LMFDB - Embedded newform 700.2.g.j.251.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(251,700)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, 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("700.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.g (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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.4
Root			$0.599676 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	700.251
Dual form			700.2.g.j.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28078 + 0.599676i) q^{2} +0.936426 q^{3} +(1.28078 - 1.53610i) q^{4} +(-1.19935 + 0.561553i) q^{6} +(-2.60399 - 0.468213i) q^{7} +(-0.719224 + 2.73546i) q^{8} -2.12311 q^{9} +O(q^{10})$	\(q+(-1.28078 + 0.599676i) q^{2} +0.936426 q^{3} +(1.28078 - 1.53610i) q^{4} +(-1.19935 + 0.561553i) q^{6} +(-2.60399 - 0.468213i) q^{7} +(-0.719224 + 2.73546i) q^{8} -2.12311 q^{9} +2.39871i q^{11} +(1.19935 - 1.43845i) q^{12} +2.00000i q^{13} +(3.61591 - 0.961876i) q^{14} +(-0.719224 - 3.93481i) q^{16} -7.12311i q^{17} +(2.71922 - 1.27318i) q^{18} -2.39871 q^{19} +(-2.43845 - 0.438447i) q^{21} +(-1.43845 - 3.07221i) q^{22} -5.73384i q^{23} +(-0.673500 + 2.56155i) q^{24} +(-1.19935 - 2.56155i) q^{26} -4.79741 q^{27} +(-4.05436 + 3.40032i) q^{28} -2.00000 q^{29} -6.67026 q^{31} +(3.28078 + 4.60831i) q^{32} +2.24621i q^{33} +(4.27156 + 9.12311i) q^{34} +(-2.71922 + 3.26131i) q^{36} -2.00000 q^{37} +(3.07221 - 1.43845i) q^{38} +1.87285i q^{39} -7.12311i q^{41} +(3.38603 - 0.900726i) q^{42} +7.60669i q^{43} +(3.68466 + 3.07221i) q^{44} +(3.43845 + 7.34376i) q^{46} -10.0054 q^{47} +(-0.673500 - 3.68466i) q^{48} +(6.56155 + 2.43845i) q^{49} -6.67026i q^{51} +(3.07221 + 2.56155i) q^{52} -2.00000 q^{53} +(6.14441 - 2.87689i) q^{54} +(3.15363 - 6.78636i) q^{56} -2.24621 q^{57} +(2.56155 - 1.19935i) q^{58} -10.9418 q^{59} -2.00000i q^{61} +(8.54312 - 4.00000i) q^{62} +(5.52855 + 0.994066i) q^{63} +(-6.96543 - 3.93481i) q^{64} +(-1.34700 - 2.87689i) q^{66} +14.2770i q^{67} +(-10.9418 - 9.12311i) q^{68} -5.36932i q^{69} +6.14441i q^{71} +(1.52699 - 5.80766i) q^{72} -9.36932i q^{73} +(2.56155 - 1.19935i) q^{74} +(-3.07221 + 3.68466i) q^{76} +(1.12311 - 6.24621i) q^{77} +(-1.12311 - 2.39871i) q^{78} -4.27156i q^{79} +1.87689 q^{81} +(4.27156 + 9.12311i) q^{82} +0.936426 q^{83} +(-3.79661 + 3.18415i) q^{84} +(-4.56155 - 9.74247i) q^{86} -1.87285 q^{87} +(-6.56155 - 1.72521i) q^{88} -12.0000i q^{89} +(0.936426 - 5.20798i) q^{91} +(-8.80776 - 7.34376i) q^{92} -6.24621 q^{93} +(12.8147 - 6.00000i) q^{94} +(3.07221 + 4.31534i) q^{96} +7.12311i q^{97} +(-9.86616 + 0.811703i) q^{98} -5.09271i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 16 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^4 - 14 * q^8 + 16 * q^9	$ 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 16 q^{9} - 6 q^{14} - 14 q^{16} + 30 q^{18} - 36 q^{21} - 28 q^{22} - 14 q^{28} - 16 q^{29} + 18 q^{32} - 30 q^{36} - 16 q^{37} - 8 q^{42} - 20 q^{44} + 44 q^{46} + 36 q^{49} - 16 q^{53} + 2 q^{56} + 48 q^{57} + 4 q^{58} + 2 q^{64} - 62 q^{72} + 4 q^{74} - 24 q^{77} + 24 q^{78} + 48 q^{81} + 8 q^{84} - 20 q^{86} - 36 q^{88} + 12 q^{92} + 16 q^{93} - 26 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^4 - 14 * q^8 + 16 * q^9 - 6 * q^14 - 14 * q^16 + 30 * q^18 - 36 * q^21 - 28 * q^22 - 14 * q^28 - 16 * q^29 + 18 * q^32 - 30 * q^36 - 16 * q^37 - 8 * q^42 - 20 * q^44 + 44 * q^46 + 36 * q^49 - 16 * q^53 + 2 * q^56 + 48 * q^57 + 4 * q^58 + 2 * q^64 - 62 * q^72 + 4 * q^74 - 24 * q^77 + 24 * q^78 + 48 * q^81 + 8 * q^84 - 20 * q^86 - 36 * q^88 + 12 * q^92 + 16 * q^93 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.28078	+	0.599676i	−0.905646	+	0.424035i
$2$	−1.28078	+	0.599676i	−0.905646	+	0.424035i
$3$	0.936426			0.540646			0.270323	−	0.962770i	$-0.412870\pi$
$3$	0.936426			0.540646			0.270323	+	0.962770i	$0.412870\pi$
$4$	1.28078	−	1.53610i	0.640388	−	0.768051i
$5$		0			0
$5$		0			0
$6$	−1.19935	+	0.561553i	−0.489634	+	0.229253i
$7$	−2.60399	−	0.468213i	−0.984217	−	0.176968i
$7$	−2.60399	−	0.468213i	−0.984217	−	0.176968i
$8$	−0.719224	+	2.73546i	−0.254284	+	0.967130i
$9$	−2.12311			−0.707702
$10$		0			0
$11$			2.39871i			0.723237i	0.932326	+	0.361618i	$0.117776\pi$
$11$			2.39871i			0.723237i	−0.932326	+	0.361618i	$0.882224\pi$
$12$	1.19935	−	1.43845i	0.346223	−	0.415244i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	3.61591	−	0.961876i	0.966392	−	0.257072i
$15$		0			0
$16$	−0.719224	−	3.93481i	−0.179806	−	0.983702i
$17$		−	7.12311i		−	1.72761i	−0.503829	−	0.863803i	$-0.668076\pi$
$17$		−	7.12311i		−	1.72761i	0.503829	−	0.863803i	$-0.331924\pi$
$18$	2.71922	−	1.27318i	0.640927	−	0.300091i
$19$	−2.39871			−0.550301			−0.275150	−	0.961401i	$-0.588728\pi$
$19$	−2.39871			−0.550301			−0.275150	+	0.961401i	$0.588728\pi$
$20$		0			0
$21$	−2.43845	−	0.438447i	−0.532113	−	0.0956770i
$22$	−1.43845	−	3.07221i	−0.306678	−	0.654996i
$23$		−	5.73384i		−	1.19559i	−0.801650	−	0.597794i	$-0.796044\pi$
$23$		−	5.73384i		−	1.19559i	0.801650	−	0.597794i	$-0.203956\pi$
$24$	−0.673500	+	2.56155i	−0.137478	+	0.522875i
$25$		0			0
$26$	−1.19935	−	2.56155i	−0.235212	−	0.502362i
$27$	−4.79741			−0.923262
$28$	−4.05436	+	3.40032i	−0.766201	+	0.642601i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	−6.67026			−1.19801			−0.599007	−	0.800743i	$-0.704438\pi$
$31$	−6.67026			−1.19801			−0.599007	+	0.800743i	$0.704438\pi$
$32$	3.28078	+	4.60831i	0.579965	+	0.814642i
$33$			2.24621i			0.391015i
$34$	4.27156	+	9.12311i	0.732566	+	1.56460i
$35$		0			0
$36$	−2.71922	+	3.26131i	−0.453204	+	0.543551i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	3.07221	−	1.43845i	0.498378	−	0.233347i
$39$			1.87285i			0.299896i
$40$		0			0
$41$		−	7.12311i		−	1.11244i	−0.831034	−	0.556221i	$-0.812251\pi$
$41$		−	7.12311i		−	1.11244i	0.831034	−	0.556221i	$-0.187749\pi$
$42$	3.38603	−	0.900726i	0.522476	−	0.138985i
$43$			7.60669i			1.16001i	0.814613	+	0.580005i	$0.196949\pi$
$43$			7.60669i			1.16001i	−0.814613	+	0.580005i	$0.803051\pi$
$44$	3.68466	+	3.07221i	0.555483	+	0.463152i
$45$		0			0
$46$	3.43845	+	7.34376i	0.506971	+	1.08278i
$47$	−10.0054			−1.45944			−0.729719	−	0.683748i	$-0.760349\pi$
$47$	−10.0054			−1.45944			−0.729719	+	0.683748i	$0.760349\pi$
$48$	−0.673500	−	3.68466i	−0.0972113	−	0.531835i
$49$	6.56155	+	2.43845i	0.937365	+	0.348350i
$50$		0			0
$51$		−	6.67026i		−	0.934024i
$52$	3.07221	+	2.56155i	0.426038	+	0.355223i
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$	6.14441	−	2.87689i	0.836148	−	0.391496i
$55$		0			0
$56$	3.15363	−	6.78636i	0.421421	−	0.906865i
$57$	−2.24621			−0.297518
$58$	2.56155	−	1.19935i	0.336348	−	0.157483i
$59$	−10.9418			−1.42450			−0.712252	−	0.701924i	$-0.752325\pi$
$59$	−10.9418			−1.42450			−0.712252	+	0.701924i	$0.752325\pi$
$60$		0			0
$61$		−	2.00000i		−	0.256074i	−0.991769	−	0.128037i	$-0.959132\pi$
$61$		−	2.00000i		−	0.256074i	0.991769	−	0.128037i	$-0.0408676\pi$
$62$	8.54312	−	4.00000i	1.08498	−	0.508001i
$63$	5.52855	+	0.994066i	0.696532	+	0.125241i
$64$	−6.96543	−	3.93481i	−0.870679	−	0.491851i
$65$		0			0
$66$	−1.34700	−	2.87689i	−0.165804	−	0.354121i
$67$			14.2770i			1.74421i	0.489321	+	0.872104i	$0.337245\pi$
$67$			14.2770i			1.74421i	−0.489321	+	0.872104i	$0.662755\pi$
$68$	−10.9418	−	9.12311i	−1.32689	−	1.10634i
$69$		−	5.36932i		−	0.646390i
$70$		0			0
$71$			6.14441i			0.729207i	0.931163	+	0.364604i	$0.118796\pi$
$71$			6.14441i			0.729207i	−0.931163	+	0.364604i	$0.881204\pi$
$72$	1.52699	−	5.80766i	0.179957	−	0.684439i
$73$		−	9.36932i		−	1.09660i	−0.836283	−	0.548298i	$-0.815276\pi$
$73$		−	9.36932i		−	1.09660i	0.836283	−	0.548298i	$-0.184724\pi$
$74$	2.56155	−	1.19935i	0.297774	−	0.139422i
$75$		0			0
$76$	−3.07221	+	3.68466i	−0.352406	+	0.422659i
$77$	1.12311	−	6.24621i	0.127990	−	0.711822i
$78$	−1.12311	−	2.39871i	−0.127167	−	0.271600i
$79$		−	4.27156i		−	0.480588i	−0.970700	−	0.240294i	$-0.922756\pi$
$79$		−	4.27156i		−	0.480588i	0.970700	−	0.240294i	$-0.0772438\pi$
$80$		0			0
$81$	1.87689			0.208544
$82$	4.27156	+	9.12311i	0.471715	+	1.00748i
$83$	0.936426			0.102786			0.0513931	−	0.998679i	$-0.483634\pi$
$83$	0.936426			0.102786			0.0513931	+	0.998679i	$0.483634\pi$
$84$	−3.79661	+	3.18415i	−0.414244	+	0.347420i
$85$		0			0
$86$	−4.56155	−	9.74247i	−0.491885	−	1.05056i
$87$	−1.87285			−0.200791
$88$	−6.56155	−	1.72521i	−0.699464	−	0.183908i
$89$		−	12.0000i		−	1.27200i	−0.771690	−	0.635999i	$-0.780588\pi$
$89$		−	12.0000i		−	1.27200i	0.771690	−	0.635999i	$-0.219412\pi$
$90$		0			0
$91$	0.936426	−	5.20798i	0.0981642	−	0.545945i
$92$	−8.80776	−	7.34376i	−0.918273	−	0.765640i
$93$	−6.24621			−0.647702
$94$	12.8147	−	6.00000i	1.32173	−	0.618853i
$95$		0			0
$96$	3.07221	+	4.31534i	0.313556	+	0.440433i
$97$			7.12311i			0.723242i	0.932325	+	0.361621i	$0.117777\pi$
$97$			7.12311i			0.723242i	−0.932325	+	0.361621i	$0.882223\pi$
$98$	−9.86616	+	0.811703i	−0.996633	+	0.0819944i
$99$		−	5.09271i		−	0.511836i
$100$		0			0
$101$			6.87689i			0.684277i	0.939650	+	0.342138i	$0.111151\pi$
$101$			6.87689i			0.684277i	−0.939650	+	0.342138i	$0.888849\pi$
$102$	4.00000	+	8.54312i	0.396059	+	0.845895i
$103$	1.46228			0.144083			0.0720413	−	0.997402i	$-0.477049\pi$
$103$	1.46228			0.144083			0.0720413	+	0.997402i	$0.477049\pi$
$104$	−5.47091	−	1.43845i	−0.536467	−	0.141051i
$105$		0			0
$106$	2.56155	−	1.19935i	0.248800	−	0.116491i
$107$		−	9.47954i		−	0.916422i	−0.888843	−	0.458211i	$-0.848490\pi$
$107$		−	9.47954i		−	0.916422i	0.888843	−	0.458211i	$-0.151510\pi$
$108$	−6.14441	+	7.36932i	−0.591246	+	0.709113i
$109$	1.12311			0.107574			0.0537870	−	0.998552i	$-0.482871\pi$
$109$	1.12311			0.107574			0.0537870	+	0.998552i	$0.482871\pi$
$110$		0			0
$111$	−1.87285			−0.177763
$112$	0.0305236	+	10.5830i	0.00288420	+	0.999996i
$113$	14.4924			1.36333			0.681666	−	0.731663i	$-0.261256\pi$
$113$	14.4924			1.36333			0.681666	+	0.731663i	$0.261256\pi$
$114$	2.87689	−	1.34700i	0.269446	−	0.126158i
$115$		0			0
$116$	−2.56155	+	3.07221i	−0.237834	+	0.285247i
$117$		−	4.24621i		−	0.392562i
$118$	14.0140	−	6.56155i	1.29010	−	0.604040i
$119$	−3.33513	+	18.5485i	−0.305731	+	1.70034i
$120$		0			0
$121$	5.24621			0.476928
$122$	1.19935	+	2.56155i	0.108584	+	0.231912i
$123$		−	6.67026i		−	0.601437i
$124$	−8.54312	+	10.2462i	−0.767195	+	0.920137i
$125$		0			0
$126$	−7.67696	+	2.04217i	−0.683918	+	0.181931i
$127$		−	13.2252i		−	1.17355i	−0.809750	−	0.586776i	$-0.800397\pi$
$127$		−	13.2252i		−	1.17355i	0.809750	−	0.586776i	$-0.199603\pi$
$128$	11.2808	+	0.862603i	0.997089	+	0.0762440i
$129$			7.12311i			0.627154i
$130$		0			0
$131$	13.8664			1.21151			0.605756	−	0.795651i	$-0.292871\pi$
$131$	13.8664			1.21151			0.605756	+	0.795651i	$0.292871\pi$
$132$	3.45041	+	2.87689i	0.300320	+	0.250402i
$133$	6.24621	+	1.12311i	0.541615	+	0.0973856i
$134$	−8.56155	−	18.2856i	−0.739606	−	1.57963i
$135$		0			0
$136$	19.4849	+	5.12311i	1.67082	+	0.439303i
$137$	14.0000			1.19610			0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000			1.19610			0.598050	+	0.801459i	$0.295942\pi$
$138$	3.21985	+	6.87689i	0.274092	+	0.585400i
$139$	−1.34700			−0.114251			−0.0571255	−	0.998367i	$-0.518194\pi$
$139$	−1.34700			−0.114251			−0.0571255	+	0.998367i	$0.518194\pi$
$140$		0			0
$141$	−9.36932			−0.789039
$142$	−3.68466	−	7.86962i	−0.309210	−	0.660404i
$143$	−4.79741			−0.401180
$144$	1.52699	+	8.35401i	0.127249	+	0.696168i
$145$		0			0
$146$	5.61856	+	12.0000i	0.464995	+	0.993127i
$147$	6.14441	+	2.28343i	0.506782	+	0.188334i
$148$	−2.56155	+	3.07221i	−0.210558	+	0.252534i
$149$	−19.3693			−1.58680			−0.793398	−	0.608703i	$-0.791690\pi$
$149$	−19.3693			−1.58680			−0.793398	+	0.608703i	$0.791690\pi$
$150$		0			0
$151$			14.6875i			1.19525i	0.801774	+	0.597627i	$0.203890\pi$
$151$			14.6875i			1.19525i	−0.801774	+	0.597627i	$0.796110\pi$
$152$	1.72521	−	6.56155i	0.139933	−	0.532212i
$153$			15.1231i			1.22263i
$154$	2.30726	+	8.67350i	0.185924	+	0.698931i
$155$		0			0
$156$	2.87689	+	2.39871i	0.230336	+	0.192050i
$157$			16.2462i			1.29659i	0.761390	+	0.648294i	$0.224517\pi$
$157$			16.2462i			1.29659i	−0.761390	+	0.648294i	$0.775483\pi$
$158$	2.56155	+	5.47091i	0.203786	+	0.435242i
$159$	−1.87285			−0.148527
$160$		0			0
$161$	−2.68466	+	14.9309i	−0.211581	+	1.17672i
$162$	−2.40388	+	1.12553i	−0.188867	+	0.0884299i
$163$			0.936426i			0.0733466i	0.999327	+	0.0366733i	$0.0116761\pi$
$163$			0.936426i			0.0733466i	−0.999327	+	0.0366733i	$0.988324\pi$
$164$	−10.9418	−	9.12311i	−0.854413	−	0.712395i
$165$		0			0
$166$	−1.19935	+	0.561553i	−0.0930878	+	0.0435850i
$167$	−2.28343			−0.176697			−0.0883484	−	0.996090i	$-0.528159\pi$
$167$	−2.28343			−0.176697			−0.0883484	+	0.996090i	$0.528159\pi$
$168$	2.95314	−	6.35492i	0.227840	−	0.490293i
$169$	9.00000			0.692308
$170$		0			0
$171$	5.09271			0.389449
$172$	11.6847	+	9.74247i	0.890947	+	0.742856i
$173$			0.246211i			0.0187191i	0.999956	+	0.00935955i	$0.00297928\pi$
$173$			0.246211i			0.0187191i	−0.999956	+	0.00935955i	$0.997021\pi$
$174$	2.39871	−	1.12311i	0.181845	−	0.0851424i
$175$		0			0
$176$	9.43845	−	1.72521i	0.711450	−	0.130042i
$177$	−10.2462			−0.770152
$178$	7.19612	+	15.3693i	0.539372	+	1.15198i
$179$		−	0.525853i		−	0.0393041i	−0.999807	−	0.0196520i	$-0.993744\pi$
$179$		−	0.525853i		−	0.0393041i	0.999807	−	0.0196520i	$-0.00625584\pi$
$180$		0			0
$181$			6.87689i			0.511156i	0.966789	+	0.255578i	$0.0822657\pi$
$181$			6.87689i			0.511156i	−0.966789	+	0.255578i	$0.917734\pi$
$182$	1.92375	+	7.23182i	0.142598	+	0.536058i
$183$		−	1.87285i		−	0.138445i
$184$	15.6847	+	4.12391i	1.15629	+	0.304019i
$185$		0			0
$186$	8.00000	−	3.74571i	0.586588	−	0.274648i
$187$	17.0862			1.24947
$188$	−12.8147	+	15.3693i	−0.934606	+	1.12092i
$189$	12.4924	+	2.24621i	0.908690	+	0.163388i
$190$		0			0
$191$		−	1.34700i		−	0.0974655i	−0.998812	−	0.0487327i	$-0.984482\pi$
$191$		−	1.34700i		−	0.0974655i	0.998812	−	0.0487327i	$-0.0155183\pi$
$192$	−6.52262	−	3.68466i	−0.470729	−	0.265917i
$193$	−10.4924			−0.755261			−0.377631	−	0.925956i	$-0.623261\pi$
$193$	−10.4924			−0.755261			−0.377631	+	0.925956i	$0.623261\pi$
$194$	−4.27156	−	9.12311i	−0.306680	−	0.655001i
$195$		0			0
$196$	12.1496	−	6.95611i	0.867828	−	0.496865i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	3.05398	+	6.52262i	0.217037	+	0.463542i
$199$	16.0345			1.13666			0.568329	−	0.822802i	$-0.307590\pi$
$199$	16.0345			1.13666			0.568329	+	0.822802i	$0.307590\pi$
$200$		0			0
$201$			13.3693i			0.942999i
$202$	−4.12391	−	8.80776i	−0.290157	−	0.619712i
$203$	5.20798	+	0.936426i	0.365529	+	0.0657242i
$204$	−10.2462	−	8.54312i	−0.717378	−	0.598138i
$205$		0			0
$206$	−1.87285	+	0.876894i	−0.130488	+	0.0610961i
$207$			12.1735i			0.846120i
$208$	7.86962	−	1.43845i	0.545660	−	0.0997384i
$209$		−	5.75379i		−	0.397998i
$210$		0			0
$211$		−	18.4332i		−	1.26900i	−0.772924	−	0.634498i	$-0.781207\pi$
$211$		−	18.4332i		−	1.26900i	0.772924	−	0.634498i	$-0.218793\pi$
$212$	−2.56155	+	3.07221i	−0.175928	+	0.211000i
$213$			5.75379i			0.394243i
$214$	5.68466	+	12.1412i	0.388595	+	0.829954i
$215$		0			0
$216$	3.45041	−	13.1231i	0.234771	−	0.892914i
$217$	17.3693	+	3.12311i	1.17911	+	0.212010i
$218$	−1.43845	+	0.673500i	−0.0974239	+	0.0456152i
$219$		−	8.77368i		−	0.592870i
$220$		0			0
$221$	14.2462			0.958304
$222$	2.39871	−	1.12311i	0.160991	−	0.0753779i
$223$	−12.9300			−0.865854			−0.432927	−	0.901429i	$-0.642519\pi$
$223$	−12.9300			−0.865854			−0.432927	+	0.901429i	$0.642519\pi$
$224$	−6.38545	−	13.5361i	−0.426646	−	0.904419i
$225$		0			0
$226$	−18.5616	+	8.69076i	−1.23470	+	0.578101i
$227$	14.2770			0.947595			0.473797	−	0.880634i	$-0.342883\pi$
$227$	14.2770			0.947595			0.473797	+	0.880634i	$0.342883\pi$
$228$	−2.87689	+	3.45041i	−0.190527	+	0.228509i
$229$			21.1231i			1.39585i	0.716169	+	0.697927i	$0.245894\pi$
$229$			21.1231i			1.39585i	−0.716169	+	0.697927i	$0.754106\pi$
$230$		0			0
$231$	1.05171	−	5.84912i	0.0691972	−	0.384844i
$232$	1.43845	−	5.47091i	0.0944387	−	0.359183i
$233$	−24.2462			−1.58842			−0.794211	−	0.607642i	$-0.792116\pi$
$233$	−24.2462			−1.58842			−0.794211	+	0.607642i	$0.792116\pi$
$234$	2.54635	+	5.43845i	0.166460	+	0.355522i
$235$		0			0
$236$	−14.0140	+	16.8078i	−0.912236	+	1.09409i
$237$		−	4.00000i		−	0.259828i
$238$	−6.85155	−	25.7565i	−0.444120	−	1.66955i
$239$		−	12.8147i		−	0.828912i	−0.910069	−	0.414456i	$-0.863972\pi$
$239$		−	12.8147i		−	0.828912i	0.910069	−	0.414456i	$-0.136028\pi$
$240$		0			0
$241$		−	15.6155i		−	1.00588i	−0.864320	−	0.502942i	$-0.832251\pi$
$241$		−	15.6155i		−	1.00588i	0.864320	−	0.502942i	$-0.167749\pi$
$242$	−6.71922	+	3.14603i	−0.431928	+	0.202234i
$243$	16.1498			1.03601
$244$	−3.07221	−	2.56155i	−0.196678	−	0.163987i
$245$		0			0
$246$	4.00000	+	8.54312i	0.255031	+	0.544689i
$247$		−	4.79741i		−	0.305252i
$248$	4.79741	−	18.2462i	0.304636	−	1.15864i
$249$	0.876894			0.0555709
$250$		0			0
$251$	16.5604			1.04528			0.522641	−	0.852553i	$-0.324947\pi$
$251$	16.5604			1.04528			0.522641	+	0.852553i	$0.324947\pi$
$252$	8.60783	−	7.21925i	0.542242	−	0.454770i
$253$	13.7538			0.864693
$254$	7.93087	+	16.9386i	0.497627	+	1.06282i
$255$		0			0
$256$	−14.9654	+	5.66001i	−0.935340	+	0.353751i
$257$			13.3693i			0.833955i	0.908917	+	0.416978i	$0.136911\pi$
$257$			13.3693i			0.833955i	−0.908917	+	0.416978i	$0.863089\pi$
$258$	−4.27156	−	9.12311i	−0.265936	−	0.567980i
$259$	5.20798	+	0.936426i	0.323608	+	0.0581867i
$260$		0			0
$261$	4.24621			0.262834
$262$	−17.7597	+	8.31534i	−1.09720	+	0.513724i
$263$			1.98813i			0.122593i	0.998120	+	0.0612967i	$0.0195236\pi$
$263$			1.98813i			0.122593i	−0.998120	+	0.0612967i	$0.980476\pi$
$264$	−6.14441	−	1.61553i	−0.378162	−	0.0994289i
$265$		0			0
$266$	−8.67350	+	2.30726i	−0.531806	+	0.141467i
$267$		−	11.2371i		−	0.687700i
$268$	21.9309	+	18.2856i	1.33964	+	1.11697i
$269$		−	16.2462i		−	0.990549i	−0.868737	−	0.495274i	$-0.835067\pi$
$269$		−	16.2462i		−	0.990549i	0.868737	−	0.495274i	$-0.164933\pi$
$270$		0			0
$271$	−23.7565			−1.44310			−0.721552	−	0.692360i	$-0.756571\pi$
$271$	−23.7565			−1.44310			−0.721552	+	0.692360i	$0.756571\pi$
$272$	−28.0281	+	5.12311i	−1.69945	+	0.310634i
$273$	0.876894	−	4.87689i	0.0530721	−	0.295163i
$274$	−17.9309	+	8.39547i	−1.08324	+	0.507189i
$275$		0			0
$276$	−8.24782	−	6.87689i	−0.496461	−	0.413940i
$277$	4.24621			0.255130			0.127565	−	0.991830i	$-0.459284\pi$
$277$	4.24621			0.255130			0.127565	+	0.991830i	$0.459284\pi$
$278$	1.72521	−	0.807764i	0.103471	−	0.0484465i
$279$	14.1617			0.847837
$280$		0			0
$281$	−4.63068			−0.276243			−0.138122	−	0.990415i	$-0.544107\pi$
$281$	−4.63068			−0.276243			−0.138122	+	0.990415i	$0.544107\pi$
$282$	12.0000	−	5.61856i	0.714590	−	0.334580i
$283$	−24.6929			−1.46784			−0.733921	−	0.679235i	$-0.762312\pi$
$283$	−24.6929			−1.46784			−0.733921	+	0.679235i	$0.762312\pi$
$284$	9.43845	+	7.86962i	0.560069	+	0.466976i
$285$		0			0
$286$	6.14441	−	2.87689i	0.363327	−	0.170114i
$287$	−3.33513	+	18.5485i	−0.196867	+	1.09488i
$288$	−6.96543	−	9.78393i	−0.410442	−	0.576523i
$289$	−33.7386			−1.98463
$290$		0			0
$291$			6.67026i			0.391018i
$292$	−14.3922	−	12.0000i	−0.842242	−	0.702247i
$293$		−	32.2462i		−	1.88384i	−0.335832	−	0.941922i	$-0.609017\pi$
$293$		−	32.2462i		−	1.88384i	0.335832	−	0.941922i	$-0.390983\pi$
$294$	−9.23893	+	0.760100i	−0.538826	+	0.0443299i
$295$		0			0
$296$	1.43845	−	5.47091i	0.0836080	−	0.317990i
$297$		−	11.5076i		−	0.667737i
$298$	24.8078	−	11.6153i	1.43708	−	0.672858i
$299$	11.4677			0.663193
$300$		0			0
$301$	3.56155	−	19.8078i	0.205284	−	1.14170i
$302$	−8.80776	−	18.8114i	−0.506830	−	1.08248i
$303$			6.43971i			0.369951i
$304$	1.72521	+	9.43845i	0.0989473	+	0.541332i
$305$		0			0
$306$	−9.06897	−	19.3693i	−0.518438	−	1.10727i
$307$	31.3632			1.78999			0.894996	−	0.446074i	$-0.147178\pi$
$307$	31.3632			1.78999			0.894996	+	0.446074i	$0.147178\pi$
$308$	−8.15638	−	9.72521i	−0.464753	−	0.554145i
$309$	1.36932			0.0778977
$310$		0			0
$311$	−9.36426			−0.530999			−0.265499	−	0.964111i	$-0.585537\pi$
$311$	−9.36426			−0.530999			−0.265499	+	0.964111i	$0.585537\pi$
$312$	−5.12311	−	1.34700i	−0.290039	−	0.0762589i
$313$		−	7.61553i		−	0.430455i	−0.976564	−	0.215228i	$-0.930951\pi$
$313$		−	7.61553i		−	0.430455i	0.976564	−	0.215228i	$-0.0690493\pi$
$314$	−9.74247	−	20.8078i	−0.549799	−	1.17425i
$315$		0			0
$316$	−6.56155	−	5.47091i	−0.369116	−	0.307763i
$317$	4.24621			0.238491			0.119245	−	0.992865i	$-0.461952\pi$
$317$	4.24621			0.238491			0.119245	+	0.992865i	$0.461952\pi$
$318$	2.39871	−	1.12311i	0.134513	−	0.0629806i
$319$		−	4.79741i		−	0.268603i
$320$		0			0
$321$		−	8.87689i		−	0.495460i
$322$	−5.51524	−	20.7330i	−0.307352	−	1.15541i
$323$			17.0862i			0.950703i
$324$	2.40388	−	2.88310i	0.133549	−	0.160172i
$325$		0			0
$326$	−0.561553	−	1.19935i	−0.0311015	−	0.0664260i
$327$	1.05171			0.0581595
$328$	19.4849	+	5.12311i	1.07588	+	0.282876i
$329$	26.0540	+	4.68466i	1.43640	+	0.258274i
$330$		0			0
$331$			29.0798i			1.59837i	0.601086	+	0.799184i	$0.294735\pi$
$331$			29.0798i			1.59837i	−0.601086	+	0.799184i	$0.705265\pi$
$332$	1.19935	−	1.43845i	0.0658230	−	0.0789450i
$333$	4.24621			0.232691
$334$	2.92456	−	1.36932i	0.160025	−	0.0749257i
$335$		0			0
$336$	0.0285831	+	9.91016i	0.00155933	+	0.540644i
$337$	−4.24621			−0.231306			−0.115653	−	0.993290i	$-0.536896\pi$
$337$	−4.24621			−0.231306			−0.115653	+	0.993290i	$0.536896\pi$
$338$	−11.5270	+	5.39709i	−0.626985	+	0.293563i
$339$	13.5711			0.737080
$340$		0			0
$341$		−	16.0000i		−	0.866449i
$342$	−6.52262	+	3.05398i	−0.352703	+	0.165140i
$343$	−15.9445	−	9.42190i	−0.860923	−	0.508735i
$344$	−20.8078	−	5.47091i	−1.12188	−	0.294972i
$345$		0			0
$346$	−0.147647	−	0.315342i	−0.00793756	−	0.0169529i
$347$		−	9.47954i		−	0.508889i	−0.967087	−	0.254444i	$-0.918107\pi$
$347$		−	9.47954i		−	0.508889i	0.967087	−	0.254444i	$-0.0818925\pi$
$348$	−2.39871	+	2.87689i	−0.128584	+	0.154218i
$349$			27.8617i			1.49140i	0.666279	+	0.745702i	$0.267886\pi$
$349$			27.8617i			1.49140i	−0.666279	+	0.745702i	$0.732114\pi$
$350$		0			0
$351$		−	9.59482i		−	0.512134i
$352$	−11.0540	+	7.86962i	−0.589179	+	0.419452i
$353$			5.36932i			0.285780i	0.989739	+	0.142890i	$0.0456395\pi$
$353$			5.36932i			0.285780i	−0.989739	+	0.142890i	$0.954361\pi$
$354$	13.1231	−	6.14441i	0.697485	−	0.326572i
$355$		0			0
$356$	−18.4332	−	15.3693i	−0.976959	−	0.814572i
$357$	−3.12311	+	17.3693i	−0.165292	+	0.919282i
$358$	0.315342	+	0.673500i	0.0166663	+	0.0355956i
$359$		−	16.5604i		−	0.874023i	−0.899456	−	0.437012i	$-0.856037\pi$
$359$		−	16.5604i		−	0.874023i	0.899456	−	0.437012i	$-0.143963\pi$
$360$		0			0
$361$	−13.2462			−0.697169
$362$	−4.12391	−	8.80776i	−0.216748	−	0.462926i
$363$	4.91269			0.257849
$364$	−6.80065	−	8.10871i	−0.356451	−	0.425012i
$365$		0			0
$366$	1.12311	+	2.39871i	0.0587057	+	0.125382i
$367$	−7.08084			−0.369617			−0.184808	−	0.982775i	$-0.559166\pi$
$367$	−7.08084			−0.369617			−0.184808	+	0.982775i	$0.559166\pi$
$368$	−22.5616	+	4.12391i	−1.17610	+	0.214974i
$369$			15.1231i			0.787277i
$370$		0			0
$371$	5.20798	+	0.936426i	0.270385	+	0.0486168i
$372$	−8.00000	+	9.59482i	−0.414781	+	0.497468i
$373$	−22.4924			−1.16461			−0.582307	−	0.812969i	$-0.697850\pi$
$373$	−22.4924			−1.16461			−0.582307	+	0.812969i	$0.697850\pi$
$374$	−21.8836	+	10.2462i	−1.13158	+	0.529819i
$375$		0			0
$376$	7.19612	−	27.3693i	0.371111	−	1.41146i
$377$		−	4.00000i		−	0.206010i
$378$	−17.3470	+	4.61452i	−0.892233	+	0.237345i
$379$			22.4095i			1.15110i	0.817767	+	0.575549i	$0.195212\pi$
$379$			22.4095i			1.15110i	−0.817767	+	0.575549i	$0.804788\pi$
$380$		0			0
$381$		−	12.3845i		−	0.634476i
$382$	0.807764	+	1.72521i	0.0413288	+	0.0882692i
$383$	−17.4968			−0.894045			−0.447023	−	0.894523i	$-0.647516\pi$
$383$	−17.4968			−0.894045			−0.447023	+	0.894523i	$0.647516\pi$
$384$	10.5636	+	0.807764i	0.539072	+	0.0412210i
$385$		0			0
$386$	13.4384	−	6.29206i	0.683999	−	0.320257i
$387$		−	16.1498i		−	0.820941i
$388$	10.9418	+	9.12311i	0.555487	+	0.463156i
$389$	1.12311			0.0569437			0.0284719	−	0.999595i	$-0.490936\pi$
$389$	1.12311			0.0569437			0.0284719	+	0.999595i	$0.490936\pi$
$390$		0			0
$391$	−40.8427			−2.06551
$392$	−11.3895	+	16.1950i	−0.575256	+	0.817973i
$393$	12.9848			0.654999
$394$	23.0540	−	10.7942i	1.16144	−	0.543803i
$395$		0			0
$396$	−7.82292	−	6.52262i	−0.393116	−	0.327774i
$397$		−	14.0000i		−	0.702640i	−0.936255	−	0.351320i	$-0.885733\pi$
$397$		−	14.0000i		−	0.702640i	0.936255	−	0.351320i	$-0.114267\pi$
$398$	−20.5366	+	9.61553i	−1.02941	+	0.481983i
$399$	5.84912	+	1.05171i	0.292822	+	0.0526511i
$400$		0			0
$401$	6.00000			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$402$	−8.01726	−	17.1231i	−0.399865	−	0.854023i
$403$		−	13.3405i		−	0.664539i
$404$	10.5636	+	8.80776i	0.525560	+	0.438203i
$405$		0			0
$406$	−7.23182	+	1.92375i	−0.358909	+	0.0954742i
$407$		−	4.79741i		−	0.237799i
$408$	18.2462	+	4.79741i	0.903322	+	0.237507i
$409$			8.87689i			0.438934i	0.975620	+	0.219467i	$0.0704319\pi$
$409$			8.87689i			0.438934i	−0.975620	+	0.219467i	$0.929568\pi$
$410$		0			0
$411$	13.1100			0.646667
$412$	1.87285	−	2.24621i	0.0922688	−	0.110663i
$413$	28.4924	+	5.12311i	1.40202	+	0.252092i
$414$	−7.30019	−	15.5916i	−0.358785	−	0.766285i
$415$		0			0
$416$	−9.21662	+	6.56155i	−0.451882	+	0.321707i
$417$	−1.26137			−0.0617694
$418$	3.45041	+	7.36932i	0.168765	+	0.360445i
$419$	−11.9935			−0.585922			−0.292961	−	0.956124i	$-0.594641\pi$
$419$	−11.9935			−0.585922			−0.292961	+	0.956124i	$0.594641\pi$
$420$		0			0
$421$	−17.6155			−0.858528			−0.429264	−	0.903179i	$-0.641227\pi$
$421$	−17.6155			−0.858528			−0.429264	+	0.903179i	$0.641227\pi$
$422$	11.0540	+	23.6089i	0.538099	+	1.14926i
$423$	21.2425			1.03285
$424$	1.43845	−	5.47091i	0.0698572	−	0.265691i
$425$		0			0
$426$	−3.45041	−	7.36932i	−0.167173	−	0.357045i
$427$	−0.936426	+	5.20798i	−0.0453168	+	0.252032i
$428$	−14.5616	−	12.1412i	−0.703859	−	0.586866i
$429$	−4.49242			−0.216896
$430$		0			0
$431$		−	36.5712i		−	1.76157i	−0.473515	−	0.880786i	$-0.657015\pi$
$431$		−	36.5712i		−	1.76157i	0.473515	−	0.880786i	$-0.342985\pi$
$432$	3.45041	+	18.8769i	0.166008	+	0.908215i
$433$		−	11.6155i		−	0.558207i	−0.960261	−	0.279103i	$-0.909963\pi$
$433$		−	11.6155i		−	0.558207i	0.960261	−	0.279103i	$-0.0900372\pi$
$434$	−24.1191	+	6.41597i	−1.15775	+	0.307976i
$435$		0			0
$436$	1.43845	−	1.72521i	0.0688891	−	0.0826224i
$437$			13.7538i			0.657933i
$438$	5.26137	+	11.2371i	0.251398	+	0.536930i
$439$	18.1379			0.865677			0.432838	−	0.901472i	$-0.357512\pi$
$439$	18.1379			0.865677			0.432838	+	0.901472i	$0.357512\pi$
$440$		0			0
$441$	−13.9309	−	5.17708i	−0.663375	−	0.246528i
$442$	−18.2462	+	8.54312i	−0.867884	+	0.406355i
$443$		−	30.3115i		−	1.44014i	−0.693900	−	0.720071i	$-0.744109\pi$
$443$		−	30.3115i		−	1.44014i	0.693900	−	0.720071i	$-0.255891\pi$
$444$	−2.39871	+	2.87689i	−0.113838	+	0.136531i
$445$		0			0
$446$	16.5604	−	7.75379i	0.784157	−	0.367153i
$447$	−18.1379			−0.857895
$448$	16.2956	+	13.5075i	0.769895	+	0.638170i
$449$	25.6155			1.20887			0.604436	−	0.796654i	$-0.293399\pi$
$449$	25.6155			1.20887			0.604436	+	0.796654i	$0.293399\pi$
$450$		0			0
$451$	17.0862			0.804559
$452$	18.5616	−	22.2619i	0.873062	−	1.04711i
$453$			13.7538i			0.646209i
$454$	−18.2856	+	8.56155i	−0.858185	+	0.401814i
$455$		0			0
$456$	1.61553	−	6.14441i	0.0756540	−	0.287738i
$457$	−6.00000			−0.280668			−0.140334	−	0.990104i	$-0.544818\pi$
$457$	−6.00000			−0.280668			−0.140334	+	0.990104i	$0.544818\pi$
$458$	−12.6670	−	27.0540i	−0.591891	−	1.26415i
$459$			34.1725i			1.59503i
$460$		0			0
$461$			37.6155i			1.75193i	0.482375	+	0.875965i	$0.339774\pi$
$461$			37.6155i			1.75193i	−0.482375	+	0.875965i	$0.660226\pi$
$462$	2.16058	+	8.12209i	0.100519	+	0.377874i
$463$			21.9989i			1.02238i	0.859469	+	0.511188i	$0.170795\pi$
$463$			21.9989i			1.02238i	−0.859469	+	0.511188i	$0.829205\pi$
$464$	1.43845	+	7.86962i	0.0667782	+	0.365338i
$465$		0			0
$466$	31.0540	−	14.5399i	1.43855	−	0.673547i
$467$	−1.98813			−0.0919998			−0.0459999	−	0.998941i	$-0.514647\pi$
$467$	−1.98813			−0.0919998			−0.0459999	+	0.998941i	$0.514647\pi$
$468$	−6.52262	−	5.43845i	−0.301508	−	0.251392i
$469$	6.68466	−	37.1771i	0.308669	−	1.71668i
$470$		0			0
$471$			15.2134i			0.700996i
$472$	7.86962	−	29.9309i	0.362228	−	1.37768i
$473$	−18.2462			−0.838962
$474$	2.39871	+	5.12311i	0.110176	+	0.235312i
$475$		0			0
$476$	24.2209	+	28.8796i	1.11016	+	1.32369i
$477$	4.24621			0.194421
$478$	7.68466	+	16.4127i	0.351488	+	0.750701i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$		−	4.00000i		−	0.182384i
$482$	9.36426	+	20.0000i	0.426531	+	0.910975i
$483$	−2.51398	+	13.9817i	−0.114390	+	0.636188i
$484$	6.71922	−	8.05872i	0.305419	−	0.366305i
$485$		0			0
$486$	−20.6843	+	9.68466i	−0.938259	+	0.439305i
$487$		−	19.0744i		−	0.864342i	−0.901792	−	0.432171i	$-0.857748\pi$
$487$		−	19.0744i		−	0.864342i	0.901792	−	0.432171i	$-0.142252\pi$
$488$	5.47091	+	1.43845i	0.247657	+	0.0651154i
$489$			0.876894i			0.0396545i
$490$		0			0
$491$			13.6358i			0.615376i	0.951487	+	0.307688i	$0.0995553\pi$
$491$			13.6358i			0.615376i	−0.951487	+	0.307688i	$0.900445\pi$
$492$	−10.2462	−	8.54312i	−0.461935	−	0.385153i
$493$			14.2462i			0.641617i
$494$	2.87689	+	6.14441i	0.129438	+	0.276450i
$495$		0			0
$496$	4.79741	+	26.2462i	0.215410	+	1.17849i
$497$	2.87689	−	16.0000i	0.129046	−	0.717698i
$498$	−1.12311	+	0.525853i	−0.0503276	+	0.0235640i
$499$		−	27.2069i		−	1.21795i	−0.793190	−	0.608974i	$-0.791581\pi$
$499$		−	27.2069i		−	1.21795i	0.793190	−	0.608974i	$-0.208419\pi$
$500$		0			0
$501$	−2.13826			−0.0955304
$502$	−21.2101	+	9.93087i	−0.946655	+	0.443236i
$503$	21.4731			0.957437			0.478718	−	0.877968i	$-0.341101\pi$
$503$	21.4731			0.957437			0.478718	+	0.877968i	$0.341101\pi$
$504$	−6.69549	+	14.4081i	−0.298241	+	0.641790i
$505$		0			0
$506$	−17.6155	+	8.24782i	−0.783106	+	0.366660i
$507$	8.42784			0.374293
$508$	−20.3153	−	16.9386i	−0.901348	−	0.751528i
$509$		−	17.6155i		−	0.780795i	−0.920646	−	0.390397i	$-0.872338\pi$
$509$		−	17.6155i		−	0.780795i	0.920646	−	0.390397i	$-0.127662\pi$
$510$		0			0
$511$	−4.38684	+	24.3976i	−0.194062	+	1.07929i
$512$	15.7732	−	16.2236i	0.697083	−	0.716990i
$513$	11.5076			0.508072
$514$	−8.01726	−	17.1231i	−0.353626	−	0.755268i
$515$		0			0
$516$	10.9418	+	9.12311i	0.481687	+	0.401622i
$517$		−	24.0000i		−	1.05552i
$518$	−7.23182	+	1.92375i	−0.317748	+	0.0845248i
$519$			0.230559i			0.0101204i
$520$		0			0
$521$			26.2462i			1.14987i	0.818200	+	0.574934i	$0.194972\pi$
$521$			26.2462i			1.14987i	−0.818200	+	0.574934i	$0.805028\pi$
$522$	−5.43845	+	2.54635i	−0.238034	+	0.111451i
$523$	−17.2015			−0.752170			−0.376085	−	0.926585i	$-0.622730\pi$
$523$	−17.2015			−0.752170			−0.376085	+	0.926585i	$0.622730\pi$
$524$	17.7597	−	21.3002i	0.775838	−	0.930503i
$525$		0			0
$526$	−1.19224	−	2.54635i	−0.0519840	−	0.111026i
$527$			47.5130i			2.06970i
$528$	8.83841	−	1.61553i	0.384642	−	0.0703068i
$529$	−9.87689			−0.429430
$530$		0			0
$531$	23.2306			1.00812
$532$	9.72521	−	8.15638i	0.421641	−	0.353624i
$533$	14.2462			0.617072
$534$	6.73863	+	14.3922i	0.291609	+	0.622813i
$535$		0			0
$536$	−39.0540	−	10.2683i	−1.68687	−	0.443524i
$537$		−	0.492423i		−	0.0212496i
$538$	9.74247	+	20.8078i	0.420028	+	0.897086i
$539$	−5.84912	+	15.7392i	−0.251939	+	0.677937i
$540$		0			0
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$	30.4268	−	14.2462i	1.30694	−	0.611927i
$543$			6.43971i			0.276354i
$544$	32.8255	−	23.3693i	1.40738	−	1.00195i
$545$		0			0
$546$	1.80145	+	6.77206i	0.0770951	+	0.289818i
$547$			1.75757i			0.0751484i	0.999294	+	0.0375742i	$0.0119631\pi$
$547$			1.75757i			0.0751484i	−0.999294	+	0.0375742i	$0.988037\pi$
$548$	17.9309	−	21.5054i	0.765969	−	0.918667i
$549$			4.24621i			0.181224i
$550$		0			0
$551$	4.79741			0.204377
$552$	14.6875	+	3.86174i	0.625143	+	0.164367i
$553$	−2.00000	+	11.1231i	−0.0850487	+	0.473003i
$554$	−5.43845	+	2.54635i	−0.231057	+	0.108184i
$555$		0			0
$556$	−1.72521	+	2.06913i	−0.0731650	+	0.0877507i
$557$	−6.49242			−0.275093			−0.137546	−	0.990495i	$-0.543922\pi$
$557$	−6.49242			−0.275093			−0.137546	+	0.990495i	$0.543922\pi$
$558$	−18.1379	+	8.49242i	−0.767840	+	0.359513i
$559$	−15.2134			−0.643457
$560$		0			0
$561$	16.0000			0.675521
$562$	5.93087	−	2.77691i	0.250179	−	0.117137i
$563$	26.7963			1.12933			0.564665	−	0.825320i	$-0.309005\pi$
$563$	26.7963			1.12933			0.564665	+	0.825320i	$0.309005\pi$
$564$	−12.0000	+	14.3922i	−0.505291	+	0.606022i
$565$		0			0
$566$	31.6261	−	14.8078i	1.32934	−	0.622417i
$567$	−4.88742	−	0.878787i	−0.205252	−	0.0369056i
$568$	−16.8078	−	4.41921i	−0.705238	−	0.185426i
$569$	−37.1231			−1.55628			−0.778141	−	0.628090i	$-0.783837\pi$
$569$	−37.1231			−1.55628			−0.778141	+	0.628090i	$0.783837\pi$
$570$		0			0
$571$		−	28.0281i		−	1.17294i	−0.809972	−	0.586469i	$-0.800518\pi$
$571$		−	28.0281i		−	1.17294i	0.809972	−	0.586469i	$-0.199482\pi$
$572$	−6.14441	+	7.36932i	−0.256911	+	0.308127i
$573$		−	1.26137i		−	0.0526943i
$574$	−6.85155	−	25.7565i	−0.285978	−	1.07506i
$575$		0			0
$576$	14.7884	+	8.35401i	0.616181	+	0.348084i
$577$			4.38447i			0.182528i	0.995827	+	0.0912640i	$0.0290907\pi$
$577$			4.38447i			0.182528i	−0.995827	+	0.0912640i	$0.970909\pi$
$578$	43.2116	−	20.2323i	1.79737	−	0.841551i
$579$	−9.82538			−0.408329
$580$		0			0
$581$	−2.43845	−	0.438447i	−0.101164	−	0.0181899i
$582$	−4.00000	−	8.54312i	−0.165805	−	0.354124i
$583$		−	4.79741i		−	0.198688i
$584$	25.6294	+	6.73863i	1.06055	+	0.278847i
$585$		0			0
$586$	19.3373	+	41.3002i	0.798816	+	1.70609i
$587$	8.65840			0.357370			0.178685	−	0.983906i	$-0.442816\pi$
$587$	8.65840			0.357370			0.178685	+	0.983906i	$0.442816\pi$
$588$	11.3772	−	6.51389i	0.469188	−	0.268628i
$589$	16.0000			0.659269
$590$		0			0
$591$	−16.8557			−0.693350
$592$	1.43845	+	7.86962i	0.0591198	+	0.323439i
$593$			13.3693i			0.549012i	0.961585	+	0.274506i	$0.0885143\pi$
$593$			13.3693i			0.549012i	−0.961585	+	0.274506i	$0.911486\pi$
$594$	6.90082	+	14.7386i	0.283144	+	0.604733i
$595$		0			0
$596$	−24.8078	+	29.7533i	−1.01617	+	1.21874i
$597$	15.0152			0.614529
$598$	−14.6875	+	6.87689i	−0.600618	+	0.281217i
$599$		−	10.1207i		−	0.413520i	−0.978392	−	0.206760i	$-0.933708\pi$
$599$		−	10.1207i		−	0.413520i	0.978392	−	0.206760i	$-0.0662919\pi$
$600$		0			0
$601$		−	8.87689i		−	0.362096i	−0.983474	−	0.181048i	$-0.942051\pi$
$601$		−	8.87689i		−	0.362096i	0.983474	−	0.181048i	$-0.0579489\pi$
$602$	7.31670	+	27.5051i	0.298206	+	1.12102i
$603$		−	30.3115i		−	1.23438i
$604$	22.5616	+	18.8114i	0.918017	+	0.765427i
$605$		0			0
$606$	−3.86174	−	8.24782i	−0.156872	−	0.335045i
$607$	−7.90198			−0.320732			−0.160366	−	0.987058i	$-0.551267\pi$
$607$	−7.90198			−0.320732			−0.160366	+	0.987058i	$0.551267\pi$
$608$	−7.86962	−	11.0540i	−0.319155	−	0.448298i
$609$	4.87689	+	0.876894i	0.197622	+	0.0355336i
$610$		0			0
$611$		−	20.0108i		−	0.809550i
$612$	23.2306	+	19.3693i	0.939043	+	0.782958i
$613$	−11.7538			−0.474731			−0.237366	−	0.971420i	$-0.576284\pi$
$613$	−11.7538			−0.474731			−0.237366	+	0.971420i	$0.576284\pi$
$614$	−40.1692	+	18.8078i	−1.62110	+	0.759020i
$615$		0			0
$616$	16.2785	+	7.56463i	0.655878	+	0.304788i
$617$	26.0000			1.04672			0.523360	−	0.852111i	$-0.324678\pi$
$617$	26.0000			1.04672			0.523360	+	0.852111i	$0.324678\pi$
$618$	−1.75379	+	0.821147i	−0.0705477	+	0.0330314i
$619$	−48.8600			−1.96385			−0.981925	−	0.189273i	$-0.939387\pi$
$619$	−48.8600			−1.96385			−0.981925	+	0.189273i	$0.939387\pi$
$620$		0			0
$621$			27.5076i			1.10384i
$622$	11.9935	−	5.61553i	0.480897	−	0.225162i
$623$	−5.61856	+	31.2479i	−0.225103	+	1.25192i
$624$	7.36932	−	1.34700i	0.295009	−	0.0539232i
$625$		0			0
$626$	4.56685	+	9.75379i	0.182528	+	0.389840i
$627$		−	5.38800i		−	0.215176i
$628$	24.9559	+	20.8078i	0.995847	+	0.830320i
$629$			14.2462i			0.568034i
$630$		0			0
$631$		−	7.19612i		−	0.286473i	−0.989688	−	0.143236i	$-0.954249\pi$
$631$		−	7.19612i		−	0.286473i	0.989688	−	0.143236i	$-0.0457509\pi$
$632$	11.6847	+	3.07221i	0.464791	+	0.122206i
$633$		−	17.2614i		−	0.686078i
$634$	−5.43845	+	2.54635i	−0.215988	+	0.101129i
$635$		0			0
$636$	−2.39871	+	2.87689i	−0.0951149	+	0.114076i
$637$	−4.87689	+	13.1231i	−0.193230	+	0.519956i
$638$	2.87689	+	6.14441i	0.113897	+	0.243260i
$639$		−	13.0452i		−	0.516061i
$640$		0			0
$641$	1.12311			0.0443600			0.0221800	−	0.999754i	$-0.492939\pi$
$641$	1.12311			0.0443600			0.0221800	+	0.999754i	$0.492939\pi$
$642$	5.32326	+	11.3693i	0.210092	+	0.448711i
$643$	−4.91269			−0.193738			−0.0968688	−	0.995297i	$-0.530883\pi$
$643$	−4.91269			−0.193738			−0.0968688	+	0.995297i	$0.530883\pi$
$644$	19.4969	+	23.2470i	0.768286	+	0.916061i
$645$		0			0
$646$	−10.2462	−	21.8836i	−0.403132	−	0.861000i
$647$	−37.7382			−1.48364			−0.741820	−	0.670599i	$-0.766037\pi$
$647$	−37.7382			−1.48364			−0.741820	+	0.670599i	$0.766037\pi$
$648$	−1.34991	+	5.13416i	−0.0530293	+	0.201689i
$649$		−	26.2462i		−	1.03025i
$650$		0			0
$651$	16.2651	+	2.92456i	0.637479	+	0.114622i
$652$	1.43845	+	1.19935i	0.0563339	+	0.0469703i
$653$	−42.9848			−1.68213			−0.841063	−	0.540936i	$-0.818070\pi$
$653$	−42.9848			−1.68213			−0.841063	+	0.540936i	$0.818070\pi$
$654$	−1.34700	+	0.630683i	−0.0526719	+	0.0246617i
$655$		0			0
$656$	−28.0281	+	5.12311i	−1.09431	+	0.200024i
$657$			19.8920i			0.776063i
$658$	−36.1786	+	9.62395i	−1.41039	+	0.375181i
$659$		−	4.27156i		−	0.166396i	−0.996533	−	0.0831981i	$-0.973487\pi$
$659$		−	4.27156i		−	0.166396i	0.996533	−	0.0831981i	$-0.0265134\pi$
$660$		0			0
$661$		−	4.24621i		−	0.165158i	−0.996585	−	0.0825792i	$-0.973684\pi$
$661$		−	4.24621i		−	0.165158i	0.996585	−	0.0825792i	$-0.0263158\pi$
$662$	−17.4384	−	37.2447i	−0.677764	−	1.44756i
$663$	13.3405			0.518103
$664$	−0.673500	+	2.56155i	−0.0261369	+	0.0994075i
$665$		0			0
$666$	−5.43845	+	2.54635i	−0.210736	+	0.0986692i
$667$			11.4677i			0.444030i
$668$	−2.92456	+	3.50758i	−0.113155	+	0.135712i
$669$	−12.1080			−0.468120
$670$		0			0
$671$	4.79741			0.185202
$672$	−5.97950	−	12.6756i	−0.230664	−	0.488970i
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$	5.43845	−	2.54635i	0.209481	−	0.0980818i
$675$		0			0
$676$	11.5270	−	13.8249i	0.443346	−	0.531728i
$677$			16.7386i			0.643318i	0.946856	+	0.321659i	$0.104240\pi$
$677$			16.7386i			0.643318i	−0.946856	+	0.321659i	$0.895760\pi$
$678$	−17.3815	+	8.13826i	−0.667534	+	0.312548i
$679$	3.33513	−	18.5485i	0.127991	−	0.711827i
$680$		0			0
$681$	13.3693			0.512313
$682$	9.59482	+	20.4924i	0.367405	+	0.784695i
$683$			7.60669i			0.291062i	0.989354	+	0.145531i	$0.0464890\pi$
$683$			7.60669i			0.291062i	−0.989354	+	0.145531i	$0.953511\pi$
$684$	6.52262	−	7.82292i	0.249398	−	0.299117i
$685$		0			0
$686$	26.0715	+	2.50580i	0.995413	+	0.0956718i
$687$			19.7802i			0.754663i
$688$	29.9309	−	5.47091i	1.14110	−	0.208577i
$689$		−	4.00000i		−	0.152388i
$690$		0			0
$691$	−22.4095			−0.852497			−0.426249	−	0.904606i	$-0.640165\pi$
$691$	−22.4095			−0.852497			−0.426249	+	0.904606i	$0.640165\pi$
$692$	0.378206	+	0.315342i	0.0143772	+	0.0119875i
$693$	−2.38447	+	13.2614i	−0.0905786	+	0.503758i
$694$	5.68466	+	12.1412i	0.215787	+	0.460873i
$695$		0			0
$696$	1.34700	−	5.12311i	0.0510579	−	0.194191i
$697$	−50.7386			−1.92186
$698$	−16.7080	−	35.6847i	−0.632408	−	1.35068i
$699$	−22.7048			−0.858774
$700$		0			0
$701$	2.87689			0.108659			0.0543294	−	0.998523i	$-0.482698\pi$
$701$	2.87689			0.108659			0.0543294	+	0.998523i	$0.482698\pi$
$702$	5.75379	+	12.2888i	0.217163	+	0.463812i
$703$	4.79741			0.180938
$704$	9.43845	−	16.7080i	0.355725	−	0.629707i
$705$		0			0
$706$	−3.21985	−	6.87689i	−0.121181	−	0.258815i
$707$	3.21985	−	17.9074i	0.121095	−	0.673476i
$708$	−13.1231	+	15.7392i	−0.493197	+	0.591517i
$709$	−4.73863			−0.177963			−0.0889816	−	0.996033i	$-0.528361\pi$
$709$	−4.73863			−0.177963			−0.0889816	+	0.996033i	$0.528361\pi$
$710$		0			0
$711$			9.06897i			0.340113i
$712$	32.8255	+	8.63068i	1.23019	+	0.323449i
$713$			38.2462i			1.43233i
$714$	−6.41597	−	24.1191i	−0.240112	−	0.902633i
$715$		0			0
$716$	−0.807764	−	0.673500i	−0.0301876	−	0.0251699i
$717$		−	12.0000i		−	0.448148i
$718$	9.93087	+	21.2101i	0.370617	+	0.791556i
$719$	−37.9182			−1.41411			−0.707055	−	0.707159i	$-0.749977\pi$
$719$	−37.9182			−1.41411			−0.707055	+	0.707159i	$0.749977\pi$
$720$		0			0
$721$	−3.80776	−	0.684658i	−0.141809	−	0.0254980i
$722$	16.9654	−	7.94344i	0.631388	−	0.295624i
$723$		−	14.6228i		−	0.543828i
$724$	10.5636	+	8.80776i	0.392594	+	0.327338i
$725$		0			0
$726$	−6.29206	+	2.94602i	−0.233520	+	0.109337i
$727$	−22.2942			−0.826847			−0.413423	−	0.910539i	$-0.635667\pi$
$727$	−22.2942			−0.826847			−0.413423	+	0.910539i	$0.635667\pi$
$728$	13.5727	+	6.30726i	0.503038	+	0.233763i
$729$	9.49242			0.351571
$730$		0			0
$731$	54.1833			2.00404
$732$	−2.87689	−	2.39871i	−0.106333	−	0.0886587i
$733$		−	48.7386i		−	1.80020i	−0.435681	−	0.900101i	$-0.643492\pi$
$733$		−	48.7386i		−	1.80020i	0.435681	−	0.900101i	$-0.356508\pi$
$734$	9.06897	−	4.24621i	0.334742	−	0.156731i
$735$		0			0
$736$	26.4233	−	18.8114i	0.973975	−	0.693399i
$737$	−34.2462			−1.26148
$738$	−9.06897	−	19.3693i	−0.333833	−	0.712994i
$739$		−	15.5087i		−	0.570496i	−0.958454	−	0.285248i	$-0.907924\pi$
$739$		−	15.5087i		−	0.570496i	0.958454	−	0.285248i	$-0.0920759\pi$
$740$		0			0
$741$		−	4.49242i		−	0.165033i
$742$	−7.23182	+	1.92375i	−0.265488	+	0.0706232i
$743$			15.0981i			0.553896i	0.960885	+	0.276948i	$0.0893229\pi$
$743$			15.0981i			0.553896i	−0.960885	+	0.276948i	$0.910677\pi$
$744$	4.49242	−	17.0862i	0.164700	−	0.626412i
$745$		0			0
$746$	28.8078	−	13.4882i	1.05473	−	0.493837i
$747$	−1.98813			−0.0727420
$748$	21.8836	−	26.2462i	0.800145	−	0.959657i
$749$	−4.43845	+	24.6847i	−0.162177	+	0.901958i
$750$		0			0
$751$			5.09271i			0.185835i	0.995674	+	0.0929177i	$0.0296194\pi$
$751$			5.09271i			0.185835i	−0.995674	+	0.0929177i	$0.970381\pi$
$752$	7.19612	+	39.3693i	0.262415	+	1.43565i
$753$	15.5076			0.565128
$754$	2.39871	+	5.12311i	0.0873557	+	0.186573i
$755$		0			0
$756$	19.4504	−	16.3128i	0.707405	−	0.593289i
$757$	12.2462			0.445096			0.222548	−	0.974922i	$-0.428563\pi$
$757$	12.2462			0.445096			0.222548	+	0.974922i	$0.428563\pi$
$758$	−13.4384	−	28.7016i	−0.488106	−	1.04249i
$759$	12.8794			0.467493
$760$		0			0
$761$		−	35.2311i		−	1.27712i	−0.769570	−	0.638562i	$-0.779529\pi$
$761$		−	35.2311i		−	1.27712i	0.769570	−	0.638562i	$-0.220471\pi$
$762$	7.42668	+	15.8617i	0.269040	+	0.574610i
$763$	−2.92456	−	0.525853i	−0.105876	−	0.0190372i
$764$	−2.06913	−	1.72521i	−0.0748585	−	0.0624158i
$765$		0			0
$766$	22.4095	−	10.4924i	0.809688	−	0.379107i
$767$		−	21.8836i		−	0.790173i
$768$	−14.0140	+	5.30019i	−0.505688	+	0.191254i
$769$		−	55.2311i		−	1.99168i	−0.0911037	−	0.995841i	$-0.529039\pi$
$769$		−	55.2311i		−	1.99168i	0.0911037	−	0.995841i	$-0.470961\pi$
$770$		0			0
$771$			12.5194i			0.450874i
$772$	−13.4384	+	16.1174i	−0.483660	+	0.580079i
$773$			16.7386i			0.602047i	0.953617	+	0.301023i	$0.0973282\pi$
$773$			16.7386i			0.602047i	−0.953617	+	0.301023i	$0.902672\pi$
$774$	9.68466	+	20.6843i	0.348108	+	0.743482i
$775$		0			0
$776$	−19.4849	−	5.12311i	−0.699469	−	0.183909i
$777$	4.87689	+	0.876894i	0.174958	+	0.0314584i
$778$	−1.43845	+	0.673500i	−0.0515708	+	0.0241461i
$779$			17.0862i			0.612178i
$780$		0			0
$781$	−14.7386			−0.527390
$782$	52.3104	−	24.4924i	1.87062	−	0.875847i
$783$	9.59482			0.342891
$784$	4.87560	−	27.5722i	0.174129	−	0.984723i
$785$		0			0
$786$	−16.6307	+	7.78671i	−0.593197	+	0.277743i
$787$	0.936426			0.0333800			0.0166900	−	0.999861i	$-0.494687\pi$
$787$	0.936426			0.0333800			0.0166900	+	0.999861i	$0.494687\pi$
$788$	−23.0540	+	27.6499i	−0.821264	+	0.984985i
$789$			1.86174i			0.0662797i
$790$		0			0
$791$	−37.7382	−	6.78554i	−1.34181	−	0.241266i
$792$	13.9309	+	3.66279i	0.495012	+	0.130152i
$793$	4.00000			0.142044
$794$	8.39547	+	17.9309i	0.297944	+	0.636343i
$795$		0			0
$796$	20.5366	−	24.6307i	0.727902	−	0.873011i
$797$		−	20.2462i		−	0.717158i	−0.933499	−	0.358579i	$-0.883261\pi$
$797$		−	20.2462i		−	0.717158i	0.933499	−	0.358579i	$-0.116739\pi$
$798$	−8.12209	+	2.16058i	−0.287519	+	0.0764836i
$799$			71.2695i			2.52133i
$800$		0			0
$801$			25.4773i			0.900195i
$802$	−7.68466	+	3.59806i	−0.271355	+	0.127052i
$803$	22.4742			0.793098
$804$	20.5366	+	17.1231i	0.724272	+	0.603885i
$805$		0			0
$806$	8.00000	+	17.0862i	0.281788	+	0.601837i
$807$		−	15.2134i		−	0.535536i
$808$	−18.8114	−	4.94602i	−0.661784	−	0.174001i
$809$	−18.9848			−0.667472			−0.333736	−	0.942667i	$-0.608309\pi$
$809$	−18.9848			−0.667472			−0.333736	+	0.942667i	$0.608309\pi$
$810$		0			0
$811$	9.06897			0.318455			0.159227	−	0.987242i	$-0.449100\pi$
$811$	9.06897			0.318455			0.159227	+	0.987242i	$0.449100\pi$
$812$	8.10871	−	6.80065i	0.284560	−	0.238656i
$813$	−22.2462			−0.780209
$814$	2.87689	+	6.14441i	0.100835	+	0.215362i
$815$		0			0
$816$	−26.2462	+	4.79741i	−0.918801	+	0.167943i
$817$		−	18.2462i		−	0.638354i
$818$	−5.32326	−	11.3693i	−0.186124	−	0.397519i
$819$	−1.98813	+	11.0571i	−0.0694710	+	0.386366i
$820$		0			0
$821$	−25.6155			−0.893988			−0.446994	−	0.894537i	$-0.647505\pi$
$821$	−25.6155			−0.893988			−0.446994	+	0.894537i	$0.647505\pi$
$822$	−16.7909	+	7.86174i	−0.585651	+	0.274210i
$823$		−	32.1843i		−	1.12188i	−0.827858	−	0.560938i	$-0.810441\pi$
$823$		−	32.1843i		−	1.12188i	0.827858	−	0.560938i	$-0.189559\pi$
$824$	−1.05171	+	4.00000i	−0.0366379	+	0.139347i
$825$		0			0
$826$	−39.5646	+	10.5247i	−1.37663	+	0.366200i
$827$			0.115279i			0.00400866i	0.999998	+	0.00200433i	$0.000637998\pi$
$827$			0.115279i			0.00400866i	−0.999998	+	0.00200433i	$0.999362\pi$
$828$	18.6998	+	15.5916i	0.649863	+	0.541845i
$829$		−	32.2462i		−	1.11996i	−0.828507	−	0.559979i	$-0.810809\pi$
$829$		−	32.2462i		−	1.11996i	0.828507	−	0.559979i	$-0.189191\pi$
$830$		0			0
$831$	3.97626			0.137935
$832$	7.86962	−	13.9309i	0.272830	−	0.482966i
$833$	17.3693	−	46.7386i	0.601811	−	1.61940i
$834$	1.61553	−	0.756412i	0.0559412	−	0.0261924i
$835$		0			0
$836$	−8.83841	−	7.36932i	−0.305683	−	0.254873i
$837$	32.0000			1.10608
$838$	15.3610	−	7.19224i	0.530638	−	0.248452i
$839$	35.2242			1.21607			0.608037	−	0.793909i	$-0.291957\pi$
$839$	35.2242			1.21607			0.608037	+	0.793909i	$0.291957\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	22.5616	−	10.5636i	0.777522	−	0.364046i
$843$	−4.33629			−0.149350
$844$	−28.3153	−	23.6089i	−0.974654	−	0.812650i
$845$		0			0
$846$	−27.2069	+	12.7386i	−0.935393	+	0.437963i
$847$	−13.6611	−	2.45635i	−0.469401	−	0.0844010i
$848$	1.43845	+	7.86962i	0.0493965	+	0.270244i
$849$	−23.1231			−0.793583
$850$		0			0
$851$			11.4677i			0.393107i
$852$	8.83841	+	7.36932i	0.302799	+	0.252469i
$853$			7.75379i			0.265485i	0.991151	+	0.132742i	$0.0423783\pi$
$853$			7.75379i			0.265485i	−0.991151	+	0.132742i	$0.957622\pi$
$854$	−1.92375	−	7.23182i	−0.0658295	−	0.247468i
$855$		0			0
$856$	25.9309	+	6.81791i	0.886299	+	0.233031i
$857$		−	15.6155i		−	0.533416i	−0.963777	−	0.266708i	$-0.914064\pi$
$857$		−	15.6155i		−	0.533416i	0.963777	−	0.266708i	$-0.0859360\pi$
$858$	5.75379	−	2.69400i	0.196431	−	0.0919716i
$859$	−41.3686			−1.41148			−0.705739	−	0.708472i	$-0.749385\pi$
$859$	−41.3686			−1.41148			−0.705739	+	0.708472i	$0.749385\pi$
$860$		0			0
$861$	−3.12311	+	17.3693i	−0.106435	+	0.591945i
$862$	21.9309	+	46.8395i	0.746968	+	1.59536i
$863$		−	41.7792i		−	1.42218i	−0.703101	−	0.711090i	$-0.748202\pi$
$863$		−	41.7792i		−	1.42218i	0.703101	−	0.711090i	$-0.251798\pi$
$864$	−15.7392	−	22.1080i	−0.535460	−	0.752128i
$865$		0			0
$866$	6.96556	+	14.8769i	0.236699	+	0.505537i
$867$	−31.5937			−1.07298
$868$	27.0436	−	22.6811i	0.917920	−	0.769845i
$869$	10.2462			0.347579
$870$		0			0
$871$	−28.5539			−0.967512
$872$	−0.807764	+	3.07221i	−0.0273543	+	0.104038i
$873$		−	15.1231i		−	0.511840i
$874$	−8.24782	−	17.6155i	−0.278987	−	0.595854i
$875$		0			0
$876$	−13.4773	−	11.2371i	−0.455355	−	0.379667i
$877$	48.7386			1.64579			0.822893	−	0.568196i	$-0.192358\pi$
$877$	48.7386			1.64579			0.822893	+	0.568196i	$0.192358\pi$
$878$	−23.2306	+	10.8769i	−0.783996	+	0.367077i
$879$		−	30.1962i		−	1.01849i
$880$		0			0
$881$		−	6.63068i		−	0.223393i	−0.993742	−	0.111697i	$-0.964371\pi$
$881$		−	6.63068i		−	0.223393i	0.993742	−	0.111697i	$-0.0356285\pi$
$882$	20.9469	−	1.72333i	0.705319	−	0.0580276i
$883$			13.4558i			0.452824i	0.974032	+	0.226412i	$0.0726996\pi$
$883$			13.4558i			0.452824i	−0.974032	+	0.226412i	$0.927300\pi$
$884$	18.2462	−	21.8836i	0.613686	−	0.736027i
$885$		0			0
$886$	18.1771	+	38.8222i	0.610671	+	1.30426i
$887$	−17.7274			−0.595227			−0.297613	−	0.954686i	$-0.596191\pi$
$887$	−17.7274			−0.595227			−0.297613	+	0.954686i	$0.596191\pi$
$888$	1.34700	−	5.12311i	0.0452024	−	0.171920i
$889$	−6.19224	+	34.4384i	−0.207681	+	1.15503i
$890$		0			0
$891$			4.50212i			0.150827i
$892$	−16.5604	+	19.8617i	−0.554483	+	0.665020i
$893$	24.0000			0.803129
$894$	23.2306	−	10.8769i	0.776949	−	0.363778i
$895$		0			0
$896$	−28.9712	−	7.52802i	−0.967859	−	0.251493i
$897$	10.7386			0.358553
$898$	−32.8078	+	15.3610i	−1.09481	+	0.512604i
$899$	13.3405			0.444932
$900$		0			0
$901$			14.2462i			0.474610i
$902$	−21.8836	+	10.2462i	−0.728646	+	0.341162i
$903$	3.33513	−	18.5485i	0.110986	−	0.617256i
$904$	−10.4233	+	39.6434i	−0.346674	+	1.31852i
$905$		0			0
$906$	−8.24782	−	17.6155i	−0.274016	−	0.585237i
$907$		−	14.5075i		−	0.481714i	−0.970561	−	0.240857i	$-0.922572\pi$
$907$		−	14.5075i		−	0.481714i	0.970561	−	0.240857i	$-0.0774285\pi$
$908$	18.2856	−	21.9309i	0.606829	−	0.727801i
$909$		−	14.6004i		−	0.484264i
$910$		0			0
$911$			10.9418i			0.362519i	0.983435	+	0.181259i	$0.0580174\pi$
$911$			10.9418i			0.362519i	−0.983435	+	0.181259i	$0.941983\pi$
$912$	1.61553	+	8.83841i	0.0534955	+	0.292669i
$913$			2.24621i			0.0743387i
$914$	7.68466	−	3.59806i	0.254186	−	0.119013i
$915$		0			0
$916$	32.4473	+	27.0540i	1.07209	+	0.893889i
$917$	−36.1080	−	6.49242i	−1.19239	−	0.214399i
$918$	−20.4924	−	43.7673i	−0.676351	−	1.44454i
$919$			29.9009i			0.986340i	0.869933	+	0.493170i	$0.164162\pi$
$919$			29.9009i			0.986340i	−0.869933	+	0.493170i	$0.835838\pi$
$920$		0			0
$921$	29.3693			0.967752
$922$	−22.5571	−	48.1771i	−0.742880	−	1.58663i
$923$	−12.2888			−0.404492
$924$	−7.63785	−	9.10694i	−0.251267	−	0.299596i
$925$		0			0
$926$	−13.1922	−	28.1757i	−0.433524	−	0.925911i
$927$	−3.10457			−0.101968
$928$	−6.56155	−	9.21662i	−0.215394	−	0.302550i
$929$			12.8769i			0.422477i	0.977435	+	0.211239i	$0.0677497\pi$
$929$			12.8769i			0.422477i	−0.977435	+	0.211239i	$0.932250\pi$
$930$		0			0
$931$	−15.7392	−	5.84912i	−0.515833	−	0.191697i
$932$	−31.0540	+	37.2447i	−1.01721	+	1.21999i
$933$	−8.76894			−0.287082
$934$	2.54635	−	1.19224i	0.0833192	−	0.0390112i
$935$		0			0
$936$	11.6153	+	3.05398i	0.379659	+	0.0998223i
$937$			36.1080i			1.17960i	0.807551	+	0.589798i	$0.200793\pi$
$937$			36.1080i			1.17960i	−0.807551	+	0.589798i	$0.799207\pi$
$938$	13.7327	+	51.6242i	0.448387	+	1.68559i
$939$		−	7.13138i		−	0.232724i
$940$		0			0
$941$		−	51.3693i		−	1.67459i	−0.546750	−	0.837296i	$-0.684135\pi$
$941$		−	51.3693i		−	1.67459i	0.546750	−	0.837296i	$-0.315865\pi$
$942$	−9.12311	−	19.4849i	−0.297247	−	0.634854i
$943$	−40.8427			−1.33002
$944$	7.86962	+	43.0540i	0.256134	+	1.40129i
$945$		0			0
$946$	23.3693	−	10.9418i	0.759802	−	0.355749i
$947$			18.8438i			0.612341i	0.951977	+	0.306171i	$0.0990478\pi$
$947$			18.8438i			0.612341i	−0.951977	+	0.306171i	$0.900952\pi$
$948$	−6.14441	−	5.12311i	−0.199561	−	0.166391i
$949$	18.7386			0.608282
$950$		0			0
$951$	3.97626			0.128939
$952$	−48.3399	−	22.4636i	−1.56671	−	0.728051i
$953$	−11.7538			−0.380743			−0.190371	−	0.981712i	$-0.560969\pi$
$953$	−11.7538			−0.380743			−0.190371	+	0.981712i	$0.560969\pi$
$954$	−5.43845	+	2.54635i	−0.176076	+	0.0824412i
$955$		0			0
$956$	−19.6847	−	16.4127i	−0.636647	−	0.530826i
$957$		−	4.49242i		−	0.145219i
$958$		0			0
$959$	−36.4559	−	6.55498i	−1.17722	−	0.211671i
$960$		0			0
$961$	13.4924			0.435239
$962$	2.39871	+	5.12311i	0.0773374	+	0.165176i
$963$			20.1261i			0.648554i
$964$	−23.9871	−	20.0000i	−0.772571	−	0.644157i
$965$		0			0
$966$	−5.16462	−	19.4150i	−0.166169	−	0.624666i
$967$			55.1197i			1.77253i	0.463179	+	0.886265i	$0.346709\pi$
$967$			55.1197i			1.77253i	−0.463179	+	0.886265i	$0.653291\pi$
$968$	−3.77320	+	14.3508i	−0.121275	+	0.461251i
$969$			16.0000i			0.513994i
$970$		0			0
$971$	−0.525853			−0.0168754			−0.00843771	−	0.999964i	$-0.502686\pi$
$971$	−0.525853			−0.0168754			−0.00843771	+	0.999964i	$0.502686\pi$
$972$	20.6843	−	24.8078i	0.663449	−	0.795709i
$973$	3.50758	+	0.630683i	0.112448	+	0.0202188i
$974$	11.4384	+	24.4300i	0.366511	+	0.782788i
$975$		0			0
$976$	−7.86962	+	1.43845i	−0.251900	+	0.0460436i
$977$	10.4924			0.335682			0.167841	−	0.985814i	$-0.446320\pi$
$977$	10.4924			0.335682			0.167841	+	0.985814i	$0.446320\pi$
$978$	−0.525853	−	1.12311i	−0.0168149	−	0.0359130i
$979$	28.7845			0.919956
$980$		0			0
$981$	−2.38447			−0.0761303
$982$	−8.17708	−	17.4644i	−0.260941	−	0.557313i
$983$	12.6994			0.405048			0.202524	−	0.979277i	$-0.435086\pi$
$983$	12.6994			0.405048			0.202524	+	0.979277i	$0.435086\pi$
$984$	18.2462	+	4.79741i	0.581668	+	0.152936i
$985$		0			0
$986$	−8.54312	−	18.2462i	−0.272068	−	0.581078i
$987$	24.3976	+	4.38684i	0.776585	+	0.139635i
$988$	−7.36932	−	6.14441i	−0.234449	−	0.195480i
$989$	43.6155			1.38689
$990$		0			0
$991$			34.4678i			1.09490i	0.836837	+	0.547452i	$0.184402\pi$
$991$			34.4678i			1.09490i	−0.836837	+	0.547452i	$0.815598\pi$
$992$	−21.8836	−	30.7386i	−0.694806	−	0.975953i
$993$			27.2311i			0.864151i
$994$	5.91016	+	22.2176i	0.187459	+	0.704700i
$995$		0			0
$996$	1.12311	−	1.34700i	0.0355870	−	0.0426813i
$997$		−	38.4924i		−	1.21907i	−0.792760	−	0.609534i	$-0.791357\pi$
$997$		−	38.4924i		−	1.21907i	0.792760	−	0.609534i	$-0.208643\pi$
$998$	16.3153	+	34.8460i	0.516453	+	1.10303i
$999$	9.59482			0.303567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.g.j.251.4		8
4.3	odd	2	inner	700.2.g.j.251.1		8
5.2	odd	4		700.2.c.j.699.3		8
5.3	odd	4		700.2.c.i.699.6		8
5.4	even	2		140.2.g.c.111.5	✓	8
7.6	odd	2	inner	700.2.g.j.251.3		8
15.14	odd	2		1260.2.c.c.811.4		8
20.3	even	4		700.2.c.i.699.4		8
20.7	even	4		700.2.c.j.699.5		8
20.19	odd	2		140.2.g.c.111.8	yes	8
28.27	even	2	inner	700.2.g.j.251.2		8
35.4	even	6		980.2.o.e.411.6		16
35.9	even	6		980.2.o.e.31.2		16
35.13	even	4		700.2.c.j.699.6		8
35.19	odd	6		980.2.o.e.31.1		16
35.24	odd	6		980.2.o.e.411.5		16
35.27	even	4		700.2.c.i.699.3		8
35.34	odd	2		140.2.g.c.111.6	yes	8
40.19	odd	2		2240.2.k.e.1791.4		8
40.29	even	2		2240.2.k.e.1791.6		8
60.59	even	2		1260.2.c.c.811.2		8
105.104	even	2		1260.2.c.c.811.3		8
140.19	even	6		980.2.o.e.31.6		16
140.27	odd	4		700.2.c.i.699.5		8
140.39	odd	6		980.2.o.e.411.1		16
140.59	even	6		980.2.o.e.411.2		16
140.79	odd	6		980.2.o.e.31.5		16
140.83	odd	4		700.2.c.j.699.4		8
140.139	even	2		140.2.g.c.111.7	yes	8
280.69	odd	2		2240.2.k.e.1791.3		8
280.139	even	2		2240.2.k.e.1791.5		8
420.419	odd	2		1260.2.c.c.811.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.c.111.5	✓	8	5.4	even	2
140.2.g.c.111.6	yes	8	35.34	odd	2
140.2.g.c.111.7	yes	8	140.139	even	2
140.2.g.c.111.8	yes	8	20.19	odd	2
700.2.c.i.699.3		8	35.27	even	4
700.2.c.i.699.4		8	20.3	even	4
700.2.c.i.699.5		8	140.27	odd	4
700.2.c.i.699.6		8	5.3	odd	4
700.2.c.j.699.3		8	5.2	odd	4
700.2.c.j.699.4		8	140.83	odd	4
700.2.c.j.699.5		8	20.7	even	4
700.2.c.j.699.6		8	35.13	even	4
700.2.g.j.251.1		8	4.3	odd	2	inner
700.2.g.j.251.2		8	28.27	even	2	inner
700.2.g.j.251.3		8	7.6	odd	2	inner
700.2.g.j.251.4		8	1.1	even	1	trivial
980.2.o.e.31.1		16	35.19	odd	6
980.2.o.e.31.2		16	35.9	even	6
980.2.o.e.31.5		16	140.79	odd	6
980.2.o.e.31.6		16	140.19	even	6
980.2.o.e.411.1		16	140.39	odd	6
980.2.o.e.411.2		16	140.59	even	6
980.2.o.e.411.5		16	35.24	odd	6
980.2.o.e.411.6		16	35.4	even	6
1260.2.c.c.811.1		8	420.419	odd	2
1260.2.c.c.811.2		8	60.59	even	2
1260.2.c.c.811.3		8	105.104	even	2
1260.2.c.c.811.4		8	15.14	odd	2
2240.2.k.e.1791.3		8	280.69	odd	2
2240.2.k.e.1791.4		8	40.19	odd	2
2240.2.k.e.1791.5		8	280.139	even	2
2240.2.k.e.1791.6		8	40.29	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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28078 + 0.599676i) q^{2} +0.936426 q^{3} +(1.28078 - 1.53610i) q^{4} +(-1.19935 + 0.561553i) q^{6} +(-2.60399 - 0.468213i) q^{7} +(-0.719224 + 2.73546i) q^{8} -2.12311 q^{9} +O(q^{10})\)	\(q+(-1.28078 + 0.599676i) q^{2} +0.936426 q^{3} +(1.28078 - 1.53610i) q^{4} +(-1.19935 + 0.561553i) q^{6} +(-2.60399 - 0.468213i) q^{7} +(-0.719224 + 2.73546i) q^{8} -2.12311 q^{9} +2.39871i q^{11} +(1.19935 - 1.43845i) q^{12} +2.00000i q^{13} +(3.61591 - 0.961876i) q^{14} +(-0.719224 - 3.93481i) q^{16} -7.12311i q^{17} +(2.71922 - 1.27318i) q^{18} -2.39871 q^{19} +(-2.43845 - 0.438447i) q^{21} +(-1.43845 - 3.07221i) q^{22} -5.73384i q^{23} +(-0.673500 + 2.56155i) q^{24} +(-1.19935 - 2.56155i) q^{26} -4.79741 q^{27} +(-4.05436 + 3.40032i) q^{28} -2.00000 q^{29} -6.67026 q^{31} +(3.28078 + 4.60831i) q^{32} +2.24621i q^{33} +(4.27156 + 9.12311i) q^{34} +(-2.71922 + 3.26131i) q^{36} -2.00000 q^{37} +(3.07221 - 1.43845i) q^{38} +1.87285i q^{39} -7.12311i q^{41} +(3.38603 - 0.900726i) q^{42} +7.60669i q^{43} +(3.68466 + 3.07221i) q^{44} +(3.43845 + 7.34376i) q^{46} -10.0054 q^{47} +(-0.673500 - 3.68466i) q^{48} +(6.56155 + 2.43845i) q^{49} -6.67026i q^{51} +(3.07221 + 2.56155i) q^{52} -2.00000 q^{53} +(6.14441 - 2.87689i) q^{54} +(3.15363 - 6.78636i) q^{56} -2.24621 q^{57} +(2.56155 - 1.19935i) q^{58} -10.9418 q^{59} -2.00000i q^{61} +(8.54312 - 4.00000i) q^{62} +(5.52855 + 0.994066i) q^{63} +(-6.96543 - 3.93481i) q^{64} +(-1.34700 - 2.87689i) q^{66} +14.2770i q^{67} +(-10.9418 - 9.12311i) q^{68} -5.36932i q^{69} +6.14441i q^{71} +(1.52699 - 5.80766i) q^{72} -9.36932i q^{73} +(2.56155 - 1.19935i) q^{74} +(-3.07221 + 3.68466i) q^{76} +(1.12311 - 6.24621i) q^{77} +(-1.12311 - 2.39871i) q^{78} -4.27156i q^{79} +1.87689 q^{81} +(4.27156 + 9.12311i) q^{82} +0.936426 q^{83} +(-3.79661 + 3.18415i) q^{84} +(-4.56155 - 9.74247i) q^{86} -1.87285 q^{87} +(-6.56155 - 1.72521i) q^{88} -12.0000i q^{89} +(0.936426 - 5.20798i) q^{91} +(-8.80776 - 7.34376i) q^{92} -6.24621 q^{93} +(12.8147 - 6.00000i) q^{94} +(3.07221 + 4.31534i) q^{96} +7.12311i q^{97} +(-9.86616 + 0.811703i) q^{98} -5.09271i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 16 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^4 - 14 * q^8 + 16 * q^9	\( 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 16 q^{9} - 6 q^{14} - 14 q^{16} + 30 q^{18} - 36 q^{21} - 28 q^{22} - 14 q^{28} - 16 q^{29} + 18 q^{32} - 30 q^{36} - 16 q^{37} - 8 q^{42} - 20 q^{44} + 44 q^{46} + 36 q^{49} - 16 q^{53} + 2 q^{56} + 48 q^{57} + 4 q^{58} + 2 q^{64} - 62 q^{72} + 4 q^{74} - 24 q^{77} + 24 q^{78} + 48 q^{81} + 8 q^{84} - 20 q^{86} - 36 q^{88} + 12 q^{92} + 16 q^{93} - 26 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^4 - 14 * q^8 + 16 * q^9 - 6 * q^14 - 14 * q^16 + 30 * q^18 - 36 * q^21 - 28 * q^22 - 14 * q^28 - 16 * q^29 + 18 * q^32 - 30 * q^36 - 16 * q^37 - 8 * q^42 - 20 * q^44 + 44 * q^46 + 36 * q^49 - 16 * q^53 + 2 * q^56 + 48 * q^57 + 4 * q^58 + 2 * q^64 - 62 * q^72 + 4 * q^74 - 24 * q^77 + 24 * q^78 + 48 * q^81 + 8 * q^84 - 20 * q^86 - 36 * q^88 + 12 * q^92 + 16 * q^93 - 26 * q^98

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