LMFDB - Embedded newform 429.2.e.b.428.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(428,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("429.428");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.e (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3317760000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			428.4
Root			$-0.578737 + 2.15988i$ of defining polynomial
Character	$\chi$	$=$	429.428
Dual form			429.2.e.b.428.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.73205i q^{3} +1.00000 q^{4} +3.16228 q^{5} +1.73205 q^{6} +3.46410 q^{7} -3.00000i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.73205i q^{3} +1.00000 q^{4} +3.16228 q^{5} +1.73205 q^{6} +3.46410 q^{7} -3.00000i q^{8} -3.00000 q^{9} -3.16228i q^{10} +(-3.16228 + 1.00000i) q^{11} +1.73205i q^{12} +(1.73205 - 3.16228i) q^{13} -3.46410i q^{14} +5.47723i q^{15} -1.00000 q^{16} -5.47723 q^{17} +3.00000i q^{18} -3.46410 q^{19} +3.16228 q^{20} +6.00000i q^{21} +(1.00000 + 3.16228i) q^{22} +6.92820i q^{23} +5.19615 q^{24} +5.00000 q^{25} +(-3.16228 - 1.73205i) q^{26} -5.19615i q^{27} +3.46410 q^{28} -5.47723 q^{29} +5.47723 q^{30} -5.47723i q^{31} -5.00000i q^{32} +(-1.73205 - 5.47723i) q^{33} +5.47723i q^{34} +10.9545 q^{35} -3.00000 q^{36} +3.46410i q^{38} +(5.47723 + 3.00000i) q^{39} -9.48683i q^{40} +2.00000i q^{41} +6.00000 q^{42} +9.48683i q^{43} +(-3.16228 + 1.00000i) q^{44} -9.48683 q^{45} +6.92820 q^{46} +6.32456 q^{47} -1.73205i q^{48} +5.00000 q^{49} -5.00000i q^{50} -9.48683i q^{51} +(1.73205 - 3.16228i) q^{52} -6.92820i q^{53} -5.19615 q^{54} +(-10.0000 + 3.16228i) q^{55} -10.3923i q^{56} -6.00000i q^{57} +5.47723i q^{58} +6.32456 q^{59} +5.47723i q^{60} +12.6491i q^{61} -5.47723 q^{62} -10.3923 q^{63} -7.00000 q^{64} +(5.47723 - 10.0000i) q^{65} +(-5.47723 + 1.73205i) q^{66} +5.47723i q^{67} -5.47723 q^{68} -12.0000 q^{69} -10.9545i q^{70} -6.32456 q^{71} +9.00000i q^{72} -6.92820 q^{73} +8.66025i q^{75} -3.46410 q^{76} +(-10.9545 + 3.46410i) q^{77} +(3.00000 - 5.47723i) q^{78} +3.16228i q^{79} -3.16228 q^{80} +9.00000 q^{81} +2.00000 q^{82} -2.00000i q^{83} +6.00000i q^{84} -17.3205 q^{85} +9.48683 q^{86} -9.48683i q^{87} +(3.00000 + 9.48683i) q^{88} +3.16228 q^{89} +9.48683i q^{90} +(6.00000 - 10.9545i) q^{91} +6.92820i q^{92} +9.48683 q^{93} -6.32456i q^{94} -10.9545 q^{95} +8.66025 q^{96} -10.9545i q^{97} -5.00000i q^{98} +(9.48683 - 3.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 24 q^{9}+O(q^{10}) $ 8 * q + 8 * q^4 - 24 * q^9	$ 8 q + 8 q^{4} - 24 q^{9} - 8 q^{16} + 8 q^{22} + 40 q^{25} - 24 q^{36} + 48 q^{42} + 40 q^{49} - 80 q^{55} - 56 q^{64} - 96 q^{69} + 24 q^{78} + 72 q^{81} + 16 q^{82} + 24 q^{88} + 48 q^{91}+O(q^{100}) $ 8 * q + 8 * q^4 - 24 * q^9 - 8 * q^16 + 8 * q^22 + 40 * q^25 - 24 * q^36 + 48 * q^42 + 40 * q^49 - 80 * q^55 - 56 * q^64 - 96 * q^69 + 24 * q^78 + 72 * q^81 + 16 * q^82 + 24 * q^88 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$-1$	$-1$

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	−0.935414	−	0.353553i	$-0.884973\pi$
$2$		−	1.00000i		−	0.707107i	0.935414	−	0.353553i	$-0.115027\pi$
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$	1.00000			0.500000
$5$	3.16228			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$5$	3.16228			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$6$	1.73205			0.707107
$7$	3.46410			1.30931			0.654654	−	0.755929i	$-0.272814\pi$
$7$	3.46410			1.30931			0.654654	+	0.755929i	$0.272814\pi$
$8$		−	3.00000i		−	1.06066i
$9$	−3.00000			−1.00000
$10$		−	3.16228i		−	1.00000i
$11$	−3.16228	+	1.00000i	−0.953463	+	0.301511i
$11$	−3.16228	+	1.00000i	−0.953463	+	0.301511i
$12$			1.73205i			0.500000i
$13$	1.73205	−	3.16228i	0.480384	−	0.877058i
$13$	1.73205	−	3.16228i	0.480384	−	0.877058i
$14$		−	3.46410i		−	0.925820i
$15$			5.47723i			1.41421i
$16$	−1.00000			−0.250000
$17$	−5.47723			−1.32842			−0.664211	−	0.747545i	$-0.731232\pi$
$17$	−5.47723			−1.32842			−0.664211	+	0.747545i	$0.731232\pi$
$18$			3.00000i			0.707107i
$19$	−3.46410			−0.794719			−0.397360	−	0.917663i	$-0.630073\pi$
$19$	−3.46410			−0.794719			−0.397360	+	0.917663i	$0.630073\pi$
$20$	3.16228			0.707107
$21$			6.00000i			1.30931i
$22$	1.00000	+	3.16228i	0.213201	+	0.674200i
$23$			6.92820i			1.44463i	0.691564	+	0.722315i	$0.256922\pi$
$23$			6.92820i			1.44463i	−0.691564	+	0.722315i	$0.743078\pi$
$24$	5.19615			1.06066
$25$	5.00000			1.00000
$26$	−3.16228	−	1.73205i	−0.620174	−	0.339683i
$27$		−	5.19615i		−	1.00000i
$28$	3.46410			0.654654
$29$	−5.47723			−1.01710			−0.508548	−	0.861034i	$-0.669817\pi$
$29$	−5.47723			−1.01710			−0.508548	+	0.861034i	$0.669817\pi$
$30$	5.47723			1.00000
$31$		−	5.47723i		−	0.983739i	−0.870669	−	0.491869i	$-0.836314\pi$
$31$		−	5.47723i		−	0.983739i	0.870669	−	0.491869i	$-0.163686\pi$
$32$		−	5.00000i		−	0.883883i
$33$	−1.73205	−	5.47723i	−0.301511	−	0.953463i
$34$			5.47723i			0.939336i
$35$	10.9545			1.85164
$36$	−3.00000			−0.500000
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$			3.46410i			0.561951i
$39$	5.47723	+	3.00000i	0.877058	+	0.480384i
$40$		−	9.48683i		−	1.50000i
$41$			2.00000i			0.312348i	0.987730	+	0.156174i	$0.0499160\pi$
$41$			2.00000i			0.312348i	−0.987730	+	0.156174i	$0.950084\pi$
$42$	6.00000			0.925820
$43$			9.48683i			1.44673i	0.690467	+	0.723364i	$0.257405\pi$
$43$			9.48683i			1.44673i	−0.690467	+	0.723364i	$0.742595\pi$
$44$	−3.16228	+	1.00000i	−0.476731	+	0.150756i
$45$	−9.48683			−1.41421
$46$	6.92820			1.02151
$47$	6.32456			0.922531			0.461266	−	0.887262i	$-0.347396\pi$
$47$	6.32456			0.922531			0.461266	+	0.887262i	$0.347396\pi$
$48$		−	1.73205i		−	0.250000i
$49$	5.00000			0.714286
$50$		−	5.00000i		−	0.707107i
$51$		−	9.48683i		−	1.32842i
$52$	1.73205	−	3.16228i	0.240192	−	0.438529i
$53$		−	6.92820i		−	0.951662i	−0.879537	−	0.475831i	$-0.842147\pi$
$53$		−	6.92820i		−	0.951662i	0.879537	−	0.475831i	$-0.157853\pi$
$54$	−5.19615			−0.707107
$55$	−10.0000	+	3.16228i	−1.34840	+	0.426401i
$56$		−	10.3923i		−	1.38873i
$57$		−	6.00000i		−	0.794719i
$58$			5.47723i			0.719195i
$59$	6.32456			0.823387			0.411693	−	0.911322i	$-0.364937\pi$
$59$	6.32456			0.823387			0.411693	+	0.911322i	$0.364937\pi$
$60$			5.47723i			0.707107i
$61$			12.6491i			1.61955i	0.586739	+	0.809776i	$0.300412\pi$
$61$			12.6491i			1.61955i	−0.586739	+	0.809776i	$0.699588\pi$
$62$	−5.47723			−0.695608
$63$	−10.3923			−1.30931
$64$	−7.00000			−0.875000
$65$	5.47723	−	10.0000i	0.679366	−	1.24035i
$66$	−5.47723	+	1.73205i	−0.674200	+	0.213201i
$67$			5.47723i			0.669150i	0.942369	+	0.334575i	$0.108593\pi$
$67$			5.47723i			0.669150i	−0.942369	+	0.334575i	$0.891407\pi$
$68$	−5.47723			−0.664211
$69$	−12.0000			−1.44463
$70$		−	10.9545i		−	1.30931i
$71$	−6.32456			−0.750587			−0.375293	−	0.926906i	$-0.622458\pi$
$71$	−6.32456			−0.750587			−0.375293	+	0.926906i	$0.622458\pi$
$72$			9.00000i			1.06066i
$73$	−6.92820			−0.810885			−0.405442	−	0.914121i	$-0.632883\pi$
$73$	−6.92820			−0.810885			−0.405442	+	0.914121i	$0.632883\pi$
$74$		0			0
$75$			8.66025i			1.00000i
$76$	−3.46410			−0.397360
$77$	−10.9545	+	3.46410i	−1.24838	+	0.394771i
$78$	3.00000	−	5.47723i	0.339683	−	0.620174i
$79$			3.16228i			0.355784i	0.984050	+	0.177892i	$0.0569278\pi$
$79$			3.16228i			0.355784i	−0.984050	+	0.177892i	$0.943072\pi$
$80$	−3.16228			−0.353553
$81$	9.00000			1.00000
$82$	2.00000			0.220863
$83$		−	2.00000i		−	0.219529i	−0.993958	−	0.109764i	$-0.964990\pi$
$83$		−	2.00000i		−	0.219529i	0.993958	−	0.109764i	$-0.0350096\pi$
$84$			6.00000i			0.654654i
$85$	−17.3205			−1.87867
$86$	9.48683			1.02299
$87$		−	9.48683i		−	1.01710i
$88$	3.00000	+	9.48683i	0.319801	+	1.01130i
$89$	3.16228			0.335201			0.167600	−	0.985855i	$-0.446398\pi$
$89$	3.16228			0.335201			0.167600	+	0.985855i	$0.446398\pi$
$90$			9.48683i			1.00000i
$91$	6.00000	−	10.9545i	0.628971	−	1.14834i
$92$			6.92820i			0.722315i
$93$	9.48683			0.983739
$94$		−	6.32456i		−	0.652328i
$95$	−10.9545			−1.12390
$96$	8.66025			0.883883
$97$		−	10.9545i		−	1.11226i	−0.831097	−	0.556128i	$-0.812286\pi$
$97$		−	10.9545i		−	1.11226i	0.831097	−	0.556128i	$-0.187714\pi$
$98$		−	5.00000i		−	0.505076i
$99$	9.48683	−	3.00000i	0.953463	−	0.301511i
$100$	5.00000			0.500000
$101$	5.47723			0.545004			0.272502	−	0.962155i	$-0.412149\pi$
$101$	5.47723			0.545004			0.272502	+	0.962155i	$0.412149\pi$
$102$	−9.48683			−0.939336
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$	−9.48683	−	5.19615i	−0.930261	−	0.509525i
$105$			18.9737i			1.85164i
$106$	−6.92820			−0.672927
$107$	10.9545			1.05901			0.529503	−	0.848308i	$-0.322378\pi$
$107$	10.9545			1.05901			0.529503	+	0.848308i	$0.322378\pi$
$108$		−	5.19615i		−	0.500000i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	3.16228	+	10.0000i	0.301511	+	0.953463i
$111$		0			0
$112$	−3.46410			−0.327327
$113$			6.92820i			0.651751i	0.945413	+	0.325875i	$0.105659\pi$
$113$			6.92820i			0.651751i	−0.945413	+	0.325875i	$0.894341\pi$
$114$	−6.00000			−0.561951
$115$			21.9089i			2.04302i
$116$	−5.47723			−0.508548
$117$	−5.19615	+	9.48683i	−0.480384	+	0.877058i
$118$		−	6.32456i		−	0.582223i
$119$	−18.9737			−1.73931
$120$	16.4317			1.50000
$121$	9.00000	−	6.32456i	0.818182	−	0.574960i
$122$	12.6491			1.14520
$123$	−3.46410			−0.312348
$124$		−	5.47723i		−	0.491869i
$125$		0			0
$126$			10.3923i			0.925820i
$127$		−	3.16228i		−	0.280607i	−0.990109	−	0.140303i	$-0.955192\pi$
$127$		−	3.16228i		−	0.280607i	0.990109	−	0.140303i	$-0.0448078\pi$
$128$		−	3.00000i		−	0.265165i
$129$	−16.4317			−1.44673
$130$	−10.0000	−	5.47723i	−0.877058	−	0.480384i
$131$	10.9545			0.957095			0.478547	−	0.878062i	$-0.341163\pi$
$131$	10.9545			0.957095			0.478547	+	0.878062i	$0.341163\pi$
$132$	−1.73205	−	5.47723i	−0.150756	−	0.476731i
$133$	−12.0000			−1.04053
$134$	5.47723			0.473160
$135$		−	16.4317i		−	1.41421i
$136$			16.4317i			1.40900i
$137$	3.16228			0.270172			0.135086	−	0.990834i	$-0.456869\pi$
$137$	3.16228			0.270172			0.135086	+	0.990834i	$0.456869\pi$
$138$			12.0000i			1.02151i
$139$		−	9.48683i		−	0.804663i	−0.915494	−	0.402331i	$-0.868200\pi$
$139$		−	9.48683i		−	0.804663i	0.915494	−	0.402331i	$-0.131800\pi$
$140$	10.9545			0.925820
$141$			10.9545i			0.922531i
$142$			6.32456i			0.530745i
$143$	−2.31495	+	11.7321i	−0.193586	+	0.981083i
$144$	3.00000			0.250000
$145$	−17.3205			−1.43839
$146$			6.92820i			0.573382i
$147$			8.66025i			0.714286i
$148$		0			0
$149$		−	22.0000i		−	1.80231i	−0.433497	−	0.901155i	$-0.642720\pi$
$149$		−	22.0000i		−	1.80231i	0.433497	−	0.901155i	$-0.357280\pi$
$150$	8.66025			0.707107
$151$	10.3923			0.845714			0.422857	−	0.906196i	$-0.361027\pi$
$151$	10.3923			0.845714			0.422857	+	0.906196i	$0.361027\pi$
$152$			10.3923i			0.842927i
$153$	16.4317			1.32842
$154$	3.46410	+	10.9545i	0.279145	+	0.882735i
$155$		−	17.3205i		−	1.39122i
$156$	5.47723	+	3.00000i	0.438529	+	0.240192i
$157$	−16.0000			−1.27694			−0.638470	−	0.769647i	$-0.720432\pi$
$157$	−16.0000			−1.27694			−0.638470	+	0.769647i	$0.720432\pi$
$158$	3.16228			0.251577
$159$	12.0000			0.951662
$160$		−	15.8114i		−	1.25000i
$161$			24.0000i			1.89146i
$162$		−	9.00000i		−	0.707107i
$163$		−	5.47723i		−	0.429009i	−0.976723	−	0.214505i	$-0.931186\pi$
$163$		−	5.47723i		−	0.429009i	0.976723	−	0.214505i	$-0.0688137\pi$
$164$			2.00000i			0.156174i
$165$	−5.47723	−	17.3205i	−0.426401	−	1.34840i
$166$	−2.00000			−0.155230
$167$			10.0000i			0.773823i	0.922117	+	0.386912i	$0.126458\pi$
$167$			10.0000i			0.773823i	−0.922117	+	0.386912i	$0.873542\pi$
$168$	18.0000			1.38873
$169$	−7.00000	−	10.9545i	−0.538462	−	0.842650i
$170$			17.3205i			1.32842i
$171$	10.3923			0.794719
$172$			9.48683i			0.723364i
$173$	−16.4317			−1.24928			−0.624639	−	0.780914i	$-0.714754\pi$
$173$	−16.4317			−1.24928			−0.624639	+	0.780914i	$0.714754\pi$
$174$	−9.48683			−0.719195
$175$	17.3205			1.30931
$176$	3.16228	−	1.00000i	0.238366	−	0.0753778i
$177$			10.9545i			0.823387i
$178$		−	3.16228i		−	0.237023i
$179$		−	13.8564i		−	1.03568i	−0.855479	−	0.517838i	$-0.826737\pi$
$179$		−	13.8564i		−	1.03568i	0.855479	−	0.517838i	$-0.173263\pi$
$180$	−9.48683			−0.707107
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	−10.9545	−	6.00000i	−0.811998	−	0.444750i
$183$	−21.9089			−1.61955
$184$	20.7846			1.53226
$185$		0			0
$186$		−	9.48683i		−	0.695608i
$187$	17.3205	−	5.47723i	1.26660	−	0.400534i
$188$	6.32456			0.461266
$189$		−	18.0000i		−	1.30931i
$190$			10.9545i			0.794719i
$191$		−	10.3923i		−	0.751961i	−0.926628	−	0.375980i	$-0.877306\pi$
$191$		−	10.3923i		−	0.751961i	0.926628	−	0.375980i	$-0.122694\pi$
$192$		−	12.1244i		−	0.875000i
$193$	−20.7846			−1.49611			−0.748054	−	0.663637i	$-0.769012\pi$
$193$	−20.7846			−1.49611			−0.748054	+	0.663637i	$0.769012\pi$
$194$	−10.9545			−0.786484
$195$	17.3205	+	9.48683i	1.24035	+	0.679366i
$196$	5.00000			0.357143
$197$		−	14.0000i		−	0.997459i	−0.866758	−	0.498729i	$-0.833800\pi$
$197$		−	14.0000i		−	0.997459i	0.866758	−	0.498729i	$-0.166200\pi$
$198$	−3.00000	−	9.48683i	−0.213201	−	0.674200i
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$		−	15.0000i		−	1.06066i
$201$	−9.48683			−0.669150
$202$		−	5.47723i		−	0.385376i
$203$	−18.9737			−1.33169
$204$		−	9.48683i		−	0.664211i
$205$			6.32456i			0.441726i
$206$			8.00000i			0.557386i
$207$		−	20.7846i		−	1.44463i
$208$	−1.73205	+	3.16228i	−0.120096	+	0.219265i
$209$	10.9545	−	3.46410i	0.757735	−	0.239617i
$210$	18.9737			1.30931
$211$		−	3.16228i		−	0.217700i	−0.994058	−	0.108850i	$-0.965283\pi$
$211$		−	3.16228i		−	0.217700i	0.994058	−	0.108850i	$-0.0347168\pi$
$212$		−	6.92820i		−	0.475831i
$213$		−	10.9545i		−	0.750587i
$214$		−	10.9545i		−	0.748831i
$215$			30.0000i			2.04598i
$216$	−15.5885			−1.06066
$217$		−	18.9737i		−	1.28802i
$218$		0			0
$219$		−	12.0000i		−	0.810885i
$220$	−10.0000	+	3.16228i	−0.674200	+	0.213201i
$221$	−9.48683	+	17.3205i	−0.638153	+	1.16510i
$222$		0			0
$223$			16.4317i			1.10035i	0.835051	+	0.550173i	$0.185438\pi$
$223$			16.4317i			1.10035i	−0.835051	+	0.550173i	$0.814562\pi$
$224$		−	17.3205i		−	1.15728i
$225$	−15.0000			−1.00000
$226$	6.92820			0.460857
$227$			4.00000i			0.265489i	0.991150	+	0.132745i	$0.0423790\pi$
$227$			4.00000i			0.265489i	−0.991150	+	0.132745i	$0.957621\pi$
$228$		−	6.00000i		−	0.397360i
$229$			21.9089i			1.44778i	0.689915	+	0.723891i	$0.257648\pi$
$229$			21.9089i			1.44778i	−0.689915	+	0.723891i	$0.742352\pi$
$230$	21.9089			1.44463
$231$	−6.00000	−	18.9737i	−0.394771	−	1.24838i
$232$			16.4317i			1.07879i
$233$	27.3861			1.79412			0.897062	−	0.441904i	$-0.145697\pi$
$233$	27.3861			1.79412			0.897062	+	0.441904i	$0.145697\pi$
$234$	9.48683	+	5.19615i	0.620174	+	0.339683i
$235$	20.0000			1.30466
$236$	6.32456			0.411693
$237$	−5.47723			−0.355784
$238$			18.9737i			1.22988i
$239$		−	8.00000i		−	0.517477i	−0.965947	−	0.258738i	$-0.916693\pi$
$239$		−	8.00000i		−	0.517477i	0.965947	−	0.258738i	$-0.0833068\pi$
$240$		−	5.47723i		−	0.353553i
$241$	24.2487			1.56200			0.780998	−	0.624533i	$-0.214711\pi$
$241$	24.2487			1.56200			0.780998	+	0.624533i	$0.214711\pi$
$242$	−6.32456	−	9.00000i	−0.406558	−	0.578542i
$243$			15.5885i			1.00000i
$244$			12.6491i			0.809776i
$245$	15.8114			1.01015
$246$			3.46410i			0.220863i
$247$	−6.00000	+	10.9545i	−0.381771	+	0.697015i
$248$	−16.4317			−1.04341
$249$	3.46410			0.219529
$250$		0			0
$251$			24.2487i			1.53057i	0.643695	+	0.765283i	$0.277401\pi$
$251$			24.2487i			1.53057i	−0.643695	+	0.765283i	$0.722599\pi$
$252$	−10.3923			−0.654654
$253$	−6.92820	−	21.9089i	−0.435572	−	1.37740i
$254$	−3.16228			−0.198419
$255$		−	30.0000i		−	1.87867i
$256$	−17.0000			−1.06250
$257$		−	6.92820i		−	0.432169i	−0.976375	−	0.216085i	$-0.930671\pi$
$257$		−	6.92820i		−	0.432169i	0.976375	−	0.216085i	$-0.0693287\pi$
$258$			16.4317i			1.02299i
$259$		0			0
$260$	5.47723	−	10.0000i	0.339683	−	0.620174i
$261$	16.4317			1.01710
$262$		−	10.9545i		−	0.676768i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	−16.4317	+	5.19615i	−1.01130	+	0.319801i
$265$		−	21.9089i		−	1.34585i
$266$			12.0000i			0.735767i
$267$			5.47723i			0.335201i
$268$			5.47723i			0.334575i
$269$		−	13.8564i		−	0.844840i	−0.906400	−	0.422420i	$-0.861181\pi$
$269$		−	13.8564i		−	0.844840i	0.906400	−	0.422420i	$-0.138819\pi$
$270$	−16.4317			−1.00000
$271$	24.2487			1.47300			0.736502	−	0.676435i	$-0.236476\pi$
$271$	24.2487			1.47300			0.736502	+	0.676435i	$0.236476\pi$
$272$	5.47723			0.332106
$273$	18.9737	+	10.3923i	1.14834	+	0.628971i
$274$		−	3.16228i		−	0.191040i
$275$	−15.8114	+	5.00000i	−0.953463	+	0.301511i
$276$	−12.0000			−0.722315
$277$		−	18.9737i		−	1.14002i	−0.821639	−	0.570009i	$-0.806940\pi$
$277$		−	18.9737i		−	1.14002i	0.821639	−	0.570009i	$-0.193060\pi$
$278$	−9.48683			−0.568982
$279$			16.4317i			0.983739i
$280$		−	32.8634i		−	1.96396i
$281$			14.0000i			0.835170i	0.908638	+	0.417585i	$0.137123\pi$
$281$			14.0000i			0.835170i	−0.908638	+	0.417585i	$0.862877\pi$
$282$	10.9545			0.652328
$283$			3.16228i			0.187978i	0.995573	+	0.0939889i	$0.0299618\pi$
$283$			3.16228i			0.187978i	−0.995573	+	0.0939889i	$0.970038\pi$
$284$	−6.32456			−0.375293
$285$		−	18.9737i		−	1.12390i
$286$	11.7321	+	2.31495i	0.693731	+	0.136886i
$287$			6.92820i			0.408959i
$288$			15.0000i			0.883883i
$289$	13.0000			0.764706
$290$			17.3205i			1.01710i
$291$	18.9737			1.11226
$292$	−6.92820			−0.405442
$293$		−	2.00000i		−	0.116841i	−0.998292	−	0.0584206i	$-0.981394\pi$
$293$		−	2.00000i		−	0.116841i	0.998292	−	0.0584206i	$-0.0186065\pi$
$294$	8.66025			0.505076
$295$	20.0000			1.16445
$296$		0			0
$297$	5.19615	+	16.4317i	0.301511	+	0.953463i
$298$	−22.0000			−1.27443
$299$	21.9089	+	12.0000i	1.26702	+	0.693978i
$300$			8.66025i			0.500000i
$301$			32.8634i			1.89421i
$302$		−	10.3923i		−	0.598010i
$303$			9.48683i			0.545004i
$304$	3.46410			0.198680
$305$			40.0000i			2.29039i
$306$		−	16.4317i		−	0.939336i
$307$	−3.46410			−0.197707			−0.0988534	−	0.995102i	$-0.531517\pi$
$307$	−3.46410			−0.197707			−0.0988534	+	0.995102i	$0.531517\pi$
$308$	−10.9545	+	3.46410i	−0.624188	+	0.197386i
$309$		−	13.8564i		−	0.788263i
$310$	−17.3205			−0.983739
$311$		−	6.92820i		−	0.392862i	−0.980518	−	0.196431i	$-0.937065\pi$
$311$		−	6.92820i		−	0.392862i	0.980518	−	0.196431i	$-0.0629352\pi$
$312$	9.00000	−	16.4317i	0.509525	−	0.930261i
$313$	−12.0000			−0.678280			−0.339140	−	0.940736i	$-0.610136\pi$
$313$	−12.0000			−0.678280			−0.339140	+	0.940736i	$0.610136\pi$
$314$			16.0000i			0.902932i
$315$	−32.8634			−1.85164
$316$			3.16228i			0.177892i
$317$	−3.16228			−0.177611			−0.0888056	−	0.996049i	$-0.528305\pi$
$317$	−3.16228			−0.177611			−0.0888056	+	0.996049i	$0.528305\pi$
$318$		−	12.0000i		−	0.672927i
$319$	17.3205	−	5.47723i	0.969762	−	0.306666i
$320$	−22.1359			−1.23744
$321$			18.9737i			1.05901i
$322$	24.0000			1.33747
$323$	18.9737			1.05572
$324$	9.00000			0.500000
$325$	8.66025	−	15.8114i	0.480384	−	0.877058i
$326$	−5.47723			−0.303355
$327$		0			0
$328$	6.00000			0.331295
$329$	21.9089			1.20788
$330$	−17.3205	+	5.47723i	−0.953463	+	0.301511i
$331$		−	5.47723i		−	0.301056i	−0.988606	−	0.150528i	$-0.951903\pi$
$331$		−	5.47723i		−	0.301056i	0.988606	−	0.150528i	$-0.0480973\pi$
$332$		−	2.00000i		−	0.109764i
$333$		0			0
$334$	10.0000			0.547176
$335$			17.3205i			0.946320i
$336$		−	6.00000i		−	0.327327i
$337$			25.2982i			1.37808i	0.724722	+	0.689041i	$0.241968\pi$
$337$			25.2982i			1.37808i	−0.724722	+	0.689041i	$0.758032\pi$
$338$	−10.9545	+	7.00000i	−0.595844	+	0.380750i
$339$	−12.0000			−0.651751
$340$	−17.3205			−0.939336
$341$	5.47723	+	17.3205i	0.296608	+	0.937958i
$342$		−	10.3923i		−	0.561951i
$343$	−6.92820			−0.374088
$344$	28.4605			1.53449
$345$	−37.9473			−2.04302
$346$			16.4317i			0.883372i
$347$		0			0			−	1.00000i	$-0.5\pi$
$347$		0			0				1.00000i	$0.5\pi$
$348$		−	9.48683i		−	0.508548i
$349$	−17.3205			−0.927146			−0.463573	−	0.886059i	$-0.653433\pi$
$349$	−17.3205			−0.927146			−0.463573	+	0.886059i	$0.653433\pi$
$350$		−	17.3205i		−	0.925820i
$351$	−16.4317	−	9.00000i	−0.877058	−	0.480384i
$352$	5.00000	+	15.8114i	0.266501	+	0.842750i
$353$	−15.8114			−0.841555			−0.420778	−	0.907164i	$-0.638243\pi$
$353$	−15.8114			−0.841555			−0.420778	+	0.907164i	$0.638243\pi$
$354$	10.9545			0.582223
$355$	−20.0000			−1.06149
$356$	3.16228			0.167600
$357$		−	32.8634i		−	1.73931i
$358$	−13.8564			−0.732334
$359$			32.0000i			1.68890i	0.535638	+	0.844448i	$0.320071\pi$
$359$			32.0000i			1.68890i	−0.535638	+	0.844448i	$0.679929\pi$
$360$			28.4605i			1.50000i
$361$	−7.00000			−0.368421
$362$		−	8.00000i		−	0.420471i
$363$	10.9545	+	15.5885i	0.574960	+	0.818182i
$364$	6.00000	−	10.9545i	0.314485	−	0.574169i
$365$	−21.9089			−1.14676
$366$			21.9089i			1.14520i
$367$	−16.0000			−0.835193			−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000			−0.835193			−0.417597	+	0.908633i	$0.637127\pi$
$368$		−	6.92820i		−	0.361158i
$369$		−	6.00000i		−	0.312348i
$370$		0			0
$371$		−	24.0000i		−	1.24602i
$372$	9.48683			0.491869
$373$			31.6228i			1.63737i	0.574246	+	0.818683i	$0.305295\pi$
$373$			31.6228i			1.63737i	−0.574246	+	0.818683i	$0.694705\pi$
$374$	−5.47723	−	17.3205i	−0.283221	−	0.895622i
$375$		0			0
$376$		−	18.9737i		−	0.978492i
$377$	−9.48683	+	17.3205i	−0.488597	+	0.892052i
$378$	−18.0000			−0.925820
$379$		−	27.3861i		−	1.40673i	−0.710828	−	0.703365i	$-0.751680\pi$
$379$		−	27.3861i		−	1.40673i	0.710828	−	0.703365i	$-0.248320\pi$
$380$	−10.9545			−0.561951
$381$	5.47723			0.280607
$382$	−10.3923			−0.531717
$383$	25.2982			1.29268			0.646339	−	0.763050i	$-0.276299\pi$
$383$	25.2982			1.29268			0.646339	+	0.763050i	$0.276299\pi$
$384$	5.19615			0.265165
$385$	−34.6410	+	10.9545i	−1.76547	+	0.558291i
$386$			20.7846i			1.05791i
$387$		−	28.4605i		−	1.44673i
$388$		−	10.9545i		−	0.556128i
$389$			20.7846i			1.05382i	0.849921	+	0.526911i	$0.176650\pi$
$389$			20.7846i			1.05382i	−0.849921	+	0.526911i	$0.823350\pi$
$390$	9.48683	−	17.3205i	0.480384	−	0.877058i
$391$		−	37.9473i		−	1.91908i
$392$		−	15.0000i		−	0.757614i
$393$			18.9737i			0.957095i
$394$	−14.0000			−0.705310
$395$			10.0000i			0.503155i
$396$	9.48683	−	3.00000i	0.476731	−	0.150756i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		−	24.0000i		−	1.20301i
$399$		−	20.7846i		−	1.04053i
$400$	−5.00000			−0.250000
$401$	22.1359			1.10542			0.552708	−	0.833375i	$-0.313594\pi$
$401$	22.1359			1.10542			0.552708	+	0.833375i	$0.313594\pi$
$402$			9.48683i			0.473160i
$403$	−17.3205	−	9.48683i	−0.862796	−	0.472573i
$404$	5.47723			0.272502
$405$	28.4605			1.41421
$406$			18.9737i			0.941647i
$407$		0			0
$408$	−28.4605			−1.40900
$409$	20.7846			1.02773			0.513866	−	0.857870i	$-0.328213\pi$
$409$	20.7846			1.02773			0.513866	+	0.857870i	$0.328213\pi$
$410$	6.32456			0.312348
$411$			5.47723i			0.270172i
$412$	−8.00000			−0.394132
$413$	21.9089			1.07807
$414$	−20.7846			−1.02151
$415$		−	6.32456i		−	0.310460i
$416$	−15.8114	−	8.66025i	−0.775217	−	0.424604i
$417$	16.4317			0.804663
$418$	−3.46410	−	10.9545i	−0.169435	−	0.535800i
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$			18.9737i			0.925820i
$421$		−	32.8634i		−	1.60166i	−0.598891	−	0.800831i	$-0.704392\pi$
$421$		−	32.8634i		−	1.60166i	0.598891	−	0.800831i	$-0.295608\pi$
$422$	−3.16228			−0.153937
$423$	−18.9737			−0.922531
$424$	−20.7846			−1.00939
$425$	−27.3861			−1.32842
$426$	−10.9545			−0.530745
$427$			43.8178i			2.12049i
$428$	10.9545			0.529503
$429$	−20.3205	−	4.00961i	−0.981083	−	0.193586i
$430$	30.0000			1.44673
$431$		−	14.0000i		−	0.674356i	−0.941441	−	0.337178i	$-0.890528\pi$
$431$		−	14.0000i		−	0.674356i	0.941441	−	0.337178i	$-0.109472\pi$
$432$			5.19615i			0.250000i
$433$	18.0000			0.865025			0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000			0.865025			0.432512	+	0.901628i	$0.357627\pi$
$434$	−18.9737			−0.910765
$435$		−	30.0000i		−	1.43839i
$436$		0			0
$437$		−	24.0000i		−	1.14808i
$438$	−12.0000			−0.573382
$439$			28.4605i			1.35835i	0.733978	+	0.679173i	$0.237661\pi$
$439$			28.4605i			1.35835i	−0.733978	+	0.679173i	$0.762339\pi$
$440$	9.48683	+	30.0000i	0.452267	+	1.43019i
$441$	−15.0000			−0.714286
$442$	17.3205	+	9.48683i	0.823853	+	0.451243i
$443$		−	10.3923i		−	0.493753i	−0.969047	−	0.246877i	$-0.920596\pi$
$443$		−	10.3923i		−	0.493753i	0.969047	−	0.246877i	$-0.0794043\pi$
$444$		0			0
$445$	10.0000			0.474045
$446$	16.4317			0.778062
$447$	38.1051			1.80231
$448$	−24.2487			−1.14564
$449$	−15.8114			−0.746186			−0.373093	−	0.927794i	$-0.621703\pi$
$449$	−15.8114			−0.746186			−0.373093	+	0.927794i	$0.621703\pi$
$450$			15.0000i			0.707107i
$451$	−2.00000	−	6.32456i	−0.0941763	−	0.297812i
$452$			6.92820i			0.325875i
$453$			18.0000i			0.845714i
$454$	4.00000			0.187729
$455$	18.9737	−	34.6410i	0.889499	−	1.62400i
$456$	−18.0000			−0.842927
$457$	3.46410			0.162044			0.0810219	−	0.996712i	$-0.474182\pi$
$457$	3.46410			0.162044			0.0810219	+	0.996712i	$0.474182\pi$
$458$	21.9089			1.02374
$459$			28.4605i			1.32842i
$460$			21.9089i			1.02151i
$461$		−	14.0000i		−	0.652045i	−0.945362	−	0.326023i	$-0.894291\pi$
$461$		−	14.0000i		−	0.652045i	0.945362	−	0.326023i	$-0.105709\pi$
$462$	−18.9737	+	6.00000i	−0.882735	+	0.279145i
$463$		−	16.4317i		−	0.763645i	−0.924236	−	0.381822i	$-0.875297\pi$
$463$		−	16.4317i		−	0.763645i	0.924236	−	0.381822i	$-0.124703\pi$
$464$	5.47723			0.254274
$465$	30.0000			1.39122
$466$		−	27.3861i		−	1.26864i
$467$			20.7846i			0.961797i	0.876776	+	0.480899i	$0.159689\pi$
$467$			20.7846i			0.961797i	−0.876776	+	0.480899i	$0.840311\pi$
$468$	−5.19615	+	9.48683i	−0.240192	+	0.438529i
$469$			18.9737i			0.876122i
$470$		−	20.0000i		−	0.922531i
$471$		−	27.7128i		−	1.27694i
$472$		−	18.9737i		−	0.873334i
$473$	−9.48683	−	30.0000i	−0.436205	−	1.37940i
$474$			5.47723i			0.251577i
$475$	−17.3205			−0.794719
$476$	−18.9737			−0.869657
$477$			20.7846i			0.951662i
$478$	−8.00000			−0.365911
$479$		−	8.00000i		−	0.365529i	−0.983157	−	0.182765i	$-0.941495\pi$
$479$		−	8.00000i		−	0.365529i	0.983157	−	0.182765i	$-0.0585046\pi$
$480$	27.3861			1.25000
$481$		0			0
$482$		−	24.2487i		−	1.10450i
$483$	−41.5692			−1.89146
$484$	9.00000	−	6.32456i	0.409091	−	0.287480i
$485$		−	34.6410i		−	1.57297i
$486$	15.5885			0.707107
$487$			27.3861i			1.24098i	0.784213	+	0.620492i	$0.213067\pi$
$487$			27.3861i			1.24098i	−0.784213	+	0.620492i	$0.786933\pi$
$488$	37.9473			1.71780
$489$	9.48683			0.429009
$490$		−	15.8114i		−	0.714286i
$491$	−21.9089			−0.988735			−0.494367	−	0.869253i	$-0.664600\pi$
$491$	−21.9089			−0.988735			−0.494367	+	0.869253i	$0.664600\pi$
$492$	−3.46410			−0.156174
$493$	30.0000			1.35113
$494$	10.9545	+	6.00000i	0.492864	+	0.269953i
$495$	30.0000	−	9.48683i	1.34840	−	0.426401i
$496$			5.47723i			0.245935i
$497$	−21.9089			−0.982749
$498$		−	3.46410i		−	0.155230i
$499$		−	38.3406i		−	1.71636i	−0.513349	−	0.858180i	$-0.671595\pi$
$499$		−	38.3406i		−	1.71636i	0.513349	−	0.858180i	$-0.328405\pi$
$500$		0			0
$501$	−17.3205			−0.773823
$502$	24.2487			1.08227
$503$	−21.9089			−0.976870			−0.488435	−	0.872600i	$-0.662432\pi$
$503$	−21.9089			−0.976870			−0.488435	+	0.872600i	$0.662432\pi$
$504$			31.1769i			1.38873i
$505$	17.3205			0.770752
$506$	−21.9089	+	6.92820i	−0.973970	+	0.307996i
$507$	18.9737	−	12.1244i	0.842650	−	0.538462i
$508$		−	3.16228i		−	0.140303i
$509$	−15.8114			−0.700827			−0.350414	−	0.936595i	$-0.613959\pi$
$509$	−15.8114			−0.700827			−0.350414	+	0.936595i	$0.613959\pi$
$510$	−30.0000			−1.32842
$511$	−24.0000			−1.06170
$512$			11.0000i			0.486136i
$513$			18.0000i			0.794719i
$514$	−6.92820			−0.305590
$515$	−25.2982			−1.11477
$516$	−16.4317			−0.723364
$517$	−20.0000	+	6.32456i	−0.879599	+	0.278154i
$518$		0			0
$519$		−	28.4605i		−	1.24928i
$520$	−30.0000	−	16.4317i	−1.31559	−	0.720577i
$521$		−	6.92820i		−	0.303530i	−0.988417	−	0.151765i	$-0.951504\pi$
$521$		−	6.92820i		−	0.303530i	0.988417	−	0.151765i	$-0.0484957\pi$
$522$		−	16.4317i		−	0.719195i
$523$			9.48683i			0.414830i	0.978253	+	0.207415i	$0.0665051\pi$
$523$			9.48683i			0.414830i	−0.978253	+	0.207415i	$0.933495\pi$
$524$	10.9545			0.478547
$525$			30.0000i			1.30931i
$526$		0			0
$527$			30.0000i			1.30682i
$528$	1.73205	+	5.47723i	0.0753778	+	0.238366i
$529$	−25.0000			−1.08696
$530$	−21.9089			−0.951662
$531$	−18.9737			−0.823387
$532$	−12.0000			−0.520266
$533$	6.32456	+	3.46410i	0.273947	+	0.150047i
$534$	5.47723			0.237023
$535$	34.6410			1.49766
$536$	16.4317			0.709740
$537$	24.0000			1.03568
$538$	−13.8564			−0.597392
$539$	−15.8114	+	5.00000i	−0.681045	+	0.215365i
$540$		−	16.4317i		−	0.707107i
$541$	45.0333			1.93613			0.968067	−	0.250692i	$-0.0806582\pi$
$541$	45.0333			1.93613			0.968067	+	0.250692i	$0.0806582\pi$
$542$		−	24.2487i		−	1.04157i
$543$			13.8564i			0.594635i
$544$			27.3861i			1.17417i
$545$		0			0
$546$	10.3923	−	18.9737i	0.444750	−	0.811998i
$547$		−	9.48683i		−	0.405628i	−0.979217	−	0.202814i	$-0.934991\pi$
$547$		−	9.48683i		−	0.405628i	0.979217	−	0.202814i	$-0.0650086\pi$
$548$	3.16228			0.135086
$549$		−	37.9473i		−	1.61955i
$550$	5.00000	+	15.8114i	0.213201	+	0.674200i
$551$	18.9737			0.808305
$552$			36.0000i			1.53226i
$553$			10.9545i			0.465831i
$554$	−18.9737			−0.806114
$555$		0			0
$556$		−	9.48683i		−	0.402331i
$557$			14.0000i			0.593199i	0.955002	+	0.296600i	$0.0958526\pi$
$557$			14.0000i			0.593199i	−0.955002	+	0.296600i	$0.904147\pi$
$558$	16.4317			0.695608
$559$	30.0000	+	16.4317i	1.26886	+	0.694986i
$560$	−10.9545			−0.462910
$561$	9.48683	+	30.0000i	0.400534	+	1.26660i
$562$	14.0000			0.590554
$563$	10.9545			0.461675			0.230838	−	0.972992i	$-0.425853\pi$
$563$	10.9545			0.461675			0.230838	+	0.972992i	$0.425853\pi$
$564$			10.9545i			0.461266i
$565$			21.9089i			0.921714i
$566$	3.16228			0.132920
$567$	31.1769			1.30931
$568$			18.9737i			0.796117i
$569$	−5.47723			−0.229617			−0.114809	−	0.993388i	$-0.536625\pi$
$569$	−5.47723			−0.229617			−0.114809	+	0.993388i	$0.536625\pi$
$570$	−18.9737			−0.794719
$571$			22.1359i			0.926360i	0.886264	+	0.463180i	$0.153292\pi$
$571$			22.1359i			0.926360i	−0.886264	+	0.463180i	$0.846708\pi$
$572$	−2.31495	+	11.7321i	−0.0967928	+	0.490542i
$573$	18.0000			0.751961
$574$	6.92820			0.289178
$575$			34.6410i			1.44463i
$576$	21.0000			0.875000
$577$			21.9089i			0.912080i	0.889959	+	0.456040i	$0.150733\pi$
$577$			21.9089i			0.912080i	−0.889959	+	0.456040i	$0.849267\pi$
$578$		−	13.0000i		−	0.540729i
$579$		−	36.0000i		−	1.49611i
$580$	−17.3205			−0.719195
$581$		−	6.92820i		−	0.287430i
$582$		−	18.9737i		−	0.786484i
$583$	6.92820	+	21.9089i	0.286937	+	0.907374i
$584$			20.7846i			0.860073i
$585$	−16.4317	+	30.0000i	−0.679366	+	1.24035i
$586$	−2.00000			−0.0826192
$587$	−6.32456			−0.261042			−0.130521	−	0.991446i	$-0.541665\pi$
$587$	−6.32456			−0.261042			−0.130521	+	0.991446i	$0.541665\pi$
$588$			8.66025i			0.357143i
$589$			18.9737i			0.781796i
$590$		−	20.0000i		−	0.823387i
$591$	24.2487			0.997459
$592$		0			0
$593$		−	2.00000i		−	0.0821302i	−0.999156	−	0.0410651i	$-0.986925\pi$
$593$		−	2.00000i		−	0.0821302i	0.999156	−	0.0410651i	$-0.0130751\pi$
$594$	16.4317	−	5.19615i	0.674200	−	0.213201i
$595$	−60.0000			−2.45976
$596$		−	22.0000i		−	0.901155i
$597$			41.5692i			1.70131i
$598$	12.0000	−	21.9089i	0.490716	−	0.895922i
$599$			17.3205i			0.707697i	0.935303	+	0.353848i	$0.115127\pi$
$599$			17.3205i			0.707697i	−0.935303	+	0.353848i	$0.884873\pi$
$600$	25.9808			1.06066
$601$		−	12.6491i		−	0.515968i	−0.966149	−	0.257984i	$-0.916942\pi$
$601$		−	12.6491i		−	0.515968i	0.966149	−	0.257984i	$-0.0830582\pi$
$602$	32.8634			1.33941
$603$		−	16.4317i		−	0.669150i
$604$	10.3923			0.422857
$605$	28.4605	−	20.0000i	1.15708	−	0.813116i
$606$	9.48683			0.385376
$607$		−	28.4605i		−	1.15518i	−0.816328	−	0.577588i	$-0.803994\pi$
$607$		−	28.4605i		−	1.15518i	0.816328	−	0.577588i	$-0.196006\pi$
$608$			17.3205i			0.702439i
$609$		−	32.8634i		−	1.33169i
$610$	40.0000			1.61955
$611$	10.9545	−	20.0000i	0.443170	−	0.809113i
$612$	16.4317			0.664211
$613$	−13.8564			−0.559655			−0.279827	−	0.960050i	$-0.590277\pi$
$613$	−13.8564			−0.559655			−0.279827	+	0.960050i	$0.590277\pi$
$614$			3.46410i			0.139800i
$615$	−10.9545			−0.441726
$616$	10.3923	+	32.8634i	0.418718	+	1.32410i
$617$	34.7851			1.40039			0.700197	−	0.713950i	$-0.253096\pi$
$617$	34.7851			1.40039			0.700197	+	0.713950i	$0.253096\pi$
$618$	−13.8564			−0.557386
$619$		−	5.47723i		−	0.220148i	−0.993923	−	0.110074i	$-0.964891\pi$
$619$		−	5.47723i		−	0.220148i	0.993923	−	0.110074i	$-0.0351088\pi$
$620$		−	17.3205i		−	0.695608i
$621$	36.0000			1.44463
$622$	−6.92820			−0.277796
$623$	10.9545			0.438881
$624$	−5.47723	−	3.00000i	−0.219265	−	0.120096i
$625$	−25.0000			−1.00000
$626$			12.0000i			0.479616i
$627$	6.00000	+	18.9737i	0.239617	+	0.757735i
$628$	−16.0000			−0.638470
$629$		0			0
$630$			32.8634i			1.30931i
$631$			49.2950i			1.96240i	0.192983	+	0.981202i	$0.438184\pi$
$631$			49.2950i			1.96240i	−0.192983	+	0.981202i	$0.561816\pi$
$632$	9.48683			0.377366
$633$	5.47723			0.217700
$634$			3.16228i			0.125590i
$635$		−	10.0000i		−	0.396838i
$636$	12.0000			0.475831
$637$	8.66025	−	15.8114i	0.343132	−	0.626470i
$638$	−5.47723	−	17.3205i	−0.216845	−	0.685725i
$639$	18.9737			0.750587
$640$		−	9.48683i		−	0.375000i
$641$		−	41.5692i		−	1.64189i	−0.571011	−	0.820943i	$-0.693448\pi$
$641$		−	41.5692i		−	1.64189i	0.571011	−	0.820943i	$-0.306552\pi$
$642$	18.9737			0.748831
$643$		−	38.3406i		−	1.51200i	−0.654569	−	0.756002i	$-0.727150\pi$
$643$		−	38.3406i		−	1.51200i	0.654569	−	0.756002i	$-0.272850\pi$
$644$			24.0000i			0.945732i
$645$	−51.9615			−2.04598
$646$		−	18.9737i		−	0.746509i
$647$			31.1769i			1.22569i	0.790203	+	0.612845i	$0.209975\pi$
$647$			31.1769i			1.22569i	−0.790203	+	0.612845i	$0.790025\pi$
$648$		−	27.0000i		−	1.06066i
$649$	−20.0000	+	6.32456i	−0.785069	+	0.248261i
$650$	−15.8114	−	8.66025i	−0.620174	−	0.339683i
$651$	32.8634			1.28802
$652$		−	5.47723i		−	0.214505i
$653$		−	6.92820i		−	0.271122i	−0.990769	−	0.135561i	$-0.956716\pi$
$653$		−	6.92820i		−	0.271122i	0.990769	−	0.135561i	$-0.0432836\pi$
$654$		0			0
$655$	34.6410			1.35354
$656$		−	2.00000i		−	0.0780869i
$657$	20.7846			0.810885
$658$		−	21.9089i		−	0.854098i
$659$	−43.8178			−1.70690			−0.853450	−	0.521175i	$-0.825494\pi$
$659$	−43.8178			−1.70690			−0.853450	+	0.521175i	$0.825494\pi$
$660$	−5.47723	−	17.3205i	−0.213201	−	0.674200i
$661$		−	32.8634i		−	1.27824i	−0.769109	−	0.639118i	$-0.779299\pi$
$661$		−	32.8634i		−	1.27824i	0.769109	−	0.639118i	$-0.220701\pi$
$662$	−5.47723			−0.212878
$663$	−30.0000	−	16.4317i	−1.16510	−	0.638153i
$664$	−6.00000			−0.232845
$665$	−37.9473			−1.47153
$666$		0			0
$667$		−	37.9473i		−	1.46933i
$668$			10.0000i			0.386912i
$669$	−28.4605			−1.10035
$670$	17.3205			0.669150
$671$	−12.6491	−	40.0000i	−0.488314	−	1.54418i
$672$	30.0000			1.15728
$673$			18.9737i			0.731381i	0.930736	+	0.365691i	$0.119167\pi$
$673$			18.9737i			0.731381i	−0.930736	+	0.365691i	$0.880833\pi$
$674$	25.2982			0.974451
$675$		−	25.9808i		−	1.00000i
$676$	−7.00000	−	10.9545i	−0.269231	−	0.421325i
$677$	38.3406			1.47355			0.736774	−	0.676139i	$-0.236348\pi$
$677$	38.3406			1.47355			0.736774	+	0.676139i	$0.236348\pi$
$678$			12.0000i			0.460857i
$679$		−	37.9473i		−	1.45628i
$680$			51.9615i			1.99263i
$681$	−6.92820			−0.265489
$682$	17.3205	−	5.47723i	0.663237	−	0.209734i
$683$	12.6491			0.484005			0.242002	−	0.970276i	$-0.422196\pi$
$683$	12.6491			0.484005			0.242002	+	0.970276i	$0.422196\pi$
$684$	10.3923			0.397360
$685$	10.0000			0.382080
$686$			6.92820i			0.264520i
$687$	−37.9473			−1.44778
$688$		−	9.48683i		−	0.361682i
$689$	−21.9089	−	12.0000i	−0.834663	−	0.457164i
$690$			37.9473i			1.44463i
$691$			16.4317i			0.625090i	0.949903	+	0.312545i	$0.101182\pi$
$691$			16.4317i			0.625090i	−0.949903	+	0.312545i	$0.898818\pi$
$692$	−16.4317			−0.624639
$693$	32.8634	−	10.3923i	1.24838	−	0.394771i
$694$		0			0
$695$		−	30.0000i		−	1.13796i
$696$	−28.4605			−1.07879
$697$		−	10.9545i		−	0.414929i
$698$			17.3205i			0.655591i
$699$			47.4342i			1.79412i
$700$	17.3205			0.654654
$701$	−16.4317			−0.620616			−0.310308	−	0.950636i	$-0.600432\pi$
$701$	−16.4317			−0.620616			−0.310308	+	0.950636i	$0.600432\pi$
$702$	−9.00000	+	16.4317i	−0.339683	+	0.620174i
$703$		0			0
$704$	22.1359	−	7.00000i	0.834280	−	0.263822i
$705$			34.6410i			1.30466i
$706$			15.8114i			0.595069i
$707$	18.9737			0.713578
$708$			10.9545i			0.411693i
$709$			21.9089i			0.822806i	0.911454	+	0.411403i	$0.134961\pi$
$709$			21.9089i			0.822806i	−0.911454	+	0.411403i	$0.865039\pi$
$710$			20.0000i			0.750587i
$711$		−	9.48683i		−	0.355784i
$712$		−	9.48683i		−	0.355534i
$713$	37.9473			1.42114
$714$	−32.8634			−1.22988
$715$	−7.32051	+	37.1000i	−0.273771	+	1.38746i
$716$		−	13.8564i		−	0.517838i
$717$	13.8564			0.517477
$718$	32.0000			1.19423
$719$			38.1051i			1.42108i	0.703656	+	0.710541i	$0.251550\pi$
$719$			38.1051i			1.42108i	−0.703656	+	0.710541i	$0.748450\pi$
$720$	9.48683			0.353553
$721$	−27.7128			−1.03208
$722$			7.00000i			0.260513i
$723$			42.0000i			1.56200i
$724$	8.00000			0.297318
$725$	−27.3861			−1.01710
$726$	15.5885	−	10.9545i	0.578542	−	0.406558i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	−32.8634	−	18.0000i	−1.21800	−	0.667124i
$729$	−27.0000			−1.00000
$730$			21.9089i			0.810885i
$731$		−	51.9615i		−	1.92187i
$732$	−21.9089			−0.809776
$733$	−13.8564			−0.511798			−0.255899	−	0.966704i	$-0.582371\pi$
$733$	−13.8564			−0.511798			−0.255899	+	0.966704i	$0.582371\pi$
$734$			16.0000i			0.590571i
$735$			27.3861i			1.01015i
$736$	34.6410			1.27688
$737$	−5.47723	−	17.3205i	−0.201756	−	0.638009i
$738$	−6.00000			−0.220863
$739$	−38.1051			−1.40172			−0.700860	−	0.713299i	$-0.747200\pi$
$739$	−38.1051			−1.40172			−0.700860	+	0.713299i	$0.747200\pi$
$740$		0			0
$741$	−18.9737	−	10.3923i	−0.697015	−	0.381771i
$742$	−24.0000			−0.881068
$743$		−	10.0000i		−	0.366864i	−0.983032	−	0.183432i	$-0.941279\pi$
$743$		−	10.0000i		−	0.366864i	0.983032	−	0.183432i	$-0.0587208\pi$
$744$		−	28.4605i		−	1.04341i
$745$		−	69.5701i		−	2.54885i
$746$	31.6228			1.15779
$747$			6.00000i			0.219529i
$748$	17.3205	−	5.47723i	0.633300	−	0.200267i
$749$	37.9473			1.38657
$750$		0			0
$751$	44.0000			1.60558			0.802791	−	0.596260i	$-0.203347\pi$
$751$	44.0000			1.60558			0.802791	+	0.596260i	$0.203347\pi$
$752$	−6.32456			−0.230633
$753$	−42.0000			−1.53057
$754$	17.3205	+	9.48683i	0.630776	+	0.345490i
$755$	32.8634			1.19602
$756$		−	18.0000i		−	0.654654i
$757$	−24.0000			−0.872295			−0.436147	−	0.899875i	$-0.643657\pi$
$757$	−24.0000			−0.872295			−0.436147	+	0.899875i	$0.643657\pi$
$758$	−27.3861			−0.994709
$759$	37.9473	−	12.0000i	1.37740	−	0.435572i
$760$			32.8634i			1.19208i
$761$			14.0000i			0.507500i	0.967270	+	0.253750i	$0.0816640\pi$
$761$			14.0000i			0.507500i	−0.967270	+	0.253750i	$0.918336\pi$
$762$		−	5.47723i		−	0.198419i
$763$		0			0
$764$		−	10.3923i		−	0.375980i
$765$	51.9615			1.87867
$766$		−	25.2982i		−	0.914062i
$767$	10.9545	−	20.0000i	0.395542	−	0.722158i
$768$		−	29.4449i		−	1.06250i
$769$	−38.1051			−1.37411			−0.687053	−	0.726607i	$-0.741096\pi$
$769$	−38.1051			−1.37411			−0.687053	+	0.726607i	$0.741096\pi$
$770$	10.9545	+	34.6410i	0.394771	+	1.24838i
$771$	12.0000			0.432169
$772$	−20.7846			−0.748054
$773$	−41.1096			−1.47861			−0.739305	−	0.673371i	$-0.764846\pi$
$773$	−41.1096			−1.47861			−0.739305	+	0.673371i	$0.764846\pi$
$774$	−28.4605			−1.02299
$775$		−	27.3861i		−	0.983739i
$776$	−32.8634			−1.17973
$777$		0			0
$778$	20.7846			0.745164
$779$		−	6.92820i		−	0.248229i
$780$	17.3205	+	9.48683i	0.620174	+	0.339683i
$781$	20.0000	−	6.32456i	0.715656	−	0.226310i
$782$	−37.9473			−1.35699
$783$			28.4605i			1.01710i
$784$	−5.00000			−0.178571
$785$	−50.5964			−1.80586
$786$	18.9737			0.676768
$787$	10.3923			0.370446			0.185223	−	0.982697i	$-0.440699\pi$
$787$	10.3923			0.370446			0.185223	+	0.982697i	$0.440699\pi$
$788$		−	14.0000i		−	0.498729i
$789$		0			0
$790$	10.0000			0.355784
$791$			24.0000i			0.853342i
$792$	−9.00000	−	28.4605i	−0.319801	−	1.01130i
$793$	40.0000	+	21.9089i	1.42044	+	0.778008i
$794$		0			0
$795$	37.9473			1.34585
$796$	24.0000			0.850657
$797$		−	6.92820i		−	0.245410i	−0.992443	−	0.122705i	$-0.960843\pi$
$797$		−	6.92820i		−	0.245410i	0.992443	−	0.122705i	$-0.0391568\pi$
$798$	−20.7846			−0.735767
$799$	−34.6410			−1.22551
$800$		−	25.0000i		−	0.883883i
$801$	−9.48683			−0.335201
$802$		−	22.1359i		−	0.781647i
$803$	21.9089	−	6.92820i	0.773148	−	0.244491i
$804$	−9.48683			−0.334575
$805$			75.8947i			2.67494i
$806$	−9.48683	+	17.3205i	−0.334159	+	0.610089i
$807$	24.0000			0.844840
$808$		−	16.4317i		−	0.578064i
$809$	38.3406			1.34798			0.673991	−	0.738739i	$-0.264578\pi$
$809$	38.3406			1.34798			0.673991	+	0.738739i	$0.264578\pi$
$810$		−	28.4605i		−	1.00000i
$811$	−10.3923			−0.364923			−0.182462	−	0.983213i	$-0.558407\pi$
$811$	−10.3923			−0.364923			−0.182462	+	0.983213i	$0.558407\pi$
$812$	−18.9737			−0.665845
$813$			42.0000i			1.47300i
$814$		0			0
$815$		−	17.3205i		−	0.606711i
$816$			9.48683i			0.332106i
$817$		−	32.8634i		−	1.14974i
$818$		−	20.7846i		−	0.726717i
$819$	−18.0000	+	32.8634i	−0.628971	+	1.14834i
$820$			6.32456i			0.220863i
$821$		−	26.0000i		−	0.907406i	−0.891153	−	0.453703i	$-0.850103\pi$
$821$		−	26.0000i		−	0.907406i	0.891153	−	0.453703i	$-0.149897\pi$
$822$	5.47723			0.191040
$823$	−20.0000			−0.697156			−0.348578	−	0.937280i	$-0.613335\pi$
$823$	−20.0000			−0.697156			−0.348578	+	0.937280i	$0.613335\pi$
$824$			24.0000i			0.836080i
$825$	−8.66025	−	27.3861i	−0.301511	−	0.953463i
$826$		−	21.9089i		−	0.762308i
$827$			20.0000i			0.695468i	0.937593	+	0.347734i	$0.113049\pi$
$827$			20.0000i			0.695468i	−0.937593	+	0.347734i	$0.886951\pi$
$828$		−	20.7846i		−	0.722315i
$829$	−42.0000			−1.45872			−0.729360	−	0.684130i	$-0.760182\pi$
$829$	−42.0000			−1.45872			−0.729360	+	0.684130i	$0.760182\pi$
$830$	−6.32456			−0.219529
$831$	32.8634			1.14002
$832$	−12.1244	+	22.1359i	−0.420336	+	0.767426i
$833$	−27.3861			−0.948873
$834$		−	16.4317i		−	0.568982i
$835$			31.6228i			1.09435i
$836$	10.9545	−	3.46410i	0.378868	−	0.119808i
$837$	−28.4605			−0.983739
$838$		0			0
$839$	25.2982			0.873392			0.436696	−	0.899609i	$-0.356149\pi$
$839$	25.2982			0.873392			0.436696	+	0.899609i	$0.356149\pi$
$840$	56.9210			1.96396
$841$	1.00000			0.0344828
$842$	−32.8634			−1.13255
$843$	−24.2487			−0.835170
$844$		−	3.16228i		−	0.108850i
$845$	−22.1359	−	34.6410i	−0.761500	−	1.19169i
$846$			18.9737i			0.652328i
$847$	31.1769	−	21.9089i	1.07125	−	0.752799i
$848$			6.92820i			0.237915i
$849$	−5.47723			−0.187978
$850$			27.3861i			0.939336i
$851$		0			0
$852$		−	10.9545i		−	0.375293i
$853$	−24.2487			−0.830260			−0.415130	−	0.909762i	$-0.636264\pi$
$853$	−24.2487			−0.830260			−0.415130	+	0.909762i	$0.636264\pi$
$854$	43.8178			1.49941
$855$	32.8634			1.12390
$856$		−	32.8634i		−	1.12325i
$857$	27.3861			0.935492			0.467746	−	0.883863i	$-0.345066\pi$
$857$	27.3861			0.935492			0.467746	+	0.883863i	$0.345066\pi$
$858$	−4.00961	+	20.3205i	−0.136886	+	0.693731i
$859$	12.0000			0.409435			0.204717	−	0.978821i	$-0.434372\pi$
$859$	12.0000			0.409435			0.204717	+	0.978821i	$0.434372\pi$
$860$			30.0000i			1.02299i
$861$	−12.0000			−0.408959
$862$	−14.0000			−0.476842
$863$	−50.5964			−1.72232			−0.861161	−	0.508332i	$-0.830262\pi$
$863$	−50.5964			−1.72232			−0.861161	+	0.508332i	$0.830262\pi$
$864$	−25.9808			−0.883883
$865$	−51.9615			−1.76674
$866$		−	18.0000i		−	0.611665i
$867$			22.5167i			0.764706i
$868$		−	18.9737i		−	0.644008i
$869$	−3.16228	−	10.0000i	−0.107273	−	0.339227i
$870$	−30.0000			−1.01710
$871$	17.3205	+	9.48683i	0.586883	+	0.321449i
$872$		0			0
$873$			32.8634i			1.11226i
$874$	−24.0000			−0.811812
$875$		0			0
$876$		−	12.0000i		−	0.405442i
$877$	24.2487			0.818821			0.409410	−	0.912350i	$-0.365734\pi$
$877$	24.2487			0.818821			0.409410	+	0.912350i	$0.365734\pi$
$878$	28.4605			0.960495
$879$	3.46410			0.116841
$880$	10.0000	−	3.16228i	0.337100	−	0.106600i
$881$		−	34.6410i		−	1.16709i	−0.812082	−	0.583543i	$-0.801666\pi$
$881$		−	34.6410i		−	1.16709i	0.812082	−	0.583543i	$-0.198334\pi$
$882$			15.0000i			0.505076i
$883$	12.0000			0.403832			0.201916	−	0.979403i	$-0.435283\pi$
$883$	12.0000			0.403832			0.201916	+	0.979403i	$0.435283\pi$
$884$	−9.48683	+	17.3205i	−0.319077	+	0.582552i
$885$			34.6410i			1.16445i
$886$	−10.3923			−0.349136
$887$	10.9545			0.367814			0.183907	−	0.982944i	$-0.441125\pi$
$887$	10.9545			0.367814			0.183907	+	0.982944i	$0.441125\pi$
$888$		0			0
$889$		−	10.9545i		−	0.367400i
$890$		−	10.0000i		−	0.335201i
$891$	−28.4605	+	9.00000i	−0.953463	+	0.301511i
$892$			16.4317i			0.550173i
$893$	−21.9089			−0.733153
$894$		−	38.1051i		−	1.27443i
$895$		−	43.8178i		−	1.46467i
$896$		−	10.3923i		−	0.347183i
$897$	−20.7846	+	37.9473i	−0.693978	+	1.26702i
$898$			15.8114i			0.527633i
$899$			30.0000i			1.00056i
$900$	−15.0000			−0.500000
$901$			37.9473i			1.26421i
$902$	−6.32456	+	2.00000i	−0.210585	+	0.0665927i
$903$	−56.9210			−1.89421
$904$	20.7846			0.691286
$905$	25.2982			0.840941
$906$	18.0000			0.598010
$907$	36.0000			1.19536			0.597680	−	0.801735i	$-0.296089\pi$
$907$	36.0000			1.19536			0.597680	+	0.801735i	$0.296089\pi$
$908$			4.00000i			0.132745i
$909$	−16.4317			−0.545004
$910$	−34.6410	−	18.9737i	−1.14834	−	0.628971i
$911$			17.3205i			0.573854i	0.957952	+	0.286927i	$0.0926337\pi$
$911$			17.3205i			0.573854i	−0.957952	+	0.286927i	$0.907366\pi$
$912$			6.00000i			0.198680i
$913$	2.00000	+	6.32456i	0.0661903	+	0.209312i
$914$		−	3.46410i		−	0.114582i
$915$	−69.2820			−2.29039
$916$			21.9089i			0.723891i
$917$	37.9473			1.25313
$918$	28.4605			0.939336
$919$		−	3.16228i		−	0.104314i	−0.998639	−	0.0521570i	$-0.983390\pi$
$919$		−	3.16228i		−	0.104314i	0.998639	−	0.0521570i	$-0.0166096\pi$
$920$	65.7267			2.16695
$921$		−	6.00000i		−	0.197707i
$922$	−14.0000			−0.461065
$923$	−10.9545	+	20.0000i	−0.360570	+	0.658308i
$924$	−6.00000	−	18.9737i	−0.197386	−	0.624188i
$925$		0			0
$926$	−16.4317			−0.539978
$927$	24.0000			0.788263
$928$			27.3861i			0.898994i
$929$	15.8114			0.518755			0.259377	−	0.965776i	$-0.416483\pi$
$929$	15.8114			0.518755			0.259377	+	0.965776i	$0.416483\pi$
$930$		−	30.0000i		−	0.983739i
$931$	−17.3205			−0.567657
$932$	27.3861			0.897062
$933$	12.0000			0.392862
$934$	20.7846			0.680093
$935$	54.7723	−	17.3205i	1.79124	−	0.566441i
$936$	28.4605	+	15.5885i	0.930261	+	0.509525i
$937$		−	6.32456i		−	0.206614i	−0.994650	−	0.103307i	$-0.967058\pi$
$937$		−	6.32456i		−	0.206614i	0.994650	−	0.103307i	$-0.0329424\pi$
$938$	18.9737			0.619512
$939$		−	20.7846i		−	0.678280i
$940$	20.0000			0.652328
$941$		−	38.0000i		−	1.23876i	−0.785090	−	0.619382i	$-0.787383\pi$
$941$		−	38.0000i		−	1.23876i	0.785090	−	0.619382i	$-0.212617\pi$
$942$	−27.7128			−0.902932
$943$	−13.8564			−0.451227
$944$	−6.32456			−0.205847
$945$		−	56.9210i		−	1.85164i
$946$	−30.0000	+	9.48683i	−0.975384	+	0.308444i
$947$	−12.6491			−0.411041			−0.205520	−	0.978653i	$-0.565889\pi$
$947$	−12.6491			−0.411041			−0.205520	+	0.978653i	$0.565889\pi$
$948$	−5.47723			−0.177892
$949$	−12.0000	+	21.9089i	−0.389536	+	0.711193i
$950$			17.3205i			0.561951i
$951$		−	5.47723i		−	0.177611i
$952$			56.9210i			1.84482i
$953$	5.47723			0.177425			0.0887124	−	0.996057i	$-0.471725\pi$
$953$	5.47723			0.177425			0.0887124	+	0.996057i	$0.471725\pi$
$954$	20.7846			0.672927
$955$		−	32.8634i		−	1.06343i
$956$		−	8.00000i		−	0.258738i
$957$	9.48683	+	30.0000i	0.306666	+	0.969762i
$958$	−8.00000			−0.258468
$959$	10.9545			0.353738
$960$		−	38.3406i		−	1.23744i
$961$	1.00000			0.0322581
$962$		0			0
$963$	−32.8634			−1.05901
$964$	24.2487			0.780998
$965$	−65.7267			−2.11582
$966$			41.5692i			1.33747i
$967$	−31.1769			−1.00258			−0.501291	−	0.865279i	$-0.667141\pi$
$967$	−31.1769			−1.00258			−0.501291	+	0.865279i	$0.667141\pi$
$968$	−18.9737	−	27.0000i	−0.609837	−	0.867813i
$969$			32.8634i			1.05572i
$970$	−34.6410			−1.11226
$971$			34.6410i			1.11168i	0.831288	+	0.555842i	$0.187604\pi$
$971$			34.6410i			1.11168i	−0.831288	+	0.555842i	$0.812396\pi$
$972$			15.5885i			0.500000i
$973$		−	32.8634i		−	1.05355i
$974$	27.3861			0.877508
$975$	27.3861	+	15.0000i	0.877058	+	0.480384i
$976$		−	12.6491i		−	0.404888i
$977$	−22.1359			−0.708192			−0.354096	−	0.935209i	$-0.615211\pi$
$977$	−22.1359			−0.708192			−0.354096	+	0.935209i	$0.615211\pi$
$978$		−	9.48683i		−	0.303355i
$979$	−10.0000	+	3.16228i	−0.319601	+	0.101067i
$980$	15.8114			0.505076
$981$		0			0
$982$			21.9089i			0.699141i
$983$	−25.2982			−0.806888			−0.403444	−	0.915004i	$-0.632187\pi$
$983$	−25.2982			−0.806888			−0.403444	+	0.915004i	$0.632187\pi$
$984$			10.3923i			0.331295i
$985$		−	44.2719i		−	1.41062i
$986$		−	30.0000i		−	0.955395i
$987$			37.9473i			1.20788i
$988$	−6.00000	+	10.9545i	−0.190885	+	0.348508i
$989$	−65.7267			−2.08999
$990$	−9.48683	−	30.0000i	−0.301511	−	0.953463i
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$	−27.3861			−0.869510
$993$	9.48683			0.301056
$994$			21.9089i			0.694908i
$995$	75.8947			2.40602
$996$	3.46410			0.109764
$997$			56.9210i			1.80271i	0.433085	+	0.901353i	$0.357425\pi$
$997$			56.9210i			1.80271i	−0.433085	+	0.901353i	$0.642575\pi$
$998$	−38.3406			−1.21365
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.e.b.428.4	yes	8
3.2	odd	2	inner	429.2.e.b.428.5	yes	8
11.10	odd	2	inner	429.2.e.b.428.8	yes	8
13.12	even	2	inner	429.2.e.b.428.7	yes	8
33.32	even	2	inner	429.2.e.b.428.1	✓	8
39.38	odd	2	inner	429.2.e.b.428.2	yes	8
143.142	odd	2	inner	429.2.e.b.428.3	yes	8
429.428	even	2	inner	429.2.e.b.428.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.e.b.428.1	✓	8	33.32	even	2	inner
429.2.e.b.428.2	yes	8	39.38	odd	2	inner
429.2.e.b.428.3	yes	8	143.142	odd	2	inner
429.2.e.b.428.4	yes	8	1.1	even	1	trivial
429.2.e.b.428.5	yes	8	3.2	odd	2	inner
429.2.e.b.428.6	yes	8	429.428	even	2	inner
429.2.e.b.428.7	yes	8	13.12	even	2	inner
429.2.e.b.428.8	yes	8	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.73205i q^{3} +1.00000 q^{4} +3.16228 q^{5} +1.73205 q^{6} +3.46410 q^{7} -3.00000i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.73205i q^{3} +1.00000 q^{4} +3.16228 q^{5} +1.73205 q^{6} +3.46410 q^{7} -3.00000i q^{8} -3.00000 q^{9} -3.16228i q^{10} +(-3.16228 + 1.00000i) q^{11} +1.73205i q^{12} +(1.73205 - 3.16228i) q^{13} -3.46410i q^{14} +5.47723i q^{15} -1.00000 q^{16} -5.47723 q^{17} +3.00000i q^{18} -3.46410 q^{19} +3.16228 q^{20} +6.00000i q^{21} +(1.00000 + 3.16228i) q^{22} +6.92820i q^{23} +5.19615 q^{24} +5.00000 q^{25} +(-3.16228 - 1.73205i) q^{26} -5.19615i q^{27} +3.46410 q^{28} -5.47723 q^{29} +5.47723 q^{30} -5.47723i q^{31} -5.00000i q^{32} +(-1.73205 - 5.47723i) q^{33} +5.47723i q^{34} +10.9545 q^{35} -3.00000 q^{36} +3.46410i q^{38} +(5.47723 + 3.00000i) q^{39} -9.48683i q^{40} +2.00000i q^{41} +6.00000 q^{42} +9.48683i q^{43} +(-3.16228 + 1.00000i) q^{44} -9.48683 q^{45} +6.92820 q^{46} +6.32456 q^{47} -1.73205i q^{48} +5.00000 q^{49} -5.00000i q^{50} -9.48683i q^{51} +(1.73205 - 3.16228i) q^{52} -6.92820i q^{53} -5.19615 q^{54} +(-10.0000 + 3.16228i) q^{55} -10.3923i q^{56} -6.00000i q^{57} +5.47723i q^{58} +6.32456 q^{59} +5.47723i q^{60} +12.6491i q^{61} -5.47723 q^{62} -10.3923 q^{63} -7.00000 q^{64} +(5.47723 - 10.0000i) q^{65} +(-5.47723 + 1.73205i) q^{66} +5.47723i q^{67} -5.47723 q^{68} -12.0000 q^{69} -10.9545i q^{70} -6.32456 q^{71} +9.00000i q^{72} -6.92820 q^{73} +8.66025i q^{75} -3.46410 q^{76} +(-10.9545 + 3.46410i) q^{77} +(3.00000 - 5.47723i) q^{78} +3.16228i q^{79} -3.16228 q^{80} +9.00000 q^{81} +2.00000 q^{82} -2.00000i q^{83} +6.00000i q^{84} -17.3205 q^{85} +9.48683 q^{86} -9.48683i q^{87} +(3.00000 + 9.48683i) q^{88} +3.16228 q^{89} +9.48683i q^{90} +(6.00000 - 10.9545i) q^{91} +6.92820i q^{92} +9.48683 q^{93} -6.32456i q^{94} -10.9545 q^{95} +8.66025 q^{96} -10.9545i q^{97} -5.00000i q^{98} +(9.48683 - 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 24 q^{9}+O(q^{10}) \) 8 * q + 8 * q^4 - 24 * q^9	\( 8 q + 8 q^{4} - 24 q^{9} - 8 q^{16} + 8 q^{22} + 40 q^{25} - 24 q^{36} + 48 q^{42} + 40 q^{49} - 80 q^{55} - 56 q^{64} - 96 q^{69} + 24 q^{78} + 72 q^{81} + 16 q^{82} + 24 q^{88} + 48 q^{91}+O(q^{100}) \) 8 * q + 8 * q^4 - 24 * q^9 - 8 * q^16 + 8 * q^22 + 40 * q^25 - 24 * q^36 + 48 * q^42 + 40 * q^49 - 80 * q^55 - 56 * q^64 - 96 * q^69 + 24 * q^78 + 72 * q^81 + 16 * q^82 + 24 * q^88 + 48 * q^91

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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