LMFDB - Embedded newform 429.2.bb.a.25.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(25,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, degree $4$, 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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.12
Character	$\chi$	$=$	429.25
Dual form			429.2.bb.a.103.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22454 + 1.68544i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.723159 + 2.22565i) q^{4} +(-1.88056 + 2.58836i) q^{5} +(-1.22454 + 1.68544i) q^{6} +(-3.04968 - 0.990901i) q^{7} +(-0.674037 + 0.219008i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.22454 + 1.68544i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.723159 + 2.22565i) q^{4} +(-1.88056 + 2.58836i) q^{5} +(-1.22454 + 1.68544i) q^{6} +(-3.04968 - 0.990901i) q^{7} +(-0.674037 + 0.219008i) q^{8} +(-0.809017 + 0.587785i) q^{9} -6.66533 q^{10} +(2.40241 + 2.28658i) q^{11} -2.34019 q^{12} +(0.230320 - 3.59819i) q^{13} +(-2.06436 - 6.35343i) q^{14} +(-3.04280 - 0.988666i) q^{15} +(2.59200 + 1.88320i) q^{16} +(1.41451 + 1.02770i) q^{17} +(-1.98135 - 0.643779i) q^{18} +(-3.35723 + 1.09083i) q^{19} +(-4.40086 - 6.05726i) q^{20} -3.20662i q^{21} +(-0.912029 + 6.84911i) q^{22} +1.60097 q^{23} +(-0.416578 - 0.573370i) q^{24} +(-1.61805 - 4.97984i) q^{25} +(6.34655 - 4.01794i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(4.41080 - 6.07095i) q^{28} +(-0.938995 + 2.88993i) q^{29} +(-2.05970 - 6.33911i) q^{30} +(5.10418 + 7.02530i) q^{31} +8.09215i q^{32} +(-1.43228 + 2.99142i) q^{33} +3.64253i q^{34} +(8.29990 - 6.03023i) q^{35} +(-0.723159 - 2.22565i) q^{36} +(6.56363 + 2.13265i) q^{37} +(-5.94959 - 4.32263i) q^{38} +(3.49325 - 0.892854i) q^{39} +(0.700692 - 2.15651i) q^{40} +(-8.55686 + 2.78029i) q^{41} +(5.40455 - 3.92664i) q^{42} -4.21694 q^{43} +(-6.82645 + 3.69337i) q^{44} -3.19939i q^{45} +(1.96045 + 2.69833i) q^{46} +(4.01150 - 1.30342i) q^{47} +(-0.990056 + 3.04708i) q^{48} +(2.65554 + 1.92936i) q^{49} +(6.41183 - 8.82512i) q^{50} +(-0.540295 + 1.66286i) q^{51} +(7.84176 + 3.11467i) q^{52} +(7.92169 - 5.75545i) q^{53} -2.08331i q^{54} +(-10.4364 + 1.91827i) q^{55} +2.27261 q^{56} +(-2.07488 - 2.85583i) q^{57} +(-6.02063 + 1.95622i) q^{58} +(8.46988 + 2.75203i) q^{59} +(4.40086 - 6.05726i) q^{60} +(1.51477 + 1.10055i) q^{61} +(-5.59042 + 17.2055i) q^{62} +(3.04968 - 0.990901i) q^{63} +(-8.45479 + 6.14277i) q^{64} +(8.88028 + 7.36274i) q^{65} +(-6.79572 + 1.24910i) q^{66} -5.94123i q^{67} +(-3.31023 + 2.40502i) q^{68} +(0.494727 + 1.52261i) q^{69} +(20.3271 + 6.60468i) q^{70} +(3.93528 - 5.41645i) q^{71} +(0.416578 - 0.573370i) q^{72} +(-10.8194 - 3.51543i) q^{73} +(4.44298 + 13.6741i) q^{74} +(4.23610 - 3.07771i) q^{75} -8.26088i q^{76} +(-5.06081 - 9.35387i) q^{77} +(5.78248 + 4.79432i) q^{78} +(6.78636 - 4.93058i) q^{79} +(-9.74880 + 3.16758i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-15.1642 - 11.0174i) q^{82} +(5.61343 - 7.72622i) q^{83} +(7.13683 + 2.31890i) q^{84} +(-5.32013 + 1.72862i) q^{85} +(-5.16381 - 7.10738i) q^{86} -3.03865 q^{87} +(-2.12009 - 1.01509i) q^{88} -17.4105i q^{89} +(5.39237 - 3.91778i) q^{90} +(-4.26785 + 10.7451i) q^{91} +(-1.15776 + 3.56320i) q^{92} +(-5.10418 + 7.02530i) q^{93} +(7.10907 + 5.16504i) q^{94} +(3.49000 - 10.7411i) q^{95} +(-7.69609 + 2.50061i) q^{96} +(8.76328 + 12.0616i) q^{97} +6.83832i q^{98} +(-3.28761 - 0.437778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	1.22454	+	1.68544i	0.865881	+	1.19178i	0.980135	+	0.198331i	$0.0635521\pi$
$2$	1.22454	+	1.68544i	0.865881	+	1.19178i	−0.114254	+	0.993452i	$0.536448\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.723159	+	2.22565i	−0.361579	+	1.11283i
$5$	−1.88056	+	2.58836i	−0.841010	+	1.15755i	0.144763	+	0.989466i	$0.453758\pi$
$5$	−1.88056	+	2.58836i	−0.841010	+	1.15755i	−0.985773	+	0.168084i	$0.946242\pi$
$6$	−1.22454	+	1.68544i	−0.499917	+	0.688076i
$7$	−3.04968	−	0.990901i	−1.15267	−	0.374525i	−0.330522	−	0.943798i	$-0.607225\pi$
$7$	−3.04968	−	0.990901i	−1.15267	−	0.374525i	−0.822148	+	0.569273i	$0.807225\pi$
$8$	−0.674037	+	0.219008i	−0.238308	+	0.0774310i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−6.66533			−2.10776
$11$	2.40241	+	2.28658i	0.724354	+	0.689429i
$11$	2.40241	+	2.28658i	0.724354	+	0.689429i
$12$	−2.34019			−0.675555
$13$	0.230320	−	3.59819i	0.0638793	−	0.997958i
$13$	0.230320	−	3.59819i	0.0638793	−	0.997958i
$14$	−2.06436	−	6.35343i	−0.551722	−	1.69803i
$15$	−3.04280	−	0.988666i	−0.785648	−	0.255273i
$16$	2.59200	+	1.88320i	0.648000	+	0.470799i
$17$	1.41451	+	1.02770i	0.343069	+	0.249254i	0.745956	−	0.665996i	$-0.231993\pi$
$17$	1.41451	+	1.02770i	0.343069	+	0.249254i	−0.402886	+	0.915250i	$0.631993\pi$
$18$	−1.98135	−	0.643779i	−0.467008	−	0.151740i
$19$	−3.35723	+	1.09083i	−0.770202	+	0.250254i	−0.667652	−	0.744474i	$-0.732700\pi$
$19$	−3.35723	+	1.09083i	−0.770202	+	0.250254i	−0.102551	+	0.994728i	$0.532700\pi$
$20$	−4.40086	−	6.05726i	−0.984062	−	1.35445i
$21$		−	3.20662i		−	0.699742i
$22$	−0.912029	+	6.84911i	−0.194445	+	1.46024i
$23$	1.60097			0.333825			0.166913	−	0.985972i	$-0.446620\pi$
$23$	1.60097			0.333825			0.166913	+	0.985972i	$0.446620\pi$
$24$	−0.416578	−	0.573370i	−0.0850336	−	0.117039i
$25$	−1.61805	−	4.97984i	−0.323609	−	0.995967i
$26$	6.34655	−	4.01794i	1.24466	−	0.787982i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	4.41080	−	6.07095i	0.833564	−	1.14730i
$29$	−0.938995	+	2.88993i	−0.174367	+	0.536647i	−0.999604	−	0.0281401i	$-0.991042\pi$
$29$	−0.938995	+	2.88993i	−0.174367	+	0.536647i	0.825237	+	0.564787i	$0.191042\pi$
$30$	−2.05970	−	6.33911i	−0.376048	−	1.15736i
$31$	5.10418	+	7.02530i	0.916738	+	1.26178i	0.964813	+	0.262938i	$0.0846914\pi$
$31$	5.10418	+	7.02530i	0.916738	+	1.26178i	−0.0480748	+	0.998844i	$0.515309\pi$
$32$			8.09215i			1.43050i
$33$	−1.43228	+	2.99142i	−0.249328	+	0.520739i
$34$			3.64253i			0.624689i
$35$	8.29990	−	6.03023i	1.40294	−	1.01929i
$36$	−0.723159	−	2.22565i	−0.120526	−	0.370942i
$37$	6.56363	+	2.13265i	1.07905	+	0.350606i	0.794007	−	0.607908i	$-0.207991\pi$
$37$	6.56363	+	2.13265i	1.07905	+	0.350606i	0.285046	+	0.958514i	$0.407991\pi$
$38$	−5.94959	−	4.32263i	−0.965151	−	0.701224i
$39$	3.49325	−	0.892854i	0.559368	−	0.142971i
$40$	0.700692	−	2.15651i	0.110789	−	0.340974i
$41$	−8.55686	+	2.78029i	−1.33636	+	0.434209i	−0.888081	−	0.459687i	$-0.847962\pi$
$41$	−8.55686	+	2.78029i	−1.33636	+	0.434209i	−0.448276	+	0.893895i	$0.647962\pi$
$42$	5.40455	−	3.92664i	0.833941	−	0.605893i
$43$	−4.21694			−0.643078			−0.321539	−	0.946896i	$-0.604200\pi$
$43$	−4.21694			−0.643078			−0.321539	+	0.946896i	$0.604200\pi$
$44$	−6.82645	+	3.69337i	−1.02913	+	0.556797i
$45$		−	3.19939i		−	0.476937i
$46$	1.96045	+	2.69833i	0.289053	+	0.397847i
$47$	4.01150	−	1.30342i	0.585137	−	0.190123i	−0.00146333	−	0.999999i	$-0.500466\pi$
$47$	4.01150	−	1.30342i	0.585137	−	0.190123i	0.586601	+	0.809876i	$0.300466\pi$
$48$	−0.990056	+	3.04708i	−0.142902	+	0.439808i
$49$	2.65554	+	1.92936i	0.379362	+	0.275623i
$50$	6.41183	−	8.82512i	0.906769	−	1.24806i
$51$	−0.540295	+	1.66286i	−0.0756565	+	0.232847i
$52$	7.84176	+	3.11467i	1.08746	+	0.431928i
$53$	7.92169	−	5.75545i	1.08813	−	0.790572i	0.109046	−	0.994037i	$-0.465220\pi$
$53$	7.92169	−	5.75545i	1.08813	−	0.790572i	0.979082	+	0.203465i	$0.0652203\pi$
$54$		−	2.08331i		−	0.283503i
$55$	−10.4364	+	1.91827i	−1.40724	+	0.258660i
$56$	2.27261			0.303690
$57$	−2.07488	−	2.85583i	−0.274825	−	0.378264i
$58$	−6.02063	+	1.95622i	−0.790547	+	0.256864i
$59$	8.46988	+	2.75203i	1.10268	+	0.358284i	0.803135	−	0.595797i	$-0.203164\pi$
$59$	8.46988	+	2.75203i	1.10268	+	0.358284i	0.299549	+	0.954081i	$0.403164\pi$
$60$	4.40086	−	6.05726i	0.568148	−	0.781989i
$61$	1.51477	+	1.10055i	0.193946	+	0.140910i	0.680521	−	0.732729i	$-0.261754\pi$
$61$	1.51477	+	1.10055i	0.193946	+	0.140910i	−0.486574	+	0.873639i	$0.661754\pi$
$62$	−5.59042	+	17.2055i	−0.709984	+	2.18510i
$63$	3.04968	−	0.990901i	0.384223	−	0.124842i
$64$	−8.45479	+	6.14277i	−1.05685	+	0.767846i
$65$	8.88028	+	7.36274i	1.10146	+	0.913236i
$66$	−6.79572	+	1.24910i	−0.836496	+	0.153754i
$67$		−	5.94123i		−	0.725837i	−0.931821	−	0.362918i	$-0.881780\pi$
$67$		−	5.94123i		−	0.725837i	0.931821	−	0.362918i	$-0.118220\pi$
$68$	−3.31023	+	2.40502i	−0.401424	+	0.291652i
$69$	0.494727	+	1.52261i	0.0595581	+	0.183301i
$70$	20.3271	+	6.60468i	2.42956	+	0.789411i
$71$	3.93528	−	5.41645i	0.467032	−	0.642814i	−0.508917	−	0.860816i	$-0.669954\pi$
$71$	3.93528	−	5.41645i	0.467032	−	0.642814i	0.975948	+	0.218002i	$0.0699539\pi$
$72$	0.416578	−	0.573370i	0.0490942	−	0.0675723i
$73$	−10.8194	−	3.51543i	−1.26631	−	0.411450i	−0.402574	−	0.915387i	$-0.631884\pi$
$73$	−10.8194	−	3.51543i	−1.26631	−	0.411450i	−0.863740	+	0.503937i	$0.831884\pi$
$74$	4.44298	+	13.6741i	0.516486	+	1.58958i
$75$	4.23610	−	3.07771i	0.489143	−	0.355383i
$76$		−	8.26088i		−	0.947588i
$77$	−5.06081	−	9.35387i	−0.576732	−	1.06597i
$78$	5.78248	+	4.79432i	0.654736	+	0.542849i
$79$	6.78636	−	4.93058i	0.763526	−	0.554734i	−0.136464	−	0.990645i	$-0.543574\pi$
$79$	6.78636	−	4.93058i	0.763526	−	0.554734i	0.899990	+	0.435911i	$0.143574\pi$
$80$	−9.74880	+	3.16758i	−1.08995	+	0.354146i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−15.1642	−	11.0174i	−1.67461	−	1.21667i
$83$	5.61343	−	7.72622i	0.616154	−	0.848063i	−0.380912	−	0.924611i	$-0.624390\pi$
$83$	5.61343	−	7.72622i	0.616154	−	0.848063i	0.997066	+	0.0765480i	$0.0243899\pi$
$84$	7.13683	+	2.31890i	0.778692	+	0.253012i
$85$	−5.32013	+	1.72862i	−0.577049	+	0.187495i
$86$	−5.16381	−	7.10738i	−0.556828	−	0.766409i
$87$	−3.03865			−0.325778
$88$	−2.12009	−	1.01509i	−0.226002	−	0.108209i
$89$		−	17.4105i		−	1.84551i	−0.385387	−	0.922755i	$-0.625932\pi$
$89$		−	17.4105i		−	1.84551i	0.385387	−	0.922755i	$-0.374068\pi$
$90$	5.39237	−	3.91778i	0.568405	−	0.412971i
$91$	−4.26785	+	10.7451i	−0.447392	+	1.12639i
$92$	−1.15776	+	3.56320i	−0.120704	+	0.371490i
$93$	−5.10418	+	7.02530i	−0.529279	+	0.728490i
$94$	7.10907	+	5.16504i	0.733244	+	0.532733i
$95$	3.49000	−	10.7411i	0.358066	−	1.10201i
$96$	−7.69609	+	2.50061i	−0.785479	+	0.255218i
$97$	8.76328	+	12.0616i	0.889777	+	1.22467i	0.973616	+	0.228193i	$0.0732818\pi$
$97$	8.76328	+	12.0616i	0.889777	+	1.22467i	−0.0838392	+	0.996479i	$0.526718\pi$
$98$			6.83832i			0.690774i
$99$	−3.28761	−	0.437778i	−0.330417	−	0.0439984i
$100$	12.2535			1.22535
$101$	−3.00177	+	2.18091i	−0.298687	+	0.217009i	−0.727027	−	0.686609i	$-0.759099\pi$
$101$	−3.00177	+	2.18091i	−0.298687	+	0.217009i	0.428340	+	0.903618i	$0.359099\pi$
$102$	−3.46425	+	1.12560i	−0.343012	+	0.111451i
$103$	1.24103	−	3.81948i	0.122282	−	0.376345i	−0.871114	−	0.491080i	$-0.836602\pi$
$103$	1.24103	−	3.81948i	0.122282	−	0.376345i	0.993396	+	0.114736i	$0.0366021\pi$
$104$	0.632787	+	2.47575i	0.0620499	+	0.242768i
$105$	8.29990	+	6.03023i	0.809987	+	0.588490i
$106$	19.4009	+	6.30372i	1.88438	+	0.612272i
$107$	0.604070	+	1.85914i	0.0583976	+	0.179729i	0.976000	−	0.217770i	$-0.0698782\pi$
$107$	0.604070	+	1.85914i	0.0583976	+	0.179729i	−0.917603	+	0.397499i	$0.869878\pi$
$108$	1.89325	−	1.37553i	0.182178	−	0.132360i
$109$		−	12.4894i		−	1.19627i	−0.801396	−	0.598134i	$-0.795909\pi$
$109$		−	12.4894i		−	1.19627i	0.801396	−	0.598134i	$-0.204091\pi$
$110$	−16.0129	−	15.2408i	−1.52677	−	1.45315i
$111$			6.90140i			0.655052i
$112$	−6.03870	−	8.31156i	−0.570604	−	0.785369i
$113$	5.18568	+	15.9599i	0.487827	+	1.50138i	0.827844	+	0.560959i	$0.189567\pi$
$113$	5.18568	+	15.9599i	0.487827	+	1.50138i	−0.340017	+	0.940419i	$0.610433\pi$
$114$	2.27254	−	6.99417i	0.212843	−	0.655064i
$115$	−3.01071	+	4.14389i	−0.280750	+	0.386420i
$116$	−5.75294	−	4.17976i	−0.534147	−	0.388081i
$117$	1.92863	+	3.04637i	0.178302	+	0.281637i
$118$	5.73334	+	17.6454i	0.527797	+	1.62439i
$119$	−3.29545	−	4.53580i	−0.302094	−	0.415796i
$120$	2.26749			0.206992
$121$	0.543138	+	10.9866i	0.0493762	+	0.998780i
$122$			3.90071i			0.353154i
$123$	−5.28843	−	7.27890i	−0.476842	−	0.656316i
$124$	−19.3270	+	6.27973i	−1.73562	+	0.563937i
$125$	0.718431	+	0.233433i	0.0642585	+	0.0208788i
$126$	5.40455	+	3.92664i	0.481476	+	0.349813i
$127$	8.59431	+	6.24413i	0.762622	+	0.554077i	0.899713	−	0.436481i	$-0.143775\pi$
$127$	8.59431	+	6.24413i	0.762622	+	0.554077i	−0.137091	+	0.990558i	$0.543775\pi$
$128$	−5.31429	−	1.72672i	−0.469721	−	0.152622i
$129$	−1.30311	−	4.01055i	−0.114732	−	0.353109i
$130$	−1.53516	+	23.9831i	−0.134642	+	2.10346i
$131$	−8.68812			−0.759085			−0.379542	−	0.925174i	$-0.623919\pi$
$131$	−8.68812			−0.759085			−0.379542	+	0.925174i	$0.623919\pi$
$132$	−5.62210	−	5.35103i	−0.489341	−	0.465747i
$133$	11.3194			0.981515
$134$	10.0136	−	7.27528i	0.865040	−	0.628488i
$135$	3.04280	−	0.988666i	0.261883	−	0.0850909i
$136$	−1.17851	−	0.382920i	−0.101056	−	0.0328352i
$137$	−6.61105	+	9.09933i	−0.564820	+	0.777408i	−0.991929	−	0.126792i	$-0.959532\pi$
$137$	−6.61105	+	9.09933i	−0.564820	+	0.777408i	0.427109	+	0.904200i	$0.359532\pi$
$138$	−1.96045	+	2.69833i	−0.166885	+	0.229697i
$139$	−4.70410	+	14.4777i	−0.398996	+	1.22798i	0.526809	+	0.849983i	$0.323388\pi$
$139$	−4.70410	+	14.4777i	−0.398996	+	1.22798i	−0.925805	+	0.378000i	$0.876612\pi$
$140$	7.41906	+	22.8335i	0.627025	+	1.92978i
$141$	2.47924	+	3.41239i	0.208790	+	0.287375i
$142$	13.9480			1.17049
$143$	8.78085	−	8.11767i	0.734292	−	0.678834i
$144$	−3.20389			−0.266991
$145$	−5.71435	−	7.86513i	−0.474551	−	0.653164i
$146$	−7.32375	−	22.5402i	−0.606118	−	1.86544i
$147$	−1.01432	+	3.12177i	−0.0836601	+	0.257479i
$148$	−9.49309	+	13.0661i	−0.780327	+	1.07403i
$149$	8.34894	−	11.4913i	0.683972	−	0.941406i	−0.316001	−	0.948759i	$-0.602340\pi$
$149$	8.34894	−	11.4913i	0.683972	−	0.941406i	0.999973	+	0.00735254i	$0.00234041\pi$
$150$	10.3746	+	3.37090i	0.847079	+	0.275233i
$151$	12.5519	−	4.07835i	1.02146	−	0.331891i	0.250049	−	0.968233i	$-0.419553\pi$
$151$	12.5519	−	4.07835i	1.02146	−	0.331891i	0.771407	+	0.636342i	$0.219553\pi$
$152$	2.02400	−	1.47052i	0.164168	−	0.119275i
$153$	−1.74843			−0.141352
$154$	9.56818	−	19.9839i	0.771026	−	1.61034i
$155$	−27.7827			−2.23156
$156$	−0.538993	+	8.42045i	−0.0431540	+	0.674175i
$157$	−7.13744	−	21.9668i	−0.569630	−	1.75314i	−0.653778	−	0.756686i	$-0.726817\pi$
$157$	−7.13744	−	21.9668i	−0.569630	−	1.75314i	0.0841488	−	0.996453i	$-0.473183\pi$
$158$	16.6204	+	5.40028i	1.32224	+	0.429623i
$159$	7.92169	+	5.75545i	0.628231	+	0.456437i
$160$	−20.9454	−	15.2177i	−1.65588	−	1.20307i
$161$	−4.88244	−	1.58640i	−0.384790	−	0.125026i
$162$	1.98135	−	0.643779i	0.155669	−	0.0505801i
$163$	−5.33610	−	7.34451i	−0.417955	−	0.575266i	0.547181	−	0.837014i	$-0.315701\pi$
$163$	−5.33610	−	7.34451i	−0.417955	−	0.575266i	−0.965136	+	0.261748i	$0.915701\pi$
$164$		−	21.0552i		−	1.64413i
$165$	−5.04940	−	9.33278i	−0.393095	−	0.726556i
$166$	19.8959			1.54422
$167$	6.08982	+	8.38192i	0.471245	+	0.648612i	0.976793	−	0.214186i	$-0.0687098\pi$
$167$	6.08982	+	8.38192i	0.471245	+	0.648612i	−0.505548	+	0.862798i	$0.668710\pi$
$168$	0.702276	+	2.16138i	0.0541817	+	0.166754i
$169$	−12.8939	−	1.65747i	−0.991839	−	0.127498i
$170$	−9.42819	−	6.84998i	−0.723109	−	0.525369i
$171$	2.07488	−	2.85583i	0.158670	−	0.218391i
$172$	3.04952	−	9.38545i	0.232524	−	0.715634i
$173$	−3.90746	−	12.0259i	−0.297079	−	0.914315i	−0.982515	−	0.186182i	$-0.940389\pi$
$173$	−3.90746	−	12.0259i	−0.297079	−	0.914315i	0.685436	−	0.728133i	$-0.259611\pi$
$174$	−3.72095	−	5.12145i	−0.282085	−	0.388256i
$175$			16.7902i			1.26922i
$176$	1.92097	+	10.4510i	0.144798	+	0.787775i
$177$			8.90576i			0.669398i
$178$	29.3443	−	21.3199i	2.19945	−	1.59799i
$179$	4.79918	+	14.7703i	0.358707	+	1.10399i	0.953829	+	0.300352i	$0.0971041\pi$
$179$	4.79918	+	14.7703i	0.358707	+	1.10399i	−0.595121	+	0.803636i	$0.702896\pi$
$180$	7.12074	+	2.31367i	0.530749	+	0.172451i
$181$	−8.77084	−	6.37239i	−0.651932	−	0.473656i	0.211997	−	0.977270i	$-0.432003\pi$
$181$	−8.77084	−	6.37239i	−0.651932	−	0.473656i	−0.863929	+	0.503614i	$0.832003\pi$
$182$	−23.3363	+	5.96462i	−1.72980	+	0.442127i
$183$	−0.578591	+	1.78072i	−0.0427707	+	0.131635i
$184$	−1.07911	+	0.350625i	−0.0795533	+	0.0258484i
$185$	−17.8633	+	12.9785i	−1.31334	+	0.954196i
$186$	−18.0910			−1.32649
$187$	1.04831	+	5.70335i	0.0766603	+	0.417070i
$188$			9.87079i			0.719901i
$189$	1.88481	+	2.59421i	0.137099	+	0.188701i
$190$	22.3771	−	7.27075i	1.62340	−	0.527476i
$191$	0.195208	−	0.600789i	0.0141248	−	0.0434716i	−0.943746	−	0.330672i	$-0.892725\pi$
$191$	0.195208	−	0.600789i	0.0141248	−	0.0434716i	0.957870	+	0.287200i	$0.0927246\pi$
$192$	−8.45479	−	6.14277i	−0.610172	−	0.443316i
$193$	−3.12532	+	4.30163i	−0.224965	+	0.309638i	−0.906548	−	0.422103i	$-0.861292\pi$
$193$	−3.12532	+	4.30163i	−0.224965	+	0.309638i	0.681583	+	0.731741i	$0.261292\pi$
$194$	−9.59809	+	29.5399i	−0.689103	+	2.12084i
$195$	−4.25823	+	10.7209i	−0.304938	+	0.767737i
$196$	−6.21446	+	4.51507i	−0.443890	+	0.322505i
$197$		−	20.1181i		−	1.43336i	−0.697403	−	0.716679i	$-0.745661\pi$
$197$		−	20.1181i		−	1.43336i	0.697403	−	0.716679i	$-0.254339\pi$
$198$	−3.28796	−	6.07712i	−0.233665	−	0.431882i
$199$	1.92427			0.136408			0.0682039	−	0.997671i	$-0.478273\pi$
$199$	1.92427			0.136408			0.0682039	+	0.997671i	$0.478273\pi$
$200$	2.18125	+	3.00223i	0.154237	+	0.212290i
$201$	5.65044	−	1.83594i	0.398552	−	0.129497i
$202$	−7.35157	−	2.38867i	−0.517255	−	0.168066i
$203$	5.72727	−	7.88291i	0.401975	−	0.553272i
$204$	−3.31023	−	2.40502i	−0.231762	−	0.168385i
$205$	8.89524	−	27.3767i	0.621271	−	1.91207i
$206$	7.95718	−	2.58544i	0.554403	−	0.180136i
$207$	−1.29521	+	0.941026i	−0.0900234	+	0.0654059i
$208$	7.37309	−	8.89276i	0.511232	−	0.616602i
$209$	−10.5597	−	5.05595i	−0.730431	−	0.349727i
$210$			21.3732i			1.47489i
$211$	−14.8498	+	10.7890i	−1.02230	+	0.742748i	−0.966754	−	0.255708i	$-0.917691\pi$
$211$	−14.8498	+	10.7890i	−1.02230	+	0.742748i	−0.0555505	+	0.998456i	$0.517691\pi$
$212$	7.08099	+	21.7931i	0.486325	+	1.49675i
$213$	6.36742	+	2.06890i	0.436288	+	0.141759i
$214$	−2.39375	+	3.29471i	−0.163633	+	0.225222i
$215$	7.93019	−	10.9150i	0.540835	−	0.744395i
$216$	0.674037	+	0.219008i	0.0458624	+	0.0149016i
$217$	−8.60473	−	26.4827i	−0.584127	−	1.79776i
$218$	21.0501	−	15.2938i	1.42569	−	1.03583i
$219$		−	11.3762i		−	0.768731i
$220$	3.27773	−	24.6149i	0.220984	−	1.65954i
$221$	4.02366	−	4.85298i	0.270660	−	0.326446i
$222$	−11.6319	+	8.45105i	−0.780680	+	0.567197i
$223$	2.27291	−	0.738513i	0.152205	−	0.0494545i	−0.231923	−	0.972734i	$-0.574502\pi$
$223$	2.27291	−	0.738513i	0.152205	−	0.0494545i	0.384129	+	0.923280i	$0.374502\pi$
$224$	8.01852	−	24.6785i	0.535760	−	1.64890i
$225$	4.23610	+	3.07771i	0.282407	+	0.205180i
$226$	−20.5493	+	28.2836i	−1.36692	+	1.88140i
$227$	12.5839	+	4.08877i	0.835225	+	0.271381i	0.695244	−	0.718773i	$-0.255296\pi$
$227$	12.5839	+	4.08877i	0.835225	+	0.271381i	0.139980	+	0.990154i	$0.455296\pi$
$228$	7.85657	−	2.55275i	0.520314	−	0.169060i
$229$	−6.48995	−	8.93266i	−0.428868	−	0.590286i	0.538825	−	0.842418i	$-0.318868\pi$
$229$	−6.48995	−	8.93266i	−0.428868	−	0.590286i	−0.967693	+	0.252131i	$0.918868\pi$
$230$	−10.6710			−0.703625
$231$	7.33219	−	7.70362i	0.482422	−	0.506861i
$232$		−	2.15357i		−	0.141389i
$233$	18.0044	−	13.0809i	1.17951	−	0.856961i	0.187390	−	0.982286i	$-0.439997\pi$
$233$	18.0044	−	13.0809i	1.17951	−	0.856961i	0.992116	+	0.125324i	$0.0399971\pi$
$234$	−2.77278	+	6.98099i	−0.181262	+	0.456361i
$235$	−4.17014	+	12.8344i	−0.272030	+	0.837221i
$236$	−12.2501	+	16.8609i	−0.797416	+	1.09755i
$237$	6.78636	+	4.93058i	0.440822	+	0.320276i
$238$	3.60939	−	11.1085i	0.233962	−	0.720060i
$239$	−10.0513	+	3.26586i	−0.650163	+	0.211251i	−0.615486	−	0.788148i	$-0.711040\pi$
$239$	−10.0513	+	3.26586i	−0.650163	+	0.211251i	−0.0346771	+	0.999399i	$0.511040\pi$
$240$	−6.02509	−	8.29282i	−0.388918	−	0.535299i
$241$		−	27.8942i		−	1.79683i	−0.439151	−	0.898413i	$-0.644721\pi$
$241$		−	27.8942i		−	1.79683i	0.439151	−	0.898413i	$-0.355279\pi$
$242$	−17.8521	+	14.3689i	−1.14758	+	0.923670i
$243$	1.00000			0.0641500
$244$	−3.54485	+	2.57549i	−0.226936	+	0.164879i
$245$	−9.98777	+	3.24522i	−0.638095	+	0.207330i
$246$	5.79222	−	17.8266i	0.369298	−	1.13658i
$247$	3.15178	+	12.3312i	0.200543	+	0.784615i
$248$	−4.97900	−	3.61746i	−0.316167	−	0.229709i
$249$	9.08272	+	2.95116i	0.575594	+	0.187022i
$250$	0.486313	+	1.49672i	0.0307571	+	0.0946607i
$251$	7.58185	−	5.50853i	0.478562	−	0.347696i	−0.322207	−	0.946669i	$-0.604425\pi$
$251$	7.58185	−	5.50853i	0.478562	−	0.347696i	0.800769	+	0.598974i	$0.204425\pi$
$252$			7.50411i			0.472714i
$253$	3.84618	+	3.66074i	0.241808	+	0.230149i
$254$			22.1314i			1.38864i
$255$	−3.28802	−	4.52558i	−0.205904	−	0.283403i
$256$	2.86159	+	8.80708i	0.178850	+	0.550443i
$257$	−6.06902	+	18.6785i	−0.378575	+	1.16513i	0.562460	+	0.826824i	$0.309855\pi$
$257$	−6.06902	+	18.6785i	−0.378575	+	1.16513i	−0.941035	+	0.338309i	$0.890145\pi$
$258$	5.16381	−	7.10738i	0.321485	−	0.442486i
$259$	−17.9037	−	13.0078i	−1.11248	−	0.808266i
$260$	−22.8088	+	14.4400i	−1.41454	+	0.895531i
$261$	−0.938995	−	2.88993i	−0.0581223	−	0.178882i
$262$	−10.6390	−	14.6433i	−0.657277	−	0.904664i
$263$	−10.2196			−0.630168			−0.315084	−	0.949064i	$-0.602033\pi$
$263$	−10.2196			−0.630168			−0.315084	+	0.949064i	$0.602033\pi$
$264$	0.310264	−	2.33001i	0.0190954	−	0.143402i
$265$			31.3277i			1.92444i
$266$	13.8610	+	19.0781i	0.849875	+	1.16975i
$267$	16.5584	−	5.38014i	1.01336	−	0.329259i
$268$	13.2231	+	4.29645i	0.807731	+	0.262448i
$269$	−21.2512	−	15.4399i	−1.29571	−	0.941385i	−0.295802	−	0.955249i	$-0.595587\pi$
$269$	−21.2512	−	15.4399i	−1.29571	−	0.941385i	−0.999904	+	0.0138642i	$0.995587\pi$
$270$	5.39237	+	3.91778i	0.328169	+	0.238429i
$271$	−21.3452	−	6.93549i	−1.29663	−	0.421301i	−0.422223	−	0.906492i	$-0.638750\pi$
$271$	−21.3452	−	6.93549i	−1.29663	−	0.421301i	−0.874408	+	0.485191i	$0.838750\pi$
$272$	1.73104	+	5.32761i	0.104960	+	0.323034i
$273$	−11.5380	−	0.738549i	−0.698313	−	0.0446990i
$274$	−23.4318			−1.41557
$275$	7.49956	−	15.6634i	0.452241	−	0.944538i
$276$	−3.74657			−0.225517
$277$	−17.1508	+	12.4608i	−1.03049	+	0.748697i	−0.968407	−	0.249373i	$-0.919775\pi$
$277$	−17.1508	+	12.4608i	−1.03049	+	0.748697i	−0.0620861	+	0.998071i	$0.519775\pi$
$278$	−30.1616	+	9.80010i	−1.80897	+	0.587771i
$279$	−8.25874	−	2.68343i	−0.494438	−	0.160653i
$280$	−4.27377	+	5.88234i	−0.255407	+	0.351537i
$281$	−8.48090	+	11.6730i	−0.505928	+	0.696350i	−0.983226	−	0.182391i	$-0.941616\pi$
$281$	−8.48090	+	11.6730i	−0.505928	+	0.696350i	0.477298	+	0.878742i	$0.341616\pi$
$282$	−2.71542	+	8.35721i	−0.161701	+	0.497665i
$283$	−3.41117	−	10.4985i	−0.202773	−	0.624071i	−0.999797	−	0.0201242i	$-0.993594\pi$
$283$	−3.41117	−	10.4985i	−0.202773	−	0.624071i	0.797024	−	0.603947i	$-0.206406\pi$
$284$	9.20931	+	12.6755i	0.546472	+	0.752154i
$285$	11.2939			0.668991
$286$	24.4343	+	4.85914i	1.44483	+	0.287327i
$287$	28.8507			1.70300
$288$	−4.75645	−	6.54669i	−0.280276	−	0.385767i
$289$	−4.30862	−	13.2606i	−0.253448	−	0.780033i
$290$	6.25872	−	19.2623i	0.367524	−	1.13112i
$291$	−8.76328	+	12.0616i	−0.513713	+	0.707065i
$292$	15.6483	−	21.5380i	0.915746	−	1.26042i
$293$	16.7875	+	5.45458i	0.980734	+	0.318660i	0.755141	−	0.655562i	$-0.227568\pi$
$293$	16.7875	+	5.45458i	0.980734	+	0.318660i	0.225592	+	0.974222i	$0.427568\pi$
$294$	−6.50362	+	2.11316i	−0.379299	+	0.123242i
$295$	−23.0513	+	16.7478i	−1.34210	+	0.975093i
$296$	−4.89119			−0.284295
$297$	−0.599574	−	3.26198i	−0.0347908	−	0.189279i
$298$	29.5915			1.71419
$299$	0.368735	−	5.76059i	0.0213245	−	0.333143i
$300$	3.78654	+	11.6538i	0.218616	+	0.672830i
$301$	12.8603	+	4.17857i	0.741256	+	0.240849i
$302$	22.2441	+	16.1613i	1.28000	+	0.929976i
$303$	−3.00177	−	2.18091i	−0.172447	−	0.125290i
$304$	−10.7562	−	3.49490i	−0.616910	−	0.200446i
$305$	−5.69722	+	1.85114i	−0.326222	+	0.105996i
$306$	−2.14103	−	2.94687i	−0.122394	−	0.168461i
$307$			18.0428i			1.02975i	0.857264	+	0.514877i	$0.172163\pi$
$307$			18.0428i			1.02975i	−0.857264	+	0.514877i	$0.827837\pi$
$308$	24.4782	−	4.49927i	1.39478	−	0.256370i
$309$	4.01604			0.228465
$310$	−34.0211	−	46.8260i	−1.93227	−	2.65954i
$311$	9.00170	+	27.7044i	0.510440	+	1.57097i	0.791429	+	0.611261i	$0.209337\pi$
$311$	9.00170	+	27.7044i	0.510440	+	1.57097i	−0.280989	+	0.959711i	$0.590663\pi$
$312$	−2.15904	+	1.36687i	−0.122232	+	0.0773836i
$313$	6.44896	+	4.68544i	0.364517	+	0.264837i	0.754933	−	0.655801i	$-0.227669\pi$
$313$	6.44896	+	4.68544i	0.364517	+	0.264837i	−0.390417	+	0.920638i	$0.627669\pi$
$314$	28.2835	−	38.9289i	1.59613	−	2.19688i
$315$	−3.17028	+	9.75712i	−0.178625	+	0.549751i
$316$	6.06615	+	18.6697i	0.341248	+	1.05025i
$317$	9.40629	+	12.9466i	0.528310	+	0.727156i	0.986872	−	0.161507i	$-0.0516353\pi$
$317$	9.40629	+	12.9466i	0.528310	+	0.727156i	−0.458562	+	0.888662i	$0.651635\pi$
$318$			20.3993i			1.14393i
$319$	−8.86390	+	4.79571i	−0.496283	+	0.268508i
$320$		−	33.4359i		−	1.86912i
$321$	−1.58148	+	1.14901i	−0.0882694	+	0.0641315i
$322$	−3.30497	−	10.1717i	−0.184179	−	0.566844i
$323$	−5.86989	−	1.90724i	−0.326610	−	0.106122i
$324$	1.89325	+	1.37553i	0.105181	+	0.0764183i
$325$	−18.2910	+	4.67508i	−1.01460	+	0.259327i
$326$	5.84443	−	17.9873i	0.323693	−	0.996224i
$327$	11.8781	−	3.85944i	0.656862	−	0.213427i
$328$	5.15873	−	3.74804i	0.284843	−	0.206951i
$329$	−13.5253			−0.745676
$330$	9.54661	−	19.9388i	0.525524	−	1.09759i
$331$			4.64779i			0.255466i	0.991809	+	0.127733i	$0.0407700\pi$
$331$			4.64779i			0.255466i	−0.991809	+	0.127733i	$0.959230\pi$
$332$	13.1365	+	18.0808i	0.720959	+	0.992315i
$333$	−6.56363	+	2.13265i	−0.359684	+	0.116869i
$334$	−6.66995	+	20.5280i	−0.364963	+	1.12324i
$335$	15.3781	+	11.1728i	0.840193	+	0.610436i
$336$	6.03870	−	8.31156i	0.329438	−	0.453433i
$337$	9.45092	−	29.0869i	0.514825	−	1.58447i	−0.268777	−	0.963203i	$-0.586619\pi$
$337$	9.45092	−	29.0869i	0.514825	−	1.58447i	0.783601	−	0.621264i	$-0.213381\pi$
$338$	−12.9956	−	23.7615i	−0.706865	−	1.29245i
$339$	−13.5763	+	9.86374i	−0.737362	+	0.535725i
$340$		−	13.0908i		−	0.709950i
$341$	−3.80156	+	28.5487i	−0.205866	+	1.54600i
$342$	7.35410			0.397664
$343$	7.00691	+	9.64418i	0.378337	+	0.520737i
$344$	2.84237	−	0.923543i	0.153251	−	0.0497941i
$345$	−4.87143	−	1.58282i	−0.262269	−	0.0852164i
$346$	15.4841	−	21.3120i	0.832430	−	1.14574i
$347$	17.6947	+	12.8559i	0.949899	+	0.690142i	0.950783	−	0.309857i	$-0.100281\pi$
$347$	17.6947	+	12.8559i	0.949899	+	0.690142i	−0.000883675		1.00000i	$0.500281\pi$
$348$	2.19743	−	6.76299i	0.117795	−	0.362534i
$349$	−28.5654	+	9.28147i	−1.52907	+	0.496826i	−0.948336	−	0.317267i	$-0.897235\pi$
$349$	−28.5654	+	9.28147i	−1.52907	+	0.496826i	−0.580736	+	0.814092i	$0.697235\pi$
$350$	−28.2988	+	20.5603i	−1.51264	+	1.09899i
$351$	−2.30129	+	2.77562i	−0.122834	+	0.148151i
$352$	−18.5033	+	19.4407i	−0.986230	+	1.03619i
$353$			28.6624i			1.52555i	0.646666	+	0.762773i	$0.276163\pi$
$353$			28.6624i			1.52555i	−0.646666	+	0.762773i	$0.723837\pi$
$354$	−15.0101	+	10.9055i	−0.797777	+	0.579619i
$355$	6.61922	+	20.3719i	0.351312	+	1.08123i
$356$	38.7498	+	12.5906i	2.05373	+	0.667298i
$357$	3.29545	−	4.53580i	0.174414	−	0.240060i
$358$	−19.0177	+	26.1756i	−1.00512	+	1.38342i
$359$	13.2322	+	4.29939i	0.698367	+	0.226913i	0.636619	−	0.771179i	$-0.280332\pi$
$359$	13.2322	+	4.29939i	0.698367	+	0.226913i	0.0617481	+	0.998092i	$0.480332\pi$
$360$	0.700692	+	2.15651i	0.0369297	+	0.113658i
$361$	−5.29022	+	3.84357i	−0.278433	+	0.202293i
$362$		−	22.5859i		−	1.18709i
$363$	−10.2810	+	3.91160i	−0.539614	+	0.205306i
$364$	−20.8285	−	17.2692i	−1.09171	−	0.905150i
$365$	29.4457	−	21.3935i	1.54126	−	1.11979i
$366$	−3.70980	+	1.20539i	−0.193914	+	0.0630065i
$367$	5.59524	−	17.2204i	0.292069	−	0.898896i	−0.692121	−	0.721781i	$-0.743324\pi$
$367$	5.59524	−	17.2204i	0.292069	−	0.898896i	0.984190	−	0.177115i	$-0.0566763\pi$
$368$	4.14971	+	3.01494i	0.216319	+	0.157165i
$369$	5.28843	−	7.27890i	0.275305	−	0.378924i
$370$	−43.7488	−	14.2148i	−2.27439	−	0.738994i
$371$	−29.8617	+	9.70265i	−1.55034	+	0.503737i
$372$	−11.9448	−	16.4406i	−0.619307	−	0.852403i
$373$	11.8019			0.611078			0.305539	−	0.952180i	$-0.401163\pi$
$373$	11.8019			0.611078			0.305539	+	0.952180i	$0.401163\pi$
$374$	−8.32892	+	8.75085i	−0.430678	+	0.452496i
$375$			0.755403i			0.0390089i
$376$	−2.41844	+	1.75710i	−0.124722	+	0.0906155i
$377$	10.1822	+	4.04429i	0.524412	+	0.208292i
$378$	−2.06436	+	6.35343i	−0.106179	+	0.326785i
$379$	7.98346	−	10.9883i	0.410083	−	0.564431i	−0.553156	−	0.833078i	$-0.686577\pi$
$379$	7.98346	−	10.9883i	0.410083	−	0.564431i	0.963239	+	0.268647i	$0.0865765\pi$
$380$	21.3822	+	15.5351i	1.09688	+	0.796931i
$381$	−3.28274	+	10.1032i	−0.168180	+	0.517604i
$382$	1.25163	−	0.406680i	0.0640391	−	0.0208076i
$383$	6.94472	+	9.55859i	0.354859	+	0.488421i	0.948707	−	0.316156i	$-0.102392\pi$
$383$	6.94472	+	9.55859i	0.354859	+	0.488421i	−0.593849	+	0.804577i	$0.702392\pi$
$384$		−	5.58778i		−	0.285150i
$385$	33.7283	+	4.49127i	1.71896	+	0.228897i
$386$	−11.0772			−0.563814
$387$	3.41158	−	2.47866i	0.173420	−	0.125997i
$388$	−33.1823	+	10.7816i	−1.68457	+	0.547351i
$389$	6.62070	−	20.3764i	0.335683	−	1.03313i	−0.630702	−	0.776025i	$-0.717233\pi$
$389$	6.62070	−	20.3764i	0.335683	−	1.03313i	0.966385	−	0.257101i	$-0.0827672\pi$
$390$	−23.2837	+	5.95117i	−1.17902	+	0.301349i
$391$	2.26459	+	1.64532i	0.114525	+	0.0832074i
$392$	−2.21248	−	0.718877i	−0.111747	−	0.0363088i
$393$	−2.68478	−	8.26290i	−0.135429	−	0.416808i
$394$	33.9078	−	24.6355i	1.70825	−	1.24112i
$395$			26.8378i			1.35036i
$396$	3.35180	−	7.00049i	0.168435	−	0.351788i
$397$		−	15.0529i		−	0.755483i	−0.925911	−	0.377741i	$-0.876701\pi$
$397$		−	15.0529i		−	0.755483i	0.925911	−	0.377741i	$-0.123299\pi$
$398$	2.35634	+	3.24323i	0.118113	+	0.162568i
$399$	3.49788	+	10.7654i	0.175113	+	0.538943i
$400$	5.18404	−	15.9548i	0.259202	−	0.797742i
$401$	2.99865	−	4.12729i	0.149746	−	0.206107i	−0.727554	−	0.686051i	$-0.759343\pi$
$401$	2.99865	−	4.12729i	0.149746	−	0.206107i	0.877299	+	0.479943i	$0.159343\pi$
$402$	10.0136	+	7.27528i	0.499431	+	0.362858i
$403$	26.4539	−	16.7477i	1.31777	−	0.834264i
$404$	−2.68320	−	8.25804i	−0.133494	−	0.410853i
$405$	1.88056	+	2.58836i	0.0934455	+	0.128617i
$406$	20.2994			1.00744
$407$	10.8920	+	20.1317i	0.539899	+	0.997893i
$408$		−	1.23916i		−	0.0613474i
$409$	8.32734	+	11.4616i	0.411761	+	0.566740i	0.963647	−	0.267180i	$-0.0860917\pi$
$409$	8.32734	+	11.4616i	0.411761	+	0.566740i	−0.551886	+	0.833919i	$0.686092\pi$
$410$	57.0343	−	18.5316i	2.81672	−	0.915209i
$411$	−10.6969	−	3.47563i	−0.527639	−	0.171440i
$412$	7.60339	+	5.52419i	0.374592	+	0.272157i
$413$	−23.1034	−	16.7856i	−1.13685	−	0.825966i
$414$	−3.17208	−	1.03067i	−0.155899	−	0.0506547i
$415$	9.44190	+	29.0592i	0.463485	+	1.42646i
$416$	29.1171	+	1.86378i	1.42758	+	0.0913795i
$417$	−15.2228			−0.745462
$418$	−4.40933	−	23.9889i	−0.215667	−	1.17334i
$419$	−21.5995			−1.05520			−0.527602	−	0.849492i	$-0.676909\pi$
$419$	−21.5995			−1.05520			−0.527602	+	0.849492i	$0.676909\pi$
$420$	−19.4234	+	14.1119i	−0.947763	+	0.688590i
$421$	−28.2401	+	9.17576i	−1.37634	+	0.447199i	−0.901463	−	0.432855i	$-0.857506\pi$
$421$	−28.2401	+	9.17576i	−1.37634	+	0.447199i	−0.474873	+	0.880054i	$0.657506\pi$
$422$	−36.3684	−	11.8168i	−1.77039	−	0.575234i
$423$	−2.47924	+	3.41239i	−0.120545	+	0.165916i
$424$	−4.07903	+	5.61430i	−0.198095	+	0.272654i
$425$	2.82904	−	8.70690i	0.137229	−	0.422347i
$426$	4.31016	+	13.2653i	0.208828	+	0.642707i
$427$	−3.52903	−	4.85730i	−0.170782	−	0.235061i
$428$	−4.57463			−0.221123
$429$	10.4338	+	5.84259i	0.503749	+	0.282083i
$430$	28.1073			1.35546
$431$	14.2665	+	19.6362i	0.687195	+	0.945842i	0.999992	−	0.00397766i	$-0.00126613\pi$
$431$	14.2665	+	19.6362i	0.687195	+	0.945842i	−0.312798	+	0.949820i	$0.601266\pi$
$432$	−0.990056	−	3.04708i	−0.0476341	−	0.146603i
$433$	−1.92831	+	5.93474i	−0.0926688	+	0.285205i	−0.986639	−	0.162921i	$-0.947908\pi$
$433$	−1.92831	+	5.93474i	−0.0926688	+	0.285205i	0.893970	+	0.448126i	$0.147908\pi$
$434$	34.0979	−	46.9318i	1.63675	−	2.25280i
$435$	5.71435	−	7.86513i	0.273982	−	0.377104i
$436$	27.7971	+	9.03182i	1.33124	+	0.432546i
$437$	−5.37483	+	1.74639i	−0.257113	+	0.0835411i
$438$	19.1738	−	13.9306i	0.916161	−	0.665630i
$439$	1.25217			0.0597626			0.0298813	−	0.999553i	$-0.490487\pi$
$439$	1.25217			0.0597626			0.0298813	+	0.999553i	$0.490487\pi$
$440$	6.61437	−	3.57863i	0.315328	−	0.170604i
$441$	−3.28242			−0.156306
$442$	13.1065	+	0.838947i	0.623413	+	0.0399047i
$443$	−8.10043	−	24.9306i	−0.384863	−	1.18449i	−0.936580	−	0.350455i	$-0.886027\pi$
$443$	−8.10043	−	24.9306i	−0.384863	−	1.18449i	0.551717	−	0.834032i	$-0.313973\pi$
$444$	−15.3601	−	4.99081i	−0.728960	−	0.236853i
$445$	45.0647	+	32.7414i	2.13627	+	1.55209i
$446$	4.02799	+	2.92650i	0.190731	+	0.138574i
$447$	13.5089	+	4.38930i	0.638947	+	0.207607i
$448$	31.8713	−	10.3556i	1.50578	−	0.489256i
$449$	−5.55251	−	7.64237i	−0.262039	−	0.360666i	0.657643	−	0.753330i	$-0.271554\pi$
$449$	−5.55251	−	7.64237i	−0.262039	−	0.360666i	−0.919682	+	0.392664i	$0.871554\pi$
$450$			10.9085i			0.514229i
$451$	−26.9144	−	12.8865i	−1.26735	−	0.606802i
$452$	−39.2712			−1.84716
$453$	7.75748	+	10.6773i	0.364478	+	0.501661i
$454$	8.51818	+	26.2163i	0.399778	+	1.23039i
$455$	−19.7863	−	31.2535i	−0.927594	−	1.46519i
$456$	2.02400	+	1.47052i	0.0947824	+	0.0688635i
$457$	7.39305	−	10.1757i	0.345832	−	0.475997i	−0.600301	−	0.799774i	$-0.704953\pi$
$457$	7.39305	−	10.1757i	0.345832	−	0.475997i	0.946134	+	0.323777i	$0.104953\pi$
$458$	7.10820	−	21.8768i	0.332144	−	1.02224i
$459$	−0.540295	−	1.66286i	−0.0252188	−	0.0776155i
$460$	−7.04564	−	9.69749i	−0.328505	−	0.452148i
$461$		−	16.0559i		−	0.747796i	−0.927470	−	0.373898i	$-0.878021\pi$
$461$		−	16.0559i		−	0.747796i	0.927470	−	0.373898i	$-0.121979\pi$
$462$	21.9625	+	2.92453i	1.02179	+	0.136062i
$463$		−	23.2864i		−	1.08221i	−0.840954	−	0.541106i	$-0.818006\pi$
$463$		−	23.2864i		−	1.08221i	0.840954	−	0.541106i	$-0.181994\pi$
$464$	−7.87619	+	5.72238i	−0.365643	+	0.265655i
$465$	−8.58533	−	26.4229i	−0.398135	−	1.22533i
$466$	44.0942	+	14.3271i	2.04262	+	0.663689i
$467$	20.9990	+	15.2567i	0.971717	+	0.705994i	0.955842	−	0.293880i	$-0.0949467\pi$
$467$	20.9990	+	15.2567i	0.971717	+	0.705994i	0.0158747	+	0.999874i	$0.494947\pi$
$468$	−8.17488	+	2.08945i	−0.377884	+	0.0965848i
$469$	−5.88717	+	18.1188i	−0.271844	+	0.836650i
$470$	−26.7380	+	8.68770i	−1.23333	+	0.400734i
$471$	18.6861	−	13.5762i	0.861008	−	0.625559i
$472$	−6.31173			−0.290521
$473$	−10.1308	−	9.64236i	−0.465815	−	0.443356i
$474$			17.4757i			0.802684i
$475$	10.8643	+	14.9535i	0.498489	+	0.686111i
$476$	12.4783	−	4.05443i	0.571940	−	0.185835i
$477$	−3.02582	+	9.31251i	−0.138543	+	0.426391i
$478$	−17.8126	−	12.9416i	−0.814729	−	0.591935i
$479$	5.77968	−	7.95504i	0.264080	−	0.363475i	−0.656300	−	0.754500i	$-0.727879\pi$
$479$	5.77968	−	7.95504i	0.264080	−	0.363475i	0.920380	+	0.391025i	$0.127879\pi$
$480$	8.00044	−	24.6228i	0.365168	−	1.12387i
$481$	9.18541	−	23.1260i	0.418819	−	1.05445i
$482$	47.0139	−	34.1576i	2.14143	−	1.55584i
$483$		−	5.13370i		−	0.233592i
$484$	−24.8451	−	6.73621i	−1.12932	−	0.306191i
$485$	−47.6997			−2.16593
$486$	1.22454	+	1.68544i	0.0555463	+	0.0764529i
$487$	40.8378	−	13.2690i	1.85054	−	0.601276i	0.853795	−	0.520609i	$-0.174295\pi$
$487$	40.8378	−	13.2690i	1.85054	−	0.601276i	0.996741	−	0.0806662i	$-0.0257048\pi$
$488$	−1.26204	−	0.410061i	−0.0571298	−	0.0185626i
$489$	5.33610	−	7.34451i	0.241307	−	0.332130i
$490$	−17.7000	−	12.8598i	−0.799606	−	0.580948i
$491$	−1.38246	+	4.25478i	−0.0623896	+	0.192015i	−0.977393	−	0.211431i	$-0.932188\pi$
$491$	−1.38246	+	4.25478i	−0.0623896	+	0.192015i	0.915003	+	0.403446i	$0.132188\pi$
$492$	20.0247	−	6.50641i	0.902782	−	0.293332i
$493$	−4.29821	+	3.12283i	−0.193582	+	0.140645i
$494$	−16.9240	+	20.4122i	−0.761445	+	0.918387i
$495$	7.31565	−	7.68625i	0.328814	−	0.345471i
$496$			27.8218i			1.24923i
$497$	−17.3685	+	12.6190i	−0.779084	+	0.566037i
$498$	6.14818	+	18.9221i	0.275506	+	0.847922i
$499$	24.2399	+	7.87602i	1.08513	+	0.352579i	0.796362	−	0.604821i	$-0.206755\pi$
$499$	24.2399	+	7.87602i	1.08513	+	0.352579i	0.288765	+	0.957400i	$0.406755\pi$
$500$	−1.03908	+	1.43017i	−0.0464691	+	0.0639592i
$501$	−6.08982	+	8.38192i	−0.272073	+	0.374477i
$502$	18.5686	+	6.03329i	0.828755	+	0.269279i
$503$	6.86325	+	21.1229i	0.306017	+	0.941825i	0.979296	+	0.202435i	$0.0648856\pi$
$503$	6.86325	+	21.1229i	0.306017	+	0.941825i	−0.673278	+	0.739389i	$0.735114\pi$
$504$	−1.83858	+	1.33581i	−0.0818969	+	0.0595016i
$505$		−	11.8710i		−	0.528252i
$506$	−1.46013	+	10.9652i	−0.0649107	+	0.487463i
$507$	−2.40809	−	12.7750i	−0.106947	−	0.567359i
$508$	−20.1123	+	14.6125i	−0.892341	+	0.648323i
$509$	−1.68289	+	0.546803i	−0.0745926	+	0.0242366i	−0.346076	−	0.938207i	$-0.612486\pi$
$509$	−1.68289	+	0.546803i	−0.0745926	+	0.0242366i	0.271483	+	0.962443i	$0.412486\pi$
$510$	3.60125	−	11.0835i	0.159466	−	0.490786i
$511$	29.5122	+	21.4419i	1.30554	+	0.948533i
$512$	−17.9085	+	24.6489i	−0.791449	+	1.08934i
$513$	3.35723	+	1.09083i	0.148225	+	0.0481614i
$514$	−38.9132	+	12.6437i	−1.71639	+	0.557688i
$515$	7.55239	+	10.3950i	0.332798	+	0.458057i
$516$	9.86845			0.434434
$517$	12.6176	+	6.04126i	0.554922	+	0.265694i
$518$		−	46.1041i		−	2.02570i
$519$	10.2299	−	7.43244i	0.449041	−	0.326248i
$520$	−7.59814	−	3.01791i	−0.333200	−	0.132344i
$521$	−6.36445	+	19.5878i	−0.278832	+	0.858156i	0.709348	+	0.704858i	$0.248989\pi$
$521$	−6.36445	+	19.5878i	−0.278832	+	0.858156i	−0.988180	+	0.153298i	$0.951011\pi$
$522$	3.72095	−	5.12145i	0.162862	−	0.224160i
$523$	−18.3761	−	13.3510i	−0.803529	−	0.583798i	0.108418	−	0.994105i	$-0.465422\pi$
$523$	−18.3761	−	13.3510i	−0.803529	−	0.583798i	−0.911947	+	0.410307i	$0.865422\pi$
$524$	6.28289	−	19.3368i	0.274469	−	0.844730i
$525$	−15.9684	+	5.18846i	−0.696920	+	0.226443i
$526$	−12.5143	−	17.2245i	−0.545651	−	0.751024i
$527$			15.1829i			0.661380i
$528$	−9.34590	+	5.05649i	−0.406728	+	0.220056i
$529$	−20.4369			−0.888561
$530$	−52.8007	+	38.3620i	−2.29352	+	1.66634i
$531$	−8.46988	+	2.75203i	−0.367561	+	0.119428i
$532$	−8.18572	+	25.1930i	−0.354896	+	1.09226i
$533$	8.03319	+	31.4295i	0.347956	+	1.36136i
$534$	29.3443	+	21.3199i	1.26985	+	0.922601i
$535$	−5.94811	−	1.93266i	−0.257159	−	0.0835560i
$536$	1.30118	+	4.00461i	0.0562023	+	0.172973i
$537$	−12.5644	+	9.12858i	−0.542194	+	0.393927i
$538$		−	54.7242i		−	2.35933i
$539$	1.96806	+	10.7072i	0.0847702	+	0.461192i
$540$			7.48719i			0.322197i
$541$	10.0830	+	13.8781i	0.433502	+	0.596664i	0.968753	−	0.248029i	$-0.0797828\pi$
$541$	10.0830	+	13.8781i	0.433502	+	0.596664i	−0.535251	+	0.844693i	$0.679783\pi$
$542$	−14.4488	−	44.4688i	−0.620629	−	1.91010i
$543$	3.35016	−	10.3107i	0.143769	−	0.442476i
$544$	−8.31632	+	11.4464i	−0.356559	+	0.490762i
$545$	32.3271	+	23.4870i	1.38474	+	1.00607i
$546$	−12.8840	−	20.3510i	−0.551384	−	0.870942i
$547$	−4.39773	−	13.5348i	−0.188033	−	0.578707i	0.811954	−	0.583721i	$-0.198404\pi$
$547$	−4.39773	−	13.5348i	−0.188033	−	0.578707i	−0.999987	+	0.00501441i	$0.998404\pi$
$548$	−15.4711	−	21.2942i	−0.660893	−	0.909642i
$549$	−1.87236			−0.0799103
$550$	35.5831	−	6.54042i	1.51727	−	0.278885i
$551$		−	10.7265i		−	0.456962i
$552$	−0.666928	−	0.917948i	−0.0283864	−	0.0390705i
$553$	−25.5819	+	8.31208i	−1.08786	+	0.353466i
$554$	−42.0038	−	13.6479i	−1.78457	−	0.579842i
$555$	−17.8633	−	12.9785i	−0.758256	−	0.550906i
$556$	−28.8206	−	20.9394i	−1.22226	−	0.888027i
$557$	1.06907	+	0.347362i	0.0452980	+	0.0147182i	0.331578	−	0.943428i	$-0.392419\pi$
$557$	1.06907	+	0.347362i	0.0452980	+	0.0147182i	−0.286280	+	0.958146i	$0.592419\pi$
$558$	−5.59042	−	17.2055i	−0.236661	−	0.728368i
$559$	−0.971246	+	15.1733i	−0.0410793	+	0.641764i
$560$	32.8695			1.38899
$561$	−5.10026	+	2.75944i	−0.215333	+	0.116504i
$562$	−30.0592			−1.26797
$563$	5.67612	−	4.12394i	0.239220	−	0.173803i	−0.461716	−	0.887028i	$-0.652766\pi$
$563$	5.67612	−	4.12394i	0.239220	−	0.173803i	0.700936	+	0.713225i	$0.252766\pi$
$564$	−9.38768	+	3.05024i	−0.395293	+	0.128438i
$565$	−51.0619	−	16.5910i	−2.14819	−	0.697989i
$566$	13.5174	−	18.6051i	0.568180	−	0.782033i
$567$	−1.88481	+	2.59421i	−0.0791544	+	0.108947i
$568$	−1.46628	+	4.51274i	−0.0615237	+	0.189351i
$569$	−1.75468	−	5.40035i	−0.0735600	−	0.226394i	0.907516	−	0.420018i	$-0.137976\pi$
$569$	−1.75468	−	5.40035i	−0.0735600	−	0.226394i	−0.981076	+	0.193623i	$0.937976\pi$
$570$	13.8298	+	19.0351i	0.579266	+	0.797292i
$571$	19.6856			0.823816			0.411908	−	0.911225i	$-0.364862\pi$
$571$	19.6856			0.823816			0.411908	+	0.911225i	$0.364862\pi$
$572$	11.7172	+	25.4135i	0.489920	+	1.06259i
$573$	0.631707			0.0263900
$574$	35.3288	+	48.6259i	1.47460	+	2.02961i
$575$	−2.59044	−	7.97256i	−0.108029	−	0.332479i
$576$	3.22944	−	9.93921i	0.134560	−	0.414134i
$577$	26.3711	−	36.2968i	1.09784	−	1.51105i	0.259634	−	0.965707i	$-0.416398\pi$
$577$	26.3711	−	36.2968i	1.09784	−	1.51105i	0.838211	−	0.545346i	$-0.183602\pi$
$578$	17.0737	−	23.5000i	0.710174	−	0.977471i
$579$	−5.05687	−	1.64308i	−0.210156	−	0.0682839i
$580$	21.6375	−	7.03043i	0.898446	−	0.291923i
$581$	−24.7751	+	18.0002i	−1.02784	+	0.746772i
$582$	−31.0601			−1.28748
$583$	32.1914	+	4.28662i	1.33323	+	0.177534i
$584$	8.06258			0.333632
$585$	−11.5120	−	0.736884i	−0.475963	−	0.0304664i
$586$	11.3636	+	34.9735i	0.469425	+	1.44474i
$587$	−28.1775	−	9.15543i	−1.16301	−	0.377885i	−0.336981	−	0.941512i	$-0.609406\pi$
$587$	−28.1775	−	9.15543i	−1.16301	−	0.377885i	−0.826030	+	0.563627i	$0.809406\pi$
$588$	−6.21446	−	4.51507i	−0.256280	−	0.186198i
$589$	−24.7993	−	18.0178i	−1.02184	−	0.742410i
$590$	−56.4546	−	18.3432i	−2.32420	−	0.755178i
$591$	19.1335	−	6.21685i	0.787046	−	0.255727i
$592$	12.9967	+	17.8884i	0.534162	+	0.735210i
$593$			10.9147i			0.448212i	0.974565	+	0.224106i	$0.0719461\pi$
$593$			10.9147i			0.448212i	−0.974565	+	0.224106i	$0.928054\pi$
$594$	4.76365	−	5.00497i	0.195455	−	0.205356i
$595$	17.9376			0.735369
$596$	19.5381	+	26.8919i	0.800312	+	1.10154i
$597$	0.594632	+	1.83009i	0.0243367	+	0.0749005i
$598$	10.1606	−	6.43259i	0.415499	−	0.263048i
$599$	21.5772	+	15.6768i	0.881620	+	0.640535i	0.933680	−	0.358109i	$-0.116578\pi$
$599$	21.5772	+	15.6768i	0.881620	+	0.640535i	−0.0520593	+	0.998644i	$0.516578\pi$
$600$	−2.18125	+	3.00223i	−0.0890490	+	0.122565i
$601$	2.23203	−	6.86948i	0.0910463	−	0.280212i	−0.895157	−	0.445751i	$-0.852937\pi$
$601$	2.23203	−	6.86948i	0.0910463	−	0.280212i	0.986203	+	0.165540i	$0.0529366\pi$
$602$	8.70527	+	26.7921i	0.354800	+	1.09196i
$603$	3.49217	+	4.80656i	0.142212	+	0.195738i
$604$			30.8854i			1.25671i
$605$	−29.4587	−	19.2550i	−1.19766	−	0.782829i
$606$		−	7.72990i		−	0.314006i
$607$	−12.2669	+	8.91242i	−0.497898	+	0.361744i	−0.808214	−	0.588890i	$-0.799565\pi$
$607$	−12.2669	+	8.91242i	−0.497898	+	0.361744i	0.310316	+	0.950634i	$0.399565\pi$
$608$	−8.82717	−	27.1672i	−0.357989	−	1.10178i
$609$	9.26691	+	3.01100i	0.375514	+	0.122012i
$610$	−10.0965	−	7.33550i	−0.408793	−	0.297006i
$611$	−3.76600	−	14.7343i	−0.152356	−	0.596087i
$612$	1.26439	−	3.89140i	0.0511101	−	0.157301i
$613$	−26.6880	+	8.67145i	−1.07792	+	0.350237i	−0.793567	−	0.608484i	$-0.791778\pi$
$613$	−26.6880	+	8.67145i	−1.07792	+	0.350237i	−0.284351	+	0.958720i	$0.591778\pi$
$614$	−30.4099	+	22.0941i	−1.22724	+	0.891645i
$615$	28.7856			1.16075
$616$	5.45974	+	5.19650i	0.219979	+	0.209373i
$617$			17.3937i			0.700242i	0.936704	+	0.350121i	$0.113860\pi$
$617$			17.3937i			0.700242i	−0.936704	+	0.350121i	$0.886140\pi$
$618$	4.91781	+	6.76878i	0.197823	+	0.272280i
$619$	−6.23452	+	2.02572i	−0.250587	+	0.0814206i	−0.431617	−	0.902057i	$-0.642057\pi$
$619$	−6.23452	+	2.02572i	−0.250587	+	0.0814206i	0.181030	+	0.983478i	$0.442057\pi$
$620$	20.0913	−	61.8347i	0.806887	−	2.48334i
$621$	−1.29521	−	0.941026i	−0.0519751	−	0.0377621i
$622$	−35.6710	+	49.0969i	−1.43028	+	1.96861i
$623$	−17.2521	+	53.0964i	−0.691190	+	2.12726i
$624$	10.7359	+	4.26421i	0.429781	+	0.170705i
$625$	19.2252	−	13.9680i	0.769010	−	0.558718i
$626$			16.6068i			0.663742i
$627$	1.54536	−	11.6053i	0.0617157	−	0.463469i
$628$	54.0519			2.15691
$629$	7.09259	+	9.76211i	0.282800	+	0.389241i
$630$	−20.3271	+	6.60468i	−0.809852	+	0.263137i
$631$	−36.2956	−	11.7931i	−1.44490	−	0.469478i	−0.521482	−	0.853263i	$-0.674620\pi$
$631$	−36.2956	−	11.7931i	−1.44490	−	0.469478i	−0.923423	+	0.383785i	$0.874620\pi$
$632$	−3.49442	+	4.80966i	−0.139001	+	0.191318i
$633$	−14.8498	−	10.7890i	−0.590228	−	0.428826i
$634$	−10.3023	+	31.7074i	−0.409159	+	1.25926i
$635$	−32.3242	+	10.5028i	−1.28275	+	0.416789i
$636$	−18.5383	+	13.4688i	−0.735091	+	0.534075i
$637$	7.55382	−	9.11075i	0.299293	−	0.360981i
$638$	−18.9371	−	9.06698i	−0.749725	−	0.358965i
$639$			6.69510i			0.264854i
$640$	14.4632	−	10.5081i	0.571708	−	0.415370i
$641$	−9.57526	−	29.4696i	−0.378200	−	1.16398i	−0.941294	−	0.337587i	$-0.890389\pi$
$641$	−9.57526	−	29.4696i	−0.378200	−	1.16398i	0.563094	−	0.826393i	$-0.309611\pi$
$642$	−3.87316	−	1.25847i	−0.152862	−	0.0496677i
$643$	−17.1392	+	23.5901i	−0.675904	+	0.930302i	−0.999876	−	0.0157650i	$-0.994982\pi$
$643$	−17.1392	+	23.5901i	−0.675904	+	0.930302i	0.323972	+	0.946067i	$0.394982\pi$
$644$	7.06156	−	9.71941i	0.278265	−	0.382998i
$645$	12.8313	+	4.16915i	0.505233	+	0.164160i
$646$	−3.97339	−	12.2288i	−0.156331	−	0.481137i
$647$	5.69761	−	4.13955i	0.223996	−	0.162743i	−0.470128	−	0.882598i	$-0.655792\pi$
$647$	5.69761	−	4.13955i	0.223996	−	0.162743i	0.694124	+	0.719856i	$0.255792\pi$
$648$			0.708724i			0.0278413i
$649$	14.0554	+	25.9785i	0.551722	+	1.01975i
$650$	−30.2777	−	25.1036i	−1.18759	−	0.984642i
$651$	22.5275	−	16.3672i	0.882922	−	0.641480i
$652$	20.2052	−	6.56506i	0.791296	−	0.257108i
$653$	−1.43180	+	4.40663i	−0.0560307	+	0.172445i	−0.975155	−	0.221522i	$-0.928898\pi$
$653$	−1.43180	+	4.40663i	−0.0560307	+	0.172445i	0.919125	+	0.393967i	$0.128898\pi$
$654$	21.0501	+	15.2938i	0.823123	+	0.598034i
$655$	16.3385	−	22.4880i	0.638398	−	0.878679i
$656$	−27.4152	−	8.90774i	−1.07038	−	0.347789i
$657$	10.8194	−	3.51543i	0.422105	−	0.137150i
$658$	−16.5623	−	22.7961i	−0.645667	−	0.888684i
$659$	−23.5299			−0.916594			−0.458297	−	0.888799i	$-0.651540\pi$
$659$	−23.5299			−0.916594			−0.458297	+	0.888799i	$0.651540\pi$
$660$	24.4231	−	4.48912i	0.950666	−	0.174739i
$661$			11.2697i			0.438341i	0.975687	+	0.219170i	$0.0703351\pi$
$661$			11.2697i			0.438341i	−0.975687	+	0.219170i	$0.929665\pi$
$662$	−7.83355	+	5.69140i	−0.304459	+	0.221203i
$663$	5.85883	+	2.32707i	0.227538	+	0.0903760i
$664$	−2.09156	+	6.43715i	−0.0811681	+	0.249810i
$665$	−21.2867	+	29.2987i	−0.825464	+	1.13615i
$666$	−11.6319	−	8.45105i	−0.450726	−	0.327471i
$667$	−1.50330	+	4.62669i	−0.0582081	+	0.179146i
$668$	−23.0592	+	7.49238i	−0.892186	+	0.289889i
$669$	1.40474	+	1.93345i	0.0543102	+	0.0747516i
$670$			39.6003i			1.52989i
$671$	1.12262	+	6.10760i	0.0433382	+	0.235781i
$672$	25.9485			1.00098
$673$	−11.2269	+	8.15684i	−0.432766	+	0.314423i	−0.782754	−	0.622331i	$-0.786186\pi$
$673$	−11.2269	+	8.15684i	−0.432766	+	0.314423i	0.349988	+	0.936754i	$0.386186\pi$
$674$	60.5972	−	19.6892i	2.33412	−	0.758401i
$675$	−1.61805	+	4.97984i	−0.0622786	+	0.191674i
$676$	13.0133	−	27.4988i	0.500511	−	1.05764i
$677$	12.2017	+	8.86506i	0.468950	+	0.340712i	0.797032	−	0.603937i	$-0.206402\pi$
$677$	12.2017	+	8.86506i	0.468950	+	0.340712i	−0.328082	+	0.944649i	$0.606402\pi$
$678$	−33.2494	−	10.8034i	−1.27694	−	0.414901i
$679$	−14.7733	−	45.4676i	−0.566948	−	1.74489i
$680$	3.20739	−	2.33030i	0.122998	−	0.0893630i
$681$			13.2315i			0.507033i
$682$	−52.7722	+	28.5518i	−2.02075	+	1.09331i
$683$		−	24.0917i		−	0.921843i	−0.887441	−	0.460922i	$-0.847519\pi$
$683$		−	24.0917i		−	0.921843i	0.887441	−	0.460922i	$-0.152481\pi$
$684$	4.85563	+	6.68320i	0.185659	+	0.255538i
$685$	−11.1199	−	34.2236i	−0.424870	−	1.30762i
$686$	−7.67440	+	23.6194i	−0.293010	+	0.901792i
$687$	6.48995	−	8.93266i	0.247607	−	0.340802i
$688$	−10.9303	−	7.94133i	−0.416714	−	0.302761i
$689$	−18.8847	−	29.8293i	−0.719448	−	1.13641i
$690$	−3.29752	−	10.1487i	−0.125534	−	0.386355i
$691$	15.1445	+	20.8446i	0.576124	+	0.792967i	0.993264	−	0.115875i	$-0.0369673\pi$
$691$	15.1445	+	20.8446i	0.576124	+	0.792967i	−0.417139	+	0.908842i	$0.636967\pi$
$692$	29.5913			1.12489
$693$	9.59235	+	4.59277i	0.364383	+	0.174465i
$694$			45.5658i			1.72965i
$695$	−28.6273	−	39.4020i	−1.08589	−	1.49460i
$696$	2.04816	−	0.665489i	0.0776355	−	0.0252253i
$697$	−14.9611	−	4.86115i	−0.566691	−	0.184129i
$698$	−50.6228	−	36.7796i	−1.91610	−	1.39213i
$699$	18.0044	+	13.0809i	0.680988	+	0.494767i
$700$	−37.3692	−	12.1420i	−1.41242	−	0.458924i
$701$	9.18576	+	28.2709i	0.346941	+	1.06778i	0.960536	+	0.278155i	$0.0897227\pi$
$701$	9.18576	+	28.2709i	0.346941	+	1.06778i	−0.613595	+	0.789621i	$0.710277\pi$
$702$	−7.49615	−	0.479829i	−0.282924	−	0.0181100i
$703$	−24.3620			−0.918830
$704$	−34.3578	−	4.57509i	−1.29491	−	0.172430i
$705$	−13.4948			−0.508245
$706$	−48.3087	+	35.0983i	−1.81812	+	1.32094i
$707$	11.3155	−	3.67663i	0.425563	−	0.138274i
$708$	−19.8211	−	6.44028i	−0.744924	−	0.242040i
$709$	−1.93658	+	2.66547i	−0.0727298	+	0.100104i	−0.843832	−	0.536607i	$-0.819706\pi$
$709$	−1.93658	+	2.66547i	−0.0727298	+	0.100104i	0.771102	+	0.636711i	$0.219706\pi$
$710$	−26.2299	+	36.1024i	−0.984392	+	1.35490i
$711$	−2.59216	+	7.97785i	−0.0972136	+	0.299193i
$712$	3.81304	+	11.7353i	0.142900	+	0.439800i
$713$	8.17164	+	11.2473i	0.306030	+	0.421215i
$714$	11.6802			0.437121
$715$	4.49860	+	37.9938i	0.168238	+	1.42089i
$716$	−36.3443			−1.35825
$717$	−6.21203	−	8.55013i	−0.231993	−	0.319310i
$718$	8.95698	+	27.5667i	0.334271	+	1.02878i
$719$	12.5626	−	38.6636i	0.468504	−	1.44191i	−0.386017	−	0.922492i	$-0.626149\pi$
$719$	12.5626	−	38.6636i	0.468504	−	1.44191i	0.854521	−	0.519417i	$-0.173851\pi$
$720$	6.02509	−	8.29282i	0.224542	−	0.309055i
$721$	−7.56946	+	10.4185i	−0.281901	+	0.388004i
$722$	−12.9562	−	4.20972i	−0.482179	−	0.156669i
$723$	26.5290	−	8.61980i	0.986624	−	0.320574i
$724$	20.5255	−	14.9126i	0.762822	−	0.554223i
$725$	15.9107			0.590909
$726$	−19.1823	−	12.5381i	−0.711921	−	0.465332i
$727$	−24.5162			−0.909254			−0.454627	−	0.890682i	$-0.650227\pi$
$727$	−24.5162			−0.909254			−0.454627	+	0.890682i	$0.650227\pi$
$728$	0.523428	−	8.17728i	0.0193995	−	0.303070i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	72.1149	+	23.4315i	2.66909	+	0.867240i
$731$	−5.96491	−	4.33376i	−0.220620	−	0.160290i
$732$	−3.54485	−	2.57549i	−0.131022	−	0.0951927i
$733$	2.10609	+	0.684311i	0.0777903	+	0.0252756i	0.347654	−	0.937623i	$-0.386979\pi$
$733$	2.10609	+	0.684311i	0.0777903	+	0.0252756i	−0.269863	+	0.962899i	$0.586979\pi$
$734$	35.8754	−	11.6566i	1.32419	−	0.430254i
$735$	−6.17278	−	8.49610i	−0.227686	−	0.313383i
$736$			12.9553i			0.477538i
$737$	13.5851	−	14.2733i	0.500413	−	0.525762i
$738$	18.7440			0.689976
$739$	13.9740	+	19.2336i	0.514043	+	0.707520i	0.984595	−	0.174853i	$-0.0559449\pi$
$739$	13.9740	+	19.2336i	0.514043	+	0.707520i	−0.470551	+	0.882373i	$0.655945\pi$
$740$	−15.9676	−	49.1431i	−0.586979	−	1.80654i
$741$	−10.7537	+	6.80807i	−0.395047	+	0.250101i
$742$	−52.9201	−	38.4487i	−1.94276	−	1.41150i
$743$	13.5253	−	18.6160i	0.496196	−	0.682955i	−0.485320	−	0.874337i	$-0.661297\pi$
$743$	13.5253	−	18.6160i	0.496196	−	0.682955i	0.981516	+	0.191381i	$0.0612968\pi$
$744$	1.90181	−	5.85317i	0.0697237	−	0.214588i
$745$	14.0431	+	43.2202i	0.514499	+	1.58346i
$746$	14.4519	+	19.8913i	0.529121	+	0.728272i
$747$			9.55014i			0.349421i
$748$	−13.4518	−	1.79124i	−0.491846	−	0.0654943i
$749$		−	6.26834i		−	0.229040i
$750$	−1.27318	+	0.925022i	−0.0464901	+	0.0337770i
$751$	−1.26596	−	3.89623i	−0.0461956	−	0.142176i	0.925298	−	0.379240i	$-0.123815\pi$
$751$	−1.26596	−	3.89623i	−0.0461956	−	0.142176i	−0.971494	+	0.237065i	$0.923815\pi$
$752$	12.8524	+	4.17600i	0.468679	+	0.152283i
$753$	7.58185	+	5.50853i	0.276298	+	0.200742i
$754$	5.65218	+	22.1139i	0.205840	+	0.805341i
$755$	−13.0482	+	40.1583i	−0.474874	+	1.46151i
$756$	−7.13683	+	2.31890i	−0.259564	+	0.0843375i
$757$	1.90136	−	1.38142i	0.0691063	−	0.0502086i	−0.552696	−	0.833383i	$-0.686401\pi$
$757$	1.90136	−	1.38142i	0.0691063	−	0.0502086i	0.621802	+	0.783174i	$0.286401\pi$
$758$	28.2961			1.02776
$759$	−2.29303	+	4.78917i	−0.0832318	+	0.173836i
$760$			8.00424i			0.290344i
$761$	−23.2895	−	32.0552i	−0.844243	−	1.16200i	−0.985102	−	0.171971i	$-0.944987\pi$
$761$	−23.2895	−	32.0552i	−0.844243	−	1.16200i	0.140860	−	0.990030i	$-0.455013\pi$
$762$	−21.0482	+	6.83896i	−0.762495	+	0.247750i
$763$	−12.3758	+	38.0887i	−0.448032	+	1.37890i
$764$	1.19598	+	0.868932i	0.0432691	+	0.0314369i
$765$	3.28802	−	4.52558i	0.118879	−	0.163623i
$766$	−7.60629	+	23.4098i	−0.274826	+	0.845829i
$767$	11.8531	−	29.8424i	0.427991	−	1.07755i
$768$	−7.49175	+	5.44308i	−0.270335	+	0.196410i
$769$		−	13.2522i		−	0.477886i	−0.971034	−	0.238943i	$-0.923199\pi$
$769$		−	13.2522i		−	0.477886i	0.971034	−	0.238943i	$-0.0768010\pi$
$770$	33.7320	+	62.3467i	1.21562	+	2.24682i
$771$	−19.6397			−0.707308
$772$	−7.31384	−	10.0666i	−0.263231	−	0.362306i
$773$	24.2204	−	7.86967i	0.871146	−	0.283052i	0.160870	−	0.986976i	$-0.448570\pi$
$773$	24.2204	−	7.86967i	0.871146	−	0.283052i	0.710276	+	0.703923i	$0.248570\pi$
$774$	8.35523	+	2.71478i	0.300322	+	0.0975807i
$775$	26.7260	−	36.7852i	0.960028	−	1.32136i
$776$	−8.54837	−	6.21075i	−0.306869	−	0.222953i
$777$	6.83861	−	21.0471i	0.245334	−	0.755059i
$778$	42.4505	−	13.7930i	1.52192	−	0.494503i
$779$	25.6945	−	18.6682i	0.920602	−	0.668857i
$780$	−20.7816	−	17.2302i	−0.744099	−	0.616941i
$781$	21.8393	−	4.01421i	0.781471	−	0.143640i
$782$			5.83158i			0.208537i
$783$	2.45832	−	1.78608i	0.0878532	−	0.0638291i
$784$	3.24978	+	10.0018i	0.116064	+	0.357207i
$785$	70.2803	+	22.8355i	2.50841	+	0.815032i
$786$	10.6390	−	14.6433i	0.379479	−	0.522308i
$787$	−7.65132	+	10.5311i	−0.272740	+	0.375394i	−0.923312	−	0.384050i	$-0.874529\pi$
$787$	−7.65132	+	10.5311i	−0.272740	+	0.375394i	0.650572	+	0.759444i	$0.274529\pi$
$788$	44.7760	+	14.5486i	1.59508	+	0.518273i
$789$	−3.15803	−	9.71943i	−0.112429	−	0.346021i
$790$	−45.2334	+	32.8640i	−1.60933	+	1.16925i
$791$		−	53.8110i		−	1.91330i
$792$	2.31184	−	0.424933i	0.0821478	−	0.0150993i
$793$	4.30885	−	5.19695i	0.153012	−	0.184549i
$794$	25.3707	−	18.4329i	0.900371	−	0.654158i
$795$	−29.7944	+	9.68078i	−1.05670	+	0.343342i
$796$	−1.39155	+	4.28276i	−0.0493223	+	0.151798i
$797$	−20.7481	−	15.0744i	−0.734935	−	0.533962i	0.156186	−	0.987728i	$-0.450080\pi$
$797$	−20.7481	−	15.0744i	−0.734935	−	0.533962i	−0.891121	+	0.453766i	$0.850080\pi$
$798$	−13.8610	+	19.0781i	−0.490676	+	0.675357i
$799$	7.01383	+	2.27893i	0.248132	+	0.0806229i
$800$	40.2976	−	13.0935i	1.42473	−	0.462924i
$801$	10.2336	+	14.0854i	0.361588	+	0.497683i
$802$	10.6283			0.375297
$803$	−17.9543	−	33.1849i	−0.633594	−	1.17107i
$804$			13.9036i			0.490343i
$805$	13.2879	−	9.65422i	0.468336	−	0.340266i
$806$	60.6211	+	24.0781i	2.13529	+	0.848116i
$807$	8.11722	−	24.9822i	0.285740	−	0.879416i
$808$	1.54567	−	2.12743i	0.0543763	−	0.0748426i
$809$	−27.4545	−	19.9468i	−0.965248	−	0.701293i	−0.0108840	−	0.999941i	$-0.503465\pi$
$809$	−27.4545	−	19.9468i	−0.965248	−	0.701293i	−0.954364	+	0.298647i	$0.903465\pi$
$810$	−2.05970	+	6.33911i	−0.0723705	+	0.222734i
$811$	35.9056	−	11.6665i	1.26082	−	0.409665i	0.399032	−	0.916937i	$-0.369346\pi$
$811$	35.9056	−	11.6665i	1.26082	−	0.409665i	0.861786	+	0.507272i	$0.169346\pi$
$812$	13.4029	+	18.4475i	0.470350	+	0.647381i
$813$		−	22.4437i		−	0.787136i
$814$	−20.5930	+	43.0100i	−0.721784	+	1.50750i
$815$	29.0451			1.01740
$816$	−4.53193	+	3.29264i	−0.158649	+	0.115266i
$817$	14.1573	−	4.59997i	0.495300	−	0.160933i
$818$	−9.12062	+	28.0704i	−0.318895	+	0.981458i
$819$	−2.86304	−	11.2015i	−0.100043	−	0.391413i
$820$	54.4985	+	39.5955i	1.90317	+	1.38273i
$821$	−19.1535	−	6.22335i	−0.668462	−	0.217196i	−0.0449249	−	0.998990i	$-0.514305\pi$
$821$	−19.1535	−	6.22335i	−0.668462	−	0.217196i	−0.623537	+	0.781794i	$0.714305\pi$
$822$	−7.24083	−	22.2850i	−0.252553	−	0.777278i
$823$	12.5203	−	9.09653i	0.436430	−	0.317085i	−0.347785	−	0.937574i	$-0.613066\pi$
$823$	12.5203	−	9.09653i	0.436430	−	0.317085i	0.784215	+	0.620489i	$0.213066\pi$
$824$			2.84627i			0.0991544i
$825$	17.2143	+	2.29226i	0.599324	+	0.0798061i
$826$		−	59.4940i		−	2.07006i
$827$	−21.4487	−	29.5215i	−0.745843	−	1.02656i	−0.998261	−	0.0589463i	$-0.981226\pi$
$827$	−21.4487	−	29.5215i	−0.745843	−	1.02656i	0.252418	−	0.967618i	$-0.418774\pi$
$828$	−1.15776	−	3.56320i	−0.0402348	−	0.123830i
$829$	13.9781	−	43.0201i	0.485478	−	1.49415i	−0.345809	−	0.938305i	$-0.612395\pi$
$829$	13.9781	−	43.0201i	0.485478	−	1.49415i	0.831287	−	0.555843i	$-0.187605\pi$
$830$	−37.4154	+	51.4979i	−1.29871	+	1.78752i
$831$	−17.1508	−	12.4608i	−0.594956	−	0.432261i
$832$	20.1555	+	31.8367i	0.698767	+	1.10374i
$833$	1.77348	+	5.45820i	0.0614474	+	0.189116i
$834$	−18.6409	−	25.6570i	−0.645482	−	0.888429i
$835$	−33.1477			−1.14712
$836$	18.8891	−	19.8460i	0.653295	−	0.686389i
$837$		−	8.68375i		−	0.300154i
$838$	−26.4494	−	36.4045i	−0.913681	−	1.25757i
$839$	−0.763942	+	0.248220i	−0.0263742	+	0.00856950i	−0.322174	−	0.946680i	$-0.604414\pi$
$839$	−0.763942	+	0.248220i	−0.0263742	+	0.00856950i	0.295800	+	0.955250i	$0.404414\pi$
$840$	−6.91511	−	2.24685i	−0.238594	−	0.0775239i
$841$	15.9915	+	11.6185i	0.551431	+	0.400638i
$842$	−50.0462	−	36.3607i	−1.72471	−	1.25307i
$843$	−13.7224	−	4.45867i	−0.472624	−	0.153565i
$844$	−13.2739	−	40.8528i	−0.456905	−	1.40621i
$845$	28.5378	−	30.2571i	0.981731	−	1.04088i
$846$	−8.78729			−0.302113
$847$	9.23021	−	34.0437i	0.317154	−	1.16976i
$848$	31.3717			1.07731
$849$	8.93056	−	6.48843i	0.306496	−	0.222682i
$850$	18.1392	−	5.89378i	0.622169	−	0.202155i
$851$	10.5082	+	3.41431i	0.360215	+	0.117041i
$852$	−9.20931	+	12.6755i	−0.315506	+	0.434256i
$853$	−29.3689	+	40.4228i	−1.00557	+	1.38405i	−0.0837278	+	0.996489i	$0.526683\pi$
$853$	−29.3689	+	40.4228i	−1.00557	+	1.38405i	−0.921844	+	0.387562i	$0.873317\pi$
$854$	3.86522	−	11.8959i	0.132265	−	0.407070i
$855$	3.49000	+	10.7411i	0.119355	+	0.367338i
$856$	−0.814331	−	1.12083i	−0.0278333	−	0.0383092i
$857$	35.7355			1.22070			0.610351	−	0.792131i	$-0.291029\pi$
$857$	35.7355			1.22070			0.610351	+	0.792131i	$0.291029\pi$
$858$	2.92930	+	24.7400i	0.100005	+	0.844609i
$859$	−29.0097			−0.989798			−0.494899	−	0.868950i	$-0.664795\pi$
$859$	−29.0097			−0.989798			−0.494899	+	0.868950i	$0.664795\pi$
$860$	18.5582	+	25.5431i	0.632828	+	0.871013i
$861$	8.91534	+	27.4386i	0.303834	+	0.935105i
$862$	−15.6256	+	48.0906i	−0.532210	+	1.63797i
$863$	−13.6124	+	18.7359i	−0.463372	+	0.637777i	−0.975204	−	0.221309i	$-0.928967\pi$
$863$	−13.6124	+	18.7359i	−0.463372	+	0.637777i	0.511832	+	0.859086i	$0.328967\pi$
$864$	4.75645	−	6.54669i	0.161818	−	0.222723i
$865$	38.4757	+	12.5015i	1.30821	+	0.425064i
$866$	−12.3639	+	4.01728i	−0.420143	+	0.136513i
$867$	11.2801	−	8.19548i	0.383093	−	0.278333i
$868$	65.1638			2.21180
$869$	27.5778	+	3.67226i	0.935512	+	0.124573i
$870$	20.2536			0.686662
$871$	−21.3777	−	1.36838i	−0.724354	−	0.0463659i
$872$	2.73528	+	8.41832i	0.0926282	+	0.285080i
$873$	−14.1793	−	4.60713i	−0.479896	−	0.155928i
$874$	−9.52512	−	6.92040i	−0.322192	−	0.234086i
$875$	−1.95968	−	1.42379i	−0.0662492	−	0.0481328i
$876$	25.3195	+	8.22679i	0.855465	+	0.277957i
$877$	−4.40249	+	1.43046i	−0.148662	+	0.0483031i	−0.382403	−	0.923996i	$-0.624903\pi$
$877$	−4.40249	+	1.43046i	−0.148662	+	0.0483031i	0.233741	+	0.972299i	$0.424903\pi$
$878$	1.53333	+	2.11044i	0.0517473	+	0.0712240i
$879$			17.6514i			0.595366i
$880$	−30.6635	−	14.6816i	−1.03367	−	0.494915i
$881$	12.2483			0.412655			0.206327	−	0.978483i	$-0.433849\pi$
$881$	12.2483			0.412655			0.206327	+	0.978483i	$0.433849\pi$
$882$	−4.01946	−	5.53231i	−0.135342	−	0.186283i
$883$	−10.0119	−	30.8136i	−0.336928	−	1.03696i	−0.965764	−	0.259421i	$-0.916468\pi$
$883$	−10.0119	−	30.8136i	−0.336928	−	1.03696i	0.628836	−	0.777538i	$-0.283532\pi$
$884$	7.89130	+	12.4647i	0.265413	+	0.419235i
$885$	−23.0513	−	16.7478i	−0.774862	−	0.562970i
$886$	32.0995	−	44.1812i	1.07841	−	1.48430i
$887$	2.97866	−	9.16739i	0.100014	−	0.307811i	−0.888514	−	0.458849i	$-0.848262\pi$
$887$	2.97866	−	9.16739i	0.100014	−	0.307811i	0.988528	+	0.151039i	$0.0482618\pi$
$888$	−1.51146	−	4.65180i	−0.0507214	−	0.156104i
$889$	−20.0226	−	27.5587i	−0.671536	−	0.924290i
$890$			116.047i			3.88990i
$891$	2.91705	−	1.57824i	0.0977248	−	0.0528729i
$892$			5.59277i			0.187260i
$893$	−12.0457	+	8.75174i	−0.403095	+	0.292866i
$894$	9.14428	+	28.1432i	0.305830	+	0.941249i
$895$	−47.2561	−	15.3544i	−1.57960	−	0.513243i
$896$	14.4959	+	10.5319i	0.484273	+	0.351845i
$897$	5.59259	−	1.42943i	0.186731	−	0.0477273i
$898$	6.08145	−	18.7168i	0.202941	−	0.624587i
$899$	−25.0954	+	8.15400i	−0.836980	+	0.271951i
$900$	−9.91329	+	7.20242i	−0.330443	+	0.240081i
$901$	17.1202			0.570357
$902$	−11.2384	−	61.1426i	−0.374198	−	2.03582i
$903$			13.5221i			0.449989i
$904$	−6.99067	−	9.62184i	−0.232506	−	0.320018i
$905$	32.9881	−	10.7185i	1.09656	−	0.356295i
$906$	−8.49648	+	26.1495i	−0.282277	+	0.868758i
$907$	19.8839	+	14.4465i	0.660235	+	0.479689i	0.866742	−	0.498756i	$-0.166210\pi$
$907$	19.8839	+	14.4465i	0.660235	+	0.479689i	−0.206507	+	0.978445i	$0.566210\pi$
$908$	−18.2004	+	25.0506i	−0.604000	+	0.831335i
$909$	1.14657	−	3.52879i	0.0380294	−	0.117043i
$910$	28.4466	−	71.6196i	0.942997	−	2.37417i
$911$	−20.7370	+	15.0663i	−0.687047	+	0.499169i	−0.875688	−	0.482877i	$-0.839592\pi$
$911$	−20.7370	+	15.0663i	−0.687047	+	0.499169i	0.188641	+	0.982046i	$0.439592\pi$
$912$		−	11.3097i		−	0.374503i
$913$	31.1524	−	5.72601i	1.03099	−	0.189503i
$914$	26.2035			0.866735
$915$	−3.52108	−	4.84634i	−0.116403	−	0.160215i
$916$	24.5743	−	7.98466i	0.811957	−	0.263821i
$917$	26.4960	+	8.60907i	0.874974	+	0.284296i
$918$	2.14103	−	2.94687i	0.0706644	−	0.0972612i
$919$	8.50894	+	6.18211i	0.280684	+	0.203929i	0.719216	−	0.694787i	$-0.244501\pi$
$919$	8.50894	+	6.18211i	0.280684	+	0.203929i	−0.438532	+	0.898716i	$0.644501\pi$
$920$	1.12179	−	3.45250i	0.0369842	−	0.113826i
$921$	−17.1597	+	5.57552i	−0.565431	+	0.183720i
$922$	27.0611	−	19.6611i	0.891210	−	0.647502i
$923$	−18.5830	−	15.4074i	−0.611668	−	0.507140i
$924$	11.8433	+	21.8898i	0.389614	+	0.720123i
$925$		−	36.1365i		−	1.18816i
$926$	39.2478	−	28.5152i	1.28976	−	0.937067i
$927$	1.24103	+	3.81948i	0.0407606	+	0.125448i
$928$	−23.3857	−	7.59849i	−0.767675	−	0.249433i
$929$	−4.27207	+	5.88000i	−0.140162	+	0.192916i	−0.873327	−	0.487134i	$-0.838042\pi$
$929$	−4.27207	+	5.88000i	−0.140162	+	0.192916i	0.733165	+	0.680051i	$0.238042\pi$
$930$	34.0211	−	46.8260i	1.11559	−	1.53548i
$931$	−11.0199	−	3.58057i	−0.361161	−	0.117348i
$932$	16.0936	+	49.5311i	0.527165	+	1.62245i
$933$	−23.5668	+	17.1223i	−0.771541	+	0.560557i
$934$			54.0748i			1.76938i
$935$	−16.7337	−	8.01205i	−0.547252	−	0.262022i
$936$	−1.96715	−	1.63098i	−0.0642982	−	0.0533104i
$937$	39.9065	−	28.9938i	1.30369	−	0.947186i	0.303705	−	0.952766i	$-0.401776\pi$
$937$	39.9065	−	28.9938i	1.30369	−	0.947186i	0.999984	+	0.00558032i	$0.00177628\pi$
$938$	−37.7472	+	12.2648i	−1.23249	+	0.400460i
$939$	−2.46328	+	7.58120i	−0.0803862	+	0.247403i
$940$	−25.5492	−	18.5626i	−0.833322	−	0.605444i
$941$	−6.20724	+	8.54353i	−0.202350	+	0.278511i	−0.898117	−	0.439757i	$-0.855065\pi$
$941$	−6.20724	+	8.54353i	−0.202350	+	0.278511i	0.695767	+	0.718268i	$0.255065\pi$
$942$	45.7637	+	14.8695i	1.49106	+	0.484475i
$943$	−13.6993	+	4.45116i	−0.446110	+	0.144950i
$944$	16.7713	+	23.0837i	0.545859	+	0.751311i
$945$	−10.2592			−0.333733
$946$	3.84597	−	28.8823i	0.125043	−	0.939044i
$947$			22.2849i			0.724161i	0.932147	+	0.362081i	$0.117933\pi$
$947$			22.2849i			0.724161i	−0.932147	+	0.362081i	$0.882067\pi$
$948$	−15.8814	+	11.5385i	−0.515804	+	0.374753i
$949$	−15.1411	+	38.1205i	−0.491501	+	1.23744i
$950$	−11.8993	+	36.6222i	−0.386064	+	1.18818i
$951$	−9.40629	+	12.9466i	−0.305020	+	0.419824i
$952$	3.21463	+	2.33557i	0.104187	+	0.0756962i
$953$	9.46236	−	29.1221i	0.306516	−	0.943359i	−0.672591	−	0.740014i	$-0.734819\pi$
$953$	9.46236	−	29.1221i	0.306516	−	0.943359i	0.979107	−	0.203345i	$-0.0651812\pi$
$954$	−19.4009	+	6.30372i	−0.628126	+	0.204091i
$955$	1.18796	+	1.63509i	0.0384415	+	0.0529102i
$956$		−	24.7324i		−	0.799903i
$957$	−7.30009	−	6.94811i	−0.235978	−	0.224601i
$958$	20.4852			0.661845
$959$	29.1781	−	21.1991i	0.942210	−	0.684556i
$960$	31.7994	−	10.3323i	1.02632	−	0.333472i
$961$	−13.7227	+	42.2341i	−0.442667	+	1.36239i
$962$	50.2252	−	12.8373i	1.61933	−	0.413890i
$963$	−1.58148	−	1.14901i	−0.0509623	−	0.0370263i
$964$	62.0829	+	20.1720i	1.99956	+	0.649695i
$965$	−5.25684	−	16.1789i	−0.169224	−	0.520817i
$966$	8.65253	−	6.28643i	0.278390	−	0.202263i
$967$		−	46.9451i		−	1.50965i	−0.655925	−	0.754826i	$-0.727721\pi$
$967$		−	46.9451i		−	1.50965i	0.655925	−	0.754826i	$-0.272279\pi$
$968$	−2.77224	−	7.28641i	−0.0891033	−	0.234194i
$969$		−	6.17197i		−	0.198272i
$970$	−58.4102	−	80.3947i	−1.87544	−	2.58132i
$971$	−2.83376	−	8.72142i	−0.0909397	−	0.279884i	0.895235	−	0.445595i	$-0.147008\pi$
$971$	−2.83376	−	8.72142i	−0.0909397	−	0.279884i	−0.986174	+	0.165712i	$0.947008\pi$
$972$	−0.723159	+	2.22565i	−0.0231953	+	0.0713879i
$973$	28.6920	−	39.4911i	0.919822	−	1.26603i
$974$	72.3715	+	52.5810i	2.31893	+	1.68480i
$975$	−10.0985	−	15.9511i	−0.323411	−	0.510845i
$976$	1.85374	+	5.70523i	0.0593368	+	0.182620i
$977$	−2.10981	−	2.90391i	−0.0674988	−	0.0929042i	0.773933	−	0.633268i	$-0.218287\pi$
$977$	−2.10981	−	2.90391i	−0.0674988	−	0.0929042i	−0.841432	+	0.540363i	$0.818287\pi$
$978$	18.9130			0.604770
$979$	39.8104	−	41.8272i	1.27235	−	1.33680i
$980$		−	24.5761i		−	0.785056i
$981$	7.34109	+	10.1041i	0.234383	+	0.322600i
$982$	−8.86403	+	2.88010i	−0.282863	+	0.0919076i
$983$	−43.4579	−	14.1203i	−1.38609	−	0.450368i	−0.481424	−	0.876488i	$-0.659880\pi$
$983$	−43.4579	−	14.1203i	−1.38609	−	0.450368i	−0.904667	+	0.426120i	$0.859880\pi$
$984$	5.15873	+	3.74804i	0.164454	+	0.119483i
$985$	52.0730	+	37.8333i	1.65918	+	1.20547i
$986$	−10.5267	−	3.42032i	−0.335237	−	0.108925i
$987$	−4.17956	−	12.8634i	−0.133037	−	0.409445i
$988$	−29.7242	−	1.90265i	−0.945653	−	0.0605313i
$989$	−6.75119			−0.214676
$990$	21.9130	+	2.91794i	0.696440	+	0.0927382i
$991$	−22.3667			−0.710501			−0.355250	−	0.934771i	$-0.615604\pi$
$991$	−22.3667			−0.710501			−0.355250	+	0.934771i	$0.615604\pi$
$992$	−56.8498	+	41.3038i	−1.80498	+	1.31140i
$993$	−4.42031	+	1.43625i	−0.140274	+	0.0455779i
$994$	−42.5369	−	13.8211i	−1.34919	−	0.438377i
$995$	−3.61869	+	4.98070i	−0.114720	+	0.157899i
$996$	−13.1365	+	18.0808i	−0.416246	+	0.572913i
$997$	−3.98426	+	12.2623i	−0.126183	+	0.388351i	−0.994115	−	0.108332i	$-0.965449\pi$
$997$	−3.98426	+	12.2623i	−0.126183	+	0.388351i	0.867932	+	0.496683i	$0.165449\pi$
$998$	16.4082	+	50.4993i	0.519393	+	1.59853i
$999$	−4.05654	−	5.58335i	−0.128343	−	0.176649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.a.25.12	yes	56
11.4	even	5	inner	429.2.bb.a.103.3	yes	56
13.12	even	2	inner	429.2.bb.a.25.3	✓	56
143.103	even	10	inner	429.2.bb.a.103.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.a.25.3	✓	56	13.12	even	2	inner
429.2.bb.a.25.12	yes	56	1.1	even	1	trivial
429.2.bb.a.103.3	yes	56	11.4	even	5	inner
429.2.bb.a.103.12	yes	56	143.103	even	10	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.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22454 + 1.68544i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.723159 + 2.22565i) q^{4} +(-1.88056 + 2.58836i) q^{5} +(-1.22454 + 1.68544i) q^{6} +(-3.04968 - 0.990901i) q^{7} +(-0.674037 + 0.219008i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.22454 + 1.68544i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.723159 + 2.22565i) q^{4} +(-1.88056 + 2.58836i) q^{5} +(-1.22454 + 1.68544i) q^{6} +(-3.04968 - 0.990901i) q^{7} +(-0.674037 + 0.219008i) q^{8} +(-0.809017 + 0.587785i) q^{9} -6.66533 q^{10} +(2.40241 + 2.28658i) q^{11} -2.34019 q^{12} +(0.230320 - 3.59819i) q^{13} +(-2.06436 - 6.35343i) q^{14} +(-3.04280 - 0.988666i) q^{15} +(2.59200 + 1.88320i) q^{16} +(1.41451 + 1.02770i) q^{17} +(-1.98135 - 0.643779i) q^{18} +(-3.35723 + 1.09083i) q^{19} +(-4.40086 - 6.05726i) q^{20} -3.20662i q^{21} +(-0.912029 + 6.84911i) q^{22} +1.60097 q^{23} +(-0.416578 - 0.573370i) q^{24} +(-1.61805 - 4.97984i) q^{25} +(6.34655 - 4.01794i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(4.41080 - 6.07095i) q^{28} +(-0.938995 + 2.88993i) q^{29} +(-2.05970 - 6.33911i) q^{30} +(5.10418 + 7.02530i) q^{31} +8.09215i q^{32} +(-1.43228 + 2.99142i) q^{33} +3.64253i q^{34} +(8.29990 - 6.03023i) q^{35} +(-0.723159 - 2.22565i) q^{36} +(6.56363 + 2.13265i) q^{37} +(-5.94959 - 4.32263i) q^{38} +(3.49325 - 0.892854i) q^{39} +(0.700692 - 2.15651i) q^{40} +(-8.55686 + 2.78029i) q^{41} +(5.40455 - 3.92664i) q^{42} -4.21694 q^{43} +(-6.82645 + 3.69337i) q^{44} -3.19939i q^{45} +(1.96045 + 2.69833i) q^{46} +(4.01150 - 1.30342i) q^{47} +(-0.990056 + 3.04708i) q^{48} +(2.65554 + 1.92936i) q^{49} +(6.41183 - 8.82512i) q^{50} +(-0.540295 + 1.66286i) q^{51} +(7.84176 + 3.11467i) q^{52} +(7.92169 - 5.75545i) q^{53} -2.08331i q^{54} +(-10.4364 + 1.91827i) q^{55} +2.27261 q^{56} +(-2.07488 - 2.85583i) q^{57} +(-6.02063 + 1.95622i) q^{58} +(8.46988 + 2.75203i) q^{59} +(4.40086 - 6.05726i) q^{60} +(1.51477 + 1.10055i) q^{61} +(-5.59042 + 17.2055i) q^{62} +(3.04968 - 0.990901i) q^{63} +(-8.45479 + 6.14277i) q^{64} +(8.88028 + 7.36274i) q^{65} +(-6.79572 + 1.24910i) q^{66} -5.94123i q^{67} +(-3.31023 + 2.40502i) q^{68} +(0.494727 + 1.52261i) q^{69} +(20.3271 + 6.60468i) q^{70} +(3.93528 - 5.41645i) q^{71} +(0.416578 - 0.573370i) q^{72} +(-10.8194 - 3.51543i) q^{73} +(4.44298 + 13.6741i) q^{74} +(4.23610 - 3.07771i) q^{75} -8.26088i q^{76} +(-5.06081 - 9.35387i) q^{77} +(5.78248 + 4.79432i) q^{78} +(6.78636 - 4.93058i) q^{79} +(-9.74880 + 3.16758i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-15.1642 - 11.0174i) q^{82} +(5.61343 - 7.72622i) q^{83} +(7.13683 + 2.31890i) q^{84} +(-5.32013 + 1.72862i) q^{85} +(-5.16381 - 7.10738i) q^{86} -3.03865 q^{87} +(-2.12009 - 1.01509i) q^{88} -17.4105i q^{89} +(5.39237 - 3.91778i) q^{90} +(-4.26785 + 10.7451i) q^{91} +(-1.15776 + 3.56320i) q^{92} +(-5.10418 + 7.02530i) q^{93} +(7.10907 + 5.16504i) q^{94} +(3.49000 - 10.7411i) q^{95} +(-7.69609 + 2.50061i) q^{96} +(8.76328 + 12.0616i) q^{97} +6.83832i q^{98} +(-3.28761 - 0.437778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

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