LMFDB - Embedded newform 133.2.s.d.103.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(31,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("133.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.s (of order $6$, degree $2$, 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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26x^{14} + 265x^{12} + 1335x^{10} + 3450x^{8} + 4344x^{6} + 2376x^{4} + 423x^{2} + 9 $ x^16 + 26x^14 + 265x^12 + 1335x^10 + 3450x^8 + 4344x^6 + 2376x^4 + 423*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.1
Root			$2.69097i$ of defining polynomial
Character	$\chi$	$=$	133.103
Dual form			133.2.s.d.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.33045 + 1.34549i) q^{2} -1.67620 q^{3} +(2.62067 - 4.53913i) q^{4} +(0.109680 - 0.0633240i) q^{5} +(3.90630 - 2.25530i) q^{6} +(2.64467 - 0.0757760i) q^{7} +8.72235i q^{8} -0.190360 q^{9} +O(q^{10})$	\(q+(-2.33045 + 1.34549i) q^{2} -1.67620 q^{3} +(2.62067 - 4.53913i) q^{4} +(0.109680 - 0.0633240i) q^{5} +(3.90630 - 2.25530i) q^{6} +(2.64467 - 0.0757760i) q^{7} +8.72235i q^{8} -0.190360 q^{9} +(-0.170403 + 0.295147i) q^{10} +(-0.136041 - 0.235630i) q^{11} +(-4.39276 + 7.60848i) q^{12} +(2.09320 + 3.62554i) q^{13} +(-6.06131 + 3.73495i) q^{14} +(-0.183846 + 0.106144i) q^{15} +(-6.49447 - 11.2487i) q^{16} +3.99752i q^{17} +(0.443624 - 0.256127i) q^{18} +(4.28308 + 0.809469i) q^{19} -0.663805i q^{20} +(-4.43298 + 0.127016i) q^{21} +(0.634074 + 0.366083i) q^{22} +5.90199 q^{23} -14.6204i q^{24} +(-2.49198 + 4.31624i) q^{25} +(-9.75622 - 5.63276i) q^{26} +5.34768 q^{27} +(6.58683 - 12.2031i) q^{28} +(6.55245 - 3.78306i) q^{29} +(0.285630 - 0.494725i) q^{30} +(0.804591 + 1.39359i) q^{31} +(15.1625 + 8.75408i) q^{32} +(0.228032 + 0.394963i) q^{33} +(-5.37860 - 9.31601i) q^{34} +(0.285270 - 0.175782i) q^{35} +(-0.498870 + 0.864068i) q^{36} +(-8.34178 - 4.81613i) q^{37} +(-11.0706 + 3.87640i) q^{38} +(-3.50862 - 6.07712i) q^{39} +(0.552334 + 0.956671i) q^{40} +(-2.22506 + 3.85392i) q^{41} +(10.1600 - 6.26052i) q^{42} +(0.387957 - 0.671961i) q^{43} -1.42607 q^{44} +(-0.0208788 + 0.0120544i) q^{45} +(-13.7543 + 7.94105i) q^{46} +1.57697i q^{47} +(10.8860 + 18.8551i) q^{48} +(6.98852 - 0.400805i) q^{49} -13.4117i q^{50} -6.70063i q^{51} +21.9424 q^{52} +(-3.05534 - 1.76400i) q^{53} +(-12.4625 + 7.19522i) q^{54} +(-0.0298421 - 0.0172293i) q^{55} +(0.660945 + 23.0677i) q^{56} +(-7.17929 - 1.35683i) q^{57} +(-10.1801 + 17.6325i) q^{58} +4.88026 q^{59} +1.11267i q^{60} +0.160767i q^{61} +(-3.75012 - 2.16513i) q^{62} +(-0.503438 + 0.0144247i) q^{63} -21.1361 q^{64} +(0.459167 + 0.265100i) q^{65} +(-1.06283 - 0.613627i) q^{66} +(-5.79400 - 3.34517i) q^{67} +(18.1452 + 10.4762i) q^{68} -9.89291 q^{69} +(-0.428295 + 0.793478i) q^{70} +(-5.63464 - 3.25316i) q^{71} -1.66038i q^{72} +14.8619i q^{73} +25.9201 q^{74} +(4.17705 - 7.23487i) q^{75} +(14.8988 - 17.3201i) q^{76} +(-0.377638 - 0.612854i) q^{77} +(16.3534 + 9.44162i) q^{78} +(9.55897 - 5.51887i) q^{79} +(-1.42463 - 0.822512i) q^{80} -8.39268 q^{81} -11.9752i q^{82} -17.7150i q^{83} +(-11.0408 + 20.4548i) q^{84} +(0.253139 + 0.438449i) q^{85} +2.08796i q^{86} +(-10.9832 + 6.34116i) q^{87} +(2.05525 - 1.18660i) q^{88} +1.98873 q^{89} +(0.0324379 - 0.0561842i) q^{90} +(5.81055 + 9.42972i) q^{91} +(15.4672 - 26.7899i) q^{92} +(-1.34865 - 2.33594i) q^{93} +(-2.12179 - 3.67505i) q^{94} +(0.521029 - 0.182439i) q^{95} +(-25.4154 - 14.6736i) q^{96} +(-5.94274 + 10.2931i) q^{97} +(-15.7471 + 10.3370i) q^{98} +(0.0258967 + 0.0448545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9	$ 16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9} - 2 q^{10} - 9 q^{11} - 17 q^{12} + 15 q^{13} + 3 q^{14} - 12 q^{15} - 22 q^{16} - 3 q^{18} + 8 q^{19} - 10 q^{21} - 27 q^{22} + 30 q^{23} + 13 q^{25} - 9 q^{26} - 38 q^{27} + 35 q^{28} - 18 q^{29} - 32 q^{30} - 27 q^{31} + 27 q^{32} - 12 q^{33} - 16 q^{34} - 6 q^{35} + 4 q^{36} - 39 q^{37} + 27 q^{38} - 9 q^{39} + 9 q^{40} + 9 q^{41} + 48 q^{42} - 9 q^{43} + 18 q^{44} + 75 q^{45} - 36 q^{46} + 35 q^{48} - 8 q^{49} + 18 q^{53} - 18 q^{54} + 15 q^{56} - 22 q^{57} - 20 q^{58} + 18 q^{59} - 45 q^{62} - 46 q^{63} - 22 q^{64} - 36 q^{65} - 45 q^{66} + 18 q^{67} + 63 q^{68} + 30 q^{69} - 19 q^{70} - 9 q^{71} + 18 q^{74} + 10 q^{75} + 98 q^{76} + 30 q^{77} + 54 q^{78} + 21 q^{79} + 27 q^{80} + 40 q^{81} - 34 q^{84} + 31 q^{85} - 48 q^{87} + 18 q^{88} + 24 q^{89} + 28 q^{90} + 15 q^{91} + 54 q^{92} + 6 q^{93} - 49 q^{94} - 66 q^{95} - 69 q^{96} + q^{97} + 15 q^{98} + 18 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9 - 2 * q^10 - 9 * q^11 - 17 * q^12 + 15 * q^13 + 3 * q^14 - 12 * q^15 - 22 * q^16 - 3 * q^18 + 8 * q^19 - 10 * q^21 - 27 * q^22 + 30 * q^23 + 13 * q^25 - 9 * q^26 - 38 * q^27 + 35 * q^28 - 18 * q^29 - 32 * q^30 - 27 * q^31 + 27 * q^32 - 12 * q^33 - 16 * q^34 - 6 * q^35 + 4 * q^36 - 39 * q^37 + 27 * q^38 - 9 * q^39 + 9 * q^40 + 9 * q^41 + 48 * q^42 - 9 * q^43 + 18 * q^44 + 75 * q^45 - 36 * q^46 + 35 * q^48 - 8 * q^49 + 18 * q^53 - 18 * q^54 + 15 * q^56 - 22 * q^57 - 20 * q^58 + 18 * q^59 - 45 * q^62 - 46 * q^63 - 22 * q^64 - 36 * q^65 - 45 * q^66 + 18 * q^67 + 63 * q^68 + 30 * q^69 - 19 * q^70 - 9 * q^71 + 18 * q^74 + 10 * q^75 + 98 * q^76 + 30 * q^77 + 54 * q^78 + 21 * q^79 + 27 * q^80 + 40 * q^81 - 34 * q^84 + 31 * q^85 - 48 * q^87 + 18 * q^88 + 24 * q^89 + 28 * q^90 + 15 * q^91 + 54 * q^92 + 6 * q^93 - 49 * q^94 - 66 * q^95 - 69 * q^96 + q^97 + 15 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.33045	+	1.34549i	−1.64788	+	0.951403i	−0.669964	+	0.742394i	$0.733690\pi$
$2$	−2.33045	+	1.34549i	−1.64788	+	0.951403i	−0.977914	+	0.209009i	$0.932976\pi$
$3$	−1.67620			−0.967753			−0.483877	−	0.875136i	$-0.660772\pi$
$3$	−1.67620			−0.967753			−0.483877	+	0.875136i	$0.660772\pi$
$4$	2.62067	−	4.53913i	1.31033	−	2.26957i
$5$	0.109680	−	0.0633240i	0.0490506	−	0.0283194i	−0.475274	−	0.879838i	$-0.657651\pi$
$5$	0.109680	−	0.0633240i	0.0490506	−	0.0283194i	0.524325	+	0.851518i	$0.324318\pi$
$6$	3.90630	−	2.25530i	1.59474	−	0.920723i
$7$	2.64467	−	0.0757760i	0.999590	−	0.0286406i
$7$	2.64467	−	0.0757760i	0.999590	−	0.0286406i
$8$			8.72235i			3.08382i
$9$	−0.190360			−0.0634533
$10$	−0.170403	+	0.295147i	−0.0538863	+	0.0933337i
$11$	−0.136041	−	0.235630i	−0.0410179	−	0.0710451i	0.844788	−	0.535102i	$-0.179727\pi$
$11$	−0.136041	−	0.235630i	−0.0410179	−	0.0710451i	−0.885806	+	0.464057i	$0.846393\pi$
$12$	−4.39276	+	7.60848i	−1.26808	+	2.19638i
$13$	2.09320	+	3.62554i	0.580550	+	1.00554i	0.995414	+	0.0956592i	$0.0304959\pi$
$13$	2.09320	+	3.62554i	0.580550	+	1.00554i	−0.414864	+	0.909884i	$0.636171\pi$
$14$	−6.06131	+	3.73495i	−1.61995	+	0.998209i
$15$	−0.183846	+	0.106144i	−0.0474689	+	0.0274062i
$16$	−6.49447	−	11.2487i	−1.62362	−	2.81219i
$17$			3.99752i			0.969540i	0.874642	+	0.484770i	$0.161097\pi$
$17$			3.99752i			0.969540i	−0.874642	+	0.484770i	$0.838903\pi$
$18$	0.443624	−	0.256127i	0.104563	−	0.0603696i
$19$	4.28308	+	0.809469i	0.982606	+	0.185705i
$19$	4.28308	+	0.809469i	0.982606	+	0.185705i
$20$		−	0.663805i		−	0.148431i
$21$	−4.43298	+	0.127016i	−0.967356	+	0.0277171i
$22$	0.634074	+	0.366083i	0.135185	+	0.0780491i
$23$	5.90199			1.23065			0.615325	−	0.788273i	$-0.289025\pi$
$23$	5.90199			1.23065			0.615325	+	0.788273i	$0.289025\pi$
$24$		−	14.6204i		−	2.98437i
$25$	−2.49198	+	4.31624i	−0.498396	+	0.863247i
$26$	−9.75622	−	5.63276i	−1.91335	−	1.10467i
$27$	5.34768			1.02916
$28$	6.58683	−	12.2031i	1.24479	−	2.30616i
$29$	6.55245	−	3.78306i	1.21676	−	0.702497i	0.252537	−	0.967587i	$-0.418735\pi$
$29$	6.55245	−	3.78306i	1.21676	−	0.702497i	0.964224	+	0.265091i	$0.0854019\pi$
$30$	0.285630	−	0.494725i	0.0521486	−	0.0903240i
$31$	0.804591	+	1.39359i	0.144509	+	0.250297i	0.929190	−	0.369603i	$-0.120506\pi$
$31$	0.804591	+	1.39359i	0.144509	+	0.250297i	−0.784681	+	0.619900i	$0.787173\pi$
$32$	15.1625	+	8.75408i	2.68038	+	1.54752i
$33$	0.228032	+	0.394963i	0.0396952	+	0.0687542i
$34$	−5.37860	−	9.31601i	−0.922423	−	1.59768i
$35$	0.285270	−	0.175782i	0.0482194	−	0.0297126i
$36$	−0.498870	+	0.864068i	−0.0831450	+	0.144011i
$37$	−8.34178	−	4.81613i	−1.37138	−	0.791767i	−0.380278	−	0.924872i	$-0.624172\pi$
$37$	−8.34178	−	4.81613i	−1.37138	−	0.791767i	−0.991102	+	0.133105i	$0.957505\pi$
$38$	−11.0706	+	3.87640i	−1.79589	+	0.628834i
$39$	−3.50862	−	6.07712i	−0.561830	−	0.973117i
$40$	0.552334	+	0.956671i	0.0873317	+	0.151263i
$41$	−2.22506	+	3.85392i	−0.347496	+	0.601882i	−0.985804	−	0.167900i	$-0.946301\pi$
$41$	−2.22506	+	3.85392i	−0.347496	+	0.601882i	0.638308	+	0.769781i	$0.279635\pi$
$42$	10.1600	−	6.26052i	1.56772	−	0.966020i
$43$	0.387957	−	0.671961i	0.0591629	−	0.102473i	−0.834927	−	0.550361i	$-0.814490\pi$
$43$	0.387957	−	0.671961i	0.0591629	−	0.102473i	0.894090	+	0.447888i	$0.147824\pi$
$44$	−1.42607			−0.214989
$45$	−0.0208788	+	0.0120544i	−0.00311242	+	0.00179696i
$46$	−13.7543	+	7.94105i	−2.02796	+	1.17084i
$47$			1.57697i			0.230024i	0.993364	+	0.115012i	$0.0366907\pi$
$47$			1.57697i			0.230024i	−0.993364	+	0.115012i	$0.963309\pi$
$48$	10.8860	+	18.8551i	1.57126	+	2.72150i
$49$	6.98852	−	0.400805i	0.998359	−	0.0572578i
$50$		−	13.4117i		−	1.89670i
$51$		−	6.70063i		−	0.938276i
$52$	21.9424			3.04286
$53$	−3.05534	−	1.76400i	−0.419683	−	0.242304i	0.275259	−	0.961370i	$-0.411236\pi$
$53$	−3.05534	−	1.76400i	−0.419683	−	0.242304i	−0.694942	+	0.719066i	$0.744570\pi$
$54$	−12.4625	+	7.19522i	−1.69593	+	0.979146i
$55$	−0.0298421	−	0.0172293i	−0.00402391	−	0.00232320i
$56$	0.660945	+	23.0677i	0.0883225	+	3.08255i
$57$	−7.17929	−	1.35683i	−0.950920	−	0.179717i
$58$	−10.1801	+	17.6325i	−1.33671	+	2.31526i
$59$	4.88026			0.635356			0.317678	−	0.948199i	$-0.397097\pi$
$59$	4.88026			0.635356			0.317678	+	0.948199i	$0.397097\pi$
$60$			1.11267i			0.143645i
$61$			0.160767i			0.0205841i	0.999947	+	0.0102920i	$0.00327612\pi$
$61$			0.160767i			0.0205841i	−0.999947	+	0.0102920i	$0.996724\pi$
$62$	−3.75012	−	2.16513i	−0.476266	−	0.274972i
$63$	−0.503438	+	0.0144247i	−0.0634272	+	0.00181734i
$64$	−21.1361			−2.64202
$65$	0.459167	+	0.265100i	0.0569527	+	0.0328816i
$66$	−1.06283	−	0.613627i	−0.130826	−	0.0755323i
$67$	−5.79400	−	3.34517i	−0.707849	−	0.408677i	0.102415	−	0.994742i	$-0.467343\pi$
$67$	−5.79400	−	3.34517i	−0.707849	−	0.408677i	−0.810264	+	0.586065i	$0.800676\pi$
$68$	18.1452	+	10.4762i	2.20043	+	1.27042i
$69$	−9.89291			−1.19097
$70$	−0.428295	+	0.793478i	−0.0511910	+	0.0948388i
$71$	−5.63464	−	3.25316i	−0.668709	−	0.386079i	0.126878	−	0.991918i	$-0.459504\pi$
$71$	−5.63464	−	3.25316i	−0.668709	−	0.386079i	−0.795587	+	0.605839i	$0.792838\pi$
$72$		−	1.66038i		−	0.195678i
$73$			14.8619i			1.73946i	0.493529	+	0.869730i	$0.335707\pi$
$73$			14.8619i			1.73946i	−0.493529	+	0.869730i	$0.664293\pi$
$74$	25.9201			3.01316
$75$	4.17705	−	7.23487i	0.482324	−	0.835410i
$76$	14.8988	−	17.3201i	1.70901	−	1.98675i
$77$	−0.377638	−	0.612854i	−0.0430359	−	0.0698412i
$78$	16.3534	+	9.44162i	1.85165	+	1.06905i
$79$	9.55897	−	5.51887i	1.07547	−	0.620922i	0.145798	−	0.989314i	$-0.453425\pi$
$79$	9.55897	−	5.51887i	1.07547	−	0.620922i	0.929670	+	0.368393i	$0.120092\pi$
$80$	−1.42463	−	0.822512i	−0.159279	−	0.0919596i
$81$	−8.39268			−0.932520
$82$		−	11.9752i		−	1.32244i
$83$		−	17.7150i		−	1.94447i	−0.234006	−	0.972235i	$-0.575183\pi$
$83$		−	17.7150i		−	1.94447i	0.234006	−	0.972235i	$-0.424817\pi$
$84$	−11.0408	+	20.4548i	−1.20465	+	2.23180i
$85$	0.253139	+	0.438449i	0.0274568	+	0.0475565i
$86$			2.08796i			0.225151i
$87$	−10.9832	+	6.34116i	−1.17752	+	0.679844i
$88$	2.05525	−	1.18660i	0.219090	−	0.126492i
$89$	1.98873			0.210805			0.105402	−	0.994430i	$-0.466387\pi$
$89$	1.98873			0.210805			0.105402	+	0.994430i	$0.466387\pi$
$90$	0.0324379	−	0.0561842i	0.00341926	−	0.00592233i
$91$	5.81055	+	9.42972i	0.609112	+	0.988503i
$92$	15.4672	−	26.7899i	1.61256	−	2.79304i
$93$	−1.34865	−	2.33594i	−0.139849	−	0.242225i
$94$	−2.12179	−	3.67505i	−0.218846	−	0.379052i
$95$	0.521029	−	0.182439i	0.0534564	−	0.0187178i
$96$	−25.4154	−	14.6736i	−2.59395	−	1.49762i
$97$	−5.94274	+	10.2931i	−0.603394	+	1.04511i	0.388909	+	0.921276i	$0.372852\pi$
$97$	−5.94274	+	10.2931i	−0.603394	+	1.04511i	−0.992303	+	0.123833i	$0.960481\pi$
$98$	−15.7471	+	10.3370i	−1.59070	+	1.04420i
$99$	0.0258967	+	0.0448545i	0.00260272	+	0.00450805i
$100$	13.0613	+	22.6228i	1.30613	+	2.26228i
$101$	−7.09443	−	4.09597i	−0.705922	−	0.407564i	0.103627	−	0.994616i	$-0.466955\pi$
$101$	−7.09443	−	4.09597i	−0.705922	−	0.407564i	−0.809549	+	0.587052i	$0.800288\pi$
$102$	9.01560	+	15.6155i	0.892678	+	1.54616i
$103$	1.36143	−	2.35807i	0.134146	−	0.232347i	−0.791125	−	0.611654i	$-0.790504\pi$
$103$	1.36143	−	2.35807i	0.134146	−	0.232347i	0.925271	+	0.379307i	$0.123838\pi$
$104$	−31.6232	+	18.2577i	−3.10091	+	1.79031i
$105$	−0.478169	+	0.294646i	−0.0466645	+	0.0287545i
$106$	9.49375			0.922114
$107$	−3.99290	−	2.30530i	−0.386008	−	0.222862i	0.294421	−	0.955676i	$-0.404873\pi$
$107$	−3.99290	−	2.30530i	−0.386008	−	0.222862i	−0.680429	+	0.732814i	$0.738207\pi$
$108$	14.0145	−	24.2738i	1.34854	−	2.33575i
$109$		−	3.99746i		−	0.382887i	−0.981504	−	0.191443i	$-0.938683\pi$
$109$		−	3.99746i		−	0.382887i	0.981504	−	0.191443i	$-0.0613168\pi$
$110$	0.0927274			0.00884121
$111$	13.9825	+	8.07279i	1.32716	+	0.766235i
$112$	−18.0281	−	29.2570i	−1.70349	−	2.76453i
$113$			7.72422i			0.726633i	0.931666	+	0.363317i	$0.118356\pi$
$113$			7.72422i			0.726633i	−0.931666	+	0.363317i	$0.881644\pi$
$114$	18.5566	−	6.49761i	1.73798	−	0.608557i
$115$	0.647333	−	0.373738i	0.0603641	−	0.0348513i
$116$		−	39.6566i		−	3.68202i
$117$	−0.398462	−	0.690156i	−0.0368378	−	0.0638050i
$118$	−11.3732	+	6.56633i	−1.04699	+	0.604479i
$119$	0.302916	+	10.5721i	0.0277682	+	0.969142i
$120$	−0.925822	−	1.60357i	−0.0845156	−	0.146385i
$121$	5.46299	−	9.46217i	0.496635	−	0.860197i
$122$	−0.216310	−	0.374659i	−0.0195838	−	0.0339201i
$123$	3.72965	−	6.45994i	0.336291	−	0.582473i
$124$	8.43426			0.757419
$125$			1.26445i			0.113096i
$126$	1.15383	−	0.710985i	0.102791	−	0.0633396i
$127$	−2.85316	+	1.64727i	−0.253177	+	0.146172i	−0.621218	−	0.783638i	$-0.713362\pi$
$127$	−2.85316	+	1.64727i	−0.253177	+	0.146172i	0.368041	+	0.929809i	$0.380029\pi$
$128$	18.9317	−	10.9302i	1.67334	−	0.966105i
$129$	−0.650293	+	1.12634i	−0.0572551	+	0.0991687i
$130$	−1.42676			−0.125135
$131$	−7.01331	+	4.04914i	−0.612756	+	0.353775i	−0.774043	−	0.633133i	$-0.781769\pi$
$131$	−7.01331	+	4.04914i	−0.612756	+	0.353775i	0.161287	+	0.986908i	$0.448435\pi$
$132$	2.39038			0.208056
$133$	11.3886	+	1.81622i	0.987521	+	0.157486i
$134$	18.0035			1.55527
$135$	0.586535	−	0.338636i	0.0504809	−	0.0291452i
$136$	−34.8677			−2.98988
$137$	2.01967	−	3.49818i	0.172552	−	0.298870i	−0.766759	−	0.641935i	$-0.778132\pi$
$137$	2.01967	−	3.49818i	0.172552	−	0.298870i	0.939312	+	0.343065i	$0.111465\pi$
$138$	23.0549	−	13.3108i	1.96257	−	1.13309i
$139$	−14.3376	+	8.27784i	−1.21610	+	0.702117i	−0.964082	−	0.265605i	$-0.914428\pi$
$139$	−14.3376	+	8.27784i	−1.21610	+	0.702117i	−0.252020	+	0.967722i	$0.581095\pi$
$140$	−0.0503005	−	1.75554i	−0.00425117	−	0.148370i
$141$		−	2.64331i		−	0.222607i
$142$	17.5083			1.46927
$143$	0.569523	−	0.986443i	0.0476259	−	0.0824905i
$144$	1.23629	+	2.14131i	0.103024	+	0.178442i
$145$	0.479117	−	0.829856i	0.0397885	−	0.0689158i
$146$	−19.9965	−	34.6350i	−1.65493	−	2.86642i
$147$	−11.7141	+	0.671828i	−0.966166	+	0.0554114i
$148$	−43.7221	+	25.2429i	−3.59393	+	2.07496i
$149$	6.24327	+	10.8137i	0.511469	+	0.885890i	0.999912	+	0.0132943i	$0.00423183\pi$
$149$	6.24327	+	10.8137i	0.511469	+	0.885890i	−0.488443	+	0.872596i	$0.662435\pi$
$150$			22.4807i			1.83554i
$151$	0.736019	−	0.424941i	0.0598964	−	0.0345812i	−0.469753	−	0.882798i	$-0.655657\pi$
$151$	0.736019	−	0.424941i	0.0598964	−	0.0345812i	0.529649	+	0.848217i	$0.322324\pi$
$152$	−7.06047	+	37.3585i	−0.572680	+	3.03017i
$153$		−	0.760966i		−	0.0615205i
$154$	1.70465	+	0.920119i	0.137365	+	0.0741453i
$155$	0.176496	+	0.101900i	0.0141765	+	0.00818480i
$156$	−36.7798			−2.94474
$157$		−	13.6787i		−	1.09168i	−0.837890	−	0.545839i	$-0.816211\pi$
$157$		−	13.6787i		−	1.09168i	0.837890	−	0.545839i	$-0.183789\pi$
$158$	−14.8511	+	25.7229i	−1.18149	+	2.04641i
$159$	5.12135	+	2.95681i	0.406149	+	0.234490i
$160$	2.21738			0.175299
$161$	15.6088	−	0.447230i	1.23015	−	0.0352466i
$162$	19.5587	−	11.2922i	1.53668	−	0.887202i
$163$	−3.93840	+	6.82151i	−0.308479	+	0.534302i	−0.978030	−	0.208465i	$-0.933153\pi$
$163$	−3.93840	+	6.82151i	−0.308479	+	0.534302i	0.669551	+	0.742766i	$0.266487\pi$
$164$	11.6623	+	20.1997i	0.910673	+	1.57733i
$165$	0.0500213	+	0.0288798i	0.00389415	+	0.00224829i
$166$	23.8353	+	41.2839i	1.84997	+	3.20425i
$167$	4.81135	+	8.33351i	0.372314	+	0.644866i	0.989921	−	0.141620i	$-0.0452312\pi$
$167$	4.81135	+	8.33351i	0.372314	+	0.644866i	−0.617607	+	0.786487i	$0.711898\pi$
$168$	−1.10787	−	38.6660i	−0.0854744	−	2.98315i
$169$	−2.26301	+	3.91964i	−0.174077	+	0.301511i
$170$	−1.17986	−	0.681190i	−0.0904908	−	0.0522449i
$171$	−0.815326	−	0.154090i	−0.0623495	−	0.0117836i
$172$	−2.03341	−	3.52197i	−0.155046	−	0.268548i
$173$	−6.72839	−	11.6539i	−0.511550	−	0.886031i	−0.999910	−	0.0133887i	$-0.995738\pi$
$173$	−6.72839	−	11.6539i	−0.511550	−	0.886031i	0.488360	−	0.872642i	$-0.337595\pi$
$174$	17.0639	−	29.5555i	1.29361	−	2.24060i
$175$	−6.26339	+	11.6038i	−0.473468	+	0.877167i
$176$	−1.76703	+	3.06058i	−0.133195	+	0.230700i
$177$	−8.18029			−0.614868
$178$	−4.63464	+	2.67581i	−0.347381	+	0.200560i
$179$	5.83565	−	3.36921i	0.436177	−	0.251827i	−0.265798	−	0.964029i	$-0.585635\pi$
$179$	5.83565	−	3.36921i	0.436177	−	0.251827i	0.701975	+	0.712202i	$0.252302\pi$
$180$			0.126362i			0.00941845i
$181$	2.72765	+	4.72443i	0.202745	+	0.351164i	0.949412	−	0.314034i	$-0.101681\pi$
$181$	2.72765	+	4.72443i	0.202745	+	0.351164i	−0.746667	+	0.665198i	$0.768347\pi$
$182$	−26.2288	−	14.1575i	−1.94421	−	1.04942i
$183$		−	0.269477i		−	0.0199203i
$184$			51.4792i			3.79510i
$185$	−1.21991			−0.0896893
$186$	6.28594	+	3.62919i	0.460908	+	0.266105i
$187$	0.941935	−	0.543826i	0.0688811	−	0.0397685i
$188$	7.15806	+	4.13271i	0.522055	+	0.301409i
$189$	14.1428	−	0.405226i	1.02874	−	0.0294758i
$190$	−0.968763	+	1.12620i	−0.0702815	+	0.0817033i
$191$	−0.00688022	+	0.0119169i	−0.000497835	+	0.000862276i	−0.866274	−	0.499569i	$-0.833492\pi$
$191$	−0.00688022	+	0.0119169i	−0.000497835	+	0.000862276i	0.865776	+	0.500431i	$0.166825\pi$
$192$	35.4284			2.55682
$193$		−	3.10690i		−	0.223640i	−0.993728	−	0.111820i	$-0.964332\pi$
$193$		−	3.10690i		−	0.223640i	0.993728	−	0.111820i	$-0.0356679\pi$
$194$		−	31.9835i		−	2.29628i
$195$	−0.769655	−	0.444361i	−0.0551162	−	0.0318213i
$196$	16.4953	−	32.7722i	1.17823	−	2.34087i
$197$	−5.99147			−0.426874			−0.213437	−	0.976957i	$-0.568466\pi$
$197$	−5.99147			−0.426874			−0.213437	+	0.976957i	$0.568466\pi$
$198$	−0.120702	−	0.0696875i	−0.00857793	−	0.00495247i
$199$	8.68412	+	5.01378i	0.615601	+	0.355417i	0.775154	−	0.631772i	$-0.217672\pi$
$199$	8.68412	+	5.01378i	0.615601	+	0.355417i	−0.159553	+	0.987189i	$0.551005\pi$
$200$	−37.6477	−	21.7359i	−2.66210	−	1.53696i
$201$	9.71189	+	5.60716i	0.685024	+	0.395499i
$202$	22.0443			1.55103
$203$	17.0424	−	10.5015i	1.19614	−	0.737057i
$204$	−30.4150	−	17.5601i	−2.12948	−	1.22945i
$205$			0.563600i			0.0393635i
$206$			7.32714i			0.510506i
$207$	−1.12350			−0.0780888
$208$	27.1885	−	47.0918i	1.88518	−	3.26523i
$209$	−0.391939	−	1.11934i	−0.0271110	−	0.0774266i
$210$	0.717907	−	1.33003i	0.0495403	−	0.0917806i
$211$	−2.83332	−	1.63582i	−0.195054	−	0.112614i	0.399292	−	0.916824i	$-0.369256\pi$
$211$	−2.83332	−	1.63582i	−0.195054	−	0.112614i	−0.594346	+	0.804209i	$0.702589\pi$
$212$	−16.0140	+	9.24571i	−1.09985	+	0.634998i
$213$	9.44477	+	5.45294i	0.647145	+	0.373629i
$214$	12.4070			0.848126
$215$		−	0.0982680i		−	0.00670182i
$216$			46.6443i			3.17374i
$217$	2.23348	+	3.62462i	0.151618	+	0.246055i
$218$	5.37852	+	9.31587i	0.364279	+	0.630951i
$219$		−	24.9116i		−	1.68337i
$220$	−0.156412	+	0.0903048i	−0.0105453	+	0.00608835i
$221$	−14.4931	+	8.36762i	−0.974914	+	0.562867i
$222$	−43.4473			−2.91599
$223$	10.4876	−	18.1651i	0.702305	−	1.21643i	−0.265350	−	0.964152i	$-0.585488\pi$
$223$	10.4876	−	18.1651i	0.702305	−	1.21643i	0.967655	−	0.252276i	$-0.0811790\pi$
$224$	40.7631	+	22.0027i	2.72360	+	1.47012i
$225$	0.474373	−	0.821638i	0.0316249	−	0.0547759i
$226$	−10.3928	−	18.0009i	−0.691321	−	1.19740i
$227$	−2.62739	−	4.55078i	−0.174386	−	0.302046i	0.765563	−	0.643361i	$-0.222461\pi$
$227$	−2.62739	−	4.55078i	−0.174386	−	0.302046i	−0.939949	+	0.341316i	$0.889127\pi$
$228$	−24.9734	+	29.0319i	−1.65390	+	1.92269i
$229$	−6.95308	−	4.01436i	−0.459472	−	0.265276i	0.252350	−	0.967636i	$-0.418797\pi$
$229$	−6.95308	−	4.01436i	−0.459472	−	0.265276i	−0.711822	+	0.702360i	$0.752130\pi$
$230$	−1.00572	+	1.74196i	−0.0663151	+	0.114861i
$231$	0.632996	+	1.02726i	0.0416481	+	0.0675891i
$232$	32.9972	+	57.1528i	2.16637	+	3.75226i
$233$	−10.2213	−	17.7039i	−0.669623	−	1.15982i	−0.978010	−	0.208560i	$-0.933122\pi$
$233$	−10.2213	−	17.7039i	−0.669623	−	1.15982i	0.308387	−	0.951261i	$-0.400211\pi$
$234$	1.85719	+	1.07225i	0.121408	+	0.0700952i
$235$	0.0998600	+	0.172963i	0.00651415	+	0.0112828i
$236$	12.7895	−	22.1521i	0.832529	−	1.44198i
$237$	−16.0227	+	9.25073i	−1.04079	+	0.600899i
$238$	−14.9305	−	24.2302i	−0.967803	−	1.57061i
$239$	−10.4011			−0.672790			−0.336395	−	0.941721i	$-0.609208\pi$
$239$	−10.4011			−0.672790			−0.336395	+	0.941721i	$0.609208\pi$
$240$	2.38797	+	1.37869i	0.154142	+	0.0889942i
$241$	7.25492	−	12.5659i	0.467330	−	0.809440i	−0.531973	−	0.846761i	$-0.678549\pi$
$241$	7.25492	−	12.5659i	0.467330	−	0.809440i	0.999303	+	0.0373215i	$0.0118826\pi$
$242$			29.4015i			1.89000i
$243$	−1.97522			−0.126711
$244$	0.729742	+	0.421317i	0.0467169	+	0.0269720i
$245$	0.741123	−	0.486502i	0.0473486	−	0.0310814i
$246$			20.0728i			1.27979i
$247$	6.03060	+	17.2228i	0.383718	+	1.09586i
$248$	−12.1554	+	7.01792i	−0.771869	+	0.445639i
$249$			29.6938i			1.88177i
$250$	−1.70130	−	2.94674i	−0.107600	−	0.186368i
$251$	1.02258	−	0.590388i	0.0645448	−	0.0372649i	−0.467380	−	0.884056i	$-0.654802\pi$
$251$	1.02258	−	0.590388i	0.0645448	−	0.0372649i	0.531925	+	0.846791i	$0.321469\pi$
$252$	−1.25387	+	2.32297i	−0.0789863	+	0.146334i
$253$	−0.802913	−	1.39069i	−0.0504787	−	0.0874317i
$254$	4.43276	−	7.67777i	0.278136	−	0.481746i
$255$	−0.424311	−	0.734928i	−0.0265714	−	0.0460230i
$256$	−8.27681	+	14.3359i	−0.517301	+	0.895991i
$257$	−23.6050			−1.47244			−0.736220	−	0.676742i	$-0.763391\pi$
$257$	−23.6050			−1.47244			−0.736220	+	0.676742i	$0.763391\pi$
$258$		−	3.49984i		−	0.217891i
$259$	−22.4262	−	12.1049i	−1.39349	−	0.752165i
$260$	2.40665	−	1.38948i	0.149254	−	0.0861719i
$261$	−1.24732	+	0.720143i	−0.0772074	+	0.0445757i
$262$	10.8961	−	18.8726i	0.673165	−	1.16596i
$263$	2.01671			0.124356			0.0621779	−	0.998065i	$-0.480195\pi$
$263$	2.01671			0.124356			0.0621779	+	0.998065i	$0.480195\pi$
$264$	−3.44500	+	1.98897i	−0.212025	+	0.122413i
$265$	−0.446814			−0.0274476
$266$	−28.9844	+	11.0907i	−1.77715	+	0.680012i
$267$	−3.33350			−0.204007
$268$	−30.3683	+	17.5331i	−1.85504	+	1.07101i
$269$	27.0789			1.65103			0.825516	−	0.564379i	$-0.190884\pi$
$269$	27.0789			1.65103			0.825516	+	0.564379i	$0.190884\pi$
$270$	−0.911261	+	1.57835i	−0.0554576	+	0.0960554i
$271$	−23.2068	+	13.3985i	−1.40971	+	0.813898i	−0.995360	−	0.0962186i	$-0.969325\pi$
$271$	−23.2068	+	13.3985i	−1.40971	+	0.813898i	−0.414352	+	0.910117i	$0.635992\pi$
$272$	44.9670	−	25.9617i	2.72653	−	1.57416i
$273$	−9.73964	−	15.8061i	−0.589470	−	0.956627i
$274$			10.8698i			0.656667i
$275$	1.35605			0.0817727
$276$	−25.9260	+	44.9052i	−1.56056	+	2.70298i
$277$	−3.98141	−	6.89601i	−0.239220	−	0.414341i	0.721271	−	0.692653i	$-0.243558\pi$
$277$	−3.98141	−	6.89601i	−0.239220	−	0.414341i	−0.960491	+	0.278312i	$0.910225\pi$
$278$	22.2754	−	38.5822i	1.33599	−	2.31401i
$279$	−0.153162	−	0.265284i	−0.00916956	−	0.0158821i
$280$	1.53323	+	2.48822i	0.0916282	+	0.148700i
$281$	24.3836	−	14.0779i	1.45460	−	0.839816i	0.455867	−	0.890048i	$-0.349329\pi$
$281$	24.3836	−	14.0779i	1.45460	−	0.839816i	0.998738	+	0.0502319i	$0.0159960\pi$
$282$	3.55654	+	6.16011i	0.211789	+	0.366829i
$283$		−	20.2050i		−	1.20106i	−0.799601	−	0.600532i	$-0.794956\pi$
$283$		−	20.2050i		−	1.20106i	0.799601	−	0.600532i	$-0.205044\pi$
$284$	−29.5330	+	17.0509i	−1.75246	+	1.01179i
$285$	−0.873348	+	0.305804i	−0.0517326	+	0.0181142i
$286$			3.06514i			0.181246i
$287$	−5.59251	+	10.3609i	−0.330116	+	0.611587i
$288$	−2.88633	−	1.66643i	−0.170079	−	0.0981951i
$289$	1.01987			0.0599924
$290$			2.57858i			0.151420i
$291$	9.96121	−	17.2533i	0.583936	−	1.01141i
$292$	67.4603	+	38.9482i	3.94782	+	2.27927i
$293$	17.0035			0.993357			0.496678	−	0.867935i	$-0.334553\pi$
$293$	17.0035			0.993357			0.496678	+	0.867935i	$0.334553\pi$
$294$	26.3953	−	17.3269i	1.53940	−	1.01052i
$295$	0.535269	−	0.309038i	0.0311646	−	0.0179929i
$296$	42.0079	−	72.7599i	2.44166	−	4.22908i
$297$	−0.727503	−	1.26007i	−0.0422140	−	0.0731168i
$298$	−29.0993	−	16.8005i	−1.68568	−	0.973226i
$299$	12.3541	+	21.3979i	0.714455	+	1.23747i
$300$	−21.8933	−	37.9204i	−1.26401	−	2.18933i
$301$	0.975098	−	1.80651i	0.0562037	−	0.104126i
$302$	−1.14350	+	1.98061i	−0.0658013	+	0.113971i
$303$	11.8917	+	6.86566i	0.683159	+	0.394422i
$304$	−18.7108	−	53.4363i	−1.07314	−	3.06478i
$305$	0.0101804	+	0.0176330i	0.000582928	+	0.00100966i
$306$	1.02387	+	1.77339i	0.0585307	+	0.101378i
$307$	3.76338	−	6.51836i	0.214787	−	0.372023i	−0.738419	−	0.674342i	$-0.764427\pi$
$307$	3.76338	−	6.51836i	0.214787	−	0.372023i	0.953207	+	0.302319i	$0.0977608\pi$
$308$	−3.77149	+	0.108062i	−0.214900	+	0.00615741i
$309$	−2.28203	+	3.95259i	−0.129820	+	0.224855i
$310$	−0.548420			−0.0311482
$311$	0.826081	−	0.476938i	0.0468428	−	0.0270447i	−0.476396	−	0.879231i	$-0.658057\pi$
$311$	0.826081	−	0.476938i	0.0468428	−	0.0270447i	0.523238	+	0.852186i	$0.324724\pi$
$312$	53.0067	−	30.6034i	3.00091	−	1.73258i
$313$		−	5.61998i		−	0.317660i	−0.987306	−	0.158830i	$-0.949228\pi$
$313$		−	5.61998i		−	0.317660i	0.987306	−	0.158830i	$-0.0507722\pi$
$314$	18.4045	+	31.8775i	1.03863	+	1.79895i
$315$	−0.0543039	+	0.0334618i	−0.00305968	+	0.00188536i
$316$		−	57.8525i		−	3.25446i
$317$			21.6156i			1.21405i	0.794682	+	0.607026i	$0.207638\pi$
$317$			21.6156i			1.21405i	−0.794682	+	0.607026i	$0.792362\pi$
$318$	−15.9134			−0.892379
$319$	−1.78281	−	1.02930i	−0.0998179	−	0.0576299i
$320$	−2.31822	+	1.33843i	−0.129593	+	0.0748203i
$321$	6.69289	+	3.86414i	0.373561	+	0.215676i
$322$	−35.7738	+	22.0437i	−1.99360	+	1.22845i
$323$	−3.23587	+	17.1217i	−0.180048	+	0.952675i
$324$	−21.9944	+	38.0955i	−1.22191	+	2.11642i
$325$	−20.8649			−1.15738
$326$		−	21.1962i		−	1.17395i
$327$			6.70053i			0.370540i
$328$	−33.6152	−	19.4078i	−1.85609	−	1.07161i
$329$	0.119496	+	4.17055i	0.00658805	+	0.229930i
$330$	−0.155429			−0.00855611
$331$	1.88643	+	1.08913i	0.103688	+	0.0598641i	0.550947	−	0.834540i	$-0.314267\pi$
$331$	1.88643	+	1.08913i	0.103688	+	0.0598641i	−0.447259	+	0.894404i	$0.647600\pi$
$332$	−80.4105	−	46.4251i	−4.41310	−	2.54791i
$333$	1.58794	+	0.916797i	0.0870186	+	0.0502402i
$334$	−22.4253	−	12.9472i	−1.22706	−	0.708441i
$335$	−0.847318			−0.0462939
$336$	30.2186	+	49.0406i	1.64856	+	2.67538i
$337$	−27.6548	−	15.9665i	−1.50645	−	0.869752i	−0.999972	−	0.00750145i	$-0.997612\pi$
$337$	−27.6548	−	15.9665i	−1.50645	−	0.869752i	−0.506482	−	0.862250i	$-0.669054\pi$
$338$		−	12.1794i		−	0.662471i
$339$		−	12.9473i		−	0.703202i
$340$	2.65357			0.143910
$341$	0.218915	−	0.379172i	0.0118549	−	0.0205333i
$342$	2.10740	−	0.737910i	0.113955	−	0.0399016i
$343$	18.4519	−	1.58956i	0.996310	−	0.0858280i
$344$	5.86108	+	3.38390i	0.316008	+	0.182447i
$345$	−1.08506	+	0.626459i	−0.0584176	+	0.0337274i
$346$	31.3604	+	18.1059i	1.68594	+	0.973380i
$347$	31.1334			1.67133			0.835663	−	0.549242i	$-0.185083\pi$
$347$	31.1334			1.67133			0.835663	+	0.549242i	$0.185083\pi$
$348$			66.4723i			3.56329i
$349$			13.9720i			0.747906i	0.927448	+	0.373953i	$0.121998\pi$
$349$			13.9720i			0.747906i	−0.927448	+	0.373953i	$0.878002\pi$
$350$	−1.01629	−	35.4695i	−0.0543227	−	1.89592i
$351$	11.1938	+	19.3882i	0.597480	+	1.03486i
$352$		−	4.76366i		−	0.253904i
$353$	1.05903	−	0.611431i	0.0563665	−	0.0325432i	−0.471552	−	0.881838i	$-0.656306\pi$
$353$	1.05903	−	0.611431i	0.0563665	−	0.0325432i	0.527918	+	0.849295i	$0.322973\pi$
$354$	19.0638	−	11.0065i	1.01323	−	0.584987i
$355$	−0.824013			−0.0437341
$356$	5.21180	−	9.02710i	0.276225	−	0.478435i
$357$	−0.507747	−	17.7209i	−0.0268728	−	0.937891i
$358$	−9.06646	+	15.7036i	−0.479177	+	0.829959i
$359$	0.730326	+	1.26496i	0.0385452	+	0.0667622i	0.884654	−	0.466247i	$-0.154394\pi$
$359$	0.730326	+	1.26496i	0.0385452	+	0.0667622i	−0.846109	+	0.533010i	$0.821061\pi$
$360$	−0.105142	−	0.182112i	−0.00554148	−	0.00959813i
$361$	17.6895	+	6.93404i	0.931027	+	0.364949i
$362$	−12.7133	−	7.34004i	−0.668197	−	0.385784i
$363$	−9.15705	+	15.8605i	−0.480620	+	0.832459i
$364$	58.0302	−	1.66271i	3.04161	−	0.0871495i
$365$	0.941118	+	1.63007i	0.0492604	+	0.0853215i
$366$	0.362578	+	0.628003i	0.0189522	+	0.0328263i
$367$	−6.65661	−	3.84319i	−0.347472	−	0.200613i	0.316099	−	0.948726i	$-0.397627\pi$
$367$	−6.65661	−	3.84319i	−0.347472	−	0.200613i	−0.663571	+	0.748113i	$0.730960\pi$
$368$	−38.3303	−	66.3900i	−1.99810	−	3.46082i
$369$	0.423563	−	0.733632i	0.0220498	−	0.0381914i
$370$	2.84293	−	1.64137i	0.147797	−	0.0853307i
$371$	−8.21401	−	4.43367i	−0.426450	−	0.230184i
$372$	−14.1375			−0.732995
$373$	26.0912	+	15.0638i	1.35095	+	0.779973i	0.988383	−	0.151983i	$-0.0485659\pi$
$373$	26.0912	+	15.0638i	1.35095	+	0.779973i	0.362570	+	0.931956i	$0.381899\pi$
$374$	−1.46342	+	2.53472i	−0.0756717	+	0.131067i
$375$		−	2.11947i		−	0.109449i
$376$	−13.7549			−0.709353
$377$	27.4312	+	15.8374i	1.41278	+	0.815670i
$378$	−32.4139	+	19.9733i	−1.66719	+	1.02732i
$379$		−	9.59543i		−	0.492884i	−0.969158	−	0.246442i	$-0.920739\pi$
$379$		−	9.59543i		−	0.492884i	0.969158	−	0.246442i	$-0.0792615\pi$
$380$	0.537330	−	2.84313i	0.0275644	−	0.145849i
$381$	4.78246	−	2.76115i	0.245013	−	0.141458i
$382$		−	0.0370290i		−	0.00189457i
$383$	8.11196	+	14.0503i	0.414502	+	0.717938i	0.995376	−	0.0960554i	$-0.0306226\pi$
$383$	8.11196	+	14.0503i	0.414502	+	0.717938i	−0.580874	+	0.813993i	$0.697289\pi$
$384$	−31.7333	+	18.3212i	−1.61938	+	0.934951i
$385$	−0.0802279	−	0.0433045i	−0.00408879	−	0.00220700i
$386$	4.18029	+	7.24048i	0.212771	+	0.368531i
$387$	−0.0738514	+	0.127914i	−0.00375408	+	0.00650225i
$388$	31.1479	+	53.9497i	1.58129	+	2.73888i
$389$	−8.31716	+	14.4057i	−0.421697	+	0.730400i	−0.996106	−	0.0881683i	$-0.971899\pi$
$389$	−8.31716	+	14.4057i	−0.421697	+	0.730400i	0.574409	+	0.818569i	$0.305232\pi$
$390$	2.39152			0.121100
$391$			23.5933i			1.19316i
$392$	3.49596	+	60.9563i	0.176572	+	3.07876i
$393$	11.7557	−	6.78716i	0.592997	−	0.342367i
$394$	13.9628	−	8.06144i	0.703437	−	0.406129i
$395$	0.698955	−	1.21063i	0.0351682	−	0.0609132i
$396$	0.271467			0.0136417
$397$	21.9739	−	12.6866i	1.10284	−	0.636723i	0.165872	−	0.986147i	$-0.446956\pi$
$397$	21.9739	−	12.6866i	1.10284	−	0.636723i	0.936964	+	0.349425i	$0.113623\pi$
$398$	−26.9839			−1.35258
$399$	−19.0896	−	3.04435i	−0.955677	−	0.152408i
$400$	64.7363			3.23682
$401$	−21.3389	+	12.3200i	−1.06561	+	0.615233i	−0.926980	−	0.375111i	$-0.877605\pi$
$401$	−21.3389	+	12.3200i	−1.06561	+	0.615233i	−0.138635	+	0.990344i	$0.544271\pi$
$402$	−30.1774			−1.50511
$403$	−3.36835	+	5.83415i	−0.167789	+	0.290620i
$404$	−37.1843	+	21.4684i	−1.84999	+	1.06809i
$405$	−0.920513	+	0.531459i	−0.0457407	+	0.0264084i
$406$	−25.5869	+	47.4034i	−1.26986	+	2.35259i
$407$			2.62076i			0.129906i
$408$	58.4452			2.89347
$409$	1.22087	−	2.11460i	0.0603679	−	0.104560i	−0.834262	−	0.551368i	$-0.814106\pi$
$409$	1.22087	−	2.11460i	0.0603679	−	0.104560i	0.894630	+	0.446808i	$0.147439\pi$
$410$	−0.758316	−	1.31344i	−0.0374506	−	0.0648663i
$411$	−3.38537	+	5.86364i	−0.166988	+	0.289232i
$412$	−7.13571	−	12.3594i	−0.351551	−	0.608905i
$413$	12.9067	−	0.369807i	0.635095	−	0.0181970i
$414$	2.61827	−	1.51166i	0.128681	−	0.0742939i
$415$	−1.12178	−	1.94299i	−0.0550662	−	0.0953774i
$416$			73.2963i			3.59365i
$417$	24.0327	−	13.8753i	1.17689	−	0.679476i
$418$	2.41946	+	2.08122i	0.118339	+	0.101796i
$419$		−	13.3026i		−	0.649873i	−0.945736	−	0.324937i	$-0.894657\pi$
$419$		−	13.3026i		−	0.649873i	0.945736	−	0.324937i	$-0.105343\pi$
$420$	0.0843136	+	2.94264i	0.00411408	+	0.143586i
$421$	−20.6049	−	11.8962i	−1.00422	−	0.579787i	−0.0947268	−	0.995503i	$-0.530198\pi$
$421$	−20.6049	−	11.8962i	−1.00422	−	0.579787i	−0.909495	+	0.415716i	$0.863531\pi$
$422$	8.80389			0.428567
$423$		−	0.300191i		−	0.0145958i
$424$	15.3862	−	26.6497i	0.747220	−	1.29422i
$425$	−17.2542	−	9.96173i	−0.836953	−	0.483215i
$426$	−29.3474			−1.42189
$427$	0.0121823	+	0.425175i	0.000589542	+	0.0205756i
$428$	−20.9281	+	12.0829i	−1.01160	+	0.584047i
$429$	−0.954634	+	1.65347i	−0.0460902	+	0.0798305i
$430$	0.132218	+	0.229009i	0.00637613	+	0.0110438i
$431$	4.25689	+	2.45771i	0.205047	+	0.118384i	0.599007	−	0.800743i	$-0.295562\pi$
$431$	4.25689	+	2.45771i	0.205047	+	0.118384i	−0.393960	+	0.919127i	$0.628895\pi$
$432$	−34.7303	−	60.1546i	−1.67096	−	2.89419i
$433$	−8.26480	−	14.3151i	−0.397181	−	0.687937i	0.596196	−	0.802839i	$-0.296678\pi$
$433$	−8.26480	−	14.3151i	−0.397181	−	0.687937i	−0.993377	+	0.114901i	$0.963345\pi$
$434$	−10.0819	−	5.44188i	−0.483946	−	0.261219i
$435$	−0.803096	+	1.39100i	−0.0385055	+	0.0666935i
$436$	−18.1450	−	10.4760i	−0.868986	−	0.501710i
$437$	25.2787	+	4.77748i	1.20924	+	0.228538i
$438$	33.5182	+	58.0552i	1.60156	+	2.77398i
$439$	−15.3534	−	26.5929i	−0.732777	−	1.26921i	−0.955692	−	0.294370i	$-0.904890\pi$
$439$	−15.3534	−	26.5929i	−0.732777	−	1.26921i	0.222914	−	0.974838i	$-0.428443\pi$
$440$	0.150280	−	0.260293i	0.00716433	−	0.0124090i
$441$	−1.33033	+	0.0762971i	−0.0633492	+	0.00363319i
$442$	22.5170	−	39.0006i	1.07103	−	1.85507i
$443$	−5.20118			−0.247116			−0.123558	−	0.992337i	$-0.539430\pi$
$443$	−5.20118			−0.247116			−0.123558	+	0.992337i	$0.539430\pi$
$444$	73.2868	−	42.3122i	3.47804	−	2.00805i
$445$	0.218125	−	0.125934i	0.0103401	−	0.00596986i
$446$			56.4440i			2.67270i
$447$	−10.4650	−	18.1259i	−0.494976	−	0.857323i
$448$	−55.8980	+	1.60161i	−2.64093	+	0.0756691i
$449$			30.9166i			1.45904i	0.683958	+	0.729521i	$0.260257\pi$
$449$			30.9166i			1.45904i	−0.683958	+	0.729521i	$0.739743\pi$
$450$			2.55305i			0.120352i
$451$	1.21080			0.0570143
$452$	35.0612	+	20.2426i	1.64914	+	0.952132i
$453$	−1.23371	+	0.712285i	−0.0579649	+	0.0334661i
$454$	12.2460	+	7.07024i	0.574734	+	0.331823i
$455$	1.23443	+	0.666308i	0.0578711	+	0.0312370i
$456$	11.8347	−	62.6202i	0.554213	−	2.93246i
$457$	4.08985	−	7.08382i	0.191315	−	0.331367i	−0.754371	−	0.656448i	$-0.772058\pi$
$457$	4.08985	−	7.08382i	0.191315	−	0.331367i	0.945686	+	0.325081i	$0.105391\pi$
$458$	21.6051			1.00954
$459$			21.3774i			0.997812i
$460$		−	3.91777i		−	0.182667i
$461$	−21.9952	−	12.6990i	−1.02442	−	0.591450i	−0.109039	−	0.994037i	$-0.534777\pi$
$461$	−21.9952	−	12.6990i	−1.02442	−	0.591450i	−0.915381	+	0.402588i	$0.868111\pi$
$462$	−2.85734	−	1.54230i	−0.132935	−	0.0717544i
$463$	−16.1315			−0.749696			−0.374848	−	0.927086i	$-0.622305\pi$
$463$	−16.1315			−0.749696			−0.374848	+	0.927086i	$0.622305\pi$
$464$	−85.1094	−	49.1379i	−3.95110	−	2.28117i
$465$	−0.295842	−	0.170804i	−0.0137193	−	0.00792087i
$466$	47.6407	+	27.5054i	2.20691	+	1.27416i
$467$	8.65065	+	4.99446i	0.400304	+	0.231116i	0.686615	−	0.727021i	$-0.259096\pi$
$467$	8.65065	+	4.99446i	0.400304	+	0.231116i	−0.286311	+	0.958137i	$0.592429\pi$
$468$	−4.17695			−0.193079
$469$	−15.5767	−	8.40780i	−0.719264	−	0.388236i
$470$	−0.465438	−	0.268721i	−0.0214690	−	0.0123952i
$471$			22.9282i			1.05648i
$472$			42.5674i			1.95932i
$473$	−0.211112			−0.00970695
$474$	24.8935	−	43.1167i	1.14339	−	1.98042i
$475$	−14.1672	+	16.4696i	−0.650036	+	0.755677i
$476$	48.7819	+	26.3310i	2.23592	+	1.20688i
$477$	0.581613	+	0.335794i	0.0266302	+	0.0153750i
$478$	24.2392	−	13.9945i	1.10868	−	0.640094i
$479$	−32.7340	−	18.8990i	−1.49565	−	0.863516i	−0.495665	−	0.868514i	$-0.665076\pi$
$479$	−32.7340	−	18.8990i	−1.49565	−	0.863516i	−0.999988	+	0.00499790i	$0.998409\pi$
$480$	−3.71676			−0.169646
$481$		−	40.3246i		−	1.83864i
$482$			39.0456i			1.77848i
$483$	−26.1634	+	0.749645i	−1.19048	+	0.0341100i
$484$	−28.6333	−	49.5944i	−1.30152	−	2.25429i
$485$			1.50527i			0.0683509i
$486$	4.60316	−	2.65764i	0.208804	−	0.120553i
$487$	−26.5268	+	15.3153i	−1.20205	+	0.694001i	−0.961010	−	0.276515i	$-0.910820\pi$
$487$	−26.5268	+	15.3153i	−1.20205	+	0.694001i	−0.241036	+	0.970516i	$0.577487\pi$
$488$	−1.40226			−0.0634775
$489$	6.60154	−	11.4342i	0.298532	−	0.517072i
$490$	−1.07257	+	2.13094i	−0.0484538	+	0.0962660i
$491$	9.20497	−	15.9435i	0.415415	−	0.719519i	−0.580057	−	0.814576i	$-0.696970\pi$
$491$	9.20497	−	15.9435i	0.415415	−	0.719519i	0.995472	+	0.0950565i	$0.0303032\pi$
$492$	−19.5483	−	33.8587i	−0.881307	−	1.52647i
$493$	15.1228	+	26.1935i	0.681099	+	1.17970i
$494$	−37.2271	−	32.0229i	−1.67493	−	1.44078i
$495$	0.00568073	+	0.00327977i	0.000255330	+	0.000147415i
$496$	10.4508	−	18.1013i	0.469254	−	0.812771i
$497$	−15.1483	−	8.17655i	−0.679492	−	0.366769i
$498$	−39.9526	−	69.1999i	−1.79032	−	3.10092i
$499$	−5.42264	−	9.39229i	−0.242751	−	0.420457i	0.718746	−	0.695273i	$-0.244716\pi$
$499$	−5.42264	−	9.39229i	−0.242751	−	0.420457i	−0.961497	+	0.274816i	$0.911383\pi$
$500$	5.73950	+	3.31370i	0.256678	+	0.148193i
$501$	−8.06478	−	13.9686i	−0.360308	−	0.624072i
$502$	−1.58872	+	2.75174i	−0.0709079	+	0.122816i
$503$	25.0660	−	14.4719i	1.11764	−	0.645269i	0.176842	−	0.984239i	$-0.443412\pi$
$503$	25.0660	−	14.4719i	1.11764	−	0.645269i	0.940797	+	0.338970i	$0.110079\pi$
$504$	−0.125817	−	4.39116i	−0.00560435	−	0.195598i
$505$	−1.03749			−0.0461679
$506$	3.74230	+	2.16062i	0.166366	+	0.0960512i
$507$	3.79325	−	6.57010i	0.168464	−	0.291788i
$508$			17.2678i			0.766135i
$509$	−16.1379			−0.715299			−0.357650	−	0.933856i	$-0.616422\pi$
$509$	−16.1379			−0.715299			−0.357650	+	0.933856i	$0.616422\pi$
$510$	1.97767	+	1.14181i	0.0875728	+	0.0505602i
$511$	1.12618	+	39.3049i	0.0498192	+	1.73875i
$512$		−	0.824426i		−	0.0364348i
$513$	22.9045	+	4.32878i	1.01126	+	0.191120i
$514$	55.0103	−	31.7602i	2.42640	−	1.40088i
$515$		−	0.344845i		−	0.0151957i
$516$	3.40840	+	5.90353i	0.150047	+	0.259888i
$517$	0.371581	−	0.214532i	0.0163421	−	0.00943512i
$518$	68.5501	−	1.96413i	3.01192	−	0.0862987i
$519$	11.2781	+	19.5343i	0.495054	+	0.857459i
$520$	−2.31230	+	4.00502i	−0.101401	+	0.175632i
$521$	8.61550	+	14.9225i	0.377452	+	0.653766i	0.990691	−	0.136131i	$-0.0434670\pi$
$521$	8.61550	+	14.9225i	0.377452	+	0.653766i	−0.613239	+	0.789898i	$0.710134\pi$
$522$	1.93788	−	3.35651i	0.0848189	−	0.146911i
$523$	2.45138			0.107191			0.0535957	−	0.998563i	$-0.482932\pi$
$523$	2.45138			0.107191			0.0535957	+	0.998563i	$0.482932\pi$
$524$			42.4458i			1.85425i
$525$	10.4987	−	19.4503i	0.458200	−	0.848882i
$526$	−4.69985	+	2.71346i	−0.204923	+	0.118312i
$527$	−5.57091	+	3.21637i	−0.242673	+	0.140107i
$528$	2.96189	−	5.13014i	0.128900	−	0.223261i
$529$	11.8335			0.514501
$530$	1.04128	−	0.601182i	0.0452302	−	0.0261137i
$531$	−0.929006			−0.0403154
$532$	38.0899	−	46.9349i	1.65141	−	2.03488i
$533$	−18.6300			−0.806957
$534$	7.76857	−	4.48518i	0.336179	−	0.194093i
$535$	−0.583924			−0.0252453
$536$	29.1777	−	50.5373i	1.26028	−	2.18288i
$537$	−9.78170	+	5.64747i	−0.422112	+	0.243706i
$538$	−63.1061	+	36.4343i	−2.72070	+	1.57080i
$539$	−1.04517	−	1.59218i	−0.0450185	−	0.0685800i
$540$		−	3.54981i		−	0.152760i
$541$	−3.02526			−0.130066			−0.0650330	−	0.997883i	$-0.520715\pi$
$541$	−3.02526			−0.130066			−0.0650330	+	0.997883i	$0.520715\pi$
$542$	36.0549	−	62.4489i	1.54869	−	2.68241i
$543$	−4.57208	−	7.91908i	−0.196207	−	0.339840i
$544$	−34.9946	+	60.6124i	−1.50038	+	2.59874i
$545$	−0.253135	−	0.438443i	−0.0108431	−	0.0187808i
$546$	43.9646	+	23.7307i	1.88151	+	1.01558i
$547$	−13.9695	+	8.06531i	−0.597294	+	0.344848i	−0.767976	−	0.640478i	$-0.778736\pi$
$547$	−13.9695	+	8.06531i	−0.597294	+	0.344848i	0.170682	+	0.985326i	$0.445403\pi$
$548$	−10.5858	−	18.3351i	−0.452203	−	0.783238i
$549$		−	0.0306036i		−	0.00130613i
$550$	−3.16020	+	1.82454i	−0.134751	+	0.0777987i
$551$	31.1269	−	10.8991i	1.32605	−	0.464319i
$552$		−	86.2894i		−	3.67272i
$553$	24.8621	−	15.3199i	1.05724	−	0.651469i
$554$	18.5570	+	10.7139i	0.788410	+	0.455189i
$555$	2.04481			0.0867972
$556$			86.7738i			3.68003i
$557$	−5.07899	+	8.79708i	−0.215204	+	0.372744i	−0.953336	−	0.301913i	$-0.902375\pi$
$557$	−5.07899	+	8.79708i	−0.215204	+	0.372744i	0.738132	+	0.674657i	$0.235708\pi$
$558$	0.713872	+	0.412154i	0.0302206	+	0.0174479i
$559$	3.24829			0.137388
$560$	−3.83000	−	2.06732i	−0.161847	−	0.0873600i
$561$	−1.57887	+	0.911560i	−0.0666599	+	0.0384861i
$562$	−37.8832	+	65.6156i	−1.59801	+	2.76783i
$563$	−17.3744	−	30.0933i	−0.732243	−	1.26828i	−0.955923	−	0.293619i	$-0.905140\pi$
$563$	−17.3744	−	30.0933i	−0.732243	−	1.26828i	0.223680	−	0.974663i	$-0.428193\pi$
$564$	−11.9983	−	6.92724i	−0.505221	−	0.291689i
$565$	0.489129	+	0.847196i	0.0205778	+	0.0356418i
$566$	27.1856	+	47.0868i	1.14270	+	1.97921i
$567$	−22.1958	+	0.635964i	−0.932138	+	0.0267080i
$568$	28.3752	−	49.1473i	1.19060	−	2.06217i
$569$	−23.9526	−	13.8290i	−1.00415	−	0.579744i	−0.0946735	−	0.995508i	$-0.530181\pi$
$569$	−23.9526	−	13.8290i	−1.00415	−	0.579744i	−0.909472	+	0.415765i	$0.863514\pi$
$570$	1.62384	−	1.88774i	0.0680151	−	0.0790686i
$571$	−17.5951	−	30.4755i	−0.736330	−	1.27536i	−0.954137	−	0.299369i	$-0.903224\pi$
$571$	−17.5951	−	30.4755i	−0.736330	−	1.27536i	0.217807	−	0.975992i	$-0.430110\pi$
$572$	−2.98506	−	5.17028i	−0.124812	−	0.216180i
$573$	0.0115326	−	0.0199751i	0.000481782	−	0.000834471i
$574$	−0.907431	−	31.6703i	−0.0378754	−	1.32189i
$575$	−14.7076	+	25.4744i	−0.613351	+	1.06236i
$576$	4.02347			0.167645
$577$	12.3184	−	7.11201i	0.512820	−	0.296077i	−0.221172	−	0.975235i	$-0.570988\pi$
$577$	12.3184	−	7.11201i	0.512820	−	0.296077i	0.733992	+	0.679158i	$0.237655\pi$
$578$	−2.37676	+	1.37222i	−0.0988601	+	0.0570769i
$579$			5.20778i			0.216428i
$580$	−2.51122	−	4.34955i	−0.104273	−	0.180605i
$581$	−1.34237	−	46.8502i	−0.0556909	−	1.94367i
$582$			53.6107i			2.22223i
$583$			0.959905i			0.0397552i
$584$	−129.631			−5.36417
$585$	−0.0874070	−	0.0504644i	−0.00361383	−	0.00208645i
$586$	−39.6259	+	22.8780i	−1.63693	+	0.945082i
$587$	−28.9712	−	16.7265i	−1.19577	−	0.690377i	−0.236160	−	0.971714i	$-0.575889\pi$
$587$	−28.9712	−	16.7265i	−1.19577	−	0.690377i	−0.959609	+	0.281337i	$0.909222\pi$
$588$	−27.6494	+	54.9326i	−1.14024	+	2.26538i
$589$	2.31806	+	6.62016i	0.0955139	+	0.272779i
$590$	−0.831613	+	1.44040i	−0.0342370	+	0.0593002i
$591$	10.0429			0.413109
$592$			125.113i			5.14210i
$593$			46.1450i			1.89495i	0.319832	+	0.947474i	$0.396373\pi$
$593$			46.1450i			1.89495i	−0.319832	+	0.947474i	$0.603627\pi$
$594$	3.39082	+	1.95769i	0.139127	+	0.0803251i
$595$	0.702692	+	1.14037i	0.0288075	+	0.0467506i
$596$	65.4462			2.68078
$597$	−14.5563	−	8.40409i	−0.595750	−	0.343956i
$598$	−57.5811	−	33.2445i	−2.35467	−	1.35947i
$599$	19.5863	+	11.3081i	0.800273	+	0.462038i	0.843567	−	0.537024i	$-0.180452\pi$
$599$	19.5863	+	11.3081i	0.800273	+	0.462038i	−0.0432933	+	0.999062i	$0.513785\pi$
$600$	63.1050	+	36.4337i	2.57625	+	1.48740i
$601$	−12.3958			−0.505633			−0.252817	−	0.967514i	$-0.581357\pi$
$601$	−12.3958			−0.505633			−0.252817	+	0.967514i	$0.581357\pi$
$602$	0.158218	+	5.52197i	0.00644847	+	0.225059i
$603$	1.10294	+	0.636785i	0.0449154	+	0.0259319i
$604$		−	4.45452i		−	0.181252i
$605$		−	1.38375i		−	0.0562576i
$606$	−36.9506			−1.50102
$607$	−8.64849	+	14.9796i	−0.351031	+	0.608004i	−0.986430	−	0.164180i	$-0.947502\pi$
$607$	−8.64849	+	14.9796i	−0.351031	+	0.608004i	0.635399	+	0.772184i	$0.280836\pi$
$608$	57.8561	+	49.7680i	2.34637	+	2.01836i
$609$	−28.5664	+	17.6025i	−1.15757	+	0.713290i
$610$	−0.0474499	−	0.0273952i	−0.00192119	−	0.00110920i
$611$	−5.71735	+	3.30092i	−0.231299	+	0.133541i
$612$	−3.45412	−	1.99424i	−0.139625	−	0.0806124i
$613$	22.6801			0.916041			0.458021	−	0.888942i	$-0.348559\pi$
$613$	22.6801			0.916041			0.458021	+	0.888942i	$0.348559\pi$
$614$			20.2543i			0.817397i
$615$		−	0.944705i		−	0.0380942i
$616$	5.34553	−	3.29389i	0.215377	−	0.132715i
$617$	−11.2707	−	19.5215i	−0.453742	−	0.785905i	0.544873	−	0.838519i	$-0.316578\pi$
$617$	−11.2707	−	19.5215i	−0.453742	−	0.785905i	−0.998615	+	0.0526142i	$0.983245\pi$
$618$		−	12.2817i		−	0.494044i
$619$	−22.7017	+	13.1069i	−0.912460	+	0.526809i	−0.881222	−	0.472703i	$-0.843278\pi$
$619$	−22.7017	+	13.1069i	−0.912460	+	0.526809i	−0.0312382	+	0.999512i	$0.509945\pi$
$620$	0.925074	−	0.534092i	0.0371519	−	0.0214496i
$621$	31.5619			1.26654
$622$	−1.28343	+	2.22296i	−0.0514608	+	0.0891326i
$623$	5.25952	−	0.150698i	0.210718	−	0.00603759i
$624$	−45.5733	+	78.9352i	−1.82439	+	3.15994i
$625$	−12.3798	−	21.4425i	−0.495193	−	0.857700i
$626$	7.56161	+	13.0971i	0.302223	+	0.523465i
$627$	0.656968	+	1.87624i	0.0262368	+	0.0749298i
$628$	−62.0893	−	35.8473i	−2.47763	−	1.43046i
$629$	19.2525	−	33.3464i	0.767649	−	1.32961i
$630$	0.0815301	−	0.151046i	0.00324824	−	0.00601783i
$631$	7.89100	+	13.6676i	0.314136	+	0.544099i	0.979253	−	0.202639i	$-0.0649519\pi$
$631$	7.89100	+	13.6676i	0.314136	+	0.544099i	−0.665118	+	0.746739i	$0.731619\pi$
$632$	48.1375	+	83.3767i	1.91481	+	3.31655i
$633$	4.74921	+	2.74196i	0.188764	+	0.108983i
$634$	−29.0835	−	50.3741i	−1.15505	−	2.00061i
$635$	−0.208624	+	0.361347i	−0.00827898	+	0.0143396i
$636$	26.8427	−	15.4976i	1.06438	−	0.614521i
$637$	16.0815	+	24.4982i	0.637173	+	0.970652i
$638$	5.53965			0.219317
$639$	1.07261	+	0.619271i	0.0424318	+	0.0244980i
$640$	1.38429	−	2.39767i	0.0547190	−	0.0947760i
$641$		−	10.5735i		−	0.417628i	−0.977955	−	0.208814i	$-0.933040\pi$
$641$		−	10.5735i		−	0.417628i	0.977955	−	0.208814i	$-0.0669604\pi$
$642$	−20.7966			−0.820777
$643$	−40.5307	−	23.4004i	−1.59838	−	0.922822i	−0.991800	−	0.127796i	$-0.959210\pi$
$643$	−40.5307	−	23.4004i	−1.59838	−	0.922822i	−0.606575	−	0.795026i	$-0.707457\pi$
$644$	38.8754	−	72.0224i	1.53191	−	2.83808i
$645$			0.164717i			0.00648571i
$646$	−15.4960	−	44.2550i	−0.609680	−	1.74119i
$647$	−11.1187	+	6.41939i	−0.437121	+	0.252372i	−0.702376	−	0.711806i	$-0.747877\pi$
$647$	−11.1187	+	6.41939i	−0.437121	+	0.252372i	0.265255	+	0.964178i	$0.414544\pi$
$648$		−	73.2039i		−	2.87572i
$649$	−0.663916	−	1.14994i	−0.0260610	−	0.0451390i
$650$	48.6246	−	28.0734i	1.90721	−	1.10113i
$651$	−3.74375	−	6.07558i	−0.146729	−	0.238121i
$652$	20.6425	+	35.7538i	0.808421	+	1.40023i
$653$	1.49515	−	2.58968i	0.0585098	−	0.101342i	−0.835287	−	0.549814i	$-0.814698\pi$
$653$	1.49515	−	2.58968i	0.0585098	−	0.101342i	0.893797	+	0.448472i	$0.148032\pi$
$654$	−9.01547	−	15.6153i	−0.352533	−	0.610605i
$655$	−0.512816	+	0.888223i	−0.0200374	+	0.0347057i
$656$	57.8024			2.25680
$657$		−	2.82912i		−	0.110374i
$658$	−5.88990	−	9.55849i	−0.229612	−	0.372629i
$659$	29.4316	−	16.9924i	1.14649	−	0.661928i	0.198463	−	0.980108i	$-0.436405\pi$
$659$	29.4316	−	16.9924i	1.14649	−	0.661928i	0.948030	+	0.318180i	$0.103072\pi$
$660$	0.262178	−	0.151369i	0.0102053	−	0.00589202i
$661$	0.999203	−	1.73067i	0.0388645	−	0.0673153i	−0.845939	−	0.533280i	$-0.820959\pi$
$661$	0.999203	−	1.73067i	0.0388645	−	0.0673153i	0.884803	+	0.465965i	$0.154293\pi$
$662$	−5.86165			−0.227819
$663$	24.2934	−	14.0258i	0.943476	−	0.544716i
$664$	154.516			5.99639
$665$	1.36412	−	0.521971i	0.0528984	−	0.0202412i
$666$	−4.93415			−0.191195
$667$	38.6725	−	22.3276i	1.49741	−	0.864528i
$668$	50.4358			1.95142
$669$	−17.5794	+	30.4484i	−0.679658	+	1.17720i
$670$	1.97463	−	1.14005i	0.0762867	−	0.0440441i
$671$	0.0378815	−	0.0218709i	0.00146240	−	0.000844316i
$672$	−68.3271	−	36.8808i	−2.63578	−	1.42271i
$673$		−	29.4453i		−	1.13503i	−0.823362	−	0.567517i	$-0.807904\pi$
$673$		−	29.4453i		−	1.13503i	0.823362	−	0.567517i	$-0.192096\pi$
$674$	85.9309			3.30994
$675$	−13.3263	+	23.0818i	−0.512930	+	0.888420i
$676$	11.8612	+	20.5442i	0.456199	+	0.790160i
$677$	11.2661	−	19.5134i	0.432991	−	0.749963i	−0.564138	−	0.825680i	$-0.690791\pi$
$677$	11.2661	−	19.5134i	0.432991	−	0.749963i	0.997129	+	0.0757178i	$0.0241248\pi$
$678$	17.4204	+	30.1731i	0.669028	+	1.15879i
$679$	−14.9366	+	27.6722i	−0.573214	+	1.06196i
$680$	−3.82431	+	2.20796i	−0.146655	+	0.0846716i
$681$	4.40403	+	7.62800i	0.168763	+	0.292306i
$682$			1.17819i			0.0451151i
$683$	29.4817	−	17.0212i	1.12808	−	0.651300i	0.184632	−	0.982808i	$-0.440891\pi$
$683$	29.4817	−	17.0212i	1.12808	−	0.651300i	0.943452	+	0.331508i	$0.107557\pi$
$684$	−2.83614	+	3.29705i	−0.108442	+	0.126066i
$685$		−	0.511576i		−	0.0195463i
$686$	−40.8626	+	28.5312i	−1.56014	+	1.08933i
$687$	11.6547	+	6.72886i	0.444656	+	0.256722i
$688$	−10.0783			−0.384231
$689$		−	14.7696i		−	0.562678i
$690$	1.68578	−	2.91986i	0.0641767	−	0.111157i
$691$	−24.8441	−	14.3437i	−0.945113	−	0.545661i	−0.0535535	−	0.998565i	$-0.517055\pi$
$691$	−24.8441	−	14.3437i	−0.945113	−	0.545661i	−0.891559	+	0.452904i	$0.850388\pi$
$692$	−70.5315			−2.68121
$693$	0.0718871	+	0.116663i	0.00273077	+	0.00443165i
$694$	−72.5548	+	41.8895i	−2.75414	+	1.59010i
$695$	−1.04837	+	1.81583i	−0.0397670	+	0.0688785i
$696$	−55.3098	−	95.7994i	−2.09651	−	3.63127i
$697$	−15.4061	−	8.89472i	−0.583548	−	0.336912i
$698$	−18.7992	−	32.5612i	−0.711560	−	1.23246i
$699$	17.1330	+	29.6752i	0.648030	+	1.12242i
$700$	36.2571	+	58.8401i	1.37039	+	2.22395i
$701$	−15.8211	+	27.4030i	−0.597555	+	1.03500i	0.395626	+	0.918412i	$0.370528\pi$
$701$	−15.8211	+	27.4030i	−0.597555	+	1.03500i	−0.993181	+	0.116584i	$0.962806\pi$
$702$	−52.1731	−	30.1221i	−1.96915	−	1.13689i
$703$	−31.8300	−	27.3803i	−1.20049	−	1.03267i
$704$	2.87538	+	4.98031i	0.108370	+	0.187702i
$705$	−0.167385	−	0.289920i	−0.00630409	−	0.0109190i
$706$	−1.64534	+	2.84982i	−0.0619234	+	0.107254i
$707$	−19.0728	−	10.2949i	−0.717305	−	0.387179i
$708$	−21.4378	+	37.1314i	−0.805683	+	1.39548i
$709$	21.5060			0.807676			0.403838	−	0.914830i	$-0.367676\pi$
$709$	21.5060			0.807676			0.403838	+	0.914830i	$0.367676\pi$
$710$	1.92032	−	1.10870i	0.0720684	−	0.0416087i
$711$	−1.81964	+	1.05057i	−0.0682420	+	0.0393995i
$712$			17.3464i			0.650083i
$713$	4.74869	+	8.22497i	0.177840	+	0.308028i
$714$	25.0265	+	40.6146i	0.936595	+	1.51996i
$715$		−	0.144258i		−	0.00539495i
$716$		−	35.3183i		−	1.31991i
$717$	17.4343			0.651095
$718$	−3.40398	−	1.96529i	−0.127035	−	0.0733439i
$719$	8.40991	−	4.85547i	0.313637	−	0.181078i	−0.334916	−	0.942248i	$-0.608708\pi$
$719$	8.40991	−	4.85547i	0.313637	−	0.181078i	0.648553	+	0.761170i	$0.275375\pi$
$720$	0.271193	+	0.156573i	0.0101068	+	0.00583514i
$721$	3.42184	−	6.33946i	0.127436	−	0.236094i
$722$	−50.5542	+	7.64157i	−1.88143	+	0.284390i
$723$	−12.1607	+	21.0629i	−0.452261	+	0.783338i
$724$	28.5931			1.06265
$725$			37.7093i			1.40049i
$726$		−	49.2827i		−	1.82905i
$727$	34.1447	+	19.7135i	1.26636	+	0.731132i	0.974297	−	0.225268i	$-0.0723258\pi$
$727$	34.1447	+	19.7135i	1.26636	+	0.731132i	0.292060	+	0.956400i	$0.405659\pi$
$728$	−82.2493	+	50.6817i	−3.04836	+	1.87839i
$729$	28.4889			1.05515
$730$	−4.38646	−	2.53252i	−0.162350	−	0.0937329i
$731$	2.68617	+	1.55086i	0.0993518	+	0.0573608i
$732$	−1.22319	−	0.706210i	−0.0452105	−	0.0261023i
$733$	22.2094	+	12.8226i	0.820325	+	0.473615i	0.850528	−	0.525929i	$-0.176282\pi$
$733$	22.2094	+	12.8226i	0.820325	+	0.473615i	−0.0302038	+	0.999544i	$0.509616\pi$
$734$	20.6839			0.763455
$735$	−1.24227	+	0.815473i	−0.0458218	+	0.0300792i
$736$	89.4891	+	51.6665i	3.29861	+	1.90445i
$737$			1.82032i			0.0670523i
$738$			2.27959i			0.0839129i
$739$	29.6252			1.08978			0.544890	−	0.838508i	$-0.316572\pi$
$739$	29.6252			1.08978			0.544890	+	0.838508i	$0.316572\pi$
$740$	−3.19697	+	5.53732i	−0.117523	+	0.203556i
$741$	−10.1085	−	28.8689i	−0.371344	−	1.06053i
$742$	25.1078	−	0.719398i	0.921736	−	0.0264099i
$743$	33.2909	+	19.2205i	1.22133	+	0.705133i	0.965201	−	0.261511i	$-0.0842207\pi$
$743$	33.2909	+	19.2205i	1.22133	+	0.705133i	0.256125	+	0.966644i	$0.417554\pi$
$744$	20.3749	−	11.7634i	0.746979	−	0.431268i
$745$	1.36953	+	0.790699i	0.0501757	+	0.0289690i
$746$	−81.0725			−2.96827
$747$			3.37222i			0.123383i
$748$		−	5.70075i		−	0.208440i
$749$	−10.7346	−	5.79419i	−0.392233	−	0.211715i
$750$	2.85172	+	4.93932i	0.104130	+	0.180358i
$751$		−	5.86604i		−	0.214055i	−0.994256	−	0.107027i	$-0.965867\pi$
$751$		−	5.86604i		−	0.214055i	0.994256	−	0.107027i	$-0.0341333\pi$
$752$	17.7389	−	10.2416i	0.646872	−	0.373471i
$753$	−1.71405	+	0.989607i	−0.0624634	+	0.0360633i
$754$	−85.2362			−3.10412
$755$	0.0538179	−	0.0932154i	0.00195864	−	0.00339246i
$756$	35.2242	−	65.2580i	1.28109	−	2.37341i
$757$	−6.95292	+	12.0428i	−0.252708	+	0.437704i	−0.964271	−	0.264919i	$-0.914655\pi$
$757$	−6.95292	+	12.0428i	−0.252708	+	0.437704i	0.711562	+	0.702623i	$0.247988\pi$
$758$	12.9105	+	22.3617i	0.468931	+	0.812212i
$759$	1.34584	+	2.33107i	0.0488510	+	0.0846123i
$760$	1.59130	+	4.54459i	0.0577224	+	0.164850i
$761$	27.6597	+	15.9693i	1.00266	+	0.578888i	0.909035	−	0.416719i	$-0.136820\pi$
$761$	27.6597	+	15.9693i	1.00266	+	0.578888i	0.0936283	+	0.995607i	$0.470153\pi$
$762$	−7.43019	+	12.8695i	−0.269167	+	0.466211i
$763$	−0.302911	−	10.5719i	−0.0109661	−	0.382730i
$764$	0.0360616	+	0.0624604i	0.00130466	+	0.00225974i
$765$	−0.0481875	−	0.0834631i	−0.00174222	−	0.00301762i
$766$	−37.8090	−	21.8291i	−1.36610	−	0.788716i
$767$	10.2154	+	17.6936i	0.368856	+	0.638878i
$768$	13.8736	−	24.0297i	0.500619	−	0.867098i
$769$	−10.9992	+	6.35037i	−0.396640	+	0.229000i	−0.685033	−	0.728512i	$-0.740212\pi$
$769$	−10.9992	+	6.35037i	−0.396640	+	0.229000i	0.288393	+	0.957512i	$0.406879\pi$
$770$	0.245233	−	0.00702651i	0.00883758	−	0.000253218i
$771$	39.5667			1.42496
$772$	−14.1026	−	8.14216i	−0.507565	−	0.293043i
$773$	−27.3436	+	47.3605i	−0.983481	+	1.70344i	−0.334982	+	0.942225i	$0.608730\pi$
$773$	−27.3436	+	47.3605i	−0.983481	+	1.70344i	−0.648500	+	0.761215i	$0.724603\pi$
$774$		−	0.397464i		−	0.0142866i
$775$	−8.02010			−0.288091
$776$	−89.7802	−	51.8346i	−3.22292	−	1.86076i
$777$	37.5907	+	20.2903i	1.34856	+	0.727910i
$778$		−	44.7625i		−	1.60481i
$779$	−12.6497	+	14.7055i	−0.453224	+	0.526880i
$780$	−4.03402	+	2.32904i	−0.144441	+	0.0833931i
$781$			1.77025i			0.0633447i
$782$	−31.7445	−	54.9830i	−1.13518	−	1.96619i
$783$	35.0404	−	20.2306i	1.25224	−	0.722982i
$784$	−49.8952	−	76.0090i	−1.78197	−	2.71461i
$785$	−0.866190	−	1.50028i	−0.0309156	−	0.0535475i
$786$	−18.2641	+	31.6343i	−0.651458	+	1.12836i
$787$	23.3167	+	40.3858i	0.831152	+	1.43960i	0.897126	+	0.441775i	$0.145651\pi$
$787$	23.3167	+	40.3858i	0.831152	+	1.43960i	−0.0659741	+	0.997821i	$0.521015\pi$
$788$	−15.7016	+	27.1960i	−0.559348	+	0.968819i
$789$	−3.38041			−0.120346
$790$			3.76174i			0.133837i
$791$	0.585310	+	20.4280i	0.0208112	+	0.726335i
$792$	−0.391236	+	0.225880i	−0.0139020	+	0.00802631i
$793$	−0.582866	+	0.336518i	−0.0206982	+	0.0119501i
$794$	−34.1393	+	59.1311i	−1.21156	+	2.09848i
$795$	0.748949			0.0265625
$796$	45.5164	−	26.2789i	1.61329	−	0.931431i
$797$	−1.22513			−0.0433965			−0.0216982	−	0.999765i	$-0.506907\pi$
$797$	−1.22513			−0.0433965			−0.0216982	+	0.999765i	$0.506907\pi$
$798$	48.5836	−	18.5901i	1.71984	−	0.658084i
$799$	−6.30395			−0.223018
$800$	−75.5694	+	43.6300i	−2.67178	+	1.54255i
$801$	−0.378574			−0.0133763
$802$	33.1529	−	57.4225i	1.17067	−	2.02766i
$803$	3.50192	−	2.02183i	0.123580	−	0.0713490i
$804$	50.9033	−	29.3890i	1.79522	−	1.03647i
$805$	1.68366	−	1.03746i	0.0593412	−	0.0365658i
$806$		−	18.1283i		−	0.638541i
$807$	−45.3896			−1.59779
$808$	35.7265	−	61.8801i	1.25685	−	2.17693i
$809$	−7.17891	−	12.4342i	−0.252397	−	0.437164i	0.711788	−	0.702394i	$-0.247886\pi$
$809$	−7.17891	−	12.4342i	−0.252397	−	0.437164i	−0.964185	+	0.265230i	$0.914552\pi$
$810$	1.43014	−	2.47708i	0.0502500	−	0.0870356i
$811$	21.9700	+	38.0532i	0.771473	+	1.33623i	0.936756	+	0.349984i	$0.113813\pi$
$811$	21.9700	+	38.0532i	0.771473	+	1.33623i	−0.165283	+	0.986246i	$0.552854\pi$
$812$	−3.00502	−	104.878i	−0.105455	−	3.68051i
$813$	38.8992	−	22.4585i	1.36425	−	0.787653i
$814$	−3.52620	−	6.10756i	−0.123593	−	0.214070i
$815$			0.997581i			0.0349437i
$816$	−75.3736	+	43.5170i	−2.63861	+	1.52340i
$817$	2.20558	−	2.56402i	0.0771635	−	0.0897038i
$818$			6.57063i			0.229737i
$819$	−1.10610	−	1.79504i	−0.0386501	−	0.0627237i
$820$	2.55825	+	1.47701i	0.0893381	+	0.0515794i
$821$	−26.5661			−0.927162			−0.463581	−	0.886055i	$-0.653436\pi$
$821$	−26.5661			−0.927162			−0.463581	+	0.886055i	$0.653436\pi$
$822$		−	18.2199i		−	0.635492i
$823$	14.3654	−	24.8815i	0.500745	−	0.867316i	−0.499255	−	0.866455i	$-0.666393\pi$
$823$	14.3654	−	24.8815i	0.500745	−	0.867316i	1.00000		0.000860496i	$-0.000273905\pi$
$824$	20.5679	+	11.8749i	0.716516	+	0.413681i
$825$	−2.27300			−0.0791358
$826$	−29.5808	+	18.2276i	−1.02925	+	0.634218i
$827$	34.5971	−	19.9746i	1.20306	−	0.694586i	0.241824	−	0.970320i	$-0.422254\pi$
$827$	34.5971	−	19.9746i	1.20306	−	0.694586i	0.961234	+	0.275735i	$0.0889211\pi$
$828$	−2.94433	+	5.09972i	−0.102322	+	0.177228i
$829$	16.6735	+	28.8794i	0.579096	+	1.00302i	0.995583	+	0.0938824i	$0.0299278\pi$
$829$	16.6735	+	28.8794i	0.579096	+	1.00302i	−0.416487	+	0.909142i	$0.636739\pi$
$830$	5.22852	+	3.01869i	0.181485	+	0.104780i
$831$	6.67363	+	11.5591i	0.231506	+	0.400980i
$832$	−44.2423	−	76.6298i	−1.53382	−	2.65666i
$833$	1.60222	+	27.9367i	0.0555137	+	0.967949i
$834$	−37.3380	+	64.6714i	−1.29291	+	2.23939i
$835$	1.05542	+	0.609349i	0.0365244	+	0.0210874i
$836$	−6.10799	−	1.15436i	−0.211249	−	0.0399245i
$837$	4.30269	+	7.45248i	0.148723	+	0.257595i
$838$	17.8984	+	31.0010i	0.618291	+	1.07091i
$839$	−7.43354	+	12.8753i	−0.256634	+	0.444504i	−0.965338	−	0.261002i	$-0.915947\pi$
$839$	−7.43354	+	12.8753i	−0.256634	+	0.444504i	0.708704	+	0.705506i	$0.249280\pi$
$840$	−2.57000	−	4.17075i	−0.0886735	−	0.143905i
$841$	14.1231	−	24.4619i	0.487003	−	0.843515i
$842$	64.0249			2.20645
$843$	−40.8718	+	23.5973i	−1.40770	+	0.812735i
$844$	−14.8504	+	8.57388i	−0.511172	+	0.295125i
$845$			0.573211i			0.0197191i
$846$	0.403903	+	0.699581i	0.0138865	+	0.0240521i
$847$	13.7308	−	25.4382i	0.471795	−	0.874068i
$848$			45.8249i			1.57363i
$849$			33.8676i			1.16233i
$850$	53.6135			1.83893
$851$	−49.2331	−	28.4248i	−1.68769	−	0.974388i
$852$	49.5032	−	28.5807i	1.69595	−	0.979159i
$853$	−7.84936	−	4.53183i	−0.268757	−	0.155167i	0.359566	−	0.933120i	$-0.382925\pi$
$853$	−7.84936	−	4.53183i	−0.268757	−	0.155167i	−0.628323	+	0.777953i	$0.716258\pi$
$854$	−0.600457	−	0.974458i	−0.0205472	−	0.0333453i
$855$	−0.0991830	+	0.0347290i	−0.00339199	+	0.00118771i
$856$	20.1077	−	34.8275i	0.687265	−	1.19038i
$857$	23.9678			0.818723			0.409362	−	0.912372i	$-0.365751\pi$
$857$	23.9678			0.818723			0.409362	+	0.912372i	$0.365751\pi$
$858$		−	5.13779i		−	0.175401i
$859$			26.9123i			0.918236i	0.888375	+	0.459118i	$0.151834\pi$
$859$			26.9123i			0.918236i	−0.888375	+	0.459118i	$0.848166\pi$
$860$	−0.446051	−	0.257528i	−0.0152102	−	0.00878163i
$861$	9.37416	−	17.3670i	0.319471	−	0.591866i
$862$	−13.2273			−0.450523
$863$	6.58569	+	3.80225i	0.224179	+	0.129430i	0.607884	−	0.794026i	$-0.292019\pi$
$863$	6.58569	+	3.80225i	0.224179	+	0.129430i	−0.383705	+	0.923456i	$0.625352\pi$
$864$	81.0842	+	46.8140i	2.75854	+	1.59264i
$865$	−1.47595	−	0.852138i	−0.0501837	−	0.0289736i
$866$	38.5214	+	22.2404i	1.30901	+	0.755758i
$867$	−1.70951			−0.0580578
$868$	22.3058	−	0.639115i	0.757109	−	0.0216930i
$869$	−2.60082	−	1.50159i	−0.0882269	−	0.0509378i
$870$		−	4.32222i		−	0.146537i
$871$		−	28.0085i		−	0.949030i
$872$	34.8672			1.18075
$873$	1.13126	−	1.95940i	0.0382873	−	0.0663156i
$874$	−65.3388	+	22.8785i	−2.21012	+	0.773876i
$875$	0.0958149	+	3.34405i	0.00323914	+	0.113049i
$876$	−113.077	−	65.2849i	−3.82051	−	2.20577i
$877$	−12.5573	+	7.24994i	−0.424029	+	0.244813i	−0.696800	−	0.717266i	$-0.745393\pi$
$877$	−12.5573	+	7.24994i	−0.424029	+	0.244813i	0.272771	+	0.962079i	$0.412060\pi$
$878$	71.5607	+	41.3156i	2.41506	+	1.39433i
$879$	−28.5013			−0.961324
$880$			0.447581i			0.0150880i
$881$			4.60281i			0.155073i	0.996990	+	0.0775363i	$0.0247054\pi$
$881$			4.60281i			0.155073i	−0.996990	+	0.0775363i	$0.975295\pi$
$882$	2.99762	−	1.96775i	0.100935	−	0.0662576i
$883$	1.55869	+	2.69974i	0.0524543	+	0.0908534i	0.891060	−	0.453885i	$-0.149962\pi$
$883$	1.55869	+	2.69974i	0.0524543	+	0.0908534i	−0.838606	+	0.544738i	$0.816629\pi$
$884$			87.7150i			2.95017i
$885$	−0.897218	+	0.518009i	−0.0301596	+	0.0174127i
$886$	12.1211	−	6.99812i	0.407216	−	0.235107i
$887$	−6.75321			−0.226751			−0.113375	−	0.993552i	$-0.536166\pi$
$887$	−6.75321			−0.226751			−0.113375	+	0.993552i	$0.536166\pi$
$888$	−70.4136	+	121.960i	−2.36293	+	4.09271i
$889$	−7.42082	+	4.57268i	−0.248886	+	0.153363i
$890$	−0.338886	+	0.586968i	−0.0113595	+	0.0196752i
$891$	1.14175	+	1.97757i	0.0382500	+	0.0662510i
$892$	−54.9693	−	95.2096i	−1.84051	−	3.18785i
$893$	−1.27651	+	6.75428i	−0.0427167	+	0.226023i
$894$	48.7762	+	28.1609i	1.63132	+	0.941843i
$895$	0.426704	−	0.739073i	0.0142632	−	0.0247045i
$896$	49.2398	−	30.3414i	1.64499	−	1.01363i
$897$	−20.7079	−	35.8671i	−0.691416	−	1.19757i
$898$	−41.5978	−	72.0495i	−1.38814	−	2.40432i
$899$	10.5441	+	6.08763i	0.351665	+	0.203034i
$900$	−2.48635	−	4.30648i	−0.0828783	−	0.143549i
$901$	7.05161	−	12.2138i	0.234923	−	0.406899i
$902$	−2.82171	+	1.62911i	−0.0939526	+	0.0542436i
$903$	−1.63446	+	3.02807i	−0.0543913	+	0.100768i
$904$	−67.3733			−2.24080
$905$	0.598340	+	0.345452i	0.0198895	+	0.0114832i
$906$	1.91674	−	3.31989i	0.0636794	−	0.110296i
$907$		−	13.3638i		−	0.443736i	−0.975077	−	0.221868i	$-0.928785\pi$
$907$		−	13.3638i		−	0.443736i	0.975077	−	0.221868i	$-0.0712154\pi$
$908$	−27.5421			−0.914016
$909$	1.35049	+	0.779708i	0.0447931	+	0.0258613i
$910$	−3.77329	+	0.108114i	−0.125083	+	0.00358394i
$911$		−	43.1749i		−	1.43045i	−0.698895	−	0.715224i	$-0.746325\pi$
$911$		−	43.1749i		−	1.43045i	0.698895	−	0.715224i	$-0.253675\pi$
$912$	31.3630	+	89.5699i	1.03853	+	2.96595i
$913$	−4.17418	+	2.40996i	−0.138145	+	0.0797581i
$914$			22.0113i			0.728070i
$915$	−0.0170644	−	0.0295564i	−0.000564131	−	0.000977104i
$916$	−36.4434	+	21.0406i	−1.20412	+	0.695201i
$917$	−18.2410	+	11.2401i	−0.602372	+	0.371180i
$918$	−28.7630	−	49.8190i	−0.949321	−	1.64427i
$919$	23.0514	−	39.9262i	0.760396	−	1.31704i	−0.182251	−	0.983252i	$-0.558338\pi$
$919$	23.0514	−	39.9262i	0.760396	−	1.31704i	0.942647	−	0.333792i	$-0.108328\pi$
$920$	3.25987	+	5.64627i	0.107475	+	0.186152i
$921$	−6.30817	+	10.9261i	−0.207861	+	0.360026i
$922$	68.3451			2.25083
$923$		−	27.2381i		−	0.896554i
$924$	6.32176	−	0.181134i	0.207971	−	0.00595886i
$925$	41.5751	−	24.0034i	1.36698	−	0.789227i
$926$	37.5937	−	21.7048i	1.23541	−	0.713262i
$927$	−0.259162	+	0.448881i	−0.00851198	+	0.0147432i
$928$	132.469			4.34851
$929$	−23.1452	+	13.3629i	−0.759369	+	0.438422i	−0.829069	−	0.559146i	$-0.811129\pi$
$929$	−23.1452	+	13.3629i	−0.759369	+	0.438422i	0.0697003	+	0.997568i	$0.477796\pi$
$930$	0.919260			0.0301437
$931$	30.2568	+	3.94031i	0.991627	+	0.129138i
$932$	−107.147			−3.50972
$933$	−1.38468	+	0.799443i	−0.0453322	+	0.0261726i
$934$	−26.8799			−0.879537
$935$	0.0688745	−	0.119294i	0.00225244	−	0.00390134i
$936$	6.01978	−	3.47552i	0.196763	−	0.113601i
$937$	−10.5920	+	6.11528i	−0.346025	+	0.199778i	−0.662933	−	0.748679i	$-0.730689\pi$
$937$	−10.5920	+	6.11528i	−0.346025	+	0.199778i	0.316908	+	0.948456i	$0.397355\pi$
$938$	47.6132	−	1.36423i	1.55463	−	0.0445438i
$939$			9.42021i			0.307417i
$940$	1.04680			0.0341428
$941$	−12.3506	+	21.3919i	−0.402619	+	0.697356i	−0.994041	−	0.109006i	$-0.965233\pi$
$941$	−12.3506	+	21.3919i	−0.402619	+	0.697356i	0.591422	+	0.806362i	$0.298567\pi$
$942$	−30.8496	−	53.4330i	−1.00513	−	1.74094i
$943$	−13.1323	+	22.7458i	−0.427647	+	0.740706i
$944$	−31.6947	−	54.8968i	−1.03157	−	1.78674i
$945$	1.52553	−	0.940026i	0.0496255	−	0.0305790i
$946$	0.491987	−	0.284049i	0.0159959	−	0.00923522i
$947$	−25.5341	−	44.2264i	−0.829748	−	1.43716i	−0.898236	−	0.439513i	$-0.855151\pi$
$947$	−25.5341	−	44.2264i	−0.829748	−	1.43716i	0.0684887	−	0.997652i	$-0.478182\pi$
$948$			96.9723i			3.14951i
$949$	−53.8825	+	31.1091i	−1.74910	+	1.00984i
$950$	10.8564	−	57.4434i	0.352227	−	1.86371i
$951$		−	36.2320i		−	1.17490i
$952$	−92.2135	+	2.64214i	−2.98866	+	0.0856322i
$953$	−33.4935	−	19.3375i	−1.08496	−	0.626402i	−0.152729	−	0.988268i	$-0.548806\pi$
$953$	−33.4935	−	19.3375i	−1.08496	−	0.626402i	−0.932230	+	0.361866i	$0.882140\pi$
$954$	−1.80723			−0.0585112
$955$			0.00174273i			5.63935e-5i
$956$	−27.2578	+	47.2118i	−0.881579	+	1.52694i
$957$	2.98833	+	1.72532i	0.0965992	+	0.0557715i
$958$	101.713			3.28620
$959$	5.07629	−	9.40456i	0.163922	−	0.303689i
$960$	3.88580	−	2.24347i	0.125414	−	0.0724076i
$961$	14.2053	−	24.6042i	0.458234	−	0.793685i
$962$	54.2562	+	93.9744i	1.74929	+	3.02986i
$963$	0.760088	+	0.438837i	0.0244935	+	0.0141413i
$964$	−38.0255	−	65.8620i	−1.22472	−	2.12127i
$965$	−0.196742	−	0.340766i	−0.00633333	−	0.0109697i
$966$	59.9640	−	36.9496i	1.92931	−	1.18883i
$967$	2.60618	−	4.51404i	0.0838092	−	0.145162i	−0.821074	−	0.570822i	$-0.806625\pi$
$967$	2.60618	−	4.51404i	0.0838092	−	0.145162i	0.904883	+	0.425660i	$0.139958\pi$
$968$	82.5323	+	47.6501i	2.65269	+	1.53153i
$969$	5.42395	−	28.6993i	0.174242	−	0.921955i
$970$	−2.02532	−	3.50797i	−0.0650293	−	0.112634i
$971$	−16.1434	−	27.9612i	−0.518066	−	0.897317i	−0.999780	−	0.0209884i	$-0.993319\pi$
$971$	−16.1434	−	27.9612i	−0.518066	−	0.897317i	0.481713	−	0.876329i	$-0.340015\pi$
$972$	−5.17641	+	8.96580i	−0.166033	+	0.287578i
$973$	−37.2910	+	22.9786i	−1.19549	+	0.736659i
$974$	41.2130	−	71.3830i	1.32055	−	2.28726i
$975$	34.9737			1.12005
$976$	1.80843	−	1.04409i	0.0578863	−	0.0334207i
$977$	−29.7229	+	17.1605i	−0.950918	+	0.549013i	−0.893366	−	0.449330i	$-0.851663\pi$
$977$	−29.7229	+	17.1605i	−0.950918	+	0.549013i	−0.0575522	+	0.998342i	$0.518330\pi$
$978$			35.5291i			1.13610i
$979$	−0.270549	−	0.468604i	−0.00864678	−	0.0149767i
$980$	−0.266056	−	4.63901i	−0.00849885	−	0.148188i
$981$			0.760955i			0.0242954i
$982$			49.5407i			1.58091i
$983$	−44.4390			−1.41739			−0.708693	−	0.705517i	$-0.750715\pi$
$983$	−44.4390			−1.41739			−0.708693	+	0.705517i	$0.750715\pi$
$984$	56.3458	+	32.5313i	1.79624	+	1.03706i
$985$	−0.657147	+	0.379404i	−0.0209384	+	0.0120888i
$986$	−70.4861	−	40.6952i	−2.24473	−	1.29600i
$987$	−0.200300	−	6.99067i	−0.00637561	−	0.222516i
$988$	93.9809	+	17.7617i	2.98993	+	0.565074i
$989$	2.28972	−	3.96591i	0.0728088	−	0.126109i
$990$	−0.0176516			−0.000561004
$991$		−	13.6035i		−	0.432129i	−0.976379	−	0.216065i	$-0.930678\pi$
$991$		−	13.6035i		−	0.432129i	0.976379	−	0.216065i	$-0.0693222\pi$
$992$			28.1738i			0.894520i
$993$	−3.16203	−	1.82560i	−0.100344	−	0.0579337i
$994$	46.3037	−	1.32671i	1.46866	−	0.0420807i
$995$	1.26997			0.0402608
$996$	134.784	+	77.8176i	4.27079	+	2.46574i
$997$	9.44958	+	5.45572i	0.299271	+	0.172784i	0.642115	−	0.766608i	$-0.278057\pi$
$997$	9.44958	+	5.45572i	0.299271	+	0.172784i	−0.342844	+	0.939392i	$0.611390\pi$
$998$	25.2744	+	14.5922i	0.800047	+	0.461907i
$999$	−44.6091	−	25.7551i	−1.41137	−	0.814855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.s.d.103.1	yes	16
7.2	even	3		931.2.p.h.293.8		16
7.3	odd	6		133.2.i.d.122.1	yes	16
7.4	even	3		931.2.i.g.521.1		16
7.5	odd	6		931.2.p.g.293.8		16
7.6	odd	2		931.2.s.g.901.1		16
19.12	odd	6		133.2.i.d.12.8	✓	16
133.12	even	6		931.2.p.h.734.8		16
133.31	even	6	inner	133.2.s.d.31.1	yes	16
133.69	even	6		931.2.i.g.411.8		16
133.88	odd	6		931.2.s.g.31.1		16
133.107	odd	6		931.2.p.g.734.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.i.d.12.8	✓	16	19.12	odd	6
133.2.i.d.122.1	yes	16	7.3	odd	6
133.2.s.d.31.1	yes	16	133.31	even	6	inner
133.2.s.d.103.1	yes	16	1.1	even	1	trivial
931.2.i.g.411.8		16	133.69	even	6
931.2.i.g.521.1		16	7.4	even	3
931.2.p.g.293.8		16	7.5	odd	6
931.2.p.g.734.8		16	133.107	odd	6
931.2.p.h.293.8		16	7.2	even	3
931.2.p.h.734.8		16	133.12	even	6
931.2.s.g.31.1		16	133.88	odd	6
931.2.s.g.901.1		16	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.33045 + 1.34549i) q^{2} -1.67620 q^{3} +(2.62067 - 4.53913i) q^{4} +(0.109680 - 0.0633240i) q^{5} +(3.90630 - 2.25530i) q^{6} +(2.64467 - 0.0757760i) q^{7} +8.72235i q^{8} -0.190360 q^{9} +O(q^{10})\)	\(q+(-2.33045 + 1.34549i) q^{2} -1.67620 q^{3} +(2.62067 - 4.53913i) q^{4} +(0.109680 - 0.0633240i) q^{5} +(3.90630 - 2.25530i) q^{6} +(2.64467 - 0.0757760i) q^{7} +8.72235i q^{8} -0.190360 q^{9} +(-0.170403 + 0.295147i) q^{10} +(-0.136041 - 0.235630i) q^{11} +(-4.39276 + 7.60848i) q^{12} +(2.09320 + 3.62554i) q^{13} +(-6.06131 + 3.73495i) q^{14} +(-0.183846 + 0.106144i) q^{15} +(-6.49447 - 11.2487i) q^{16} +3.99752i q^{17} +(0.443624 - 0.256127i) q^{18} +(4.28308 + 0.809469i) q^{19} -0.663805i q^{20} +(-4.43298 + 0.127016i) q^{21} +(0.634074 + 0.366083i) q^{22} +5.90199 q^{23} -14.6204i q^{24} +(-2.49198 + 4.31624i) q^{25} +(-9.75622 - 5.63276i) q^{26} +5.34768 q^{27} +(6.58683 - 12.2031i) q^{28} +(6.55245 - 3.78306i) q^{29} +(0.285630 - 0.494725i) q^{30} +(0.804591 + 1.39359i) q^{31} +(15.1625 + 8.75408i) q^{32} +(0.228032 + 0.394963i) q^{33} +(-5.37860 - 9.31601i) q^{34} +(0.285270 - 0.175782i) q^{35} +(-0.498870 + 0.864068i) q^{36} +(-8.34178 - 4.81613i) q^{37} +(-11.0706 + 3.87640i) q^{38} +(-3.50862 - 6.07712i) q^{39} +(0.552334 + 0.956671i) q^{40} +(-2.22506 + 3.85392i) q^{41} +(10.1600 - 6.26052i) q^{42} +(0.387957 - 0.671961i) q^{43} -1.42607 q^{44} +(-0.0208788 + 0.0120544i) q^{45} +(-13.7543 + 7.94105i) q^{46} +1.57697i q^{47} +(10.8860 + 18.8551i) q^{48} +(6.98852 - 0.400805i) q^{49} -13.4117i q^{50} -6.70063i q^{51} +21.9424 q^{52} +(-3.05534 - 1.76400i) q^{53} +(-12.4625 + 7.19522i) q^{54} +(-0.0298421 - 0.0172293i) q^{55} +(0.660945 + 23.0677i) q^{56} +(-7.17929 - 1.35683i) q^{57} +(-10.1801 + 17.6325i) q^{58} +4.88026 q^{59} +1.11267i q^{60} +0.160767i q^{61} +(-3.75012 - 2.16513i) q^{62} +(-0.503438 + 0.0144247i) q^{63} -21.1361 q^{64} +(0.459167 + 0.265100i) q^{65} +(-1.06283 - 0.613627i) q^{66} +(-5.79400 - 3.34517i) q^{67} +(18.1452 + 10.4762i) q^{68} -9.89291 q^{69} +(-0.428295 + 0.793478i) q^{70} +(-5.63464 - 3.25316i) q^{71} -1.66038i q^{72} +14.8619i q^{73} +25.9201 q^{74} +(4.17705 - 7.23487i) q^{75} +(14.8988 - 17.3201i) q^{76} +(-0.377638 - 0.612854i) q^{77} +(16.3534 + 9.44162i) q^{78} +(9.55897 - 5.51887i) q^{79} +(-1.42463 - 0.822512i) q^{80} -8.39268 q^{81} -11.9752i q^{82} -17.7150i q^{83} +(-11.0408 + 20.4548i) q^{84} +(0.253139 + 0.438449i) q^{85} +2.08796i q^{86} +(-10.9832 + 6.34116i) q^{87} +(2.05525 - 1.18660i) q^{88} +1.98873 q^{89} +(0.0324379 - 0.0561842i) q^{90} +(5.81055 + 9.42972i) q^{91} +(15.4672 - 26.7899i) q^{92} +(-1.34865 - 2.33594i) q^{93} +(-2.12179 - 3.67505i) q^{94} +(0.521029 - 0.182439i) q^{95} +(-25.4154 - 14.6736i) q^{96} +(-5.94274 + 10.2931i) q^{97} +(-15.7471 + 10.3370i) q^{98} +(0.0258967 + 0.0448545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9	\( 16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9} - 2 q^{10} - 9 q^{11} - 17 q^{12} + 15 q^{13} + 3 q^{14} - 12 q^{15} - 22 q^{16} - 3 q^{18} + 8 q^{19} - 10 q^{21} - 27 q^{22} + 30 q^{23} + 13 q^{25} - 9 q^{26} - 38 q^{27} + 35 q^{28} - 18 q^{29} - 32 q^{30} - 27 q^{31} + 27 q^{32} - 12 q^{33} - 16 q^{34} - 6 q^{35} + 4 q^{36} - 39 q^{37} + 27 q^{38} - 9 q^{39} + 9 q^{40} + 9 q^{41} + 48 q^{42} - 9 q^{43} + 18 q^{44} + 75 q^{45} - 36 q^{46} + 35 q^{48} - 8 q^{49} + 18 q^{53} - 18 q^{54} + 15 q^{56} - 22 q^{57} - 20 q^{58} + 18 q^{59} - 45 q^{62} - 46 q^{63} - 22 q^{64} - 36 q^{65} - 45 q^{66} + 18 q^{67} + 63 q^{68} + 30 q^{69} - 19 q^{70} - 9 q^{71} + 18 q^{74} + 10 q^{75} + 98 q^{76} + 30 q^{77} + 54 q^{78} + 21 q^{79} + 27 q^{80} + 40 q^{81} - 34 q^{84} + 31 q^{85} - 48 q^{87} + 18 q^{88} + 24 q^{89} + 28 q^{90} + 15 q^{91} + 54 q^{92} + 6 q^{93} - 49 q^{94} - 66 q^{95} - 69 q^{96} + q^{97} + 15 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9 - 2 * q^10 - 9 * q^11 - 17 * q^12 + 15 * q^13 + 3 * q^14 - 12 * q^15 - 22 * q^16 - 3 * q^18 + 8 * q^19 - 10 * q^21 - 27 * q^22 + 30 * q^23 + 13 * q^25 - 9 * q^26 - 38 * q^27 + 35 * q^28 - 18 * q^29 - 32 * q^30 - 27 * q^31 + 27 * q^32 - 12 * q^33 - 16 * q^34 - 6 * q^35 + 4 * q^36 - 39 * q^37 + 27 * q^38 - 9 * q^39 + 9 * q^40 + 9 * q^41 + 48 * q^42 - 9 * q^43 + 18 * q^44 + 75 * q^45 - 36 * q^46 + 35 * q^48 - 8 * q^49 + 18 * q^53 - 18 * q^54 + 15 * q^56 - 22 * q^57 - 20 * q^58 + 18 * q^59 - 45 * q^62 - 46 * q^63 - 22 * q^64 - 36 * q^65 - 45 * q^66 + 18 * q^67 + 63 * q^68 + 30 * q^69 - 19 * q^70 - 9 * q^71 + 18 * q^74 + 10 * q^75 + 98 * q^76 + 30 * q^77 + 54 * q^78 + 21 * q^79 + 27 * q^80 + 40 * q^81 - 34 * q^84 + 31 * q^85 - 48 * q^87 + 18 * q^88 + 24 * q^89 + 28 * q^90 + 15 * q^91 + 54 * q^92 + 6 * q^93 - 49 * q^94 - 66 * q^95 - 69 * q^96 + q^97 + 15 * q^98 + 18 * q^99

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