LMFDB - Embedded newform 429.2.n.b.313.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, 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:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 4 x^{18} + 4 x^{17} + 37 x^{16} - 74 x^{15} + 398 x^{14} - 224 x^{13} + 978 x^{12} + \cdots + 121 $ x^20 - x^19 + 4x^18 + 4x^17 + 37x^16 - 74x^15 + 398x^14 - 224x^13 + 978x^12 + 115x^11 + 1963x^10 + 323x^9 + 3007x^8 + 1828x^7 + 6736x^6 + 4512x^5 + 5197x^4 + 2152x^3 + 1259x^2 + 495x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			313.2
Root			$-0.262109 + 0.806688i$ of defining polynomial
Character	$\chi$	$=$	429.313
Dual form			429.2.n.b.196.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.262109 - 0.806688i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.03599 - 0.752690i) q^{4} +(-1.08398 + 3.33616i) q^{5} +(0.262109 - 0.806688i) q^{6} +(-2.82268 + 2.05079i) q^{7} +(-2.25115 - 1.63555i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.262109 - 0.806688i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.03599 - 0.752690i) q^{4} +(-1.08398 + 3.33616i) q^{5} +(0.262109 - 0.806688i) q^{6} +(-2.82268 + 2.05079i) q^{7} +(-2.25115 - 1.63555i) q^{8} +(0.309017 + 0.951057i) q^{9} +2.97536 q^{10} +(0.233160 + 3.30842i) q^{11} +1.28055 q^{12} +(-0.309017 - 0.951057i) q^{13} +(2.39420 + 1.73949i) q^{14} +(-2.83791 + 2.06186i) q^{15} +(0.0620883 - 0.191088i) q^{16} +(-1.81366 + 5.58187i) q^{17} +(0.686210 - 0.498561i) q^{18} +(-0.666652 - 0.484351i) q^{19} +(1.38810 + 4.27213i) q^{20} -3.48902 q^{21} +(2.60775 - 1.05525i) q^{22} +2.78699 q^{23} +(-0.859862 - 2.64638i) q^{24} +(-5.90987 - 4.29377i) q^{25} +(-0.686210 + 0.498561i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-1.38065 + 4.24920i) q^{28} +(5.89094 - 4.28002i) q^{29} +(2.40712 + 1.74888i) q^{30} +(0.0338344 + 0.104131i) q^{31} -5.73557 q^{32} +(-1.75601 + 2.81362i) q^{33} +4.97821 q^{34} +(-3.78204 - 11.6399i) q^{35} +(1.03599 + 0.752690i) q^{36} +(2.59738 - 1.88711i) q^{37} +(-0.215985 + 0.664733i) q^{38} +(0.309017 - 0.951057i) q^{39} +(7.89669 - 5.73728i) q^{40} +(-4.80992 - 3.49461i) q^{41} +(0.914503 + 2.81455i) q^{42} +7.10223 q^{43} +(2.73177 + 3.25199i) q^{44} -3.50785 q^{45} +(-0.730494 - 2.24823i) q^{46} +(9.12990 + 6.63326i) q^{47} +(0.162549 - 0.118099i) q^{48} +(1.59863 - 4.92007i) q^{49} +(-1.91471 + 5.89286i) q^{50} +(-4.74823 + 3.44979i) q^{51} +(-1.03599 - 0.752690i) q^{52} +(3.67522 + 11.3112i) q^{53} +0.848202 q^{54} +(-11.2902 - 2.80841i) q^{55} +9.70845 q^{56} +(-0.254638 - 0.783696i) q^{57} +(-4.99671 - 3.63032i) q^{58} +(-0.764686 + 0.555577i) q^{59} +(-1.38810 + 4.27213i) q^{60} +(0.355976 - 1.09558i) q^{61} +(0.0751333 - 0.0545876i) q^{62} +(-2.82268 - 2.05079i) q^{63} +(1.37917 + 4.24464i) q^{64} +3.50785 q^{65} +(2.72998 + 0.679078i) q^{66} +12.3918 q^{67} +(2.32249 + 7.14789i) q^{68} +(2.25472 + 1.63815i) q^{69} +(-8.39849 + 6.10186i) q^{70} +(4.48919 - 13.8163i) q^{71} +(0.859862 - 2.64638i) q^{72} +(-3.69827 + 2.68695i) q^{73} +(-2.20311 - 1.60065i) q^{74} +(-2.25737 - 6.94747i) q^{75} -1.05521 q^{76} +(-7.44302 - 8.86043i) q^{77} -0.848202 q^{78} +(-2.66845 - 8.21263i) q^{79} +(0.570198 + 0.414273i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.55834 + 4.79608i) q^{82} +(-1.43435 + 4.41447i) q^{83} +(-3.61459 + 2.62615i) q^{84} +(-16.6561 - 12.1013i) q^{85} +(-1.86156 - 5.72929i) q^{86} +7.28160 q^{87} +(4.88622 - 7.82909i) q^{88} -15.0285 q^{89} +(0.919438 + 2.82974i) q^{90} +(2.82268 + 2.05079i) q^{91} +(2.88729 - 2.09774i) q^{92} +(-0.0338344 + 0.104131i) q^{93} +(2.95795 - 9.10362i) q^{94} +(2.33851 - 1.69903i) q^{95} +(-4.64017 - 3.37128i) q^{96} +(-2.67243 - 8.22490i) q^{97} -4.38797 q^{98} +(-3.07444 + 1.24411i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9 - 2 * q^10 + 14 * q^11 - 18 * q^12 + 5 * q^13 - q^14 - 4 * q^15 - 35 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 45 * q^20 - 2 * q^21 + 11 * q^22 + 6 * q^23 + 2 * q^24 - 7 * q^25 + 4 * q^26 + 5 * q^27 + 12 * q^28 + 26 * q^29 - 3 * q^30 + 20 * q^31 + 42 * q^32 + q^33 - 24 * q^34 - 18 * q^35 + 3 * q^36 - 6 * q^37 - 3 * q^38 - 5 * q^39 - 26 * q^41 - 9 * q^42 + 28 * q^43 - 38 * q^44 - 16 * q^45 - 17 * q^46 + 8 * q^47 - 20 * q^48 + 2 * q^49 - 29 * q^50 + 3 * q^51 - 3 * q^52 + q^53 - 6 * q^54 - 36 * q^56 - 8 * q^57 + 22 * q^58 - 21 * q^59 - 45 * q^60 + 26 * q^61 - 10 * q^62 - 3 * q^63 - 87 * q^64 + 16 * q^65 + 14 * q^66 + 56 * q^67 + 65 * q^68 + 4 * q^69 - 24 * q^70 - 28 * q^71 - 2 * q^72 + 45 * q^73 - 29 * q^74 - 3 * q^75 + 60 * q^76 + 4 * q^77 + 6 * q^78 - 15 * q^79 - 7 * q^80 - 5 * q^81 - 46 * q^82 + 36 * q^83 + 8 * q^84 + 39 * q^86 + 24 * q^87 + 73 * q^88 - 126 * q^89 - 2 * q^90 + 3 * q^91 + 2 * q^92 - 20 * q^93 - 3 * q^94 + 47 * q^95 - 47 * q^96 + 18 * q^97 - 54 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.262109	−	0.806688i	−0.185339	−	0.570415i	0.814615	−	0.580002i	$-0.196948\pi$
$2$	−0.262109	−	0.806688i	−0.185339	−	0.570415i	−0.999954	+	0.00958726i	$0.996948\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	1.03599	−	0.752690i	0.517995	−	0.376345i
$5$	−1.08398	+	3.33616i	−0.484773	+	1.49198i	0.347537	+	0.937666i	$0.387018\pi$
$5$	−1.08398	+	3.33616i	−0.484773	+	1.49198i	−0.832310	+	0.554311i	$0.812982\pi$
$6$	0.262109	−	0.806688i	0.107006	−	0.329329i
$7$	−2.82268	+	2.05079i	−1.06687	+	0.775128i	−0.975347	−	0.220675i	$-0.929174\pi$
$7$	−2.82268	+	2.05079i	−1.06687	+	0.775128i	−0.0915242	+	0.995803i	$0.529174\pi$
$8$	−2.25115	−	1.63555i	−0.795901	−	0.578256i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	2.97536			0.940893
$11$	0.233160	+	3.30842i	0.0703005	+	0.997526i
$11$	0.233160	+	3.30842i	0.0703005	+	0.997526i
$12$	1.28055			0.369664
$13$	−0.309017	−	0.951057i	−0.0857059	−	0.263776i
$13$	−0.309017	−	0.951057i	−0.0857059	−	0.263776i
$14$	2.39420	+	1.73949i	0.639877	+	0.464898i
$15$	−2.83791	+	2.06186i	−0.732745	+	0.532370i
$16$	0.0620883	−	0.191088i	0.0155221	−	0.0477720i
$17$	−1.81366	+	5.58187i	−0.439877	+	1.35380i	0.448128	+	0.893970i	$0.352091\pi$
$17$	−1.81366	+	5.58187i	−0.439877	+	1.35380i	−0.888005	+	0.459834i	$0.847909\pi$
$18$	0.686210	−	0.498561i	0.161741	−	0.117512i
$19$	−0.666652	−	0.484351i	−0.152940	−	0.111118i	0.508683	−	0.860954i	$-0.330132\pi$
$19$	−0.666652	−	0.484351i	−0.152940	−	0.111118i	−0.661624	+	0.749836i	$0.730132\pi$
$20$	1.38810	+	4.27213i	0.310389	+	0.955278i
$21$	−3.48902			−0.761367
$22$	2.60775	−	1.05525i	0.555974	−	0.224981i
$23$	2.78699			0.581127			0.290564	−	0.956856i	$-0.406157\pi$
$23$	2.78699			0.581127			0.290564	+	0.956856i	$0.406157\pi$
$24$	−0.859862	−	2.64638i	−0.175519	−	0.540191i
$25$	−5.90987	−	4.29377i	−1.18197	−	0.858754i
$26$	−0.686210	+	0.498561i	−0.134577	+	0.0977758i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−1.38065	+	4.24920i	−0.260918	+	0.803024i
$29$	5.89094	−	4.28002i	1.09392	−	0.794779i	0.113863	−	0.993496i	$-0.463678\pi$
$29$	5.89094	−	4.28002i	1.09392	−	0.794779i	0.980057	+	0.198717i	$0.0636776\pi$
$30$	2.40712	+	1.74888i	0.439478	+	0.319300i
$31$	0.0338344	+	0.104131i	0.00607683	+	0.0187026i	0.954049	−	0.299651i	$-0.0968702\pi$
$31$	0.0338344	+	0.104131i	0.00607683	+	0.0187026i	−0.947972	+	0.318353i	$0.896870\pi$
$32$	−5.73557			−1.01391
$33$	−1.75601	+	2.81362i	−0.305682	+	0.489788i
$34$	4.97821			0.853756
$35$	−3.78204	−	11.6399i	−0.639282	−	1.96751i
$36$	1.03599	+	0.752690i	0.172665	+	0.125448i
$37$	2.59738	−	1.88711i	0.427007	−	0.310239i	−0.353444	−	0.935456i	$-0.614989\pi$
$37$	2.59738	−	1.88711i	0.427007	−	0.310239i	0.780451	+	0.625217i	$0.214989\pi$
$38$	−0.215985	+	0.664733i	−0.0350374	+	0.107834i
$39$	0.309017	−	0.951057i	0.0494823	−	0.152291i
$40$	7.89669	−	5.73728i	1.24858	−	0.907143i
$41$	−4.80992	−	3.49461i	−0.751184	−	0.545767i	0.145010	−	0.989430i	$-0.453679\pi$
$41$	−4.80992	−	3.49461i	−0.751184	−	0.545767i	−0.896194	+	0.443663i	$0.853679\pi$
$42$	0.914503	+	2.81455i	0.141111	+	0.434295i
$43$	7.10223			1.08308			0.541540	−	0.840675i	$-0.317841\pi$
$43$	7.10223			1.08308			0.541540	+	0.840675i	$0.317841\pi$
$44$	2.73177	+	3.25199i	0.411829	+	0.490256i
$45$	−3.50785			−0.522919
$46$	−0.730494	−	2.24823i	−0.107706	−	0.331483i
$47$	9.12990	+	6.63326i	1.33173	+	0.967560i	0.999705	+	0.0242909i	$0.00773280\pi$
$47$	9.12990	+	6.63326i	1.33173	+	0.967560i	0.332028	+	0.943270i	$0.392267\pi$
$48$	0.162549	−	0.118099i	0.0234620	−	0.0170461i
$49$	1.59863	−	4.92007i	0.228375	−	0.702866i
$50$	−1.91471	+	5.89286i	−0.270780	+	0.833376i
$51$	−4.74823	+	3.44979i	−0.664885	+	0.483067i
$52$	−1.03599	−	0.752690i	−0.143666	−	0.104379i
$53$	3.67522	+	11.3112i	0.504830	+	1.55371i	0.801057	+	0.598588i	$0.204272\pi$
$53$	3.67522	+	11.3112i	0.504830	+	1.55371i	−0.296227	+	0.955118i	$0.595728\pi$
$54$	0.848202			0.115426
$55$	−11.2902	−	2.80841i	−1.52237	−	0.378687i
$56$	9.70845			1.29735
$57$	−0.254638	−	0.783696i	−0.0337277	−	0.103803i
$58$	−4.99671	−	3.63032i	−0.656100	−	0.476684i
$59$	−0.764686	+	0.555577i	−0.0995537	+	0.0723300i	−0.636448	−	0.771319i	$-0.719597\pi$
$59$	−0.764686	+	0.555577i	−0.0995537	+	0.0723300i	0.536895	+	0.843649i	$0.319597\pi$
$60$	−1.38810	+	4.27213i	−0.179203	+	0.551530i
$61$	0.355976	−	1.09558i	0.0455780	−	0.140275i	−0.925678	−	0.378313i	$-0.876504\pi$
$61$	0.355976	−	1.09558i	0.0455780	−	0.140275i	0.971256	+	0.238038i	$0.0765043\pi$
$62$	0.0751333	−	0.0545876i	0.00954194	−	0.00693263i
$63$	−2.82268	−	2.05079i	−0.355624	−	0.258376i
$64$	1.37917	+	4.24464i	0.172396	+	0.530580i
$65$	3.50785			0.435095
$66$	2.72998	+	0.679078i	0.336037	+	0.0835888i
$67$	12.3918			1.51390			0.756949	−	0.653475i	$-0.226689\pi$
$67$	12.3918			1.51390			0.756949	+	0.653475i	$0.226689\pi$
$68$	2.32249	+	7.14789i	0.281643	+	0.866808i
$69$	2.25472	+	1.63815i	0.271436	+	0.197210i
$70$	−8.39849	+	6.10186i	−1.00381	+	0.729312i
$71$	4.48919	−	13.8163i	0.532769	−	1.63969i	−0.215653	−	0.976470i	$-0.569188\pi$
$71$	4.48919	−	13.8163i	0.532769	−	1.63969i	0.748422	−	0.663223i	$-0.230812\pi$
$72$	0.859862	−	2.64638i	0.101336	−	0.311879i
$73$	−3.69827	+	2.68695i	−0.432850	+	0.314484i	−0.782788	−	0.622289i	$-0.786203\pi$
$73$	−3.69827	+	2.68695i	−0.432850	+	0.314484i	0.349937	+	0.936773i	$0.386203\pi$
$74$	−2.20311	−	1.60065i	−0.256106	−	0.186072i
$75$	−2.25737	−	6.94747i	−0.260659	−	0.802224i
$76$	−1.05521			−0.121041
$77$	−7.44302	−	8.86043i	−0.848211	−	1.00974i
$78$	−0.848202			−0.0960400
$79$	−2.66845	−	8.21263i	−0.300224	−	0.923993i	−0.981417	−	0.191889i	$-0.938539\pi$
$79$	−2.66845	−	8.21263i	−0.300224	−	0.923993i	0.681193	−	0.732104i	$-0.261461\pi$
$80$	0.570198	+	0.414273i	0.0637501	+	0.0463172i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−1.55834	+	4.79608i	−0.172090	+	0.529638i
$83$	−1.43435	+	4.41447i	−0.157440	+	0.484551i	−0.998400	−	0.0565466i	$-0.981991\pi$
$83$	−1.43435	+	4.41447i	−0.157440	+	0.484551i	0.840960	+	0.541098i	$0.181991\pi$
$84$	−3.61459	+	2.62615i	−0.394384	+	0.286537i
$85$	−16.6561	−	12.1013i	−1.80660	−	1.31257i
$86$	−1.86156	−	5.72929i	−0.200737	−	0.617805i
$87$	7.28160			0.780669
$88$	4.88622	−	7.82909i	0.520873	−	0.834584i
$89$	−15.0285			−1.59302			−0.796509	−	0.604626i	$-0.793323\pi$
$89$	−15.0285			−1.59302			−0.796509	+	0.604626i	$0.793323\pi$
$90$	0.919438	+	2.82974i	0.0969173	+	0.298281i
$91$	2.82268	+	2.05079i	0.295897	+	0.214982i
$92$	2.88729	−	2.09774i	0.301021	−	0.218704i
$93$	−0.0338344	+	0.104131i	−0.00350846	+	0.0107979i
$94$	2.95795	−	9.10362i	0.305089	−	0.938967i
$95$	2.33851	−	1.69903i	0.239926	−	0.174317i
$96$	−4.64017	−	3.37128i	−0.473585	−	0.344080i
$97$	−2.67243	−	8.22490i	−0.271344	−	0.835112i	−0.990164	−	0.139915i	$-0.955317\pi$
$97$	−2.67243	−	8.22490i	−0.271344	−	0.835112i	0.718819	−	0.695197i	$-0.244683\pi$
$98$	−4.38797			−0.443252
$99$	−3.07444	+	1.24411i	−0.308993	+	0.125037i
$100$	−9.35444			−0.935444
$101$	2.63044	+	8.09567i	0.261739	+	0.805549i	0.992427	+	0.122838i	$0.0391995\pi$
$101$	2.63044	+	8.09567i	0.261739	+	0.805549i	−0.730688	+	0.682712i	$0.760801\pi$
$102$	4.02746	+	2.92612i	0.398778	+	0.289729i
$103$	−5.89972	+	4.28640i	−0.581317	+	0.422351i	−0.839199	−	0.543825i	$-0.816975\pi$
$103$	−5.89972	+	4.28640i	−0.581317	+	0.422351i	0.257882	+	0.966176i	$0.416975\pi$
$104$	−0.859862	+	2.64638i	−0.0843164	+	0.259499i
$105$	3.78204	−	11.6399i	0.369090	−	1.13594i
$106$	8.16127	−	5.92951i	0.792692	−	0.575925i
$107$	−9.97009	−	7.24369i	−0.963845	−	0.700274i	−0.00980420	−	0.999952i	$-0.503121\pi$
$107$	−9.97009	−	7.24369i	−0.963845	−	0.700274i	−0.954040	+	0.299678i	$0.903121\pi$
$108$	0.395713	+	1.21788i	0.0380775	+	0.117190i
$109$	20.8006			1.99233			0.996166	−	0.0874813i	$-0.0278818\pi$
$109$	20.8006			1.99233			0.996166	+	0.0874813i	$0.0278818\pi$
$110$	0.693737	+	9.84375i	0.0661453	+	0.938565i
$111$	3.21054			0.304731
$112$	0.216627	+	0.666711i	0.0204694	+	0.0629982i
$113$	5.15758	+	3.74720i	0.485185	+	0.352507i	0.803330	−	0.595535i	$-0.203060\pi$
$113$	5.15758	+	3.74720i	0.485185	+	0.352507i	−0.318145	+	0.948042i	$0.603060\pi$
$114$	−0.565456	+	0.410828i	−0.0529598	+	0.0384775i
$115$	−3.02105	+	9.29784i	−0.281715	+	0.867028i
$116$	2.88142	−	8.86810i	0.267533	−	0.823383i
$117$	0.809017	−	0.587785i	0.0747936	−	0.0543408i
$118$	0.648608	+	0.471242i	0.0597092	+	0.0433813i
$119$	−6.32790	−	19.4753i	−0.580078	−	1.78530i
$120$	9.76084			0.891039
$121$	−10.8913	+	1.54278i	−0.990116	+	0.140253i
$122$	−0.977097			−0.0884622
$123$	−1.83723	−	5.65440i	−0.165657	−	0.509840i
$124$	0.113431	+	0.0824123i	0.0101864	+	0.00740084i
$125$	6.54138	−	4.75259i	0.585079	−	0.425085i
$126$	−0.914503	+	2.81455i	−0.0814704	+	0.250740i
$127$	−3.20922	+	9.87695i	−0.284772	+	0.876438i	0.701695	+	0.712478i	$0.252427\pi$
$127$	−3.20922	+	9.87695i	−0.284772	+	0.876438i	−0.986467	+	0.163960i	$0.947573\pi$
$128$	−6.21773	+	4.51745i	−0.549575	+	0.399290i
$129$	5.74583	+	4.17459i	0.505892	+	0.367552i
$130$	−0.919438	−	2.82974i	−0.0806401	−	0.248185i
$131$	−12.0936			−1.05662			−0.528311	−	0.849051i	$-0.677174\pi$
$131$	−12.0936			−1.05662			−0.528311	+	0.849051i	$0.677174\pi$
$132$	0.298574	+	4.23661i	0.0259876	+	0.368749i
$133$	2.87505			0.249298
$134$	−3.24800	−	9.99630i	−0.280584	−	0.863549i
$135$	−2.83791	−	2.06186i	−0.244248	−	0.177457i
$136$	13.2123	−	9.59928i	1.13294	−	0.823132i
$137$	−2.12115	+	6.52823i	−0.181222	+	0.557744i	−0.999863	−	0.0165618i	$-0.994728\pi$
$137$	−2.12115	+	6.52823i	−0.181222	+	0.557744i	0.818641	+	0.574306i	$0.194728\pi$
$138$	0.730494	−	2.24823i	0.0621838	−	0.191382i
$139$	6.74706	−	4.90203i	0.572278	−	0.415784i	−0.263654	−	0.964617i	$-0.584928\pi$
$139$	6.74706	−	4.90203i	0.572278	−	0.415784i	0.835932	+	0.548833i	$0.184928\pi$
$140$	−12.6794	−	9.21214i	−1.07161	−	0.778568i
$141$	3.48731	+	10.7328i	0.293685	+	0.903868i
$142$	−12.3221			−1.03405
$143$	3.07444	−	1.24411i	0.257098	−	0.104037i
$144$	0.200922			0.0167435
$145$	7.89314	+	24.2926i	0.655490	+	2.01739i
$146$	3.13688	+	2.27908i	0.259610	+	0.188618i
$147$	4.18526	−	3.04077i	0.345194	−	0.250798i
$148$	1.27045	−	3.91005i	0.104431	−	0.321404i
$149$	3.37668	−	10.3923i	0.276628	−	0.851373i	−0.712156	−	0.702021i	$-0.752281\pi$
$149$	3.37668	−	10.3923i	0.276628	−	0.851373i	0.988784	−	0.149352i	$-0.0477188\pi$
$150$	−5.01276	+	3.64199i	−0.409290	+	0.297367i
$151$	16.2845	+	11.8314i	1.32521	+	0.962823i	0.999851	+	0.0172335i	$0.00548587\pi$
$151$	16.2845	+	11.8314i	1.32521	+	0.962823i	0.325361	+	0.945590i	$0.394514\pi$
$152$	0.708550	+	2.18069i	0.0574710	+	0.176877i
$153$	−5.86913			−0.474491
$154$	−5.19672	+	8.32660i	−0.418764	+	0.670976i
$155$	−0.384075			−0.0308497
$156$	−0.395713	−	1.21788i	−0.0316824	−	0.0975083i
$157$	−14.7583	−	10.7225i	−1.17784	−	0.855749i	−0.185912	−	0.982566i	$-0.559524\pi$
$157$	−14.7583	−	10.7225i	−1.17784	−	0.855749i	−0.991926	+	0.126817i	$0.959524\pi$
$158$	−5.92561	+	4.30521i	−0.471416	+	0.342504i
$159$	−3.67522	+	11.3112i	−0.291464	+	0.897033i
$160$	6.21727	−	19.1348i	0.491518	−	1.51274i
$161$	−7.86677	+	5.71554i	−0.619988	+	0.450448i
$162$	0.686210	+	0.498561i	0.0539137	+	0.0391706i
$163$	2.26694	+	6.97692i	0.177560	+	0.546474i	0.999741	−	0.0227521i	$-0.00724284\pi$
$163$	2.26694	+	6.97692i	0.177560	+	0.546474i	−0.822181	+	0.569226i	$0.807243\pi$
$164$	−7.61339			−0.594506
$165$	−7.48319	−	8.90825i	−0.582566	−	0.693506i
$166$	3.93706			0.305575
$167$	−2.54901	−	7.84506i	−0.197249	−	0.607069i	−0.999943	−	0.0106781i	$-0.996601\pi$
$167$	−2.54901	−	7.84506i	−0.197249	−	0.607069i	0.802694	−	0.596391i	$-0.203399\pi$
$168$	7.85430	+	5.70648i	0.605973	+	0.440265i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−5.39630	+	16.6081i	−0.413877	+	1.27378i
$171$	0.254638	−	0.783696i	0.0194727	−	0.0599308i
$172$	7.35783	−	5.34578i	0.561030	−	0.407612i
$173$	−5.95146	−	4.32399i	−0.452481	−	0.328747i	0.338093	−	0.941113i	$-0.390218\pi$
$173$	−5.95146	−	4.32399i	−0.452481	−	0.328747i	−0.790575	+	0.612366i	$0.790218\pi$
$174$	−1.90857	−	5.87398i	−0.144688	−	0.445305i
$175$	25.4873			1.92666
$176$	0.646676	+	0.160860i	0.0487451	+	0.0121253i
$177$	−0.945204			−0.0710459
$178$	3.93911	+	12.1233i	0.295248	+	0.908681i
$179$	−9.03960	−	6.56765i	−0.675651	−	0.490889i	0.196261	−	0.980552i	$-0.437120\pi$
$179$	−9.03960	−	6.56765i	−0.675651	−	0.490889i	−0.871912	+	0.489662i	$0.837120\pi$
$180$	−3.63409	+	2.64032i	−0.270869	+	0.196798i
$181$	−4.17170	+	12.8392i	−0.310080	+	0.954328i	0.667653	+	0.744473i	$0.267299\pi$
$181$	−4.17170	+	12.8392i	−0.310080	+	0.954328i	−0.977733	+	0.209855i	$0.932701\pi$
$182$	0.914503	−	2.81455i	0.0677875	−	0.208628i
$183$	0.931957	−	0.677106i	0.0688922	−	0.0500531i
$184$	−6.27392	−	4.55827i	−0.462520	−	0.336040i
$185$	3.48018	+	10.7109i	0.255868	+	0.787481i
$186$	0.0928699			0.00680955
$187$	−18.8901	−	4.69888i	−1.38138	−	0.343616i
$188$	14.4513			1.05397
$189$	−1.07817	−	3.31826i	−0.0784251	−	0.241368i
$190$	−1.98353	−	1.44112i	−0.143901	−	0.104550i
$191$	17.1204	−	12.4387i	1.23879	−	0.900032i	0.241271	−	0.970458i	$-0.422436\pi$
$191$	17.1204	−	12.4387i	1.23879	−	0.900032i	0.997517	+	0.0704259i	$0.0224358\pi$
$192$	−1.37917	+	4.24464i	−0.0995328	+	0.306330i
$193$	−3.79983	+	11.6947i	−0.273518	+	0.841802i	0.716090	+	0.698008i	$0.245930\pi$
$193$	−3.79983	+	11.6947i	−0.273518	+	0.841802i	−0.989608	+	0.143794i	$0.954070\pi$
$194$	−5.93446	+	4.31164i	−0.426069	+	0.309558i
$195$	2.83791	+	2.06186i	0.203227	+	0.147653i
$196$	−2.04713	−	6.30040i	−0.146223	−	0.450029i
$197$	1.76574			0.125804			0.0629018	−	0.998020i	$-0.479964\pi$
$197$	1.76574			0.125804			0.0629018	+	0.998020i	$0.479964\pi$
$198$	1.80944	+	2.15403i	0.128592	+	0.153080i
$199$	16.5373			1.17230			0.586149	−	0.810203i	$-0.300643\pi$
$199$	16.5373			1.17230			0.586149	+	0.810203i	$0.300643\pi$
$200$	6.28129	+	19.3318i	0.444154	+	1.36697i
$201$	10.0252	+	7.28371i	0.707120	+	0.513753i
$202$	5.84122	−	4.24390i	0.410987	−	0.298599i
$203$	−7.85078	+	24.1622i	−0.551016	+	1.69585i
$204$	−2.32249	+	7.14789i	−0.162607	+	0.500452i
$205$	16.8725	−	12.2586i	1.17843	−	0.856176i
$206$	5.00416	+	3.63573i	0.348656	+	0.253313i
$207$	0.861227	+	2.65058i	0.0598594	+	0.184228i
$208$	−0.200922			−0.0139314
$209$	1.44700	−	2.31850i	0.100091	−	0.160374i
$210$	−10.3811			−0.716364
$211$	7.37650	+	22.7025i	0.507819	+	1.56291i	0.795979	+	0.605324i	$0.206956\pi$
$211$	7.37650	+	22.7025i	0.507819	+	1.56291i	−0.288160	+	0.957582i	$0.593044\pi$
$212$	12.3213	+	8.95193i	0.846229	+	0.614821i
$213$	11.7528	−	8.53894i	0.805292	−	0.585079i
$214$	−3.23015	+	9.94139i	−0.220809	+	0.679579i
$215$	−7.69871	+	23.6942i	−0.525048	+	1.61593i
$216$	2.25115	−	1.63555i	0.153171	−	0.111285i
$217$	−0.309056	−	0.224542i	−0.0209801	−	0.0152429i
$218$	−5.45201	−	16.7796i	−0.369257	−	1.13646i
$219$	−4.57132			−0.308901
$220$	−13.8104	+	5.58851i	−0.931094	+	0.376777i
$221$	5.86913			0.394800
$222$	−0.841512	−	2.58991i	−0.0564786	−	0.173823i
$223$	17.0267	+	12.3706i	1.14019	+	0.828399i	0.987146	−	0.159820i	$-0.0510915\pi$
$223$	17.0267	+	12.3706i	1.14019	+	0.828399i	0.153047	+	0.988219i	$0.451092\pi$
$224$	16.1897	−	11.7625i	1.08172	−	0.785913i
$225$	2.25737	−	6.94747i	0.150491	−	0.463164i
$226$	1.67098	−	5.14274i	0.111152	−	0.342090i
$227$	19.9497	−	14.4943i	1.32411	−	0.962022i	0.324239	−	0.945975i	$-0.394892\pi$
$227$	19.9497	−	14.4943i	1.32411	−	0.962022i	0.999871	−	0.0160467i	$-0.00510806\pi$
$228$	−0.853683	−	0.620237i	−0.0565365	−	0.0410762i
$229$	−1.59254	−	4.90132i	−0.105238	−	0.323889i	0.884548	−	0.466448i	$-0.154467\pi$
$229$	−1.59254	−	4.90132i	−0.105238	−	0.323889i	−0.989786	+	0.142560i	$0.954467\pi$
$230$	8.29231			0.546778
$231$	−0.813501	−	11.5431i	−0.0535245	−	0.759483i
$232$	−20.2616			−1.33024
$233$	−0.0253492	−	0.0780169i	−0.00166068	−	0.00511106i	0.950223	−	0.311571i	$-0.100855\pi$
$233$	−0.0253492	−	0.0780169i	−0.00166068	−	0.00511106i	−0.951883	+	0.306460i	$0.900855\pi$
$234$	−0.686210	−	0.498561i	−0.0448590	−	0.0325919i
$235$	−32.0263	+	23.2685i	−2.08917	+	1.51787i
$236$	−0.374029	+	1.15114i	−0.0243472	+	0.0749331i
$237$	2.66845	−	8.21263i	0.173334	−	0.533468i
$238$	−14.0519	+	10.2093i	−0.910848	+	0.661770i
$239$	8.13196	+	5.90821i	0.526013	+	0.382171i	0.818864	−	0.573987i	$-0.194604\pi$
$239$	8.13196	+	5.90821i	0.526013	+	0.382171i	−0.292852	+	0.956158i	$0.594604\pi$
$240$	0.217796	+	0.670308i	0.0140587	+	0.0432682i
$241$	12.4838			0.804150			0.402075	−	0.915607i	$-0.368289\pi$
$241$	12.4838			0.804150			0.402075	+	0.915607i	$0.368289\pi$
$242$	4.09925	+	8.38148i	0.263509	+	0.538782i
$243$	−1.00000			−0.0641500
$244$	−0.455846	−	1.40295i	−0.0291825	−	0.0898146i
$245$	14.6812	+	10.6666i	0.937951	+	0.681461i
$246$	−4.07979	+	2.96414i	−0.260118	+	0.188987i
$247$	−0.254638	+	0.783696i	−0.0162023	+	0.0498654i
$248$	0.0941466	−	0.289753i	0.00597831	−	0.0183994i
$249$	−3.75517	+	2.72829i	−0.237974	+	0.172898i
$250$	−5.54841	−	4.03116i	−0.350912	−	0.254953i
$251$	−4.11882	−	12.6764i	−0.259977	−	0.800128i	−0.992808	−	0.119717i	$-0.961801\pi$
$251$	−4.11882	−	12.6764i	−0.259977	−	0.800128i	0.732831	−	0.680411i	$-0.238199\pi$
$252$	−4.46788			−0.281450
$253$	0.649815	+	9.22052i	0.0408535	+	0.579689i
$254$	8.80879			0.552712
$255$	−6.36205	−	19.5804i	−0.398407	−	1.22617i
$256$	12.4953	+	9.07837i	0.780957	+	0.567398i
$257$	1.33653	−	0.971043i	0.0833702	−	0.0605720i	−0.545319	−	0.838228i	$-0.683592\pi$
$257$	1.33653	−	0.971043i	0.0833702	−	0.0605720i	0.628690	+	0.777656i	$0.283592\pi$
$258$	1.86156	−	5.72929i	0.115896	−	0.356690i
$259$	−3.46150	+	10.6534i	−0.215087	+	0.661970i
$260$	3.63409	−	2.64032i	0.225377	−	0.163746i
$261$	5.89094	+	4.28002i	0.364640	+	0.264926i
$262$	3.16984	+	9.75575i	0.195833	+	0.602712i
$263$	10.2804			0.633916			0.316958	−	0.948440i	$-0.397339\pi$
$263$	10.2804			0.633916			0.316958	+	0.948440i	$0.397339\pi$
$264$	8.55486	−	3.46182i	0.526515	−	0.213060i
$265$	−41.7197			−2.56282
$266$	−0.753575	−	2.31927i	−0.0462047	−	0.142203i
$267$	−12.1583	−	8.83354i	−0.744077	−	0.540604i
$268$	12.8378	−	9.32717i	0.784190	−	0.569748i
$269$	−3.53956	+	10.8936i	−0.215811	+	0.664198i	0.783284	+	0.621664i	$0.213543\pi$
$269$	−3.53956	+	10.8936i	−0.215811	+	0.664198i	−0.999095	+	0.0425337i	$0.986457\pi$
$270$	−0.919438	+	2.82974i	−0.0559552	+	0.172212i
$271$	10.4392	−	7.58449i	0.634134	−	0.460725i	−0.223696	−	0.974659i	$-0.571812\pi$
$271$	10.4392	−	7.58449i	0.634134	−	0.460725i	0.857830	+	0.513934i	$0.171812\pi$
$272$	0.954023	+	0.693138i	0.0578461	+	0.0420277i
$273$	1.07817	+	3.31826i	0.0652536	+	0.200830i
$274$	5.82222			0.351733
$275$	12.8276	−	20.5535i	0.773536	−	1.23942i
$276$	3.56889			0.214822
$277$	−7.99064	−	24.5927i	−0.480111	−	1.47763i	−0.838939	−	0.544226i	$-0.816823\pi$
$277$	−7.99064	−	24.5927i	−0.480111	−	1.47763i	0.358827	−	0.933404i	$-0.383177\pi$
$278$	−5.72287	−	4.15791i	−0.343235	−	0.249375i
$279$	−0.0885795	+	0.0643568i	−0.00530312	+	0.00385294i
$280$	−10.5238	+	32.3890i	−0.628918	+	1.93561i
$281$	−0.437638	+	1.34691i	−0.0261073	+	0.0803500i	−0.963261	−	0.268566i	$-0.913450\pi$
$281$	−0.437638	+	1.34691i	−0.0261073	+	0.0803500i	0.937154	+	0.348916i	$0.113450\pi$
$282$	7.74400	−	5.62635i	0.461149	−	0.335044i
$283$	6.06695	+	4.40790i	0.360643	+	0.262022i	0.753320	−	0.657654i	$-0.228451\pi$
$283$	6.06695	+	4.40790i	0.360643	+	0.262022i	−0.392677	+	0.919676i	$0.628451\pi$
$284$	−5.74864	−	17.6925i	−0.341119	−	1.04986i
$285$	2.89056			0.171222
$286$	−1.80944	−	2.15403i	−0.106995	−	0.127370i
$287$	20.7436			1.22446
$288$	−1.77239	−	5.45485i	−0.104439	−	0.321430i
$289$	−14.1147	−	10.2549i	−0.830274	−	0.603230i
$290$	17.5277	−	12.7346i	1.02926	−	0.747802i
$291$	2.67243	−	8.22490i	0.156661	−	0.482152i
$292$	−1.80893	+	5.56731i	−0.105860	+	0.325802i
$293$	−5.56260	+	4.04146i	−0.324970	+	0.236105i	−0.738293	−	0.674480i	$-0.764368\pi$
$293$	−5.56260	+	4.04146i	−0.324970	+	0.236105i	0.413323	+	0.910584i	$0.364368\pi$
$294$	−3.54994	−	2.57919i	−0.207037	−	0.150421i
$295$	−1.02459	−	3.15335i	−0.0596537	−	0.183595i
$296$	−8.93357			−0.519253
$297$	−3.21854	−	0.800609i	−0.186759	−	0.0464560i
$298$	−9.26843			−0.536906
$299$	−0.861227	−	2.65058i	−0.0498060	−	0.153287i
$300$	−7.56790	−	5.49840i	−0.436933	−	0.317450i
$301$	−20.0473	+	14.5652i	−1.15551	+	0.839525i
$302$	5.27592	−	16.2376i	0.303595	−	0.934370i
$303$	−2.63044	+	8.09567i	−0.151115	+	0.465084i
$304$	−0.133945	+	0.0973168i	−0.00768228	+	0.00558150i
$305$	3.26916	+	2.37519i	0.187192	+	0.136003i
$306$	1.53835	+	4.73456i	0.0879417	+	0.270657i
$307$	−9.95198			−0.567989			−0.283995	−	0.958826i	$-0.591660\pi$
$307$	−9.95198			−0.567989			−0.283995	+	0.958826i	$0.591660\pi$
$308$	−14.3801	−	3.57702i	−0.819380	−	0.203820i
$309$	−7.29246			−0.414853
$310$	0.100670	+	0.309829i	0.00571765	+	0.0175971i
$311$	19.1637	+	13.9232i	1.08667	+	0.789515i	0.978834	−	0.204654i	$-0.0656068\pi$
$311$	19.1637	+	13.9232i	1.08667	+	0.789515i	0.107839	+	0.994168i	$0.465607\pi$
$312$	−2.25115	+	1.63555i	−0.127446	+	0.0925951i
$313$	2.20149	−	6.77550i	0.124436	−	0.382974i	−0.869362	−	0.494176i	$-0.835470\pi$
$313$	2.20149	−	6.77550i	0.124436	−	0.382974i	0.993798	+	0.111202i	$0.0354700\pi$
$314$	−4.78145	+	14.7158i	−0.269833	+	0.830460i
$315$	9.90152	−	7.19388i	0.557888	−	0.405329i
$316$	−8.94605	−	6.49969i	−0.503255	−	0.365636i
$317$	−6.59598	−	20.3003i	−0.370467	−	1.14018i	−0.946486	−	0.322744i	$-0.895395\pi$
$317$	−6.59598	−	20.3003i	−0.370467	−	1.14018i	0.576019	−	0.817436i	$-0.304605\pi$
$318$	10.0879			0.565700
$319$	15.5336	+	18.4918i	0.869716	+	1.03534i
$320$	−15.6558			−0.875186
$321$	−3.80823	−	11.7205i	−0.212555	−	0.654177i
$322$	6.67261	+	4.84793i	0.371850	+	0.270165i
$323$	3.91267	−	2.84272i	0.217707	−	0.158173i
$324$	−0.395713	+	1.21788i	−0.0219840	+	0.0676599i
$325$	−2.25737	+	6.94747i	−0.125216	+	0.385376i
$326$	5.03401	−	3.65742i	0.278808	−	0.202566i
$327$	16.8280	+	12.2263i	0.930591	+	0.676114i
$328$	5.11222	+	15.7338i	0.282275	+	0.868753i
$329$	−39.3742			−2.17077
$330$	−5.22477	+	8.37153i	−0.287614	+	0.460838i
$331$	−16.5033			−0.907105			−0.453552	−	0.891230i	$-0.649844\pi$
$331$	−16.5033			−0.907105			−0.453552	+	0.891230i	$0.649844\pi$
$332$	1.83676	+	5.65296i	0.100805	+	0.310247i
$333$	2.59738	+	1.88711i	0.142336	+	0.103413i
$334$	−5.66040	+	4.11252i	−0.309723	+	0.225027i
$335$	−13.4325	+	41.3410i	−0.733896	+	2.25870i
$336$	−0.216627	+	0.666711i	−0.0118180	+	0.0363720i
$337$	−11.6301	+	8.44977i	−0.633533	+	0.460288i	−0.857622	−	0.514280i	$-0.828059\pi$
$337$	−11.6301	+	8.44977i	−0.633533	+	0.460288i	0.224090	+	0.974569i	$0.428059\pi$
$338$	0.686210	+	0.498561i	0.0373249	+	0.0271181i
$339$	1.97002	+	6.06310i	0.106997	+	0.329303i
$340$	−26.3640			−1.42979
$341$	−0.336622	+	0.136218i	−0.0182291	+	0.00737660i
$342$	−0.698942			−0.0377944
$343$	−1.96953	−	6.06158i	−0.106344	−	0.327295i
$344$	−15.9882	−	11.6161i	−0.862025	−	0.626298i
$345$	−7.90922	+	5.74638i	−0.425818	+	0.309375i
$346$	−1.92818	+	5.93433i	−0.103660	+	0.319032i
$347$	2.68999	−	8.27894i	0.144406	−	0.444437i	−0.852528	−	0.522682i	$-0.824932\pi$
$347$	2.68999	−	8.27894i	0.144406	−	0.444437i	0.996934	+	0.0782449i	$0.0249316\pi$
$348$	7.54366	−	5.48079i	0.404382	−	0.293801i
$349$	5.85607	+	4.25469i	0.313468	+	0.227748i	0.733383	−	0.679815i	$-0.237940\pi$
$349$	5.85607	+	4.25469i	0.313468	+	0.227748i	−0.419915	+	0.907563i	$0.637940\pi$
$350$	−6.68045	−	20.5603i	−0.357085	−	1.09899i
$351$	1.00000			0.0533761
$352$	−1.33731	−	18.9757i	−0.0712787	−	1.01141i
$353$	−8.38751			−0.446422			−0.223211	−	0.974770i	$-0.571654\pi$
$353$	−8.38751			−0.446422			−0.223211	+	0.974770i	$0.571654\pi$
$354$	0.247746	+	0.762485i	0.0131676	+	0.0405256i
$355$	41.2272	+	29.9533i	2.18811	+	1.58976i
$356$	−15.5694	+	11.3118i	−0.825175	+	0.599525i
$357$	6.32790	−	19.4753i	0.334908	−	1.03074i
$358$	−2.92869	+	9.01358i	−0.154786	+	0.476382i
$359$	2.29669	−	1.66864i	0.121215	−	0.0880675i	−0.525526	−	0.850777i	$-0.676132\pi$
$359$	2.29669	−	1.66864i	0.121215	−	0.0880675i	0.646741	+	0.762710i	$0.276132\pi$
$360$	7.89669	+	5.73728i	0.416192	+	0.302381i
$361$	−5.66149	−	17.4243i	−0.297973	−	0.917068i
$362$	11.4506			0.601832
$363$	−9.71805	−	5.15359i	−0.510065	−	0.270493i
$364$	4.46788			0.234180
$365$	−4.95524	−	15.2507i	−0.259369	−	0.798256i
$366$	−0.790488	−	0.574323i	−0.0413195	−	0.0300203i
$367$	9.85854	−	7.16265i	0.514612	−	0.373887i	−0.299959	−	0.953952i	$-0.596973\pi$
$367$	9.85854	−	7.16265i	0.514612	−	0.373887i	0.814570	+	0.580065i	$0.196973\pi$
$368$	0.173039	−	0.532560i	0.00902030	−	0.0277616i
$369$	1.83723	−	5.65440i	0.0956422	−	0.294357i
$370$	7.72817	−	5.61484i	0.401768	−	0.291902i
$371$	−33.5708	−	24.3906i	−1.74291	−	1.26630i
$372$	0.0433267	+	0.133346i	0.00224638	+	0.00691366i
$373$	−2.51168			−0.130050			−0.0650250	−	0.997884i	$-0.520713\pi$
$373$	−2.51168			−0.130050			−0.0650250	+	0.997884i	$0.520713\pi$
$374$	1.16072	+	16.4700i	0.0600195	+	0.851643i
$375$	8.08559			0.417538
$376$	−9.70370	−	29.8649i	−0.500430	−	1.54016i
$377$	−5.89094	−	4.28002i	−0.303399	−	0.220432i
$378$	−2.39420	+	1.73949i	−0.123144	+	0.0894696i
$379$	9.85154	−	30.3199i	0.506039	−	1.55743i	−0.292977	−	0.956120i	$-0.594646\pi$
$379$	9.85154	−	30.3199i	0.506039	−	1.55743i	0.799016	−	0.601310i	$-0.205354\pi$
$380$	1.14383	−	3.52035i	0.0586773	−	0.180590i
$381$	−8.40184	+	6.10429i	−0.430439	+	0.312732i
$382$	−14.5216	−	10.5505i	−0.742987	−	0.539812i
$383$	2.42592	+	7.46622i	0.123959	+	0.381506i	0.993710	−	0.111985i	$-0.0357208\pi$
$383$	2.42592	+	7.46622i	0.123959	+	0.381506i	−0.869751	+	0.493491i	$0.835721\pi$
$384$	−7.68554			−0.392201
$385$	37.6280	−	15.2266i	1.91770	−	0.776017i
$386$	10.4299			0.530870
$387$	2.19471	+	6.75462i	0.111563	+	0.343357i
$388$	−8.95941	−	6.50939i	−0.454845	−	0.330464i
$389$	−25.6685	+	18.6493i	−1.30145	+	0.945556i	−0.999969	−	0.00791700i	$-0.997480\pi$
$389$	−25.6685	+	18.6493i	−1.30145	+	0.945556i	−0.301478	+	0.953473i	$0.597480\pi$
$390$	0.919438	−	2.82974i	0.0465576	−	0.143289i
$391$	−5.05465	+	15.5566i	−0.255625	+	0.786732i
$392$	−11.6458	+	8.46116i	−0.588201	+	0.427353i
$393$	−9.78392	−	7.10843i	−0.493533	−	0.358573i
$394$	−0.462816	−	1.42440i	−0.0233163	−	0.0717603i
$395$	30.2912			1.52412
$396$	−2.24866	+	3.60298i	−0.113000	+	0.181057i
$397$	−1.57175			−0.0788839			−0.0394420	−	0.999222i	$-0.512558\pi$
$397$	−1.57175			−0.0788839			−0.0394420	+	0.999222i	$0.512558\pi$
$398$	−4.33458	−	13.3405i	−0.217273	−	0.668696i
$399$	2.32596	+	1.68991i	0.116444	+	0.0846013i
$400$	−1.18742	+	0.862713i	−0.0593711	+	0.0431357i
$401$	5.09155	−	15.6702i	0.254260	−	0.782532i	−0.739715	−	0.672921i	$-0.765040\pi$
$401$	5.09155	−	15.6702i	0.254260	−	0.782532i	0.993975	−	0.109611i	$-0.0349605\pi$
$402$	3.24800	−	9.99630i	0.161995	−	0.498570i
$403$	0.0885795	−	0.0643568i	0.00441246	−	0.00320584i
$404$	8.81864	+	6.40712i	0.438744	+	0.318766i
$405$	−1.08398	−	3.33616i	−0.0538636	−	0.165775i
$406$	21.5491			1.06947
$407$	6.84896	+	8.15324i	0.339490	+	0.404141i
$408$	16.3313			0.808519
$409$	2.86426	+	8.81530i	0.141629	+	0.435888i	0.996562	−	0.0828495i	$-0.0264021\pi$
$409$	2.86426	+	8.81530i	0.141629	+	0.435888i	−0.854933	+	0.518738i	$0.826402\pi$
$410$	−14.3113	−	10.3978i	−0.706784	−	0.513508i
$411$	−5.55324	+	4.03467i	−0.273921	+	0.199015i
$412$	−2.88572	+	8.88132i	−0.142169	+	0.437551i
$413$	1.01909	−	3.13643i	0.0501460	−	0.154334i
$414$	1.91246	−	1.38948i	0.0939922	−	0.0682894i
$415$	−13.1726	−	9.57043i	−0.646616	−	0.469794i
$416$	1.77239	+	5.45485i	0.0868985	+	0.267446i
$417$	8.33982			0.408403
$418$	−2.24957	−	0.559579i	−0.110030	−	0.0273699i
$419$	−15.4569			−0.755121			−0.377560	−	0.925985i	$-0.623237\pi$
$419$	−15.4569			−0.755121			−0.377560	+	0.925985i	$0.623237\pi$
$420$	−4.84311	−	14.9056i	−0.236320	−	0.727317i
$421$	15.1476	+	11.0054i	0.738250	+	0.536370i	0.892163	−	0.451715i	$-0.149187\pi$
$421$	15.1476	+	11.0054i	0.738250	+	0.536370i	−0.153913	+	0.988084i	$0.549187\pi$
$422$	16.3804	−	11.9011i	0.797386	−	0.579335i
$423$	−3.48731	+	10.7328i	−0.169559	+	0.521849i
$424$	10.2266	−	31.4741i	0.496645	−	1.52852i
$425$	34.6858	−	25.2007i	1.68251	−	1.22241i
$426$	−9.96879	−	7.24275i	−0.482990	−	0.350912i
$427$	1.24201	+	3.82250i	0.0601049	+	0.184984i
$428$	−15.7812			−0.762811
$429$	3.21854	+	0.800609i	0.155393	+	0.0386538i
$430$	21.1317			1.01906
$431$	2.16702	+	6.66942i	0.104382	+	0.321254i	0.989585	−	0.143951i	$-0.0459806\pi$
$431$	2.16702	+	6.66942i	0.104382	+	0.321254i	−0.885203	+	0.465205i	$0.845981\pi$
$432$	0.162549	+	0.118099i	0.00782066	+	0.00568204i
$433$	15.8549	−	11.5192i	0.761937	−	0.553579i	−0.137567	−	0.990492i	$-0.543928\pi$
$433$	15.8549	−	11.5192i	0.761937	−	0.553579i	0.899504	+	0.436913i	$0.143928\pi$
$434$	−0.100129	+	0.308166i	−0.00480636	+	0.0147924i
$435$	−7.89314	+	24.2926i	−0.378447	+	1.16474i
$436$	21.5492	−	15.6564i	1.03202	−	0.749804i
$437$	−1.85795	−	1.34988i	−0.0888778	−	0.0645735i
$438$	1.19818	+	3.68763i	0.0572514	+	0.176202i
$439$	27.7208			1.32304			0.661522	−	0.749926i	$-0.269911\pi$
$439$	27.7208			1.32304			0.661522	+	0.749926i	$0.269911\pi$
$440$	20.8225	+	24.7878i	0.992675	+	1.18171i
$441$	5.17326			0.246346
$442$	−1.53835	−	4.73456i	−0.0731719	−	0.225200i
$443$	14.5301	+	10.5568i	0.690348	+	0.501567i	0.876775	−	0.480902i	$-0.159691\pi$
$443$	14.5301	+	10.5568i	0.690348	+	0.501567i	−0.186426	+	0.982469i	$0.559691\pi$
$444$	3.32609	−	2.41655i	0.157849	−	0.114684i
$445$	16.2907	−	50.1375i	0.772252	−	2.37675i
$446$	5.51639	−	16.9777i	0.261209	−	0.803917i
$447$	8.84025	−	6.42282i	0.418129	−	0.303789i
$448$	−12.5978	−	9.15285i	−0.595191	−	0.432432i
$449$	−10.0273	−	30.8609i	−0.473219	−	1.45642i	−0.848345	−	0.529444i	$-0.822401\pi$
$449$	−10.0273	−	30.8609i	−0.473219	−	1.45642i	0.375126	−	0.926974i	$-0.377599\pi$
$450$	−6.19612			−0.292088
$451$	10.4402	−	16.7280i	0.491608	−	0.787693i
$452$	8.16369			0.383987
$453$	6.22012	+	19.1436i	0.292247	+	0.899443i
$454$	−16.9214	−	12.2941i	−0.794161	−	0.576992i
$455$	−9.90152	+	7.19388i	−0.464190	+	0.337254i
$456$	−0.708550	+	2.18069i	−0.0331809	+	0.102120i
$457$	−2.12743	+	6.54757i	−0.0995172	+	0.306282i	−0.988405	−	0.151843i	$-0.951479\pi$
$457$	−2.12743	+	6.54757i	−0.0995172	+	0.306282i	0.888887	+	0.458126i	$0.151479\pi$
$458$	−3.53642	+	2.56936i	−0.165246	+	0.120058i
$459$	−4.74823	−	3.44979i	−0.221628	−	0.161022i
$460$	3.86862	+	11.9064i	0.180375	+	0.555138i
$461$	−3.80133			−0.177045			−0.0885227	−	0.996074i	$-0.528215\pi$
$461$	−3.80133			−0.177045			−0.0885227	+	0.996074i	$0.528215\pi$
$462$	−9.09849	+	3.68180i	−0.423300	+	0.171293i
$463$	−18.1865			−0.845198			−0.422599	−	0.906317i	$-0.638882\pi$
$463$	−18.1865			−0.845198			−0.422599	+	0.906317i	$0.638882\pi$
$464$	−0.452102	−	1.39143i	−0.0209883	−	0.0645954i
$465$	−0.310724	−	0.225754i	−0.0144095	−	0.0104691i
$466$	−0.0562911	+	0.0408978i	−0.00260763	+	0.00189456i
$467$	−4.81990	+	14.8341i	−0.223038	+	0.686442i	0.775446	+	0.631413i	$0.217525\pi$
$467$	−4.81990	+	14.8341i	−0.223038	+	0.686442i	−0.998485	+	0.0550282i	$0.982475\pi$
$468$	0.395713	−	1.21788i	0.0182918	−	0.0562964i
$469$	−34.9780	+	25.4130i	−1.61513	+	1.17346i
$470$	27.1648	+	19.7364i	1.25302	+	0.910371i
$471$	−5.63716	−	17.3494i	−0.259746	−	0.799417i
$472$	2.63010			0.121060
$473$	1.65596	+	23.4972i	0.0761411	+	1.08040i
$474$	−7.32446			−0.336423
$475$	1.86013	+	5.72490i	0.0853488	+	0.262676i
$476$	−21.2145	−	15.4132i	−0.972364	−	0.706464i
$477$	−9.62184	+	6.99068i	−0.440554	+	0.320081i
$478$	2.63463	−	8.10855i	0.120505	−	0.370876i
$479$	8.15298	−	25.0923i	0.372519	−	1.14650i	−0.572618	−	0.819823i	$-0.694072\pi$
$479$	8.15298	−	25.0923i	0.372519	−	1.14650i	0.945137	−	0.326674i	$-0.105928\pi$
$480$	16.2770	−	11.8259i	0.742941	−	0.539778i
$481$	−2.59738	−	1.88711i	−0.118431	−	0.0860448i
$482$	−3.27211	−	10.0705i	−0.149040	−	0.458699i
$483$	−9.72386			−0.442451
$484$	−10.1220	+	9.79606i	−0.460091	+	0.445276i
$485$	30.3365			1.37751
$486$	0.262109	+	0.806688i	0.0118895	+	0.0365921i
$487$	10.8781	+	7.90342i	0.492935	+	0.358138i	0.806312	−	0.591491i	$-0.201460\pi$
$487$	10.8781	+	7.90342i	0.492935	+	0.358138i	−0.313377	+	0.949629i	$0.601460\pi$
$488$	−2.59324	+	1.88410i	−0.117390	+	0.0852891i
$489$	−2.26694	+	6.97692i	−0.102514	+	0.315507i
$490$	4.75650	−	14.6390i	0.214877	−	0.661322i
$491$	6.53077	−	4.74488i	0.294729	−	0.214134i	−0.430587	−	0.902549i	$-0.641693\pi$
$491$	6.53077	−	4.74488i	0.294729	−	0.214134i	0.725316	+	0.688416i	$0.241693\pi$
$492$	−6.15936	−	4.47504i	−0.277685	−	0.201750i
$493$	13.2063	+	40.6450i	0.594784	+	1.83056i
$494$	0.698942			0.0314469
$495$	−0.817891	−	11.6054i	−0.0367615	−	0.521625i
$496$	0.0219990			0.000987785
$497$	15.6629	+	48.2054i	0.702576	+	2.16231i
$498$	3.18515	+	2.31414i	0.142730	+	0.103699i
$499$	−15.1784	+	11.0277i	−0.679477	+	0.493669i	−0.873184	−	0.487390i	$-0.837949\pi$
$499$	−15.1784	+	11.0277i	−0.679477	+	0.493669i	0.193707	+	0.981059i	$0.437949\pi$
$500$	3.19957	−	9.84726i	0.143089	−	0.440383i
$501$	2.54901	−	7.84506i	0.113882	−	0.350491i
$502$	−9.14634	+	6.64520i	−0.408221	+	0.296590i
$503$	5.27977	+	3.83597i	0.235413	+	0.171038i	0.699237	−	0.714890i	$-0.253523\pi$
$503$	5.27977	+	3.83597i	0.235413	+	0.171038i	−0.463824	+	0.885927i	$0.653523\pi$
$504$	3.00008	+	9.23329i	0.133634	+	0.411283i
$505$	−29.8598			−1.32875
$506$	7.26777	−	2.94098i	0.323092	−	0.130742i
$507$	−1.00000			−0.0444116
$508$	4.10957	+	12.6480i	0.182333	+	0.561163i
$509$	−32.7860	−	23.8204i	−1.45322	−	1.05582i	−0.985067	−	0.172173i	$-0.944921\pi$
$509$	−32.7860	−	23.8204i	−1.45322	−	1.05582i	−0.468148	−	0.883650i	$-0.655079\pi$
$510$	−14.1277	+	10.2644i	−0.625585	+	0.454514i
$511$	4.92864	−	15.1688i	0.218030	−	0.671028i
$512$	−0.701642	+	2.15943i	−0.0310085	+	0.0954343i
$513$	0.666652	−	0.484351i	0.0294334	−	0.0213846i
$514$	−1.13364	−	0.823641i	−0.0500029	−	0.0363293i
$515$	−7.90491	−	24.3288i	−0.348332	−	1.07206i
$516$	9.09478			0.400376
$517$	−19.8169	+	31.7521i	−0.871545	+	1.39646i
$518$	9.50127			0.417462
$519$	−2.27326	−	6.99637i	−0.0997849	−	0.307106i
$520$	−7.89669	−	5.73728i	−0.346293	−	0.251596i
$521$	5.26509	−	3.82531i	0.230668	−	0.167590i	−0.466448	−	0.884549i	$-0.654466\pi$
$521$	5.26509	−	3.82531i	0.230668	−	0.167590i	0.697115	+	0.716959i	$0.254466\pi$
$522$	1.90857	−	5.87398i	0.0835359	−	0.257097i
$523$	−10.5776	+	32.5546i	−0.462527	+	1.42351i	0.399538	+	0.916717i	$0.369170\pi$
$523$	−10.5776	+	32.5546i	−0.462527	+	1.42351i	−0.862066	+	0.506797i	$0.830830\pi$
$524$	−12.5288	+	9.10272i	−0.547324	+	0.397654i
$525$	20.6197	+	14.9811i	0.899915	+	0.653827i
$526$	−2.69458	−	8.29307i	−0.117489	−	0.361595i
$527$	−0.642613			−0.0279927
$528$	0.428621	+	0.510245i	0.0186533	+	0.0222056i
$529$	−15.2327			−0.662291
$530$	10.9351	+	33.6548i	0.474991	+	1.46187i
$531$	−0.764686	−	0.555577i	−0.0331846	−	0.0241100i
$532$	2.97852	−	2.16402i	0.129135	−	0.0938222i
$533$	−1.83723	+	5.65440i	−0.0795791	+	0.244919i
$534$	−3.93911	+	12.1233i	−0.170462	+	0.524627i
$535$	34.9736	−	25.4098i	1.51204	−	1.09856i
$536$	−27.8957	−	20.2674i	−1.20491	−	0.875420i
$537$	−3.45282	−	10.6267i	−0.149000	−	0.458575i
$538$	9.71553			0.418866
$539$	16.6504	+	4.14176i	0.717182	+	0.178398i
$540$	−4.49199			−0.193304
$541$	−1.50103	−	4.61968i	−0.0645341	−	0.198616i	0.913590	−	0.406636i	$-0.133298\pi$
$541$	−1.50103	−	4.61968i	−0.0645341	−	0.198616i	−0.978125	+	0.208020i	$0.933298\pi$
$542$	−8.85452	−	6.43318i	−0.380334	−	0.276329i
$543$	−10.9216	+	7.93504i	−0.468693	+	0.340525i
$544$	10.4024	−	32.0152i	0.445998	−	1.37264i
$545$	−22.5475	+	69.3940i	−0.965828	+	2.97251i
$546$	2.39420	−	1.73949i	0.102462	−	0.0744432i
$547$	5.38299	+	3.91097i	0.230160	+	0.167221i	0.696888	−	0.717180i	$-0.254567\pi$
$547$	5.38299	+	3.91097i	0.230160	+	0.167221i	−0.466728	+	0.884401i	$0.654567\pi$
$548$	2.71624	+	8.35974i	0.116032	+	0.357110i
$549$	1.15196			0.0491645
$550$	−19.9425	−	4.96067i	−0.850350	−	0.211524i
$551$	−6.00023			−0.255619
$552$	−2.39643	−	7.37544i	−0.101999	−	0.313920i
$553$	24.3746	+	17.7092i	1.03651	+	0.753071i
$554$	−17.7442	+	12.8919i	−0.753879	+	0.547725i
$555$	−3.48018	+	10.7109i	−0.147725	+	0.454652i
$556$	3.30017	−	10.1569i	0.139959	−	0.430748i
$557$	−30.5083	+	22.1656i	−1.29268	+	0.939186i	−0.999856	−	0.0169807i	$-0.994595\pi$
$557$	−30.5083	+	22.1656i	−1.29268	+	0.939186i	−0.292823	+	0.956167i	$0.594595\pi$
$558$	0.0751333	+	0.0545876i	0.00318065	+	0.00231088i
$559$	−2.19471	−	6.75462i	−0.0928263	−	0.285690i
$560$	−2.45908			−0.103915
$561$	−12.5204	−	14.9048i	−0.528613	−	0.629280i
$562$	1.20125			0.0506715
$563$	−1.00579	−	3.09552i	−0.0423892	−	0.130461i	0.927622	−	0.373520i	$-0.121849\pi$
$563$	−1.00579	−	3.09552i	−0.0423892	−	0.130461i	−0.970011	+	0.243059i	$0.921849\pi$
$564$	11.6913	+	8.49424i	0.492293	+	0.357672i
$565$	−18.0920	+	13.1446i	−0.761137	+	0.552999i
$566$	1.96560	−	6.04948i	0.0826202	−	0.254279i
$567$	1.07817	−	3.31826i	0.0452787	−	0.139354i
$568$	−32.7032	+	23.7602i	−1.37219	+	0.996957i
$569$	17.2282	+	12.5170i	0.722244	+	0.524741i	0.887100	−	0.461577i	$-0.152716\pi$
$569$	17.2282	+	12.5170i	0.722244	+	0.524741i	−0.164856	+	0.986318i	$0.552716\pi$
$570$	−0.757642	−	2.33178i	−0.0317341	−	0.0976676i
$571$	−23.5011			−0.983489			−0.491745	−	0.870739i	$-0.663641\pi$
$571$	−23.5011			−0.983489			−0.491745	+	0.870739i	$0.663641\pi$
$572$	2.24866	−	3.60298i	0.0940213	−	0.150648i
$573$	21.1620			0.884054
$574$	−5.43708	−	16.7336i	−0.226939	−	0.698448i
$575$	−16.4707	−	11.9667i	−0.686877	−	0.499045i
$576$	−3.61070	+	2.62333i	−0.150446	+	0.109305i
$577$	9.84831	−	30.3100i	0.409991	−	1.26182i	−0.506665	−	0.862143i	$-0.669122\pi$
$577$	9.84831	−	30.3100i	0.409991	−	1.26182i	0.916656	−	0.399678i	$-0.130878\pi$
$578$	−4.57293	+	14.0740i	−0.190209	+	0.585403i
$579$	−9.94809	+	7.22771i	−0.413429	+	0.300374i
$580$	26.4620	+	19.2258i	1.09877	+	0.798307i
$581$	−5.00447	−	15.4022i	−0.207620	−	0.638990i
$582$	−7.33540			−0.304062
$583$	−36.5651	+	14.7965i	−1.51437	+	0.612807i
$584$	12.7200			0.526358
$585$	1.08398	+	3.33616i	0.0448173	+	0.137933i
$586$	4.71821	+	3.42798i	0.194907	+	0.141608i
$587$	21.7833	−	15.8265i	0.899094	−	0.653230i	−0.0391394	−	0.999234i	$-0.512462\pi$
$587$	21.7833	−	15.8265i	0.899094	−	0.653230i	0.938233	+	0.346004i	$0.112462\pi$
$588$	2.04713	−	6.30040i	0.0844220	−	0.259824i
$589$	0.0278804	−	0.0858072i	0.00114879	−	0.00353562i
$590$	−2.27522	+	1.65304i	−0.0936693	+	0.0680548i
$591$	1.42851	+	1.03788i	0.0587612	+	0.0426925i
$592$	−0.199337	−	0.613497i	−0.00819271	−	0.0252146i
$593$	1.93122			0.0793057			0.0396528	−	0.999214i	$-0.487375\pi$
$593$	1.93122			0.0793057			0.0396528	+	0.999214i	$0.487375\pi$
$594$	0.197767	+	2.80621i	0.00811449	+	0.115140i
$595$	71.8320			2.94483
$596$	−4.32401	−	13.3079i	−0.177118	−	0.545114i
$597$	13.3790	+	9.72038i	0.547564	+	0.397829i
$598$	−1.91246	+	1.38948i	−0.0782063	+	0.0568202i
$599$	0.482454	−	1.48484i	0.0197126	−	0.0606690i	−0.940716	−	0.339194i	$-0.889846\pi$
$599$	0.482454	−	1.48484i	0.0197126	−	0.0606690i	0.960429	+	0.278525i	$0.0898456\pi$
$600$	−6.28129	+	19.3318i	−0.256433	+	0.789219i
$601$	−17.4228	+	12.6584i	−0.710689	+	0.516346i	−0.883396	−	0.468627i	$-0.844749\pi$
$601$	−17.4228	+	12.6584i	−0.710689	+	0.516346i	0.172707	+	0.984973i	$0.444749\pi$
$602$	17.0042	+	12.3543i	0.693038	+	0.503522i
$603$	3.82927	+	11.7853i	0.155940	+	0.479934i
$604$	25.7759			1.04881
$605$	6.65899	−	38.0074i	0.270727	−	1.54522i
$606$	7.22015			0.293298
$607$	−7.08778	−	21.8140i	−0.287684	−	0.885401i	−0.985581	−	0.169203i	$-0.945881\pi$
$607$	−7.08778	−	21.8140i	−0.287684	−	0.885401i	0.697897	−	0.716198i	$-0.254119\pi$
$608$	3.82363	+	2.77803i	0.155069	+	0.112664i
$609$	−20.5536	+	14.9331i	−0.832874	+	0.605118i
$610$	1.05916	−	3.25975i	0.0428841	−	0.131984i
$611$	3.48731	−	10.7328i	0.141082	−	0.434204i
$612$	−6.08035	+	4.41764i	−0.245784	+	0.178572i
$613$	−23.4619	−	17.0460i	−0.947616	−	0.688483i	0.00262596	−	0.999997i	$-0.499164\pi$
$613$	−23.4619	−	17.0460i	−0.947616	−	0.688483i	−0.950242	+	0.311513i	$0.899164\pi$
$614$	2.60850	+	8.02814i	0.105271	+	0.323990i
$615$	20.8555			0.840976
$616$	2.26363	+	32.1196i	0.0912041	+	1.29414i
$617$	−42.5248			−1.71198			−0.855992	−	0.516990i	$-0.827053\pi$
$617$	−42.5248			−1.71198			−0.855992	+	0.516990i	$0.827053\pi$
$618$	1.91142	+	5.88274i	0.0768885	+	0.236638i
$619$	24.4574	+	17.7693i	0.983024	+	0.714209i	0.958382	−	0.285487i	$-0.0921554\pi$
$619$	24.4574	+	17.7693i	0.983024	+	0.714209i	0.0246419	+	0.999696i	$0.492155\pi$
$620$	−0.397898	+	0.289090i	−0.0159800	+	0.0116101i
$621$	−0.861227	+	2.65058i	−0.0345598	+	0.106364i
$622$	6.20874	−	19.1085i	0.248948	−	0.766182i
$623$	42.4206	−	30.8204i	1.69955	−	1.23479i
$624$	−0.162549	−	0.118099i	−0.00650718	−	0.00472774i
$625$	−2.52219	−	7.76250i	−0.100888	−	0.310500i
$626$	−6.04274			−0.241517
$627$	2.53342	−	1.02518i	0.101175	−	0.0409416i
$628$	−23.3601			−0.932171
$629$	5.82284	+	17.9209i	0.232172	+	0.714551i
$630$	−8.39849	−	6.10186i	−0.334604	−	0.243104i
$631$	13.6656	−	9.92867i	0.544021	−	0.395254i	−0.281555	−	0.959545i	$-0.590850\pi$
$631$	13.6656	−	9.92867i	0.544021	−	0.395254i	0.825576	+	0.564291i	$0.190850\pi$
$632$	−7.42514	+	22.8522i	−0.295356	+	0.909013i
$633$	−7.37650	+	22.7025i	−0.293189	+	0.902344i
$634$	−14.6472	+	10.6418i	−0.581714	+	0.422640i
$635$	−29.4724	−	21.4129i	−1.16958	−	0.849746i
$636$	4.70631	+	14.4845i	0.186617	+	0.574349i
$637$	−5.17326			−0.204972
$638$	10.8456	−	17.3776i	0.429381	−	0.687987i
$639$	14.5273			0.574692
$640$	−8.33101	−	25.6402i	−0.329312	−	1.01352i
$641$	32.5771	+	23.6687i	1.28672	+	0.934856i	0.999734	−	0.0230792i	$-0.00734698\pi$
$641$	32.5771	+	23.6687i	1.28672	+	0.934856i	0.286985	+	0.957935i	$0.407347\pi$
$642$	−8.45665	+	6.14412i	−0.333757	+	0.242489i
$643$	10.8809	−	33.4880i	0.429101	−	1.32064i	−0.469912	−	0.882713i	$-0.655714\pi$
$643$	10.8809	−	33.4880i	0.429101	−	1.32064i	0.899013	−	0.437923i	$-0.144286\pi$
$644$	−3.84785	+	11.8425i	−0.151627	+	0.466659i
$645$	−20.1555	+	14.6438i	−0.793621	+	0.576600i
$646$	−3.31873	−	2.41120i	−0.130574	−	0.0948674i
$647$	−4.30825	−	13.2594i	−0.169375	−	0.521282i	0.829957	−	0.557827i	$-0.188365\pi$
$647$	−4.30825	−	13.2594i	−0.169375	−	0.521282i	−0.999332	+	0.0365452i	$0.988365\pi$
$648$	2.78257			0.109310
$649$	−2.01638	−	2.40036i	−0.0791497	−	0.0942225i
$650$	6.19612			0.243032
$651$	−0.118049	−	0.363317i	−0.00462670	−	0.0142395i
$652$	7.59998	+	5.52171i	0.297638	+	0.216247i
$653$	18.4489	−	13.4039i	0.721962	−	0.524536i	−0.165048	−	0.986286i	$-0.552778\pi$
$653$	18.4489	−	13.4039i	0.721962	−	0.524536i	0.887011	+	0.461749i	$0.152778\pi$
$654$	5.45201	−	16.7796i	0.213191	−	0.656133i
$655$	13.1093	−	40.3462i	0.512221	−	1.57645i
$656$	−0.966420	+	0.702145i	−0.0377323	+	0.0274142i
$657$	−3.69827	−	2.68695i	−0.144283	−	0.104828i
$658$	10.3203	+	31.7627i	0.402328	+	1.23824i
$659$	5.26528			0.205106			0.102553	−	0.994728i	$-0.467299\pi$
$659$	5.26528			0.205106			0.102553	+	0.994728i	$0.467299\pi$
$660$	−14.4577	−	3.59632i	−0.562763	−	0.139987i
$661$	−28.4438			−1.10634			−0.553168	−	0.833070i	$-0.686581\pi$
$661$	−28.4438			−1.10634			−0.553168	+	0.833070i	$0.686581\pi$
$662$	4.32567	+	13.3130i	0.168122	+	0.517426i
$663$	4.74823	+	3.44979i	0.184406	+	0.133979i
$664$	10.4490	−	7.59167i	0.405501	−	0.294614i
$665$	−3.11651	+	9.59162i	−0.120853	+	0.371947i
$666$	0.841512	−	2.58991i	0.0326079	−	0.100357i
$667$	16.4180	−	11.9284i	0.635706	−	0.461868i
$668$	−8.54565	−	6.20878i	−0.330641	−	0.240225i
$669$	6.50362	+	20.0161i	0.251445	+	0.773867i
$670$	36.8701			1.42442
$671$	3.70764	+	0.922271i	0.143132	+	0.0356039i
$672$	20.0115			0.771961
$673$	5.51996	+	16.9887i	0.212779	+	0.654866i	0.999304	+	0.0373073i	$0.0118780\pi$
$673$	5.51996	+	16.9887i	0.212779	+	0.654866i	−0.786525	+	0.617558i	$0.788122\pi$
$674$	9.86469	+	7.16712i	0.379974	+	0.276067i
$675$	5.90987	−	4.29377i	0.227471	−	0.165267i
$676$	−0.395713	+	1.21788i	−0.0152197	+	0.0468415i
$677$	9.77585	−	30.0870i	0.375716	−	1.15634i	−0.567278	−	0.823527i	$-0.692003\pi$
$677$	9.77585	−	30.0870i	0.375716	−	1.15634i	0.942994	−	0.332810i	$-0.107997\pi$
$678$	4.37467	−	3.17839i	0.168008	−	0.122065i
$679$	24.4110	+	17.7356i	0.936808	+	0.680631i
$680$	17.7029	+	54.4838i	0.678874	+	2.08936i
$681$	24.6592			0.944943
$682$	0.198117	+	0.235845i	0.00758628	+	0.00903097i
$683$	−30.9484			−1.18421			−0.592104	−	0.805862i	$-0.701703\pi$
$683$	−30.9484			−1.18421			−0.592104	+	0.805862i	$0.701703\pi$
$684$	−0.326078	−	1.00356i	−0.0124679	−	0.0383723i
$685$	−19.4799	−	14.1530i	−0.744290	−	0.540758i
$686$	−4.37358	+	3.17759i	−0.166984	+	0.121321i
$687$	1.59254	−	4.90132i	0.0607591	−	0.186997i
$688$	0.440966	−	1.35715i	0.0168117	−	0.0517410i
$689$	9.62184	−	6.99068i	0.366563	−	0.266324i
$690$	6.70862	+	4.87409i	0.255393	+	0.185554i
$691$	−3.86624	−	11.8991i	−0.147079	−	0.452662i	0.850194	−	0.526470i	$-0.176485\pi$
$691$	−3.86624	−	11.8991i	−0.147079	−	0.452662i	−0.997272	+	0.0738082i	$0.976485\pi$
$692$	−9.42028			−0.358105
$693$	6.12675	−	9.81676i	0.232736	−	0.372908i
$694$	−7.38360			−0.280277
$695$	9.04024	+	27.8230i	0.342916	+	1.05539i
$696$	−16.3920	−	11.9095i	−0.621336	−	0.451427i
$697$	28.2301	−	20.5103i	1.06929	−	0.776885i
$698$	1.89728	−	5.83922i	0.0718130	−	0.221018i
$699$	0.0253492	−	0.0780169i	0.000958796	−	0.00295087i
$700$	26.4046	−	19.1840i	0.997998	−	0.725088i
$701$	24.1941	+	17.5780i	0.913798	+	0.663913i	0.941973	−	0.335690i	$-0.108969\pi$
$701$	24.1941	+	17.5780i	0.913798	+	0.663913i	−0.0281743	+	0.999603i	$0.508969\pi$
$702$	−0.262109	−	0.806688i	−0.00989266	−	0.0304465i
$703$	−2.64558			−0.0997798
$704$	−13.7215	+	5.55254i	−0.517148	+	0.209269i
$705$	−39.5867			−1.49092
$706$	2.19844	+	6.76610i	0.0827394	+	0.254646i
$707$	−24.0275	−	17.4570i	−0.903645	−	0.656537i
$708$	−0.979221	+	0.711446i	−0.0368014	+	0.0267378i
$709$	−1.15941	+	3.56831i	−0.0435427	+	0.134011i	−0.970465	−	0.241244i	$-0.922445\pi$
$709$	−1.15941	+	3.56831i	−0.0435427	+	0.134011i	0.926922	+	0.375254i	$0.122445\pi$
$710$	13.3570	−	41.1085i	0.501278	−	1.54278i
$711$	6.98608	−	5.07569i	0.261999	−	0.190353i
$712$	33.8314	+	24.5800i	1.26789	+	0.921173i
$713$	0.0942960	+	0.290213i	0.00353141	+	0.0108686i
$714$	−17.3691			−0.650021
$715$	0.817891	+	11.6054i	0.0305874	+	0.434019i
$716$	−14.3083			−0.534728
$717$	3.10613	+	9.55969i	0.116001	+	0.357013i
$718$	−1.94806	−	1.41535i	−0.0727008	−	0.0528202i
$719$	−31.0697	+	22.5734i	−1.15870	+	0.841847i	−0.989613	−	0.143754i	$-0.954083\pi$
$719$	−31.0697	+	22.5734i	−1.15870	+	0.841847i	−0.169089	+	0.985601i	$0.554083\pi$
$720$	−0.217796	+	0.670308i	−0.00811679	+	0.0249809i
$721$	7.86248	−	24.1982i	0.292814	−	0.901189i
$722$	−12.5720	+	9.13412i	−0.467883	+	0.339937i
$723$	10.0996	+	7.33777i	0.375607	+	0.272895i
$724$	5.34208	+	16.4412i	0.198537	+	0.611034i
$725$	−53.1921			−1.97550
$726$	−1.61015	+	9.19024i	−0.0597584	+	0.341082i
$727$	30.3570			1.12588			0.562940	−	0.826498i	$-0.309670\pi$
$727$	30.3570			1.12588			0.562940	+	0.826498i	$0.309670\pi$
$728$	−3.00008	−	9.23329i	−0.111190	−	0.342208i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−11.0037	+	7.99467i	−0.407266	+	0.295896i
$731$	−12.8810	+	39.6438i	−0.476422	+	1.46628i
$732$	0.455846	−	1.40295i	0.0168486	−	0.0518545i
$733$	−33.1238	+	24.0658i	−1.22345	+	0.888892i	−0.996382	−	0.0849859i	$-0.972915\pi$
$733$	−33.1238	+	24.0658i	−1.22345	+	0.888892i	−0.227073	+	0.973878i	$0.572915\pi$
$734$	−8.36203	−	6.07537i	−0.308648	−	0.224246i
$735$	5.60774	+	17.2588i	0.206845	+	0.636602i
$736$	−15.9850			−0.589213
$737$	2.88927	+	40.9972i	0.106428	+	1.51015i
$738$	−5.04289			−0.185632
$739$	−4.41222	−	13.5794i	−0.162306	−	0.499527i	0.836522	−	0.547934i	$-0.184585\pi$
$739$	−4.41222	−	13.5794i	−0.162306	−	0.499527i	−0.998828	+	0.0484072i	$0.984585\pi$
$740$	11.6674	+	8.47687i	0.428903	+	0.311616i
$741$	−0.666652	+	0.484351i	−0.0244901	+	0.0177931i
$742$	−10.8764	+	33.4742i	−0.399286	+	1.22888i
$743$	−10.2536	+	31.5574i	−0.376168	+	1.15773i	0.566519	+	0.824049i	$0.308290\pi$
$743$	−10.2536	+	31.5574i	−0.376168	+	1.15773i	−0.942687	+	0.333678i	$0.891710\pi$
$744$	0.246479	−	0.179077i	0.00903636	−	0.00656530i
$745$	31.0103	+	22.5303i	1.13613	+	0.825445i
$746$	0.658335	+	2.02615i	0.0241033	+	0.0741825i
$747$	−4.64165			−0.169829
$748$	−23.1067	+	9.35037i	−0.844864	+	0.341883i
$749$	42.9977			1.57110
$750$	−2.11930	−	6.52255i	−0.0773861	−	0.238170i
$751$	−23.7156	−	17.2304i	−0.865394	−	0.628745i	0.0639533	−	0.997953i	$-0.479629\pi$
$751$	−23.7156	−	17.2304i	−0.865394	−	0.628745i	−0.929347	+	0.369208i	$0.879629\pi$
$752$	1.83440	−	1.33277i	0.0668936	−	0.0486011i
$753$	4.11882	−	12.6764i	0.150098	−	0.461954i
$754$	−1.90857	+	5.87398i	−0.0695061	+	0.213918i
$755$	−57.1235	+	41.5027i	−2.07894	+	1.51044i
$756$	−3.61459	−	2.62615i	−0.131461	−	0.0955122i
$757$	−4.00785	−	12.3349i	−0.145668	−	0.448319i	0.851429	−	0.524471i	$-0.175737\pi$
$757$	−4.00785	−	12.3349i	−0.145668	−	0.448319i	−0.997096	+	0.0761514i	$0.975737\pi$
$758$	−27.0409			−0.982169
$759$	−4.89398	+	7.84151i	−0.177640	+	0.284629i
$760$	−8.04320			−0.291757
$761$	−3.47434	−	10.6929i	−0.125945	−	0.387618i	0.868127	−	0.496342i	$-0.165324\pi$
$761$	−3.47434	−	10.6929i	−0.125945	−	0.387618i	−0.994072	+	0.108724i	$0.965324\pi$
$762$	7.12646	+	5.17768i	0.258164	+	0.187567i
$763$	−58.7133	+	42.6577i	−2.12556	+	1.54431i
$764$	8.37406	−	25.7727i	0.302963	−	0.932423i
$765$	6.36205	−	19.5804i	0.230020	−	0.707930i
$766$	5.38705	−	3.91392i	0.194642	−	0.141416i
$767$	0.764686	+	0.555577i	0.0276112	+	0.0200607i
$768$	4.77278	+	14.6891i	0.172223	+	0.530048i
$769$	−0.957410			−0.0345251			−0.0172625	−	0.999851i	$-0.505495\pi$
$769$	−0.957410			−0.0345251			−0.0172625	+	0.999851i	$0.505495\pi$
$770$	−22.1457	−	26.3630i	−0.798076	−	0.950057i
$771$	1.65204			0.0594967
$772$	4.86589	+	14.9757i	0.175127	+	0.538986i
$773$	−40.4485	−	29.3875i	−1.45483	−	1.05700i	−0.984672	−	0.174414i	$-0.944197\pi$
$773$	−40.4485	−	29.3875i	−1.45483	−	1.05700i	−0.470158	−	0.882582i	$-0.655803\pi$
$774$	4.87362	−	3.54089i	0.175179	−	0.127275i
$775$	0.247160	−	0.760680i	0.00887825	−	0.0273244i
$776$	−7.43623	+	22.8864i	−0.266945	+	0.821573i
$777$	−9.06233	+	6.58417i	−0.325109	+	0.236206i
$778$	21.7721	+	15.8184i	0.780568	+	0.567116i
$779$	1.51393	+	4.65938i	0.0542420	+	0.166940i
$780$	4.49199			0.160839
$781$	46.7568	+	11.6307i	1.67309	+	0.416179i
$782$	13.8742			0.496141
$783$	2.25014	+	6.92521i	0.0804134	+	0.247487i
$784$	−0.840910	−	0.610957i	−0.0300325	−	0.0218199i
$785$	51.7698	−	37.6129i	1.84774	−	1.34246i
$786$	−3.16984	+	9.75575i	−0.113064	+	0.347976i
$787$	11.6391	−	35.8215i	0.414890	−	1.27690i	−0.497459	−	0.867487i	$-0.665734\pi$
$787$	11.6391	−	35.8215i	0.414890	−	1.27690i	0.912349	−	0.409413i	$-0.134266\pi$
$788$	1.82929	−	1.32905i	0.0651656	−	0.0473456i
$789$	8.31701	+	6.04266i	0.296093	+	0.215124i
$790$	−7.93960	−	24.4356i	−0.282478	−	0.869379i
$791$	−22.2429			−0.790868
$792$	8.95583	+	2.22775i	0.318232	+	0.0791597i
$793$	−1.15196			−0.0409074
$794$	0.411970	+	1.26791i	0.0146203	+	0.0449966i
$795$	−33.7520	−	24.5222i	−1.19706	−	0.869714i
$796$	17.1325	−	12.4475i	0.607244	−	0.441189i
$797$	−2.55629	+	7.86746i	−0.0905485	+	0.278680i	−0.986068	−	0.166343i	$-0.946804\pi$
$797$	−2.55629	+	7.86746i	−0.0905485	+	0.278680i	0.895520	+	0.445022i	$0.146804\pi$
$798$	0.753575	−	2.31927i	0.0266763	−	0.0821012i
$799$	−53.5846	+	38.9315i	−1.89569	+	1.37730i
$800$	33.8964	+	24.6272i	1.19842	+	0.870703i
$801$	−4.64406	−	14.2930i	−0.164090	−	0.505017i
$802$	−13.9755			−0.493492
$803$	−9.75186	−	11.6089i	−0.344136	−	0.409671i
$804$	15.8683			0.559633
$805$	−10.5405	−	32.4404i	−0.371504	−	1.14337i
$806$	−0.0751333	−	0.0545876i	−0.00264646	−	0.00192277i
$807$	−9.26669	+	6.73265i	−0.326203	+	0.237000i
$808$	7.31940	−	22.5268i	0.257496	−	0.792490i
$809$	0.0709547	−	0.218376i	0.00249464	−	0.00767770i	−0.949801	−	0.312853i	$-0.898715\pi$
$809$	0.0709547	−	0.218376i	0.00249464	−	0.00767770i	0.952296	+	0.305176i	$0.0987152\pi$
$810$	−2.40712	+	1.74888i	−0.0845776	+	0.0614492i
$811$	−21.8888	−	15.9032i	−0.768621	−	0.558435i	0.132922	−	0.991127i	$-0.457564\pi$
$811$	−21.8888	−	15.9032i	−0.768621	−	0.558435i	−0.901542	+	0.432691i	$0.857564\pi$
$812$	10.0533	+	30.9410i	0.352803	+	1.08582i
$813$	12.9035			0.452546
$814$	4.78195	−	7.66201i	0.167607	−	0.268553i
$815$	−25.7334			−0.901403
$816$	0.364404	+	1.12152i	0.0127567	+	0.0392611i
$817$	−4.73472	−	3.43997i	−0.165647	−	0.120349i
$818$	6.36045	−	4.62114i	0.222388	−	0.161574i
$819$	−1.07817	+	3.31826i	−0.0376742	+	0.115949i
$820$	8.25280	−	25.3995i	0.288200	−	0.886989i
$821$	19.8248	−	14.4036i	0.691891	−	0.502688i	−0.185390	−	0.982665i	$-0.559355\pi$
$821$	19.8248	−	14.4036i	0.691891	−	0.502688i	0.877281	+	0.479977i	$0.159355\pi$
$822$	4.71027	+	3.42221i	0.164290	+	0.119363i
$823$	−13.9026	−	42.7878i	−0.484614	−	1.49149i	−0.832539	−	0.553966i	$-0.813114\pi$
$823$	−13.9026	−	42.7878i	−0.484614	−	1.49149i	0.347925	−	0.937522i	$-0.386886\pi$
$824$	20.2918			0.706898
$825$	22.4588	−	9.08820i	0.781915	−	0.316410i
$826$	−2.79723			−0.0973281
$827$	3.49840	+	10.7670i	0.121651	+	0.374405i	0.993276	−	0.115769i	$-0.0369333\pi$
$827$	3.49840	+	10.7670i	0.121651	+	0.374405i	−0.871625	+	0.490174i	$0.836933\pi$
$828$	2.88729	+	2.09774i	0.100340	+	0.0729014i
$829$	20.5794	−	14.9518i	0.714752	−	0.519298i	−0.169951	−	0.985452i	$-0.554361\pi$
$829$	20.5794	−	14.9518i	0.714752	−	0.519298i	0.884703	+	0.466155i	$0.154361\pi$
$830$	−4.26771	+	13.1347i	−0.148134	+	0.455911i
$831$	7.99064	−	24.5927i	0.277192	−	0.853110i
$832$	3.61070	−	2.62333i	0.125179	−	0.0909476i
$833$	24.5638	+	17.8467i	0.851086	+	0.618350i
$834$	−2.18594	−	6.72764i	−0.0756930	−	0.232959i
$835$	28.9355			1.00135
$836$	−0.246033	−	3.49108i	−0.00850924	−	0.120741i
$837$	−0.109490			−0.00378454
$838$	4.05140	+	12.4689i	0.139953	+	0.430732i
$839$	35.5072	+	25.7975i	1.22585	+	0.890629i	0.996572	−	0.0827326i	$-0.0263647\pi$
$839$	35.5072	+	25.7975i	1.22585	+	0.890629i	0.229274	+	0.973362i	$0.426365\pi$
$840$	−27.5517	+	20.0175i	−0.950624	+	0.690669i
$841$	7.42311	−	22.8460i	0.255969	−	0.787792i
$842$	4.90759	−	15.1040i	0.169127	−	0.520519i
$843$	−1.14575	+	0.832437i	−0.0394618	+	0.0286706i
$844$	24.7299	+	17.9673i	0.851239	+	0.618462i
$845$	−1.08398	−	3.33616i	−0.0372902	−	0.114767i
$846$	9.57211			0.329096
$847$	27.5786	−	26.6905i	0.947612	−	0.917098i
$848$	2.38962			0.0820597
$849$	2.31737	+	7.13212i	0.0795319	+	0.244774i
$850$	−29.4206	−	21.3753i	−1.00912	−	0.733166i
$851$	7.23888	−	5.25935i	0.248146	−	0.180288i
$852$	5.74864	−	17.6925i	0.196945	−	0.606135i
$853$	−3.07573	+	9.46613i	−0.105311	+	0.324114i	−0.989803	−	0.142441i	$-0.954505\pi$
$853$	−3.07573	+	9.46613i	−0.105311	+	0.324114i	0.884492	+	0.466555i	$0.154505\pi$
$854$	2.75803	−	2.00382i	0.0943778	−	0.0685695i
$855$	2.33851	+	1.69903i	0.0799755	+	0.0581056i
$856$	10.5967	+	32.6132i	0.362187	+	1.11470i
$857$	36.8045			1.25722			0.628609	−	0.777721i	$-0.283625\pi$
$857$	36.8045			1.25722			0.628609	+	0.777721i	$0.283625\pi$
$858$	−0.197767	−	2.80621i	−0.00675166	−	0.0958024i
$859$	15.9907			0.545595			0.272798	−	0.962071i	$-0.412051\pi$
$859$	15.9907			0.545595			0.272798	+	0.962071i	$0.412051\pi$
$860$	9.85861	+	30.3417i	0.336176	+	1.03464i
$861$	16.7819	+	12.1928i	0.571926	+	0.415529i
$862$	4.81214	−	3.49623i	0.163902	−	0.119082i
$863$	4.31972	−	13.2947i	0.147045	−	0.452558i	−0.850223	−	0.526422i	$-0.823533\pi$
$863$	4.31972	−	13.2947i	0.147045	−	0.452558i	0.997268	+	0.0738645i	$0.0235332\pi$
$864$	1.77239	−	5.45485i	0.0602979	−	0.185578i
$865$	20.8768	−	15.1679i	0.709834	−	0.515724i
$866$	−13.4481	−	9.77064i	−0.456986	−	0.332020i
$867$	−5.39132	−	16.5928i	−0.183099	−	0.563520i
$868$	−0.489189			−0.0166042
$869$	26.5487	−	10.7432i	0.900601	−	0.364438i
$870$	21.6654			0.734526
$871$	−3.82927	−	11.7853i	−0.129750	−	0.399329i
$872$	−46.8251	−	34.0205i	−1.58570	−	1.15208i
$873$	6.99652	−	5.08327i	0.236796	−	0.172043i
$874$	−0.601947	+	1.85260i	−0.0203612	+	0.0626652i
$875$	−8.71761	+	26.8300i	−0.294709	+	0.907021i
$876$	−4.73584	+	3.44079i	−0.160009	+	0.116253i
$877$	36.5739	+	26.5725i	1.23501	+	0.897290i	0.997256	−	0.0740346i	$-0.0235875\pi$
$877$	36.5739	+	26.5725i	1.23501	+	0.897290i	0.237758	+	0.971324i	$0.423588\pi$
$878$	−7.26588	−	22.3621i	−0.245212	−	0.754684i
$879$	−6.87575			−0.231913
$880$	−1.23764	+	1.98305i	−0.0417209	+	0.0668485i
$881$	−48.1142			−1.62101			−0.810504	−	0.585733i	$-0.800807\pi$
$881$	−48.1142			−1.62101			−0.810504	+	0.585733i	$0.800807\pi$
$882$	−1.35596	−	4.17321i	−0.0456575	−	0.140519i
$883$	−20.5684	−	14.9438i	−0.692183	−	0.502900i	0.185194	−	0.982702i	$-0.440709\pi$
$883$	−20.5684	−	14.9438i	−0.692183	−	0.502900i	−0.877377	+	0.479802i	$0.840709\pi$
$884$	6.08035	−	4.41764i	0.204504	−	0.148581i
$885$	1.02459	−	3.15335i	0.0344411	−	0.105999i
$886$	4.70754	−	14.4883i	0.158153	−	0.486745i
$887$	37.7731	−	27.4438i	1.26830	−	0.921471i	0.269163	−	0.963095i	$-0.413253\pi$
$887$	37.7731	−	27.4438i	1.26830	−	0.921471i	0.999133	+	0.0416233i	$0.0132529\pi$
$888$	−7.22741	−	5.25102i	−0.242536	−	0.176213i
$889$	−11.1970	−	34.4609i	−0.375536	−	1.15578i
$890$	−44.7153			−1.49886
$891$	−2.13327	−	2.53952i	−0.0714673	−	0.0850771i
$892$	26.9507			0.902377
$893$	−2.87364	−	8.84415i	−0.0961627	−	0.295958i
$894$	−7.49832	−	5.44785i	−0.250781	−	0.182203i
$895$	31.7095	−	23.0383i	1.05993	−	0.770086i
$896$	8.28630	−	25.5026i	0.276826	−	0.851982i
$897$	0.861227	−	2.65058i	0.0287555	−	0.0885004i
$898$	−22.2669	+	16.1778i	−0.743056	+	0.539862i
$899$	0.645001	+	0.468620i	0.0215120	+	0.0156294i
$900$	−2.89068	−	8.89660i	−0.0963560	−	0.296553i
$901$	−69.8030			−2.32548
$902$	−16.2308	−	4.03739i	−0.540426	−	0.134430i
$903$	−24.7798			−0.824621
$904$	−5.48173	−	16.8710i	−0.182320	−	0.561122i
$905$	−38.3115	−	27.8349i	−1.27352	−	0.925264i
$906$	13.8125	−	10.0354i	0.458891	−	0.333404i
$907$	−4.82072	+	14.8367i	−0.160070	+	0.492643i	−0.998639	−	0.0521510i	$-0.983392\pi$
$907$	−4.82072	+	14.8367i	−0.160070	+	0.492643i	0.838570	+	0.544794i	$0.183392\pi$
$908$	9.75796	−	30.0319i	0.323829	−	0.996644i
$909$	−6.88659	+	5.00340i	−0.228414	+	0.165952i
$910$	8.39849	+	6.10186i	0.278407	+	0.202275i
$911$	−5.57498	−	17.1580i	−0.184707	−	0.568470i	0.815236	−	0.579129i	$-0.196607\pi$
$911$	−5.57498	−	17.1580i	−0.184707	−	0.568470i	−0.999943	+	0.0106586i	$0.996607\pi$
$912$	−0.165565			−0.00548241
$913$	−14.9393	−	3.71614i	−0.494420	−	0.122986i
$914$	5.83947			0.193152
$915$	1.24871	+	3.84313i	0.0412811	+	0.127050i
$916$	−5.33903	−	3.87903i	−0.176406	−	0.128167i
$917$	34.1363	−	24.8015i	1.12728	−	0.819016i
$918$	−1.53835	+	4.73456i	−0.0507732	+	0.156264i
$919$	6.46852	−	19.9081i	0.213377	−	0.656707i	−0.785888	−	0.618369i	$-0.787794\pi$
$919$	6.46852	−	19.9081i	0.213377	−	0.656707i	0.999265	−	0.0383377i	$-0.0122063\pi$
$920$	22.0080	−	15.9897i	0.725581	−	0.527166i
$921$	−8.05132	−	5.84963i	−0.265300	−	0.192752i
$922$	0.996362	+	3.06649i	0.0328134	+	0.100989i
$923$	−14.5273			−0.478173
$924$	−9.53119	−	11.3463i	−0.313553	−	0.373264i
$925$	−23.4530			−0.771131
$926$	4.76684	+	14.6708i	0.156648	+	0.482114i
$927$	−5.89972	−	4.28640i	−0.193772	−	0.140784i
$928$	−33.7879	+	24.5483i	−1.10914	+	0.805838i
$929$	−4.51672	+	13.9010i	−0.148189	+	0.456078i	−0.997407	−	0.0719634i	$-0.977074\pi$
$929$	−4.51672	+	13.9010i	−0.148189	+	0.456078i	0.849218	+	0.528042i	$0.177074\pi$
$930$	−0.100670	+	0.309829i	−0.00330109	+	0.0101597i
$931$	−3.44877	+	2.50567i	−0.113029	+	0.0821202i
$932$	−0.0849841	−	0.0617445i	−0.00278375	−	0.00202251i
$933$	7.31988	+	22.5283i	0.239642	+	0.737543i
$934$	13.2299			0.432894
$935$	36.1527	−	57.9268i	1.18232	−	1.89441i
$936$	−2.78257			−0.0909512
$937$	−11.2700	−	34.6856i	−0.368176	−	1.13313i	−0.947968	−	0.318365i	$-0.896866\pi$
$937$	−11.2700	−	34.6856i	−0.368176	−	1.13313i	0.579792	−	0.814765i	$-0.303134\pi$
$938$	29.6684	+	21.5554i	0.968708	+	0.703808i
$939$	5.76358	−	4.18749i	0.188087	−	0.136653i
$940$	−15.6650	+	48.2118i	−0.510934	+	1.57249i
$941$	7.91634	−	24.3640i	0.258065	−	0.794244i	−0.735145	−	0.677910i	$-0.762886\pi$
$941$	7.91634	−	24.3640i	0.258065	−	0.794244i	0.993210	−	0.116334i	$-0.0371142\pi$
$942$	−12.5180	+	9.09485i	−0.407858	+	0.296326i
$943$	−13.4052	−	9.73945i	−0.436533	−	0.317160i
$944$	0.0586861	+	0.180617i	0.00191007	+	0.00587859i
$945$	12.2390			0.398133
$946$	18.5208	−	7.49466i	0.602164	−	0.243672i
$947$	−41.6979			−1.35500			−0.677501	−	0.735522i	$-0.736937\pi$
$947$	−41.6979			−1.35500			−0.677501	+	0.735522i	$0.736937\pi$
$948$	−3.41709	−	10.5167i	−0.110982	−	0.341567i
$949$	3.69827	+	2.68695i	0.120051	+	0.0872222i
$950$	4.13065	−	3.00110i	0.134016	−	0.0973684i
$951$	6.59598	−	20.3003i	0.213889	−	0.658284i
$952$	−17.6078	+	54.1914i	−0.570673	+	1.75635i
$953$	−7.92951	+	5.76112i	−0.256862	+	0.186621i	−0.708762	−	0.705447i	$-0.750746\pi$
$953$	−7.92951	+	5.76112i	−0.256862	+	0.186621i	0.451901	+	0.892068i	$0.350746\pi$
$954$	8.16127	+	5.92951i	0.264231	+	0.191975i
$955$	22.9392	+	70.5997i	0.742297	+	2.28455i
$956$	12.8717			0.416300
$957$	1.69778	+	24.0906i	0.0548815	+	0.778738i
$958$	−22.3786			−0.723021
$959$	−7.40073	−	22.7771i	−0.238982	−	0.735511i
$960$	−12.6658	−	9.20225i	−0.408787	−	0.297001i
$961$	25.0698	−	18.2143i	0.808704	−	0.587558i
$962$	−0.841512	+	2.58991i	−0.0271314	+	0.0835020i
$963$	3.80823	−	11.7205i	0.122719	−	0.377689i
$964$	12.9330	−	9.39641i	0.416545	−	0.302638i
$965$	−34.8964	−	25.3537i	−1.12335	−	0.816165i
$966$	2.54871	+	7.84412i	0.0820034	+	0.252380i
$967$	−43.0593			−1.38469			−0.692347	−	0.721565i	$-0.743423\pi$
$967$	−43.0593			−1.38469			−0.692347	+	0.721565i	$0.743423\pi$
$968$	27.0412	+	14.3402i	0.869136	+	0.460913i
$969$	4.83632			0.155365
$970$	−7.95146	−	24.4721i	−0.255306	−	0.785751i
$971$	34.5213	+	25.0812i	1.10784	+	0.804895i	0.982322	−	0.187197i	$-0.0599401\pi$
$971$	34.5213	+	25.0812i	1.10784	+	0.804895i	0.125520	+	0.992091i	$0.459940\pi$
$972$	−1.03599	+	0.752690i	−0.0332294	+	0.0241425i
$973$	−8.99172	+	27.6737i	−0.288261	+	0.887177i
$974$	3.52434	−	10.8468i	0.112927	−	0.347554i
$975$	−5.90987	+	4.29377i	−0.189267	+	0.137511i
$976$	−0.187251	−	0.136046i	−0.00599375	−	0.00435471i
$977$	17.9469	+	55.2350i	0.574174	+	1.76712i	0.638976	+	0.769226i	$0.279358\pi$
$977$	17.9469	+	55.2350i	0.574174	+	1.76712i	−0.0648029	+	0.997898i	$0.520642\pi$
$978$	6.22238			0.198970
$979$	−3.50405	−	49.7206i	−0.111990	−	1.58908i
$980$	23.2382			0.742318
$981$	6.42773	+	19.7825i	0.205222	+	0.631607i
$982$	−5.53941	−	4.02462i	−0.176770	−	0.128431i
$983$	−0.816723	+	0.593384i	−0.0260494	+	0.0189260i	−0.600734	−	0.799449i	$-0.705125\pi$
$983$	−0.816723	+	0.593384i	−0.0260494	+	0.0189260i	0.574684	+	0.818375i	$0.305125\pi$
$984$	−5.11222	+	15.7338i	−0.162972	+	0.501575i
$985$	−1.91403	+	5.89079i	−0.0609862	+	0.187696i
$986$	29.3263	−	21.3068i	0.933940	−	0.678547i
$987$	−31.8544	−	23.1436i	−1.01394	−	0.736668i
$988$	0.326078	+	1.00356i	0.0103739	+	0.0319276i
$989$	19.7938			0.629407
$990$	−9.14759	+	3.70167i	−0.290729	+	0.117647i
$991$	−32.2166			−1.02339			−0.511697	−	0.859166i	$-0.670983\pi$
$991$	−32.2166			−1.02339			−0.511697	+	0.859166i	$0.670983\pi$
$992$	−0.194059	−	0.597253i	−0.00616139	−	0.0189628i
$993$	−13.3515	−	9.70041i	−0.423696	−	0.307833i
$994$	34.7813	−	25.2701i	1.10320	−	0.801519i
$995$	−17.9262	+	55.1711i	−0.568298	+	1.74904i
$996$	−1.83676	+	5.65296i	−0.0581999	+	0.179121i
$997$	15.4843	−	11.2500i	0.490393	−	0.356291i	−0.314943	−	0.949111i	$-0.601985\pi$
$997$	15.4843	−	11.2500i	0.490393	−	0.356291i	0.805335	+	0.592820i	$0.201985\pi$
$998$	12.8743	+	9.35374i	0.407530	+	0.296088i
$999$	0.992113	+	3.05341i	0.0313891	+	0.0966056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.b.313.2	yes	20
11.3	even	5		4719.2.a.bn.1.4		10
11.8	odd	10		4719.2.a.bi.1.7		10
11.9	even	5	inner	429.2.n.b.196.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.b.196.2	✓	20	11.9	even	5	inner
429.2.n.b.313.2	yes	20	1.1	even	1	trivial
4719.2.a.bi.1.7		10	11.8	odd	10
4719.2.a.bn.1.4		10	11.3	even	5

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.262109 - 0.806688i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.03599 - 0.752690i) q^{4} +(-1.08398 + 3.33616i) q^{5} +(0.262109 - 0.806688i) q^{6} +(-2.82268 + 2.05079i) q^{7} +(-2.25115 - 1.63555i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.262109 - 0.806688i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.03599 - 0.752690i) q^{4} +(-1.08398 + 3.33616i) q^{5} +(0.262109 - 0.806688i) q^{6} +(-2.82268 + 2.05079i) q^{7} +(-2.25115 - 1.63555i) q^{8} +(0.309017 + 0.951057i) q^{9} +2.97536 q^{10} +(0.233160 + 3.30842i) q^{11} +1.28055 q^{12} +(-0.309017 - 0.951057i) q^{13} +(2.39420 + 1.73949i) q^{14} +(-2.83791 + 2.06186i) q^{15} +(0.0620883 - 0.191088i) q^{16} +(-1.81366 + 5.58187i) q^{17} +(0.686210 - 0.498561i) q^{18} +(-0.666652 - 0.484351i) q^{19} +(1.38810 + 4.27213i) q^{20} -3.48902 q^{21} +(2.60775 - 1.05525i) q^{22} +2.78699 q^{23} +(-0.859862 - 2.64638i) q^{24} +(-5.90987 - 4.29377i) q^{25} +(-0.686210 + 0.498561i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-1.38065 + 4.24920i) q^{28} +(5.89094 - 4.28002i) q^{29} +(2.40712 + 1.74888i) q^{30} +(0.0338344 + 0.104131i) q^{31} -5.73557 q^{32} +(-1.75601 + 2.81362i) q^{33} +4.97821 q^{34} +(-3.78204 - 11.6399i) q^{35} +(1.03599 + 0.752690i) q^{36} +(2.59738 - 1.88711i) q^{37} +(-0.215985 + 0.664733i) q^{38} +(0.309017 - 0.951057i) q^{39} +(7.89669 - 5.73728i) q^{40} +(-4.80992 - 3.49461i) q^{41} +(0.914503 + 2.81455i) q^{42} +7.10223 q^{43} +(2.73177 + 3.25199i) q^{44} -3.50785 q^{45} +(-0.730494 - 2.24823i) q^{46} +(9.12990 + 6.63326i) q^{47} +(0.162549 - 0.118099i) q^{48} +(1.59863 - 4.92007i) q^{49} +(-1.91471 + 5.89286i) q^{50} +(-4.74823 + 3.44979i) q^{51} +(-1.03599 - 0.752690i) q^{52} +(3.67522 + 11.3112i) q^{53} +0.848202 q^{54} +(-11.2902 - 2.80841i) q^{55} +9.70845 q^{56} +(-0.254638 - 0.783696i) q^{57} +(-4.99671 - 3.63032i) q^{58} +(-0.764686 + 0.555577i) q^{59} +(-1.38810 + 4.27213i) q^{60} +(0.355976 - 1.09558i) q^{61} +(0.0751333 - 0.0545876i) q^{62} +(-2.82268 - 2.05079i) q^{63} +(1.37917 + 4.24464i) q^{64} +3.50785 q^{65} +(2.72998 + 0.679078i) q^{66} +12.3918 q^{67} +(2.32249 + 7.14789i) q^{68} +(2.25472 + 1.63815i) q^{69} +(-8.39849 + 6.10186i) q^{70} +(4.48919 - 13.8163i) q^{71} +(0.859862 - 2.64638i) q^{72} +(-3.69827 + 2.68695i) q^{73} +(-2.20311 - 1.60065i) q^{74} +(-2.25737 - 6.94747i) q^{75} -1.05521 q^{76} +(-7.44302 - 8.86043i) q^{77} -0.848202 q^{78} +(-2.66845 - 8.21263i) q^{79} +(0.570198 + 0.414273i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.55834 + 4.79608i) q^{82} +(-1.43435 + 4.41447i) q^{83} +(-3.61459 + 2.62615i) q^{84} +(-16.6561 - 12.1013i) q^{85} +(-1.86156 - 5.72929i) q^{86} +7.28160 q^{87} +(4.88622 - 7.82909i) q^{88} -15.0285 q^{89} +(0.919438 + 2.82974i) q^{90} +(2.82268 + 2.05079i) q^{91} +(2.88729 - 2.09774i) q^{92} +(-0.0338344 + 0.104131i) q^{93} +(2.95795 - 9.10362i) q^{94} +(2.33851 - 1.69903i) q^{95} +(-4.64017 - 3.37128i) q^{96} +(-2.67243 - 8.22490i) q^{97} -4.38797 q^{98} +(-3.07444 + 1.24411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9 - 2 * q^10 + 14 * q^11 - 18 * q^12 + 5 * q^13 - q^14 - 4 * q^15 - 35 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 45 * q^20 - 2 * q^21 + 11 * q^22 + 6 * q^23 + 2 * q^24 - 7 * q^25 + 4 * q^26 + 5 * q^27 + 12 * q^28 + 26 * q^29 - 3 * q^30 + 20 * q^31 + 42 * q^32 + q^33 - 24 * q^34 - 18 * q^35 + 3 * q^36 - 6 * q^37 - 3 * q^38 - 5 * q^39 - 26 * q^41 - 9 * q^42 + 28 * q^43 - 38 * q^44 - 16 * q^45 - 17 * q^46 + 8 * q^47 - 20 * q^48 + 2 * q^49 - 29 * q^50 + 3 * q^51 - 3 * q^52 + q^53 - 6 * q^54 - 36 * q^56 - 8 * q^57 + 22 * q^58 - 21 * q^59 - 45 * q^60 + 26 * q^61 - 10 * q^62 - 3 * q^63 - 87 * q^64 + 16 * q^65 + 14 * q^66 + 56 * q^67 + 65 * q^68 + 4 * q^69 - 24 * q^70 - 28 * q^71 - 2 * q^72 + 45 * q^73 - 29 * q^74 - 3 * q^75 + 60 * q^76 + 4 * q^77 + 6 * q^78 - 15 * q^79 - 7 * q^80 - 5 * q^81 - 46 * q^82 + 36 * q^83 + 8 * q^84 + 39 * q^86 + 24 * q^87 + 73 * q^88 - 126 * q^89 - 2 * q^90 + 3 * q^91 + 2 * q^92 - 20 * q^93 - 3 * q^94 + 47 * q^95 - 47 * q^96 + 18 * q^97 - 54 * q^98 - 16 * q^99

Introduction

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