LMFDB - Embedded newform 429.2.n.d.157.6

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:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.6
Character	$\chi$	$=$	429.157
Dual form			429.2.n.d.235.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19143 - 0.865625i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.0521663 - 0.160551i) q^{4} +(-0.917011 - 0.666248i) q^{5} +(1.19143 + 0.865625i) q^{6} +(-1.26104 + 3.88108i) q^{7} +(0.833347 + 2.56478i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.19143 - 0.865625i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.0521663 - 0.160551i) q^{4} +(-0.917011 - 0.666248i) q^{5} +(1.19143 + 0.865625i) q^{6} +(-1.26104 + 3.88108i) q^{7} +(0.833347 + 2.56478i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.66928 q^{10} +(-1.60839 + 2.90053i) q^{11} +0.168814 q^{12} +(0.809017 - 0.587785i) q^{13} +(1.85712 + 5.71562i) q^{14} +(0.350267 - 1.07801i) q^{15} +(3.48616 + 2.53284i) q^{16} +(2.56801 + 1.86577i) q^{17} +(-0.455086 + 1.40061i) q^{18} +(-2.63260 - 8.10232i) q^{19} +(-0.154804 + 0.112472i) q^{20} -4.08081 q^{21} +(0.594492 + 4.84804i) q^{22} +7.96906 q^{23} +(-2.18173 + 1.58512i) q^{24} +(-1.14806 - 3.53337i) q^{25} +(0.455086 - 1.40061i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.557328 + 0.404923i) q^{28} +(0.151356 - 0.465826i) q^{29} +(-0.515835 - 1.58758i) q^{30} +(3.62713 - 2.63526i) q^{31} +0.952471 q^{32} +(-3.25559 - 0.633353i) q^{33} +4.67465 q^{34} +(3.74215 - 2.71883i) q^{35} +(0.0521663 + 0.160551i) q^{36} +(-2.89587 + 8.91257i) q^{37} +(-10.1501 - 7.37450i) q^{38} +(0.809017 + 0.587785i) q^{39} +(0.944590 - 2.90715i) q^{40} +(2.30462 + 7.09288i) q^{41} +(-4.86200 + 3.53245i) q^{42} +7.71864 q^{43} +(0.381781 + 0.409538i) q^{44} +1.13349 q^{45} +(9.49458 - 6.89821i) q^{46} +(-0.00750832 - 0.0231082i) q^{47} +(-1.33159 + 4.09823i) q^{48} +(-7.80942 - 5.67388i) q^{49} +(-4.42641 - 3.21597i) q^{50} +(-0.980891 + 3.01887i) q^{51} +(-0.0521663 - 0.160551i) q^{52} +(-1.60751 + 1.16793i) q^{53} -1.47269 q^{54} +(3.40738 - 1.58824i) q^{55} -11.0050 q^{56} +(6.89224 - 5.00751i) q^{57} +(-0.222900 - 0.686016i) q^{58} +(1.41498 - 4.35485i) q^{59} +(-0.154804 - 0.112472i) q^{60} +(-10.3038 - 7.48614i) q^{61} +(2.04032 - 6.27946i) q^{62} +(-1.26104 - 3.88108i) q^{63} +(-5.83751 + 4.24120i) q^{64} -1.13349 q^{65} +(-4.42706 + 2.06352i) q^{66} +1.26089 q^{67} +(0.433514 - 0.314966i) q^{68} +(2.46257 + 7.57902i) q^{69} +(2.10502 - 6.47859i) q^{70} +(-0.793661 - 0.576628i) q^{71} +(-2.18173 - 1.58512i) q^{72} +(-0.843861 + 2.59714i) q^{73} +(4.26472 + 13.1254i) q^{74} +(3.00566 - 2.18374i) q^{75} -1.43817 q^{76} +(-9.22895 - 9.89996i) q^{77} +1.47269 q^{78} +(11.6813 - 8.48699i) q^{79} +(-1.50935 - 4.64529i) q^{80} +(0.309017 - 0.951057i) q^{81} +(8.88557 + 6.45574i) q^{82} +(3.10363 + 2.25492i) q^{83} +(-0.212880 + 0.655178i) q^{84} +(-1.11183 - 3.42186i) q^{85} +(9.19622 - 6.68145i) q^{86} +0.489798 q^{87} +(-8.77957 - 1.70801i) q^{88} +17.8685 q^{89} +(1.35047 - 0.981176i) q^{90} +(1.26104 + 3.88108i) q^{91} +(0.415716 - 1.27944i) q^{92} +(3.62713 + 2.63526i) q^{93} +(-0.0289487 - 0.0210325i) q^{94} +(-2.98402 + 9.18388i) q^{95} +(0.294330 + 0.905854i) q^{96} +(0.293923 - 0.213548i) q^{97} -14.2158 q^{98} +(-0.403678 - 3.29197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) $ 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.19143	−	0.865625i	0.842469	−	0.612089i	−0.0805905	−	0.996747i	$-0.525681\pi$
$2$	1.19143	−	0.865625i	0.842469	−	0.612089i	0.923059	+	0.384658i	$0.125681\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.0521663	−	0.160551i	0.0260831	−	0.0802756i
$5$	−0.917011	−	0.666248i	−0.410100	−	0.297955i	0.363542	−	0.931578i	$-0.381567\pi$
$5$	−0.917011	−	0.666248i	−0.410100	−	0.297955i	−0.773642	+	0.633623i	$0.781567\pi$
$6$	1.19143	+	0.865625i	0.486400	+	0.353390i
$7$	−1.26104	+	3.88108i	−0.476628	+	1.46691i	0.367122	+	0.930173i	$0.380343\pi$
$7$	−1.26104	+	3.88108i	−0.476628	+	1.46691i	−0.843750	+	0.536737i	$0.819657\pi$
$8$	0.833347	+	2.56478i	0.294633	+	0.906786i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−1.66928			−0.527872
$11$	−1.60839	+	2.90053i	−0.484947	+	0.874544i
$11$	−1.60839	+	2.90053i	−0.484947	+	0.874544i
$12$	0.168814			0.0487323
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	1.85712	+	5.71562i	0.496336	+	1.52756i
$15$	0.350267	−	1.07801i	0.0904386	−	0.278341i
$16$	3.48616	+	2.53284i	0.871540	+	0.633211i
$17$	2.56801	+	1.86577i	0.622833	+	0.452515i	0.853910	−	0.520421i	$-0.174225\pi$
$17$	2.56801	+	1.86577i	0.622833	+	0.452515i	−0.231077	+	0.972935i	$0.574225\pi$
$18$	−0.455086	+	1.40061i	−0.107265	+	0.330127i
$19$	−2.63260	−	8.10232i	−0.603960	−	1.85880i	−0.503785	−	0.863829i	$-0.668060\pi$
$19$	−2.63260	−	8.10232i	−0.603960	−	1.85880i	−0.100175	−	0.994970i	$-0.531940\pi$
$20$	−0.154804	+	0.112472i	−0.0346152	+	0.0251494i
$21$	−4.08081			−0.890505
$22$	0.594492	+	4.84804i	0.126746	+	1.03361i
$23$	7.96906			1.66166			0.830832	−	0.556524i	$-0.187865\pi$
$23$	7.96906			1.66166			0.830832	+	0.556524i	$0.187865\pi$
$24$	−2.18173	+	1.58512i	−0.445344	+	0.323561i
$25$	−1.14806	−	3.53337i	−0.229612	−	0.706674i
$26$	0.455086	−	1.40061i	0.0892497	−	0.274682i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.557328	+	0.404923i	0.105325	+	0.0765232i
$29$	0.151356	−	0.465826i	0.0281061	−	0.0865016i	−0.936020	−	0.351948i	$-0.885519\pi$
$29$	0.151356	−	0.465826i	0.0281061	−	0.0865016i	0.964126	+	0.265446i	$0.0855194\pi$
$30$	−0.515835	−	1.58758i	−0.0941781	−	0.289850i
$31$	3.62713	−	2.63526i	0.651451	−	0.473307i	−0.212314	−	0.977201i	$-0.568100\pi$
$31$	3.62713	−	2.63526i	0.651451	−	0.473307i	0.863765	+	0.503895i	$0.168100\pi$
$32$	0.952471			0.168375
$33$	−3.25559	−	0.633353i	−0.566725	−	0.110253i
$34$	4.67465			0.801696
$35$	3.74215	−	2.71883i	0.632538	−	0.459566i
$36$	0.0521663	+	0.160551i	0.00869438	+	0.0267585i
$37$	−2.89587	+	8.91257i	−0.476078	+	1.46522i	0.368420	+	0.929659i	$0.379899\pi$
$37$	−2.89587	+	8.91257i	−0.476078	+	1.46522i	−0.844498	+	0.535558i	$0.820101\pi$
$38$	−10.1501	−	7.37450i	−1.64657	−	1.19630i
$39$	0.809017	+	0.587785i	0.129546	+	0.0941210i
$40$	0.944590	−	2.90715i	0.149353	−	0.459660i
$41$	2.30462	+	7.09288i	0.359921	+	1.10772i	0.953101	+	0.302653i	$0.0978722\pi$
$41$	2.30462	+	7.09288i	0.359921	+	1.10772i	−0.593180	+	0.805070i	$0.702128\pi$
$42$	−4.86200	+	3.53245i	−0.750222	+	0.545069i
$43$	7.71864			1.17708			0.588541	−	0.808468i	$-0.299703\pi$
$43$	7.71864			1.17708			0.588541	+	0.808468i	$0.299703\pi$
$44$	0.381781	+	0.409538i	0.0575556	+	0.0617402i
$45$	1.13349			0.168970
$46$	9.49458	−	6.89821i	1.39990	−	1.01709i
$47$	−0.00750832	−	0.0231082i	−0.00109520	−	0.00337068i	0.950507	−	0.310702i	$-0.100564\pi$
$47$	−0.00750832	−	0.0231082i	−0.00109520	−	0.00337068i	−0.951603	+	0.307331i	$0.900564\pi$
$48$	−1.33159	+	4.09823i	−0.192199	+	0.591528i
$49$	−7.80942	−	5.67388i	−1.11563	−	0.810554i
$50$	−4.42641	−	3.21597i	−0.625989	−	0.454807i
$51$	−0.980891	+	3.01887i	−0.137352	+	0.422727i
$52$	−0.0521663	−	0.160551i	−0.00723416	−	0.0222645i
$53$	−1.60751	+	1.16793i	−0.220809	+	0.160427i	−0.692691	−	0.721235i	$-0.743575\pi$
$53$	−1.60751	+	1.16793i	−0.220809	+	0.160427i	0.471882	+	0.881662i	$0.343575\pi$
$54$	−1.47269			−0.200408
$55$	3.40738	−	1.58824i	0.459451	−	0.214158i
$56$	−11.0050			−1.47060
$57$	6.89224	−	5.00751i	0.912900	−	0.663260i
$58$	−0.222900	−	0.686016i	−0.0292682	−	0.0900783i
$59$	1.41498	−	4.35485i	0.184214	−	0.566953i	−0.815720	−	0.578447i	$-0.803659\pi$
$59$	1.41498	−	4.35485i	0.184214	−	0.566953i	0.999934	+	0.0114944i	$0.00365886\pi$
$60$	−0.154804	−	0.112472i	−0.0199851	−	0.0145200i
$61$	−10.3038	−	7.48614i	−1.31926	−	0.958501i	−0.999941	−	0.0108555i	$-0.996545\pi$
$61$	−10.3038	−	7.48614i	−1.31926	−	0.958501i	−0.319323	−	0.947646i	$-0.603455\pi$
$62$	2.04032	−	6.27946i	0.259121	−	0.797492i
$63$	−1.26104	−	3.88108i	−0.158876	−	0.488970i
$64$	−5.83751	+	4.24120i	−0.729689	+	0.530150i
$65$	−1.13349			−0.140592
$66$	−4.42706	+	2.06352i	−0.544933	+	0.254002i
$67$	1.26089			0.154042			0.0770208	−	0.997029i	$-0.475459\pi$
$67$	1.26089			0.154042			0.0770208	+	0.997029i	$0.475459\pi$
$68$	0.433514	−	0.314966i	0.0525713	−	0.0381953i
$69$	2.46257	+	7.57902i	0.296459	+	0.912407i
$70$	2.10502	−	6.47859i	0.251598	−	0.774340i
$71$	−0.793661	−	0.576628i	−0.0941902	−	0.0684332i	0.539693	−	0.841862i	$-0.318540\pi$
$71$	−0.793661	−	0.576628i	−0.0941902	−	0.0684332i	−0.633884	+	0.773428i	$0.718540\pi$
$72$	−2.18173	−	1.58512i	−0.257120	−	0.186808i
$73$	−0.843861	+	2.59714i	−0.0987664	+	0.303972i	−0.988217	−	0.153060i	$-0.951087\pi$
$73$	−0.843861	+	2.59714i	−0.0987664	+	0.303972i	0.889451	+	0.457031i	$0.151087\pi$
$74$	4.26472	+	13.1254i	0.495763	+	1.52580i
$75$	3.00566	−	2.18374i	0.347064	−	0.252157i
$76$	−1.43817			−0.164969
$77$	−9.22895	−	9.89996i	−1.05174	−	1.12820i
$78$	1.47269			0.166749
$79$	11.6813	−	8.48699i	1.31425	−	0.954861i	0.314268	−	0.949334i	$-0.398241\pi$
$79$	11.6813	−	8.48699i	1.31425	−	0.954861i	0.999985	−	0.00552625i	$-0.00175907\pi$
$80$	−1.50935	−	4.64529i	−0.168750	−	0.519359i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	8.88557	+	6.45574i	0.981247	+	0.712918i
$83$	3.10363	+	2.25492i	0.340668	+	0.247510i	0.744944	−	0.667127i	$-0.232476\pi$
$83$	3.10363	+	2.25492i	0.340668	+	0.247510i	−0.404276	+	0.914637i	$0.632476\pi$
$84$	−0.212880	+	0.655178i	−0.0232272	+	0.0714858i
$85$	−1.11183	−	3.42186i	−0.120595	−	0.371152i
$86$	9.19622	−	6.68145i	0.991654	−	0.720479i
$87$	0.489798			0.0525119
$88$	−8.77957	−	1.70801i	−0.935906	−	0.182074i
$89$	17.8685			1.89405			0.947027	−	0.321155i	$-0.104071\pi$
$89$	17.8685			1.89405			0.947027	+	0.321155i	$0.104071\pi$
$90$	1.35047	−	0.981176i	0.142352	−	0.103425i
$91$	1.26104	+	3.88108i	0.132193	+	0.406847i
$92$	0.415716	−	1.27944i	0.0433414	−	0.133391i
$93$	3.62713	+	2.63526i	0.376115	+	0.273264i
$94$	−0.0289487	−	0.0210325i	−0.00298583	−	0.00216933i
$95$	−2.98402	+	9.18388i	−0.306154	+	0.942246i
$96$	0.294330	+	0.905854i	0.0300399	+	0.0924533i
$97$	0.293923	−	0.213548i	0.0298434	−	0.0216825i	−0.572764	−	0.819721i	$-0.694129\pi$
$97$	0.293923	−	0.213548i	0.0298434	−	0.0216825i	0.602607	+	0.798038i	$0.294129\pi$
$98$	−14.2158			−1.43602
$99$	−0.403678	−	3.29197i	−0.0405712	−	0.330855i
$100$	−0.627177			−0.0627177
$101$	−6.84215	+	4.97112i	−0.680820	+	0.494644i	−0.873630	−	0.486592i	$-0.838240\pi$
$101$	−6.84215	+	4.97112i	−0.680820	+	0.494644i	0.192810	+	0.981236i	$0.438240\pi$
$102$	1.44455	+	4.44586i	0.143031	+	0.440206i
$103$	5.55247	−	17.0887i	0.547101	−	1.68380i	−0.168841	−	0.985643i	$-0.554002\pi$
$103$	5.55247	−	17.0887i	0.547101	−	1.68380i	0.715942	−	0.698160i	$-0.245998\pi$
$104$	2.18173	+	1.58512i	0.213936	+	0.155434i
$105$	3.74215	+	2.71883i	0.365196	+	0.265330i
$106$	−0.904254	+	2.78301i	−0.0878289	+	0.270310i
$107$	3.57040	+	10.9886i	0.345164	+	1.06230i	0.961496	+	0.274819i	$0.0886178\pi$
$107$	3.57040	+	10.9886i	0.345164	+	1.06230i	−0.616332	+	0.787486i	$0.711382\pi$
$108$	−0.136573	+	0.0992261i	−0.0131417	+	0.00954804i
$109$	−8.03958			−0.770052			−0.385026	−	0.922906i	$-0.625808\pi$
$109$	−8.03958			−0.770052			−0.385026	+	0.922906i	$0.625808\pi$
$110$	2.68484	−	4.84179i	0.255990	−	0.461647i
$111$	−9.37123			−0.889478
$112$	−14.2263	+	10.3360i	−1.34426	+	0.976664i
$113$	−3.72579	−	11.4668i	−0.350493	−	1.07871i	−0.958577	−	0.284834i	$-0.908061\pi$
$113$	−3.72579	−	11.4668i	−0.350493	−	1.07871i	0.608083	−	0.793873i	$-0.291939\pi$
$114$	3.87700	−	11.9322i	0.363115	−	1.11755i
$115$	−7.30772	−	5.30937i	−0.681448	−	0.495101i
$116$	−0.0668932	−	0.0486008i	−0.00621088	−	0.00451247i
$117$	−0.309017	+	0.951057i	−0.0285686	+	0.0879252i
$118$	−2.08382	−	6.41334i	−0.191831	−	0.590396i
$119$	−10.4795	+	7.61383i	−0.960657	+	0.697958i
$120$	3.05676			0.279042
$121$	−5.82618	−	9.33036i	−0.529653	−	0.848214i
$122$	−18.7564			−1.69813
$123$	−6.03357	+	4.38364i	−0.544028	+	0.395260i
$124$	−0.233881	−	0.719811i	−0.0210031	−	0.0646409i
$125$	−3.05265	+	9.39509i	−0.273037	+	0.840322i
$126$	−4.86200	−	3.53245i	−0.433141	−	0.314695i
$127$	13.3040	+	9.66590i	1.18054	+	0.857710i	0.992232	−	0.124400i	$-0.0397007\pi$
$127$	13.3040	+	9.66590i	1.18054	+	0.857710i	0.188305	+	0.982111i	$0.439701\pi$
$128$	−3.87236	+	11.9179i	−0.342272	+	1.05340i
$129$	2.38519	+	7.34086i	0.210004	+	0.646327i
$130$	−1.35047	+	0.981176i	−0.118444	+	0.0860548i
$131$	−9.94840			−0.869195			−0.434598	−	0.900625i	$-0.643109\pi$
$131$	−9.94840			−0.869195			−0.434598	+	0.900625i	$0.643109\pi$
$132$	−0.271518	+	0.489649i	−0.0236326	+	0.0426185i
$133$	34.7655			3.01455
$134$	1.50226	−	1.09145i	0.129775	−	0.0942873i
$135$	0.350267	+	1.07801i	0.0301462	+	0.0927805i
$136$	−2.64524	+	8.14120i	−0.226827	+	0.698102i
$137$	−3.86607	−	2.80886i	−0.330301	−	0.239977i	0.410258	−	0.911970i	$-0.365439\pi$
$137$	−3.86607	−	2.80886i	−0.330301	−	0.239977i	−0.740558	+	0.671992i	$0.765439\pi$
$138$	9.49458	+	6.89821i	0.808232	+	0.587215i
$139$	0.129061	−	0.397208i	0.0109468	−	0.0336908i	−0.945434	−	0.325814i	$-0.894362\pi$
$139$	0.129061	−	0.397208i	0.0109468	−	0.0336908i	0.956381	+	0.292123i	$0.0943617\pi$
$140$	−0.241297	−	0.742637i	−0.0203934	−	0.0627643i
$141$	0.0196570	−	0.0142817i	0.00165542	−	0.00120273i
$142$	−1.44474			−0.121240
$143$	0.403678	+	3.29197i	0.0337573	+	0.275288i
$144$	−4.30913			−0.359094
$145$	−0.449150	+	0.326327i	−0.0372999	+	0.0271000i
$146$	1.24274	+	3.82477i	0.102850	+	0.316541i
$147$	2.98293	−	9.18053i	0.246028	−	0.757197i
$148$	1.27986	+	0.929871i	0.105204	+	0.0764349i
$149$	−8.67046	−	6.29945i	−0.710311	−	0.516071i	0.172963	−	0.984928i	$-0.444666\pi$
$149$	−8.67046	−	6.29945i	−0.710311	−	0.516071i	−0.883274	+	0.468857i	$0.844666\pi$
$150$	1.69074	−	5.20355i	0.138048	−	0.424868i
$151$	1.55672	+	4.79110i	0.126684	+	0.389894i	0.994204	−	0.107508i	$-0.0342873\pi$
$151$	1.55672	+	4.79110i	0.126684	+	0.389894i	−0.867520	+	0.497402i	$0.834287\pi$
$152$	18.5868	−	13.5041i	1.50759	−	1.09533i
$153$	−3.17423			−0.256621
$154$	−19.5653	−	3.80630i	−1.57662	−	0.306720i
$155$	−5.08185			−0.408184
$156$	0.136573	−	0.0992261i	0.0109346	−	0.00794445i
$157$	−1.24951	−	3.84559i	−0.0997217	−	0.306912i	0.888734	−	0.458424i	$-0.151586\pi$
$157$	−1.24951	−	3.84559i	−0.0997217	−	0.306912i	−0.988455	+	0.151512i	$0.951586\pi$
$158$	6.57095	−	20.2233i	0.522757	−	1.60888i
$159$	−1.60751	−	1.16793i	−0.127484	−	0.0926226i
$160$	−0.873427	−	0.634582i	−0.0690504	−	0.0501681i
$161$	−10.0493	+	30.9285i	−0.791995	+	2.43751i
$162$	−0.455086	−	1.40061i	−0.0357549	−	0.110042i
$163$	−10.8156	+	7.85796i	−0.847139	+	0.615483i	−0.924356	−	0.381531i	$-0.875397\pi$
$163$	−10.8156	+	7.85796i	−0.847139	+	0.615483i	0.0772164	+	0.997014i	$0.475397\pi$
$164$	1.25899			0.0983110
$165$	2.56344	+	2.74982i	0.199564	+	0.214073i
$166$	5.64968			0.438500
$167$	3.58950	−	2.60792i	0.277764	−	0.201807i	−0.440178	−	0.897911i	$-0.645085\pi$
$167$	3.58950	−	2.60792i	0.277764	−	0.201807i	0.717941	+	0.696103i	$0.245085\pi$
$168$	−3.40073	−	10.4664i	−0.262372	−	0.807498i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−4.28671	−	3.11448i	−0.328776	−	0.238870i
$171$	6.89224	+	5.00751i	0.527063	+	0.382934i
$172$	0.402652	−	1.23924i	0.0307020	−	0.0944909i
$173$	6.64724	+	20.4581i	0.505380	+	1.55540i	0.800130	+	0.599826i	$0.204764\pi$
$173$	6.64724	+	20.4581i	0.505380	+	1.55540i	−0.294750	+	0.955574i	$0.595236\pi$
$174$	0.583560	−	0.423981i	0.0442396	−	0.0321419i
$175$	15.1610			1.14607
$176$	−12.9537	+	6.03793i	−0.976421	+	0.455126i
$177$	4.57896			0.344176
$178$	21.2890	−	15.4674i	1.59568	−	1.15933i
$179$	−4.37999	−	13.4802i	−0.327376	−	1.00756i	−0.970357	−	0.241677i	$-0.922303\pi$
$179$	−4.37999	−	13.4802i	−0.327376	−	1.00756i	0.642981	−	0.765882i	$-0.277697\pi$
$180$	0.0591299	−	0.181983i	0.00440728	−	0.0135642i
$181$	−0.339720	−	0.246821i	−0.0252512	−	0.0183460i	0.575088	−	0.818091i	$-0.304968\pi$
$181$	−0.339720	−	0.246821i	−0.0252512	−	0.0183460i	−0.600339	+	0.799745i	$0.704968\pi$
$182$	4.86200	+	3.53245i	0.360395	+	0.261842i
$183$	3.93569	−	12.1128i	0.290935	−	0.895406i
$184$	6.64099	+	20.4389i	0.489580	+	1.50677i
$185$	8.59353	−	6.24356i	0.631809	−	0.459036i
$186$	6.60262			0.484127
$187$	−9.54206	+	4.44771i	−0.697785	+	0.325249i
$188$	−0.00410174			−0.000299150
$189$	3.30144	−	2.39864i	0.240145	−	0.174475i
$190$	4.39454	+	13.5250i	0.318813	+	0.981207i
$191$	3.05923	−	9.41533i	0.221358	−	0.681270i	−0.777283	−	0.629151i	$-0.783403\pi$
$191$	3.05923	−	9.41533i	0.221358	−	0.681270i	0.998641	−	0.0521185i	$-0.0165974\pi$
$192$	−5.83751	−	4.24120i	−0.421286	−	0.306082i
$193$	−7.90500	−	5.74332i	−0.569014	−	0.413413i	0.265733	−	0.964047i	$-0.414386\pi$
$193$	−7.90500	−	5.74332i	−0.569014	−	0.413413i	−0.834747	+	0.550634i	$0.814386\pi$
$194$	0.165337	−	0.508855i	0.0118705	−	0.0365336i
$195$	−0.350267	−	1.07801i	−0.0250832	−	0.0771980i
$196$	−1.31834	+	0.957827i	−0.0941669	+	0.0684162i
$197$	17.8319			1.27047			0.635234	−	0.772320i	$-0.280904\pi$
$197$	17.8319			1.27047			0.635234	+	0.772320i	$0.280904\pi$
$198$	−3.33056	−	3.57272i	−0.236693	−	0.253902i
$199$	20.6076			1.46084			0.730418	−	0.683001i	$-0.239325\pi$
$199$	20.6076			1.46084			0.730418	+	0.683001i	$0.239325\pi$
$200$	8.10558	−	5.88905i	0.573151	−	0.416418i
$201$	0.389635	+	1.19917i	0.0274827	+	0.0845832i
$202$	−3.84883	+	11.8455i	−0.270803	+	0.833445i
$203$	1.61704	+	1.17485i	0.113494	+	0.0824581i
$204$	0.433514	+	0.314966i	0.0303521	+	0.0220521i
$205$	2.61226	−	8.03970i	0.182448	−	0.561517i
$206$	−8.17706	−	25.1664i	−0.569723	−	1.75343i
$207$	−6.44710	+	4.68409i	−0.448105	+	0.325567i
$208$	4.30913			0.298784
$209$	27.7353	+	5.39571i	1.91849	+	0.373229i
$210$	6.81199			0.470072
$211$	−12.8965	+	9.36986i	−0.887832	+	0.645048i	−0.935312	−	0.353825i	$-0.884881\pi$
$211$	−12.8965	+	9.36986i	−0.887832	+	0.645048i	0.0474799	+	0.998872i	$0.484881\pi$
$212$	0.103654	+	0.319015i	0.00711900	+	0.0219100i
$213$	0.303151	−	0.933004i	0.0207716	−	0.0639284i
$214$	13.7659	+	10.0015i	0.941015	+	0.683687i
$215$	−7.07808	−	5.14253i	−0.482721	−	0.350717i
$216$	0.833347	−	2.56478i	0.0567021	−	0.174511i
$217$	5.65371	+	17.4003i	0.383799	+	1.18121i
$218$	−9.57860	+	6.95926i	−0.648745	+	0.471341i
$219$	−2.73079			−0.184530
$220$	−0.0772431	−	0.629912i	−0.00520773	−	0.0424687i
$221$	3.17423			0.213522
$222$	−11.1652	+	8.11197i	−0.749357	+	0.544440i
$223$	−3.32211	−	10.2244i	−0.222465	−	0.684678i	−0.998539	−	0.0540355i	$-0.982792\pi$
$223$	−3.32211	−	10.2244i	−0.222465	−	0.684678i	0.776074	−	0.630642i	$-0.217208\pi$
$224$	−1.20110	+	3.69661i	−0.0802520	+	0.246990i
$225$	3.00566	+	2.18374i	0.200378	+	0.145583i
$226$	−14.3650	−	10.4368i	−0.955545	−	0.694244i
$227$	3.26658	−	10.0535i	0.216810	−	0.667273i	−0.782210	−	0.623015i	$-0.785908\pi$
$227$	3.26658	−	10.0535i	0.216810	−	0.667273i	0.999020	−	0.0442583i	$-0.0140925\pi$
$228$	−0.444419	−	1.36778i	−0.0294324	−	0.0905835i
$229$	8.96843	−	6.51594i	0.592650	−	0.430586i	−0.250612	−	0.968088i	$-0.580632\pi$
$229$	8.96843	−	6.51594i	0.592650	−	0.430586i	0.843263	+	0.537502i	$0.180632\pi$
$230$	−13.3026			−0.877145
$231$	6.56351	−	11.8365i	0.431848	−	0.778785i
$232$	1.32087			0.0867195
$233$	−17.3224	+	12.5855i	−1.13483	+	0.824502i	−0.986390	−	0.164420i	$-0.947425\pi$
$233$	−17.3224	+	12.5855i	−1.13483	+	0.824502i	−0.148439	+	0.988922i	$0.547425\pi$
$234$	0.455086	+	1.40061i	0.0297499	+	0.0915608i
$235$	−0.00851059	+	0.0261929i	−0.000555170	+	0.00170864i
$236$	−0.625362	−	0.454352i	−0.0407076	−	0.0295758i
$237$	11.6813	+	8.48699i	0.758784	+	0.551289i
$238$	−5.89492	+	18.1427i	−0.382111	+	1.17602i
$239$	2.69174	+	8.28434i	0.174114	+	0.535869i	0.999592	−	0.0285659i	$-0.00909404\pi$
$239$	2.69174	+	8.28434i	0.174114	+	0.535869i	−0.825477	+	0.564435i	$0.809094\pi$
$240$	3.95152	−	2.87095i	0.255070	−	0.185319i
$241$	−23.0096			−1.48218			−0.741090	−	0.671406i	$-0.765691\pi$
$241$	−23.0096			−1.48218			−0.741090	+	0.671406i	$0.765691\pi$
$242$	−15.0181	−	6.07319i	−0.965399	−	0.390399i
$243$	1.00000			0.0641500
$244$	−1.73942	+	1.26376i	−0.111355	+	0.0809040i
$245$	3.38112	+	10.4060i	0.216012	+	0.664816i
$246$	−3.39399	+	10.4456i	−0.216393	+	0.665988i
$247$	−6.89224	−	5.00751i	−0.438543	−	0.318620i
$248$	9.78152	+	7.10669i	0.621127	+	0.451275i
$249$	−1.18548	+	3.64854i	−0.0751269	+	0.231217i
$250$	4.49560	+	13.8360i	0.284327	+	0.875069i
$251$	10.3410	−	7.51321i	0.652721	−	0.474229i	−0.211476	−	0.977383i	$-0.567827\pi$
$251$	10.3410	−	7.51321i	0.652721	−	0.474229i	0.864197	+	0.503154i	$0.167827\pi$
$252$	−0.688895			−0.0433963
$253$	−12.8173	+	23.1145i	−0.805818	+	1.45320i
$254$	24.2178			1.51956
$255$	2.91080	−	2.11482i	0.182282	−	0.132435i
$256$	1.24332	+	3.82655i	0.0777076	+	0.239159i
$257$	3.57845	−	11.0133i	0.223218	−	0.686994i	−0.775250	−	0.631655i	$-0.782376\pi$
$257$	3.57845	−	11.0133i	0.223218	−	0.686994i	0.998468	−	0.0553390i	$-0.0176240\pi$
$258$	9.19622	+	6.68145i	0.572532	+	0.415969i
$259$	−30.9386	−	22.4782i	−1.92243	−	1.39673i
$260$	−0.0591299	+	0.181983i	−0.00366708	+	0.0112861i
$261$	0.151356	+	0.465826i	0.00936869	+	0.0288339i
$262$	−11.8528	+	8.61158i	−0.732270	+	0.532025i
$263$	−3.08778			−0.190401			−0.0952003	−	0.995458i	$-0.530349\pi$
$263$	−3.08778			−0.190401			−0.0952003	+	0.995458i	$0.530349\pi$
$264$	−1.08863	−	8.87767i	−0.0670003	−	0.546383i
$265$	2.25224			0.138354
$266$	41.4207	−	30.0939i	2.53967	−	1.84518i
$267$	5.52166	+	16.9939i	0.337920	+	1.04001i
$268$	0.0657757	−	0.202437i	0.00401789	−	0.0123658i
$269$	23.7556	+	17.2595i	1.44840	+	1.05233i	0.986201	+	0.165554i	$0.0529412\pi$
$269$	23.7556	+	17.2595i	1.44840	+	1.05233i	0.462204	+	0.886774i	$0.347059\pi$
$270$	1.35047	+	0.981176i	0.0821872	+	0.0597125i
$271$	0.950695	−	2.92594i	0.0577506	−	0.177738i	−0.918020	−	0.396534i	$-0.870213\pi$
$271$	0.950695	−	2.92594i	0.0577506	−	0.177738i	0.975771	+	0.218796i	$0.0702129\pi$
$272$	4.22679	+	13.0087i	0.256286	+	0.788769i
$273$	−3.30144	+	2.39864i	−0.199812	+	0.145172i
$274$	−7.03758			−0.425156
$275$	12.0952	+	2.35304i	0.729367	+	0.141893i
$276$	1.34528			0.0809766
$277$	3.57549	−	2.59775i	0.214830	−	0.156083i	−0.475166	−	0.879896i	$-0.657612\pi$
$277$	3.57549	−	2.59775i	0.214830	−	0.156083i	0.689997	+	0.723813i	$0.257612\pi$
$278$	−0.190066	−	0.584964i	−0.0113994	−	0.0350838i
$279$	−1.38544	+	4.26394i	−0.0829440	+	0.255275i
$280$	10.0917	+	7.33205i	0.603094	+	0.438174i
$281$	−3.84579	−	2.79413i	−0.229421	−	0.166684i	0.467136	−	0.884185i	$-0.345286\pi$
$281$	−3.84579	−	2.79413i	−0.229421	−	0.166684i	−0.696557	+	0.717501i	$0.745286\pi$
$282$	0.0110574	−	0.0340312i	0.000658460	−	0.00202653i
$283$	−0.815669	−	2.51037i	−0.0484865	−	0.149226i	0.923882	−	0.382678i	$-0.124998\pi$
$283$	−0.815669	−	2.51037i	−0.0484865	−	0.149226i	−0.972368	+	0.233452i	$0.924998\pi$
$284$	−0.133981	+	0.0973427i	−0.00795029	+	0.00577622i
$285$	−9.65650			−0.572002
$286$	3.33056	+	3.57272i	0.196940	+	0.211259i
$287$	−30.4342			−1.79648
$288$	−0.770565	+	0.559848i	−0.0454060	+	0.0329894i
$289$	−2.13972	−	6.58537i	−0.125866	−	0.387375i
$290$	−0.252655	+	0.777592i	−0.0148364	+	0.0456617i
$291$	0.293923	+	0.213548i	0.0172301	+	0.0125184i
$292$	0.372952	+	0.270966i	0.0218254	+	0.0158571i
$293$	9.52746	−	29.3225i	0.556600	−	1.71304i	−0.135079	−	0.990835i	$-0.543129\pi$
$293$	9.52746	−	29.3225i	0.556600	−	1.71304i	0.691679	−	0.722205i	$-0.256871\pi$
$294$	−4.39293	−	13.5201i	−0.256201	−	0.788506i
$295$	−4.19896	+	3.05072i	−0.244473	+	0.177620i
$296$	−25.2720			−1.46891
$297$	3.00610	−	1.40119i	0.174432	−	0.0813055i
$298$	−15.7832			−0.914297
$299$	6.44710	−	4.68409i	0.372846	−	0.270888i
$300$	−0.193808	−	0.596481i	−0.0111895	−	0.0344378i
$301$	−9.73350	+	29.9566i	−0.561029	+	1.72667i
$302$	6.00202	+	4.36072i	0.345377	+	0.250931i
$303$	−6.84215	−	4.97112i	−0.393071	−	0.285583i
$304$	11.3442	−	34.9139i	0.650636	−	2.00245i
$305$	4.46106	+	13.7297i	0.255440	+	0.786163i
$306$	−3.78187	+	2.74769i	−0.216195	+	0.157075i
$307$	−16.6915			−0.952632			−0.476316	−	0.879274i	$-0.658028\pi$
$307$	−16.6915			−0.952632			−0.476316	+	0.879274i	$0.658028\pi$
$308$	−2.07089	+	0.965276i	−0.118000	+	0.0550017i
$309$	17.9682			1.02217
$310$	−6.05467	+	4.39898i	−0.343882	+	0.249845i
$311$	−0.194815	−	0.599579i	−0.0110469	−	0.0339990i	0.945381	−	0.325967i	$-0.105690\pi$
$311$	−0.194815	−	0.599579i	−0.0110469	−	0.0339990i	−0.956428	+	0.291968i	$0.905690\pi$
$312$	−0.833347	+	2.56478i	−0.0471790	+	0.145202i
$313$	−8.47954	−	6.16074i	−0.479292	−	0.348226i	0.321760	−	0.946821i	$-0.395726\pi$
$313$	−8.47954	−	6.16074i	−0.479292	−	0.348226i	−0.801051	+	0.598596i	$0.795726\pi$
$314$	−4.81754	−	3.50015i	−0.271870	−	0.197525i
$315$	−1.42937	+	4.39916i	−0.0805360	+	0.247864i
$316$	−0.753225	−	2.31819i	−0.0423722	−	0.130408i
$317$	−10.0852	+	7.32730i	−0.566439	+	0.411542i	−0.833810	−	0.552051i	$-0.813845\pi$
$317$	−10.0852	+	7.32730i	−0.566439	+	0.411542i	0.267371	+	0.963594i	$0.413845\pi$
$318$	−2.92623			−0.164095
$319$	1.10770	+	1.18824i	0.0620195	+	0.0665287i
$320$	8.17876			0.457207
$321$	−9.34743	+	6.79131i	−0.521723	+	0.379054i
$322$	14.7995	+	45.5481i	0.824742	+	2.53830i
$323$	8.35648	−	25.7186i	0.464967	−	1.43102i
$324$	−0.136573	−	0.0992261i	−0.00758739	−	0.00551256i
$325$	−3.00566	−	2.18374i	−0.166724	−	0.121132i
$326$	−6.08393	+	18.7244i	−0.336958	+	1.03705i
$327$	−2.48437	−	7.64609i	−0.137386	−	0.422830i
$328$	−16.2711	+	11.8217i	−0.898423	+	0.652743i
$329$	0.0991531			0.00546649
$330$	5.43448	+	1.05724i	0.299158	+	0.0581992i
$331$	6.64087			0.365015			0.182508	−	0.983204i	$-0.441579\pi$
$331$	6.64087			0.365015			0.182508	+	0.983204i	$0.441579\pi$
$332$	0.523936	−	0.380661i	0.0287547	−	0.0208915i
$333$	−2.89587	−	8.91257i	−0.158693	−	0.488406i
$334$	2.01916	−	6.21432i	0.110483	−	0.340033i
$335$	−1.15625	−	0.840062i	−0.0631725	−	0.0458975i
$336$	−14.2263	−	10.3360i	−0.776110	−	0.563877i
$337$	4.88307	−	15.0285i	0.265998	−	0.818656i	−0.725464	−	0.688260i	$-0.758375\pi$
$337$	4.88307	−	15.0285i	0.265998	−	0.818656i	0.991462	−	0.130396i	$-0.0416250\pi$
$338$	−0.455086	−	1.40061i	−0.0247534	−	0.0761832i
$339$	9.75426	−	7.08688i	0.529779	−	0.384907i
$340$	−0.607383			−0.0329400
$341$	1.80984	+	14.7591i	0.0980083	+	0.799251i
$342$	12.5462			0.678423
$343$	8.75865	−	6.36353i	0.472923	−	0.343598i
$344$	6.43231	+	19.7966i	0.346807	+	1.06736i
$345$	2.79130	−	8.59074i	0.150278	−	0.462510i
$346$	25.6288	+	18.6204i	1.37781	+	1.00104i
$347$	11.7681	+	8.55004i	0.631746	+	0.458990i	0.857005	−	0.515309i	$-0.172323\pi$
$347$	11.7681	+	8.55004i	0.631746	+	0.458990i	−0.225259	+	0.974299i	$0.572323\pi$
$348$	0.0255509	−	0.0786377i	0.00136967	−	0.00421542i
$349$	4.38270	+	13.4886i	0.234601	+	0.722027i	0.997174	+	0.0751250i	$0.0239356\pi$
$349$	4.38270	+	13.4886i	0.234601	+	0.722027i	−0.762573	+	0.646902i	$0.776064\pi$
$350$	18.0633	−	13.1238i	0.965525	−	0.701495i
$351$	−1.00000			−0.0533761
$352$	−1.53194	+	2.76267i	−0.0816528	+	0.147251i
$353$	−32.4634			−1.72785			−0.863926	−	0.503619i	$-0.832001\pi$
$353$	−32.4634			−1.72785			−0.863926	+	0.503619i	$0.832001\pi$
$354$	5.45551	−	3.96366i	0.289957	−	0.210666i
$355$	0.343619	+	1.05755i	0.0182374	+	0.0561289i
$356$	0.932131	−	2.86880i	0.0494028	−	0.152046i
$357$	−10.4795	−	7.61383i	−0.554636	−	0.402966i
$358$	−16.8873	−	12.2693i	−0.892520	−	0.648454i
$359$	−6.86148	+	21.1175i	−0.362135	+	1.11454i	0.589621	+	0.807680i	$0.299277\pi$
$359$	−6.86148	+	21.1175i	−0.362135	+	1.11454i	−0.951756	+	0.306857i	$0.900723\pi$
$360$	0.944590	+	2.90715i	0.0497842	+	0.153220i
$361$	−43.3456	+	31.4924i	−2.28135	+	1.65750i
$362$	−0.618406			−0.0325027
$363$	7.07331	−	8.42427i	0.371252	−	0.442159i
$364$	0.688895			0.0361079
$365$	2.50417	−	1.81938i	0.131074	−	0.0952309i
$366$	−5.79605	−	17.8384i	−0.302965	−	0.932429i
$367$	1.88118	−	5.78968i	0.0981968	−	0.302219i	−0.889877	−	0.456201i	$-0.849210\pi$
$367$	1.88118	−	5.78968i	0.0981968	−	0.302219i	0.988074	+	0.153982i	$0.0492098\pi$
$368$	27.7814	+	20.1844i	1.44821	+	1.05218i
$369$	−6.03357	−	4.38364i	−0.314095	−	0.228203i
$370$	4.83401	−	14.8775i	0.251308	−	0.773447i
$371$	−2.50568	−	7.71168i	−0.130088	−	0.400371i
$372$	0.612308	−	0.444868i	0.0317467	−	0.0230653i
$373$	−21.8465			−1.13117			−0.565584	−	0.824691i	$-0.691349\pi$
$373$	−21.8465			−1.13117			−0.565584	+	0.824691i	$0.691349\pi$
$374$	−7.51865	+	13.5590i	−0.388780	+	0.701118i
$375$	−9.87858			−0.510128
$376$	0.0530105	−	0.0385144i	0.00273381	−	0.00198623i
$377$	−0.151356	−	0.465826i	−0.00779523	−	0.0239912i
$378$	1.85712	−	5.71562i	0.0955198	−	0.293980i
$379$	−17.4431	−	12.6732i	−0.895993	−	0.650977i	0.0414407	−	0.999141i	$-0.486805\pi$
$379$	−17.4431	−	12.6732i	−0.895993	−	0.650977i	−0.937434	+	0.348164i	$0.886805\pi$
$380$	1.31882	+	0.958177i	0.0676539	+	0.0491535i
$381$	−5.08167	+	15.6398i	−0.260342	+	0.801249i
$382$	−4.50529	−	13.8659i	−0.230511	−	0.709439i
$383$	18.2664	−	13.2713i	0.933367	−	0.678131i	−0.0134475	−	0.999910i	$-0.504281\pi$
$383$	18.2664	−	13.2713i	0.933367	−	0.678131i	0.946815	+	0.321778i	$0.104281\pi$
$384$	−12.5312			−0.639481
$385$	1.86723	+	15.2271i	0.0951630	+	0.776047i
$386$	−14.3898			−0.732422
$387$	−6.24451	+	4.53690i	−0.317426	+	0.230624i
$388$	−0.0189525	−	0.0583297i	−0.000962166	−	0.00296124i
$389$	5.61212	−	17.2723i	0.284546	−	0.875741i	−0.701989	−	0.712188i	$-0.747704\pi$
$389$	5.61212	−	17.2723i	0.284546	−	0.875741i	0.986534	−	0.163553i	$-0.0522956\pi$
$390$	−1.35047	−	0.981176i	−0.0683839	−	0.0496838i
$391$	20.4646	+	14.8684i	1.03494	+	0.751927i
$392$	8.04428	−	24.7578i	0.406298	−	1.25046i
$393$	−3.07422	−	9.46149i	−0.155074	−	0.477269i
$394$	21.2454	−	15.4357i	1.07033	−	0.777640i
$395$	−16.3664			−0.823481
$396$	−0.549588	−	0.106919i	−0.0276178	−	0.00537286i
$397$	−10.7060			−0.537317			−0.268659	−	0.963235i	$-0.586580\pi$
$397$	−10.7060			−0.537317			−0.268659	+	0.963235i	$0.586580\pi$
$398$	24.5526	−	17.8385i	1.23071	−	0.894162i
$399$	10.7431	+	33.0640i	0.537830	+	1.65527i
$400$	4.94714	−	15.2257i	0.247357	−	0.761287i
$401$	−10.0854	−	7.32745i	−0.503640	−	0.365916i	0.306766	−	0.951785i	$-0.400753\pi$
$401$	−10.0854	−	7.32745i	−0.503640	−	0.365916i	−0.810405	+	0.585869i	$0.800753\pi$
$402$	1.50226	+	1.09145i	0.0749258	+	0.0544368i
$403$	1.38544	−	4.26394i	0.0690136	−	0.212402i
$404$	0.441189	+	1.35784i	0.0219500	+	0.0675551i
$405$	−0.917011	+	0.666248i	−0.0455667	+	0.0331061i
$406$	2.94357			0.146087
$407$	−21.1935	−	22.7344i	−1.05052	−	1.12690i
$408$	−8.56016			−0.423791
$409$	−22.3794	+	16.2596i	−1.10659	+	0.803987i	−0.982124	−	0.188237i	$-0.939723\pi$
$409$	−22.3794	+	16.2596i	−1.10659	+	0.803987i	−0.124469	+	0.992224i	$0.539723\pi$
$410$	−3.84704	−	11.8400i	−0.189992	−	0.584735i
$411$	1.47671	−	4.54484i	0.0728406	−	0.224180i
$412$	−2.45397	−	1.78291i	−0.120898	−	0.0878377i
$413$	15.1172	+	10.9833i	0.743867	+	0.540451i
$414$	−3.62661	+	11.1615i	−0.178238	+	0.548560i
$415$	−1.34373	−	4.13558i	−0.0659612	−	0.203008i
$416$	0.770565	−	0.559848i	0.0377801	−	0.0274488i
$417$	0.417650			0.0204524
$418$	37.7153	−	17.5797i	1.84472	−	0.859853i
$419$	−13.0558			−0.637817			−0.318908	−	0.947786i	$-0.603316\pi$
$419$	−13.0558			−0.637817			−0.318908	+	0.947786i	$0.603316\pi$
$420$	0.631725	−	0.458975i	0.0308250	−	0.0223957i
$421$	−4.47256	−	13.7651i	−0.217979	−	0.670871i	−0.998929	−	0.0462768i	$-0.985264\pi$
$421$	−4.47256	−	13.7651i	−0.217979	−	0.670871i	0.780949	−	0.624594i	$-0.214736\pi$
$422$	−7.25451	+	22.3271i	−0.353144	+	1.08686i
$423$	0.0196570	+	0.0142817i	0.000955758	+	0.000694399i
$424$	−4.33509	−	3.14963i	−0.210531	−	0.152959i
$425$	3.64421	−	11.2157i	0.176770	−	0.544042i
$426$	−0.446448	−	1.37403i	−0.0216305	−	0.0665717i
$427$	42.0477	−	30.5495i	2.03483	−	1.47839i
$428$	1.95048			0.0942801
$429$	−3.00610	+	1.40119i	−0.145136	+	0.0676503i
$430$	−12.8845			−0.621348
$431$	−3.12704	+	2.27193i	−0.150624	+	0.109435i	−0.660545	−	0.750786i	$-0.729675\pi$
$431$	−3.12704	+	2.27193i	−0.150624	+	0.109435i	0.509921	+	0.860221i	$0.329675\pi$
$432$	−1.33159	−	4.09823i	−0.0640664	−	0.197176i
$433$	3.67490	−	11.3102i	0.176604	−	0.543532i	−0.823099	−	0.567898i	$-0.807757\pi$
$433$	3.67490	−	11.3102i	0.176604	−	0.543532i	0.999703	+	0.0243659i	$0.00775668\pi$
$434$	21.7981	+	15.8373i	1.04634	+	0.760214i
$435$	−0.449150	−	0.326327i	−0.0215351	−	0.0156462i
$436$	−0.419395	+	1.29076i	−0.0200854	+	0.0618164i
$437$	−20.9794	−	64.5678i	−1.00358	−	3.08870i
$438$	−3.25355	+	2.36384i	−0.155461	+	0.112949i
$439$	34.6288			1.65274			0.826371	−	0.563126i	$-0.190401\pi$
$439$	34.6288			1.65274			0.826371	+	0.563126i	$0.190401\pi$
$440$	6.91301	+	7.41563i	0.329565	+	0.353526i
$441$	9.65298			0.459666
$442$	3.78187	−	2.74769i	0.179885	−	0.130694i
$443$	0.251206	+	0.773134i	0.0119352	+	0.0367327i	0.956847	−	0.290593i	$-0.0938526\pi$
$443$	0.251206	+	0.773134i	0.0119352	+	0.0367327i	−0.944912	+	0.327326i	$0.893853\pi$
$444$	−0.488862	+	1.50456i	−0.0232004	+	0.0714034i
$445$	−16.3856	−	11.9048i	−0.776751	−	0.564343i
$446$	−12.8086	−	9.30598i	−0.606504	−	0.440651i
$447$	3.31182	−	10.1927i	0.156644	−	0.482100i
$448$	−9.09910	−	28.0042i	−0.429892	−	1.32307i
$449$	9.42030	−	6.84425i	0.444571	−	0.323000i	−0.342877	−	0.939380i	$-0.611402\pi$
$449$	9.42030	−	6.84425i	0.444571	−	0.323000i	0.787449	+	0.616380i	$0.211402\pi$
$450$	5.47134			0.257921
$451$	−24.2799	−	4.72348i	−1.14329	−	0.222420i
$452$	−2.03537			−0.0957359
$453$	−4.07555	+	2.96106i	−0.191486	+	0.139123i
$454$	−4.81065	−	14.8057i	−0.225775	−	0.694864i
$455$	1.42937	−	4.39916i	0.0670100	−	0.206236i
$456$	18.5868	+	13.5041i	0.870406	+	0.632387i
$457$	−8.44160	−	6.13318i	−0.394881	−	0.286898i	0.372571	−	0.928003i	$-0.378476\pi$
$457$	−8.44160	−	6.13318i	−0.394881	−	0.286898i	−0.767453	+	0.641105i	$0.778476\pi$
$458$	5.04490	−	15.5266i	0.235732	−	0.725510i
$459$	−0.980891	−	3.01887i	−0.0457841	−	0.140909i
$460$	−1.23364	+	0.896293i	−0.0575188	+	0.0417899i
$461$	25.6140			1.19296			0.596482	−	0.802627i	$-0.296565\pi$
$461$	25.6140			1.19296			0.596482	+	0.802627i	$0.296565\pi$
$462$	−2.42601	−	19.7839i	−0.112868	−	0.920432i
$463$	−5.26896			−0.244870			−0.122435	−	0.992477i	$-0.539070\pi$
$463$	−5.26896			−0.244870			−0.122435	+	0.992477i	$0.539070\pi$
$464$	1.70751	−	1.24058i	0.0792693	−	0.0575925i
$465$	−1.57038	−	4.83313i	−0.0728246	−	0.224131i
$466$	−9.74416	+	29.9894i	−0.451389	+	1.38923i
$467$	−25.7230	−	18.6888i	−1.19032	−	0.864817i	−0.197020	−	0.980399i	$-0.563126\pi$
$467$	−25.7230	−	18.6888i	−1.19032	−	0.864817i	−0.993298	+	0.115583i	$0.963126\pi$
$468$	0.136573	+	0.0992261i	0.00631309	+	0.00458673i
$469$	−1.59003	+	4.89359i	−0.0734205	+	0.225965i
$470$	0.0125335	+	0.0385740i	0.000578125	+	0.00177929i
$471$	3.27126	−	2.37671i	0.150732	−	0.109513i
$472$	12.3484			0.568381
$473$	−12.4146	+	22.3882i	−0.570822	+	1.02941i
$474$	21.2640			0.976690
$475$	−25.6061	+	18.6039i	−1.17489	+	0.853606i
$476$	0.675731	+	2.07969i	0.0309721	+	0.0953223i
$477$	0.614015	−	1.88975i	0.0281138	−	0.0865255i
$478$	10.3782	+	7.54017i	0.474686	+	0.344879i
$479$	−11.8614	−	8.61785i	−0.541963	−	0.393759i	0.282850	−	0.959164i	$-0.408720\pi$
$479$	−11.8614	−	8.61785i	−0.541963	−	0.393759i	−0.824814	+	0.565405i	$0.808720\pi$
$480$	0.333619	−	1.02677i	0.0152276	−	0.0468656i
$481$	2.89587	+	8.91257i	0.132040	+	0.406378i
$482$	−27.4144	+	19.9177i	−1.24869	+	0.907227i
$483$	−32.5202			−1.47972
$484$	−1.80193	+	0.448671i	−0.0819059	+	0.0203941i
$485$	−0.411807			−0.0186992
$486$	1.19143	−	0.865625i	0.0540444	−	0.0392655i
$487$	4.38199	+	13.4864i	0.198567	+	0.611126i	0.999916	+	0.0129295i	$0.00411570\pi$
$487$	4.38199	+	13.4864i	0.198567	+	0.611126i	−0.801350	+	0.598196i	$0.795884\pi$
$488$	10.6137	−	32.6655i	0.480458	−	1.47870i
$489$	−10.8156	−	7.85796i	−0.489096	−	0.355349i
$490$	13.0361	+	9.47127i	0.588910	+	0.427868i
$491$	−1.46715	+	4.51543i	−0.0662117	+	0.203779i	−0.978689	−	0.205349i	$-0.934167\pi$
$491$	−1.46715	+	4.51543i	−0.0662117	+	0.203779i	0.912477	+	0.409128i	$0.134167\pi$
$492$	0.389051	+	1.19737i	0.0175398	+	0.0539818i
$493$	1.25780	−	0.913848i	0.0566486	−	0.0411576i
$494$	−12.5462			−0.564482
$495$	−1.82309	+	3.28772i	−0.0819417	+	0.147772i
$496$	19.3194			0.867468
$497$	3.23878	−	2.35311i	0.145279	−	0.105551i
$498$	1.74585	+	5.37317i	0.0782333	+	0.240777i
$499$	0.493000	−	1.51730i	0.0220697	−	0.0679236i	−0.939415	−	0.342782i	$-0.888631\pi$
$499$	0.493000	−	1.51730i	0.0220697	−	0.0679236i	0.961485	+	0.274858i	$0.0886309\pi$
$500$	1.34915	+	0.980213i	0.0603357	+	0.0438365i
$501$	3.58950	+	2.60792i	0.160367	+	0.116513i
$502$	5.81701	−	17.9029i	0.259626	−	0.799047i
$503$	5.02859	+	15.4764i	0.224214	+	0.690060i	0.998370	+	0.0570653i	$0.0181743\pi$
$503$	5.02859	+	15.4764i	0.224214	+	0.690060i	−0.774157	+	0.632994i	$0.781826\pi$
$504$	8.90322	−	6.46857i	0.396581	−	0.288133i
$505$	9.58633			0.426586
$506$	4.73754	+	38.6343i	0.210610	+	1.71751i
$507$	1.00000			0.0444116
$508$	2.24589	−	1.63174i	0.0996453	−	0.0723966i
$509$	6.31739	+	19.4429i	0.280013	+	0.861793i	0.987849	+	0.155416i	$0.0496717\pi$
$509$	6.31739	+	19.4429i	0.280013	+	0.861793i	−0.707836	+	0.706377i	$0.750328\pi$
$510$	1.63738	−	5.03933i	0.0725043	−	0.223145i
$511$	−9.01555	−	6.55018i	−0.398824	−	0.289763i
$512$	−15.4823	−	11.2485i	−0.684226	−	0.497119i
$513$	−2.63260	+	8.10232i	−0.116232	+	0.357726i
$514$	−5.26995	−	16.2192i	−0.232448	−	0.715400i
$515$	−16.4770	+	11.9712i	−0.726064	+	0.527516i
$516$	1.30301			0.0573618
$517$	0.0791025	+	0.0153888i	0.00347892	+	0.000676801i
$518$	−56.3188			−2.47451
$519$	−17.4027	+	12.6438i	−0.763894	+	0.555001i
$520$	−0.944590	−	2.90715i	−0.0414230	−	0.127487i
$521$	6.34922	−	19.5409i	0.278164	−	0.856101i	−0.710201	−	0.703999i	$-0.751396\pi$
$521$	6.34922	−	19.5409i	0.278164	−	0.856101i	0.988365	−	0.152102i	$-0.0486042\pi$
$522$	0.583560	+	0.423981i	0.0255417	+	0.0185572i
$523$	−14.1636	−	10.2905i	−0.619332	−	0.449971i	0.233356	−	0.972391i	$-0.425029\pi$
$523$	−14.1636	−	10.2905i	−0.619332	−	0.449971i	−0.852688	+	0.522420i	$0.825029\pi$
$524$	−0.518971	+	1.59723i	−0.0226713	+	0.0697752i
$525$	4.68501	+	14.4190i	0.204471	+	0.629296i
$526$	−3.67887	+	2.67286i	−0.160406	+	0.116542i
$527$	14.2313			0.619923
$528$	−9.74532	−	10.4539i	−0.424111	−	0.454946i
$529$	40.5059			1.76112
$530$	2.68338	−	1.94959i	0.116559	−	0.0846849i
$531$	1.41498	+	4.35485i	0.0614047	+	0.188984i
$532$	1.81359	−	5.58165i	0.0786290	−	0.241995i
$533$	6.03357	+	4.38364i	0.261343	+	0.189877i
$534$	21.2890	+	15.4674i	0.921267	+	0.669339i
$535$	4.04701	−	12.4554i	0.174967	−	0.538494i
$536$	1.05076	+	3.23389i	0.0453857	+	0.139683i
$537$	11.4670	−	8.33123i	0.494836	−	0.359519i
$538$	43.2434			1.86435
$539$	29.0178	−	13.5257i	1.24989	−	0.582593i
$540$	0.191348			0.00823432
$541$	−12.8087	+	9.30605i	−0.550688	+	0.400098i	−0.828039	−	0.560670i	$-0.810544\pi$
$541$	−12.8087	+	9.30605i	−0.550688	+	0.400098i	0.277351	+	0.960769i	$0.410544\pi$
$542$	−1.40008	−	4.30900i	−0.0601385	−	0.185087i
$543$	0.129761	−	0.399364i	0.00556859	−	0.0171384i
$544$	2.44595	+	1.77709i	0.104869	+	0.0761920i
$545$	7.37239	+	5.35635i	0.315798	+	0.229441i
$546$	−1.85712	+	5.71562i	−0.0794773	+	0.244606i
$547$	−2.18730	−	6.73183i	−0.0935223	−	0.287832i	0.893343	−	0.449375i	$-0.148353\pi$
$547$	−2.18730	−	6.73183i	−0.0935223	−	0.287832i	−0.986866	+	0.161542i	$0.948353\pi$
$548$	−0.652645	+	0.474174i	−0.0278796	+	0.0202557i
$549$	12.7362			0.543567
$550$	16.4474	−	7.66641i	0.701320	−	0.326897i
$551$	−4.17273			−0.177764
$552$	−17.3863	+	12.6319i	−0.740012	+	0.537650i
$553$	18.2080	+	56.0386i	0.774284	+	2.38300i
$554$	2.01128	−	6.19007i	0.0854509	−	0.262991i
$555$	8.59353	+	6.24356i	0.364775	+	0.265024i
$556$	−0.0570397	−	0.0414417i	−0.00241902	−	0.00175752i
$557$	−4.21093	+	12.9599i	−0.178423	+	0.549129i	−0.999773	−	0.0212950i	$-0.993221\pi$
$557$	−4.21093	+	12.9599i	−0.178423	+	0.549129i	0.821350	+	0.570424i	$0.193221\pi$
$558$	2.04032	+	6.27946i	0.0863736	+	0.265831i
$559$	6.24451	−	4.53690i	0.264115	−	0.191890i
$560$	19.9321			0.842284
$561$	−7.17868	−	7.70062i	−0.303084	−	0.325120i
$562$	−7.00066			−0.295305
$563$	−10.2027	+	7.41272i	−0.429994	+	0.312409i	−0.781647	−	0.623722i	$-0.785620\pi$
$563$	−10.2027	+	7.41272i	−0.429994	+	0.312409i	0.351652	+	0.936131i	$0.385620\pi$
$564$	−0.00126751	−	0.00390098i	−5.33716e−5	−	0.000164261i
$565$	−4.22315	+	12.9975i	−0.177669	+	0.546809i
$566$	−3.14485	−	2.28487i	−0.132188	−	0.0960402i
$567$	3.30144	+	2.39864i	0.138648	+	0.100733i
$568$	0.817529	−	2.51610i	0.0343028	−	0.105573i
$569$	13.2807	+	40.8737i	0.556754	+	1.71351i	0.691265	+	0.722601i	$0.257054\pi$
$569$	13.2807	+	40.8737i	0.556754	+	1.71351i	−0.134511	+	0.990912i	$0.542946\pi$
$570$	−11.5051	+	8.35891i	−0.481894	+	0.350116i
$571$	−8.47191			−0.354538			−0.177269	−	0.984162i	$-0.556726\pi$
$571$	−8.47191			−0.354538			−0.177269	+	0.984162i	$0.556726\pi$
$572$	0.549588	+	0.106919i	0.0229794	+	0.00447049i
$573$	9.89987			0.413573
$574$	−36.2603	+	26.3446i	−1.51348	+	1.09960i
$575$	−9.14896	−	28.1576i	−0.381538	−	1.17425i
$576$	2.22973	−	6.86241i	0.0929055	−	0.285934i
$577$	10.9304	+	7.94141i	0.455039	+	0.330605i	0.791582	−	0.611063i	$-0.209258\pi$
$577$	10.9304	+	7.94141i	0.455039	+	0.330605i	−0.336543	+	0.941668i	$0.609258\pi$
$578$	−8.24979	−	5.99382i	−0.343146	−	0.249310i
$579$	3.01944	−	9.29288i	0.125484	−	0.386199i
$580$	0.0289617	+	0.0891349i	0.00120257	+	0.00370112i
$581$	−12.6653	+	9.20190i	−0.525446	+	0.381759i
$582$	0.535041			0.0221782
$583$	−0.802107	−	6.54112i	−0.0332199	−	0.270906i
$584$	−7.36431			−0.304737
$585$	0.917011	−	0.666248i	0.0379138	−	0.0275460i
$586$	−14.0310	−	43.1830i	−0.579615	−	1.78387i
$587$	−8.39894	+	25.8493i	−0.346661	+	1.06691i	0.614027	+	0.789285i	$0.289548\pi$
$587$	−8.39894	+	25.8493i	−0.346661	+	1.06691i	−0.960688	+	0.277629i	$0.910452\pi$
$588$	−1.31834	−	0.957827i	−0.0543673	−	0.0395001i
$589$	−30.9005	−	22.4505i	−1.27323	−	0.925058i
$590$	−2.36199	+	7.26944i	−0.0972414	+	0.299278i
$591$	5.51035	+	16.9591i	0.226666	+	0.697605i
$592$	−32.6696	+	23.7359i	−1.34271	+	0.975538i
$593$	25.9550			1.06584			0.532922	−	0.846165i	$-0.321094\pi$
$593$	25.9550			1.06584			0.532922	+	0.846165i	$0.321094\pi$
$594$	2.36865	−	4.27158i	0.0971871	−	0.175265i
$595$	14.6825			0.601926
$596$	−1.46369	+	1.06343i	−0.0599551	+	0.0435599i
$597$	6.36811	+	19.5990i	0.260629	+	0.802134i
$598$	3.62661	−	11.1615i	0.148303	−	0.456430i
$599$	3.03382	+	2.20420i	0.123959	+	0.0900611i	0.648037	−	0.761609i	$-0.275590\pi$
$599$	3.03382	+	2.20420i	0.123959	+	0.0900611i	−0.524079	+	0.851670i	$0.675590\pi$
$600$	8.10558	+	5.88905i	0.330909	+	0.240419i
$601$	6.75656	−	20.7945i	0.275606	−	0.848227i	−0.713453	−	0.700703i	$-0.752870\pi$
$601$	6.75656	−	20.7945i	0.275606	−	0.848227i	0.989059	−	0.147524i	$-0.0471303\pi$
$602$	14.3344	+	44.1168i	0.584227	+	1.79807i
$603$	−1.02008	+	0.741130i	−0.0415408	+	0.0301811i
$604$	0.850425			0.0346033
$605$	−0.873655	+	12.4377i	−0.0355191	+	0.505666i
$606$	−12.4551			−0.505953
$607$	10.6733	−	7.75460i	0.433216	−	0.314750i	−0.349718	−	0.936855i	$-0.613723\pi$
$607$	10.6733	−	7.75460i	0.433216	−	0.314750i	0.782933	+	0.622106i	$0.213723\pi$
$608$	−2.50748	−	7.71722i	−0.101692	−	0.312975i
$609$	−0.617654	+	1.90094i	−0.0250286	+	0.0770301i
$610$	17.1999	+	12.4964i	0.696402	+	0.505966i
$611$	−0.0196570	−	0.0142817i	−0.000795238	−	0.000577775i
$612$	−0.165588	+	0.509626i	−0.00669348	+	0.0206004i
$613$	1.85129	+	5.69767i	0.0747727	+	0.230127i	0.981457	−	0.191684i	$-0.0613948\pi$
$613$	1.85129	+	5.69767i	0.0747727	+	0.230127i	−0.906684	+	0.421810i	$0.861395\pi$
$614$	−19.8867	+	14.4485i	−0.802563	+	0.583096i
$615$	8.45344			0.340876
$616$	17.7003	−	31.9203i	0.713165	−	1.28611i
$617$	−24.3197			−0.979074			−0.489537	−	0.871983i	$-0.662834\pi$
$617$	−24.3197			−0.979074			−0.489537	+	0.871983i	$0.662834\pi$
$618$	21.4078	−	15.5537i	0.861149	−	0.625661i
$619$	−0.323142	−	0.994529i	−0.0129882	−	0.0399735i	0.944352	−	0.328935i	$-0.106690\pi$
$619$	−0.323142	−	0.994529i	−0.0129882	−	0.0399735i	−0.957341	+	0.288962i	$0.906690\pi$
$620$	−0.265101	+	0.815898i	−0.0106467	+	0.0327672i
$621$	−6.44710	−	4.68409i	−0.258713	−	0.187966i
$622$	−0.751119	−	0.545720i	−0.0301171	−	0.0218814i
$623$	−22.5328	+	69.3489i	−0.902758	+	2.77840i
$624$	1.33159	+	4.09823i	0.0533064	+	0.164060i
$625$	−5.96954	+	4.33713i	−0.238782	+	0.173485i
$626$	−15.4357			−0.616934
$627$	3.43905	+	28.0452i	0.137342	+	1.12002i
$628$	−0.682597			−0.0272386
$629$	−24.0654	+	17.4845i	−0.959549	+	0.697153i
$630$	2.10502	+	6.47859i	0.0838661	+	0.258113i
$631$	0.230907	−	0.710658i	0.00919225	−	0.0282909i	−0.946355	−	0.323128i	$-0.895265\pi$
$631$	0.230907	−	0.710658i	0.00919225	−	0.0282909i	0.955547	+	0.294837i	$0.0952655\pi$
$632$	31.5019	+	22.8874i	1.25308	+	0.910413i
$633$	−12.8965	−	9.36986i	−0.512590	−	0.372418i
$634$	−5.67308	+	17.4599i	−0.225307	+	0.693423i
$635$	−5.76001	−	17.7275i	−0.228579	−	0.703494i
$636$	−0.271370	+	0.197162i	−0.0107605	+	0.00781798i
$637$	−9.65298			−0.382465
$638$	2.34832	+	0.456850i	0.0929710	+	0.0180869i
$639$	0.981019			0.0388085
$640$	11.4913	−	8.34890i	0.454233	−	0.330019i
$641$	9.29081	+	28.5942i	0.366965	+	1.12940i	0.948741	+	0.316053i	$0.102358\pi$
$641$	9.29081	+	28.5942i	0.366965	+	1.12940i	−0.581777	+	0.813349i	$0.697642\pi$
$642$	−5.25809	+	16.1827i	−0.207520	+	0.638682i
$643$	3.58755	+	2.60651i	0.141479	+	0.102791i	0.656274	−	0.754523i	$-0.272132\pi$
$643$	3.58755	+	2.60651i	0.141479	+	0.102791i	−0.514794	+	0.857314i	$0.672132\pi$
$644$	4.44138	+	3.22685i	0.175015	+	0.127156i
$645$	2.70359	−	8.32078i	0.106454	−	0.327630i
$646$	−12.3065	−	37.8755i	−0.484193	−	1.49019i
$647$	8.38038	−	6.08870i	0.329467	−	0.239372i	−0.410738	−	0.911754i	$-0.634729\pi$
$647$	8.38038	−	6.08870i	0.329467	−	0.239372i	0.740204	+	0.672382i	$0.234729\pi$
$648$	2.69677			0.105939
$649$	10.3556	+	11.1085i	0.406491	+	0.436045i
$650$	−5.47134			−0.214604
$651$	−14.8016	+	10.7540i	−0.580120	+	0.421482i
$652$	0.697398	+	2.14637i	0.0273122	+	0.0840584i
$653$	10.5220	−	32.3834i	0.411757	−	1.26726i	−0.503362	−	0.864076i	$-0.667904\pi$
$653$	10.5220	−	32.3834i	0.411757	−	1.26726i	0.915119	−	0.403183i	$-0.132096\pi$
$654$	−9.57860	−	6.95926i	−0.374553	−	0.272129i
$655$	9.12279	+	6.62810i	0.356457	+	0.258981i
$656$	−9.93089	+	30.5642i	−0.387736	+	1.19333i
$657$	−0.843861	−	2.59714i	−0.0329221	−	0.101324i
$658$	0.118134	−	0.0858294i	0.00460534	−	0.00334598i
$659$	−26.3568			−1.02672			−0.513359	−	0.858174i	$-0.671599\pi$
$659$	−26.3568			−1.02672			−0.513359	+	0.858174i	$0.671599\pi$
$660$	0.575212	−	0.268116i	0.0223901	−	0.0104364i
$661$	25.5578			0.994085			0.497042	−	0.867726i	$-0.334419\pi$
$661$	25.5578			0.994085			0.497042	+	0.867726i	$0.334419\pi$
$662$	7.91214	−	5.74850i	0.307514	−	0.223422i
$663$	0.980891	+	3.01887i	0.0380946	+	0.117243i
$664$	−3.19697	+	9.83927i	−0.124067	+	0.381838i
$665$	−31.8804	−	23.1625i	−1.23627	−	0.898201i
$666$	−11.1652	−	8.11197i	−0.432642	−	0.314333i
$667$	1.20616	−	3.71219i	0.0467028	−	0.143737i
$668$	−0.231455	−	0.712344i	−0.00895525	−	0.0275614i
$669$	8.69741	−	6.31904i	0.336261	−	0.244308i
$670$	−2.10477			−0.0813142
$671$	38.2862	−	17.8459i	1.47802	−	0.688932i
$672$	−3.88685			−0.149938
$673$	21.6809	−	15.7521i	0.835738	−	0.607199i	−0.0854388	−	0.996343i	$-0.527229\pi$
$673$	21.6809	−	15.7521i	0.835738	−	0.607199i	0.921177	+	0.389144i	$0.127229\pi$
$674$	−7.19124	−	22.1324i	−0.276996	−	0.852506i
$675$	−1.14806	+	3.53337i	−0.0441889	+	0.135999i
$676$	−0.136573	−	0.0992261i	−0.00525281	−	0.00381639i
$677$	−15.6797	−	11.3920i	−0.602621	−	0.437830i	0.244187	−	0.969728i	$-0.421479\pi$
$677$	−15.6797	−	11.3920i	−0.602621	−	0.437830i	−0.846808	+	0.531898i	$0.821479\pi$
$678$	5.48694	−	16.8871i	0.210725	−	0.648544i
$679$	0.458147	+	1.41003i	0.0175821	+	0.0541120i
$680$	7.84977	−	5.70319i	0.301025	−	0.218707i
$681$	10.5709			0.405076
$682$	14.9322	+	16.0178i	0.571782	+	0.613354i
$683$	−1.56333			−0.0598190			−0.0299095	−	0.999553i	$-0.509522\pi$
$683$	−1.56333			−0.0598190			−0.0299095	+	0.999553i	$0.509522\pi$
$684$	1.16350	−	0.845335i	0.0444877	−	0.0323222i
$685$	1.67383	+	5.15152i	0.0639538	+	0.196830i
$686$	4.92689	−	15.1634i	0.188110	−	0.578942i
$687$	8.96843	+	6.51594i	0.342167	+	0.248599i
$688$	26.9084	+	19.5501i	1.02587	+	0.745340i
$689$	−0.614015	+	1.88975i	−0.0233921	+	0.0719936i
$690$	−4.11072	−	12.6515i	−0.156492	−	0.481634i
$691$	20.0694	−	14.5812i	0.763474	−	0.554697i	−0.136500	−	0.990640i	$-0.543585\pi$
$691$	20.0694	−	14.5812i	0.763474	−	0.554697i	0.899974	+	0.435944i	$0.143585\pi$
$692$	3.63133			0.138043
$693$	13.2854	+	2.58459i	0.504672	+	0.0981805i
$694$	21.4220			0.813169
$695$	−0.382989	+	0.278258i	−0.0145276	+	0.0105549i
$696$	0.408172	+	1.25622i	0.0154717	+	0.0476170i
$697$	−7.31538	+	22.5144i	−0.277090	+	0.852795i
$698$	16.8977	+	12.2769i	0.639588	+	0.464688i
$699$	−17.3224	−	12.5855i	−0.655194	−	0.476026i
$700$	0.790894	−	2.43412i	0.0298930	−	0.0920011i
$701$	9.40264	+	28.9384i	0.355133	+	1.09299i	0.955932	+	0.293587i	$0.0948490\pi$
$701$	9.40264	+	28.9384i	0.355133	+	1.09299i	−0.600800	+	0.799400i	$0.705151\pi$
$702$	−1.19143	+	0.865625i	−0.0449677	+	0.0326709i
$703$	79.8361			3.01108
$704$	−2.91277	−	23.7534i	−0.109779	−	0.895240i
$705$	−0.0275409			−0.00103725
$706$	−38.6779	+	28.1011i	−1.45566	+	1.05760i
$707$	−10.6651	−	32.8237i	−0.401101	−	1.23446i
$708$	0.238867	−	0.735157i	0.00897718	−	0.0276289i
$709$	−3.88549	−	2.82298i	−0.145923	−	0.106019i	0.512429	−	0.858730i	$-0.328746\pi$
$709$	−3.88549	−	2.82298i	−0.145923	−	0.106019i	−0.658351	+	0.752711i	$0.728746\pi$
$710$	1.32484	+	0.962552i	0.0497203	+	0.0361239i
$711$	−4.46187	+	13.7322i	−0.167333	+	0.514999i
$712$	14.8906	+	45.8287i	0.558050	+	1.71750i
$713$	28.9048	−	21.0005i	1.08249	−	0.786476i
$714$	−19.0764			−0.713915
$715$	1.82309	−	3.28772i	0.0681796	−	0.122954i
$716$	−2.39275			−0.0894214
$717$	−7.04708	+	5.12000i	−0.263178	+	0.191210i
$718$	10.1048	+	31.0995i	0.377109	+	1.16062i
$719$	−7.20209	+	22.1657i	−0.268592	+	0.826643i	0.722251	+	0.691631i	$0.243107\pi$
$719$	−7.20209	+	22.1657i	−0.268592	+	0.826643i	−0.990844	+	0.135012i	$0.956893\pi$
$720$	3.95152	+	2.87095i	0.147264	+	0.106994i
$721$	59.3208	+	43.0991i	2.20922	+	1.60509i
$722$	−24.3826	+	75.0421i	−0.907428	+	2.79278i
$723$	−7.11037	−	21.8835i	−0.264437	−	0.813854i
$724$	−0.0573493	+	0.0416667i	−0.00213137	+	0.00154853i
$725$	−1.81970			−0.0675819
$726$	1.13510	−	16.1598i	0.0421275	−	0.599745i
$727$	−5.67539			−0.210489			−0.105244	−	0.994446i	$-0.533562\pi$
$727$	−5.67539			−0.210489			−0.105244	+	0.994446i	$0.533562\pi$
$728$	−8.90322	+	6.46857i	−0.329975	+	0.239741i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	1.40864	−	4.33534i	0.0521360	−	0.160458i
$731$	19.8215	+	14.4012i	0.733125	+	0.532646i
$732$	−1.73942	−	1.26376i	−0.0642907	−	0.0467100i
$733$	7.25908	−	22.3411i	0.268120	−	0.825189i	−0.722838	−	0.691018i	$-0.757163\pi$
$733$	7.25908	−	22.3411i	0.268120	−	0.825189i	0.990958	−	0.134171i	$-0.0428373\pi$
$734$	−2.77039	−	8.52640i	−0.102257	−	0.314715i
$735$	−8.85189	+	6.43127i	−0.326507	+	0.237221i
$736$	7.59029			0.279782
$737$	−2.02799	+	3.65724i	−0.0747020	+	0.134716i
$738$	−10.9832			−0.404296
$739$	4.55702	−	3.31087i	0.167633	−	0.121792i	−0.500806	−	0.865560i	$-0.666963\pi$
$739$	4.55702	−	3.31087i	0.167633	−	0.121792i	0.668439	+	0.743767i	$0.266963\pi$
$740$	−0.554120	−	1.70540i	−0.0203698	−	0.0626919i
$741$	2.63260	−	8.10232i	0.0967110	−	0.297646i
$742$	−9.66077	−	7.01896i	−0.354658	−	0.257674i
$743$	13.7071	+	9.95881i	0.502866	+	0.365353i	0.810110	−	0.586277i	$-0.199407\pi$
$743$	13.7071	+	9.95881i	0.502866	+	0.365353i	−0.307245	+	0.951630i	$0.599407\pi$
$744$	−3.73621	+	11.4989i	−0.136976	+	0.421569i
$745$	3.75391	+	11.5533i	0.137533	+	0.423282i
$746$	−26.0285	+	18.9108i	−0.952973	+	0.692375i
$747$	−3.83630			−0.140363
$748$	0.216312	+	1.76401i	0.00790915	+	0.0644986i
$749$	−47.1499			−1.72282
$750$	−11.7696	+	8.55115i	−0.429767	+	0.312244i
$751$	1.08324	+	3.33387i	0.0395280	+	0.121655i	0.968873	−	0.247557i	$-0.0796277\pi$
$751$	1.08324	+	3.33387i	0.0395280	+	0.121655i	−0.929345	+	0.369212i	$0.879628\pi$
$752$	0.0323543	−	0.0995763i	0.00117984	−	0.00363118i
$753$	10.3410	+	7.51321i	0.376849	+	0.273796i
$754$	−0.583560	−	0.423981i	−0.0212520	−	0.0154405i
$755$	1.76453	−	5.43065i	0.0642177	−	0.197642i
$756$	−0.212880	−	0.655178i	−0.00774238	−	0.0238286i
$757$	9.41530	−	6.84062i	0.342205	−	0.248627i	−0.403387	−	0.915030i	$-0.632167\pi$
$757$	9.41530	−	6.84062i	0.342205	−	0.248627i	0.745592	+	0.666403i	$0.232167\pi$
$758$	−31.7525			−1.15330
$759$	−25.9440	−	5.04722i	−0.941707	−	0.183203i
$760$	−26.0414			−0.944619
$761$	−3.98403	+	2.89456i	−0.144421	+	0.104928i	−0.657650	−	0.753324i	$-0.728449\pi$
$761$	−3.98403	+	2.89456i	−0.144421	+	0.104928i	0.513229	+	0.858252i	$0.328449\pi$
$762$	7.48372	+	23.0325i	0.271106	+	0.834380i
$763$	10.1382	−	31.2022i	0.367028	−	1.12960i
$764$	−1.35206	−	0.982326i	−0.0489156	−	0.0355393i
$765$	2.91080	+	2.11482i	0.105240	+	0.0764616i
$766$	10.2751	−	31.6236i	0.371256	−	1.14261i
$767$	−1.41498	−	4.35485i	−0.0510918	−	0.157244i
$768$	−3.25506	+	2.36494i	−0.117457	+	0.0853373i
$769$	−47.3002			−1.70569			−0.852844	−	0.522165i	$-0.825124\pi$
$769$	−47.3002			−1.70569			−0.852844	+	0.522165i	$0.825124\pi$
$770$	15.4057	+	16.5258i	0.555182	+	0.595547i
$771$	11.5801			0.417048
$772$	−1.33447	+	0.969550i	−0.0480287	+	0.0348949i
$773$	−10.0975	−	31.0768i	−0.363181	−	1.11776i	−0.951112	−	0.308845i	$-0.900058\pi$
$773$	−10.0975	−	31.0768i	−0.363181	−	1.11776i	0.587931	−	0.808911i	$-0.299942\pi$
$774$	−3.51264	+	10.8108i	−0.126259	+	0.388586i
$775$	−13.4755	−	9.79053i	−0.484055	−	0.351686i
$776$	0.792643	+	0.575889i	0.0284542	+	0.0206732i
$777$	11.8175	−	36.3705i	0.423950	−	1.30478i
$778$	−8.26490	−	25.4368i	−0.296311	−	0.911952i
$779$	51.4016	−	37.3455i	1.84165	−	1.33804i
$780$	−0.191348			−0.00685137
$781$	2.94904	−	1.37460i	0.105525	−	0.0491870i
$782$	37.2526			1.33215
$783$	−0.396255	+	0.287896i	−0.0141610	+	0.0102886i
$784$	−12.8538	−	39.5601i	−0.459066	−	1.41286i
$785$	−1.41630	+	4.35893i	−0.0505501	+	0.155577i
$786$	−11.8528	−	8.61158i	−0.422776	−	0.307165i
$787$	15.2736	+	11.0969i	0.544445	+	0.395562i	0.825733	−	0.564061i	$-0.190762\pi$
$787$	15.2736	+	11.0969i	0.544445	+	0.395562i	−0.281288	+	0.959623i	$0.590762\pi$
$788$	0.930222	−	2.86293i	0.0331378	−	0.101988i
$789$	−0.954176	−	2.93665i	−0.0339696	−	0.104548i
$790$	−19.4994	+	14.1671i	−0.693757	+	0.504044i
$791$	49.2020			1.74942
$792$	8.10676	−	3.77870i	0.288061	−	0.134270i
$793$	−12.7362			−0.452275
$794$	−12.7554	+	9.26735i	−0.452673	+	0.328886i
$795$	0.695979	+	2.14200i	0.0246838	+	0.0759691i
$796$	1.07502	−	3.30858i	0.0381032	−	0.117269i
$797$	−8.17982	−	5.94299i	−0.289744	−	0.210511i	0.433412	−	0.901196i	$-0.357309\pi$
$797$	−8.17982	−	5.94299i	−0.289744	−	0.210511i	−0.723156	+	0.690684i	$0.757309\pi$
$798$	41.4207	+	30.0939i	1.46628	+	1.06531i
$799$	0.0238331	−	0.0733508i	0.000843155	−	0.00259497i
$800$	−1.09349	−	3.36543i	−0.0386609	−	0.118986i
$801$	−14.4559	+	10.5028i	−0.510774	+	0.371099i
$802$	−18.3589			−0.648274
$803$	−6.17583	−	6.62485i	−0.217940	−	0.233786i
$804$	0.212855			0.00750680
$805$	29.8214	−	21.6665i	1.05107	−	0.763644i
$806$	−2.04032	−	6.27946i	−0.0718672	−	0.221185i
$807$	−9.07383	+	27.9264i	−0.319414	+	0.983055i
$808$	−18.4517	−	13.4059i	−0.649129	−	0.471620i
$809$	−17.5973	−	12.7852i	−0.618689	−	0.449504i	0.233775	−	0.972291i	$-0.424892\pi$
$809$	−17.5973	−	12.7852i	−0.618689	−	0.449504i	−0.852463	+	0.522787i	$0.824892\pi$
$810$	−0.515835	+	1.58758i	−0.0181246	+	0.0557817i
$811$	−10.3013	−	31.7040i	−0.361726	−	1.11328i	−0.952006	−	0.306079i	$-0.900983\pi$
$811$	−10.3013	−	31.7040i	−0.361726	−	1.11328i	0.590280	−	0.807199i	$-0.299017\pi$
$812$	0.272978	−	0.198330i	0.00957966	−	0.00696003i
$813$	3.07651			0.107898
$814$	−44.9301	−	8.74085i	−1.57480	−	0.306367i
$815$	15.1533			0.530798
$816$	−11.0659	+	8.03982i	−0.387383	+	0.281450i
$817$	−20.3201	−	62.5388i	−0.710910	−	2.18796i
$818$	−12.5888	+	38.7444i	−0.440158	+	1.35467i
$819$	−3.30144	−	2.39864i	−0.115362	−	0.0838152i
$820$	−1.15451	−	0.838802i	−0.0403173	−	0.0292922i
$821$	9.92110	−	30.5340i	0.346249	−	1.06564i	−0.614663	−	0.788790i	$-0.710708\pi$
$821$	9.92110	−	30.5340i	0.346249	−	1.06564i	0.960912	−	0.276854i	$-0.0892919\pi$
$822$	−2.17473	−	6.69313i	−0.0758525	−	0.233450i
$823$	33.9767	−	24.6855i	1.18435	−	0.860484i	0.191698	−	0.981454i	$-0.438601\pi$
$823$	33.9767	−	24.6855i	1.18435	−	0.860484i	0.992656	+	0.120970i	$0.0386006\pi$
$824$	48.4560			1.68804
$825$	1.49975	+	12.2303i	0.0522145	+	0.425805i
$826$	27.5184			0.957489
$827$	−23.4216	+	17.0168i	−0.814448	+	0.591731i	−0.915117	−	0.403189i	$-0.867902\pi$
$827$	−23.4216	+	17.0168i	−0.814448	+	0.591731i	0.100669	+	0.994920i	$0.467902\pi$
$828$	0.415716	+	1.27944i	0.0144471	+	0.0444637i
$829$	1.58636	−	4.88232i	0.0550966	−	0.169570i	−0.919721	−	0.392572i	$-0.871586\pi$
$829$	1.58636	−	4.88232i	0.0550966	−	0.169570i	0.974818	+	0.223002i	$0.0715855\pi$
$830$	−5.18082	−	3.76409i	−0.179829	−	0.130653i
$831$	3.57549	+	2.59775i	0.124032	+	0.0901148i
$832$	−2.22973	+	6.86241i	−0.0773021	+	0.237911i
$833$	−9.46852	−	29.1411i	−0.328065	−	1.00968i
$834$	0.497601	−	0.361528i	0.0172305	−	0.0125187i
$835$	−5.02914			−0.174040
$836$	2.31313	−	4.17146i	0.0800014	−	0.144273i
$837$	−4.48337			−0.154968
$838$	−15.5551	+	11.3014i	−0.537341	+	0.390401i
$839$	−4.70556	−	14.4822i	−0.162454	−	0.499982i	0.836386	−	0.548141i	$-0.184664\pi$
$839$	−4.70556	−	14.4822i	−0.162454	−	0.499982i	−0.998840	+	0.0481597i	$0.984664\pi$
$840$	−3.85469	+	11.8635i	−0.132999	+	0.409330i
$841$	23.2674	+	16.9048i	0.802324	+	0.582923i
$842$	−17.2442	−	12.5286i	−0.594274	−	0.431765i
$843$	1.46896	−	4.52100i	0.0505937	−	0.155711i
$844$	0.831580	+	2.55934i	0.0286242	+	0.0880961i
$845$	−0.917011	+	0.666248i	−0.0315462	+	0.0229196i
$846$	0.0357826			0.00123023
$847$	43.5589	−	10.8459i	1.49670	−	0.372670i
$848$	−8.56222			−0.294028
$849$	2.13545	−	1.55149i	0.0732884	−	0.0532471i
$850$	−5.36679	−	16.5173i	−0.184079	−	0.566538i
$851$	−23.0774	+	71.0248i	−0.791081	+	2.43470i
$852$	−0.133981	−	0.0973427i	−0.00459010	−	0.00333490i
$853$	27.8038	+	20.2007i	0.951985	+	0.691658i	0.951276	−	0.308342i	$-0.0997741\pi$
$853$	27.8038	+	20.2007i	0.951985	+	0.691658i	0.000709712		1.00000i	$0.499774\pi$
$854$	23.6526	−	72.7951i	0.809374	−	2.49100i
$855$	−2.98402	−	9.18388i	−0.102051	−	0.314082i
$856$	−25.2079	+	18.3146i	−0.861587	+	0.625980i
$857$	38.7974			1.32529			0.662647	−	0.748932i	$-0.269433\pi$
$857$	38.7974			1.32529			0.662647	+	0.748932i	$0.269433\pi$
$858$	−2.36865	+	4.27158i	−0.0808645	+	0.145829i
$859$	−45.3237			−1.54642			−0.773212	−	0.634148i	$-0.781351\pi$
$859$	−45.3237			−1.54642			−0.773212	+	0.634148i	$0.781351\pi$
$860$	−1.19488	+	0.868128i	−0.0407449	+	0.0296029i
$861$	−9.40470	−	28.9447i	−0.320511	−	0.986432i
$862$	−1.75901	+	5.41369i	−0.0599122	+	0.184391i
$863$	13.1666	+	9.56609i	0.448196	+	0.325633i	0.788883	−	0.614543i	$-0.210660\pi$
$863$	13.1666	+	9.56609i	0.448196	+	0.325633i	−0.340687	+	0.940177i	$0.610660\pi$
$864$	−0.770565	−	0.559848i	−0.0262152	−	0.0190464i
$865$	7.53457	−	23.1890i	0.256183	−	0.788450i
$866$	−5.41198	−	16.6564i	−0.183907	−	0.566007i
$867$	5.60185	−	4.06998i	0.190249	−	0.138224i
$868$	3.08858			0.104833
$869$	5.82868	+	47.5325i	0.197724	+	1.61243i
$870$	−0.817608			−0.0277195
$871$	1.02008	−	0.741130i	0.0345640	−	0.0251122i
$872$	−6.69976	−	20.6197i	−0.226883	−	0.698273i
$873$	−0.112269	+	0.345527i	−0.00379972	+	0.0116943i
$874$	−80.8870	−	58.7678i	−2.73604	−	1.98785i
$875$	−32.6136	−	23.6951i	−1.10254	−	0.801042i
$876$	−0.142455	+	0.438432i	−0.00481311	+	0.0148132i
$877$	−16.6153	−	51.1365i	−0.561058	−	1.72676i	−0.679383	−	0.733784i	$-0.737753\pi$
$877$	−16.6153	−	51.1365i	−0.561058	−	1.72676i	0.118325	−	0.992975i	$-0.462247\pi$
$878$	41.2578	−	29.9756i	1.39238	−	1.01163i
$879$	30.8315			1.03992
$880$	15.9014	+	3.09352i	0.536037	+	0.104282i
$881$	5.86140			0.197476			0.0987378	−	0.995113i	$-0.468519\pi$
$881$	5.86140			0.197476			0.0987378	+	0.995113i	$0.468519\pi$
$882$	11.5009	−	8.35586i	0.387254	−	0.281356i
$883$	2.55461	+	7.86228i	0.0859695	+	0.264587i	0.984795	−	0.173719i	$-0.0555785\pi$
$883$	2.55461	+	7.86228i	0.0859695	+	0.264587i	−0.898826	+	0.438306i	$0.855579\pi$
$884$	0.165588	−	0.509626i	0.00556932	−	0.0171406i
$885$	−4.19896	−	3.05072i	−0.141146	−	0.102549i
$886$	0.968539	+	0.703685i	0.0325387	+	0.0236407i
$887$	0.100987	−	0.310806i	0.00339081	−	0.0104358i	−0.949347	−	0.314230i	$-0.898254\pi$
$887$	0.100987	−	0.310806i	0.00339081	−	0.0104358i	0.952738	+	0.303794i	$0.0982536\pi$
$888$	−7.80949	−	24.0351i	−0.262069	−	0.806567i
$889$	−54.2909	+	39.4447i	−1.82086	+	1.32293i
$890$	−29.8274			−0.999817
$891$	2.26155	+	2.42598i	0.0757648	+	0.0812734i
$892$	−1.81485			−0.0607655
$893$	−0.167464	+	0.121670i	−0.00560396	+	0.00407152i
$894$	−4.87728	−	15.0107i	−0.163121	−	0.502034i
$895$	−4.96467	+	15.2797i	−0.165951	+	0.510743i
$896$	−41.3711	−	30.0579i	−1.38211	−	1.00416i
$897$	6.44710	+	4.68409i	0.215262	+	0.156397i
$898$	5.29908	−	16.3089i	0.176833	−	0.544235i
$899$	−0.678585	−	2.08847i	−0.0226321	−	0.0696544i
$900$	0.507397	−	0.368645i	0.0169132	−	0.0122882i
$901$	−6.30718			−0.210123
$902$	−33.0165	+	15.3896i	−1.09933	+	0.512416i
$903$	−31.4983			−1.04820
$904$	26.3050	−	19.1117i	0.874890	−	0.635645i
$905$	0.147083	+	0.452675i	0.00488920	+	0.0150474i
$906$	−2.29257	+	7.05580i	−0.0761655	+	0.234413i
$907$	18.3849	+	13.3574i	0.610461	+	0.443526i	0.849577	−	0.527465i	$-0.176857\pi$
$907$	18.3849	+	13.3574i	0.610461	+	0.443526i	−0.239116	+	0.970991i	$0.576857\pi$
$908$	−1.44369	−	1.04891i	−0.0479107	−	0.0348092i
$909$	2.61347	−	8.04343i	0.0866833	−	0.266784i
$910$	−2.10502	−	6.47859i	−0.0697808	−	0.214763i
$911$	−22.8674	+	16.6141i	−0.757630	+	0.550450i	−0.898183	−	0.439623i	$-0.855112\pi$
$911$	−22.8674	+	16.6141i	−0.757630	+	0.550450i	0.140552	+	0.990073i	$0.455112\pi$
$912$	36.7107			1.21561
$913$	−11.5323	+	5.37541i	−0.381664	+	0.177900i
$914$	−15.3666			−0.508282
$915$	−11.6792	+	8.48545i	−0.386103	+	0.280520i
$916$	−0.578294	−	1.77980i	−0.0191074	−	0.0588064i
$917$	12.5453	−	38.6105i	0.414283	−	1.27503i
$918$	−3.78187	−	2.74769i	−0.124820	−	0.0906874i
$919$	−33.9366	−	24.6564i	−1.11946	−	0.813339i	−0.135337	−	0.990800i	$-0.543212\pi$
$919$	−33.9366	−	24.6564i	−1.11946	−	0.813339i	−0.984128	+	0.177461i	$0.943212\pi$
$920$	7.52749	−	23.1672i	0.248174	−	0.763801i
$921$	−5.15795	−	15.8745i	−0.169960	−	0.523083i
$922$	30.5173	−	22.1721i	1.00503	−	0.730200i
$923$	−0.981019			−0.0322906
$924$	−1.55797	−	1.67125i	−0.0512535	−	0.0549800i
$925$	34.8160			1.14474
$926$	−6.27761	+	4.56095i	−0.206295	+	0.149882i
$927$	5.55247	+	17.0887i	0.182367	+	0.561268i
$928$	0.144162	−	0.443685i	0.00473235	−	0.0145647i
$929$	−15.2327	−	11.0672i	−0.499770	−	0.363104i	0.309159	−	0.951010i	$-0.399952\pi$
$929$	−15.2327	−	11.0672i	−0.499770	−	0.363104i	−0.808929	+	0.587906i	$0.799952\pi$
$930$	−6.05467	−	4.39898i	−0.198541	−	0.144248i
$931$	−25.4124	+	78.2115i	−0.832859	+	2.56328i
$932$	1.11697	+	3.43767i	0.0365875	+	0.112605i
$933$	0.510032	−	0.370560i	0.0166977	−	0.0121316i
$934$	−46.8247			−1.53215
$935$	11.7135	+	2.27877i	0.383071	+	0.0745239i
$936$	−2.69677			−0.0881466
$937$	2.14252	−	1.55663i	0.0699931	−	0.0508530i	−0.552239	−	0.833686i	$-0.686226\pi$
$937$	2.14252	−	1.55663i	0.0699931	−	0.0508530i	0.622232	+	0.782833i	$0.286226\pi$
$938$	2.34161	+	7.20674i	0.0764564	+	0.235309i
$939$	3.23889	−	9.96829i	0.105697	−	0.325303i
$940$	0.00376134	+	0.00273277i	0.000122681	+	8.91332e-5i
$941$	−3.88937	−	2.82580i	−0.126790	−	0.0921183i	0.522583	−	0.852588i	$-0.324969\pi$
$941$	−3.88937	−	2.82580i	−0.126790	−	0.0921183i	−0.649373	+	0.760470i	$0.724969\pi$
$942$	1.84014	−	5.66336i	0.0599549	−	0.184522i
$943$	18.3656	+	56.5236i	0.598067	+	1.84066i
$944$	15.9630	−	11.5978i	0.519551	−	0.377476i
$945$	−4.62555			−0.150469
$946$	4.58867	+	37.4203i	0.149191	+	1.21664i
$947$	19.0767			0.619911			0.309955	−	0.950751i	$-0.399686\pi$
$947$	19.0767			0.619911			0.309955	+	0.950751i	$0.399686\pi$
$948$	1.97197	−	1.43272i	0.0640465	−	0.0465325i
$949$	0.843861	+	2.59714i	0.0273929	+	0.0843066i
$950$	−14.4039	+	44.3305i	−0.467323	+	1.43827i
$951$	−10.0852	−	7.32730i	−0.327034	−	0.237604i
$952$	−28.2609	−	20.5327i	−0.915940	−	0.665469i
$953$	8.70833	−	26.8015i	0.282090	−	0.868185i	−0.705165	−	0.709043i	$-0.749127\pi$
$953$	8.70833	−	26.8015i	0.282090	−	0.868185i	0.987256	−	0.159142i	$-0.0508728\pi$
$954$	−0.904254	−	2.78301i	−0.0292763	−	0.0901032i
$955$	−9.07829	+	6.59577i	−0.293767	+	0.213434i
$956$	1.47048			0.0475587
$957$	−0.787785	+	1.42068i	−0.0254655	+	0.0459239i
$958$	−21.5919			−0.697603
$959$	15.7767	−	11.4624i	0.509456	−	0.370141i
$960$	2.52738	+	7.77846i	0.0815707	+	0.251049i
$961$	−3.36809	+	10.3659i	−0.108648	+	0.334384i
$962$	11.1652	+	8.11197i	0.359980	+	0.261541i
$963$	−9.34743	−	6.79131i	−0.301217	−	0.218847i
$964$	−1.20033	+	3.69422i	−0.0386599	+	0.118983i
$965$	3.42250	+	10.5334i	0.110174	+	0.339081i
$966$	−38.7455	+	28.1503i	−1.24662	+	0.905720i
$967$	−13.5446			−0.435564			−0.217782	−	0.975997i	$-0.569882\pi$
$967$	−13.5446			−0.435564			−0.217782	+	0.975997i	$0.569882\pi$
$968$	19.0751	−	22.7183i	0.613096	−	0.730194i
$969$	27.0421			0.868719
$970$	−0.490639	+	0.356470i	−0.0157535	+	0.0114456i
$971$	11.9566	+	36.7985i	0.383705	+	1.18092i	0.937416	+	0.348213i	$0.113211\pi$
$971$	11.9566	+	36.7985i	0.383705	+	1.18092i	−0.553711	+	0.832709i	$0.686789\pi$
$972$	0.0521663	−	0.160551i	0.00167323	−	0.00514968i
$973$	1.37885	+	1.00179i	0.0442038	+	0.0321159i
$974$	16.8950	+	12.2749i	0.541350	+	0.393314i
$975$	1.14806	−	3.53337i	0.0367674	−	0.113158i
$976$	−16.9594	−	52.1957i	−0.542858	−	1.67074i
$977$	42.3788	−	30.7900i	1.35582	−	0.985059i	0.357119	−	0.934059i	$-0.383759\pi$
$977$	42.3788	−	30.7900i	1.35582	−	0.985059i	0.998699	−	0.0510000i	$-0.0162409\pi$
$978$	−19.6880			−0.629554
$979$	−28.7394	+	51.8281i	−0.918515	+	1.65643i
$980$	1.84708			0.0590028
$981$	6.50416	−	4.72555i	0.207662	−	0.150875i
$982$	2.16066	+	6.64983i	0.0689494	+	0.212205i
$983$	9.70250	−	29.8612i	0.309462	−	0.952425i	−0.668513	−	0.743701i	$-0.733069\pi$
$983$	9.70250	−	29.8612i	0.309462	−	0.952425i	0.977974	−	0.208725i	$-0.0669312\pi$
$984$	−16.2711	−	11.8217i	−0.518705	−	0.376861i
$985$	−16.3520	−	11.8804i	−0.521019	−	0.378542i
$986$	0.707536	−	2.17757i	0.0225325	−	0.0693480i
$987$	0.0306400	+	0.0943002i	0.000975282	+	0.00300161i
$988$	−1.16350	+	0.845335i	−0.0370160	+	0.0268937i
$989$	61.5103			1.95591
$990$	0.673850	+	5.49520i	0.0214164	+	0.174649i
$991$	41.5862			1.32103			0.660514	−	0.750814i	$-0.270338\pi$
$991$	41.5862			1.32103			0.660514	+	0.750814i	$0.270338\pi$
$992$	3.45473	−	2.51001i	0.109688	−	0.0796929i
$993$	2.05214	+	6.31584i	0.0651228	+	0.200427i
$994$	1.82187	−	5.60713i	0.0577861	−	0.177847i
$995$	−18.8974	−	13.7298i	−0.599089	−	0.435263i
$996$	0.523936	+	0.380661i	0.0166015	+	0.0120617i
$997$	−18.8567	+	58.0349i	−0.597197	+	1.83798i	−0.0537253	+	0.998556i	$0.517110\pi$
$997$	−18.8567	+	58.0349i	−0.597197	+	1.83798i	−0.543472	+	0.839428i	$0.682890\pi$
$998$	−0.726036	−	2.23451i	−0.0229823	−	0.0707322i
$999$	7.58149	−	5.50827i	0.239868	−	0.174274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.d.157.6	✓	36
11.2	odd	10		4719.2.a.br.1.13		18
11.4	even	5	inner	429.2.n.d.235.6	yes	36
11.9	even	5		4719.2.a.bq.1.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.d.157.6	✓	36	1.1	even	1	trivial
429.2.n.d.235.6	yes	36	11.4	even	5	inner
4719.2.a.bq.1.6		18	11.9	even	5
4719.2.a.br.1.13		18	11.2	odd	10

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)

\(f(q)\)	\(=\)	\(q+(1.19143 - 0.865625i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.0521663 - 0.160551i) q^{4} +(-0.917011 - 0.666248i) q^{5} +(1.19143 + 0.865625i) q^{6} +(-1.26104 + 3.88108i) q^{7} +(0.833347 + 2.56478i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.19143 - 0.865625i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.0521663 - 0.160551i) q^{4} +(-0.917011 - 0.666248i) q^{5} +(1.19143 + 0.865625i) q^{6} +(-1.26104 + 3.88108i) q^{7} +(0.833347 + 2.56478i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.66928 q^{10} +(-1.60839 + 2.90053i) q^{11} +0.168814 q^{12} +(0.809017 - 0.587785i) q^{13} +(1.85712 + 5.71562i) q^{14} +(0.350267 - 1.07801i) q^{15} +(3.48616 + 2.53284i) q^{16} +(2.56801 + 1.86577i) q^{17} +(-0.455086 + 1.40061i) q^{18} +(-2.63260 - 8.10232i) q^{19} +(-0.154804 + 0.112472i) q^{20} -4.08081 q^{21} +(0.594492 + 4.84804i) q^{22} +7.96906 q^{23} +(-2.18173 + 1.58512i) q^{24} +(-1.14806 - 3.53337i) q^{25} +(0.455086 - 1.40061i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.557328 + 0.404923i) q^{28} +(0.151356 - 0.465826i) q^{29} +(-0.515835 - 1.58758i) q^{30} +(3.62713 - 2.63526i) q^{31} +0.952471 q^{32} +(-3.25559 - 0.633353i) q^{33} +4.67465 q^{34} +(3.74215 - 2.71883i) q^{35} +(0.0521663 + 0.160551i) q^{36} +(-2.89587 + 8.91257i) q^{37} +(-10.1501 - 7.37450i) q^{38} +(0.809017 + 0.587785i) q^{39} +(0.944590 - 2.90715i) q^{40} +(2.30462 + 7.09288i) q^{41} +(-4.86200 + 3.53245i) q^{42} +7.71864 q^{43} +(0.381781 + 0.409538i) q^{44} +1.13349 q^{45} +(9.49458 - 6.89821i) q^{46} +(-0.00750832 - 0.0231082i) q^{47} +(-1.33159 + 4.09823i) q^{48} +(-7.80942 - 5.67388i) q^{49} +(-4.42641 - 3.21597i) q^{50} +(-0.980891 + 3.01887i) q^{51} +(-0.0521663 - 0.160551i) q^{52} +(-1.60751 + 1.16793i) q^{53} -1.47269 q^{54} +(3.40738 - 1.58824i) q^{55} -11.0050 q^{56} +(6.89224 - 5.00751i) q^{57} +(-0.222900 - 0.686016i) q^{58} +(1.41498 - 4.35485i) q^{59} +(-0.154804 - 0.112472i) q^{60} +(-10.3038 - 7.48614i) q^{61} +(2.04032 - 6.27946i) q^{62} +(-1.26104 - 3.88108i) q^{63} +(-5.83751 + 4.24120i) q^{64} -1.13349 q^{65} +(-4.42706 + 2.06352i) q^{66} +1.26089 q^{67} +(0.433514 - 0.314966i) q^{68} +(2.46257 + 7.57902i) q^{69} +(2.10502 - 6.47859i) q^{70} +(-0.793661 - 0.576628i) q^{71} +(-2.18173 - 1.58512i) q^{72} +(-0.843861 + 2.59714i) q^{73} +(4.26472 + 13.1254i) q^{74} +(3.00566 - 2.18374i) q^{75} -1.43817 q^{76} +(-9.22895 - 9.89996i) q^{77} +1.47269 q^{78} +(11.6813 - 8.48699i) q^{79} +(-1.50935 - 4.64529i) q^{80} +(0.309017 - 0.951057i) q^{81} +(8.88557 + 6.45574i) q^{82} +(3.10363 + 2.25492i) q^{83} +(-0.212880 + 0.655178i) q^{84} +(-1.11183 - 3.42186i) q^{85} +(9.19622 - 6.68145i) q^{86} +0.489798 q^{87} +(-8.77957 - 1.70801i) q^{88} +17.8685 q^{89} +(1.35047 - 0.981176i) q^{90} +(1.26104 + 3.88108i) q^{91} +(0.415716 - 1.27944i) q^{92} +(3.62713 + 2.63526i) q^{93} +(-0.0289487 - 0.0210325i) q^{94} +(-2.98402 + 9.18388i) q^{95} +(0.294330 + 0.905854i) q^{96} +(0.293923 - 0.213548i) q^{97} -14.2158 q^{98} +(-0.403678 - 3.29197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Introduction

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