LMFDB - Embedded newform 155.2.h.b.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [155,2,Mod(16,155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(155, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("155.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.h (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:	$1.23768123133$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			16.6
Character	$\chi$	$=$	155.16
Dual form			155.2.h.b.126.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00060 - 1.45352i) q^{2} +(0.632602 + 0.459612i) q^{3} +(1.27165 - 3.91373i) q^{4} -1.00000 q^{5} +1.93364 q^{6} +(-1.33011 + 4.09364i) q^{7} +(-1.61631 - 4.97449i) q^{8} +(-0.738109 - 2.27167i) q^{9} +O(q^{10})$	\(q+(2.00060 - 1.45352i) q^{2} +(0.632602 + 0.459612i) q^{3} +(1.27165 - 3.91373i) q^{4} -1.00000 q^{5} +1.93364 q^{6} +(-1.33011 + 4.09364i) q^{7} +(-1.61631 - 4.97449i) q^{8} +(-0.738109 - 2.27167i) q^{9} +(-2.00060 + 1.45352i) q^{10} +(-1.15195 + 3.54532i) q^{11} +(2.60325 - 1.89137i) q^{12} +(-2.67324 - 1.94223i) q^{13} +(3.28919 + 10.1231i) q^{14} +(-0.632602 - 0.459612i) q^{15} +(-3.80569 - 2.76500i) q^{16} +(-1.00411 - 3.09033i) q^{17} +(-4.77858 - 3.47184i) q^{18} +(5.91714 - 4.29905i) q^{19} +(-1.27165 + 3.91373i) q^{20} +(-2.72292 + 1.97832i) q^{21} +(2.84862 + 8.76716i) q^{22} +(2.01811 + 6.21110i) q^{23} +(1.26386 - 3.88975i) q^{24} +1.00000 q^{25} -8.17117 q^{26} +(1.30205 - 4.00731i) q^{27} +(14.3300 + 10.4113i) q^{28} +(-0.994509 + 0.722553i) q^{29} -1.93364 q^{30} +(-5.01907 - 2.41018i) q^{31} -1.17168 q^{32} +(-2.35820 + 1.71333i) q^{33} +(-6.50069 - 4.72303i) q^{34} +(1.33011 - 4.09364i) q^{35} -9.82930 q^{36} -0.157243 q^{37} +(5.58907 - 17.2014i) q^{38} +(-0.798430 - 2.45731i) q^{39} +(1.61631 + 4.97449i) q^{40} +(1.20494 - 0.875439i) q^{41} +(-2.57195 + 7.91565i) q^{42} +(-0.704059 + 0.511528i) q^{43} +(12.4106 + 9.01681i) q^{44} +(0.738109 + 2.27167i) q^{45} +(13.0654 + 9.49258i) q^{46} +(-0.610075 - 0.443246i) q^{47} +(-1.13666 - 3.49828i) q^{48} +(-9.32562 - 6.77546i) q^{49} +(2.00060 - 1.45352i) q^{50} +(0.785153 - 2.41645i) q^{51} +(-11.0008 + 7.99253i) q^{52} +(3.95496 + 12.1721i) q^{53} +(-3.21982 - 9.90960i) q^{54} +(1.15195 - 3.54532i) q^{55} +22.5136 q^{56} +5.71909 q^{57} +(-0.939370 + 2.89108i) q^{58} +(-5.45570 - 3.96380i) q^{59} +(-2.60325 + 1.89137i) q^{60} +8.35420 q^{61} +(-13.5444 + 2.47352i) q^{62} +10.2812 q^{63} +(5.26731 - 3.82692i) q^{64} +(2.67324 + 1.94223i) q^{65} +(-2.22745 + 6.85539i) q^{66} -1.93853 q^{67} -13.3716 q^{68} +(-1.57804 + 4.85671i) q^{69} +(-3.28919 - 10.1231i) q^{70} +(-2.28875 - 7.04404i) q^{71} +(-10.1074 + 7.34343i) q^{72} +(1.97141 - 6.06738i) q^{73} +(-0.314581 + 0.228557i) q^{74} +(0.632602 + 0.459612i) q^{75} +(-9.30082 - 28.6250i) q^{76} +(-12.9811 - 9.43131i) q^{77} +(-5.16910 - 3.75557i) q^{78} +(-1.31037 - 4.03290i) q^{79} +(3.80569 + 2.76500i) q^{80} +(-3.13169 + 2.27531i) q^{81} +(1.13813 - 3.50281i) q^{82} +(-11.1369 + 8.09141i) q^{83} +(4.28000 + 13.1725i) q^{84} +(1.00411 + 3.09033i) q^{85} +(-0.665023 + 2.04673i) q^{86} -0.961224 q^{87} +19.4981 q^{88} +(-0.793685 + 2.44271i) q^{89} +(4.77858 + 3.47184i) q^{90} +(11.5065 - 8.35995i) q^{91} +26.8749 q^{92} +(-2.06733 - 3.83151i) q^{93} -1.86479 q^{94} +(-5.91714 + 4.29905i) q^{95} +(-0.741209 - 0.538520i) q^{96} +(-1.57861 + 4.85845i) q^{97} -28.5052 q^{98} +8.90405 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 6 q^{4} - 24 q^{5} - 16 q^{6} - 9 q^{7} + 11 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 6 * q^4 - 24 * q^5 - 16 * q^6 - 9 * q^7 + 11 * q^8 - 6 * q^9	\( 24 q + 2 q^{2} - 6 q^{4} - 24 q^{5} - 16 q^{6} - 9 q^{7} + 11 q^{8} - 6 q^{9} - 2 q^{10} + q^{11} + 18 q^{12} - 5 q^{13} + 6 q^{14} - 24 q^{16} + 7 q^{17} - 18 q^{18} + 2 q^{19} + 6 q^{20} - 10 q^{21} + 28 q^{22} - 15 q^{23} - 32 q^{24} + 24 q^{25} + 22 q^{26} + 9 q^{27} + 38 q^{28} + 15 q^{29} + 16 q^{30} + 6 q^{31} + 74 q^{32} + 5 q^{33} - 20 q^{34} + 9 q^{35} - 58 q^{36} - 56 q^{37} - 21 q^{38} - 10 q^{39} - 11 q^{40} - 24 q^{41} - 38 q^{42} + 21 q^{43} + 41 q^{44} + 6 q^{45} + 48 q^{46} - 8 q^{47} - 26 q^{48} - 23 q^{49} + 2 q^{50} + 26 q^{51} - 27 q^{52} + 26 q^{53} + 11 q^{54} - q^{55} - 48 q^{56} + 62 q^{57} + 52 q^{58} + 10 q^{59} - 18 q^{60} - 40 q^{61} - 28 q^{62} + 26 q^{63} + 9 q^{64} + 5 q^{65} - 2 q^{66} - 26 q^{67} - 8 q^{68} + 64 q^{69} - 6 q^{70} - 7 q^{71} - 127 q^{72} - 51 q^{73} - q^{74} + 43 q^{76} - 39 q^{77} - 31 q^{78} + 31 q^{79} + 24 q^{80} + 34 q^{81} + 58 q^{82} + 6 q^{83} + 113 q^{84} - 7 q^{85} - 22 q^{86} + 4 q^{87} - 28 q^{88} + 13 q^{89} + 18 q^{90} + 54 q^{91} - 2 q^{92} - 72 q^{93} - 10 q^{94} - 2 q^{95} + 101 q^{96} - 39 q^{97} - 220 q^{98} - 170 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 6 * q^4 - 24 * q^5 - 16 * q^6 - 9 * q^7 + 11 * q^8 - 6 * q^9 - 2 * q^10 + q^11 + 18 * q^12 - 5 * q^13 + 6 * q^14 - 24 * q^16 + 7 * q^17 - 18 * q^18 + 2 * q^19 + 6 * q^20 - 10 * q^21 + 28 * q^22 - 15 * q^23 - 32 * q^24 + 24 * q^25 + 22 * q^26 + 9 * q^27 + 38 * q^28 + 15 * q^29 + 16 * q^30 + 6 * q^31 + 74 * q^32 + 5 * q^33 - 20 * q^34 + 9 * q^35 - 58 * q^36 - 56 * q^37 - 21 * q^38 - 10 * q^39 - 11 * q^40 - 24 * q^41 - 38 * q^42 + 21 * q^43 + 41 * q^44 + 6 * q^45 + 48 * q^46 - 8 * q^47 - 26 * q^48 - 23 * q^49 + 2 * q^50 + 26 * q^51 - 27 * q^52 + 26 * q^53 + 11 * q^54 - q^55 - 48 * q^56 + 62 * q^57 + 52 * q^58 + 10 * q^59 - 18 * q^60 - 40 * q^61 - 28 * q^62 + 26 * q^63 + 9 * q^64 + 5 * q^65 - 2 * q^66 - 26 * q^67 - 8 * q^68 + 64 * q^69 - 6 * q^70 - 7 * q^71 - 127 * q^72 - 51 * q^73 - q^74 + 43 * q^76 - 39 * q^77 - 31 * q^78 + 31 * q^79 + 24 * q^80 + 34 * q^81 + 58 * q^82 + 6 * q^83 + 113 * q^84 - 7 * q^85 - 22 * q^86 + 4 * q^87 - 28 * q^88 + 13 * q^89 + 18 * q^90 + 54 * q^91 - 2 * q^92 - 72 * q^93 - 10 * q^94 - 2 * q^95 + 101 * q^96 - 39 * q^97 - 220 * q^98 - 170 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/155\mathbb{Z}\right)^\times$.

$n$	$32$	$96$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	2.00060	−	1.45352i	1.41464	−	1.02780i	0.422012	−	0.906590i	$-0.361324\pi$
$2$	2.00060	−	1.45352i	1.41464	−	1.02780i	0.992627	−	0.121206i	$-0.0386761\pi$
$3$	0.632602	+	0.459612i	0.365233	+	0.265357i	0.755231	−	0.655458i	$-0.227524\pi$
$3$	0.632602	+	0.459612i	0.365233	+	0.265357i	−0.389998	+	0.920816i	$0.627524\pi$
$4$	1.27165	−	3.91373i	0.635824	−	1.95686i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.93364			0.789406
$7$	−1.33011	+	4.09364i	−0.502733	+	1.54725i	0.301816	+	0.953366i	$0.402407\pi$
$7$	−1.33011	+	4.09364i	−0.502733	+	1.54725i	−0.804549	+	0.593886i	$0.797593\pi$
$8$	−1.61631	−	4.97449i	−0.571452	−	1.75875i
$9$	−0.738109	−	2.27167i	−0.246036	−	0.757222i
$10$	−2.00060	+	1.45352i	−0.632646	+	0.459644i
$11$	−1.15195	+	3.54532i	−0.347325	+	1.06896i	0.613003	+	0.790081i	$0.289961\pi$
$11$	−1.15195	+	3.54532i	−0.347325	+	1.06896i	−0.960328	+	0.278875i	$0.910039\pi$
$12$	2.60325	−	1.89137i	0.751493	−	0.545991i
$13$	−2.67324	−	1.94223i	−0.741425	−	0.538677i	0.151732	−	0.988422i	$-0.451515\pi$
$13$	−2.67324	−	1.94223i	−0.741425	−	0.538677i	−0.893157	+	0.449745i	$0.851515\pi$
$14$	3.28919	+	10.1231i	0.879074	+	2.70551i
$15$	−0.632602	−	0.459612i	−0.163337	−	0.118671i
$16$	−3.80569	−	2.76500i	−0.951422	−	0.691249i
$17$	−1.00411	−	3.09033i	−0.243532	−	0.749515i	−0.995874	−	0.0907427i	$-0.971076\pi$
$17$	−1.00411	−	3.09033i	−0.243532	−	0.749515i	0.752342	−	0.658773i	$-0.228924\pi$
$18$	−4.77858	−	3.47184i	−1.12632	−	0.818321i
$19$	5.91714	−	4.29905i	1.35748	−	0.986271i	0.358884	−	0.933382i	$-0.383157\pi$
$19$	5.91714	−	4.29905i	1.35748	−	0.986271i	0.998600	−	0.0528885i	$-0.0168428\pi$
$20$	−1.27165	+	3.91373i	−0.284349	+	0.875137i
$21$	−2.72292	+	1.97832i	−0.594189	+	0.431704i
$22$	2.84862	+	8.76716i	0.607329	+	1.86917i
$23$	2.01811	+	6.21110i	0.420805	+	1.29510i	0.906954	+	0.421229i	$0.138401\pi$
$23$	2.01811	+	6.21110i	0.420805	+	1.29510i	−0.486149	+	0.873876i	$0.661599\pi$
$24$	1.26386	−	3.88975i	0.257984	−	0.793992i
$25$	1.00000			0.200000
$26$	−8.17117			−1.60250
$27$	1.30205	−	4.00731i	0.250580	−	0.771207i
$28$	14.3300	+	10.4113i	2.70811	+	1.96756i
$29$	−0.994509	+	0.722553i	−0.184676	+	0.134175i	−0.676282	−	0.736643i	$-0.736410\pi$
$29$	−0.994509	+	0.722553i	−0.184676	+	0.134175i	0.491606	+	0.870818i	$0.336410\pi$
$30$	−1.93364			−0.353033
$31$	−5.01907	−	2.41018i	−0.901451	−	0.432881i
$31$	−5.01907	−	2.41018i	−0.901451	−	0.432881i
$32$	−1.17168			−0.207126
$33$	−2.35820	+	1.71333i	−0.410510	+	0.298253i
$34$	−6.50069	−	4.72303i	−1.11486	−	0.809993i
$35$	1.33011	−	4.09364i	0.224829	−	0.691952i
$36$	−9.82930			−1.63822
$37$	−0.157243			−0.0258506			−0.0129253	−	0.999916i	$-0.504114\pi$
$37$	−0.157243			−0.0258506			−0.0129253	+	0.999916i	$0.504114\pi$
$38$	5.58907	−	17.2014i	0.906667	−	2.79043i
$39$	−0.798430	−	2.45731i	−0.127851	−	0.393485i
$40$	1.61631	+	4.97449i	0.255561	+	0.786536i
$41$	1.20494	−	0.875439i	0.188180	−	0.136721i	−0.489707	−	0.871887i	$-0.662896\pi$
$41$	1.20494	−	0.875439i	0.188180	−	0.136721i	0.677886	+	0.735167i	$0.262896\pi$
$42$	−2.57195	+	7.91565i	−0.396860	+	1.22141i
$43$	−0.704059	+	0.511528i	−0.107368	+	0.0780074i	−0.640174	−	0.768230i	$-0.721138\pi$
$43$	−0.704059	+	0.511528i	−0.107368	+	0.0780074i	0.532806	+	0.846238i	$0.321138\pi$
$44$	12.4106	+	9.01681i	1.87096	+	1.35933i
$45$	0.738109	+	2.27167i	0.110031	+	0.338640i
$46$	13.0654	+	9.49258i	1.92639	+	1.39960i
$47$	−0.610075	−	0.443246i	−0.0889887	−	0.0646540i	0.542401	−	0.840120i	$-0.317515\pi$
$47$	−0.610075	−	0.443246i	−0.0889887	−	0.0646540i	−0.631390	+	0.775465i	$0.717515\pi$
$48$	−1.13666	−	3.49828i	−0.164063	−	0.504934i
$49$	−9.32562	−	6.77546i	−1.33223	−	0.967923i
$50$	2.00060	−	1.45352i	0.282928	−	0.205559i
$51$	0.785153	−	2.41645i	0.109943	−	0.338371i
$52$	−11.0008	+	7.99253i	−1.52553	+	1.10836i
$53$	3.95496	+	12.1721i	0.543256	+	1.67197i	0.725101	+	0.688642i	$0.241793\pi$
$53$	3.95496	+	12.1721i	0.543256	+	1.67197i	−0.181845	+	0.983327i	$0.558207\pi$
$54$	−3.21982	−	9.90960i	−0.438163	−	1.34853i
$55$	1.15195	−	3.54532i	0.155328	−	0.478051i
$56$	22.5136			3.00851
$57$	5.71909			0.757513
$58$	−0.939370	+	2.89108i	−0.123345	+	0.379618i
$59$	−5.45570	−	3.96380i	−0.710272	−	0.516042i	0.172990	−	0.984924i	$-0.444657\pi$
$59$	−5.45570	−	3.96380i	−0.710272	−	0.516042i	−0.883261	+	0.468881i	$0.844657\pi$
$60$	−2.60325	+	1.89137i	−0.336078	+	0.244175i
$61$	8.35420			1.06965			0.534823	−	0.844964i	$-0.320378\pi$
$61$	8.35420			1.06965			0.534823	+	0.844964i	$0.320378\pi$
$62$	−13.5444	+	2.47352i	−1.72014	+	0.314138i
$63$	10.2812			1.29530
$64$	5.26731	−	3.82692i	0.658413	−	0.478365i
$65$	2.67324	+	1.94223i	0.331575	+	0.240903i
$66$	−2.22745	+	6.85539i	−0.274180	+	0.843840i
$67$	−1.93853			−0.236830			−0.118415	−	0.992964i	$-0.537781\pi$
$67$	−1.93853			−0.236830			−0.118415	+	0.992964i	$0.537781\pi$
$68$	−13.3716			−1.62154
$69$	−1.57804	+	4.85671i	−0.189974	+	0.584679i
$70$	−3.28919	−	10.1231i	−0.393134	−	1.20994i
$71$	−2.28875	−	7.04404i	−0.271624	−	0.835974i	−0.990093	−	0.140414i	$-0.955157\pi$
$71$	−2.28875	−	7.04404i	−0.271624	−	0.835974i	0.718469	−	0.695559i	$-0.244843\pi$
$72$	−10.1074	+	7.34343i	−1.19116	+	0.865431i
$73$	1.97141	−	6.06738i	0.230736	−	0.710134i	−0.766922	−	0.641740i	$-0.778213\pi$
$73$	1.97141	−	6.06738i	0.230736	−	0.710134i	0.997658	−	0.0683933i	$-0.0217873\pi$
$74$	−0.314581	+	0.228557i	−0.0365693	+	0.0265692i
$75$	0.632602	+	0.459612i	0.0730466	+	0.0530715i
$76$	−9.30082	−	28.6250i	−1.06688	−	3.28351i
$77$	−12.9811	−	9.43131i	−1.47933	−	1.07480i
$78$	−5.16910	−	3.75557i	−0.585285	−	0.425235i
$79$	−1.31037	−	4.03290i	−0.147428	−	0.453737i	0.849887	−	0.526965i	$-0.176670\pi$
$79$	−1.31037	−	4.03290i	−0.147428	−	0.453737i	−0.997315	+	0.0732278i	$0.976670\pi$
$80$	3.80569	+	2.76500i	0.425489	+	0.309136i
$81$	−3.13169	+	2.27531i	−0.347966	+	0.252812i
$82$	1.13813	−	3.50281i	0.125686	−	0.386821i
$83$	−11.1369	+	8.09141i	−1.22243	+	0.888148i	−0.996300	−	0.0859494i	$-0.972608\pi$
$83$	−11.1369	+	8.09141i	−1.22243	+	0.888148i	−0.226131	+	0.974097i	$0.572608\pi$
$84$	4.28000	+	13.1725i	0.466986	+	1.43724i
$85$	1.00411	+	3.09033i	0.108911	+	0.335193i
$86$	−0.665023	+	2.04673i	−0.0717113	+	0.220705i
$87$	−0.961224			−0.103054
$88$	19.4981			2.07850
$89$	−0.793685	+	2.44271i	−0.0841305	+	0.258927i	−0.984269	−	0.176677i	$-0.943465\pi$
$89$	−0.793685	+	2.44271i	−0.0841305	+	0.258927i	0.900138	+	0.435604i	$0.143465\pi$
$90$	4.77858	+	3.47184i	0.503707	+	0.365964i
$91$	11.5065	−	8.35995i	1.20621	−	0.876361i
$92$	26.8749			2.80190
$93$	−2.06733	−	3.83151i	−0.214372	−	0.397309i
$94$	−1.86479			−0.192338
$95$	−5.91714	+	4.29905i	−0.607086	+	0.441074i
$96$	−0.741209	−	0.538520i	−0.0756493	−	0.0549625i
$97$	−1.57861	+	4.85845i	−0.160283	+	0.493301i	−0.998658	−	0.0517938i	$-0.983506\pi$
$97$	−1.57861	+	4.85845i	−0.160283	+	0.493301i	0.838375	+	0.545094i	$0.183506\pi$
$98$	−28.5052			−2.87946
$99$	8.90405			0.894891
$100$	1.27165	−	3.91373i	0.127165	−	0.391373i
$101$	0.953730	+	2.93528i	0.0948997	+	0.292071i	0.987228	−	0.159317i	$-0.0509291\pi$
$101$	0.953730	+	2.93528i	0.0948997	+	0.292071i	−0.892328	+	0.451388i	$0.850929\pi$
$102$	−1.94159	−	5.97560i	−0.192246	−	0.591672i
$103$	10.9262	−	7.93833i	1.07659	−	0.782187i	0.0995035	−	0.995037i	$-0.468275\pi$
$103$	10.9262	−	7.93833i	1.07659	−	0.782187i	0.977085	+	0.212850i	$0.0682746\pi$
$104$	−5.34079	+	16.4373i	−0.523708	+	1.61181i
$105$	2.72292	−	1.97832i	0.265730	−	0.193064i
$106$	25.6048	+	18.6030i	2.48695	+	1.80688i
$107$	1.50607	+	4.63521i	0.145597	+	0.448103i	0.997087	−	0.0762683i	$-0.0243005\pi$
$107$	1.50607	+	4.63521i	0.145597	+	0.448103i	−0.851490	+	0.524371i	$0.824301\pi$
$108$	−14.0278	−	10.1918i	−1.34982	−	0.980704i
$109$	−12.6738	−	9.20803i	−1.21393	−	0.881969i	−0.218345	−	0.975872i	$-0.570066\pi$
$109$	−12.6738	−	9.20803i	−1.21393	−	0.881969i	−0.995581	+	0.0939024i	$0.970066\pi$
$110$	−2.84862	−	8.76716i	−0.271606	−	0.835916i
$111$	−0.0994725	−	0.0722710i	−0.00944151	−	0.00685966i
$112$	16.3809	−	11.9014i	1.54785	−	1.12458i
$113$	−1.38944	+	4.27625i	−0.130707	+	0.402276i	−0.994898	−	0.100889i	$-0.967831\pi$
$113$	−1.38944	+	4.27625i	−0.130707	+	0.402276i	0.864190	+	0.503165i	$0.167831\pi$
$114$	11.4416	−	8.31283i	1.07161	−	0.778568i
$115$	−2.01811	−	6.21110i	−0.188190	−	0.579188i
$116$	1.56321	+	4.81107i	0.145141	+	0.446697i
$117$	−2.43894	+	7.50629i	−0.225480	+	0.693957i
$118$	−16.6762			−1.53516
$119$	13.9863			1.28212
$120$	−1.26386	+	3.88975i	−0.115374	+	0.355084i
$121$	−2.34315	−	1.70240i	−0.213014	−	0.154764i
$122$	16.7134	−	12.1430i	1.51316	−	1.09938i
$123$	1.16461			0.105009
$124$	−15.8153	+	16.5784i	−1.42025	+	1.48878i
$125$	−1.00000			−0.0894427
$126$	20.5685	−	14.9439i	1.83239	−	1.33131i
$127$	9.64838	+	7.00996i	0.856155	+	0.622033i	0.926836	−	0.375466i	$-0.122517\pi$
$127$	9.64838	+	7.00996i	0.856155	+	0.622033i	−0.0706813	+	0.997499i	$0.522517\pi$
$128$	5.69941	−	17.5410i	0.503761	−	1.55042i
$129$	−0.680494			−0.0599142
$130$	8.17117			0.716659
$131$	−0.621621	+	1.91315i	−0.0543113	+	0.167153i	−0.974533	−	0.224245i	$-0.928008\pi$
$131$	−0.621621	+	1.91315i	−0.0543113	+	0.167153i	0.920222	+	0.391398i	$0.128008\pi$
$132$	3.70672	+	11.4081i	0.322628	+	0.992948i
$133$	9.72838	+	29.9409i	0.843557	+	2.59620i
$134$	−3.87824	+	2.81770i	−0.335029	+	0.243412i
$135$	−1.30205	+	4.00731i	−0.112063	+	0.344894i
$136$	−13.7499	+	9.98986i	−1.17904	+	0.856624i
$137$	−1.37359	−	0.997971i	−0.117354	−	0.0852624i	0.527560	−	0.849518i	$-0.323107\pi$
$137$	−1.37359	−	0.997971i	−0.117354	−	0.0852624i	−0.644914	+	0.764255i	$0.723107\pi$
$138$	3.90230	+	12.0101i	0.332186	+	1.02236i
$139$	17.5533	+	12.7532i	1.48885	+	1.08171i	0.974569	+	0.224088i	$0.0719405\pi$
$139$	17.5533	+	12.7532i	1.48885	+	1.08171i	0.514279	+	0.857623i	$0.328060\pi$
$140$	−14.3300	−	10.4113i	−1.21111	−	0.879920i
$141$	−0.182214	−	0.560797i	−0.0153452	−	0.0472276i
$142$	−14.8175	−	10.7656i	−1.24346	−	0.903427i
$143$	9.96525	−	7.24018i	0.833336	−	0.605454i
$144$	−3.47213	+	10.6861i	−0.289344	+	0.890510i
$145$	0.994509	−	0.722553i	0.0825895	−	0.0600048i
$146$	−4.87507	−	15.0039i	−0.403464	−	1.24173i
$147$	−2.78532	−	8.57235i	−0.229730	−	0.707035i
$148$	−0.199958	+	0.615408i	−0.0164365	+	0.0505862i
$149$	−12.6966			−1.04015			−0.520073	−	0.854122i	$-0.674095\pi$
$149$	−12.6966			−1.04015			−0.520073	+	0.854122i	$0.674095\pi$
$150$	1.93364			0.157881
$151$	−6.54274	+	20.1365i	−0.532440	+	1.63868i	0.216675	+	0.976244i	$0.430479\pi$
$151$	−6.54274	+	20.1365i	−0.532440	+	1.63868i	−0.749116	+	0.662439i	$0.769521\pi$
$152$	−30.9495	−	22.4861i	−2.51034	−	1.82387i
$153$	−6.27906	+	4.56200i	−0.507632	+	0.368816i
$154$	−39.6786			−3.19739
$155$	5.01907	+	2.41018i	0.403141	+	0.193590i
$156$	−10.6326			−0.851288
$157$	10.4877	−	7.61977i	0.837010	−	0.608124i	−0.0845236	−	0.996421i	$-0.526937\pi$
$157$	10.4877	−	7.61977i	0.837010	−	0.608124i	0.921534	+	0.388298i	$0.126937\pi$
$158$	−8.48344	−	6.16358i	−0.674907	−	0.490348i
$159$	−3.09254	+	9.51786i	−0.245254	+	0.754816i
$160$	1.17168			0.0926297
$161$	−28.1103			−2.21541
$162$	−2.95806	+	9.10397i	−0.232407	+	0.715275i
$163$	4.92844	+	15.1682i	0.386026	+	1.18806i	0.935734	+	0.352708i	$0.114739\pi$
$163$	4.92844	+	15.1682i	0.386026	+	1.18806i	−0.549708	+	0.835357i	$0.685261\pi$
$164$	−1.89397	−	5.82905i	−0.147895	−	0.455173i
$165$	2.35820	−	1.71333i	0.183585	−	0.133383i
$166$	−10.5194	+	32.3754i	−0.816464	+	2.51282i
$167$	−15.2139	+	11.0536i	−1.17729	+	0.855351i	−0.991863	−	0.127307i	$-0.959367\pi$
$167$	−15.2139	+	11.0536i	−1.17729	+	0.855351i	−0.185426	+	0.982658i	$0.559367\pi$
$168$	14.2422	+	10.3476i	1.09881	+	0.798331i
$169$	−0.643225	−	1.97964i	−0.0494788	−	0.152280i
$170$	6.50069	+	4.72303i	0.498580	+	0.362240i
$171$	−14.1335	−	10.2686i	−1.08082	−	0.785259i
$172$	1.10667	+	3.40598i	0.0843828	+	0.259703i
$173$	8.47992	+	6.16102i	0.644716	+	0.468414i	0.861467	−	0.507813i	$-0.169546\pi$
$173$	8.47992	+	6.16102i	0.644716	+	0.468414i	−0.216751	+	0.976227i	$0.569546\pi$
$174$	−1.92303	+	1.39716i	−0.145784	+	0.105918i
$175$	−1.33011	+	4.09364i	−0.100547	+	0.309450i
$176$	14.1867	−	10.3073i	1.06937	−	0.776940i
$177$	−1.62948	−	5.01501i	−0.122479	−	0.376952i
$178$	1.96269	+	6.04054i	0.147110	+	0.452757i
$179$	5.43590	−	16.7300i	0.406298	−	1.25046i	−0.513508	−	0.858085i	$-0.671654\pi$
$179$	5.43590	−	16.7300i	0.406298	−	1.25046i	0.919806	−	0.392373i	$-0.128346\pi$
$180$	9.82930			0.732633
$181$	−2.25085			−0.167305			−0.0836524	−	0.996495i	$-0.526659\pi$
$181$	−2.25085			−0.167305			−0.0836524	+	0.996495i	$0.526659\pi$
$182$	10.8685	−	33.4499i	0.805628	−	2.47947i
$183$	5.28489	+	3.83969i	0.390670	+	0.283838i
$184$	27.6352	−	20.0781i	2.03729	−	1.48018i
$185$	0.157243			0.0115608
$186$	−9.70509	−	4.66042i	−0.711611	−	0.341719i
$187$	12.1129			0.885783
$188$	−2.51055	+	1.82402i	−0.183100	+	0.133030i
$189$	14.6726	+	10.6603i	1.06728	+	0.775422i
$190$	−5.58907	+	17.2014i	−0.405474	+	1.24792i
$191$	16.2975			1.17925			0.589623	−	0.807679i	$-0.299276\pi$
$191$	16.2975			1.17925			0.589623	+	0.807679i	$0.299276\pi$
$192$	5.09101			0.367412
$193$	5.48198	−	16.8718i	0.394602	−	1.21446i	−0.534670	−	0.845061i	$-0.679564\pi$
$193$	5.48198	−	16.8718i	0.394602	−	1.21446i	0.929271	−	0.369398i	$-0.120436\pi$
$194$	3.90370	+	12.0144i	0.280269	+	0.862581i
$195$	0.798430	+	2.45731i	0.0571767	+	0.175972i
$196$	−38.3762	+	27.8820i	−2.74116	+	1.99157i
$197$	−4.92921	+	15.1705i	−0.351191	+	1.08086i	0.606994	+	0.794707i	$0.292375\pi$
$197$	−4.92921	+	15.1705i	−0.351191	+	1.08086i	−0.958185	+	0.286149i	$0.907625\pi$
$198$	17.8135	−	12.9422i	1.26595	−	0.919765i
$199$	−11.8937	−	8.64129i	−0.843123	−	0.612565i	0.0801180	−	0.996785i	$-0.474470\pi$
$199$	−11.8937	−	8.64129i	−0.843123	−	0.612565i	−0.923241	+	0.384220i	$0.874470\pi$
$200$	−1.61631	−	4.97449i	−0.114290	−	0.351749i
$201$	−1.22632	−	0.890974i	−0.0864980	−	0.0628445i
$202$	6.17453	+	4.48606i	0.434438	+	0.315638i
$203$	−1.63507	−	5.03224i	−0.114760	−	0.353194i
$204$	−8.45890	−	6.14575i	−0.592242	−	0.430289i
$205$	−1.20494	+	0.875439i	−0.0841566	+	0.0611433i
$206$	10.3204	−	31.7629i	0.719056	−	2.21303i
$207$	12.6200	−	9.16894i	0.877148	−	0.637286i
$208$	4.80329	+	14.7830i	0.333049	+	1.02502i
$209$	8.42531	+	25.9304i	0.582791	+	1.79365i
$210$	2.57195	−	7.91565i	0.177481	−	0.546232i
$211$	6.62890			0.456352			0.228176	−	0.973620i	$-0.426724\pi$
$211$	6.62890			0.456352			0.228176	+	0.973620i	$0.426724\pi$
$212$	52.6677			3.61723
$213$	1.78966	−	5.50801i	0.122626	−	0.377403i
$214$	9.75043	+	7.08410i	0.666526	+	0.484259i
$215$	0.704059	−	0.511528i	0.0480164	−	0.0348860i
$216$	−22.0388			−1.49955
$217$	16.5423	−	17.3405i	1.12296	−	1.17715i
$218$	−38.7392			−2.62375
$219$	4.03577	−	2.93216i	0.272712	−	0.198137i
$220$	−12.4106	−	9.01681i	−0.836720	−	0.607913i
$221$	−3.31789	+	10.2114i	−0.223186	+	0.686894i
$222$	−0.304053			−0.0204067
$223$	6.66925			0.446606			0.223303	−	0.974749i	$-0.428316\pi$
$223$	6.66925			0.446606			0.223303	+	0.974749i	$0.428316\pi$
$224$	1.55846	−	4.79645i	0.104129	−	0.320476i
$225$	−0.738109	−	2.27167i	−0.0492073	−	0.151444i
$226$	3.43592	+	10.5747i	0.228554	+	0.703416i
$227$	−3.71651	+	2.70020i	−0.246673	+	0.179219i	−0.704251	−	0.709951i	$-0.748717\pi$
$227$	−3.71651	+	2.70020i	−0.246673	+	0.179219i	0.457578	+	0.889170i	$0.348717\pi$
$228$	7.27267	−	22.3830i	0.481645	−	1.48235i
$229$	0.998589	−	0.725517i	0.0659886	−	0.0479435i	−0.554302	−	0.832316i	$-0.687015\pi$
$229$	0.998589	−	0.725517i	0.0659886	−	0.0479435i	0.620291	+	0.784372i	$0.287015\pi$
$230$	−13.0654	−	9.49258i	−0.861508	−	0.625922i
$231$	−3.87712	−	11.9325i	−0.255096	−	0.785103i
$232$	5.20177	+	3.77931i	0.341513	+	0.248124i
$233$	−11.5557	−	8.39574i	−0.757042	−	0.550023i	0.140960	−	0.990015i	$-0.454981\pi$
$233$	−11.5557	−	8.39574i	−0.757042	−	0.550023i	−0.898002	+	0.439992i	$0.854981\pi$
$234$	6.03121	+	18.5622i	0.394273	+	1.21345i
$235$	0.610075	+	0.443246i	0.0397969	+	0.0289142i
$236$	−22.4510	+	16.3116i	−1.46143	+	1.06179i
$237$	1.02463	−	3.15349i	0.0665568	−	0.204841i
$238$	27.9810	−	20.3294i	1.81374	−	1.31776i
$239$	−6.87217	−	21.1504i	−0.444524	−	1.36810i	−0.883005	−	0.469363i	$-0.844483\pi$
$239$	−6.87217	−	21.1504i	−0.444524	−	1.36810i	0.438481	−	0.898740i	$-0.355517\pi$
$240$	1.13666	+	3.49828i	0.0733712	+	0.225813i
$241$	5.24003	−	16.1272i	0.337540	−	1.03884i	−0.627917	−	0.778280i	$-0.716092\pi$
$241$	5.24003	−	16.1272i	0.337540	−	1.03884i	0.965457	−	0.260561i	$-0.0839076\pi$
$242$	−7.16219			−0.460403
$243$	−15.6675			−1.00507
$244$	10.6236	−	32.6961i	0.680106	−	2.09315i
$245$	9.32562	+	6.77546i	0.595792	+	0.432868i
$246$	2.32992	−	1.69279i	0.148550	−	0.107928i
$247$	−24.1677			−1.53775
$248$	−3.87704	+	28.8629i	−0.246192	+	1.83280i
$249$	−10.7641			−0.682149
$250$	−2.00060	+	1.45352i	−0.126529	+	0.0919289i
$251$	0.796039	+	0.578356i	0.0502456	+	0.0365055i	0.612625	−	0.790374i	$-0.290114\pi$
$251$	0.796039	+	0.578356i	0.0502456	+	0.0365055i	−0.562379	+	0.826880i	$0.690114\pi$
$252$	13.0740	−	40.2377i	0.823585	−	2.53473i
$253$	−24.3451			−1.53056
$254$	29.4917			1.85047
$255$	−0.785153	+	2.41645i	−0.0491682	+	0.151324i
$256$	−10.0701	−	30.9926i	−0.629381	−	1.93703i
$257$	1.44166	+	4.43698i	0.0899283	+	0.276771i	0.985899	−	0.167343i	$-0.0535186\pi$
$257$	1.44166	+	4.43698i	0.0899283	+	0.276771i	−0.895970	+	0.444114i	$0.853519\pi$
$258$	−1.36140	+	0.989114i	−0.0847569	+	0.0615795i
$259$	0.209150	−	0.643698i	0.0129960	−	0.0399975i
$260$	11.0008	−	7.99253i	0.682239	−	0.495676i
$261$	2.37546	+	1.72587i	0.147037	+	0.106829i
$262$	1.53719	+	4.73100i	0.0949681	+	0.292282i
$263$	−3.55365	−	2.58188i	−0.219128	−	0.159206i	0.472806	−	0.881166i	$-0.343241\pi$
$263$	−3.55365	−	2.58188i	−0.219128	−	0.159206i	−0.691934	+	0.721961i	$0.743241\pi$
$264$	12.3345	+	8.96156i	0.759137	+	0.551546i
$265$	−3.95496	−	12.1721i	−0.242951	−	0.747728i
$266$	62.9823	+	45.7593i	3.86169	+	2.80569i
$267$	−1.62479	+	1.18048i	−0.0994354	+	0.0722441i
$268$	−2.46513	+	7.58690i	−0.150582	+	0.463444i
$269$	−16.2829	+	11.8302i	−0.992786	+	0.721301i	−0.960529	−	0.278179i	$-0.910269\pi$
$269$	−16.2829	+	11.8302i	−0.992786	+	0.721301i	−0.0322563	+	0.999480i	$0.510269\pi$
$270$	3.21982	+	9.90960i	0.195952	+	0.603079i
$271$	−2.27744	−	7.00925i	−0.138345	−	0.425781i	0.857750	−	0.514066i	$-0.171861\pi$
$271$	−2.27744	−	7.00925i	−0.138345	−	0.425781i	−0.996095	+	0.0882848i	$0.971861\pi$
$272$	−4.72342	+	14.5372i	−0.286400	+	0.881447i
$273$	11.1214			0.673096
$274$	−4.19858			−0.253646
$275$	−1.15195	+	3.54532i	−0.0694649	+	0.213791i
$276$	17.0011	+	12.3520i	1.02335	+	0.743506i
$277$	2.62982	−	1.91067i	0.158010	−	0.114801i	−0.505971	−	0.862551i	$-0.668866\pi$
$277$	2.62982	−	1.91067i	0.158010	−	0.114801i	0.663981	+	0.747749i	$0.268866\pi$
$278$	53.6541			3.21796
$279$	−1.77050	+	13.1806i	−0.105997	+	0.789103i
$280$	−22.5136			−1.34545
$281$	−3.05408	+	2.21892i	−0.182191	+	0.132370i	−0.675143	−	0.737687i	$-0.735918\pi$
$281$	−3.05408	+	2.21892i	−0.182191	+	0.132370i	0.492952	+	0.870057i	$0.335918\pi$
$282$	−1.17967	−	0.857079i	−0.0702482	−	0.0510383i
$283$	−1.56938	+	4.83007i	−0.0932902	+	0.287118i	−0.986804	−	0.161917i	$-0.948232\pi$
$283$	−1.56938	+	4.83007i	−0.0932902	+	0.287118i	0.893514	+	0.449035i	$0.148232\pi$
$284$	−30.4789			−1.80859
$285$	−5.71909			−0.338770
$286$	9.41274	−	28.9694i	0.556587	−	1.71300i
$287$	1.98104	+	6.09702i	0.116937	+	0.359895i
$288$	0.864829	+	2.66167i	0.0509606	+	0.156840i
$289$	5.21138	−	3.78629i	0.306552	−	0.222723i
$290$	0.939370	−	2.89108i	0.0551617	−	0.169770i
$291$	−3.23163	+	2.34792i	−0.189442	+	0.137637i
$292$	−21.2392	−	15.4312i	−1.24293	−	0.903040i
$293$	−2.99886	−	9.22954i	−0.175195	−	0.539196i	0.824447	−	0.565939i	$-0.191486\pi$
$293$	−2.99886	−	9.22954i	−0.175195	−	0.539196i	−0.999642	+	0.0267435i	$0.991486\pi$
$294$	−18.0324	−	13.1013i	−1.05167	−	0.764085i
$295$	5.45570	+	3.96380i	0.317643	+	0.230781i
$296$	0.254154	+	0.782205i	0.0147724	+	0.0454648i
$297$	12.7073	+	9.23241i	0.737353	+	0.535719i
$298$	−25.4009	+	18.4548i	−1.47143	+	1.06906i
$299$	6.66847	−	20.5234i	0.385647	−	1.18690i
$300$	2.60325	−	1.89137i	0.150299	−	0.109198i
$301$	−1.15754	−	3.56255i	−0.0667197	−	0.205342i
$302$	16.1794	+	49.7951i	0.931020	+	2.86539i
$303$	−0.745759	+	2.29521i	−0.0428428	+	0.131856i
$304$	−34.4057			−1.97330
$305$	−8.35420			−0.478360
$306$	−5.93092	+	18.2535i	−0.339048	+	1.04348i
$307$	−10.6960	−	7.77109i	−0.610452	−	0.443519i	0.239121	−	0.970990i	$-0.423141\pi$
$307$	−10.6960	−	7.77109i	−0.610452	−	0.443519i	−0.849573	+	0.527470i	$0.823141\pi$
$308$	−53.4190	+	38.8111i	−3.04383	+	2.21147i
$309$	10.5605			0.600765
$310$	13.5444	−	2.47352i	0.769271	−	0.140487i
$311$	10.0107			0.567652			0.283826	−	0.958876i	$-0.408396\pi$
$311$	10.0107			0.567652			0.283826	+	0.958876i	$0.408396\pi$
$312$	−10.9334	+	7.94356i	−0.618980	+	0.449715i
$313$	−21.2220	−	15.4187i	−1.19954	−	0.871515i	−0.205299	−	0.978699i	$-0.565817\pi$
$313$	−21.2220	−	15.4187i	−1.19954	−	0.871515i	−0.994239	+	0.107184i	$0.965817\pi$
$314$	9.90623	−	30.4883i	0.559041	−	1.72055i
$315$	−10.2812			−0.579277
$316$	−17.4500			−0.981640
$317$	8.23267	−	25.3375i	0.462393	−	1.42310i	−0.399840	−	0.916585i	$-0.630934\pi$
$317$	8.23267	−	25.3375i	0.462393	−	1.42310i	0.862232	−	0.506513i	$-0.169066\pi$
$318$	7.64749	+	23.5365i	0.428850	+	1.31986i
$319$	−1.41606	−	4.35820i	−0.0792844	−	0.244012i
$320$	−5.26731	+	3.82692i	−0.294451	+	0.213931i
$321$	−1.17766	+	3.62445i	−0.0657304	+	0.202297i
$322$	−56.2376	+	40.8590i	−3.13400	+	2.27698i
$323$	−19.2270	−	13.9692i	−1.06982	−	0.777267i
$324$	4.92253	+	15.1500i	0.273474	+	0.841665i
$325$	−2.67324	−	1.94223i	−0.148285	−	0.107735i
$326$	31.9072	+	23.1819i	1.76717	+	1.28393i
$327$	−3.78533	−	11.6500i	−0.209329	−	0.644249i
$328$	−6.30241	−	4.57897i	−0.347993	−	0.252831i
$329$	2.62596	−	1.90787i	0.144774	−	0.105184i
$330$	2.22745	−	6.85539i	0.122617	−	0.377377i
$331$	9.70610	−	7.05189i	0.533495	−	0.387607i	−0.288168	−	0.957580i	$-0.593046\pi$
$331$	9.70610	−	7.05189i	0.533495	−	0.387607i	0.821664	+	0.569973i	$0.193046\pi$
$332$	17.5054	+	53.8761i	0.960734	+	2.95684i
$333$	0.116063	+	0.357204i	0.00636020	+	0.0195747i
$334$	−14.3704	+	44.2276i	−0.786314	+	2.42003i
$335$	1.93853			0.105913
$336$	15.8326			0.863740
$337$	2.56009	−	7.87915i	0.139457	−	0.429204i	−0.856800	−	0.515649i	$-0.827551\pi$
$337$	2.56009	−	7.87915i	0.139457	−	0.429204i	0.996257	+	0.0864450i	$0.0275507\pi$
$338$	−4.16429	−	3.02554i	−0.226508	−	0.164567i
$339$	−2.84438	+	2.06656i	−0.154486	+	0.112240i
$340$	13.3716			0.725177
$341$	14.3266	−	15.0178i	0.775826	−	0.813261i
$342$	−43.2012			−2.33605
$343$	15.7646	−	11.4536i	0.851207	−	0.618438i
$344$	3.68257	+	2.67554i	0.198551	+	0.144256i
$345$	1.57804	−	4.85671i	0.0849588	−	0.261476i
$346$	25.9201			1.39348
$347$	−21.0006			−1.12737			−0.563687	−	0.825989i	$-0.690617\pi$
$347$	−21.0006			−1.12737			−0.563687	+	0.825989i	$0.690617\pi$
$348$	−1.22234	+	3.76197i	−0.0655242	+	0.201663i
$349$	6.74719	+	20.7657i	0.361169	+	1.11156i	0.952346	+	0.305021i	$0.0986635\pi$
$349$	6.74719	+	20.7657i	0.361169	+	1.11156i	−0.591177	+	0.806542i	$0.701337\pi$
$350$	3.28919	+	10.1231i	0.175815	+	0.541102i
$351$	−11.2638	+	8.18364i	−0.601218	+	0.436810i
$352$	1.34971	−	4.15399i	0.0719400	−	0.221409i
$353$	13.3399	−	9.69203i	0.710013	−	0.515855i	−0.173165	−	0.984893i	$-0.555399\pi$
$353$	13.3399	−	9.69203i	0.710013	−	0.515855i	0.883178	+	0.469038i	$0.155399\pi$
$354$	−10.5494	−	7.66457i	−0.560693	−	0.407367i
$355$	2.28875	+	7.04404i	0.121474	+	0.373859i
$356$	8.55083	+	6.21254i	0.453193	+	0.329264i
$357$	8.84776	+	6.42827i	0.468273	+	0.340220i
$358$	−13.4423	−	41.3713i	−0.710450	−	2.18654i
$359$	19.0301	+	13.8262i	1.00437	+	0.729717i	0.963021	−	0.269427i	$-0.0868344\pi$
$359$	19.0301	+	13.8262i	1.00437	+	0.729717i	0.0413491	+	0.999145i	$0.486834\pi$
$360$	10.1074	−	7.34343i	0.532705	−	0.387033i
$361$	10.6594	−	32.8061i	0.561019	−	1.72664i
$362$	−4.50307	+	3.27167i	−0.236676	+	0.171955i
$363$	−0.699839	−	2.15388i	−0.0367320	−	0.113050i
$364$	−18.0864	−	55.6642i	−0.947984	−	2.91760i
$365$	−1.97141	+	6.06738i	−0.103188	+	0.317581i
$366$	16.1540			0.844385
$367$	−15.2190			−0.794423			−0.397211	−	0.917727i	$-0.630022\pi$
$367$	−15.2190			−0.794423			−0.397211	+	0.917727i	$0.630022\pi$
$368$	9.49337	−	29.2176i	0.494876	−	1.52307i
$369$	−2.87808	−	2.09105i	−0.149827	−	0.108856i
$370$	0.314581	−	0.228557i	0.0163543	−	0.0118821i
$371$	−55.0889			−2.86007
$372$	−17.6244	+	3.21862i	−0.913783	+	0.166878i
$373$	10.1560			0.525857			0.262928	−	0.964815i	$-0.415312\pi$
$373$	10.1560			0.525857			0.262928	+	0.964815i	$0.415312\pi$
$374$	24.2331	−	17.6064i	1.25306	−	0.910404i
$375$	−0.632602	−	0.459612i	−0.0326674	−	0.0237343i
$376$	−1.21885	+	3.75124i	−0.0628574	+	0.193455i
$377$	4.06193			0.209200
$378$	44.8491			2.30679
$379$	−6.63409	+	20.4176i	−0.340771	+	1.04878i	0.623039	+	0.782191i	$0.285898\pi$
$379$	−6.63409	+	20.4176i	−0.340771	+	1.04878i	−0.963809	+	0.266593i	$0.914102\pi$
$380$	9.30082	+	28.6250i	0.477122	+	1.46843i
$381$	2.88172	+	8.86903i	0.147635	+	0.454374i
$382$	32.6048	−	23.6888i	1.66821	−	1.21202i
$383$	8.65025	−	26.6227i	0.442007	−	1.36036i	−0.443726	−	0.896163i	$-0.646344\pi$
$383$	8.65025	−	26.6227i	0.442007	−	1.36036i	0.885733	−	0.464195i	$-0.153656\pi$
$384$	11.6675	−	8.47694i	0.595405	−	0.432587i
$385$	12.9811	+	9.43131i	0.661577	+	0.480664i
$386$	−13.5563	−	41.7219i	−0.689997	−	2.12359i
$387$	1.68169	+	1.22182i	0.0854853	+	0.0621087i
$388$	17.0072	+	12.3565i	0.863411	+	0.627305i
$389$	10.5864	+	32.5816i	0.536752	+	1.65195i	0.739834	+	0.672790i	$0.234904\pi$
$389$	10.5864	+	32.5816i	0.536752	+	1.65195i	−0.203082	+	0.979162i	$0.565096\pi$
$390$	5.16910	+	3.75557i	0.261748	+	0.190171i
$391$	17.1680	−	12.4733i	0.868221	−	0.630800i
$392$	−18.6314	+	57.3414i	−0.941026	+	2.89618i
$393$	−1.27255	+	0.924560i	−0.0641915	+	0.0466379i
$394$	12.1893	+	37.5149i	0.614090	+	1.88997i
$395$	1.31037	+	4.03290i	0.0659318	+	0.202917i
$396$	11.3228	−	34.8480i	0.568993	−	1.75118i
$397$	−33.3545			−1.67401			−0.837006	−	0.547194i	$-0.815696\pi$
$397$	−33.3545			−1.67401			−0.837006	+	0.547194i	$0.815696\pi$
$398$	−36.3549			−1.82231
$399$	−7.60700	+	23.4119i	−0.380826	+	1.17206i
$400$	−3.80569	−	2.76500i	−0.190284	−	0.138250i
$401$	13.1955	−	9.58708i	0.658951	−	0.478756i	−0.207357	−	0.978265i	$-0.566486\pi$
$401$	13.1955	−	9.58708i	0.658951	−	0.478756i	0.866309	+	0.499509i	$0.166486\pi$
$402$	−3.74843			−0.186955
$403$	8.73609	+	16.1912i	0.435176	+	0.806539i
$404$	12.7007			0.631883
$405$	3.13169	−	2.27531i	0.155615	−	0.113061i
$406$	−10.5856	−	7.69090i	−0.525355	−	0.381693i
$407$	0.181136	−	0.557478i	0.00897857	−	0.0276332i
$408$	−13.2897			−0.657936
$409$	−19.5489			−0.966630			−0.483315	−	0.875447i	$-0.660567\pi$
$409$	−19.5489			−0.966630			−0.483315	+	0.875447i	$0.660567\pi$
$410$	−1.13813	+	3.50281i	−0.0562084	+	0.172992i
$411$	−0.410256	−	1.26264i	−0.0202364	−	0.0622813i
$412$	−17.1742	−	52.8569i	−0.846114	−	2.60407i
$413$	23.4830	−	17.0614i	1.15552	−	0.839538i
$414$	11.9203	−	36.6868i	0.585849	−	1.80306i
$415$	11.1369	−	8.09141i	0.546687	−	0.397192i
$416$	3.13219	+	2.27567i	0.153568	+	0.111574i
$417$	5.24271	+	16.1354i	0.256736	+	0.790154i
$418$	54.5462	+	39.6301i	2.66794	+	1.93837i
$419$	−8.45963	−	6.14628i	−0.413280	−	0.300266i	0.361648	−	0.932315i	$-0.382214\pi$
$419$	−8.45963	−	6.14628i	−0.413280	−	0.300266i	−0.774928	+	0.632049i	$0.782214\pi$
$420$	−4.28000	−	13.1725i	−0.208843	−	0.642752i
$421$	−18.3728	−	13.3486i	−0.895433	−	0.650571i	0.0418555	−	0.999124i	$-0.486673\pi$
$421$	−18.3728	−	13.3486i	−0.895433	−	0.650571i	−0.937289	+	0.348553i	$0.886673\pi$
$422$	13.2618	−	9.63525i	0.645574	−	0.469037i
$423$	−0.556604	+	1.71305i	−0.0270630	+	0.0832914i
$424$	54.1576	−	39.3478i	2.63013	−	1.91090i
$425$	−1.00411	−	3.09033i	−0.0487065	−	0.149903i
$426$	−4.42562	−	13.6207i	−0.214422	−	0.659923i
$427$	−11.1120	+	34.1991i	−0.537746	+	1.65501i
$428$	20.0561			0.969451
$429$	9.63172			0.465024
$430$	0.665023	−	2.04673i	0.0320703	−	0.0987021i
$431$	26.6234	+	19.3430i	1.28240	+	0.931719i	0.999623	−	0.0274657i	$-0.00874372\pi$
$431$	26.6234	+	19.3430i	1.28240	+	0.931719i	0.282779	+	0.959185i	$0.408744\pi$
$432$	−16.0354	+	11.6504i	−0.771504	+	0.560530i
$433$	−17.0605			−0.819876			−0.409938	−	0.912113i	$-0.634450\pi$
$433$	−17.0605			−0.819876			−0.409938	+	0.912113i	$0.634450\pi$
$434$	7.88978	−	58.7360i	0.378721	−	2.81942i
$435$	0.961224			0.0460871
$436$	−52.1543	+	37.8923i	−2.49774	+	1.81471i
$437$	38.6433	+	28.0760i	1.84856	+	1.34306i
$438$	3.81201	−	11.7322i	0.182145	−	0.560584i
$439$	−19.1266			−0.912865			−0.456432	−	0.889758i	$-0.650873\pi$
$439$	−19.1266			−0.912865			−0.456432	+	0.889758i	$0.650873\pi$
$440$	−19.4981			−0.929534
$441$	−8.50826	+	26.1857i	−0.405155	+	1.24694i
$442$	8.20475	+	25.2516i	0.390260	+	1.20110i
$443$	3.83798	+	11.8121i	0.182348	+	0.561209i	0.999893	−	0.0146563i	$-0.00466541\pi$
$443$	3.83798	+	11.8121i	0.182348	+	0.561209i	−0.817545	+	0.575865i	$0.804665\pi$
$444$	−0.409343	+	0.297405i	−0.0194266	+	0.0141142i
$445$	0.793685	−	2.44271i	0.0376243	−	0.115796i
$446$	13.3425	−	9.69391i	0.631787	−	0.459020i
$447$	−8.03190	−	5.83552i	−0.379896	−	0.276010i
$448$	8.65999	+	26.6527i	0.409146	+	1.25922i
$449$	−28.7166	−	20.8638i	−1.35522	−	0.984626i	−0.998733	−	0.0503259i	$-0.983974\pi$
$449$	−28.7166	−	20.8638i	−1.35522	−	0.984626i	−0.356488	−	0.934300i	$-0.616026\pi$
$450$	−4.77858	−	3.47184i	−0.225264	−	0.163664i
$451$	1.71569	+	5.28035i	0.0807887	+	0.248642i
$452$	14.9692	+	10.8758i	0.704093	+	0.511553i
$453$	−13.3939	+	9.73126i	−0.629302	+	0.457214i
$454$	−3.51045	+	10.8041i	−0.164754	+	0.507060i
$455$	−11.5065	+	8.35995i	−0.539432	+	0.391920i
$456$	−9.24383	−	28.4496i	−0.432882	−	1.33227i
$457$	−6.32157	−	19.4558i	−0.295710	−	0.910103i	−0.982982	−	0.183703i	$-0.941192\pi$
$457$	−6.32157	−	19.4558i	−0.295710	−	0.910103i	0.687271	−	0.726401i	$-0.258808\pi$
$458$	0.943223	−	2.90294i	0.0440739	−	0.135646i
$459$	−13.6913			−0.639056
$460$	−26.8749			−1.25305
$461$	−8.46443	+	26.0508i	−0.394228	+	1.21331i	0.535334	+	0.844641i	$0.320186\pi$
$461$	−8.46443	+	26.0508i	−0.394228	+	1.21331i	−0.929561	+	0.368667i	$0.879814\pi$
$462$	−25.1008	−	18.2368i	−1.16779	−	0.848452i
$463$	16.8492	−	12.2417i	0.783051	−	0.568920i	−0.122842	−	0.992426i	$-0.539201\pi$
$463$	16.8492	−	12.2417i	0.783051	−	0.568920i	0.905893	+	0.423506i	$0.139201\pi$
$464$	5.78265			0.268453
$465$	2.06733	+	3.83151i	0.0958700	+	0.177682i
$466$	−35.3218			−1.63625
$467$	−7.29610	+	5.30093i	−0.337623	+	0.245298i	−0.743658	−	0.668560i	$-0.766911\pi$
$467$	−7.29610	+	5.30093i	−0.337623	+	0.245298i	0.406035	+	0.913858i	$0.366911\pi$
$468$	26.2761	+	19.0907i	1.21461	+	0.882469i
$469$	2.57846	−	7.93567i	0.119062	−	0.366435i
$470$	1.86479			0.0860162
$471$	10.1367			0.467074
$472$	−10.8998	+	33.5460i	−0.501702	+	1.54408i
$473$	−1.00250	−	3.08537i	−0.0460949	−	0.141865i
$474$	−2.53379	−	7.79819i	−0.116381	−	0.358183i
$475$	5.91714	−	4.29905i	0.271497	−	0.197254i
$476$	17.7856	−	54.7386i	0.815203	−	2.50894i
$477$	24.7318	−	17.9687i	1.13239	−	0.822730i
$478$	−44.4910	−	32.3246i	−2.03497	−	1.47849i
$479$	−1.15483	−	3.55421i	−0.0527656	−	0.162396i	0.921201	−	0.389087i	$-0.127209\pi$
$479$	−1.15483	−	3.55421i	−0.0527656	−	0.162396i	−0.973967	+	0.226691i	$0.927209\pi$
$480$	0.741209	+	0.538520i	0.0338314	+	0.0245800i
$481$	0.420350	+	0.305402i	0.0191663	+	0.0139251i
$482$	−12.9580	−	39.8805i	−0.590219	−	1.81651i
$483$	−17.7827	−	12.9199i	−0.809140	−	0.587874i
$484$	−9.64239	+	7.00561i	−0.438291	+	0.318437i
$485$	1.57861	−	4.85845i	0.0716808	−	0.220611i
$486$	−31.3444	+	22.7730i	−1.42181	+	1.03301i
$487$	−5.78164	−	17.7941i	−0.261991	−	0.806326i	−0.992371	−	0.123285i	$-0.960657\pi$
$487$	−5.78164	−	17.7941i	−0.261991	−	0.806326i	0.730380	−	0.683041i	$-0.239343\pi$
$488$	−13.5030	−	41.5579i	−0.611251	−	1.88124i
$489$	−3.85375	+	11.8606i	−0.174272	+	0.536355i
$490$	28.5052			1.28773
$491$	13.3373			0.601906			0.300953	−	0.953639i	$-0.402695\pi$
$491$	13.3373			0.601906			0.300953	+	0.953639i	$0.402695\pi$
$492$	1.48097	−	4.55797i	0.0667674	−	0.205489i
$493$	3.23153	+	2.34784i	0.145541	+	0.105741i
$494$	−48.3500	+	35.1283i	−2.17537	+	1.58050i
$495$	−8.90405			−0.400207
$496$	12.4369	+	23.0501i	0.558433	+	1.03498i
$497$	31.8801			1.43002
$498$	−21.5347	+	15.6459i	−0.964994	+	0.701109i
$499$	35.1027	+	25.5036i	1.57141	+	1.14170i	0.925790	+	0.378039i	$0.123402\pi$
$499$	35.1027	+	25.5036i	1.57141	+	1.14170i	0.645621	+	0.763658i	$0.276598\pi$
$500$	−1.27165	+	3.91373i	−0.0568698	+	0.175027i
$501$	−14.7047			−0.656959
$502$	2.43321			0.108600
$503$	−9.65548	+	29.7165i	−0.430517	+	1.32499i	0.467095	+	0.884207i	$0.345300\pi$
$503$	−9.65548	+	29.7165i	−0.430517	+	1.32499i	−0.897612	+	0.440787i	$0.854700\pi$
$504$	−16.6175	−	51.1435i	−0.740203	−	2.27811i
$505$	−0.953730	−	2.93528i	−0.0424404	−	0.130618i
$506$	−48.7049	+	35.3862i	−2.16520	+	1.57311i
$507$	0.502963	−	1.54796i	0.0223374	−	0.0687473i
$508$	39.7044	−	28.8469i	1.76160	−	1.27988i
$509$	12.8560	+	9.34043i	0.569832	+	0.414007i	0.835044	−	0.550183i	$-0.185442\pi$
$509$	12.8560	+	9.34043i	0.569832	+	0.414007i	−0.265212	+	0.964190i	$0.585442\pi$
$510$	1.94159	+	5.97560i	0.0859750	+	0.264604i
$511$	22.2155	+	16.1405i	0.982757	+	0.714015i
$512$	−35.3522	−	25.6848i	−1.56236	−	1.13512i
$513$	−9.52321	−	29.3094i	−0.420460	−	1.29404i
$514$	9.33343	+	6.78114i	0.411680	+	0.299103i
$515$	−10.9262	+	7.93833i	−0.481465	+	0.349805i
$516$	−0.865349	+	2.66327i	−0.0380949	+	0.117244i
$517$	2.27422	−	1.65232i	0.100020	−	0.0726689i
$518$	−0.517204	−	1.59179i	−0.0227246	−	0.0699392i
$519$	2.53273	+	7.79496i	0.111175	+	0.342161i
$520$	5.34079	−	16.4373i	0.234209	−	0.720822i
$521$	33.2690			1.45754			0.728771	−	0.684757i	$-0.240092\pi$
$521$	33.2690			1.45754			0.728771	+	0.684757i	$0.240092\pi$
$522$	7.26093			0.317802
$523$	−3.50033	+	10.7729i	−0.153059	+	0.471066i	−0.997959	−	0.0638576i	$-0.979660\pi$
$523$	−3.50033	+	10.7729i	−0.153059	+	0.471066i	0.844900	+	0.534924i	$0.179660\pi$
$524$	6.69708	+	4.86571i	0.292563	+	0.212560i
$525$	−2.72292	+	1.97832i	−0.118838	+	0.0863408i
$526$	−10.8623			−0.473618
$527$	−2.40855	+	17.9307i	−0.104918	+	0.781072i
$528$	13.7119			0.596735
$529$	−15.8976	+	11.5503i	−0.691202	+	0.502188i
$530$	−25.6048	−	18.6030i	−1.11220	−	0.808061i
$531$	−4.97752	+	15.3192i	−0.216006	+	0.664798i
$532$	129.552			5.61677
$533$	−4.92140			−0.213169
$534$	−1.53470	+	4.72333i	−0.0664131	+	0.204399i
$535$	−1.50607	−	4.63521i	−0.0651131	−	0.200398i
$536$	3.13327	+	9.64321i	0.135337	+	0.416523i
$537$	11.1281	−	8.08502i	0.480212	−	0.348894i
$538$	−15.3801	+	47.3351i	−0.663084	+	2.04076i
$539$	34.7638	−	25.2574i	1.49738	−	1.08791i
$540$	14.0278	+	10.1918i	0.603659	+	0.438584i
$541$	4.73314	+	14.5671i	0.203494	+	0.626289i	0.999772	+	0.0213587i	$0.00679920\pi$
$541$	4.73314	+	14.5671i	0.203494	+	0.626289i	−0.796278	+	0.604931i	$0.793201\pi$
$542$	−14.7444	−	10.7124i	−0.633324	−	0.460137i
$543$	−1.42390	−	1.03452i	−0.0611052	−	0.0443955i
$544$	1.17650	+	3.62089i	0.0504419	+	0.155244i
$545$	12.6738	+	9.20803i	0.542884	+	0.394429i
$546$	22.2494	−	16.1652i	0.952188	−	0.691805i
$547$	−9.76272	+	30.0466i	−0.417424	+	1.28470i	0.492641	+	0.870232i	$0.336031\pi$
$547$	−9.76272	+	30.0466i	−0.417424	+	1.28470i	−0.910065	+	0.414465i	$0.863969\pi$
$548$	−5.65251	+	4.10679i	−0.241463	+	0.175433i
$549$	−6.16631	−	18.9779i	−0.263172	−	0.809959i
$550$	2.84862	+	8.76716i	0.121466	+	0.373833i
$551$	−2.77836	+	8.55090i	−0.118362	+	0.364281i
$552$	26.7102			1.13686
$553$	18.2522			0.776162
$554$	2.48401	−	7.64500i	0.105535	−	0.324805i
$555$	0.0994725	+	0.0722710i	0.00422237	+	0.00306773i
$556$	72.2341	−	52.4811i	3.06341	−	2.22570i
$557$	2.49093			0.105544			0.0527720	−	0.998607i	$-0.483194\pi$
$557$	2.49093			0.105544			0.0527720	+	0.998607i	$0.483194\pi$
$558$	15.6163	+	28.9426i	0.661089	+	1.22524i
$559$	2.87562			0.121626
$560$	−16.3809	+	11.9014i	−0.692218	+	0.502926i
$561$	7.66265	+	5.56724i	0.323517	+	0.235049i
$562$	−2.88475	+	8.87835i	−0.121686	+	0.374511i
$563$	13.8735			0.584700			0.292350	−	0.956311i	$-0.405563\pi$
$563$	13.8735			0.584700			0.292350	+	0.956311i	$0.405563\pi$
$564$	−2.42652			−0.102175
$565$	1.38944	−	4.27625i	0.0584541	−	0.179903i
$566$	3.88090	+	11.9442i	0.163126	+	0.502051i
$567$	−5.14881	−	15.8464i	−0.216230	−	0.665487i
$568$	−31.3412	+	22.7707i	−1.31505	+	0.955437i
$569$	3.81522	−	11.7420i	0.159942	−	0.492251i	−0.838686	−	0.544615i	$-0.816676\pi$
$569$	3.81522	−	11.7420i	0.159942	−	0.492251i	0.998628	+	0.0523641i	$0.0166756\pi$
$570$	−11.4416	+	8.31283i	−0.479237	+	0.348186i
$571$	−2.95894	−	2.14979i	−0.123828	−	0.0899661i	0.524148	−	0.851627i	$-0.324384\pi$
$571$	−2.95894	−	2.14979i	−0.123828	−	0.0899661i	−0.647975	+	0.761661i	$0.724384\pi$
$572$	−15.6638	−	48.2083i	−0.654937	−	2.01569i
$573$	10.3098	+	7.49054i	0.430700	+	0.312922i
$574$	12.8254	+	9.31822i	0.535323	+	0.388935i
$575$	2.01811	+	6.21110i	0.0841610	+	0.259021i
$576$	−12.5813	−	9.14088i	−0.524222	−	0.380870i
$577$	5.83976	−	4.24283i	0.243112	−	0.176631i	−0.459556	−	0.888149i	$-0.651992\pi$
$577$	5.83976	−	4.24283i	0.243112	−	0.176631i	0.702669	+	0.711517i	$0.251992\pi$
$578$	4.92244	−	15.1497i	0.204747	−	0.630145i
$579$	11.2224	−	8.15355i	0.466387	−	0.338850i
$580$	−1.56321	−	4.81107i	−0.0649089	−	0.199769i
$581$	−18.3101	−	56.3528i	−0.759633	−	2.33791i
$582$	−3.05246	+	9.39450i	−0.126528	+	0.389415i
$583$	−47.7100			−1.97595
$584$	−33.3685			−1.38080
$585$	2.43894	−	7.50629i	0.100838	−	0.310347i
$586$	−19.4149	−	14.1057i	−0.802021	−	0.582702i
$587$	1.61755	−	1.17522i	0.0667632	−	0.0485063i	−0.553903	−	0.832581i	$-0.686862\pi$
$587$	1.61755	−	1.17522i	0.0667632	−	0.0485063i	0.620666	+	0.784075i	$0.286862\pi$
$588$	−37.0918			−1.52964
$589$	−40.0600	+	7.31588i	−1.65064	+	0.301446i
$590$	16.6762			0.686546
$591$	−10.0908	+	7.33139i	−0.415080	+	0.301573i
$592$	0.598419	+	0.434777i	0.0245949	+	0.0178692i
$593$	−0.198711	+	0.611571i	−0.00816010	+	0.0251142i	−0.955054	−	0.296433i	$-0.904203\pi$
$593$	−0.198711	+	0.611571i	−0.00816010	+	0.0251142i	0.946894	+	0.321547i	$0.104203\pi$
$594$	38.8418			1.59370
$595$	−13.9863			−0.573382
$596$	−16.1456	+	49.6911i	−0.661350	+	2.03543i
$597$	−3.55235	−	10.9330i	−0.145388	−	0.447458i
$598$	−16.4903	−	50.7520i	−0.674339	−	2.07540i
$599$	23.2703	−	16.9069i	0.950799	−	0.690796i	−0.000196345	−	1.00000i	$-0.500062\pi$
$599$	23.2703	−	16.9069i	0.950799	−	0.690796i	0.950996	+	0.309204i	$0.100062\pi$
$600$	1.26386	−	3.88975i	0.0515967	−	0.158798i
$601$	2.44203	−	1.77424i	0.0996125	−	0.0723727i	−0.536864	−	0.843669i	$-0.680391\pi$
$601$	2.44203	−	1.77424i	0.0996125	−	0.0723727i	0.636477	+	0.771296i	$0.280391\pi$
$602$	−7.49404	−	5.44474i	−0.305434	−	0.221911i
$603$	1.43085	+	4.40370i	0.0582687	+	0.179333i
$604$	70.4887	+	51.2130i	2.86814	+	2.08383i
$605$	2.34315	+	1.70240i	0.0952626	+	0.0692124i
$606$	1.84417	+	5.67578i	0.0749144	+	0.230563i
$607$	−35.4947	−	25.7884i	−1.44068	−	1.04672i	−0.987899	−	0.155099i	$-0.950430\pi$
$607$	−35.4947	−	25.7884i	−1.44068	−	1.04672i	−0.452785	−	0.891620i	$-0.649570\pi$
$608$	−6.93301	+	5.03713i	−0.281171	+	0.204282i
$609$	1.27853	−	3.93491i	0.0518086	−	0.159451i
$610$	−16.7134	+	12.1430i	−0.676707	+	0.491657i
$611$	0.769998	+	2.36981i	0.0311508	+	0.0958722i
$612$	9.86969	+	30.3758i	0.398959	+	1.22787i
$613$	−14.5194	+	44.6861i	−0.586433	+	1.80485i	0.00700749	+	0.999975i	$0.497769\pi$
$613$	−14.5194	+	44.6861i	−0.586433	+	1.80485i	−0.593440	+	0.804878i	$0.702231\pi$
$614$	−32.6939			−1.31942
$615$	−1.16461			−0.0469616
$616$	−25.9345	+	79.8182i	−1.04493	+	3.21597i
$617$	15.1718	+	11.0230i	0.610795	+	0.443768i	0.849694	−	0.527276i	$-0.176787\pi$
$617$	15.1718	+	11.0230i	0.610795	+	0.443768i	−0.238899	+	0.971044i	$0.576787\pi$
$618$	21.1273	−	15.3499i	0.849866	−	0.617464i
$619$	43.9014			1.76455			0.882274	−	0.470737i	$-0.156012\pi$
$619$	43.9014			1.76455			0.882274	+	0.470737i	$0.156012\pi$
$620$	15.8153	−	16.5784i	0.635157	−	0.665804i
$621$	27.5175			1.10424
$622$	20.0273	−	14.5507i	0.803023	−	0.583430i
$623$	−8.94391	−	6.49813i	−0.358330	−	0.260342i
$624$	−3.75589	+	11.5594i	−0.150356	+	0.462747i
$625$	1.00000			0.0400000
$626$	−64.8682			−2.59265
$627$	−6.58808	+	20.2760i	−0.263103	+	0.809747i
$628$	−16.4850	−	50.7357i	−0.657825	−	2.02458i
$629$	0.157890	+	0.485934i	0.00629547	+	0.0193755i
$630$	−20.5685	+	14.9439i	−0.819469	+	0.595379i
$631$	1.58279	−	4.87133i	0.0630099	−	0.193925i	−0.914596	−	0.404369i	$-0.867491\pi$
$631$	1.58279	−	4.87133i	0.0630099	−	0.193925i	0.977606	+	0.210445i	$0.0674911\pi$
$632$	−17.9437	+	13.0368i	−0.713761	+	0.518577i
$633$	4.19345	+	3.04672i	0.166675	+	0.121096i
$634$	−20.3584	−	62.6567i	−0.808535	−	2.48842i
$635$	−9.64838	−	7.00996i	−0.382884	−	0.278182i
$636$	33.3177	+	24.2067i	1.32113	+	0.959860i
$637$	11.7702	+	36.2249i	0.466352	+	1.43528i
$638$	−9.16773	−	6.66074i	−0.362954	−	0.263701i
$639$	−14.3124	+	10.3985i	−0.566188	+	0.411360i
$640$	−5.69941	+	17.5410i	−0.225289	+	0.693368i
$641$	−17.6720	+	12.8395i	−0.698003	+	0.507129i	−0.879281	−	0.476303i	$-0.841976\pi$
$641$	−17.6720	+	12.8395i	−0.698003	+	0.507129i	0.181279	+	0.983432i	$0.441976\pi$
$642$	2.91220	+	8.96284i	0.114935	+	0.353735i
$643$	−11.0814	−	34.1050i	−0.437007	−	1.34497i	−0.891016	−	0.453972i	$-0.850007\pi$
$643$	−11.0814	−	34.1050i	−0.437007	−	1.34497i	0.454009	−	0.890997i	$-0.349993\pi$
$644$	−35.7465	+	110.016i	−1.40861	+	4.33525i
$645$	0.680494			0.0267944
$646$	−58.7700			−2.31228
$647$	4.06772	−	12.5191i	0.159918	−	0.492178i	−0.838708	−	0.544582i	$-0.816688\pi$
$647$	4.06772	−	12.5191i	0.159918	−	0.492178i	0.998626	+	0.0524039i	$0.0166883\pi$
$648$	16.3803	+	11.9010i	0.643477	+	0.467514i
$649$	20.3376	−	14.7761i	0.798321	−	0.580014i
$650$	−8.17117			−0.320500
$651$	18.4346	−	3.36658i	0.722509	−	0.131947i
$652$	65.6315			2.57033
$653$	8.44186	−	6.13337i	0.330355	−	0.240017i	−0.410226	−	0.911984i	$-0.634550\pi$
$653$	8.44186	−	6.13337i	0.330355	−	0.240017i	0.740581	+	0.671967i	$0.234550\pi$
$654$	−24.5065	−	17.8050i	−0.958281	−	0.696232i
$655$	0.621621	−	1.91315i	0.0242887	−	0.0747530i
$656$	−7.00621			−0.273546
$657$	−15.2382			−0.594498
$658$	2.48036	−	7.63377i	0.0966946	−	0.297595i
$659$	−2.62300	−	8.07277i	−0.102178	−	0.314471i	0.886880	−	0.462000i	$-0.152868\pi$
$659$	−2.62300	−	8.07277i	−0.102178	−	0.314471i	−0.989058	+	0.147529i	$0.952868\pi$
$660$	−3.70672	−	11.4081i	−0.144284	−	0.444060i
$661$	10.2547	−	7.45049i	0.398862	−	0.289790i	−0.370215	−	0.928946i	$-0.620716\pi$
$661$	10.2547	−	7.45049i	0.398862	−	0.289790i	0.769077	+	0.639156i	$0.220716\pi$
$662$	9.16795	−	28.2161i	0.356323	−	1.09665i
$663$	−6.79220	+	4.93482i	−0.263787	+	0.191653i
$664$	58.2512	+	42.3220i	2.26059	+	1.64241i
$665$	−9.72838	−	29.9409i	−0.377250	−	1.16106i
$666$	0.751400	+	0.545924i	0.0291162	+	0.0211541i
$667$	−6.49488	−	4.71881i	−0.251483	−	0.182713i
$668$	23.9139	+	73.5995i	0.925257	+	2.84765i
$669$	4.21899	+	3.06527i	0.163115	+	0.118510i
$670$	3.87824	−	2.81770i	0.149829	−	0.108857i
$671$	−9.62358	+	29.6183i	−0.371514	+	1.14340i
$672$	3.19040	−	2.31796i	0.123072	−	0.0894172i
$673$	2.45769	+	7.56398i	0.0947368	+	0.291570i	0.987185	−	0.159580i	$-0.0510140\pi$
$673$	2.45769	+	7.56398i	0.0947368	+	0.291570i	−0.892448	+	0.451150i	$0.851014\pi$
$674$	−6.33080	−	19.4842i	−0.243853	−	0.750503i
$675$	1.30205	−	4.00731i	0.0501161	−	0.154241i
$676$	−8.56574			−0.329452
$677$	30.3994			1.16835			0.584173	−	0.811629i	$-0.301419\pi$
$677$	30.3994			1.16835			0.584173	+	0.811629i	$0.301419\pi$
$678$	−2.68668	+	8.26875i	−0.103181	+	0.317559i
$679$	−17.7890	−	12.9245i	−0.682681	−	0.495997i
$680$	13.7499	−	9.98986i	0.527283	−	0.383094i
$681$	−3.59212			−0.137650
$682$	6.83298	−	50.8687i	0.261648	−	1.94786i
$683$	3.50808			0.134233			0.0671165	−	0.997745i	$-0.478620\pi$
$683$	3.50808			0.134233			0.0671165	+	0.997745i	$0.478620\pi$
$684$	−58.1613	+	42.2567i	−2.22385	+	1.61572i
$685$	1.37359	+	0.997971i	0.0524822	+	0.0381305i
$686$	14.8905	−	45.8283i	0.568523	−	1.74973i
$687$	0.965166			0.0368234
$688$	4.09380			0.156075
$689$	13.0684	−	40.2205i	0.497868	−	1.53228i
$690$	−3.90230	−	12.0101i	−0.148558	−	0.457215i
$691$	4.92655	+	15.1624i	0.187415	+	0.576803i	0.999982	−	0.00606485i	$-0.00193051\pi$
$691$	4.92655	+	15.1624i	0.187415	+	0.576803i	−0.812567	+	0.582868i	$0.801931\pi$
$692$	34.8961	−	25.3535i	1.32655	−	0.963794i
$693$	−11.8433	+	36.4500i	−0.449891	+	1.38462i
$694$	−42.0139	+	30.5249i	−1.59483	+	1.15871i
$695$	−17.5533	−	12.7532i	−0.665833	−	0.483756i
$696$	1.55363	+	4.78160i	0.0588904	+	0.181246i
$697$	−3.91529	−	2.84462i	−0.148302	−	0.107748i
$698$	43.6819	+	31.7367i	1.65338	+	1.20125i
$699$	−3.45140	−	10.6223i	−0.130544	−	0.401773i
$700$	14.3300	+	10.4113i	0.541623	+	0.393512i
$701$	−19.9610	+	14.5025i	−0.753918	+	0.547753i	−0.897039	−	0.441952i	$-0.854286\pi$
$701$	−19.9610	+	14.5025i	−0.753918	+	0.547753i	0.143121	+	0.989705i	$0.454286\pi$
$702$	−10.6393	+	32.7444i	−0.401555	+	1.23586i
$703$	−0.930431	+	0.675998i	−0.0350919	+	0.0254957i
$704$	7.50003	+	23.0827i	0.282668	+	0.869962i
$705$	0.182214	+	0.560797i	0.00686257	+	0.0211208i
$706$	12.6003	−	38.7798i	0.474219	−	1.45950i
$707$	−13.2846			−0.499617
$708$	−21.6995			−0.815518
$709$	9.33878	−	28.7418i	0.350725	−	1.07942i	−0.607722	−	0.794150i	$-0.707916\pi$
$709$	9.33878	−	28.7418i	0.350725	−	1.07942i	0.958447	−	0.285271i	$-0.0920837\pi$
$710$	14.8175	+	10.7656i	0.556093	+	0.404025i
$711$	−8.19421	+	5.95344i	−0.307307	+	0.223272i
$712$	13.4341			0.503464
$713$	4.84083	−	36.0380i	0.181291	−	1.34963i
$714$	27.0445			1.01211
$715$	−9.96525	+	7.24018i	−0.372679	+	0.270767i
$716$	−58.5641	−	42.5493i	−2.18864	−	1.59014i
$717$	5.37362	−	16.5383i	0.200682	−	0.617634i
$718$	58.1683			2.17082
$719$	−15.2082			−0.567172			−0.283586	−	0.958947i	$-0.591524\pi$
$719$	−15.2082			−0.567172			−0.283586	+	0.958947i	$0.591524\pi$
$720$	3.47213	−	10.6861i	0.129399	−	0.398248i
$721$	17.9637	+	55.2867i	0.669005	+	2.05898i
$722$	−26.3593	−	81.1256i	−0.980992	−	3.01918i
$723$	10.7271	−	7.79369i	0.398945	−	0.289851i
$724$	−2.86229	+	8.80924i	−0.106376	+	0.327393i
$725$	−0.994509	+	0.722553i	−0.0369352	+	0.0268350i
$726$	−4.53082	−	3.29183i	−0.168154	−	0.122171i
$727$	7.97917	+	24.5574i	0.295931	+	0.910782i	0.982907	+	0.184102i	$0.0589377\pi$
$727$	7.97917	+	24.5574i	0.295931	+	0.910782i	−0.686976	+	0.726680i	$0.741062\pi$
$728$	−60.1845	−	43.7266i	−2.23059	−	1.62062i
$729$	−0.516215	−	0.375053i	−0.0191191	−	0.0138908i
$730$	4.87507	+	15.0039i	0.180434	+	0.555320i
$731$	2.28774	+	1.66214i	0.0846153	+	0.0614766i
$732$	21.7480	−	15.8009i	0.803831	−	0.584017i
$733$	−7.51092	+	23.1162i	−0.277422	+	0.853818i	0.711146	+	0.703044i	$0.248176\pi$
$733$	−7.51092	+	23.1162i	−0.277422	+	0.853818i	−0.988568	+	0.150774i	$0.951824\pi$
$734$	−30.4471	+	22.1211i	−1.12382	+	0.816505i
$735$	2.78532	+	8.57235i	0.102738	+	0.316196i
$736$	−2.36458	−	7.27744i	−0.0871597	−	0.268250i
$737$	2.23309	−	6.87273i	0.0822567	−	0.253160i
$738$	−8.79728			−0.323832
$739$	−8.21144			−0.302063			−0.151031	−	0.988529i	$-0.548259\pi$
$739$	−8.21144			−0.302063			−0.151031	+	0.988529i	$0.548259\pi$
$740$	0.199958	−	0.615408i	0.00735061	−	0.0226228i
$741$	−15.2885	−	11.1078i	−0.561639	−	0.408054i
$742$	−110.211	+	80.0729i	−4.04597	+	2.93957i
$743$	−17.6744			−0.648413			−0.324206	−	0.945986i	$-0.605097\pi$
$743$	−17.6744			−0.648413			−0.324206	+	0.945986i	$0.605097\pi$
$744$	−15.7184	+	16.4768i	−0.576263	+	0.604069i
$745$	12.6966			0.465168
$746$	20.3181	−	14.7619i	0.743898	−	0.540473i
$747$	26.6012	+	19.3269i	0.973287	+	0.707134i
$748$	15.4033	−	47.4066i	0.563202	−	1.73336i
$749$	−20.9781			−0.766524
$750$	−1.93364			−0.0706067
$751$	4.42836	−	13.6291i	0.161593	−	0.497333i	−0.837176	−	0.546934i	$-0.815795\pi$
$751$	4.42836	−	13.6291i	0.161593	−	0.497333i	0.998769	+	0.0496009i	$0.0157949\pi$
$752$	1.09619	+	3.37371i	0.0399738	+	0.123027i
$753$	0.237756	+	0.731739i	0.00866433	+	0.0266661i
$754$	8.12631	−	5.90411i	0.295943	−	0.215015i
$755$	6.54274	−	20.1365i	0.238115	−	0.732841i
$756$	60.3799	−	43.8686i	2.19600	−	1.59549i
$757$	−20.3918	−	14.8155i	−0.741153	−	0.538480i	0.151919	−	0.988393i	$-0.451455\pi$
$757$	−20.3918	−	14.8155i	−0.741153	−	0.538480i	−0.893072	+	0.449913i	$0.851455\pi$
$758$	16.4053	+	50.4904i	0.595868	+	1.83389i
$759$	−15.4008	−	11.1893i	−0.559013	−	0.406147i
$760$	30.9495	+	22.4861i	1.12266	+	0.815658i
$761$	−7.60526	−	23.4066i	−0.275690	−	0.848487i	−0.989036	−	0.147675i	$-0.952821\pi$
$761$	−7.60526	−	23.4066i	−0.275690	−	0.848487i	0.713346	−	0.700812i	$-0.247179\pi$
$762$	18.6565	+	13.5548i	0.675854	+	0.491037i
$763$	54.5518	−	39.6342i	1.97491	−	1.43486i
$764$	20.7247	−	63.7840i	0.749793	−	2.30763i
$765$	6.27906	−	4.56200i	0.227020	−	0.164940i
$766$	−21.3910	−	65.8348i	−0.772890	−	2.37871i
$767$	6.88583	+	21.1924i	0.248633	+	0.765213i
$768$	7.87420	−	24.2343i	0.284136	−	0.874480i
$769$	9.24398			0.333346			0.166673	−	0.986012i	$-0.446698\pi$
$769$	9.24398			0.333346			0.166673	+	0.986012i	$0.446698\pi$
$770$	39.6786			1.42992
$771$	−1.12729	+	3.46945i	−0.0405984	+	0.124949i
$772$	−59.0605	−	42.9100i	−2.12563	−	1.54436i
$773$	−16.3568	+	11.8839i	−0.588314	+	0.427435i	−0.841712	−	0.539927i	$-0.818452\pi$
$773$	−16.3568	+	11.8839i	−0.588314	+	0.427435i	0.253398	+	0.967362i	$0.418452\pi$
$774$	5.14035			0.184766
$775$	−5.01907	−	2.41018i	−0.180290	−	0.0865761i
$776$	26.7198			0.959185
$777$	0.428161	−	0.311077i	0.0153602	−	0.0111598i
$778$	68.5372	+	49.7952i	2.45718	+	1.78524i
$779$	3.36623	−	10.3602i	0.120608	−	0.371192i
$780$	10.6326			0.380708
$781$	27.6099			0.987960
$782$	16.2161	−	49.9081i	0.579887	−	1.78471i
$783$	1.60059	+	4.92611i	0.0572005	+	0.176045i
$784$	16.7563	+	51.5706i	0.598440	+	1.84181i
$785$	−10.4877	+	7.61977i	−0.374322	+	0.271961i
$786$	−1.20199	+	3.69935i	−0.0428737	+	0.131952i
$787$	19.4832	−	14.1554i	0.694501	−	0.504585i	−0.183636	−	0.982994i	$-0.558787\pi$
$787$	19.4832	−	14.1554i	0.694501	−	0.504585i	0.878137	+	0.478410i	$0.158787\pi$
$788$	53.1052	+	38.5832i	1.89179	+	1.37447i
$789$	−1.06139	−	3.26661i	−0.0377863	−	0.116294i
$790$	8.48344	+	6.16358i	0.301827	+	0.219290i
$791$	−15.6574	−	11.3757i	−0.556712	−	0.404475i
$792$	−14.3917	−	44.2931i	−0.511387	−	1.57389i
$793$	−22.3328	−	16.2257i	−0.793062	−	0.576193i
$794$	−66.7290	+	48.4815i	−2.36812	+	1.72054i
$795$	3.09254	−	9.51786i	0.109681	−	0.337564i
$796$	−48.9443	+	35.5601i	−1.73478	+	1.26040i
$797$	3.07468	+	9.46290i	0.108911	+	0.335193i	0.990628	−	0.136584i	$-0.0436125\pi$
$797$	3.07468	+	9.46290i	0.108911	+	0.335193i	−0.881718	+	0.471778i	$0.843613\pi$
$798$	18.8112	+	57.8949i	0.665909	+	2.04946i
$799$	−0.757194	+	2.33040i	−0.0267876	+	0.0824437i
$800$	−1.17168			−0.0414252
$801$	6.13485			0.216764
$802$	12.4639	−	38.3599i	0.440115	−	1.35453i
$803$	19.2399	+	13.9786i	0.678961	+	0.493294i
$804$	−5.04648	+	3.66648i	−0.177976	+	0.129307i
$805$	28.1103			0.990760
$806$	41.0117	+	19.6940i	1.44457	+	0.693691i
$807$	−15.7379			−0.554001
$808$	13.0600	−	9.48864i	0.459449	−	0.333809i
$809$	19.2640	+	13.9961i	0.677288	+	0.492078i	0.872457	−	0.488691i	$-0.162526\pi$
$809$	19.2640	+	13.9961i	0.677288	+	0.492078i	−0.195169	+	0.980770i	$0.562526\pi$
$810$	2.95806	−	9.10397i	0.103936	−	0.319881i
$811$	14.5393			0.510546			0.255273	−	0.966869i	$-0.417835\pi$
$811$	14.5393			0.510546			0.255273	+	0.966869i	$0.417835\pi$
$812$	−21.7741			−0.764120
$813$	1.78082	−	5.48081i	0.0624562	−	0.192220i
$814$	−0.447927	−	1.37858i	−0.0156998	−	0.0483191i
$815$	−4.92844	−	15.1682i	−0.172636	−	0.531319i
$816$	−9.66953	+	7.02532i	−0.338501	+	0.245935i
$817$	−1.96692	+	6.05357i	−0.0688140	+	0.211788i
$818$	−39.1095	+	28.4147i	−1.36743	+	0.993498i
$819$	−27.4840	−	19.9683i	−0.960370	−	0.697750i
$820$	1.89397	+	5.82905i	0.0661405	+	0.203559i
$821$	7.35265	+	5.34201i	0.256609	+	0.186438i	0.708651	−	0.705559i	$-0.249304\pi$
$821$	7.35265	+	5.34201i	0.256609	+	0.186438i	−0.452042	+	0.891997i	$0.649304\pi$
$822$	−2.65603	−	1.92972i	−0.0926397	−	0.0673067i
$823$	−0.612654	−	1.88555i	−0.0213558	−	0.0657263i	0.939811	−	0.341696i	$-0.111001\pi$
$823$	−0.612654	−	1.88555i	−0.0213558	−	0.0657263i	−0.961166	+	0.275969i	$0.911001\pi$
$824$	−57.1492	−	41.5213i	−1.99089	−	1.44646i
$825$	−2.35820	+	1.71333i	−0.0821019	+	0.0596505i
$826$	22.1810	−	68.2662i	0.771777	−	2.37529i
$827$	0.626819	−	0.455410i	0.0217966	−	0.0158362i	−0.576834	−	0.816862i	$-0.695712\pi$
$827$	0.626819	−	0.455410i	0.0217966	−	0.0158362i	0.598630	+	0.801025i	$0.295712\pi$
$828$	−19.8366	−	61.0508i	−0.689370	−	2.12166i
$829$	−1.77583	−	5.46544i	−0.0616771	−	0.189823i	0.915470	−	0.402386i	$-0.131819\pi$
$829$	−1.77583	−	5.46544i	−0.0616771	−	0.189823i	−0.977147	+	0.212563i	$0.931819\pi$
$830$	10.5194	−	32.3754i	0.365134	−	1.12377i
$831$	2.54180			0.0881740
$832$	−21.5136			−0.745848
$833$	−11.5745	+	35.6226i	−0.401032	+	1.23425i
$834$	33.9417	+	24.6601i	1.17531	+	0.853910i
$835$	15.2139	−	11.0536i	0.526500	−	0.382525i
$836$	112.199			3.88048
$837$	−16.1934	+	16.9748i	−0.559727	+	0.586734i
$838$	−25.8581			−0.893254
$839$	−10.2549	+	7.45059i	−0.354037	+	0.257223i	−0.750561	−	0.660801i	$-0.770217\pi$
$839$	−10.2549	+	7.45059i	−0.354037	+	0.257223i	0.396524	+	0.918025i	$0.370217\pi$
$840$	−14.2422	−	10.3476i	−0.491402	−	0.357025i
$841$	−8.49453	+	26.1435i	−0.292915	+	0.901499i
$842$	−56.1591			−1.93537
$843$	−2.95186			−0.101668
$844$	8.42962	−	25.9437i	0.290160	−	0.893019i
$845$	0.643225	+	1.97964i	0.0221276	+	0.0681018i
$846$	1.37642	+	4.23617i	0.0473221	+	0.145643i
$847$	10.0857	−	7.32766i	0.346547	−	0.251781i
$848$	18.6045	−	57.2588i	0.638881	−	1.96627i
$849$	−3.21276	+	2.33420i	−0.110261	+	0.0801097i
$850$	−6.50069	−	4.72303i	−0.222972	−	0.161999i
$851$	−0.317334	−	0.976655i	−0.0108781	−	0.0334793i
$852$	−19.2811	−	14.0085i	−0.660558	−	0.479923i
$853$	−7.52689	−	5.46861i	−0.257716	−	0.187241i	0.451424	−	0.892310i	$-0.350916\pi$
$853$	−7.52689	−	5.46861i	−0.257716	−	0.187241i	−0.709139	+	0.705068i	$0.750916\pi$
$854$	27.4786	+	84.5704i	0.940297	+	2.89394i
$855$	14.1335	+	10.2686i	0.483356	+	0.351178i
$856$	20.6235	−	14.9839i	0.704897	−	0.512138i
$857$	10.3563	−	31.8735i	0.353766	−	1.08878i	−0.602956	−	0.797775i	$-0.706010\pi$
$857$	10.3563	−	31.8735i	0.353766	−	1.08878i	0.956722	−	0.291005i	$-0.0939896\pi$
$858$	19.2692	−	13.9999i	0.657841	−	0.477949i
$859$	10.9698	+	33.7615i	0.374284	+	1.15193i	0.943960	+	0.330058i	$0.107068\pi$
$859$	10.9698	+	33.7615i	0.374284	+	1.15193i	−0.569677	+	0.821869i	$0.692932\pi$
$860$	−1.10667	−	3.40598i	−0.0377371	−	0.116143i
$861$	−1.54905	+	4.76750i	−0.0527916	+	0.162476i
$862$	81.3782			2.77175
$863$	−19.3026			−0.657068			−0.328534	−	0.944492i	$-0.606555\pi$
$863$	−19.3026			−0.657068			−0.328534	+	0.944492i	$0.606555\pi$
$864$	−1.52559	+	4.69530i	−0.0519018	+	0.159737i
$865$	−8.47992	−	6.16102i	−0.288326	−	0.209481i
$866$	−34.1313	+	24.7978i	−1.15983	+	0.842665i
$867$	5.03696			0.171064
$868$	−46.8300	−	86.7931i	−1.58951	−	2.94595i
$869$	15.8074			0.536230
$870$	1.92303	−	1.39716i	0.0651967	−	0.0473682i
$871$	5.18218	+	3.76507i	0.175591	+	0.127575i
$872$	−25.3205	+	77.9285i	−0.857461	+	2.63899i
$873$	12.2019			0.412973
$874$	118.119			3.99543
$875$	1.33011	−	4.09364i	0.0449658	−	0.138390i
$876$	−6.34359	−	19.5236i	−0.214330	−	0.659640i
$877$	0.200452	+	0.616927i	0.00676877	+	0.0208321i	0.954384	−	0.298582i	$-0.0965138\pi$
$877$	0.200452	+	0.616927i	0.00676877	+	0.0208321i	−0.947615	+	0.319415i	$0.896514\pi$
$878$	−38.2648	+	27.8010i	−1.29137	+	0.938238i
$879$	2.34493	−	7.21694i	0.0790924	−	0.243421i
$880$	−14.1867	+	10.3073i	−0.478235	+	0.347458i
$881$	27.2520	+	19.7998i	0.918144	+	0.667071i	0.943061	−	0.332619i	$-0.107932\pi$
$881$	27.2520	+	19.7998i	0.918144	+	0.667071i	−0.0249171	+	0.999690i	$0.507932\pi$
$882$	21.0399	+	64.7542i	0.708451	+	2.18039i
$883$	−15.0925	−	10.9654i	−0.507904	−	0.369014i	0.304124	−	0.952632i	$-0.401636\pi$
$883$	−15.0925	−	10.9654i	−0.507904	−	0.369014i	−0.812028	+	0.583619i	$0.801636\pi$
$884$	35.7455	+	25.9707i	1.20225	+	0.873488i
$885$	1.62948	+	5.01501i	0.0547743	+	0.168578i
$886$	24.8474	+	18.0527i	0.834764	+	0.606492i
$887$	−39.5663	+	28.7466i	−1.32851	+	0.965217i	−0.328724	+	0.944426i	$0.606618\pi$
$887$	−39.5663	+	28.7466i	−1.32851	+	0.965217i	−0.999784	+	0.0207910i	$0.993382\pi$
$888$	−0.198733	+	0.611637i	−0.00666904	+	0.0205252i
$889$	−41.5296	+	30.1730i	−1.39286	+	1.01197i
$890$	−1.96269	−	6.04054i	−0.0657895	−	0.202479i
$891$	−4.45916	−	13.7239i	−0.149387	−	0.459767i
$892$	8.48094	−	26.1017i	0.283963	−	0.873948i
$893$	−5.51544			−0.184567
$894$	−24.5507			−0.821098
$895$	−5.43590	+	16.7300i	−0.181702	+	0.559222i
$896$	64.2257	+	46.6627i	2.14563	+	1.55889i
$897$	13.6513	−	9.91826i	0.455804	−	0.331161i
$898$	−87.7766			−2.92914
$899$	6.73299	−	1.22960i	0.224558	−	0.0410095i
$900$	−9.82930			−0.327643
$901$	33.6447	−	24.4443i	1.12087	−	0.814357i
$902$	11.1075	+	8.07009i	0.369840	+	0.268705i
$903$	0.905129	−	2.78570i	0.0301208	−	0.0927023i
$904$	23.5179			0.782195
$905$	2.25085			0.0748209
$906$	−12.6513	+	38.9368i	−0.420312	+	1.29359i
$907$	11.6370	+	35.8150i	0.386400	+	1.18922i	0.935460	+	0.353434i	$0.114986\pi$
$907$	11.6370	+	35.8150i	0.386400	+	1.18922i	−0.549059	+	0.835783i	$0.685014\pi$
$908$	5.84177	+	17.9791i	0.193866	+	0.596658i
$909$	5.96402	−	4.33311i	0.197814	−	0.143720i
$910$	−10.8685	+	33.4499i	−0.360288	+	1.10885i
$911$	1.65486	−	1.20232i	0.0548279	−	0.0398348i	−0.560034	−	0.828470i	$-0.689212\pi$
$911$	1.65486	−	1.20232i	0.0548279	−	0.0398348i	0.614862	+	0.788635i	$0.289212\pi$
$912$	−21.7651	−	15.8133i	−0.720714	−	0.523630i
$913$	−15.8576	−	48.8047i	−0.524810	−	1.61520i
$914$	−40.9264	−	29.7348i	−1.35372	−	0.983538i
$915$	−5.28489	−	3.83969i	−0.174713	−	0.126936i
$916$	−1.56962	−	4.83081i	−0.0518619	−	0.159614i
$917$	−7.00494	−	5.08939i	−0.231324	−	0.168066i
$918$	−27.3909	+	19.9006i	−0.904034	+	0.656819i
$919$	−3.49186	+	10.7468i	−0.115186	+	0.354505i	−0.991986	−	0.126350i	$-0.959674\pi$
$919$	−3.49186	+	10.7468i	−0.115186	+	0.354505i	0.876800	+	0.480855i	$0.159674\pi$
$920$	−27.6352	+	20.0781i	−0.911105	+	0.661956i
$921$	−3.19462	−	9.83202i	−0.105266	−	0.323976i
$922$	20.9315	+	64.4206i	0.689343	+	2.12158i
$923$	−7.56273	+	23.2757i	−0.248930	+	0.766129i
$924$	−51.6310			−1.69854
$925$	−0.157243			−0.00517013
$926$	15.9151	−	48.9815i	0.523001	−	1.60963i
$927$	−26.0980	−	18.9613i	−0.857169	−	0.622770i
$928$	1.16525	−	0.846603i	0.0382512	−	0.0277911i
$929$	−19.4155			−0.637002			−0.318501	−	0.947922i	$-0.603179\pi$
$929$	−19.4155			−0.637002			−0.318501	+	0.947922i	$0.603179\pi$
$930$	9.70509	+	4.66042i	0.318242	+	0.152821i
$931$	−84.3091			−2.76312
$932$	−47.5535	+	34.5496i	−1.55767	+	1.13171i
$933$	6.33276	+	4.60102i	0.207325	+	0.150631i
$934$	−6.89158	+	21.2101i	−0.225499	+	0.694016i
$935$	−12.1129			−0.396134
$936$	41.2821			1.34935
$937$	−8.82451	+	27.1590i	−0.288284	+	0.887247i	0.697111	+	0.716963i	$0.254468\pi$
$937$	−8.82451	+	27.1590i	−0.288284	+	0.887247i	−0.985395	+	0.170284i	$0.945532\pi$
$938$	−6.37621	−	19.6240i	−0.208191	−	0.640745i
$939$	−6.33846	−	19.5078i	−0.206848	−	0.636613i
$940$	2.51055	−	1.82402i	0.0818850	−	0.0594929i
$941$	−8.10330	+	24.9394i	−0.264160	+	0.813001i	0.727726	+	0.685868i	$0.240577\pi$
$941$	−8.10330	+	24.9394i	−0.264160	+	0.813001i	−0.991886	+	0.127133i	$0.959423\pi$
$942$	20.2795	−	14.7339i	0.660741	−	0.480057i
$943$	7.86914	+	5.71727i	0.256254	+	0.186180i
$944$	9.80282	+	30.1700i	0.319054	+	0.981949i
$945$	−14.6726	−	10.6603i	−0.477301	−	0.346779i
$946$	−6.49025	−	4.71544i	−0.211016	−	0.153312i
$947$	−9.65045	−	29.7010i	−0.313598	−	0.965154i	−0.976328	−	0.216296i	$-0.930602\pi$
$947$	−9.65045	−	29.7010i	−0.313598	−	0.965154i	0.662730	−	0.748858i	$-0.269398\pi$
$948$	−11.0389	−	8.02025i	−0.358528	−	0.260485i
$949$	−17.0543	+	12.3907i	−0.553606	+	0.402218i
$950$	5.58907	−	17.2014i	0.181333	−	0.558087i
$951$	16.8535	−	12.2448i	0.546511	−	0.397063i
$952$	−22.6062	−	69.5746i	−0.732670	−	2.25493i
$953$	4.99523	+	15.3737i	0.161811	+	0.498004i	0.998787	−	0.0492356i	$-0.0156785\pi$
$953$	4.99523	+	15.3737i	0.161811	+	0.498004i	−0.836976	+	0.547240i	$0.815679\pi$
$954$	23.3606	−	71.8965i	0.756327	−	2.32773i
$955$	−16.2975			−0.527375
$956$	−91.5158			−2.95983
$957$	1.10728	−	3.40785i	0.0357932	−	0.110160i
$958$	−7.47648	−	5.43198i	−0.241554	−	0.175499i
$959$	5.91236	−	4.29558i	0.190920	−	0.138712i
$960$	−5.09101			−0.164312
$961$	19.3821	+	24.1937i	0.625229	+	0.780442i
$962$	1.28486			0.0414256
$963$	9.41800	−	6.84258i	0.303491	−	0.220499i
$964$	−56.4539	−	41.0161i	−1.81826	−	1.32104i
$965$	−5.48198	+	16.8718i	−0.176471	+	0.543122i
$966$	−54.3554			−1.74886
$967$	39.4371			1.26821			0.634106	−	0.773246i	$-0.281368\pi$
$967$	39.4371			1.26821			0.634106	+	0.773246i	$0.281368\pi$
$968$	−4.68131	+	14.4076i	−0.150463	+	0.463077i
$969$	−5.74260	−	17.6739i	−0.184479	−	0.567767i
$970$	−3.90370	−	12.0144i	−0.125340	−	0.385758i
$971$	32.0663	−	23.2975i	1.02906	−	0.747652i	0.0609359	−	0.998142i	$-0.480591\pi$
$971$	32.0663	−	23.2975i	1.02906	−	0.747652i	0.968119	+	0.250489i	$0.0805915\pi$
$972$	−19.9235	+	61.3183i	−0.639047	+	1.96679i
$973$	−75.5547	+	54.8937i	−2.42217	+	1.75981i
$974$	−37.4308	−	27.1951i	−1.19936	−	0.871387i
$975$	−0.798430	−	2.45731i	−0.0255702	−	0.0786970i
$976$	−31.7935	−	23.0993i	−1.01768	−	0.739391i
$977$	−24.7906	−	18.0114i	−0.793121	−	0.576236i	0.115767	−	0.993276i	$-0.463067\pi$
$977$	−24.7906	−	18.0114i	−0.793121	−	0.576236i	−0.908888	+	0.417040i	$0.863067\pi$
$978$	9.52985	+	29.3299i	0.304731	+	0.937866i
$979$	−7.74592	−	5.62774i	−0.247561	−	0.179863i
$980$	38.3762	−	27.8820i	1.22588	−	0.890657i
$981$	−11.5629	+	35.5871i	−0.369176	+	1.13621i
$982$	26.6827	−	19.3861i	0.851480	−	0.618637i
$983$	0.589619	+	1.81466i	0.0188059	+	0.0578787i	0.960019	−	0.279935i	$-0.0903128\pi$
$983$	0.589619	+	1.81466i	0.0188059	+	0.0578787i	−0.941213	+	0.337813i	$0.890313\pi$
$984$	−1.88237	−	5.79334i	−0.0600077	−	0.184685i
$985$	4.92921	−	15.1705i	0.157058	−	0.483373i
$986$	9.87764			0.314568
$987$	2.53807			0.0807875
$988$	−30.7328	+	94.5858i	−0.977741	+	3.00918i
$989$	−4.59802	−	3.34066i	−0.146209	−	0.106227i
$990$	−17.8135	+	12.9422i	−0.566149	+	0.411331i
$991$	3.11839			0.0990590			0.0495295	−	0.998773i	$-0.484228\pi$
$991$	3.11839			0.0990590			0.0495295	+	0.998773i	$0.484228\pi$
$992$	5.88076	+	2.82396i	0.186714	+	0.0896609i
$993$	9.38124			0.297705
$994$	63.7793	−	46.3384i	2.02296	−	1.46976i
$995$	11.8937	+	8.64129i	0.377056	+	0.273947i
$996$	−13.6882	+	42.1279i	−0.433726	+	1.33487i
$997$	10.2924			0.325965			0.162982	−	0.986629i	$-0.447889\pi$
$997$	10.2924			0.325965			0.162982	+	0.986629i	$0.447889\pi$
$998$	107.297			3.39641
$999$	−0.204739	+	0.630123i	−0.00647767	+	0.0199362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.h.b.16.6	✓	24
5.2	odd	4		775.2.bf.c.574.11		48
5.3	odd	4		775.2.bf.c.574.2		48
5.4	even	2		775.2.k.d.326.1		24
31.2	even	5	inner	155.2.h.b.126.6	yes	24
31.8	even	5		4805.2.a.u.1.2		12
31.23	odd	10		4805.2.a.v.1.2		12
155.2	odd	20		775.2.bf.c.374.2		48
155.33	odd	20		775.2.bf.c.374.11		48
155.64	even	10		775.2.k.d.126.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.h.b.16.6	✓	24	1.1	even	1	trivial
155.2.h.b.126.6	yes	24	31.2	even	5	inner
775.2.k.d.126.1		24	155.64	even	10
775.2.k.d.326.1		24	5.4	even	2
775.2.bf.c.374.2		48	155.2	odd	20
775.2.bf.c.374.11		48	155.33	odd	20
775.2.bf.c.574.2		48	5.3	odd	4
775.2.bf.c.574.11		48	5.2	odd	4
4805.2.a.u.1.2		12	31.8	even	5
4805.2.a.v.1.2		12	31.23	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:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00060 - 1.45352i) q^{2} +(0.632602 + 0.459612i) q^{3} +(1.27165 - 3.91373i) q^{4} -1.00000 q^{5} +1.93364 q^{6} +(-1.33011 + 4.09364i) q^{7} +(-1.61631 - 4.97449i) q^{8} +(-0.738109 - 2.27167i) q^{9} +O(q^{10})\)	\(q+(2.00060 - 1.45352i) q^{2} +(0.632602 + 0.459612i) q^{3} +(1.27165 - 3.91373i) q^{4} -1.00000 q^{5} +1.93364 q^{6} +(-1.33011 + 4.09364i) q^{7} +(-1.61631 - 4.97449i) q^{8} +(-0.738109 - 2.27167i) q^{9} +(-2.00060 + 1.45352i) q^{10} +(-1.15195 + 3.54532i) q^{11} +(2.60325 - 1.89137i) q^{12} +(-2.67324 - 1.94223i) q^{13} +(3.28919 + 10.1231i) q^{14} +(-0.632602 - 0.459612i) q^{15} +(-3.80569 - 2.76500i) q^{16} +(-1.00411 - 3.09033i) q^{17} +(-4.77858 - 3.47184i) q^{18} +(5.91714 - 4.29905i) q^{19} +(-1.27165 + 3.91373i) q^{20} +(-2.72292 + 1.97832i) q^{21} +(2.84862 + 8.76716i) q^{22} +(2.01811 + 6.21110i) q^{23} +(1.26386 - 3.88975i) q^{24} +1.00000 q^{25} -8.17117 q^{26} +(1.30205 - 4.00731i) q^{27} +(14.3300 + 10.4113i) q^{28} +(-0.994509 + 0.722553i) q^{29} -1.93364 q^{30} +(-5.01907 - 2.41018i) q^{31} -1.17168 q^{32} +(-2.35820 + 1.71333i) q^{33} +(-6.50069 - 4.72303i) q^{34} +(1.33011 - 4.09364i) q^{35} -9.82930 q^{36} -0.157243 q^{37} +(5.58907 - 17.2014i) q^{38} +(-0.798430 - 2.45731i) q^{39} +(1.61631 + 4.97449i) q^{40} +(1.20494 - 0.875439i) q^{41} +(-2.57195 + 7.91565i) q^{42} +(-0.704059 + 0.511528i) q^{43} +(12.4106 + 9.01681i) q^{44} +(0.738109 + 2.27167i) q^{45} +(13.0654 + 9.49258i) q^{46} +(-0.610075 - 0.443246i) q^{47} +(-1.13666 - 3.49828i) q^{48} +(-9.32562 - 6.77546i) q^{49} +(2.00060 - 1.45352i) q^{50} +(0.785153 - 2.41645i) q^{51} +(-11.0008 + 7.99253i) q^{52} +(3.95496 + 12.1721i) q^{53} +(-3.21982 - 9.90960i) q^{54} +(1.15195 - 3.54532i) q^{55} +22.5136 q^{56} +5.71909 q^{57} +(-0.939370 + 2.89108i) q^{58} +(-5.45570 - 3.96380i) q^{59} +(-2.60325 + 1.89137i) q^{60} +8.35420 q^{61} +(-13.5444 + 2.47352i) q^{62} +10.2812 q^{63} +(5.26731 - 3.82692i) q^{64} +(2.67324 + 1.94223i) q^{65} +(-2.22745 + 6.85539i) q^{66} -1.93853 q^{67} -13.3716 q^{68} +(-1.57804 + 4.85671i) q^{69} +(-3.28919 - 10.1231i) q^{70} +(-2.28875 - 7.04404i) q^{71} +(-10.1074 + 7.34343i) q^{72} +(1.97141 - 6.06738i) q^{73} +(-0.314581 + 0.228557i) q^{74} +(0.632602 + 0.459612i) q^{75} +(-9.30082 - 28.6250i) q^{76} +(-12.9811 - 9.43131i) q^{77} +(-5.16910 - 3.75557i) q^{78} +(-1.31037 - 4.03290i) q^{79} +(3.80569 + 2.76500i) q^{80} +(-3.13169 + 2.27531i) q^{81} +(1.13813 - 3.50281i) q^{82} +(-11.1369 + 8.09141i) q^{83} +(4.28000 + 13.1725i) q^{84} +(1.00411 + 3.09033i) q^{85} +(-0.665023 + 2.04673i) q^{86} -0.961224 q^{87} +19.4981 q^{88} +(-0.793685 + 2.44271i) q^{89} +(4.77858 + 3.47184i) q^{90} +(11.5065 - 8.35995i) q^{91} +26.8749 q^{92} +(-2.06733 - 3.83151i) q^{93} -1.86479 q^{94} +(-5.91714 + 4.29905i) q^{95} +(-0.741209 - 0.538520i) q^{96} +(-1.57861 + 4.85845i) q^{97} -28.5052 q^{98} +8.90405 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 6 q^{4} - 24 q^{5} - 16 q^{6} - 9 q^{7} + 11 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 6 * q^4 - 24 * q^5 - 16 * q^6 - 9 * q^7 + 11 * q^8 - 6 * q^9	\( 24 q + 2 q^{2} - 6 q^{4} - 24 q^{5} - 16 q^{6} - 9 q^{7} + 11 q^{8} - 6 q^{9} - 2 q^{10} + q^{11} + 18 q^{12} - 5 q^{13} + 6 q^{14} - 24 q^{16} + 7 q^{17} - 18 q^{18} + 2 q^{19} + 6 q^{20} - 10 q^{21} + 28 q^{22} - 15 q^{23} - 32 q^{24} + 24 q^{25} + 22 q^{26} + 9 q^{27} + 38 q^{28} + 15 q^{29} + 16 q^{30} + 6 q^{31} + 74 q^{32} + 5 q^{33} - 20 q^{34} + 9 q^{35} - 58 q^{36} - 56 q^{37} - 21 q^{38} - 10 q^{39} - 11 q^{40} - 24 q^{41} - 38 q^{42} + 21 q^{43} + 41 q^{44} + 6 q^{45} + 48 q^{46} - 8 q^{47} - 26 q^{48} - 23 q^{49} + 2 q^{50} + 26 q^{51} - 27 q^{52} + 26 q^{53} + 11 q^{54} - q^{55} - 48 q^{56} + 62 q^{57} + 52 q^{58} + 10 q^{59} - 18 q^{60} - 40 q^{61} - 28 q^{62} + 26 q^{63} + 9 q^{64} + 5 q^{65} - 2 q^{66} - 26 q^{67} - 8 q^{68} + 64 q^{69} - 6 q^{70} - 7 q^{71} - 127 q^{72} - 51 q^{73} - q^{74} + 43 q^{76} - 39 q^{77} - 31 q^{78} + 31 q^{79} + 24 q^{80} + 34 q^{81} + 58 q^{82} + 6 q^{83} + 113 q^{84} - 7 q^{85} - 22 q^{86} + 4 q^{87} - 28 q^{88} + 13 q^{89} + 18 q^{90} + 54 q^{91} - 2 q^{92} - 72 q^{93} - 10 q^{94} - 2 q^{95} + 101 q^{96} - 39 q^{97} - 220 q^{98} - 170 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 6 * q^4 - 24 * q^5 - 16 * q^6 - 9 * q^7 + 11 * q^8 - 6 * q^9 - 2 * q^10 + q^11 + 18 * q^12 - 5 * q^13 + 6 * q^14 - 24 * q^16 + 7 * q^17 - 18 * q^18 + 2 * q^19 + 6 * q^20 - 10 * q^21 + 28 * q^22 - 15 * q^23 - 32 * q^24 + 24 * q^25 + 22 * q^26 + 9 * q^27 + 38 * q^28 + 15 * q^29 + 16 * q^30 + 6 * q^31 + 74 * q^32 + 5 * q^33 - 20 * q^34 + 9 * q^35 - 58 * q^36 - 56 * q^37 - 21 * q^38 - 10 * q^39 - 11 * q^40 - 24 * q^41 - 38 * q^42 + 21 * q^43 + 41 * q^44 + 6 * q^45 + 48 * q^46 - 8 * q^47 - 26 * q^48 - 23 * q^49 + 2 * q^50 + 26 * q^51 - 27 * q^52 + 26 * q^53 + 11 * q^54 - q^55 - 48 * q^56 + 62 * q^57 + 52 * q^58 + 10 * q^59 - 18 * q^60 - 40 * q^61 - 28 * q^62 + 26 * q^63 + 9 * q^64 + 5 * q^65 - 2 * q^66 - 26 * q^67 - 8 * q^68 + 64 * q^69 - 6 * q^70 - 7 * q^71 - 127 * q^72 - 51 * q^73 - q^74 + 43 * q^76 - 39 * q^77 - 31 * q^78 + 31 * q^79 + 24 * q^80 + 34 * q^81 + 58 * q^82 + 6 * q^83 + 113 * q^84 - 7 * q^85 - 22 * q^86 + 4 * q^87 - 28 * q^88 + 13 * q^89 + 18 * q^90 + 54 * q^91 - 2 * q^92 - 72 * q^93 - 10 * q^94 - 2 * q^95 + 101 * q^96 - 39 * q^97 - 220 * q^98 - 170 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more