LMFDB - Embedded newform 273.2.j.c.172.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(100,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("273.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.4
Root			$0.613260 + 1.06220i$ of defining polynomial
Character	$\chi$	$=$	273.172
Dual form			273.2.j.c.100.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.613260 + 1.06220i) q^{2} +1.00000 q^{3} +(0.247823 + 0.429243i) q^{4} +(-2.10660 - 3.64874i) q^{5} +(-0.613260 + 1.06220i) q^{6} +(2.23241 - 1.41998i) q^{7} -3.06096 q^{8} +1.00000 q^{9} +5.16759 q^{10} +5.52538 q^{11} +(0.247823 + 0.429243i) q^{12} +(3.59845 + 0.226101i) q^{13} +(0.139251 + 3.24208i) q^{14} +(-2.10660 - 3.64874i) q^{15} +(1.38152 - 2.39286i) q^{16} +(-0.0891447 - 0.154403i) q^{17} +(-0.613260 + 1.06220i) q^{18} -4.51901 q^{19} +(1.04413 - 1.80849i) q^{20} +(2.23241 - 1.41998i) q^{21} +(-3.38850 + 5.86905i) q^{22} +(-0.543523 + 0.941410i) q^{23} -3.06096 q^{24} +(-6.37556 + 11.0428i) q^{25} +(-2.44695 + 3.68361i) q^{26} +1.00000 q^{27} +(1.16276 + 0.606342i) q^{28} +(-0.0731926 - 0.126773i) q^{29} +5.16759 q^{30} +(4.19459 - 7.26525i) q^{31} +(-1.36650 - 2.36685i) q^{32} +5.52538 q^{33} +0.218676 q^{34} +(-9.88395 - 5.15416i) q^{35} +(0.247823 + 0.429243i) q^{36} +(-2.15922 + 3.73988i) q^{37} +(2.77133 - 4.80008i) q^{38} +(3.59845 + 0.226101i) q^{39} +(6.44824 + 11.1687i) q^{40} +(0.782385 + 1.35513i) q^{41} +(0.139251 + 3.24208i) q^{42} +(-1.66752 + 2.88823i) q^{43} +(1.36932 + 2.37173i) q^{44} +(-2.10660 - 3.64874i) q^{45} +(-0.666643 - 1.15466i) q^{46} +(0.636455 + 1.10237i) q^{47} +(1.38152 - 2.39286i) q^{48} +(2.96732 - 6.33996i) q^{49} +(-7.81976 - 13.5442i) q^{50} +(-0.0891447 - 0.154403i) q^{51} +(0.794729 + 1.60064i) q^{52} +(-3.93930 + 6.82307i) q^{53} +(-0.613260 + 1.06220i) q^{54} +(-11.6398 - 20.1607i) q^{55} +(-6.83333 + 4.34650i) q^{56} -4.51901 q^{57} +0.179545 q^{58} +(1.01059 + 1.75040i) q^{59} +(1.04413 - 1.80849i) q^{60} -3.76557 q^{61} +(5.14476 + 8.91098i) q^{62} +(2.23241 - 1.41998i) q^{63} +8.87816 q^{64} +(-6.75553 - 13.6061i) q^{65} +(-3.38850 + 5.86905i) q^{66} -0.307378 q^{67} +(0.0441842 - 0.0765294i) q^{68} +(-0.543523 + 0.941410i) q^{69} +(11.5362 - 7.33787i) q^{70} +(-1.62940 + 2.82220i) q^{71} -3.06096 q^{72} +(-3.53172 + 6.11712i) q^{73} +(-2.64833 - 4.58704i) q^{74} +(-6.37556 + 11.0428i) q^{75} +(-1.11992 - 1.93975i) q^{76} +(12.3349 - 7.84593i) q^{77} +(-2.44695 + 3.68361i) q^{78} +(-2.30707 - 3.99596i) q^{79} -11.6413 q^{80} +1.00000 q^{81} -1.91922 q^{82} -8.85136 q^{83} +(1.16276 + 0.606342i) q^{84} +(-0.375585 + 0.650532i) q^{85} +(-2.04525 - 3.54248i) q^{86} +(-0.0731926 - 0.126773i) q^{87} -16.9130 q^{88} +(-6.59852 + 11.4290i) q^{89} +5.16759 q^{90} +(8.35429 - 4.60498i) q^{91} -0.538791 q^{92} +(4.19459 - 7.26525i) q^{93} -1.56125 q^{94} +(9.51976 + 16.4887i) q^{95} +(-1.36650 - 2.36685i) q^{96} +(1.17499 - 2.03514i) q^{97} +(4.91455 + 7.03992i) q^{98} +5.52538 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) $ 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.613260	+	1.06220i	−0.433641	+	0.751088i	−0.997184	−	0.0749992i	$-0.976105\pi$
$2$	−0.613260	+	1.06220i	−0.433641	+	0.751088i	0.563543	+	0.826087i	$0.309438\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.247823	+	0.429243i	0.123912	+	0.214621i
$5$	−2.10660	−	3.64874i	−0.942102	−	1.63177i	−0.761452	−	0.648221i	$-0.775513\pi$
$5$	−2.10660	−	3.64874i	−0.942102	−	1.63177i	−0.180649	−	0.983548i	$-0.557820\pi$
$6$	−0.613260	+	1.06220i	−0.250363	+	0.433641i
$7$	2.23241	−	1.41998i	0.843772	−	0.536702i
$7$	2.23241	−	1.41998i	0.843772	−	0.536702i
$8$	−3.06096			−1.08221
$9$	1.00000			0.333333
$10$	5.16759			1.63413
$11$	5.52538			1.66596			0.832982	−	0.553300i	$-0.186632\pi$
$11$	5.52538			1.66596			0.832982	+	0.553300i	$0.186632\pi$
$12$	0.247823	+	0.429243i	0.0715404	+	0.123912i
$13$	3.59845	+	0.226101i	0.998032	+	0.0627091i
$13$	3.59845	+	0.226101i	0.998032	+	0.0627091i
$14$	0.139251	+	3.24208i	0.0372163	+	0.866482i
$15$	−2.10660	−	3.64874i	−0.543923	−	0.942102i
$16$	1.38152	−	2.39286i	0.345380	−	0.598216i
$17$	−0.0891447	−	0.154403i	−0.0216208	−	0.0374482i	0.855013	−	0.518607i	$-0.173549\pi$
$17$	−0.0891447	−	0.154403i	−0.0216208	−	0.0374482i	−0.876633	+	0.481159i	$0.840216\pi$
$18$	−0.613260	+	1.06220i	−0.144547	+	0.250363i
$19$	−4.51901			−1.03673			−0.518366	−	0.855159i	$-0.673459\pi$
$19$	−4.51901			−1.03673			−0.518366	+	0.855159i	$0.673459\pi$
$20$	1.04413	−	1.80849i	0.233475	−	0.404390i
$21$	2.23241	−	1.41998i	0.487152	−	0.309865i
$22$	−3.38850	+	5.86905i	−0.722430	+	1.25129i
$23$	−0.543523	+	0.941410i	−0.113332	+	0.196298i	−0.917112	−	0.398630i	$-0.869486\pi$
$23$	−0.543523	+	0.941410i	−0.113332	+	0.196298i	0.803779	+	0.594927i	$0.202819\pi$
$24$	−3.06096			−0.624816
$25$	−6.37556	+	11.0428i	−1.27511	+	2.20856i
$26$	−2.44695	+	3.68361i	−0.479887	+	0.722416i
$27$	1.00000			0.192450
$28$	1.16276	+	0.606342i	0.219741	+	0.114588i
$29$	−0.0731926	−	0.126773i	−0.0135915	−	0.0235412i	0.859150	−	0.511724i	$-0.170993\pi$
$29$	−0.0731926	−	0.126773i	−0.0135915	−	0.0235412i	−0.872741	+	0.488183i	$0.837660\pi$
$30$	5.16759			0.943468
$31$	4.19459	−	7.26525i	0.753371	−	1.30488i	−0.192809	−	0.981236i	$-0.561760\pi$
$31$	4.19459	−	7.26525i	0.753371	−	1.30488i	0.946180	−	0.323641i	$-0.104907\pi$
$32$	−1.36650	−	2.36685i	−0.241565	−	0.418403i
$33$	5.52538			0.961845
$34$	0.218676			0.0375026
$35$	−9.88395	−	5.15416i	−1.67069	−	0.871213i
$36$	0.247823	+	0.429243i	0.0413039	+	0.0715404i
$37$	−2.15922	+	3.73988i	−0.354973	+	0.614832i	−0.987113	−	0.160022i	$-0.948843\pi$
$37$	−2.15922	+	3.73988i	−0.354973	+	0.614832i	0.632140	+	0.774854i	$0.282177\pi$
$38$	2.77133	−	4.80008i	0.449569	−	0.778676i
$39$	3.59845	+	0.226101i	0.576214	+	0.0362051i
$40$	6.44824	+	11.1687i	1.01956	+	1.76592i
$41$	0.782385	+	1.35513i	0.122188	+	0.211636i	0.920630	−	0.390436i	$-0.127676\pi$
$41$	0.782385	+	1.35513i	0.122188	+	0.211636i	−0.798442	+	0.602071i	$0.794342\pi$
$42$	0.139251	+	3.24208i	0.0214869	+	0.500264i
$43$	−1.66752	+	2.88823i	−0.254295	+	0.440452i	−0.964704	−	0.263338i	$-0.915177\pi$
$43$	−1.66752	+	2.88823i	−0.254295	+	0.440452i	0.710409	+	0.703789i	$0.248510\pi$
$44$	1.36932	+	2.37173i	0.206432	+	0.357551i
$45$	−2.10660	−	3.64874i	−0.314034	−	0.543923i
$46$	−0.666643	−	1.15466i	−0.0982911	−	0.170245i
$47$	0.636455	+	1.10237i	0.0928365	+	0.160798i	0.908704	−	0.417442i	$-0.137073\pi$
$47$	0.636455	+	1.10237i	0.0928365	+	0.160798i	−0.815867	+	0.578239i	$0.803740\pi$
$48$	1.38152	−	2.39286i	0.199405	−	0.345380i
$49$	2.96732	−	6.33996i	0.423902	−	0.905708i
$50$	−7.81976	−	13.5442i	−1.10588	−	1.91544i
$51$	−0.0891447	−	0.154403i	−0.0124827	−	0.0216208i
$52$	0.794729	+	1.60064i	0.110209	+	0.221969i
$53$	−3.93930	+	6.82307i	−0.541105	+	0.937221i	0.457736	+	0.889088i	$0.348660\pi$
$53$	−3.93930	+	6.82307i	−0.541105	+	0.937221i	−0.998841	+	0.0481326i	$0.984673\pi$
$54$	−0.613260	+	1.06220i	−0.0834542	+	0.144547i
$55$	−11.6398	−	20.1607i	−1.56951	−	2.71847i
$56$	−6.83333	+	4.34650i	−0.913142	+	0.580826i
$57$	−4.51901			−0.598557
$58$	0.179545			0.0235753
$59$	1.01059	+	1.75040i	0.131568	+	0.227883i	0.924281	−	0.381712i	$-0.124665\pi$
$59$	1.01059	+	1.75040i	0.131568	+	0.227883i	−0.792713	+	0.609595i	$0.791332\pi$
$60$	1.04413	−	1.80849i	0.134797	−	0.233475i
$61$	−3.76557			−0.482132			−0.241066	−	0.970509i	$-0.577497\pi$
$61$	−3.76557			−0.482132			−0.241066	+	0.970509i	$0.577497\pi$
$62$	5.14476	+	8.91098i	0.653385	+	1.13170i
$63$	2.23241	−	1.41998i	0.281257	−	0.178901i
$64$	8.87816			1.10977
$65$	−6.75553	−	13.6061i	−0.837921	−	1.68764i
$66$	−3.38850	+	5.86905i	−0.417095	+	0.722430i
$67$	−0.307378			−0.0375522			−0.0187761	−	0.999824i	$-0.505977\pi$
$67$	−0.307378			−0.0375522			−0.0187761	+	0.999824i	$0.505977\pi$
$68$	0.0441842	−	0.0765294i	0.00535813	−	0.00928055i
$69$	−0.543523	+	0.941410i	−0.0654325	+	0.113332i
$70$	11.5362	−	7.33787i	1.37884	−	0.877043i
$71$	−1.62940	+	2.82220i	−0.193374	+	0.334933i	−0.946366	−	0.323096i	$-0.895276\pi$
$71$	−1.62940	+	2.82220i	−0.193374	+	0.334933i	0.752992	+	0.658029i	$0.228610\pi$
$72$	−3.06096			−0.360738
$73$	−3.53172	+	6.11712i	−0.413356	+	0.715954i	−0.995254	−	0.0973075i	$-0.968977\pi$
$73$	−3.53172	+	6.11712i	−0.413356	+	0.715954i	0.581898	+	0.813262i	$0.302310\pi$
$74$	−2.64833	−	4.58704i	−0.307862	−	0.533232i
$75$	−6.37556	+	11.0428i	−0.736186	+	1.27511i
$76$	−1.11992	−	1.93975i	−0.128463	−	0.222505i
$77$	12.3349	−	7.84593i	1.40569	−	0.894126i
$78$	−2.44695	+	3.68361i	−0.277063	+	0.417087i
$79$	−2.30707	−	3.99596i	−0.259566	−	0.449581i	0.706560	−	0.707653i	$-0.250246\pi$
$79$	−2.30707	−	3.99596i	−0.259566	−	0.449581i	−0.966126	+	0.258072i	$0.916913\pi$
$80$	−11.6413			−1.30153
$81$	1.00000			0.111111
$82$	−1.91922			−0.211943
$83$	−8.85136			−0.971563			−0.485782	−	0.874080i	$-0.661465\pi$
$83$	−8.85136			−0.971563			−0.485782	+	0.874080i	$0.661465\pi$
$84$	1.16276	+	0.606342i	0.126867	+	0.0661573i
$85$	−0.375585	+	0.650532i	−0.0407379	+	0.0705601i
$86$	−2.04525	−	3.54248i	−0.220545	−	0.381995i
$87$	−0.0731926	−	0.126773i	−0.00784707	−	0.0135915i
$88$	−16.9130			−1.80293
$89$	−6.59852	+	11.4290i	−0.699442	+	1.21147i	0.269219	+	0.963079i	$0.413235\pi$
$89$	−6.59852	+	11.4290i	−0.699442	+	1.21147i	−0.968660	+	0.248389i	$0.920099\pi$
$90$	5.16759			0.544712
$91$	8.35429	−	4.60498i	0.875767	−	0.482733i
$92$	−0.538791			−0.0561729
$93$	4.19459	−	7.26525i	0.434959	−	0.753371i
$94$	−1.56125			−0.161031
$95$	9.51976	+	16.4887i	0.976707	+	1.69171i
$96$	−1.36650	−	2.36685i	−0.139468	−	0.241565i
$97$	1.17499	−	2.03514i	0.119302	−	0.206637i	−0.800189	−	0.599748i	$-0.795268\pi$
$97$	1.17499	−	2.03514i	0.119302	−	0.206637i	0.919491	+	0.393110i	$0.128601\pi$
$98$	4.91455	+	7.03992i	0.496445	+	0.711139i
$99$	5.52538			0.555322
$100$	−6.32005			−0.632005
$101$	10.1397			1.00894			0.504469	−	0.863430i	$-0.331688\pi$
$101$	10.1397			1.00894			0.504469	+	0.863430i	$0.331688\pi$
$102$	0.218676			0.0216521
$103$	−5.01549	−	8.68709i	−0.494191	−	0.855964i	0.505786	−	0.862659i	$-0.331202\pi$
$103$	−5.01549	−	8.68709i	−0.494191	−	0.855964i	−0.999978	+	0.00669444i	$0.997869\pi$
$104$	−11.0147	−	0.692086i	−1.08008	−	0.0678647i
$105$	−9.88395	−	5.15416i	−0.964575	−	0.502995i
$106$	−4.83163	−	8.36864i	−0.469290	−	0.812834i
$107$	−6.92606	+	11.9963i	−0.669567	+	1.15972i	0.308458	+	0.951238i	$0.400187\pi$
$107$	−6.92606	+	11.9963i	−0.669567	+	1.15972i	−0.978025	+	0.208486i	$0.933146\pi$
$108$	0.247823	+	0.429243i	0.0238468	+	0.0413039i
$109$	0.471229	−	0.816192i	0.0451355	−	0.0781770i	−0.842575	−	0.538579i	$-0.818961\pi$
$109$	0.471229	−	0.816192i	0.0451355	−	0.0781770i	0.887711	+	0.460402i	$0.152295\pi$
$110$	28.5529			2.72241
$111$	−2.15922	+	3.73988i	−0.204944	+	0.354973i
$112$	−0.313697	−	7.30359i	−0.0296415	−	0.690124i
$113$	2.86292	−	4.95873i	0.269321	−	0.466478i	−0.699366	−	0.714764i	$-0.746534\pi$
$113$	2.86292	−	4.95873i	0.269321	−	0.466478i	0.968687	+	0.248286i	$0.0798674\pi$
$114$	2.77133	−	4.80008i	0.259559	−	0.449569i
$115$	4.57995			0.427083
$116$	0.0362777	−	0.0628348i	0.00336830	−	0.00583406i
$117$	3.59845	+	0.226101i	0.332677	+	0.0209030i
$118$	−2.47903			−0.228213
$119$	−0.418257	−	0.218107i	−0.0383415	−	0.0199939i
$120$	6.44824	+	11.1687i	0.588641	+	1.01956i
$121$	19.5298			1.77544
$122$	2.30928	−	3.99979i	0.209072	−	0.362124i
$123$	0.782385	+	1.35513i	0.0705453	+	0.122188i
$124$	4.15807			0.373406
$125$	32.6571			2.92094
$126$	0.139251	+	3.24208i	0.0124054	+	0.288827i
$127$	6.56642	+	11.3734i	0.582676	+	1.00922i	0.995161	+	0.0982595i	$0.0313275\pi$
$127$	6.56642	+	11.3734i	0.582676	+	1.00922i	−0.412485	+	0.910964i	$0.635339\pi$
$128$	−2.71163	+	4.69668i	−0.239676	+	0.415131i
$129$	−1.66752	+	2.88823i	−0.146817	+	0.254295i
$130$	18.5953	+	1.16840i	1.63092	+	0.102475i
$131$	5.95196	+	10.3091i	0.520025	+	0.900710i	0.999729	+	0.0232796i	$0.00741081\pi$
$131$	5.95196	+	10.3091i	0.520025	+	0.900710i	−0.479704	+	0.877431i	$0.659256\pi$
$132$	1.36932	+	2.37173i	0.119184	+	0.206432i
$133$	−10.0883	+	6.41690i	−0.874765	+	0.556416i
$134$	0.188503	−	0.326496i	0.0162842	−	0.0282050i
$135$	−2.10660	−	3.64874i	−0.181308	−	0.314034i
$136$	0.272868	+	0.472622i	0.0233983	+	0.0405270i
$137$	−6.76423	−	11.7160i	−0.577907	−	1.00096i	−0.995719	−	0.0924312i	$-0.970536\pi$
$137$	−6.76423	−	11.7160i	−0.577907	−	1.00096i	0.417812	−	0.908534i	$-0.362797\pi$
$138$	−0.666643	−	1.15466i	−0.0567484	−	0.0982911i
$139$	−10.9150	+	18.9053i	−0.925796	+	1.60353i	−0.135521	+	0.990774i	$0.543271\pi$
$139$	−10.9150	+	18.9053i	−0.925796	+	1.60353i	−0.790275	+	0.612752i	$0.790062\pi$
$140$	−0.237087	−	5.51993i	−0.0200375	−	0.466519i
$141$	0.636455	+	1.10237i	0.0535992	+	0.0928365i
$142$	−1.99849	−	3.46149i	−0.167710	−	0.290481i
$143$	19.8828	+	1.24929i	1.66269	+	0.104471i
$144$	1.38152	−	2.39286i	0.115127	−	0.199405i
$145$	−0.308376	+	0.534122i	−0.0256092	+	0.0443564i
$146$	−4.33173	−	7.50277i	−0.358496	−	0.620934i
$147$	2.96732	−	6.33996i	0.244740	−	0.522911i
$148$	−2.14042			−0.175941
$149$	7.66408			0.627866			0.313933	−	0.949445i	$-0.398353\pi$
$149$	7.66408			0.627866			0.313933	+	0.949445i	$0.398353\pi$
$150$	−7.81976	−	13.5442i	−0.638480	−	1.10588i
$151$	−1.87363	+	3.24522i	−0.152474	+	0.264092i	−0.932136	−	0.362108i	$-0.882057\pi$
$151$	−1.87363	+	3.24522i	−0.152474	+	0.264092i	0.779663	+	0.626200i	$0.215391\pi$
$152$	13.8325			1.12197
$153$	−0.0891447	−	0.154403i	−0.00720692	−	0.0124827i
$154$	0.769413	+	17.9137i	0.0620011	+	1.44353i
$155$	−35.3454			−2.83901
$156$	0.794729	+	1.60064i	0.0636292	+	0.128154i
$157$	1.63089	−	2.82478i	0.130159	−	0.225442i	−0.793579	−	0.608467i	$-0.791785\pi$
$157$	1.63089	−	2.82478i	0.130159	−	0.225442i	0.923738	+	0.383026i	$0.125118\pi$
$158$	5.65934			0.450233
$159$	−3.93930	+	6.82307i	−0.312407	+	0.541105i
$160$	−5.75734	+	9.97201i	−0.455158	+	0.788357i
$161$	0.123416	+	2.87341i	0.00972653	+	0.226456i
$162$	−0.613260	+	1.06220i	−0.0481823	+	0.0834542i
$163$	−10.4509			−0.818576			−0.409288	−	0.912405i	$-0.634223\pi$
$163$	−10.4509			−0.818576			−0.409288	+	0.912405i	$0.634223\pi$
$164$	−0.387787	+	0.671666i	−0.0302810	+	0.0524483i
$165$	−11.6398	−	20.1607i	−0.906156	−	1.56951i
$166$	5.42819	−	9.40190i	0.421309	−	0.729729i
$167$	5.58474	+	9.67305i	0.432160	+	0.748523i	0.997059	−	0.0766369i	$-0.0244182\pi$
$167$	5.58474	+	9.67305i	0.432160	+	0.748523i	−0.564899	+	0.825160i	$0.691085\pi$
$168$	−6.83333	+	4.34650i	−0.527203	+	0.335340i
$169$	12.8978	+	1.62723i	0.992135	+	0.125171i
$170$	−0.460663	−	0.797891i	−0.0353312	−	0.0611955i
$171$	−4.51901			−0.345577
$172$	−1.65300			−0.126040
$173$	−12.7666			−0.970630			−0.485315	−	0.874339i	$-0.661295\pi$
$173$	−12.7666			−0.970630			−0.485315	+	0.874339i	$0.661295\pi$
$174$	0.179545			0.0136112
$175$	1.44767	+	33.7052i	0.109434	+	2.54787i
$176$	7.63343	−	13.2215i	0.575391	−	0.996607i
$177$	1.01059	+	1.75040i	0.0759610	+	0.131568i
$178$	−8.09322	−	14.0179i	−0.606613	−	1.05068i
$179$	−12.5526			−0.938228			−0.469114	−	0.883138i	$-0.655427\pi$
$179$	−12.5526			−0.938228			−0.469114	+	0.883138i	$0.655427\pi$
$180$	1.04413	−	1.80849i	0.0778249	−	0.134797i
$181$	13.6821			1.01698			0.508491	−	0.861067i	$-0.330204\pi$
$181$	13.6821			1.01698			0.508491	+	0.861067i	$0.330204\pi$
$182$	−0.231950	+	11.6980i	−0.0171933	+	0.867111i
$183$	−3.76557			−0.278359
$184$	1.66371	−	2.88162i	0.122650	−	0.212436i
$185$	18.1945			1.33768
$186$	5.14476	+	8.91098i	0.377232	+	0.653385i
$187$	−0.492558	−	0.853136i	−0.0360194	−	0.0623875i
$188$	−0.315457	+	0.546387i	−0.0230070	+	0.0398494i
$189$	2.23241	−	1.41998i	0.162384	−	0.103288i
$190$	−23.3524			−1.69416
$191$	24.4136			1.76650			0.883252	−	0.468899i	$-0.155349\pi$
$191$	24.4136			1.76650			0.883252	+	0.468899i	$0.155349\pi$
$192$	8.87816			0.640726
$193$	−12.5094			−0.900445			−0.450223	−	0.892916i	$-0.648655\pi$
$193$	−12.5094			−0.900445			−0.450223	+	0.892916i	$0.648655\pi$
$194$	1.44115	+	2.49614i	0.103468	+	0.179213i
$195$	−6.75553	−	13.6061i	−0.483774	−	0.974357i
$196$	3.45675	−	0.297491i	0.246911	−	0.0212493i
$197$	−9.75853	−	16.9023i	−0.695266	−	1.20424i	−0.970091	−	0.242742i	$-0.921953\pi$
$197$	−9.75853	−	16.9023i	−0.695266	−	1.20424i	0.274825	−	0.961494i	$-0.411380\pi$
$198$	−3.38850	+	5.86905i	−0.240810	+	0.417095i
$199$	2.39385	+	4.14627i	0.169695	+	0.293921i	0.938313	−	0.345788i	$-0.112388\pi$
$199$	2.39385	+	4.14627i	0.169695	+	0.293921i	−0.768617	+	0.639709i	$0.779055\pi$
$200$	19.5153	−	33.8016i	1.37994	−	2.39013i
$201$	−0.307378			−0.0216808
$202$	−6.21828	+	10.7704i	−0.437517	+	0.757801i
$203$	−0.343411	−	0.179078i	−0.0241028	−	0.0125688i
$204$	0.0441842	−	0.0765294i	0.00309352	−	0.00535813i
$205$	3.29635	−	5.70945i	0.230227	−	0.398765i
$206$	12.3032			0.857206
$207$	−0.543523	+	0.941410i	−0.0377775	+	0.0654325i
$208$	5.51237	−	8.29825i	0.382214	−	0.575380i
$209$	−24.9692			−1.72716
$210$	11.5362	−	7.33787i	0.796072	−	0.506361i
$211$	−2.28135	−	3.95141i	−0.157054	−	0.272026i	0.776751	−	0.629808i	$-0.216866\pi$
$211$	−2.28135	−	3.95141i	−0.157054	−	0.272026i	−0.933805	+	0.357782i	$0.883533\pi$
$212$	−3.90500			−0.268197
$213$	−1.62940	+	2.82220i	−0.111644	+	0.193374i
$214$	−8.49495	−	14.7137i	−0.580703	−	1.00581i
$215$	14.0512			0.958287
$216$	−3.06096			−0.208272
$217$	−0.952450	−	22.1753i	−0.0646565	−	1.50535i
$218$	0.577972	+	1.00108i	0.0391452	+	0.0678015i
$219$	−3.53172	+	6.11712i	−0.238651	+	0.413356i
$220$	5.76922	−	9.99258i	0.388961	−	0.673700i
$221$	−0.285872	−	0.575768i	−0.0192299	−	0.0387304i
$222$	−2.64833	−	4.58704i	−0.177744	−	0.307862i
$223$	−3.76290	−	6.51754i	−0.251983	−	0.436447i	0.712089	−	0.702089i	$-0.247749\pi$
$223$	−3.76290	−	6.51754i	−0.251983	−	0.436447i	−0.964072	+	0.265643i	$0.914416\pi$
$224$	−6.41146	−	3.34337i	−0.428384	−	0.223388i
$225$	−6.37556	+	11.0428i	−0.425037	+	0.736186i
$226$	3.51143	+	6.08198i	0.233577	+	0.404567i
$227$	1.84054	+	3.18791i	0.122161	+	0.211589i	0.920620	−	0.390460i	$-0.127684\pi$
$227$	1.84054	+	3.18791i	0.122161	+	0.211589i	−0.798459	+	0.602050i	$0.794351\pi$
$228$	−1.11992	−	1.93975i	−0.0741682	−	0.128463i
$229$	−2.35083	−	4.07176i	−0.155347	−	0.269069i	0.777838	−	0.628465i	$-0.216316\pi$
$229$	−2.35083	−	4.07176i	−0.155347	−	0.269069i	−0.933185	+	0.359395i	$0.882983\pi$
$230$	−2.80871	+	4.86482i	−0.185201	+	0.320777i
$231$	12.3349	−	7.84593i	0.811578	−	0.516224i
$232$	0.224040	+	0.388048i	0.0147089	+	0.0254766i
$233$	1.20491	+	2.08697i	0.0789365	+	0.136722i	0.902791	−	0.430079i	$-0.141514\pi$
$233$	1.20491	+	2.08697i	0.0789365	+	0.136722i	−0.823855	+	0.566801i	$0.808181\pi$
$234$	−2.44695	+	3.68361i	−0.159962	+	0.240805i
$235$	2.68152	−	4.64452i	0.174923	−	0.302975i
$236$	−0.500898	+	0.867581i	−0.0326057	+	0.0564747i
$237$	−2.30707	−	3.99596i	−0.149860	−	0.259566i
$238$	0.488174	−	0.310515i	0.0316436	−	0.0201277i
$239$	7.96050			0.514922			0.257461	−	0.966289i	$-0.417114\pi$
$239$	7.96050			0.514922			0.257461	+	0.966289i	$0.417114\pi$
$240$	−11.6413			−0.751441
$241$	−14.9378	−	25.8730i	−0.962225	−	1.66662i	−0.716892	−	0.697185i	$-0.754436\pi$
$241$	−14.9378	−	25.8730i	−0.962225	−	1.66662i	−0.245334	−	0.969439i	$-0.578898\pi$
$242$	−11.9769	+	20.7445i	−0.769902	+	1.33351i
$243$	1.00000			0.0641500
$244$	−0.933197	−	1.61634i	−0.0597418	−	0.103476i
$245$	−29.3838	+	2.52880i	−1.87726	+	0.161559i
$246$	−1.91922			−0.122365
$247$	−16.2614	−	1.02175i	−1.03469	−	0.0650125i
$248$	−12.8395	+	22.2387i	−0.815309	+	1.41216i
$249$	−8.85136			−0.560932
$250$	−20.0273	+	34.6883i	−1.26664	+	2.19388i
$251$	11.1062	−	19.2366i	0.701019	−	1.21420i	−0.267090	−	0.963672i	$-0.586062\pi$
$251$	11.1062	−	19.2366i	0.701019	−	1.21420i	0.968109	−	0.250529i	$-0.0806045\pi$
$252$	1.16276	+	0.606342i	0.0732469	+	0.0381959i
$253$	−3.00317	+	5.20165i	−0.188808	+	0.327025i
$254$	−16.1077			−1.01069
$255$	−0.375585	+	0.650532i	−0.0235200	+	0.0407379i
$256$	5.55229	+	9.61685i	0.347018	+	0.601053i
$257$	1.61677	−	2.80033i	0.100851	−	0.174680i	−0.811184	−	0.584791i	$-0.801177\pi$
$257$	1.61677	−	2.80033i	0.100851	−	0.174680i	0.912036	+	0.410111i	$0.134510\pi$
$258$	−2.04525	−	3.54248i	−0.127332	−	0.220545i
$259$	0.490285	+	11.4150i	0.0304649	+	0.709293i
$260$	4.16616	−	6.27168i	0.258374	−	0.388953i
$261$	−0.0731926	−	0.126773i	−0.00453051	−	0.00784707i
$262$	−14.6004			−0.902016
$263$	7.48246			0.461388			0.230694	−	0.973026i	$-0.425900\pi$
$263$	7.48246			0.461388			0.230694	+	0.973026i	$0.425900\pi$
$264$	−16.9130			−1.04092
$265$	33.1942			2.03910
$266$	−0.629275	−	14.6510i	−0.0385833	−	0.898310i
$267$	−6.59852	+	11.4290i	−0.403823	+	0.699442i
$268$	−0.0761754	−	0.131940i	−0.00465316	−	0.00805950i
$269$	1.51589	+	2.62560i	0.0924253	+	0.160085i	0.908531	−	0.417817i	$-0.137205\pi$
$269$	1.51589	+	2.62560i	0.0924253	+	0.160085i	−0.816106	+	0.577902i	$0.803871\pi$
$270$	5.16759			0.314489
$271$	10.8080	−	18.7200i	0.656540	−	1.13716i	−0.324965	−	0.945726i	$-0.605352\pi$
$271$	10.8080	−	18.7200i	0.656540	−	1.13716i	0.981505	−	0.191435i	$-0.0613142\pi$
$272$	−0.492621			−0.0298695
$273$	8.35429	−	4.60498i	0.505625	−	0.278706i
$274$	16.5929			1.00242
$275$	−35.2274	+	61.0156i	−2.12429	+	3.67938i
$276$	−0.538791			−0.0324314
$277$	4.75341	+	8.23314i	0.285604	+	0.494681i	0.972756	−	0.231833i	$-0.0744723\pi$
$277$	4.75341	+	8.23314i	0.285604	+	0.494681i	−0.687151	+	0.726514i	$0.741139\pi$
$278$	−13.3874	−	23.1877i	−0.802926	−	1.39071i
$279$	4.19459	−	7.26525i	0.251124	−	0.434959i
$280$	30.2544	+	15.7767i	1.80805	+	0.942838i
$281$	31.6740			1.88951			0.944757	−	0.327771i	$-0.106297\pi$
$281$	31.6740			1.88951			0.944757	+	0.327771i	$0.106297\pi$
$282$	−1.56125			−0.0929711
$283$	−14.5144			−0.862792			−0.431396	−	0.902163i	$-0.641979\pi$
$283$	−14.5144			−0.862792			−0.431396	+	0.902163i	$0.641979\pi$
$284$	−1.61521			−0.0958451
$285$	9.51976	+	16.4887i	0.563902	+	0.976707i
$286$	−13.5203	+	20.3534i	−0.799475	+	1.20352i
$287$	3.67086	+	1.91424i	0.216684	+	0.112994i
$288$	−1.36650	−	2.36685i	−0.0805217	−	0.139468i
$289$	8.48411	−	14.6949i	0.499065	−	0.864406i
$290$	−0.378229	−	0.655112i	−0.0222104	−	0.0384695i
$291$	1.17499	−	2.03514i	0.0688791	−	0.119302i
$292$	−3.50097			−0.204879
$293$	−10.3725	+	17.9658i	−0.605970	+	1.04957i	0.385927	+	0.922529i	$0.373882\pi$
$293$	−10.3725	+	17.9658i	−0.605970	+	1.04957i	−0.991897	+	0.127042i	$0.959452\pi$
$294$	4.91455	+	7.03992i	0.286623	+	0.410577i
$295$	4.25785	−	7.37481i	0.247901	−	0.429378i
$296$	6.60929	−	11.4476i	0.384157	−	0.665379i
$297$	5.52538			0.320615
$298$	−4.70008	+	8.14078i	−0.272268	+	0.471583i
$299$	−2.16870	+	3.26473i	−0.125419	+	0.188804i
$300$	−6.32005			−0.364888
$301$	0.378638	+	8.81557i	0.0218243	+	0.508121i
$302$	−2.29804	−	3.98033i	−0.132237	−	0.229042i
$303$	10.1397			0.582511
$304$	−6.24310	+	10.8134i	−0.358067	+	0.620189i
$305$	7.93257	+	13.7396i	0.454218	+	0.786728i
$306$	0.218676			0.0125009
$307$	13.9276			0.794892			0.397446	−	0.917625i	$-0.369897\pi$
$307$	13.9276			0.794892			0.397446	+	0.917625i	$0.369897\pi$
$308$	6.42468	+	3.35027i	0.366080	+	0.190899i
$309$	−5.01549	−	8.68709i	−0.285321	−	0.494191i
$310$	21.6759	−	37.5438i	1.23111	−	2.13234i
$311$	−2.28996	+	3.96633i	−0.129852	+	0.224910i	−0.923619	−	0.383312i	$-0.874784\pi$
$311$	−2.28996	+	3.96633i	−0.129852	+	0.224910i	0.793767	+	0.608222i	$0.208117\pi$
$312$	−11.0147	−	0.692086i	−0.623587	−	0.0391817i
$313$	6.75197	+	11.6948i	0.381644	+	0.661026i	0.991297	−	0.131642i	$-0.0420248\pi$
$313$	6.75197	+	11.6948i	0.381644	+	0.661026i	−0.609654	+	0.792668i	$0.708691\pi$
$314$	2.00032	+	3.46465i	0.112884	+	0.195521i
$315$	−9.88395	−	5.15416i	−0.556897	−	0.290404i
$316$	1.14349	−	1.98059i	0.0643264	−	0.111417i
$317$	2.86564	+	4.96343i	0.160950	+	0.278774i	0.935210	−	0.354094i	$-0.115211\pi$
$317$	2.86564	+	4.96343i	0.160950	+	0.278774i	−0.774259	+	0.632868i	$0.781877\pi$
$318$	−4.83163	−	8.36864i	−0.270945	−	0.469290i
$319$	−0.404417	−	0.700471i	−0.0226430	−	0.0392188i
$320$	−18.7028	−	32.3941i	−1.04552	−	1.81089i
$321$	−6.92606	+	11.9963i	−0.386575	+	0.669567i
$322$	−3.12781	−	1.63105i	−0.174306	−	0.0908951i
$323$	0.402845	+	0.697749i	0.0224149	+	0.0388238i
$324$	0.247823	+	0.429243i	0.0137680	+	0.0238468i
$325$	−25.4390	+	38.2955i	−1.41110	+	2.12425i
$326$	6.40911	−	11.1009i	0.354968	−	0.614822i
$327$	0.471229	−	0.816192i	0.0260590	−	0.0451355i
$328$	−2.39485	−	4.14801i	−0.132234	−	0.229035i
$329$	2.98618	+	1.55719i	0.164633	+	0.0858509i
$330$	28.5529			1.57178
$331$	−24.5183			−1.34765			−0.673824	−	0.738892i	$-0.735349\pi$
$331$	−24.5183			−1.34765			−0.673824	+	0.738892i	$0.735349\pi$
$332$	−2.19357	−	3.79938i	−0.120388	−	0.208518i
$333$	−2.15922	+	3.73988i	−0.118324	+	0.204944i
$334$	−13.6996			−0.749609
$335$	0.647524	+	1.12154i	0.0353780	+	0.0612765i
$336$	−0.313697	−	7.30359i	−0.0171136	−	0.398443i
$337$	23.7122			1.29168			0.645842	−	0.763471i	$-0.276506\pi$
$337$	23.7122			1.29168			0.645842	+	0.763471i	$0.276506\pi$
$338$	−9.63812	+	12.7021i	−0.524245	+	0.690901i
$339$	2.86292	−	4.95873i	0.155493	−	0.269321i
$340$	−0.372315			−0.0201916
$341$	23.1767	−	40.1433i	1.25509	−	2.17388i
$342$	2.77133	−	4.80008i	0.149856	−	0.259559i
$343$	−2.37834	−	18.3669i	−0.128418	−	0.991720i
$344$	5.10422	−	8.84078i	0.275201	−	0.476663i
$345$	4.57995			0.246576
$346$	7.82928	−	13.5607i	0.420905	−	0.729028i
$347$	1.09374	+	1.89441i	0.0587150	+	0.101697i	0.893889	−	0.448289i	$-0.147966\pi$
$347$	1.09374	+	1.89441i	0.0587150	+	0.101697i	−0.835174	+	0.549986i	$0.814633\pi$
$348$	0.0362777	−	0.0628348i	0.00194469	−	0.00336830i
$349$	−14.2613	−	24.7014i	−0.763392	−	1.32223i	−0.941092	−	0.338149i	$-0.890199\pi$
$349$	−14.2613	−	24.7014i	−0.763392	−	1.32223i	0.177700	−	0.984085i	$-0.443134\pi$
$350$	−36.6894	−	19.1324i	−1.96113	−	1.02267i
$351$	3.59845	+	0.226101i	0.192071	+	0.0120684i
$352$	−7.55042	−	13.0777i	−0.402439	−	0.697045i
$353$	10.2865			0.547494			0.273747	−	0.961802i	$-0.411737\pi$
$353$	10.2865			0.547494			0.273747	+	0.961802i	$0.411737\pi$
$354$	−2.47903			−0.131759
$355$	13.7300			0.728712
$356$	−6.54107			−0.346676
$357$	−0.418257	−	0.218107i	−0.0221365	−	0.0115435i
$358$	7.69804	−	13.3334i	0.406854	−	0.704691i
$359$	0.247010	+	0.427834i	0.0130367	+	0.0225802i	0.872470	−	0.488667i	$-0.162517\pi$
$359$	0.247010	+	0.427834i	0.0130367	+	0.0225802i	−0.859433	+	0.511248i	$0.829184\pi$
$360$	6.44824	+	11.1687i	0.339852	+	0.588641i
$361$	1.42144			0.0748125
$362$	−8.39068	+	14.5331i	−0.441004	+	0.763842i
$363$	19.5298			1.02505
$364$	4.04704	+	2.44479i	0.212123	+	0.128142i
$365$	29.7597			1.55770
$366$	2.30928	−	3.99979i	0.120708	−	0.209072i
$367$	−20.9488			−1.09352			−0.546759	−	0.837290i	$-0.684139\pi$
$367$	−20.9488			−1.09352			−0.546759	+	0.837290i	$0.684139\pi$
$368$	1.50178	+	2.60116i	0.0782856	+	0.135595i
$369$	0.782385	+	1.35513i	0.0407294	+	0.0705453i
$370$	−11.1579	+	19.3261i	−0.580074	+	1.00472i
$371$	0.894482	+	20.8256i	0.0464392	+	1.08121i
$372$	4.15807			0.215586
$373$	28.4170			1.47138			0.735689	−	0.677319i	$-0.236858\pi$
$373$	28.4170			1.47138			0.735689	+	0.677319i	$0.236858\pi$
$374$	1.20827			0.0624779
$375$	32.6571			1.68640
$376$	−1.94817	−	3.37432i	−0.100469	−	0.174017i
$377$	−0.234717	−	0.472737i	−0.0120885	−	0.0243472i
$378$	0.139251	+	3.24208i	0.00716228	+	0.166755i
$379$	17.5547	+	30.4056i	0.901724	+	1.56183i	0.825255	+	0.564760i	$0.191031\pi$
$379$	17.5547	+	30.4056i	0.901724	+	1.56183i	0.0764691	+	0.997072i	$0.475635\pi$
$380$	−4.71844	+	8.17257i	−0.242051	+	0.419244i
$381$	6.56642	+	11.3734i	0.336408	+	0.582676i
$382$	−14.9719	+	25.9320i	−0.766028	+	1.32680i
$383$	−36.2451			−1.85204			−0.926020	−	0.377475i	$-0.876792\pi$
$383$	−36.2451			−1.85204			−0.926020	+	0.377475i	$0.876792\pi$
$384$	−2.71163	+	4.69668i	−0.138377	+	0.239676i
$385$	−54.6126	−	28.4787i	−2.78331	−	1.45141i
$386$	7.67151	−	13.2874i	0.390470	−	0.676313i
$387$	−1.66752	+	2.88823i	−0.0847649	+	0.146817i
$388$	1.16476			0.0591317
$389$	18.5269	−	32.0895i	0.939349	−	1.62700i	0.172661	−	0.984981i	$-0.444763\pi$
$389$	18.5269	−	32.0895i	0.939349	−	1.62700i	0.766688	−	0.642020i	$-0.221903\pi$
$390$	18.5953	+	1.16840i	0.941611	+	0.0591640i
$391$	0.193809			0.00980134
$392$	−9.08284	+	19.4064i	−0.458753	+	0.980170i
$393$	5.95196	+	10.3091i	0.300237	+	0.520025i
$394$	23.9381			1.20598
$395$	−9.72017	+	16.8358i	−0.489075	+	0.847102i
$396$	1.36932	+	2.37173i	0.0688108	+	0.119184i
$397$	−30.9842			−1.55505			−0.777527	−	0.628849i	$-0.783526\pi$
$397$	−30.9842			−1.55505			−0.777527	+	0.628849i	$0.783526\pi$
$398$	−5.87221			−0.294347
$399$	−10.0883	+	6.41690i	−0.505046	+	0.321247i
$400$	17.6159	+	30.5117i	0.880797	+	1.52558i
$401$	15.1060	−	26.1644i	0.754359	−	1.30659i	−0.191334	−	0.981525i	$-0.561281\pi$
$401$	15.1060	−	26.1644i	0.754359	−	1.30659i	0.945693	−	0.325062i	$-0.105385\pi$
$402$	0.188503	−	0.326496i	0.00940167	−	0.0162842i
$403$	16.7367	−	25.1953i	0.833716	−	1.25507i
$404$	2.51286	+	4.35239i	0.125019	+	0.216540i
$405$	−2.10660	−	3.64874i	−0.104678	−	0.181308i
$406$	0.400817	−	0.254950i	0.0198922	−	0.0126529i
$407$	−11.9305	+	20.6642i	−0.591373	+	1.02429i
$408$	0.272868	+	0.472622i	0.0135090	+	0.0233983i
$409$	6.92988	+	12.0029i	0.342661	+	0.593506i	0.984926	−	0.172977i	$-0.0553386\pi$
$409$	6.92988	+	12.0029i	0.342661	+	0.593506i	−0.642265	+	0.766482i	$0.722005\pi$
$410$	4.04304	+	7.00276i	0.199672	+	0.345842i
$411$	−6.76423	−	11.7160i	−0.333655	−	0.577907i
$412$	2.48591	−	4.30573i	0.122472	−	0.212128i
$413$	4.74160	+	2.47259i	0.233319	+	0.121668i
$414$	−0.666643	−	1.15466i	−0.0327637	−	0.0567484i
$415$	18.6463	+	32.2964i	0.915311	+	1.58537i
$416$	−4.38214	−	8.82595i	−0.214852	−	0.432728i
$417$	−10.9150	+	18.9053i	−0.534509	+	0.925796i
$418$	15.3126	−	26.5223i	0.748966	−	1.29725i
$419$	−10.3550	−	17.9355i	−0.505877	−	0.876204i	−0.999977	−	0.00679920i	$-0.997836\pi$
$419$	−10.3550	−	17.9355i	−0.505877	−	0.876204i	0.494100	−	0.869405i	$-0.335498\pi$
$420$	−0.237087	−	5.51993i	−0.0115687	−	0.269345i
$421$	−37.6001			−1.83252			−0.916259	−	0.400586i	$-0.868806\pi$
$421$	−37.6001			−1.83252			−0.916259	+	0.400586i	$0.868806\pi$
$422$	5.59624			0.272421
$423$	0.636455	+	1.10237i	0.0309455	+	0.0535992i
$424$	12.0581	−	20.8852i	0.585591	−	1.01427i
$425$	2.27339			0.110276
$426$	−1.99849	−	3.46149i	−0.0968271	−	0.167710i
$427$	−8.40631	+	5.34704i	−0.406810	+	0.258761i
$428$	−6.86575			−0.331869
$429$	19.8828	+	1.24929i	0.959952	+	0.0603165i
$430$	−8.61707	+	14.9252i	−0.415552	+	0.719757i
$431$	−24.8176			−1.19542			−0.597712	−	0.801711i	$-0.703923\pi$
$431$	−24.8176			−1.19542			−0.597712	+	0.801711i	$0.703923\pi$
$432$	1.38152	−	2.39286i	0.0664684	−	0.115127i
$433$	12.3713	−	21.4277i	0.594526	−	1.02975i	−0.399087	−	0.916913i	$-0.630673\pi$
$433$	12.3713	−	21.4277i	0.594526	−	1.02975i	0.993614	−	0.112837i	$-0.0359937\pi$
$434$	24.1386	+	12.5875i	1.15869	+	0.604220i
$435$	−0.308376	+	0.534122i	−0.0147855	+	0.0256092i
$436$	0.467126			0.0223713
$437$	2.45619	−	4.25424i	0.117495	−	0.203508i
$438$	−4.33173	−	7.50277i	−0.206978	−	0.358496i
$439$	14.0060	−	24.2592i	0.668472	−	1.15783i	−0.309860	−	0.950782i	$-0.600282\pi$
$439$	14.0060	−	24.2592i	0.668472	−	1.15783i	0.978331	−	0.207045i	$-0.0663846\pi$
$440$	35.6289	+	61.7112i	1.69854	+	2.94196i
$441$	2.96732	−	6.33996i	0.141301	−	0.301903i
$442$	0.786894	+	0.0494427i	0.0374287	+	0.00235175i
$443$	−14.5799	−	25.2531i	−0.692711	−	1.19981i	−0.970946	−	0.239298i	$-0.923083\pi$
$443$	−14.5799	−	25.2531i	−0.692711	−	1.19981i	0.278235	−	0.960513i	$-0.410251\pi$
$444$	−2.14042			−0.101580
$445$	55.6019			2.63578
$446$	9.23056			0.437079
$447$	7.66408			0.362499
$448$	19.8197	−	12.6068i	0.936393	−	0.595616i
$449$	−12.6725	+	21.9494i	−0.598052	+	1.03586i	0.395056	+	0.918657i	$0.370725\pi$
$449$	−12.6725	+	21.9494i	−0.598052	+	1.03586i	−0.993108	+	0.117200i	$0.962608\pi$
$450$	−7.81976	−	13.5442i	−0.368627	−	0.638480i
$451$	4.32298	+	7.48761i	0.203561	+	0.352578i
$452$	2.83800			0.133488
$453$	−1.87363	+	3.24522i	−0.0880307	+	0.152474i
$454$	−4.51493			−0.211896
$455$	−34.4016	−	20.7818i	−1.61277	−	0.974265i
$456$	13.8325			0.647767
$457$	−6.36623	+	11.0266i	−0.297799	+	0.515804i	−0.975632	−	0.219412i	$-0.929586\pi$
$457$	−6.36623	+	11.0266i	−0.297799	+	0.515804i	0.677833	+	0.735216i	$0.262919\pi$
$458$	5.76669			0.269460
$459$	−0.0891447	−	0.154403i	−0.00416092	−	0.00720692i
$460$	1.13502	+	1.96591i	0.0529206	+	0.0916611i
$461$	−0.654119	+	1.13297i	−0.0304653	+	0.0527675i	−0.880856	−	0.473384i	$-0.843032\pi$
$461$	−0.654119	+	1.13297i	−0.0304653	+	0.0527675i	0.850391	+	0.526152i	$0.176366\pi$
$462$	0.769413	+	17.9137i	0.0357963	+	0.833422i
$463$	17.5365			0.814992			0.407496	−	0.913207i	$-0.366402\pi$
$463$	17.5365			0.814992			0.407496	+	0.913207i	$0.366402\pi$
$464$	−0.404468			−0.0187770
$465$	−35.3454			−1.63910
$466$	−2.95570			−0.136920
$467$	−21.5106	−	37.2575i	−0.995392	−	1.72407i	−0.580735	−	0.814092i	$-0.697235\pi$
$467$	−21.5106	−	37.2575i	−0.995392	−	1.72407i	−0.414657	−	0.909978i	$-0.636098\pi$
$468$	0.794729	+	1.60064i	0.0367364	+	0.0739897i
$469$	−0.686194	+	0.436471i	−0.0316855	+	0.0201543i
$470$	3.28894	+	5.69661i	0.151707	+	0.262765i
$471$	1.63089	−	2.82478i	0.0751473	−	0.130159i
$472$	−3.09339	−	5.35791i	−0.142385	−	0.246618i
$473$	−9.21370	+	15.9586i	−0.423646	+	0.733777i
$474$	5.65934			0.259942
$475$	28.8112	−	49.9025i	1.32195	−	2.28968i
$476$	−0.0100327	−	0.233586i	−0.000459850	−	0.0107064i
$477$	−3.93930	+	6.82307i	−0.180368	+	0.312407i
$478$	−4.88186	+	8.45563i	−0.223291	+	0.386752i
$479$	9.45378			0.431954			0.215977	−	0.976398i	$-0.430706\pi$
$479$	9.45378			0.431954			0.215977	+	0.976398i	$0.430706\pi$
$480$	−5.75734	+	9.97201i	−0.262786	+	0.455158i
$481$	−8.61544	+	12.9696i	−0.392830	+	0.591362i
$482$	36.6429			1.66904
$483$	0.123416	+	2.87341i	0.00561561	+	0.130745i
$484$	4.83994	+	8.38303i	0.219997	+	0.381047i
$485$	−9.90095			−0.449579
$486$	−0.613260	+	1.06220i	−0.0278181	+	0.0481823i
$487$	−3.93156	−	6.80966i	−0.178156	−	0.308575i	0.763093	−	0.646289i	$-0.223680\pi$
$487$	−3.93156	−	6.80966i	−0.178156	−	0.308575i	−0.941249	+	0.337714i	$0.890346\pi$
$488$	11.5263			0.521770
$489$	−10.4509			−0.472605
$490$	15.3339	−	32.7623i	0.692713	−	1.48005i
$491$	−14.7190	−	25.4941i	−0.664261	−	1.15053i	−0.979485	−	0.201516i	$-0.935413\pi$
$491$	−14.7190	−	25.4941i	−0.664261	−	1.15053i	0.315224	−	0.949017i	$-0.397920\pi$
$492$	−0.387787	+	0.671666i	−0.0174828	+	0.0302810i
$493$	−0.0130495	+	0.0226023i	−0.000587718	+	0.00101796i
$494$	11.0578	−	16.6463i	0.497514	−	0.748952i
$495$	−11.6398	−	20.1607i	−0.523169	−	0.906156i
$496$	−11.5898	−	20.0742i	−0.520399	−	0.901357i
$497$	0.369981	+	8.61402i	0.0165959	+	0.386392i
$498$	5.42819	−	9.40190i	0.243243	−	0.421309i
$499$	−4.14699	−	7.18281i	−0.185645	−	0.321547i	0.758149	−	0.652082i	$-0.226104\pi$
$499$	−4.14699	−	7.18281i	−0.185645	−	0.321547i	−0.943794	+	0.330535i	$0.892771\pi$
$500$	8.09318	+	14.0178i	0.361938	+	0.626895i
$501$	5.58474	+	9.67305i	0.249508	+	0.432160i
$502$	13.6220	+	23.5940i	0.607981	+	1.05305i
$503$	1.86348	−	3.22764i	0.0830885	−	0.143913i	−0.821487	−	0.570228i	$-0.806855\pi$
$503$	1.86348	−	3.22764i	0.0830885	−	0.143913i	0.904575	+	0.426314i	$0.140188\pi$
$504$	−6.83333	+	4.34650i	−0.304381	+	0.193609i
$505$	−21.3603	−	36.9972i	−0.950523	−	1.64635i
$506$	−3.68346	−	6.37993i	−0.163750	−	0.283623i
$507$	12.8978	+	1.62723i	0.572809	+	0.0722677i
$508$	−3.25462	+	5.63717i	−0.144401	+	0.250109i
$509$	0.636994	−	1.10331i	0.0282342	−	0.0489032i	−0.851563	−	0.524252i	$-0.824345\pi$
$509$	0.636994	−	1.10331i	0.0282342	−	0.0489032i	0.879797	+	0.475349i	$0.157678\pi$
$510$	−0.460663	−	0.797891i	−0.0203985	−	0.0353312i
$511$	0.801934	+	18.6709i	0.0354755	+	0.825951i
$512$	−24.4665			−1.08128
$513$	−4.51901			−0.199519
$514$	1.98300	+	3.43466i	0.0874665	+	0.151496i
$515$	−21.1313	+	36.6005i	−0.931157	+	1.61281i
$516$	−1.65300			−0.0727694
$517$	3.51666	+	6.09103i	0.154662	+	0.267883i
$518$	−12.4256	−	6.47958i	−0.545952	−	0.284696i
$519$	−12.7666			−0.560393
$520$	20.6784	+	41.6479i	0.906810	+	1.82638i
$521$	3.53913	−	6.12995i	0.155052	−	0.268558i	−0.778026	−	0.628232i	$-0.783779\pi$
$521$	3.53913	−	6.12995i	0.155052	−	0.268558i	0.933078	+	0.359674i	$0.117112\pi$
$522$	0.179545			0.00785845
$523$	−6.12307	+	10.6055i	−0.267743	+	0.463745i	−0.968279	−	0.249873i	$-0.919611\pi$
$523$	−6.12307	+	10.6055i	−0.267743	+	0.463745i	0.700535	+	0.713618i	$0.252945\pi$
$524$	−2.95007	+	5.10967i	−0.128874	+	0.223217i
$525$	1.44767	+	33.7052i	0.0631817	+	1.47102i
$526$	−4.58870	+	7.94786i	−0.200077	+	0.346543i
$527$	−1.49570			−0.0651538
$528$	7.63343	−	13.2215i	0.332202	−	0.575391i
$529$	10.9092	+	18.8952i	0.474311	+	0.821532i
$530$	−20.3567	+	35.2588i	−0.884238	+	1.53154i
$531$	1.01059	+	1.75040i	0.0438561	+	0.0759610i
$532$	−5.25452	−	2.74006i	−0.227812	−	0.118797i
$533$	2.50898	+	5.05328i	0.108676	+	0.218882i
$534$	−8.09322	−	14.0179i	−0.350228	−	0.606613i
$535$	58.3618			2.52320
$536$	0.940873			0.0406395
$537$	−12.5526			−0.541686
$538$	−3.71854			−0.160317
$539$	16.3955	−	35.0307i	0.706206	−	1.50888i
$540$	1.04413	−	1.80849i	0.0449322	−	0.0778249i
$541$	12.5429	+	21.7249i	0.539261	+	0.934027i	0.998944	+	0.0459441i	$0.0146296\pi$
$541$	12.5429	+	21.7249i	0.539261	+	0.934027i	−0.459683	+	0.888083i	$0.652037\pi$
$542$	13.2563	+	22.9605i	0.569405	+	0.986239i
$543$	13.6821			0.587155
$544$	−0.243632	+	0.421983i	−0.0104456	+	0.0180924i
$545$	−3.97077			−0.170089
$546$	−0.231950	+	11.6980i	−0.00992654	+	0.500627i
$547$	−1.32955			−0.0568473			−0.0284236	−	0.999596i	$-0.509049\pi$
$547$	−1.32955			−0.0568473			−0.0284236	+	0.999596i	$0.509049\pi$
$548$	3.35267	−	5.80699i	0.143219	−	0.248062i
$549$	−3.76557			−0.160711
$550$	−43.2071	−	74.8369i	−1.84236	−	3.19106i
$551$	0.330758	+	0.572890i	0.0140908	+	0.0244059i
$552$	1.66371	−	2.88162i	0.0708120	−	0.122650i
$553$	−10.8245	−	5.64464i	−0.460305	−	0.240034i
$554$	−11.6603			−0.495399
$555$	18.1945			0.772312
$556$	−10.8199			−0.458868
$557$	−7.92132			−0.335637			−0.167819	−	0.985818i	$-0.553672\pi$
$557$	−7.92132			−0.335637			−0.167819	+	0.985818i	$0.553672\pi$
$558$	5.14476	+	8.91098i	0.217795	+	0.377232i
$559$	−6.65354	+	10.0162i	−0.281415	+	0.423638i
$560$	−25.9881	+	16.5304i	−1.09820	+	0.698535i
$561$	−0.492558	−	0.853136i	−0.0207958	−	0.0360194i
$562$	−19.4244	+	33.6441i	−0.819370	+	1.41919i
$563$	−2.87547	−	4.98046i	−0.121187	−	0.209901i	0.799049	−	0.601266i	$-0.205337\pi$
$563$	−2.87547	−	4.98046i	−0.121187	−	0.209901i	−0.920236	+	0.391364i	$0.872003\pi$
$564$	−0.315457	+	0.546387i	−0.0132831	+	0.0230070i
$565$	−24.1242			−1.01491
$566$	8.90111	−	15.4172i	0.374141	−	0.648032i
$567$	2.23241	−	1.41998i	0.0937524	−	0.0596335i
$568$	4.98752	−	8.63864i	0.209272	−	0.362469i
$569$	3.22149	−	5.57978i	0.135052	−	0.233917i	−0.790565	−	0.612378i	$-0.790213\pi$
$569$	3.22149	−	5.57978i	0.135052	−	0.233917i	0.925617	+	0.378461i	$0.123547\pi$
$570$	−23.3524			−0.978123
$571$	−16.3076	+	28.2456i	−0.682451	+	1.18204i	0.291779	+	0.956486i	$0.405753\pi$
$571$	−16.3076	+	28.2456i	−0.682451	+	1.18204i	−0.974231	+	0.225555i	$0.927581\pi$
$572$	4.39118	+	8.84416i	0.183604	+	0.369793i
$573$	24.4136			1.01989
$574$	−4.28450	+	2.72526i	−0.178831	+	0.113750i
$575$	−6.93053	−	12.0040i	−0.289023	−	0.500603i
$576$	8.87816			0.369923
$577$	−10.1701	+	17.6152i	−0.423388	+	0.733330i	−0.996268	−	0.0863089i	$-0.972493\pi$
$577$	−10.1701	+	17.6152i	−0.423388	+	0.733330i	0.572880	+	0.819639i	$0.305826\pi$
$578$	10.4059	+	18.0236i	0.432830	+	0.749683i
$579$	−12.5094			−0.519872
$580$	−0.305691			−0.0126931
$581$	−19.7599	+	12.5688i	−0.819778	+	0.521440i
$582$	1.44115	+	2.49614i	0.0597376	+	0.103468i
$583$	−21.7661	+	37.7000i	−0.901461	+	1.56138i
$584$	10.8105	−	18.7243i	0.447340	−	0.774816i
$585$	−6.75553	−	13.6061i	−0.279307	−	0.562545i
$586$	−12.7221	−	22.0354i	−0.525547	−	0.910274i
$587$	−14.8490	−	25.7192i	−0.612883	−	1.06154i	−0.990752	−	0.135685i	$-0.956676\pi$
$587$	−14.8490	−	25.7192i	−0.612883	−	1.06154i	0.377869	−	0.925859i	$-0.376657\pi$
$588$	3.45675	−	0.297491i	0.142554	−	0.0122683i
$589$	−18.9554	+	32.8317i	−0.781044	+	1.35281i
$590$	5.22234	+	9.04535i	0.215000	+	0.372391i
$591$	−9.75853	−	16.9023i	−0.401412	−	0.695266i
$592$	5.96601	+	10.3334i	0.245201	+	0.424701i
$593$	8.00200	+	13.8599i	0.328603	+	0.569157i	0.982235	−	0.187656i	$-0.0600889\pi$
$593$	8.00200	+	13.8599i	0.328603	+	0.569157i	−0.653632	+	0.756813i	$0.726756\pi$
$594$	−3.38850	+	5.86905i	−0.139032	+	0.240810i
$595$	0.0852827	+	1.98558i	0.00349625	+	0.0814008i
$596$	1.89934	+	3.28975i	0.0777999	+	0.134753i
$597$	2.39385	+	4.14627i	0.0979737	+	0.169695i
$598$	−2.13781	−	4.30572i	−0.0874218	−	0.176074i
$599$	−8.13858	+	14.0964i	−0.332533	+	0.575965i	−0.983008	−	0.183563i	$-0.941237\pi$
$599$	−8.13858	+	14.0964i	−0.332533	+	0.575965i	0.650475	+	0.759528i	$0.274570\pi$
$600$	19.5153	−	33.8016i	0.796711	−	1.37994i
$601$	21.2956	+	36.8850i	0.868664	+	1.50457i	0.863362	+	0.504585i	$0.168354\pi$
$601$	21.2956	+	36.8850i	0.868664	+	1.50457i	0.00530223	+	0.999986i	$0.498312\pi$
$602$	−9.59609	−	5.00405i	−0.391107	−	0.203950i
$603$	−0.307378			−0.0125174
$604$	−1.85731			−0.0755730
$605$	−41.1416	−	71.2593i	−1.67264	−	2.89710i
$606$	−6.21828	+	10.7704i	−0.252600	+	0.437517i
$607$	−18.6270			−0.756045			−0.378022	−	0.925796i	$-0.623396\pi$
$607$	−18.6270			−0.756045			−0.378022	+	0.925796i	$0.623396\pi$
$608$	6.17522	+	10.6958i	0.250438	+	0.433772i
$609$	−0.343411	−	0.179078i	−0.0139157	−	0.00725661i
$610$	−19.4589			−0.787869
$611$	2.04101	+	4.11074i	0.0825703	+	0.166303i
$612$	0.0441842	−	0.0765294i	0.00178604	−	0.00309352i
$613$	20.3580			0.822252			0.411126	−	0.911579i	$-0.365136\pi$
$613$	20.3580			0.822252			0.411126	+	0.911579i	$0.365136\pi$
$614$	−8.54127	+	14.7939i	−0.344698	+	0.597034i
$615$	3.29635	−	5.70945i	0.132922	−	0.230227i
$616$	−37.7567	+	24.0161i	−1.52126	+	0.967636i
$617$	15.7193	−	27.2266i	0.632835	−	1.09610i	−0.354134	−	0.935195i	$-0.615224\pi$
$617$	15.7193	−	27.2266i	0.632835	−	1.09610i	0.986969	−	0.160908i	$-0.0514423\pi$
$618$	12.3032			0.494908
$619$	4.84802	−	8.39703i	0.194859	−	0.337505i	−0.751996	−	0.659168i	$-0.770909\pi$
$619$	4.84802	−	8.39703i	0.194859	−	0.337505i	0.946854	+	0.321663i	$0.104242\pi$
$620$	−8.75941	−	15.1717i	−0.351786	−	0.609312i
$621$	−0.543523	+	0.941410i	−0.0218108	+	0.0377775i
$622$	−2.80869	−	4.86479i	−0.112618	−	0.195060i
$623$	1.49830	+	34.8839i	0.0600281	+	1.39759i
$624$	5.51237	−	8.29825i	0.220671	−	0.332196i
$625$	−36.9177	−	63.9434i	−1.47671	−	2.55773i
$626$	−16.5629			−0.661985
$627$	−24.9692			−0.997175
$628$	1.61669			0.0645128
$629$	0.769931			0.0306992
$630$	11.5362	−	7.33787i	0.459612	−	0.292348i
$631$	−9.65738	+	16.7271i	−0.384454	+	0.665895i	−0.991693	−	0.128625i	$-0.958944\pi$
$631$	−9.65738	+	16.7271i	−0.384454	+	0.665895i	0.607239	+	0.794519i	$0.292277\pi$
$632$	7.06186	+	12.2315i	0.280906	+	0.486543i
$633$	−2.28135	−	3.95141i	−0.0906753	−	0.157054i
$634$	−7.02953			−0.279178
$635$	27.6657	−	47.9184i	1.09788	−	1.90158i
$636$	−3.90500			−0.154843
$637$	12.1112	−	22.1431i	0.479864	−	0.877343i
$638$	0.992052			0.0392757
$639$	−1.62940	+	2.82220i	−0.0644580	+	0.111644i
$640$	22.8493			0.903198
$641$	−9.22686	−	15.9814i	−0.364439	−	0.631227i	0.624247	−	0.781227i	$-0.285406\pi$
$641$	−9.22686	−	15.9814i	−0.364439	−	0.631227i	−0.988686	+	0.150000i	$0.952073\pi$
$642$	−8.49495	−	14.7137i	−0.335269	−	0.580703i
$643$	10.8340	−	18.7650i	0.427250	−	0.740019i	−0.569378	−	0.822076i	$-0.692816\pi$
$643$	10.8340	−	18.7650i	0.427250	−	0.740019i	0.996628	+	0.0820574i	$0.0261491\pi$
$644$	−1.20280	+	0.765072i	−0.0473971	+	0.0301481i
$645$	14.0512			0.553267
$646$	−0.988197			−0.0388801
$647$	−21.7371			−0.854573			−0.427287	−	0.904116i	$-0.640530\pi$
$647$	−21.7371			−0.854573			−0.427287	+	0.904116i	$0.640530\pi$
$648$	−3.06096			−0.120246
$649$	5.58392	+	9.67163i	0.219188	+	0.379645i
$650$	−25.0767	−	50.5063i	−0.983588	−	1.98102i
$651$	−0.952450	−	22.1753i	−0.0373295	−	0.869117i
$652$	−2.58997	−	4.48596i	−0.101431	−	0.175684i
$653$	11.2916	−	19.5576i	0.441875	−	0.765350i	−0.555954	−	0.831213i	$-0.687647\pi$
$653$	11.2916	−	19.5576i	0.441875	−	0.765350i	0.997829	+	0.0658635i	$0.0209802\pi$
$654$	0.577972	+	1.00108i	0.0226005	+	0.0391452i
$655$	25.0768	−	43.4344i	0.979834	−	1.69712i
$656$	4.32353			0.168805
$657$	−3.53172	+	6.11712i	−0.137785	+	0.238651i
$658$	−3.48535	+	2.21694i	−0.135873	+	0.0864255i
$659$	1.42864	−	2.47447i	0.0556517	−	0.0963916i	−0.836857	−	0.547421i	$-0.815610\pi$
$659$	1.42864	−	2.47447i	0.0556517	−	0.0963916i	0.892509	+	0.451029i	$0.148943\pi$
$660$	5.76922	−	9.99258i	0.224567	−	0.388961i
$661$	9.63310			0.374684			0.187342	−	0.982295i	$-0.440013\pi$
$661$	9.63310			0.374684			0.187342	+	0.982295i	$0.440013\pi$
$662$	15.0361	−	26.0433i	0.584395	−	1.01220i
$663$	−0.285872	−	0.575768i	−0.0111024	−	0.0223610i
$664$	27.0937			1.05144
$665$	44.6656	+	23.2917i	1.73206	+	0.903214i
$666$	−2.64833	−	4.58704i	−0.102621	−	0.177744i
$667$	0.159128			0.00616144
$668$	−2.76806	+	4.79441i	−0.107099	+	0.185501i
$669$	−3.76290	−	6.51754i	−0.145482	−	0.251983i
$670$	−1.58840			−0.0613654
$671$	−20.8062			−0.803216
$672$	−6.41146	−	3.34337i	−0.247327	−	0.128973i
$673$	15.4999	+	26.8466i	0.597476	+	1.03486i	0.993192	+	0.116486i	$0.0371631\pi$
$673$	15.4999	+	26.8466i	0.597476	+	1.03486i	−0.395716	+	0.918373i	$0.629504\pi$
$674$	−14.5417	+	25.1870i	−0.560127	+	0.970168i
$675$	−6.37556	+	11.0428i	−0.245395	+	0.425037i
$676$	2.49789	+	5.93953i	0.0960727	+	0.228443i
$677$	−5.44610	−	9.43293i	−0.209311	−	0.362537i	0.742187	−	0.670193i	$-0.233789\pi$
$677$	−5.44610	−	9.43293i	−0.209311	−	0.362537i	−0.951498	+	0.307656i	$0.900455\pi$
$678$	3.51143	+	6.08198i	0.134856	+	0.233577i
$679$	−0.266800	−	6.21173i	−0.0102389	−	0.238384i
$680$	1.14965	−	1.99125i	0.0440871	−	0.0763611i
$681$	1.84054	+	3.18791i	0.0705298	+	0.122161i
$682$	28.4267	+	49.2365i	1.08852	+	1.88536i
$683$	13.2641	+	22.9742i	0.507538	+	0.879082i	0.999962	+	0.00872632i	$0.00277771\pi$
$683$	13.2641	+	22.9742i	0.507538	+	0.879082i	−0.492424	+	0.870356i	$0.663889\pi$
$684$	−1.11992	−	1.93975i	−0.0428210	−	0.0741682i
$685$	−28.4991	+	49.3619i	−1.08890	+	1.88602i
$686$	20.9678	+	8.73743i	0.800556	+	0.333597i
$687$	−2.35083	−	4.07176i	−0.0896898	−	0.155347i
$688$	4.60743	+	7.98031i	0.175657	+	0.304246i
$689$	−15.7181	+	23.6618i	−0.598812	+	0.901444i
$690$	−2.80871	+	4.86482i	−0.106926	+	0.185201i
$691$	2.37760	−	4.11812i	0.0904480	−	0.156661i	−0.817252	−	0.576281i	$-0.804503\pi$
$691$	2.37760	−	4.11812i	0.0904480	−	0.156661i	0.907700	+	0.419620i	$0.137837\pi$
$692$	−3.16387	−	5.47999i	−0.120272	−	0.208318i
$693$	12.3349	−	7.84593i	0.468565	−	0.298042i
$694$	−2.68299			−0.101845
$695$	91.9741			3.48878
$696$	0.224040	+	0.388048i	0.00849221	+	0.0147089i
$697$	0.139491	−	0.241605i	0.00528360	−	0.00915146i
$698$	34.9837			1.32415
$699$	1.20491	+	2.08697i	0.0455740	+	0.0789365i
$700$	−14.1089	+	8.97434i	−0.533268	+	0.339198i
$701$	19.5899			0.739898			0.369949	−	0.929052i	$-0.379375\pi$
$701$	19.5899			0.739898			0.369949	+	0.929052i	$0.379375\pi$
$702$	−2.44695	+	3.68361i	−0.0923543	+	0.139029i
$703$	9.75753	−	16.9005i	0.368012	−	0.637416i
$704$	49.0552			1.84884
$705$	2.68152	−	4.64452i	0.100992	−	0.174923i
$706$	−6.30829	+	10.9263i	−0.237416	+	0.411216i
$707$	22.6360	−	14.3982i	0.851314	−	0.541499i
$708$	−0.500898	+	0.867581i	−0.0188249	+	0.0326057i
$709$	−16.1980			−0.608327			−0.304164	−	0.952620i	$-0.598377\pi$
$709$	−16.1980			−0.608327			−0.304164	+	0.952620i	$0.598377\pi$
$710$	−8.42005	+	14.5840i	−0.315999	+	0.547326i
$711$	−2.30707	−	3.99596i	−0.0865219	−	0.149860i
$712$	20.1978	−	34.9836i	0.756945	−	1.31107i
$713$	4.55972	+	7.89767i	0.170763	+	0.295770i
$714$	0.488174	−	0.310515i	0.0182694	−	0.0116207i
$715$	−37.3269	−	75.1791i	−1.39595	−	2.81154i
$716$	−3.11084	−	5.38813i	−0.116257	−	0.201364i
$717$	7.96050			0.297290
$718$	−0.605926			−0.0226129
$719$	−27.6928			−1.03277			−0.516384	−	0.856357i	$-0.672722\pi$
$719$	−27.6928			−1.03277			−0.516384	+	0.856357i	$0.672722\pi$
$720$	−11.6413			−0.433844
$721$	−23.5321	−	12.2713i	−0.876382	−	0.457005i
$722$	−0.871712	+	1.50985i	−0.0324418	+	0.0561908i
$723$	−14.9378	−	25.8730i	−0.555541	−	0.962225i
$724$	3.39074	+	5.87293i	0.126016	+	0.218266i
$725$	1.86658			0.0693229
$726$	−11.9769	+	20.7445i	−0.444503	+	0.769902i
$727$	29.2681			1.08549			0.542746	−	0.839897i	$-0.317384\pi$
$727$	29.2681			1.08549			0.542746	+	0.839897i	$0.317384\pi$
$728$	−25.5722	+	14.0957i	−0.947767	+	0.522421i
$729$	1.00000			0.0370370
$730$	−18.2505	+	31.6107i	−0.675480	+	1.16997i
$731$	0.594603			0.0219922
$732$	−0.933197	−	1.61634i	−0.0344920	−	0.0597418i
$733$	11.0284	+	19.1017i	0.407343	+	0.705538i	0.994591	−	0.103869i	$-0.0331222\pi$
$733$	11.0284	+	19.1017i	0.407343	+	0.705538i	−0.587248	+	0.809407i	$0.699789\pi$
$734$	12.8471	−	22.2518i	0.474194	−	0.821328i
$735$	−29.3838	+	2.52880i	−1.08384	+	0.0932761i
$736$	2.97090			0.109509
$737$	−1.69838			−0.0625606
$738$	−1.91922			−0.0706476
$739$	−9.72468			−0.357728			−0.178864	−	0.983874i	$-0.557242\pi$
$739$	−9.72468			−0.357728			−0.178864	+	0.983874i	$0.557242\pi$
$740$	4.50901	+	7.80984i	0.165755	+	0.287095i
$741$	−16.2614	−	1.02175i	−0.597379	−	0.0375350i
$742$	−22.6695	−	11.8214i	−0.832223	−	0.433978i
$743$	18.6574	+	32.3156i	0.684475	+	1.18554i	0.973602	+	0.228254i	$0.0733016\pi$
$743$	18.6574	+	32.3156i	0.684475	+	1.18554i	−0.289127	+	0.957291i	$0.593365\pi$
$744$	−12.8395	+	22.2387i	−0.470719	+	0.815309i
$745$	−16.1452	−	27.9643i	−0.591514	−	1.02453i
$746$	−17.4270	+	30.1845i	−0.638049	+	1.10513i
$747$	−8.85136			−0.323854
$748$	0.244135	−	0.422854i	0.00892645	−	0.0154611i
$749$	1.57267	+	36.6155i	0.0574642	+	1.33790i
$750$	−20.0273	+	34.6883i	−0.731293	+	1.26664i
$751$	−0.911661	+	1.57904i	−0.0332670	+	0.0576201i	−0.882180	−	0.470913i	$-0.843924\pi$
$751$	−0.911661	+	1.57904i	−0.0332670	+	0.0576201i	0.848913	+	0.528533i	$0.177258\pi$
$752$	3.51710			0.128256
$753$	11.1062	−	19.2366i	0.404733	−	0.701019i
$754$	0.646083	+	0.0405952i	0.0235289	+	0.00147839i
$755$	15.7880			0.574583
$756$	1.16276	+	0.606342i	0.0422891	+	0.0220524i
$757$	−4.43646	−	7.68417i	−0.161246	−	0.279286i	0.774070	−	0.633100i	$-0.218218\pi$
$757$	−4.43646	−	7.68417i	−0.161246	−	0.279286i	−0.935316	+	0.353814i	$0.884885\pi$
$758$	−43.0624			−1.56410
$759$	−3.00317	+	5.20165i	−0.109008	+	0.188808i
$760$	−29.1396	−	50.4713i	−1.05701	−	1.83079i
$761$	24.0973			0.873527			0.436764	−	0.899576i	$-0.356125\pi$
$761$	24.0973			0.873527			0.436764	+	0.899576i	$0.356125\pi$
$762$	−16.1077			−0.583521
$763$	−0.107000	−	2.49121i	−0.00387367	−	0.0901879i
$764$	6.05025	+	10.4793i	0.218890	+	0.379129i
$765$	−0.375585	+	0.650532i	−0.0135793	+	0.0235200i
$766$	22.2277	−	38.4995i	0.803119	−	1.39104i
$767$	3.24081	+	6.52724i	0.117019	+	0.235685i
$768$	5.55229	+	9.61685i	0.200351	+	0.347018i
$769$	−20.3128	−	35.1829i	−0.732499	−	1.26873i	−0.955812	−	0.293979i	$-0.905020\pi$
$769$	−20.3128	−	35.1829i	−0.732499	−	1.26873i	0.223312	−	0.974747i	$-0.428313\pi$
$770$	63.7418	−	40.5445i	2.29709	−	1.46112i
$771$	1.61677	−	2.80033i	0.0582266	−	0.100851i
$772$	−3.10012	−	5.36956i	−0.111576	−	0.193255i
$773$	0.0147281	+	0.0255098i	0.000529733	+	0.000917524i	0.866290	−	0.499541i	$-0.166498\pi$
$773$	0.0147281	+	0.0255098i	0.000529733	+	0.000917524i	−0.865760	+	0.500459i	$0.833165\pi$
$774$	−2.04525	−	3.54248i	−0.0735150	−	0.127332i
$775$	53.4858	+	92.6400i	1.92126	+	3.32773i
$776$	−3.59660	+	6.22949i	−0.129110	+	0.223626i
$777$	0.490285	+	11.4150i	0.0175889	+	0.409510i
$778$	22.7236	+	39.3584i	0.814680	+	1.41107i
$779$	−3.53561	−	6.12385i	−0.126676	−	0.219410i
$780$	4.16616	−	6.27168i	0.149172	−	0.224562i
$781$	−9.00304	+	15.5937i	−0.322154	+	0.557987i
$782$	−0.118855	+	0.205863i	−0.00425026	+	0.00736166i
$783$	−0.0731926	−	0.126773i	−0.00261569	−	0.00453051i
$784$	−11.0712	−	15.8592i	−0.395402	−	0.566399i
$785$	−13.7425			−0.490492
$786$	−14.6004			−0.520779
$787$	22.5887	+	39.1247i	0.805199	+	1.39465i	0.916156	+	0.400821i	$0.131275\pi$
$787$	22.5887	+	39.1247i	0.805199	+	1.39465i	−0.110957	+	0.993825i	$0.535392\pi$
$788$	4.83678	−	8.37755i	0.172303	−	0.298438i
$789$	7.48246			0.266383
$790$	−11.9220	−	20.6495i	−0.424165	−	0.734676i
$791$	−0.650073	−	15.1352i	−0.0231139	−	0.538146i
$792$	−16.9130			−0.600977
$793$	−13.5503	−	0.851400i	−0.481184	−	0.0302341i
$794$	19.0014	−	32.9114i	0.674335	−	1.16798i
$795$	33.1942			1.17728
$796$	−1.18650	+	2.05508i	−0.0420545	+	0.0728405i
$797$	−6.89239	+	11.9380i	−0.244141	+	0.422864i	−0.961890	−	0.273438i	$-0.911839\pi$
$797$	−6.89239	+	11.9380i	−0.244141	+	0.422864i	0.717749	+	0.696302i	$0.245173\pi$
$798$	−0.629275	−	14.6510i	−0.0222761	−	0.518639i
$799$	0.113473	−	0.196541i	0.00401439	−	0.00695313i
$800$	34.8488			1.23209
$801$	−6.59852	+	11.4290i	−0.233147	+	0.403823i
$802$	18.5278	+	32.0912i	0.654241	+	1.13318i
$803$	−19.5141	+	33.7994i	−0.688637	+	1.19275i
$804$	−0.0761754	−	0.131940i	−0.00268650	−	0.00465316i
$805$	10.2243	−	6.50344i	0.360361	−	0.229216i
$806$	16.4984	+	33.2290i	0.581131	+	1.17044i
$807$	1.51589	+	2.62560i	0.0533618	+	0.0924253i
$808$	−31.0373			−1.09189
$809$	−18.3976			−0.646825			−0.323413	−	0.946258i	$-0.604830\pi$
$809$	−18.3976			−0.646825			−0.323413	+	0.946258i	$0.604830\pi$
$810$	5.16759			0.181571
$811$	−28.7233			−1.00861			−0.504306	−	0.863525i	$-0.668252\pi$
$811$	−28.7233			−1.00861			−0.504306	+	0.863525i	$0.668252\pi$
$812$	−0.00823743	−	0.191787i	−0.000289077	−	0.00673039i
$813$	10.8080	−	18.7200i	0.379054	−	0.656540i
$814$	−14.6330	−	25.3451i	−0.512887	−	0.888346i
$815$	22.0159	+	38.1326i	0.771182	+	1.33573i
$816$	−0.492621			−0.0172452
$817$	7.53555	−	13.0520i	0.263635	−	0.456630i
$818$	−16.9993			−0.594366
$819$	8.35429	−	4.60498i	0.291922	−	0.160911i
$820$	3.26765			0.114111
$821$	−6.08215	+	10.5346i	−0.212268	+	0.367660i	−0.952424	−	0.304776i	$-0.901418\pi$
$821$	−6.08215	+	10.5346i	−0.212268	+	0.367660i	0.740156	+	0.672436i	$0.234752\pi$
$822$	16.5929			0.578745
$823$	−6.64923	−	11.5168i	−0.231777	−	0.401450i	0.726554	−	0.687110i	$-0.241121\pi$
$823$	−6.64923	−	11.5168i	−0.231777	−	0.401450i	−0.958331	+	0.285659i	$0.907787\pi$
$824$	15.3522	+	26.5909i	0.534821	+	0.926336i
$825$	−35.2274	+	61.0156i	−1.22646	+	2.12429i
$826$	−5.53422	+	3.52017i	−0.192560	+	0.122483i
$827$	39.3333			1.36775			0.683876	−	0.729598i	$-0.260293\pi$
$827$	39.3333			1.36775			0.683876	+	0.729598i	$0.260293\pi$
$828$	−0.538791			−0.0187243
$829$	5.37918			0.186827			0.0934134	−	0.995627i	$-0.470222\pi$
$829$	5.37918			0.186827			0.0934134	+	0.995627i	$0.470222\pi$
$830$	−45.7402			−1.58766
$831$	4.75341	+	8.23314i	0.164894	+	0.285604i
$832$	31.9477	+	2.00736i	1.10759	+	0.0695927i
$833$	−1.24343	+	0.107011i	−0.0430823	+	0.00370770i
$834$	−13.3874	−	23.1877i	−0.463569	−	0.802926i
$835$	23.5297	−	40.7546i	0.814278	−	1.41037i
$836$	−6.18796	−	10.7179i	−0.214015	−	0.370685i
$837$	4.19459	−	7.26525i	0.144986	−	0.251124i
$838$	25.4013			0.877475
$839$	−14.7620	+	25.5686i	−0.509642	+	0.882726i	0.490295	+	0.871556i	$0.336889\pi$
$839$	−14.7620	+	25.5686i	−0.509642	+	0.882726i	−0.999938	+	0.0111700i	$0.996444\pi$
$840$	30.2544	+	15.7767i	1.04388	+	0.544348i
$841$	14.4893	−	25.0962i	0.499631	−	0.865385i
$842$	23.0587	−	39.9388i	0.794654	−	1.37638i
$843$	31.6740			1.09091
$844$	1.13074	−	1.95850i	0.0389217	−	0.0674144i
$845$	−21.2331	−	50.4885i	−0.730442	−	1.73686i
$846$	−1.56125			−0.0536769
$847$	43.5986	−	27.7319i	1.49806	−	0.952881i
$848$	10.8845	+	18.8524i	0.373774	+	0.647395i
$849$	−14.5144			−0.498133
$850$	−1.39418	+	2.41479i	−0.0478200	+	0.0828266i
$851$	−2.34717	−	4.06542i	−0.0804600	−	0.139361i
$852$	−1.61521			−0.0553362
$853$	−12.4764			−0.427184			−0.213592	−	0.976923i	$-0.568516\pi$
$853$	−12.4764			−0.427184			−0.213592	+	0.976923i	$0.568516\pi$
$854$	−0.524359	−	12.2083i	−0.0179432	−	0.417759i
$855$	9.51976	+	16.4887i	0.325569	+	0.563902i
$856$	21.2004	−	36.7202i	0.724615	−	1.25507i
$857$	−22.7205	+	39.3531i	−0.776118	+	1.34428i	0.158046	+	0.987432i	$0.449481\pi$
$857$	−22.7205	+	39.3531i	−0.776118	+	1.34428i	−0.934164	+	0.356844i	$0.883853\pi$
$858$	−13.5203	+	20.3534i	−0.461577	+	0.694852i
$859$	26.2027	+	45.3845i	0.894026	+	1.54850i	0.835006	+	0.550241i	$0.185464\pi$
$859$	26.2027	+	45.3845i	0.894026	+	1.54850i	0.0590202	+	0.998257i	$0.481202\pi$
$860$	3.48222	+	6.03139i	0.118743	+	0.205669i
$861$	3.67086	+	1.91424i	0.125103	+	0.0652371i
$862$	15.2197	−	26.3613i	0.518384	−	0.897868i
$863$	−12.9896	−	22.4986i	−0.442170	−	0.765862i	0.555680	−	0.831396i	$-0.312458\pi$
$863$	−12.9896	−	22.4986i	−0.442170	−	0.765862i	−0.997850	+	0.0655347i	$0.979125\pi$
$864$	−1.36650	−	2.36685i	−0.0464892	−	0.0805217i
$865$	26.8943	+	46.5822i	0.914432	+	1.58384i
$866$	15.1736	+	26.2815i	0.515621	+	0.893083i
$867$	8.48411	−	14.6949i	0.288135	−	0.499065i
$868$	9.28252	−	5.90438i	0.315069	−	0.200408i
$869$	−12.7474	−	22.0792i	−0.432427	−	0.748986i
$870$	−0.378229	−	0.655112i	−0.0128232	−	0.0222104i
$871$	−1.10609	−	0.0694985i	−0.0374783	−	0.00235487i
$872$	−1.44241	+	2.49833i	−0.0488463	+	0.0846043i
$873$	1.17499	−	2.03514i	0.0397674	−	0.0688791i
$874$	3.01256	+	5.21792i	0.101902	+	0.176499i
$875$	72.9040	−	46.3724i	2.46461	−	1.56767i
$876$	−3.50097			−0.118287
$877$	−6.98130			−0.235742			−0.117871	−	0.993029i	$-0.537607\pi$
$877$	−6.98130			−0.235742			−0.117871	+	0.993029i	$0.537607\pi$
$878$	17.1787	+	29.7544i	0.579753	+	1.00416i
$879$	−10.3725	+	17.9658i	−0.349857	+	0.605970i
$880$	−64.3224			−2.16831
$881$	−10.2063	−	17.6779i	−0.343859	−	0.595582i	0.641286	−	0.767302i	$-0.278401\pi$
$881$	−10.2063	−	17.6779i	−0.343859	−	0.595582i	−0.985146	+	0.171720i	$0.945068\pi$
$882$	4.91455	+	7.03992i	0.165482	+	0.237046i
$883$	2.69268			0.0906160			0.0453080	−	0.998973i	$-0.485573\pi$
$883$	2.69268			0.0906160			0.0453080	+	0.998973i	$0.485573\pi$
$884$	0.176298	−	0.265397i	0.00592956	−	0.00892628i
$885$	4.25785	−	7.37481i	0.143126	−	0.247901i
$886$	35.7651			1.20155
$887$	12.7982	−	22.1672i	0.429722	−	0.744300i	−0.567126	−	0.823631i	$-0.691945\pi$
$887$	12.7982	−	22.1672i	0.429722	−	0.744300i	0.996848	+	0.0793304i	$0.0252782\pi$
$888$	6.60929	−	11.4476i	0.221793	−	0.384157i
$889$	30.8089	+	16.0659i	1.03330	+	0.538832i
$890$	−34.0984	+	59.0602i	−1.14298	+	1.97970i
$891$	5.52538			0.185107
$892$	1.86507	−	3.23039i	0.0624471	−	0.108162i
$893$	−2.87615	−	4.98163i	−0.0962465	−	0.166704i
$894$	−4.70008	+	8.14078i	−0.157194	+	0.272268i
$895$	26.4434	+	45.8014i	0.883906	+	1.53097i
$896$	0.615719	+	14.3354i	0.0205697	+	0.478911i
$897$	−2.16870	+	3.26473i	−0.0724107	+	0.109006i
$898$	−15.5431	−	26.9214i	−0.518679	−	0.898379i
$899$	−1.22805			−0.0409578
$900$	−6.32005			−0.210668
$901$	1.40467			0.0467964
$902$	−10.6044			−0.353089
$903$	0.378638	+	8.81557i	0.0126003	+	0.293364i
$904$	−8.76330	+	15.1785i	−0.291463	+	0.504829i
$905$	−28.8227	−	49.9224i	−0.958100	−	1.65948i
$906$	−2.29804	−	3.98033i	−0.0763473	−	0.132237i
$907$	−56.9819			−1.89205			−0.946027	−	0.324088i	$-0.894943\pi$
$907$	−56.9819			−1.89205			−0.946027	+	0.324088i	$0.894943\pi$
$908$	−0.912259	+	1.58008i	−0.0302744	+	0.0524368i
$909$	10.1397			0.336313
$910$	43.1715	−	23.7967i	1.43112	−	0.788851i
$911$	43.0338			1.42577			0.712887	−	0.701279i	$-0.247387\pi$
$911$	43.0338			1.42577			0.712887	+	0.701279i	$0.247387\pi$
$912$	−6.24310	+	10.8134i	−0.206730	+	0.358067i
$913$	−48.9071			−1.61859
$914$	−7.80831	−	13.5244i	−0.258276	−	0.447347i
$915$	7.93257	+	13.7396i	0.262243	+	0.454218i
$916$	1.16518	−	2.01815i	0.0384987	−	0.0666817i
$917$	27.9259	+	14.5625i	0.922196	+	0.480895i
$918$	0.218676			0.00721737
$919$	−6.10412			−0.201356			−0.100678	−	0.994919i	$-0.532101\pi$
$919$	−6.10412			−0.201356			−0.100678	+	0.994919i	$0.532101\pi$
$920$	−14.0191			−0.462195
$921$	13.9276			0.458931
$922$	−0.802290	−	1.38961i	−0.0264220	−	0.0457643i
$923$	−6.50141	+	9.78715i	−0.213997	+	0.322148i
$924$	6.42468	+	3.35027i	0.211357	+	0.110216i
$925$	−27.5324	−	47.6876i	−0.905261	−	1.56796i
$926$	−10.7545	+	18.6273i	−0.353413	+	0.612130i
$927$	−5.01549	−	8.68709i	−0.164730	−	0.285321i
$928$	−0.200035	+	0.346471i	−0.00656648	+	0.0113735i
$929$	1.89800			0.0622713			0.0311357	−	0.999515i	$-0.490088\pi$
$929$	1.89800			0.0622713			0.0311357	+	0.999515i	$0.490088\pi$
$930$	21.6759	−	37.5438i	0.710782	−	1.23111i
$931$	−13.4093	+	28.6503i	−0.439473	+	0.938976i
$932$	−0.597211	+	1.03440i	−0.0195623	+	0.0338829i
$933$	−2.28996	+	3.96633i	−0.0749700	+	0.129852i
$934$	52.7664			1.72657
$935$	−2.07525	+	3.59444i	−0.0678679	+	0.117551i
$936$	−11.0147	−	0.692086i	−0.360028	−	0.0226216i
$937$	6.34000			0.207119			0.103559	−	0.994623i	$-0.466977\pi$
$937$	6.34000			0.207119			0.103559	+	0.994623i	$0.466977\pi$
$938$	−0.0428026	−	0.996544i	−0.00139755	−	0.0325383i
$939$	6.75197	+	11.6948i	0.220342	+	0.381644i
$940$	2.65817			0.0866999
$941$	8.66104	−	15.0014i	0.282342	−	0.489030i	−0.689619	−	0.724172i	$-0.742222\pi$
$941$	8.66104	−	15.0014i	0.282342	−	0.489030i	0.971961	+	0.235142i	$0.0755554\pi$
$942$	2.00032	+	3.46465i	0.0651738	+	0.112884i
$943$	−1.70098			−0.0553915
$944$	5.58463			0.181764
$945$	−9.88395	−	5.15416i	−0.321525	−	0.167665i
$946$	−11.3008	−	19.5735i	−0.367420	−	0.636391i
$947$	−11.0324	+	19.1086i	−0.358503	+	0.620946i	−0.987711	−	0.156291i	$-0.950046\pi$
$947$	−11.0324	+	19.1086i	−0.358503	+	0.620946i	0.629208	+	0.777237i	$0.283380\pi$
$948$	1.14349	−	1.98059i	0.0371389	−	0.0643264i
$949$	−14.0918	+	21.2136i	−0.457440	+	0.688624i
$950$	35.3375	+	61.2064i	1.14650	+	1.98580i
$951$	2.86564	+	4.96343i	0.0929247	+	0.160950i
$952$	1.28027	+	0.667619i	0.0414937	+	0.0216377i
$953$	9.89509	−	17.1388i	0.320533	−	0.555180i	−0.660065	−	0.751209i	$-0.729471\pi$
$953$	9.89509	−	17.1388i	0.320533	−	0.555180i	0.980598	+	0.196028i	$0.0628045\pi$
$954$	−4.83163	−	8.36864i	−0.156430	−	0.270945i
$955$	−51.4297	−	89.0789i	−1.66423	−	2.88252i
$956$	1.97280	+	3.41699i	0.0638048	+	0.110513i
$957$	−0.404417	−	0.700471i	−0.0130729	−	0.0226430i
$958$	−5.79763	+	10.0418i	−0.187313	+	0.324436i
$959$	−31.7370	−	16.5498i	−1.02484	−	0.534422i
$960$	−18.7028	−	32.3941i	−0.603629	−	1.04552i
$961$	−19.6892	−	34.1027i	−0.635136	−	1.10009i
$962$	−8.49275	−	17.1050i	−0.273817	−	0.551488i
$963$	−6.92606	+	11.9963i	−0.223189	+	0.386575i
$964$	7.40385	−	12.8238i	0.238462	−	0.413028i
$965$	26.3523	+	45.6436i	0.848311	+	1.46932i
$966$	−3.12781	−	1.63105i	−0.100636	−	0.0524783i
$967$	−40.1430			−1.29091			−0.645457	−	0.763797i	$-0.723333\pi$
$967$	−40.1430			−1.29091			−0.645457	+	0.763797i	$0.723333\pi$
$968$	−59.7800			−1.92140
$969$	0.402845	+	0.697749i	0.0129413	+	0.0224149i
$970$	6.07186	−	10.5168i	0.194956	−	0.337673i
$971$	−30.8635			−0.990458			−0.495229	−	0.868762i	$-0.664916\pi$
$971$	−30.8635			−0.990458			−0.495229	+	0.868762i	$0.664916\pi$
$972$	0.247823	+	0.429243i	0.00794894	+	0.0137680i
$973$	2.47842	+	57.7034i	0.0794546	+	1.84989i
$974$	9.64428			0.309023
$975$	−25.4390	+	38.2955i	−0.814698	+	1.22644i
$976$	−5.20222	+	9.01051i	−0.166519	+	0.288419i
$977$	21.3229			0.682181			0.341090	−	0.940031i	$-0.389204\pi$
$977$	21.3229			0.682181			0.341090	+	0.940031i	$0.389204\pi$
$978$	6.40911	−	11.1009i	0.204941	−	0.354968i
$979$	−36.4593	+	63.1494i	−1.16524	+	2.01826i
$980$	−8.36747	−	11.9861i	−0.267289	−	0.382882i
$981$	0.471229	−	0.816192i	0.0150452	−	0.0260590i
$982$	36.1064			1.15220
$983$	18.7115	−	32.4092i	0.596803	−	1.03369i	−0.396487	−	0.918040i	$-0.629771\pi$
$983$	18.7115	−	32.4092i	0.596803	−	1.03369i	0.993290	−	0.115652i	$-0.0368959\pi$
$984$	−2.39485	−	4.14801i	−0.0763451	−	0.132234i
$985$	−41.1147	+	71.2128i	−1.31002	+	2.26903i
$986$	−0.0160054	−	0.0277222i	−0.000509717	−	0.000882855i
$987$	2.98618	+	1.55719i	0.0950510	+	0.0495661i
$988$	−3.59139	−	7.23332i	−0.114257	−	0.230123i
$989$	−1.81268	−	3.13965i	−0.0576397	−	0.0998349i
$990$	28.5529			0.907470
$991$	3.31902			0.105432			0.0527161	−	0.998610i	$-0.483212\pi$
$991$	3.31902			0.105432			0.0527161	+	0.998610i	$0.483212\pi$
$992$	−22.9276			−0.727953
$993$	−24.5183			−0.778065
$994$	−9.37669	−	4.88964i	−0.297411	−	0.155090i
$995$	10.0858	−	17.4691i	0.319741	−	0.553807i
$996$	−2.19357	−	3.79938i	−0.0695060	−	0.120388i
$997$	−12.0627	−	20.8932i	−0.382029	−	0.661693i	0.609323	−	0.792922i	$-0.291441\pi$
$997$	−12.0627	−	20.8932i	−0.382029	−	0.661693i	−0.991352	+	0.131229i	$0.958108\pi$
$998$	10.1728			0.322013
$999$	−2.15922	+	3.73988i	−0.0683146	+	0.118324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.j.c.172.4	yes	20
3.2	odd	2		819.2.n.f.172.7		20
7.2	even	3		273.2.l.c.16.7	yes	20
13.9	even	3		273.2.l.c.256.7	yes	20
21.2	odd	6		819.2.s.f.289.4		20
39.35	odd	6		819.2.s.f.802.4		20
91.9	even	3	inner	273.2.j.c.100.4	✓	20
273.191	odd	6		819.2.n.f.100.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.4	✓	20	91.9	even	3	inner
273.2.j.c.172.4	yes	20	1.1	even	1	trivial
273.2.l.c.16.7	yes	20	7.2	even	3
273.2.l.c.256.7	yes	20	13.9	even	3
819.2.n.f.100.7		20	273.191	odd	6
819.2.n.f.172.7		20	3.2	odd	2
819.2.s.f.289.4		20	21.2	odd	6
819.2.s.f.802.4		20	39.35	odd	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.613260 + 1.06220i) q^{2} +1.00000 q^{3} +(0.247823 + 0.429243i) q^{4} +(-2.10660 - 3.64874i) q^{5} +(-0.613260 + 1.06220i) q^{6} +(2.23241 - 1.41998i) q^{7} -3.06096 q^{8} +1.00000 q^{9} +5.16759 q^{10} +5.52538 q^{11} +(0.247823 + 0.429243i) q^{12} +(3.59845 + 0.226101i) q^{13} +(0.139251 + 3.24208i) q^{14} +(-2.10660 - 3.64874i) q^{15} +(1.38152 - 2.39286i) q^{16} +(-0.0891447 - 0.154403i) q^{17} +(-0.613260 + 1.06220i) q^{18} -4.51901 q^{19} +(1.04413 - 1.80849i) q^{20} +(2.23241 - 1.41998i) q^{21} +(-3.38850 + 5.86905i) q^{22} +(-0.543523 + 0.941410i) q^{23} -3.06096 q^{24} +(-6.37556 + 11.0428i) q^{25} +(-2.44695 + 3.68361i) q^{26} +1.00000 q^{27} +(1.16276 + 0.606342i) q^{28} +(-0.0731926 - 0.126773i) q^{29} +5.16759 q^{30} +(4.19459 - 7.26525i) q^{31} +(-1.36650 - 2.36685i) q^{32} +5.52538 q^{33} +0.218676 q^{34} +(-9.88395 - 5.15416i) q^{35} +(0.247823 + 0.429243i) q^{36} +(-2.15922 + 3.73988i) q^{37} +(2.77133 - 4.80008i) q^{38} +(3.59845 + 0.226101i) q^{39} +(6.44824 + 11.1687i) q^{40} +(0.782385 + 1.35513i) q^{41} +(0.139251 + 3.24208i) q^{42} +(-1.66752 + 2.88823i) q^{43} +(1.36932 + 2.37173i) q^{44} +(-2.10660 - 3.64874i) q^{45} +(-0.666643 - 1.15466i) q^{46} +(0.636455 + 1.10237i) q^{47} +(1.38152 - 2.39286i) q^{48} +(2.96732 - 6.33996i) q^{49} +(-7.81976 - 13.5442i) q^{50} +(-0.0891447 - 0.154403i) q^{51} +(0.794729 + 1.60064i) q^{52} +(-3.93930 + 6.82307i) q^{53} +(-0.613260 + 1.06220i) q^{54} +(-11.6398 - 20.1607i) q^{55} +(-6.83333 + 4.34650i) q^{56} -4.51901 q^{57} +0.179545 q^{58} +(1.01059 + 1.75040i) q^{59} +(1.04413 - 1.80849i) q^{60} -3.76557 q^{61} +(5.14476 + 8.91098i) q^{62} +(2.23241 - 1.41998i) q^{63} +8.87816 q^{64} +(-6.75553 - 13.6061i) q^{65} +(-3.38850 + 5.86905i) q^{66} -0.307378 q^{67} +(0.0441842 - 0.0765294i) q^{68} +(-0.543523 + 0.941410i) q^{69} +(11.5362 - 7.33787i) q^{70} +(-1.62940 + 2.82220i) q^{71} -3.06096 q^{72} +(-3.53172 + 6.11712i) q^{73} +(-2.64833 - 4.58704i) q^{74} +(-6.37556 + 11.0428i) q^{75} +(-1.11992 - 1.93975i) q^{76} +(12.3349 - 7.84593i) q^{77} +(-2.44695 + 3.68361i) q^{78} +(-2.30707 - 3.99596i) q^{79} -11.6413 q^{80} +1.00000 q^{81} -1.91922 q^{82} -8.85136 q^{83} +(1.16276 + 0.606342i) q^{84} +(-0.375585 + 0.650532i) q^{85} +(-2.04525 - 3.54248i) q^{86} +(-0.0731926 - 0.126773i) q^{87} -16.9130 q^{88} +(-6.59852 + 11.4290i) q^{89} +5.16759 q^{90} +(8.35429 - 4.60498i) q^{91} -0.538791 q^{92} +(4.19459 - 7.26525i) q^{93} -1.56125 q^{94} +(9.51976 + 16.4887i) q^{95} +(-1.36650 - 2.36685i) q^{96} +(1.17499 - 2.03514i) q^{97} +(4.91455 + 7.03992i) q^{98} +5.52538 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) \) 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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