LMFDB - Embedded newform 342.2.h.e.277.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(121,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("342.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.h (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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	342.277
Dual form			342.2.h.e.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.72474 + 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-0.724745 - 1.57313i) q^{6} +(1.72474 - 2.98735i) q^{7} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.72474 + 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-0.724745 - 1.57313i) q^{6} +(1.72474 - 2.98735i) q^{7} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +(1.50000 + 2.59808i) q^{10} +(0.275255 - 0.476756i) q^{11} +(-1.00000 + 1.41421i) q^{12} +(2.00000 - 3.46410i) q^{13} -3.44949 q^{14} +(-5.17423 - 0.476756i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.00000 - 2.82843i) q^{18} +(1.00000 - 4.24264i) q^{19} +(1.50000 - 2.59808i) q^{20} +(3.44949 - 4.87832i) q^{21} -0.550510 q^{22} +(-2.44949 + 4.24264i) q^{23} +(1.72474 + 0.158919i) q^{24} +4.00000 q^{25} -4.00000 q^{26} +(5.00000 + 1.41421i) q^{27} +(1.72474 + 2.98735i) q^{28} +1.89898 q^{29} +(2.17423 + 4.71940i) q^{30} +(1.72474 + 2.98735i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.550510 - 0.778539i) q^{33} -3.00000 q^{34} +(-5.17423 + 8.96204i) q^{35} +(-1.94949 + 2.28024i) q^{36} -8.89898 q^{37} +(-4.17423 + 1.25529i) q^{38} +(4.00000 - 5.65685i) q^{39} -3.00000 q^{40} +7.89898 q^{41} +(-5.94949 - 0.548188i) q^{42} +(3.89898 + 6.75323i) q^{43} +(0.275255 + 0.476756i) q^{44} +(-8.84847 - 1.64456i) q^{45} +4.89898 q^{46} -11.4495 q^{47} +(-0.724745 - 1.57313i) q^{48} +(-2.44949 - 4.24264i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(3.00000 - 4.24264i) q^{51} +(2.00000 + 3.46410i) q^{52} +(0.949490 + 1.64456i) q^{53} +(-1.27526 - 5.03723i) q^{54} +(-0.825765 + 1.43027i) q^{55} +(1.72474 - 2.98735i) q^{56} +(2.39898 - 7.15855i) q^{57} +(-0.949490 - 1.64456i) q^{58} -5.44949 q^{59} +(3.00000 - 4.24264i) q^{60} +3.89898 q^{61} +(1.72474 - 2.98735i) q^{62} +(6.72474 - 7.86566i) q^{63} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(-0.949490 - 0.0874863i) q^{66} +(-2.89898 + 5.02118i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-4.89898 + 6.92820i) q^{69} +10.3485 q^{70} +(3.27526 - 5.67291i) q^{71} +(2.94949 + 0.548188i) q^{72} +(-7.39898 + 12.8154i) q^{73} +(4.44949 + 7.70674i) q^{74} +(6.89898 + 0.635674i) q^{75} +(3.17423 + 2.98735i) q^{76} +(-0.949490 - 1.64456i) q^{77} +(-6.89898 - 0.635674i) q^{78} +(5.00000 + 8.66025i) q^{79} +(1.50000 + 2.59808i) q^{80} +(8.39898 + 3.23375i) q^{81} +(-3.94949 - 6.84072i) q^{82} +(8.17423 - 14.1582i) q^{83} +(2.50000 + 5.42650i) q^{84} +(-4.50000 + 7.79423i) q^{85} +(3.89898 - 6.75323i) q^{86} +(3.27526 + 0.301783i) q^{87} +(0.275255 - 0.476756i) q^{88} +(4.50000 + 7.79423i) q^{89} +(3.00000 + 8.48528i) q^{90} +(-6.89898 - 11.9494i) q^{91} +(-2.44949 - 4.24264i) q^{92} +(2.50000 + 5.42650i) q^{93} +(5.72474 + 9.91555i) q^{94} +(-3.00000 + 12.7279i) q^{95} +(-1.00000 + 1.41421i) q^{96} +(2.00000 + 3.46410i) q^{97} +(-2.44949 + 4.24264i) q^{98} +(1.07321 - 1.25529i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 12 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 12 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 12 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 2 q^{9} + 6 q^{10} + 6 q^{11} - 4 q^{12} + 8 q^{13} - 4 q^{14} - 6 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 6 q^{20} + 4 q^{21} - 12 q^{22} + 2 q^{24} + 16 q^{25} - 16 q^{26} + 20 q^{27} + 2 q^{28} - 12 q^{29} - 6 q^{30} + 2 q^{31} - 2 q^{32} + 12 q^{33} - 12 q^{34} - 6 q^{35} + 2 q^{36} - 16 q^{37} - 2 q^{38} + 16 q^{39} - 12 q^{40} + 12 q^{41} - 14 q^{42} - 4 q^{43} + 6 q^{44} - 6 q^{45} - 36 q^{47} + 2 q^{48} - 8 q^{50} + 12 q^{51} + 8 q^{52} - 6 q^{53} - 10 q^{54} - 18 q^{55} + 2 q^{56} - 10 q^{57} + 6 q^{58} - 12 q^{59} + 12 q^{60} - 4 q^{61} + 2 q^{62} + 22 q^{63} + 4 q^{64} - 24 q^{65} + 6 q^{66} + 8 q^{67} + 6 q^{68} + 12 q^{70} + 18 q^{71} + 2 q^{72} - 10 q^{73} + 8 q^{74} + 8 q^{75} - 2 q^{76} + 6 q^{77} - 8 q^{78} + 20 q^{79} + 6 q^{80} + 14 q^{81} - 6 q^{82} + 18 q^{83} + 10 q^{84} - 18 q^{85} - 4 q^{86} + 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{90} - 8 q^{91} + 10 q^{93} + 18 q^{94} - 12 q^{95} - 4 q^{96} + 8 q^{97} - 30 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 12 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 2 * q^9 + 6 * q^10 + 6 * q^11 - 4 * q^12 + 8 * q^13 - 4 * q^14 - 6 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 6 * q^20 + 4 * q^21 - 12 * q^22 + 2 * q^24 + 16 * q^25 - 16 * q^26 + 20 * q^27 + 2 * q^28 - 12 * q^29 - 6 * q^30 + 2 * q^31 - 2 * q^32 + 12 * q^33 - 12 * q^34 - 6 * q^35 + 2 * q^36 - 16 * q^37 - 2 * q^38 + 16 * q^39 - 12 * q^40 + 12 * q^41 - 14 * q^42 - 4 * q^43 + 6 * q^44 - 6 * q^45 - 36 * q^47 + 2 * q^48 - 8 * q^50 + 12 * q^51 + 8 * q^52 - 6 * q^53 - 10 * q^54 - 18 * q^55 + 2 * q^56 - 10 * q^57 + 6 * q^58 - 12 * q^59 + 12 * q^60 - 4 * q^61 + 2 * q^62 + 22 * q^63 + 4 * q^64 - 24 * q^65 + 6 * q^66 + 8 * q^67 + 6 * q^68 + 12 * q^70 + 18 * q^71 + 2 * q^72 - 10 * q^73 + 8 * q^74 + 8 * q^75 - 2 * q^76 + 6 * q^77 - 8 * q^78 + 20 * q^79 + 6 * q^80 + 14 * q^81 - 6 * q^82 + 18 * q^83 + 10 * q^84 - 18 * q^85 - 4 * q^86 + 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^90 - 8 * q^91 + 10 * q^93 + 18 * q^94 - 12 * q^95 - 4 * q^96 + 8 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.72474	+	0.158919i	0.995782	+	0.0917517i
$3$	1.72474	+	0.158919i	0.995782	+	0.0917517i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$	−0.724745	−	1.57313i	−0.295876	−	0.642229i
$7$	1.72474	−	2.98735i	0.651892	−	1.12911i	−0.330771	−	0.943711i	$-0.607309\pi$
$7$	1.72474	−	2.98735i	0.651892	−	1.12911i	0.982663	−	0.185399i	$-0.0593579\pi$
$8$	1.00000			0.353553
$9$	2.94949	+	0.548188i	0.983163	+	0.182729i
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	0.275255	−	0.476756i	0.0829925	−	0.143747i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	0.275255	−	0.476756i	0.0829925	−	0.143747i	0.904534	+	0.426401i	$0.140219\pi$
$12$	−1.00000	+	1.41421i	−0.288675	+	0.408248i
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$	−3.44949			−0.921915
$15$	−5.17423	−	0.476756i	−1.33598	−	0.123098i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	−1.00000	−	2.82843i	−0.235702	−	0.666667i
$19$	1.00000	−	4.24264i	0.229416	−	0.973329i
$19$	1.00000	−	4.24264i	0.229416	−	0.973329i
$20$	1.50000	−	2.59808i	0.335410	−	0.580948i
$21$	3.44949	−	4.87832i	0.752740	−	1.06454i
$22$	−0.550510			−0.117369
$23$	−2.44949	+	4.24264i	−0.510754	+	0.884652i	0.489168	+	0.872189i	$0.337300\pi$
$23$	−2.44949	+	4.24264i	−0.510754	+	0.884652i	−0.999922	+	0.0124624i	$0.996033\pi$
$24$	1.72474	+	0.158919i	0.352062	+	0.0324391i
$25$	4.00000			0.800000
$26$	−4.00000			−0.784465
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$	1.72474	+	2.98735i	0.325946	+	0.564555i
$29$	1.89898			0.352632			0.176316	−	0.984334i	$-0.443582\pi$
$29$	1.89898			0.352632			0.176316	+	0.984334i	$0.443582\pi$
$30$	2.17423	+	4.71940i	0.396959	+	0.861640i
$31$	1.72474	+	2.98735i	0.309773	+	0.536543i	0.978313	−	0.207134i	$-0.0664135\pi$
$31$	1.72474	+	2.98735i	0.309773	+	0.536543i	−0.668539	+	0.743677i	$0.733080\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.550510	−	0.778539i	0.0958315	−	0.135526i
$34$	−3.00000			−0.514496
$35$	−5.17423	+	8.96204i	−0.874605	+	1.51486i
$36$	−1.94949	+	2.28024i	−0.324915	+	0.380040i
$37$	−8.89898			−1.46298			−0.731492	−	0.681850i	$-0.761175\pi$
$37$	−8.89898			−1.46298			−0.731492	+	0.681850i	$0.761175\pi$
$38$	−4.17423	+	1.25529i	−0.677150	+	0.203636i
$39$	4.00000	−	5.65685i	0.640513	−	0.905822i
$40$	−3.00000			−0.474342
$41$	7.89898			1.23361			0.616807	−	0.787115i	$-0.288426\pi$
$41$	7.89898			1.23361			0.616807	+	0.787115i	$0.288426\pi$
$42$	−5.94949	−	0.548188i	−0.918026	−	0.0845873i
$43$	3.89898	+	6.75323i	0.594589	+	1.02986i	0.993605	+	0.112914i	$0.0360185\pi$
$43$	3.89898	+	6.75323i	0.594589	+	1.02986i	−0.399016	+	0.916944i	$0.630648\pi$
$44$	0.275255	+	0.476756i	0.0414963	+	0.0718737i
$45$	−8.84847	−	1.64456i	−1.31905	−	0.245157i
$46$	4.89898			0.722315
$47$	−11.4495			−1.67008			−0.835040	−	0.550189i	$-0.814555\pi$
$47$	−11.4495			−1.67008			−0.835040	+	0.550189i	$0.814555\pi$
$48$	−0.724745	−	1.57313i	−0.104608	−	0.227062i
$49$	−2.44949	−	4.24264i	−0.349927	−	0.606092i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$	3.00000	−	4.24264i	0.420084	−	0.594089i
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	0.949490	+	1.64456i	0.130422	+	0.225898i	0.923839	−	0.382780i	$-0.125033\pi$
$53$	0.949490	+	1.64456i	0.130422	+	0.225898i	−0.793417	+	0.608678i	$0.791700\pi$
$54$	−1.27526	−	5.03723i	−0.173540	−	0.685481i
$55$	−0.825765	+	1.43027i	−0.111346	+	0.192857i
$56$	1.72474	−	2.98735i	0.230479	−	0.399201i
$57$	2.39898	−	7.15855i	0.317753	−	0.948174i
$58$	−0.949490	−	1.64456i	−0.124674	−	0.215942i
$59$	−5.44949			−0.709463			−0.354732	−	0.934968i	$-0.615428\pi$
$59$	−5.44949			−0.709463			−0.354732	+	0.934968i	$0.615428\pi$
$60$	3.00000	−	4.24264i	0.387298	−	0.547723i
$61$	3.89898			0.499213			0.249607	−	0.968347i	$-0.419699\pi$
$61$	3.89898			0.499213			0.249607	+	0.968347i	$0.419699\pi$
$62$	1.72474	−	2.98735i	0.219043	−	0.379393i
$63$	6.72474	−	7.86566i	0.847238	−	0.990980i
$64$	1.00000			0.125000
$65$	−6.00000	+	10.3923i	−0.744208	+	1.28901i
$66$	−0.949490	−	0.0874863i	−0.116874	−	0.0107688i
$67$	−2.89898	+	5.02118i	−0.354167	+	0.613435i	−0.986975	−	0.160874i	$-0.948569\pi$
$67$	−2.89898	+	5.02118i	−0.354167	+	0.613435i	0.632808	+	0.774309i	$0.281902\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	−4.89898	+	6.92820i	−0.589768	+	0.834058i
$70$	10.3485			1.23688
$71$	3.27526	−	5.67291i	0.388701	−	0.673250i	−0.603574	−	0.797307i	$-0.706257\pi$
$71$	3.27526	−	5.67291i	0.388701	−	0.673250i	0.992275	+	0.124057i	$0.0395905\pi$
$72$	2.94949	+	0.548188i	0.347601	+	0.0646046i
$73$	−7.39898	+	12.8154i	−0.865985	+	1.49993i	8.07078e−5		1.00000i	$0.499974\pi$
$73$	−7.39898	+	12.8154i	−0.865985	+	1.49993i	−0.866066	+	0.499930i	$0.833359\pi$
$74$	4.44949	+	7.70674i	0.517243	+	0.895891i
$75$	6.89898	+	0.635674i	0.796626	+	0.0734014i
$76$	3.17423	+	2.98735i	0.364110	+	0.342672i
$77$	−0.949490	−	1.64456i	−0.108204	−	0.187416i
$78$	−6.89898	−	0.635674i	−0.781156	−	0.0719760i
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	8.39898	+	3.23375i	0.933220	+	0.359306i
$82$	−3.94949	−	6.84072i	−0.436148	−	0.755431i
$83$	8.17423	−	14.1582i	0.897239	−	1.55406i	0.0662297	−	0.997804i	$-0.478903\pi$
$83$	8.17423	−	14.1582i	0.897239	−	1.55406i	0.831009	−	0.556259i	$-0.187764\pi$
$84$	2.50000	+	5.42650i	0.272772	+	0.592080i
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$	3.89898	−	6.75323i	0.420438	−	0.728220i
$87$	3.27526	+	0.301783i	0.351144	+	0.0323546i
$88$	0.275255	−	0.476756i	0.0293423	−	0.0508223i
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	0.999653	−	0.0263586i	$-0.00839118\pi$
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	−0.522654	+	0.852545i	$0.675058\pi$
$90$	3.00000	+	8.48528i	0.316228	+	0.894427i
$91$	−6.89898	−	11.9494i	−0.723210	−	1.25264i
$92$	−2.44949	−	4.24264i	−0.255377	−	0.442326i
$93$	2.50000	+	5.42650i	0.259238	+	0.562702i
$94$	5.72474	+	9.91555i	0.590462	+	1.02271i
$95$	−3.00000	+	12.7279i	−0.307794	+	1.30586i
$96$	−1.00000	+	1.41421i	−0.102062	+	0.144338i
$97$	2.00000	+	3.46410i	0.203069	+	0.351726i	0.949516	−	0.313719i	$-0.101575\pi$
$97$	2.00000	+	3.46410i	0.203069	+	0.351726i	−0.746447	+	0.665445i	$0.768242\pi$
$98$	−2.44949	+	4.24264i	−0.247436	+	0.428571i
$99$	1.07321	−	1.25529i	0.107862	−	0.126162i
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−17.6969			−1.76091			−0.880456	−	0.474129i	$-0.842763\pi$
$101$	−17.6969			−1.76091			−0.880456	+	0.474129i	$0.842763\pi$
$102$	−5.17423	−	0.476756i	−0.512326	−	0.0472059i
$103$	6.62372	+	11.4726i	0.652655	+	1.13043i	0.982476	+	0.186388i	$0.0596782\pi$
$103$	6.62372	+	11.4726i	0.652655	+	1.13043i	−0.329821	+	0.944043i	$0.606988\pi$
$104$	2.00000	−	3.46410i	0.196116	−	0.339683i
$105$	−10.3485	+	14.6349i	−1.00991	+	1.42822i
$106$	0.949490	−	1.64456i	0.0922226	−	0.159734i
$107$	−4.89898			−0.473602			−0.236801	−	0.971558i	$-0.576099\pi$
$107$	−4.89898			−0.473602			−0.236801	+	0.971558i	$0.576099\pi$
$108$	−3.72474	+	3.62302i	−0.358414	+	0.348625i
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	−0.841086	−	0.540901i	$-0.818083\pi$
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	0.888977	+	0.457951i	$0.151417\pi$
$110$	1.65153			0.157467
$111$	−15.3485	−	1.41421i	−1.45681	−	0.134231i
$112$	−3.44949			−0.325946
$113$	2.05051	+	3.55159i	0.192896	+	0.334105i	0.946209	−	0.323557i	$-0.104879\pi$
$113$	2.05051	+	3.55159i	0.192896	+	0.334105i	−0.753313	+	0.657662i	$0.771545\pi$
$114$	−7.39898	+	1.50170i	−0.692978	+	0.140647i
$115$	7.34847	−	12.7279i	0.685248	−	1.18688i
$116$	−0.949490	+	1.64456i	−0.0881579	+	0.152694i
$117$	7.79796	−	9.12096i	0.720922	−	0.843233i
$118$	2.72474	+	4.71940i	0.250833	+	0.434456i
$119$	−5.17423	−	8.96204i	−0.474321	−	0.821549i
$120$	−5.17423	−	0.476756i	−0.472341	−	0.0435217i
$121$	5.34847	+	9.26382i	0.486224	+	0.842165i
$122$	−1.94949	−	3.37662i	−0.176499	−	0.305704i
$123$	13.6237	+	1.25529i	1.22841	+	0.113186i
$124$	−3.44949			−0.309773
$125$	3.00000			0.268328
$126$	−10.1742	−	1.89097i	−0.906393	−	0.168461i
$127$	−6.17423	−	10.6941i	−0.547875	−	0.948947i	−0.998420	−	0.0561932i	$-0.982104\pi$
$127$	−6.17423	−	10.6941i	−0.547875	−	0.948947i	0.450545	−	0.892754i	$-0.351230\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	5.65153	+	12.2672i	0.497590	+	1.08007i
$130$	12.0000			1.05247
$131$	20.1464			1.76020			0.880101	−	0.474787i	$-0.157475\pi$
$131$	20.1464			1.76020			0.880101	+	0.474787i	$0.157475\pi$
$132$	0.398979	+	0.866025i	0.0347267	+	0.0753778i
$133$	−10.9495	−	10.3048i	−0.949441	−	0.893541i
$134$	5.79796			0.500867
$135$	−15.0000	−	4.24264i	−1.29099	−	0.365148i
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	11.6969			0.999337			0.499668	−	0.866217i	$-0.333455\pi$
$137$	11.6969			0.999337			0.499668	+	0.866217i	$0.333455\pi$
$138$	8.44949	+	0.778539i	0.719268	+	0.0662736i
$139$	5.55051	−	9.61377i	0.470788	−	0.815429i	−0.528654	−	0.848838i	$-0.677303\pi$
$139$	5.55051	−	9.61377i	0.470788	−	0.815429i	0.999442	+	0.0334087i	$0.0106363\pi$
$140$	−5.17423	−	8.96204i	−0.437303	−	0.757430i
$141$	−19.7474	−	1.81954i	−1.66304	−	0.153233i
$142$	−6.55051			−0.549707
$143$	−1.10102	−	1.90702i	−0.0920720	−	0.159473i
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$	−5.69694			−0.473105
$146$	14.7980			1.22469
$147$	−3.55051	−	7.70674i	−0.292841	−	0.635641i
$148$	4.44949	−	7.70674i	0.365746	−	0.633490i
$149$	0.797959			0.0653713			0.0326857	−	0.999466i	$-0.489594\pi$
$149$	0.797959			0.0653713			0.0326857	+	0.999466i	$0.489594\pi$
$150$	−2.89898	−	6.29253i	−0.236701	−	0.513783i
$151$	10.1742	−	17.6223i	0.827967	−	1.43408i	−0.0716626	−	0.997429i	$-0.522830\pi$
$151$	10.1742	−	17.6223i	0.827967	−	1.43408i	0.899630	−	0.436653i	$-0.143836\pi$
$152$	1.00000	−	4.24264i	0.0811107	−	0.344124i
$153$	5.84847	−	6.84072i	0.472821	−	0.553039i
$154$	−0.949490	+	1.64456i	−0.0765121	+	0.132523i
$155$	−5.17423	−	8.96204i	−0.415605	−	0.719848i
$156$	2.89898	+	6.29253i	0.232104	+	0.503806i
$157$	−2.10102			−0.167680			−0.0838398	−	0.996479i	$-0.526718\pi$
$157$	−2.10102			−0.167680			−0.0838398	+	0.996479i	$0.526718\pi$
$158$	5.00000	−	8.66025i	0.397779	−	0.688973i
$159$	1.37628	+	2.98735i	0.109146	+	0.236912i
$160$	1.50000	−	2.59808i	0.118585	−	0.205396i
$161$	8.44949	+	14.6349i	0.665913	+	1.15340i
$162$	−1.39898	−	8.89060i	−0.109914	−	0.698512i
$163$	−20.8990			−1.63693			−0.818467	−	0.574553i	$-0.805176\pi$
$163$	−20.8990			−1.63693			−0.818467	+	0.574553i	$0.805176\pi$
$164$	−3.94949	+	6.84072i	−0.308403	+	0.534170i
$165$	−1.65153	+	2.33562i	−0.128571	+	0.181828i
$166$	−16.3485			−1.26889
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	−0.958440	−	0.285295i	$-0.907908\pi$
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	0.726293	+	0.687386i	$0.241242\pi$
$168$	3.44949	−	4.87832i	0.266134	−	0.376370i
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	9.00000			0.690268
$171$	5.27526	−	11.9654i	0.403409	−	0.915020i
$172$	−7.79796			−0.594589
$173$	3.55051	+	6.14966i	0.269940	+	0.467550i	0.968846	−	0.247663i	$-0.0796627\pi$
$173$	3.55051	+	6.14966i	0.269940	+	0.467550i	−0.698906	+	0.715214i	$0.746329\pi$
$174$	−1.37628	−	2.98735i	−0.104335	−	0.226470i
$175$	6.89898	−	11.9494i	0.521514	−	0.903288i
$176$	−0.550510			−0.0414963
$177$	−9.39898	−	0.866025i	−0.706471	−	0.0650945i
$178$	4.50000	−	7.79423i	0.337289	−	0.584202i
$179$	−16.8990			−1.26309			−0.631545	−	0.775340i	$-0.717579\pi$
$179$	−16.8990			−1.26309			−0.631545	+	0.775340i	$0.717579\pi$
$180$	5.84847	−	6.84072i	0.435919	−	0.509877i
$181$	−5.50000	−	9.52628i	−0.408812	−	0.708083i	0.585945	−	0.810351i	$-0.300723\pi$
$181$	−5.50000	−	9.52628i	−0.408812	−	0.708083i	−0.994757	+	0.102268i	$0.967390\pi$
$182$	−6.89898	+	11.9494i	−0.511386	+	0.885747i
$183$	6.72474	+	0.619620i	0.497107	+	0.0458037i
$184$	−2.44949	+	4.24264i	−0.180579	+	0.312772i
$185$	26.6969			1.96280
$186$	3.44949	−	4.87832i	0.252929	−	0.357695i
$187$	−0.825765	−	1.43027i	−0.0603859	−	0.104592i
$188$	5.72474	−	9.91555i	0.417520	−	0.723166i
$189$	12.8485	−	12.4976i	0.934589	−	0.909065i
$190$	12.5227	−	3.76588i	0.908492	−	0.273206i
$191$	1.62372	−	2.81237i	0.117489	−	0.203496i	−0.801283	−	0.598285i	$-0.795849\pi$
$191$	1.62372	−	2.81237i	0.117489	−	0.203496i	0.918772	+	0.394789i	$0.129182\pi$
$192$	1.72474	+	0.158919i	0.124473	+	0.0114690i
$193$	−20.5959			−1.48253			−0.741263	−	0.671214i	$-0.765773\pi$
$193$	−20.5959			−1.48253			−0.741263	+	0.671214i	$0.765773\pi$
$194$	2.00000	−	3.46410i	0.143592	−	0.248708i
$195$	−12.0000	+	16.9706i	−0.859338	+	1.21529i
$196$	4.89898			0.349927
$197$	−2.20204			−0.156889			−0.0784445	−	0.996918i	$-0.524995\pi$
$197$	−2.20204			−0.156889			−0.0784445	+	0.996918i	$0.524995\pi$
$198$	−1.62372	−	0.301783i	−0.115393	−	0.0214468i
$199$	−0.174235	−	0.301783i	−0.0123512	−	0.0213928i	0.859784	−	0.510658i	$-0.170598\pi$
$199$	−0.174235	−	0.301783i	−0.0123512	−	0.0213928i	−0.872135	+	0.489265i	$0.837265\pi$
$200$	4.00000			0.282843
$201$	−5.79796	+	8.19955i	−0.408956	+	0.578352i
$202$	8.84847	+	15.3260i	0.622576	+	1.07833i
$203$	3.27526	−	5.67291i	0.229878	−	0.398160i
$204$	2.17423	+	4.71940i	0.152227	+	0.330424i
$205$	−23.6969			−1.65507
$206$	6.62372	−	11.4726i	0.461497	−	0.799336i
$207$	−9.55051	+	11.1708i	−0.663806	+	0.776427i
$208$	−4.00000			−0.277350
$209$	−1.74745	−	1.64456i	−0.120874	−	0.113757i
$210$	17.8485	+	1.64456i	1.23166	+	0.113486i
$211$	−23.0454			−1.58651			−0.793256	−	0.608889i	$-0.791616\pi$
$211$	−23.0454			−1.58651			−0.793256	+	0.608889i	$0.791616\pi$
$212$	−1.89898			−0.130422
$213$	6.55051	−	9.26382i	0.448834	−	0.634747i
$214$	2.44949	+	4.24264i	0.167444	+	0.290021i
$215$	−11.6969	−	20.2597i	−0.797725	−	1.38170i
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$	11.8990			0.807755
$218$	−1.00000			−0.0677285
$219$	−14.7980	+	20.9275i	−0.999953	+	1.41415i
$220$	−0.825765	−	1.43027i	−0.0556731	−	0.0964286i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	6.44949	+	13.9993i	0.432861	+	0.939570i
$223$	−0.449490	−	0.778539i	−0.0301001	−	0.0521348i	0.850583	−	0.525841i	$-0.176249\pi$
$223$	−0.449490	−	0.778539i	−0.0301001	−	0.0521348i	−0.880683	+	0.473706i	$0.842916\pi$
$224$	1.72474	+	2.98735i	0.115239	+	0.199600i
$225$	11.7980	+	2.19275i	0.786531	+	0.146184i
$226$	2.05051	−	3.55159i	0.136398	−	0.236248i
$227$	8.72474	−	15.1117i	0.579082	−	1.00300i	−0.416503	−	0.909134i	$-0.636745\pi$
$227$	8.72474	−	15.1117i	0.579082	−	1.00300i	0.995585	−	0.0938647i	$-0.0299221\pi$
$228$	5.00000	+	5.65685i	0.331133	+	0.374634i
$229$	13.2980	+	23.0327i	0.878754	+	1.52205i	0.852709	+	0.522386i	$0.174958\pi$
$229$	13.2980	+	23.0327i	0.878754	+	1.52205i	0.0260445	+	0.999661i	$0.491709\pi$
$230$	−14.6969			−0.969087
$231$	−1.37628	−	2.98735i	−0.0905523	−	0.196553i
$232$	1.89898			0.124674
$233$	−9.94949	+	17.2330i	−0.651813	+	1.12897i	0.330870	+	0.943676i	$0.392658\pi$
$233$	−9.94949	+	17.2330i	−0.651813	+	1.12897i	−0.982683	+	0.185296i	$0.940675\pi$
$234$	−11.7980	−	2.19275i	−0.771257	−	0.143345i
$235$	34.3485			2.24065
$236$	2.72474	−	4.71940i	0.177366	−	0.307207i
$237$	7.24745	+	15.7313i	0.470772	+	1.02186i
$238$	−5.17423	+	8.96204i	−0.335396	+	0.580923i
$239$	2.72474	+	4.71940i	0.176249	+	0.305272i	0.940593	−	0.339537i	$-0.110270\pi$
$239$	2.72474	+	4.71940i	0.176249	+	0.305272i	−0.764344	+	0.644809i	$0.776937\pi$
$240$	2.17423	+	4.71940i	0.140346	+	0.304636i
$241$	−22.7980			−1.46855			−0.734273	−	0.678854i	$-0.762477\pi$
$241$	−22.7980			−1.46855			−0.734273	+	0.678854i	$0.762477\pi$
$242$	5.34847	−	9.26382i	0.343813	−	0.595501i
$243$	13.9722	+	6.91215i	0.896317	+	0.443415i
$244$	−1.94949	+	3.37662i	−0.124803	+	0.216166i
$245$	7.34847	+	12.7279i	0.469476	+	0.813157i
$246$	−5.72474	−	12.4261i	−0.364996	−	0.792262i
$247$	−12.6969	−	11.9494i	−0.807887	−	0.760321i
$248$	1.72474	+	2.98735i	0.109521	+	0.189697i
$249$	16.3485	−	23.1202i	1.03604	−	1.46518i
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	3.82577	+	6.62642i	0.241480	+	0.418256i	0.961136	−	0.276075i	$-0.0890338\pi$
$251$	3.82577	+	6.62642i	0.241480	+	0.418256i	−0.719656	+	0.694331i	$0.755700\pi$
$252$	3.44949	+	9.75663i	0.217297	+	0.614610i
$253$	1.34847	+	2.33562i	0.0847775	+	0.146839i
$254$	−6.17423	+	10.6941i	−0.387406	+	0.671007i
$255$	−9.00000	+	12.7279i	−0.563602	+	0.797053i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.10102	−	1.90702i	0.0686798	−	0.118957i	−0.829641	−	0.558298i	$-0.811455\pi$
$257$	1.10102	−	1.90702i	0.0686798	−	0.118957i	0.898320	+	0.439341i	$0.144788\pi$
$258$	7.79796	−	11.0280i	0.485480	−	0.686572i
$259$	−15.3485	+	26.5843i	−0.953707	+	1.65187i
$260$	−6.00000	−	10.3923i	−0.372104	−	0.644503i
$261$	5.60102	+	1.04100i	0.346694	+	0.0644362i
$262$	−10.0732	−	17.4473i	−0.622325	−	1.07790i
$263$	4.89898	+	8.48528i	0.302084	+	0.523225i	0.976608	−	0.215028i	$-0.0689843\pi$
$263$	4.89898	+	8.48528i	0.302084	+	0.523225i	−0.674524	+	0.738253i	$0.735651\pi$
$264$	0.550510	−	0.778539i	0.0338816	−	0.0479158i
$265$	−2.84847	−	4.93369i	−0.174980	−	0.303074i
$266$	−3.44949	+	14.6349i	−0.211502	+	0.897326i
$267$	6.52270	+	14.1582i	0.399183	+	0.866467i
$268$	−2.89898	−	5.02118i	−0.177083	−	0.306717i
$269$	−6.94949	+	12.0369i	−0.423718	+	0.733901i	−0.996300	−	0.0859467i	$-0.972609\pi$
$269$	−6.94949	+	12.0369i	−0.423718	+	0.733901i	0.572582	+	0.819848i	$0.305942\pi$
$270$	3.82577	+	15.1117i	0.232829	+	0.919669i
$271$	10.1742	−	17.6223i	0.618041	−	1.07048i	−0.371802	−	0.928312i	$-0.621260\pi$
$271$	10.1742	−	17.6223i	0.618041	−	1.07048i	0.989843	−	0.142166i	$-0.0454067\pi$
$272$	−3.00000			−0.181902
$273$	−10.0000	−	21.7060i	−0.605228	−	1.31371i
$274$	−5.84847	−	10.1298i	−0.353319	−	0.611966i
$275$	1.10102	−	1.90702i	0.0663940	−	0.114998i
$276$	−3.55051	−	7.70674i	−0.213716	−	0.463891i
$277$	13.8485	−	23.9863i	0.832074	−	1.44119i	−0.0643169	−	0.997930i	$-0.520487\pi$
$277$	13.8485	−	23.9863i	0.832074	−	1.44119i	0.896391	−	0.443265i	$-0.146180\pi$
$278$	−11.1010			−0.665795
$279$	3.44949	+	9.75663i	0.206516	+	0.584114i
$280$	−5.17423	+	8.96204i	−0.309220	+	0.535584i
$281$	21.0000			1.25275			0.626377	−	0.779520i	$-0.284537\pi$
$281$	21.0000			1.25275			0.626377	+	0.779520i	$0.284537\pi$
$282$	8.29796	+	18.0116i	0.494136	+	1.07257i
$283$	24.3485			1.44737			0.723683	−	0.690132i	$-0.242448\pi$
$283$	24.3485			1.44737			0.723683	+	0.690132i	$0.242448\pi$
$284$	3.27526	+	5.67291i	0.194351	+	0.336625i
$285$	−7.19694	+	21.4757i	−0.426310	+	1.27211i
$286$	−1.10102	+	1.90702i	−0.0651047	+	0.112765i
$287$	13.6237	−	23.5970i	0.804183	−	1.39289i
$288$	−1.94949	+	2.28024i	−0.114875	+	0.134364i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	2.84847	+	4.93369i	0.167268	+	0.289716i
$291$	2.89898	+	6.29253i	0.169941	+	0.368875i
$292$	−7.39898	−	12.8154i	−0.432993	−	0.749965i
$293$	−14.8485	−	25.7183i	−0.867457	−	1.50248i	−0.864587	−	0.502483i	$-0.832420\pi$
$293$	−14.8485	−	25.7183i	−0.867457	−	1.50248i	−0.00286999	−	0.999996i	$-0.500914\pi$
$294$	−4.89898	+	6.92820i	−0.285714	+	0.404061i
$295$	16.3485			0.951845
$296$	−8.89898			−0.517243
$297$	2.05051	−	1.99451i	0.118983	−	0.115733i
$298$	−0.398979	−	0.691053i	−0.0231123	−	0.0400316i
$299$	9.79796	+	16.9706i	0.566631	+	0.981433i
$300$	−4.00000	+	5.65685i	−0.230940	+	0.326599i
$301$	26.8990			1.55043
$302$	−20.3485			−1.17092
$303$	−30.5227	−	2.81237i	−1.75348	−	0.161567i
$304$	−4.17423	+	1.25529i	−0.239409	+	0.0719961i
$305$	−11.6969			−0.669765
$306$	−8.84847	−	1.64456i	−0.505833	−	0.0940135i
$307$	−3.17423	+	5.49794i	−0.181163	+	0.313784i	−0.942277	−	0.334835i	$-0.891320\pi$
$307$	−3.17423	+	5.49794i	−0.181163	+	0.313784i	0.761114	+	0.648618i	$0.224653\pi$
$308$	1.89898			0.108204
$309$	9.60102	+	20.8400i	0.546183	+	1.18555i
$310$	−5.17423	+	8.96204i	−0.293877	+	0.509010i
$311$	6.82577	+	11.8226i	0.387054	+	0.670397i	0.992052	−	0.125830i	$-0.0401595\pi$
$311$	6.82577	+	11.8226i	0.387054	+	0.670397i	−0.604998	+	0.796227i	$0.706826\pi$
$312$	4.00000	−	5.65685i	0.226455	−	0.320256i
$313$	−1.00000			−0.0565233			−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000			−0.0565233			−0.0282617	+	0.999601i	$0.508997\pi$
$314$	1.05051	+	1.81954i	0.0592837	+	0.102682i
$315$	−20.1742	+	23.5970i	−1.13669	+	1.32954i
$316$	−10.0000			−0.562544
$317$	11.6969			0.656966			0.328483	−	0.944510i	$-0.393463\pi$
$317$	11.6969			0.656966			0.328483	+	0.944510i	$0.393463\pi$
$318$	1.89898	−	2.68556i	0.106489	−	0.150599i
$319$	0.522704	−	0.905350i	0.0292658	−	0.0506898i
$320$	−3.00000			−0.167705
$321$	−8.44949	−	0.778539i	−0.471605	−	0.0434538i
$322$	8.44949	−	14.6349i	0.470872	−	0.815574i
$323$	−9.52270	−	8.96204i	−0.529857	−	0.498661i
$324$	−7.00000	+	5.65685i	−0.388889	+	0.314270i
$325$	8.00000	−	13.8564i	0.443760	−	0.768615i
$326$	10.4495	+	18.0990i	0.578744	+	1.00241i
$327$	1.00000	−	1.41421i	0.0553001	−	0.0782062i
$328$	7.89898			0.436148
$329$	−19.7474	+	34.2036i	−1.08871	+	1.88570i
$330$	2.84847	+	0.262459i	0.156803	+	0.0144479i
$331$	−0.174235	+	0.301783i	−0.00957680	+	0.0165875i	−0.870774	−	0.491683i	$-0.836382\pi$
$331$	−0.174235	+	0.301783i	−0.00957680	+	0.0165875i	0.861197	+	0.508271i	$0.169715\pi$
$332$	8.17423	+	14.1582i	0.448619	+	0.777032i
$333$	−26.2474	−	4.87832i	−1.43835	−	0.267330i
$334$	6.00000			0.328305
$335$	8.69694	−	15.0635i	0.475165	−	0.823009i
$336$	−5.94949	−	0.548188i	−0.324571	−	0.0299061i
$337$	−2.10102			−0.114450			−0.0572249	−	0.998361i	$-0.518225\pi$
$337$	−2.10102			−0.114450			−0.0572249	+	0.998361i	$0.518225\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$	2.97219	+	6.45145i	0.161427	+	0.350395i
$340$	−4.50000	−	7.79423i	−0.244047	−	0.422701i
$341$	1.89898			0.102836
$342$	−13.0000	+	1.41421i	−0.702959	+	0.0764719i
$343$	7.24745			0.391325
$344$	3.89898	+	6.75323i	0.210219	+	0.364110i
$345$	14.6969	−	20.7846i	0.791257	−	1.11901i
$346$	3.55051	−	6.14966i	0.190877	−	0.330608i
$347$	12.5505			0.673747			0.336873	−	0.941550i	$-0.390631\pi$
$347$	12.5505			0.673747			0.336873	+	0.941550i	$0.390631\pi$
$348$	−1.89898	+	2.68556i	−0.101796	+	0.143961i
$349$	−9.05051	+	15.6759i	−0.484463	+	0.839114i	−0.999841	−	0.0178489i	$-0.994318\pi$
$349$	−9.05051	+	15.6759i	−0.484463	+	0.839114i	0.515378	+	0.856963i	$0.327652\pi$
$350$	−13.7980			−0.737532
$351$	14.8990	−	14.4921i	0.795249	−	0.773530i
$352$	0.275255	+	0.476756i	0.0146711	+	0.0254112i
$353$	−0.949490	+	1.64456i	−0.0505362	+	0.0875313i	−0.890187	−	0.455595i	$-0.849426\pi$
$353$	−0.949490	+	1.64456i	−0.0505362	+	0.0875313i	0.839651	+	0.543127i	$0.182760\pi$
$354$	3.94949	+	8.57277i	0.209913	+	0.455637i
$355$	−9.82577	+	17.0187i	−0.521497	+	0.903260i
$356$	−9.00000			−0.476999
$357$	−7.50000	−	16.2795i	−0.396942	−	0.861603i
$358$	8.44949	+	14.6349i	0.446569	+	0.773481i
$359$	11.7247	−	20.3079i	0.618808	−	1.07181i	−0.370895	−	0.928675i	$-0.620949\pi$
$359$	11.7247	−	20.3079i	0.618808	−	1.07181i	0.989703	−	0.143133i	$-0.0457176\pi$
$360$	−8.84847	−	1.64456i	−0.466355	−	0.0866762i
$361$	−17.0000	−	8.48528i	−0.894737	−	0.446594i
$362$	−5.50000	+	9.52628i	−0.289074	+	0.500690i
$363$	7.75255	+	16.8277i	0.406903	+	0.883225i
$364$	13.7980			0.723210
$365$	22.1969	−	38.4462i	1.16184	−	2.01237i
$366$	−2.82577	−	6.13361i	−0.147705	−	0.320609i
$367$	8.55051			0.446333			0.223167	−	0.974780i	$-0.428361\pi$
$367$	8.55051			0.446333			0.223167	+	0.974780i	$0.428361\pi$
$368$	4.89898			0.255377
$369$	23.2980	+	4.33013i	1.21284	+	0.225417i
$370$	−13.3485	−	23.1202i	−0.693954	−	1.20196i
$371$	6.55051			0.340086
$372$	−5.94949	−	0.548188i	−0.308467	−	0.0284222i
$373$	−12.8485	−	22.2542i	−0.665269	−	1.15228i	−0.979212	−	0.202837i	$-0.934984\pi$
$373$	−12.8485	−	22.2542i	−0.665269	−	1.15228i	0.313944	−	0.949442i	$-0.398350\pi$
$374$	−0.825765	+	1.43027i	−0.0426993	+	0.0739574i
$375$	5.17423	+	0.476756i	0.267196	+	0.0246196i
$376$	−11.4495			−0.590462
$377$	3.79796	−	6.57826i	0.195605	−	0.338798i
$378$	−17.2474	−	4.87832i	−0.887113	−	0.250913i
$379$	15.5959			0.801108			0.400554	−	0.916273i	$-0.368818\pi$
$379$	15.5959			0.801108			0.400554	+	0.916273i	$0.368818\pi$
$380$	−9.52270	−	8.96204i	−0.488504	−	0.459743i
$381$	−8.94949	−	19.4258i	−0.458496	−	0.995213i
$382$	−3.24745			−0.166154
$383$	−28.8434			−1.47383			−0.736914	−	0.675987i	$-0.763718\pi$
$383$	−28.8434			−1.47383			−0.736914	+	0.675987i	$0.763718\pi$
$384$	−0.724745	−	1.57313i	−0.0369845	−	0.0802786i
$385$	2.84847	+	4.93369i	0.145171	+	0.251444i
$386$	10.2980	+	17.8366i	0.524152	+	0.907858i
$387$	7.79796	+	22.0560i	0.396393	+	1.12117i
$388$	−4.00000			−0.203069
$389$	−18.7980			−0.953094			−0.476547	−	0.879149i	$-0.658112\pi$
$389$	−18.7980			−0.953094			−0.476547	+	0.879149i	$0.658112\pi$
$390$	20.6969	+	1.90702i	1.04803	+	0.0965659i
$391$	7.34847	+	12.7279i	0.371628	+	0.643679i
$392$	−2.44949	−	4.24264i	−0.123718	−	0.214286i
$393$	34.7474	+	3.20164i	1.75278	+	0.161502i
$394$	1.10102	+	1.90702i	0.0554686	+	0.0960745i
$395$	−15.0000	−	25.9808i	−0.754732	−	1.30723i
$396$	0.550510	+	1.55708i	0.0276642	+	0.0782461i
$397$	−12.2980	+	21.3007i	−0.617217	+	1.06905i	0.372774	+	0.927922i	$0.378407\pi$
$397$	−12.2980	+	21.3007i	−0.617217	+	1.06905i	−0.989991	+	0.141129i	$0.954927\pi$
$398$	−0.174235	+	0.301783i	−0.00873359	+	0.0151270i
$399$	−17.2474	−	19.5133i	−0.863452	−	0.976885i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−11.2020			−0.559403			−0.279702	−	0.960087i	$-0.590236\pi$
$401$	−11.2020			−0.559403			−0.279702	+	0.960087i	$0.590236\pi$
$402$	10.0000	+	0.921404i	0.498755	+	0.0459554i
$403$	13.7980			0.687325
$404$	8.84847	−	15.3260i	0.440228	−	0.762497i
$405$	−25.1969	−	9.70125i	−1.25205	−	0.482059i
$406$	−6.55051			−0.325096
$407$	−2.44949	+	4.24264i	−0.121417	+	0.210300i
$408$	3.00000	−	4.24264i	0.148522	−	0.210042i
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$	11.8485	+	20.5222i	0.585154	+	1.01352i
$411$	20.1742	+	1.85886i	0.995122	+	0.0916909i
$412$	−13.2474			−0.652655
$413$	−9.39898	+	16.2795i	−0.462494	+	0.801062i
$414$	14.4495	+	2.68556i	0.710154	+	0.131988i
$415$	−24.5227	+	42.4746i	−1.20377	+	2.08499i
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$	11.1010	−	15.6992i	0.543619	−	0.768794i
$418$	−0.550510	+	2.33562i	−0.0269263	+	0.114239i
$419$	−7.62372	−	13.2047i	−0.372443	−	0.645091i	0.617498	−	0.786573i	$-0.288147\pi$
$419$	−7.62372	−	13.2047i	−0.372443	−	0.645091i	−0.989941	+	0.141482i	$0.954813\pi$
$420$	−7.50000	−	16.2795i	−0.365963	−	0.794359i
$421$	9.34847	+	16.1920i	0.455617	+	0.789151i	0.998723	−	0.0505126i	$-0.0160855\pi$
$421$	9.34847	+	16.1920i	0.455617	+	0.789151i	−0.543107	+	0.839664i	$0.682752\pi$
$422$	11.5227	+	19.9579i	0.560916	+	0.971536i
$423$	−33.7702	−	6.27647i	−1.64196	−	0.305173i
$424$	0.949490	+	1.64456i	0.0461113	+	0.0798671i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$	−11.2980	−	1.04100i	−0.547388	−	0.0504365i
$427$	6.72474	−	11.6476i	0.325433	−	0.563667i
$428$	2.44949	−	4.24264i	0.118401	−	0.205076i
$429$	−1.59592	−	3.46410i	−0.0770516	−	0.167248i
$430$	−11.6969	+	20.2597i	−0.564076	+	0.977009i
$431$	4.62372	+	8.00853i	0.222717	+	0.385757i	0.955632	−	0.294563i	$-0.0951741\pi$
$431$	4.62372	+	8.00853i	0.222717	+	0.385757i	−0.732915	+	0.680320i	$0.761841\pi$
$432$	−1.27526	−	5.03723i	−0.0613557	−	0.242354i
$433$	8.39898	+	14.5475i	0.403629	+	0.699106i	0.994161	−	0.107908i	$-0.0344153\pi$
$433$	8.39898	+	14.5475i	0.403629	+	0.699106i	−0.590532	+	0.807014i	$0.701082\pi$
$434$	−5.94949	−	10.3048i	−0.285585	−	0.494647i
$435$	−9.82577	−	0.905350i	−0.471109	−	0.0434082i
$436$	0.500000	+	0.866025i	0.0239457	+	0.0414751i
$437$	15.5505	+	14.6349i	0.743882	+	0.700084i
$438$	25.5227	+	2.35167i	1.21952	+	0.112367i
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	−0.825765	+	1.43027i	−0.0393668	+	0.0681853i
$441$	−4.89898	−	13.8564i	−0.233285	−	0.659829i
$442$	−6.00000	+	10.3923i	−0.285391	+	0.494312i
$443$	−38.1464			−1.81239			−0.906196	−	0.422858i	$-0.861027\pi$
$443$	−38.1464			−1.81239			−0.906196	+	0.422858i	$0.861027\pi$
$444$	8.89898	−	12.5851i	0.422327	−	0.597260i
$445$	−13.5000	−	23.3827i	−0.639961	−	1.10845i
$446$	−0.449490	+	0.778539i	−0.0212840	+	0.0368649i
$447$	1.37628	+	0.126811i	0.0650956	+	0.00599793i
$448$	1.72474	−	2.98735i	0.0814865	−	0.141139i
$449$	2.20204			0.103921			0.0519604	−	0.998649i	$-0.483453\pi$
$449$	2.20204			0.103921			0.0519604	+	0.998649i	$0.483453\pi$
$450$	−4.00000	−	11.3137i	−0.188562	−	0.533333i
$451$	2.17423	−	3.76588i	0.102381	−	0.177329i
$452$	−4.10102			−0.192896
$453$	20.3485	−	28.7771i	0.956054	−	1.35207i
$454$	−17.4495			−0.818945
$455$	20.6969	+	35.8481i	0.970287	+	1.68059i
$456$	2.39898	−	7.15855i	0.112343	−	0.335230i
$457$	10.6010	−	18.3615i	0.495895	−	0.858915i	−0.504094	−	0.863649i	$-0.668173\pi$
$457$	10.6010	−	18.3615i	0.495895	−	0.858915i	0.999989	+	0.00473378i	$0.00150681\pi$
$458$	13.2980	−	23.0327i	0.621373	−	1.07625i
$459$	11.1742	−	10.8691i	0.521569	−	0.507324i
$460$	7.34847	+	12.7279i	0.342624	+	0.593442i
$461$	14.6969	+	25.4558i	0.684505	+	1.18560i	0.973592	+	0.228294i	$0.0733148\pi$
$461$	14.6969	+	25.4558i	0.684505	+	1.18560i	−0.289088	+	0.957303i	$0.593352\pi$
$462$	−1.89898	+	2.68556i	−0.0883485	+	0.124944i
$463$	−4.82577	−	8.35847i	−0.224272	−	0.388451i	0.731829	−	0.681489i	$-0.238667\pi$
$463$	−4.82577	−	8.35847i	−0.224272	−	0.388451i	−0.956101	+	0.293038i	$0.905334\pi$
$464$	−0.949490	−	1.64456i	−0.0440790	−	0.0763470i
$465$	−7.50000	−	16.2795i	−0.347804	−	0.754944i
$466$	19.8990			0.921802
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$	4.00000	+	11.3137i	0.184900	+	0.522976i
$469$	10.0000	+	17.3205i	0.461757	+	0.799787i
$470$	−17.1742	−	29.7466i	−0.792188	−	1.37211i
$471$	−3.62372	−	0.333891i	−0.166972	−	0.0153849i
$472$	−5.44949			−0.250833
$473$	4.29286			0.197386
$474$	10.0000	−	14.1421i	0.459315	−	0.649570i
$475$	4.00000	−	16.9706i	0.183533	−	0.778663i
$476$	10.3485			0.474321
$477$	1.89898	+	5.37113i	0.0869483	+	0.245927i
$478$	2.72474	−	4.71940i	0.124627	−	0.215860i
$479$	5.44949			0.248994			0.124497	−	0.992220i	$-0.460268\pi$
$479$	5.44949			0.248994			0.124497	+	0.992220i	$0.460268\pi$
$480$	3.00000	−	4.24264i	0.136931	−	0.193649i
$481$	−17.7980	+	30.8270i	−0.811517	+	1.40559i
$482$	11.3990	+	19.7436i	0.519209	+	0.899297i
$483$	12.2474	+	26.5843i	0.557278	+	1.20963i
$484$	−10.6969			−0.486224
$485$	−6.00000	−	10.3923i	−0.272446	−	0.471890i
$486$	−1.00000	−	15.5563i	−0.0453609	−	0.705650i
$487$	−21.3939			−0.969449			−0.484725	−	0.874667i	$-0.661080\pi$
$487$	−21.3939			−0.969449			−0.484725	+	0.874667i	$0.661080\pi$
$488$	3.89898			0.176499
$489$	−36.0454	−	3.32124i	−1.63003	−	0.150192i
$490$	7.34847	−	12.7279i	0.331970	−	0.574989i
$491$	−39.7423			−1.79355			−0.896773	−	0.442490i	$-0.854095\pi$
$491$	−39.7423			−1.79355			−0.896773	+	0.442490i	$0.854095\pi$
$492$	−7.89898	+	11.1708i	−0.356113	+	0.503621i
$493$	2.84847	−	4.93369i	0.128289	−	0.222202i
$494$	−4.00000	+	16.9706i	−0.179969	+	0.763542i
$495$	−3.21964	+	3.76588i	−0.144712	+	0.169264i
$496$	1.72474	−	2.98735i	0.0774433	−	0.134136i
$497$	−11.2980	−	19.5686i	−0.506783	−	0.877773i
$498$	−28.1969	−	2.59808i	−1.26354	−	0.116423i
$499$	15.0454			0.673525			0.336762	−	0.941590i	$-0.390668\pi$
$499$	15.0454			0.673525			0.336762	+	0.941590i	$0.390668\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	−6.00000	+	8.48528i	−0.268060	+	0.379094i
$502$	3.82577	−	6.62642i	0.170752	−	0.295752i
$503$	6.27526	+	10.8691i	0.279800	+	0.484627i	0.971335	−	0.237715i	$-0.0763986\pi$
$503$	6.27526	+	10.8691i	0.279800	+	0.484627i	−0.691535	+	0.722343i	$0.743065\pi$
$504$	6.72474	−	7.86566i	0.299544	−	0.350364i
$505$	53.0908			2.36251
$506$	1.34847	−	2.33562i	0.0599468	−	0.103831i
$507$	−2.17423	−	4.71940i	−0.0965611	−	0.209596i
$508$	12.3485			0.547875
$509$	−8.44949	+	14.6349i	−0.374517	+	0.648683i	−0.990255	−	0.139269i	$-0.955525\pi$
$509$	−8.44949	+	14.6349i	−0.374517	+	0.648683i	0.615738	+	0.787951i	$0.288858\pi$
$510$	15.5227	+	1.43027i	0.687357	+	0.0633333i
$511$	25.5227	+	44.2066i	1.12906	+	1.95559i
$512$	1.00000			0.0441942
$513$	11.0000	−	19.7990i	0.485662	−	0.874147i
$514$	−2.20204			−0.0971279
$515$	−19.8712	−	34.4179i	−0.875629	−	1.51663i
$516$	−13.4495	−	1.23924i	−0.592081	−	0.0545545i
$517$	−3.15153	+	5.45861i	−0.138604	+	0.240069i
$518$	30.6969			1.34875
$519$	5.14643	+	11.1708i	0.225903	+	0.490346i
$520$	−6.00000	+	10.3923i	−0.263117	+	0.455733i
$521$	28.8990			1.26609			0.633044	−	0.774116i	$-0.281805\pi$
$521$	28.8990			1.26609			0.633044	+	0.774116i	$0.281805\pi$
$522$	−1.89898	−	5.37113i	−0.0831161	−	0.235088i
$523$	−15.9722	−	27.6647i	−0.698415	−	1.20969i	−0.969016	−	0.246999i	$-0.920556\pi$
$523$	−15.9722	−	27.6647i	−0.698415	−	1.20969i	0.270600	−	0.962692i	$-0.412778\pi$
$524$	−10.0732	+	17.4473i	−0.440050	+	0.762190i
$525$	13.7980	−	19.5133i	0.602192	−	0.851629i
$526$	4.89898	−	8.48528i	0.213606	−	0.369976i
$527$	10.3485			0.450786
$528$	−0.949490	−	0.0874863i	−0.0413212	−	0.00380735i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−2.84847	+	4.93369i	−0.123730	+	0.214306i
$531$	−16.0732	−	2.98735i	−0.697518	−	0.129640i
$532$	14.3990	−	4.33013i	0.624275	−	0.187735i
$533$	15.7980	−	27.3629i	0.684286	−	1.18522i
$534$	9.00000	−	12.7279i	0.389468	−	0.550791i
$535$	14.6969			0.635404
$536$	−2.89898	+	5.02118i	−0.125217	+	0.216882i
$537$	−29.1464	−	2.68556i	−1.25776	−	0.115891i
$538$	13.8990			0.599228
$539$	−2.69694			−0.116165
$540$	11.1742	−	10.8691i	0.480862	−	0.467730i
$541$	5.94949	+	10.3048i	0.255789	+	0.443039i	0.965109	−	0.261847i	$-0.0843316\pi$
$541$	5.94949	+	10.3048i	0.255789	+	0.443039i	−0.709321	+	0.704886i	$0.750998\pi$
$542$	−20.3485			−0.874042
$543$	−7.97219	−	17.3045i	−0.342120	−	0.742605i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	−1.50000	+	2.59808i	−0.0642529	+	0.111289i
$546$	−13.7980	+	19.5133i	−0.590498	+	0.835090i
$547$	−26.8434			−1.14774			−0.573870	−	0.818947i	$-0.694558\pi$
$547$	−26.8434			−1.14774			−0.573870	+	0.818947i	$0.694558\pi$
$548$	−5.84847	+	10.1298i	−0.249834	+	0.432726i
$549$	11.5000	+	2.13737i	0.490808	+	0.0912209i
$550$	−2.20204			−0.0938953
$551$	1.89898	−	8.05669i	0.0808992	−	0.343226i
$552$	−4.89898	+	6.92820i	−0.208514	+	0.294884i
$553$	34.4949			1.46687
$554$	−27.6969			−1.17673
$555$	46.0454	+	4.24264i	1.95452	+	0.180090i
$556$	5.55051	+	9.61377i	0.235394	+	0.407714i
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	0.896053	−	0.443947i	$-0.146422\pi$
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	−0.832496	+	0.554031i	$0.813089\pi$
$558$	6.72474	−	7.86566i	0.284681	−	0.332980i
$559$	31.1918			1.31927
$560$	10.3485			0.437303
$561$	−1.19694	−	2.59808i	−0.0505348	−	0.109691i
$562$	−10.5000	−	18.1865i	−0.442916	−	0.767153i
$563$	−15.2753	−	26.4575i	−0.643775	−	1.11505i	−0.984583	−	0.174918i	$-0.944034\pi$
$563$	−15.2753	−	26.4575i	−0.643775	−	1.11505i	0.340808	−	0.940133i	$-0.389299\pi$
$564$	11.4495	−	16.1920i	0.482110	−	0.681807i
$565$	−6.15153	−	10.6548i	−0.258797	−	0.448249i
$566$	−12.1742	−	21.0864i	−0.511721	−	0.886327i
$567$	24.1464	−	19.5133i	1.01405	−	0.819480i
$568$	3.27526	−	5.67291i	0.137427	−	0.238030i
$569$	−2.84847	+	4.93369i	−0.119414	+	0.206831i	−0.919536	−	0.393007i	$-0.871435\pi$
$569$	−2.84847	+	4.93369i	−0.119414	+	0.206831i	0.800122	+	0.599838i	$0.204768\pi$
$570$	22.1969	−	4.50510i	0.929727	−	0.188698i
$571$	−12.4217	−	21.5150i	−0.519831	−	0.900374i	−0.999734	−	0.0230526i	$-0.992661\pi$
$571$	−12.4217	−	21.5150i	−0.519831	−	0.900374i	0.479903	−	0.877322i	$-0.340672\pi$
$572$	2.20204			0.0920720
$573$	3.24745	−	4.59259i	0.135664	−	0.191858i
$574$	−27.2474			−1.13729
$575$	−9.79796	+	16.9706i	−0.408603	+	0.707721i
$576$	2.94949	+	0.548188i	0.122895	+	0.0228412i
$577$	8.00000			0.333044			0.166522	−	0.986038i	$-0.446746\pi$
$577$	8.00000			0.333044			0.166522	+	0.986038i	$0.446746\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−35.5227	−	3.27307i	−1.47627	−	0.136024i
$580$	2.84847	−	4.93369i	0.118276	−	0.204860i
$581$	−28.1969	−	48.8385i	−1.16981	−	2.02616i
$582$	4.00000	−	5.65685i	0.165805	−	0.234484i
$583$	1.04541			0.0432964
$584$	−7.39898	+	12.8154i	−0.306172	+	0.530305i
$585$	−23.3939	+	27.3629i	−0.967218	+	1.13132i
$586$	−14.8485	+	25.7183i	−0.613385	+	1.06241i
$587$	12.2474	+	21.2132i	0.505506	+	0.875563i	0.999980	+	0.00636985i	$0.00202760\pi$
$587$	12.2474	+	21.2132i	0.505506	+	0.875563i	−0.494473	+	0.869193i	$0.664639\pi$
$588$	8.44949	+	0.778539i	0.348451	+	0.0321064i
$589$	14.3990	−	4.33013i	0.593300	−	0.178420i
$590$	−8.17423	−	14.1582i	−0.336528	−	0.582883i
$591$	−3.79796	−	0.349945i	−0.156227	−	0.0143948i
$592$	4.44949	+	7.70674i	0.182873	+	0.316745i
$593$	−7.50000	−	12.9904i	−0.307988	−	0.533451i	0.669934	−	0.742421i	$-0.266322\pi$
$593$	−7.50000	−	12.9904i	−0.307988	−	0.533451i	−0.977922	+	0.208970i	$0.932989\pi$
$594$	−2.75255	−	0.778539i	−0.112939	−	0.0319438i
$595$	15.5227	+	26.8861i	0.636369	+	1.10222i
$596$	−0.398979	+	0.691053i	−0.0163428	+	0.0283066i
$597$	−0.252551	−	0.548188i	−0.0103362	−	0.0224358i
$598$	9.79796	−	16.9706i	0.400668	−	0.693978i
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	−0.798206	−	0.602384i	$-0.794218\pi$
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	0.920783	+	0.390075i	$0.127551\pi$
$600$	6.89898	+	0.635674i	0.281650	+	0.0259513i
$601$	−9.60102	+	16.6295i	−0.391634	+	0.678330i	−0.992665	−	0.120896i	$-0.961423\pi$
$601$	−9.60102	+	16.6295i	−0.391634	+	0.678330i	0.601031	+	0.799225i	$0.294757\pi$
$602$	−13.4495	−	23.2952i	−0.548160	−	0.949441i
$603$	−11.3031	+	13.2207i	−0.460296	+	0.538390i
$604$	10.1742	+	17.6223i	0.413984	+	0.717041i
$605$	−16.0454	−	27.7915i	−0.652339	−	1.12988i
$606$	12.8258	+	27.8396i	0.521011	+	1.13091i
$607$	−7.27526	−	12.6011i	−0.295293	−	0.511463i	0.679760	−	0.733435i	$-0.262084\pi$
$607$	−7.27526	−	12.6011i	−0.295293	−	0.511463i	−0.975053	+	0.221972i	$0.928751\pi$
$608$	3.17423	+	2.98735i	0.128732	+	0.121153i
$609$	6.55051	−	9.26382i	0.265440	−	0.375389i
$610$	5.84847	+	10.1298i	0.236798	+	0.410145i
$611$	−22.8990	+	39.6622i	−0.926394	+	1.60456i
$612$	3.00000	+	8.48528i	0.121268	+	0.342997i
$613$	4.84847	−	8.39780i	0.195828	−	0.339184i	−0.751344	−	0.659911i	$-0.770594\pi$
$613$	4.84847	−	8.39780i	0.195828	−	0.339184i	0.947172	+	0.320727i	$0.103927\pi$
$614$	6.34847			0.256203
$615$	−40.8712	−	3.76588i	−1.64808	−	0.151855i
$616$	−0.949490	−	1.64456i	−0.0382560	−	0.0662614i
$617$	19.3485	−	33.5125i	0.778940	−	1.34916i	−0.153613	−	0.988131i	$-0.549091\pi$
$617$	19.3485	−	33.5125i	0.778940	−	1.34916i	0.932553	−	0.361033i	$-0.117576\pi$
$618$	13.2474	−	18.7347i	0.532891	−	0.753621i
$619$	4.72474	−	8.18350i	0.189904	−	0.328923i	−0.755314	−	0.655363i	$-0.772516\pi$
$619$	4.72474	−	8.18350i	0.189904	−	0.328923i	0.945218	+	0.326440i	$0.105849\pi$
$620$	10.3485			0.415605
$621$	−18.2474	+	17.7491i	−0.732245	+	0.712247i
$622$	6.82577	−	11.8226i	0.273688	−	0.474042i
$623$	31.0454			1.24381
$624$	−6.89898	−	0.635674i	−0.276180	−	0.0254473i
$625$	−29.0000			−1.16000
$626$	0.500000	+	0.866025i	0.0199840	+	0.0346133i
$627$	−2.75255	−	3.11416i	−0.109926	−	0.124367i
$628$	1.05051	−	1.81954i	0.0419199	−	0.0726074i
$629$	−13.3485	+	23.1202i	−0.532238	+	0.921864i
$630$	30.5227	+	5.67291i	1.21605	+	0.226014i
$631$	−5.37628	−	9.31198i	−0.214026	−	0.370704i	0.738945	−	0.673766i	$-0.235324\pi$
$631$	−5.37628	−	9.31198i	−0.214026	−	0.370704i	−0.952971	+	0.303062i	$0.901991\pi$
$632$	5.00000	+	8.66025i	0.198889	+	0.344486i
$633$	−39.7474	−	3.66234i	−1.57982	−	0.145565i
$634$	−5.84847	−	10.1298i	−0.232272	−	0.402308i
$635$	18.5227	+	32.0823i	0.735051	+	1.27315i
$636$	−3.27526	−	0.301783i	−0.129872	−	0.0119665i
$637$	−19.5959			−0.776419
$638$	−1.04541			−0.0413881
$639$	12.7702	−	14.9367i	0.505179	−	0.590888i
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	0.631721	−	0.775196i	$-0.282349\pi$
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	−0.987200	+	0.159489i	$0.949015\pi$
$642$	3.55051	+	7.70674i	0.140127	+	0.304161i
$643$	27.6515			1.09047			0.545235	−	0.838283i	$-0.316440\pi$
$643$	27.6515			1.09047			0.545235	+	0.838283i	$0.316440\pi$
$644$	−16.8990			−0.665913
$645$	−16.9546	−	36.8017i	−0.667586	−	1.44906i
$646$	−3.00000	+	12.7279i	−0.118033	+	0.500773i
$647$	−4.89898			−0.192599			−0.0962994	−	0.995352i	$-0.530701\pi$
$647$	−4.89898			−0.192599			−0.0962994	+	0.995352i	$0.530701\pi$
$648$	8.39898	+	3.23375i	0.329943	+	0.127034i
$649$	−1.50000	+	2.59808i	−0.0588802	+	0.101983i
$650$	−16.0000			−0.627572
$651$	20.5227	+	1.89097i	0.804348	+	0.0741129i
$652$	10.4495	−	18.0990i	0.409234	−	0.708813i
$653$	13.7474	+	23.8113i	0.537979	+	0.931807i	0.999013	+	0.0444246i	$0.0141455\pi$
$653$	13.7474	+	23.8113i	0.537979	+	0.931807i	−0.461033	+	0.887383i	$0.652521\pi$
$654$	−1.72474	−	0.158919i	−0.0674429	−	0.00621421i
$655$	−60.4393			−2.36156
$656$	−3.94949	−	6.84072i	−0.154202	−	0.267085i
$657$	−28.8485	+	33.7429i	−1.12549	+	1.31644i
$658$	39.4949			1.53967
$659$	−40.8434			−1.59103			−0.795516	−	0.605933i	$-0.792800\pi$
$659$	−40.8434			−1.59103			−0.795516	+	0.605933i	$0.792800\pi$
$660$	−1.19694	−	2.59808i	−0.0465908	−	0.101130i
$661$	−18.6969	+	32.3840i	−0.727227	+	1.25959i	0.230824	+	0.972995i	$0.425858\pi$
$661$	−18.6969	+	32.3840i	−0.727227	+	1.25959i	−0.958051	+	0.286598i	$0.907476\pi$
$662$	0.348469			0.0135436
$663$	−8.69694	−	18.8776i	−0.337761	−	0.733145i
$664$	8.17423	−	14.1582i	0.317222	−	0.549444i
$665$	32.8485	+	30.9145i	1.27381	+	1.19881i
$666$	8.89898	+	25.1701i	0.344828	+	0.975322i
$667$	−4.65153	+	8.05669i	−0.180108	+	0.311956i
$668$	−3.00000	−	5.19615i	−0.116073	−	0.201045i
$669$	−0.651531	−	1.41421i	−0.0251896	−	0.0546767i
$670$	−17.3939			−0.671984
$671$	1.07321	−	1.85886i	0.0414310	−	0.0717605i
$672$	2.50000	+	5.42650i	0.0964396	+	0.209332i
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	−0.952343	−	0.305028i	$-0.901334\pi$
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	0.740334	+	0.672239i	$0.234667\pi$
$674$	1.05051	+	1.81954i	0.0404641	+	0.0700860i
$675$	20.0000	+	5.65685i	0.769800	+	0.217732i
$676$	3.00000			0.115385
$677$	2.60102	−	4.50510i	0.0999653	−	0.173145i	−0.811705	−	0.584068i	$-0.801460\pi$
$677$	2.60102	−	4.50510i	0.0999653	−	0.173145i	0.911670	+	0.410923i	$0.134793\pi$
$678$	4.10102	−	5.79972i	0.157499	−	0.222737i
$679$	13.7980			0.529517
$680$	−4.50000	+	7.79423i	−0.172567	+	0.298895i
$681$	17.4495	−	24.6773i	0.668666	−	0.945636i
$682$	−0.949490	−	1.64456i	−0.0363578	−	0.0629736i
$683$	−21.7980			−0.834076			−0.417038	−	0.908889i	$-0.636932\pi$
$683$	−21.7980			−0.834076			−0.417038	+	0.908889i	$0.636932\pi$
$684$	7.72474	+	10.5512i	0.295363	+	0.403436i
$685$	−35.0908			−1.34075
$686$	−3.62372	−	6.27647i	−0.138354	−	0.239637i
$687$	19.2753	+	41.8389i	0.735397	+	1.59625i
$688$	3.89898	−	6.75323i	0.148647	−	0.257465i
$689$	7.59592			0.289381
$690$	−25.3485	−	2.33562i	−0.965000	−	0.0889154i
$691$	2.52270	−	4.36945i	0.0959682	−	0.166222i	−0.814044	−	0.580803i	$-0.802739\pi$
$691$	2.52270	−	4.36945i	0.0959682	−	0.166222i	0.910012	+	0.414581i	$0.136072\pi$
$692$	−7.10102			−0.269940
$693$	−1.89898	−	5.37113i	−0.0721363	−	0.204032i
$694$	−6.27526	−	10.8691i	−0.238205	−	0.412584i
$695$	−16.6515	+	28.8413i	−0.631629	+	1.09401i
$696$	3.27526	+	0.301783i	0.124148	+	0.0114391i
$697$	11.8485	−	20.5222i	0.448793	−	0.777332i
$698$	18.1010			0.685134
$699$	−19.8990	+	28.1414i	−0.752649	+	1.06441i
$700$	6.89898	+	11.9494i	0.260757	+	0.451644i
$701$	17.8485	−	30.9145i	0.674127	−	1.16762i	−0.302596	−	0.953119i	$-0.597853\pi$
$701$	17.8485	−	30.9145i	0.674127	−	1.16762i	0.976723	−	0.214504i	$-0.0688135\pi$
$702$	−20.0000	−	5.65685i	−0.754851	−	0.213504i
$703$	−8.89898	+	37.7552i	−0.335631	+	1.42396i
$704$	0.275255	−	0.476756i	0.0103741	−	0.0179684i
$705$	59.2423	+	5.45861i	2.23120	+	0.205583i
$706$	1.89898			0.0714690
$707$	−30.5227	+	52.8669i	−1.14792	+	1.98826i
$708$	5.44949	−	7.70674i	0.204804	−	0.289637i
$709$	46.3939			1.74236			0.871179	−	0.490965i	$-0.163356\pi$
$709$	46.3939			1.74236			0.871179	+	0.490965i	$0.163356\pi$
$710$	19.6515			0.737509
$711$	10.0000	+	28.2843i	0.375029	+	1.06074i
$712$	4.50000	+	7.79423i	0.168645	+	0.292101i
$713$	−16.8990			−0.632872
$714$	−10.3485	+	14.6349i	−0.387282	+	0.547699i
$715$	3.30306	+	5.72107i	0.123527	+	0.213956i
$716$	8.44949	−	14.6349i	0.315772	−	0.546934i
$717$	3.94949	+	8.57277i	0.147496	+	0.320156i
$718$	−23.4495			−0.875127
$719$	4.62372	−	8.00853i	0.172436	−	0.298668i	−0.766835	−	0.641844i	$-0.778170\pi$
$719$	4.62372	−	8.00853i	0.172436	−	0.298668i	0.939271	+	0.343177i	$0.111503\pi$
$720$	3.00000	+	8.48528i	0.111803	+	0.316228i
$721$	45.6969			1.70184
$722$	1.15153	+	18.9651i	0.0428555	+	0.705807i
$723$	−39.3207	−	3.62302i	−1.46235	−	0.134742i
$724$	11.0000			0.408812
$725$	7.59592			0.282105
$726$	10.6969	−	15.1278i	0.397001	−	0.561444i
$727$	0.651531	+	1.12848i	0.0241639	+	0.0418532i	0.877855	−	0.478927i	$-0.158974\pi$
$727$	0.651531	+	1.12848i	0.0241639	+	0.0418532i	−0.853691	+	0.520781i	$0.825641\pi$
$728$	−6.89898	−	11.9494i	−0.255693	−	0.442874i
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	−44.3939			−1.64309
$731$	23.3939			0.865254
$732$	−3.89898	+	5.51399i	−0.144110	+	0.203803i
$733$	−11.5000	−	19.9186i	−0.424762	−	0.735710i	0.571636	−	0.820507i	$-0.306309\pi$
$733$	−11.5000	−	19.9186i	−0.424762	−	0.735710i	−0.996398	+	0.0847976i	$0.972976\pi$
$734$	−4.27526	−	7.40496i	−0.157803	−	0.273322i
$735$	10.6515	+	23.1202i	0.392888	+	0.852802i
$736$	−2.44949	−	4.24264i	−0.0902894	−	0.156386i
$737$	1.59592	+	2.76421i	0.0587864	+	0.101821i
$738$	−7.89898	−	22.3417i	−0.290765	−	0.822409i
$739$	9.62372	−	16.6688i	0.354014	−	0.613171i	−0.632934	−	0.774205i	$-0.718150\pi$
$739$	9.62372	−	16.6688i	0.354014	−	0.613171i	0.986949	+	0.161034i	$0.0514830\pi$
$740$	−13.3485	+	23.1202i	−0.490699	+	0.849916i
$741$	−20.0000	−	22.6274i	−0.734718	−	0.831239i
$742$	−3.27526	−	5.67291i	−0.120238	−	0.208259i
$743$	−11.4495			−0.420041			−0.210021	−	0.977697i	$-0.567353\pi$
$743$	−11.4495			−0.420041			−0.210021	+	0.977697i	$0.567353\pi$
$744$	2.50000	+	5.42650i	0.0916544	+	0.198945i
$745$	−2.39388			−0.0877049
$746$	−12.8485	+	22.2542i	−0.470416	+	0.814784i
$747$	31.8712	−	37.2784i	1.16611	−	1.36395i
$748$	1.65153			0.0603859
$749$	−8.44949	+	14.6349i	−0.308738	+	0.534749i
$750$	−2.17423	−	4.71940i	−0.0793918	−	0.172328i
$751$	−13.5505	+	23.4702i	−0.494465	+	0.856439i	−0.999980	−	0.00637936i	$-0.997969\pi$
$751$	−13.5505	+	23.4702i	−0.494465	+	0.856439i	0.505515	+	0.862818i	$0.331303\pi$
$752$	5.72474	+	9.91555i	0.208760	+	0.361583i
$753$	5.54541	+	12.0369i	0.202086	+	0.438648i
$754$	−7.59592			−0.276627
$755$	−30.5227	+	52.8669i	−1.11083	+	1.92402i
$756$	4.39898	+	17.3759i	0.159989	+	0.631955i
$757$	−7.64643	+	13.2440i	−0.277914	+	0.481361i	−0.970866	−	0.239622i	$-0.922976\pi$
$757$	−7.64643	+	13.2440i	−0.277914	+	0.481361i	0.692952	+	0.720984i	$0.256310\pi$
$758$	−7.79796	−	13.5065i	−0.283235	−	0.490577i
$759$	1.95459	+	4.24264i	0.0709472	+	0.153998i
$760$	−3.00000	+	12.7279i	−0.108821	+	0.461690i
$761$	−19.7474	−	34.2036i	−0.715844	−	1.23988i	−0.962633	−	0.270810i	$-0.912709\pi$
$761$	−19.7474	−	34.2036i	−0.715844	−	1.23988i	0.246788	−	0.969069i	$-0.420625\pi$
$762$	−12.3485	+	17.4634i	−0.447338	+	0.632631i
$763$	−1.72474	−	2.98735i	−0.0624400	−	0.108149i
$764$	1.62372	+	2.81237i	0.0587443	+	0.101748i
$765$	−17.5454	+	20.5222i	−0.634356	+	0.741980i
$766$	14.4217	+	24.9791i	0.521077	+	0.902531i
$767$	−10.8990	+	18.8776i	−0.393539	+	0.681630i
$768$	−1.00000	+	1.41421i	−0.0360844	+	0.0510310i
$769$	3.34847	−	5.79972i	0.120749	−	0.209143i	−0.799314	−	0.600913i	$-0.794804\pi$
$769$	3.34847	−	5.79972i	0.120749	−	0.209143i	0.920063	+	0.391770i	$0.128137\pi$
$770$	2.84847	−	4.93369i	0.102652	−	0.177798i
$771$	2.20204	−	3.11416i	0.0793046	−	0.112154i
$772$	10.2980	−	17.8366i	0.370632	−	0.641953i
$773$	−1.50000	−	2.59808i	−0.0539513	−	0.0934463i	0.837788	−	0.545995i	$-0.183848\pi$
$773$	−1.50000	−	2.59808i	−0.0539513	−	0.0934463i	−0.891740	+	0.452549i	$0.850515\pi$
$774$	15.2020	−	17.7812i	0.546426	−	0.639132i
$775$	6.89898	+	11.9494i	0.247819	+	0.429235i
$776$	2.00000	+	3.46410i	0.0717958	+	0.124354i
$777$	−30.6969	+	43.4120i	−1.10125	+	1.55740i
$778$	9.39898	+	16.2795i	0.336970	+	0.583649i
$779$	7.89898	−	33.5125i	0.283010	−	1.20071i
$780$	−8.69694	−	18.8776i	−0.311400	−	0.675926i
$781$	−1.80306	−	3.12299i	−0.0645186	−	0.111750i
$782$	7.34847	−	12.7279i	0.262781	−	0.455150i
$783$	9.49490	+	2.68556i	0.339320	+	0.0959742i
$784$	−2.44949	+	4.24264i	−0.0874818	+	0.151523i
$785$	6.30306			0.224966
$786$	−14.6010	−	31.6930i	−0.520801	−	1.13045i
$787$	−4.27526	−	7.40496i	−0.152396	−	0.263958i	0.779712	−	0.626139i	$-0.215366\pi$
$787$	−4.27526	−	7.40496i	−0.152396	−	0.263958i	−0.932108	+	0.362181i	$0.882032\pi$
$788$	1.10102	−	1.90702i	0.0392222	−	0.0679349i
$789$	7.10102	+	15.4135i	0.252803	+	0.548735i
$790$	−15.0000	+	25.9808i	−0.533676	+	0.924354i
$791$	14.1464			0.502989
$792$	1.07321	−	1.25529i	0.0381350	−	0.0446050i
$793$	7.79796	−	13.5065i	0.276914	−	0.479628i
$794$	24.5959			0.872876
$795$	−4.12883	−	8.96204i	−0.146434	−	0.317851i
$796$	0.348469			0.0123512
$797$	20.0505	+	34.7285i	0.710226	+	1.23015i	0.964772	+	0.263086i	$0.0847404\pi$
$797$	20.0505	+	34.7285i	0.710226	+	1.23015i	−0.254547	+	0.967060i	$0.581926\pi$
$798$	−8.27526	+	24.6934i	−0.292941	+	0.874135i
$799$	−17.1742	+	29.7466i	−0.607581	+	1.05236i
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$	9.00000	+	25.4558i	0.317999	+	0.899438i
$802$	5.60102	+	9.70125i	0.197779	+	0.342563i
$803$	4.07321	+	7.05501i	0.143741	+	0.248966i
$804$	−4.20204	−	9.12096i	−0.148195	−	0.321671i
$805$	−25.3485	−	43.9048i	−0.893416	−	1.54744i
$806$	−6.89898	−	11.9494i	−0.243006	−	0.420899i
$807$	−13.8990	+	19.6561i	−0.489267	+	0.691928i
$808$	−17.6969			−0.622576
$809$	0.494897			0.0173997			0.00869983	−	0.999962i	$-0.497231\pi$
$809$	0.494897			0.0173997			0.00869983	+	0.999962i	$0.497231\pi$
$810$	4.19694	+	26.6718i	0.147465	+	0.937152i
$811$	−16.5227	−	28.6182i	−0.580191	−	1.00492i	−0.995456	−	0.0952194i	$-0.969645\pi$
$811$	−16.5227	−	28.6182i	−0.580191	−	1.00492i	0.415266	−	0.909700i	$-0.363689\pi$
$812$	3.27526	+	5.67291i	0.114939	+	0.199080i
$813$	20.3485	−	28.7771i	0.713652	−	1.00926i
$814$	4.89898			0.171709
$815$	62.6969			2.19618
$816$	−5.17423	−	0.476756i	−0.181134	−	0.0166898i
$817$	32.5505	−	9.78874i	1.13880	−	0.342465i
$818$	14.0000			0.489499
$819$	−13.7980	−	39.0265i	−0.482140	−	1.36370i
$820$	11.8485	−	20.5222i	0.413766	−	0.716665i
$821$	−25.2929			−0.882727			−0.441363	−	0.897328i	$-0.645505\pi$
$821$	−25.2929			−0.882727			−0.441363	+	0.897328i	$0.645505\pi$
$822$	−8.47730	−	18.4008i	−0.295680	−	0.641803i
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	6.62372	+	11.4726i	0.230748	+	0.399668i
$825$	2.20204	−	3.11416i	0.0766652	−	0.108421i
$826$	18.7980			0.654065
$827$	−16.0732	−	27.8396i	−0.558920	−	0.968079i	−0.997587	−	0.0694286i	$-0.977882\pi$
$827$	−16.0732	−	27.8396i	−0.558920	−	0.968079i	0.438667	−	0.898650i	$-0.355451\pi$
$828$	−4.89898	−	13.8564i	−0.170251	−	0.481543i
$829$	−45.3939			−1.57659			−0.788297	−	0.615295i	$-0.789037\pi$
$829$	−45.3939			−1.57659			−0.788297	+	0.615295i	$0.789037\pi$
$830$	49.0454			1.70239
$831$	27.6969	−	39.1694i	0.960796	−	1.35877i
$832$	2.00000	−	3.46410i	0.0693375	−	0.120096i
$833$	−14.6969			−0.509219
$834$	−19.1464	−	1.76416i	−0.662987	−	0.0610878i
$835$	9.00000	−	15.5885i	0.311458	−	0.539461i
$836$	2.29796	−	0.691053i	0.0794766	−	0.0239006i
$837$	4.39898	+	17.3759i	0.152051	+	0.600598i
$838$	−7.62372	+	13.2047i	−0.263357	+	0.456148i
$839$	−9.79796	−	16.9706i	−0.338263	−	0.585889i	0.645843	−	0.763470i	$-0.276506\pi$
$839$	−9.79796	−	16.9706i	−0.338263	−	0.585889i	−0.984106	+	0.177581i	$0.943173\pi$
$840$	−10.3485	+	14.6349i	−0.357056	+	0.504954i
$841$	−25.3939			−0.875651
$842$	9.34847	−	16.1920i	0.322170	−	0.558014i
$843$	36.2196	+	3.33729i	1.24747	+	0.114942i
$844$	11.5227	−	19.9579i	0.396628	−	0.686980i
$845$	4.50000	+	7.79423i	0.154805	+	0.268130i
$846$	11.4495	+	32.3840i	0.393642	+	1.11339i
$847$	36.8990			1.26786
$848$	0.949490	−	1.64456i	0.0326056	−	0.0564746i
$849$	41.9949	+	3.86943i	1.44126	+	0.132798i
$850$	−12.0000			−0.411597
$851$	21.7980	−	37.7552i	0.747224	−	1.29423i
$852$	4.74745	+	10.3048i	0.162645	+	0.353037i
$853$	−23.5959	−	40.8693i	−0.807909	−	1.39934i	−0.914310	−	0.405016i	$-0.867266\pi$
$853$	−23.5959	−	40.8693i	−0.807909	−	1.39934i	0.106401	−	0.994323i	$-0.466067\pi$
$854$	−13.4495			−0.460232
$855$	−15.8258	+	35.8963i	−0.541230	+	1.22763i
$856$	−4.89898			−0.167444
$857$	21.5505	+	37.3266i	0.736151	+	1.27505i	0.954216	+	0.299117i	$0.0966922\pi$
$857$	21.5505	+	37.3266i	0.736151	+	1.27505i	−0.218065	+	0.975934i	$0.569974\pi$
$858$	−2.20204	+	3.11416i	−0.0751764	+	0.106316i
$859$	11.7980	−	20.4347i	0.402541	−	0.697222i	−0.591491	−	0.806312i	$-0.701460\pi$
$859$	11.7980	−	20.4347i	0.402541	−	0.697222i	0.994032	+	0.109090i	$0.0347937\pi$
$860$	23.3939			0.797725
$861$	27.2474	−	38.5337i	0.928591	−	1.31323i
$862$	4.62372	−	8.00853i	0.157485	−	0.272771i
$863$	−16.8990			−0.575248			−0.287624	−	0.957743i	$-0.592865\pi$
$863$	−16.8990			−0.575248			−0.287624	+	0.957743i	$0.592865\pi$
$864$	−3.72474	+	3.62302i	−0.126718	+	0.123258i
$865$	−10.6515	−	18.4490i	−0.362163	−	0.627285i
$866$	8.39898	−	14.5475i	0.285409	−	0.494343i
$867$	5.79796	+	12.5851i	0.196909	+	0.427411i
$868$	−5.94949	+	10.3048i	−0.201939	+	0.349768i
$869$	5.50510			0.186748
$870$	4.12883	+	8.96204i	0.139980	+	0.303842i
$871$	11.5959	+	20.0847i	0.392913	+	0.680545i
$872$	0.500000	−	0.866025i	0.0169321	−	0.0293273i
$873$	4.00000	+	11.3137i	0.135379	+	0.382911i
$874$	4.89898	−	20.7846i	0.165710	−	0.703050i
$875$	5.17423	−	8.96204i	0.174921	−	0.302972i
$876$	−10.7247	−	23.2791i	−0.362356	−	0.786529i
$877$	−35.2929			−1.19176			−0.595878	−	0.803075i	$-0.703196\pi$
$877$	−35.2929			−1.19176			−0.595878	+	0.803075i	$0.703196\pi$
$878$	8.00000	−	13.8564i	0.269987	−	0.467631i
$879$	−21.5227	−	46.7172i	−0.725943	−	1.57573i
$880$	1.65153			0.0556731
$881$	2.20204			0.0741886			0.0370943	−	0.999312i	$-0.488190\pi$
$881$	2.20204			0.0741886			0.0370943	+	0.999312i	$0.488190\pi$
$882$	−9.55051	+	11.1708i	−0.321582	+	0.376142i
$883$	−4.82577	−	8.35847i	−0.162400	−	0.281285i	0.773329	−	0.634005i	$-0.218590\pi$
$883$	−4.82577	−	8.35847i	−0.162400	−	0.281285i	−0.935729	+	0.352720i	$0.885257\pi$
$884$	12.0000			0.403604
$885$	28.1969	+	2.59808i	0.947830	+	0.0873334i
$886$	19.0732	+	33.0358i	0.640777	+	1.10986i
$887$	−14.4495	+	25.0273i	−0.485166	+	0.840333i	−0.999855	−	0.0170445i	$-0.994574\pi$
$887$	−14.4495	+	25.0273i	−0.485166	+	0.840333i	0.514688	+	0.857377i	$0.327908\pi$
$888$	−15.3485	−	1.41421i	−0.515061	−	0.0474579i
$889$	−42.5959			−1.42862
$890$	−13.5000	+	23.3827i	−0.452521	+	0.783789i
$891$	3.85357	−	3.11416i	0.129100	−	0.104328i
$892$	0.898979			0.0301001
$893$	−11.4495	+	48.5761i	−0.383143	+	1.62554i
$894$	−0.578317	−	1.25529i	−0.0193418	−	0.0419833i
$895$	50.6969			1.69461
$896$	−3.44949			−0.115239
$897$	14.2020	+	30.8270i	0.474192	+	1.02928i
$898$	−1.10102	−	1.90702i	−0.0367415	−	0.0636382i
$899$	3.27526	+	5.67291i	0.109236	+	0.189202i
$900$	−7.79796	+	9.12096i	−0.259932	+	0.304032i
$901$	5.69694			0.189793
$902$	−4.34847			−0.144788
$903$	46.3939	+	4.27475i	1.54389	+	0.142255i
$904$	2.05051	+	3.55159i	0.0681990	+	0.118124i
$905$	16.5000	+	28.5788i	0.548479	+	0.949993i
$906$	−35.0959	−	3.23375i	−1.16598	−	0.107434i
$907$	−21.6969	−	37.5802i	−0.720435	−	1.24783i	−0.960826	−	0.277154i	$-0.910609\pi$
$907$	−21.6969	−	37.5802i	−0.720435	−	1.24783i	0.240391	−	0.970676i	$-0.422724\pi$
$908$	8.72474	+	15.1117i	0.289541	+	0.501499i
$909$	−52.1969	−	9.70125i	−1.73126	−	0.321770i
$910$	20.6969	−	35.8481i	0.686097	−	1.18835i
$911$	13.3763	−	23.1684i	0.443176	−	0.767603i	−0.554747	−	0.832019i	$-0.687185\pi$
$911$	13.3763	−	23.1684i	0.443176	−	0.767603i	0.997923	+	0.0644159i	$0.0205184\pi$
$912$	−7.39898	+	1.50170i	−0.245005	+	0.0497263i
$913$	−4.50000	−	7.79423i	−0.148928	−	0.257951i
$914$	−21.2020			−0.701301
$915$	−20.1742	−	1.85886i	−0.666940	−	0.0614521i
$916$	−26.5959			−0.878754
$917$	34.7474	−	60.1843i	1.14746	−	1.98746i
$918$	−15.0000	−	4.24264i	−0.495074	−	0.140028i
$919$	−22.0000			−0.725713			−0.362857	−	0.931845i	$-0.618198\pi$
$919$	−22.0000			−0.725713			−0.362857	+	0.931845i	$0.618198\pi$
$920$	7.34847	−	12.7279i	0.242272	−	0.419627i
$921$	−6.34847	+	8.97809i	−0.209189	+	0.295838i
$922$	14.6969	−	25.4558i	0.484018	−	0.838344i
$923$	−13.1010	−	22.6916i	−0.431225	−	0.746904i
$924$	3.27526	+	0.301783i	0.107748	+	0.00992794i
$925$	−35.5959			−1.17039
$926$	−4.82577	+	8.35847i	−0.158584	+	0.274676i
$927$	13.2474	+	37.4694i	0.435103	+	1.23066i
$928$	−0.949490	+	1.64456i	−0.0311685	+	0.0539855i
$929$	6.79796	+	11.7744i	0.223034	+	0.386306i	0.955728	−	0.294252i	$-0.0950706\pi$
$929$	6.79796	+	11.7744i	0.223034	+	0.386306i	−0.732694	+	0.680558i	$0.761737\pi$
$930$	−10.3485	+	14.6349i	−0.339340	+	0.479899i
$931$	−20.4495	+	6.14966i	−0.670205	+	0.201547i
$932$	−9.94949	−	17.2330i	−0.325906	−	0.564486i
$933$	9.89388	+	21.4757i	0.323911	+	0.703082i
$934$	−9.00000	−	15.5885i	−0.294489	−	0.510070i
$935$	2.47730	+	4.29080i	0.0810162	+	0.140324i
$936$	7.79796	−	9.12096i	0.254884	−	0.298128i
$937$	−1.70204	−	2.94802i	−0.0556033	−	0.0963077i	0.836884	−	0.547380i	$-0.184375\pi$
$937$	−1.70204	−	2.94802i	−0.0556033	−	0.0963077i	−0.892487	+	0.451073i	$0.851042\pi$
$938$	10.0000	−	17.3205i	0.326512	−	0.565535i
$939$	−1.72474	−	0.158919i	−0.0562849	−	0.00518611i
$940$	−17.1742	+	29.7466i	−0.560162	+	0.970229i
$941$	−15.5505	+	26.9343i	−0.506932	+	0.878032i	0.493036	+	0.870009i	$0.335887\pi$
$941$	−15.5505	+	26.9343i	−0.506932	+	0.878032i	−0.999968	+	0.00802314i	$0.997446\pi$
$942$	1.52270	+	3.30518i	0.0496124	+	0.107689i
$943$	−19.3485	+	33.5125i	−0.630073	+	1.09132i
$944$	2.72474	+	4.71940i	0.0886829	+	0.153603i
$945$	−38.5454	+	37.4927i	−1.25388	+	1.21964i
$946$	−2.14643	−	3.71772i	−0.0697864	−	0.120874i
$947$	−10.8990	−	18.8776i	−0.354169	−	0.613439i	0.632806	−	0.774310i	$-0.281903\pi$
$947$	−10.8990	−	18.8776i	−0.354169	−	0.613439i	−0.986975	+	0.160871i	$0.948570\pi$
$948$	−17.2474	−	1.58919i	−0.560171	−	0.0516144i
$949$	29.5959	+	51.2616i	0.960724	+	1.66402i
$950$	−16.6969	+	5.02118i	−0.541720	+	0.162909i
$951$	20.1742	+	1.85886i	0.654194	+	0.0602777i
$952$	−5.17423	−	8.96204i	−0.167698	−	0.290461i
$953$	−12.3990	+	21.4757i	−0.401642	+	0.695665i	−0.993924	−	0.110066i	$-0.964894\pi$
$953$	−12.3990	+	21.4757i	−0.401642	+	0.695665i	0.592282	+	0.805731i	$0.298227\pi$
$954$	3.70204	−	4.33013i	0.119858	−	0.140193i
$955$	−4.87117	+	8.43712i	−0.157627	+	0.273019i
$956$	−5.44949			−0.176249
$957$	1.04541	−	1.47843i	0.0337932	−	0.0477908i
$958$	−2.72474	−	4.71940i	−0.0880325	−	0.152477i
$959$	20.1742	−	34.9428i	0.651460	−	1.12836i
$960$	−5.17423	−	0.476756i	−0.166998	−	0.0153872i
$961$	9.55051	−	16.5420i	0.308081	−	0.533612i
$962$	35.5959			1.14766
$963$	−14.4495	−	2.68556i	−0.465628	−	0.0865410i
$964$	11.3990	−	19.7436i	0.367136	−	0.635899i
$965$	61.7878			1.98902
$966$	16.8990	−	23.8988i	0.543716	−	0.768930i
$967$	−28.5505			−0.918123			−0.459061	−	0.888405i	$-0.651814\pi$
$967$	−28.5505			−0.918123			−0.459061	+	0.888405i	$0.651814\pi$
$968$	5.34847	+	9.26382i	0.171906	+	0.297750i
$969$	−15.0000	−	16.9706i	−0.481869	−	0.545173i
$970$	−6.00000	+	10.3923i	−0.192648	+	0.333677i
$971$	25.8712	−	44.8102i	0.830245	−	1.43803i	−0.0675981	−	0.997713i	$-0.521534\pi$
$971$	25.8712	−	44.8102i	0.830245	−	1.43803i	0.897844	−	0.440315i	$-0.145133\pi$
$972$	−12.9722	+	8.64420i	−0.416083	+	0.277263i
$973$	−19.1464	−	33.1626i	−0.613806	−	1.06314i
$974$	10.6969	+	18.5276i	0.342752	+	0.593664i
$975$	16.0000	−	22.6274i	0.512410	−	0.724657i
$976$	−1.94949	−	3.37662i	−0.0624016	−	0.108083i
$977$	−8.29796	−	14.3725i	−0.265475	−	0.459817i	0.702213	−	0.711967i	$-0.252196\pi$
$977$	−8.29796	−	14.3725i	−0.265475	−	0.459817i	−0.967688	+	0.252151i	$0.918862\pi$
$978$	15.1464	+	32.8769i	0.484329	+	1.05129i
$979$	4.95459			0.158349
$980$	−14.6969			−0.469476
$981$	1.94949	−	2.28024i	0.0622424	−	0.0728024i
$982$	19.8712	+	34.4179i	0.634115	+	1.09832i
$983$	−6.24745	−	10.8209i	−0.199263	−	0.345133i	0.749027	−	0.662540i	$-0.230521\pi$
$983$	−6.24745	−	10.8209i	−0.199263	−	0.345133i	−0.948290	+	0.317407i	$0.897188\pi$
$984$	13.6237	+	1.25529i	0.434308	+	0.0400173i
$985$	6.60612			0.210489
$986$	−5.69694			−0.181427
$987$	−39.4949	+	55.8542i	−1.25714	+	1.77786i
$988$	16.6969	−	5.02118i	0.531200	−	0.159745i
$989$	−38.2020			−1.21475
$990$	4.87117	+	0.905350i	0.154816	+	0.0287739i
$991$	15.3763	−	26.6325i	0.488443	−	0.846009i	−0.511468	−	0.859302i	$-0.670898\pi$
$991$	15.3763	−	26.6325i	0.488443	−	0.846009i	0.999912	+	0.0132933i	$0.00423151\pi$
$992$	−3.44949			−0.109521
$993$	−0.348469	+	0.492810i	−0.0110583	+	0.0156388i
$994$	−11.2980	+	19.5686i	−0.358349	+	0.620680i
$995$	0.522704	+	0.905350i	0.0165708	+	0.0287015i
$996$	11.8485	+	25.7183i	0.375433	+	0.814916i
$997$	25.6969			0.813830			0.406915	−	0.913466i	$-0.366604\pi$
$997$	25.6969			0.813830			0.406915	+	0.913466i	$0.366604\pi$
$998$	−7.52270	−	13.0297i	−0.238127	−	0.412448i
$999$	−44.4949	−	12.5851i	−1.40776	−	0.398174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.h.e.277.2	yes	4
3.2	odd	2		1026.2.h.e.505.2		4
9.4	even	3		342.2.f.e.49.1	yes	4
9.5	odd	6		1026.2.f.e.847.2		4
19.7	even	3		342.2.f.e.7.2	✓	4
57.26	odd	6		1026.2.f.e.235.2		4
171.121	even	3	inner	342.2.h.e.121.2	yes	4
171.140	odd	6		1026.2.h.e.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.e.7.2	✓	4	19.7	even	3
342.2.f.e.49.1	yes	4	9.4	even	3
342.2.h.e.121.2	yes	4	171.121	even	3	inner
342.2.h.e.277.2	yes	4	1.1	even	1	trivial
1026.2.f.e.235.2		4	57.26	odd	6
1026.2.f.e.847.2		4	9.5	odd	6
1026.2.h.e.505.2		4	3.2	odd	2
1026.2.h.e.577.2		4	171.140	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.72474 + 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-0.724745 - 1.57313i) q^{6} +(1.72474 - 2.98735i) q^{7} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.72474 + 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-0.724745 - 1.57313i) q^{6} +(1.72474 - 2.98735i) q^{7} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +(1.50000 + 2.59808i) q^{10} +(0.275255 - 0.476756i) q^{11} +(-1.00000 + 1.41421i) q^{12} +(2.00000 - 3.46410i) q^{13} -3.44949 q^{14} +(-5.17423 - 0.476756i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.00000 - 2.82843i) q^{18} +(1.00000 - 4.24264i) q^{19} +(1.50000 - 2.59808i) q^{20} +(3.44949 - 4.87832i) q^{21} -0.550510 q^{22} +(-2.44949 + 4.24264i) q^{23} +(1.72474 + 0.158919i) q^{24} +4.00000 q^{25} -4.00000 q^{26} +(5.00000 + 1.41421i) q^{27} +(1.72474 + 2.98735i) q^{28} +1.89898 q^{29} +(2.17423 + 4.71940i) q^{30} +(1.72474 + 2.98735i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.550510 - 0.778539i) q^{33} -3.00000 q^{34} +(-5.17423 + 8.96204i) q^{35} +(-1.94949 + 2.28024i) q^{36} -8.89898 q^{37} +(-4.17423 + 1.25529i) q^{38} +(4.00000 - 5.65685i) q^{39} -3.00000 q^{40} +7.89898 q^{41} +(-5.94949 - 0.548188i) q^{42} +(3.89898 + 6.75323i) q^{43} +(0.275255 + 0.476756i) q^{44} +(-8.84847 - 1.64456i) q^{45} +4.89898 q^{46} -11.4495 q^{47} +(-0.724745 - 1.57313i) q^{48} +(-2.44949 - 4.24264i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(3.00000 - 4.24264i) q^{51} +(2.00000 + 3.46410i) q^{52} +(0.949490 + 1.64456i) q^{53} +(-1.27526 - 5.03723i) q^{54} +(-0.825765 + 1.43027i) q^{55} +(1.72474 - 2.98735i) q^{56} +(2.39898 - 7.15855i) q^{57} +(-0.949490 - 1.64456i) q^{58} -5.44949 q^{59} +(3.00000 - 4.24264i) q^{60} +3.89898 q^{61} +(1.72474 - 2.98735i) q^{62} +(6.72474 - 7.86566i) q^{63} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(-0.949490 - 0.0874863i) q^{66} +(-2.89898 + 5.02118i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-4.89898 + 6.92820i) q^{69} +10.3485 q^{70} +(3.27526 - 5.67291i) q^{71} +(2.94949 + 0.548188i) q^{72} +(-7.39898 + 12.8154i) q^{73} +(4.44949 + 7.70674i) q^{74} +(6.89898 + 0.635674i) q^{75} +(3.17423 + 2.98735i) q^{76} +(-0.949490 - 1.64456i) q^{77} +(-6.89898 - 0.635674i) q^{78} +(5.00000 + 8.66025i) q^{79} +(1.50000 + 2.59808i) q^{80} +(8.39898 + 3.23375i) q^{81} +(-3.94949 - 6.84072i) q^{82} +(8.17423 - 14.1582i) q^{83} +(2.50000 + 5.42650i) q^{84} +(-4.50000 + 7.79423i) q^{85} +(3.89898 - 6.75323i) q^{86} +(3.27526 + 0.301783i) q^{87} +(0.275255 - 0.476756i) q^{88} +(4.50000 + 7.79423i) q^{89} +(3.00000 + 8.48528i) q^{90} +(-6.89898 - 11.9494i) q^{91} +(-2.44949 - 4.24264i) q^{92} +(2.50000 + 5.42650i) q^{93} +(5.72474 + 9.91555i) q^{94} +(-3.00000 + 12.7279i) q^{95} +(-1.00000 + 1.41421i) q^{96} +(2.00000 + 3.46410i) q^{97} +(-2.44949 + 4.24264i) q^{98} +(1.07321 - 1.25529i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 12 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 12 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 12 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 2 q^{9} + 6 q^{10} + 6 q^{11} - 4 q^{12} + 8 q^{13} - 4 q^{14} - 6 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 6 q^{20} + 4 q^{21} - 12 q^{22} + 2 q^{24} + 16 q^{25} - 16 q^{26} + 20 q^{27} + 2 q^{28} - 12 q^{29} - 6 q^{30} + 2 q^{31} - 2 q^{32} + 12 q^{33} - 12 q^{34} - 6 q^{35} + 2 q^{36} - 16 q^{37} - 2 q^{38} + 16 q^{39} - 12 q^{40} + 12 q^{41} - 14 q^{42} - 4 q^{43} + 6 q^{44} - 6 q^{45} - 36 q^{47} + 2 q^{48} - 8 q^{50} + 12 q^{51} + 8 q^{52} - 6 q^{53} - 10 q^{54} - 18 q^{55} + 2 q^{56} - 10 q^{57} + 6 q^{58} - 12 q^{59} + 12 q^{60} - 4 q^{61} + 2 q^{62} + 22 q^{63} + 4 q^{64} - 24 q^{65} + 6 q^{66} + 8 q^{67} + 6 q^{68} + 12 q^{70} + 18 q^{71} + 2 q^{72} - 10 q^{73} + 8 q^{74} + 8 q^{75} - 2 q^{76} + 6 q^{77} - 8 q^{78} + 20 q^{79} + 6 q^{80} + 14 q^{81} - 6 q^{82} + 18 q^{83} + 10 q^{84} - 18 q^{85} - 4 q^{86} + 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{90} - 8 q^{91} + 10 q^{93} + 18 q^{94} - 12 q^{95} - 4 q^{96} + 8 q^{97} - 30 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 12 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 2 * q^9 + 6 * q^10 + 6 * q^11 - 4 * q^12 + 8 * q^13 - 4 * q^14 - 6 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 6 * q^20 + 4 * q^21 - 12 * q^22 + 2 * q^24 + 16 * q^25 - 16 * q^26 + 20 * q^27 + 2 * q^28 - 12 * q^29 - 6 * q^30 + 2 * q^31 - 2 * q^32 + 12 * q^33 - 12 * q^34 - 6 * q^35 + 2 * q^36 - 16 * q^37 - 2 * q^38 + 16 * q^39 - 12 * q^40 + 12 * q^41 - 14 * q^42 - 4 * q^43 + 6 * q^44 - 6 * q^45 - 36 * q^47 + 2 * q^48 - 8 * q^50 + 12 * q^51 + 8 * q^52 - 6 * q^53 - 10 * q^54 - 18 * q^55 + 2 * q^56 - 10 * q^57 + 6 * q^58 - 12 * q^59 + 12 * q^60 - 4 * q^61 + 2 * q^62 + 22 * q^63 + 4 * q^64 - 24 * q^65 + 6 * q^66 + 8 * q^67 + 6 * q^68 + 12 * q^70 + 18 * q^71 + 2 * q^72 - 10 * q^73 + 8 * q^74 + 8 * q^75 - 2 * q^76 + 6 * q^77 - 8 * q^78 + 20 * q^79 + 6 * q^80 + 14 * q^81 - 6 * q^82 + 18 * q^83 + 10 * q^84 - 18 * q^85 - 4 * q^86 + 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^90 - 8 * q^91 + 10 * q^93 + 18 * q^94 - 12 * q^95 - 4 * q^96 + 8 * q^97 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more