LMFDB - Embedded newform 138.2.e.d.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	138.85
Dual form			138.2.e.d.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-1.37787 - 3.01713i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(3.66820 - 1.07708i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-1.37787 - 3.01713i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(3.66820 - 1.07708i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-3.18251 - 0.934468i) q^{10} +(0.230471 + 0.265977i) q^{11} +(0.654861 + 0.755750i) q^{12} +(-0.367451 - 0.107893i) q^{13} +(1.58816 - 3.47758i) q^{14} +(2.79032 + 1.79323i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-1.03578 + 7.20399i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(0.592229 + 4.11904i) q^{19} +(-2.79032 + 1.79323i) q^{20} +(-2.50357 + 2.88927i) q^{21} +0.351939 q^{22} +(-0.368423 - 4.78166i) q^{23} +1.00000 q^{24} +(-3.93020 + 4.53569i) q^{25} +(-0.322170 + 0.207046i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-1.58816 - 3.47758i) q^{28} +(0.637728 - 4.43549i) q^{29} +(3.18251 - 0.934468i) q^{30} +(3.65812 + 2.35093i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-0.337683 - 0.0991526i) q^{33} +(4.76612 + 5.50040i) q^{34} +(-8.30400 - 9.58333i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-3.04045 + 6.65767i) q^{37} +(3.50079 + 2.24982i) q^{38} +(0.367451 - 0.107893i) q^{39} +(-0.472039 + 3.28310i) q^{40} +(2.92426 + 6.40324i) q^{41} +(0.544078 + 3.78415i) q^{42} +(7.42019 - 4.76867i) q^{43} +(0.230471 - 0.265977i) q^{44} -3.31686 q^{45} +(-3.85500 - 2.85288i) q^{46} +10.6682 q^{47} +(0.654861 - 0.755750i) q^{48} +(6.40680 - 4.11740i) q^{49} +(0.854114 + 5.94049i) q^{50} +(-3.02342 - 6.62036i) q^{51} +(-0.0545015 + 0.379066i) q^{52} +(-2.43282 + 0.714342i) q^{53} +(0.841254 + 0.540641i) q^{54} +(0.484927 - 1.06184i) q^{55} +(-3.66820 - 1.07708i) q^{56} +(-2.72514 - 3.14498i) q^{57} +(-2.93450 - 3.38659i) q^{58} +(-7.57270 - 2.22355i) q^{59} +(1.37787 - 3.01713i) q^{60} +(-10.6433 - 6.84001i) q^{61} +(4.17227 - 1.22509i) q^{62} +(0.544078 - 3.78415i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.180774 + 1.25731i) q^{65} +(-0.296070 + 0.190272i) q^{66} +(-3.67231 + 4.23807i) q^{67} +7.27807 q^{68} +(2.89510 + 3.82340i) q^{69} -12.6806 q^{70} +(0.217114 - 0.250563i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(-0.0995577 - 0.692439i) q^{73} +(3.04045 + 6.65767i) q^{74} +(0.854114 - 5.94049i) q^{75} +(3.99283 - 1.17240i) q^{76} +(1.13189 + 0.727422i) q^{77} +(0.159089 - 0.348356i) q^{78} +(-15.4749 - 4.54383i) q^{79} +(2.17208 + 2.50672i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(6.75423 + 1.98322i) q^{82} +(-1.92508 + 4.21533i) q^{83} +(3.21616 + 2.06690i) q^{84} +(23.1625 - 6.80112i) q^{85} +(1.25527 - 8.73062i) q^{86} +(1.86152 + 4.07616i) q^{87} +(-0.0500861 - 0.348356i) q^{88} +(-7.41760 + 4.76700i) q^{89} +(-2.17208 + 2.50672i) q^{90} -1.46409 q^{91} +(-4.68056 + 1.04517i) q^{92} -4.34841 q^{93} +(6.98617 - 8.06247i) q^{94} +(11.6116 - 7.46235i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-4.66501 - 10.2150i) q^{97} +(1.08384 - 7.53826i) q^{98} +(0.337683 - 0.0991526i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9} - 13 q^{10} - 5 q^{11} + q^{12} + 13 q^{13} + 9 q^{14} + 9 q^{15} - q^{16} + q^{18} - 9 q^{20} - 13 q^{21} - 6 q^{22} - 32 q^{23} + 10 q^{24} + q^{25} - 13 q^{26} + q^{27} - 9 q^{28} + 27 q^{29} + 13 q^{30} - 8 q^{31} + q^{32} - 6 q^{33} - 11 q^{34} - 26 q^{35} - q^{36} - 11 q^{37} + 11 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} + 2 q^{42} + 34 q^{43} - 5 q^{44} + 2 q^{45} - q^{46} + 8 q^{47} + q^{48} + 25 q^{49} + 21 q^{50} - 11 q^{51} + 2 q^{52} + 9 q^{53} - q^{54} - 23 q^{55} - 2 q^{56} - 11 q^{57} - 5 q^{58} - 21 q^{59} - 2 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{63} - q^{64} + 29 q^{65} + 6 q^{66} - 32 q^{67} + 22 q^{68} - q^{69} - 18 q^{70} + 22 q^{71} + q^{72} + 43 q^{73} + 11 q^{74} + 21 q^{75} + 10 q^{77} + 2 q^{78} - 16 q^{79} + 2 q^{80} - q^{81} + 32 q^{82} - 3 q^{83} + 9 q^{84} + 33 q^{85} + 32 q^{86} + 6 q^{87} - 6 q^{88} - 11 q^{89} - 2 q^{90} - 70 q^{91} - 21 q^{92} + 8 q^{93} + 3 q^{94} - q^{96} + 39 q^{97} - 14 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9 - 13 * q^10 - 5 * q^11 + q^12 + 13 * q^13 + 9 * q^14 + 9 * q^15 - q^16 + q^18 - 9 * q^20 - 13 * q^21 - 6 * q^22 - 32 * q^23 + 10 * q^24 + q^25 - 13 * q^26 + q^27 - 9 * q^28 + 27 * q^29 + 13 * q^30 - 8 * q^31 + q^32 - 6 * q^33 - 11 * q^34 - 26 * q^35 - q^36 - 11 * q^37 + 11 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 + 2 * q^42 + 34 * q^43 - 5 * q^44 + 2 * q^45 - q^46 + 8 * q^47 + q^48 + 25 * q^49 + 21 * q^50 - 11 * q^51 + 2 * q^52 + 9 * q^53 - q^54 - 23 * q^55 - 2 * q^56 - 11 * q^57 - 5 * q^58 - 21 * q^59 - 2 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^63 - q^64 + 29 * q^65 + 6 * q^66 - 32 * q^67 + 22 * q^68 - q^69 - 18 * q^70 + 22 * q^71 + q^72 + 43 * q^73 + 11 * q^74 + 21 * q^75 + 10 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 - q^81 + 32 * q^82 - 3 * q^83 + 9 * q^84 + 33 * q^85 + 32 * q^86 + 6 * q^87 - 6 * q^88 - 11 * q^89 - 2 * q^90 - 70 * q^91 - 21 * q^92 + 8 * q^93 + 3 * q^94 - q^96 + 39 * q^97 - 14 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	−1.37787	−	3.01713i	−0.616204	−	1.34930i	−0.918248	−	0.396005i	$-0.870396\pi$
$5$	−1.37787	−	3.01713i	−0.616204	−	1.34930i	0.302044	−	0.953294i	$-0.402331\pi$
$6$	−0.142315	+	0.989821i	−0.0580998	+	0.404093i
$7$	3.66820	−	1.07708i	1.38645	−	0.407098i	0.498440	−	0.866924i	$-0.333907\pi$
$7$	3.66820	−	1.07708i	1.38645	−	0.407098i	0.888009	+	0.459826i	$0.152088\pi$
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−3.18251	−	0.934468i	−1.00640	−	0.295505i
$11$	0.230471	+	0.265977i	0.0694895	+	0.0801952i	0.789430	−	0.613841i	$-0.210376\pi$
$11$	0.230471	+	0.265977i	0.0694895	+	0.0801952i	−0.719940	+	0.694036i	$0.755831\pi$
$12$	0.654861	+	0.755750i	0.189042	+	0.218166i
$13$	−0.367451	−	0.107893i	−0.101913	−	0.0299243i	0.230379	−	0.973101i	$-0.426004\pi$
$13$	−0.367451	−	0.107893i	−0.101913	−	0.0299243i	−0.332291	+	0.943177i	$0.607822\pi$
$14$	1.58816	−	3.47758i	0.424453	−	0.929421i
$15$	2.79032	+	1.79323i	0.720458	+	0.463010i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−1.03578	+	7.20399i	−0.251213	+	1.74722i	0.339742	+	0.940519i	$0.389660\pi$
$17$	−1.03578	+	7.20399i	−0.251213	+	1.74722i	−0.590955	+	0.806705i	$0.701249\pi$
$18$	−0.415415	−	0.909632i	−0.0979143	−	0.214402i
$19$	0.592229	+	4.11904i	0.135867	+	0.944973i	0.937705	+	0.347432i	$0.112946\pi$
$19$	0.592229	+	4.11904i	0.135867	+	0.944973i	−0.801839	+	0.597541i	$0.796145\pi$
$20$	−2.79032	+	1.79323i	−0.623935	+	0.400979i
$21$	−2.50357	+	2.88927i	−0.546324	+	0.630491i
$22$	0.351939			0.0750336
$23$	−0.368423	−	4.78166i	−0.0768216	−	0.997045i
$23$	−0.368423	−	4.78166i	−0.0768216	−	0.997045i
$24$	1.00000			0.204124
$25$	−3.93020	+	4.53569i	−0.786040	+	0.907139i
$26$	−0.322170	+	0.207046i	−0.0631827	+	0.0406051i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	−1.58816	−	3.47758i	−0.300133	−	0.657200i
$29$	0.637728	−	4.43549i	0.118423	−	0.823650i	−0.840870	−	0.541237i	$-0.817956\pi$
$29$	0.637728	−	4.43549i	0.118423	−	0.823650i	0.959293	−	0.282413i	$-0.0911348\pi$
$30$	3.18251	−	0.934468i	0.581044	−	0.170610i
$31$	3.65812	+	2.35093i	0.657017	+	0.422239i	0.826224	−	0.563341i	$-0.190484\pi$
$31$	3.65812	+	2.35093i	0.657017	+	0.422239i	−0.169207	+	0.985581i	$0.554121\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	−0.337683	−	0.0991526i	−0.0587830	−	0.0172602i
$34$	4.76612	+	5.50040i	0.817383	+	0.943310i
$35$	−8.30400	−	9.58333i	−1.40363	−	1.61988i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	−3.04045	+	6.65767i	−0.499848	+	1.09451i	0.476671	+	0.879082i	$0.341843\pi$
$37$	−3.04045	+	6.65767i	−0.499848	+	1.09451i	−0.976519	+	0.215432i	$0.930884\pi$
$38$	3.50079	+	2.24982i	0.567903	+	0.364969i
$39$	0.367451	−	0.107893i	0.0588393	−	0.0172768i
$40$	−0.472039	+	3.28310i	−0.0746359	+	0.519104i
$41$	2.92426	+	6.40324i	0.456693	+	1.00002i	0.988229	+	0.152982i	$0.0488878\pi$
$41$	2.92426	+	6.40324i	0.456693	+	1.00002i	−0.531536	+	0.847036i	$0.678385\pi$
$42$	0.544078	+	3.78415i	0.0839531	+	0.583906i
$43$	7.42019	−	4.76867i	1.13157	−	0.727215i	0.165681	−	0.986179i	$-0.447018\pi$
$43$	7.42019	−	4.76867i	1.13157	−	0.727215i	0.965887	+	0.258965i	$0.0833813\pi$
$44$	0.230471	−	0.265977i	0.0347448	−	0.0400976i
$45$	−3.31686			−0.494449
$46$	−3.85500	−	2.85288i	−0.568389	−	0.420635i
$47$	10.6682			1.55611			0.778056	−	0.628194i	$-0.216206\pi$
$47$	10.6682			1.55611			0.778056	+	0.628194i	$0.216206\pi$
$48$	0.654861	−	0.755750i	0.0945210	−	0.109083i
$49$	6.40680	−	4.11740i	0.915257	−	0.588200i
$50$	0.854114	+	5.94049i	0.120790	+	0.840113i
$51$	−3.02342	−	6.62036i	−0.423363	−	0.927036i
$52$	−0.0545015	+	0.379066i	−0.00755799	+	0.0525670i
$53$	−2.43282	+	0.714342i	−0.334174	+	0.0981224i	−0.444515	−	0.895771i	$-0.646624\pi$
$53$	−2.43282	+	0.714342i	−0.334174	+	0.0981224i	0.110341	+	0.993894i	$0.464806\pi$
$54$	0.841254	+	0.540641i	0.114480	+	0.0735719i
$55$	0.484927	−	1.06184i	0.0653876	−	0.143179i
$56$	−3.66820	−	1.07708i	−0.490184	−	0.143931i
$57$	−2.72514	−	3.14498i	−0.360953	−	0.416562i
$58$	−2.93450	−	3.38659i	−0.385319	−	0.444681i
$59$	−7.57270	−	2.22355i	−0.985882	−	0.289481i	−0.251232	−	0.967927i	$-0.580836\pi$
$59$	−7.57270	−	2.22355i	−0.985882	−	0.289481i	−0.734650	+	0.678446i	$0.762654\pi$
$60$	1.37787	−	3.01713i	0.177883	−	0.389509i
$61$	−10.6433	−	6.84001i	−1.36273	−	0.875774i	−0.364273	−	0.931292i	$-0.618683\pi$
$61$	−10.6433	−	6.84001i	−1.36273	−	0.875774i	−0.998458	+	0.0555183i	$0.982319\pi$
$62$	4.17227	−	1.22509i	0.529879	−	0.155586i
$63$	0.544078	−	3.78415i	0.0685474	−	0.476757i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	0.180774	+	1.25731i	0.0224222	+	0.155950i
$66$	−0.296070	+	0.190272i	−0.0364436	+	0.0234209i
$67$	−3.67231	+	4.23807i	−0.448644	+	0.517763i	−0.934349	−	0.356360i	$-0.884018\pi$
$67$	−3.67231	+	4.23807i	−0.448644	+	0.517763i	0.485705	+	0.874123i	$0.338563\pi$
$68$	7.27807			0.882595
$69$	2.89510	+	3.82340i	0.348529	+	0.460284i
$70$	−12.6806			−1.51562
$71$	0.217114	−	0.250563i	0.0257667	−	0.0297363i	−0.742720	−	0.669602i	$-0.766465\pi$
$71$	0.217114	−	0.250563i	0.0257667	−	0.0297363i	0.768487	+	0.639866i	$0.221010\pi$
$72$	−0.841254	+	0.540641i	−0.0991427	+	0.0637151i
$73$	−0.0995577	−	0.692439i	−0.0116524	−	0.0810439i	0.983165	−	0.182717i	$-0.0584894\pi$
$73$	−0.0995577	−	0.692439i	−0.0116524	−	0.0810439i	−0.994818	+	0.101674i	$0.967580\pi$
$74$	3.04045	+	6.65767i	0.353446	+	0.773938i
$75$	0.854114	−	5.94049i	0.0986246	−	0.685949i
$76$	3.99283	−	1.17240i	0.458009	−	0.134484i
$77$	1.13189	+	0.727422i	0.128991	+	0.0828975i
$78$	0.159089	−	0.348356i	0.0180133	−	0.0394436i
$79$	−15.4749	−	4.54383i	−1.74106	−	0.511221i	−0.752054	−	0.659102i	$-0.770937\pi$
$79$	−15.4749	−	4.54383i	−1.74106	−	0.511221i	−0.989005	+	0.147881i	$0.952755\pi$
$80$	2.17208	+	2.50672i	0.242846	+	0.280260i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	6.75423	+	1.98322i	0.745880	+	0.219010i
$83$	−1.92508	+	4.21533i	−0.211304	+	0.462692i	−0.985373	−	0.170409i	$-0.945491\pi$
$83$	−1.92508	+	4.21533i	−0.211304	+	0.462692i	0.774069	+	0.633101i	$0.218218\pi$
$84$	3.21616	+	2.06690i	0.350912	+	0.225517i
$85$	23.1625	−	6.80112i	2.51233	−	0.737685i
$86$	1.25527	−	8.73062i	0.135360	−	0.941447i
$87$	1.86152	+	4.07616i	0.199576	+	0.437010i
$88$	−0.0500861	−	0.348356i	−0.00533919	−	0.0371349i
$89$	−7.41760	+	4.76700i	−0.786264	+	0.505301i	−0.871107	−	0.491093i	$-0.836598\pi$
$89$	−7.41760	+	4.76700i	−0.786264	+	0.505301i	0.0848429	+	0.996394i	$0.472961\pi$
$90$	−2.17208	+	2.50672i	−0.228958	+	0.264231i
$91$	−1.46409			−0.153479
$92$	−4.68056	+	1.04517i	−0.487982	+	0.108967i
$93$	−4.34841			−0.450909
$94$	6.98617	−	8.06247i	0.720568	−	0.831580i
$95$	11.6116	−	7.46235i	1.19133	−	0.765621i
$96$	−0.142315	−	0.989821i	−0.0145249	−	0.101023i
$97$	−4.66501	−	10.2150i	−0.473660	−	1.03717i	−0.984158	−	0.177293i	$-0.943266\pi$
$97$	−4.66501	−	10.2150i	−0.473660	−	1.03717i	0.510498	−	0.859879i	$-0.329461\pi$
$98$	1.08384	−	7.53826i	0.109484	−	0.761479i
$99$	0.337683	−	0.0991526i	0.0339384	−	0.00996521i
$100$	5.04885	+	3.24470i	0.504885	+	0.324470i
$101$	−2.30782	+	5.05341i	−0.229636	+	0.502833i	−0.989015	−	0.147816i	$-0.952776\pi$
$101$	−2.30782	+	5.05341i	−0.229636	+	0.502833i	0.759379	+	0.650649i	$0.225503\pi$
$102$	−6.98325	−	2.05047i	−0.691445	−	0.203027i
$103$	6.71619	+	7.75090i	0.661766	+	0.763718i	0.983065	−	0.183259i	$-0.0586648\pi$
$103$	6.71619	+	7.75090i	0.661766	+	0.763718i	−0.321299	+	0.946978i	$0.604119\pi$
$104$	0.250788	+	0.289425i	0.0245918	+	0.0283804i
$105$	12.1669	+	3.57253i	1.18737	+	0.348643i
$106$	−1.05330	+	2.30640i	−0.102305	+	0.224017i
$107$	8.99116	+	5.77827i	0.869208	+	0.558606i	0.897510	−	0.440993i	$-0.145374\pi$
$107$	8.99116	+	5.77827i	0.869208	+	0.558606i	−0.0283023	+	0.999599i	$0.509010\pi$
$108$	0.959493	−	0.281733i	0.0923273	−	0.0271097i
$109$	2.35760	−	16.3975i	0.225817	−	1.57059i	−0.489632	−	0.871929i	$-0.662869\pi$
$109$	2.35760	−	16.3975i	0.225817	−	1.57059i	0.715449	−	0.698665i	$-0.246222\pi$
$110$	−0.484927	−	1.06184i	−0.0462360	−	0.101243i
$111$	−1.04161	−	7.24458i	−0.0988655	−	0.687625i
$112$	−3.21616	+	2.06690i	−0.303899	+	0.195304i
$113$	−8.58753	+	9.91053i	−0.807847	+	0.932305i	−0.998784	−	0.0492976i	$-0.984302\pi$
$113$	−8.58753	+	9.91053i	−0.807847	+	0.932305i	0.190938	+	0.981602i	$0.438847\pi$
$114$	−4.16140			−0.389751
$115$	−13.9192	+	7.70011i	−1.29797	+	0.718039i
$116$	−4.48110			−0.416060
$117$	−0.250788	+	0.289425i	−0.0231854	+	0.0267573i
$118$	−6.63951	+	4.26695i	−0.611216	+	0.392805i
$119$	3.95984	+	27.5413i	0.362998	+	2.52470i
$120$	−1.37787	−	3.01713i	−0.125782	−	0.275425i
$121$	1.54784	−	10.7654i	0.140712	−	0.978676i
$122$	−12.1392	+	3.56439i	−1.09903	+	0.322705i
$123$	−5.92190	−	3.80577i	−0.533960	−	0.343155i
$124$	1.80640	−	3.95545i	0.162219	−	0.355210i
$125$	3.18754	+	0.935947i	0.285103	+	0.0837137i
$126$	−2.50357	−	2.88927i	−0.223036	−	0.257397i
$127$	9.98886	+	11.5278i	0.886368	+	1.02292i	0.999569	+	0.0293507i	$0.00934396\pi$
$127$	9.98886	+	11.5278i	0.886368	+	1.02292i	−0.113202	+	0.993572i	$0.536111\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	−3.66412	+	8.02331i	−0.322608	+	0.706413i
$130$	1.06859	+	0.686743i	0.0937218	+	0.0602314i
$131$	3.87151	−	1.13678i	0.338255	−	0.0993207i	−0.108194	−	0.994130i	$-0.534507\pi$
$131$	3.87151	−	1.13678i	0.338255	−	0.0993207i	0.446449	+	0.894809i	$0.352688\pi$
$132$	−0.0500861	+	0.348356i	−0.00435943	+	0.0303205i
$133$	6.60895	+	14.4716i	0.573069	+	1.25485i
$134$	0.798069	+	5.55069i	0.0689427	+	0.479507i
$135$	2.79032	−	1.79323i	0.240153	−	0.154337i
$136$	4.76612	−	5.50040i	0.408691	−	0.471655i
$137$	4.16447			0.355795			0.177898	−	0.984049i	$-0.443070\pi$
$137$	4.16447			0.355795			0.177898	+	0.984049i	$0.443070\pi$
$138$	4.78542	+	0.315828i	0.407362	+	0.0268850i
$139$	2.19178			0.185904			0.0929521	−	0.995671i	$-0.470370\pi$
$139$	2.19178			0.185904			0.0929521	+	0.995671i	$0.470370\pi$
$140$	−8.30400	+	9.58333i	−0.701816	+	0.809939i
$141$	−8.97464	+	5.76765i	−0.755801	+	0.485724i
$142$	−0.0471833	−	0.328167i	−0.00395954	−	0.0275392i
$143$	−0.0559896	−	0.122600i	−0.00468208	−	0.0102523i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	−14.2611	+	4.18745i	−1.18432	+	0.347749i
$146$	−0.588507	−	0.378211i	−0.0487052	−	0.0313009i
$147$	−3.16371	+	6.92755i	−0.260938	+	0.571375i
$148$	7.02260	+	2.06202i	0.577254	+	0.169497i
$149$	0.901293	+	1.04015i	0.0738368	+	0.0852122i	0.791466	−	0.611213i	$-0.209318\pi$
$149$	0.901293	+	1.04015i	0.0738368	+	0.0852122i	−0.717629	+	0.696425i	$0.754773\pi$
$150$	−3.93020	−	4.53569i	−0.320900	−	0.370338i
$151$	−12.9802	−	3.81132i	−1.05631	−	0.310161i	−0.292946	−	0.956129i	$-0.594636\pi$
$151$	−12.9802	−	3.81132i	−1.05631	−	0.310161i	−0.763364	+	0.645968i	$0.776454\pi$
$152$	1.72871	−	3.78534i	0.140217	−	0.307032i
$153$	6.12270	+	3.93482i	0.494991	+	0.318111i
$154$	1.29098	−	0.379066i	0.104030	−	0.0305460i
$155$	2.05262	−	14.2763i	0.164870	−	1.14670i
$156$	−0.159089	−	0.348356i	−0.0127373	−	0.0278908i
$157$	2.04059	+	14.1926i	0.162857	+	1.13270i	0.893215	+	0.449630i	$0.148444\pi$
$157$	2.04059	+	14.1926i	0.162857	+	1.13270i	−0.730358	+	0.683065i	$0.760647\pi$
$158$	−13.5679	+	8.71955i	−1.07940	+	0.693690i
$159$	1.66042	−	1.91623i	0.131680	−	0.151967i
$160$	3.31686			0.262221
$161$	−6.50168	−	17.1433i	−0.512404	−	1.35108i
$162$	−1.00000			−0.0785674
$163$	4.88246	−	5.63466i	0.382424	−	0.441341i	−0.531603	−	0.846993i	$-0.678410\pi$
$163$	4.88246	−	5.63466i	0.382424	−	0.441341i	0.914027	+	0.405653i	$0.132956\pi$
$164$	5.92190	−	3.80577i	0.462423	−	0.297181i
$165$	0.166129	+	1.15545i	0.0129331	+	0.0899517i
$166$	1.92508	+	4.21533i	0.149415	+	0.327173i
$167$	−0.0534699	+	0.371891i	−0.00413763	+	0.0287778i	−0.991786	−	0.127911i	$-0.959173\pi$
$167$	−0.0534699	+	0.371891i	−0.00413763	+	0.0287778i	0.987648	+	0.156689i	$0.0500819\pi$
$168$	3.66820	−	1.07708i	0.283008	−	0.0830985i
$169$	−10.8129	−	6.94904i	−0.831763	−	0.534541i
$170$	10.0283	−	21.9588i	0.769133	−	1.68417i
$171$	3.99283	+	1.17240i	0.305340	+	0.0896558i
$172$	−5.77613	−	6.66601i	−0.440426	−	0.508279i
$173$	−10.3056	−	11.8933i	−0.783519	−	0.904229i	0.213840	−	0.976869i	$-0.431403\pi$
$173$	−10.3056	−	11.8933i	−0.783519	−	0.904229i	−0.997358	+	0.0726401i	$0.976858\pi$
$174$	4.29959	+	1.26247i	0.325951	+	0.0957078i
$175$	−9.53145	+	20.8710i	−0.720510	+	1.57770i
$176$	−0.296070	−	0.190272i	−0.0223171	−	0.0143423i
$177$	7.57270	−	2.22355i	0.569199	−	0.167132i
$178$	−1.25484	+	8.72757i	−0.0940539	+	0.654159i
$179$	−2.48154	−	5.43382i	−0.185479	−	0.406143i	0.793935	−	0.608002i	$-0.208029\pi$
$179$	−2.48154	−	5.43382i	−0.185479	−	0.406143i	−0.979415	+	0.201859i	$0.935302\pi$
$180$	0.472039	+	3.28310i	0.0351837	+	0.244708i
$181$	−15.4007	+	9.89742i	−1.14472	+	0.735669i	−0.968582	−	0.248696i	$-0.919998\pi$
$181$	−15.4007	+	9.89742i	−1.14472	+	0.735669i	−0.176142	+	0.984365i	$0.556362\pi$
$182$	−0.958778	+	1.10649i	−0.0710693	+	0.0820184i
$183$	12.6517			0.935239
$184$	−2.27522	+	4.22177i	−0.167732	+	0.311233i
$185$	24.2764			1.78483
$186$	−2.84760	+	3.28631i	−0.208796	+	0.240964i
$187$	−2.15481	+	1.38481i	−0.157576	+	0.101268i
$188$	−1.51824	−	10.5596i	−0.110729	−	0.770137i
$189$	1.58816	+	3.47758i	0.115521	+	0.252956i
$190$	1.96434	−	13.6623i	0.142508	−	0.991167i
$191$	7.79149	−	2.28779i	0.563773	−	0.165539i	0.0125864	−	0.999921i	$-0.495994\pi$
$191$	7.79149	−	2.28779i	0.563773	−	0.165539i	0.551186	+	0.834382i	$0.314175\pi$
$192$	−0.841254	−	0.540641i	−0.0607122	−	0.0390174i
$193$	6.21393	−	13.6066i	0.447288	−	0.979425i	−0.542914	−	0.839788i	$-0.682679\pi$
$193$	6.21393	−	13.6066i	0.447288	−	0.979425i	0.990203	−	0.139637i	$-0.0445935\pi$
$194$	−10.7749	−	3.16379i	−0.773591	−	0.227147i
$195$	−0.831830	−	0.959983i	−0.0595686	−	0.0687458i
$196$	−4.98727	−	5.75562i	−0.356234	−	0.411116i
$197$	19.6536	+	5.77082i	1.40026	+	0.411154i	0.892774	−	0.450505i	$-0.148756\pi$
$197$	19.6536	+	5.77082i	1.40026	+	0.411154i	0.507487	+	0.861659i	$0.330574\pi$
$198$	0.146201	−	0.320135i	0.0103900	−	0.0227510i
$199$	11.8433	+	7.61124i	0.839551	+	0.539547i	0.888300	−	0.459264i	$-0.151887\pi$
$199$	11.8433	+	7.61124i	0.839551	+	0.539547i	−0.0487487	+	0.998811i	$0.515523\pi$
$200$	5.75848	−	1.69084i	0.407186	−	0.119561i
$201$	0.798069	−	5.55069i	0.0562914	−	0.391516i
$202$	2.30782	+	5.05341i	0.162377	+	0.355557i
$203$	−2.43807	−	16.9571i	−0.171119	−	1.19016i
$204$	−6.12270	+	3.93482i	−0.428675	+	0.275492i
$205$	15.2901	−	17.6457i	1.06791	−	1.23243i
$206$	10.2559			0.714563
$207$	−4.50260	−	1.65124i	−0.312952	−	0.114769i
$208$	0.382964			0.0265538
$209$	−0.959081	+	1.10684i	−0.0663410	+	0.0765616i
$210$	10.6676	−	6.85563i	0.736132	−	0.473083i
$211$	−0.569168	−	3.95865i	−0.0391832	−	0.272525i	0.960806	−	0.277222i	$-0.0894139\pi$
$211$	−0.569168	−	3.95865i	−0.0391832	−	0.272525i	−0.999989	+	0.00469740i	$0.998505\pi$
$212$	1.05330	+	2.30640i	0.0723408	+	0.158404i
$213$	−0.0471833	+	0.328167i	−0.00323295	+	0.0224857i
$214$	10.2549	−	3.01110i	0.701009	−	0.205835i
$215$	−24.6118	−	15.8170i	−1.67851	−	1.07871i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	15.9508	+	4.68359i	1.08281	+	0.317943i
$218$	−10.8485	−	12.5198i	−0.734753	−	0.847950i
$219$	0.458114	+	0.528692i	0.0309565	+	0.0357257i
$220$	−1.12005	−	0.328875i	−0.0755136	−	0.0221728i
$221$	1.15786	−	2.53536i	0.0778861	−	0.170547i
$222$	−6.15720	−	3.95699i	−0.413244	−	0.265576i
$223$	−5.76119	+	1.69164i	−0.385798	+	0.113280i	−0.468879	−	0.883262i	$-0.655342\pi$
$223$	−5.76119	+	1.69164i	−0.385798	+	0.113280i	0.0830815	+	0.996543i	$0.473524\pi$
$224$	−0.544078	+	3.78415i	−0.0363527	+	0.252839i
$225$	2.49315	+	5.45923i	0.166210	+	0.363949i
$226$	1.86625	+	12.9800i	0.124141	+	0.863419i
$227$	0.363529	−	0.233626i	0.0241283	−	0.0155063i	−0.528521	−	0.848920i	$-0.677253\pi$
$227$	0.363529	−	0.233626i	0.0241283	−	0.0155063i	0.552649	+	0.833414i	$0.313617\pi$
$228$	−2.72514	+	3.14498i	−0.180477	+	0.208281i
$229$	−9.80029			−0.647621			−0.323811	−	0.946122i	$-0.604964\pi$
$229$	−9.80029			−0.647621			−0.323811	+	0.946122i	$0.604964\pi$
$230$	−3.29580	+	15.5619i	−0.217319	+	1.02612i
$231$	−1.34548			−0.0885262
$232$	−2.93450	+	3.38659i	−0.192659	+	0.222341i
$233$	−7.41438	+	4.76493i	−0.485732	+	0.312161i	−0.760487	−	0.649353i	$-0.775040\pi$
$233$	−7.41438	+	4.76493i	−0.485732	+	0.312161i	0.274755	+	0.961514i	$0.411403\pi$
$234$	0.0545015	+	0.379066i	0.00356287	+	0.0247803i
$235$	−14.6994	−	32.1872i	−0.958884	−	2.09966i
$236$	−1.12321	+	7.81207i	−0.0731145	+	0.508522i
$237$	15.4749	−	4.54383i	1.00520	−	0.295154i
$238$	23.4074	+	15.0430i	1.51728	+	0.975096i
$239$	−8.09697	+	17.7299i	−0.523750	+	1.14685i	0.444251	+	0.895903i	$0.353470\pi$
$239$	−8.09697	+	17.7299i	−0.523750	+	1.14685i	−0.968000	+	0.250949i	$0.919257\pi$
$240$	−3.18251	−	0.934468i	−0.205430	−	0.0603197i
$241$	1.52599	+	1.76108i	0.0982974	+	0.113441i	0.802767	−	0.596293i	$-0.203360\pi$
$241$	1.52599	+	1.76108i	0.0982974	+	0.113441i	−0.704469	+	0.709734i	$0.748815\pi$
$242$	−7.12236	−	8.21964i	−0.457842	−	0.528378i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	−5.25570	+	11.5084i	−0.336461	+	0.736748i
$245$	−21.2505	−	13.6569i	−1.35764	−	0.872504i
$246$	−6.75423	+	1.98322i	−0.430634	+	0.126446i
$247$	0.226802	−	1.57744i	0.0144311	−	0.100370i
$248$	−1.80640	−	3.95545i	−0.114706	−	0.251172i
$249$	−0.659501	−	4.58693i	−0.0417942	−	0.290685i
$250$	2.79474	−	1.79607i	0.176755	−	0.113593i
$251$	−9.69515	+	11.1888i	−0.611953	+	0.706231i	−0.974158	−	0.225867i	$-0.927478\pi$
$251$	−9.69515	+	11.1888i	−0.611953	+	0.706231i	0.362205	+	0.932098i	$0.382024\pi$
$252$	−3.82306			−0.240830
$253$	1.18690	−	1.20002i	0.0746199	−	0.0754449i
$254$	15.2534			0.957084
$255$	−15.8086	+	18.2441i	−0.989971	+	1.14249i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−3.52467	−	24.5146i	−0.219863	−	1.52918i	−0.738540	−	0.674209i	$-0.764485\pi$
$257$	−3.52467	−	24.5146i	−0.219863	−	1.52918i	0.518678	−	0.854970i	$-0.326425\pi$
$258$	3.66412	+	8.02331i	0.228118	+	0.499510i
$259$	−3.98215	+	27.6964i	−0.247439	+	1.72097i
$260$	1.21879	−	0.357868i	0.0755859	−	0.0221940i
$261$	−3.76974	−	2.42267i	−0.233341	−	0.149959i
$262$	1.67618	−	3.67032i	0.103555	−	0.226753i
$263$	−2.48394	−	0.729350i	−0.153166	−	0.0449736i	0.204251	−	0.978919i	$-0.434524\pi$
$263$	−2.48394	−	0.729350i	−0.153166	−	0.0449736i	−0.357417	+	0.933945i	$0.616342\pi$
$264$	0.230471	+	0.265977i	0.0141845	+	0.0163698i
$265$	5.50739	+	6.35586i	0.338316	+	0.390438i
$266$	15.2648	+	4.48216i	0.935947	+	0.274819i
$267$	3.66285	−	8.02052i	0.224163	−	0.490848i
$268$	4.71756	+	3.03179i	0.288171	+	0.185196i
$269$	12.4123	−	3.64457i	0.756790	−	0.222214i	0.119496	−	0.992835i	$-0.461872\pi$
$269$	12.4123	−	3.64457i	0.756790	−	0.222214i	0.637294	+	0.770621i	$0.280054\pi$
$270$	0.472039	−	3.28310i	0.0287274	−	0.199803i
$271$	−4.85060	−	10.6213i	−0.294653	−	0.645199i	0.703179	−	0.711013i	$-0.251763\pi$
$271$	−4.85060	−	10.6213i	−0.294653	−	0.645199i	−0.997832	+	0.0658132i	$0.979036\pi$
$272$	−1.03578	−	7.20399i	−0.0628032	−	0.436806i
$273$	1.23167	−	0.791549i	0.0745443	−	0.0479067i
$274$	2.72715	−	3.14730i	0.164753	−	0.190135i
$275$	−2.11219			−0.127370
$276$	3.37247	−	3.40976i	0.202999	−	0.205243i
$277$	14.2109			0.853849			0.426925	−	0.904287i	$-0.359597\pi$
$277$	14.2109			0.853849			0.426925	+	0.904287i	$0.359597\pi$
$278$	1.43531	−	1.65644i	0.0860842	−	0.0993464i
$279$	3.65812	−	2.35093i	0.219006	−	0.140746i
$280$	1.80463	+	12.5515i	0.107847	+	0.750095i
$281$	−5.30272	−	11.6113i	−0.316334	−	0.692674i	0.682952	−	0.730463i	$-0.260696\pi$
$281$	−5.30272	−	11.6113i	−0.316334	−	0.692674i	−0.999286	+	0.0377891i	$0.987968\pi$
$282$	−1.51824	+	10.5596i	−0.0904098	+	0.628814i
$283$	2.55003	−	0.748757i	0.151584	−	0.0445090i	−0.205060	−	0.978749i	$-0.565739\pi$
$283$	2.55003	−	0.748757i	0.151584	−	0.0445090i	0.356644	+	0.934240i	$0.383921\pi$
$284$	−0.278911	−	0.179245i	−0.0165503	−	0.0106362i
$285$	−5.73389	+	12.5555i	−0.339646	+	0.743721i
$286$	−0.129320	−	0.0379719i	−0.00764687	−	0.00224532i
$287$	17.6236	+	20.3387i	1.04029	+	1.20055i
$288$	0.654861	+	0.755750i	0.0385880	+	0.0445330i
$289$	−34.5132	−	10.1340i	−2.03019	−	0.596117i
$290$	−6.17440	+	13.5200i	−0.362573	+	0.793925i
$291$	9.44708	+	6.07127i	0.553798	+	0.355904i
$292$	−0.671223	+	0.197089i	−0.0392803	+	0.0115337i
$293$	−1.55113	+	10.7883i	−0.0906178	+	0.630261i	0.893008	+	0.450040i	$0.148590\pi$
$293$	−1.55113	+	10.7883i	−0.0906178	+	0.630261i	−0.983626	+	0.180221i	$0.942319\pi$
$294$	3.16371	+	6.92755i	0.184511	+	0.404023i
$295$	3.72552	+	25.9116i	0.216908	+	1.50863i
$296$	6.15720	−	3.95699i	0.357880	−	0.229995i
$297$	−0.230471	+	0.265977i	−0.0133733	+	0.0154336i
$298$	1.37631			0.0797276
$299$	−0.380532	+	1.79678i	−0.0220067	+	0.103910i
$300$	−6.00158			−0.346502
$301$	22.0825	−	25.4845i	1.27281	−	1.46890i
$302$	−11.3806	+	7.31387i	−0.654880	+	0.420866i
$303$	−0.790623	−	5.49890i	−0.0454201	−	0.315904i
$304$	−1.72871	−	3.78534i	−0.0991482	−	0.217104i
$305$	−5.97208	+	41.5368i	−0.341960	+	2.37839i
$306$	6.98325	−	2.05047i	0.399206	−	0.117217i
$307$	−9.08434	−	5.83815i	−0.518471	−	0.333201i	0.255096	−	0.966916i	$-0.417893\pi$
$307$	−9.08434	−	5.83815i	−0.518471	−	0.333201i	−0.773567	+	0.633715i	$0.781529\pi$
$308$	0.558933	−	1.22389i	0.0318482	−	0.0697378i
$309$	−9.84047	−	2.88942i	−0.559805	−	0.164373i
$310$	−9.44511	−	10.9002i	−0.536446	−	0.619092i
$311$	−4.92470	−	5.68341i	−0.279254	−	0.322276i	0.598744	−	0.800940i	$-0.295667\pi$
$311$	−4.92470	−	5.68341i	−0.279254	−	0.322276i	−0.877998	+	0.478664i	$0.841121\pi$
$312$	−0.367451	−	0.107893i	−0.0208028	−	0.00610826i
$313$	−6.73499	+	14.7476i	−0.380684	+	0.833582i	0.618185	+	0.786033i	$0.287868\pi$
$313$	−6.73499	+	14.7476i	−0.380684	+	0.833582i	−0.998869	+	0.0475490i	$0.984859\pi$
$314$	12.0624	+	7.75202i	0.680719	+	0.437472i
$315$	−12.1669	+	3.57253i	−0.685528	+	0.201289i
$316$	−2.29528	+	15.9640i	−0.129119	+	0.898046i
$317$	2.40859	+	5.27407i	0.135280	+	0.296221i	0.965133	−	0.261761i	$-0.0843031\pi$
$317$	2.40859	+	5.27407i	0.135280	+	0.296221i	−0.829853	+	0.557982i	$0.811576\pi$
$318$	−0.360844	−	2.50972i	−0.0202351	−	0.140738i
$319$	1.32672	−	0.852630i	0.0742820	−	0.0477381i
$320$	2.17208	−	2.50672i	0.121423	−	0.140130i
$321$	−10.6878			−0.596535
$322$	−17.2137	−	6.31280i	−0.959282	−	0.351799i
$323$	−30.2869			−1.68521
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	1.93353	−	1.24260i	0.107253	−	0.0689272i
$326$	−1.06106	−	7.37984i	−0.0587667	−	0.408731i
$327$	6.88181	+	15.0691i	0.380565	+	0.833321i
$328$	1.00181	−	6.96772i	0.0553156	−	0.384728i
$329$	39.1330	−	11.4905i	2.15747	−	0.633490i
$330$	0.982022	+	0.631107i	0.0540585	+	0.0347413i
$331$	−1.76651	+	3.86811i	−0.0970959	+	0.212610i	−0.951947	−	0.306263i	$-0.900921\pi$
$331$	−1.76651	+	3.86811i	−0.0970959	+	0.212610i	0.854851	+	0.518874i	$0.173648\pi$
$332$	4.44639	+	1.30558i	0.244027	+	0.0716529i
$333$	4.79298	+	5.53139i	0.262653	+	0.303118i
$334$	0.246041	+	0.283947i	0.0134628	+	0.0155369i
$335$	17.8468	+	5.24028i	0.975073	+	0.286307i
$336$	1.58816	−	3.47758i	0.0866410	−	0.189717i
$337$	−6.14322	−	3.94801i	−0.334642	−	0.215062i	0.362518	−	0.931977i	$-0.381917\pi$
$337$	−6.14322	−	3.94801i	−0.334642	−	0.215062i	−0.697160	+	0.716915i	$0.745553\pi$
$338$	−12.3327	+	3.62120i	−0.670810	+	0.196968i
$339$	1.86625	−	12.9800i	0.101361	−	0.704979i
$340$	−10.0283	−	21.9588i	−0.543859	−	1.19089i
$341$	0.217795	+	1.51480i	0.0117943	+	0.0820309i
$342$	3.50079	−	2.24982i	0.189301	−	0.121656i
$343$	1.54164	−	1.77915i	0.0832408	−	0.0960650i
$344$	−8.82040			−0.475564
$345$	7.54660	−	14.0030i	0.406295	−	0.753898i
$346$	−15.7371			−0.846029
$347$	14.7553	−	17.0285i	0.792104	−	0.914137i	−0.205817	−	0.978591i	$-0.565985\pi$
$347$	14.7553	−	17.0285i	0.792104	−	0.914137i	0.997921	+	0.0644537i	$0.0205305\pi$
$348$	3.76974	−	2.42267i	0.202079	−	0.129869i
$349$	−3.00628	−	20.9092i	−0.160923	−	1.11924i	−0.896899	−	0.442235i	$-0.854186\pi$
$349$	−3.00628	−	20.9092i	−0.160923	−	1.11924i	0.735976	−	0.677007i	$-0.236723\pi$
$350$	9.53145	+	20.8710i	0.509477	+	1.11560i
$351$	0.0545015	−	0.379066i	0.00290907	−	0.0202330i
$352$	−0.337683	+	0.0991526i	−0.0179985	+	0.00528485i
$353$	14.3088	+	9.19572i	0.761581	+	0.489439i	0.862875	−	0.505418i	$-0.168662\pi$
$353$	14.3088	+	9.19572i	0.761581	+	0.489439i	−0.101293	+	0.994857i	$0.532298\pi$
$354$	3.27862	−	7.17918i	0.174257	−	0.381569i
$355$	−1.05513	−	0.309815i	−0.0560007	−	0.0164433i
$356$	5.77412	+	6.66369i	0.306028	+	0.353175i
$357$	−18.2212	−	21.0283i	−0.964366	−	1.11294i
$358$	−5.73167	−	1.68297i	−0.302928	−	0.0889478i
$359$	4.13610	−	9.05680i	0.218295	−	0.478000i	−0.768525	−	0.639820i	$-0.779009\pi$
$359$	4.13610	−	9.05680i	0.218295	−	0.478000i	0.986820	+	0.161820i	$0.0517363\pi$
$360$	2.79032	+	1.79323i	0.147063	+	0.0945116i
$361$	1.61460	−	0.474089i	0.0849789	−	0.0249521i
$362$	−2.60533	+	18.1205i	−0.136933	+	0.952392i
$363$	4.51811	+	9.89328i	0.237139	+	0.519263i
$364$	0.208362	+	1.44919i	0.0109212	+	0.0759583i
$365$	−1.95200	+	1.25447i	−0.102172	+	0.0656621i
$366$	8.28509	−	9.56150i	0.433068	−	0.499788i
$367$	24.3414			1.27061			0.635306	−	0.772261i	$-0.280874\pi$
$367$	24.3414			1.27061			0.635306	+	0.772261i	$0.280874\pi$
$368$	1.70065	+	4.48417i	0.0886524	+	0.233754i
$369$	7.03938			0.366455
$370$	15.8976	−	18.3469i	0.826479	−	0.953808i
$371$	−8.15468	+	5.24069i	−0.423370	+	0.272083i
$372$	0.618844	+	4.30415i	0.0320855	+	0.223160i
$373$	14.4280	+	31.5930i	0.747056	+	1.63582i	0.771586	+	0.636125i	$0.219464\pi$
$373$	14.4280	+	31.5930i	0.747056	+	1.63582i	−0.0245297	+	0.999699i	$0.507809\pi$
$374$	−0.364530	+	2.53536i	−0.0188494	+	0.131100i
$375$	−3.18754	+	0.935947i	−0.164604	+	0.0483321i
$376$	−8.97464	−	5.76765i	−0.462832	−	0.297444i
$377$	−0.712894	+	1.56102i	−0.0367159	+	0.0803967i
$378$	3.66820	+	1.07708i	0.188672	+	0.0553990i
$379$	16.5256	+	19.0715i	0.848862	+	0.979639i	0.999961	−	0.00887990i	$-0.00282660\pi$
$379$	16.5256	+	19.0715i	0.848862	+	0.979639i	−0.151099	+	0.988519i	$0.548281\pi$
$380$	−9.03891	−	10.4315i	−0.463686	−	0.535122i
$381$	−14.6355	−	4.29738i	−0.749801	−	0.220161i
$382$	3.37335	−	7.38660i	0.172596	−	0.377931i
$383$	−23.2551	−	14.9451i	−1.18828	−	0.763660i	−0.211389	−	0.977402i	$-0.567799\pi$
$383$	−23.2551	−	14.9451i	−1.18828	−	0.763660i	−0.976890	+	0.213742i	$0.931435\pi$
$384$	−0.959493	+	0.281733i	−0.0489639	+	0.0143771i
$385$	0.635120	−	4.41735i	0.0323687	−	0.225129i
$386$	−6.21393	−	13.6066i	−0.316281	−	0.692558i
$387$	−1.25527	−	8.73062i	−0.0638091	−	0.443802i
$388$	−9.44708	+	6.07127i	−0.479603	+	0.308222i
$389$	−9.83860	+	11.3544i	−0.498837	+	0.575688i	−0.948205	−	0.317658i	$-0.897104\pi$
$389$	−9.83860	+	11.3544i	−0.498837	+	0.575688i	0.449368	+	0.893347i	$0.351649\pi$
$390$	−1.27024			−0.0643211
$391$	34.8286	+	2.29861i	1.76136	+	0.116246i
$392$	−7.61578			−0.384655
$393$	−2.64233	+	3.04941i	−0.133288	+	0.153823i
$394$	17.2317	−	11.0741i	0.868119	−	0.557906i
$395$	7.61312	+	52.9504i	0.383058	+	2.66423i
$396$	−0.146201	−	0.320135i	−0.00734686	−	0.0160874i
$397$	2.65753	−	18.4835i	0.133378	−	0.927663i	−0.807729	−	0.589554i	$-0.799304\pi$
$397$	2.65753	−	18.4835i	0.133378	−	0.927663i	0.941107	−	0.338109i	$-0.109787\pi$
$398$	13.5079	−	3.96628i	0.677091	−	0.198812i
$399$	−13.3837	−	8.60120i	−0.670025	−	0.430599i
$400$	2.49315	−	5.45923i	0.124657	−	0.272962i
$401$	31.0836	+	9.12697i	1.55224	+	0.455779i	0.941770	−	0.336258i	$-0.109162\pi$
$401$	31.0836	+	9.12697i	1.55224	+	0.455779i	0.610472	+	0.792038i	$0.290980\pi$
$402$	−3.67231	−	4.23807i	−0.183158	−	0.211376i
$403$	−1.09053	−	1.25854i	−0.0543232	−	0.0626923i
$404$	5.33041	+	1.56515i	0.265198	+	0.0778691i
$405$	−1.37787	+	3.01713i	−0.0684672	+	0.149922i
$406$	−14.4120	−	9.26200i	−0.715253	−	0.459665i
$407$	−2.47152	+	0.725705i	−0.122509	+	0.0359719i
$408$	−1.03578	+	7.20399i	−0.0512786	+	0.356650i
$409$	−5.58677	−	12.2333i	−0.276248	−	0.604898i	0.719754	−	0.694229i	$-0.244254\pi$
$409$	−5.58677	−	12.2333i	−0.276248	−	0.604898i	−0.996002	+	0.0893307i	$0.971527\pi$
$410$	−3.32286	−	23.1110i	−0.164104	−	1.14137i
$411$	−3.50338	+	2.25149i	−0.172809	+	0.111058i
$412$	6.71619	−	7.75090i	0.330883	−	0.381859i
$413$	−30.1731			−1.48472
$414$	−4.19650	+	2.32150i	−0.206247	+	0.114096i
$415$	15.3707			0.754517
$416$	0.250788	−	0.289425i	0.0122959	−	0.0141902i
$417$	−1.84384	+	1.18496i	−0.0902933	+	0.0580280i
$418$	0.208428	+	1.44965i	0.0101946	+	0.0709047i
$419$	−5.62009	−	12.3063i	−0.274559	−	0.601201i	0.721248	−	0.692677i	$-0.243569\pi$
$419$	−5.62009	−	12.3063i	−0.274559	−	0.601201i	−0.995807	+	0.0914759i	$0.970842\pi$
$420$	1.80463	−	12.5515i	0.0880570	−	0.612450i
$421$	−24.6050	+	7.22468i	−1.19917	+	0.352109i	−0.819537	−	0.573026i	$-0.805769\pi$
$421$	−24.6050	+	7.22468i	−1.19917	+	0.352109i	−0.379637	+	0.925135i	$0.623951\pi$
$422$	−3.36448	−	2.16222i	−0.163780	−	0.105255i
$423$	4.43172	−	9.70411i	0.215478	−	0.471830i
$424$	2.43282	+	0.714342i	0.118148	+	0.0346915i
$425$	−28.6043	−	33.0111i	−1.38751	−	1.60127i
$426$	0.217114	+	0.250563i	0.0105192	+	0.0121398i
$427$	−46.4089	−	13.6269i	−2.24588	−	0.659450i
$428$	4.43988	−	9.72197i	0.214610	−	0.469929i
$429$	0.113384	+	0.0728675i	0.00547423	+	0.00351807i
$430$	−28.0710	+	8.24238i	−1.35370	+	0.397483i
$431$	2.44186	−	16.9835i	0.117620	−	0.818068i	−0.842543	−	0.538629i	$-0.818942\pi$
$431$	2.44186	−	16.9835i	0.117620	−	0.818068i	0.960163	−	0.279439i	$-0.0901485\pi$
$432$	−0.415415	−	0.909632i	−0.0199867	−	0.0437647i
$433$	1.35870	+	9.44994i	0.0652948	+	0.454135i	0.996072	+	0.0885481i	$0.0282227\pi$
$433$	1.35870	+	9.44994i	0.0652948	+	0.454135i	−0.930777	+	0.365587i	$0.880868\pi$
$434$	13.9852	−	8.98774i	0.671311	−	0.431425i
$435$	9.73333	−	11.2329i	0.466678	−	0.538575i
$436$	−16.5661			−0.793373
$437$	19.4777	−	4.34939i	0.931743	−	0.208059i
$438$	0.699560			0.0334263
$439$	15.6250	−	18.0322i	0.745742	−	0.860632i	−0.248407	−	0.968656i	$-0.579907\pi$
$439$	15.6250	−	18.0322i	0.745742	−	0.860632i	0.994148	+	0.108024i	$0.0344523\pi$
$440$	−0.982022	+	0.631107i	−0.0468161	+	0.0300869i
$441$	−1.08384	−	7.53826i	−0.0516113	−	0.358965i
$442$	−1.15786	−	2.53536i	−0.0550738	−	0.120595i
$443$	1.00236	−	6.97159i	0.0476237	−	0.331230i	−0.952056	−	0.305924i	$-0.901035\pi$
$443$	1.00236	−	6.97159i	0.0476237	−	0.331230i	0.999680	−	0.0253065i	$-0.00805616\pi$
$444$	−7.02260	+	2.06202i	−0.333278	+	0.0978592i
$445$	24.6032	+	15.8115i	1.16630	+	0.749537i
$446$	−2.49432	+	5.46180i	−0.118110	+	0.258624i
$447$	−1.32056	−	0.387752i	−0.0624604	−	0.0183400i
$448$	2.50357	+	2.88927i	0.118283	+	0.136505i
$449$	24.6978	+	28.5028i	1.16556	+	1.34513i	0.927475	+	0.373885i	$0.121975\pi$
$449$	24.6978	+	28.5028i	1.16556	+	1.34513i	0.238086	+	0.971244i	$0.423480\pi$
$450$	5.75848	+	1.69084i	0.271457	+	0.0797070i
$451$	−1.02916	+	2.25355i	−0.0484613	+	0.106115i
$452$	11.0318	+	7.08970i	0.518892	+	0.333472i
$453$	12.9802	−	3.81132i	0.609861	−	0.179071i
$454$	0.0614982	−	0.427730i	0.00288626	−	0.0200743i
$455$	2.01734	+	4.41735i	0.0945743	+	0.207089i
$456$	0.592229	+	4.11904i	0.0277337	+	0.192892i
$457$	−1.64284	+	1.05579i	−0.0768490	+	0.0493879i	−0.578501	−	0.815682i	$-0.696362\pi$
$457$	−1.64284	+	1.05579i	−0.0768490	+	0.0493879i	0.501652	+	0.865069i	$0.332726\pi$
$458$	−6.41782	+	7.40656i	−0.299885	+	0.346086i
$459$	−7.27807			−0.339711
$460$	9.60264	+	12.6817i	0.447726	+	0.591288i
$461$	6.85072			0.319070			0.159535	−	0.987192i	$-0.449001\pi$
$461$	6.85072			0.319070			0.159535	+	0.987192i	$0.449001\pi$
$462$	−0.881103	+	1.01685i	−0.0409926	+	0.0473080i
$463$	−1.24196	+	0.798159i	−0.0577188	+	0.0370936i	−0.569182	−	0.822212i	$-0.692740\pi$
$463$	−1.24196	+	0.798159i	−0.0577188	+	0.0370936i	0.511463	+	0.859305i	$0.329104\pi$
$464$	0.637728	+	4.43549i	0.0296058	+	0.205913i
$465$	5.99157	+	13.1197i	0.277852	+	0.608412i
$466$	−1.25429	+	8.72378i	−0.0581039	+	0.404121i
$467$	−10.9280	+	3.20875i	−0.505687	+	0.148483i	−0.524618	−	0.851338i	$-0.675792\pi$
$467$	−10.9280	+	3.20875i	−0.505687	+	0.148483i	0.0189309	+	0.999821i	$0.493974\pi$
$468$	0.322170	+	0.207046i	0.0148923	+	0.00957070i
$469$	−8.90601	+	19.5015i	−0.411242	+	0.900493i
$470$	−33.9515	−	9.96907i	−1.56607	−	0.459839i
$471$	−9.38977	−	10.8364i	−0.432658	−	0.499314i
$472$	5.16842	+	5.96468i	0.237896	+	0.274547i
$473$	2.97849	+	0.874565i	0.136951	+	0.0402125i
$474$	6.69989	−	14.6707i	0.307736	−	0.673848i
$475$	−21.0103	−	13.5025i	−0.964018	−	0.619537i
$476$	26.6974	−	7.83906i	1.22367	−	0.359303i
$477$	−0.360844	+	2.50972i	−0.0165219	+	0.114912i
$478$	8.09697	+	17.7299i	0.370347	+	0.810947i
$479$	−2.54204	−	17.6802i	−0.116149	−	0.807831i	−0.961733	−	0.273989i	$-0.911657\pi$
$479$	−2.54204	−	17.6802i	−0.116149	−	0.807831i	0.845584	−	0.533842i	$-0.179252\pi$
$480$	−2.79032	+	1.79323i	−0.127360	+	0.0818495i
$481$	1.83554	−	2.11832i	0.0836933	−	0.0965872i
$482$	2.33025			0.106140
$483$	14.7379	+	10.9067i	0.670598	+	0.496274i
$484$	−10.8761			−0.494370
$485$	−24.3920	+	28.1499i	−1.10758	+	1.27822i
$486$	0.841254	−	0.540641i	0.0381600	−	0.0245240i
$487$	−1.29822	−	9.02935i	−0.0588281	−	0.409159i	−0.997863	−	0.0653374i	$-0.979188\pi$
$487$	−1.29822	−	9.02935i	−0.0588281	−	0.409159i	0.939035	−	0.343821i	$-0.111721\pi$
$488$	5.25570	+	11.5084i	0.237914	+	0.520959i
$489$	−1.06106	+	7.37984i	−0.0479828	+	0.333728i
$490$	−24.2373	+	7.11670i	−1.09493	+	0.321500i
$491$	27.7836	+	17.8554i	1.25385	+	0.805803i	0.987431	−	0.158053i	$-0.0505216\pi$
$491$	27.7836	+	17.8554i	1.25385	+	0.805803i	0.266424	+	0.963856i	$0.414158\pi$
$492$	−2.92426	+	6.40324i	−0.131836	+	0.288680i
$493$	31.2927	+	9.18836i	1.40935	+	0.413823i
$494$	−1.04363	−	1.20441i	−0.0469551	−	0.0541891i
$495$	−0.764440	−	0.882211i	−0.0343590	−	0.0396524i
$496$	−4.17227	−	1.22509i	−0.187340	−	0.0550081i
$497$	0.526540	−	1.15296i	0.0236186	−	0.0517174i
$498$	−3.89845	−	2.50538i	−0.174694	−	0.112269i
$499$	−7.78105	+	2.28472i	−0.348328	+	0.102278i	−0.451216	−	0.892415i	$-0.649010\pi$
$499$	−7.78105	+	2.28472i	−0.348328	+	0.102278i	0.102889	+	0.994693i	$0.467191\pi$
$500$	0.472786	−	3.28830i	0.0211436	−	0.147057i
$501$	−0.156078	−	0.341763i	−0.00697305	−	0.0152688i
$502$	2.10696	+	14.6542i	0.0940381	+	0.654050i
$503$	15.7802	−	10.1413i	0.703604	−	0.452179i	−0.139295	−	0.990251i	$-0.544484\pi$
$503$	15.7802	−	10.1413i	0.703604	−	0.452179i	0.842899	+	0.538072i	$0.180847\pi$
$504$	−2.50357	+	2.88927i	−0.111518	+	0.128699i
$505$	18.4267			0.819976
$506$	−0.129662	−	1.68285i	−0.00576420	−	0.0748118i
$507$	12.8533			0.570837
$508$	9.98886	−	11.5278i	0.443184	−	0.511461i
$509$	−9.03662	+	5.80748i	−0.400541	+	0.257412i	−0.725368	−	0.688361i	$-0.758330\pi$
$509$	−9.03662	+	5.80748i	−0.400541	+	0.257412i	0.324827	+	0.945774i	$0.394694\pi$
$510$	3.43553	+	23.8946i	0.152128	+	1.05807i
$511$	−1.11101	−	2.43277i	−0.0491482	−	0.107620i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	−3.99283	+	1.17240i	−0.176288	+	0.0517628i
$514$	−20.8351	−	13.3899i	−0.918996	−	0.590603i
$515$	14.1314	−	30.9433i	0.622702	−	1.36353i
$516$	8.46311	+	2.48499i	0.372568	+	0.109396i
$517$	2.45870	+	2.83749i	0.108134	+	0.124793i
$518$	18.3238	+	21.1468i	0.805103	+	0.929138i
$519$	15.0996	+	4.43364i	0.662799	+	0.194615i
$520$	0.527677	−	1.15545i	0.0231401	−	0.0506699i
$521$	5.58535	+	3.58949i	0.244699	+	0.157258i	0.657242	−	0.753680i	$-0.271723\pi$
$521$	5.58535	+	3.58949i	0.244699	+	0.157258i	−0.412543	+	0.910938i	$0.635359\pi$
$522$	−4.29959	+	1.26247i	−0.188188	+	0.0552569i
$523$	−5.27639	+	36.6981i	−0.230720	+	1.60469i	0.464282	+	0.885687i	$0.346312\pi$
$523$	−5.27639	+	36.6981i	−0.230720	+	1.60469i	−0.695002	+	0.719007i	$0.744597\pi$
$524$	−1.67618	−	3.67032i	−0.0732242	−	0.160339i
$525$	−3.26533	−	22.7109i	−0.142511	−	0.991183i
$526$	−2.17784	+	1.39961i	−0.0949583	+	0.0610260i
$527$	−20.7251	+	23.9180i	−0.902797	+	1.04188i
$528$	0.351939			0.0153162
$529$	−22.7285	+	3.52335i	−0.988197	+	0.153189i
$530$	8.41001			0.365308
$531$	−5.16842	+	5.96468i	−0.224290	+	0.258845i
$532$	13.3837	−	8.60120i	0.580258	−	0.372909i
$533$	−0.383656	−	2.66839i	−0.0166180	−	0.115581i
$534$	−3.66285	−	8.02052i	−0.158507	−	0.347082i
$535$	5.04506	−	35.0892i	0.218117	−	1.51704i
$536$	5.38062	−	1.57989i	0.232407	−	0.0682409i
$537$	5.02535	+	3.22960i	0.216860	+	0.139367i
$538$	5.37393	−	11.7673i	0.231687	−	0.507323i
$539$	2.57172	+	0.755124i	0.110772	+	0.0325255i
$540$	−2.17208	−	2.50672i	−0.0934716	−	0.107872i
$541$	16.6529	+	19.2184i	0.715963	+	0.826266i	0.990815	−	0.135221i	$-0.0431744\pi$
$541$	16.6529	+	19.2184i	0.715963	+	0.826266i	−0.274852	+	0.961486i	$0.588629\pi$
$542$	−11.2035	−	3.28965i	−0.481233	−	0.141303i
$543$	7.60493	−	16.6525i	0.326359	−	0.714626i
$544$	−6.12270	−	3.93482i	−0.262509	−	0.168704i
$545$	−52.7218	+	15.4805i	−2.25835	+	0.663112i
$546$	0.208362	−	1.44919i	0.00891708	−	0.0620197i
$547$	1.41850	+	3.10609i	0.0606508	+	0.132807i	0.937530	−	0.347903i	$-0.113106\pi$
$547$	1.41850	+	3.10609i	0.0606508	+	0.132807i	−0.876880	+	0.480710i	$0.840379\pi$
$548$	−0.592667	−	4.12209i	−0.0253175	−	0.176087i
$549$	−10.6433	+	6.84001i	−0.454244	+	0.291925i
$550$	−1.38319	+	1.59629i	−0.0589794	+	0.0680658i
$551$	18.6477			0.794417
$552$	−0.368423	−	4.78166i	−0.0156811	−	0.203521i
$553$	−61.6590			−2.62201
$554$	9.30615	−	10.7399i	0.395380	−	0.456293i
$555$	−20.4226	+	13.1248i	−0.866890	+	0.557117i
$556$	−0.311923	−	2.16947i	−0.0132285	−	0.0920060i
$557$	−9.17672	−	20.0942i	−0.388830	−	0.851420i	−0.998282	−	0.0585962i	$-0.981338\pi$
$557$	−9.17672	−	20.0942i	−0.388830	−	0.851420i	0.609452	−	0.792823i	$-0.291390\pi$
$558$	0.618844	−	4.30415i	0.0261977	−	0.182209i
$559$	−3.24107	+	0.951663i	−0.137082	+	0.0402511i
$560$	10.6676	+	6.85563i	0.450787	+	0.289703i
$561$	1.06406	−	2.32996i	0.0449245	−	0.0983710i
$562$	−12.2478	−	3.59628i	−0.516642	−	0.151700i
$563$	−17.7737	−	20.5119i	−0.749071	−	0.864474i	0.245407	−	0.969420i	$-0.421079\pi$
$563$	−17.7737	−	20.5119i	−0.749071	−	0.864474i	−0.994478	+	0.104946i	$0.966533\pi$
$564$	6.98617	+	8.06247i	0.294171	+	0.339491i
$565$	41.7339	+	12.2542i	1.75576	+	0.515537i
$566$	1.10404	−	2.41752i	0.0464064	−	0.101616i
$567$	−3.21616	−	2.06690i	−0.135066	−	0.0868017i
$568$	−0.318112	+	0.0934062i	−0.0133477	+	0.00391924i
$569$	3.96731	−	27.5933i	0.166318	−	1.15677i	−0.720095	−	0.693875i	$-0.755902\pi$
$569$	3.96731	−	27.5933i	0.166318	−	1.15677i	0.886414	−	0.462894i	$-0.153189\pi$
$570$	5.73389	+	12.5555i	0.240166	+	0.525890i
$571$	−1.42324	−	9.89886i	−0.0595608	−	0.414255i	−0.997688	−	0.0679632i	$-0.978350\pi$
$571$	−1.42324	−	9.89886i	−0.0595608	−	0.414255i	0.938127	−	0.346291i	$-0.112559\pi$
$572$	−0.113384	+	0.0728675i	−0.00474082	+	0.00304674i
$573$	−5.31775	+	6.13701i	−0.222152	+	0.256377i
$574$	26.9119			1.12328
$575$	23.1361	+	17.1218i	0.964843	+	0.714029i
$576$	1.00000			0.0416667
$577$	−22.6238	+	26.1092i	−0.941839	+	1.08694i	0.0542445	+	0.998528i	$0.482725\pi$
$577$	−22.6238	+	26.1092i	−0.941839	+	1.08694i	−0.996084	+	0.0884129i	$0.971821\pi$
$578$	−30.2601	+	19.4470i	−1.25865	+	0.808888i
$579$	2.12880	+	14.8061i	0.0884698	+	0.615321i
$580$	6.17440	+	13.5200i	0.256378	+	0.561389i
$581$	−2.52131	+	17.5361i	−0.104602	+	0.727520i
$582$	10.7749	−	3.16379i	0.446633	−	0.131143i
$583$	−0.750694	−	0.482442i	−0.0310906	−	0.0199807i
$584$	−0.290608	+	0.636342i	−0.0120254	+	0.0263320i
$585$	1.21879	+	0.357868i	0.0503906	+	0.0147960i
$586$	7.13750	+	8.23711i	0.294847	+	0.340272i
$587$	19.2179	+	22.1787i	0.793209	+	0.915412i	0.997988	−	0.0633958i	$-0.0201930\pi$
$587$	19.2179	+	22.1787i	0.793209	+	0.915412i	−0.204779	+	0.978808i	$0.565648\pi$
$588$	7.30728	+	2.14561i	0.301347	+	0.0884836i
$589$	−7.51713	+	16.4602i	−0.309738	+	0.678232i
$590$	22.0223	+	14.1529i	0.906646	+	0.582666i
$591$	−19.6536	+	5.77082i	−0.808441	+	0.237380i
$592$	1.04161	−	7.24458i	0.0428100	−	0.297750i
$593$	−17.5461	−	38.4205i	−0.720530	−	1.57774i	−0.813160	−	0.582041i	$-0.802254\pi$
$593$	−17.5461	−	38.4205i	−0.720530	−	1.57774i	0.0926291	−	0.995701i	$-0.470473\pi$
$594$	0.0500861	+	0.348356i	0.00205506	+	0.0142932i
$595$	77.6393	−	49.8957i	3.18290	−	2.04553i
$596$	0.901293	−	1.04015i	0.0369184	−	0.0426061i
$597$	−14.0782			−0.576182
$598$	1.10872	+	1.46423i	0.0453389	+	0.0598766i
$599$	−19.2147			−0.785092			−0.392546	−	0.919732i	$-0.628406\pi$
$599$	−19.2147			−0.785092			−0.392546	+	0.919732i	$0.628406\pi$
$600$	−3.93020	+	4.53569i	−0.160450	+	0.185169i
$601$	−10.9196	+	7.01758i	−0.445418	+	0.286253i	−0.744061	−	0.668112i	$-0.767103\pi$
$601$	−10.9196	+	7.01758i	−0.445418	+	0.286253i	0.298642	+	0.954365i	$0.403466\pi$
$602$	−4.79898	−	33.3777i	−0.195592	−	1.36037i
$603$	2.32955	+	5.10101i	0.0948667	+	0.207729i
$604$	−1.92526	+	13.3904i	−0.0783375	+	0.544850i
$605$	−34.6134	+	10.1634i	−1.40723	+	0.413201i
$606$	−4.67354	−	3.00350i	−0.189850	−	0.122009i
$607$	−10.4445	+	22.8703i	−0.423930	+	0.928277i	0.570343	+	0.821407i	$0.306810\pi$
$607$	−10.4445	+	22.8703i	−0.423930	+	0.928277i	−0.994273	+	0.106871i	$0.965917\pi$
$608$	−3.99283	−	1.17240i	−0.161931	−	0.0475472i
$609$	11.2188	+	12.9471i	0.454607	+	0.524645i
$610$	27.4805	+	31.7142i	1.11265	+	1.28407i
$611$	−3.92003	−	1.15103i	−0.158588	−	0.0465655i
$612$	3.02342	−	6.62036i	0.122214	−	0.267612i
$613$	−16.1352	−	10.3695i	−0.651696	−	0.418819i	0.172590	−	0.984994i	$-0.444787\pi$
$613$	−16.1352	−	10.3695i	−0.651696	−	0.418819i	−0.824285	+	0.566174i	$0.808423\pi$
$614$	−10.3612	+	3.04231i	−0.418142	+	0.122778i
$615$	−3.32286	+	23.1110i	−0.133991	+	0.931925i
$616$	−0.558933	−	1.22389i	−0.0225201	−	0.0493121i
$617$	−4.21557	−	29.3199i	−0.169712	−	1.18037i	−0.879479	−	0.475938i	$-0.842109\pi$
$617$	−4.21557	−	29.3199i	−0.169712	−	1.18037i	0.709767	−	0.704437i	$-0.248800\pi$
$618$	−8.62782	+	5.54476i	−0.347062	+	0.223043i
$619$	30.2148	−	34.8697i	1.21444	−	1.40153i	0.324226	−	0.945979i	$-0.394896\pi$
$619$	30.2148	−	34.8697i	1.21444	−	1.40153i	0.890209	−	0.455553i	$-0.150559\pi$
$620$	−14.4231			−0.579245
$621$	4.68056	−	1.04517i	0.187824	−	0.0419414i
$622$	−7.52022			−0.301533
$623$	−22.0748	+	25.4757i	−0.884408	+	1.02066i
$624$	−0.322170	+	0.207046i	−0.0128971	+	0.00828847i
$625$	2.70241	+	18.7956i	0.108096	+	0.751826i
$626$	6.73499	+	14.7476i	0.269184	+	0.589431i
$627$	0.208428	−	1.44965i	0.00832382	−	0.0578934i
$628$	13.7578	−	4.03964i	0.548995	−	0.161199i
$629$	−44.8125	−	28.7992i	−1.78679	−	1.14830i
$630$	−5.26770	+	11.5346i	−0.209870	+	0.459551i
$631$	13.7896	+	4.04900i	0.548956	+	0.161188i	0.544437	−	0.838802i	$-0.316743\pi$
$631$	13.7896	+	4.04900i	0.548956	+	0.161188i	0.00451927	+	0.999990i	$0.498561\pi$
$632$	10.5617	+	12.1889i	0.420122	+	0.484847i
$633$	2.61902	+	3.02252i	0.104097	+	0.120134i
$634$	5.56316	+	1.63349i	0.220941	+	0.0648742i
$635$	21.0173	−	46.0214i	0.834045	−	1.82630i
$636$	−2.13303	−	1.37081i	−0.0845799	−	0.0543562i
$637$	−2.79843	+	0.821692i	−0.110878	+	0.0325566i
$638$	0.224441	−	1.56102i	0.00888570	−	0.0618014i
$639$	−0.137728	−	0.301581i	−0.00544842	−	0.0119304i
$640$	−0.472039	−	3.28310i	−0.0186590	−	0.129776i
$641$	4.83962	−	3.11024i	0.191154	−	0.122847i	−0.441563	−	0.897230i	$-0.645576\pi$
$641$	4.83962	−	3.11024i	0.191154	−	0.122847i	0.632717	+	0.774383i	$0.281940\pi$
$642$	−6.99903	+	8.07731i	−0.276230	+	0.318786i
$643$	10.2171			0.402924			0.201462	−	0.979496i	$-0.435431\pi$
$643$	10.2171			0.402924			0.201462	+	0.979496i	$0.435431\pi$
$644$	−16.0435	+	8.87524i	−0.632201	+	0.349733i
$645$	29.2560			1.15196
$646$	−19.8337	+	22.8893i	−0.780347	+	0.900569i
$647$	24.8914	−	15.9967i	0.978581	−	0.628896i	0.0495008	−	0.998774i	$-0.484237\pi$
$647$	24.8914	−	15.9967i	0.978581	−	0.628896i	0.929080	+	0.369878i	$0.120601\pi$
$648$	0.142315	+	0.989821i	0.00559065	+	0.0388839i
$649$	−1.15387	−	2.52663i	−0.0452935	−	0.0991789i
$650$	0.327095	−	2.27500i	0.0128297	−	0.0892327i
$651$	−15.9508	+	4.68359i	−0.625163	+	0.183564i
$652$	−6.27216	−	4.03087i	−0.245637	−	0.157861i
$653$	3.23536	−	7.08445i	0.126609	−	0.277236i	−0.835703	−	0.549181i	$-0.814940\pi$
$653$	3.23536	−	7.08445i	0.126609	−	0.277236i	0.962313	+	0.271945i	$0.0876670\pi$
$654$	15.8951	+	4.66721i	0.621546	+	0.182502i
$655$	−8.76425	−	10.1145i	−0.342448	−	0.395206i
$656$	−4.60981	−	5.32001i	−0.179983	−	0.207711i
$657$	−0.671223	−	0.197089i	−0.0261869	−	0.00768916i
$658$	16.9427	−	37.0994i	0.660496	−	1.44628i
$659$	−7.83147	−	5.03298i	−0.305071	−	0.196057i	0.379144	−	0.925338i	$-0.376219\pi$
$659$	−7.83147	−	5.03298i	−0.305071	−	0.196057i	−0.684215	+	0.729281i	$0.739855\pi$
$660$	1.12005	−	0.328875i	0.0435978	−	0.0128015i
$661$	3.60225	−	25.0542i	0.140111	−	0.974494i	−0.791534	−	0.611125i	$-0.790717\pi$
$661$	3.60225	−	25.0542i	0.140111	−	0.974494i	0.931645	−	0.363369i	$-0.118374\pi$
$662$	1.76651	+	3.86811i	0.0686572	+	0.150338i
$663$	0.396665	+	2.75887i	0.0154052	+	0.107146i
$664$	3.89845	−	2.50538i	0.151289	−	0.0972278i
$665$	34.5563	−	39.8801i	1.34003	−	1.54648i
$666$	7.31908			0.283608
$667$	−21.4440	−	1.41526i	−0.830314	−	0.0547989i
$668$	0.375716			0.0145369
$669$	3.93205	−	4.53783i	0.152022	−	0.175443i
$670$	15.6475	−	10.0560i	0.604515	−	0.388498i
$671$	−0.633673	−	4.40729i	−0.0244627	−	0.170142i
$672$	−1.58816	−	3.47758i	−0.0612644	−	0.134150i
$673$	−3.37850	+	23.4980i	−0.130232	+	0.905780i	0.815019	+	0.579434i	$0.196727\pi$
$673$	−3.37850	+	23.4980i	−0.130232	+	0.905780i	−0.945250	+	0.326346i	$0.894183\pi$
$674$	−7.00666	+	2.05734i	−0.269886	+	0.0792458i
$675$	−5.04885	−	3.24470i	−0.194330	−	0.124889i
$676$	−5.33947	+	11.6918i	−0.205364	+	0.449685i
$677$	1.40913	+	0.413758i	0.0541572	+	0.0159020i	0.308699	−	0.951160i	$-0.400106\pi$
$677$	1.40913	+	0.413758i	0.0541572	+	0.0159020i	−0.254542	+	0.967062i	$0.581925\pi$
$678$	−8.58753	−	9.91053i	−0.329802	−	0.380612i
$679$	−28.1145	−	32.4459i	−1.07894	−	1.24516i
$680$	−23.1625	−	6.80112i	−0.888241	−	0.260811i
$681$	−0.179512	+	0.393077i	−0.00687893	+	0.0150628i
$682$	1.28743	+	0.827383i	0.0492983	+	0.0316821i
$683$	19.5561	−	5.74219i	0.748293	−	0.219719i	0.114716	−	0.993398i	$-0.463404\pi$
$683$	19.5561	−	5.74219i	0.748293	−	0.219719i	0.633577	+	0.773680i	$0.281586\pi$
$684$	0.592229	−	4.11904i	0.0226444	−	0.157495i
$685$	−5.73812	−	12.5647i	−0.219242	−	0.480074i
$686$	−0.335031	−	2.33019i	−0.0127915	−	0.0889670i
$687$	8.24452	−	5.29843i	0.314548	−	0.202148i
$688$	−5.77613	+	6.66601i	−0.220213	+	0.254139i
$689$	0.971018			0.0369928
$690$	−5.64082	−	14.8734i	−0.214742	−	0.566220i
$691$	27.6880			1.05330			0.526650	−	0.850082i	$-0.323448\pi$
$691$	27.6880			1.05330			0.526650	+	0.850082i	$0.323448\pi$
$692$	−10.3056	+	11.8933i	−0.391759	+	0.452114i
$693$	1.13189	−	0.727422i	0.0429970	−	0.0276325i
$694$	−3.20663	−	22.3026i	−0.121722	−	0.846594i
$695$	−3.02000	−	6.61287i	−0.114555	−	0.250840i
$696$	0.637728	−	4.43549i	0.0241730	−	0.168127i
$697$	−49.1577	+	14.4340i	−1.86198	+	0.546727i
$698$	−17.7708	−	11.4206i	−0.672634	−	0.432276i
$699$	3.66126	−	8.01703i	0.138481	−	0.303232i
$700$	22.0150	+	6.46418i	0.832088	+	0.244323i
$701$	7.33904	+	8.46970i	0.277192	+	0.319896i	0.877226	−	0.480078i	$-0.159392\pi$
$701$	7.33904	+	8.46970i	0.277192	+	0.319896i	−0.600034	+	0.799974i	$0.704846\pi$
$702$	−0.250788	−	0.289425i	−0.00946539	−	0.0109236i
$703$	−29.2238	−	8.58089i	−1.10220	−	0.323635i
$704$	−0.146201	+	0.320135i	−0.00551014	+	0.0120655i
$705$	29.7676	+	19.1305i	1.12111	+	0.720496i
$706$	16.3199	−	4.79197i	0.614209	−	0.180348i
$707$	−3.02260	+	21.0226i	−0.113676	+	0.790637i
$708$	−3.27862	−	7.17918i	−0.123218	−	0.269810i
$709$	−0.537380	−	3.73756i	−0.0201817	−	0.140367i	0.977239	−	0.212140i	$-0.0680434\pi$
$709$	−0.537380	−	3.73756i	−0.0201817	−	0.140367i	−0.997421	+	0.0717731i	$0.977134\pi$
$710$	−0.925109	+	0.594532i	−0.0347187	+	0.0223124i
$711$	−10.5617	+	12.1889i	−0.396095	+	0.457118i
$712$	8.81732			0.330443
$713$	9.89360	−	18.3580i	0.370518	−	0.687513i
$714$	−27.8245			−1.04130
$715$	−0.292753	+	0.337855i	−0.0109483	+	0.0126351i
$716$	−5.02535	+	3.22960i	−0.187806	+	0.120696i
$717$	−2.77390	−	19.2929i	−0.103593	−	0.720506i
$718$	−4.13610	−	9.05680i	−0.154358	−	0.337997i
$719$	4.98867	−	34.6969i	0.186046	−	1.29398i	−0.656078	−	0.754693i	$-0.727786\pi$
$719$	4.98867	−	34.6969i	0.186046	−	1.29398i	0.842124	−	0.539284i	$-0.181305\pi$
$720$	3.18251	−	0.934468i	0.118605	−	0.0348256i
$721$	32.9846	+	21.1979i	1.22841	+	0.789453i
$722$	0.699045	−	1.53069i	0.0260158	−	0.0569666i
$723$	−2.23585	−	0.656506i	−0.0831523	−	0.0244157i
$724$	11.9884	+	13.8354i	0.445546	+	0.514188i
$725$	17.6116	+	20.3249i	0.654080	+	0.754848i
$726$	10.4356	+	3.06416i	0.387301	+	0.113722i
$727$	14.3475	−	31.4165i	0.532118	−	1.16517i	−0.432527	−	0.901621i	$-0.642378\pi$
$727$	14.3475	−	31.4165i	0.532118	−	1.16517i	0.964645	−	0.263554i	$-0.0848947\pi$
$728$	1.23167	+	0.791549i	0.0456489	+	0.0293368i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−0.330219	+	2.29673i	−0.0122220	+	0.0850056i
$731$	26.6677	+	58.3942i	0.986342	+	2.15979i
$732$	−1.80052	−	12.5229i	−0.0665492	−	0.462860i
$733$	8.18277	−	5.25875i	0.302237	−	0.194236i	−0.380728	−	0.924687i	$-0.624326\pi$
$733$	8.18277	−	5.25875i	0.302237	−	0.194236i	0.682965	+	0.730451i	$0.260690\pi$
$734$	15.9402	−	18.3960i	0.588365	−	0.679009i
$735$	25.2605			0.931747
$736$	4.50260	+	1.65124i	0.165968	+	0.0608656i
$737$	−1.97359			−0.0726982
$738$	4.60981	−	5.32001i	0.169689	−	0.195832i
$739$	−16.3220	+	10.4895i	−0.600414	+	0.385863i	−0.805252	−	0.592933i	$-0.797970\pi$
$739$	−16.3220	+	10.4895i	−0.600414	+	0.385863i	0.204837	+	0.978796i	$0.434333\pi$
$740$	−3.45489	−	24.0293i	−0.127004	−	0.883334i
$741$	0.662033	+	1.44965i	0.0243204	+	0.0532542i
$742$	−1.37953	+	9.59482i	−0.0506440	+	0.352237i
$743$	−3.68671	+	1.08251i	−0.135252	+	0.0397136i	−0.348658	−	0.937250i	$-0.613363\pi$
$743$	−3.68671	+	1.08251i	−0.135252	+	0.0397136i	0.213406	+	0.976964i	$0.431544\pi$
$744$	3.65812	+	2.35093i	0.134113	+	0.0861892i
$745$	1.89639	−	4.15251i	0.0694782	−	0.152136i
$746$	33.3248	+	9.78504i	1.22011	+	0.358256i
$747$	3.03469	+	3.50222i	0.111034	+	0.128140i
$748$	1.67738	+	1.93580i	0.0613311	+	0.0707799i
$749$	39.2050	+	11.5116i	1.43252	+	0.420626i
$750$	−1.38006	+	3.02190i	−0.0503925	+	0.110344i
$751$	−13.5502	−	8.70815i	−0.494452	−	0.317765i	0.269542	−	0.962989i	$-0.413128\pi$
$751$	−13.5502	−	8.70815i	−0.494452	−	0.317765i	−0.763994	+	0.645224i	$0.776764\pi$
$752$	−10.2360	+	3.00557i	−0.373270	+	0.109602i
$753$	2.10696	−	14.6542i	0.0767818	−	0.534029i
$754$	0.712894	+	1.56102i	0.0259621	+	0.0568490i
$755$	6.38581	+	44.4143i	0.232403	+	1.61640i
$756$	3.21616	−	2.06690i	0.116971	−	0.0751725i
$757$	−1.71316	+	1.97709i	−0.0622658	+	0.0718586i	−0.786028	−	0.618191i	$-0.787866\pi$
$757$	−1.71316	+	1.97709i	−0.0622658	+	0.0718586i	0.723762	+	0.690050i	$0.242411\pi$
$758$	25.2353			0.916586
$759$	−0.349704	+	1.65121i	−0.0126934	+	0.0599352i
$760$	−13.8028			−0.500680
$761$	−16.1066	+	18.5880i	−0.583863	+	0.673813i	−0.968431	−	0.249283i	$-0.919805\pi$
$761$	−16.1066	+	18.5880i	−0.583863	+	0.673813i	0.384568	+	0.923097i	$0.374350\pi$
$762$	−12.8320	+	8.24661i	−0.464854	+	0.298743i
$763$	−9.01325	−	62.6886i	−0.326302	−	2.26948i
$764$	−3.37335	−	7.38660i	−0.122043	−	0.267238i
$765$	3.43553	−	23.8946i	0.124212	−	0.863912i
$766$	−26.5236	+	7.78803i	−0.958337	+	0.281393i
$767$	2.54269	+	1.63409i	0.0918113	+	0.0590036i
$768$	−0.415415	+	0.909632i	−0.0149900	+	0.0328235i
$769$	−30.2906	−	8.89412i	−1.09231	−	0.320730i	−0.314515	−	0.949252i	$-0.601842\pi$
$769$	−30.2906	−	8.89412i	−1.09231	−	0.320730i	−0.777792	+	0.628522i	$0.783660\pi$
$770$	−2.92250	−	3.37274i	−0.105320	−	0.121545i
$771$	16.2187	+	18.7174i	0.584104	+	0.674091i
$772$	−14.3524	−	4.21426i	−0.516556	−	0.151674i
$773$	19.8367	−	43.4363i	0.713477	−	1.56230i	−0.109349	−	0.994003i	$-0.534877\pi$
$773$	19.8367	−	43.4363i	0.713477	−	1.56230i	0.822826	−	0.568293i	$-0.192396\pi$
$774$	−7.42019	−	4.76867i	−0.266713	−	0.171406i
$775$	−25.0402	+	7.35247i	−0.899471	+	0.264109i
$776$	−1.59816	+	11.1155i	−0.0573707	+	0.399022i
$777$	−11.6238	−	25.4526i	−0.417003	−	0.913109i
$778$	2.13813	+	14.8710i	0.0766558	+	0.533153i
$779$	−24.6434	+	15.8373i	−0.882941	+	0.567432i
$780$	−0.831830	+	0.959983i	−0.0297843	+	0.0343729i
$781$	0.116682			0.00417522
$782$	24.5451	−	24.8164i	0.877730	−	0.887434i
$783$	4.48110			0.160142
$784$	−4.98727	+	5.75562i	−0.178117	+	0.205558i
$785$	40.0093	−	25.7124i	1.42799	−	0.917715i
$786$	0.574233	+	3.99388i	0.0204822	+	0.142457i
$787$	13.9057	+	30.4493i	0.495686	+	1.08540i	0.977847	+	0.209319i	$0.0671247\pi$
$787$	13.9057	+	30.4493i	0.495686	+	1.08540i	−0.482161	+	0.876083i	$0.660148\pi$
$788$	2.91508	−	20.2748i	0.103845	−	0.722261i
$789$	2.48394	−	0.729350i	0.0884305	−	0.0259655i
$790$	45.0028	+	28.9216i	1.60113	+	1.02898i
$791$	−20.8263	+	45.6033i	−0.740498	+	1.62146i
$792$	−0.337683	−	0.0991526i	−0.0119990	−	0.00352323i
$793$	3.17289	+	3.66171i	0.112673	+	0.130031i
$794$	−12.2286	−	14.1126i	−0.433977	−	0.500837i
$795$	−8.06935	−	2.36937i	−0.286190	−	0.0840330i
$796$	5.84829	−	12.8060i	0.207287	−	0.453895i
$797$	12.9998	+	8.35449i	0.460478	+	0.295931i	0.750238	−	0.661168i	$-0.229939\pi$
$797$	12.9998	+	8.35449i	0.460478	+	0.295931i	−0.289760	+	0.957099i	$0.593575\pi$
$798$	−15.2648	+	4.48216i	−0.540369	+	0.158667i
$799$	−11.0498	+	76.8534i	−0.390915	+	2.71888i
$800$	−2.49315	−	5.45923i	−0.0881461	−	0.193013i
$801$	1.25484	+	8.72757i	0.0443374	+	0.308374i
$802$	27.2531	−	17.5145i	0.962342	−	0.618460i
$803$	0.161228	−	0.186067i	0.00568961	−	0.00656617i
$804$	−5.60777			−0.197771
$805$	−42.7648	+	43.2376i	−1.50726	+	1.52393i
$806$	−1.66529			−0.0586572
$807$	−8.47147	+	9.77659i	−0.298210	+	0.344152i
$808$	4.67354	−	3.00350i	0.164415	−	0.105663i
$809$	0.913503	+	6.35355i	0.0321171	+	0.223379i	0.999558	−	0.0297164i	$-0.00946042\pi$
$809$	0.913503	+	6.35355i	0.0321171	+	0.223379i	−0.967441	+	0.253095i	$0.918551\pi$
$810$	1.37787	+	3.01713i	0.0484136	+	0.106011i
$811$	−5.58616	+	38.8526i	−0.196156	+	1.36430i	0.619152	+	0.785271i	$0.287476\pi$
$811$	−5.58616	+	38.8526i	−0.196156	+	1.36430i	−0.815308	+	0.579027i	$0.803433\pi$
$812$	−16.4376	+	4.82651i	−0.576846	+	0.169377i
$813$	9.82290	+	6.31280i	0.344504	+	0.221399i
$814$	−1.07005	+	2.34309i	−0.0375053	+	0.0821252i
$815$	−23.7279	−	6.96714i	−0.831152	−	0.244048i
$816$	4.76612	+	5.50040i	0.166848	+	0.192552i
$817$	24.0368	+	27.7399i	0.840941	+	0.970497i
$818$	−12.9039	−	3.78892i	−0.451173	−	0.132476i
$819$	−0.608207	+	1.33179i	−0.0212525	+	0.0465364i
$820$	−19.6421	−	12.6232i	−0.685933	−	0.440822i
$821$	−49.1161	+	14.4218i	−1.71416	+	0.503323i	−0.983729	−	0.179660i	$-0.942500\pi$
$821$	−49.1161	+	14.4218i	−1.71416	+	0.503323i	−0.730434	+	0.682984i	$0.760682\pi$
$822$	−0.592667	+	4.12209i	−0.0206716	+	0.143774i
$823$	−20.9730	−	45.9244i	−0.731072	−	1.60082i	−0.797706	−	0.603046i	$-0.793953\pi$
$823$	−20.9730	−	45.9244i	−0.731072	−	1.60082i	0.0666347	−	0.997777i	$-0.478774\pi$
$824$	−1.45957	−	10.1515i	−0.0508464	−	0.353645i
$825$	1.77689	−	1.14194i	0.0618632	−	0.0397571i
$826$	−19.7592	+	22.8033i	−0.687510	+	0.793429i
$827$	−48.0754			−1.67174			−0.835872	−	0.548924i	$-0.815038\pi$
$827$	−48.0754			−1.67174			−0.835872	+	0.548924i	$0.815038\pi$
$828$	−0.993649	+	4.69177i	−0.0345317	+	0.163050i
$829$	27.4066			0.951871			0.475936	−	0.879480i	$-0.342110\pi$
$829$	27.4066			0.951871			0.475936	+	0.879480i	$0.342110\pi$
$830$	10.0657	−	11.6164i	0.349384	−	0.403211i
$831$	−11.9550	+	7.68298i	−0.414713	+	0.266520i
$832$	−0.0545015	−	0.379066i	−0.00188950	−	0.0131418i
$833$	23.0257	+	50.4192i	0.797792	+	1.74692i
$834$	−0.311923	+	2.16947i	−0.0108010	+	0.0751226i
$835$	1.19572	−	0.351094i	0.0413795	−	0.0121501i
$836$	1.23206	+	0.791799i	0.0426118	+	0.0273849i
$837$	−1.80640	+	3.95545i	−0.0624382	+	0.136721i
$838$	−12.9808	−	3.81152i	−0.448416	−	0.131667i
$839$	−12.9755	−	14.9745i	−0.447962	−	0.516976i	0.486189	−	0.873854i	$-0.338387\pi$
$839$	−12.9755	−	14.9745i	−0.447962	−	0.516976i	−0.934151	+	0.356878i	$0.883841\pi$
$840$	−8.30400	−	9.58333i	−0.286515	−	0.330656i
$841$	8.55840	+	2.51297i	0.295117	+	0.0866543i
$842$	−10.6528	+	23.3264i	−0.367120	+	0.803880i
$843$	10.7385	+	6.90121i	0.369853	+	0.237690i
$844$	−3.83736	+	1.12675i	−0.132087	+	0.0387843i
$845$	−6.06728	+	42.1988i	−0.208721	+	1.45168i
$846$	−4.43172	−	9.70411i	−0.152366	−	0.333634i
$847$	−5.91747	−	41.1569i	−0.203327	−	1.41417i
$848$	2.13303	−	1.37081i	0.0732484	−	0.0470739i
$849$	−1.74041	+	2.00855i	−0.0597309	+	0.0689331i
$850$	−43.6799			−1.49821
$851$	32.9549	+	12.0856i	1.12968	+	0.414288i
$852$	0.331542			0.0113584
$853$	13.4772	−	15.5536i	0.461452	−	0.532544i	−0.476562	−	0.879141i	$-0.658117\pi$
$853$	13.4772	−	15.5536i	0.461452	−	0.532544i	0.938014	+	0.346597i	$0.112663\pi$
$854$	−40.6898	+	26.1498i	−1.39238	+	0.894827i
$855$	−1.96434	−	13.6623i	−0.0671791	−	0.467241i
$856$	−4.43988	−	9.72197i	−0.151752	−	0.332290i
$857$	1.22485	−	8.51902i	0.0418401	−	0.291004i	−0.958149	−	0.286271i	$-0.907584\pi$
$857$	1.22485	−	8.51902i	0.0418401	−	0.291004i	0.999989	−	0.00473330i	$-0.00150666\pi$
$858$	0.129320	−	0.0379719i	0.00441492	−	0.00129634i
$859$	34.9945	+	22.4896i	1.19400	+	0.767336i	0.977908	−	0.209038i	$-0.0670331\pi$
$859$	34.9945	+	22.4896i	1.19400	+	0.767336i	0.216090	+	0.976373i	$0.430669\pi$
$860$	−12.1534	+	26.6122i	−0.414428	+	0.907470i
$861$	−25.8218	−	7.58197i	−0.880005	−	0.258393i
$862$	−11.2362	−	12.9673i	−0.382707	−	0.441668i
$863$	−9.11321	−	10.5172i	−0.310217	−	0.358010i	0.579136	−	0.815231i	$-0.303390\pi$
$863$	−9.11321	−	10.5172i	−0.310217	−	0.358010i	−0.889353	+	0.457221i	$0.848845\pi$
$864$	−0.959493	−	0.281733i	−0.0326426	−	0.00958474i
$865$	−21.6837	+	47.4807i	−0.737268	+	1.61439i
$866$	8.03155	+	5.16156i	0.272923	+	0.175397i
$867$	34.5132	−	10.1340i	1.17213	−	0.344168i
$868$	2.36588	−	16.4550i	0.0803030	−	0.558520i
$869$	−2.35795	−	5.16319i	−0.0799879	−	0.175149i
$870$	−2.11525	−	14.7119i	−0.0717139	−	0.498781i
$871$	1.80665	−	1.16107i	0.0612162	−	0.0393412i
$872$	−10.8485	+	12.5198i	−0.367376	+	0.423975i
$873$	−11.2298			−0.380070
$874$	9.46811	−	17.5685i	0.320264	−	0.594263i
$875$	12.7006			0.429360
$876$	0.458114	−	0.528692i	0.0154782	−	0.0178628i
$877$	8.64520	−	5.55594i	0.291928	−	0.187611i	−0.386477	−	0.922299i	$-0.626308\pi$
$877$	8.64520	−	5.55594i	0.291928	−	0.187611i	0.678405	+	0.734689i	$0.262672\pi$
$878$	−3.39564	−	23.6172i	−0.114597	−	0.797042i
$879$	−4.52772	−	9.91432i	−0.152716	−	0.334402i
$880$	−0.166129	+	1.15545i	−0.00560020	+	0.0389502i
$881$	17.8776	−	5.24934i	0.602312	−	0.176855i	0.0336603	−	0.999433i	$-0.489284\pi$
$881$	17.8776	−	5.24934i	0.602312	−	0.176855i	0.568651	+	0.822579i	$0.307465\pi$
$882$	−6.40680	−	4.11740i	−0.215728	−	0.138640i
$883$	8.20154	−	17.9589i	0.276004	−	0.604364i	−0.719970	−	0.694005i	$-0.755845\pi$
$883$	8.20154	−	17.9589i	0.276004	−	0.604364i	0.995974	+	0.0896408i	$0.0285719\pi$
$884$	−2.67434	−	0.785256i	−0.0899476	−	0.0264110i
$885$	−17.1430	−	19.7840i	−0.576254	−	0.665033i
$886$	−4.61237	−	5.32296i	−0.154955	−	0.178828i
$887$	−21.9589	−	6.44772i	−0.737308	−	0.216493i	−0.108547	−	0.994091i	$-0.534620\pi$
$887$	−21.9589	−	6.44772i	−0.737308	−	0.216493i	−0.628762	+	0.777598i	$0.716438\pi$
$888$	−3.04045	+	6.65767i	−0.102031	+	0.223417i
$889$	49.0574	+	31.5273i	1.64533	+	1.05739i
$890$	28.0612	−	8.23951i	0.940613	−	0.276189i
$891$	0.0500861	−	0.348356i	0.00167795	−	0.0116704i
$892$	2.49432	+	5.46180i	0.0835160	+	0.182875i
$893$	6.31800	+	43.9426i	0.211424	+	1.47048i
$894$	−1.15783	+	0.744091i	−0.0387235	+	0.0248861i
$895$	−12.9753	+	14.9743i	−0.433715	+	0.500534i
$896$	3.82306			0.127719
$897$	−0.651287	−	1.71728i	−0.0217459	−	0.0573382i
$898$	37.7146			1.25855
$899$	12.7604	−	14.7263i	0.425583	−	0.491150i
$900$	5.04885	−	3.24470i	0.168295	−	0.108157i
$901$	−2.62625	−	18.2659i	−0.0874929	−	0.608527i
$902$	1.02916	+	2.25355i	0.0342673	+	0.0750349i
$903$	−4.79898	+	33.3777i	−0.159700	+	1.11074i
$904$	12.5823	−	3.69450i	0.418482	−	0.122877i
$905$	51.0820	+	32.8284i	1.69802	+	1.09125i
$906$	5.61979	−	12.3056i	0.186705	−	0.408827i
$907$	19.0109	+	5.58211i	0.631247	+	0.185351i	0.581677	−	0.813420i	$-0.302397\pi$
$907$	19.0109	+	5.58211i	0.631247	+	0.185351i	0.0495699	+	0.998771i	$0.484215\pi$
$908$	−0.282984	−	0.326581i	−0.00939114	−	0.0108380i
$909$	3.63804	+	4.19853i	0.120666	+	0.139256i
$910$	4.65949	+	1.36815i	0.154461	+	0.0453537i
$911$	−8.70510	+	19.0615i	−0.288413	+	0.631536i	−0.997272	−	0.0738141i	$-0.976483\pi$
$911$	−8.70510	+	19.0615i	−0.288413	+	0.631536i	0.708859	+	0.705350i	$0.249210\pi$
$912$	3.50079	+	2.24982i	0.115923	+	0.0744990i
$913$	−1.56486	+	0.459483i	−0.0517891	+	0.0152067i
$914$	−0.277920	+	1.93298i	−0.00919278	+	0.0639372i
$915$	−17.4324	−	38.1717i	−0.576298	−	1.26192i
$916$	1.39473	+	9.70053i	0.0460830	+	0.320515i
$917$	12.9771	−	8.33985i	0.428540	−	0.275406i
$918$	−4.76612	+	5.50040i	−0.157305	+	0.181540i
$919$	−33.7364			−1.11286			−0.556431	−	0.830894i	$-0.687830\pi$
$919$	−33.7364			−1.11286			−0.556431	+	0.830894i	$0.687830\pi$
$920$	15.8726	+	1.04756i	0.523304	+	0.0345369i
$921$	10.7986			0.355825
$922$	4.48627	−	5.17743i	0.147747	−	0.170510i
$923$	−0.106813	+	0.0686444i	−0.00351579	+	0.00225946i
$924$	0.191482	+	1.33179i	0.00629930	+	0.0438126i
$925$	−18.2475	−	39.9565i	−0.599975	−	1.31376i
$926$	−0.210102	+	1.46129i	−0.00690439	+	0.0480211i
$927$	9.84047	−	2.88942i	0.323203	−	0.0949011i
$928$	3.76974	+	2.42267i	0.123748	+	0.0795280i
$929$	−18.8567	+	41.2904i	−0.618668	+	1.35469i	0.297816	+	0.954623i	$0.403742\pi$
$929$	−18.8567	+	41.2904i	−0.618668	+	1.35469i	−0.916484	+	0.400071i	$0.868985\pi$
$930$	13.8389	+	4.06345i	0.453794	+	0.133246i
$931$	20.7540	+	23.9514i	0.680186	+	0.784976i
$932$	5.77161	+	6.66079i	0.189055	+	0.218181i
$933$	7.21560	+	2.11869i	0.236228	+	0.0693629i
$934$	−4.73130	+	10.3601i	−0.154813	+	0.338993i
$935$	7.14722	+	4.59324i	0.233739	+	0.150215i
$936$	0.367451	−	0.107893i	0.0120105	−	0.00352661i
$937$	8.53433	−	59.3575i	0.278804	−	1.93913i	−0.0598305	−	0.998209i	$-0.519056\pi$
$937$	8.53433	−	59.3575i	0.278804	−	1.93913i	0.338635	−	0.940918i	$-0.390035\pi$
$938$	8.90601	+	19.5015i	0.290792	+	0.636745i
$939$	−2.30730	−	16.0477i	−0.0752960	−	0.523695i
$940$	−29.7676	+	19.1305i	−0.970914	+	0.623968i
$941$	32.8241	−	37.8811i	1.07004	−	1.23489i	0.0992194	−	0.995066i	$-0.468365\pi$
$941$	32.8241	−	37.8811i	1.07004	−	1.23489i	0.970817	−	0.239822i	$-0.0770891\pi$
$942$	−14.3386			−0.467176
$943$	29.5408	−	16.3419i	0.961979	−	0.532166i
$944$	7.89240			0.256876
$945$	8.30400	−	9.58333i	0.270129	−	0.311746i
$946$	2.61145	−	1.67828i	0.0849056	−	0.0545655i
$947$	3.06937	+	21.3479i	0.0997411	+	0.693715i	0.976929	+	0.213566i	$0.0685080\pi$
$947$	3.06937	+	21.3479i	0.0997411	+	0.693715i	−0.877187	+	0.480148i	$0.840583\pi$
$948$	−6.69989	−	14.6707i	−0.217602	−	0.476482i
$949$	−0.0381270	+	0.265179i	−0.00123766	+	0.00860808i
$950$	−23.9633	+	7.03626i	−0.777473	+	0.228287i
$951$	−4.87761	−	3.13465i	−0.158167	−	0.101648i
$952$	11.5587	−	25.3100i	0.374620	−	0.820303i
$953$	13.7135	+	4.02664i	0.444224	+	0.130436i	0.496192	−	0.868213i	$-0.334731\pi$
$953$	13.7135	+	4.02664i	0.444224	+	0.130436i	−0.0519682	+	0.998649i	$0.516549\pi$
$954$	1.66042	+	1.91623i	0.0537581	+	0.0620401i
$955$	−17.6383	−	20.3556i	−0.570760	−	0.658693i
$956$	18.7018	+	5.49133i	0.604858	+	0.177602i
$957$	−0.655140	+	1.43456i	−0.0211777	+	0.0463726i
$958$	−15.0265	−	9.65696i	−0.485485	−	0.312002i
$959$	15.2761	−	4.48547i	0.493292	−	0.144843i
$960$	−0.472039	+	3.28310i	−0.0152350	+	0.105962i
$961$	−5.02291	−	10.9986i	−0.162029	−	0.354795i
$962$	−0.398900	−	2.77441i	−0.0128611	−	0.0894507i
$963$	8.99116	−	5.77827i	0.289736	−	0.186202i
$964$	1.52599	−	1.76108i	0.0491487	−	0.0567206i
$965$	−49.6148			−1.59716
$966$	17.8940	−	3.99576i	0.575731	−	0.128562i
$967$	−52.3238			−1.68262			−0.841310	−	0.540553i	$-0.818215\pi$
$967$	−52.3238			−1.68262			−0.841310	+	0.540553i	$0.818215\pi$
$968$	−7.12236	+	8.21964i	−0.228921	+	0.264189i
$969$	25.4790	−	16.3744i	0.818503	−	0.526020i
$970$	5.30089	+	36.8685i	0.170201	+	1.18378i
$971$	3.43811	+	7.52842i	0.110334	+	0.241598i	0.956742	−	0.290936i	$-0.0939668\pi$
$971$	3.43811	+	7.52842i	0.110334	+	0.241598i	−0.846408	+	0.532535i	$0.821240\pi$
$972$	0.142315	−	0.989821i	0.00456475	−	0.0317485i
$973$	8.03988	−	2.36072i	0.257747	−	0.0756812i
$974$	−7.67408	−	4.93183i	−0.245893	−	0.158026i
$975$	−0.954786	+	2.09069i	−0.0305776	+	0.0669556i
$976$	12.1392	+	3.56439i	0.388566	+	0.114093i
$977$	−1.32060	−	1.52405i	−0.0422496	−	0.0487587i	0.734231	−	0.678899i	$-0.237543\pi$
$977$	−1.32060	−	1.52405i	−0.0422496	−	0.0487587i	−0.776481	+	0.630141i	$0.782997\pi$
$978$	4.88246	+	5.63466i	0.156124	+	0.180177i
$979$	−2.97746	−	0.874260i	−0.0951599	−	0.0279415i
$980$	−10.4936	+	22.9778i	−0.335205	+	0.733997i
$981$	−13.9363	−	8.95631i	−0.444952	−	0.285953i
$982$	31.6886	−	9.30461i	1.01122	−	0.296922i
$983$	−1.79669	+	12.4963i	−0.0573055	+	0.398569i	0.940900	+	0.338685i	$0.109982\pi$
$983$	−1.79669	+	12.4963i	−0.0573055	+	0.398569i	−0.998205	+	0.0598838i	$0.980927\pi$
$984$	2.92426	+	6.40324i	0.0932221	+	0.204128i
$985$	−9.66892	−	67.2488i	−0.308078	−	2.14273i
$986$	27.4364	−	17.6323i	0.873754	−	0.561528i
$987$	−26.7085	+	30.8233i	−0.850142	+	0.981116i
$988$	−1.59367			−0.0507013
$989$	−25.5359	−	33.7239i	−0.811995	−	1.07236i
$990$	−1.16733			−0.0371003
$991$	17.3281	−	19.9978i	0.550447	−	0.635249i	−0.410540	−	0.911842i	$-0.634660\pi$
$991$	17.3281	−	19.9978i	0.550447	−	0.635249i	0.960987	+	0.276593i	$0.0892054\pi$
$992$	−3.65812	+	2.35093i	−0.116145	+	0.0746421i
$993$	−0.605178	−	4.20910i	−0.0192047	−	0.133572i
$994$	−0.526540	−	1.15296i	−0.0167008	−	0.0365698i
$995$	6.64545	−	46.2201i	0.210675	−	1.46528i
$996$	−4.44639	+	1.30558i	−0.140889	+	0.0413688i
$997$	−28.8712	−	18.5544i	−0.914359	−	0.587623i	−0.00334331	−	0.999994i	$-0.501064\pi$
$997$	−28.8712	−	18.5544i	−0.914359	−	0.587623i	−0.911016	+	0.412372i	$0.864701\pi$
$998$	−3.36883	+	7.37670i	−0.106638	+	0.233505i
$999$	−7.02260	−	2.06202i	−0.222185	−	0.0652395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.d.85.1	yes	10
3.2	odd	2		414.2.i.a.361.1		10
23.6	even	11		3174.2.a.x.1.1		5
23.13	even	11	inner	138.2.e.d.13.1	✓	10
23.17	odd	22		3174.2.a.w.1.5		5
69.17	even	22		9522.2.a.by.1.1		5
69.29	odd	22		9522.2.a.bx.1.5		5
69.59	odd	22		414.2.i.a.289.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.d.13.1	✓	10	23.13	even	11	inner
138.2.e.d.85.1	yes	10	1.1	even	1	trivial
414.2.i.a.289.1		10	69.59	odd	22
414.2.i.a.361.1		10	3.2	odd	2
3174.2.a.w.1.5		5	23.17	odd	22
3174.2.a.x.1.1		5	23.6	even	11
9522.2.a.bx.1.5		5	69.29	odd	22
9522.2.a.by.1.1		5	69.17	even	22

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-1.37787 - 3.01713i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(3.66820 - 1.07708i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-1.37787 - 3.01713i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(3.66820 - 1.07708i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-3.18251 - 0.934468i) q^{10} +(0.230471 + 0.265977i) q^{11} +(0.654861 + 0.755750i) q^{12} +(-0.367451 - 0.107893i) q^{13} +(1.58816 - 3.47758i) q^{14} +(2.79032 + 1.79323i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-1.03578 + 7.20399i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(0.592229 + 4.11904i) q^{19} +(-2.79032 + 1.79323i) q^{20} +(-2.50357 + 2.88927i) q^{21} +0.351939 q^{22} +(-0.368423 - 4.78166i) q^{23} +1.00000 q^{24} +(-3.93020 + 4.53569i) q^{25} +(-0.322170 + 0.207046i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-1.58816 - 3.47758i) q^{28} +(0.637728 - 4.43549i) q^{29} +(3.18251 - 0.934468i) q^{30} +(3.65812 + 2.35093i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-0.337683 - 0.0991526i) q^{33} +(4.76612 + 5.50040i) q^{34} +(-8.30400 - 9.58333i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-3.04045 + 6.65767i) q^{37} +(3.50079 + 2.24982i) q^{38} +(0.367451 - 0.107893i) q^{39} +(-0.472039 + 3.28310i) q^{40} +(2.92426 + 6.40324i) q^{41} +(0.544078 + 3.78415i) q^{42} +(7.42019 - 4.76867i) q^{43} +(0.230471 - 0.265977i) q^{44} -3.31686 q^{45} +(-3.85500 - 2.85288i) q^{46} +10.6682 q^{47} +(0.654861 - 0.755750i) q^{48} +(6.40680 - 4.11740i) q^{49} +(0.854114 + 5.94049i) q^{50} +(-3.02342 - 6.62036i) q^{51} +(-0.0545015 + 0.379066i) q^{52} +(-2.43282 + 0.714342i) q^{53} +(0.841254 + 0.540641i) q^{54} +(0.484927 - 1.06184i) q^{55} +(-3.66820 - 1.07708i) q^{56} +(-2.72514 - 3.14498i) q^{57} +(-2.93450 - 3.38659i) q^{58} +(-7.57270 - 2.22355i) q^{59} +(1.37787 - 3.01713i) q^{60} +(-10.6433 - 6.84001i) q^{61} +(4.17227 - 1.22509i) q^{62} +(0.544078 - 3.78415i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.180774 + 1.25731i) q^{65} +(-0.296070 + 0.190272i) q^{66} +(-3.67231 + 4.23807i) q^{67} +7.27807 q^{68} +(2.89510 + 3.82340i) q^{69} -12.6806 q^{70} +(0.217114 - 0.250563i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(-0.0995577 - 0.692439i) q^{73} +(3.04045 + 6.65767i) q^{74} +(0.854114 - 5.94049i) q^{75} +(3.99283 - 1.17240i) q^{76} +(1.13189 + 0.727422i) q^{77} +(0.159089 - 0.348356i) q^{78} +(-15.4749 - 4.54383i) q^{79} +(2.17208 + 2.50672i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(6.75423 + 1.98322i) q^{82} +(-1.92508 + 4.21533i) q^{83} +(3.21616 + 2.06690i) q^{84} +(23.1625 - 6.80112i) q^{85} +(1.25527 - 8.73062i) q^{86} +(1.86152 + 4.07616i) q^{87} +(-0.0500861 - 0.348356i) q^{88} +(-7.41760 + 4.76700i) q^{89} +(-2.17208 + 2.50672i) q^{90} -1.46409 q^{91} +(-4.68056 + 1.04517i) q^{92} -4.34841 q^{93} +(6.98617 - 8.06247i) q^{94} +(11.6116 - 7.46235i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-4.66501 - 10.2150i) q^{97} +(1.08384 - 7.53826i) q^{98} +(0.337683 - 0.0991526i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9} - 13 q^{10} - 5 q^{11} + q^{12} + 13 q^{13} + 9 q^{14} + 9 q^{15} - q^{16} + q^{18} - 9 q^{20} - 13 q^{21} - 6 q^{22} - 32 q^{23} + 10 q^{24} + q^{25} - 13 q^{26} + q^{27} - 9 q^{28} + 27 q^{29} + 13 q^{30} - 8 q^{31} + q^{32} - 6 q^{33} - 11 q^{34} - 26 q^{35} - q^{36} - 11 q^{37} + 11 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} + 2 q^{42} + 34 q^{43} - 5 q^{44} + 2 q^{45} - q^{46} + 8 q^{47} + q^{48} + 25 q^{49} + 21 q^{50} - 11 q^{51} + 2 q^{52} + 9 q^{53} - q^{54} - 23 q^{55} - 2 q^{56} - 11 q^{57} - 5 q^{58} - 21 q^{59} - 2 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{63} - q^{64} + 29 q^{65} + 6 q^{66} - 32 q^{67} + 22 q^{68} - q^{69} - 18 q^{70} + 22 q^{71} + q^{72} + 43 q^{73} + 11 q^{74} + 21 q^{75} + 10 q^{77} + 2 q^{78} - 16 q^{79} + 2 q^{80} - q^{81} + 32 q^{82} - 3 q^{83} + 9 q^{84} + 33 q^{85} + 32 q^{86} + 6 q^{87} - 6 q^{88} - 11 q^{89} - 2 q^{90} - 70 q^{91} - 21 q^{92} + 8 q^{93} + 3 q^{94} - q^{96} + 39 q^{97} - 14 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9 - 13 * q^10 - 5 * q^11 + q^12 + 13 * q^13 + 9 * q^14 + 9 * q^15 - q^16 + q^18 - 9 * q^20 - 13 * q^21 - 6 * q^22 - 32 * q^23 + 10 * q^24 + q^25 - 13 * q^26 + q^27 - 9 * q^28 + 27 * q^29 + 13 * q^30 - 8 * q^31 + q^32 - 6 * q^33 - 11 * q^34 - 26 * q^35 - q^36 - 11 * q^37 + 11 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 + 2 * q^42 + 34 * q^43 - 5 * q^44 + 2 * q^45 - q^46 + 8 * q^47 + q^48 + 25 * q^49 + 21 * q^50 - 11 * q^51 + 2 * q^52 + 9 * q^53 - q^54 - 23 * q^55 - 2 * q^56 - 11 * q^57 - 5 * q^58 - 21 * q^59 - 2 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^63 - q^64 + 29 * q^65 + 6 * q^66 - 32 * q^67 + 22 * q^68 - q^69 - 18 * q^70 + 22 * q^71 + q^72 + 43 * q^73 + 11 * q^74 + 21 * q^75 + 10 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 - q^81 + 32 * q^82 - 3 * q^83 + 9 * q^84 + 33 * q^85 + 32 * q^86 + 6 * q^87 - 6 * q^88 - 11 * q^89 - 2 * q^90 - 70 * q^91 - 21 * q^92 + 8 * q^93 + 3 * q^94 - q^96 + 39 * q^97 - 14 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more