LMFDB - Embedded newform 414.2.i.a.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$414 = 2 \cdot 3^{2} \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	414.i (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:	$3.30580664368$
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:	no (minimal twist has level 138)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			361.1
Root			$-0.841254 - 0.540641i$ of defining polynomial
Character	$\chi$	$=$	414.361
Dual form			414.2.i.a.289.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$ .

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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			0
$3$		0			0
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	1.37787	+	3.01713i	0.616204	+	1.34930i	0.918248	+	0.396005i	$0.129604\pi$
$5$	1.37787	+	3.01713i	0.616204	+	1.34930i	−0.302044	+	0.953294i	$0.597669\pi$
$6$		0			0
$7$	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			0
$10$	−3.18251	−	0.934468i	−1.00640	−	0.295505i
$11$	−0.230471	−	0.265977i	−0.0694895	−	0.0801952i	0.719940	−	0.694036i	$-0.244169\pi$
$11$	−0.230471	−	0.265977i	−0.0694895	−	0.0801952i	−0.789430	+	0.613841i	$0.789624\pi$
$12$		0			0
$13$	−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
$15$		0			0
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	1.03578	−	7.20399i	0.251213	−	1.74722i	−0.339742	−	0.940519i	$-0.610340\pi$
$17$	1.03578	−	7.20399i	0.251213	−	1.74722i	0.590955	−	0.806705i	$-0.298751\pi$
$18$		0			0
$19$	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
$21$		0			0
$22$	0.351939			0.0750336
$23$	0.368423	+	4.78166i	0.0768216	+	0.997045i
$23$	0.368423	+	4.78166i	0.0768216	+	0.997045i
$24$		0			0
$25$	−3.93020	+	4.53569i	−0.786040	+	0.907139i
$26$	0.322170	−	0.207046i	0.0631827	−	0.0406051i
$27$		0			0
$28$	−1.58816	−	3.47758i	−0.300133	−	0.657200i
$29$	−0.637728	+	4.43549i	−0.118423	+	0.823650i	0.840870	+	0.541237i	$0.182044\pi$
$29$	−0.637728	+	4.43549i	−0.118423	+	0.823650i	−0.959293	+	0.282413i	$0.908865\pi$
$30$		0			0
$31$	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			0
$34$	4.76612	+	5.50040i	0.817383	+	0.943310i
$35$	8.30400	+	9.58333i	1.40363	+	1.61988i
$36$		0			0
$37$	−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			0
$40$	−0.472039	+	3.28310i	−0.0746359	+	0.519104i
$41$	−2.92426	−	6.40324i	−0.456693	−	1.00002i	−0.988229	−	0.152982i	$-0.951112\pi$
$41$	−2.92426	−	6.40324i	−0.456693	−	1.00002i	0.531536	−	0.847036i	$-0.321615\pi$
$42$		0			0
$43$	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
$45$		0			0
$46$	−3.85500	−	2.85288i	−0.568389	−	0.420635i
$47$	−10.6682			−1.55611			−0.778056	−	0.628194i	$-0.783794\pi$
$47$	−10.6682			−1.55611			−0.778056	+	0.628194i	$0.783794\pi$
$48$		0			0
$49$	6.40680	−	4.11740i	0.915257	−	0.588200i
$50$	−0.854114	−	5.94049i	−0.120790	−	0.840113i
$51$		0			0
$52$	−0.0545015	+	0.379066i	−0.00755799	+	0.0525670i
$53$	2.43282	−	0.714342i	0.334174	−	0.0981224i	−0.110341	−	0.993894i	$-0.535194\pi$
$53$	2.43282	−	0.714342i	0.334174	−	0.0981224i	0.444515	+	0.895771i	$0.353376\pi$
$54$		0			0
$55$	0.484927	−	1.06184i	0.0653876	−	0.143179i
$56$	3.66820	+	1.07708i	0.490184	+	0.143931i
$57$		0			0
$58$	−2.93450	−	3.38659i	−0.385319	−	0.444681i
$59$	7.57270	+	2.22355i	0.985882	+	0.289481i	0.734650	−	0.678446i	$-0.237346\pi$
$59$	7.57270	+	2.22355i	0.985882	+	0.289481i	0.251232	+	0.967927i	$0.419164\pi$
$60$		0			0
$61$	−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			0
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−0.180774	−	1.25731i	−0.0224222	−	0.155950i
$66$		0			0
$67$	−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
$69$		0			0
$70$	−12.6806			−1.51562
$71$	−0.217114	+	0.250563i	−0.0257667	+	0.0297363i	−0.768487	−	0.639866i	$-0.778990\pi$
$71$	−0.217114	+	0.250563i	−0.0257667	+	0.0297363i	0.742720	+	0.669602i	$0.233535\pi$
$72$		0			0
$73$	−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			0
$76$	3.99283	−	1.17240i	0.458009	−	0.134484i
$77$	−1.13189	−	0.727422i	−0.128991	−	0.0828975i
$78$		0			0
$79$	−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			0
$82$	6.75423	+	1.98322i	0.745880	+	0.219010i
$83$	1.92508	−	4.21533i	0.211304	−	0.462692i	−0.774069	−	0.633101i	$-0.781782\pi$
$83$	1.92508	−	4.21533i	0.211304	−	0.462692i	0.985373	+	0.170409i	$0.0545089\pi$
$84$		0			0
$85$	23.1625	−	6.80112i	2.51233	−	0.737685i
$86$	−1.25527	+	8.73062i	−0.135360	+	0.941447i
$87$		0			0
$88$	−0.0500861	−	0.348356i	−0.00533919	−	0.0371349i
$89$	7.41760	−	4.76700i	0.786264	−	0.505301i	−0.0848429	−	0.996394i	$-0.527039\pi$
$89$	7.41760	−	4.76700i	0.786264	−	0.505301i	0.871107	+	0.491093i	$0.163402\pi$
$90$		0			0
$91$	−1.46409			−0.153479
$92$	4.68056	−	1.04517i	0.487982	−	0.108967i
$93$		0			0
$94$	6.98617	−	8.06247i	0.720568	−	0.831580i
$95$	−11.6116	+	7.46235i	−1.19133	+	0.765621i
$96$		0			0
$97$	−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			0
$100$	5.04885	+	3.24470i	0.504885	+	0.324470i
$101$	2.30782	−	5.05341i	0.229636	−	0.502833i	−0.759379	−	0.650649i	$-0.774497\pi$
$101$	2.30782	−	5.05341i	0.229636	−	0.502833i	0.989015	+	0.147816i	$0.0472242\pi$
$102$		0			0
$103$	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
$105$		0			0
$106$	−1.05330	+	2.30640i	−0.102305	+	0.224017i
$107$	−8.99116	−	5.77827i	−0.869208	−	0.558606i	0.0283023	−	0.999599i	$-0.490990\pi$
$107$	−8.99116	−	5.77827i	−0.869208	−	0.558606i	−0.897510	+	0.440993i	$0.854626\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−3.21616	+	2.06690i	−0.303899	+	0.195304i
$113$	8.58753	−	9.91053i	0.807847	−	0.932305i	−0.190938	−	0.981602i	$-0.561153\pi$
$113$	8.58753	−	9.91053i	0.807847	−	0.932305i	0.998784	+	0.0492976i	$0.0156983\pi$
$114$		0			0
$115$	−13.9192	+	7.70011i	−1.29797	+	0.718039i
$116$	4.48110			0.416060
$117$		0			0
$118$	−6.63951	+	4.26695i	−0.611216	+	0.392805i
$119$	−3.95984	−	27.5413i	−0.362998	−	2.52470i
$120$		0			0
$121$	1.54784	−	10.7654i	0.140712	−	0.978676i
$122$	12.1392	−	3.56439i	1.09903	−	0.322705i
$123$		0			0
$124$	1.80640	−	3.95545i	0.162219	−	0.355210i
$125$	−3.18754	−	0.935947i	−0.285103	−	0.0837137i
$126$		0			0
$127$	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
$129$		0			0
$130$	1.06859	+	0.686743i	0.0937218	+	0.0602314i
$131$	−3.87151	+	1.13678i	−0.338255	+	0.0993207i	−0.446449	−	0.894809i	$-0.647312\pi$
$131$	−3.87151	+	1.13678i	−0.338255	+	0.0993207i	0.108194	+	0.994130i	$0.465493\pi$
$132$		0			0
$133$	6.60895	+	14.4716i	0.573069	+	1.25485i
$134$	−0.798069	−	5.55069i	−0.0689427	−	0.479507i
$135$		0			0
$136$	4.76612	−	5.50040i	0.408691	−	0.471655i
$137$	−4.16447			−0.355795			−0.177898	−	0.984049i	$-0.556930\pi$
$137$	−4.16447			−0.355795			−0.177898	+	0.984049i	$0.556930\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	−0.0471833	−	0.328167i	−0.00395954	−	0.0275392i
$143$	0.0559896	+	0.122600i	0.00468208	+	0.0102523i
$144$		0			0
$145$	−14.2611	+	4.18745i	−1.18432	+	0.347749i
$146$	0.588507	+	0.378211i	0.0487052	+	0.0313009i
$147$		0			0
$148$	7.02260	+	2.06202i	0.577254	+	0.169497i
$149$	−0.901293	−	1.04015i	−0.0738368	−	0.0852122i	0.717629	−	0.696425i	$-0.245227\pi$
$149$	−0.901293	−	1.04015i	−0.0738368	−	0.0852122i	−0.791466	+	0.611213i	$0.790682\pi$
$150$		0			0
$151$	−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
$153$		0			0
$154$	1.29098	−	0.379066i	0.104030	−	0.0305460i
$155$	−2.05262	+	14.2763i	−0.164870	+	1.14670i
$156$		0			0
$157$	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
$159$		0			0
$160$	3.31686			0.262221
$161$	6.50168	+	17.1433i	0.512404	+	1.35108i
$162$		0			0
$163$	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			0
$166$	1.92508	+	4.21533i	0.149415	+	0.327173i
$167$	0.0534699	−	0.371891i	0.00413763	−	0.0287778i	−0.987648	−	0.156689i	$-0.949918\pi$
$167$	0.0534699	−	0.371891i	0.00413763	−	0.0287778i	0.991786	+	0.127911i	$0.0408272\pi$
$168$		0			0
$169$	−10.8129	−	6.94904i	−0.831763	−	0.534541i
$170$	−10.0283	+	21.9588i	−0.769133	+	1.68417i
$171$		0			0
$172$	−5.77613	−	6.66601i	−0.440426	−	0.508279i
$173$	10.3056	+	11.8933i	0.783519	+	0.904229i	0.997358	−	0.0726401i	$-0.0231424\pi$
$173$	10.3056	+	11.8933i	0.783519	+	0.904229i	−0.213840	+	0.976869i	$0.568597\pi$
$174$		0			0
$175$	−9.53145	+	20.8710i	−0.720510	+	1.57770i
$176$	0.296070	+	0.190272i	0.0223171	+	0.0143423i
$177$		0			0
$178$	−1.25484	+	8.72757i	−0.0940539	+	0.654159i
$179$	2.48154	+	5.43382i	0.185479	+	0.406143i	0.979415	−	0.201859i	$-0.0646984\pi$
$179$	2.48154	+	5.43382i	0.185479	+	0.406143i	−0.793935	+	0.608002i	$0.791971\pi$
$180$		0			0
$181$	−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
$183$		0			0
$184$	−2.27522	+	4.22177i	−0.167732	+	0.311233i
$185$	−24.2764			−1.78483
$186$		0			0
$187$	−2.15481	+	1.38481i	−0.157576	+	0.101268i
$188$	1.51824	+	10.5596i	0.110729	+	0.770137i
$189$		0			0
$190$	1.96434	−	13.6623i	0.142508	−	0.991167i
$191$	−7.79149	+	2.28779i	−0.563773	+	0.165539i	−0.551186	−	0.834382i	$-0.685825\pi$
$191$	−7.79149	+	2.28779i	−0.563773	+	0.165539i	−0.0125864	+	0.999921i	$0.504006\pi$
$192$		0			0
$193$	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			0
$196$	−4.98727	−	5.75562i	−0.356234	−	0.411116i
$197$	−19.6536	−	5.77082i	−1.40026	−	0.411154i	−0.507487	−	0.861659i	$-0.669426\pi$
$197$	−19.6536	−	5.77082i	−1.40026	−	0.411154i	−0.892774	+	0.450505i	$0.851244\pi$
$198$		0			0
$199$	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			0
$202$	2.30782	+	5.05341i	0.162377	+	0.355557i
$203$	2.43807	+	16.9571i	0.171119	+	1.19016i
$204$		0			0
$205$	15.2901	−	17.6457i	1.06791	−	1.23243i
$206$	−10.2559			−0.714563
$207$		0			0
$208$	0.382964			0.0265538
$209$	0.959081	−	1.10684i	0.0663410	−	0.0765616i
$210$		0			0
$211$	−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			0
$214$	10.2549	−	3.01110i	0.701009	−	0.205835i
$215$	24.6118	+	15.8170i	1.67851	+	1.07871i
$216$		0			0
$217$	15.9508	+	4.68359i	1.08281	+	0.317943i
$218$	10.8485	+	12.5198i	0.734753	+	0.847950i
$219$		0			0
$220$	−1.12005	−	0.328875i	−0.0755136	−	0.0221728i
$221$	−1.15786	+	2.53536i	−0.0778861	+	0.170547i
$222$		0			0
$223$	−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
$225$		0			0
$226$	1.86625	+	12.9800i	0.124141	+	0.863419i
$227$	−0.363529	+	0.233626i	−0.0241283	+	0.0155063i	−0.552649	−	0.833414i	$-0.686383\pi$
$227$	−0.363529	+	0.233626i	−0.0241283	+	0.0155063i	0.528521	+	0.848920i	$0.322747\pi$
$228$		0			0
$229$	−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
$231$		0			0
$232$	−2.93450	+	3.38659i	−0.192659	+	0.222341i
$233$	7.41438	−	4.76493i	0.485732	−	0.312161i	−0.274755	−	0.961514i	$-0.588597\pi$
$233$	7.41438	−	4.76493i	0.485732	−	0.312161i	0.760487	+	0.649353i	$0.224960\pi$
$234$		0			0
$235$	−14.6994	−	32.1872i	−0.958884	−	2.09966i
$236$	1.12321	−	7.81207i	0.0731145	−	0.508522i
$237$		0			0
$238$	23.4074	+	15.0430i	1.51728	+	0.975096i
$239$	8.09697	−	17.7299i	0.523750	−	1.14685i	−0.444251	−	0.895903i	$-0.646530\pi$
$239$	8.09697	−	17.7299i	0.523750	−	1.14685i	0.968000	−	0.250949i	$-0.0807427\pi$
$240$		0			0
$241$	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			0
$244$	−5.25570	+	11.5084i	−0.336461	+	0.736748i
$245$	21.2505	+	13.6569i	1.35764	+	0.872504i
$246$		0			0
$247$	0.226802	−	1.57744i	0.0144311	−	0.100370i
$248$	1.80640	+	3.95545i	0.114706	+	0.251172i
$249$		0			0
$250$	2.79474	−	1.79607i	0.176755	−	0.113593i
$251$	9.69515	−	11.1888i	0.611953	−	0.706231i	−0.362205	−	0.932098i	$-0.617976\pi$
$251$	9.69515	−	11.1888i	0.611953	−	0.706231i	0.974158	+	0.225867i	$0.0725216\pi$
$252$		0			0
$253$	1.18690	−	1.20002i	0.0746199	−	0.0754449i
$254$	−15.2534			−0.957084
$255$		0			0
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	3.52467	+	24.5146i	0.219863	+	1.52918i	0.738540	+	0.674209i	$0.235515\pi$
$257$	3.52467	+	24.5146i	0.219863	+	1.52918i	−0.518678	+	0.854970i	$0.673575\pi$
$258$		0			0
$259$	−3.98215	+	27.6964i	−0.247439	+	1.72097i
$260$	−1.21879	+	0.357868i	−0.0755859	+	0.0221940i
$261$		0			0
$262$	1.67618	−	3.67032i	0.103555	−	0.226753i
$263$	2.48394	+	0.729350i	0.153166	+	0.0449736i	0.357417	−	0.933945i	$-0.383658\pi$
$263$	2.48394	+	0.729350i	0.153166	+	0.0449736i	−0.204251	+	0.978919i	$0.565476\pi$
$264$		0			0
$265$	5.50739	+	6.35586i	0.338316	+	0.390438i
$266$	−15.2648	−	4.48216i	−0.935947	−	0.274819i
$267$		0			0
$268$	4.71756	+	3.03179i	0.288171	+	0.185196i
$269$	−12.4123	+	3.64457i	−0.756790	+	0.222214i	−0.637294	−	0.770621i	$-0.719946\pi$
$269$	−12.4123	+	3.64457i	−0.756790	+	0.222214i	−0.119496	+	0.992835i	$0.538128\pi$
$270$		0			0
$271$	−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
$273$		0			0
$274$	2.72715	−	3.14730i	0.164753	−	0.190135i
$275$	2.11219			0.127370
$276$		0			0
$277$	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
$279$		0			0
$280$	1.80463	+	12.5515i	0.107847	+	0.750095i
$281$	5.30272	+	11.6113i	0.316334	+	0.692674i	0.999286	−	0.0377891i	$-0.0120315\pi$
$281$	5.30272	+	11.6113i	0.316334	+	0.692674i	−0.682952	+	0.730463i	$0.739304\pi$
$282$		0			0
$283$	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
$285$		0			0
$286$	−0.129320	−	0.0379719i	−0.00764687	−	0.00224532i
$287$	−17.6236	−	20.3387i	−1.04029	−	1.20055i
$288$		0			0
$289$	−34.5132	−	10.1340i	−2.03019	−	0.596117i
$290$	6.17440	−	13.5200i	0.362573	−	0.793925i
$291$		0			0
$292$	−0.671223	+	0.197089i	−0.0392803	+	0.0115337i
$293$	1.55113	−	10.7883i	0.0906178	−	0.630261i	−0.893008	−	0.450040i	$-0.851410\pi$
$293$	1.55113	−	10.7883i	0.0906178	−	0.630261i	0.983626	−	0.180221i	$-0.0576812\pi$
$294$		0			0
$295$	3.72552	+	25.9116i	0.216908	+	1.50863i
$296$	−6.15720	+	3.95699i	−0.357880	+	0.229995i
$297$		0			0
$298$	1.37631			0.0797276
$299$	0.380532	−	1.79678i	0.0220067	−	0.103910i
$300$		0			0
$301$	22.0825	−	25.4845i	1.27281	−	1.46890i
$302$	11.3806	−	7.31387i	0.654880	−	0.420866i
$303$		0			0
$304$	−1.72871	−	3.78534i	−0.0991482	−	0.217104i
$305$	5.97208	−	41.5368i	0.341960	−	2.37839i
$306$		0			0
$307$	−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
$309$		0			0
$310$	−9.44511	−	10.9002i	−0.536446	−	0.619092i
$311$	4.92470	+	5.68341i	0.279254	+	0.322276i	0.877998	−	0.478664i	$-0.158879\pi$
$311$	4.92470	+	5.68341i	0.279254	+	0.322276i	−0.598744	+	0.800940i	$0.704333\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	−2.29528	+	15.9640i	−0.129119	+	0.898046i
$317$	−2.40859	−	5.27407i	−0.135280	−	0.296221i	0.829853	−	0.557982i	$-0.188424\pi$
$317$	−2.40859	−	5.27407i	−0.135280	−	0.296221i	−0.965133	+	0.261761i	$0.915697\pi$
$318$		0			0
$319$	1.32672	−	0.852630i	0.0742820	−	0.0477381i
$320$	−2.17208	+	2.50672i	−0.121423	+	0.140130i
$321$		0			0
$322$	−17.2137	−	6.31280i	−0.959282	−	0.351799i
$323$	30.2869			1.68521
$324$		0			0
$325$	1.93353	−	1.24260i	0.107253	−	0.0689272i
$326$	1.06106	+	7.37984i	0.0587667	+	0.408731i
$327$		0			0
$328$	1.00181	−	6.96772i	0.0553156	−	0.384728i
$329$	−39.1330	+	11.4905i	−2.15747	+	0.633490i
$330$		0			0
$331$	−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
$333$		0			0
$334$	0.246041	+	0.283947i	0.0134628	+	0.0155369i
$335$	−17.8468	−	5.24028i	−0.975073	−	0.286307i
$336$		0			0
$337$	−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
$339$		0			0
$340$	−10.0283	−	21.9588i	−0.543859	−	1.19089i
$341$	−0.217795	−	1.51480i	−0.0117943	−	0.0820309i
$342$		0			0
$343$	1.54164	−	1.77915i	0.0832408	−	0.0960650i
$344$	8.82040			0.475564
$345$		0			0
$346$	−15.7371			−0.846029
$347$	−14.7553	+	17.0285i	−0.792104	+	0.914137i	−0.997921	−	0.0644537i	$-0.979470\pi$
$347$	−14.7553	+	17.0285i	−0.792104	+	0.914137i	0.205817	+	0.978591i	$0.434015\pi$
$348$		0			0
$349$	−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			0
$352$	−0.337683	+	0.0991526i	−0.0179985	+	0.00528485i
$353$	−14.3088	−	9.19572i	−0.761581	−	0.489439i	0.101293	−	0.994857i	$-0.467702\pi$
$353$	−14.3088	−	9.19572i	−0.761581	−	0.489439i	−0.862875	+	0.505418i	$0.831338\pi$
$354$		0			0
$355$	−1.05513	−	0.309815i	−0.0560007	−	0.0164433i
$356$	−5.77412	−	6.66369i	−0.306028	−	0.353175i
$357$		0			0
$358$	−5.73167	−	1.68297i	−0.302928	−	0.0889478i
$359$	−4.13610	+	9.05680i	−0.218295	+	0.478000i	−0.986820	−	0.161820i	$-0.948264\pi$
$359$	−4.13610	+	9.05680i	−0.218295	+	0.478000i	0.768525	+	0.639820i	$0.220991\pi$
$360$		0			0
$361$	1.61460	−	0.474089i	0.0849789	−	0.0249521i
$362$	2.60533	−	18.1205i	0.136933	−	0.952392i
$363$		0			0
$364$	0.208362	+	1.44919i	0.0109212	+	0.0759583i
$365$	1.95200	−	1.25447i	0.102172	−	0.0656621i
$366$		0			0
$367$	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
$369$		0			0
$370$	15.8976	−	18.3469i	0.826479	−	0.953808i
$371$	8.15468	−	5.24069i	0.423370	−	0.272083i
$372$		0			0
$373$	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
$375$		0			0
$376$	−8.97464	−	5.76765i	−0.462832	−	0.297444i
$377$	0.712894	−	1.56102i	0.0367159	−	0.0803967i
$378$		0			0
$379$	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
$381$		0			0
$382$	3.37335	−	7.38660i	0.172596	−	0.377931i
$383$	23.2551	+	14.9451i	1.18828	+	0.763660i	0.976890	−	0.213742i	$-0.0685651\pi$
$383$	23.2551	+	14.9451i	1.18828	+	0.763660i	0.211389	+	0.977402i	$0.432201\pi$
$384$		0			0
$385$	0.635120	−	4.41735i	0.0323687	−	0.225129i
$386$	6.21393	+	13.6066i	0.316281	+	0.692558i
$387$		0			0
$388$	−9.44708	+	6.07127i	−0.479603	+	0.308222i
$389$	9.83860	−	11.3544i	0.498837	−	0.575688i	−0.449368	−	0.893347i	$-0.648351\pi$
$389$	9.83860	−	11.3544i	0.498837	−	0.575688i	0.948205	+	0.317658i	$0.102896\pi$
$390$		0			0
$391$	34.8286	+	2.29861i	1.76136	+	0.116246i
$392$	7.61578			0.384655
$393$		0			0
$394$	17.2317	−	11.0741i	0.868119	−	0.557906i
$395$	−7.61312	−	52.9504i	−0.383058	−	2.66423i
$396$		0			0
$397$	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
$399$		0			0
$400$	2.49315	−	5.45923i	0.124657	−	0.272962i
$401$	−31.0836	−	9.12697i	−1.55224	−	0.455779i	−0.610472	−	0.792038i	$-0.709020\pi$
$401$	−31.0836	−	9.12697i	−1.55224	−	0.455779i	−0.941770	+	0.336258i	$0.890838\pi$
$402$		0			0
$403$	−1.09053	−	1.25854i	−0.0543232	−	0.0626923i
$404$	−5.33041	−	1.56515i	−0.265198	−	0.0778691i
$405$		0			0
$406$	−14.4120	−	9.26200i	−0.715253	−	0.459665i
$407$	2.47152	−	0.725705i	0.122509	−	0.0359719i
$408$		0			0
$409$	−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
$411$		0			0
$412$	6.71619	−	7.75090i	0.330883	−	0.381859i
$413$	30.1731			1.48472
$414$		0			0
$415$	15.3707			0.754517
$416$	−0.250788	+	0.289425i	−0.0122959	+	0.0141902i
$417$		0			0
$418$	0.208428	+	1.44965i	0.0101946	+	0.0709047i
$419$	5.62009	+	12.3063i	0.274559	+	0.601201i	0.995807	−	0.0914759i	$-0.0291585\pi$
$419$	5.62009	+	12.3063i	0.274559	+	0.601201i	−0.721248	+	0.692677i	$0.756431\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	2.43282	+	0.714342i	0.118148	+	0.0346915i
$425$	28.6043	+	33.0111i	1.38751	+	1.60127i
$426$		0			0
$427$	−46.4089	−	13.6269i	−2.24588	−	0.659450i
$428$	−4.43988	+	9.72197i	−0.214610	+	0.469929i
$429$		0			0
$430$	−28.0710	+	8.24238i	−1.35370	+	0.397483i
$431$	−2.44186	+	16.9835i	−0.117620	+	0.818068i	0.842543	+	0.538629i	$0.181058\pi$
$431$	−2.44186	+	16.9835i	−0.117620	+	0.818068i	−0.960163	+	0.279439i	$0.909852\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	−16.5661			−0.793373
$437$	−19.4777	+	4.34939i	−0.931743	+	0.208059i
$438$		0			0
$439$	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
$441$		0			0
$442$	−1.15786	−	2.53536i	−0.0550738	−	0.120595i
$443$	−1.00236	+	6.97159i	−0.0476237	+	0.331230i	0.952056	+	0.305924i	$0.0989652\pi$
$443$	−1.00236	+	6.97159i	−0.0476237	+	0.331230i	−0.999680	+	0.0253065i	$0.991944\pi$
$444$		0			0
$445$	24.6032	+	15.8115i	1.16630	+	0.749537i
$446$	2.49432	−	5.46180i	0.118110	−	0.258624i
$447$		0			0
$448$	2.50357	+	2.88927i	0.118283	+	0.136505i
$449$	−24.6978	−	28.5028i	−1.16556	−	1.34513i	−0.927475	−	0.373885i	$-0.878025\pi$
$449$	−24.6978	−	28.5028i	−1.16556	−	1.34513i	−0.238086	−	0.971244i	$-0.576520\pi$
$450$		0			0
$451$	−1.02916	+	2.25355i	−0.0484613	+	0.106115i
$452$	−11.0318	−	7.08970i	−0.518892	−	0.333472i
$453$		0			0
$454$	0.0614982	−	0.427730i	0.00288626	−	0.0200743i
$455$	−2.01734	−	4.41735i	−0.0945743	−	0.207089i
$456$		0			0
$457$	−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
$459$		0			0
$460$	9.60264	+	12.6817i	0.447726	+	0.591288i
$461$	−6.85072			−0.319070			−0.159535	−	0.987192i	$-0.550999\pi$
$461$	−6.85072			−0.319070			−0.159535	+	0.987192i	$0.550999\pi$
$462$		0			0
$463$	−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
$465$		0			0
$466$	−1.25429	+	8.72378i	−0.0581039	+	0.404121i
$467$	10.9280	−	3.20875i	0.505687	−	0.148483i	−0.0189309	−	0.999821i	$-0.506026\pi$
$467$	10.9280	−	3.20875i	0.505687	−	0.148483i	0.524618	+	0.851338i	$0.324208\pi$
$468$		0			0
$469$	−8.90601	+	19.5015i	−0.411242	+	0.900493i
$470$	33.9515	+	9.96907i	1.56607	+	0.459839i
$471$		0			0
$472$	5.16842	+	5.96468i	0.237896	+	0.274547i
$473$	−2.97849	−	0.874565i	−0.136951	−	0.0402125i
$474$		0			0
$475$	−21.0103	−	13.5025i	−0.964018	−	0.619537i
$476$	−26.6974	+	7.83906i	−1.22367	+	0.359303i
$477$		0			0
$478$	8.09697	+	17.7299i	0.370347	+	0.810947i
$479$	2.54204	+	17.6802i	0.116149	+	0.807831i	0.961733	+	0.273989i	$0.0883432\pi$
$479$	2.54204	+	17.6802i	0.116149	+	0.807831i	−0.845584	+	0.533842i	$0.820748\pi$
$480$		0			0
$481$	1.83554	−	2.11832i	0.0836933	−	0.0965872i
$482$	−2.33025			−0.106140
$483$		0			0
$484$	−10.8761			−0.494370
$485$	24.3920	−	28.1499i	1.10758	−	1.27822i
$486$		0			0
$487$	−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
$489$		0			0
$490$	−24.2373	+	7.11670i	−1.09493	+	0.321500i
$491$	−27.7836	−	17.8554i	−1.25385	−	0.805803i	−0.266424	−	0.963856i	$-0.585842\pi$
$491$	−27.7836	−	17.8554i	−1.25385	−	0.805803i	−0.987431	+	0.158053i	$0.949478\pi$
$492$		0			0
$493$	31.2927	+	9.18836i	1.40935	+	0.413823i
$494$	1.04363	+	1.20441i	0.0469551	+	0.0541891i
$495$		0			0
$496$	−4.17227	−	1.22509i	−0.187340	−	0.0550081i
$497$	−0.526540	+	1.15296i	−0.0236186	+	0.0517174i
$498$		0			0
$499$	−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			0
$502$	2.10696	+	14.6542i	0.0940381	+	0.654050i
$503$	−15.7802	+	10.1413i	−0.703604	+	0.452179i	−0.842899	−	0.538072i	$-0.819153\pi$
$503$	−15.7802	+	10.1413i	−0.703604	+	0.452179i	0.139295	+	0.990251i	$0.455516\pi$
$504$		0			0
$505$	18.4267			0.819976
$506$	0.129662	+	1.68285i	0.00576420	+	0.0748118i
$507$		0			0
$508$	9.98886	−	11.5278i	0.443184	−	0.511461i
$509$	9.03662	−	5.80748i	0.400541	−	0.257412i	−0.324827	−	0.945774i	$-0.605306\pi$
$509$	9.03662	−	5.80748i	0.400541	−	0.257412i	0.725368	+	0.688361i	$0.241670\pi$
$510$		0			0
$511$	−1.11101	−	2.43277i	−0.0491482	−	0.107620i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$		0			0
$514$	−20.8351	−	13.3899i	−0.918996	−	0.590603i
$515$	−14.1314	+	30.9433i	−0.622702	+	1.36353i
$516$		0			0
$517$	2.45870	+	2.83749i	0.108134	+	0.124793i
$518$	−18.3238	−	21.1468i	−0.805103	−	0.929138i
$519$		0			0
$520$	0.527677	−	1.15545i	0.0231401	−	0.0506699i
$521$	−5.58535	−	3.58949i	−0.244699	−	0.157258i	0.412543	−	0.910938i	$-0.364641\pi$
$521$	−5.58535	−	3.58949i	−0.244699	−	0.157258i	−0.657242	+	0.753680i	$0.728277\pi$
$522$		0			0
$523$	−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
$525$		0			0
$526$	−2.17784	+	1.39961i	−0.0949583	+	0.0610260i
$527$	20.7251	−	23.9180i	0.902797	−	1.04188i
$528$		0			0
$529$	−22.7285	+	3.52335i	−0.988197	+	0.153189i
$530$	−8.41001			−0.365308
$531$		0			0
$532$	13.3837	−	8.60120i	0.580258	−	0.372909i
$533$	0.383656	+	2.66839i	0.0166180	+	0.115581i
$534$		0			0
$535$	5.04506	−	35.0892i	0.218117	−	1.51704i
$536$	−5.38062	+	1.57989i	−0.232407	+	0.0682409i
$537$		0			0
$538$	5.37393	−	11.7673i	0.231687	−	0.507323i
$539$	−2.57172	−	0.755124i	−0.110772	−	0.0325255i
$540$		0			0
$541$	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
$543$		0			0
$544$	−6.12270	−	3.93482i	−0.262509	−	0.168704i
$545$	52.7218	−	15.4805i	2.25835	−	0.663112i
$546$		0			0
$547$	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
$549$		0			0
$550$	−1.38319	+	1.59629i	−0.0589794	+	0.0680658i
$551$	−18.6477			−0.794417
$552$		0			0
$553$	−61.6590			−2.62201
$554$	−9.30615	+	10.7399i	−0.395380	+	0.456293i
$555$		0			0
$556$	−0.311923	−	2.16947i	−0.0132285	−	0.0920060i
$557$	9.17672	+	20.0942i	0.388830	+	0.851420i	0.998282	+	0.0585962i	$0.0186624\pi$
$557$	9.17672	+	20.0942i	0.388830	+	0.851420i	−0.609452	+	0.792823i	$0.708610\pi$
$558$		0			0
$559$	−3.24107	+	0.951663i	−0.137082	+	0.0402511i
$560$	−10.6676	−	6.85563i	−0.450787	−	0.289703i
$561$		0			0
$562$	−12.2478	−	3.59628i	−0.516642	−	0.151700i
$563$	17.7737	+	20.5119i	0.749071	+	0.864474i	0.994478	−	0.104946i	$-0.0334669\pi$
$563$	17.7737	+	20.5119i	0.749071	+	0.864474i	−0.245407	+	0.969420i	$0.578921\pi$
$564$		0			0
$565$	41.7339	+	12.2542i	1.75576	+	0.515537i
$566$	−1.10404	+	2.41752i	−0.0464064	+	0.101616i
$567$		0			0
$568$	−0.318112	+	0.0934062i	−0.0133477	+	0.00391924i
$569$	−3.96731	+	27.5933i	−0.166318	+	1.15677i	0.720095	+	0.693875i	$0.244098\pi$
$569$	−3.96731	+	27.5933i	−0.166318	+	1.15677i	−0.886414	+	0.462894i	$0.846811\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	26.9119			1.12328
$575$	−23.1361	−	17.1218i	−0.964843	−	0.714029i
$576$		0			0
$577$	−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
$579$		0			0
$580$	6.17440	+	13.5200i	0.256378	+	0.561389i
$581$	2.52131	−	17.5361i	0.104602	−	0.727520i
$582$		0			0
$583$	−0.750694	−	0.482442i	−0.0310906	−	0.0199807i
$584$	0.290608	−	0.636342i	0.0120254	−	0.0263320i
$585$		0			0
$586$	7.13750	+	8.23711i	0.294847	+	0.340272i
$587$	−19.2179	−	22.1787i	−0.793209	−	0.915412i	0.204779	−	0.978808i	$-0.434352\pi$
$587$	−19.2179	−	22.1787i	−0.793209	−	0.915412i	−0.997988	+	0.0633958i	$0.979807\pi$
$588$		0			0
$589$	−7.51713	+	16.4602i	−0.309738	+	0.678232i
$590$	−22.0223	−	14.1529i	−0.906646	−	0.582666i
$591$		0			0
$592$	1.04161	−	7.24458i	0.0428100	−	0.297750i
$593$	17.5461	+	38.4205i	0.720530	+	1.57774i	0.813160	+	0.582041i	$0.197746\pi$
$593$	17.5461	+	38.4205i	0.720530	+	1.57774i	−0.0926291	+	0.995701i	$0.529527\pi$
$594$		0			0
$595$	77.6393	−	49.8957i	3.18290	−	2.04553i
$596$	−0.901293	+	1.04015i	−0.0369184	+	0.0426061i
$597$		0			0
$598$	1.10872	+	1.46423i	0.0453389	+	0.0598766i
$599$	19.2147			0.785092			0.392546	−	0.919732i	$-0.371594\pi$
$599$	19.2147			0.785092			0.392546	+	0.919732i	$0.371594\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	−1.92526	+	13.3904i	−0.0783375	+	0.544850i
$605$	34.6134	−	10.1634i	1.40723	−	0.413201i
$606$		0			0
$607$	−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
$609$		0			0
$610$	27.4805	+	31.7142i	1.11265	+	1.28407i
$611$	3.92003	+	1.15103i	0.158588	+	0.0465655i
$612$		0			0
$613$	−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
$615$		0			0
$616$	−0.558933	−	1.22389i	−0.0225201	−	0.0493121i
$617$	4.21557	+	29.3199i	0.169712	+	1.18037i	0.879479	+	0.475938i	$0.157891\pi$
$617$	4.21557	+	29.3199i	0.169712	+	1.18037i	−0.709767	+	0.704437i	$0.751200\pi$
$618$		0			0
$619$	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
$621$		0			0
$622$	−7.52022			−0.301533
$623$	22.0748	−	25.4757i	0.884408	−	1.02066i
$624$		0			0
$625$	2.70241	+	18.7956i	0.108096	+	0.751826i
$626$	−6.73499	−	14.7476i	−0.269184	−	0.589431i
$627$		0			0
$628$	13.7578	−	4.03964i	0.548995	−	0.161199i
$629$	44.8125	+	28.7992i	1.78679	+	1.14830i
$630$		0			0
$631$	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
$633$		0			0
$634$	5.56316	+	1.63349i	0.220941	+	0.0648742i
$635$	−21.0173	+	46.0214i	−0.834045	+	1.82630i
$636$		0			0
$637$	−2.79843	+	0.821692i	−0.110878	+	0.0325566i
$638$	−0.224441	+	1.56102i	−0.00888570	+	0.0618014i
$639$		0			0
$640$	−0.472039	−	3.28310i	−0.0186590	−	0.129776i
$641$	−4.83962	+	3.11024i	−0.191154	+	0.122847i	−0.632717	−	0.774383i	$-0.718060\pi$
$641$	−4.83962	+	3.11024i	−0.191154	+	0.122847i	0.441563	+	0.897230i	$0.354424\pi$
$642$		0			0
$643$	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
$645$		0			0
$646$	−19.8337	+	22.8893i	−0.780347	+	0.900569i
$647$	−24.8914	+	15.9967i	−0.978581	+	0.628896i	−0.929080	−	0.369878i	$-0.879399\pi$
$647$	−24.8914	+	15.9967i	−0.978581	+	0.628896i	−0.0495008	+	0.998774i	$0.515763\pi$
$648$		0			0
$649$	−1.15387	−	2.52663i	−0.0452935	−	0.0991789i
$650$	−0.327095	+	2.27500i	−0.0128297	+	0.0892327i
$651$		0			0
$652$	−6.27216	−	4.03087i	−0.245637	−	0.157861i
$653$	−3.23536	+	7.08445i	−0.126609	+	0.277236i	−0.962313	−	0.271945i	$-0.912333\pi$
$653$	−3.23536	+	7.08445i	−0.126609	+	0.277236i	0.835703	+	0.549181i	$0.185060\pi$
$654$		0			0
$655$	−8.76425	−	10.1145i	−0.342448	−	0.395206i
$656$	4.60981	+	5.32001i	0.179983	+	0.207711i
$657$		0			0
$658$	16.9427	−	37.0994i	0.660496	−	1.44628i
$659$	7.83147	+	5.03298i	0.305071	+	0.196057i	0.684215	−	0.729281i	$-0.260145\pi$
$659$	7.83147	+	5.03298i	0.305071	+	0.196057i	−0.379144	+	0.925338i	$0.623781\pi$
$660$		0			0
$661$	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			0
$664$	3.89845	−	2.50538i	0.151289	−	0.0972278i
$665$	−34.5563	+	39.8801i	−1.34003	+	1.54648i
$666$		0			0
$667$	−21.4440	−	1.41526i	−0.830314	−	0.0547989i
$668$	−0.375716			−0.0145369
$669$		0			0
$670$	15.6475	−	10.0560i	0.604515	−	0.388498i
$671$	0.633673	+	4.40729i	0.0244627	+	0.170142i
$672$		0			0
$673$	−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
$675$		0			0
$676$	−5.33947	+	11.6918i	−0.205364	+	0.449685i
$677$	−1.40913	−	0.413758i	−0.0541572	−	0.0159020i	0.254542	−	0.967062i	$-0.418075\pi$
$677$	−1.40913	−	0.413758i	−0.0541572	−	0.0159020i	−0.308699	+	0.951160i	$0.599894\pi$
$678$		0			0
$679$	−28.1145	−	32.4459i	−1.07894	−	1.24516i
$680$	23.1625	+	6.80112i	0.888241	+	0.260811i
$681$		0			0
$682$	1.28743	+	0.827383i	0.0492983	+	0.0316821i
$683$	−19.5561	+	5.74219i	−0.748293	+	0.219719i	−0.633577	−	0.773680i	$-0.718414\pi$
$683$	−19.5561	+	5.74219i	−0.748293	+	0.219719i	−0.114716	+	0.993398i	$0.536596\pi$
$684$		0			0
$685$	−5.73812	−	12.5647i	−0.219242	−	0.480074i
$686$	0.335031	+	2.33019i	0.0127915	+	0.0889670i
$687$		0			0
$688$	−5.77613	+	6.66601i	−0.220213	+	0.254139i
$689$	−0.971018			−0.0369928
$690$		0			0
$691$	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
$693$		0			0
$694$	−3.20663	−	22.3026i	−0.121722	−	0.846594i
$695$	3.02000	+	6.61287i	0.114555	+	0.250840i
$696$		0			0
$697$	−49.1577	+	14.4340i	−1.86198	+	0.546727i
$698$	17.7708	+	11.4206i	0.672634	+	0.432276i
$699$		0			0
$700$	22.0150	+	6.46418i	0.832088	+	0.244323i
$701$	−7.33904	−	8.46970i	−0.277192	−	0.319896i	0.600034	−	0.799974i	$-0.295154\pi$
$701$	−7.33904	−	8.46970i	−0.277192	−	0.319896i	−0.877226	+	0.480078i	$0.840608\pi$
$702$		0			0
$703$	−29.2238	−	8.58089i	−1.10220	−	0.323635i
$704$	0.146201	−	0.320135i	0.00551014	−	0.0120655i
$705$		0			0
$706$	16.3199	−	4.79197i	0.614209	−	0.180348i
$707$	3.02260	−	21.0226i	0.113676	−	0.790637i
$708$		0			0
$709$	−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
$711$		0			0
$712$	8.81732			0.330443
$713$	−9.89360	+	18.3580i	−0.370518	+	0.687513i
$714$		0			0
$715$	−0.292753	+	0.337855i	−0.0109483	+	0.0126351i
$716$	5.02535	−	3.22960i	0.187806	−	0.120696i
$717$		0			0
$718$	−4.13610	−	9.05680i	−0.154358	−	0.337997i
$719$	−4.98867	+	34.6969i	−0.186046	+	1.29398i	0.656078	+	0.754693i	$0.272214\pi$
$719$	−4.98867	+	34.6969i	−0.186046	+	1.29398i	−0.842124	+	0.539284i	$0.818695\pi$
$720$		0			0
$721$	32.9846	+	21.1979i	1.22841	+	0.789453i
$722$	−0.699045	+	1.53069i	−0.0260158	+	0.0569666i
$723$		0			0
$724$	11.9884	+	13.8354i	0.445546	+	0.514188i
$725$	−17.6116	−	20.3249i	−0.654080	−	0.754848i
$726$		0			0
$727$	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			0
$730$	−0.330219	+	2.29673i	−0.0122220	+	0.0850056i
$731$	−26.6677	−	58.3942i	−0.986342	−	2.15979i
$732$		0			0
$733$	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
$735$		0			0
$736$	4.50260	+	1.65124i	0.165968	+	0.0608656i
$737$	1.97359			0.0726982
$738$		0			0
$739$	−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			0
$742$	−1.37953	+	9.59482i	−0.0506440	+	0.352237i
$743$	3.68671	−	1.08251i	0.135252	−	0.0397136i	−0.213406	−	0.976964i	$-0.568456\pi$
$743$	3.68671	−	1.08251i	0.135252	−	0.0397136i	0.348658	+	0.937250i	$0.386637\pi$
$744$		0			0
$745$	1.89639	−	4.15251i	0.0694782	−	0.152136i
$746$	−33.3248	−	9.78504i	−1.22011	−	0.358256i
$747$		0			0
$748$	1.67738	+	1.93580i	0.0613311	+	0.0707799i
$749$	−39.2050	−	11.5116i	−1.43252	−	0.420626i
$750$		0			0
$751$	−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
$753$		0			0
$754$	0.712894	+	1.56102i	0.0259621	+	0.0568490i
$755$	−6.38581	−	44.4143i	−0.232403	−	1.61640i
$756$		0			0
$757$	−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			0
$760$	−13.8028			−0.500680
$761$	16.1066	−	18.5880i	0.583863	−	0.673813i	−0.384568	−	0.923097i	$-0.625650\pi$
$761$	16.1066	−	18.5880i	0.583863	−	0.673813i	0.968431	+	0.249283i	$0.0801950\pi$
$762$		0			0
$763$	−9.01325	−	62.6886i	−0.326302	−	2.26948i
$764$	3.37335	+	7.38660i	0.122043	+	0.267238i
$765$		0			0
$766$	−26.5236	+	7.78803i	−0.958337	+	0.281393i
$767$	−2.54269	−	1.63409i	−0.0918113	−	0.0590036i
$768$		0			0
$769$	−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
$771$		0			0
$772$	−14.3524	−	4.21426i	−0.516556	−	0.151674i
$773$	−19.8367	+	43.4363i	−0.713477	+	1.56230i	0.109349	+	0.994003i	$0.465123\pi$
$773$	−19.8367	+	43.4363i	−0.713477	+	1.56230i	−0.822826	+	0.568293i	$0.807604\pi$
$774$		0			0
$775$	−25.0402	+	7.35247i	−0.899471	+	0.264109i
$776$	1.59816	−	11.1155i	0.0573707	−	0.399022i
$777$		0			0
$778$	2.13813	+	14.8710i	0.0766558	+	0.533153i
$779$	24.6434	−	15.8373i	0.882941	−	0.567432i
$780$		0			0
$781$	0.116682			0.00417522
$782$	−24.5451	+	24.8164i	−0.877730	+	0.887434i
$783$		0			0
$784$	−4.98727	+	5.75562i	−0.178117	+	0.205558i
$785$	−40.0093	+	25.7124i	−1.42799	+	0.917715i
$786$		0			0
$787$	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
$789$		0			0
$790$	45.0028	+	28.9216i	1.60113	+	1.02898i
$791$	20.8263	−	45.6033i	0.740498	−	1.62146i
$792$		0			0
$793$	3.17289	+	3.66171i	0.112673	+	0.130031i
$794$	12.2286	+	14.1126i	0.433977	+	0.500837i
$795$		0			0
$796$	5.84829	−	12.8060i	0.207287	−	0.453895i
$797$	−12.9998	−	8.35449i	−0.460478	−	0.295931i	0.289760	−	0.957099i	$-0.406425\pi$
$797$	−12.9998	−	8.35449i	−0.460478	−	0.295931i	−0.750238	+	0.661168i	$0.770061\pi$
$798$		0			0
$799$	−11.0498	+	76.8534i	−0.390915	+	2.71888i
$800$	2.49315	+	5.45923i	0.0881461	+	0.193013i
$801$		0			0
$802$	27.2531	−	17.5145i	0.962342	−	0.618460i
$803$	−0.161228	+	0.186067i	−0.00568961	+	0.00656617i
$804$		0			0
$805$	−42.7648	+	43.2376i	−1.50726	+	1.52393i
$806$	1.66529			0.0586572
$807$		0			0
$808$	4.67354	−	3.00350i	0.164415	−	0.105663i
$809$	−0.913503	−	6.35355i	−0.0321171	−	0.223379i	0.967441	−	0.253095i	$-0.0814487\pi$
$809$	−0.913503	−	6.35355i	−0.0321171	−	0.223379i	−0.999558	+	0.0297164i	$0.990540\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	−1.07005	+	2.34309i	−0.0375053	+	0.0821252i
$815$	23.7279	+	6.96714i	0.831152	+	0.244048i
$816$		0			0
$817$	24.0368	+	27.7399i	0.840941	+	0.970497i
$818$	12.9039	+	3.78892i	0.451173	+	0.132476i
$819$		0			0
$820$	−19.6421	−	12.6232i	−0.685933	−	0.440822i
$821$	49.1161	−	14.4218i	1.71416	−	0.503323i	0.730434	−	0.682984i	$-0.239318\pi$
$821$	49.1161	−	14.4218i	1.71416	−	0.503323i	0.983729	+	0.179660i	$0.0574999\pi$
$822$		0			0
$823$	−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
$825$		0			0
$826$	−19.7592	+	22.8033i	−0.687510	+	0.793429i
$827$	48.0754			1.67174			0.835872	−	0.548924i	$-0.184962\pi$
$827$	48.0754			1.67174			0.835872	+	0.548924i	$0.184962\pi$
$828$		0			0
$829$	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
$831$		0			0
$832$	−0.0545015	−	0.379066i	−0.00188950	−	0.0131418i
$833$	−23.0257	−	50.4192i	−0.797792	−	1.74692i
$834$		0			0
$835$	1.19572	−	0.351094i	0.0413795	−	0.0121501i
$836$	−1.23206	−	0.791799i	−0.0426118	−	0.0273849i
$837$		0			0
$838$	−12.9808	−	3.81152i	−0.448416	−	0.131667i
$839$	12.9755	+	14.9745i	0.447962	+	0.516976i	0.934151	−	0.356878i	$-0.116159\pi$
$839$	12.9755	+	14.9745i	0.447962	+	0.516976i	−0.486189	+	0.873854i	$0.661613\pi$
$840$		0			0
$841$	8.55840	+	2.51297i	0.295117	+	0.0866543i
$842$	10.6528	−	23.3264i	0.367120	−	0.803880i
$843$		0			0
$844$	−3.83736	+	1.12675i	−0.132087	+	0.0387843i
$845$	6.06728	−	42.1988i	0.208721	−	1.45168i
$846$		0			0
$847$	−5.91747	−	41.1569i	−0.203327	−	1.41417i
$848$	−2.13303	+	1.37081i	−0.0732484	+	0.0470739i
$849$		0			0
$850$	−43.6799			−1.49821
$851$	−32.9549	−	12.0856i	−1.12968	−	0.414288i
$852$		0			0
$853$	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
$855$		0			0
$856$	−4.43988	−	9.72197i	−0.151752	−	0.332290i
$857$	−1.22485	+	8.51902i	−0.0418401	+	0.291004i	0.958149	+	0.286271i	$0.0924158\pi$
$857$	−1.22485	+	8.51902i	−0.0418401	+	0.291004i	−0.999989	+	0.00473330i	$0.998493\pi$
$858$		0			0
$859$	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
$861$		0			0
$862$	−11.2362	−	12.9673i	−0.382707	−	0.441668i
$863$	9.11321	+	10.5172i	0.310217	+	0.358010i	0.889353	−	0.457221i	$-0.151155\pi$
$863$	9.11321	+	10.5172i	0.310217	+	0.358010i	−0.579136	+	0.815231i	$0.696610\pi$
$864$		0			0
$865$	−21.6837	+	47.4807i	−0.737268	+	1.61439i
$866$	−8.03155	−	5.16156i	−0.272923	−	0.175397i
$867$		0			0
$868$	2.36588	−	16.4550i	0.0803030	−	0.558520i
$869$	2.35795	+	5.16319i	0.0799879	+	0.175149i
$870$		0			0
$871$	1.80665	−	1.16107i	0.0612162	−	0.0393412i
$872$	10.8485	−	12.5198i	0.367376	−	0.423975i
$873$		0			0
$874$	9.46811	−	17.5685i	0.320264	−	0.594263i
$875$	−12.7006			−0.429360
$876$		0			0
$877$	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
$879$		0			0
$880$	−0.166129	+	1.15545i	−0.00560020	+	0.0389502i
$881$	−17.8776	+	5.24934i	−0.602312	+	0.176855i	−0.568651	−	0.822579i	$-0.692535\pi$
$881$	−17.8776	+	5.24934i	−0.602312	+	0.176855i	−0.0336603	+	0.999433i	$0.510716\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	−4.61237	−	5.32296i	−0.154955	−	0.178828i
$887$	21.9589	+	6.44772i	0.737308	+	0.216493i	0.628762	−	0.777598i	$-0.283562\pi$
$887$	21.9589	+	6.44772i	0.737308	+	0.216493i	0.108547	+	0.994091i	$0.465380\pi$
$888$		0			0
$889$	49.0574	+	31.5273i	1.64533	+	1.05739i
$890$	−28.0612	+	8.23951i	−0.940613	+	0.276189i
$891$		0			0
$892$	2.49432	+	5.46180i	0.0835160	+	0.182875i
$893$	−6.31800	−	43.9426i	−0.211424	−	1.47048i
$894$		0			0
$895$	−12.9753	+	14.9743i	−0.433715	+	0.500534i
$896$	−3.82306			−0.127719
$897$		0			0
$898$	37.7146			1.25855
$899$	−12.7604	+	14.7263i	−0.425583	+	0.491150i
$900$		0			0
$901$	−2.62625	−	18.2659i	−0.0874929	−	0.608527i
$902$	−1.02916	−	2.25355i	−0.0342673	−	0.0750349i
$903$		0			0
$904$	12.5823	−	3.69450i	0.418482	−	0.122877i
$905$	−51.0820	−	32.8284i	−1.69802	−	1.09125i
$906$		0			0
$907$	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
$909$		0			0
$910$	4.65949	+	1.36815i	0.154461	+	0.0453537i
$911$	8.70510	−	19.0615i	0.288413	−	0.631536i	−0.708859	−	0.705350i	$-0.750790\pi$
$911$	8.70510	−	19.0615i	0.288413	−	0.631536i	0.997272	+	0.0738141i	$0.0235171\pi$
$912$		0			0
$913$	−1.56486	+	0.459483i	−0.0517891	+	0.0152067i
$914$	0.277920	−	1.93298i	0.00919278	−	0.0639372i
$915$		0			0
$916$	1.39473	+	9.70053i	0.0460830	+	0.320515i
$917$	−12.9771	+	8.33985i	−0.428540	+	0.275406i
$918$		0			0
$919$	−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
$921$		0			0
$922$	4.48627	−	5.17743i	0.147747	−	0.170510i
$923$	0.106813	−	0.0686444i	0.00351579	−	0.00225946i
$924$		0			0
$925$	−18.2475	−	39.9565i	−0.599975	−	1.31376i
$926$	0.210102	−	1.46129i	0.00690439	−	0.0480211i
$927$		0			0
$928$	3.76974	+	2.42267i	0.123748	+	0.0795280i
$929$	18.8567	−	41.2904i	0.618668	−	1.35469i	−0.297816	−	0.954623i	$-0.596258\pi$
$929$	18.8567	−	41.2904i	0.618668	−	1.35469i	0.916484	−	0.400071i	$-0.131015\pi$
$930$		0			0
$931$	20.7540	+	23.9514i	0.680186	+	0.784976i
$932$	−5.77161	−	6.66079i	−0.189055	−	0.218181i
$933$		0			0
$934$	−4.73130	+	10.3601i	−0.154813	+	0.338993i
$935$	−7.14722	−	4.59324i	−0.233739	−	0.150215i
$936$		0			0
$937$	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
$939$		0			0
$940$	−29.7676	+	19.1305i	−0.970914	+	0.623968i
$941$	−32.8241	+	37.8811i	−1.07004	+	1.23489i	−0.0992194	+	0.995066i	$0.531635\pi$
$941$	−32.8241	+	37.8811i	−1.07004	+	1.23489i	−0.970817	+	0.239822i	$0.922911\pi$
$942$		0			0
$943$	29.5408	−	16.3419i	0.961979	−	0.532166i
$944$	−7.89240			−0.256876
$945$		0			0
$946$	2.61145	−	1.67828i	0.0849056	−	0.0545655i
$947$	−3.06937	−	21.3479i	−0.0997411	−	0.693715i	−0.976929	−	0.213566i	$-0.931492\pi$
$947$	−3.06937	−	21.3479i	−0.0997411	−	0.693715i	0.877187	−	0.480148i	$-0.159417\pi$
$948$		0			0
$949$	−0.0381270	+	0.265179i	−0.00123766	+	0.00860808i
$950$	23.9633	−	7.03626i	0.777473	−	0.228287i
$951$		0			0
$952$	11.5587	−	25.3100i	0.374620	−	0.820303i
$953$	−13.7135	−	4.02664i	−0.444224	−	0.130436i	0.0519682	−	0.998649i	$-0.483451\pi$
$953$	−13.7135	−	4.02664i	−0.444224	−	0.130436i	−0.496192	+	0.868213i	$0.665269\pi$
$954$		0			0
$955$	−17.6383	−	20.3556i	−0.570760	−	0.658693i
$956$	−18.7018	−	5.49133i	−0.604858	−	0.177602i
$957$		0			0
$958$	−15.0265	−	9.65696i	−0.485485	−	0.312002i
$959$	−15.2761	+	4.48547i	−0.493292	+	0.144843i
$960$		0			0
$961$	−5.02291	−	10.9986i	−0.162029	−	0.354795i
$962$	0.398900	+	2.77441i	0.0128611	+	0.0894507i
$963$		0			0
$964$	1.52599	−	1.76108i	0.0491487	−	0.0567206i
$965$	49.6148			1.59716
$966$		0			0
$967$	−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
$969$		0			0
$970$	5.30089	+	36.8685i	0.170201	+	1.18378i
$971$	−3.43811	−	7.52842i	−0.110334	−	0.241598i	0.846408	−	0.532535i	$-0.178760\pi$
$971$	−3.43811	−	7.52842i	−0.110334	−	0.241598i	−0.956742	+	0.290936i	$0.906033\pi$
$972$		0			0
$973$	8.03988	−	2.36072i	0.257747	−	0.0756812i
$974$	7.67408	+	4.93183i	0.245893	+	0.158026i
$975$		0			0
$976$	12.1392	+	3.56439i	0.388566	+	0.114093i
$977$	1.32060	+	1.52405i	0.0422496	+	0.0487587i	0.776481	−	0.630141i	$-0.217003\pi$
$977$	1.32060	+	1.52405i	0.0422496	+	0.0487587i	−0.734231	+	0.678899i	$0.762457\pi$
$978$		0			0
$979$	−2.97746	−	0.874260i	−0.0951599	−	0.0279415i
$980$	10.4936	−	22.9778i	0.335205	−	0.733997i
$981$		0			0
$982$	31.6886	−	9.30461i	1.01122	−	0.296922i
$983$	1.79669	−	12.4963i	0.0573055	−	0.398569i	−0.940900	−	0.338685i	$-0.890018\pi$
$983$	1.79669	−	12.4963i	0.0573055	−	0.398569i	0.998205	−	0.0598838i	$-0.0190730\pi$
$984$		0			0
$985$	−9.66892	−	67.2488i	−0.308078	−	2.14273i
$986$	−27.4364	+	17.6323i	−0.873754	+	0.561528i
$987$		0			0
$988$	−1.59367			−0.0507013
$989$	25.5359	+	33.7239i	0.811995	+	1.07236i
$990$		0			0
$991$	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			0
$994$	−0.526540	−	1.15296i	−0.0167008	−	0.0365698i
$995$	−6.64545	+	46.2201i	−0.210675	+	1.46528i
$996$		0			0
$997$	−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
$999$		0			0

Display

a_p

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p

up to: 50 250 1000 (See

a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

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

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

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Elliptic curves over $\Q$
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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	414.2.i.a.361.1

Level	$414$
Weight	$2$
Character	414.361
Analytic conductor	$3.306$
Analytic rank	$0$
Dimension	$10$
Inner twists	$2$