LMFDB - Embedded newform 289.3.e.d.40.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,3,Mod(40,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([15]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("289.40");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, 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:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			40.1
Root			$0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.40
Dual form			289.3.e.d.224.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.79690 - 1.15851i) q^{2} +(-0.796897 + 0.158513i) q^{3} +(3.65205 + 3.65205i) q^{4} +(-4.46088 + 6.67619i) q^{5} +(2.41248 + 0.479872i) q^{6} +(4.36370 + 6.53073i) q^{7} +(-1.34942 - 3.25778i) q^{8} +(-7.70500 + 3.19151i) q^{9} +O(q^{10})$	\(q+(-2.79690 - 1.15851i) q^{2} +(-0.796897 + 0.158513i) q^{3} +(3.65205 + 3.65205i) q^{4} +(-4.46088 + 6.67619i) q^{5} +(2.41248 + 0.479872i) q^{6} +(4.36370 + 6.53073i) q^{7} +(-1.34942 - 3.25778i) q^{8} +(-7.70500 + 3.19151i) q^{9} +(20.2111 - 13.5046i) q^{10} +(-1.57545 + 7.92030i) q^{11} +(-3.48921 - 2.33141i) q^{12} +(0.798835 - 0.798835i) q^{13} +(-4.63887 - 23.3212i) q^{14} +(2.49661 - 6.02734i) q^{15} -9.98414i q^{16} +25.2475 q^{18} +(2.59882 + 1.07647i) q^{19} +(-40.6732 + 8.09040i) q^{20} +(-4.51262 - 4.51262i) q^{21} +(13.5821 - 20.3271i) q^{22} +(-8.41543 - 1.67393i) q^{23} +(1.59175 + 2.38222i) q^{24} +(-15.1049 - 36.4664i) q^{25} +(-3.15972 + 1.30880i) q^{26} +(11.7144 - 7.82730i) q^{27} +(-7.91414 + 39.7870i) q^{28} +(2.55301 + 1.70587i) q^{29} +(-13.9655 + 13.9655i) q^{30} +(2.50461 + 12.5915i) q^{31} +(-16.9644 + 40.9557i) q^{32} -6.56139i q^{33} -63.0663 q^{35} +(-39.7946 - 16.4835i) q^{36} +(23.2161 - 4.61798i) q^{37} +(-6.02153 - 6.02153i) q^{38} +(-0.509964 + 0.763215i) q^{39} +(27.7692 + 5.52363i) q^{40} +(-12.1338 - 18.1595i) q^{41} +(7.39341 + 17.8493i) q^{42} +(-21.4671 + 8.89197i) q^{43} +(-34.6790 + 23.1717i) q^{44} +(13.0640 - 65.6770i) q^{45} +(21.5978 + 14.4312i) q^{46} +(-55.6597 + 55.6597i) q^{47} +(1.58261 + 7.95633i) q^{48} +(-4.85715 + 11.7262i) q^{49} +119.492i q^{50} +5.83478 q^{52} +(-55.5080 - 22.9922i) q^{53} +(-41.8320 + 8.32089i) q^{54} +(-45.8495 - 45.8495i) q^{55} +(15.3873 - 23.0287i) q^{56} +(-2.24162 - 0.445887i) q^{57} +(-5.16424 - 7.72882i) q^{58} +(10.5100 + 25.3733i) q^{59} +(31.1299 - 12.8944i) q^{60} +(-30.3155 + 20.2562i) q^{61} +(7.58231 - 38.1189i) q^{62} +(-54.4652 - 36.3925i) q^{63} +(66.6561 - 66.6561i) q^{64} +(1.76966 + 8.89668i) q^{65} +(-7.60145 + 18.3515i) q^{66} -117.219i q^{67} +6.97157 q^{69} +(176.390 + 73.0632i) q^{70} +(103.934 - 20.6737i) q^{71} +(20.7945 + 20.7945i) q^{72} +(33.9091 - 50.7486i) q^{73} +(-70.2832 - 13.9802i) q^{74} +(17.8174 + 26.6657i) q^{75} +(5.55971 + 13.4223i) q^{76} +(-58.6001 + 24.2730i) q^{77} +(2.31051 - 1.54383i) q^{78} +(-18.5894 + 93.4553i) q^{79} +(66.6560 + 44.5381i) q^{80} +(44.9799 - 44.9799i) q^{81} +(12.8989 + 64.8474i) q^{82} +(45.4770 - 109.791i) q^{83} -32.9607i q^{84} +70.3428 q^{86} +(-2.30489 - 0.954715i) q^{87} +(27.9285 - 5.55533i) q^{88} +(61.4534 + 61.4534i) q^{89} +(-112.626 + 168.557i) q^{90} +(8.70285 + 1.73111i) q^{91} +(-24.6203 - 36.8469i) q^{92} +(-3.99184 - 9.63715i) q^{93} +(220.157 - 91.1920i) q^{94} +(-18.7797 + 12.5482i) q^{95} +(7.02689 - 35.3266i) q^{96} +(-20.4467 - 13.6621i) q^{97} +(27.1699 - 27.1699i) q^{98} +(-13.1389 - 66.0539i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{3} + 32 q^{6} + 8 q^{7} - 40 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^3 + 32 * q^6 + 8 * q^7 - 40 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{3} + 32 q^{6} + 8 q^{7} - 40 q^{8} + 8 q^{9} + 32 q^{10} - 24 q^{11} - 8 q^{12} - 16 q^{13} + 24 q^{14} + 56 q^{18} - 48 q^{19} - 80 q^{20} + 64 q^{21} + 48 q^{22} + 24 q^{23} - 120 q^{24} - 32 q^{25} - 48 q^{26} + 80 q^{27} - 120 q^{28} + 16 q^{29} - 16 q^{30} - 40 q^{31} - 88 q^{32} - 160 q^{35} - 24 q^{36} + 16 q^{37} + 120 q^{38} + 160 q^{39} + 48 q^{40} - 40 q^{41} + 128 q^{42} - 112 q^{43} - 64 q^{44} + 128 q^{45} - 8 q^{46} - 192 q^{47} - 96 q^{48} - 80 q^{49} - 384 q^{52} - 128 q^{53} - 168 q^{54} - 224 q^{55} - 264 q^{56} - 80 q^{57} + 368 q^{58} - 120 q^{59} + 48 q^{60} - 96 q^{61} + 120 q^{62} - 184 q^{63} + 64 q^{64} - 96 q^{66} + 240 q^{69} + 480 q^{70} + 280 q^{71} - 40 q^{72} + 208 q^{73} - 224 q^{74} - 136 q^{75} + 160 q^{76} + 80 q^{77} - 64 q^{78} + 24 q^{79} + 240 q^{80} + 424 q^{81} + 272 q^{82} + 336 q^{83} + 832 q^{86} - 80 q^{87} + 72 q^{88} - 160 q^{89} - 384 q^{90} - 248 q^{92} - 208 q^{93} + 432 q^{94} - 192 q^{95} - 88 q^{96} + 176 q^{97} + 120 q^{98} - 216 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 32 * q^6 + 8 * q^7 - 40 * q^8 + 8 * q^9 + 32 * q^10 - 24 * q^11 - 8 * q^12 - 16 * q^13 + 24 * q^14 + 56 * q^18 - 48 * q^19 - 80 * q^20 + 64 * q^21 + 48 * q^22 + 24 * q^23 - 120 * q^24 - 32 * q^25 - 48 * q^26 + 80 * q^27 - 120 * q^28 + 16 * q^29 - 16 * q^30 - 40 * q^31 - 88 * q^32 - 160 * q^35 - 24 * q^36 + 16 * q^37 + 120 * q^38 + 160 * q^39 + 48 * q^40 - 40 * q^41 + 128 * q^42 - 112 * q^43 - 64 * q^44 + 128 * q^45 - 8 * q^46 - 192 * q^47 - 96 * q^48 - 80 * q^49 - 384 * q^52 - 128 * q^53 - 168 * q^54 - 224 * q^55 - 264 * q^56 - 80 * q^57 + 368 * q^58 - 120 * q^59 + 48 * q^60 - 96 * q^61 + 120 * q^62 - 184 * q^63 + 64 * q^64 - 96 * q^66 + 240 * q^69 + 480 * q^70 + 280 * q^71 - 40 * q^72 + 208 * q^73 - 224 * q^74 - 136 * q^75 + 160 * q^76 + 80 * q^77 - 64 * q^78 + 24 * q^79 + 240 * q^80 + 424 * q^81 + 272 * q^82 + 336 * q^83 + 832 * q^86 - 80 * q^87 + 72 * q^88 - 160 * q^89 - 384 * q^90 - 248 * q^92 - 208 * q^93 + 432 * q^94 - 192 * q^95 - 88 * q^96 + 176 * q^97 + 120 * q^98 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{15}{16}\right)$

Coefficient data

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

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

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

$2$	−2.79690	−	1.15851i	−1.39845	−	0.579256i	−0.449100	−	0.893481i	$-0.648255\pi$
$2$	−2.79690	−	1.15851i	−1.39845	−	0.579256i	−0.949348	+	0.314225i	$0.898255\pi$
$3$	−0.796897	+	0.158513i	−0.265632	+	0.0528376i	−0.326109	−	0.945332i	$-0.605738\pi$
$3$	−0.796897	+	0.158513i	−0.265632	+	0.0528376i	0.0604771	+	0.998170i	$0.480738\pi$
$4$	3.65205	+	3.65205i	0.913014	+	0.913014i
$5$	−4.46088	+	6.67619i	−0.892177	+	1.33524i	0.0495193	+	0.998773i	$0.484231\pi$
$5$	−4.46088	+	6.67619i	−0.892177	+	1.33524i	−0.941696	+	0.336464i	$0.890769\pi$
$6$	2.41248	+	0.479872i	0.402080	+	0.0799786i
$7$	4.36370	+	6.53073i	0.623385	+	0.932962i	0.999978	+	0.00658318i	$0.00209551\pi$
$7$	4.36370	+	6.53073i	0.623385	+	0.932962i	−0.376593	+	0.926379i	$0.622904\pi$
$8$	−1.34942	−	3.25778i	−0.168677	−	0.407223i
$9$	−7.70500	+	3.19151i	−0.856111	+	0.354613i
$10$	20.2111	−	13.5046i	2.02111	−	1.35046i
$11$	−1.57545	+	7.92030i	−0.143222	+	0.720027i	0.840710	+	0.541486i	$0.182138\pi$
$11$	−1.57545	+	7.92030i	−0.143222	+	0.720027i	−0.983932	+	0.178542i	$0.942862\pi$
$12$	−3.48921	−	2.33141i	−0.290767	−	0.194285i
$13$	0.798835	−	0.798835i	0.0614489	−	0.0614489i	−0.675715	−	0.737163i	$-0.736165\pi$
$13$	0.798835	−	0.798835i	0.0614489	−	0.0614489i	0.737163	+	0.675715i	$0.236165\pi$
$14$	−4.63887	−	23.3212i	−0.331348	−	1.66580i
$15$	2.49661	−	6.02734i	0.166440	−	0.401823i
$16$		−	9.98414i		−	0.624009i
$17$		0			0
$17$		0			0
$18$	25.2475			1.40264
$19$	2.59882	+	1.07647i	0.136780	+	0.0566561i	0.450023	−	0.893017i	$-0.351416\pi$
$19$	2.59882	+	1.07647i	0.136780	+	0.0566561i	−0.313244	+	0.949673i	$0.601416\pi$
$20$	−40.6732	+	8.09040i	−2.03366	+	0.404520i
$21$	−4.51262	−	4.51262i	−0.214887	−	0.214887i
$22$	13.5821	−	20.3271i	0.617369	−	0.923958i
$23$	−8.41543	−	1.67393i	−0.365888	−	0.0727797i	0.00872222	−	0.999962i	$-0.497224\pi$
$23$	−8.41543	−	1.67393i	−0.365888	−	0.0727797i	−0.374611	+	0.927182i	$0.622224\pi$
$24$	1.59175	+	2.38222i	0.0663228	+	0.0992590i
$25$	−15.1049	−	36.4664i	−0.604195	−	1.45866i
$26$	−3.15972	+	1.30880i	−0.121528	+	0.0503384i
$27$	11.7144	−	7.82730i	0.433866	−	0.289900i
$28$	−7.91414	+	39.7870i	−0.282648	+	1.42097i
$29$	2.55301	+	1.70587i	0.0880348	+	0.0588230i	0.598809	−	0.800892i	$-0.295641\pi$
$29$	2.55301	+	1.70587i	0.0880348	+	0.0588230i	−0.510774	+	0.859715i	$0.670641\pi$
$30$	−13.9655	+	13.9655i	−0.465517	+	0.465517i
$31$	2.50461	+	12.5915i	0.0807940	+	0.406179i	0.999925	+	0.0122273i	$0.00389218\pi$
$31$	2.50461	+	12.5915i	0.0807940	+	0.406179i	−0.919131	+	0.393951i	$0.871108\pi$
$32$	−16.9644	+	40.9557i	−0.530138	+	1.27987i
$33$		−	6.56139i		−	0.198830i
$34$		0			0
$35$	−63.0663			−1.80190
$36$	−39.7946	−	16.4835i	−1.10541	−	0.457875i
$37$	23.2161	−	4.61798i	0.627463	−	0.124810i	0.128892	−	0.991659i	$-0.458858\pi$
$37$	23.2161	−	4.61798i	0.627463	−	0.124810i	0.498572	+	0.866848i	$0.333858\pi$
$38$	−6.02153	−	6.02153i	−0.158461	−	0.158461i
$39$	−0.509964	+	0.763215i	−0.0130760	+	0.0195696i
$40$	27.7692	+	5.52363i	0.694229	+	0.138091i
$41$	−12.1338	−	18.1595i	−0.295946	−	0.442914i	0.653462	−	0.756959i	$-0.273316\pi$
$41$	−12.1338	−	18.1595i	−0.295946	−	0.442914i	−0.949408	+	0.314045i	$0.898316\pi$
$42$	7.39341	+	17.8493i	0.176034	+	0.424982i
$43$	−21.4671	+	8.89197i	−0.499235	+	0.206790i	−0.618069	−	0.786124i	$-0.712085\pi$
$43$	−21.4671	+	8.89197i	−0.499235	+	0.206790i	0.118833	+	0.992914i	$0.462085\pi$
$44$	−34.6790	+	23.1717i	−0.788158	+	0.526631i
$45$	13.0640	−	65.6770i	0.290310	−	1.45949i
$46$	21.5978	+	14.4312i	0.469518	+	0.313722i
$47$	−55.6597	+	55.6597i	−1.18425	+	1.18425i	−0.205617	+	0.978632i	$0.565920\pi$
$47$	−55.6597	+	55.6597i	−1.18425	+	1.18425i	−0.978632	+	0.205617i	$0.934080\pi$
$48$	1.58261	+	7.95633i	0.0329711	+	0.165757i
$49$	−4.85715	+	11.7262i	−0.0991254	+	0.239310i
$50$			119.492i			2.38984i
$51$		0			0
$52$	5.83478			0.112207
$53$	−55.5080	−	22.9922i	−1.04732	−	0.433815i	−0.208386	−	0.978047i	$-0.566821\pi$
$53$	−55.5080	−	22.9922i	−1.04732	−	0.433815i	−0.838935	+	0.544232i	$0.816821\pi$
$54$	−41.8320	+	8.32089i	−0.774666	+	0.154091i
$55$	−45.8495	−	45.8495i	−0.833627	−	0.833627i
$56$	15.3873	−	23.0287i	0.274772	−	0.411226i
$57$	−2.24162	−	0.445887i	−0.0393267	−	0.00782257i
$58$	−5.16424	−	7.72882i	−0.0890385	−	0.133256i
$59$	10.5100	+	25.3733i	0.178135	+	0.430057i	0.987575	−	0.157146i	$-0.0502292\pi$
$59$	10.5100	+	25.3733i	0.178135	+	0.430057i	−0.809440	+	0.587202i	$0.800229\pi$
$60$	31.1299	−	12.8944i	0.518832	−	0.214907i
$61$	−30.3155	+	20.2562i	−0.496976	+	0.332068i	−0.778668	−	0.627436i	$-0.784104\pi$
$61$	−30.3155	+	20.2562i	−0.496976	+	0.332068i	0.281692	+	0.959505i	$0.409104\pi$
$62$	7.58231	−	38.1189i	0.122295	−	0.614820i
$63$	−54.4652	−	36.3925i	−0.864527	−	0.577658i
$64$	66.6561	−	66.6561i	1.04150	−	1.04150i
$65$	1.76966	+	8.89668i	0.0272255	+	0.136872i
$66$	−7.60145	+	18.3515i	−0.115174	+	0.278054i
$67$		−	117.219i		−	1.74953i	−0.484544	−	0.874767i	$-0.661015\pi$
$67$		−	117.219i		−	1.74953i	0.484544	−	0.874767i	$-0.338985\pi$
$68$		0			0
$69$	6.97157			0.101037
$70$	176.390	+	73.0632i	2.51986	+	1.04376i
$71$	103.934	−	20.6737i	1.46386	−	0.291179i	0.602067	−	0.798446i	$-0.294344\pi$
$71$	103.934	−	20.6737i	1.46386	−	0.291179i	0.861789	+	0.507266i	$0.169344\pi$
$72$	20.7945	+	20.7945i	0.288813	+	0.288813i
$73$	33.9091	−	50.7486i	0.464508	−	0.695186i	−0.523074	−	0.852287i	$-0.675215\pi$
$73$	33.9091	−	50.7486i	0.464508	−	0.695186i	0.987583	+	0.157101i	$0.0502149\pi$
$74$	−70.2832	−	13.9802i	−0.949772	−	0.188921i
$75$	17.8174	+	26.6657i	0.237566	+	0.355542i
$76$	5.55971	+	13.4223i	0.0731541	+	0.176610i
$77$	−58.6001	+	24.2730i	−0.761041	+	0.315233i
$78$	2.31051	−	1.54383i	0.0296219	−	0.0197927i
$79$	−18.5894	+	93.4553i	−0.235309	+	1.18298i	0.664701	+	0.747109i	$0.268559\pi$
$79$	−18.5894	+	93.4553i	−0.235309	+	1.18298i	−0.900010	+	0.435869i	$0.856441\pi$
$80$	66.6560	+	44.5381i	0.833200	+	0.556726i
$81$	44.9799	−	44.9799i	0.555308	−	0.555308i
$82$	12.8989	+	64.8474i	0.157304	+	0.790821i
$83$	45.4770	−	109.791i	0.547916	−	1.32279i	−0.371110	−	0.928589i	$-0.621023\pi$
$83$	45.4770	−	109.791i	0.547916	−	1.32279i	0.919026	−	0.394197i	$-0.128977\pi$
$84$		−	32.9607i		−	0.392389i
$85$		0			0
$86$	70.3428			0.817939
$87$	−2.30489	−	0.954715i	−0.0264929	−	0.0109737i
$88$	27.9285	−	5.55533i	0.317370	−	0.0631288i
$89$	61.4534	+	61.4534i	0.690488	+	0.690488i	0.962339	−	0.271851i	$-0.0876359\pi$
$89$	61.4534	+	61.4534i	0.690488	+	0.690488i	−0.271851	+	0.962339i	$0.587636\pi$
$90$	−112.626	+	168.557i	−1.25140	+	1.87286i
$91$	8.70285	+	1.73111i	0.0956357	+	0.0190231i
$92$	−24.6203	−	36.8469i	−0.267612	−	0.400510i
$93$	−3.99184	−	9.63715i	−0.0429230	−	0.103625i
$94$	220.157	−	91.1920i	2.34210	−	0.970128i
$95$	−18.7797	+	12.5482i	−0.197681	+	0.132086i
$96$	7.02689	−	35.3266i	0.0731968	−	0.367985i
$97$	−20.4467	−	13.6621i	−0.210791	−	0.140846i	0.445693	−	0.895186i	$-0.352957\pi$
$97$	−20.4467	−	13.6621i	−0.210791	−	0.140846i	−0.656484	+	0.754340i	$0.727957\pi$
$98$	27.1699	−	27.1699i	0.277244	−	0.277244i
$99$	−13.1389	−	66.0539i	−0.132717	−	0.667211i
$100$	78.0135	−	188.341i	0.780135	−	1.88341i
$101$			7.70266i			0.0762640i	0.999273	+	0.0381320i	$0.0121407\pi$
$101$			7.70266i			0.0762640i	−0.999273	+	0.0381320i	$0.987859\pi$
$102$		0			0
$103$	41.5688			0.403581			0.201790	−	0.979429i	$-0.435324\pi$
$103$	41.5688			0.403581			0.201790	+	0.979429i	$0.435324\pi$
$104$	−3.68039	−	1.52447i	−0.0353884	−	0.0146584i
$105$	50.2574	−	9.99681i	0.478642	−	0.0952078i
$106$	128.614	+	128.614i	1.21333	+	1.21333i
$107$	−49.1193	+	73.5122i	−0.459059	+	0.687030i	−0.986721	−	0.162424i	$-0.948069\pi$
$107$	−49.1193	+	73.5122i	−0.459059	+	0.687030i	0.527662	+	0.849454i	$0.323069\pi$
$108$	71.3673	+	14.1958i	0.660808	+	0.131443i
$109$	−10.3522	−	15.4932i	−0.0949743	−	0.142139i	0.780940	−	0.624607i	$-0.214741\pi$
$109$	−10.3522	−	15.4932i	−0.0949743	−	0.142139i	−0.875914	+	0.482467i	$0.839741\pi$
$110$	75.1191	+	181.354i	0.682901	+	1.64867i
$111$	−17.7689	+	7.36011i	−0.160080	+	0.0663073i
$112$	65.2038	−	43.5678i	0.582176	−	0.388998i
$113$	11.8307	−	59.4768i	0.104696	−	0.526343i	−0.892470	−	0.451108i	$-0.851029\pi$
$113$	11.8307	−	59.4768i	0.104696	−	0.526343i	0.997166	−	0.0752358i	$-0.0239709\pi$
$114$	5.75303	+	3.84405i	0.0504651	+	0.0337197i
$115$	48.7158	−	48.7158i	0.423615	−	0.423615i
$116$	3.09381	+	15.5536i	0.0266708	+	0.134083i
$117$	−3.60553	+	8.70452i	−0.0308165	+	0.0743976i
$118$		−	83.1426i		−	0.704598i
$119$		0			0
$120$	−23.0047			−0.191706
$121$	51.5403	+	21.3487i	0.425953	+	0.176436i
$122$	108.256	−	21.5335i	0.887347	−	0.176504i
$123$	12.5479	+	12.5479i	0.102015	+	0.102015i
$124$	−36.8380	+	55.1320i	−0.297081	+	0.444613i
$125$	113.960	+	22.6681i	0.911682	+	0.181345i
$126$	110.172	+	164.885i	0.874384	+	1.30861i
$127$	−45.6333	−	110.168i	−0.359317	−	0.867468i	−0.995396	−	0.0958444i	$-0.969445\pi$
$127$	−45.6333	−	110.168i	−0.359317	−	0.867468i	0.636079	−	0.771624i	$-0.280555\pi$
$128$	−99.8291	+	41.3506i	−0.779915	+	0.323051i
$129$	15.6976	−	10.4888i	0.121687	−	0.0813085i
$130$	5.35736	−	26.9333i	0.0412105	−	0.207179i
$131$	−142.451	−	95.1830i	−1.08742	−	0.726588i	−0.123380	−	0.992360i	$-0.539373\pi$
$131$	−142.451	−	95.1830i	−1.08742	−	0.726588i	−0.964036	+	0.265772i	$0.914373\pi$
$132$	23.9626	−	23.9626i	0.181534	−	0.181534i
$133$	4.31034	+	21.6696i	0.0324086	+	0.162929i
$134$	−135.799	+	327.849i	−1.01343	+	2.44663i
$135$			113.124i			0.837956i
$136$		0			0
$137$	−173.113			−1.26360			−0.631799	−	0.775132i	$-0.717683\pi$
$137$	−173.113			−1.26360			−0.631799	+	0.775132i	$0.717683\pi$
$138$	−19.4988	−	8.07666i	−0.141295	−	0.0585265i
$139$	−176.119	+	35.0323i	−1.26705	+	0.252031i	−0.782454	−	0.622709i	$-0.786032\pi$
$139$	−176.119	+	35.0323i	−1.26705	+	0.252031i	−0.484593	+	0.874740i	$0.661032\pi$
$140$	−230.322	−	230.322i	−1.64515	−	1.64515i
$141$	35.5323	−	53.1779i	0.252002	−	0.377148i
$142$	−314.643	−	62.5864i	−2.21579	−	0.440749i
$143$	5.06849	+	7.58553i	0.0354440	+	0.0530457i
$144$	31.8645	+	76.9278i	0.221281	+	0.534221i
$145$	−22.7774	+	9.43469i	−0.157085	+	0.0650668i
$146$	−153.633	+	102.654i	−1.05228	+	0.703112i
$147$	2.01190	−	10.1145i	0.0136864	−	0.0688060i
$148$	101.652	+	67.9215i	0.686836	+	0.458929i
$149$	−31.6842	+	31.6842i	−0.212646	+	0.212646i	−0.805391	−	0.592745i	$-0.798044\pi$
$149$	−31.6842	+	31.6842i	−0.212646	+	0.212646i	0.592745	+	0.805391i	$0.298044\pi$
$150$	−18.9410	−	95.2228i	−0.126273	−	0.634819i
$151$	50.2789	−	121.384i	0.332973	−	0.803868i	−0.665380	−	0.746504i	$-0.731731\pi$
$151$	50.2789	−	121.384i	0.332973	−	0.803868i	0.998353	−	0.0573634i	$-0.0182694\pi$
$152$		−	9.91898i		−	0.0652565i
$153$		0			0
$154$	192.019			1.24688
$155$	−95.2363	−	39.4482i	−0.614428	−	0.254504i
$156$	−4.64972	+	0.924886i	−0.0298059	+	0.00592876i
$157$	−25.4694	−	25.4694i	−0.162225	−	0.162225i	0.621327	−	0.783552i	$-0.286594\pi$
$157$	−25.4694	−	25.4694i	−0.162225	−	0.162225i	−0.783552	+	0.621327i	$0.786594\pi$
$158$	160.262	−	239.849i	1.01432	−	1.51803i
$159$	47.8787	+	9.52367i	0.301124	+	0.0598973i
$160$	−197.752	−	295.956i	−1.23595	−	1.84973i
$161$	−25.7904	−	62.2635i	−0.160189	−	0.386730i
$162$	−177.914	+	73.6944i	−1.09823	+	0.454904i
$163$	−132.801	+	88.7349i	−0.814731	+	0.544386i	−0.891689	−	0.452648i	$-0.850479\pi$
$163$	−132.801	+	88.7349i	−0.814731	+	0.544386i	0.0769579	+	0.997034i	$0.475479\pi$
$164$	22.0062	−	110.633i	0.134184	−	0.674589i
$165$	43.8051	+	29.2696i	0.265485	+	0.177392i
$166$	−254.389	+	254.389i	−1.53246	+	1.53246i
$167$	21.6035	+	108.608i	0.129362	+	0.650347i	0.989993	+	0.141117i	$0.0450695\pi$
$167$	21.6035	+	108.608i	0.129362	+	0.650347i	−0.860631	+	0.509229i	$0.829930\pi$
$168$	−8.61173	+	20.7905i	−0.0512603	+	0.123753i
$169$			167.724i			0.992448i
$170$		0			0
$171$	−23.4594			−0.137190
$172$	−110.873	−	45.9251i	−0.644611	−	0.267006i
$173$	−174.633	+	34.7367i	−1.00944	+	0.200790i	−0.671995	−	0.740556i	$-0.734562\pi$
$173$	−174.633	+	34.7367i	−1.00944	+	0.200790i	−0.337444	+	0.941346i	$0.609562\pi$
$174$	5.34048	+	5.34048i	0.0306924	+	0.0306924i
$175$	172.239	−	257.774i	0.984224	−	1.47300i
$176$	79.0774	+	15.7295i	0.449303	+	0.0893720i
$177$	−12.3974	−	18.5540i	−0.0700417	−	0.104825i
$178$	−100.684	−	243.074i	−0.565642	−	1.36558i
$179$	232.978	−	96.5028i	1.30155	−	0.539122i	0.379146	−	0.925337i	$-0.376218\pi$
$179$	232.978	−	96.5028i	1.30155	−	0.539122i	0.922409	+	0.386215i	$0.126218\pi$
$180$	287.566	−	192.146i	1.59759	−	1.06748i
$181$	−58.7904	+	295.559i	−0.324809	+	1.63292i	0.381038	+	0.924559i	$0.375567\pi$
$181$	−58.7904	+	295.559i	−0.324809	+	1.63292i	−0.705847	+	0.708365i	$0.749433\pi$
$182$	−22.3355	−	14.9241i	−0.122722	−	0.0820005i
$183$	20.9475	−	20.9475i	0.114467	−	0.114467i
$184$	5.90262	+	29.6745i	0.0320795	+	0.161274i
$185$	−72.7341	+	175.596i	−0.393157	+	0.949165i
$186$			31.5787i			0.169778i
$187$		0			0
$188$	−406.545			−2.16247
$189$	102.236	+	42.3476i	0.540931	+	0.224061i
$190$	67.0622	−	13.3395i	0.352959	−	0.0702079i
$191$	−93.7287	−	93.7287i	−0.490726	−	0.490726i	0.417809	−	0.908535i	$-0.362798\pi$
$191$	−93.7287	−	93.7287i	−0.490726	−	0.490726i	−0.908535	+	0.417809i	$0.862798\pi$
$192$	−42.5522	+	63.6839i	−0.221626	+	0.331687i
$193$	312.491	+	62.1584i	1.61913	+	0.322064i	0.919694	−	0.392635i	$-0.128436\pi$
$193$	312.491	+	62.1584i	1.61913	+	0.322064i	0.699432	+	0.714699i	$0.253436\pi$
$194$	41.3597	+	61.8991i	0.213194	+	0.319068i
$195$	−2.82047	−	6.80923i	−0.0144640	−	0.0349191i
$196$	−60.5632	+	25.0861i	−0.308996	+	0.127990i
$197$	−96.1714	+	64.2597i	−0.488180	+	0.326191i	−0.775181	−	0.631739i	$-0.782341\pi$
$197$	−96.1714	+	64.2597i	−0.488180	+	0.326191i	0.287002	+	0.957930i	$0.407341\pi$
$198$	−39.7760	+	199.968i	−0.200889	+	1.00994i
$199$	245.987	+	164.363i	1.23611	+	0.825944i	0.989691	−	0.143218i	$-0.0457451\pi$
$199$	245.987	+	164.363i	1.23611	+	0.825944i	0.246422	+	0.969163i	$0.420745\pi$
$200$	−98.4168	+	98.4168i	−0.492084	+	0.492084i
$201$	18.5807	+	93.4113i	0.0924411	+	0.464733i
$202$	8.92363	−	21.5436i	0.0441764	−	0.106651i
$203$			24.1169i			0.118802i
$204$		0			0
$205$	175.364			0.855432
$206$	−116.264	−	48.1580i	−0.564387	−	0.233777i
$207$	70.1833	−	13.9603i	0.339050	−	0.0674412i
$208$	−7.97568	−	7.97568i	−0.0383446	−	0.0383446i
$209$	−12.6202	+	18.8875i	−0.0603839	+	0.0903708i
$210$	−152.146	−	30.2638i	−0.724505	−	0.144113i
$211$	127.636	+	191.021i	0.604912	+	0.905315i	0.999911	−	0.0133670i	$-0.00425497\pi$
$211$	127.636	+	191.021i	0.604912	+	0.905315i	−0.394999	+	0.918682i	$0.629255\pi$
$212$	−118.750	−	286.687i	−0.560140	−	1.35230i
$213$	−79.5475	+	32.9496i	−0.373462	+	0.154693i
$214$	222.546	−	148.701i	1.03994	−	0.694863i
$215$	36.3979	−	182.985i	0.169292	−	0.851091i
$216$	−41.3072	−	27.6006i	−0.191237	−	0.127781i
$217$	−71.3026	+	71.3026i	−0.328584	+	0.328584i
$218$	11.0050	+	55.3260i	0.0504817	+	0.253789i
$219$	−18.9778	+	45.8164i	−0.0866565	+	0.209207i
$220$		−	334.890i		−	1.52223i
$221$		0			0
$222$	58.2245			0.262272
$223$	−335.723	−	139.061i	−1.50549	−	0.623593i	−0.530865	−	0.847456i	$-0.678133\pi$
$223$	−335.723	−	139.061i	−1.50549	−	0.623593i	−0.974621	+	0.223863i	$0.928133\pi$
$224$	−341.499	+	67.9283i	−1.52455	+	0.303251i
$225$	232.766	+	232.766i	1.03452	+	1.03452i
$226$	−101.994	+	152.645i	−0.451300	+	0.675418i
$227$	−95.0611	−	18.9088i	−0.418772	−	0.0832988i	−0.0187931	−	0.999823i	$-0.505982\pi$
$227$	−95.0611	−	18.9088i	−0.418772	−	0.0832988i	−0.399978	+	0.916525i	$0.630982\pi$
$228$	−6.55813	−	9.81493i	−0.0287637	−	0.0430480i
$229$	138.397	+	334.120i	0.604353	+	1.45904i	0.869059	+	0.494708i	$0.164725\pi$
$229$	138.397	+	334.120i	0.604353	+	1.45904i	−0.264706	+	0.964329i	$0.585275\pi$
$230$	−192.691	+	79.8152i	−0.837786	+	0.347022i
$231$	42.8507	−	28.6319i	0.185501	−	0.123948i
$232$	2.11226	−	10.6191i	0.00910459	−	0.0457719i
$233$	−232.935	−	155.642i	−0.999720	−	0.667991i	−0.0558946	−	0.998437i	$-0.517801\pi$
$233$	−232.935	−	155.642i	−0.999720	−	0.667991i	−0.943825	+	0.330445i	$0.892801\pi$
$234$	20.1686	−	20.1686i	0.0861905	−	0.0861905i
$235$	−123.303	−	619.886i	−0.524694	−	2.63781i
$236$	−54.2818	+	131.048i	−0.230008	+	0.555288i
$237$		−	77.4209i		−	0.326670i
$238$		0			0
$239$	328.551			1.37469			0.687345	−	0.726331i	$-0.258776\pi$
$239$	328.551			1.37469			0.687345	+	0.726331i	$0.258776\pi$
$240$	−60.1778	−	24.9265i	−0.250741	−	0.103860i
$241$	−237.756	+	47.2927i	−0.986541	+	0.196235i	−0.661892	−	0.749599i	$-0.730246\pi$
$241$	−237.756	+	47.2927i	−0.986541	+	0.196235i	−0.324649	+	0.945835i	$0.605246\pi$
$242$	−119.420	−	119.420i	−0.493472	−	0.493472i
$243$	−99.1602	+	148.404i	−0.408067	+	0.610715i
$244$	−184.691	−	36.7372i	−0.756928	−	0.150562i
$245$	−56.6190	−	84.7364i	−0.231098	−	0.345863i
$246$	−20.5583	−	49.6320i	−0.0835701	−	0.201756i
$247$	2.93595	−	1.21611i	0.0118864	−	0.00492352i
$248$	37.6407	−	25.1507i	0.151777	−	0.101414i
$249$	−18.8372	+	94.7010i	−0.0756514	+	0.380325i
$250$	−292.474	−	195.425i	−1.16989	−	0.781699i
$251$	155.463	−	155.463i	0.619375	−	0.619375i	−0.325996	−	0.945371i	$-0.605700\pi$
$251$	155.463	−	155.463i	0.619375	−	0.619375i	0.945371	+	0.325996i	$0.105700\pi$
$252$	−66.0025	−	331.817i	−0.261915	−	1.31673i
$253$	26.5161	−	64.0155i	0.104807	−	0.253026i
$254$			360.996i			1.42125i
$255$		0			0
$256$	−49.9468			−0.195105
$257$	300.480	+	124.463i	1.16918	+	0.484292i	0.880923	−	0.473260i	$-0.156923\pi$
$257$	300.480	+	124.463i	1.16918	+	0.484292i	0.288261	+	0.957552i	$0.406923\pi$
$258$	−56.0559	+	11.1502i	−0.217271	+	0.0432179i
$259$	131.467	+	131.467i	0.507595	+	0.507595i
$260$	−26.0283	+	38.9541i	−0.100109	+	0.149823i
$261$	−25.1152	−	4.99573i	−0.0962269	−	0.0191407i
$262$	288.151	+	431.249i	1.09981	+	1.64599i
$263$	−53.0907	−	128.172i	−0.201866	−	0.487347i	0.790233	−	0.612806i	$-0.209959\pi$
$263$	−53.0907	−	128.172i	−0.201866	−	0.487347i	−0.992099	+	0.125460i	$0.959959\pi$
$264$	−21.3756	+	8.85405i	−0.0809681	+	0.0335381i
$265$	401.115	−	268.016i	1.51364	−	1.01138i
$266$	13.0489	−	65.6011i	0.0490559	−	0.246621i
$267$	−58.7132	−	39.2309i	−0.219900	−	0.146932i
$268$	428.089	−	428.089i	1.59735	−	1.59735i
$269$	63.3806	+	318.636i	0.235615	+	1.18452i	0.899580	+	0.436755i	$0.143872\pi$
$269$	63.3806	+	318.636i	0.235615	+	1.18452i	−0.663965	+	0.747764i	$0.731128\pi$
$270$	131.056	−	316.396i	0.485391	−	1.17184i
$271$			19.1867i			0.0707996i	0.999373	+	0.0353998i	$0.0112705\pi$
$271$			19.1867i			0.0707996i	−0.999373	+	0.0353998i	$0.988730\pi$
$272$		0			0
$273$	−7.20968			−0.0264091
$274$	484.179	+	200.554i	1.76708	+	0.731947i
$275$	312.622	−	62.1843i	1.13681	−	0.226125i
$276$	25.4606	+	25.4606i	0.0922484	+	0.0922484i
$277$	−171.117	+	256.095i	−0.617751	+	0.924529i	0.382249	+	0.924059i	$0.375150\pi$
$277$	−171.117	+	256.095i	−0.617751	+	0.924529i	−1.00000		0.000470113i	$0.999850\pi$
$278$	533.173	+	106.055i	1.91789	+	0.381492i
$279$	−59.4841	−	89.0243i	−0.213205	−	0.319083i
$280$	85.1028	+	205.456i	0.303939	+	0.733773i
$281$	−79.9361	+	33.1106i	−0.284470	+	0.117831i	−0.520356	−	0.853949i	$-0.674201\pi$
$281$	−79.9361	+	33.1106i	−0.284470	+	0.117831i	0.235886	+	0.971781i	$0.424201\pi$
$282$	−160.987	+	107.568i	−0.570877	+	0.381448i
$283$	−1.45959	+	7.33785i	−0.00515756	+	0.0259288i	−0.983278	−	0.182109i	$-0.941708\pi$
$283$	−1.45959	+	7.33785i	−0.00515756	+	0.0259288i	0.978121	+	0.208038i	$0.0667077\pi$
$284$	455.073	+	304.070i	1.60237	+	1.07067i
$285$	12.9764	−	12.9764i	0.0455314	−	0.0455314i
$286$	−5.38811	−	27.0879i	−0.0188396	−	0.0947128i
$287$	65.6466	−	158.485i	0.228734	−	0.552213i
$288$		−	369.706i		−	1.28370i
$289$		0			0
$290$	74.6361			0.257366
$291$	18.4595	+	7.64619i	0.0634348	+	0.0262756i
$292$	309.174	−	61.4986i	1.05882	−	0.210612i
$293$	−54.4583	−	54.4583i	−0.185864	−	0.185864i	0.608041	−	0.793906i	$-0.291956\pi$
$293$	−54.4583	−	54.4583i	−0.185864	−	0.185864i	−0.793906	+	0.608041i	$0.791956\pi$
$294$	−17.3448	+	25.9584i	−0.0589960	+	0.0882937i
$295$	−216.281	−	43.0210i	−0.733156	−	0.145834i
$296$	−46.3726	−	69.4016i	−0.156664	−	0.234465i
$297$	43.5392	+	105.113i	0.146597	+	0.353915i
$298$	125.324	−	51.9110i	0.420551	−	0.174198i
$299$	−8.05974	+	5.38535i	−0.0269557	+	0.0180112i
$300$	−32.3142	+	162.455i	−0.107714	+	0.541515i
$301$	−151.747	−	101.394i	−0.504143	−	0.336858i
$302$	−281.250	+	281.250i	−0.931291	+	0.931291i
$303$	−1.22097	−	6.13823i	−0.00402960	−	0.0202582i
$304$	10.7476	−	25.9470i	0.0353539	−	0.0853519i
$305$		−	292.752i		−	0.959844i
$306$		0			0
$307$	−159.680			−0.520132			−0.260066	−	0.965591i	$-0.583744\pi$
$307$	−159.680			−0.520132			−0.260066	+	0.965591i	$0.583744\pi$
$308$	−302.657	−	125.365i	−0.982653	−	0.407028i
$309$	−33.1261	+	6.58918i	−0.107204	+	0.0213242i
$310$	220.665	+	220.665i	0.711822	+	0.711822i
$311$	185.013	−	276.891i	0.594896	−	0.890324i	−0.404814	−	0.914399i	$-0.632664\pi$
$311$	185.013	−	276.891i	0.594896	−	0.890324i	0.999710	+	0.0240745i	$0.00766388\pi$
$312$	3.17454	+	0.631456i	0.0101748	+	0.00202390i
$313$	−219.210	−	328.071i	−0.700351	−	1.04815i	−0.995689	−	0.0927565i	$-0.970432\pi$
$313$	−219.210	−	328.071i	−0.700351	−	1.04815i	0.295338	−	0.955393i	$-0.404568\pi$
$314$	41.7286	+	100.742i	0.132894	+	0.320834i
$315$	485.926	−	201.277i	1.54262	−	0.638975i
$316$	−409.193	+	273.414i	−1.29492	+	0.865235i
$317$	27.1362	−	136.423i	0.0856033	−	0.430357i	−0.914088	−	0.405516i	$-0.867092\pi$
$317$	27.1362	−	136.423i	0.0856033	−	0.430357i	0.999691	−	0.0248412i	$-0.00790801\pi$
$318$	−122.879	−	82.1048i	−0.386411	−	0.258191i
$319$	−17.5331	+	17.5331i	−0.0549627	+	0.0549627i
$320$	147.663	+	742.353i	0.461448	+	2.31985i
$321$	27.4904	−	66.3677i	0.0856399	−	0.206753i
$322$			204.023i			0.633612i
$323$		0			0
$324$	328.538			1.01401
$325$	−41.1970	−	17.0643i	−0.126760	−	0.0525057i
$326$	474.232	−	94.3306i	1.45470	−	0.289358i
$327$	10.7055	+	10.7055i	0.0327385	+	0.0327385i
$328$	−42.7861	+	64.0340i	−0.130445	+	0.195225i
$329$	−606.381	−	120.617i	−1.84310	−	0.366616i
$330$	−88.6090	−	132.613i	−0.268512	−	0.401857i
$331$	−60.7720	−	146.717i	−0.183601	−	0.443252i	0.805103	−	0.593136i	$-0.202110\pi$
$331$	−60.7720	−	146.717i	−0.183601	−	0.443252i	−0.988704	+	0.149883i	$0.952110\pi$
$332$	567.048	−	234.879i	1.70798	−	0.707467i
$333$	−164.142	+	109.676i	−0.492919	+	0.329358i
$334$	65.4010	−	328.793i	0.195811	−	0.984410i
$335$	782.574	+	522.899i	2.33604	+	1.56089i
$336$	−45.0546	+	45.0546i	−0.134091	+	0.134091i
$337$	94.1023	+	473.084i	0.279235	+	1.40381i	0.824649	+	0.565644i	$0.191372\pi$
$337$	94.1023	+	473.084i	0.279235	+	1.40381i	−0.545414	+	0.838167i	$0.683628\pi$
$338$	194.310	−	469.106i	0.574882	−	1.38789i
$339$			49.2722i			0.145346i
$340$		0			0
$341$	−103.675			−0.304031
$342$	65.6136	+	27.1781i	0.191853	+	0.0794680i
$343$	279.697	−	55.6352i	0.815443	−	0.162202i
$344$	57.9362	+	57.9362i	0.168419	+	0.168419i
$345$	−31.0994	+	46.5435i	−0.0901431	+	0.134909i
$346$	528.673	+	105.160i	1.52796	+	0.303930i
$347$	10.9946	+	16.4546i	0.0316848	+	0.0474197i	0.846974	−	0.531634i	$-0.178422\pi$
$347$	10.9946	+	16.4546i	0.0316848	+	0.0474197i	−0.815289	+	0.579054i	$0.803422\pi$
$348$	−4.93090	−	11.9042i	−0.0141692	−	0.0342076i
$349$	−361.651	+	149.801i	−1.03625	+	0.429229i	−0.834965	−	0.550304i	$-0.814512\pi$
$349$	−361.651	+	149.801i	−1.03625	+	0.429229i	−0.201286	+	0.979533i	$0.564512\pi$
$350$	−780.370	+	521.427i	−2.22963	+	1.48979i
$351$	3.10514	−	15.6106i	0.00884655	−	0.0444746i
$352$	−297.655	−	198.887i	−0.845611	−	0.565019i
$353$	−138.024	+	138.024i	−0.391003	+	0.391003i	−0.875045	−	0.484042i	$-0.839168\pi$
$353$	−138.024	+	138.024i	−0.391003	+	0.391003i	0.484042	+	0.875045i	$0.339168\pi$
$354$	13.1792	+	66.2561i	0.0372293	+	0.187164i
$355$	−325.615	+	786.104i	−0.917226	+	2.21438i
$356$			448.863i			1.26085i
$357$		0			0
$358$	−763.416			−2.13245
$359$	328.726	+	136.163i	0.915672	+	0.379284i	0.790225	−	0.612817i	$-0.209964\pi$
$359$	328.726	+	136.163i	0.915672	+	0.379284i	0.125447	+	0.992100i	$0.459964\pi$
$360$	−231.590	+	46.0661i	−0.643306	+	0.127961i
$361$	−249.670	−	249.670i	−0.691608	−	0.691608i
$362$	506.840	−	758.539i	1.40011	−	2.09541i
$363$	−44.4564	−	8.84292i	−0.122469	−	0.0243607i
$364$	25.4612	+	38.1054i	0.0699484	+	0.104685i
$365$	187.542	+	452.767i	0.513814	+	1.24046i
$366$	−82.8558	+	34.3200i	−0.226382	+	0.0937705i
$367$	67.9537	−	45.4052i	0.185160	−	0.123720i	−0.459536	−	0.888159i	$-0.651984\pi$
$367$	67.9537	−	45.4052i	0.185160	−	0.123720i	0.644696	+	0.764439i	$0.276984\pi$
$368$	−16.7128	+	84.0209i	−0.0454152	+	0.228318i
$369$	151.447	+	101.194i	0.410426	+	0.274238i
$370$	406.859	−	406.859i	1.09962	−	1.09962i
$371$	−92.0644	−	462.839i	−0.248152	−	1.24754i
$372$	20.6170	−	49.7738i	0.0554220	−	0.133801i
$373$			76.8209i			0.205954i	0.994684	+	0.102977i	$0.0328368\pi$
$373$			76.8209i			0.205954i	−0.994684	+	0.102977i	$0.967163\pi$
$374$		0			0
$375$	−94.4077			−0.251754
$376$	256.436	+	106.219i	0.682009	+	0.282498i
$377$	3.40214	−	0.676727i	0.00902424	−	0.00179503i
$378$	−236.883	−	236.883i	−0.626676	−	0.626676i
$379$	−327.377	+	489.954i	−0.863791	+	1.29275i	0.0911132	+	0.995841i	$0.470957\pi$
$379$	−327.377	+	489.954i	−0.863791	+	1.29275i	−0.954904	+	0.296914i	$0.904043\pi$
$380$	−114.411	−	22.7578i	−0.301082	−	0.0598890i
$381$	53.8281	+	80.5594i	0.141281	+	0.211442i
$382$	153.564	+	370.735i	0.401999	+	0.970511i
$383$	−215.834	+	89.4016i	−0.563537	+	0.233424i	−0.646220	−	0.763151i	$-0.723651\pi$
$383$	−215.834	+	89.4016i	−0.563537	+	0.233424i	0.0826832	+	0.996576i	$0.473651\pi$
$384$	72.9989	−	48.7763i	0.190101	−	0.127022i
$385$	99.3576	−	499.504i	0.258072	−	1.29741i
$386$	−801.995	−	535.876i	−2.07771	−	1.38828i
$387$	137.025	−	137.025i	0.354070	−	0.354070i
$388$	−24.7779	−	124.567i	−0.0638606	−	0.321049i
$389$	−154.467	+	372.916i	−0.397087	+	0.958653i	0.591266	+	0.806477i	$0.298628\pi$
$389$	−154.467	+	372.916i	−0.397087	+	0.958653i	−0.988353	+	0.152177i	$0.951372\pi$
$390$			22.3123i			0.0572109i
$391$		0			0
$392$	44.7557			0.114173
$393$	128.607	+	53.2707i	0.327244	+	0.135549i
$394$	343.427	−	68.3119i	0.871642	−	0.173380i
$395$	−541.000	−	541.000i	−1.36962	−	1.36962i
$396$	193.248	−	289.217i	0.488001	−	0.730345i
$397$	258.720	+	51.4626i	0.651688	+	0.129629i	0.509853	−	0.860262i	$-0.329700\pi$
$397$	258.720	+	51.4626i	0.651688	+	0.129629i	0.141835	+	0.989890i	$0.454700\pi$
$398$	−497.582	−	744.685i	−1.25021	−	1.87107i
$399$	−6.86980	−	16.5852i	−0.0172175	−	0.0415668i
$400$	−364.086	+	150.809i	−0.910214	+	0.377023i
$401$	−198.962	+	132.942i	−0.496164	+	0.331526i	−0.778347	−	0.627835i	$-0.783941\pi$
$401$	−198.962	+	132.942i	−0.496164	+	0.331526i	0.282183	+	0.959361i	$0.408941\pi$
$402$	56.2499	−	282.788i	0.139925	−	0.703452i
$403$	12.0593	+	8.05779i	0.0299239	+	0.0199945i
$404$	−28.1305	+	28.1305i	−0.0696300	+	0.0696300i
$405$	99.6441	+	500.945i	0.246035	+	1.23690i
$406$	27.9397	−	67.4525i	0.0688171	−	0.166139i
$407$			191.154i			0.469666i
$408$		0			0
$409$	259.903			0.635461			0.317730	−	0.948181i	$-0.397079\pi$
$409$	259.903			0.635461			0.317730	+	0.948181i	$0.397079\pi$
$410$	−490.474	−	203.161i	−1.19628	−	0.495514i
$411$	137.953	−	27.4406i	0.335652	−	0.0667654i
$412$	151.812	+	151.812i	0.368475	+	0.368475i
$413$	−119.844	+	179.360i	−0.290180	+	0.434285i
$414$	−212.469	−	42.2626i	−0.513209	−	0.102084i
$415$	530.119	+	793.379i	1.27740	+	1.91176i
$416$	19.1651	+	46.2687i	0.0460700	+	0.111223i
$417$	134.796	−	55.8343i	0.323252	−	0.133895i
$418$	57.1789	−	38.2057i	0.136792	−	0.0914012i
$419$	33.4680	−	168.255i	0.0798758	−	0.401563i	−0.920076	−	0.391740i	$-0.871873\pi$
$419$	33.4680	−	168.255i	0.0798758	−	0.401563i	0.999952	−	0.00982284i	$-0.00312676\pi$
$420$	220.052	+	147.034i	0.523932	+	0.350080i
$421$	−443.214	+	443.214i	−1.05276	+	1.05276i	−0.0542356	+	0.998528i	$0.517272\pi$
$421$	−443.214	+	443.214i	−1.05276	+	1.05276i	−0.998528	+	0.0542356i	$0.982728\pi$
$422$	−135.685	−	682.136i	−0.321529	−	1.61644i
$423$	251.219	−	606.497i	0.593899	−	1.43380i
$424$			211.859i			0.499668i
$425$		0			0
$426$	260.659			0.611875
$427$	−264.575	−	109.591i	−0.619614	−	0.256653i
$428$	−447.857	+	89.0843i	−1.04639	+	0.208141i
$429$	−5.24147	−	5.24147i	−0.0122179	−	0.0122179i
$430$	−313.791	+	469.621i	−0.729747	+	1.09214i
$431$	−747.540	−	148.695i	−1.73443	−	0.345000i	−0.776089	−	0.630623i	$-0.782799\pi$
$431$	−747.540	−	148.695i	−1.73443	−	0.345000i	−0.958342	+	0.285623i	$0.907799\pi$
$432$	−78.1489	−	116.958i	−0.180900	−	0.270736i
$433$	−36.2305	−	87.4681i	−0.0836732	−	0.202005i	0.876505	−	0.481392i	$-0.159869\pi$
$433$	−36.2305	−	87.4681i	−0.0836732	−	0.202005i	−0.960179	+	0.279387i	$0.909869\pi$
$434$	282.031	−	116.821i	0.649841	−	0.269173i
$435$	16.6557	−	11.1290i	0.0382889	−	0.0255839i
$436$	18.7751	−	94.3887i	0.0430621	−	0.216488i
$437$	−20.0682	−	13.4092i	−0.0459228	−	0.0306846i
$438$	106.158	−	106.158i	0.242369	−	0.242369i
$439$	7.21414	+	36.2679i	0.0164331	+	0.0826149i	0.988132	−	0.153610i	$-0.0490899\pi$
$439$	7.21414	+	36.2679i	0.0164331	+	0.0826149i	−0.971698	+	0.236225i	$0.924090\pi$
$440$	−87.4976	+	211.238i	−0.198858	+	0.480086i
$441$		−	105.852i		−	0.240027i
$442$		0			0
$443$	−634.146			−1.43148			−0.715740	−	0.698367i	$-0.753911\pi$
$443$	−634.146			−1.43148			−0.715740	+	0.698367i	$0.753911\pi$
$444$	−91.7724	−	38.0134i	−0.206695	−	0.0856157i
$445$	−684.411	+	136.138i	−1.53800	+	0.305928i
$446$	777.880	+	777.880i	1.74412	+	1.74412i
$447$	20.2267	−	30.2714i	0.0452499	−	0.0677213i
$448$	726.180	+	144.446i	1.62094	+	0.322424i
$449$	−245.465	−	367.365i	−0.546693	−	0.818184i	0.450522	−	0.892765i	$-0.351238\pi$
$449$	−245.465	−	367.365i	−0.546693	−	0.818184i	−0.997215	+	0.0745814i	$0.976238\pi$
$450$	−381.360	−	920.685i	−0.847468	−	2.04597i
$451$	162.945	−	67.4939i	0.361296	−	0.149654i
$452$	260.419	−	174.006i	0.576148	−	0.384970i
$453$	−20.8262	+	104.700i	−0.0459740	+	0.231127i
$454$	243.970	+	163.016i	0.537379	+	0.359065i
$455$	−50.3796	+	50.3796i	−0.110724	+	0.110724i
$456$	1.57228	+	7.90441i	0.00344799	+	0.0173342i
$457$	−102.104	+	246.501i	−0.223423	+	0.539390i	−0.995350	−	0.0963202i	$-0.969293\pi$
$457$	−102.104	+	246.501i	−0.223423	+	0.539390i	0.771928	+	0.635710i	$0.219293\pi$
$458$		−	1094.83i		−	2.39046i
$459$		0			0
$460$	355.825			0.773533
$461$	417.100	+	172.768i	0.904772	+	0.374769i	0.786053	−	0.618159i	$-0.212121\pi$
$461$	417.100	+	172.768i	0.904772	+	0.374769i	0.118719	+	0.992928i	$0.462121\pi$
$462$	−153.019	+	30.4375i	−0.331211	+	0.0658819i
$463$	57.1171	+	57.1171i	0.123363	+	0.123363i	0.766093	−	0.642730i	$-0.222198\pi$
$463$	57.1171	+	57.1171i	0.123363	+	0.123363i	−0.642730	+	0.766093i	$0.722198\pi$
$464$	17.0316	−	25.4896i	0.0367060	−	0.0549345i
$465$	82.1465	+	16.3400i	0.176659	+	0.0351397i
$466$	471.181	+	705.172i	1.01112	+	1.51325i
$467$	−31.5580	−	76.1879i	−0.0675761	−	0.163143i	0.886483	−	0.462760i	$-0.153141\pi$
$467$	−31.5580	−	76.1879i	−0.0675761	−	0.163143i	−0.954059	+	0.299617i	$0.903141\pi$
$468$	−44.9569	+	18.6218i	−0.0960619	+	0.0397901i
$469$	765.524	−	511.507i	1.63225	−	1.09063i
$470$	−373.280	+	1876.61i	−0.794213	+	3.99278i
$471$	24.3337	+	16.2592i	0.0516638	+	0.0345207i
$472$	68.4785	−	68.4785i	0.145082	−	0.145082i
$473$	−36.6068	−	184.035i	−0.0773928	−	0.389080i
$474$	−89.6931	+	216.538i	−0.189226	+	0.456832i
$475$		−	111.029i		−	0.233746i
$476$		0			0
$477$	501.069			1.05046
$478$	−918.923	−	380.630i	−1.92243	−	0.796298i
$479$	451.536	−	89.8162i	0.942665	−	0.187508i	0.300246	−	0.953862i	$-0.402931\pi$
$479$	451.536	−	89.8162i	0.942665	−	0.187508i	0.642418	+	0.766354i	$0.277931\pi$
$480$	204.501	+	204.501i	0.426043	+	0.426043i
$481$	14.8569	−	22.2349i	0.0308875	−	0.0462264i
$482$	719.769	+	143.171i	1.49330	+	0.297035i
$483$	30.4218	+	45.5295i	0.0629852	+	0.0942639i
$484$	110.261	+	266.195i	0.227813	+	0.549989i
$485$	182.421	−	75.5612i	0.376125	−	0.155796i
$486$	449.268	−	300.192i	0.924421	−	0.617678i
$487$	−102.061	+	513.097i	−0.209571	+	1.05359i	0.722516	+	0.691354i	$0.242985\pi$
$487$	−102.061	+	513.097i	−0.209571	+	1.05359i	−0.932088	+	0.362233i	$0.882015\pi$
$488$	106.898	+	71.4273i	0.219054	+	0.146367i
$489$	91.7633	−	91.7633i	0.187655	−	0.187655i
$490$	60.1894	+	302.593i	0.122836	+	0.617536i
$491$	187.167	−	451.862i	0.381196	−	0.920289i	−0.610539	−	0.791986i	$-0.709047\pi$
$491$	187.167	−	451.862i	0.381196	−	0.920289i	0.991735	−	0.128303i	$-0.0409530\pi$
$492$			91.6511i			0.186283i
$493$		0			0
$494$	−9.62041			−0.0194745
$495$	499.600	+	206.941i	1.00929	+	0.418063i
$496$	125.716	−	25.0064i	0.253459	−	0.0504161i
$497$	588.550	+	588.550i	1.18421	+	1.18421i
$498$	162.398	−	243.046i	0.326100	−	0.488044i
$499$	−497.323	−	98.9237i	−0.996639	−	0.198244i	−0.330287	−	0.943881i	$-0.607145\pi$
$499$	−497.323	−	98.9237i	−0.996639	−	0.198244i	−0.666353	+	0.745637i	$0.732145\pi$
$500$	333.404	+	498.974i	0.666807	+	0.997948i
$501$	−34.4315	−	83.1249i	−0.0687255	−	0.165918i
$502$	−614.921	+	254.709i	−1.22494	+	0.507388i
$503$	560.779	−	374.700i	1.11487	−	0.744931i	0.145211	−	0.989401i	$-0.453614\pi$
$503$	560.779	−	374.700i	1.11487	−	0.744931i	0.969657	+	0.244470i	$0.0786138\pi$
$504$	−45.0625	+	226.544i	−0.0894097	+	0.449493i
$505$	−51.4244	−	34.3607i	−0.101831	−	0.0680410i
$506$	−148.326	+	148.326i	−0.293134	+	0.293134i
$507$	−26.5863	−	133.659i	−0.0524385	−	0.263626i
$508$	235.686	−	568.996i	0.463949	−	1.12007i
$509$		−	349.504i		−	0.686648i	−0.939217	−	0.343324i	$-0.888447\pi$
$509$		−	349.504i		−	0.686648i	0.939217	−	0.343324i	$-0.111553\pi$
$510$		0			0
$511$	479.395			0.938150
$512$	539.012	+	223.266i	1.05276	+	0.436067i
$513$	38.8694	−	7.73160i	0.0757688	−	0.0150713i
$514$	−696.221	−	696.221i	−1.35451	−	1.35451i
$515$	−185.434	+	277.521i	−0.360065	+	0.538876i
$516$	95.6341	+	19.0228i	0.185337	+	0.0368659i
$517$	−353.153	−	528.531i	−0.683081	−	1.02230i
$518$	−215.393	−	520.006i	−0.415818	−	1.00387i
$519$	133.658	−	55.3631i	0.257530	−	0.106673i
$520$	26.5954	−	17.7705i	0.0511451	−	0.0341741i
$521$	61.5301	−	309.333i	0.118100	−	0.593729i	−0.875729	−	0.482803i	$-0.839619\pi$
$521$	61.5301	−	309.333i	0.118100	−	0.593729i	0.993829	−	0.110925i	$-0.0353814\pi$
$522$	64.4571	+	43.0688i	0.123481	+	0.0825074i
$523$	145.221	−	145.221i	0.277669	−	0.277669i	−0.554509	−	0.832178i	$-0.687094\pi$
$523$	145.221	−	145.221i	0.277669	−	0.277669i	0.832178	+	0.554509i	$0.187094\pi$
$524$	−172.627	−	867.854i	−0.329441	−	1.65621i
$525$	−96.3965	+	232.722i	−0.183612	+	0.443279i
$526$			419.991i			0.798461i
$527$		0			0
$528$	−65.5098			−0.124072
$529$	−420.715	−	174.266i	−0.795302	−	0.329425i
$530$	−1432.38	+	284.918i	−2.70260	+	0.537580i
$531$	−161.959	−	161.959i	−0.305007	−	0.305007i
$532$	−63.3968	+	94.8800i	−0.119167	+	0.178346i
$533$	−24.1993	−	4.81355i	−0.0454021	−	0.00903104i
$534$	118.765	+	177.745i	0.222407	+	0.332855i
$535$	−271.666	−	655.859i	−0.507786	−	1.22590i
$536$	−381.873	+	158.177i	−0.712450	+	0.295106i
$537$	−170.363	+	113.833i	−0.317249	+	0.211979i
$538$	191.874	−	964.618i	0.356644	−	1.79297i
$539$	−85.2227	−	56.9440i	−0.158113	−	0.105648i
$540$	−413.135	+	413.135i	−0.765065	+	0.765065i
$541$	−154.255	−	775.493i	−0.285130	−	1.43344i	−0.812079	−	0.583547i	$-0.801664\pi$
$541$	−154.255	−	775.493i	−0.285130	−	1.43344i	0.526949	−	0.849897i	$-0.323336\pi$
$542$	22.2280	−	53.6632i	0.0410111	−	0.0990096i
$543$		−	244.849i		−	0.450919i
$544$		0			0
$545$	149.615			0.274523
$546$	20.1647	+	8.35251i	0.0369317	+	0.0152976i
$547$	−924.626	+	183.920i	−1.69036	+	0.336233i	−0.944159	−	0.329490i	$-0.893123\pi$
$547$	−924.626	+	183.920i	−1.69036	+	0.336233i	−0.746199	+	0.665723i	$0.768123\pi$
$548$	−632.218	−	632.218i	−1.15368	−	1.15368i
$549$	168.933	−	252.826i	0.307710	−	0.460521i
$550$	−946.412	−	188.253i	−1.72075	−	0.342278i
$551$	4.79850	+	7.18146i	0.00870871	+	0.0130335i
$552$	−9.40756	−	22.7119i	−0.0170427	−	0.0411447i
$553$	−691.450	+	286.408i	−1.25036	+	0.517917i
$554$	775.285	−	518.029i	1.39943	−	0.935071i
$555$	30.1274	−	151.461i	0.0542837	−	0.272902i
$556$	−771.138	−	515.258i	−1.38694	−	0.926723i
$557$	303.284	−	303.284i	0.544495	−	0.544495i	−0.380348	−	0.924843i	$-0.624196\pi$
$557$	303.284	−	303.284i	0.544495	−	0.544495i	0.924843	+	0.380348i	$0.124196\pi$
$558$	63.2352	+	317.905i	0.113325	+	0.569722i
$559$	−10.0455	+	24.2519i	−0.0179704	+	0.0433844i
$560$			629.663i			1.12440i
$561$		0			0
$562$	261.932			0.466071
$563$	−639.473	−	264.879i	−1.13583	−	0.470477i	−0.266072	−	0.963953i	$-0.585726\pi$
$563$	−639.473	−	264.879i	−1.13583	−	0.470477i	−0.869759	+	0.493476i	$0.835726\pi$
$564$	323.974	−	64.4425i	0.574423	−	0.114260i
$565$	344.303	+	344.303i	0.609386	+	0.609386i
$566$	12.5833	−	18.8323i	0.0222320	−	0.0332725i
$567$	490.031	+	97.4731i	0.864251	+	0.171910i
$568$	−207.601	−	310.696i	−0.365494	−	0.547000i
$569$	153.331	+	370.173i	0.269474	+	0.650567i	0.999459	−	0.0328958i	$-0.0104730\pi$
$569$	153.331	+	370.173i	0.269474	+	0.650567i	−0.729985	+	0.683463i	$0.760473\pi$
$570$	−51.3272	+	21.2604i	−0.0900477	+	0.0372990i
$571$	−541.876	+	362.070i	−0.948995	+	0.634098i	−0.930719	−	0.365734i	$-0.880818\pi$
$571$	−541.876	+	362.070i	−0.948995	+	0.634098i	−0.0182762	+	0.999833i	$0.505818\pi$
$572$	−9.19237	+	46.2132i	−0.0160706	+	0.0807923i
$573$	89.5493	+	59.8349i	0.156281	+	0.104424i
$574$	−367.214	+	367.214i	−0.639745	+	0.639745i
$575$	66.0718	+	332.165i	0.114907	+	0.577679i
$576$	−300.851	+	726.319i	−0.522311	+	1.26097i
$577$			684.109i			1.18563i	0.805339	+	0.592815i	$0.201983\pi$
$577$			684.109i			1.18563i	−0.805339	+	0.592815i	$0.798017\pi$
$578$		0			0
$579$	−258.876			−0.447109
$580$	−117.640	−	48.7281i	−0.202828	−	0.0840140i
$581$	915.465	−	182.097i	1.57567	−	0.313421i
$582$	−42.7712	−	42.7712i	−0.0734900	−	0.0734900i
$583$	269.555	−	403.417i	0.462358	−	0.691968i
$584$	−211.085	−	41.9875i	−0.361448	−	0.0718964i
$585$	−42.0291	−	62.9010i	−0.0718446	−	0.107523i
$586$	89.2236	+	215.405i	0.152259	+	0.367585i
$587$	−342.216	+	141.750i	−0.582991	+	0.241483i	−0.654632	−	0.755948i	$-0.727176\pi$
$587$	−342.216	+	141.750i	−0.582991	+	0.241483i	0.0716408	+	0.997430i	$0.477176\pi$
$588$	44.2862	−	29.5911i	0.0753166	−	0.0503250i
$589$	−7.04533	+	35.4193i	−0.0119615	+	0.0601346i
$590$	555.075	+	370.890i	0.940806	+	0.628626i
$591$	66.4527	−	66.4527i	0.112441	−	0.112441i
$592$	−46.1065	−	231.793i	−0.0778827	−	0.391543i
$593$	−242.416	+	585.245i	−0.408797	+	0.986922i	0.576658	+	0.816985i	$0.304356\pi$
$593$	−242.416	+	585.245i	−0.408797	+	0.986922i	−0.985455	+	0.169937i	$0.945644\pi$
$594$		−	344.431i		−	0.579850i
$595$		0			0
$596$	−231.425			−0.388297
$597$	−222.080	−	91.9883i	−0.371992	−	0.154084i
$598$	28.7813	−	5.72495i	0.0481292	−	0.00957349i
$599$	−315.855	−	315.855i	−0.527304	−	0.527304i	0.392463	−	0.919768i	$-0.371623\pi$
$599$	−315.855	−	315.855i	−0.527304	−	0.527304i	−0.919768	+	0.392463i	$0.871623\pi$
$600$	62.8278	−	94.0284i	0.104713	−	0.156714i
$601$	427.337	+	85.0027i	0.711044	+	0.141435i	0.537344	−	0.843363i	$-0.319428\pi$
$601$	427.337	+	85.0027i	0.711044	+	0.141435i	0.173700	+	0.984799i	$0.444428\pi$
$602$	306.955	+	459.390i	0.509891	+	0.763106i
$603$	374.105	+	903.170i	0.620407	+	1.49779i
$604$	626.922	−	259.680i	1.03795	−	0.429933i
$605$	−372.443	+	248.859i	−0.615609	+	0.411337i
$606$	−3.69629	+	18.5825i	−0.00609949	+	0.0306642i
$607$	−527.645	−	352.561i	−0.869267	−	0.580826i	0.0389892	−	0.999240i	$-0.487586\pi$
$607$	−527.645	−	352.561i	−0.869267	−	0.580826i	−0.908257	+	0.418414i	$0.862586\pi$
$608$	−88.1749	+	88.1749i	−0.145025	+	0.145025i
$609$	−3.82283	−	19.2187i	−0.00627723	−	0.0315578i
$610$	−339.157	+	818.798i	−0.555996	+	1.34229i
$611$			88.9259i			0.145542i
$612$		0			0
$613$	−692.422			−1.12956			−0.564782	−	0.825240i	$-0.691040\pi$
$613$	−692.422			−1.12956			−0.564782	+	0.825240i	$0.691040\pi$
$614$	446.610	+	184.992i	0.727377	+	0.301290i
$615$	−139.747	+	27.7973i	−0.227230	+	0.0451989i
$616$	158.152	+	158.152i	0.256740	+	0.256740i
$617$	149.021	−	223.026i	0.241525	−	0.361468i	−0.690827	−	0.723021i	$-0.742753\pi$
$617$	149.021	−	223.026i	0.241525	−	0.361468i	0.932352	+	0.361553i	$0.117753\pi$
$618$	100.284	+	19.9477i	0.162272	+	0.0322778i
$619$	86.9787	+	130.173i	0.140515	+	0.210295i	0.895052	−	0.445962i	$-0.147138\pi$
$619$	86.9787	+	130.173i	0.140515	+	0.210295i	−0.754537	+	0.656258i	$0.772138\pi$
$620$	−203.741	−	491.875i	−0.328615	−	0.793346i
$621$	−111.684	+	46.2610i	−0.179845	+	0.0744944i
$622$	−838.243	+	560.096i	−1.34766	+	0.900476i
$623$	−133.172	+	669.500i	−0.213759	+	1.07464i
$624$	7.62004	+	5.09155i	0.0122116	+	0.00815953i
$625$	38.0547	−	38.0547i	0.0608875	−	0.0608875i
$626$	233.033	+	1171.54i	0.372258	+	1.87147i
$627$	7.06311	−	17.0519i	0.0112649	−	0.0271959i
$628$		−	186.031i		−	0.296228i
$629$		0			0
$630$	−1592.27			−2.52741
$631$	−289.230	−	119.803i	−0.458368	−	0.189862i	0.141538	−	0.989933i	$-0.454795\pi$
$631$	−289.230	−	119.803i	−0.458368	−	0.189862i	−0.599906	+	0.800071i	$0.704795\pi$
$632$	329.542	−	65.5499i	0.521427	−	0.103718i
$633$	−131.992	−	131.992i	−0.208519	−	0.208519i
$634$	−233.945	+	350.124i	−0.368999	+	0.552246i
$635$	939.070	+	186.793i	1.47885	+	0.294162i
$636$	140.075	+	209.637i	0.220243	+	0.329617i
$637$	5.48723	+	13.2473i	0.00861418	+	0.0207965i
$638$	69.3506	−	28.7259i	0.108700	−	0.0450250i
$639$	−734.829	+	490.997i	−1.14997	+	0.768384i
$640$	169.262	−	850.938i	0.264472	−	1.32959i
$641$	307.746	+	205.629i	0.480103	+	0.320794i	0.771964	−	0.635666i	$-0.219275\pi$
$641$	307.746	+	205.629i	0.480103	+	0.320794i	−0.291861	+	0.956461i	$0.594275\pi$
$642$	−153.776	+	153.776i	−0.239526	+	0.239526i
$643$	42.9179	+	215.763i	0.0667463	+	0.335556i	0.999701	−	0.0244365i	$-0.00777915\pi$
$643$	42.9179	+	215.763i	0.0667463	+	0.335556i	−0.932955	+	0.359993i	$0.882779\pi$
$644$	133.202	−	321.577i	0.206835	−	0.499344i
$645$			151.589i			0.235022i
$646$		0			0
$647$	769.098			1.18871			0.594357	−	0.804201i	$-0.297407\pi$
$647$	769.098			1.18871			0.594357	+	0.804201i	$0.297407\pi$
$648$	−207.231	−	85.8381i	−0.319802	−	0.132466i
$649$	−217.522	+	43.2679i	−0.335165	+	0.0666686i
$650$	95.4544	+	95.4544i	0.146853	+	0.146853i
$651$	45.5185	−	68.1232i	0.0699209	−	0.104644i
$652$	−809.062	−	160.932i	−1.24089	−	0.246829i
$653$	23.5759	+	35.2838i	0.0361040	+	0.0540334i	0.849083	−	0.528260i	$-0.177155\pi$
$653$	23.5759	+	35.2838i	0.0361040	+	0.0540334i	−0.812979	+	0.582294i	$0.802155\pi$
$654$	−17.5397	−	42.3446i	−0.0268192	−	0.0647472i
$655$	1270.92	−	526.432i	1.94033	−	0.803713i
$656$	−181.307	+	121.145i	−0.276382	+	0.184673i
$657$	−99.3048	+	499.239i	−0.151149	+	0.759877i
$658$	1556.25	+	1039.85i	2.36512	+	1.58032i
$659$	−472.719	+	472.719i	−0.717328	+	0.717328i	−0.968057	−	0.250729i	$-0.919330\pi$
$659$	−472.719	+	472.719i	−0.717328	+	0.717328i	0.250729	+	0.968057i	$0.419330\pi$
$660$	53.0843	+	266.873i	0.0804307	+	0.404352i
$661$	157.467	−	380.158i	0.238225	−	0.575126i	−0.758874	−	0.651237i	$-0.774250\pi$
$661$	157.467	−	380.158i	0.238225	−	0.575126i	0.997099	+	0.0761113i	$0.0242504\pi$
$662$			480.756i			0.726218i
$663$		0			0
$664$	−419.043			−0.631089
$665$	−163.898	−	67.8888i	−0.246463	−	0.102088i
$666$	586.150	−	116.592i	0.880104	−	0.175064i
$667$	−18.6292	−	18.6292i	−0.0279298	−	0.0279298i
$668$	−317.745	+	475.539i	−0.475666	+	0.711885i
$669$	289.580	+	57.6010i	0.432855	+	0.0861002i
$670$	−1582.99	−	2369.12i	−2.36268	−	3.53600i
$671$	−112.675	−	272.020i	−0.167920	−	0.405395i
$672$	261.372	−	108.264i	0.388946	−	0.161107i
$673$	−13.4837	+	9.00950i	−0.0200352	+	0.0133871i	−0.565547	−	0.824716i	$-0.691335\pi$
$673$	−13.4837	+	9.00950i	−0.0200352	+	0.0133871i	0.545512	+	0.838103i	$0.316335\pi$
$674$	284.880	−	1432.19i	0.422670	−	2.12491i
$675$	−462.378	−	308.951i	−0.685004	−	0.457705i
$676$	−612.536	+	612.536i	−0.906119	+	0.906119i
$677$	200.593	+	1008.45i	0.296297	+	1.48958i	0.786290	+	0.617858i	$0.211999\pi$
$677$	200.593	+	1008.45i	0.296297	+	1.48958i	−0.489993	+	0.871726i	$0.663001\pi$
$678$	57.0825	−	137.809i	0.0841924	−	0.203258i
$679$		−	193.149i		−	0.284461i
$680$		0			0
$681$	78.7512			0.115641
$682$	289.967	+	120.108i	0.425172	+	0.176112i
$683$	221.999	−	44.1583i	0.325035	−	0.0646534i	−0.0298760	−	0.999554i	$-0.509511\pi$
$683$	221.999	−	44.1583i	0.325035	−	0.0646534i	0.354911	+	0.934900i	$0.384511\pi$
$684$	−85.6752	−	85.6752i	−0.125256	−	0.125256i
$685$	772.237	−	1155.73i	1.12735	−	1.68720i
$686$	−846.738	−	168.427i	−1.23431	−	0.245520i
$687$	−163.250	−	244.321i	−0.237628	−	0.355635i
$688$	88.7787	+	214.331i	0.129039	+	0.311527i
$689$	−62.7087	+	25.9748i	−0.0910141	+	0.0376993i
$690$	140.903	−	94.1484i	0.204207	−	0.136447i
$691$	7.62208	−	38.3188i	0.0110305	−	0.0554541i	−0.974878	−	0.222739i	$-0.928500\pi$
$691$	7.62208	−	38.3188i	0.0110305	−	0.0554541i	0.985909	+	0.167285i	$0.0535001\pi$
$692$	−764.629	−	510.909i	−1.10496	−	0.738308i
$693$	374.046	−	374.046i	0.539749	−	0.539749i
$694$	−11.6880	−	58.7593i	−0.0168414	−	0.0846676i
$695$	551.766	−	1332.08i	0.793908	−	1.91666i
$696$			8.79713i			0.0126395i
$697$		0			0
$698$	1185.05			1.69778
$699$	210.296	+	87.1075i	0.300853	+	0.124617i
$700$	1570.43	−	312.379i	2.24348	−	0.446255i
$701$	401.261	+	401.261i	0.572412	+	0.572412i	0.932802	−	0.360390i	$-0.117356\pi$
$701$	401.261	+	401.261i	0.572412	+	0.572412i	−0.360390	+	0.932802i	$0.617356\pi$
$702$	−26.7698	+	40.0639i	−0.0381336	+	0.0570710i
$703$	65.3056	+	12.9901i	0.0928956	+	0.0184781i
$704$	422.923	+	632.949i	0.600743	+	0.899075i
$705$	196.520	+	474.441i	0.278751	+	0.672965i
$706$	545.941	−	226.136i	0.773288	−	0.320306i
$707$	−50.3040	+	33.6121i	−0.0711514	+	0.0475418i
$708$	22.4843	−	113.036i	0.0317574	−	0.159655i
$709$	−237.289	−	158.551i	−0.334681	−	0.223627i	0.376862	−	0.926270i	$-0.377003\pi$
$709$	−237.289	−	158.551i	−0.334681	−	0.223627i	−0.711543	+	0.702643i	$0.752003\pi$
$710$	1821.42	−	1821.42i	2.56539	−	2.56539i
$711$	−155.033	−	779.401i	−0.218049	−	1.09620i
$712$	117.276	−	283.128i	0.164713	−	0.397652i
$713$		−	110.156i		−	0.154496i
$714$		0			0
$715$	−73.2524			−0.102451
$716$	1203.28	+	498.416i	1.68056	+	0.696112i
$717$	−261.821	+	52.0795i	−0.365162	+	0.0726353i
$718$	−761.667	−	761.667i	−1.06082	−	1.06082i
$719$	−340.804	+	510.049i	−0.473997	+	0.709387i	−0.989019	−	0.147790i	$-0.952784\pi$
$719$	−340.804	+	510.049i	−0.473997	+	0.709387i	0.515022	+	0.857177i	$0.327784\pi$
$720$	−655.728	−	130.432i	−0.910733	−	0.181156i
$721$	181.394	+	271.475i	0.251586	+	0.376525i
$722$	409.056	+	987.549i	0.566560	+	1.36780i
$723$	181.971	−	75.3748i	0.251689	−	0.104253i
$724$	−1294.10	+	864.693i	−1.78744	+	1.19433i
$725$	23.6439	−	118.866i	0.0326123	−	0.163953i
$726$	114.095	+	76.2360i	0.157156	+	0.105008i
$727$	−244.413	+	244.413i	−0.336194	+	0.336194i	−0.854933	−	0.518739i	$-0.826402\pi$
$727$	−244.413	+	244.413i	−0.336194	+	0.336194i	0.518739	+	0.854933i	$0.326402\pi$
$728$	−6.10422	−	30.6880i	−0.00838492	−	0.0421538i
$729$	−163.590	+	394.941i	−0.224403	+	0.541758i
$730$		−	1483.61i		−	2.03235i
$731$		0			0
$732$	153.003			0.209020
$733$	1246.38	+	516.266i	1.70038	+	0.704319i	0.999956	−	0.00941053i	$-0.00299551\pi$
$733$	1246.38	+	516.266i	1.70038	+	0.704319i	0.700421	+	0.713730i	$0.252996\pi$
$734$	−242.662	+	48.2685i	−0.330602	+	0.0657608i
$735$	58.5513	+	58.5513i	0.0796617	+	0.0796617i
$736$	211.320	−	316.263i	0.287120	−	0.429705i
$737$	928.407	+	184.672i	1.25971	+	0.250572i
$738$	−306.348	−	458.482i	−0.415105	−	0.621249i
$739$	−249.740	−	602.925i	−0.337943	−	0.815866i	−0.997913	−	0.0645741i	$-0.979431\pi$
$739$	−249.740	−	602.925i	−0.337943	−	0.815866i	0.659970	−	0.751292i	$-0.270569\pi$
$740$	−906.913	+	375.656i	−1.22556	+	0.507643i
$741$	−2.14688	+	1.43450i	−0.00289727	+	0.00193589i
$742$	−278.710	+	1401.17i	−0.375620	+	1.88837i
$743$	185.415	+	123.890i	0.249548	+	0.166743i	0.674053	−	0.738683i	$-0.264552\pi$
$743$	185.415	+	123.890i	0.249548	+	0.166743i	−0.424505	+	0.905426i	$0.639552\pi$
$744$	−26.0091	+	26.0091i	−0.0349584	+	0.0349584i
$745$	−70.1902	−	352.870i	−0.0942150	−	0.473651i
$746$	88.9980	−	214.860i	0.119300	−	0.288016i
$747$			991.082i			1.32675i
$748$		0			0
$749$	−694.430			−0.927143
$750$	264.049	+	109.373i	0.352065	+	0.145830i
$751$	−440.400	+	87.6011i	−0.586419	+	0.116646i	−0.479378	−	0.877609i	$-0.659138\pi$
$751$	−440.400	+	87.6011i	−0.586419	+	0.116646i	−0.107041	+	0.994255i	$0.534138\pi$
$752$	555.715	+	555.715i	0.738982	+	0.738982i
$753$	−99.2453	+	148.531i	−0.131800	+	0.197252i
$754$	−10.2994	−	2.04868i	−0.0136597	−	0.00271709i
$755$	586.094	+	877.152i	0.776283	+	1.16179i
$756$	218.716	+	528.027i	0.289307	+	0.698449i
$757$	−42.5792	+	17.6369i	−0.0562473	+	0.0232984i	−0.410630	−	0.911802i	$-0.634691\pi$
$757$	−42.5792	+	17.6369i	−0.0562473	+	0.0232984i	0.354382	+	0.935101i	$0.384691\pi$
$758$	1483.26	−	991.081i	1.95680	−	1.30749i
$759$	−10.9833	+	55.2169i	−0.0144708	+	0.0727496i
$760$	66.2210	+	44.2475i	0.0871329	+	0.0582203i
$761$	552.081	−	552.081i	0.725467	−	0.725467i	−0.244246	−	0.969713i	$-0.578540\pi$
$761$	552.081	−	552.081i	0.725467	−	0.725467i	0.969713	+	0.244246i	$0.0785404\pi$
$762$	−57.2225	−	287.677i	−0.0750952	−	0.377529i
$763$	56.0079	−	135.215i	0.0734048	−	0.177215i
$764$		−	684.604i		−	0.896079i
$765$		0			0
$766$	707.240			0.923289
$767$	28.6649	+	11.8734i	0.0373727	+	0.0154803i
$768$	39.8024	−	7.91719i	0.0518261	−	0.0103088i
$769$	625.504	+	625.504i	0.813400	+	0.813400i	0.985142	−	0.171742i	$-0.0549396\pi$
$769$	625.504	+	625.504i	0.813400	+	0.813400i	−0.171742	+	0.985142i	$0.554940\pi$
$770$	−856.575	+	1281.95i	−1.11243	+	1.66488i
$771$	−259.181	−	51.5543i	−0.336162	−	0.0668668i
$772$	914.229	+	1368.24i	1.18424	+	1.77233i
$773$	−465.474	−	1123.75i	−0.602166	−	1.45376i	−0.871347	−	0.490667i	$-0.836753\pi$
$773$	−465.474	−	1123.75i	−0.602166	−	1.45376i	0.269181	−	0.963090i	$-0.413247\pi$
$774$	−541.991	+	224.500i	−0.700247	+	0.290052i
$775$	421.336	−	281.528i	0.543660	−	0.363262i
$776$	−16.9169	+	85.0468i	−0.0218001	+	0.109596i
$777$	−125.605	−	83.9265i	−0.161654	−	0.108013i
$778$	864.056	−	864.056i	1.11061	−	1.11061i
$779$	−11.9854	−	60.2548i	−0.0153857	−	0.0773489i
$780$	14.5671	−	35.1682i	0.0186758	−	0.0450874i
$781$			855.757i			1.09572i
$782$		0			0
$783$	43.2592			0.0552481
$784$	117.076	+	48.4944i	0.149331	+	0.0618551i
$785$	283.654	−	56.4223i	0.361343	−	0.0718755i
$786$	−297.985	−	297.985i	−0.379116	−	0.379116i
$787$	107.816	−	161.359i	0.136997	−	0.205030i	−0.756627	−	0.653846i	$-0.773154\pi$
$787$	107.816	−	161.359i	0.136997	−	0.205030i	0.893624	+	0.448816i	$0.148154\pi$
$788$	−585.903	−	116.543i	−0.743532	−	0.147898i
$789$	62.6247	+	93.7245i	0.0793723	+	0.118789i
$790$	886.365	+	2139.88i	1.12198	+	2.70870i
$791$	440.053	−	182.276i	0.556324	−	0.230437i
$792$	−197.459	+	131.938i	−0.249317	+	0.166589i
$793$	−8.03575	+	40.3984i	−0.0101334	+	0.0509438i
$794$	−663.993	−	443.666i	−0.836263	−	0.558773i
$795$	−277.163	+	277.163i	−0.348633	+	0.348633i
$796$	298.094	+	1498.62i	0.374490	+	1.88269i
$797$	−49.1164	+	118.577i	−0.0616266	+	0.148780i	−0.951693	−	0.307051i	$-0.900658\pi$
$797$	−49.1164	+	118.577i	−0.0616266	+	0.148780i	0.890066	+	0.455831i	$0.150658\pi$
$798$			54.3457i			0.0681024i
$799$		0			0
$800$	1749.75			2.18719
$801$	−669.628	−	277.369i	−0.835990	−	0.346278i
$802$	710.490	−	141.325i	0.885898	−	0.176216i
$803$	348.522	+	348.522i	0.434025	+	0.434025i
$804$	−273.285	+	409.001i	−0.339907	+	0.508707i
$805$	530.731	+	105.569i	0.659293	+	0.131141i
$806$	−24.3937	−	36.5077i	−0.0302651	−	0.0452949i
$807$	−101.016	−	243.873i	−0.125174	−	0.302197i
$808$	25.0936	−	10.3941i	0.0310564	−	0.0128640i
$809$	−290.282	+	193.960i	−0.358816	+	0.239753i	−0.721891	−	0.692007i	$-0.756727\pi$
$809$	−290.282	+	193.960i	−0.358816	+	0.239753i	0.363075	+	0.931760i	$0.381727\pi$
$810$	301.656	−	1516.53i	0.372415	−	1.87226i
$811$	−154.347	−	103.131i	−0.190317	−	0.127166i	0.456761	−	0.889589i	$-0.349009\pi$
$811$	−154.347	−	103.131i	−0.190317	−	0.127166i	−0.647078	+	0.762423i	$0.724009\pi$
$812$	−88.0762	+	88.0762i	−0.108468	+	0.108468i
$813$	−3.04133	−	15.2898i	−0.00374088	−	0.0188067i
$814$	221.455	−	534.639i	0.272057	−	0.656804i
$815$		−	1282.44i		−	1.57355i
$816$		0			0
$817$	−65.3610			−0.0800013
$818$	−726.923	−	301.101i	−0.888659	−	0.368095i
$819$	−72.5803	+	14.4371i	−0.0886206	+	0.0176277i
$820$	640.437	+	640.437i	0.781021	+	0.781021i
$821$	−875.613	+	1310.45i	−1.06652	+	1.59616i	−0.300001	+	0.953939i	$0.596987\pi$
$821$	−875.613	+	1310.45i	−1.06652	+	1.59616i	−0.766519	+	0.642221i	$0.778013\pi$
$822$	−417.631	−	83.0720i	−0.508067	−	0.101061i
$823$	−558.689	−	836.137i	−0.678844	−	1.01596i	−0.997675	−	0.0681507i	$-0.978290\pi$
$823$	−558.689	−	836.137i	−0.678844	−	1.01596i	0.318831	−	0.947812i	$-0.396710\pi$
$824$	−56.0937	−	135.422i	−0.0680749	−	0.164347i
$825$	−239.270	+	99.1090i	−0.290025	+	0.120132i
$826$	542.982	−	362.809i	0.657363	−	0.439236i
$827$	310.073	−	1558.84i	0.374937	−	1.88494i	−0.0839938	−	0.996466i	$-0.526768\pi$
$827$	310.073	−	1558.84i	0.374937	−	1.88494i	0.458931	−	0.888472i	$-0.348232\pi$
$828$	307.297	+	205.329i	0.371132	+	0.247982i
$829$	269.747	−	269.747i	0.325388	−	0.325388i	−0.525442	−	0.850830i	$-0.676100\pi$
$829$	269.747	−	269.747i	0.325388	−	0.325388i	0.850830	+	0.525442i	$0.176100\pi$
$830$	−563.548	−	2833.15i	−0.678974	−	3.41343i
$831$	95.7684	−	231.205i	0.115245	−	0.278225i
$832$		−	106.494i		−	0.127998i
$833$		0			0
$834$	−441.695			−0.529611
$835$	−821.457	−	340.259i	−0.983781	−	0.407495i
$836$	−115.068	+	22.8884i	−0.137641	+	0.0273785i
$837$	127.898	+	127.898i	0.152805	+	0.152805i
$838$	−288.532	+	431.818i	−0.344310	+	0.515297i
$839$	−36.3072	−	7.22195i	−0.0432744	−	0.00860781i	0.173406	−	0.984850i	$-0.444523\pi$
$839$	−36.3072	−	7.22195i	−0.0432744	−	0.00860781i	−0.216680	+	0.976243i	$0.569523\pi$
$840$	−100.386	−	150.238i	−0.119507	−	0.178854i
$841$	−318.229	−	768.273i	−0.378393	−	0.913523i
$842$	1753.09	−	726.154i	2.08206	−	0.862416i
$843$	58.4524	−	39.0566i	0.0693386	−	0.0463305i
$844$	−231.485	+	1163.76i	−0.274272	+	1.37886i
$845$	−1119.75	−	748.196i	−1.32515	−	0.885439i
$846$	−1405.27	+	1405.27i	−1.66107	+	1.66107i
$847$	85.4837	+	429.755i	0.100925	+	0.507385i
$848$	−229.557	+	554.200i	−0.270704	+	0.653538i
$849$		−	6.07887i		−	0.00716004i
$850$		0			0
$851$	−203.104			−0.238665
$852$	−410.846	−	170.178i	−0.482213	−	0.199739i
$853$	−77.3472	+	15.3853i	−0.0906767	+	0.0180367i	−0.240220	−	0.970718i	$-0.577220\pi$
$853$	−77.3472	+	15.3853i	−0.0906767	+	0.0180367i	0.149543	+	0.988755i	$0.452220\pi$
$854$	613.028	+	613.028i	0.717831	+	0.717831i
$855$	104.650	−	156.620i	0.122398	−	0.183181i
$856$	305.769	+	60.8213i	0.357207	+	0.0710529i
$857$	370.058	+	553.831i	0.431806	+	0.646244i	0.982019	−	0.188780i	$-0.0604535\pi$
$857$	370.058	+	553.831i	0.431806	+	0.646244i	−0.550213	+	0.835024i	$0.685453\pi$
$858$	8.58754	+	20.7322i	0.0100088	+	0.0241634i
$859$	−1281.10	+	530.649i	−1.49138	+	0.617752i	−0.971618	−	0.236556i	$-0.923981\pi$
$859$	−1281.10	+	530.649i	−1.49138	+	0.617752i	−0.519767	+	0.854308i	$0.673981\pi$
$860$	801.196	−	535.342i	0.931624	−	0.622491i
$861$	−27.1917	+	136.702i	−0.0315816	+	0.158771i
$862$	1918.53	+	1281.92i	2.22567	+	1.48714i
$863$	375.548	−	375.548i	0.435166	−	0.435166i	−0.455215	−	0.890381i	$-0.650438\pi$
$863$	375.548	−	375.548i	0.435166	−	0.435166i	0.890381	+	0.455215i	$0.150438\pi$
$864$	121.845	+	612.557i	0.141024	+	0.708978i
$865$	547.109	−	1320.84i	0.632496	−	1.52698i
$866$			286.613i			0.330962i
$867$		0			0
$868$	−520.802			−0.600002
$869$	−710.907	−	294.467i	−0.818075	−	0.338858i
$870$	−59.4773	+	11.8308i	−0.0683647	+	0.0135986i
$871$	−93.6384	−	93.6384i	−0.107507	−	0.107507i
$872$	−36.5039	+	54.6320i	−0.0418623	+	0.0626513i
$873$	201.145	+	40.0101i	0.230406	+	0.0458306i
$874$	40.5941	+	60.7534i	0.0464464	+	0.0695119i
$875$	349.249	+	843.160i	0.399141	+	0.963612i
$876$	−236.632	+	98.0161i	−0.270128	+	0.111891i
$877$	206.666	−	138.090i	0.235652	−	0.157457i	−0.432138	−	0.901808i	$-0.642241\pi$
$877$	206.666	−	138.090i	0.235652	−	0.157457i	0.667789	+	0.744350i	$0.267241\pi$
$878$	21.8396	−	109.795i	0.0248743	−	0.125052i
$879$	52.0300	+	34.7653i	0.0591922	+	0.0395510i
$880$	−457.768	+	457.768i	−0.520191	+	0.520191i
$881$	28.5729	+	143.646i	0.0324324	+	0.163048i	0.993607	−	0.112891i	$-0.0360111\pi$
$881$	28.5729	+	143.646i	0.0324324	+	0.163048i	−0.961175	+	0.275939i	$0.911011\pi$
$882$	−122.631	+	296.057i	−0.139037	+	0.335665i
$883$			322.505i			0.365237i	0.983184	+	0.182619i	$0.0584574\pi$
$883$			322.505i			0.365237i	−0.983184	+	0.182619i	$0.941543\pi$
$884$		0			0
$885$	179.173			0.202455
$886$	1773.64	+	734.666i	2.00185	+	0.829194i
$887$	−61.6470	+	12.2623i	−0.0695005	+	0.0138245i	−0.229718	−	0.973257i	$-0.573780\pi$
$887$	−61.6470	+	12.2623i	−0.0695005	+	0.0138245i	0.160218	+	0.987082i	$0.448780\pi$
$888$	47.9552	+	47.9552i	0.0540037	+	0.0540037i
$889$	520.351	−	778.760i	0.585322	−	0.875996i
$890$	2071.95	+	412.136i	2.32803	+	0.463074i
$891$	285.391	+	427.118i	0.320304	+	0.479369i
$892$	−718.221	−	1733.94i	−0.805180	−	1.94388i
$893$	−204.565	+	84.7337i	−0.229077	+	0.0948866i
$894$	−91.6419	+	61.2332i	−0.102508	+	0.0684935i
$895$	−395.019	+	1985.89i	−0.441362	+	2.21888i
$896$	−705.674	−	471.516i	−0.787582	−	0.526246i
$897$	5.56914	−	5.56914i	0.00620863	−	0.00620863i
$898$	260.944	+	1311.86i	0.290584	+	1.46086i
$899$	−15.0852	+	36.4189i	−0.0167800	+	0.0405104i
$900$			1700.15i			1.88905i
$901$		0			0
$902$	−533.932			−0.591942
$903$	136.999	+	56.7469i	0.151715	+	0.0628426i
$904$	−209.727	+	41.7173i	−0.231999	+	0.0461474i
$905$	−1710.95	−	1710.95i	−1.89055	−	1.89055i
$906$	179.546	−	268.709i	0.198174	−	0.296588i
$907$	−215.586	−	42.8827i	−0.237691	−	0.0472797i	0.0748072	−	0.997198i	$-0.476166\pi$
$907$	−215.586	−	42.8827i	−0.237691	−	0.0472797i	−0.312498	+	0.949918i	$0.601166\pi$
$908$	−278.112	−	416.225i	−0.306291	−	0.458397i
$909$	−24.5832	−	59.3490i	−0.0270442	−	0.0652904i
$910$	199.272	−	82.5412i	0.218980	−	0.0907046i
$911$	−420.193	+	280.764i	−0.461244	+	0.308193i	−0.764394	−	0.644750i	$-0.776962\pi$
$911$	−420.193	+	280.764i	−0.461244	+	0.308193i	0.303150	+	0.952943i	$0.401962\pi$
$912$	−4.45180	+	22.3807i	−0.00488135	+	0.0245402i
$913$	797.933	+	533.162i	0.873968	+	0.583967i
$914$	571.150	−	571.150i	0.624890	−	0.624890i
$915$	46.4050	+	233.294i	0.0507158	+	0.254966i
$916$	−714.790	+	1725.66i	−0.780338	+	1.88390i
$917$		−	1345.66i		−	1.46746i
$918$		0			0
$919$	−930.196			−1.01218			−0.506091	−	0.862480i	$-0.668910\pi$
$919$	−930.196			−1.01218			−0.506091	+	0.862480i	$0.668910\pi$
$920$	−224.443	−	92.9674i	−0.243960	−	0.101052i
$921$	127.249	−	25.3114i	0.138164	−	0.0274825i
$922$	−966.431	−	966.431i	−1.04819	−	1.04819i
$923$	66.5111	−	99.5409i	0.0720597	−	0.107845i
$924$	261.058	+	51.9277i	0.282531	+	0.0561988i
$925$	−519.078	−	776.855i	−0.561166	−	0.839844i
$926$	−93.5798	−	225.922i	−0.101058	−	0.243976i
$927$	−320.288	+	132.667i	−0.345510	+	0.143115i
$928$	−113.175	+	75.6213i	−0.121956	+	0.0814885i
$929$	−223.893	+	1125.58i	−0.241004	+	1.21161i	0.650822	+	0.759230i	$0.274424\pi$
$929$	−223.893	+	1125.58i	−0.241004	+	1.21161i	−0.891826	+	0.452378i	$0.850576\pi$
$930$	−210.825	−	140.869i	−0.226694	−	0.151472i
$931$	−25.2457	+	25.2457i	−0.0271167	+	0.0271167i
$932$	−282.277	−	1419.10i	−0.302872	−	1.52264i
$933$	−103.545	+	249.980i	−0.110981	+	0.267932i
$934$			249.650i			0.267291i
$935$		0			0
$936$	33.2228			0.0354944
$937$	1249.07	+	517.380i	1.33305	+	0.552166i	0.931523	−	0.363682i	$-0.118481\pi$
$937$	1249.07	+	517.380i	1.33305	+	0.552166i	0.401524	+	0.915848i	$0.368481\pi$
$938$	−2733.68	+	543.763i	−2.91437	+	0.579704i
$939$	226.691	+	226.691i	0.241418	+	0.241418i
$940$	1813.55	−	2714.17i	1.92931	−	2.88741i
$941$	−1804.40	−	358.917i	−1.91753	−	0.381421i	−0.917661	−	0.397365i	$-0.869925\pi$
$941$	−1804.40	−	358.917i	−1.91753	−	0.381421i	−0.999873	+	0.0159438i	$0.994925\pi$
$942$	−49.2222	−	73.6663i	−0.0522529	−	0.0782020i
$943$	71.7133	+	173.131i	0.0760480	+	0.183596i
$944$	253.331	−	104.933i	0.268359	−	0.111158i
$945$	−738.783	+	493.639i	−0.781781	+	0.522370i
$946$	−110.821	+	557.136i	−0.117147	+	0.588938i
$947$	32.7188	+	21.8620i	0.0345499	+	0.0230855i	0.572725	−	0.819747i	$-0.305886\pi$
$947$	32.7188	+	21.8620i	0.0345499	+	0.0230855i	−0.538175	+	0.842833i	$0.680886\pi$
$948$	282.745	−	282.745i	0.298255	−	0.298255i
$949$	−13.4520	−	67.6275i	−0.0141749	−	0.0712619i
$950$	−128.629	+	310.538i	−0.135399	+	0.326882i
$951$			113.017i			0.118840i
$952$		0			0
$953$	183.445			0.192492			0.0962458	−	0.995358i	$-0.469317\pi$
$953$	183.445			0.192492			0.0962458	+	0.995358i	$0.469317\pi$
$954$	−1401.44	−	580.495i	−1.46901	−	0.608485i
$955$	1043.86	−	207.637i	1.09305	−	0.217421i
$956$	1199.89	+	1199.89i	1.25511	+	1.25511i
$957$	11.1929	−	16.7513i	0.0116958	−	0.0175040i
$958$	−1366.95	−	271.904i	−1.42688	−	0.283825i
$959$	−755.412	−	1130.55i	−0.787708	−	1.17889i
$960$	−235.345	−	568.173i	−0.245151	−	0.591847i
$961$	735.574	−	304.685i	0.765426	−	0.317050i
$962$	−67.3125	+	44.9768i	−0.0699714	+	0.0467534i
$963$	143.849	−	723.176i	0.149376	−	0.750962i
$964$	−1041.01	−	695.584i	−1.07989	−	0.721560i
$965$	−1808.97	+	1808.97i	−1.87458	+	1.87458i
$966$	−32.3402	−	162.585i	−0.0334785	−	0.168308i
$967$	−489.471	+	1181.69i	−0.506175	+	1.22201i	0.439894	+	0.898050i	$0.355016\pi$
$967$	−489.471	+	1181.69i	−0.506175	+	1.22201i	−0.946069	+	0.323965i	$0.894984\pi$
$968$		−	196.715i		−	0.203218i
$969$		0			0
$970$	−597.751			−0.616238
$971$	−844.437	−	349.777i	−0.869657	−	0.360224i	−0.0971803	−	0.995267i	$-0.530982\pi$
$971$	−844.437	−	349.777i	−0.869657	−	0.360224i	−0.772477	+	0.635043i	$0.780982\pi$
$972$	−904.117	+	179.840i	−0.930161	+	0.185021i
$973$	−997.319	−	997.319i	−1.02499	−	1.02499i
$974$	879.884	−	1316.84i	0.903371	−	1.35199i
$975$	35.5346	+	7.06828i	0.0364458	+	0.00724952i
$976$	202.240	+	302.674i	0.207214	+	0.310117i
$977$	169.210	+	408.510i	0.173194	+	0.418126i	0.986511	−	0.163694i	$-0.0523408\pi$
$977$	169.210	+	408.510i	0.173194	+	0.418126i	−0.813318	+	0.581820i	$0.802341\pi$
$978$	−362.961	+	150.343i	−0.371126	+	0.153725i
$979$	−583.546	+	389.913i	−0.596063	+	0.398277i
$980$	102.686	−	516.238i	0.104782	−	0.526773i
$981$	129.210	+	86.3356i	0.131713	+	0.0880078i
$982$	−1046.98	+	1046.98i	−1.06617	+	1.06617i
$983$	−129.820	−	652.647i	−0.132065	−	0.663934i	−0.988929	−	0.148391i	$-0.952590\pi$
$983$	−129.820	−	652.647i	−0.132065	−	0.663934i	0.856864	−	0.515542i	$-0.172410\pi$
$984$	23.9459	−	57.8106i	0.0243353	−	0.0587506i
$985$		−	928.713i		−	0.942856i
$986$		0			0
$987$	502.343			0.508959
$988$	15.1635	+	6.28094i	0.0153477	+	0.00635723i
$989$	195.540	−	38.8953i	0.197714	−	0.0393279i
$990$	−1157.59	−	1157.59i	−1.16928	−	1.16928i
$991$	869.394	−	1301.14i	0.877289	−	1.31296i	−0.0716278	−	0.997431i	$-0.522819\pi$
$991$	869.394	−	1301.14i	0.877289	−	1.31296i	0.948917	−	0.315525i	$-0.102181\pi$
$992$	−558.185	−	111.030i	−0.562687	−	0.111925i
$993$	71.6854	+	107.285i	0.0721908	+	0.108041i
$994$	−964.271	−	2327.96i	−0.970092	−	2.34201i
$995$	−2194.64	+	909.048i	−2.20566	+	0.913616i
$996$	−414.648	+	277.059i	−0.416313	+	0.278171i
$997$	300.460	−	1510.52i	0.301364	−	1.51506i	−0.472284	−	0.881446i	$-0.656570\pi$
$997$	300.460	−	1510.52i	0.301364	−	1.51506i	0.773649	−	0.633615i	$-0.218430\pi$
$998$	1276.36	+	852.835i	1.27891	+	0.854544i
$999$	235.817	−	235.817i	0.236053	−	0.236053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.d.40.1		8
17.2	even	8		289.3.e.i.75.1		8
17.3	odd	16	inner	289.3.e.d.224.1		8
17.4	even	4		289.3.e.l.249.1		8
17.5	odd	16		289.3.e.l.65.1		8
17.6	odd	16		17.3.e.a.12.1	yes	8
17.7	odd	16		289.3.e.m.158.1		8
17.8	even	8		289.3.e.c.214.1		8
17.9	even	8		17.3.e.a.10.1	✓	8
17.10	odd	16		289.3.e.i.158.1		8
17.11	odd	16		289.3.e.c.131.1		8
17.12	odd	16		289.3.e.k.65.1		8
17.13	even	4		289.3.e.k.249.1		8
17.14	odd	16		289.3.e.b.224.1		8
17.15	even	8		289.3.e.m.75.1		8
17.16	even	2		289.3.e.b.40.1		8
51.23	even	16		153.3.p.b.46.1		8
51.26	odd	8		153.3.p.b.10.1		8
68.23	even	16		272.3.bh.c.97.1		8
68.43	odd	8		272.3.bh.c.129.1		8
85.9	even	8		425.3.u.b.401.1		8
85.23	even	16		425.3.t.a.199.1		8
85.43	odd	8		425.3.t.c.299.1		8
85.57	even	16		425.3.t.c.199.1		8
85.74	odd	16		425.3.u.b.301.1		8
85.77	odd	8		425.3.t.a.299.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.10.1	✓	8	17.9	even	8
17.3.e.a.12.1	yes	8	17.6	odd	16
153.3.p.b.10.1		8	51.26	odd	8
153.3.p.b.46.1		8	51.23	even	16
272.3.bh.c.97.1		8	68.23	even	16
272.3.bh.c.129.1		8	68.43	odd	8
289.3.e.b.40.1		8	17.16	even	2
289.3.e.b.224.1		8	17.14	odd	16
289.3.e.c.131.1		8	17.11	odd	16
289.3.e.c.214.1		8	17.8	even	8
289.3.e.d.40.1		8	1.1	even	1	trivial
289.3.e.d.224.1		8	17.3	odd	16	inner
289.3.e.i.75.1		8	17.2	even	8
289.3.e.i.158.1		8	17.10	odd	16
289.3.e.k.65.1		8	17.12	odd	16
289.3.e.k.249.1		8	17.13	even	4
289.3.e.l.65.1		8	17.5	odd	16
289.3.e.l.249.1		8	17.4	even	4
289.3.e.m.75.1		8	17.15	even	8
289.3.e.m.158.1		8	17.7	odd	16
425.3.t.a.199.1		8	85.23	even	16
425.3.t.a.299.1		8	85.77	odd	8
425.3.t.c.199.1		8	85.57	even	16
425.3.t.c.299.1		8	85.43	odd	8
425.3.u.b.301.1		8	85.74	odd	16
425.3.u.b.401.1		8	85.9	even	8

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.79690 - 1.15851i) q^{2} +(-0.796897 + 0.158513i) q^{3} +(3.65205 + 3.65205i) q^{4} +(-4.46088 + 6.67619i) q^{5} +(2.41248 + 0.479872i) q^{6} +(4.36370 + 6.53073i) q^{7} +(-1.34942 - 3.25778i) q^{8} +(-7.70500 + 3.19151i) q^{9} +O(q^{10})\)	\(q+(-2.79690 - 1.15851i) q^{2} +(-0.796897 + 0.158513i) q^{3} +(3.65205 + 3.65205i) q^{4} +(-4.46088 + 6.67619i) q^{5} +(2.41248 + 0.479872i) q^{6} +(4.36370 + 6.53073i) q^{7} +(-1.34942 - 3.25778i) q^{8} +(-7.70500 + 3.19151i) q^{9} +(20.2111 - 13.5046i) q^{10} +(-1.57545 + 7.92030i) q^{11} +(-3.48921 - 2.33141i) q^{12} +(0.798835 - 0.798835i) q^{13} +(-4.63887 - 23.3212i) q^{14} +(2.49661 - 6.02734i) q^{15} -9.98414i q^{16} +25.2475 q^{18} +(2.59882 + 1.07647i) q^{19} +(-40.6732 + 8.09040i) q^{20} +(-4.51262 - 4.51262i) q^{21} +(13.5821 - 20.3271i) q^{22} +(-8.41543 - 1.67393i) q^{23} +(1.59175 + 2.38222i) q^{24} +(-15.1049 - 36.4664i) q^{25} +(-3.15972 + 1.30880i) q^{26} +(11.7144 - 7.82730i) q^{27} +(-7.91414 + 39.7870i) q^{28} +(2.55301 + 1.70587i) q^{29} +(-13.9655 + 13.9655i) q^{30} +(2.50461 + 12.5915i) q^{31} +(-16.9644 + 40.9557i) q^{32} -6.56139i q^{33} -63.0663 q^{35} +(-39.7946 - 16.4835i) q^{36} +(23.2161 - 4.61798i) q^{37} +(-6.02153 - 6.02153i) q^{38} +(-0.509964 + 0.763215i) q^{39} +(27.7692 + 5.52363i) q^{40} +(-12.1338 - 18.1595i) q^{41} +(7.39341 + 17.8493i) q^{42} +(-21.4671 + 8.89197i) q^{43} +(-34.6790 + 23.1717i) q^{44} +(13.0640 - 65.6770i) q^{45} +(21.5978 + 14.4312i) q^{46} +(-55.6597 + 55.6597i) q^{47} +(1.58261 + 7.95633i) q^{48} +(-4.85715 + 11.7262i) q^{49} +119.492i q^{50} +5.83478 q^{52} +(-55.5080 - 22.9922i) q^{53} +(-41.8320 + 8.32089i) q^{54} +(-45.8495 - 45.8495i) q^{55} +(15.3873 - 23.0287i) q^{56} +(-2.24162 - 0.445887i) q^{57} +(-5.16424 - 7.72882i) q^{58} +(10.5100 + 25.3733i) q^{59} +(31.1299 - 12.8944i) q^{60} +(-30.3155 + 20.2562i) q^{61} +(7.58231 - 38.1189i) q^{62} +(-54.4652 - 36.3925i) q^{63} +(66.6561 - 66.6561i) q^{64} +(1.76966 + 8.89668i) q^{65} +(-7.60145 + 18.3515i) q^{66} -117.219i q^{67} +6.97157 q^{69} +(176.390 + 73.0632i) q^{70} +(103.934 - 20.6737i) q^{71} +(20.7945 + 20.7945i) q^{72} +(33.9091 - 50.7486i) q^{73} +(-70.2832 - 13.9802i) q^{74} +(17.8174 + 26.6657i) q^{75} +(5.55971 + 13.4223i) q^{76} +(-58.6001 + 24.2730i) q^{77} +(2.31051 - 1.54383i) q^{78} +(-18.5894 + 93.4553i) q^{79} +(66.6560 + 44.5381i) q^{80} +(44.9799 - 44.9799i) q^{81} +(12.8989 + 64.8474i) q^{82} +(45.4770 - 109.791i) q^{83} -32.9607i q^{84} +70.3428 q^{86} +(-2.30489 - 0.954715i) q^{87} +(27.9285 - 5.55533i) q^{88} +(61.4534 + 61.4534i) q^{89} +(-112.626 + 168.557i) q^{90} +(8.70285 + 1.73111i) q^{91} +(-24.6203 - 36.8469i) q^{92} +(-3.99184 - 9.63715i) q^{93} +(220.157 - 91.1920i) q^{94} +(-18.7797 + 12.5482i) q^{95} +(7.02689 - 35.3266i) q^{96} +(-20.4467 - 13.6621i) q^{97} +(27.1699 - 27.1699i) q^{98} +(-13.1389 - 66.0539i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{3} + 32 q^{6} + 8 q^{7} - 40 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^3 + 32 * q^6 + 8 * q^7 - 40 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{3} + 32 q^{6} + 8 q^{7} - 40 q^{8} + 8 q^{9} + 32 q^{10} - 24 q^{11} - 8 q^{12} - 16 q^{13} + 24 q^{14} + 56 q^{18} - 48 q^{19} - 80 q^{20} + 64 q^{21} + 48 q^{22} + 24 q^{23} - 120 q^{24} - 32 q^{25} - 48 q^{26} + 80 q^{27} - 120 q^{28} + 16 q^{29} - 16 q^{30} - 40 q^{31} - 88 q^{32} - 160 q^{35} - 24 q^{36} + 16 q^{37} + 120 q^{38} + 160 q^{39} + 48 q^{40} - 40 q^{41} + 128 q^{42} - 112 q^{43} - 64 q^{44} + 128 q^{45} - 8 q^{46} - 192 q^{47} - 96 q^{48} - 80 q^{49} - 384 q^{52} - 128 q^{53} - 168 q^{54} - 224 q^{55} - 264 q^{56} - 80 q^{57} + 368 q^{58} - 120 q^{59} + 48 q^{60} - 96 q^{61} + 120 q^{62} - 184 q^{63} + 64 q^{64} - 96 q^{66} + 240 q^{69} + 480 q^{70} + 280 q^{71} - 40 q^{72} + 208 q^{73} - 224 q^{74} - 136 q^{75} + 160 q^{76} + 80 q^{77} - 64 q^{78} + 24 q^{79} + 240 q^{80} + 424 q^{81} + 272 q^{82} + 336 q^{83} + 832 q^{86} - 80 q^{87} + 72 q^{88} - 160 q^{89} - 384 q^{90} - 248 q^{92} - 208 q^{93} + 432 q^{94} - 192 q^{95} - 88 q^{96} + 176 q^{97} + 120 q^{98} - 216 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 32 * q^6 + 8 * q^7 - 40 * q^8 + 8 * q^9 + 32 * q^10 - 24 * q^11 - 8 * q^12 - 16 * q^13 + 24 * q^14 + 56 * q^18 - 48 * q^19 - 80 * q^20 + 64 * q^21 + 48 * q^22 + 24 * q^23 - 120 * q^24 - 32 * q^25 - 48 * q^26 + 80 * q^27 - 120 * q^28 + 16 * q^29 - 16 * q^30 - 40 * q^31 - 88 * q^32 - 160 * q^35 - 24 * q^36 + 16 * q^37 + 120 * q^38 + 160 * q^39 + 48 * q^40 - 40 * q^41 + 128 * q^42 - 112 * q^43 - 64 * q^44 + 128 * q^45 - 8 * q^46 - 192 * q^47 - 96 * q^48 - 80 * q^49 - 384 * q^52 - 128 * q^53 - 168 * q^54 - 224 * q^55 - 264 * q^56 - 80 * q^57 + 368 * q^58 - 120 * q^59 + 48 * q^60 - 96 * q^61 + 120 * q^62 - 184 * q^63 + 64 * q^64 - 96 * q^66 + 240 * q^69 + 480 * q^70 + 280 * q^71 - 40 * q^72 + 208 * q^73 - 224 * q^74 - 136 * q^75 + 160 * q^76 + 80 * q^77 - 64 * q^78 + 24 * q^79 + 240 * q^80 + 424 * q^81 + 272 * q^82 + 336 * q^83 + 832 * q^86 - 80 * q^87 + 72 * q^88 - 160 * q^89 - 384 * q^90 - 248 * q^92 - 208 * q^93 + 432 * q^94 - 192 * q^95 - 88 * q^96 + 176 * q^97 + 120 * q^98 - 216 * q^99

Introduction

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