LMFDB - Embedded newform 750.2.l.c.143.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			143.6
Character	$\chi$	$=$	750.143
Dual form			750.2.l.c.257.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.453990 - 0.891007i) q^{2} +(-1.69234 + 0.368756i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.439743 + 1.67530i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(2.72804 - 1.24812i) q^{9} +O(q^{10})$	\(q+(0.453990 - 0.891007i) q^{2} +(-1.69234 + 0.368756i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.439743 + 1.67530i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(2.72804 - 1.24812i) q^{9} +(-0.335657 + 0.109061i) q^{11} +(1.29306 + 1.15238i) q^{12} +(2.20817 - 1.12512i) q^{13} +(1.19166 + 3.66754i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.554059 - 3.49819i) q^{17} +(0.126420 - 2.99734i) q^{18} +(3.84926 - 5.29805i) q^{19} +(3.60915 - 5.62020i) q^{21} +(-0.0552105 + 0.348585i) q^{22} +(6.98347 + 3.55825i) q^{23} +(1.61382 - 0.628956i) q^{24} -2.47829i q^{26} +(-4.15652 + 3.11823i) q^{27} +(3.80880 + 0.603255i) q^{28} +(5.05137 - 3.67003i) q^{29} +(-3.39184 - 2.46432i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.527829 - 0.308344i) q^{33} +(-3.36845 - 1.09448i) q^{34} +(-2.61325 - 1.47340i) q^{36} +(-2.20890 - 4.33521i) q^{37} +(-2.97307 - 5.83498i) q^{38} +(-3.32209 + 2.71836i) q^{39} +(8.06531 + 2.62058i) q^{41} +(-3.36911 - 5.76730i) q^{42} +(-5.16349 - 5.16349i) q^{43} +(0.285527 + 0.207447i) q^{44} +(6.34085 - 4.60690i) q^{46} +(4.22323 + 0.668895i) q^{47} +(0.172255 - 1.72346i) q^{48} -7.87088i q^{49} +(2.22763 + 5.71582i) q^{51} +(-2.20817 - 1.12512i) q^{52} +(0.688494 - 4.34698i) q^{53} +(0.891339 + 5.11913i) q^{54} +(2.26666 - 3.11979i) q^{56} +(-4.56057 + 10.3855i) q^{57} +(-0.976751 - 6.16696i) q^{58} +(-0.713107 + 2.19472i) q^{59} +(0.0451729 + 0.139028i) q^{61} +(-3.73559 + 1.90338i) q^{62} +(-4.03544 + 10.8422i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-0.0351078 - 0.610284i) q^{66} +(7.47829 - 1.18445i) q^{67} +(-2.50443 + 2.50443i) q^{68} +(-13.1305 - 3.44659i) q^{69} +(3.62303 + 4.98667i) q^{71} +(-2.49920 + 1.65951i) q^{72} +(4.74043 - 9.30362i) q^{73} -4.86552 q^{74} -6.54875 q^{76} +(0.617880 - 1.21266i) q^{77} +(0.913883 + 4.19411i) q^{78} +(-0.803169 - 1.10547i) q^{79} +(5.88439 - 6.80984i) q^{81} +(5.99652 - 5.99652i) q^{82} +(-5.77823 + 0.915181i) q^{83} +(-6.66824 + 0.383604i) q^{84} +(-6.94488 + 2.25653i) q^{86} +(-7.19529 + 8.07367i) q^{87} +(0.314463 - 0.160227i) q^{88} +(-0.633239 - 1.94891i) q^{89} +(-2.95327 + 9.08922i) q^{91} +(-1.22609 - 7.74123i) q^{92} +(6.64888 + 2.91971i) q^{93} +(2.51330 - 3.45926i) q^{94} +(-1.45742 - 0.935916i) q^{96} +(1.09907 - 6.93926i) q^{97} +(-7.01300 - 3.57330i) q^{98} +(-0.779562 + 0.716464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$-1$

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 $

$2$	0.453990	−	0.891007i	0.321020	−	0.630037i
$2$	0.453990	−	0.891007i	0.321020	−	0.630037i
$3$	−1.69234	+	0.368756i	−0.977074	+	0.212901i
$3$	−1.69234	+	0.368756i	−0.977074	+	0.212901i
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	−0.439743	+	1.67530i	−0.179524	+	0.683938i
$7$	−2.72680	+	2.72680i	−1.03063	+	1.03063i	−0.0311178	+	0.999516i	$0.509907\pi$
$7$	−2.72680	+	2.72680i	−1.03063	+	1.03063i	−0.999516	+	0.0311178i	$0.990093\pi$
$8$	−0.987688	+	0.156434i	−0.349201	+	0.0553079i
$9$	2.72804	−	1.24812i	0.909346	−	0.416040i
$10$		0			0
$11$	−0.335657	+	0.109061i	−0.101204	+	0.0328833i	−0.359181	−	0.933268i	$-0.616944\pi$
$11$	−0.335657	+	0.109061i	−0.101204	+	0.0328833i	0.257977	+	0.966151i	$0.416944\pi$
$12$	1.29306	+	1.15238i	0.373275	+	0.332665i
$13$	2.20817	−	1.12512i	0.612437	−	0.312052i	−0.120119	−	0.992760i	$-0.538327\pi$
$13$	2.20817	−	1.12512i	0.612437	−	0.312052i	0.732555	+	0.680707i	$0.238327\pi$
$14$	1.19166	+	3.66754i	0.318483	+	0.980191i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−0.554059	−	3.49819i	−0.134379	−	0.848436i	−0.959135	−	0.282948i	$-0.908688\pi$
$17$	−0.554059	−	3.49819i	−0.134379	−	0.848436i	0.824756	−	0.565488i	$-0.191312\pi$
$18$	0.126420	−	2.99734i	0.0297975	−	0.706479i
$19$	3.84926	−	5.29805i	0.883080	−	1.21546i	−0.0924780	−	0.995715i	$-0.529479\pi$
$19$	3.84926	−	5.29805i	0.883080	−	1.21546i	0.975558	−	0.219741i	$-0.0705212\pi$
$20$		0			0
$21$	3.60915	−	5.62020i	0.787582	−	1.22643i
$22$	−0.0552105	+	0.348585i	−0.0117709	+	0.0743186i
$23$	6.98347	+	3.55825i	1.45615	+	0.741947i	0.989775	−	0.142638i	$-0.0455585\pi$
$23$	6.98347	+	3.55825i	1.45615	+	0.741947i	0.466378	+	0.884585i	$0.345559\pi$
$24$	1.61382	−	0.628956i	0.329420	−	0.128385i
$25$		0			0
$26$		−	2.47829i		−	0.486033i
$27$	−4.15652	+	3.11823i	−0.799923	+	0.600103i
$28$	3.80880	+	0.603255i	0.719796	+	0.114004i
$29$	5.05137	−	3.67003i	0.938015	−	0.681508i	−0.00992666	−	0.999951i	$-0.503160\pi$
$29$	5.05137	−	3.67003i	0.938015	−	0.681508i	0.947942	+	0.318443i	$0.103160\pi$
$30$		0			0
$31$	−3.39184	−	2.46432i	−0.609193	−	0.442604i	0.239937	−	0.970788i	$-0.422873\pi$
$31$	−3.39184	−	2.46432i	−0.609193	−	0.442604i	−0.849130	+	0.528184i	$0.822873\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.527829	−	0.308344i	0.0918832	−	0.0536759i
$34$	−3.36845	−	1.09448i	−0.577684	−	0.187701i
$35$		0			0
$36$	−2.61325	−	1.47340i	−0.435542	−	0.245567i
$37$	−2.20890	−	4.33521i	−0.363141	−	0.712704i	0.635073	−	0.772452i	$-0.280970\pi$
$37$	−2.20890	−	4.33521i	−0.363141	−	0.712704i	−0.998213	+	0.0597483i	$0.980970\pi$
$38$	−2.97307	−	5.83498i	−0.482296	−	0.946558i
$39$	−3.32209	+	2.71836i	−0.531960	+	0.435286i
$40$		0			0
$41$	8.06531	+	2.62058i	1.25959	+	0.409265i	0.861348	−	0.508015i	$-0.169621\pi$
$41$	8.06531	+	2.62058i	1.25959	+	0.409265i	0.398241	+	0.917281i	$0.369621\pi$
$42$	−3.36911	−	5.76730i	−0.519865	−	0.889913i
$43$	−5.16349	−	5.16349i	−0.787425	−	0.787425i	0.193647	−	0.981071i	$-0.437969\pi$
$43$	−5.16349	−	5.16349i	−0.787425	−	0.787425i	−0.981071	+	0.193647i	$0.937969\pi$
$44$	0.285527	+	0.207447i	0.0430448	+	0.0312738i
$45$		0			0
$46$	6.34085	−	4.60690i	0.934908	−	0.679250i
$47$	4.22323	+	0.668895i	0.616022	+	0.0975683i	0.456644	−	0.889649i	$-0.349051\pi$
$47$	4.22323	+	0.668895i	0.616022	+	0.0975683i	0.159378	+	0.987218i	$0.449051\pi$
$48$	0.172255	−	1.72346i	0.0248628	−	0.248761i
$49$		−	7.87088i		−	1.12441i
$50$		0			0
$51$	2.22763	+	5.71582i	0.311931	+	0.800375i
$52$	−2.20817	−	1.12512i	−0.306218	−	0.156026i
$53$	0.688494	−	4.34698i	0.0945719	−	0.597103i	−0.894200	−	0.447668i	$-0.852255\pi$
$53$	0.688494	−	4.34698i	0.0945719	−	0.597103i	0.988772	−	0.149435i	$-0.0477455\pi$
$54$	0.891339	+	5.11913i	0.121296	+	0.696626i
$55$		0			0
$56$	2.26666	−	3.11979i	0.302896	−	0.416900i
$57$	−4.56057	+	10.3855i	−0.604063	+	1.37560i
$58$	−0.976751	−	6.16696i	−0.128254	−	0.809762i
$59$	−0.713107	+	2.19472i	−0.0928386	+	0.285728i	−0.986684	−	0.162647i	$-0.947997\pi$
$59$	−0.713107	+	2.19472i	−0.0928386	+	0.285728i	0.893846	+	0.448375i	$0.147997\pi$
$60$		0			0
$61$	0.0451729	+	0.139028i	0.00578380	+	0.0178007i	0.953907	−	0.300103i	$-0.0970211\pi$
$61$	0.0451729	+	0.139028i	0.00578380	+	0.0178007i	−0.948123	+	0.317904i	$0.897021\pi$
$62$	−3.73559	+	1.90338i	−0.474420	+	0.241729i
$63$	−4.03544	+	10.8422i	−0.508418	+	1.36599i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	−0.0351078	−	0.610284i	−0.00432147	−	0.0751208i
$67$	7.47829	−	1.18445i	0.913619	−	0.144703i	0.318112	−	0.948053i	$-0.396951\pi$
$67$	7.47829	−	1.18445i	0.913619	−	0.144703i	0.595507	+	0.803350i	$0.296951\pi$
$68$	−2.50443	+	2.50443i	−0.303707	+	0.303707i
$69$	−13.1305	−	3.44659i	−1.58073	−	0.414920i
$70$		0			0
$71$	3.62303	+	4.98667i	0.429974	+	0.591809i	0.967947	−	0.251153i	$-0.0808098\pi$
$71$	3.62303	+	4.98667i	0.429974	+	0.591809i	−0.537973	+	0.842962i	$0.680810\pi$
$72$	−2.49920	+	1.65951i	−0.294534	+	0.195576i
$73$	4.74043	−	9.30362i	0.554825	−	1.08891i	−0.427898	−	0.903827i	$-0.640746\pi$
$73$	4.74043	−	9.30362i	0.554825	−	1.08891i	0.982724	−	0.185079i	$-0.0592542\pi$
$74$	−4.86552			−0.565605
$75$		0			0
$76$	−6.54875			−0.751193
$77$	0.617880	−	1.21266i	0.0704139	−	0.138195i
$78$	0.913883	+	4.19411i	0.103477	+	0.474890i
$79$	−0.803169	−	1.10547i	−0.0903636	−	0.124375i	0.761442	−	0.648234i	$-0.224492\pi$
$79$	−0.803169	−	1.10547i	−0.0903636	−	0.124375i	−0.851805	+	0.523859i	$0.824492\pi$
$80$		0			0
$81$	5.88439	−	6.80984i	0.653821	−	0.756649i
$82$	5.99652	−	5.99652i	0.662205	−	0.662205i
$83$	−5.77823	+	0.915181i	−0.634243	+	0.100454i	−0.465273	−	0.885167i	$-0.654044\pi$
$83$	−5.77823	+	0.915181i	−0.634243	+	0.100454i	−0.168969	+	0.985621i	$0.554044\pi$
$84$	−6.66824	+	0.383604i	−0.727565	+	0.0418546i
$85$		0			0
$86$	−6.94488	+	2.25653i	−0.748886	+	0.243328i
$87$	−7.19529	+	8.07367i	−0.771416	+	0.865588i
$88$	0.314463	−	0.160227i	0.0335219	−	0.0170803i
$89$	−0.633239	−	1.94891i	−0.0671232	−	0.206584i	0.911869	−	0.410481i	$-0.134639\pi$
$89$	−0.633239	−	1.94891i	−0.0671232	−	0.206584i	−0.978992	+	0.203897i	$0.934639\pi$
$90$		0			0
$91$	−2.95327	+	9.08922i	−0.309587	+	0.952809i
$92$	−1.22609	−	7.74123i	−0.127829	−	0.807079i
$93$	6.64888	+	2.91971i	0.689457	+	0.302759i
$94$	2.51330	−	3.45926i	0.259227	−	0.356795i
$95$		0			0
$96$	−1.45742	−	0.935916i	−0.148747	−	0.0955216i
$97$	1.09907	−	6.93926i	0.111594	−	0.704575i	−0.866928	−	0.498433i	$-0.833909\pi$
$97$	1.09907	−	6.93926i	0.111594	−	0.704575i	0.978522	−	0.206142i	$-0.0660910\pi$
$98$	−7.01300	−	3.57330i	−0.708420	−	0.360958i
$99$	−0.779562	+	0.716464i	−0.0783490	+	0.0720073i
$100$		0			0
$101$			9.58679i			0.953921i	0.878925	+	0.476961i	$0.158262\pi$
$101$			9.58679i			0.953921i	−0.878925	+	0.476961i	$0.841738\pi$
$102$	6.10416	+	0.610091i	0.604402	+	0.0604081i
$103$	6.57102	+	1.04075i	0.647462	+	0.102548i	0.471524	−	0.881853i	$-0.343704\pi$
$103$	6.57102	+	1.04075i	0.647462	+	0.102548i	0.175938	+	0.984401i	$0.443704\pi$
$104$	−2.00498	+	1.45670i	−0.196604	+	0.142841i
$105$		0			0
$106$	−3.56062	−	2.58694i	−0.345838	−	0.251266i
$107$	10.4337	+	10.4337i	1.00866	+	1.00866i	0.999962	+	0.00870186i	$0.00276992\pi$
$107$	10.4337	+	10.4337i	1.00866	+	1.00866i	0.00870186	+	0.999962i	$0.497230\pi$
$108$	4.96584	+	1.52985i	0.477838	+	0.147210i
$109$	10.5722	+	3.43511i	1.01263	+	0.329024i	0.767902	−	0.640568i	$-0.221301\pi$
$109$	10.5722	+	3.43511i	1.01263	+	0.329024i	0.244729	+	0.969592i	$0.421301\pi$
$110$		0			0
$111$	5.33685	+	6.52211i	0.506551	+	0.619051i
$112$	−1.75071	−	3.43597i	−0.165427	−	0.324668i
$113$	−0.799015	−	1.56816i	−0.0751650	−	0.147520i	0.850366	−	0.526192i	$-0.176381\pi$
$113$	−0.799015	−	1.56816i	−0.0751650	−	0.147520i	−0.925531	+	0.378672i	$0.876381\pi$
$114$	7.18313	+	8.77844i	0.672762	+	0.822176i
$115$		0			0
$116$	−5.93824	−	1.92945i	−0.551352	−	0.179145i
$117$	4.61969	−	5.82544i	0.427091	−	0.538562i
$118$	1.63176	+	1.63176i	0.150216	+	0.150216i
$119$	11.0497	+	8.02806i	1.01292	+	0.735931i
$120$		0			0
$121$	−8.79842	+	6.39242i	−0.799856	+	0.581129i
$122$	0.144383	+	0.0228680i	0.0130718	+	0.00207037i
$123$	−14.6156	−	1.46078i	−1.31784	−	0.131714i
$124$			4.19255i			0.376502i
$125$		0			0
$126$	7.82841	+	8.51786i	0.697410	+	0.758831i
$127$	−4.80592	−	2.44874i	−0.426457	−	0.217290i	0.227571	−	0.973762i	$-0.426922\pi$
$127$	−4.80592	−	2.44874i	−0.426457	−	0.217290i	−0.654027	+	0.756471i	$0.726922\pi$
$128$	0.156434	−	0.987688i	0.0138270	−	0.0873001i
$129$	10.6425	+	6.83432i	0.937016	+	0.601728i
$130$		0			0
$131$	10.2354	−	14.0878i	0.894273	−	1.23086i	−0.0779865	−	0.996954i	$-0.524849\pi$
$131$	10.2354	−	14.0878i	0.894273	−	1.23086i	0.972259	−	0.233906i	$-0.0751509\pi$
$132$	−0.559706	−	0.245782i	−0.0487161	−	0.0213926i
$133$	3.95056	+	24.9429i	0.342557	+	2.16282i
$134$	2.33973	−	7.20094i	0.202122	−	0.622066i
$135$		0			0
$136$	1.09448	+	3.36845i	0.0938505	+	0.288842i
$137$	−15.9727	+	8.13848i	−1.36464	+	0.695317i	−0.974279	−	0.225346i	$-0.927649\pi$
$137$	−15.9727	+	8.13848i	−1.36464	+	0.695317i	−0.390358	+	0.920663i	$0.627649\pi$
$138$	−9.03207	+	10.1347i	−0.768861	+	0.862721i
$139$	−17.1405	+	5.56927i	−1.45383	+	0.472379i	−0.926181	−	0.377080i	$-0.876928\pi$
$139$	−17.1405	+	5.56927i	−1.45383	+	0.472379i	−0.527654	+	0.849459i	$0.676928\pi$
$140$		0			0
$141$	−7.39381	+	0.425343i	−0.622671	+	0.0358204i
$142$	6.08797	−	0.964240i	0.510891	−	0.0809172i
$143$	−0.618480	+	0.618480i	−0.0517199	+	0.0517199i
$144$	0.344023	+	2.98021i	0.0286686	+	0.248351i
$145$		0			0
$146$	−6.13747	−	8.44751i	−0.507941	−	0.699121i
$147$	2.90243	+	13.3202i	0.239388	+	1.09863i
$148$	−2.20890	+	4.33521i	−0.181570	+	0.356352i
$149$	−4.64891			−0.380854			−0.190427	−	0.981701i	$-0.560987\pi$
$149$	−4.64891			−0.380854			−0.190427	+	0.981701i	$0.560987\pi$
$150$		0			0
$151$	−14.6548			−1.19259			−0.596295	−	0.802765i	$-0.703361\pi$
$151$	−14.6548			−1.19259			−0.596295	+	0.802765i	$0.703361\pi$
$152$	−2.97307	+	5.83498i	−0.241148	+	0.473279i
$153$	−5.87766	−	8.85167i	−0.475181	−	0.715615i
$154$	−0.799974	−	1.10107i	−0.0644637	−	0.0887267i
$155$		0			0
$156$	4.15188	+	1.08981i	0.332416	+	0.0872547i
$157$	3.17235	−	3.17235i	0.253181	−	0.253181i	−0.569093	−	0.822273i	$-0.692705\pi$
$157$	3.17235	−	3.17235i	0.253181	−	0.253181i	0.822273	+	0.569093i	$0.192705\pi$
$158$	−1.34961	+	0.213757i	−0.107369	+	0.0170056i
$159$	0.437806	+	7.61046i	0.0347203	+	0.603548i
$160$		0			0
$161$	−28.7452	+	9.33987i	−2.26544	+	0.736085i
$162$	−3.39616	−	8.33463i	−0.266827	−	0.654831i
$163$	9.64088	−	4.91227i	0.755132	−	0.384759i	−0.0336487	−	0.999434i	$-0.510713\pi$
$163$	9.64088	−	4.91227i	0.755132	−	0.384759i	0.788781	+	0.614675i	$0.210713\pi$
$164$	−2.62058	−	8.06531i	−0.204633	−	0.629795i
$165$		0			0
$166$	−1.80783	+	5.56392i	−0.140315	+	0.431844i
$167$	−2.62714	−	16.5871i	−0.203295	−	1.28355i	−0.852415	−	0.522866i	$-0.824863\pi$
$167$	−2.62714	−	16.5871i	−0.203295	−	1.28355i	0.649120	−	0.760686i	$-0.275137\pi$
$168$	−2.68553	+	6.11560i	−0.207193	+	0.471829i
$169$	−4.03108	+	5.54830i	−0.310083	+	0.426793i
$170$		0			0
$171$	3.88832	−	19.2576i	0.297347	−	1.47267i
$172$	−1.14233	+	7.21237i	−0.0871017	+	0.549938i
$173$	15.5207	+	7.90821i	1.18002	+	0.601250i	0.930204	−	0.367043i	$-0.119630\pi$
$173$	15.5207	+	7.90821i	1.18002	+	0.601250i	0.249816	+	0.968293i	$0.419630\pi$
$174$	3.92710	+	10.0764i	0.297713	+	0.763892i
$175$		0			0
$176$		−	0.352930i		−	0.0266031i
$177$	0.397506	−	3.97717i	0.0298784	−	0.298943i
$178$	−2.02397	−	0.320566i	−0.151703	−	0.0240274i
$179$	−5.94519	+	4.31943i	−0.444364	+	0.322849i	−0.787367	−	0.616485i	$-0.788556\pi$
$179$	−5.94519	+	4.31943i	−0.444364	+	0.322849i	0.343002	+	0.939334i	$0.388556\pi$
$180$		0			0
$181$	−0.543117	−	0.394597i	−0.0403695	−	0.0293302i	0.567418	−	0.823430i	$-0.307943\pi$
$181$	−0.543117	−	0.394597i	−0.0403695	−	0.0293302i	−0.607787	+	0.794100i	$0.707943\pi$
$182$	6.75780	+	6.75780i	0.500922	+	0.500922i
$183$	−0.127715	−	0.218625i	−0.00944098	−	0.0161612i
$184$	−7.45412	−	2.42199i	−0.549525	−	0.178552i
$185$		0			0
$186$	5.62001	−	4.59868i	0.412079	−	0.337192i
$187$	0.567491	+	1.11376i	0.0414991	+	0.0814465i
$188$	−1.94121	−	3.80983i	−0.141577	−	0.277861i
$189$	2.83122	−	19.8368i	0.205941	−	1.44291i
$190$		0			0
$191$	13.4008	+	4.35419i	0.969650	+	0.315058i	0.750675	−	0.660672i	$-0.229729\pi$
$191$	13.4008	+	4.35419i	0.969650	+	0.315058i	0.218975	+	0.975730i	$0.429729\pi$
$192$	−1.49556	+	0.873670i	−0.107933	+	0.0630517i
$193$	−2.89340	−	2.89340i	−0.208271	−	0.208271i	0.595261	−	0.803532i	$-0.297049\pi$
$193$	−2.89340	−	2.89340i	−0.208271	−	0.208271i	−0.803532	+	0.595261i	$0.797049\pi$
$194$	−5.68396	−	4.12964i	−0.408085	−	0.296491i
$195$		0			0
$196$	−6.36767	+	4.62638i	−0.454834	+	0.330456i
$197$	22.4605	+	3.55739i	1.60024	+	0.253454i	0.891839	−	0.452353i	$-0.149415\pi$
$197$	22.4605	+	3.55739i	1.60024	+	0.253454i	0.708405	+	0.705806i	$0.249415\pi$
$198$	0.284460	+	1.01986i	0.0202157	+	0.0724785i
$199$			6.31867i			0.447919i	0.974598	+	0.223959i	$0.0718983\pi$
$199$			6.31867i			0.447919i	−0.974598	+	0.223959i	$0.928102\pi$
$200$		0			0
$201$	−12.2191	+	4.76215i	−0.861866	+	0.335896i
$202$	8.54189	+	4.35231i	0.601006	+	0.306228i
$203$	−3.76662	+	23.7815i	−0.264365	+	1.66914i
$204$	3.31483	−	5.16187i	0.232084	−	0.361403i
$205$		0			0
$206$	3.91049	−	5.38233i	0.272457	−	0.375005i
$207$	23.4923	+	0.990845i	1.63283	+	0.0688685i
$208$	0.387690	+	2.44778i	0.0268815	+	0.169723i
$209$	−0.714216	+	2.19813i	−0.0494033	+	0.152048i
$210$		0			0
$211$	−1.28435	−	3.95283i	−0.0884185	−	0.272124i	0.897064	−	0.441900i	$-0.145696\pi$
$211$	−1.28435	−	3.95283i	−0.0884185	−	0.272124i	−0.985483	+	0.169776i	$0.945696\pi$
$212$	−3.92147	+	1.99809i	−0.269327	+	0.137229i
$213$	−7.97026	−	7.10313i	−0.546113	−	0.486699i
$214$	14.0333	−	4.55969i	0.959296	−	0.311694i
$215$		0			0
$216$	3.61755	−	3.73006i	0.246143	−	0.253798i
$217$	15.9686	−	2.52917i	1.08402	−	0.171691i
$218$	7.86037	−	7.86037i	0.532371	−	0.532371i
$219$	−4.59166	+	17.4930i	−0.310276	+	1.18206i
$220$		0			0
$221$	−5.15934	−	7.10123i	−0.347055	−	0.477680i
$222$	8.23412	−	1.79419i	0.552638	−	0.120418i
$223$	−6.97753	+	13.6942i	−0.467250	+	0.917030i	0.530349	+	0.847779i	$0.322061\pi$
$223$	−6.97753	+	13.6942i	−0.467250	+	0.917030i	−0.997599	+	0.0692509i	$0.977939\pi$
$224$	−3.85628			−0.257658
$225$		0			0
$226$	−1.75998			−0.117072
$227$	6.36747	−	12.4969i	0.422624	−	0.829445i	−0.577293	−	0.816537i	$-0.695891\pi$
$227$	6.36747	−	12.4969i	0.422624	−	0.829445i	0.999917	−	0.0129084i	$-0.00410898\pi$
$228$	11.0827	−	2.41489i	0.733971	−	0.159930i
$229$	−10.1878	−	14.0224i	−0.673232	−	0.926624i	0.326596	−	0.945164i	$-0.394098\pi$
$229$	−10.1878	−	14.0224i	−0.673232	−	0.926624i	−0.999828	+	0.0185396i	$0.994098\pi$
$230$		0			0
$231$	−0.598489	+	2.28008i	−0.0393777	+	0.150018i
$232$	−4.41506	+	4.41506i	−0.289863	+	0.289863i
$233$	2.43006	−	0.384884i	0.159199	−	0.0252146i	−0.0763263	−	0.997083i	$-0.524319\pi$
$233$	2.43006	−	0.384884i	0.159199	−	0.0252146i	0.235525	+	0.971868i	$0.424319\pi$
$234$	−3.09320	−	6.76087i	−0.202209	−	0.441972i
$235$		0			0
$236$	2.19472	−	0.713107i	0.142864	−	0.0464193i
$237$	1.76688	+	1.57466i	0.114771	+	0.102285i
$238$	12.1695	−	6.20067i	0.788831	−	0.401930i
$239$	−0.751883	−	2.31406i	−0.0486352	−	0.149684i	0.923790	−	0.382901i	$-0.125075\pi$
$239$	−0.751883	−	2.31406i	−0.0486352	−	0.149684i	−0.972425	+	0.233217i	$0.925075\pi$
$240$		0			0
$241$	0.500207	−	1.53948i	0.0322212	−	0.0991666i	−0.933653	−	0.358180i	$-0.883397\pi$
$241$	0.500207	−	1.53948i	0.0322212	−	0.0991666i	0.965874	+	0.259013i	$0.0833974\pi$
$242$	1.70129	+	10.7415i	0.109363	+	0.690493i
$243$	−7.44723	+	13.6945i	−0.477740	+	0.878501i
$244$	0.0859239	−	0.118264i	0.00550072	−	0.00757109i
$245$		0			0
$246$	−7.93691	+	12.3594i	−0.506039	+	0.788008i
$247$	2.53888	−	16.0299i	0.161545	−	1.01996i
$248$	3.73559	+	1.90338i	0.237210	+	0.120865i
$249$	9.44125	−	3.67955i	0.598315	−	0.233182i
$250$		0			0
$251$		−	24.7263i		−	1.56071i	−0.625335	−	0.780357i	$-0.715038\pi$
$251$		−	24.7263i		−	1.56071i	0.625335	−	0.780357i	$-0.284962\pi$
$252$	11.1435	−	3.10814i	0.701974	−	0.195794i
$253$	−2.73211	−	0.432724i	−0.171767	−	0.0272052i
$254$	−4.36369	+	3.17040i	−0.273802	+	0.198929i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−20.2470	−	20.2470i	−1.26297	−	1.26297i	−0.949646	−	0.313326i	$-0.898557\pi$
$257$	−20.2470	−	20.2470i	−1.26297	−	1.26297i	−0.313326	−	0.949646i	$-0.601443\pi$
$258$	10.9210	−	6.37978i	0.679912	−	0.397188i
$259$	17.8445	+	5.79802i	1.10880	+	0.360272i
$260$		0			0
$261$	9.19968	−	16.3167i	0.569446	−	1.00998i
$262$	−7.90558	−	15.5156i	−0.488408	−	0.958555i
$263$	1.36671	+	2.68232i	0.0842750	+	0.165399i	0.929298	−	0.369331i	$-0.120413\pi$
$263$	1.36671	+	2.68232i	0.0842750	+	0.165399i	−0.845023	+	0.534730i	$0.820413\pi$
$264$	−0.473094	+	0.387119i	−0.0291169	+	0.0238255i
$265$		0			0
$266$	24.0178	+	7.80385i	1.47262	+	0.478485i
$267$	1.79033	+	3.06471i	0.109566	+	0.187557i
$268$	−5.35387	−	5.35387i	−0.327039	−	0.327039i
$269$	−10.4918	−	7.62274i	−0.639697	−	0.464767i	0.220049	−	0.975489i	$-0.429378\pi$
$269$	−10.4918	−	7.62274i	−0.639697	−	0.464767i	−0.859746	+	0.510722i	$0.829378\pi$
$270$		0			0
$271$	13.7784	−	10.0106i	0.836981	−	0.608102i	−0.0845447	−	0.996420i	$-0.526944\pi$
$271$	13.7784	−	10.0106i	0.836981	−	0.608102i	0.921526	+	0.388317i	$0.126944\pi$
$272$	3.49819	+	0.554059i	0.212109	+	0.0335948i
$273$	1.64623	−	16.4711i	0.0996347	−	0.996876i
$274$			17.9265i			1.08298i
$275$		0			0
$276$	4.92959	+	12.6487i	0.296726	+	0.761361i
$277$	9.46812	+	4.82425i	0.568884	+	0.289861i	0.714677	−	0.699454i	$-0.246573\pi$
$277$	9.46812	+	4.82425i	0.568884	+	0.289861i	−0.145793	+	0.989315i	$0.546573\pi$
$278$	−2.81935	+	17.8007i	−0.169093	+	1.06761i
$279$	−12.3288	−	2.48932i	−0.738108	−	0.149032i
$280$		0			0
$281$	−16.4932	+	22.7009i	−0.983902	+	1.35422i	−0.0492011	+	0.998789i	$0.515668\pi$
$281$	−16.4932	+	22.7009i	−0.983902	+	1.35422i	−0.934701	+	0.355436i	$0.884332\pi$
$282$	−2.97774	+	6.78104i	−0.177322	+	0.403805i
$283$	−4.01611	−	25.3567i	−0.238733	−	1.50730i	−0.757755	−	0.652539i	$-0.773704\pi$
$283$	−4.01611	−	25.3567i	−0.238733	−	1.50730i	0.519022	−	0.854761i	$-0.326296\pi$
$284$	1.90474	−	5.86218i	0.113025	−	0.347856i
$285$		0			0
$286$	0.270286	+	0.831854i	0.0159823	+	0.0491886i
$287$	−29.1383	+	14.8467i	−1.71998	+	0.876372i
$288$	2.81157	+	1.04646i	0.165673	+	0.0616632i
$289$	4.23760	−	1.37688i	0.249271	−	0.0809930i
$290$		0			0
$291$	0.698888	+	12.1489i	0.0409696	+	0.712181i
$292$	−10.3131	+	1.63344i	−0.603531	+	0.0955899i
$293$	24.1559	−	24.1559i	1.41120	−	1.41120i	0.659495	−	0.751709i	$-0.270770\pi$
$293$	24.1559	−	24.1559i	1.41120	−	1.41120i	0.751709	−	0.659495i	$-0.229230\pi$
$294$	13.1861	+	3.46116i	0.769027	+	0.201859i
$295$		0			0
$296$	2.85988	+	3.93629i	0.166227	+	0.228792i
$297$	1.05509	−	1.49997i	0.0612223	−	0.0870370i
$298$	−2.11056	+	4.14221i	−0.122262	+	0.239952i
$299$	19.4242			1.12333
$300$		0			0
$301$	28.1596			1.62309
$302$	−6.65314	+	13.0575i	−0.382845	+	0.751376i
$303$	−3.53518	−	16.2241i	−0.203091	−	0.932051i
$304$	3.84926	+	5.29805i	0.220770	+	0.303864i
$305$		0			0
$306$	−10.5553	+	1.21846i	−0.603406	+	0.0696547i
$307$	−12.8970	+	12.8970i	−0.736071	+	0.736071i	−0.971815	−	0.235744i	$-0.924247\pi$
$307$	−12.8970	+	12.8970i	−0.736071	+	0.736071i	0.235744	+	0.971815i	$0.424247\pi$
$308$	−1.34424	+	0.212907i	−0.0765952	+	0.0121315i
$309$	−11.5042	+	0.661801i	−0.654451	+	0.0376485i
$310$		0			0
$311$	−15.4255	+	5.01205i	−0.874699	+	0.284207i	−0.711755	−	0.702428i	$-0.752099\pi$
$311$	−15.4255	+	5.01205i	−0.874699	+	0.284207i	−0.162945	+	0.986635i	$0.552099\pi$
$312$	2.85594	−	3.20458i	0.161686	−	0.181424i
$313$	−4.81228	+	2.45198i	−0.272006	+	0.138594i	−0.584674	−	0.811269i	$-0.698777\pi$
$313$	−4.81228	+	2.45198i	−0.272006	+	0.138594i	0.312668	+	0.949863i	$0.398777\pi$
$314$	−1.38637	−	4.26680i	−0.0782372	−	0.240789i
$315$		0			0
$316$	−0.422251	+	1.29956i	−0.0237535	+	0.0731057i
$317$	−1.34202	−	8.47316i	−0.0753752	−	0.475900i	−0.996284	−	0.0861233i	$-0.972552\pi$
$317$	−1.34202	−	8.47316i	−0.0753752	−	0.475900i	0.920909	−	0.389777i	$-0.127448\pi$
$318$	6.97973	+	3.06499i	0.391404	+	0.171876i
$319$	−1.29527	+	1.78278i	−0.0725210	+	0.0998166i
$320$		0			0
$321$	−21.5049	−	13.8099i	−1.20028	−	0.770793i
$322$	−4.72815	+	29.8523i	−0.263489	+	1.66361i
$323$	−20.6663	−	10.5300i	−1.14990	−	0.585905i
$324$	−8.96804	−	0.757846i	−0.498224	−	0.0421025i
$325$		0			0
$326$		−	10.8202i		−	0.599276i
$327$	−19.1584	−	1.91483i	−1.05946	−	0.105890i
$328$	−8.37596	−	1.32662i	−0.462485	−	0.0732504i
$329$	−13.3399	+	9.69197i	−0.735450	+	0.534336i
$330$		0			0
$331$	22.9895	+	16.7029i	1.26362	+	0.918073i	0.998929	−	0.0462607i	$-0.0147305\pi$
$331$	22.9895	+	16.7029i	1.26362	+	0.918073i	0.264690	+	0.964334i	$0.414731\pi$
$332$	4.13675	+	4.13675i	0.227034	+	0.227034i
$333$	−11.4368	−	9.06965i	−0.626734	−	0.497014i
$334$	−15.9719	−	5.18960i	−0.873946	−	0.283962i
$335$		0			0
$336$	4.22984	+	5.16925i	0.230757	+	0.282005i
$337$	2.15464	+	4.22871i	0.117371	+	0.230353i	0.942216	−	0.335005i	$-0.108738\pi$
$337$	2.15464	+	4.22871i	0.117371	+	0.230353i	−0.824846	+	0.565358i	$0.808738\pi$
$338$	3.11350	+	6.11059i	0.169352	+	0.332372i
$339$	1.93047	+	2.35921i	0.104849	+	0.128135i
$340$		0			0
$341$	1.40726	+	0.457245i	0.0762072	+	0.0247612i
$342$	−15.3934	−	12.2073i	−0.832380	−	0.660095i
$343$	2.37470	+	2.37470i	0.128222	+	0.128222i
$344$	5.90767	+	4.29217i	0.318520	+	0.231418i
$345$		0			0
$346$	14.0925	−	10.2388i	0.757620	−	0.550443i
$347$	−7.92843	−	1.25574i	−0.425620	−	0.0674116i	−0.0600500	−	0.998195i	$-0.519126\pi$
$347$	−7.92843	−	1.25574i	−0.425620	−	0.0674116i	−0.365570	+	0.930784i	$0.619126\pi$
$348$	10.7610	+	1.07553i	0.576851	+	0.0576545i
$349$		−	18.9234i		−	1.01295i	−0.862256	−	0.506474i	$-0.830949\pi$
$349$		−	18.9234i		−	1.01295i	0.862256	−	0.506474i	$-0.169051\pi$
$350$		0			0
$351$	−5.66994	+	11.5622i	−0.302639	+	0.617143i
$352$	−0.314463	−	0.160227i	−0.0167609	−	0.00854013i
$353$	0.739053	−	4.66620i	0.0393358	−	0.248357i	−0.960183	−	0.279371i	$-0.909874\pi$
$353$	0.739053	−	4.66620i	0.0393358	−	0.248357i	0.999519	+	0.0310149i	$0.00987393\pi$
$354$	−3.36322	−	2.15978i	−0.178753	−	0.114791i
$355$		0			0
$356$	−1.20449	+	1.65784i	−0.0638379	+	0.0878654i
$357$	−21.6602	−	9.51159i	−1.14638	−	0.503406i
$358$	1.14958	+	7.25818i	0.0607573	+	0.383607i
$359$	−4.67561	+	14.3900i	−0.246769	+	0.759478i	0.748571	+	0.663054i	$0.230740\pi$
$359$	−4.67561	+	14.3900i	−0.246769	+	0.759478i	−0.995340	+	0.0964232i	$0.969260\pi$
$360$		0			0
$361$	−7.38121	−	22.7170i	−0.388485	−	1.19563i
$362$	−0.598158	+	0.304777i	−0.0314385	+	0.0160187i
$363$	12.5327	−	14.0626i	0.657795	−	0.738097i
$364$	9.08922	−	2.95327i	0.476405	−	0.154793i
$365$		0			0
$366$	−0.252778	+	0.0145415i	−0.0132129	+	0.000760098i
$367$	−36.1791	+	5.73021i	−1.88853	+	0.299114i	−0.990140	−	0.140078i	$-0.955265\pi$
$367$	−36.1791	+	5.73021i	−1.88853	+	0.299114i	−0.898393	+	0.439193i	$0.855265\pi$
$368$	−5.54211	+	5.54211i	−0.288902	+	0.288902i
$369$	25.2733	−	2.91744i	1.31567	−	0.151876i
$370$		0			0
$371$	9.97595	+	13.7307i	0.517926	+	0.712864i
$372$	−1.54603	−	7.09522i	−0.0801577	−	0.367870i
$373$	1.00640	−	1.97517i	0.0521093	−	0.102270i	−0.863483	−	0.504377i	$-0.831722\pi$
$373$	1.00640	−	1.97517i	0.0521093	−	0.102270i	0.915593	+	0.402107i	$0.131722\pi$
$374$	1.25001			0.0646363
$375$		0			0
$376$	−4.27588			−0.220512
$377$	7.02506	−	13.7875i	0.361809	−	0.710090i
$378$	−16.3894	−	11.5283i	−0.842977	−	0.592954i
$379$	−4.15559	−	5.71968i	−0.213458	−	0.293800i	0.688839	−	0.724914i	$-0.258121\pi$
$379$	−4.15559	−	5.71968i	−0.213458	−	0.293800i	−0.902297	+	0.431114i	$0.858121\pi$
$380$		0			0
$381$	9.03625	+	2.37189i	0.462941	+	0.121516i
$382$	9.96347	−	9.96347i	0.509775	−	0.509775i
$383$	−13.7450	+	2.17700i	−0.702339	+	0.111240i	−0.497382	−	0.867532i	$-0.665705\pi$
$383$	−13.7450	+	2.17700i	−0.702339	+	0.111240i	−0.204957	+	0.978771i	$0.565705\pi$
$384$	0.0994751	+	1.72919i	0.00507632	+	0.0882425i
$385$		0			0
$386$	−3.89161	+	1.26446i	−0.198078	+	0.0643593i
$387$	−20.5309	−	7.64154i	−1.04364	−	0.388441i
$388$	−6.26000	+	3.18963i	−0.317803	+	0.161929i
$389$	4.65972	+	14.3411i	0.236257	+	0.727125i	0.996952	+	0.0780155i	$0.0248584\pi$
$389$	4.65972	+	14.3411i	0.236257	+	0.727125i	−0.760695	+	0.649110i	$0.775142\pi$
$390$		0			0
$391$	8.57820	−	26.4010i	0.433818	−	1.33515i
$392$	1.23128	+	7.77397i	0.0621888	+	0.392645i
$393$	−12.1268	+	27.6158i	−0.611719	+	1.39303i
$394$	13.3665	−	18.3974i	0.673395	−	0.926849i
$395$		0			0
$396$	1.03785	+	0.209552i	0.0521538	+	0.0105304i
$397$	−2.15808	+	13.6256i	−0.108311	+	0.683849i	0.872460	+	0.488686i	$0.162524\pi$
$397$	−2.15808	+	13.6256i	−0.108311	+	0.683849i	−0.980771	+	0.195163i	$0.937476\pi$
$398$	5.62998	+	2.86862i	0.282205	+	0.143791i
$399$	−15.8835	−	40.7551i	−0.795171	−	2.04031i
$400$		0			0
$401$			15.8196i			0.789991i	0.918683	+	0.394995i	$0.129254\pi$
$401$			15.8196i			0.789991i	−0.918683	+	0.394995i	$0.870746\pi$
$402$	−1.30423	+	13.0492i	−0.0650490	+	0.650836i
$403$	−10.2624	−	1.62541i	−0.511208	−	0.0809674i
$404$	7.75588	−	5.63497i	0.385869	−	0.280350i
$405$		0			0
$406$	19.4795	+	14.1527i	0.966750	+	0.702385i
$407$	1.21424	+	1.21424i	0.0601875	+	0.0601875i
$408$	−3.09436	−	5.29697i	−0.153194	−	0.262239i
$409$	5.65867	+	1.83861i	0.279803	+	0.0909136i	0.445557	−	0.895254i	$-0.353006\pi$
$409$	5.65867	+	1.83861i	0.279803	+	0.0909136i	−0.165754	+	0.986167i	$0.553006\pi$
$410$		0			0
$411$	24.0301	−	19.6631i	1.18532	−	0.969909i
$412$	−3.02037	−	5.92780i	−0.148803	−	0.292042i
$413$	−4.04005	−	7.92905i	−0.198798	−	0.390163i
$414$	11.5481	−	20.4820i	0.567559	−	1.00663i
$415$		0			0
$416$	2.35699	+	0.765834i	0.115561	+	0.0375481i
$417$	26.9538	−	15.7457i	1.31993	−	0.771073i
$418$	1.63430	+	1.63430i	0.0799363	+	0.0799363i
$419$	3.49605	+	2.54003i	0.170793	+	0.124088i	0.669898	−	0.742453i	$-0.266338\pi$
$419$	3.49605	+	2.54003i	0.170793	+	0.124088i	−0.499105	+	0.866542i	$0.666338\pi$
$420$		0			0
$421$	−20.2471	+	14.7103i	−0.986781	+	0.716939i	−0.959214	−	0.282681i	$-0.908776\pi$
$421$	−20.2471	+	14.7103i	−0.986781	+	0.716939i	−0.0275674	+	0.999620i	$0.508776\pi$
$422$	−4.10508	−	0.650182i	−0.199832	−	0.0316503i
$423$	12.3560	−	3.44634i	0.600770	−	0.167567i
$424$			4.40116i			0.213739i
$425$		0			0
$426$	−9.94736	+	3.87680i	−0.481951	+	0.187831i
$427$	−0.502279	−	0.255924i	−0.0243070	−	0.0123850i
$428$	2.30827	−	14.5738i	0.111574	−	0.704452i
$429$	0.818612	−	1.27475i	0.0395230	−	0.0615454i
$430$		0			0
$431$	4.11469	−	5.66339i	0.198198	−	0.272796i	−0.698337	−	0.715769i	$-0.746076\pi$
$431$	4.11469	−	5.66339i	0.198198	−	0.272796i	0.896535	+	0.442973i	$0.146076\pi$
$432$	−1.68117	−	4.91667i	−0.0808855	−	0.236553i
$433$	−1.54377	−	9.74698i	−0.0741889	−	0.468410i	−0.996613	−	0.0822322i	$-0.973795\pi$
$433$	−1.54377	−	9.74698i	−0.0741889	−	0.468410i	0.922424	−	0.386178i	$-0.126205\pi$
$434$	4.99607	−	15.3763i	0.239819	−	0.738087i
$435$		0			0
$436$	−3.43511	−	10.5722i	−0.164512	−	0.506315i
$437$	45.7330	−	23.3021i	2.18770	−	1.11469i
$438$	13.5018	+	12.0328i	0.645139	+	0.574951i
$439$	0.555271	−	0.180419i	0.0265016	−	0.00861091i	−0.295736	−	0.955270i	$-0.595565\pi$
$439$	0.555271	−	0.180419i	0.0265016	−	0.00861091i	0.322238	+	0.946659i	$0.395565\pi$
$440$		0			0
$441$	−9.82380	−	21.4721i	−0.467800	−	1.02248i
$442$	−8.66953	+	1.37312i	−0.412368	+	0.0653126i
$443$	−6.33032	+	6.33032i	−0.300763	+	0.300763i	−0.841312	−	0.540549i	$-0.818216\pi$
$443$	−6.33032	+	6.33032i	−0.300763	+	0.300763i	0.540549	+	0.841312i	$0.318216\pi$
$444$	2.13958	−	8.15120i	0.101540	−	0.386839i
$445$		0			0
$446$	9.03387	+	12.4341i	0.427766	+	0.588770i
$447$	7.86754	−	1.71431i	0.372122	−	0.0810842i
$448$	−1.75071	+	3.43597i	−0.0827134	+	0.162334i
$449$	18.3782			0.867322			0.433661	−	0.901076i	$-0.357221\pi$
$449$	18.3782			0.867322			0.433661	+	0.901076i	$0.357221\pi$
$450$		0			0
$451$	−2.99298			−0.140934
$452$	−0.799015	+	1.56816i	−0.0375825	+	0.0737598i
$453$	24.8009	−	5.40404i	1.16525	−	0.253904i
$454$	−8.24401	−	11.3469i	−0.386911	−	0.532537i
$455$		0			0
$456$	2.87977	−	10.9711i	0.134857	−	0.513769i
$457$	−24.7918	+	24.7918i	−1.15971	+	1.15971i	−0.175174	+	0.984537i	$0.556049\pi$
$457$	−24.7918	+	24.7918i	−1.15971	+	1.15971i	−0.984537	+	0.175174i	$0.943951\pi$
$458$	−17.1192	+	2.71142i	−0.799928	+	0.126696i
$459$	13.2111	+	12.8126i	0.616642	+	0.598042i
$460$		0			0
$461$	0.133994	−	0.0435374i	0.00624074	−	0.00202774i	−0.305895	−	0.952065i	$-0.598956\pi$
$461$	0.133994	−	0.0435374i	0.00624074	−	0.00202774i	0.312136	+	0.950038i	$0.398956\pi$
$462$	1.75985	+	1.56839i	0.0818758	+	0.0729681i
$463$	7.90552	−	4.02806i	0.367401	−	0.187200i	−0.260537	−	0.965464i	$-0.583899\pi$
$463$	7.90552	−	4.02806i	0.367401	−	0.187200i	0.627937	+	0.778264i	$0.283899\pi$
$464$	1.92945	+	5.93824i	0.0895725	+	0.275676i
$465$		0			0
$466$	0.760291	−	2.33993i	0.0352198	−	0.108395i
$467$	0.762590	+	4.81480i	0.0352885	+	0.222803i	0.999030	−	0.0440349i	$-0.0140213\pi$
$467$	0.762590	+	4.81480i	0.0352885	+	0.222803i	−0.963742	+	0.266838i	$0.914021\pi$
$468$	−7.42827	−	0.313305i	−0.343372	−	0.0144825i
$469$	−17.1621	+	23.6216i	−0.792470	+	1.09074i
$470$		0			0
$471$	−4.19887	+	6.53851i	−0.193474	+	0.301279i
$472$	0.360998	−	2.27925i	0.0166163	−	0.104911i
$473$	2.29630	+	1.17002i	0.105584	+	0.0537977i
$474$	2.20518	−	0.859427i	0.101287	−	0.0394748i
$475$		0			0
$476$		−	13.6581i		−	0.626020i
$477$	−3.54732	−	12.7180i	−0.162420	−	0.582319i
$478$	−2.40319	−	0.380627i	−0.109919	−	0.0174095i
$479$	11.5308	−	8.37759i	0.526854	−	0.382782i	−0.292326	−	0.956319i	$-0.594429\pi$
$479$	11.5308	−	8.37759i	0.526854	−	0.382782i	0.819180	+	0.573537i	$0.194429\pi$
$480$		0			0
$481$	−9.75526	−	7.08761i	−0.444802	−	0.323167i
$482$	−1.14460	−	1.14460i	−0.0521349	−	0.0521349i
$483$	45.2025	−	26.4062i	2.05678	−	1.20152i
$484$	10.3432	+	3.36070i	0.470144	+	0.152759i
$485$		0			0
$486$	8.82090	+	12.8527i	0.400124	+	0.583010i
$487$	15.8349	+	31.0777i	0.717547	+	1.40827i	0.904749	+	0.425945i	$0.140058\pi$
$487$	15.8349	+	31.0777i	0.717547	+	1.40827i	−0.187202	+	0.982321i	$0.559942\pi$
$488$	−0.0663655	−	0.130250i	−0.00300422	−	0.00589612i
$489$	−14.5042	+	11.8684i	−0.655904	+	0.536706i
$490$		0			0
$491$	−5.09165	−	1.65438i	−0.229783	−	0.0746610i	0.191862	−	0.981422i	$-0.438547\pi$
$491$	−5.09165	−	1.65438i	−0.229783	−	0.0746610i	−0.421645	+	0.906761i	$0.638547\pi$
$492$	7.40904	+	12.6829i	0.334025	+	0.571789i
$493$	−15.6372	−	15.6372i	−0.704266	−	0.704266i
$494$	−13.1301	−	9.53958i	−0.590751	−	0.429206i
$495$		0			0
$496$	3.39184	−	2.46432i	0.152298	−	0.110651i
$497$	−23.4769	−	3.71838i	−1.05308	−	0.166792i
$498$	1.00773	−	10.0827i	0.0451576	−	0.451817i
$499$			8.93736i			0.400091i	0.979787	+	0.200046i	$0.0641090\pi$
$499$			8.93736i			0.400091i	−0.979787	+	0.200046i	$0.935891\pi$
$500$		0			0
$501$	10.5626	+	27.1023i	0.471903	+	1.21084i
$502$	−22.0313	−	11.2255i	−0.983307	−	0.501020i
$503$	−0.456793	+	2.88408i	−0.0203674	+	0.128595i	−0.995777	−	0.0918053i	$-0.970736\pi$
$503$	−0.456793	+	2.88408i	−0.0203674	+	0.128595i	0.975410	+	0.220400i	$0.0707363\pi$
$504$	2.28966	−	11.3400i	0.101990	−	0.505123i
$505$		0			0
$506$	−1.62591	+	2.23788i	−0.0722807	+	0.0994859i
$507$	4.77599	−	10.8761i	0.212109	−	0.483025i
$508$	0.843778	+	5.32741i	0.0374366	+	0.236365i
$509$	3.24395	−	9.98385i	0.143786	−	0.442527i	−0.853067	−	0.521801i	$-0.825260\pi$
$509$	3.24395	−	9.98385i	0.143786	−	0.442527i	0.996853	+	0.0792745i	$0.0252604\pi$
$510$		0			0
$511$	12.4429	+	38.2953i	0.550441	+	1.69408i
$512$	−0.891007	+	0.453990i	−0.0393773	+	0.0200637i
$513$	0.520992	+	34.0243i	0.0230023	+	1.50221i
$514$	−27.2321	+	8.84825i	−1.20116	+	0.390280i
$515$		0			0
$516$	−0.726395	−	12.6270i	−0.0319777	−	0.555874i
$517$	−1.49051	+	0.236073i	−0.0655524	+	0.0103825i
$518$	13.2673	−	13.2673i	0.582932	−	0.582932i
$519$	−29.1826	−	7.66004i	−1.28097	−	0.336238i
$520$		0			0
$521$	11.1471	+	15.3427i	0.488364	+	0.672175i	0.980085	−	0.198578i	$-0.0636322\pi$
$521$	11.1471	+	15.3427i	0.488364	+	0.672175i	−0.491722	+	0.870753i	$0.663632\pi$
$522$	−10.3617	−	15.6046i	−0.453520	−	0.682995i
$523$	−11.0596	+	21.7058i	−0.483604	+	0.949127i	0.512308	+	0.858802i	$0.328791\pi$
$523$	−11.0596	+	21.7058i	−0.483604	+	0.949127i	−0.995912	+	0.0903250i	$0.971209\pi$
$524$	−17.4135			−0.760714
$525$		0			0
$526$	3.01044			0.131261
$527$	−6.74137	+	13.2307i	−0.293659	+	0.576338i
$528$	0.130145	+	0.597278i	0.00566383	+	0.0259932i
$529$	22.5886	+	31.0905i	0.982111	+	1.35176i
$530$		0			0
$531$	0.793889	+	6.87732i	0.0344518	+	0.298450i
$532$	17.8571	−	17.8571i	0.774205	−	0.774205i
$533$	20.7580	−	3.28775i	0.899131	−	0.142408i
$534$	3.54347	−	0.203845i	0.153341	−	0.00882122i
$535$		0			0
$536$	−7.20094	+	2.33973i	−0.311033	+	0.101061i
$537$	8.46847	−	9.50227i	0.365441	−	0.410053i
$538$	−11.5551	+	5.88761i	−0.498175	+	0.253833i
$539$	0.858409	+	2.64191i	0.0369743	+	0.113795i
$540$		0			0
$541$	8.94591	−	27.5327i	0.384615	−	1.18372i	−0.552144	−	0.833749i	$-0.686190\pi$
$541$	8.94591	−	27.5327i	0.384615	−	1.18372i	0.936759	−	0.349974i	$-0.113810\pi$
$542$	−2.66425	−	16.8214i	−0.114439	−	0.722542i
$543$	1.06465	+	0.467516i	0.0456884	+	0.0200630i
$544$	2.08182	−	2.86537i	0.0892571	−	0.122852i
$545$		0			0
$546$	−13.9285	−	8.94453i	−0.596084	−	0.382790i
$547$	2.05584	−	12.9801i	0.0879014	−	0.554988i	−0.903955	−	0.427627i	$-0.859350\pi$
$547$	2.05584	−	12.9801i	0.0879014	−	0.554988i	0.991857	−	0.127360i	$-0.0406505\pi$
$548$	15.9727	+	8.13848i	0.682319	+	0.347659i
$549$	0.296757	+	0.322892i	0.0126653	+	0.0137807i
$550$		0			0
$551$		−	40.8893i		−	1.74194i
$552$	13.5080	+	1.35009i	0.574940	+	0.0574635i
$553$	5.20447	+	0.824307i	0.221317	+	0.0350531i
$554$	8.59687	−	6.24599i	0.365246	−	0.265367i
$555$		0			0
$556$	14.5805	+	10.5934i	0.618353	+	0.449260i
$557$	24.6270	+	24.6270i	1.04348	+	1.04348i	0.999011	+	0.0444707i	$0.0141601\pi$
$557$	24.6270	+	24.6270i	1.04348	+	1.04348i	0.0444707	+	0.999011i	$0.485840\pi$
$558$	−7.81518	+	9.85495i	−0.330843	+	0.417193i
$559$	−17.2114	−	5.59233i	−0.727966	−	0.236530i
$560$		0			0
$561$	−1.37110	−	1.67560i	−0.0578877	−	0.0707441i
$562$	12.7389	+	25.0016i	0.537359	+	1.05463i
$563$	−4.44165	−	8.71723i	−0.187193	−	0.367388i	0.778269	−	0.627931i	$-0.216098\pi$
$563$	−4.44165	−	8.71723i	−0.187193	−	0.367388i	−0.965462	+	0.260544i	$0.916098\pi$
$564$	4.69008	+	5.73171i	0.197488	+	0.241348i
$565$		0			0
$566$	−24.4163	−	7.93332i	−1.02629	−	0.333462i
$567$	2.52353	+	34.6146i	0.105978	+	1.45368i
$568$	−4.35851	−	4.35851i	−0.182879	−	0.182879i
$569$	−8.66014	−	6.29196i	−0.363052	−	0.263773i	0.391272	−	0.920275i	$-0.372035\pi$
$569$	−8.66014	−	6.29196i	−0.363052	−	0.263773i	−0.754324	+	0.656502i	$0.772035\pi$
$570$		0			0
$571$	12.5798	−	9.13980i	0.526450	−	0.382489i	−0.292578	−	0.956242i	$-0.594513\pi$
$571$	12.5798	−	9.13980i	0.526450	−	0.382489i	0.819028	+	0.573753i	$0.194513\pi$
$572$	0.863895	+	0.136828i	0.0361213	+	0.00572105i
$573$	−24.2844	−	2.42715i	−1.01450	−	0.101396i
$574$			32.7026i			1.36498i
$575$		0			0
$576$	2.20883	−	2.03004i	0.0920345	−	0.0845852i
$577$	13.2712	+	6.76199i	0.552485	+	0.281505i	0.707863	−	0.706350i	$-0.249659\pi$
$577$	13.2712	+	6.76199i	0.552485	+	0.281505i	−0.155378	+	0.987855i	$0.549659\pi$
$578$	0.697022	−	4.40082i	0.0289923	−	0.183050i
$579$	5.96357	+	3.82966i	0.247837	+	0.159155i
$580$		0			0
$581$	13.2606	−	18.2516i	0.550140	−	0.757203i
$582$	11.1420	+	4.89277i	0.461852	+	0.202812i
$583$	0.242990	+	1.53418i	0.0100636	+	0.0635392i
$584$	−3.22666	+	9.93064i	−0.133520	+	0.410933i
$585$		0			0
$586$	−10.5565	−	32.4896i	−0.436086	−	1.34213i
$587$	22.7817	−	11.6079i	0.940302	−	0.479108i	0.0845070	−	0.996423i	$-0.473068\pi$
$587$	22.7817	−	11.6079i	0.940302	−	0.479108i	0.855795	+	0.517315i	$0.173068\pi$
$588$	9.07027	−	10.1775i	0.374052	−	0.419715i
$589$	−26.1121	+	8.48435i	−1.07593	+	0.349592i
$590$		0			0
$591$	−39.3226	+	2.26211i	−1.61752	+	0.0930508i
$592$	4.80562	−	0.761135i	0.197510	−	0.0312825i
$593$	5.46116	−	5.46116i	0.224263	−	0.224263i	−0.586028	−	0.810291i	$-0.699309\pi$
$593$	5.46116	−	5.46116i	0.224263	−	0.224263i	0.810291	+	0.586028i	$0.199309\pi$
$594$	−0.857484	−	1.62106i	−0.0351830	−	0.0665129i
$595$		0			0
$596$	2.73256	+	3.76105i	0.111930	+	0.154058i
$597$	−2.33005	−	10.6933i	−0.0953624	−	0.437650i
$598$	8.81838	−	17.3071i	0.360611	−	0.707738i
$599$	20.6409			0.843363			0.421681	−	0.906744i	$-0.361440\pi$
$599$	20.6409			0.843363			0.421681	+	0.906744i	$0.361440\pi$
$600$		0			0
$601$	17.9854			0.733642			0.366821	−	0.930292i	$-0.380446\pi$
$601$	17.9854			0.733642			0.366821	+	0.930292i	$0.380446\pi$
$602$	12.7842	−	25.0904i	0.521045	−	1.02261i
$603$	18.9227	−	12.5650i	0.770594	−	0.511687i
$604$	8.61387	+	11.8560i	0.350494	+	0.482413i
$605$		0			0
$606$	−16.0607	−	4.21573i	−0.652423	−	0.171252i
$607$	5.54524	−	5.54524i	0.225074	−	0.225074i	−0.585557	−	0.810631i	$-0.699124\pi$
$607$	5.54524	−	5.54524i	0.225074	−	0.225074i	0.810631	+	0.585557i	$0.199124\pi$
$608$	6.46812	−	1.02445i	0.262317	−	0.0415469i
$609$	−2.39516	−	41.6354i	−0.0970567	−	1.68715i
$610$		0			0
$611$	10.0782	−	3.27461i	0.407721	−	0.132477i
$612$	−3.70635	+	9.95800i	−0.149820	+	0.402528i
$613$	4.19191	−	2.13588i	0.169310	−	0.0862676i	−0.367282	−	0.930110i	$-0.619712\pi$
$613$	4.19191	−	2.13588i	0.169310	−	0.0862676i	0.536592	+	0.843842i	$0.319712\pi$
$614$	5.63620	+	17.3464i	0.227459	+	0.700045i
$615$		0			0
$616$	−0.420571	+	1.29439i	−0.0169453	+	0.0521523i
$617$	6.41977	+	40.5328i	0.258450	+	1.63179i	0.685861	+	0.727733i	$0.259426\pi$
$617$	6.41977	+	40.5328i	0.258450	+	1.63179i	−0.427410	+	0.904058i	$0.640574\pi$
$618$	−4.63313	+	10.5508i	−0.186372	+	0.424414i
$619$	10.1486	−	13.9684i	0.407908	−	0.561438i	−0.554798	−	0.831985i	$-0.687205\pi$
$619$	10.1486	−	13.9684i	0.407908	−	0.561438i	0.962707	+	0.270547i	$0.0872046\pi$
$620$		0			0
$621$	−40.1224	+	6.98607i	−1.61005	+	0.280341i
$622$	−2.53726	+	16.0196i	−0.101735	+	0.642329i
$623$	7.04100	+	3.58757i	0.282092	+	0.143733i
$624$	−1.55874	−	3.99951i	−0.0623994	−	0.160109i
$625$		0			0
$626$			5.40095i			0.215865i
$627$	0.398124	−	3.98336i	0.0158995	−	0.159080i
$628$	−4.43114	−	0.701824i	−0.176822	−	0.0280058i
$629$	−13.9415	+	10.1291i	−0.555885	+	0.403874i
$630$		0			0
$631$	−29.4746	−	21.4146i	−1.17337	−	0.852501i	−0.181959	−	0.983306i	$-0.558244\pi$
$631$	−29.4746	−	21.4146i	−1.17337	−	0.852501i	−0.991408	+	0.130805i	$0.958244\pi$
$632$	0.966214	+	0.966214i	0.0384339	+	0.0384339i
$633$	3.63119	+	6.21593i	0.144327	+	0.247061i
$634$	−8.15891	−	2.65099i	−0.324032	−	0.105284i
$635$		0			0
$636$	5.89965	−	4.82751i	0.233936	−	0.191423i
$637$	−8.85568	−	17.3803i	−0.350875	−	0.688631i
$638$	1.00043	+	1.96346i	0.0396074	+	0.0777340i
$639$	16.1077	+	9.08185i	0.637212	+	0.359272i
$640$		0			0
$641$	28.1775	+	9.15543i	1.11294	+	0.361618i	0.807071	−	0.590454i	$-0.201051\pi$
$641$	28.1775	+	9.15543i	1.11294	+	0.361618i	0.305874	+	0.952072i	$0.401051\pi$
$642$	−22.0677	+	12.8914i	−0.870943	+	0.508784i
$643$	16.2471	+	16.2471i	0.640721	+	0.640721i	0.950733	−	0.310012i	$-0.100333\pi$
$643$	16.2471	+	16.2471i	0.640721	+	0.640721i	−0.310012	+	0.950733i	$0.600333\pi$
$644$	24.4521	+	17.7655i	0.963547	+	0.700058i
$645$		0			0
$646$	−18.7646	+	13.6333i	−0.738284	+	0.536394i
$647$	−1.77157	−	0.280589i	−0.0696477	−	0.0110311i	0.121513	−	0.992590i	$-0.461225\pi$
$647$	−1.77157	−	0.280589i	−0.0696477	−	0.0110311i	−0.191161	+	0.981559i	$0.561225\pi$
$648$	−4.74665	+	7.64652i	−0.186466	+	0.300384i
$649$		−	0.814444i		−	0.0319697i
$650$		0			0
$651$	−26.0916	+	10.1687i	−1.02261	+	0.398544i
$652$	−9.64088	−	4.91227i	−0.377566	−	0.192379i
$653$	−4.16803	+	26.3159i	−0.163107	+	1.02982i	0.761296	+	0.648404i	$0.224563\pi$
$653$	−4.16803	+	26.3159i	−0.163107	+	1.02982i	−0.924404	+	0.381416i	$0.875437\pi$
$654$	−10.4039	+	16.2010i	−0.406824	+	0.633509i
$655$		0			0
$656$	−4.98463	+	6.86076i	−0.194617	+	0.267868i
$657$	1.32004	−	31.2973i	0.0514996	−	1.22102i
$658$	2.57944	+	16.2860i	0.100557	+	0.634893i
$659$	2.02081	−	6.21940i	0.0787195	−	0.242274i	−0.903951	−	0.427637i	$-0.859346\pi$
$659$	2.02081	−	6.21940i	0.0787195	−	0.242274i	0.982670	+	0.185363i	$0.0593462\pi$
$660$		0			0
$661$	5.97584	+	18.3917i	0.232433	+	0.715356i	0.997452	+	0.0713473i	$0.0227299\pi$
$661$	5.97584	+	18.3917i	0.232433	+	0.715356i	−0.765018	+	0.644008i	$0.777270\pi$
$662$	25.3194	−	12.9009i	0.984066	−	0.501407i
$663$	11.3500	+	10.1152i	0.440797	+	0.392840i
$664$	5.56392	−	1.80783i	0.215922	−	0.0701573i
$665$		0			0
$666$	−13.2733	+	6.07276i	−0.514331	+	0.235315i
$667$	48.3350	−	7.65551i	1.87154	−	0.296422i
$668$	−11.8751	+	11.8751i	−0.459461	+	0.459461i
$669$	6.75856	−	25.7482i	0.261301	−	0.995484i
$670$		0			0
$671$	−0.0303252	−	0.0417390i	−0.00117069	−	0.00161132i
$672$	6.52614	−	1.42202i	0.251751	−	0.0548558i
$673$	−19.9723	+	39.1978i	−0.769874	+	1.51096i	0.0874407	+	0.996170i	$0.472131\pi$
$673$	−19.9723	+	39.1978i	−0.769874	+	1.51096i	−0.857315	+	0.514793i	$0.827869\pi$
$674$	4.74599			0.182809
$675$		0			0
$676$	6.85808			0.263772
$677$	−17.0020	+	33.3683i	−0.653440	+	1.28245i	0.291927	+	0.956441i	$0.405704\pi$
$677$	−17.0020	+	33.3683i	−0.653440	+	1.28245i	−0.945367	+	0.326008i	$0.894296\pi$
$678$	2.97849	−	0.649003i	0.114388	−	0.0249248i
$679$	15.9250	+	21.9189i	0.611147	+	0.841171i
$680$		0			0
$681$	−6.16764	+	23.4970i	−0.236344	+	0.900406i
$682$	1.04629	−	1.04629i	0.0400645	−	0.0400645i
$683$	−33.7054	+	5.33840i	−1.28970	+	0.204268i	−0.763342	−	0.645995i	$-0.776443\pi$
$683$	−33.7054	+	5.33840i	−1.28970	+	0.204268i	−0.526358	+	0.850263i	$0.676443\pi$
$684$	−17.8652	+	8.17363i	−0.683094	+	0.312526i
$685$		0			0
$686$	3.19397	−	1.03778i	0.121946	−	0.0396228i
$687$	22.4121	+	19.9738i	0.855077	+	0.762049i
$688$	6.50638	−	3.31516i	0.248053	−	0.126389i
$689$	−3.37056	−	10.3735i	−0.128408	−	0.395199i
$690$		0			0
$691$	−9.75674	+	30.0282i	−0.371164	+	1.14232i	0.574867	+	0.818247i	$0.305054\pi$
$691$	−9.75674	+	30.0282i	−0.371164	+	1.14232i	−0.946030	+	0.324078i	$0.894946\pi$
$692$	−2.72498	−	17.2049i	−0.103588	−	0.654031i
$693$	0.172057	−	4.07936i	0.00653591	−	0.154962i
$694$	−4.71830	+	6.49419i	−0.179104	+	0.246516i
$695$		0			0
$696$	5.84371	−	9.09986i	0.221505	−	0.344929i
$697$	4.69862	−	29.6659i	0.177973	−	1.12368i
$698$	−16.8609	−	8.59105i	−0.638194	−	0.325176i
$699$	−3.97056	+	1.54745i	−0.150181	+	0.0585301i
$700$		0			0
$701$		−	41.1349i		−	1.55364i	−0.629720	−	0.776822i	$-0.716830\pi$
$701$		−	41.1349i		−	1.55364i	0.629720	−	0.776822i	$-0.283170\pi$
$702$	7.72787	+	10.3011i	0.291670	+	0.388789i
$703$	−31.4708	−	4.98448i	−1.18694	−	0.187993i
$704$	−0.285527	+	0.207447i	−0.0107612	+	0.00781846i
$705$		0			0
$706$	−3.82209	−	2.77691i	−0.143846	−	0.104510i
$707$	−26.1413	−	26.1413i	−0.983143	−	0.983143i
$708$	−3.45125	+	2.01613i	−0.129706	+	0.0757710i
$709$	48.5191	+	15.7648i	1.82217	+	0.592060i	0.999731	+	0.0232123i	$0.00738937\pi$
$709$	48.5191	+	15.7648i	1.82217	+	0.592060i	0.822443	+	0.568848i	$0.192611\pi$
$710$		0			0
$711$	−3.57083	−	2.01331i	−0.133917	−	0.0755049i
$712$	0.930319	+	1.82585i	0.0348652	+	0.0684268i
$713$	−14.9181	−	29.2785i	−0.558689	−	1.09649i
$714$	−18.3084	+	14.9812i	−0.685175	+	0.560658i
$715$		0			0
$716$	6.98899	+	2.27086i	0.261191	+	0.0848660i
$717$	2.12576	+	3.63891i	0.0793881	+	0.135898i
$718$	10.6989	+	10.6989i	0.399281	+	0.399281i
$719$	−29.8994	−	21.7232i	−1.11506	−	0.810138i	−0.131606	−	0.991302i	$-0.542013\pi$
$719$	−29.8994	−	21.7232i	−1.11506	−	0.810138i	−0.983453	+	0.181164i	$0.942013\pi$
$720$		0			0
$721$	−20.7558	+	15.0800i	−0.772985	+	0.561607i
$722$	−23.5920	−	3.73661i	−0.878004	−	0.139062i
$723$	−0.278830	+	2.78978i	−0.0103698	+	0.103753i
$724$			0.671329i			0.0249497i
$725$		0			0
$726$	−6.84017	−	17.5510i	−0.253863	−	0.651379i
$727$	−16.7818	−	8.55075i	−0.622402	−	0.317130i	0.114198	−	0.993458i	$-0.463570\pi$
$727$	−16.7818	−	8.55075i	−0.622402	−	0.317130i	−0.736600	+	0.676328i	$0.763570\pi$
$728$	1.49504	−	9.43931i	0.0554099	−	0.349844i
$729$	7.55333	−	25.9219i	0.279753	−	0.960072i
$730$		0			0
$731$	−15.2020	+	20.9238i	−0.562266	+	0.773893i
$732$	−0.101802	+	0.231828i	−0.00376271	+	0.00856862i
$733$	5.43410	+	34.3095i	0.200713	+	1.26725i	0.858015	+	0.513625i	$0.171698\pi$
$733$	5.43410	+	34.3095i	0.200713	+	1.26725i	−0.657302	+	0.753627i	$0.728302\pi$
$734$	−11.3193	+	34.8373i	−0.417804	+	1.28587i
$735$		0			0
$736$	2.42199	+	7.45412i	0.0892758	+	0.274763i
$737$	−2.38096	+	1.21316i	−0.0877038	+	0.0446873i
$738$	8.87436	−	23.8431i	0.326670	−	0.877678i
$739$	−2.70309	+	0.878288i	−0.0994348	+	0.0323083i	−0.358312	−	0.933602i	$-0.616648\pi$
$739$	−2.70309	+	0.878288i	−0.0994348	+	0.0323083i	0.258877	+	0.965910i	$0.416648\pi$
$740$		0			0
$741$	1.61445	+	28.0643i	0.0593083	+	1.03097i
$742$	16.7632	−	2.65502i	0.615395	−	0.0974689i
$743$	−19.3245	+	19.3245i	−0.708947	+	0.708947i	−0.966314	−	0.257367i	$-0.917145\pi$
$743$	−19.3245	+	19.3245i	−0.708947	+	0.708947i	0.257367	+	0.966314i	$0.417145\pi$
$744$	−7.02377	−	1.84364i	−0.257504	−	0.0675913i
$745$		0			0
$746$	−1.30299	−	1.79341i	−0.0477059	−	0.0656615i
$747$	−14.6210	+	9.70857i	−0.534953	+	0.355218i
$748$	0.567491	−	1.11376i	0.0207495	−	0.0407233i
$749$	−56.9012			−2.07913
$750$		0			0
$751$	13.6596			0.498445			0.249222	−	0.968446i	$-0.419825\pi$
$751$	13.6596			0.498445			0.249222	+	0.968446i	$0.419825\pi$
$752$	−1.94121	+	3.80983i	−0.0707886	+	0.138930i
$753$	9.11798	+	41.8454i	0.332278	+	1.52493i
$754$	−9.09541	−	12.5188i	−0.331235	−	0.455906i
$755$		0			0
$756$	−17.7124	+	9.36926i	−0.644195	+	0.340757i
$757$	−11.1659	+	11.1659i	−0.405833	+	0.405833i	−0.880283	−	0.474450i	$-0.842647\pi$
$757$	−11.1659	+	11.1659i	−0.405833	+	0.405833i	0.474450	+	0.880283i	$0.342647\pi$
$758$	−6.98287	+	1.10598i	−0.253629	+	0.0401710i
$759$	4.78324	−	0.275165i	0.173621	−	0.00998786i
$760$		0			0
$761$	−13.3455	+	4.33621i	−0.483774	+	0.157188i	−0.540742	−	0.841188i	$-0.681857\pi$
$761$	−13.3455	+	4.33621i	−0.483774	+	0.157188i	0.0569686	+	0.998376i	$0.481857\pi$
$762$	6.21574	−	6.97454i	0.225173	−	0.252661i
$763$	−38.1951	+	19.4614i	−1.38275	+	0.704548i
$764$	−4.35419	−	13.4008i	−0.157529	−	0.484825i
$765$		0			0
$766$	−4.30040	+	13.2353i	−0.155380	+	0.478209i
$767$	0.894657	+	5.64864i	0.0323042	+	0.203961i
$768$	1.58588	+	0.696404i	0.0572256	+	0.0251293i
$769$	−13.0082	+	17.9042i	−0.469087	+	0.645643i	−0.976362	−	0.216141i	$-0.930653\pi$
$769$	−13.0082	+	17.9042i	−0.469087	+	0.645643i	0.507275	+	0.861784i	$0.330653\pi$
$770$		0			0
$771$	41.7310	+	26.7986i	1.50290	+	0.965128i
$772$	−0.640111	+	4.04150i	−0.0230381	+	0.145457i
$773$	37.7774	+	19.2486i	1.35876	+	0.692323i	0.973114	−	0.230324i	$-0.0739785\pi$
$773$	37.7774	+	19.2486i	1.35876	+	0.692323i	0.385646	+	0.922647i	$0.373979\pi$
$774$	−16.1295	+	14.8239i	−0.579762	+	0.532836i
$775$		0			0
$776$			7.02576i			0.252210i
$777$	−32.3370	−	3.23198i	−1.16008	−	0.115947i
$778$	14.8935	+	2.35890i	0.533959	+	0.0845708i
$779$	44.9294	−	32.6431i	1.60976	−	1.16956i
$780$		0			0
$781$	−1.75995	−	1.27868i	−0.0629758	−	0.0457546i
$782$	−19.6290	−	19.6290i	−0.701932	−	0.701932i
$783$	−9.55212	+	31.0059i	−0.341365	+	1.10806i
$784$	7.48565	+	2.43223i	0.267345	+	0.0868655i
$785$		0			0
$786$	19.1004	+	23.3424i	0.681288	+	0.832596i
$787$	13.1408	+	25.7904i	0.468420	+	0.919327i	0.997494	+	0.0707509i	$0.0225396\pi$
$787$	13.1408	+	25.7904i	0.468420	+	0.919327i	−0.529074	+	0.848576i	$0.677460\pi$
$788$	−10.3240	−	20.2619i	−0.367776	−	0.721800i
$789$	−3.30206	−	4.03542i	−0.117557	−	0.143665i
$790$		0			0
$791$	6.45480	+	2.09729i	0.229506	+	0.0745711i
$792$	0.657885	−	0.829593i	0.0233769	−	0.0294783i
$793$	0.256173	+	0.256173i	0.00909695	+	0.00909695i
$794$	11.1607	+	8.10876i	0.396080	+	0.287769i
$795$		0			0
$796$	5.11191	−	3.71402i	0.181187	−	0.131640i
$797$	−17.0659	−	2.70297i	−0.604505	−	0.0957441i	−0.153323	−	0.988176i	$-0.548997\pi$
$797$	−17.0659	−	2.70297i	−0.604505	−	0.0957441i	−0.451182	+	0.892432i	$0.648997\pi$
$798$	−43.5240	−	4.35009i	−1.54073	−	0.153991i
$799$		−	15.1443i		−	0.535766i
$800$		0			0
$801$	−4.15997	−	4.52634i	−0.146985	−	0.159930i
$802$	14.0953	+	7.18193i	0.497723	+	0.253603i
$803$	−0.576491	+	3.63982i	−0.0203439	+	0.128446i
$804$	11.0348	+	7.08630i	0.389169	+	0.249915i
$805$		0			0
$806$	−6.10729	+	8.40597i	−0.215120	+	0.296088i
$807$	20.5666	+	9.03137i	0.723980	+	0.317919i
$808$	−1.49970	−	9.46876i	−0.0527594	−	0.333110i
$809$	−14.1884	+	43.6674i	−0.498837	+	1.53526i	0.312054	+	0.950064i	$0.398983\pi$
$809$	−14.1884	+	43.6674i	−0.498837	+	1.53526i	−0.810891	+	0.585198i	$0.801017\pi$
$810$		0			0
$811$	14.2314	+	43.7999i	0.499733	+	1.53802i	0.809448	+	0.587192i	$0.199767\pi$
$811$	14.2314	+	43.7999i	0.499733	+	1.53802i	−0.309714	+	0.950830i	$0.600233\pi$
$812$	21.4536	−	10.9312i	0.752874	−	0.383609i
$813$	−19.6264	+	22.0223i	−0.688326	+	0.772355i
$814$	1.63314	−	0.530641i	0.0572417	−	0.0185989i
$815$		0			0
$816$	−6.12445	+	0.352321i	−0.214398	+	0.0123337i
$817$	−47.2320	+	7.48082i	−1.65244	+	0.261721i
$818$	4.20720	−	4.20720i	0.147101	−	0.147101i
$819$	3.28782	+	28.4818i	0.114886	+	0.995234i
$820$		0			0
$821$	13.3733	+	18.4068i	0.466731	+	0.642400i	0.975888	−	0.218274i	$-0.0700425\pi$
$821$	13.3733	+	18.4068i	0.466731	+	0.642400i	−0.509156	+	0.860674i	$0.670043\pi$
$822$	−6.61051	−	30.3378i	−0.230568	−	1.05815i
$823$	16.8780	−	33.1249i	0.588330	−	1.15466i	−0.384496	−	0.923127i	$-0.625625\pi$
$823$	16.8780	−	33.1249i	0.588330	−	1.15466i	0.972826	−	0.231536i	$-0.0743752\pi$
$824$	−6.65293			−0.231766
$825$		0			0
$826$	−8.89898			−0.309635
$827$	4.78802	−	9.39702i	0.166496	−	0.326766i	−0.792651	−	0.609676i	$-0.791300\pi$
$827$	4.78802	−	9.39702i	0.166496	−	0.326766i	0.959147	+	0.282910i	$0.0912996\pi$
$828$	−13.0068	−	19.5881i	−0.452018	−	0.680732i
$829$	−7.78028	−	10.7086i	−0.270220	−	0.371926i	0.652244	−	0.758009i	$-0.273828\pi$
$829$	−7.78028	−	10.7086i	−0.270220	−	0.371926i	−0.922464	+	0.386083i	$0.873828\pi$
$830$		0			0
$831$	−17.8023	−	4.67285i	−0.617553	−	0.162099i
$832$	1.75242	−	1.75242i	0.0607541	−	0.0607541i
$833$	−27.5338	+	4.36093i	−0.953990	+	0.151097i
$834$	−1.79279	−	31.1644i	−0.0620794	−	1.07914i
$835$		0			0
$836$	2.19813	−	0.714216i	0.0760239	−	0.0247017i
$837$	21.7826	−	0.333542i	0.752915	−	0.0115289i
$838$	3.85035	−	1.96185i	0.133008	−	0.0677711i
$839$	0.944989	+	2.90838i	0.0326247	+	0.100408i	0.966043	−	0.258382i	$-0.0831893\pi$
$839$	0.944989	+	2.90838i	0.0326247	+	0.100408i	−0.933418	+	0.358790i	$0.883189\pi$
$840$		0			0
$841$	3.08568	−	9.49674i	0.106403	−	0.327474i
$842$	3.91504	+	24.7186i	0.134921	+	0.851860i
$843$	19.5410	−	44.4997i	0.673029	−	1.53265i
$844$	−2.44299	+	3.36248i	−0.0840910	+	0.115741i
$845$		0			0
$846$	2.53880	−	12.5739i	0.0872858	−	0.432299i
$847$	6.56066	−	41.4224i	0.225427	−	1.42329i
$848$	3.92147	+	1.99809i	0.134664	+	0.0686146i
$849$	16.1471	+	41.4312i	0.554165	+	1.42192i
$850$		0			0
$851$		−	38.1346i		−	1.30724i
$852$	−1.06175	+	10.6232i	−0.0363751	+	0.363945i
$853$	37.2390	+	5.89808i	1.27504	+	0.201946i	0.757003	−	0.653412i	$-0.226663\pi$
$853$	37.2390	+	5.89808i	1.27504	+	0.201946i	0.518037	+	0.855358i	$0.326663\pi$
$854$	−0.456059	+	0.331347i	−0.0156060	+	0.0113384i
$855$		0			0
$856$	−11.9374	−	8.67305i	−0.408013	−	0.296439i
$857$	3.57064	+	3.57064i	0.121971	+	0.121971i	0.765457	−	0.643487i	$-0.222513\pi$
$857$	3.57064	+	3.57064i	0.121971	+	0.121971i	−0.643487	+	0.765457i	$0.722513\pi$
$858$	−0.764167	−	1.30811i	−0.0260882	−	0.0446582i
$859$	−33.5736	−	10.9087i	−1.14552	−	0.372201i	−0.326064	−	0.945348i	$-0.605722\pi$
$859$	−33.5736	−	10.9087i	−1.14552	−	0.372201i	−0.819453	+	0.573147i	$0.805722\pi$
$860$		0			0
$861$	43.8371	−	35.8706i	1.49396	−	1.22247i
$862$	−3.17809	−	6.23735i	−0.108246	−	0.212445i
$863$	−9.14003	−	17.9383i	−0.311130	−	0.610628i	0.681499	−	0.731819i	$-0.261328\pi$
$863$	−9.14003	−	17.9383i	−0.311130	−	0.610628i	−0.992629	+	0.121191i	$0.961328\pi$
$864$	−5.14402	−	0.734186i	−0.175003	−	0.0249775i
$865$		0			0
$866$	−9.38548	−	3.04953i	−0.318932	−	0.103627i
$867$	−6.66374	+	3.89279i	−0.226312	+	0.132206i
$868$	−11.4322	−	11.4322i	−0.388035	−	0.388035i
$869$	0.390153	+	0.283463i	0.0132350	+	0.00961581i
$870$		0			0
$871$	15.1807	−	11.0294i	0.514379	−	0.373718i
$872$	−10.9794	−	1.73896i	−0.371809	−	0.0588887i
$873$	−5.66273	−	20.3024i	−0.191654	−	0.687131i
$874$		−	51.3273i		−	1.73617i
$875$		0			0
$876$	16.8510	−	6.56737i	0.569343	−	0.221891i
$877$	37.5805	+	19.1482i	1.26900	+	0.646590i	0.953230	−	0.302244i	$-0.0977359\pi$
$877$	37.5805	+	19.1482i	1.26900	+	0.646590i	0.315774	+	0.948834i	$0.397736\pi$
$878$	0.0913337	−	0.576659i	0.00308236	−	0.0194613i
$879$	−31.9724	+	49.7877i	−1.07840	+	1.67930i
$880$		0			0
$881$	−22.4775	+	30.9376i	−0.757285	+	1.04231i	0.240150	+	0.970736i	$0.422803\pi$
$881$	−22.4775	+	30.9376i	−0.757285	+	1.04231i	−0.997435	+	0.0715779i	$0.977197\pi$
$882$	−23.5917	−	0.995035i	−0.794372	−	0.0335046i
$883$	−2.18763	−	13.8121i	−0.0736196	−	0.464816i	−0.996765	−	0.0803657i	$-0.974391\pi$
$883$	−2.18763	−	13.8121i	−0.0736196	−	0.464816i	0.923146	−	0.384450i	$-0.125609\pi$
$884$	−2.71243	+	8.34799i	−0.0912288	+	0.280773i
$885$		0			0
$886$	2.76645	+	8.51427i	0.0929408	+	0.286042i
$887$	18.4621	−	9.40690i	0.619896	−	0.315853i	−0.115689	−	0.993285i	$-0.536908\pi$
$887$	18.4621	−	9.40690i	0.619896	−	0.315853i	0.735585	+	0.677433i	$0.236908\pi$
$888$	−6.29142	−	5.60695i	−0.211126	−	0.188157i
$889$	19.7820	−	6.42756i	0.663467	−	0.215574i
$890$		0			0
$891$	−1.23244	+	2.92753i	−0.0412884	+	0.0980759i
$892$	15.1801	−	2.40429i	0.508268	−	0.0805017i
$893$	19.8002	−	19.8002i	0.662587	−	0.662587i
$894$	2.04433	−	7.78831i	0.0683725	−	0.260480i
$895$		0			0
$896$	2.26666	+	3.11979i	0.0757239	+	0.104225i
$897$	−32.8723	+	7.16277i	−1.09757	+	0.239158i
$898$	8.34354	−	16.3751i	0.278428	−	0.546445i
$899$	−26.1776			−0.873071
$900$		0			0
$901$	−15.5880			−0.519312
$902$	−1.35878	+	2.66676i	−0.0452425	+	0.0887935i
$903$	−47.6557	+	10.3840i	−1.58588	+	0.345558i
$904$	1.03449	+	1.42386i	0.0344067	+	0.0473567i
$905$		0			0
$906$	6.44435	−	24.5512i	0.214099	−	0.815658i
$907$	8.19678	−	8.19678i	0.272170	−	0.272170i	−0.557803	−	0.829973i	$-0.688356\pi$
$907$	8.19678	−	8.19678i	0.272170	−	0.272170i	0.829973	+	0.557803i	$0.188356\pi$
$908$	−13.8529	+	2.19408i	−0.459724	+	0.0728131i
$909$	11.9655	+	26.1531i	0.396870	+	0.867445i
$910$		0			0
$911$	4.38290	−	1.42409i	0.145212	−	0.0471822i	−0.235509	−	0.971872i	$-0.575676\pi$
$911$	4.38290	−	1.42409i	0.145212	−	0.0471822i	0.380721	+	0.924690i	$0.375676\pi$
$912$	−8.46794	−	7.54667i	−0.280402	−	0.249895i
$913$	1.83969	−	0.937368i	0.0608848	−	0.0310224i
$914$	10.8344	+	33.3449i	0.358371	+	1.10295i
$915$		0			0
$916$	−5.35607	+	16.4843i	−0.176970	+	0.544656i
$917$	10.5048	+	66.3247i	0.346899	+	2.19023i
$918$	17.4138	−	5.95437i	0.574743	−	0.196524i
$919$	−1.33595	+	1.83878i	−0.0440689	+	0.0606557i	−0.830483	−	0.557044i	$-0.811935\pi$
$919$	−1.33595	+	1.83878i	−0.0440689	+	0.0606557i	0.786414	+	0.617700i	$0.211935\pi$
$920$		0			0
$921$	17.0703	−	26.5820i	0.562485	−	0.875906i
$922$	0.0220400	−	0.139155i	0.000725850	−	0.00458284i
$923$	13.6109	+	6.93508i	0.448007	+	0.228271i
$924$	2.19640	−	0.856007i	0.0722564	−	0.0281606i
$925$		0			0
$926$		−	8.87257i		−	0.291571i
$927$	19.2250	−	5.36223i	0.631431	−	0.176119i
$928$	6.16696	+	0.976751i	0.202440	+	0.0320634i
$929$	12.0105	−	8.72617i	0.394053	−	0.286296i	−0.373061	−	0.927807i	$-0.621692\pi$
$929$	12.0105	−	8.72617i	0.394053	−	0.286296i	0.767114	+	0.641510i	$0.221692\pi$
$930$		0			0
$931$	−41.7003	−	30.2970i	−1.36667	−	0.992945i
$932$	−1.73973	−	1.73973i	−0.0569868	−	0.0569868i
$933$	24.2570	−	14.1703i	0.794138	−	0.463916i
$934$	4.63623	+	1.50640i	0.151702	+	0.0492910i
$935$		0			0
$936$	−3.65152	+	6.47640i	−0.119354	+	0.211688i
$937$	−6.76373	−	13.2746i	−0.220961	−	0.433661i	0.753740	−	0.657173i	$-0.228248\pi$
$937$	−6.76373	−	13.2746i	−0.220961	−	0.433661i	−0.974701	+	0.223512i	$0.928248\pi$
$938$	13.2555	+	26.0155i	0.432809	+	0.849435i
$939$	7.23984	−	5.92414i	0.236263	−	0.193327i
$940$		0			0
$941$	−29.4117	−	9.55645i	−0.958795	−	0.311531i	−0.212511	−	0.977159i	$-0.568164\pi$
$941$	−29.4117	−	9.55645i	−0.958795	−	0.311531i	−0.746284	+	0.665627i	$0.768164\pi$
$942$	3.91961	+	6.70965i	0.127708	+	0.218612i
$943$	46.9991	+	46.9991i	1.53050	+	1.53050i
$944$	−1.86694	−	1.35641i	−0.0607636	−	0.0441474i
$945$		0			0
$946$	2.08499	−	1.51484i	0.0677890	−	0.0492516i
$947$	8.98080	+	1.42242i	0.291837	+	0.0462224i	0.300636	−	0.953739i	$-0.402801\pi$
$947$	8.98080	+	1.42242i	0.291837	+	0.0462224i	−0.00879948	+	0.999961i	$0.502801\pi$
$948$	0.235375	−	2.35500i	0.00764461	−	0.0764868i
$949$		−	25.8775i		−	0.840021i
$950$		0			0
$951$	5.39568	+	13.8446i	0.174967	+	0.448942i
$952$	−12.1695	−	6.20067i	−0.394416	−	0.200965i
$953$	−2.99474	+	18.9081i	−0.0970093	+	0.612493i	0.890506	+	0.454971i	$0.150350\pi$
$953$	−2.99474	+	18.9081i	−0.0970093	+	0.612493i	−0.987516	+	0.157522i	$0.949650\pi$
$954$	−12.9423	−	2.61319i	−0.419023	−	0.0846052i
$955$		0			0
$956$	−1.43017	+	1.96845i	−0.0462549	+	0.0636644i
$957$	1.53462	−	3.49471i	0.0496073	−	0.112968i
$958$	−2.22963	−	14.0773i	−0.0720361	−	0.454818i
$959$	21.3623	−	65.7463i	0.689823	−	2.12306i
$960$		0			0
$961$	−4.14780	−	12.7656i	−0.133800	−	0.411794i
$962$	−10.7439	+	5.47429i	−0.346397	+	0.176498i
$963$	41.4861	+	15.4410i	1.33687	+	0.497580i
$964$	−1.53948	+	0.500207i	−0.0495833	+	0.0161106i
$965$		0			0
$966$	−3.00658	−	52.2639i	−0.0967351	−	1.68156i
$967$	−43.4603	+	6.88343i	−1.39759	+	0.221356i	−0.809347	−	0.587330i	$-0.800179\pi$
$967$	−43.4603	+	6.88343i	−1.39759	+	0.221356i	−0.588240	+	0.808686i	$0.700179\pi$
$968$	7.69010	−	7.69010i	0.247169	−	0.247169i
$969$	38.8574	+	10.1995i	1.24828	+	0.327657i
$970$		0			0
$971$	18.1657	+	25.0030i	0.582965	+	0.802383i	0.994017	−	0.109229i	$-0.0348383\pi$
$971$	18.1657	+	25.0030i	0.582965	+	0.802383i	−0.411051	+	0.911612i	$0.634838\pi$
$972$	15.4564	−	2.02448i	0.495765	−	0.0649352i
$973$	31.5523	−	61.9249i	1.01152	−	1.98522i
$974$	34.8793			1.11761
$975$		0			0
$976$	−0.146183			−0.00467919
$977$	−21.5434	+	42.2813i	−0.689235	+	1.35270i	0.235420	+	0.971894i	$0.424354\pi$
$977$	−21.5434	+	42.2813i	−0.689235	+	1.35270i	−0.924655	+	0.380806i	$0.875646\pi$
$978$	3.99001	+	18.3115i	0.127587	+	0.585537i
$979$	0.425102	+	0.585102i	0.0135863	+	0.0186999i
$980$		0			0
$981$	33.1287	−	3.82424i	1.05772	−	0.122099i
$982$	−3.78562	+	3.78562i	−0.120804	+	0.120804i
$983$	34.4243	−	5.45227i	1.09796	−	0.173900i	0.418938	−	0.908015i	$-0.362402\pi$
$983$	34.4243	−	5.45227i	1.09796	−	0.173900i	0.679026	+	0.734114i	$0.262402\pi$
$984$	14.6642	−	0.843585i	0.467477	−	0.0268925i
$985$		0			0
$986$	−21.0320	+	6.83372i	−0.669796	+	0.217630i
$987$	19.0016	−	21.3213i	0.604828	−	0.678664i
$988$	−14.4608	+	7.36813i	−0.460058	+	0.234411i
$989$	−17.6860	−	54.4321i	−0.562384	−	1.73084i
$990$		0			0
$991$	1.45449	−	4.47645i	0.0462033	−	0.142199i	−0.925293	−	0.379252i	$-0.876181\pi$
$991$	1.45449	−	4.47645i	0.0462033	−	0.142199i	0.971497	+	0.237053i	$0.0761814\pi$
$992$	−0.655859	−	4.14093i	−0.0208235	−	0.131475i
$993$	−45.0654	−	19.7894i	−1.43011	−	0.627999i
$994$	−13.9714	+	19.2300i	−0.443146	+	0.609938i
$995$		0			0
$996$	−8.52625	−	5.47535i	−0.270165	−	0.173493i
$997$	−3.24377	+	20.4803i	−0.102731	+	0.648619i	0.881561	+	0.472070i	$0.156493\pi$
$997$	−3.24377	+	20.4803i	−0.102731	+	0.648619i	−0.984292	+	0.176548i	$0.943507\pi$
$998$	7.96325	+	4.05748i	0.252072	+	0.128437i
$999$	22.6995	+	11.1315i	0.718180	+	0.352186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.c.143.6		80
3.2	odd	2	inner	750.2.l.c.143.1		80
5.2	odd	4		150.2.l.a.17.8	yes	80
5.3	odd	4		750.2.l.b.107.3		80
5.4	even	2		750.2.l.a.143.5		80
15.2	even	4		150.2.l.a.17.2	✓	80
15.8	even	4		750.2.l.b.107.9		80
15.14	odd	2		750.2.l.a.143.10		80
25.3	odd	20		750.2.l.a.257.10		80
25.4	even	10		750.2.l.b.743.9		80
25.21	even	5		150.2.l.a.53.2	yes	80
25.22	odd	20	inner	750.2.l.c.257.1		80
75.29	odd	10		750.2.l.b.743.3		80
75.47	even	20	inner	750.2.l.c.257.6		80
75.53	even	20		750.2.l.a.257.5		80
75.71	odd	10		150.2.l.a.53.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.2	✓	80	15.2	even	4
150.2.l.a.17.8	yes	80	5.2	odd	4
150.2.l.a.53.2	yes	80	25.21	even	5
150.2.l.a.53.8	yes	80	75.71	odd	10
750.2.l.a.143.5		80	5.4	even	2
750.2.l.a.143.10		80	15.14	odd	2
750.2.l.a.257.5		80	75.53	even	20
750.2.l.a.257.10		80	25.3	odd	20
750.2.l.b.107.3		80	5.3	odd	4
750.2.l.b.107.9		80	15.8	even	4
750.2.l.b.743.3		80	75.29	odd	10
750.2.l.b.743.9		80	25.4	even	10
750.2.l.c.143.1		80	3.2	odd	2	inner
750.2.l.c.143.6		80	1.1	even	1	trivial
750.2.l.c.257.1		80	25.22	odd	20	inner
750.2.l.c.257.6		80	75.47	even	20	inner

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.453990 - 0.891007i) q^{2} +(-1.69234 + 0.368756i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.439743 + 1.67530i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(2.72804 - 1.24812i) q^{9} +O(q^{10})\)	\(q+(0.453990 - 0.891007i) q^{2} +(-1.69234 + 0.368756i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.439743 + 1.67530i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(2.72804 - 1.24812i) q^{9} +(-0.335657 + 0.109061i) q^{11} +(1.29306 + 1.15238i) q^{12} +(2.20817 - 1.12512i) q^{13} +(1.19166 + 3.66754i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.554059 - 3.49819i) q^{17} +(0.126420 - 2.99734i) q^{18} +(3.84926 - 5.29805i) q^{19} +(3.60915 - 5.62020i) q^{21} +(-0.0552105 + 0.348585i) q^{22} +(6.98347 + 3.55825i) q^{23} +(1.61382 - 0.628956i) q^{24} -2.47829i q^{26} +(-4.15652 + 3.11823i) q^{27} +(3.80880 + 0.603255i) q^{28} +(5.05137 - 3.67003i) q^{29} +(-3.39184 - 2.46432i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.527829 - 0.308344i) q^{33} +(-3.36845 - 1.09448i) q^{34} +(-2.61325 - 1.47340i) q^{36} +(-2.20890 - 4.33521i) q^{37} +(-2.97307 - 5.83498i) q^{38} +(-3.32209 + 2.71836i) q^{39} +(8.06531 + 2.62058i) q^{41} +(-3.36911 - 5.76730i) q^{42} +(-5.16349 - 5.16349i) q^{43} +(0.285527 + 0.207447i) q^{44} +(6.34085 - 4.60690i) q^{46} +(4.22323 + 0.668895i) q^{47} +(0.172255 - 1.72346i) q^{48} -7.87088i q^{49} +(2.22763 + 5.71582i) q^{51} +(-2.20817 - 1.12512i) q^{52} +(0.688494 - 4.34698i) q^{53} +(0.891339 + 5.11913i) q^{54} +(2.26666 - 3.11979i) q^{56} +(-4.56057 + 10.3855i) q^{57} +(-0.976751 - 6.16696i) q^{58} +(-0.713107 + 2.19472i) q^{59} +(0.0451729 + 0.139028i) q^{61} +(-3.73559 + 1.90338i) q^{62} +(-4.03544 + 10.8422i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-0.0351078 - 0.610284i) q^{66} +(7.47829 - 1.18445i) q^{67} +(-2.50443 + 2.50443i) q^{68} +(-13.1305 - 3.44659i) q^{69} +(3.62303 + 4.98667i) q^{71} +(-2.49920 + 1.65951i) q^{72} +(4.74043 - 9.30362i) q^{73} -4.86552 q^{74} -6.54875 q^{76} +(0.617880 - 1.21266i) q^{77} +(0.913883 + 4.19411i) q^{78} +(-0.803169 - 1.10547i) q^{79} +(5.88439 - 6.80984i) q^{81} +(5.99652 - 5.99652i) q^{82} +(-5.77823 + 0.915181i) q^{83} +(-6.66824 + 0.383604i) q^{84} +(-6.94488 + 2.25653i) q^{86} +(-7.19529 + 8.07367i) q^{87} +(0.314463 - 0.160227i) q^{88} +(-0.633239 - 1.94891i) q^{89} +(-2.95327 + 9.08922i) q^{91} +(-1.22609 - 7.74123i) q^{92} +(6.64888 + 2.91971i) q^{93} +(2.51330 - 3.45926i) q^{94} +(-1.45742 - 0.935916i) q^{96} +(1.09907 - 6.93926i) q^{97} +(-7.01300 - 3.57330i) q^{98} +(-0.779562 + 0.716464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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