LMFDB - Embedded newform 750.2.l.c.143.1

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			143.1
Character	$\chi$	$=$	750.143
Dual form			750.2.l.c.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(-1.49556 - 0.873670i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.45742 - 0.935916i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.47340 + 2.61325i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(-1.49556 - 0.873670i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.45742 - 0.935916i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.47340 + 2.61325i) q^{9} +(0.335657 - 0.109061i) q^{11} +(0.172255 + 1.72346i) 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} +(-2.99734 + 0.126420i) q^{18} +(3.84926 - 5.29805i) q^{19} +(6.46042 - 1.69577i) q^{21} +(-0.0552105 + 0.348585i) q^{22} +(-6.98347 - 3.55825i) q^{23} +(-1.61382 - 0.628956i) q^{24} +2.47829i q^{26} +(0.0795559 - 5.19554i) 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} +(-0.597278 - 0.130145i) q^{33} +(-3.36845 - 1.09448i) q^{34} +(1.24812 - 2.72804i) q^{36} +(-2.20890 - 4.33521i) q^{37} +(2.97307 + 5.83498i) q^{38} +(-4.28544 - 0.246528i) q^{39} +(-8.06531 - 2.62058i) q^{41} +(-1.42202 + 6.52614i) 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} +(1.29306 - 1.15238i) q^{48} -7.87088i q^{49} +(2.22763 - 5.71582i) q^{51} +(-2.20817 - 1.12512i) q^{52} +(-0.688494 + 4.34698i) q^{53} +(4.59315 + 2.42961i) q^{54} +(-2.26666 + 3.11979i) q^{56} +(-10.3855 + 4.56057i) 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} +(-11.1435 - 3.10814i) q^{63} +(0.951057 - 0.309017i) q^{64} +(0.387119 - 0.473094i) q^{66} +(7.47829 - 1.18445i) q^{67} +(2.50443 - 2.50443i) q^{68} +(7.33546 + 11.4228i) q^{69} +(-3.62303 - 4.98667i) q^{71} +(1.86407 + 2.35059i) q^{72} +(4.74043 - 9.30362i) q^{73} +4.86552 q^{74} -6.54875 q^{76} +(-0.617880 + 1.21266i) q^{77} +(2.16521 - 3.70643i) q^{78} +(-0.803169 - 1.10547i) q^{79} +(-4.65817 + 7.70074i) q^{81} +(5.99652 - 5.99652i) q^{82} +(5.77823 - 0.915181i) q^{83} +(-5.16925 - 4.22984i) q^{84} +(6.94488 - 2.25653i) q^{86} +(10.7610 - 1.07553i) 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} +(2.91971 + 6.64888i) q^{93} +(2.51330 - 3.45926i) q^{94} +(0.439743 + 1.67530i) 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
$3$	−1.49556	−	0.873670i	−0.863462	−	0.504413i
$3$	−1.49556	−	0.873670i	−0.863462	−	0.504413i
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	1.45742	−	0.935916i	0.594987	−	0.382086i
$7$	−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
$9$	1.47340	+	2.61325i	0.491134	+	0.871084i
$10$		0			0
$11$	0.335657	−	0.109061i	0.101204	−	0.0328833i	−0.257977	−	0.966151i	$-0.583056\pi$
$11$	0.335657	−	0.109061i	0.101204	−	0.0328833i	0.359181	+	0.933268i	$0.383056\pi$
$12$	0.172255	+	1.72346i	0.0497257	+	0.497521i
$13$	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	$0.0913123\pi$
$17$	0.554059	+	3.49819i	0.134379	+	0.848436i	−0.824756	+	0.565488i	$0.808688\pi$
$18$	−2.99734	+	0.126420i	−0.706479	+	0.0297975i
$19$	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
$21$	6.46042	−	1.69577i	1.40978	−	0.370048i
$22$	−0.0552105	+	0.348585i	−0.0117709	+	0.0743186i
$23$	−6.98347	−	3.55825i	−1.45615	−	0.741947i	−0.466378	−	0.884585i	$-0.654441\pi$
$23$	−6.98347	−	3.55825i	−1.45615	−	0.741947i	−0.989775	+	0.142638i	$0.954441\pi$
$24$	−1.61382	−	0.628956i	−0.329420	−	0.128385i
$25$		0			0
$26$			2.47829i			0.486033i
$27$	0.0795559	−	5.19554i	0.0153105	−	0.999883i
$28$	3.80880	+	0.603255i	0.719796	+	0.114004i
$29$	−5.05137	+	3.67003i	−0.938015	+	0.681508i	−0.947942	−	0.318443i	$-0.896840\pi$
$29$	−5.05137	+	3.67003i	−0.938015	+	0.681508i	0.00992666	+	0.999951i	$0.496840\pi$
$30$		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
$33$	−0.597278	−	0.130145i	−0.103973	−	0.0226553i
$34$	−3.36845	−	1.09448i	−0.577684	−	0.187701i
$35$		0			0
$36$	1.24812	−	2.72804i	0.208020	−	0.454673i
$37$	−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
$39$	−4.28544	−	0.246528i	−0.686219	−	0.0394761i
$40$		0			0
$41$	−8.06531	−	2.62058i	−1.25959	−	0.409265i	−0.398241	−	0.917281i	$-0.630379\pi$
$41$	−8.06531	−	2.62058i	−1.25959	−	0.409265i	−0.861348	+	0.508015i	$0.830379\pi$
$42$	−1.42202	+	6.52614i	−0.219423	+	1.00700i
$43$	−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	−0.159378	−	0.987218i	$-0.550949\pi$
$47$	−4.22323	−	0.668895i	−0.616022	−	0.0975683i	−0.456644	+	0.889649i	$0.650949\pi$
$48$	1.29306	−	1.15238i	0.186638	−	0.166332i
$49$		−	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	$0.147745\pi$
$53$	−0.688494	+	4.34698i	−0.0945719	+	0.597103i	−0.988772	+	0.149435i	$0.952255\pi$
$54$	4.59315	+	2.42961i	0.625048	+	0.330628i
$55$		0			0
$56$	−2.26666	+	3.11979i	−0.302896	+	0.416900i
$57$	−10.3855	+	4.56057i	−1.37560	+	0.604063i
$58$	−0.976751	−	6.16696i	−0.128254	−	0.809762i
$59$	0.713107	−	2.19472i	0.0928386	−	0.285728i	−0.893846	−	0.448375i	$-0.852003\pi$
$59$	0.713107	−	2.19472i	0.0928386	−	0.285728i	0.986684	+	0.162647i	$0.0520031\pi$
$60$		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
$63$	−11.1435	−	3.10814i	−1.40395	−	0.391589i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	0.387119	−	0.473094i	0.0476510	−	0.0582339i
$67$	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
$69$	7.33546	+	11.4228i	0.883085	+	1.37515i
$70$		0			0
$71$	−3.62303	−	4.98667i	−0.429974	−	0.591809i	0.537973	−	0.842962i	$-0.319190\pi$
$71$	−3.62303	−	4.98667i	−0.429974	−	0.591809i	−0.967947	+	0.251153i	$0.919190\pi$
$72$	1.86407	+	2.35059i	0.219682	+	0.277019i
$73$	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
$78$	2.16521	−	3.70643i	0.245161	−	0.419671i
$79$	−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
$81$	−4.65817	+	7.70074i	−0.517574	+	0.855638i
$82$	5.99652	−	5.99652i	0.662205	−	0.662205i
$83$	5.77823	−	0.915181i	0.634243	−	0.100454i	0.168969	−	0.985621i	$-0.445956\pi$
$83$	5.77823	−	0.915181i	0.634243	−	0.100454i	0.465273	+	0.885167i	$0.345956\pi$
$84$	−5.16925	−	4.22984i	−0.564011	−	0.461513i
$85$		0			0
$86$	6.94488	−	2.25653i	0.748886	−	0.243328i
$87$	10.7610	−	1.07553i	1.15370	−	0.115309i
$88$	0.314463	−	0.160227i	0.0335219	−	0.0170803i
$89$	0.633239	+	1.94891i	0.0671232	+	0.206584i	0.978992	−	0.203897i	$-0.0653608\pi$
$89$	0.633239	+	1.94891i	0.0671232	+	0.206584i	−0.911869	+	0.410481i	$0.865361\pi$
$90$		0			0
$91$	−2.95327	+	9.08922i	−0.309587	+	0.952809i
$92$	1.22609	+	7.74123i	0.127829	+	0.807079i
$93$	2.91971	+	6.64888i	0.302759	+	0.689457i
$94$	2.51330	−	3.45926i	0.259227	−	0.356795i
$95$		0			0
$96$	0.439743	+	1.67530i	0.0448811	+	0.170984i
$97$	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	$-0.841738\pi$
$101$		−	9.58679i		−	0.953921i	0.878925	−	0.476961i	$-0.158262\pi$
$102$	4.08151	+	4.57976i	0.404130	+	0.453464i
$103$	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	$-0.997230\pi$
$107$	−10.4337	−	10.4337i	−1.00866	−	1.00866i	−0.00870186	−	0.999962i	$-0.502770\pi$
$108$	−4.25004	+	2.98950i	−0.408961	+	0.287665i
$109$	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
$111$	−0.483998	+	8.41342i	−0.0459391	+	0.798566i
$112$	−1.75071	−	3.43597i	−0.165427	−	0.324668i
$113$	0.799015	+	1.56816i	0.0751650	+	0.147520i	0.925531	−	0.378672i	$-0.123619\pi$
$113$	0.799015	+	1.56816i	0.0751650	+	0.147520i	−0.850366	+	0.526192i	$0.823619\pi$
$114$	0.651437	−	11.3240i	0.0610127	−	1.06059i
$115$		0			0
$116$	5.93824	+	1.92945i	0.551352	+	0.179145i
$117$	6.19375	+	4.11276i	0.572612	+	0.380224i
$118$	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
$123$	9.77263	+	10.9656i	0.881169	+	0.988739i
$124$			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
$129$	3.21113	+	12.2335i	0.282724	+	1.07710i
$130$		0			0
$131$	−10.2354	+	14.0878i	−0.894273	+	1.23086i	0.0779865	+	0.996954i	$0.475151\pi$
$131$	−10.2354	+	14.0878i	−0.894273	+	1.23086i	−0.972259	+	0.233906i	$0.924849\pi$
$132$	0.245782	+	0.559706i	0.0213926	+	0.0487161i
$133$	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	0.390358	−	0.920663i	$-0.372351\pi$
$137$	15.9727	−	8.13848i	1.36464	−	0.695317i	0.974279	+	0.225346i	$0.0723511\pi$
$138$	−13.5080	+	1.35009i	−1.14988	+	0.114927i
$139$	−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
$141$	5.73171	+	4.69008i	0.482697	+	0.394976i
$142$	6.08797	−	0.964240i	0.510891	−	0.0809172i
$143$	0.618480	−	0.618480i	0.0517199	−	0.0517199i
$144$	−2.94066	+	0.593750i	−0.245055	+	0.0494792i
$145$		0			0
$146$	6.13747	+	8.44751i	0.507941	+	0.699121i
$147$	−6.87655	+	11.7714i	−0.567168	+	0.970886i
$148$	−2.20890	+	4.33521i	−0.181570	+	0.356352i
$149$	4.64891			0.380854			0.190427	−	0.981701i	$-0.439013\pi$
$149$	4.64891			0.380854			0.190427	+	0.981701i	$0.439013\pi$
$150$		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
$153$	−8.32530	+	6.60214i	−0.673061	+	0.533751i
$154$	−0.799974	−	1.10107i	−0.0644637	−	0.0887267i
$155$		0			0
$156$	2.31947	+	3.61190i	0.185706	+	0.289183i
$157$	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
$159$	4.82751	−	5.89965i	0.382846	−	0.467873i
$160$		0			0
$161$	28.7452	−	9.33987i	2.26544	−	0.736085i
$162$	−4.74665	−	7.64652i	−0.372932	−	0.600768i
$163$	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	$0.175137\pi$
$167$	2.62714	+	16.5871i	0.203295	+	1.28355i	−0.649120	+	0.760686i	$0.724863\pi$
$168$	6.11560	−	2.68553i	0.471829	−	0.207193i
$169$	−4.03108	+	5.54830i	−0.310083	+	0.426793i
$170$		0			0
$171$	19.5166	+	2.25292i	1.49247	+	0.172285i
$172$	−1.14233	+	7.21237i	−0.0871017	+	0.549938i
$173$	−15.5207	−	7.90821i	−1.18002	−	0.601250i	−0.249816	−	0.968293i	$-0.580370\pi$
$173$	−15.5207	−	7.90821i	−1.18002	−	0.601250i	−0.930204	+	0.367043i	$0.880370\pi$
$174$	−3.92710	+	10.0764i	−0.297713	+	0.763892i
$175$		0			0
$176$			0.352930i			0.0266031i
$177$	−2.98395	+	2.65931i	−0.224288	+	0.199886i
$178$	−2.02397	−	0.320566i	−0.151703	−	0.0240274i
$179$	5.94519	−	4.31943i	0.444364	−	0.322849i	−0.343002	−	0.939334i	$-0.611444\pi$
$179$	5.94519	−	4.31943i	0.444364	−	0.322849i	0.787367	+	0.616485i	$0.211444\pi$
$180$		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
$183$	0.0539056	−	0.247391i	0.00398482	−	0.0182877i
$184$	−7.45412	−	2.42199i	−0.549525	−	0.178552i
$185$		0			0
$186$	−7.24972	−	0.417054i	−0.531575	−	0.0305799i
$187$	0.567491	+	1.11376i	0.0414991	+	0.0814465i
$188$	1.94121	+	3.80983i	0.141577	+	0.277861i
$189$	13.9503	+	14.3841i	1.01473	+	1.04629i
$190$		0			0
$191$	−13.4008	−	4.35419i	−0.969650	−	0.315058i	−0.218975	−	0.975730i	$-0.570271\pi$
$191$	−13.4008	−	4.35419i	−0.969650	−	0.315058i	−0.750675	+	0.660672i	$0.770271\pi$
$192$	−1.69234	−	0.368756i	−0.122134	−	0.0266126i
$193$	−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	−0.708405	−	0.705806i	$-0.750585\pi$
$197$	−22.4605	−	3.55739i	−1.60024	−	0.253454i	−0.891839	+	0.452353i	$0.850585\pi$
$198$	−0.992288	+	0.369327i	−0.0705188	+	0.0262470i
$199$			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
$204$	−5.93357	+	1.55748i	−0.415433	+	0.109045i
$205$		0			0
$206$	−3.91049	+	5.38233i	−0.272457	+	0.375005i
$207$	−0.990845	−	23.4923i	−0.0688685	−	1.63283i
$208$	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
$213$	1.06175	+	10.6232i	0.0727502	+	0.727889i
$214$	14.0333	−	4.55969i	0.959296	−	0.311694i
$215$		0			0
$216$	−0.734186	−	5.14402i	−0.0499550	−	0.350006i
$217$	15.9686	−	2.52917i	1.08402	−	0.171691i
$218$	−7.86037	+	7.86037i	−0.532371	+	0.532371i
$219$	−15.2179	+	9.77255i	−1.02833	+	0.660368i
$220$		0			0
$221$	5.15934	+	7.10123i	0.347055	+	0.477680i
$222$	−7.27668	−	4.25086i	−0.488379	−	0.285299i
$223$	−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	$0.304109\pi$
$227$	−6.36747	+	12.4969i	−0.422624	+	0.829445i	−0.999917	+	0.0129084i	$0.995891\pi$
$228$	9.79405	+	5.72144i	0.648627	+	0.378912i
$229$	−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
$231$	1.98354	−	1.27378i	0.130507	−	0.0838085i
$232$	−4.41506	+	4.41506i	−0.289863	+	0.289863i
$233$	−2.43006	+	0.384884i	−0.159199	+	0.0252146i	−0.235525	−	0.971868i	$-0.575681\pi$
$233$	−2.43006	+	0.384884i	−0.159199	+	0.0252146i	0.0763263	+	0.997083i	$0.475681\pi$
$234$	−6.47640	+	3.65152i	−0.423375	+	0.238707i
$235$		0			0
$236$	−2.19472	+	0.713107i	−0.142864	+	0.0464193i
$237$	0.235375	+	2.35500i	0.0152892	+	0.152974i
$238$	12.1695	−	6.20067i	0.788831	−	0.401930i
$239$	0.751883	+	2.31406i	0.0486352	+	0.149684i	0.972425	−	0.233217i	$-0.0749252\pi$
$239$	0.751883	+	2.31406i	0.0486352	+	0.149684i	−0.923790	+	0.382901i	$0.874925\pi$
$240$		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
$243$	13.6945	−	7.44723i	0.878501	−	0.477740i
$244$	0.0859239	−	0.118264i	0.00550072	−	0.00757109i
$245$		0			0
$246$	−14.2071	+	3.72918i	−0.905814	+	0.237764i
$247$	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	$0.284962\pi$
$251$			24.7263i			1.56071i	−0.625335	+	0.780357i	$0.715038\pi$
$252$	4.03544	+	10.8422i	0.254209	+	0.682994i
$253$	−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	$0.101443\pi$
$257$	20.2470	+	20.2470i	1.26297	+	1.26297i	0.313326	+	0.949646i	$0.398557\pi$
$258$	−12.3579	−	2.69276i	−0.769372	−	0.167644i
$259$	17.8445	+	5.79802i	1.10880	+	0.360272i
$260$		0			0
$261$	−17.0334	−	7.79306i	−1.05434	−	0.482378i
$262$	−7.90558	−	15.5156i	−0.488408	−	0.958555i
$263$	−1.36671	−	2.68232i	−0.0842750	−	0.165399i	0.845023	−	0.534730i	$-0.179587\pi$
$263$	−1.36671	−	2.68232i	−0.0842750	−	0.165399i	−0.929298	+	0.369331i	$0.879587\pi$
$264$	−0.610284	−	0.0351078i	−0.0375604	−	0.00216073i
$265$		0			0
$266$	−24.0178	−	7.80385i	−1.47262	−	0.478485i
$267$	0.755655	−	3.46795i	0.0462454	−	0.212235i
$268$	−5.35387	−	5.35387i	−0.327039	−	0.327039i
$269$	10.4918	+	7.62274i	0.639697	+	0.464767i	0.859746	−	0.510722i	$-0.170622\pi$
$269$	10.4918	+	7.62274i	0.639697	+	0.464767i	−0.220049	+	0.975489i	$0.570622\pi$
$270$		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
$273$	12.3578	−	11.0133i	0.747926	−	0.666555i
$274$			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
$279$	1.44233	−	12.4947i	0.0863502	−	0.748036i
$280$		0			0
$281$	16.4932	−	22.7009i	0.983902	−	1.35422i	0.0492011	−	0.998789i	$-0.484332\pi$
$281$	16.4932	−	22.7009i	0.983902	−	1.35422i	0.934701	−	0.355436i	$-0.115668\pi$
$282$	−6.78104	+	2.97774i	−0.403805	+	0.177322i
$283$	−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
$288$	0.805995	−	2.88970i	0.0474937	−	0.170277i
$289$	4.23760	−	1.37688i	0.249271	−	0.0809930i
$290$		0			0
$291$	−7.70635	+	9.41786i	−0.451754	+	0.552085i
$292$	−10.3131	+	1.63344i	−0.603531	+	0.0955899i
$293$	−24.1559	+	24.1559i	−1.41120	+	1.41120i	−0.659495	+	0.751709i	$0.729230\pi$
$293$	−24.1559	+	24.1559i	−1.41120	+	1.41120i	−0.751709	+	0.659495i	$0.770770\pi$
$294$	−7.36648	−	11.4711i	−0.429622	−	0.669010i
$295$		0			0
$296$	−2.85988	−	3.93629i	−0.166227	−	0.228792i
$297$	−0.539930	−	1.75260i	−0.0313299	−	0.101696i
$298$	−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
$303$	−8.37569	+	14.3376i	−0.481171	+	0.823675i
$304$	3.84926	+	5.29805i	0.220770	+	0.303864i
$305$		0			0
$306$	−2.10294	−	10.4152i	−0.120217	−	0.595398i
$307$	−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
$309$	−8.91809	−	7.29740i	−0.507333	−	0.415135i
$310$		0			0
$311$	15.4255	−	5.01205i	0.874699	−	0.284207i	0.162945	−	0.986635i	$-0.447901\pi$
$311$	15.4255	−	5.01205i	0.874699	−	0.284207i	0.711755	+	0.702428i	$0.247901\pi$
$312$	−4.27124	+	0.426897i	−0.241812	+	0.0241683i
$313$	−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	$0.0274479\pi$
$317$	1.34202	+	8.47316i	0.0753752	+	0.475900i	−0.920909	+	0.389777i	$0.872552\pi$
$318$	3.06499	+	6.97973i	0.171876	+	0.391404i
$319$	−1.29527	+	1.78278i	−0.0725210	+	0.0998166i
$320$		0			0
$321$	6.48862	+	24.7198i	0.362160	+	1.37973i
$322$	−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
$327$	−12.8102	−	14.3740i	−0.708404	−	0.794884i
$328$	−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
$333$	8.07440	−	12.1599i	0.442474	−	0.666360i
$334$	−15.9719	−	5.18960i	−0.873946	−	0.283962i
$335$		0			0
$336$	−0.383604	+	6.66824i	−0.0209273	+	0.363783i
$337$	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
$339$	0.175074	−	3.04335i	0.00950874	−	0.165292i
$340$		0			0
$341$	−1.40726	−	0.457245i	−0.0762072	−	0.0247612i
$342$	−10.8677	+	16.3666i	−0.587660	+	0.885007i
$343$	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	0.365570	−	0.930784i	$-0.380874\pi$
$347$	7.92843	+	1.25574i	0.425620	+	0.0674116i	0.0600500	+	0.998195i	$0.480874\pi$
$348$	−7.19529	−	8.07367i	−0.385708	−	0.432794i
$349$		−	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	−0.999519	−	0.0310149i	$-0.990126\pi$
$353$	−0.739053	+	4.66620i	−0.0393358	+	0.248357i	0.960183	+	0.279371i	$0.0901261\pi$
$354$	−1.01478	−	3.86602i	−0.0539349	−	0.205477i
$355$		0			0
$356$	1.20449	−	1.65784i	0.0638379	−	0.0878654i
$357$	9.51159	+	21.6602i	0.503406	+	1.14638i
$358$	1.14958	+	7.25818i	0.0607573	+	0.383607i
$359$	4.67561	−	14.3900i	0.246769	−	0.759478i	−0.748571	−	0.663054i	$-0.769260\pi$
$359$	4.67561	−	14.3900i	0.246769	−	0.759478i	0.995340	−	0.0964232i	$-0.0307402\pi$
$360$		0			0
$361$	−7.38121	−	22.7170i	−0.388485	−	1.19563i
$362$	0.598158	−	0.304777i	0.0314385	−	0.0160187i
$363$	18.7434	−	1.87335i	0.983775	−	0.0983252i
$364$	9.08922	−	2.95327i	0.476405	−	0.154793i
$365$		0			0
$366$	0.195954	+	0.160343i	0.0102427	+	0.00838128i
$367$	−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
$369$	−5.03522	−	24.9378i	−0.262123	−	1.29821i
$370$		0			0
$371$	−9.97595	−	13.7307i	−0.517926	−	0.712864i
$372$	3.66290	−	6.27021i	0.189913	−	0.325095i
$373$	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
$378$	−19.1497	+	5.89952i	−0.984952	+	0.303439i
$379$	−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
$381$	5.04816	+	7.86103i	0.258625	+	0.402733i
$382$	9.96347	−	9.96347i	0.509775	−	0.509775i
$383$	13.7450	−	2.17700i	0.702339	−	0.111240i	0.204957	−	0.978771i	$-0.434295\pi$
$383$	13.7450	−	2.17700i	0.702339	−	0.111240i	0.497382	+	0.867532i	$0.334295\pi$
$384$	1.09687	−	1.34048i	0.0559744	−	0.0684059i
$385$		0			0
$386$	3.89161	−	1.26446i	0.198078	−	0.0643593i
$387$	5.88560	−	21.1014i	0.299182	−	1.07264i
$388$	−6.26000	+	3.18963i	−0.317803	+	0.161929i
$389$	−4.65972	−	14.3411i	−0.236257	−	0.727125i	−0.996952	−	0.0780155i	$-0.975142\pi$
$389$	−4.65972	−	14.3411i	−0.236257	−	0.727125i	0.760695	−	0.649110i	$-0.224858\pi$
$390$		0			0
$391$	8.57820	−	26.4010i	0.433818	−	1.33515i
$392$	−1.23128	−	7.77397i	−0.0621888	−	0.392645i
$393$	27.6158	−	12.1268i	1.39303	−	0.611719i
$394$	13.3665	−	18.3974i	0.673395	−	0.926849i
$395$		0			0
$396$	0.121416	−	1.05181i	0.00610139	−	0.0528552i
$397$	−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	$-0.870746\pi$
$401$		−	15.8196i		−	0.789991i	0.918683	−	0.394995i	$-0.129254\pi$
$402$	9.79044	−	8.72529i	0.488303	−	0.435178i
$403$	−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
$408$	1.30606	−	5.99393i	0.0646595	−	0.296744i
$409$	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
$411$	−30.9984	−	1.78324i	−1.52904	−	0.0879610i
$412$	−3.02037	−	5.92780i	−0.148803	−	0.292042i
$413$	4.04005	+	7.92905i	0.198798	+	0.390163i
$414$	21.3816	+	9.78243i	1.05085	+	0.480780i
$415$		0			0
$416$	−2.35699	−	0.765834i	−0.115561	−	0.0375481i
$417$	30.5003	+	6.64591i	1.49361	+	0.325452i
$418$	1.63430	+	1.63430i	0.0799363	+	0.0799363i
$419$	−3.49605	−	2.54003i	−0.170793	−	0.124088i	0.499105	−	0.866542i	$-0.333662\pi$
$419$	−3.49605	−	2.54003i	−0.170793	−	0.124088i	−0.669898	+	0.742453i	$0.733662\pi$
$420$		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
$423$	−4.47453	−	12.0219i	−0.217559	−	0.584526i
$424$			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
$429$	−1.46532	+	0.384627i	−0.0707464	+	0.0185700i
$430$		0			0
$431$	−4.11469	+	5.66339i	−0.198198	+	0.272796i	−0.896535	−	0.442973i	$-0.853924\pi$
$431$	−4.11469	+	5.66339i	−0.198198	+	0.272796i	0.698337	+	0.715769i	$0.253924\pi$
$432$	4.91667	+	1.68117i	0.236553	+	0.0808855i
$433$	−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
$438$	−1.79863	−	17.9959i	−0.0859420	−	0.859877i
$439$	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
$441$	20.5686	−	11.5970i	0.979456	−	0.552237i
$442$	−8.66953	+	1.37312i	−0.412368	+	0.0653126i
$443$	6.33032	−	6.33032i	0.300763	−	0.300763i	−0.540549	−	0.841312i	$-0.681784\pi$
$443$	6.33032	−	6.33032i	0.300763	−	0.300763i	0.841312	+	0.540549i	$0.181784\pi$
$444$	7.09108	−	4.55372i	0.336528	−	0.216110i
$445$		0			0
$446$	−9.03387	−	12.4341i	−0.427766	−	0.588770i
$447$	−6.95273	−	4.06161i	−0.328853	−	0.192108i
$448$	−1.75071	+	3.43597i	−0.0827134	+	0.162334i
$449$	−18.3782			−0.867322			−0.433661	−	0.901076i	$-0.642779\pi$
$449$	−18.3782			−0.867322			−0.433661	+	0.901076i	$0.642779\pi$
$450$		0			0
$451$	−2.99298			−0.140934
$452$	0.799015	−	1.56816i	0.0375825	−	0.0737598i
$453$	21.9171	+	12.8035i	1.02976	+	0.601559i
$454$	−8.24401	−	11.3469i	−0.386911	−	0.532537i
$455$		0			0
$456$	−9.54425	+	6.12908i	−0.446950	+	0.287021i
$457$	−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
$459$	18.2191	−	2.60034i	0.850394	−	0.121373i
$460$		0			0
$461$	−0.133994	+	0.0435374i	−0.00624074	+	0.00202774i	−0.312136	−	0.950038i	$-0.601044\pi$
$461$	−0.133994	+	0.0435374i	−0.00624074	+	0.00202774i	0.305895	+	0.952065i	$0.401044\pi$
$462$	0.234438	+	2.34563i	0.0109071	+	0.109129i
$463$	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	0.963742	−	0.266838i	$-0.0859787\pi$
$467$	−0.762590	−	4.81480i	−0.0352885	−	0.222803i	−0.999030	+	0.0440349i	$0.985979\pi$
$468$	−0.313305	−	7.42827i	−0.0144825	−	0.343372i
$469$	−17.1621	+	23.6216i	−0.792470	+	1.09074i
$470$		0			0
$471$	−7.51602	+	1.97285i	−0.346320	+	0.0909043i
$472$	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
$477$	−12.3742	+	4.60564i	−0.566575	+	0.210878i
$478$	−2.40319	−	0.380627i	−0.109919	−	0.0174095i
$479$	−11.5308	+	8.37759i	−0.526854	+	0.382782i	−0.819180	−	0.573537i	$-0.805571\pi$
$479$	−11.5308	+	8.37759i	−0.526854	+	0.382782i	0.292326	+	0.956319i	$0.405571\pi$
$480$		0			0
$481$	−9.75526	−	7.08761i	−0.444802	−	0.323167i
$482$	1.14460	+	1.14460i	0.0521349	+	0.0521349i
$483$	−51.1501	−	11.1454i	−2.32741	−	0.507135i
$484$	10.3432	+	3.36070i	0.470144	+	0.152759i
$485$		0			0
$486$	0.418364	+	15.5828i	0.0189774	+	0.706852i
$487$	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
$489$	−18.7102	−	1.07634i	−0.846106	−	0.0486739i
$490$		0			0
$491$	5.09165	+	1.65438i	0.229783	+	0.0746610i	0.421645	−	0.906761i	$-0.361453\pi$
$491$	5.09165	+	1.65438i	0.229783	+	0.0746610i	−0.191862	+	0.981422i	$0.561453\pi$
$492$	3.12718	−	14.3517i	0.140984	−	0.647023i
$493$	−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
$498$	7.56474	−	6.74174i	0.338984	−	0.302104i
$499$			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	−0.975410	−	0.220400i	$-0.929264\pi$
$503$	0.456793	−	2.88408i	0.0203674	−	0.128595i	0.995777	+	0.0918053i	$0.0292637\pi$
$504$	−11.4925	−	1.32665i	−0.511917	−	0.0590936i
$505$		0			0
$506$	1.62591	−	2.23788i	0.0722807	−	0.0994859i
$507$	10.8761	−	4.77599i	0.483025	−	0.212109i
$508$	0.843778	+	5.32741i	0.0374366	+	0.236365i
$509$	−3.24395	+	9.98385i	−0.143786	+	0.442527i	−0.996853	−	0.0792745i	$-0.974740\pi$
$509$	−3.24395	+	9.98385i	−0.143786	+	0.442527i	0.853067	+	0.521801i	$0.174740\pi$
$510$		0			0
$511$	12.4429	+	38.2953i	0.550441	+	1.69408i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	−27.2200	−	20.4205i	−1.20179	−	0.901586i
$514$	−27.2321	+	8.84825i	−1.20116	+	0.390280i
$515$		0			0
$516$	8.00965	−	9.78853i	0.352605	−	0.430916i
$517$	−1.49051	+	0.236073i	−0.0655524	+	0.0103825i
$518$	−13.2673	+	13.2673i	−0.582932	+	0.582932i
$519$	16.3030	+	25.3872i	0.715624	+	1.11437i
$520$		0			0
$521$	−11.1471	−	15.3427i	−0.488364	−	0.672175i	0.491722	−	0.870753i	$-0.336368\pi$
$521$	−11.1471	−	15.3427i	−0.488364	−	0.672175i	−0.980085	+	0.198578i	$0.936368\pi$
$522$	14.6767	−	11.6389i	0.642381	−	0.509421i
$523$	−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
$528$	0.308344	−	0.527829i	0.0134190	−	0.0229708i
$529$	22.5886	+	31.0905i	0.982111	+	1.35176i
$530$		0			0
$531$	6.78604	−	1.37017i	0.294489	−	0.0594605i
$532$	17.8571	−	17.8571i	0.774205	−	0.774205i
$533$	−20.7580	+	3.28775i	−0.899131	+	0.142408i
$534$	2.74691	+	2.24771i	0.118870	+	0.0972680i
$535$		0			0
$536$	7.20094	−	2.33973i	0.311033	−	0.101061i
$537$	−12.6651	+	1.26584i	−0.546541	+	0.0546251i
$538$	−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
$543$	0.467516	+	1.06465i	0.0200630	+	0.0456884i
$544$	2.08182	−	2.86537i	0.0892571	−	0.122852i
$545$		0			0
$546$	4.20261	+	16.0108i	0.179855	+	0.685198i
$547$	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
$552$	9.03207	+	10.1347i	0.384430	+	0.431360i
$553$	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	$-0.985840\pi$
$557$	−24.6270	−	24.6270i	−1.04348	−	1.04348i	−0.0444707	−	0.999011i	$-0.514160\pi$
$558$	10.4780	+	6.95759i	0.443570	+	0.294538i
$559$	−17.2114	−	5.59233i	−0.727966	−	0.236530i
$560$		0			0
$561$	0.124345	−	2.16150i	0.00524983	−	0.0912587i
$562$	12.7389	+	25.0016i	0.537359	+	1.05463i
$563$	4.44165	+	8.71723i	0.187193	+	0.367388i	0.965462	−	0.260544i	$-0.0839018\pi$
$563$	4.44165	+	8.71723i	0.187193	+	0.367388i	−0.778269	+	0.627931i	$0.783902\pi$
$564$	0.425343	−	7.39381i	0.0179102	−	0.311336i
$565$		0			0
$566$	24.4163	+	7.93332i	1.02629	+	0.333462i
$567$	−8.29649	−	33.7003i	−0.348420	−	1.41528i
$568$	−4.35851	−	4.35851i	−0.182879	−	0.182879i
$569$	8.66014	+	6.29196i	0.363052	+	0.263773i	0.754324	−	0.656502i	$-0.227965\pi$
$569$	8.66014	+	6.29196i	0.363052	+	0.263773i	−0.391272	+	0.920275i	$0.627965\pi$
$570$		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
$573$	16.2376	+	18.2199i	0.678337	+	0.761146i
$574$			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
$579$	1.79938	+	6.85512i	0.0747795	+	0.284889i
$580$		0			0
$581$	−13.2606	+	18.2516i	−0.550140	+	0.757203i
$582$	−4.89277	−	11.1420i	−0.202812	−	0.461852i
$583$	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	−0.855795	−	0.517315i	$-0.826932\pi$
$587$	−22.7817	+	11.6079i	−0.940302	+	0.479108i	−0.0845070	+	0.996423i	$0.526932\pi$
$588$	13.5652	−	1.35580i	0.559418	−	0.0559121i
$589$	−26.1121	+	8.48435i	−1.07593	+	0.349592i
$590$		0			0
$591$	30.4830	+	24.9433i	1.25390	+	1.02603i
$592$	4.80562	−	0.761135i	0.197510	−	0.0312825i
$593$	−5.46116	+	5.46116i	−0.224263	+	0.224263i	−0.810291	−	0.586028i	$-0.800691\pi$
$593$	−5.46116	+	5.46116i	−0.224263	+	0.224263i	0.586028	+	0.810291i	$0.300691\pi$
$594$	1.80670	+	0.314580i	0.0741297	+	0.0129074i
$595$		0			0
$596$	−2.73256	−	3.76105i	−0.111930	−	0.154058i
$597$	5.52043	−	9.44996i	0.225936	−	0.386761i
$598$	8.81838	−	17.3071i	0.360611	−	0.707738i
$599$	−20.6409			−0.843363			−0.421681	−	0.906744i	$-0.638560\pi$
$599$	−20.6409			−0.843363			−0.421681	+	0.906744i	$0.638560\pi$
$600$		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
$603$	14.1138	+	17.7975i	0.574758	+	0.724770i
$604$	8.61387	+	11.8560i	0.350494	+	0.482413i
$605$		0			0
$606$	−8.97244	−	13.9719i	−0.364480	−	0.567571i
$607$	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
$609$	−26.4104	+	32.2759i	−1.07020	+	1.30789i
$610$		0			0
$611$	−10.0782	+	3.27461i	−0.407721	+	0.132477i
$612$	10.2347	+	2.85467i	0.413715	+	0.115393i
$613$	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	$-0.740574\pi$
$617$	−6.41977	−	40.5328i	−0.258450	−	1.63179i	0.427410	−	0.904058i	$-0.359426\pi$
$618$	10.5508	−	4.63313i	0.424414	−	0.186372i
$619$	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
$621$	−19.0426	+	35.9998i	−0.764155	+	1.44462i
$622$	−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
$627$	−2.98859	+	2.66345i	−0.119353	+	0.106368i
$628$	−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
$633$	−1.53264	+	7.03380i	−0.0609171	+	0.279569i
$634$	−8.15891	−	2.65099i	−0.324032	−	0.105284i
$635$		0			0
$636$	−7.61046	−	0.437806i	−0.301774	−	0.0173601i
$637$	−8.85568	−	17.3803i	−0.350875	−	0.688631i
$638$	−1.00043	−	1.96346i	−0.0396074	−	0.0777340i
$639$	7.69324	−	16.8152i	0.304340	−	0.665201i
$640$		0			0
$641$	−28.1775	−	9.15543i	−1.11294	−	0.361618i	−0.305874	−	0.952072i	$-0.598949\pi$
$641$	−28.1775	−	9.15543i	−1.11294	−	0.361618i	−0.807071	+	0.590454i	$0.798949\pi$
$642$	−24.9713	−	5.44117i	−0.985539	−	0.214746i
$643$	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	0.191161	−	0.981559i	$-0.438775\pi$
$647$	1.77157	+	0.280589i	0.0696477	+	0.0110311i	−0.121513	+	0.992590i	$0.538775\pi$
$648$	−3.39616	+	8.33463i	−0.133414	+	0.327415i
$649$		−	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	$-0.775437\pi$
$653$	4.16803	−	26.3159i	0.163107	−	1.02982i	0.924404	−	0.381416i	$-0.124563\pi$
$654$	18.6230	−	4.88829i	0.728218	−	0.191147i
$655$		0			0
$656$	4.98463	−	6.86076i	0.194617	−	0.267868i
$657$	31.2973	−	1.32004i	1.22102	−	0.0514996i
$658$	2.57944	+	16.2860i	0.100557	+	0.634893i
$659$	−2.02081	+	6.21940i	−0.0787195	+	0.242274i	−0.982670	−	0.185363i	$-0.940654\pi$
$659$	−2.02081	+	6.21940i	−0.0787195	+	0.242274i	0.903951	+	0.427637i	$0.140654\pi$
$660$		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
$663$	−1.51198	−	15.1279i	−0.0587206	−	0.587518i
$664$	5.56392	−	1.80783i	0.215922	−	0.0701573i
$665$		0			0
$666$	7.16887	+	12.7148i	0.277788	+	0.492690i
$667$	48.3350	−	7.65551i	1.87154	−	0.296422i
$668$	11.8751	−	11.8751i	0.459461	−	0.459461i
$669$	22.3995	−	14.3844i	0.866015	−	0.556134i
$670$		0			0
$671$	0.0303252	+	0.0417390i	0.00117069	+	0.00161132i
$672$	−5.76730	−	3.36911i	−0.222478	−	0.129966i
$673$	−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	$-0.594296\pi$
$677$	17.0020	−	33.3683i	0.653440	−	1.28245i	0.945367	−	0.326008i	$-0.105704\pi$
$678$	2.63216	+	1.53764i	0.101087	+	0.0590528i
$679$	15.9250	+	21.9189i	0.611147	+	0.841171i
$680$		0			0
$681$	20.4411	−	13.1267i	0.783303	−	0.503018i
$682$	1.04629	−	1.04629i	0.0400645	−	0.0400645i
$683$	33.7054	−	5.33840i	1.28970	−	0.204268i	0.526358	−	0.850263i	$-0.323557\pi$
$683$	33.7054	−	5.33840i	1.28970	−	0.204268i	0.763342	+	0.645995i	$0.223557\pi$
$684$	−9.64894	−	17.1135i	−0.368937	−	0.654352i
$685$		0			0
$686$	−3.19397	+	1.03778i	−0.121946	+	0.0396228i
$687$	2.98562	+	29.8721i	0.113909	+	1.13969i
$688$	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
$693$	−4.07936	+	0.172057i	−0.154962	+	0.00653591i
$694$	−4.71830	+	6.49419i	−0.179104	+	0.246516i
$695$		0			0
$696$	10.4603	−	2.74568i	0.396496	−	0.104075i
$697$	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	$0.283170\pi$
$701$			41.1349i			1.55364i	−0.629720	+	0.776822i	$0.716830\pi$
$702$	12.8761	+	0.197163i	0.485976	+	0.00744143i
$703$	−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
$708$	3.90535	+	0.850963i	0.146772	+	0.0319812i
$709$	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
$711$	1.70547	−	3.72768i	0.0639603	−	0.139799i
$712$	0.930319	+	1.82585i	0.0348652	+	0.0684268i
$713$	14.9181	+	29.2785i	0.558689	+	1.09649i
$714$	−23.6176	−	1.35865i	−0.883865	−	0.0508460i
$715$		0			0
$716$	−6.98899	−	2.27086i	−0.261191	−	0.0848660i
$717$	0.897235	−	4.11771i	0.0335079	−	0.153779i
$718$	10.6989	+	10.6989i	0.399281	+	0.399281i
$719$	29.8994	+	21.7232i	1.11506	+	0.810138i	0.983453	−	0.181164i	$-0.0579866\pi$
$719$	29.8994	+	21.7232i	1.11506	+	0.810138i	0.131606	+	0.991302i	$0.457987\pi$
$720$		0			0
$721$	−20.7558	+	15.0800i	−0.772985	+	0.561607i
$722$	23.5920	+	3.73661i	0.878004	+	0.139062i
$723$	−2.09309	+	1.86537i	−0.0778427	+	0.0693738i
$724$			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
$729$	−26.9873	−	0.826673i	−0.999531	−	0.0306175i
$730$		0			0
$731$	15.2020	−	20.9238i	0.562266	−	0.773893i
$732$	−0.231828	+	0.101802i	−0.00856862	+	0.00376271i
$733$	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
$738$	24.5057	+	6.83513i	0.902068	+	0.251605i
$739$	−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
$741$	−17.8019	+	21.7555i	−0.653968	+	0.799209i
$742$	16.7632	−	2.65502i	0.615395	−	0.0974689i
$743$	19.3245	−	19.3245i	0.708947	−	0.708947i	−0.257367	−	0.966314i	$-0.582855\pi$
$743$	19.3245	−	19.3245i	0.708947	−	0.708947i	0.966314	+	0.257367i	$0.0828549\pi$
$744$	3.92387	+	6.11028i	0.143856	+	0.224014i
$745$		0			0
$746$	1.30299	+	1.79341i	0.0477059	+	0.0656615i
$747$	10.9053	+	13.7515i	0.399002	+	0.503142i
$748$	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
$753$	21.6027	−	36.9797i	0.787245	−	1.34762i
$754$	−9.09541	−	12.5188i	−0.331235	−	0.455906i
$755$		0			0
$756$	3.43725	−	19.7408i	0.125012	−	0.717966i
$757$	−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
$759$	3.70798	+	3.03413i	0.134591	+	0.110132i
$760$		0			0
$761$	13.3455	−	4.33621i	0.483774	−	0.157188i	−0.0569686	−	0.998376i	$-0.518143\pi$
$761$	13.3455	−	4.33621i	0.483774	−	0.157188i	0.540742	+	0.841188i	$0.318143\pi$
$762$	−9.29604	+	0.929110i	−0.336760	+	0.0336581i
$763$	−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
$768$	0.696404	+	1.58588i	0.0251293	+	0.0572256i
$769$	−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
$771$	−12.5914	−	47.9697i	−0.453468	−	1.72759i
$772$	−0.640111	+	4.04150i	−0.0230381	+	0.145457i
$773$	−37.7774	−	19.2486i	−1.35876	−	0.692323i	−0.385646	−	0.922647i	$-0.626021\pi$
$773$	−37.7774	−	19.2486i	−1.35876	−	0.692323i	−0.973114	+	0.230324i	$0.926021\pi$
$774$	16.1295	+	14.8239i	0.579762	+	0.532836i
$775$		0			0
$776$		−	7.02576i		−	0.252210i
$777$	−21.6219	−	24.2615i	−0.775683	−	0.870376i
$778$	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
$783$	18.6660	+	26.5366i	0.667067	+	0.948340i
$784$	7.48565	+	2.43223i	0.267345	+	0.0868655i
$785$		0			0
$786$	−1.73221	+	30.1113i	−0.0617860	+	1.07404i
$787$	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
$789$	−0.299464	+	5.20563i	−0.0106612	+	0.185325i
$790$		0			0
$791$	−6.45480	−	2.09729i	−0.229506	−	0.0745711i
$792$	0.882044	+	0.585693i	0.0313421	+	0.0208117i
$793$	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	0.451182	−	0.892432i	$-0.351003\pi$
$797$	17.0659	+	2.70297i	0.604505	+	0.0957441i	0.153323	+	0.988176i	$0.451003\pi$
$798$	29.1021	+	32.6547i	1.03020	+	1.15597i
$799$		−	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
$804$	3.32952	+	12.6845i	0.117423	+	0.447349i
$805$		0			0
$806$	6.10729	−	8.40597i	0.215120	−	0.296088i
$807$	−9.03137	−	20.5666i	−0.317919	−	0.723980i
$808$	−1.49970	−	9.46876i	−0.0527594	−	0.333110i
$809$	14.1884	−	43.6674i	0.498837	−	1.53526i	−0.312054	−	0.950064i	$-0.601017\pi$
$809$	14.1884	−	43.6674i	0.498837	−	1.53526i	0.810891	−	0.585198i	$-0.198983\pi$
$810$		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
$813$	−29.3525	+	2.93369i	−1.02944	+	0.102889i
$814$	1.63314	−	0.530641i	0.0572417	−	0.0185989i
$815$		0			0
$816$	4.74769	+	3.88489i	0.166202	+	0.135998i
$817$	−47.2320	+	7.48082i	−1.65244	+	0.261721i
$818$	−4.20720	+	4.20720i	−0.147101	+	0.147101i
$819$	−28.1038	+	5.67445i	−0.982025	+	0.198281i
$820$		0			0
$821$	−13.3733	−	18.4068i	−0.466731	−	0.642400i	0.509156	−	0.860674i	$-0.329957\pi$
$821$	−13.3733	−	18.4068i	−0.466731	−	0.642400i	−0.975888	+	0.218274i	$0.929957\pi$
$822$	15.6619	−	26.8102i	0.546271	−	0.935114i
$823$	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	−0.959147	−	0.282910i	$-0.908700\pi$
$827$	−4.78802	+	9.39702i	−0.166496	+	0.326766i	0.792651	+	0.609676i	$0.208700\pi$
$828$	−18.4233	+	14.6100i	−0.640253	+	0.507734i
$829$	−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
$831$	−9.94535	−	15.4870i	−0.345000	−	0.537237i
$832$	1.75242	−	1.75242i	0.0607541	−	0.0607541i
$833$	27.5338	−	4.36093i	0.953990	−	0.151097i
$834$	−19.7684	+	24.1588i	−0.684524	+	0.836550i
$835$		0			0
$836$	−2.19813	+	0.714216i	−0.0760239	+	0.0247017i
$837$	−13.0733	+	17.4264i	−0.451880	+	0.602345i
$838$	3.85035	−	1.96185i	0.133008	−	0.0677711i
$839$	−0.944989	−	2.90838i	−0.0326247	−	0.100408i	0.933418	−	0.358790i	$-0.116811\pi$
$839$	−0.944989	−	2.90838i	−0.0326247	−	0.100408i	−0.966043	+	0.258382i	$0.916811\pi$
$840$		0			0
$841$	3.08568	−	9.49674i	0.106403	−	0.327474i
$842$	−3.91504	−	24.7186i	−0.134921	−	0.851860i
$843$	−44.4997	+	19.5410i	−1.53265	+	0.673029i
$844$	−2.44299	+	3.36248i	−0.0840910	+	0.115741i
$845$		0			0
$846$	12.7430	+	1.47100i	0.438114	+	0.0505740i
$847$	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
$852$	7.97026	−	7.10313i	0.273057	−	0.243349i
$853$	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	0.643487	−	0.765457i	$-0.277487\pi$
$857$	−3.57064	−	3.57064i	−0.121971	−	0.121971i	−0.765457	+	0.643487i	$0.777487\pi$
$858$	0.322537	−	1.48023i	0.0110112	−	0.0505342i
$859$	−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
$861$	−56.5491	−	3.25310i	−1.92719	−	0.110865i
$862$	−3.17809	−	6.23735i	−0.108246	−	0.212445i
$863$	9.14003	+	17.9383i	0.311130	+	0.610628i	0.992629	−	0.121191i	$-0.0386715\pi$
$863$	9.14003	+	17.9383i	0.311130	+	0.610628i	−0.681499	+	0.731819i	$0.738672\pi$
$864$	−3.73006	+	3.61755i	−0.126899	+	0.123072i
$865$		0			0
$866$	9.38548	+	3.04953i	0.318932	+	0.103627i
$867$	−7.54053	−	1.64306i	−0.256090	−	0.0558011i
$868$	−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
$873$	19.7534	−	7.35218i	0.668552	−	0.248834i
$874$		−	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
$879$	57.2309	−	15.0223i	1.93035	−	0.506691i
$880$		0			0
$881$	22.4775	−	30.9376i	0.757285	−	1.04231i	−0.240150	−	0.970736i	$-0.577197\pi$
$881$	22.4775	−	30.9376i	0.757285	−	1.04231i	0.997435	−	0.0715779i	$-0.0228035\pi$
$882$	0.995035	+	23.5917i	0.0335046	+	0.794372i
$883$	−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	−0.735585	−	0.677433i	$-0.763092\pi$
$887$	−18.4621	+	9.40690i	−0.619896	+	0.315853i	0.115689	+	0.993285i	$0.463092\pi$
$888$	0.838109	+	8.38555i	0.0281251	+	0.281401i
$889$	19.7820	−	6.42756i	0.663467	−	0.215574i
$890$		0			0
$891$	−0.723691	+	3.09283i	−0.0242446	+	0.103614i
$892$	15.1801	−	2.40429i	0.508268	−	0.0805017i
$893$	−19.8002	+	19.8002i	−0.662587	+	0.662587i
$894$	6.77539	−	4.35099i	0.226603	−	0.145519i
$895$		0			0
$896$	−2.26666	−	3.11979i	−0.0757239	−	0.104225i
$897$	29.0500	+	16.9703i	0.969951	+	0.566622i
$898$	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
$903$	−42.1144	−	24.6022i	−1.40148	−	0.818710i
$904$	1.03449	+	1.42386i	0.0344067	+	0.0473567i
$905$		0			0
$906$	−21.3581	+	13.7157i	−0.709576	+	0.455672i
$907$	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
$909$	25.0527	−	14.1252i	0.830946	−	0.468503i
$910$		0			0
$911$	−4.38290	+	1.42409i	−0.145212	+	0.0471822i	−0.380721	−	0.924690i	$-0.624324\pi$
$911$	−4.38290	+	1.42409i	−0.145212	+	0.0471822i	0.235509	+	0.971872i	$0.424324\pi$
$912$	−1.12805	−	11.2865i	−0.0373536	−	0.373734i
$913$	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
$918$	−5.95437	+	17.4138i	−0.196524	+	0.574743i
$919$	−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
$921$	30.5560	−	8.02053i	1.00685	−	0.264286i
$922$	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
$927$	6.96203	+	18.7052i	0.228663	+	0.614359i
$928$	6.16696	+	0.976751i	0.202440	+	0.0320634i
$929$	−12.0105	+	8.72617i	−0.394053	+	0.286296i	−0.767114	−	0.641510i	$-0.778308\pi$
$929$	−12.0105	+	8.72617i	−0.394053	+	0.286296i	0.373061	+	0.927807i	$0.378308\pi$
$930$		0			0
$931$	−41.7003	−	30.2970i	−1.36667	−	0.992945i
$932$	1.73973	+	1.73973i	0.0569868	+	0.0569868i
$933$	−27.4486	−	5.98097i	−0.898628	−	0.195808i
$934$	4.63623	+	1.50640i	0.151702	+	0.0492910i
$935$		0			0
$936$	6.76087	+	3.09320i	0.220986	+	0.101105i
$937$	−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
$939$	9.33928	+	0.537260i	0.304776	+	0.0175328i
$940$		0			0
$941$	29.4117	+	9.55645i	0.958795	+	0.311531i	0.746284	−	0.665627i	$-0.231836\pi$
$941$	29.4117	+	9.55645i	0.958795	+	0.311531i	0.212511	+	0.977159i	$0.431836\pi$
$942$	1.65438	−	7.59248i	0.0539025	−	0.247376i
$943$	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	0.00879948	−	0.999961i	$-0.497199\pi$
$947$	−8.98080	−	1.42242i	−0.291837	−	0.0462224i	−0.300636	+	0.953739i	$0.597199\pi$
$948$	1.76688	−	1.57466i	0.0573857	−	0.0511424i
$949$		−	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	$-0.849650\pi$
$953$	2.99474	−	18.9081i	0.0970093	−	0.612493i	0.987516	−	0.157522i	$-0.0503504\pi$
$954$	1.51410	−	13.1164i	0.0490209	−	0.424659i
$955$		0			0
$956$	1.43017	−	1.96845i	0.0462549	−	0.0636644i
$957$	3.49471	−	1.53462i	0.112968	−	0.0496073i
$958$	−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
$963$	11.8928	−	42.6389i	0.383242	−	1.37402i
$964$	−1.53948	+	0.500207i	−0.0495833	+	0.0161106i
$965$		0			0
$966$	33.1523	−	40.5151i	1.06666	−	1.30355i
$967$	−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
$969$	−21.7080	−	33.8038i	−0.697360	−	1.08593i
$970$		0			0
$971$	−18.1657	−	25.0030i	−0.582965	−	0.802383i	0.411051	−	0.911612i	$-0.365162\pi$
$971$	−18.1657	−	25.0030i	−0.582965	−	0.802383i	−0.994017	+	0.109229i	$0.965162\pi$
$972$	−14.0743	−	6.70170i	−0.451435	−	0.214957i
$973$	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	$-0.575646\pi$
$977$	21.5434	−	42.2813i	0.689235	−	1.35270i	0.924655	−	0.380806i	$-0.124354\pi$
$978$	9.45329	−	16.1823i	0.302283	−	0.517452i
$979$	0.425102	+	0.585102i	0.0135863	+	0.0186999i
$980$		0			0
$981$	6.60027	+	32.6890i	0.210730	+	1.04368i
$982$	−3.78562	+	3.78562i	−0.120804	+	0.120804i
$983$	−34.4243	+	5.45227i	−1.09796	+	0.173900i	−0.679026	−	0.734114i	$-0.737598\pi$
$983$	−34.4243	+	5.45227i	−1.09796	+	0.173900i	−0.418938	+	0.908015i	$0.637598\pi$
$984$	11.3677	+	9.30186i	0.362390	+	0.296533i
$985$		0			0
$986$	21.0320	−	6.83372i	0.669796	−	0.217630i
$987$	−28.4181	+	2.84030i	−0.904560	+	0.0904079i
$988$	−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
$993$	−19.7894	−	45.0654i	−0.627999	−	1.43011i
$994$	−13.9714	+	19.2300i	−0.443146	+	0.609938i
$995$		0			0
$996$	2.57261	+	9.80092i	0.0815162	+	0.310554i
$997$	−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.143.1		80
3.2	odd	2	inner	750.2.l.c.143.6		80
5.2	odd	4		150.2.l.a.17.2	✓	80
5.3	odd	4		750.2.l.b.107.9		80
5.4	even	2		750.2.l.a.143.10		80
15.2	even	4		150.2.l.a.17.8	yes	80
15.8	even	4		750.2.l.b.107.3		80
15.14	odd	2		750.2.l.a.143.5		80
25.3	odd	20		750.2.l.a.257.5		80
25.4	even	10		750.2.l.b.743.3		80
25.21	even	5		150.2.l.a.53.8	yes	80
25.22	odd	20	inner	750.2.l.c.257.6		80
75.29	odd	10		750.2.l.b.743.9		80
75.47	even	20	inner	750.2.l.c.257.1		80
75.53	even	20		750.2.l.a.257.10		80
75.71	odd	10		150.2.l.a.53.2	yes	80

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

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-1.49556 - 0.873670i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.45742 - 0.935916i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.47340 + 2.61325i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-1.49556 - 0.873670i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.45742 - 0.935916i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.47340 + 2.61325i) q^{9} +(0.335657 - 0.109061i) q^{11} +(0.172255 + 1.72346i) 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} +(-2.99734 + 0.126420i) q^{18} +(3.84926 - 5.29805i) q^{19} +(6.46042 - 1.69577i) q^{21} +(-0.0552105 + 0.348585i) q^{22} +(-6.98347 - 3.55825i) q^{23} +(-1.61382 - 0.628956i) q^{24} +2.47829i q^{26} +(0.0795559 - 5.19554i) 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} +(-0.597278 - 0.130145i) q^{33} +(-3.36845 - 1.09448i) q^{34} +(1.24812 - 2.72804i) q^{36} +(-2.20890 - 4.33521i) q^{37} +(2.97307 + 5.83498i) q^{38} +(-4.28544 - 0.246528i) q^{39} +(-8.06531 - 2.62058i) q^{41} +(-1.42202 + 6.52614i) 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} +(1.29306 - 1.15238i) q^{48} -7.87088i q^{49} +(2.22763 - 5.71582i) q^{51} +(-2.20817 - 1.12512i) q^{52} +(-0.688494 + 4.34698i) q^{53} +(4.59315 + 2.42961i) q^{54} +(-2.26666 + 3.11979i) q^{56} +(-10.3855 + 4.56057i) 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} +(-11.1435 - 3.10814i) q^{63} +(0.951057 - 0.309017i) q^{64} +(0.387119 - 0.473094i) q^{66} +(7.47829 - 1.18445i) q^{67} +(2.50443 - 2.50443i) q^{68} +(7.33546 + 11.4228i) q^{69} +(-3.62303 - 4.98667i) q^{71} +(1.86407 + 2.35059i) q^{72} +(4.74043 - 9.30362i) q^{73} +4.86552 q^{74} -6.54875 q^{76} +(-0.617880 + 1.21266i) q^{77} +(2.16521 - 3.70643i) q^{78} +(-0.803169 - 1.10547i) q^{79} +(-4.65817 + 7.70074i) q^{81} +(5.99652 - 5.99652i) q^{82} +(5.77823 - 0.915181i) q^{83} +(-5.16925 - 4.22984i) q^{84} +(6.94488 - 2.25653i) q^{86} +(10.7610 - 1.07553i) 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} +(2.91971 + 6.64888i) q^{93} +(2.51330 - 3.45926i) q^{94} +(0.439743 + 1.67530i) 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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