LMFDB - Embedded newform 750.2.l.b.743.9

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			743.9
Character	$\chi$	$=$	750.743
Dual form			750.2.l.b.107.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 - 0.453990i) q^{2} +(0.873670 + 1.49556i) q^{3} +(0.587785 - 0.809017i) q^{4} +(1.45742 + 0.935916i) q^{6} +(2.72680 - 2.72680i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.47340 + 2.61325i) q^{9} +O(q^{10})$	\(q+(0.891007 - 0.453990i) q^{2} +(0.873670 + 1.49556i) q^{3} +(0.587785 - 0.809017i) q^{4} +(1.45742 + 0.935916i) q^{6} +(2.72680 - 2.72680i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.47340 + 2.61325i) q^{9} +(0.335657 + 0.109061i) q^{11} +(1.72346 + 0.172255i) q^{12} +(1.12512 - 2.20817i) q^{13} +(1.19166 - 3.66754i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(3.49819 + 0.554059i) q^{17} +(-0.126420 + 2.99734i) q^{18} +(-3.84926 - 5.29805i) q^{19} +(6.46042 + 1.69577i) q^{21} +(0.348585 - 0.0552105i) q^{22} +(3.55825 + 6.98347i) q^{23} +(1.61382 - 0.628956i) q^{24} -2.47829i q^{26} +(-5.19554 + 0.0795559i) q^{27} +(-0.603255 - 3.80880i) q^{28} +(5.05137 + 3.67003i) q^{29} +(-3.39184 + 2.46432i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.130145 + 0.597278i) q^{33} +(3.36845 - 1.09448i) q^{34} +(1.24812 + 2.72804i) q^{36} +(-4.33521 - 2.20890i) q^{37} +(-5.83498 - 2.97307i) q^{38} +(4.28544 - 0.246528i) q^{39} +(-8.06531 + 2.62058i) q^{41} +(6.52614 - 1.42202i) q^{42} +(5.16349 + 5.16349i) q^{43} +(0.285527 - 0.207447i) q^{44} +(6.34085 + 4.60690i) q^{46} +(-0.668895 - 4.22323i) q^{47} +(1.15238 - 1.29306i) q^{48} -7.87088i q^{49} +(2.22763 + 5.71582i) q^{51} +(-1.12512 - 2.20817i) q^{52} +(-4.34698 + 0.688494i) q^{53} +(-4.59315 + 2.42961i) q^{54} +(-2.26666 - 3.11979i) q^{56} +(4.56057 - 10.3855i) q^{57} +(6.16696 + 0.976751i) q^{58} +(-0.713107 - 2.19472i) q^{59} +(0.0451729 - 0.139028i) q^{61} +(-1.90338 + 3.73559i) q^{62} +(3.10814 + 11.1435i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(0.387119 + 0.473094i) q^{66} +(-1.18445 + 7.47829i) q^{67} +(2.50443 - 2.50443i) q^{68} +(-7.33546 + 11.4228i) q^{69} +(-3.62303 + 4.98667i) q^{71} +(2.35059 + 1.86407i) q^{72} +(9.30362 - 4.74043i) q^{73} -4.86552 q^{74} -6.54875 q^{76} +(1.21266 - 0.617880i) q^{77} +(3.70643 - 2.16521i) q^{78} +(0.803169 - 1.10547i) q^{79} +(-4.65817 - 7.70074i) q^{81} +(-5.99652 + 5.99652i) q^{82} +(0.915181 - 5.77823i) q^{83} +(5.16925 - 4.22984i) q^{84} +(6.94488 + 2.25653i) q^{86} +(-1.07553 + 10.7610i) q^{87} +(0.160227 - 0.314463i) q^{88} +(-0.633239 + 1.94891i) q^{89} +(-2.95327 - 9.08922i) q^{91} +(7.74123 + 1.22609i) q^{92} +(-6.64888 - 2.91971i) q^{93} +(-2.51330 - 3.45926i) q^{94} +(0.439743 - 1.67530i) q^{96} +(-6.93926 + 1.09907i) q^{97} +(-3.57330 - 7.01300i) 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} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$-1$

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 $

$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$3$	0.873670	+	1.49556i	0.504413	+	0.863462i
$3$	0.873670	+	1.49556i	0.504413	+	0.863462i
$4$	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	$-0.490093\pi$
$7$	2.72680	−	2.72680i	1.03063	−	1.03063i	0.999516	−	0.0311178i	$-0.00990669\pi$
$8$	0.156434	−	0.987688i	0.0553079	−	0.349201i
$9$	−1.47340	+	2.61325i	−0.491134	+	0.871084i
$10$		0			0
$11$	0.335657	+	0.109061i	0.101204	+	0.0328833i	0.359181	−	0.933268i	$-0.383056\pi$
$11$	0.335657	+	0.109061i	0.101204	+	0.0328833i	−0.257977	+	0.966151i	$0.583056\pi$
$12$	1.72346	+	0.172255i	0.497521	+	0.0497257i
$13$	1.12512	−	2.20817i	0.312052	−	0.612437i	−0.680707	−	0.732555i	$-0.738327\pi$
$13$	1.12512	−	2.20817i	0.312052	−	0.612437i	0.992760	+	0.120119i	$0.0383275\pi$
$14$	1.19166	−	3.66754i	0.318483	−	0.980191i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	3.49819	+	0.554059i	0.848436	+	0.134379i	0.565488	−	0.824756i	$-0.308688\pi$
$17$	3.49819	+	0.554059i	0.848436	+	0.134379i	0.282948	+	0.959135i	$0.408688\pi$
$18$	−0.126420	+	2.99734i	−0.0297975	+	0.706479i
$19$	−3.84926	−	5.29805i	−0.883080	−	1.21546i	−0.975558	−	0.219741i	$-0.929479\pi$
$19$	−3.84926	−	5.29805i	−0.883080	−	1.21546i	0.0924780	−	0.995715i	$-0.470521\pi$
$20$		0			0
$21$	6.46042	+	1.69577i	1.40978	+	0.370048i
$22$	0.348585	−	0.0552105i	0.0743186	−	0.0117709i
$23$	3.55825	+	6.98347i	0.741947	+	1.45615i	0.884585	+	0.466378i	$0.154441\pi$
$23$	3.55825	+	6.98347i	0.741947	+	1.45615i	−0.142638	+	0.989775i	$0.545559\pi$
$24$	1.61382	−	0.628956i	0.329420	−	0.128385i
$25$		0			0
$26$		−	2.47829i		−	0.486033i
$27$	−5.19554	+	0.0795559i	−0.999883	+	0.0153105i
$28$	−0.603255	−	3.80880i	−0.114004	−	0.719796i
$29$	5.05137	+	3.67003i	0.938015	+	0.681508i	0.947942	−	0.318443i	$-0.103160\pi$
$29$	5.05137	+	3.67003i	0.938015	+	0.681508i	−0.00992666	+	0.999951i	$0.503160\pi$
$30$		0			0
$31$	−3.39184	+	2.46432i	−0.609193	+	0.442604i	−0.849130	−	0.528184i	$-0.822873\pi$
$31$	−3.39184	+	2.46432i	−0.609193	+	0.442604i	0.239937	+	0.970788i	$0.422873\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.130145	+	0.597278i	0.0226553	+	0.103973i
$34$	3.36845	−	1.09448i	0.577684	−	0.187701i
$35$		0			0
$36$	1.24812	+	2.72804i	0.208020	+	0.454673i
$37$	−4.33521	−	2.20890i	−0.712704	−	0.363141i	0.0597483	−	0.998213i	$-0.480970\pi$
$37$	−4.33521	−	2.20890i	−0.712704	−	0.363141i	−0.772452	+	0.635073i	$0.780970\pi$
$38$	−5.83498	−	2.97307i	−0.946558	−	0.482296i
$39$	4.28544	−	0.246528i	0.686219	−	0.0394761i
$40$		0			0
$41$	−8.06531	+	2.62058i	−1.25959	+	0.409265i	−0.861348	−	0.508015i	$-0.830379\pi$
$41$	−8.06531	+	2.62058i	−1.25959	+	0.409265i	−0.398241	+	0.917281i	$0.630379\pi$
$42$	6.52614	−	1.42202i	1.00700	−	0.219423i
$43$	5.16349	+	5.16349i	0.787425	+	0.787425i	0.981071	−	0.193647i	$-0.0620315\pi$
$43$	5.16349	+	5.16349i	0.787425	+	0.787425i	−0.193647	+	0.981071i	$0.562031\pi$
$44$	0.285527	−	0.207447i	0.0430448	−	0.0312738i
$45$		0			0
$46$	6.34085	+	4.60690i	0.934908	+	0.679250i
$47$	−0.668895	−	4.22323i	−0.0975683	−	0.616022i	−0.987218	−	0.159378i	$-0.949051\pi$
$47$	−0.668895	−	4.22323i	−0.0975683	−	0.616022i	0.889649	−	0.456644i	$-0.150949\pi$
$48$	1.15238	−	1.29306i	0.166332	−	0.186638i
$49$		−	7.87088i		−	1.12441i
$50$		0			0
$51$	2.22763	+	5.71582i	0.311931	+	0.800375i
$52$	−1.12512	−	2.20817i	−0.156026	−	0.306218i
$53$	−4.34698	+	0.688494i	−0.597103	+	0.0945719i	−0.447668	−	0.894200i	$-0.647745\pi$
$53$	−4.34698	+	0.688494i	−0.597103	+	0.0945719i	−0.149435	+	0.988772i	$0.547745\pi$
$54$	−4.59315	+	2.42961i	−0.625048	+	0.330628i
$55$		0			0
$56$	−2.26666	−	3.11979i	−0.302896	−	0.416900i
$57$	4.56057	−	10.3855i	0.604063	−	1.37560i
$58$	6.16696	+	0.976751i	0.809762	+	0.128254i
$59$	−0.713107	−	2.19472i	−0.0928386	−	0.285728i	0.893846	−	0.448375i	$-0.147997\pi$
$59$	−0.713107	−	2.19472i	−0.0928386	−	0.285728i	−0.986684	+	0.162647i	$0.947997\pi$
$60$		0			0
$61$	0.0451729	−	0.139028i	0.00578380	−	0.0178007i	−0.948123	−	0.317904i	$-0.897021\pi$
$61$	0.0451729	−	0.139028i	0.00578380	−	0.0178007i	0.953907	+	0.300103i	$0.0970211\pi$
$62$	−1.90338	+	3.73559i	−0.241729	+	0.474420i
$63$	3.10814	+	11.1435i	0.391589	+	1.40395i
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$		0			0
$66$	0.387119	+	0.473094i	0.0476510	+	0.0582339i
$67$	−1.18445	+	7.47829i	−0.144703	+	0.913619i	0.803350	+	0.595507i	$0.203049\pi$
$67$	−1.18445	+	7.47829i	−0.144703	+	0.913619i	−0.948053	+	0.318112i	$0.896951\pi$
$68$	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	−0.967947	−	0.251153i	$-0.919190\pi$
$71$	−3.62303	+	4.98667i	−0.429974	+	0.591809i	0.537973	+	0.842962i	$0.319190\pi$
$72$	2.35059	+	1.86407i	0.277019	+	0.219682i
$73$	9.30362	−	4.74043i	1.08891	−	0.554825i	0.185079	−	0.982724i	$-0.440746\pi$
$73$	9.30362	−	4.74043i	1.08891	−	0.554825i	0.903827	+	0.427898i	$0.140746\pi$
$74$	−4.86552			−0.565605
$75$		0			0
$76$	−6.54875			−0.751193
$77$	1.21266	−	0.617880i	0.138195	−	0.0704139i
$78$	3.70643	−	2.16521i	0.419671	−	0.245161i
$79$	0.803169	−	1.10547i	0.0903636	−	0.124375i	−0.761442	−	0.648234i	$-0.775508\pi$
$79$	0.803169	−	1.10547i	0.0903636	−	0.124375i	0.851805	+	0.523859i	$0.175508\pi$
$80$		0			0
$81$	−4.65817	−	7.70074i	−0.517574	−	0.855638i
$82$	−5.99652	+	5.99652i	−0.662205	+	0.662205i
$83$	0.915181	−	5.77823i	0.100454	−	0.634243i	−0.885167	−	0.465273i	$-0.845956\pi$
$83$	0.915181	−	5.77823i	0.100454	−	0.634243i	0.985621	−	0.168969i	$-0.0540439\pi$
$84$	5.16925	−	4.22984i	0.564011	−	0.461513i
$85$		0			0
$86$	6.94488	+	2.25653i	0.748886	+	0.243328i
$87$	−1.07553	+	10.7610i	−0.115309	+	1.15370i
$88$	0.160227	−	0.314463i	0.0170803	−	0.0335219i
$89$	−0.633239	+	1.94891i	−0.0671232	+	0.206584i	−0.978992	−	0.203897i	$-0.934639\pi$
$89$	−0.633239	+	1.94891i	−0.0671232	+	0.206584i	0.911869	+	0.410481i	$0.134639\pi$
$90$		0			0
$91$	−2.95327	−	9.08922i	−0.309587	−	0.952809i
$92$	7.74123	+	1.22609i	0.807079	+	0.127829i
$93$	−6.64888	−	2.91971i	−0.689457	−	0.302759i
$94$	−2.51330	−	3.45926i	−0.259227	−	0.356795i
$95$		0			0
$96$	0.439743	−	1.67530i	0.0448811	−	0.170984i
$97$	−6.93926	+	1.09907i	−0.704575	+	0.111594i	−0.498433	−	0.866928i	$-0.666091\pi$
$97$	−6.93926	+	1.09907i	−0.704575	+	0.111594i	−0.206142	+	0.978522i	$0.566091\pi$
$98$	−3.57330	−	7.01300i	−0.360958	−	0.708420i
$99$	−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	$0.841738\pi$
$102$	4.57976	+	4.08151i	0.453464	+	0.404130i
$103$	−1.04075	−	6.57102i	−0.102548	−	0.647462i	−0.984401	−	0.175938i	$-0.943704\pi$
$103$	−1.04075	−	6.57102i	−0.102548	−	0.647462i	0.881853	−	0.471524i	$-0.156296\pi$
$104$	−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	$-0.502770\pi$
$108$	−2.98950	+	4.25004i	−0.287665	+	0.408961i
$109$	−10.5722	+	3.43511i	−1.01263	+	0.329024i	−0.767902	−	0.640568i	$-0.778699\pi$
$109$	−10.5722	+	3.43511i	−1.01263	+	0.329024i	−0.244729	+	0.969592i	$0.578699\pi$
$110$		0			0
$111$	−0.483998	−	8.41342i	−0.0459391	−	0.798566i
$112$	−3.43597	−	1.75071i	−0.324668	−	0.165427i
$113$	−1.56816	−	0.799015i	−0.147520	−	0.0751650i	0.378672	−	0.925531i	$-0.376381\pi$
$113$	−1.56816	−	0.799015i	−0.147520	−	0.0751650i	−0.526192	+	0.850366i	$0.676381\pi$
$114$	−0.651437	−	11.3240i	−0.0610127	−	1.06059i
$115$		0			0
$116$	5.93824	−	1.92945i	0.551352	−	0.179145i
$117$	4.11276	+	6.19375i	0.380224	+	0.572612i
$118$	−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
$122$	−0.0228680	−	0.144383i	−0.00207037	−	0.0130718i
$123$	−10.9656	−	9.77263i	−0.988739	−	0.881169i
$124$			4.19255i			0.376502i
$125$		0			0
$126$	7.82841	+	8.51786i	0.697410	+	0.758831i
$127$	−2.44874	−	4.80592i	−0.217290	−	0.426457i	0.756471	−	0.654027i	$-0.226922\pi$
$127$	−2.44874	−	4.80592i	−0.217290	−	0.426457i	−0.973762	+	0.227571i	$0.926922\pi$
$128$	−0.987688	+	0.156434i	−0.0873001	+	0.0138270i
$129$	−3.21113	+	12.2335i	−0.282724	+	1.07710i
$130$		0			0
$131$	−10.2354	−	14.0878i	−0.894273	−	1.23086i	−0.972259	−	0.233906i	$-0.924849\pi$
$131$	−10.2354	−	14.0878i	−0.894273	−	1.23086i	0.0779865	−	0.996954i	$-0.475151\pi$
$132$	0.559706	+	0.245782i	0.0487161	+	0.0213926i
$133$	−24.9429	−	3.95056i	−2.16282	−	0.342557i
$134$	2.33973	+	7.20094i	0.202122	+	0.622066i
$135$		0			0
$136$	1.09448	−	3.36845i	0.0938505	−	0.288842i
$137$	−8.13848	+	15.9727i	−0.695317	+	1.36464i	0.225346	+	0.974279i	$0.427649\pi$
$137$	−8.13848	+	15.9727i	−0.695317	+	1.36464i	−0.920663	+	0.390358i	$0.872351\pi$
$138$	−1.35009	+	13.5080i	−0.114927	+	1.14988i
$139$	17.1405	+	5.56927i	1.45383	+	0.472379i	0.926181	−	0.377080i	$-0.123072\pi$
$139$	17.1405	+	5.56927i	1.45383	+	0.472379i	0.527654	+	0.849459i	$0.323072\pi$
$140$		0			0
$141$	5.73171	−	4.69008i	0.482697	−	0.394976i
$142$	−0.964240	+	6.08797i	−0.0809172	+	0.510891i
$143$	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
$147$	11.7714	−	6.87655i	0.970886	−	0.567168i
$148$	−4.33521	+	2.20890i	−0.356352	+	0.181570i
$149$	−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	$0.703361\pi$
$152$	−5.83498	+	2.97307i	−0.473279	+	0.241148i
$153$	−6.60214	+	8.32530i	−0.533751	+	0.673061i
$154$	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	−0.822273	−	0.569093i	$-0.807295\pi$
$157$	−3.17235	+	3.17235i	−0.253181	+	0.253181i	0.569093	+	0.822273i	$0.307295\pi$
$158$	0.213757	−	1.34961i	0.0170056	−	0.107369i
$159$	−4.82751	−	5.89965i	−0.382846	−	0.467873i
$160$		0			0
$161$	28.7452	+	9.33987i	2.26544	+	0.736085i
$162$	−7.64652	−	4.74665i	−0.600768	−	0.372932i
$163$	4.91227	−	9.64088i	0.384759	−	0.755132i	−0.614675	−	0.788781i	$-0.710713\pi$
$163$	4.91227	−	9.64088i	0.384759	−	0.755132i	0.999434	+	0.0336487i	$0.0107127\pi$
$164$	−2.62058	+	8.06531i	−0.204633	+	0.629795i
$165$		0			0
$166$	−1.80783	−	5.56392i	−0.140315	−	0.431844i
$167$	16.5871	+	2.62714i	1.28355	+	0.203295i	0.760686	−	0.649120i	$-0.224863\pi$
$167$	16.5871	+	2.62714i	1.28355	+	0.203295i	0.522866	+	0.852415i	$0.324863\pi$
$168$	2.68553	−	6.11560i	0.207193	−	0.471829i
$169$	4.03108	+	5.54830i	0.310083	+	0.426793i
$170$		0			0
$171$	19.5166	−	2.25292i	1.49247	−	0.172285i
$172$	7.21237	−	1.14233i	0.549938	−	0.0871017i
$173$	7.90821	+	15.5207i	0.601250	+	1.18002i	0.968293	+	0.249816i	$0.0803702\pi$
$173$	7.90821	+	15.5207i	0.601250	+	1.18002i	−0.367043	+	0.930204i	$0.619630\pi$
$174$	3.92710	+	10.0764i	0.297713	+	0.763892i
$175$		0			0
$176$		−	0.352930i		−	0.0266031i
$177$	2.65931	−	2.98395i	0.199886	−	0.224288i
$178$	0.320566	+	2.02397i	0.0240274	+	0.151703i
$179$	−5.94519	−	4.31943i	−0.444364	−	0.322849i	0.343002	−	0.939334i	$-0.388556\pi$
$179$	−5.94519	−	4.31943i	−0.444364	−	0.322849i	−0.787367	+	0.616485i	$0.788556\pi$
$180$		0			0
$181$	−0.543117	+	0.394597i	−0.0403695	+	0.0293302i	−0.607787	−	0.794100i	$-0.707943\pi$
$181$	−0.543117	+	0.394597i	−0.0403695	+	0.0293302i	0.567418	+	0.823430i	$0.307943\pi$
$182$	−6.75780	−	6.75780i	−0.500922	−	0.500922i
$183$	0.247391	−	0.0539056i	0.0182877	−	0.00398482i
$184$	7.45412	−	2.42199i	0.549525	−	0.178552i
$185$		0			0
$186$	−7.24972	+	0.417054i	−0.531575	+	0.0305799i
$187$	1.11376	+	0.567491i	0.0814465	+	0.0414991i
$188$	−3.80983	−	1.94121i	−0.277861	−	0.141577i
$189$	−13.9503	+	14.3841i	−1.01473	+	1.04629i
$190$		0			0
$191$	−13.4008	+	4.35419i	−0.969650	+	0.315058i	−0.750675	−	0.660672i	$-0.770271\pi$
$191$	−13.4008	+	4.35419i	−0.969650	+	0.315058i	−0.218975	+	0.975730i	$0.570271\pi$
$192$	−0.368756	−	1.69234i	−0.0266126	−	0.122134i
$193$	2.89340	+	2.89340i	0.208271	+	0.208271i	0.803532	−	0.595261i	$-0.202951\pi$
$193$	2.89340	+	2.89340i	0.208271	+	0.208271i	−0.595261	+	0.803532i	$0.702951\pi$
$194$	−5.68396	+	4.12964i	−0.408085	+	0.296491i
$195$		0			0
$196$	−6.36767	−	4.62638i	−0.454834	−	0.330456i
$197$	−3.55739	−	22.4605i	−0.253454	−	1.60024i	−0.705806	−	0.708405i	$-0.749415\pi$
$197$	−3.55739	−	22.4605i	−0.253454	−	1.60024i	0.452353	−	0.891839i	$-0.350585\pi$
$198$	−0.369327	+	0.992288i	−0.0262470	+	0.0705188i
$199$			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
$202$	4.35231	+	8.54189i	0.306228	+	0.601006i
$203$	23.7815	−	3.76662i	1.66914	−	0.264365i
$204$	5.93357	+	1.55748i	0.415433	+	0.109045i
$205$		0			0
$206$	−3.91049	−	5.38233i	−0.272457	−	0.375005i
$207$	−23.4923	−	0.990845i	−1.63283	−	0.0688685i
$208$	−2.44778	−	0.387690i	−0.169723	−	0.0268815i
$209$	−0.714216	−	2.19813i	−0.0494033	−	0.152048i
$210$		0			0
$211$	−1.28435	+	3.95283i	−0.0884185	+	0.272124i	−0.985483	−	0.169776i	$-0.945696\pi$
$211$	−1.28435	+	3.95283i	−0.0884185	+	0.272124i	0.897064	+	0.441900i	$0.145696\pi$
$212$	−1.99809	+	3.92147i	−0.137229	+	0.269327i
$213$	−10.6232	−	1.06175i	−0.727889	−	0.0727502i
$214$	−14.0333	−	4.55969i	−0.959296	−	0.311694i
$215$		0			0
$216$	−0.734186	+	5.14402i	−0.0499550	+	0.350006i
$217$	−2.52917	+	15.9686i	−0.171691	+	1.08402i
$218$	−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
$222$	−4.25086	−	7.27668i	−0.285299	−	0.488379i
$223$	−13.6942	+	6.97753i	−0.917030	+	0.467250i	−0.847779	−	0.530349i	$-0.822061\pi$
$223$	−13.6942	+	6.97753i	−0.917030	+	0.467250i	−0.0692509	+	0.997599i	$0.522061\pi$
$224$	−3.85628			−0.257658
$225$		0			0
$226$	−1.75998			−0.117072
$227$	12.4969	−	6.36747i	0.829445	−	0.422624i	0.0129084	−	0.999917i	$-0.495891\pi$
$227$	12.4969	−	6.36747i	0.829445	−	0.422624i	0.816537	+	0.577293i	$0.195891\pi$
$228$	−5.72144	−	9.79405i	−0.378912	−	0.648627i
$229$	10.1878	−	14.0224i	0.673232	−	0.926624i	−0.326596	−	0.945164i	$-0.605902\pi$
$229$	10.1878	−	14.0224i	0.673232	−	0.926624i	0.999828	+	0.0185396i	$0.00590167\pi$
$230$		0			0
$231$	1.98354	+	1.27378i	0.130507	+	0.0838085i
$232$	4.41506	−	4.41506i	0.289863	−	0.289863i
$233$	−0.384884	+	2.43006i	−0.0252146	+	0.159199i	−0.997083	−	0.0763263i	$-0.975681\pi$
$233$	−0.384884	+	2.43006i	−0.0252146	+	0.159199i	0.971868	+	0.235525i	$0.0756809\pi$
$234$	6.47640	+	3.65152i	0.423375	+	0.238707i
$235$		0			0
$236$	−2.19472	−	0.713107i	−0.142864	−	0.0464193i
$237$	2.35500	+	0.235375i	0.152974	+	0.0152892i
$238$	6.20067	−	12.1695i	0.401930	−	0.788831i
$239$	−0.751883	+	2.31406i	−0.0486352	+	0.149684i	−0.972425	−	0.233217i	$-0.925075\pi$
$239$	−0.751883	+	2.31406i	−0.0486352	+	0.149684i	0.923790	+	0.382901i	$0.125075\pi$
$240$		0			0
$241$	0.500207	+	1.53948i	0.0322212	+	0.0991666i	0.965874	−	0.259013i	$-0.0833974\pi$
$241$	0.500207	+	1.53948i	0.0322212	+	0.0991666i	−0.933653	+	0.358180i	$0.883397\pi$
$242$	−10.7415	−	1.70129i	−0.690493	−	0.109363i
$243$	7.44723	−	13.6945i	0.477740	−	0.878501i
$244$	−0.0859239	−	0.118264i	−0.00550072	−	0.00757109i
$245$		0			0
$246$	−14.2071	−	3.72918i	−0.905814	−	0.237764i
$247$	−16.0299	+	2.53888i	−1.01996	+	0.161545i
$248$	1.90338	+	3.73559i	0.120865	+	0.237210i
$249$	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	$-0.284962\pi$
$252$	10.8422	+	4.03544i	0.682994	+	0.254209i
$253$	0.432724	+	2.73211i	0.0272052	+	0.171767i
$254$	−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	$0.398557\pi$
$258$	2.69276	+	12.3579i	0.167644	+	0.769372i
$259$	−17.8445	+	5.79802i	−1.10880	+	0.360272i
$260$		0			0
$261$	−17.0334	+	7.79306i	−1.05434	+	0.482378i
$262$	−15.5156	−	7.90558i	−0.958555	−	0.488408i
$263$	2.68232	+	1.36671i	0.165399	+	0.0842750i	0.534730	−	0.845023i	$-0.320413\pi$
$263$	2.68232	+	1.36671i	0.165399	+	0.0842750i	−0.369331	+	0.929298i	$0.620413\pi$
$264$	0.610284	−	0.0351078i	0.0375604	−	0.00216073i
$265$		0			0
$266$	−24.0178	+	7.80385i	−1.47262	+	0.478485i
$267$	−3.46795	+	0.755655i	−0.212235	+	0.0462454i
$268$	5.35387	+	5.35387i	0.327039	+	0.327039i
$269$	−10.4918	+	7.62274i	−0.639697	+	0.464767i	−0.859746	−	0.510722i	$-0.829378\pi$
$269$	−10.4918	+	7.62274i	−0.639697	+	0.464767i	0.220049	+	0.975489i	$0.429378\pi$
$270$		0			0
$271$	13.7784	+	10.0106i	0.836981	+	0.608102i	0.921526	−	0.388317i	$-0.126944\pi$
$271$	13.7784	+	10.0106i	0.836981	+	0.608102i	−0.0845447	+	0.996420i	$0.526944\pi$
$272$	−0.554059	−	3.49819i	−0.0335948	−	0.212109i
$273$	11.0133	−	12.3578i	0.666555	−	0.747926i
$274$			17.9265i			1.08298i
$275$		0			0
$276$	4.92959	+	12.6487i	0.296726	+	0.761361i
$277$	4.82425	+	9.46812i	0.289861	+	0.568884i	0.989315	−	0.145793i	$-0.0465735\pi$
$277$	4.82425	+	9.46812i	0.289861	+	0.568884i	−0.699454	+	0.714677i	$0.746573\pi$
$278$	17.8007	−	2.81935i	1.06761	−	0.169093i
$279$	−1.44233	−	12.4947i	−0.0863502	−	0.748036i
$280$		0			0
$281$	16.4932	+	22.7009i	0.983902	+	1.35422i	0.934701	+	0.355436i	$0.115668\pi$
$281$	16.4932	+	22.7009i	0.983902	+	1.35422i	0.0492011	+	0.998789i	$0.484332\pi$
$282$	2.97774	−	6.78104i	0.177322	−	0.403805i
$283$	25.3567	+	4.01611i	1.50730	+	0.238733i	0.854761	−	0.519022i	$-0.173704\pi$
$283$	25.3567	+	4.01611i	1.50730	+	0.238733i	0.652539	+	0.757755i	$0.273704\pi$
$284$	1.90474	+	5.86218i	0.113025	+	0.347856i
$285$		0			0
$286$	0.270286	−	0.831854i	0.0159823	−	0.0491886i
$287$	−14.8467	+	29.1383i	−0.876372	+	1.71998i
$288$	2.88970	−	0.805995i	0.170277	−	0.0474937i
$289$	−4.23760	−	1.37688i	−0.249271	−	0.0809930i
$290$		0			0
$291$	−7.70635	−	9.41786i	−0.451754	−	0.552085i
$292$	1.63344	−	10.3131i	0.0955899	−	0.603531i
$293$	−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
$297$	−1.75260	−	0.539930i	−0.101696	−	0.0313299i
$298$	−4.14221	+	2.11056i	−0.239952	+	0.122262i
$299$	19.4242			1.12333
$300$		0			0
$301$	28.1596			1.62309
$302$	−13.0575	+	6.65314i	−0.751376	+	0.382845i
$303$	−14.3376	+	8.37569i	−0.823675	+	0.481171i
$304$	−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	−0.235744	−	0.971815i	$-0.575753\pi$
$307$	12.8970	−	12.8970i	0.736071	−	0.736071i	0.971815	+	0.235744i	$0.0757527\pi$
$308$	0.212907	−	1.34424i	0.0121315	−	0.0765952i
$309$	8.91809	−	7.29740i	0.507333	−	0.415135i
$310$		0			0
$311$	15.4255	+	5.01205i	0.874699	+	0.284207i	0.711755	−	0.702428i	$-0.247901\pi$
$311$	15.4255	+	5.01205i	0.874699	+	0.284207i	0.162945	+	0.986635i	$0.447901\pi$
$312$	0.426897	−	4.27124i	0.0241683	−	0.241812i
$313$	−2.45198	+	4.81228i	−0.138594	+	0.272006i	−0.949863	−	0.312668i	$-0.898777\pi$
$313$	−2.45198	+	4.81228i	−0.138594	+	0.272006i	0.811269	+	0.584674i	$0.198777\pi$
$314$	−1.38637	+	4.26680i	−0.0782372	+	0.240789i
$315$		0			0
$316$	−0.422251	−	1.29956i	−0.0237535	−	0.0731057i
$317$	8.47316	+	1.34202i	0.475900	+	0.0753752i	0.389777	−	0.920909i	$-0.372552\pi$
$317$	8.47316	+	1.34202i	0.475900	+	0.0753752i	0.0861233	+	0.996284i	$0.472552\pi$
$318$	−6.97973	−	3.06499i	−0.391404	−	0.171876i
$319$	1.29527	+	1.78278i	0.0725210	+	0.0998166i
$320$		0			0
$321$	6.48862	−	24.7198i	0.362160	−	1.37973i
$322$	29.8523	−	4.72815i	1.66361	−	0.263489i
$323$	−10.5300	−	20.6663i	−0.585905	−	1.14990i
$324$	−8.96804	−	0.757846i	−0.498224	−	0.0421025i
$325$		0			0
$326$		−	10.8202i		−	0.599276i
$327$	−14.3740	−	12.8102i	−0.794884	−	0.708404i
$328$	1.32662	+	8.37596i	0.0732504	+	0.462485i
$329$	−13.3399	−	9.69197i	−0.735450	−	0.534336i
$330$		0			0
$331$	22.9895	−	16.7029i	1.26362	−	0.918073i	0.264690	−	0.964334i	$-0.414731\pi$
$331$	22.9895	−	16.7029i	1.26362	−	0.918073i	0.998929	+	0.0462607i	$0.0147305\pi$
$332$	−4.13675	−	4.13675i	−0.227034	−	0.227034i
$333$	12.1599	−	8.07440i	0.666360	−	0.442474i
$334$	15.9719	−	5.18960i	0.873946	−	0.283962i
$335$		0			0
$336$	−0.383604	−	6.66824i	−0.0209273	−	0.363783i
$337$	4.22871	+	2.15464i	0.230353	+	0.117371i	0.565358	−	0.824846i	$-0.308738\pi$
$337$	4.22871	+	2.15464i	0.230353	+	0.117371i	−0.335005	+	0.942216i	$0.608738\pi$
$338$	6.11059	+	3.11350i	0.332372	+	0.169352i
$339$	−0.175074	−	3.04335i	−0.00950874	−	0.165292i
$340$		0			0
$341$	−1.40726	+	0.457245i	−0.0762072	+	0.0247612i
$342$	16.3666	−	10.8677i	0.885007	−	0.587660i
$343$	−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
$347$	1.25574	+	7.92843i	0.0674116	+	0.425620i	0.998195	+	0.0600500i	$0.0191260\pi$
$347$	1.25574	+	7.92843i	0.0674116	+	0.425620i	−0.930784	+	0.365570i	$0.880874\pi$
$348$	8.07367	+	7.19529i	0.432794	+	0.385708i
$349$		−	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
$352$	−0.160227	−	0.314463i	−0.00854013	−	0.0167609i
$353$	−4.66620	+	0.739053i	−0.248357	+	0.0393358i	−0.279371	−	0.960183i	$-0.590126\pi$
$353$	−4.66620	+	0.739053i	−0.248357	+	0.0393358i	0.0310149	+	0.999519i	$0.490126\pi$
$354$	1.01478	−	3.86602i	0.0539349	−	0.205477i
$355$		0			0
$356$	1.20449	+	1.65784i	0.0638379	+	0.0878654i
$357$	21.6602	+	9.51159i	1.14638	+	0.503406i
$358$	−7.25818	−	1.14958i	−0.383607	−	0.0607573i
$359$	−4.67561	−	14.3900i	−0.246769	−	0.759478i	−0.995340	−	0.0964232i	$-0.969260\pi$
$359$	−4.67561	−	14.3900i	−0.246769	−	0.759478i	0.748571	−	0.663054i	$-0.230740\pi$
$360$		0			0
$361$	−7.38121	+	22.7170i	−0.388485	+	1.19563i
$362$	−0.304777	+	0.598158i	−0.0160187	+	0.0314385i
$363$	1.87335	−	18.7434i	0.0983252	−	0.983775i
$364$	−9.08922	−	2.95327i	−0.476405	−	0.154793i
$365$		0			0
$366$	0.195954	−	0.160343i	0.0102427	−	0.00838128i
$367$	5.73021	−	36.1791i	0.299114	−	1.88853i	−0.140078	−	0.990140i	$-0.544735\pi$
$367$	5.73021	−	36.1791i	0.299114	−	1.88853i	0.439193	−	0.898393i	$-0.355265\pi$
$368$	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
$372$	−6.27021	+	3.66290i	−0.325095	+	0.189913i
$373$	1.97517	−	1.00640i	0.102270	−	0.0521093i	−0.402107	−	0.915593i	$-0.631722\pi$
$373$	1.97517	−	1.00640i	0.102270	−	0.0521093i	0.504377	+	0.863483i	$0.331722\pi$
$374$	1.25001			0.0646363
$375$		0			0
$376$	−4.27588			−0.220512
$377$	13.7875	−	7.02506i	0.710090	−	0.361809i
$378$	−5.89952	+	19.1497i	−0.303439	+	0.984952i
$379$	4.15559	−	5.71968i	0.213458	−	0.293800i	−0.688839	−	0.724914i	$-0.741879\pi$
$379$	4.15559	−	5.71968i	0.213458	−	0.293800i	0.902297	+	0.431114i	$0.141879\pi$
$380$		0			0
$381$	5.04816	−	7.86103i	0.258625	−	0.402733i
$382$	−9.96347	+	9.96347i	−0.509775	+	0.509775i
$383$	2.17700	−	13.7450i	0.111240	−	0.702339i	−0.867532	−	0.497382i	$-0.834295\pi$
$383$	2.17700	−	13.7450i	0.111240	−	0.702339i	0.978771	−	0.204957i	$-0.0657053\pi$
$384$	−1.09687	−	1.34048i	−0.0559744	−	0.0684059i
$385$		0			0
$386$	3.89161	+	1.26446i	0.198078	+	0.0643593i
$387$	−21.1014	+	5.88560i	−1.07264	+	0.299182i
$388$	−3.18963	+	6.26000i	−0.161929	+	0.317803i
$389$	4.65972	−	14.3411i	0.236257	−	0.727125i	−0.760695	−	0.649110i	$-0.775142\pi$
$389$	4.65972	−	14.3411i	0.236257	−	0.727125i	0.996952	−	0.0780155i	$-0.0248584\pi$
$390$		0			0
$391$	8.57820	+	26.4010i	0.433818	+	1.33515i
$392$	−7.77397	−	1.23128i	−0.392645	−	0.0621888i
$393$	12.1268	−	27.6158i	0.611719	−	1.39303i
$394$	−13.3665	−	18.3974i	−0.673395	−	0.926849i
$395$		0			0
$396$	0.121416	+	1.05181i	0.00610139	+	0.0528552i
$397$	13.6256	−	2.15808i	0.683849	−	0.108311i	0.195163	−	0.980771i	$-0.437476\pi$
$397$	13.6256	−	2.15808i	0.683849	−	0.108311i	0.488686	+	0.872460i	$0.337476\pi$
$398$	2.86862	+	5.62998i	0.143791	+	0.282205i
$399$	−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	$0.870746\pi$
$402$	−8.72529	+	9.79044i	−0.435178	+	0.488303i
$403$	1.62541	+	10.2624i	0.0809674	+	0.511208i
$404$	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
$408$	5.99393	−	1.30606i	0.296744	−	0.0646595i
$409$	−5.65867	+	1.83861i	−0.279803	+	0.0909136i	−0.445557	−	0.895254i	$-0.646994\pi$
$409$	−5.65867	+	1.83861i	−0.279803	+	0.0909136i	0.165754	+	0.986167i	$0.446994\pi$
$410$		0			0
$411$	−30.9984	+	1.78324i	−1.52904	+	0.0879610i
$412$	−5.92780	−	3.02037i	−0.292042	−	0.148803i
$413$	−7.92905	−	4.04005i	−0.390163	−	0.198798i
$414$	−21.3816	+	9.78243i	−1.05085	+	0.480780i
$415$		0			0
$416$	−2.35699	+	0.765834i	−0.115561	+	0.0375481i
$417$	6.64591	+	30.5003i	0.325452	+	1.49361i
$418$	−1.63430	−	1.63430i	−0.0799363	−	0.0799363i
$419$	3.49605	−	2.54003i	0.170793	−	0.124088i	−0.499105	−	0.866542i	$-0.666338\pi$
$419$	3.49605	−	2.54003i	0.170793	−	0.124088i	0.669898	+	0.742453i	$0.266338\pi$
$420$		0			0
$421$	−20.2471	−	14.7103i	−0.986781	−	0.716939i	−0.0275674	−	0.999620i	$-0.508776\pi$
$421$	−20.2471	−	14.7103i	−0.986781	−	0.716939i	−0.959214	+	0.282681i	$0.908776\pi$
$422$	0.650182	+	4.10508i	0.0316503	+	0.199832i
$423$	12.0219	+	4.47453i	0.584526	+	0.217559i
$424$			4.40116i			0.213739i
$425$		0			0
$426$	−9.94736	+	3.87680i	−0.481951	+	0.187831i
$427$	−0.255924	−	0.502279i	−0.0123850	−	0.0243070i
$428$	−14.5738	+	2.30827i	−0.704452	+	0.111574i
$429$	1.46532	+	0.384627i	0.0707464	+	0.0185700i
$430$		0			0
$431$	−4.11469	−	5.66339i	−0.198198	−	0.272796i	0.698337	−	0.715769i	$-0.253924\pi$
$431$	−4.11469	−	5.66339i	−0.198198	−	0.272796i	−0.896535	+	0.442973i	$0.853924\pi$
$432$	1.68117	+	4.91667i	0.0808855	+	0.236553i
$433$	9.74698	+	1.54377i	0.468410	+	0.0741889i	0.386178	−	0.922424i	$-0.373795\pi$
$433$	9.74698	+	1.54377i	0.468410	+	0.0741889i	0.0822322	+	0.996613i	$0.473795\pi$
$434$	4.99607	+	15.3763i	0.239819	+	0.738087i
$435$		0			0
$436$	−3.43511	+	10.5722i	−0.164512	+	0.506315i
$437$	23.3021	−	45.7330i	1.11469	−	2.18770i
$438$	17.9959	+	1.79863i	0.859877	+	0.0859420i
$439$	−0.555271	−	0.180419i	−0.0265016	−	0.00861091i	0.295736	−	0.955270i	$-0.404435\pi$
$439$	−0.555271	−	0.180419i	−0.0265016	−	0.00861091i	−0.322238	+	0.946659i	$0.604435\pi$
$440$		0			0
$441$	20.5686	+	11.5970i	0.979456	+	0.552237i
$442$	1.37312	−	8.66953i	0.0653126	−	0.412368i
$443$	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
$447$	−4.06161	−	6.95273i	−0.192108	−	0.328853i
$448$	−3.43597	+	1.75071i	−0.162334	+	0.0827134i
$449$	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
$452$	−1.56816	+	0.799015i	−0.0737598	+	0.0375825i
$453$	−12.8035	−	21.9171i	−0.601559	−	1.02976i
$454$	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	$-0.443951\pi$
$457$	24.7918	−	24.7918i	1.15971	−	1.15971i	0.984537	−	0.175174i	$-0.0560488\pi$
$458$	2.71142	−	17.1192i	0.126696	−	0.799928i
$459$	−18.2191	−	2.60034i	−0.850394	−	0.121373i
$460$		0			0
$461$	−0.133994	−	0.0435374i	−0.00624074	−	0.00202774i	0.305895	−	0.952065i	$-0.401044\pi$
$461$	−0.133994	−	0.0435374i	−0.00624074	−	0.00202774i	−0.312136	+	0.950038i	$0.601044\pi$
$462$	2.34563	+	0.234438i	0.109129	+	0.0109071i
$463$	4.02806	−	7.90552i	0.187200	−	0.367401i	−0.778264	−	0.627937i	$-0.783899\pi$
$463$	4.02806	−	7.90552i	0.187200	−	0.367401i	0.965464	+	0.260537i	$0.0838995\pi$
$464$	1.92945	−	5.93824i	0.0895725	−	0.275676i
$465$		0			0
$466$	0.760291	+	2.33993i	0.0352198	+	0.108395i
$467$	−4.81480	−	0.762590i	−0.222803	−	0.0352885i	0.0440349	−	0.999030i	$-0.485979\pi$
$467$	−4.81480	−	0.762590i	−0.222803	−	0.0352885i	−0.266838	+	0.963742i	$0.585979\pi$
$468$	7.42827	+	0.313305i	0.343372	+	0.0144825i
$469$	17.1621	+	23.6216i	0.792470	+	1.09074i
$470$		0			0
$471$	−7.51602	−	1.97285i	−0.346320	−	0.0909043i
$472$	−2.27925	+	0.360998i	−0.104911	+	0.0166163i
$473$	1.17002	+	2.29630i	0.0537977	+	0.105584i
$474$	2.20518	−	0.859427i	0.101287	−	0.0394748i
$475$		0			0
$476$		−	13.6581i		−	0.626020i
$477$	4.60564	−	12.3742i	0.210878	−	0.566575i
$478$	0.380627	+	2.40319i	0.0174095	+	0.109919i
$479$	11.5308	+	8.37759i	0.526854	+	0.382782i	0.819180	−	0.573537i	$-0.194429\pi$
$479$	11.5308	+	8.37759i	0.526854	+	0.382782i	−0.292326	+	0.956319i	$0.594429\pi$
$480$		0			0
$481$	−9.75526	+	7.08761i	−0.444802	+	0.323167i
$482$	1.14460	+	1.14460i	0.0521349	+	0.0521349i
$483$	11.1454	+	51.1501i	0.507135	+	2.32741i
$484$	−10.3432	+	3.36070i	−0.470144	+	0.152759i
$485$		0			0
$486$	0.418364	−	15.5828i	0.0189774	−	0.706852i
$487$	31.0777	+	15.8349i	1.40827	+	0.717547i	0.982321	−	0.187202i	$-0.0599418\pi$
$487$	31.0777	+	15.8349i	1.40827	+	0.717547i	0.425945	+	0.904749i	$0.359942\pi$
$488$	−0.130250	−	0.0663655i	−0.00589612	−	0.00300422i
$489$	18.7102	−	1.07634i	0.846106	−	0.0486739i
$490$		0			0
$491$	5.09165	−	1.65438i	0.229783	−	0.0746610i	−0.191862	−	0.981422i	$-0.561453\pi$
$491$	5.09165	−	1.65438i	0.229783	−	0.0746610i	0.421645	+	0.906761i	$0.361453\pi$
$492$	−14.3517	+	3.12718i	−0.647023	+	0.140984i
$493$	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
$497$	3.71838	+	23.4769i	0.166792	+	1.05308i
$498$	6.74174	−	7.56474i	0.302104	−	0.338984i
$499$			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
$502$	−11.2255	−	22.0313i	−0.501020	−	0.983307i
$503$	2.88408	−	0.456793i	0.128595	−	0.0203674i	−0.0918053	−	0.995777i	$-0.529264\pi$
$503$	2.88408	−	0.456793i	0.128595	−	0.0203674i	0.220400	+	0.975410i	$0.429264\pi$
$504$	11.4925	−	1.32665i	0.511917	−	0.0590936i
$505$		0			0
$506$	1.62591	+	2.23788i	0.0722807	+	0.0994859i
$507$	−4.77599	+	10.8761i	−0.212109	+	0.483025i
$508$	−5.32741	−	0.843778i	−0.236365	−	0.0374366i
$509$	3.24395	+	9.98385i	0.143786	+	0.442527i	0.996853	−	0.0792745i	$-0.0252604\pi$
$509$	3.24395	+	9.98385i	0.143786	+	0.442527i	−0.853067	+	0.521801i	$0.825260\pi$
$510$		0			0
$511$	12.4429	−	38.2953i	0.550441	−	1.69408i
$512$	−0.453990	+	0.891007i	−0.0200637	+	0.0393773i
$513$	20.4205	+	27.2200i	0.901586	+	1.20179i
$514$	27.2321	+	8.84825i	1.20116	+	0.390280i
$515$		0			0
$516$	8.00965	+	9.78853i	0.352605	+	0.430916i
$517$	0.236073	−	1.49051i	0.0103825	−	0.0655524i
$518$	−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	−0.980085	−	0.198578i	$-0.936368\pi$
$521$	−11.1471	+	15.3427i	−0.488364	+	0.672175i	0.491722	+	0.870753i	$0.336368\pi$
$522$	−11.6389	+	14.6767i	−0.509421	+	0.642381i
$523$	−21.7058	+	11.0596i	−0.949127	+	0.483604i	−0.858802	−	0.512308i	$-0.828791\pi$
$523$	−21.7058	+	11.0596i	−0.949127	+	0.483604i	−0.0903250	+	0.995912i	$0.528791\pi$
$524$	−17.4135			−0.760714
$525$		0			0
$526$	3.01044			0.131261
$527$	−13.2307	+	6.74137i	−0.576338	+	0.293659i
$528$	0.527829	−	0.308344i	0.0229708	−	0.0134190i
$529$	−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
$533$	−3.28775	+	20.7580i	−0.142408	+	0.899131i
$534$	−2.74691	+	2.24771i	−0.118870	+	0.0972680i
$535$		0			0
$536$	7.20094	+	2.33973i	0.311033	+	0.101061i
$537$	1.26584	−	12.6651i	0.0546251	−	0.546541i
$538$	−5.88761	+	11.5551i	−0.253833	+	0.498175i
$539$	0.858409	−	2.64191i	0.0369743	−	0.113795i
$540$		0			0
$541$	8.94591	+	27.5327i	0.384615	+	1.18372i	0.936759	+	0.349974i	$0.113810\pi$
$541$	8.94591	+	27.5327i	0.384615	+	1.18372i	−0.552144	+	0.833749i	$0.686190\pi$
$542$	16.8214	+	2.66425i	0.722542	+	0.114439i
$543$	−1.06465	−	0.467516i	−0.0456884	−	0.0200630i
$544$	−2.08182	−	2.86537i	−0.0892571	−	0.122852i
$545$		0			0
$546$	4.20261	−	16.0108i	0.179855	−	0.685198i
$547$	−12.9801	+	2.05584i	−0.554988	+	0.0879014i	−0.427627	−	0.903955i	$-0.640650\pi$
$547$	−12.9801	+	2.05584i	−0.554988	+	0.0879014i	−0.127360	+	0.991857i	$0.540650\pi$
$548$	8.13848	+	15.9727i	0.347659	+	0.682319i
$549$	0.296757	+	0.322892i	0.0126653	+	0.0137807i
$550$		0			0
$551$		−	40.8893i		−	1.74194i
$552$	10.1347	+	9.03207i	0.431360	+	0.384430i
$553$	−0.824307	−	5.20447i	−0.0350531	−	0.221317i
$554$	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	$-0.514160\pi$
$558$	−6.95759	−	10.4780i	−0.294538	−	0.443570i
$559$	17.2114	−	5.59233i	0.727966	−	0.236530i
$560$		0			0
$561$	0.124345	+	2.16150i	0.00524983	+	0.0912587i
$562$	25.0016	+	12.7389i	1.05463	+	0.537359i
$563$	−8.71723	−	4.44165i	−0.367388	−	0.187193i	0.260544	−	0.965462i	$-0.416098\pi$
$563$	−8.71723	−	4.44165i	−0.367388	−	0.187193i	−0.627931	+	0.778269i	$0.716098\pi$
$564$	−0.425343	−	7.39381i	−0.0179102	−	0.311336i
$565$		0			0
$566$	24.4163	−	7.93332i	1.02629	−	0.333462i
$567$	−33.7003	−	8.29649i	−1.41528	−	0.348420i
$568$	4.35851	+	4.35851i	0.182879	+	0.182879i
$569$	−8.66014	+	6.29196i	−0.363052	+	0.263773i	−0.754324	−	0.656502i	$-0.772035\pi$
$569$	−8.66014	+	6.29196i	−0.363052	+	0.263773i	0.391272	+	0.920275i	$0.372035\pi$
$570$		0			0
$571$	12.5798	+	9.13980i	0.526450	+	0.382489i	0.819028	−	0.573753i	$-0.194513\pi$
$571$	12.5798	+	9.13980i	0.526450	+	0.382489i	−0.292578	+	0.956242i	$0.594513\pi$
$572$	−0.136828	−	0.863895i	−0.00572105	−	0.0361213i
$573$	−18.2199	−	16.2376i	−0.761146	−	0.678337i
$574$			32.7026i			1.36498i
$575$		0			0
$576$	2.20883	−	2.03004i	0.0920345	−	0.0845852i
$577$	6.76199	+	13.2712i	0.281505	+	0.552485i	0.987855	−	0.155378i	$-0.0496594\pi$
$577$	6.76199	+	13.2712i	0.281505	+	0.552485i	−0.706350	+	0.707863i	$0.749659\pi$
$578$	−4.40082	+	0.697022i	−0.183050	+	0.0289923i
$579$	−1.79938	+	6.85512i	−0.0747795	+	0.284889i
$580$		0			0
$581$	−13.2606	−	18.2516i	−0.550140	−	0.757203i
$582$	−11.1420	−	4.89277i	−0.461852	−	0.202812i
$583$	−1.53418	−	0.242990i	−0.0635392	−	0.0100636i
$584$	−3.22666	−	9.93064i	−0.133520	−	0.410933i
$585$		0			0
$586$	−10.5565	+	32.4896i	−0.436086	+	1.34213i
$587$	11.6079	−	22.7817i	0.479108	−	0.940302i	−0.517315	−	0.855795i	$-0.673068\pi$
$587$	11.6079	−	22.7817i	0.479108	−	0.940302i	0.996423	−	0.0845070i	$-0.0269315\pi$
$588$	1.35580	−	13.5652i	0.0559121	−	0.559418i
$589$	26.1121	+	8.48435i	1.07593	+	0.349592i
$590$		0			0
$591$	30.4830	−	24.9433i	1.25390	−	1.02603i
$592$	−0.761135	+	4.80562i	−0.0312825	+	0.197510i
$593$	−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
$597$	−9.44996	+	5.52043i	−0.386761	+	0.225936i
$598$	17.3071	−	8.81838i	0.707738	−	0.360611i
$599$	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	$0.380446\pi$
$602$	25.0904	−	12.7842i	1.02261	−	0.521045i
$603$	−17.7975	−	14.1138i	−0.724770	−	0.574758i
$604$	−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	−0.810631	−	0.585557i	$-0.800876\pi$
$607$	−5.54524	+	5.54524i	−0.225074	+	0.225074i	0.585557	+	0.810631i	$0.300876\pi$
$608$	−1.02445	+	6.46812i	−0.0415469	+	0.262317i
$609$	26.4104	+	32.2759i	1.07020	+	1.30789i
$610$		0			0
$611$	−10.0782	−	3.27461i	−0.407721	−	0.132477i
$612$	2.85467	+	10.2347i	0.115393	+	0.413715i
$613$	2.13588	−	4.19191i	0.0862676	−	0.169310i	−0.843842	−	0.536592i	$-0.819712\pi$
$613$	2.13588	−	4.19191i	0.0862676	−	0.169310i	0.930110	+	0.367282i	$0.119712\pi$
$614$	5.63620	−	17.3464i	0.227459	−	0.700045i
$615$		0			0
$616$	−0.420571	−	1.29439i	−0.0169453	−	0.0521523i
$617$	−40.5328	−	6.41977i	−1.63179	−	0.258450i	−0.727733	−	0.685861i	$-0.759426\pi$
$617$	−40.5328	−	6.41977i	−1.63179	−	0.258450i	−0.904058	+	0.427410i	$0.859426\pi$
$618$	4.63313	−	10.5508i	0.186372	−	0.424414i
$619$	−10.1486	−	13.9684i	−0.407908	−	0.561438i	0.554798	−	0.831985i	$-0.312795\pi$
$619$	−10.1486	−	13.9684i	−0.407908	−	0.561438i	−0.962707	+	0.270547i	$0.912795\pi$
$620$		0			0
$621$	−19.0426	−	35.9998i	−0.764155	−	1.44462i
$622$	16.0196	−	2.53726i	0.642329	−	0.101735i
$623$	3.58757	+	7.04100i	0.143733	+	0.282092i
$624$	−1.55874	−	3.99951i	−0.0623994	−	0.160109i
$625$		0			0
$626$			5.40095i			0.215865i
$627$	2.66345	−	2.98859i	0.106368	−	0.119353i
$628$	0.701824	+	4.43114i	0.0280058	+	0.176822i
$629$	−13.9415	−	10.1291i	−0.555885	−	0.403874i
$630$		0			0
$631$	−29.4746	+	21.4146i	−1.17337	+	0.852501i	−0.991408	−	0.130805i	$-0.958244\pi$
$631$	−29.4746	+	21.4146i	−1.17337	+	0.852501i	−0.181959	+	0.983306i	$0.558244\pi$
$632$	−0.966214	−	0.966214i	−0.0384339	−	0.0384339i
$633$	−7.03380	+	1.53264i	−0.279569	+	0.0609171i
$634$	8.15891	−	2.65099i	0.324032	−	0.105284i
$635$		0			0
$636$	−7.61046	+	0.437806i	−0.301774	+	0.0173601i
$637$	−17.3803	−	8.85568i	−0.688631	−	0.350875i
$638$	1.96346	+	1.00043i	0.0777340	+	0.0396074i
$639$	−7.69324	−	16.8152i	−0.304340	−	0.665201i
$640$		0			0
$641$	−28.1775	+	9.15543i	−1.11294	+	0.361618i	−0.807071	−	0.590454i	$-0.798949\pi$
$641$	−28.1775	+	9.15543i	−1.11294	+	0.361618i	−0.305874	+	0.952072i	$0.598949\pi$
$642$	−5.44117	−	24.9713i	−0.214746	−	0.985539i
$643$	−16.2471	−	16.2471i	−0.640721	−	0.640721i	0.310012	−	0.950733i	$-0.399667\pi$
$643$	−16.2471	−	16.2471i	−0.640721	−	0.640721i	−0.950733	+	0.310012i	$0.899667\pi$
$644$	24.4521	−	17.7655i	0.963547	−	0.700058i
$645$		0			0
$646$	−18.7646	−	13.6333i	−0.738284	−	0.536394i
$647$	0.280589	+	1.77157i	0.0110311	+	0.0696477i	0.992590	−	0.121513i	$-0.0387747\pi$
$647$	0.280589	+	1.77157i	0.0110311	+	0.0696477i	−0.981559	+	0.191161i	$0.938775\pi$
$648$	−8.33463	+	3.39616i	−0.327415	+	0.133414i
$649$		−	0.814444i		−	0.0319697i
$650$		0			0
$651$	−26.0916	+	10.1687i	−1.02261	+	0.398544i
$652$	−4.91227	−	9.64088i	−0.192379	−	0.377566i
$653$	26.3159	−	4.16803i	1.02982	−	0.163107i	0.381416	−	0.924404i	$-0.375437\pi$
$653$	26.3159	−	4.16803i	1.02982	−	0.163107i	0.648404	+	0.761296i	$0.275437\pi$
$654$	−18.6230	−	4.88829i	−0.728218	−	0.191147i
$655$		0			0
$656$	4.98463	+	6.86076i	0.194617	+	0.267868i
$657$	−1.32004	+	31.2973i	−0.0514996	+	1.22102i
$658$	−16.2860	−	2.57944i	−0.634893	−	0.100557i
$659$	2.02081	+	6.21940i	0.0787195	+	0.242274i	0.982670	−	0.185363i	$-0.0593462\pi$
$659$	2.02081	+	6.21940i	0.0787195	+	0.242274i	−0.903951	+	0.427637i	$0.859346\pi$
$660$		0			0
$661$	5.97584	−	18.3917i	0.232433	−	0.715356i	−0.765018	−	0.644008i	$-0.777270\pi$
$661$	5.97584	−	18.3917i	0.232433	−	0.715356i	0.997452	−	0.0713473i	$-0.0227299\pi$
$662$	12.9009	−	25.3194i	0.501407	−	0.984066i
$663$	15.1279	+	1.51198i	0.587518	+	0.0587206i
$664$	−5.56392	−	1.80783i	−0.215922	−	0.0701573i
$665$		0			0
$666$	7.16887	−	12.7148i	0.277788	−	0.492690i
$667$	−7.65551	+	48.3350i	−0.296422	+	1.87154i
$668$	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
$672$	−3.36911	−	5.76730i	−0.129966	−	0.222478i
$673$	−39.1978	+	19.9723i	−1.51096	+	0.769874i	−0.996170	−	0.0874407i	$-0.972131\pi$
$673$	−39.1978	+	19.9723i	−1.51096	+	0.769874i	−0.514793	+	0.857315i	$0.672131\pi$
$674$	4.74599			0.182809
$675$		0			0
$676$	6.85808			0.263772
$677$	−33.3683	+	17.0020i	−1.28245	+	0.653440i	−0.956441	−	0.291927i	$-0.905704\pi$
$677$	−33.3683	+	17.0020i	−1.28245	+	0.653440i	−0.326008	+	0.945367i	$0.605704\pi$
$678$	−1.53764	−	2.63216i	−0.0590528	−	0.101087i
$679$	−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
$683$	5.33840	−	33.7054i	0.204268	−	1.28970i	−0.645995	−	0.763342i	$-0.723557\pi$
$683$	5.33840	−	33.7054i	0.204268	−	1.28970i	0.850263	−	0.526358i	$-0.176443\pi$
$684$	9.64894	−	17.1135i	0.368937	−	0.654352i
$685$		0			0
$686$	−3.19397	−	1.03778i	−0.121946	−	0.0396228i
$687$	29.8721	+	2.98562i	1.13969	+	0.113909i
$688$	3.31516	−	6.50638i	0.126389	−	0.248053i
$689$	−3.37056	+	10.3735i	−0.128408	+	0.395199i
$690$		0			0
$691$	−9.75674	−	30.0282i	−0.371164	−	1.14232i	−0.946030	−	0.324078i	$-0.894946\pi$
$691$	−9.75674	−	30.0282i	−0.371164	−	1.14232i	0.574867	−	0.818247i	$-0.305054\pi$
$692$	17.2049	+	2.72498i	0.654031	+	0.103588i
$693$	−0.172057	+	4.07936i	−0.00653591	+	0.154962i
$694$	4.71830	+	6.49419i	0.179104	+	0.246516i
$695$		0			0
$696$	10.4603	+	2.74568i	0.396496	+	0.104075i
$697$	−29.6659	+	4.69862i	−1.12368	+	0.177973i
$698$	−8.59105	−	16.8609i	−0.325176	−	0.638194i
$699$	−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	$-0.283170\pi$
$702$	0.197163	+	12.8761i	0.00744143	+	0.485976i
$703$	4.98448	+	31.4708i	0.187993	+	1.18694i
$704$	−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
$708$	−0.850963	−	3.90535i	−0.0319812	−	0.146772i
$709$	−48.5191	+	15.7648i	−1.82217	+	0.592060i	−0.822443	+	0.568848i	$0.807389\pi$
$709$	−48.5191	+	15.7648i	−1.82217	+	0.592060i	−0.999731	+	0.0232123i	$0.992611\pi$
$710$		0			0
$711$	1.70547	+	3.72768i	0.0639603	+	0.139799i
$712$	1.82585	+	0.930319i	0.0684268	+	0.0348652i
$713$	−29.2785	−	14.9181i	−1.09649	−	0.558689i
$714$	23.6176	−	1.35865i	0.883865	−	0.0508460i
$715$		0			0
$716$	−6.98899	+	2.27086i	−0.261191	+	0.0848660i
$717$	−4.11771	+	0.897235i	−0.153779	+	0.0335079i
$718$	−10.6989	−	10.6989i	−0.399281	−	0.399281i
$719$	−29.8994	+	21.7232i	−1.11506	+	0.810138i	−0.983453	−	0.181164i	$-0.942013\pi$
$719$	−29.8994	+	21.7232i	−1.11506	+	0.810138i	−0.131606	+	0.991302i	$0.542013\pi$
$720$		0			0
$721$	−20.7558	−	15.0800i	−0.772985	−	0.561607i
$722$	3.73661	+	23.5920i	0.139062	+	0.878004i
$723$	−1.86537	+	2.09309i	−0.0693738	+	0.0778427i
$724$			0.671329i			0.0249497i
$725$		0			0
$726$	−6.84017	−	17.5510i	−0.253863	−	0.651379i
$727$	−8.55075	−	16.7818i	−0.317130	−	0.622402i	0.676328	−	0.736600i	$-0.263570\pi$
$727$	−8.55075	−	16.7818i	−0.317130	−	0.622402i	−0.993458	+	0.114198i	$0.963570\pi$
$728$	−9.43931	+	1.49504i	−0.349844	+	0.0554099i
$729$	26.9873	−	0.826673i	0.999531	−	0.0306175i
$730$		0			0
$731$	15.2020	+	20.9238i	0.562266	+	0.773893i
$732$	0.101802	−	0.231828i	0.00376271	−	0.00856862i
$733$	−34.3095	−	5.43410i	−1.26725	−	0.200713i	−0.513625	−	0.858015i	$-0.671698\pi$
$733$	−34.3095	−	5.43410i	−1.26725	−	0.200713i	−0.753627	+	0.657302i	$0.771698\pi$
$734$	−11.3193	−	34.8373i	−0.417804	−	1.28587i
$735$		0			0
$736$	2.42199	−	7.45412i	0.0892758	−	0.274763i
$737$	−1.21316	+	2.38096i	−0.0446873	+	0.0877038i
$738$	−6.83513	−	24.5057i	−0.251605	−	0.902068i
$739$	2.70309	+	0.878288i	0.0994348	+	0.0323083i	0.358312	−	0.933602i	$-0.383352\pi$
$739$	2.70309	+	0.878288i	0.0994348	+	0.0323083i	−0.258877	+	0.965910i	$0.583352\pi$
$740$		0			0
$741$	−17.8019	−	21.7555i	−0.653968	−	0.799209i
$742$	−2.65502	+	16.7632i	−0.0974689	+	0.615395i
$743$	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
$747$	13.7515	+	10.9053i	0.503142	+	0.399002i
$748$	1.11376	−	0.567491i	0.0407233	−	0.0207495i
$749$	−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	$0.419825\pi$
$752$	−3.80983	+	1.94121i	−0.138930	+	0.0707886i
$753$	36.9797	−	21.6027i	1.34762	−	0.787245i
$754$	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	−0.474450	−	0.880283i	$-0.657353\pi$
$757$	11.1659	−	11.1659i	0.405833	−	0.405833i	0.880283	+	0.474450i	$0.157353\pi$
$758$	1.10598	−	6.98287i	0.0401710	−	0.253629i
$759$	−3.70798	+	3.03413i	−0.134591	+	0.110132i
$760$		0			0
$761$	13.3455	+	4.33621i	0.483774	+	0.157188i	0.540742	−	0.841188i	$-0.318143\pi$
$761$	13.3455	+	4.33621i	0.483774	+	0.157188i	−0.0569686	+	0.998376i	$0.518143\pi$
$762$	0.929110	−	9.29604i	0.0336581	−	0.336760i
$763$	−19.4614	+	38.1951i	−0.704548	+	1.38275i
$764$	−4.35419	+	13.4008i	−0.157529	+	0.484825i
$765$		0			0
$766$	−4.30040	−	13.2353i	−0.155380	−	0.478209i
$767$	−5.64864	−	0.894657i	−0.203961	−	0.0323042i
$768$	−1.58588	−	0.696404i	−0.0572256	−	0.0251293i
$769$	13.0082	+	17.9042i	0.469087	+	0.645643i	0.976362	−	0.216141i	$-0.0693471\pi$
$769$	13.0082	+	17.9042i	0.469087	+	0.645643i	−0.507275	+	0.861784i	$0.669347\pi$
$770$		0			0
$771$	−12.5914	+	47.9697i	−0.453468	+	1.72759i
$772$	4.04150	−	0.640111i	0.145457	−	0.0230381i
$773$	19.2486	+	37.7774i	0.692323	+	1.35876i	0.922647	+	0.385646i	$0.126021\pi$
$773$	19.2486	+	37.7774i	0.692323	+	1.35876i	−0.230324	+	0.973114i	$0.573979\pi$
$774$	−16.1295	+	14.8239i	−0.579762	+	0.532836i
$775$		0			0
$776$			7.02576i			0.252210i
$777$	−24.2615	−	21.6219i	−0.870376	−	0.775683i
$778$	−2.35890	−	14.8935i	−0.0845708	−	0.533959i
$779$	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
$783$	−26.5366	−	18.6660i	−0.948340	−	0.667067i
$784$	−7.48565	+	2.43223i	−0.267345	+	0.0868655i
$785$		0			0
$786$	−1.73221	−	30.1113i	−0.0617860	−	1.07404i
$787$	25.7904	+	13.1408i	0.919327	+	0.468420i	0.848576	−	0.529074i	$-0.177460\pi$
$787$	25.7904	+	13.1408i	0.919327	+	0.468420i	0.0707509	+	0.997494i	$0.477460\pi$
$788$	−20.2619	−	10.3240i	−0.721800	−	0.367776i
$789$	0.299464	+	5.20563i	0.0106612	+	0.185325i
$790$		0			0
$791$	−6.45480	+	2.09729i	−0.229506	+	0.0745711i
$792$	0.585693	+	0.882044i	0.0208117	+	0.0313421i
$793$	−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
$797$	2.70297	+	17.0659i	0.0957441	+	0.604505i	0.988176	+	0.153323i	$0.0489974\pi$
$797$	2.70297	+	17.0659i	0.0957441	+	0.604505i	−0.892432	+	0.451182i	$0.851003\pi$
$798$	−32.6547	−	29.1021i	−1.15597	−	1.03020i
$799$		−	15.1443i		−	0.535766i
$800$		0			0
$801$	−4.15997	−	4.52634i	−0.146985	−	0.159930i
$802$	7.18193	+	14.0953i	0.253603	+	0.497723i
$803$	3.63982	−	0.576491i	0.128446	−	0.0203439i
$804$	−3.32952	+	12.6845i	−0.117423	+	0.447349i
$805$		0			0
$806$	6.10729	+	8.40597i	0.215120	+	0.296088i
$807$	−20.5666	−	9.03137i	−0.723980	−	0.317919i
$808$	9.46876	+	1.49970i	0.333110	+	0.0527594i
$809$	−14.1884	−	43.6674i	−0.498837	−	1.53526i	−0.810891	−	0.585198i	$-0.801017\pi$
$809$	−14.1884	−	43.6674i	−0.498837	−	1.53526i	0.312054	−	0.950064i	$-0.398983\pi$
$810$		0			0
$811$	14.2314	−	43.7999i	0.499733	−	1.53802i	−0.309714	−	0.950830i	$-0.600233\pi$
$811$	14.2314	−	43.7999i	0.499733	−	1.53802i	0.809448	−	0.587192i	$-0.199767\pi$
$812$	10.9312	−	21.4536i	0.383609	−	0.752874i
$813$	−2.93369	+	29.3525i	−0.102889	+	1.02944i
$814$	−1.63314	−	0.530641i	−0.0572417	−	0.0185989i
$815$		0			0
$816$	4.74769	−	3.88489i	0.166202	−	0.135998i
$817$	7.48082	−	47.2320i	0.261721	−	1.65244i
$818$	−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	−0.975888	−	0.218274i	$-0.929957\pi$
$821$	−13.3733	+	18.4068i	−0.466731	+	0.642400i	0.509156	+	0.860674i	$0.329957\pi$
$822$	−26.8102	+	15.6619i	−0.935114	+	0.546271i
$823$	33.1249	−	16.8780i	1.15466	−	0.588330i	0.231536	−	0.972826i	$-0.425625\pi$
$823$	33.1249	−	16.8780i	1.15466	−	0.588330i	0.923127	+	0.384496i	$0.125625\pi$
$824$	−6.65293			−0.231766
$825$		0			0
$826$	−8.89898			−0.309635
$827$	9.39702	−	4.78802i	0.326766	−	0.166496i	−0.282910	−	0.959147i	$-0.591300\pi$
$827$	9.39702	−	4.78802i	0.326766	−	0.166496i	0.609676	+	0.792651i	$0.291300\pi$
$828$	−14.6100	+	18.4233i	−0.507734	+	0.640253i
$829$	7.78028	−	10.7086i	0.270220	−	0.371926i	−0.652244	−	0.758009i	$-0.726172\pi$
$829$	7.78028	−	10.7086i	0.270220	−	0.371926i	0.922464	+	0.386083i	$0.126172\pi$
$830$		0			0
$831$	−9.94535	+	15.4870i	−0.345000	+	0.537237i
$832$	−1.75242	+	1.75242i	−0.0607541	+	0.0607541i
$833$	4.36093	−	27.5338i	0.151097	−	0.953990i
$834$	19.7684	+	24.1588i	0.684524	+	0.836550i
$835$		0			0
$836$	−2.19813	−	0.714216i	−0.0760239	−	0.0247017i
$837$	17.4264	−	13.0733i	0.602345	−	0.451880i
$838$	1.96185	−	3.85035i	0.0677711	−	0.133008i
$839$	0.944989	−	2.90838i	0.0326247	−	0.100408i	−0.933418	−	0.358790i	$-0.883189\pi$
$839$	0.944989	−	2.90838i	0.0326247	−	0.100408i	0.966043	+	0.258382i	$0.0831893\pi$
$840$		0			0
$841$	3.08568	+	9.49674i	0.106403	+	0.327474i
$842$	−24.7186	−	3.91504i	−0.851860	−	0.134921i
$843$	−19.5410	+	44.4997i	−0.673029	+	1.53265i
$844$	2.44299	+	3.36248i	0.0840910	+	0.115741i
$845$		0			0
$846$	12.7430	−	1.47100i	0.438114	−	0.0505740i
$847$	−41.4224	+	6.56066i	−1.42329	+	0.225427i
$848$	1.99809	+	3.92147i	0.0686146	+	0.134664i
$849$	16.1471	+	41.4312i	0.554165	+	1.42192i
$850$		0			0
$851$		−	38.1346i		−	1.30724i
$852$	−7.10313	+	7.97026i	−0.243349	+	0.273057i
$853$	−5.89808	−	37.2390i	−0.201946	−	1.27504i	−0.855358	−	0.518037i	$-0.826663\pi$
$853$	−5.89808	−	37.2390i	−0.201946	−	1.27504i	0.653412	−	0.757003i	$-0.273337\pi$
$854$	−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	$0.777487\pi$
$858$	1.48023	−	0.322537i	0.0505342	−	0.0110112i
$859$	33.5736	−	10.9087i	1.14552	−	0.372201i	0.326064	−	0.945348i	$-0.394278\pi$
$859$	33.5736	−	10.9087i	1.14552	−	0.372201i	0.819453	+	0.573147i	$0.194278\pi$
$860$		0			0
$861$	−56.5491	+	3.25310i	−1.92719	+	0.110865i
$862$	−6.23735	−	3.17809i	−0.212445	−	0.108246i
$863$	−17.9383	−	9.14003i	−0.610628	−	0.311130i	0.121191	−	0.992629i	$-0.461328\pi$
$863$	−17.9383	−	9.14003i	−0.610628	−	0.311130i	−0.731819	+	0.681499i	$0.761328\pi$
$864$	3.73006	+	3.61755i	0.126899	+	0.123072i
$865$		0			0
$866$	9.38548	−	3.04953i	0.318932	−	0.103627i
$867$	−1.64306	−	7.54053i	−0.0558011	−	0.256090i
$868$	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
$872$	1.73896	+	10.9794i	0.0588887	+	0.371809i
$873$	7.35218	−	19.7534i	0.248834	−	0.668552i
$874$		−	51.3273i		−	1.73617i
$875$		0			0
$876$	16.8510	−	6.56737i	0.569343	−	0.221891i
$877$	19.1482	+	37.5805i	0.646590	+	1.26900i	0.948834	+	0.315774i	$0.102264\pi$
$877$	19.1482	+	37.5805i	0.646590	+	1.26900i	−0.302244	+	0.953230i	$0.597736\pi$
$878$	−0.576659	+	0.0913337i	−0.0194613	+	0.00308236i
$879$	−57.2309	−	15.0223i	−1.93035	−	0.506691i
$880$		0			0
$881$	22.4775	+	30.9376i	0.757285	+	1.04231i	0.997435	+	0.0715779i	$0.0228035\pi$
$881$	22.4775	+	30.9376i	0.757285	+	1.04231i	−0.240150	+	0.970736i	$0.577197\pi$
$882$	23.5917	+	0.995035i	0.794372	+	0.0335046i
$883$	13.8121	+	2.18763i	0.464816	+	0.0736196i	0.384450	−	0.923146i	$-0.374391\pi$
$883$	13.8121	+	2.18763i	0.464816	+	0.0736196i	0.0803657	+	0.996765i	$0.474391\pi$
$884$	−2.71243	−	8.34799i	−0.0912288	−	0.280773i
$885$		0			0
$886$	2.76645	−	8.51427i	0.0929408	−	0.286042i
$887$	9.40690	−	18.4621i	0.315853	−	0.619896i	−0.677433	−	0.735585i	$-0.736908\pi$
$887$	9.40690	−	18.4621i	0.315853	−	0.619896i	0.993285	+	0.115689i	$0.0369076\pi$
$888$	−8.38555	−	0.838109i	−0.281401	−	0.0281251i
$889$	−19.7820	−	6.42756i	−0.663467	−	0.215574i
$890$		0			0
$891$	−0.723691	−	3.09283i	−0.0242446	−	0.103614i
$892$	−2.40429	+	15.1801i	−0.0805017	+	0.508268i
$893$	−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
$897$	16.9703	+	29.0500i	0.566622	+	0.969951i
$898$	16.3751	−	8.34354i	0.546445	−	0.278428i
$899$	−26.1776			−0.873071
$900$		0			0
$901$	−15.5880			−0.519312
$902$	−2.66676	+	1.35878i	−0.0887935	+	0.0452425i
$903$	24.6022	+	42.1144i	0.818710	+	1.40148i
$904$	−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	−0.829973	−	0.557803i	$-0.811644\pi$
$907$	−8.19678	+	8.19678i	−0.272170	+	0.272170i	0.557803	+	0.829973i	$0.311644\pi$
$908$	2.19408	−	13.8529i	0.0728131	−	0.459724i
$909$	−25.0527	−	14.1252i	−0.830946	−	0.468503i
$910$		0			0
$911$	−4.38290	−	1.42409i	−0.145212	−	0.0471822i	0.235509	−	0.971872i	$-0.424324\pi$
$911$	−4.38290	−	1.42409i	−0.145212	−	0.0471822i	−0.380721	+	0.924690i	$0.624324\pi$
$912$	−11.2865	−	1.12805i	−0.373734	−	0.0373536i
$913$	0.937368	−	1.83969i	0.0310224	−	0.0608848i
$914$	10.8344	−	33.3449i	0.358371	−	1.10295i
$915$		0			0
$916$	−5.35607	−	16.4843i	−0.176970	−	0.544656i
$917$	−66.3247	−	10.5048i	−2.19023	−	0.346899i
$918$	−17.4138	+	5.95437i	−0.574743	+	0.196524i
$919$	1.33595	+	1.83878i	0.0440689	+	0.0606557i	0.830483	−	0.557044i	$-0.188065\pi$
$919$	1.33595	+	1.83878i	0.0440689	+	0.0606557i	−0.786414	+	0.617700i	$0.788065\pi$
$920$		0			0
$921$	30.5560	+	8.02053i	1.00685	+	0.264286i
$922$	−0.139155	+	0.0220400i	−0.00458284	+	0.000725850i
$923$	6.93508	+	13.6109i	0.228271	+	0.448007i
$924$	2.19640	−	0.856007i	0.0722564	−	0.0281606i
$925$		0			0
$926$		−	8.87257i		−	0.291571i
$927$	18.7052	+	6.96203i	0.614359	+	0.228663i
$928$	−0.976751	−	6.16696i	−0.0320634	−	0.202440i
$929$	12.0105	+	8.72617i	0.394053	+	0.286296i	0.767114	−	0.641510i	$-0.221692\pi$
$929$	12.0105	+	8.72617i	0.394053	+	0.286296i	−0.373061	+	0.927807i	$0.621692\pi$
$930$		0			0
$931$	−41.7003	+	30.2970i	−1.36667	+	0.992945i
$932$	1.73973	+	1.73973i	0.0569868	+	0.0569868i
$933$	5.98097	+	27.4486i	0.195808	+	0.898628i
$934$	−4.63623	+	1.50640i	−0.151702	+	0.0492910i
$935$		0			0
$936$	6.76087	−	3.09320i	0.220986	−	0.101105i
$937$	−13.2746	−	6.76373i	−0.433661	−	0.220961i	0.223512	−	0.974701i	$-0.428248\pi$
$937$	−13.2746	−	6.76373i	−0.433661	−	0.220961i	−0.657173	+	0.753740i	$0.728248\pi$
$938$	26.0155	+	13.2555i	0.849435	+	0.432809i
$939$	−9.33928	+	0.537260i	−0.304776	+	0.0175328i
$940$		0			0
$941$	29.4117	−	9.55645i	0.958795	−	0.311531i	0.212511	−	0.977159i	$-0.431836\pi$
$941$	29.4117	−	9.55645i	0.958795	−	0.311531i	0.746284	+	0.665627i	$0.231836\pi$
$942$	−7.59248	+	1.65438i	−0.247376	+	0.0539025i
$943$	−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
$947$	−1.42242	−	8.98080i	−0.0462224	−	0.291837i	0.953739	−	0.300636i	$-0.0971990\pi$
$947$	−1.42242	−	8.98080i	−0.0462224	−	0.291837i	−0.999961	+	0.00879948i	$0.997199\pi$
$948$	1.57466	−	1.76688i	0.0511424	−	0.0573857i
$949$		−	25.8775i		−	0.840021i
$950$		0			0
$951$	5.39568	+	13.8446i	0.174967	+	0.448942i
$952$	−6.20067	−	12.1695i	−0.200965	−	0.394416i
$953$	18.9081	−	2.99474i	0.612493	−	0.0970093i	0.157522	−	0.987516i	$-0.449650\pi$
$953$	18.9081	−	2.99474i	0.612493	−	0.0970093i	0.454971	+	0.890506i	$0.349650\pi$
$954$	−1.51410	−	13.1164i	−0.0490209	−	0.424659i
$955$		0			0
$956$	1.43017	+	1.96845i	0.0462549	+	0.0636644i
$957$	−1.53462	+	3.49471i	−0.0496073	+	0.112968i
$958$	14.0773	+	2.22963i	0.454818	+	0.0720361i
$959$	21.3623	+	65.7463i	0.689823	+	2.12306i
$960$		0			0
$961$	−4.14780	+	12.7656i	−0.133800	+	0.411794i
$962$	−5.47429	+	10.7439i	−0.176498	+	0.346397i
$963$	42.6389	−	11.8928i	1.37402	−	0.383242i
$964$	1.53948	+	0.500207i	0.0495833	+	0.0161106i
$965$		0			0
$966$	33.1523	+	40.5151i	1.06666	+	1.30355i
$967$	6.88343	−	43.4603i	0.221356	−	1.39759i	−0.587330	−	0.809347i	$-0.699821\pi$
$967$	6.88343	−	43.4603i	0.221356	−	1.39759i	0.808686	−	0.588240i	$-0.200179\pi$
$968$	−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	−0.994017	−	0.109229i	$-0.965162\pi$
$971$	−18.1657	+	25.0030i	−0.582965	+	0.802383i	0.411051	+	0.911612i	$0.365162\pi$
$972$	−6.70170	−	14.0743i	−0.214957	−	0.451435i
$973$	61.9249	−	31.5523i	1.98522	−	1.01152i
$974$	34.8793			1.11761
$975$		0			0
$976$	−0.146183			−0.00467919
$977$	−42.2813	+	21.5434i	−1.35270	+	0.689235i	−0.971894	−	0.235420i	$-0.924354\pi$
$977$	−42.2813	+	21.5434i	−1.35270	+	0.689235i	−0.380806	+	0.924655i	$0.624354\pi$
$978$	16.1823	−	9.45329i	0.517452	−	0.302283i
$979$	−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
$983$	−5.45227	+	34.4243i	−0.173900	+	1.09796i	0.734114	+	0.679026i	$0.237598\pi$
$983$	−5.45227	+	34.4243i	−0.173900	+	1.09796i	−0.908015	+	0.418938i	$0.862402\pi$
$984$	−11.3677	+	9.30186i	−0.362390	+	0.296533i
$985$		0			0
$986$	21.0320	+	6.83372i	0.669796	+	0.217630i
$987$	2.84030	−	28.4181i	0.0904079	−	0.904560i
$988$	−7.36813	+	14.4608i	−0.234411	+	0.460058i
$989$	−17.6860	+	54.4321i	−0.562384	+	1.73084i
$990$		0			0
$991$	1.45449	+	4.47645i	0.0462033	+	0.142199i	0.971497	−	0.237053i	$-0.0761814\pi$
$991$	1.45449	+	4.47645i	0.0462033	+	0.142199i	−0.925293	+	0.379252i	$0.876181\pi$
$992$	4.14093	+	0.655859i	0.131475	+	0.0208235i
$993$	45.0654	+	19.7894i	1.43011	+	0.627999i
$994$	13.9714	+	19.2300i	0.443146	+	0.609938i
$995$		0			0
$996$	2.57261	−	9.80092i	0.0815162	−	0.310554i
$997$	20.4803	−	3.24377i	0.648619	−	0.102731i	0.176548	−	0.984292i	$-0.443507\pi$
$997$	20.4803	−	3.24377i	0.648619	−	0.102731i	0.472070	+	0.881561i	$0.343507\pi$
$998$	4.05748	+	7.96325i	0.128437	+	0.252072i
$999$	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.b.743.9		80
3.2	odd	2	inner	750.2.l.b.743.3		80
5.2	odd	4		750.2.l.a.257.10		80
5.3	odd	4		750.2.l.c.257.1		80
5.4	even	2		150.2.l.a.53.2	yes	80
15.2	even	4		750.2.l.a.257.5		80
15.8	even	4		750.2.l.c.257.6		80
15.14	odd	2		150.2.l.a.53.8	yes	80
25.6	even	5		750.2.l.a.143.5		80
25.8	odd	20		150.2.l.a.17.8	yes	80
25.17	odd	20	inner	750.2.l.b.107.3		80
25.19	even	10		750.2.l.c.143.6		80
75.8	even	20		150.2.l.a.17.2	✓	80
75.17	even	20	inner	750.2.l.b.107.9		80
75.44	odd	10		750.2.l.c.143.1		80
75.56	odd	10		750.2.l.a.143.10		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.2	✓	80	75.8	even	20
150.2.l.a.17.8	yes	80	25.8	odd	20
150.2.l.a.53.2	yes	80	5.4	even	2
150.2.l.a.53.8	yes	80	15.14	odd	2
750.2.l.a.143.5		80	25.6	even	5
750.2.l.a.143.10		80	75.56	odd	10
750.2.l.a.257.5		80	15.2	even	4
750.2.l.a.257.10		80	5.2	odd	4
750.2.l.b.107.3		80	25.17	odd	20	inner
750.2.l.b.107.9		80	75.17	even	20	inner
750.2.l.b.743.3		80	3.2	odd	2	inner
750.2.l.b.743.9		80	1.1	even	1	trivial
750.2.l.c.143.1		80	75.44	odd	10
750.2.l.c.143.6		80	25.19	even	10
750.2.l.c.257.1		80	5.3	odd	4
750.2.l.c.257.6		80	15.8	even	4

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)

\(f(q)\)	\(=\)	\(q+(0.891007 - 0.453990i) q^{2} +(0.873670 + 1.49556i) q^{3} +(0.587785 - 0.809017i) q^{4} +(1.45742 + 0.935916i) q^{6} +(2.72680 - 2.72680i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.47340 + 2.61325i) q^{9} +O(q^{10})\)	\(q+(0.891007 - 0.453990i) q^{2} +(0.873670 + 1.49556i) q^{3} +(0.587785 - 0.809017i) q^{4} +(1.45742 + 0.935916i) q^{6} +(2.72680 - 2.72680i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.47340 + 2.61325i) q^{9} +(0.335657 + 0.109061i) q^{11} +(1.72346 + 0.172255i) q^{12} +(1.12512 - 2.20817i) q^{13} +(1.19166 - 3.66754i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(3.49819 + 0.554059i) q^{17} +(-0.126420 + 2.99734i) q^{18} +(-3.84926 - 5.29805i) q^{19} +(6.46042 + 1.69577i) q^{21} +(0.348585 - 0.0552105i) q^{22} +(3.55825 + 6.98347i) q^{23} +(1.61382 - 0.628956i) q^{24} -2.47829i q^{26} +(-5.19554 + 0.0795559i) q^{27} +(-0.603255 - 3.80880i) q^{28} +(5.05137 + 3.67003i) q^{29} +(-3.39184 + 2.46432i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.130145 + 0.597278i) q^{33} +(3.36845 - 1.09448i) q^{34} +(1.24812 + 2.72804i) q^{36} +(-4.33521 - 2.20890i) q^{37} +(-5.83498 - 2.97307i) q^{38} +(4.28544 - 0.246528i) q^{39} +(-8.06531 + 2.62058i) q^{41} +(6.52614 - 1.42202i) q^{42} +(5.16349 + 5.16349i) q^{43} +(0.285527 - 0.207447i) q^{44} +(6.34085 + 4.60690i) q^{46} +(-0.668895 - 4.22323i) q^{47} +(1.15238 - 1.29306i) q^{48} -7.87088i q^{49} +(2.22763 + 5.71582i) q^{51} +(-1.12512 - 2.20817i) q^{52} +(-4.34698 + 0.688494i) q^{53} +(-4.59315 + 2.42961i) q^{54} +(-2.26666 - 3.11979i) q^{56} +(4.56057 - 10.3855i) q^{57} +(6.16696 + 0.976751i) q^{58} +(-0.713107 - 2.19472i) q^{59} +(0.0451729 - 0.139028i) q^{61} +(-1.90338 + 3.73559i) q^{62} +(3.10814 + 11.1435i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(0.387119 + 0.473094i) q^{66} +(-1.18445 + 7.47829i) q^{67} +(2.50443 - 2.50443i) q^{68} +(-7.33546 + 11.4228i) q^{69} +(-3.62303 + 4.98667i) q^{71} +(2.35059 + 1.86407i) q^{72} +(9.30362 - 4.74043i) q^{73} -4.86552 q^{74} -6.54875 q^{76} +(1.21266 - 0.617880i) q^{77} +(3.70643 - 2.16521i) q^{78} +(0.803169 - 1.10547i) q^{79} +(-4.65817 - 7.70074i) q^{81} +(-5.99652 + 5.99652i) q^{82} +(0.915181 - 5.77823i) q^{83} +(5.16925 - 4.22984i) q^{84} +(6.94488 + 2.25653i) q^{86} +(-1.07553 + 10.7610i) q^{87} +(0.160227 - 0.314463i) q^{88} +(-0.633239 + 1.94891i) q^{89} +(-2.95327 - 9.08922i) q^{91} +(7.74123 + 1.22609i) q^{92} +(-6.64888 - 2.91971i) q^{93} +(-2.51330 - 3.45926i) q^{94} +(0.439743 - 1.67530i) q^{96} +(-6.93926 + 1.09907i) q^{97} +(-3.57330 - 7.01300i) 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	\( 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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