LMFDB - Embedded newform 750.2.l.b.107.3

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			107.3
Character	$\chi$	$=$	750.107
Dual form			750.2.l.b.743.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(-0.368756 - 1.69234i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.439743 + 1.67530i) q^{6} +(2.72680 + 2.72680i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.72804 + 1.24812i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(-0.368756 - 1.69234i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.439743 + 1.67530i) q^{6} +(2.72680 + 2.72680i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.72804 + 1.24812i) q^{9} +(-0.335657 + 0.109061i) q^{11} +(1.15238 - 1.29306i) 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} +(2.99734 + 0.126420i) q^{18} +(-3.84926 + 5.29805i) q^{19} +(3.60915 - 5.62020i) q^{21} +(0.348585 + 0.0552105i) q^{22} +(-3.55825 + 6.98347i) q^{23} +(-1.61382 + 0.628956i) q^{24} -2.47829i q^{26} +(3.11823 + 4.15652i) 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} +(0.308344 + 0.527829i) q^{33} +(3.36845 + 1.09448i) q^{34} +(-2.61325 - 1.47340i) q^{36} +(-4.33521 + 2.20890i) q^{37} +(5.83498 - 2.97307i) q^{38} +(3.32209 - 2.71836i) q^{39} +(8.06531 + 2.62058i) q^{41} +(-5.76730 + 3.36911i) 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} +(1.72346 + 0.172255i) q^{48} +7.87088i q^{49} +(2.22763 + 5.71582i) q^{51} +(-1.12512 + 2.20817i) q^{52} +(4.34698 + 0.688494i) q^{53} +(-0.891339 - 5.11913i) q^{54} +(2.26666 - 3.11979i) q^{56} +(10.3855 + 4.56057i) 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} +(-10.8422 - 4.03544i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-0.0351078 - 0.610284i) q^{66} +(-1.18445 - 7.47829i) q^{67} +(-2.50443 - 2.50443i) q^{68} +(13.1305 + 3.44659i) q^{69} +(3.62303 + 4.98667i) q^{71} +(1.65951 + 2.49920i) q^{72} +(9.30362 + 4.74043i) q^{73} +4.86552 q^{74} -6.54875 q^{76} +(-1.21266 - 0.617880i) q^{77} +(-4.19411 + 0.913883i) q^{78} +(0.803169 + 1.10547i) q^{79} +(5.88439 - 6.80984i) q^{81} +(-5.99652 - 5.99652i) q^{82} +(-0.915181 - 5.77823i) q^{83} +(6.66824 - 0.383604i) q^{84} +(-6.94488 + 2.25653i) q^{86} +(8.07367 + 7.19529i) 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} +(-2.91971 + 6.64888i) q^{93} +(-2.51330 + 3.45926i) q^{94} +(-1.45742 - 0.935916i) 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

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
$3$	−0.368756	−	1.69234i	−0.212901	−	0.977074i
$3$	−0.368756	−	1.69234i	−0.212901	−	0.977074i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	−0.439743	+	1.67530i	−0.179524	+	0.683938i
$7$	2.72680	+	2.72680i	1.03063	+	1.03063i	0.999516	+	0.0311178i	$0.00990669\pi$
$7$	2.72680	+	2.72680i	1.03063	+	1.03063i	0.0311178	+	0.999516i	$0.490093\pi$
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	−2.72804	+	1.24812i	−0.909346	+	0.416040i
$10$		0			0
$11$	−0.335657	+	0.109061i	−0.101204	+	0.0328833i	−0.359181	−	0.933268i	$-0.616944\pi$
$11$	−0.335657	+	0.109061i	−0.101204	+	0.0328833i	0.257977	+	0.966151i	$0.416944\pi$
$12$	1.15238	−	1.29306i	0.332665	−	0.373275i
$13$	1.12512	+	2.20817i	0.312052	+	0.612437i	0.992760	−	0.120119i	$-0.0383275\pi$
$13$	1.12512	+	2.20817i	0.312052	+	0.612437i	−0.680707	+	0.732555i	$0.738327\pi$
$14$	−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	$-0.691312\pi$
$17$	−3.49819	+	0.554059i	−0.848436	+	0.134379i	−0.282948	+	0.959135i	$0.591312\pi$
$18$	2.99734	+	0.126420i	0.706479	+	0.0297975i
$19$	−3.84926	+	5.29805i	−0.883080	+	1.21546i	0.0924780	+	0.995715i	$0.470521\pi$
$19$	−3.84926	+	5.29805i	−0.883080	+	1.21546i	−0.975558	+	0.219741i	$0.929479\pi$
$20$		0			0
$21$	3.60915	−	5.62020i	0.787582	−	1.22643i
$22$	0.348585	+	0.0552105i	0.0743186	+	0.0117709i
$23$	−3.55825	+	6.98347i	−0.741947	+	1.45615i	0.142638	+	0.989775i	$0.454441\pi$
$23$	−3.55825	+	6.98347i	−0.741947	+	1.45615i	−0.884585	+	0.466378i	$0.845559\pi$
$24$	−1.61382	+	0.628956i	−0.329420	+	0.128385i
$25$		0			0
$26$		−	2.47829i		−	0.486033i
$27$	3.11823	+	4.15652i	0.600103	+	0.799923i
$28$	−0.603255	+	3.80880i	−0.114004	+	0.719796i
$29$	−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
$33$	0.308344	+	0.527829i	0.0536759	+	0.0918832i
$34$	3.36845	+	1.09448i	0.577684	+	0.187701i
$35$		0			0
$36$	−2.61325	−	1.47340i	−0.435542	−	0.245567i
$37$	−4.33521	+	2.20890i	−0.712704	+	0.363141i	−0.772452	−	0.635073i	$-0.780970\pi$
$37$	−4.33521	+	2.20890i	−0.712704	+	0.363141i	0.0597483	+	0.998213i	$0.480970\pi$
$38$	5.83498	−	2.97307i	0.946558	−	0.482296i
$39$	3.32209	−	2.71836i	0.531960	−	0.435286i
$40$		0			0
$41$	8.06531	+	2.62058i	1.25959	+	0.409265i	0.861348	−	0.508015i	$-0.169621\pi$
$41$	8.06531	+	2.62058i	1.25959	+	0.409265i	0.398241	+	0.917281i	$0.369621\pi$
$42$	−5.76730	+	3.36911i	−0.889913	+	0.519865i
$43$	5.16349	−	5.16349i	0.787425	−	0.787425i	−0.193647	−	0.981071i	$-0.562031\pi$
$43$	5.16349	−	5.16349i	0.787425	−	0.787425i	0.981071	+	0.193647i	$0.0620315\pi$
$44$	−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	−0.889649	−	0.456644i	$-0.849051\pi$
$47$	0.668895	−	4.22323i	0.0975683	−	0.616022i	0.987218	−	0.159378i	$-0.0509488\pi$
$48$	1.72346	+	0.172255i	0.248761	+	0.0248628i
$49$			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	$-0.352255\pi$
$53$	4.34698	+	0.688494i	0.597103	+	0.0945719i	0.149435	+	0.988772i	$0.452255\pi$
$54$	−0.891339	−	5.11913i	−0.121296	−	0.696626i
$55$		0			0
$56$	2.26666	−	3.11979i	0.302896	−	0.416900i
$57$	10.3855	+	4.56057i	1.37560	+	0.604063i
$58$	6.16696	−	0.976751i	0.809762	−	0.128254i
$59$	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	$0.897021\pi$
$62$	1.90338	+	3.73559i	0.241729	+	0.474420i
$63$	−10.8422	−	4.03544i	−1.36599	−	0.508418i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$		0			0
$66$	−0.0351078	−	0.610284i	−0.00432147	−	0.0751208i
$67$	−1.18445	−	7.47829i	−0.144703	−	0.913619i	−0.948053	−	0.318112i	$-0.896951\pi$
$67$	−1.18445	−	7.47829i	−0.144703	−	0.913619i	0.803350	−	0.595507i	$-0.203049\pi$
$68$	−2.50443	−	2.50443i	−0.303707	−	0.303707i
$69$	13.1305	+	3.44659i	1.58073	+	0.414920i
$70$		0			0
$71$	3.62303	+	4.98667i	0.429974	+	0.591809i	0.967947	−	0.251153i	$-0.0808098\pi$
$71$	3.62303	+	4.98667i	0.429974	+	0.591809i	−0.537973	+	0.842962i	$0.680810\pi$
$72$	1.65951	+	2.49920i	0.195576	+	0.294534i
$73$	9.30362	+	4.74043i	1.08891	+	0.554825i	0.903827	−	0.427898i	$-0.140746\pi$
$73$	9.30362	+	4.74043i	1.08891	+	0.554825i	0.185079	+	0.982724i	$0.440746\pi$
$74$	4.86552			0.565605
$75$		0			0
$76$	−6.54875			−0.751193
$77$	−1.21266	−	0.617880i	−0.138195	−	0.0704139i
$78$	−4.19411	+	0.913883i	−0.474890	+	0.103477i
$79$	0.803169	+	1.10547i	0.0903636	+	0.124375i	0.851805	−	0.523859i	$-0.175508\pi$
$79$	0.803169	+	1.10547i	0.0903636	+	0.124375i	−0.761442	+	0.648234i	$0.775508\pi$
$80$		0			0
$81$	5.88439	−	6.80984i	0.653821	−	0.756649i
$82$	−5.99652	−	5.99652i	−0.662205	−	0.662205i
$83$	−0.915181	−	5.77823i	−0.100454	−	0.634243i	−0.985621	−	0.168969i	$-0.945956\pi$
$83$	−0.915181	−	5.77823i	−0.100454	−	0.634243i	0.885167	−	0.465273i	$-0.154044\pi$
$84$	6.66824	−	0.383604i	0.727565	−	0.0418546i
$85$		0			0
$86$	−6.94488	+	2.25653i	−0.748886	+	0.243328i
$87$	8.07367	+	7.19529i	0.865588	+	0.771416i
$88$	0.160227	+	0.314463i	0.0170803	+	0.0335219i
$89$	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
$92$	−7.74123	+	1.22609i	−0.807079	+	0.127829i
$93$	−2.91971	+	6.64888i	−0.302759	+	0.689457i
$94$	−2.51330	+	3.45926i	−0.259227	+	0.356795i
$95$		0			0
$96$	−1.45742	−	0.935916i	−0.148747	−	0.0955216i
$97$	−6.93926	−	1.09907i	−0.704575	−	0.111594i	−0.206142	−	0.978522i	$-0.566091\pi$
$97$	−6.93926	−	1.09907i	−0.704575	−	0.111594i	−0.498433	+	0.866928i	$0.666091\pi$
$98$	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	$0.841738\pi$
$102$	0.610091	−	6.10416i	0.0604081	−	0.604402i
$103$	−1.04075	+	6.57102i	−0.102548	+	0.647462i	0.881853	+	0.471524i	$0.156296\pi$
$103$	−1.04075	+	6.57102i	−0.102548	+	0.647462i	−0.984401	+	0.175938i	$0.943704\pi$
$104$	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	0.00870186	−	0.999962i	$-0.497230\pi$
$107$	10.4337	−	10.4337i	1.00866	−	1.00866i	0.999962	−	0.00870186i	$-0.00276992\pi$
$108$	−1.52985	+	4.96584i	−0.147210	+	0.477838i
$109$	−10.5722	−	3.43511i	−1.01263	−	0.329024i	−0.244729	−	0.969592i	$-0.578699\pi$
$109$	−10.5722	−	3.43511i	−1.01263	−	0.329024i	−0.767902	+	0.640568i	$0.778699\pi$
$110$		0			0
$111$	5.33685	+	6.52211i	0.506551	+	0.619051i
$112$	−3.43597	+	1.75071i	−0.324668	+	0.165427i
$113$	1.56816	−	0.799015i	0.147520	−	0.0751650i	−0.378672	−	0.925531i	$-0.623619\pi$
$113$	1.56816	−	0.799015i	0.147520	−	0.0751650i	0.526192	+	0.850366i	$0.323619\pi$
$114$	−7.18313	−	8.77844i	−0.672762	−	0.822176i
$115$		0			0
$116$	−5.93824	−	1.92945i	−0.551352	−	0.179145i
$117$	−5.82544	−	4.61969i	−0.538562	−	0.427091i
$118$	−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
$123$	1.46078	−	14.6156i	0.131714	−	1.31784i
$124$		−	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	−0.973762	−	0.227571i	$-0.926922\pi$
$127$	−2.44874	+	4.80592i	−0.217290	+	0.426457i	0.756471	+	0.654027i	$0.226922\pi$
$128$	0.987688	+	0.156434i	0.0873001	+	0.0138270i
$129$	−10.6425	−	6.83432i	−0.937016	−	0.601728i
$130$		0			0
$131$	10.2354	−	14.0878i	0.894273	−	1.23086i	−0.0779865	−	0.996954i	$-0.524849\pi$
$131$	10.2354	−	14.0878i	0.894273	−	1.23086i	0.972259	−	0.233906i	$-0.0751509\pi$
$132$	−0.245782	+	0.559706i	−0.0213926	+	0.0487161i
$133$	−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	0.920663	+	0.390358i	$0.127649\pi$
$137$	8.13848	+	15.9727i	0.695317	+	1.36464i	−0.225346	+	0.974279i	$0.572351\pi$
$138$	−10.1347	−	9.03207i	−0.862721	−	0.768861i
$139$	17.1405	−	5.56927i	1.45383	−	0.472379i	0.527654	−	0.849459i	$-0.323072\pi$
$139$	17.1405	−	5.56927i	1.45383	−	0.472379i	0.926181	+	0.377080i	$0.123072\pi$
$140$		0			0
$141$	−7.39381	+	0.425343i	−0.622671	+	0.0358204i
$142$	−0.964240	−	6.08797i	−0.0809172	−	0.510891i
$143$	−0.618480	−	0.618480i	−0.0517199	−	0.0517199i
$144$	−0.344023	−	2.98021i	−0.0286686	−	0.248351i
$145$		0			0
$146$	−6.13747	−	8.44751i	−0.507941	−	0.699121i
$147$	13.3202	−	2.90243i	1.09863	−	0.239388i
$148$	−4.33521	−	2.20890i	−0.356352	−	0.181570i
$149$	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	$0.703361\pi$
$152$	5.83498	+	2.97307i	0.473279	+	0.241148i
$153$	8.85167	−	5.87766i	0.715615	−	0.475181i
$154$	0.799974	+	1.10107i	0.0644637	+	0.0887267i
$155$		0			0
$156$	4.15188	+	1.08981i	0.332416	+	0.0872547i
$157$	−3.17235	−	3.17235i	−0.253181	−	0.253181i	0.569093	−	0.822273i	$-0.307295\pi$
$157$	−3.17235	−	3.17235i	−0.253181	−	0.253181i	−0.822273	+	0.569093i	$0.807295\pi$
$158$	−0.213757	−	1.34961i	−0.0170056	−	0.107369i
$159$	−0.437806	−	7.61046i	−0.0347203	−	0.603548i
$160$		0			0
$161$	−28.7452	+	9.33987i	−2.26544	+	0.736085i
$162$	−8.33463	+	3.39616i	−0.654831	+	0.266827i
$163$	4.91227	+	9.64088i	0.384759	+	0.755132i	0.999434	−	0.0336487i	$-0.0107127\pi$
$163$	4.91227	+	9.64088i	0.384759	+	0.755132i	−0.614675	+	0.788781i	$0.710713\pi$
$164$	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	$-0.775137\pi$
$167$	−16.5871	+	2.62714i	−1.28355	+	0.203295i	−0.522866	+	0.852415i	$0.675137\pi$
$168$	−6.11560	−	2.68553i	−0.471829	−	0.207193i
$169$	4.03108	−	5.54830i	0.310083	−	0.426793i
$170$		0			0
$171$	3.88832	−	19.2576i	0.297347	−	1.47267i
$172$	7.21237	+	1.14233i	0.549938	+	0.0871017i
$173$	−7.90821	+	15.5207i	−0.601250	+	1.18002i	0.367043	+	0.930204i	$0.380370\pi$
$173$	−7.90821	+	15.5207i	−0.601250	+	1.18002i	−0.968293	+	0.249816i	$0.919630\pi$
$174$	−3.92710	−	10.0764i	−0.297713	−	0.763892i
$175$		0			0
$176$		−	0.352930i		−	0.0266031i
$177$	−3.97717	−	0.397506i	−0.298943	−	0.0298784i
$178$	0.320566	−	2.02397i	0.0240274	−	0.151703i
$179$	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
$183$	0.218625	−	0.127715i	0.0161612	−	0.00944098i
$184$	7.45412	+	2.42199i	0.549525	+	0.178552i
$185$		0			0
$186$	5.62001	−	4.59868i	0.412079	−	0.337192i
$187$	1.11376	−	0.567491i	0.0814465	−	0.0414991i
$188$	3.80983	−	1.94121i	0.277861	−	0.141577i
$189$	−2.83122	+	19.8368i	−0.205941	+	1.44291i
$190$		0			0
$191$	13.4008	+	4.35419i	0.969650	+	0.315058i	0.750675	−	0.660672i	$-0.229729\pi$
$191$	13.4008	+	4.35419i	0.969650	+	0.315058i	0.218975	+	0.975730i	$0.429729\pi$
$192$	0.873670	+	1.49556i	0.0630517	+	0.107933i
$193$	2.89340	−	2.89340i	0.208271	−	0.208271i	−0.595261	−	0.803532i	$-0.702951\pi$
$193$	2.89340	−	2.89340i	0.208271	−	0.208271i	0.803532	+	0.595261i	$0.202951\pi$
$194$	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	−0.452353	−	0.891839i	$-0.649415\pi$
$197$	3.55739	−	22.4605i	0.253454	−	1.60024i	0.705806	−	0.708405i	$-0.250585\pi$
$198$	−1.01986	+	0.284460i	−0.0724785	+	0.0202157i
$199$		−	6.31867i		−	0.447919i	−0.974598	−	0.223959i	$-0.928102\pi$
$199$		−	6.31867i		−	0.447919i	0.974598	−	0.223959i	$-0.0718983\pi$
$200$		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
$204$	−3.31483	+	5.16187i	−0.232084	+	0.361403i
$205$		0			0
$206$	3.91049	−	5.38233i	0.272457	−	0.375005i
$207$	0.990845	−	23.4923i	0.0688685	−	1.63283i
$208$	−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	0.897064	−	0.441900i	$-0.145696\pi$
$211$	−1.28435	−	3.95283i	−0.0884185	−	0.272124i	−0.985483	+	0.169776i	$0.945696\pi$
$212$	1.99809	+	3.92147i	0.137229	+	0.269327i
$213$	7.10313	−	7.97026i	0.486699	−	0.546113i
$214$	−14.0333	+	4.55969i	−0.959296	+	0.311694i
$215$		0			0
$216$	3.61755	−	3.73006i	0.246143	−	0.253798i
$217$	−2.52917	−	15.9686i	−0.171691	−	1.08402i
$218$	7.86037	+	7.86037i	0.532371	+	0.532371i
$219$	4.59166	−	17.4930i	0.310276	−	1.18206i
$220$		0			0
$221$	−5.15934	−	7.10123i	−0.347055	−	0.477680i
$222$	−1.79419	−	8.23412i	−0.120418	−	0.552638i
$223$	−13.6942	−	6.97753i	−0.917030	−	0.467250i	−0.0692509	−	0.997599i	$-0.522061\pi$
$223$	−13.6942	−	6.97753i	−0.917030	−	0.467250i	−0.847779	+	0.530349i	$0.822061\pi$
$224$	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	$-0.504109\pi$
$227$	−12.4969	−	6.36747i	−0.829445	−	0.422624i	−0.816537	+	0.577293i	$0.804109\pi$
$228$	2.41489	+	11.0827i	0.159930	+	0.733971i
$229$	10.1878	+	14.0224i	0.673232	+	0.926624i	0.999828	−	0.0185396i	$-0.00590167\pi$
$229$	10.1878	+	14.0224i	0.673232	+	0.926624i	−0.326596	+	0.945164i	$0.605902\pi$
$230$		0			0
$231$	−0.598489	+	2.28008i	−0.0393777	+	0.150018i
$232$	4.41506	+	4.41506i	0.289863	+	0.289863i
$233$	0.384884	+	2.43006i	0.0252146	+	0.159199i	0.997083	−	0.0763263i	$-0.0243191\pi$
$233$	0.384884	+	2.43006i	0.0252146	+	0.159199i	−0.971868	+	0.235525i	$0.924319\pi$
$234$	3.09320	+	6.76087i	0.202209	+	0.441972i
$235$		0			0
$236$	2.19472	−	0.713107i	0.142864	−	0.0464193i
$237$	1.57466	−	1.76688i	0.102285	−	0.114771i
$238$	6.20067	+	12.1695i	0.401930	+	0.788831i
$239$	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	$0.0833974\pi$
$242$	10.7415	−	1.70129i	0.690493	−	0.109363i
$243$	−13.6945	−	7.44723i	−0.878501	−	0.477740i
$244$	−0.0859239	+	0.118264i	−0.00550072	+	0.00757109i
$245$		0			0
$246$	−7.93691	+	12.3594i	−0.506039	+	0.788008i
$247$	−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	$-0.284962\pi$
$252$	−3.10814	−	11.1435i	−0.195794	−	0.701974i
$253$	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	−0.313326	+	0.949646i	$0.601443\pi$
$257$	−20.2470	+	20.2470i	−1.26297	+	1.26297i	−0.949646	+	0.313326i	$0.898557\pi$
$258$	6.37978	+	10.9210i	0.397188	+	0.679912i
$259$	−17.8445	−	5.79802i	−1.10880	−	0.360272i
$260$		0			0
$261$	9.19968	−	16.3167i	0.569446	−	1.00998i
$262$	−15.5156	+	7.90558i	−0.958555	+	0.488408i
$263$	−2.68232	+	1.36671i	−0.165399	+	0.0842750i	−0.534730	−	0.845023i	$-0.679587\pi$
$263$	−2.68232	+	1.36671i	−0.165399	+	0.0842750i	0.369331	+	0.929298i	$0.379587\pi$
$264$	0.473094	−	0.387119i	0.0291169	−	0.0238255i
$265$		0			0
$266$	24.0178	+	7.80385i	1.47262	+	0.478485i
$267$	3.06471	−	1.79033i	0.187557	−	0.109566i
$268$	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	$0.126944\pi$
$272$	0.554059	−	3.49819i	0.0335948	−	0.212109i
$273$	16.4711	+	1.64623i	0.996876	+	0.0996347i
$274$		−	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	−0.699454	−	0.714677i	$-0.746573\pi$
$277$	4.82425	−	9.46812i	0.289861	−	0.568884i	0.989315	+	0.145793i	$0.0465735\pi$
$278$	−17.8007	−	2.81935i	−1.06761	−	0.169093i
$279$	12.3288	+	2.48932i	0.738108	+	0.149032i
$280$		0			0
$281$	−16.4932	+	22.7009i	−0.983902	+	1.35422i	−0.0492011	+	0.998789i	$0.515668\pi$
$281$	−16.4932	+	22.7009i	−0.983902	+	1.35422i	−0.934701	+	0.355436i	$0.884332\pi$
$282$	6.78104	+	2.97774i	0.403805	+	0.177322i
$283$	25.3567	−	4.01611i	1.50730	−	0.238733i	0.652539	−	0.757755i	$-0.273704\pi$
$283$	25.3567	−	4.01611i	1.50730	−	0.238733i	0.854761	+	0.519022i	$0.173704\pi$
$284$	−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
$288$	−1.04646	+	2.81157i	−0.0616632	+	0.165673i
$289$	−4.23760	+	1.37688i	−0.249271	+	0.0809930i
$290$		0			0
$291$	0.698888	+	12.1489i	0.0409696	+	0.712181i
$292$	1.63344	+	10.3131i	0.0955899	+	0.603531i
$293$	24.1559	+	24.1559i	1.41120	+	1.41120i	0.751709	+	0.659495i	$0.229230\pi$
$293$	24.1559	+	24.1559i	1.41120	+	1.41120i	0.659495	+	0.751709i	$0.270770\pi$
$294$	−13.1861	−	3.46116i	−0.769027	−	0.201859i
$295$		0			0
$296$	2.85988	+	3.93629i	0.166227	+	0.228792i
$297$	−1.49997	−	1.05509i	−0.0870370	−	0.0612223i
$298$	−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
$303$	16.2241	−	3.53518i	0.932051	−	0.203091i
$304$	−3.84926	−	5.29805i	−0.220770	−	0.303864i
$305$		0			0
$306$	−10.5553	+	1.21846i	−0.603406	+	0.0696547i
$307$	12.8970	+	12.8970i	0.736071	+	0.736071i	0.971815	−	0.235744i	$-0.0757527\pi$
$307$	12.8970	+	12.8970i	0.736071	+	0.736071i	−0.235744	+	0.971815i	$0.575753\pi$
$308$	−0.212907	−	1.34424i	−0.0121315	−	0.0765952i
$309$	11.5042	−	0.661801i	0.654451	−	0.0376485i
$310$		0			0
$311$	−15.4255	+	5.01205i	−0.874699	+	0.284207i	−0.711755	−	0.702428i	$-0.752099\pi$
$311$	−15.4255	+	5.01205i	−0.874699	+	0.284207i	−0.162945	+	0.986635i	$0.552099\pi$
$312$	−3.20458	−	2.85594i	−0.181424	−	0.161686i
$313$	−2.45198	−	4.81228i	−0.138594	−	0.272006i	0.811269	−	0.584674i	$-0.198777\pi$
$313$	−2.45198	−	4.81228i	−0.138594	−	0.272006i	−0.949863	+	0.312668i	$0.898777\pi$
$314$	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	$-0.627448\pi$
$317$	−8.47316	+	1.34202i	−0.475900	+	0.0753752i	−0.0861233	+	0.996284i	$0.527448\pi$
$318$	−3.06499	+	6.97973i	−0.171876	+	0.391404i
$319$	1.29527	−	1.78278i	0.0725210	−	0.0998166i
$320$		0			0
$321$	−21.5049	−	13.8099i	−1.20028	−	0.770793i
$322$	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
$327$	−1.91483	+	19.1584i	−0.105890	+	1.05946i
$328$	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	0.998929	−	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
$333$	9.06965	−	11.4368i	0.497014	−	0.626734i
$334$	15.9719	+	5.18960i	0.873946	+	0.283962i
$335$		0			0
$336$	4.22984	+	5.16925i	0.230757	+	0.282005i
$337$	4.22871	−	2.15464i	0.230353	−	0.117371i	−0.335005	−	0.942216i	$-0.608738\pi$
$337$	4.22871	−	2.15464i	0.230353	−	0.117371i	0.565358	+	0.824846i	$0.308738\pi$
$338$	−6.11059	+	3.11350i	−0.332372	+	0.169352i
$339$	−1.93047	−	2.35921i	−0.104849	−	0.128135i
$340$		0			0
$341$	1.40726	+	0.457245i	0.0762072	+	0.0247612i
$342$	−12.2073	+	15.3934i	−0.660095	+	0.832380i
$343$	−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	0.930784	+	0.365570i	$0.119126\pi$
$347$	−1.25574	+	7.92843i	−0.0674116	+	0.425620i	−0.998195	+	0.0600500i	$0.980874\pi$
$348$	−1.07553	+	10.7610i	−0.0576545	+	0.576851i
$349$			18.9234i			1.01295i	0.862256	+	0.506474i	$0.169051\pi$
$349$			18.9234i			1.01295i	−0.862256	+	0.506474i	$0.830949\pi$
$350$		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	$-0.409874\pi$
$353$	4.66620	+	0.739053i	0.248357	+	0.0393358i	−0.0310149	+	0.999519i	$0.509874\pi$
$354$	3.36322	+	2.15978i	0.178753	+	0.114791i
$355$		0			0
$356$	−1.20449	+	1.65784i	−0.0638379	+	0.0878654i
$357$	−9.51159	+	21.6602i	−0.503406	+	1.14638i
$358$	−7.25818	+	1.14958i	−0.383607	+	0.0607573i
$359$	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
$362$	0.304777	+	0.598158i	0.0160187	+	0.0314385i
$363$	14.0626	+	12.5327i	0.738097	+	0.657795i
$364$	−9.08922	+	2.95327i	−0.476405	+	0.154793i
$365$		0			0
$366$	−0.252778	+	0.0145415i	−0.0132129	+	0.000760098i
$367$	5.73021	+	36.1791i	0.299114	+	1.88853i	0.439193	+	0.898393i	$0.355265\pi$
$367$	5.73021	+	36.1791i	0.299114	+	1.88853i	−0.140078	+	0.990140i	$0.544735\pi$
$368$	−5.54211	−	5.54211i	−0.288902	−	0.288902i
$369$	−25.2733	+	2.91744i	−1.31567	+	0.151876i
$370$		0			0
$371$	9.97595	+	13.7307i	0.517926	+	0.712864i
$372$	−7.09522	+	1.54603i	−0.367870	+	0.0801577i
$373$	1.97517	+	1.00640i	0.102270	+	0.0521093i	0.504377	−	0.863483i	$-0.331722\pi$
$373$	1.97517	+	1.00640i	0.102270	+	0.0521093i	−0.402107	+	0.915593i	$0.631722\pi$
$374$	−1.25001			−0.0646363
$375$		0			0
$376$	−4.27588			−0.220512
$377$	−13.7875	−	7.02506i	−0.710090	−	0.361809i
$378$	11.5283	−	16.3894i	0.592954	−	0.842977i
$379$	4.15559	+	5.71968i	0.213458	+	0.293800i	0.902297	−	0.431114i	$-0.141879\pi$
$379$	4.15559	+	5.71968i	0.213458	+	0.293800i	−0.688839	+	0.724914i	$0.741879\pi$
$380$		0			0
$381$	9.03625	+	2.37189i	0.462941	+	0.121516i
$382$	−9.96347	−	9.96347i	−0.509775	−	0.509775i
$383$	−2.17700	−	13.7450i	−0.111240	−	0.702339i	−0.978771	−	0.204957i	$-0.934295\pi$
$383$	−2.17700	−	13.7450i	−0.111240	−	0.702339i	0.867532	−	0.497382i	$-0.165705\pi$
$384$	−0.0994751	−	1.72919i	−0.00507632	−	0.0882425i
$385$		0			0
$386$	−3.89161	+	1.26446i	−0.198078	+	0.0643593i
$387$	−7.64154	+	20.5309i	−0.388441	+	1.04364i
$388$	−3.18963	−	6.26000i	−0.161929	−	0.317803i
$389$	−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
$392$	7.77397	−	1.23128i	0.392645	−	0.0621888i
$393$	−27.6158	−	12.1268i	−1.39303	−	0.611719i
$394$	−13.3665	+	18.3974i	−0.673395	+	0.926849i
$395$		0			0
$396$	1.03785	+	0.209552i	0.0521538	+	0.0105304i
$397$	13.6256	+	2.15808i	0.683849	+	0.108311i	0.488686	−	0.872460i	$-0.337476\pi$
$397$	13.6256	+	2.15808i	0.683849	+	0.108311i	0.195163	+	0.980771i	$0.437476\pi$
$398$	−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	$0.870746\pi$
$402$	13.0492	+	1.30423i	0.650836	+	0.0650490i
$403$	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
$408$	5.29697	−	3.09436i	0.262239	−	0.153194i
$409$	−5.65867	−	1.83861i	−0.279803	−	0.0909136i	0.165754	−	0.986167i	$-0.446994\pi$
$409$	−5.65867	−	1.83861i	−0.279803	−	0.0909136i	−0.445557	+	0.895254i	$0.646994\pi$
$410$		0			0
$411$	24.0301	−	19.6631i	1.18532	−	0.969909i
$412$	−5.92780	+	3.02037i	−0.292042	+	0.148803i
$413$	7.92905	−	4.04005i	0.390163	−	0.198798i
$414$	−11.5481	+	20.4820i	−0.567559	+	1.00663i
$415$		0			0
$416$	2.35699	+	0.765834i	0.115561	+	0.0375481i
$417$	−15.7457	−	26.9538i	−0.771073	−	1.31993i
$418$	−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	$0.508776\pi$
$422$	−0.650182	+	4.10508i	−0.0316503	+	0.199832i
$423$	3.44634	+	12.3560i	0.167567	+	0.600770i
$424$		−	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
$429$	−0.818612	+	1.27475i	−0.0395230	+	0.0615454i
$430$		0			0
$431$	4.11469	−	5.66339i	0.198198	−	0.272796i	−0.698337	−	0.715769i	$-0.746076\pi$
$431$	4.11469	−	5.66339i	0.198198	−	0.272796i	0.896535	+	0.442973i	$0.146076\pi$
$432$	−4.91667	+	1.68117i	−0.236553	+	0.0808855i
$433$	9.74698	−	1.54377i	0.468410	−	0.0741889i	0.0822322	−	0.996613i	$-0.473795\pi$
$433$	9.74698	−	1.54377i	0.468410	−	0.0741889i	0.386178	+	0.922424i	$0.373795\pi$
$434$	−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
$438$	−12.0328	+	13.5018i	−0.574951	+	0.645139i
$439$	−0.555271	+	0.180419i	−0.0265016	+	0.00861091i	−0.322238	−	0.946659i	$-0.604435\pi$
$439$	−0.555271	+	0.180419i	−0.0265016	+	0.00861091i	0.295736	+	0.955270i	$0.404435\pi$
$440$		0			0
$441$	−9.82380	−	21.4721i	−0.467800	−	1.02248i
$442$	1.37312	+	8.66953i	0.0653126	+	0.412368i
$443$	−6.33032	−	6.33032i	−0.300763	−	0.300763i	0.540549	−	0.841312i	$-0.318216\pi$
$443$	−6.33032	−	6.33032i	−0.300763	−	0.300763i	−0.841312	+	0.540549i	$0.818216\pi$
$444$	−2.13958	+	8.15120i	−0.101540	+	0.386839i
$445$		0			0
$446$	9.03387	+	12.4341i	0.427766	+	0.588770i
$447$	−1.71431	−	7.86754i	−0.0810842	−	0.372122i
$448$	−3.43597	−	1.75071i	−0.162334	−	0.0827134i
$449$	−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
$452$	1.56816	+	0.799015i	0.0737598	+	0.0375825i
$453$	5.40404	+	24.8009i	0.253904	+	1.16525i
$454$	8.24401	+	11.3469i	0.386911	+	0.532537i
$455$		0			0
$456$	2.87977	−	10.9711i	0.134857	−	0.513769i
$457$	24.7918	+	24.7918i	1.15971	+	1.15971i	0.984537	+	0.175174i	$0.0560488\pi$
$457$	24.7918	+	24.7918i	1.15971	+	1.15971i	0.175174	+	0.984537i	$0.443951\pi$
$458$	−2.71142	−	17.1192i	−0.126696	−	0.799928i
$459$	−13.2111	−	12.8126i	−0.616642	−	0.598042i
$460$		0			0
$461$	0.133994	−	0.0435374i	0.00624074	−	0.00202774i	−0.305895	−	0.952065i	$-0.598956\pi$
$461$	0.133994	−	0.0435374i	0.00624074	−	0.00202774i	0.312136	+	0.950038i	$0.398956\pi$
$462$	1.56839	−	1.75985i	0.0729681	−	0.0818758i
$463$	4.02806	+	7.90552i	0.187200	+	0.367401i	0.965464	−	0.260537i	$-0.0838995\pi$
$463$	4.02806	+	7.90552i	0.187200	+	0.367401i	−0.778264	+	0.627937i	$0.783899\pi$
$464$	−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	$-0.514021\pi$
$467$	4.81480	−	0.762590i	0.222803	−	0.0352885i	0.266838	+	0.963742i	$0.414021\pi$
$468$	0.313305	−	7.42827i	0.0144825	−	0.343372i
$469$	17.1621	−	23.6216i	0.792470	−	1.09074i
$470$		0			0
$471$	−4.19887	+	6.53851i	−0.193474	+	0.301279i
$472$	−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
$477$	−12.7180	+	3.54732i	−0.582319	+	0.162420i
$478$	0.380627	−	2.40319i	0.0174095	−	0.109919i
$479$	−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
$483$	26.4062	+	45.2025i	1.20152	+	2.05678i
$484$	−10.3432	−	3.36070i	−0.470144	−	0.152759i
$485$		0			0
$486$	8.82090	+	12.8527i	0.400124	+	0.583010i
$487$	31.0777	−	15.8349i	1.40827	−	0.717547i	0.425945	−	0.904749i	$-0.359942\pi$
$487$	31.0777	−	15.8349i	1.40827	−	0.717547i	0.982321	+	0.187202i	$0.0599418\pi$
$488$	0.130250	−	0.0663655i	0.00589612	−	0.00300422i
$489$	14.5042	−	11.8684i	0.655904	−	0.536706i
$490$		0			0
$491$	−5.09165	−	1.65438i	−0.229783	−	0.0746610i	0.191862	−	0.981422i	$-0.438547\pi$
$491$	−5.09165	−	1.65438i	−0.229783	−	0.0746610i	−0.421645	+	0.906761i	$0.638547\pi$
$492$	12.6829	−	7.40904i	0.571789	−	0.334025i
$493$	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
$498$	10.0827	+	1.00773i	0.451817	+	0.0451576i
$499$		−	8.93736i		−	0.400091i	−0.979787	−	0.200046i	$-0.935891\pi$
$499$		−	8.93736i		−	0.400091i	0.979787	−	0.200046i	$-0.0641090\pi$
$500$		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	$-0.470736\pi$
$503$	−2.88408	−	0.456793i	−0.128595	−	0.0203674i	−0.220400	+	0.975410i	$0.570736\pi$
$504$	−2.28966	+	11.3400i	−0.101990	+	0.505123i
$505$		0			0
$506$	−1.62591	+	2.23788i	−0.0722807	+	0.0994859i
$507$	−10.8761	−	4.77599i	−0.483025	−	0.212109i
$508$	−5.32741	+	0.843778i	−0.236365	+	0.0374366i
$509$	−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
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	−34.0243	+	0.520992i	−1.50221	+	0.0230023i
$514$	27.2321	−	8.84825i	1.20116	−	0.390280i
$515$		0			0
$516$	−0.726395	−	12.6270i	−0.0319777	−	0.555874i
$517$	0.236073	+	1.49051i	0.0103825	+	0.0655524i
$518$	13.2673	+	13.2673i	0.582932	+	0.582932i
$519$	29.1826	+	7.66004i	1.28097	+	0.336238i
$520$		0			0
$521$	11.1471	+	15.3427i	0.488364	+	0.672175i	0.980085	−	0.198578i	$-0.0636322\pi$
$521$	11.1471	+	15.3427i	0.488364	+	0.672175i	−0.491722	+	0.870753i	$0.663632\pi$
$522$	−15.6046	+	10.3617i	−0.682995	+	0.453520i
$523$	−21.7058	−	11.0596i	−0.949127	−	0.483604i	−0.0903250	−	0.995912i	$-0.528791\pi$
$523$	−21.7058	−	11.0596i	−0.949127	−	0.483604i	−0.858802	+	0.512308i	$0.828791\pi$
$524$	17.4135			0.760714
$525$		0			0
$526$	3.01044			0.131261
$527$	13.2307	+	6.74137i	0.576338	+	0.293659i
$528$	−0.597278	+	0.130145i	−0.0259932	+	0.00566383i
$529$	−22.5886	−	31.0905i	−0.982111	−	1.35176i
$530$		0			0
$531$	0.793889	+	6.87732i	0.0344518	+	0.298450i
$532$	−17.8571	−	17.8571i	−0.774205	−	0.774205i
$533$	3.28775	+	20.7580i	0.142408	+	0.899131i
$534$	−3.54347	+	0.203845i	−0.153341	+	0.00882122i
$535$		0			0
$536$	−7.20094	+	2.33973i	−0.311033	+	0.101061i
$537$	−9.50227	−	8.46847i	−0.410053	−	0.365441i
$538$	−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	−0.552144	−	0.833749i	$-0.686190\pi$
$541$	8.94591	−	27.5327i	0.384615	−	1.18372i	0.936759	−	0.349974i	$-0.113810\pi$
$542$	−16.8214	+	2.66425i	−0.722542	+	0.114439i
$543$	−0.467516	+	1.06465i	−0.0200630	+	0.0456884i
$544$	−2.08182	+	2.86537i	−0.0892571	+	0.122852i
$545$		0			0
$546$	−13.9285	−	8.94453i	−0.596084	−	0.382790i
$547$	−12.9801	−	2.05584i	−0.554988	−	0.0879014i	−0.127360	−	0.991857i	$-0.540650\pi$
$547$	−12.9801	−	2.05584i	−0.554988	−	0.0879014i	−0.427627	+	0.903955i	$0.640650\pi$
$548$	−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
$552$	1.35009	−	13.5080i	0.0574635	−	0.574940i
$553$	−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	0.0444707	−	0.999011i	$-0.485840\pi$
$557$	24.6270	−	24.6270i	1.04348	−	1.04348i	0.999011	−	0.0444707i	$-0.0141601\pi$
$558$	−9.85495	−	7.81518i	−0.417193	−	0.330843i
$559$	17.2114	+	5.59233i	0.727966	+	0.236530i
$560$		0			0
$561$	−1.37110	−	1.67560i	−0.0578877	−	0.0707441i
$562$	25.0016	−	12.7389i	1.05463	−	0.537359i
$563$	8.71723	−	4.44165i	0.367388	−	0.187193i	−0.260544	−	0.965462i	$-0.583902\pi$
$563$	8.71723	−	4.44165i	0.367388	−	0.187193i	0.627931	+	0.778269i	$0.283902\pi$
$564$	−4.69008	−	5.73171i	−0.197488	−	0.241348i
$565$		0			0
$566$	−24.4163	−	7.93332i	−1.02629	−	0.333462i
$567$	34.6146	−	2.52353i	1.45368	−	0.105978i
$568$	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	$0.194513\pi$
$572$	0.136828	−	0.863895i	0.00572105	−	0.0361213i
$573$	2.42715	−	24.2844i	0.101396	−	1.01450i
$574$		−	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	−0.706350	−	0.707863i	$-0.749659\pi$
$577$	6.76199	−	13.2712i	0.281505	−	0.552485i	0.987855	+	0.155378i	$0.0496594\pi$
$578$	4.40082	+	0.697022i	0.183050	+	0.0289923i
$579$	−5.96357	−	3.82966i	−0.247837	−	0.159155i
$580$		0			0
$581$	13.2606	−	18.2516i	0.550140	−	0.757203i
$582$	4.89277	−	11.1420i	0.202812	−	0.461852i
$583$	−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	−0.996423	−	0.0845070i	$-0.973068\pi$
$587$	−11.6079	−	22.7817i	−0.479108	−	0.940302i	0.517315	−	0.855795i	$-0.326932\pi$
$588$	10.1775	+	9.07027i	0.419715	+	0.374052i
$589$	26.1121	−	8.48435i	1.07593	−	0.349592i
$590$		0			0
$591$	−39.3226	+	2.26211i	−1.61752	+	0.0930508i
$592$	−0.761135	−	4.80562i	−0.0312825	−	0.197510i
$593$	5.46116	+	5.46116i	0.224263	+	0.224263i	0.810291	−	0.586028i	$-0.199309\pi$
$593$	5.46116	+	5.46116i	0.224263	+	0.224263i	−0.586028	+	0.810291i	$0.699309\pi$
$594$	0.857484	+	1.62106i	0.0351830	+	0.0665129i
$595$		0			0
$596$	2.73256	+	3.76105i	0.111930	+	0.154058i
$597$	−10.6933	+	2.33005i	−0.437650	+	0.0953624i
$598$	17.3071	+	8.81838i	0.707738	+	0.360611i
$599$	−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	$0.380446\pi$
$602$	−25.0904	−	12.7842i	−1.02261	−	0.521045i
$603$	12.5650	+	18.9227i	0.511687	+	0.770594i
$604$	−8.61387	−	11.8560i	−0.350494	−	0.482413i
$605$		0			0
$606$	−16.0607	−	4.21573i	−0.652423	−	0.171252i
$607$	−5.54524	−	5.54524i	−0.225074	−	0.225074i	0.585557	−	0.810631i	$-0.300876\pi$
$607$	−5.54524	−	5.54524i	−0.225074	−	0.225074i	−0.810631	+	0.585557i	$0.800876\pi$
$608$	1.02445	+	6.46812i	0.0415469	+	0.262317i
$609$	2.39516	+	41.6354i	0.0970567	+	1.68715i
$610$		0			0
$611$	10.0782	−	3.27461i	0.407721	−	0.132477i
$612$	9.95800	+	3.70635i	0.402528	+	0.149820i
$613$	2.13588	+	4.19191i	0.0862676	+	0.169310i	0.930110	−	0.367282i	$-0.119712\pi$
$613$	2.13588	+	4.19191i	0.0862676	+	0.169310i	−0.843842	+	0.536592i	$0.819712\pi$
$614$	−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	$-0.240574\pi$
$617$	40.5328	−	6.41977i	1.63179	−	0.258450i	0.904058	+	0.427410i	$0.140574\pi$
$618$	−10.5508	−	4.63313i	−0.424414	−	0.186372i
$619$	−10.1486	+	13.9684i	−0.407908	+	0.561438i	−0.962707	−	0.270547i	$-0.912795\pi$
$619$	−10.1486	+	13.9684i	−0.407908	+	0.561438i	0.554798	+	0.831985i	$0.312795\pi$
$620$		0			0
$621$	−40.1224	+	6.98607i	−1.61005	+	0.280341i
$622$	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
$627$	−3.98336	−	0.398124i	−0.159080	−	0.0158995i
$628$	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	−0.181959	−	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
$633$	−6.21593	+	3.63119i	−0.247061	+	0.144327i
$634$	8.15891	+	2.65099i	0.324032	+	0.105284i
$635$		0			0
$636$	5.89965	−	4.82751i	0.233936	−	0.191423i
$637$	−17.3803	+	8.85568i	−0.688631	+	0.350875i
$638$	−1.96346	+	1.00043i	−0.0777340	+	0.0396074i
$639$	−16.1077	−	9.08185i	−0.637212	−	0.359272i
$640$		0			0
$641$	28.1775	+	9.15543i	1.11294	+	0.361618i	0.807071	−	0.590454i	$-0.201051\pi$
$641$	28.1775	+	9.15543i	1.11294	+	0.361618i	0.305874	+	0.952072i	$0.401051\pi$
$642$	12.8914	+	22.0677i	0.508784	+	0.870943i
$643$	−16.2471	+	16.2471i	−0.640721	+	0.640721i	−0.950733	−	0.310012i	$-0.899667\pi$
$643$	−16.2471	+	16.2471i	−0.640721	+	0.640721i	0.310012	+	0.950733i	$0.399667\pi$
$644$	−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	$-0.961225\pi$
$647$	−0.280589	+	1.77157i	−0.0110311	+	0.0696477i	0.981559	+	0.191161i	$0.0612253\pi$
$648$	−7.64652	−	4.74665i	−0.300384	−	0.186466i
$649$			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	$-0.624563\pi$
$653$	−26.3159	−	4.16803i	−1.02982	−	0.163107i	−0.648404	+	0.761296i	$0.724563\pi$
$654$	10.4039	−	16.2010i	0.406824	−	0.633509i
$655$		0			0
$656$	−4.98463	+	6.86076i	−0.194617	+	0.267868i
$657$	−31.2973	−	1.32004i	−1.22102	−	0.0514996i
$658$	−16.2860	+	2.57944i	−0.634893	+	0.100557i
$659$	−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	$0.777270\pi$
$662$	−12.9009	−	25.3194i	−0.501407	−	0.984066i
$663$	−10.1152	+	11.3500i	−0.392840	+	0.440797i
$664$	−5.56392	+	1.80783i	−0.215922	+	0.0701573i
$665$		0			0
$666$	−13.2733	+	6.07276i	−0.514331	+	0.235315i
$667$	−7.65551	−	48.3350i	−0.296422	−	1.87154i
$668$	−11.8751	−	11.8751i	−0.459461	−	0.459461i
$669$	−6.75856	+	25.7482i	−0.261301	+	0.995484i
$670$		0			0
$671$	−0.0303252	−	0.0417390i	−0.00117069	−	0.00161132i
$672$	−1.42202	−	6.52614i	−0.0548558	−	0.251751i
$673$	−39.1978	−	19.9723i	−1.51096	−	0.769874i	−0.514793	−	0.857315i	$-0.672131\pi$
$673$	−39.1978	−	19.9723i	−1.51096	−	0.769874i	−0.996170	+	0.0874407i	$0.972131\pi$
$674$	−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	$-0.0942963\pi$
$677$	33.3683	+	17.0020i	1.28245	+	0.653440i	0.326008	+	0.945367i	$0.394296\pi$
$678$	0.649003	+	2.97849i	0.0249248	+	0.114388i
$679$	−15.9250	−	21.9189i	−0.611147	−	0.841171i
$680$		0			0
$681$	−6.16764	+	23.4970i	−0.236344	+	0.900406i
$682$	−1.04629	−	1.04629i	−0.0400645	−	0.0400645i
$683$	−5.33840	−	33.7054i	−0.204268	−	1.28970i	−0.850263	−	0.526358i	$-0.823557\pi$
$683$	−5.33840	−	33.7054i	−0.204268	−	1.28970i	0.645995	−	0.763342i	$-0.276443\pi$
$684$	17.8652	−	8.17363i	0.683094	−	0.312526i
$685$		0			0
$686$	3.19397	−	1.03778i	0.121946	−	0.0396228i
$687$	19.9738	−	22.4121i	0.762049	−	0.855077i
$688$	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	0.574867	+	0.818247i	$0.305054\pi$
$691$	−9.75674	+	30.0282i	−0.371164	+	1.14232i	−0.946030	+	0.324078i	$0.894946\pi$
$692$	−17.2049	+	2.72498i	−0.654031	+	0.103588i
$693$	4.07936	+	0.172057i	0.154962	+	0.00653591i
$694$	4.71830	−	6.49419i	0.179104	−	0.246516i
$695$		0			0
$696$	5.84371	−	9.09986i	0.221505	−	0.344929i
$697$	−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	$-0.283170\pi$
$702$	10.3011	−	7.72787i	0.388789	−	0.291670i
$703$	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
$708$	−2.01613	−	3.45125i	−0.0757710	−	0.129706i
$709$	−48.5191	−	15.7648i	−1.82217	−	0.592060i	−0.999731	−	0.0232123i	$-0.992611\pi$
$709$	−48.5191	−	15.7648i	−1.82217	−	0.592060i	−0.822443	−	0.568848i	$-0.807389\pi$
$710$		0			0
$711$	−3.57083	−	2.01331i	−0.133917	−	0.0755049i
$712$	1.82585	−	0.930319i	0.0684268	−	0.0348652i
$713$	29.2785	−	14.9181i	1.09649	−	0.558689i
$714$	18.3084	−	14.9812i	0.685175	−	0.560658i
$715$		0			0
$716$	6.98899	+	2.27086i	0.261191	+	0.0848660i
$717$	3.63891	−	2.12576i	0.135898	−	0.0793881i
$718$	−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
$722$	−3.73661	+	23.5920i	−0.139062	+	0.878004i
$723$	−2.78978	−	0.278830i	−0.103753	−	0.0103698i
$724$		−	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	−0.993458	−	0.114198i	$-0.963570\pi$
$727$	−8.55075	+	16.7818i	−0.317130	+	0.622402i	0.676328	+	0.736600i	$0.263570\pi$
$728$	9.43931	+	1.49504i	0.349844	+	0.0554099i
$729$	−7.55333	+	25.9219i	−0.279753	+	0.960072i
$730$		0			0
$731$	−15.2020	+	20.9238i	−0.562266	+	0.773893i
$732$	0.231828	+	0.101802i	0.00856862	+	0.00376271i
$733$	−34.3095	+	5.43410i	−1.26725	+	0.200713i	−0.753627	−	0.657302i	$-0.771698\pi$
$733$	−34.3095	+	5.43410i	−1.26725	+	0.200713i	−0.513625	+	0.858015i	$0.671698\pi$
$734$	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
$738$	23.8431	+	8.87436i	0.877678	+	0.326670i
$739$	2.70309	−	0.878288i	0.0994348	−	0.0323083i	−0.258877	−	0.965910i	$-0.583352\pi$
$739$	2.70309	−	0.878288i	0.0994348	−	0.0323083i	0.358312	+	0.933602i	$0.383352\pi$
$740$		0			0
$741$	1.61445	+	28.0643i	0.0593083	+	1.03097i
$742$	−2.65502	−	16.7632i	−0.0974689	−	0.615395i
$743$	−19.3245	−	19.3245i	−0.708947	−	0.708947i	0.257367	−	0.966314i	$-0.417145\pi$
$743$	−19.3245	−	19.3245i	−0.708947	−	0.708947i	−0.966314	+	0.257367i	$0.917145\pi$
$744$	7.02377	+	1.84364i	0.257504	+	0.0675913i
$745$		0			0
$746$	−1.30299	−	1.79341i	−0.0477059	−	0.0656615i
$747$	9.70857	+	14.6210i	0.355218	+	0.534953i
$748$	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
$753$	−41.8454	+	9.11798i	−1.52493	+	0.332278i
$754$	9.09541	+	12.5188i	0.331235	+	0.455906i
$755$		0			0
$756$	−17.7124	+	9.36926i	−0.644195	+	0.340757i
$757$	11.1659	+	11.1659i	0.405833	+	0.405833i	0.880283	−	0.474450i	$-0.157353\pi$
$757$	11.1659	+	11.1659i	0.405833	+	0.405833i	−0.474450	+	0.880283i	$0.657353\pi$
$758$	−1.10598	−	6.98287i	−0.0401710	−	0.253629i
$759$	−4.78324	+	0.275165i	−0.173621	+	0.00998786i
$760$		0			0
$761$	−13.3455	+	4.33621i	−0.483774	+	0.157188i	−0.540742	−	0.841188i	$-0.681857\pi$
$761$	−13.3455	+	4.33621i	−0.483774	+	0.157188i	0.0569686	+	0.998376i	$0.481857\pi$
$762$	−6.97454	−	6.21574i	−0.252661	−	0.225173i
$763$	−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
$768$	−0.696404	+	1.58588i	−0.0251293	+	0.0572256i
$769$	13.0082	−	17.9042i	0.469087	−	0.645643i	−0.507275	−	0.861784i	$-0.669347\pi$
$769$	13.0082	−	17.9042i	0.469087	−	0.645643i	0.976362	+	0.216141i	$0.0693471\pi$
$770$		0			0
$771$	41.7310	+	26.7986i	1.50290	+	0.965128i
$772$	4.04150	+	0.640111i	0.145457	+	0.0230381i
$773$	−19.2486	+	37.7774i	−0.692323	+	1.35876i	0.230324	+	0.973114i	$0.426021\pi$
$773$	−19.2486	+	37.7774i	−0.692323	+	1.35876i	−0.922647	+	0.385646i	$0.873979\pi$
$774$	16.1295	−	14.8239i	0.579762	−	0.532836i
$775$		0			0
$776$			7.02576i			0.252210i
$777$	−3.23198	+	32.3370i	−0.115947	+	1.16008i
$778$	−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
$783$	−31.0059	−	9.55212i	−1.10806	−	0.341365i
$784$	−7.48565	−	2.43223i	−0.267345	−	0.0868655i
$785$		0			0
$786$	19.1004	+	23.3424i	0.681288	+	0.832596i
$787$	25.7904	−	13.1408i	0.919327	−	0.468420i	0.0707509	−	0.997494i	$-0.477460\pi$
$787$	25.7904	−	13.1408i	0.919327	−	0.468420i	0.848576	+	0.529074i	$0.177460\pi$
$788$	20.2619	−	10.3240i	0.721800	−	0.367776i
$789$	3.30206	+	4.03542i	0.117557	+	0.143665i
$790$		0			0
$791$	6.45480	+	2.09729i	0.229506	+	0.0745711i
$792$	−0.829593	−	0.657885i	−0.0294783	−	0.0233769i
$793$	−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	0.892432	+	0.451182i	$0.148997\pi$
$797$	−2.70297	+	17.0659i	−0.0957441	+	0.604505i	−0.988176	+	0.153323i	$0.951003\pi$
$798$	4.35009	−	43.5240i	0.153991	−	1.54073i
$799$			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
$804$	−11.0348	−	7.08630i	−0.389169	−	0.249915i
$805$		0			0
$806$	−6.10729	+	8.40597i	−0.215120	+	0.296088i
$807$	9.03137	−	20.5666i	0.317919	−	0.723980i
$808$	9.46876	−	1.49970i	0.333110	−	0.0527594i
$809$	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	$0.600233\pi$
$812$	−10.9312	−	21.4536i	−0.383609	−	0.752874i
$813$	−22.0223	−	19.6264i	−0.772355	−	0.688326i
$814$	−1.63314	+	0.530641i	−0.0572417	+	0.0185989i
$815$		0			0
$816$	−6.12445	+	0.352321i	−0.214398	+	0.0123337i
$817$	7.48082	+	47.2320i	0.261721	+	1.65244i
$818$	4.20720	+	4.20720i	0.147101	+	0.147101i
$819$	−3.28782	−	28.4818i	−0.114886	−	0.995234i
$820$		0			0
$821$	13.3733	+	18.4068i	0.466731	+	0.642400i	0.975888	−	0.218274i	$-0.0700425\pi$
$821$	13.3733	+	18.4068i	0.466731	+	0.642400i	−0.509156	+	0.860674i	$0.670043\pi$
$822$	−30.3378	+	6.61051i	−1.05815	+	0.230568i
$823$	33.1249	+	16.8780i	1.15466	+	0.588330i	0.923127	−	0.384496i	$-0.125625\pi$
$823$	33.1249	+	16.8780i	1.15466	+	0.588330i	0.231536	+	0.972826i	$0.425625\pi$
$824$	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	$-0.408700\pi$
$827$	−9.39702	−	4.78802i	−0.326766	−	0.166496i	−0.609676	+	0.792651i	$0.708700\pi$
$828$	19.5881	−	13.0068i	0.680732	−	0.452018i
$829$	7.78028	+	10.7086i	0.270220	+	0.371926i	0.922464	−	0.386083i	$-0.126172\pi$
$829$	7.78028	+	10.7086i	0.270220	+	0.371926i	−0.652244	+	0.758009i	$0.726172\pi$
$830$		0			0
$831$	−17.8023	−	4.67285i	−0.617553	−	0.162099i
$832$	−1.75242	−	1.75242i	−0.0607541	−	0.0607541i
$833$	−4.36093	−	27.5338i	−0.151097	−	0.953990i
$834$	1.79279	+	31.1644i	0.0620794	+	1.07914i
$835$		0			0
$836$	2.19813	−	0.714216i	0.0760239	−	0.0247017i
$837$	−0.333542	−	21.7826i	−0.0115289	−	0.752915i
$838$	1.96185	+	3.85035i	0.0677711	+	0.133008i
$839$	−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
$842$	24.7186	−	3.91504i	0.851860	−	0.134921i
$843$	44.4997	+	19.5410i	1.53265	+	0.673029i
$844$	2.44299	−	3.36248i	0.0840910	−	0.115741i
$845$		0			0
$846$	2.53880	−	12.5739i	0.0872858	−	0.432299i
$847$	−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
$852$	10.6232	+	1.06175i	0.363945	+	0.0363751i
$853$	−5.89808	+	37.2390i	−0.201946	+	1.27504i	0.653412	+	0.757003i	$0.273337\pi$
$853$	−5.89808	+	37.2390i	−0.201946	+	1.27504i	−0.855358	+	0.518037i	$0.826663\pi$
$854$	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	$-0.722513\pi$
$857$	3.57064	−	3.57064i	0.121971	−	0.121971i	0.765457	+	0.643487i	$0.222513\pi$
$858$	1.30811	−	0.764167i	0.0446582	−	0.0260882i
$859$	33.5736	+	10.9087i	1.14552	+	0.372201i	0.819453	−	0.573147i	$-0.194278\pi$
$859$	33.5736	+	10.9087i	1.14552	+	0.372201i	0.326064	+	0.945348i	$0.394278\pi$
$860$		0			0
$861$	43.8371	−	35.8706i	1.49396	−	1.22247i
$862$	−6.23735	+	3.17809i	−0.212445	+	0.108246i
$863$	17.9383	−	9.14003i	0.610628	−	0.311130i	−0.121191	−	0.992629i	$-0.538672\pi$
$863$	17.9383	−	9.14003i	0.610628	−	0.311130i	0.731819	+	0.681499i	$0.238672\pi$
$864$	5.14402	+	0.734186i	0.175003	+	0.0249775i
$865$		0			0
$866$	−9.38548	−	3.04953i	−0.318932	−	0.103627i
$867$	3.89279	+	6.66374i	0.132206	+	0.226312i
$868$	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
$873$	20.3024	−	5.66273i	0.687131	−	0.191654i
$874$			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	−0.302244	−	0.953230i	$-0.597736\pi$
$877$	19.1482	−	37.5805i	0.646590	−	1.26900i	0.948834	−	0.315774i	$-0.102264\pi$
$878$	0.576659	+	0.0913337i	0.0194613	+	0.00308236i
$879$	31.9724	−	49.7877i	1.07840	−	1.67930i
$880$		0			0
$881$	−22.4775	+	30.9376i	−0.757285	+	1.04231i	0.240150	+	0.970736i	$0.422803\pi$
$881$	−22.4775	+	30.9376i	−0.757285	+	1.04231i	−0.997435	+	0.0715779i	$0.977197\pi$
$882$	−0.995035	+	23.5917i	−0.0335046	+	0.794372i
$883$	13.8121	−	2.18763i	0.464816	−	0.0736196i	0.0803657	−	0.996765i	$-0.474391\pi$
$883$	13.8121	−	2.18763i	0.464816	−	0.0736196i	0.384450	+	0.923146i	$0.374391\pi$
$884$	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	$-0.263092\pi$
$887$	−9.40690	−	18.4621i	−0.315853	−	0.619896i	−0.993285	+	0.115689i	$0.963092\pi$
$888$	5.60695	−	6.29142i	0.188157	−	0.211126i
$889$	−19.7820	+	6.42756i	−0.663467	+	0.215574i
$890$		0			0
$891$	−1.23244	+	2.92753i	−0.0412884	+	0.0980759i
$892$	−2.40429	−	15.1801i	−0.0805017	−	0.508268i
$893$	19.8002	+	19.8002i	0.662587	+	0.662587i
$894$	−2.04433	+	7.78831i	−0.0683725	+	0.260480i
$895$		0			0
$896$	2.26666	+	3.11979i	0.0757239	+	0.104225i
$897$	7.16277	+	32.8723i	0.239158	+	1.09757i
$898$	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
$903$	−10.3840	−	47.6557i	−0.345558	−	1.58588i
$904$	−1.03449	−	1.42386i	−0.0344067	−	0.0473567i
$905$		0			0
$906$	6.44435	−	24.5512i	0.214099	−	0.815658i
$907$	−8.19678	−	8.19678i	−0.272170	−	0.272170i	0.557803	−	0.829973i	$-0.311644\pi$
$907$	−8.19678	−	8.19678i	−0.272170	−	0.272170i	−0.829973	+	0.557803i	$0.811644\pi$
$908$	−2.19408	−	13.8529i	−0.0728131	−	0.459724i
$909$	−11.9655	−	26.1531i	−0.396870	−	0.867445i
$910$		0			0
$911$	4.38290	−	1.42409i	0.145212	−	0.0471822i	−0.235509	−	0.971872i	$-0.575676\pi$
$911$	4.38290	−	1.42409i	0.145212	−	0.0471822i	0.380721	+	0.924690i	$0.375676\pi$
$912$	−7.54667	+	8.46794i	−0.249895	+	0.280402i
$913$	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
$918$	5.95437	+	17.4138i	0.196524	+	0.574743i
$919$	1.33595	−	1.83878i	0.0440689	−	0.0606557i	−0.786414	−	0.617700i	$-0.788065\pi$
$919$	1.33595	−	1.83878i	0.0440689	−	0.0606557i	0.830483	+	0.557044i	$0.188065\pi$
$920$		0			0
$921$	17.0703	−	26.5820i	0.562485	−	0.875906i
$922$	−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
$927$	−5.36223	−	19.2250i	−0.176119	−	0.631431i
$928$	−0.976751	+	6.16696i	−0.0320634	+	0.202440i
$929$	−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
$933$	14.1703	+	24.2570i	0.463916	+	0.794138i
$934$	−4.63623	−	1.50640i	−0.151702	−	0.0492910i
$935$		0			0
$936$	−3.65152	+	6.47640i	−0.119354	+	0.211688i
$937$	−13.2746	+	6.76373i	−0.433661	+	0.220961i	−0.657173	−	0.753740i	$-0.728248\pi$
$937$	−13.2746	+	6.76373i	−0.433661	+	0.220961i	0.223512	+	0.974701i	$0.428248\pi$
$938$	−26.0155	+	13.2555i	−0.849435	+	0.432809i
$939$	−7.23984	+	5.92414i	−0.236263	+	0.193327i
$940$		0			0
$941$	−29.4117	−	9.55645i	−0.958795	−	0.311531i	−0.212511	−	0.977159i	$-0.568164\pi$
$941$	−29.4117	−	9.55645i	−0.958795	−	0.311531i	−0.746284	+	0.665627i	$0.768164\pi$
$942$	6.70965	−	3.91961i	0.218612	−	0.127708i
$943$	−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	$-0.902801\pi$
$947$	1.42242	−	8.98080i	0.0462224	−	0.291837i	0.999961	+	0.00879948i	$0.00280100\pi$
$948$	2.35500	+	0.235375i	0.0764868	+	0.00764461i
$949$			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	$-0.550350\pi$
$953$	−18.9081	−	2.99474i	−0.612493	−	0.0970093i	−0.454971	+	0.890506i	$0.650350\pi$
$954$	12.9423	+	2.61319i	0.419023	+	0.0846052i
$955$		0			0
$956$	−1.43017	+	1.96845i	−0.0462549	+	0.0636644i
$957$	−3.49471	−	1.53462i	−0.112968	−	0.0496073i
$958$	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
$963$	−15.4410	+	41.4861i	−0.497580	+	1.33687i
$964$	1.53948	−	0.500207i	0.0495833	−	0.0161106i
$965$		0			0
$966$	−3.00658	−	52.2639i	−0.0967351	−	1.68156i
$967$	6.88343	+	43.4603i	0.221356	+	1.39759i	0.808686	+	0.588240i	$0.200179\pi$
$967$	6.88343	+	43.4603i	0.221356	+	1.39759i	−0.587330	+	0.809347i	$0.699821\pi$
$968$	7.69010	+	7.69010i	0.247169	+	0.247169i
$969$	−38.8574	−	10.1995i	−1.24828	−	0.327657i
$970$		0			0
$971$	18.1657	+	25.0030i	0.582965	+	0.802383i	0.994017	−	0.109229i	$-0.0348383\pi$
$971$	18.1657	+	25.0030i	0.582965	+	0.802383i	−0.411051	+	0.911612i	$0.634838\pi$
$972$	−2.02448	−	15.4564i	−0.0649352	−	0.495765i
$973$	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	$-0.0756465\pi$
$977$	42.2813	+	21.5434i	1.35270	+	0.689235i	0.380806	+	0.924655i	$0.375646\pi$
$978$	−18.3115	+	3.99001i	−0.585537	+	0.127587i
$979$	−0.425102	−	0.585102i	−0.0135863	−	0.0186999i
$980$		0			0
$981$	33.1287	−	3.82424i	1.05772	−	0.122099i
$982$	3.78562	+	3.78562i	0.120804	+	0.120804i
$983$	5.45227	+	34.4243i	0.173900	+	1.09796i	0.908015	+	0.418938i	$0.137598\pi$
$983$	5.45227	+	34.4243i	0.173900	+	1.09796i	−0.734114	+	0.679026i	$0.762402\pi$
$984$	−14.6642	+	0.843585i	−0.467477	+	0.0268925i
$985$		0			0
$986$	−21.0320	+	6.83372i	−0.669796	+	0.217630i
$987$	−21.3213	−	19.0016i	−0.678664	−	0.604828i
$988$	−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	−0.925293	−	0.379252i	$-0.876181\pi$
$991$	1.45449	−	4.47645i	0.0462033	−	0.142199i	0.971497	+	0.237053i	$0.0761814\pi$
$992$	−4.14093	+	0.655859i	−0.131475	+	0.0208235i
$993$	19.7894	−	45.0654i	0.627999	−	1.43011i
$994$	13.9714	−	19.2300i	0.443146	−	0.609938i
$995$		0			0
$996$	−8.52625	−	5.47535i	−0.270165	−	0.173493i
$997$	20.4803	+	3.24377i	0.648619	+	0.102731i	0.472070	−	0.881561i	$-0.343507\pi$
$997$	20.4803	+	3.24377i	0.648619	+	0.102731i	0.176548	+	0.984292i	$0.443507\pi$
$998$	−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.107.3		80
3.2	odd	2	inner	750.2.l.b.107.9		80
5.2	odd	4		750.2.l.c.143.6		80
5.3	odd	4		750.2.l.a.143.5		80
5.4	even	2		150.2.l.a.17.8	yes	80
15.2	even	4		750.2.l.c.143.1		80
15.8	even	4		750.2.l.a.143.10		80
15.14	odd	2		150.2.l.a.17.2	✓	80
25.3	odd	20	inner	750.2.l.b.743.9		80
25.4	even	10		750.2.l.c.257.1		80
25.21	even	5		750.2.l.a.257.10		80
25.22	odd	20		150.2.l.a.53.2	yes	80
75.29	odd	10		750.2.l.c.257.6		80
75.47	even	20		150.2.l.a.53.8	yes	80
75.53	even	20	inner	750.2.l.b.743.3		80
75.71	odd	10		750.2.l.a.257.5		80

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

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)

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(-0.368756 - 1.69234i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.439743 + 1.67530i) q^{6} +(2.72680 + 2.72680i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.72804 + 1.24812i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(-0.368756 - 1.69234i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.439743 + 1.67530i) q^{6} +(2.72680 + 2.72680i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.72804 + 1.24812i) q^{9} +(-0.335657 + 0.109061i) q^{11} +(1.15238 - 1.29306i) 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} +(2.99734 + 0.126420i) q^{18} +(-3.84926 + 5.29805i) q^{19} +(3.60915 - 5.62020i) q^{21} +(0.348585 + 0.0552105i) q^{22} +(-3.55825 + 6.98347i) q^{23} +(-1.61382 + 0.628956i) q^{24} -2.47829i q^{26} +(3.11823 + 4.15652i) 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} +(0.308344 + 0.527829i) q^{33} +(3.36845 + 1.09448i) q^{34} +(-2.61325 - 1.47340i) q^{36} +(-4.33521 + 2.20890i) q^{37} +(5.83498 - 2.97307i) q^{38} +(3.32209 - 2.71836i) q^{39} +(8.06531 + 2.62058i) q^{41} +(-5.76730 + 3.36911i) 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} +(1.72346 + 0.172255i) q^{48} +7.87088i q^{49} +(2.22763 + 5.71582i) q^{51} +(-1.12512 + 2.20817i) q^{52} +(4.34698 + 0.688494i) q^{53} +(-0.891339 - 5.11913i) q^{54} +(2.26666 - 3.11979i) q^{56} +(10.3855 + 4.56057i) 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} +(-10.8422 - 4.03544i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-0.0351078 - 0.610284i) q^{66} +(-1.18445 - 7.47829i) q^{67} +(-2.50443 - 2.50443i) q^{68} +(13.1305 + 3.44659i) q^{69} +(3.62303 + 4.98667i) q^{71} +(1.65951 + 2.49920i) q^{72} +(9.30362 + 4.74043i) q^{73} +4.86552 q^{74} -6.54875 q^{76} +(-1.21266 - 0.617880i) q^{77} +(-4.19411 + 0.913883i) q^{78} +(0.803169 + 1.10547i) q^{79} +(5.88439 - 6.80984i) q^{81} +(-5.99652 - 5.99652i) q^{82} +(-0.915181 - 5.77823i) q^{83} +(6.66824 - 0.383604i) q^{84} +(-6.94488 + 2.25653i) q^{86} +(8.07367 + 7.19529i) 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} +(-2.91971 + 6.64888i) q^{93} +(-2.51330 + 3.45926i) q^{94} +(-1.45742 - 0.935916i) 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

Fields

Representations

Groups

Database

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