LMFDB - Embedded newform 483.2.q.b.232.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(64,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("483.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 12])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,5,-1,-1,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			232.1
Root			$0.142315 - 0.989821i$ of defining polynomial
Character	$\chi$	$=$	483.232
Dual form			483.2.q.b.127.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0741615 + 0.0476607i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(-0.827602 - 1.81219i) q^{4} +(-1.48357 - 0.435615i) q^{5} +(0.0366213 - 0.0801894i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(0.0500861 - 0.348356i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-0.0892619 - 0.103014i) q^{10} +(0.0405070 - 0.0260323i) q^{11} +(-1.67597 + 1.07708i) q^{12} +(-1.24690 - 1.43900i) q^{13} +(-0.0845850 + 0.0248364i) q^{14} +(-0.220047 + 1.53046i) q^{15} +(-2.58895 + 2.98780i) q^{16} +(-0.415415 + 0.909632i) q^{17} +(-0.0845850 - 0.0248364i) q^{18} +(-0.953800 - 2.08853i) q^{19} +(0.438384 + 3.04903i) q^{20} +(0.841254 + 0.540641i) q^{21} +0.00424478 q^{22} +(-3.50654 + 3.27173i) q^{23} -0.351939 q^{24} +(-2.19505 - 1.41067i) q^{25} +(-0.0238883 - 0.166147i) q^{26} +(0.415415 + 0.909632i) q^{27} +(1.91153 + 0.561276i) q^{28} +(-3.80306 + 8.32753i) q^{29} +(-0.0892619 + 0.103014i) q^{30} +(0.284630 - 1.97964i) q^{31} +(-1.00977 + 0.296494i) q^{32} +(-0.0315321 - 0.0363899i) q^{33} +(-0.0741615 + 0.0476607i) q^{34} +(1.30075 - 0.835939i) q^{35} +(1.30463 + 1.50563i) q^{36} +(-2.34811 + 0.689466i) q^{37} +(0.0288056 - 0.200347i) q^{38} +(-1.24690 + 1.43900i) q^{39} +(-0.226055 + 0.494992i) q^{40} +(1.26946 + 0.372747i) q^{41} +(0.0366213 + 0.0801894i) q^{42} +(-0.525696 - 3.65630i) q^{43} +(-0.0806993 - 0.0518623i) q^{44} +1.54620 q^{45} +(-0.415983 + 0.0755121i) q^{46} +0.701665 q^{47} +(3.32584 + 2.13739i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.0955546 - 0.209235i) q^{50} +(0.959493 + 0.281733i) q^{51} +(-1.57581 + 3.45055i) q^{52} +(7.68576 - 8.86984i) q^{53} +(-0.0125459 + 0.0872586i) q^{54} +(-0.0714350 + 0.0209752i) q^{55} +(0.230471 + 0.265977i) q^{56} +(-1.93153 + 1.24132i) q^{57} +(-0.678936 + 0.436326i) q^{58} +(-5.26786 - 6.07944i) q^{59} +(2.95561 - 0.867845i) q^{60} +(2.12854 - 14.8043i) q^{61} +(0.115460 - 0.133248i) q^{62} +(0.415415 - 0.909632i) q^{63} +(7.49756 + 2.20148i) q^{64} +(1.22301 + 2.67803i) q^{65} +(-0.000604095 - 0.00420157i) q^{66} +(-9.85039 - 6.33046i) q^{67} +1.99223 q^{68} +(3.73746 + 3.00523i) q^{69} +0.136307 q^{70} +(4.02068 + 2.58393i) q^{71} +(0.0500861 + 0.348356i) q^{72} +(-4.64381 - 10.1685i) q^{73} +(-0.206999 - 0.0607805i) q^{74} +(-1.08393 + 2.37347i) q^{75} +(-2.99546 + 3.45694i) q^{76} +(-0.00685257 + 0.0476607i) q^{77} +(-0.161056 + 0.0472903i) q^{78} +(-0.288649 - 0.333119i) q^{79} +(5.14241 - 3.30483i) q^{80} +(0.841254 - 0.540641i) q^{81} +(0.0763796 + 0.0881468i) q^{82} +(-1.68427 + 0.494546i) q^{83} +(0.283524 - 1.97195i) q^{84} +(1.01255 - 1.16854i) q^{85} +(0.135275 - 0.296211i) q^{86} +(8.78400 + 2.57922i) q^{87} +(-0.00703967 - 0.0154147i) q^{88} +(-0.146185 - 1.01674i) q^{89} +(0.114669 + 0.0736930i) q^{90} +1.90407 q^{91} +(8.83102 + 3.64684i) q^{92} -2.00000 q^{93} +(0.0520365 + 0.0334418i) q^{94} +(0.505232 + 3.51397i) q^{95} +(0.437181 + 0.957293i) q^{96} +(-6.26007 - 1.83812i) q^{97} +(0.0366213 - 0.0801894i) q^{98} +(-0.0315321 + 0.0363899i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - q^{3} - q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - q^{9} + 3 q^{10} + 9 q^{11} - 12 q^{12} - 15 q^{13} - 6 q^{14} + 6 q^{15} + 5 q^{16} + q^{17} - 6 q^{18} - 19 q^{19} - 5 q^{20}+ \cdots - 2 q^{99}+O(q^{100}) $ 10 * q + 5 * q^2 - q^3 - q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - q^9 + 3 * q^10 + 9 * q^11 - 12 * q^12 - 15 * q^13 - 6 * q^14 + 6 * q^15 + 5 * q^16 + q^17 - 6 * q^18 - 19 * q^19 - 5 * q^20 - q^21 - 12 * q^22 - 21 * q^23 + 6 * q^24 + 2 * q^25 - 13 * q^26 - q^27 - q^28 + 3 * q^30 + 2 * q^31 + 7 * q^32 - 2 * q^33 - 5 * q^34 - 5 * q^35 + 10 * q^36 - 27 * q^37 + 18 * q^38 - 15 * q^39 - 3 * q^40 + 10 * q^41 - 6 * q^42 + 15 * q^43 + 9 * q^44 + 6 * q^45 - 5 * q^46 - 18 * q^47 + 5 * q^48 - q^49 + 34 * q^50 + q^51 + 18 * q^52 + 19 * q^53 + 5 * q^54 - 21 * q^55 - 5 * q^56 + 3 * q^57 - 13 * q^59 + 6 * q^60 - 18 * q^61 - 10 * q^62 - q^63 + 54 * q^64 + 2 * q^65 + 10 * q^66 - 18 * q^67 - 10 * q^68 + q^69 - 8 * q^70 + 38 * q^71 + 6 * q^72 + 14 * q^73 + 14 * q^74 + 2 * q^75 + 3 * q^76 - 13 * q^77 + 9 * q^78 + 25 * q^79 + 25 * q^80 - q^81 - 72 * q^82 - 19 * q^83 - q^84 + 5 * q^85 + 2 * q^86 + 33 * q^87 + q^88 - 17 * q^89 + 14 * q^90 - 4 * q^91 + 67 * q^92 - 20 * q^93 + 13 * q^94 + 37 * q^95 + 18 * q^96 - 49 * q^97 - 6 * q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{11}\right)$

Coefficient data

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

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

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

$2$	0.0741615	+	0.0476607i	0.0524401	+	0.0337012i	0.566598	−	0.823994i	$-0.308259\pi$
$2$	0.0741615	+	0.0476607i	0.0524401	+	0.0337012i	−0.514158	+	0.857695i	$0.671896\pi$
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$4$	−0.827602	−	1.81219i	−0.413801	−	0.906097i
$5$	−1.48357	−	0.435615i	−0.663472	−	0.194813i	−0.0673779	−	0.997728i	$-0.521463\pi$
$5$	−1.48357	−	0.435615i	−0.663472	−	0.194813i	−0.596094	+	0.802915i	$0.703281\pi$
$6$	0.0366213	−	0.0801894i	0.0149506	−	0.0327372i
$7$	−0.654861	+	0.755750i	−0.247514	+	0.285646i
$7$	−0.654861	+	0.755750i	−0.247514	+	0.285646i
$8$	0.0500861	−	0.348356i	0.0177081	−	0.123163i
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$	−0.0892619	−	0.103014i	−0.0282271	−	0.0325758i
$11$	0.0405070	−	0.0260323i	0.0122133	−	0.00784903i	−0.534520	−	0.845156i	$-0.679508\pi$
$11$	0.0405070	−	0.0260323i	0.0122133	−	0.00784903i	0.546733	+	0.837307i	$0.315871\pi$
$12$	−1.67597	+	1.07708i	−0.483811	+	0.310926i
$13$	−1.24690	−	1.43900i	−0.345828	−	0.399107i	0.556014	−	0.831173i	$-0.312330\pi$
$13$	−1.24690	−	1.43900i	−0.345828	−	0.399107i	−0.901842	+	0.432066i	$0.857785\pi$
$14$	−0.0845850	+	0.0248364i	−0.0226063	+	0.00663781i
$15$	−0.220047	+	1.53046i	−0.0568160	+	0.395164i
$16$	−2.58895	+	2.98780i	−0.647237	+	0.746951i
$17$	−0.415415	+	0.909632i	−0.100753	+	0.220618i	−0.953295	−	0.302040i	$-0.902332\pi$
$17$	−0.415415	+	0.909632i	−0.100753	+	0.220618i	0.852542	+	0.522658i	$0.175060\pi$
$18$	−0.0845850	−	0.0248364i	−0.0199369	−	0.00585399i
$19$	−0.953800	−	2.08853i	−0.218817	−	0.479142i	0.768109	−	0.640319i	$-0.221198\pi$
$19$	−0.953800	−	2.08853i	−0.218817	−	0.479142i	−0.986925	+	0.161178i	$0.948471\pi$
$20$	0.438384	+	3.04903i	0.0980257	+	0.681784i
$21$	0.841254	+	0.540641i	0.183577	+	0.117977i
$22$	0.00424478			0.000904990
$23$	−3.50654	+	3.27173i	−0.731164	+	0.682202i
$23$	−3.50654	+	3.27173i	−0.731164	+	0.682202i
$24$	−0.351939			−0.0718392
$25$	−2.19505	−	1.41067i	−0.439011	−	0.282135i
$26$	−0.0238883	−	0.166147i	−0.00468488	−	0.0325841i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	1.91153	+	0.561276i	0.361245	+	0.106071i
$29$	−3.80306	+	8.32753i	−0.706210	+	1.54638i	0.126066	+	0.992022i	$0.459765\pi$
$29$	−3.80306	+	8.32753i	−0.706210	+	1.54638i	−0.832276	+	0.554362i	$0.812962\pi$
$30$	−0.0892619	+	0.103014i	−0.0162969	+	0.0188077i
$31$	0.284630	−	1.97964i	0.0511210	−	0.355554i	−0.948165	−	0.317778i	$-0.897063\pi$
$31$	0.284630	−	1.97964i	0.0511210	−	0.355554i	0.999286	−	0.0377766i	$-0.0120275\pi$
$32$	−1.00977	+	0.296494i	−0.178503	+	0.0524132i
$33$	−0.0315321	−	0.0363899i	−0.00548903	−	0.00633468i
$34$	−0.0741615	+	0.0476607i	−0.0127186	+	0.00817374i
$35$	1.30075	−	0.835939i	0.219866	−	0.141299i
$36$	1.30463	+	1.50563i	0.217439	+	0.250938i
$37$	−2.34811	+	0.689466i	−0.386026	+	0.113348i	−0.468987	−	0.883205i	$-0.655381\pi$
$37$	−2.34811	+	0.689466i	−0.386026	+	0.113348i	0.0829603	+	0.996553i	$0.473563\pi$
$38$	0.0288056	−	0.200347i	0.00467288	−	0.0325006i
$39$	−1.24690	+	1.43900i	−0.199664	+	0.230425i
$40$	−0.226055	+	0.494992i	−0.0357425	+	0.0782651i
$41$	1.26946	+	0.372747i	0.198256	+	0.0582133i	0.379353	−	0.925252i	$-0.376147\pi$
$41$	1.26946	+	0.372747i	0.198256	+	0.0582133i	−0.181097	+	0.983465i	$0.557965\pi$
$42$	0.0366213	+	0.0801894i	0.00565079	+	0.0123735i
$43$	−0.525696	−	3.65630i	−0.0801679	−	0.557580i	−0.989833	−	0.142237i	$-0.954571\pi$
$43$	−0.525696	−	3.65630i	−0.0801679	−	0.557580i	0.909665	−	0.415343i	$-0.136338\pi$
$44$	−0.0806993	−	0.0518623i	−0.0121659	−	0.00781853i
$45$	1.54620			0.230494
$46$	−0.415983	+	0.0755121i	−0.0613333	+	0.0111336i
$47$	0.701665			0.102348			0.0511742	−	0.998690i	$-0.483704\pi$
$47$	0.701665			0.102348			0.0511742	+	0.998690i	$0.483704\pi$
$48$	3.32584	+	2.13739i	0.480043	+	0.308505i
$49$	−0.142315	−	0.989821i	−0.0203307	−	0.141403i
$50$	−0.0955546	−	0.209235i	−0.0135135	−	0.0295904i
$51$	0.959493	+	0.281733i	0.134356	+	0.0394504i
$52$	−1.57581	+	3.45055i	−0.218526	+	0.478505i
$53$	7.68576	−	8.86984i	1.05572	−	1.21837i	0.0805875	−	0.996748i	$-0.474320\pi$
$53$	7.68576	−	8.86984i	1.05572	−	1.21837i	0.975133	−	0.221619i	$-0.0711342\pi$
$54$	−0.0125459	+	0.0872586i	−0.00170728	+	0.0118744i
$55$	−0.0714350	+	0.0209752i	−0.00963229	+	0.00282830i
$56$	0.230471	+	0.265977i	0.0307980	+	0.0355427i
$57$	−1.93153	+	1.24132i	−0.255838	+	0.164417i
$58$	−0.678936	+	0.436326i	−0.0891487	+	0.0572924i
$59$	−5.26786	−	6.07944i	−0.685817	−	0.791475i	0.300946	−	0.953641i	$-0.402698\pi$
$59$	−5.26786	−	6.07944i	−0.685817	−	0.791475i	−0.986764	+	0.162166i	$0.948152\pi$
$60$	2.95561	−	0.867845i	0.381567	−	0.112038i
$61$	2.12854	−	14.8043i	0.272531	−	1.89549i	−0.149254	−	0.988799i	$-0.547687\pi$
$61$	2.12854	−	14.8043i	0.272531	−	1.89549i	0.421785	−	0.906696i	$-0.361404\pi$
$62$	0.115460	−	0.133248i	0.0146634	−	0.0169225i
$63$	0.415415	−	0.909632i	0.0523374	−	0.114603i
$64$	7.49756	+	2.20148i	0.937195	+	0.275185i
$65$	1.22301	+	2.67803i	0.151696	+	0.332168i
$66$	−0.000604095	−	0.00420157i	−7.43589e−5	−	0.000517178i
$67$	−9.85039	−	6.33046i	−1.20342	−	0.773389i	−0.223873	−	0.974618i	$-0.571870\pi$
$67$	−9.85039	−	6.33046i	−1.20342	−	0.773389i	−0.979544	+	0.201229i	$0.935506\pi$
$68$	1.99223			0.241593
$69$	3.73746	+	3.00523i	0.449937	+	0.361787i
$70$	0.136307			0.0162918
$71$	4.02068	+	2.58393i	0.477167	+	0.306656i	0.757026	−	0.653385i	$-0.226652\pi$
$71$	4.02068	+	2.58393i	0.477167	+	0.306656i	−0.279860	+	0.960041i	$0.590288\pi$
$72$	0.0500861	+	0.348356i	0.00590270	+	0.0410542i
$73$	−4.64381	−	10.1685i	−0.543517	−	1.19014i	−0.959744	−	0.280875i	$-0.909375\pi$
$73$	−4.64381	−	10.1685i	−0.543517	−	1.19014i	0.416228	−	0.909260i	$-0.363352\pi$
$74$	−0.206999	−	0.0607805i	−0.0240632	−	0.00706559i
$75$	−1.08393	+	2.37347i	−0.125161	+	0.274065i
$76$	−2.99546	+	3.45694i	−0.343602	+	0.396538i
$77$	−0.00685257	+	0.0476607i	−0.000780923	+	0.00543144i
$78$	−0.161056	+	0.0472903i	−0.0182360	+	0.00535457i
$79$	−0.288649	−	0.333119i	−0.0324756	−	0.0374788i	0.739279	−	0.673399i	$-0.235166\pi$
$79$	−0.288649	−	0.333119i	−0.0324756	−	0.0374788i	−0.771755	+	0.635920i	$0.780621\pi$
$80$	5.14241	−	3.30483i	0.574939	−	0.369491i
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	0.0763796	+	0.0881468i	0.00843472	+	0.00973418i
$83$	−1.68427	+	0.494546i	−0.184873	+	0.0542835i	−0.372858	−	0.927888i	$-0.621622\pi$
$83$	−1.68427	+	0.494546i	−0.184873	+	0.0542835i	0.187986	+	0.982172i	$0.439804\pi$
$84$	0.283524	−	1.97195i	0.0309350	−	0.215157i
$85$	1.01255	−	1.16854i	0.109826	−	0.126746i
$86$	0.135275	−	0.296211i	0.0145871	−	0.0319413i
$87$	8.78400	+	2.57922i	0.941744	+	0.276521i
$88$	−0.00703967	−	0.0154147i	−0.000750432	−	0.00164322i
$89$	−0.146185	−	1.01674i	−0.0154956	−	0.107774i	0.980606	−	0.195991i	$-0.0627923\pi$
$89$	−0.146185	−	1.01674i	−0.0154956	−	0.107774i	−0.996101	+	0.0882166i	$0.971883\pi$
$90$	0.114669	+	0.0736930i	0.0120871	+	0.00776792i
$91$	1.90407			0.199601
$92$	8.83102	+	3.64684i	0.920698	+	0.380210i
$93$	−2.00000			−0.207390
$94$	0.0520365	+	0.0334418i	0.00536716	+	0.00344926i
$95$	0.505232	+	3.51397i	0.0518357	+	0.360525i
$96$	0.437181	+	0.957293i	0.0446196	+	0.0977033i
$97$	−6.26007	−	1.83812i	−0.635614	−	0.186633i	−0.0519774	−	0.998648i	$-0.516552\pi$
$97$	−6.26007	−	1.83812i	−0.635614	−	0.186633i	−0.583636	+	0.812015i	$0.698371\pi$
$98$	0.0366213	−	0.0801894i	0.00369931	−	0.00810036i
$99$	−0.0315321	+	0.0363899i	−0.00316909	+	0.00365733i
$100$	−0.739788	+	5.14534i	−0.0739788	+	0.514534i
$101$	2.90274	−	0.852322i	0.288834	−	0.0848092i	−0.134106	−	0.990967i	$-0.542816\pi$
$101$	2.90274	−	0.852322i	0.288834	−	0.0848092i	0.422940	+	0.906158i	$0.360998\pi$
$102$	0.0577299	+	0.0666238i	0.00571611	+	0.00659674i
$103$	10.2185	−	6.56703i	1.00686	−	0.647069i	0.0702804	−	0.997527i	$-0.477611\pi$
$103$	10.2185	−	6.56703i	1.00686	−	0.647069i	0.936578	+	0.350459i	$0.113974\pi$
$104$	−0.563738	+	0.362292i	−0.0552791	+	0.0355257i
$105$	−1.01255	−	1.16854i	−0.0988144	−	0.114038i
$106$	0.992730	−	0.291492i	0.0964225	−	0.0283122i
$107$	−1.22449	+	8.51650i	−0.118376	+	0.823321i	0.840969	+	0.541084i	$0.181986\pi$
$107$	−1.22449	+	8.51650i	−0.118376	+	0.823321i	−0.959345	+	0.282238i	$0.908923\pi$
$108$	1.30463	−	1.50563i	0.125538	−	0.144879i
$109$	−2.08020	+	4.55501i	−0.199247	+	0.436290i	−0.982711	−	0.185147i	$-0.940724\pi$
$109$	−2.08020	+	4.55501i	−0.199247	+	0.436290i	0.783464	+	0.621438i	$0.213451\pi$
$110$	−0.00629742	−	0.00184909i	−0.000600435	−	0.000176304i
$111$	1.01662	+	2.22608i	0.0964932	+	0.211291i
$112$	−0.562632	−	3.91319i	−0.0531637	−	0.369762i
$113$	−12.8633	−	8.26675i	−1.21008	−	0.777670i	−0.229407	−	0.973331i	$-0.573679\pi$
$113$	−12.8633	−	8.26675i	−1.21008	−	0.777670i	−0.980672	+	0.195660i	$0.937315\pi$
$114$	−0.202407			−0.0189572
$115$	6.62740	−	3.32633i	0.618008	−	0.310182i
$116$	18.2385			1.69340
$117$	1.60181	+	1.02942i	0.148087	+	0.0951699i
$118$	−0.100922	−	0.701930i	−0.00929065	−	0.0646179i
$119$	−0.415415	−	0.909632i	−0.0380810	−	0.0833858i
$120$	0.522125	+	0.153310i	0.0476633	+	0.0139952i
$121$	−4.56860	+	10.0038i	−0.415327	+	0.909440i
$122$	0.863438	−	0.996460i	0.0781720	−	0.0902153i
$123$	0.188290	−	1.30959i	0.0169775	−	0.118081i
$124$	−3.82306	+	1.12255i	−0.343321	+	0.100808i
$125$	7.70473	+	8.89173i	0.689132	+	0.795301i
$126$	0.0741615	−	0.0476607i	0.00660683	−	0.00424595i
$127$	−2.36789	+	1.52175i	−0.210116	+	0.135034i	−0.641467	−	0.767151i	$-0.721674\pi$
$127$	−2.36789	+	1.52175i	−0.210116	+	0.135034i	0.431350	+	0.902185i	$0.358037\pi$
$128$	1.82945	+	2.11130i	0.161702	+	0.186614i
$129$	−3.54427	+	1.04069i	−0.312055	+	0.0916277i
$130$	−0.0369361	+	0.256896i	−0.00323951	+	0.0225313i
$131$	2.08531	−	2.40657i	0.182194	−	0.210263i	−0.657304	−	0.753625i	$-0.728303\pi$
$131$	2.08531	−	2.40657i	0.182194	−	0.210263i	0.839499	+	0.543362i	$0.182849\pi$
$132$	−0.0398497	+	0.0872586i	−0.00346847	+	0.00759489i
$133$	2.20301	+	0.646863i	0.191025	+	0.0560901i
$134$	−0.428805	−	0.938953i	−0.0370431	−	0.0811132i
$135$	−0.220047	−	1.53046i	−0.0189387	−	0.131721i
$136$	0.296070	+	0.190272i	0.0253878	+	0.0163157i
$137$	7.98235			0.681978			0.340989	−	0.940067i	$-0.389238\pi$
$137$	7.98235			0.681978			0.340989	+	0.940067i	$0.389238\pi$
$138$	0.133944	+	0.401002i	0.0114021	+	0.0341356i
$139$	−3.65196			−0.309755			−0.154878	−	0.987934i	$-0.549498\pi$
$139$	−3.65196			−0.309755			−0.154878	+	0.987934i	$0.549498\pi$
$140$	−2.59138	−	1.66538i	−0.219012	−	0.140750i
$141$	−0.0998574	−	0.694523i	−0.00840951	−	0.0584894i
$142$	0.175027	+	0.383256i	0.0146880	+	0.0321622i
$143$	−0.0879688	−	0.0258300i	−0.00735632	−	0.00216001i
$144$	1.64231	−	3.59617i	0.136860	−	0.299681i
$145$	9.26969	−	10.6978i	0.769806	−	0.888403i
$146$	0.140247	−	0.975440i	0.0116069	−	0.0807280i
$147$	−0.959493	+	0.281733i	−0.0791376	+	0.0232369i
$148$	3.19274	+	3.68462i	0.262442	+	0.302874i
$149$	−2.82110	+	1.81301i	−0.231114	+	0.148528i	−0.651073	−	0.759015i	$-0.725681\pi$
$149$	−2.82110	+	1.81301i	−0.231114	+	0.148528i	0.419959	+	0.907543i	$0.362044\pi$
$150$	−0.193507	+	0.124359i	−0.0157998	+	0.0101539i
$151$	8.52847	+	9.84237i	0.694037	+	0.800961i	0.987934	−	0.154876i	$-0.0494978\pi$
$151$	8.52847	+	9.84237i	0.694037	+	0.800961i	−0.293897	+	0.955837i	$0.594952\pi$
$152$	−0.775325	+	0.227656i	−0.0628871	+	0.0184653i
$153$	0.142315	−	0.989821i	0.0115055	−	0.0800223i
$154$	−0.00277974	+	0.00320799i	−0.000223998	+	0.000258507i
$155$	−1.28463	+	2.81295i	−0.103184	+	0.225941i
$156$	3.63969	+	1.06871i	0.291408	+	0.0855652i
$157$	−6.42579	−	14.0705i	−0.512834	−	1.12295i	−0.972082	−	0.234642i	$-0.924608\pi$
$157$	−6.42579	−	14.0705i	−0.512834	−	1.12295i	0.459248	−	0.888308i	$-0.348119\pi$
$158$	−0.00552997	−	0.0384618i	−0.000439941	−	0.00305986i
$159$	−9.87336	−	6.34522i	−0.783008	−	0.503209i
$160$	1.62721			0.128643
$161$	−0.176312	−	4.79259i	−0.0138953	−	0.377709i
$162$	0.0881559			0.00692618
$163$	16.5768	+	10.6533i	1.29840	+	0.834428i	0.993036	−	0.117809i	$-0.0375871\pi$
$163$	16.5768	+	10.6533i	1.29840	+	0.834428i	0.305359	+	0.952237i	$0.401223\pi$
$164$	−0.375117	−	2.60899i	−0.0292917	−	0.203728i
$165$	0.0309280	+	0.0677228i	0.00240774	+	0.00527221i
$166$	−0.148478	−	0.0435972i	−0.0115242	−	0.00338380i
$167$	−8.56540	+	18.7556i	−0.662811	+	1.45135i	0.217069	+	0.976156i	$0.430350\pi$
$167$	−8.56540	+	18.7556i	−0.662811	+	1.45135i	−0.879880	+	0.475197i	$0.842377\pi$
$168$	0.230471	−	0.265977i	0.0177812	−	0.0205206i
$169$	1.33413	−	9.27909i	0.102626	−	0.713776i
$170$	0.130785	−	0.0384020i	0.0100308	−	0.00294530i
$171$	1.50357	+	1.73521i	0.114981	+	0.132695i
$172$	−6.19085	+	3.97862i	−0.472048	+	0.303367i
$173$	4.25717	−	2.73592i	0.323667	−	0.208008i	−0.368709	−	0.929545i	$-0.620200\pi$
$173$	4.25717	−	2.73592i	0.323667	−	0.208008i	0.692376	+	0.721537i	$0.256564\pi$
$174$	0.528507	+	0.609930i	0.0400660	+	0.0462387i
$175$	2.50357	−	0.735115i	0.189252	−	0.0555695i
$176$	−0.0270912	+	0.188423i	−0.00204207	+	0.0142029i
$177$	−5.26786	+	6.07944i	−0.395957	+	0.456959i
$178$	0.0376173	−	0.0823704i	0.00281954	−	0.00617392i
$179$	−6.17296	−	1.81254i	−0.461389	−	0.135476i	0.0427738	−	0.999085i	$-0.486381\pi$
$179$	−6.17296	−	1.81254i	−0.461389	−	0.135476i	−0.504162	+	0.863609i	$0.668199\pi$
$180$	−1.27964	−	2.80202i	−0.0953786	−	0.208850i
$181$	−2.14959	−	14.9507i	−0.159778	−	1.11128i	−0.899041	−	0.437864i	$-0.855735\pi$
$181$	−2.14959	−	14.9507i	−0.159778	−	1.11128i	0.739263	−	0.673416i	$-0.235174\pi$
$182$	0.141209	+	0.0907494i	0.0104671	+	0.00672679i
$183$	−14.9565			−1.10562
$184$	0.964098	+	1.38539i	0.0710742	+	0.102133i
$185$	3.78392			0.278199
$186$	−0.148323	−	0.0953214i	−0.0108756	−	0.00698930i
$187$	0.00685257	+	0.0476607i	0.000501110	+	0.00348529i
$188$	−0.580699	−	1.27155i	−0.0423518	−	0.0927376i
$189$	−0.959493	−	0.281733i	−0.0697928	−	0.0204930i
$190$	−0.130009	+	0.284681i	−0.00943187	+	0.0206529i
$191$	0.507125	−	0.585254i	0.0366943	−	0.0423475i	−0.737106	−	0.675777i	$-0.763808\pi$
$191$	0.507125	−	0.585254i	0.0366943	−	0.0423475i	0.773800	+	0.633430i	$0.218354\pi$
$192$	1.11206	−	7.73455i	0.0802561	−	0.558193i
$193$	−3.01461	+	0.885169i	−0.216996	+	0.0637159i	−0.388424	−	0.921481i	$-0.626980\pi$
$193$	−3.01461	+	0.885169i	−0.216996	+	0.0637159i	0.171427	+	0.985197i	$0.445162\pi$
$194$	−0.376650	−	0.434677i	−0.0270419	−	0.0312080i
$195$	2.47672	−	1.59169i	0.177361	−	0.113983i
$196$	−1.67597	+	1.07708i	−0.119712	+	0.0769343i
$197$	−11.4742	−	13.2419i	−0.817501	−	0.943446i	0.181703	−	0.983353i	$-0.441839\pi$
$197$	−11.4742	−	13.2419i	−0.817501	−	0.943446i	−0.999203	+	0.0399075i	$0.987294\pi$
$198$	−0.00407283	+	0.00119589i	−0.000289444	+	8.49883e-5i
$199$	−1.19930	+	8.34130i	−0.0850160	+	0.591299i	0.902128	+	0.431468i	$0.142004\pi$
$199$	−1.19930	+	8.34130i	−0.0850160	+	0.591299i	−0.987144	+	0.159831i	$0.948905\pi$
$200$	−0.601359	+	0.694005i	−0.0425225	+	0.0490736i
$201$	−4.86417	+	10.6510i	−0.343092	+	0.751267i
$202$	0.255894	+	0.0751372i	0.0180046	+	0.00528664i
$203$	−3.80306	−	8.32753i	−0.266922	−	0.584478i
$204$	−0.283524	−	1.97195i	−0.0198506	−	0.138064i
$205$	−1.72096	−	1.10599i	−0.120197	−	0.0772458i
$206$	1.07081			0.0746067
$207$	2.44275	−	4.12710i	0.169783	−	0.286854i
$208$	7.52762			0.521947
$209$	−0.0930048	−	0.0597706i	−0.00643328	−	0.00413442i
$210$	−0.0193985	−	0.134919i	−0.00133862	−	0.00931032i
$211$	4.67332	+	10.2331i	0.321725	+	0.704478i	0.999527	−	0.0307660i	$-0.00979465\pi$
$211$	4.67332	+	10.2331i	0.321725	+	0.704478i	−0.677802	+	0.735244i	$0.737067\pi$
$212$	−22.4346	−	6.58740i	−1.54082	−	0.452425i
$213$	1.98543	−	4.34748i	0.136039	−	0.297885i
$214$	−0.496712	+	0.573236i	−0.0339545	+	0.0391856i
$215$	−0.812831	+	5.65336i	−0.0554346	+	0.385556i
$216$	0.337683	−	0.0991526i	0.0229764	−	0.00674648i
$217$	1.30972	+	1.51150i	0.0889097	+	0.102607i
$218$	−0.371366	+	0.238662i	−0.0251520	+	0.0161642i
$219$	−9.40414	+	6.04367i	−0.635473	+	0.408393i
$220$	0.0971309	+	0.112095i	0.00654856	+	0.00755744i
$221$	1.82694	−	0.536439i	0.122894	−	0.0360848i
$222$	−0.0307028	+	0.213542i	−0.00206064	+	0.0143320i
$223$	−10.7680	+	12.4269i	−0.721075	+	0.832165i	−0.991436	−	0.130594i	$-0.958312\pi$
$223$	−10.7680	+	12.4269i	−0.721075	+	0.832165i	0.270360	+	0.962759i	$0.412857\pi$
$224$	0.437181	−	0.957293i	0.0292104	−	0.0639618i
$225$	2.50357	+	0.735115i	0.166905	+	0.0490077i
$226$	−0.559963	−	1.22615i	−0.0372482	−	0.0815622i
$227$	0.385683	+	2.68248i	0.0255987	+	0.178043i	0.998610	−	0.0527168i	$-0.0167881\pi$
$227$	0.385683	+	2.68248i	0.0255987	+	0.178043i	−0.973011	+	0.230759i	$0.925879\pi$
$228$	3.84805	+	2.47299i	0.254844	+	0.163778i
$229$	22.7039			1.50031			0.750157	−	0.661260i	$-0.229978\pi$
$229$	22.7039			1.50031			0.750157	+	0.661260i	$0.229978\pi$
$230$	0.650033	+	0.0691810i	0.0428619	+	0.00456166i
$231$	0.0481508			0.00316809
$232$	2.71047	+	1.74191i	0.177951	+	0.114362i
$233$	2.42072	+	16.8365i	0.158586	+	1.10299i	0.901241	+	0.433318i	$0.142657\pi$
$233$	2.42072	+	16.8365i	0.158586	+	1.10299i	−0.742655	+	0.669675i	$0.766434\pi$
$234$	0.0697296	+	0.152687i	0.00455837	+	0.00998143i
$235$	−1.04097	−	0.305656i	−0.0679053	−	0.0199388i
$236$	−6.65743	+	14.5777i	−0.433362	+	0.948931i
$237$	−0.288649	+	0.333119i	−0.0187498	+	0.0216384i
$238$	0.0125459	−	0.0872586i	0.000813230	−	0.00565614i
$239$	−20.7258	+	6.08564i	−1.34064	+	0.393647i	−0.871898	−	0.489688i	$-0.837111\pi$
$239$	−20.7258	+	6.08564i	−1.34064	+	0.393647i	−0.468741	+	0.883335i	$0.655292\pi$
$240$	−4.00303	−	4.61974i	−0.258395	−	0.298203i
$241$	−1.28323	+	0.824685i	−0.0826604	+	0.0531226i	−0.581318	−	0.813676i	$-0.697463\pi$
$241$	−1.28323	+	0.824685i	−0.0826604	+	0.0531226i	0.498658	+	0.866799i	$0.333826\pi$
$242$	−0.815604	+	0.524157i	−0.0524290	+	0.0336941i
$243$	−0.654861	−	0.755750i	−0.0420093	−	0.0484814i
$244$	−28.5898	+	8.39473i	−1.83028	+	0.537418i
$245$	−0.220047	+	1.53046i	−0.0140583	+	0.0977776i
$246$	0.0763796	−	0.0881468i	0.00486979	−	0.00562003i
$247$	−1.81610	+	3.97671i	−0.115556	+	0.253032i
$248$	−0.675365	−	0.198305i	−0.0428857	−	0.0125924i
$249$	0.729209	+	1.59675i	0.0462118	+	0.101190i
$250$	0.147608	+	1.02664i	0.00933555	+	0.0649302i
$251$	−6.89077	−	4.42843i	−0.434942	−	0.279520i	0.304793	−	0.952419i	$-0.401413\pi$
$251$	−6.89077	−	4.42843i	−0.434942	−	0.279520i	−0.739735	+	0.672898i	$0.765049\pi$
$252$	−1.99223			−0.125499
$253$	−0.0568689	+	0.223811i	−0.00357532	+	0.0140709i
$254$	−0.248134			−0.0155693
$255$	−1.30075	−	0.835939i	−0.0814559	−	0.0523485i
$256$	−2.18907	−	15.2253i	−0.136817	−	0.951583i
$257$	−11.3313	−	24.8121i	−0.706829	−	1.54774i	−0.831490	−	0.555540i	$-0.812512\pi$
$257$	−11.3313	−	24.8121i	−0.706829	−	1.54774i	0.124661	−	0.992199i	$-0.460216\pi$
$258$	−0.312448	−	0.0917430i	−0.0194522	−	0.00571167i
$259$	1.01662	−	2.22608i	0.0631696	−	0.138322i
$260$	3.84094	−	4.43268i	0.238205	−	0.274903i
$261$	1.30287	−	9.06165i	0.0806456	−	0.560902i
$262$	0.269348	−	0.0790878i	0.0166404	−	0.00488606i
$263$	−4.82837	−	5.57224i	−0.297730	−	0.343599i	0.587099	−	0.809516i	$-0.300270\pi$
$263$	−4.82837	−	5.57224i	−0.297730	−	0.343599i	−0.884829	+	0.465917i	$0.845725\pi$
$264$	−0.0142560	+	0.00916177i	−0.000877395	+	0.000563868i
$265$	−15.2662	+	9.81099i	−0.937795	+	0.602684i
$266$	0.132549	+	0.152969i	0.00812708	+	0.00937915i
$267$	−0.985589	+	0.289395i	−0.0603170	+	0.0177107i
$268$	−3.31983	+	23.0899i	−0.202791	+	1.41044i
$269$	8.46257	−	9.76632i	0.515972	−	0.595463i	−0.436646	−	0.899633i	$-0.643834\pi$
$269$	8.46257	−	9.76632i	0.515972	−	0.595463i	0.952618	+	0.304170i	$0.0983792\pi$
$270$	0.0566239	−	0.123989i	0.00344602	−	0.00754573i
$271$	22.0284	+	6.46812i	1.33813	+	0.392910i	0.871002	−	0.491280i	$-0.163471\pi$
$271$	22.0284	+	6.46812i	1.33813	+	0.392910i	0.467127	+	0.884190i	$0.345289\pi$
$272$	−1.64231	−	3.59617i	−0.0995800	−	0.218050i
$273$	−0.270978	−	1.88469i	−0.0164003	−	0.114067i
$274$	0.591983	+	0.380444i	0.0357630	+	0.0229835i
$275$	−0.125638			−0.00757627
$276$	2.35294	−	9.26013i	0.141630	−	0.557395i
$277$	−9.46932			−0.568957			−0.284478	−	0.958682i	$-0.591820\pi$
$277$	−9.46932			−0.568957			−0.284478	+	0.958682i	$0.591820\pi$
$278$	−0.270835	−	0.174055i	−0.0162436	−	0.0104391i
$279$	0.284630	+	1.97964i	0.0170403	+	0.118518i
$280$	−0.226055	−	0.494992i	−0.0135094	−	0.0295814i
$281$	3.29361	+	0.967091i	0.196480	+	0.0576918i	0.378492	−	0.925605i	$-0.376443\pi$
$281$	3.29361	+	0.967091i	0.196480	+	0.0576918i	−0.182012	+	0.983296i	$0.558261\pi$
$282$	0.0256959	−	0.0562661i	0.00153017	−	0.00335060i
$283$	−4.24828	+	4.90278i	−0.252534	+	0.291440i	−0.867835	−	0.496852i	$-0.834489\pi$
$283$	−4.24828	+	4.90278i	−0.252534	+	0.291440i	0.615301	+	0.788292i	$0.289034\pi$
$284$	1.35507	−	9.42472i	0.0804086	−	0.559254i
$285$	3.40630	−	1.00018i	0.201772	−	0.0592455i
$286$	−0.00529282	−	0.00610824i	−0.000312971	−	0.000361188i
$287$	−1.11302	+	0.715296i	−0.0656996	+	0.0422226i
$288$	0.885331	−	0.568968i	0.0521687	−	0.0335268i
$289$	10.4778	+	12.0920i	0.616340	+	0.711294i
$290$	1.19732	−	0.351564i	0.0703089	−	0.0206446i
$291$	−0.928512	+	6.45794i	−0.0544303	+	0.378571i
$292$	−14.5841	+	16.8310i	−0.853471	+	0.984958i
$293$	12.5019	−	27.3752i	0.730366	−	1.59928i	−0.0684146	−	0.997657i	$-0.521794\pi$
$293$	12.5019	−	27.3752i	0.730366	−	1.59928i	0.798781	−	0.601622i	$-0.205479\pi$
$294$	−0.0845850	−	0.0248364i	−0.00493310	−	0.00144849i
$295$	5.16694	+	11.3140i	0.300831	+	0.658728i
$296$	0.122572	+	0.852510i	0.00712438	+	0.0495512i
$297$	0.0405070	+	0.0260323i	0.00235046	+	0.00151055i
$298$	−0.295626			−0.0171252
$299$	9.08033	+	0.966392i	0.525129	+	0.0558879i
$300$	5.19825			0.300121
$301$	3.10750	+	1.99707i	0.179113	+	0.115109i
$302$	0.163389	+	1.13640i	0.00940200	+	0.0653923i
$303$	−1.25675	−	2.75190i	−0.0721984	−	0.158092i
$304$	8.70946	+	2.55733i	0.499522	+	0.146673i
$305$	−9.60680	+	21.0360i	−0.550084	+	1.20452i
$306$	0.0577299	−	0.0666238i	0.00330020	−	0.00380863i
$307$	0.557310	−	3.87618i	0.0318074	−	0.221225i	−0.967718	−	0.252036i	$-0.918900\pi$
$307$	0.557310	−	3.87618i	0.0318074	−	0.221225i	0.999525	+	0.0308108i	$0.00980895\pi$
$308$	0.0920417	−	0.0270259i	0.00524456	−	0.00153994i
$309$	−7.95443	−	9.17990i	−0.452512	−	0.522226i
$310$	−0.229337	+	0.147386i	−0.0130255	+	0.00837096i
$311$	−7.78868	+	5.00548i	−0.441656	+	0.283835i	−0.742510	−	0.669835i	$-0.766365\pi$
$311$	−7.78868	+	5.00548i	−0.441656	+	0.283835i	0.300854	+	0.953670i	$0.402728\pi$
$312$	0.438833	+	0.506440i	0.0248440	+	0.0286715i
$313$	−20.3969	+	5.98907i	−1.15290	+	0.338522i	−0.801670	−	0.597767i	$-0.796055\pi$
$313$	−20.3969	+	5.98907i	−1.15290	+	0.338522i	−0.351230	+	0.936289i	$0.614237\pi$
$314$	0.194065	−	1.34975i	0.0109517	−	0.0761707i
$315$	−1.01255	+	1.16854i	−0.0570505	+	0.0658398i
$316$	−0.364790	+	0.798779i	−0.0205210	+	0.0449348i
$317$	5.72643	+	1.68143i	0.321628	+	0.0944386i	0.438561	−	0.898701i	$-0.355488\pi$
$317$	5.72643	+	1.68143i	0.321628	+	0.0944386i	−0.116933	+	0.993140i	$0.537306\pi$
$318$	−0.429805	−	0.941142i	−0.0241023	−	0.0527766i
$319$	0.0627342	+	0.436326i	0.00351244	+	0.0244296i
$320$	−10.1641	−	6.53210i	−0.568193	−	0.365156i
$321$	8.60408			0.480233
$322$	0.215343	−	0.363829i	0.0120006	−	0.0202754i
$323$	2.29602			0.127754
$324$	−1.67597	−	1.07708i	−0.0931094	−	0.0598378i
$325$	0.707053	+	4.91766i	0.0392202	+	0.272783i
$326$	0.721618	+	1.58012i	0.0399667	+	0.0875150i
$327$	4.80469	+	1.41078i	0.265700	+	0.0780165i
$328$	0.193431	−	0.423555i	0.0106804	−	0.0233869i
$329$	−0.459493	+	0.530283i	−0.0253327	+	0.0292355i
$330$	−0.000934052		0.00649647i	−5.14179e−5		0.000357619i
$331$	20.5946	−	6.04711i	1.13198	−	0.332379i	0.338494	−	0.940969i	$-0.390083\pi$
$331$	20.5946	−	6.04711i	1.13198	−	0.332379i	0.793485	+	0.608589i	$0.208264\pi$
$332$	2.29012	+	2.64294i	0.125687	+	0.145050i
$333$	2.05875	−	1.32308i	0.112819	−	0.0725041i
$334$	−1.52913	+	0.982711i	−0.0836702	+	0.0537716i
$335$	11.8561	+	13.6826i	0.647767	+	0.747563i
$336$	−3.79329	+	1.11381i	−0.206941	+	0.0607633i
$337$	−0.178107	+	1.23876i	−0.00970210	+	0.0674796i	−0.994097	−	0.108492i	$-0.965398\pi$
$337$	−0.178107	+	1.23876i	−0.00970210	+	0.0674796i	0.984395	+	0.175972i	$0.0563068\pi$
$338$	0.541189	−	0.624565i	0.0294368	−	0.0339719i
$339$	−6.35197	+	13.9089i	−0.344991	+	0.755426i
$340$	−2.95561	−	0.867845i	−0.160290	−	0.0470655i
$341$	−0.0400051	−	0.0875990i	−0.00216640	−	0.00474375i
$342$	0.0288056	+	0.200347i	0.00155763	+	0.0108335i
$343$	0.841254	+	0.540641i	0.0454234	+	0.0291919i
$344$	−1.30002			−0.0700926
$345$	−4.23565	−	6.08656i	−0.228040	−	0.327689i
$346$	0.446114			0.0239832
$347$	−18.5945	−	11.9500i	−0.998205	−	0.641507i	−0.0638903	−	0.997957i	$-0.520351\pi$
$347$	−18.5945	−	11.9500i	−0.998205	−	0.641507i	−0.934315	+	0.356450i	$0.883987\pi$
$348$	−2.59561	−	18.0529i	−0.139139	−	0.967736i
$349$	−1.95583	−	4.28267i	−0.104693	−	0.229246i	0.850035	−	0.526727i	$-0.176581\pi$
$349$	−1.95583	−	4.28267i	−0.104693	−	0.229246i	−0.954728	+	0.297481i	$0.903854\pi$
$350$	0.220705	+	0.0648047i	0.0117972	+	0.00346396i
$351$	0.790980	−	1.73201i	0.0422194	−	0.0924476i
$352$	−0.0331842	+	0.0382966i	−0.00176872	+	0.00204122i
$353$	1.77303	−	12.3317i	0.0943691	−	0.656351i	−0.886650	−	0.462441i	$-0.846974\pi$
$353$	1.77303	−	12.3317i	0.0943691	−	0.656351i	0.981019	−	0.193911i	$-0.0621172\pi$
$354$	−0.680423	+	0.199790i	−0.0361641	+	0.0106187i
$355$	−4.83935	−	5.58491i	−0.256846	−	0.296416i
$356$	−1.72155	+	1.10637i	−0.0912420	+	0.0586377i
$357$	−0.841254	+	0.540641i	−0.0445239	+	0.0286137i
$358$	−0.371409	−	0.428628i	−0.0196296	−	0.0226537i
$359$	−14.6760	+	4.30927i	−0.774571	+	0.227435i	−0.645048	−	0.764142i	$-0.723163\pi$
$359$	−14.6760	+	4.30927i	−0.774571	+	0.227435i	−0.129523	+	0.991576i	$0.541345\pi$
$360$	0.0774431	−	0.538629i	0.00408161	−	0.0283882i
$361$	8.99013	−	10.3752i	0.473165	−	0.546061i
$362$	0.553146	−	1.21122i	0.0290727	−	0.0636603i
$363$	10.5522	+	3.09840i	0.553847	+	0.162624i
$364$	−1.57581	−	3.45055i	−0.0825951	−	0.180858i
$365$	2.45985	+	17.1086i	0.128754	+	0.895505i
$366$	−1.10920	−	0.712838i	−0.0579787	−	0.0372607i
$367$	4.31700			0.225346			0.112673	−	0.993632i	$-0.464059\pi$
$367$	4.31700			0.225346			0.112673	+	0.993632i	$0.464059\pi$
$368$	−0.697037	−	18.9472i	−0.0363356	−	0.987690i
$369$	−1.32305			−0.0688754
$370$	0.280621	+	0.180344i	0.0145888	+	0.00937564i
$371$	1.67028	+	11.6170i	0.0867164	+	0.603126i
$372$	1.65520	+	3.62439i	0.0858183	+	0.187916i
$373$	19.6268	+	5.76295i	1.01624	+	0.298394i	0.747103	−	0.664708i	$-0.231444\pi$
$373$	19.6268	+	5.76295i	1.01624	+	0.298394i	0.269135	+	0.963103i	$0.413262\pi$
$374$	−0.00176334	+	0.00386119i	−9.11804e−5	+	0.000199657i
$375$	7.70473	−	8.89173i	0.397871	−	0.459167i
$376$	0.0351437	−	0.244430i	0.00181240	−	0.0126055i
$377$	16.7254	−	4.91101i	0.861401	−	0.252930i
$378$	−0.0577299	−	0.0666238i	−0.00296930	−	0.00342676i
$379$	−10.5609	+	6.78710i	−0.542479	+	0.348630i	−0.783008	−	0.622012i	$-0.786316\pi$
$379$	−10.5609	+	6.78710i	−0.542479	+	0.348630i	0.240529	+	0.970642i	$0.422679\pi$
$380$	5.94986	−	3.82374i	0.305221	−	0.196154i
$381$	1.84325	+	2.12722i	0.0944325	+	0.108981i
$382$	0.0655028	−	0.0192333i	0.00335141	−	0.000984064i
$383$	0.869367	−	6.04658i	0.0444226	−	0.308966i	−0.955481	−	0.295054i	$-0.904662\pi$
$383$	0.869367	−	6.04658i	0.0444226	−	0.308966i	0.999903	−	0.0139120i	$-0.00442847\pi$
$384$	1.82945	−	2.11130i	0.0933588	−	0.107742i
$385$	0.0309280	−	0.0677228i	0.00157624	−	0.00345147i
$386$	−0.265756	−	0.0780329i	−0.0135266	−	0.00397177i
$387$	1.53450	+	3.36008i	0.0780030	+	0.170803i
$388$	1.84981	+	12.8657i	0.0939098	+	0.653157i
$389$	9.98252	+	6.41537i	0.506134	+	0.325272i	0.768665	−	0.639651i	$-0.220921\pi$
$389$	9.98252	+	6.41537i	0.506134	+	0.325272i	−0.262532	+	0.964923i	$0.584557\pi$
$390$	0.259538			0.0131422
$391$	−1.51940	−	4.54878i	−0.0768393	−	0.230042i
$392$	−0.351939			−0.0177756
$393$	−2.67885	−	1.72159i	−0.135130	−	0.0868427i
$394$	−0.219823	−	1.52891i	−0.0110745	−	0.0770251i
$395$	0.283119	+	0.619945i	0.0142453	+	0.0311928i
$396$	0.0920417	+	0.0270259i	0.00462527	+	0.00135810i
$397$	−7.72901	+	16.9242i	−0.387908	+	0.849399i	0.610447	+	0.792057i	$0.290990\pi$
$397$	−7.72901	+	16.9242i	−0.387908	+	0.849399i	−0.998355	+	0.0573422i	$0.981737\pi$
$398$	−0.486494	+	0.561444i	−0.0243857	+	0.0281426i
$399$	0.326757	−	2.27265i	0.0163583	−	0.113775i
$400$	9.89770	−	2.90623i	0.494885	−	0.145311i
$401$	−11.4191	−	13.1784i	−0.570244	−	0.658097i	0.395234	−	0.918580i	$-0.370663\pi$
$401$	−11.4191	−	13.1784i	−0.570244	−	0.658097i	−0.965478	+	0.260484i	$0.916118\pi$
$402$	−0.868370	+	0.558068i	−0.0433104	+	0.0278339i
$403$	−3.20362	+	2.05884i	−0.159583	+	0.102558i
$404$	−3.94689	−	4.55495i	−0.196365	−	0.226617i
$405$	−1.48357	+	0.435615i	−0.0737191	+	0.0216459i
$406$	0.114856	−	0.798838i	0.00570019	−	0.0396457i
$407$	−0.0771664	+	0.0890548i	−0.00382500	+	0.00441428i
$408$	0.146201	−	0.320135i	0.00723801	−	0.0158490i
$409$	5.96936	+	1.75276i	0.295166	+	0.0866685i	0.425963	−	0.904741i	$-0.359935\pi$
$409$	5.96936	+	1.75276i	0.295166	+	0.0866685i	−0.130797	+	0.991409i	$0.541754\pi$
$410$	−0.0749163	−	0.164044i	−0.00369985	−	0.00810155i
$411$	−1.13601	−	7.90110i	−0.0560351	−	0.389733i
$412$	−20.3576	−	13.0830i	−1.00295	−	0.644554i
$413$	8.04425			0.395832
$414$	0.377858	−	0.189649i	0.0185707	−	0.00932075i
$415$	2.71416			0.133233
$416$	1.68574	+	1.08336i	0.0826500	+	0.0531159i
$417$	0.519728	+	3.61479i	0.0254512	+	0.177017i
$418$	−0.00404867	−	0.00886535i	−0.000198027	−	0.000433618i
$419$	24.4797	+	7.18790i	1.19591	+	0.351152i	0.818289	−	0.574807i	$-0.194923\pi$
$419$	24.4797	+	7.18790i	1.19591	+	0.351152i	0.377624	+	0.925959i	$0.376741\pi$
$420$	−1.27964	+	2.80202i	−0.0624399	+	0.136724i
$421$	14.4799	−	16.7107i	0.705707	−	0.814430i	−0.283804	−	0.958882i	$-0.591597\pi$
$421$	14.4799	−	16.7107i	0.705707	−	0.814430i	0.989512	+	0.144452i	$0.0461421\pi$
$422$	−0.141138	+	0.981638i	−0.00687050	+	0.0477854i
$423$	−0.673243	+	0.197682i	−0.0327342	+	0.00961162i
$424$	−2.70492	−	3.12164i	−0.131362	−	0.151600i
$425$	2.19505	−	1.41067i	0.106476	−	0.0684278i
$426$	0.354446	−	0.227789i	0.0171730	−	0.0110364i
$427$	9.79444	+	11.3034i	0.473986	+	0.547009i
$428$	16.4469	−	4.82926i	0.794993	−	0.233431i
$429$	−0.0130478	+	0.0907494i	−0.000629954	+	0.00438142i
$430$	−0.329724	+	0.380522i	−0.0159007	+	0.0183504i
$431$	8.42458	−	18.4472i	0.405798	−	0.888573i	−0.590852	−	0.806780i	$-0.701208\pi$
$431$	8.42458	−	18.4472i	0.405798	−	0.888573i	0.996649	−	0.0817926i	$-0.0260645\pi$
$432$	−3.79329	−	1.11381i	−0.182505	−	0.0535882i
$433$	−3.39700	−	7.43840i	−0.163250	−	0.357467i	0.810275	−	0.586050i	$-0.199318\pi$
$433$	−3.39700	−	7.43840i	−0.163250	−	0.357467i	−0.973524	+	0.228583i	$0.926591\pi$
$434$	0.0250918	+	0.174517i	0.00120444	+	0.00837710i
$435$	−11.9081	−	7.65288i	−0.570951	−	0.366928i
$436$	9.97614			0.477770
$437$	10.1776	+	4.20294i	0.486862	+	0.201054i
$438$	−0.985470			−0.0470876
$439$	27.1791	+	17.4669i	1.29719	+	0.833652i	0.992903	−	0.118929i	$-0.0379462\pi$
$439$	27.1791	+	17.4669i	1.29719	+	0.833652i	0.304285	+	0.952581i	$0.401583\pi$
$440$	0.00372895	+	0.0259354i	0.000177771	+	0.00123642i
$441$	0.415415	+	0.909632i	0.0197817	+	0.0433158i
$442$	0.161056	+	0.0472903i	0.00766065	+	0.00224937i
$443$	−7.03718	+	15.4093i	−0.334346	+	0.732117i	−0.999899	−	0.0142347i	$-0.995469\pi$
$443$	−7.03718	+	15.4093i	−0.334346	+	0.732117i	0.665552	+	0.746351i	$0.268196\pi$
$444$	3.19274	−	3.68462i	0.151521	−	0.174864i
$445$	−0.226032	+	1.57209i	−0.0107149	+	0.0745241i
$446$	−1.39084	+	0.408388i	−0.0658582	+	0.0193377i
$447$	2.19604	+	2.53437i	0.103869	+	0.119871i
$448$	−6.57363	+	4.22462i	−0.310575	+	0.199594i
$449$	−2.19152	+	1.40840i	−0.103424	+	0.0664666i	−0.591330	−	0.806429i	$-0.701397\pi$
$449$	−2.19152	+	1.40840i	−0.103424	+	0.0664666i	0.487906	+	0.872896i	$0.337761\pi$
$450$	0.150632	+	0.173839i	0.00710088	+	0.00819485i
$451$	0.0611255	−	0.0179481i	0.00287829	−	0.000845141i
$452$	−4.33526	+	30.1524i	−0.203914	+	1.41825i
$453$	8.52847	−	9.84237i	0.400702	−	0.462435i
$454$	−0.0992461	+	0.217319i	−0.00465785	+	0.0101993i
$455$	−2.82482	−	0.829443i	−0.132430	−	0.0388849i
$456$	0.335679	+	0.735034i	0.0157196	+	0.0344211i
$457$	−4.11375	−	28.6118i	−0.192433	−	1.33840i	−0.825542	−	0.564340i	$-0.809131\pi$
$457$	−4.11375	−	28.6118i	−0.192433	−	1.33840i	0.633109	−	0.774063i	$-0.281779\pi$
$458$	1.68375	+	1.08208i	0.0786766	+	0.0505624i
$459$	−1.00000			−0.0466760
$460$	−11.5128	−	9.25727i	−0.536787	−	0.431622i
$461$	37.1520			1.73034			0.865170	−	0.501478i	$-0.167210\pi$
$461$	37.1520			1.73034			0.865170	+	0.501478i	$0.167210\pi$
$462$	0.00357093	+	0.00229490i	0.000166135	+	0.000106768i
$463$	3.94008	+	27.4038i	0.183111	+	1.27356i	0.849351	+	0.527828i	$0.176993\pi$
$463$	3.94008	+	27.4038i	0.183111	+	1.27356i	−0.666240	+	0.745737i	$0.732098\pi$
$464$	−15.0351	−	32.9223i	−0.697988	−	1.52838i
$465$	2.96714	+	0.871230i	0.137598	+	0.0404023i
$466$	−0.622913	+	1.36399i	−0.0288559	+	0.0631856i
$467$	−3.55967	+	4.10808i	−0.164722	+	0.190099i	−0.832110	−	0.554611i	$-0.812867\pi$
$467$	−3.55967	+	4.10808i	−0.164722	+	0.190099i	0.667388	+	0.744710i	$0.267412\pi$
$468$	0.539850	−	3.75474i	0.0249546	−	0.173563i
$469$	11.2349	−	3.29886i	0.518778	−	0.152327i
$470$	−0.0626320	−	0.0722812i	−0.00288900	−	0.00333408i
$471$	−13.0128	+	8.36283i	−0.599599	+	0.385339i
$472$	−2.38166	+	1.53060i	−0.109625	+	0.0704515i
$473$	−0.116476	−	0.134421i	−0.00535558	−	0.00618066i
$474$	−0.0372833	+	0.0109474i	−0.00171248	+	0.000502830i
$475$	−0.852596	+	5.92993i	−0.0391198	+	0.272084i
$476$	−1.30463	+	1.50563i	−0.0597977	+	0.0690102i
$477$	−4.87551	+	10.6759i	−0.223234	+	0.488815i
$478$	−1.82710	−	0.536485i	−0.0835696	−	0.0245382i
$479$	−2.42846	−	5.31758i	−0.110959	−	0.242966i	0.846004	−	0.533177i	$-0.179002\pi$
$479$	−2.42846	−	5.31758i	−0.110959	−	0.242966i	−0.956963	+	0.290211i	$0.906275\pi$
$480$	−0.231577	−	1.61065i	−0.0105700	−	0.0735159i
$481$	3.92000	+	2.51923i	0.178737	+	0.114867i
$482$	−0.134472			−0.00612501
$483$	−4.71872	+	0.856574i	−0.214709	+	0.0389755i
$484$	21.9099			0.995904
$485$	8.48652	+	5.45396i	0.385353	+	0.247651i
$486$	−0.0125459	−	0.0872586i	−0.000569093	−	0.00395813i
$487$	−12.6536	−	27.7074i	−0.573388	−	1.25554i	−0.944974	−	0.327145i	$-0.893913\pi$
$487$	−12.6536	−	27.7074i	−0.573388	−	1.25554i	0.371586	−	0.928398i	$-0.378814\pi$
$488$	−5.05056	−	1.48298i	−0.228628	−	0.0671312i
$489$	8.18571	−	17.9242i	0.370170	−	0.810560i
$490$	−0.0892619	+	0.103014i	−0.00403244	+	0.00465369i
$491$	3.34437	−	23.2606i	0.150929	−	1.04974i	−0.763737	−	0.645528i	$-0.776637\pi$
$491$	3.34437	−	23.2606i	0.150929	−	1.04974i	0.914666	−	0.404210i	$-0.132453\pi$
$492$	−2.52905	+	0.742597i	−0.114019	+	0.0334789i
$493$	−5.99514	−	6.91876i	−0.270008	−	0.311605i
$494$	−0.324218	+	0.208362i	−0.0145872	+	0.00937466i
$495$	0.0626320	−	0.0402511i	0.00281510	−	0.00180915i
$496$	5.17789	+	5.97561i	0.232494	+	0.268313i
$497$	−4.58579	+	1.34651i	−0.205701	+	0.0603992i
$498$	−0.0220228	+	0.153172i	−0.000986863	+	0.00686379i
$499$	14.6404	−	16.8959i	0.655393	−	0.756364i	−0.326624	−	0.945154i	$-0.605911\pi$
$499$	14.6404	−	16.8959i	0.655393	−	0.756364i	0.982017	+	0.188790i	$0.0604565\pi$
$500$	9.73710	−	21.3213i	0.435457	−	0.953517i
$501$	19.7837	+	5.80902i	0.883870	+	0.259528i
$502$	−0.299968	−	0.656838i	−0.0133882	−	0.0293161i
$503$	2.15699	+	15.0022i	0.0961754	+	0.668915i	0.979691	+	0.200513i	$0.0642609\pi$
$503$	2.15699	+	15.0022i	0.0961754	+	0.668915i	−0.883516	+	0.468402i	$0.844830\pi$
$504$	−0.296070	−	0.190272i	−0.0131880	−	0.00847540i
$505$	−4.67770			−0.208155
$506$	−0.0148845	+	0.0138878i	−0.000661696	+	0.000617386i
$507$	−9.37451			−0.416336
$508$	4.71738	+	3.03168i	0.209300	+	0.134509i
$509$	1.63942	+	11.4024i	0.0726660	+	0.505403i	0.993354	+	0.115103i	$0.0367198\pi$
$509$	1.63942	+	11.4024i	0.0726660	+	0.505403i	−0.920688	+	0.390300i	$0.872371\pi$
$510$	−0.0566239	−	0.123989i	−0.00250735	−	0.00549032i
$511$	10.7259	+	3.14941i	0.474486	+	0.139322i
$512$	2.88435	−	6.31585i	0.127472	−	0.279124i
$513$	1.50357	−	1.73521i	0.0663843	−	0.0766115i
$514$	0.342216	−	2.38016i	0.0150945	−	0.104985i
$515$	−18.0205	+	5.29131i	−0.794080	+	0.233163i
$516$	4.81917	+	5.56162i	0.212152	+	0.244837i
$517$	0.0284224	−	0.0182659i	0.00125001	−	0.000803335i
$518$	0.181491	−	0.116637i	0.00797424	−	0.00512473i
$519$	−3.31393	−	3.82448i	−0.145465	−	0.167876i
$520$	0.994164	−	0.291913i	0.0435970	−	0.0128012i
$521$	−6.22011	+	43.2618i	−0.272508	+	1.89533i	0.149533	+	0.988757i	$0.452223\pi$
$521$	−6.22011	+	43.2618i	−0.272508	+	1.89533i	−0.422041	+	0.906577i	$0.638686\pi$
$522$	0.528507	−	0.609930i	0.0231321	−	0.0266959i
$523$	−0.0285746	+	0.0625696i	−0.00124948	+	0.00273598i	−0.910256	−	0.414047i	$-0.864115\pi$
$523$	−0.0285746	+	0.0625696i	−0.00124948	+	0.00273598i	0.909006	+	0.416783i	$0.136842\pi$
$524$	−6.08698	−	1.78730i	−0.265911	−	0.0780785i
$525$	−1.08393	−	2.37347i	−0.0473065	−	0.103587i
$526$	−0.0925025	−	0.643369i	−0.00403330	−	0.0280522i
$527$	1.68251	+	1.08128i	0.0732912	+	0.0471014i
$528$	0.190361			0.00828439
$529$	1.59161	−	22.9449i	0.0692006	−	0.997603i
$530$	−1.59976			−0.0694892
$531$	6.76725	+	4.34905i	0.293674	+	0.188733i
$532$	−0.650975	−	4.52763i	−0.0282233	−	0.196298i
$533$	−1.04651	−	2.29153i	−0.0453293	−	0.0992574i
$534$	−0.0868855	−	0.0255119i	−0.00375990	−	0.00110401i
$535$	5.52653	−	12.1014i	0.238933	−	0.523189i
$536$	−2.69862	+	3.11438i	−0.116563	+	0.134521i
$537$	−0.915592	+	6.36808i	−0.0395107	+	0.274803i
$538$	1.09307	−	0.320953i	0.0471254	−	0.0138373i
$539$	−0.0315321	−	0.0363899i	−0.00135818	−	0.00156743i
$540$	−2.59138	+	1.66538i	−0.111515	+	0.0716666i
$541$	22.5323	−	14.4806i	0.968740	−	0.622571i	0.0423362	−	0.999103i	$-0.486520\pi$
$541$	22.5323	−	14.4806i	0.968740	−	0.622571i	0.926404	+	0.376532i	$0.122884\pi$
$542$	1.32538	+	1.52957i	0.0569301	+	0.0657008i
$543$	−14.4926	+	4.25543i	−0.621939	+	0.182618i
$544$	0.149772	−	1.04168i	0.00642140	−	0.0446618i
$545$	5.07035	−	5.85150i	0.217190	−	0.250651i
$546$	0.0697296	−	0.152687i	0.00298415	−	0.00653438i
$547$	28.2177	+	8.28548i	1.20650	+	0.354261i	0.822336	−	0.569002i	$-0.192670\pi$
$547$	28.2177	+	8.28548i	1.20650	+	0.354261i	0.384167	+	0.923264i	$0.374489\pi$
$548$	−6.60621	−	14.4656i	−0.282203	−	0.617939i
$549$	2.12854	+	14.8043i	0.0908437	+	0.631832i
$550$	−0.00931751	−	0.00598800i	−0.000397300	−	0.000255329i
$551$	21.0197			0.895467
$552$	1.23409	−	1.15145i	0.0525262	−	0.0490088i
$553$	0.440780			0.0187439
$554$	−0.702259	−	0.451315i	−0.0298361	−	0.0191745i
$555$	−0.538508	−	3.74540i	−0.0228584	−	0.158983i
$556$	3.02237	+	6.61807i	0.128177	+	0.280669i
$557$	15.2785	+	4.48616i	0.647369	+	0.190085i	0.588902	−	0.808205i	$-0.299560\pi$
$557$	15.2785	+	4.48616i	0.647369	+	0.190085i	0.0584674	+	0.998289i	$0.481379\pi$
$558$	−0.0732426	+	0.160379i	−0.00310061	+	0.00678938i
$559$	−4.60592	+	5.31552i	−0.194810	+	0.224823i
$560$	−0.869942	+	6.05058i	−0.0367617	+	0.255684i
$561$	0.0462003	−	0.0135656i	0.00195058	−	0.000572742i
$562$	0.198167	+	0.228697i	0.00835916	+	0.00964699i
$563$	−31.0391	+	19.9476i	−1.30814	+	0.840692i	−0.994074	−	0.108708i	$-0.965329\pi$
$563$	−31.0391	+	19.9476i	−1.30814	+	0.840692i	−0.314069	+	0.949400i	$0.601692\pi$
$564$	−1.17597	+	0.755750i	−0.0495172	+	0.0318228i
$565$	15.4825	+	17.8677i	0.651353	+	0.751702i
$566$	−0.548729	+	0.161121i	−0.0230648	+	0.00677243i
$567$	−0.142315	+	0.989821i	−0.00597666	+	0.0415686i
$568$	1.10151	−	1.27121i	0.0462183	−	0.0533388i
$569$	16.8257	−	36.8432i	0.705370	−	1.54455i	−0.127966	−	0.991779i	$-0.540845\pi$
$569$	16.8257	−	36.8432i	0.705370	−	1.54455i	0.833336	−	0.552767i	$-0.186428\pi$
$570$	0.300285	+	0.0881717i	0.0125776	+	0.00369311i
$571$	12.1756	+	26.6608i	0.509533	+	1.11572i	0.973252	+	0.229739i	$0.0737872\pi$
$571$	12.1756	+	26.6608i	0.509533	+	1.11572i	−0.463720	+	0.885982i	$0.653485\pi$
$572$	0.0259942	+	0.180794i	0.00108687	+	0.00755936i
$573$	−0.651468	−	0.418673i	−0.0272155	−	0.0174903i
$574$	−0.116635			−0.00486825
$575$	12.3124	−	2.23503i	0.513462	−	0.0932071i
$576$	−7.81409			−0.325587
$577$	−27.2597	−	17.5187i	−1.13483	−	0.729314i	−0.168271	−	0.985741i	$-0.553818\pi$
$577$	−27.2597	−	17.5187i	−1.13483	−	0.729314i	−0.966564	+	0.256427i	$0.917455\pi$
$578$	0.200734	+	1.39614i	0.00834945	+	0.0580717i
$579$	1.30518	+	2.85795i	0.0542416	+	0.118772i
$580$	−27.0581	−	7.94497i	−1.12353	−	0.329897i
$581$	0.729209	−	1.59675i	0.0302527	−	0.0662442i
$582$	−0.376650	+	0.434677i	−0.0156126	+	0.0180179i
$583$	0.0804251	−	0.559369i	0.00333087	−	0.0231667i
$584$	−3.77486	+	1.10840i	−0.156205	+	0.0458659i
$585$	−1.92796	−	2.22499i	−0.0797114	−	0.0919918i
$586$	2.23188	−	1.43434i	0.0921981	−	0.0592521i
$587$	−7.18584	+	4.61806i	−0.296591	+	0.190608i	−0.680470	−	0.732776i	$-0.738224\pi$
$587$	−7.18584	+	4.61806i	−0.296591	+	0.190608i	0.383879	+	0.923383i	$0.374588\pi$
$588$	1.30463	+	1.50563i	0.0538021	+	0.0620910i
$589$	−4.40602	+	1.29373i	−0.181547	+	0.0533070i
$590$	−0.156046	+	1.08532i	−0.00642432	+	0.0446821i
$591$	−11.4742	+	13.2419i	−0.471984	+	0.544699i
$592$	4.01913	−	8.80067i	0.165185	−	0.361705i
$593$	−42.2378	−	12.4021i	−1.73450	−	0.509295i	−0.746717	−	0.665142i	$-0.768371\pi$
$593$	−42.2378	−	12.4021i	−1.73450	−	0.509295i	−0.987781	+	0.155847i	$0.950189\pi$
$594$	0.00176334	+	0.00386119i	7.23509e−5	+	0.000158426i
$595$	0.220047	+	1.53046i	0.00902106	+	0.0627428i
$596$	5.62028	+	3.61193i	0.230215	+	0.147951i
$597$	8.42707			0.344897
$598$	0.627352	+	0.504444i	0.0256543	+	0.0206282i
$599$	−30.0823			−1.22913			−0.614565	−	0.788866i	$-0.710669\pi$
$599$	−30.0823			−1.22913			−0.614565	+	0.788866i	$0.710669\pi$
$600$	0.772524	+	0.496471i	0.0315382	+	0.0202683i
$601$	−1.12881	−	7.85103i	−0.0460450	−	0.320250i	−0.999806	−	0.0196849i	$-0.993734\pi$
$601$	−1.12881	−	7.85103i	−0.0460450	−	0.320250i	0.953761	−	0.300565i	$-0.0971754\pi$
$602$	0.135275	+	0.296211i	0.00551340	+	0.0120727i
$603$	11.2349	+	3.29886i	0.457520	+	0.134340i
$604$	10.7781	−	23.6008i	0.438556	−	0.960303i
$605$	11.1357	−	12.8512i	0.452729	−	0.522477i
$606$	0.0379549	−	0.263982i	0.00154181	−	0.0107236i
$607$	−21.4147	+	6.28793i	−0.869197	+	0.255219i	−0.685774	−	0.727815i	$-0.740536\pi$
$607$	−21.4147	+	6.28793i	−0.869197	+	0.255219i	−0.183423	+	0.983034i	$0.558718\pi$
$608$	1.58235	+	1.82613i	0.0641728	+	0.0740594i
$609$	−7.70154	+	4.94948i	−0.312082	+	0.200563i
$610$	−1.71504	+	1.10219i	−0.0694400	+	0.0446264i
$611$	−0.874908	−	1.00970i	−0.0353950	−	0.0408480i
$612$	−1.91153	+	0.561276i	−0.0772690	+	0.0226882i
$613$	−5.08018	+	35.3335i	−0.205187	+	1.42711i	0.583402	+	0.812184i	$0.301721\pi$
$613$	−5.08018	+	35.3335i	−0.205187	+	1.42711i	−0.788588	+	0.614921i	$0.789188\pi$
$614$	0.226072	−	0.260901i	0.00912353	−	0.0105291i
$615$	−0.849816	+	1.86084i	−0.0342679	+	0.0750362i
$616$	0.0162597	+	0.00477427i	0.000655121	+	0.000192361i
$617$	−17.7855	−	38.9447i	−0.716015	−	1.56786i	−0.819406	−	0.573214i	$-0.805696\pi$
$617$	−17.7855	−	38.9447i	−0.716015	−	1.56786i	0.103390	−	0.994641i	$-0.467031\pi$
$618$	−0.152392	−	1.05991i	−0.00613010	−	0.0426358i
$619$	−37.9375	−	24.3810i	−1.52484	−	0.979954i	−0.990925	−	0.134415i	$-0.957084\pi$
$619$	−37.9375	−	24.3810i	−1.52484	−	0.979954i	−0.533914	−	0.845539i	$-0.679279\pi$
$620$	6.16077			0.247422
$621$	−4.43274	−	1.83053i	−0.177880	−	0.0734568i
$622$	−0.816185			−0.0327260
$623$	0.864133	+	0.555345i	0.0346208	+	0.0222494i
$624$	−1.07129	−	7.45100i	−0.0428860	−	0.298279i
$625$	−2.13748	−	4.68044i	−0.0854993	−	0.187217i
$626$	−1.79811	−	0.527972i	−0.0718668	−	0.0211020i
$627$	−0.0459262	+	0.100564i	−0.00183412	+	0.00401615i
$628$	−20.1805	+	23.2896i	−0.805291	+	0.929355i
$629$	0.348278	−	2.42233i	0.0138868	−	0.0965845i
$630$	−0.130785	+	0.0384020i	−0.00521061	+	0.00152997i
$631$	2.93776	+	3.39035i	0.116950	+	0.134968i	0.811206	−	0.584761i	$-0.198812\pi$
$631$	2.93776	+	3.39035i	0.116950	+	0.134968i	−0.694255	+	0.719729i	$0.744266\pi$
$632$	−0.130501	+	0.0838682i	−0.00519107	+	0.00333610i
$633$	9.46390	−	6.08208i	0.376156	−	0.241741i
$634$	0.344542	+	0.397623i	0.0136835	+	0.0157916i
$635$	4.17583	−	1.22613i	0.165713	−	0.0486576i
$636$	−3.32757	+	23.1438i	−0.131947	+	0.917710i
$637$	−1.24690	+	1.43900i	−0.0494041	+	0.0570153i
$638$	−0.0161431	+	0.0353485i	−0.000639113	+	0.00139946i
$639$	−4.58579	−	1.34651i	−0.181411	−	0.0532671i
$640$	−1.79440	−	3.92919i	−0.0709300	−	0.155315i
$641$	5.37759	+	37.4020i	0.212402	+	1.47729i	0.765103	+	0.643908i	$0.222688\pi$
$641$	5.37759	+	37.4020i	0.212402	+	1.47729i	−0.552701	+	0.833380i	$0.686403\pi$
$642$	0.638091	+	0.410076i	0.0251835	+	0.0161844i
$643$	9.18900			0.362379			0.181189	−	0.983448i	$-0.442005\pi$
$643$	9.18900			0.362379			0.181189	+	0.983448i	$0.442005\pi$
$644$	−8.53919	+	4.28587i	−0.336491	+	0.168887i
$645$	5.71150			0.224890
$646$	0.170276	+	0.109430i	0.00669942	+	0.00430545i
$647$	6.27746	+	43.6607i	0.246792	+	1.71648i	0.616520	+	0.787339i	$0.288542\pi$
$647$	6.27746	+	43.6607i	0.246792	+	1.71648i	−0.369728	+	0.929140i	$0.620549\pi$
$648$	−0.146201	−	0.320135i	−0.00574330	−	0.0125761i
$649$	−0.371647	−	0.109125i	−0.0145884	−	0.00428355i
$650$	−0.181943	+	0.398400i	−0.00713639	+	0.0156265i
$651$	1.30972	−	1.51150i	0.0513320	−	0.0592403i
$652$	5.58680	−	38.8571i	0.218796	−	1.52176i
$653$	−19.0026	+	5.57967i	−0.743630	+	0.218349i	−0.631534	−	0.775348i	$-0.717575\pi$
$653$	−19.0026	+	5.57967i	−0.743630	+	0.218349i	−0.112096	+	0.993697i	$0.535756\pi$
$654$	0.289084	+	0.333620i	0.0113041	+	0.0130456i
$655$	−4.14203	+	2.66192i	−0.161843	+	0.104010i
$656$	−4.40026	+	2.82787i	−0.171801	+	0.110410i
$657$	7.32050	+	8.44831i	0.285600	+	0.329600i
$658$	−0.0593503	+	0.0174268i	−0.00231372	+	0.000679369i
$659$	−2.80789	+	19.5293i	−0.109380	+	0.760754i	0.859126	+	0.511764i	$0.171008\pi$
$659$	−2.80789	+	19.5293i	−0.109380	+	0.760754i	−0.968506	+	0.248990i	$0.919901\pi$
$660$	0.0971309	−	0.112095i	0.00378081	−	0.00436329i
$661$	−6.84945	+	14.9982i	−0.266413	+	0.583362i	−0.994805	−	0.101798i	$-0.967541\pi$
$661$	−6.84945	+	14.9982i	−0.266413	+	0.583362i	0.728392	+	0.685160i	$0.240268\pi$
$662$	1.81553	+	0.533088i	0.0705627	+	0.0207191i
$663$	−0.790980	−	1.73201i	−0.0307191	−	0.0672655i
$664$	0.0879199	+	0.611496i	0.00341195	+	0.0237307i
$665$	−2.98654	−	1.91933i	−0.115813	−	0.0744284i
$666$	0.215738			0.00835969
$667$	−13.9098	−	41.6434i	−0.538591	−	1.61244i
$668$	41.0776			1.58934
$669$	13.8328	+	8.88982i	0.534808	+	0.343700i
$670$	0.227140	+	1.57979i	0.00877519	+	0.0610328i
$671$	−0.299169	−	0.655088i	−0.0115493	−	0.0252894i
$672$	−1.00977	−	0.296494i	−0.0389526	−	0.0114375i
$673$	−12.2653	+	26.8572i	−0.472792	+	1.03527i	0.511591	+	0.859229i	$0.329056\pi$
$673$	−12.2653	+	26.8572i	−0.472792	+	1.03527i	−0.984383	+	0.176040i	$0.943671\pi$
$674$	−0.0722488	+	0.0833796i	−0.00278292	+	0.00321166i
$675$	0.371337	−	2.58271i	0.0142928	−	0.0994084i
$676$	−17.9196	+	5.26168i	−0.689217	+	0.202372i
$677$	5.60102	+	6.46392i	0.215265	+	0.248429i	0.853104	−	0.521741i	$-0.174717\pi$
$677$	5.60102	+	6.46392i	0.215265	+	0.248429i	−0.637840	+	0.770169i	$0.720172\pi$
$678$	−1.13398	+	0.728763i	−0.0435501	+	0.0279880i
$679$	5.48863	−	3.52733i	0.210634	−	0.135366i
$680$	−0.356354	−	0.411254i	−0.0136656	−	0.0157709i
$681$	2.60029	−	0.763514i	0.0996433	−	0.0292579i
$682$	0.00120819	−	0.00840314i	4.62640e−5	−	0.000321773i
$683$	10.5374	−	12.1608i	0.403201	−	0.465318i	−0.517446	−	0.855716i	$-0.673117\pi$
$683$	10.5374	−	12.1608i	0.403201	−	0.465318i	0.920646	+	0.390398i	$0.127663\pi$
$684$	1.90019	−	4.16083i	0.0726555	−	0.159093i
$685$	−11.8424	−	3.47723i	−0.452473	−	0.132858i
$686$	0.0366213	+	0.0801894i	0.00139821	+	0.00306165i
$687$	−3.23110	−	22.4728i	−0.123274	−	0.857390i
$688$	12.2853	+	7.89528i	0.468372	+	0.301005i
$689$	−22.3471			−0.851357
$690$	−0.0240325	−	0.653262i	−0.000914901	−	0.0248693i
$691$	−15.9086			−0.605191			−0.302595	−	0.953119i	$-0.597853\pi$
$691$	−15.9086			−0.605191			−0.302595	+	0.953119i	$0.597853\pi$
$692$	−8.48126	−	5.45058i	−0.322409	−	0.207200i
$693$	−0.00685257	−	0.0476607i	−0.000260308	−	0.00181048i
$694$	−0.809452	−	1.77245i	−0.0307264	−	0.0672814i
$695$	5.41794	+	1.59085i	0.205514	+	0.0603444i
$696$	1.33844	−	2.93078i	0.0507335	−	0.111091i
$697$	−0.866415	+	0.999896i	−0.0328178	+	0.0378738i
$698$	0.0590678	−	0.410826i	0.00223575	−	0.0155500i
$699$	16.3206	−	4.79215i	0.617301	−	0.181256i
$700$	−3.40413	−	3.92858i	−0.128664	−	0.148486i
$701$	−18.8778	+	12.1320i	−0.713003	+	0.458220i	−0.846197	−	0.532871i	$-0.821113\pi$
$701$	−18.8778	+	12.1320i	−0.713003	+	0.458220i	0.133193	+	0.991090i	$0.457477\pi$
$702$	0.141209	−	0.0907494i	0.00532958	−	0.00342512i
$703$	3.67959	+	4.24648i	0.138778	+	0.160159i
$704$	0.361014	−	0.106003i	0.0136062	−	0.00399514i
$705$	−0.154399	+	1.07387i	−0.00581502	+	0.0404444i
$706$	0.719229	−	0.830035i	0.0270686	−	0.0312388i
$707$	−1.25675	+	2.75190i	−0.0472649	+	0.103496i
$708$	15.3768	+	4.51504i	0.577896	+	0.169686i
$709$	−2.17960	−	4.77266i	−0.0818566	−	0.179241i	0.864278	−	0.503014i	$-0.167776\pi$
$709$	−2.17960	−	4.77266i	−0.0818566	−	0.179241i	−0.946135	+	0.323773i	$0.895048\pi$
$710$	−0.0927128	−	0.644832i	−0.00347945	−	0.0242001i
$711$	0.370807	+	0.238303i	0.0139064	+	0.00893708i
$712$	−0.361510			−0.0135482
$713$	5.47878	+	7.87292i	0.205182	+	0.294843i
$714$	−0.0881559			−0.00329915
$715$	0.119256	+	0.0766411i	0.00445992	+	0.00286621i
$716$	1.82407	+	12.6867i	0.0681686	+	0.474123i
$717$	8.97328	+	19.6487i	0.335113	+	0.733796i
$718$	−1.29378	−	0.379888i	−0.0482834	−	0.0141773i
$719$	−15.5919	+	34.1414i	−0.581478	+	1.27326i	0.358978	+	0.933346i	$0.383125\pi$
$719$	−15.5919	+	34.1414i	−0.581478	+	1.27326i	−0.940456	+	0.339914i	$0.889602\pi$
$720$	−4.00303	+	4.61974i	−0.149184	+	0.172168i
$721$	−1.72866	+	12.0231i	−0.0643788	+	0.447764i
$722$	1.16121	−	0.340962i	0.0432157	−	0.0126893i
$723$	0.998914	+	1.15281i	0.0371500	+	0.0428734i
$724$	−25.3147	+	16.2687i	−0.940812	+	0.604623i
$725$	20.0953	−	12.9145i	0.746322	−	0.479632i
$726$	0.634895	+	0.732707i	0.0235631	+	0.0271933i
$727$	−46.9192	+	13.7767i	−1.74014	+	0.510950i	−0.988836	−	0.149011i	$-0.952391\pi$
$727$	−46.9192	+	13.7767i	−1.74014	+	0.510950i	−0.751300	+	0.659961i	$0.770573\pi$
$728$	0.0953675	−	0.663296i	0.00353456	−	0.0245834i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	−0.632982	+	1.38604i	−0.0234277	+	0.0512996i
$731$	3.54427	+	1.04069i	0.131089	+	0.0384913i
$732$	12.3780	+	27.1041i	0.457506	+	1.00180i
$733$	−3.68490	−	25.6291i	−0.136105	−	0.946631i	−0.937373	−	0.348326i	$-0.886750\pi$
$733$	−3.68490	−	25.6291i	−0.136105	−	0.946631i	0.801268	−	0.598305i	$-0.204159\pi$
$734$	0.320155	+	0.205751i	0.0118171	+	0.00759442i
$735$	1.54620			0.0570325
$736$	2.57074	−	4.34335i	0.0947586	−	0.160098i
$737$	−0.563806			−0.0207681
$738$	−0.0981195	−	0.0630576i	−0.00361183	−	0.00232118i
$739$	0.715234	+	4.97456i	0.0263103	+	0.182992i	0.998739	−	0.0502094i	$-0.0159889\pi$
$739$	0.715234	+	4.97456i	0.0263103	+	0.182992i	−0.972428	+	0.233202i	$0.925080\pi$
$740$	−3.13158	−	6.85720i	−0.115119	−	0.252076i
$741$	4.19469	+	1.23167i	0.154096	+	0.0452466i
$742$	−0.429805	+	0.941142i	−0.0157786	+	0.0345504i
$743$	18.7895	−	21.6842i	0.689318	−	0.795516i	−0.297950	−	0.954582i	$-0.596303\pi$
$743$	18.7895	−	21.6842i	0.689318	−	0.795516i	0.987268	+	0.159066i	$0.0508483\pi$
$744$	−0.100172	+	0.696713i	−0.00367249	+	0.0255427i
$745$	4.97507	−	1.46081i	0.182272	−	0.0535200i
$746$	1.18089	+	1.36282i	0.0432354	+	0.0498963i
$747$	1.47672	−	0.949028i	0.0540302	−	0.0347231i
$748$	0.0806993	−	0.0518623i	0.00295066	−	0.00189627i
$749$	−5.63447	−	6.50253i	−0.205879	−	0.237597i
$750$	0.995180	−	0.292211i	0.0363388	−	0.0106700i
$751$	4.88246	−	33.9583i	0.178164	−	1.23916i	−0.682844	−	0.730564i	$-0.739257\pi$
$751$	4.88246	−	33.9583i	0.178164	−	1.23916i	0.861008	−	0.508591i	$-0.169834\pi$
$752$	−1.81657	+	2.09644i	−0.0662436	+	0.0764492i
$753$	−3.40270	+	7.45087i	−0.124001	+	0.271525i
$754$	1.47444	+	0.432935i	0.0536960	+	0.0157666i
$755$	−8.36508	−	18.3170i	−0.304436	−	0.666622i
$756$	0.283524	+	1.97195i	0.0103117	+	0.0717191i
$757$	−21.4661	−	13.7955i	−0.780200	−	0.501404i	0.0888998	−	0.996041i	$-0.471665\pi$
$757$	−21.4661	−	13.7955i	−0.780200	−	0.501404i	−0.869100	+	0.494636i	$0.835301\pi$
$758$	−1.10669			−0.0401969
$759$	0.229626	+	0.0244384i	0.00833491	+	0.000887059i
$760$	1.24942			0.0453211
$761$	40.8175	+	26.2318i	1.47963	+	0.950902i	0.997185	+	0.0749767i	$0.0238882\pi$
$761$	40.8175	+	26.2318i	1.47963	+	0.950902i	0.482447	+	0.875925i	$0.339748\pi$
$762$	0.0353132	+	0.245608i	0.00127926	+	0.00889745i
$763$	−2.08020	−	4.55501i	−0.0753083	−	0.164902i
$764$	−1.48029	−	0.434653i	−0.0535551	−	0.0157252i
$765$	−0.642315	+	1.40647i	−0.0232229	+	0.0508511i
$766$	0.352658	−	0.406989i	0.0127420	−	0.0147051i
$767$	−2.17981	+	15.1609i	−0.0787085	+	0.547430i
$768$	−14.7588	+	4.33358i	−0.532563	+	0.156375i
$769$	−13.7508	−	15.8693i	−0.495866	−	0.572260i	0.451557	−	0.892242i	$-0.350869\pi$
$769$	−13.7508	−	15.8693i	−0.495866	−	0.572260i	−0.947424	+	0.319982i	$0.896323\pi$
$770$	0.00552138	−	0.00354838i	0.000198977	−	0.000127875i
$771$	−22.9470	+	14.7471i	−0.826415	+	0.531105i
$772$	4.09900	+	4.73049i	0.147526	+	0.170254i
$773$	−46.1444	+	13.5492i	−1.65970	+	0.487332i	−0.971272	−	0.237974i	$-0.923517\pi$
$773$	−46.1444	+	13.5492i	−1.65970	+	0.487332i	−0.688428	+	0.725305i	$0.741699\pi$
$774$	−0.0463432	+	0.322324i	−0.00166577	+	0.0115857i
$775$	−3.41741	+	3.94390i	−0.122757	+	0.141669i
$776$	−0.953864	+	2.08867i	−0.0342417	+	0.0749789i
$777$	−2.34811	−	0.689466i	−0.0842378	−	0.0247345i
$778$	0.434557	+	0.951547i	0.0155796	+	0.0341146i
$779$	−0.432317	−	3.00683i	−0.0154894	−	0.107731i
$780$	−4.93418	−	3.17101i	−0.176672	−	0.113540i
$781$	0.230131			0.00823475
$782$	0.104117	−	0.409760i	0.00372323	−	0.0146530i
$783$	−9.15484			−0.327167
$784$	3.32584	+	2.13739i	0.118780	+	0.0763352i
$785$	3.40377	+	23.6738i	0.121486	+	0.844952i
$786$	−0.116615	−	0.255351i	−0.00415952	−	0.00910808i
$787$	−5.57562	−	1.63715i	−0.198749	−	0.0583581i	0.180843	−	0.983512i	$-0.442118\pi$
$787$	−5.57562	−	1.63715i	−0.198749	−	0.0583581i	−0.379592	+	0.925154i	$0.623936\pi$
$788$	−14.5009	+	31.7524i	−0.516572	+	1.13113i
$789$	−4.82837	+	5.57224i	−0.171895	+	0.198377i
$790$	−0.00855045	+	0.0594697i	−0.000304211	+	0.00211584i
$791$	14.6713	−	4.30787i	0.521650	−	0.153170i
$792$	0.0110974	+	0.0128070i	0.000394327	+	0.000455078i
$793$	−23.9575	+	15.3965i	−0.850755	+	0.546747i
$794$	−1.37981	+	0.886751i	−0.0489677	+	0.0314696i
$795$	11.8837	+	13.7146i	0.421472	+	0.486405i
$796$	16.1086	−	4.72991i	0.570954	−	0.167647i
$797$	6.69593	−	46.5712i	0.237182	−	1.64964i	−0.428603	−	0.903493i	$-0.640994\pi$
$797$	6.69593	−	46.5712i	0.237182	−	1.64964i	0.665785	−	0.746144i	$-0.268097\pi$
$798$	0.132549	−	0.152969i	0.00469217	−	0.00541506i
$799$	−0.291482	+	0.638257i	−0.0103119	+	0.0225799i
$800$	2.63475	+	0.773632i	0.0931524	+	0.0273520i
$801$	0.426713	+	0.934372i	0.0150772	+	0.0330144i
$802$	−0.218769	−	1.52157i	−0.00772500	−	0.0537285i
$803$	−0.452817	−	0.291008i	−0.0159796	−	0.0102694i
$804$	23.3274			0.822693
$805$	−1.82615	+	7.18694i	−0.0643634	+	0.253306i
$806$	−0.335711			−0.0118249
$807$	−10.8713	−	6.98654i	−0.382687	−	0.245938i
$808$	−0.151525	−	1.05388i	−0.00533062	−	0.0370753i
$809$	13.5630	+	29.6988i	0.476849	+	1.04415i	0.983318	+	0.181895i	$0.0582231\pi$
$809$	13.5630	+	29.6988i	0.476849	+	1.04415i	−0.506469	+	0.862258i	$0.669050\pi$
$810$	−0.130785	−	0.0384020i	−0.00459533	−	0.00134931i
$811$	17.3178	−	37.9208i	0.608112	−	1.33158i	−0.315746	−	0.948844i	$-0.602255\pi$
$811$	17.3178	−	37.9208i	0.608112	−	1.33158i	0.923858	−	0.382735i	$-0.125018\pi$
$812$	−11.9437	+	13.7838i	−0.419141	+	0.483715i
$813$	3.26732	−	22.7247i	0.114590	−	0.796989i
$814$	−0.00996719	+	0.00292663i	−0.000349350	+	0.000102578i
$815$	−19.9521	−	23.0260i	−0.698892	−	0.806564i
$816$	−3.32584	+	2.13739i	−0.116428	+	0.0748235i
$817$	−7.13487	+	4.58530i	−0.249618	+	0.160420i
$818$	0.359159	+	0.414491i	0.0125577	+	0.0144924i
$819$	−1.82694	+	0.536439i	−0.0638386	+	0.0187447i
$820$	−0.580006	+	4.03403i	−0.0202547	+	0.140874i
$821$	23.8273	−	27.4982i	0.831578	−	0.959693i	−0.168081	−	0.985773i	$-0.553757\pi$
$821$	23.8273	−	27.4982i	0.831578	−	0.959693i	0.999660	+	0.0260804i	$0.00830259\pi$
$822$	0.292324	−	0.640100i	0.0101960	−	0.0223261i
$823$	−13.1631	−	3.86505i	−0.458838	−	0.134727i	0.0441415	−	0.999025i	$-0.485945\pi$
$823$	−13.1631	−	3.86505i	−0.458838	−	0.134727i	−0.502980	+	0.864298i	$0.667763\pi$
$824$	−1.77586	−	3.88860i	−0.0618651	−	0.135466i
$825$	0.0178802	+	0.124359i	0.000622508	+	0.00432964i
$826$	0.596573	+	0.383394i	0.0207574	+	0.0133400i
$827$	−33.1922			−1.15421			−0.577104	−	0.816671i	$-0.695817\pi$
$827$	−33.1922			−1.15421			−0.577104	+	0.816671i	$0.695817\pi$
$828$	−9.50074	−	1.01113i	−0.330173	−	0.0351393i
$829$	−38.1240			−1.32410			−0.662051	−	0.749459i	$-0.730314\pi$
$829$	−38.1240			−1.32410			−0.662051	+	0.749459i	$0.730314\pi$
$830$	0.201286	+	0.129359i	0.00698675	+	0.00449011i
$831$	1.34763	+	9.37294i	0.0467486	+	0.325144i
$832$	−6.18079	−	13.5340i	−0.214280	−	0.469209i
$833$	0.959493	+	0.281733i	0.0332445	+	0.00976145i
$834$	−0.133740	+	0.292849i	−0.00463102	+	0.0101405i
$835$	20.8776	−	24.0940i	0.722499	−	0.833808i
$836$	−0.0313450	+	0.218009i	−0.00108409	+	0.00754000i
$837$	1.91899	−	0.563465i	0.0663299	−	0.0194762i
$838$	1.47287	+	1.69979i	0.0508796	+	0.0587181i
$839$	16.0232	−	10.2975i	0.553182	−	0.355509i	−0.233993	−	0.972238i	$-0.575179\pi$
$839$	16.0232	−	10.2975i	0.553182	−	0.355509i	0.787175	+	0.616730i	$0.211543\pi$
$840$	−0.457783	+	0.294199i	−0.0157950	+	0.0101508i
$841$	−35.8936	−	41.4234i	−1.23771	−	1.42839i
$842$	1.87029	−	0.549168i	0.0644546	−	0.0189256i
$843$	0.488518	−	3.39772i	0.0168255	−	0.117024i
$844$	14.6768	−	16.9379i	0.505196	−	0.583028i
$845$	−6.02139	+	13.1850i	−0.207142	+	0.453578i
$846$	−0.0593503	−	0.0174268i	−0.00204051	−	0.000599147i
$847$	−4.56860	−	10.0038i	−0.156979	−	0.343736i
$848$	6.60332	+	45.9271i	0.226759	+	1.57714i
$849$	5.45747	+	3.50730i	0.187300	+	0.120370i
$850$	0.230022			0.00788969
$851$	5.97798	−	10.1000i	0.204922	−	0.346224i
$852$	−9.52163			−0.326206
$853$	−4.31822	−	2.77515i	−0.147853	−	0.0950193i	0.464623	−	0.885509i	$-0.346190\pi$
$853$	−4.31822	−	2.77515i	−0.147853	−	0.0950193i	−0.612476	+	0.790489i	$0.709826\pi$
$854$	0.187643	+	1.30509i	0.00642101	+	0.0446591i
$855$	−1.47477	−	3.22929i	−0.0504359	−	0.110439i
$856$	2.90545	+	0.853116i	0.0993062	+	0.0291589i
$857$	−2.01816	+	4.41915i	−0.0689390	+	0.150955i	−0.940965	−	0.338505i	$-0.890079\pi$
$857$	−2.01816	+	4.41915i	−0.0689390	+	0.150955i	0.872026	+	0.489460i	$0.162806\pi$
$858$	−0.00529282	+	0.00610824i	−0.000180694	+	0.000208532i
$859$	−0.125356	+	0.871868i	−0.00427708	+	0.0297478i	−0.991848	−	0.127425i	$-0.959329\pi$
$859$	−0.125356	+	0.871868i	−0.00427708	+	0.0297478i	0.987571	+	0.157173i	$0.0502379\pi$
$860$	10.9177	−	3.20573i	0.372290	−	0.109314i
$861$	0.866415	+	0.999896i	0.0295273	+	0.0340764i
$862$	1.50399	−	0.966554i	0.0512260	−	0.0329210i
$863$	26.5318	−	17.0510i	0.903154	−	0.580422i	−0.00456991	−	0.999990i	$-0.501455\pi$
$863$	26.5318	−	17.0510i	0.903154	−	0.580422i	0.907724	+	0.419568i	$0.137818\pi$
$864$	−0.689173	−	0.795348i	−0.0234461	−	0.0270583i
$865$	−7.50761	+	2.20443i	−0.255267	+	0.0749530i
$866$	0.102592	−	0.713546i	0.00348623	−	0.0242473i
$867$	10.4778	−	12.0920i	0.355844	−	0.410666i
$868$	1.65520	−	3.62439i	0.0561813	−	0.123020i
$869$	−0.0203642	−	0.00597946i	−0.000690807	−	0.000202839i
$870$	−0.518382	−	1.13510i	−0.0175748	−	0.0384834i
$871$	3.17293	+	22.0682i	0.107511	+	0.747752i
$872$	1.48258	+	0.952794i	0.0502064	+	0.0322657i
$873$	6.52435			0.220816
$874$	0.554473	+	0.796769i	0.0187553	+	0.0269511i
$875$	−11.7654			−0.397745
$876$	18.7352	+	12.0404i	0.633003	+	0.406807i
$877$	−0.554894	−	3.85937i	−0.0187374	−	0.130322i	0.978306	−	0.207167i	$-0.0664244\pi$
$877$	−0.554894	−	3.85937i	−0.0187374	−	0.130322i	−0.997043	+	0.0768452i	$0.975515\pi$
$878$	1.18316	+	2.59075i	0.0399296	+	0.0874335i
$879$	−28.8758	−	8.47870i	−0.973957	−	0.285980i
$880$	0.122272	−	0.267737i	0.00412178	−	0.00902543i
$881$	−6.59328	+	7.60905i	−0.222133	+	0.256355i	−0.855867	−	0.517196i	$-0.826976\pi$
$881$	−6.59328	+	7.60905i	−0.222133	+	0.256355i	0.633734	+	0.773551i	$0.281521\pi$
$882$	−0.0125459	+	0.0872586i	−0.000422442	+	0.00293815i
$883$	−23.7615	+	6.97702i	−0.799639	+	0.234795i	−0.655927	−	0.754824i	$-0.727722\pi$
$883$	−23.7615	+	6.97702i	−0.799639	+	0.234795i	−0.143712	+	0.989620i	$0.545904\pi$
$884$	−2.48411	−	2.86682i	−0.0835498	−	0.0964216i
$885$	10.4635	−	6.72450i	0.351728	−	0.226042i
$886$	−1.25630	+	0.807378i	−0.0422064	+	0.0271244i
$887$	1.81219	+	2.09138i	0.0608475	+	0.0702218i	0.785357	−	0.619043i	$-0.212479\pi$
$887$	1.81219	+	2.09138i	0.0608475	+	0.0702218i	−0.724510	+	0.689265i	$0.757934\pi$
$888$	0.826389	−	0.242650i	0.0277318	−	0.00814279i
$889$	0.400576	−	2.78607i	0.0134349	−	0.0934417i
$890$	−0.0916896	+	0.105815i	−0.00307344	+	0.00354694i
$891$	0.0200026	−	0.0437995i	0.000670111	−	0.00146734i
$892$	31.4315	+	9.22912i	1.05240	+	0.309014i
$893$	−0.669248	−	1.46545i	−0.0223955	−	0.0490394i
$894$	0.0420720	+	0.292617i	0.00140710	+	0.00978659i
$895$	8.36844	+	5.37807i	0.279726	+	0.179769i
$896$	−2.79365			−0.0933293
$897$	−0.335711	−	9.12544i	−0.0112090	−	0.304690i
$898$	−0.229652			−0.00766357
$899$	15.4031	+	9.89896i	0.513721	+	0.330149i
$900$	−0.739788	−	5.14534i	−0.0246596	−	0.171511i
$901$	4.87551	+	10.6759i	0.162427	+	0.355665i
$902$	0.00538857	+	0.00158223i	0.000179420	+	5.26824e-5i
$903$	1.53450	−	3.36008i	0.0510649	−	0.111817i
$904$	−3.52405	+	4.06697i	−0.117208	+	0.135265i
$905$	−3.32370	+	23.1168i	−0.110484	+	0.768430i
$906$	1.10158	−	0.323452i	0.0365975	−	0.0107460i
$907$	−21.8803	−	25.2512i	−0.726523	−	0.838452i	0.265552	−	0.964096i	$-0.414446\pi$
$907$	−21.8803	−	25.2512i	−0.726523	−	0.838452i	−0.992075	+	0.125644i	$0.959900\pi$
$908$	4.54199	−	2.91896i	0.150731	−	0.0968690i
$909$	−2.54503	+	1.63559i	−0.0844134	+	0.0542492i
$910$	−0.169961	−	0.196146i	−0.00563416	−	0.00650216i
$911$	−9.32398	+	2.73777i	−0.308917	+	0.0907063i	−0.432517	−	0.901626i	$-0.642374\pi$
$911$	−9.32398	+	2.73777i	−0.308917	+	0.0907063i	0.123600	+	0.992332i	$0.460556\pi$
$912$	1.29181	−	8.98475i	0.0427762	−	0.297515i
$913$	−0.0553506	+	0.0638780i	−0.00183184	+	0.00211405i
$914$	1.05858	−	2.31796i	0.0350146	−	0.0766712i
$915$	22.1890	+	6.51529i	0.733547	+	0.215389i
$916$	−18.7898	−	41.1438i	−0.620831	−	1.35943i
$917$	0.453180	+	3.15194i	0.0149653	+	0.104086i
$918$	−0.0741615	−	0.0476607i	−0.00244769	−	0.00157304i
$919$	22.8433			0.753532			0.376766	−	0.926309i	$-0.377036\pi$
$919$	22.8433			0.753532			0.376766	+	0.926309i	$0.377036\pi$
$920$	−0.826807	−	2.47530i	−0.0272590	−	0.0816082i
$921$	−3.91604			−0.129038
$922$	2.75525	+	1.77069i	0.0907392	+	0.0583146i
$923$	−1.29511	−	9.00767i	−0.0426290	−	0.296491i
$924$	−0.0398497	−	0.0872586i	−0.00131096	−	0.00287060i
$925$	6.12683	+	1.79900i	0.201449	+	0.0591507i
$926$	−1.01388	+	2.22010i	−0.0333183	+	0.0729569i
$927$	−7.95443	+	9.17990i	−0.261258	+	0.301508i
$928$	1.37113	−	9.53644i	0.0450097	−	0.313049i
$929$	11.5787	−	3.39982i	0.379886	−	0.111545i	−0.0862139	−	0.996277i	$-0.527477\pi$
$929$	11.5787	−	3.39982i	0.379886	−	0.111545i	0.466100	+	0.884732i	$0.345659\pi$
$930$	0.178524	+	0.206027i	0.00585403	+	0.00675591i
$931$	−1.93153	+	1.24132i	−0.0633034	+	0.0406826i
$932$	28.5075	−	18.3207i	0.933796	−	0.600114i
$933$	6.06298	+	6.99705i	0.198493	+	0.229073i
$934$	−0.459784	+	0.135005i	−0.0150446	+	0.00441749i
$935$	0.0105955	−	0.0736930i	0.000346508	−	0.00241002i
$936$	0.438833	−	0.506440i	0.0143437	−	0.0165535i
$937$	−0.418270	+	0.915883i	−0.0136643	+	0.0299206i	−0.916341	−	0.400399i	$-0.868872\pi$
$937$	−0.418270	+	0.915883i	−0.0136643	+	0.0299206i	0.902677	+	0.430319i	$0.141599\pi$
$938$	0.990421	+	0.290814i	0.0323384	+	0.00949541i
$939$	8.83089	+	19.3369i	0.288185	+	0.631037i
$940$	0.307599	+	2.13940i	0.0100328	+	0.0697795i
$941$	4.59323	+	2.95189i	0.149735	+	0.0962288i	0.613363	−	0.789801i	$-0.289816\pi$
$941$	4.59323	+	2.95189i	0.149735	+	0.0962288i	−0.463628	+	0.886030i	$0.653453\pi$
$942$	−1.36363			−0.0444294
$943$	−5.67093	+	2.84627i	−0.184671	+	0.0926874i
$944$	31.8024			1.03508
$945$	1.30075	+	0.835939i	0.0423133	+	0.0271931i
$946$	−0.00223146	−	0.0155202i	−7.25511e−5	−	0.000504604i
$947$	−3.63380	−	7.95691i	−0.118083	−	0.258565i	0.841357	−	0.540480i	$-0.181757\pi$
$947$	−3.63380	−	7.95691i	−0.118083	−	0.258565i	−0.959439	+	0.281916i	$0.909030\pi$
$948$	0.842563	+	0.247399i	0.0273652	+	0.00803514i
$949$	−8.84215	+	19.3616i	−0.287028	+	0.628504i
$950$	−0.345855	+	0.399137i	−0.0112210	+	0.0129497i
$951$	0.849361	−	5.90743i	0.0275424	−	0.191562i
$952$	−0.337683	+	0.0991526i	−0.0109444	+	0.00321355i
$953$	−19.4239	−	22.4164i	−0.629203	−	0.726139i	0.348224	−	0.937411i	$-0.386785\pi$
$953$	−19.4239	−	22.4164i	−0.629203	−	0.726139i	−0.977427	+	0.211272i	$0.932239\pi$
$954$	−0.870395	+	0.559369i	−0.0281801	+	0.0181102i
$955$	−1.00730	+	0.647353i	−0.0325955	+	0.0209478i
$956$	28.1810	+	32.5227i	0.911440	+	1.05186i
$957$	0.422957	−	0.124191i	0.0136722	−	0.00401453i
$958$	0.0733415	−	0.510101i	0.00236956	−	0.0164806i
$959$	−5.22733	+	6.03266i	−0.168799	+	0.194805i
$960$	−5.01910	+	10.9903i	−0.161991	+	0.354711i
$961$	25.9063	+	7.60678i	0.835687	+	0.245380i
$962$	0.170645	+	0.373660i	0.00550181	+	0.0120473i
$963$	−1.22449	−	8.51650i	−0.0394586	−	0.274440i
$964$	2.55650	+	1.64296i	0.0823392	+	0.0529162i
$965$	4.85797			0.156384
$966$	−0.390772	−	0.161372i	−0.0125729	−	0.00519207i
$967$	25.2952			0.813438			0.406719	−	0.913553i	$-0.366673\pi$
$967$	25.2952			0.813438			0.406719	+	0.913553i	$0.366673\pi$
$968$	3.25608	+	2.09255i	0.104654	+	0.0672573i
$969$	−0.326757	−	2.27265i	−0.0104970	−	0.0730079i
$970$	0.369434	+	0.808947i	0.0118618	+	0.0259737i
$971$	−19.6680	−	5.77506i	−0.631178	−	0.185330i	−0.0495317	−	0.998773i	$-0.515773\pi$
$971$	−19.6680	−	5.77506i	−0.631178	−	0.185330i	−0.581646	+	0.813442i	$0.697591\pi$
$972$	−0.827602	+	1.81219i	−0.0265453	+	0.0581262i
$973$	2.39153	−	2.75997i	0.0766688	−	0.0884805i
$974$	0.382149	−	2.65790i	0.0122448	−	0.0851647i
$975$	4.76698	−	1.39971i	0.152666	−	0.0448267i
$976$	38.7216	+	44.6872i	1.23945	+	1.43040i
$977$	32.9981	−	21.2066i	1.05570	−	0.678459i	0.106881	−	0.994272i	$-0.465913\pi$
$977$	32.9981	−	21.2066i	1.05570	−	0.678459i	0.948822	+	0.315813i	$0.102277\pi$
$978$	1.46134	−	0.939148i	0.0467286	−	0.0300307i
$979$	−0.0323897	−	0.0373796i	−0.00103518	−	0.00119466i
$980$	2.95561	−	0.867845i	0.0944134	−	0.0277223i
$981$	0.712645	−	4.95656i	0.0227530	−	0.158251i
$982$	1.35664	−	1.56565i	0.0432922	−	0.0499618i
$983$	21.1549	−	46.3228i	0.674737	−	1.47747i	−0.193387	−	0.981122i	$-0.561947\pi$
$983$	21.1549	−	46.3228i	0.674737	−	1.47747i	0.868125	−	0.496346i	$-0.165325\pi$
$984$	−0.446772	−	0.131184i	−0.0142426	−	0.00418199i
$985$	11.2543	+	24.6436i	0.358593	+	0.785210i
$986$	−0.114856	−	0.798838i	−0.00365775	−	0.0254402i
$987$	0.590278	+	0.379349i	0.0187888	+	0.0120748i
$988$	8.70959			0.277089
$989$	13.8058	+	11.1010i	0.438998	+	0.352991i
$990$	0.00656328			0.000208595
$991$	−1.12941	−	0.725825i	−0.0358767	−	0.0230566i	0.522580	−	0.852591i	$-0.324970\pi$
$991$	−1.12941	−	0.725825i	−0.0358767	−	0.0230566i	−0.558456	+	0.829534i	$0.688606\pi$
$992$	0.299543	+	2.08337i	0.00951050	+	0.0661470i
$993$	−8.91647	−	19.5243i	−0.282956	−	0.619586i
$994$	−0.404264	−	0.118703i	−0.0128225	−	0.00376502i
$995$	5.41283	−	11.8525i	0.171598	−	0.375748i
$996$	2.29012	−	2.64294i	0.0725652	−	0.0837447i
$997$	8.26090	−	57.4559i	0.261625	−	1.81965i	−0.259020	−	0.965872i	$-0.583399\pi$
$997$	8.26090	−	57.4559i	0.261625	−	1.81965i	0.520645	−	0.853773i	$-0.325691\pi$
$998$	1.89102	−	0.555254i	0.0598593	−	0.0175763i
$999$	−1.60260	−	1.84950i	−0.0507040	−	0.0585155i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.b.232.1	yes	10
23.12	even	11	inner	483.2.q.b.127.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.b.127.1	✓	10	23.12	even	11	inner
483.2.q.b.232.1	yes	10	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0741615 + 0.0476607i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(-0.827602 - 1.81219i) q^{4} +(-1.48357 - 0.435615i) q^{5} +(0.0366213 - 0.0801894i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(0.0500861 - 0.348356i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-0.0892619 - 0.103014i) q^{10} +(0.0405070 - 0.0260323i) q^{11} +(-1.67597 + 1.07708i) q^{12} +(-1.24690 - 1.43900i) q^{13} +(-0.0845850 + 0.0248364i) q^{14} +(-0.220047 + 1.53046i) q^{15} +(-2.58895 + 2.98780i) q^{16} +(-0.415415 + 0.909632i) q^{17} +(-0.0845850 - 0.0248364i) q^{18} +(-0.953800 - 2.08853i) q^{19} +(0.438384 + 3.04903i) q^{20} +(0.841254 + 0.540641i) q^{21} +0.00424478 q^{22} +(-3.50654 + 3.27173i) q^{23} -0.351939 q^{24} +(-2.19505 - 1.41067i) q^{25} +(-0.0238883 - 0.166147i) q^{26} +(0.415415 + 0.909632i) q^{27} +(1.91153 + 0.561276i) q^{28} +(-3.80306 + 8.32753i) q^{29} +(-0.0892619 + 0.103014i) q^{30} +(0.284630 - 1.97964i) q^{31} +(-1.00977 + 0.296494i) q^{32} +(-0.0315321 - 0.0363899i) q^{33} +(-0.0741615 + 0.0476607i) q^{34} +(1.30075 - 0.835939i) q^{35} +(1.30463 + 1.50563i) q^{36} +(-2.34811 + 0.689466i) q^{37} +(0.0288056 - 0.200347i) q^{38} +(-1.24690 + 1.43900i) q^{39} +(-0.226055 + 0.494992i) q^{40} +(1.26946 + 0.372747i) q^{41} +(0.0366213 + 0.0801894i) q^{42} +(-0.525696 - 3.65630i) q^{43} +(-0.0806993 - 0.0518623i) q^{44} +1.54620 q^{45} +(-0.415983 + 0.0755121i) q^{46} +0.701665 q^{47} +(3.32584 + 2.13739i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.0955546 - 0.209235i) q^{50} +(0.959493 + 0.281733i) q^{51} +(-1.57581 + 3.45055i) q^{52} +(7.68576 - 8.86984i) q^{53} +(-0.0125459 + 0.0872586i) q^{54} +(-0.0714350 + 0.0209752i) q^{55} +(0.230471 + 0.265977i) q^{56} +(-1.93153 + 1.24132i) q^{57} +(-0.678936 + 0.436326i) q^{58} +(-5.26786 - 6.07944i) q^{59} +(2.95561 - 0.867845i) q^{60} +(2.12854 - 14.8043i) q^{61} +(0.115460 - 0.133248i) q^{62} +(0.415415 - 0.909632i) q^{63} +(7.49756 + 2.20148i) q^{64} +(1.22301 + 2.67803i) q^{65} +(-0.000604095 - 0.00420157i) q^{66} +(-9.85039 - 6.33046i) q^{67} +1.99223 q^{68} +(3.73746 + 3.00523i) q^{69} +0.136307 q^{70} +(4.02068 + 2.58393i) q^{71} +(0.0500861 + 0.348356i) q^{72} +(-4.64381 - 10.1685i) q^{73} +(-0.206999 - 0.0607805i) q^{74} +(-1.08393 + 2.37347i) q^{75} +(-2.99546 + 3.45694i) q^{76} +(-0.00685257 + 0.0476607i) q^{77} +(-0.161056 + 0.0472903i) q^{78} +(-0.288649 - 0.333119i) q^{79} +(5.14241 - 3.30483i) q^{80} +(0.841254 - 0.540641i) q^{81} +(0.0763796 + 0.0881468i) q^{82} +(-1.68427 + 0.494546i) q^{83} +(0.283524 - 1.97195i) q^{84} +(1.01255 - 1.16854i) q^{85} +(0.135275 - 0.296211i) q^{86} +(8.78400 + 2.57922i) q^{87} +(-0.00703967 - 0.0154147i) q^{88} +(-0.146185 - 1.01674i) q^{89} +(0.114669 + 0.0736930i) q^{90} +1.90407 q^{91} +(8.83102 + 3.64684i) q^{92} -2.00000 q^{93} +(0.0520365 + 0.0334418i) q^{94} +(0.505232 + 3.51397i) q^{95} +(0.437181 + 0.957293i) q^{96} +(-6.26007 - 1.83812i) q^{97} +(0.0366213 - 0.0801894i) q^{98} +(-0.0315321 + 0.0363899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - q^{3} - q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - q^{9} + 3 q^{10} + 9 q^{11} - 12 q^{12} - 15 q^{13} - 6 q^{14} + 6 q^{15} + 5 q^{16} + q^{17} - 6 q^{18} - 19 q^{19} - 5 q^{20}+ \cdots - 2 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - q^3 - q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - q^9 + 3 * q^10 + 9 * q^11 - 12 * q^12 - 15 * q^13 - 6 * q^14 + 6 * q^15 + 5 * q^16 + q^17 - 6 * q^18 - 19 * q^19 - 5 * q^20 - q^21 - 12 * q^22 - 21 * q^23 + 6 * q^24 + 2 * q^25 - 13 * q^26 - q^27 - q^28 + 3 * q^30 + 2 * q^31 + 7 * q^32 - 2 * q^33 - 5 * q^34 - 5 * q^35 + 10 * q^36 - 27 * q^37 + 18 * q^38 - 15 * q^39 - 3 * q^40 + 10 * q^41 - 6 * q^42 + 15 * q^43 + 9 * q^44 + 6 * q^45 - 5 * q^46 - 18 * q^47 + 5 * q^48 - q^49 + 34 * q^50 + q^51 + 18 * q^52 + 19 * q^53 + 5 * q^54 - 21 * q^55 - 5 * q^56 + 3 * q^57 - 13 * q^59 + 6 * q^60 - 18 * q^61 - 10 * q^62 - q^63 + 54 * q^64 + 2 * q^65 + 10 * q^66 - 18 * q^67 - 10 * q^68 + q^69 - 8 * q^70 + 38 * q^71 + 6 * q^72 + 14 * q^73 + 14 * q^74 + 2 * q^75 + 3 * q^76 - 13 * q^77 + 9 * q^78 + 25 * q^79 + 25 * q^80 - q^81 - 72 * q^82 - 19 * q^83 - q^84 + 5 * q^85 + 2 * q^86 + 33 * q^87 + q^88 - 17 * q^89 + 14 * q^90 - 4 * q^91 + 67 * q^92 - 20 * q^93 + 13 * q^94 + 37 * q^95 + 18 * q^96 - 49 * q^97 - 6 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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