LMFDB - Embedded newform 804.2.l.a.431.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(431,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("804.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.l (of order $6$, degree $2$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$132$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.17
Character	$\chi$	$=$	804.431
Dual form			804.2.l.a.707.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27761 - 0.606402i) q^{2} +(-0.369021 + 1.69228i) q^{3} +(1.26455 + 1.54948i) q^{4} -0.628413i q^{5} +(1.49767 - 1.93830i) q^{6} +(1.58089 - 0.912727i) q^{7} +(-0.675992 - 2.74646i) q^{8} +(-2.72765 - 1.24898i) q^{9} +O(q^{10})$	\(q+(-1.27761 - 0.606402i) q^{2} +(-0.369021 + 1.69228i) q^{3} +(1.26455 + 1.54948i) q^{4} -0.628413i q^{5} +(1.49767 - 1.93830i) q^{6} +(1.58089 - 0.912727i) q^{7} +(-0.675992 - 2.74646i) q^{8} +(-2.72765 - 1.24898i) q^{9} +(-0.381071 + 0.802864i) q^{10} +(1.13269 + 1.96187i) q^{11} +(-3.08881 + 1.56819i) q^{12} +(-2.71636 + 4.70488i) q^{13} +(-2.57323 + 0.207452i) q^{14} +(1.06345 + 0.231897i) q^{15} +(-0.801806 + 3.91881i) q^{16} +(-0.0570386 - 0.0329313i) q^{17} +(2.72748 + 3.24975i) q^{18} +(0.370018 + 0.213630i) q^{19} +(0.973716 - 0.794662i) q^{20} +(0.961212 + 3.01213i) q^{21} +(-0.257445 - 3.19336i) q^{22} +(-0.209633 + 0.363096i) q^{23} +(4.89724 - 0.130470i) q^{24} +4.60510 q^{25} +(6.32348 - 4.36377i) q^{26} +(3.12018 - 4.15506i) q^{27} +(3.41338 + 1.29537i) q^{28} +(-4.16787 + 2.40632i) q^{29} +(-1.21805 - 0.941153i) q^{30} +(5.22798 - 3.01837i) q^{31} +(3.40077 - 4.52048i) q^{32} +(-3.73802 + 1.19285i) q^{33} +(0.0529033 + 0.0766615i) q^{34} +(-0.573569 - 0.993451i) q^{35} +(-1.51399 - 5.80584i) q^{36} +(-2.50243 + 4.33434i) q^{37} +(-0.343191 - 0.497314i) q^{38} +(-6.95959 - 6.33305i) q^{39} +(-1.72591 + 0.424802i) q^{40} +(-6.76463 + 3.90556i) q^{41} +(0.598510 - 4.43119i) q^{42} +5.23747i q^{43} +(-1.60754 + 4.23597i) q^{44} +(-0.784872 + 1.71409i) q^{45} +(0.488011 - 0.336771i) q^{46} +(5.12132 + 8.87039i) q^{47} +(-6.33586 - 2.80301i) q^{48} +(-1.83386 + 3.17634i) q^{49} +(-5.88350 - 2.79254i) q^{50} +(0.0767775 - 0.0843732i) q^{51} +(-10.7251 + 1.74061i) q^{52} +7.94642i q^{53} +(-6.50599 + 3.41644i) q^{54} +(1.23286 - 0.711794i) q^{55} +(-3.57544 - 3.72485i) q^{56} +(-0.498066 + 0.547341i) q^{57} +(6.78410 - 0.546927i) q^{58} -1.76671 q^{59} +(0.985472 + 1.94105i) q^{60} +(0.214096 - 0.370826i) q^{61} +(-8.50964 + 0.686039i) q^{62} +(-5.45208 + 0.515106i) q^{63} +(-7.08607 + 3.71317i) q^{64} +(2.95660 + 1.70700i) q^{65} +(5.49907 + 0.742744i) q^{66} +(-8.11496 - 1.07116i) q^{67} +(-0.0211019 - 0.130024i) q^{68} +(-0.537102 - 0.488749i) q^{69} +(0.130365 + 1.61705i) q^{70} +(-5.27204 - 9.13145i) q^{71} +(-1.58639 + 8.33567i) q^{72} +(1.28646 - 2.22822i) q^{73} +(5.82547 - 4.02010i) q^{74} +(-1.69938 + 7.79313i) q^{75} +(0.136891 + 0.843483i) q^{76} +(3.58130 + 2.06766i) q^{77} +(5.05124 + 12.3114i) q^{78} +(1.06036 - 0.612201i) q^{79} +(2.46263 + 0.503865i) q^{80} +(5.88012 + 6.81353i) q^{81} +(11.0109 - 0.887686i) q^{82} +(-7.52293 + 13.0301i) q^{83} +(-3.45174 + 5.29838i) q^{84} +(-0.0206944 + 0.0358438i) q^{85} +(3.17601 - 6.69142i) q^{86} +(-2.53415 - 7.94121i) q^{87} +(4.62250 - 4.43708i) q^{88} -1.29595i q^{89} +(2.04218 - 1.71398i) q^{90} +9.91719i q^{91} +(-0.827704 + 0.134330i) q^{92} +(3.17871 + 9.96106i) q^{93} +(-1.16401 - 14.4384i) q^{94} +(0.134248 - 0.232524i) q^{95} +(6.39499 + 7.42321i) q^{96} +(-2.16361 + 3.74748i) q^{97} +(4.26908 - 2.94605i) q^{98} +(-0.639241 - 6.76598i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.27761	−	0.606402i	−0.903404	−	0.428791i
$2$	−1.27761	−	0.606402i	−0.903404	−	0.428791i
$3$	−0.369021	+	1.69228i	−0.213054	+	0.977040i
$3$	−0.369021	+	1.69228i	−0.213054	+	0.977040i
$4$	1.26455	+	1.54948i	0.632277	+	0.774742i
$5$		−	0.628413i		−	0.281035i	−0.990078	−	0.140517i	$-0.955123\pi$
$5$		−	0.628413i		−	0.281035i	0.990078	−	0.140517i	$-0.0448766\pi$
$6$	1.49767	−	1.93830i	0.611420	−	0.791306i
$7$	1.58089	−	0.912727i	0.597520	−	0.344978i	−0.170545	−	0.985350i	$-0.554553\pi$
$7$	1.58089	−	0.912727i	0.597520	−	0.344978i	0.768065	+	0.640371i	$0.221220\pi$
$8$	−0.675992	−	2.74646i	−0.238999	−	0.971020i
$9$	−2.72765	−	1.24898i	−0.909216	−	0.416325i
$10$	−0.381071	+	0.802864i	−0.120505	+	0.253888i
$11$	1.13269	+	1.96187i	0.341517	+	0.591525i	0.984715	−	0.174175i	$-0.0557258\pi$
$11$	1.13269	+	1.96187i	0.341517	+	0.591525i	−0.643197	+	0.765700i	$0.722393\pi$
$12$	−3.08881	+	1.56819i	−0.891664	+	0.452698i
$13$	−2.71636	+	4.70488i	−0.753383	+	1.30490i	0.192791	+	0.981240i	$0.438246\pi$
$13$	−2.71636	+	4.70488i	−0.753383	+	1.30490i	−0.946174	+	0.323658i	$0.895087\pi$
$14$	−2.57323	+	0.207452i	−0.687726	+	0.0554438i
$15$	1.06345	+	0.231897i	0.274582	+	0.0598756i
$16$	−0.801806	+	3.91881i	−0.200451	+	0.979704i
$17$	−0.0570386	−	0.0329313i	−0.0138339	−	0.00798701i	0.493067	−	0.869991i	$-0.335876\pi$
$17$	−0.0570386	−	0.0329313i	−0.0138339	−	0.00798701i	−0.506901	+	0.862004i	$0.669209\pi$
$18$	2.72748	+	3.24975i	0.642873	+	0.765973i
$19$	0.370018	+	0.213630i	0.0848878	+	0.0490100i	0.541843	−	0.840480i	$-0.317727\pi$
$19$	0.370018	+	0.213630i	0.0848878	+	0.0490100i	−0.456955	+	0.889490i	$0.651060\pi$
$20$	0.973716	−	0.794662i	0.217730	−	0.177692i
$21$	0.961212	+	3.01213i	0.209754	+	0.657300i
$22$	−0.257445	−	3.19336i	−0.0548875	−	0.680826i
$23$	−0.209633	+	0.363096i	−0.0437116	+	0.0757107i	−0.887053	−	0.461667i	$-0.847252\pi$
$23$	−0.209633	+	0.363096i	−0.0437116	+	0.0757107i	0.843342	+	0.537377i	$0.180585\pi$
$24$	4.89724	−	0.130470i	0.999645	−	0.0266321i
$25$	4.60510			0.921019
$26$	6.32348	−	4.36377i	1.24014	−	0.855806i
$27$	3.12018	−	4.15506i	0.600479	−	0.799641i
$28$	3.41338	+	1.29537i	0.645068	+	0.244802i
$29$	−4.16787	+	2.40632i	−0.773955	+	0.446843i	−0.834284	−	0.551336i	$-0.814118\pi$
$29$	−4.16787	+	2.40632i	−0.773955	+	0.446843i	0.0603289	+	0.998179i	$0.480785\pi$
$30$	−1.21805	−	0.941153i	−0.222385	−	0.171830i
$31$	5.22798	−	3.01837i	0.938973	−	0.542116i	0.0493345	−	0.998782i	$-0.484290\pi$
$31$	5.22798	−	3.01837i	0.938973	−	0.542116i	0.889638	+	0.456666i	$0.150957\pi$
$32$	3.40077	−	4.52048i	0.601176	−	0.799116i
$33$	−3.73802	+	1.19285i	−0.650706	+	0.207649i
$34$	0.0529033	+	0.0766615i	0.00907285	+	0.0131473i
$35$	−0.573569	−	0.993451i	−0.0969509	−	0.167924i
$36$	−1.51399	−	5.80584i	−0.252332	−	0.967641i
$37$	−2.50243	+	4.33434i	−0.411397	+	0.712560i	−0.995043	−	0.0994480i	$-0.968292\pi$
$37$	−2.50243	+	4.33434i	−0.411397	+	0.712560i	0.583646	+	0.812008i	$0.301626\pi$
$38$	−0.343191	−	0.497314i	−0.0556730	−	0.0806750i
$39$	−6.95959	−	6.33305i	−1.11443	−	1.01410i
$40$	−1.72591	+	0.424802i	−0.272890	+	0.0671671i
$41$	−6.76463	+	3.90556i	−1.05646	+	0.609947i	−0.924450	−	0.381302i	$-0.875476\pi$
$41$	−6.76463	+	3.90556i	−1.05646	+	0.609947i	−0.132008	+	0.991249i	$0.542142\pi$
$42$	0.598510	−	4.43119i	0.0923520	−	0.683748i
$43$			5.23747i			0.798707i	0.916797	+	0.399353i	$0.130765\pi$
$43$			5.23747i			0.798707i	−0.916797	+	0.399353i	$0.869235\pi$
$44$	−1.60754	+	4.23597i	−0.242346	+	0.638596i
$45$	−0.784872	+	1.71409i	−0.117002	+	0.255521i
$46$	0.488011	−	0.336771i	0.0719533	−	0.0496542i
$47$	5.12132	+	8.87039i	0.747022	+	1.29388i	0.949244	+	0.314540i	$0.101850\pi$
$47$	5.12132	+	8.87039i	0.747022	+	1.29388i	−0.202223	+	0.979340i	$0.564816\pi$
$48$	−6.33586	−	2.80301i	−0.914503	−	0.404579i
$49$	−1.83386	+	3.17634i	−0.261980	+	0.453762i
$50$	−5.88350	−	2.79254i	−0.832053	−	0.394925i
$51$	0.0767775	−	0.0843732i	0.0107510	−	0.0118146i
$52$	−10.7251	+	1.74061i	−1.48731	+	0.241379i
$53$			7.94642i			1.09152i	0.837940	+	0.545762i	$0.183760\pi$
$53$			7.94642i			1.09152i	−0.837940	+	0.545762i	$0.816240\pi$
$54$	−6.50599	+	3.41644i	−0.885353	+	0.464919i
$55$	1.23286	−	0.711794i	0.166239	−	0.0959783i
$56$	−3.57544	−	3.72485i	−0.477788	−	0.497754i
$57$	−0.498066	+	0.547341i	−0.0659705	+	0.0724971i
$58$	6.78410	−	0.546927i	0.890796	−	0.0718151i
$59$	−1.76671			−0.230007			−0.115003	−	0.993365i	$-0.536688\pi$
$59$	−1.76671			−0.230007			−0.115003	+	0.993365i	$0.536688\pi$
$60$	0.985472	+	1.94105i	0.127224	+	0.250589i
$61$	0.214096	−	0.370826i	0.0274122	−	0.0474793i	−0.851994	−	0.523552i	$-0.824607\pi$
$61$	0.214096	−	0.370826i	0.0274122	−	0.0474793i	0.879406	+	0.476072i	$0.157940\pi$
$62$	−8.50964	+	0.686039i	−1.08073	+	0.0871271i
$63$	−5.45208	+	0.515106i	−0.686898	+	0.0648972i
$64$	−7.08607	+	3.71317i	−0.885759	+	0.464146i
$65$	2.95660	+	1.70700i	0.366722	+	0.211727i
$66$	5.49907	+	0.742744i	0.676888	+	0.0914255i
$67$	−8.11496	−	1.07116i	−0.991400	−	0.130864i
$67$	−8.11496	−	1.07116i	−0.991400	−	0.130864i
$68$	−0.0211019	−	0.130024i	−0.00255899	−	0.0157677i
$69$	−0.537102	−	0.488749i	−0.0646595	−	0.0588385i
$70$	0.130365	+	1.61705i	0.0155816	+	0.193275i
$71$	−5.27204	−	9.13145i	−0.625677	−	1.08370i	−0.988410	−	0.151810i	$-0.951490\pi$
$71$	−5.27204	−	9.13145i	−0.625677	−	1.08370i	0.362733	−	0.931893i	$-0.381844\pi$
$72$	−1.58639	+	8.33567i	−0.186958	+	0.982368i
$73$	1.28646	−	2.22822i	0.150569	−	0.260794i	−0.780868	−	0.624696i	$-0.785223\pi$
$73$	1.28646	−	2.22822i	0.150569	−	0.260794i	0.931437	+	0.363903i	$0.118556\pi$
$74$	5.82547	−	4.02010i	0.677197	−	0.467327i
$75$	−1.69938	+	7.79313i	−0.196227	+	0.899873i
$76$	0.136891	+	0.843483i	0.0157025	+	0.0967541i
$77$	3.58130	+	2.06766i	0.408127	+	0.235632i
$78$	5.05124	+	12.3114i	0.571941	+	1.39400i
$79$	1.06036	−	0.612201i	0.119300	−	0.0688780i	−0.439162	−	0.898408i	$-0.644725\pi$
$79$	1.06036	−	0.612201i	0.119300	−	0.0688780i	0.558463	+	0.829530i	$0.311391\pi$
$80$	2.46263	+	0.503865i	0.275331	+	0.0563338i
$81$	5.88012	+	6.81353i	0.653347	+	0.757059i
$82$	11.0109	−	0.887686i	1.21595	−	0.0980285i
$83$	−7.52293	+	13.0301i	−0.825749	+	1.43024i	0.0755968	+	0.997138i	$0.475914\pi$
$83$	−7.52293	+	13.0301i	−0.825749	+	1.43024i	−0.901346	+	0.433100i	$0.857420\pi$
$84$	−3.45174	+	5.29838i	−0.376616	+	0.578101i
$85$	−0.0206944	+	0.0358438i	−0.00224463	+	0.00388781i
$86$	3.17601	−	6.69142i	0.342478	−	0.721555i
$87$	−2.53415	−	7.94121i	−0.271689	−	0.851387i
$88$	4.62250	−	4.43708i	0.492761	−	0.472994i
$89$		−	1.29595i		−	0.137370i	−0.997638	−	0.0686852i	$-0.978120\pi$
$89$		−	1.29595i		−	0.137370i	0.997638	−	0.0686852i	$-0.0218804\pi$
$90$	2.04218	−	1.71398i	0.215265	−	0.180670i
$91$			9.91719i			1.03960i
$92$	−0.827704	+	0.134330i	−0.0862941	+	0.0140049i
$93$	3.17871	+	9.96106i	0.329617	+	1.03291i
$94$	−1.16401	−	14.4384i	−0.120059	−	1.48921i
$95$	0.134248	−	0.232524i	0.0137735	−	0.0238564i
$96$	6.39499	+	7.42321i	0.652686	+	0.757629i
$97$	−2.16361	+	3.74748i	−0.219681	+	0.380499i	−0.954710	−	0.297536i	$-0.903835\pi$
$97$	−2.16361	+	3.74748i	−0.219681	+	0.380499i	0.735029	+	0.678035i	$0.237168\pi$
$98$	4.26908	−	2.94605i	0.431243	−	0.297596i
$99$	−0.639241	−	6.76598i	−0.0642461	−	0.680007i
$100$	5.82339	+	7.13553i	0.582339	+	0.713553i
$101$	−7.84972	+	4.53204i	−0.781077	+	0.450955i	−0.836812	−	0.547491i	$-0.815583\pi$
$101$	−7.84972	+	4.53204i	−0.781077	+	0.450955i	0.0557352	+	0.998446i	$0.482250\pi$
$102$	−0.149255	+	0.0612377i	−0.0147785	+	0.00606344i
$103$	9.83064	−	5.67572i	0.968642	−	0.559245i	0.0698197	−	0.997560i	$-0.477758\pi$
$103$	9.83064	−	5.67572i	0.968642	−	0.559245i	0.898822	+	0.438314i	$0.144424\pi$
$104$	14.7580	+	4.27992i	1.44714	+	0.419680i
$105$	1.89286	−	0.604038i	0.184724	−	0.0589481i
$106$	4.81872	−	10.1524i	0.468036	−	0.986087i
$107$	2.82554			0.273155			0.136577	−	0.990629i	$-0.456390\pi$
$107$	2.82554			0.273155			0.136577	+	0.990629i	$0.456390\pi$
$108$	10.3838	−	0.419623i	0.999184	−	0.0403783i
$109$	0.695969			0.0666617			0.0333309	−	0.999444i	$-0.489388\pi$
$109$	0.695969			0.0666617			0.0333309	+	0.999444i	$0.489388\pi$
$110$	−2.00675	+	0.161782i	−0.191336	+	0.0154253i
$111$	−6.41148	−	5.83428i	−0.608550	−	0.553765i
$112$	2.30924	+	6.92704i	0.218203	+	0.654544i
$113$	−10.5043	+	6.06463i	−0.988157	+	0.570513i	−0.904723	−	0.426001i	$-0.859922\pi$
$113$	−10.5043	+	6.06463i	−0.988157	+	0.570513i	−0.0834339	+	0.996513i	$0.526589\pi$
$114$	0.968241	−	0.397258i	0.0906840	−	0.0372066i
$115$	0.228174	+	0.131736i	0.0212773	+	0.0122845i
$116$	−8.99906	−	3.41513i	−0.835542	−	0.317087i
$117$	13.2855	−	9.44057i	1.22825	−	0.872781i
$118$	2.25716	+	1.07134i	0.207789	+	0.0986247i
$119$	−0.120229			−0.0110214
$120$	−0.0819891	−	3.07749i	−0.00748454	−	0.280935i
$121$	2.93405	−	5.08192i	0.266732	−	0.461993i
$122$	−0.498400	+	0.343941i	−0.0451230	+	0.0311389i
$123$	−4.11303	−	12.8889i	−0.370859	−	1.16215i
$124$	11.2880	+	4.28377i	1.01369	+	0.384694i
$125$		−	6.03597i		−	0.539873i
$126$	7.27798	+	2.64805i	0.648374	+	0.235907i
$127$	0.572523	−	0.330546i	0.0508032	−	0.0293312i	−0.474383	−	0.880318i	$-0.657329\pi$
$127$	0.572523	−	0.330546i	0.0508032	−	0.0293312i	0.525186	+	0.850987i	$0.323996\pi$
$128$	11.3049	−	0.446961i	0.999219	−	0.0395062i
$129$	−8.86328	−	1.93273i	−0.780369	−	0.170168i
$130$	−2.74225	−	3.97376i	−0.240511	−	0.348522i
$131$	15.5282			1.35670			0.678352	−	0.734737i	$-0.262695\pi$
$131$	15.5282			1.35670			0.678352	+	0.734737i	$0.262695\pi$
$132$	−6.57524	−	4.28358i	−0.572301	−	0.372838i
$133$	0.779942			0.0676296
$134$	9.71817	+	6.28945i	0.839522	+	0.543326i
$135$	−2.61109	−	1.96076i	−0.224727	−	0.168755i
$136$	−0.0518867	+	0.178916i	−0.00444925	+	0.0153419i
$137$			6.71866i			0.574014i	0.957928	+	0.287007i	$0.0926603\pi$
$137$			6.71866i			0.574014i	−0.957928	+	0.287007i	$0.907340\pi$
$138$	0.389826	+	0.950128i	0.0331842	+	0.0808803i
$139$			4.61117i			0.391114i	0.980692	+	0.195557i	$0.0626515\pi$
$139$			4.61117i			0.391114i	−0.980692	+	0.195557i	$0.937349\pi$
$140$	0.814028	−	2.14501i	0.0687979	−	0.181286i
$141$	−16.9011	+	5.39337i	−1.42333	+	0.454204i
$142$	1.19827	+	14.8634i	0.100557	+	1.24731i
$143$	−12.3071			−1.02917
$144$	7.08155	−	9.68771i	0.590129	−	0.807309i
$145$	1.51216	+	2.61915i	0.125578	+	0.217508i
$146$	−2.99479	+	2.06667i	−0.247851	+	0.171039i
$147$	−4.69853	−	4.27554i	−0.387528	−	0.352641i
$148$	−9.88044	+	1.60353i	−0.812168	+	0.131809i
$149$		−	19.4452i		−	1.59302i	−0.604628	−	0.796508i	$-0.706678\pi$
$149$		−	19.4452i		−	1.59302i	0.604628	−	0.796508i	$-0.293322\pi$
$150$	6.89690	−	8.92605i	0.563130	−	0.728809i
$151$	19.3843	+	11.1915i	1.57747	+	0.910755i	0.995211	+	0.0977543i	$0.0311659\pi$
$151$	19.3843	+	11.1915i	1.57747	+	0.910755i	0.582263	+	0.813000i	$0.302167\pi$
$152$	0.336596	−	1.16065i	0.0273016	−	0.0941411i
$153$	0.114451	+	0.161065i	0.00925281	+	0.0130213i
$154$	−3.32166	−	4.81337i	−0.267667	−	0.387872i
$155$	−1.89679	−	3.28533i	−0.152353	−	0.263884i
$156$	1.01218	−	18.7923i	0.0810397	−	1.50459i
$157$	7.27034	−	12.5926i	0.580236	−	1.00500i	−0.415215	−	0.909723i	$-0.636294\pi$
$157$	7.27034	−	12.5926i	0.580236	−	1.00500i	0.995451	−	0.0952752i	$-0.0303731\pi$
$158$	−1.72597	+	0.139146i	−0.137310	+	0.0110698i
$159$	−13.4476	−	2.93239i	−1.06646	−	0.232554i
$160$	−2.84073	−	2.13709i	−0.224580	−	0.168951i
$161$			0.765352i			0.0603182i
$162$	−3.38074	−	12.2707i	−0.265616	−	0.964079i
$163$	−17.3821	+	10.0356i	−1.36147	+	0.786046i	−0.989820	−	0.142326i	$-0.954542\pi$
$163$	−17.3821	+	10.0356i	−1.36147	+	0.786046i	−0.371652	+	0.928372i	$0.621209\pi$
$164$	−14.6059	−	5.54290i	−1.14053	−	0.432828i
$165$	0.749605	+	2.34902i	0.0583567	+	0.182871i
$166$	17.5128	−	12.0854i	1.35926	−	0.938010i
$167$	2.15803	+	3.73781i	0.166993	+	0.289240i	0.937361	−	0.348359i	$-0.113261\pi$
$167$	2.15803	+	3.73781i	0.166993	+	0.289240i	−0.770368	+	0.637599i	$0.779928\pi$
$168$	7.62292	−	4.67610i	0.588121	−	0.360769i
$169$	−8.25723	−	14.3019i	−0.635172	−	1.10015i
$170$	0.0481751	−	0.0332451i	0.00369486	−	0.00254979i
$171$	−0.742459	−	1.04485i	−0.0567773	−	0.0799016i
$172$	−8.11538	+	6.62306i	−0.618792	+	0.505004i
$173$	−3.41512	−	1.97172i	−0.259646	−	0.149907i	0.364527	−	0.931193i	$-0.381231\pi$
$173$	−3.41512	−	1.97172i	−0.259646	−	0.149907i	−0.624173	+	0.781286i	$0.714564\pi$
$174$	−1.57792	+	11.6824i	−0.119622	+	0.885644i
$175$	7.28015	−	4.20320i	0.550328	−	0.317732i
$176$	−8.59639	+	2.86575i	−0.647977	+	0.216014i
$177$	0.651954	−	2.98978i	0.0490039	−	0.224726i
$178$	−0.785866	+	1.65571i	−0.0589031	+	0.124101i
$179$	18.3886			1.37443			0.687213	−	0.726456i	$-0.258834\pi$
$179$	18.3886			1.37443			0.687213	+	0.726456i	$0.258834\pi$
$180$	−3.64847	+	0.951411i	−0.271941	+	0.0709140i
$181$	3.39464	+	5.87970i	0.252322	+	0.437034i	0.964165	−	0.265305i	$-0.0854725\pi$
$181$	3.39464	+	5.87970i	0.252322	+	0.437034i	−0.711843	+	0.702339i	$0.752139\pi$
$182$	6.01380	−	12.6703i	0.445772	−	0.939182i
$183$	0.548536	+	0.499154i	0.0405490	+	0.0368985i
$184$	1.13894	+	0.330300i	0.0839636	+	0.0243500i
$185$	2.72375	+	1.57256i	0.200254	+	0.115617i
$186$	1.97926	−	14.6539i	0.145127	−	1.07448i
$187$		−	0.149203i		−	0.0109108i
$188$	−7.26835	+	19.1525i	−0.530099	+	1.39684i
$189$	1.14023	−	9.41656i	0.0829393	−	0.684954i
$190$	−0.312518	+	0.215666i	−0.0226725	+	0.0156460i
$191$	9.40405	−	16.2883i	0.680453	−	1.17858i	−0.294389	−	0.955686i	$-0.595116\pi$
$191$	9.40405	−	16.2883i	0.680453	−	1.17858i	0.974843	−	0.222894i	$-0.0715505\pi$
$192$	−3.66883	−	13.3619i	−0.264775	−	0.964310i
$193$	−9.03880			−0.650627			−0.325313	−	0.945606i	$-0.605470\pi$
$193$	−9.03880			−0.650627			−0.325313	+	0.945606i	$0.605470\pi$
$194$	5.03672	−	3.47579i	0.361615	−	0.249547i
$195$	−3.97977	+	4.37350i	−0.284997	+	0.313193i
$196$	−7.24070	+	1.17511i	−0.517193	+	0.0839367i
$197$	4.20221	−	2.42615i	0.299395	−	0.172856i	−0.342776	−	0.939417i	$-0.611367\pi$
$197$	4.20221	−	2.42615i	0.299395	−	0.172856i	0.642171	+	0.766561i	$0.278034\pi$
$198$	−3.28620	+	9.03189i	−0.233540	+	0.641869i
$199$	0.814838	+	0.470447i	0.0577623	+	0.0333491i	0.528603	−	0.848869i	$-0.322716\pi$
$199$	0.814838	+	0.470447i	0.0577623	+	0.0333491i	−0.470841	+	0.882218i	$0.656049\pi$
$200$	−3.11301	−	12.6477i	−0.220123	−	0.894328i
$201$	4.80730	−	13.3375i	0.339081	−	0.940757i
$202$	12.7771	−	1.03008i	0.898993	−	0.0724759i
$203$	−4.39263	+	7.60826i	−0.308302	+	0.533995i
$204$	0.227824	+	0.0122710i	0.0159509	+	0.000859144i
$205$	2.45431	+	4.25098i	0.171416	+	0.296902i
$206$	−16.0014	+	1.29002i	−1.11487	+	0.0898800i
$207$	1.02530	−	0.728570i	0.0712635	−	0.0506391i
$208$	−16.2595	−	14.4173i	−1.12740	−	0.999661i
$209$			0.967901i			0.0669511i
$210$	−2.78462	−	0.376111i	−0.192157	−	0.0259541i
$211$	3.09511	+	1.78696i	0.213076	+	0.123019i	0.602740	−	0.797938i	$-0.294076\pi$
$211$	3.09511	+	1.78696i	0.213076	+	0.123019i	−0.389664	+	0.920957i	$0.627409\pi$
$212$	−12.3129	+	10.0487i	−0.845650	+	0.690146i
$213$	17.3985	−	5.55210i	1.19213	−	0.380424i
$214$	−3.60992	−	1.71341i	−0.246769	−	0.117126i
$215$	3.29129			0.224464
$216$	−13.5209	−	5.76066i	−0.919981	−	0.391963i
$217$	5.50990	−	9.54344i	0.374037	−	0.647851i
$218$	−0.889174	−	0.422036i	−0.0602224	−	0.0285839i
$219$	3.29605	+	2.99932i	0.222726	+	0.202675i
$220$	2.66194	+	1.01020i	0.179468	+	0.0681077i
$221$	0.309875	−	0.178906i	0.0208445	−	0.0120345i
$222$	4.65342	+	11.3418i	0.312317	+	0.761215i
$223$		−	25.1877i		−	1.68669i	−0.537371	−	0.843346i	$-0.680583\pi$
$223$		−	25.1877i		−	1.68669i	0.537371	−	0.843346i	$-0.319417\pi$
$224$	1.25027	−	10.2504i	0.0835371	−	0.684881i
$225$	−12.5611	−	5.75165i	−0.837405	−	0.383444i
$226$	17.0979	−	1.37842i	1.13734	−	0.0916908i
$227$	8.79470	+	15.2329i	0.583725	+	1.01104i	0.995033	+	0.0995450i	$0.0317387\pi$
$227$	8.79470	+	15.2329i	0.583725	+	1.01104i	−0.411308	+	0.911496i	$0.634928\pi$
$228$	−1.47793	−	0.0796038i	−0.0978782	−	0.00527189i
$229$	2.57678	−	4.46311i	0.170278	−	0.294931i	−0.768239	−	0.640163i	$-0.778867\pi$
$229$	2.57678	−	4.46311i	0.170278	−	0.294931i	0.938517	+	0.345233i	$0.112200\pi$
$230$	−0.211631	−	0.306672i	−0.0139546	−	0.0202214i
$231$	−4.82065	+	5.29756i	−0.317175	+	0.348554i
$232$	9.42632	+	9.82024i	0.618868	+	0.644730i
$233$	−5.10552	+	2.94767i	−0.334474	+	0.193109i	−0.657826	−	0.753170i	$-0.728524\pi$
$233$	−5.10552	+	2.94767i	−0.334474	+	0.193109i	0.323352	+	0.946279i	$0.395190\pi$
$234$	−22.6985	+	4.00496i	−1.48385	+	0.261812i
$235$	5.57427	−	3.21831i	0.363625	−	0.209939i
$236$	−2.23411	−	2.73750i	−0.145428	−	0.178196i
$237$	0.644722	+	2.02035i	0.0418792	+	0.131236i
$238$	0.153605	+	0.0729071i	0.00995676	+	0.00472586i
$239$	13.8768	+	24.0353i	0.897615	+	1.55472i	0.830534	+	0.556968i	$0.188035\pi$
$239$	13.8768	+	24.0353i	0.897615	+	1.55472i	0.0670812	+	0.997748i	$0.478631\pi$
$240$	−1.76145	+	3.98154i	−0.113701	+	0.257007i
$241$	−13.3552			−0.860281			−0.430141	−	0.902762i	$-0.641536\pi$
$241$	−13.3552			−0.860281			−0.430141	+	0.902762i	$0.641536\pi$
$242$	−6.83024	+	4.71348i	−0.439065	+	0.302994i
$243$	−13.7003	+	7.43650i	−0.878875	+	0.477052i
$244$	0.845325	−	0.137190i	0.0541164	−	0.00878270i
$245$	1.99605	+	1.15242i	0.127523	+	0.0736254i
$246$	−2.56102	+	18.9611i	−0.163285	+	1.20892i
$247$	−2.01020	+	1.16059i	−0.127906	+	0.0738466i
$248$	−11.8239	−	12.3180i	−0.750819	−	0.782196i
$249$	−19.2745	−	17.5393i	−1.22147	−	1.11151i
$250$	−3.66022	+	7.71159i	−0.231493	+	0.487724i
$251$	8.37072	−	14.4985i	0.528355	−	0.915138i	−0.471098	−	0.882081i	$-0.656142\pi$
$251$	8.37072	−	14.4985i	0.528355	−	0.915138i	0.999453	−	0.0330571i	$-0.0105243\pi$
$252$	−7.69260	−	7.79654i	−0.484588	−	0.491136i
$253$	−0.949794			−0.0597131
$254$	−0.931903	+	0.0751291i	−0.0584728	+	0.00471402i
$255$	−0.0530212	−	0.0482480i	−0.00332032	−	0.00302140i
$256$	−14.7142	−	6.28425i	−0.919638	−	0.392766i
$257$	14.8816	−	8.59187i	0.928286	−	0.535946i	0.0420172	−	0.999117i	$-0.486622\pi$
$257$	14.8816	−	8.59187i	0.928286	−	0.535946i	0.886269	+	0.463170i	$0.153288\pi$
$258$	10.1518	+	7.84398i	0.632022	+	0.488345i
$259$			9.13614i			0.567692i
$260$	1.09382	+	6.73980i	0.0678359	+	0.417985i
$261$	14.3739	−	1.35803i	0.889724	−	0.0840599i
$262$	−19.8389	−	9.41632i	−1.22565	−	0.581742i
$263$	18.1057			1.11645			0.558223	−	0.829691i	$-0.311483\pi$
$263$	18.1057			1.11645			0.558223	+	0.829691i	$0.311483\pi$
$264$	5.80300	+	9.45996i	0.357150	+	0.582220i
$265$	4.99363			0.306756
$266$	−0.996459	−	0.472958i	−0.0610968	−	0.0289989i
$267$	2.19311	+	0.478232i	0.134216	+	0.0292673i
$268$	−8.60206	−	13.9286i	−0.525454	−	0.850822i
$269$		−	29.9350i		−	1.82517i	−0.408890	−	0.912584i	$-0.634084\pi$
$269$		−	29.9350i		−	1.82517i	0.408890	−	0.912584i	$-0.365916\pi$
$270$	2.14694	+	4.08845i	0.130658	+	0.248815i
$271$		−	1.84711i		−	0.112204i	−0.998425	−	0.0561020i	$-0.982133\pi$
$271$		−	1.84711i		−	0.112204i	0.998425	−	0.0561020i	$-0.0178672\pi$
$272$	0.174785	−	0.197119i	0.0105979	−	0.0119521i
$273$	−16.7827	−	3.65965i	−1.01573	−	0.221492i
$274$	4.07421	−	8.58380i	0.246132	−	0.518566i
$275$	5.21612	+	9.03459i	0.314544	+	0.544806i
$276$	0.0781147	−	1.45028i	0.00470195	−	0.0872966i
$277$	27.3477			1.64316			0.821581	−	0.570091i	$-0.193092\pi$
$277$	27.3477			1.64316			0.821581	+	0.570091i	$0.193092\pi$
$278$	2.79622	−	5.89125i	0.167706	−	0.353334i
$279$	−18.0300	+	1.70345i	−1.07943	+	0.101983i
$280$	−2.34075	+	2.24685i	−0.139886	+	0.134275i
$281$	−10.0390	−	5.79605i	−0.598879	−	0.345763i	0.169721	−	0.985492i	$-0.445713\pi$
$281$	−10.0390	−	5.79605i	−0.598879	−	0.345763i	−0.768601	+	0.639729i	$0.779047\pi$
$282$	24.8635	+	3.35824i	1.48060	+	0.199981i
$283$		−	23.2660i		−	1.38302i	−0.722367	−	0.691510i	$-0.756946\pi$
$283$		−	23.2660i		−	1.38302i	0.722367	−	0.691510i	$-0.243054\pi$
$284$	7.48225	−	19.7162i	0.443990	−	1.16994i
$285$	0.343956	+	0.312991i	0.0203742	+	0.0185400i
$286$	15.7237	+	7.46306i	0.929759	+	0.441300i
$287$	−7.12943	+	12.3485i	−0.420837	+	0.728911i
$288$	−14.9221	+	8.08281i	−0.879291	+	0.476284i
$289$	−8.49783	−	14.7187i	−0.499872	−	0.865804i
$290$	−0.343696	−	4.26322i	−0.0201825	−	0.250345i
$291$	−5.54338	−	5.04434i	−0.324959	−	0.295704i
$292$	5.07940	−	0.824350i	0.297249	−	0.0482414i
$293$			1.99695i			0.116663i	0.998297	+	0.0583316i	$0.0185781\pi$
$293$			1.99695i			0.116663i	−0.998297	+	0.0583316i	$0.981422\pi$
$294$	3.41017	+	8.31165i	0.198885	+	0.484746i
$295$			1.11023i			0.0646399i
$296$	13.5957	+	3.94284i	0.790234	+	0.229173i
$297$	11.6859	+	1.41501i	0.678082	+	0.0821072i
$298$	−11.7916	+	24.8434i	−0.683070	+	1.43914i
$299$	−1.13888	−	1.97260i	−0.0658631	−	0.114078i
$300$	−14.2243	+	7.22168i	−0.821240	+	0.416944i
$301$	4.78038	+	8.27986i	0.275537	+	0.477243i
$302$	−17.9790	−	26.0531i	−1.03457	−	1.49919i
$303$	−4.77279	−	14.9564i	−0.274189	−	0.859221i
$304$	−1.13386	+	1.27874i	−0.0650312	+	0.0733408i
$305$	−0.233032	−	0.134541i	−0.0133433	−	0.00770379i
$306$	−0.0485533	−	0.275181i	−0.00277561	−	0.0157310i
$307$	−10.6402	−	6.14314i	−0.607270	−	0.350607i	0.164626	−	0.986356i	$-0.447358\pi$
$307$	−10.6402	−	6.14314i	−0.607270	−	0.350607i	−0.771896	+	0.635749i	$0.780692\pi$
$308$	1.32493	+	8.16384i	0.0754951	+	0.465178i
$309$	5.97722	+	18.7307i	0.340032	+	1.06555i
$310$	0.431116	+	5.34757i	0.0244857	+	0.303722i
$311$	21.6237			1.22617			0.613084	−	0.790018i	$-0.289929\pi$
$311$	21.6237			1.22617			0.613084	+	0.790018i	$0.289929\pi$
$312$	−12.6888	+	23.3953i	−0.718364	+	1.32450i
$313$	5.10662			0.288643			0.144322	−	0.989531i	$-0.453900\pi$
$313$	5.10662			0.288643			0.144322	+	0.989531i	$0.453900\pi$
$314$	−16.9248	+	11.6796i	−0.955122	+	0.659120i
$315$	0.323699	+	3.42616i	0.0182384	+	0.193042i
$316$	2.28948	+	0.868855i	0.128793	+	0.0488769i
$317$	15.6078	+	9.01117i	0.876622	+	0.506118i	0.869543	−	0.493857i	$-0.164413\pi$
$317$	15.6078	+	9.01117i	0.876622	+	0.506118i	0.00707882	+	0.999975i	$0.497747\pi$
$318$	15.4025	+	11.9011i	0.863730	+	0.667380i
$319$	−9.44178	−	5.45121i	−0.528638	−	0.305209i
$320$	2.33340	+	4.45298i	0.130441	+	0.248929i
$321$	−1.04268	+	4.78161i	−0.0581968	+	0.266883i
$322$	0.464111	−	0.977819i	0.0258639	−	0.0544917i
$323$	−0.0140702	−	0.0243703i	−0.000782887	−	0.00135600i
$324$	−3.12173	+	17.7272i	−0.173429	+	0.984846i
$325$	−12.5091	+	21.6664i	−0.693880	+	1.20184i
$326$	28.2931	−	2.28096i	1.56701	−	0.126331i
$327$	−0.256827	+	1.17778i	−0.0142026	+	0.0651312i
$328$	15.2993	+	15.9387i	0.844763	+	0.880065i
$329$	16.1925	+	9.34874i	0.892721	+	0.515413i
$330$	0.466750	−	3.45568i	0.0256937	−	0.190229i
$331$	14.8370	−	8.56615i	0.815516	−	0.470838i	−0.0333519	−	0.999444i	$-0.510618\pi$
$331$	14.8370	−	8.56615i	0.815516	−	0.470838i	0.848868	+	0.528605i	$0.177285\pi$
$332$	−29.7031	+	4.82060i	−1.63017	+	0.264565i
$333$	12.2392	−	8.69707i	0.670705	−	0.476596i
$334$	−0.490493	−	6.08408i	−0.0268386	−	0.332906i
$335$	−0.673133	+	5.09955i	−0.0367772	+	0.278618i
$336$	−12.5747	+	1.35167i	−0.686005	+	0.0737397i
$337$	−12.2157	+	21.1583i	−0.665433	+	1.15256i	0.313735	+	0.949511i	$0.398420\pi$
$337$	−12.2157	+	21.1583i	−0.665433	+	1.15256i	−0.979168	+	0.203053i	$0.934914\pi$
$338$	1.87677	+	23.2795i	0.102083	+	1.26624i
$339$	−6.38679	−	20.0141i	−0.346883	−	1.08702i
$340$	−0.0817087	+	0.0132607i	−0.00443128	+	0.000719164i
$341$	11.8433	+	6.83774i	0.641351	+	0.370284i
$342$	0.314972	+	1.78513i	0.0170317	+	0.0965290i
$343$			19.4734i			1.05147i
$344$	14.3845	−	3.54049i	0.775560	−	0.190890i
$345$	−0.307136	+	0.337522i	−0.0165357	+	0.0181716i
$346$	3.16752	+	4.59001i	0.170287	+	0.246761i
$347$	10.8661	+	18.8206i	0.583323	+	1.01034i	0.995082	+	0.0990520i	$0.0315810\pi$
$347$	10.8661	+	18.8206i	0.583323	+	1.01034i	−0.411760	+	0.911293i	$0.635086\pi$
$348$	9.10021	−	13.9687i	0.487822	−	0.748802i
$349$	−10.8609			−0.581372			−0.290686	−	0.956819i	$-0.593883\pi$
$349$	−10.8609			−0.581372			−0.290686	+	0.956819i	$0.593883\pi$
$350$	−11.8500	+	0.955334i	−0.633409	+	0.0510648i
$351$	11.0735	+	25.9667i	0.591059	+	1.38600i
$352$	12.7206	+	1.55157i	0.678010	+	0.0826990i
$353$	21.4915	+	12.4082i	1.14388	+	0.660419i	0.947388	−	0.320086i	$-0.103712\pi$
$353$	21.4915	+	12.4082i	1.14388	+	0.660419i	0.196491	+	0.980506i	$0.437045\pi$
$354$	−2.64595	+	3.42442i	−0.140631	+	0.182006i
$355$	−5.73832	+	3.31302i	−0.304558	+	0.175837i
$356$	2.00805	−	1.63880i	0.106427	−	0.0868561i
$357$	0.0443670	−	0.203462i	0.00234815	−	0.0107683i
$358$	−23.4933	−	11.1509i	−1.24166	−	0.589341i
$359$	−34.3809			−1.81455			−0.907277	−	0.420535i	$-0.861843\pi$
$359$	−34.3809			−1.81455			−0.907277	+	0.420535i	$0.861843\pi$
$360$	5.23824	+	0.996909i	0.276080	+	0.0525417i
$361$	−9.40872	−	16.2964i	−0.495196	−	0.857705i
$362$	−0.771560	−	9.57045i	−0.0405523	−	0.503012i
$363$	7.51733	+	6.84058i	0.394557	+	0.359037i
$364$	−15.3665	+	12.5408i	−0.805425	+	0.657317i
$365$	−1.40024	−	0.808430i	−0.0732920	−	0.0423152i
$366$	−0.398125	−	0.970355i	−0.0208103	−	0.0507213i
$367$	6.15053	−	3.55101i	0.321055	−	0.185361i	−0.330808	−	0.943698i	$-0.607321\pi$
$367$	6.15053	−	3.55101i	0.321055	−	0.185361i	0.651863	+	0.758337i	$0.273988\pi$
$368$	−1.25482	−	1.11265i	−0.0654120	−	0.0580007i
$369$	23.3295	−	2.20414i	1.21448	−	0.114743i
$370$	−2.52628	−	3.66080i	−0.131335	−	0.190316i
$371$	7.25291	+	12.5624i	0.376552	+	0.652208i
$372$	−11.4149	+	17.5217i	−0.591833	+	0.908456i
$373$	15.1394	+	26.2221i	0.783886	+	1.35773i	0.929662	+	0.368413i	$0.120099\pi$
$373$	15.1394	+	26.2221i	0.783886	+	1.35773i	−0.145776	+	0.989318i	$0.546568\pi$
$374$	−0.0904770	+	0.190623i	−0.00467845	+	0.00985686i
$375$	10.2146	+	2.22740i	0.527478	+	0.115022i
$376$	20.9002	−	20.0618i	1.07784	−	1.03461i
$377$		−	26.1458i		−	1.34658i
$378$	−7.16698	+	11.3392i	−0.368629	+	0.583226i
$379$	−9.64639	−	5.56935i	−0.495502	−	0.286078i	0.231352	−	0.972870i	$-0.425685\pi$
$379$	−9.64639	−	5.56935i	−0.495502	−	0.286078i	−0.726854	+	0.686792i	$0.759018\pi$
$380$	0.530055	−	0.0860242i	0.0271913	−	0.00441295i
$381$	0.348105	+	1.09085i	0.0178340	+	0.0558859i
$382$	−21.8919	+	15.1074i	−1.12009	+	0.772962i
$383$	−7.48054	+	12.9567i	−0.382238	+	0.662055i	−0.991382	−	0.131005i	$-0.958180\pi$
$383$	−7.48054	+	12.9567i	−0.382238	+	0.662055i	0.609144	+	0.793059i	$0.291513\pi$
$384$	−3.41535	+	19.2960i	−0.174289	+	0.984695i
$385$	1.29935	−	2.25054i	0.0662209	−	0.114698i
$386$	11.5480	+	5.48114i	0.587779	+	0.278983i
$387$	6.54147	−	14.2860i	0.332522	−	0.726197i
$388$	−8.54266	+	1.38641i	−0.433688	+	0.0703845i
$389$	26.6025	+	15.3589i	1.34880	+	0.778729i	0.988079	−	0.153946i	$-0.0491981\pi$
$389$	26.6025	+	15.3589i	1.34880	+	0.778729i	0.360719	+	0.932675i	$0.382531\pi$
$390$	7.73667	−	3.17427i	0.391762	−	0.160735i
$391$	0.0239144	−	0.0138070i	0.00120940	−	0.000698249i
$392$	9.96335	+	2.88944i	0.503225	+	0.145939i
$393$	−5.73022	+	26.2781i	−0.289051	+	1.32555i
$394$	−6.83999	+	0.551433i	−0.344594	+	0.0277808i
$395$	−0.384715	−	0.666346i	−0.0193571	−	0.0335275i
$396$	9.67543	−	9.54644i	0.486209	−	0.479727i
$397$	2.21239			0.111037			0.0555185	−	0.998458i	$-0.482319\pi$
$397$	2.21239			0.111037			0.0555185	+	0.998458i	$0.482319\pi$
$398$	−0.755762	−	1.09516i	−0.0378829	−	0.0548956i
$399$	−0.287815	+	1.31988i	−0.0144088	+	0.0660768i
$400$	−3.69239	+	18.0465i	−0.184620	+	0.902326i
$401$			0.812009i			0.0405498i	0.999794	+	0.0202749i	$0.00645414\pi$
$401$			0.812009i			0.0405498i	−0.999794	+	0.0202749i	$0.993546\pi$
$402$	−14.2297	+	14.1250i	−0.709715	+	0.704489i
$403$			32.7960i			1.63368i
$404$	−16.9487	−	6.43201i	−0.843231	−	0.320005i
$405$	4.28171	−	3.69514i	0.212760	−	0.183613i
$406$	10.2257	−	7.05666i	0.507494	−	0.350216i
$407$	−11.3379			−0.561997
$408$	−0.283629	−	0.153831i	−0.0140417	−	0.00761575i
$409$	−16.8414	−	29.1702i	−0.832755	−	1.44237i	−0.895845	−	0.444366i	$-0.853429\pi$
$409$	−16.8414	−	29.1702i	−0.832755	−	1.44237i	0.0630907	−	0.998008i	$-0.479904\pi$
$410$	−0.557833	−	6.91938i	−0.0275494	−	0.341724i
$411$	−11.3699	−	2.47932i	−0.560835	−	0.122296i
$412$	21.2258	+	8.05517i	1.04572	+	0.396850i
$413$	−2.79298	+	1.61253i	−0.137434	+	0.0793473i
$414$	−1.75174	+	0.309080i	−0.0860933	+	0.0151904i
$415$	8.18828	+	4.72751i	0.401947	+	0.232064i
$416$	12.0306	+	28.2795i	0.589849	+	1.38651i
$417$	−7.80340	−	1.70162i	−0.382134	−	0.0833285i
$418$	0.586937	−	1.23660i	0.0287080	−	0.0604839i
$419$	9.57619	−	16.5864i	0.467827	−	0.810301i	−0.531497	−	0.847060i	$-0.678370\pi$
$419$	9.57619	−	16.5864i	0.467827	−	0.810301i	0.999324	+	0.0367596i	$0.0117036\pi$
$420$	3.32957	+	2.16912i	0.162467	+	0.105842i
$421$	−4.64901	+	8.05233i	−0.226579	+	0.392446i	−0.956792	−	0.290773i	$-0.906087\pi$
$421$	−4.64901	+	8.05233i	−0.226579	+	0.392446i	0.730213	+	0.683220i	$0.239421\pi$
$422$	−2.87071	−	4.15991i	−0.139744	−	0.202501i
$423$	−2.89026	−	30.5917i	−0.140529	−	1.48742i
$424$	21.8245	−	5.37171i	1.05989	−	0.260874i
$425$	−0.262668	−	0.151652i	−0.0127413	−	0.00735619i
$426$	−25.5952	−	3.45708i	−1.24009	−	0.167496i
$427$		−	0.781646i		−	0.0378265i
$428$	3.57304	+	4.37813i	0.172710	+	0.211625i
$429$	4.54158	−	20.8271i	0.219270	−	1.00554i
$430$	−4.20498	−	1.99585i	−0.202782	−	0.0962482i
$431$	−18.0857	−	31.3253i	−0.871156	−	1.50889i	−0.860802	−	0.508939i	$-0.830038\pi$
$431$	−18.0857	−	31.3253i	−0.871156	−	1.50889i	−0.0103532	−	0.999946i	$-0.503296\pi$
$432$	13.7811	+	15.5589i	0.663044	+	0.748580i
$433$	6.72410	+	11.6465i	0.323140	+	0.559694i	0.981134	−	0.193329i	$-0.0619283\pi$
$433$	6.72410	+	11.6465i	0.323140	+	0.559694i	−0.657994	+	0.753023i	$0.728595\pi$
$434$	−12.8266	+	8.85153i	−0.615699	+	0.424887i
$435$	−4.99036	+	1.59249i	−0.239269	+	0.0763542i
$436$	0.880090	+	1.07839i	0.0421487	+	0.0516456i
$437$	−0.155136	+	0.0895678i	−0.00742116	+	0.00428461i
$438$	−2.39226	−	5.83068i	−0.114307	−	0.278601i
$439$	0.854266	+	0.493211i	0.0407719	+	0.0235397i	0.520247	−	0.854016i	$-0.325840\pi$
$439$	0.854266	+	0.493211i	0.0407719	+	0.0235397i	−0.479476	+	0.877555i	$0.659173\pi$
$440$	−2.78832	−	2.90484i	−0.132928	−	0.138483i
$441$	8.96928	−	6.37348i	0.427109	−	0.303499i
$442$	−0.504387	+	0.0406632i	−0.0239913	+	0.00193415i
$443$	−9.35621	−	16.2054i	−0.444527	−	0.769944i	0.553492	−	0.832854i	$-0.313295\pi$
$443$	−9.35621	−	16.2054i	−0.444527	−	0.769944i	−0.998019	+	0.0629109i	$0.979962\pi$
$444$	0.932469	−	17.3122i	0.0442530	−	0.821603i
$445$	−0.814391			−0.0386059
$446$	−15.2738	+	32.1799i	−0.723238	+	1.52376i
$447$	32.9069	+	7.17570i	1.55644	+	0.339399i
$448$	−7.81319	+	12.3378i	−0.369138	+	0.582904i
$449$	−20.9173	+	12.0766i	−0.987146	+	0.569929i	−0.904420	−	0.426643i	$-0.859696\pi$
$449$	−20.9173	+	12.0766i	−0.987146	+	0.569929i	−0.0827261	+	0.996572i	$0.526363\pi$
$450$	12.5603	+	14.9654i	0.592098	+	0.705476i
$451$	−15.3244	−	8.84755i	−0.721598	−	0.416615i
$452$	−22.6802	−	8.60712i	−1.06679	−	0.404845i
$453$	−26.0925	+	28.6739i	−1.22593	+	1.34722i
$454$	−1.99893	−	24.7947i	−0.0938143	−	1.16367i
$455$	6.23209			0.292165
$456$	1.83994	+	0.997920i	0.0861630	+	0.0467319i
$457$	0.215249	+	0.372823i	0.0100689	+	0.0174399i	0.871016	−	0.491255i	$-0.163462\pi$
$457$	0.215249	+	0.372823i	0.0100689	+	0.0174399i	−0.860947	+	0.508695i	$0.830128\pi$
$458$	−5.99854	+	4.13953i	−0.280294	+	0.193428i
$459$	−0.314802	+	0.134247i	−0.0146937	+	0.00626612i
$460$	0.0844150	+	0.520140i	0.00393587	+	0.0242516i
$461$			9.52819i			0.443772i	0.975073	+	0.221886i	$0.0712213\pi$
$461$			9.52819i			0.443772i	−0.975073	+	0.221886i	$0.928779\pi$
$462$	9.37134	−	3.84495i	0.435994	−	0.178883i
$463$	−5.69009	−	3.28517i	−0.264441	−	0.152675i	0.361918	−	0.932210i	$-0.382122\pi$
$463$	−5.69009	−	3.28517i	−0.264441	−	0.152675i	−0.626359	+	0.779535i	$0.715455\pi$
$464$	−6.08811	−	18.2625i	−0.282633	−	0.847817i
$465$	6.25966	−	1.99754i	0.290285	−	0.0926339i
$466$	8.31032	−	0.669970i	0.384968	−	0.0310358i
$467$	−14.9636	+	25.9177i	−0.692433	+	1.19933i	0.278605	+	0.960406i	$0.410128\pi$
$467$	−14.9636	+	25.9177i	−0.692433	+	1.19933i	−0.971038	+	0.238924i	$0.923205\pi$
$468$	31.4283	+	8.64764i	1.45277	+	0.399737i
$469$	−13.8065	+	5.71335i	−0.637527	+	0.263818i
$470$	−9.07330	+	0.731481i	−0.418520	+	0.0337407i
$471$	18.6273	+	16.9504i	0.858302	+	0.781033i
$472$	1.19428	+	4.85221i	0.0549714	+	0.223341i
$473$	−10.2752	+	5.93240i	−0.472455	+	0.272772i
$474$	0.401443	−	2.97217i	0.0184389	−	0.136516i
$475$	1.70397	+	0.983786i	0.0781834	+	0.0451392i
$476$	−0.152036	−	0.186293i	−0.00696857	−	0.00853873i
$477$	9.92488	−	21.6750i	0.454429	−	0.992431i
$478$	−3.15402	−	39.1226i	−0.144262	−	1.78942i
$479$	17.9195	−	31.0375i	0.818764	−	1.41814i	−0.0878290	−	0.996136i	$-0.527993\pi$
$479$	17.9195	−	31.0375i	0.818764	−	1.41814i	0.906593	−	0.422006i	$-0.138674\pi$
$480$	4.66484	−	4.01869i	0.212920	−	0.183427i
$481$	−13.5950	−	23.5472i	−0.619879	−	1.07366i
$482$	17.0626	+	8.09859i	0.777181	+	0.368881i
$483$	−1.29519	−	0.282431i	−0.0589333	−	0.0128510i
$484$	11.5846	−	1.88010i	0.526574	−	0.0854592i
$485$	2.35496	+	1.35964i	0.106933	+	0.0617381i
$486$	22.0131	−	1.19303i	0.998535	−	0.0541168i
$487$	−10.7088	−	6.18271i	−0.485261	−	0.280166i	0.237345	−	0.971425i	$-0.423723\pi$
$487$	−10.7088	−	6.18271i	−0.485261	−	0.280166i	−0.722606	+	0.691260i	$0.757056\pi$
$488$	−1.16318	−	0.337331i	−0.0526549	−	0.0152703i
$489$	−10.5687	−	33.1188i	−0.477932	−	1.49768i
$490$	−1.85134	−	2.68275i	−0.0836349	−	0.121194i
$491$	2.85354			0.128779			0.0643893	−	0.997925i	$-0.479490\pi$
$491$	2.85354			0.128779			0.0643893	+	0.997925i	$0.479490\pi$
$492$	14.7700	−	22.6718i	0.665884	−	1.02212i
$493$	0.316973			0.0142757
$494$	3.27203	−	0.263788i	0.147216	−	0.0118684i
$495$	−4.25183	+	0.401707i	−0.191106	+	0.0180554i
$496$	7.63663	+	22.9076i	0.342895	+	1.02858i
$497$	−16.6690	−	9.62387i	−0.747709	−	0.431690i
$498$	13.9894	+	34.0964i	0.626878	+	1.52790i
$499$	−11.0683	−	6.39027i	−0.495484	−	0.286068i	0.231363	−	0.972868i	$-0.425682\pi$
$499$	−11.0683	−	6.39027i	−0.495484	−	0.286068i	−0.726847	+	0.686800i	$0.759015\pi$
$500$	9.35264	−	7.63281i	0.418263	−	0.341350i
$501$	−7.12179	+	2.27266i	−0.318178	+	0.101535i
$502$	−19.4864	+	13.4474i	−0.869721	+	0.600185i
$503$	8.12287	+	14.0692i	0.362181	+	0.627316i	0.988320	−	0.152396i	$-0.0486989\pi$
$503$	8.12287	+	14.0692i	0.362181	+	0.627316i	−0.626139	+	0.779712i	$0.715366\pi$
$504$	5.10028	+	14.6257i	0.227185	+	0.651481i
$505$	2.84799	+	4.93287i	0.126734	+	0.219510i
$506$	1.21346	+	0.575957i	0.0539450	+	0.0256044i
$507$	27.2500	−	8.69587i	1.21022	−	0.386197i
$508$	1.23616	+	0.469122i	0.0548459	+	0.0208139i
$509$		−	24.0533i		−	1.06614i	−0.846070	−	0.533072i	$-0.821037\pi$
$509$		−	24.0533i		−	1.06614i	0.846070	−	0.533072i	$-0.178963\pi$
$510$	0.0384826	+	0.0937940i	0.00170404	+	0.00415327i
$511$		−	4.69676i		−	0.207772i
$512$	14.9882	+	16.9515i	0.662391	+	0.749159i
$513$	2.04216	−	0.870880i	0.0901637	−	0.0384503i
$514$	−24.2229	+	1.95283i	−1.06843	+	0.0861355i
$515$	−3.56670	−	6.17770i	−0.157167	−	0.272222i
$516$	−8.21336	−	16.1776i	−0.361573	−	0.712178i
$517$	−11.6017	+	20.0947i	−0.510242	+	0.883765i
$518$	5.54017	−	11.6724i	0.243421	−	0.512855i
$519$	4.59696	−	5.05174i	0.201784	−	0.221747i
$520$	2.68955	−	9.27411i	0.117945	−	0.406697i
$521$		−	15.1409i		−	0.663335i	−0.943396	−	0.331668i	$-0.892389\pi$
$521$		−	15.1409i		−	0.663335i	0.943396	−	0.331668i	$-0.107611\pi$
$522$	−19.1877	−	6.98135i	−0.839824	−	0.305565i
$523$	−18.6031	−	10.7405i	−0.813456	−	0.469649i	0.0346985	−	0.999398i	$-0.488953\pi$
$523$	−18.6031	−	10.7405i	−0.813456	−	0.469649i	−0.848155	+	0.529749i	$0.822286\pi$
$524$	19.6362	+	24.0607i	0.857813	+	1.05110i
$525$	4.42648	+	13.8711i	0.193187	+	0.605386i
$526$	−23.1320	−	10.9793i	−1.00860	−	0.478722i
$527$	−0.397596			−0.0173195
$528$	−1.67741	−	15.6050i	−0.0729999	−	0.679123i
$529$	11.4121	+	19.7664i	0.496179	+	0.859407i
$530$	−6.37989	−	3.02815i	−0.277125	−	0.131534i
$531$	4.81897	+	2.20658i	0.209126	+	0.0957575i
$532$	0.986280	+	1.20851i	0.0427606	+	0.0523955i
$533$		−	42.4357i		−	1.83809i
$534$	−2.51193	−	1.94090i	−0.108702	−	0.0839910i
$535$		−	1.77560i		−	0.0767660i
$536$	2.54374	+	23.0115i	0.109873	+	0.993946i
$537$	−6.78576	+	31.1187i	−0.292827	+	1.34287i
$538$	−18.1526	+	38.2451i	−0.782615	+	1.64886i
$539$	−8.30874			−0.357883
$540$	−0.263697	−	6.52533i	−0.0113477	−	0.280806i
$541$	16.7038			0.718154			0.359077	−	0.933308i	$-0.383091\pi$
$541$	16.7038			0.718154			0.359077	+	0.933308i	$0.383091\pi$
$542$	−1.12009	+	2.35988i	−0.0481120	+	0.101365i
$543$	−11.2028	+	3.57497i	−0.480758	+	0.153417i
$544$	−0.342840	+	0.145851i	−0.0146992	+	0.00625330i
$545$		−	0.437356i		−	0.0187343i
$546$	19.2224	+	14.8526i	0.822645	+	0.635634i
$547$	−20.9033	+	12.0685i	−0.893760	+	0.516012i	−0.875170	−	0.483815i	$-0.839251\pi$
$547$	−20.9033	+	12.0685i	−0.893760	+	0.516012i	−0.0185893	+	0.999827i	$0.505918\pi$
$548$	−10.4105	+	8.49611i	−0.444713	+	0.362936i
$549$	−1.04713	+	0.744081i	−0.0446905	+	0.0317566i
$550$	−1.18556	−	14.7057i	−0.0505525	−	0.627054i
$551$	−2.05625			−0.0875991
$552$	−0.979252	+	1.80552i	−0.0416797	+	0.0768480i
$553$	1.11754	−	1.93564i	0.0475228	−	0.0823120i
$554$	−34.9396	−	16.5837i	−1.48444	−	0.704573i
$555$	−3.66634	+	4.02905i	−0.155627	+	0.171024i
$556$	−7.14493	+	5.83107i	−0.303013	+	0.247292i
$557$	−7.63815	+	4.40989i	−0.323639	+	0.186853i	−0.653013	−	0.757346i	$-0.726495\pi$
$557$	−7.63815	+	4.40989i	−0.323639	+	0.186853i	0.329375	+	0.944199i	$0.393162\pi$
$558$	24.0682	+	8.75706i	1.01889	+	0.370716i
$559$	−24.6416	−	14.2269i	−1.04223	−	0.601732i
$560$	4.35304	−	1.45116i	0.183950	−	0.0613226i
$561$	0.252494	+	0.0550590i	0.0106603	+	0.00232459i
$562$	9.31121	+	13.4928i	0.392770	+	0.569158i
$563$	4.98959			0.210286			0.105143	−	0.994457i	$-0.466470\pi$
$563$	4.98959			0.210286			0.105143	+	0.994457i	$0.466470\pi$
$564$	−29.7293	−	19.3678i	−1.25183	−	0.815530i
$565$	3.81109	+	6.60101i	0.160334	+	0.277706i
$566$	−14.1085	+	29.7248i	−0.593026	+	1.24942i
$567$	15.5147	+	5.40449i	0.651557	+	0.226967i
$568$	−21.5153	+	20.6522i	−0.902761	+	0.866549i
$569$	24.0262	−	13.8715i	1.00723	−	0.581524i	0.0968498	−	0.995299i	$-0.469123\pi$
$569$	24.0262	−	13.8715i	1.00723	−	0.581524i	0.910379	+	0.413775i	$0.135790\pi$
$570$	−0.249642	−	0.608455i	−0.0104563	−	0.0254854i
$571$	−22.0540	+	12.7329i	−0.922931	+	0.532855i	−0.884569	−	0.466409i	$-0.845547\pi$
$571$	−22.0540	+	12.7329i	−0.922931	+	0.532855i	−0.0383621	+	0.999264i	$0.512214\pi$
$572$	−15.5630	−	19.0697i	−0.650723	−	0.797344i
$573$	24.0941	+	21.9250i	1.00655	+	0.915932i
$574$	16.5968	−	11.4533i	0.692736	−	0.478050i
$575$	−0.965382	+	1.67209i	−0.0402592	+	0.0697310i
$576$	23.9660	−	1.27789i	0.998581	−	0.0532453i
$577$	−16.3309	−	28.2860i	−0.679865	−	1.17756i	−0.975021	−	0.222111i	$-0.928705\pi$
$577$	−16.3309	−	28.2860i	−0.679865	−	1.17756i	0.295157	−	0.955449i	$-0.404628\pi$
$578$	1.93145	+	23.9578i	0.0803378	+	0.996512i
$579$	3.33550	−	15.2962i	0.138619	−	0.635689i
$580$	−2.14611	+	5.65513i	−0.0891125	+	0.234816i
$581$			27.4655i			1.13946i
$582$	4.02336	+	9.80619i	0.166774	+	0.406480i
$583$	−15.5898	+	9.00079i	−0.645665	+	0.372775i
$584$	−6.98936	−	2.02696i	−0.289222	−	0.0838762i
$585$	−5.93258	−	8.34881i	−0.245282	−	0.345181i
$586$	1.21095	−	2.55132i	0.0500241	−	0.105394i
$587$	15.5222	−	26.8852i	0.640670	−	1.10967i	−0.344614	−	0.938745i	$-0.611990\pi$
$587$	15.5222	−	26.8852i	0.640670	−	1.10967i	0.985283	−	0.170928i	$-0.0546766\pi$
$588$	0.683342	−	12.6870i	0.0281806	−	0.523201i
$589$	2.57926			0.106276
$590$	0.673243	−	1.41843i	0.0277170	−	0.0583959i
$591$	2.55503	+	8.00663i	0.105100	+	0.329349i
$592$	−14.9790	−	13.2819i	−0.615633	−	0.545881i
$593$	33.5979	+	19.3978i	1.37970	+	0.796570i	0.992123	−	0.125267i	$-0.0399787\pi$
$593$	33.5979	+	19.3978i	1.37970	+	0.796570i	0.387577	+	0.921837i	$0.373312\pi$
$594$	−14.0718	−	8.89414i	−0.577375	−	0.364931i
$595$			0.0755535i			0.00309739i
$596$	30.1301	−	24.5896i	1.23418	−	1.00723i
$597$	−1.09682	+	1.20533i	−0.0448899	+	0.0493309i
$598$	0.258853	+	3.21082i	0.0105853	+	0.131300i
$599$	−0.910006	−	1.57618i	−0.0371818	−	0.0644008i	0.846836	−	0.531855i	$-0.178505\pi$
$599$	−0.910006	−	1.57618i	−0.0371818	−	0.0644008i	−0.884017	+	0.467454i	$0.845171\pi$
$600$	22.5523	−	0.600827i	0.920693	−	0.0245287i
$601$	6.08570	−	10.5407i	0.248241	−	0.429966i	−0.714797	−	0.699332i	$-0.753481\pi$
$601$	6.08570	−	10.5407i	0.248241	−	0.429966i	0.963038	+	0.269366i	$0.0868142\pi$
$602$	−1.08652	−	13.4772i	−0.0442833	−	0.549291i
$603$	20.7969	+	13.0571i	0.846915	+	0.531728i
$604$	7.17140	+	44.1880i	0.291800	+	1.79798i
$605$	−3.19355	−	1.84379i	−0.129836	−	0.0749609i
$606$	−2.97183	+	22.0026i	−0.120722	+	0.893793i
$607$	−15.7434	+	9.08944i	−0.639004	+	0.368929i	−0.784231	−	0.620469i	$-0.786942\pi$
$607$	−15.7434	+	9.08944i	−0.639004	+	0.368929i	0.145227	+	0.989398i	$0.453609\pi$
$608$	2.22405	−	0.946154i	0.0901973	−	0.0383716i
$609$	−11.2544	−	10.2412i	−0.456050	−	0.414994i
$610$	0.216137	+	0.313201i	0.00875112	+	0.0126811i
$611$	−55.6454			−2.25117
$612$	−0.104838	+	0.381015i	−0.00423782	+	0.0154016i
$613$	5.42549	−	9.39723i	0.219134	−	0.379551i	−0.735410	−	0.677623i	$-0.763010\pi$
$613$	5.42549	−	9.39723i	0.219134	−	0.379551i	0.954543	+	0.298072i	$0.0963436\pi$
$614$	9.86881	+	14.3008i	0.398273	+	0.577132i
$615$	−8.09956	+	2.58468i	−0.326606	+	0.104224i
$616$	3.25783	−	11.2336i	0.131262	−	0.452615i
$617$		−	46.0369i		−	1.85337i	−0.375833	−	0.926687i	$-0.622643\pi$
$617$		−	46.0369i		−	1.85337i	0.375833	−	0.926687i	$-0.377357\pi$
$618$	3.72178	−	27.5550i	0.149712	−	1.10843i
$619$	33.5036	+	19.3433i	1.34662	+	0.777473i	0.987770	−	0.155921i	$-0.0498344\pi$
$619$	33.5036	+	19.3433i	1.34662	+	0.777473i	0.358854	+	0.933394i	$0.383168\pi$
$620$	2.69198	−	7.09352i	0.108112	−	0.284882i
$621$	0.854589	+	2.00396i	0.0342935	+	0.0804162i
$622$	−27.6266	−	13.1127i	−1.10772	−	0.525769i
$623$	−1.18285	−	2.04875i	−0.0473898	−	0.0820816i
$624$	30.3983	−	22.1955i	1.21691	−	0.888530i
$625$	19.2324			0.769296
$626$	−6.52425	−	3.09666i	−0.260761	−	0.123767i
$627$	−1.63796	−	0.357175i	−0.0654139	−	0.0142642i
$628$	28.7058	−	4.65874i	1.14549	−	0.185904i
$629$	0.285470	−	0.164816i	0.0113824	−	0.00657166i
$630$	1.66407	−	4.57357i	0.0662981	−	0.182216i
$631$	−16.2279	−	9.36917i	−0.646022	−	0.372981i	0.140909	−	0.990023i	$-0.454998\pi$
$631$	−16.2279	−	9.36917i	−0.646022	−	0.372981i	−0.786930	+	0.617042i	$0.788331\pi$
$632$	−2.39818	−	2.49840i	−0.0953945	−	0.0993810i
$633$	−4.16620	+	4.57837i	−0.165592	+	0.181974i
$634$	−14.4762	−	20.9773i	−0.574925	−	0.833116i
$635$	−0.207720	−	0.359781i	−0.00824310	−	0.0142775i
$636$	−12.4615	−	24.5450i	−0.494131	−	0.973273i
$637$	−9.96284	−	17.2562i	−0.394742	−	0.683714i
$638$	8.75725	+	12.6900i	0.346703	+	0.502402i
$639$	2.97532	+	31.4920i	0.117702	+	1.24581i
$640$	−0.280876	−	7.10413i	−0.0111026	−	0.280815i
$641$	−22.7290	+	13.1226i	−0.897740	+	0.518310i	−0.876466	−	0.481463i	$-0.840105\pi$
$641$	−22.7290	+	13.1226i	−0.897740	+	0.518310i	−0.0212735	+	0.999774i	$0.506772\pi$
$642$	4.23171	−	5.47673i	0.167012	−	0.216149i
$643$			0.105938i			0.00417777i	0.999998	+	0.00208888i	$0.000664913\pi$
$643$			0.105938i			0.00417777i	−0.999998	+	0.00208888i	$0.999335\pi$
$644$	−1.18590	+	0.967829i	−0.0467311	+	0.0381378i
$645$	−1.21456	+	5.56980i	−0.0478231	+	0.219311i
$646$	0.00319798	+	0.0396678i	0.000125823	+	0.00156071i
$647$	−4.06702	+	7.04428i	−0.159891	+	0.276939i	−0.934829	−	0.355098i	$-0.884448\pi$
$647$	−4.06702	+	7.04428i	−0.159891	+	0.276939i	0.774938	+	0.632037i	$0.217781\pi$
$648$	14.7382	−	20.7554i	0.578970	−	0.815349i
$649$	−2.00113	−	3.46606i	−0.0785513	−	0.136055i
$650$	29.1203	−	20.0956i	1.14219	−	0.788214i
$651$	14.1169	+	12.8460i	0.553286	+	0.503476i
$652$	−37.5306	−	14.2428i	−1.46981	−	0.557791i
$653$	9.50353	+	5.48686i	0.371902	+	0.214718i	0.674289	−	0.738468i	$-0.264450\pi$
$653$	9.50353	+	5.48686i	0.371902	+	0.214718i	−0.302387	+	0.953185i	$0.597784\pi$
$654$	1.04233	−	1.34899i	0.0407583	−	0.0527498i
$655$		−	9.75811i		−	0.381281i
$656$	−9.88126	−	29.6408i	−0.385798	−	1.15728i
$657$	−6.29201	+	4.47104i	−0.245475	+	0.174432i
$658$	−15.0185	−	21.7632i	−0.585483	−	0.848416i
$659$	−16.6716	−	28.8761i	−0.649435	−	1.12485i	−0.983258	−	0.182219i	$-0.941672\pi$
$659$	−16.6716	−	28.8761i	−0.649435	−	1.12485i	0.333823	−	0.942636i	$-0.391661\pi$
$660$	−2.69186	+	4.13197i	−0.104780	+	0.160837i
$661$	46.8293			1.82145			0.910724	−	0.413016i	$-0.135525\pi$
$661$	46.8293			1.82145			0.910724	+	0.413016i	$0.135525\pi$
$662$	−24.1504	+	1.94698i	−0.938631	+	0.0756715i
$663$	0.188410	+	0.590417i	0.00731724	+	0.0229299i
$664$	40.8721	+	11.8532i	1.58614	+	0.459992i
$665$		−	0.490126i		−	0.0190063i
$666$	−20.9108	+	3.68954i	−0.810278	+	0.142967i
$667$		−	2.01778i		−	0.0781289i
$668$	−3.06274	+	8.07049i	−0.118501	+	0.312257i
$669$	42.6247	+	9.29477i	1.64797	+	0.359357i
$670$	3.95237	−	6.10702i	0.152693	−	0.235935i
$671$	0.970014			0.0374470
$672$	16.8851	+	5.89840i	0.651358	+	0.227536i
$673$	−7.49593			−0.288947			−0.144473	−	0.989509i	$-0.546149\pi$
$673$	−7.49593			−0.288947			−0.144473	+	0.989509i	$0.546149\pi$
$674$	28.4373	−	19.6243i	1.09536	−	0.755899i
$675$	14.3687	−	19.1344i	0.553053	−	0.736485i
$676$	11.7189	−	30.8800i	0.450728	−	1.18769i
$677$	−10.9269	+	6.30862i	−0.419953	+	0.242460i	−0.695057	−	0.718954i	$-0.744621\pi$
$677$	−10.9269	+	6.30862i	−0.419953	+	0.242460i	0.275104	+	0.961414i	$0.411288\pi$
$678$	−3.97681	+	29.4432i	−0.152728	+	1.13076i
$679$			7.89914i			0.303141i
$680$	0.112433	+	0.0326063i	0.00431160	+	0.00125039i
$681$	−29.0238	+	9.26189i	−1.11219	+	0.354916i
$682$	−10.9847	−	15.9177i	−0.420625	−	0.609521i
$683$	−12.5352	+	21.7115i	−0.479644	+	0.830768i	−0.999727	−	0.0233474i	$-0.992568\pi$
$683$	−12.5352	+	21.7115i	−0.479644	+	0.830768i	0.520083	+	0.854116i	$0.325901\pi$
$684$	0.680098	−	2.47170i	0.0260042	−	0.0945077i
$685$	4.22209			0.161318
$686$	11.8087	−	24.8794i	0.450859	−	0.949899i
$687$	6.60196	+	6.00762i	0.251881	+	0.229205i
$688$	−20.5247	−	4.19943i	−0.782496	−	0.160102i
$689$	−37.3869	−	21.5853i	−1.42433	−	0.822336i
$690$	0.597073	−	0.244972i	0.0227302	−	0.00932592i
$691$	30.7460	−	17.7512i	1.16963	−	0.675288i	0.216040	−	0.976385i	$-0.430686\pi$
$691$	30.7460	−	17.7512i	1.16963	−	0.675288i	0.953594	+	0.301096i	$0.0973526\pi$
$692$	−1.26345	−	7.78502i	−0.0480292	−	0.295942i
$693$	−7.18606	−	10.1128i	−0.272976	−	0.384154i
$694$	−2.46973	−	30.6346i	−0.0937496	−	1.16287i
$695$	2.89772			0.109917
$696$	−20.0971	+	12.3281i	−0.761780	+	0.467296i
$697$	0.514461			0.0194866
$698$	13.8760	+	6.58608i	0.525214	+	0.249287i
$699$	−3.10426	−	9.72774i	−0.117414	−	0.367937i
$700$	15.7189	+	5.96531i	0.594120	+	0.225468i
$701$	−32.9163	+	19.0042i	−1.24323	+	0.717779i	−0.969750	−	0.244099i	$-0.921508\pi$
$701$	−32.9163	+	19.0042i	−1.24323	+	0.717779i	−0.273479	+	0.961878i	$0.588175\pi$
$702$	1.59869	−	39.8902i	0.0603386	−	1.50556i
$703$	−1.85189	+	1.06919i	−0.0698452	+	0.0403251i
$704$	−15.3110	−	9.69608i	−0.577056	−	0.365435i
$705$	3.38926	+	10.6209i	0.127647	+	0.400005i
$706$	−19.9334	−	28.8852i	−0.750204	−	1.08711i
$707$	−8.27303	+	14.3293i	−0.311139	+	0.538909i
$708$	5.45705	−	2.77055i	0.205089	−	0.104124i
$709$	−18.1334	+	31.4081i	−0.681016	+	1.17955i	0.293655	+	0.955911i	$0.405128\pi$
$709$	−18.1334	+	31.4081i	−0.681016	+	1.17955i	−0.974671	+	0.223643i	$0.928205\pi$
$710$	9.34033	−	0.753008i	0.350536	−	0.0282599i
$711$	−3.65692	+	0.345501i	−0.137145	+	0.0129573i
$712$	−3.55927	+	0.876051i	−0.133389	+	0.0328314i
$713$			2.53101i			0.0947870i
$714$	−0.180063	+	0.233040i	−0.00673869	+	0.00872129i
$715$			7.73396i			0.289234i
$716$	23.2533	+	28.4928i	0.869018	+	1.06483i
$717$	−45.7954	+	14.6139i	−1.71026	+	0.545768i
$718$	43.9252	+	20.8486i	1.63927	+	0.778063i
$719$	−10.7067	+	18.5445i	−0.399292	+	0.691594i	−0.993639	−	0.112615i	$-0.964077\pi$
$719$	−10.7067	+	18.5445i	−0.399292	+	0.691594i	0.594347	+	0.804209i	$0.297411\pi$
$720$	−6.08788	−	4.45013i	−0.226882	−	0.165847i
$721$	10.3608	−	17.9454i	0.385855	−	0.668321i
$722$	2.13849	+	26.5258i	0.0795862	+	0.987189i
$723$	4.92833	−	22.6007i	0.183287	−	0.840529i
$724$	−4.81779	+	12.6951i	−0.179052	+	0.471811i
$725$	−19.1935	+	11.0814i	−0.712827	+	0.411551i
$726$	−5.45605	−	13.2981i	−0.202493	−	0.493538i
$727$	28.0058	+	16.1691i	1.03868	+	0.599680i	0.919458	−	0.393188i	$-0.128628\pi$
$727$	28.0058	+	16.1691i	1.03868	+	0.599680i	0.119218	+	0.992868i	$0.461961\pi$
$728$	27.2371	−	6.70394i	1.00948	−	0.248464i
$729$	−7.52897	−	25.9290i	−0.278851	−	0.960334i
$730$	1.29872	+	1.88197i	0.0480680	+	0.0696547i
$731$	0.172477	−	0.298738i	0.00637927	−	0.0110492i
$732$	−0.0797777	+	1.48116i	−0.00294867	+	0.0547451i
$733$	−4.32291	−	7.48750i	−0.159670	−	0.276557i	0.775079	−	0.631864i	$-0.217710\pi$
$733$	−4.32291	−	7.48750i	−0.159670	−	0.276557i	−0.934750	+	0.355307i	$0.884376\pi$
$734$	−10.0113	+	0.807101i	−0.369524	+	0.0297906i
$735$	−2.68681	+	2.95262i	−0.0991043	+	0.108909i
$736$	0.928454	+	2.18245i	0.0342233	+	0.0804461i
$737$	−7.09021	−	17.1338i	−0.261171	−	0.631131i
$738$	−31.1425	−	11.3310i	−1.14637	−	0.417101i
$739$	34.4758	+	19.9046i	1.26821	+	0.732202i	0.974649	−	0.223737i	$-0.0718258\pi$
$739$	34.4758	+	19.9046i	1.26821	+	0.732202i	0.293562	+	0.955940i	$0.405159\pi$
$740$	1.00768	+	6.20900i	0.0370429	+	0.228247i
$741$	−1.22224	−	3.83011i	−0.0449002	−	0.140703i
$742$	−1.64850	−	20.4480i	−0.0605182	−	0.750669i
$743$	11.9270	−	20.6582i	0.437559	−	0.757875i	−0.559941	−	0.828532i	$-0.689176\pi$
$743$	11.9270	−	20.6582i	0.437559	−	0.757875i	0.997501	+	0.0706572i	$0.0225096\pi$
$744$	25.2089	−	15.4638i	0.924202	−	0.566931i
$745$	−12.2196			−0.447693
$746$	−3.44099	−	42.6821i	−0.125984	−	1.56270i
$747$	36.7942	−	26.1456i	1.34623	−	0.956616i
$748$	0.231188	−	0.188675i	0.00845306	−	0.00689865i
$749$	4.46686	−	2.57894i	0.163216	−	0.0942326i
$750$	−11.6995	−	9.03987i	−0.427205	−	0.330089i
$751$		−	10.0182i		−	0.365568i	−0.983153	−	0.182784i	$-0.941489\pi$
$751$		−	10.0182i		−	0.365568i	0.983153	−	0.182784i	$-0.0585109\pi$
$752$	−38.8677	+	12.9572i	−1.41736	+	0.472500i
$753$	21.4466	+	19.5159i	0.781558	+	0.711198i
$754$	−15.8548	+	33.4040i	−0.577399	+	1.21650i
$755$	7.03291	−	12.1814i	0.255954	−	0.443325i
$756$	16.0327	−	10.1410i	0.583103	−	0.368824i
$757$	−3.17198	−	5.49403i	−0.115288	−	0.199684i	0.802607	−	0.596508i	$-0.203446\pi$
$757$	−3.17198	−	5.49403i	−0.115288	−	0.199684i	−0.917895	+	0.396824i	$0.870112\pi$
$758$	8.94703	+	12.9650i	0.324971	+	0.470911i
$759$	0.350494	−	1.60732i	0.0127221	−	0.0583421i
$760$	−0.729367	−	0.211521i	−0.0264569	−	0.00767269i
$761$			44.6992i			1.62035i	0.586191	+	0.810173i	$0.300627\pi$
$761$			44.6992i			1.62035i	−0.586191	+	0.810173i	$0.699373\pi$
$762$	0.216752	−	1.60477i	0.00785209	−	0.0581346i
$763$	1.10025	−	0.635229i	0.0398317	−	0.0229968i
$764$	37.1304	−	6.02600i	1.34333	−	0.218013i
$765$	0.101215	−	0.0719224i	0.00365944	−	0.00260036i
$766$	17.4141	−	12.0173i	0.629198	−	0.434203i
$767$	4.79903	−	8.31217i	0.173283	−	0.300135i
$768$	16.0646	−	22.5816i	0.579681	−	0.814844i
$769$	−9.95427	−	17.2413i	−0.358960	−	0.621737i	0.628827	−	0.777545i	$-0.283535\pi$
$769$	−9.95427	−	17.2413i	−0.358960	−	0.621737i	−0.987787	+	0.155808i	$0.950202\pi$
$770$	−3.02478	+	2.08737i	−0.109006	+	0.0752236i
$771$	9.04828	+	28.3544i	0.325866	+	1.02116i
$772$	−11.4300	−	14.0055i	−0.411376	−	0.504068i
$773$	−7.05889	+	4.07545i	−0.253891	+	0.146584i	−0.621544	−	0.783379i	$-0.713494\pi$
$773$	−7.05889	+	4.07545i	−0.253891	+	0.146584i	0.367654	+	0.929963i	$0.380161\pi$
$774$	−17.0205	+	14.2851i	−0.611788	+	0.513467i
$775$	24.0753	−	13.8999i	0.864812	−	0.499299i
$776$	11.7549	+	3.40900i	0.421976	+	0.122376i
$777$	−15.4609	−	3.37143i	−0.554658	−	0.120949i
$778$	−24.6738	−	35.7544i	−0.884598	−	1.28186i
$779$	−3.33738			−0.119574
$780$	−11.8093	−	0.636070i	−0.422841	−	0.0227750i
$781$	11.9431	−	20.6861i	0.427359	−	0.740207i
$782$	−0.0389258	+	0.00313816i	−0.00139198	+	0.000112220i
$783$	−3.00611	+	24.8259i	−0.107429	+	0.887205i
$784$	−10.9771	−	9.73336i	−0.392038	−	0.347620i
$785$	−7.91335	−	4.56877i	−0.282440	−	0.163067i
$786$	23.2560	−	30.0982i	0.829516	−	1.07357i
$787$	−11.3496	−	6.55267i	−0.404568	−	0.233577i	0.283885	−	0.958858i	$-0.408377\pi$
$787$	−11.3496	−	6.55267i	−0.404568	−	0.233577i	−0.688453	+	0.725281i	$0.741710\pi$
$788$	9.07320	+	3.44327i	0.323220	+	0.122661i
$789$	−6.68139	+	30.6400i	−0.237864	+	1.09081i
$790$	0.0874409	+	1.08462i	0.00311101	+	0.0385890i
$791$	−11.0707	+	19.1750i	−0.393629	+	0.681785i
$792$	−18.1504	+	6.32940i	−0.644945	+	0.224905i
$793$	1.16313	+	2.01459i	0.0413038	+	0.0715403i
$794$	−2.82657	−	1.34160i	−0.100311	−	0.0476116i
$795$	−1.84275	+	8.45064i	−0.0653557	+	0.299713i
$796$	0.301456	+	1.85748i	0.0106848	+	0.0658368i
$797$	−15.1020	+	8.71914i	−0.534940	+	0.308848i	−0.743026	−	0.669263i	$-0.766610\pi$
$797$	−15.1020	+	8.71914i	−0.534940	+	0.308848i	0.208086	+	0.978111i	$0.433277\pi$
$798$	1.16809	−	1.51176i	0.0413501	−	0.0535157i
$799$		−	0.674607i		−	0.0238659i
$800$	15.6609	−	20.8173i	0.553695	−	0.736002i
$801$	−1.61861	+	3.53489i	−0.0571907	+	0.124899i
$802$	0.492404	−	1.03743i	0.0173874	−	0.0366329i
$803$	5.82863			0.205688
$804$	26.7454	−	9.41719i	0.943238	−	0.332119i
$805$	0.480957			0.0169515
$806$	19.8875	−	41.9003i	0.700509	−	1.47588i
$807$	50.6585	+	11.0466i	1.78326	+	0.388859i
$808$	17.7534	+	18.4953i	0.624563	+	0.650663i
$809$			40.6750i			1.43006i	0.699095	+	0.715028i	$0.253586\pi$
$809$			40.6750i			1.43006i	−0.699095	+	0.715028i	$0.746414\pi$
$810$	−7.71108	+	2.12450i	−0.270940	+	0.0746474i
$811$	−1.15108	+	0.664576i	−0.0404199	+	0.0233364i	−0.520074	−	0.854121i	$-0.674096\pi$
$811$	−1.15108	+	0.664576i	−0.0404199	+	0.0233364i	0.479654	+	0.877458i	$0.340762\pi$
$812$	−17.3436	+	2.81474i	−0.608641	+	0.0987781i
$813$	3.12583	+	0.681622i	0.109628	+	0.0239055i
$814$	14.4853	+	6.87530i	0.507710	+	0.240979i
$815$	6.30648	+	10.9231i	0.220906	+	0.382621i
$816$	0.269082	+	0.368528i	0.00941977	+	0.0129010i
$817$	−1.11888	+	1.93796i	−0.0391446	+	0.0678005i
$818$	3.82785	+	47.4807i	0.133838	+	1.66012i
$819$	12.3863	−	27.0506i	0.432813	−	0.945224i
$820$	−3.48323	+	9.17851i	−0.121640	+	0.320527i
$821$	−6.04767	−	3.49162i	−0.211065	−	0.121859i	0.390741	−	0.920501i	$-0.372219\pi$
$821$	−6.04767	−	3.49162i	−0.211065	−	0.121859i	−0.601806	+	0.798642i	$0.705552\pi$
$822$	13.0228	+	10.0623i	0.454221	+	0.350963i
$823$	−34.7072	−	20.0382i	−1.20982	−	0.698487i	−0.247096	−	0.968991i	$-0.579476\pi$
$823$	−34.7072	−	20.0382i	−1.20982	−	0.698487i	−0.962719	+	0.270504i	$0.912810\pi$
$824$	−22.2336	−	23.1627i	−0.774543	−	0.806911i
$825$	−17.2140	+	5.49321i	−0.599313	+	0.191249i
$826$	4.54617	−	0.366508i	0.158181	−	0.0127524i
$827$	−2.32296	+	4.02349i	−0.0807773	+	0.139910i	−0.903584	−	0.428411i	$-0.859074\pi$
$827$	−2.32296	+	4.02349i	−0.0807773	+	0.139910i	0.822807	+	0.568321i	$0.192407\pi$
$828$	2.42546	+	0.667376i	0.0842906	+	0.0231929i
$829$	41.9693			1.45766			0.728828	−	0.684697i	$-0.240066\pi$
$829$	41.9693			1.45766			0.728828	+	0.684697i	$0.240066\pi$
$830$	−7.59463	−	11.0053i	−0.263613	−	0.381999i
$831$	−10.0919	+	46.2800i	−0.350083	+	1.60544i
$832$	1.77833	−	43.4254i	0.0616526	−	1.50550i
$833$	0.209202	−	0.120783i	0.00724840	−	0.00418487i
$834$	8.93781	+	6.90599i	0.309491	+	0.239135i
$835$	2.34889	−	1.35613i	0.0812866	−	0.0469309i
$836$	−1.49975	+	1.22396i	−0.0518698	+	0.0423316i
$837$	3.77071	−	31.1404i	0.130335	−	1.07637i
$838$	−22.2926	+	15.3839i	−0.770086	+	0.531429i
$839$	−7.10595	−	12.3079i	−0.245325	−	0.424915i	0.716898	−	0.697178i	$-0.245561\pi$
$839$	−7.10595	−	12.3079i	−0.245325	−	0.424915i	−0.962223	+	0.272263i	$0.912228\pi$
$840$	−2.93852	−	4.79034i	−0.101389	−	0.165282i
$841$	−2.91922	+	5.05624i	−0.100663	+	0.174353i
$842$	10.8225	−	7.46853i	0.372970	−	0.257383i
$843$	13.5132	−	14.8500i	0.465418	−	0.511463i
$844$	1.14506	+	7.05553i	0.0394147	+	0.242861i
$845$	−8.98753	+	5.18895i	−0.309180	+	0.178505i
$846$	−14.8582	+	40.8368i	−0.510837	+	1.40400i
$847$		−	10.7119i		−	0.368067i
$848$	−31.1405	−	6.37148i	−1.06937	−	0.218798i
$849$	39.3726	+	8.58563i	1.35127	+	0.294658i
$850$	0.243625	+	0.353034i	0.00835627	+	0.0121090i
$851$	−1.04919	−	1.81724i	−0.0359656	−	0.0622943i
$852$	30.6042	+	19.9378i	1.04848	+	0.683057i
$853$	−4.99381	+	8.64953i	−0.170985	+	0.296154i	−0.938764	−	0.344560i	$-0.888028\pi$
$853$	−4.99381	+	8.64953i	−0.170985	+	0.296154i	0.767780	+	0.640714i	$0.221362\pi$
$854$	−0.473991	+	0.998635i	−0.0162196	+	0.0341726i
$855$	−0.656597	+	0.466571i	−0.0224551	+	0.0159564i
$856$	−1.91004	−	7.76022i	−0.0652838	−	0.265239i
$857$			38.9394i			1.33014i	0.746779	+	0.665072i	$0.231599\pi$
$857$			38.9394i			1.33014i	−0.746779	+	0.665072i	$0.768401\pi$
$858$	−18.4320	+	23.8549i	−0.629257	+	0.814392i
$859$	−5.06225	+	2.92269i	−0.172722	+	0.0997209i	−0.583869	−	0.811848i	$-0.698462\pi$
$859$	−5.06225	+	2.92269i	−0.172722	+	0.0997209i	0.411147	+	0.911569i	$0.365128\pi$
$860$	4.16202	+	5.09981i	0.141924	+	0.173902i
$861$	−18.2663	−	16.6219i	−0.622514	−	0.566472i
$862$	4.11065	+	50.9885i	0.140009	+	1.73668i
$863$	6.72638			0.228969			0.114484	−	0.993425i	$-0.463478\pi$
$863$	6.72638			0.228969			0.114484	+	0.993425i	$0.463478\pi$
$864$	−8.17186	−	28.2351i	−0.278012	−	0.960577i
$865$	−1.23905	+	2.14610i	−0.0421291	+	0.0729697i
$866$	−1.52830	−	18.9571i	−0.0519339	−	0.644189i
$867$	28.0440	−	8.94924i	0.952426	−	0.303932i
$868$	21.7550	−	3.53068i	0.738412	−	0.119839i
$869$	2.40212	+	1.38686i	0.0814862	+	0.0470461i
$870$	7.34140	+	0.991583i	0.248897	+	0.0336178i
$871$	27.0829	−	35.2702i	0.917668	−	1.19509i
$872$	−0.470469	−	1.91145i	−0.0159321	−	0.0647298i
$873$	10.5821	−	7.51951i	0.358149	−	0.254497i
$874$	0.252517	−	0.0203577i	0.00854151	−	0.000688608i
$875$	−5.50919	−	9.54220i	−0.186245	−	0.322585i
$876$	−0.479369	+	8.89998i	−0.0161964	+	0.300703i
$877$	24.3625	−	42.1971i	0.822664	−	1.42490i	−0.0810278	−	0.996712i	$-0.525820\pi$
$877$	24.3625	−	42.1971i	0.822664	−	1.42490i	0.903692	−	0.428184i	$-0.140846\pi$
$878$	−0.792332	−	1.14816i	−0.0267399	−	0.0387484i
$879$	−3.37941	−	0.736916i	−0.113985	−	0.0248556i
$880$	1.80087	+	5.40208i	0.0607074	+	0.182104i
$881$	6.45557	+	3.72713i	0.217494	+	0.125570i	0.604789	−	0.796386i	$-0.293257\pi$
$881$	6.45557	+	3.72713i	0.217494	+	0.125570i	−0.387295	+	0.921956i	$0.626591\pi$
$882$	−15.3241	+	2.70381i	−0.515989	+	0.0910420i
$883$	−25.0366	+	14.4549i	−0.842547	+	0.486445i	−0.858129	−	0.513434i	$-0.828373\pi$
$883$	−25.0366	+	14.4549i	−0.842547	+	0.486445i	0.0155821	+	0.999879i	$0.495040\pi$
$884$	0.669067	+	0.253910i	0.0225031	+	0.00853991i
$885$	−1.87882	−	0.409696i	−0.0631558	−	0.0137718i
$886$	2.12655	+	26.3778i	0.0714429	+	0.886179i
$887$	0.418006	−	0.724008i	0.0140353	−	0.0243098i	−0.858922	−	0.512106i	$-0.828866\pi$
$887$	0.418006	−	0.724008i	0.0140353	−	0.0243098i	0.872958	+	0.487796i	$0.162199\pi$
$888$	−11.6895	+	21.5528i	−0.392274	+	0.723264i
$889$	0.603397	−	1.04511i	0.0202373	−	0.0350520i
$890$	1.04047	+	0.493848i	0.0348767	+	0.0165538i
$891$	−6.70692	+	19.2536i	−0.224690	+	0.645020i
$892$	39.0279	−	31.8512i	1.30675	−	1.06646i
$893$			4.37627i			0.146446i
$894$	−37.6906	−	29.1225i	−1.26056	−	0.974002i
$895$		−	11.5556i		−	0.386262i
$896$	17.4638	−	11.0249i	0.583425	−	0.368315i
$897$	3.75847	−	1.19938i	0.125492	−	0.0400461i
$898$	34.0473	−	2.74486i	1.13617	−	0.0915971i
$899$	−14.5264	+	25.1604i	−0.484482	+	0.839147i
$900$	−6.97207	−	26.7365i	−0.232402	−	0.891216i
$901$	0.261686	−	0.453253i	0.00871801	−	0.0151000i
$902$	14.2134	+	20.5964i	0.473254	+	0.685786i
$903$	−15.7759	+	5.03432i	−0.524990	+	0.167532i
$904$	23.7570	+	24.7498i	0.790148	+	0.823168i
$905$	3.69488	−	2.13324i	0.122822	−	0.0709112i
$906$	50.7238	−	20.8114i	1.68518	−	0.691411i
$907$	46.4573	−	26.8221i	1.54259	−	0.890614i	0.543914	−	0.839141i	$-0.316942\pi$
$907$	46.4573	−	26.8221i	1.54259	−	0.890614i	0.998674	−	0.0514723i	$-0.0163914\pi$
$908$	−12.4817	+	32.8901i	−0.414221	+	1.09149i
$909$	27.0717	−	2.55770i	0.897911	−	0.0848334i
$910$	−7.96215	−	3.77915i	−0.263943	−	0.125278i
$911$	−23.0944			−0.765153			−0.382577	−	0.923924i	$-0.624963\pi$
$911$	−23.0944			−0.765153			−0.382577	+	0.923924i	$0.624963\pi$
$912$	−1.74557	−	2.39069i	−0.0578018	−	0.0791637i
$913$	−34.0844			−1.12803
$914$	−0.0489235	−	0.606848i	−0.00161825	−	0.0200728i
$915$	0.313675	−	0.344707i	0.0103698	−	0.0113957i
$916$	10.1740	−	1.65117i	0.336158	−	0.0545561i
$917$	24.5483	−	14.1730i	0.810658	−	0.468033i
$918$	0.483601	+	0.0193814i	0.0159612	+	0.000639681i
$919$	44.5788	+	25.7376i	1.47052	+	0.849005i	0.999452	−	0.0330921i	$-0.0105355\pi$
$919$	44.5788	+	25.7376i	1.47052	+	0.849005i	0.471068	+	0.882097i	$0.343869\pi$
$920$	0.207565	−	0.715723i	0.00684320	−	0.0235967i
$921$	14.3224	−	15.7393i	0.471939	−	0.518629i
$922$	5.77791	−	12.1733i	0.190285	−	0.400906i
$923$	57.2831			1.88550
$924$	−14.3045	−	0.770464i	−0.470582	−	0.0253464i
$925$	−11.5239	+	19.9600i	−0.378905	+	0.656282i
$926$	5.27756	+	7.64764i	0.173431	+	0.251317i
$927$	−33.9034	+	3.20314i	−1.11353	+	0.105205i
$928$	−3.29622	+	27.0242i	−0.108204	+	0.887111i
$929$			30.7981i			1.01045i	0.862987	+	0.505226i	$0.168591\pi$
$929$			30.7981i			1.01045i	−0.862987	+	0.505226i	$0.831409\pi$
$930$	−9.20870	−	1.24379i	−0.301965	−	0.0407856i
$931$	−1.35712	+	0.783533i	−0.0444778	+	0.0256793i
$932$	−11.0236	−	4.18343i	−0.361090	−	0.137033i
$933$	−7.97960	+	36.5934i	−0.261240	+	1.19802i
$934$	34.8342	−	24.0387i	1.13981	−	0.786570i
$935$	−0.0937611			−0.00306632
$936$	−34.9091	−	30.1065i	−1.14104	−	0.984060i
$937$	−22.8394			−0.746130			−0.373065	−	0.927805i	$-0.621693\pi$
$937$	−22.8394			−0.746130			−0.373065	+	0.927805i	$0.621693\pi$
$938$	21.1039	+	1.07289i	0.689067	+	0.0350312i
$939$	−1.88445	+	8.64185i	−0.0614966	+	0.282016i
$940$	12.0357	+	4.56752i	0.392561	+	0.148976i
$941$			7.49915i			0.244465i	0.992501	+	0.122233i	$0.0390054\pi$
$941$			7.49915i			0.244465i	−0.992501	+	0.122233i	$0.960995\pi$
$942$	−13.5196	−	32.9516i	−0.440494	−	1.07362i
$943$		−	3.27495i		−	0.106647i
$944$	1.41656	−	6.92343i	0.0461051	−	0.225338i
$945$	−5.91749	−	0.716533i	−0.192496	−	0.0233088i
$946$	16.7251	−	1.34836i	0.543780	−	0.0438390i
$947$	−42.7136			−1.38801			−0.694003	−	0.719972i	$-0.744155\pi$
$947$	−42.7136			−1.38801			−0.694003	+	0.719972i	$0.744155\pi$
$948$	−2.31522	+	3.55383i	−0.0751947	+	0.115423i
$949$	6.98900	+	12.1053i	0.226873	+	0.392955i
$950$	−1.58043	−	2.29018i	−0.0512759	−	0.0743032i
$951$	−21.0091	+	23.0875i	−0.681266	+	0.748664i
$952$	0.0812739	+	0.330204i	0.00263410	+	0.0107020i
$953$		−	36.5897i		−	1.18526i	−0.805476	−	0.592628i	$-0.798091\pi$
$953$		−	36.5897i		−	1.18526i	0.805476	−	0.592628i	$-0.201909\pi$
$954$	−25.8239	+	21.6737i	−0.836078	+	0.701711i
$955$	−10.2358	−	5.90963i	−0.331222	−	0.191231i
$956$	−19.6944	+	51.8958i	−0.636962	+	1.67843i
$957$	12.7092	−	13.9666i	0.410830	−	0.451475i
$958$	−41.7153	+	28.7873i	−1.34776	+	0.930076i
$959$	6.13230	+	10.6215i	0.198022	+	0.342985i
$960$	−8.39677	+	2.30554i	−0.271005	+	0.0744109i
$961$	2.72117	−	4.71321i	0.0877797	−	0.152039i
$962$	3.08998	+	38.3281i	0.0996248	+	1.23575i
$963$	−7.70707	−	3.52903i	−0.248357	−	0.113721i
$964$	−16.8883	−	20.6936i	−0.543936	−	0.666496i
$965$			5.68010i			0.182849i
$966$	1.48348	+	1.14624i	0.0477302	+	0.0368797i
$967$	11.6077	−	6.70173i	0.373280	−	0.215513i	−0.301611	−	0.953431i	$-0.597524\pi$
$967$	11.6077	−	6.70173i	0.373280	−	0.215513i	0.674890	+	0.737918i	$0.264191\pi$
$968$	−15.9407	−	4.62291i	−0.512353	−	0.148586i
$969$	0.0464336	−	0.0148176i	0.00149166	−	0.000476010i
$970$	−2.18423	−	3.16514i	−0.0701314	−	0.101626i
$971$	−27.5678	−	47.7488i	−0.884692	−	1.53233i	−0.846066	−	0.533078i	$-0.821035\pi$
$971$	−27.5678	−	47.7488i	−0.884692	−	1.53233i	−0.0386259	−	0.999254i	$-0.512298\pi$
$972$	−28.8475	−	11.8246i	−0.925285	−	0.379273i
$973$	4.20874	+	7.28974i	0.134926	+	0.233698i
$974$	9.93239	+	14.3929i	0.318254	+	0.461178i
$975$	−32.0496	−	29.1643i	−1.02641	−	0.934005i
$976$	1.28153	+	1.13633i	0.0410209	+	0.0363731i
$977$	−6.06290	−	3.50041i	−0.193969	−	0.111988i	0.399870	−	0.916572i	$-0.369055\pi$
$977$	−6.06290	−	3.50041i	−0.193969	−	0.111988i	−0.593839	+	0.804584i	$0.702389\pi$
$978$	−6.58070	+	48.7216i	−0.210428	+	1.55795i
$979$	2.54248	−	1.46790i	0.0812581	−	0.0469144i
$980$	0.738456	+	4.55015i	0.0235891	+	0.145349i
$981$	−1.89836	−	0.869248i	−0.0606099	−	0.0277529i
$982$	−3.64570	−	1.73039i	−0.116339	−	0.0552191i
$983$	32.0301			1.02160			0.510800	−	0.859700i	$-0.329349\pi$
$983$	32.0301			1.02160			0.510800	+	0.859700i	$0.329349\pi$
$984$	−32.6185	+	20.0091i	−1.03984	+	0.637866i
$985$	−1.52462	−	2.64072i	−0.0485785	−	0.0841405i
$986$	−0.404967	−	0.192213i	−0.0128968	−	0.00612131i
$987$	−21.7961	+	23.9524i	−0.693777	+	0.762414i
$988$	−4.34033	−	1.64715i	−0.138084	−	0.0524027i
$989$	−1.90170	−	1.09795i	−0.0604706	−	0.0349127i
$990$	5.67576	+	2.06509i	0.180387	+	0.0656330i
$991$			1.34279i			0.0426551i	0.999773	+	0.0213275i	$0.00678928\pi$
$991$			1.34279i			0.0426551i	−0.999773	+	0.0213275i	$0.993211\pi$
$992$	4.13462	−	33.8978i	0.131274	−	1.07626i
$993$	9.02119	+	28.2695i	0.286279	+	0.897106i
$994$	15.4605	+	22.4037i	0.490378	+	0.710601i
$995$	0.295635	−	0.512054i	0.00937225	−	0.0162332i
$996$	2.80323	−	52.0449i	0.0888239	−	1.64911i
$997$	−21.2349			−0.672515			−0.336257	−	0.941770i	$-0.609161\pi$
$997$	−21.2349			−0.672515			−0.336257	+	0.941770i	$0.609161\pi$
$998$	10.2658	+	14.8761i	0.324959	+	0.470893i
$999$	10.2014	+	23.9216i	0.322757	+	0.756847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.l.a.431.17	✓	264
3.2	odd	2	inner	804.2.l.a.431.116	yes	264
4.3	odd	2	inner	804.2.l.a.431.26	yes	264
12.11	even	2	inner	804.2.l.a.431.107	yes	264
67.37	even	3	inner	804.2.l.a.707.107	yes	264
201.104	odd	6	inner	804.2.l.a.707.26	yes	264
268.171	odd	6	inner	804.2.l.a.707.116	yes	264
804.707	even	6	inner	804.2.l.a.707.17	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.l.a.431.17	✓	264	1.1	even	1	trivial
804.2.l.a.431.26	yes	264	4.3	odd	2	inner
804.2.l.a.431.107	yes	264	12.11	even	2	inner
804.2.l.a.431.116	yes	264	3.2	odd	2	inner
804.2.l.a.707.17	yes	264	804.707	even	6	inner
804.2.l.a.707.26	yes	264	201.104	odd	6	inner
804.2.l.a.707.107	yes	264	67.37	even	3	inner
804.2.l.a.707.116	yes	264	268.171	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27761 - 0.606402i) q^{2} +(-0.369021 + 1.69228i) q^{3} +(1.26455 + 1.54948i) q^{4} -0.628413i q^{5} +(1.49767 - 1.93830i) q^{6} +(1.58089 - 0.912727i) q^{7} +(-0.675992 - 2.74646i) q^{8} +(-2.72765 - 1.24898i) q^{9} +O(q^{10})\)	\(q+(-1.27761 - 0.606402i) q^{2} +(-0.369021 + 1.69228i) q^{3} +(1.26455 + 1.54948i) q^{4} -0.628413i q^{5} +(1.49767 - 1.93830i) q^{6} +(1.58089 - 0.912727i) q^{7} +(-0.675992 - 2.74646i) q^{8} +(-2.72765 - 1.24898i) q^{9} +(-0.381071 + 0.802864i) q^{10} +(1.13269 + 1.96187i) q^{11} +(-3.08881 + 1.56819i) q^{12} +(-2.71636 + 4.70488i) q^{13} +(-2.57323 + 0.207452i) q^{14} +(1.06345 + 0.231897i) q^{15} +(-0.801806 + 3.91881i) q^{16} +(-0.0570386 - 0.0329313i) q^{17} +(2.72748 + 3.24975i) q^{18} +(0.370018 + 0.213630i) q^{19} +(0.973716 - 0.794662i) q^{20} +(0.961212 + 3.01213i) q^{21} +(-0.257445 - 3.19336i) q^{22} +(-0.209633 + 0.363096i) q^{23} +(4.89724 - 0.130470i) q^{24} +4.60510 q^{25} +(6.32348 - 4.36377i) q^{26} +(3.12018 - 4.15506i) q^{27} +(3.41338 + 1.29537i) q^{28} +(-4.16787 + 2.40632i) q^{29} +(-1.21805 - 0.941153i) q^{30} +(5.22798 - 3.01837i) q^{31} +(3.40077 - 4.52048i) q^{32} +(-3.73802 + 1.19285i) q^{33} +(0.0529033 + 0.0766615i) q^{34} +(-0.573569 - 0.993451i) q^{35} +(-1.51399 - 5.80584i) q^{36} +(-2.50243 + 4.33434i) q^{37} +(-0.343191 - 0.497314i) q^{38} +(-6.95959 - 6.33305i) q^{39} +(-1.72591 + 0.424802i) q^{40} +(-6.76463 + 3.90556i) q^{41} +(0.598510 - 4.43119i) q^{42} +5.23747i q^{43} +(-1.60754 + 4.23597i) q^{44} +(-0.784872 + 1.71409i) q^{45} +(0.488011 - 0.336771i) q^{46} +(5.12132 + 8.87039i) q^{47} +(-6.33586 - 2.80301i) q^{48} +(-1.83386 + 3.17634i) q^{49} +(-5.88350 - 2.79254i) q^{50} +(0.0767775 - 0.0843732i) q^{51} +(-10.7251 + 1.74061i) q^{52} +7.94642i q^{53} +(-6.50599 + 3.41644i) q^{54} +(1.23286 - 0.711794i) q^{55} +(-3.57544 - 3.72485i) q^{56} +(-0.498066 + 0.547341i) q^{57} +(6.78410 - 0.546927i) q^{58} -1.76671 q^{59} +(0.985472 + 1.94105i) q^{60} +(0.214096 - 0.370826i) q^{61} +(-8.50964 + 0.686039i) q^{62} +(-5.45208 + 0.515106i) q^{63} +(-7.08607 + 3.71317i) q^{64} +(2.95660 + 1.70700i) q^{65} +(5.49907 + 0.742744i) q^{66} +(-8.11496 - 1.07116i) q^{67} +(-0.0211019 - 0.130024i) q^{68} +(-0.537102 - 0.488749i) q^{69} +(0.130365 + 1.61705i) q^{70} +(-5.27204 - 9.13145i) q^{71} +(-1.58639 + 8.33567i) q^{72} +(1.28646 - 2.22822i) q^{73} +(5.82547 - 4.02010i) q^{74} +(-1.69938 + 7.79313i) q^{75} +(0.136891 + 0.843483i) q^{76} +(3.58130 + 2.06766i) q^{77} +(5.05124 + 12.3114i) q^{78} +(1.06036 - 0.612201i) q^{79} +(2.46263 + 0.503865i) q^{80} +(5.88012 + 6.81353i) q^{81} +(11.0109 - 0.887686i) q^{82} +(-7.52293 + 13.0301i) q^{83} +(-3.45174 + 5.29838i) q^{84} +(-0.0206944 + 0.0358438i) q^{85} +(3.17601 - 6.69142i) q^{86} +(-2.53415 - 7.94121i) q^{87} +(4.62250 - 4.43708i) q^{88} -1.29595i q^{89} +(2.04218 - 1.71398i) q^{90} +9.91719i q^{91} +(-0.827704 + 0.134330i) q^{92} +(3.17871 + 9.96106i) q^{93} +(-1.16401 - 14.4384i) q^{94} +(0.134248 - 0.232524i) q^{95} +(6.39499 + 7.42321i) q^{96} +(-2.16361 + 3.74748i) q^{97} +(4.26908 - 2.94605i) q^{98} +(-0.639241 - 6.76598i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

Introduction

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