LMFDB - Embedded newform 570.2.q.b.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(49,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("570.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.q (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.1
Root			$-0.531325 + 1.98293i$ of defining polynomial
Character	$\chi$	$=$	570.349
Dual form			570.2.q.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.837733 - 2.07321i) q^{5} +(0.500000 - 0.866025i) q^{6} +0.785680i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.837733 - 2.07321i) q^{5} +(0.500000 - 0.866025i) q^{6} +0.785680i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.76210 + 1.37659i) q^{10} -0.377784 q^{11} +1.00000i q^{12} +(2.51426 + 1.45161i) q^{13} +(-0.392840 - 0.680419i) q^{14} +(1.76210 + 1.37659i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.45651 + 1.41827i) q^{17} +1.00000i q^{18} +(-2.82148 - 3.32254i) q^{19} +(-2.21432 - 0.311108i) q^{20} +(-0.392840 - 0.680419i) q^{21} +(0.327171 - 0.188892i) q^{22} +(-7.86994 - 4.54371i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.59641 + 3.47359i) q^{25} -2.90321 q^{26} +1.00000i q^{27} +(0.680419 + 0.392840i) q^{28} +(2.01037 - 3.48207i) q^{29} +(-2.21432 - 0.311108i) q^{30} -4.42864 q^{31} +(0.866025 + 0.500000i) q^{32} +(0.327171 - 0.188892i) q^{33} +(1.41827 - 2.45651i) q^{34} +(1.62888 - 0.658190i) q^{35} +(-0.500000 - 0.866025i) q^{36} -0.0967881i q^{37} +(4.10474 + 1.46666i) q^{38} -2.90321 q^{39} +(2.07321 - 0.837733i) q^{40} +(-1.43655 - 2.48818i) q^{41} +(0.680419 + 0.392840i) q^{42} +(0.371213 - 0.214320i) q^{43} +(-0.188892 + 0.327171i) q^{44} +(-2.21432 - 0.311108i) q^{45} +9.08742 q^{46} +(-10.4680 - 6.04371i) q^{47} +(0.866025 + 0.500000i) q^{48} +6.38271 q^{49} +(1.37778 - 4.80642i) q^{50} +(1.41827 - 2.45651i) q^{51} +(2.51426 - 1.45161i) q^{52} +(-6.00443 - 3.46666i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.316482 + 0.783227i) q^{55} -0.785680 q^{56} +(4.10474 + 1.46666i) q^{57} +4.02074i q^{58} +(-4.88025 - 8.45283i) q^{59} +(2.07321 - 0.837733i) q^{60} +(-2.27777 + 3.94521i) q^{61} +(3.83531 - 2.21432i) q^{62} +(0.680419 + 0.392840i) q^{63} -1.00000 q^{64} +(0.903212 - 6.42864i) q^{65} +(-0.188892 + 0.327171i) q^{66} +(-7.31738 - 4.22469i) q^{67} +2.83654i q^{68} +9.08742 q^{69} +(-1.08156 + 1.38445i) q^{70} +(5.86987 + 10.1669i) q^{71} +(0.866025 + 0.500000i) q^{72} +(1.95744 - 1.13013i) q^{73} +(0.0483940 + 0.0838209i) q^{74} +(1.37778 - 4.80642i) q^{75} +(-4.28814 + 0.782204i) q^{76} -0.296818i q^{77} +(2.51426 - 1.45161i) q^{78} +(-0.785680 - 1.36084i) q^{79} +(-1.37659 + 1.76210i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.48818 + 1.43655i) q^{82} +2.75557i q^{83} -0.785680 q^{84} +(4.99827 + 3.90474i) q^{85} +(-0.214320 + 0.371213i) q^{86} +4.02074i q^{87} -0.377784i q^{88} +(5.96912 - 10.3388i) q^{89} +(2.07321 - 0.837733i) q^{90} +(-1.14050 + 1.97540i) q^{91} +(-7.86994 + 4.54371i) q^{92} +(3.83531 - 2.21432i) q^{93} +12.0874 q^{94} +(-4.52468 + 8.63292i) q^{95} -1.00000 q^{96} +(-2.98299 + 1.72223i) q^{97} +(-5.52759 + 3.19135i) q^{98} +(-0.188892 + 0.327171i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 6 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 + 6 * q^6 + 6 * q^9	$ 12 q + 6 q^{4} + 6 q^{6} + 6 q^{9} - 2 q^{10} - 4 q^{11} - 18 q^{14} - 2 q^{15} - 6 q^{16} + 6 q^{19} - 18 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 4 q^{34} + 2 q^{35} - 6 q^{36} - 8 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} + 28 q^{46} - 56 q^{49} + 16 q^{50} + 4 q^{51} - 6 q^{54} - 8 q^{55} - 36 q^{56} + 8 q^{59} + 2 q^{60} - 28 q^{61} - 12 q^{64} - 16 q^{65} - 2 q^{66} + 28 q^{69} + 16 q^{70} + 44 q^{71} + 14 q^{74} + 16 q^{75} - 12 q^{76} - 36 q^{79} - 6 q^{81} - 36 q^{84} - 32 q^{85} + 24 q^{86} + 6 q^{89} + 2 q^{90} + 64 q^{94} - 12 q^{95} - 12 q^{96} - 2 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 + 6 * q^6 + 6 * q^9 - 2 * q^10 - 4 * q^11 - 18 * q^14 - 2 * q^15 - 6 * q^16 + 6 * q^19 - 18 * q^21 - 6 * q^24 - 2 * q^25 - 8 * q^26 - 16 * q^29 + 4 * q^34 + 2 * q^35 - 6 * q^36 - 8 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 + 28 * q^46 - 56 * q^49 + 16 * q^50 + 4 * q^51 - 6 * q^54 - 8 * q^55 - 36 * q^56 + 8 * q^59 + 2 * q^60 - 28 * q^61 - 12 * q^64 - 16 * q^65 - 2 * q^66 + 28 * q^69 + 16 * q^70 + 44 * q^71 + 14 * q^74 + 16 * q^75 - 12 * q^76 - 36 * q^79 - 6 * q^81 - 36 * q^84 - 32 * q^85 + 24 * q^86 + 6 * q^89 + 2 * q^90 + 64 * q^94 - 12 * q^95 - 12 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.837733	−	2.07321i	−0.374645	−	0.927168i
$5$	−0.837733	−	2.07321i	−0.374645	−	0.927168i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$			0.785680i			0.296959i	0.988915	+	0.148480i	$0.0474379\pi$
$7$			0.785680i			0.296959i	−0.988915	+	0.148480i	$0.952562\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.76210	+	1.37659i	0.557226	+	0.435315i
$11$	−0.377784			−0.113906			−0.0569531	−	0.998377i	$-0.518139\pi$
$11$	−0.377784			−0.113906			−0.0569531	+	0.998377i	$0.518139\pi$
$12$			1.00000i			0.288675i
$13$	2.51426	+	1.45161i	0.697329	+	0.402603i	0.806352	−	0.591436i	$-0.201439\pi$
$13$	2.51426	+	1.45161i	0.697329	+	0.402603i	−0.109023	+	0.994039i	$0.534772\pi$
$14$	−0.392840	−	0.680419i	−0.104991	−	0.181850i
$15$	1.76210	+	1.37659i	0.454973	+	0.355433i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.45651	+	1.41827i	−0.595792	+	0.343980i	−0.767384	−	0.641188i	$-0.778442\pi$
$17$	−2.45651	+	1.41827i	−0.595792	+	0.343980i	0.171593	+	0.985168i	$0.445109\pi$
$18$			1.00000i			0.235702i
$19$	−2.82148	−	3.32254i	−0.647292	−	0.762242i
$19$	−2.82148	−	3.32254i	−0.647292	−	0.762242i
$20$	−2.21432	−	0.311108i	−0.495137	−	0.0695658i
$21$	−0.392840	−	0.680419i	−0.0857247	−	0.148480i
$22$	0.327171	−	0.188892i	0.0697531	−	0.0402719i
$23$	−7.86994	−	4.54371i	−1.64100	−	0.947429i	−0.980481	−	0.196616i	$-0.937005\pi$
$23$	−7.86994	−	4.54371i	−1.64100	−	0.947429i	−0.660515	−	0.750813i	$-0.729662\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−3.59641	+	3.47359i	−0.719282	+	0.694719i
$26$	−2.90321			−0.569367
$27$			1.00000i			0.192450i
$28$	0.680419	+	0.392840i	0.128587	+	0.0742398i
$29$	2.01037	−	3.48207i	0.373317	−	0.646603i	−0.616757	−	0.787154i	$-0.711554\pi$
$29$	2.01037	−	3.48207i	0.373317	−	0.646603i	0.990074	+	0.140550i	$0.0448872\pi$
$30$	−2.21432	−	0.311108i	−0.404278	−	0.0568003i
$31$	−4.42864			−0.795407			−0.397704	−	0.917514i	$-0.630193\pi$
$31$	−4.42864			−0.795407			−0.397704	+	0.917514i	$0.630193\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.327171	−	0.188892i	0.0569531	−	0.0328819i
$34$	1.41827	−	2.45651i	0.243231	−	0.421288i
$35$	1.62888	−	0.658190i	0.275331	−	0.111254i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$		−	0.0967881i		−	0.0159119i	−0.999968	−	0.00795593i	$-0.997468\pi$
$37$		−	0.0967881i		−	0.0159119i	0.999968	−	0.00795593i	$-0.00253248\pi$
$38$	4.10474	+	1.46666i	0.665877	+	0.237924i
$39$	−2.90321			−0.464886
$40$	2.07321	−	0.837733i	0.327803	−	0.132457i
$41$	−1.43655	−	2.48818i	−0.224351	−	0.388588i	0.731773	−	0.681548i	$-0.238693\pi$
$41$	−1.43655	−	2.48818i	−0.224351	−	0.388588i	−0.956125	+	0.292960i	$0.905360\pi$
$42$	0.680419	+	0.392840i	0.104991	+	0.0606165i
$43$	0.371213	−	0.214320i	0.0566094	−	0.0326835i	−0.471428	−	0.881904i	$-0.656261\pi$
$43$	0.371213	−	0.214320i	0.0566094	−	0.0326835i	0.528038	+	0.849221i	$0.322928\pi$
$44$	−0.188892	+	0.327171i	−0.0284766	+	0.0493229i
$45$	−2.21432	−	0.311108i	−0.330091	−	0.0463772i
$46$	9.08742			1.33987
$47$	−10.4680	−	6.04371i	−1.52692	−	0.881566i	−0.999489	−	0.0319658i	$-0.989823\pi$
$47$	−10.4680	−	6.04371i	−1.52692	−	0.881566i	−0.527428	−	0.849600i	$-0.676843\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	6.38271			0.911815
$50$	1.37778	−	4.80642i	0.194848	−	0.679731i
$51$	1.41827	−	2.45651i	0.198597	−	0.343980i
$52$	2.51426	−	1.45161i	0.348664	−	0.201302i
$53$	−6.00443	−	3.46666i	−0.824772	−	0.476183i	0.0272870	−	0.999628i	$-0.491313\pi$
$53$	−6.00443	−	3.46666i	−0.824772	−	0.476183i	−0.852059	+	0.523445i	$0.824647\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	0.316482	+	0.783227i	0.0426745	+	0.105610i
$56$	−0.785680			−0.104991
$57$	4.10474	+	1.46666i	0.543686	+	0.194264i
$58$			4.02074i			0.527949i
$59$	−4.88025	−	8.45283i	−0.635354	−	1.10047i	−0.986440	−	0.164122i	$-0.947521\pi$
$59$	−4.88025	−	8.45283i	−0.635354	−	1.10047i	0.351086	−	0.936343i	$-0.385812\pi$
$60$	2.07321	−	0.837733i	0.267650	−	0.108151i
$61$	−2.27777	+	3.94521i	−0.291639	+	0.505133i	−0.974197	−	0.225698i	$-0.927534\pi$
$61$	−2.27777	+	3.94521i	−0.291639	+	0.505133i	0.682559	+	0.730831i	$0.260867\pi$
$62$	3.83531	−	2.21432i	0.487085	−	0.281219i
$63$	0.680419	+	0.392840i	0.0857247	+	0.0494932i
$64$	−1.00000			−0.125000
$65$	0.903212	−	6.42864i	0.112030	−	0.797375i
$66$	−0.188892	+	0.327171i	−0.0232510	+	0.0402719i
$67$	−7.31738	−	4.22469i	−0.893960	−	0.516128i	−0.0187245	−	0.999825i	$-0.505961\pi$
$67$	−7.31738	−	4.22469i	−0.893960	−	0.516128i	−0.875236	+	0.483696i	$0.839294\pi$
$68$			2.83654i			0.343980i
$69$	9.08742			1.09400
$70$	−1.08156	+	1.38445i	−0.129271	+	0.165473i
$71$	5.86987	+	10.1669i	0.696626	+	1.20659i	0.969630	+	0.244578i	$0.0786495\pi$
$71$	5.86987	+	10.1669i	0.696626	+	1.20659i	−0.273004	+	0.962013i	$0.588017\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	1.95744	−	1.13013i	0.229101	−	0.132271i	−0.381056	−	0.924552i	$-0.624440\pi$
$73$	1.95744	−	1.13013i	0.229101	−	0.132271i	0.610157	+	0.792280i	$0.291106\pi$
$74$	0.0483940	+	0.0838209i	0.00562569	+	0.00974399i
$75$	1.37778	−	4.80642i	0.159093	−	0.554998i
$76$	−4.28814	+	0.782204i	−0.491884	+	0.0897250i
$77$		−	0.296818i		−	0.0338255i
$78$	2.51426	−	1.45161i	0.284683	−	0.164362i
$79$	−0.785680	−	1.36084i	−0.0883959	−	0.153106i	0.818437	−	0.574596i	$-0.194841\pi$
$79$	−0.785680	−	1.36084i	−0.0883959	−	0.153106i	−0.906833	+	0.421490i	$0.861507\pi$
$80$	−1.37659	+	1.76210i	−0.153907	+	0.197009i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.48818	+	1.43655i	0.274773	+	0.158640i
$83$			2.75557i			0.302463i	0.988498	+	0.151231i	$0.0483239\pi$
$83$			2.75557i			0.302463i	−0.988498	+	0.151231i	$0.951676\pi$
$84$	−0.785680			−0.0857247
$85$	4.99827	+	3.90474i	0.542138	+	0.423528i
$86$	−0.214320	+	0.371213i	−0.0231107	+	0.0400289i
$87$			4.02074i			0.431069i
$88$		−	0.377784i		−	0.0402719i
$89$	5.96912	−	10.3388i	0.632726	−	1.09591i	−0.354266	−	0.935145i	$-0.615269\pi$
$89$	5.96912	−	10.3388i	0.632726	−	1.09591i	0.986992	−	0.160769i	$-0.0513973\pi$
$90$	2.07321	−	0.837733i	0.218536	−	0.0883048i
$91$	−1.14050	+	1.97540i	−0.119557	+	0.207078i
$92$	−7.86994	+	4.54371i	−0.820498	+	0.473715i
$93$	3.83531	−	2.21432i	0.397704	−	0.229614i
$94$	12.0874			1.24672
$95$	−4.52468	+	8.63292i	−0.464222	+	0.885719i
$96$	−1.00000			−0.102062
$97$	−2.98299	+	1.72223i	−0.302877	+	0.174866i	−0.643735	−	0.765249i	$-0.722616\pi$
$97$	−2.98299	+	1.72223i	−0.302877	+	0.174866i	0.340858	+	0.940115i	$0.389283\pi$
$98$	−5.52759	+	3.19135i	−0.558371	+	0.322375i
$99$	−0.188892	+	0.327171i	−0.0189844	+	0.0328819i
$100$	1.21002	+	4.85138i	0.121002	+	0.485138i
$101$	−8.54617	+	14.8024i	−0.850376	+	1.47289i	0.0304937	+	0.999535i	$0.490292\pi$
$101$	−8.54617	+	14.8024i	−0.850376	+	1.47289i	−0.880870	+	0.473359i	$0.843041\pi$
$102$			2.83654i			0.280859i
$103$		−	8.11753i		−	0.799844i	−0.916549	−	0.399922i	$-0.869037\pi$
$103$		−	8.11753i		−	0.799844i	0.916549	−	0.399922i	$-0.130963\pi$
$104$	−1.45161	+	2.51426i	−0.142342	+	0.246543i
$105$	−1.08156	+	1.38445i	−0.105549	+	0.135108i
$106$	6.93332			0.673424
$107$			17.7812i			1.71898i	0.511155	+	0.859488i	$0.329218\pi$
$107$			17.7812i			1.71898i	−0.511155	+	0.859488i	$0.670782\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	0.722230	+	1.25094i	0.0691771	+	0.119818i	0.898539	−	0.438893i	$-0.144629\pi$
$109$	0.722230	+	1.25094i	0.0691771	+	0.119818i	−0.829362	+	0.558711i	$0.811296\pi$
$110$	−0.665695	−	0.520053i	−0.0634715	−	0.0495851i
$111$	0.0483940	+	0.0838209i	0.00459336	+	0.00795593i
$112$	0.680419	−	0.392840i	0.0642936	−	0.0371199i
$113$		−	14.3160i		−	1.34674i	−0.739306	−	0.673369i	$-0.764846\pi$
$113$		−	14.3160i		−	1.34674i	0.739306	−	0.673369i	$-0.235154\pi$
$114$	−4.28814	+	0.782204i	−0.401621	+	0.0732602i
$115$	−2.82717	+	20.1225i	−0.263635	+	1.87643i
$116$	−2.01037	−	3.48207i	−0.186658	−	0.323302i
$117$	2.51426	−	1.45161i	0.232443	−	0.134201i
$118$	8.45283	+	4.88025i	0.778146	+	0.449263i
$119$	−1.11430	−	1.93003i	−0.102148	−	0.176926i
$120$	−1.37659	+	1.76210i	−0.125665	+	0.160857i
$121$	−10.8573			−0.987025
$122$		−	4.55554i		−	0.412439i
$123$	2.48818	+	1.43655i	0.224351	+	0.129529i
$124$	−2.21432	+	3.83531i	−0.198852	+	0.344421i
$125$	10.2143	+	4.54617i	0.913597	+	0.406622i
$126$	−0.785680			−0.0699940
$127$	3.14252	+	1.81433i	0.278854	+	0.160996i	0.632904	−	0.774230i	$-0.281863\pi$
$127$	3.14252	+	1.81433i	0.278854	+	0.160996i	−0.354051	+	0.935226i	$0.615196\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−0.214320	+	0.371213i	−0.0188698	+	0.0326835i
$130$	2.43212	+	6.01897i	0.213311	+	0.527899i
$131$	8.40321	+	14.5548i	0.734192	+	1.27166i	0.955077	+	0.296358i	$0.0957722\pi$
$131$	8.40321	+	14.5548i	0.734192	+	1.27166i	−0.220885	+	0.975300i	$0.570895\pi$
$132$		−	0.377784i		−	0.0328819i
$133$	2.61045	−	2.21678i	0.226355	−	0.192219i
$134$	8.44938			0.729916
$135$	2.07321	−	0.837733i	0.178434	−	0.0721005i
$136$	−1.41827	−	2.45651i	−0.121615	−	0.210644i
$137$	1.89969	+	1.09679i	0.162302	+	0.0937049i	0.578951	−	0.815362i	$-0.303462\pi$
$137$	1.89969	+	1.09679i	0.162302	+	0.0937049i	−0.416649	+	0.909067i	$0.636796\pi$
$138$	−7.86994	+	4.54371i	−0.669934	+	0.386786i
$139$	0.836535	−	1.44892i	0.0709540	−	0.122896i	−0.828366	−	0.560188i	$-0.810729\pi$
$139$	0.836535	−	1.44892i	0.0709540	−	0.122896i	0.899320	+	0.437292i	$0.144062\pi$
$140$	0.244431	−	1.73975i	0.0206582	−	0.147035i
$141$	12.0874			1.01794
$142$	−10.1669	−	5.86987i	−0.853189	−	0.492589i
$143$	−0.949846	−	0.548394i	−0.0794301	−	0.0458590i
$144$	−1.00000			−0.0833333
$145$	−8.90321	−	1.25088i	−0.739372	−	0.103880i
$146$	−1.13013	+	1.95744i	−0.0935299	+	0.161999i
$147$	−5.52759	+	3.19135i	−0.455908	+	0.263218i
$148$	−0.0838209	−	0.0483940i	−0.00689004	−	0.00397797i
$149$	2.69926	+	4.67526i	0.221132	+	0.383012i	0.955152	−	0.296116i	$-0.0956914\pi$
$149$	2.69926	+	4.67526i	0.221132	+	0.383012i	−0.734020	+	0.679128i	$0.762358\pi$
$150$	1.21002	+	4.85138i	0.0987974	+	0.396113i
$151$	9.07160			0.738236			0.369118	−	0.929382i	$-0.379660\pi$
$151$	9.07160			0.738236			0.369118	+	0.929382i	$0.379660\pi$
$152$	3.32254	−	2.82148i	0.269493	−	0.228852i
$153$			2.83654i			0.229320i
$154$	0.148409	+	0.257052i	0.0119591	+	0.0207138i
$155$	3.71002	+	9.18150i	0.297996	+	0.737476i
$156$	−1.45161	+	2.51426i	−0.116221	+	0.201302i
$157$	13.3094	−	7.68421i	1.06221	−	0.613267i	0.136166	−	0.990686i	$-0.456522\pi$
$157$	13.3094	−	7.68421i	1.06221	−	0.613267i	0.926042	+	0.377419i	$0.123188\pi$
$158$	1.36084	+	0.785680i	0.108262	+	0.0625054i
$159$	6.93332			0.549848
$160$	0.311108	−	2.21432i	0.0245952	−	0.175057i
$161$	3.56990	−	6.18325i	0.281348	−	0.487309i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$			7.31756i			0.573156i	0.958057	+	0.286578i	$0.0925177\pi$
$163$			7.31756i			0.573156i	−0.958057	+	0.286578i	$0.907482\pi$
$164$	−2.87310			−0.224351
$165$	−0.665695	−	0.520053i	−0.0518243	−	0.0404861i
$166$	−1.37778	−	2.38639i	−0.106937	−	0.185220i
$167$	−5.03277	−	2.90567i	−0.389448	−	0.224848i	0.292473	−	0.956274i	$-0.405522\pi$
$167$	−5.03277	−	2.90567i	−0.389448	−	0.224848i	−0.681921	+	0.731426i	$0.738855\pi$
$168$	0.680419	−	0.392840i	0.0524955	−	0.0303083i
$169$	−2.28568	−	3.95891i	−0.175822	−	0.304532i
$170$	−6.28100	−	0.882468i	−0.481730	−	0.0676822i
$171$	−4.28814	+	0.782204i	−0.327922	+	0.0598167i
$172$		−	0.428639i		−	0.0326835i
$173$	7.55647	−	4.36273i	0.574508	−	0.331692i	−0.184440	−	0.982844i	$-0.559047\pi$
$173$	7.55647	−	4.36273i	0.574508	−	0.331692i	0.758948	+	0.651152i	$0.225714\pi$
$174$	−2.01037	−	3.48207i	−0.152406	−	0.263975i
$175$	−2.72913	−	2.82563i	−0.206303	−	0.213597i
$176$	0.188892	+	0.327171i	0.0142383	+	0.0246614i
$177$	8.45283	+	4.88025i	0.635354	+	0.366822i
$178$			11.9382i			0.894809i
$179$	23.2306			1.73634			0.868169	−	0.496269i	$-0.165297\pi$
$179$	23.2306			1.73634			0.868169	+	0.496269i	$0.165297\pi$
$180$	−1.37659	+	1.76210i	−0.102605	+	0.131339i
$181$	−3.77309	+	6.53518i	−0.280451	+	0.485756i	−0.971496	−	0.237056i	$-0.923817\pi$
$181$	−3.77309	+	6.53518i	−0.280451	+	0.485756i	0.691045	+	0.722812i	$0.257151\pi$
$182$		−	2.28100i		−	0.169079i
$183$		−	4.55554i		−	0.336755i
$184$	4.54371	−	7.86994i	0.334967	−	0.580179i
$185$	−0.200662	+	0.0810825i	−0.0147530	+	0.00596131i
$186$	−2.21432	+	3.83531i	−0.162362	+	0.281219i
$187$	0.928032	−	0.535799i	0.0678644	−	0.0391815i
$188$	−10.4680	+	6.04371i	−0.763458	+	0.440783i
$189$	−0.785680			−0.0571498
$190$	−0.397977	−	9.73867i	−0.0288723	−	0.706517i
$191$	−20.4701			−1.48117			−0.740583	−	0.671965i	$-0.765451\pi$
$191$	−20.4701			−1.48117			−0.740583	+	0.671965i	$0.765451\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	16.3886	−	9.46198i	1.17968	−	0.681088i	0.223739	−	0.974649i	$-0.428174\pi$
$193$	16.3886	−	9.46198i	1.17968	−	0.681088i	0.955940	+	0.293561i	$0.0948404\pi$
$194$	1.72223	−	2.98299i	0.123649	−	0.214166i
$195$	2.43212	+	6.01897i	0.174167	+	0.431027i
$196$	3.19135	−	5.52759i	0.227954	−	0.394828i
$197$			1.73038i			0.123284i	0.998098	+	0.0616422i	$0.0196338\pi$
$197$			1.73038i			0.123284i	−0.998098	+	0.0616422i	$0.980366\pi$
$198$		−	0.377784i		−	0.0268480i
$199$	7.53580	−	13.0524i	0.534199	−	0.925259i	−0.465003	−	0.885309i	$-0.653947\pi$
$199$	7.53580	−	13.0524i	0.534199	−	0.925259i	0.999202	−	0.0399501i	$-0.0127199\pi$
$200$	−3.47359	−	3.59641i	−0.245620	−	0.254304i
$201$	8.44938			0.595974
$202$		−	17.0923i		−	1.20261i
$203$	2.73579	+	1.57951i	0.192015	+	0.110860i
$204$	−1.41827	−	2.45651i	−0.0992986	−	0.171990i
$205$	−3.95507	+	5.06270i	−0.276234	+	0.353594i
$206$	4.05877	+	7.02999i	0.282788	+	0.489803i
$207$	−7.86994	+	4.54371i	−0.546998	+	0.315810i
$208$		−	2.90321i		−	0.201302i
$209$	1.06591	+	1.25520i	0.0737306	+	0.0868242i
$210$	0.244431	−	1.73975i	0.0168674	−	0.120054i
$211$	−6.65801	−	11.5320i	−0.458357	−	0.793897i	0.540518	−	0.841333i	$-0.318228\pi$
$211$	−6.65801	−	11.5320i	−0.458357	−	0.793897i	−0.998874	+	0.0474357i	$0.984895\pi$
$212$	−6.00443	+	3.46666i	−0.412386	+	0.238091i
$213$	−10.1669	−	5.86987i	−0.696626	−	0.402197i
$214$	−8.89062	−	15.3990i	−0.607750	−	1.05265i
$215$	−0.755307	−	0.590060i	−0.0515115	−	0.0402417i
$216$	−1.00000			−0.0680414
$217$		−	3.47949i		−	0.236203i
$218$	−1.25094	−	0.722230i	−0.0847243	−	0.0489156i
$219$	−1.13013	+	1.95744i	−0.0763669	+	0.132271i
$220$	0.836535	+	0.117532i	0.0563992	+	0.00792398i
$221$	−8.23506			−0.553950
$222$	−0.0838209	−	0.0483940i	−0.00562569	−	0.00324800i
$223$	−16.6003	+	9.58419i	−1.11164	+	0.641805i	−0.939253	−	0.343224i	$-0.888481\pi$
$223$	−16.6003	+	9.58419i	−1.11164	+	0.641805i	−0.172386	+	0.985030i	$0.555148\pi$
$224$	−0.392840	+	0.680419i	−0.0262477	+	0.0454624i
$225$	1.21002	+	4.85138i	0.0806677	+	0.323425i
$226$	7.15801	+	12.3980i	0.476144	+	0.824706i
$227$			6.88247i			0.456805i	0.973567	+	0.228403i	$0.0733503\pi$
$227$			6.88247i			0.456805i	−0.973567	+	0.228403i	$0.926650\pi$
$228$	3.32254	−	2.82148i	0.220040	−	0.186857i
$229$	−13.7462			−0.908375			−0.454187	−	0.890906i	$-0.650070\pi$
$229$	−13.7462			−0.908375			−0.454187	+	0.890906i	$0.650070\pi$
$230$	−7.61283	−	18.8401i	−0.501975	−	1.24228i
$231$	0.148409	+	0.257052i	0.00976459	+	0.0169128i
$232$	3.48207	+	2.01037i	0.228609	+	0.131987i
$233$	5.88642	−	3.39853i	0.385632	−	0.222645i	−0.294634	−	0.955610i	$-0.595198\pi$
$233$	5.88642	−	3.39853i	0.385632	−	0.222645i	0.680266	+	0.732965i	$0.261864\pi$
$234$	−1.45161	+	2.51426i	−0.0948945	+	0.164362i
$235$	−3.76049	+	26.7654i	−0.245307	+	1.74598i
$236$	−9.76049			−0.635354
$237$	1.36084	+	0.785680i	0.0883959	+	0.0510354i
$238$	1.93003	+	1.11430i	0.125105	+	0.0722297i
$239$	10.8573			0.702299			0.351149	−	0.936319i	$-0.385791\pi$
$239$	10.8573			0.702299			0.351149	+	0.936319i	$0.385791\pi$
$240$	0.311108	−	2.21432i	0.0200819	−	0.142934i
$241$	4.84368	−	8.38950i	0.312009	−	0.540415i	−0.666788	−	0.745247i	$-0.732331\pi$
$241$	4.84368	−	8.38950i	0.312009	−	0.540415i	0.978797	+	0.204832i	$0.0656648\pi$
$242$	9.40268	−	5.42864i	0.604427	−	0.348966i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	2.27777	+	3.94521i	0.145819	+	0.252566i
$245$	−5.34700	−	13.2327i	−0.341607	−	0.845406i
$246$	−2.87310			−0.183182
$247$	−2.27091	−	12.4494i	−0.144494	−	0.792135i
$248$		−	4.42864i		−	0.281219i
$249$	−1.37778	−	2.38639i	−0.0873135	−	0.151231i
$250$	−11.1189	+	1.17006i	−0.703224	+	0.0740011i
$251$	−7.54617	+	13.0704i	−0.476310	+	0.824993i	−0.999632	−	0.0271420i	$-0.991359\pi$
$251$	−7.54617	+	13.0704i	−0.476310	+	0.824993i	0.523321	+	0.852135i	$0.324693\pi$
$252$	0.680419	−	0.392840i	0.0428624	−	0.0247466i
$253$	2.97314	+	1.71654i	0.186920	+	0.107918i
$254$	−3.62867			−0.227683
$255$	−6.28100	−	0.882468i	−0.393331	−	0.0552623i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	19.7676	+	11.4128i	1.23307	+	0.711912i	0.967668	−	0.252226i	$-0.0811628\pi$
$257$	19.7676	+	11.4128i	1.23307	+	0.711912i	0.265400	+	0.964139i	$0.414496\pi$
$258$		−	0.428639i		−	0.0266859i
$259$	0.0760445			0.00472517
$260$	−5.11576	−	3.99652i	−0.317266	−	0.247854i
$261$	−2.01037	−	3.48207i	−0.124439	−	0.215534i
$262$	−14.5548	−	8.40321i	−0.899198	−	0.519152i
$263$	10.4885	−	6.05554i	0.646749	−	0.373401i	−0.140461	−	0.990086i	$-0.544858\pi$
$263$	10.4885	−	6.05554i	0.646749	−	0.373401i	0.787209	+	0.616686i	$0.211525\pi$
$264$	0.188892	+	0.327171i	0.0116255	+	0.0201360i
$265$	−2.15701	+	15.3526i	−0.132504	+	0.943102i
$266$	−1.15233	+	3.22501i	−0.0706537	+	0.197738i
$267$			11.9382i			0.730609i
$268$	−7.31738	+	4.22469i	−0.446980	+	0.258064i
$269$	−12.6168	−	21.8529i	−0.769258	−	1.33239i	−0.937966	−	0.346728i	$-0.887293\pi$
$269$	−12.6168	−	21.8529i	−0.769258	−	1.33239i	0.168708	−	0.985666i	$-0.446040\pi$
$270$	−1.37659	+	1.76210i	−0.0837764	+	0.107238i
$271$	−15.4652	−	26.7865i	−0.939444	−	1.62717i	−0.766511	−	0.642232i	$-0.778009\pi$
$271$	−15.4652	−	26.7865i	−0.939444	−	1.62717i	−0.172934	−	0.984933i	$-0.555325\pi$
$272$	2.45651	+	1.41827i	0.148948	+	0.0859951i
$273$		−	2.28100i		−	0.138052i
$274$	−2.19358			−0.132519
$275$	1.35867	−	1.31227i	0.0819307	−	0.0791328i
$276$	4.54371	−	7.86994i	0.273499	−	0.473715i
$277$		−	19.4938i		−	1.17127i	−0.810576	−	0.585634i	$-0.800846\pi$
$277$		−	19.4938i		−	1.17127i	0.810576	−	0.585634i	$-0.199154\pi$
$278$			1.67307i			0.100344i
$279$	−2.21432	+	3.83531i	−0.132568	+	0.229614i
$280$	0.658190	+	1.62888i	0.0393344	+	0.0973443i
$281$	3.71755	−	6.43898i	0.221770	−	0.384117i	−0.733575	−	0.679608i	$-0.762150\pi$
$281$	3.71755	−	6.43898i	0.221770	−	0.384117i	0.955346	+	0.295491i	$0.0954832\pi$
$282$	−10.4680	+	6.04371i	−0.623361	+	0.359898i
$283$	1.48485	−	0.857279i	0.0882652	−	0.0509599i	−0.455218	−	0.890380i	$-0.650439\pi$
$283$	1.48485	−	0.857279i	0.0882652	−	0.0509599i	0.543483	+	0.839420i	$0.317105\pi$
$284$	11.7397			0.696626
$285$	−0.397977	−	9.73867i	−0.0235741	−	0.576869i
$286$	1.09679			0.0648544
$287$	1.95491	−	1.12867i	0.115395	−	0.0666232i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−4.47703	+	7.75445i	−0.263355	+	0.456144i
$290$	8.33585	−	3.36831i	0.489498	−	0.197794i
$291$	1.72223	−	2.98299i	0.100959	−	0.174866i
$292$		−	2.26025i		−	0.132271i
$293$		−	7.93825i		−	0.463757i	−0.972745	−	0.231879i	$-0.925513\pi$
$293$		−	7.93825i		−	0.463757i	0.972745	−	0.231879i	$-0.0744872\pi$
$294$	3.19135	−	5.52759i	0.186124	−	0.322375i
$295$	−13.4362	+	17.1990i	−0.782284	+	1.00136i
$296$	0.0967881			0.00562569
$297$		−	0.377784i		−	0.0219213i
$298$	−4.67526	−	2.69926i	−0.270831	−	0.156364i
$299$	−13.1914	−	22.8481i	−0.762876	−	1.32134i
$300$	−3.47359	−	3.59641i	−0.200548	−	0.207639i
$301$	0.168387	+	0.291654i	0.00970565	+	0.0168107i
$302$	−7.85623	+	4.53580i	−0.452076	+	0.261006i
$303$		−	17.0923i		−	0.981929i
$304$	−1.46666	+	4.10474i	−0.0841188	+	0.235423i
$305$	10.0874	+	1.41726i	0.577604	+	0.0811523i
$306$	−1.41827	−	2.45651i	−0.0810770	−	0.140429i
$307$	−0.919506	+	0.530877i	−0.0524790	+	0.0302988i	−0.526010	−	0.850478i	$-0.676313\pi$
$307$	−0.919506	+	0.530877i	−0.0524790	+	0.0302988i	0.473531	+	0.880777i	$0.342979\pi$
$308$	−0.257052	−	0.148409i	−0.0146469	−	0.00845638i
$309$	4.05877	+	7.02999i	0.230895	+	0.399922i
$310$	−7.80372	−	6.09641i	−0.443222	−	0.346253i
$311$	17.5210			0.993524			0.496762	−	0.867887i	$-0.334522\pi$
$311$	17.5210			0.993524			0.496762	+	0.867887i	$0.334522\pi$
$312$		−	2.90321i		−	0.164362i
$313$	−10.6480	−	6.14764i	−0.601862	−	0.347485i	0.167912	−	0.985802i	$-0.446298\pi$
$313$	−10.6480	−	6.14764i	−0.601862	−	0.347485i	−0.769774	+	0.638317i	$0.779631\pi$
$314$	−7.68421	+	13.3094i	−0.433645	+	0.751095i
$315$	0.244431	−	1.73975i	0.0137721	−	0.0980237i
$316$	−1.57136			−0.0883959
$317$	20.7188	+	11.9620i	1.16368	+	0.671852i	0.952183	−	0.305527i	$-0.0988326\pi$
$317$	20.7188	+	11.9620i	1.16368	+	0.671852i	0.211498	+	0.977379i	$0.432166\pi$
$318$	−6.00443	+	3.46666i	−0.336712	+	0.194401i
$319$	−0.759487	+	1.31547i	−0.0425231	+	0.0736522i
$320$	0.837733	+	2.07321i	0.0468307	+	0.115896i
$321$	−8.89062	−	15.3990i	−0.496226	−	0.859488i
$322$			7.13981i			0.397886i
$323$	11.6432	+	4.16024i	0.647847	+	0.231482i
$324$	−1.00000			−0.0555556
$325$	−14.0846	+	3.51293i	−0.781272	+	0.194862i
$326$	−3.65878	−	6.33719i	−0.202641	−	0.350985i
$327$	−1.25094	−	0.722230i	−0.0691771	−	0.0399394i
$328$	2.48818	−	1.43655i	0.137387	−	0.0793202i
$329$	4.74842	−	8.22451i	0.261789	−	0.453432i
$330$	0.836535	+	0.117532i	0.0460498	+	0.00646991i
$331$	13.0810			0.718995			0.359497	−	0.933146i	$-0.382948\pi$
$331$	13.0810			0.718995			0.359497	+	0.933146i	$0.382948\pi$
$332$	2.38639	+	1.37778i	0.130970	+	0.0756157i
$333$	−0.0838209	−	0.0483940i	−0.00459336	−	0.00265198i
$334$	5.81135			0.317983
$335$	−2.62867	+	18.7096i	−0.143620	+	1.02222i
$336$	−0.392840	+	0.680419i	−0.0214312	+	0.0371199i
$337$	14.3953	−	8.31111i	0.784160	−	0.452735i	−0.0537427	−	0.998555i	$-0.517115\pi$
$337$	14.3953	−	8.31111i	0.784160	−	0.452735i	0.837903	+	0.545820i	$0.183782\pi$
$338$	3.95891	+	2.28568i	0.215337	+	0.124325i
$339$	7.15801	+	12.3980i	0.388770	+	0.673369i
$340$	5.88074	−	2.37626i	0.318928	−	0.128871i
$341$	1.67307			0.0906019
$342$	3.32254	−	2.82148i	0.179662	−	0.152568i
$343$			10.5145i			0.567731i
$344$	0.214320	+	0.371213i	0.0115553	+	0.0200144i
$345$	−7.61283	−	18.8401i	−0.409861	−	1.01432i
$346$	−4.36273	+	7.55647i	−0.234542	+	0.406238i
$347$	4.62989	−	2.67307i	0.248546	−	0.143498i	−0.370552	−	0.928812i	$-0.620832\pi$
$347$	4.62989	−	2.67307i	0.248546	−	0.143498i	0.619098	+	0.785314i	$0.287498\pi$
$348$	3.48207	+	2.01037i	0.186658	+	0.107767i
$349$	−0.882468			−0.0472374			−0.0236187	−	0.999721i	$-0.507519\pi$
$349$	−0.882468			−0.0472374			−0.0236187	+	0.999721i	$0.507519\pi$
$350$	3.77631	+	1.08250i	0.201852	+	0.0578620i
$351$	−1.45161	+	2.51426i	−0.0774810	+	0.134201i
$352$	−0.327171	−	0.188892i	−0.0174383	−	0.0100680i
$353$			15.1032i			0.803864i	0.915669	+	0.401932i	$0.131661\pi$
$353$			15.1032i			0.803864i	−0.915669	+	0.401932i	$0.868339\pi$
$354$	−9.76049			−0.518764
$355$	16.1608	−	20.6866i	0.857725	−	1.09793i
$356$	−5.96912	−	10.3388i	−0.316363	−	0.547957i
$357$	1.93003	+	1.11430i	0.102148	+	0.0589753i
$358$	−20.1183	+	11.6153i	−1.06329	+	0.613888i
$359$	−7.82394	−	13.5515i	−0.412932	−	0.715219i	0.582277	−	0.812990i	$-0.302162\pi$
$359$	−7.82394	−	13.5515i	−0.412932	−	0.715219i	−0.995209	+	0.0977715i	$0.968829\pi$
$360$	0.311108	−	2.21432i	0.0163968	−	0.116705i
$361$	−3.07851	+	18.7489i	−0.162027	+	0.986786i
$362$		−	7.54617i		−	0.396618i
$363$	9.40268	−	5.42864i	0.493513	−	0.284930i
$364$	1.14050	+	1.97540i	0.0597783	+	0.103539i
$365$	−3.98280	−	3.11143i	−0.208469	−	0.162860i
$366$	2.27777	+	3.94521i	0.119061	+	0.206220i
$367$	−27.8642	−	16.0874i	−1.45450	−	0.839756i	−0.455769	−	0.890098i	$-0.650636\pi$
$367$	−27.8642	−	16.0874i	−1.45450	−	0.839756i	−0.998732	+	0.0503417i	$0.983969\pi$
$368$			9.08742i			0.473715i
$369$	−2.87310			−0.149568
$370$	0.133237	−	0.170551i	0.00692667	−	0.00886650i
$371$	2.72369	−	4.71757i	0.141407	−	0.244924i
$372$		−	4.42864i		−	0.229614i
$373$			15.1160i			0.782677i	0.920247	+	0.391338i	$0.127988\pi$
$373$			15.1160i			0.782677i	−0.920247	+	0.391338i	$0.872012\pi$
$374$	−0.535799	+	0.928032i	−0.0277055	+	0.0479874i
$375$	−11.1189	+	1.17006i	−0.574180	+	0.0604216i
$376$	6.04371	−	10.4680i	0.311681	−	0.539847i
$377$	10.1092	−	5.83654i	0.520649	−	0.300597i
$378$	0.680419	−	0.392840i	0.0349970	−	0.0202055i
$379$	0.907658			0.0466232			0.0233116	−	0.999728i	$-0.492579\pi$
$379$	0.907658			0.0466232			0.0233116	+	0.999728i	$0.492579\pi$
$380$	5.21399	+	8.23494i	0.267472	+	0.422444i
$381$	−3.62867			−0.185902
$382$	17.7276	−	10.2351i	0.907025	−	0.523671i
$383$	0.526479	−	0.303963i	0.0269018	−	0.0155318i	−0.486489	−	0.873687i	$-0.661723\pi$
$383$	0.526479	−	0.303963i	0.0269018	−	0.0155318i	0.513391	+	0.858155i	$0.328389\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−0.615366	+	0.248654i	−0.0313619	+	0.0126726i
$386$	−9.46198	+	16.3886i	−0.481602	+	0.834159i
$387$		−	0.428639i		−	0.0217890i
$388$			3.44446i			0.174866i
$389$	−6.04048	+	10.4624i	−0.306265	+	0.530466i	−0.977542	−	0.210740i	$-0.932413\pi$
$389$	−6.04048	+	10.4624i	−0.306265	+	0.530466i	0.671277	+	0.741206i	$0.265746\pi$
$390$	−5.11576	−	3.99652i	−0.259047	−	0.202372i
$391$	25.7768			1.30359
$392$			6.38271i			0.322375i
$393$	−14.5548	−	8.40321i	−0.734192	−	0.423886i
$394$	−0.865190	−	1.49855i	−0.0435876	−	0.0754960i
$395$	−2.16311	+	2.76890i	−0.108838	+	0.139318i
$396$	0.188892	+	0.327171i	0.00949219	+	0.0164410i
$397$	16.3351	−	9.43110i	0.819837	−	0.473333i	−0.0305230	−	0.999534i	$-0.509717\pi$
$397$	16.3351	−	9.43110i	0.819837	−	0.473333i	0.850360	+	0.526201i	$0.176384\pi$
$398$			15.0716i			0.755471i
$399$	−1.15233	+	3.22501i	−0.0576885	+	0.161453i
$400$	4.80642	+	1.37778i	0.240321	+	0.0688892i
$401$	−4.88739	−	8.46521i	−0.244065	−	0.422732i	0.717804	−	0.696246i	$-0.245148\pi$
$401$	−4.88739	−	8.46521i	−0.244065	−	0.422732i	−0.961868	+	0.273513i	$0.911814\pi$
$402$	−7.31738	+	4.22469i	−0.364958	+	0.210708i
$403$	−11.1347	−	6.42864i	−0.554660	−	0.320233i
$404$	8.54617	+	14.8024i	0.425188	+	0.736447i
$405$	−1.37659	+	1.76210i	−0.0684032	+	0.0875596i
$406$	−3.15902			−0.156779
$407$			0.0365650i			0.00181246i
$408$	2.45651	+	1.41827i	0.121615	+	0.0702147i
$409$	−19.1916	+	33.2408i	−0.948963	+	1.64365i	−0.201348	+	0.979520i	$0.564532\pi$
$409$	−19.1916	+	33.2408i	−0.948963	+	1.64365i	−0.747615	+	0.664133i	$0.768801\pi$
$410$	0.893844	−	6.36196i	0.0441438	−	0.314195i
$411$	−2.19358			−0.108201
$412$	−7.02999	−	4.05877i	−0.346343	−	0.199961i
$413$	6.64122	−	3.83431i	0.326793	−	0.188674i
$414$	4.54371	−	7.86994i	0.223311	−	0.386786i
$415$	5.71288	−	2.30843i	0.280434	−	0.113316i
$416$	1.45161	+	2.51426i	0.0711708	+	0.123272i
$417$			1.67307i			0.0819306i
$418$	−1.55071	−	0.554082i	−0.0758476	−	0.0271010i
$419$	−30.7560			−1.50253			−0.751266	−	0.660000i	$-0.770556\pi$
$419$	−30.7560			−1.50253			−0.751266	+	0.660000i	$0.770556\pi$
$420$	0.658190	+	1.62888i	0.0321164	+	0.0794813i
$421$	6.31433	+	10.9367i	0.307742	+	0.533024i	0.977868	−	0.209223i	$-0.0670934\pi$
$421$	6.31433	+	10.9367i	0.307742	+	0.533024i	−0.670126	+	0.742247i	$0.733760\pi$
$422$	11.5320	+	6.65801i	0.561370	+	0.324107i
$423$	−10.4680	+	6.04371i	−0.508972	+	0.293855i
$424$	3.46666	−	6.00443i	0.168356	−	0.291601i
$425$	3.90813	−	13.6336i	0.189572	−	0.661326i
$426$	11.7397			0.568793
$427$	−3.09968	−	1.78960i	−0.150004	−	0.0866047i
$428$	15.3990	+	8.89062i	0.744339	+	0.429744i
$429$	1.09679			0.0529534
$430$	0.949145	+	0.133353i	0.0457718	+	0.00643086i
$431$	17.6763	−	30.6162i	0.851437	−	1.47473i	−0.0284739	−	0.999595i	$-0.509065\pi$
$431$	17.6763	−	30.6162i	0.851437	−	1.47473i	0.879911	−	0.475138i	$-0.157602\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−18.0052	−	10.3953i	−0.865274	−	0.499566i	0.000500727	−	1.00000i	$-0.499841\pi$
$433$	−18.0052	−	10.3953i	−0.865274	−	0.499566i	−0.865775	+	0.500434i	$0.833174\pi$
$434$	1.73975	+	3.01333i	0.0835105	+	0.144645i
$435$	8.33585	−	3.36831i	0.399673	−	0.161498i
$436$	1.44446			0.0691771
$437$	7.10822	+	38.9681i	0.340032	+	1.86410i
$438$		−	2.26025i		−	0.107999i
$439$	−1.96444	−	3.40251i	−0.0937576	−	0.162393i	0.815332	−	0.578994i	$-0.196555\pi$
$439$	−1.96444	−	3.40251i	−0.0937576	−	0.162393i	−0.909089	+	0.416601i	$0.863221\pi$
$440$	−0.783227	+	0.316482i	−0.0373389	+	0.0150877i
$441$	3.19135	−	5.52759i	0.151969	−	0.263218i
$442$	7.13177	−	4.11753i	0.339224	−	0.195851i
$443$	1.38265	+	0.798275i	0.0656918	+	0.0379272i	0.532486	−	0.846439i	$-0.321258\pi$
$443$	1.38265	+	0.798275i	0.0656918	+	0.0379272i	−0.466794	+	0.884366i	$0.654591\pi$
$444$	0.0967881			0.00459336
$445$	−26.4351	−	3.71408i	−1.25314	−	0.176064i
$446$	9.58419	−	16.6003i	0.453825	−	0.786047i
$447$	−4.67526	−	2.69926i	−0.221132	−	0.127671i
$448$		−	0.785680i		−	0.0371199i
$449$	14.4588			0.682351			0.341175	−	0.940000i	$-0.389175\pi$
$449$	14.4588			0.682351			0.341175	+	0.940000i	$0.389175\pi$
$450$	−3.47359	−	3.59641i	−0.163747	−	0.169536i
$451$	0.542706	+	0.939995i	0.0255550	+	0.0442626i
$452$	−12.3980	−	7.15801i	−0.583155	−	0.336685i
$453$	−7.85623	+	4.53580i	−0.369118	+	0.213110i
$454$	−3.44123	−	5.96039i	−0.161505	−	0.279735i
$455$	5.05086	+	0.709636i	0.236788	+	0.0332682i
$456$	−1.46666	+	4.10474i	−0.0686827	+	0.192222i
$457$			28.9052i			1.35213i	0.736842	+	0.676065i	$0.236316\pi$
$457$			28.9052i			1.35213i	−0.736842	+	0.676065i	$0.763684\pi$
$458$	11.9046	−	6.87310i	0.556264	−	0.321159i
$459$	−1.41827	−	2.45651i	−0.0661991	−	0.114660i
$460$	16.0130	+	12.5096i	0.746609	+	0.583264i
$461$	−1.22369	−	2.11949i	−0.0569928	−	0.0987145i	0.836121	−	0.548545i	$-0.184818\pi$
$461$	−1.22369	−	2.11949i	−0.0569928	−	0.0987145i	−0.893114	+	0.449830i	$0.851485\pi$
$462$	−0.257052	−	0.148409i	−0.0119591	−	0.00690460i
$463$		−	7.67460i		−	0.356669i	−0.983970	−	0.178335i	$-0.942929\pi$
$463$		−	7.67460i		−	0.356669i	0.983970	−	0.178335i	$-0.0570709\pi$
$464$	−4.02074			−0.186658
$465$	−7.80372	−	6.09641i	−0.361889	−	0.282714i
$466$	−3.39853	+	5.88642i	−0.157434	+	0.272683i
$467$			9.78123i			0.452622i	0.974055	+	0.226311i	$0.0726665\pi$
$467$			9.78123i			0.452622i	−0.974055	+	0.226311i	$0.927334\pi$
$468$		−	2.90321i		−	0.134201i
$469$	3.31926	−	5.74912i	0.153269	−	0.265470i
$470$	−10.1260	−	25.0598i	−0.467079	−	1.15592i
$471$	−7.68421	+	13.3094i	−0.354070	+	0.613267i
$472$	8.45283	−	4.88025i	0.389073	−	0.224632i
$473$	−0.140238	+	0.0809666i	−0.00644817	+	0.00372285i
$474$	−1.57136			−0.0721750
$475$	21.6883	+	2.14853i	0.995129	+	0.0985812i
$476$	−2.22861			−0.102148
$477$	−6.00443	+	3.46666i	−0.274924	+	0.158728i
$478$	−9.40268	+	5.42864i	−0.430069	+	0.248300i
$479$	−16.9716	+	29.3956i	−0.775451	+	1.34312i	0.159089	+	0.987264i	$0.449144\pi$
$479$	−16.9716	+	29.3956i	−0.775451	+	1.34312i	−0.934540	+	0.355857i	$0.884189\pi$
$480$	0.837733	+	2.07321i	0.0382371	+	0.0946287i
$481$	0.140498	−	0.243350i	0.00640616	−	0.0110958i
$482$			9.68736i			0.441247i
$483$			7.13981i			0.324872i
$484$	−5.42864	+	9.40268i	−0.246756	+	0.427395i
$485$	6.06950	+	4.74160i	0.275602	+	0.215305i
$486$	−1.00000			−0.0453609
$487$		−	33.8780i		−	1.53516i	−0.640953	−	0.767580i	$-0.721461\pi$
$487$		−	33.8780i		−	1.53516i	0.640953	−	0.767580i	$-0.278539\pi$
$488$	−3.94521	−	2.27777i	−0.178591	−	0.103110i
$489$	−3.65878	−	6.33719i	−0.165456	−	0.286578i
$490$	11.2470	+	8.78635i	0.508087	+	0.396927i
$491$	20.5622	+	35.6148i	0.927960	+	1.60727i	0.786729	+	0.617298i	$0.211773\pi$
$491$	20.5622	+	35.6148i	0.927960	+	1.60727i	0.141231	+	0.989977i	$0.454894\pi$
$492$	2.48818	−	1.43655i	0.112176	−	0.0647647i
$493$			11.4050i			0.513655i
$494$	8.19135	+	9.64603i	0.368546	+	0.433995i
$495$	0.836535	+	0.117532i	0.0375995	+	0.00528266i
$496$	2.21432	+	3.83531i	0.0994259	+	0.172211i
$497$	−7.98795	+	4.61184i	−0.358308	+	0.206869i
$498$	2.38639	+	1.37778i	0.106937	+	0.0617400i
$499$	9.98987	+	17.3030i	0.447208	+	0.774587i	0.998203	−	0.0599217i	$-0.0190851\pi$
$499$	9.98987	+	17.3030i	0.447208	+	0.774587i	−0.550995	+	0.834508i	$0.685752\pi$
$500$	9.04426	−	6.57277i	0.404472	−	0.293943i
$501$	5.81135			0.259632
$502$		−	15.0923i		−	0.673604i
$503$	−18.2708	−	10.5486i	−0.814653	−	0.470340i	0.0339160	−	0.999425i	$-0.489202\pi$
$503$	−18.2708	−	10.5486i	−0.814653	−	0.470340i	−0.848569	+	0.529084i	$0.822535\pi$
$504$	−0.392840	+	0.680419i	−0.0174985	+	0.0303083i
$505$	37.8479	+	5.31756i	1.68421	+	0.236628i
$506$	−3.43309			−0.152619
$507$	3.95891	+	2.28568i	0.175822	+	0.101511i
$508$	3.14252	−	1.81433i	0.139427	−	0.0804981i
$509$	−11.3620	+	19.6795i	−0.503610	+	0.872278i	0.496381	+	0.868105i	$0.334662\pi$
$509$	−11.3620	+	19.6795i	−0.503610	+	0.872278i	−0.999991	+	0.00417367i	$0.998671\pi$
$510$	5.88074	−	2.37626i	0.260403	−	0.105222i
$511$	0.887918	+	1.53792i	0.0392792	+	0.0680335i
$512$		−	1.00000i		−	0.0441942i
$513$	3.32254	−	2.82148i	0.146694	−	0.124571i
$514$	−22.8256			−1.00680
$515$	−16.8294	+	6.80032i	−0.741590	+	0.299658i
$516$	0.214320	+	0.371213i	0.00943490	+	0.0163417i
$517$	3.95465	+	2.28322i	0.173925	+	0.100416i
$518$	−0.0658565	+	0.0380222i	−0.00289357	+	0.00167060i
$519$	−4.36273	+	7.55647i	−0.191503	+	0.331692i
$520$	6.42864	+	0.903212i	0.281914	+	0.0396085i
$521$	29.0923			1.27456			0.637279	−	0.770633i	$-0.280060\pi$
$521$	29.0923			1.27456			0.637279	+	0.770633i	$0.280060\pi$
$522$	3.48207	+	2.01037i	0.152406	+	0.0879916i
$523$	−6.84186	−	3.95015i	−0.299174	−	0.172728i	0.342898	−	0.939373i	$-0.388591\pi$
$523$	−6.84186	−	3.95015i	−0.299174	−	0.172728i	−0.642072	+	0.766645i	$0.721925\pi$
$524$	16.8064			0.734192
$525$	3.77631	+	1.08250i	0.164812	+	0.0472441i
$526$	−6.05554	+	10.4885i	−0.264034	+	0.457320i
$527$	10.8790	−	6.28100i	0.473897	−	0.273604i
$528$	−0.327171	−	0.188892i	−0.0142383	−	0.00822048i
$529$	29.7906	+	51.5988i	1.29524	+	2.24343i
$530$	−5.80827	−	14.3742i	−0.252295	−	0.624377i
$531$	−9.76049			−0.423569
$532$	−0.614563	−	3.36911i	−0.0266447	−	0.146069i
$533$		−	8.34122i		−	0.361298i
$534$	−5.96912	−	10.3388i	−0.258309	−	0.447405i
$535$	36.8643	−	14.8959i	1.59378	−	0.644007i
$536$	4.22469	−	7.31738i	0.182479	−	0.316063i
$537$	−20.1183	+	11.6153i	−0.868169	+	0.501238i
$538$	21.8529	+	12.6168i	0.942145	+	0.543947i
$539$	−2.41129			−0.103861
$540$	0.311108	−	2.21432i	0.0133879	−	0.0952891i
$541$	10.3160	−	17.8679i	0.443521	−	0.768201i	−0.554427	−	0.832232i	$-0.687063\pi$
$541$	10.3160	−	17.8679i	0.443521	−	0.768201i	0.997948	+	0.0640318i	$0.0203959\pi$
$542$	26.7865	+	15.4652i	1.15058	+	0.664287i
$543$		−	7.54617i		−	0.323837i
$544$	−2.83654			−0.121615
$545$	1.98843	−	2.54529i	0.0851748	−	0.109028i
$546$	1.14050	+	1.97540i	0.0488088	+	0.0845393i
$547$	−7.43965	−	4.29529i	−0.318097	−	0.183653i	0.332447	−	0.943122i	$-0.392126\pi$
$547$	−7.43965	−	4.29529i	−0.318097	−	0.183653i	−0.650544	+	0.759469i	$0.725459\pi$
$548$	1.89969	−	1.09679i	0.0811508	−	0.0468525i
$549$	2.27777	+	3.94521i	0.0972128	+	0.168378i
$550$	−0.520505	+	1.81579i	−0.0221944	+	0.0774256i
$551$	−17.2415	+	3.14504i	−0.734513	+	0.133983i
$552$			9.08742i			0.386786i
$553$	1.06918	−	0.617293i	0.0454663	−	0.0262500i
$554$	9.74689	+	16.8821i	0.414106	+	0.717252i
$555$	0.133237	−	0.170551i	0.00565560	−	0.00723947i
$556$	−0.836535	−	1.44892i	−0.0354770	−	0.0614480i
$557$	−21.3209	−	12.3097i	−0.903397	−	0.521577i	−0.0250964	−	0.999685i	$-0.507989\pi$
$557$	−21.3209	−	12.3097i	−0.903397	−	0.521577i	−0.878301	+	0.478108i	$0.841323\pi$
$558$		−	4.42864i		−	0.187479i
$559$	1.24443			0.0526338
$560$	−1.38445	−	1.08156i	−0.0585037	−	0.0457041i
$561$	−0.535799	+	0.928032i	−0.0226215	+	0.0391815i
$562$			7.43509i			0.313630i
$563$			33.6958i			1.42011i	0.704146	+	0.710055i	$0.251330\pi$
$563$			33.6958i			1.42011i	−0.704146	+	0.710055i	$0.748670\pi$
$564$	6.04371	−	10.4680i	0.254486	−	0.440783i
$565$	−29.6802	+	11.9930i	−1.24865	+	0.504550i
$566$	−0.857279	+	1.48485i	−0.0360341	+	0.0624129i
$567$	0.680419	−	0.392840i	0.0285749	−	0.0164977i
$568$	−10.1669	+	5.86987i	−0.426594	+	0.246294i
$569$	3.59703			0.150795			0.0753976	−	0.997154i	$-0.475977\pi$
$569$	3.59703			0.150795			0.0753976	+	0.997154i	$0.475977\pi$
$570$	5.21399	+	8.23494i	0.218390	+	0.344924i
$571$	22.2623			0.931647			0.465823	−	0.884878i	$-0.345758\pi$
$571$	22.2623			0.931647			0.465823	+	0.884878i	$0.345758\pi$
$572$	−0.949846	+	0.548394i	−0.0397151	+	0.0229295i
$573$	17.7276	−	10.2351i	0.740583	−	0.427576i
$574$	−1.12867	+	1.95491i	−0.0471097	+	0.0815965i
$575$	44.0865	−	10.9959i	1.83853	−	0.458562i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$		−	34.7719i		−	1.44757i	−0.690025	−	0.723786i	$-0.742400\pi$
$577$		−	34.7719i		−	1.44757i	0.690025	−	0.723786i	$-0.257600\pi$
$578$		−	8.95407i		−	0.372440i
$579$	−9.46198	+	16.3886i	−0.393226	+	0.681088i
$580$	−5.53490	+	7.08497i	−0.229824	+	0.294187i
$581$	−2.16500			−0.0898192
$582$			3.44446i			0.142777i
$583$	2.26838	+	1.30965i	0.0939468	+	0.0542402i
$584$	1.13013	+	1.95744i	0.0467650	+	0.0809993i
$585$	−5.11576	−	3.99652i	−0.211511	−	0.165236i
$586$	3.96912	+	6.87472i	0.163963	+	0.283992i
$587$	−21.7306	+	12.5462i	−0.896918	+	0.517836i	−0.876199	−	0.481949i	$-0.839929\pi$
$587$	−21.7306	+	12.5462i	−0.896918	+	0.517836i	−0.0207191	+	0.999785i	$0.506596\pi$
$588$			6.38271i			0.263218i
$589$	12.4953	+	14.7143i	0.514861	+	0.606293i
$590$	3.03657	−	21.6128i	0.125013	−	0.889787i
$591$	−0.865190	−	1.49855i	−0.0355891	−	0.0616422i
$592$	−0.0838209	+	0.0483940i	−0.00344502	+	0.00198898i
$593$	−36.9025	−	21.3057i	−1.51540	−	0.874919i	−0.999837	−	0.0180690i	$-0.994248\pi$
$593$	−36.9025	−	21.3057i	−1.51540	−	0.874919i	−0.515567	−	0.856850i	$-0.672419\pi$
$594$	0.188892	+	0.327171i	0.00775034	+	0.0134240i
$595$	−3.06788	+	3.92704i	−0.125771	+	0.160993i
$596$	5.39853			0.221132
$597$			15.0716i			0.616839i
$598$	22.8481	+	13.1914i	0.934328	+	0.539435i
$599$	−21.3652	+	37.0056i	−0.872958	+	1.51201i	−0.0140358	+	0.999901i	$0.504468\pi$
$599$	−21.3652	+	37.0056i	−0.872958	+	1.51201i	−0.858922	+	0.512106i	$0.828865\pi$
$600$	4.80642	+	1.37778i	0.196221	+	0.0562478i
$601$	−40.1481			−1.63768			−0.818838	−	0.574025i	$-0.805381\pi$
$601$	−40.1481			−1.63768			−0.818838	+	0.574025i	$0.805381\pi$
$602$	−0.291654	−	0.168387i	−0.0118869	−	0.00686293i
$603$	−7.31738	+	4.22469i	−0.297987	+	0.172043i
$604$	4.53580	−	7.85623i	0.184559	−	0.319666i
$605$	9.09550	+	22.5094i	0.369785	+	0.915138i
$606$	8.54617	+	14.8024i	0.347164	+	0.601307i
$607$		−	36.0988i		−	1.46520i	−0.680657	−	0.732602i	$-0.738305\pi$
$607$		−	36.0988i		−	1.46520i	0.680657	−	0.732602i	$-0.261695\pi$
$608$	−0.782204	−	4.28814i	−0.0317226	−	0.173907i
$609$	−3.15902			−0.128010
$610$	−9.44459	+	3.81632i	−0.382400	+	0.154518i
$611$	−17.5462	−	30.3909i	−0.709842	−	1.22948i
$612$	2.45651	+	1.41827i	0.0992986	+	0.0573301i
$613$	−21.8144	+	12.5946i	−0.881076	+	0.508690i	−0.871013	−	0.491260i	$-0.836537\pi$
$613$	−21.8144	+	12.5946i	−0.881076	+	0.508690i	−0.0100632	+	0.999949i	$0.503203\pi$
$614$	0.530877	−	0.919506i	0.0214245	−	0.0371083i
$615$	0.893844	−	6.36196i	0.0360433	−	0.256539i
$616$	0.296818			0.0119591
$617$	−2.97740	−	1.71900i	−0.119866	−	0.0692045i	0.438868	−	0.898551i	$-0.355379\pi$
$617$	−2.97740	−	1.71900i	−0.119866	−	0.0692045i	−0.558734	+	0.829347i	$0.688713\pi$
$618$	−7.02999	−	4.05877i	−0.282788	−	0.163268i
$619$	20.7397			0.833601			0.416800	−	0.908998i	$-0.363151\pi$
$619$	20.7397			0.833601			0.416800	+	0.908998i	$0.363151\pi$
$620$	9.80642	+	1.37778i	0.393835	+	0.0553332i
$621$	4.54371	−	7.86994i	0.182333	−	0.315810i
$622$	−15.1736	+	8.76049i	−0.608407	+	0.351264i
$623$	8.12301	+	4.68982i	0.325442	+	0.187894i
$624$	1.45161	+	2.51426i	0.0581107	+	0.100651i
$625$	0.868304	−	24.9849i	0.0347321	−	0.999397i
$626$	12.2953			0.491418
$627$	−1.55071	−	0.554082i	−0.0619293	−	0.0221279i
$628$		−	15.3684i		−	0.613267i
$629$	0.137271	+	0.237761i	0.00547337	+	0.00948015i
$630$	0.658190	+	1.62888i	0.0262229	+	0.0648962i
$631$	−17.1629	+	29.7271i	−0.683246	+	1.18342i	0.290739	+	0.956802i	$0.406099\pi$
$631$	−17.1629	+	29.7271i	−0.683246	+	1.18342i	−0.973985	+	0.226614i	$0.927234\pi$
$632$	1.36084	−	0.785680i	0.0541312	−	0.0312527i
$633$	11.5320	+	6.65801i	0.458357	+	0.264632i
$634$	−23.9240			−0.950142
$635$	1.12891	−	8.03503i	0.0447993	−	0.318861i
$636$	3.46666	−	6.00443i	0.137462	−	0.238091i
$637$	16.0478	+	9.26517i	0.635835	+	0.367100i
$638$		−	1.51897i		−	0.0601368i
$639$	11.7397			0.464417
$640$	−1.76210	−	1.37659i	−0.0696532	−	0.0544144i
$641$	1.54125	+	2.66952i	0.0608757	+	0.105440i	0.894857	−	0.446353i	$-0.147277\pi$
$641$	1.54125	+	2.66952i	0.0608757	+	0.105440i	−0.833981	+	0.551793i	$0.813944\pi$
$642$	15.3990	+	8.89062i	0.607750	+	0.350885i
$643$	27.9069	−	16.1121i	1.10054	−	0.635398i	0.164179	−	0.986431i	$-0.447503\pi$
$643$	27.9069	−	16.1121i	1.10054	−	0.635398i	0.936363	+	0.351032i	$0.114169\pi$
$644$	−3.56990	−	6.18325i	−0.140674	−	0.243654i
$645$	0.949145	+	0.133353i	0.0373725	+	0.00525077i
$646$	−12.1635	+	2.21875i	−0.478565	+	0.0872956i
$647$		−	4.90813i		−	0.192959i	−0.995335	−	0.0964793i	$-0.969242\pi$
$647$		−	4.90813i		−	0.192959i	0.995335	−	0.0964793i	$-0.0307582\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	1.84368	+	3.19335i	0.0723708	+	0.125350i
$650$	10.4411	−	10.0846i	0.409535	−	0.395550i
$651$	1.73975	+	3.01333i	0.0681861	+	0.118102i
$652$	6.33719	+	3.65878i	0.248184	+	0.143289i
$653$		−	41.4405i		−	1.62169i	−0.585260	−	0.810846i	$-0.699007\pi$
$653$		−	41.4405i		−	1.62169i	0.585260	−	0.810846i	$-0.300993\pi$
$654$	1.44446			0.0564829
$655$	23.1355	−	29.6147i	0.903979	−	1.15714i
$656$	−1.43655	+	2.48818i	−0.0560879	+	0.0971470i
$657$		−	2.26025i		−	0.0881809i
$658$			9.49685i			0.370226i
$659$	−0.665688	+	1.15300i	−0.0259315	+	0.0449147i	−0.878700	−	0.477375i	$-0.841589\pi$
$659$	−0.665688	+	1.15300i	−0.0259315	+	0.0449147i	0.852768	+	0.522289i	$0.174922\pi$
$660$	−0.783227	+	0.316482i	−0.0304871	+	0.0123191i
$661$	18.1891	−	31.5045i	0.707475	−	1.22538i	−0.258316	−	0.966061i	$-0.583167\pi$
$661$	18.1891	−	31.5045i	0.707475	−	1.22538i	0.965791	−	0.259322i	$-0.0834992\pi$
$662$	−11.3284	+	6.54048i	−0.440293	+	0.254203i
$663$	7.13177	−	4.11753i	0.276975	−	0.159912i
$664$	−2.75557			−0.106937
$665$	−6.78272	−	3.55495i	−0.263022	−	0.137855i
$666$	0.0967881			0.00375046
$667$	−31.6430	+	18.2691i	−1.22522	+	0.707382i
$668$	−5.03277	+	2.90567i	−0.194724	+	0.112424i
$669$	9.58419	−	16.6003i	0.370546	−	0.641805i
$670$	−7.07832	−	17.5174i	−0.273459	−	0.676754i
$671$	0.860506	−	1.49044i	0.0332195	−	0.0575378i
$672$		−	0.785680i		−	0.0303083i
$673$			38.8069i			1.49590i	0.663757	+	0.747948i	$0.268961\pi$
$673$			38.8069i			1.49590i	−0.663757	+	0.747948i	$0.731039\pi$
$674$	−8.31111	+	14.3953i	−0.320132	+	0.554485i
$675$	−3.47359	−	3.59641i	−0.133699	−	0.138426i
$676$	−4.57136			−0.175822
$677$		−	31.6242i		−	1.21542i	−0.794160	−	0.607709i	$-0.792089\pi$
$677$		−	31.6242i		−	1.21542i	0.794160	−	0.607709i	$-0.207911\pi$
$678$	−12.3980	−	7.15801i	−0.476144	−	0.274902i
$679$	−1.35312	−	2.34368i	−0.0519281	−	0.0899421i
$680$	−3.90474	+	4.99827i	−0.149740	+	0.191675i
$681$	−3.44123	−	5.96039i	−0.131868	−	0.228403i
$682$	−1.44892	+	0.836535i	−0.0554821	+	0.0320326i
$683$		−	24.2000i		−	0.925988i	−0.886361	−	0.462994i	$-0.846775\pi$
$683$		−	24.2000i		−	0.925988i	0.886361	−	0.462994i	$-0.153225\pi$
$684$	−1.46666	+	4.10474i	−0.0560792	+	0.156949i
$685$	0.682439	−	4.85728i	0.0260746	−	0.185587i
$686$	−5.25726	−	9.10585i	−0.200723	−	0.347663i
$687$	11.9046	−	6.87310i	0.454187	−	0.262225i
$688$	−0.371213	−	0.214320i	−0.0141524	−	0.00817086i
$689$	−10.0645	−	17.4321i	−0.383425	−	0.664112i
$690$	16.0130	+	12.5096i	0.609603	+	0.476233i
$691$	−21.1782			−0.805658			−0.402829	−	0.915275i	$-0.631973\pi$
$691$	−21.1782			−0.805658			−0.402829	+	0.915275i	$0.631973\pi$
$692$		−	8.72546i		−	0.331692i
$693$	−0.257052	−	0.148409i	−0.00976459	−	0.00563759i
$694$	−2.67307	+	4.62989i	−0.101468	+	0.175748i
$695$	−3.70471	−	0.520505i	−0.140528	−	0.0197439i
$696$	−4.02074			−0.152406
$697$	7.05780	+	4.07483i	0.267333	+	0.154345i
$698$	0.764240	−	0.441234i	0.0289269	−	0.0167010i
$699$	−3.39853	+	5.88642i	−0.128544	+	0.222645i
$700$	−3.81163	+	0.950685i	−0.144066	+	0.0359325i
$701$	11.1635	+	19.3357i	0.421638	+	0.730299i	0.996100	−	0.0882326i	$-0.0281219\pi$
$701$	11.1635	+	19.3357i	0.421638	+	0.730299i	−0.574462	+	0.818531i	$0.694789\pi$
$702$		−	2.90321i		−	0.109575i
$703$	−0.321582	+	0.273086i	−0.0121287	+	0.0102996i
$704$	0.377784			0.0142383
$705$	−10.1260	−	25.0598i	−0.381368	−	0.943806i
$706$	−7.55162	−	13.0798i	−0.284209	−	0.492264i
$707$	−11.6300	−	6.71456i	−0.437389	−	0.252527i
$708$	8.45283	−	4.88025i	0.317677	−	0.183411i
$709$	−11.2733	+	19.5260i	−0.423379	+	0.733313i	−0.996267	−	0.0863198i	$-0.972489\pi$
$709$	−11.2733	+	19.5260i	−0.423379	+	0.733313i	0.572889	+	0.819633i	$0.305823\pi$
$710$	−3.65233	+	25.9956i	−0.137069	+	0.975596i
$711$	−1.57136			−0.0589306
$712$	10.3388	+	5.96912i	0.387464	+	0.223702i
$713$	34.8531	+	20.1225i	1.30526	+	0.753592i
$714$	−2.22861			−0.0834036
$715$	−0.341219	+	2.42864i	−0.0127609	+	0.0908260i
$716$	11.6153	−	20.1183i	0.434084	−	0.751856i
$717$	−9.40268	+	5.42864i	−0.351149	+	0.202736i
$718$	13.5515	+	7.82394i	0.505736	+	0.291987i
$719$	−16.3111	−	28.2517i	−0.608302	−	1.05361i	−0.991520	−	0.129952i	$-0.958518\pi$
$719$	−16.3111	−	28.2517i	−0.608302	−	1.05361i	0.383219	−	0.923658i	$-0.374816\pi$
$720$	0.837733	+	2.07321i	0.0312205	+	0.0772640i
$721$	6.37778			0.237521
$722$	−6.70841	−	17.7763i	−0.249661	−	0.661566i
$723$			9.68736i			0.360277i
$724$	3.77309	+	6.53518i	0.140226	+	0.242878i
$725$	4.86516	+	19.5061i	0.180688	+	0.724440i
$726$	−5.42864	+	9.40268i	−0.201476	+	0.348966i
$727$	−32.6741	+	18.8644i	−1.21182	+	0.699643i	−0.963155	−	0.268948i	$-0.913324\pi$
$727$	−32.6741	+	18.8644i	−1.21182	+	0.699643i	−0.248662	+	0.968590i	$0.579991\pi$
$728$	−1.97540	−	1.14050i	−0.0732132	−	0.0422697i
$729$	−1.00000			−0.0370370
$730$	5.00492	+	0.703182i	0.185240	+	0.0260259i
$731$	−0.607926	+	1.05296i	−0.0224849	+	0.0389451i
$732$	−3.94521	−	2.27777i	−0.145819	−	0.0841888i
$733$		−	47.5531i		−	1.75641i	−0.478281	−	0.878207i	$-0.658740\pi$
$733$		−	47.5531i		−	1.75641i	0.478281	−	0.878207i	$-0.341260\pi$
$734$	32.1748			1.18760
$735$	11.2470	+	8.78635i	0.414851	+	0.324089i
$736$	−4.54371	−	7.86994i	−0.167483	−	0.290090i
$737$	2.76439	+	1.59602i	0.101828	+	0.0587902i
$738$	2.48818	−	1.43655i	0.0915911	−	0.0528801i
$739$	−14.6602	−	25.3923i	−0.539286	−	0.934070i	−0.998943	−	0.0459735i	$-0.985361\pi$
$739$	−14.6602	−	25.3923i	−0.539286	−	0.934070i	0.459657	−	0.888096i	$-0.347972\pi$
$740$	−0.0301115	+	0.214320i	−0.00110692	+	0.00787855i
$741$	8.19135	+	9.64603i	0.300917	+	0.354356i
$742$			5.44738i			0.199979i
$743$	−7.39176	+	4.26764i	−0.271177	+	0.156564i	−0.629423	−	0.777063i	$-0.716709\pi$
$743$	−7.39176	+	4.26764i	−0.271177	+	0.156564i	0.358245	+	0.933628i	$0.383375\pi$
$744$	2.21432	+	3.83531i	0.0811809	+	0.140609i
$745$	7.43154	−	9.51276i	0.272271	−	0.348521i
$746$	−7.55800	−	13.0908i	−0.276718	−	0.479290i
$747$	2.38639	+	1.37778i	0.0873135	+	0.0504105i
$748$		−	1.07160i		−	0.0391815i
$749$	−13.9704			−0.510466
$750$	9.04426	−	6.57277i	0.330250	−	0.240004i
$751$	3.79213	−	6.56817i	0.138377	−	0.239676i	−0.788505	−	0.615028i	$-0.789145\pi$
$751$	3.79213	−	6.56817i	0.138377	−	0.239676i	0.926882	+	0.375352i	$0.122478\pi$
$752$			12.0874i			0.440783i
$753$		−	15.0923i		−	0.549996i
$754$	−5.83654	+	10.1092i	−0.212554	+	0.368154i
$755$	−7.59957	−	18.8073i	−0.276577	−	0.684469i
$756$	−0.392840	+	0.680419i	−0.0142875	+	0.0247466i
$757$	−26.1600	+	15.1035i	−0.950801	+	0.548945i	−0.893330	−	0.449402i	$-0.851637\pi$
$757$	−26.1600	+	15.1035i	−0.950801	+	0.548945i	−0.0574714	+	0.998347i	$0.518304\pi$
$758$	−0.786055	+	0.453829i	−0.0285508	+	0.0164838i
$759$	−3.43309			−0.124613
$760$	−8.63292	−	4.52468i	−0.313149	−	0.164127i
$761$	−46.3526			−1.68028			−0.840140	−	0.542369i	$-0.817527\pi$
$761$	−46.3526			−1.68028			−0.840140	+	0.542369i	$0.817527\pi$
$762$	3.14252	−	1.81433i	0.113841	−	0.0657264i
$763$	−0.982839	+	0.567442i	−0.0355812	+	0.0205428i
$764$	−10.2351	+	17.7276i	−0.370292	+	0.641364i
$765$	5.88074	−	2.37626i	0.212618	−	0.0859138i
$766$	−0.303963	+	0.526479i	−0.0109826	+	0.0190225i
$767$		−	28.3368i		−	1.02318i
$768$		−	1.00000i		−	0.0360844i
$769$	3.85950	−	6.68485i	0.139177	−	0.241062i	−0.788008	−	0.615665i	$-0.788888\pi$
$769$	3.85950	−	6.68485i	0.139177	−	0.241062i	0.927185	+	0.374603i	$0.122221\pi$
$770$	0.408595	−	0.523023i	0.0147248	−	0.0188485i
$771$	−22.8256			−0.822045
$772$		−	18.9240i		−	0.681088i
$773$	−18.0095	−	10.3978i	−0.647755	−	0.373982i	0.139841	−	0.990174i	$-0.455341\pi$
$773$	−18.0095	−	10.3978i	−0.647755	−	0.373982i	−0.787596	+	0.616193i	$0.788674\pi$
$774$	0.214320	+	0.371213i	0.00770356	+	0.0133430i
$775$	15.9272	−	15.3833i	0.572122	−	0.552584i
$776$	−1.72223	−	2.98299i	−0.0618245	−	0.107083i
$777$	−0.0658565	+	0.0380222i	−0.00236259	+	0.00136404i
$778$		−	12.0810i		−	0.433124i
$779$	−4.21387	+	11.7933i	−0.150977	+	0.422540i
$780$	6.42864	+	0.903212i	0.230182	+	0.0323402i
$781$	−2.21755	−	3.84090i	−0.0793501	−	0.137438i
$782$	−22.3234	+	12.8884i	−0.798282	+	0.460888i
$783$	3.48207	+	2.01037i	0.124439	+	0.0718448i
$784$	−3.19135	−	5.52759i	−0.113977	−	0.197414i
$785$	−27.0807	−	21.1560i	−0.966553	−	0.755089i
$786$	16.8064			0.599465
$787$			31.7255i			1.13089i	0.824786	+	0.565445i	$0.191296\pi$
$787$			31.7255i			1.13089i	−0.824786	+	0.565445i	$0.808704\pi$
$788$	1.49855	+	0.865190i	0.0533837	+	0.0308211i
$789$	−6.05554	+	10.4885i	−0.215583	+	0.373401i
$790$	0.488863	−	3.47949i	0.0173929	−	0.123795i
$791$	11.2478			0.399927
$792$	−0.327171	−	0.188892i	−0.0116255	−	0.00671199i
$793$	−11.4538	+	6.61285i	−0.406736	+	0.234829i
$794$	−9.43110	+	16.3351i	−0.334697	+	0.579713i
$795$	−5.80827	−	14.3742i	−0.205998	−	0.509802i
$796$	−7.53580	−	13.0524i	−0.267099	−	0.462630i
$797$			54.5417i			1.93197i	0.258604	+	0.965984i	$0.416738\pi$
$797$			54.5417i			1.93197i	−0.258604	+	0.965984i	$0.583262\pi$
$798$	−0.614563	−	3.36911i	−0.0217553	−	0.119265i
$799$	34.2864			1.21297
$800$	−4.85138	+	1.21002i	−0.171522	+	0.0427805i
$801$	−5.96912	−	10.3388i	−0.210909	−	0.365304i
$802$	8.46521	+	4.88739i	0.298917	+	0.172580i
$803$	−0.739489	+	0.426944i	−0.0260960	+	0.0150665i
$804$	4.22469	−	7.31738i	0.148993	−	0.258064i
$805$	−15.8098	−	2.22125i	−0.557223	−	0.0782888i
$806$	12.8573			0.452878
$807$	21.8529	+	12.6168i	0.769258	+	0.444131i
$808$	−14.8024	−	8.54617i	−0.520747	−	0.300653i
$809$	14.4429			0.507786			0.253893	−	0.967232i	$-0.418289\pi$
$809$	14.4429			0.507786			0.253893	+	0.967232i	$0.418289\pi$
$810$	0.311108	−	2.21432i	0.0109312	−	0.0778033i
$811$	16.0079	−	27.7265i	0.562114	−	0.973610i	−0.435198	−	0.900335i	$-0.643322\pi$
$811$	16.0079	−	27.7265i	0.562114	−	0.973610i	0.997312	−	0.0732748i	$-0.0233450\pi$
$812$	2.73579	−	1.57951i	0.0960074	−	0.0554299i
$813$	26.7865	+	15.4652i	0.939444	+	0.542388i
$814$	−0.0182825	−	0.0316662i	−0.000640802	−	0.00110990i
$815$	15.1708	−	6.13016i	0.531412	−	0.214730i
$816$	−2.83654			−0.0992986
$817$	−1.75945	−	0.628669i	−0.0615555	−	0.0219943i
$818$		−	38.3832i		−	1.34204i
$819$	1.14050	+	1.97540i	0.0398522	+	0.0690261i
$820$	2.40689	+	5.95654i	0.0840522	+	0.208012i
$821$	2.73038	−	4.72916i	0.0952909	−	0.165049i	−0.814439	−	0.580249i	$-0.802955\pi$
$821$	2.73038	−	4.72916i	0.0952909	−	0.165049i	0.909730	+	0.415200i	$0.136289\pi$
$822$	1.89969	−	1.09679i	0.0662594	−	0.0382549i
$823$	45.4901	+	26.2637i	1.58568	+	0.915496i	0.994006	+	0.109322i	$0.0348679\pi$
$823$	45.4901	+	26.2637i	1.58568	+	0.915496i	0.591679	+	0.806174i	$0.298465\pi$
$824$	8.11753			0.282788
$825$	−0.520505	+	1.81579i	−0.0181217	+	0.0632178i
$826$	−3.83431	+	6.64122i	−0.133413	+	0.231078i
$827$	−18.7229	−	10.8097i	−0.651058	−	0.375888i	0.137804	−	0.990460i	$-0.455996\pi$
$827$	−18.7229	−	10.8097i	−0.651058	−	0.375888i	−0.788861	+	0.614571i	$0.789329\pi$
$828$			9.08742i			0.315810i
$829$	−22.1432			−0.769065			−0.384533	−	0.923111i	$-0.625637\pi$
$829$	−22.1432			−0.769065			−0.384533	+	0.923111i	$0.625637\pi$
$830$	−3.79328	+	4.85560i	−0.131667	+	0.168540i
$831$	9.74689	+	16.8821i	0.338116	+	0.585634i
$832$	−2.51426	−	1.45161i	−0.0871661	−	0.0503254i
$833$	−15.6792	+	9.05239i	−0.543252	+	0.313647i
$834$	−0.836535	−	1.44892i	−0.0289669	−	0.0501721i
$835$	−1.80796	+	12.8682i	−0.0625669	+	0.445322i
$836$	1.61999	−	0.295505i	0.0560286	−	0.0102202i
$837$		−	4.42864i		−	0.153076i
$838$	26.6355	−	15.3780i	0.920109	−	0.531225i
$839$	−15.0622	−	26.0885i	−0.520006	−	0.900677i	−0.999730	−	0.0232570i	$-0.992596\pi$
$839$	−15.0622	−	26.0885i	−0.520006	−	0.900677i	0.479724	−	0.877420i	$-0.340737\pi$
$840$	−1.38445	−	1.08156i	−0.0477681	−	0.0373173i
$841$	6.41681	+	11.1142i	0.221269	+	0.383250i
$842$	−10.9367	−	6.31433i	−0.376905	−	0.217606i
$843$			7.43509i			0.256078i
$844$	−13.3160			−0.458357
$845$	−6.29288	+	8.05521i	−0.216482	+	0.277108i
$846$	6.04371	−	10.4680i	0.207787	−	0.359898i
$847$		−	8.53035i		−	0.293106i
$848$			6.93332i			0.238091i
$849$	−0.857279	+	1.48485i	−0.0294217	+	0.0509599i
$850$	3.43225	+	13.7611i	0.117725	+	0.472002i
$851$	−0.439777	+	0.761716i	−0.0150754	+	0.0261113i
$852$	−10.1669	+	5.86987i	−0.348313	+	0.201099i
$853$	−20.1303	+	11.6222i	−0.689247	+	0.397937i	−0.803330	−	0.595534i	$-0.796940\pi$
$853$	−20.1303	+	11.6222i	−0.689247	+	0.397937i	0.114083	+	0.993471i	$0.463607\pi$
$854$	3.57920			0.122478
$855$	5.21399	+	8.23494i	0.178315	+	0.281629i
$856$	−17.7812			−0.607750
$857$	−31.9390	+	18.4400i	−1.09102	+	0.629899i	−0.933847	−	0.357673i	$-0.883570\pi$
$857$	−31.9390	+	18.4400i	−1.09102	+	0.629899i	−0.157170	+	0.987572i	$0.550237\pi$
$858$	−0.949846	+	0.548394i	−0.0324272	+	0.0187219i
$859$	14.2057	−	24.6050i	0.484693	−	0.839513i	−0.515153	−	0.857099i	$-0.672265\pi$
$859$	14.2057	−	24.6050i	0.484693	−	0.839513i	0.999845	+	0.0175859i	$0.00559806\pi$
$860$	−0.888660	+	0.359085i	−0.0303031	+	0.0122447i
$861$	−1.12867	+	1.95491i	−0.0384649	+	0.0666232i
$862$			35.3526i			1.20411i
$863$		−	15.3082i		−	0.521097i	−0.965461	−	0.260548i	$-0.916097\pi$
$863$		−	15.3082i		−	0.521097i	0.965461	−	0.260548i	$-0.0839034\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−15.3752	−	12.0114i	−0.522771	−	0.408398i
$866$	20.7906			0.706493
$867$		−	8.95407i		−	0.304096i
$868$	−3.01333	−	1.73975i	−0.102279	−	0.0590509i
$869$	0.296818	+	0.514103i	0.0100689	+	0.0174398i
$870$	−5.53490	+	7.08497i	−0.187651	+	0.240203i
$871$	−12.2652	−	21.2439i	−0.415590	−	0.719822i
$872$	−1.25094	+	0.722230i	−0.0423622	+	0.0244578i
$873$			3.44446i			0.116577i
$874$	−25.6400	−	30.1933i	−0.867285	−	1.02130i
$875$	−3.57184	+	8.02519i	−0.120750	+	0.271301i
$876$	1.13013	+	1.95744i	0.0381834	+	0.0661356i
$877$	23.8022	−	13.7422i	0.803743	−	0.464041i	−0.0410351	−	0.999158i	$-0.513066\pi$
$877$	23.8022	−	13.7422i	0.803743	−	0.464041i	0.844778	+	0.535116i	$0.179732\pi$
$878$	3.40251	+	1.96444i	0.114829	+	0.0662966i
$879$	3.96912	+	6.87472i	0.133875	+	0.231879i
$880$	0.520053	−	0.665695i	0.0175310	−	0.0224406i
$881$	−20.3210			−0.684630			−0.342315	−	0.939585i	$-0.611211\pi$
$881$	−20.3210			−0.684630			−0.342315	+	0.939585i	$0.611211\pi$
$882$			6.38271i			0.214917i
$883$	27.8026	+	16.0519i	0.935633	+	0.540188i	0.888589	−	0.458705i	$-0.151686\pi$
$883$	27.8026	+	16.0519i	0.935633	+	0.540188i	0.0470444	+	0.998893i	$0.485020\pi$
$884$	−4.11753	+	7.13177i	−0.138488	+	0.239868i
$885$	3.03657	−	21.6128i	0.102073	−	0.726508i
$886$	−1.59655			−0.0536371
$887$	−21.1520	−	12.2121i	−0.710214	−	0.410042i	0.100926	−	0.994894i	$-0.467819\pi$
$887$	−21.1520	−	12.2121i	−0.710214	−	0.410042i	−0.811140	+	0.584852i	$0.801153\pi$
$888$	−0.0838209	+	0.0483940i	−0.00281285	+	0.00162400i
$889$	−1.42549	+	2.46902i	−0.0478093	+	0.0828081i
$890$	24.7505	−	10.0011i	0.829639	−	0.335236i
$891$	0.188892	+	0.327171i	0.00632813	+	0.0109606i
$892$			19.1684i			0.641805i
$893$	9.45483	+	51.8326i	0.316394	+	1.73451i
$894$	5.39853			0.180554
$895$	−19.4610	−	48.1620i	−0.650511	−	1.60988i
$896$	0.392840	+	0.680419i	0.0131239	+	0.0227312i
$897$	22.8481	+	13.1914i	0.762876	+	0.440446i
$898$	−12.5216	+	7.22938i	−0.417853	+	0.241247i
$899$	−8.90321	+	15.4208i	−0.296939	+	0.514313i
$900$	4.80642	+	1.37778i	0.160214	+	0.0459261i
$901$	19.6666			0.655190
$902$	−0.939995	−	0.542706i	−0.0312984	−	0.0180701i
$903$	−0.291654	−	0.168387i	−0.00970565	−	0.00560356i
$904$	14.3160			0.476144
$905$	16.7096	+	2.34767i	0.555447	+	0.0780393i
$906$	4.53580	−	7.85623i	0.150692	−	0.261006i
$907$	0.681745	−	0.393606i	0.0226370	−	0.0130695i	−0.488639	−	0.872486i	$-0.662506\pi$
$907$	0.681745	−	0.393606i	0.0226370	−	0.0130695i	0.511276	+	0.859417i	$0.329173\pi$
$908$	5.96039	+	3.44123i	0.197803	+	0.114201i
$909$	8.54617	+	14.8024i	0.283459	+	0.490965i
$910$	−4.72899	+	1.91086i	−0.156764	+	0.0633446i
$911$	5.93978			0.196794			0.0983968	−	0.995147i	$-0.468629\pi$
$911$	5.93978			0.196794			0.0983968	+	0.995147i	$0.468629\pi$
$912$	−0.782204	−	4.28814i	−0.0259014	−	0.141995i
$913$		−	1.04101i		−	0.0344524i
$914$	−14.4526	−	25.0327i	−0.478050	−	0.828007i
$915$	−9.44459	+	3.81632i	−0.312229	+	0.126164i
$916$	−6.87310	+	11.9046i	−0.227094	+	0.393338i
$917$	−11.4354	+	6.60224i	−0.377631	+	0.218025i
$918$	2.45651	+	1.41827i	0.0810770	+	0.0468098i
$919$	−28.5096			−0.940445			−0.470223	−	0.882548i	$-0.655826\pi$
$919$	−28.5096			−0.940445			−0.470223	+	0.882548i	$0.655826\pi$
$920$	−20.1225	−	2.82717i	−0.663418	−	0.0932090i
$921$	0.530877	−	0.919506i	0.0174930	−	0.0302988i
$922$	2.11949	+	1.22369i	0.0698017	+	0.0403000i
$923$			34.0830i			1.12185i
$924$	0.296818			0.00976459
$925$	0.336202	+	0.348089i	0.0110543	+	0.0114451i
$926$	3.83730	+	6.64640i	0.126102	+	0.218414i
$927$	−7.02999	−	4.05877i	−0.230895	−	0.133307i
$928$	3.48207	−	2.01037i	0.114304	−	0.0659937i
$929$	−1.34199	−	2.32439i	−0.0440291	−	0.0762606i	0.843171	−	0.537645i	$-0.180686\pi$
$929$	−1.34199	−	2.32439i	−0.0440291	−	0.0762606i	−0.887200	+	0.461385i	$0.847353\pi$
$930$	9.80642	+	1.37778i	0.321565	+	0.0451793i
$931$	−18.0087	−	21.2068i	−0.590211	−	0.695024i
$932$		−	6.79706i		−	0.222645i
$933$	−15.1736	+	8.76049i	−0.496762	+	0.286806i
$934$	−4.89062	−	8.47080i	−0.160026	−	0.277173i
$935$	−1.88827	−	1.47515i	−0.0617530	−	0.0482425i
$936$	1.45161	+	2.51426i	0.0474472	+	0.0821810i
$937$	42.3258	+	24.4368i	1.38272	+	0.798315i	0.992481	−	0.122398i	$-0.0390583\pi$
$937$	42.3258	+	24.4368i	1.38272	+	0.798315i	0.390241	+	0.920713i	$0.372392\pi$
$938$			6.63851i			0.216755i
$939$	12.2953			0.401242
$940$	21.2993	+	16.6394i	0.694706	+	0.542717i
$941$	28.7961	−	49.8762i	0.938724	−	1.62592i	0.170871	−	0.985293i	$-0.445342\pi$
$941$	28.7961	−	49.8762i	0.938724	−	1.62592i	0.767854	−	0.640625i	$-0.221325\pi$
$942$		−	15.3684i		−	0.500730i
$943$			26.1091i			0.850228i
$944$	−4.88025	+	8.45283i	−0.158838	+	0.275116i
$945$	0.658190	+	1.62888i	0.0214109	+	0.0529875i
$946$	0.0809666	−	0.140238i	0.00263245	−	0.00455954i
$947$	24.0430	−	13.8812i	0.781293	−	0.451080i	−0.0555950	−	0.998453i	$-0.517706\pi$
$947$	24.0430	−	13.8812i	0.781293	−	0.451080i	0.836888	+	0.547373i	$0.184372\pi$
$948$	1.36084	−	0.785680i	0.0441980	−	0.0255177i
$949$	6.56199			0.213011
$950$	−19.8569	+	8.98349i	−0.644243	+	0.291463i
$951$	−23.9240			−0.775787
$952$	1.93003	−	1.11430i	0.0625527	−	0.0361148i
$953$	−23.3993	+	13.5096i	−0.757978	+	0.437619i	−0.828569	−	0.559886i	$-0.810845\pi$
$953$	−23.3993	+	13.5096i	−0.757978	+	0.437619i	0.0705910	+	0.997505i	$0.477511\pi$
$954$	3.46666	−	6.00443i	0.112237	−	0.194401i
$955$	17.1485	+	42.4389i	0.554912	+	1.37329i
$956$	5.42864	−	9.40268i	0.175575	−	0.304104i
$957$		−	1.51897i		−	0.0491015i
$958$		−	33.9432i		−	1.09665i
$959$	−0.861725	+	1.49255i	−0.0278265	+	0.0481970i
$960$	−1.76210	−	1.37659i	−0.0568716	−	0.0444292i
$961$	−11.3872			−0.367327
$962$			0.280996i			0.00905968i
$963$	15.3990	+	8.89062i	0.496226	+	0.286496i
$964$	−4.84368	−	8.38950i	−0.156004	−	0.270208i
$965$	−33.3460	−	26.0505i	−1.07344	−	0.838594i
$966$	−3.56990	−	6.18325i	−0.114860	−	0.198943i
$967$	47.4916	−	27.4193i	1.52723	−	0.881744i	0.527749	−	0.849400i	$-0.323036\pi$
$967$	47.4916	−	27.4193i	1.52723	−	0.881744i	0.999477	−	0.0323441i	$-0.0102972\pi$
$968$		−	10.8573i		−	0.348966i
$969$	−12.1635	+	2.21875i	−0.390747	+	0.0712765i
$970$	−7.62714	−	1.07160i	−0.244893	−	0.0344070i
$971$	9.23575	+	15.9968i	0.296389	+	0.513362i	0.975307	−	0.220853i	$-0.0708840\pi$
$971$	9.23575	+	15.9968i	0.296389	+	0.513362i	−0.678918	+	0.734214i	$0.737551\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	1.13839	+	0.657249i	0.0364951	+	0.0210704i
$974$	16.9390	+	29.3392i	0.542761	+	0.940090i
$975$	10.4411	−	10.0846i	0.334384	−	0.322965i
$976$	4.55554			0.145819
$977$			21.1131i			0.675467i	0.941242	+	0.337734i	$0.109660\pi$
$977$			21.1131i			0.675467i	−0.941242	+	0.337734i	$0.890340\pi$
$978$	6.33719	+	3.65878i	0.202641	+	0.116995i
$979$	−2.25504	+	3.90585i	−0.0720714	+	0.124831i
$980$	−14.1334	−	1.98571i	−0.451473	−	0.0634312i
$981$	1.44446			0.0461181
$982$	−35.6148	−	20.5622i	−1.13651	−	0.656167i
$983$	29.0617	−	16.7788i	0.926924	−	0.535160i	0.0410865	−	0.999156i	$-0.486918\pi$
$983$	29.0617	−	16.7788i	0.926924	−	0.535160i	0.885837	+	0.463996i	$0.153585\pi$
$984$	−1.43655	+	2.48818i	−0.0457955	+	0.0793202i
$985$	3.58744	−	1.44960i	0.114305	−	0.0461879i
$986$	−5.70249	−	9.87700i	−0.181604	−	0.314548i
$987$			9.49685i			0.302288i
$988$	−11.9169	−	4.25803i	−0.379128	−	0.135466i
$989$	−3.89523			−0.123861
$990$	−0.783227	+	0.316482i	−0.0248926	+	0.0100585i
$991$	7.88347	+	13.6546i	0.250427	+	0.433752i	0.963643	−	0.267192i	$-0.0860957\pi$
$991$	7.88347	+	13.6546i	0.250427	+	0.433752i	−0.713217	+	0.700944i	$0.752762\pi$
$992$	−3.83531	−	2.21432i	−0.121771	−	0.0703047i
$993$	−11.3284	+	6.54048i	−0.359497	+	0.207556i
$994$	4.61184	−	7.98795i	0.146279	−	0.253362i
$995$	−33.3733	−	4.68889i	−1.05801	−	0.148648i
$996$	−2.75557			−0.0873135
$997$	−29.9992	−	17.3200i	−0.950083	−	0.548531i	−0.0569762	−	0.998376i	$-0.518146\pi$
$997$	−29.9992	−	17.3200i	−0.950083	−	0.548531i	−0.893107	+	0.449845i	$0.851479\pi$
$998$	−17.3030	−	9.98987i	−0.547716	−	0.316224i
$999$	0.0967881			0.00306224

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.q.b.349.1	yes	12
3.2	odd	2		1710.2.t.b.919.6		12
5.4	even	2	inner	570.2.q.b.349.5	yes	12
15.14	odd	2		1710.2.t.b.919.2		12
19.11	even	3	inner	570.2.q.b.49.5	yes	12
57.11	odd	6		1710.2.t.b.1189.2		12
95.49	even	6	inner	570.2.q.b.49.1	✓	12
285.239	odd	6		1710.2.t.b.1189.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.b.49.1	✓	12	95.49	even	6	inner
570.2.q.b.49.5	yes	12	19.11	even	3	inner
570.2.q.b.349.1	yes	12	1.1	even	1	trivial
570.2.q.b.349.5	yes	12	5.4	even	2	inner
1710.2.t.b.919.2		12	15.14	odd	2
1710.2.t.b.919.6		12	3.2	odd	2
1710.2.t.b.1189.2		12	57.11	odd	6
1710.2.t.b.1189.6		12	285.239	odd	6

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.837733 - 2.07321i) q^{5} +(0.500000 - 0.866025i) q^{6} +0.785680i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.837733 - 2.07321i) q^{5} +(0.500000 - 0.866025i) q^{6} +0.785680i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.76210 + 1.37659i) q^{10} -0.377784 q^{11} +1.00000i q^{12} +(2.51426 + 1.45161i) q^{13} +(-0.392840 - 0.680419i) q^{14} +(1.76210 + 1.37659i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.45651 + 1.41827i) q^{17} +1.00000i q^{18} +(-2.82148 - 3.32254i) q^{19} +(-2.21432 - 0.311108i) q^{20} +(-0.392840 - 0.680419i) q^{21} +(0.327171 - 0.188892i) q^{22} +(-7.86994 - 4.54371i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.59641 + 3.47359i) q^{25} -2.90321 q^{26} +1.00000i q^{27} +(0.680419 + 0.392840i) q^{28} +(2.01037 - 3.48207i) q^{29} +(-2.21432 - 0.311108i) q^{30} -4.42864 q^{31} +(0.866025 + 0.500000i) q^{32} +(0.327171 - 0.188892i) q^{33} +(1.41827 - 2.45651i) q^{34} +(1.62888 - 0.658190i) q^{35} +(-0.500000 - 0.866025i) q^{36} -0.0967881i q^{37} +(4.10474 + 1.46666i) q^{38} -2.90321 q^{39} +(2.07321 - 0.837733i) q^{40} +(-1.43655 - 2.48818i) q^{41} +(0.680419 + 0.392840i) q^{42} +(0.371213 - 0.214320i) q^{43} +(-0.188892 + 0.327171i) q^{44} +(-2.21432 - 0.311108i) q^{45} +9.08742 q^{46} +(-10.4680 - 6.04371i) q^{47} +(0.866025 + 0.500000i) q^{48} +6.38271 q^{49} +(1.37778 - 4.80642i) q^{50} +(1.41827 - 2.45651i) q^{51} +(2.51426 - 1.45161i) q^{52} +(-6.00443 - 3.46666i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.316482 + 0.783227i) q^{55} -0.785680 q^{56} +(4.10474 + 1.46666i) q^{57} +4.02074i q^{58} +(-4.88025 - 8.45283i) q^{59} +(2.07321 - 0.837733i) q^{60} +(-2.27777 + 3.94521i) q^{61} +(3.83531 - 2.21432i) q^{62} +(0.680419 + 0.392840i) q^{63} -1.00000 q^{64} +(0.903212 - 6.42864i) q^{65} +(-0.188892 + 0.327171i) q^{66} +(-7.31738 - 4.22469i) q^{67} +2.83654i q^{68} +9.08742 q^{69} +(-1.08156 + 1.38445i) q^{70} +(5.86987 + 10.1669i) q^{71} +(0.866025 + 0.500000i) q^{72} +(1.95744 - 1.13013i) q^{73} +(0.0483940 + 0.0838209i) q^{74} +(1.37778 - 4.80642i) q^{75} +(-4.28814 + 0.782204i) q^{76} -0.296818i q^{77} +(2.51426 - 1.45161i) q^{78} +(-0.785680 - 1.36084i) q^{79} +(-1.37659 + 1.76210i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.48818 + 1.43655i) q^{82} +2.75557i q^{83} -0.785680 q^{84} +(4.99827 + 3.90474i) q^{85} +(-0.214320 + 0.371213i) q^{86} +4.02074i q^{87} -0.377784i q^{88} +(5.96912 - 10.3388i) q^{89} +(2.07321 - 0.837733i) q^{90} +(-1.14050 + 1.97540i) q^{91} +(-7.86994 + 4.54371i) q^{92} +(3.83531 - 2.21432i) q^{93} +12.0874 q^{94} +(-4.52468 + 8.63292i) q^{95} -1.00000 q^{96} +(-2.98299 + 1.72223i) q^{97} +(-5.52759 + 3.19135i) q^{98} +(-0.188892 + 0.327171i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 6 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 + 6 * q^6 + 6 * q^9	\( 12 q + 6 q^{4} + 6 q^{6} + 6 q^{9} - 2 q^{10} - 4 q^{11} - 18 q^{14} - 2 q^{15} - 6 q^{16} + 6 q^{19} - 18 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 4 q^{34} + 2 q^{35} - 6 q^{36} - 8 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} + 28 q^{46} - 56 q^{49} + 16 q^{50} + 4 q^{51} - 6 q^{54} - 8 q^{55} - 36 q^{56} + 8 q^{59} + 2 q^{60} - 28 q^{61} - 12 q^{64} - 16 q^{65} - 2 q^{66} + 28 q^{69} + 16 q^{70} + 44 q^{71} + 14 q^{74} + 16 q^{75} - 12 q^{76} - 36 q^{79} - 6 q^{81} - 36 q^{84} - 32 q^{85} + 24 q^{86} + 6 q^{89} + 2 q^{90} + 64 q^{94} - 12 q^{95} - 12 q^{96} - 2 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 + 6 * q^6 + 6 * q^9 - 2 * q^10 - 4 * q^11 - 18 * q^14 - 2 * q^15 - 6 * q^16 + 6 * q^19 - 18 * q^21 - 6 * q^24 - 2 * q^25 - 8 * q^26 - 16 * q^29 + 4 * q^34 + 2 * q^35 - 6 * q^36 - 8 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 + 28 * q^46 - 56 * q^49 + 16 * q^50 + 4 * q^51 - 6 * q^54 - 8 * q^55 - 36 * q^56 + 8 * q^59 + 2 * q^60 - 28 * q^61 - 12 * q^64 - 16 * q^65 - 2 * q^66 + 28 * q^69 + 16 * q^70 + 44 * q^71 + 14 * q^74 + 16 * q^75 - 12 * q^76 - 36 * q^79 - 6 * q^81 - 36 * q^84 - 32 * q^85 + 24 * q^86 + 6 * q^89 + 2 * q^90 + 64 * q^94 - 12 * q^95 - 12 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more