LMFDB - Embedded newform 462.2.k.e.89.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(89,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("462.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.k (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.3
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.e.353.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.10721 - 1.33195i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.241181 + 0.417738i) q^{5} +(1.62484 - 0.599900i) q^{6} +(1.48356 - 2.19067i) q^{7} +1.00000i q^{8} +(-0.548188 - 2.94949i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.10721 - 1.33195i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.241181 + 0.417738i) q^{5} +(1.62484 - 0.599900i) q^{6} +(1.48356 - 2.19067i) q^{7} +1.00000i q^{8} +(-0.548188 - 2.94949i) q^{9} +(-0.417738 + 0.241181i) q^{10} +(0.866025 - 0.500000i) q^{11} +(1.70711 + 0.292893i) q^{12} -0.550510i q^{13} +(2.38014 - 1.15539i) q^{14} +(0.289369 + 0.783763i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.926868 + 1.60538i) q^{17} +(1.00000 - 2.82843i) q^{18} +(-0.334273 - 0.192993i) q^{19} -0.482362 q^{20} +(-1.27526 - 4.40156i) q^{21} +1.00000 q^{22} +(-0.216237 - 0.124844i) q^{23} +(1.33195 + 1.10721i) q^{24} +(2.38366 + 4.12863i) q^{25} +(0.275255 - 0.476756i) q^{26} +(-4.53553 - 2.53553i) q^{27} +(2.63896 + 0.189469i) q^{28} +4.48477i q^{29} +(-0.141281 + 0.823443i) q^{30} +(1.08018 - 0.623642i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.292893 - 1.70711i) q^{33} +1.85374i q^{34} +(0.557318 + 1.14809i) q^{35} +(2.28024 - 1.94949i) q^{36} +(-2.72853 + 4.72595i) q^{37} +(-0.192993 - 0.334273i) q^{38} +(-0.733253 - 0.609528i) q^{39} +(-0.417738 - 0.241181i) q^{40} -5.67387 q^{41} +(1.09638 - 4.44949i) q^{42} -0.682163 q^{43} +(0.866025 + 0.500000i) q^{44} +(1.36433 + 0.482362i) q^{45} +(-0.124844 - 0.216237i) q^{46} +(4.41421 - 7.64564i) q^{47} +(0.599900 + 1.62484i) q^{48} +(-2.59808 - 6.50000i) q^{49} +4.76733i q^{50} +(3.16452 + 0.542947i) q^{51} +(0.476756 - 0.275255i) q^{52} +(-6.54441 + 3.77841i) q^{53} +(-2.66012 - 4.46360i) q^{54} +0.482362i q^{55} +(2.19067 + 1.48356i) q^{56} +(-0.627167 + 0.231553i) q^{57} +(-2.24238 + 3.88392i) q^{58} +(1.82465 + 3.16038i) q^{59} +(-0.534074 + 0.642483i) q^{60} +(-7.63593 - 4.40861i) q^{61} +1.24728 q^{62} +(-7.27463 - 3.17486i) q^{63} -1.00000 q^{64} +(0.229969 + 0.132773i) q^{65} +(1.10721 - 1.33195i) q^{66} +(4.35690 + 7.54636i) q^{67} +(-0.926868 + 1.60538i) q^{68} +(-0.405706 + 0.149788i) q^{69} +(-0.0913925 + 1.27293i) q^{70} +5.76028i q^{71} +(2.94949 - 0.548188i) q^{72} +(-1.94534 + 1.12314i) q^{73} +(-4.72595 + 2.72853i) q^{74} +(8.13834 + 1.39632i) q^{75} -0.385986i q^{76} +(0.189469 - 2.63896i) q^{77} +(-0.330251 - 0.894494i) q^{78} +(-6.71587 + 11.6322i) q^{79} +(-0.241181 - 0.417738i) q^{80} +(-8.39898 + 3.23375i) q^{81} +(-4.91372 - 2.83694i) q^{82} -6.48941 q^{83} +(3.17423 - 3.30518i) q^{84} -0.894171 q^{85} +(-0.590770 - 0.341081i) q^{86} +(5.97349 + 4.96556i) q^{87} +(0.500000 + 0.866025i) q^{88} +(5.64394 - 9.77559i) q^{89} +(0.940360 + 1.09990i) q^{90} +(-1.20599 - 0.816717i) q^{91} -0.249689i q^{92} +(0.365321 - 2.12925i) q^{93} +(7.64564 - 4.41421i) q^{94} +(0.161241 - 0.0930924i) q^{95} +(-0.292893 + 1.70711i) q^{96} +16.8389i q^{97} +(1.00000 - 6.92820i) q^{98} +(-1.94949 - 2.28024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 8 q^{12} - 4 q^{16} + 20 q^{17} + 8 q^{18} - 12 q^{19} - 8 q^{20} - 20 q^{21} + 8 q^{22} - 12 q^{23} - 4 q^{24} + 8 q^{25} + 12 q^{26} - 8 q^{27} - 4 q^{30} + 12 q^{31} + 8 q^{33} + 16 q^{35} - 8 q^{38} + 24 q^{39} + 40 q^{41} - 8 q^{43} + 16 q^{45} + 8 q^{46} + 24 q^{47} + 4 q^{48} + 32 q^{51} - 60 q^{53} - 4 q^{54} - 20 q^{57} - 4 q^{58} + 4 q^{59} - 12 q^{60} - 36 q^{61} + 24 q^{62} - 32 q^{63} - 8 q^{64} - 12 q^{65} + 4 q^{66} + 12 q^{67} - 20 q^{68} - 12 q^{69} - 20 q^{70} + 4 q^{72} + 48 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{79} - 4 q^{80} - 28 q^{81} - 24 q^{82} - 72 q^{83} - 4 q^{84} - 32 q^{85} + 12 q^{86} + 16 q^{87} + 4 q^{88} - 4 q^{89} - 28 q^{90} + 36 q^{91} + 16 q^{93} + 24 q^{95} - 8 q^{96} + 8 q^{98} + 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 8 * q^12 - 4 * q^16 + 20 * q^17 + 8 * q^18 - 12 * q^19 - 8 * q^20 - 20 * q^21 + 8 * q^22 - 12 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 - 8 * q^27 - 4 * q^30 + 12 * q^31 + 8 * q^33 + 16 * q^35 - 8 * q^38 + 24 * q^39 + 40 * q^41 - 8 * q^43 + 16 * q^45 + 8 * q^46 + 24 * q^47 + 4 * q^48 + 32 * q^51 - 60 * q^53 - 4 * q^54 - 20 * q^57 - 4 * q^58 + 4 * q^59 - 12 * q^60 - 36 * q^61 + 24 * q^62 - 32 * q^63 - 8 * q^64 - 12 * q^65 + 4 * q^66 + 12 * q^67 - 20 * q^68 - 12 * q^69 - 20 * q^70 + 4 * q^72 + 48 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^79 - 4 * q^80 - 28 * q^81 - 24 * q^82 - 72 * q^83 - 4 * q^84 - 32 * q^85 + 12 * q^86 + 16 * q^87 + 4 * q^88 - 4 * q^89 - 28 * q^90 + 36 * q^91 + 16 * q^93 + 24 * q^95 - 8 * q^96 + 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	1.10721	−	1.33195i	0.639246	−	0.769002i
$3$	1.10721	−	1.33195i	0.639246	−	0.769002i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.241181	+	0.417738i	−0.107859	+	0.186818i	−0.914903	−	0.403674i	$-0.867733\pi$
$5$	−0.241181	+	0.417738i	−0.107859	+	0.186818i	0.807043	+	0.590492i	$0.201066\pi$
$6$	1.62484	−	0.599900i	0.663340	−	0.244908i
$7$	1.48356	−	2.19067i	0.560734	−	0.827996i
$7$	1.48356	−	2.19067i	0.560734	−	0.827996i
$8$			1.00000i			0.353553i
$9$	−0.548188	−	2.94949i	−0.182729	−	0.983163i
$10$	−0.417738	+	0.241181i	−0.132100	+	0.0762681i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	1.70711	+	0.292893i	0.492799	+	0.0845510i
$13$		−	0.550510i		−	0.152684i	−0.997082	−	0.0763420i	$-0.975676\pi$
$13$		−	0.550510i		−	0.152684i	0.997082	−	0.0763420i	$-0.0243241\pi$
$14$	2.38014	−	1.15539i	0.636119	−	0.308792i
$15$	0.289369	+	0.783763i	0.0747148	+	0.202367i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.926868	+	1.60538i	0.224798	+	0.389362i	0.956259	−	0.292521i	$-0.0944943\pi$
$17$	0.926868	+	1.60538i	0.224798	+	0.389362i	−0.731460	+	0.681884i	$0.761161\pi$
$18$	1.00000	−	2.82843i	0.235702	−	0.666667i
$19$	−0.334273	−	0.192993i	−0.0766876	−	0.0442756i	0.461166	−	0.887314i	$-0.347431\pi$
$19$	−0.334273	−	0.192993i	−0.0766876	−	0.0442756i	−0.537853	+	0.843038i	$0.680765\pi$
$20$	−0.482362			−0.107859
$21$	−1.27526	−	4.40156i	−0.278283	−	0.960499i
$22$	1.00000			0.213201
$23$	−0.216237	−	0.124844i	−0.0450885	−	0.0260319i	0.477286	−	0.878748i	$-0.341620\pi$
$23$	−0.216237	−	0.124844i	−0.0450885	−	0.0260319i	−0.522375	+	0.852716i	$0.674954\pi$
$24$	1.33195	+	1.10721i	0.271883	+	0.226008i
$25$	2.38366	+	4.12863i	0.476733	+	0.825725i
$26$	0.275255	−	0.476756i	0.0539820	−	0.0934995i
$27$	−4.53553	−	2.53553i	−0.872864	−	0.487964i
$28$	2.63896	+	0.189469i	0.498716	+	0.0358062i
$29$			4.48477i			0.832800i	0.909181	+	0.416400i	$0.136708\pi$
$29$			4.48477i			0.832800i	−0.909181	+	0.416400i	$0.863292\pi$
$30$	−0.141281	+	0.823443i	−0.0257942	+	0.150339i
$31$	1.08018	−	0.623642i	0.194006	−	0.112009i	−0.399851	−	0.916580i	$-0.630938\pi$
$31$	1.08018	−	0.623642i	0.194006	−	0.112009i	0.593857	+	0.804571i	$0.297605\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.292893	−	1.70711i	0.0509862	−	0.297169i
$34$			1.85374i			0.317913i
$35$	0.557318	+	1.14809i	0.0942040	+	0.194062i
$36$	2.28024	−	1.94949i	0.380040	−	0.324915i
$37$	−2.72853	+	4.72595i	−0.448567	+	0.776941i	−0.998293	−	0.0584042i	$-0.981399\pi$
$37$	−2.72853	+	4.72595i	−0.448567	+	0.776941i	0.549726	+	0.835345i	$0.314732\pi$
$38$	−0.192993	−	0.334273i	−0.0313076	−	0.0542263i
$39$	−0.733253	−	0.609528i	−0.117414	−	0.0976027i
$40$	−0.417738	−	0.241181i	−0.0660501	−	0.0381341i
$41$	−5.67387			−0.886110			−0.443055	−	0.896495i	$-0.646105\pi$
$41$	−5.67387			−0.886110			−0.443055	+	0.896495i	$0.646105\pi$
$42$	1.09638	−	4.44949i	0.169175	−	0.686571i
$43$	−0.682163			−0.104029			−0.0520144	−	0.998646i	$-0.516564\pi$
$43$	−0.682163			−0.104029			−0.0520144	+	0.998646i	$0.516564\pi$
$44$	0.866025	+	0.500000i	0.130558	+	0.0753778i
$45$	1.36433	+	0.482362i	0.203382	+	0.0719063i
$46$	−0.124844	−	0.216237i	−0.0184073	−	0.0318824i
$47$	4.41421	−	7.64564i	0.643879	−	1.11523i	−0.340680	−	0.940179i	$-0.610657\pi$
$47$	4.41421	−	7.64564i	0.643879	−	1.11523i	0.984559	−	0.175052i	$-0.0560094\pi$
$48$	0.599900	+	1.62484i	0.0865882	+	0.234526i
$49$	−2.59808	−	6.50000i	−0.371154	−	0.928571i
$50$			4.76733i			0.674202i
$51$	3.16452	+	0.542947i	0.443122	+	0.0760277i
$52$	0.476756	−	0.275255i	0.0661141	−	0.0381710i
$53$	−6.54441	+	3.77841i	−0.898943	+	0.519005i	−0.876857	−	0.480751i	$-0.840364\pi$
$53$	−6.54441	+	3.77841i	−0.898943	+	0.519005i	−0.0220861	+	0.999756i	$0.507031\pi$
$54$	−2.66012	−	4.46360i	−0.361997	−	0.607420i
$55$			0.482362i			0.0650417i
$56$	2.19067	+	1.48356i	0.292741	+	0.198250i
$57$	−0.627167	+	0.231553i	−0.0830702	+	0.0306699i
$58$	−2.24238	+	3.88392i	−0.294439	+	0.509984i
$59$	1.82465	+	3.16038i	0.237549	+	0.411446i	0.960010	−	0.279965i	$-0.0903228\pi$
$59$	1.82465	+	3.16038i	0.237549	+	0.411446i	−0.722462	+	0.691411i	$0.756989\pi$
$60$	−0.534074	+	0.642483i	−0.0689487	+	0.0829441i
$61$	−7.63593	−	4.40861i	−0.977681	−	0.564464i	−0.0761117	−	0.997099i	$-0.524251\pi$
$61$	−7.63593	−	4.40861i	−0.977681	−	0.564464i	−0.901569	+	0.432635i	$0.857584\pi$
$62$	1.24728			0.158405
$63$	−7.27463	−	3.17486i	−0.916518	−	0.399994i
$64$	−1.00000			−0.125000
$65$	0.229969	+	0.132773i	0.0285241	+	0.0164684i
$66$	1.10721	−	1.33195i	0.136288	−	0.163952i
$67$	4.35690	+	7.54636i	0.532279	+	0.921935i	0.999290	+	0.0376832i	$0.0119978\pi$
$67$	4.35690	+	7.54636i	0.532279	+	0.921935i	−0.467010	+	0.884252i	$0.654669\pi$
$68$	−0.926868	+	1.60538i	−0.112399	+	0.194681i
$69$	−0.405706	+	0.149788i	−0.0488412	+	0.0180324i
$70$	−0.0913925	+	1.27293i	−0.0109235	+	0.152145i
$71$			5.76028i			0.683619i	0.939769	+	0.341810i	$0.111040\pi$
$71$			5.76028i			0.683619i	−0.939769	+	0.341810i	$0.888960\pi$
$72$	2.94949	−	0.548188i	0.347601	−	0.0646046i
$73$	−1.94534	+	1.12314i	−0.227685	+	0.131454i	−0.609504	−	0.792783i	$-0.708631\pi$
$73$	−1.94534	+	1.12314i	−0.227685	+	0.131454i	0.381819	+	0.924237i	$0.375298\pi$
$74$	−4.72595	+	2.72853i	−0.549380	+	0.317185i
$75$	8.13834	+	1.39632i	0.939734	+	0.161233i
$76$		−	0.385986i		−	0.0442756i
$77$	0.189469	−	2.63896i	0.0215920	−	0.300737i
$78$	−0.330251	−	0.894494i	−0.0373936	−	0.101281i
$79$	−6.71587	+	11.6322i	−0.755595	+	1.30873i	0.189483	+	0.981884i	$0.439319\pi$
$79$	−6.71587	+	11.6322i	−0.755595	+	1.30873i	−0.945078	+	0.326844i	$0.894015\pi$
$80$	−0.241181	−	0.417738i	−0.0269649	−	0.0467045i
$81$	−8.39898	+	3.23375i	−0.933220	+	0.359306i
$82$	−4.91372	−	2.83694i	−0.542629	−	0.313287i
$83$	−6.48941			−0.712305			−0.356153	−	0.934428i	$-0.615912\pi$
$83$	−6.48941			−0.712305			−0.356153	+	0.934428i	$0.615912\pi$
$84$	3.17423	−	3.30518i	0.346337	−	0.360625i
$85$	−0.894171			−0.0969865
$86$	−0.590770	−	0.341081i	−0.0637044	−	0.0367798i
$87$	5.97349	+	4.96556i	0.640425	+	0.532364i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	5.64394	−	9.77559i	0.598257	−	1.03621i	−0.394822	−	0.918758i	$-0.629194\pi$
$89$	5.64394	−	9.77559i	0.598257	−	1.03621i	0.993078	−	0.117453i	$-0.0374730\pi$
$90$	0.940360	+	1.09990i	0.0991226	+	0.115940i
$91$	−1.20599	−	0.816717i	−0.126422	−	0.0856152i
$92$		−	0.249689i		−	0.0260319i
$93$	0.365321	−	2.12925i	0.0378821	−	0.220793i
$94$	7.64564	−	4.41421i	0.788588	−	0.455291i
$95$	0.161241	−	0.0930924i	0.0165429	−	0.00955108i
$96$	−0.292893	+	1.70711i	−0.0298933	+	0.174231i
$97$			16.8389i			1.70973i	0.518849	+	0.854866i	$0.326361\pi$
$97$			16.8389i			1.70973i	−0.518849	+	0.854866i	$0.673639\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$	−1.94949	−	2.28024i	−0.195931	−	0.229173i
$100$	−2.38366	+	4.12863i	−0.238366	+	0.412863i
$101$	−0.855693	−	1.48210i	−0.0851447	−	0.147475i	0.820308	−	0.571922i	$-0.193802\pi$
$101$	−0.855693	−	1.48210i	−0.0851447	−	0.147475i	−0.905453	+	0.424447i	$0.860469\pi$
$102$	2.46909	+	2.05247i	0.244476	+	0.203225i
$103$	0.170088	+	0.0982005i	0.0167593	+	0.00967599i	0.508356	−	0.861147i	$-0.330253\pi$
$103$	0.170088	+	0.0982005i	0.0167593	+	0.00967599i	−0.491597	+	0.870823i	$0.663587\pi$
$104$	0.550510			0.0539820
$105$	2.14626	+	0.528850i	0.209454	+	0.0516105i
$106$	−7.55683			−0.733984
$107$	8.08991	+	4.67071i	0.782081	+	0.451535i	0.837167	−	0.546947i	$-0.184210\pi$
$107$	8.08991	+	4.67071i	0.782081	+	0.451535i	−0.0550863	+	0.998482i	$0.517543\pi$
$108$	−0.0719302	−	5.19565i	−0.00692148	−	0.499952i
$109$	3.15161	+	5.45875i	0.301870	+	0.522854i	0.976559	−	0.215248i	$-0.0690559\pi$
$109$	3.15161	+	5.45875i	0.301870	+	0.522854i	−0.674690	+	0.738101i	$0.735723\pi$
$110$	−0.241181	+	0.417738i	−0.0229957	+	0.0398297i
$111$	3.27369	+	8.86686i	0.310725	+	0.841605i
$112$	1.15539	+	2.38014i	0.109175	+	0.224902i
$113$		−	19.8084i		−	1.86342i	−0.363201	−	0.931711i	$-0.618316\pi$
$113$		−	19.8084i		−	1.86342i	0.363201	−	0.931711i	$-0.381684\pi$
$114$	−0.658919	−	0.113053i	−0.0617134	−	0.0105883i
$115$	0.104304	−	0.0602202i	0.00972644	−	0.00561556i
$116$	−3.88392	+	2.24238i	−0.360613	+	0.208200i
$117$	−1.62372	+	0.301783i	−0.150113	+	0.0278999i
$118$			3.64929i			0.335944i
$119$	4.89193	+	0.351225i	0.448443	+	0.0321967i
$120$	−0.783763	+	0.289369i	−0.0715475	+	0.0264157i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−4.40861	−	7.63593i	−0.399137	−	0.691325i
$123$	−6.28215	+	7.55732i	−0.566442	+	0.681420i
$124$	1.08018	+	0.623642i	0.0970031	+	0.0560047i
$125$	−4.71139			−0.421399
$126$	−4.71259	−	6.38682i	−0.419831	−	0.568983i
$127$	−21.1440			−1.87623			−0.938114	−	0.346326i	$-0.887429\pi$
$127$	−21.1440			−1.87623			−0.938114	+	0.346326i	$0.887429\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−0.755295	+	0.908608i	−0.0665000	+	0.0799984i
$130$	0.132773	+	0.229969i	0.0116449	+	0.0201696i
$131$	8.17009	−	14.1510i	0.713824	−	1.23638i	−0.249587	−	0.968352i	$-0.580295\pi$
$131$	8.17009	−	14.1510i	0.713824	−	1.23638i	0.963411	−	0.268027i	$-0.0863717\pi$
$132$	1.62484	−	0.599900i	0.141425	−	0.0522146i
$133$	−0.918700	+	0.445966i	−0.0796614	+	0.0386701i
$134$			8.71379i			0.752757i
$135$	2.15307	−	1.28314i	0.185307	−	0.110435i
$136$	−1.60538	+	0.926868i	−0.137660	+	0.0794783i
$137$	9.95875	−	5.74969i	0.850834	−	0.491229i	−0.0100984	−	0.999949i	$-0.503214\pi$
$137$	9.95875	−	5.74969i	0.850834	−	0.491229i	0.860932	+	0.508720i	$0.169881\pi$
$138$	−0.426246	−	0.0731322i	−0.0362844	−	0.00622543i
$139$		−	3.37945i		−	0.286641i	−0.989676	−	0.143321i	$-0.954222\pi$
$139$		−	3.37945i		−	0.286641i	0.989676	−	0.143321i	$-0.0457780\pi$
$140$	−0.715615	+	1.05670i	−0.0604805	+	0.0893071i
$141$	−5.29618	−	14.3448i	−0.446019	−	1.20805i
$142$	−2.88014	+	4.98855i	−0.241696	+	0.418630i
$143$	−0.275255	−	0.476756i	−0.0230180	−	0.0398683i
$144$	2.82843	+	1.00000i	0.235702	+	0.0833333i
$145$	−1.87346	−	1.08164i	−0.155582	−	0.0898253i
$146$	−2.24629			−0.185904
$147$	−11.5343	−	3.73633i	−0.951332	−	0.308167i
$148$	−5.45705			−0.448567
$149$	−14.3154	−	8.26500i	−1.17276	−	0.677096i	−0.218434	−	0.975852i	$-0.570095\pi$
$149$	−14.3154	−	8.26500i	−1.17276	−	0.677096i	−0.954330	+	0.298756i	$0.903428\pi$
$150$	6.34985	+	5.27841i	0.518463	+	0.430981i
$151$	−0.0763986	−	0.132326i	−0.00621723	−	0.0107686i	0.862900	−	0.505375i	$-0.168646\pi$
$151$	−0.0763986	−	0.132326i	−0.00621723	−	0.0107686i	−0.869117	+	0.494606i	$0.835312\pi$
$152$	0.192993	−	0.334273i	0.0156538	−	0.0271131i
$153$	4.22696	−	3.61384i	0.341729	−	0.292162i
$154$	1.48356	−	2.19067i	0.119549	−	0.176529i
$155$			0.601643i			0.0483251i
$156$	0.161241	−	0.939780i	0.0129096	−	0.0752426i
$157$	9.11357	−	5.26172i	0.727342	−	0.419931i	−0.0901071	−	0.995932i	$-0.528721\pi$
$157$	9.11357	−	5.26172i	0.727342	−	0.419931i	0.817449	+	0.576001i	$0.195388\pi$
$158$	−11.6322	+	6.71587i	−0.925411	+	0.534286i
$159$	−2.21334	+	12.9003i	−0.175530	+	1.02306i
$160$		−	0.482362i		−	0.0381341i
$161$	−0.594294	+	0.288489i	−0.0468370	+	0.0227361i
$162$	−8.89060	−	1.39898i	−0.698512	−	0.109914i
$163$	−4.34228	+	7.52106i	−0.340114	+	0.589095i	−0.984454	−	0.175645i	$-0.943799\pi$
$163$	−4.34228	+	7.52106i	−0.340114	+	0.589095i	0.644340	+	0.764739i	$0.277132\pi$
$164$	−2.83694	−	4.91372i	−0.221527	−	0.383697i
$165$	0.642483	+	0.534074i	0.0500172	+	0.0415776i
$166$	−5.61999	−	3.24471i	−0.436196	−	0.251838i
$167$	−2.01096			−0.155613			−0.0778065	−	0.996968i	$-0.524792\pi$
$167$	−2.01096			−0.155613			−0.0778065	+	0.996968i	$0.524792\pi$
$168$	4.40156	−	1.27526i	0.339588	−	0.0983881i
$169$	12.6969			0.976688
$170$	−0.774375	−	0.447086i	−0.0593919	−	0.0342899i
$171$	−0.385986	+	1.09173i	−0.0295171	+	0.0834868i
$172$	−0.341081	−	0.590770i	−0.0260072	−	0.0450458i
$173$	−6.58140	+	11.3993i	−0.500375	+	0.866674i	0.499625	+	0.866242i	$0.333471\pi$
$173$	−6.58140	+	11.3993i	−0.500375	+	0.866674i	−1.00000		0.000432574i	$0.999862\pi$
$174$	2.69041	+	7.28705i	0.203960	+	0.552430i
$175$	12.5808	+	0.903259i	0.951017	+	0.0682800i
$176$			1.00000i			0.0753778i
$177$	6.22973	+	1.06885i	0.468255	+	0.0803399i
$178$	9.77559	−	5.64394i	0.732712	−	0.423031i
$179$	11.4624	−	6.61780i	0.856737	−	0.494637i	−0.00618127	−	0.999981i	$-0.501968\pi$
$179$	11.4624	−	6.61780i	0.856737	−	0.494637i	0.862918	+	0.505344i	$0.168634\pi$
$180$	0.264425	+	1.42272i	0.0197091	+	0.106043i
$181$		−	25.8936i		−	1.92466i	−0.271890	−	0.962328i	$-0.587649\pi$
$181$		−	25.8936i		−	1.92466i	0.271890	−	0.962328i	$-0.412351\pi$
$182$	−0.636057	−	1.31029i	−0.0471476	−	0.0971252i
$183$	−14.3266	+	5.28945i	−1.05905	+	0.391007i
$184$	0.124844	−	0.216237i	0.00920365	−	0.0159412i
$185$	−1.31614	−	2.27962i	−0.0967643	−	0.167601i
$186$	1.38100	−	1.66132i	0.101260	−	0.121814i
$187$	1.60538	+	0.926868i	0.117397	+	0.0677793i
$188$	8.82843			0.643879
$189$	−12.2833	+	6.17423i	−0.893477	+	0.449109i
$190$	0.186185			0.0135073
$191$	15.1791	+	8.76368i	1.09832	+	0.634118i	0.935780	−	0.352584i	$-0.114697\pi$
$191$	15.1791	+	8.76368i	1.09832	+	0.634118i	0.162544	+	0.986701i	$0.448030\pi$
$192$	−1.10721	+	1.33195i	−0.0799057	+	0.0961253i
$193$	3.68204	+	6.37748i	0.265039	+	0.459061i	0.967574	−	0.252588i	$-0.0812819\pi$
$193$	3.68204	+	6.37748i	0.265039	+	0.459061i	−0.702535	+	0.711649i	$0.747949\pi$
$194$	−8.41946	+	14.5829i	−0.604482	+	1.04699i
$195$	0.431470	−	0.159301i	0.0308982	−	0.0114078i
$196$	4.33013	−	5.50000i	0.309295	−	0.392857i
$197$		−	19.2932i		−	1.37458i	−0.726381	−	0.687292i	$-0.758799\pi$
$197$		−	19.2932i		−	1.37458i	0.726381	−	0.687292i	$-0.241201\pi$
$198$	−0.548188	−	2.94949i	−0.0389580	−	0.209611i
$199$	17.4020	−	10.0471i	1.23360	−	0.712218i	0.265819	−	0.964023i	$-0.414358\pi$
$199$	17.4020	−	10.0471i	1.23360	−	0.712218i	0.967778	+	0.251805i	$0.0810242\pi$
$200$	−4.12863	+	2.38366i	−0.291938	+	0.168550i
$201$	14.8754	+	2.55221i	1.04923	+	0.180019i
$202$		−	1.71139i		−	0.120413i
$203$	9.82465	+	6.65344i	0.689555	+	0.466980i
$204$	1.11206	+	3.01203i	0.0778595	+	0.210884i
$205$	1.36843	−	2.37019i	0.0955753	−	0.165541i
$206$	0.0982005	+	0.170088i	0.00684196	+	0.0118506i
$207$	−0.249689	+	0.706227i	−0.0173546	+	0.0490862i
$208$	0.476756	+	0.275255i	0.0330571	+	0.0190855i
$209$	−0.385986			−0.0266992
$210$	1.59429	+	1.53113i	0.110017	+	0.105658i
$211$	−4.98514			−0.343191			−0.171596	−	0.985167i	$-0.554892\pi$
$211$	−4.98514			−0.343191			−0.171596	+	0.985167i	$0.554892\pi$
$212$	−6.54441	−	3.77841i	−0.449472	−	0.259503i
$213$	7.67241	+	6.37782i	0.525705	+	0.437001i
$214$	4.67071	+	8.08991i	0.319283	+	0.553015i
$215$	0.164525	−	0.284965i	0.0112205	−	0.0194345i
$216$	2.53553	−	4.53553i	0.172521	−	0.308604i
$217$	0.236321	−	3.29153i	0.0160425	−	0.223444i
$218$			6.30323i			0.426908i
$219$	−0.657923	+	3.83466i	−0.0444583	+	0.259122i
$220$	−0.417738	+	0.241181i	−0.0281639	+	0.0162604i
$221$	0.883779	−	0.510250i	0.0594494	−	0.0343231i
$222$	−1.59833	+	9.31577i	−0.107273	+	0.625234i
$223$		−	13.2416i		−	0.886726i	−0.896342	−	0.443363i	$-0.853785\pi$
$223$		−	13.2416i		−	0.886726i	0.896342	−	0.443363i	$-0.146215\pi$
$224$	−0.189469	+	2.63896i	−0.0126594	+	0.176323i
$225$	10.8706	−	9.29386i	0.724710	−	0.619590i
$226$	9.90422	−	17.1546i	0.658819	−	1.14111i
$227$	13.8591	+	24.0046i	0.919858	+	1.59324i	0.799629	+	0.600495i	$0.205030\pi$
$227$	13.8591	+	24.0046i	0.919858	+	1.59324i	0.120229	+	0.992746i	$0.461637\pi$
$228$	−0.514114	−	0.427366i	−0.0340480	−	0.0283030i
$229$	7.21733	+	4.16693i	0.476935	+	0.275358i	0.719138	−	0.694867i	$-0.244537\pi$
$229$	7.21733	+	4.16693i	0.476935	+	0.275358i	−0.242203	+	0.970225i	$0.577870\pi$
$230$	0.120440			0.00794161
$231$	−3.30518	−	3.17423i	−0.217465	−	0.208849i
$232$	−4.48477			−0.294439
$233$	−7.01267	−	4.04877i	−0.459415	−	0.265244i	0.252383	−	0.967627i	$-0.418786\pi$
$233$	−7.01267	−	4.04877i	−0.459415	−	0.265244i	−0.711798	+	0.702384i	$0.752119\pi$
$234$	−1.55708	−	0.550510i	−0.101789	−	0.0359880i
$235$	2.12925	+	3.68797i	0.138897	+	0.240576i
$236$	−1.82465	+	3.16038i	−0.118774	+	0.205723i
$237$	8.05771	+	21.8245i	0.523404	+	1.41765i
$238$	4.06092	+	2.75014i	0.263231	+	0.178265i
$239$			23.6386i			1.52905i	0.644592	+	0.764527i	$0.277027\pi$
$239$			23.6386i			1.52905i	−0.644592	+	0.764527i	$0.722973\pi$
$240$	−0.823443	−	0.141281i	−0.0531530	−	0.00911962i
$241$	14.7528	−	8.51751i	0.950309	−	0.548661i	0.0571323	−	0.998367i	$-0.481804\pi$
$241$	14.7528	−	8.51751i	0.950309	−	0.548661i	0.893177	+	0.449705i	$0.148471\pi$
$242$	0.866025	−	0.500000i	0.0556702	−	0.0321412i
$243$	−4.99221	+	14.7675i	−0.320250	+	0.947333i
$244$		−	8.81722i		−	0.564464i
$245$	3.34190	+	0.482362i	0.213506	+	0.0308170i
$246$	−9.21916	+	3.40376i	−0.587792	+	0.217016i
$247$	−0.106245	+	0.184021i	−0.00676018	+	0.0117090i
$248$	0.623642	+	1.08018i	0.0396013	+	0.0685915i
$249$	−7.18512	+	8.64358i	−0.455338	+	0.547764i
$250$	−4.08018	−	2.35569i	−0.258053	−	0.148987i
$251$	12.6075			0.795777			0.397889	−	0.917434i	$-0.369743\pi$
$251$	12.6075			0.795777			0.397889	+	0.917434i	$0.369743\pi$
$252$	−0.887810	−	7.88745i	−0.0559268	−	0.496862i
$253$	−0.249689			−0.0156978
$254$	−18.3113	−	10.5720i	−1.14895	−	0.663347i
$255$	−0.990032	+	1.19099i	−0.0619982	+	0.0745829i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.204527	−	0.354251i	0.0127580	−	0.0220976i	−0.859576	−	0.511008i	$-0.829272\pi$
$257$	0.204527	−	0.354251i	0.0127580	−	0.0220976i	0.872334	+	0.488911i	$0.162606\pi$
$258$	−1.10841	+	0.409230i	−0.0690065	+	0.0254775i
$259$	6.30505	+	12.9885i	0.391777	+	0.807069i
$260$			0.265545i			0.0164684i
$261$	13.2278	−	2.45850i	0.818778	−	0.152177i
$262$	14.1510	−	8.17009i	0.874252	−	0.504750i
$263$	12.6093	−	7.28000i	0.777524	−	0.448904i	−0.0580278	−	0.998315i	$-0.518481\pi$
$263$	12.6093	−	7.28000i	0.777524	−	0.448904i	0.835552	+	0.549411i	$0.185148\pi$
$264$	1.70711	+	0.292893i	0.105065	+	0.0180263i
$265$		−	3.64513i		−	0.223918i
$266$	−1.01860	−	0.0731322i	−0.0624544	−	0.00448402i
$267$	−6.77161	−	18.3411i	−0.414416	−	1.12245i
$268$	−4.35690	+	7.54636i	−0.266140	+	0.460968i
$269$	12.3960	+	21.4704i	0.755795	+	1.30907i	0.944978	+	0.327133i	$0.106082\pi$
$269$	12.3960	+	21.4704i	0.755795	+	1.30907i	−0.189184	+	0.981942i	$0.560584\pi$
$270$	2.50619	−	0.0346964i	0.152522	−	0.00211155i
$271$	−24.6174	−	14.2128i	−1.49540	−	0.863369i	−0.495413	−	0.868658i	$-0.664983\pi$
$271$	−24.6174	−	14.2128i	−1.49540	−	0.863369i	−0.999986	+	0.00528874i	$0.998317\pi$
$272$	−1.85374			−0.112399
$273$	−2.42310	+	0.702041i	−0.146653	+	0.0424895i
$274$	11.4994			0.694703
$275$	4.12863	+	2.38366i	0.248966	+	0.143740i
$276$	−0.332573	−	0.276457i	−0.0200186	−	0.0166408i
$277$	−1.73179	−	2.99955i	−0.104053	−	0.180226i	0.809298	−	0.587399i	$-0.199848\pi$
$277$	−1.73179	−	2.99955i	−0.104053	−	0.180226i	−0.913351	+	0.407173i	$0.866515\pi$
$278$	1.68973	−	2.92669i	0.101343	−	0.175531i
$279$	−2.43157	−	2.84411i	−0.145574	−	0.170272i
$280$	−1.14809	+	0.557318i	−0.0686114	+	0.0333061i
$281$		−	20.5607i		−	1.22655i	−0.789869	−	0.613276i	$-0.789852\pi$
$281$		−	20.5607i		−	1.22655i	0.789869	−	0.613276i	$-0.210148\pi$
$282$	2.58579	−	15.0711i	0.153981	−	0.897469i
$283$	6.42343	−	3.70857i	0.381833	−	0.220451i	−0.296782	−	0.954945i	$-0.595914\pi$
$283$	6.42343	−	3.70857i	0.381833	−	0.220451i	0.678615	+	0.734494i	$0.262580\pi$
$284$	−4.98855	+	2.88014i	−0.296016	+	0.170905i
$285$	0.0545323	−	0.317837i	0.00323021	−	0.0188271i
$286$		−	0.550510i		−	0.0325524i
$287$	−8.41755	+	12.4296i	−0.496872	+	0.733695i
$288$	1.94949	+	2.28024i	0.114875	+	0.134364i
$289$	6.78183	−	11.7465i	0.398931	−	0.690969i
$290$	−1.08164	−	1.87346i	−0.0635161	−	0.110013i
$291$	22.4286	+	18.6441i	1.31479	+	1.09294i
$292$	−1.94534	−	1.12314i	−0.113843	−	0.0657271i
$293$	−33.1199			−1.93488			−0.967442	−	0.253093i	$-0.918552\pi$
$293$	−33.1199			−1.93488			−0.967442	+	0.253093i	$0.918552\pi$
$294$	−8.12082	−	9.00290i	−0.473616	−	0.525060i
$295$	−1.76028			−0.102487
$296$	−4.72595	−	2.72853i	−0.274690	−	0.158592i
$297$	−5.19565	+	0.0719302i	−0.301482	+	0.00417381i
$298$	−8.26500	−	14.3154i	−0.478779	−	0.829269i
$299$	−0.0687281	+	0.119041i	−0.00397465	+	0.00688430i
$300$	2.85992	+	7.74616i	0.165118	+	0.447225i
$301$	−1.01203	+	1.49439i	−0.0583326	+	0.0861354i
$302$		−	0.152797i		−	0.00879249i
$303$	−2.92152	−	0.501254i	−0.167837	−	0.0287963i
$304$	0.334273	−	0.192993i	0.0191719	−	0.0110689i
$305$	3.68328	−	2.12654i	0.210904	−	0.121766i
$306$	5.46757	−	1.01620i	0.312560	−	0.0580921i
$307$		−	11.6047i		−	0.662317i	−0.943575	−	0.331158i	$-0.892561\pi$
$307$		−	11.6047i		−	0.662317i	0.943575	−	0.331158i	$-0.107439\pi$
$308$	2.38014	−	1.15539i	0.135621	−	0.0658347i
$309$	0.319121	−	0.117821i	0.0181542	−	0.00670261i
$310$	−0.300821	+	0.521038i	−0.0170855	+	0.0295930i
$311$	−1.12484	−	1.94829i	−0.0637841	−	0.110477i	0.832370	−	0.554220i	$-0.186984\pi$
$311$	−1.12484	−	1.94829i	−0.0637841	−	0.110477i	−0.896154	+	0.443743i	$0.853650\pi$
$312$	0.609528	−	0.733253i	0.0345078	−	0.0415123i
$313$	−8.92899	−	5.15515i	−0.504696	−	0.291387i	0.225955	−	0.974138i	$-0.427450\pi$
$313$	−8.92899	−	5.15515i	−0.504696	−	0.291387i	−0.730651	+	0.682751i	$0.760783\pi$
$314$	10.5234			0.593872
$315$	3.08076	−	2.27317i	0.173581	−	0.128079i
$316$	−13.4317			−0.755595
$317$	13.7259	+	7.92463i	0.770921	+	0.445091i	0.833203	−	0.552967i	$-0.186505\pi$
$317$	13.7259	+	7.92463i	0.770921	+	0.445091i	−0.0622821	+	0.998059i	$0.519838\pi$
$318$	−8.36697	+	10.0653i	−0.469196	+	0.564436i
$319$	2.24238	+	3.88392i	0.125549	+	0.217458i
$320$	0.241181	−	0.417738i	0.0134824	−	0.0233522i
$321$	15.1784	−	5.60392i	0.847173	−	0.312780i
$322$	−0.658919	−	0.0473082i	−0.0367201	−	0.00263638i
$323$		−	0.715515i		−	0.0398123i
$324$	−7.00000	−	5.65685i	−0.388889	−	0.314270i
$325$	2.27285	−	1.31223i	0.126075	−	0.0727895i
$326$	−7.52106	+	4.34228i	−0.416553	+	0.240497i
$327$	10.7603	+	1.84617i	0.595045	+	0.102094i
$328$		−	5.67387i		−	0.313287i
$329$	−10.2003	−	21.0129i	−0.562362	−	1.15848i
$330$	0.289369	+	0.783763i	0.0159292	+	0.0431447i
$331$	−3.37516	+	5.84594i	−0.185515	+	0.321322i	−0.943750	−	0.330660i	$-0.892729\pi$
$331$	−3.37516	+	5.84594i	−0.185515	+	0.321322i	0.758235	+	0.651982i	$0.226062\pi$
$332$	−3.24471	−	5.61999i	−0.178076	−	0.308437i
$333$	15.4349	+	5.45705i	0.845826	+	0.299045i
$334$	−1.74155	−	1.00548i	−0.0952931	−	0.0550175i
$335$	−4.20320			−0.229645
$336$	4.44949	+	1.09638i	0.242740	+	0.0598122i
$337$	1.02093			0.0556137			0.0278068	−	0.999613i	$-0.491148\pi$
$337$	1.02093			0.0556137			0.0278068	+	0.999613i	$0.491148\pi$
$338$	10.9959	+	6.34847i	0.598097	+	0.345311i
$339$	−26.3839	−	21.9320i	−1.43298	−	1.19118i
$340$	−0.447086	−	0.774375i	−0.0242466	−	0.0419964i
$341$	0.623642	−	1.08018i	0.0337721	−	0.0584950i
$342$	−0.880139	+	0.752475i	−0.0475925	+	0.0406892i
$343$	−18.0938	−	3.95164i	−0.976972	−	0.213368i
$344$		−	0.682163i		−	0.0367798i
$345$	0.0352762	−	0.205605i	0.00189921	−	0.0110694i
$346$	−11.3993	+	6.58140i	−0.612831	+	0.353818i
$347$	24.6613	−	14.2382i	1.32389	−	0.764349i	0.339544	−	0.940590i	$-0.389727\pi$
$347$	24.6613	−	14.2382i	1.32389	−	0.764349i	0.984347	+	0.176242i	$0.0563940\pi$
$348$	−1.31356	+	7.65597i	−0.0704141	+	0.410403i
$349$			12.9437i			0.692861i	0.938076	+	0.346430i	$0.112606\pi$
$349$			12.9437i			0.692861i	−0.938076	+	0.346430i	$0.887394\pi$
$350$	10.4436	+	7.07263i	0.558236	+	0.378048i
$351$	−1.39584	+	2.49686i	−0.0745043	+	0.133272i
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−8.66631	−	15.0105i	−0.461261	−	0.798927i	0.537763	−	0.843096i	$-0.319269\pi$
$353$	−8.66631	−	15.0105i	−0.461261	−	0.798927i	−0.999024	+	0.0441686i	$0.985936\pi$
$354$	4.86068	+	4.04052i	0.258342	+	0.214751i
$355$	−2.40629	−	1.38927i	−0.127712	−	0.0737348i
$356$	11.2879			0.598257
$357$	5.88419	−	6.12694i	0.311424	−	0.324272i
$358$	13.2356			0.699523
$359$	−6.33088	−	3.65514i	−0.334131	−	0.192911i	0.323543	−	0.946214i	$-0.395126\pi$
$359$	−6.33088	−	3.65514i	−0.334131	−	0.192911i	−0.657674	+	0.753303i	$0.728459\pi$
$360$	−0.482362	+	1.36433i	−0.0254227	+	0.0719063i
$361$	−9.42551	−	16.3255i	−0.496079	−	0.859235i
$362$	12.9468	−	22.4245i	0.680469	−	1.17861i
$363$	−0.599900	−	1.62484i	−0.0314866	−	0.0852822i
$364$	0.104304	−	1.45277i	0.00546704	−	0.0761460i
$365$		−	1.08352i		−	0.0567143i
$366$	−15.0519	−	2.58250i	−0.786777	−	0.134990i
$367$	8.47438	−	4.89269i	0.442359	−	0.255396i	−0.262239	−	0.965003i	$-0.584461\pi$
$367$	8.47438	−	4.89269i	0.442359	−	0.255396i	0.704598	+	0.709607i	$0.251127\pi$
$368$	0.216237	−	0.124844i	0.0112721	−	0.00650797i
$369$	3.11035	+	16.7350i	0.161918	+	0.871190i
$370$		−	2.63227i		−	0.136845i
$371$	−1.43178	+	19.9422i	−0.0743344	+	1.03535i
$372$	2.02664	−	0.748247i	0.105077	−	0.0387948i
$373$	−14.0289	+	24.2988i	−0.726391	+	1.25815i	0.232008	+	0.972714i	$0.425470\pi$
$373$	−14.0289	+	24.2988i	−0.726391	+	1.25815i	−0.958399	+	0.285432i	$0.907863\pi$
$374$	0.926868	+	1.60538i	0.0479272	+	0.0830123i
$375$	−5.21648	+	6.27534i	−0.269378	+	0.324057i
$376$	7.64564	+	4.41421i	0.394294	+	0.227646i
$377$	2.46891			0.127155
$378$	−13.7247	−	0.794593i	−0.705925	−	0.0408695i
$379$	29.2641			1.50320			0.751598	−	0.659622i	$-0.229284\pi$
$379$	29.2641			1.50320			0.751598	+	0.659622i	$0.229284\pi$
$380$	0.161241	+	0.0930924i	0.00827147	+	0.00477554i
$381$	−23.4108	+	28.1628i	−1.19937	+	1.44282i
$382$	8.76368	+	15.1791i	0.448389	+	0.776632i
$383$	−4.89376	+	8.47623i	−0.250059	+	0.433115i	−0.963542	−	0.267558i	$-0.913783\pi$
$383$	−4.89376	+	8.47623i	−0.250059	+	0.433115i	0.713483	+	0.700673i	$0.247117\pi$
$384$	−1.62484	+	0.599900i	−0.0829175	+	0.0306135i
$385$	1.05670	+	0.715615i	0.0538542	+	0.0364711i
$386$			7.36408i			0.374822i
$387$	0.373954	+	2.01203i	0.0190091	+	0.102277i
$388$	−14.5829	+	8.41946i	−0.740336	+	0.427433i
$389$	−32.1589	+	18.5669i	−1.63052	+	0.941380i	−0.646586	+	0.762841i	$0.723804\pi$
$389$	−32.1589	+	18.5669i	−1.63052	+	0.941380i	−0.983933	+	0.178539i	$0.942863\pi$
$390$	0.453314	+	0.0777764i	0.0229544	+	0.00393836i
$391$		−	0.462857i		−	0.0234077i
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$	−9.80248	−	26.5502i	−0.494470	−	1.33928i
$394$	9.64660	−	16.7084i	0.485989	−	0.841757i
$395$	−3.23948	−	5.61095i	−0.162996	−	0.282317i
$396$	1.00000	−	2.82843i	0.0502519	−	0.142134i
$397$	−31.3992	−	18.1283i	−1.57588	−	0.909835i	−0.995425	−	0.0955439i	$-0.969541\pi$
$397$	−31.3992	−	18.1283i	−1.57588	−	0.909835i	−0.580456	−	0.814292i	$-0.697126\pi$
$398$	20.0941			1.00723
$399$	−0.423185	+	1.71744i	−0.0211858	+	0.0859795i
$400$	−4.76733			−0.238366
$401$	−23.6204	−	13.6373i	−1.17955	−	0.681013i	−0.223638	−	0.974672i	$-0.571793\pi$
$401$	−23.6204	−	13.6373i	−1.17955	−	0.681013i	−0.955910	+	0.293660i	$0.905127\pi$
$402$	11.6063	+	9.64796i	0.578872	+	0.481197i
$403$	−0.343322	−	0.594650i	−0.0171021	−	0.0296216i
$404$	0.855693	−	1.48210i	0.0425723	−	0.0737374i
$405$	0.674814	−	4.28849i	0.0335318	−	0.213097i
$406$	5.18167	+	10.6744i	0.257162	+	0.529760i
$407$			5.45705i			0.270496i
$408$	−0.542947	+	3.16452i	−0.0268799	+	0.156667i
$409$	10.8109	−	6.24170i	0.534566	−	0.308632i	−0.208308	−	0.978063i	$-0.566796\pi$
$409$	10.8109	−	6.24170i	0.534566	−	0.308632i	0.742874	+	0.669431i	$0.233462\pi$
$410$	2.37019	−	1.36843i	0.117055	−	0.0675819i
$411$	3.36809	−	19.6307i	0.166136	−	0.968309i
$412$			0.196401i			0.00967599i
$413$	9.63033	+	0.691426i	0.473877	+	0.0340229i
$414$	−0.569350	+	0.486766i	−0.0279820	+	0.0239232i
$415$	1.56512	−	2.71087i	0.0768288	−	0.133071i
$416$	0.275255	+	0.476756i	0.0134955	+	0.0233749i
$417$	−4.50127	−	3.74175i	−0.220428	−	0.183234i
$418$	−0.334273	−	0.192993i	−0.0163498	−	0.00943959i
$419$	−14.3077			−0.698975			−0.349487	−	0.936941i	$-0.613644\pi$
$419$	−14.3077			−0.698975			−0.349487	+	0.936941i	$0.613644\pi$
$420$	0.615134	+	2.12314i	0.0300155	+	0.103599i
$421$	15.2015			0.740875			0.370437	−	0.928857i	$-0.379208\pi$
$421$	15.2015			0.740875			0.370437	+	0.928857i	$0.379208\pi$
$422$	−4.31726	−	2.49257i	−0.210161	−	0.121336i
$423$	−24.9706	−	8.82843i	−1.21411	−	0.429253i
$424$	−3.77841	−	6.54441i	−0.183496	−	0.317824i
$425$	−4.41868	+	7.65338i	−0.214338	+	0.371244i
$426$	3.45559	+	9.35956i	0.167424	+	0.453472i
$427$	−20.9862	+	10.1874i	−1.01559	+	0.493001i
$428$			9.34142i			0.451535i
$429$	−0.939780	−	0.161241i	−0.0453730	−	0.00778478i
$430$	0.284965	−	0.164525i	0.0137422	−	0.00793408i
$431$	1.44564	−	0.834638i	0.0696338	−	0.0402031i	−0.464779	−	0.885427i	$-0.653866\pi$
$431$	1.44564	−	0.834638i	0.0696338	−	0.0402031i	0.534413	+	0.845224i	$0.320533\pi$
$432$	4.46360	−	2.66012i	0.214755	−	0.127985i
$433$		−	10.5393i		−	0.506486i	−0.967403	−	0.253243i	$-0.918503\pi$
$433$		−	10.5393i		−	0.506486i	0.967403	−	0.253243i	$-0.0814973\pi$
$434$	1.85043	−	2.73239i	0.0888233	−	0.131159i
$435$	−3.51499	+	1.29775i	−0.168531	+	0.0622225i
$436$	−3.15161	+	5.45875i	−0.150935	+	0.261427i
$437$	0.0481882	+	0.0834643i	0.00230515	+	0.00399264i
$438$	−2.48711	+	2.99195i	−0.118839	+	0.142961i
$439$	19.4237	+	11.2143i	0.927041	+	0.535227i	0.885874	−	0.463925i	$-0.153559\pi$
$439$	19.4237	+	11.2143i	0.927041	+	0.535227i	0.0411662	+	0.999152i	$0.486893\pi$
$440$	−0.482362			−0.0229957
$441$	−17.7474	+	11.2262i	−0.845117	+	0.534582i
$442$	1.02050			0.0485403
$443$	5.36156	+	3.09550i	0.254735	+	0.147071i	0.621931	−	0.783072i	$-0.286349\pi$
$443$	5.36156	+	3.09550i	0.254735	+	0.147071i	−0.367195	+	0.930144i	$0.619682\pi$
$444$	−6.04208	+	7.26853i	−0.286745	+	0.344949i
$445$	2.72242	+	4.71537i	0.129055	+	0.223530i
$446$	6.62082	−	11.4676i	0.313505	−	0.543007i
$447$	−26.8587	+	9.91636i	−1.27037	+	0.469028i
$448$	−1.48356	+	2.19067i	−0.0700918	+	0.103499i
$449$		−	1.55464i		−	0.0733680i	−0.999327	−	0.0366840i	$-0.988321\pi$
$449$		−	1.55464i		−	0.0733680i	0.999327	−	0.0366840i	$-0.0116795\pi$
$450$	14.0612	−	2.61339i	0.662850	−	0.123196i
$451$	−4.91372	+	2.83694i	−0.231378	+	0.133586i
$452$	17.1546	−	9.90422i	0.806885	−	0.465855i
$453$	−0.260841	−	0.0447532i	−0.0122554	−	0.00210269i
$454$			27.7181i			1.30088i
$455$	0.632035	−	0.306809i	0.0296302	−	0.0143834i
$456$	−0.231553	−	0.627167i	−0.0108435	−	0.0293698i
$457$	−8.17556	+	14.1605i	−0.382437	+	0.662400i	−0.991410	−	0.130791i	$-0.958248\pi$
$457$	−8.17556	+	14.1605i	−0.382437	+	0.662400i	0.608973	+	0.793191i	$0.291582\pi$
$458$	4.16693	+	7.21733i	0.194708	+	0.337244i
$459$	−0.133340	−	9.63137i	−0.00622376	−	0.449554i
$460$	0.104304	+	0.0602202i	0.00486322	+	0.00280778i
$461$	−20.2754			−0.944321			−0.472160	−	0.881513i	$-0.656526\pi$
$461$	−20.2754			−0.944321			−0.472160	+	0.881513i	$0.656526\pi$
$462$	−1.27526	−	4.40156i	−0.0593302	−	0.204779i
$463$	5.63443			0.261854			0.130927	−	0.991392i	$-0.458205\pi$
$463$	5.63443			0.261854			0.130927	+	0.991392i	$0.458205\pi$
$464$	−3.88392	−	2.24238i	−0.180307	−	0.104100i
$465$	0.801359	+	0.666143i	0.0371621	+	0.0308916i
$466$	−4.04877	−	7.01267i	−0.187556	−	0.324856i
$467$	−18.8229	+	32.6022i	−0.871020	+	1.50865i	−0.0100773	+	0.999949i	$0.503208\pi$
$467$	−18.8229	+	32.6022i	−0.871020	+	1.50865i	−0.860943	+	0.508702i	$0.830126\pi$
$468$	−1.07321	−	1.25529i	−0.0496093	−	0.0580260i
$469$	22.9953	+	1.65099i	1.06183	+	0.0762357i
$470$			4.25850i			0.196430i
$471$	3.08224	−	17.9646i	0.142022	−	0.827767i
$472$	−3.16038	+	1.82465i	−0.145468	+	0.0839861i
$473$	−0.590770	+	0.341081i	−0.0271636	+	0.0156829i
$474$	−3.93407	+	22.9294i	−0.180698	+	1.05318i
$475$		−	1.84012i		−	0.0844305i
$476$	2.14180	+	4.41215i	0.0981691	+	0.202231i
$477$	14.7320	+	17.2314i	0.674530	+	0.788971i
$478$	−11.8193	+	20.4716i	−0.540602	+	0.936350i
$479$	−8.08725	−	14.0075i	−0.369516	−	0.640020i	0.619974	−	0.784622i	$-0.287143\pi$
$479$	−8.08725	−	14.0075i	−0.369516	−	0.640020i	−0.989490	+	0.144602i	$0.953810\pi$
$480$	−0.642483	−	0.534074i	−0.0293252	−	0.0243770i
$481$	2.60168	+	1.50208i	0.118626	+	0.0684890i
$482$	17.0350			0.775924
$483$	−0.273753	+	1.11099i	−0.0124562	+	0.0505517i
$484$	1.00000			0.0454545
$485$	−7.03425	−	4.06122i	−0.319409	−	0.184411i
$486$	−11.7071	+	10.2929i	−0.531045	+	0.466895i
$487$	−10.8869	−	18.8567i	−0.493335	−	0.854481i	0.506636	−	0.862160i	$-0.330889\pi$
$487$	−10.8869	−	18.8567i	−0.493335	−	0.854481i	−0.999971	+	0.00767942i	$0.997556\pi$
$488$	4.40861	−	7.63593i	0.199568	−	0.345662i
$489$	5.20988	+	14.1111i	0.235599	+	0.638125i
$490$	2.65299	+	2.08869i	0.119850	+	0.0943573i
$491$			14.3125i			0.645912i	0.946414	+	0.322956i	$0.104677\pi$
$491$			14.3125i			0.645912i	−0.946414	+	0.322956i	$0.895323\pi$
$492$	−9.68590	−	1.66184i	−0.436674	−	0.0749214i
$493$	−7.19976	+	4.15679i	−0.324261	+	0.187212i
$494$	−0.184021	+	0.106245i	−0.00827949	+	0.00478017i
$495$	1.42272	−	0.264425i	0.0639466	−	0.0118850i
$496$			1.24728i			0.0560047i
$497$	12.6189	+	8.54574i	0.566034	+	0.383329i
$498$	−10.5443	+	3.89300i	−0.472501	+	0.174449i
$499$	−4.02874	+	6.97799i	−0.180351	+	0.312378i	−0.942000	−	0.335612i	$-0.891057\pi$
$499$	−4.02874	+	6.97799i	−0.180351	+	0.312378i	0.761649	+	0.647990i	$0.224390\pi$
$500$	−2.35569	−	4.08018i	−0.105350	−	0.182471i
$501$	−2.22655	+	2.67851i	−0.0994750	+	0.119667i
$502$	10.9184	+	6.30374i	0.487312	+	0.281350i
$503$	−20.9014			−0.931947			−0.465973	−	0.884799i	$-0.654296\pi$
$503$	−20.9014			−0.931947			−0.465973	+	0.884799i	$0.654296\pi$
$504$	3.17486	−	7.27463i	0.141419	−	0.324038i
$505$	0.825508			0.0367346
$506$	−0.216237	−	0.124844i	−0.00961290	−	0.00555001i
$507$	14.0581	−	16.9117i	0.624344	−	0.751075i
$508$	−10.5720	−	18.3113i	−0.469057	−	0.812431i
$509$	−20.0442	+	34.7175i	−0.888442	+	1.53883i	−0.0467259	+	0.998908i	$0.514879\pi$
$509$	−20.0442	+	34.7175i	−0.888442	+	1.53883i	−0.841717	+	0.539920i	$0.818455\pi$
$510$	−1.45289	+	0.536414i	−0.0643350	+	0.0237528i
$511$	−0.425601	+	5.92786i	−0.0188275	+	0.262233i
$512$		−	1.00000i		−	0.0441942i
$513$	1.02677	+	1.72289i	0.0453329	+	0.0760673i
$514$	0.354251	−	0.204527i	0.0156253	−	0.00902130i
$515$	−0.0820441	+	0.0473682i	−0.00361530	+	0.00208729i
$516$	−1.16452	−	0.199801i	−0.0512653	−	0.00879574i
$517$		−	8.82843i		−	0.388274i
$518$	−1.03394	+	14.4009i	−0.0454287	+	0.632741i
$519$	7.89637	+	21.3875i	0.346612	+	0.938807i
$520$	−0.132773	+	0.229969i	−0.00582246	+	0.0100848i
$521$	2.01266	+	3.48604i	0.0881764	+	0.152726i	0.906740	−	0.421689i	$-0.138563\pi$
$521$	2.01266	+	3.48604i	0.0881764	+	0.152726i	−0.818564	+	0.574415i	$0.805229\pi$
$522$	12.6848	+	4.48477i	0.555200	+	0.196293i
$523$	−22.8435	−	13.1887i	−0.998876	−	0.576701i	−0.0909602	−	0.995855i	$-0.528994\pi$
$523$	−22.8435	−	13.1887i	−0.998876	−	0.576701i	−0.907915	+	0.419153i	$0.862327\pi$
$524$	16.3402			0.713824
$525$	15.1326	−	15.7569i	0.660441	−	0.687687i
$526$	14.5600			0.634846
$527$	2.00237	+	1.15607i	0.0872246	+	0.0503591i
$528$	1.33195	+	1.10721i	0.0579657	+	0.0481850i
$529$	−11.4688	−	19.8646i	−0.498645	−	0.863678i
$530$	1.82256	−	3.15677i	0.0791671	−	0.137121i
$531$	8.32125	−	7.11425i	0.361112	−	0.308732i
$532$	−0.845567	−	0.572634i	−0.0366600	−	0.0248268i
$533$			3.12352i			0.135295i
$534$	3.30614	−	19.2696i	0.143071	−	0.833878i
$535$	−3.90226	+	2.25297i	−0.168710	+	0.0974045i
$536$	−7.54636	+	4.35690i	−0.325953	+	0.188189i
$537$	3.87662	−	22.5946i	0.167288	−	0.975028i
$538$			24.7919i			1.06885i
$539$	−5.50000	−	4.33013i	−0.236902	−	0.186512i
$540$	2.18777	+	1.22304i	0.0941466	+	0.0526315i
$541$	−9.66000	+	16.7316i	−0.415316	+	0.719348i	−0.995462	−	0.0951647i	$-0.969662\pi$
$541$	−9.66000	+	16.7316i	−0.415316	+	0.719348i	0.580146	+	0.814513i	$0.302996\pi$
$542$	−14.2128	−	24.6174i	−0.610494	−	1.05741i
$543$	−34.4890	−	28.6696i	−1.48007	−	1.23033i
$544$	−1.60538	−	0.926868i	−0.0688302	−	0.0397391i
$545$	−3.04044			−0.130238
$546$	−2.44949	−	0.603566i	−0.104828	−	0.0258303i
$547$	6.96837			0.297946			0.148973	−	0.988841i	$-0.452403\pi$
$547$	6.96837			0.297946			0.148973	+	0.988841i	$0.452403\pi$
$548$	9.95875	+	5.74969i	0.425417	+	0.245615i
$549$	−8.81722	+	24.9389i	−0.376310	+	1.06436i
$550$	2.38366	+	4.12863i	0.101640	+	0.176045i
$551$	0.865528	−	1.49914i	0.0368727	−	0.0638654i
$552$	−0.149788	−	0.405706i	−0.00637542	−	0.0172680i
$553$	15.5190	+	31.9694i	0.659933	+	1.35948i
$554$		−	3.46359i		−	0.147154i
$555$	−4.49357	−	0.770975i	−0.190742	−	0.0327261i
$556$	2.92669	−	1.68973i	0.124119	−	0.0716604i
$557$	12.4468	−	7.18616i	0.527388	−	0.304487i	−0.212564	−	0.977147i	$-0.568182\pi$
$557$	12.4468	−	7.18616i	0.527388	−	0.304487i	0.739952	+	0.672660i	$0.234848\pi$
$558$	−0.683747	−	3.67885i	−0.0289453	−	0.155738i
$559$			0.375538i			0.0158835i
$560$	−1.27293	−	0.0913925i	−0.0537912	−	0.00386204i
$561$	3.01203	−	1.11206i	0.127168	−	0.0469511i
$562$	10.2804	−	17.8061i	0.433651	−	0.751106i
$563$	−15.5721	−	26.9717i	−0.656286	−	1.13672i	−0.981570	−	0.191104i	$-0.938793\pi$
$563$	−15.5721	−	26.9717i	−0.656286	−	1.13672i	0.325284	−	0.945616i	$-0.394540\pi$
$564$	9.77489	−	11.7590i	0.411597	−	0.495145i
$565$	8.27473	+	4.77742i	0.348121	+	0.200988i
$566$	7.41713			0.311765
$567$	−5.37634	+	23.1969i	−0.225785	+	0.974177i
$568$	−5.76028			−0.241696
$569$	26.5762	+	15.3438i	1.11413	+	0.643244i	0.939896	−	0.341461i	$-0.110922\pi$
$569$	26.5762	+	15.3438i	1.11413	+	0.643244i	0.174234	+	0.984704i	$0.444255\pi$
$570$	0.206145	−	0.247989i	0.00863446	−	0.0103871i
$571$	7.29934	+	12.6428i	0.305468	+	0.529086i	0.977365	−	0.211558i	$-0.0678539\pi$
$571$	7.29934	+	12.6428i	0.305468	+	0.529086i	−0.671898	+	0.740644i	$0.734521\pi$
$572$	0.275255	−	0.476756i	0.0115090	−	0.0199342i
$573$	28.4792	−	10.5147i	1.18974	−	0.439257i
$574$	−13.5046	+	6.55556i	−0.563671	+	0.273624i
$575$		−	1.19035i		−	0.0496410i
$576$	0.548188	+	2.94949i	0.0228412	+	0.122895i
$577$	−23.3520	+	13.4823i	−0.972154	+	0.561274i	−0.899892	−	0.436112i	$-0.856355\pi$
$577$	−23.3520	+	13.4823i	−0.972154	+	0.561274i	−0.0722621	+	0.997386i	$0.523022\pi$
$578$	11.7465	−	6.78183i	0.488589	−	0.282087i
$579$	12.5713	+	2.15689i	0.522444	+	0.0896372i
$580$		−	2.16328i		−	0.0898253i
$581$	−9.62745	+	14.2162i	−0.399414	+	0.589786i
$582$	10.1017	+	27.3606i	0.418728	+	1.13413i
$583$	−3.77841	+	6.54441i	−0.156486	+	0.271042i
$584$	−1.12314	−	1.94534i	−0.0464761	−	0.0804989i
$585$	0.265545	−	0.751075i	0.0109789	−	0.0310531i
$586$	−28.6827	−	16.5599i	−1.18487	−	0.684085i
$587$	−4.39307			−0.181321			−0.0906607	−	0.995882i	$-0.528898\pi$
$587$	−4.39307			−0.181321			−0.0906607	+	0.995882i	$0.528898\pi$
$588$	−2.53139	−	11.8572i	−0.104393	−	0.488981i
$589$	−0.481434			−0.0198371
$590$	−1.52445	−	0.880139i	−0.0627605	−	0.0362348i
$591$	−25.6976	−	21.3616i	−1.05706	−	0.878697i
$592$	−2.72853	−	4.72595i	−0.112142	−	0.194235i
$593$	20.1436	−	34.8897i	0.827197	−	1.43275i	−0.0730318	−	0.997330i	$-0.523267\pi$
$593$	20.1436	−	34.8897i	0.827197	−	1.43275i	0.900229	−	0.435417i	$-0.143399\pi$
$594$	−4.53553	−	2.53553i	−0.186095	−	0.104034i
$595$	−1.32656	+	1.95884i	−0.0543837	+	0.0803044i
$596$		−	16.5300i		−	0.677096i
$597$	5.88544	−	34.3028i	0.240875	−	1.40392i
$598$	−0.119041	+	0.0687281i	−0.00486793	+	0.00281050i
$599$	24.9757	−	14.4197i	1.02048	−	0.589173i	0.106236	−	0.994341i	$-0.466120\pi$
$599$	24.9757	−	14.4197i	1.02048	−	0.589173i	0.914242	+	0.405167i	$0.132787\pi$
$600$	−1.39632	+	8.13834i	−0.0570044	+	0.332246i
$601$			24.5161i			1.00003i	0.866015	+	0.500017i	$0.166673\pi$
$601$			24.5161i			1.00003i	−0.866015	+	0.500017i	$0.833327\pi$
$602$	−1.62364	+	0.788167i	−0.0661747	+	0.0321233i
$603$	19.8695	−	16.9874i	0.809150	−	0.691782i
$604$	0.0763986	−	0.132326i	0.00310861	−	0.00538428i
$605$	0.241181	+	0.417738i	0.00980540	+	0.0169835i
$606$	−2.27948	−	1.89486i	−0.0925977	−	0.0769733i
$607$	−7.37857	−	4.26002i	−0.299487	−	0.172909i	0.342725	−	0.939436i	$-0.388650\pi$
$607$	−7.37857	−	4.26002i	−0.299487	−	0.172909i	−0.642212	+	0.766527i	$0.721983\pi$
$608$	0.385986			0.0156538
$609$	19.7400	−	5.71922i	0.799904	−	0.231755i
$610$	4.25309			0.172203
$611$	−4.20900	−	2.43007i	−0.170278	−	0.0983101i
$612$	5.24316	+	1.85374i	0.211942	+	0.0749328i
$613$	−22.8423	−	39.5640i	−0.922592	−	1.59798i	−0.795388	−	0.606100i	$-0.792733\pi$
$613$	−22.8423	−	39.5640i	−0.922592	−	1.59798i	−0.127204	−	0.991877i	$-0.540600\pi$
$614$	5.80236	−	10.0500i	0.234164	−	0.405584i
$615$	−1.64184	−	4.44697i	−0.0662055	−	0.179319i
$616$	2.63896	+	0.189469i	0.106327	+	0.00763391i
$617$		−	20.7786i		−	0.836513i	−0.908329	−	0.418257i	$-0.862641\pi$
$617$		−	20.7786i		−	0.836513i	0.908329	−	0.418257i	$-0.137359\pi$
$618$	0.335278	+	0.0575245i	0.0134868	+	0.00231398i
$619$	17.3550	−	10.0199i	0.697558	−	0.402735i	−0.108879	−	0.994055i	$-0.534726\pi$
$619$	17.3550	−	10.0199i	0.697558	−	0.402735i	0.806437	+	0.591320i	$0.201393\pi$
$620$	−0.521038	+	0.300821i	−0.0209254	+	0.0120813i
$621$	0.664203	+	1.11451i	0.0266535	+	0.0447238i
$622$		−	2.24969i		−	0.0902043i
$623$	−13.0420	−	26.8667i	−0.522515	−	1.07639i
$624$	0.894494	−	0.330251i	0.0358084	−	0.0132206i
$625$	−10.7820	+	18.6750i	−0.431281	+	0.747000i
$626$	−5.15515	−	8.92899i	−0.206041	−	0.356874i
$627$	−0.427366	+	0.514114i	−0.0170673	+	0.0205317i
$628$	9.11357	+	5.26172i	0.363671	+	0.209966i
$629$	−10.1159			−0.403349
$630$	3.80460	−	0.428246i	0.151579	−	0.0170617i
$631$	6.16436			0.245399			0.122700	−	0.992444i	$-0.460845\pi$
$631$	6.16436			0.245399			0.122700	+	0.992444i	$0.460845\pi$
$632$	−11.6322	−	6.71587i	−0.462705	−	0.267143i
$633$	−5.51958	+	6.63996i	−0.219384	+	0.263915i
$634$	7.92463	+	13.7259i	0.314727	+	0.545123i
$635$	5.09954	−	8.83266i	0.202369	−	0.350513i
$636$	−12.2787	+	4.53335i	−0.486881	+	0.179759i
$637$	−3.57832	+	1.43027i	−0.141778	+	0.0566693i
$638$			4.48477i			0.177554i
$639$	16.9899	−	3.15772i	0.672109	−	0.124917i
$640$	0.417738	−	0.241181i	0.0165125	−	0.00953351i
$641$	−21.4440	+	12.3807i	−0.846988	+	0.489009i	−0.859634	−	0.510911i	$-0.829308\pi$
$641$	−21.4440	+	12.3807i	−0.846988	+	0.489009i	0.0126451	+	0.999920i	$0.495975\pi$
$642$	15.9468	+	2.73604i	0.629370	+	0.107983i
$643$		−	32.9650i		−	1.30001i	−0.759929	−	0.650006i	$-0.774766\pi$
$643$		−	32.9650i		−	1.30001i	0.759929	−	0.650006i	$-0.225234\pi$
$644$	−0.546986	−	0.370429i	−0.0215543	−	0.0145970i
$645$	−0.197397	−	0.534654i	−0.00777249	−	0.0210520i
$646$	0.357758	−	0.619654i	0.0140758	−	0.0243800i
$647$	6.74037	+	11.6747i	0.264991	+	0.458978i	0.967561	−	0.252636i	$-0.0812976\pi$
$647$	6.74037	+	11.6747i	0.264991	+	0.458978i	−0.702570	+	0.711615i	$0.747964\pi$
$648$	−3.23375	−	8.39898i	−0.127034	−	0.329943i
$649$	3.16038	+	1.82465i	0.124056	+	0.0716236i
$650$	2.62446			0.102940
$651$	−4.12250	−	3.95917i	−0.161574	−	0.155172i
$652$	−8.68457			−0.340114
$653$	12.6035	+	7.27663i	0.493213	+	0.284757i	0.725906	−	0.687793i	$-0.241421\pi$
$653$	12.6035	+	7.27663i	0.493213	+	0.284757i	−0.232693	+	0.972550i	$0.574754\pi$
$654$	8.39559	+	6.97897i	0.328294	+	0.272899i
$655$	3.94094	+	6.82591i	0.153985	+	0.266710i
$656$	2.83694	−	4.91372i	0.110764	−	0.191848i
$657$	4.37912	+	5.12208i	0.170846	+	0.199831i
$658$	1.67271	−	23.2979i	0.0652090	−	0.908245i
$659$			30.1076i			1.17283i	0.810012	+	0.586413i	$0.199460\pi$
$659$			30.1076i			1.17283i	−0.810012	+	0.586413i	$0.800540\pi$
$660$	−0.141281	+	0.823443i	−0.00549934	+	0.0320525i
$661$	−30.8753	+	17.8258i	−1.20091	+	0.693345i	−0.960757	−	0.277390i	$-0.910530\pi$
$661$	−30.8753	+	17.8258i	−1.20091	+	0.693345i	−0.240152	+	0.970735i	$0.577197\pi$
$662$	−5.84594	+	3.37516i	−0.227209	+	0.131179i
$663$	0.298898	−	1.74210i	0.0116082	−	0.0676577i
$664$		−	6.48941i		−	0.251838i
$665$	0.0352762	−	0.491334i	0.00136795	−	0.0190531i
$666$	10.6385	+	12.4434i	0.412232	+	0.482171i
$667$	0.559898	−	0.969772i	0.0216793	−	0.0375497i
$668$	−1.00548	−	1.74155i	−0.0389033	−	0.0673824i
$669$	−17.6372	−	14.6612i	−0.681895	−	0.566836i
$670$	−3.64008	−	2.10160i	−0.140629	−	0.0811919i
$671$	−8.81722			−0.340385
$672$	3.30518	+	3.17423i	0.127500	+	0.122449i
$673$	47.2677			1.82203			0.911017	−	0.412369i	$-0.135298\pi$
$673$	47.2677			1.82203			0.911017	+	0.412369i	$0.135298\pi$
$674$	0.884152	+	0.510466i	0.0340563	+	0.0196624i
$675$	−0.342915	−	24.7694i	−0.0131988	−	0.953374i
$676$	6.34847	+	10.9959i	0.244172	+	0.422918i
$677$	−16.9764	+	29.4040i	−0.652456	+	1.13009i	0.330069	+	0.943957i	$0.392928\pi$
$677$	−16.9764	+	29.4040i	−0.652456	+	1.13009i	−0.982525	+	0.186130i	$0.940406\pi$
$678$	−11.8831	−	32.1856i	−0.456367	−	1.23608i
$679$	36.8885	+	24.9816i	1.41565	+	0.958706i
$680$		−	0.894171i		−	0.0342899i
$681$	47.3178	+	8.11845i	1.81322	+	0.311100i
$682$	1.08018	−	0.623642i	0.0413622	−	0.0238805i
$683$	30.2293	−	17.4529i	1.15669	−	0.667817i	0.206184	−	0.978513i	$-0.433896\pi$
$683$	30.2293	−	17.4529i	1.15669	−	0.667817i	0.950509	+	0.310696i	$0.100562\pi$
$684$	−1.13846	+	0.211593i	−0.0435301	+	0.00809045i
$685$			5.54686i			0.211935i
$686$	−13.6938	−	12.4691i	−0.522834	−	0.476073i
$687$	13.5412	−	4.99948i	0.516630	−	0.190742i
$688$	0.341081	−	0.590770i	0.0130036	−	0.0225229i
$689$	2.08006	+	3.60276i	0.0792438	+	0.137254i
$690$	0.133352	−	0.160421i	0.00507664	−	0.00610711i
$691$	8.04299	+	4.64362i	0.305970	+	0.176652i	0.645122	−	0.764080i	$-0.276807\pi$
$691$	8.04299	+	4.64362i	0.305970	+	0.176652i	−0.339152	+	0.940732i	$0.610140\pi$
$692$	−13.1628			−0.500375
$693$	−7.88745	+	0.887810i	−0.299619	+	0.0337251i
$694$	28.4765			1.08095
$695$	1.41172	+	0.815060i	0.0535498	+	0.0309170i
$696$	−4.96556	+	5.97349i	−0.188219	+	0.226425i
$697$	−5.25893	−	9.10873i	−0.199196	−	0.345018i
$698$	−6.47185	+	11.2096i	−0.244963	+	0.424289i
$699$	−13.1572	+	4.85772i	−0.497652	+	0.183736i
$700$	5.50814	+	11.3469i	0.208188	+	0.428873i
$701$			32.9715i			1.24531i	0.782495	+	0.622657i	$0.213947\pi$
$701$			32.9715i			1.24531i	−0.782495	+	0.622657i	$0.786053\pi$
$702$	−2.45726	+	1.46442i	−0.0927433	+	0.0552711i
$703$	1.82415	−	1.05317i	0.0687990	−	0.0397211i
$704$	−0.866025	+	0.500000i	−0.0326396	+	0.0188445i
$705$	7.26971	+	1.24728i	0.273793	+	0.0469755i
$706$		−	17.3326i		−	0.652321i
$707$	−4.51628	−	0.324254i	−0.169852	−	0.0121948i
$708$	2.18921	+	5.92953i	0.0822756	+	0.222845i
$709$	8.32304	−	14.4159i	0.312578	−	0.541401i	−0.666342	−	0.745647i	$-0.732141\pi$
$709$	8.32304	−	14.4159i	0.312578	−	0.541401i	0.978920	+	0.204245i	$0.0654740\pi$
$710$	−1.38927	−	2.40629i	−0.0521384	−	0.0903063i
$711$	37.9907	+	13.4317i	1.42476	+	0.503730i
$712$	9.77559	+	5.64394i	0.366356	+	0.211516i
$713$	−0.311433			−0.0116633
$714$	8.15933	−	2.36399i	0.305355	−	0.0884699i
$715$	0.265545			0.00993083
$716$	11.4624	+	6.61780i	0.428368	+	0.247319i
$717$	31.4855	+	26.1728i	1.17585	+	0.977441i
$718$	−3.65514	−	6.33088i	−0.136408	−	0.236266i
$719$	21.6348	−	37.4725i	0.806841	−	1.39749i	−0.108201	−	0.994129i	$-0.534509\pi$
$719$	21.6348	−	37.4725i	0.806841	−	1.39749i	0.915041	−	0.403360i	$-0.132158\pi$
$720$	−1.09990	+	0.940360i	−0.0409909	+	0.0350451i
$721$	0.467462	−	0.226921i	0.0174092	−	0.00845097i
$722$		−	18.8510i		−	0.701562i
$723$	4.98944	−	29.0806i	0.185559	−	1.08152i
$724$	22.4245	−	12.9468i	0.833401	−	0.481164i
$725$	−18.5159	+	10.6902i	−0.687664	+	0.397023i
$726$	0.292893	−	1.70711i	0.0108703	−	0.0633567i
$727$			41.7432i			1.54817i	0.633082	+	0.774085i	$0.281790\pi$
$727$			41.7432i			1.54817i	−0.633082	+	0.774085i	$0.718210\pi$
$728$	0.816717	−	1.20599i	0.0302696	−	0.0446968i
$729$	14.1421	+	23.0000i	0.523783	+	0.851852i
$730$	0.541762	−	0.938360i	0.0200515	−	0.0347302i
$731$	−0.632275	−	1.09513i	−0.0233855	−	0.0405049i
$732$	−11.7441	−	9.76248i	−0.434074	−	0.360832i
$733$	2.60675	+	1.50501i	0.0962826	+	0.0555888i	0.547368	−	0.836892i	$-0.315630\pi$
$733$	2.60675	+	1.50501i	0.0962826	+	0.0555888i	−0.451086	+	0.892481i	$0.648963\pi$
$734$	9.78537			0.361185
$735$	4.34266	−	3.91718i	0.160181	−	0.144487i
$736$	0.249689			0.00920365
$737$	7.54636	+	4.35690i	0.277974	+	0.160488i
$738$	−5.67387	+	16.0481i	−0.208858	+	0.590740i
$739$	−5.43041	−	9.40575i	−0.199761	−	0.345996i	0.748690	−	0.662920i	$-0.230683\pi$
$739$	−5.43041	−	9.40575i	−0.199761	−	0.345996i	−0.948451	+	0.316924i	$0.897350\pi$
$740$	1.31614	−	2.27962i	0.0483822	−	0.0838004i
$741$	0.127472	+	0.345262i	0.00468281	+	0.0126835i
$742$	−11.2110	+	16.5545i	−0.411570	+	0.607736i
$743$		−	32.1359i		−	1.17895i	−0.807786	−	0.589476i	$-0.799334\pi$
$743$		−	32.1359i		−	1.17895i	0.807786	−	0.589476i	$-0.200666\pi$
$744$	2.12925	+	0.365321i	0.0780620	+	0.0133933i
$745$	6.90521	−	3.98672i	0.252987	−	0.146062i
$746$	−24.2988	+	14.0289i	−0.889644	+	0.513636i
$747$	3.55742	+	19.1404i	0.130159	+	0.700312i
$748$			1.85374i			0.0677793i
$749$	22.2339	−	10.7930i	0.812408	−	0.394369i
$750$	−7.65527	+	2.82636i	−0.279531	+	0.103204i
$751$	14.4715	−	25.0654i	0.528072	−	0.914648i	−0.471392	−	0.881924i	$-0.656248\pi$
$751$	14.4715	−	25.0654i	0.528072	−	0.914648i	0.999464	−	0.0327241i	$-0.0104183\pi$
$752$	4.41421	+	7.64564i	0.160970	+	0.278808i
$753$	13.9591	−	16.7926i	0.508697	−	0.611955i
$754$	2.13814	+	1.23445i	0.0778664	+	0.0449562i
$755$	0.0737035			0.00268235
$756$	−11.4887	−	7.55051i	−0.417839	−	0.274609i
$757$	11.8099			0.429239			0.214619	−	0.976698i	$-0.431149\pi$
$757$	11.8099			0.429239			0.214619	+	0.976698i	$0.431149\pi$
$758$	25.3434	+	14.6320i	0.920515	+	0.531460i
$759$	−0.276457	+	0.332573i	−0.0100348	+	0.0120717i
$760$	0.0930924	+	0.161241i	0.00337682	+	0.00584882i
$761$	2.72848	−	4.72586i	0.0989071	−	0.171312i	−0.812325	−	0.583204i	$-0.801799\pi$
$761$	2.72848	−	4.72586i	0.0989071	−	0.171312i	0.911233	+	0.411892i	$0.135132\pi$
$762$	−34.3558	+	12.6843i	−1.24458	+	0.459504i
$763$	16.6339	+	1.19426i	0.602189	+	0.0432353i
$764$			17.5274i			0.634118i
$765$	0.490174	+	2.63735i	0.0177223	+	0.0953536i
$766$	−8.47623	+	4.89376i	−0.306259	+	0.176819i
$767$	1.73982	−	1.00449i	0.0628213	−	0.0362699i
$768$	−1.70711	−	0.292893i	−0.0615999	−	0.0105689i
$769$		−	20.7871i		−	0.749602i	−0.927105	−	0.374801i	$-0.877711\pi$
$769$		−	20.7871i		−	0.749602i	0.927105	−	0.374801i	$-0.122289\pi$
$770$	0.557318	+	1.14809i	0.0200844	+	0.0413742i
$771$	−0.245392	−	0.664649i	−0.00883756	−	0.0239367i
$772$	−3.68204	+	6.37748i	−0.132519	+	0.229530i
$773$	23.4534	+	40.6225i	0.843560	+	1.46109i	0.886866	+	0.462027i	$0.152878\pi$
$773$	23.4534	+	40.6225i	0.843560	+	1.46109i	−0.0433053	+	0.999062i	$0.513789\pi$
$774$	−0.682163	+	1.92945i	−0.0245198	+	0.0693526i
$775$	5.14957	+	2.97311i	0.184978	+	0.106797i
$776$	−16.8389			−0.604482
$777$	24.2811	+	5.98298i	0.871080	+	0.214638i
$778$	−37.1338			−1.33131
$779$	1.89662	+	1.09502i	0.0679536	+	0.0392330i
$780$	0.353693	+	0.294013i	0.0126642	+	0.0105274i
$781$	2.88014	+	4.98855i	0.103059	+	0.178504i
$782$	0.231429	−	0.400846i	0.00827587	−	0.0143342i
$783$	11.3713	−	20.3408i	0.406376	−	0.726921i
$784$	6.92820	+	1.00000i	0.247436	+	0.0357143i
$785$			5.07611i			0.181174i
$786$	4.78593	−	27.8944i	0.170708	−	0.994961i
$787$	−22.6920	+	13.1012i	−0.808881	+	0.467008i	−0.846567	−	0.532282i	$-0.821335\pi$
$787$	−22.6920	+	13.1012i	−0.808881	+	0.467008i	0.0376861	+	0.999290i	$0.488001\pi$
$788$	16.7084	−	9.64660i	0.595212	−	0.343646i
$789$	4.26452	−	24.8555i	0.151821	−	0.884878i
$790$		−	6.47896i		−	0.230511i
$791$	−43.3938	−	29.3871i	−1.54290	−	1.04488i
$792$	2.28024	−	1.94949i	0.0810248	−	0.0692721i
$793$	−2.42698	+	4.20366i	−0.0861847	+	0.149276i
$794$	−18.1283	−	31.3992i	−0.643351	−	1.11432i
$795$	−4.85513	−	4.03591i	−0.172194	−	0.143139i
$796$	17.4020	+	10.0471i	0.616799	+	0.356109i
$797$	5.14751			0.182334			0.0911671	−	0.995836i	$-0.470940\pi$
$797$	5.14751			0.182334			0.0911671	+	0.995836i	$0.470940\pi$
$798$	−1.22521	+	1.27575i	−0.0433719	+	0.0451612i
$799$	16.3656			0.578972
$800$	−4.12863	−	2.38366i	−0.145969	−	0.0842752i
$801$	−31.9270	−	11.2879i	−1.12808	−	0.398838i
$802$	−13.6373	−	23.6204i	−0.481549	−	0.834067i
$803$	−1.12314	+	1.94534i	−0.0396349	+	0.0686497i
$804$	5.22741	+	14.1586i	0.184356	+	0.499334i
$805$	0.0228197	−	0.317837i	0.000804288	−	0.0112023i
$806$		−	0.686643i		−	0.0241860i
$807$	42.3224	+	7.26138i	1.48982	+	0.255613i
$808$	1.48210	−	0.855693i	0.0521402	−	0.0301032i
$809$	−6.76716	+	3.90702i	−0.237921	+	0.137364i	−0.614221	−	0.789134i	$-0.710530\pi$
$809$	−6.76716	+	3.90702i	−0.237921	+	0.137364i	0.376300	+	0.926498i	$0.377196\pi$
$810$	2.72865	−	3.37653i	0.0958750	−	0.118639i
$811$			9.92215i			0.348414i	0.984709	+	0.174207i	$0.0557362\pi$
$811$			9.92215i			0.348414i	−0.984709	+	0.174207i	$0.944264\pi$
$812$	−0.849723	+	11.8351i	−0.0298194	+	0.415331i
$813$	−46.1873	+	17.0526i	−1.61986	+	0.598060i
$814$	−2.72853	+	4.72595i	−0.0956348	+	0.165644i
$815$	−2.09455	−	3.62787i	−0.0733690	−	0.127079i
$816$	−2.05247	+	2.46909i	−0.0718507	+	0.0864353i
$817$	0.228029	+	0.131652i	0.00797772	+	0.00460594i
$818$	12.4834			0.436472
$819$	−1.74779	+	4.00476i	−0.0610728	+	0.139938i
$820$	2.73686			0.0955753
$821$	16.6405	+	9.60741i	0.580758	+	0.335301i	0.761435	−	0.648242i	$-0.224495\pi$
$821$	16.6405	+	9.60741i	0.580758	+	0.335301i	−0.180676	+	0.983543i	$0.557829\pi$
$822$	12.7322	−	15.3166i	0.444086	−	0.534228i
$823$	−9.79913	−	16.9726i	−0.341576	−	0.591627i	0.643149	−	0.765741i	$-0.277627\pi$
$823$	−9.79913	−	16.9726i	−0.341576	−	0.591627i	−0.984726	+	0.174113i	$0.944294\pi$
$824$	−0.0982005	+	0.170088i	−0.00342098	+	0.00592531i
$825$	7.74616	−	2.85992i	0.269687	−	0.0995697i
$826$	7.99439	+	5.41396i	0.278161	+	0.188376i
$827$			3.35552i			0.116683i	0.998297	+	0.0583414i	$0.0185812\pi$
$827$			3.35552i			0.116683i	−0.998297	+	0.0583414i	$0.981419\pi$
$828$	−0.736455	+	0.136876i	−0.0255936	+	0.00475679i
$829$	−33.3865	+	19.2757i	−1.15956	+	0.669474i	−0.951199	−	0.308578i	$-0.900147\pi$
$829$	−33.3865	+	19.2757i	−1.15956	+	0.669474i	−0.208363	+	0.978051i	$0.566814\pi$
$830$	2.71087	−	1.56512i	0.0940957	−	0.0543262i
$831$	−5.91271	−	1.01446i	−0.205110	−	0.0351913i
$832$			0.550510i			0.0190855i
$833$	8.02691	−	10.1955i	0.278116	−	0.353255i
$834$	−2.02734	−	5.49109i	−0.0702009	−	0.190141i
$835$	0.485006	−	0.840055i	0.0167843	−	0.0290713i
$836$	−0.192993	−	0.334273i	−0.00667480	−	0.0115611i
$837$	−6.48046	+	0.0897174i	−0.223998	+	0.00310109i
$838$	−12.3908	−	7.15383i	−0.428033	−	0.247125i
$839$	33.3680			1.15199			0.575996	−	0.817452i	$-0.304614\pi$
$839$	33.3680			1.15199			0.575996	+	0.817452i	$0.304614\pi$
$840$	−0.528850	+	2.14626i	−0.0182471	+	0.0740532i
$841$	8.88687			0.306444
$842$	13.1649	+	7.60074i	0.453691	+	0.261939i
$843$	−27.3859	−	22.7650i	−0.943221	−	0.784068i
$844$	−2.49257	−	4.31726i	−0.0857978	−	0.148606i
$845$	−3.06226	+	5.30399i	−0.105345	+	0.182463i
$846$	−17.2109	−	20.1309i	−0.591724	−	0.692115i
$847$	−1.15539	−	2.38014i	−0.0396998	−	0.0817826i
$848$		−	7.55683i		−	0.259503i
$849$	2.17243	−	12.6618i	0.0745575	−	0.434553i
$850$	−7.65338	+	4.41868i	−0.262509	+	0.151560i
$851$	1.18002	−	0.681283i	0.0404504	−	0.0233541i
$852$	−1.68715	+	9.83341i	−0.0578007	+	0.336887i
$853$		−	7.56740i		−	0.259103i	−0.991573	−	0.129551i	$-0.958646\pi$
$853$		−	7.56740i		−	0.259103i	0.991573	−	0.129551i	$-0.0413537\pi$
$854$	−23.2683	−	1.67059i	−0.796224	−	0.0571663i
$855$	−0.362965	−	0.424546i	−0.0124131	−	0.0145192i
$856$	−4.67071	+	8.08991i	−0.159642	+	0.276507i
$857$	22.1795	+	38.4160i	0.757636	+	1.31226i	0.944053	+	0.329794i	$0.106979\pi$
$857$	22.1795	+	38.4160i	0.757636	+	1.31226i	−0.186416	+	0.982471i	$0.559687\pi$
$858$	−0.733253	−	0.609528i	−0.0250328	−	0.0208090i
$859$	15.3094	+	8.83889i	0.522350	+	0.301579i	0.737896	−	0.674915i	$-0.235820\pi$
$859$	15.3094	+	8.83889i	0.522350	+	0.301579i	−0.215545	+	0.976494i	$0.569153\pi$
$860$	0.329049			0.0112205
$861$	7.23563	+	24.9739i	0.246590	+	0.851107i
$862$	1.66928			0.0568558
$863$	−27.0927	−	15.6420i	−0.922248	−	0.532460i	−0.0378962	−	0.999282i	$-0.512066\pi$
$863$	−27.0927	−	15.6420i	−0.922248	−	0.532460i	−0.884351	+	0.466822i	$0.845399\pi$
$864$	5.19565	−	0.0719302i	0.176760	−	0.00244711i
$865$	−3.17462	−	5.49860i	−0.107940	−	0.186958i
$866$	5.26965	−	9.12730i	0.179070	−	0.310158i
$867$	−8.13685	−	22.0388i	−0.276342	−	0.748478i
$868$	2.96871	−	1.44111i	0.100765	−	0.0489143i
$869$			13.4317i			0.455641i
$870$	−3.69295	−	0.633610i	−0.125203	−	0.0214814i
$871$	4.15435	−	2.39852i	0.140765	−	0.0812706i
$872$	−5.45875	+	3.15161i	−0.184857	+	0.106727i
$873$	49.6662	−	9.23089i	1.68095	−	0.312418i
$874$			0.0963763i			0.00325998i
$875$	−6.98964	+	10.3211i	−0.236293	+	0.348917i
$876$	−3.64987	+	1.34755i	−0.123318	+	0.0455295i
$877$	6.71183	−	11.6252i	0.226642	−	0.392556i	−0.730168	−	0.683267i	$-0.760558\pi$
$877$	6.71183	−	11.6252i	0.226642	−	0.392556i	0.956811	+	0.290711i	$0.0938918\pi$
$878$	11.2143	+	19.4237i	0.378463	+	0.655517i
$879$	−36.6705	+	44.1141i	−1.23687	+	1.48793i
$880$	−0.417738	−	0.241181i	−0.0140819	−	0.00813021i
$881$	17.4395			0.587551			0.293775	−	0.955874i	$-0.405088\pi$
$881$	17.4395			0.587551			0.293775	+	0.955874i	$0.405088\pi$
$882$	−20.9829	+	0.848469i	−0.706529	+	0.0285694i
$883$	−46.0054			−1.54820			−0.774102	−	0.633061i	$-0.781798\pi$
$883$	−46.0054			−1.54820			−0.774102	+	0.633061i	$0.781798\pi$
$884$	0.883779	+	0.510250i	0.0297247	+	0.0171616i
$885$	−1.94899	+	2.34461i	−0.0655146	+	0.0788131i
$886$	3.09550	+	5.36156i	0.103995	+	0.180125i
$887$	16.2645	−	28.1710i	0.546109	−	0.945888i	−0.452428	−	0.891801i	$-0.649442\pi$
$887$	16.2645	−	28.1710i	0.546109	−	0.945888i	0.998536	−	0.0540868i	$-0.0172248\pi$
$888$	−8.86686	+	3.27369i	−0.297552	+	0.109858i
$889$	−31.3685	+	46.3196i	−1.05207	+	1.55351i
$890$			5.44485i			0.182512i
$891$	−5.65685	+	7.00000i	−0.189512	+	0.234509i
$892$	11.4676	−	6.62082i	0.383964	−	0.221682i
$893$	−2.95111	+	1.70382i	−0.0987551	+	0.0570163i
$894$	−28.2185	−	4.84153i	−0.943768	−	0.161925i
$895$			6.38435i			0.213405i
$896$	−2.38014	+	1.15539i	−0.0795149	+	0.0385990i
$897$	0.0824601	+	0.223345i	0.00275326	+	0.00745728i
$898$	0.777320	−	1.34636i	0.0259395	−	0.0449285i
$899$	2.79689	+	4.84436i	0.0932815	+	0.161568i
$900$	13.4840	+	4.76733i	0.449468	+	0.158911i
$901$	−12.1316	−	7.00418i	−0.404162	−	0.233343i
$902$	−5.67387			−0.188919
$903$	0.869932	+	3.00258i	0.0289495	+	0.0999196i
$904$	19.8084			0.658819
$905$	10.8167	+	6.24504i	0.359560	+	0.207592i
$906$	−0.203518	−	0.169178i	−0.00676144	−	0.00562056i
$907$	1.11719	+	1.93503i	0.0370957	+	0.0642517i	0.883977	−	0.467530i	$-0.154856\pi$
$907$	1.11719	+	1.93503i	0.0370957	+	0.0642517i	−0.846881	+	0.531782i	$0.821523\pi$
$908$	−13.8591	+	24.0046i	−0.459929	+	0.796620i
$909$	−3.90237	+	3.33633i	−0.129433	+	0.110659i
$910$	0.700763	+	0.0503125i	0.0232301	+	0.00166784i
$911$			30.4938i			1.01030i	0.863030	+	0.505152i	$0.168564\pi$
$911$			30.4938i			1.01030i	−0.863030	+	0.505152i	$0.831436\pi$
$912$	0.113053	−	0.658919i	0.00374354	−	0.0218190i
$913$	−5.61999	+	3.24471i	−0.185995	+	0.107384i
$914$	−14.1605	+	8.17556i	−0.468387	+	0.270424i
$915$	1.24570	−	7.26048i	0.0411816	−	0.240024i
$916$			8.33386i			0.275358i
$917$	−18.8794	−	38.8919i	−0.623451	−	1.28432i
$918$	4.70021	−	8.40768i	0.155130	−	0.277495i
$919$	1.57169	−	2.72225i	0.0518453	−	0.0897986i	−0.838938	−	0.544227i	$-0.816823\pi$
$919$	1.57169	−	2.72225i	0.0518453	−	0.0897986i	0.890783	+	0.454428i	$0.150156\pi$
$920$	0.0602202	+	0.104304i	0.00198540	+	0.00343882i
$921$	−15.4569	−	12.8488i	−0.509323	−	0.423383i
$922$	−17.5590	−	10.1377i	−0.578276	−	0.333868i
$923$	3.17109			0.104378
$924$	1.09638	−	4.44949i	0.0360681	−	0.146377i
$925$	−26.0156			−0.855386
$926$	4.87956	+	2.81722i	0.160352	+	0.0925794i
$927$	0.196401	−	0.555506i	0.00645066	−	0.0182452i
$928$	−2.24238	−	3.88392i	−0.0736098	−	0.127496i
$929$	−23.0663	+	39.9519i	−0.756779	+	1.31078i	0.187706	+	0.982225i	$0.439895\pi$
$929$	−23.0663	+	39.9519i	−0.756779	+	1.31078i	−0.944485	+	0.328555i	$0.893438\pi$
$930$	0.360926	+	0.977576i	0.0118352	+	0.0320560i
$931$	−0.385986	+	2.67419i	−0.0126502	+	0.0876429i
$932$		−	8.09754i		−	0.265244i
$933$	−3.84046	−	0.658919i	−0.125731	−	0.0215720i
$934$	−32.6022	+	18.8229i	−1.06678	+	0.615904i
$935$	−0.774375	+	0.447086i	−0.0253248	+	0.0146213i
$936$	−0.301783	−	1.62372i	−0.00986409	−	0.0530731i
$937$			29.7606i			0.972236i	0.873893	+	0.486118i	$0.161587\pi$
$937$			29.7606i			0.972236i	−0.873893	+	0.486118i	$0.838413\pi$
$938$	19.0890	+	12.9275i	0.623279	+	0.422097i
$939$	−16.7526	+	6.18516i	−0.546702	+	0.201845i
$940$	−2.12925	+	3.68797i	−0.0694484	+	0.120288i
$941$	3.16738	+	5.48605i	0.103253	+	0.178840i	0.913023	−	0.407907i	$-0.133741\pi$
$941$	3.16738	+	5.48605i	0.103253	+	0.178840i	−0.809770	+	0.586748i	$0.800408\pi$
$942$	11.6516	−	14.0167i	0.379630	−	0.456689i
$943$	1.22690	+	0.708351i	0.0399534	+	0.0230671i
$944$	−3.64929			−0.118774
$945$	0.383281	−	6.62029i	0.0124681	−	0.215358i
$946$	−0.682163			−0.0221790
$947$	−38.3205	−	22.1244i	−1.24525	−	0.718945i	−0.275091	−	0.961418i	$-0.588708\pi$
$947$	−38.3205	−	22.1244i	−1.24525	−	0.718945i	−0.970158	+	0.242473i	$0.922041\pi$
$948$	−14.8717	+	17.8904i	−0.483011	+	0.581054i
$949$	0.618303	+	1.07093i	0.0200710	+	0.0347639i
$950$	0.920060	−	1.59359i	0.0298507	−	0.0517029i
$951$	25.7526	−	9.50797i	0.835084	−	0.308317i
$952$	−0.351225	+	4.89193i	−0.0113833	+	0.158548i
$953$		−	49.7571i		−	1.61179i	−0.592059	−	0.805895i	$-0.701685\pi$
$953$		−	49.7571i		−	1.61179i	0.592059	−	0.805895i	$-0.298315\pi$
$954$	4.14256	+	22.2888i	0.134120	+	0.721626i
$955$	−7.32184	+	4.22726i	−0.236929	+	0.136791i
$956$	−20.4716	+	11.8193i	−0.662100	+	0.382263i
$957$	7.65597	+	1.31356i	0.247483	+	0.0424613i
$958$		−	16.1745i		−	0.522574i
$959$	2.17877	−	30.3464i	0.0703562	−	0.979936i
$960$	−0.289369	−	0.783763i	−0.00933935	−	0.0252958i
$961$	−14.7221	+	25.4995i	−0.474908	+	0.822564i
$962$	1.50208	+	2.60168i	0.0484291	+	0.0838816i
$963$	9.34142	−	26.4215i	0.301023	−	0.851422i
$964$	14.7528	+	8.51751i	0.475155	+	0.274331i
$965$	−3.55215			−0.114348
$966$	−0.792571	+	0.825267i	−0.0255006	+	0.0265525i
$967$	−31.3556			−1.00833			−0.504164	−	0.863608i	$-0.668199\pi$
$967$	−31.3556			−1.00833			−0.504164	+	0.863608i	$0.668199\pi$
$968$	0.866025	+	0.500000i	0.0278351	+	0.0160706i
$969$	−0.953031	−	0.792223i	−0.0306158	−	0.0254499i
$970$	−4.06122	−	7.03425i	−0.130398	−	0.225856i
$971$	−26.2882	+	45.5325i	−0.843628	+	1.46121i	0.0431796	+	0.999067i	$0.486251\pi$
$971$	−26.2882	+	45.5325i	−0.843628	+	1.46121i	−0.886807	+	0.462139i	$0.847082\pi$
$972$	−15.2851	+	3.06035i	−0.490270	+	0.0981609i
$973$	−7.40327	−	5.01363i	−0.237338	−	0.160730i
$974$		−	21.7739i		−	0.697681i
$975$	0.768687	−	4.48024i	0.0246177	−	0.143482i
$976$	7.63593	−	4.40861i	0.244420	−	0.141116i
$977$	−27.9026	+	16.1096i	−0.892682	+	0.515390i	−0.874819	−	0.484450i	$-0.839020\pi$
$977$	−27.9026	+	16.1096i	−0.892682	+	0.515390i	−0.0178633	+	0.999840i	$0.505686\pi$
$978$	−2.54365	+	14.8255i	−0.0813370	+	0.474067i
$979$		−	11.2879i		−	0.360762i
$980$	1.25321	+	3.13535i	0.0400324	+	0.100155i
$981$	14.3729	−	12.2881i	0.458890	−	0.392328i
$982$	−7.15623	+	12.3950i	−0.228365	+	0.395539i
$983$	−9.07712	−	15.7220i	−0.289515	−	0.501455i	0.684179	−	0.729314i	$-0.260161\pi$
$983$	−9.07712	−	15.7220i	−0.289515	−	0.501455i	−0.973694	+	0.227859i	$0.926827\pi$
$984$	−7.55732	−	6.28215i	−0.240919	−	0.200267i
$985$	8.05950	+	4.65315i	0.256797	+	0.148262i
$986$	−8.31357			−0.264758
$987$	−39.2820	−	9.67928i	−1.25036	−	0.308095i
$988$	−0.212489			−0.00676018
$989$	0.147509	+	0.0851642i	0.00469051	+	0.00270807i
$990$	1.36433	+	0.482362i	0.0433611	+	0.0153305i
$991$	24.0610	+	41.6748i	0.764321	+	1.32384i	0.940605	+	0.339504i	$0.110259\pi$
$991$	24.0610	+	41.6748i	0.764321	+	1.32384i	−0.176283	+	0.984339i	$0.556408\pi$
$992$	−0.623642	+	1.08018i	−0.0198007	+	0.0342958i
$993$	4.04951	+	10.9682i	0.128507	+	0.348065i
$994$	6.65539	+	13.7103i	0.211096	+	0.434863i
$995$			9.69265i			0.307278i
$996$	−11.0781	−	1.90070i	−0.351024	−	0.0602261i
$997$	−5.51486	+	3.18400i	−0.174657	+	0.100838i	−0.584780	−	0.811192i	$-0.698819\pi$
$997$	−5.51486	+	3.18400i	−0.174657	+	0.100838i	0.410123	+	0.912030i	$0.365486\pi$
$998$	−6.97799	+	4.02874i	−0.220884	+	0.127528i
$999$	24.3581	−	14.5164i	0.770657	−	0.459279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.k.e.89.3	✓	8
3.2	odd	2		462.2.k.f.89.2	yes	8
7.3	odd	6		462.2.k.f.353.2	yes	8
21.17	even	6	inner	462.2.k.e.353.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.e.89.3	✓	8	1.1	even	1	trivial
462.2.k.e.353.3	yes	8	21.17	even	6	inner
462.2.k.f.89.2	yes	8	3.2	odd	2
462.2.k.f.353.2	yes	8	7.3	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.10721 - 1.33195i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.241181 + 0.417738i) q^{5} +(1.62484 - 0.599900i) q^{6} +(1.48356 - 2.19067i) q^{7} +1.00000i q^{8} +(-0.548188 - 2.94949i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.10721 - 1.33195i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.241181 + 0.417738i) q^{5} +(1.62484 - 0.599900i) q^{6} +(1.48356 - 2.19067i) q^{7} +1.00000i q^{8} +(-0.548188 - 2.94949i) q^{9} +(-0.417738 + 0.241181i) q^{10} +(0.866025 - 0.500000i) q^{11} +(1.70711 + 0.292893i) q^{12} -0.550510i q^{13} +(2.38014 - 1.15539i) q^{14} +(0.289369 + 0.783763i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.926868 + 1.60538i) q^{17} +(1.00000 - 2.82843i) q^{18} +(-0.334273 - 0.192993i) q^{19} -0.482362 q^{20} +(-1.27526 - 4.40156i) q^{21} +1.00000 q^{22} +(-0.216237 - 0.124844i) q^{23} +(1.33195 + 1.10721i) q^{24} +(2.38366 + 4.12863i) q^{25} +(0.275255 - 0.476756i) q^{26} +(-4.53553 - 2.53553i) q^{27} +(2.63896 + 0.189469i) q^{28} +4.48477i q^{29} +(-0.141281 + 0.823443i) q^{30} +(1.08018 - 0.623642i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.292893 - 1.70711i) q^{33} +1.85374i q^{34} +(0.557318 + 1.14809i) q^{35} +(2.28024 - 1.94949i) q^{36} +(-2.72853 + 4.72595i) q^{37} +(-0.192993 - 0.334273i) q^{38} +(-0.733253 - 0.609528i) q^{39} +(-0.417738 - 0.241181i) q^{40} -5.67387 q^{41} +(1.09638 - 4.44949i) q^{42} -0.682163 q^{43} +(0.866025 + 0.500000i) q^{44} +(1.36433 + 0.482362i) q^{45} +(-0.124844 - 0.216237i) q^{46} +(4.41421 - 7.64564i) q^{47} +(0.599900 + 1.62484i) q^{48} +(-2.59808 - 6.50000i) q^{49} +4.76733i q^{50} +(3.16452 + 0.542947i) q^{51} +(0.476756 - 0.275255i) q^{52} +(-6.54441 + 3.77841i) q^{53} +(-2.66012 - 4.46360i) q^{54} +0.482362i q^{55} +(2.19067 + 1.48356i) q^{56} +(-0.627167 + 0.231553i) q^{57} +(-2.24238 + 3.88392i) q^{58} +(1.82465 + 3.16038i) q^{59} +(-0.534074 + 0.642483i) q^{60} +(-7.63593 - 4.40861i) q^{61} +1.24728 q^{62} +(-7.27463 - 3.17486i) q^{63} -1.00000 q^{64} +(0.229969 + 0.132773i) q^{65} +(1.10721 - 1.33195i) q^{66} +(4.35690 + 7.54636i) q^{67} +(-0.926868 + 1.60538i) q^{68} +(-0.405706 + 0.149788i) q^{69} +(-0.0913925 + 1.27293i) q^{70} +5.76028i q^{71} +(2.94949 - 0.548188i) q^{72} +(-1.94534 + 1.12314i) q^{73} +(-4.72595 + 2.72853i) q^{74} +(8.13834 + 1.39632i) q^{75} -0.385986i q^{76} +(0.189469 - 2.63896i) q^{77} +(-0.330251 - 0.894494i) q^{78} +(-6.71587 + 11.6322i) q^{79} +(-0.241181 - 0.417738i) q^{80} +(-8.39898 + 3.23375i) q^{81} +(-4.91372 - 2.83694i) q^{82} -6.48941 q^{83} +(3.17423 - 3.30518i) q^{84} -0.894171 q^{85} +(-0.590770 - 0.341081i) q^{86} +(5.97349 + 4.96556i) q^{87} +(0.500000 + 0.866025i) q^{88} +(5.64394 - 9.77559i) q^{89} +(0.940360 + 1.09990i) q^{90} +(-1.20599 - 0.816717i) q^{91} -0.249689i q^{92} +(0.365321 - 2.12925i) q^{93} +(7.64564 - 4.41421i) q^{94} +(0.161241 - 0.0930924i) q^{95} +(-0.292893 + 1.70711i) q^{96} +16.8389i q^{97} +(1.00000 - 6.92820i) q^{98} +(-1.94949 - 2.28024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 8 q^{12} - 4 q^{16} + 20 q^{17} + 8 q^{18} - 12 q^{19} - 8 q^{20} - 20 q^{21} + 8 q^{22} - 12 q^{23} - 4 q^{24} + 8 q^{25} + 12 q^{26} - 8 q^{27} - 4 q^{30} + 12 q^{31} + 8 q^{33} + 16 q^{35} - 8 q^{38} + 24 q^{39} + 40 q^{41} - 8 q^{43} + 16 q^{45} + 8 q^{46} + 24 q^{47} + 4 q^{48} + 32 q^{51} - 60 q^{53} - 4 q^{54} - 20 q^{57} - 4 q^{58} + 4 q^{59} - 12 q^{60} - 36 q^{61} + 24 q^{62} - 32 q^{63} - 8 q^{64} - 12 q^{65} + 4 q^{66} + 12 q^{67} - 20 q^{68} - 12 q^{69} - 20 q^{70} + 4 q^{72} + 48 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{79} - 4 q^{80} - 28 q^{81} - 24 q^{82} - 72 q^{83} - 4 q^{84} - 32 q^{85} + 12 q^{86} + 16 q^{87} + 4 q^{88} - 4 q^{89} - 28 q^{90} + 36 q^{91} + 16 q^{93} + 24 q^{95} - 8 q^{96} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 8 * q^12 - 4 * q^16 + 20 * q^17 + 8 * q^18 - 12 * q^19 - 8 * q^20 - 20 * q^21 + 8 * q^22 - 12 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 - 8 * q^27 - 4 * q^30 + 12 * q^31 + 8 * q^33 + 16 * q^35 - 8 * q^38 + 24 * q^39 + 40 * q^41 - 8 * q^43 + 16 * q^45 + 8 * q^46 + 24 * q^47 + 4 * q^48 + 32 * q^51 - 60 * q^53 - 4 * q^54 - 20 * q^57 - 4 * q^58 + 4 * q^59 - 12 * q^60 - 36 * q^61 + 24 * q^62 - 32 * q^63 - 8 * q^64 - 12 * q^65 + 4 * q^66 + 12 * q^67 - 20 * q^68 - 12 * q^69 - 20 * q^70 + 4 * q^72 + 48 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^79 - 4 * q^80 - 28 * q^81 - 24 * q^82 - 72 * q^83 - 4 * q^84 - 32 * q^85 + 12 * q^86 + 16 * q^87 + 4 * q^88 - 4 * q^89 - 28 * q^90 + 36 * q^91 + 16 * q^93 + 24 * q^95 - 8 * q^96 + 8 * q^98 + 4 * q^99

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