LMFDB - Embedded newform 462.2.k.e.353.3

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			353.3
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	462.353
Dual form			462.2.k.e.89.3

$q$-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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

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

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	0.807043	−	0.590492i	$-0.201066\pi$
$5$	−0.241181	−	0.417738i	−0.107859	−	0.186818i	−0.914903	+	0.403674i	$0.867733\pi$
$6$	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	$0.0243241\pi$
$13$			0.550510i			0.152684i	−0.997082	+	0.0763420i	$0.975676\pi$
$14$	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	−0.731460	−	0.681884i	$-0.761161\pi$
$17$	0.926868	−	1.60538i	0.224798	−	0.389362i	0.956259	+	0.292521i	$0.0944943\pi$
$18$	1.00000	+	2.82843i	0.235702	+	0.666667i
$19$	−0.334273	+	0.192993i	−0.0766876	+	0.0442756i	−0.537853	−	0.843038i	$-0.680765\pi$
$19$	−0.334273	+	0.192993i	−0.0766876	+	0.0442756i	0.461166	+	0.887314i	$0.347431\pi$
$20$	−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	−0.522375	−	0.852716i	$-0.674954\pi$
$23$	−0.216237	+	0.124844i	−0.0450885	+	0.0260319i	0.477286	+	0.878748i	$0.341620\pi$
$24$	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	$-0.863292\pi$
$29$		−	4.48477i		−	0.832800i	0.909181	−	0.416400i	$-0.136708\pi$
$30$	−0.141281	−	0.823443i	−0.0257942	−	0.150339i
$31$	1.08018	+	0.623642i	0.194006	+	0.112009i	0.593857	−	0.804571i	$-0.297605\pi$
$31$	1.08018	+	0.623642i	0.194006	+	0.112009i	−0.399851	+	0.916580i	$0.630938\pi$
$32$	−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	0.549726	−	0.835345i	$-0.314732\pi$
$37$	−2.72853	−	4.72595i	−0.448567	−	0.776941i	−0.998293	+	0.0584042i	$0.981399\pi$
$38$	−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	0.984559	+	0.175052i	$0.0560094\pi$
$47$	4.41421	+	7.64564i	0.643879	+	1.11523i	−0.340680	+	0.940179i	$0.610657\pi$
$48$	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	−0.0220861	−	0.999756i	$-0.507031\pi$
$53$	−6.54441	−	3.77841i	−0.898943	−	0.519005i	−0.876857	+	0.480751i	$0.840364\pi$
$54$	−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	−0.722462	−	0.691411i	$-0.756989\pi$
$59$	1.82465	−	3.16038i	0.237549	−	0.411446i	0.960010	+	0.279965i	$0.0903228\pi$
$60$	−0.534074	−	0.642483i	−0.0689487	−	0.0829441i
$61$	−7.63593	+	4.40861i	−0.977681	+	0.564464i	−0.901569	−	0.432635i	$-0.857584\pi$
$61$	−7.63593	+	4.40861i	−0.977681	+	0.564464i	−0.0761117	+	0.997099i	$0.524251\pi$
$62$	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	−0.467010	−	0.884252i	$-0.654669\pi$
$67$	4.35690	−	7.54636i	0.532279	−	0.921935i	0.999290	−	0.0376832i	$-0.0119978\pi$
$68$	−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	$-0.888960\pi$
$71$		−	5.76028i		−	0.683619i	0.939769	−	0.341810i	$-0.111040\pi$
$72$	2.94949	+	0.548188i	0.347601	+	0.0646046i
$73$	−1.94534	−	1.12314i	−0.227685	−	0.131454i	0.381819	−	0.924237i	$-0.375298\pi$
$73$	−1.94534	−	1.12314i	−0.227685	−	0.131454i	−0.609504	+	0.792783i	$0.708631\pi$
$74$	−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	−0.945078	−	0.326844i	$-0.894015\pi$
$79$	−6.71587	−	11.6322i	−0.755595	−	1.30873i	0.189483	−	0.981884i	$-0.439319\pi$
$80$	−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	0.993078	+	0.117453i	$0.0374730\pi$
$89$	5.64394	+	9.77559i	0.598257	+	1.03621i	−0.394822	+	0.918758i	$0.629194\pi$
$90$	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	$-0.673639\pi$
$97$		−	16.8389i		−	1.70973i	0.518849	−	0.854866i	$-0.326361\pi$
$98$	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	−0.905453	−	0.424447i	$-0.860469\pi$
$101$	−0.855693	+	1.48210i	−0.0851447	+	0.147475i	0.820308	+	0.571922i	$0.193802\pi$
$102$	2.46909	−	2.05247i	0.244476	−	0.203225i
$103$	0.170088	−	0.0982005i	0.0167593	−	0.00967599i	−0.491597	−	0.870823i	$-0.663587\pi$
$103$	0.170088	−	0.0982005i	0.0167593	−	0.00967599i	0.508356	+	0.861147i	$0.330253\pi$
$104$	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	−0.0550863	−	0.998482i	$-0.517543\pi$
$107$	8.08991	−	4.67071i	0.782081	−	0.451535i	0.837167	+	0.546947i	$0.184210\pi$
$108$	−0.0719302	+	5.19565i	−0.00692148	+	0.499952i
$109$	3.15161	−	5.45875i	0.301870	−	0.522854i	−0.674690	−	0.738101i	$-0.735723\pi$
$109$	3.15161	−	5.45875i	0.301870	−	0.522854i	0.976559	+	0.215248i	$0.0690559\pi$
$110$	−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	$0.381684\pi$
$113$			19.8084i			1.86342i	−0.363201	+	0.931711i	$0.618316\pi$
$114$	−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	0.963411	+	0.268027i	$0.0863717\pi$
$131$	8.17009	+	14.1510i	0.713824	+	1.23638i	−0.249587	+	0.968352i	$0.580295\pi$
$132$	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	0.860932	−	0.508720i	$-0.169881\pi$
$137$	9.95875	+	5.74969i	0.850834	+	0.491229i	−0.0100984	+	0.999949i	$0.503214\pi$
$138$	−0.426246	+	0.0731322i	−0.0362844	+	0.00622543i
$139$			3.37945i			0.286641i	0.989676	+	0.143321i	$0.0457780\pi$
$139$			3.37945i			0.286641i	−0.989676	+	0.143321i	$0.954222\pi$
$140$	−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	−0.954330	−	0.298756i	$-0.903428\pi$
$149$	−14.3154	+	8.26500i	−1.17276	+	0.677096i	−0.218434	+	0.975852i	$0.570095\pi$
$150$	6.34985	−	5.27841i	0.518463	−	0.430981i
$151$	−0.0763986	+	0.132326i	−0.00621723	+	0.0107686i	−0.869117	−	0.494606i	$-0.835312\pi$
$151$	−0.0763986	+	0.132326i	−0.00621723	+	0.0107686i	0.862900	+	0.505375i	$0.168646\pi$
$152$	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	0.817449	−	0.576001i	$-0.195388\pi$
$157$	9.11357	+	5.26172i	0.727342	+	0.419931i	−0.0901071	+	0.995932i	$0.528721\pi$
$158$	−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	0.644340	−	0.764739i	$-0.277132\pi$
$163$	−4.34228	−	7.52106i	−0.340114	−	0.589095i	−0.984454	+	0.175645i	$0.943799\pi$
$164$	−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	−1.00000		0.000432574i	$-0.999862\pi$
$173$	−6.58140	−	11.3993i	−0.500375	−	0.866674i	0.499625	−	0.866242i	$-0.333471\pi$
$174$	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	0.862918	−	0.505344i	$-0.168634\pi$
$179$	11.4624	+	6.61780i	0.856737	+	0.494637i	−0.00618127	+	0.999981i	$0.501968\pi$
$180$	0.264425	−	1.42272i	0.0197091	−	0.106043i
$181$			25.8936i			1.92466i	0.271890	+	0.962328i	$0.412351\pi$
$181$			25.8936i			1.92466i	−0.271890	+	0.962328i	$0.587649\pi$
$182$	−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	0.162544	−	0.986701i	$-0.448030\pi$
$191$	15.1791	−	8.76368i	1.09832	−	0.634118i	0.935780	+	0.352584i	$0.114697\pi$
$192$	−1.10721	−	1.33195i	−0.0799057	−	0.0961253i
$193$	3.68204	−	6.37748i	0.265039	−	0.459061i	−0.702535	−	0.711649i	$-0.747949\pi$
$193$	3.68204	−	6.37748i	0.265039	−	0.459061i	0.967574	+	0.252588i	$0.0812819\pi$
$194$	−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	$0.241201\pi$
$197$			19.2932i			1.37458i	−0.726381	+	0.687292i	$0.758799\pi$
$198$	−0.548188	+	2.94949i	−0.0389580	+	0.209611i
$199$	17.4020	+	10.0471i	1.23360	+	0.712218i	0.967778	−	0.251805i	$-0.0810242\pi$
$199$	17.4020	+	10.0471i	1.23360	+	0.712218i	0.265819	+	0.964023i	$0.414358\pi$
$200$	−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	$0.146215\pi$
$223$			13.2416i			0.886726i	−0.896342	+	0.443363i	$0.853785\pi$
$224$	−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	0.120229	−	0.992746i	$-0.461637\pi$
$227$	13.8591	−	24.0046i	0.919858	−	1.59324i	0.799629	−	0.600495i	$-0.205030\pi$
$228$	−0.514114	+	0.427366i	−0.0340480	+	0.0283030i
$229$	7.21733	−	4.16693i	0.476935	−	0.275358i	−0.242203	−	0.970225i	$-0.577870\pi$
$229$	7.21733	−	4.16693i	0.476935	−	0.275358i	0.719138	+	0.694867i	$0.244537\pi$
$230$	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	−0.711798	−	0.702384i	$-0.752119\pi$
$233$	−7.01267	+	4.04877i	−0.459415	+	0.265244i	0.252383	+	0.967627i	$0.418786\pi$
$234$	−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	$-0.722973\pi$
$239$		−	23.6386i		−	1.52905i	0.644592	−	0.764527i	$-0.277027\pi$
$240$	−0.823443	+	0.141281i	−0.0531530	+	0.00911962i
$241$	14.7528	+	8.51751i	0.950309	+	0.548661i	0.893177	−	0.449705i	$-0.148471\pi$
$241$	14.7528	+	8.51751i	0.950309	+	0.548661i	0.0571323	+	0.998367i	$0.481804\pi$
$242$	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	0.872334	−	0.488911i	$-0.162606\pi$
$257$	0.204527	+	0.354251i	0.0127580	+	0.0220976i	−0.859576	+	0.511008i	$0.829272\pi$
$258$	−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	0.835552	−	0.549411i	$-0.185148\pi$
$263$	12.6093	+	7.28000i	0.777524	+	0.448904i	−0.0580278	+	0.998315i	$0.518481\pi$
$264$	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	−0.189184	−	0.981942i	$-0.560584\pi$
$269$	12.3960	−	21.4704i	0.755795	−	1.30907i	0.944978	−	0.327133i	$-0.106082\pi$
$270$	2.50619	+	0.0346964i	0.152522	+	0.00211155i
$271$	−24.6174	+	14.2128i	−1.49540	+	0.863369i	−0.999986	−	0.00528874i	$-0.998317\pi$
$271$	−24.6174	+	14.2128i	−1.49540	+	0.863369i	−0.495413	+	0.868658i	$0.664983\pi$
$272$	−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	−0.913351	−	0.407173i	$-0.866515\pi$
$277$	−1.73179	+	2.99955i	−0.104053	+	0.180226i	0.809298	+	0.587399i	$0.199848\pi$
$278$	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	$0.210148\pi$
$281$			20.5607i			1.22655i	−0.789869	+	0.613276i	$0.789852\pi$
$282$	2.58579	+	15.0711i	0.153981	+	0.897469i
$283$	6.42343	+	3.70857i	0.381833	+	0.220451i	0.678615	−	0.734494i	$-0.262580\pi$
$283$	6.42343	+	3.70857i	0.381833	+	0.220451i	−0.296782	+	0.954945i	$0.595914\pi$
$284$	−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	$0.107439\pi$
$307$			11.6047i			0.662317i	−0.943575	+	0.331158i	$0.892561\pi$
$308$	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	−0.896154	−	0.443743i	$-0.853650\pi$
$311$	−1.12484	+	1.94829i	−0.0637841	+	0.110477i	0.832370	+	0.554220i	$0.186984\pi$
$312$	0.609528	+	0.733253i	0.0345078	+	0.0415123i
$313$	−8.92899	+	5.15515i	−0.504696	+	0.291387i	−0.730651	−	0.682751i	$-0.760783\pi$
$313$	−8.92899	+	5.15515i	−0.504696	+	0.291387i	0.225955	+	0.974138i	$0.427450\pi$
$314$	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	−0.0622821	−	0.998059i	$-0.519838\pi$
$317$	13.7259	−	7.92463i	0.770921	−	0.445091i	0.833203	+	0.552967i	$0.186505\pi$
$318$	−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	0.758235	−	0.651982i	$-0.226062\pi$
$331$	−3.37516	−	5.84594i	−0.185515	−	0.321322i	−0.943750	+	0.330660i	$0.892729\pi$
$332$	−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	0.984347	−	0.176242i	$-0.0563940\pi$
$347$	24.6613	+	14.2382i	1.32389	+	0.764349i	0.339544	+	0.940590i	$0.389727\pi$
$348$	−1.31356	−	7.65597i	−0.0704141	−	0.410403i
$349$		−	12.9437i		−	0.692861i	−0.938076	−	0.346430i	$-0.887394\pi$
$349$		−	12.9437i		−	0.692861i	0.938076	−	0.346430i	$-0.112606\pi$
$350$	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	−0.999024	−	0.0441686i	$-0.985936\pi$
$353$	−8.66631	+	15.0105i	−0.461261	+	0.798927i	0.537763	+	0.843096i	$0.319269\pi$
$354$	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	−0.657674	−	0.753303i	$-0.728459\pi$
$359$	−6.33088	+	3.65514i	−0.334131	+	0.192911i	0.323543	+	0.946214i	$0.395126\pi$
$360$	−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	0.704598	−	0.709607i	$-0.251127\pi$
$367$	8.47438	+	4.89269i	0.442359	+	0.255396i	−0.262239	+	0.965003i	$0.584461\pi$
$368$	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	−0.958399	−	0.285432i	$-0.907863\pi$
$373$	−14.0289	−	24.2988i	−0.726391	−	1.25815i	0.232008	−	0.972714i	$-0.425470\pi$
$374$	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	0.713483	−	0.700673i	$-0.247117\pi$
$383$	−4.89376	−	8.47623i	−0.250059	−	0.433115i	−0.963542	+	0.267558i	$0.913783\pi$
$384$	−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	−0.983933	−	0.178539i	$-0.942863\pi$
$389$	−32.1589	−	18.5669i	−1.63052	−	0.941380i	−0.646586	−	0.762841i	$-0.723804\pi$
$390$	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	−0.580456	+	0.814292i	$0.697126\pi$
$397$	−31.3992	+	18.1283i	−1.57588	+	0.909835i	−0.995425	+	0.0955439i	$0.969541\pi$
$398$	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	−0.955910	−	0.293660i	$-0.905127\pi$
$401$	−23.6204	+	13.6373i	−1.17955	+	0.681013i	−0.223638	+	0.974672i	$0.571793\pi$
$402$	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	0.742874	−	0.669431i	$-0.233462\pi$
$409$	10.8109	+	6.24170i	0.534566	+	0.308632i	−0.208308	+	0.978063i	$0.566796\pi$
$410$	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	0.534413	−	0.845224i	$-0.320533\pi$
$431$	1.44564	+	0.834638i	0.0696338	+	0.0402031i	−0.464779	+	0.885427i	$0.653866\pi$
$432$	4.46360	+	2.66012i	0.214755	+	0.127985i
$433$			10.5393i			0.506486i	0.967403	+	0.253243i	$0.0814973\pi$
$433$			10.5393i			0.506486i	−0.967403	+	0.253243i	$0.918503\pi$
$434$	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	0.0411662	−	0.999152i	$-0.486893\pi$
$439$	19.4237	−	11.2143i	0.927041	−	0.535227i	0.885874	+	0.463925i	$0.153559\pi$
$440$	−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	−0.367195	−	0.930144i	$-0.619682\pi$
$443$	5.36156	−	3.09550i	0.254735	−	0.147071i	0.621931	+	0.783072i	$0.286349\pi$
$444$	−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	$0.0116795\pi$
$449$			1.55464i			0.0733680i	−0.999327	+	0.0366840i	$0.988321\pi$
$450$	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	0.608973	−	0.793191i	$-0.291582\pi$
$457$	−8.17556	−	14.1605i	−0.382437	−	0.662400i	−0.991410	+	0.130791i	$0.958248\pi$
$458$	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	−0.860943	−	0.508702i	$-0.830126\pi$
$467$	−18.8229	−	32.6022i	−0.871020	−	1.50865i	−0.0100773	−	0.999949i	$-0.503208\pi$
$468$	−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	−0.989490	−	0.144602i	$-0.953810\pi$
$479$	−8.08725	+	14.0075i	−0.369516	+	0.640020i	0.619974	+	0.784622i	$0.287143\pi$
$480$	−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	−0.999971	−	0.00767942i	$-0.997556\pi$
$487$	−10.8869	+	18.8567i	−0.493335	+	0.854481i	0.506636	+	0.862160i	$0.330889\pi$
$488$	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	$-0.895323\pi$
$491$		−	14.3125i		−	0.645912i	0.946414	−	0.322956i	$-0.104677\pi$
$492$	−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	0.761649	−	0.647990i	$-0.224390\pi$
$499$	−4.02874	−	6.97799i	−0.180351	−	0.312378i	−0.942000	+	0.335612i	$0.891057\pi$
$500$	−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	−0.841717	−	0.539920i	$-0.818455\pi$
$509$	−20.0442	−	34.7175i	−0.888442	−	1.53883i	−0.0467259	−	0.998908i	$-0.514879\pi$
$510$	−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	−0.818564	−	0.574415i	$-0.805229\pi$
$521$	2.01266	−	3.48604i	0.0881764	−	0.152726i	0.906740	+	0.421689i	$0.138563\pi$
$522$	12.6848	−	4.48477i	0.555200	−	0.196293i
$523$	−22.8435	+	13.1887i	−0.998876	+	0.576701i	−0.907915	−	0.419153i	$-0.862327\pi$
$523$	−22.8435	+	13.1887i	−0.998876	+	0.576701i	−0.0909602	+	0.995855i	$0.528994\pi$
$524$	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	0.580146	−	0.814513i	$-0.302996\pi$
$541$	−9.66000	−	16.7316i	−0.415316	−	0.719348i	−0.995462	+	0.0951647i	$0.969662\pi$
$542$	−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	0.739952	−	0.672660i	$-0.234848\pi$
$557$	12.4468	+	7.18616i	0.527388	+	0.304487i	−0.212564	+	0.977147i	$0.568182\pi$
$558$	−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	0.325284	+	0.945616i	$0.394540\pi$
$563$	−15.5721	+	26.9717i	−0.656286	+	1.13672i	−0.981570	+	0.191104i	$0.938793\pi$
$564$	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	0.174234	−	0.984704i	$-0.444255\pi$
$569$	26.5762	−	15.3438i	1.11413	−	0.643244i	0.939896	+	0.341461i	$0.110922\pi$
$570$	0.206145	+	0.247989i	0.00863446	+	0.0103871i
$571$	7.29934	−	12.6428i	0.305468	−	0.529086i	−0.671898	−	0.740644i	$-0.734521\pi$
$571$	7.29934	−	12.6428i	0.305468	−	0.529086i	0.977365	+	0.211558i	$0.0678539\pi$
$572$	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	−0.0722621	−	0.997386i	$-0.523022\pi$
$577$	−23.3520	−	13.4823i	−0.972154	−	0.561274i	−0.899892	+	0.436112i	$0.856355\pi$
$578$	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	0.900229	+	0.435417i	$0.143399\pi$
$593$	20.1436	+	34.8897i	0.827197	+	1.43275i	−0.0730318	+	0.997330i	$0.523267\pi$
$594$	−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	0.914242	−	0.405167i	$-0.132787\pi$
$599$	24.9757	+	14.4197i	1.02048	+	0.589173i	0.106236	+	0.994341i	$0.466120\pi$
$600$	−1.39632	−	8.13834i	−0.0570044	−	0.332246i
$601$		−	24.5161i		−	1.00003i	−0.866015	−	0.500017i	$-0.833327\pi$
$601$		−	24.5161i		−	1.00003i	0.866015	−	0.500017i	$-0.166673\pi$
$602$	−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	−0.642212	−	0.766527i	$-0.721983\pi$
$607$	−7.37857	+	4.26002i	−0.299487	+	0.172909i	0.342725	+	0.939436i	$0.388650\pi$
$608$	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	−0.127204	+	0.991877i	$0.540600\pi$
$613$	−22.8423	+	39.5640i	−0.922592	+	1.59798i	−0.795388	+	0.606100i	$0.792733\pi$
$614$	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	$0.137359\pi$
$617$			20.7786i			0.836513i	−0.908329	+	0.418257i	$0.862641\pi$
$618$	0.335278	−	0.0575245i	0.0134868	−	0.00231398i
$619$	17.3550	+	10.0199i	0.697558	+	0.402735i	0.806437	−	0.591320i	$-0.201393\pi$
$619$	17.3550	+	10.0199i	0.697558	+	0.402735i	−0.108879	+	0.994055i	$0.534726\pi$
$620$	−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	0.0126451	−	0.999920i	$-0.495975\pi$
$641$	−21.4440	−	12.3807i	−0.846988	−	0.489009i	−0.859634	+	0.510911i	$0.829308\pi$
$642$	15.9468	−	2.73604i	0.629370	−	0.107983i
$643$			32.9650i			1.30001i	0.759929	+	0.650006i	$0.225234\pi$
$643$			32.9650i			1.30001i	−0.759929	+	0.650006i	$0.774766\pi$
$644$	−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	−0.702570	−	0.711615i	$-0.747964\pi$
$647$	6.74037	−	11.6747i	0.264991	−	0.458978i	0.967561	+	0.252636i	$0.0812976\pi$
$648$	−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	−0.232693	−	0.972550i	$-0.574754\pi$
$653$	12.6035	−	7.27663i	0.493213	−	0.284757i	0.725906	+	0.687793i	$0.241421\pi$
$654$	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	$-0.800540\pi$
$659$		−	30.1076i		−	1.17283i	0.810012	−	0.586413i	$-0.199460\pi$
$660$	−0.141281	−	0.823443i	−0.00549934	−	0.0320525i
$661$	−30.8753	−	17.8258i	−1.20091	−	0.693345i	−0.240152	−	0.970735i	$-0.577197\pi$
$661$	−30.8753	−	17.8258i	−1.20091	−	0.693345i	−0.960757	+	0.277390i	$0.910530\pi$
$662$	−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	−0.982525	−	0.186130i	$-0.940406\pi$
$677$	−16.9764	−	29.4040i	−0.652456	−	1.13009i	0.330069	−	0.943957i	$-0.392928\pi$
$678$	−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	0.950509	−	0.310696i	$-0.100562\pi$
$683$	30.2293	+	17.4529i	1.15669	+	0.667817i	0.206184	+	0.978513i	$0.433896\pi$
$684$	−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	−0.339152	−	0.940732i	$-0.610140\pi$
$691$	8.04299	−	4.64362i	0.305970	−	0.176652i	0.645122	+	0.764080i	$0.276807\pi$
$692$	−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	$-0.786053\pi$
$701$		−	32.9715i		−	1.24531i	0.782495	−	0.622657i	$-0.213947\pi$
$702$	−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	0.978920	−	0.204245i	$-0.0654740\pi$
$709$	8.32304	+	14.4159i	0.312578	+	0.541401i	−0.666342	+	0.745647i	$0.732141\pi$
$710$	−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	0.915041	+	0.403360i	$0.132158\pi$
$719$	21.6348	+	37.4725i	0.806841	+	1.39749i	−0.108201	+	0.994129i	$0.534509\pi$
$720$	−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	$-0.718210\pi$
$727$		−	41.7432i		−	1.54817i	0.633082	−	0.774085i	$-0.281790\pi$
$728$	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	−0.451086	−	0.892481i	$-0.648963\pi$
$733$	2.60675	−	1.50501i	0.0962826	−	0.0555888i	0.547368	+	0.836892i	$0.315630\pi$
$734$	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	−0.948451	−	0.316924i	$-0.897350\pi$
$739$	−5.43041	+	9.40575i	−0.199761	+	0.345996i	0.748690	+	0.662920i	$0.230683\pi$
$740$	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	$0.200666\pi$
$743$			32.1359i			1.17895i	−0.807786	+	0.589476i	$0.799334\pi$
$744$	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	0.999464	+	0.0327241i	$0.0104183\pi$
$751$	14.4715	+	25.0654i	0.528072	+	0.914648i	−0.471392	+	0.881924i	$0.656248\pi$
$752$	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	0.911233	−	0.411892i	$-0.135132\pi$
$761$	2.72848	+	4.72586i	0.0989071	+	0.171312i	−0.812325	+	0.583204i	$0.801799\pi$
$762$	−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	$0.122289\pi$
$769$			20.7871i			0.749602i	−0.927105	+	0.374801i	$0.877711\pi$
$770$	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	−0.0433053	−	0.999062i	$-0.513789\pi$
$773$	23.4534	−	40.6225i	0.843560	−	1.46109i	0.886866	−	0.462027i	$-0.152878\pi$
$774$	−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	0.0376861	−	0.999290i	$-0.488001\pi$
$787$	−22.6920	−	13.1012i	−0.808881	−	0.467008i	−0.846567	+	0.532282i	$0.821335\pi$
$788$	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	0.376300	−	0.926498i	$-0.377196\pi$
$809$	−6.76716	−	3.90702i	−0.237921	−	0.137364i	−0.614221	+	0.789134i	$0.710530\pi$
$810$	2.72865	+	3.37653i	0.0958750	+	0.118639i
$811$		−	9.92215i		−	0.348414i	−0.984709	−	0.174207i	$-0.944264\pi$
$811$		−	9.92215i		−	0.348414i	0.984709	−	0.174207i	$-0.0557362\pi$
$812$	−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	−0.180676	−	0.983543i	$-0.557829\pi$
$821$	16.6405	−	9.60741i	0.580758	−	0.335301i	0.761435	+	0.648242i	$0.224495\pi$
$822$	12.7322	+	15.3166i	0.444086	+	0.534228i
$823$	−9.79913	+	16.9726i	−0.341576	+	0.591627i	−0.984726	−	0.174113i	$-0.944294\pi$
$823$	−9.79913	+	16.9726i	−0.341576	+	0.591627i	0.643149	+	0.765741i	$0.277627\pi$
$824$	−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	$-0.981419\pi$
$827$		−	3.35552i		−	0.116683i	0.998297	−	0.0583414i	$-0.0185812\pi$
$828$	−0.736455	−	0.136876i	−0.0255936	−	0.00475679i
$829$	−33.3865	−	19.2757i	−1.15956	−	0.669474i	−0.208363	−	0.978051i	$-0.566814\pi$
$829$	−33.3865	−	19.2757i	−1.15956	−	0.669474i	−0.951199	+	0.308578i	$0.900147\pi$
$830$	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	$0.0413537\pi$
$853$			7.56740i			0.259103i	−0.991573	+	0.129551i	$0.958646\pi$
$854$	−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	−0.186416	−	0.982471i	$-0.559687\pi$
$857$	22.1795	−	38.4160i	0.757636	−	1.31226i	0.944053	−	0.329794i	$-0.106979\pi$
$858$	−0.733253	+	0.609528i	−0.0250328	+	0.0208090i
$859$	15.3094	−	8.83889i	0.522350	−	0.301579i	−0.215545	−	0.976494i	$-0.569153\pi$
$859$	15.3094	−	8.83889i	0.522350	−	0.301579i	0.737896	+	0.674915i	$0.235820\pi$
$860$	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	−0.884351	−	0.466822i	$-0.845399\pi$
$863$	−27.0927	+	15.6420i	−0.922248	+	0.532460i	−0.0378962	+	0.999282i	$0.512066\pi$
$864$	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	0.956811	−	0.290711i	$-0.0938918\pi$
$877$	6.71183	+	11.6252i	0.226642	+	0.392556i	−0.730168	+	0.683267i	$0.760558\pi$
$878$	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	0.998536	+	0.0540868i	$0.0172248\pi$
$887$	16.2645	+	28.1710i	0.546109	+	0.945888i	−0.452428	+	0.891801i	$0.649442\pi$
$888$	−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	−0.846881	−	0.531782i	$-0.821523\pi$
$907$	1.11719	−	1.93503i	0.0370957	−	0.0642517i	0.883977	+	0.467530i	$0.154856\pi$
$908$	−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	$-0.831436\pi$
$911$		−	30.4938i		−	1.01030i	0.863030	−	0.505152i	$-0.168564\pi$
$912$	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	0.890783	−	0.454428i	$-0.150156\pi$
$919$	1.57169	+	2.72225i	0.0518453	+	0.0897986i	−0.838938	+	0.544227i	$0.816823\pi$
$920$	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	−0.944485	−	0.328555i	$-0.893438\pi$
$929$	−23.0663	−	39.9519i	−0.756779	−	1.31078i	0.187706	−	0.982225i	$-0.439895\pi$
$930$	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	$-0.838413\pi$
$937$		−	29.7606i		−	0.972236i	0.873893	−	0.486118i	$-0.161587\pi$
$938$	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	−0.809770	−	0.586748i	$-0.800408\pi$
$941$	3.16738	−	5.48605i	0.103253	−	0.178840i	0.913023	+	0.407907i	$0.133741\pi$
$942$	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	−0.970158	−	0.242473i	$-0.922041\pi$
$947$	−38.3205	+	22.1244i	−1.24525	+	0.718945i	−0.275091	+	0.961418i	$0.588708\pi$
$948$	−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	$0.298315\pi$
$953$			49.7571i			1.61179i	−0.592059	+	0.805895i	$0.701685\pi$
$954$	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	−0.886807	−	0.462139i	$-0.847082\pi$
$971$	−26.2882	−	45.5325i	−0.843628	−	1.46121i	0.0431796	−	0.999067i	$-0.486251\pi$
$972$	−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	−0.0178633	−	0.999840i	$-0.505686\pi$
$977$	−27.9026	−	16.1096i	−0.892682	−	0.515390i	−0.874819	+	0.484450i	$0.839020\pi$
$978$	−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	−0.973694	−	0.227859i	$-0.926827\pi$
$983$	−9.07712	+	15.7220i	−0.289515	+	0.501455i	0.684179	+	0.729314i	$0.260161\pi$
$984$	−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	−0.176283	−	0.984339i	$-0.556408\pi$
$991$	24.0610	−	41.6748i	0.764321	−	1.32384i	0.940605	−	0.339504i	$-0.110259\pi$
$992$	−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	0.410123	−	0.912030i	$-0.365486\pi$
$997$	−5.51486	−	3.18400i	−0.174657	−	0.100838i	−0.584780	+	0.811192i	$0.698819\pi$
$998$	−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.353.3	yes	8
3.2	odd	2		462.2.k.f.353.2	yes	8
7.5	odd	6		462.2.k.f.89.2	yes	8
21.5	even	6	inner	462.2.k.e.89.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.e.89.3	✓	8	21.5	even	6	inner
462.2.k.e.353.3	yes	8	1.1	even	1	trivial
462.2.k.f.89.2	yes	8	7.5	odd	6
462.2.k.f.353.2	yes	8	3.2	odd	2

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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