LMFDB - Embedded newform 462.2.k.e.89.1

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			89.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.e.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.465926 - 0.807007i) q^{5} +(0.599900 + 1.62484i) q^{6} +(2.19067 + 1.48356i) q^{7} -1.00000i q^{8} +(0.548188 + 2.94949i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.465926 - 0.807007i) q^{5} +(0.599900 + 1.62484i) q^{6} +(2.19067 + 1.48356i) q^{7} -1.00000i q^{8} +(0.548188 + 2.94949i) q^{9} +(-0.807007 + 0.465926i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(0.292893 - 1.70711i) q^{12} +0.550510i q^{13} +(-1.15539 - 2.38014i) q^{14} +(-1.51411 + 0.559018i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.07313 + 7.05487i) q^{17} +(1.00000 - 2.82843i) q^{18} +(1.00851 + 0.582262i) q^{19} +0.931852 q^{20} +(-1.27526 - 4.40156i) q^{21} +1.00000 q^{22} +(-1.55902 - 0.900100i) q^{23} +(-1.10721 + 1.33195i) q^{24} +(2.06583 + 3.57812i) q^{25} +(0.275255 - 0.476756i) q^{26} +(2.53553 - 4.53553i) q^{27} +(-0.189469 + 2.63896i) q^{28} -7.31319i q^{29} +(1.59077 + 0.272933i) q^{30} +(4.36931 - 2.52262i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.70711 + 0.292893i) q^{33} -8.14626i q^{34} +(2.21794 - 1.07666i) q^{35} +(-2.28024 + 1.94949i) q^{36} +(3.95327 - 6.84727i) q^{37} +(-0.582262 - 1.00851i) q^{38} +(0.609528 - 0.733253i) q^{39} +(-0.807007 - 0.465926i) q^{40} +8.32540 q^{41} +(-1.09638 + 4.44949i) q^{42} -1.31784 q^{43} +(-0.866025 - 0.500000i) q^{44} +(2.63567 + 0.931852i) q^{45} +(0.900100 + 1.55902i) q^{46} +(1.58579 - 2.74666i) q^{47} +(1.62484 - 0.599900i) q^{48} +(2.59808 + 6.50000i) q^{49} -4.13165i q^{50} +(2.38599 - 13.9065i) q^{51} +(-0.476756 + 0.275255i) q^{52} +(-12.1298 + 7.00316i) q^{53} +(-4.46360 + 2.66012i) q^{54} +0.931852i q^{55} +(1.48356 - 2.19067i) q^{56} +(-0.698599 - 1.89217i) q^{57} +(-3.65660 + 6.33341i) q^{58} +(2.84959 + 4.93563i) q^{59} +(-1.24118 - 1.03175i) q^{60} +(3.53491 + 2.04088i) q^{61} -5.04524 q^{62} +(-3.17486 + 7.27463i) q^{63} -1.00000 q^{64} +(0.444266 + 0.256497i) q^{65} +(-1.33195 - 1.10721i) q^{66} +(-0.132150 - 0.228891i) q^{67} +(-4.07313 + 7.05487i) q^{68} +(1.07994 + 2.92504i) q^{69} +(-2.45912 - 0.176557i) q^{70} +1.31079i q^{71} +(2.94949 - 0.548188i) q^{72} +(5.37213 - 3.10160i) q^{73} +(-6.84727 + 3.95327i) q^{74} +(1.21013 - 7.05317i) q^{75} +1.16452i q^{76} +(-2.63896 - 0.189469i) q^{77} +(-0.894494 + 0.330251i) q^{78} +(5.94062 - 10.2895i) q^{79} +(0.465926 + 0.807007i) q^{80} +(-8.39898 + 3.23375i) q^{81} +(-7.21001 - 4.16270i) q^{82} -11.5106 q^{83} +(3.17423 - 3.30518i) q^{84} +7.59111 q^{85} +(1.14128 + 0.658919i) q^{86} +(-8.09721 + 9.74082i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-1.74496 + 3.02236i) q^{89} +(-1.81664 - 2.12484i) q^{90} +(-0.816717 + 1.20599i) q^{91} -1.80020i q^{92} +(-8.61277 - 1.47772i) q^{93} +(-2.74666 + 1.58579i) q^{94} +(0.939780 - 0.542582i) q^{95} +(-1.70711 - 0.292893i) q^{96} +17.7379i 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
$3$	−1.33195	−	1.10721i	−0.769002	−	0.639246i
$3$	−1.33195	−	1.10721i	−0.769002	−	0.639246i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.465926	−	0.807007i	0.208368	−	0.360905i	−0.742832	−	0.669478i	$-0.766518\pi$
$5$	0.465926	−	0.807007i	0.208368	−	0.360905i	0.951201	+	0.308573i	$0.0998514\pi$
$6$	0.599900	+	1.62484i	0.244908	+	0.663340i
$7$	2.19067	+	1.48356i	0.827996	+	0.560734i
$7$	2.19067	+	1.48356i	0.827996	+	0.560734i
$8$		−	1.00000i		−	0.353553i
$9$	0.548188	+	2.94949i	0.182729	+	0.983163i
$10$	−0.807007	+	0.465926i	−0.255198	+	0.147339i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	0.292893	−	1.70711i	0.0845510	−	0.492799i
$13$			0.550510i			0.152684i	0.997082	+	0.0763420i	$0.0243241\pi$
$13$			0.550510i			0.152684i	−0.997082	+	0.0763420i	$0.975676\pi$
$14$	−1.15539	−	2.38014i	−0.308792	−	0.636119i
$15$	−1.51411	+	0.559018i	−0.390943	+	0.144338i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.07313	+	7.05487i	0.987880	+	1.71106i	0.628366	+	0.777918i	$0.283724\pi$
$17$	4.07313	+	7.05487i	0.987880	+	1.71106i	0.359514	+	0.933140i	$0.382943\pi$
$18$	1.00000	−	2.82843i	0.235702	−	0.666667i
$19$	1.00851	+	0.582262i	0.231368	+	0.133580i	0.611203	−	0.791474i	$-0.290686\pi$
$19$	1.00851	+	0.582262i	0.231368	+	0.133580i	−0.379835	+	0.925054i	$0.624019\pi$
$20$	0.931852			0.208368
$21$	−1.27526	−	4.40156i	−0.278283	−	0.960499i
$22$	1.00000			0.213201
$23$	−1.55902	−	0.900100i	−0.325078	−	0.187684i	0.328576	−	0.944478i	$-0.393431\pi$
$23$	−1.55902	−	0.900100i	−0.325078	−	0.187684i	−0.653654	+	0.756794i	$0.726765\pi$
$24$	−1.10721	+	1.33195i	−0.226008	+	0.271883i
$25$	2.06583	+	3.57812i	0.413165	+	0.715623i
$26$	0.275255	−	0.476756i	0.0539820	−	0.0934995i
$27$	2.53553	−	4.53553i	0.487964	−	0.872864i
$28$	−0.189469	+	2.63896i	−0.0358062	+	0.498716i
$29$		−	7.31319i		−	1.35803i	−0.734126	−	0.679013i	$-0.762408\pi$
$29$		−	7.31319i		−	1.35803i	0.734126	−	0.679013i	$-0.237592\pi$
$30$	1.59077	+	0.272933i	0.290434	+	0.0498305i
$31$	4.36931	−	2.52262i	0.784751	−	0.453076i	−0.0533603	−	0.998575i	$-0.516993\pi$
$31$	4.36931	−	2.52262i	0.784751	−	0.453076i	0.838111	+	0.545499i	$0.183660\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.70711	+	0.292893i	0.297169	+	0.0509862i
$34$		−	8.14626i		−	1.39707i
$35$	2.21794	−	1.07666i	0.374900	−	0.181988i
$36$	−2.28024	+	1.94949i	−0.380040	+	0.324915i
$37$	3.95327	−	6.84727i	0.649914	−	1.12568i	−0.333229	−	0.942846i	$-0.608138\pi$
$37$	3.95327	−	6.84727i	0.649914	−	1.12568i	0.983143	−	0.182838i	$-0.0585284\pi$
$38$	−0.582262	−	1.00851i	−0.0944554	−	0.163602i
$39$	0.609528	−	0.733253i	0.0976027	−	0.117414i
$40$	−0.807007	−	0.465926i	−0.127599	−	0.0736693i
$41$	8.32540			1.30021			0.650105	−	0.759845i	$-0.274725\pi$
$41$	8.32540			1.30021			0.650105	+	0.759845i	$0.274725\pi$
$42$	−1.09638	+	4.44949i	−0.169175	+	0.686571i
$43$	−1.31784			−0.200968			−0.100484	−	0.994939i	$-0.532039\pi$
$43$	−1.31784			−0.200968			−0.100484	+	0.994939i	$0.532039\pi$
$44$	−0.866025	−	0.500000i	−0.130558	−	0.0753778i
$45$	2.63567	+	0.931852i	0.392903	+	0.138912i
$46$	0.900100	+	1.55902i	0.132712	+	0.229865i
$47$	1.58579	−	2.74666i	0.231311	−	0.400642i	−0.726883	−	0.686761i	$-0.759032\pi$
$47$	1.58579	−	2.74666i	0.231311	−	0.400642i	0.958194	+	0.286119i	$0.0923653\pi$
$48$	1.62484	−	0.599900i	0.234526	−	0.0865882i
$49$	2.59808	+	6.50000i	0.371154	+	0.928571i
$50$		−	4.13165i		−	0.584304i
$51$	2.38599	−	13.9065i	0.334105	−	1.94731i
$52$	−0.476756	+	0.275255i	−0.0661141	+	0.0381710i
$53$	−12.1298	+	7.00316i	−1.66616	+	0.961958i	−0.696481	+	0.717575i	$0.745252\pi$
$53$	−12.1298	+	7.00316i	−1.66616	+	0.961958i	−0.969679	+	0.244383i	$0.921415\pi$
$54$	−4.46360	+	2.66012i	−0.607420	+	0.361997i
$55$			0.931852i			0.125651i
$56$	1.48356	−	2.19067i	0.198250	−	0.292741i
$57$	−0.698599	−	1.89217i	−0.0925317	−	0.250624i
$58$	−3.65660	+	6.33341i	−0.480135	+	0.831618i
$59$	2.84959	+	4.93563i	0.370985	+	0.642565i	0.989717	−	0.143037i	$-0.0456868\pi$
$59$	2.84959	+	4.93563i	0.370985	+	0.642565i	−0.618732	+	0.785602i	$0.712353\pi$
$60$	−1.24118	−	1.03175i	−0.160236	−	0.133199i
$61$	3.53491	+	2.04088i	0.452599	+	0.261308i	0.708927	−	0.705282i	$-0.249179\pi$
$61$	3.53491	+	2.04088i	0.452599	+	0.261308i	−0.256328	+	0.966590i	$0.582513\pi$
$62$	−5.04524			−0.640747
$63$	−3.17486	+	7.27463i	−0.399994	+	0.916518i
$64$	−1.00000			−0.125000
$65$	0.444266	+	0.256497i	0.0551044	+	0.0318145i
$66$	−1.33195	−	1.10721i	−0.163952	−	0.136288i
$67$	−0.132150	−	0.228891i	−0.0161447	−	0.0279635i	0.857840	−	0.513917i	$-0.171806\pi$
$67$	−0.132150	−	0.228891i	−0.0161447	−	0.0279635i	−0.873985	+	0.485953i	$0.838473\pi$
$68$	−4.07313	+	7.05487i	−0.493940	+	0.855529i
$69$	1.07994	+	2.92504i	0.130010	+	0.352134i
$70$	−2.45912	−	0.176557i	−0.293921	−	0.0211026i
$71$			1.31079i			0.155562i	0.996970	+	0.0777810i	$0.0247835\pi$
$71$			1.31079i			0.155562i	−0.996970	+	0.0777810i	$0.975217\pi$
$72$	2.94949	−	0.548188i	0.347601	−	0.0646046i
$73$	5.37213	−	3.10160i	0.628760	−	0.363015i	−0.151512	−	0.988455i	$-0.548414\pi$
$73$	5.37213	−	3.10160i	0.628760	−	0.363015i	0.780272	+	0.625441i	$0.215081\pi$
$74$	−6.84727	+	3.95327i	−0.795979	+	0.459558i
$75$	1.21013	−	7.05317i	0.139734	−	0.814430i
$76$			1.16452i			0.133580i
$77$	−2.63896	−	0.189469i	−0.300737	−	0.0215920i
$78$	−0.894494	+	0.330251i	−0.101281	+	0.0373936i
$79$	5.94062	−	10.2895i	0.668372	−	1.15765i	−0.309988	−	0.950741i	$-0.600325\pi$
$79$	5.94062	−	10.2895i	0.668372	−	1.15765i	0.978359	−	0.206913i	$-0.0663417\pi$
$80$	0.465926	+	0.807007i	0.0520921	+	0.0902261i
$81$	−8.39898	+	3.23375i	−0.933220	+	0.359306i
$82$	−7.21001	−	4.16270i	−0.796212	−	0.459693i
$83$	−11.5106			−1.26345			−0.631726	−	0.775192i	$-0.717653\pi$
$83$	−11.5106			−1.26345			−0.631726	+	0.775192i	$0.717653\pi$
$84$	3.17423	−	3.30518i	0.346337	−	0.360625i
$85$	7.59111			0.823371
$86$	1.14128	+	0.658919i	0.123067	+	0.0710530i
$87$	−8.09721	+	9.74082i	−0.868112	+	1.04433i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−1.74496	+	3.02236i	−0.184966	+	0.320370i	−0.943565	−	0.331188i	$-0.892551\pi$
$89$	−1.74496	+	3.02236i	−0.184966	+	0.320370i	0.758599	+	0.651557i	$0.225884\pi$
$90$	−1.81664	−	2.12484i	−0.191490	−	0.223978i
$91$	−0.816717	+	1.20599i	−0.0856152	+	0.126422i
$92$		−	1.80020i		−	0.187684i
$93$	−8.61277	−	1.47772i	−0.893103	−	0.153232i
$94$	−2.74666	+	1.58579i	−0.283297	+	0.163561i
$95$	0.939780	−	0.542582i	0.0964194	−	0.0556678i
$96$	−1.70711	−	0.292893i	−0.174231	−	0.0298933i
$97$			17.7379i			1.80101i	0.434846	+	0.900505i	$0.356803\pi$
$97$			17.7379i			1.80101i	−0.434846	+	0.900505i	$0.643197\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$	−1.94949	−	2.28024i	−0.195931	−	0.229173i
$100$	−2.06583	+	3.57812i	−0.206583	+	0.357812i
$101$	5.75467	+	9.96739i	0.572611	+	0.991792i	0.996297	+	0.0859825i	$0.0274029\pi$
$101$	5.75467	+	9.96739i	0.572611	+	0.991792i	−0.423685	+	0.905809i	$0.639264\pi$
$102$	−9.01960	+	10.8504i	−0.893073	+	1.07435i
$103$	−7.14738	−	4.12654i	−0.704253	−	0.406600i	0.104677	−	0.994506i	$-0.466619\pi$
$103$	−7.14738	−	4.12654i	−0.704253	−	0.406600i	−0.808929	+	0.587906i	$0.799953\pi$
$104$	0.550510			0.0539820
$105$	−4.14626	−	1.02166i	−0.404634	−	0.0997038i
$106$	14.0063			1.36041
$107$	−2.51669	−	1.45301i	−0.243298	−	0.140468i	0.373394	−	0.927673i	$-0.378194\pi$
$107$	−2.51669	−	1.45301i	−0.243298	−	0.140468i	−0.616692	+	0.787205i	$0.711527\pi$
$108$	5.19565	−	0.0719302i	0.499952	−	0.00692148i
$109$	6.29788	+	10.9082i	0.603227	+	1.04482i	0.992329	+	0.123625i	$0.0394521\pi$
$109$	6.29788	+	10.9082i	0.603227	+	1.04482i	−0.389102	+	0.921195i	$0.627215\pi$
$110$	0.465926	−	0.807007i	0.0444243	−	0.0769451i
$111$	−12.8469	+	4.74314i	−1.21937	+	0.450199i
$112$	−2.38014	+	1.15539i	−0.224902	+	0.109175i
$113$		−	9.11150i		−	0.857138i	−0.903509	−	0.428569i	$-0.859018\pi$
$113$		−	9.11150i		−	0.857138i	0.903509	−	0.428569i	$-0.140982\pi$
$114$	−0.341081	+	1.98797i	−0.0319452	+	0.186190i
$115$	−1.45277	+	0.838759i	−0.135472	+	0.0782147i
$116$	6.33341	−	3.65660i	0.588042	−	0.339506i
$117$	−1.62372	+	0.301783i	−0.150113	+	0.0278999i
$118$		−	5.69918i		−	0.524652i
$119$	−1.54346	+	21.4977i	−0.141489	+	1.97069i
$120$	0.559018	+	1.51411i	0.0510311	+	0.138219i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−2.04088	−	3.53491i	−0.184773	−	0.320036i
$123$	−11.0890	−	9.21794i	−0.999864	−	0.831153i
$124$	4.36931	+	2.52262i	0.392376	+	0.226538i
$125$	8.50935			0.761099
$126$	6.38682	−	4.71259i	0.568983	−	0.419831i
$127$	−16.9014			−1.49976			−0.749878	−	0.661577i	$-0.769888\pi$
$127$	−16.9014			−1.49976			−0.749878	+	0.661577i	$0.769888\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	1.75529	+	1.45912i	0.154545	+	0.128468i
$130$	−0.256497	−	0.444266i	−0.0224963	−	0.0389647i
$131$	0.852616	−	1.47677i	0.0744934	−	0.129026i	−0.826372	−	0.563124i	$-0.809599\pi$
$131$	0.852616	−	1.47677i	0.0744934	−	0.129026i	0.900866	+	0.434098i	$0.142933\pi$
$132$	0.599900	+	1.62484i	0.0522146	+	0.141425i
$133$	1.34549	+	2.77173i	0.116668	+	0.240340i
$134$			0.264301i			0.0228321i
$135$	−2.47884	−	4.15942i	−0.213344	−	0.357986i
$136$	7.05487	−	4.07313i	0.604950	−	0.349268i
$137$	−6.40824	+	3.69980i	−0.547493	+	0.316095i	−0.748110	−	0.663574i	$-0.769039\pi$
$137$	−6.40824	+	3.69980i	−0.547493	+	0.316095i	0.200617	+	0.979670i	$0.435705\pi$
$138$	0.527266	−	3.07313i	0.0448839	−	0.261602i
$139$		−	22.0764i		−	1.87250i	−0.351341	−	0.936248i	$-0.614274\pi$
$139$		−	22.0764i		−	1.87250i	0.351341	−	0.936248i	$-0.385726\pi$
$140$	2.04138	+	1.38246i	0.172528	+	0.116839i
$141$	−5.15331	+	1.90263i	−0.433987	+	0.160230i
$142$	0.655395	−	1.13518i	0.0549995	−	0.0952619i
$143$	−0.275255	−	0.476756i	−0.0230180	−	0.0398683i
$144$	−2.82843	−	1.00000i	−0.235702	−	0.0833333i
$145$	−5.90180	−	3.40741i	−0.490118	−	0.282970i
$146$	−6.20320			−0.513381
$147$	3.73633	−	11.5343i	0.308167	−	0.951332i
$148$	7.90654			0.649914
$149$	11.3154	+	6.53295i	0.926994	+	0.535200i	0.885860	−	0.463953i	$-0.153569\pi$
$149$	11.3154	+	6.53295i	0.926994	+	0.535200i	0.0411346	+	0.999154i	$0.486903\pi$
$150$	−4.57459	+	5.50316i	−0.373514	+	0.449331i
$151$	−10.0473	−	17.4025i	−0.817640	−	1.41619i	−0.907417	−	0.420232i	$-0.861949\pi$
$151$	−10.0473	−	17.4025i	−0.817640	−	1.41619i	0.0897770	−	0.995962i	$-0.471385\pi$
$152$	0.582262	−	1.00851i	0.0472277	−	0.0818008i
$153$	−18.5754	+	15.8811i	−1.50173	+	1.28391i
$154$	2.19067	+	1.48356i	0.176529	+	0.119549i
$155$		−	4.70142i		−	0.377627i
$156$	0.939780	+	0.161241i	0.0752426	+	0.0129096i
$157$	−8.81051	+	5.08675i	−0.703155	+	0.405967i	−0.808521	−	0.588467i	$-0.799732\pi$
$157$	−8.81051	+	5.08675i	−0.703155	+	0.405967i	0.105366	+	0.994433i	$0.466398\pi$
$158$	−10.2895	+	5.94062i	−0.818585	+	0.472610i
$159$	23.9103	+	4.10236i	1.89621	+	0.325338i
$160$		−	0.931852i		−	0.0736693i
$161$	−2.07994	−	4.28472i	−0.163922	−	0.337684i
$162$	8.89060	+	1.39898i	0.698512	+	0.109914i
$163$	−6.78144	+	11.7458i	−0.531163	+	0.920002i	0.468175	+	0.883636i	$0.344912\pi$
$163$	−6.78144	+	11.7458i	−0.531163	+	0.920002i	−0.999339	+	0.0363664i	$0.988422\pi$
$164$	4.16270	+	7.21001i	0.325052	+	0.563007i
$165$	1.03175	−	1.24118i	0.0803218	−	0.0966258i
$166$	9.96846	+	5.75529i	0.773703	+	0.446698i
$167$	17.3594			1.34331			0.671657	−	0.740863i	$-0.265583\pi$
$167$	17.3594			1.34331			0.671657	+	0.740863i	$0.265583\pi$
$168$	−4.40156	+	1.27526i	−0.339588	+	0.0983881i
$169$	12.6969			0.976688
$170$	−6.57409	−	3.79555i	−0.504210	−	0.291106i
$171$	−1.16452	+	3.29377i	−0.0890534	+	0.251881i
$172$	−0.658919	−	1.14128i	−0.0502421	−	0.0870218i
$173$	2.68242	−	4.64609i	0.203941	−	0.353236i	−0.745854	−	0.666109i	$-0.767958\pi$
$173$	2.68242	−	4.64609i	0.203941	−	0.353236i	0.949795	+	0.312874i	$0.101292\pi$
$174$	11.8828	−	4.38719i	0.900833	−	0.332592i
$175$	−0.782819	+	10.9033i	−0.0591755	+	0.824209i
$176$		−	1.00000i		−	0.0753778i
$177$	1.66925	−	9.72911i	0.125469	−	0.731284i
$178$	3.02236	−	1.74496i	0.226536	−	0.130790i
$179$	1.45932	−	0.842541i	0.109075	−	0.0629745i	−0.444470	−	0.895794i	$-0.646608\pi$
$179$	1.45932	−	0.842541i	0.109075	−	0.0629745i	0.553545	+	0.832819i	$0.313275\pi$
$180$	0.510830	+	2.74849i	0.0380750	+	0.204860i
$181$		−	4.29769i		−	0.319445i	−0.987162	−	0.159722i	$-0.948940\pi$
$181$		−	4.29769i		−	0.319445i	0.987162	−	0.159722i	$-0.0510599\pi$
$182$	1.31029	−	0.636057i	0.0971252	−	0.0471476i
$183$	−2.44865	−	6.63223i	−0.181010	−	0.490269i
$184$	−0.900100	+	1.55902i	−0.0663562	+	0.114932i
$185$	−3.68386	−	6.38064i	−0.270843	−	0.469114i
$186$	6.72002	+	5.58613i	0.492736	+	0.409595i
$187$	−7.05487	−	4.07313i	−0.515903	−	0.297857i
$188$	3.17157			0.231311
$189$	12.2833	−	6.17423i	0.893477	−	0.449109i
$190$	−1.08516			−0.0787261
$191$	7.47239	+	4.31419i	0.540683	+	0.312164i	0.745356	−	0.666667i	$-0.232280\pi$
$191$	7.47239	+	4.31419i	0.540683	+	0.312164i	−0.204672	+	0.978831i	$0.565613\pi$
$192$	1.33195	+	1.10721i	0.0961253	+	0.0799057i
$193$	−4.90678	−	8.49880i	−0.353198	−	0.611757i	0.633610	−	0.773653i	$-0.281572\pi$
$193$	−4.90678	−	8.49880i	−0.353198	−	0.611757i	−0.986808	+	0.161896i	$0.948239\pi$
$194$	8.86894	−	15.3615i	0.636753	−	1.10289i
$195$	−0.307745	−	0.833535i	−0.0220381	−	0.0596907i
$196$	−4.33013	+	5.50000i	−0.309295	+	0.392857i
$197$		−	6.79831i		−	0.484360i	−0.970231	−	0.242180i	$-0.922138\pi$
$197$		−	6.79831i		−	0.484360i	0.970231	−	0.242180i	$-0.0778624\pi$
$198$	0.548188	+	2.94949i	0.0389580	+	0.209611i
$199$	−17.2783	+	9.97564i	−1.22483	+	0.707154i	−0.965943	−	0.258754i	$-0.916688\pi$
$199$	−17.2783	+	9.97564i	−1.22483	+	0.707154i	−0.258884	+	0.965909i	$0.583355\pi$
$200$	3.57812	−	2.06583i	0.253011	−	0.146076i
$201$	−0.0774119	+	0.451190i	−0.00546021	+	0.0318245i
$202$		−	11.5093i		−	0.809795i
$203$	10.8496	−	16.0208i	0.761492	−	1.12444i
$204$	13.2364	−	4.88695i	0.926734	−	0.342155i
$205$	3.87902	−	6.71866i	0.270922	−	0.469251i
$206$	4.12654	+	7.14738i	0.287510	+	0.497982i
$207$	1.80020	−	5.09173i	0.125122	−	0.353900i
$208$	−0.476756	−	0.275255i	−0.0330571	−	0.0190855i
$209$	−1.16452			−0.0805519
$210$	3.07994	+	2.95792i	0.212536	+	0.204116i
$211$	6.53565			0.449933			0.224966	−	0.974367i	$-0.427773\pi$
$211$	6.53565			0.449933			0.224966	+	0.974367i	$0.427773\pi$
$212$	−12.1298	−	7.00316i	−0.833080	−	0.480979i
$213$	1.45131	−	1.74591i	0.0994424	−	0.119628i
$214$	1.45301	+	2.51669i	0.0993260	+	0.172038i
$215$	−0.614014	+	1.06350i	−0.0418754	+	0.0725304i
$216$	−4.53553	−	2.53553i	−0.308604	−	0.172521i
$217$	13.3142	+	0.955916i	0.903826	+	0.0648918i
$218$		−	12.5958i		−	0.853092i
$219$	−10.5895	−	1.81688i	−0.715574	−	0.122773i
$220$	−0.807007	+	0.465926i	−0.0544084	+	0.0314127i
$221$	−3.88378	+	2.24230i	−0.261251	+	0.150833i
$222$	13.4973	+	2.31577i	0.905880	+	0.155424i
$223$			15.0058i			1.00486i	0.864617	+	0.502431i	$0.167561\pi$
$223$			15.0058i			1.00486i	−0.864617	+	0.502431i	$0.832439\pi$
$224$	2.63896	+	0.189469i	0.176323	+	0.0126594i
$225$	−9.42116	+	8.05461i	−0.628077	+	0.536974i
$226$	−4.55575	+	7.89079i	−0.303044	+	0.524888i
$227$	8.83788	+	15.3077i	0.586591	+	1.01600i	0.994675	+	0.103061i	$0.0328636\pi$
$227$	8.83788	+	15.3077i	0.586591	+	1.01600i	−0.408084	+	0.912944i	$0.633803\pi$
$228$	1.28937	−	1.55109i	0.0853906	−	0.102723i
$229$	−13.2173	−	7.63103i	−0.873426	−	0.504273i	−0.00494071	−	0.999988i	$-0.501573\pi$
$229$	−13.2173	−	7.63103i	−0.873426	−	0.504273i	−0.868485	+	0.495715i	$0.834906\pi$
$230$	1.67752			0.110612
$231$	3.30518	+	3.17423i	0.217465	+	0.208849i
$232$	−7.31319			−0.480135
$233$	1.68691	+	0.973936i	0.110513	+	0.0638047i	0.554238	−	0.832358i	$-0.313010\pi$
$233$	1.68691	+	0.973936i	0.110513	+	0.0638047i	−0.443725	+	0.896163i	$0.646343\pi$
$234$	1.55708	+	0.550510i	0.101789	+	0.0359880i
$235$	−1.47772	−	2.55948i	−0.0963957	−	0.166962i
$236$	−2.84959	+	4.93563i	−0.185492	+	0.321282i
$237$	−19.3052	+	7.12756i	−1.25400	+	0.462985i
$238$	12.0855	−	17.8458i	0.783387	−	1.15677i
$239$		−	6.81090i		−	0.440560i	−0.975437	−	0.220280i	$-0.929303\pi$
$239$		−	6.81090i		−	0.440560i	0.975437	−	0.220280i	$-0.0706971\pi$
$240$	0.272933	−	1.59077i	0.0176178	−	0.102684i
$241$	−1.22496	+	0.707231i	−0.0789066	+	0.0455568i	−0.538934	−	0.842348i	$-0.681173\pi$
$241$	−1.22496	+	0.707231i	−0.0789066	+	0.0455568i	0.460028	+	0.887905i	$0.347840\pi$
$242$	−0.866025	+	0.500000i	−0.0556702	+	0.0321412i
$243$	14.7675	+	4.99221i	0.947333	+	0.320250i
$244$			4.08176i			0.261308i
$245$	6.45606	+	0.931852i	0.412462	+	0.0595338i
$246$	4.99441	+	13.5275i	0.318432	+	0.862481i
$247$	−0.320541	+	0.555194i	−0.0203956	+	0.0353261i
$248$	−2.52262	−	4.36931i	−0.160187	−	0.277451i
$249$	15.3315	+	12.7446i	0.971597	+	0.807656i
$250$	−7.36931	−	4.25467i	−0.466076	−	0.269089i
$251$	−14.4054			−0.909263			−0.454632	−	0.890680i	$-0.650229\pi$
$251$	−14.4054			−0.909263			−0.454632	+	0.890680i	$0.650229\pi$
$252$	−7.88745	+	0.887810i	−0.496862	+	0.0559268i
$253$	1.80020			0.113178
$254$	14.6370	+	8.45069i	0.918409	+	0.530244i
$255$	−10.1110	−	8.40493i	−0.633175	−	0.526337i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.59343	−	13.1522i	0.473665	−	0.820412i	−0.525880	−	0.850559i	$-0.676264\pi$
$257$	7.59343	−	13.1522i	0.473665	−	0.820412i	0.999545	+	0.0301463i	$0.00959732\pi$
$258$	−0.790571	−	2.14128i	−0.0492188	−	0.133310i
$259$	18.8187	−	9.13518i	1.16934	−	0.567632i
$260$			0.512994i			0.0318145i
$261$	21.5702	−	4.00901i	1.33516	−	0.248151i
$262$	−1.47677	+	0.852616i	−0.0912354	+	0.0526748i
$263$	3.55980	−	2.05525i	0.219507	−	0.126732i	−0.386215	−	0.922409i	$-0.626218\pi$
$263$	3.55980	−	2.05525i	0.219507	−	0.126732i	0.605722	+	0.795676i	$0.292884\pi$
$264$	0.292893	−	1.70711i	0.0180263	−	0.105065i
$265$			13.0518i			0.801766i
$266$	0.220641	−	3.07313i	0.0135284	−	0.188426i
$267$	5.67059	−	2.09361i	0.347034	−	0.128127i
$268$	0.132150	−	0.228891i	0.00807237	−	0.0139818i
$269$	4.05354	+	7.02093i	0.247148	+	0.428074i	0.962733	−	0.270452i	$-0.0871731\pi$
$269$	4.05354	+	7.02093i	0.247148	+	0.428074i	−0.715585	+	0.698526i	$0.753840\pi$
$270$	0.0670283	+	4.84158i	0.00407921	+	0.294649i
$271$	−11.7538	−	6.78606i	−0.713993	−	0.412224i	0.0985450	−	0.995133i	$-0.468581\pi$
$271$	−11.7538	−	6.78606i	−0.713993	−	0.412224i	−0.812538	+	0.582909i	$0.801914\pi$
$272$	−8.14626			−0.493940
$273$	2.42310	−	0.702041i	0.146653	−	0.0424895i
$274$	7.39960			0.447026
$275$	−3.57812	−	2.06583i	−0.215769	−	0.124574i
$276$	−1.99319	+	2.39778i	−0.119976	+	0.144329i
$277$	−8.16719	−	14.1460i	−0.490719	−	0.849950i	0.509224	−	0.860634i	$-0.329932\pi$
$277$	−8.16719	−	14.1460i	−0.490719	−	0.849950i	−0.999943	+	0.0106842i	$0.996599\pi$
$278$	−11.0382	+	19.1187i	−0.662027	+	1.14666i
$279$	9.83565	+	11.5044i	0.588845	+	0.688748i
$280$	−1.07666	−	2.21794i	−0.0643425	−	0.132547i
$281$		−	26.8082i		−	1.59924i	−0.600505	−	0.799621i	$-0.705034\pi$
$281$		−	26.8082i		−	1.59924i	0.600505	−	0.799621i	$-0.294966\pi$
$282$	5.41421	+	0.928932i	0.322412	+	0.0553171i
$283$	9.49826	−	5.48382i	0.564613	−	0.325979i	−0.190382	−	0.981710i	$-0.560973\pi$
$283$	9.49826	−	5.48382i	0.564613	−	0.325979i	0.754995	+	0.655731i	$0.227639\pi$
$284$	−1.13518	+	0.655395i	−0.0673603	+	0.0388905i
$285$	−1.85249	−	0.317837i	−0.109732	−	0.0188271i
$286$			0.550510i			0.0325524i
$287$	18.2382	+	12.3513i	1.07657	+	0.729072i
$288$	1.94949	+	2.28024i	0.114875	+	0.134364i
$289$	−24.6808	+	42.7484i	−1.45181	+	2.51461i
$290$	3.40741	+	5.90180i	0.200090	+	0.346566i
$291$	19.6395	−	23.6260i	1.15129	−	1.38498i
$292$	5.37213	+	3.10160i	0.314380	+	0.181507i
$293$	−12.9709			−0.757770			−0.378885	−	0.925444i	$-0.623692\pi$
$293$	−12.9709			−0.757770			−0.378885	+	0.925444i	$0.623692\pi$
$294$	−9.00290	+	8.12082i	−0.525060	+	0.473616i
$295$	5.31079			0.309206
$296$	−6.84727	−	3.95327i	−0.397989	−	0.229779i
$297$	0.0719302	+	5.19565i	0.00417381	+	0.301482i
$298$	−6.53295	−	11.3154i	−0.378444	−	0.655484i
$299$	0.495514	−	0.858256i	0.0286563	−	0.0496342i
$300$	6.71329	−	2.47858i	0.387592	−	0.143101i
$301$	−2.88695	−	1.95510i	−0.166401	−	0.112690i
$302$			20.0947i			1.15632i
$303$	3.37101	−	19.6477i	0.193659	−	1.12873i
$304$	−1.00851	+	0.582262i	−0.0578419	+	0.0333950i
$305$	3.29401	−	1.90180i	0.188615	−	0.108897i
$306$	24.0273	−	4.46569i	1.37355	−	0.255286i
$307$			6.44068i			0.367589i	0.982965	+	0.183795i	$0.0588381\pi$
$307$			6.44068i			0.367589i	−0.982965	+	0.183795i	$0.941162\pi$
$308$	−1.15539	−	2.38014i	−0.0658347	−	0.135621i
$309$	4.95103	+	13.4100i	0.281654	+	0.762867i
$310$	−2.35071	+	4.07155i	−0.133511	+	0.231248i
$311$	−0.0999004	−	0.173033i	−0.00566483	−	0.00981178i	0.863179	−	0.504898i	$-0.168470\pi$
$311$	−0.0999004	−	0.173033i	−0.00566483	−	0.00981178i	−0.868844	+	0.495086i	$0.835137\pi$
$312$	−0.733253	−	0.609528i	−0.0415123	−	0.0345078i
$313$	−5.46489	−	3.15515i	−0.308894	−	0.178340i	0.337538	−	0.941312i	$-0.390406\pi$
$313$	−5.46489	−	3.15515i	−0.308894	−	0.178340i	−0.646431	+	0.762972i	$0.723739\pi$
$314$	10.1735			0.574124
$315$	4.39143	+	5.95157i	0.247429	+	0.335333i
$316$	11.8812			0.668372
$317$	−22.7259	−	13.1208i	−1.27641	−	0.736936i	−0.300225	−	0.953869i	$-0.597062\pi$
$317$	−22.7259	−	13.1208i	−1.27641	−	0.736936i	−0.976187	+	0.216932i	$0.930395\pi$
$318$	−18.6557	−	15.5079i	−1.04616	−	0.869639i
$319$	3.65660	+	6.33341i	0.204730	+	0.354603i
$320$	−0.465926	+	0.807007i	−0.0260460	+	0.0451131i
$321$	1.74333	+	4.72184i	0.0973030	+	0.263548i
$322$	−0.341081	+	4.75065i	−0.0190077	+	0.264743i
$323$			9.48653i			0.527844i
$324$	−7.00000	−	5.65685i	−0.388889	−	0.314270i
$325$	−1.96979	+	1.13726i	−0.109264	+	0.0630838i
$326$	11.7458	−	6.78144i	0.650540	−	0.375589i
$327$	3.68921	−	21.5023i	0.204014	−	1.18908i
$328$		−	8.32540i		−	0.459693i
$329$	7.54879	−	3.66442i	0.416178	−	0.202026i
$330$	−1.51411	+	0.559018i	−0.0833492	+	0.0307729i
$331$	−4.40010	+	7.62120i	−0.241851	+	0.418899i	−0.961242	−	0.275707i	$-0.911088\pi$
$331$	−4.40010	+	7.62120i	−0.241851	+	0.418899i	0.719390	+	0.694606i	$0.244421\pi$
$332$	−5.75529	−	9.96846i	−0.315863	−	0.547090i
$333$	22.3631	+	7.90654i	1.22549	+	0.433276i
$334$	−15.0337	−	8.67972i	−0.822608	−	0.474933i
$335$	−0.246289			−0.0134562
$336$	4.44949	+	1.09638i	0.242740	+	0.0598122i
$337$	−27.4704			−1.49641			−0.748205	−	0.663468i	$-0.769084\pi$
$337$	−27.4704			−1.49641			−0.748205	+	0.663468i	$0.769084\pi$
$338$	−10.9959	−	6.34847i	−0.598097	−	0.345311i
$339$	−10.0883	+	12.1361i	−0.547922	+	0.659141i
$340$	3.79555	+	6.57409i	0.205843	+	0.356530i
$341$	−2.52262	+	4.36931i	−0.136608	+	0.236611i
$342$	2.65539	−	2.27023i	0.143587	−	0.122760i
$343$	−3.95164	+	18.0938i	−0.213368	+	0.976972i
$344$			1.31784i			0.0710530i
$345$	2.86370	+	0.491334i	0.154177	+	0.0264525i
$346$	−4.64609	+	2.68242i	−0.249775	+	0.144208i
$347$	−14.4366	+	8.33498i	−0.774998	+	0.447445i	−0.834654	−	0.550774i	$-0.814333\pi$
$347$	−14.4366	+	8.33498i	−0.774998	+	0.447445i	0.0596570	+	0.998219i	$0.480999\pi$
$348$	−12.4844	−	2.14198i	−0.669234	−	0.114822i
$349$		−	26.4502i		−	1.41585i	−0.706290	−	0.707923i	$-0.749633\pi$
$349$		−	26.4502i		−	1.41585i	0.706290	−	0.707923i	$-0.250367\pi$
$350$	6.12957	−	9.05109i	0.327639	−	0.483801i
$351$	2.49686	+	1.39584i	0.133272	+	0.0745043i
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−8.03063	−	13.9095i	−0.427427	−	0.740326i	0.569216	−	0.822188i	$-0.307247\pi$
$353$	−8.03063	−	13.9095i	−0.427427	−	0.740326i	−0.996644	+	0.0818618i	$0.973913\pi$
$354$	−6.31017	+	7.59103i	−0.335382	+	0.403459i
$355$	1.05782	+	0.610730i	0.0561431	+	0.0324142i
$356$	−3.48993			−0.184966
$357$	25.8582	−	26.9249i	1.36856	−	1.42502i
$358$	−1.68508			−0.0890594
$359$	17.3536	+	10.0191i	0.915887	+	0.528788i	0.882321	−	0.470649i	$-0.155980\pi$
$359$	17.3536	+	10.0191i	0.915887	+	0.528788i	0.0335666	+	0.999436i	$0.489313\pi$
$360$	0.931852	−	2.63567i	0.0491129	−	0.138912i
$361$	−8.82194	−	15.2801i	−0.464313	−	0.804213i
$362$	−2.14884	+	3.72191i	−0.112941	+	0.195619i
$363$	−1.62484	+	0.599900i	−0.0852822	+	0.0314866i
$364$	−1.45277	−	0.104304i	−0.0761460	−	0.00546704i
$365$		−	5.78046i		−	0.302563i
$366$	−1.19552	+	6.96801i	−0.0624909	+	0.364224i
$367$	28.6947	−	16.5669i	1.49785	−	0.864786i	0.497857	−	0.867259i	$-0.334121\pi$
$367$	28.6947	−	16.5669i	1.49785	−	0.864786i	0.999997	+	0.00247299i	$0.000787176\pi$
$368$	1.55902	−	0.900100i	0.0812694	−	0.0469209i
$369$	4.56389	+	24.5557i	0.237586	+	1.27832i
$370$			7.36773i			0.383030i
$371$	−36.9621	−	2.65376i	−1.91898	−	0.137776i
$372$	−3.02664	−	8.19774i	−0.156924	−	0.425033i
$373$	10.6805	−	18.4991i	0.553014	−	0.957848i	−0.445041	−	0.895510i	$-0.646811\pi$
$373$	10.6805	−	18.4991i	0.553014	−	0.957848i	0.998055	−	0.0623380i	$-0.0198557\pi$
$374$	4.07313	+	7.05487i	0.210617	+	0.364799i
$375$	−11.3340	−	9.42160i	−0.585287	−	0.486529i
$376$	−2.74666	−	1.58579i	−0.141648	−	0.0817807i
$377$	4.02599			0.207349
$378$	−13.7247	−	0.794593i	−0.705925	−	0.0408695i
$379$	−27.5115			−1.41317			−0.706586	−	0.707627i	$-0.749766\pi$
$379$	−27.5115			−1.41317			−0.706586	+	0.707627i	$0.749766\pi$
$380$	0.939780	+	0.542582i	0.0482097	+	0.0278339i
$381$	22.5118	+	18.7133i	1.15332	+	0.958712i
$382$	−4.31419	−	7.47239i	−0.220733	−	0.382321i
$383$	−4.67946	+	8.10506i	−0.239109	+	0.414149i	−0.960459	−	0.278422i	$-0.910189\pi$
$383$	−4.67946	+	8.10506i	−0.239109	+	0.414149i	0.721350	+	0.692571i	$0.243522\pi$
$384$	−0.599900	−	1.62484i	−0.0306135	−	0.0829175i
$385$	−1.38246	+	2.04138i	−0.0704568	+	0.104038i
$386$			9.81357i			0.499497i
$387$	−0.722423	−	3.88695i	−0.0367228	−	0.197585i
$388$	−15.3615	+	8.86894i	−0.779860	+	0.450252i
$389$	−5.01028	+	2.89269i	−0.254031	+	0.146665i	−0.621609	−	0.783328i	$-0.713521\pi$
$389$	−5.01028	+	2.89269i	−0.254031	+	0.146665i	0.367577	+	0.929993i	$0.380187\pi$
$390$	−0.150252	+	0.875735i	−0.00760833	+	0.0443446i
$391$		−	14.6649i		−	0.741636i
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$	−2.77074	+	1.02297i	−0.139765	+	0.0516020i
$394$	−3.39916	+	5.88751i	−0.171247	+	0.296608i
$395$	−5.53577	−	9.58824i	−0.278535	−	0.482437i
$396$	1.00000	−	2.82843i	0.0502519	−	0.142134i
$397$	−0.747216	−	0.431405i	−0.0375017	−	0.0216516i	0.481132	−	0.876648i	$-0.340226\pi$
$397$	−0.747216	−	0.431405i	−0.0375017	−	0.0216516i	−0.518634	+	0.854997i	$0.673559\pi$
$398$	19.9513			1.00007
$399$	1.27676	−	5.18154i	0.0639178	−	0.259401i
$400$	−4.13165			−0.206583
$401$	−25.1775	−	14.5362i	−1.25731	−	0.725906i	−0.284755	−	0.958600i	$-0.591912\pi$
$401$	−25.1775	−	14.5362i	−1.25731	−	0.725906i	−0.972550	+	0.232695i	$0.925246\pi$
$402$	0.292635	−	0.352036i	0.0145953	−	0.0175579i
$403$	1.38873	+	2.40535i	0.0691775	+	0.119819i
$404$	−5.75467	+	9.96739i	−0.286306	+	0.495896i
$405$	−1.30364	+	8.28472i	−0.0647785	+	0.411671i
$406$	−17.4064	+	8.44962i	−0.863866	+	0.419348i
$407$			7.90654i			0.391913i
$408$	−13.9065	−	2.38599i	−0.688476	−	0.118124i
$409$	24.7067	−	14.2644i	1.22167	−	0.705329i	0.256393	−	0.966573i	$-0.417466\pi$
$409$	24.7067	−	14.2644i	1.22167	−	0.705329i	0.965273	+	0.261243i	$0.0841325\pi$
$410$	−6.71866	+	3.87902i	−0.331811	+	0.191571i
$411$	12.6319	+	2.16729i	0.623086	+	0.106905i
$412$		−	8.25309i		−	0.406600i
$413$	−1.07982	+	15.0399i	−0.0531343	+	0.740065i
$414$	−4.10488	+	3.50947i	−0.201744	+	0.172481i
$415$	−5.36308	+	9.28913i	−0.263263	+	0.455985i
$416$	0.275255	+	0.476756i	0.0134955	+	0.0233749i
$417$	−24.4431	+	29.4047i	−1.19698	+	1.43995i
$418$	1.00851	+	0.582262i	0.0493277	+	0.0284794i
$419$	25.0046			1.22155			0.610777	−	0.791803i	$-0.290857\pi$
$419$	25.0046			1.22155			0.610777	+	0.791803i	$0.290857\pi$
$420$	−1.18835	−	4.10160i	−0.0579855	−	0.200138i
$421$	−6.50454			−0.317012			−0.158506	−	0.987358i	$-0.550668\pi$
$421$	−6.50454			−0.317012			−0.158506	+	0.987358i	$0.550668\pi$
$422$	−5.66004	−	3.26782i	−0.275526	−	0.159075i
$423$	8.97056	+	3.17157i	0.436164	+	0.154207i
$424$	7.00316	+	12.1298i	0.340103	+	0.589077i
$425$	−16.8288	+	29.1483i	−0.816315	+	1.41390i
$426$	−2.12983	+	0.786343i	−0.103191	+	0.0380984i
$427$	4.71605	+	9.71517i	0.228226	+	0.470150i
$428$		−	2.90603i		−	0.140468i
$429$	−0.161241	+	0.939780i	−0.00778478	+	0.0453730i
$430$	1.06350	−	0.614014i	0.0512867	−	0.0296104i
$431$	−23.3673	+	13.4911i	−1.12556	+	0.649845i	−0.942816	−	0.333315i	$-0.891833\pi$
$431$	−23.3673	+	13.4911i	−1.12556	+	0.649845i	−0.182749	+	0.983160i	$0.558499\pi$
$432$	2.66012	+	4.46360i	0.127985	+	0.214755i
$433$			11.4607i			0.550766i	0.961335	+	0.275383i	$0.0888047\pi$
$433$			11.4607i			0.550766i	−0.961335	+	0.275383i	$0.911195\pi$
$434$	−11.0525	−	7.48494i	−0.530535	−	0.359289i
$435$	4.08821	+	11.0730i	0.196015	+	0.530910i
$436$	−6.29788	+	10.9082i	−0.301614	+	0.522410i
$437$	−1.04819	−	1.81552i	−0.0501416	−	0.0868479i
$438$	8.26236	+	6.86822i	0.394791	+	0.328176i
$439$	−8.15351	−	4.70743i	−0.389146	−	0.224673i	0.292644	−	0.956221i	$-0.405465\pi$
$439$	−8.15351	−	4.70743i	−0.389146	−	0.224673i	−0.681790	+	0.731548i	$0.738798\pi$
$440$	0.931852			0.0444243
$441$	−17.7474	+	11.2262i	−0.845117	+	0.534582i
$442$	4.48460			0.213311
$443$	−11.6090	−	6.70246i	−0.551561	−	0.318444i	0.198191	−	0.980163i	$-0.436493\pi$
$443$	−11.6090	−	6.70246i	−0.551561	−	0.318444i	−0.749751	+	0.661720i	$0.769827\pi$
$444$	−10.5311	−	8.75417i	−0.499785	−	0.415455i
$445$	1.62605	+	2.81640i	0.0770820	+	0.133510i
$446$	7.50290	−	12.9954i	0.355273	−	0.615350i
$447$	−7.83824	−	21.2301i	−0.370736	−	1.00415i
$448$	−2.19067	−	1.48356i	−0.103499	−	0.0700918i
$449$			23.5464i			1.11122i	0.831442	+	0.555611i	$0.187516\pi$
$449$			23.5464i			1.11122i	−0.831442	+	0.555611i	$0.812484\pi$
$450$	12.1863	−	2.26492i	0.574466	−	0.106769i
$451$	−7.21001	+	4.16270i	−0.339506	+	0.196014i
$452$	7.89079	−	4.55575i	0.371152	−	0.214285i
$453$	−5.88559	+	34.3037i	−0.276529	+	1.61173i
$454$		−	17.6758i		−	0.829564i
$455$	0.592710	+	1.22100i	0.0277867	+	0.0572412i
$456$	−1.89217	+	0.698599i	−0.0886090	+	0.0327149i
$457$	−19.5214	+	33.8120i	−0.913172	+	1.58166i	−0.103615	+	0.994617i	$0.533041\pi$
$457$	−19.5214	+	33.8120i	−0.913172	+	1.58166i	−0.809556	+	0.587042i	$0.800292\pi$
$458$	7.63103	+	13.2173i	0.356575	+	0.617605i
$459$	42.3252	−	0.585962i	1.97557	−	0.0273504i
$460$	−1.45277	−	0.838759i	−0.0677359	−	0.0391074i
$461$	1.78053			0.0829276			0.0414638	−	0.999140i	$-0.486798\pi$
$461$	1.78053			0.0829276			0.0414638	+	0.999140i	$0.486798\pi$
$462$	−1.27526	−	4.40156i	−0.0593302	−	0.204779i
$463$	−3.83647			−0.178296			−0.0891480	−	0.996018i	$-0.528414\pi$
$463$	−3.83647			−0.178296			−0.0891480	+	0.996018i	$0.528414\pi$
$464$	6.33341	+	3.65660i	0.294021	+	0.169753i
$465$	−5.20544	+	6.26206i	−0.241397	+	0.290396i
$466$	−0.973936	−	1.68691i	−0.0451167	−	0.0781444i
$467$	−16.7730	+	29.0517i	−0.776163	+	1.34435i	0.157976	+	0.987443i	$0.449503\pi$
$467$	−16.7730	+	29.0517i	−0.776163	+	1.34435i	−0.934139	+	0.356910i	$0.883830\pi$
$468$	−1.07321	−	1.25529i	−0.0496093	−	0.0580260i
$469$	0.0500767	−	0.697479i	0.00231233	−	0.0322066i
$470$			2.95544i			0.136324i
$471$	17.3672	+	2.97975i	0.800240	+	0.137300i
$472$	4.93563	−	2.84959i	0.227181	−	0.131163i
$473$	1.14128	−	0.658919i	0.0524761	−	0.0302971i
$474$	20.2825	+	3.47993i	0.931608	+	0.159839i
$475$			4.81141i			0.220763i
$476$	−19.3892	+	9.41215i	−0.888705	+	0.431405i
$477$	−27.3052	−	31.9378i	−1.25022	−	1.46233i
$478$	−3.40545	+	5.89841i	−0.155762	+	0.269787i
$479$	−3.13750	−	5.43431i	−0.143356	−	0.248300i	0.785402	−	0.618986i	$-0.212456\pi$
$479$	−3.13750	−	5.43431i	−0.143356	−	0.248300i	−0.928758	+	0.370686i	$0.879123\pi$
$480$	−1.03175	+	1.24118i	−0.0470928	+	0.0566519i
$481$	3.76949	+	2.17632i	0.171874	+	0.0992315i
$482$	1.41446			0.0644270
$483$	−1.97370	+	8.00997i	−0.0898063	+	0.364466i
$484$	1.00000			0.0454545
$485$	14.3146	+	8.26454i	0.649993	+	0.375273i
$486$	−10.2929	−	11.7071i	−0.466895	−	0.531045i
$487$	−9.01203	−	15.6093i	−0.408374	−	0.707325i	0.586334	−	0.810070i	$-0.300571\pi$
$487$	−9.01203	−	15.6093i	−0.408374	−	0.707325i	−0.994708	+	0.102745i	$0.967237\pi$
$488$	2.04088	−	3.53491i	0.0923864	−	0.160018i
$489$	22.0376	−	8.13638i	0.996574	−	0.367940i
$490$	−5.12518	−	4.03504i	−0.231532	−	0.182284i
$491$			16.5145i			0.745289i	0.927974	+	0.372645i	$0.121549\pi$
$491$			16.5145i			0.745289i	−0.927974	+	0.372645i	$0.878451\pi$
$492$	2.43845	−	14.2123i	0.109934	−	0.640742i
$493$	51.5936	−	29.7876i	2.32366	−	1.34157i
$494$	0.555194	−	0.320541i	0.0249794	−	0.0144218i
$495$	−2.74849	+	0.510830i	−0.123535	+	0.0229601i
$496$			5.04524i			0.226538i
$497$	−1.94464	+	2.87151i	−0.0872290	+	0.128805i
$498$	−6.90521	−	18.7029i	−0.309430	−	0.838098i
$499$	19.3772	−	33.5623i	0.867443	−	1.50246i	0.00284253	−	0.999996i	$-0.499095\pi$
$499$	19.3772	−	33.5623i	0.867443	−	1.50246i	0.864601	−	0.502460i	$-0.167571\pi$
$500$	4.25467	+	7.36931i	0.190275	+	0.329566i
$501$	−23.1219	−	19.2205i	−1.03301	−	0.858707i
$502$	12.4755	+	7.20272i	0.556808	+	0.321473i
$503$	−25.1440			−1.12112			−0.560558	−	0.828115i	$-0.689413\pi$
$503$	−25.1440			−1.12112			−0.560558	+	0.828115i	$0.689413\pi$
$504$	7.27463	+	3.17486i	0.324038	+	0.141419i
$505$	10.7250			0.477256
$506$	−1.55902	−	0.900100i	−0.0693068	−	0.0400143i
$507$	−16.9117	−	14.0581i	−0.751075	−	0.624344i
$508$	−8.45069	−	14.6370i	−0.374939	−	0.649413i
$509$	7.49367	−	12.9794i	0.332151	−	0.575302i	−0.650782	−	0.759264i	$-0.725559\pi$
$509$	7.49367	−	12.9794i	0.332151	−	0.575302i	0.982933	+	0.183962i	$0.0588924\pi$
$510$	4.55391	+	12.3344i	0.201651	+	0.546175i
$511$	16.3700	+	1.17531i	0.724166	+	0.0519928i
$512$			1.00000i			0.0441942i
$513$	5.19798	−	3.09778i	0.229496	−	0.136770i
$514$	−13.1522	+	7.59343i	−0.580119	+	0.334932i
$515$	−6.66030	+	3.84533i	−0.293488	+	0.169445i
$516$	−0.385986	+	2.24969i	−0.0169921	+	0.0990370i
$517$			3.17157i			0.139486i
$518$	−20.8650	−	1.49804i	−0.916757	−	0.0658202i
$519$	−8.71703	+	3.21837i	−0.382635	+	0.141271i
$520$	0.256497	−	0.444266i	0.0112481	−	0.0194823i
$521$	−20.3611	−	35.2665i	−0.892037	−	1.54505i	−0.837429	−	0.546546i	$-0.815942\pi$
$521$	−20.3611	−	35.2665i	−0.892037	−	1.54505i	−0.0546085	−	0.998508i	$-0.517391\pi$
$522$	−20.6848	−	7.31319i	−0.905351	−	0.320090i
$523$	8.02282	+	4.63197i	0.350813	+	0.202542i	0.665043	−	0.746805i	$-0.268413\pi$
$523$	8.02282	+	4.63197i	0.350813	+	0.202542i	−0.314230	+	0.949347i	$0.601746\pi$
$524$	1.70523			0.0744934
$525$	13.1148	−	13.6559i	0.572378	−	0.595991i
$526$	−4.11051			−0.179227
$527$	35.5935	+	20.5499i	1.55048	+	0.895170i
$528$	−1.10721	+	1.33195i	−0.0481850	+	0.0579657i
$529$	−9.87964	−	17.1120i	−0.429550	−	0.744002i
$530$	6.52591	−	11.3032i	0.283467	−	0.490980i
$531$	−12.9955	+	11.1105i	−0.563956	+	0.482154i
$532$	−1.72765	+	2.55109i	−0.0749030	+	0.110604i
$533$			4.58322i			0.198521i
$534$	−5.95768	−	1.02218i	−0.257814	−	0.0442339i
$535$	−2.34519	+	1.35399i	−0.101391	+	0.0585382i
$536$	−0.228891	+	0.132150i	−0.00988659	+	0.00570803i
$537$	−2.87662	−	0.493549i	−0.124135	−	0.0212982i
$538$		−	8.10707i		−	0.349521i
$539$	−5.50000	−	4.33013i	−0.236902	−	0.186512i
$540$	2.36274	−	4.22644i	0.101676	−	0.181877i
$541$	−2.23898	+	3.87803i	−0.0962614	+	0.166730i	−0.910134	−	0.414313i	$-0.864022\pi$
$541$	−2.23898	+	3.87803i	−0.0962614	+	0.166730i	0.813873	+	0.581043i	$0.197355\pi$
$542$	6.78606	+	11.7538i	0.291486	+	0.504869i
$543$	−4.75843	+	5.72431i	−0.204204	+	0.245654i
$544$	7.05487	+	4.07313i	0.302475	+	0.174634i
$545$	11.7374			0.502774
$546$	−2.44949	−	0.603566i	−0.104828	−	0.0258303i
$547$	16.5821			0.709001			0.354501	−	0.935056i	$-0.384651\pi$
$547$	16.5821			0.709001			0.354501	+	0.935056i	$0.384651\pi$
$548$	−6.40824	−	3.69980i	−0.273747	−	0.158048i
$549$	−4.08176	+	11.5450i	−0.174205	+	0.492727i
$550$	2.06583	+	3.57812i	0.0880871	+	0.152571i
$551$	4.25820	−	7.37541i	0.181405	−	0.314203i
$552$	2.92504	−	1.07994i	0.124498	−	0.0459653i
$553$	28.2790	−	13.7275i	1.20255	−	0.583753i
$554$			16.3344i			0.693981i
$555$	−2.15796	+	12.5775i	−0.0916002	+	0.533885i
$556$	19.1187	−	11.0382i	0.810814	−	0.468124i
$557$	25.6996	−	14.8377i	1.08893	−	0.628693i	0.155637	−	0.987814i	$-0.450257\pi$
$557$	25.6996	−	14.8377i	1.08893	−	0.628693i	0.933291	+	0.359121i	$0.116924\pi$
$558$	−2.76574	−	14.8809i	−0.117083	−	0.629959i
$559$		−	0.725483i		−	0.0306847i
$560$	−0.176557	+	2.45912i	−0.00746088	+	0.103917i
$561$	4.88695	+	13.2364i	0.206327	+	0.558842i
$562$	−13.4041	+	23.2166i	−0.565418	+	0.979332i
$563$	−16.5970	−	28.7469i	−0.699482	−	1.21154i	−0.968646	−	0.248444i	$-0.920081\pi$
$563$	−16.5970	−	28.7469i	−0.699482	−	1.21154i	0.269165	−	0.963094i	$-0.413252\pi$
$564$	−4.22438	−	3.51159i	−0.177879	−	0.147864i
$565$	−7.35305	−	4.24528i	−0.309345	−	0.178600i
$566$	−10.9676			−0.461004
$567$	−23.1969	−	5.37634i	−0.974177	−	0.225785i
$568$	1.31079			0.0549995
$569$	31.7723	+	18.3438i	1.33196	+	0.769010i	0.985601	−	0.169090i	$-0.0540829\pi$
$569$	31.7723	+	18.3438i	1.33196	+	0.769010i	0.346364	+	0.938100i	$0.387416\pi$
$570$	1.44539	+	1.20150i	0.0605406	+	0.0503253i
$571$	−3.62510	−	6.27886i	−0.151706	−	0.262762i	0.780149	−	0.625594i	$-0.215143\pi$
$571$	−3.62510	−	6.27886i	−0.151706	−	0.262762i	−0.931855	+	0.362832i	$0.881810\pi$
$572$	0.275255	−	0.476756i	0.0115090	−	0.0199342i
$573$	−5.17617	−	14.0198i	−0.216237	−	0.585684i
$574$	−9.61912	−	19.8156i	−0.401494	−	0.827088i
$575$		−	7.43780i		−	0.310178i
$576$	−0.548188	−	2.94949i	−0.0228412	−	0.122895i
$577$	−20.4914	+	11.8307i	−0.853069	+	0.492520i	−0.861685	−	0.507443i	$-0.830591\pi$
$577$	−20.4914	+	11.8307i	−0.853069	+	0.492520i	0.00861630	+	0.999963i	$0.497257\pi$
$578$	42.7484	−	24.6808i	1.77810	−	1.02659i
$579$	−2.87433	+	16.7528i	−0.119453	+	0.696223i
$580$		−	6.81481i		−	0.282970i
$581$	−25.2159	−	17.0767i	−1.04613	−	0.708461i
$582$	−28.8213	+	10.6410i	−1.19468	+	0.441082i
$583$	7.00316	−	12.1298i	0.290041	−	0.502366i
$584$	−3.10160	−	5.37213i	−0.128345	−	0.222300i
$585$	−0.512994	+	1.45097i	−0.0212097	+	0.0599901i
$586$	11.2332	+	6.48547i	0.464038	+	0.267912i
$587$	17.7415			0.732272			0.366136	−	0.930561i	$-0.380681\pi$
$587$	17.7415			0.732272			0.366136	+	0.930561i	$0.380681\pi$
$588$	11.8572	−	2.53139i	0.488981	−	0.104393i
$589$	5.87531			0.242088
$590$	−4.59928	−	2.65539i	−0.189349	−	0.109321i
$591$	−7.52713	+	9.05502i	−0.309625	+	0.372474i
$592$	3.95327	+	6.84727i	0.162478	+	0.281421i
$593$	13.4297	−	23.2608i	0.551490	−	0.955208i	−0.446678	−	0.894695i	$-0.647393\pi$
$593$	13.4297	−	23.2608i	0.551490	−	0.955208i	0.998167	−	0.0605133i	$-0.0192738\pi$
$594$	2.53553	−	4.53553i	0.104034	−	0.186095i
$595$	16.6296	+	11.2619i	0.681748	+	0.461693i
$596$			13.0659i			0.535200i
$597$	34.0590	+	5.84359i	1.39394	+	0.239162i
$598$	−0.858256	+	0.495514i	−0.0350967	+	0.0202631i
$599$	22.1151	−	12.7682i	0.903600	−	0.521694i	0.0252337	−	0.999682i	$-0.491967\pi$
$599$	22.1151	−	12.7682i	0.903600	−	0.521694i	0.878366	+	0.477988i	$0.158634\pi$
$600$	−7.05317	−	1.21013i	−0.287945	−	0.0494035i
$601$			0.718186i			0.0292954i	0.999893	+	0.0146477i	$0.00466268\pi$
$601$			0.718186i			0.0292954i	−0.999893	+	0.0146477i	$0.995337\pi$
$602$	1.52262	+	3.13664i	0.0620574	+	0.127840i
$603$	0.602669	−	0.515252i	0.0245426	−	0.0209827i
$604$	10.0473	−	17.4025i	0.408820	−	0.708097i
$605$	−0.465926	−	0.807007i	−0.0189426	−	0.0328095i
$606$	−12.7432	+	15.3299i	−0.517658	+	0.622734i
$607$	12.2776	+	7.08845i	0.498330	+	0.287711i	0.728024	−	0.685552i	$-0.240439\pi$
$607$	12.2776	+	7.08845i	0.498330	+	0.287711i	−0.229693	+	0.973263i	$0.573772\pi$
$608$	1.16452			0.0472277
$609$	−32.1895	+	9.32619i	−1.30438	+	0.377916i
$610$	−3.80360			−0.154003
$611$	1.51207	+	0.872992i	0.0611716	+	0.0353175i
$612$	−23.0411	−	8.14626i	−0.931382	−	0.329293i
$613$	17.7413	+	30.7288i	0.716564	+	1.24113i	0.962353	+	0.271802i	$0.0876195\pi$
$613$	17.7413	+	30.7288i	0.716564	+	1.24113i	−0.245789	+	0.969323i	$0.579047\pi$
$614$	3.22034	−	5.57779i	0.129962	−	0.225101i
$615$	−12.6056	+	4.65405i	−0.508307	+	0.187669i
$616$	−0.189469	+	2.63896i	−0.00763391	+	0.106327i
$617$		−	37.4755i		−	1.50871i	−0.656469	−	0.754353i	$-0.727951\pi$
$617$		−	37.4755i		−	1.50871i	0.656469	−	0.754353i	$-0.272049\pi$
$618$	2.41727	−	14.0889i	0.0972370	−	0.566739i
$619$	14.2409	−	8.22198i	0.572389	−	0.330469i	−0.185714	−	0.982604i	$-0.559460\pi$
$619$	14.2409	−	8.22198i	0.572389	−	0.330469i	0.758103	+	0.652135i	$0.226126\pi$
$620$	4.07155	−	2.35071i	0.163517	−	0.0944068i
$621$	−8.03538	+	4.78875i	−0.322449	+	0.192166i
$622$			0.199801i			0.00801128i
$623$	−8.30651	+	4.03224i	−0.332793	+	0.161548i
$624$	0.330251	+	0.894494i	0.0132206	+	0.0358084i
$625$	−6.36441	+	11.0235i	−0.254576	+	0.440939i
$626$	3.15515	+	5.46489i	0.126105	+	0.218421i
$627$	1.55109	+	1.28937i	0.0619446	+	0.0514924i
$628$	−8.81051	−	5.08675i	−0.351577	−	0.202983i
$629$	64.4088			2.56815
$630$	−0.827307	−	7.34993i	−0.0329607	−	0.292828i
$631$	−0.906707			−0.0360954			−0.0180477	−	0.999837i	$-0.505745\pi$
$631$	−0.906707			−0.0360954			−0.0180477	+	0.999837i	$0.505745\pi$
$632$	−10.2895	−	5.94062i	−0.409292	−	0.236305i
$633$	−8.70517	−	7.23631i	−0.345999	−	0.287618i
$634$	13.1208	+	22.7259i	0.521093	+	0.902559i
$635$	−7.87479	+	13.6395i	−0.312502	+	0.541269i
$636$	8.40240	+	22.7581i	0.333177	+	0.902417i
$637$	−3.57832	+	1.43027i	−0.141778	+	0.0566693i
$638$		−	7.31319i		−	0.289532i
$639$	−3.86616	+	0.718559i	−0.152943	+	0.0284258i
$640$	0.807007	−	0.465926i	0.0318998	−	0.0184173i
$641$	11.8935	−	6.86673i	0.469766	−	0.271220i	−0.246376	−	0.969174i	$-0.579240\pi$
$641$	11.8935	−	6.86673i	0.469766	−	0.271220i	0.716142	+	0.697955i	$0.245906\pi$
$642$	0.851156	−	4.96090i	0.0335924	−	0.195791i
$643$		−	8.11142i		−	0.319883i	−0.987126	−	0.159942i	$-0.948869\pi$
$643$		−	8.11142i		−	0.319883i	0.987126	−	0.159942i	$-0.0511306\pi$
$644$	2.67071	−	3.94364i	0.105241	−	0.155401i
$645$	1.99536	−	0.736695i	0.0785671	−	0.0290073i
$646$	4.74326	−	8.21557i	0.186621	−	0.323237i
$647$	−25.1115	−	43.4945i	−0.987237	−	1.70994i	−0.631542	−	0.775342i	$-0.717578\pi$
$647$	−25.1115	−	43.4945i	−0.987237	−	1.70994i	−0.355695	−	0.934602i	$-0.615756\pi$
$648$	3.23375	+	8.39898i	0.127034	+	0.329943i
$649$	−4.93563	−	2.84959i	−0.193741	−	0.111856i
$650$	2.27452			0.0892139
$651$	−16.6755	−	16.0148i	−0.653563	−	0.627669i
$652$	−13.5629			−0.531163
$653$	6.31819	+	3.64781i	0.247250	+	0.142750i	0.618504	−	0.785781i	$-0.287739\pi$
$653$	6.31819	+	3.64781i	0.247250	+	0.142750i	−0.371255	+	0.928531i	$0.621072\pi$
$654$	−13.9461	+	16.7769i	−0.545336	+	0.656030i
$655$	−0.794511	−	1.37613i	−0.0310441	−	0.0537700i
$656$	−4.16270	+	7.21001i	−0.162526	+	0.281504i
$657$	12.0931	+	14.1448i	0.471796	+	0.551840i
$658$	−8.36965	−	0.600914i	−0.326283	−	0.0234261i
$659$			29.7035i			1.15709i	0.815652	+	0.578543i	$0.196378\pi$
$659$			29.7035i			1.15709i	−0.815652	+	0.578543i	$0.803622\pi$
$660$	1.59077	+	0.272933i	0.0619206	+	0.0106239i
$661$	36.3248	−	20.9721i	1.41287	−	0.815721i	0.417212	−	0.908809i	$-0.363007\pi$
$661$	36.3248	−	20.9721i	1.41287	−	0.815721i	0.995658	+	0.0930887i	$0.0296740\pi$
$662$	7.62120	−	4.40010i	0.296206	−	0.171015i
$663$	7.65569	+	1.31351i	0.297323	+	0.0510125i
$664$			11.5106i			0.446698i
$665$	2.86370	+	0.205605i	0.111050	+	0.00797301i
$666$	−15.4137	−	18.0288i	−0.597270	−	0.698602i
$667$	−6.58260	+	11.4014i	−0.254879	+	0.441464i
$668$	8.67972	+	15.0337i	0.335828	+	0.581672i
$669$	16.6145	−	19.9870i	0.642355	−	0.772742i
$670$	0.213293	+	0.123145i	0.00824021	+	0.00475749i
$671$	−4.08176			−0.157575
$672$	−3.30518	−	3.17423i	−0.127500	−	0.122449i
$673$	−9.22224			−0.355491			−0.177746	−	0.984076i	$-0.556880\pi$
$673$	−9.22224			−0.355491			−0.177746	+	0.984076i	$0.556880\pi$
$674$	23.7901	+	13.7352i	0.916360	+	0.529061i
$675$	21.4666	−	0.297191i	0.826251	−	0.0114389i
$676$	6.34847	+	10.9959i	0.244172	+	0.422918i
$677$	−2.02361	+	3.50499i	−0.0777736	+	0.134708i	−0.902289	−	0.431132i	$-0.858114\pi$
$677$	−2.02361	+	3.50499i	−0.0777736	+	0.134708i	0.824515	+	0.565839i	$0.191448\pi$
$678$	14.8048	−	5.46599i	0.568574	−	0.209920i
$679$	−26.3153	+	38.8579i	−1.00989	+	1.49123i
$680$		−	7.59111i		−	0.291106i
$681$	5.17711	−	30.1744i	0.198387	−	1.15629i
$682$	4.36931	−	2.52262i	0.167310	−	0.0965962i
$683$	5.59134	−	3.22816i	0.213947	−	0.123522i	−0.389198	−	0.921154i	$-0.627248\pi$
$683$	5.59134	−	3.22816i	0.213947	−	0.123522i	0.603144	+	0.797632i	$0.293914\pi$
$684$	−3.43475	+	0.638379i	−0.131331	+	0.0244090i
$685$			6.89533i			0.263457i
$686$	12.4691	−	13.6938i	0.476073	−	0.522834i
$687$	9.15572	+	24.7985i	0.349312	+	0.946121i
$688$	0.658919	−	1.14128i	0.0251210	−	0.0435109i
$689$	−3.85531	−	6.67759i	−0.146876	−	0.254396i
$690$	−2.23437	−	1.85736i	−0.0850611	−	0.0707085i
$691$	18.4746	+	10.6663i	0.702807	+	0.405766i	0.808392	−	0.588644i	$-0.200338\pi$
$691$	18.4746	+	10.6663i	0.702807	+	0.405766i	−0.105585	+	0.994410i	$0.533671\pi$
$692$	5.36484			0.203941
$693$	−0.887810	−	7.88745i	−0.0337251	−	0.299619i
$694$	16.6700			0.632783
$695$	−17.8158	−	10.2860i	−0.675792	−	0.390169i
$696$	9.74082	+	8.09721i	0.369225	+	0.306924i
$697$	33.9105	+	58.7346i	1.28445	+	2.22473i
$698$	−13.2251	+	22.9065i	−0.500577	+	0.867025i
$699$	−1.16853	−	3.16499i	−0.0441978	−	0.119711i
$700$	−9.83391	+	4.77369i	−0.371687	+	0.180428i
$701$		−	33.3214i		−	1.25853i	−0.777190	−	0.629266i	$-0.783356\pi$
$701$		−	33.3214i		−	1.25853i	0.777190	−	0.629266i	$-0.216644\pi$
$702$	−1.46442	−	2.45726i	−0.0552711	−	0.0927433i
$703$	7.97381	−	4.60368i	0.300738	−	0.173631i
$704$	0.866025	−	0.500000i	0.0326396	−	0.0188445i
$705$	−0.865627	+	5.04524i	−0.0326014	+	0.190015i
$706$			16.0613i			0.604474i
$707$	−2.18066	+	30.3727i	−0.0820122	+	1.14228i
$708$	9.26028	−	3.41894i	0.348023	−	0.128492i
$709$	−12.8508	+	22.2583i	−0.482624	+	0.835928i	−0.999801	−	0.0199497i	$-0.993649\pi$
$709$	−12.8508	+	22.2583i	−0.482624	+	0.835928i	0.517177	+	0.855878i	$0.326983\pi$
$710$	−0.610730	−	1.05782i	−0.0229203	−	0.0396991i
$711$	33.6052	+	11.8812i	1.26029	+	0.445581i
$712$	3.02236	+	1.74496i	0.113268	+	0.0653952i
$713$	−9.08244			−0.340140
$714$	−35.8563	+	10.3886i	−1.34189	+	0.388782i
$715$	−0.512994			−0.0191849
$716$	1.45932	+	0.842541i	0.0545375	+	0.0314872i
$717$	−7.54107	+	9.07178i	−0.281626	+	0.338792i
$718$	−10.0191	−	17.3536i	−0.373909	−	0.647630i
$719$	5.41064	−	9.37150i	0.201783	−	0.349498i	−0.747320	−	0.664464i	$-0.768660\pi$
$719$	5.41064	−	9.37150i	0.201783	−	0.349498i	0.949103	+	0.314966i	$0.101993\pi$
$720$	−2.12484	+	1.81664i	−0.0791883	+	0.0677020i
$721$	−9.53557	−	19.6435i	−0.355123	−	0.731562i
$722$			17.6439i			0.656637i
$723$	2.41464	+	0.414286i	0.0898014	+	0.0154075i
$724$	3.72191	−	2.14884i	0.138324	−	0.0798612i
$725$	26.1675	−	15.1078i	0.971835	−	0.561089i
$726$	1.70711	+	0.292893i	0.0633567	+	0.0108703i
$727$			4.14730i			0.153815i	0.997038	+	0.0769073i	$0.0245046\pi$
$727$			4.14730i			0.153815i	−0.997038	+	0.0769073i	$0.975495\pi$
$728$	1.20599	+	0.816717i	0.0446968	+	0.0302696i
$729$	−14.1421	−	23.0000i	−0.523783	−	0.851852i
$730$	−2.89023	+	5.00603i	−0.106972	+	0.185281i
$731$	−5.36773	−	9.29717i	−0.198532	−	0.343868i
$732$	4.51936	−	5.43671i	0.167040	−	0.200947i
$733$	−30.6522	−	17.6970i	−1.13216	−	0.653655i	−0.187685	−	0.982229i	$-0.560098\pi$
$733$	−30.6522	−	17.6970i	−1.13216	−	0.653655i	−0.944478	+	0.328574i	$0.893432\pi$
$734$	−33.1338			−1.22299
$735$	−7.56740	−	8.38937i	−0.279128	−	0.309447i
$736$	−1.80020			−0.0663562
$737$	0.228891	+	0.132150i	0.00843132	+	0.00486782i
$738$	8.32540	−	23.5478i	0.306462	−	0.866806i
$739$	2.87990	+	4.98813i	0.105939	+	0.183491i	0.914121	−	0.405441i	$-0.132882\pi$
$739$	2.87990	+	4.98813i	0.105939	+	0.183491i	−0.808183	+	0.588932i	$0.799549\pi$
$740$	3.68386	−	6.38064i	0.135421	−	0.234557i
$741$	1.04166	−	0.384586i	0.0382663	−	0.0141281i
$742$	30.6832	+	20.7793i	1.12642	+	0.762831i
$743$			19.5508i			0.717251i	0.933482	+	0.358625i	$0.116754\pi$
$743$			19.5508i			0.717251i	−0.933482	+	0.358625i	$0.883246\pi$
$744$	−1.47772	+	8.61277i	−0.0541758	+	0.315759i
$745$	10.5443	−	6.08774i	0.386313	−	0.223038i
$746$	−18.4991	+	10.6805i	−0.677301	+	0.391040i
$747$	−6.30997	−	33.9504i	−0.230870	−	1.24218i
$748$		−	8.14626i		−	0.297857i
$749$	−3.35761	−	6.91675i	−0.122684	−	0.252733i
$750$	5.10476	+	13.8264i	0.186399	+	0.504867i
$751$	7.22545	−	12.5148i	0.263660	−	0.456673i	−0.703551	−	0.710644i	$-0.748404\pi$
$751$	7.22545	−	12.5148i	0.263660	−	0.456673i	0.967212	+	0.253971i	$0.0817368\pi$
$752$	1.58579	+	2.74666i	0.0578277	+	0.100160i
$753$	19.1873	+	15.9498i	0.699226	+	0.581243i
$754$	−3.48661	−	2.01299i	−0.126975	−	0.0733089i
$755$	−18.7252			−0.681481
$756$	11.4887	+	7.55051i	0.417839	+	0.274609i
$757$	−17.8099			−0.647312			−0.323656	−	0.946175i	$-0.604912\pi$
$757$	−17.8099			−0.647312			−0.323656	+	0.946175i	$0.604912\pi$
$758$	23.8257	+	13.7558i	0.865388	+	0.499632i
$759$	−2.39778	−	1.99319i	−0.0870338	−	0.0723483i
$760$	−0.542582	−	0.939780i	−0.0196815	−	0.0340894i
$761$	18.3169	−	31.7259i	0.663988	−	1.15006i	−0.315570	−	0.948902i	$-0.602196\pi$
$761$	18.3169	−	31.7259i	0.663988	−	1.15006i	0.979559	−	0.201159i	$-0.0644709\pi$
$762$	−10.1391	−	27.4621i	−0.367303	−	0.994848i
$763$	−2.38650	+	33.2397i	−0.0863971	+	1.20336i
$764$			8.62838i			0.312164i
$765$	4.16136	+	22.3899i	0.150454	+	0.809509i
$766$	8.10506	−	4.67946i	0.292848	−	0.169076i
$767$	−2.71712	+	1.56873i	−0.0981094	+	0.0566435i
$768$	−0.292893	+	1.70711i	−0.0105689	+	0.0615999i
$769$		−	4.38302i		−	0.158056i	−0.996872	−	0.0790278i	$-0.974818\pi$
$769$		−	4.38302i		−	0.158056i	0.996872	−	0.0790278i	$-0.0251816\pi$
$770$	2.21794	−	1.07666i	0.0799289	−	0.0388000i
$771$	−24.6763	+	9.11061i	−0.888695	+	0.328110i
$772$	4.90678	−	8.49880i	0.176599	−	0.305878i
$773$	−2.35238	−	4.07445i	−0.0846094	−	0.146548i	0.820615	−	0.571481i	$-0.193631\pi$
$773$	−2.35238	−	4.07445i	−0.0846094	−	0.146548i	−0.905225	+	0.424933i	$0.860298\pi$
$774$	−1.31784	+	3.72741i	−0.0473687	+	0.133979i
$775$	18.0525	+	10.4226i	0.648464	+	0.374391i
$776$	17.7379			0.636753
$777$	−35.1801	−	8.66855i	−1.26208	−	0.310982i
$778$	5.78537			0.207416
$779$	8.39623	+	4.84757i	0.300826	+	0.173682i
$780$	0.567990	−	0.683283i	0.0203373	−	0.0244655i
$781$	−0.655395	−	1.13518i	−0.0234519	−	0.0406198i
$782$	−7.33245	+	12.7002i	−0.262208	+	0.454157i
$783$	−33.1692	−	18.5428i	−1.18537	−	0.662667i
$784$	−6.92820	−	1.00000i	−0.247436	−	0.0357143i
$785$			9.48019i			0.338362i
$786$	2.91101	+	0.499451i	0.103832	+	0.0178148i
$787$	−40.9267	+	23.6290i	−1.45888	+	0.842284i	−0.998956	−	0.0456761i	$-0.985456\pi$
$787$	−40.9267	+	23.6290i	−1.45888	+	0.842284i	−0.459922	+	0.887960i	$0.652122\pi$
$788$	5.88751	−	3.39916i	0.209734	−	0.121090i
$789$	−7.01708	−	1.20394i	−0.249815	−	0.0428614i
$790$			11.0715i			0.393908i
$791$	13.5175	−	19.9603i	0.480627	−	0.709707i
$792$	−2.28024	+	1.94949i	−0.0810248	+	0.0692721i
$793$	−1.12353	+	1.94601i	−0.0398976	+	0.0691047i
$794$	0.431405	+	0.747216i	0.0153100	+	0.0265177i
$795$	14.4510	−	17.3844i	0.512526	−	0.616560i
$796$	−17.2783	−	9.97564i	−0.612413	−	0.353577i
$797$	7.05453			0.249884			0.124942	−	0.992164i	$-0.460125\pi$
$797$	7.05453			0.249884			0.124942	+	0.992164i	$0.460125\pi$
$798$	−3.69647	+	3.84897i	−0.130854	+	0.136252i
$799$	25.8365			0.914029
$800$	3.57812	+	2.06583i	0.126506	+	0.0730380i
$801$	−9.87100	−	3.48993i	−0.348775	−	0.123310i
$802$	14.5362	+	25.1775i	0.513293	+	0.889049i
$803$	−3.10160	+	5.37213i	−0.109453	+	0.189578i
$804$	−0.429448	+	0.158554i	−0.0151455	+	0.00559177i
$805$	−4.42690	−	0.317837i	−0.156028	−	0.0112023i
$806$		−	2.77746i		−	0.0978318i
$807$	2.37451	−	13.8396i	0.0835866	−	0.487178i
$808$	9.96739	−	5.75467i	0.350651	−	0.202449i
$809$	0.161040	−	0.0929765i	0.00566187	−	0.00326888i	−0.497166	−	0.867655i	$-0.665626\pi$
$809$	0.161040	−	0.0929765i	0.00566187	−	0.00326888i	0.502828	+	0.864386i	$0.332293\pi$
$810$	5.27135	−	6.52296i	0.185216	−	0.229194i
$811$			20.6191i			0.724034i	0.932171	+	0.362017i	$0.117912\pi$
$811$			20.6191i			0.724034i	−0.932171	+	0.362017i	$0.882088\pi$
$812$	19.2992	+	1.38562i	0.677270	+	0.0486258i
$813$	8.14192	+	22.0526i	0.285550	+	0.773418i
$814$	3.95327	−	6.84727i	0.138562	−	0.239997i
$815$	6.31930	+	10.9453i	0.221355	+	0.383399i
$816$	10.8504	+	9.01960i	0.379841	+	0.315749i
$817$	−1.32905	−	0.767327i	−0.0464976	−	0.0268454i
$818$	−28.5288			−0.997486
$819$	−4.00476	−	1.74779i	−0.139938	−	0.0610728i
$820$	7.75804			0.270922
$821$	−33.8426	−	19.5390i	−1.18111	−	0.681916i	−0.224842	−	0.974395i	$-0.572187\pi$
$821$	−33.8426	−	19.5390i	−1.18111	−	0.681916i	−0.956272	+	0.292479i	$0.905520\pi$
$822$	−9.85591	−	8.19289i	−0.343764	−	0.285760i
$823$	13.4961	+	23.3759i	0.470443	+	0.814832i	0.999429	−	0.0337992i	$-0.0107607\pi$
$823$	13.4961	+	23.3759i	0.470443	+	0.814832i	−0.528985	+	0.848631i	$0.677427\pi$
$824$	−4.12654	+	7.14738i	−0.143755	+	0.248991i
$825$	2.47858	+	6.71329i	0.0862931	+	0.233727i
$826$	8.45510	−	12.4850i	0.294190	−	0.434410i
$827$		−	9.79091i		−	0.340463i	−0.985404	−	0.170232i	$-0.945548\pi$
$827$		−	9.79091i		−	0.340463i	0.985404	−	0.170232i	$-0.0544516\pi$
$828$	5.30967	−	0.986848i	0.184524	−	0.0342953i
$829$	−11.4341	+	6.60149i	−0.397123	+	0.229279i	−0.685242	−	0.728315i	$-0.740304\pi$
$829$	−11.4341	+	6.60149i	−0.397123	+	0.229279i	0.288119	+	0.957595i	$0.406970\pi$
$830$	9.28913	−	5.36308i	0.322430	−	0.186155i
$831$	−4.78423	+	27.8845i	−0.165963	+	0.967303i
$832$		−	0.550510i		−	0.0190855i
$833$	−35.2744	+	44.8045i	−1.22218	+	1.55238i
$834$	35.8707	−	13.2436i	1.24210	−	0.458590i
$835$	8.08821	−	14.0092i	0.279904	−	0.484808i
$836$	−0.582262	−	1.00851i	−0.0201380	−	0.0348800i
$837$	−0.362905	−	26.2133i	−0.0125438	−	0.906066i
$838$	−21.6546	−	12.5023i	−0.748046	−	0.431885i
$839$	−38.9639			−1.34518			−0.672592	−	0.740013i	$-0.734819\pi$
$839$	−38.9639			−1.34518			−0.672592	+	0.740013i	$0.734819\pi$
$840$	−1.02166	+	4.14626i	−0.0352506	+	0.143060i
$841$	−24.4828			−0.844234
$842$	5.63309	+	3.25227i	0.194129	+	0.112081i
$843$	−29.6822	+	35.7072i	−1.02231	+	1.22982i
$844$	3.26782	+	5.66004i	0.112483	+	0.194827i
$845$	5.91583	−	10.2465i	0.203511	−	0.352491i
$846$	−6.18295	−	7.23194i	−0.212574	−	0.248639i
$847$	2.38014	−	1.15539i	0.0817826	−	0.0396998i
$848$		−	14.0063i		−	0.480979i
$849$	−18.7229	−	3.21235i	−0.642570	−	0.110248i
$850$	29.1483	−	16.8288i	0.999778	−	0.577222i
$851$	−12.3264	+	7.11668i	−0.422545	+	0.243957i
$852$	2.23766	+	0.383921i	0.0766609	+	0.0131529i
$853$		−	30.7592i		−	1.05318i	−0.850121	−	0.526588i	$-0.823471\pi$
$853$		−	30.7592i		−	1.05318i	0.850121	−	0.526588i	$-0.176529\pi$
$854$	0.773367	−	10.7716i	0.0264641	−	0.368597i
$855$	2.11552	+	2.47443i	0.0723491	+	0.0846238i
$856$	−1.45301	+	2.51669i	−0.0496630	+	0.0860188i
$857$	7.71950	+	13.3706i	0.263693	+	0.456730i	0.967220	−	0.253938i	$-0.0817260\pi$
$857$	7.71950	+	13.3706i	0.263693	+	0.456730i	−0.703527	+	0.710668i	$0.748393\pi$
$858$	0.609528	−	0.733253i	0.0208090	−	0.0250328i
$859$	19.1628	+	11.0636i	0.653826	+	0.377486i	0.789920	−	0.613209i	$-0.210122\pi$
$859$	19.1628	+	11.0636i	0.653826	+	0.377486i	−0.136095	+	0.990696i	$0.543455\pi$
$860$	−1.22803			−0.0418754
$861$	−10.6170	−	36.6447i	−0.361827	−	1.24885i
$862$	26.9823			0.919019
$863$	11.2267	+	6.48172i	0.382160	+	0.220640i	0.678758	−	0.734362i	$-0.262519\pi$
$863$	11.2267	+	6.48172i	0.382160	+	0.220640i	−0.296597	+	0.955003i	$0.595852\pi$
$864$	−0.0719302	−	5.19565i	−0.00244711	−	0.176760i
$865$	−2.49962	−	4.32947i	−0.0849896	−	0.147206i
$866$	5.73035	−	9.92526i	0.194725	−	0.337274i
$867$	80.2050	−	29.6121i	2.72390	−	1.00568i
$868$	5.82925	+	12.0084i	0.197858	+	0.407591i
$869$			11.8812i			0.403043i
$870$	1.99601	−	11.6336i	0.0676711	−	0.394416i
$871$	0.126007	−	0.0727501i	0.00426958	−	0.00246504i
$872$	10.9082	−	6.29788i	0.369400	−	0.213273i
$873$	−52.3177	+	9.72370i	−1.77069	+	0.329097i
$874$			2.09638i			0.0709110i
$875$	18.6412	+	12.6242i	0.630187	+	0.426774i
$876$	−3.72130	−	10.0792i	−0.125731	−	0.340546i
$877$	10.6366	−	18.4232i	0.359174	−	0.622107i	−0.628649	−	0.777689i	$-0.716392\pi$
$877$	10.6366	−	18.4232i	0.359174	−	0.622107i	0.987823	+	0.155582i	$0.0497252\pi$
$878$	4.70743	+	8.15351i	0.158868	+	0.275167i
$879$	17.2767	+	14.3615i	0.582727	+	0.484402i
$880$	−0.807007	−	0.465926i	−0.0272042	−	0.0157064i
$881$	−14.9446			−0.503496			−0.251748	−	0.967793i	$-0.581005\pi$
$881$	−14.9446			−0.503496			−0.251748	+	0.967793i	$0.581005\pi$
$882$	20.9829	−	0.848469i	0.706529	−	0.0285694i
$883$	51.3538			1.72819			0.864097	−	0.503325i	$-0.167890\pi$
$883$	51.3538			1.72819			0.864097	+	0.503325i	$0.167890\pi$
$884$	−3.88378	−	2.24230i	−0.130626	−	0.0754167i
$885$	−7.07371	−	5.88014i	−0.237780	−	0.197659i
$886$	6.70246	+	11.6090i	0.225174	+	0.390012i
$887$	19.6572	−	34.0472i	0.660023	−	1.14319i	−0.320586	−	0.947220i	$-0.603880\pi$
$887$	19.6572	−	34.0472i	0.660023	−	1.14319i	0.980609	−	0.195974i	$-0.0627870\pi$
$888$	4.74314	+	12.8469i	0.159169	+	0.431114i
$889$	−37.0254	−	25.0743i	−1.24179	−	0.840964i
$890$		−	3.25209i		−	0.109010i
$891$	5.65685	−	7.00000i	0.189512	−	0.234509i
$892$	−12.9954	+	7.50290i	−0.435118	+	0.251216i
$893$	3.19856	−	1.84669i	0.107036	−	0.0617970i
$894$	−3.82692	+	22.3049i	−0.127991	+	0.745987i
$895$		−	1.57025i		−	0.0524876i
$896$	1.15539	+	2.38014i	0.0385990	+	0.0795149i
$897$	−1.61027	+	0.594518i	−0.0537652	+	0.0198504i
$898$	11.7732	−	20.3918i	0.392876	−	0.680482i
$899$	−18.4484	−	31.9536i	−0.615289	−	1.06571i
$900$	−11.6861	−	4.13165i	−0.389536	−	0.137722i
$901$	−98.8128	−	57.0496i	−3.29193	−	1.90060i
$902$	8.32540			0.277206
$903$	1.68058	+	5.80054i	0.0559262	+	0.193030i
$904$	−9.11150			−0.303044
$905$	−3.46827	−	2.00240i	−0.115289	−	0.0665622i
$906$	22.2489	−	26.7651i	0.739171	−	0.889211i
$907$	−25.1172	−	43.5043i	−0.834003	−	1.44453i	−0.894840	−	0.446387i	$-0.852710\pi$
$907$	−25.1172	−	43.5043i	−0.834003	−	1.44453i	0.0608372	−	0.998148i	$-0.480623\pi$
$908$	−8.83788	+	15.3077i	−0.293295	+	0.508002i
$909$	−26.2441	+	22.4374i	−0.870460	+	0.744200i
$910$	0.0971963	−	1.35377i	0.00322203	−	0.0448770i
$911$			51.5948i			1.70941i	0.519112	+	0.854706i	$0.326263\pi$
$911$			51.5948i			1.70941i	−0.519112	+	0.854706i	$0.673737\pi$
$912$	1.98797	+	0.341081i	0.0658282	+	0.0112943i
$913$	9.96846	−	5.75529i	0.329908	−	0.190472i
$914$	33.8120	−	19.5214i	1.11840	−	0.645710i
$915$	−6.49315	−	1.11405i	−0.214657	−	0.0368293i
$916$		−	15.2621i		−	0.504273i
$917$	4.05869	−	1.97021i	0.134030	−	0.0650622i
$918$	−36.9477	−	20.6551i	−1.21945	−	0.681721i
$919$	−8.47067	+	14.6716i	−0.279422	+	0.483972i	−0.971241	−	0.238098i	$-0.923476\pi$
$919$	−8.47067	+	14.6716i	−0.279422	+	0.483972i	0.691820	+	0.722070i	$0.256809\pi$
$920$	0.838759	+	1.45277i	0.0276531	+	0.0478965i
$921$	7.13116	−	8.57867i	0.234980	−	0.282677i
$922$	−1.54198	−	0.890265i	−0.0507826	−	0.0293193i
$923$	−0.721603			−0.0237518
$924$	−1.09638	+	4.44949i	−0.0360681	+	0.146377i
$925$	32.6671			1.07409
$926$	3.32248	+	1.91824i	0.109184	+	0.0630371i
$927$	8.25309	−	23.3433i	0.271067	−	0.766693i
$928$	−3.65660	−	6.33341i	−0.120034	−	0.207904i
$929$	8.57136	−	14.8460i	0.281217	−	0.487082i	−0.690468	−	0.723363i	$-0.742595\pi$
$929$	8.57136	−	14.8460i	0.281217	−	0.487082i	0.971685	+	0.236281i	$0.0759285\pi$
$930$	7.63907	−	2.82038i	0.250495	−	0.0924840i
$931$	−1.16452	+	8.06806i	−0.0381658	+	0.264420i
$932$			1.94787i			0.0638047i
$933$	−0.0585203	+	0.341081i	−0.00191587	+	0.0111665i
$934$	29.0517	−	16.7730i	0.950601	−	0.548830i
$935$	−6.57409	+	3.79555i	−0.214996	+	0.124128i
$936$	0.301783	+	1.62372i	0.00986409	+	0.0530731i
$937$			44.9070i			1.46705i	0.679664	+	0.733524i	$0.262126\pi$
$937$			44.9070i			1.46705i	−0.679664	+	0.733524i	$0.737874\pi$
$938$	−0.392107	+	0.578996i	−0.0128028	+	0.0189049i
$939$	3.78556	+	10.2533i	0.123537	+	0.334603i
$940$	1.47772	−	2.55948i	0.0481978	−	0.0834811i
$941$	23.7770	+	41.1830i	0.775108	+	1.34253i	0.934734	+	0.355349i	$0.115638\pi$
$941$	23.7770	+	41.1830i	0.775108	+	1.34253i	−0.159625	+	0.987178i	$0.551029\pi$
$942$	−13.5506	−	11.2642i	−0.441502	−	0.367006i
$943$	−12.9795	−	7.49369i	−0.422669	−	0.244028i
$944$	−5.69918			−0.185492
$945$	0.740443	−	12.7894i	0.0240866	−	0.416040i
$946$	−1.31784			−0.0428466
$947$	−3.67949	−	2.12436i	−0.119567	−	0.0690323i	0.439024	−	0.898476i	$-0.355324\pi$
$947$	−3.67949	−	2.12436i	−0.119567	−	0.0690323i	−0.558591	+	0.829443i	$0.688658\pi$
$948$	−15.8252	−	13.1550i	−0.513979	−	0.427254i
$949$	1.70746	+	2.95741i	0.0554266	+	0.0960017i
$950$	2.40571	−	4.16680i	0.0780514	−	0.135189i
$951$	15.7423	+	42.6385i	0.510480	+	1.38265i
$952$	21.4977	+	1.54346i	0.696743	+	0.0500239i
$953$		−	1.71165i		−	0.0554459i	−0.999616	−	0.0277229i	$-0.991174\pi$
$953$		−	1.71165i		−	0.0554459i	0.999616	−	0.0277229i	$-0.00882562\pi$
$954$	7.67810	+	41.3115i	0.248588	+	1.33751i
$955$	6.96316	−	4.02018i	0.225323	−	0.130090i
$956$	5.89841	−	3.40545i	0.190768	−	0.110140i
$957$	2.14198	−	12.4844i	0.0692405	−	0.403563i
$958$			6.27500i			0.202736i
$959$	−19.5272	−	1.40199i	−0.630568	−	0.0452727i
$960$	1.51411	−	0.559018i	0.0488678	−	0.0180422i
$961$	−2.77276	+	4.80256i	−0.0894438	+	0.154921i
$962$	−2.17632	−	3.76949i	−0.0701673	−	0.121533i
$963$	2.90603	−	8.21949i	0.0936454	−	0.264869i
$964$	−1.22496	−	0.707231i	−0.0394533	−	0.0227784i
$965$	−9.14479			−0.294381
$966$	5.71425	−	5.94999i	0.183853	−	0.191438i
$967$	48.2546			1.55176			0.775881	−	0.630879i	$-0.217306\pi$
$967$	48.2546			1.55176			0.775881	+	0.630879i	$0.217306\pi$
$968$	−0.866025	−	0.500000i	−0.0278351	−	0.0160706i
$969$	10.5035	−	12.6356i	0.337422	−	0.405914i
$970$	−8.26454	−	14.3146i	−0.265358	−	0.459614i
$971$	1.32109	−	2.28820i	0.0423958	−	0.0734317i	−0.844049	−	0.536266i	$-0.819834\pi$
$971$	1.32109	−	2.28820i	0.0423958	−	0.0734317i	0.886445	+	0.462835i	$0.153168\pi$
$972$	3.06035	+	15.2851i	0.0981609	+	0.490270i
$973$	32.7517	−	48.3621i	1.04997	−	1.55042i
$974$			18.0241i			0.577528i
$975$	3.88284	+	0.666191i	0.124351	+	0.0213352i
$976$	−3.53491	+	2.04088i	−0.113150	+	0.0653270i
$977$	−48.9408	+	28.2560i	−1.56575	+	0.903989i	−0.569100	+	0.822269i	$0.692708\pi$
$977$	−48.9408	+	28.2560i	−1.56575	+	0.903989i	−0.996655	+	0.0817204i	$0.973959\pi$
$978$	−23.1533	−	3.97248i	−0.740361	−	0.127026i
$979$		−	3.48993i		−	0.111539i
$980$	2.42102	+	6.05704i	0.0773367	+	0.193485i
$981$	−28.7213	+	24.5553i	−0.917001	+	0.783990i
$982$	8.25725	−	14.3020i	0.263500	−	0.456395i
$983$	−11.6198	−	20.1261i	−0.370615	−	0.641923i	0.619046	−	0.785355i	$-0.287520\pi$
$983$	−11.6198	−	20.1261i	−0.370615	−	0.641923i	−0.989660	+	0.143432i	$0.954186\pi$
$984$	−9.21794	+	11.0890i	−0.293857	+	0.353505i
$985$	−5.48629	−	3.16751i	−0.174808	−	0.100925i
$986$	−59.5752			−1.89726
$987$	−14.1119	−	3.47724i	−0.449186	−	0.110682i
$988$	−0.641083			−0.0203956
$989$	2.05453	+	1.18618i	0.0653303	+	0.0377185i
$990$	2.63567	+	0.931852i	0.0837672	+	0.0296162i
$991$	−10.9372	−	18.9438i	−0.347432	−	0.601771i	0.638360	−	0.769738i	$-0.279613\pi$
$991$	−10.9372	−	18.9438i	−0.347432	−	0.601771i	−0.985793	+	0.167967i	$0.946280\pi$
$992$	2.52262	−	4.36931i	0.0800933	−	0.138726i
$993$	14.2990	−	5.27924i	0.453764	−	0.167532i
$994$	3.11986	−	1.51448i	0.0989560	−	0.0480363i
$995$			18.5916i			0.589394i
$996$	−3.37137	+	19.6498i	−0.106826	+	0.622628i
$997$	−8.02545	+	4.63349i	−0.254168	+	0.146744i	−0.621671	−	0.783278i	$-0.713546\pi$
$997$	−8.02545	+	4.63349i	−0.254168	+	0.146744i	0.367503	+	0.930022i	$0.380213\pi$
$998$	−33.5623	+	19.3772i	−1.06240	+	0.613375i
$999$	−21.0324	−	35.2917i	−0.665434	−	1.11658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.k.e.89.1	✓	8
3.2	odd	2		462.2.k.f.89.3	yes	8
7.3	odd	6		462.2.k.f.353.3	yes	8
21.17	even	6	inner	462.2.k.e.353.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.e.89.1	✓	8	1.1	even	1	trivial
462.2.k.e.353.1	yes	8	21.17	even	6	inner
462.2.k.f.89.3	yes	8	3.2	odd	2
462.2.k.f.353.3	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.465926 - 0.807007i) q^{5} +(0.599900 + 1.62484i) q^{6} +(2.19067 + 1.48356i) q^{7} -1.00000i q^{8} +(0.548188 + 2.94949i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.465926 - 0.807007i) q^{5} +(0.599900 + 1.62484i) q^{6} +(2.19067 + 1.48356i) q^{7} -1.00000i q^{8} +(0.548188 + 2.94949i) q^{9} +(-0.807007 + 0.465926i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(0.292893 - 1.70711i) q^{12} +0.550510i q^{13} +(-1.15539 - 2.38014i) q^{14} +(-1.51411 + 0.559018i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.07313 + 7.05487i) q^{17} +(1.00000 - 2.82843i) q^{18} +(1.00851 + 0.582262i) q^{19} +0.931852 q^{20} +(-1.27526 - 4.40156i) q^{21} +1.00000 q^{22} +(-1.55902 - 0.900100i) q^{23} +(-1.10721 + 1.33195i) q^{24} +(2.06583 + 3.57812i) q^{25} +(0.275255 - 0.476756i) q^{26} +(2.53553 - 4.53553i) q^{27} +(-0.189469 + 2.63896i) q^{28} -7.31319i q^{29} +(1.59077 + 0.272933i) q^{30} +(4.36931 - 2.52262i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.70711 + 0.292893i) q^{33} -8.14626i q^{34} +(2.21794 - 1.07666i) q^{35} +(-2.28024 + 1.94949i) q^{36} +(3.95327 - 6.84727i) q^{37} +(-0.582262 - 1.00851i) q^{38} +(0.609528 - 0.733253i) q^{39} +(-0.807007 - 0.465926i) q^{40} +8.32540 q^{41} +(-1.09638 + 4.44949i) q^{42} -1.31784 q^{43} +(-0.866025 - 0.500000i) q^{44} +(2.63567 + 0.931852i) q^{45} +(0.900100 + 1.55902i) q^{46} +(1.58579 - 2.74666i) q^{47} +(1.62484 - 0.599900i) q^{48} +(2.59808 + 6.50000i) q^{49} -4.13165i q^{50} +(2.38599 - 13.9065i) q^{51} +(-0.476756 + 0.275255i) q^{52} +(-12.1298 + 7.00316i) q^{53} +(-4.46360 + 2.66012i) q^{54} +0.931852i q^{55} +(1.48356 - 2.19067i) q^{56} +(-0.698599 - 1.89217i) q^{57} +(-3.65660 + 6.33341i) q^{58} +(2.84959 + 4.93563i) q^{59} +(-1.24118 - 1.03175i) q^{60} +(3.53491 + 2.04088i) q^{61} -5.04524 q^{62} +(-3.17486 + 7.27463i) q^{63} -1.00000 q^{64} +(0.444266 + 0.256497i) q^{65} +(-1.33195 - 1.10721i) q^{66} +(-0.132150 - 0.228891i) q^{67} +(-4.07313 + 7.05487i) q^{68} +(1.07994 + 2.92504i) q^{69} +(-2.45912 - 0.176557i) q^{70} +1.31079i q^{71} +(2.94949 - 0.548188i) q^{72} +(5.37213 - 3.10160i) q^{73} +(-6.84727 + 3.95327i) q^{74} +(1.21013 - 7.05317i) q^{75} +1.16452i q^{76} +(-2.63896 - 0.189469i) q^{77} +(-0.894494 + 0.330251i) q^{78} +(5.94062 - 10.2895i) q^{79} +(0.465926 + 0.807007i) q^{80} +(-8.39898 + 3.23375i) q^{81} +(-7.21001 - 4.16270i) q^{82} -11.5106 q^{83} +(3.17423 - 3.30518i) q^{84} +7.59111 q^{85} +(1.14128 + 0.658919i) q^{86} +(-8.09721 + 9.74082i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-1.74496 + 3.02236i) q^{89} +(-1.81664 - 2.12484i) q^{90} +(-0.816717 + 1.20599i) q^{91} -1.80020i q^{92} +(-8.61277 - 1.47772i) q^{93} +(-2.74666 + 1.58579i) q^{94} +(0.939780 - 0.542582i) q^{95} +(-1.70711 - 0.292893i) q^{96} +17.7379i 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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