LMFDB - Embedded newform 462.2.k.e.353.1

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			353.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	462.353
Dual form			462.2.k.e.89.1

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

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

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
$3$	−1.33195	+	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	0.951201	−	0.308573i	$-0.0998514\pi$
$5$	0.465926	+	0.807007i	0.208368	+	0.360905i	−0.742832	+	0.669478i	$0.766518\pi$
$6$	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	$-0.975676\pi$
$13$		−	0.550510i		−	0.152684i	0.997082	−	0.0763420i	$-0.0243241\pi$
$14$	−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	0.359514	−	0.933140i	$-0.382943\pi$
$17$	4.07313	−	7.05487i	0.987880	−	1.71106i	0.628366	−	0.777918i	$-0.283724\pi$
$18$	1.00000	+	2.82843i	0.235702	+	0.666667i
$19$	1.00851	−	0.582262i	0.231368	−	0.133580i	−0.379835	−	0.925054i	$-0.624019\pi$
$19$	1.00851	−	0.582262i	0.231368	−	0.133580i	0.611203	+	0.791474i	$0.290686\pi$
$20$	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	−0.653654	−	0.756794i	$-0.726765\pi$
$23$	−1.55902	+	0.900100i	−0.325078	+	0.187684i	0.328576	+	0.944478i	$0.393431\pi$
$24$	−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	$0.237592\pi$
$29$			7.31319i			1.35803i	−0.734126	+	0.679013i	$0.762408\pi$
$30$	1.59077	−	0.272933i	0.290434	−	0.0498305i
$31$	4.36931	+	2.52262i	0.784751	+	0.453076i	0.838111	−	0.545499i	$-0.183660\pi$
$31$	4.36931	+	2.52262i	0.784751	+	0.453076i	−0.0533603	+	0.998575i	$0.516993\pi$
$32$	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	0.983143	+	0.182838i	$0.0585284\pi$
$37$	3.95327	+	6.84727i	0.649914	+	1.12568i	−0.333229	+	0.942846i	$0.608138\pi$
$38$	−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	0.958194	−	0.286119i	$-0.0923653\pi$
$47$	1.58579	+	2.74666i	0.231311	+	0.400642i	−0.726883	+	0.686761i	$0.759032\pi$
$48$	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	−0.969679	−	0.244383i	$-0.921415\pi$
$53$	−12.1298	−	7.00316i	−1.66616	−	0.961958i	−0.696481	−	0.717575i	$-0.745252\pi$
$54$	−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	−0.618732	−	0.785602i	$-0.712353\pi$
$59$	2.84959	−	4.93563i	0.370985	−	0.642565i	0.989717	+	0.143037i	$0.0456868\pi$
$60$	−1.24118	+	1.03175i	−0.160236	+	0.133199i
$61$	3.53491	−	2.04088i	0.452599	−	0.261308i	−0.256328	−	0.966590i	$-0.582513\pi$
$61$	3.53491	−	2.04088i	0.452599	−	0.261308i	0.708927	+	0.705282i	$0.249179\pi$
$62$	−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	−0.873985	−	0.485953i	$-0.838473\pi$
$67$	−0.132150	+	0.228891i	−0.0161447	+	0.0279635i	0.857840	+	0.513917i	$0.171806\pi$
$68$	−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	$-0.975217\pi$
$71$		−	1.31079i		−	0.155562i	0.996970	−	0.0777810i	$-0.0247835\pi$
$72$	2.94949	+	0.548188i	0.347601	+	0.0646046i
$73$	5.37213	+	3.10160i	0.628760	+	0.363015i	0.780272	−	0.625441i	$-0.215081\pi$
$73$	5.37213	+	3.10160i	0.628760	+	0.363015i	−0.151512	+	0.988455i	$0.548414\pi$
$74$	−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	0.978359	+	0.206913i	$0.0663417\pi$
$79$	5.94062	+	10.2895i	0.668372	+	1.15765i	−0.309988	+	0.950741i	$0.600325\pi$
$80$	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	0.758599	−	0.651557i	$-0.225884\pi$
$89$	−1.74496	−	3.02236i	−0.184966	−	0.320370i	−0.943565	+	0.331188i	$0.892551\pi$
$90$	−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	$-0.643197\pi$
$97$		−	17.7379i		−	1.80101i	0.434846	−	0.900505i	$-0.356803\pi$
$98$	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	−0.423685	−	0.905809i	$-0.639264\pi$
$101$	5.75467	−	9.96739i	0.572611	−	0.991792i	0.996297	−	0.0859825i	$-0.0274029\pi$
$102$	−9.01960	−	10.8504i	−0.893073	−	1.07435i
$103$	−7.14738	+	4.12654i	−0.704253	+	0.406600i	−0.808929	−	0.587906i	$-0.799953\pi$
$103$	−7.14738	+	4.12654i	−0.704253	+	0.406600i	0.104677	+	0.994506i	$0.466619\pi$
$104$	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	−0.616692	−	0.787205i	$-0.711527\pi$
$107$	−2.51669	+	1.45301i	−0.243298	+	0.140468i	0.373394	+	0.927673i	$0.378194\pi$
$108$	5.19565	+	0.0719302i	0.499952	+	0.00692148i
$109$	6.29788	−	10.9082i	0.603227	−	1.04482i	−0.389102	−	0.921195i	$-0.627215\pi$
$109$	6.29788	−	10.9082i	0.603227	−	1.04482i	0.992329	−	0.123625i	$-0.0394521\pi$
$110$	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	$0.140982\pi$
$113$			9.11150i			0.857138i	−0.903509	+	0.428569i	$0.859018\pi$
$114$	−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	0.900866	−	0.434098i	$-0.142933\pi$
$131$	0.852616	+	1.47677i	0.0744934	+	0.129026i	−0.826372	+	0.563124i	$0.809599\pi$
$132$	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	0.200617	−	0.979670i	$-0.435705\pi$
$137$	−6.40824	−	3.69980i	−0.547493	−	0.316095i	−0.748110	+	0.663574i	$0.769039\pi$
$138$	0.527266	+	3.07313i	0.0448839	+	0.261602i
$139$			22.0764i			1.87250i	0.351341	+	0.936248i	$0.385726\pi$
$139$			22.0764i			1.87250i	−0.351341	+	0.936248i	$0.614274\pi$
$140$	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	0.0411346	−	0.999154i	$-0.486903\pi$
$149$	11.3154	−	6.53295i	0.926994	−	0.535200i	0.885860	+	0.463953i	$0.153569\pi$
$150$	−4.57459	−	5.50316i	−0.373514	−	0.449331i
$151$	−10.0473	+	17.4025i	−0.817640	+	1.41619i	0.0897770	+	0.995962i	$0.471385\pi$
$151$	−10.0473	+	17.4025i	−0.817640	+	1.41619i	−0.907417	+	0.420232i	$0.861949\pi$
$152$	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	0.105366	−	0.994433i	$-0.466398\pi$
$157$	−8.81051	−	5.08675i	−0.703155	−	0.405967i	−0.808521	+	0.588467i	$0.799732\pi$
$158$	−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	−0.999339	−	0.0363664i	$-0.988422\pi$
$163$	−6.78144	−	11.7458i	−0.531163	−	0.920002i	0.468175	−	0.883636i	$-0.344912\pi$
$164$	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	0.949795	−	0.312874i	$-0.101292\pi$
$173$	2.68242	+	4.64609i	0.203941	+	0.353236i	−0.745854	+	0.666109i	$0.767958\pi$
$174$	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	0.553545	−	0.832819i	$-0.313275\pi$
$179$	1.45932	+	0.842541i	0.109075	+	0.0629745i	−0.444470	+	0.895794i	$0.646608\pi$
$180$	0.510830	−	2.74849i	0.0380750	−	0.204860i
$181$			4.29769i			0.319445i	0.987162	+	0.159722i	$0.0510599\pi$
$181$			4.29769i			0.319445i	−0.987162	+	0.159722i	$0.948940\pi$
$182$	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	−0.204672	−	0.978831i	$-0.565613\pi$
$191$	7.47239	−	4.31419i	0.540683	−	0.312164i	0.745356	+	0.666667i	$0.232280\pi$
$192$	1.33195	−	1.10721i	0.0961253	−	0.0799057i
$193$	−4.90678	+	8.49880i	−0.353198	+	0.611757i	−0.986808	−	0.161896i	$-0.948239\pi$
$193$	−4.90678	+	8.49880i	−0.353198	+	0.611757i	0.633610	+	0.773653i	$0.281572\pi$
$194$	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	$0.0778624\pi$
$197$			6.79831i			0.484360i	−0.970231	+	0.242180i	$0.922138\pi$
$198$	0.548188	−	2.94949i	0.0389580	−	0.209611i
$199$	−17.2783	−	9.97564i	−1.22483	−	0.707154i	−0.258884	−	0.965909i	$-0.583355\pi$
$199$	−17.2783	−	9.97564i	−1.22483	−	0.707154i	−0.965943	+	0.258754i	$0.916688\pi$
$200$	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	$-0.832439\pi$
$223$		−	15.0058i		−	1.00486i	0.864617	−	0.502431i	$-0.167561\pi$
$224$	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	−0.408084	−	0.912944i	$-0.633803\pi$
$227$	8.83788	−	15.3077i	0.586591	−	1.01600i	0.994675	−	0.103061i	$-0.0328636\pi$
$228$	1.28937	+	1.55109i	0.0853906	+	0.102723i
$229$	−13.2173	+	7.63103i	−0.873426	+	0.504273i	−0.868485	−	0.495715i	$-0.834906\pi$
$229$	−13.2173	+	7.63103i	−0.873426	+	0.504273i	−0.00494071	+	0.999988i	$0.501573\pi$
$230$	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	−0.443725	−	0.896163i	$-0.646343\pi$
$233$	1.68691	−	0.973936i	0.110513	−	0.0638047i	0.554238	+	0.832358i	$0.313010\pi$
$234$	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	$0.0706971\pi$
$239$			6.81090i			0.440560i	−0.975437	+	0.220280i	$0.929303\pi$
$240$	0.272933	+	1.59077i	0.0176178	+	0.102684i
$241$	−1.22496	−	0.707231i	−0.0789066	−	0.0455568i	0.460028	−	0.887905i	$-0.347840\pi$
$241$	−1.22496	−	0.707231i	−0.0789066	−	0.0455568i	−0.538934	+	0.842348i	$0.681173\pi$
$242$	−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	0.999545	−	0.0301463i	$-0.00959732\pi$
$257$	7.59343	+	13.1522i	0.473665	+	0.820412i	−0.525880	+	0.850559i	$0.676264\pi$
$258$	−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	0.605722	−	0.795676i	$-0.292884\pi$
$263$	3.55980	+	2.05525i	0.219507	+	0.126732i	−0.386215	+	0.922409i	$0.626218\pi$
$264$	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	−0.715585	−	0.698526i	$-0.753840\pi$
$269$	4.05354	−	7.02093i	0.247148	−	0.428074i	0.962733	+	0.270452i	$0.0871731\pi$
$270$	0.0670283	−	4.84158i	0.00407921	−	0.294649i
$271$	−11.7538	+	6.78606i	−0.713993	+	0.412224i	−0.812538	−	0.582909i	$-0.801914\pi$
$271$	−11.7538	+	6.78606i	−0.713993	+	0.412224i	0.0985450	+	0.995133i	$0.468581\pi$
$272$	−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	−0.999943	−	0.0106842i	$-0.996599\pi$
$277$	−8.16719	+	14.1460i	−0.490719	+	0.849950i	0.509224	+	0.860634i	$0.329932\pi$
$278$	−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	$0.294966\pi$
$281$			26.8082i			1.59924i	−0.600505	+	0.799621i	$0.705034\pi$
$282$	5.41421	−	0.928932i	0.322412	−	0.0553171i
$283$	9.49826	+	5.48382i	0.564613	+	0.325979i	0.754995	−	0.655731i	$-0.227639\pi$
$283$	9.49826	+	5.48382i	0.564613	+	0.325979i	−0.190382	+	0.981710i	$0.560973\pi$
$284$	−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	$-0.941162\pi$
$307$		−	6.44068i		−	0.367589i	0.982965	−	0.183795i	$-0.0588381\pi$
$308$	−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	−0.868844	−	0.495086i	$-0.835137\pi$
$311$	−0.0999004	+	0.173033i	−0.00566483	+	0.00981178i	0.863179	+	0.504898i	$0.168470\pi$
$312$	−0.733253	+	0.609528i	−0.0415123	+	0.0345078i
$313$	−5.46489	+	3.15515i	−0.308894	+	0.178340i	−0.646431	−	0.762972i	$-0.723739\pi$
$313$	−5.46489	+	3.15515i	−0.308894	+	0.178340i	0.337538	+	0.941312i	$0.390406\pi$
$314$	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	−0.976187	−	0.216932i	$-0.930395\pi$
$317$	−22.7259	+	13.1208i	−1.27641	+	0.736936i	−0.300225	+	0.953869i	$0.597062\pi$
$318$	−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	0.719390	−	0.694606i	$-0.244421\pi$
$331$	−4.40010	−	7.62120i	−0.241851	−	0.418899i	−0.961242	+	0.275707i	$0.911088\pi$
$332$	−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	0.0596570	−	0.998219i	$-0.480999\pi$
$347$	−14.4366	−	8.33498i	−0.774998	−	0.447445i	−0.834654	+	0.550774i	$0.814333\pi$
$348$	−12.4844	+	2.14198i	−0.669234	+	0.114822i
$349$			26.4502i			1.41585i	0.706290	+	0.707923i	$0.250367\pi$
$349$			26.4502i			1.41585i	−0.706290	+	0.707923i	$0.749633\pi$
$350$	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	−0.996644	−	0.0818618i	$-0.973913\pi$
$353$	−8.03063	+	13.9095i	−0.427427	+	0.740326i	0.569216	+	0.822188i	$0.307247\pi$
$354$	−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	0.0335666	−	0.999436i	$-0.489313\pi$
$359$	17.3536	−	10.0191i	0.915887	−	0.528788i	0.882321	+	0.470649i	$0.155980\pi$
$360$	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	0.999997	−	0.00247299i	$-0.000787176\pi$
$367$	28.6947	+	16.5669i	1.49785	+	0.864786i	0.497857	+	0.867259i	$0.334121\pi$
$368$	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	0.998055	+	0.0623380i	$0.0198557\pi$
$373$	10.6805	+	18.4991i	0.553014	+	0.957848i	−0.445041	+	0.895510i	$0.646811\pi$
$374$	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	0.721350	−	0.692571i	$-0.243522\pi$
$383$	−4.67946	−	8.10506i	−0.239109	−	0.414149i	−0.960459	+	0.278422i	$0.910189\pi$
$384$	−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	0.367577	−	0.929993i	$-0.380187\pi$
$389$	−5.01028	−	2.89269i	−0.254031	−	0.146665i	−0.621609	+	0.783328i	$0.713521\pi$
$390$	−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	−0.518634	−	0.854997i	$-0.673559\pi$
$397$	−0.747216	+	0.431405i	−0.0375017	+	0.0216516i	0.481132	+	0.876648i	$0.340226\pi$
$398$	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	−0.972550	−	0.232695i	$-0.925246\pi$
$401$	−25.1775	+	14.5362i	−1.25731	+	0.725906i	−0.284755	+	0.958600i	$0.591912\pi$
$402$	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	0.965273	−	0.261243i	$-0.0841325\pi$
$409$	24.7067	+	14.2644i	1.22167	+	0.705329i	0.256393	+	0.966573i	$0.417466\pi$
$410$	−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	−0.182749	−	0.983160i	$-0.558499\pi$
$431$	−23.3673	−	13.4911i	−1.12556	−	0.649845i	−0.942816	+	0.333315i	$0.891833\pi$
$432$	2.66012	−	4.46360i	0.127985	−	0.214755i
$433$		−	11.4607i		−	0.550766i	−0.961335	−	0.275383i	$-0.911195\pi$
$433$		−	11.4607i		−	0.550766i	0.961335	−	0.275383i	$-0.0888047\pi$
$434$	−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	−0.681790	−	0.731548i	$-0.738798\pi$
$439$	−8.15351	+	4.70743i	−0.389146	+	0.224673i	0.292644	+	0.956221i	$0.405465\pi$
$440$	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	−0.749751	−	0.661720i	$-0.769827\pi$
$443$	−11.6090	+	6.70246i	−0.551561	+	0.318444i	0.198191	+	0.980163i	$0.436493\pi$
$444$	−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	$-0.812484\pi$
$449$		−	23.5464i		−	1.11122i	0.831442	−	0.555611i	$-0.187516\pi$
$450$	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	−0.809556	−	0.587042i	$-0.800292\pi$
$457$	−19.5214	−	33.8120i	−0.913172	−	1.58166i	−0.103615	−	0.994617i	$-0.533041\pi$
$458$	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	−0.934139	−	0.356910i	$-0.883830\pi$
$467$	−16.7730	−	29.0517i	−0.776163	−	1.34435i	0.157976	−	0.987443i	$-0.449503\pi$
$468$	−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	−0.928758	−	0.370686i	$-0.879123\pi$
$479$	−3.13750	+	5.43431i	−0.143356	+	0.248300i	0.785402	+	0.618986i	$0.212456\pi$
$480$	−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	−0.994708	−	0.102745i	$-0.967237\pi$
$487$	−9.01203	+	15.6093i	−0.408374	+	0.707325i	0.586334	+	0.810070i	$0.300571\pi$
$488$	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	$-0.878451\pi$
$491$		−	16.5145i		−	0.745289i	0.927974	−	0.372645i	$-0.121549\pi$
$492$	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	0.864601	+	0.502460i	$0.167571\pi$
$499$	19.3772	+	33.5623i	0.867443	+	1.50246i	0.00284253	+	0.999996i	$0.499095\pi$
$500$	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	0.982933	−	0.183962i	$-0.0588924\pi$
$509$	7.49367	+	12.9794i	0.332151	+	0.575302i	−0.650782	+	0.759264i	$0.725559\pi$
$510$	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	−0.0546085	+	0.998508i	$0.517391\pi$
$521$	−20.3611	+	35.2665i	−0.892037	+	1.54505i	−0.837429	+	0.546546i	$0.815942\pi$
$522$	−20.6848	+	7.31319i	−0.905351	+	0.320090i
$523$	8.02282	−	4.63197i	0.350813	−	0.202542i	−0.314230	−	0.949347i	$-0.601746\pi$
$523$	8.02282	−	4.63197i	0.350813	−	0.202542i	0.665043	+	0.746805i	$0.268413\pi$
$524$	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	0.813873	−	0.581043i	$-0.197355\pi$
$541$	−2.23898	−	3.87803i	−0.0962614	−	0.166730i	−0.910134	+	0.414313i	$0.864022\pi$
$542$	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	0.933291	−	0.359121i	$-0.116924\pi$
$557$	25.6996	+	14.8377i	1.08893	+	0.628693i	0.155637	+	0.987814i	$0.450257\pi$
$558$	−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	0.269165	+	0.963094i	$0.413252\pi$
$563$	−16.5970	+	28.7469i	−0.699482	+	1.21154i	−0.968646	+	0.248444i	$0.920081\pi$
$564$	−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	0.346364	−	0.938100i	$-0.387416\pi$
$569$	31.7723	−	18.3438i	1.33196	−	0.769010i	0.985601	+	0.169090i	$0.0540829\pi$
$570$	1.44539	−	1.20150i	0.0605406	−	0.0503253i
$571$	−3.62510	+	6.27886i	−0.151706	+	0.262762i	−0.931855	−	0.362832i	$-0.881810\pi$
$571$	−3.62510	+	6.27886i	−0.151706	+	0.262762i	0.780149	+	0.625594i	$0.215143\pi$
$572$	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	0.00861630	−	0.999963i	$-0.497257\pi$
$577$	−20.4914	−	11.8307i	−0.853069	−	0.492520i	−0.861685	+	0.507443i	$0.830591\pi$
$578$	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	0.998167	+	0.0605133i	$0.0192738\pi$
$593$	13.4297	+	23.2608i	0.551490	+	0.955208i	−0.446678	+	0.894695i	$0.647393\pi$
$594$	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	0.878366	−	0.477988i	$-0.158634\pi$
$599$	22.1151	+	12.7682i	0.903600	+	0.521694i	0.0252337	+	0.999682i	$0.491967\pi$
$600$	−7.05317	+	1.21013i	−0.287945	+	0.0494035i
$601$		−	0.718186i		−	0.0292954i	−0.999893	−	0.0146477i	$-0.995337\pi$
$601$		−	0.718186i		−	0.0292954i	0.999893	−	0.0146477i	$-0.00466268\pi$
$602$	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	−0.229693	−	0.973263i	$-0.573772\pi$
$607$	12.2776	−	7.08845i	0.498330	−	0.287711i	0.728024	+	0.685552i	$0.240439\pi$
$608$	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	−0.245789	−	0.969323i	$-0.579047\pi$
$613$	17.7413	−	30.7288i	0.716564	−	1.24113i	0.962353	−	0.271802i	$-0.0876195\pi$
$614$	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	$0.272049\pi$
$617$			37.4755i			1.50871i	−0.656469	+	0.754353i	$0.727951\pi$
$618$	2.41727	+	14.0889i	0.0972370	+	0.566739i
$619$	14.2409	+	8.22198i	0.572389	+	0.330469i	0.758103	−	0.652135i	$-0.226126\pi$
$619$	14.2409	+	8.22198i	0.572389	+	0.330469i	−0.185714	+	0.982604i	$0.559460\pi$
$620$	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	0.716142	−	0.697955i	$-0.245906\pi$
$641$	11.8935	+	6.86673i	0.469766	+	0.271220i	−0.246376	+	0.969174i	$0.579240\pi$
$642$	0.851156	+	4.96090i	0.0335924	+	0.195791i
$643$			8.11142i			0.319883i	0.987126	+	0.159942i	$0.0511306\pi$
$643$			8.11142i			0.319883i	−0.987126	+	0.159942i	$0.948869\pi$
$644$	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	−0.355695	+	0.934602i	$0.615756\pi$
$647$	−25.1115	+	43.4945i	−0.987237	+	1.70994i	−0.631542	+	0.775342i	$0.717578\pi$
$648$	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	−0.371255	−	0.928531i	$-0.621072\pi$
$653$	6.31819	−	3.64781i	0.247250	−	0.142750i	0.618504	+	0.785781i	$0.287739\pi$
$654$	−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	$-0.803622\pi$
$659$		−	29.7035i		−	1.15709i	0.815652	−	0.578543i	$-0.196378\pi$
$660$	1.59077	−	0.272933i	0.0619206	−	0.0106239i
$661$	36.3248	+	20.9721i	1.41287	+	0.815721i	0.995658	−	0.0930887i	$-0.0296740\pi$
$661$	36.3248	+	20.9721i	1.41287	+	0.815721i	0.417212	+	0.908809i	$0.363007\pi$
$662$	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	0.824515	−	0.565839i	$-0.191448\pi$
$677$	−2.02361	−	3.50499i	−0.0777736	−	0.134708i	−0.902289	+	0.431132i	$0.858114\pi$
$678$	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	0.603144	−	0.797632i	$-0.293914\pi$
$683$	5.59134	+	3.22816i	0.213947	+	0.123522i	−0.389198	+	0.921154i	$0.627248\pi$
$684$	−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	−0.105585	−	0.994410i	$-0.533671\pi$
$691$	18.4746	−	10.6663i	0.702807	−	0.405766i	0.808392	+	0.588644i	$0.200338\pi$
$692$	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	$0.216644\pi$
$701$			33.3214i			1.25853i	−0.777190	+	0.629266i	$0.783356\pi$
$702$	−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	0.517177	−	0.855878i	$-0.326983\pi$
$709$	−12.8508	−	22.2583i	−0.482624	−	0.835928i	−0.999801	+	0.0199497i	$0.993649\pi$
$710$	−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	0.949103	−	0.314966i	$-0.101993\pi$
$719$	5.41064	+	9.37150i	0.201783	+	0.349498i	−0.747320	+	0.664464i	$0.768660\pi$
$720$	−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	$-0.975495\pi$
$727$		−	4.14730i		−	0.153815i	0.997038	−	0.0769073i	$-0.0245046\pi$
$728$	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	−0.944478	−	0.328574i	$-0.893432\pi$
$733$	−30.6522	+	17.6970i	−1.13216	+	0.653655i	−0.187685	+	0.982229i	$0.560098\pi$
$734$	−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	−0.808183	−	0.588932i	$-0.799549\pi$
$739$	2.87990	−	4.98813i	0.105939	−	0.183491i	0.914121	+	0.405441i	$0.132882\pi$
$740$	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	$-0.883246\pi$
$743$		−	19.5508i		−	0.717251i	0.933482	−	0.358625i	$-0.116754\pi$
$744$	−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	0.967212	−	0.253971i	$-0.0817368\pi$
$751$	7.22545	+	12.5148i	0.263660	+	0.456673i	−0.703551	+	0.710644i	$0.748404\pi$
$752$	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	0.979559	+	0.201159i	$0.0644709\pi$
$761$	18.3169	+	31.7259i	0.663988	+	1.15006i	−0.315570	+	0.948902i	$0.602196\pi$
$762$	−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	$0.0251816\pi$
$769$			4.38302i			0.158056i	−0.996872	+	0.0790278i	$0.974818\pi$
$770$	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	−0.905225	−	0.424933i	$-0.860298\pi$
$773$	−2.35238	+	4.07445i	−0.0846094	+	0.146548i	0.820615	+	0.571481i	$0.193631\pi$
$774$	−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	−0.459922	−	0.887960i	$-0.652122\pi$
$787$	−40.9267	−	23.6290i	−1.45888	−	0.842284i	−0.998956	+	0.0456761i	$0.985456\pi$
$788$	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	0.502828	−	0.864386i	$-0.332293\pi$
$809$	0.161040	+	0.0929765i	0.00566187	+	0.00326888i	−0.497166	+	0.867655i	$0.665626\pi$
$810$	5.27135	+	6.52296i	0.185216	+	0.229194i
$811$		−	20.6191i		−	0.724034i	−0.932171	−	0.362017i	$-0.882088\pi$
$811$		−	20.6191i		−	0.724034i	0.932171	−	0.362017i	$-0.117912\pi$
$812$	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	−0.956272	−	0.292479i	$-0.905520\pi$
$821$	−33.8426	+	19.5390i	−1.18111	+	0.681916i	−0.224842	+	0.974395i	$0.572187\pi$
$822$	−9.85591	+	8.19289i	−0.343764	+	0.285760i
$823$	13.4961	−	23.3759i	0.470443	−	0.814832i	−0.528985	−	0.848631i	$-0.677427\pi$
$823$	13.4961	−	23.3759i	0.470443	−	0.814832i	0.999429	+	0.0337992i	$0.0107607\pi$
$824$	−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	$0.0544516\pi$
$827$			9.79091i			0.340463i	−0.985404	+	0.170232i	$0.945548\pi$
$828$	5.30967	+	0.986848i	0.184524	+	0.0342953i
$829$	−11.4341	−	6.60149i	−0.397123	−	0.229279i	0.288119	−	0.957595i	$-0.406970\pi$
$829$	−11.4341	−	6.60149i	−0.397123	−	0.229279i	−0.685242	+	0.728315i	$0.740304\pi$
$830$	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	$0.176529\pi$
$853$			30.7592i			1.05318i	−0.850121	+	0.526588i	$0.823471\pi$
$854$	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	−0.703527	−	0.710668i	$-0.748393\pi$
$857$	7.71950	−	13.3706i	0.263693	−	0.456730i	0.967220	+	0.253938i	$0.0817260\pi$
$858$	0.609528	+	0.733253i	0.0208090	+	0.0250328i
$859$	19.1628	−	11.0636i	0.653826	−	0.377486i	−0.136095	−	0.990696i	$-0.543455\pi$
$859$	19.1628	−	11.0636i	0.653826	−	0.377486i	0.789920	+	0.613209i	$0.210122\pi$
$860$	−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	−0.296597	−	0.955003i	$-0.595852\pi$
$863$	11.2267	−	6.48172i	0.382160	−	0.220640i	0.678758	+	0.734362i	$0.262519\pi$
$864$	−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	0.987823	−	0.155582i	$-0.0497252\pi$
$877$	10.6366	+	18.4232i	0.359174	+	0.622107i	−0.628649	+	0.777689i	$0.716392\pi$
$878$	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	0.980609	+	0.195974i	$0.0627870\pi$
$887$	19.6572	+	34.0472i	0.660023	+	1.14319i	−0.320586	+	0.947220i	$0.603880\pi$
$888$	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	0.0608372	+	0.998148i	$0.480623\pi$
$907$	−25.1172	+	43.5043i	−0.834003	+	1.44453i	−0.894840	+	0.446387i	$0.852710\pi$
$908$	−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	$-0.673737\pi$
$911$		−	51.5948i		−	1.70941i	0.519112	−	0.854706i	$-0.326263\pi$
$912$	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	0.691820	−	0.722070i	$-0.256809\pi$
$919$	−8.47067	−	14.6716i	−0.279422	−	0.483972i	−0.971241	+	0.238098i	$0.923476\pi$
$920$	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	0.971685	−	0.236281i	$-0.0759285\pi$
$929$	8.57136	+	14.8460i	0.281217	+	0.487082i	−0.690468	+	0.723363i	$0.742595\pi$
$930$	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	$-0.737874\pi$
$937$		−	44.9070i		−	1.46705i	0.679664	−	0.733524i	$-0.262126\pi$
$938$	−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	−0.159625	−	0.987178i	$-0.551029\pi$
$941$	23.7770	−	41.1830i	0.775108	−	1.34253i	0.934734	−	0.355349i	$-0.115638\pi$
$942$	−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	−0.558591	−	0.829443i	$-0.688658\pi$
$947$	−3.67949	+	2.12436i	−0.119567	+	0.0690323i	0.439024	+	0.898476i	$0.355324\pi$
$948$	−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	$0.00882562\pi$
$953$			1.71165i			0.0554459i	−0.999616	+	0.0277229i	$0.991174\pi$
$954$	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	0.886445	−	0.462835i	$-0.153168\pi$
$971$	1.32109	+	2.28820i	0.0423958	+	0.0734317i	−0.844049	+	0.536266i	$0.819834\pi$
$972$	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	−0.996655	−	0.0817204i	$-0.973959\pi$
$977$	−48.9408	−	28.2560i	−1.56575	−	0.903989i	−0.569100	−	0.822269i	$-0.692708\pi$
$978$	−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	−0.989660	−	0.143432i	$-0.954186\pi$
$983$	−11.6198	+	20.1261i	−0.370615	+	0.641923i	0.619046	+	0.785355i	$0.287520\pi$
$984$	−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	−0.985793	−	0.167967i	$-0.946280\pi$
$991$	−10.9372	+	18.9438i	−0.347432	+	0.601771i	0.638360	+	0.769738i	$0.279613\pi$
$992$	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	0.367503	−	0.930022i	$-0.380213\pi$
$997$	−8.02545	−	4.63349i	−0.254168	−	0.146744i	−0.621671	+	0.783278i	$0.713546\pi$
$998$	−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.353.1	yes	8
3.2	odd	2		462.2.k.f.353.3	yes	8
7.5	odd	6		462.2.k.f.89.3	yes	8
21.5	even	6	inner	462.2.k.e.89.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.e.89.1	✓	8	21.5	even	6	inner
462.2.k.e.353.1	yes	8	1.1	even	1	trivial
462.2.k.f.89.3	yes	8	7.5	odd	6
462.2.k.f.353.3	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.33195 + 1.10721i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.465926 + 0.807007i) q^{5} +(0.599900 - 1.62484i) q^{6} +(2.19067 - 1.48356i) q^{7} +1.00000i q^{8} +(0.548188 - 2.94949i) q^{9} +O(q^{10})\)	\(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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