LMFDB - Embedded newform 546.2.cg.b.271.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.7
Character	$\chi$	$=$	546.271
Dual form			546.2.cg.b.409.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-0.367885 - 1.37297i) q^{5} +(0.258819 + 0.965926i) q^{6} +(1.50946 + 2.17291i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-0.367885 - 1.37297i) q^{5} +(0.258819 + 0.965926i) q^{6} +(1.50946 + 2.17291i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.710699 - 1.23097i) q^{10} +(0.998376 + 3.72599i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.74539 - 3.15494i) q^{13} +(-0.469134 + 2.60383i) q^{14} +(0.367885 - 1.37297i) q^{15} -1.00000 q^{16} +2.36042 q^{17} +(-0.258819 + 0.965926i) q^{18} +(-5.84150 - 1.56523i) q^{19} +(1.37297 - 0.367885i) q^{20} +(0.220772 + 2.63652i) q^{21} +(-1.92872 + 3.34063i) q^{22} +8.10794i q^{23} +(-0.965926 + 0.258819i) q^{24} +(2.58043 - 1.48981i) q^{25} +(3.46505 - 0.996704i) q^{26} +1.00000i q^{27} +(-2.17291 + 1.50946i) q^{28} +(-0.220739 - 0.382331i) q^{29} +(1.23097 - 0.710699i) q^{30} +(3.19195 + 0.855281i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.998376 + 3.72599i) q^{33} +(1.66907 + 1.66907i) q^{34} +(2.42803 - 2.87181i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(5.36507 - 5.36507i) q^{37} +(-3.02378 - 5.23735i) q^{38} +(3.08902 - 1.85956i) q^{39} +(1.23097 + 0.710699i) q^{40} +(1.33418 + 0.357492i) q^{41} +(-1.70820 + 2.02041i) q^{42} +(-7.53977 - 4.35309i) q^{43} +(-3.72599 + 0.998376i) q^{44} +(1.00508 - 1.00508i) q^{45} +(-5.73318 + 5.73318i) q^{46} +(-6.14515 + 1.64659i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-2.44309 + 6.55983i) q^{49} +(2.87810 + 0.771184i) q^{50} +(2.04418 + 1.18021i) q^{51} +(3.15494 + 1.74539i) q^{52} +(-4.08469 - 7.07489i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(4.74837 - 2.74147i) q^{55} +(-2.60383 - 0.469134i) q^{56} +(-4.27628 - 4.27628i) q^{57} +(0.114263 - 0.426435i) q^{58} +(-5.93929 - 5.93929i) q^{59} +(1.37297 + 0.367885i) q^{60} +(9.22941 - 5.32860i) q^{61} +(1.65228 + 2.86183i) q^{62} +(-1.12707 + 2.39368i) q^{63} -1.00000i q^{64} +(-4.97372 - 1.23570i) q^{65} +(-3.34063 + 1.92872i) q^{66} +(0.0380657 - 0.0101997i) q^{67} +2.36042i q^{68} +(-4.05397 + 7.02168i) q^{69} +(3.74755 - 0.313804i) q^{70} +(-12.2523 + 3.28299i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(2.06986 - 7.72484i) q^{73} +7.58736 q^{74} +2.97962 q^{75} +(1.56523 - 5.84150i) q^{76} +(-6.58924 + 7.79360i) q^{77} +(3.49917 + 0.869355i) q^{78} +(6.14585 - 10.6449i) q^{79} +(0.367885 + 1.37297i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.690622 + 1.19619i) q^{82} +(9.37857 - 9.37857i) q^{83} +(-2.63652 + 0.220772i) q^{84} +(-0.868362 - 3.24077i) q^{85} +(-2.25332 - 8.40952i) q^{86} -0.441478i q^{87} +(-3.34063 - 1.92872i) q^{88} +(1.45796 + 1.45796i) q^{89} +1.42140 q^{90} +(9.48998 - 0.969671i) q^{91} -8.10794 q^{92} +(2.33667 + 2.33667i) q^{93} +(-5.50959 - 3.18096i) q^{94} +8.59601i q^{95} +(-0.258819 - 0.965926i) q^{96} +(-3.62024 - 13.5109i) q^{97} +(-6.36602 + 2.91098i) q^{98} +(-2.72762 + 2.72762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$			1.00000i			0.500000i
$5$	−0.367885	−	1.37297i	−0.164523	−	0.614009i	−0.998101	−	0.0616062i	$-0.980378\pi$
$5$	−0.367885	−	1.37297i	−0.164523	−	0.614009i	0.833577	−	0.552403i	$-0.186289\pi$
$6$	0.258819	+	0.965926i	0.105662	+	0.394338i
$7$	1.50946	+	2.17291i	0.570521	+	0.821283i
$7$	1.50946	+	2.17291i	0.570521	+	0.821283i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.710699	−	1.23097i	0.224743	−	0.389266i
$11$	0.998376	+	3.72599i	0.301022	+	1.12343i	0.936316	+	0.351158i	$0.114212\pi$
$11$	0.998376	+	3.72599i	0.301022	+	1.12343i	−0.635294	+	0.772270i	$0.719121\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.74539	−	3.15494i	0.484083	−	0.875022i
$13$	1.74539	−	3.15494i	0.484083	−	0.875022i
$14$	−0.469134	+	2.60383i	−0.125381	+	0.695902i
$15$	0.367885	−	1.37297i	0.0949875	−	0.354498i
$16$	−1.00000			−0.250000
$17$	2.36042			0.572485			0.286243	−	0.958157i	$-0.407594\pi$
$17$	2.36042			0.572485			0.286243	+	0.958157i	$0.407594\pi$
$18$	−0.258819	+	0.965926i	−0.0610042	+	0.227671i
$19$	−5.84150	−	1.56523i	−1.34013	−	0.359087i	−0.483649	−	0.875262i	$-0.660689\pi$
$19$	−5.84150	−	1.56523i	−1.34013	−	0.359087i	−0.856483	+	0.516175i	$0.827356\pi$
$20$	1.37297	−	0.367885i	0.307005	−	0.0822616i
$21$	0.220772	+	2.63652i	0.0481763	+	0.575337i
$22$	−1.92872	+	3.34063i	−0.411203	+	0.712225i
$23$			8.10794i			1.69062i	0.534274	+	0.845311i	$0.320585\pi$
$23$			8.10794i			1.69062i	−0.534274	+	0.845311i	$0.679415\pi$
$24$	−0.965926	+	0.258819i	−0.197169	+	0.0528312i
$25$	2.58043	−	1.48981i	0.516086	−	0.297962i
$26$	3.46505	−	0.996704i	0.679552	−	0.195470i
$27$			1.00000i			0.192450i
$28$	−2.17291	+	1.50946i	−0.410642	+	0.285260i
$29$	−0.220739	−	0.382331i	−0.0409902	−	0.0709971i	0.844802	−	0.535078i	$-0.179718\pi$
$29$	−0.220739	−	0.382331i	−0.0409902	−	0.0709971i	−0.885793	+	0.464081i	$0.846385\pi$
$30$	1.23097	−	0.710699i	0.224743	−	0.129755i
$31$	3.19195	+	0.855281i	0.573292	+	0.153613i	0.533806	−	0.845607i	$-0.320761\pi$
$31$	3.19195	+	0.855281i	0.573292	+	0.153613i	0.0394858	+	0.999220i	$0.487428\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.998376	+	3.72599i	−0.173795	+	0.648612i
$34$	1.66907	+	1.66907i	0.286243	+	0.286243i
$35$	2.42803	−	2.87181i	0.410411	−	0.485425i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	5.36507	−	5.36507i	0.882013	−	0.882013i	−0.111726	−	0.993739i	$-0.535638\pi$
$37$	5.36507	−	5.36507i	0.882013	−	0.882013i	0.993739	+	0.111726i	$0.0356380\pi$
$38$	−3.02378	−	5.23735i	−0.490522	−	0.849610i
$39$	3.08902	−	1.85956i	0.494639	−	0.297768i
$40$	1.23097	+	0.710699i	0.194633	+	0.112371i
$41$	1.33418	+	0.357492i	0.208364	+	0.0558309i	0.361491	−	0.932376i	$-0.382268\pi$
$41$	1.33418	+	0.357492i	0.208364	+	0.0558309i	−0.153127	+	0.988206i	$0.548934\pi$
$42$	−1.70820	+	2.02041i	−0.263580	+	0.311757i
$43$	−7.53977	−	4.35309i	−1.14980	−	0.663840i	−0.200964	−	0.979599i	$-0.564408\pi$
$43$	−7.53977	−	4.35309i	−1.14980	−	0.663840i	−0.948839	+	0.315759i	$0.897741\pi$
$44$	−3.72599	+	0.998376i	−0.561714	+	0.150511i
$45$	1.00508	−	1.00508i	0.149829	−	0.149829i
$46$	−5.73318	+	5.73318i	−0.845311	+	0.845311i
$47$	−6.14515	+	1.64659i	−0.896362	+	0.240179i	−0.677453	−	0.735566i	$-0.736916\pi$
$47$	−6.14515	+	1.64659i	−0.896362	+	0.240179i	−0.218909	+	0.975745i	$0.570250\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−2.44309	+	6.55983i	−0.349012	+	0.937118i
$50$	2.87810	+	0.771184i	0.407024	+	0.109062i
$51$	2.04418	+	1.18021i	0.286243	+	0.165262i
$52$	3.15494	+	1.74539i	0.437511	+	0.242041i
$53$	−4.08469	−	7.07489i	−0.561076	−	0.971811i	−0.997403	−	0.0720233i	$-0.977054\pi$
$53$	−4.08469	−	7.07489i	−0.561076	−	0.971811i	0.436327	−	0.899788i	$-0.356279\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	4.74837	−	2.74147i	0.640270	−	0.369660i
$56$	−2.60383	−	0.469134i	−0.347951	−	0.0626906i
$57$	−4.27628	−	4.27628i	−0.566407	−	0.566407i
$58$	0.114263	−	0.426435i	0.0150035	−	0.0559937i
$59$	−5.93929	−	5.93929i	−0.773230	−	0.773230i	0.205440	−	0.978670i	$-0.434137\pi$
$59$	−5.93929	−	5.93929i	−0.773230	−	0.773230i	−0.978670	+	0.205440i	$0.934137\pi$
$60$	1.37297	+	0.367885i	0.177249	+	0.0474938i
$61$	9.22941	−	5.32860i	1.18170	−	0.682257i	0.225296	−	0.974290i	$-0.427665\pi$
$61$	9.22941	−	5.32860i	1.18170	−	0.682257i	0.956408	+	0.292033i	$0.0943317\pi$
$62$	1.65228	+	2.86183i	0.209839	+	0.363452i
$63$	−1.12707	+	2.39368i	−0.141997	+	0.301576i
$64$		−	1.00000i		−	0.125000i
$65$	−4.97372	−	1.23570i	−0.616914	−	0.153270i
$66$	−3.34063	+	1.92872i	−0.411203	+	0.237408i
$67$	0.0380657	−	0.0101997i	0.00465047	−	0.00124609i	−0.256493	−	0.966546i	$-0.582567\pi$
$67$	0.0380657	−	0.0101997i	0.00465047	−	0.00124609i	0.261144	+	0.965300i	$0.415900\pi$
$68$			2.36042i			0.286243i
$69$	−4.05397	+	7.02168i	−0.488041	+	0.845311i
$70$	3.74755	−	0.313804i	0.447918	−	0.0375068i
$71$	−12.2523	+	3.28299i	−1.45408	+	0.389619i	−0.897440	−	0.441137i	$-0.854575\pi$
$71$	−12.2523	+	3.28299i	−1.45408	+	0.389619i	−0.556637	+	0.830756i	$0.687909\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	2.06986	−	7.72484i	0.242259	−	0.904124i	−0.732482	−	0.680786i	$-0.761638\pi$
$73$	2.06986	−	7.72484i	0.242259	−	0.904124i	0.974741	−	0.223337i	$-0.0716952\pi$
$74$	7.58736			0.882013
$75$	2.97962			0.344057
$76$	1.56523	−	5.84150i	0.179544	−	0.670066i
$77$	−6.58924	+	7.79360i	−0.750914	+	0.888163i
$78$	3.49917	+	0.869355i	0.396203	+	0.0984351i
$79$	6.14585	−	10.6449i	0.691462	−	1.19765i	−0.279896	−	0.960030i	$-0.590300\pi$
$79$	6.14585	−	10.6449i	0.691462	−	1.19765i	0.971359	−	0.237618i	$-0.0763666\pi$
$80$	0.367885	+	1.37297i	0.0411308	+	0.153502i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.690622	+	1.19619i	0.0762664	+	0.132097i
$83$	9.37857	−	9.37857i	1.02943	−	1.02943i	0.0298777	−	0.999554i	$-0.490488\pi$
$83$	9.37857	−	9.37857i	1.02943	−	1.02943i	0.999554	−	0.0298777i	$-0.00951178\pi$
$84$	−2.63652	+	0.220772i	−0.287668	+	0.0240881i
$85$	−0.868362	−	3.24077i	−0.0941871	−	0.351511i
$86$	−2.25332	−	8.40952i	−0.242982	−	0.906822i
$87$		−	0.441478i		−	0.0473314i
$88$	−3.34063	−	1.92872i	−0.356113	−	0.205602i
$89$	1.45796	+	1.45796i	0.154544	+	0.154544i	0.780144	−	0.625600i	$-0.215146\pi$
$89$	1.45796	+	1.45796i	0.154544	+	0.154544i	−0.625600	+	0.780144i	$0.715146\pi$
$90$	1.42140			0.149829
$91$	9.48998	−	0.969671i	0.994820	−	0.101649i
$92$	−8.10794			−0.845311
$93$	2.33667	+	2.33667i	0.242302	+	0.242302i
$94$	−5.50959	−	3.18096i	−0.568270	−	0.328091i
$95$			8.59601i			0.881932i
$96$	−0.258819	−	0.965926i	−0.0264156	−	0.0985844i
$97$	−3.62024	−	13.5109i	−0.367580	−	1.37183i	−0.863889	−	0.503681i	$-0.831979\pi$
$97$	−3.62024	−	13.5109i	−0.367580	−	1.37183i	0.496310	−	0.868146i	$-0.334688\pi$
$98$	−6.36602	+	2.91098i	−0.643065	+	0.294053i
$99$	−2.72762	+	2.72762i	−0.274136	+	0.274136i
$100$	1.48981	+	2.58043i	0.148981	+	0.258043i
$101$	2.30534	−	3.99296i	0.229390	−	0.397315i	−0.728238	−	0.685325i	$-0.759660\pi$
$101$	2.30534	−	3.99296i	0.229390	−	0.397315i	0.957627	+	0.288010i	$0.0929936\pi$
$102$	0.610921	+	2.27999i	0.0604902	+	0.225752i
$103$	−6.27668	+	10.8715i	−0.618460	+	1.07120i	0.371307	+	0.928510i	$0.378910\pi$
$103$	−6.27668	+	10.8715i	−0.618460	+	1.07120i	−0.989767	+	0.142694i	$0.954424\pi$
$104$	0.996704	+	3.46505i	0.0977348	+	0.339776i
$105$	3.53864	−	1.27305i	0.345336	−	0.124237i
$106$	2.11439	−	7.89102i	0.205368	−	0.766443i
$107$	0.574182			0.0555083			0.0277541	−	0.999615i	$-0.491164\pi$
$107$	0.574182			0.0555083			0.0277541	+	0.999615i	$0.491164\pi$
$108$	−1.00000			−0.0962250
$109$	−5.04790	+	18.8390i	−0.483501	+	1.80445i	0.103218	+	0.994659i	$0.467086\pi$
$109$	−5.04790	+	18.8390i	−0.483501	+	1.80445i	−0.586718	+	0.809791i	$0.699580\pi$
$110$	5.29612	+	1.41909i	0.504965	+	0.135305i
$111$	7.32883	−	1.96375i	0.695622	−	0.186391i
$112$	−1.50946	−	2.17291i	−0.142630	−	0.205321i
$113$	5.28204	−	9.14876i	0.496892	−	0.860643i	−0.503101	−	0.864227i	$-0.667808\pi$
$113$	5.28204	−	9.14876i	0.496892	−	0.860643i	0.999994	+	0.00358469i	$0.00114104\pi$
$114$		−	6.04757i		−	0.566407i
$115$	11.1319	−	2.98279i	1.03806	−	0.278147i
$116$	0.382331	−	0.220739i	0.0354986	−	0.0204951i
$117$	3.60495	−	0.0659206i	0.333278	−	0.00609436i
$118$		−	8.39942i		−	0.773230i
$119$	3.56294	+	5.12898i	0.326615	+	0.470172i
$120$	0.710699	+	1.23097i	0.0648777	+	0.112371i
$121$	−3.35998	+	1.93988i	−0.305452	+	0.176353i
$122$	10.2941	+	2.75829i	0.931981	+	0.249724i
$123$	0.976687	+	0.976687i	0.0880649	+	0.0880649i
$124$	−0.855281	+	3.19195i	−0.0768065	+	0.286646i
$125$	−8.02017	−	8.02017i	−0.717346	−	0.717346i
$126$	−2.48955	+	0.895632i	−0.221786	+	0.0797892i
$127$	13.6070	−	7.85602i	1.20743	−	0.697109i	0.245232	−	0.969465i	$-0.421136\pi$
$127$	13.6070	−	7.85602i	1.20743	−	0.697109i	0.962197	+	0.272355i	$0.0878027\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−4.35309	−	7.53977i	−0.383268	−	0.663840i
$130$	−2.64318	−	4.39073i	−0.231822	−	0.385092i
$131$	12.0386	+	6.95051i	1.05182	+	0.607269i	0.923159	−	0.384420i	$-0.125598\pi$
$131$	12.0386	+	6.95051i	1.05182	+	0.607269i	0.128662	+	0.991688i	$0.458932\pi$
$132$	−3.72599	−	0.998376i	−0.324306	−	0.0868975i
$133$	−5.41639	−	15.0557i	−0.469661	−	1.30550i
$134$	0.0341288	+	0.0197043i	0.00294828	+	0.00170219i
$135$	1.37297	−	0.367885i	0.118166	−	0.0316625i
$136$	−1.66907	+	1.66907i	−0.143121	+	0.143121i
$137$	−7.51981	+	7.51981i	−0.642461	+	0.642461i	−0.951160	−	0.308699i	$-0.900106\pi$
$137$	−7.51981	+	7.51981i	−0.642461	+	0.642461i	0.308699	+	0.951160i	$0.400106\pi$
$138$	−7.83167	+	2.09849i	−0.666676	+	0.178635i
$139$	−4.31229	−	2.48970i	−0.365764	−	0.211174i	0.305842	−	0.952082i	$-0.401062\pi$
$139$	−4.31229	−	2.48970i	−0.365764	−	0.211174i	−0.671606	+	0.740908i	$0.734395\pi$
$140$	2.87181	+	2.42803i	0.242713	+	0.205206i
$141$	−6.14515	−	1.64659i	−0.517515	−	0.138668i
$142$	−10.9851	−	6.34224i	−0.921848	−	0.532229i
$143$	13.4978	+	3.35348i	1.12874	+	0.280432i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.443721	+	0.443721i	−0.0368490	+	0.0368490i
$146$	6.92590	−	3.99867i	0.573192	−	0.330932i
$147$	−5.39569	+	4.45943i	−0.445029	+	0.367808i
$148$	5.36507	+	5.36507i	0.441006	+	0.441006i
$149$	−2.03574	+	7.59748i	−0.166774	+	0.622410i	0.831033	+	0.556223i	$0.187750\pi$
$149$	−2.03574	+	7.59748i	−0.166774	+	0.622410i	−0.997807	+	0.0661868i	$0.978917\pi$
$150$	2.10691	+	2.10691i	0.172029	+	0.172029i
$151$	−14.8742	−	3.98554i	−1.21045	−	0.324338i	−0.403510	−	0.914975i	$-0.632210\pi$
$151$	−14.8742	−	3.98554i	−1.21045	−	0.324338i	−0.806937	+	0.590637i	$0.798877\pi$
$152$	5.23735	−	3.02378i	0.424805	−	0.245261i
$153$	1.18021	+	2.04418i	0.0954142	+	0.165262i
$154$	−10.1702	+	0.851611i	−0.819539	+	0.0686248i
$155$		−	4.69709i		−	0.377279i
$156$	1.85956	+	3.08902i	0.148884	+	0.247319i
$157$	−8.88249	+	5.12831i	−0.708900	+	0.409283i	−0.810653	−	0.585526i	$-0.800888\pi$
$157$	−8.88249	+	5.12831i	−0.708900	+	0.409283i	0.101754	+	0.994810i	$0.467555\pi$
$158$	11.8729	−	3.18133i	0.944555	−	0.253093i
$159$		−	8.16938i		−	0.647874i
$160$	−0.710699	+	1.23097i	−0.0561857	+	0.0973165i
$161$	−17.6178	+	12.2386i	−1.38848	+	0.964535i
$162$	−0.965926	+	0.258819i	−0.0758903	+	0.0203347i
$163$	−1.72071	−	0.461062i	−0.134776	−	0.0361132i	0.190800	−	0.981629i	$-0.438892\pi$
$163$	−1.72071	−	0.461062i	−0.134776	−	0.0361132i	−0.325576	+	0.945516i	$0.605558\pi$
$164$	−0.357492	+	1.33418i	−0.0279154	+	0.104182i
$165$	5.48295			0.426847
$166$	13.2633			1.02943
$167$	−0.545200	+	2.03471i	−0.0421888	+	0.157451i	−0.983807	−	0.179233i	$-0.942639\pi$
$167$	−0.545200	+	2.03471i	−0.0421888	+	0.157451i	0.941618	+	0.336683i	$0.109305\pi$
$168$	−2.02041	−	1.70820i	−0.155878	−	0.131790i
$169$	−6.90726	−	11.0132i	−0.531328	−	0.847166i
$170$	1.67755	−	2.90560i	0.128662	−	0.222849i
$171$	−1.56523	−	5.84150i	−0.119696	−	0.446711i
$172$	4.35309	−	7.53977i	0.331920	−	0.574902i
$173$	2.20729	+	3.82314i	0.167817	+	0.290668i	0.937652	−	0.347575i	$-0.112995\pi$
$173$	2.20729	+	3.82314i	0.167817	+	0.290668i	−0.769835	+	0.638243i	$0.779661\pi$
$174$	0.312172	−	0.312172i	0.0236657	−	0.0236657i
$175$	7.13228	+	3.35824i	0.539149	+	0.253859i
$176$	−0.998376	−	3.72599i	−0.0752555	−	0.280857i
$177$	−2.17393	−	8.11322i	−0.163403	−	0.609827i
$178$			2.06187i			0.154544i
$179$	−19.6430	−	11.3409i	−1.46819	−	0.847660i	−0.468825	−	0.883291i	$-0.655322\pi$
$179$	−19.6430	−	11.3409i	−1.46819	−	0.847660i	−0.999365	+	0.0356312i	$0.988656\pi$
$180$	1.00508	+	1.00508i	0.0749143	+	0.0749143i
$181$	4.69879			0.349259			0.174629	−	0.984634i	$-0.444127\pi$
$181$	4.69879			0.349259			0.174629	+	0.984634i	$0.444127\pi$
$182$	7.39609	+	6.02477i	0.548235	+	0.446586i
$183$	10.6572			0.787803
$184$	−5.73318	−	5.73318i	−0.422656	−	0.422656i
$185$	−9.33980	−	5.39233i	−0.686675	−	0.396452i
$186$			3.30455i			0.242302i
$187$	2.35658	+	8.79489i	0.172330	+	0.643146i
$188$	−1.64659	−	6.14515i	−0.120090	−	0.448181i
$189$	−2.17291	+	1.50946i	−0.158056	+	0.109797i
$190$	−6.07829	+	6.07829i	−0.440966	+	0.440966i
$191$	11.5048	+	19.9269i	0.832457	+	1.44186i	0.896084	+	0.443885i	$0.146400\pi$
$191$	11.5048	+	19.9269i	0.832457	+	1.44186i	−0.0636265	+	0.997974i	$0.520267\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	1.13349	+	4.23024i	0.0815904	+	0.304499i	0.994647	−	0.103334i	$-0.0329511\pi$
$193$	1.13349	+	4.23024i	0.0815904	+	0.304499i	−0.913056	+	0.407833i	$0.866284\pi$
$194$	6.99377	−	12.1136i	0.502124	−	0.869703i
$195$	−3.68952	−	3.55701i	−0.264212	−	0.254723i
$196$	−6.55983	−	2.44309i	−0.468559	−	0.174506i
$197$	−2.73968	+	10.2246i	−0.195194	+	0.728476i	0.797022	+	0.603950i	$0.206407\pi$
$197$	−2.73968	+	10.2246i	−0.195194	+	0.728476i	−0.992216	+	0.124525i	$0.960259\pi$
$198$	−3.85743			−0.274136
$199$	10.2868			0.729215			0.364608	−	0.931161i	$-0.381203\pi$
$199$	10.2868			0.729215			0.364608	+	0.931161i	$0.381203\pi$
$200$	−0.771184	+	2.87810i	−0.0545309	+	0.203512i
$201$	0.0380657	+	0.0101997i	0.00268495	+	0.000719430i
$202$	4.45357	−	1.19333i	0.313352	−	0.0839625i
$203$	0.497576	−	1.05676i	0.0349230	−	0.0741699i
$204$	−1.18021	+	2.04418i	−0.0826311	+	0.143121i
$205$		−	1.96330i		−	0.137123i
$206$	−12.1256	+	3.24905i	−0.844832	+	0.226372i
$207$	−7.02168	+	4.05397i	−0.488041	+	0.281770i
$208$	−1.74539	+	3.15494i	−0.121021	+	0.218756i
$209$		−	23.3281i		−	1.61364i
$210$	3.40238	+	1.60201i	0.234786	+	0.110549i
$211$	−5.66861	−	9.81832i	−0.390243	−	0.675921i	0.602238	−	0.798317i	$-0.294276\pi$
$211$	−5.66861	−	9.81832i	−0.390243	−	0.675921i	−0.992481	+	0.122395i	$0.960942\pi$
$212$	7.07489	−	4.08469i	0.485906	−	0.280538i
$213$	−12.2523	−	3.28299i	−0.839512	−	0.224946i
$214$	0.406008	+	0.406008i	0.0277541	+	0.0277541i
$215$	−3.20287	+	11.9533i	−0.218434	+	0.815207i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	2.95966	+	8.22684i	0.200915	+	0.558474i
$218$	−16.8906	+	9.75179i	−1.14398	+	0.660474i
$219$	5.65497	−	5.65497i	0.382128	−	0.382128i
$220$	2.74147	+	4.74837i	0.184830	+	0.320135i
$221$	4.11984	−	7.44697i	0.277130	−	0.500937i
$222$	6.57085	+	3.79368i	0.441006	+	0.254615i
$223$	4.73346	+	1.26833i	0.316976	+	0.0849335i	0.413799	−	0.910368i	$-0.364201\pi$
$223$	4.73346	+	1.26833i	0.316976	+	0.0849335i	−0.0968232	+	0.995302i	$0.530868\pi$
$224$	0.469134	−	2.60383i	0.0313453	−	0.173975i
$225$	2.58043	+	1.48981i	0.172029	+	0.0993208i
$226$	10.2041	−	2.73418i	0.678768	−	0.181875i
$227$	−5.20069	+	5.20069i	−0.345182	+	0.345182i	−0.858311	−	0.513129i	$-0.828486\pi$
$227$	−5.20069	+	5.20069i	−0.345182	+	0.345182i	0.513129	+	0.858311i	$0.328486\pi$
$228$	4.27628	−	4.27628i	0.283203	−	0.283203i
$229$	4.83929	−	1.29668i	0.319789	−	0.0856873i	−0.0953536	−	0.995443i	$-0.530398\pi$
$229$	4.83929	−	1.29668i	0.319789	−	0.0856873i	0.415143	+	0.909756i	$0.363732\pi$
$230$	9.98061	+	5.76231i	0.658102	+	0.379955i
$231$	−9.60325	+	3.45484i	−0.631848	+	0.227312i
$232$	0.426435	+	0.114263i	0.0279968	+	0.00750173i
$233$	9.40002	+	5.42710i	0.615816	+	0.355541i	0.775238	−	0.631669i	$-0.217630\pi$
$233$	9.40002	+	5.42710i	0.615816	+	0.355541i	−0.159422	+	0.987210i	$0.550963\pi$
$234$	2.59570	+	2.50247i	0.169686	+	0.163592i
$235$	4.52142	+	7.83132i	0.294945	+	0.510859i
$236$	5.93929	−	5.93929i	0.386615	−	0.386615i
$237$	10.6449	−	6.14585i	0.691462	−	0.399216i
$238$	−1.10735	+	6.14612i	−0.0717789	+	0.398393i
$239$	6.33211	+	6.33211i	0.409590	+	0.409590i	0.881596	−	0.472006i	$-0.156470\pi$
$239$	6.33211	+	6.33211i	0.409590	+	0.409590i	−0.472006	+	0.881596i	$0.656470\pi$
$240$	−0.367885	+	1.37297i	−0.0237469	+	0.0886246i
$241$	14.3855	+	14.3855i	0.926649	+	0.926649i	0.997488	−	0.0708386i	$-0.0225675\pi$
$241$	14.3855	+	14.3855i	0.926649	+	0.926649i	−0.0708386	+	0.997488i	$0.522568\pi$
$242$	−3.74757	−	1.00416i	−0.240903	−	0.0645497i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	5.32860	+	9.22941i	0.341129	+	0.590852i
$245$	9.90519	+	0.941011i	0.632820	+	0.0601190i
$246$			1.38124i			0.0880649i
$247$	−15.1339	+	15.6976i	−0.962944	+	0.998818i
$248$	−2.86183	+	1.65228i	−0.181726	+	0.104920i
$249$	12.8114	−	3.43279i	0.811887	−	0.217544i
$250$		−	11.3422i		−	0.717346i
$251$	−0.890713	+	1.54276i	−0.0562213	+	0.0973782i	−0.892766	−	0.450520i	$-0.851239\pi$
$251$	−0.890713	+	1.54276i	−0.0562213	+	0.0973782i	0.836545	+	0.547898i	$0.184572\pi$
$252$	−2.39368	−	1.12707i	−0.150788	−	0.0709986i
$253$	−30.2101	+	8.09478i	−1.89929	+	0.508914i
$254$	15.1767	+	4.06658i	0.952269	+	0.255160i
$255$	0.868362	−	3.24077i	0.0543789	−	0.202945i
$256$	1.00000			0.0625000
$257$	3.89260			0.242814			0.121407	−	0.992603i	$-0.461259\pi$
$257$	3.89260			0.242814			0.121407	+	0.992603i	$0.461259\pi$
$258$	2.25332	−	8.40952i	0.140286	−	0.523554i
$259$	19.7562	+	3.55949i	1.22759	+	0.221176i
$260$	1.23570	−	4.97372i	0.0766349	−	0.308457i
$261$	0.220739	−	0.382331i	0.0136634	−	0.0236657i
$262$	3.59785	+	13.4274i	0.222276	+	0.829545i
$263$	−1.66195	+	2.87858i	−0.102480	+	0.177501i	−0.912706	−	0.408617i	$-0.866011\pi$
$263$	−1.66195	+	2.87858i	−0.102480	+	0.177501i	0.810226	+	0.586118i	$0.199344\pi$
$264$	−1.92872	−	3.34063i	−0.118704	−	0.205602i
$265$	−8.21089	+	8.21089i	−0.504391	+	0.504391i
$266$	6.81602	−	14.4760i	0.417917	−	0.887578i
$267$	0.533652	+	1.99161i	0.0326589	+	0.121885i
$268$	0.0101997	+	0.0380657i	0.000623044	+	0.00232523i
$269$		−	13.0921i		−	0.798242i	−0.916898	−	0.399121i	$-0.869315\pi$
$269$		−	13.0921i		−	0.798242i	0.916898	−	0.399121i	$-0.130685\pi$
$270$	1.23097	+	0.710699i	0.0749143	+	0.0432518i
$271$	−17.1585	−	17.1585i	−1.04231	−	1.04231i	−0.999065	−	0.0432406i	$-0.986232\pi$
$271$	−17.1585	−	17.1585i	−1.04231	−	1.04231i	−0.0432406	−	0.999065i	$-0.513768\pi$
$272$	−2.36042			−0.143121
$273$	8.70340	+	3.90523i	0.526754	+	0.236355i
$274$	−10.6346			−0.642461
$275$	8.12727	+	8.12727i	0.490093	+	0.490093i
$276$	−7.02168	−	4.05397i	−0.422656	−	0.244020i
$277$			29.9233i			1.79792i	0.438032	+	0.898959i	$0.355676\pi$
$277$			29.9233i			1.79792i	−0.438032	+	0.898959i	$0.644324\pi$
$278$	−1.28877	−	4.80974i	−0.0772950	−	0.288469i
$279$	0.855281	+	3.19195i	0.0512043	+	0.191097i
$280$	0.313804	+	3.74755i	0.0187534	+	0.223959i
$281$	−14.1065	+	14.1065i	−0.841521	+	0.841521i	−0.989057	−	0.147535i	$-0.952866\pi$
$281$	−14.1065	+	14.1065i	−0.841521	+	0.841521i	0.147535	+	0.989057i	$0.452866\pi$
$282$	−3.18096	−	5.50959i	−0.189423	−	0.328091i
$283$	−8.34190	+	14.4486i	−0.495874	+	0.858880i	−0.999989	−	0.00475723i	$-0.998486\pi$
$283$	−8.34190	+	14.4486i	−0.495874	+	0.858880i	0.504114	+	0.863637i	$0.331819\pi$
$284$	−3.28299	−	12.2523i	−0.194809	−	0.727038i
$285$	−4.29800	+	7.44436i	−0.254592	+	0.440966i
$286$	7.17314	+	11.9157i	0.424156	+	0.704588i
$287$	1.23709	+	3.43867i	0.0730228	+	0.202978i
$288$	0.258819	−	0.965926i	0.0152511	−	0.0569177i
$289$	−11.4284			−0.672261
$290$	−0.627516			−0.0368490
$291$	3.62024	−	13.5109i	0.212222	−	0.792025i
$292$	7.72484	+	2.06986i	0.452062	+	0.121130i
$293$	−31.5634	+	8.45739i	−1.84395	+	0.494086i	−0.999159	−	0.0410025i	$-0.986945\pi$
$293$	−31.5634	+	8.45739i	−1.84395	+	0.494086i	−0.844796	+	0.535089i	$0.820278\pi$
$294$	−6.96862	−	0.662032i	−0.406418	−	0.0386105i
$295$	−5.96947	+	10.3394i	−0.347556	+	0.601984i
$296$			7.58736i			0.441006i
$297$	−3.72599	+	0.998376i	−0.216204	+	0.0579317i
$298$	−6.81171	+	3.93275i	−0.394592	+	0.227818i
$299$	25.5800	+	14.1515i	1.47933	+	0.818401i
$300$			2.97962i			0.172029i
$301$	−1.92208	−	22.9540i	−0.110787	−	1.32305i
$302$	−7.69947	−	13.3359i	−0.443054	−	0.767393i
$303$	3.99296	−	2.30534i	0.229390	−	0.132438i
$304$	5.84150	+	1.56523i	0.335033	+	0.0897718i
$305$	−10.7113	−	10.7113i	−0.613330	−	0.613330i
$306$	−0.610921	+	2.27999i	−0.0349240	+	0.130338i
$307$	3.32023	+	3.32023i	0.189496	+	0.189496i	0.795478	−	0.605982i	$-0.207220\pi$
$307$	3.32023	+	3.32023i	0.189496	+	0.189496i	−0.605982	+	0.795478i	$0.707220\pi$
$308$	−7.79360	−	6.58924i	−0.444082	−	0.375457i
$309$	−10.8715	+	6.27668i	−0.618460	+	0.357068i
$310$	3.32134	−	3.32134i	0.188640	−	0.188640i
$311$	13.3219	+	23.0743i	0.755417	+	1.30842i	0.945167	+	0.326588i	$0.105899\pi$
$311$	13.3219	+	23.0743i	0.755417	+	1.30842i	−0.189749	+	0.981833i	$0.560768\pi$
$312$	−0.869355	+	3.49917i	−0.0492175	+	0.198102i
$313$	6.79782	+	3.92473i	0.384236	+	0.221839i	0.679660	−	0.733528i	$-0.262128\pi$
$313$	6.79782	+	3.92473i	0.384236	+	0.221839i	−0.295424	+	0.955366i	$0.595461\pi$
$314$	−9.90713	−	2.65461i	−0.559091	−	0.149808i
$315$	3.70108	+	0.666826i	0.208532	+	0.0375714i
$316$	10.6449	+	6.14585i	0.598824	+	0.345731i
$317$	−4.83309	+	1.29502i	−0.271454	+	0.0727358i	−0.391978	−	0.919975i	$-0.628209\pi$
$317$	−4.83309	+	1.29502i	−0.271454	+	0.0727358i	0.120524	+	0.992710i	$0.461542\pi$
$318$	5.77663	−	5.77663i	0.323937	−	0.323937i
$319$	1.20418	−	1.20418i	0.0674213	−	0.0674213i
$320$	−1.37297	+	0.367885i	−0.0767511	+	0.0205654i
$321$	0.497256	+	0.287091i	0.0277541	+	0.0160239i
$322$	−21.1117	−	3.80371i	−1.17651	−	0.211972i
$323$	−13.7884	−	3.69458i	−0.767206	−	0.205572i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	−0.196419	−	10.7414i	−0.0108953	−	0.595825i
$326$	−0.890703	−	1.54274i	−0.0493315	−	0.0854447i
$327$	−13.7911	+	13.7911i	−0.762650	+	0.762650i
$328$	−1.19619	+	0.690622i	−0.0660487	+	0.0381332i
$329$	−12.8537	−	10.8674i	−0.708648	−	0.599139i
$330$	3.87703	+	3.87703i	0.213423	+	0.213423i
$331$	−1.80754	+	6.74583i	−0.0993513	+	0.370784i	−0.997643	−	0.0686150i	$-0.978142\pi$
$331$	−1.80754	+	6.74583i	−0.0993513	+	0.370784i	0.898292	+	0.439399i	$0.144809\pi$
$332$	9.37857	+	9.37857i	0.514716	+	0.514716i
$333$	7.32883	+	1.96375i	0.401617	+	0.107613i
$334$	−1.82427	+	1.05324i	−0.0998198	+	0.0576310i
$335$	−0.0280076	−	0.0485106i	−0.00153022	−	0.00265042i
$336$	−0.220772	−	2.63652i	−0.0120441	−	0.143834i
$337$		−	11.2260i		−	0.611518i	−0.952109	−	0.305759i	$-0.901090\pi$
$337$		−	11.2260i		−	0.611518i	0.952109	−	0.305759i	$-0.0989101\pi$
$338$	2.90331	−	12.6717i	0.157919	−	0.689247i
$339$	9.14876	−	5.28204i	0.496892	−	0.286881i
$340$	3.24077	−	0.868362i	0.175756	−	0.0470935i
$341$			12.7471i			0.690293i
$342$	3.02378	−	5.23735i	0.163507	−	0.283203i
$343$	−17.9417	+	4.59316i	−0.968758	+	0.248007i
$344$	8.40952	−	2.25332i	0.453411	−	0.121491i
$345$	11.1319	+	2.98279i	0.599323	+	0.160588i
$346$	−1.14258	+	4.26416i	−0.0614254	+	0.229243i
$347$	32.2202			1.72967			0.864836	−	0.502055i	$-0.167423\pi$
$347$	32.2202			1.72967			0.864836	+	0.502055i	$0.167423\pi$
$348$	0.441478			0.0236657
$349$	−0.290712	+	1.08495i	−0.0155614	+	0.0580761i	−0.973270	−	0.229664i	$-0.926237\pi$
$349$	−0.290712	+	1.08495i	−0.0155614	+	0.0580761i	0.957709	+	0.287740i	$0.0929039\pi$
$350$	2.66865	+	7.41792i	0.142645	+	0.396504i
$351$	3.15494	+	1.74539i	0.168398	+	0.0931618i
$352$	1.92872	−	3.34063i	0.102801	−	0.178056i
$353$	−2.30028	−	8.58477i	−0.122432	−	0.456921i	0.877303	−	0.479936i	$-0.159340\pi$
$353$	−2.30028	−	8.58477i	−0.122432	−	0.456921i	−0.999735	+	0.0230148i	$0.992674\pi$
$354$	4.19971	−	7.27411i	0.223212	−	0.386615i
$355$	9.01485	+	15.6142i	0.478459	+	0.828715i
$356$	−1.45796	+	1.45796i	−0.0772719	+	0.0772719i
$357$	0.521113	+	6.22330i	0.0275802	+	0.329372i
$358$	−5.87049	−	21.9090i	−0.310265	−	1.15792i
$359$	−2.50353	−	9.34329i	−0.132131	−	0.493120i	0.867862	−	0.496805i	$-0.165494\pi$
$359$	−2.50353	−	9.34329i	−0.132131	−	0.493120i	−0.999993	+	0.00368517i	$0.998827\pi$
$360$			1.42140i			0.0749143i
$361$	15.2187	+	8.78654i	0.800986	+	0.462449i
$362$	3.32255	+	3.32255i	0.174629	+	0.174629i
$363$	−3.87977			−0.203635
$364$	0.969671	+	9.48998i	0.0508246	+	0.497410i
$365$	−11.3674			−0.594997
$366$	7.53578	+	7.53578i	0.393902	+	0.393902i
$367$	23.0143	+	13.2873i	1.20134	+	0.693591i	0.960852	−	0.277062i	$-0.0893607\pi$
$367$	23.0143	+	13.2873i	1.20134	+	0.693591i	0.240483	+	0.970653i	$0.422694\pi$
$368$		−	8.10794i		−	0.422656i
$369$	0.357492	+	1.33418i	0.0186103	+	0.0694546i
$370$	−2.79128	−	10.4172i	−0.145112	−	0.541564i
$371$	9.20745	−	19.5549i	0.478027	−	1.01524i
$372$	−2.33667	+	2.33667i	−0.121151	+	0.121151i
$373$	4.87556	+	8.44473i	0.252447	+	0.437251i	0.964199	−	0.265180i	$-0.0854313\pi$
$373$	4.87556	+	8.44473i	0.252447	+	0.437251i	−0.711752	+	0.702431i	$0.752098\pi$
$374$	−4.55257	+	7.88528i	−0.235408	+	0.407738i
$375$	−2.93559	−	10.9558i	−0.151593	−	0.565753i
$376$	3.18096	−	5.50959i	0.164046	−	0.284135i
$377$	−1.59151	+	0.0291025i	−0.0819667	+	0.00149885i
$378$	−2.60383	−	0.469134i	−0.133926	−	0.0241296i
$379$	7.08824	−	26.4537i	0.364098	−	1.35883i	−0.504541	−	0.863388i	$-0.668338\pi$
$379$	7.08824	−	26.4537i	0.364098	−	1.35883i	0.868639	−	0.495445i	$-0.164995\pi$
$380$	−8.59601			−0.440966
$381$	15.7120			0.804952
$382$	−5.95532	+	22.2255i	−0.304701	+	1.13716i
$383$	−29.6308	−	7.93955i	−1.51406	−	0.405692i	−0.596281	−	0.802776i	$-0.703356\pi$
$383$	−29.6308	−	7.93955i	−1.51406	−	0.405692i	−0.917783	+	0.397083i	$0.870022\pi$
$384$	0.965926	−	0.258819i	0.0492922	−	0.0132078i
$385$	13.1244	+	6.17966i	0.668883	+	0.314944i
$386$	−2.18973	+	3.79273i	−0.111455	+	0.193045i
$387$		−	8.70617i		−	0.442560i
$388$	13.5109	−	3.62024i	0.685914	−	0.183790i
$389$	−2.94763	+	1.70182i	−0.149451	+	0.0862855i	−0.572861	−	0.819653i	$-0.694166\pi$
$389$	−2.94763	+	1.70182i	−0.149451	+	0.0862855i	0.423410	+	0.905938i	$0.360833\pi$
$390$	−0.0936995	−	5.12407i	−0.00474466	−	0.259467i
$391$			19.1381i			0.967856i
$392$	−2.91098	−	6.36602i	−0.147026	−	0.321533i
$393$	6.95051	+	12.0386i	0.350607	+	0.607269i
$394$	−9.16716	+	5.29266i	−0.461835	+	0.266641i
$395$	−16.8761	−	4.52194i	−0.849128	−	0.227523i
$396$	−2.72762	−	2.72762i	−0.137068	−	0.137068i
$397$	−6.61809	+	24.6991i	−0.332153	+	1.23961i	0.574771	+	0.818315i	$0.305091\pi$
$397$	−6.61809	+	24.6991i	−0.332153	+	1.23961i	−0.906923	+	0.421296i	$0.861575\pi$
$398$	7.27390	+	7.27390i	0.364608	+	0.364608i
$399$	2.83712	−	15.7468i	0.142034	−	0.788327i
$400$	−2.58043	+	1.48981i	−0.129022	+	0.0744906i
$401$	−1.51269	+	1.51269i	−0.0755399	+	0.0755399i	−0.743867	−	0.668327i	$-0.767011\pi$
$401$	−1.51269	+	1.51269i	−0.0755399	+	0.0755399i	0.668327	+	0.743867i	$0.267011\pi$
$402$	0.0197043	+	0.0341288i	0.000982759	+	0.00170219i
$403$	8.26955	−	8.57762i	0.411935	−	0.427281i
$404$	3.99296	+	2.30534i	0.198657	+	0.114695i
$405$	1.37297	+	0.367885i	0.0682232	+	0.0182804i
$406$	1.09908	−	0.395402i	0.0545464	−	0.0196235i
$407$	25.3466	+	14.6339i	1.25638	+	0.725373i
$408$	−2.27999	+	0.610921i	−0.112876	+	0.0302451i
$409$	−13.0979	+	13.0979i	−0.647652	+	0.647652i	−0.952425	−	0.304773i	$-0.901419\pi$
$409$	−13.0979	+	13.0979i	−0.647652	+	0.647652i	0.304773	+	0.952425i	$0.401419\pi$
$410$	1.38826	−	1.38826i	0.0685613	−	0.0685613i
$411$	−10.2723	+	2.75244i	−0.506693	+	0.135768i
$412$	−10.8715	−	6.27668i	−0.535602	−	0.309230i
$413$	3.94045	−	21.8706i	0.193897	−	1.07618i
$414$	−7.83167	−	2.09849i	−0.384905	−	0.103135i
$415$	−16.3267	−	9.42622i	−0.801445	−	0.462715i
$416$	−3.46505	+	0.996704i	−0.169888	+	0.0488674i
$417$	−2.48970	−	4.31229i	−0.121921	−	0.211174i
$418$	16.4954	−	16.4954i	0.806818	−	0.806818i
$419$	28.4741	−	16.4395i	1.39105	−	0.803124i	0.397620	−	0.917550i	$-0.369836\pi$
$419$	28.4741	−	16.4395i	1.39105	−	0.803124i	0.993432	+	0.114426i	$0.0365028\pi$
$420$	1.27305	+	3.53864i	0.0621185	+	0.172668i
$421$	11.1258	+	11.1258i	0.542238	+	0.542238i	0.924185	−	0.381946i	$-0.124746\pi$
$421$	11.1258	+	11.1258i	0.542238	+	0.542238i	−0.381946	+	0.924185i	$0.624746\pi$
$422$	2.93429	−	10.9509i	0.142839	−	0.533082i
$423$	−4.49856	−	4.49856i	−0.218727	−	0.218727i
$424$	7.89102	+	2.11439i	0.383222	+	0.102684i
$425$	6.09089	−	3.51658i	0.295452	−	0.170579i
$426$	−6.34224	−	10.9851i	−0.307283	−	0.532229i
$427$	25.5100	+	12.0114i	1.23451	+	0.581272i
$428$			0.574182i			0.0277541i
$429$	10.0127	+	9.65311i	0.483419	+	0.466056i
$430$	−10.7170	+	6.18747i	−0.516821	+	0.298386i
$431$	11.4795	−	3.07591i	0.552946	−	0.148162i	0.0284825	−	0.999594i	$-0.490932\pi$
$431$	11.4795	−	3.07591i	0.552946	−	0.148162i	0.524464	+	0.851433i	$0.324266\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	1.73495	−	3.00502i	0.0833765	−	0.144412i	−0.821322	−	0.570465i	$-0.806763\pi$
$433$	1.73495	−	3.00502i	0.0833765	−	0.144412i	0.904698	+	0.426053i	$0.140096\pi$
$434$	−3.72446	+	7.91005i	−0.178780	+	0.379695i
$435$	−0.606134	+	0.162413i	−0.0290619	+	0.00778712i
$436$	−18.8390	−	5.04790i	−0.902225	−	0.241750i
$437$	12.6908	−	47.3625i	0.607081	−	2.26566i
$438$	7.99734			0.382128
$439$	−16.8928			−0.806250			−0.403125	−	0.915145i	$-0.632076\pi$
$439$	−16.8928			−0.806250			−0.403125	+	0.915145i	$0.632076\pi$
$440$	−1.41909	+	5.29612i	−0.0676525	+	0.252483i
$441$	−6.90252	+	1.16414i	−0.328691	+	0.0554352i
$442$	8.17896	−	2.35264i	0.389034	−	0.111903i
$443$	0.108413	−	0.187777i	0.00515086	−	0.00892155i	−0.863438	−	0.504454i	$-0.831694\pi$
$443$	0.108413	−	0.187777i	0.00515086	−	0.00892155i	0.868589	+	0.495533i	$0.165027\pi$
$444$	1.96375	+	7.32883i	0.0931956	+	0.347811i
$445$	1.46537	−	2.53810i	0.0694652	−	0.120317i
$446$	2.45022	+	4.24391i	0.116021	+	0.200955i
$447$	−5.56174	+	5.56174i	−0.263061	+	0.263061i
$448$	2.17291	−	1.50946i	0.102660	−	0.0713151i
$449$	2.07566	+	7.74645i	0.0979562	+	0.365578i	0.997451	−	0.0713537i	$-0.0227319\pi$
$449$	2.07566	+	7.74645i	0.0979562	+	0.365578i	−0.899495	+	0.436931i	$0.856065\pi$
$450$	0.771184	+	2.87810i	0.0363539	+	0.135675i
$451$			5.32805i			0.250888i
$452$	9.14876	+	5.28204i	0.430321	+	0.248446i
$453$	−10.8887	−	10.8887i	−0.511595	−	0.511595i
$454$	−7.35489			−0.345182
$455$	−4.82255	−	12.6727i	−0.226085	−	0.594105i
$456$	6.04757			0.283203
$457$	22.0099	+	22.0099i	1.02958	+	1.02958i	0.999549	+	0.0300309i	$0.00956058\pi$
$457$	22.0099	+	22.0099i	1.02958	+	1.02958i	0.0300309	+	0.999549i	$0.490439\pi$
$458$	4.33879	+	2.50500i	0.202738	+	0.117051i
$459$			2.36042i			0.110175i
$460$	2.98279	+	11.1319i	0.139073	+	0.519029i
$461$	−10.2018	−	38.0738i	−0.475147	−	1.77327i	−0.620835	−	0.783941i	$-0.713206\pi$
$461$	−10.2018	−	38.0738i	−0.475147	−	1.77327i	0.145689	−	0.989331i	$-0.453460\pi$
$462$	−9.23346	−	4.34759i	−0.429580	−	0.202268i
$463$	6.13141	−	6.13141i	0.284951	−	0.284951i	−0.550129	−	0.835080i	$-0.685421\pi$
$463$	6.13141	−	6.13141i	0.284951	−	0.284951i	0.835080	+	0.550129i	$0.185421\pi$
$464$	0.220739	+	0.382331i	0.0102476	+	0.0177493i
$465$	2.34854	−	4.06780i	0.108911	−	0.188640i
$466$	2.80927	+	10.4844i	0.130137	+	0.485678i
$467$	−6.52135	+	11.2953i	−0.301772	+	0.522684i	−0.976537	−	0.215348i	$-0.930911\pi$
$467$	−6.52135	+	11.2953i	−0.301772	+	0.522684i	0.674765	+	0.738032i	$0.264245\pi$
$468$	0.0659206	+	3.60495i	0.00304718	+	0.166639i
$469$	0.0796215	+	0.0673174i	0.00367658	+	0.00310843i
$470$	−2.34046	+	8.73470i	−0.107957	+	0.402902i
$471$	−10.2566			−0.472600
$472$	8.39942			0.386615
$473$	8.69204	−	32.4391i	0.399660	−	1.49155i
$474$	11.8729	+	3.18133i	0.545339	+	0.146123i
$475$	−17.4055	+	4.66379i	−0.798618	+	0.213989i
$476$	−5.12898	+	3.56294i	−0.235086	+	0.163307i
$477$	4.08469	−	7.07489i	0.187025	−	0.323937i
$478$			8.95495i			0.409590i
$479$	−33.7720	+	9.04918i	−1.54308	+	0.413467i	−0.927260	−	0.374418i	$-0.877842\pi$
$479$	−33.7720	+	9.04918i	−1.54308	+	0.413467i	−0.615821	+	0.787886i	$0.711176\pi$
$480$	−1.23097	+	0.710699i	−0.0561857	+	0.0324388i
$481$	−7.56235	−	26.2906i	−0.344814	−	1.19875i
$482$			20.3441i			0.926649i
$483$	−21.3768	+	1.79000i	−0.972677	+	0.0814479i
$484$	−1.93988	−	3.35998i	−0.0881765	−	0.152726i
$485$	−17.2182	+	9.94094i	−0.781839	+	0.451395i
$486$	−0.965926	−	0.258819i	−0.0438153	−	0.0117403i
$487$	−23.3442	−	23.3442i	−1.05783	−	1.05783i	−0.998222	−	0.0596036i	$-0.981016\pi$
$487$	−23.3442	−	23.3442i	−1.05783	−	1.05783i	−0.0596036	−	0.998222i	$-0.518984\pi$
$488$	−2.75829	+	10.2941i	−0.124862	+	0.465991i
$489$	−1.25964	−	1.25964i	−0.0569631	−	0.0569631i
$490$	6.33863	+	7.66943i	0.286350	+	0.346469i
$491$	36.0599	−	20.8192i	1.62736	−	0.939556i	0.642482	−	0.766301i	$-0.277905\pi$
$491$	36.0599	−	20.8192i	1.62736	−	0.939556i	0.984877	−	0.173256i	$-0.0554287\pi$
$492$	−0.976687	+	0.976687i	−0.0440324	+	0.0440324i
$493$	−0.521036	−	0.902461i	−0.0234663	−	0.0406448i
$494$	−21.8012	+	0.398659i	−0.980881	+	0.0179365i
$495$	4.74837	+	2.74147i	0.213423	+	0.123220i
$496$	−3.19195	−	0.855281i	−0.143323	−	0.0384033i
$497$	−25.6279	−	21.6676i	−1.14957	−	0.971923i
$498$	11.4863	+	6.63165i	0.514716	+	0.297171i
$499$	−6.56533	+	1.75918i	−0.293905	+	0.0787515i	−0.402759	−	0.915306i	$-0.631949\pi$
$499$	−6.56533	+	1.75918i	−0.293905	+	0.0787515i	0.108854	+	0.994058i	$0.465282\pi$
$500$	8.02017	−	8.02017i	0.358673	−	0.358673i
$501$	−1.48951	+	1.48951i	−0.0665465	+	0.0665465i
$502$	−1.72073	+	0.461067i	−0.0767997	+	0.0205784i
$503$	−7.14428	−	4.12475i	−0.318548	−	0.183914i	0.332197	−	0.943210i	$-0.392210\pi$
$503$	−7.14428	−	4.12475i	−0.318548	−	0.183914i	−0.650745	+	0.759296i	$0.725543\pi$
$504$	−0.895632	−	2.48955i	−0.0398946	−	0.110893i
$505$	−6.33030	−	1.69620i	−0.281695	−	0.0754799i
$506$	−27.0856	−	15.6379i	−1.20410	−	0.695190i
$507$	−0.475281	−	12.9913i	−0.0211080	−	0.576964i
$508$	7.85602	+	13.6070i	0.348555	+	0.603714i
$509$	24.2138	−	24.2138i	1.07326	−	1.07326i	0.0761637	−	0.997095i	$-0.475733\pi$
$509$	24.2138	−	24.2138i	1.07326	−	1.07326i	0.997095	−	0.0761637i	$-0.0242672\pi$
$510$	2.90560	−	1.67755i	0.128662	−	0.0742830i
$511$	19.9098	−	7.16267i	0.880756	−	0.316858i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.56523	−	5.84150i	0.0691064	−	0.257909i
$514$	2.75249	+	2.75249i	0.121407	+	0.121407i
$515$	17.2353	+	4.61820i	0.759480	+	0.203502i
$516$	7.53977	−	4.35309i	0.331920	−	0.191634i
$517$	−12.2703	−	21.2528i	−0.539649	−	0.934699i
$518$	11.4528	+	16.4867i	0.503207	+	0.724382i
$519$			4.41458i			0.193779i
$520$	4.39073	−	2.64318i	0.192546	−	0.115911i
$521$	18.7607	−	10.8315i	0.821921	−	0.474536i	−0.0291576	−	0.999575i	$-0.509282\pi$
$521$	18.7607	−	10.8315i	0.821921	−	0.474536i	0.851078	+	0.525039i	$0.175949\pi$
$522$	0.426435	−	0.114263i	0.0186646	−	0.00500115i
$523$		−	30.1085i		−	1.31655i	−0.752776	−	0.658277i	$-0.771286\pi$
$523$		−	30.1085i		−	1.31655i	0.752776	−	0.658277i	$-0.228714\pi$
$524$	−6.95051	+	12.0386i	−0.303634	+	0.525910i
$525$	4.49761	+	6.47446i	0.196292	+	0.282569i
$526$	−3.21064	+	0.860288i	−0.139990	+	0.0375103i
$527$	7.53434	+	2.01882i	0.328201	+	0.0879412i
$528$	0.998376	−	3.72599i	0.0434488	−	0.162153i
$529$	−42.7387			−1.85820
$530$	−11.6120			−0.504391
$531$	2.17393	−	8.11322i	0.0943406	−	0.352084i
$532$	15.0557	−	5.41639i	0.652748	−	0.234830i
$533$	3.45652	−	3.58529i	0.149719	−	0.155296i
$534$	−1.03094	+	1.78563i	−0.0446129	+	0.0772719i
$535$	−0.211233	−	0.788333i	−0.00913240	−	0.0340826i
$536$	−0.0197043	+	0.0341288i	−0.000851094	+	0.00147414i
$537$	−11.3409	−	19.6430i	−0.489397	−	0.847660i
$538$	9.25754	−	9.25754i	0.399121	−	0.399121i
$539$	−26.8810	−	2.55374i	−1.15785	−	0.109997i
$540$	0.367885	+	1.37297i	0.0158313	+	0.0590830i
$541$	0.354527	+	1.32311i	0.0152423	+	0.0568850i	0.973128	−	0.230264i	$-0.0739591\pi$
$541$	0.354527	+	1.32311i	0.0152423	+	0.0568850i	−0.957886	+	0.287149i	$0.907292\pi$
$542$		−	24.2658i		−	1.04231i
$543$	4.06927	+	2.34940i	0.174629	+	0.100822i
$544$	−1.66907	−	1.66907i	−0.0715606	−	0.0715606i
$545$	27.7224			1.18750
$546$	3.39282	+	8.91565i	0.145199	+	0.381555i
$547$	13.2992			0.568632			0.284316	−	0.958731i	$-0.408233\pi$
$547$	13.2992			0.568632			0.284316	+	0.958731i	$0.408233\pi$
$548$	−7.51981	−	7.51981i	−0.321231	−	0.321231i
$549$	9.22941	+	5.32860i	0.393902	+	0.227419i
$550$			11.4937i			0.490093i
$551$	0.691013	+	2.57889i	0.0294381	+	0.109865i
$552$	−2.09849	−	7.83167i	−0.0893176	−	0.333338i
$553$	32.4074	−	2.71366i	1.37810	−	0.115396i
$554$	−21.1590	+	21.1590i	−0.898959	+	0.898959i
$555$	−5.39233	−	9.33980i	−0.228892	−	0.396452i
$556$	2.48970	−	4.31229i	0.105587	−	0.182882i
$557$	4.55371	+	16.9947i	0.192947	+	0.720088i	0.992789	+	0.119877i	$0.0382500\pi$
$557$	4.55371	+	16.9947i	0.192947	+	0.720088i	−0.799842	+	0.600211i	$0.795083\pi$
$558$	−1.65228	+	2.86183i	−0.0699464	+	0.121151i
$559$	−26.8935	+	16.1897i	−1.13747	+	0.684751i
$560$	−2.42803	+	2.87181i	−0.102603	+	0.121356i
$561$	−2.35658	+	8.79489i	−0.0994951	+	0.371321i
$562$	−19.9496			−0.841521
$563$	−20.7446			−0.874280			−0.437140	−	0.899394i	$-0.644009\pi$
$563$	−20.7446			−0.874280			−0.437140	+	0.899394i	$0.644009\pi$
$564$	1.64659	−	6.14515i	0.0693338	−	0.258757i
$565$	−14.5041	−	3.88637i	−0.610193	−	0.163501i
$566$	−16.1153	+	4.31808i	−0.677377	+	0.181503i
$567$	−2.63652	+	0.220772i	−0.110724	+	0.00927153i
$568$	6.34224	−	10.9851i	0.266114	−	0.460924i
$569$		−	6.93297i		−	0.290645i	−0.989384	−	0.145323i	$-0.953578\pi$
$569$		−	6.93297i		−	0.290645i	0.989384	−	0.145323i	$-0.0464220\pi$
$570$	−8.30310	+	2.22481i	−0.347779	+	0.0931870i
$571$	−25.9520	+	14.9834i	−1.08606	+	0.627035i	−0.932524	−	0.361108i	$-0.882398\pi$
$571$	−25.9520	+	14.9834i	−1.08606	+	0.627035i	−0.153533	+	0.988144i	$0.549065\pi$
$572$	−3.35348	+	13.4978i	−0.140216	+	0.564372i
$573$			23.0096i			0.961239i
$574$	−1.55676	+	3.30626i	−0.0649777	+	0.138001i
$575$	12.0793	+	20.9220i	0.503742	+	0.872507i
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	24.1396	+	6.46820i	1.00495	+	0.269275i	0.723516	−	0.690307i	$-0.242525\pi$
$577$	24.1396	+	6.46820i	1.00495	+	0.269275i	0.281430	+	0.959582i	$0.409191\pi$
$578$	−8.08112	−	8.08112i	−0.336130	−	0.336130i
$579$	−1.13349	+	4.23024i	−0.0471062	+	0.175803i
$580$	−0.443721	−	0.443721i	−0.0184245	−	0.0184245i
$581$	34.5353	+	6.22226i	1.43277	+	0.258143i
$582$	12.1136	−	6.99377i	0.502124	−	0.289901i
$583$	22.2829	−	22.2829i	0.922865	−	0.922865i
$584$	3.99867	+	6.92590i	0.165466	+	0.286596i
$585$	−1.41671	−	4.92522i	−0.0585739	−	0.203633i
$586$	−28.2990	−	16.3384i	−1.16902	−	0.674934i
$587$	−16.4638	−	4.41145i	−0.679532	−	0.182080i	−0.0974873	−	0.995237i	$-0.531081\pi$
$587$	−16.4638	−	4.41145i	−0.679532	−	0.182080i	−0.582045	+	0.813157i	$0.697747\pi$
$588$	−4.45943	−	5.39569i	−0.183904	−	0.222514i
$589$	−17.3071	−	9.99225i	−0.713126	−	0.411724i
$590$	−11.5321	+	3.09002i	−0.474770	+	0.127214i
$591$	−7.48496	+	7.48496i	−0.307890	+	0.307890i
$592$	−5.36507	+	5.36507i	−0.220503	+	0.220503i
$593$	−40.5737	+	10.8717i	−1.66616	+	0.446447i	−0.964072	−	0.265642i	$-0.914416\pi$
$593$	−40.5737	+	10.8717i	−1.66616	+	0.446447i	−0.702090	+	0.712089i	$0.747749\pi$
$594$	−3.34063	−	1.92872i	−0.137068	−	0.0791361i
$595$	5.73115	−	6.77868i	0.234954	−	0.277899i
$596$	−7.59748	−	2.03574i	−0.311205	−	0.0833871i
$597$	8.90867	+	5.14342i	0.364608	+	0.210506i
$598$	8.08121	+	28.0944i	0.330465	+	1.14887i
$599$	11.3993	+	19.7442i	0.465764	+	0.806727i	0.999236	−	0.0390909i	$-0.0124462\pi$
$599$	11.3993	+	19.7442i	0.465764	+	0.806727i	−0.533472	+	0.845818i	$0.679113\pi$
$600$	−2.10691	+	2.10691i	−0.0860144	+	0.0860144i
$601$	−24.1075	+	13.9185i	−0.983364	+	0.567745i	−0.903284	−	0.429043i	$-0.858851\pi$
$601$	−24.1075	+	13.9185i	−0.983364	+	0.567745i	−0.0800799	+	0.996788i	$0.525518\pi$
$602$	14.8718	−	17.5901i	0.606131	−	0.716918i
$603$	0.0278660	+	0.0278660i	0.00113479	+	0.00113479i
$604$	3.98554	−	14.8742i	0.162169	−	0.605224i
$605$	3.89948	+	3.89948i	0.158536	+	0.158536i
$606$	4.45357	+	1.19333i	0.180914	+	0.0484758i
$607$	−35.8112	+	20.6756i	−1.45353	+	0.839196i	−0.998680	−	0.0513721i	$-0.983641\pi$
$607$	−35.8112	+	20.6756i	−1.45353	+	0.839196i	−0.454850	+	0.890568i	$0.650307\pi$
$608$	3.02378	+	5.23735i	0.122631	+	0.212402i
$609$	0.959293	−	0.666392i	0.0388725	−	0.0270036i
$610$		−	15.1481i		−	0.613330i
$611$	−5.53077	+	22.2615i	−0.223751	+	0.900603i
$612$	−2.04418	+	1.18021i	−0.0826311	+	0.0477071i
$613$	17.4917	−	4.68689i	0.706484	−	0.189302i	0.112351	−	0.993669i	$-0.464162\pi$
$613$	17.4917	−	4.68689i	0.706484	−	0.189302i	0.594133	+	0.804367i	$0.297495\pi$
$614$			4.69552i			0.189496i
$615$	0.981649	−	1.70027i	0.0395839	−	0.0685613i
$616$	−0.851611	−	10.1702i	−0.0343124	−	0.409769i
$617$	32.3546	−	8.66940i	1.30255	−	0.349017i	0.460135	−	0.887849i	$-0.347801\pi$
$617$	32.3546	−	8.66940i	1.30255	−	0.349017i	0.842413	+	0.538832i	$0.181134\pi$
$618$	−12.1256	−	3.24905i	−0.487764	−	0.130696i
$619$	11.2933	−	42.1473i	0.453917	−	1.69404i	−0.237335	−	0.971428i	$-0.576274\pi$
$619$	11.2933	−	42.1473i	0.453917	−	1.69404i	0.691252	−	0.722613i	$-0.257059\pi$
$620$	4.69709			0.188640
$621$	−8.10794			−0.325360
$622$	−6.89594	+	25.7360i	−0.276502	+	1.03192i
$623$	−0.967293	+	5.36876i	−0.0387538	+	0.215095i
$624$	−3.08902	+	1.85956i	−0.123660	+	0.0744421i
$625$	−0.611855	+	1.05976i	−0.0244742	+	0.0423906i
$626$	2.03159	+	7.58199i	0.0811986	+	0.303037i
$627$	11.6640	−	20.2027i	0.465817	−	0.806818i
$628$	−5.12831	−	8.88249i	−0.204642	−	0.354450i
$629$	12.6638	−	12.6638i	0.504939	−	0.504939i
$630$	2.14554	+	3.08857i	0.0854803	+	0.123052i
$631$	−3.74651	−	13.9822i	−0.149146	−	0.556622i	−0.999536	−	0.0304680i	$-0.990300\pi$
$631$	−3.74651	−	13.9822i	−0.149146	−	0.556622i	0.850389	−	0.526154i	$-0.176366\pi$
$632$	3.18133	+	11.8729i	0.126546	+	0.472278i
$633$		−	11.3372i		−	0.450614i
$634$	−4.33323	−	2.50179i	−0.172095	−	0.0993589i
$635$	−15.7919	−	15.7919i	−0.626681	−	0.626681i
$636$	8.16938			0.323937
$637$	16.4317	+	19.1572i	0.651048	+	0.759036i
$638$	1.70297			0.0674213
$639$	−8.96928	−	8.96928i	−0.354819	−	0.354819i
$640$	−1.23097	−	0.710699i	−0.0486583	−	0.0280929i
$641$		−	24.2666i		−	0.958472i	−0.877686	−	0.479236i	$-0.840914\pi$
$641$		−	24.2666i		−	0.958472i	0.877686	−	0.479236i	$-0.159086\pi$
$642$	0.148609	+	0.554617i	0.00586514	+	0.0218890i
$643$	0.634628	+	2.36846i	0.0250273	+	0.0934031i	0.977310	−	0.211815i	$-0.0679374\pi$
$643$	0.634628	+	2.36846i	0.0250273	+	0.0934031i	−0.952283	+	0.305218i	$0.901271\pi$
$644$	−12.2386	−	17.6178i	−0.482267	−	0.694240i
$645$	−8.75041	+	8.75041i	−0.344547	+	0.344547i
$646$	−7.13739	−	12.3623i	−0.280817	−	0.486389i
$647$	−0.925328	+	1.60272i	−0.0363784	+	0.0630092i	−0.883641	−	0.468164i	$-0.844915\pi$
$647$	−0.925328	+	1.60272i	−0.0363784	+	0.0630092i	0.847263	+	0.531174i	$0.178249\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	16.2001	−	28.0594i	0.635909	−	1.10143i
$650$	7.45642	−	7.73420i	0.292465	−	0.303360i
$651$	−1.55028	+	8.60448i	−0.0607602	+	0.337236i
$652$	0.461062	−	1.72071i	0.0180566	−	0.0673881i
$653$	25.6874			1.00522			0.502612	−	0.864512i	$-0.332372\pi$
$653$	25.6874			1.00522			0.502612	+	0.864512i	$0.332372\pi$
$654$	−19.5036			−0.762650
$655$	5.11398	−	19.0856i	0.199820	−	0.745737i
$656$	−1.33418	−	0.357492i	−0.0520909	−	0.0139577i
$657$	7.72484	−	2.06986i	0.301375	−	0.0807531i
$658$	−1.40453	−	16.7734i	−0.0547543	−	0.653894i
$659$	20.2039	−	34.9941i	0.787031	−	1.36318i	−0.140747	−	0.990046i	$-0.544950\pi$
$659$	20.2039	−	34.9941i	0.787031	−	1.36318i	0.927778	−	0.373133i	$-0.121716\pi$
$660$			5.48295i			0.213423i
$661$	8.08720	−	2.16696i	0.314555	−	0.0842849i	−0.0980873	−	0.995178i	$-0.531272\pi$
$661$	8.08720	−	2.16696i	0.314555	−	0.0842849i	0.412643	+	0.910893i	$0.364606\pi$
$662$	−6.04814	+	3.49190i	−0.235068	+	0.135716i
$663$	7.29137	−	4.38934i	0.283173	−	0.170468i
$664$			13.2633i			0.514716i
$665$	−18.6784	+	12.9753i	−0.724316	+	0.503160i
$666$	3.79368	+	6.57085i	0.147002	+	0.254615i
$667$	3.09992	−	1.78974i	0.120029	−	0.0692990i
$668$	−2.03471	−	0.545200i	−0.0787254	−	0.0210944i
$669$	3.46514	+	3.46514i	0.133970	+	0.133970i
$670$	0.0144978	−	0.0541066i	0.000560099	−	0.00209032i
$671$	29.0687	+	29.0687i	1.12219	+	1.12219i
$672$	1.70820	−	2.02041i	0.0658951	−	0.0779391i
$673$	0.338909	−	0.195669i	0.0130640	−	0.00754250i	−0.493454	−	0.869772i	$-0.664266\pi$
$673$	0.338909	−	0.195669i	0.0130640	−	0.00754250i	0.506518	+	0.862230i	$0.330932\pi$
$674$	7.93796	−	7.93796i	0.305759	−	0.305759i
$675$	1.48981	+	2.58043i	0.0573429	+	0.0993208i
$676$	11.0132	−	6.90726i	0.423583	−	0.265664i
$677$	22.1437	+	12.7847i	0.851052	+	0.491355i	0.861006	−	0.508595i	$-0.169835\pi$
$677$	22.1437	+	12.7847i	0.851052	+	0.491355i	−0.00995355	+	0.999950i	$0.503168\pi$
$678$	10.2041	+	2.73418i	0.391887	+	0.105006i
$679$	23.8935	−	28.2606i	0.916947	−	1.08454i
$680$	2.90560	+	1.67755i	0.111425	+	0.0643310i
$681$	−7.10428	+	1.90358i	−0.272236	+	0.0729455i
$682$	−9.01355	+	9.01355i	−0.345147	+	0.345147i
$683$	3.89025	−	3.89025i	0.148856	−	0.148856i	−0.628751	−	0.777607i	$-0.716433\pi$
$683$	3.89025	−	3.89025i	0.148856	−	0.148856i	0.777607	+	0.628751i	$0.216433\pi$
$684$	5.84150	−	1.56523i	0.223355	−	0.0598479i
$685$	13.0909	+	7.55802i	0.500177	+	0.288777i
$686$	−15.9345	−	9.43881i	−0.608383	−	0.360375i
$687$	4.83929	+	1.29668i	0.184631	+	0.0494716i
$688$	7.53977	+	4.35309i	0.287451	+	0.165960i
$689$	−29.4502	+	0.538531i	−1.12196	+	0.0205164i
$690$	5.76231	+	9.98061i	0.219367	+	0.379955i
$691$	19.0641	−	19.0641i	0.725234	−	0.725234i	−0.244432	−	0.969666i	$-0.578602\pi$
$691$	19.0641	−	19.0641i	0.725234	−	0.725234i	0.969666	+	0.244432i	$0.0786016\pi$
$692$	−3.82314	+	2.20729i	−0.145334	+	0.0839086i
$693$	−10.0441	−	1.80965i	−0.381543	−	0.0687429i
$694$	22.7831	+	22.7831i	0.864836	+	0.864836i
$695$	−1.83185	+	6.83655i	−0.0694860	+	0.259325i
$696$	0.312172	+	0.312172i	0.0118329	+	0.0118329i
$697$	3.14922	+	0.843830i	0.119285	+	0.0319624i
$698$	−0.972741	+	0.561612i	−0.0368188	+	0.0212573i
$699$	5.42710	+	9.40002i	0.205272	+	0.355541i
$700$	−3.35824	+	7.13228i	−0.126930	+	0.269575i
$701$			41.8639i			1.58118i	0.612348	+	0.790588i	$0.290225\pi$
$701$			41.8639i			1.58118i	−0.612348	+	0.790588i	$0.709775\pi$
$702$	0.996704	+	3.46505i	0.0376182	+	0.130780i
$703$	−39.7376	+	22.9425i	−1.49873	+	0.865294i
$704$	3.72599	−	0.998376i	0.140429	−	0.0376277i
$705$			9.04283i			0.340573i
$706$	4.44381	−	7.69690i	0.167245	−	0.289677i
$707$	12.1562	−	1.01791i	0.457180	−	0.0382823i
$708$	8.11322	−	2.17393i	0.304913	−	0.0817013i
$709$	−9.73333	−	2.60804i	−0.365543	−	0.0979469i	0.0713720	−	0.997450i	$-0.477262\pi$
$709$	−9.73333	−	2.60804i	−0.365543	−	0.0979469i	−0.436915	+	0.899503i	$0.643929\pi$
$710$	−4.66643	+	17.4154i	−0.175128	+	0.653587i
$711$	12.2917			0.460975
$712$	−2.06187			−0.0772719
$713$	−6.93457	+	25.8802i	−0.259702	+	0.969220i
$714$	−4.03205	+	4.76902i	−0.150896	+	0.178476i
$715$	−0.361439	−	19.7657i	−0.0135171	−	0.739197i
$716$	11.3409	−	19.6430i	0.423830	−	0.734095i
$717$	2.31771	+	8.64982i	0.0865565	+	0.323033i
$718$	4.83644	−	8.37696i	0.180494	−	0.312626i
$719$	−21.2034	−	36.7253i	−0.790753	−	1.36962i	−0.925501	−	0.378744i	$-0.876356\pi$
$719$	−21.2034	−	36.7253i	−0.790753	−	1.36962i	0.134749	−	0.990880i	$-0.456977\pi$
$720$	−1.00508	+	1.00508i	−0.0374572	+	0.0374572i
$721$	−33.0973	+	2.77143i	−1.23261	+	0.103213i
$722$	4.54825	+	16.9743i	0.169268	+	0.631717i
$723$	5.26545	+	19.6509i	0.195824	+	0.730825i
$724$			4.69879i			0.174629i
$725$	−1.13920	−	0.657720i	−0.0423090	−	0.0244271i
$726$	−2.74341	−	2.74341i	−0.101817	−	0.101817i
$727$	16.8790			0.626008			0.313004	−	0.949752i	$-0.398665\pi$
$727$	16.8790			0.626008			0.313004	+	0.949752i	$0.398665\pi$
$728$	−6.02477	+	7.39609i	−0.223293	+	0.274117i
$729$	−1.00000			−0.0370370
$730$	−8.03797	−	8.03797i	−0.297499	−	0.297499i
$731$	−17.7970	−	10.2751i	−0.658246	−	0.380038i
$732$			10.6572i			0.393902i
$733$	3.72135	+	13.8883i	0.137451	+	0.512975i	0.999976	+	0.00695978i	$0.00221538\pi$
$733$	3.72135	+	13.8883i	0.137451	+	0.512975i	−0.862525	+	0.506015i	$0.831118\pi$
$734$	6.87801	+	25.6691i	0.253872	+	0.947463i
$735$	8.10764	+	5.76754i	0.299055	+	0.212739i
$736$	5.73318	−	5.73318i	0.211328	−	0.211328i
$737$	0.0760078	+	0.131649i	0.00279978	+	0.00484937i
$738$	−0.690622	+	1.19619i	−0.0254221	+	0.0440324i
$739$	−4.23566	−	15.8077i	−0.155811	−	0.581496i	−0.999035	−	0.0439322i	$-0.986011\pi$
$739$	−4.23566	−	15.8077i	−0.155811	−	0.581496i	0.843223	−	0.537564i	$-0.180655\pi$
$740$	5.39233	−	9.33980i	0.198226	−	0.343338i
$741$	−20.9551	+	6.02763i	−0.769806	+	0.221431i
$742$	20.3381	−	7.31676i	0.746634	−	0.268607i
$743$	−0.834271	+	3.11354i	−0.0306064	+	0.114225i	−0.979539	−	0.201254i	$-0.935498\pi$
$743$	−0.834271	+	3.11354i	−0.0306064	+	0.114225i	0.948933	+	0.315479i	$0.102165\pi$
$744$	−3.30455			−0.121151
$745$	11.1800			0.409603
$746$	−2.52378	+	9.41887i	−0.0924021	+	0.344849i
$747$	12.8114	+	3.43279i	0.468743	+	0.125599i
$748$	−8.79489	+	2.35658i	−0.321573	+	0.0861652i
$749$	0.866703	+	1.24765i	0.0316686	+	0.0455880i
$750$	5.67112	−	9.82266i	0.207080	−	0.358673i
$751$		−	21.0279i		−	0.767320i	−0.923474	−	0.383660i	$-0.874664\pi$
$751$		−	21.0279i		−	0.767320i	0.923474	−	0.383660i	$-0.125336\pi$
$752$	6.14515	−	1.64659i	0.224090	−	0.0600448i
$753$	−1.54276	+	0.890713i	−0.0562213	+	0.0324594i
$754$	−1.14594	−	1.10479i	−0.0417328	−	0.0402339i
$755$			21.8880i			0.796587i
$756$	−1.50946	−	2.17291i	−0.0548984	−	0.0790280i
$757$	25.1659	+	43.5887i	0.914672	+	1.58426i	0.807381	+	0.590030i	$0.200884\pi$
$757$	25.1659	+	43.5887i	0.914672	+	1.58426i	0.107290	+	0.994228i	$0.465783\pi$
$758$	23.7177	−	13.6934i	0.861466	−	0.497367i
$759$	−30.2101	−	8.09478i	−1.09656	−	0.293822i
$760$	−6.07829	−	6.07829i	−0.220483	−	0.220483i
$761$	−4.29477	+	16.0283i	−0.155685	+	0.581025i	0.843361	+	0.537348i	$0.180574\pi$
$761$	−4.29477	+	16.0283i	−0.155685	+	0.581025i	−0.999046	+	0.0436767i	$0.986093\pi$
$762$	11.1101	+	11.1101i	0.402476	+	0.402476i
$763$	−48.5551	+	17.4680i	−1.75781	+	0.632385i
$764$	−19.9269	+	11.5048i	−0.720929	+	0.416229i
$765$	2.37241	−	2.37241i	0.0857746	−	0.0857746i
$766$	−15.3380	−	26.5663i	−0.554186	−	0.959878i
$767$	−29.1044	+	8.37174i	−1.05090	+	0.302286i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−13.0827	−	3.50549i	−0.471773	−	0.126411i	0.0150963	−	0.999886i	$-0.495195\pi$
$769$	−13.0827	−	3.50549i	−0.471773	−	0.126411i	−0.486869	+	0.873475i	$0.661861\pi$
$770$	4.91070	+	13.6501i	0.176969	+	0.491914i
$771$	3.37109	+	1.94630i	0.121407	+	0.0700943i
$772$	−4.23024	+	1.13349i	−0.152250	+	0.0407952i
$773$	−27.0387	+	27.0387i	−0.972515	+	0.972515i	−0.999632	−	0.0271176i	$-0.991367\pi$
$773$	−27.0387	+	27.0387i	−0.972515	+	0.972515i	0.0271176	+	0.999632i	$0.491367\pi$
$774$	6.15620	−	6.15620i	0.221280	−	0.221280i
$775$	9.51082	−	2.54842i	0.341639	−	0.0915418i
$776$	12.1136	+	6.99377i	0.434852	+	0.251062i
$777$	15.3296	+	12.9607i	0.549947	+	0.464962i
$778$	−3.28766	−	0.880925i	−0.117868	−	0.0315827i
$779$	−7.23405	−	4.17658i	−0.259187	−	0.149642i
$780$	3.55701	−	3.68952i	0.127361	−	0.132106i
$781$	−24.4647	−	42.3742i	−0.875418	−	1.51627i
$782$	−13.5327	+	13.5327i	−0.483928	+	0.483928i
$783$	0.382331	−	0.220739i	0.0136634	−	0.00788857i
$784$	2.44309	−	6.55983i	0.0872531	−	0.234280i
$785$	10.3087	+	10.3087i	0.367934	+	0.367934i
$786$	−3.59785	+	13.4274i	−0.128331	+	0.478938i
$787$	19.2036	+	19.2036i	0.684534	+	0.684534i	0.961018	−	0.276484i	$-0.0891694\pi$
$787$	19.2036	+	19.2036i	0.684534	+	0.684534i	−0.276484	+	0.961018i	$0.589169\pi$
$788$	−10.2246	−	2.73968i	−0.364238	−	0.0975972i
$789$	−2.87858	+	1.66195i	−0.102480	+	0.0591669i
$790$	−8.73571	−	15.1307i	−0.310803	−	0.538326i
$791$	27.8524	−	2.33225i	0.990319	−	0.0829252i
$792$		−	3.85743i		−	0.137068i
$793$	−0.702529	−	38.4187i	−0.0249475	−	1.36429i
$794$	−22.1446	+	12.7852i	−0.785882	+	0.453729i
$795$	−11.2163	+	3.00539i	−0.397801	+	0.106590i
$796$			10.2868i			0.364608i
$797$	8.46109	−	14.6550i	0.299707	−	0.519108i	−0.676362	−	0.736570i	$-0.736444\pi$
$797$	8.46109	−	14.6550i	0.299707	−	0.519108i	0.976069	+	0.217462i	$0.0697777\pi$
$798$	13.1408	−	9.12854i	0.465180	−	0.323147i
$799$	−14.5051	+	3.88663i	−0.513154	+	0.137499i
$800$	−2.87810	−	0.771184i	−0.101756	−	0.0272655i
$801$	−0.533652	+	1.99161i	−0.0188557	+	0.0703702i
$802$	−2.13926			−0.0755399
$803$	30.8492			1.08864
$804$	−0.0101997	+	0.0380657i	−0.000359715	+	0.00134247i
$805$	23.2845	+	19.6863i	0.820670	+	0.693851i
$806$	11.9127	−	0.217838i	0.419608	−	0.00767302i
$807$	6.54607	−	11.3381i	0.230432	−	0.399121i
$808$	1.19333	+	4.45357i	0.0419812	+	0.156676i
$809$	−4.55573	+	7.89075i	−0.160171	+	0.277424i	−0.934930	−	0.354833i	$-0.884538\pi$
$809$	−4.55573	+	7.89075i	−0.160171	+	0.277424i	0.774759	+	0.632257i	$0.217871\pi$
$810$	0.710699	+	1.23097i	0.0249714	+	0.0432518i
$811$	−0.850909	+	0.850909i	−0.0298795	+	0.0298795i	−0.721889	−	0.692009i	$-0.756726\pi$
$811$	−0.850909	+	0.850909i	−0.0298795	+	0.0298795i	0.692009	+	0.721889i	$0.256726\pi$
$812$	1.05676	+	0.497576i	0.0370849	+	0.0174615i
$813$	−6.28045	−	23.4390i	−0.220265	−	0.822040i
$814$	7.57504	+	28.2704i	0.265505	+	0.990879i
$815$			2.53209i			0.0886952i
$816$	−2.04418	−	1.18021i	−0.0715606	−	0.0413156i
$817$	37.2300	+	37.2300i	1.30251	+	1.30251i
$818$	−18.5233			−0.647652
$819$	5.58475	+	7.73373i	0.195147	+	0.270238i
$820$	1.96330			0.0685613
$821$	31.4951	+	31.4951i	1.09919	+	1.09919i	0.994506	+	0.104679i	$0.0333816\pi$
$821$	31.4951	+	31.4951i	1.09919	+	1.09919i	0.104679	+	0.994506i	$0.466618\pi$
$822$	−9.20985	−	5.31731i	−0.321231	−	0.185463i
$823$			51.5547i			1.79708i	0.438887	+	0.898542i	$0.355373\pi$
$823$			51.5547i			1.79708i	−0.438887	+	0.898542i	$0.644627\pi$
$824$	−3.24905	−	12.1256i	−0.113186	−	0.422416i
$825$	2.97479	+	11.1021i	0.103569	+	0.386524i
$826$	18.2512	−	12.6786i	0.635041	−	0.441144i
$827$	−11.5383	+	11.5383i	−0.401227	+	0.401227i	−0.878665	−	0.477439i	$-0.841565\pi$
$827$	−11.5383	+	11.5383i	−0.401227	+	0.401227i	0.477439	+	0.878665i	$0.341565\pi$
$828$	−4.05397	−	7.02168i	−0.140885	−	0.244020i
$829$	−6.52441	+	11.3006i	−0.226602	+	0.392487i	−0.956799	−	0.290750i	$-0.906095\pi$
$829$	−6.52441	+	11.3006i	−0.226602	+	0.392487i	0.730197	+	0.683237i	$0.239428\pi$
$830$	−4.87937	−	18.2101i	−0.169365	−	0.632080i
$831$	−14.9617	+	25.9144i	−0.519014	+	0.898959i
$832$	−3.15494	−	1.74539i	−0.109378	−	0.0605104i
$833$	−5.76670	+	15.4839i	−0.199804	+	0.536486i
$834$	1.28877	−	4.80974i	0.0446263	−	0.166548i
$835$	2.99416			0.103617
$836$	23.3281			0.806818
$837$	−0.855281	+	3.19195i	−0.0295628	+	0.110330i
$838$	31.7588	+	8.50973i	1.09709	+	0.293964i
$839$	4.77327	−	1.27899i	0.164792	−	0.0441558i	−0.175480	−	0.984483i	$-0.556148\pi$
$839$	4.77327	−	1.27899i	0.164792	−	0.0441558i	0.340272	+	0.940327i	$0.389481\pi$
$840$	−1.60201	+	3.40238i	−0.0552747	+	0.117393i
$841$	14.4025	−	24.9459i	0.496640	−	0.860205i
$842$			15.7343i			0.542238i
$843$	−19.2698	+	5.16333i	−0.663687	+	0.177834i
$844$	9.81832	−	5.66861i	0.337961	−	0.195122i
$845$	−12.5796	+	13.5350i	−0.432752	+	0.465619i
$846$		−	6.36192i		−	0.218727i
$847$	−9.28693	−	4.37276i	−0.319103	−	0.150250i
$848$	4.08469	+	7.07489i	0.140269	+	0.242953i
$849$	−14.4486	+	8.34190i	−0.495874	+	0.286293i
$850$	6.79351	+	1.82031i	0.233015	+	0.0624363i
$851$	43.4997	+	43.4997i	1.49115	+	1.49115i
$852$	3.28299	−	12.2523i	0.112473	−	0.419756i
$853$	27.1995	+	27.1995i	0.931292	+	0.931292i	0.997787	−	0.0664946i	$-0.0211815\pi$
$853$	27.1995	+	27.1995i	0.931292	+	0.931292i	−0.0664946	+	0.997787i	$0.521182\pi$
$854$	9.54493	+	26.5316i	0.326621	+	0.907893i
$855$	−7.44436	+	4.29800i	−0.254592	+	0.146989i
$856$	−0.406008	+	0.406008i	−0.0138771	+	0.0138771i
$857$	−2.53008	−	4.38222i	−0.0864258	−	0.149694i	0.819572	−	0.572976i	$-0.194211\pi$
$857$	−2.53008	−	4.38222i	−0.0864258	−	0.149694i	−0.905998	+	0.423282i	$0.860878\pi$
$858$	0.254284	+	13.9058i	0.00868112	+	0.474737i
$859$	−47.6367	−	27.5031i	−1.62534	−	0.938393i	−0.985457	−	0.169924i	$-0.945648\pi$
$859$	−47.6367	−	27.5031i	−1.62534	−	0.938393i	−0.639887	−	0.768469i	$-0.721019\pi$
$860$	−11.9533	−	3.20287i	−0.407604	−	0.109217i
$861$	−0.647988	+	3.59652i	−0.0220834	+	0.122569i
$862$	10.2922	+	5.94221i	0.350554	+	0.202392i
$863$	−2.73644	+	0.733228i	−0.0931496	+	0.0249594i	−0.305093	−	0.952323i	$-0.598687\pi$
$863$	−2.73644	+	0.733228i	−0.0931496	+	0.0249594i	0.211943	+	0.977282i	$0.432021\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	4.43701	−	4.43701i	0.150863	−	0.150863i
$866$	3.35167	−	0.898077i	0.113894	−	0.0305179i
$867$	−9.89731	−	5.71422i	−0.336130	−	0.194065i
$868$	−8.22684	+	2.95966i	−0.279237	+	0.100457i
$869$	45.7988	+	12.2717i	1.55362	+	0.416291i
$870$	−0.543445	−	0.313758i	−0.0184245	−	0.0106374i
$871$	0.0342600	−	0.137897i	0.00116086	−	0.00467247i
$872$	−9.75179	−	16.8906i	−0.330237	−	0.571988i
$873$	9.89069	−	9.89069i	0.334749	−	0.334749i
$874$	42.4641	−	24.5167i	1.43637	−	0.829288i
$875$	5.32102	−	29.5332i	0.179883	−	0.998404i
$876$	5.65497	+	5.65497i	0.191064	+	0.191064i
$877$	0.135105	−	0.504219i	0.00456218	−	0.0170263i	−0.963607	−	0.267322i	$-0.913861\pi$
$877$	0.135105	−	0.504219i	0.00456218	−	0.0170263i	0.968169	+	0.250296i	$0.0805279\pi$
$878$	−11.9450	−	11.9450i	−0.403125	−	0.403125i
$879$	−31.5634	−	8.45739i	−1.06461	−	0.285261i
$880$	−4.74837	+	2.74147i	−0.160068	+	0.0924151i
$881$	−8.60734	−	14.9083i	−0.289989	−	0.502275i	0.683818	−	0.729653i	$-0.260318\pi$
$881$	−8.60734	−	14.9083i	−0.289989	−	0.502275i	−0.973807	+	0.227378i	$0.926985\pi$
$882$	−5.70399	−	4.05765i	−0.192063	−	0.136628i
$883$		−	2.32270i		−	0.0781651i	−0.999236	−	0.0390825i	$-0.987556\pi$
$883$		−	2.32270i		−	0.0781651i	0.999236	−	0.0390825i	$-0.0124435\pi$
$884$	7.44697	+	4.11984i	0.250469	+	0.138565i
$885$	−10.3394	+	5.96947i	−0.347556	+	0.200661i
$886$	0.209438	−	0.0561187i	0.00703621	−	0.00188535i
$887$		−	17.4348i		−	0.585402i	−0.956204	−	0.292701i	$-0.905446\pi$
$887$		−	17.4348i		−	0.585402i	0.956204	−	0.292701i	$-0.0945541\pi$
$888$	−3.79368	+	6.57085i	−0.127308	+	0.220503i
$889$	37.6096	+	17.7085i	1.26139	+	0.593925i
$890$	2.83088	−	0.758532i	0.0948913	−	0.0254260i
$891$	−3.72599	−	0.998376i	−0.124825	−	0.0334469i
$892$	−1.26833	+	4.73346i	−0.0424668	+	0.158488i
$893$	38.4742			1.28749
$894$	−7.86549			−0.263061
$895$	−8.34431	+	31.1414i	−0.278919	+	1.04094i
$896$	2.60383	+	0.469134i	0.0869877	+	0.0156727i
$897$	15.0772	+	25.0456i	0.503414	+	0.836247i
$898$	−4.00986	+	6.94528i	−0.133811	+	0.231767i
$899$	−0.377588	−	1.40918i	−0.0125933	−	0.0469987i
$900$	−1.48981	+	2.58043i	−0.0496604	+	0.0860144i
$901$	−9.64157	−	16.6997i	−0.321207	−	0.556347i
$902$	−3.76750	+	3.76750i	−0.125444	+	0.125444i
$903$	9.81245	−	20.8398i	0.326538	−	0.693506i
$904$	2.73418	+	10.2041i	0.0909376	+	0.339384i
$905$	−1.72862	−	6.45128i	−0.0574611	−	0.214448i
$906$		−	15.3989i		−	0.511595i
$907$	−22.7524	−	13.1361i	−0.755481	−	0.436177i	0.0721897	−	0.997391i	$-0.477001\pi$
$907$	−22.7524	−	13.1361i	−0.755481	−	0.436177i	−0.827671	+	0.561214i	$0.810335\pi$
$908$	−5.20069	−	5.20069i	−0.172591	−	0.172591i
$909$	4.61068			0.152927
$910$	5.55089	−	12.3710i	0.184010	−	0.410095i
$911$	16.3508			0.541727			0.270863	−	0.962618i	$-0.412691\pi$
$911$	16.3508			0.541727			0.270863	+	0.962618i	$0.412691\pi$
$912$	4.27628	+	4.27628i	0.141602	+	0.141602i
$913$	44.3078	+	25.5811i	1.46637	+	0.846611i
$914$			31.1267i			1.02958i
$915$	−3.92063	−	14.6320i	−0.129612	−	0.483718i
$916$	1.29668	+	4.83929i	0.0428437	+	0.159895i
$917$	3.06895	+	36.6504i	0.101346	+	1.21030i
$918$	−1.66907	+	1.66907i	−0.0550874	+	0.0550874i
$919$	16.3833	+	28.3767i	0.540435	+	0.936061i	0.998879	+	0.0473375i	$0.0150736\pi$
$919$	16.3833	+	28.3767i	0.540435	+	0.936061i	−0.458444	+	0.888723i	$0.651593\pi$
$920$	−5.76231	+	9.98061i	−0.189978	+	0.329051i
$921$	1.21529	+	4.53552i	0.0400451	+	0.149450i
$922$	19.7084	−	34.1360i	0.649062	−	1.12421i
$923$	−11.0273	+	44.3852i	−0.362969	+	1.46096i
$924$	−3.45484	−	9.60325i	−0.113656	−	0.315924i
$925$	5.85125	−	21.8372i	0.192388	−	0.718001i
$926$	8.67112			0.284951
$927$	−12.5534			−0.412307
$928$	−0.114263	+	0.426435i	−0.00375086	+	0.0139984i
$929$	0.281735	+	0.0754906i	0.00924342	+	0.00247677i	0.263438	−	0.964676i	$-0.415144\pi$
$929$	0.281735	+	0.0754906i	0.00924342	+	0.00247677i	−0.254194	+	0.967153i	$0.581810\pi$
$930$	4.53704	−	1.21570i	0.148775	−	0.0398642i
$931$	24.5389	−	34.4953i	0.804230	−	1.13054i
$932$	−5.42710	+	9.40002i	−0.177771	+	0.307908i
$933$			26.6439i			0.872281i
$934$	−12.5983	+	3.37570i	−0.412228	+	0.110456i
$935$	11.2081	−	6.47102i	0.366545	−	0.211625i
$936$	−2.50247	+	2.59570i	−0.0817958	+	0.0848430i
$937$			6.39250i			0.208834i	0.994534	+	0.104417i	$0.0332976\pi$
$937$			6.39250i			0.208834i	−0.994534	+	0.104417i	$0.966702\pi$
$938$	0.00870028	+	0.103902i	0.000284074	+	0.00339251i
$939$	3.92473	+	6.79782i	0.128079	+	0.221839i
$940$	−7.83132	+	4.52142i	−0.255430	+	0.147472i
$941$	−23.4153	−	6.27411i	−0.763317	−	0.204530i	−0.143900	−	0.989592i	$-0.545964\pi$
$941$	−23.4153	−	6.27411i	−0.763317	−	0.204530i	−0.619417	+	0.785062i	$0.712631\pi$
$942$	−7.25252	−	7.25252i	−0.236300	−	0.236300i
$943$	−2.89852	+	10.8174i	−0.0943889	+	0.352264i
$944$	5.93929	+	5.93929i	0.193307	+	0.193307i
$945$	2.87181	+	2.42803i	0.0934201	+	0.0789837i
$946$	29.0841	−	16.7917i	0.945607	−	0.545946i
$947$	−40.3919	+	40.3919i	−1.31256	+	1.31256i	−0.393041	+	0.919521i	$0.628577\pi$
$947$	−40.3919	+	40.3919i	−1.31256	+	1.31256i	−0.919521	+	0.393041i	$0.871423\pi$
$948$	6.14585	+	10.6449i	0.199608	+	0.345731i
$949$	−20.7587	−	20.0131i	−0.673855	−	0.649653i
$950$	−15.6053	−	9.00974i	−0.506304	−	0.292315i
$951$	−4.83309	−	1.29502i	−0.156724	−	0.0419940i
$952$	−6.14612	−	1.10735i	−0.199197	−	0.0358895i
$953$	−29.1590	−	16.8350i	−0.944553	−	0.545338i	−0.0531686	−	0.998586i	$-0.516932\pi$
$953$	−29.1590	−	16.8350i	−0.944553	−	0.545338i	−0.891385	+	0.453247i	$0.850265\pi$
$954$	7.89102	−	2.11439i	0.255481	−	0.0684560i
$955$	23.1265	−	23.1265i	0.748356	−	0.748356i
$956$	−6.33211	+	6.33211i	−0.204795	+	0.204795i
$957$	1.64494	−	0.440761i	0.0531735	−	0.0142478i
$958$	−30.2791	−	17.4817i	−0.978274	−	0.564807i
$959$	−27.6907	−	4.98906i	−0.894180	−	0.161105i
$960$	−1.37297	−	0.367885i	−0.0443123	−	0.0118734i
$961$	−17.3897	−	10.0400i	−0.560959	−	0.323870i
$962$	13.2429	−	23.9377i	0.426967	−	0.771781i
$963$	0.287091	+	0.497256i	0.00925138	+	0.0160239i
$964$	−14.3855	+	14.3855i	−0.463325	+	0.463325i
$965$	5.39098	−	3.11249i	0.173542	−	0.100194i
$966$	−16.3814	−	13.8499i	−0.527063	−	0.445615i
$967$	−6.11427	−	6.11427i	−0.196622	−	0.196622i	0.601928	−	0.798550i	$-0.294399\pi$
$967$	−6.11427	−	6.11427i	−0.196622	−	0.196622i	−0.798550	+	0.601928i	$0.794399\pi$
$968$	1.00416	−	3.74757i	0.0322749	−	0.120451i
$969$	−10.0938	−	10.0938i	−0.324259	−	0.324259i
$970$	−19.2044	−	5.14581i	−0.616617	−	0.165222i
$971$	−27.8426	+	16.0750i	−0.893513	+	0.515870i	−0.875090	−	0.483960i	$-0.839198\pi$
$971$	−27.8426	+	16.0750i	−0.893513	+	0.515870i	−0.0184231	+	0.999830i	$0.505865\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−1.09931	−	13.1283i	−0.0352423	−	0.420875i
$974$		−	33.0137i		−	1.05783i
$975$	5.20059	−	9.40053i	0.166552	−	0.301058i
$976$	−9.22941	+	5.32860i	−0.295426	+	0.170564i
$977$	−1.63311	+	0.437589i	−0.0522477	+	0.0139997i	−0.284848	−	0.958573i	$-0.591943\pi$
$977$	−1.63311	+	0.437589i	−0.0522477	+	0.0139997i	0.232601	+	0.972572i	$0.425277\pi$
$978$		−	1.78141i		−	0.0569631i
$979$	−3.97676	+	6.88795i	−0.127098	+	0.220140i
$980$	−0.941011	+	9.90519i	−0.0300595	+	0.316410i
$981$	−18.8390	+	5.04790i	−0.601483	+	0.161167i
$982$	40.2196	+	10.7768i	1.28346	+	0.343901i
$983$	−4.75086	+	17.7305i	−0.151529	+	0.565514i	0.847849	+	0.530238i	$0.177898\pi$
$983$	−4.75086	+	17.7305i	−0.151529	+	0.565514i	−0.999378	+	0.0352757i	$0.988769\pi$
$984$	−1.38124			−0.0440324
$985$	15.0460			0.479405
$986$	0.269708	−	1.00656i	0.00858926	−	0.0320555i
$987$	−5.69794	−	15.8383i	−0.181367	−	0.504139i
$988$	−15.6976	−	15.1339i	−0.499409	−	0.481472i
$989$	35.2946	−	61.1320i	1.12230	−	1.94388i
$990$	1.41909	+	5.29612i	0.0451017	+	0.168322i
$991$	−2.21869	+	3.84289i	−0.0704791	+	0.122073i	−0.899111	−	0.437720i	$-0.855786\pi$
$991$	−2.21869	+	3.84289i	−0.0704791	+	0.122073i	0.828632	+	0.559793i	$0.189119\pi$
$992$	−1.65228	−	2.86183i	−0.0524598	−	0.0908631i
$993$	−4.93829	+	4.93829i	−0.156712	+	0.156712i
$994$	−2.80037	−	33.4429i	−0.0888224	−	1.06075i
$995$	−3.78438	−	14.1235i	−0.119973	−	0.447745i
$996$	3.43279	+	12.8114i	0.108772	+	0.405943i
$997$			35.8562i			1.13558i	0.823175	+	0.567788i	$0.192201\pi$
$997$			35.8562i			1.13558i	−0.823175	+	0.567788i	$0.807799\pi$
$998$	−5.88632	−	3.39847i	−0.186328	−	0.107577i
$999$	5.36507	+	5.36507i	0.169743	+	0.169743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.b.271.7	yes	40
7.3	odd	6		546.2.by.b.115.2	yes	40
13.6	odd	12		546.2.by.b.19.2	✓	40
91.45	even	12	inner	546.2.cg.b.409.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.2	✓	40	13.6	odd	12
546.2.by.b.115.2	yes	40	7.3	odd	6
546.2.cg.b.271.7	yes	40	1.1	even	1	trivial
546.2.cg.b.409.7	yes	40	91.45	even	12	inner

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-0.367885 - 1.37297i) q^{5} +(0.258819 + 0.965926i) q^{6} +(1.50946 + 2.17291i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-0.367885 - 1.37297i) q^{5} +(0.258819 + 0.965926i) q^{6} +(1.50946 + 2.17291i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.710699 - 1.23097i) q^{10} +(0.998376 + 3.72599i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.74539 - 3.15494i) q^{13} +(-0.469134 + 2.60383i) q^{14} +(0.367885 - 1.37297i) q^{15} -1.00000 q^{16} +2.36042 q^{17} +(-0.258819 + 0.965926i) q^{18} +(-5.84150 - 1.56523i) q^{19} +(1.37297 - 0.367885i) q^{20} +(0.220772 + 2.63652i) q^{21} +(-1.92872 + 3.34063i) q^{22} +8.10794i q^{23} +(-0.965926 + 0.258819i) q^{24} +(2.58043 - 1.48981i) q^{25} +(3.46505 - 0.996704i) q^{26} +1.00000i q^{27} +(-2.17291 + 1.50946i) q^{28} +(-0.220739 - 0.382331i) q^{29} +(1.23097 - 0.710699i) q^{30} +(3.19195 + 0.855281i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.998376 + 3.72599i) q^{33} +(1.66907 + 1.66907i) q^{34} +(2.42803 - 2.87181i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(5.36507 - 5.36507i) q^{37} +(-3.02378 - 5.23735i) q^{38} +(3.08902 - 1.85956i) q^{39} +(1.23097 + 0.710699i) q^{40} +(1.33418 + 0.357492i) q^{41} +(-1.70820 + 2.02041i) q^{42} +(-7.53977 - 4.35309i) q^{43} +(-3.72599 + 0.998376i) q^{44} +(1.00508 - 1.00508i) q^{45} +(-5.73318 + 5.73318i) q^{46} +(-6.14515 + 1.64659i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-2.44309 + 6.55983i) q^{49} +(2.87810 + 0.771184i) q^{50} +(2.04418 + 1.18021i) q^{51} +(3.15494 + 1.74539i) q^{52} +(-4.08469 - 7.07489i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(4.74837 - 2.74147i) q^{55} +(-2.60383 - 0.469134i) q^{56} +(-4.27628 - 4.27628i) q^{57} +(0.114263 - 0.426435i) q^{58} +(-5.93929 - 5.93929i) q^{59} +(1.37297 + 0.367885i) q^{60} +(9.22941 - 5.32860i) q^{61} +(1.65228 + 2.86183i) q^{62} +(-1.12707 + 2.39368i) q^{63} -1.00000i q^{64} +(-4.97372 - 1.23570i) q^{65} +(-3.34063 + 1.92872i) q^{66} +(0.0380657 - 0.0101997i) q^{67} +2.36042i q^{68} +(-4.05397 + 7.02168i) q^{69} +(3.74755 - 0.313804i) q^{70} +(-12.2523 + 3.28299i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(2.06986 - 7.72484i) q^{73} +7.58736 q^{74} +2.97962 q^{75} +(1.56523 - 5.84150i) q^{76} +(-6.58924 + 7.79360i) q^{77} +(3.49917 + 0.869355i) q^{78} +(6.14585 - 10.6449i) q^{79} +(0.367885 + 1.37297i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.690622 + 1.19619i) q^{82} +(9.37857 - 9.37857i) q^{83} +(-2.63652 + 0.220772i) q^{84} +(-0.868362 - 3.24077i) q^{85} +(-2.25332 - 8.40952i) q^{86} -0.441478i q^{87} +(-3.34063 - 1.92872i) q^{88} +(1.45796 + 1.45796i) q^{89} +1.42140 q^{90} +(9.48998 - 0.969671i) q^{91} -8.10794 q^{92} +(2.33667 + 2.33667i) q^{93} +(-5.50959 - 3.18096i) q^{94} +8.59601i q^{95} +(-0.258819 - 0.965926i) q^{96} +(-3.62024 - 13.5109i) q^{97} +(-6.36602 + 2.91098i) q^{98} +(-2.72762 + 2.72762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

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