LMFDB - Embedded newform 546.2.by.b.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (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			19.4
Character	$\chi$	$=$	546.19
Dual form			546.2.by.b.115.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(1.30611 - 0.349971i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(2.64352 - 0.108591i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(1.30611 - 0.349971i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(2.64352 - 0.108591i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -1.35218 q^{10} +(0.402566 + 0.402566i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.33605 + 1.36776i) q^{13} +(-2.58155 - 0.579303i) q^{14} +(-0.349971 - 1.30611i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.487543 - 0.844450i) q^{17} +(0.965926 + 0.258819i) q^{18} +(2.29914 + 2.29914i) q^{19} +(1.30611 + 0.349971i) q^{20} +(-0.108591 - 2.64352i) q^{21} +(-0.284657 - 0.493040i) q^{22} +(-0.0701717 + 0.0405137i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(-2.74668 + 1.58580i) q^{25} +(-2.86837 - 2.18459i) q^{26} +1.00000i q^{27} +(2.34365 + 1.22772i) q^{28} +(-0.139785 + 0.242115i) q^{29} +1.35218i q^{30} +(0.665884 - 2.48511i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.402566 - 0.402566i) q^{33} +(-0.689491 + 0.689491i) q^{34} +(3.41473 - 1.06699i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(0.419419 - 1.56529i) q^{37} +(-1.62574 - 2.81586i) q^{38} +(1.36776 - 3.33605i) q^{39} +(-1.17103 - 0.676092i) q^{40} +(-2.23576 + 0.599071i) q^{41} +(-0.579303 + 2.58155i) q^{42} +(9.48543 - 5.47642i) q^{43} +(0.147349 + 0.549915i) q^{44} +(-1.30611 + 0.349971i) q^{45} +(0.0782664 - 0.0209714i) q^{46} +(-1.48771 - 5.55221i) q^{47} +(0.866025 - 0.500000i) q^{48} +(6.97642 - 0.574124i) q^{49} +(3.06353 - 0.820870i) q^{50} +(-0.844450 - 0.487543i) q^{51} +(2.20522 + 2.85254i) q^{52} +(-4.54058 - 7.86452i) q^{53} +(0.258819 - 0.965926i) q^{54} +(0.666681 + 0.384909i) q^{55} +(-1.94604 - 1.79247i) q^{56} +(2.29914 - 2.29914i) q^{57} +(0.197686 - 0.197686i) q^{58} +(-1.84934 - 6.90183i) q^{59} +(0.349971 - 1.30611i) q^{60} +5.72178i q^{61} +(-1.28639 + 2.22809i) q^{62} +(-2.64352 + 0.108591i) q^{63} +1.00000i q^{64} +(4.83592 + 0.618927i) q^{65} +(-0.493040 + 0.284657i) q^{66} +(-1.53445 + 1.53445i) q^{67} +(0.844450 - 0.487543i) q^{68} +(0.0405137 + 0.0701717i) q^{69} +(-3.57453 + 0.146835i) q^{70} +(0.466117 + 0.124896i) q^{71} +(0.707107 + 0.707107i) q^{72} +(-2.81084 - 0.753163i) q^{73} +(-0.810255 + 1.40340i) q^{74} +(1.58580 + 2.74668i) q^{75} +(0.841543 + 3.14068i) q^{76} +(1.10791 + 1.02048i) q^{77} +(-2.18459 + 2.86837i) q^{78} +(1.45438 - 2.51907i) q^{79} +(0.956138 + 0.956138i) q^{80} +1.00000 q^{81} +2.31463 q^{82} +(2.22649 + 2.22649i) q^{83} +(1.22772 - 2.34365i) q^{84} +(0.341252 - 1.27357i) q^{85} +(-10.5796 + 2.83480i) q^{86} +(0.242115 + 0.139785i) q^{87} -0.569314i q^{88} +(-10.2243 - 2.73959i) q^{89} +1.35218 q^{90} +(8.96745 + 3.25345i) q^{91} -0.0810273 q^{92} +(-2.48511 - 0.665884i) q^{93} +5.74807i q^{94} +(3.80756 + 2.19829i) q^{95} +(-0.965926 + 0.258819i) q^{96} +(-4.34344 + 16.2099i) q^{97} +(-6.88729 - 1.25107i) q^{98} +(-0.402566 - 0.402566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.30611	−	0.349971i	0.584110	−	0.156512i	0.0453500	−	0.998971i	$-0.485560\pi$
$5$	1.30611	−	0.349971i	0.584110	−	0.156512i	0.538760	+	0.842459i	$0.318893\pi$
$6$	−0.258819	+	0.965926i	−0.105662	+	0.394338i
$7$	2.64352	−	0.108591i	0.999157	−	0.0410434i
$7$	2.64352	−	0.108591i	0.999157	−	0.0410434i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	−1.35218			−0.427598
$11$	0.402566	+	0.402566i	0.121378	+	0.121378i	0.765187	−	0.643808i	$-0.222647\pi$
$11$	0.402566	+	0.402566i	0.121378	+	0.121378i	−0.643808	+	0.765187i	$0.722647\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	3.33605	+	1.36776i	0.925254	+	0.379349i
$13$	3.33605	+	1.36776i	0.925254	+	0.379349i
$14$	−2.58155	−	0.579303i	−0.689949	−	0.154825i
$15$	−0.349971	−	1.30611i	−0.0903621	−	0.337236i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.487543	−	0.844450i	0.118247	−	0.204809i	−0.800826	−	0.598897i	$-0.795606\pi$
$17$	0.487543	−	0.844450i	0.118247	−	0.204809i	0.919073	+	0.394088i	$0.128939\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	2.29914	+	2.29914i	0.527459	+	0.527459i	0.919814	−	0.392355i	$-0.128340\pi$
$19$	2.29914	+	2.29914i	0.527459	+	0.527459i	−0.392355	+	0.919814i	$0.628340\pi$
$20$	1.30611	+	0.349971i	0.292055	+	0.0782559i
$21$	−0.108591	−	2.64352i	−0.0236964	−	0.576864i
$22$	−0.284657	−	0.493040i	−0.0606891	−	0.105117i
$23$	−0.0701717	+	0.0405137i	−0.0146318	+	0.00844768i	−0.507298	−	0.861771i	$-0.669356\pi$
$23$	−0.0701717	+	0.0405137i	−0.0146318	+	0.00844768i	0.492666	+	0.870218i	$0.336022\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−2.74668	+	1.58580i	−0.549337	+	0.317160i
$26$	−2.86837	−	2.18459i	−0.562534	−	0.428433i
$27$			1.00000i			0.192450i
$28$	2.34365	+	1.22772i	0.442909	+	0.232017i
$29$	−0.139785	+	0.242115i	−0.0259574	+	0.0449596i	−0.878712	−	0.477352i	$-0.841597\pi$
$29$	−0.139785	+	0.242115i	−0.0259574	+	0.0449596i	0.852755	+	0.522311i	$0.174930\pi$
$30$			1.35218i			0.246874i
$31$	0.665884	−	2.48511i	0.119596	−	0.446339i	−0.879993	−	0.474986i	$-0.842453\pi$
$31$	0.665884	−	2.48511i	0.119596	−	0.446339i	0.999590	+	0.0286467i	$0.00911977\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	0.402566	−	0.402566i	0.0700777	−	0.0700777i
$34$	−0.689491	+	0.689491i	−0.118247	+	0.118247i
$35$	3.41473	−	1.06699i	0.577194	−	0.180354i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	0.419419	−	1.56529i	0.0689520	−	0.257332i	−0.922842	−	0.385179i	$-0.874140\pi$
$37$	0.419419	−	1.56529i	0.0689520	−	0.257332i	0.991794	+	0.127846i	$0.0408064\pi$
$38$	−1.62574	−	2.81586i	−0.263729	−	0.456793i
$39$	1.36776	−	3.33605i	0.219017	−	0.534195i
$40$	−1.17103	−	0.676092i	−0.185155	−	0.106900i
$41$	−2.23576	+	0.599071i	−0.349168	+	0.0935592i	−0.429140	−	0.903238i	$-0.641183\pi$
$41$	−2.23576	+	0.599071i	−0.349168	+	0.0935592i	0.0799726	+	0.996797i	$0.474517\pi$
$42$	−0.579303	+	2.58155i	−0.0893884	+	0.398342i
$43$	9.48543	−	5.47642i	1.44651	−	0.835146i	0.448243	−	0.893912i	$-0.352050\pi$
$43$	9.48543	−	5.47642i	1.44651	−	0.835146i	0.998272	+	0.0587660i	$0.0187166\pi$
$44$	0.147349	+	0.549915i	0.0222137	+	0.0829028i
$45$	−1.30611	+	0.349971i	−0.194703	+	0.0521706i
$46$	0.0782664	−	0.0209714i	0.0115398	−	0.00309207i
$47$	−1.48771	−	5.55221i	−0.217005	−	0.809873i	−0.985451	−	0.169959i	$-0.945637\pi$
$47$	−1.48771	−	5.55221i	−0.217005	−	0.809873i	0.768446	−	0.639914i	$-0.221030\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	6.97642	−	0.574124i	0.996631	−	0.0820177i
$50$	3.06353	−	0.820870i	0.433248	−	0.116089i
$51$	−0.844450	−	0.487543i	−0.118247	−	0.0682697i
$52$	2.20522	+	2.85254i	0.305809	+	0.395576i
$53$	−4.54058	−	7.86452i	−0.623697	−	1.08027i	−0.988791	−	0.149304i	$-0.952297\pi$
$53$	−4.54058	−	7.86452i	−0.623697	−	1.08027i	0.365095	−	0.930970i	$-0.381037\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	0.666681	+	0.384909i	0.0898953	+	0.0519011i
$56$	−1.94604	−	1.79247i	−0.260050	−	0.239528i
$57$	2.29914	−	2.29914i	0.304528	−	0.304528i
$58$	0.197686	−	0.197686i	0.0259574	−	0.0259574i
$59$	−1.84934	−	6.90183i	−0.240763	−	0.898541i	−0.975466	−	0.220152i	$-0.929345\pi$
$59$	−1.84934	−	6.90183i	−0.240763	−	0.898541i	0.734702	−	0.678390i	$-0.237322\pi$
$60$	0.349971	−	1.30611i	0.0451811	−	0.168618i
$61$			5.72178i			0.732599i	0.930497	+	0.366299i	$0.119375\pi$
$61$			5.72178i			0.732599i	−0.930497	+	0.366299i	$0.880625\pi$
$62$	−1.28639	+	2.22809i	−0.163372	+	0.282968i
$63$	−2.64352	+	0.108591i	−0.333052	+	0.0136811i
$64$			1.00000i			0.125000i
$65$	4.83592	+	0.618927i	0.599822	+	0.0767685i
$66$	−0.493040	+	0.284657i	−0.0606891	+	0.0350389i
$67$	−1.53445	+	1.53445i	−0.187463	+	0.187463i	−0.794598	−	0.607135i	$-0.792319\pi$
$67$	−1.53445	+	1.53445i	−0.187463	+	0.187463i	0.607135	+	0.794598i	$0.292319\pi$
$68$	0.844450	−	0.487543i	0.102405	−	0.0591233i
$69$	0.0405137	+	0.0701717i	0.00487727	+	0.00844768i
$70$	−3.57453	+	0.146835i	−0.427238	+	0.0175501i
$71$	0.466117	+	0.124896i	0.0553179	+	0.0148224i	0.286372	−	0.958119i	$-0.407551\pi$
$71$	0.466117	+	0.124896i	0.0553179	+	0.0148224i	−0.231054	+	0.972941i	$0.574217\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	−2.81084	−	0.753163i	−0.328984	−	0.0881510i	0.0905465	−	0.995892i	$-0.471139\pi$
$73$	−2.81084	−	0.753163i	−0.328984	−	0.0881510i	−0.419531	+	0.907741i	$0.637805\pi$
$74$	−0.810255	+	1.40340i	−0.0941902	+	0.163142i
$75$	1.58580	+	2.74668i	0.183112	+	0.317160i
$76$	0.841543	+	3.14068i	0.0965316	+	0.360261i
$77$	1.10791	+	1.02048i	0.126258	+	0.116294i
$78$	−2.18459	+	2.86837i	−0.247356	+	0.324779i
$79$	1.45438	−	2.51907i	0.163631	−	0.283417i	−0.772537	−	0.634969i	$-0.781013\pi$
$79$	1.45438	−	2.51907i	0.163631	−	0.283417i	0.936168	+	0.351552i	$0.114346\pi$
$80$	0.956138	+	0.956138i	0.106900	+	0.106900i
$81$	1.00000			0.111111
$82$	2.31463			0.255608
$83$	2.22649	+	2.22649i	0.244389	+	0.244389i	0.818663	−	0.574274i	$-0.194716\pi$
$83$	2.22649	+	2.22649i	0.244389	+	0.244389i	−0.574274	+	0.818663i	$0.694716\pi$
$84$	1.22772	−	2.34365i	0.133955	−	0.255713i
$85$	0.341252	−	1.27357i	0.0370140	−	0.138138i
$86$	−10.5796	+	2.83480i	−1.14083	+	0.305685i
$87$	0.242115	+	0.139785i	0.0259574	+	0.0149865i
$88$		−	0.569314i		−	0.0606891i
$89$	−10.2243	−	2.73959i	−1.08377	−	0.290396i	−0.327633	−	0.944805i	$-0.606251\pi$
$89$	−10.2243	−	2.73959i	−1.08377	−	0.290396i	−0.756141	+	0.654409i	$0.772918\pi$
$90$	1.35218			0.142533
$91$	8.96745	+	3.25345i	0.940044	+	0.341054i
$92$	−0.0810273			−0.00844768
$93$	−2.48511	−	0.665884i	−0.257694	−	0.0690489i
$94$			5.74807i			0.592868i
$95$	3.80756	+	2.19829i	0.390647	+	0.225540i
$96$	−0.965926	+	0.258819i	−0.0985844	+	0.0264156i
$97$	−4.34344	+	16.2099i	−0.441009	+	1.64587i	0.285254	+	0.958452i	$0.407922\pi$
$97$	−4.34344	+	16.2099i	−0.441009	+	1.64587i	−0.726263	+	0.687417i	$0.758745\pi$
$98$	−6.88729	−	1.25107i	−0.695722	−	0.126377i
$99$	−0.402566	−	0.402566i	−0.0404594	−	0.0404594i
$100$	−3.17160			−0.317160
$101$	−1.56526			−0.155749			−0.0778744	−	0.996963i	$-0.524813\pi$
$101$	−1.56526			−0.155749			−0.0778744	+	0.996963i	$0.524813\pi$
$102$	0.689491	+	0.689491i	0.0682697	+	0.0682697i
$103$	−3.08156	+	5.33742i	−0.303635	+	0.525911i	−0.976957	−	0.213439i	$-0.931534\pi$
$103$	−3.08156	+	5.33742i	−0.303635	+	0.525911i	0.673321	+	0.739350i	$0.264867\pi$
$104$	−1.39179	−	3.32610i	−0.136476	−	0.326151i
$105$	−1.06699	−	3.41473i	−0.104127	−	0.333243i
$106$	2.35038	+	8.77173i	0.228289	+	0.851986i
$107$	7.03449	+	12.1841i	0.680050	+	1.17788i	0.974965	+	0.222358i	$0.0713753\pi$
$107$	7.03449	+	12.1841i	0.680050	+	1.17788i	−0.294915	+	0.955523i	$0.595291\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−18.3713	−	4.92259i	−1.75966	−	0.471498i	−0.773012	−	0.634392i	$-0.781251\pi$
$109$	−18.3713	−	4.92259i	−1.75966	−	0.471498i	−0.986644	+	0.162893i	$0.947917\pi$
$110$	−0.544343	−	0.544343i	−0.0519011	−	0.0519011i
$111$	−1.56529	−	0.419419i	−0.148571	−	0.0398095i
$112$	1.41580	+	2.23506i	0.133781	+	0.211193i
$113$	9.09354	+	15.7505i	0.855448	+	1.48168i	0.876229	+	0.481896i	$0.160052\pi$
$113$	9.09354	+	15.7505i	0.855448	+	1.48168i	−0.0207805	+	0.999784i	$0.506615\pi$
$114$	−2.81586	+	1.62574i	−0.263729	+	0.152264i
$115$	−0.0774734	+	0.0774734i	−0.00722443	+	0.00722443i
$116$	−0.242115	+	0.139785i	−0.0224798	+	0.0129787i
$117$	−3.33605	−	1.36776i	−0.308418	−	0.126450i
$118$			7.14530i			0.657778i
$119$	1.19713	−	2.28526i	0.109741	−	0.209490i
$120$	−0.676092	+	1.17103i	−0.0617185	+	0.106900i
$121$		−	10.6759i		−	0.970535i
$122$	1.48091	−	5.52681i	0.134075	−	0.500374i
$123$	0.599071	+	2.23576i	0.0540164	+	0.201592i
$124$	1.81923	−	1.81923i	0.163372	−	0.163372i
$125$	−7.81318	+	7.81318i	−0.698832	+	0.698832i
$126$	2.58155	+	0.579303i	0.229983	+	0.0516084i
$127$	7.52749	+	4.34600i	0.667957	+	0.385645i	0.795302	−	0.606213i	$-0.207312\pi$
$127$	7.52749	+	4.34600i	0.667957	+	0.385645i	−0.127345	+	0.991858i	$0.540646\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−5.47642	−	9.48543i	−0.482172	−	0.835146i
$130$	−4.51095	−	1.84947i	−0.395637	−	0.162209i
$131$	−5.23185	−	3.02061i	−0.457109	−	0.263912i	0.253719	−	0.967278i	$-0.418346\pi$
$131$	−5.23185	−	3.02061i	−0.457109	−	0.263912i	−0.710828	+	0.703366i	$0.751679\pi$
$132$	0.549915	−	0.147349i	0.0478640	−	0.0128251i
$133$	6.32749	+	5.82816i	0.548663	+	0.505365i
$134$	1.87931	−	1.08502i	0.162348	−	0.0937316i
$135$	0.349971	+	1.30611i	0.0301207	+	0.112412i
$136$	−0.941862	+	0.252371i	−0.0807640	+	0.0216406i
$137$	−4.25919	+	1.14125i	−0.363888	+	0.0975034i	−0.436130	−	0.899884i	$-0.643651\pi$
$137$	−4.25919	+	1.14125i	−0.363888	+	0.0975034i	0.0722423	+	0.997387i	$0.476985\pi$
$138$	−0.0209714	−	0.0782664i	−0.00178521	−	0.00666248i
$139$	−3.93291	+	2.27067i	−0.333585	+	0.192596i	−0.657432	−	0.753514i	$-0.728357\pi$
$139$	−3.93291	+	2.27067i	−0.333585	+	0.192596i	0.323846	+	0.946110i	$0.395024\pi$
$140$	3.49073	+	0.783325i	0.295021	+	0.0662030i
$141$	−5.55221	+	1.48771i	−0.467580	+	0.125288i
$142$	−0.417909	−	0.241280i	−0.0350702	−	0.0202478i
$143$	0.792365	+	1.89359i	0.0662609	+	0.158350i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.0978414	+	0.365149i	−0.00812528	+	0.0303240i
$146$	2.52013	+	1.45500i	0.208568	+	0.120417i
$147$	−0.574124	−	6.97642i	−0.0473529	−	0.575405i
$148$	1.14587	−	1.14587i	0.0941902	−	0.0941902i
$149$	−8.07270	+	8.07270i	−0.661341	+	0.661341i	−0.955696	−	0.294355i	$-0.904895\pi$
$149$	−8.07270	+	8.07270i	−0.661341	+	0.661341i	0.294355	+	0.955696i	$0.404895\pi$
$150$	−0.820870	−	3.06353i	−0.0670238	−	0.250136i
$151$	0.614206	−	2.29225i	0.0499834	−	0.186541i	−0.936420	−	0.350880i	$-0.885883\pi$
$151$	0.614206	−	2.29225i	0.0499834	−	0.186541i	0.986404	+	0.164339i	$0.0525492\pi$
$152$		−	3.25147i		−	0.263729i
$153$	−0.487543	+	0.844450i	−0.0394156	+	0.0682697i
$154$	−0.806037	−	1.27245i	−0.0649523	−	0.102537i
$155$		−	3.47887i		−	0.279429i
$156$	2.85254	−	2.20522i	0.228386	−	0.176559i
$157$	−15.0264	+	8.67548i	−1.19924	+	0.692379i	−0.960385	−	0.278677i	$-0.910104\pi$
$157$	−15.0264	+	8.67548i	−1.19924	+	0.692379i	−0.238851	+	0.971056i	$0.576771\pi$
$158$	−2.05681	+	2.05681i	−0.163631	+	0.163631i
$159$	−7.86452	+	4.54058i	−0.623697	+	0.360091i
$160$	−0.676092	−	1.17103i	−0.0534498	−	0.0925777i
$161$	−0.181101	+	0.114719i	−0.0142728	+	0.00904111i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	−5.99975	−	5.99975i	−0.469937	−	0.469937i	0.431957	−	0.901894i	$-0.357823\pi$
$163$	−5.99975	−	5.99975i	−0.469937	−	0.469937i	−0.901894	+	0.431957i	$0.857823\pi$
$164$	−2.23576	−	0.599071i	−0.174584	−	0.0467796i
$165$	0.384909	−	0.666681i	0.0299651	−	0.0519011i
$166$	−1.57437	−	2.72689i	−0.122195	−	0.211647i
$167$	4.82117	+	17.9928i	0.373073	+	1.39233i	0.856140	+	0.516744i	$0.172856\pi$
$167$	4.82117	+	17.9928i	0.373073	+	1.39233i	−0.483067	+	0.875583i	$0.660477\pi$
$168$	−1.79247	+	1.94604i	−0.138292	+	0.150140i
$169$	9.25845	+	9.12585i	0.712189	+	0.701988i
$170$	−0.659248	+	1.14185i	−0.0505620	+	0.0875760i
$171$	−2.29914	−	2.29914i	−0.175820	−	0.175820i
$172$	10.9528			0.835146
$173$	−10.2465			−0.779027			−0.389514	−	0.921021i	$-0.627357\pi$
$173$	−10.2465			−0.779027			−0.389514	+	0.921021i	$0.627357\pi$
$174$	−0.197686	−	0.197686i	−0.0149865	−	0.0149865i
$175$	−7.08872	+	4.49036i	−0.535857	+	0.339439i
$176$	−0.147349	+	0.549915i	−0.0111069	+	0.0414514i
$177$	−6.90183	+	1.84934i	−0.518773	+	0.139005i
$178$	9.16686	+	5.29249i	0.687085	+	0.396689i
$179$			5.16079i			0.385736i	0.981225	+	0.192868i	$0.0617789\pi$
$179$			5.16079i			0.385736i	−0.981225	+	0.192868i	$0.938221\pi$
$180$	−1.30611	−	0.349971i	−0.0973516	−	0.0260853i
$181$	−4.50812			−0.335086			−0.167543	−	0.985865i	$-0.553583\pi$
$181$	−4.50812			−0.335086			−0.167543	+	0.985865i	$0.553583\pi$
$182$	−7.81983	−	5.46353i	−0.579645	−	0.404984i
$183$	5.72178			0.422966
$184$	0.0782664	+	0.0209714i	0.00576988	+	0.00154603i
$185$		−	2.19123i		−	0.161102i
$186$	2.22809	+	1.28639i	0.163372	+	0.0943226i
$187$	0.536215	−	0.143678i	0.0392119	−	0.0105068i
$188$	1.48771	−	5.55221i	0.108502	−	0.404936i
$189$	0.108591	+	2.64352i	0.00789881	+	0.192288i
$190$	−3.10886	−	3.10886i	−0.225540	−	0.225540i
$191$	14.5531			1.05302			0.526512	−	0.850168i	$-0.323500\pi$
$191$	14.5531			1.05302			0.526512	+	0.850168i	$0.323500\pi$
$192$	1.00000			0.0721688
$193$	−15.1981	−	15.1981i	−1.09398	−	1.09398i	−0.995099	−	0.0988833i	$-0.968473\pi$
$193$	−15.1981	−	15.1981i	−1.09398	−	1.09398i	−0.0988833	−	0.995099i	$-0.531527\pi$
$194$	8.39088	−	14.5334i	0.602430	−	1.04344i
$195$	0.618927	−	4.83592i	0.0443223	−	0.346308i
$196$	6.32882	+	2.99100i	0.452058	+	0.213643i
$197$	3.63389	+	13.5619i	0.258904	+	0.966243i	0.965877	+	0.259002i	$0.0833937\pi$
$197$	3.63389	+	13.5619i	0.258904	+	0.966243i	−0.706973	+	0.707241i	$0.749940\pi$
$198$	0.284657	+	0.493040i	0.0202297	+	0.0350389i
$199$	2.55850	−	4.43145i	0.181367	−	0.314137i	−0.760979	−	0.648776i	$-0.775281\pi$
$199$	2.55850	−	4.43145i	0.181367	−	0.314137i	0.942346	+	0.334639i	$0.108614\pi$
$200$	3.06353	+	0.820870i	0.216624	+	0.0580443i
$201$	1.53445	+	1.53445i	0.108232	+	0.108232i
$202$	1.51192	+	0.405118i	0.106378	+	0.0285040i
$203$	−0.343233	+	0.655215i	−0.0240903	+	0.0459871i
$204$	−0.487543	−	0.844450i	−0.0341349	−	0.0591233i
$205$	−2.71049	+	1.56490i	−0.189309	+	0.109298i
$206$	4.35798	−	4.35798i	0.303635	−	0.303635i
$207$	0.0701717	−	0.0405137i	0.00487727	−	0.00281589i
$208$	0.483507	+	3.57298i	0.0335252	+	0.247742i
$209$			1.85111i			0.128044i
$210$	0.146835	+	3.57453i	0.0101326	+	0.246666i
$211$	5.94537	−	10.2977i	0.409296	−	0.708922i	−0.585515	−	0.810662i	$-0.699108\pi$
$211$	5.94537	−	10.2977i	0.409296	−	0.708922i	0.994811	+	0.101740i	$0.0324408\pi$
$212$		−	9.08116i		−	0.623697i
$213$	0.124896	−	0.466117i	0.00855771	−	0.0319378i
$214$	−3.64132	−	13.5896i	−0.248916	−	0.928966i
$215$	10.4724	−	10.4724i	0.714213	−	0.714213i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	1.49042	−	6.64176i	0.101176	−	0.450872i
$218$	16.4713	+	9.50971i	1.11558	+	0.644079i
$219$	−0.753163	+	2.81084i	−0.0508940	+	0.189939i
$220$	0.384909	+	0.666681i	0.0259505	+	0.0449477i
$221$	2.78148	−	2.15028i	0.187102	−	0.144644i
$222$	1.40340	+	0.810255i	0.0941902	+	0.0543807i
$223$	7.79102	−	2.08760i	0.521725	−	0.139796i	0.0116608	−	0.999932i	$-0.496288\pi$
$223$	7.79102	−	2.08760i	0.521725	−	0.139796i	0.510065	+	0.860136i	$0.329622\pi$
$224$	−0.789084	−	2.52534i	−0.0527229	−	0.168731i
$225$	2.74668	−	1.58580i	0.183112	−	0.105720i
$226$	−4.70716	−	17.5674i	−0.313116	−	1.16856i
$227$	−15.6448	+	4.19201i	−1.03838	+	0.278233i	−0.737442	−	0.675410i	$-0.763967\pi$
$227$	−15.6448	+	4.19201i	−1.03838	+	0.278233i	−0.300938	+	0.953644i	$0.597300\pi$
$228$	3.14068	−	0.841543i	0.207997	−	0.0557326i
$229$	−6.94386	−	25.9148i	−0.458863	−	1.71250i	−0.676475	−	0.736465i	$-0.736493\pi$
$229$	−6.94386	−	25.9148i	−0.458863	−	1.71250i	0.217612	−	0.976035i	$-0.430173\pi$
$230$	0.0948851	−	0.0547819i	0.00625654	−	0.00361221i
$231$	1.02048	−	1.10791i	0.0671424	−	0.0728949i
$232$	0.270044	−	0.0723580i	0.0177292	−	0.00475054i
$233$	22.8801	+	13.2098i	1.49893	+	0.865406i	0.999999	−	0.00123761i	$-0.000393945\pi$
$233$	22.8801	+	13.2098i	1.49893	+	0.865406i	0.498928	+	0.866644i	$0.333727\pi$
$234$	2.86837	+	2.18459i	0.187511	+	0.142811i
$235$	−3.88622	−	6.73113i	−0.253509	−	0.439091i
$236$	1.84934	−	6.90183i	0.120382	−	0.449271i
$237$	−2.51907	−	1.45438i	−0.163631	−	0.0944723i
$238$	−1.74781	+	1.89756i	−0.113294	+	0.123000i
$239$	7.85321	−	7.85321i	0.507982	−	0.507982i	−0.405925	−	0.913907i	$-0.633050\pi$
$239$	7.85321	−	7.85321i	0.507982	−	0.507982i	0.913907	+	0.405925i	$0.133050\pi$
$240$	0.956138	−	0.956138i	0.0617185	−	0.0617185i
$241$	−1.17845	−	4.39803i	−0.0759106	−	0.283302i	0.917528	−	0.397672i	$-0.130182\pi$
$241$	−1.17845	−	4.39803i	−0.0759106	−	0.283302i	−0.993438	+	0.114370i	$0.963515\pi$
$242$	−2.76312	+	10.3121i	−0.177620	+	0.662888i
$243$		−	1.00000i		−	0.0641500i
$244$	−2.86089	+	4.95521i	−0.183150	+	0.317225i
$245$	8.91104	−	3.19141i	0.569305	−	0.203892i
$246$		−	2.31463i		−	0.147576i
$247$	4.52536	+	10.8147i	0.287942	+	0.688124i
$248$	−2.22809	+	1.28639i	−0.141484	+	0.0816858i
$249$	2.22649	−	2.22649i	0.141098	−	0.141098i
$250$	9.56915	−	5.52475i	0.605206	−	0.349416i
$251$	4.91255	+	8.50878i	0.310077	+	0.537069i	0.978379	−	0.206821i	$-0.0663118\pi$
$251$	4.91255	+	8.50878i	0.310077	+	0.537069i	−0.668302	+	0.743890i	$0.732978\pi$
$252$	−2.34365	−	1.22772i	−0.147636	−	0.0773390i
$253$	−0.0445582	−	0.0119393i	−0.00280135	−	0.000750619i
$254$	−6.14617	−	6.14617i	−0.385645	−	0.385645i
$255$	−1.27357	−	0.341252i	−0.0797541	−	0.0213700i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.49748	−	11.2540i	−0.405302	−	0.702003i	0.589055	−	0.808093i	$-0.299500\pi$
$257$	−6.49748	−	11.2540i	−0.405302	−	0.702003i	−0.994357	+	0.106090i	$0.966167\pi$
$258$	2.83480	+	10.5796i	0.176487	+	0.658659i
$259$	0.938766	−	4.18343i	0.0583321	−	0.259946i
$260$	3.87857	+	2.95397i	0.240539	+	0.183197i
$261$	0.139785	−	0.242115i	0.00865247	−	0.0149865i
$262$	4.27179	+	4.27179i	0.263912	+	0.263912i
$263$	19.5019			1.20254			0.601270	−	0.799046i	$-0.294662\pi$
$263$	19.5019			1.20254			0.601270	+	0.799046i	$0.294662\pi$
$264$	−0.569314			−0.0350389
$265$	−8.68285	−	8.68285i	−0.533383	−	0.533383i
$266$	−4.60345	−	7.26724i	−0.282255	−	0.445583i
$267$	−2.73959	+	10.2243i	−0.167660	+	0.625717i
$268$	−2.09610	+	0.561649i	−0.128040	+	0.0343082i
$269$	25.5520	+	14.7525i	1.55794	+	0.899475i	0.997454	+	0.0713074i	$0.0227171\pi$
$269$	25.5520	+	14.7525i	1.55794	+	0.899475i	0.560481	+	0.828167i	$0.310616\pi$
$270$		−	1.35218i		−	0.0822913i
$271$	−7.27817	−	1.95018i	−0.442117	−	0.118465i	0.0308915	−	0.999523i	$-0.490165\pi$
$271$	−7.27817	−	1.95018i	−0.442117	−	0.118465i	−0.473009	+	0.881058i	$0.656832\pi$
$272$	0.975087			0.0591233
$273$	3.25345	−	8.96745i	0.196908	−	0.542735i
$274$	4.40944			0.266384
$275$	−1.74411	−	0.467333i	−0.105174	−	0.0281812i
$276$			0.0810273i			0.00487727i
$277$	6.80836	+	3.93081i	0.409075	+	0.236179i	0.690392	−	0.723435i	$-0.257438\pi$
$277$	6.80836	+	3.93081i	0.409075	+	0.236179i	−0.281317	+	0.959615i	$0.590771\pi$
$278$	4.38659	−	1.17538i	0.263090	−	0.0704949i
$279$	−0.665884	+	2.48511i	−0.0398654	+	0.148780i
$280$	−3.16905	−	1.66010i	−0.189387	−	0.0992100i
$281$	−14.1756	−	14.1756i	−0.845648	−	0.845648i	0.143939	−	0.989587i	$-0.454023\pi$
$281$	−14.1756	−	14.1756i	−0.845648	−	0.845648i	−0.989587	+	0.143939i	$0.954023\pi$
$282$	5.74807			0.342292
$283$	−19.8154			−1.17791			−0.588953	−	0.808167i	$-0.700460\pi$
$283$	−19.8154			−1.17791			−0.588953	+	0.808167i	$0.700460\pi$
$284$	0.341221	+	0.341221i	0.0202478	+	0.0202478i
$285$	2.19829	−	3.80756i	0.130216	−	0.225540i
$286$	−0.275268	−	2.03415i	−0.0162769	−	0.120282i
$287$	−5.84524	+	1.82644i	−0.345033	+	0.107811i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	8.02460	+	13.8990i	0.472035	+	0.817589i
$290$	0.189015	−	0.327384i	0.0110993	−	0.0192246i
$291$	16.2099	+	4.34344i	0.950243	+	0.254617i
$292$	−2.05768	−	2.05768i	−0.120417	−	0.120417i
$293$	−28.8649	−	7.73434i	−1.68631	−	0.451845i	−0.716875	−	0.697202i	$-0.754428\pi$
$293$	−28.8649	−	7.73434i	−1.68631	−	0.451845i	−0.969433	+	0.245357i	$0.921095\pi$
$294$	−1.25107	+	6.88729i	−0.0729638	+	0.401675i
$295$	−4.83088	−	8.36733i	−0.281265	−	0.487165i
$296$	−1.40340	+	0.810255i	−0.0815711	+	0.0470951i
$297$	−0.402566	+	0.402566i	−0.0233592	+	0.0233592i
$298$	9.88700	−	5.70826i	0.572738	−	0.330671i
$299$	−0.289509	+	0.0391773i	−0.0167428	+	0.00226568i
$300$			3.17160i			0.183112i
$301$	24.4803	−	15.5071i	1.41102	−	0.893812i
$302$	−1.18656	+	2.05517i	−0.0682786	+	0.118262i
$303$			1.56526i			0.0899216i
$304$	−0.841543	+	3.14068i	−0.0482658	+	0.180130i
$305$	2.00246	+	7.47327i	0.114660	+	0.427918i
$306$	0.689491	−	0.689491i	0.0394156	−	0.0394156i
$307$	−1.31631	+	1.31631i	−0.0751256	+	0.0751256i	−0.743671	−	0.668546i	$-0.766917\pi$
$307$	−1.31631	+	1.31631i	−0.0751256	+	0.0751256i	0.668546	+	0.743671i	$0.266917\pi$
$308$	0.449237	+	1.43771i	0.0255976	+	0.0819213i
$309$	5.33742	+	3.08156i	0.303635	+	0.175304i
$310$	−0.900397	+	3.36033i	−0.0511391	+	0.190854i
$311$	−11.9503	−	20.6986i	−0.677641	−	1.17371i	−0.975689	−	0.219158i	$-0.929669\pi$
$311$	−11.9503	−	20.6986i	−0.677641	−	1.17371i	0.298049	−	0.954551i	$-0.403664\pi$
$312$	−3.32610	+	1.39179i	−0.188303	+	0.0787945i
$313$	3.83190	+	2.21235i	0.216592	+	0.125049i	0.604371	−	0.796703i	$-0.293424\pi$
$313$	3.83190	+	2.21235i	0.216592	+	0.125049i	−0.387779	+	0.921752i	$0.626758\pi$
$314$	16.7597	−	4.49076i	0.945807	−	0.253428i
$315$	−3.41473	+	1.06699i	−0.192398	+	0.0601179i
$316$	2.51907	−	1.45438i	0.141709	−	0.0818154i
$317$	3.50687	+	13.0878i	0.196966	+	0.735086i	0.991749	+	0.128193i	$0.0409177\pi$
$317$	3.50687	+	13.0878i	0.196966	+	0.735086i	−0.794784	+	0.606893i	$0.792416\pi$
$318$	8.77173	−	2.35038i	0.491894	−	0.131803i
$319$	−0.153740	+	0.0411945i	−0.00860778	+	0.00230645i
$320$	0.349971	+	1.30611i	0.0195640	+	0.0730137i
$321$	12.1841	−	7.03449i	0.680050	−	0.392627i
$322$	0.204622	−	0.0639374i	0.0114031	−	0.00356309i
$323$	3.06244	−	0.820578i	0.170399	−	0.0456582i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	−11.3321	+	1.53349i	−0.628590	+	0.0850628i
$326$	4.24247	+	7.34817i	0.234968	+	0.406977i
$327$	−4.92259	+	18.3713i	−0.272220	+	1.01594i
$328$	2.00453	+	1.15732i	0.110682	+	0.0639021i
$329$	−4.53571	−	14.5158i	−0.250062	−	0.800284i
$330$	−0.544343	+	0.544343i	−0.0299651	+	0.0299651i
$331$	−12.2693	+	12.2693i	−0.674384	+	0.674384i	−0.958724	−	0.284339i	$-0.908226\pi$
$331$	−12.2693	+	12.2693i	−0.674384	+	0.674384i	0.284339	+	0.958724i	$0.408226\pi$
$332$	0.814953	+	3.04145i	0.0447263	+	0.166921i
$333$	−0.419419	+	1.56529i	−0.0229840	+	0.0857775i
$334$		−	18.6276i		−	1.01925i
$335$	−1.46715	+	2.54118i	−0.0801589	+	0.138839i
$336$	2.23506	−	1.41580i	0.121933	−	0.0772384i
$337$		−	11.6579i		−	0.635046i	−0.948251	−	0.317523i	$-0.897149\pi$
$337$		−	11.6579i		−	0.635046i	0.948251	−	0.317523i	$-0.102851\pi$
$338$	−6.58103	−	11.2112i	−0.357961	−	0.609806i
$339$	15.7505	−	9.09354i	0.855448	−	0.493893i
$340$	0.932318	−	0.932318i	0.0505620	−	0.0505620i
$341$	1.26848	−	0.732359i	0.0686922	−	0.0396595i
$342$	1.62574	+	2.81586i	0.0879098	+	0.152264i
$343$	18.3800	−	2.27528i	0.992425	−	0.122854i
$344$	−10.5796	−	2.83480i	−0.570415	−	0.152842i
$345$	0.0774734	+	0.0774734i	0.00417102	+	0.00417102i
$346$	9.89737	+	2.65199i	0.532086	+	0.142572i
$347$	0.632772	−	1.09599i	0.0339690	−	0.0588360i	−0.848541	−	0.529129i	$-0.822519\pi$
$347$	0.632772	−	1.09599i	0.0339690	−	0.0588360i	0.882510	+	0.470293i	$0.155852\pi$
$348$	0.139785	+	0.242115i	0.00749326	+	0.0129787i
$349$	−1.87703	−	7.00518i	−0.100475	−	0.374979i	0.897317	−	0.441386i	$-0.145513\pi$
$349$	−1.87703	−	7.00518i	−0.100475	−	0.374979i	−0.997793	+	0.0664071i	$0.978846\pi$
$350$	8.00937	−	2.50266i	0.428119	−	0.133773i
$351$	−1.36776	+	3.33605i	−0.0730058	+	0.178065i
$352$	0.284657	−	0.493040i	0.0151723	−	0.0262791i
$353$	15.5796	+	15.5796i	0.829220	+	0.829220i	0.987409	−	0.158189i	$-0.0505656\pi$
$353$	15.5796	+	15.5796i	0.829220	+	0.829220i	−0.158189	+	0.987409i	$0.550566\pi$
$354$	7.14530			0.379768
$355$	0.652510			0.0346316
$356$	−7.48471	−	7.48471i	−0.396689	−	0.396689i
$357$	−2.28526	−	1.19713i	−0.120949	−	0.0633590i
$358$	1.33571	−	4.98494i	0.0705945	−	0.263462i
$359$	7.87503	−	2.11011i	0.415628	−	0.111367i	−0.0449440	−	0.998990i	$-0.514311\pi$
$359$	7.87503	−	2.11011i	0.415628	−	0.111367i	0.460572	+	0.887622i	$0.347644\pi$
$360$	1.17103	+	0.676092i	0.0617185	+	0.0356332i
$361$		−	8.42792i		−	0.443575i
$362$	4.35451	+	1.16679i	0.228868	+	0.0613250i
$363$	−10.6759			−0.560338
$364$	6.13931	+	7.30129i	0.321787	+	0.382692i
$365$	−3.93485			−0.205960
$366$	−5.52681	−	1.48091i	−0.288891	−	0.0774082i
$367$			29.9706i			1.56445i	0.622996	+	0.782225i	$0.285915\pi$
$367$			29.9706i			1.56445i	−0.622996	+	0.782225i	$0.714085\pi$
$368$	−0.0701717	−	0.0405137i	−0.00365795	−	0.00211192i
$369$	2.23576	−	0.599071i	0.116389	−	0.0311864i
$370$	−0.567131	+	2.11656i	−0.0294837	+	0.110035i
$371$	−12.8571	−	20.2970i	−0.667509	−	1.05377i
$372$	−1.81923	−	1.81923i	−0.0943226	−	0.0943226i
$373$	−9.22385			−0.477593			−0.238796	−	0.971070i	$-0.576753\pi$
$373$	−9.22385			−0.477593			−0.238796	+	0.971070i	$0.576753\pi$
$374$	−0.555131			−0.0287051
$375$	7.81318	+	7.81318i	0.403471	+	0.403471i
$376$	−2.87403	+	4.97797i	−0.148217	+	0.256719i
$377$	−0.797485	+	0.616514i	−0.0410726	+	0.0317521i
$378$	0.579303	−	2.58155i	0.0297961	−	0.132781i
$379$	0.121145	+	0.452118i	0.00622278	+	0.0232237i	0.968967	−	0.247188i	$-0.0795067\pi$
$379$	0.121145	+	0.452118i	0.00622278	+	0.0232237i	−0.962745	+	0.270412i	$0.912840\pi$
$380$	2.19829	+	3.80756i	0.112770	+	0.195324i
$381$	4.34600	−	7.52749i	0.222652	−	0.385645i
$382$	−14.0572	−	3.76661i	−0.719228	−	0.192717i
$383$	2.50918	+	2.50918i	0.128213	+	0.128213i	0.768301	−	0.640088i	$-0.221102\pi$
$383$	2.50918	+	2.50918i	0.128213	+	0.128213i	−0.640088	+	0.768301i	$0.721102\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	1.80418	+	0.945119i	0.0919498	+	0.0481677i
$386$	10.7467	+	18.6138i	0.546991	+	0.947416i
$387$	−9.48543	+	5.47642i	−0.482172	+	0.278382i
$388$	−11.8665	+	11.8665i	−0.602430	+	0.602430i
$389$	−23.1285	+	13.3533i	−1.17266	+	0.677037i	−0.954306	−	0.298832i	$-0.903403\pi$
$389$	−23.1285	+	13.3533i	−1.17266	+	0.677037i	−0.218357	+	0.975869i	$0.570070\pi$
$390$	−1.84947	+	4.51095i	−0.0936514	+	0.228421i
$391$			0.0790087i			0.00399564i
$392$	−5.33904	−	4.52710i	−0.269662	−	0.228653i
$393$	−3.02061	+	5.23185i	−0.152370	+	0.263912i
$394$		−	14.0403i		−	0.707339i
$395$	1.01798	−	3.79917i	0.0512203	−	0.191157i
$396$	−0.147349	−	0.549915i	−0.00740458	−	0.0276343i
$397$	−2.38711	+	2.38711i	−0.119806	+	0.119806i	−0.764468	−	0.644662i	$-0.776998\pi$
$397$	−2.38711	+	2.38711i	−0.119806	+	0.119806i	0.644662	+	0.764468i	$0.276998\pi$
$398$	−3.61827	+	3.61827i	−0.181367	+	0.181367i
$399$	5.82816	−	6.32749i	0.291773	−	0.316771i
$400$	−2.74668	−	1.58580i	−0.137334	−	0.0792900i
$401$	3.48631	−	13.0111i	0.174098	−	0.649743i	−0.822605	−	0.568613i	$-0.807480\pi$
$401$	3.48631	−	13.0111i	0.174098	−	0.649743i	0.996704	−	0.0811303i	$-0.0258530\pi$
$402$	−1.08502	−	1.87931i	−0.0541160	−	0.0937316i
$403$	5.62047	−	7.37969i	0.279975	−	0.367608i
$404$	−1.35555	−	0.782628i	−0.0674412	−	0.0389372i
$405$	1.30611	−	0.349971i	0.0649011	−	0.0173902i
$406$	0.501120	−	0.544054i	0.0248702	−	0.0270009i
$407$	0.798977	−	0.461289i	0.0396038	−	0.0228653i
$408$	0.252371	+	0.941862i	0.0124942	+	0.0466291i
$409$	−34.1501	+	9.15050i	−1.68861	+	0.452463i	−0.970032	−	0.242978i	$-0.921876\pi$
$409$	−34.1501	+	9.15050i	−1.68861	+	0.452463i	−0.718583	+	0.695441i	$0.755209\pi$
$410$	3.02316	−	0.810054i	0.149303	−	0.0400057i
$411$	1.14125	+	4.25919i	0.0562936	+	0.210091i
$412$	−5.33742	+	3.08156i	−0.262956	+	0.151818i
$413$	−5.63824	−	18.0443i	−0.277440	−	0.887902i
$414$	−0.0782664	+	0.0209714i	−0.00384658	+	0.00103069i
$415$	3.68725	+	2.12883i	0.181000	+	0.104500i
$416$	0.457724	−	3.57638i	0.0224418	−	0.175346i
$417$	2.27067	+	3.93291i	0.111195	+	0.192596i
$418$	0.479102	−	1.78803i	0.0234337	−	0.0874556i
$419$	−20.6288	−	11.9100i	−1.00778	−	0.581843i	−0.0972406	−	0.995261i	$-0.531002\pi$
$419$	−20.6288	−	11.9100i	−1.00778	−	0.581843i	−0.910542	+	0.413418i	$0.864335\pi$
$420$	0.783325	−	3.49073i	0.0382223	−	0.170330i
$421$	18.6380	−	18.6380i	0.908362	−	0.908362i	−0.0877779	−	0.996140i	$-0.527977\pi$
$421$	18.6380	−	18.6380i	0.908362	−	0.908362i	0.996140	+	0.0877779i	$0.0279766\pi$
$422$	−8.40803	+	8.40803i	−0.409296	+	0.409296i
$423$	1.48771	+	5.55221i	0.0723349	+	0.269958i
$424$	−2.35038	+	8.77173i	−0.114144	+	0.425993i
$425$			3.09258i			0.150012i
$426$	−0.241280	+	0.417909i	−0.0116901	+	0.0202478i
$427$	0.621332	+	15.1256i	0.0300684	+	0.731981i
$428$			14.0690i			0.680050i
$429$	1.89359	−	0.792365i	0.0914236	−	0.0382557i
$430$	−12.8260	+	7.40512i	−0.618527	+	0.357107i
$431$	3.20968	−	3.20968i	0.154605	−	0.154605i	−0.625566	−	0.780171i	$-0.715132\pi$
$431$	3.20968	−	3.20968i	0.154605	−	0.154605i	0.780171	+	0.625566i	$0.215132\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−14.8827	−	25.7776i	−0.715218	−	1.23879i	−0.962875	−	0.269947i	$-0.912994\pi$
$433$	−14.8827	−	25.7776i	−0.715218	−	1.23879i	0.247657	−	0.968848i	$-0.420339\pi$
$434$	−3.15865	+	6.02970i	−0.151620	+	0.289435i
$435$	0.365149	+	0.0978414i	0.0175076	+	0.00469113i
$436$	−13.4488	−	13.4488i	−0.644079	−	0.644079i
$437$	−0.254481	−	0.0681880i	−0.0121735	−	0.00326187i
$438$	1.45500	−	2.52013i	0.0695225	−	0.120417i
$439$	3.93301	+	6.81217i	0.187712	+	0.325127i	0.944487	−	0.328548i	$-0.106559\pi$
$439$	3.93301	+	6.81217i	0.187712	+	0.325127i	−0.756775	+	0.653676i	$0.773226\pi$
$440$	−0.199243	−	0.743587i	−0.00949856	−	0.0354491i
$441$	−6.97642	+	0.574124i	−0.332210	+	0.0273392i
$442$	−3.24323	+	1.35712i	−0.154265	+	0.0645514i
$443$	19.0667	−	33.0246i	0.905888	−	1.56904i	0.0861680	−	0.996281i	$-0.472538\pi$
$443$	19.0667	−	33.0246i	0.905888	−	1.56904i	0.819720	−	0.572764i	$-0.194129\pi$
$444$	−1.14587	−	1.14587i	−0.0543807	−	0.0543807i
$445$	−14.3128			−0.678493
$446$	−8.06586			−0.381929
$447$	8.07270	+	8.07270i	0.381826	+	0.381826i
$448$	0.108591	+	2.64352i	0.00513043	+	0.124895i
$449$	−6.92757	+	25.8540i	−0.326932	+	1.22013i	0.585423	+	0.810728i	$0.300928\pi$
$449$	−6.92757	+	25.8540i	−0.326932	+	1.22013i	−0.912355	+	0.409399i	$0.865738\pi$
$450$	−3.06353	+	0.820870i	−0.144416	+	0.0386962i
$451$	−1.14121	−	0.658877i	−0.0537374	−	0.0310253i
$452$			18.1871i			0.855448i
$453$	−2.29225	−	0.614206i	−0.107699	−	0.0288579i
$454$	16.1967			0.760147
$455$	12.8511	+	1.11101i	0.602468	+	0.0520850i
$456$	−3.25147			−0.152264
$457$	−5.16300	−	1.38342i	−0.241515	−	0.0647137i	0.136031	−	0.990705i	$-0.456565\pi$
$457$	−5.16300	−	1.38342i	−0.241515	−	0.0647137i	−0.377546	+	0.925991i	$0.623232\pi$
$458$			26.8290i			1.25364i
$459$	0.844450	+	0.487543i	0.0394156	+	0.0227566i
$460$	−0.105831	+	0.0283572i	−0.00493438	+	0.00132216i
$461$	−9.44607	+	35.2532i	−0.439947	+	1.64191i	0.288995	+	0.957330i	$0.406679\pi$
$461$	−9.44607	+	35.2532i	−0.439947	+	1.64191i	−0.728943	+	0.684575i	$0.759988\pi$
$462$	−1.27245	+	0.806037i	−0.0591998	+	0.0375002i
$463$	−8.27330	−	8.27330i	−0.384493	−	0.384493i	0.488225	−	0.872718i	$-0.337645\pi$
$463$	−8.27330	−	8.27330i	−0.384493	−	0.384493i	−0.872718	+	0.488225i	$0.837645\pi$
$464$	−0.279570			−0.0129787
$465$	−3.47887			−0.161329
$466$	−18.6815	−	18.6815i	−0.865406	−	0.865406i
$467$	−19.1690	+	33.2016i	−0.887035	+	1.53639i	−0.0436707	+	0.999046i	$0.513905\pi$
$467$	−19.1690	+	33.2016i	−0.887035	+	1.53639i	−0.843364	+	0.537343i	$0.819428\pi$
$468$	−2.20522	−	2.85254i	−0.101936	−	0.131859i
$469$	−3.88973	+	4.22299i	−0.179611	+	0.194999i
$470$	2.01166	+	7.50760i	0.0927908	+	0.346300i
$471$	8.67548	+	15.0264i	0.399745	+	0.692379i
$472$	−3.57265	+	6.18801i	−0.164444	+	0.284826i
$473$	6.02313	+	1.61389i	0.276944	+	0.0742069i
$474$	2.05681	+	2.05681i	0.0944723	+	0.0944723i
$475$	−9.96098	−	2.66904i	−0.457041	−	0.122464i
$476$	2.17938	−	1.38053i	0.0998917	−	0.0632765i
$477$	4.54058	+	7.86452i	0.207899	+	0.360091i
$478$	−9.61818	+	5.55306i	−0.439925	+	0.253991i
$479$	15.5390	−	15.5390i	0.709995	−	0.709995i	−0.256539	−	0.966534i	$-0.582582\pi$
$479$	15.5390	−	15.5390i	0.709995	−	0.709995i	0.966534	+	0.256539i	$0.0825821\pi$
$480$	−1.17103	+	0.676092i	−0.0534498	+	0.0308592i
$481$	3.54015	−	4.64823i	0.161417	−	0.211941i
$482$			4.55318i			0.207392i
$483$	0.114719	+	0.181101i	0.00521988	+	0.00824039i
$484$	5.33794	−	9.24558i	0.242634	−	0.420254i
$485$			22.6920i			1.03039i
$486$	−0.258819	+	0.965926i	−0.0117403	+	0.0438153i
$487$	7.80281	+	29.1205i	0.353579	+	1.31957i	0.882263	+	0.470756i	$0.156019\pi$
$487$	7.80281	+	29.1205i	0.353579	+	1.31957i	−0.528684	+	0.848818i	$0.677315\pi$
$488$	4.04591	−	4.04591i	0.183150	−	0.183150i
$489$	−5.99975	+	5.99975i	−0.271318	+	0.271318i
$490$	−9.43340	+	0.776321i	−0.426157	+	0.0350706i
$491$	−23.9198	−	13.8101i	−1.07949	−	0.623242i	−0.148729	−	0.988878i	$-0.547518\pi$
$491$	−23.9198	−	13.8101i	−1.07949	−	0.623242i	−0.930758	+	0.365636i	$0.880852\pi$
$492$	−0.599071	+	2.23576i	−0.0270082	+	0.100796i
$493$	0.136303	+	0.236083i	0.00613876	+	0.0106326i
$494$	−1.57211	−	11.6175i	−0.0707326	−	0.522694i
$495$	−0.666681	−	0.384909i	−0.0299651	−	0.0173004i
$496$	2.48511	−	0.665884i	0.111585	−	0.0298991i
$497$	1.24575	+	0.279549i	0.0558797	+	0.0125395i
$498$	−2.72689	+	1.57437i	−0.122195	+	0.0705491i
$499$	−6.58713	−	24.5835i	−0.294881	−	1.10051i	−0.941312	−	0.337537i	$-0.890406\pi$
$499$	−6.58713	−	24.5835i	−0.294881	−	1.10051i	0.646431	−	0.762972i	$-0.276261\pi$
$500$	−10.6730	+	2.85982i	−0.477311	+	0.127895i
$501$	17.9928	−	4.82117i	0.803861	−	0.215394i
$502$	−2.54292	−	9.49031i	−0.113496	−	0.423573i
$503$	36.0023	−	20.7860i	1.60527	−	0.926800i	0.614855	−	0.788640i	$-0.289214\pi$
$503$	36.0023	−	20.7860i	1.60527	−	0.926800i	0.990410	−	0.138161i	$-0.0441190\pi$
$504$	1.94604	+	1.79247i	0.0866834	+	0.0798428i
$505$	−2.04439	+	0.547794i	−0.0909744	+	0.0243765i
$506$	0.0399498	+	0.0230650i	0.00177598	+	0.00102536i
$507$	9.12585	−	9.25845i	0.405293	−	0.411182i
$508$	4.34600	+	7.52749i	0.192822	+	0.333978i
$509$	−9.41318	+	35.1305i	−0.417232	+	1.55713i	0.363091	+	0.931753i	$0.381721\pi$
$509$	−9.41318	+	35.1305i	−0.417232	+	1.55713i	−0.780323	+	0.625376i	$0.784945\pi$
$510$	1.14185	+	0.659248i	0.0505620	+	0.0291920i
$511$	−7.51231	−	1.68577i	−0.332325	−	0.0745741i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−2.29914	+	2.29914i	−0.101509	+	0.101509i
$514$	3.36334	+	12.5522i	0.148351	+	0.553652i
$515$	−2.15691	+	8.04971i	−0.0950449	+	0.354713i
$516$		−	10.9528i		−	0.482172i
$517$	1.63623	−	2.83403i	0.0719612	−	0.124640i
$518$	−1.98953	+	3.79791i	−0.0874149	+	0.166871i
$519$			10.2465i			0.449772i
$520$	−2.98187	−	3.85716i	−0.130763	−	0.169148i
$521$	6.43659	−	3.71616i	0.281992	−	0.162808i	−0.352333	−	0.935875i	$-0.614612\pi$
$521$	6.43659	−	3.71616i	0.281992	−	0.162808i	0.634325	+	0.773067i	$0.281278\pi$
$522$	−0.197686	+	0.197686i	−0.00865247	+	0.00865247i
$523$	−25.7430	+	14.8628i	−1.12566	+	0.649903i	−0.942841	−	0.333243i	$-0.891857\pi$
$523$	−25.7430	+	14.8628i	−1.12566	+	0.649903i	−0.182824	+	0.983146i	$0.558524\pi$
$524$	−3.02061	−	5.23185i	−0.131956	−	0.228554i
$525$	4.49036	+	7.08872i	0.195975	+	0.309377i
$526$	−18.8374	−	5.04747i	−0.821350	−	0.220080i
$527$	−1.77391	−	1.77391i	−0.0772726	−	0.0772726i
$528$	0.549915	+	0.147349i	0.0239320	+	0.00641256i
$529$	−11.4967	+	19.9129i	−0.499857	+	0.865778i
$530$	6.13970	+	10.6343i	0.266692	+	0.461923i
$531$	1.84934	+	6.90183i	0.0802545	+	0.299514i
$532$	2.56569	+	8.21108i	0.111237	+	0.355995i
$533$	−8.27801	−	1.05946i	−0.358560	−	0.0458905i
$534$	5.29249	−	9.16686i	0.229028	−	0.396689i
$535$	13.4519	+	13.4519i	0.581576	+	0.581576i
$536$	2.17004			0.0937316
$537$	5.16079			0.222705
$538$	−20.8632	−	20.8632i	−0.899475	−	0.899475i
$539$	3.03959	+	2.57734i	0.130924	+	0.111014i
$540$	−0.349971	+	1.30611i	−0.0150604	+	0.0562060i
$541$	24.6032	−	6.59240i	1.05777	−	0.283429i	0.312313	−	0.949979i	$-0.398896\pi$
$541$	24.6032	−	6.59240i	1.05777	−	0.283429i	0.745460	+	0.666550i	$0.232230\pi$
$542$	6.52542	+	3.76746i	0.280291	+	0.161826i
$543$			4.50812i			0.193462i
$544$	−0.941862	−	0.252371i	−0.0403820	−	0.0108203i
$545$	−25.7177			−1.10163
$546$	−5.46353	+	7.81983i	−0.233818	+	0.334658i
$547$	14.1002			0.602880			0.301440	−	0.953485i	$-0.402533\pi$
$547$	14.1002			0.602880			0.301440	+	0.953485i	$0.402533\pi$
$548$	−4.25919	−	1.14125i	−0.181944	−	0.0487517i
$549$		−	5.72178i		−	0.244200i
$550$	1.56373	+	0.902818i	0.0666775	+	0.0384963i
$551$	−0.878040	+	0.235270i	−0.0374058	+	0.0100228i
$552$	0.0209714	−	0.0782664i	0.000892603	−	0.00333124i
$553$	3.57115	−	6.81714i	0.151861	−	0.289894i
$554$	−5.55901	−	5.55901i	−0.236179	−	0.236179i
$555$	−2.19123			−0.0930124
$556$	−4.54134			−0.192596
$557$	10.5717	+	10.5717i	0.447938	+	0.447938i	0.894668	−	0.446731i	$-0.147412\pi$
$557$	10.5717	+	10.5717i	0.447938	+	0.447938i	−0.446731	+	0.894668i	$0.647412\pi$
$558$	1.28639	−	2.22809i	0.0544572	−	0.0943226i
$559$	39.1343	−	5.29578i	1.65520	−	0.223987i
$560$	2.63140	+	2.42375i	0.111197	+	0.102422i
$561$	−0.143678	−	0.536215i	−0.00606611	−	0.0226390i
$562$	10.0237	+	17.3615i	0.422824	+	0.732352i
$563$	12.0849	−	20.9316i	0.509316	−	0.882161i	−0.490626	−	0.871370i	$-0.663232\pi$
$563$	12.0849	−	20.9316i	0.509316	−	0.882161i	0.999942	−	0.0107905i	$-0.00343480\pi$
$564$	−5.55221	−	1.48771i	−0.233790	−	0.0626439i
$565$	17.3894	+	17.3894i	0.731576	+	0.731576i
$566$	19.1402	+	5.12861i	0.804525	+	0.215572i
$567$	2.64352	−	0.108591i	0.111017	−	0.00456038i
$568$	−0.241280	−	0.417909i	−0.0101239	−	0.0175351i
$569$	25.5109	−	14.7287i	1.06947	−	0.617461i	0.141436	−	0.989947i	$-0.454828\pi$
$569$	25.5109	−	14.7287i	1.06947	−	0.617461i	0.928038	+	0.372487i	$0.121495\pi$
$570$	−3.10886	+	3.10886i	−0.130216	+	0.130216i
$571$	−19.6643	+	11.3532i	−0.822924	+	0.475116i	−0.851424	−	0.524478i	$-0.824260\pi$
$571$	−19.6643	+	11.3532i	−0.822924	+	0.475116i	0.0284996	+	0.999594i	$0.490927\pi$
$572$	−0.260589	+	2.03608i	−0.0108958	+	0.0851329i
$573$		−	14.5531i		−	0.607963i
$574$	6.11878	−	0.251348i	0.255393	−	0.0104910i
$575$	0.128493	−	0.222557i	0.00535853	−	0.00928125i
$576$		−	1.00000i		−	0.0416667i
$577$	1.27121	−	4.74423i	0.0529212	−	0.197505i	−0.934404	−	0.356215i	$-0.884067\pi$
$577$	1.27121	−	4.74423i	0.0529212	−	0.197505i	0.987325	+	0.158711i	$0.0507337\pi$
$578$	−4.15384	−	15.5023i	−0.172777	−	0.644812i
$579$	−15.1981	+	15.1981i	−0.631611	+	0.631611i
$580$	−0.267308	+	0.267308i	−0.0110993	+	0.0110993i
$581$	6.12756	+	5.64400i	0.254214	+	0.234153i
$582$	−14.5334	−	8.39088i	−0.602430	−	0.347813i
$583$	1.33810	−	4.99387i	0.0554186	−	0.206825i
$584$	1.45500	+	2.52013i	0.0602083	+	0.104284i
$585$	−4.83592	−	0.618927i	−0.199941	−	0.0255895i
$586$	25.8796	+	14.9416i	1.06908	+	0.617231i
$587$	−12.4252	+	3.32932i	−0.512842	+	0.137416i	−0.505954	−	0.862561i	$-0.668859\pi$
$587$	−12.4252	+	3.32932i	−0.512842	+	0.137416i	−0.00688845	+	0.999976i	$0.502193\pi$
$588$	2.99100	−	6.32882i	0.123347	−	0.260996i
$589$	7.24458	−	4.18266i	0.298508	−	0.172343i
$590$	2.50065	+	9.33254i	0.102950	+	0.384215i
$591$	13.5619	−	3.63389i	0.557861	−	0.149478i
$592$	1.56529	−	0.419419i	0.0643331	−	0.0172380i
$593$	−3.12251	−	11.6534i	−0.128226	−	0.478547i	0.871708	−	0.490026i	$-0.163013\pi$
$593$	−3.12251	−	11.6534i	−0.128226	−	0.478547i	−0.999934	+	0.0114792i	$0.996346\pi$
$594$	0.493040	−	0.284657i	0.0202297	−	0.0116796i
$595$	0.763810	−	3.40377i	0.0313131	−	0.139541i
$596$	−11.0275	+	2.95481i	−0.451705	+	0.121034i
$597$	−4.43145	−	2.55850i	−0.181367	−	0.104712i
$598$	0.289784	+	0.0370882i	0.0118502	+	0.00151665i
$599$	−10.2865	−	17.8168i	−0.420296	−	0.727975i	0.575672	−	0.817681i	$-0.304741\pi$
$599$	−10.2865	−	17.8168i	−0.420296	−	0.727975i	−0.995968	+	0.0897062i	$0.971407\pi$
$600$	0.820870	−	3.06353i	0.0335119	−	0.125068i
$601$	−20.0939	−	11.6012i	−0.819648	−	0.473224i	0.0306468	−	0.999530i	$-0.490243\pi$
$601$	−20.0939	−	11.6012i	−0.819648	−	0.473224i	−0.850295	+	0.526306i	$0.823577\pi$
$602$	−27.6596	+	8.64271i	−1.12732	+	0.352251i
$603$	1.53445	−	1.53445i	0.0624877	−	0.0624877i
$604$	1.67804	−	1.67804i	0.0682786	−	0.0682786i
$605$	−3.73625	−	13.9439i	−0.151900	−	0.566899i
$606$	0.405118	−	1.51192i	0.0164568	−	0.0614176i
$607$			21.6565i			0.879011i	0.898240	+	0.439505i	$0.144846\pi$
$607$			21.6565i			0.879011i	−0.898240	+	0.439505i	$0.855154\pi$
$608$	1.62574	−	2.81586i	0.0659323	−	0.114198i
$609$	0.655215	+	0.343233i	0.0265506	+	0.0139085i
$610$		−	7.73690i		−	0.313258i
$611$	2.63103	−	20.5573i	0.106440	−	0.831658i
$612$	−0.844450	+	0.487543i	−0.0341349	+	0.0197078i
$613$	28.1755	−	28.1755i	1.13800	−	1.13800i	0.149189	−	0.988809i	$-0.452334\pi$
$613$	28.1755	−	28.1755i	1.13800	−	1.13800i	0.988809	−	0.149189i	$-0.0476663\pi$
$614$	1.61214	−	0.930769i	0.0650606	−	0.0375628i
$615$	1.56490	+	2.71049i	0.0631030	+	0.109298i
$616$	−0.0618222	−	1.50499i	−0.00249089	−	0.0606380i
$617$	−18.2128	−	4.88010i	−0.733218	−	0.196465i	−0.127156	−	0.991883i	$-0.540585\pi$
$617$	−18.2128	−	4.88010i	−0.733218	−	0.196465i	−0.606062	+	0.795417i	$0.707252\pi$
$618$	−4.35798	−	4.35798i	−0.175304	−	0.175304i
$619$	42.5998	+	11.4146i	1.71223	+	0.458790i	0.975969	−	0.217909i	$-0.0699236\pi$
$619$	42.5998	+	11.4146i	1.71223	+	0.458790i	0.736260	+	0.676699i	$0.236590\pi$
$620$	1.73943	−	3.01279i	0.0698574	−	0.120996i
$621$	−0.0405137	−	0.0701717i	−0.00162576	−	0.00281589i
$622$	6.18594	+	23.0863i	0.248034	+	0.925674i
$623$	−27.3257	−	6.13191i	−1.09478	−	0.245670i
$624$	3.57298	−	0.483507i	0.143034	−	0.0193558i
$625$	0.458516	−	0.794172i	0.0183406	−	0.0317669i
$626$	−3.12873	−	3.12873i	−0.125049	−	0.125049i
$627$	1.85111			0.0739262
$628$	−17.3510			−0.692379
$629$	−1.11733	−	1.11733i	−0.0445507	−	0.0445507i
$630$	3.57453	−	0.146835i	0.142413	−	0.00585003i
$631$	−4.22390	+	15.7638i	−0.168151	+	0.627547i	0.829467	+	0.558556i	$0.188645\pi$
$631$	−4.22390	+	15.7638i	−0.168151	+	0.627547i	−0.997617	+	0.0689908i	$0.978022\pi$
$632$	−2.80965	+	0.752844i	−0.111762	+	0.0299465i
$633$	−10.2977	−	5.94537i	−0.409296	−	0.236307i
$634$		−	13.5495i		−	0.538120i
$635$	11.3527	+	3.04195i	0.450518	+	0.120716i
$636$	−9.08116			−0.360091
$637$	24.0589	+	7.62678i	0.953250	+	0.302184i
$638$	0.159163			0.00630133
$639$	−0.466117	−	0.124896i	−0.0184393	−	0.00494080i
$640$		−	1.35218i		−	0.0534498i
$641$	26.5384	+	15.3219i	1.04820	+	0.605180i	0.922146	−	0.386843i	$-0.126434\pi$
$641$	26.5384	+	15.3219i	1.04820	+	0.605180i	0.126057	+	0.992023i	$0.459768\pi$
$642$	−13.5896	+	3.64132i	−0.536339	+	0.143711i
$643$	6.79028	−	25.3417i	0.267783	−	0.999379i	−0.692742	−	0.721185i	$-0.743598\pi$
$643$	6.79028	−	25.3417i	0.267783	−	0.999379i	0.960525	−	0.278193i	$-0.0897356\pi$
$644$	−0.214198	+	0.00879882i	−0.00844057	+	0.000346722i
$645$	−10.4724	−	10.4724i	−0.412351	−	0.412351i
$646$	−3.17047			−0.124740
$647$	−34.0582			−1.33897			−0.669484	−	0.742827i	$-0.733485\pi$
$647$	−34.0582			−1.33897			−0.669484	+	0.742827i	$0.733485\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	2.03396	−	3.52292i	0.0798399	−	0.138287i
$650$	11.3428	+	1.45172i	0.444903	+	0.0569410i
$651$	−6.64176	−	1.49042i	−0.260311	−	0.0584141i
$652$	−2.19606	−	8.19581i	−0.0860044	−	0.320973i
$653$	−6.84461	−	11.8552i	−0.267850	−	0.463930i	0.700456	−	0.713695i	$-0.252980\pi$
$653$	−6.84461	−	11.8552i	−0.267850	−	0.463930i	−0.968306	+	0.249765i	$0.919647\pi$
$654$	9.50971	−	16.4713i	0.371859	−	0.644079i
$655$	−7.89049	−	2.11425i	−0.308307	−	0.0826106i
$656$	−1.63669	−	1.63669i	−0.0639021	−	0.0639021i
$657$	2.81084	+	0.753163i	0.109661	+	0.0293837i
$658$	0.624187	+	15.1951i	0.0243333	+	0.592368i
$659$	−20.2242	−	35.0293i	−0.787822	−	1.36455i	−0.927299	−	0.374322i	$-0.877875\pi$
$659$	−20.2242	−	35.0293i	−0.787822	−	1.36455i	0.139477	−	0.990225i	$-0.455458\pi$
$660$	0.666681	−	0.384909i	0.0259505	−	0.0149826i
$661$	3.49101	−	3.49101i	0.135785	−	0.135785i	−0.635948	−	0.771732i	$-0.719391\pi$
$661$	3.49101	−	3.49101i	0.135785	−	0.135785i	0.771732	+	0.635948i	$0.219391\pi$
$662$	15.0268	−	8.67574i	0.584034	−	0.337192i
$663$	−2.15028	−	2.78148i	−0.0835101	−	0.108024i
$664$		−	3.14874i		−	0.122195i
$665$	10.3041	+	5.39778i	0.399575	+	0.209317i
$666$	0.810255	−	1.40340i	0.0313967	−	0.0543807i
$667$		−	0.0226528i		−	0.000877120i
$668$	−4.82117	+	17.9928i	−0.186537	+	0.696164i
$669$	−2.08760	−	7.79102i	−0.0807112	−	0.301218i
$670$	2.07486	−	2.07486i	0.0801589	−	0.0801589i
$671$	−2.30339	+	2.30339i	−0.0889215	+	0.0889215i
$672$	−2.52534	+	0.789084i	−0.0974171	+	0.0304396i
$673$	13.7664	+	7.94802i	0.530655	+	0.306374i	0.741283	−	0.671193i	$-0.234218\pi$
$673$	13.7664	+	7.94802i	0.530655	+	0.306374i	−0.210628	+	0.977566i	$0.567551\pi$
$674$	−3.01729	+	11.2607i	−0.116222	+	0.433745i
$675$	−1.58580	−	2.74668i	−0.0610374	−	0.105720i
$676$	3.45513	+	12.5324i	0.132890	+	0.482017i
$677$	16.1179	+	9.30568i	0.619462	+	0.357646i	0.776659	−	0.629921i	$-0.216913\pi$
$677$	16.1179	+	9.30568i	0.619462	+	0.357646i	−0.157198	+	0.987567i	$0.550246\pi$
$678$	−17.5674	+	4.70716i	−0.674671	+	0.180777i
$679$	−9.72172	+	43.3230i	−0.373085	+	1.66258i
$680$	−1.14185	+	0.659248i	−0.0437880	+	0.0252810i
$681$	4.19201	+	15.6448i	0.160638	+	0.599509i
$682$	−1.41481	+	0.379097i	−0.0541759	+	0.0145164i
$683$	19.6827	−	5.27396i	0.753137	−	0.201802i	0.138228	−	0.990400i	$-0.455859\pi$
$683$	19.6827	−	5.27396i	0.753137	−	0.201802i	0.614909	+	0.788598i	$0.289193\pi$
$684$	−0.841543	−	3.14068i	−0.0321772	−	0.120087i
$685$	−5.16357	+	2.98119i	−0.197290	+	0.113905i
$686$	−18.3426	−	2.55933i	−0.700323	−	0.0977157i
$687$	−25.9148	+	6.94386i	−0.988713	+	0.264925i
$688$	9.48543	+	5.47642i	0.361629	+	0.208786i
$689$	−4.39081	−	32.4469i	−0.167277	−	1.23613i
$690$	−0.0547819	−	0.0948851i	−0.00208551	−	0.00361221i
$691$	−3.68070	+	13.7365i	−0.140020	+	0.522563i	0.859906	+	0.510452i	$0.170522\pi$
$691$	−3.68070	+	13.7365i	−0.140020	+	0.522563i	−0.999927	+	0.0121110i	$0.996145\pi$
$692$	−8.87374	−	5.12325i	−0.337329	−	0.194757i
$693$	−1.10791	−	1.02048i	−0.0420859	−	0.0387647i
$694$	−0.894875	+	0.894875i	−0.0339690	+	0.0339690i
$695$	−4.34215	+	4.34215i	−0.164707	+	0.164707i
$696$	−0.0723580	−	0.270044i	−0.00274272	−	0.0102360i
$697$	−0.584146	+	2.18006i	−0.0221261	+	0.0825758i
$698$			7.25230i			0.274504i
$699$	13.2098	−	22.8801i	0.499642	−	0.865406i
$700$	−8.38419	+	0.344406i	−0.316893	+	0.0130173i
$701$			22.7395i			0.858858i	0.903101	+	0.429429i	$0.141285\pi$
$701$			22.7395i			0.858858i	−0.903101	+	0.429429i	$0.858715\pi$
$702$	2.18459	−	2.86837i	0.0824521	−	0.108260i
$703$	4.56312	−	2.63452i	0.172102	−	0.0993629i
$704$	−0.402566	+	0.402566i	−0.0151723	+	0.0151723i
$705$	−6.73113	+	3.88622i	−0.253509	+	0.146364i
$706$	−11.0165	−	19.0811i	−0.414610	−	0.718125i
$707$	−4.13779	+	0.169972i	−0.155618	+	0.00639246i
$708$	−6.90183	−	1.84934i	−0.259387	−	0.0695024i
$709$	−7.83733	−	7.83733i	−0.294337	−	0.294337i	0.544454	−	0.838791i	$-0.316737\pi$
$709$	−7.83733	−	7.83733i	−0.294337	−	0.294337i	−0.838791	+	0.544454i	$0.816737\pi$
$710$	−0.630276	−	0.168882i	−0.0236538	−	0.00633803i
$711$	−1.45438	+	2.51907i	−0.0545436	+	0.0944723i
$712$	5.29249	+	9.16686i	0.198344	+	0.343543i
$713$	0.0539548	+	0.201362i	0.00202062	+	0.00754107i
$714$	1.89756	+	1.74781i	0.0710142	+	0.0654102i
$715$	1.69762	+	2.19594i	0.0634873	+	0.0821234i
$716$	−2.58040	+	4.46938i	−0.0964339	+	0.167028i
$717$	−7.85321	−	7.85321i	−0.293283	−	0.293283i
$718$	−8.15283			−0.304261
$719$	−0.543752			−0.0202785			−0.0101393	−	0.999949i	$-0.503227\pi$
$719$	−0.543752			−0.0202785			−0.0101393	+	0.999949i	$0.503227\pi$
$720$	−0.956138	−	0.956138i	−0.0356332	−	0.0356332i
$721$	−7.56658	+	14.4442i	−0.281794	+	0.537930i
$722$	−2.18131	+	8.14075i	−0.0811798	+	0.302967i
$723$	−4.39803	+	1.17845i	−0.163565	+	0.0438270i
$724$	−3.90415	−	2.25406i	−0.145096	−	0.0837715i
$725$		−	0.886684i		−	0.0329306i
$726$	10.3121	+	2.76312i	0.382718	+	0.102549i
$727$	34.4524			1.27777			0.638884	−	0.769303i	$-0.279396\pi$
$727$	34.4524			1.27777			0.638884	+	0.769303i	$0.279396\pi$
$728$	−4.04041	−	8.64148i	−0.149747	−	0.320274i
$729$	−1.00000			−0.0370370
$730$	3.80077	+	1.01841i	0.140673	+	0.0376932i
$731$		−	10.6800i		−	0.395013i
$732$	4.95521	+	2.86089i	0.183150	+	0.105742i
$733$	25.1359	−	6.73516i	0.928417	−	0.248769i	0.237238	−	0.971452i	$-0.423758\pi$
$733$	25.1359	−	6.73516i	0.928417	−	0.248769i	0.691180	+	0.722683i	$0.257091\pi$
$734$	7.75695	−	28.9493i	0.286314	−	1.06854i
$735$	−3.19141	−	8.91104i	−0.117717	−	0.328689i
$736$	0.0572950	+	0.0572950i	0.00211192	+	0.00211192i
$737$	−1.23544			−0.0455079
$738$	−2.31463			−0.0852028
$739$	−29.7898	−	29.7898i	−1.09583	−	1.09583i	−0.994892	−	0.100942i	$-0.967814\pi$
$739$	−29.7898	−	29.7898i	−1.09583	−	1.09583i	−0.100942	−	0.994892i	$-0.532186\pi$
$740$	1.09561	−	1.89766i	0.0402755	−	0.0697593i
$741$	10.8147	−	4.52536i	0.397289	−	0.166243i
$742$	7.16580	+	22.9330i	0.263065	+	0.841898i
$743$	−9.68987	−	36.1631i	−0.355487	−	1.32670i	−0.879871	−	0.475213i	$-0.842371\pi$
$743$	−9.68987	−	36.1631i	−0.355487	−	1.32670i	0.524384	−	0.851482i	$-0.324296\pi$
$744$	1.28639	+	2.22809i	0.0471613	+	0.0816858i
$745$	−7.71862	+	13.3690i	−0.282788	+	0.489804i
$746$	8.90955	+	2.38731i	0.326202	+	0.0874055i
$747$	−2.22649	−	2.22649i	−0.0814631	−	0.0814631i
$748$	0.536215	+	0.143678i	0.0196060	+	0.00525340i
$749$	19.9189	+	31.4450i	0.727821	+	1.14898i
$750$	−5.52475	−	9.56915i	−0.201735	−	0.349416i
$751$	1.85585	−	1.07147i	0.0677208	−	0.0390986i	−0.465757	−	0.884913i	$-0.654218\pi$
$751$	1.85585	−	1.07147i	0.0677208	−	0.0390986i	0.533478	+	0.845814i	$0.320885\pi$
$752$	4.06450	−	4.06450i	0.148217	−	0.148217i
$753$	8.50878	−	4.91255i	0.310077	−	0.179023i
$754$	0.929877	−	0.389102i	0.0338641	−	0.0141703i
$755$		−	3.20888i		−	0.116783i
$756$	−1.22772	+	2.34365i	−0.0446517	+	0.0852378i
$757$	13.5526	−	23.4737i	0.492577	−	0.853168i	−0.507387	−	0.861718i	$-0.669388\pi$
$757$	13.5526	−	23.4737i	0.492577	−	0.853168i	0.999963	+	0.00855073i	$0.00272181\pi$
$758$		−	0.468067i		−	0.0170010i
$759$	−0.0119393	+	0.0445582i	−0.000433370	+	0.00161736i
$760$	−1.13792	−	4.24678i	−0.0412767	−	0.154047i
$761$	36.0858	−	36.0858i	1.30811	−	1.30811i	0.385331	−	0.922779i	$-0.374087\pi$
$761$	36.0858	−	36.0858i	1.30811	−	1.30811i	0.922779	−	0.385331i	$-0.125913\pi$
$762$	−6.14617	+	6.14617i	−0.222652	+	0.222652i
$763$	−49.0996	−	11.0180i	−1.77752	−	0.398879i
$764$	12.6033	+	7.27654i	0.455973	+	0.263256i
$765$	−0.341252	+	1.27357i	−0.0123380	+	0.0460460i
$766$	−1.77426	−	3.07310i	−0.0641065	−	0.111036i
$767$	3.27058	−	25.5543i	0.118094	−	0.922712i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	30.8477	−	8.26561i	1.11240	−	0.298066i	0.344594	−	0.938752i	$-0.388017\pi$
$769$	30.8477	−	8.26561i	1.11240	−	0.298066i	0.767803	+	0.640686i	$0.221350\pi$
$770$	−1.49809	−	1.37987i	−0.0539875	−	0.0497271i
$771$	−11.2540	+	6.49748i	−0.405302	+	0.234001i
$772$	−5.56289	−	20.7610i	−0.200213	−	0.747204i
$773$	24.9169	−	6.67648i	0.896200	−	0.240136i	0.218817	−	0.975766i	$-0.429780\pi$
$773$	24.9169	−	6.67648i	0.896200	−	0.240136i	0.677384	+	0.735630i	$0.263114\pi$
$774$	10.5796	−	2.83480i	0.380277	−	0.101895i
$775$	2.11192	+	7.88178i	0.0758623	+	0.283122i
$776$	14.5334	−	8.39088i	0.521719	−	0.301215i
$777$	−4.18343	−	0.938766i	−0.150080	−	0.0336781i
$778$	25.7965	−	6.91216i	0.924850	−	0.247813i
$779$	−6.51768	−	3.76298i	−0.233520	−	0.134823i
$780$	2.95397	−	3.87857i	0.105769	−	0.138875i
$781$	0.137364	+	0.237922i	0.00491527	+	0.00851350i
$782$	0.0204490	−	0.0763165i	0.000731253	−	0.00272907i
$783$	−0.242115	−	0.139785i	−0.00865247	−	0.00499551i
$784$	3.98541	+	5.75469i	0.142336	+	0.205525i
$785$	−16.5899	+	16.5899i	−0.592120	+	0.592120i
$786$	4.27179	−	4.27179i	0.152370	−	0.152370i
$787$	1.92321	+	7.17753i	0.0685551	+	0.255851i	0.991695	−	0.128614i	$-0.0410527\pi$
$787$	1.92321	+	7.17753i	0.0685551	+	0.255851i	−0.923140	+	0.384465i	$0.874386\pi$
$788$	−3.63389	+	13.5619i	−0.129452	+	0.483122i
$789$		−	19.5019i		−	0.694287i
$790$	−1.96659	+	3.40624i	−0.0699683	+	0.121189i
$791$	25.7493	+	40.6492i	0.915541	+	1.44532i
$792$			0.569314i			0.0202297i
$793$	−7.82604	+	19.0881i	−0.277911	+	0.677840i
$794$	2.92360	−	1.68794i	0.103755	−	0.0599028i
$795$	−8.68285	+	8.68285i	−0.307949	+	0.307949i
$796$	4.43145	−	2.55850i	0.157069	−	0.0906836i
$797$	16.4874	+	28.5569i	0.584012	+	1.01154i	0.994998	+	0.0998967i	$0.0318512\pi$
$797$	16.4874	+	28.5569i	0.584012	+	1.01154i	−0.410986	+	0.911642i	$0.634815\pi$
$798$	−7.26724	+	4.60345i	−0.257258	+	0.162960i
$799$	−5.41388	−	1.45065i	−0.191529	−	0.0513202i
$800$	2.24266	+	2.24266i	0.0792900	+	0.0792900i
$801$	10.2243	+	2.73959i	0.361258	+	0.0967988i
$802$	−6.73504	+	11.6654i	−0.237822	+	0.411921i
$803$	−0.828351	−	1.43475i	−0.0292319	−	0.0506311i
$804$	0.561649	+	2.09610i	0.0198078	+	0.0739238i
$805$	−0.196390	+	0.213215i	−0.00692182	+	0.00751485i
$806$	−7.33896	+	5.67355i	−0.258504	+	0.199842i
$807$	14.7525	−	25.5520i	0.519312	−	0.899475i
$808$	1.10680	+	1.10680i	0.0389372	+	0.0389372i
$809$	31.8139			1.11852			0.559259	−	0.828993i	$-0.311086\pi$
$809$	31.8139			1.11852			0.559259	+	0.828993i	$0.311086\pi$
$810$	−1.35218			−0.0475109
$811$	−31.9059	−	31.9059i	−1.12037	−	1.12037i	−0.991686	−	0.128680i	$-0.958926\pi$
$811$	−31.9059	−	31.9059i	−1.12037	−	1.12037i	−0.128680	−	0.991686i	$-0.541074\pi$
$812$	−0.624856	+	0.395816i	−0.0219282	+	0.0138904i
$813$	−1.95018	+	7.27817i	−0.0683957	+	0.255256i
$814$	−0.891143	+	0.238781i	−0.0312345	+	0.00836927i
$815$	−9.93607	−	5.73659i	−0.348045	−	0.200944i
$816$		−	0.975087i		−	0.0341349i
$817$	34.3994	+	9.21728i	1.20348	+	0.322472i
$818$	35.3548			1.23615
$819$	−8.96745	−	3.25345i	−0.313348	−	0.113685i
$820$	−3.12981			−0.109298
$821$	−30.4055	−	8.14712i	−1.06116	−	0.284337i	−0.314303	−	0.949323i	$-0.601771\pi$
$821$	−30.4055	−	8.14712i	−1.06116	−	0.284337i	−0.746856	+	0.664986i	$0.768437\pi$
$822$		−	4.40944i		−	0.153797i
$823$	10.0280	+	5.78966i	0.349553	+	0.201815i	0.664489	−	0.747298i	$-0.268649\pi$
$823$	10.0280	+	5.78966i	0.349553	+	0.201815i	−0.314935	+	0.949113i	$0.601983\pi$
$824$	5.95312	−	1.59513i	0.207387	−	0.0555691i
$825$	−0.467333	+	1.74411i	−0.0162704	+	0.0607221i
$826$	0.775913	+	18.8887i	0.0269975	+	0.657224i
$827$	−37.5272	−	37.5272i	−1.30495	−	1.30495i	−0.925014	−	0.379933i	$-0.875947\pi$
$827$	−37.5272	−	37.5272i	−1.30495	−	1.30495i	−0.379933	−	0.925014i	$-0.624053\pi$
$828$	0.0810273			0.00281589
$829$	17.5873			0.610832			0.305416	−	0.952219i	$-0.401204\pi$
$829$	17.5873			0.610832			0.305416	+	0.952219i	$0.401204\pi$
$830$	−3.01063	−	3.01063i	−0.104500	−	0.104500i
$831$	3.93081	−	6.80836i	0.136358	−	0.236179i
$832$	−1.36776	+	3.33605i	−0.0474186	+	0.115657i
$833$	2.91649	−	6.17115i	0.101050	−	0.213818i
$834$	−1.17538	−	4.38659i	−0.0407002	−	0.151895i
$835$	12.5939	+	21.8133i	0.435831	+	0.754882i
$836$	−0.925555	+	1.60311i	−0.0320110	+	0.0554447i
$837$	2.48511	+	0.665884i	0.0858980	+	0.0230163i
$838$	16.8433	+	16.8433i	0.581843	+	0.581843i
$839$	29.4347	+	7.88700i	1.01620	+	0.272290i	0.728217	−	0.685346i	$-0.240349\pi$
$839$	29.4347	+	7.88700i	1.01620	+	0.272290i	0.287981	+	0.957636i	$0.407016\pi$
$840$	−1.66010	+	3.16905i	−0.0572789	+	0.109343i
$841$	14.4609	+	25.0470i	0.498652	+	0.863691i
$842$	−22.8268	+	13.1791i	−0.786665	+	0.454181i
$843$	−14.1756	+	14.1756i	−0.488235	+	0.488235i
$844$	10.2977	−	5.94537i	0.354461	−	0.204648i
$845$	15.2863	+	8.67917i	0.525866	+	0.298572i
$846$		−	5.74807i		−	0.197623i
$847$	−1.15930	−	28.2219i	−0.0398341	−	0.969717i
$848$	4.54058	−	7.86452i	0.155924	−	0.270069i
$849$			19.8154i			0.680064i
$850$	0.800420	−	2.98721i	0.0274542	−	0.102460i
$851$	0.0339844	+	0.126831i	0.00116497	+	0.00434773i
$852$	0.341221	−	0.341221i	0.0116901	−	0.0116901i
$853$	−3.62993	+	3.62993i	−0.124287	+	0.124287i	−0.766514	−	0.642228i	$-0.778010\pi$
$853$	−3.62993	+	3.62993i	−0.124287	+	0.124287i	0.642228	+	0.766514i	$0.278010\pi$
$854$	3.31465	−	14.7711i	0.113425	−	0.505456i
$855$	−3.80756	−	2.19829i	−0.130216	−	0.0751801i
$856$	3.64132	−	13.5896i	0.124458	−	0.464483i
$857$	−15.3895	−	26.6554i	−0.525696	−	0.910532i	−0.999552	−	0.0299299i	$-0.990472\pi$
$857$	−15.3895	−	26.6554i	−0.525696	−	0.910532i	0.473856	−	0.880602i	$-0.342862\pi$
$858$	−2.03415	+	0.275268i	−0.0694448	+	0.00939748i
$859$	7.66671	+	4.42637i	0.261585	+	0.151026i	0.625057	−	0.780579i	$-0.285076\pi$
$859$	7.66671	+	4.42637i	0.261585	+	0.151026i	−0.363473	+	0.931605i	$0.618409\pi$
$860$	14.3056	−	3.83317i	0.487817	−	0.130710i
$861$	1.82644	+	5.84524i	0.0622449	+	0.199205i
$862$	−3.93104	+	2.26958i	−0.133892	+	0.0773024i
$863$	11.1633	+	41.6620i	0.380003	+	1.41819i	0.845895	+	0.533350i	$0.179067\pi$
$863$	11.1633	+	41.6620i	0.380003	+	1.41819i	−0.465891	+	0.884842i	$0.654266\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	−13.3831	+	3.58598i	−0.455038	+	0.121927i
$866$	7.70387	+	28.7512i	0.261788	+	0.977006i
$867$	13.8990	−	8.02460i	0.472035	−	0.272530i
$868$	4.61162	−	5.00672i	0.156529	−	0.169939i
$869$	1.59957	−	0.428605i	0.0542619	−	0.0145394i
$870$	−0.327384	−	0.189015i	−0.0110993	−	0.00640821i
$871$	−7.21778	+	3.02024i	−0.244565	+	0.102337i
$872$	9.50971	+	16.4713i	0.322039	+	0.557788i
$873$	4.34344	−	16.2099i	0.147003	−	0.548623i
$874$	0.228162	+	0.131729i	0.00771768	+	0.00445580i
$875$	−19.8059	+	21.5027i	−0.669561	+	0.726926i
$876$	−2.05768	+	2.05768i	−0.0695225	+	0.0695225i
$877$	0.821015	−	0.821015i	0.0277237	−	0.0277237i	−0.693109	−	0.720833i	$-0.743760\pi$
$877$	0.821015	−	0.821015i	0.0277237	−	0.0277237i	0.720833	+	0.693109i	$0.243760\pi$
$878$	−2.03588	−	7.59799i	−0.0687075	−	0.256420i
$879$	−7.73434	+	28.8649i	−0.260873	+	0.973590i
$880$			0.769817i			0.0259505i
$881$	16.0134	−	27.7360i	0.539505	−	0.934451i	−0.459425	−	0.888216i	$-0.651945\pi$
$881$	16.0134	−	27.7360i	0.539505	−	0.934451i	0.998931	−	0.0462344i	$-0.0147221\pi$
$882$	6.88729	+	1.25107i	0.231907	+	0.0421257i
$883$		−	10.0658i		−	0.338742i	−0.985552	−	0.169371i	$-0.945826\pi$
$883$		−	10.0658i		−	0.338742i	0.985552	−	0.169371i	$-0.0541736\pi$
$884$	3.48397	−	0.471462i	0.117179	−	0.0158570i
$885$	−8.36733	+	4.83088i	−0.281265	+	0.162388i
$886$	−26.9644	+	26.9644i	−0.905888	+	0.905888i
$887$	−15.0283	+	8.67659i	−0.504601	+	0.291331i	−0.730611	−	0.682794i	$-0.760765\pi$
$887$	−15.0283	+	8.67659i	−0.504601	+	0.291331i	0.226011	+	0.974125i	$0.427432\pi$
$888$	0.810255	+	1.40340i	0.0271904	+	0.0470951i
$889$	20.3710	+	10.6713i	0.683222	+	0.357905i
$890$	13.8251	+	3.70443i	0.463420	+	0.124173i
$891$	0.402566	+	0.402566i	0.0134865	+	0.0134865i
$892$	7.79102	+	2.08760i	0.260863	+	0.0698979i
$893$	9.34484	−	16.1857i	0.312713	−	0.541635i
$894$	−5.70826	−	9.88700i	−0.190913	−	0.330671i
$895$	1.80613	+	6.74056i	0.0603722	+	0.225312i
$896$	0.579303	−	2.58155i	0.0193532	−	0.0862436i
$897$	0.0391773	+	0.289509i	0.00130809	+	0.00966644i
$898$	13.3830	−	23.1801i	0.446598	−	0.773530i
$899$	0.508602	+	0.508602i	0.0169628	+	0.0169628i
$900$	3.17160			0.105720
$901$	−8.85492			−0.295000
$902$	0.931792	+	0.931792i	0.0310253	+	0.0310253i
$903$	−15.5071	−	24.4803i	−0.516043	−	0.814652i
$904$	4.70716	−	17.5674i	0.156558	−	0.584282i
$905$	−5.88810	+	1.57771i	−0.195727	+	0.0524449i
$906$	2.05517	+	1.18656i	0.0682786	+	0.0394207i
$907$			7.26534i			0.241242i	0.992699	+	0.120621i	$0.0384885\pi$
$907$			7.26534i			0.241242i	−0.992699	+	0.120621i	$0.961511\pi$
$908$	−15.6448	−	4.19201i	−0.519190	−	0.139117i
$909$	1.56526			0.0519162
$910$	−12.1256	−	4.39926i	−0.401961	−	0.145834i
$911$	−40.1352			−1.32974			−0.664869	−	0.746960i	$-0.731513\pi$
$911$	−40.1352			−1.32974			−0.664869	+	0.746960i	$0.731513\pi$
$912$	3.14068	+	0.841543i	0.103998	+	0.0278663i
$913$			1.79262i			0.0593271i
$914$	4.62902	+	2.67256i	0.153114	+	0.0884006i
$915$	7.47327	−	2.00246i	0.247059	−	0.0661992i
$916$	6.94386	−	25.9148i	0.229432	−	0.856250i
$917$	−14.1585	−	7.41691i	−0.467555	−	0.244928i
$918$	−0.689491	−	0.689491i	−0.0227566	−	0.0227566i
$919$	−58.5985			−1.93299			−0.966493	−	0.256691i	$-0.917368\pi$
$919$	−58.5985			−1.93299			−0.966493	+	0.256691i	$0.917368\pi$
$920$	0.109564			0.00361221
$921$	1.31631	+	1.31631i	0.0433738	+	0.0433738i
$922$	18.2484	−	31.6072i	0.600979	−	1.04093i
$923$	1.38416	+	1.05420i	0.0455603	+	0.0346993i
$924$	1.43771	−	0.449237i	0.0472973	−	0.0147788i
$925$	1.33023	+	4.96448i	0.0437376	+	0.163231i
$926$	5.85010	+	10.1327i	0.192246	+	0.332980i
$927$	3.08156	−	5.33742i	0.101212	−	0.175304i
$928$	0.270044	+	0.0723580i	0.00886462	+	0.00237527i
$929$	−17.8564	−	17.8564i	−0.585851	−	0.585851i	0.350654	−	0.936505i	$-0.385959\pi$
$929$	−17.8564	−	17.8564i	−0.585851	−	0.585851i	−0.936505	+	0.350654i	$0.885959\pi$
$930$	3.36033	+	0.900397i	0.110190	+	0.0295252i
$931$	17.3597	+	14.7198i	0.568942	+	0.482421i
$932$	13.2098	+	22.8801i	0.432703	+	0.749464i
$933$	−20.6986	+	11.9503i	−0.677641	+	0.391236i
$934$	27.1090	−	27.1090i	0.887035	−	0.887035i
$935$	0.650072	−	0.375319i	0.0212596	−	0.0122743i
$936$	1.39179	+	3.32610i	0.0454920	+	0.108717i
$937$			57.5907i			1.88141i	0.339232	+	0.940703i	$0.389833\pi$
$937$			57.5907i			1.88141i	−0.339232	+	0.940703i	$0.610167\pi$
$938$	4.85018	−	3.07235i	0.158364	−	0.100316i
$939$	2.21235	−	3.83190i	0.0721973	−	0.125049i
$940$		−	7.77244i		−	0.253509i
$941$	−1.63921	+	6.11763i	−0.0534368	+	0.199429i	−0.987484	−	0.157722i	$-0.949585\pi$
$941$	−1.63921	+	6.11763i	−0.0534368	+	0.199429i	0.934047	+	0.357151i	$0.116252\pi$
$942$	−4.49076	−	16.7597i	−0.146317	−	0.546062i
$943$	0.132617	−	0.132617i	0.00431860	−	0.00431860i
$944$	5.05249	−	5.05249i	0.164444	−	0.164444i
$945$	1.06699	+	3.41473i	0.0347091	+	0.111081i
$946$	−5.40019	−	3.11780i	−0.175575	−	0.101368i
$947$	4.38404	−	16.3614i	0.142462	−	0.531675i	−0.857393	−	0.514662i	$-0.827917\pi$
$947$	4.38404	−	16.3614i	0.142462	−	0.531675i	0.999855	−	0.0170136i	$-0.00541586\pi$
$948$	−1.45438	−	2.51907i	−0.0472362	−	0.0818154i
$949$	−8.34696	−	6.35715i	−0.270954	−	0.206362i
$950$	8.93077	+	5.15618i	0.289753	+	0.167289i
$951$	13.0878	−	3.50687i	0.424402	−	0.113718i
$952$	−2.46243	+	0.769426i	−0.0798077	+	0.0249372i
$953$	−11.1246	+	6.42281i	−0.360362	+	0.208055i	−0.669240	−	0.743047i	$-0.733380\pi$
$953$	−11.1246	+	6.42281i	−0.360362	+	0.208055i	0.308878	+	0.951102i	$0.400047\pi$
$954$	−2.35038	−	8.77173i	−0.0760963	−	0.283995i
$955$	19.0079	−	5.09315i	0.615081	−	0.164811i
$956$	10.7277	−	2.87447i	0.346958	−	0.0929671i
$957$	0.0411945	+	0.153740i	0.00133163	+	0.00496970i
$958$	−19.0313	+	10.9877i	−0.614874	+	0.354998i
$959$	−11.1353	+	3.47942i	−0.359579	+	0.112356i
$960$	1.30611	−	0.349971i	0.0421545	−	0.0112953i
$961$	21.1144	+	12.1904i	0.681110	+	0.393239i
$962$	−4.62257	+	3.57358i	−0.149038	+	0.115217i
$963$	−7.03449	−	12.1841i	−0.226683	−	0.392627i
$964$	1.17845	−	4.39803i	0.0379553	−	0.141651i
$965$	−25.1693	−	14.5315i	−0.810227	−	0.467785i
$966$	−0.0639374	−	0.204622i	−0.00205715	−	0.00658359i
$967$	2.56512	−	2.56512i	0.0824888	−	0.0824888i	−0.664659	−	0.747147i	$-0.731423\pi$
$967$	2.56512	−	2.56512i	0.0824888	−	0.0824888i	0.747147	+	0.664659i	$0.231423\pi$
$968$	−7.54899	+	7.54899i	−0.242634	+	0.242634i
$969$	−0.820578	−	3.06244i	−0.0263608	−	0.0983797i
$970$	5.87313	−	21.9188i	0.188575	−	0.703770i
$971$			0.0707086i			0.00226915i	0.999999	+	0.00113457i	$0.000361146\pi$
$971$			0.0707086i			0.00226915i	−0.999999	+	0.00113457i	$0.999639\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−10.1502	+	6.42964i	−0.325399	+	0.206125i
$974$		−	30.1477i		−	0.965996i
$975$	1.53349	+	11.3321i	0.0491110	+	0.362917i
$976$	−4.95521	+	2.86089i	−0.158612	+	0.0915749i
$977$	−18.2334	+	18.2334i	−0.583339	+	0.583339i	−0.935819	−	0.352480i	$-0.885338\pi$
$977$	−18.2334	+	18.2334i	−0.583339	+	0.583339i	0.352480	+	0.935819i	$0.385338\pi$
$978$	7.34817	−	4.24247i	0.234968	−	0.135659i
$979$	−3.01309	−	5.21882i	−0.0962987	−	0.166794i
$980$	9.31289	+	1.69167i	0.297489	+	0.0540386i
$981$	18.3713	+	4.92259i	0.586552	+	0.157166i
$982$	19.5305	+	19.5305i	0.623242	+	0.623242i
$983$	37.1942	+	9.96615i	1.18631	+	0.317871i	0.797427	−	0.603416i	$-0.206194\pi$
$983$	37.1942	+	9.96615i	1.18631	+	0.317871i	0.388884	+	0.921287i	$0.372861\pi$
$984$	1.15732	−	2.00453i	0.0368939	−	0.0639021i
$985$	9.49252	+	16.4415i	0.302457	+	0.523871i
$986$	−0.0705554	−	0.263316i	−0.00224694	−	0.00838570i
$987$	−14.5158	+	4.53571i	−0.462044	+	0.144373i
$988$	−1.48828	+	11.6285i	−0.0473484	+	0.369952i
$989$	−0.443739	+	0.768579i	−0.0141101	+	0.0244394i
$990$	0.544343	+	0.544343i	0.0173004	+	0.0173004i
$991$	−25.6351			−0.814325			−0.407162	−	0.913356i	$-0.633482\pi$
$991$	−25.6351			−0.814325			−0.407162	+	0.913356i	$0.633482\pi$
$992$	−2.57278			−0.0816858
$993$	12.2693	+	12.2693i	0.389356	+	0.389356i
$994$	−1.13095	−	0.592448i	−0.0358716	−	0.0187913i
$995$	1.79080	−	6.68336i	0.0567722	−	0.211877i
$996$	3.04145	−	0.814953i	0.0963719	−	0.0258228i
$997$	−10.2019	−	5.89007i	−0.323097	−	0.186540i	0.329675	−	0.944094i	$-0.393061\pi$
$997$	−10.2019	−	5.89007i	−0.323097	−	0.186540i	−0.652772	+	0.757554i	$0.726394\pi$
$998$			25.4507i			0.805629i
$999$	1.56529	+	0.419419i	0.0495236	+	0.0132698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.19.4	✓	40
7.3	odd	6		546.2.cg.b.409.9	yes	40
13.11	odd	12		546.2.cg.b.271.9	yes	40
91.24	even	12	inner	546.2.by.b.115.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.4	✓	40	1.1	even	1	trivial
546.2.by.b.115.4	yes	40	91.24	even	12	inner
546.2.cg.b.271.9	yes	40	13.11	odd	12
546.2.cg.b.409.9	yes	40	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(1.30611 - 0.349971i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(2.64352 - 0.108591i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(1.30611 - 0.349971i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(2.64352 - 0.108591i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -1.35218 q^{10} +(0.402566 + 0.402566i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.33605 + 1.36776i) q^{13} +(-2.58155 - 0.579303i) q^{14} +(-0.349971 - 1.30611i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.487543 - 0.844450i) q^{17} +(0.965926 + 0.258819i) q^{18} +(2.29914 + 2.29914i) q^{19} +(1.30611 + 0.349971i) q^{20} +(-0.108591 - 2.64352i) q^{21} +(-0.284657 - 0.493040i) q^{22} +(-0.0701717 + 0.0405137i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(-2.74668 + 1.58580i) q^{25} +(-2.86837 - 2.18459i) q^{26} +1.00000i q^{27} +(2.34365 + 1.22772i) q^{28} +(-0.139785 + 0.242115i) q^{29} +1.35218i q^{30} +(0.665884 - 2.48511i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.402566 - 0.402566i) q^{33} +(-0.689491 + 0.689491i) q^{34} +(3.41473 - 1.06699i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(0.419419 - 1.56529i) q^{37} +(-1.62574 - 2.81586i) q^{38} +(1.36776 - 3.33605i) q^{39} +(-1.17103 - 0.676092i) q^{40} +(-2.23576 + 0.599071i) q^{41} +(-0.579303 + 2.58155i) q^{42} +(9.48543 - 5.47642i) q^{43} +(0.147349 + 0.549915i) q^{44} +(-1.30611 + 0.349971i) q^{45} +(0.0782664 - 0.0209714i) q^{46} +(-1.48771 - 5.55221i) q^{47} +(0.866025 - 0.500000i) q^{48} +(6.97642 - 0.574124i) q^{49} +(3.06353 - 0.820870i) q^{50} +(-0.844450 - 0.487543i) q^{51} +(2.20522 + 2.85254i) q^{52} +(-4.54058 - 7.86452i) q^{53} +(0.258819 - 0.965926i) q^{54} +(0.666681 + 0.384909i) q^{55} +(-1.94604 - 1.79247i) q^{56} +(2.29914 - 2.29914i) q^{57} +(0.197686 - 0.197686i) q^{58} +(-1.84934 - 6.90183i) q^{59} +(0.349971 - 1.30611i) q^{60} +5.72178i q^{61} +(-1.28639 + 2.22809i) q^{62} +(-2.64352 + 0.108591i) q^{63} +1.00000i q^{64} +(4.83592 + 0.618927i) q^{65} +(-0.493040 + 0.284657i) q^{66} +(-1.53445 + 1.53445i) q^{67} +(0.844450 - 0.487543i) q^{68} +(0.0405137 + 0.0701717i) q^{69} +(-3.57453 + 0.146835i) q^{70} +(0.466117 + 0.124896i) q^{71} +(0.707107 + 0.707107i) q^{72} +(-2.81084 - 0.753163i) q^{73} +(-0.810255 + 1.40340i) q^{74} +(1.58580 + 2.74668i) q^{75} +(0.841543 + 3.14068i) q^{76} +(1.10791 + 1.02048i) q^{77} +(-2.18459 + 2.86837i) q^{78} +(1.45438 - 2.51907i) q^{79} +(0.956138 + 0.956138i) q^{80} +1.00000 q^{81} +2.31463 q^{82} +(2.22649 + 2.22649i) q^{83} +(1.22772 - 2.34365i) q^{84} +(0.341252 - 1.27357i) q^{85} +(-10.5796 + 2.83480i) q^{86} +(0.242115 + 0.139785i) q^{87} -0.569314i q^{88} +(-10.2243 - 2.73959i) q^{89} +1.35218 q^{90} +(8.96745 + 3.25345i) q^{91} -0.0810273 q^{92} +(-2.48511 - 0.665884i) q^{93} +5.74807i q^{94} +(3.80756 + 2.19829i) q^{95} +(-0.965926 + 0.258819i) q^{96} +(-4.34344 + 16.2099i) q^{97} +(-6.88729 - 1.25107i) q^{98} +(-0.402566 - 0.402566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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