LMFDB - Embedded newform 546.2.cg.a.145.6

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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.6
Character	$\chi$	$=$	546.145
Dual form			546.2.cg.a.241.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(-0.864363 + 0.231605i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-1.65489 - 2.06430i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(-0.864363 + 0.231605i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-1.65489 - 2.06430i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.447427 + 0.774967i) q^{10} +(4.73077 - 1.26761i) q^{11} +(0.500000 - 0.866025i) q^{12} +(2.86336 - 2.19116i) q^{13} +(-2.62987 - 0.289497i) q^{14} +(-0.864363 - 0.231605i) q^{15} -1.00000 q^{16} +2.68269 q^{17} +(0.965926 + 0.258819i) q^{18} +(0.864559 - 3.22658i) q^{19} +(0.231605 + 0.864363i) q^{20} +(-0.401026 - 2.61518i) q^{21} +(2.44883 - 4.24149i) q^{22} -6.85473i q^{23} +(-0.258819 - 0.965926i) q^{24} +(-3.63664 + 2.09962i) q^{25} +(0.475319 - 3.57408i) q^{26} +1.00000i q^{27} +(-2.06430 + 1.65489i) q^{28} +(-1.14028 - 1.97502i) q^{29} +(-0.774967 + 0.447427i) q^{30} +(-2.07202 + 7.73290i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.73077 + 1.26761i) q^{33} +(1.89695 - 1.89695i) q^{34} +(1.90853 + 1.40102i) q^{35} +(0.866025 - 0.500000i) q^{36} +(5.39888 + 5.39888i) q^{37} +(-1.67020 - 2.89287i) q^{38} +(3.57532 - 0.465918i) q^{39} +(0.774967 + 0.447427i) q^{40} +(-0.707984 + 2.64223i) q^{41} +(-2.13278 - 1.56564i) q^{42} +(-4.45888 - 2.57433i) q^{43} +(-1.26761 - 4.73077i) q^{44} +(-0.632758 - 0.632758i) q^{45} +(-4.84703 - 4.84703i) q^{46} +(3.25361 + 12.1426i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-1.52268 + 6.83238i) q^{49} +(-1.08684 + 4.05615i) q^{50} +(2.32327 + 1.34134i) q^{51} +(-2.19116 - 2.86336i) q^{52} +(-4.53418 - 7.85343i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-3.79552 + 2.19134i) q^{55} +(-0.289497 + 2.62987i) q^{56} +(2.36202 - 2.36202i) q^{57} +(-2.20285 - 0.590253i) q^{58} +(2.39350 - 2.39350i) q^{59} +(-0.231605 + 0.864363i) q^{60} +(-11.9938 + 6.92464i) q^{61} +(4.00284 + 6.93313i) q^{62} +(0.960292 - 2.46533i) q^{63} +1.00000i q^{64} +(-1.96750 + 2.55713i) q^{65} +(4.24149 - 2.44883i) q^{66} +(3.46789 + 12.9423i) q^{67} -2.68269i q^{68} +(3.42737 - 5.93637i) q^{69} +(2.34021 - 0.358860i) q^{70} +(-2.94672 - 10.9973i) q^{71} +(0.258819 - 0.965926i) q^{72} +(13.1396 + 3.52074i) q^{73} +7.63517 q^{74} -4.19924 q^{75} +(-3.22658 - 0.864559i) q^{76} +(-10.4456 - 7.66798i) q^{77} +(2.19868 - 2.85759i) q^{78} +(3.28194 - 5.68448i) q^{79} +(0.864363 - 0.231605i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.36772 + 2.36896i) q^{82} +(-2.49869 - 2.49869i) q^{83} +(-2.61518 + 0.401026i) q^{84} +(-2.31882 + 0.621325i) q^{85} +(-4.97323 + 1.33257i) q^{86} -2.28056i q^{87} +(-4.24149 - 2.44883i) q^{88} +(-7.19838 + 7.19838i) q^{89} -0.894855 q^{90} +(-9.26175 - 2.28471i) q^{91} -6.85473 q^{92} +(-5.66087 + 5.66087i) q^{93} +(10.8868 + 6.28549i) q^{94} +2.98917i q^{95} +(-0.965926 + 0.258819i) q^{96} +(-3.09903 + 0.830382i) q^{97} +(3.75453 + 5.90792i) q^{98} +(3.46316 + 3.46316i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7} + 16 q^{9}+O(q^{10}) $ 32 * q - 4 * q^7 + 16 * q^9	$ 32 q - 4 q^{7} + 16 q^{9} + 8 q^{11} + 16 q^{12} + 4 q^{14} - 32 q^{16} - 16 q^{17} + 24 q^{19} + 8 q^{21} - 4 q^{22} + 24 q^{25} - 8 q^{26} + 8 q^{28} - 12 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} + 40 q^{35} - 12 q^{37} - 8 q^{38} + 28 q^{39} + 28 q^{41} - 12 q^{42} + 84 q^{43} - 4 q^{44} - 40 q^{46} - 4 q^{47} - 36 q^{49} - 16 q^{50} - 20 q^{52} - 4 q^{53} - 48 q^{55} + 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{59} - 36 q^{61} + 40 q^{62} + 4 q^{63} + 44 q^{65} - 16 q^{67} + 8 q^{69} + 40 q^{70} + 20 q^{71} - 16 q^{73} - 40 q^{74} + 16 q^{75} - 36 q^{76} + 12 q^{77} - 20 q^{78} - 16 q^{81} - 24 q^{82} - 12 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 60 q^{89} - 48 q^{91} - 16 q^{92} - 32 q^{93} - 76 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 16 * q^9 + 8 * q^11 + 16 * q^12 + 4 * q^14 - 32 * q^16 - 16 * q^17 + 24 * q^19 + 8 * q^21 - 4 * q^22 + 24 * q^25 - 8 * q^26 + 8 * q^28 - 12 * q^29 + 4 * q^31 + 8 * q^33 + 8 * q^34 + 40 * q^35 - 12 * q^37 - 8 * q^38 + 28 * q^39 + 28 * q^41 - 12 * q^42 + 84 * q^43 - 4 * q^44 - 40 * q^46 - 4 * q^47 - 36 * q^49 - 16 * q^50 - 20 * q^52 - 4 * q^53 - 48 * q^55 + 12 * q^56 + 12 * q^57 + 12 * q^58 - 24 * q^59 - 36 * q^61 + 40 * q^62 + 4 * q^63 + 44 * q^65 - 16 * q^67 + 8 * q^69 + 40 * q^70 + 20 * q^71 - 16 * q^73 - 40 * q^74 + 16 * q^75 - 36 * q^76 + 12 * q^77 - 20 * q^78 - 16 * q^81 - 24 * q^82 - 12 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 60 * q^89 - 48 * q^91 - 16 * q^92 - 32 * q^93 - 76 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−0.864363	+	0.231605i	−0.386555	+	0.103577i	−0.446862	−	0.894603i	$-0.647459\pi$
$5$	−0.864363	+	0.231605i	−0.386555	+	0.103577i	0.0603073	+	0.998180i	$0.480792\pi$
$6$	0.965926	−	0.258819i	0.394338	−	0.105662i
$7$	−1.65489	−	2.06430i	−0.625490	−	0.780232i
$7$	−1.65489	−	2.06430i	−0.625490	−	0.780232i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.447427	+	0.774967i	−0.141489	+	0.245066i
$11$	4.73077	−	1.26761i	1.42638	−	0.382197i	0.538637	−	0.842538i	$-0.318939\pi$
$11$	4.73077	−	1.26761i	1.42638	−	0.382197i	0.887743	+	0.460340i	$0.152273\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	2.86336	−	2.19116i	0.794153	−	0.607718i
$13$	2.86336	−	2.19116i	0.794153	−	0.607718i
$14$	−2.62987	−	0.289497i	−0.702861	−	0.0773714i
$15$	−0.864363	−	0.231605i	−0.223178	−	0.0598003i
$16$	−1.00000			−0.250000
$17$	2.68269			0.650647			0.325324	−	0.945603i	$-0.394527\pi$
$17$	2.68269			0.650647			0.325324	+	0.945603i	$0.394527\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	0.864559	−	3.22658i	0.198343	−	0.740228i	−0.793033	−	0.609179i	$-0.791499\pi$
$19$	0.864559	−	3.22658i	0.198343	−	0.740228i	0.991376	−	0.131048i	$-0.0418343\pi$
$20$	0.231605	+	0.864363i	0.0517885	+	0.193277i
$21$	−0.401026	−	2.61518i	−0.0875111	−	0.570680i
$22$	2.44883	−	4.24149i	0.522091	−	0.904289i
$23$		−	6.85473i		−	1.42931i	−0.699477	−	0.714655i	$-0.746584\pi$
$23$		−	6.85473i		−	1.42931i	0.699477	−	0.714655i	$-0.253416\pi$
$24$	−0.258819	−	0.965926i	−0.0528312	−	0.197169i
$25$	−3.63664	+	2.09962i	−0.727329	+	0.419924i
$26$	0.475319	−	3.57408i	0.0932178	−	0.700935i
$27$			1.00000i			0.192450i
$28$	−2.06430	+	1.65489i	−0.390116	+	0.312745i
$29$	−1.14028	−	1.97502i	−0.211745	−	0.366753i	0.740516	−	0.672039i	$-0.234581\pi$
$29$	−1.14028	−	1.97502i	−0.211745	−	0.366753i	−0.952261	+	0.305286i	$0.901248\pi$
$30$	−0.774967	+	0.447427i	−0.141489	+	0.0816887i
$31$	−2.07202	+	7.73290i	−0.372146	+	1.38887i	0.485323	+	0.874335i	$0.338702\pi$
$31$	−2.07202	+	7.73290i	−0.372146	+	1.38887i	−0.857470	+	0.514534i	$0.827965\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	4.73077	+	1.26761i	0.823521	+	0.220662i
$34$	1.89695	−	1.89695i	0.325324	−	0.325324i
$35$	1.90853	+	1.40102i	0.322600	+	0.236816i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	5.39888	+	5.39888i	0.887570	+	0.887570i	0.994289	−	0.106719i	$-0.0340345\pi$
$37$	5.39888	+	5.39888i	0.887570	+	0.887570i	−0.106719	+	0.994289i	$0.534034\pi$
$38$	−1.67020	−	2.89287i	−0.270942	−	0.469285i
$39$	3.57532	−	0.465918i	0.572510	−	0.0746065i
$40$	0.774967	+	0.447427i	0.122533	+	0.0707445i
$41$	−0.707984	+	2.64223i	−0.110569	+	0.412648i	−0.998917	−	0.0465219i	$-0.985186\pi$
$41$	−0.707984	+	2.64223i	−0.110569	+	0.412648i	0.888349	+	0.459169i	$0.151853\pi$
$42$	−2.13278	−	1.56564i	−0.329095	−	0.241584i
$43$	−4.45888	−	2.57433i	−0.679972	−	0.392582i	0.119872	−	0.992789i	$-0.461752\pi$
$43$	−4.45888	−	2.57433i	−0.679972	−	0.392582i	−0.799845	+	0.600207i	$0.795085\pi$
$44$	−1.26761	−	4.73077i	−0.191099	−	0.713190i
$45$	−0.632758	−	0.632758i	−0.0943260	−	0.0943260i
$46$	−4.84703	−	4.84703i	−0.714655	−	0.714655i
$47$	3.25361	+	12.1426i	0.474588	+	1.77119i	0.622959	+	0.782254i	$0.285930\pi$
$47$	3.25361	+	12.1426i	0.474588	+	1.77119i	−0.148371	+	0.988932i	$0.547403\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−1.52268	+	6.83238i	−0.217525	+	0.976055i
$50$	−1.08684	+	4.05615i	−0.153703	+	0.573626i
$51$	2.32327	+	1.34134i	0.325324	+	0.187826i
$52$	−2.19116	−	2.86336i	−0.303859	−	0.397077i
$53$	−4.53418	−	7.85343i	−0.622817	−	1.07875i	−0.988959	−	0.148192i	$-0.952655\pi$
$53$	−4.53418	−	7.85343i	−0.622817	−	1.07875i	0.366141	−	0.930559i	$-0.380679\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−3.79552	+	2.19134i	−0.511787	+	0.295481i
$56$	−0.289497	+	2.62987i	−0.0386857	+	0.351431i
$57$	2.36202	−	2.36202i	0.312857	−	0.312857i
$58$	−2.20285	−	0.590253i	−0.289249	−	0.0775040i
$59$	2.39350	−	2.39350i	0.311608	−	0.311608i	−0.533924	−	0.845532i	$-0.679283\pi$
$59$	2.39350	−	2.39350i	0.311608	−	0.311608i	0.845532	+	0.533924i	$0.179283\pi$
$60$	−0.231605	+	0.864363i	−0.0299001	+	0.111589i
$61$	−11.9938	+	6.92464i	−1.53565	+	0.886610i	−0.536567	+	0.843857i	$0.680279\pi$
$61$	−11.9938	+	6.92464i	−1.53565	+	0.886610i	−0.999086	+	0.0427524i	$0.986387\pi$
$62$	4.00284	+	6.93313i	0.508361	+	0.880508i
$63$	0.960292	−	2.46533i	0.120985	−	0.310602i
$64$			1.00000i			0.125000i
$65$	−1.96750	+	2.55713i	−0.244038	+	0.317172i
$66$	4.24149	−	2.44883i	0.522091	−	0.301430i
$67$	3.46789	+	12.9423i	0.423670	+	1.58116i	0.766811	+	0.641873i	$0.221843\pi$
$67$	3.46789	+	12.9423i	0.423670	+	1.58116i	−0.343141	+	0.939284i	$0.611491\pi$
$68$		−	2.68269i		−	0.325324i
$69$	3.42737	−	5.93637i	0.412606	−	0.714655i
$70$	2.34021	−	0.358860i	0.279708	−	0.0428920i
$71$	−2.94672	−	10.9973i	−0.349711	−	1.30514i	−0.887011	−	0.461749i	$-0.847222\pi$
$71$	−2.94672	−	10.9973i	−0.349711	−	1.30514i	0.537299	−	0.843392i	$-0.319445\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	13.1396	+	3.52074i	1.53787	+	0.412072i	0.925578	−	0.378557i	$-0.123580\pi$
$73$	13.1396	+	3.52074i	1.53787	+	0.412072i	0.612296	+	0.790629i	$0.290246\pi$
$74$	7.63517			0.887570
$75$	−4.19924			−0.484886
$76$	−3.22658	−	0.864559i	−0.370114	−	0.0991717i
$77$	−10.4456	−	7.66798i	−1.19039	−	0.873847i
$78$	2.19868	−	2.85759i	0.248952	−	0.323558i
$79$	3.28194	−	5.68448i	0.369247	−	0.639554i	−0.620201	−	0.784443i	$-0.712949\pi$
$79$	3.28194	−	5.68448i	0.369247	−	0.639554i	0.989448	+	0.144888i	$0.0462823\pi$
$80$	0.864363	−	0.231605i	0.0966387	−	0.0258943i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.36772	+	2.36896i	0.151040	+	0.261608i
$83$	−2.49869	−	2.49869i	−0.274267	−	0.274267i	0.556549	−	0.830815i	$-0.312125\pi$
$83$	−2.49869	−	2.49869i	−0.274267	−	0.274267i	−0.830815	+	0.556549i	$0.812125\pi$
$84$	−2.61518	+	0.401026i	−0.285340	+	0.0437556i
$85$	−2.31882	+	0.621325i	−0.251511	+	0.0673921i
$86$	−4.97323	+	1.33257i	−0.536277	+	0.143695i
$87$		−	2.28056i		−	0.244502i
$88$	−4.24149	−	2.44883i	−0.452144	−	0.261046i
$89$	−7.19838	+	7.19838i	−0.763027	+	0.763027i	−0.976868	−	0.213842i	$-0.931402\pi$
$89$	−7.19838	+	7.19838i	−0.763027	+	0.763027i	0.213842	+	0.976868i	$0.431402\pi$
$90$	−0.894855			−0.0943260
$91$	−9.26175	−	2.28471i	−0.970896	−	0.239503i
$92$	−6.85473			−0.714655
$93$	−5.66087	+	5.66087i	−0.587005	+	0.587005i
$94$	10.8868	+	6.28549i	1.12289	+	0.648299i
$95$			2.98917i			0.306682i
$96$	−0.965926	+	0.258819i	−0.0985844	+	0.0264156i
$97$	−3.09903	+	0.830382i	−0.314659	+	0.0843125i	−0.412692	−	0.910871i	$-0.635411\pi$
$97$	−3.09903	+	0.830382i	−0.314659	+	0.0843125i	0.0980335	+	0.995183i	$0.468745\pi$
$98$	3.75453	+	5.90792i	0.379265	+	0.596790i
$99$	3.46316	+	3.46316i	0.348061	+	0.348061i
$100$	2.09962	+	3.63664i	0.209962	+	0.363664i
$101$	2.03035	−	3.51667i	0.202027	−	0.349922i	−0.747154	−	0.664651i	$-0.768580\pi$
$101$	2.03035	−	3.51667i	0.202027	−	0.349922i	0.949182	+	0.314729i	$0.101914\pi$
$102$	2.59128	−	0.694330i	0.256575	−	0.0687490i
$103$	−4.22153	+	7.31190i	−0.415960	+	0.720463i	−0.995529	−	0.0944598i	$-0.969888\pi$
$103$	−4.22153	+	7.31190i	−0.415960	+	0.720463i	0.579569	+	0.814923i	$0.303221\pi$
$104$	−3.57408	−	0.475319i	−0.350468	−	0.0466089i
$105$	0.952323	+	2.16759i	0.0929372	+	0.211535i
$106$	−8.75936	−	2.34706i	−0.850784	−	0.227967i
$107$	17.4652			1.68842			0.844212	−	0.536010i	$-0.180069\pi$
$107$	17.4652			1.68842			0.844212	+	0.536010i	$0.180069\pi$
$108$	1.00000			0.0962250
$109$	−8.41024	−	2.25352i	−0.805555	−	0.215848i	−0.167534	−	0.985866i	$-0.553580\pi$
$109$	−8.41024	−	2.25352i	−0.805555	−	0.215848i	−0.638022	+	0.770018i	$0.720247\pi$
$110$	−1.13432	+	4.23335i	−0.108153	+	0.403634i
$111$	1.97613	+	7.37501i	0.187566	+	0.700005i
$112$	1.65489	+	2.06430i	0.156372	+	0.195058i
$113$	0.00987908	−	0.0171111i	0.000929346	−	0.00160967i	−0.865560	−	0.500805i	$-0.833038\pi$
$113$	0.00987908	−	0.0171111i	0.000929346	−	0.00160967i	0.866490	+	0.499195i	$0.166371\pi$
$114$		−	3.34040i		−	0.312857i
$115$	1.58759	+	5.92498i	0.148044	+	0.552507i
$116$	−1.97502	+	1.14028i	−0.183376	+	0.105872i
$117$	3.32928	+	1.38416i	0.307792	+	0.127966i
$118$		−	3.38493i		−	0.311608i
$119$	−4.43955	−	5.53787i	−0.406973	−	0.507656i
$120$	0.447427	+	0.774967i	0.0408443	+	0.0707445i
$121$	11.2471	−	6.49349i	1.02246	−	0.590317i
$122$	−3.58446	+	13.3774i	−0.324522	+	1.21113i
$123$	−1.93425	+	1.93425i	−0.174405	+	0.174405i
$124$	7.73290	+	2.07202i	0.694435	+	0.186073i
$125$	5.82089	−	5.82089i	0.520636	−	0.520636i
$126$	−1.06422	−	2.42228i	−0.0948083	−	0.215794i
$127$	−7.61500	+	4.39652i	−0.675722	+	0.390129i	−0.798241	−	0.602338i	$-0.794236\pi$
$127$	−7.61500	+	4.39652i	−0.675722	+	0.390129i	0.122519	+	0.992466i	$0.460903\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−2.57433	−	4.45888i	−0.226657	−	0.392582i
$130$	0.416929	+	3.19939i	0.0365671	+	0.280605i
$131$	14.8953	+	8.59980i	1.30141	+	0.751368i	0.980646	−	0.195792i	$-0.0627276\pi$
$131$	14.8953	+	8.59980i	1.30141	+	0.751368i	0.320762	+	0.947160i	$0.396061\pi$
$132$	1.26761	−	4.73077i	0.110331	−	0.411760i
$133$	−8.09138	+	3.55492i	−0.701611	+	0.308251i
$134$	11.6038	+	6.69944i	1.00241	+	0.578744i
$135$	−0.231605	−	0.864363i	−0.0199334	−	0.0743925i
$136$	−1.89695	−	1.89695i	−0.162662	−	0.162662i
$137$	7.90217	+	7.90217i	0.675128	+	0.675128i	0.958894	−	0.283765i	$-0.0915837\pi$
$137$	7.90217	+	7.90217i	0.675128	+	0.675128i	−0.283765	+	0.958894i	$0.591584\pi$
$138$	−1.77414	−	6.62116i	−0.151024	−	0.563631i
$139$	−2.36040	−	1.36278i	−0.200206	−	0.115589i	0.396545	−	0.918015i	$-0.370209\pi$
$139$	−2.36040	−	1.36278i	−0.200206	−	0.115589i	−0.596752	+	0.802426i	$0.703542\pi$
$140$	1.40102	−	1.90853i	0.118408	−	0.161300i
$141$	−3.25361	+	12.1426i	−0.274003	+	1.02259i
$142$	−9.85992	−	5.69263i	−0.827426	−	0.477715i
$143$	10.7684	−	13.9955i	0.900496	−	1.17036i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.44304	+	1.44304i	0.119838	+	0.119838i
$146$	11.7806	−	6.80156i	0.974973	−	0.562901i
$147$	−4.73487	+	5.15568i	−0.390525	+	0.425233i
$148$	5.39888	−	5.39888i	0.443785	−	0.443785i
$149$	−16.7983	−	4.50108i	−1.37617	−	0.368743i	−0.506440	−	0.862275i	$-0.669039\pi$
$149$	−16.7983	−	4.50108i	−1.37617	−	0.368743i	−0.869728	+	0.493532i	$0.835706\pi$
$150$	−2.96931	+	2.96931i	−0.242443	+	0.242443i
$151$	2.97701	−	11.1104i	0.242266	−	0.904148i	−0.732472	−	0.680797i	$-0.761634\pi$
$151$	2.97701	−	11.1104i	0.242266	−	0.904148i	0.974738	−	0.223351i	$-0.0716997\pi$
$152$	−2.89287	+	1.67020i	−0.234643	+	0.135471i
$153$	1.34134	+	2.32327i	0.108441	+	0.187826i
$154$	−12.8082	+	1.96409i	−1.03212	+	0.158271i
$155$		−	7.16392i		−	0.575420i
$156$	−0.465918	−	3.57532i	−0.0373033	−	0.286255i
$157$	1.34763	−	0.778054i	0.107552	−	0.0620954i	−0.445259	−	0.895402i	$-0.646888\pi$
$157$	1.34763	−	0.778054i	0.107552	−	0.0620954i	0.552811	+	0.833306i	$0.313555\pi$
$158$	−1.69886	−	6.34022i	−0.135154	−	0.504401i
$159$		−	9.06836i		−	0.719167i
$160$	0.447427	−	0.774967i	0.0353722	−	0.0612665i
$161$	−14.1502	+	11.3438i	−1.11519	+	0.894019i
$162$	0.258819	+	0.965926i	0.0203347	+	0.0758903i
$163$	−4.24835	+	15.8551i	−0.332756	+	1.24186i	0.573525	+	0.819188i	$0.305576\pi$
$163$	−4.24835	+	15.8551i	−0.332756	+	1.24186i	−0.906281	+	0.422676i	$0.861091\pi$
$164$	2.64223	+	0.707984i	0.206324	+	0.0552843i
$165$	−4.38269			−0.341192
$166$	−3.53368			−0.274267
$167$	17.9445	+	4.80822i	1.38859	+	0.372071i	0.874233	−	0.485506i	$-0.161365\pi$
$167$	17.9445	+	4.80822i	1.38859	+	0.372071i	0.514355	+	0.857577i	$0.328031\pi$
$168$	−1.56564	+	2.13278i	−0.120792	+	0.164548i
$169$	3.39766	−	12.5481i	0.261359	−	0.965242i
$170$	−1.20031	+	2.07899i	−0.0920594	+	0.159452i
$171$	3.22658	−	0.864559i	0.246743	−	0.0661145i
$172$	−2.57433	+	4.45888i	−0.196291	+	0.339986i
$173$	3.86192	+	6.68903i	0.293616	+	0.508558i	0.974662	−	0.223683i	$-0.0718080\pi$
$173$	3.86192	+	6.68903i	0.293616	+	0.508558i	−0.681046	+	0.732241i	$0.738475\pi$
$174$	−1.61260	−	1.61260i	−0.122251	−	0.122251i
$175$	10.3525	+	4.03249i	0.782575	+	0.304828i
$176$	−4.73077	+	1.26761i	−0.356595	+	0.0955493i
$177$	3.26959	−	0.876083i	0.245757	−	0.0658505i
$178$			10.1800i			0.763027i
$179$	11.6004	+	6.69750i	0.867055	+	0.500594i	0.866368	−	0.499405i	$-0.166448\pi$
$179$	11.6004	+	6.69750i	0.867055	+	0.500594i	0.000686434		1.00000i	$0.499782\pi$
$180$	−0.632758	+	0.632758i	−0.0471630	+	0.0471630i
$181$	−4.29894			−0.319538			−0.159769	−	0.987154i	$-0.551075\pi$
$181$	−4.29894			−0.319538			−0.159769	+	0.987154i	$0.551075\pi$
$182$	−8.16459	+	4.93351i	−0.605199	+	0.365696i
$183$	−13.8493			−1.02377
$184$	−4.84703	+	4.84703i	−0.357328	+	0.357328i
$185$	−5.91700	−	3.41618i	−0.435027	−	0.251163i
$186$			8.00568i			0.587005i
$187$	12.6912	−	3.40059i	0.928070	−	0.248676i
$188$	12.1426	−	3.25361i	0.885593	−	0.237294i
$189$	2.06430	−	1.65489i	0.150156	−	0.120376i
$190$	2.11366	+	2.11366i	0.153341	+	0.153341i
$191$	−4.00394	−	6.93503i	−0.289715	−	0.501801i	0.684027	−	0.729457i	$-0.260227\pi$
$191$	−4.00394	−	6.93503i	−0.289715	−	0.501801i	−0.973742	+	0.227656i	$0.926894\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−26.0747	+	6.98670i	−1.87690	+	0.502914i	−0.877159	+	0.480201i	$0.840564\pi$
$193$	−26.0747	+	6.98670i	−1.87690	+	0.502914i	−0.999742	+	0.0227130i	$0.992770\pi$
$194$	−1.60417	+	2.77851i	−0.115173	+	0.199486i
$195$	−2.98247	+	1.23079i	−0.213579	+	0.0881384i
$196$	6.83238	+	1.52268i	0.488027	+	0.108763i
$197$	−1.44240	−	0.386491i	−0.102767	−	0.0275363i	0.207069	−	0.978326i	$-0.433608\pi$
$197$	−1.44240	−	0.386491i	−0.102767	−	0.0275363i	−0.309836	+	0.950790i	$0.600274\pi$
$198$	4.89765			0.348061
$199$	1.75468			0.124386			0.0621930	−	0.998064i	$-0.480191\pi$
$199$	1.75468			0.124386			0.0621930	+	0.998064i	$0.480191\pi$
$200$	4.05615	+	1.08684i	0.286813	+	0.0768513i
$201$	−3.46789	+	12.9423i	−0.244606	+	0.912882i
$202$	−1.05099	−	3.92233i	−0.0739471	−	0.275974i
$203$	−2.19001	+	5.62233i	−0.153708	+	0.394610i
$204$	1.34134	−	2.32327i	0.0939128	−	0.162662i
$205$		−	2.44782i		−	0.170963i
$206$	2.18522	+	8.15537i	0.152252	+	0.568212i
$207$	5.93637	−	3.42737i	0.412606	−	0.238218i
$208$	−2.86336	+	2.19116i	−0.198538	+	0.151929i
$209$		−	16.3601i		−	1.13165i
$210$	2.20611	+	0.859322i	0.152236	+	0.0592988i
$211$	−4.10487	−	7.10985i	−0.282591	−	0.489462i	0.689431	−	0.724351i	$-0.257861\pi$
$211$	−4.10487	−	7.10985i	−0.282591	−	0.489462i	−0.972022	+	0.234889i	$0.924527\pi$
$212$	−7.85343	+	4.53418i	−0.539376	+	0.311409i
$213$	2.94672	−	10.9973i	0.201906	−	0.753523i
$214$	12.3497	−	12.3497i	0.844212	−	0.844212i
$215$	4.45032	+	1.19246i	0.303509	+	0.0813251i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	19.3920	−	8.51981i	1.31641	−	0.578363i
$218$	−7.54042	+	4.35346i	−0.510702	+	0.294854i
$219$	9.61885	+	9.61885i	0.649982	+	0.649982i
$220$	2.19134	+	3.79552i	0.147740	+	0.255894i
$221$	7.68150	−	5.87819i	0.516713	−	0.395410i
$222$	6.61225	+	3.81758i	0.443785	+	0.256220i
$223$	−0.791992	+	2.95575i	−0.0530357	+	0.197932i	−0.987360	−	0.158491i	$-0.949337\pi$
$223$	−0.791992	+	2.95575i	−0.0530357	+	0.197932i	0.934325	+	0.356423i	$0.116004\pi$
$224$	2.62987	+	0.289497i	0.175715	+	0.0193428i
$225$	−3.63664	−	2.09962i	−0.242443	−	0.139975i
$226$	−0.00511379	−	0.0190849i	−0.000340164	−	0.00126951i
$227$	−8.78932	−	8.78932i	−0.583368	−	0.583368i	0.352459	−	0.935827i	$-0.385345\pi$
$227$	−8.78932	−	8.78932i	−0.583368	−	0.583368i	−0.935827	+	0.352459i	$0.885345\pi$
$228$	−2.36202	−	2.36202i	−0.156428	−	0.156428i
$229$	3.54780	+	13.2406i	0.234445	+	0.874961i	0.978398	+	0.206729i	$0.0662819\pi$
$229$	3.54780	+	13.2406i	0.234445	+	0.874961i	−0.743953	+	0.668232i	$0.767051\pi$
$230$	5.31219	+	3.06700i	0.350276	+	0.202232i
$231$	−5.21218	−	11.8635i	−0.342936	−	0.780559i
$232$	−0.590253	+	2.20285i	−0.0387520	+	0.144624i
$233$	6.60661	+	3.81433i	0.432813	+	0.249885i	0.700544	−	0.713609i	$-0.252941\pi$
$233$	6.60661	+	3.81433i	0.432813	+	0.249885i	−0.267731	+	0.963494i	$0.586274\pi$
$234$	3.33291	−	1.37540i	0.217879	−	0.0899129i
$235$	−5.62460	−	9.74210i	−0.366909	−	0.635504i
$236$	−2.39350	−	2.39350i	−0.155804	−	0.155804i
$237$	5.68448	−	3.28194i	0.369247	−	0.213185i
$238$	−7.05510	−	0.776630i	−0.457314	−	0.0503415i
$239$	6.59105	−	6.59105i	0.426339	−	0.426339i	−0.461040	−	0.887379i	$-0.652524\pi$
$239$	6.59105	−	6.59105i	0.426339	−	0.426339i	0.887379	+	0.461040i	$0.152524\pi$
$240$	0.864363	+	0.231605i	0.0557944	+	0.0149501i
$241$	−9.83659	+	9.83659i	−0.633630	+	0.633630i	−0.948977	−	0.315346i	$-0.897879\pi$
$241$	−9.83659	+	9.83659i	−0.633630	+	0.633630i	0.315346	+	0.948977i	$0.397879\pi$
$242$	3.36128	−	12.5445i	0.216071	−	0.806388i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	6.92464	+	11.9938i	0.443305	+	0.767827i
$245$	−0.266270	−	6.25832i	−0.0170114	−	0.399829i
$246$			2.73544i			0.174405i
$247$	−4.59439	−	11.1332i	−0.292334	−	0.708391i
$248$	6.93313	−	4.00284i	0.440254	−	0.254181i
$249$	−0.914583	−	3.41327i	−0.0579594	−	0.216307i
$250$		−	8.23198i		−	0.520636i
$251$	1.11432	−	1.93005i	0.0703350	−	0.121824i	−0.828713	−	0.559674i	$-0.810927\pi$
$251$	1.11432	−	1.93005i	0.0703350	−	0.121824i	0.899048	+	0.437850i	$0.144260\pi$
$252$	−2.46533	−	0.960292i	−0.155301	−	0.0604927i
$253$	−8.68910	−	32.4281i	−0.546279	−	2.03874i
$254$	−2.27581	+	8.49343i	−0.142797	+	0.532925i
$255$	−2.31882	−	0.621325i	−0.145210	−	0.0389089i
$256$	1.00000			0.0625000
$257$	−21.3865			−1.33405			−0.667027	−	0.745034i	$-0.732433\pi$
$257$	−21.3865			−1.33405			−0.667027	+	0.745034i	$0.732433\pi$
$258$	−4.97323	−	1.33257i	−0.309620	−	0.0829624i
$259$	2.21036	−	20.0795i	0.137345	−	1.24768i
$260$	2.55713	+	1.96750i	0.158586	+	0.122019i
$261$	1.14028	−	1.97502i	0.0705816	−	0.122251i
$262$	16.6135	−	4.45158i	1.02639	−	0.275020i
$263$	−2.26722	+	3.92693i	−0.139803	+	0.242145i	−0.927422	−	0.374017i	$-0.877980\pi$
$263$	−2.26722	+	3.92693i	−0.139803	+	0.242145i	0.787619	+	0.616162i	$0.211313\pi$
$264$	−2.44883	−	4.24149i	−0.150715	−	0.261046i
$265$	5.73807	+	5.73807i	0.352487	+	0.352487i
$266$	−3.20776	+	8.23518i	−0.196680	+	0.504931i
$267$	−9.83317	+	2.63479i	−0.601780	+	0.161247i
$268$	12.9423	−	3.46789i	0.790579	−	0.211835i
$269$			17.0025i			1.03666i	0.855181	+	0.518330i	$0.173446\pi$
$269$			17.0025i			1.03666i	−0.855181	+	0.518330i	$0.826554\pi$
$270$	−0.774967	−	0.447427i	−0.0471630	−	0.0272296i
$271$	19.8451	−	19.8451i	1.20550	−	1.20550i	0.233035	−	0.972468i	$-0.425134\pi$
$271$	19.8451	−	19.8451i	1.20550	−	1.20550i	0.972468	−	0.233035i	$-0.0748657\pi$
$272$	−2.68269			−0.162662
$273$	−6.87856	−	6.60950i	−0.416309	−	0.400025i
$274$	11.1754			0.675128
$275$	−14.5426	+	14.5426i	−0.876954	+	0.876954i
$276$	−5.93637	−	3.42737i	−0.357328	−	0.206303i
$277$			9.94711i			0.597664i	0.954306	+	0.298832i	$0.0965970\pi$
$277$			9.94711i			0.597664i	−0.954306	+	0.298832i	$0.903403\pi$
$278$	−2.63268	+	0.705425i	−0.157898	+	0.0423086i
$279$	−7.73290	+	2.07202i	−0.462956	+	0.124049i
$280$	−0.358860	−	2.34021i	−0.0214460	−	0.139854i
$281$	−9.92606	−	9.92606i	−0.592139	−	0.592139i	0.346070	−	0.938209i	$-0.387516\pi$
$281$	−9.92606	−	9.92606i	−0.592139	−	0.592139i	−0.938209	+	0.346070i	$0.887516\pi$
$282$	6.28549	+	10.8868i	0.374296	+	0.648299i
$283$	2.27723	−	3.94428i	0.135367	−	0.234463i	−0.790370	−	0.612629i	$-0.790112\pi$
$283$	2.27723	−	3.94428i	0.135367	−	0.234463i	0.925738	+	0.378166i	$0.123445\pi$
$284$	−10.9973	+	2.94672i	−0.652570	+	0.174856i
$285$	−1.49459	+	2.58870i	−0.0885316	+	0.153341i
$286$	−2.28190	−	17.5107i	−0.134932	−	1.03543i
$287$	6.62600	−	2.91111i	0.391121	−	0.171838i
$288$	−0.965926	−	0.258819i	−0.0569177	−	0.0152511i
$289$	−9.80319			−0.576658
$290$	2.04077			0.119838
$291$	−3.09903	−	0.830382i	−0.181668	−	0.0486778i
$292$	3.52074	−	13.1396i	0.206036	−	0.768937i
$293$	−2.86889	−	10.7068i	−0.167602	−	0.625500i	−0.997694	−	0.0678734i	$-0.978379\pi$
$293$	−2.86889	−	10.7068i	−0.167602	−	0.625500i	0.830092	−	0.557627i	$-0.188288\pi$
$294$	0.297557	+	6.99367i	0.0173539	+	0.407879i
$295$	−1.51451	+	2.62321i	−0.0881781	+	0.152729i
$296$		−	7.63517i		−	0.443785i
$297$	1.26761	+	4.73077i	0.0735539	+	0.274507i
$298$	−15.0609	+	8.69542i	−0.872455	+	0.503712i
$299$	−15.0198	−	19.6276i	−0.868617	−	1.13509i
$300$			4.19924i			0.242443i
$301$	2.06475	+	13.4647i	0.119010	+	0.776093i
$302$	−5.75115	−	9.96128i	−0.330941	−	0.573207i
$303$	3.51667	−	2.03035i	0.202027	−	0.116641i
$304$	−0.864559	+	3.22658i	−0.0495858	+	0.185057i
$305$	8.76324	−	8.76324i	0.501782	−	0.501782i
$306$	2.59128	+	0.694330i	0.148133	+	0.0396922i
$307$	19.1117	−	19.1117i	1.09076	−	1.09076i	0.0953121	−	0.995447i	$-0.469615\pi$
$307$	19.1117	−	19.1117i	1.09076	−	1.09076i	0.995447	−	0.0953121i	$-0.0303849\pi$
$308$	−7.66798	+	10.4456i	−0.436924	+	0.595194i
$309$	−7.31190	+	4.22153i	−0.415960	+	0.240154i
$310$	−5.06566	−	5.06566i	−0.287710	−	0.287710i
$311$	−15.7308	−	27.2465i	−0.892011	−	1.54501i	−0.837460	−	0.546498i	$-0.815961\pi$
$311$	−15.7308	−	27.2465i	−0.892011	−	1.54501i	−0.0545511	−	0.998511i	$-0.517373\pi$
$312$	−2.85759	−	2.19868i	−0.161779	−	0.124476i
$313$	0.370324	+	0.213807i	0.0209319	+	0.0120851i	0.510429	−	0.859920i	$-0.329486\pi$
$313$	0.370324	+	0.213807i	0.0209319	+	0.0120851i	−0.489498	+	0.872005i	$0.662820\pi$
$314$	0.402750	−	1.50308i	0.0227285	−	0.0848239i
$315$	−0.259058	+	2.35335i	−0.0145963	+	0.132596i
$316$	−5.68448	−	3.28194i	−0.319777	−	0.184623i
$317$	4.08574	+	15.2482i	0.229478	+	0.856423i	0.980561	+	0.196215i	$0.0628652\pi$
$317$	4.08574	+	15.2482i	0.229478	+	0.856423i	−0.751083	+	0.660208i	$0.770468\pi$
$318$	−6.41230	−	6.41230i	−0.359584	−	0.359584i
$319$	−7.89795	−	7.89795i	−0.442201	−	0.442201i
$320$	−0.231605	−	0.864363i	−0.0129471	−	0.0483194i
$321$	15.1253	+	8.73259i	0.844212	+	0.487406i
$322$	−1.98443	+	18.0270i	−0.110588	+	1.00461i
$323$	2.31934	−	8.65590i	0.129052	−	0.481627i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	−5.81243	+	13.9804i	−0.322416	+	0.775494i
$326$	8.20718	+	14.2153i	0.454554	+	0.787310i
$327$	−6.15673	−	6.15673i	−0.340468	−	0.340468i
$328$	2.36896	−	1.36772i	0.130804	−	0.0755198i
$329$	19.6817	−	26.8112i	1.08509	−	1.47815i
$330$	−3.09903	+	3.09903i	−0.170596	+	0.170596i
$331$	29.5958	+	7.93018i	1.62673	+	0.435882i	0.952970	−	0.303064i	$-0.0980096\pi$
$331$	29.5958	+	7.93018i	1.62673	+	0.435882i	0.673764	+	0.738946i	$0.264676\pi$
$332$	−2.49869	+	2.49869i	−0.137133	+	0.137133i
$333$	−1.97613	+	7.37501i	−0.108291	+	0.404148i
$334$	16.0886	−	9.28877i	0.880330	−	0.508259i
$335$	−5.99503	−	10.3837i	−0.327543	−	0.567322i
$336$	0.401026	+	2.61518i	0.0218778	+	0.142670i
$337$		−	21.8065i		−	1.18787i	−0.804511	−	0.593937i	$-0.797573\pi$
$337$		−	21.8065i		−	1.18787i	0.804511	−	0.593937i	$-0.202427\pi$
$338$	−6.47037	−	11.2754i	−0.351942	−	0.613300i
$339$	0.0171111	−	0.00987908i	0.000929346	−	0.000536558i
$340$	0.621325	+	2.31882i	0.0336961	+	0.125755i
$341$			39.2090i			2.12329i
$342$	1.67020	−	2.89287i	0.0903140	−	0.156428i
$343$	16.6240	−	8.16358i	0.897609	−	0.440792i
$344$	1.33257	+	4.97323i	0.0718475	+	0.268139i
$345$	−1.58759	+	5.92498i	−0.0854732	+	0.318990i
$346$	7.46065	+	1.99907i	0.401087	+	0.107471i
$347$	9.73495			0.522600			0.261300	−	0.965258i	$-0.415849\pi$
$347$	9.73495			0.522600			0.261300	+	0.965258i	$0.415849\pi$
$348$	−2.28056			−0.122251
$349$	−10.7437	−	2.87876i	−0.575097	−	0.154097i	−0.0404636	−	0.999181i	$-0.512883\pi$
$349$	−10.7437	−	2.87876i	−0.575097	−	0.154097i	−0.534633	+	0.845084i	$0.679550\pi$
$350$	10.1717	−	4.46891i	0.543701	−	0.238873i
$351$	2.19116	+	2.86336i	0.116955	+	0.152835i
$352$	−2.44883	+	4.24149i	−0.130523	+	0.226072i
$353$	−4.89282	+	1.31103i	−0.260419	+	0.0697789i	−0.386666	−	0.922220i	$-0.626373\pi$
$353$	−4.89282	+	1.31103i	−0.260419	+	0.0697789i	0.126247	+	0.991999i	$0.459707\pi$
$354$	1.69246	−	2.93143i	0.0899534	−	0.155804i
$355$	5.09407	+	8.82319i	0.270365	+	0.468286i
$356$	7.19838	+	7.19838i	0.381513	+	0.381513i
$357$	−1.07583	−	7.01571i	−0.0569389	−	0.371311i
$358$	12.9386	−	3.46688i	0.683825	−	0.183230i
$359$	23.2678	−	6.23458i	1.22803	−	0.329049i	0.414216	−	0.910179i	$-0.364056\pi$
$359$	23.2678	−	6.23458i	1.22803	−	0.329049i	0.813811	+	0.581130i	$0.197389\pi$
$360$			0.894855i			0.0471630i
$361$	6.79115	+	3.92087i	0.357429	+	0.206362i
$362$	−3.03981	+	3.03981i	−0.159769	+	0.159769i
$363$	12.9870			0.681640
$364$	−2.28471	+	9.26175i	−0.119751	+	0.485448i
$365$	−12.1728			−0.637154
$366$	−9.79293	+	9.79293i	−0.511884	+	0.511884i
$367$	−26.4680	−	15.2813i	−1.38162	−	0.797679i	−0.389269	−	0.921124i	$-0.627272\pi$
$367$	−26.4680	−	15.2813i	−1.38162	−	0.797679i	−0.992351	+	0.123445i	$0.960606\pi$
$368$			6.85473i			0.357328i
$369$	−2.64223	+	0.707984i	−0.137549	+	0.0368562i
$370$	−6.59956	+	1.76835i	−0.343095	+	0.0919320i
$371$	−8.70827	+	22.3565i	−0.452111	+	1.16069i
$372$	5.66087	+	5.66087i	0.293503	+	0.293503i
$373$	−6.20944	−	10.7551i	−0.321513	−	0.556876i	0.659288	−	0.751891i	$-0.270858\pi$
$373$	−6.20944	−	10.7551i	−0.321513	−	0.556876i	−0.980800	+	0.195015i	$0.937525\pi$
$374$	6.56943	−	11.3786i	0.339697	−	0.588373i
$375$	7.95148	−	2.13059i	0.410613	−	0.110023i
$376$	6.28549	−	10.8868i	0.324150	−	0.561443i
$377$	−7.59262	−	3.15667i	−0.391040	−	0.162577i
$378$	0.289497	−	2.62987i	0.0148901	−	0.135266i
$379$	8.06020	+	2.15972i	0.414025	+	0.110938i	0.459818	−	0.888013i	$-0.347915\pi$
$379$	8.06020	+	2.15972i	0.414025	+	0.110938i	−0.0457929	+	0.998951i	$0.514581\pi$
$380$	2.98917			0.153341
$381$	−8.79305			−0.450482
$382$	−7.73502	−	2.07259i	−0.395758	−	0.106043i
$383$	0.905709	−	3.38015i	0.0462795	−	0.172718i	−0.938918	−	0.344141i	$-0.888170\pi$
$383$	0.905709	−	3.38015i	0.0462795	−	0.172718i	0.985197	+	0.171424i	$0.0548367\pi$
$384$	0.258819	+	0.965926i	0.0132078	+	0.0492922i
$385$	10.8048	+	4.20866i	0.550661	+	0.214493i
$386$	−13.4973	+	23.3780i	−0.686993	+	1.18991i
$387$		−	5.14867i		−	0.261722i
$388$	0.830382	+	3.09903i	0.0421563	+	0.157329i
$389$	−17.0504	+	9.84407i	−0.864492	+	0.499114i	−0.865514	−	0.500885i	$-0.833008\pi$
$389$	−17.0504	+	9.84407i	−0.864492	+	0.499114i	0.00102229	+	0.999999i	$0.499675\pi$
$390$	−1.23863	+	2.97922i	−0.0627202	+	0.150859i
$391$		−	18.3891i		−	0.929977i
$392$	5.90792	−	3.75453i	0.298395	−	0.189632i
$393$	8.59980	+	14.8953i	0.433803	+	0.751368i
$394$	−1.29322	+	0.746643i	−0.0651516	+	0.0376153i
$395$	−1.52023	+	5.67357i	−0.0764911	+	0.285468i
$396$	3.46316	−	3.46316i	0.174030	−	0.174030i
$397$	2.70666	+	0.725247i	0.135843	+	0.0363991i	0.326100	−	0.945335i	$-0.394265\pi$
$397$	2.70666	+	0.725247i	0.135843	+	0.0363991i	−0.190257	+	0.981734i	$0.560932\pi$
$398$	1.24075	−	1.24075i	0.0621930	−	0.0621930i
$399$	−8.78480	−	0.967036i	−0.439790	−	0.0484124i
$400$	3.63664	−	2.09962i	0.181832	−	0.104981i
$401$	4.78757	+	4.78757i	0.239080	+	0.239080i	0.816469	−	0.577389i	$-0.195928\pi$
$401$	4.78757	+	4.78757i	0.239080	+	0.239080i	−0.577389	+	0.816469i	$0.695928\pi$
$402$	6.69944	+	11.6038i	0.334138	+	0.578744i
$403$	11.0110	+	26.6822i	0.548499	+	1.32913i
$404$	−3.51667	−	2.03035i	−0.174961	−	0.101014i
$405$	0.231605	−	0.864363i	0.0115086	−	0.0429506i
$406$	2.42702	+	5.52416i	0.120451	+	0.274159i
$407$	32.3845	+	18.6972i	1.60524	+	0.926786i
$408$	−0.694330	−	2.59128i	−0.0343745	−	0.128287i
$409$	10.7235	+	10.7235i	0.530244	+	0.530244i	0.920645	−	0.390401i	$-0.127664\pi$
$409$	10.7235	+	10.7235i	0.530244	+	0.530244i	−0.390401	+	0.920645i	$0.627664\pi$
$410$	−1.73087	−	1.73087i	−0.0854817	−	0.0854817i
$411$	2.89240	+	10.7946i	0.142671	+	0.532457i
$412$	7.31190	+	4.22153i	0.360232	+	0.207980i
$413$	−8.90190	−	0.979927i	−0.438034	−	0.0482191i
$414$	1.77414	−	6.62116i	0.0871940	−	0.325412i
$415$	2.73848	+	1.58106i	0.134427	+	0.0776114i
$416$	−0.475319	+	3.57408i	−0.0233044	+	0.175234i
$417$	−1.36278	−	2.36040i	−0.0667355	−	0.115589i
$418$	−11.5683	−	11.5683i	−0.565826	−	0.565826i
$419$	−12.2187	+	7.05447i	−0.596923	+	0.344634i	−0.767830	−	0.640654i	$-0.778663\pi$
$419$	−12.2187	+	7.05447i	−0.596923	+	0.344634i	0.170907	+	0.985287i	$0.445330\pi$
$420$	2.16759	−	0.952323i	0.105767	−	0.0464686i
$421$	4.54790	−	4.54790i	0.221651	−	0.221651i	−0.587542	−	0.809193i	$-0.699904\pi$
$421$	4.54790	−	4.54790i	0.221651	−	0.221651i	0.809193	+	0.587542i	$0.199904\pi$
$422$	−7.93001	−	2.12484i	−0.386027	−	0.103436i
$423$	−8.88903	+	8.88903i	−0.432199	+	0.432199i
$424$	−2.34706	+	8.75936i	−0.113983	+	0.425392i
$425$	−9.75598	+	5.63262i	−0.473234	+	0.273222i
$426$	−5.69263	−	9.85992i	−0.275809	−	0.477715i
$427$	34.1430	+	13.2994i	1.65230	+	0.643601i
$428$		−	17.4652i		−	0.844212i
$429$	16.3234	−	6.73624i	0.788102	−	0.325229i
$430$	3.99005	−	2.30365i	0.192417	−	0.111092i
$431$	0.965690	+	3.60400i	0.0465156	+	0.173599i	0.985276	−	0.170973i	$-0.0546910\pi$
$431$	0.965690	+	3.60400i	0.0465156	+	0.173599i	−0.938760	+	0.344571i	$0.888024\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	11.5943	−	20.0819i	0.557186	−	0.965075i	−0.440544	−	0.897731i	$-0.645214\pi$
$433$	11.5943	−	20.0819i	0.557186	−	0.965075i	0.997730	−	0.0673436i	$-0.0214524\pi$
$434$	7.68779	−	19.7366i	0.369026	−	0.947389i
$435$	0.528190	+	1.97123i	0.0253248	+	0.0945134i
$436$	−2.25352	+	8.41024i	−0.107924	+	0.402778i
$437$	−22.1173	−	5.92632i	−1.05802	−	0.283494i
$438$	13.6031			0.649982
$439$	−2.85069			−0.136056			−0.0680279	−	0.997683i	$-0.521671\pi$
$439$	−2.85069			−0.136056			−0.0680279	+	0.997683i	$0.521671\pi$
$440$	4.23335	+	1.13432i	0.201817	+	0.0540767i
$441$	−6.67836	+	2.09751i	−0.318017	+	0.0998816i
$442$	1.27513	−	9.58815i	0.0606519	−	0.456062i
$443$	5.33971	−	9.24865i	0.253697	−	0.439417i	−0.710844	−	0.703350i	$-0.751687\pi$
$443$	5.33971	−	9.24865i	0.253697	−	0.439417i	0.964541	+	0.263933i	$0.0850199\pi$
$444$	7.37501	−	1.97613i	0.350002	−	0.0937828i
$445$	4.55483	−	7.88920i	0.215920	−	0.373984i
$446$	1.53001	+	2.65006i	0.0724481	+	0.125484i
$447$	−12.2972	−	12.2972i	−0.581637	−	0.581637i
$448$	2.06430	−	1.65489i	0.0975291	−	0.0781862i
$449$	−15.0474	+	4.03194i	−0.710131	+	0.190279i	−0.595764	−	0.803160i	$-0.703151\pi$
$449$	−15.0474	+	4.03194i	−0.710131	+	0.190279i	−0.114367	+	0.993439i	$0.536484\pi$
$450$	−4.05615	+	1.08684i	−0.191209	+	0.0512342i
$451$			13.3972i			0.630851i
$452$	−0.0171111	−	0.00987908i	−0.000804837	−	0.000464673i
$453$	8.13335	−	8.13335i	0.382138	−	0.382138i
$454$	−12.4300			−0.583368
$455$	8.53467	−	0.170251i	0.400112	−	0.00798147i
$456$	−3.34040			−0.156428
$457$	−12.3773	+	12.3773i	−0.578984	+	0.578984i	−0.934623	−	0.355639i	$-0.884263\pi$
$457$	−12.3773	+	12.3773i	−0.578984	+	0.578984i	0.355639	+	0.934623i	$0.384263\pi$
$458$	11.8712	+	6.85382i	0.554703	+	0.320258i
$459$			2.68269i			0.125217i
$460$	5.92498	−	1.58759i	0.276254	−	0.0740219i
$461$	−26.8170	+	7.18559i	−1.24899	+	0.334666i	−0.821947	−	0.569564i	$-0.807112\pi$
$461$	−26.8170	+	7.18559i	−1.24899	+	0.334666i	−0.427045	+	0.904231i	$0.640445\pi$
$462$	−12.0743	−	4.70317i	−0.561748	−	0.218811i
$463$	16.6449	+	16.6449i	0.773555	+	0.773555i	0.978726	−	0.205171i	$-0.0657751\pi$
$463$	16.6449	+	16.6449i	0.773555	+	0.773555i	−0.205171	+	0.978726i	$0.565775\pi$
$464$	1.14028	+	1.97502i	0.0529362	+	0.0916882i
$465$	3.58196	−	6.20414i	0.166110	−	0.287710i
$466$	7.36872	−	1.97444i	0.341349	−	0.0914642i
$467$	−3.11839	+	5.40121i	−0.144302	+	0.249938i	−0.929112	−	0.369798i	$-0.879427\pi$
$467$	−3.11839	+	5.40121i	−0.144302	+	0.249938i	0.784810	+	0.619736i	$0.212760\pi$
$468$	1.38416	−	3.32928i	0.0639830	−	0.153896i
$469$	20.9779	−	28.5769i	0.968669	−	1.31956i
$470$	−10.8659	−	2.91151i	−0.501206	−	0.134298i
$471$	1.55611			0.0717016
$472$	−3.38493			−0.155804
$473$	−24.3571	−	6.52648i	−1.11994	−	0.300088i
$474$	1.69886	−	6.34022i	0.0780311	−	0.291216i
$475$	3.63049	+	13.5492i	0.166578	+	0.621678i
$476$	−5.53787	+	4.43955i	−0.253828	+	0.203487i
$477$	4.53418	−	7.85343i	0.207606	−	0.359584i
$478$		−	9.32115i		−	0.426339i
$479$	7.58213	+	28.2969i	0.346436	+	1.29292i	0.890925	+	0.454150i	$0.150057\pi$
$479$	7.58213	+	28.2969i	0.346436	+	1.29292i	−0.544489	+	0.838768i	$0.683276\pi$
$480$	0.774967	−	0.447427i	0.0353722	−	0.0204222i
$481$	27.2887	+	3.62914i	1.24426	+	0.165475i
$482$			13.9110i			0.633630i
$483$	−17.9264	+	2.74893i	−0.815678	+	0.125081i
$484$	−6.49349	−	11.2471i	−0.295159	−	0.511230i
$485$	2.48636	−	1.43550i	0.112900	−	0.0651828i
$486$	−0.258819	+	0.965926i	−0.0117403	+	0.0438153i
$487$	−29.2606	+	29.2606i	−1.32592	+	1.32592i	−0.417031	+	0.908892i	$0.636929\pi$
$487$	−29.2606	+	29.2606i	−1.32592	+	1.32592i	−0.908892	+	0.417031i	$0.863071\pi$
$488$	13.3774	+	3.58446i	0.605566	+	0.162261i
$489$	−11.6067	+	11.6067i	−0.524873	+	0.524873i
$490$	−4.61358	−	4.23702i	−0.208420	−	0.191409i
$491$	−16.2647	+	9.39045i	−0.734017	+	0.423785i	−0.819890	−	0.572521i	$-0.805965\pi$
$491$	−16.2647	+	9.39045i	−0.734017	+	0.423785i	0.0858727	+	0.996306i	$0.472632\pi$
$492$	1.93425	+	1.93425i	0.0872027	+	0.0872027i
$493$	−3.05902	−	5.29837i	−0.137771	−	0.238627i
$494$	−11.1211	−	4.62366i	−0.500363	−	0.208028i
$495$	−3.79552	−	2.19134i	−0.170596	−	0.0984935i
$496$	2.07202	−	7.73290i	0.0930366	−	0.347217i
$497$	−17.8253	+	24.2823i	−0.799572	+	1.08921i
$498$	−3.06025	−	1.76684i	−0.137133	−	0.0791739i
$499$	−6.19403	−	23.1164i	−0.277283	−	1.03483i	−0.954296	−	0.298863i	$-0.903393\pi$
$499$	−6.19403	−	23.1164i	−0.277283	−	1.03483i	0.677013	−	0.735971i	$-0.263274\pi$
$500$	−5.82089	−	5.82089i	−0.260318	−	0.260318i
$501$	13.1363	+	13.1363i	0.586887	+	0.586887i
$502$	−0.576812	−	2.15269i	−0.0257444	−	0.0960794i
$503$	−15.2647	−	8.81310i	−0.680621	−	0.392957i	0.119468	−	0.992838i	$-0.461881\pi$
$503$	−15.2647	−	8.81310i	−0.680621	−	0.392957i	−0.800089	+	0.599881i	$0.795214\pi$
$504$	−2.42228	+	1.06422i	−0.107897	+	0.0474042i
$505$	−0.940480	+	3.50992i	−0.0418508	+	0.156189i
$506$	−29.0743	−	16.7860i	−1.29251	−	0.746231i
$507$	9.21653	−	9.16818i	0.409321	−	0.407173i
$508$	4.39652	+	7.61500i	0.195064	+	0.337861i
$509$	5.18819	+	5.18819i	0.229962	+	0.229962i	0.812677	−	0.582715i	$-0.198009\pi$
$509$	5.18819	+	5.18819i	0.229962	+	0.229962i	−0.582715	+	0.812677i	$0.698009\pi$
$510$	−2.07899	+	1.20031i	−0.0920594	+	0.0531505i
$511$	−14.4767	−	32.9505i	−0.640412	−	1.45765i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	3.22658	+	0.864559i	0.142457	+	0.0381712i
$514$	−15.1225	+	15.1225i	−0.667027	+	0.667027i
$515$	1.95546	−	7.29787i	0.0861678	−	0.321583i
$516$	−4.45888	+	2.57433i	−0.196291	+	0.113329i
$517$	30.7841	+	53.3197i	1.35389	+	2.34500i
$518$	−12.6354	−	15.7613i	−0.555166	−	0.692511i
$519$			7.72383i			0.339039i
$520$	3.19939	−	0.416929i	0.140303	−	0.0182835i
$521$	20.1210	−	11.6169i	0.881517	−	0.508944i	0.0103586	−	0.999946i	$-0.496703\pi$
$521$	20.1210	−	11.6169i	0.881517	−	0.508944i	0.871158	+	0.491002i	$0.163369\pi$
$522$	−0.590253	−	2.20285i	−0.0258347	−	0.0964163i
$523$			11.9955i			0.524526i	0.964996	+	0.262263i	$0.0844687\pi$
$523$			11.9955i			0.524526i	−0.964996	+	0.262263i	$0.915531\pi$
$524$	8.59980	−	14.8953i	0.375684	−	0.650704i
$525$	6.94927	+	8.66849i	0.303291	+	0.378324i
$526$	1.17360	+	4.37993i	0.0511713	+	0.190974i
$527$	−5.55859	+	20.7449i	−0.242136	+	0.903664i
$528$	−4.73077	−	1.26761i	−0.205880	−	0.0551654i
$529$	−23.9874			−1.04293
$530$	8.11486			0.352487
$531$	3.26959	+	0.876083i	0.141888	+	0.0380188i
$532$	3.55492	+	8.09138i	0.154125	+	0.350806i
$533$	3.76234	+	9.11697i	0.162965	+	0.394900i
$534$	−5.09002	+	8.81618i	−0.220267	+	0.381513i
$535$	−15.0963	+	4.04503i	−0.652668	+	0.174882i
$536$	6.69944	−	11.6038i	0.289372	−	0.501207i
$537$	6.69750	+	11.6004i	0.289018	+	0.500594i
$538$	12.0226	+	12.0226i	0.518330	+	0.518330i
$539$	1.45733	+	34.2526i	0.0627717	+	1.47536i
$540$	−0.864363	+	0.231605i	−0.0371963	+	0.00996671i
$541$	27.3622	−	7.33167i	1.17639	−	0.315213i	0.382897	−	0.923791i	$-0.374926\pi$
$541$	27.3622	−	7.33167i	1.17639	−	0.315213i	0.793494	+	0.608578i	$0.208260\pi$
$542$		−	28.0652i		−	1.20550i
$543$	−3.72299	−	2.14947i	−0.159769	−	0.0922426i
$544$	−1.89695	+	1.89695i	−0.0813309	+	0.0813309i
$545$	7.79143			0.333748
$546$	−9.53749	+	0.190255i	−0.408167	+	0.00814217i
$547$	−19.2616			−0.823568			−0.411784	−	0.911282i	$-0.635094\pi$
$547$	−19.2616			−0.823568			−0.411784	+	0.911282i	$0.635094\pi$
$548$	7.90217	−	7.90217i	0.337564	−	0.337564i
$549$	−11.9938	−	6.92464i	−0.511884	−	0.295537i
$550$			20.5664i			0.876954i
$551$	−7.35841	+	1.97168i	−0.313479	+	0.0839964i
$552$	−6.62116	+	1.77414i	−0.281815	+	0.0755122i
$553$	−17.1657	+	2.63229i	−0.729961	+	0.111936i
$554$	7.03367	+	7.03367i	0.298832	+	0.298832i
$555$	−3.41618	−	5.91700i	−0.145009	−	0.251163i
$556$	−1.36278	+	2.36040i	−0.0577946	+	0.100103i
$557$	41.5202	−	11.1253i	1.75927	−	0.471394i	0.772704	−	0.634767i	$-0.218904\pi$
$557$	41.5202	−	11.1253i	1.75927	−	0.471394i	0.986564	+	0.163372i	$0.0522372\pi$
$558$	−4.00284	+	6.93313i	−0.169454	+	0.293503i
$559$	−18.4081	+	2.39886i	−0.778581	+	0.101461i
$560$	−1.90853	−	1.40102i	−0.0806501	−	0.0592041i
$561$	12.6912	+	3.40059i	0.535821	+	0.143573i
$562$	−14.0376			−0.592139
$563$	−4.75604			−0.200443			−0.100222	−	0.994965i	$-0.531955\pi$
$563$	−4.75604			−0.200443			−0.100222	+	0.994965i	$0.531955\pi$
$564$	12.1426	+	3.25361i	0.511297	+	0.137002i
$565$	−0.00457610	+	0.0170782i	−0.000192518	+	0.000718487i
$566$	−1.17878	−	4.39927i	−0.0495478	−	0.184915i
$567$	2.61518	−	0.401026i	0.109827	−	0.0168415i
$568$	−5.69263	+	9.85992i	−0.238857	+	0.413713i
$569$		−	38.4712i		−	1.61280i	−0.591373	−	0.806398i	$-0.701414\pi$
$569$		−	38.4712i		−	1.61280i	0.591373	−	0.806398i	$-0.298586\pi$
$570$	0.773654	+	2.88732i	0.0324048	+	0.120936i
$571$	−19.2241	+	11.0990i	−0.804504	+	0.464480i	−0.845044	−	0.534697i	$-0.820426\pi$
$571$	−19.2241	+	11.0990i	−0.804504	+	0.464480i	0.0405398	+	0.999178i	$0.487092\pi$
$572$	−13.9955	−	10.7684i	−0.585180	−	0.450248i
$573$		−	8.00789i		−	0.334534i
$574$	2.62682	−	6.74376i	0.109641	−	0.281479i
$575$	14.3923	+	24.9282i	0.600201	+	1.03958i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	−7.67212	+	28.6327i	−0.319395	+	1.19200i	0.600433	+	0.799675i	$0.294995\pi$
$577$	−7.67212	+	28.6327i	−0.319395	+	1.19200i	−0.919828	+	0.392322i	$0.871672\pi$
$578$	−6.93190	+	6.93190i	−0.288329	+	0.288329i
$579$	−26.0747	−	6.98670i	−1.08363	−	0.290358i
$580$	1.44304	−	1.44304i	0.0599191	−	0.0599191i
$581$	−1.02299	+	9.29310i	−0.0424408	+	0.385543i
$582$	−2.77851	+	1.60417i	−0.115173	+	0.0664952i
$583$	−31.4052	−	31.4052i	−1.30067	−	1.30067i
$584$	−6.80156	−	11.7806i	−0.281450	−	0.487486i
$585$	−3.19829	−	0.425342i	−0.132233	−	0.0175857i
$586$	−9.59949	−	5.54227i	−0.396551	−	0.228949i
$587$	−4.88638	+	18.2362i	−0.201682	+	0.752689i	0.788753	+	0.614711i	$0.210727\pi$
$587$	−4.88638	+	18.2362i	−0.201682	+	0.752689i	−0.990435	+	0.137979i	$0.955939\pi$
$588$	5.15568	+	4.73487i	0.212617	+	0.195263i
$589$	23.1594	+	13.3711i	0.954267	+	0.550946i
$590$	0.783967	+	2.92581i	0.0322754	+	0.120454i
$591$	−1.05591	−	1.05591i	−0.0434344	−	0.0434344i
$592$	−5.39888	−	5.39888i	−0.221893	−	0.221893i
$593$	−0.383507	−	1.43127i	−0.0157487	−	0.0587751i	0.957604	−	0.288087i	$-0.0930192\pi$
$593$	−0.383507	−	1.43127i	−0.0157487	−	0.0587751i	−0.973353	+	0.229312i	$0.926352\pi$
$594$	4.24149	+	2.44883i	0.174030	+	0.100477i
$595$	5.11999	+	3.75851i	0.209899	+	0.154084i
$596$	−4.50108	+	16.7983i	−0.184371	+	0.688084i
$597$	1.51960	+	0.877340i	0.0621930	+	0.0359072i
$598$	−24.4994	−	3.25819i	−1.00185	−	0.133237i
$599$	6.33300	+	10.9691i	0.258759	+	0.448184i	0.965910	−	0.258879i	$-0.0833530\pi$
$599$	6.33300	+	10.9691i	0.258759	+	0.448184i	−0.707150	+	0.707063i	$0.750020\pi$
$600$	2.96931	+	2.96931i	0.121221	+	0.121221i
$601$	−13.4519	+	7.76648i	−0.548716	+	0.316801i	−0.748604	−	0.663017i	$-0.769276\pi$
$601$	−13.4519	+	7.76648i	−0.548716	+	0.316801i	0.199888	+	0.979819i	$0.435942\pi$
$602$	10.9810	+	8.06098i	0.447552	+	0.328541i
$603$	−9.47444	+	9.47444i	−0.385829	+	0.385829i
$604$	−11.1104	−	2.97701i	−0.452074	−	0.121133i
$605$	−8.21761	+	8.21761i	−0.334093	+	0.334093i
$606$	1.05099	−	3.92233i	0.0426934	−	0.159334i
$607$	−31.9370	+	18.4388i	−1.29628	+	0.748408i	−0.979760	−	0.200177i	$-0.935848\pi$
$607$	−31.9370	+	18.4388i	−1.29628	+	0.748408i	−0.316521	+	0.948585i	$0.602515\pi$
$608$	1.67020	+	2.89287i	0.0677355	+	0.117321i
$609$	−4.70777	+	3.77408i	−0.190768	+	0.152933i
$610$		−	12.3931i		−	0.501782i
$611$	35.9227	+	27.6396i	1.45328	+	1.11818i
$612$	2.32327	−	1.34134i	0.0939128	−	0.0542206i
$613$	−2.79330	−	10.4247i	−0.112820	−	0.421051i	0.886294	−	0.463123i	$-0.153271\pi$
$613$	−2.79330	−	10.4247i	−0.112820	−	0.421051i	−0.999115	+	0.0420712i	$0.986604\pi$
$614$		−	27.0280i		−	1.09076i
$615$	1.22391	−	2.11988i	0.0493529	−	0.0854817i
$616$	1.96409	+	12.8082i	0.0791353	+	0.516059i
$617$	−6.71882	−	25.0750i	−0.270490	−	1.00948i	−0.958804	−	0.284068i	$-0.908316\pi$
$617$	−6.71882	−	25.0750i	−0.270490	−	1.00948i	0.688314	−	0.725412i	$-0.258351\pi$
$618$	−2.18522	+	8.15537i	−0.0879026	+	0.328057i
$619$	2.06284	+	0.552735i	0.0829124	+	0.0222163i	0.300037	−	0.953928i	$-0.403001\pi$
$619$	2.06284	+	0.552735i	0.0829124	+	0.0222163i	−0.217124	+	0.976144i	$0.569668\pi$
$620$	−7.16392			−0.287710
$621$	6.85473			0.275071
$622$	−30.3896	−	8.14286i	−1.21851	−	0.326499i
$623$	26.7721	+	2.94710i	1.07260	+	0.118073i
$624$	−3.57532	+	0.465918i	−0.143127	+	0.0186516i
$625$	6.81488	−	11.8037i	0.272595	−	0.472148i
$626$	0.413043	−	0.110674i	0.0165085	−	0.00442344i
$627$	8.18005	−	14.1683i	0.326680	−	0.565826i
$628$	−0.778054	−	1.34763i	−0.0310477	−	0.0537762i
$629$	14.4835	+	14.4835i	0.577495	+	0.577495i
$630$	1.48089	+	1.84725i	0.0589999	+	0.0735962i
$631$	16.7045	−	4.47596i	0.664995	−	0.178185i	0.0894960	−	0.995987i	$-0.471474\pi$
$631$	16.7045	−	4.47596i	0.664995	−	0.178185i	0.575499	+	0.817802i	$0.304808\pi$
$632$	−6.34022	+	1.69886i	−0.252200	+	0.0675769i
$633$		−	8.20975i		−	0.326308i
$634$	13.6711	+	7.89304i	0.542951	+	0.313473i
$635$	5.56387	−	5.56387i	0.220795	−	0.220795i
$636$	−9.06836			−0.359584
$637$	10.6108	+	22.9000i	0.420417	+	0.907331i
$638$	−11.1694			−0.442201
$639$	8.05059	−	8.05059i	0.318476	−	0.318476i
$640$	−0.774967	−	0.447427i	−0.0306333	−	0.0176861i
$641$			4.10954i			0.162317i	0.996701	+	0.0811585i	$0.0258620\pi$
$641$			4.10954i			0.162317i	−0.996701	+	0.0811585i	$0.974138\pi$
$642$	16.8701	−	4.52032i	0.665809	−	0.178403i
$643$	−5.15585	+	1.38150i	−0.203327	+	0.0544812i	−0.359045	−	0.933320i	$-0.616898\pi$
$643$	−5.15585	+	1.38150i	−0.203327	+	0.0544812i	0.155718	+	0.987802i	$0.450231\pi$
$644$	11.3438	+	14.1502i	0.447010	+	0.557597i
$645$	3.25786	+	3.25786i	0.128278	+	0.128278i
$646$	−4.48062	−	7.76066i	−0.176288	−	0.305339i
$647$	8.28163	−	14.3442i	0.325584	−	0.563929i	−0.656046	−	0.754721i	$-0.727772\pi$
$647$	8.28163	−	14.3442i	0.325584	−	0.563929i	0.981630	+	0.190792i	$0.0611056\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	8.28909	−	14.3571i	0.325375	−	0.563567i
$650$	5.77564	+	13.9957i	0.226539	+	0.548955i
$651$	21.0539	+	2.31762i	0.825166	+	0.0908348i
$652$	15.8551	+	4.24835i	0.620932	+	0.166378i
$653$	13.3886			0.523934			0.261967	−	0.965077i	$-0.415629\pi$
$653$	13.3886			0.523934			0.261967	+	0.965077i	$0.415629\pi$
$654$	−8.70693			−0.340468
$655$	−14.8667	−	3.98352i	−0.580890	−	0.155649i
$656$	0.707984	−	2.64223i	0.0276421	−	0.103162i
$657$	3.52074	+	13.1396i	0.137357	+	0.512625i
$658$	−5.04130	−	32.8754i	−0.196530	−	1.28162i
$659$	1.41762	−	2.45539i	0.0552227	−	0.0956485i	−0.837093	−	0.547061i	$-0.815746\pi$
$659$	1.41762	−	2.45539i	0.0552227	−	0.0956485i	0.892315	+	0.451413i	$0.149080\pi$
$660$			4.38269i			0.170596i
$661$	−8.19476	−	30.5833i	−0.318739	−	1.18955i	−0.920458	−	0.390843i	$-0.872184\pi$
$661$	−8.19476	−	30.5833i	−0.318739	−	1.18955i	0.601718	−	0.798708i	$-0.294483\pi$
$662$	26.5349	−	15.3199i	1.03131	−	0.595426i
$663$	9.59147	−	1.24991i	0.372502	−	0.0485425i
$664$			3.53368i			0.137133i
$665$	6.17055	−	4.94675i	0.239284	−	0.191827i
$666$	3.81758	+	6.61225i	0.147928	+	0.256220i
$667$	−13.5383	+	7.81632i	−0.524204	+	0.302649i
$668$	4.80822	−	17.9445i	0.186036	−	0.694294i
$669$	−2.16376	+	2.16376i	−0.0836559	+	0.0836559i
$670$	−11.5815	−	3.10326i	−0.447433	−	0.119889i
$671$	−47.9623	+	47.9623i	−1.85156	+	1.85156i
$672$	2.13278	+	1.56564i	0.0822738	+	0.0603961i
$673$	8.90796	−	5.14301i	0.343377	−	0.198249i	−0.318388	−	0.947961i	$-0.603141\pi$
$673$	8.90796	−	5.14301i	0.343377	−	0.198249i	0.661764	+	0.749712i	$0.269808\pi$
$674$	−15.4195	−	15.4195i	−0.593937	−	0.593937i
$675$	−2.09962	−	3.63664i	−0.0808143	−	0.139975i
$676$	−12.5481	−	3.39766i	−0.482621	−	0.130679i
$677$	−9.98639	−	5.76565i	−0.383808	−	0.221592i	0.295666	−	0.955292i	$-0.404459\pi$
$677$	−9.98639	−	5.76565i	−0.383808	−	0.221592i	−0.679474	+	0.733700i	$0.737792\pi$
$678$	0.00511379	−	0.0190849i	0.000196394	−	0.000732952i
$679$	6.84271	+	5.02313i	0.262599	+	0.192770i
$680$	2.07899	+	1.20031i	0.0797258	+	0.0460297i
$681$	−3.21711	−	12.0064i	−0.123280	−	0.460088i
$682$	27.7250	+	27.7250i	1.06164	+	1.06164i
$683$	13.4421	+	13.4421i	0.514349	+	0.514349i	0.915856	−	0.401507i	$-0.131513\pi$
$683$	13.4421	+	13.4421i	0.514349	+	0.514349i	−0.401507	+	0.915856i	$0.631513\pi$
$684$	−0.864559	−	3.22658i	−0.0330572	−	0.123371i
$685$	−8.66053	−	5.00016i	−0.330902	−	0.191046i
$686$	5.98239	−	17.5274i	0.228409	−	0.669201i
$687$	−3.54780	+	13.2406i	−0.135357	+	0.505159i
$688$	4.45888	+	2.57433i	0.169993	+	0.0981456i
$689$	−30.1911	−	12.5521i	−1.15019	−	0.478197i
$690$	3.06700	+	5.31219i	0.116759	+	0.202232i
$691$	−18.4584	−	18.4584i	−0.702190	−	0.702190i	0.262690	−	0.964880i	$-0.415390\pi$
$691$	−18.4584	−	18.4584i	−0.702190	−	0.702190i	−0.964880	+	0.262690i	$0.915390\pi$
$692$	6.68903	−	3.86192i	0.254279	−	0.146808i
$693$	1.41786	−	12.8802i	0.0538599	−	0.489277i
$694$	6.88365	−	6.88365i	0.261300	−	0.261300i
$695$	2.35587	+	0.631253i	0.0893632	+	0.0239448i
$696$	−1.61260	+	1.61260i	−0.0611255	+	0.0611255i
$697$	−1.89930	+	7.08829i	−0.0719411	+	0.268488i
$698$	−9.63253	+	5.56134i	−0.364597	+	0.210500i
$699$	3.81433	+	6.60661i	0.144271	+	0.249885i
$700$	4.03249	−	10.3525i	0.152414	−	0.391287i
$701$		−	4.88532i		−	0.184516i	−0.995735	−	0.0922580i	$-0.970592\pi$
$701$		−	4.88532i		−	0.184516i	0.995735	−	0.0922580i	$-0.0294084\pi$
$702$	3.57408	+	0.475319i	0.134895	+	0.0179398i
$703$	22.0876	−	12.7523i	0.833048	−	0.480960i
$704$	1.26761	+	4.73077i	0.0477747	+	0.178297i
$705$		−	11.2492i		−	0.423670i
$706$	−2.53271	+	4.38678i	−0.0953198	+	0.165099i
$707$	−10.6195	+	1.62845i	−0.399386	+	0.0612440i
$708$	−0.876083	−	3.26959i	−0.0329252	−	0.122879i
$709$	11.2146	−	41.8536i	0.421175	−	1.57185i	−0.350962	−	0.936390i	$-0.614145\pi$
$709$	11.2146	−	41.8536i	0.421175	−	1.57185i	0.772137	−	0.635456i	$-0.219188\pi$
$710$	9.84099	+	2.63689i	0.369326	+	0.0989606i
$711$	6.56388			0.246165
$712$	10.1800			0.381513
$713$	53.0069	+	14.2032i	1.98513	+	0.531913i
$714$	−5.72158	−	4.20013i	−0.214125	−	0.157186i
$715$	−6.06636	+	14.5912i	−0.226869	+	0.545679i
$716$	6.69750	−	11.6004i	0.250297	−	0.433527i
$717$	9.00353	−	2.41249i	0.336243	−	0.0900961i
$718$	12.0443	−	20.8613i	0.449489	−	0.778537i
$719$	−22.5185	−	39.0033i	−0.839800	−	1.45458i	−0.890062	−	0.455840i	$-0.849339\pi$
$719$	−22.5185	−	39.0033i	−0.839800	−	1.45458i	0.0502617	−	0.998736i	$-0.483994\pi$
$720$	0.632758	+	0.632758i	0.0235815	+	0.0235815i
$721$	22.0801	−	3.38589i	0.822307	−	0.126097i
$722$	7.57454	−	2.02959i	0.281895	−	0.0755336i
$723$	−13.4370	+	3.60044i	−0.499729	+	0.133902i
$724$			4.29894i			0.159769i
$725$	8.29359	+	4.78831i	0.308016	+	0.177833i
$726$	9.18318	−	9.18318i	0.340820	−	0.340820i
$727$	−15.0517			−0.558235			−0.279118	−	0.960257i	$-0.590042\pi$
$727$	−15.0517			−0.558235			−0.279118	+	0.960257i	$0.590042\pi$
$728$	4.93351	+	8.16459i	0.182848	+	0.302600i
$729$	−1.00000			−0.0370370
$730$	−8.60748	+	8.60748i	−0.318577	+	0.318577i
$731$	−11.9618	−	6.90613i	−0.442422	−	0.255433i
$732$			13.8493i			0.511884i
$733$	10.3880	−	2.78347i	0.383691	−	0.102810i	−0.0618175	−	0.998087i	$-0.519690\pi$
$733$	10.3880	−	2.78347i	0.383691	−	0.102810i	0.445508	+	0.895278i	$0.353023\pi$
$734$	−29.5213	+	7.91020i	−1.08965	+	0.291971i
$735$	2.89856	−	5.55300i	0.106915	−	0.204825i
$736$	4.84703	+	4.84703i	0.178664	+	0.178664i
$737$	32.8115	+	56.8312i	1.20863	+	2.09341i
$738$	−1.36772	+	2.36896i	−0.0503465	+	0.0872027i
$739$	−2.12137	+	0.568419i	−0.0780359	+	0.0209096i	−0.297626	−	0.954683i	$-0.596195\pi$
$739$	−2.12137	+	0.568419i	−0.0780359	+	0.0209096i	0.219590	+	0.975592i	$0.429528\pi$
$740$	−3.41618	+	5.91700i	−0.125581	+	0.217513i
$741$	1.58776	−	11.9389i	0.0583277	−	0.438585i
$742$	9.65073	+	21.9661i	0.354290	+	0.806400i
$743$	21.9519	+	5.88199i	0.805336	+	0.215789i	0.637925	−	0.770098i	$-0.279793\pi$
$743$	21.9519	+	5.88199i	0.805336	+	0.215789i	0.167411	+	0.985887i	$0.446459\pi$
$744$	8.00568			0.293503
$745$	15.5623			0.570158
$746$	−11.9957	−	3.21424i	−0.439194	−	0.117682i
$747$	0.914583	−	3.41327i	0.0334628	−	0.124885i
$748$	−3.40059	−	12.6912i	−0.124338	−	0.464035i
$749$	−28.9030	−	36.0534i	−1.05609	−	1.31736i
$750$	4.11599	−	7.12910i	0.150295	−	0.260318i
$751$			31.0401i			1.13267i	0.824175	+	0.566335i	$0.191639\pi$
$751$			31.0401i			1.13267i	−0.824175	+	0.566335i	$0.808361\pi$
$752$	−3.25361	−	12.1426i	−0.118647	−	0.442796i
$753$	1.93005	−	1.11432i	0.0703350	−	0.0406079i
$754$	−7.60090	+	3.13669i	−0.276808	+	0.114232i
$755$			10.2929i			0.374596i
$756$	−1.65489	−	2.06430i	−0.0601878	−	0.0750779i
$757$	10.7381	+	18.5990i	0.390284	+	0.675992i	0.992487	−	0.122351i	$-0.0390434\pi$
$757$	10.7381	+	18.5990i	0.390284	+	0.675992i	−0.602203	+	0.798343i	$0.705710\pi$
$758$	7.22658	−	4.17227i	0.262481	−	0.151544i
$759$	8.68910	−	32.4281i	0.315394	−	1.17707i
$760$	2.11366	−	2.11366i	0.0766706	−	0.0766706i
$761$	−38.2504	−	10.2492i	−1.38657	−	0.371532i	−0.513070	−	0.858347i	$-0.671492\pi$
$761$	−38.2504	−	10.2492i	−1.38657	−	0.371532i	−0.873505	+	0.486815i	$0.838159\pi$
$762$	−6.21763	+	6.21763i	−0.225241	+	0.225241i
$763$	9.26609	+	21.0906i	0.335455	+	0.763531i
$764$	−6.93503	+	4.00394i	−0.250901	+	0.144858i
$765$	−1.69749	−	1.69749i	−0.0613729	−	0.0613729i
$766$	−1.74969	−	3.03056i	−0.0632190	−	0.109499i
$767$	1.60892	−	12.0980i	0.0580948	−	0.436834i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	4.86878	−	18.1706i	0.175573	−	0.655247i	−0.820880	−	0.571100i	$-0.806517\pi$
$769$	4.86878	−	18.1706i	0.175573	−	0.655247i	0.996453	−	0.0841469i	$-0.0268165\pi$
$770$	10.6161	−	4.66414i	0.382577	−	0.168084i
$771$	−18.5212	−	10.6932i	−0.667027	−	0.385108i
$772$	6.98670	+	26.0747i	0.251457	+	0.938450i
$773$	8.51198	+	8.51198i	0.306155	+	0.306155i	0.843416	−	0.537261i	$-0.180541\pi$
$773$	8.51198	+	8.51198i	0.306155	+	0.306155i	−0.537261	+	0.843416i	$0.680541\pi$
$774$	−3.64066	−	3.64066i	−0.130861	−	0.130861i
$775$	−8.70091	−	32.4723i	−0.312546	−	1.16644i
$776$	2.77851	+	1.60417i	0.0997428	+	0.0575865i
$777$	11.9540	−	16.2841i	0.428846	−	0.584191i
$778$	−5.09567	+	19.0173i	−0.182689	+	0.681803i
$779$	7.91328	+	4.56873i	0.283523	+	0.163692i
$780$	1.23079	+	2.98247i	0.0440692	+	0.106789i
$781$	−27.8805	−	48.2904i	−0.997642	−	1.72797i
$782$	−13.0031	−	13.0031i	−0.464988	−	0.464988i
$783$	1.97502	−	1.14028i	0.0705816	−	0.0407503i
$784$	1.52268	−	6.83238i	0.0543813	−	0.244014i
$785$	−0.984639	+	0.984639i	−0.0351433	+	0.0351433i
$786$	16.6135	+	4.45158i	0.592585	+	0.158783i
$787$	−8.46788	+	8.46788i	−0.301847	+	0.301847i	−0.841736	−	0.539889i	$-0.818466\pi$
$787$	−8.46788	+	8.46788i	−0.301847	+	0.301847i	0.539889	+	0.841736i	$0.318466\pi$
$788$	−0.386491	+	1.44240i	−0.0137682	+	0.0513835i
$789$	−3.92693	+	2.26722i	−0.139803	+	0.0807151i
$790$	2.93686	+	5.08679i	0.104489	+	0.180980i
$791$	−0.0516712	+	0.00792355i	−0.00183722	+	0.000281729i
$792$		−	4.89765i		−	0.174030i
$793$	−19.1697	+	46.1081i	−0.680735	+	1.63735i
$794$	2.42672	−	1.40107i	0.0861212	−	0.0497221i
$795$	2.10028	+	7.83835i	0.0744893	+	0.277998i
$796$		−	1.75468i		−	0.0621930i
$797$	3.73809	−	6.47456i	0.132410	−	0.229341i	−0.792195	−	0.610268i	$-0.791062\pi$
$797$	3.73809	−	6.47456i	0.132410	−	0.229341i	0.924605	+	0.380927i	$0.124395\pi$
$798$	−6.89559	+	5.52799i	−0.244101	+	0.195689i
$799$	8.72842	+	32.5749i	0.308789	+	1.15242i
$800$	1.08684	−	4.05615i	0.0384257	−	0.143407i
$801$	−9.83317	−	2.63479i	−0.347438	−	0.0930957i
$802$	6.77065			0.239080
$803$	66.6233			2.35108
$804$	12.9423	+	3.46789i	0.456441	+	0.122303i
$805$	9.60365	−	13.0825i	0.338484	−	0.461096i
$806$	26.6531	+	11.0812i	0.938817	+	0.390318i
$807$	−8.50124	+	14.7246i	−0.299258	+	0.518330i
$808$	−3.92233	+	1.05099i	−0.137987	+	0.0369736i
$809$	19.2858	−	33.4040i	0.678052	−	1.17442i	−0.297515	−	0.954717i	$-0.596158\pi$
$809$	19.2858	−	33.4040i	0.678052	−	1.17442i	0.975567	−	0.219703i	$-0.0705089\pi$
$810$	−0.447427	−	0.774967i	−0.0157210	−	0.0272296i
$811$	−20.7415	−	20.7415i	−0.728332	−	0.728332i	0.241955	−	0.970287i	$-0.422211\pi$
$811$	−20.7415	−	20.7415i	−0.728332	−	0.728332i	−0.970287	+	0.241955i	$0.922211\pi$
$812$	5.62233	+	2.19001i	0.197305	+	0.0768541i
$813$	27.1089	−	7.26381i	0.950751	−	0.254753i
$814$	36.1202	−	9.67838i	1.26601	−	0.339227i
$815$		−	14.6885i		−	0.514515i
$816$	−2.32327	−	1.34134i	−0.0813309	−	0.0469564i
$817$	−12.1612	+	12.1612i	−0.425468	+	0.425468i
$818$	15.1653			0.530244
$819$	−2.65226	−	9.16327i	−0.0926774	−	0.320191i
$820$	−2.44782			−0.0854817
$821$	−30.5638	+	30.5638i	−1.06668	+	1.06668i	−0.0690707	+	0.997612i	$0.522003\pi$
$821$	−30.5638	+	30.5638i	−1.06668	+	1.06668i	−0.997612	+	0.0690707i	$0.977997\pi$
$822$	9.67815	+	5.58768i	0.337564	+	0.194893i
$823$		−	49.7312i		−	1.73352i	−0.498723	−	0.866761i	$-0.666198\pi$
$823$		−	49.7312i		−	1.73352i	0.498723	−	0.866761i	$-0.333802\pi$
$824$	8.15537	−	2.18522i	0.284106	−	0.0761259i
$825$	−19.8656	+	5.32297i	−0.691632	+	0.185322i
$826$	−6.98751	+	5.60168i	−0.243126	+	0.194907i
$827$	9.13789	+	9.13789i	0.317756	+	0.317756i	0.847905	−	0.530149i	$-0.177864\pi$
$827$	9.13789	+	9.13789i	0.317756	+	0.317756i	−0.530149	+	0.847905i	$0.677864\pi$
$828$	−3.42737	−	5.93637i	−0.119109	−	0.206303i
$829$	−19.1655	+	33.1956i	−0.665646	+	1.15293i	0.313464	+	0.949600i	$0.398511\pi$
$829$	−19.1655	+	33.1956i	−0.665646	+	1.15293i	−0.979110	+	0.203332i	$0.934823\pi$
$830$	3.05438	−	0.818419i	0.106019	−	0.0284077i
$831$	−4.97355	+	8.61445i	−0.172531	+	0.298832i
$832$	2.19116	+	2.86336i	0.0759647	+	0.0992691i
$833$	−4.08487	+	18.3291i	−0.141532	+	0.635067i
$834$	−2.63268	−	0.705425i	−0.0911623	−	0.0244269i
$835$	−16.6242			−0.575304
$836$	−16.3601			−0.565826
$837$	−7.73290	−	2.07202i	−0.267288	−	0.0716196i
$838$	−3.65166	+	13.6282i	−0.126145	+	0.470778i
$839$	−13.6197	−	50.8295i	−0.470205	−	1.75483i	−0.639030	−	0.769182i	$-0.720664\pi$
$839$	−13.6197	−	50.8295i	−0.470205	−	1.75483i	0.168825	−	0.985646i	$-0.446003\pi$
$840$	0.859322	−	2.20611i	0.0296494	−	0.0761180i
$841$	11.8995	−	20.6106i	0.410328	−	0.710709i
$842$		−	6.43171i		−	0.221651i
$843$	−3.63319	−	13.5592i	−0.125134	−	0.467005i
$844$	−7.10985	+	4.10487i	−0.244731	+	0.141296i
$845$	−0.0305954	+	11.6331i	−0.00105251	+	0.400190i
$846$			12.5710i			0.432199i
$847$	−32.0172	−	12.4713i	−1.10012	−	0.428519i
$848$	4.53418	+	7.85343i	0.155704	+	0.269688i
$849$	3.94428	−	2.27723i	0.135367	−	0.0781543i
$850$	−2.91566	+	10.8814i	−0.100006	+	0.373228i
$851$	37.0079	−	37.0079i	1.26861	−	1.26861i
$852$	−10.9973	−	2.94672i	−0.376762	−	0.100953i
$853$	4.49464	−	4.49464i	0.153893	−	0.153893i	−0.625961	−	0.779854i	$-0.715293\pi$
$853$	4.49464	−	4.49464i	0.153893	−	0.153893i	0.779854	+	0.625961i	$0.215293\pi$
$854$	33.5468	−	14.7387i	1.14795	−	0.504348i
$855$	−2.58870	+	1.49459i	−0.0885316	+	0.0511137i
$856$	−12.3497	−	12.3497i	−0.422106	−	0.422106i
$857$	8.72068	+	15.1047i	0.297893	+	0.515965i	0.975654	−	0.219317i	$-0.0703829\pi$
$857$	8.72068	+	15.1047i	0.297893	+	0.515965i	−0.677761	+	0.735282i	$0.737050\pi$
$858$	6.77915	−	16.3056i	0.231436	−	0.556665i
$859$	−15.0785	−	8.70560i	−0.514473	−	0.297031i	0.220197	−	0.975455i	$-0.429330\pi$
$859$	−15.0785	−	8.70560i	−0.514473	−	0.297031i	−0.734670	+	0.678424i	$0.762663\pi$
$860$	1.19246	−	4.45032i	0.0406625	−	0.151755i
$861$	7.19384	+	0.791903i	0.245166	+	0.0269880i
$862$	3.23126	+	1.86557i	0.110057	+	0.0635415i
$863$	−4.88165	−	18.2186i	−0.166173	−	0.620168i	−0.997888	−	0.0649637i	$-0.979307\pi$
$863$	−4.88165	−	18.2186i	−0.166173	−	0.620168i	0.831714	−	0.555204i	$-0.187360\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	−4.88731	−	4.88731i	−0.166174	−	0.166174i
$866$	−6.00165	−	22.3985i	−0.203944	−	0.761130i
$867$	−8.48981	−	4.90160i	−0.288329	−	0.166467i
$868$	−8.51981	−	19.3920i	−0.289181	−	0.658207i
$869$	8.32040	−	31.0522i	0.282250	−	1.05337i
$870$	1.76736	+	1.02039i	0.0599191	+	0.0345943i
$871$	38.2885	+	29.4599i	1.29736	+	0.998210i
$872$	4.35346	+	7.54042i	0.147427	+	0.255351i
$873$	−2.26865	−	2.26865i	−0.0767820	−	0.0767820i
$874$	−19.8299	+	11.4488i	−0.670755	+	0.387260i
$875$	−21.6490	−	2.38314i	−0.731870	−	0.0805647i
$876$	9.61885	−	9.61885i	0.324991	−	0.324991i
$877$	5.13889	+	1.37696i	0.173528	+	0.0464967i	0.344537	−	0.938773i	$-0.388036\pi$
$877$	5.13889	+	1.37696i	0.173528	+	0.0464967i	−0.171009	+	0.985270i	$0.554703\pi$
$878$	−2.01574	+	2.01574i	−0.0680279	+	0.0680279i
$879$	2.86889	−	10.7068i	0.0967652	−	0.361133i
$880$	3.79552	−	2.19134i	0.127947	−	0.0738701i
$881$	−4.23040	−	7.32727i	−0.142526	−	0.246862i	0.785921	−	0.618327i	$-0.212189\pi$
$881$	−4.23040	−	7.32727i	−0.142526	−	0.246862i	−0.928447	+	0.371464i	$0.878856\pi$
$882$	−3.23914	+	6.20548i	−0.109068	+	0.208949i
$883$			21.9493i			0.738654i	0.929299	+	0.369327i	$0.120412\pi$
$883$			21.9493i			0.738654i	−0.929299	+	0.369327i	$0.879588\pi$
$884$	−5.87819	−	7.68150i	−0.197705	−	0.258357i
$885$	−2.62321	+	1.51451i	−0.0881781	+	0.0509096i
$886$	−2.76404	−	10.3155i	−0.0928597	−	0.346557i
$887$			3.98008i			0.133638i	0.997765	+	0.0668190i	$0.0212850\pi$
$887$			3.98008i			0.133638i	−0.997765	+	0.0668190i	$0.978715\pi$
$888$	3.81758	−	6.61225i	0.128110	−	0.221893i
$889$	21.6777	+	8.44390i	0.727048	+	0.283199i
$890$	−2.35775	−	8.79926i	−0.0790321	−	0.294952i
$891$	−1.26761	+	4.73077i	−0.0424664	+	0.158487i
$892$	2.95575	+	0.791992i	0.0989659	+	0.0265178i
$893$	41.9921			1.40521
$894$	−17.3908			−0.581637
$895$	−11.5781	−	3.10235i	−0.387014	−	0.103700i
$896$	0.289497	−	2.62987i	0.00967142	−	0.0878576i
$897$	−3.19374	−	24.5079i	−0.106636	−	0.818294i
$898$	−7.78911	+	13.4911i	−0.259926	+	0.450205i
$899$	17.6353	−	4.72538i	0.588172	−	0.157600i
$900$	−2.09962	+	3.63664i	−0.0699873	+	0.121221i
$901$	−12.1638	−	21.0683i	−0.405234	−	0.701886i
$902$	9.47328	+	9.47328i	0.315426	+	0.315426i
$903$	−4.94423	+	12.6932i	−0.164534	+	0.422402i
$904$	−0.0190849	+	0.00511379i	−0.000634755	+	0.000170082i
$905$	3.71585	−	0.995658i	0.123519	−	0.0330968i
$906$		−	11.5023i		−	0.382138i
$907$	−14.0659	−	8.12097i	−0.467052	−	0.269652i	0.247953	−	0.968772i	$-0.420242\pi$
$907$	−14.0659	−	8.12097i	−0.467052	−	0.269652i	−0.715005	+	0.699120i	$0.753575\pi$
$908$	−8.78932	+	8.78932i	−0.291684	+	0.291684i
$909$	4.06070			0.134685
$910$	5.91454	−	6.15531i	0.196065	−	0.204047i
$911$	46.7757			1.54975			0.774874	−	0.632115i	$-0.217813\pi$
$911$	46.7757			1.54975			0.774874	+	0.632115i	$0.217813\pi$
$912$	−2.36202	+	2.36202i	−0.0782142	+	0.0782142i
$913$	−14.9881	−	8.65336i	−0.496032	−	0.286384i
$914$			17.5041i			0.578984i
$915$	11.9708	−	3.20757i	0.395743	−	0.106039i
$916$	13.2406	−	3.54780i	0.437480	−	0.117223i
$917$	−6.89749	−	44.9801i	−0.227775	−	1.48537i
$918$	1.89695	+	1.89695i	0.0626085	+	0.0626085i
$919$	−21.7203	−	37.6207i	−0.716488	−	1.24099i	−0.962383	−	0.271697i	$-0.912415\pi$
$919$	−21.7203	−	37.6207i	−0.716488	−	1.24099i	0.245895	−	0.969296i	$-0.420918\pi$
$920$	3.06700	−	5.31219i	0.101116	−	0.175138i
$921$	26.1070	−	6.99535i	0.860255	−	0.230505i
$922$	−13.8815	+	24.0434i	−0.457163	+	0.791829i
$923$	−32.5344	−	25.0325i	−1.07088	−	0.823956i
$924$	−11.8635	+	5.21218i	−0.390280	+	0.171468i
$925$	−30.9694	−	8.29822i	−1.01827	−	0.272844i
$926$	23.5395			0.773555
$927$	−8.44306			−0.277306
$928$	2.20285	+	0.590253i	0.0723122	+	0.0193760i
$929$	11.9054	−	44.4317i	0.390605	−	1.45776i	−0.438534	−	0.898714i	$-0.644502\pi$
$929$	11.9054	−	44.4317i	0.390605	−	1.45776i	0.829139	−	0.559042i	$-0.188831\pi$
$930$	−1.85416	−	6.91982i	−0.0608003	−	0.226910i
$931$	20.7288	+	10.8200i	0.679358	+	0.354612i
$932$	3.81433	−	6.60661i	0.124942	−	0.216407i
$933$		−	31.4616i		−	1.03001i
$934$	1.61420	+	6.02426i	0.0528181	+	0.197120i
$935$	−10.1822	+	5.87869i	−0.332993	+	0.192254i
$936$	−1.37540	−	3.33291i	−0.0449565	−	0.108939i
$937$			52.1974i			1.70522i	0.522552	+	0.852608i	$0.324980\pi$
$937$			52.1974i			1.70522i	−0.522552	+	0.852608i	$0.675020\pi$
$938$	−5.37331	−	35.0405i	−0.175445	−	1.14411i
$939$	0.213807	+	0.370324i	0.00697731	+	0.0120851i
$940$	−9.74210	+	5.62460i	−0.317752	+	0.183454i
$941$	−7.99441	+	29.8356i	−0.260610	+	0.972611i	0.704272	+	0.709930i	$0.251273\pi$
$941$	−7.99441	+	29.8356i	−0.260610	+	0.972611i	−0.964883	+	0.262681i	$0.915393\pi$
$942$	1.10033	−	1.10033i	0.0358508	−	0.0358508i
$943$	18.1118	+	4.85304i	0.589802	+	0.158037i
$944$	−2.39350	+	2.39350i	−0.0779019	+	0.0779019i
$945$	−1.40102	+	1.90853i	−0.0455753	+	0.0620845i
$946$	−21.8380	+	12.6082i	−0.710015	+	0.409928i
$947$	3.65318	+	3.65318i	0.118712	+	0.118712i	0.763967	−	0.645255i	$-0.223249\pi$
$947$	3.65318	+	3.65318i	0.118712	+	0.118712i	−0.645255	+	0.763967i	$0.723249\pi$
$948$	−3.28194	−	5.68448i	−0.106592	−	0.184623i
$949$	45.3379	−	18.7098i	1.47173	−	0.607345i
$950$	12.1478	+	7.01356i	0.394128	+	0.227550i
$951$	−4.08574	+	15.2482i	−0.132489	+	0.494456i
$952$	−0.776630	+	7.05510i	−0.0251707	+	0.228657i
$953$	33.2887	+	19.2192i	1.07833	+	0.622572i	0.930445	−	0.366432i	$-0.119421\pi$
$953$	33.2887	+	19.2192i	1.07833	+	0.622572i	0.147882	+	0.989005i	$0.452754\pi$
$954$	−2.34706	−	8.75936i	−0.0759890	−	0.283595i
$955$	5.06705	+	5.06705i	0.163966	+	0.163966i
$956$	−6.59105	−	6.59105i	−0.213170	−	0.213170i
$957$	−2.89085	−	10.7888i	−0.0934480	−	0.348753i
$958$	25.3703	+	14.6476i	0.819677	+	0.473241i
$959$	3.23524	−	29.3897i	0.104471	−	0.949043i
$960$	0.231605	−	0.864363i	0.00747503	−	0.0278972i
$961$	−28.6576	−	16.5455i	−0.924439	−	0.533725i
$962$	21.8622	−	16.7299i	0.704867	−	0.539392i
$963$	8.73259	+	15.1253i	0.281404	+	0.487406i
$964$	9.83659	+	9.83659i	0.316815	+	0.316815i
$965$	20.9199	−	12.0781i	0.673435	−	0.388808i
$966$	−10.7321	+	14.6196i	−0.345299	+	0.470380i
$967$	10.3011	−	10.3011i	0.331262	−	0.331262i	−0.521804	−	0.853066i	$-0.674741\pi$
$967$	10.3011	−	10.3011i	0.331262	−	0.331262i	0.853066	+	0.521804i	$0.174741\pi$
$968$	−12.5445	−	3.36128i	−0.403194	−	0.108036i
$969$	6.33655	−	6.33655i	0.203559	−	0.203559i
$970$	0.743071	−	2.77318i	0.0238586	−	0.0890414i
$971$	34.0715	−	19.6712i	1.09341	−	0.631278i	0.158924	−	0.987291i	$-0.449197\pi$
$971$	34.0715	−	19.6712i	1.09341	−	0.631278i	0.934481	+	0.356013i	$0.115864\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	1.09302	+	7.12782i	0.0350406	+	0.228507i
$974$			41.3807i			1.32592i
$975$	−12.0239	+	9.20118i	−0.385074	+	0.294674i
$976$	11.9938	−	6.92464i	0.383913	−	0.221652i
$977$	7.08437	+	26.4392i	0.226649	+	0.845866i	0.981737	+	0.190243i	$0.0609274\pi$
$977$	7.08437	+	26.4392i	0.226649	+	0.845866i	−0.755088	+	0.655623i	$0.772406\pi$
$978$			16.4144i			0.524873i
$979$	−24.9292	+	43.1786i	−0.796739	+	1.37999i
$980$	−6.25832	+	0.266270i	−0.199915	+	0.00850570i
$981$	−2.25352	−	8.41024i	−0.0719493	−	0.268518i
$982$	−4.86085	+	18.1410i	−0.155116	+	0.578901i
$983$	−17.7220	−	4.74860i	−0.565244	−	0.151457i	−0.0351296	−	0.999383i	$-0.511184\pi$
$983$	−17.7220	−	4.74860i	−0.565244	−	0.151457i	−0.530115	+	0.847926i	$0.677851\pi$
$984$	2.73544			0.0872027
$985$	1.33627			0.0425772
$986$	−5.90957	−	1.58346i	−0.188199	−	0.0504277i
$987$	30.4504	−	13.3783i	0.969248	−	0.425836i
$988$	−11.1332	+	4.59439i	−0.354195	+	0.146167i
$989$	−17.6464	+	30.5644i	−0.561122	+	0.971892i
$990$	−4.23335	+	1.13432i	−0.134545	+	0.0360511i
$991$	0.704940	−	1.22099i	0.0223932	−	0.0387861i	−0.854612	−	0.519268i	$-0.826205\pi$
$991$	0.704940	−	1.22099i	0.0223932	−	0.0387861i	0.877005	+	0.480482i	$0.159538\pi$
$992$	−4.00284	−	6.93313i	−0.127090	−	0.220127i
$993$	21.6657	+	21.6657i	0.687539	+	0.687539i
$994$	4.56579	+	29.7745i	0.144818	+	0.944390i
$995$	−1.51668	+	0.406394i	−0.0480820	+	0.0128835i
$996$	−3.41327	+	0.914583i	−0.108154	+	0.0289797i
$997$			25.0227i			0.792478i	0.918147	+	0.396239i	$0.129685\pi$
$997$			25.0227i			0.792478i	−0.918147	+	0.396239i	$0.870315\pi$
$998$	−20.7256	−	11.9659i	−0.656058	−	0.378775i
$999$	−5.39888	+	5.39888i	−0.170813	+	0.170813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.a.145.6	yes	32
7.3	odd	6		546.2.by.a.535.6	yes	32
13.7	odd	12		546.2.by.a.397.6	✓	32
91.59	even	12	inner	546.2.cg.a.241.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.397.6	✓	32	13.7	odd	12
546.2.by.a.535.6	yes	32	7.3	odd	6
546.2.cg.a.145.6	yes	32	1.1	even	1	trivial
546.2.cg.a.241.6	yes	32	91.59	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(-0.864363 + 0.231605i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-1.65489 - 2.06430i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(-0.864363 + 0.231605i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-1.65489 - 2.06430i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.447427 + 0.774967i) q^{10} +(4.73077 - 1.26761i) q^{11} +(0.500000 - 0.866025i) q^{12} +(2.86336 - 2.19116i) q^{13} +(-2.62987 - 0.289497i) q^{14} +(-0.864363 - 0.231605i) q^{15} -1.00000 q^{16} +2.68269 q^{17} +(0.965926 + 0.258819i) q^{18} +(0.864559 - 3.22658i) q^{19} +(0.231605 + 0.864363i) q^{20} +(-0.401026 - 2.61518i) q^{21} +(2.44883 - 4.24149i) q^{22} -6.85473i q^{23} +(-0.258819 - 0.965926i) q^{24} +(-3.63664 + 2.09962i) q^{25} +(0.475319 - 3.57408i) q^{26} +1.00000i q^{27} +(-2.06430 + 1.65489i) q^{28} +(-1.14028 - 1.97502i) q^{29} +(-0.774967 + 0.447427i) q^{30} +(-2.07202 + 7.73290i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.73077 + 1.26761i) q^{33} +(1.89695 - 1.89695i) q^{34} +(1.90853 + 1.40102i) q^{35} +(0.866025 - 0.500000i) q^{36} +(5.39888 + 5.39888i) q^{37} +(-1.67020 - 2.89287i) q^{38} +(3.57532 - 0.465918i) q^{39} +(0.774967 + 0.447427i) q^{40} +(-0.707984 + 2.64223i) q^{41} +(-2.13278 - 1.56564i) q^{42} +(-4.45888 - 2.57433i) q^{43} +(-1.26761 - 4.73077i) q^{44} +(-0.632758 - 0.632758i) q^{45} +(-4.84703 - 4.84703i) q^{46} +(3.25361 + 12.1426i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-1.52268 + 6.83238i) q^{49} +(-1.08684 + 4.05615i) q^{50} +(2.32327 + 1.34134i) q^{51} +(-2.19116 - 2.86336i) q^{52} +(-4.53418 - 7.85343i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-3.79552 + 2.19134i) q^{55} +(-0.289497 + 2.62987i) q^{56} +(2.36202 - 2.36202i) q^{57} +(-2.20285 - 0.590253i) q^{58} +(2.39350 - 2.39350i) q^{59} +(-0.231605 + 0.864363i) q^{60} +(-11.9938 + 6.92464i) q^{61} +(4.00284 + 6.93313i) q^{62} +(0.960292 - 2.46533i) q^{63} +1.00000i q^{64} +(-1.96750 + 2.55713i) q^{65} +(4.24149 - 2.44883i) q^{66} +(3.46789 + 12.9423i) q^{67} -2.68269i q^{68} +(3.42737 - 5.93637i) q^{69} +(2.34021 - 0.358860i) q^{70} +(-2.94672 - 10.9973i) q^{71} +(0.258819 - 0.965926i) q^{72} +(13.1396 + 3.52074i) q^{73} +7.63517 q^{74} -4.19924 q^{75} +(-3.22658 - 0.864559i) q^{76} +(-10.4456 - 7.66798i) q^{77} +(2.19868 - 2.85759i) q^{78} +(3.28194 - 5.68448i) q^{79} +(0.864363 - 0.231605i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.36772 + 2.36896i) q^{82} +(-2.49869 - 2.49869i) q^{83} +(-2.61518 + 0.401026i) q^{84} +(-2.31882 + 0.621325i) q^{85} +(-4.97323 + 1.33257i) q^{86} -2.28056i q^{87} +(-4.24149 - 2.44883i) q^{88} +(-7.19838 + 7.19838i) q^{89} -0.894855 q^{90} +(-9.26175 - 2.28471i) q^{91} -6.85473 q^{92} +(-5.66087 + 5.66087i) q^{93} +(10.8868 + 6.28549i) q^{94} +2.98917i q^{95} +(-0.965926 + 0.258819i) q^{96} +(-3.09903 + 0.830382i) q^{97} +(3.75453 + 5.90792i) q^{98} +(3.46316 + 3.46316i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7} + 16 q^{9}+O(q^{10}) \) 32 * q - 4 * q^7 + 16 * q^9	\( 32 q - 4 q^{7} + 16 q^{9} + 8 q^{11} + 16 q^{12} + 4 q^{14} - 32 q^{16} - 16 q^{17} + 24 q^{19} + 8 q^{21} - 4 q^{22} + 24 q^{25} - 8 q^{26} + 8 q^{28} - 12 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} + 40 q^{35} - 12 q^{37} - 8 q^{38} + 28 q^{39} + 28 q^{41} - 12 q^{42} + 84 q^{43} - 4 q^{44} - 40 q^{46} - 4 q^{47} - 36 q^{49} - 16 q^{50} - 20 q^{52} - 4 q^{53} - 48 q^{55} + 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{59} - 36 q^{61} + 40 q^{62} + 4 q^{63} + 44 q^{65} - 16 q^{67} + 8 q^{69} + 40 q^{70} + 20 q^{71} - 16 q^{73} - 40 q^{74} + 16 q^{75} - 36 q^{76} + 12 q^{77} - 20 q^{78} - 16 q^{81} - 24 q^{82} - 12 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 60 q^{89} - 48 q^{91} - 16 q^{92} - 32 q^{93} - 76 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 16 * q^9 + 8 * q^11 + 16 * q^12 + 4 * q^14 - 32 * q^16 - 16 * q^17 + 24 * q^19 + 8 * q^21 - 4 * q^22 + 24 * q^25 - 8 * q^26 + 8 * q^28 - 12 * q^29 + 4 * q^31 + 8 * q^33 + 8 * q^34 + 40 * q^35 - 12 * q^37 - 8 * q^38 + 28 * q^39 + 28 * q^41 - 12 * q^42 + 84 * q^43 - 4 * q^44 - 40 * q^46 - 4 * q^47 - 36 * q^49 - 16 * q^50 - 20 * q^52 - 4 * q^53 - 48 * q^55 + 12 * q^56 + 12 * q^57 + 12 * q^58 - 24 * q^59 - 36 * q^61 + 40 * q^62 + 4 * q^63 + 44 * q^65 - 16 * q^67 + 8 * q^69 + 40 * q^70 + 20 * q^71 - 16 * q^73 - 40 * q^74 + 16 * q^75 - 36 * q^76 + 12 * q^77 - 20 * q^78 - 16 * q^81 - 24 * q^82 - 12 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 60 * q^89 - 48 * q^91 - 16 * q^92 - 32 * q^93 - 76 * q^97 - 8 * q^98 + 4 * q^99

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