LMFDB - Embedded newform 546.2.bm.a.205.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(205,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("546.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26x^{14} + 249x^{12} + 1144x^{10} + 2766x^{8} + 3554x^{6} + 2260x^{4} + 564x^{2} + 9 $ x^16 + 26x^14 + 249x^12 + 1144x^10 + 2766x^8 + 3554x^6 + 2260x^4 + 564*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.6
Root			$-2.54804i$ of defining polynomial
Character	$\chi$	$=$	546.205
Dual form			546.2.bm.a.277.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-0.825077 - 0.476358i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.63278 + 0.261643i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-0.825077 - 0.476358i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.63278 + 0.261643i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.476358 - 0.825077i) q^{10} +(0.0637835 + 0.0368254i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-3.60135 + 0.173988i) q^{13} +(-0.261643 - 2.63278i) q^{14} +(-0.825077 + 0.476358i) q^{15} +1.00000 q^{16} -2.20006 q^{17} +(0.866025 - 0.500000i) q^{18} +(-0.747223 + 0.431409i) q^{19} +(0.825077 + 0.476358i) q^{20} +(-1.08980 + 2.41088i) q^{21} +(-0.0368254 + 0.0637835i) q^{22} -8.03109 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-2.04617 - 3.54406i) q^{25} +(-0.173988 - 3.60135i) q^{26} -1.00000 q^{27} +(2.63278 - 0.261643i) q^{28} +(-2.36853 - 4.10241i) q^{29} +(-0.476358 - 0.825077i) q^{30} +(8.72813 - 5.03919i) q^{31} +1.00000i q^{32} +(0.0637835 - 0.0368254i) q^{33} -2.20006i q^{34} +(2.29688 + 1.03827i) q^{35} +(0.500000 + 0.866025i) q^{36} +11.2779i q^{37} +(-0.431409 - 0.747223i) q^{38} +(-1.65000 + 3.20586i) q^{39} +(-0.476358 + 0.825077i) q^{40} +(-5.80786 + 3.35317i) q^{41} +(-2.41088 - 1.08980i) q^{42} +(-1.23939 + 2.14669i) q^{43} +(-0.0637835 - 0.0368254i) q^{44} +0.952717i q^{45} -8.03109i q^{46} +(-8.12115 - 4.68875i) q^{47} +(0.500000 - 0.866025i) q^{48} +(6.86309 - 1.37770i) q^{49} +(3.54406 - 2.04617i) q^{50} +(-1.10003 + 1.90531i) q^{51} +(3.60135 - 0.173988i) q^{52} +(0.935404 + 1.62017i) q^{53} -1.00000i q^{54} +(-0.0350842 - 0.0607676i) q^{55} +(0.261643 + 2.63278i) q^{56} +0.862818i q^{57} +(4.10241 - 2.36853i) q^{58} -13.5969i q^{59} +(0.825077 - 0.476358i) q^{60} +(-1.78571 - 3.09294i) q^{61} +(5.03919 + 8.72813i) q^{62} +(1.54298 + 2.14923i) q^{63} -1.00000 q^{64} +(3.05427 + 1.57198i) q^{65} +(0.0368254 + 0.0637835i) q^{66} +(10.5789 + 6.10772i) q^{67} +2.20006 q^{68} +(-4.01555 + 6.95513i) q^{69} +(-1.03827 + 2.29688i) q^{70} +(8.96491 + 5.17589i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(6.76210 - 3.90410i) q^{73} -11.2779 q^{74} -4.09233 q^{75} +(0.747223 - 0.431409i) q^{76} +(-0.177563 - 0.0802648i) q^{77} +(-3.20586 - 1.65000i) q^{78} +(-1.30072 + 2.25291i) q^{79} +(-0.825077 - 0.476358i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.35317 - 5.80786i) q^{82} -11.8771i q^{83} +(1.08980 - 2.41088i) q^{84} +(1.81522 + 1.04802i) q^{85} +(-2.14669 - 1.23939i) q^{86} -4.73706 q^{87} +(0.0368254 - 0.0637835i) q^{88} +3.63181i q^{89} -0.952717 q^{90} +(9.43605 - 1.40034i) q^{91} +8.03109 q^{92} -10.0784i q^{93} +(4.68875 - 8.12115i) q^{94} +0.822022 q^{95} +(0.866025 + 0.500000i) q^{96} +(11.1324 + 6.42728i) q^{97} +(1.37770 + 6.86309i) q^{98} -0.0736508i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9} + 4 q^{10} + 6 q^{11} - 8 q^{12} - 10 q^{13} + 4 q^{14} + 16 q^{16} + 18 q^{19} + 8 q^{21} + 6 q^{22} + 32 q^{23} - 4 q^{26} - 16 q^{27} + 2 q^{28} - 4 q^{29} - 4 q^{30} - 12 q^{31} + 6 q^{33} - 2 q^{35} + 8 q^{36} - 2 q^{38} - 14 q^{39} - 4 q^{40} - 18 q^{41} + 2 q^{42} - 32 q^{43} - 6 q^{44} - 66 q^{47} + 8 q^{48} + 22 q^{49} + 36 q^{50} + 10 q^{52} + 2 q^{53} + 16 q^{55} - 4 q^{56} + 24 q^{58} + 4 q^{61} + 4 q^{62} + 10 q^{63} - 16 q^{64} + 38 q^{65} - 6 q^{66} + 36 q^{67} + 16 q^{69} + 6 q^{70} - 30 q^{71} + 18 q^{73} - 12 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 6 q^{82} - 8 q^{84} + 72 q^{85} - 8 q^{87} - 6 q^{88} - 8 q^{90} - 2 q^{91} - 32 q^{92} - 24 q^{94} + 80 q^{95} - 6 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9 + 4 * q^10 + 6 * q^11 - 8 * q^12 - 10 * q^13 + 4 * q^14 + 16 * q^16 + 18 * q^19 + 8 * q^21 + 6 * q^22 + 32 * q^23 - 4 * q^26 - 16 * q^27 + 2 * q^28 - 4 * q^29 - 4 * q^30 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 8 * q^36 - 2 * q^38 - 14 * q^39 - 4 * q^40 - 18 * q^41 + 2 * q^42 - 32 * q^43 - 6 * q^44 - 66 * q^47 + 8 * q^48 + 22 * q^49 + 36 * q^50 + 10 * q^52 + 2 * q^53 + 16 * q^55 - 4 * q^56 + 24 * q^58 + 4 * q^61 + 4 * q^62 + 10 * q^63 - 16 * q^64 + 38 * q^65 - 6 * q^66 + 36 * q^67 + 16 * q^69 + 6 * q^70 - 30 * q^71 + 18 * q^73 - 12 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 6 * q^82 - 8 * q^84 + 72 * q^85 - 8 * q^87 - 6 * q^88 - 8 * q^90 - 2 * q^91 - 32 * q^92 - 24 * q^94 + 80 * q^95 - 6 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.00000			−0.500000
$5$	−0.825077	−	0.476358i	−0.368986	−	0.213034i	0.304030	−	0.952663i	$-0.401668\pi$
$5$	−0.825077	−	0.476358i	−0.368986	−	0.213034i	−0.673015	+	0.739629i	$0.735001\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−2.63278	+	0.261643i	−0.995098	+	0.0988918i
$7$	−2.63278	+	0.261643i	−0.995098	+	0.0988918i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.476358	−	0.825077i	0.150638	−	0.260912i
$11$	0.0637835	+	0.0368254i	0.0192314	+	0.0111033i	0.509585	−	0.860420i	$-0.329799\pi$
$11$	0.0637835	+	0.0368254i	0.0192314	+	0.0111033i	−0.490353	+	0.871524i	$0.663132\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−3.60135	+	0.173988i	−0.998835	+	0.0482557i
$13$	−3.60135	+	0.173988i	−0.998835	+	0.0482557i
$14$	−0.261643	−	2.63278i	−0.0699270	−	0.703641i
$15$	−0.825077	+	0.476358i	−0.213034	+	0.122995i
$16$	1.00000			0.250000
$17$	−2.20006			−0.533594			−0.266797	−	0.963753i	$-0.585965\pi$
$17$	−2.20006			−0.533594			−0.266797	+	0.963753i	$0.585965\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−0.747223	+	0.431409i	−0.171425	+	0.0989721i	−0.583257	−	0.812287i	$-0.698222\pi$
$19$	−0.747223	+	0.431409i	−0.171425	+	0.0989721i	0.411833	+	0.911259i	$0.364889\pi$
$20$	0.825077	+	0.476358i	0.184493	+	0.106517i
$21$	−1.08980	+	2.41088i	−0.237814	+	0.526097i
$22$	−0.0368254	+	0.0637835i	−0.00785121	+	0.0135987i
$23$	−8.03109			−1.67460			−0.837299	−	0.546745i	$-0.815867\pi$
$23$	−8.03109			−1.67460			−0.837299	+	0.546745i	$0.815867\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−2.04617	−	3.54406i	−0.409233	−	0.708812i
$26$	−0.173988	−	3.60135i	−0.0341219	−	0.706283i
$27$	−1.00000			−0.192450
$28$	2.63278	−	0.261643i	0.497549	−	0.0494459i
$29$	−2.36853	−	4.10241i	−0.439825	−	0.761799i	0.557851	−	0.829941i	$-0.311626\pi$
$29$	−2.36853	−	4.10241i	−0.439825	−	0.761799i	−0.997676	+	0.0681421i	$0.978293\pi$
$30$	−0.476358	−	0.825077i	−0.0869708	−	0.150638i
$31$	8.72813	−	5.03919i	1.56762	−	0.905065i	0.571172	−	0.820830i	$-0.306489\pi$
$31$	8.72813	−	5.03919i	1.56762	−	0.905065i	0.996446	−	0.0842343i	$-0.0268444\pi$
$32$			1.00000i			0.176777i
$33$	0.0637835	−	0.0368254i	0.0111033	−	0.00641048i
$34$		−	2.20006i		−	0.377308i
$35$	2.29688	+	1.03827i	0.388244	+	0.175500i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$			11.2779i			1.85407i	0.374972	+	0.927036i	$0.377652\pi$
$37$			11.2779i			1.85407i	−0.374972	+	0.927036i	$0.622348\pi$
$38$	−0.431409	−	0.747223i	−0.0699838	−	0.121216i
$39$	−1.65000	+	3.20586i	−0.264211	+	0.513348i
$40$	−0.476358	+	0.825077i	−0.0753189	+	0.130456i
$41$	−5.80786	+	3.35317i	−0.907036	+	0.523677i	−0.879476	−	0.475943i	$-0.842107\pi$
$41$	−5.80786	+	3.35317i	−0.907036	+	0.523677i	−0.0275595	+	0.999620i	$0.508774\pi$
$42$	−2.41088	−	1.08980i	−0.372007	−	0.168160i
$43$	−1.23939	+	2.14669i	−0.189005	+	0.327367i	−0.944919	−	0.327305i	$-0.893860\pi$
$43$	−1.23939	+	2.14669i	−0.189005	+	0.327367i	0.755914	+	0.654671i	$0.227193\pi$
$44$	−0.0637835	−	0.0368254i	−0.00961572	−	0.00555164i
$45$			0.952717i			0.142023i
$46$		−	8.03109i		−	1.18412i
$47$	−8.12115	−	4.68875i	−1.18459	−	0.683924i	−0.227519	−	0.973774i	$-0.573061\pi$
$47$	−8.12115	−	4.68875i	−1.18459	−	0.683924i	−0.957072	+	0.289849i	$0.906395\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	6.86309	−	1.37770i	0.980441	−	0.196814i
$50$	3.54406	−	2.04617i	0.501206	−	0.289371i
$51$	−1.10003	+	1.90531i	−0.154035	+	0.266797i
$52$	3.60135	−	0.173988i	0.499418	−	0.0241278i
$53$	0.935404	+	1.62017i	0.128488	+	0.222547i	0.923091	−	0.384582i	$-0.125654\pi$
$53$	0.935404	+	1.62017i	0.128488	+	0.222547i	−0.794603	+	0.607129i	$0.792321\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−0.0350842	−	0.0607676i	−0.00473075	−	0.00819390i
$56$	0.261643	+	2.63278i	0.0349635	+	0.351820i
$57$			0.862818i			0.114283i
$58$	4.10241	−	2.36853i	0.538673	−	0.311003i
$59$		−	13.5969i		−	1.77017i	−0.465434	−	0.885083i	$-0.654102\pi$
$59$		−	13.5969i		−	1.77017i	0.465434	−	0.885083i	$-0.345898\pi$
$60$	0.825077	−	0.476358i	0.106517	−	0.0614976i
$61$	−1.78571	−	3.09294i	−0.228637	−	0.396011i	0.728768	−	0.684761i	$-0.240093\pi$
$61$	−1.78571	−	3.09294i	−0.228637	−	0.396011i	−0.957404	+	0.288751i	$0.906760\pi$
$62$	5.03919	+	8.72813i	0.639977	+	1.10847i
$63$	1.54298	+	2.14923i	0.194397	+	0.270778i
$64$	−1.00000			−0.125000
$65$	3.05427	+	1.57198i	0.378836	+	0.194980i
$66$	0.0368254	+	0.0637835i	0.00453290	+	0.00785121i
$67$	10.5789	+	6.10772i	1.29242	+	0.746177i	0.979082	−	0.203466i	$-0.0652206\pi$
$67$	10.5789	+	6.10772i	1.29242	+	0.746177i	0.313334	+	0.949643i	$0.398554\pi$
$68$	2.20006			0.266797
$69$	−4.01555	+	6.95513i	−0.483415	+	0.837299i
$70$	−1.03827	+	2.29688i	−0.124097	+	0.274530i
$71$	8.96491	+	5.17589i	1.06394	+	0.614265i	0.926519	−	0.376248i	$-0.122786\pi$
$71$	8.96491	+	5.17589i	1.06394	+	0.614265i	0.137420	+	0.990513i	$0.456119\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	6.76210	−	3.90410i	0.791444	−	0.456941i	−0.0490264	−	0.998797i	$-0.515612\pi$
$73$	6.76210	−	3.90410i	0.791444	−	0.456941i	0.840471	+	0.541857i	$0.182279\pi$
$74$	−11.2779			−1.31103
$75$	−4.09233			−0.472542
$76$	0.747223	−	0.431409i	0.0857123	−	0.0494860i
$77$	−0.177563	−	0.0802648i	−0.0202352	−	0.00914702i
$78$	−3.20586	−	1.65000i	−0.362992	−	0.186825i
$79$	−1.30072	+	2.25291i	−0.146342	+	0.253472i	−0.929873	−	0.367881i	$-0.880083\pi$
$79$	−1.30072	+	2.25291i	−0.146342	+	0.253472i	0.783531	+	0.621353i	$0.213417\pi$
$80$	−0.825077	−	0.476358i	−0.0922464	−	0.0532585i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.35317	−	5.80786i	−0.370296	−	0.641371i
$83$		−	11.8771i		−	1.30368i	−0.758355	−	0.651842i	$-0.773997\pi$
$83$		−	11.8771i		−	1.30368i	0.758355	−	0.651842i	$-0.226003\pi$
$84$	1.08980	−	2.41088i	0.118907	−	0.263048i
$85$	1.81522	+	1.04802i	0.196889	+	0.113674i
$86$	−2.14669	−	1.23939i	−0.231483	−	0.133647i
$87$	−4.73706			−0.507866
$88$	0.0368254	−	0.0637835i	0.00392560	−	0.00679934i
$89$			3.63181i			0.384971i	0.981300	+	0.192485i	$0.0616548\pi$
$89$			3.63181i			0.384971i	−0.981300	+	0.192485i	$0.938345\pi$
$90$	−0.952717			−0.100425
$91$	9.43605	−	1.40034i	0.989167	−	0.146796i
$92$	8.03109			0.837299
$93$		−	10.0784i		−	1.04508i
$94$	4.68875	−	8.12115i	0.483607	−	0.837633i
$95$	0.822022			0.0843376
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	11.1324	+	6.42728i	1.13032	+	0.652592i	0.944016	−	0.329900i	$-0.107015\pi$
$97$	11.1324	+	6.42728i	1.13032	+	0.652592i	0.186306	+	0.982492i	$0.440348\pi$
$98$	1.37770	+	6.86309i	0.139169	+	0.693276i
$99$		−	0.0736508i		−	0.00740219i
$100$	2.04617	+	3.54406i	0.204617	+	0.354406i
$101$	−1.70367	+	2.95085i	−0.169522	+	0.293620i	−0.938252	−	0.345953i	$-0.887556\pi$
$101$	−1.70367	+	2.95085i	−0.169522	+	0.293620i	0.768730	+	0.639573i	$0.220889\pi$
$102$	−1.90531	−	1.10003i	−0.188654	−	0.108919i
$103$	−1.18228	+	2.04778i	−0.116494	+	0.201773i	−0.918376	−	0.395709i	$-0.870499\pi$
$103$	−1.18228	+	2.04778i	−0.116494	+	0.201773i	0.801882	+	0.597482i	$0.203832\pi$
$104$	0.173988	+	3.60135i	0.0170610	+	0.353142i
$105$	2.04761	−	1.47002i	0.199827	−	0.143460i
$106$	−1.62017	+	0.935404i	−0.157365	+	0.0908545i
$107$	−9.50398			−0.918785			−0.459392	−	0.888233i	$-0.651933\pi$
$107$	−9.50398			−0.918785			−0.459392	+	0.888233i	$0.651933\pi$
$108$	1.00000			0.0962250
$109$	−6.69452	+	3.86508i	−0.641219	+	0.370208i	−0.785084	−	0.619389i	$-0.787380\pi$
$109$	−6.69452	+	3.86508i	−0.641219	+	0.370208i	0.143865	+	0.989597i	$0.454047\pi$
$110$	0.0607676	−	0.0350842i	0.00579396	−	0.00334515i
$111$	9.76693	+	5.63894i	0.927036	+	0.535224i
$112$	−2.63278	+	0.261643i	−0.248775	+	0.0247229i
$113$	−3.70956	+	6.42514i	−0.348966	+	0.604426i	−0.986066	−	0.166355i	$-0.946800\pi$
$113$	−3.70956	+	6.42514i	−0.348966	+	0.604426i	0.637100	+	0.770781i	$0.280134\pi$
$114$	−0.862818			−0.0808104
$115$	6.62627	+	3.82568i	0.617903	+	0.356746i
$116$	2.36853	+	4.10241i	0.219913	+	0.380900i
$117$	1.95135	+	3.03187i	0.180403	+	0.280296i
$118$	13.5969			1.25170
$119$	5.79229	−	0.575631i	0.530978	−	0.0527680i
$120$	0.476358	+	0.825077i	0.0434854	+	0.0753189i
$121$	−5.49729	−	9.52158i	−0.499753	−	0.865598i
$122$	3.09294	−	1.78571i	0.280022	−	0.161671i
$123$			6.70634i			0.604690i
$124$	−8.72813	+	5.03919i	−0.783809	+	0.452532i
$125$			8.66242i			0.774790i
$126$	−2.14923	+	1.54298i	−0.191469	+	0.137460i
$127$	−2.83564	−	4.91147i	−0.251622	−	0.435823i	0.712350	−	0.701824i	$-0.247631\pi$
$127$	−2.83564	−	4.91147i	−0.251622	−	0.435823i	−0.963973	+	0.266001i	$0.914297\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.23939	+	2.14669i	0.109122	+	0.189005i
$130$	−1.57198	+	3.05427i	−0.137872	+	0.267877i
$131$	10.8146	−	18.7315i	0.944877	−	1.63658i	0.188881	−	0.982000i	$-0.439514\pi$
$131$	10.8146	−	18.7315i	0.944877	−	1.63658i	0.755996	−	0.654576i	$-0.227153\pi$
$132$	−0.0637835	+	0.0368254i	−0.00555164	+	0.00320524i
$133$	1.85440	−	1.33131i	0.160797	−	0.115439i
$134$	−6.10772	+	10.5789i	−0.527627	+	0.913876i
$135$	0.825077	+	0.476358i	0.0710113	+	0.0409984i
$136$			2.20006i			0.188654i
$137$			20.2972i			1.73411i	0.498213	+	0.867054i	$0.333990\pi$
$137$			20.2972i			1.73411i	−0.498213	+	0.867054i	$0.666010\pi$
$138$	−6.95513	−	4.01555i	−0.592060	−	0.341826i
$139$	−0.0743508	+	0.128779i	−0.00630635	+	0.0109229i	−0.869161	−	0.494529i	$-0.835341\pi$
$139$	−0.0743508	+	0.128779i	−0.00630635	+	0.0109229i	0.862855	+	0.505452i	$0.168674\pi$
$140$	−2.29688	−	1.03827i	−0.194122	−	0.0877500i
$141$	−8.12115	+	4.68875i	−0.683924	+	0.394864i
$142$	−5.17589	+	8.96491i	−0.434351	+	0.752318i
$143$	−0.236114	−	0.121524i	−0.0197448	−	0.0101623i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$			4.51308i			0.374791i
$146$	3.90410	+	6.76210i	0.323106	+	0.559636i
$147$	2.23842	−	6.63246i	0.184622	−	0.547036i
$148$		−	11.2779i		−	0.927036i
$149$	−10.2125	+	5.89618i	−0.836639	+	0.483034i	−0.856120	−	0.516777i	$-0.827132\pi$
$149$	−10.2125	+	5.89618i	−0.836639	+	0.483034i	0.0194815	+	0.999810i	$0.493798\pi$
$150$		−	4.09233i		−	0.334137i
$151$	−13.7500	+	7.93859i	−1.11896	+	0.646033i	−0.941136	−	0.338028i	$-0.890240\pi$
$151$	−13.7500	+	7.93859i	−1.11896	+	0.646033i	−0.177827	+	0.984062i	$0.556907\pi$
$152$	0.431409	+	0.747223i	0.0349919	+	0.0606078i
$153$	1.10003	+	1.90531i	0.0889323	+	0.154035i
$154$	0.0802648	−	0.177563i	0.00646792	−	0.0143084i
$155$	−9.60184			−0.771238
$156$	1.65000	−	3.20586i	0.132106	−	0.256674i
$157$	−3.46211	−	5.99655i	−0.276307	−	0.478577i	0.694157	−	0.719823i	$-0.255777\pi$
$157$	−3.46211	−	5.99655i	−0.276307	−	0.478577i	−0.970464	+	0.241246i	$0.922444\pi$
$158$	−2.25291	−	1.30072i	−0.179232	−	0.103480i
$159$	1.87081			0.148365
$160$	0.476358	−	0.825077i	0.0376594	−	0.0652281i
$161$	21.1441	−	2.10128i	1.66639	−	0.165604i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	7.10668	−	4.10304i	0.556638	−	0.321375i	−0.195157	−	0.980772i	$-0.562522\pi$
$163$	7.10668	−	4.10304i	0.556638	−	0.321375i	0.751795	+	0.659397i	$0.229188\pi$
$164$	5.80786	−	3.35317i	0.453518	−	0.261839i
$165$	−0.0701684			−0.00546260
$166$	11.8771			0.921844
$167$	−15.4171	+	8.90108i	−1.19301	+	0.688786i	−0.958989	−	0.283445i	$-0.908523\pi$
$167$	−15.4171	+	8.90108i	−1.19301	+	0.688786i	−0.234024	+	0.972231i	$0.575189\pi$
$168$	2.41088	+	1.08980i	0.186003	+	0.0840800i
$169$	12.9395	−	1.25319i	0.995343	−	0.0963989i
$170$	−1.04802	+	1.81522i	−0.0803794	+	0.139221i
$171$	0.747223	+	0.431409i	0.0571415	+	0.0329907i
$172$	1.23939	−	2.14669i	0.0945027	−	0.163683i
$173$	1.38516	+	2.39917i	0.105312	+	0.182405i	0.913866	−	0.406017i	$-0.133083\pi$
$173$	1.38516	+	2.39917i	0.105312	+	0.182405i	−0.808554	+	0.588422i	$0.799749\pi$
$174$		−	4.73706i		−	0.359116i
$175$	6.31439	+	8.79538i	0.477323	+	0.664868i
$176$	0.0637835	+	0.0368254i	0.00480786	+	0.00277582i
$177$	−11.7753	−	6.79845i	−0.885083	−	0.511003i
$178$	−3.63181			−0.272216
$179$	−0.380717	+	0.659422i	−0.0284561	+	0.0492875i	−0.879903	−	0.475154i	$-0.842392\pi$
$179$	−0.380717	+	0.659422i	−0.0284561	+	0.0492875i	0.851447	+	0.524441i	$0.175726\pi$
$180$		−	0.952717i		−	0.0710113i
$181$	−15.0250			−1.11680			−0.558399	−	0.829573i	$-0.688584\pi$
$181$	−15.0250			−1.11680			−0.558399	+	0.829573i	$0.688584\pi$
$182$	1.40034	+	9.43605i	0.103800	+	0.699447i
$183$	−3.57142			−0.264007
$184$			8.03109i			0.592060i
$185$	5.37231	−	9.30512i	0.394980	−	0.684126i
$186$	10.0784			0.738982
$187$	−0.140328	−	0.0810183i	−0.0102618	−	0.00592464i
$188$	8.12115	+	4.68875i	0.592296	+	0.341962i
$189$	2.63278	−	0.261643i	0.191507	−	0.0190317i
$190$			0.822022i			0.0596357i
$191$	−2.93733	−	5.08760i	−0.212538	−	0.368126i	0.739970	−	0.672639i	$-0.234839\pi$
$191$	−2.93733	−	5.08760i	−0.212538	−	0.368126i	−0.952508	+	0.304513i	$0.901506\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−10.5808	−	6.10882i	−0.761622	−	0.439723i	0.0682556	−	0.997668i	$-0.478257\pi$
$193$	−10.5808	−	6.10882i	−0.761622	−	0.439723i	−0.829878	+	0.557945i	$0.811590\pi$
$194$	−6.42728	+	11.1324i	−0.461452	+	0.799258i
$195$	2.88851	−	1.85909i	0.206851	−	0.133132i
$196$	−6.86309	+	1.37770i	−0.490220	+	0.0984070i
$197$	11.5921	−	6.69271i	0.825904	−	0.476836i	−0.0265438	−	0.999648i	$-0.508450\pi$
$197$	11.5921	−	6.69271i	0.825904	−	0.476836i	0.852448	+	0.522811i	$0.175117\pi$
$198$	0.0736508			0.00523414
$199$	0.537059			0.0380711			0.0190355	−	0.999819i	$-0.493940\pi$
$199$	0.537059			0.0380711			0.0190355	+	0.999819i	$0.493940\pi$
$200$	−3.54406	+	2.04617i	−0.250603	+	0.144686i
$201$	10.5789	−	6.10772i	0.746177	−	0.430805i
$202$	−2.95085	−	1.70367i	−0.207621	−	0.119870i
$203$	7.30919	+	10.1811i	0.513005	+	0.714570i
$204$	1.10003	−	1.90531i	0.0770177	−	0.133398i
$205$	6.38924			0.446244
$206$	−2.04778	−	1.18228i	−0.142675	−	0.0823737i
$207$	4.01555	+	6.95513i	0.279100	+	0.483415i
$208$	−3.60135	+	0.173988i	−0.249709	+	0.0120639i
$209$	−0.0635473			−0.00439566
$210$	1.47002	+	2.04761i	0.101441	+	0.141299i
$211$	−3.36821	−	5.83390i	−0.231877	−	0.401622i	0.726484	−	0.687184i	$-0.241153\pi$
$211$	−3.36821	−	5.83390i	−0.231877	−	0.401622i	−0.958360	+	0.285561i	$0.907820\pi$
$212$	−0.935404	−	1.62017i	−0.0642438	−	0.111274i
$213$	8.96491	−	5.17589i	0.614265	−	0.354646i
$214$		−	9.50398i		−	0.649679i
$215$	2.04519	−	1.18079i	0.139481	−	0.0805291i
$216$			1.00000i			0.0680414i
$217$	−21.6608	+	15.5507i	−1.47043	+	1.05565i
$218$	−3.86508	−	6.69452i	−0.261777	−	0.453410i
$219$		−	7.80821i		−	0.527630i
$220$	0.0350842	+	0.0607676i	0.00236538	+	0.00409695i
$221$	7.92320	−	0.382785i	0.532972	−	0.0257489i
$222$	−5.63894	+	9.76693i	−0.378461	+	0.655513i
$223$	22.0208	−	12.7137i	1.47462	−	0.851372i	0.475029	−	0.879970i	$-0.342438\pi$
$223$	22.0208	−	12.7137i	1.47462	−	0.851372i	0.999591	+	0.0285982i	$0.00910434\pi$
$224$	−0.261643	−	2.63278i	−0.0174818	−	0.175910i
$225$	−2.04617	+	3.54406i	−0.136411	+	0.236271i
$226$	−6.42514	−	3.70956i	−0.427394	−	0.246756i
$227$		−	3.40559i		−	0.226037i	−0.993593	−	0.113018i	$-0.963948\pi$
$227$		−	3.40559i		−	0.226037i	0.993593	−	0.113018i	$-0.0360519\pi$
$228$		−	0.862818i		−	0.0571415i
$229$	−0.991069	−	0.572194i	−0.0654917	−	0.0378117i	0.466897	−	0.884312i	$-0.345372\pi$
$229$	−0.991069	−	0.572194i	−0.0654917	−	0.0378117i	−0.532388	+	0.846500i	$0.678705\pi$
$230$	−3.82568	+	6.62627i	−0.252258	+	0.436923i
$231$	−0.158293	+	0.113642i	−0.0104149	+	0.00747708i
$232$	−4.10241	+	2.36853i	−0.269337	+	0.155502i
$233$	1.67391	−	2.89929i	0.109661	−	0.189939i	−0.805972	−	0.591954i	$-0.798357\pi$
$233$	1.67391	−	2.89929i	0.109661	−	0.189939i	0.915633	+	0.402015i	$0.131690\pi$
$234$	−3.03187	+	1.95135i	−0.198199	+	0.127564i
$235$	4.46705	+	7.73716i	0.291398	+	0.504716i
$236$			13.5969i			0.885083i
$237$	1.30072	+	2.25291i	0.0844908	+	0.146342i
$238$	0.575631	+	5.79229i	0.0373126	+	0.375458i
$239$		−	28.9640i		−	1.87352i	−0.349968	−	0.936762i	$-0.613808\pi$
$239$		−	28.9640i		−	1.87352i	0.349968	−	0.936762i	$-0.386192\pi$
$240$	−0.825077	+	0.476358i	−0.0532585	+	0.0307488i
$241$		−	5.99770i		−	0.386346i	−0.981165	−	0.193173i	$-0.938122\pi$
$241$		−	5.99770i		−	0.386346i	0.981165	−	0.193173i	$-0.0618778\pi$
$242$	9.52158	−	5.49729i	0.612070	−	0.353379i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	1.78571	+	3.09294i	0.114318	+	0.198005i
$245$	−6.31885	−	2.13258i	−0.403697	−	0.136246i
$246$	−6.70634			−0.427581
$247$	2.61595	−	1.68366i	0.166449	−	0.107129i
$248$	−5.03919	−	8.72813i	−0.319989	−	0.554237i
$249$	−10.2859	−	5.93856i	−0.651842	−	0.376341i
$250$	−8.66242			−0.547859
$251$	1.29020	−	2.23470i	0.0814369	−	0.141053i	−0.822430	−	0.568866i	$-0.807382\pi$
$251$	1.29020	−	2.23470i	0.0814369	−	0.141053i	0.903867	+	0.427813i	$0.140716\pi$
$252$	−1.54298	−	2.14923i	−0.0971986	−	0.135389i
$253$	−0.512251	−	0.295748i	−0.0322049	−	0.0185935i
$254$	4.91147	−	2.83564i	0.308173	−	0.177924i
$255$	1.81522	−	1.04802i	0.113674	−	0.0656295i
$256$	1.00000			0.0625000
$257$	−24.5685			−1.53254			−0.766270	−	0.642518i	$-0.777890\pi$
$257$	−24.5685			−1.53254			−0.766270	+	0.642518i	$0.777890\pi$
$258$	−2.14669	+	1.23939i	−0.133647	+	0.0771611i
$259$	−2.95078	−	29.6922i	−0.183352	−	1.84498i
$260$	−3.05427	−	1.57198i	−0.189418	−	0.0974901i
$261$	−2.36853	+	4.10241i	−0.146608	+	0.253933i
$262$	18.7315	+	10.8146i	1.15723	+	0.668129i
$263$	12.1294	−	21.0087i	0.747930	−	1.29545i	−0.200883	−	0.979615i	$-0.564381\pi$
$263$	12.1294	−	21.0087i	0.747930	−	1.29545i	0.948813	−	0.315838i	$-0.102285\pi$
$264$	−0.0368254	−	0.0637835i	−0.00226645	−	0.00392560i
$265$		−	1.78235i		−	0.109489i
$266$	1.33131	+	1.85440i	0.0816280	+	0.113701i
$267$	3.14524	+	1.81590i	0.192485	+	0.111132i
$268$	−10.5789	−	6.10772i	−0.646208	−	0.373088i
$269$	−12.4381			−0.758367			−0.379183	−	0.925322i	$-0.623795\pi$
$269$	−12.4381			−0.758367			−0.379183	+	0.925322i	$0.623795\pi$
$270$	−0.476358	+	0.825077i	−0.0289903	+	0.0502126i
$271$			16.4601i			0.999882i	0.866060	+	0.499941i	$0.166645\pi$
$271$			16.4601i			0.999882i	−0.866060	+	0.499941i	$0.833355\pi$
$272$	−2.20006			−0.133398
$273$	3.50529	−	8.87203i	0.212150	−	0.536960i
$274$	−20.2972			−1.22620
$275$		−	0.301404i		−	0.0181753i
$276$	4.01555	−	6.95513i	0.241707	−	0.418650i
$277$	−22.5992			−1.35786			−0.678928	−	0.734205i	$-0.737555\pi$
$277$	−22.5992			−1.35786			−0.678928	+	0.734205i	$0.737555\pi$
$278$	−0.128779	−	0.0743508i	−0.00772367	−	0.00445926i
$279$	−8.72813	−	5.03919i	−0.522539	−	0.301688i
$280$	1.03827	−	2.29688i	0.0620486	−	0.137265i
$281$			7.34639i			0.438249i	0.975697	+	0.219125i	$0.0703201\pi$
$281$			7.34639i			0.438249i	−0.975697	+	0.219125i	$0.929680\pi$
$282$	−4.68875	−	8.12115i	−0.279211	−	0.483607i
$283$	12.5645	−	21.7624i	0.746882	−	1.29364i	−0.202428	−	0.979297i	$-0.564883\pi$
$283$	12.5645	−	21.7624i	0.746882	−	1.29364i	0.949310	−	0.314341i	$-0.101783\pi$
$284$	−8.96491	−	5.17589i	−0.531969	−	0.307133i
$285$	0.411011	−	0.711892i	0.0243462	−	0.0421688i
$286$	0.121524	−	0.236114i	0.00718585	−	0.0139617i
$287$	14.4135	−	10.3478i	0.850802	−	0.610809i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−12.1597			−0.715277
$290$	−4.51308			−0.265017
$291$	11.1324	−	6.42728i	0.652592	−	0.376774i
$292$	−6.76210	+	3.90410i	−0.395722	+	0.228470i
$293$	−15.0195	−	8.67149i	−0.877447	−	0.506594i	−0.00763096	−	0.999971i	$-0.502429\pi$
$293$	−15.0195	−	8.67149i	−0.877447	−	0.506594i	−0.869816	+	0.493377i	$0.835762\pi$
$294$	6.63246	+	2.23842i	0.386813	+	0.130547i
$295$	−6.47700	+	11.2185i	−0.377105	+	0.653166i
$296$	11.2779			0.655513
$297$	−0.0637835	−	0.0368254i	−0.00370109	−	0.00213683i
$298$	−5.89618	−	10.2125i	−0.341556	−	0.591593i
$299$	28.9228	−	1.39732i	1.67265	−	0.0808088i
$300$	4.09233			0.236271
$301$	2.70138	−	5.97604i	0.155705	−	0.344453i
$302$	−7.93859	−	13.7500i	−0.456815	−	0.791226i
$303$	1.70367	+	2.95085i	0.0978735	+	0.169522i
$304$	−0.747223	+	0.431409i	−0.0428562	+	0.0247430i
$305$			3.40255i			0.194830i
$306$	−1.90531	+	1.10003i	−0.108919	+	0.0628847i
$307$		−	27.9365i		−	1.59442i	−0.603702	−	0.797210i	$-0.706308\pi$
$307$		−	27.9365i		−	1.59442i	0.603702	−	0.797210i	$-0.293692\pi$
$308$	0.177563	+	0.0802648i	0.0101176	+	0.00457351i
$309$	1.18228	+	2.04778i	0.0672578	+	0.116494i
$310$		−	9.60184i		−	0.545348i
$311$	−3.34510	−	5.79388i	−0.189683	−	0.328541i	0.755461	−	0.655193i	$-0.227413\pi$
$311$	−3.34510	−	5.79388i	−0.189683	−	0.328541i	−0.945145	+	0.326652i	$0.894079\pi$
$312$	3.20586	+	1.65000i	0.181496	+	0.0934127i
$313$	2.67609	−	4.63512i	0.151261	−	0.261992i	−0.780430	−	0.625243i	$-0.785000\pi$
$313$	2.67609	−	4.63512i	0.151261	−	0.261992i	0.931691	+	0.363251i	$0.118333\pi$
$314$	5.99655	−	3.46211i	0.338405	−	0.195378i
$315$	−0.249272	−	2.50830i	−0.0140449	−	0.141326i
$316$	1.30072	−	2.25291i	0.0731712	−	0.126736i
$317$	−15.2431	−	8.80060i	−0.856137	−	0.494291i	0.00657993	−	0.999978i	$-0.497906\pi$
$317$	−15.2431	−	8.80060i	−0.856137	−	0.494291i	−0.862717	+	0.505688i	$0.831239\pi$
$318$			1.87081i			0.104910i
$319$		−	0.348888i		−	0.0195340i
$320$	0.825077	+	0.476358i	0.0461232	+	0.0266292i
$321$	−4.75199	+	8.23069i	−0.265230	+	0.459392i
$322$	2.10128	+	21.1441i	0.117100	+	1.17832i
$323$	1.64394	−	0.949128i	0.0914712	−	0.0528109i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	7.98558	+	12.4074i	0.442961	+	0.688239i
$326$	4.10304	+	7.10668i	0.227247	+	0.393603i
$327$			7.73017i			0.427479i
$328$	3.35317	+	5.80786i	0.185148	+	0.320686i
$329$	22.6080	+	10.2196i	1.24642	+	0.563425i
$330$		−	0.0701684i		−	0.00386264i
$331$	−25.8242	+	14.9096i	−1.41943	+	0.819507i	−0.996249	−	0.0865381i	$-0.972420\pi$
$331$	−25.8242	+	14.9096i	−1.41943	+	0.819507i	−0.423180	+	0.906046i	$0.639086\pi$
$332$			11.8771i			0.651842i
$333$	9.76693	−	5.63894i	0.535224	−	0.309012i
$334$	−8.90108	−	15.4171i	−0.487045	−	0.843587i
$335$	−5.81893	−	10.0787i	−0.317922	−	0.550657i
$336$	−1.08980	+	2.41088i	−0.0594536	+	0.131524i
$337$	−13.5126			−0.736078			−0.368039	−	0.929810i	$-0.619971\pi$
$337$	−13.5126			−0.736078			−0.368039	+	0.929810i	$0.619971\pi$
$338$	1.25319	+	12.9395i	0.0681643	+	0.703814i
$339$	3.70956	+	6.42514i	0.201475	+	0.348966i
$340$	−1.81522	−	1.04802i	−0.0984443	−	0.0568368i
$341$	0.742281			0.0401968
$342$	−0.431409	+	0.747223i	−0.0233279	+	0.0404052i
$343$	−17.7085	+	5.42286i	−0.956172	+	0.292807i
$344$	2.14669	+	1.23939i	0.115742	+	0.0668235i
$345$	6.62627	−	3.82568i	0.356746	−	0.205968i
$346$	−2.39917	+	1.38516i	−0.128980	+	0.0744667i
$347$	18.1643			0.975110			0.487555	−	0.873092i	$-0.337889\pi$
$347$	18.1643			0.975110			0.487555	+	0.873092i	$0.337889\pi$
$348$	4.73706			0.253933
$349$	−9.88831	+	5.70902i	−0.529309	+	0.305597i	−0.740735	−	0.671797i	$-0.765523\pi$
$349$	−9.88831	+	5.70902i	−0.529309	+	0.305597i	0.211426	+	0.977394i	$0.432189\pi$
$350$	−8.79538	+	6.31439i	−0.470133	+	0.337518i
$351$	3.60135	−	0.173988i	0.192226	−	0.00928681i
$352$	−0.0368254	+	0.0637835i	−0.00196280	+	0.00339967i
$353$	0.835461	+	0.482354i	0.0444671	+	0.0256731i	0.522069	−	0.852903i	$-0.325160\pi$
$353$	0.835461	+	0.482354i	0.0444671	+	0.0256731i	−0.477602	+	0.878576i	$0.658494\pi$
$354$	6.79845	−	11.7753i	0.361333	−	0.625848i
$355$	−4.93116	−	8.54102i	−0.261719	−	0.453310i
$356$		−	3.63181i		−	0.192485i
$357$	2.39763	−	5.30409i	0.126896	−	0.280722i
$358$	−0.659422	−	0.380717i	−0.0348515	−	0.0201215i
$359$	0.807380	+	0.466141i	0.0426119	+	0.0246020i	0.521155	−	0.853462i	$-0.325501\pi$
$359$	0.807380	+	0.466141i	0.0426119	+	0.0246020i	−0.478543	+	0.878064i	$0.658835\pi$
$360$	0.952717			0.0502126
$361$	−9.12777	+	15.8098i	−0.480409	+	0.832093i
$362$		−	15.0250i		−	0.789695i
$363$	−10.9946			−0.577066
$364$	−9.43605	+	1.40034i	−0.494583	+	0.0733978i
$365$	−7.43901			−0.389376
$366$		−	3.57142i		−	0.186681i
$367$	−10.9968	+	19.0471i	−0.574031	+	0.994251i	0.422115	+	0.906542i	$0.361288\pi$
$367$	−10.9968	+	19.0471i	−0.574031	+	0.994251i	−0.996146	+	0.0877085i	$0.972046\pi$
$368$	−8.03109			−0.418650
$369$	5.80786	+	3.35317i	0.302345	+	0.174559i
$370$	9.30512	+	5.37231i	0.483750	+	0.279293i
$371$	−2.88662	−	4.02081i	−0.149866	−	0.208750i
$372$			10.0784i			0.522539i
$373$	13.5772	+	23.5164i	0.703002	+	1.21763i	0.967408	+	0.253223i	$0.0814907\pi$
$373$	13.5772	+	23.5164i	0.703002	+	1.21763i	−0.264406	+	0.964411i	$0.585176\pi$
$374$	0.0810183	−	0.140328i	0.00418936	−	0.00725618i
$375$	7.50187	+	4.33121i	0.387395	+	0.223663i
$376$	−4.68875	+	8.12115i	−0.241804	+	0.418816i
$377$	9.24368	+	14.3621i	0.476074	+	0.739688i
$378$	0.261643	+	2.63278i	0.0134575	+	0.135416i
$379$	11.0569	−	6.38369i	0.567953	−	0.327908i	−0.188378	−	0.982097i	$-0.560323\pi$
$379$	11.0569	−	6.38369i	0.567953	−	0.327908i	0.756332	+	0.654189i	$0.226990\pi$
$380$	−0.822022			−0.0421688
$381$	−5.67128			−0.290548
$382$	5.08760	−	2.93733i	0.260304	−	0.150287i
$383$	−9.53385	+	5.50437i	−0.487157	+	0.281260i	−0.723394	−	0.690435i	$-0.757419\pi$
$383$	−9.53385	+	5.50437i	−0.487157	+	0.281260i	0.236237	+	0.971695i	$0.424086\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$	0.108268	+	0.150808i	0.00551787	+	0.00768591i
$386$	6.10882	−	10.5808i	0.310931	−	0.538548i
$387$	2.47878			0.126004
$388$	−11.1324	−	6.42728i	−0.565161	−	0.326296i
$389$	−6.00836	−	10.4068i	−0.304636	−	0.527645i	0.672544	−	0.740057i	$-0.265202\pi$
$389$	−6.00836	−	10.4068i	−0.304636	−	0.527645i	−0.977180	+	0.212412i	$0.931868\pi$
$390$	1.85909	+	2.88851i	0.0941386	+	0.146265i
$391$	17.6689			0.893555
$392$	−1.37770	−	6.86309i	−0.0695843	−	0.346638i
$393$	−10.8146	−	18.7315i	−0.545525	−	0.944877i
$394$	6.69271	+	11.5921i	0.337174	+	0.584003i
$395$	2.14639	−	1.23922i	0.107996	−	0.0623518i
$396$			0.0736508i			0.00370109i
$397$	14.9160	−	8.61174i	0.748611	−	0.432211i	−0.0765808	−	0.997063i	$-0.524400\pi$
$397$	14.9160	−	8.61174i	0.748611	−	0.432211i	0.825192	+	0.564853i	$0.191067\pi$
$398$			0.537059i			0.0269203i
$399$	−0.225750	−	2.27161i	−0.0113017	−	0.113723i
$400$	−2.04617	−	3.54406i	−0.102308	−	0.177203i
$401$		−	12.1457i		−	0.606528i	−0.952907	−	0.303264i	$-0.901924\pi$
$401$		−	12.1457i		−	0.606528i	0.952907	−	0.303264i	$-0.0980765\pi$
$402$	6.10772	+	10.5789i	0.304625	+	0.527627i
$403$	−30.5563	+	19.6665i	−1.52212	+	0.979657i
$404$	1.70367	−	2.95085i	0.0847609	−	0.146810i
$405$	0.825077	−	0.476358i	0.0409984	−	0.0236704i
$406$	−10.1811	+	7.30919i	−0.505277	+	0.362749i
$407$	−0.415313	+	0.719343i	−0.0205863	+	0.0356565i
$408$	1.90531	+	1.10003i	0.0943270	+	0.0544597i
$409$			24.2902i			1.20107i	0.799597	+	0.600536i	$0.205046\pi$
$409$			24.2902i			1.20107i	−0.799597	+	0.600536i	$0.794954\pi$
$410$			6.38924i			0.315542i
$411$	17.5779	+	10.1486i	0.867054	+	0.500594i
$412$	1.18228	−	2.04778i	0.0582470	−	0.100887i
$413$	3.55753	+	35.7977i	0.175055	+	1.76149i
$414$	−6.95513	+	4.01555i	−0.341826	+	0.197353i
$415$	−5.65777	+	9.79954i	−0.277729	+	0.481041i
$416$	−0.173988	−	3.60135i	−0.00853048	−	0.176571i
$417$	0.0743508	+	0.128779i	0.00364097	+	0.00630635i
$418$		−	0.0635473i		−	0.00310820i
$419$	4.86261	+	8.42229i	0.237554	+	0.411456i	0.960012	−	0.279959i	$-0.0903209\pi$
$419$	4.86261	+	8.42229i	0.237554	+	0.411456i	−0.722458	+	0.691415i	$0.756988\pi$
$420$	−2.04761	+	1.47002i	−0.0999133	+	0.0717298i
$421$		−	25.6881i		−	1.25196i	−0.779839	−	0.625980i	$-0.784699\pi$
$421$		−	25.6881i		−	1.25196i	0.779839	−	0.625980i	$-0.215301\pi$
$422$	5.83390	−	3.36821i	0.283990	−	0.163962i
$423$			9.37750i			0.455949i
$424$	1.62017	−	0.935404i	0.0786823	−	0.0454272i
$425$	4.50170	+	7.79716i	0.218364	+	0.378218i
$426$	5.17589	+	8.96491i	0.250773	+	0.434351i
$427$	5.51063	+	7.67582i	0.266678	+	0.371459i
$428$	9.50398			0.459392
$429$	−0.223300	+	0.143719i	−0.0107810	+	0.00693881i
$430$	1.18079	+	2.04519i	0.0569427	+	0.0986276i
$431$	−3.13600	−	1.81057i	−0.151056	−	0.0872122i	0.422567	−	0.906332i	$-0.361129\pi$
$431$	−3.13600	−	1.81057i	−0.151056	−	0.0872122i	−0.573623	+	0.819120i	$0.694462\pi$
$432$	−1.00000			−0.0481125
$433$	−1.43124	+	2.47898i	−0.0687809	+	0.119132i	−0.898365	−	0.439250i	$-0.855244\pi$
$433$	−1.43124	+	2.47898i	−0.0687809	+	0.119132i	0.829584	+	0.558382i	$0.188578\pi$
$434$	−15.5507	−	21.6608i	−0.746459	−	1.03975i
$435$	3.90844	+	2.25654i	0.187395	+	0.108193i
$436$	6.69452	−	3.86508i	0.320609	−	0.185104i
$437$	6.00101	−	3.46469i	0.287067	−	0.165738i
$438$	7.80821			0.373090
$439$	10.7520			0.513165			0.256582	−	0.966522i	$-0.417404\pi$
$439$	10.7520			0.513165			0.256582	+	0.966522i	$0.417404\pi$
$440$	−0.0607676	+	0.0350842i	−0.00289698	+	0.00167257i
$441$	−4.62466	−	5.25476i	−0.220222	−	0.250227i
$442$	0.382785	+	7.92320i	0.0182072	+	0.376868i
$443$	−3.00480	+	5.20447i	−0.142763	+	0.247272i	−0.928536	−	0.371242i	$-0.878932\pi$
$443$	−3.00480	+	5.20447i	−0.142763	+	0.247272i	0.785773	+	0.618515i	$0.212265\pi$
$444$	−9.76693	−	5.63894i	−0.463518	−	0.267612i
$445$	1.73004	−	2.99652i	0.0820119	−	0.142049i
$446$	12.7137	+	22.0208i	0.602011	+	1.04271i
$447$			11.7924i			0.557759i
$448$	2.63278	−	0.261643i	0.124387	−	0.0123615i
$449$	16.6165	+	9.59355i	0.784182	+	0.452748i	0.837910	−	0.545808i	$-0.183777\pi$
$449$	16.6165	+	9.59355i	0.784182	+	0.452748i	−0.0537284	+	0.998556i	$0.517111\pi$
$450$	−3.54406	−	2.04617i	−0.167069	−	0.0964572i
$451$	−0.493928			−0.0232581
$452$	3.70956	−	6.42514i	0.174483	−	0.302213i
$453$			15.8772i			0.745975i
$454$	3.40559			0.159832
$455$	−8.45253	−	3.33955i	−0.396261	−	0.156561i
$456$	0.862818			0.0404052
$457$			6.43716i			0.301118i	0.988601	+	0.150559i	$0.0481073\pi$
$457$			6.43716i			0.301118i	−0.988601	+	0.150559i	$0.951893\pi$
$458$	0.572194	−	0.991069i	0.0267369	−	0.0463096i
$459$	2.20006			0.102690
$460$	−6.62627	−	3.82568i	−0.308951	−	0.178373i
$461$	−6.89063	−	3.97831i	−0.320929	−	0.185288i	0.330878	−	0.943674i	$-0.392655\pi$
$461$	−6.89063	−	3.97831i	−0.320929	−	0.185288i	−0.651806	+	0.758385i	$0.725989\pi$
$462$	−0.113642	−	0.158293i	−0.00528710	−	0.00736445i
$463$			20.5480i			0.954947i	0.878646	+	0.477474i	$0.158447\pi$
$463$			20.5480i			0.954947i	−0.878646	+	0.477474i	$0.841553\pi$
$464$	−2.36853	−	4.10241i	−0.109956	−	0.190450i
$465$	−4.80092	+	8.31543i	−0.222637	+	0.385619i
$466$	2.89929	+	1.67391i	0.134307	+	0.0775423i
$467$	−4.15187	+	7.19125i	−0.192126	+	0.332771i	−0.945954	−	0.324299i	$-0.894871\pi$
$467$	−4.15187	+	7.19125i	−0.192126	+	0.332771i	0.753829	+	0.657071i	$0.228205\pi$
$468$	−1.95135	−	3.03187i	−0.0902014	−	0.140148i
$469$	−29.4499	−	13.3124i	−1.35987	−	0.614710i
$470$	−7.73716	+	4.46705i	−0.356888	+	0.206050i
$471$	−6.92422			−0.319051
$472$	−13.5969			−0.625848
$473$	−0.158105	+	0.0912822i	−0.00726969	+	0.00419716i
$474$	−2.25291	+	1.30072i	−0.103480	+	0.0597440i
$475$	3.05788	+	1.76547i	0.140305	+	0.0810053i
$476$	−5.79229	+	0.575631i	−0.265489	+	0.0263840i
$477$	0.935404	−	1.62017i	0.0428292	−	0.0741824i
$478$	28.9640			1.32478
$479$	−18.4037	−	10.6254i	−0.840888	−	0.485487i	0.0166781	−	0.999861i	$-0.494691\pi$
$479$	−18.4037	−	10.6254i	−0.840888	−	0.485487i	−0.857566	+	0.514374i	$0.828024\pi$
$480$	−0.476358	−	0.825077i	−0.0217427	−	0.0376594i
$481$	−1.96222	−	40.6156i	−0.0894695	−	1.85191i
$482$	5.99770			0.273188
$483$	8.75230	−	19.3620i	0.398243	−	0.881001i
$484$	5.49729	+	9.52158i	0.249877	+	0.432799i
$485$	−6.12338	−	10.6060i	−0.278048	−	0.481594i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$			24.9365i			1.12998i	0.825097	+	0.564991i	$0.191120\pi$
$487$			24.9365i			1.12998i	−0.825097	+	0.564991i	$0.808880\pi$
$488$	−3.09294	+	1.78571i	−0.140011	+	0.0808353i
$489$		−	8.20609i		−	0.371092i
$490$	2.13258	−	6.31885i	0.0963402	−	0.285457i
$491$	0.201577	+	0.349141i	0.00909703	+	0.0157565i	0.870538	−	0.492101i	$-0.163771\pi$
$491$	0.201577	+	0.349141i	0.00909703	+	0.0157565i	−0.861441	+	0.507858i	$0.830438\pi$
$492$		−	6.70634i		−	0.302345i
$493$	5.21092	+	9.02558i	0.234688	+	0.406492i
$494$	1.68366	+	2.61595i	0.0757516	+	0.117697i
$495$	−0.0350842	+	0.0607676i	−0.00157692	+	0.00273130i
$496$	8.72813	−	5.03919i	0.391905	−	0.226266i
$497$	−24.9569	−	11.2814i	−1.11947	−	0.506040i
$498$	5.93856	−	10.2859i	0.266113	−	0.460922i
$499$	22.9988	+	13.2784i	1.02957	+	0.594422i	0.916861	−	0.399206i	$-0.130714\pi$
$499$	22.9988	+	13.2784i	1.02957	+	0.594422i	0.112708	+	0.993628i	$0.464047\pi$
$500$		−	8.66242i		−	0.387395i
$501$			17.8022i			0.795342i
$502$	2.23470	+	1.29020i	0.0997394	+	0.0575846i
$503$	0.443994	−	0.769020i	0.0197967	−	0.0342889i	−0.855957	−	0.517046i	$-0.827031\pi$
$503$	0.443994	−	0.769020i	0.0197967	−	0.0342889i	0.875754	+	0.482758i	$0.160365\pi$
$504$	2.14923	−	1.54298i	0.0957345	−	0.0687298i
$505$	2.81132	−	1.62312i	0.125102	−	0.0722278i
$506$	0.295748	−	0.512251i	0.0131476	−	0.0227723i
$507$	5.38444	−	11.8325i	0.239131	−	0.525499i
$508$	2.83564	+	4.91147i	0.125811	+	0.217911i
$509$		−	18.0231i		−	0.798860i	−0.916764	−	0.399430i	$-0.869208\pi$
$509$		−	18.0231i		−	0.798860i	0.916764	−	0.399430i	$-0.130792\pi$
$510$	1.04802	+	1.81522i	0.0464071	+	0.0803794i
$511$	−16.7817	+	12.0479i	−0.742377	+	0.532968i
$512$			1.00000i			0.0441942i
$513$	0.747223	−	0.431409i	0.0329907	−	0.0190472i
$514$		−	24.5685i		−	1.08367i
$515$	1.95095	−	1.12638i	0.0859692	−	0.0496343i
$516$	−1.23939	−	2.14669i	−0.0545611	−	0.0945027i
$517$	−0.345330	−	0.598130i	−0.0151876	−	0.0263057i
$518$	29.6922	−	2.95078i	1.30460	−	0.129650i
$519$	2.77032			0.121604
$520$	1.57198	−	3.05427i	0.0689359	−	0.133939i
$521$	15.1663	+	26.2687i	0.664446	+	1.15085i	0.979435	+	0.201759i	$0.0646659\pi$
$521$	15.1663	+	26.2687i	0.664446	+	1.15085i	−0.314989	+	0.949095i	$0.602001\pi$
$522$	−4.10241	−	2.36853i	−0.179558	−	0.103668i
$523$	1.83462			0.0802222			0.0401111	−	0.999195i	$-0.487229\pi$
$523$	1.83462			0.0802222			0.0401111	+	0.999195i	$0.487229\pi$
$524$	−10.8146	+	18.7315i	−0.472439	+	0.818288i
$525$	10.7742	−	1.07073i	0.470225	−	0.0467305i
$526$	21.0087	+	12.1294i	0.916023	+	0.528866i
$527$	−19.2024	+	11.0865i	−0.836471	+	0.482937i
$528$	0.0637835	−	0.0368254i	0.00277582	−	0.00160262i
$529$	41.4984			1.80428
$530$	1.78235			0.0774203
$531$	−11.7753	+	6.79845i	−0.511003	+	0.295028i
$532$	−1.85440	+	1.33131i	−0.0803984	+	0.0577197i
$533$	20.3327	−	13.0864i	0.880709	−	0.566837i
$534$	−1.81590	+	3.14524i	−0.0785819	+	0.136108i
$535$	7.84152	+	4.52730i	0.339018	+	0.195732i
$536$	6.10772	−	10.5789i	0.263813	−	0.456938i
$537$	0.380717	+	0.659422i	0.0164292	+	0.0284561i
$538$		−	12.4381i		−	0.536246i
$539$	0.488486	+	0.164862i	0.0210406	+	0.00710109i
$540$	−0.825077	−	0.476358i	−0.0355057	−	0.0204992i
$541$	14.5108	+	8.37779i	0.623866	+	0.360189i	0.778373	−	0.627803i	$-0.216045\pi$
$541$	14.5108	+	8.37779i	0.623866	+	0.360189i	−0.154507	+	0.987992i	$0.549379\pi$
$542$	−16.4601			−0.707023
$543$	−7.51249	+	13.0120i	−0.322392	+	0.558399i
$544$		−	2.20006i		−	0.0943270i
$545$	7.36466			0.315467
$546$	8.87203	+	3.50529i	0.379688	+	0.150013i
$547$	24.6951			1.05588			0.527942	−	0.849280i	$-0.322964\pi$
$547$	24.6951			1.05588			0.527942	+	0.849280i	$0.322964\pi$
$548$		−	20.2972i		−	0.867054i
$549$	−1.78571	+	3.09294i	−0.0762123	+	0.132004i
$550$	0.301404			0.0128519
$551$	3.53964	+	2.04361i	0.150794	+	0.0870608i
$552$	6.95513	+	4.01555i	0.296030	+	0.170913i
$553$	2.83505	−	6.27175i	0.120559	−	0.266702i
$554$		−	22.5992i		−	0.960149i
$555$	−5.37231	−	9.30512i	−0.228042	−	0.394980i
$556$	0.0743508	−	0.128779i	0.00315317	−	0.00546146i
$557$	15.4200	+	8.90274i	0.653366	+	0.377221i	0.789745	−	0.613436i	$-0.210213\pi$
$557$	15.4200	+	8.90274i	0.653366	+	0.377221i	−0.136378	+	0.990657i	$0.543546\pi$
$558$	5.03919	−	8.72813i	0.213326	−	0.369491i
$559$	4.08998	−	7.94662i	0.172988	−	0.336106i
$560$	2.29688	+	1.03827i	0.0970611	+	0.0438750i
$561$	−0.140328	+	0.0810183i	−0.00592464	+	0.00342059i
$562$	−7.34639			−0.309889
$563$	−29.9144			−1.26074			−0.630372	−	0.776293i	$-0.717097\pi$
$563$	−29.9144			−1.26074			−0.630372	+	0.776293i	$0.717097\pi$
$564$	8.12115	−	4.68875i	0.341962	−	0.197432i
$565$	6.12134	−	3.53416i	0.257527	−	0.148683i
$566$	21.7624	+	12.5645i	0.914740	+	0.528126i
$567$	1.08980	−	2.41088i	0.0457674	−	0.101247i
$568$	5.17589	−	8.96491i	0.217176	−	0.376159i
$569$	−0.902108			−0.0378183			−0.0189092	−	0.999821i	$-0.506019\pi$
$569$	−0.902108			−0.0378183			−0.0189092	+	0.999821i	$0.506019\pi$
$570$	0.711892	+	0.411011i	0.0298179	+	0.0172154i
$571$	−20.8868	−	36.1770i	−0.874085	−	1.51396i	−0.857734	−	0.514094i	$-0.828128\pi$
$571$	−20.8868	−	36.1770i	−0.874085	−	1.51396i	−0.0163510	−	0.999866i	$-0.505205\pi$
$572$	0.236114	+	0.121524i	0.00987242	+	0.00508116i
$573$	−5.87466			−0.245417
$574$	10.3478	+	14.4135i	0.431907	+	0.601608i
$575$	16.4329	+	28.4627i	0.685301	+	1.18698i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−21.1876	+	12.2326i	−0.882050	+	0.509252i	−0.871334	−	0.490691i	$-0.836744\pi$
$577$	−21.1876	+	12.2326i	−0.882050	+	0.509252i	−0.0107161	+	0.999943i	$0.503411\pi$
$578$		−	12.1597i		−	0.505778i
$579$	−10.5808	+	6.10882i	−0.439723	+	0.253874i
$580$		−	4.51308i		−	0.187395i
$581$	3.10757	+	31.2699i	0.128924	+	1.29729i
$582$	6.42728	+	11.1324i	0.266419	+	0.461452i
$583$			0.137787i			0.00570654i
$584$	−3.90410	−	6.76210i	−0.161553	−	0.279818i
$585$	−0.165762	−	3.43107i	−0.00685340	−	0.141857i
$586$	8.67149	−	15.0195i	0.358216	−	0.620448i
$587$	−1.42198	+	0.820978i	−0.0586912	+	0.0338854i	−0.529058	−	0.848585i	$-0.677455\pi$
$587$	−1.42198	+	0.820978i	−0.0586912	+	0.0338854i	0.470367	+	0.882471i	$0.344121\pi$
$588$	−2.23842	+	6.63246i	−0.0923109	+	0.273518i
$589$	−4.34790	+	7.53079i	−0.179152	+	0.310301i
$590$	−11.2185	−	6.47700i	−0.461858	−	0.266654i
$591$		−	13.3854i		−	0.550603i
$592$			11.2779i			0.463518i
$593$	9.96128	+	5.75115i	0.409061	+	0.236171i	0.690386	−	0.723441i	$-0.257441\pi$
$593$	9.96128	+	5.75115i	0.409061	+	0.236171i	−0.281325	+	0.959612i	$0.590774\pi$
$594$	0.0368254	−	0.0637835i	0.00151097	−	0.00261707i
$595$	−5.05329	−	2.28427i	−0.207165	−	0.0936458i
$596$	10.2125	−	5.89618i	0.418319	−	0.241517i
$597$	0.268529	−	0.465107i	0.0109902	−	0.0190355i
$598$	1.39732	+	28.9228i	0.0571405	+	1.18274i
$599$	5.84281	+	10.1200i	0.238731	+	0.413494i	0.960350	−	0.278796i	$-0.0899353\pi$
$599$	5.84281	+	10.1200i	0.238731	+	0.413494i	−0.721620	+	0.692290i	$0.756602\pi$
$600$			4.09233i			0.167069i
$601$	−5.10939	−	8.84972i	−0.208416	−	0.360987i	0.742800	−	0.669514i	$-0.233498\pi$
$601$	−5.10939	−	8.84972i	−0.208416	−	0.360987i	−0.951216	+	0.308526i	$0.900164\pi$
$602$	5.97604	+	2.70138i	0.243565	+	0.110100i
$603$		−	12.2154i		−	0.497451i
$604$	13.7500	−	7.93859i	0.559481	−	0.323017i
$605$			10.4747i			0.425858i
$606$	−2.95085	+	1.70367i	−0.119870	+	0.0692070i
$607$	1.03671	+	1.79563i	0.0420786	+	0.0728823i	0.886298	−	0.463116i	$-0.153269\pi$
$607$	1.03671	+	1.79563i	0.0420786	+	0.0728823i	−0.844219	+	0.535998i	$0.819935\pi$
$608$	−0.431409	−	0.747223i	−0.0174960	−	0.0303039i
$609$	12.4716	−	1.23942i	0.505377	−	0.0502238i
$610$	−3.40255			−0.137765
$611$	30.0629	+	15.4728i	1.21621	+	0.625964i
$612$	−1.10003	−	1.90531i	−0.0444662	−	0.0770177i
$613$	−19.6295	−	11.3331i	−0.792830	−	0.457740i	0.0481281	−	0.998841i	$-0.484674\pi$
$613$	−19.6295	−	11.3331i	−0.792830	−	0.457740i	−0.840958	+	0.541101i	$0.818008\pi$
$614$	27.9365			1.12743
$615$	3.19462	−	5.53325i	0.128820	−	0.223122i
$616$	−0.0802648	+	0.177563i	−0.00323396	+	0.00715422i
$617$	6.40425	+	3.69750i	0.257826	+	0.148856i	0.623342	−	0.781949i	$-0.285774\pi$
$617$	6.40425	+	3.69750i	0.257826	+	0.148856i	−0.365517	+	0.930805i	$0.619108\pi$
$618$	−2.04778	+	1.18228i	−0.0823737	+	0.0475585i
$619$	16.6370	−	9.60540i	0.668699	−	0.386074i	−0.126884	−	0.991918i	$-0.540498\pi$
$619$	16.6370	−	9.60540i	0.668699	−	0.386074i	0.795584	+	0.605844i	$0.207164\pi$
$620$	9.60184			0.385619
$621$	8.03109			0.322277
$622$	5.79388	−	3.34510i	0.232314	−	0.134126i
$623$	−0.950237	−	9.56176i	−0.0380705	−	0.383084i
$624$	−1.65000	+	3.20586i	−0.0660528	+	0.128337i
$625$	−6.10441	+	10.5732i	−0.244176	+	0.422926i
$626$	4.63512	+	2.67609i	0.185257	+	0.106958i
$627$	−0.0317737	+	0.0550336i	−0.00126892	+	0.00219783i
$628$	3.46211	+	5.99655i	0.138153	+	0.239288i
$629$		−	24.8121i		−	0.989322i
$630$	2.50830	−	0.249272i	0.0999329	−	0.00993122i
$631$	−18.6803	−	10.7851i	−0.743651	−	0.429347i	0.0797444	−	0.996815i	$-0.474590\pi$
$631$	−18.6803	−	10.7851i	−0.743651	−	0.429347i	−0.823395	+	0.567468i	$0.807923\pi$
$632$	2.25291	+	1.30072i	0.0896160	+	0.0517398i
$633$	−6.73641			−0.267748
$634$	8.80060	−	15.2431i	0.349516	−	0.605380i
$635$			5.40312i			0.214416i
$636$	−1.87081			−0.0741824
$637$	−24.4767	+	6.15567i	−0.969801	+	0.243897i
$638$	0.348888			0.0138126
$639$		−	10.3518i		−	0.409510i
$640$	−0.476358	+	0.825077i	−0.0188297	+	0.0326140i
$641$	38.7828			1.53183			0.765914	−	0.642943i	$-0.222287\pi$
$641$	38.7828			1.53183			0.765914	+	0.642943i	$0.222287\pi$
$642$	−8.23069	−	4.75199i	−0.324840	−	0.187546i
$643$	−42.5539	−	24.5685i	−1.67816	−	0.968888i	−0.962832	−	0.270102i	$-0.912943\pi$
$643$	−42.5539	−	24.5685i	−1.67816	−	0.968888i	−0.715331	−	0.698786i	$-0.753724\pi$
$644$	−21.1441	+	2.10128i	−0.833195	+	0.0828020i
$645$		−	2.36158i		−	0.0929870i
$646$	0.949128	+	1.64394i	0.0373429	+	0.0646799i
$647$	−25.2258	+	43.6924i	−0.991730	+	1.71773i	−0.384715	+	0.923035i	$0.625700\pi$
$647$	−25.2258	+	43.6924i	−0.991730	+	1.71773i	−0.607014	+	0.794691i	$0.707633\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	0.500711	−	0.867258i	0.0196546	−	0.0340428i
$650$	−12.4074	+	7.98558i	−0.486658	+	0.313220i
$651$	2.63694	+	26.5342i	0.103350	+	1.03996i
$652$	−7.10668	+	4.10304i	−0.278319	+	0.160688i
$653$	12.8969			0.504694			0.252347	−	0.967637i	$-0.418798\pi$
$653$	12.8969			0.504694			0.252347	+	0.967637i	$0.418798\pi$
$654$	−7.73017			−0.302274
$655$	−17.8458	+	10.3033i	−0.697292	+	0.402582i
$656$	−5.80786	+	3.35317i	−0.226759	+	0.130919i
$657$	−6.76210	−	3.90410i	−0.263815	−	0.152314i
$658$	−10.2196	+	22.6080i	−0.398402	+	0.881352i
$659$	−16.7189	+	28.9581i	−0.651278	+	1.12805i	0.331536	+	0.943443i	$0.392433\pi$
$659$	−16.7189	+	28.9581i	−0.651278	+	1.12805i	−0.982813	+	0.184603i	$0.940900\pi$
$660$	0.0701684			0.00273130
$661$	4.62178	+	2.66839i	0.179766	+	0.103788i	0.587183	−	0.809454i	$-0.300237\pi$
$661$	4.62178	+	2.66839i	0.179766	+	0.103788i	−0.407416	+	0.913242i	$0.633570\pi$
$662$	−14.9096	−	25.8242i	−0.579479	−	1.00369i
$663$	3.63010	−	7.05309i	0.140981	−	0.273919i
$664$	−11.8771			−0.460922
$665$	−2.16420	+	0.215076i	−0.0839242	+	0.00834030i
$666$	5.63894	+	9.76693i	0.218504	+	0.378461i
$667$	19.0219	+	32.9469i	0.736530	+	1.27571i
$668$	15.4171	−	8.90108i	0.596506	−	0.344393i
$669$		−	25.4274i		−	0.983080i
$670$	10.0787	−	5.81893i	0.389373	−	0.224805i
$671$		−	0.263038i		−	0.0101545i
$672$	−2.41088	−	1.08980i	−0.0930016	−	0.0420400i
$673$	−12.3543	−	21.3983i	−0.476223	−	0.824842i	0.523406	−	0.852083i	$-0.324661\pi$
$673$	−12.3543	−	21.3983i	−0.476223	−	0.824842i	−0.999629	+	0.0272410i	$0.991328\pi$
$674$		−	13.5126i		−	0.520486i
$675$	2.04617	+	3.54406i	0.0787569	+	0.136411i
$676$	−12.9395	+	1.25319i	−0.497671	+	0.0481994i
$677$	7.32191	−	12.6819i	0.281404	−	0.487406i	−0.690327	−	0.723498i	$-0.742533\pi$
$677$	7.32191	−	12.6819i	0.281404	−	0.487406i	0.971731	+	0.236092i	$0.0758666\pi$
$678$	−6.42514	+	3.70956i	−0.246756	+	0.142465i
$679$	−30.9908	−	14.0089i	−1.18932	−	0.537613i
$680$	1.04802	−	1.81522i	0.0401897	−	0.0696106i
$681$	−2.94933	−	1.70279i	−0.113018	−	0.0652512i
$682$			0.742281i			0.0284234i
$683$		−	39.4325i		−	1.50884i	−0.656390	−	0.754421i	$-0.727918\pi$
$683$		−	39.4325i		−	1.50884i	0.656390	−	0.754421i	$-0.272082\pi$
$684$	−0.747223	−	0.431409i	−0.0285708	−	0.0164953i
$685$	9.66875	−	16.7468i	0.369424	−	0.639861i
$686$	−5.42286	−	17.7085i	−0.207046	−	0.676115i
$687$	−0.991069	+	0.572194i	−0.0378117	+	0.0218306i
$688$	−1.23939	+	2.14669i	−0.0472513	+	0.0818417i
$689$	−3.65061	−	5.67204i	−0.139077	−	0.216088i
$690$	3.82568	+	6.62627i	0.145641	+	0.252258i
$691$			28.9430i			1.10104i	0.834821	+	0.550522i	$0.185571\pi$
$691$			28.9430i			1.10104i	−0.834821	+	0.550522i	$0.814429\pi$
$692$	−1.38516	−	2.39917i	−0.0526559	−	0.0912027i
$693$	0.0192702	+	0.193907i	0.000732015	+	0.00736590i
$694$			18.1643i			0.689507i
$695$	0.122690	−	0.0708352i	0.00465391	−	0.00268693i
$696$			4.73706i			0.179558i
$697$	12.7777	−	7.37719i	0.483989	−	0.279431i
$698$	−5.70902	−	9.88831i	−0.216090	−	0.374278i
$699$	−1.67391	−	2.89929i	−0.0633130	−	0.109661i
$700$	−6.31439	−	8.79538i	−0.238661	−	0.332434i
$701$	32.2105			1.21657			0.608286	−	0.793718i	$-0.291857\pi$
$701$	32.2105			1.21657			0.608286	+	0.793718i	$0.291857\pi$
$702$	0.173988	+	3.60135i	0.00656676	+	0.135924i
$703$	−4.86538	−	8.42709i	−0.183501	−	0.317834i
$704$	−0.0637835	−	0.0368254i	−0.00240393	−	0.00138791i
$705$	8.93410			0.336478
$706$	−0.482354	+	0.835461i	−0.0181536	+	0.0314430i
$707$	3.71333	−	8.21470i	0.139654	−	0.308945i
$708$	11.7753	+	6.79845i	0.442541	+	0.255501i
$709$	31.9387	−	18.4398i	1.19948	−	0.692522i	0.239043	−	0.971009i	$-0.423166\pi$
$709$	31.9387	−	18.4398i	1.19948	−	0.692522i	0.960440	+	0.278487i	$0.0898329\pi$
$710$	8.54102	−	4.93116i	0.320539	−	0.185063i
$711$	2.60144			0.0975616
$712$	3.63181			0.136108
$713$	−70.0964	+	40.4702i	−2.62513	+	1.51562i
$714$	5.30409	+	2.39763i	0.198500	+	0.0897292i
$715$	0.136923	+	0.212741i	0.00512064	+	0.00795607i
$716$	0.380717	−	0.659422i	0.0142281	−	0.0246437i
$717$	−25.0835	−	14.4820i	−0.936762	−	0.540840i
$718$	−0.466141	+	0.807380i	−0.0173962	+	0.0301311i
$719$	−14.4977	−	25.1107i	−0.540672	−	0.936471i	−0.998866	−	0.0476185i	$-0.984837\pi$
$719$	−14.4977	−	25.1107i	−0.540672	−	0.936471i	0.458194	−	0.888852i	$-0.348496\pi$
$720$			0.952717i			0.0355057i
$721$	2.57691	−	5.70069i	0.0959692	−	0.212305i
$722$	−15.8098	−	9.12777i	−0.588379	−	0.339701i
$723$	−5.19416	−	2.99885i	−0.193173	−	0.111528i
$724$	15.0250			0.558399
$725$	−9.69281	+	16.7884i	−0.359982	+	0.623507i
$726$		−	10.9946i		−	0.408047i
$727$	4.22223			0.156594			0.0782970	−	0.996930i	$-0.475052\pi$
$727$	4.22223			0.156594			0.0782970	+	0.996930i	$0.475052\pi$
$728$	−1.40034	−	9.43605i	−0.0519001	−	0.349723i
$729$	1.00000			0.0370370
$730$		−	7.43901i		−	0.275330i
$731$	2.72674	−	4.72285i	0.100852	−	0.174681i
$732$	3.57142			0.132004
$733$	38.5274	+	22.2438i	1.42304	+	0.821593i	0.996558	−	0.0829028i	$-0.0264191\pi$
$733$	38.5274	+	22.2438i	1.42304	+	0.821593i	0.426483	+	0.904496i	$0.359752\pi$
$734$	−19.0471	−	10.9968i	−0.703041	−	0.405901i
$735$	−5.00630	+	4.40600i	−0.184660	+	0.162518i
$736$		−	8.03109i		−	0.296030i
$737$	0.449839	+	0.779144i	0.0165700	+	0.0287001i
$738$	−3.35317	+	5.80786i	−0.123432	+	0.213790i
$739$	20.1961	+	11.6602i	0.742927	+	0.428929i	0.823133	−	0.567849i	$-0.192224\pi$
$739$	20.1961	+	11.6602i	0.742927	+	0.428929i	−0.0802057	+	0.996778i	$0.525558\pi$
$740$	−5.37231	+	9.30512i	−0.197490	+	0.342063i
$741$	−0.150120	−	3.10731i	−0.00551481	−	0.114150i
$742$	4.02081	−	2.88662i	0.147608	−	0.105971i
$743$	−43.1684	+	24.9233i	−1.58369	+	0.914347i	−0.589381	+	0.807855i	$0.700628\pi$
$743$	−43.1684	+	24.9233i	−1.58369	+	0.914347i	−0.994314	+	0.106492i	$0.966038\pi$
$744$	−10.0784			−0.369491
$745$	11.2348			0.411610
$746$	−23.5164	+	13.5772i	−0.860998	+	0.497097i
$747$	−10.2859	+	5.93856i	−0.376341	+	0.217281i
$748$	0.140328	+	0.0810183i	0.00513089	+	0.00296232i
$749$	25.0219	−	2.48665i	0.914281	−	0.0908603i
$750$	−4.33121	+	7.50187i	−0.158153	+	0.273930i
$751$	−18.1413			−0.661984			−0.330992	−	0.943633i	$-0.607383\pi$
$751$	−18.1413			−0.661984			−0.330992	+	0.943633i	$0.607383\pi$
$752$	−8.12115	−	4.68875i	−0.296148	−	0.170981i
$753$	−1.29020	−	2.23470i	−0.0470176	−	0.0814369i
$754$	−14.3621	+	9.24368i	−0.523038	+	0.336635i
$755$	15.1265			0.550508
$756$	−2.63278	+	0.261643i	−0.0957534	+	0.00951586i
$757$	−6.93581	−	12.0132i	−0.252086	−	0.436626i	0.712014	−	0.702166i	$-0.247783\pi$
$757$	−6.93581	−	12.0132i	−0.252086	−	0.436626i	−0.964100	+	0.265539i	$0.914450\pi$
$758$	6.38369	+	11.0569i	0.231866	+	0.401604i
$759$	−0.512251	+	0.295748i	−0.0185935	+	0.0107350i
$760$		−	0.822022i		−	0.0298179i
$761$	−37.0181	+	21.3724i	−1.34191	+	0.774750i	−0.987087	−	0.160186i	$-0.948791\pi$
$761$	−37.0181	+	21.3724i	−1.34191	+	0.774750i	−0.354819	+	0.934935i	$0.615457\pi$
$762$		−	5.67128i		−	0.205449i
$763$	16.6139	−	11.9275i	0.601465	−	0.431805i
$764$	2.93733	+	5.08760i	0.106269	+	0.184063i
$765$		−	2.09604i		−	0.0757824i
$766$	−5.50437	−	9.53385i	−0.198881	−	0.344472i
$767$	2.36570	+	48.9672i	0.0854205	+	1.76810i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	22.4317	−	12.9509i	0.808906	−	0.467022i	−0.0376696	−	0.999290i	$-0.511993\pi$
$769$	22.4317	−	12.9509i	0.808906	−	0.467022i	0.846576	+	0.532268i	$0.178660\pi$
$770$	−0.150808	+	0.108268i	−0.00543476	+	0.00390173i
$771$	−12.2842	+	21.2769i	−0.442406	+	0.766270i
$772$	10.5808	+	6.10882i	0.380811	+	0.219861i
$773$			36.4733i			1.31185i	0.754824	+	0.655927i	$0.227722\pi$
$773$			36.4733i			1.31185i	−0.754824	+	0.655927i	$0.772278\pi$
$774$			2.47878i			0.0890980i
$775$	−35.7184	−	20.6220i	−1.28304	−	0.740765i
$776$	6.42728	−	11.1324i	0.230726	−	0.399629i
$777$	−27.1896	−	12.2907i	−0.975421	−	0.440925i
$778$	10.4068	−	6.00836i	0.373102	−	0.215410i
$779$	2.89318	−	5.01113i	0.103659	−	0.179542i
$780$	−2.88851	+	1.85909i	−0.103425	+	0.0665660i
$781$	0.381209	+	0.660273i	0.0136407	+	0.0236264i
$782$			17.6689i			0.631839i
$783$	2.36853	+	4.10241i	0.0846444	+	0.146608i
$784$	6.86309	−	1.37770i	0.245110	−	0.0492035i
$785$			6.59682i			0.235451i
$786$	18.7315	−	10.8146i	0.668129	−	0.385745i
$787$		−	7.48792i		−	0.266916i	−0.991054	−	0.133458i	$-0.957392\pi$
$787$		−	7.48792i		−	0.266916i	0.991054	−	0.133458i	$-0.0426081\pi$
$788$	−11.5921	+	6.69271i	−0.412952	+	0.238418i
$789$	−12.1294	−	21.0087i	−0.431818	−	0.747930i
$790$	1.23922	+	2.14639i	0.0440894	+	0.0763650i
$791$	8.08536	−	17.8866i	0.287482	−	0.635974i
$792$	−0.0736508			−0.00261707
$793$	6.96911	+	10.8281i	0.247480	+	0.384516i
$794$	8.61174	+	14.9160i	0.305619	+	0.529348i
$795$	−1.54356	−	0.891175i	−0.0547445	−	0.0316067i
$796$	−0.537059			−0.0190355
$797$	16.2908	−	28.2165i	0.577049	−	0.999478i	−0.418767	−	0.908094i	$-0.637537\pi$
$797$	16.2908	−	28.2165i	0.577049	−	0.999478i	0.995816	−	0.0913843i	$-0.0291292\pi$
$798$	2.27161	−	0.225750i	0.0804142	−	0.00799148i
$799$	17.8671	+	10.3155i	0.632091	+	0.364938i
$800$	3.54406	−	2.04617i	0.125302	−	0.0723429i
$801$	3.14524	−	1.81590i	0.111132	−	0.0641618i
$802$	12.1457			0.428880
$803$	0.575081			0.0202942
$804$	−10.5789	+	6.10772i	−0.373088	+	0.215403i
$805$	−18.4465	−	8.33846i	−0.650153	−	0.293892i
$806$	−19.6665	−	30.5563i	−0.692722	−	1.07630i
$807$	−6.21907	+	10.7717i	−0.218922	+	0.379183i
$808$	2.95085	+	1.70367i	0.103811	+	0.0599350i
$809$	−8.01968	+	13.8905i	−0.281957	+	0.488364i	−0.971867	−	0.235532i	$-0.924317\pi$
$809$	−8.01968	+	13.8905i	−0.281957	+	0.488364i	0.689910	+	0.723895i	$0.257650\pi$
$810$	0.476358	+	0.825077i	0.0167375	+	0.0289903i
$811$		−	35.4166i		−	1.24364i	−0.783159	−	0.621822i	$-0.786393\pi$
$811$		−	35.4166i		−	1.24364i	0.783159	−	0.621822i	$-0.213607\pi$
$812$	−7.30919	−	10.1811i	−0.256502	−	0.357285i
$813$	14.2549	+	8.23006i	0.499941	+	0.288641i
$814$	−0.719343	−	0.415313i	−0.0252129	−	0.0145567i
$815$	−7.81808			−0.273855
$816$	−1.10003	+	1.90531i	−0.0385088	+	0.0666992i
$817$		−	2.13874i		−	0.0748250i
$818$	−24.2902			−0.849287
$819$	−5.93076	−	7.47169i	−0.207237	−	0.261082i
$820$	−6.38924			−0.223122
$821$		−	21.3599i		−	0.745467i	−0.927938	−	0.372734i	$-0.878421\pi$
$821$		−	21.3599i		−	0.745467i	0.927938	−	0.372734i	$-0.121579\pi$
$822$	−10.1486	+	17.5779i	−0.353974	+	0.613100i
$823$	2.65227			0.0924524			0.0462262	−	0.998931i	$-0.485280\pi$
$823$	2.65227			0.0924524			0.0462262	+	0.998931i	$0.485280\pi$
$824$	2.04778	+	1.18228i	0.0713377	+	0.0411868i
$825$	−0.261023	−	0.150702i	−0.00908766	−	0.00524676i
$826$	−35.7977	+	3.55753i	−1.24556	+	0.123782i
$827$			41.7395i			1.45142i	0.687999	+	0.725712i	$0.258490\pi$
$827$			41.7395i			1.45142i	−0.687999	+	0.725712i	$0.741510\pi$
$828$	−4.01555	−	6.95513i	−0.139550	−	0.241707i
$829$	20.5425	−	35.5806i	0.713470	−	1.23577i	−0.250077	−	0.968226i	$-0.580456\pi$
$829$	20.5425	−	35.5806i	0.713470	−	1.23577i	0.963547	−	0.267540i	$-0.0862109\pi$
$830$	−9.79954	−	5.65777i	−0.340147	−	0.196384i
$831$	−11.2996	+	19.5715i	−0.391979	+	0.678928i
$832$	3.60135	−	0.173988i	0.124854	−	0.00603196i
$833$	−15.0992	+	3.03102i	−0.523157	+	0.105019i
$834$	−0.128779	+	0.0743508i	−0.00445926	+	0.00257456i
$835$	16.9604			0.586939
$836$	0.0635473			0.00219783
$837$	−8.72813	+	5.03919i	−0.301688	+	0.174180i
$838$	−8.42229	+	4.86261i	−0.290943	+	0.167976i
$839$	22.0532	+	12.7324i	0.761360	+	0.439572i	0.829784	−	0.558085i	$-0.188464\pi$
$839$	22.0532	+	12.7324i	0.761360	+	0.439572i	−0.0684237	+	0.997656i	$0.521797\pi$
$840$	−1.47002	−	2.04761i	−0.0507206	−	0.0706493i
$841$	3.28013	−	5.68135i	0.113108	−	0.195909i
$842$	25.6881			0.885270
$843$	6.36216	+	3.67320i	0.219125	+	0.126512i
$844$	3.36821	+	5.83390i	0.115938	+	0.200811i
$845$	−11.2730	−	5.12984i	−0.387803	−	0.176472i
$846$	−9.37750			−0.322405
$847$	16.9644	+	23.6299i	0.582904	+	0.811934i
$848$	0.935404	+	1.62017i	0.0321219	+	0.0556368i
$849$	−12.5645	−	21.7624i	−0.431213	−	0.746882i
$850$	−7.79716	+	4.50170i	−0.267441	+	0.154407i
$851$		−	90.5737i		−	3.10483i
$852$	−8.96491	+	5.17589i	−0.307133	+	0.177323i
$853$		−	22.0242i		−	0.754095i	−0.926194	−	0.377048i	$-0.876939\pi$
$853$		−	22.0242i		−	0.754095i	0.926194	−	0.377048i	$-0.123061\pi$
$854$	−7.67582	+	5.51063i	−0.262661	+	0.188570i
$855$	−0.411011	−	0.711892i	−0.0140563	−	0.0243462i
$856$			9.50398i			0.324840i
$857$	15.1598	+	26.2576i	0.517850	+	0.896942i	0.999785	+	0.0207350i	$0.00660064\pi$
$857$	15.1598	+	26.2576i	0.517850	+	0.896942i	−0.481935	+	0.876207i	$0.660066\pi$
$858$	−0.143719	−	0.223300i	−0.00490648	−	0.00762332i
$859$	1.51161	−	2.61819i	0.0515756	−	0.0893315i	−0.839085	−	0.544000i	$-0.816909\pi$
$859$	1.51161	−	2.61819i	0.0515756	−	0.0893315i	0.890661	+	0.454669i	$0.150242\pi$
$860$	−2.04519	+	1.18079i	−0.0697403	+	0.0402646i
$861$	−1.75467	−	17.6563i	−0.0597989	−	0.601726i
$862$	1.81057	−	3.13600i	0.0616683	−	0.106813i
$863$	7.87832	+	4.54855i	0.268181	+	0.154834i	0.628061	−	0.778164i	$-0.283849\pi$
$863$	7.87832	+	4.54855i	0.268181	+	0.154834i	−0.359880	+	0.932999i	$0.617182\pi$
$864$		−	1.00000i		−	0.0340207i
$865$		−	2.63933i		−	0.0897400i
$866$	−2.47898	−	1.43124i	−0.0842390	−	0.0486354i
$867$	−6.07986	+	10.5306i	−0.206483	+	0.357639i
$868$	21.6608	−	15.5507i	0.735215	−	0.527826i
$869$	−0.165929	+	0.0957991i	−0.00562875	+	0.00324976i
$870$	−2.25654	+	3.90844i	−0.0765038	+	0.132509i
$871$	−39.1609	−	20.1554i	−1.32692	−	0.682941i
$872$	3.86508	+	6.69452i	0.130888	+	0.226705i
$873$		−	12.8546i		−	0.435061i
$874$	3.46469	+	6.00101i	0.117195	+	0.202987i
$875$	−2.26646	−	22.8063i	−0.0766204	−	0.770992i
$876$			7.80821i			0.263815i
$877$	−15.3424	+	8.85792i	−0.518075	+	0.299111i	−0.736147	−	0.676822i	$-0.763357\pi$
$877$	−15.3424	+	8.85792i	−0.518075	+	0.299111i	0.218072	+	0.975933i	$0.430023\pi$
$878$			10.7520i			0.362862i
$879$	−15.0195	+	8.67149i	−0.506594	+	0.292482i
$880$	−0.0350842	−	0.0607676i	−0.00118269	−	0.00204848i
$881$	0.631977	+	1.09462i	0.0212919	+	0.0368786i	0.876475	−	0.481447i	$-0.159889\pi$
$881$	0.631977	+	1.09462i	0.0212919	+	0.0368786i	−0.855183	+	0.518326i	$0.826555\pi$
$882$	5.25476	−	4.62466i	0.176937	−	0.155721i
$883$	9.58668			0.322617			0.161309	−	0.986904i	$-0.448429\pi$
$883$	9.58668			0.322617			0.161309	+	0.986904i	$0.448429\pi$
$884$	−7.92320	+	0.382785i	−0.266486	+	0.0128745i
$885$	6.47700	+	11.2185i	0.217722	+	0.377105i
$886$	−5.20447	−	3.00480i	−0.174848	−	0.100948i
$887$	15.6377			0.525062			0.262531	−	0.964924i	$-0.415443\pi$
$887$	15.6377			0.525062			0.262531	+	0.964924i	$0.415443\pi$
$888$	5.63894	−	9.76693i	0.189230	−	0.327757i
$889$	8.75067	+	12.1889i	0.293488	+	0.408803i
$890$	2.99652	+	1.73004i	0.100444	+	0.0579912i
$891$	−0.0637835	+	0.0368254i	−0.00213683	+	0.00123370i
$892$	−22.0208	+	12.7137i	−0.737310	+	0.425686i
$893$	8.09108			0.270758
$894$	−11.7924			−0.394395
$895$	0.628242	−	0.362716i	0.0209998	−	0.0121242i
$896$	0.261643	+	2.63278i	0.00874088	+	0.0879551i
$897$	13.2513	−	25.7465i	0.442447	−	0.859651i
$898$	−9.59355	+	16.6165i	−0.320141	+	0.554500i
$899$	−41.3457	−	23.8709i	−1.37896	−	0.796140i
$900$	2.04617	−	3.54406i	0.0682055	−	0.118135i
$901$	−2.05795	−	3.56447i	−0.0685602	−	0.118750i
$902$		−	0.493928i		−	0.0164460i
$903$	−3.82471	−	5.32748i	−0.127278	−	0.177288i
$904$	6.42514	+	3.70956i	0.213697	+	0.123378i
$905$	12.3968	+	7.15727i	0.412082	+	0.237916i
$906$	−15.8772			−0.527484
$907$	24.2657	−	42.0294i	0.805730	−	1.39556i	−0.110068	−	0.993924i	$-0.535107\pi$
$907$	24.2657	−	42.0294i	0.805730	−	1.39556i	0.915797	−	0.401641i	$-0.131560\pi$
$908$			3.40559i			0.113018i
$909$	3.40735			0.113015
$910$	3.33955	−	8.45253i	0.110705	−	0.280199i
$911$	−16.8461			−0.558135			−0.279068	−	0.960271i	$-0.590025\pi$
$911$	−16.8461			−0.558135			−0.279068	+	0.960271i	$0.590025\pi$
$912$			0.862818i			0.0285708i
$913$	0.437380	−	0.757565i	0.0144752	−	0.0250717i
$914$	−6.43716			−0.212922
$915$	2.94670	+	1.70128i	0.0974148	+	0.0562425i
$916$	0.991069	+	0.572194i	0.0327459	+	0.0189058i
$917$	−23.5716	+	52.1454i	−0.778402	+	1.72199i
$918$			2.20006i			0.0726129i
$919$	17.5397	+	30.3797i	0.578582	+	1.00213i	0.995642	+	0.0932549i	$0.0297272\pi$
$919$	17.5397	+	30.3797i	0.578582	+	1.00213i	−0.417060	+	0.908879i	$0.636940\pi$
$920$	3.82568	−	6.62627i	0.126129	−	0.218462i
$921$	−24.1937	−	13.9683i	−0.797210	−	0.460270i
$922$	3.97831	−	6.89063i	0.131019	−	0.226931i
$923$	−33.1863	−	17.0804i	−1.09234	−	0.562209i
$924$	0.158293	−	0.113642i	0.00520746	−	0.00373854i
$925$	39.9695	−	23.0764i	1.31419	−	0.758748i
$926$	−20.5480			−0.675250
$927$	2.36457			0.0776626
$928$	4.10241	−	2.36853i	0.134668	−	0.0777508i
$929$	11.8242	−	6.82669i	0.387939	−	0.223976i	−0.293328	−	0.956012i	$-0.594763\pi$
$929$	11.8242	−	6.82669i	0.387939	−	0.223976i	0.681267	+	0.732035i	$0.261429\pi$
$930$	−8.31543	−	4.80092i	−0.272674	−	0.157428i
$931$	−4.53390	+	3.99025i	−0.148593	+	0.130775i
$932$	−1.67391	+	2.89929i	−0.0548307	+	0.0949695i
$933$	−6.69020			−0.219027
$934$	−7.19125	−	4.15187i	−0.235305	−	0.135853i
$935$	0.0771875	+	0.133693i	0.00252430	+	0.00437222i
$936$	3.03187	−	1.95135i	0.0990997	−	0.0637820i
$937$	−22.9765			−0.750611			−0.375306	−	0.926901i	$-0.622462\pi$
$937$	−22.9765			−0.750611			−0.375306	+	0.926901i	$0.622462\pi$
$938$	13.3124	−	29.4499i	0.434666	−	0.961575i
$939$	−2.67609	−	4.63512i	−0.0873308	−	0.151261i
$940$	−4.46705	−	7.73716i	−0.145699	−	0.252358i
$941$	−23.4793	+	13.5558i	−0.765404	+	0.441906i	−0.831233	−	0.555925i	$-0.812364\pi$
$941$	−23.4793	+	13.5558i	−0.765404	+	0.441906i	0.0658287	+	0.997831i	$0.479031\pi$
$942$		−	6.92422i		−	0.225603i
$943$	46.6435	−	26.9296i	1.51892	−	0.876949i
$944$		−	13.5969i		−	0.442541i
$945$	−2.29688	−	1.03827i	−0.0747176	−	0.0337750i
$946$	−0.0912822	−	0.158105i	−0.00296784	−	0.00514045i
$947$			4.64882i			0.151066i	0.997143	+	0.0755331i	$0.0240659\pi$
$947$			4.64882i			0.151066i	−0.997143	+	0.0755331i	$0.975934\pi$
$948$	−1.30072	−	2.25291i	−0.0422454	−	0.0731712i
$949$	−23.6734	+	15.2366i	−0.768472	+	0.494600i
$950$	−1.76547	+	3.05788i	−0.0572794	+	0.0992108i
$951$	−15.2431	+	8.80060i	−0.494291	+	0.285379i
$952$	−0.575631	−	5.79229i	−0.0186563	−	0.187729i
$953$	−13.9684	+	24.1939i	−0.452480	+	0.783718i	−0.998539	−	0.0540283i	$-0.982794\pi$
$953$	−13.9684	+	24.1939i	−0.452480	+	0.783718i	0.546060	+	0.837746i	$0.316127\pi$
$954$	1.62017	+	0.935404i	0.0524548	+	0.0302848i
$955$			5.59688i			0.181111i
$956$			28.9640i			0.936762i
$957$	−0.302146	−	0.174444i	−0.00976700	−	0.00563898i
$958$	10.6254	−	18.4037i	0.343291	−	0.594597i
$959$	−5.31063	−	53.4382i	−0.171489	−	1.72561i
$960$	0.825077	−	0.476358i	0.0266292	−	0.0153744i
$961$	35.2868	−	61.1185i	1.13828	−	1.97157i
$962$	40.6156	−	1.96222i	1.30950	−	0.0632645i
$963$	4.75199	+	8.23069i	0.153131	+	0.265230i
$964$			5.99770i			0.193173i
$965$	5.81998	+	10.0805i	0.187352	+	0.324503i
$966$	19.3620	+	8.75230i	0.622961	+	0.281601i
$967$		−	11.0007i		−	0.353760i	−0.984232	−	0.176880i	$-0.943400\pi$
$967$		−	11.0007i		−	0.353760i	0.984232	−	0.176880i	$-0.0566004\pi$
$968$	−9.52158	+	5.49729i	−0.306035	+	0.176690i
$969$		−	1.89826i		−	0.0609808i
$970$	10.6060	−	6.12338i	0.340538	−	0.196610i
$971$	2.52319	+	4.37029i	0.0809729	+	0.140249i	0.903668	−	0.428234i	$-0.140864\pi$
$971$	2.52319	+	4.37029i	0.0809729	+	0.140249i	−0.822695	+	0.568483i	$0.807531\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	0.162055	−	0.358501i	0.00519525	−	0.0114930i
$974$	−24.9365			−0.799018
$975$	14.7379	−	0.712017i	0.471991	−	0.0228028i
$976$	−1.78571	−	3.09294i	−0.0571592	−	0.0990026i
$977$	−21.5797	−	12.4591i	−0.690396	−	0.398600i	0.113364	−	0.993553i	$-0.463837\pi$
$977$	−21.5797	−	12.4591i	−0.690396	−	0.398600i	−0.803760	+	0.594953i	$0.797171\pi$
$978$	8.20609			0.262402
$979$	−0.133743	+	0.231649i	−0.00427444	+	0.00740355i
$980$	6.31885	+	2.13258i	0.201848	+	0.0681228i
$981$	6.69452	+	3.86508i	0.213740	+	0.123403i
$982$	−0.349141	+	0.201577i	−0.0111415	+	0.00643257i
$983$	−27.0541	+	15.6197i	−0.862892	+	0.498191i	−0.864980	−	0.501807i	$-0.832669\pi$
$983$	−27.0541	+	15.6197i	−0.862892	+	0.498191i	0.00208762	+	0.999998i	$0.499335\pi$
$984$	6.70634			0.213790
$985$	−12.7525			−0.406329
$986$	−9.02558	+	5.21092i	−0.287433	+	0.165949i
$987$	20.1544	−	14.4693i	0.641523	−	0.460563i
$988$	−2.61595	+	1.68366i	−0.0832245	+	0.0535645i
$989$	9.95366	−	17.2402i	0.316508	−	0.548208i
$990$	−0.0607676	−	0.0350842i	−0.00193132	−	0.00111505i
$991$	−18.5986	+	32.2137i	−0.590803	+	1.02330i	0.403322	+	0.915058i	$0.367856\pi$
$991$	−18.5986	+	32.2137i	−0.590803	+	1.02330i	−0.994125	+	0.108242i	$0.965478\pi$
$992$	5.03919	+	8.72813i	0.159994	+	0.277118i
$993$			29.8193i			0.946286i
$994$	11.2814	−	24.9569i	0.357824	−	0.791584i
$995$	−0.443115	−	0.255832i	−0.0140477	−	0.00811044i
$996$	10.2859	+	5.93856i	0.325921	+	0.188171i
$997$	37.1018			1.17503			0.587514	−	0.809214i	$-0.300107\pi$
$997$	37.1018			1.17503			0.587514	+	0.809214i	$0.300107\pi$
$998$	−13.2784	+	22.9988i	−0.420320	+	0.728016i
$999$		−	11.2779i		−	0.356816i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bm.a.205.6	yes	16
3.2	odd	2		1638.2.dt.a.1297.3		16
7.4	even	3		546.2.bd.a.361.3	yes	16
13.4	even	6		546.2.bd.a.121.3	✓	16
21.11	odd	6		1638.2.cr.a.361.6		16
39.17	odd	6		1638.2.cr.a.667.6		16
91.4	even	6	inner	546.2.bm.a.277.2	yes	16
273.95	odd	6		1638.2.dt.a.1369.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.3	✓	16	13.4	even	6
546.2.bd.a.361.3	yes	16	7.4	even	3
546.2.bm.a.205.6	yes	16	1.1	even	1	trivial
546.2.bm.a.277.2	yes	16	91.4	even	6	inner
1638.2.cr.a.361.6		16	21.11	odd	6
1638.2.cr.a.667.6		16	39.17	odd	6
1638.2.dt.a.1297.3		16	3.2	odd	2
1638.2.dt.a.1369.7		16	273.95	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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-0.825077 - 0.476358i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.63278 + 0.261643i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-0.825077 - 0.476358i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.63278 + 0.261643i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.476358 - 0.825077i) q^{10} +(0.0637835 + 0.0368254i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-3.60135 + 0.173988i) q^{13} +(-0.261643 - 2.63278i) q^{14} +(-0.825077 + 0.476358i) q^{15} +1.00000 q^{16} -2.20006 q^{17} +(0.866025 - 0.500000i) q^{18} +(-0.747223 + 0.431409i) q^{19} +(0.825077 + 0.476358i) q^{20} +(-1.08980 + 2.41088i) q^{21} +(-0.0368254 + 0.0637835i) q^{22} -8.03109 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-2.04617 - 3.54406i) q^{25} +(-0.173988 - 3.60135i) q^{26} -1.00000 q^{27} +(2.63278 - 0.261643i) q^{28} +(-2.36853 - 4.10241i) q^{29} +(-0.476358 - 0.825077i) q^{30} +(8.72813 - 5.03919i) q^{31} +1.00000i q^{32} +(0.0637835 - 0.0368254i) q^{33} -2.20006i q^{34} +(2.29688 + 1.03827i) q^{35} +(0.500000 + 0.866025i) q^{36} +11.2779i q^{37} +(-0.431409 - 0.747223i) q^{38} +(-1.65000 + 3.20586i) q^{39} +(-0.476358 + 0.825077i) q^{40} +(-5.80786 + 3.35317i) q^{41} +(-2.41088 - 1.08980i) q^{42} +(-1.23939 + 2.14669i) q^{43} +(-0.0637835 - 0.0368254i) q^{44} +0.952717i q^{45} -8.03109i q^{46} +(-8.12115 - 4.68875i) q^{47} +(0.500000 - 0.866025i) q^{48} +(6.86309 - 1.37770i) q^{49} +(3.54406 - 2.04617i) q^{50} +(-1.10003 + 1.90531i) q^{51} +(3.60135 - 0.173988i) q^{52} +(0.935404 + 1.62017i) q^{53} -1.00000i q^{54} +(-0.0350842 - 0.0607676i) q^{55} +(0.261643 + 2.63278i) q^{56} +0.862818i q^{57} +(4.10241 - 2.36853i) q^{58} -13.5969i q^{59} +(0.825077 - 0.476358i) q^{60} +(-1.78571 - 3.09294i) q^{61} +(5.03919 + 8.72813i) q^{62} +(1.54298 + 2.14923i) q^{63} -1.00000 q^{64} +(3.05427 + 1.57198i) q^{65} +(0.0368254 + 0.0637835i) q^{66} +(10.5789 + 6.10772i) q^{67} +2.20006 q^{68} +(-4.01555 + 6.95513i) q^{69} +(-1.03827 + 2.29688i) q^{70} +(8.96491 + 5.17589i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(6.76210 - 3.90410i) q^{73} -11.2779 q^{74} -4.09233 q^{75} +(0.747223 - 0.431409i) q^{76} +(-0.177563 - 0.0802648i) q^{77} +(-3.20586 - 1.65000i) q^{78} +(-1.30072 + 2.25291i) q^{79} +(-0.825077 - 0.476358i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.35317 - 5.80786i) q^{82} -11.8771i q^{83} +(1.08980 - 2.41088i) q^{84} +(1.81522 + 1.04802i) q^{85} +(-2.14669 - 1.23939i) q^{86} -4.73706 q^{87} +(0.0368254 - 0.0637835i) q^{88} +3.63181i q^{89} -0.952717 q^{90} +(9.43605 - 1.40034i) q^{91} +8.03109 q^{92} -10.0784i q^{93} +(4.68875 - 8.12115i) q^{94} +0.822022 q^{95} +(0.866025 + 0.500000i) q^{96} +(11.1324 + 6.42728i) q^{97} +(1.37770 + 6.86309i) q^{98} -0.0736508i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9} + 4 q^{10} + 6 q^{11} - 8 q^{12} - 10 q^{13} + 4 q^{14} + 16 q^{16} + 18 q^{19} + 8 q^{21} + 6 q^{22} + 32 q^{23} - 4 q^{26} - 16 q^{27} + 2 q^{28} - 4 q^{29} - 4 q^{30} - 12 q^{31} + 6 q^{33} - 2 q^{35} + 8 q^{36} - 2 q^{38} - 14 q^{39} - 4 q^{40} - 18 q^{41} + 2 q^{42} - 32 q^{43} - 6 q^{44} - 66 q^{47} + 8 q^{48} + 22 q^{49} + 36 q^{50} + 10 q^{52} + 2 q^{53} + 16 q^{55} - 4 q^{56} + 24 q^{58} + 4 q^{61} + 4 q^{62} + 10 q^{63} - 16 q^{64} + 38 q^{65} - 6 q^{66} + 36 q^{67} + 16 q^{69} + 6 q^{70} - 30 q^{71} + 18 q^{73} - 12 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 6 q^{82} - 8 q^{84} + 72 q^{85} - 8 q^{87} - 6 q^{88} - 8 q^{90} - 2 q^{91} - 32 q^{92} - 24 q^{94} + 80 q^{95} - 6 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9 + 4 * q^10 + 6 * q^11 - 8 * q^12 - 10 * q^13 + 4 * q^14 + 16 * q^16 + 18 * q^19 + 8 * q^21 + 6 * q^22 + 32 * q^23 - 4 * q^26 - 16 * q^27 + 2 * q^28 - 4 * q^29 - 4 * q^30 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 8 * q^36 - 2 * q^38 - 14 * q^39 - 4 * q^40 - 18 * q^41 + 2 * q^42 - 32 * q^43 - 6 * q^44 - 66 * q^47 + 8 * q^48 + 22 * q^49 + 36 * q^50 + 10 * q^52 + 2 * q^53 + 16 * q^55 - 4 * q^56 + 24 * q^58 + 4 * q^61 + 4 * q^62 + 10 * q^63 - 16 * q^64 + 38 * q^65 - 6 * q^66 + 36 * q^67 + 16 * q^69 + 6 * q^70 - 30 * q^71 + 18 * q^73 - 12 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 6 * q^82 - 8 * q^84 + 72 * q^85 - 8 * q^87 - 6 * q^88 - 8 * q^90 - 2 * q^91 - 32 * q^92 - 24 * q^94 + 80 * q^95 - 6 * q^97 - 60 * q^98

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