LMFDB - Embedded newform 546.2.bd.a.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(121,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bd (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			121.3
Root			$-2.54804i$ of defining polynomial
Character	$\chi$	$=$	546.121
Dual form			546.2.bd.a.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(0.825077 + 0.476358i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.08980 + 2.41088i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(0.825077 + 0.476358i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.08980 + 2.41088i) q^{7} +1.00000i q^{8} +1.00000 q^{9} -0.952717 q^{10} +0.0736508i 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} +(-0.500000 - 0.866025i) q^{16} +(1.10003 - 1.90531i) q^{17} +(-0.866025 + 0.500000i) q^{18} +0.862818i q^{19} +(0.825077 - 0.476358i) q^{20} +(1.08980 - 2.41088i) q^{21} +(-0.0368254 - 0.0637835i) q^{22} +(4.01555 + 6.95513i) q^{23} -1.00000i q^{24} +(-2.04617 - 3.54406i) q^{25} +(3.20586 - 1.65000i) q^{26} -1.00000 q^{27} +(1.54298 + 2.14923i) q^{28} +(-2.36853 + 4.10241i) q^{29} +0.952717 q^{30} +(-8.72813 + 5.03919i) q^{31} +(0.866025 + 0.500000i) q^{32} -0.0736508i q^{33} +2.20006i q^{34} +(-2.04761 + 1.47002i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-9.76693 + 5.63894i) q^{37} +(-0.431409 - 0.747223i) q^{38} +(3.60135 + 0.173988i) q^{39} +(-0.476358 + 0.825077i) q^{40} +(-5.80786 - 3.35317i) q^{41} +(0.261643 + 2.63278i) q^{42} +(-1.23939 - 2.14669i) q^{43} +(0.0637835 + 0.0368254i) q^{44} +(0.825077 + 0.476358i) q^{45} +(-6.95513 - 4.01555i) q^{46} +(8.12115 + 4.68875i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-4.62466 - 5.25476i) q^{49} +(3.54406 + 2.04617i) q^{50} +(-1.10003 + 1.90531i) q^{51} +(-1.95135 + 3.03187i) q^{52} +(0.935404 + 1.62017i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.0350842 + 0.0607676i) q^{55} +(-2.41088 - 1.08980i) q^{56} -0.862818i q^{57} -4.73706i q^{58} +(-11.7753 - 6.79845i) q^{59} +(-0.825077 + 0.476358i) q^{60} +3.57142 q^{61} +(5.03919 - 8.72813i) q^{62} +(-1.08980 + 2.41088i) q^{63} -1.00000 q^{64} +(-2.88851 - 1.85909i) q^{65} +(0.0368254 + 0.0637835i) q^{66} +12.2154i q^{67} +(-1.10003 - 1.90531i) q^{68} +(-4.01555 - 6.95513i) q^{69} +(1.03827 - 2.29688i) q^{70} +(8.96491 - 5.17589i) q^{71} +1.00000i q^{72} +(-6.76210 + 3.90410i) q^{73} +(5.63894 - 9.76693i) q^{74} +(2.04617 + 3.54406i) 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} -0.952717i q^{80} +1.00000 q^{81} +6.70634 q^{82} +11.8771i q^{83} +(-1.54298 - 2.14923i) q^{84} +(1.81522 - 1.04802i) q^{85} +(2.14669 + 1.23939i) q^{86} +(2.36853 - 4.10241i) q^{87} -0.0736508 q^{88} +(-3.14524 + 1.81590i) q^{89} -0.952717 q^{90} +(4.34422 - 8.49280i) q^{91} +8.03109 q^{92} +(8.72813 - 5.03919i) q^{93} -9.37750 q^{94} +(-0.411011 + 0.711892i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(11.1324 - 6.42728i) q^{97} +(6.63246 + 2.23842i) q^{98} +0.0736508i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9	$ 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31} + 16 q^{35} + 8 q^{36} + 30 q^{37} - 2 q^{38} + 10 q^{39} - 4 q^{40} - 18 q^{41} - 4 q^{42} - 32 q^{43} + 6 q^{44} + 12 q^{46} + 66 q^{47} + 8 q^{48} - 2 q^{49} + 36 q^{50} + 4 q^{52} + 2 q^{53} + 16 q^{55} + 2 q^{56} - 36 q^{59} - 8 q^{61} + 4 q^{62} + 8 q^{63} - 16 q^{64} - 28 q^{65} - 6 q^{66} + 16 q^{69} - 6 q^{70} - 30 q^{71} - 18 q^{73} + 6 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} + 16 q^{81} - 12 q^{82} - 10 q^{84} + 72 q^{85} + 4 q^{87} + 12 q^{88} - 42 q^{89} - 8 q^{90} - 18 q^{91} - 32 q^{92} - 12 q^{93} + 48 q^{94} - 40 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) $ 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9 - 8 * q^10 - 8 * q^12 - 10 * q^13 + 4 * q^14 - 8 * q^16 - 8 * q^21 + 6 * q^22 - 16 * q^23 + 2 * q^26 - 16 * q^27 + 10 * q^28 - 4 * q^29 + 8 * q^30 + 12 * q^31 + 16 * q^35 + 8 * q^36 + 30 * q^37 - 2 * q^38 + 10 * q^39 - 4 * q^40 - 18 * q^41 - 4 * q^42 - 32 * q^43 + 6 * q^44 + 12 * q^46 + 66 * q^47 + 8 * q^48 - 2 * q^49 + 36 * q^50 + 4 * q^52 + 2 * q^53 + 16 * q^55 + 2 * q^56 - 36 * q^59 - 8 * q^61 + 4 * q^62 + 8 * q^63 - 16 * q^64 - 28 * q^65 - 6 * q^66 + 16 * q^69 - 6 * q^70 - 30 * q^71 - 18 * q^73 + 6 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 + 16 * q^81 - 12 * q^82 - 10 * q^84 + 72 * q^85 + 4 * q^87 + 12 * q^88 - 42 * q^89 - 8 * q^90 - 18 * q^91 - 32 * q^92 - 12 * q^93 + 48 * q^94 - 40 * q^95 - 6 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.825077	+	0.476358i	0.368986	+	0.213034i	0.673015	−	0.739629i	$-0.264999\pi$
$5$	0.825077	+	0.476358i	0.368986	+	0.213034i	−0.304030	+	0.952663i	$0.598332\pi$
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−1.08980	+	2.41088i	−0.411906	+	0.911226i
$7$	−1.08980	+	2.41088i	−0.411906	+	0.911226i
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	−0.952717			−0.301276
$11$			0.0736508i			0.0222066i	0.999938	+	0.0111033i	$0.00353436\pi$
$11$			0.0736508i			0.0222066i	−0.999938	+	0.0111033i	$0.996466\pi$
$12$	−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
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.10003	−	1.90531i	0.266797	−	0.462106i	−0.701236	−	0.712929i	$-0.747368\pi$
$17$	1.10003	−	1.90531i	0.266797	−	0.462106i	0.968033	+	0.250823i	$0.0807014\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$			0.862818i			0.197944i	0.995090	+	0.0989721i	$0.0315554\pi$
$19$			0.862818i			0.197944i	−0.995090	+	0.0989721i	$0.968445\pi$
$20$	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
$23$	4.01555	+	6.95513i	0.837299	+	1.45024i	0.892145	+	0.451750i	$0.149200\pi$
$23$	4.01555	+	6.95513i	0.837299	+	1.45024i	−0.0548457	+	0.998495i	$0.517467\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−2.04617	−	3.54406i	−0.409233	−	0.708812i
$26$	3.20586	−	1.65000i	0.628720	−	0.323591i
$27$	−1.00000			−0.192450
$28$	1.54298	+	2.14923i	0.291596	+	0.406167i
$29$	−2.36853	+	4.10241i	−0.439825	+	0.761799i	−0.997676	−	0.0681421i	$-0.978293\pi$
$29$	−2.36853	+	4.10241i	−0.439825	+	0.761799i	0.557851	+	0.829941i	$0.311626\pi$
$30$	0.952717			0.173942
$31$	−8.72813	+	5.03919i	−1.56762	+	0.905065i	−0.571172	+	0.820830i	$0.693511\pi$
$31$	−8.72813	+	5.03919i	−1.56762	+	0.905065i	−0.996446	+	0.0842343i	$0.973156\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		−	0.0736508i		−	0.0128210i
$34$			2.20006i			0.377308i
$35$	−2.04761	+	1.47002i	−0.346110	+	0.248479i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−9.76693	+	5.63894i	−1.60567	+	0.927036i	−0.615351	+	0.788254i	$0.710986\pi$
$37$	−9.76693	+	5.63894i	−1.60567	+	0.927036i	−0.990323	+	0.138782i	$0.955681\pi$
$38$	−0.431409	−	0.747223i	−0.0699838	−	0.121216i
$39$	3.60135	+	0.173988i	0.576678	+	0.0278604i
$40$	−0.476358	+	0.825077i	−0.0753189	+	0.130456i
$41$	−5.80786	−	3.35317i	−0.907036	−	0.523677i	−0.0275595	−	0.999620i	$-0.508774\pi$
$41$	−5.80786	−	3.35317i	−0.907036	−	0.523677i	−0.879476	+	0.475943i	$0.842107\pi$
$42$	0.261643	+	2.63278i	0.0403724	+	0.406247i
$43$	−1.23939	−	2.14669i	−0.189005	−	0.327367i	0.755914	−	0.654671i	$-0.227193\pi$
$43$	−1.23939	−	2.14669i	−0.189005	−	0.327367i	−0.944919	+	0.327305i	$0.893860\pi$
$44$	0.0637835	+	0.0368254i	0.00961572	+	0.00555164i
$45$	0.825077	+	0.476358i	0.122995	+	0.0710113i
$46$	−6.95513	−	4.01555i	−1.02548	−	0.592060i
$47$	8.12115	+	4.68875i	1.18459	+	0.683924i	0.957072	−	0.289849i	$-0.0936052\pi$
$47$	8.12115	+	4.68875i	1.18459	+	0.683924i	0.227519	+	0.973774i	$0.426939\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−4.62466	−	5.25476i	−0.660666	−	0.750680i
$50$	3.54406	+	2.04617i	0.501206	+	0.289371i
$51$	−1.10003	+	1.90531i	−0.154035	+	0.266797i
$52$	−1.95135	+	3.03187i	−0.270604	+	0.420444i
$53$	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	$0.792321\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−0.0350842	+	0.0607676i	−0.00473075	+	0.00819390i
$56$	−2.41088	−	1.08980i	−0.322167	−	0.145631i
$57$		−	0.862818i		−	0.114283i
$58$		−	4.73706i		−	0.622007i
$59$	−11.7753	−	6.79845i	−1.53301	−	0.885083i	−0.999221	−	0.0394635i	$-0.987435\pi$
$59$	−11.7753	−	6.79845i	−1.53301	−	0.885083i	−0.533787	−	0.845619i	$-0.679232\pi$
$60$	−0.825077	+	0.476358i	−0.106517	+	0.0614976i
$61$	3.57142			0.457274			0.228637	−	0.973512i	$-0.426573\pi$
$61$	3.57142			0.457274			0.228637	+	0.973512i	$0.426573\pi$
$62$	5.03919	−	8.72813i	0.639977	−	1.10847i
$63$	−1.08980	+	2.41088i	−0.137302	+	0.303742i
$64$	−1.00000			−0.125000
$65$	−2.88851	−	1.85909i	−0.358276	−	0.230591i
$66$	0.0368254	+	0.0637835i	0.00453290	+	0.00785121i
$67$			12.2154i			1.49235i	0.665748	+	0.746177i	$0.268113\pi$
$67$			12.2154i			1.49235i	−0.665748	+	0.746177i	$0.731887\pi$
$68$	−1.10003	−	1.90531i	−0.133398	−	0.231053i
$69$	−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	0.137420	−	0.990513i	$-0.456119\pi$
$71$	8.96491	−	5.17589i	1.06394	−	0.614265i	0.926519	+	0.376248i	$0.122786\pi$
$72$			1.00000i			0.117851i
$73$	−6.76210	+	3.90410i	−0.791444	+	0.456941i	−0.840471	−	0.541857i	$-0.817721\pi$
$73$	−6.76210	+	3.90410i	−0.791444	+	0.456941i	0.0490264	+	0.998797i	$0.484388\pi$
$74$	5.63894	−	9.76693i	0.655513	−	1.13538i
$75$	2.04617	+	3.54406i	0.236271	+	0.409233i
$76$	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	$0.213417\pi$
$80$		−	0.952717i		−	0.106517i
$81$	1.00000			0.111111
$82$	6.70634			0.740592
$83$			11.8771i			1.30368i	0.758355	+	0.651842i	$0.226003\pi$
$83$			11.8771i			1.30368i	−0.758355	+	0.651842i	$0.773997\pi$
$84$	−1.54298	−	2.14923i	−0.168353	−	0.234501i
$85$	1.81522	−	1.04802i	0.196889	−	0.113674i
$86$	2.14669	+	1.23939i	0.231483	+	0.133647i
$87$	2.36853	−	4.10241i	0.253933	−	0.439825i
$88$	−0.0736508			−0.00785121
$89$	−3.14524	+	1.81590i	−0.333395	+	0.192485i	−0.657347	−	0.753588i	$-0.728321\pi$
$89$	−3.14524	+	1.81590i	−0.333395	+	0.192485i	0.323953	+	0.946073i	$0.394988\pi$
$90$	−0.952717			−0.100425
$91$	4.34422	−	8.49280i	0.455398	−	0.890288i
$92$	8.03109			0.837299
$93$	8.72813	−	5.03919i	0.905065	−	0.522539i
$94$	−9.37750			−0.967215
$95$	−0.411011	+	0.711892i	−0.0421688	+	0.0730385i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	11.1324	−	6.42728i	1.13032	−	0.652592i	0.186306	−	0.982492i	$-0.440348\pi$
$97$	11.1324	−	6.42728i	1.13032	−	0.652592i	0.944016	+	0.329900i	$0.107015\pi$
$98$	6.63246	+	2.23842i	0.669979	+	0.226115i
$99$			0.0736508i			0.00740219i
$100$	−4.09233			−0.409233
$101$	3.40735			0.339044			0.169522	−	0.985526i	$-0.445778\pi$
$101$	3.40735			0.339044			0.169522	+	0.985526i	$0.445778\pi$
$102$		−	2.20006i		−	0.217839i
$103$	−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
$107$	4.75199	+	8.23069i	0.459392	+	0.795691i	0.998929	−	0.0462712i	$-0.0147338\pi$
$107$	4.75199	+	8.23069i	0.459392	+	0.795691i	−0.539536	+	0.841962i	$0.681401\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	6.69452	−	3.86508i	0.641219	−	0.370208i	−0.143865	−	0.989597i	$-0.545953\pi$
$109$	6.69452	−	3.86508i	0.641219	−	0.370208i	0.785084	+	0.619389i	$0.212620\pi$
$110$		−	0.0701684i		−	0.00669029i
$111$	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	0.637100	−	0.770781i	$-0.280134\pi$
$113$	−3.70956	−	6.42514i	−0.348966	−	0.604426i	−0.986066	+	0.166355i	$0.946800\pi$
$114$	0.431409	+	0.747223i	0.0404052	+	0.0699838i
$115$			7.65136i			0.713493i
$116$	2.36853	+	4.10241i	0.219913	+	0.380900i
$117$	−3.60135	−	0.173988i	−0.332945	−	0.0160852i
$118$	13.5969			1.25170
$119$	3.39466	+	4.72845i	0.311188	+	0.433457i
$120$	0.476358	−	0.825077i	0.0434854	−	0.0753189i
$121$	10.9946			0.999507
$122$	−3.09294	+	1.78571i	−0.280022	+	0.161671i
$123$	5.80786	+	3.35317i	0.523677	+	0.302345i
$124$			10.0784i			0.905065i
$125$		−	8.66242i		−	0.774790i
$126$	−0.261643	−	2.63278i	−0.0233090	−	0.234547i
$127$	−2.83564	+	4.91147i	−0.251622	+	0.435823i	−0.963973	−	0.266001i	$-0.914297\pi$
$127$	−2.83564	+	4.91147i	−0.251622	+	0.435823i	0.712350	+	0.701824i	$0.247631\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	1.23939	+	2.14669i	0.109122	+	0.189005i
$130$	3.43107	+	0.165762i	0.300925	+	0.0145382i
$131$	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
$133$	−2.08015	−	0.940301i	−0.180372	−	0.0815344i
$134$	−6.10772	−	10.5789i	−0.527627	−	0.913876i
$135$	−0.825077	−	0.476358i	−0.0710113	−	0.0409984i
$136$	1.90531	+	1.10003i	0.163379	+	0.0943270i
$137$	17.5779	+	10.1486i	1.50178	+	0.867054i	0.999998	+	0.00206185i	$0.000656309\pi$
$137$	17.5779	+	10.1486i	1.50178	+	0.867054i	0.501785	+	0.864993i	$0.332677\pi$
$138$	6.95513	+	4.01555i	0.592060	+	0.341826i
$139$	−0.0743508	−	0.128779i	−0.00630635	−	0.0109229i	0.862855	−	0.505452i	$-0.168674\pi$
$139$	−0.0743508	−	0.128779i	−0.00630635	−	0.0109229i	−0.869161	+	0.494529i	$0.835341\pi$
$140$	0.249272	+	2.50830i	0.0210673	+	0.211990i
$141$	−8.12115	−	4.68875i	−0.683924	−	0.394864i
$142$	−5.17589	+	8.96491i	−0.434351	+	0.752318i
$143$	0.0128144	−	0.265243i	0.00107159	−	0.0221807i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−3.90844	+	2.25654i	−0.324578	+	0.187395i
$146$	3.90410	−	6.76210i	0.323106	−	0.559636i
$147$	4.62466	+	5.25476i	0.381436	+	0.433405i
$148$			11.2779i			0.927036i
$149$			11.7924i			0.966067i	0.875602	+	0.483034i	$0.160465\pi$
$149$			11.7924i			0.966067i	−0.875602	+	0.483034i	$0.839535\pi$
$150$	−3.54406	−	2.04617i	−0.289371	−	0.167069i
$151$	13.7500	−	7.93859i	1.11896	−	0.646033i	0.177827	−	0.984062i	$-0.443093\pi$
$151$	13.7500	−	7.93859i	1.11896	−	0.646033i	0.941136	+	0.338028i	$0.109760\pi$
$152$	−0.862818			−0.0699838
$153$	1.10003	−	1.90531i	0.0889323	−	0.154035i
$154$	0.193907	−	0.0192702i	0.0156254	−	0.00155284i
$155$	−9.60184			−0.771238
$156$	1.95135	−	3.03187i	0.156233	−	0.242744i
$157$	−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	$0.922444\pi$
$158$		−	2.60144i		−	0.206959i
$159$	−0.935404	−	1.62017i	−0.0741824	−	0.128488i
$160$	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
$163$		−	8.20609i		−	0.642750i	−0.946952	−	0.321375i	$-0.895855\pi$
$163$		−	8.20609i		−	0.642750i	0.946952	−	0.321375i	$-0.104145\pi$
$164$	−5.80786	+	3.35317i	−0.453518	+	0.261839i
$165$	0.0350842	−	0.0607676i	0.00273130	−	0.00473075i
$166$	−5.93856	−	10.2859i	−0.460922	−	0.798340i
$167$	−15.4171	−	8.90108i	−1.19301	−	0.688786i	−0.234024	−	0.972231i	$-0.575189\pi$
$167$	−15.4171	−	8.90108i	−1.19301	−	0.688786i	−0.958989	+	0.283445i	$0.908523\pi$
$168$	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
$171$			0.862818i			0.0659814i
$172$	−2.47878			−0.189005
$173$	−2.77032			−0.210624			−0.105312	−	0.994439i	$-0.533584\pi$
$173$	−2.77032			−0.210624			−0.105312	+	0.994439i	$0.533584\pi$
$174$			4.73706i			0.359116i
$175$	10.7742	−	1.07073i	0.814454	−	0.0809396i
$176$	0.0637835	−	0.0368254i	0.00480786	−	0.00277582i
$177$	11.7753	+	6.79845i	0.885083	+	0.511003i
$178$	1.81590	−	3.14524i	0.136108	−	0.235746i
$179$	0.761434			0.0569123			0.0284561	−	0.999595i	$-0.490941\pi$
$179$	0.761434			0.0569123			0.0284561	+	0.999595i	$0.490941\pi$
$180$	0.825077	−	0.476358i	0.0614976	−	0.0355057i
$181$	−15.0250			−1.11680			−0.558399	−	0.829573i	$-0.688584\pi$
$181$	−15.0250			−1.11680			−0.558399	+	0.829573i	$0.688584\pi$
$182$	0.484195	+	9.52710i	0.0358909	+	0.706195i
$183$	−3.57142			−0.264007
$184$	−6.95513	+	4.01555i	−0.512739	+	0.296030i
$185$	−10.7446			−0.789961
$186$	−5.03919	+	8.72813i	−0.369491	+	0.639977i
$187$	0.140328	+	0.0810183i	0.0102618	+	0.00592464i
$188$	8.12115	−	4.68875i	0.592296	−	0.341962i
$189$	1.08980	−	2.41088i	0.0792714	−	0.175366i
$190$		−	0.822022i		−	0.0596357i
$191$	5.87466			0.425075			0.212538	−	0.977153i	$-0.431827\pi$
$191$	5.87466			0.425075			0.212538	+	0.977153i	$0.431827\pi$
$192$	1.00000			0.0721688
$193$		−	12.2176i		−	0.879446i	−0.898134	−	0.439723i	$-0.855077\pi$
$193$		−	12.2176i		−	0.879446i	0.898134	−	0.439723i	$-0.144923\pi$
$194$	−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	0.852448	−	0.522811i	$-0.175117\pi$
$197$	11.5921	+	6.69271i	0.825904	+	0.476836i	−0.0265438	+	0.999648i	$0.508450\pi$
$198$	−0.0368254	−	0.0637835i	−0.00261707	−	0.00453290i
$199$	−0.268529	+	0.465107i	−0.0190355	+	0.0329705i	−0.875386	−	0.483424i	$-0.839393\pi$
$199$	−0.268529	+	0.465107i	−0.0190355	+	0.0329705i	0.856351	+	0.516395i	$0.172726\pi$
$200$	3.54406	−	2.04617i	0.250603	−	0.144686i
$201$		−	12.2154i		−	0.861611i
$202$	−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
$205$	−3.19462	−	5.53325i	−0.223122	−	0.386459i
$206$		−	2.36457i		−	0.164747i
$207$	4.01555	+	6.95513i	0.279100	+	0.483415i
$208$	1.65000	+	3.20586i	0.114407	+	0.222286i
$209$	−0.0635473			−0.00439566
$210$	−1.03827	+	2.29688i	−0.0716476	+	0.158500i
$211$	−3.36821	+	5.83390i	−0.231877	+	0.401622i	−0.958360	−	0.285561i	$-0.907820\pi$
$211$	−3.36821	+	5.83390i	−0.231877	+	0.401622i	0.726484	+	0.687184i	$0.241153\pi$
$212$	1.87081			0.128488
$213$	−8.96491	+	5.17589i	−0.614265	+	0.354646i
$214$	−8.23069	−	4.75199i	−0.562639	−	0.324840i
$215$		−	2.36158i		−	0.161058i
$216$		−	1.00000i		−	0.0680414i
$217$	−2.63694	−	26.5342i	−0.179007	−	1.80126i
$218$	−3.86508	+	6.69452i	−0.261777	+	0.453410i
$219$	6.76210	−	3.90410i	0.456941	−	0.263815i
$220$	0.0350842	+	0.0607676i	0.00236538	+	0.00409695i
$221$	−4.29310	+	6.67030i	−0.288785	+	0.448693i
$222$	−5.63894	+	9.76693i	−0.378461	+	0.655513i
$223$	22.0208	+	12.7137i	1.47462	+	0.851372i	0.999591	−	0.0285982i	$-0.00910434\pi$
$223$	22.0208	+	12.7137i	1.47462	+	0.851372i	0.475029	+	0.879970i	$0.342438\pi$
$224$	−2.14923	+	1.54298i	−0.143602	+	0.103095i
$225$	−2.04617	−	3.54406i	−0.136411	−	0.236271i
$226$	6.42514	+	3.70956i	0.427394	+	0.246756i
$227$	−2.94933	−	1.70279i	−0.195754	−	0.113018i	0.398920	−	0.916986i	$-0.369385\pi$
$227$	−2.94933	−	1.70279i	−0.195754	−	0.113018i	−0.594673	+	0.803967i	$0.702719\pi$
$228$	−0.747223	−	0.431409i	−0.0494860	−	0.0285708i
$229$	0.991069	+	0.572194i	0.0654917	+	0.0378117i	0.532388	−	0.846500i	$-0.321295\pi$
$229$	0.991069	+	0.572194i	0.0654917	+	0.0378117i	−0.466897	+	0.884312i	$0.654628\pi$
$230$	−3.82568	−	6.62627i	−0.252258	−	0.436923i
$231$	0.177563	+	0.0802648i	0.0116828	+	0.00528104i
$232$	−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	$0.131690\pi$
$234$	3.20586	−	1.65000i	0.209573	−	0.107864i
$235$	4.46705	+	7.73716i	0.291398	+	0.504716i
$236$	−11.7753	+	6.79845i	−0.766504	+	0.442541i
$237$	1.30072	−	2.25291i	0.0844908	−	0.146342i
$238$	−5.30409	−	2.39763i	−0.343813	−	0.155416i
$239$			28.9640i			1.87352i	0.349968	+	0.936762i	$0.386192\pi$
$239$			28.9640i			1.87352i	−0.349968	+	0.936762i	$0.613808\pi$
$240$			0.952717i			0.0614976i
$241$	−5.19416	−	2.99885i	−0.334585	−	0.193173i	0.323290	−	0.946300i	$-0.395211\pi$
$241$	−5.19416	−	2.99885i	−0.334585	−	0.193173i	−0.657875	+	0.753127i	$0.728544\pi$
$242$	−9.52158	+	5.49729i	−0.612070	+	0.353379i
$243$	−1.00000			−0.0641500
$244$	1.78571	−	3.09294i	0.114318	−	0.198005i
$245$	−1.31256	−	6.53858i	−0.0838561	−	0.417734i
$246$	−6.70634			−0.427581
$247$	0.150120	−	3.10731i	0.00955192	−	0.197714i
$248$	−5.03919	−	8.72813i	−0.319989	−	0.554237i
$249$		−	11.8771i		−	0.752682i
$250$	4.33121	+	7.50187i	0.273930	+	0.474460i
$251$	1.29020	+	2.23470i	0.0814369	+	0.141053i	0.903867	−	0.427813i	$-0.140716\pi$
$251$	1.29020	+	2.23470i	0.0814369	+	0.141053i	−0.822430	+	0.568866i	$0.807382\pi$
$252$	1.54298	+	2.14923i	0.0971986	+	0.135389i
$253$	−0.512251	+	0.295748i	−0.0322049	+	0.0185935i
$254$		−	5.67128i		−	0.355848i
$255$	−1.81522	+	1.04802i	−0.113674	+	0.0656295i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.2842	+	21.2769i	0.766270	+	1.32722i	0.939572	+	0.342351i	$0.111223\pi$
$257$	12.2842	+	21.2769i	0.766270	+	1.32722i	−0.173302	+	0.984869i	$0.555444\pi$
$258$	−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
$262$			21.6292i			1.33626i
$263$	−24.2588			−1.49586			−0.747930	−	0.663778i	$-0.768952\pi$
$263$	−24.2588			−1.49586			−0.747930	+	0.663778i	$0.768952\pi$
$264$	0.0736508			0.00453290
$265$			1.78235i			0.109489i
$266$	2.27161	−	0.225750i	0.139282	−	0.0138416i
$267$	3.14524	−	1.81590i	0.192485	−	0.111132i
$268$	10.5789	+	6.10772i	0.646208	+	0.373088i
$269$	6.21907	−	10.7717i	0.379183	−	0.656765i	−0.611760	−	0.791043i	$-0.709538\pi$
$269$	6.21907	−	10.7717i	0.379183	−	0.656765i	0.990944	+	0.134278i	$0.0428717\pi$
$270$	0.952717			0.0579805
$271$	−14.2549	+	8.23006i	−0.865923	+	0.499941i	−0.865991	−	0.500059i	$-0.833312\pi$
$271$	−14.2549	+	8.23006i	−0.865923	+	0.499941i	6.83738e−5		1.00000i	$0.499978\pi$
$272$	−2.20006			−0.133398
$273$	−4.34422	+	8.49280i	−0.262924	+	0.514008i
$274$	−20.2972			−1.22620
$275$	0.261023	−	0.150702i	0.0157403	−	0.00908766i
$276$	−8.03109			−0.483415
$277$	11.2996	−	19.5715i	0.678928	−	1.17594i	−0.296376	−	0.955071i	$-0.595778\pi$
$277$	11.2996	−	19.5715i	0.678928	−	1.17594i	0.975304	−	0.220866i	$-0.0708884\pi$
$278$	0.128779	+	0.0743508i	0.00772367	+	0.00445926i
$279$	−8.72813	+	5.03919i	−0.522539	+	0.301688i
$280$	−1.47002	−	2.04761i	−0.0878507	−	0.122368i
$281$		−	7.34639i		−	0.438249i	−0.975697	−	0.219125i	$-0.929680\pi$
$281$		−	7.34639i		−	0.438249i	0.975697	−	0.219125i	$-0.0703201\pi$
$282$	9.37750			0.558422
$283$	−25.1290			−1.49376			−0.746882	−	0.664956i	$-0.768450\pi$
$283$	−25.1290			−1.49376			−0.746882	+	0.664956i	$0.768450\pi$
$284$		−	10.3518i		−	0.614265i
$285$	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
$289$	6.07986	+	10.5306i	0.357639	+	0.619448i
$290$	2.25654	−	3.90844i	0.132509	−	0.229511i
$291$	−11.1324	+	6.42728i	−0.652592	+	0.376774i
$292$			7.80821i			0.456941i
$293$	−15.0195	+	8.67149i	−0.877447	+	0.506594i	−0.869816	−	0.493377i	$-0.835762\pi$
$293$	−15.0195	+	8.67149i	−0.877447	+	0.506594i	−0.00763096	+	0.999971i	$0.502429\pi$
$294$	−6.63246	−	2.23842i	−0.386813	−	0.130547i
$295$	−6.47700	−	11.2185i	−0.377105	−	0.653166i
$296$	−5.63894	−	9.76693i	−0.327757	−	0.567691i
$297$		−	0.0736508i		−	0.00427366i
$298$	−5.89618	−	10.2125i	−0.341556	−	0.591593i
$299$	−13.2513	−	25.7465i	−0.766341	−	1.48896i
$300$	4.09233			0.236271
$301$	6.52609	−	0.648556i	0.376158	−	0.0373821i
$302$	−7.93859	+	13.7500i	−0.456815	+	0.791226i
$303$	−3.40735			−0.195747
$304$	0.747223	−	0.431409i	0.0428562	−	0.0247430i
$305$	2.94670	+	1.70128i	0.168727	+	0.0974148i
$306$			2.20006i			0.125769i
$307$			27.9365i			1.59442i	0.603702	+	0.797210i	$0.293692\pi$
$307$			27.9365i			1.59442i	−0.603702	+	0.797210i	$0.706308\pi$
$308$	−0.158293	+	0.113642i	−0.00901958	+	0.00647534i
$309$	1.18228	−	2.04778i	0.0672578	−	0.116494i
$310$	8.31543	−	4.80092i	0.472285	−	0.272674i
$311$	−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	$0.894079\pi$
$312$	−0.173988	+	3.60135i	−0.00985015	+	0.203886i
$313$	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
$315$	−2.04761	+	1.47002i	−0.115370	+	0.0828265i
$316$	1.30072	+	2.25291i	0.0731712	+	0.126736i
$317$	15.2431	+	8.80060i	0.856137	+	0.494291i	0.862717	−	0.505688i	$-0.168761\pi$
$317$	15.2431	+	8.80060i	0.856137	+	0.494291i	−0.00657993	+	0.999978i	$0.502094\pi$
$318$	1.62017	+	0.935404i	0.0908545	+	0.0524548i
$319$	−0.302146	−	0.174444i	−0.0169169	−	0.00976700i
$320$	−0.825077	−	0.476358i	−0.0461232	−	0.0266292i
$321$	−4.75199	−	8.23069i	−0.265230	−	0.459392i
$322$	17.2607	−	12.3918i	0.961901	−	0.690569i
$323$	1.64394	+	0.949128i	0.0914712	+	0.0528109i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	6.75233	+	13.1194i	0.374552	+	0.727735i
$326$	4.10304	+	7.10668i	0.227247	+	0.393603i
$327$	−6.69452	+	3.86508i	−0.370208	+	0.213740i
$328$	3.35317	−	5.80786i	0.185148	−	0.320686i
$329$	−20.1544	+	14.4693i	−1.11115	+	0.797718i
$330$			0.0701684i			0.00386264i
$331$			29.8193i			1.63901i	0.573068	+	0.819507i	$0.305753\pi$
$331$			29.8193i			1.63901i	−0.573068	+	0.819507i	$0.694247\pi$
$332$	10.2859	+	5.93856i	0.564512	+	0.325921i
$333$	−9.76693	+	5.63894i	−0.535224	+	0.309012i
$334$	17.8022			0.974091
$335$	−5.81893	+	10.0787i	−0.317922	+	0.550657i
$336$	−2.63278	+	0.261643i	−0.143630	+	0.0142738i
$337$	−13.5126			−0.736078			−0.368039	−	0.929810i	$-0.619971\pi$
$337$	−13.5126			−0.736078			−0.368039	+	0.929810i	$0.619971\pi$
$338$	−11.8325	+	5.38444i	−0.643603	+	0.292875i
$339$	3.70956	+	6.42514i	0.201475	+	0.348966i
$340$		−	2.09604i		−	0.113674i
$341$	−0.371140	−	0.642834i	−0.0200984	−	0.0348114i
$342$	−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
$345$		−	7.65136i		−	0.411935i
$346$	2.39917	−	1.38516i	0.128980	−	0.0744667i
$347$	−9.08214	+	15.7307i	−0.487555	+	0.844470i	−0.999898	−	0.0143111i	$-0.995444\pi$
$347$	−9.08214	+	15.7307i	−0.487555	+	0.844470i	0.512343	+	0.858781i	$0.328778\pi$
$348$	−2.36853	−	4.10241i	−0.126967	−	0.219913i
$349$	−9.88831	−	5.70902i	−0.529309	−	0.305597i	0.211426	−	0.977394i	$-0.432189\pi$
$349$	−9.88831	−	5.70902i	−0.529309	−	0.305597i	−0.740735	+	0.671797i	$0.765523\pi$
$350$	−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
$353$			0.964707i			0.0513462i	0.999670	+	0.0256731i	$0.00817290\pi$
$353$			0.964707i			0.0513462i	−0.999670	+	0.0256731i	$0.991827\pi$
$354$	−13.5969			−0.722667
$355$	9.86232			0.523437
$356$			3.63181i			0.192485i
$357$	−3.39466	−	4.72845i	−0.179664	−	0.250256i
$358$	−0.659422	+	0.380717i	−0.0348515	+	0.0201215i
$359$	−0.807380	−	0.466141i	−0.0426119	−	0.0246020i	0.478543	−	0.878064i	$-0.341165\pi$
$359$	−0.807380	−	0.466141i	−0.0426119	−	0.0246020i	−0.521155	+	0.853462i	$0.674499\pi$
$360$	−0.476358	+	0.825077i	−0.0251063	+	0.0434854i
$361$	18.2555			0.960818
$362$	13.0120	−	7.51249i	0.683896	−	0.394848i
$363$	−10.9946			−0.577066
$364$	−5.18287	−	8.00861i	−0.271656	−	0.419765i
$365$	−7.43901			−0.389376
$366$	3.09294	−	1.78571i	0.161671	−	0.0933406i
$367$	21.9937			1.14806			0.574031	−	0.818834i	$-0.305379\pi$
$367$	21.9937			1.14806			0.574031	+	0.818834i	$0.305379\pi$
$368$	4.01555	−	6.95513i	0.209325	−	0.362561i
$369$	−5.80786	−	3.35317i	−0.302345	−	0.174559i
$370$	9.30512	−	5.37231i	0.483750	−	0.279293i
$371$	−4.92543	+	0.489484i	−0.255716	+	0.0254127i
$372$		−	10.0784i		−	0.522539i
$373$	−27.1544			−1.40600			−0.703002	−	0.711188i	$-0.748157\pi$
$373$	−27.1544			−1.40600			−0.703002	+	0.711188i	$0.748157\pi$
$374$	−0.162037			−0.00837871
$375$			8.66242i			0.447325i
$376$	−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	0.756332	−	0.654189i	$-0.226990\pi$
$379$	11.0569	+	6.38369i	0.567953	+	0.327908i	−0.188378	+	0.982097i	$0.560323\pi$
$380$	0.411011	+	0.711892i	0.0210844	+	0.0365193i
$381$	2.83564	−	4.91147i	0.145274	−	0.251622i
$382$	−5.08760	+	2.93733i	−0.260304	+	0.150287i
$383$			11.0087i			0.562521i	0.959632	+	0.281260i	$0.0907524\pi$
$383$			11.0087i			0.562521i	−0.959632	+	0.281260i	$0.909248\pi$
$384$	−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
$387$	−1.23939	−	2.14669i	−0.0630018	−	0.109122i
$388$		−	12.8546i		−	0.652592i
$389$	−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	$0.931868\pi$
$390$	−3.43107	−	0.165762i	−0.173739	−	0.00839366i
$391$	17.6689			0.893555
$392$	5.25476	−	4.62466i	0.265405	−	0.233581i
$393$	−10.8146	+	18.7315i	−0.545525	+	0.944877i
$394$	−13.3854			−0.674348
$395$	−2.14639	+	1.23922i	−0.107996	+	0.0623518i
$396$	0.0637835	+	0.0368254i	0.00320524	+	0.00185055i
$397$		−	17.2235i		−	0.864421i	−0.901773	−	0.432211i	$-0.857734\pi$
$397$		−	17.2235i		−	0.864421i	0.901773	−	0.432211i	$-0.142266\pi$
$398$		−	0.537059i		−	0.0269203i
$399$	2.08015	+	0.940301i	0.104138	+	0.0470739i
$400$	−2.04617	+	3.54406i	−0.102308	+	0.177203i
$401$	10.5185	−	6.07286i	0.525269	−	0.303264i	−0.213819	−	0.976873i	$-0.568590\pi$
$401$	10.5185	−	6.07286i	0.525269	−	0.303264i	0.739088	+	0.673609i	$0.235257\pi$
$402$	6.10772	+	10.5789i	0.304625	+	0.527627i
$403$	32.3098	−	16.6293i	1.60947	−	0.828364i
$404$	1.70367	−	2.95085i	0.0847609	−	0.146810i
$405$	0.825077	+	0.476358i	0.0409984	+	0.0236704i
$406$	11.4205	+	5.16246i	0.566789	+	0.256208i
$407$	−0.415313	−	0.719343i	−0.0205863	−	0.0356565i
$408$	−1.90531	−	1.10003i	−0.0943270	−	0.0544597i
$409$	21.0359	+	12.1451i	1.04016	+	0.600536i	0.919879	−	0.392203i	$-0.128287\pi$
$409$	21.0359	+	12.1451i	1.04016	+	0.600536i	0.120281	+	0.992740i	$0.461620\pi$
$410$	5.53325	+	3.19462i	0.273268	+	0.157771i
$411$	−17.5779	−	10.1486i	−0.867054	−	0.500594i
$412$	1.18228	+	2.04778i	0.0582470	+	0.100887i
$413$	29.2229	−	20.9797i	1.43797	−	1.03235i
$414$	−6.95513	−	4.01555i	−0.341826	−	0.197353i
$415$	−5.65777	+	9.79954i	−0.277729	+	0.481041i
$416$	−3.03187	−	1.95135i	−0.148650	−	0.0956730i
$417$	0.0743508	+	0.128779i	0.00364097	+	0.00630635i
$418$	0.0550336	−	0.0317737i	0.00269178	−	0.00155410i
$419$	4.86261	−	8.42229i	0.237554	−	0.411456i	−0.722458	−	0.691415i	$-0.756988\pi$
$419$	4.86261	−	8.42229i	0.237554	−	0.411456i	0.960012	+	0.279959i	$0.0903209\pi$
$420$	−0.249272	−	2.50830i	−0.0121632	−	0.122392i
$421$			25.6881i			1.25196i	0.779839	+	0.625980i	$0.215301\pi$
$421$			25.6881i			1.25196i	−0.779839	+	0.625980i	$0.784699\pi$
$422$		−	6.73641i		−	0.327923i
$423$	8.12115	+	4.68875i	0.394864	+	0.227975i
$424$	−1.62017	+	0.935404i	−0.0786823	+	0.0454272i
$425$	−9.00339			−0.436729
$426$	5.17589	−	8.96491i	0.250773	−	0.434351i
$427$	−3.89214	+	8.61026i	−0.188354	+	0.416680i
$428$	9.50398			0.459392
$429$	−0.0128144	+	0.265243i	−0.000618684	+	0.0128060i
$430$	1.18079	+	2.04519i	0.0569427	+	0.0986276i
$431$		−	3.62114i		−	0.174424i	−0.996190	−	0.0872122i	$-0.972204\pi$
$431$		−	3.62114i		−	0.174424i	0.996190	−	0.0872122i	$-0.0277958\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−1.43124	−	2.47898i	−0.0687809	−	0.119132i	0.829584	−	0.558382i	$-0.188578\pi$
$433$	−1.43124	−	2.47898i	−0.0687809	−	0.119132i	−0.898365	+	0.439250i	$0.855244\pi$
$434$	15.5507	+	21.6608i	0.746459	+	1.03975i
$435$	3.90844	−	2.25654i	0.187395	−	0.108193i
$436$		−	7.73017i		−	0.370208i
$437$	−6.00101	+	3.46469i	−0.287067	+	0.165738i
$438$	−3.90410	+	6.76210i	−0.186545	+	0.323106i
$439$	−5.37600	−	9.31150i	−0.256582	−	0.444414i	0.708742	−	0.705468i	$-0.249263\pi$
$439$	−5.37600	−	9.31150i	−0.256582	−	0.444414i	−0.965324	+	0.261054i	$0.915930\pi$
$440$	−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	$0.212265\pi$
$444$		−	11.2779i		−	0.535224i
$445$	−3.46009			−0.164024
$446$	−25.4274			−1.20402
$447$		−	11.7924i		−	0.557759i
$448$	1.08980	−	2.41088i	0.0514883	−	0.113903i
$449$	16.6165	−	9.59355i	0.784182	−	0.452748i	−0.0537284	−	0.998556i	$-0.517111\pi$
$449$	16.6165	−	9.59355i	0.784182	−	0.452748i	0.837910	+	0.545808i	$0.183777\pi$
$450$	3.54406	+	2.04617i	0.167069	+	0.0964572i
$451$	0.246964	−	0.427754i	0.0116291	−	0.0201421i
$452$	−7.41911			−0.348966
$453$	−13.7500	+	7.93859i	−0.646033	+	0.372988i
$454$	3.40559			0.159832
$455$	7.62994	−	4.93781i	0.357697	−	0.231488i
$456$	0.862818			0.0404052
$457$	−5.57475	+	3.21858i	−0.260776	+	0.150559i	−0.624688	−	0.780874i	$-0.714774\pi$
$457$	−5.57475	+	3.21858i	−0.260776	+	0.150559i	0.363913	+	0.931433i	$0.381441\pi$
$458$	−1.14439			−0.0534738
$459$	−1.10003	+	1.90531i	−0.0513451	+	0.0889323i
$460$	6.62627	+	3.82568i	0.308951	+	0.178373i
$461$	−6.89063	+	3.97831i	−0.320929	+	0.185288i	−0.651806	−	0.758385i	$-0.725989\pi$
$461$	−6.89063	+	3.97831i	−0.320929	+	0.185288i	0.330878	+	0.943674i	$0.392655\pi$
$462$	−0.193907	+	0.0192702i	−0.00902135	+	0.000896532i
$463$		−	20.5480i		−	0.954947i	−0.878646	−	0.477474i	$-0.841553\pi$
$463$		−	20.5480i		−	0.954947i	0.878646	−	0.477474i	$-0.158447\pi$
$464$	4.73706			0.219913
$465$	9.60184			0.445275
$466$			3.34782i			0.155085i
$467$	−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
$471$	3.46211	+	5.99655i	0.159526	+	0.276307i
$472$	6.79845	−	11.7753i	0.312924	−	0.542000i
$473$	0.158105	−	0.0912822i	0.00726969	−	0.00419716i
$474$			2.60144i			0.119488i
$475$	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
$478$	−14.4820	−	25.0835i	−0.662390	−	1.14729i
$479$		−	21.2508i		−	0.970974i	−0.874244	−	0.485487i	$-0.838642\pi$
$479$		−	21.2508i		−	0.970974i	0.874244	−	0.485487i	$-0.161358\pi$
$480$	−0.476358	−	0.825077i	−0.0217427	−	0.0376594i
$481$	36.1553	−	18.6085i	1.64854	−	0.848473i
$482$	5.99770			0.273188
$483$	21.1441	−	2.10128i	0.962090	−	0.0956115i
$484$	5.49729	−	9.52158i	0.249877	−	0.432799i
$485$	12.2468			0.556097
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	21.5957	+	12.4683i	0.978593	+	0.564991i	0.901845	−	0.432059i	$-0.142213\pi$
$487$	21.5957	+	12.4683i	0.978593	+	0.564991i	0.0767481	+	0.997051i	$0.475546\pi$
$488$			3.57142i			0.161671i
$489$			8.20609i			0.371092i
$490$	4.40600	+	5.00630i	0.199043	+	0.226161i
$491$	0.201577	−	0.349141i	0.00909703	−	0.0157565i	−0.861441	−	0.507858i	$-0.830438\pi$
$491$	0.201577	−	0.349141i	0.00909703	−	0.0157565i	0.870538	+	0.492101i	$0.163771\pi$
$492$	5.80786	−	3.35317i	0.261839	−	0.151173i
$493$	5.21092	+	9.02558i	0.234688	+	0.406492i
$494$	1.42365	+	2.76607i	0.0640530	+	0.124451i
$495$	−0.0350842	+	0.0607676i	−0.00157692	+	0.00273130i
$496$	8.72813	+	5.03919i	0.391905	+	0.226266i
$497$	2.70847	+	27.2540i	0.121492	+	1.22251i
$498$	5.93856	+	10.2859i	0.266113	+	0.460922i
$499$	−22.9988	−	13.2784i	−1.02957	−	0.594422i	−0.112708	−	0.993628i	$-0.535953\pi$
$499$	−22.9988	−	13.2784i	−1.02957	−	0.594422i	−0.916861	+	0.399206i	$0.869286\pi$
$500$	−7.50187	−	4.33121i	−0.335494	−	0.193698i
$501$	15.4171	+	8.90108i	0.688786	+	0.397671i
$502$	−2.23470	−	1.29020i	−0.0997394	−	0.0575846i
$503$	0.443994	+	0.769020i	0.0197967	+	0.0342889i	0.875754	−	0.482758i	$-0.160365\pi$
$503$	0.443994	+	0.769020i	0.0197967	+	0.0342889i	−0.855957	+	0.517046i	$0.827031\pi$
$504$	−2.41088	−	1.08980i	−0.107389	−	0.0485436i
$505$	2.81132	+	1.62312i	0.125102	+	0.0722278i
$506$	0.295748	−	0.512251i	0.0131476	−	0.0227723i
$507$	−12.9395	−	1.25319i	−0.574661	−	0.0556559i
$508$	2.83564	+	4.91147i	0.125811	+	0.217911i
$509$	15.6085	−	9.01155i	0.691833	−	0.399430i	−0.112465	−	0.993656i	$-0.535875\pi$
$509$	15.6085	−	9.01155i	0.691833	−	0.399430i	0.804298	+	0.594226i	$0.202541\pi$
$510$	1.04802	−	1.81522i	0.0464071	−	0.0803794i
$511$	−2.04296	−	20.5573i	−0.0903753	−	0.909402i
$512$		−	1.00000i		−	0.0441942i
$513$		−	0.862818i		−	0.0380944i
$514$	−21.2769	−	12.2842i	−0.938486	−	0.541835i
$515$	−1.95095	+	1.12638i	−0.0859692	+	0.0496343i
$516$	2.47878			0.109122
$517$	−0.345330	+	0.598130i	−0.0151876	+	0.0263057i
$518$	17.4016	+	24.2388i	0.764580	+	1.06499i
$519$	2.77032			0.121604
$520$	1.85909	−	2.88851i	0.0815264	−	0.126670i
$521$	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	$0.602001\pi$
$522$		−	4.73706i		−	0.207336i
$523$	−0.917308	−	1.58882i	−0.0401111	−	0.0694745i	0.845273	−	0.534335i	$-0.179438\pi$
$523$	−0.917308	−	1.58882i	−0.0401111	−	0.0694745i	−0.885384	+	0.464860i	$0.846105\pi$
$524$	−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
$527$			22.1731i			0.965874i
$528$	−0.0637835	+	0.0368254i	−0.00277582	+	0.00160262i
$529$	−20.7492	+	35.9387i	−0.902139	+	1.56255i
$530$	−0.891175	−	1.54356i	−0.0387102	−	0.0670480i
$531$	−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
$535$			9.05461i			0.391465i
$536$	−12.2154			−0.527627
$537$	−0.761434			−0.0328583
$538$			12.4381i			0.536246i
$539$	0.387017	−	0.340610i	0.0166700	−	0.0146711i
$540$	−0.825077	+	0.476358i	−0.0355057	+	0.0204992i
$541$	−14.5108	−	8.37779i	−0.623866	−	0.360189i	0.154507	−	0.987992i	$-0.450621\pi$
$541$	−14.5108	−	8.37779i	−0.623866	−	0.360189i	−0.778373	+	0.627803i	$0.783955\pi$
$542$	8.23006	−	14.2549i	0.353512	−	0.612300i
$543$	15.0250			0.644783
$544$	1.90531	−	1.10003i	0.0816896	−	0.0471635i
$545$	7.36466			0.315467
$546$	−0.484195	−	9.52710i	−0.0207216	−	0.407722i
$547$	24.6951			1.05588			0.527942	−	0.849280i	$-0.322964\pi$
$547$	24.6951			1.05588			0.527942	+	0.849280i	$0.322964\pi$
$548$	17.5779	−	10.1486i	0.750891	−	0.433527i
$549$	3.57142			0.152425
$550$	−0.150702	+	0.261023i	−0.00642595	+	0.0111301i
$551$	−3.53964	−	2.04361i	−0.150794	−	0.0870608i
$552$	6.95513	−	4.01555i	0.296030	−	0.170913i
$553$	−4.01397	−	5.59110i	−0.170691	−	0.237758i
$554$			22.5992i			0.960149i
$555$	10.7446			0.456084
$556$	−0.148702			−0.00630635
$557$			17.8055i			0.754443i	0.926123	+	0.377221i	$0.123120\pi$
$557$			17.8055i			0.754443i	−0.926123	+	0.377221i	$0.876880\pi$
$558$	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
$562$	3.67320	+	6.36216i	0.154944	+	0.268372i
$563$	14.9572	−	25.9067i	0.630372	−	1.09184i	−0.357104	−	0.934065i	$-0.616236\pi$
$563$	14.9572	−	25.9067i	0.630372	−	1.09184i	0.987476	−	0.157771i	$-0.0504308\pi$
$564$	−8.12115	+	4.68875i	−0.341962	+	0.197432i
$565$		−	7.06831i		−	0.297366i
$566$	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
$569$	0.451054	+	0.781249i	0.0189092	+	0.0327517i	0.875325	−	0.483535i	$-0.160647\pi$
$569$	0.451054	+	0.781249i	0.0189092	+	0.0327517i	−0.856416	+	0.516286i	$0.827314\pi$
$570$			0.822022i			0.0344307i
$571$	−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	$-0.505205\pi$
$572$	−0.223300	−	0.143719i	−0.00933662	−	0.00600919i
$573$	−5.87466			−0.245417
$574$	−7.30858	+	16.1682i	−0.305054	+	0.674846i
$575$	16.4329	−	28.4627i	0.685301	−	1.18698i
$576$	−1.00000			−0.0416667
$577$	21.1876	−	12.2326i	0.882050	−	0.509252i	0.0107161	−	0.999943i	$-0.496589\pi$
$577$	21.1876	−	12.2326i	0.882050	−	0.509252i	0.871334	+	0.490691i	$0.163256\pi$
$578$	−10.5306	−	6.07986i	−0.438016	−	0.252889i
$579$			12.2176i			0.507748i
$580$			4.51308i			0.187395i
$581$	−28.6343	−	12.9437i	−1.18795	−	0.536996i
$582$	6.42728	−	11.1324i	0.266419	−	0.461452i
$583$	−0.119327	+	0.0688933i	−0.00494201	+	0.00285327i
$584$	−3.90410	−	6.76210i	−0.161553	−	0.279818i
$585$	−2.88851	−	1.85909i	−0.119425	−	0.0768638i
$586$	8.67149	−	15.0195i	0.358216	−	0.620448i
$587$	−1.42198	−	0.820978i	−0.0586912	−	0.0338854i	0.470367	−	0.882471i	$-0.344121\pi$
$587$	−1.42198	−	0.820978i	−0.0586912	−	0.0338854i	−0.529058	+	0.848585i	$0.677455\pi$
$588$	6.86309	−	1.37770i	0.283029	−	0.0568153i
$589$	−4.34790	−	7.53079i	−0.179152	−	0.310301i
$590$	11.2185	+	6.47700i	0.461858	+	0.266654i
$591$	−11.5921	−	6.69271i	−0.476836	−	0.275301i
$592$	9.76693	+	5.63894i	0.401418	+	0.231759i
$593$	−9.96128	−	5.75115i	−0.409061	−	0.236171i	0.281325	−	0.959612i	$-0.409226\pi$
$593$	−9.96128	−	5.75115i	−0.409061	−	0.236171i	−0.690386	+	0.723441i	$0.742559\pi$
$594$	0.0368254	+	0.0637835i	0.00151097	+	0.00261707i
$595$	0.548414	+	5.51841i	0.0224828	+	0.226233i
$596$	10.2125	+	5.89618i	0.418319	+	0.241517i
$597$	0.268529	−	0.465107i	0.0109902	−	0.0190355i
$598$	24.3492	+	15.6715i	0.995713	+	0.640855i
$599$	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	$0.756602\pi$
$600$	−3.54406	+	2.04617i	−0.144686	+	0.0835343i
$601$	−5.10939	+	8.84972i	−0.208416	+	0.360987i	−0.951216	−	0.308526i	$-0.900164\pi$
$601$	−5.10939	+	8.84972i	−0.208416	+	0.360987i	0.742800	+	0.669514i	$0.233498\pi$
$602$	−5.32748	+	3.82471i	−0.217132	+	0.155884i
$603$			12.2154i			0.497451i
$604$		−	15.8772i		−	0.646033i
$605$	9.07137	+	5.23736i	0.368804	+	0.212929i
$606$	2.95085	−	1.70367i	0.119870	−	0.0692070i
$607$	−2.07341			−0.0841573			−0.0420786	−	0.999114i	$-0.513398\pi$
$607$	−2.07341			−0.0841573			−0.0420786	+	0.999114i	$0.513398\pi$
$608$	−0.431409	+	0.747223i	−0.0174960	+	0.0303039i
$609$	7.30919	+	10.1811i	0.296183	+	0.412557i
$610$	−3.40255			−0.137765
$611$	−28.4313	−	18.2988i	−1.15021	−	0.740291i
$612$	−1.10003	−	1.90531i	−0.0444662	−	0.0770177i
$613$		−	22.6662i		−	0.915481i	−0.889086	−	0.457740i	$-0.848659\pi$
$613$		−	22.6662i		−	0.915481i	0.889086	−	0.457740i	$-0.151341\pi$
$614$	−13.9683	−	24.1937i	−0.563713	−	0.976379i
$615$	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	−0.365517	−	0.930805i	$-0.619108\pi$
$617$	6.40425	−	3.69750i	0.257826	−	0.148856i	0.623342	+	0.781949i	$0.285774\pi$
$618$			2.36457i			0.0951169i
$619$	−16.6370	+	9.60540i	−0.668699	+	0.386074i	−0.795584	−	0.605844i	$-0.792836\pi$
$619$	−16.6370	+	9.60540i	−0.668699	+	0.386074i	0.126884	+	0.991918i	$0.459502\pi$
$620$	−4.80092	+	8.31543i	−0.192810	+	0.333956i
$621$	−4.01555	−	6.95513i	−0.161138	−	0.279100i
$622$	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
$626$			5.35217i			0.213916i
$627$	0.0635473			0.00253783
$628$	−6.92422			−0.276307
$629$			24.8121i			0.989322i
$630$	1.03827	−	2.29688i	0.0413658	−	0.0915100i
$631$	−18.6803	+	10.7851i	−0.743651	+	0.429347i	−0.823395	−	0.567468i	$-0.807923\pi$
$631$	−18.6803	+	10.7851i	−0.743651	+	0.429347i	0.0797444	+	0.996815i	$0.474590\pi$
$632$	−2.25291	−	1.30072i	−0.0896160	−	0.0517398i
$633$	3.36821	−	5.83390i	0.133874	−	0.231877i
$634$	−17.6012			−0.699033
$635$	−4.67924	+	2.70156i	−0.185690	+	0.107208i
$636$	−1.87081			−0.0741824
$637$	15.7408	+	19.7289i	0.623672	+	0.781686i
$638$	0.348888			0.0138126
$639$	8.96491	−	5.17589i	0.354646	−	0.204755i
$640$	0.952717			0.0376594
$641$	−19.3914	+	33.5869i	−0.765914	+	1.32660i	0.173848	+	0.984773i	$0.444380\pi$
$641$	−19.3914	+	33.5869i	−0.765914	+	1.32660i	−0.939762	+	0.341830i	$0.888953\pi$
$642$	8.23069	+	4.75199i	0.324840	+	0.187546i
$643$	−42.5539	+	24.5685i	−1.67816	+	0.968888i	−0.715331	+	0.698786i	$0.753724\pi$
$643$	−42.5539	+	24.5685i	−1.67816	+	0.968888i	−0.962832	+	0.270102i	$0.912943\pi$
$644$	−8.75230	+	19.3620i	−0.344889	+	0.762969i
$645$			2.36158i			0.0929870i
$646$	−1.89826			−0.0746859
$647$	50.4517			1.98346			0.991730	−	0.128344i	$-0.0409663\pi$
$647$	50.4517			1.98346			0.991730	+	0.128344i	$0.0409663\pi$
$648$			1.00000i			0.0392837i
$649$	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
$653$	−6.44844	−	11.1690i	−0.252347	−	0.437078i	0.711825	−	0.702357i	$-0.247869\pi$
$653$	−6.44844	−	11.1690i	−0.252347	−	0.437078i	−0.964172	+	0.265280i	$0.914536\pi$
$654$	3.86508	−	6.69452i	0.151137	−	0.261777i
$655$	17.8458	−	10.3033i	0.697292	−	0.402582i
$656$			6.70634i			0.261839i
$657$	−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	−0.982813	−	0.184603i	$-0.940900\pi$
$659$	−16.7189	−	28.9581i	−0.651278	−	1.12805i	0.331536	−	0.943443i	$-0.392433\pi$
$660$	−0.0350842	−	0.0607676i	−0.00136565	−	0.00236538i
$661$			5.33677i			0.207576i	0.994599	+	0.103788i	$0.0330964\pi$
$661$			5.33677i			0.207576i	−0.994599	+	0.103788i	$0.966904\pi$
$662$	−14.9096	−	25.8242i	−0.579479	−	1.00369i
$663$	4.29310	−	6.67030i	0.166730	−	0.259053i
$664$	−11.8771			−0.460922
$665$	−1.26836	−	1.76672i	−0.0491850	−	0.0685104i
$666$	5.63894	−	9.76693i	0.218504	−	0.378461i
$667$	−38.0438			−1.47306
$668$	−15.4171	+	8.90108i	−0.596506	+	0.344393i
$669$	−22.0208	−	12.7137i	−0.851372	−	0.491540i
$670$		−	11.6379i		−	0.449610i
$671$			0.263038i			0.0101545i
$672$	2.14923	−	1.54298i	0.0829085	−	0.0595218i
$673$	−12.3543	+	21.3983i	−0.476223	+	0.824842i	−0.999629	−	0.0272410i	$-0.991328\pi$
$673$	−12.3543	+	21.3983i	−0.476223	+	0.824842i	0.523406	+	0.852083i	$0.324661\pi$
$674$	11.7022	−	6.75630i	0.450754	−	0.260243i
$675$	2.04617	+	3.54406i	0.0787569	+	0.136411i
$676$	7.55502	−	10.5793i	0.290578	−	0.406896i
$677$	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
$679$	3.36331	+	33.8433i	0.129072	+	1.29879i
$680$	1.04802	+	1.81522i	0.0401897	+	0.0696106i
$681$	2.94933	+	1.70279i	0.113018	+	0.0652512i
$682$	0.642834	+	0.371140i	0.0246154	+	0.0142117i
$683$	−34.1496	−	19.7163i	−1.30670	−	0.754421i	−0.325153	−	0.945661i	$-0.605416\pi$
$683$	−34.1496	−	19.7163i	−1.30670	−	0.754421i	−0.981543	+	0.191240i	$0.938749\pi$
$684$	0.747223	+	0.431409i	0.0285708	+	0.0164953i
$685$	9.66875	+	16.7468i	0.369424	+	0.639861i
$686$	−12.6246	+	13.5506i	−0.482010	+	0.517365i
$687$	−0.991069	−	0.572194i	−0.0378117	−	0.0218306i
$688$	−1.23939	+	2.14669i	−0.0472513	+	0.0818417i
$689$	−3.08683	−	5.99754i	−0.117599	−	0.228488i
$690$	3.82568	+	6.62627i	0.145641	+	0.252258i
$691$	−25.0654	+	14.4715i	−0.953532	+	0.550522i	−0.894176	−	0.447715i	$-0.852238\pi$
$691$	−25.0654	+	14.4715i	−0.953532	+	0.550522i	−0.0593556	+	0.998237i	$0.518905\pi$
$692$	−1.38516	+	2.39917i	−0.0526559	+	0.0912027i
$693$	−0.177563	−	0.0802648i	−0.00674507	−	0.00304901i
$694$		−	18.1643i		−	0.689507i
$695$		−	0.141670i		−	0.00537387i
$696$	4.10241	+	2.36853i	0.155502	+	0.0897789i
$697$	−12.7777	+	7.37719i	−0.483989	+	0.279431i
$698$	11.4180			0.432179
$699$	−1.67391	+	2.89929i	−0.0633130	+	0.109661i
$700$	4.45983	−	9.86611i	0.168566	−	0.372904i
$701$	32.2105			1.21657			0.608286	−	0.793718i	$-0.291857\pi$
$701$	32.2105			1.21657			0.608286	+	0.793718i	$0.291857\pi$
$702$	−3.20586	+	1.65000i	−0.120997	+	0.0622751i
$703$	−4.86538	−	8.42709i	−0.183501	−	0.317834i
$704$		−	0.0736508i		−	0.00277582i
$705$	−4.46705	−	7.73716i	−0.168239	−	0.291398i
$706$	−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
$709$		−	36.8796i		−	1.38504i	−0.721397	−	0.692522i	$-0.756500\pi$
$709$		−	36.8796i		−	1.38504i	0.721397	−	0.692522i	$-0.243500\pi$
$710$	−8.54102	+	4.93116i	−0.320539	+	0.185063i
$711$	−1.30072	+	2.25291i	−0.0487808	+	0.0844908i
$712$	−1.81590	−	3.14524i	−0.0680539	−	0.117873i
$713$	−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
$717$		−	28.9640i		−	1.08168i
$718$	0.932282			0.0347924
$719$	28.9953			1.08134			0.540672	−	0.841234i	$-0.318170\pi$
$719$	28.9953			1.08134			0.540672	+	0.841234i	$0.318170\pi$
$720$		−	0.952717i		−	0.0355057i
$721$	−3.64848	−	5.08201i	−0.135877	−	0.189264i
$722$	−15.8098	+	9.12777i	−0.588379	+	0.339701i
$723$	5.19416	+	2.99885i	0.193173	+	0.111528i
$724$	−7.51249	+	13.0120i	−0.279199	+	0.483588i
$725$	19.3856			0.719964
$726$	9.52158	−	5.49729i	0.353379	−	0.204023i
$727$	4.22223			0.156594			0.0782970	−	0.996930i	$-0.475052\pi$
$727$	4.22223			0.156594			0.0782970	+	0.996930i	$0.475052\pi$
$728$	8.49280	+	4.34422i	0.314764	+	0.161008i
$729$	1.00000			0.0370370
$730$	6.44237	−	3.71950i	0.238443	−	0.137665i
$731$	−5.45348			−0.201704
$732$	−1.78571	+	3.09294i	−0.0660018	+	0.114318i
$733$	−38.5274	−	22.2438i	−1.42304	−	0.821593i	−0.426483	−	0.904496i	$-0.640248\pi$
$733$	−38.5274	−	22.2438i	−1.42304	−	0.821593i	−0.996558	+	0.0829028i	$0.973581\pi$
$734$	−19.0471	+	10.9968i	−0.703041	+	0.405901i
$735$	1.31256	+	6.53858i	0.0484144	+	0.241179i
$736$			8.03109i			0.296030i
$737$	−0.899678			−0.0331401
$738$	6.70634			0.246864
$739$			23.3205i			0.857858i	0.903338	+	0.428929i	$0.141109\pi$
$739$			23.3205i			0.857858i	−0.903338	+	0.428929i	$0.858891\pi$
$740$	−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	−0.994314	−	0.106492i	$-0.966038\pi$
$743$	−43.1684	−	24.9233i	−1.58369	−	0.914347i	−0.589381	−	0.807855i	$-0.700628\pi$
$744$	5.03919	+	8.72813i	0.184746	+	0.319989i
$745$	−5.61739	+	9.72960i	−0.205805	+	0.356465i
$746$	23.5164	−	13.5772i	0.860998	−	0.497097i
$747$			11.8771i			0.434561i
$748$	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
$751$	9.07064	+	15.7108i	0.330992	+	0.573295i	0.982707	−	0.185169i	$-0.0592833\pi$
$751$	9.07064	+	15.7108i	0.330992	+	0.573295i	−0.651714	+	0.758464i	$0.725950\pi$
$752$		−	9.37750i		−	0.341962i
$753$	−1.29020	−	2.23470i	−0.0470176	−	0.0814369i
$754$	−0.824193	+	17.0598i	−0.0300153	+	0.621282i
$755$	15.1265			0.550508
$756$	−1.54298	−	2.14923i	−0.0561177	−	0.0781669i
$757$	−6.93581	+	12.0132i	−0.252086	+	0.436626i	−0.964100	−	0.265539i	$-0.914450\pi$
$757$	−6.93581	+	12.0132i	−0.252086	+	0.436626i	0.712014	+	0.702166i	$0.247783\pi$
$758$	−12.7674			−0.463732
$759$	0.512251	−	0.295748i	0.0185935	−	0.0107350i
$760$	−0.711892	−	0.411011i	−0.0258230	−	0.0149089i
$761$			42.7448i			1.54950i	0.632268	+	0.774750i	$0.282124\pi$
$761$			42.7448i			1.54950i	−0.632268	+	0.774750i	$0.717876\pi$
$762$			5.67128i			0.205449i
$763$	2.02254	+	20.3519i	0.0732210	+	0.736787i
$764$	2.93733	−	5.08760i	0.106269	−	0.184063i
$765$	1.81522	−	1.04802i	0.0656295	−	0.0378912i
$766$	−5.50437	−	9.53385i	−0.198881	−	0.344472i
$767$	41.2240	+	26.5324i	1.48851	+	0.958028i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	22.4317	+	12.9509i	0.808906	+	0.467022i	0.846576	−	0.532268i	$-0.178660\pi$
$769$	22.4317	+	12.9509i	0.808906	+	0.467022i	−0.0376696	+	0.999290i	$0.511993\pi$
$770$	0.169167	+	0.0764696i	0.00609637	+	0.00275577i
$771$	−12.2842	−	21.2769i	−0.442406	−	0.766270i
$772$	−10.5808	−	6.10882i	−0.380811	−	0.219861i
$773$	31.5868	+	18.2367i	1.13610	+	0.655927i	0.945462	−	0.325733i	$-0.105611\pi$
$773$	31.5868	+	18.2367i	1.13610	+	0.655927i	0.190637	+	0.981661i	$0.438945\pi$
$774$	2.14669	+	1.23939i	0.0771611	+	0.0445490i
$775$	35.7184	+	20.6220i	1.28304	+	0.740765i
$776$	6.42728	+	11.1324i	0.230726	+	0.399629i
$777$	2.95078	+	29.6922i	0.105859	+	1.06520i
$778$	10.4068	+	6.00836i	0.373102	+	0.215410i
$779$	2.89318	−	5.01113i	0.103659	−	0.179542i
$780$	3.05427	−	1.57198i	0.109360	−	0.0562859i
$781$	0.381209	+	0.660273i	0.0136407	+	0.0236264i
$782$	−15.3017	+	8.83446i	−0.547189	+	0.315920i
$783$	2.36853	−	4.10241i	0.0846444	−	0.146608i
$784$	−2.23842	+	6.63246i	−0.0799436	+	0.236873i
$785$		−	6.59682i		−	0.235451i
$786$		−	21.6292i		−	0.771489i
$787$	−6.48473	−	3.74396i	−0.231156	−	0.133458i	0.379949	−	0.925007i	$-0.375941\pi$
$787$	−6.48473	−	3.74396i	−0.231156	−	0.133458i	−0.611105	+	0.791549i	$0.709275\pi$
$788$	11.5921	−	6.69271i	0.412952	−	0.238418i
$789$	24.2588			0.863635
$790$	1.23922	−	2.14639i	0.0440894	−	0.0763650i
$791$	19.5329	−	1.94116i	0.694510	−	0.0690197i
$792$	−0.0736508			−0.00261707
$793$	−12.8619	−	0.621385i	−0.456741	−	0.0220660i
$794$	8.61174	+	14.9160i	0.305619	+	0.529348i
$795$		−	1.78235i		−	0.0632134i
$796$	0.268529	+	0.465107i	0.00951777	+	0.0164853i
$797$	16.2908	+	28.2165i	0.577049	+	0.999478i	0.995816	+	0.0913843i	$0.0291292\pi$
$797$	16.2908	+	28.2165i	0.577049	+	0.999478i	−0.418767	+	0.908094i	$0.637537\pi$
$798$	−2.27161	+	0.225750i	−0.0804142	+	0.00799148i
$799$	17.8671	−	10.3155i	0.632091	−	0.364938i
$800$		−	4.09233i		−	0.144686i
$801$	−3.14524	+	1.81590i	−0.111132	+	0.0641618i
$802$	−6.07286	+	10.5185i	−0.214440	+	0.371421i
$803$	−0.287540	−	0.498035i	−0.0101471	−	0.0175753i
$804$	−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
$808$			3.40735i			0.119870i
$809$	16.0394			0.563914			0.281957	−	0.959427i	$-0.409017\pi$
$809$	16.0394			0.563914			0.281957	+	0.959427i	$0.409017\pi$
$810$	−0.952717			−0.0334751
$811$			35.4166i			1.24364i	0.783159	+	0.621822i	$0.213607\pi$
$811$			35.4166i			1.24364i	−0.783159	+	0.621822i	$0.786393\pi$
$812$	−12.4716	+	1.23942i	−0.437669	+	0.0434951i
$813$	14.2549	−	8.23006i	0.499941	−	0.288641i
$814$	0.719343	+	0.415313i	0.0252129	+	0.0145567i
$815$	3.90904	−	6.77065i	0.136928	−	0.237166i
$816$	2.20006			0.0770177
$817$	1.85220	−	1.06937i	0.0648003	−	0.0374125i
$818$	−24.2902			−0.849287
$819$	4.34422	−	8.49280i	0.151799	−	0.296763i
$820$	−6.38924			−0.223122
$821$	18.4983	−	10.6800i	0.645594	−	0.372734i	−0.141172	−	0.989985i	$-0.545087\pi$
$821$	18.4983	−	10.6800i	0.645594	−	0.372734i	0.786766	+	0.617251i	$0.211754\pi$
$822$	20.2972			0.707947
$823$	−1.32614	+	2.29693i	−0.0462262	+	0.0800661i	−0.888213	−	0.459432i	$-0.848053\pi$
$823$	−1.32614	+	2.29693i	−0.0462262	+	0.0800661i	0.841987	+	0.539499i	$0.181386\pi$
$824$	−2.04778	−	1.18228i	−0.0713377	−	0.0411868i
$825$	−0.261023	+	0.150702i	−0.00908766	+	0.00524676i
$826$	−14.8179	+	32.7805i	−0.515581	+	1.14058i
$827$		−	41.7395i		−	1.45142i	−0.687999	−	0.725712i	$-0.741510\pi$
$827$		−	41.7395i		−	1.45142i	0.687999	−	0.725712i	$-0.258490\pi$
$828$	8.03109			0.279100
$829$	−41.0850			−1.42694			−0.713470	−	0.700686i	$-0.752878\pi$
$829$	−41.0850			−1.42694			−0.713470	+	0.700686i	$0.752878\pi$
$830$		−	11.3155i		−	0.392768i
$831$	−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
$835$	−8.48021	−	14.6882i	−0.293470	−	0.508304i
$836$	−0.0317737	+	0.0550336i	−0.00109891	+	0.00190338i
$837$	8.72813	−	5.03919i	0.301688	−	0.174180i
$838$			9.72523i			0.335952i
$839$	22.0532	−	12.7324i	0.761360	−	0.439572i	−0.0684237	−	0.997656i	$-0.521797\pi$
$839$	22.0532	−	12.7324i	0.761360	−	0.439572i	0.829784	+	0.558085i	$0.188464\pi$
$840$	1.47002	+	2.04761i	0.0507206	+	0.0706493i
$841$	3.28013	+	5.68135i	0.113108	+	0.195909i
$842$	−12.8440	−	22.2465i	−0.442635	−	0.766666i
$843$			7.34639i			0.253023i
$844$	3.36821	+	5.83390i	0.115938	+	0.200811i
$845$	10.0791	+	7.19779i	0.346731	+	0.247612i
$846$	−9.37750			−0.322405
$847$	−11.9819	+	26.5066i	−0.411703	+	0.910777i
$848$	0.935404	−	1.62017i	0.0321219	−	0.0556368i
$849$	25.1290			0.862425
$850$	7.79716	−	4.50170i	0.267441	−	0.154407i
$851$	−78.4391	−	45.2868i	−2.68886	−	1.55241i
$852$			10.3518i			0.354646i
$853$			22.0242i			0.754095i	0.926194	+	0.377048i	$0.123061\pi$
$853$			22.0242i			0.754095i	−0.926194	+	0.377048i	$0.876939\pi$
$854$	−0.934437	−	9.40277i	−0.0319758	−	0.321756i
$855$	−0.411011	+	0.711892i	−0.0140563	+	0.0243462i
$856$	−8.23069	+	4.75199i	−0.281319	+	0.162420i
$857$	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	$0.660066\pi$
$858$	−0.121524	−	0.236114i	−0.00414875	−	0.00806080i
$859$	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
$861$	−14.4135	+	10.3478i	−0.491211	+	0.352651i
$862$	1.81057	+	3.13600i	0.0616683	+	0.106813i
$863$	−7.87832	−	4.54855i	−0.268181	−	0.154834i	0.359880	−	0.932999i	$-0.382818\pi$
$863$	−7.87832	−	4.54855i	−0.268181	−	0.154834i	−0.628061	+	0.778164i	$0.716151\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−2.28573	−	1.31967i	−0.0777171	−	0.0448700i
$866$	2.47898	+	1.43124i	0.0842390	+	0.0486354i
$867$	−6.07986	−	10.5306i	−0.206483	−	0.357639i
$868$	−24.2977	−	10.9834i	−0.824719	−	0.372802i
$869$	−0.165929	−	0.0957991i	−0.00562875	−	0.00324976i
$870$	−2.25654	+	3.90844i	−0.0765038	+	0.132509i
$871$	2.12534	−	43.9921i	0.0720145	−	1.49062i
$872$	3.86508	+	6.69452i	0.130888	+	0.226705i
$873$	11.1324	−	6.42728i	0.376774	−	0.217531i
$874$	3.46469	−	6.00101i	0.117195	−	0.202987i
$875$	20.8840	+	9.44032i	0.706009	+	0.319141i
$876$		−	7.80821i		−	0.263815i
$877$			17.7158i			0.598222i	0.954218	+	0.299111i	$0.0966900\pi$
$877$			17.7158i			0.598222i	−0.954218	+	0.299111i	$0.903310\pi$
$878$	9.31150	+	5.37600i	0.314248	+	0.181431i
$879$	15.0195	−	8.67149i	0.506594	−	0.292482i
$880$	0.0701684			0.00236538
$881$	0.631977	−	1.09462i	0.0212919	−	0.0368786i	−0.855183	−	0.518326i	$-0.826555\pi$
$881$	0.631977	−	1.09462i	0.0212919	−	0.0368786i	0.876475	+	0.481447i	$0.159889\pi$
$882$	6.63246	+	2.23842i	0.223326	+	0.0753716i
$883$	9.58668			0.322617			0.161309	−	0.986904i	$-0.448429\pi$
$883$	9.58668			0.322617			0.161309	+	0.986904i	$0.448429\pi$
$884$	3.63010	+	7.05309i	0.122093	+	0.237221i
$885$	6.47700	+	11.2185i	0.217722	+	0.377105i
$886$		−	6.00961i		−	0.201897i
$887$	−7.81884	−	13.5426i	−0.262531	−	0.454717i	0.704383	−	0.709820i	$-0.251224\pi$
$887$	−7.81884	−	13.5426i	−0.262531	−	0.454717i	−0.966914	+	0.255103i	$0.917891\pi$
$888$	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
$891$			0.0736508i			0.00246740i
$892$	22.0208	−	12.7137i	0.737310	−	0.425686i
$893$	−4.04554	+	7.00708i	−0.135379	+	0.234483i
$894$	5.89618	+	10.2125i	0.197198	+	0.341556i
$895$	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
$899$		−	47.7419i		−	1.59228i
$900$	−4.09233			−0.136411
$901$	4.11590			0.137120
$902$			0.493928i			0.0164460i
$903$	−6.52609	+	0.648556i	−0.217175	+	0.0215826i
$904$	6.42514	−	3.70956i	0.213697	−	0.123378i
$905$	−12.3968	−	7.15727i	−0.412082	−	0.237916i
$906$	7.93859	−	13.7500i	0.263742	−	0.456815i
$907$	−48.5314			−1.61146			−0.805730	−	0.592284i	$-0.798227\pi$
$907$	−48.5314			−1.61146			−0.805730	+	0.592284i	$0.798227\pi$
$908$	−2.94933	+	1.70279i	−0.0978769	+	0.0565092i
$909$	3.40735			0.113015
$910$	−4.13881	+	8.09124i	−0.137200	+	0.268222i
$911$	−16.8461			−0.558135			−0.279068	−	0.960271i	$-0.590025\pi$
$911$	−16.8461			−0.558135			−0.279068	+	0.960271i	$0.590025\pi$
$912$	−0.747223	+	0.431409i	−0.0247430	+	0.0142854i
$913$	−0.874760			−0.0289503
$914$	3.21858	−	5.57475i	0.106461	−	0.184396i
$915$	−2.94670	−	1.70128i	−0.0974148	−	0.0562425i
$916$	0.991069	−	0.572194i	0.0327459	−	0.0189058i
$917$	33.3735	+	46.4863i	1.10209	+	1.53511i
$918$		−	2.20006i		−	0.0726129i
$919$	−35.0795			−1.15716			−0.578582	−	0.815624i	$-0.696394\pi$
$919$	−35.0795			−1.15716			−0.578582	+	0.815624i	$0.696394\pi$
$920$	−7.65136			−0.252258
$921$		−	27.9365i		−	0.920539i
$922$	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
$926$	10.2740	+	17.7951i	0.337625	+	0.584784i
$927$	−1.18228	+	2.04778i	−0.0388313	+	0.0672578i
$928$	−4.10241	+	2.36853i	−0.134668	+	0.0777508i
$929$		−	13.6534i		−	0.447953i	−0.974595	−	0.223976i	$-0.928096\pi$
$929$		−	13.6534i		−	0.447953i	0.974595	−	0.223976i	$-0.0719039\pi$
$930$	−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
$933$	3.34510	+	5.79388i	0.109514	+	0.189683i
$934$		−	8.30374i		−	0.271707i
$935$	0.0771875	+	0.133693i	0.00252430	+	0.00437222i
$936$	0.173988	−	3.60135i	0.00568698	−	0.117714i
$937$	−22.9765			−0.750611			−0.375306	−	0.926901i	$-0.622462\pi$
$937$	−22.9765			−0.750611			−0.375306	+	0.926901i	$0.622462\pi$
$938$	32.1606	−	3.19609i	1.05008	−	0.104356i
$939$	−2.67609	+	4.63512i	−0.0873308	+	0.151261i
$940$	8.93410			0.291398
$941$	23.4793	−	13.5558i	0.765404	−	0.441906i	−0.0658287	−	0.997831i	$-0.520969\pi$
$941$	23.4793	−	13.5558i	0.765404	−	0.441906i	0.831233	+	0.555925i	$0.187636\pi$
$942$	−5.99655	−	3.46211i	−0.195378	−	0.112802i
$943$		−	53.8592i		−	1.75390i
$944$			13.5969i			0.442541i
$945$	2.04761	−	1.47002i	0.0666088	−	0.0478199i
$946$	−0.0912822	+	0.158105i	−0.00296784	+	0.00514045i
$947$	−4.02599	+	2.32441i	−0.130827	+	0.0755331i	−0.563985	−	0.825785i	$-0.690733\pi$
$947$	−4.02599	+	2.32441i	−0.130827	+	0.0755331i	0.433158	+	0.901318i	$0.357399\pi$
$948$	−1.30072	−	2.25291i	−0.0422454	−	0.0731712i
$949$	25.0320	−	12.8835i	0.812572	−	0.418217i
$950$	−1.76547	+	3.05788i	−0.0572794	+	0.0992108i
$951$	−15.2431	−	8.80060i	−0.494291	−	0.285379i
$952$	−4.72845	+	3.39466i	−0.153250	+	0.110021i
$953$	−13.9684	−	24.1939i	−0.452480	−	0.783718i	0.546060	−	0.837746i	$-0.316127\pi$
$953$	−13.9684	−	24.1939i	−0.452480	−	0.783718i	−0.998539	+	0.0540283i	$0.982794\pi$
$954$	−1.62017	−	0.935404i	−0.0524548	−	0.0302848i
$955$	4.84704	+	2.79844i	0.156847	+	0.0905555i
$956$	25.0835	+	14.4820i	0.811259	+	0.468381i
$957$	0.302146	+	0.174444i	0.00976700	+	0.00563898i
$958$	10.6254	+	18.4037i	0.343291	+	0.594597i
$959$	−43.6235	+	31.3182i	−1.40868	+	1.01132i
$960$	0.825077	+	0.476358i	0.0266292	+	0.0153744i
$961$	35.2868	−	61.1185i	1.13828	−	1.97157i
$962$	−22.0071	+	34.1930i	−0.709538	+	1.10243i
$963$	4.75199	+	8.23069i	0.153131	+	0.265230i
$964$	−5.19416	+	2.99885i	−0.167293	+	0.0965864i
$965$	5.81998	−	10.0805i	0.187352	−	0.324503i
$966$	−17.2607	+	12.3918i	−0.555354	+	0.398700i
$967$			11.0007i			0.353760i	0.984232	+	0.176880i	$0.0566004\pi$
$967$			11.0007i			0.353760i	−0.984232	+	0.176880i	$0.943400\pi$
$968$			10.9946i			0.353379i
$969$	−1.64394	−	0.949128i	−0.0528109	−	0.0304904i
$970$	−10.6060	+	6.12338i	−0.340538	+	0.196610i
$971$	−5.04638			−0.161946			−0.0809729	−	0.996716i	$-0.525803\pi$
$971$	−5.04638			−0.161946			−0.0809729	+	0.996716i	$0.525803\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	0.391499	−	0.0389067i	0.0125509	−	0.00124729i
$974$	−24.9365			−0.799018
$975$	−6.75233	−	13.1194i	−0.216248	−	0.420158i
$976$	−1.78571	−	3.09294i	−0.0571592	−	0.0990026i
$977$		−	24.9181i		−	0.797201i	−0.917125	−	0.398600i	$-0.869496\pi$
$977$		−	24.9181i		−	0.797201i	0.917125	−	0.398600i	$-0.130504\pi$
$978$	−4.10304	−	7.10668i	−0.131201	−	0.227247i
$979$	−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
$982$			0.403154i			0.0128651i
$983$	27.0541	−	15.6197i	0.862892	−	0.498191i	−0.00208762	−	0.999998i	$-0.500665\pi$
$983$	27.0541	−	15.6197i	0.862892	−	0.498191i	0.864980	+	0.501807i	$0.167331\pi$
$984$	−3.35317	+	5.80786i	−0.106895	+	0.185148i
$985$	6.37626	+	11.0440i	0.203165	+	0.351891i
$986$	−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
$990$		−	0.0701684i		−	0.00223010i
$991$	37.1971			1.18161			0.590803	−	0.806816i	$-0.298811\pi$
$991$	37.1971			1.18161			0.590803	+	0.806816i	$0.298811\pi$
$992$	−10.0784			−0.319989
$993$		−	29.8193i		−	0.946286i
$994$	−15.9726	−	22.2484i	−0.506620	−	0.705677i
$995$	−0.443115	+	0.255832i	−0.0140477	+	0.00811044i
$996$	−10.2859	−	5.93856i	−0.325921	−	0.188171i
$997$	−18.5509	+	32.1311i	−0.587514	+	1.01760i	0.407043	+	0.913409i	$0.366560\pi$
$997$	−18.5509	+	32.1311i	−0.587514	+	1.01760i	−0.994557	+	0.104195i	$0.966774\pi$
$998$	26.5568			0.840640
$999$	9.76693	−	5.63894i	0.309012	−	0.178408i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.3	✓	16	1.1	even	1	trivial
546.2.bd.a.361.3	yes	16	91.88	even	6	inner
546.2.bm.a.205.6	yes	16	13.10	even	6
546.2.bm.a.277.2	yes	16	7.4	even	3
1638.2.cr.a.361.6		16	273.179	odd	6
1638.2.cr.a.667.6		16	3.2	odd	2
1638.2.dt.a.1297.3		16	39.23	odd	6
1638.2.dt.a.1369.7		16	21.11	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.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(0.825077 + 0.476358i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.08980 + 2.41088i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(0.825077 + 0.476358i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.08980 + 2.41088i) q^{7} +1.00000i q^{8} +1.00000 q^{9} -0.952717 q^{10} +0.0736508i 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} +(-0.500000 - 0.866025i) q^{16} +(1.10003 - 1.90531i) q^{17} +(-0.866025 + 0.500000i) q^{18} +0.862818i q^{19} +(0.825077 - 0.476358i) q^{20} +(1.08980 - 2.41088i) q^{21} +(-0.0368254 - 0.0637835i) q^{22} +(4.01555 + 6.95513i) q^{23} -1.00000i q^{24} +(-2.04617 - 3.54406i) q^{25} +(3.20586 - 1.65000i) q^{26} -1.00000 q^{27} +(1.54298 + 2.14923i) q^{28} +(-2.36853 + 4.10241i) q^{29} +0.952717 q^{30} +(-8.72813 + 5.03919i) q^{31} +(0.866025 + 0.500000i) q^{32} -0.0736508i q^{33} +2.20006i q^{34} +(-2.04761 + 1.47002i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-9.76693 + 5.63894i) q^{37} +(-0.431409 - 0.747223i) q^{38} +(3.60135 + 0.173988i) q^{39} +(-0.476358 + 0.825077i) q^{40} +(-5.80786 - 3.35317i) q^{41} +(0.261643 + 2.63278i) q^{42} +(-1.23939 - 2.14669i) q^{43} +(0.0637835 + 0.0368254i) q^{44} +(0.825077 + 0.476358i) q^{45} +(-6.95513 - 4.01555i) q^{46} +(8.12115 + 4.68875i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-4.62466 - 5.25476i) q^{49} +(3.54406 + 2.04617i) q^{50} +(-1.10003 + 1.90531i) q^{51} +(-1.95135 + 3.03187i) q^{52} +(0.935404 + 1.62017i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.0350842 + 0.0607676i) q^{55} +(-2.41088 - 1.08980i) q^{56} -0.862818i q^{57} -4.73706i q^{58} +(-11.7753 - 6.79845i) q^{59} +(-0.825077 + 0.476358i) q^{60} +3.57142 q^{61} +(5.03919 - 8.72813i) q^{62} +(-1.08980 + 2.41088i) q^{63} -1.00000 q^{64} +(-2.88851 - 1.85909i) q^{65} +(0.0368254 + 0.0637835i) q^{66} +12.2154i q^{67} +(-1.10003 - 1.90531i) q^{68} +(-4.01555 - 6.95513i) q^{69} +(1.03827 - 2.29688i) q^{70} +(8.96491 - 5.17589i) q^{71} +1.00000i q^{72} +(-6.76210 + 3.90410i) q^{73} +(5.63894 - 9.76693i) q^{74} +(2.04617 + 3.54406i) 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} -0.952717i q^{80} +1.00000 q^{81} +6.70634 q^{82} +11.8771i q^{83} +(-1.54298 - 2.14923i) q^{84} +(1.81522 - 1.04802i) q^{85} +(2.14669 + 1.23939i) q^{86} +(2.36853 - 4.10241i) q^{87} -0.0736508 q^{88} +(-3.14524 + 1.81590i) q^{89} -0.952717 q^{90} +(4.34422 - 8.49280i) q^{91} +8.03109 q^{92} +(8.72813 - 5.03919i) q^{93} -9.37750 q^{94} +(-0.411011 + 0.711892i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(11.1324 - 6.42728i) q^{97} +(6.63246 + 2.23842i) q^{98} +0.0736508i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9	\( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31} + 16 q^{35} + 8 q^{36} + 30 q^{37} - 2 q^{38} + 10 q^{39} - 4 q^{40} - 18 q^{41} - 4 q^{42} - 32 q^{43} + 6 q^{44} + 12 q^{46} + 66 q^{47} + 8 q^{48} - 2 q^{49} + 36 q^{50} + 4 q^{52} + 2 q^{53} + 16 q^{55} + 2 q^{56} - 36 q^{59} - 8 q^{61} + 4 q^{62} + 8 q^{63} - 16 q^{64} - 28 q^{65} - 6 q^{66} + 16 q^{69} - 6 q^{70} - 30 q^{71} - 18 q^{73} + 6 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} + 16 q^{81} - 12 q^{82} - 10 q^{84} + 72 q^{85} + 4 q^{87} + 12 q^{88} - 42 q^{89} - 8 q^{90} - 18 q^{91} - 32 q^{92} - 12 q^{93} + 48 q^{94} - 40 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) \) 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9 - 8 * q^10 - 8 * q^12 - 10 * q^13 + 4 * q^14 - 8 * q^16 - 8 * q^21 + 6 * q^22 - 16 * q^23 + 2 * q^26 - 16 * q^27 + 10 * q^28 - 4 * q^29 + 8 * q^30 + 12 * q^31 + 16 * q^35 + 8 * q^36 + 30 * q^37 - 2 * q^38 + 10 * q^39 - 4 * q^40 - 18 * q^41 - 4 * q^42 - 32 * q^43 + 6 * q^44 + 12 * q^46 + 66 * q^47 + 8 * q^48 - 2 * q^49 + 36 * q^50 + 4 * q^52 + 2 * q^53 + 16 * q^55 + 2 * q^56 - 36 * q^59 - 8 * q^61 + 4 * q^62 + 8 * q^63 - 16 * q^64 - 28 * q^65 - 6 * q^66 + 16 * q^69 - 6 * q^70 - 30 * q^71 - 18 * q^73 + 6 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 + 16 * q^81 - 12 * q^82 - 10 * q^84 + 72 * q^85 + 4 * q^87 + 12 * q^88 - 42 * q^89 - 8 * q^90 - 18 * q^91 - 32 * q^92 - 12 * q^93 + 48 * q^94 - 40 * q^95 - 6 * q^97 - 12 * q^98

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