LMFDB - Embedded newform 546.2.bx.a.223.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(97,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			223.5
Character	$\chi$	$=$	546.223
Dual form			546.2.bx.a.475.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.53071 + 2.53071i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.06416 - 2.42231i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.53071 + 2.53071i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.06416 - 2.42231i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.78948 - 3.09948i) q^{10} +(1.24903 - 4.66145i) q^{11} +1.00000 q^{12} +(-3.47382 + 0.965682i) q^{13} +(0.400958 + 2.61519i) q^{14} +(3.45702 + 0.926305i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.64401 - 6.31161i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(5.46962 - 1.46558i) q^{19} +(0.926305 + 3.45702i) q^{20} +(-2.13274 - 1.56570i) q^{21} +(-2.41295 + 4.17934i) q^{22} +(-2.69208 + 1.55427i) q^{23} +(-0.965926 - 0.258819i) q^{24} +7.80902i q^{25} +(3.60539 - 0.0336851i) q^{26} -1.00000i q^{27} +(0.289566 - 2.62986i) q^{28} +(3.05124 + 5.28489i) q^{29} +(-3.09948 - 1.78948i) q^{30} +(6.07605 + 6.07605i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.24903 - 4.66145i) q^{33} +(-5.15340 + 5.15340i) q^{34} +(3.43708 - 8.82324i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-2.09834 + 7.83110i) q^{37} -5.66257 q^{38} +(-2.52558 + 2.57322i) q^{39} -3.57897i q^{40} +(0.957340 - 3.57284i) q^{41} +(1.65484 + 2.06434i) q^{42} +(-0.401200 - 0.231633i) q^{43} +(3.41242 - 3.41242i) q^{44} +(3.45702 - 0.926305i) q^{45} +(3.00263 - 0.804551i) q^{46} +(3.23615 - 3.23615i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-4.73514 + 5.15543i) q^{49} +(2.02112 - 7.54293i) q^{50} -7.28801i q^{51} +(-3.49126 - 0.900607i) q^{52} -5.63618 q^{53} +(-0.258819 + 0.965926i) q^{54} +(14.9577 - 8.63586i) q^{55} +(-0.960356 + 2.46530i) q^{56} +(4.00404 - 4.00404i) q^{57} +(-1.57944 - 5.89453i) q^{58} +(-2.29319 - 8.55829i) q^{59} +(2.53071 + 2.53071i) q^{60} +(-3.62054 - 2.09032i) q^{61} +(-4.29642 - 7.44161i) q^{62} +(-2.62986 - 0.289566i) q^{63} +1.00000i q^{64} +(-11.2351 - 6.34739i) q^{65} +4.82589i q^{66} +(4.63235 + 1.24124i) q^{67} +(6.31161 - 3.64401i) q^{68} +(-1.55427 + 2.69208i) q^{69} +(-5.60359 + 7.63301i) q^{70} +(1.02620 + 3.82981i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-0.575606 + 0.575606i) q^{73} +(4.05367 - 7.02117i) q^{74} +(3.90451 + 6.76281i) q^{75} +(5.46962 + 1.46558i) q^{76} +(-12.6206 + 1.93498i) q^{77} +(3.10552 - 1.83187i) q^{78} -13.0719 q^{79} +(-0.926305 + 3.45702i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.84944 + 3.20332i) q^{82} +(7.77258 + 7.77258i) q^{83} +(-1.06416 - 2.42231i) q^{84} +(25.1948 - 6.75093i) q^{85} +(0.327578 + 0.327578i) q^{86} +(5.28489 + 3.05124i) q^{87} +(-4.17934 + 2.41295i) q^{88} +(4.21399 + 1.12913i) q^{89} -3.57897 q^{90} +(6.03588 + 7.38703i) q^{91} -3.10855 q^{92} +(8.30004 + 2.22399i) q^{93} +(-3.96346 + 2.28830i) q^{94} +(17.5510 + 10.1331i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-14.8992 + 3.99223i) q^{97} +(5.90811 - 3.75422i) q^{98} +(-3.41242 - 3.41242i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 + 20 * q^9	$ 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	2.53071	+	2.53071i	1.13177	+	1.13177i	0.989883	+	0.141886i	$0.0453168\pi$
$5$	2.53071	+	2.53071i	1.13177	+	1.13177i	0.141886	+	0.989883i	$0.454683\pi$
$6$	−0.965926	+	0.258819i	−0.394338	+	0.105662i
$7$	−1.06416	−	2.42231i	−0.402214	−	0.915546i
$7$	−1.06416	−	2.42231i	−0.402214	−	0.915546i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.78948	−	3.09948i	−0.565885	−	0.980141i
$11$	1.24903	−	4.66145i	0.376598	−	1.40548i	−0.474399	−	0.880310i	$-0.657335\pi$
$11$	1.24903	−	4.66145i	0.376598	−	1.40548i	0.850997	−	0.525171i	$-0.175999\pi$
$12$	1.00000			0.288675
$13$	−3.47382	+	0.965682i	−0.963466	+	0.267832i
$13$	−3.47382	+	0.965682i	−0.963466	+	0.267832i
$14$	0.400958	+	2.61519i	0.107161	+	0.698940i
$15$	3.45702	+	0.926305i	0.892598	+	0.239171i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.64401	−	6.31161i	0.883802	−	1.53079i	0.0367204	−	0.999326i	$-0.488309\pi$
$17$	3.64401	−	6.31161i	0.883802	−	1.53079i	0.847081	−	0.531464i	$-0.178358\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	5.46962	−	1.46558i	1.25482	−	0.336227i	0.430622	−	0.902532i	$-0.358294\pi$
$19$	5.46962	−	1.46558i	1.25482	−	0.336227i	0.824196	+	0.566305i	$0.191628\pi$
$20$	0.926305	+	3.45702i	0.207128	+	0.773013i
$21$	−2.13274	−	1.56570i	−0.465402	−	0.341664i
$22$	−2.41295	+	4.17934i	−0.514442	+	0.891039i
$23$	−2.69208	+	1.55427i	−0.561338	+	0.324088i	−0.753682	−	0.657239i	$-0.771724\pi$
$23$	−2.69208	+	1.55427i	−0.561338	+	0.324088i	0.192345	+	0.981327i	$0.438391\pi$
$24$	−0.965926	−	0.258819i	−0.197169	−	0.0528312i
$25$			7.80902i			1.56180i
$26$	3.60539	−	0.0336851i	0.707076	−	0.00660620i
$27$		−	1.00000i		−	0.192450i
$28$	0.289566	−	2.62986i	0.0547227	−	0.496996i
$29$	3.05124	+	5.28489i	0.566600	+	0.981380i	0.996899	+	0.0786937i	$0.0250749\pi$
$29$	3.05124	+	5.28489i	0.566600	+	0.981380i	−0.430299	+	0.902687i	$0.641592\pi$
$30$	−3.09948	−	1.78948i	−0.565885	−	0.326714i
$31$	6.07605	+	6.07605i	1.09129	+	1.09129i	0.995391	+	0.0958999i	$0.0305729\pi$
$31$	6.07605	+	6.07605i	1.09129	+	1.09129i	0.0958999	+	0.995391i	$0.469427\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−1.24903	−	4.66145i	−0.217429	−	0.811455i
$34$	−5.15340	+	5.15340i	−0.883802	+	0.883802i
$35$	3.43708	−	8.82324i	0.580973	−	1.49140i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	−2.09834	+	7.83110i	−0.344964	+	1.28742i	0.547690	+	0.836682i	$0.315507\pi$
$37$	−2.09834	+	7.83110i	−0.344964	+	1.28742i	−0.892654	+	0.450743i	$0.851159\pi$
$38$	−5.66257			−0.918590
$39$	−2.52558	+	2.57322i	−0.404416	+	0.412045i
$40$		−	3.57897i		−	0.565885i
$41$	0.957340	−	3.57284i	0.149511	−	0.557984i	−0.850002	−	0.526780i	$-0.823399\pi$
$41$	0.957340	−	3.57284i	0.149511	−	0.557984i	0.999513	−	0.0312042i	$-0.00993421\pi$
$42$	1.65484	+	2.06434i	0.255347	+	0.318535i
$43$	−0.401200	−	0.231633i	−0.0611824	−	0.0353237i	0.469097	−	0.883147i	$-0.344580\pi$
$43$	−0.401200	−	0.231633i	−0.0611824	−	0.0353237i	−0.530279	+	0.847823i	$0.677913\pi$
$44$	3.41242	−	3.41242i	0.514442	−	0.514442i
$45$	3.45702	−	0.926305i	0.515342	−	0.138085i
$46$	3.00263	−	0.804551i	0.442713	−	0.118625i
$47$	3.23615	−	3.23615i	0.472041	−	0.472041i	−0.430534	−	0.902574i	$-0.641675\pi$
$47$	3.23615	−	3.23615i	0.472041	−	0.472041i	0.902574	+	0.430534i	$0.141675\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−4.73514	+	5.15543i	−0.676448	+	0.736490i
$50$	2.02112	−	7.54293i	0.285830	−	1.06673i
$51$		−	7.28801i		−	1.02053i
$52$	−3.49126	−	0.900607i	−0.484151	−	0.124892i
$53$	−5.63618			−0.774188			−0.387094	−	0.922040i	$-0.626521\pi$
$53$	−5.63618			−0.774188			−0.387094	+	0.922040i	$0.626521\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$	14.9577	−	8.63586i	2.01690	−	1.16446i
$56$	−0.960356	+	2.46530i	−0.128333	+	0.329440i
$57$	4.00404	−	4.00404i	0.530348	−	0.530348i
$58$	−1.57944	−	5.89453i	−0.207390	−	0.773990i
$59$	−2.29319	−	8.55829i	−0.298547	−	1.11419i	−0.938359	−	0.345662i	$-0.887654\pi$
$59$	−2.29319	−	8.55829i	−0.298547	−	1.11419i	0.639812	−	0.768532i	$-0.279012\pi$
$60$	2.53071	+	2.53071i	0.326714	+	0.326714i
$61$	−3.62054	−	2.09032i	−0.463563	−	0.267638i	0.249978	−	0.968251i	$-0.419576\pi$
$61$	−3.62054	−	2.09032i	−0.463563	−	0.267638i	−0.713541	+	0.700613i	$0.752910\pi$
$62$	−4.29642	−	7.44161i	−0.545645	−	0.945086i
$63$	−2.62986	−	0.289566i	−0.331331	−	0.0364818i
$64$			1.00000i			0.125000i
$65$	−11.2351	−	6.34739i	−1.39354	−	0.787297i
$66$			4.82589i			0.594026i
$67$	4.63235	+	1.24124i	0.565932	+	0.151641i	0.530430	−	0.847729i	$-0.322030\pi$
$67$	4.63235	+	1.24124i	0.565932	+	0.151641i	0.0355018	+	0.999370i	$0.488697\pi$
$68$	6.31161	−	3.64401i	0.765395	−	0.441901i
$69$	−1.55427	+	2.69208i	−0.187113	+	0.324088i
$70$	−5.60359	+	7.63301i	−0.669757	+	0.912320i
$71$	1.02620	+	3.82981i	0.121787	+	0.454515i	0.999705	−	0.0242960i	$-0.00773443\pi$
$71$	1.02620	+	3.82981i	0.121787	+	0.454515i	−0.877918	+	0.478811i	$0.841068\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	−0.575606	+	0.575606i	−0.0673696	+	0.0673696i	−0.739989	−	0.672619i	$-0.765169\pi$
$73$	−0.575606	+	0.575606i	−0.0673696	+	0.0673696i	0.672619	+	0.739989i	$0.265169\pi$
$74$	4.05367	−	7.02117i	0.471230	−	0.816194i
$75$	3.90451	+	6.76281i	0.450854	+	0.780902i
$76$	5.46962	+	1.46558i	0.627409	+	0.168114i
$77$	−12.6206	+	1.93498i	−1.43825	+	0.220512i
$78$	3.10552	−	1.83187i	0.351631	−	0.207418i
$79$	−13.0719			−1.47071			−0.735354	−	0.677683i	$-0.762984\pi$
$79$	−13.0719			−1.47071			−0.735354	+	0.677683i	$0.762984\pi$
$80$	−0.926305	+	3.45702i	−0.103564	+	0.386506i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.84944	+	3.20332i	−0.204236	+	0.353748i
$83$	7.77258	+	7.77258i	0.853151	+	0.853151i	0.990520	−	0.137369i	$-0.0438645\pi$
$83$	7.77258	+	7.77258i	0.853151	+	0.853151i	−0.137369	+	0.990520i	$0.543864\pi$
$84$	−1.06416	−	2.42231i	−0.116109	−	0.264295i
$85$	25.1948	−	6.75093i	2.73276	−	0.732241i
$86$	0.327578	+	0.327578i	0.0353237	+	0.0353237i
$87$	5.28489	+	3.05124i	0.566600	+	0.327127i
$88$	−4.17934	+	2.41295i	−0.445520	+	0.257221i
$89$	4.21399	+	1.12913i	0.446682	+	0.119688i	0.475146	−	0.879907i	$-0.342395\pi$
$89$	4.21399	+	1.12913i	0.446682	+	0.119688i	−0.0284646	+	0.999595i	$0.509062\pi$
$90$	−3.57897			−0.377256
$91$	6.03588	+	7.38703i	0.632732	+	0.774371i
$92$	−3.10855			−0.324088
$93$	8.30004	+	2.22399i	0.860674	+	0.230617i
$94$	−3.96346	+	2.28830i	−0.408799	+	0.236020i
$95$	17.5510	+	10.1331i	1.80070	+	1.03963i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−14.8992	+	3.99223i	−1.51279	+	0.405350i	−0.917359	−	0.398060i	$-0.869684\pi$
$97$	−14.8992	+	3.99223i	−1.51279	+	0.405350i	−0.595427	+	0.803410i	$0.703017\pi$
$98$	5.90811	−	3.75422i	0.596810	−	0.379234i
$99$	−3.41242	−	3.41242i	−0.342961	−	0.342961i
$100$	−3.90451	+	6.76281i	−0.390451	+	0.676281i
$101$	0.550864	+	0.954125i	0.0548130	+	0.0949390i	0.892130	−	0.451779i	$-0.149210\pi$
$101$	0.550864	+	0.954125i	0.0548130	+	0.0949390i	−0.837317	+	0.546718i	$0.815877\pi$
$102$	−1.88628	+	7.03968i	−0.186769	+	0.697032i
$103$	−16.2258			−1.59877			−0.799387	−	0.600816i	$-0.794842\pi$
$103$	−16.2258			−1.59877			−0.799387	+	0.600816i	$0.794842\pi$
$104$	3.13921	+	1.77352i	0.307824	+	0.173908i
$105$	−1.43502	−	9.35969i	−0.140043	−	0.913413i
$106$	5.44413	+	1.45875i	0.528781	+	0.141686i
$107$	−4.03650	−	6.99143i	−0.390223	−	0.675887i	0.602255	−	0.798304i	$-0.294269\pi$
$107$	−4.03650	−	6.99143i	−0.390223	−	0.675887i	−0.992479	+	0.122417i	$0.960936\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−0.225019	+	0.225019i	−0.0215529	+	0.0215529i	−0.717801	−	0.696248i	$-0.754851\pi$
$109$	−0.225019	+	0.225019i	−0.0215529	+	0.0215529i	0.696248	+	0.717801i	$0.254851\pi$
$110$	−16.6832	+	4.47025i	−1.59068	+	0.426222i
$111$	2.09834	+	7.83110i	0.199165	+	0.743295i
$112$	1.56570	−	2.13274i	0.147945	−	0.201525i
$113$	−5.93923	+	10.2871i	−0.558716	+	0.967725i	0.438888	+	0.898542i	$0.355372\pi$
$113$	−5.93923	+	10.2871i	−0.558716	+	0.967725i	−0.997604	+	0.0691828i	$0.977961\pi$
$114$	−4.90393	+	2.83129i	−0.459295	+	0.265174i
$115$	−10.7463	−	2.87946i	−1.00210	−	0.268511i
$116$			6.10247i			0.566600i
$117$	−0.900607	+	3.49126i	−0.0832612	+	0.322767i
$118$			8.86019i			0.815647i
$119$	−19.1664	−	2.11036i	−1.75698	−	0.193456i
$120$	−1.78948	−	3.09948i	−0.163357	−	0.282942i
$121$	−10.6428	−	6.14461i	−0.967526	−	0.558601i
$122$	2.95616	+	2.95616i	0.267638	+	0.267638i
$123$	−0.957340	−	3.57284i	−0.0863205	−	0.322152i
$124$	2.22399	+	8.30004i	0.199720	+	0.745366i
$125$	−7.10882	+	7.10882i	−0.635832	+	0.635832i
$126$	2.46530	+	0.960356i	0.219627	+	0.0855553i
$127$	−9.05737	+	5.22927i	−0.803711	+	0.464023i	−0.844767	−	0.535134i	$-0.820261\pi$
$127$	−9.05737	+	5.22927i	−0.803711	+	0.464023i	0.0410559	+	0.999157i	$0.486928\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−0.463266			−0.0407883
$130$	9.20947	+	9.03897i	0.807724	+	0.792770i
$131$			5.16170i			0.450980i	0.974245	+	0.225490i	$0.0723983\pi$
$131$			5.16170i			0.450980i	−0.974245	+	0.225490i	$0.927602\pi$
$132$	1.24903	−	4.66145i	0.108714	−	0.405727i
$133$	−9.37063	−	11.6895i	−0.812537	−	1.01361i
$134$	−4.15325	−	2.39788i	−0.358787	−	0.207146i
$135$	2.53071	−	2.53071i	0.217809	−	0.217809i
$136$	−7.03968	+	1.88628i	−0.603648	+	0.161747i
$137$	16.1341	−	4.32311i	1.37843	−	0.369348i	0.507877	−	0.861429i	$-0.330430\pi$
$137$	16.1341	−	4.32311i	1.37843	−	0.369348i	0.870549	+	0.492081i	$0.163764\pi$
$138$	2.19808	−	2.19808i	0.187113	−	0.187113i
$139$	4.55188	+	2.62803i	0.386085	+	0.222906i	0.680463	−	0.732783i	$-0.261779\pi$
$139$	4.55188	+	2.62803i	0.386085	+	0.222906i	−0.294377	+	0.955689i	$0.595112\pi$
$140$	7.38822	−	5.92261i	0.624419	−	0.500552i
$141$	1.18451	−	4.42066i	0.0997539	−	0.372287i
$142$		−	3.96492i		−	0.332728i
$143$	0.162561	+	17.3992i	0.0135940	+	1.45500i
$144$	1.00000			0.0833333
$145$	−5.65275	+	21.0964i	−0.469435	+	1.75196i
$146$	0.704971	−	0.407015i	0.0583438	−	0.0336848i
$147$	−1.52303	+	6.83230i	−0.125618	+	0.563519i
$148$	−5.73276	+	5.73276i	−0.471230	+	0.471230i
$149$	−2.94113	−	10.9765i	−0.240947	−	0.899227i	−0.975377	−	0.220543i	$-0.929217\pi$
$149$	−2.94113	−	10.9765i	−0.240947	−	0.899227i	0.734430	−	0.678684i	$-0.237449\pi$
$150$	−2.02112	−	7.54293i	−0.165024	−	0.615878i
$151$	−8.01079	−	8.01079i	−0.651909	−	0.651909i	0.301544	−	0.953452i	$-0.402498\pi$
$151$	−8.01079	−	8.01079i	−0.651909	−	0.651909i	−0.953452	+	0.301544i	$0.902498\pi$
$152$	−4.90393	−	2.83129i	−0.397761	−	0.229648i
$153$	−3.64401	−	6.31161i	−0.294601	−	0.510263i
$154$	12.6914	+	1.39741i	1.02270	+	0.112607i
$155$			30.7535i			2.47018i
$156$	−3.47382	+	0.965682i	−0.278129	+	0.0773164i
$157$		−	7.66324i		−	0.611593i	−0.952097	−	0.305797i	$-0.901077\pi$
$157$		−	7.66324i		−	0.611593i	0.952097	−	0.305797i	$-0.0989228\pi$
$158$	12.6265	+	3.38327i	1.00451	+	0.269158i
$159$	−4.88107	+	2.81809i	−0.387094	+	0.223489i
$160$	1.78948	−	3.09948i	0.141471	−	0.245035i
$161$	6.62973	+	4.86705i	0.522496	+	0.383578i
$162$	0.258819	+	0.965926i	0.0203347	+	0.0758903i
$163$	0.690353	−	0.184979i	0.0540726	−	0.0144887i	−0.231681	−	0.972792i	$-0.574423\pi$
$163$	0.690353	−	0.184979i	0.0540726	−	0.0144887i	0.285754	+	0.958303i	$0.407756\pi$
$164$	2.61550	−	2.61550i	0.204236	−	0.204236i
$165$	8.63586	−	14.9577i	0.672301	−	1.16446i
$166$	−5.49604	−	9.51943i	−0.426576	−	0.738851i
$167$	5.90069	+	1.58108i	0.456609	+	0.122348i	0.479790	−	0.877383i	$-0.340713\pi$
$167$	5.90069	+	1.58108i	0.456609	+	0.122348i	−0.0231813	+	0.999731i	$0.507379\pi$
$168$	0.400958	+	2.61519i	0.0309346	+	0.201766i
$169$	11.1349	−	6.70922i	0.856532	−	0.516094i
$170$	−26.0836			−2.00052
$171$	1.46558	−	5.46962i	0.112076	−	0.418273i
$172$	−0.231633	−	0.401200i	−0.0176618	−	0.0305912i
$173$	−5.94546	+	10.2978i	−0.452025	+	0.782930i	−0.998512	−	0.0545374i	$-0.982632\pi$
$173$	−5.94546	+	10.2978i	−0.452025	+	0.782930i	0.546487	+	0.837468i	$0.315965\pi$
$174$	−4.31510	−	4.31510i	−0.327127	−	0.327127i
$175$	18.9158	−	8.31003i	1.42990	−	0.628179i
$176$	4.66145	−	1.24903i	0.351370	−	0.0941494i
$177$	−6.26510	−	6.26510i	−0.470914	−	0.470914i
$178$	−3.77816	−	2.18132i	−0.283185	−	0.163497i
$179$	6.79168	−	3.92118i	0.507634	−	0.293083i	−0.224226	−	0.974537i	$-0.571986\pi$
$179$	6.79168	−	3.92118i	0.507634	−	0.293083i	0.731861	+	0.681454i	$0.238652\pi$
$180$	3.45702	+	0.926305i	0.257671	+	0.0690427i
$181$	16.6885			1.24045			0.620225	−	0.784424i	$-0.287041\pi$
$181$	16.6885			1.24045			0.620225	+	0.784424i	$0.287041\pi$
$182$	−3.91830	−	8.69752i	−0.290444	−	0.644703i
$183$	−4.18064			−0.309042
$184$	3.00263	+	0.804551i	0.221357	+	0.0593123i
$185$	−25.1285	+	14.5080i	−1.84749	+	1.06665i
$186$	−7.44161	−	4.29642i	−0.545645	−	0.315029i
$187$	−24.8698	−	24.8698i	−1.81866	−	1.81866i
$188$	4.42066	−	1.18451i	0.322410	−	0.0863894i
$189$	−2.42231	+	1.06416i	−0.176197	+	0.0774061i
$190$	−14.3303	−	14.3303i	−1.03963	−	1.03963i
$191$	−7.00231	+	12.1284i	−0.506669	+	0.877577i	0.493301	+	0.869859i	$0.335790\pi$
$191$	−7.00231	+	12.1284i	−0.506669	+	0.877577i	−0.999970	+	0.00771842i	$0.997543\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−3.74341	+	13.9706i	−0.269457	+	1.00563i	0.690009	+	0.723801i	$0.257607\pi$
$193$	−3.74341	+	13.9706i	−0.269457	+	1.00563i	−0.959466	+	0.281826i	$0.909060\pi$
$194$	15.4248			1.10744
$195$	−12.9036	+	0.120558i	−0.924046	+	0.00863334i
$196$	−6.67846	+	2.09717i	−0.477033	+	0.149798i
$197$	−9.66331	−	2.58928i	−0.688483	−	0.184478i	−0.102416	−	0.994742i	$-0.532657\pi$
$197$	−9.66331	−	2.58928i	−0.688483	−	0.184478i	−0.586066	+	0.810263i	$0.699324\pi$
$198$	2.41295	+	4.17934i	0.171481	+	0.297013i
$199$	−0.816012	+	1.41337i	−0.0578456	+	0.100191i	−0.893498	−	0.449067i	$-0.851756\pi$
$199$	−0.816012	+	1.41337i	−0.0578456	+	0.100191i	0.835653	+	0.549258i	$0.185090\pi$
$200$	5.52181	−	5.52181i	0.390451	−	0.390451i
$201$	4.63235	−	1.24124i	0.326741	−	0.0875500i
$202$	−0.285148	−	1.06419i	−0.0200630	−	0.0748760i
$203$	9.55464	−	13.0150i	0.670604	−	0.913473i
$204$	3.64401	−	6.31161i	0.255132	−	0.441901i
$205$	11.4646	−	6.61909i	0.800722	−	0.462297i
$206$	15.6729	+	4.19954i	1.09198	+	0.292596i
$207$			3.10855i			0.216059i
$208$	−2.57322	−	2.52558i	−0.178421	−	0.175117i
$209$		−	27.3270i		−	1.89024i
$210$	−1.03635	+	9.41218i	−0.0715147	+	0.649502i
$211$	10.6514	+	18.4488i	0.733274	+	1.27007i	0.955476	+	0.295068i	$0.0953422\pi$
$211$	10.6514	+	18.4488i	0.733274	+	1.27007i	−0.222202	+	0.975001i	$0.571324\pi$
$212$	−4.88107	−	2.81809i	−0.335233	−	0.193547i
$213$	2.80362	+	2.80362i	0.192101	+	0.192101i
$214$	2.08945	+	7.79792i	0.142832	+	0.533055i
$215$	−0.429125	−	1.60152i	−0.0292661	−	0.109223i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	8.25218	−	21.1839i	0.560194	−	1.43806i
$218$	0.275591	−	0.159113i	0.0186654	−	0.0107765i
$219$	−0.210687	+	0.786293i	−0.0142369	+	0.0531328i
$220$	17.2717			1.16446
$221$	−6.56364	+	25.4444i	−0.441518	+	1.71157i
$222$		−	8.10735i		−	0.544130i
$223$	1.28382	−	4.79128i	0.0859708	−	0.320848i	−0.909525	−	0.415648i	$-0.863555\pi$
$223$	1.28382	−	4.79128i	0.0859708	−	0.320848i	0.995496	+	0.0948007i	$0.0302214\pi$
$224$	−2.06434	+	1.65484i	−0.137930	+	0.110568i
$225$	6.76281	+	3.90451i	0.450854	+	0.260301i
$226$	8.39934	−	8.39934i	0.558716	−	0.558716i
$227$	8.22749	−	2.20455i	0.546078	−	0.146321i	0.0247751	−	0.999693i	$-0.492113\pi$
$227$	8.22749	−	2.20455i	0.546078	−	0.146321i	0.521302	+	0.853372i	$0.325446\pi$
$228$	5.46962	−	1.46558i	0.362235	−	0.0970605i
$229$	−3.41074	+	3.41074i	−0.225388	+	0.225388i	−0.810763	−	0.585375i	$-0.800947\pi$
$229$	−3.41074	+	3.41074i	−0.225388	+	0.225388i	0.585375	+	0.810763i	$0.300947\pi$
$230$	9.63488	+	5.56270i	0.635305	+	0.366793i
$231$	−9.96230	+	7.98606i	−0.655471	+	0.525444i
$232$	1.57944	−	5.89453i	0.103695	−	0.386995i
$233$			25.1649i			1.64861i	0.566146	+	0.824305i	$0.308434\pi$
$233$			25.1649i			1.64861i	−0.566146	+	0.824305i	$0.691566\pi$
$234$	1.77352	−	3.13921i	0.115939	−	0.205216i
$235$	16.3795			1.06848
$236$	2.29319	−	8.55829i	0.149274	−	0.557097i
$237$	−11.3206	+	6.53597i	−0.735354	+	0.424557i
$238$	17.9672	+	6.99909i	1.16464	+	0.453684i
$239$	0.0205130	−	0.0205130i	0.00132687	−	0.00132687i	−0.706443	−	0.707770i	$-0.749701\pi$
$239$	0.0205130	−	0.0205130i	0.00132687	−	0.00132687i	0.707770	+	0.706443i	$0.249701\pi$
$240$	0.926305	+	3.45702i	0.0597928	+	0.223150i
$241$	5.53103	+	20.6421i	0.356285	+	1.32967i	0.878860	+	0.477080i	$0.158305\pi$
$241$	5.53103	+	20.6421i	0.356285	+	1.32967i	−0.522575	+	0.852593i	$0.675029\pi$
$242$	8.68980	+	8.68980i	0.558601	+	0.558601i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−2.09032	−	3.62054i	−0.133819	−	0.231781i
$245$	−25.0302	+	1.06365i	−1.59912	+	0.0679540i
$246$			3.69888i			0.235832i
$247$	−17.5852	+	10.3731i	−1.11892	+	0.660024i
$248$		−	8.59283i		−	0.545645i
$249$	10.6175	+	2.84496i	0.672859	+	0.180292i
$250$	8.70649	−	5.02670i	0.550647	−	0.317916i
$251$	3.03799	−	5.26195i	0.191756	−	0.332131i	−0.754076	−	0.656787i	$-0.771915\pi$
$251$	3.03799	−	5.26195i	0.191756	−	0.332131i	0.945832	+	0.324656i	$0.105248\pi$
$252$	−2.13274	−	1.56570i	−0.134350	−	0.0986298i
$253$	3.88268	+	14.4903i	0.244102	+	0.911000i
$254$	10.1022	−	2.70687i	0.633867	−	0.169844i
$255$	18.4439	−	18.4439i	1.15500	−	1.15500i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.60816	−	7.98157i	−0.287449	−	0.497877i	0.685751	−	0.727836i	$-0.259474\pi$
$257$	−4.60816	−	7.98157i	−0.287449	−	0.497877i	−0.973200	+	0.229960i	$0.926141\pi$
$258$	0.447480	+	0.119902i	0.0278589	+	0.00746477i
$259$	21.2023	−	3.25071i	1.31745	−	0.201989i
$260$	−6.55620	−	11.1146i	−0.406598	−	0.689296i
$261$	6.10247			0.377733
$262$	1.33595	−	4.98582i	0.0825350	−	0.308025i
$263$	−10.9650	−	18.9920i	−0.676133	−	1.17110i	−0.976136	−	0.217158i	$-0.930321\pi$
$263$	−10.9650	−	18.9920i	−0.676133	−	1.17110i	0.300004	−	0.953938i	$-0.403012\pi$
$264$	−2.41295	+	4.17934i	−0.148507	+	0.257221i
$265$	−14.2635	−	14.2635i	−0.876203	−	0.876203i
$266$	6.02587	+	13.7165i	0.369470	+	0.841011i
$267$	4.21399	−	1.12913i	0.257892	−	0.0691019i
$268$	3.39112	+	3.39112i	0.207146	+	0.207146i
$269$	−2.68418	−	1.54971i	−0.163657	−	0.0944877i	0.415934	−	0.909395i	$-0.363455\pi$
$269$	−2.68418	−	1.54971i	−0.163657	−	0.0944877i	−0.579592	+	0.814907i	$0.696788\pi$
$270$	−3.09948	+	1.78948i	−0.188628	+	0.108905i
$271$	13.7109	+	3.67382i	0.832877	+	0.223169i	0.649968	−	0.759961i	$-0.274782\pi$
$271$	13.7109	+	3.67382i	0.832877	+	0.223169i	0.182908	+	0.983130i	$0.441449\pi$
$272$	7.28801			0.441901
$273$	8.92074	+	3.37942i	0.539908	+	0.204532i
$274$	−16.7032			−1.00908
$275$	36.4014	+	9.75372i	2.19509	+	0.588171i
$276$	−2.69208	+	1.55427i	−0.162044	+	0.0935563i
$277$	−14.8496	−	8.57342i	−0.892226	−	0.515127i	−0.0175560	−	0.999846i	$-0.505589\pi$
$277$	−14.8496	−	8.57342i	−0.892226	−	0.515127i	−0.874670	+	0.484719i	$0.838922\pi$
$278$	−3.71659	−	3.71659i	−0.222906	−	0.222906i
$279$	8.30004	−	2.22399i	0.496910	−	0.133147i
$280$	−8.66936	+	3.80859i	−0.518093	+	0.227607i
$281$	−2.71280	−	2.71280i	−0.161832	−	0.161832i	0.621546	−	0.783378i	$-0.286505\pi$
$281$	−2.71280	−	2.71280i	−0.161832	−	0.161832i	−0.783378	+	0.621546i	$0.786505\pi$
$282$	−2.28830	+	3.96346i	−0.136266	+	0.236020i
$283$	7.58330	+	13.1347i	0.450780	+	0.780774i	0.998435	−	0.0559304i	$-0.0178125\pi$
$283$	7.58330	+	13.1347i	0.450780	+	0.780774i	−0.547654	+	0.836705i	$0.684479\pi$
$284$	−1.02620	+	3.82981i	−0.0608935	+	0.227258i
$285$	20.2662			1.20046
$286$	4.34623	−	16.8484i	0.256998	−	0.996270i
$287$	−9.67328	+	1.48310i	−0.570996	+	0.0875444i
$288$	−0.965926	−	0.258819i	−0.0569177	−	0.0152511i
$289$	−18.0576	−	31.2766i	−1.06221	−	1.83980i
$290$	10.9203	−	18.9145i	0.641261	−	1.11070i
$291$	−10.9070	+	10.9070i	−0.639379	+	0.639379i
$292$	−0.786293	+	0.210687i	−0.0460143	+	0.0123295i
$293$	−4.58840	−	17.1241i	−0.268057	−	1.00040i	−0.960352	−	0.278789i	$-0.910067\pi$
$293$	−4.58840	−	17.1241i	−0.268057	−	1.00040i	0.692295	−	0.721615i	$-0.256600\pi$
$294$	3.23947	−	6.20531i	0.188930	−	0.361901i
$295$	15.8552	−	27.4620i	0.923124	−	1.59890i
$296$	7.02117	−	4.05367i	0.408097	−	0.235615i
$297$	−4.66145	−	1.24903i	−0.270485	−	0.0724762i
$298$			11.3637i			0.658280i
$299$	7.85088	−	7.99897i	0.454028	−	0.462592i
$300$			7.80902i			0.450854i
$301$	−0.134146	+	1.21832i	−0.00773203	+	0.0702229i
$302$	5.66448	+	9.81117i	0.325954	+	0.564569i
$303$	0.954125	+	0.550864i	0.0548130	+	0.0316463i
$304$	4.00404	+	4.00404i	0.229648	+	0.229648i
$305$	−3.87255	−	14.4526i	−0.221742	−	0.827551i
$306$	1.88628	+	7.03968i	0.107831	+	0.402432i
$307$	−7.71951	+	7.71951i	−0.440576	+	0.440576i	−0.892206	−	0.451630i	$-0.850843\pi$
$307$	−7.71951	+	7.71951i	−0.440576	+	0.440576i	0.451630	+	0.892206i	$0.350843\pi$
$308$	−11.8973	−	4.63457i	−0.677911	−	0.264079i
$309$	−14.0519	+	8.11289i	−0.799387	+	0.461526i
$310$	7.95959	−	29.7056i	0.452074	−	1.68716i
$311$	−18.2196			−1.03314			−0.516570	−	0.856245i	$-0.672791\pi$
$311$	−18.2196			−1.03314			−0.516570	+	0.856245i	$0.672791\pi$
$312$	3.60539	−	0.0336851i	0.204115	−	0.00190704i
$313$			11.2521i			0.636004i	0.948090	+	0.318002i	$0.103012\pi$
$313$			11.2521i			0.636004i	−0.948090	+	0.318002i	$0.896988\pi$
$314$	−1.98339	+	7.40212i	−0.111929	+	0.417726i
$315$	−5.92261	−	7.38822i	−0.333701	−	0.416279i
$316$	−11.3206	−	6.53597i	−0.636835	−	0.367677i
$317$	5.83611	−	5.83611i	0.327789	−	0.327789i	−0.523956	−	0.851745i	$-0.675545\pi$
$317$	5.83611	−	5.83611i	0.327789	−	0.327789i	0.851745	+	0.523956i	$0.175545\pi$
$318$	5.44413	−	1.45875i	0.305292	−	0.0818026i
$319$	28.4464	−	7.62218i	1.59269	−	0.426760i
$320$	−2.53071	+	2.53071i	−0.141471	+	0.141471i
$321$	−6.99143	−	4.03650i	−0.390223	−	0.225296i
$322$	−5.14414	−	6.41711i	−0.286672	−	0.357612i
$323$	10.6812	−	39.8627i	0.594317	−	2.21802i
$324$		−	1.00000i		−	0.0555556i
$325$	−7.54103	−	27.1272i	−0.418301	−	1.50474i
$326$	−0.714706			−0.0395839
$327$	−0.0823627	+	0.307382i	−0.00455467	+	0.0169983i
$328$	−3.20332	+	1.84944i	−0.176874	+	0.102118i
$329$	−11.2827	−	4.39517i	−0.622036	−	0.242314i
$330$	−12.2129	+	12.2129i	−0.672301	+	0.672301i
$331$	0.732111	+	2.73228i	0.0402405	+	0.150180i	0.983123	−	0.182946i	$-0.0585634\pi$
$331$	0.732111	+	2.73228i	0.0402405	+	0.150180i	−0.942882	+	0.333126i	$0.891897\pi$
$332$	2.84496	+	10.6175i	0.156138	+	0.582713i
$333$	5.73276	+	5.73276i	0.314153	+	0.314153i
$334$	−5.29041	−	3.05442i	−0.289478	−	0.167130i
$335$	8.58195	+	14.8644i	0.468882	+	0.812127i
$336$	0.289566	−	2.62986i	0.0157971	−	0.143471i
$337$			6.21918i			0.338780i	0.985549	+	0.169390i	$0.0541798\pi$
$337$			6.21918i			0.338780i	−0.985549	+	0.169390i	$0.945820\pi$
$338$	−12.4920	+	3.59868i	−0.679474	+	0.195742i
$339$			11.8785i			0.645150i
$340$	25.1948	+	6.75093i	1.36638	+	0.366120i
$341$	35.9124	−	20.7340i	1.94477	−	1.12281i
$342$	−2.83129	+	4.90393i	−0.153098	+	0.265174i
$343$	17.5270	+	5.98376i	0.946367	+	0.323093i
$344$	0.119902	+	0.447480i	0.00646468	+	0.0241265i
$345$	−10.7463	+	2.87946i	−0.578562	+	0.155025i
$346$	8.40815	−	8.40815i	0.452025	−	0.452025i
$347$	−6.40310	+	11.0905i	−0.343737	+	0.595369i	−0.985123	−	0.171848i	$-0.945026\pi$
$347$	−6.40310	+	11.0905i	−0.343737	+	0.595369i	0.641387	+	0.767218i	$0.278359\pi$
$348$	3.05124	+	5.28489i	0.163563	+	0.283300i
$349$	21.9339	+	5.87716i	1.17409	+	0.314597i	0.792581	−	0.609767i	$-0.208737\pi$
$349$	21.9339	+	5.87716i	1.17409	+	0.314597i	0.381512	+	0.924364i	$0.375404\pi$
$350$	−20.4221	+	3.13109i	−1.09161	+	0.167364i
$351$	0.965682	+	3.47382i	0.0515443	+	0.185419i
$352$	−4.82589			−0.257221
$353$	0.104416	−	0.389684i	0.00555748	−	0.0207408i	−0.963091	−	0.269175i	$-0.913249\pi$
$353$	0.104416	−	0.389684i	0.00555748	−	0.0207408i	0.968649	+	0.248434i	$0.0799158\pi$
$354$	4.43010	+	7.67315i	0.235457	+	0.407823i
$355$	−7.09516	+	12.2892i	−0.376572	+	0.652241i
$356$	3.08485	+	3.08485i	0.163497	+	0.163497i
$357$	−17.6538	+	7.75560i	−0.934338	+	0.410470i
$358$	−7.57514	+	2.02975i	−0.400358	+	0.107276i
$359$	−6.73742	−	6.73742i	−0.355587	−	0.355587i	0.506596	−	0.862183i	$-0.330904\pi$
$359$	−6.73742	−	6.73742i	−0.355587	−	0.355587i	−0.862183	+	0.506596i	$0.830904\pi$
$360$	−3.09948	−	1.78948i	−0.163357	−	0.0943141i
$361$	11.3144	−	6.53235i	0.595493	−	0.343808i
$362$	−16.1199	−	4.31931i	−0.847243	−	0.227018i
$363$	−12.2892			−0.645017
$364$	1.53371	+	9.41529i	0.0803880	+	0.493495i
$365$	−2.91339			−0.152494
$366$	4.03819	+	1.08203i	0.211080	+	0.0565586i
$367$	14.9572	−	8.63556i	0.780761	−	0.450772i	−0.0559392	−	0.998434i	$-0.517815\pi$
$367$	14.9572	−	8.63556i	0.780761	−	0.450772i	0.836700	+	0.547662i	$0.184482\pi$
$368$	−2.69208	−	1.55427i	−0.140334	−	0.0810221i
$369$	−2.61550	−	2.61550i	−0.136158	−	0.136158i
$370$	28.0273	−	7.50988i	1.45707	−	0.390420i
$371$	5.99778	+	13.6525i	0.311389	+	0.708805i
$372$	6.07605	+	6.07605i	0.315029	+	0.315029i
$373$	8.21162	−	14.2229i	0.425182	−	0.736436i	−0.571256	−	0.820772i	$-0.693544\pi$
$373$	8.21162	−	14.2229i	0.425182	−	0.736436i	0.996437	+	0.0843359i	$0.0268769\pi$
$374$	17.5856	+	30.4591i	0.909329	+	1.57500i
$375$	−2.60201	+	9.71083i	−0.134367	+	0.501465i
$376$	−4.57660			−0.236020
$377$	−15.7030	−	15.4123i	−0.808745	−	0.793772i
$378$	2.61519	−	0.400958i	0.134511	−	0.0206231i
$379$	−14.3676	−	3.84978i	−0.738013	−	0.197750i	−0.129818	−	0.991538i	$-0.541439\pi$
$379$	−14.3676	−	3.84978i	−0.738013	−	0.197750i	−0.608195	+	0.793788i	$0.708106\pi$
$380$	10.1331	+	17.5510i	0.519816	+	0.900348i
$381$	−5.22927	+	9.05737i	−0.267904	+	0.464023i
$382$	9.90276	−	9.90276i	0.506669	−	0.506669i
$383$	34.4485	−	9.23045i	1.76024	−	0.471654i	0.773474	−	0.633828i	$-0.218517\pi$
$383$	34.4485	−	9.23045i	1.76024	−	0.471654i	0.986762	+	0.162174i	$0.0518507\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	−36.8361	−	27.0423i	−1.87734	−	1.37820i
$386$	7.23172	−	12.5257i	0.368085	−	0.637542i
$387$	−0.401200	+	0.231633i	−0.0203941	+	0.0117746i
$388$	−14.8992	−	3.99223i	−0.756393	−	0.202675i
$389$			28.7218i			1.45625i	0.685442	+	0.728127i	$0.259609\pi$
$389$			28.7218i			1.45625i	−0.685442	+	0.728127i	$0.740391\pi$
$390$	12.4951	+	3.22325i	0.632715	+	0.163215i
$391$			22.6551i			1.14572i
$392$	6.99369	−	0.297194i	0.353235	−	0.0150106i
$393$	2.58085	+	4.47016i	0.130187	+	0.225490i
$394$	8.66389	+	5.00210i	0.436480	+	0.252002i
$395$	−33.0813	−	33.0813i	−1.66450	−	1.66450i
$396$	−1.24903	−	4.66145i	−0.0627663	−	0.234247i
$397$	−4.06656	−	15.1766i	−0.204095	−	0.761692i	−0.989724	−	0.142994i	$-0.954327\pi$
$397$	−4.06656	−	15.1766i	−0.204095	−	0.761692i	0.785629	−	0.618698i	$-0.212340\pi$
$398$	1.15402	−	1.15402i	0.0578456	−	0.0578456i
$399$	−13.9599	−	5.43808i	−0.698872	−	0.272245i
$400$	−6.76281	+	3.90451i	−0.338140	+	0.195225i
$401$	−4.17057	+	15.5648i	−0.208268	+	0.777268i	0.780160	+	0.625580i	$0.215138\pi$
$401$	−4.17057	+	15.5648i	−0.208268	+	0.777268i	−0.988428	+	0.151688i	$0.951529\pi$
$402$	−4.79577			−0.239191
$403$	−26.9747	−	15.2396i	−1.34370	−	0.759139i
$404$			1.10173i			0.0548130i
$405$	0.926305	−	3.45702i	0.0460285	−	0.171781i
$406$	−12.5976	+	10.0986i	−0.625208	+	0.501185i
$407$	33.8834	+	19.5626i	1.67954	+	0.969682i
$408$	−5.15340	+	5.15340i	−0.255132	+	0.255132i
$409$	−37.0126	+	9.91751i	−1.83016	+	0.490389i	−0.997945	−	0.0640692i	$-0.979592\pi$
$409$	−37.0126	+	9.91751i	−1.83016	+	0.490389i	−0.832212	+	0.554458i	$0.812926\pi$
$410$	−12.7871	+	3.42629i	−0.631510	+	0.169212i
$411$	11.8110	−	11.8110i	0.582592	−	0.582592i
$412$	−14.0519	−	8.11289i	−0.692289	−	0.399693i
$413$	−18.2905	+	14.6622i	−0.900016	+	0.721478i
$414$	0.804551	−	3.00263i	0.0395415	−	0.147571i
$415$			39.3403i			1.93114i
$416$	1.83187	+	3.10552i	0.0898148	+	0.152261i
$417$	5.25605			0.257390
$418$	−7.07274	+	26.3958i	−0.345939	+	1.29106i
$419$	−20.5146	+	11.8441i	−1.00220	+	0.578623i	−0.908900	−	0.417015i	$-0.863076\pi$
$419$	−20.5146	+	11.8441i	−1.00220	+	0.578623i	−0.0933041	+	0.995638i	$0.529743\pi$
$420$	3.43708	−	8.82324i	0.167713	−	0.430530i
$421$	−12.2619	+	12.2619i	−0.597610	+	0.597610i	−0.939676	−	0.342066i	$-0.888873\pi$
$421$	−12.2619	+	12.2619i	−0.597610	+	0.597610i	0.342066	+	0.939676i	$0.388873\pi$
$422$	−5.51358	−	20.5770i	−0.268397	−	1.00167i
$423$	−1.18451	−	4.42066i	−0.0575930	−	0.214940i
$424$	3.98538	+	3.98538i	0.193547	+	0.193547i
$425$	49.2874	+	28.4561i	2.39079	+	1.38032i
$426$	−1.98246	−	3.43372i	−0.0960504	−	0.166364i
$427$	−1.21057	+	10.9945i	−0.0585836	+	0.532061i
$428$		−	8.07301i		−	0.390223i
$429$	8.84040	+	14.9869i	0.426819	+	0.723575i
$430$			1.65801i			0.0799565i
$431$	−14.1419	−	3.78931i	−0.681191	−	0.182524i	−0.0984001	−	0.995147i	$-0.531372\pi$
$431$	−14.1419	−	3.78931i	−0.681191	−	0.182524i	−0.582790	+	0.812622i	$0.698039\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	1.49933	−	2.59691i	0.0720530	−	0.124799i	−0.827748	−	0.561100i	$-0.810378\pi$
$433$	1.49933	−	2.59691i	0.0720530	−	0.124799i	0.899801	+	0.436301i	$0.143712\pi$
$434$	−13.4538	+	18.3263i	−0.645803	+	0.879690i
$435$	5.65275	+	21.0964i	0.271029	+	1.01149i
$436$	−0.307382	+	0.0823627i	−0.0147209	+	0.00394446i
$437$	−12.4468	+	12.4468i	−0.595409	+	0.595409i
$438$	0.407015	−	0.704971i	0.0194479	−	0.0336848i
$439$	−4.55508	−	7.88962i	−0.217402	−	0.376551i	0.736611	−	0.676317i	$-0.236425\pi$
$439$	−4.55508	−	7.88962i	−0.217402	−	0.376551i	−0.954013	+	0.299766i	$0.903092\pi$
$440$	−16.6832	−	4.47025i	−0.795340	−	0.213111i
$441$	2.09717	+	6.67846i	0.0998651	+	0.318022i
$442$	12.9255	−	22.8786i	0.614802	−	1.08822i
$443$	18.3512			0.871894			0.435947	−	0.899972i	$-0.356414\pi$
$443$	18.3512			0.871894			0.435947	+	0.899972i	$0.356414\pi$
$444$	−2.09834	+	7.83110i	−0.0995826	+	0.371647i
$445$	7.80688	+	13.5219i	0.370082	+	0.641000i
$446$	−2.48015	+	4.29574i	−0.117438	+	0.203409i
$447$	−8.03533	−	8.03533i	−0.380058	−	0.380058i
$448$	2.42231	−	1.06416i	0.114443	−	0.0502767i
$449$	−10.1159	+	2.71055i	−0.477399	+	0.127919i	−0.489491	−	0.872008i	$-0.662818\pi$
$449$	−10.1159	+	2.71055i	−0.477399	+	0.127919i	0.0120921	+	0.999927i	$0.496151\pi$
$450$	−5.52181	−	5.52181i	−0.260301	−	0.260301i
$451$	−15.4589	−	8.92519i	−0.727931	−	0.420271i
$452$	−10.2871	+	5.93923i	−0.483862	+	0.279358i
$453$	−10.9429	−	2.93215i	−0.514144	−	0.137764i
$454$	−8.51772			−0.399757
$455$	−3.41939	+	33.9695i	−0.160303	+	1.59252i
$456$	−5.66257			−0.265174
$457$	28.1792	+	7.55060i	1.31817	+	0.353202i	0.848292	−	0.529529i	$-0.177631\pi$
$457$	28.1792	+	7.55060i	1.31817	+	0.353202i	0.469877	+	0.882732i	$0.344298\pi$
$458$	4.17729	−	2.41176i	0.195192	−	0.112694i
$459$	−6.31161	−	3.64401i	−0.294601	−	0.170088i
$460$	−7.86684	−	7.86684i	−0.366793	−	0.366793i
$461$	−28.5111	+	7.63952i	−1.32789	+	0.355808i	−0.851929	−	0.523657i	$-0.824567\pi$
$461$	−28.5111	+	7.63952i	−1.32789	+	0.355808i	−0.475964	+	0.879465i	$0.657901\pi$
$462$	11.6898	−	5.13551i	0.543858	−	0.238926i
$463$	−6.52384	−	6.52384i	−0.303189	−	0.303189i	0.539071	−	0.842260i	$-0.318775\pi$
$463$	−6.52384	−	6.52384i	−0.303189	−	0.303189i	−0.842260	+	0.539071i	$0.818775\pi$
$464$	−3.05124	+	5.28489i	−0.141650	+	0.245345i
$465$	15.3767	+	26.6333i	0.713079	+	1.23509i
$466$	6.51316	−	24.3075i	0.301716	−	1.12602i
$467$	−35.1033			−1.62439			−0.812193	−	0.583389i	$-0.801726\pi$
$467$	−35.1033			−1.62439			−0.812193	+	0.583389i	$0.801726\pi$
$468$	−2.52558	+	2.57322i	−0.116745	+	0.118947i
$469$	−1.92290	−	12.5419i	−0.0887914	−	0.579129i
$470$	−15.8214	−	4.23933i	−0.729787	−	0.195546i
$471$	−3.83162	−	6.63656i	−0.176552	−	0.305797i
$472$	−4.43010	+	7.67315i	−0.203912	+	0.353185i
$473$	−1.58086	+	1.58086i	−0.0726879	+	0.0726879i
$474$	12.6265	−	3.38327i	0.579956	−	0.155399i
$475$	11.4448	+	42.7124i	0.525121	+	1.95978i
$476$	−15.5434	−	11.4108i	−0.712433	−	0.523015i
$477$	−2.81809	+	4.88107i	−0.129031	+	0.223489i
$478$	−0.0251232	+	0.0145049i	−0.00114911	+	0.000663437i
$479$	21.2268	+	5.68770i	0.969877	+	0.259878i	0.708776	−	0.705434i	$-0.249248\pi$
$479$	21.2268	+	5.68770i	0.969877	+	0.259878i	0.261101	+	0.965311i	$0.415914\pi$
$480$		−	3.57897i		−	0.163357i
$481$	−0.273097	−	29.2302i	−0.0124522	−	1.33278i
$482$		−	21.3703i		−	0.973388i
$483$	8.17504	+	0.900128i	0.371977	+	0.0409573i
$484$	−6.14461	−	10.6428i	−0.279301	−	0.483763i
$485$	−47.8088	−	27.6024i	−2.17089	−	1.25336i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−3.43687	−	12.8266i	−0.155739	−	0.581227i	−0.999041	−	0.0437866i	$-0.986058\pi$
$487$	−3.43687	−	12.8266i	−0.155739	−	0.581227i	0.843302	−	0.537441i	$-0.180609\pi$
$488$	1.08203	+	4.03819i	0.0489812	+	0.182800i
$489$	0.505373	−	0.505373i	0.0228538	−	0.0228538i
$490$	24.4526	+	5.45089i	1.10466	+	0.246246i
$491$	26.0321	−	15.0296i	1.17481	−	0.678278i	0.220004	−	0.975499i	$-0.429393\pi$
$491$	26.0321	−	15.0296i	1.17481	−	0.678278i	0.954809	+	0.297221i	$0.0960597\pi$
$492$	0.957340	−	3.57284i	0.0431602	−	0.161076i
$493$	44.4749			2.00305
$494$	19.6708	−	5.46824i	0.885030	−	0.246028i
$495$		−	17.2717i		−	0.776306i
$496$	−2.22399	+	8.30004i	−0.0998600	+	0.372683i
$497$	8.18495	−	6.56129i	0.367145	−	0.294314i
$498$	−9.51943	−	5.49604i	−0.426576	−	0.246284i
$499$	21.7078	−	21.7078i	0.971773	−	0.971773i	−0.0278394	−	0.999612i	$-0.508863\pi$
$499$	21.7078	−	21.7078i	0.971773	−	0.971773i	0.999612	+	0.0278394i	$0.00886270\pi$
$500$	−9.71083	+	2.60201i	−0.434282	+	0.116365i
$501$	5.90069	−	1.58108i	0.263623	−	0.0706376i
$502$	−4.29636	+	4.29636i	−0.191756	+	0.191756i
$503$	24.3041	+	14.0320i	1.08367	+	0.625655i	0.931883	−	0.362759i	$-0.118165\pi$
$503$	24.3041	+	14.0320i	1.08367	+	0.625655i	0.151783	+	0.988414i	$0.451499\pi$
$504$	1.65484	+	2.06434i	0.0737123	+	0.0919532i
$505$	−1.02054	+	3.80870i	−0.0454133	+	0.169485i
$506$		−	15.0015i		−	0.666899i
$507$	6.28851	−	11.3778i	0.279283	−	0.505306i
$508$	−10.4585			−0.464023
$509$	−4.88320	+	18.2244i	−0.216444	+	0.807780i	0.769209	+	0.638997i	$0.220650\pi$
$509$	−4.88320	+	18.2244i	−0.216444	+	0.807780i	−0.985653	+	0.168783i	$0.946016\pi$
$510$	−22.5890	+	13.0418i	−1.00026	+	0.577500i
$511$	2.00683	+	0.781759i	0.0887770	+	0.0345830i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.46558	−	5.46962i	−0.0647070	−	0.241490i
$514$	2.38536	+	8.90229i	0.105214	+	0.392663i
$515$	−41.0628	−	41.0628i	−1.80944	−	1.80944i
$516$	−0.401200	−	0.231633i	−0.0176618	−	0.0101971i
$517$	−11.0431	−	19.1272i	−0.485675	−	0.841214i
$518$	−21.3212	−	2.34761i	−0.936798	−	0.103148i
$519$			11.8909i			0.521954i
$520$	3.45615	+	12.4327i	0.151562	+	0.545210i
$521$			38.0793i			1.66828i	0.551550	+	0.834142i	$0.314037\pi$
$521$			38.0793i			1.66828i	−0.551550	+	0.834142i	$0.685963\pi$
$522$	−5.89453	−	1.57944i	−0.257997	−	0.0691300i
$523$	−21.7435	+	12.5536i	−0.950776	+	0.548931i	−0.893322	−	0.449417i	$-0.851632\pi$
$523$	−21.7435	+	12.5536i	−0.950776	+	0.548931i	−0.0574542	+	0.998348i	$0.518298\pi$
$524$	−2.58085	+	4.47016i	−0.112745	+	0.195280i
$525$	12.2266	−	16.6546i	0.533612	−	0.726867i
$526$	5.67592	+	21.1828i	0.247482	+	0.923614i
$527$	60.4908	−	16.2085i	2.63502	−	0.706052i
$528$	3.41242	−	3.41242i	0.148507	−	0.148507i
$529$	−6.66847	+	11.5501i	−0.289933	+	0.502179i
$530$	10.0859	+	17.4692i	0.438101	+	0.758814i
$531$	−8.55829	−	2.29319i	−0.371398	−	0.0995158i
$532$	−2.27046	−	14.8087i	−0.0984367	−	0.642039i
$533$	0.124597	+	13.3359i	0.00539690	+	0.577643i
$534$	−4.36264			−0.188790
$535$	7.47807	−	27.9085i	0.323305	−	1.20659i
$536$	−2.39788	−	4.15325i	−0.103573	−	0.179393i
$537$	3.92118	−	6.79168i	0.169211	−	0.293083i
$538$	2.19163	+	2.19163i	0.0944877	+	0.0944877i
$539$	18.1175	+	28.5119i	0.780375	+	1.22810i
$540$	3.45702	−	0.926305i	0.148766	−	0.0398618i
$541$	31.1879	+	31.1879i	1.34087	+	1.34087i	0.895191	+	0.445683i	$0.147039\pi$
$541$	31.1879	+	31.1879i	1.34087	+	1.34087i	0.445683	+	0.895191i	$0.352961\pi$
$542$	−12.2928	−	7.09728i	−0.528023	−	0.304854i
$543$	14.4527	−	8.34427i	0.620225	−	0.358087i
$544$	−7.03968	−	1.88628i	−0.301824	−	0.0808735i
$545$	−1.13892			−0.0487859
$546$	−7.74211	−	5.57312i	−0.331332	−	0.238508i
$547$	−32.1361			−1.37404			−0.687021	−	0.726638i	$-0.741082\pi$
$547$	−32.1361			−1.37404			−0.687021	+	0.726638i	$0.741082\pi$
$548$	16.1341	+	4.32311i	0.689213	+	0.184674i
$549$	−3.62054	+	2.09032i	−0.154521	+	0.0892127i
$550$	−32.6366	−	18.8427i	−1.39163	−	0.803457i
$551$	24.4345	+	24.4345i	1.04095	+	1.04095i
$552$	3.00263	−	0.804551i	0.127800	−	0.0342440i
$553$	13.9106	+	31.6642i	0.591539	+	1.34650i
$554$	12.1246	+	12.1246i	0.515127	+	0.515127i
$555$	−14.5080	+	25.1285i	−0.615829	+	1.06665i
$556$	2.62803	+	4.55188i	0.111453	+	0.193043i
$557$	3.73183	−	13.9274i	0.158123	−	0.590122i	−0.840695	−	0.541509i	$-0.817853\pi$
$557$	3.73183	−	13.9274i	0.158123	−	0.590122i	0.998818	−	0.0486132i	$-0.0154802\pi$
$558$	−8.59283			−0.363764
$559$	1.61738	+	0.417220i	0.0684079	+	0.0176465i
$560$	9.35969	−	1.43502i	0.395519	−	0.0606406i
$561$	−33.9727	−	9.10297i	−1.43433	−	0.384328i
$562$	1.91824	+	3.32249i	0.0809160	+	0.140151i
$563$	12.2088	−	21.1462i	0.514538	−	0.891206i	−0.485319	−	0.874337i	$-0.661297\pi$
$563$	12.2088	−	21.1462i	0.514538	−	0.891206i	0.999858	−	0.0168695i	$-0.00536998\pi$
$564$	3.23615	−	3.23615i	0.136266	−	0.136266i
$565$	−41.0641	+	11.0031i	−1.72758	+	0.462903i
$566$	−3.92540	−	14.6498i	−0.164997	−	0.615777i
$567$	−1.56570	+	2.13274i	−0.0657532	+	0.0895667i
$568$	1.98246	−	3.43372i	0.0831821	−	0.144076i
$569$	22.6148	−	13.0567i	0.948062	−	0.547364i	0.0555834	−	0.998454i	$-0.482298\pi$
$569$	22.6148	−	13.0567i	0.948062	−	0.547364i	0.892478	+	0.451090i	$0.148965\pi$
$570$	−19.5756	−	5.24527i	−0.819932	−	0.219700i
$571$		−	41.3922i		−	1.73221i	−0.499864	−	0.866104i	$-0.666617\pi$
$571$		−	41.3922i		−	1.73221i	0.499864	−	0.866104i	$-0.333383\pi$
$572$	−8.55884	+	15.1495i	−0.357863	+	0.633431i
$573$			14.0046i			0.585051i
$574$	9.72753	+	1.07107i	0.406019	+	0.0447055i
$575$	−12.1374	−	21.0225i	−0.506163	−	0.876699i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	6.64331	+	6.64331i	0.276564	+	0.276564i	0.831736	−	0.555171i	$-0.187347\pi$
$577$	6.64331	+	6.64331i	0.276564	+	0.276564i	−0.555171	+	0.831736i	$0.687347\pi$
$578$	9.34729	+	34.8846i	0.388796	+	1.45101i
$579$	3.74341	+	13.9706i	0.155571	+	0.580599i
$580$	−15.4436	+	15.4436i	−0.641261	+	0.641261i
$581$	10.5563	−	27.0988i	0.437950	−	1.12425i
$582$	13.3583	−	7.71240i	0.553718	−	0.319689i
$583$	−7.03977	+	26.2728i	−0.291557	+	1.08811i
$584$	0.814030			0.0336848
$585$	−11.1146	+	6.55620i	−0.459531	+	0.271066i
$586$			17.7282i			0.732346i
$587$	3.45549	−	12.8961i	0.142623	−	0.532278i	−0.857226	−	0.514940i	$-0.827814\pi$
$587$	3.45549	−	12.8961i	0.142623	−	0.532278i	0.999850	−	0.0173381i	$-0.00551916\pi$
$588$	−4.73514	+	5.15543i	−0.195274	+	0.212606i
$589$	42.1387	+	24.3288i	1.73629	+	1.00245i
$590$	−22.4226	+	22.4226i	−0.923124	+	0.923124i
$591$	−9.66331	+	2.58928i	−0.397496	+	0.106509i
$592$	−7.83110	+	2.09834i	−0.321856	+	0.0862411i
$593$	12.1340	−	12.1340i	0.498285	−	0.498285i	−0.412619	−	0.910904i	$-0.635386\pi$
$593$	12.1340	−	12.1340i	0.498285	−	0.498285i	0.910904	+	0.412619i	$0.135386\pi$
$594$	4.17934	+	2.41295i	0.171481	+	0.0990044i
$595$	−43.1641	−	53.8455i	−1.76955	−	2.20745i
$596$	2.94113	−	10.9765i	0.120474	−	0.449613i
$597$			1.63202i			0.0667943i
$598$	−9.65366	+	5.69445i	−0.394767	+	0.232863i
$599$	19.0436			0.778099			0.389050	−	0.921217i	$-0.372803\pi$
$599$	19.0436			0.778099			0.389050	+	0.921217i	$0.372803\pi$
$600$	2.02112	−	7.54293i	0.0825120	−	0.307939i
$601$	37.2954	−	21.5325i	1.52131	−	0.878330i	0.521629	−	0.853172i	$-0.325324\pi$
$601$	37.2954	−	21.5325i	1.52131	−	0.878330i	0.999683	−	0.0251580i	$-0.00800887\pi$
$602$	0.444900	−	1.14209i	0.0181328	−	0.0465481i
$603$	3.39112	−	3.39112i	0.138097	−	0.138097i
$604$	−2.93215	−	10.9429i	−0.119308	−	0.445262i
$605$	−11.3836	−	42.4841i	−0.462808	−	1.72722i
$606$	−0.779040	−	0.779040i	−0.0316463	−	0.0316463i
$607$	−10.2221	−	5.90174i	−0.414902	−	0.239544i	0.277992	−	0.960584i	$-0.410331\pi$
$607$	−10.2221	−	5.90174i	−0.414902	−	0.239544i	−0.692894	+	0.721039i	$0.743665\pi$
$608$	−2.83129	−	4.90393i	−0.114824	−	0.198881i
$609$	1.76707	−	16.0486i	0.0716051	−	0.650323i
$610$			14.9624i			0.605809i
$611$	−8.11672	+	14.3669i	−0.328367	+	0.581223i
$612$		−	7.28801i		−	0.294601i
$613$	−0.0762127	−	0.0204211i	−0.00307820	−	0.000824801i	0.257280	−	0.966337i	$-0.417174\pi$
$613$	−0.0762127	−	0.0204211i	−0.00307820	−	0.000824801i	−0.260358	+	0.965512i	$0.583841\pi$
$614$	9.45443	−	5.45852i	0.381550	−	0.220288i
$615$	6.61909	−	11.4646i	0.266907	−	0.462297i
$616$	10.2924	+	7.55590i	0.414692	+	0.304436i
$617$	6.48336	+	24.1962i	0.261010	+	0.974103i	0.964647	+	0.263544i	$0.0848913\pi$
$617$	6.48336	+	24.1962i	0.261010	+	0.974103i	−0.703637	+	0.710559i	$0.748442\pi$
$618$	15.6729	−	4.19954i	0.630457	−	0.168930i
$619$	−9.02949	+	9.02949i	−0.362926	+	0.362926i	−0.864889	−	0.501963i	$-0.832611\pi$
$619$	−9.02949	+	9.02949i	−0.362926	+	0.362926i	0.501963	+	0.864889i	$0.332611\pi$
$620$	−15.3767	+	26.6333i	−0.617545	+	1.06962i
$621$	1.55427	+	2.69208i	0.0623709	+	0.108029i
$622$	17.5988	+	4.71559i	0.705648	+	0.189078i
$623$	−1.74924	−	11.4091i	−0.0700817	−	0.457098i
$624$	−3.49126	−	0.900607i	−0.139762	−	0.0360531i
$625$	3.06431			0.122572
$626$	2.91225	−	10.8687i	0.116397	−	0.434399i
$627$	−13.6635	−	23.6658i	−0.545667	−	0.945122i
$628$	3.83162	−	6.63656i	0.152898	−	0.264828i
$629$	41.7804	+	41.7804i	1.66590	+	1.66590i
$630$	3.80859	+	8.66936i	0.151738	+	0.345396i
$631$	−13.9081	+	3.72667i	−0.553674	+	0.148356i	−0.524798	−	0.851227i	$-0.675859\pi$
$631$	−13.9081	+	3.72667i	−0.553674	+	0.148356i	−0.0288754	+	0.999583i	$0.509193\pi$
$632$	9.24326	+	9.24326i	0.367677	+	0.367677i
$633$	18.4488	+	10.6514i	0.733274	+	0.423356i
$634$	−7.14775	+	4.12676i	−0.283873	+	0.163894i
$635$	−36.1554	−	9.68781i	−1.43478	−	0.384449i
$636$	−5.63618			−0.223489
$637$	11.4705	−	22.4817i	0.454479	−	0.890758i
$638$	−29.4499			−1.16593
$639$	3.82981	+	1.02620i	0.151505	+	0.0405957i
$640$	3.09948	−	1.78948i	0.122518	−	0.0707356i
$641$	8.53123	+	4.92551i	0.336963	+	0.194546i	0.658928	−	0.752206i	$-0.271010\pi$
$641$	8.53123	+	4.92551i	0.336963	+	0.194546i	−0.321965	+	0.946752i	$0.604343\pi$
$642$	5.70848	+	5.70848i	0.225296	+	0.225296i
$643$	15.5348	−	4.16254i	0.612634	−	0.164155i	0.0608569	−	0.998147i	$-0.480617\pi$
$643$	15.5348	−	4.16254i	0.612634	−	0.164155i	0.551777	+	0.833992i	$0.313950\pi$
$644$	3.30798	+	7.52985i	0.130353	+	0.296718i
$645$	−1.17239	−	1.17239i	−0.0461629	−	0.0461629i
$646$	−20.6344	+	35.7399i	−0.811851	+	1.40617i
$647$	−14.6180	−	25.3191i	−0.574694	−	0.995398i	−0.996075	−	0.0885149i	$-0.971788\pi$
$647$	−14.6180	−	25.3191i	−0.574694	−	0.995398i	0.421381	−	0.906884i	$-0.361545\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	−42.7583			−1.67841
$650$	0.263048	+	28.1546i	0.0103176	+	1.10431i
$651$	−3.44537	−	22.4719i	−0.135035	−	0.880744i
$652$	0.690353	+	0.184979i	0.0270363	+	0.00724436i
$653$	−4.55227	−	7.88477i	−0.178144	−	0.308555i	0.763101	−	0.646280i	$-0.223676\pi$
$653$	−4.55227	−	7.88477i	−0.178144	−	0.308555i	−0.941245	+	0.337725i	$0.890343\pi$
$654$	0.159113	−	0.275591i	0.00622179	−	0.0107765i
$655$	−13.0628	+	13.0628i	−0.510405	+	0.510405i
$656$	3.57284	−	0.957340i	0.139496	−	0.0373779i
$657$	0.210687	+	0.786293i	0.00821967	+	0.0306762i
$658$	9.76071	+	7.16559i	0.380512	+	0.279344i
$659$	16.5237	−	28.6199i	0.643673	−	1.11487i	−0.340933	−	0.940088i	$-0.610743\pi$
$659$	16.5237	−	28.6199i	0.643673	−	1.11487i	0.984606	−	0.174787i	$-0.0559237\pi$
$660$	14.9577	−	8.63586i	0.582229	−	0.336150i
$661$	25.4681	+	6.82417i	0.990596	+	0.265429i	0.717501	−	0.696558i	$-0.245286\pi$
$661$	25.4681	+	6.82417i	0.990596	+	0.265429i	0.273095	+	0.961987i	$0.411953\pi$
$662$		−	2.82866i		−	0.109939i
$663$	7.03790	+	25.3173i	0.273330	+	0.983242i
$664$		−	10.9921i		−	0.426576i
$665$	5.86838	−	53.2971i	0.227566	−	2.06677i
$666$	−4.05367	−	7.02117i	−0.157077	−	0.272065i
$667$	−16.4283	−	9.48491i	−0.636108	−	0.367257i
$668$	4.31960	+	4.31960i	0.167130	+	0.167130i
$669$	−1.28382	−	4.79128i	−0.0496353	−	0.185241i
$670$	−4.44234	−	16.5791i	−0.171623	−	0.640505i
$671$	−14.2661	+	14.2661i	−0.550737	+	0.550737i
$672$	−0.960356	+	2.46530i	−0.0370465	+	0.0951011i
$673$	34.9158	−	20.1587i	1.34591	−	0.777060i	0.358240	−	0.933630i	$-0.383377\pi$
$673$	34.9158	−	20.1587i	1.34591	−	0.777060i	0.987667	+	0.156570i	$0.0500436\pi$
$674$	1.60964	−	6.00726i	0.0620011	−	0.231391i
$675$	7.80902			0.300569
$676$	12.9977	−	0.242896i	0.499913	−	0.00934217i
$677$		−	14.6443i		−	0.562825i	−0.959587	−	0.281412i	$-0.909197\pi$
$677$		−	14.6443i		−	0.562825i	0.959587	−	0.281412i	$-0.0908029\pi$
$678$	3.07437	−	11.4737i	0.118071	−	0.440645i
$679$	25.5255	+	31.8421i	0.979580	+	1.22199i
$680$	−22.5890	−	13.0418i	−0.866250	−	0.500130i
$681$	6.02294	−	6.02294i	0.230800	−	0.230800i
$682$	−40.0551	+	10.7327i	−1.53379	+	0.410977i
$683$	−35.7021	+	9.56634i	−1.36610	+	0.366046i	−0.866053	−	0.499952i	$-0.833351\pi$
$683$	−35.7021	+	9.56634i	−1.36610	+	0.366046i	−0.500048	+	0.865998i	$0.666684\pi$
$684$	4.00404	−	4.00404i	0.153098	−	0.153098i
$685$	51.7713	+	29.8902i	1.97808	+	1.14204i
$686$	−15.3810	−	10.3162i	−0.587251	−	0.393874i
$687$	−1.24842	+	4.65916i	−0.0476301	+	0.177758i
$688$		−	0.463266i		−	0.0176618i
$689$	19.5791	−	5.44275i	0.745904	−	0.207352i
$690$	11.1254			0.423537
$691$	5.31536	−	19.8372i	0.202206	−	0.754642i	−0.788077	−	0.615576i	$-0.788923\pi$
$691$	5.31536	−	19.8372i	0.202206	−	0.754642i	0.990283	−	0.139066i	$-0.0444099\pi$
$692$	−10.2978	+	5.94546i	−0.391465	+	0.226013i
$693$	−4.63457	+	11.8973i	−0.176053	+	0.451940i
$694$	9.05536	−	9.05536i	0.343737	−	0.343737i
$695$	4.86871	+	18.1703i	0.184681	+	0.689238i
$696$	−1.57944	−	5.89453i	−0.0598683	−	0.223432i
$697$	−19.0618	−	19.0618i	−0.722018	−	0.722018i
$698$	−19.6654	−	11.3538i	−0.744345	−	0.429748i
$699$	12.5825	+	21.7935i	0.475913	+	0.824305i
$700$	20.5366	+	2.26122i	0.776211	+	0.0854662i
$701$		−	28.1341i		−	1.06261i	−0.847180	−	0.531306i	$-0.821701\pi$
$701$		−	28.1341i		−	1.06261i	0.847180	−	0.531306i	$-0.178299\pi$
$702$	−0.0336851	−	3.60539i	−0.00127136	−	0.136077i
$703$			45.9084i			1.73147i
$704$	4.66145	+	1.24903i	0.175685	+	0.0470747i
$705$	14.1851	−	8.18976i	0.534241	−	0.308444i
$706$	−0.201715	+	0.349381i	−0.00759166	+	0.0131491i
$707$	1.72498	−	2.34970i	0.0648744	−	0.0883696i
$708$	−2.29319	−	8.55829i	−0.0861832	−	0.321640i
$709$	−27.1515	+	7.27523i	−1.01970	+	0.273227i	−0.729676	−	0.683793i	$-0.760329\pi$
$709$	−27.1515	+	7.27523i	−1.01970	+	0.273227i	−0.290021	+	0.957020i	$0.593662\pi$
$710$	10.0341	−	10.0341i	0.376572	−	0.376572i
$711$	−6.53597	+	11.3206i	−0.245118	+	0.424557i
$712$	−2.18132	−	3.77816i	−0.0817484	−	0.141592i
$713$	−25.8011	−	6.91337i	−0.966258	−	0.258908i
$714$	19.0596	−	2.92219i	0.713286	−	0.109360i
$715$	−43.6211	+	44.4439i	−1.63134	+	1.66211i
$716$	7.84236			0.293083
$717$	0.00750827	−	0.0280212i	0.000280401	−	0.00104647i
$718$	4.76407	+	8.25162i	0.177794	+	0.307948i
$719$	4.87620	−	8.44582i	0.181852	−	0.314976i	−0.760660	−	0.649151i	$-0.775124\pi$
$719$	4.87620	−	8.44582i	0.181852	−	0.314976i	0.942511	+	0.334175i	$0.108458\pi$
$720$	2.53071	+	2.53071i	0.0943141	+	0.0943141i
$721$	17.2668	+	39.3038i	0.643049	+	1.46375i
$722$	−12.6195	+	3.38140i	−0.469651	+	0.125842i
$723$	15.1111	+	15.1111i	0.561986	+	0.561986i
$724$	14.4527	+	8.34427i	0.537130	+	0.310112i
$725$	−41.2698	+	23.8272i	−1.53272	+	0.884918i
$726$	11.8705	+	3.18069i	0.440555	+	0.118046i
$727$	7.88347			0.292382			0.146191	−	0.989256i	$-0.453299\pi$
$727$	7.88347			0.292382			0.146191	+	0.989256i	$0.453299\pi$
$728$	0.955411	−	9.49143i	0.0354099	−	0.351776i
$729$	−1.00000			−0.0370370
$730$	2.81412	+	0.754041i	0.104155	+	0.0279083i
$731$	−2.92395	+	1.68814i	−0.108146	+	0.0624382i
$732$	−3.62054	−	2.09032i	−0.133819	−	0.0772605i
$733$	−8.13863	−	8.13863i	−0.300607	−	0.300607i	0.540644	−	0.841251i	$-0.318181\pi$
$733$	−8.13863	−	8.13863i	−0.300607	−	0.300607i	−0.841251	+	0.540644i	$0.818181\pi$
$734$	−16.6826	+	4.47009i	−0.615766	+	0.164994i
$735$	−21.1450	+	13.4362i	−0.779944	+	0.495603i
$736$	2.19808	+	2.19808i	0.0810221	+	0.0810221i
$737$	11.5719	−	20.0432i	0.426257	−	0.738299i
$738$	1.84944	+	3.20332i	0.0680788	+	0.117916i
$739$	−5.14390	+	19.1973i	−0.189221	+	0.706184i	0.804466	+	0.593999i	$0.202452\pi$
$739$	−5.14390	+	19.1973i	−0.189221	+	0.706184i	−0.993687	+	0.112185i	$0.964215\pi$
$740$	−29.0159			−1.06665
$741$	−10.0427	+	17.7760i	−0.368928	+	0.653017i
$742$	−2.25987	−	14.7397i	−0.0829625	−	0.541111i
$743$	17.7324	+	4.75139i	0.650540	+	0.174312i	0.568973	−	0.822356i	$-0.307341\pi$
$743$	17.7324	+	4.75139i	0.650540	+	0.174312i	0.0815671	+	0.996668i	$0.474008\pi$
$744$	−4.29642	−	7.44161i	−0.157514	−	0.272823i
$745$	20.3351	−	35.2214i	0.745021	−	1.29041i
$746$	−11.6130	+	11.6130i	−0.425182	+	0.425182i
$747$	10.6175	−	2.84496i	0.388476	−	0.104092i
$748$	−9.10297	−	33.9727i	−0.332837	−	1.24217i
$749$	−12.6399	+	17.2176i	−0.461852	+	0.629118i
$750$	5.02670	−	8.70649i	0.183549	−	0.317916i
$751$	22.4299	−	12.9499i	0.818479	−	0.472549i	−0.0314128	−	0.999506i	$-0.510001\pi$
$751$	22.4299	−	12.9499i	0.818479	−	0.472549i	0.849892	+	0.526957i	$0.176667\pi$
$752$	4.42066	+	1.18451i	0.161205	+	0.0431947i
$753$		−	6.07598i		−	0.221421i
$754$	11.1789	+	18.9513i	0.407113	+	0.690167i
$755$		−	40.5460i		−	1.47562i
$756$	−2.62986	−	0.289566i	−0.0956470	−	0.0105314i
$757$	−4.83826	−	8.38011i	−0.175849	−	0.304580i	0.764605	−	0.644499i	$-0.222934\pi$
$757$	−4.83826	−	8.38011i	−0.175849	−	0.304580i	−0.940455	+	0.339918i	$0.889601\pi$
$758$	12.8816	+	7.43721i	0.467881	+	0.270131i
$759$	10.6077	+	10.6077i	0.385034	+	0.385034i
$760$	−5.24527	−	19.5756i	−0.190266	−	0.710082i
$761$	−3.01733	−	11.2608i	−0.109378	−	0.408205i	0.889427	−	0.457077i	$-0.151104\pi$
$761$	−3.01733	−	11.2608i	−0.109378	−	0.408205i	−0.998805	+	0.0488728i	$0.984437\pi$
$762$	7.39531	−	7.39531i	0.267904	−	0.267904i
$763$	0.784521	+	0.305610i	0.0284016	+	0.0110638i
$764$	−12.1284	+	7.00231i	−0.438789	+	0.253335i
$765$	6.75093	−	25.1948i	0.244080	−	0.910920i
$766$	−35.6637			−1.28858
$767$	16.2307	+	27.5155i	0.586057	+	0.993527i
$768$			1.00000i			0.0360844i
$769$	3.48338	−	13.0001i	0.125614	−	0.468797i	−0.874247	−	0.485481i	$-0.838644\pi$
$769$	3.48338	−	13.0001i	0.125614	−	0.468797i	0.999861	+	0.0166842i	$0.00531100\pi$
$770$	28.5819	+	35.6548i	1.03002	+	1.28491i
$771$	−7.98157	−	4.60816i	−0.287449	−	0.165959i
$772$	−10.2272	+	10.2272i	−0.368085	+	0.368085i
$773$	−24.0205	+	6.43626i	−0.863956	+	0.231496i	−0.663472	−	0.748201i	$-0.730918\pi$
$773$	−24.0205	+	6.43626i	−0.863956	+	0.231496i	−0.200484	+	0.979697i	$0.564251\pi$
$774$	0.447480	−	0.119902i	0.0160843	−	0.00430979i
$775$	−47.4480	+	47.4480i	−1.70438	+	1.70438i
$776$	13.3583	+	7.71240i	0.479534	+	0.276859i
$777$	16.7364	−	13.4163i	0.600413	−	0.481308i
$778$	7.43376	−	27.7432i	0.266513	−	0.994641i
$779$		−	20.9452i		−	0.750438i
$780$	−11.2351	−	6.34739i	−0.402282	−	0.227273i
$781$	19.1343			0.684677
$782$	5.86358	−	21.8832i	0.209681	−	0.782541i
$783$	5.28489	−	3.05124i	0.188867	−	0.109042i
$784$	−6.83230	−	1.52303i	−0.244011	−	0.0543940i
$785$	19.3935	−	19.3935i	0.692183	−	0.692183i
$786$	−1.33595	−	4.98582i	−0.0476516	−	0.177838i
$787$	−3.33860	−	12.4598i	−0.119008	−	0.444145i	0.880547	−	0.473958i	$-0.157175\pi$
$787$	−3.33860	−	12.4598i	−0.119008	−	0.444145i	−0.999555	+	0.0298135i	$0.990509\pi$
$788$	−7.07404	−	7.07404i	−0.252002	−	0.252002i
$789$	−18.9920	−	10.9650i	−0.676133	−	0.390365i
$790$	23.3920	+	40.5162i	0.832251	+	1.44150i
$791$	31.2387	+	3.43959i	1.11072	+	0.122298i
$792$			4.82589i			0.171481i
$793$	14.5957	+	3.76512i	0.518309	+	0.133703i
$794$			15.7120i			0.557597i
$795$	−19.4844	−	5.22082i	−0.691039	−	0.185163i
$796$	−1.41337	+	0.816012i	−0.0500957	+	0.0289228i
$797$	13.7851	−	23.8764i	0.488292	−	0.845747i	−0.511617	−	0.859214i	$-0.670953\pi$
$797$	13.7851	−	23.8764i	0.488292	−	0.845747i	0.999909	+	0.0134667i	$0.00428671\pi$
$798$	12.0768	+	8.86589i	0.427514	+	0.313849i
$799$	−8.63274	−	32.2178i	−0.305404	−	1.13979i
$800$	7.54293	−	2.02112i	0.266683	−	0.0714575i
$801$	3.08485	−	3.08485i	0.108998	−	0.108998i
$802$	8.05693	−	13.9550i	0.284500	−	0.492768i
$803$	1.96421	+	3.40211i	0.0693155	+	0.120058i
$804$	4.63235	+	1.24124i	0.163371	+	0.0437750i
$805$	4.46082	+	29.0951i	0.157223	+	1.02547i
$806$	22.1112	+	21.7019i	0.778835	+	0.764416i
$807$	−3.09943			−0.109105
$808$	0.285148	−	1.06419i	0.0100315	−	0.0374380i
$809$	4.78000	+	8.27921i	0.168056	+	0.291081i	0.937736	−	0.347348i	$-0.112918\pi$
$809$	4.78000	+	8.27921i	0.168056	+	0.291081i	−0.769680	+	0.638429i	$0.779584\pi$
$810$	−1.78948	+	3.09948i	−0.0628761	+	0.108905i
$811$	−30.7379	−	30.7379i	−1.07935	−	1.07935i	−0.996567	−	0.0827855i	$-0.973618\pi$
$811$	−30.7379	−	30.7379i	−1.07935	−	1.07935i	−0.0827855	−	0.996567i	$-0.526382\pi$
$812$	14.7821	−	6.49399i	0.518748	−	0.227894i
$813$	13.7109	−	3.67382i	0.480862	−	0.128846i
$814$	−27.6657	−	27.6657i	−0.969682	−	0.969682i
$815$	2.21521	+	1.27895i	0.0775956	+	0.0447998i
$816$	6.31161	−	3.64401i	0.220950	−	0.127566i
$817$	−2.53389	−	0.678953i	−0.0886495	−	0.0237536i
$818$	38.3183			1.33977
$819$	9.41529	−	1.53371i	0.328997	−	0.0535920i
$820$	13.2382			0.462297
$821$	−34.9073	−	9.35337i	−1.21827	−	0.326435i	−0.408269	−	0.912862i	$-0.633868\pi$
$821$	−34.9073	−	9.35337i	−1.21827	−	0.326435i	−0.810002	+	0.586427i	$0.800534\pi$
$822$	−14.4654	+	8.35161i	−0.504539	+	0.291296i
$823$	−20.2393	−	11.6851i	−0.705496	−	0.407318i	0.103895	−	0.994588i	$-0.466869\pi$
$823$	−20.2393	−	11.6851i	−0.705496	−	0.407318i	−0.809391	+	0.587270i	$0.800203\pi$
$824$	11.4734	+	11.4734i	0.399693	+	0.399693i
$825$	36.4014	−	9.75372i	1.26733	−	0.339581i
$826$	21.4621	−	9.42864i	0.746762	−	0.328064i
$827$	−11.2728	−	11.2728i	−0.391995	−	0.391995i	0.483403	−	0.875398i	$-0.339401\pi$
$827$	−11.2728	−	11.2728i	−0.391995	−	0.391995i	−0.875398	+	0.483403i	$0.839401\pi$
$828$	−1.55427	+	2.69208i	−0.0540147	+	0.0935563i
$829$	−2.73500	−	4.73717i	−0.0949906	−	0.164529i	0.814614	−	0.580003i	$-0.196949\pi$
$829$	−2.73500	−	4.73717i	−0.0949906	−	0.164529i	−0.909605	+	0.415475i	$0.863615\pi$
$830$	10.1820	−	37.9999i	0.353423	−	1.31899i
$831$	−17.1468			−0.594817
$832$	−0.965682	−	3.47382i	−0.0334790	−	0.120433i
$833$	15.2842	+	48.6727i	0.529566	+	1.68641i
$834$	−5.07696	−	1.36037i	−0.175801	−	0.0471057i
$835$	10.9317	+	18.9342i	0.378306	+	0.655245i
$836$	13.6635	−	23.6658i	0.472561	−	0.818500i
$837$	6.07605	−	6.07605i	0.210019	−	0.210019i
$838$	22.8811	−	6.13096i	0.790413	−	0.211791i
$839$	−2.52844	−	9.43626i	−0.0872914	−	0.325776i	0.908447	−	0.418000i	$-0.137269\pi$
$839$	−2.52844	−	9.43626i	−0.0872914	−	0.325776i	−0.995738	+	0.0922245i	$0.970602\pi$
$840$	−5.60359	+	7.63301i	−0.193342	+	0.263364i
$841$	−4.12007	+	7.13617i	−0.142071	+	0.246075i
$842$	15.0177	−	8.67050i	0.517545	−	0.298805i
$843$	−3.70575	−	0.992954i	−0.127633	−	0.0341991i
$844$			21.3028i			0.733274i
$845$	45.1584	+	11.2002i	1.55350	+	0.385298i
$846$			4.57660i			0.157347i
$847$	−3.55854	+	32.3189i	−0.122273	+	1.11049i
$848$	−2.81809	−	4.88107i	−0.0967736	−	0.167617i
$849$	13.1347	+	7.58330i	0.450780	+	0.260258i
$850$	−40.2430	−	40.2430i	−1.38032	−	1.38032i
$851$	−6.52278	−	24.3433i	−0.223598	−	0.834479i
$852$	1.02620	+	3.82981i	0.0351569	+	0.131207i
$853$	23.2249	−	23.2249i	0.795204	−	0.795204i	−0.187131	−	0.982335i	$-0.559919\pi$
$853$	23.2249	−	23.2249i	0.795204	−	0.795204i	0.982335	+	0.187131i	$0.0599188\pi$
$854$	4.01490	−	10.3065i	0.137387	−	0.352683i
$855$	17.5510	−	10.1331i	0.600232	−	0.346544i
$856$	−2.08945	+	7.79792i	−0.0714158	+	0.266528i
$857$	−27.8520			−0.951406			−0.475703	−	0.879606i	$-0.657806\pi$
$857$	−27.8520			−0.951406			−0.475703	+	0.879606i	$0.657806\pi$
$858$	−4.66028	−	16.7643i	−0.159099	−	0.572324i
$859$		−	6.44020i		−	0.219737i	−0.993946	−	0.109868i	$-0.964957\pi$
$859$		−	6.44020i		−	0.219737i	0.993946	−	0.109868i	$-0.0350429\pi$
$860$	0.429125	−	1.60152i	0.0146331	−	0.0546113i
$861$	−7.63576	+	6.12104i	−0.260226	+	0.208604i
$862$	12.6793	+	7.32038i	0.431857	+	0.249333i
$863$	−8.95459	+	8.95459i	−0.304818	+	0.304818i	−0.842895	−	0.538077i	$-0.819151\pi$
$863$	−8.95459	+	8.95459i	−0.304818	+	0.304818i	0.538077	+	0.842895i	$0.319151\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	−41.1071	+	11.0146i	−1.39768	+	0.374509i
$866$	−2.12037	+	2.12037i	−0.0720530	+	0.0720530i
$867$	−31.2766	−	18.0576i	−1.06221	−	0.613267i
$868$	17.7386	−	14.2197i	0.602086	−	0.482649i
$869$	−16.3273	+	60.9342i	−0.553865	+	2.06705i
$870$		−	21.8406i		−	0.740464i
$871$	−17.2906	+	0.161546i	−0.585870	+	0.00547378i
$872$	0.318225			0.0107765
$873$	−3.99223	+	14.8992i	−0.135117	+	0.504262i
$874$	15.2441	−	8.80119i	0.515639	−	0.297705i
$875$	24.7847	+	9.65484i	0.837874	+	0.326393i
$876$	−0.575606	+	0.575606i	−0.0194479	+	0.0194479i
$877$	−6.66354	−	24.8687i	−0.225012	−	0.839756i	−0.982400	−	0.186791i	$-0.940191\pi$
$877$	−6.66354	−	24.8687i	−0.225012	−	0.839756i	0.757388	−	0.652965i	$-0.226475\pi$
$878$	2.35788	+	8.79973i	0.0795746	+	0.296976i
$879$	−12.5357	−	12.5357i	−0.422820	−	0.422820i
$880$	14.9577	+	8.63586i	0.504225	+	0.291115i
$881$	16.5937	+	28.7411i	0.559056	+	0.968314i	0.997576	+	0.0695921i	$0.0221698\pi$
$881$	16.5937	+	28.7411i	0.559056	+	0.968314i	−0.438519	+	0.898722i	$0.644497\pi$
$882$	−0.297194	−	6.99369i	−0.0100070	−	0.235490i
$883$			29.5027i			0.992846i	0.868081	+	0.496423i	$0.165353\pi$
$883$			29.5027i			0.992846i	−0.868081	+	0.496423i	$0.834647\pi$
$884$	−18.4065	+	18.7536i	−0.619076	+	0.630753i
$885$		−	31.7103i		−	1.06593i
$886$	−17.7259	−	4.74965i	−0.595514	−	0.159568i
$887$	18.7770	−	10.8409i	0.630471	−	0.364003i	−0.150463	−	0.988616i	$-0.548077\pi$
$887$	18.7770	−	10.8409i	0.630471	−	0.364003i	0.780935	+	0.624613i	$0.214743\pi$
$888$	4.05367	−	7.02117i	0.136032	−	0.235615i
$889$	22.3054	+	16.3749i	0.748098	+	0.549198i
$890$	−4.04114	−	15.0817i	−0.135459	−	0.505541i
$891$	−4.66145	+	1.24903i	−0.156165	+	0.0418442i
$892$	3.50746	−	3.50746i	0.117438	−	0.117438i
$893$	12.9577	−	22.4433i	0.433612	−	0.751038i
$894$	5.68183	+	9.84123i	0.190029	+	0.329140i
$895$	27.1112	+	7.26442i	0.906227	+	0.242823i
$896$	−2.61519	+	0.400958i	−0.0873675	+	0.0133951i
$897$	2.79958	−	10.8528i	0.0934753	−	0.362363i
$898$	10.4728			0.349480
$899$	−13.5718	+	50.6507i	−0.452646	+	1.68930i
$900$	3.90451	+	6.76281i	0.130150	+	0.225427i
$901$	−20.5383	+	35.5733i	−0.684229	+	1.18512i
$902$	12.6221	+	12.6221i	0.420271	+	0.420271i
$903$	0.492988	+	1.12217i	0.0164056	+	0.0373435i
$904$	11.4737	−	3.07437i	0.381610	−	0.102252i
$905$	42.2339	+	42.2339i	1.40390	+	1.40390i
$906$	9.81117	+	5.66448i	0.325954	+	0.188190i
$907$	−12.7704	+	7.37298i	−0.424033	+	0.244816i	−0.696801	−	0.717264i	$-0.745394\pi$
$907$	−12.7704	+	7.37298i	−0.424033	+	0.244816i	0.272768	+	0.962080i	$0.412061\pi$
$908$	8.22749	+	2.20455i	0.273039	+	0.0731605i
$909$	1.10173			0.0365420
$910$	12.0948	−	31.9270i	0.400940	−	1.05837i
$911$	37.2050			1.23266			0.616328	−	0.787489i	$-0.288619\pi$
$911$	37.2050			1.23266			0.616328	+	0.787489i	$0.288619\pi$
$912$	5.46962	+	1.46558i	0.181117	+	0.0485302i
$913$	45.9397	−	26.5233i	1.52038	−	0.877793i
$914$	−25.2648	−	14.5866i	−0.835686	−	0.482483i
$915$	−10.5800	−	10.5800i	−0.349764	−	0.349764i
$916$	−4.65916	+	1.24842i	−0.153943	+	0.0412489i
$917$	12.5032	−	5.49286i	0.412893	−	0.181390i
$918$	5.15340	+	5.15340i	0.170088	+	0.170088i
$919$	−8.35336	+	14.4684i	−0.275552	+	0.477270i	−0.970274	−	0.242008i	$-0.922194\pi$
$919$	−8.35336	+	14.4684i	−0.275552	+	0.477270i	0.694722	+	0.719278i	$0.255527\pi$
$920$	5.56270	+	9.63488i	0.183397	+	0.317652i
$921$	−2.82554	+	10.5451i	−0.0931046	+	0.347471i
$922$	29.5168			0.972085
$923$	−7.26321	−	12.3131i	−0.239071	−	0.405291i
$924$	−12.6206	+	1.93498i	−0.415188	+	0.0636562i
$925$	−61.1532	−	16.3859i	−2.01070	−	0.538767i
$926$	4.61305	+	7.99004i	0.151594	+	0.262569i
$927$	−8.11289	+	14.0519i	−0.266462	+	0.461526i
$928$	4.31510	−	4.31510i	0.141650	−	0.141650i
$929$	3.75100	−	1.00508i	0.123066	−	0.0329755i	−0.196760	−	0.980452i	$-0.563042\pi$
$929$	3.75100	−	1.00508i	0.123066	−	0.0329755i	0.319826	+	0.947476i	$0.396375\pi$
$930$	−7.95959	−	29.7056i	−0.261005	−	0.974084i
$931$	−18.3437	+	35.1380i	−0.601191	+	1.15160i
$932$	−12.5825	+	21.7935i	−0.412152	+	0.713869i
$933$	−15.7787	+	9.10981i	−0.516570	+	0.298242i
$934$	33.9072	+	9.08540i	1.10948	+	0.297283i
$935$		−	125.877i		−	4.11660i
$936$	3.10552	−	1.83187i	0.101507	−	0.0598765i
$937$		−	9.75401i		−	0.318649i	−0.987226	−	0.159325i	$-0.949068\pi$
$937$		−	9.75401i		−	0.318649i	0.987226	−	0.159325i	$-0.0509317\pi$
$938$	−1.38869	+	12.6122i	−0.0453423	+	0.411802i
$939$	5.62603	+	9.74457i	0.183599	+	0.318002i
$940$	14.1851	+	8.18976i	0.462666	+	0.267121i
$941$	22.0554	+	22.0554i	0.718984	+	0.718984i	0.968397	−	0.249413i	$-0.0802377\pi$
$941$	22.0554	+	22.0554i	0.718984	+	0.718984i	−0.249413	+	0.968397i	$0.580238\pi$
$942$	1.98339	+	7.40212i	0.0646224	+	0.241174i
$943$	2.97594	+	11.1064i	0.0969099	+	0.361673i
$944$	6.26510	−	6.26510i	0.203912	−	0.203912i
$945$	−8.82324	−	3.43708i	−0.287020	−	0.111808i
$946$	1.93615	−	1.11783i	0.0629496	−	0.0363439i
$947$	−11.5047	+	42.9361i	−0.373853	+	1.39524i	0.481161	+	0.876632i	$0.340215\pi$
$947$	−11.5047	+	42.9361i	−0.373853	+	1.39524i	−0.855014	+	0.518605i	$0.826452\pi$
$948$	−13.0719			−0.424557
$949$	1.44370	−	2.55541i	0.0468646	−	0.0829521i
$950$		−	44.2191i		−	1.43466i
$951$	2.13617	−	7.97228i	0.0692699	−	0.258519i
$952$	12.0605	+	15.0450i	0.390882	+	0.487610i
$953$	−12.4677	−	7.19824i	−0.403869	−	0.233174i	0.284283	−	0.958740i	$-0.408244\pi$
$953$	−12.4677	−	7.19824i	−0.403869	−	0.233174i	−0.688152	+	0.725566i	$0.741578\pi$
$954$	3.98538	−	3.98538i	0.129031	−	0.129031i
$955$	−48.4142	+	12.9726i	−1.56665	+	0.419782i
$956$	0.0280212	−	0.00750827i	0.000906272	−	0.000242835i
$957$	20.8242	−	20.8242i	0.673151	−	0.673151i
$958$	−19.0314	−	10.9878i	−0.614878	−	0.355000i
$959$	−27.6411	−	34.4812i	−0.892577	−	1.11346i
$960$	−0.926305	+	3.45702i	−0.0298964	+	0.111575i
$961$			42.8368i			1.38183i
$962$	−7.30154	+	28.3049i	−0.235411	+	0.912586i
$963$	−8.07301			−0.260149
$964$	−5.53103	+	20.6421i	−0.178142	+	0.664837i
$965$	−44.8291	+	25.8821i	−1.44310	+	0.833174i
$966$	−7.66351	−	2.98531i	−0.246569	−	0.0960509i
$967$	−30.0520	+	30.0520i	−0.966406	+	0.966406i	−0.999454	−	0.0330475i	$-0.989479\pi$
$967$	−30.0520	+	30.0520i	−0.966406	+	0.966406i	0.0330475	+	0.999454i	$0.489479\pi$
$968$	3.18069	+	11.8705i	0.102231	+	0.381532i
$969$	−10.6812	−	39.8627i	−0.343129	−	1.28057i
$970$	39.0357	+	39.0357i	1.25336	+	1.25336i
$971$	−24.8050	−	14.3212i	−0.796029	−	0.459588i	0.0460514	−	0.998939i	$-0.485336\pi$
$971$	−24.8050	−	14.3212i	−0.796029	−	0.459588i	−0.842081	+	0.539351i	$0.818670\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	1.52197	−	13.8227i	0.0487922	−	0.443135i
$974$			13.2790i			0.425488i
$975$	−20.0943	−	19.7223i	−0.643533	−	0.631619i
$976$		−	4.18064i		−	0.133819i
$977$	42.0530	+	11.2681i	1.34539	+	0.360497i	0.858433	−	0.512926i	$-0.171439\pi$
$977$	42.0530	+	11.2681i	1.34539	+	0.360497i	0.486961	+	0.873424i	$0.338105\pi$
$978$	−0.618953	+	0.357353i	−0.0197919	+	0.0114269i
$979$	10.5268	−	18.2330i	0.336438	−	0.582729i
$980$	−22.2086	−	11.5940i	−0.709428	−	0.370355i
$981$	0.0823627	+	0.307382i	0.00262964	+	0.00981395i
$982$	−29.0350	+	7.77992i	−0.926545	+	0.248267i
$983$	37.1517	−	37.1517i	1.18495	−	1.18495i	0.206509	−	0.978445i	$-0.433790\pi$
$983$	37.1517	−	37.1517i	1.18495	−	1.18495i	0.978445	−	0.206509i	$-0.0662103\pi$
$984$	−1.84944	+	3.20332i	−0.0589580	+	0.102118i
$985$	−17.9024	−	31.0078i	−0.570416	−	0.987990i
$986$	−42.9594	−	11.5109i	−1.36811	−	0.366583i
$987$	−11.9687	+	1.83503i	−0.380968	+	0.0584096i
$988$	−20.4158	+	0.190744i	−0.649513	+	0.00606839i
$989$	1.44008			0.0457920
$990$	−4.47025	+	16.6832i	−0.142074	+	0.530227i
$991$	10.3883	+	17.9930i	0.329994	+	0.571567i	0.982510	−	0.186208i	$-0.0596199\pi$
$991$	10.3883	+	17.9930i	0.329994	+	0.571567i	−0.652516	+	0.757775i	$0.726287\pi$
$992$	4.29642	−	7.44161i	0.136411	−	0.236271i
$993$	2.00017	+	2.00017i	0.0634733	+	0.0634733i
$994$	−9.60424	+	4.21930i	−0.304628	+	0.133828i
$995$	−5.64194	+	1.51175i	−0.178861	+	0.0479258i
$996$	7.77258	+	7.77258i	0.246284	+	0.246284i
$997$	−26.9808	−	15.5774i	−0.854491	−	0.493341i	0.00767259	−	0.999971i	$-0.497558\pi$
$997$	−26.9808	−	15.5774i	−0.854491	−	0.493341i	−0.862164	+	0.506630i	$0.830891\pi$
$998$	−26.5865	+	15.3497i	−0.841580	+	0.485887i
$999$	7.83110	+	2.09834i	0.247765	+	0.0663884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.a.223.5	✓	40
7.6	odd	2		546.2.bx.b.223.1	yes	40
13.7	odd	12		546.2.bx.b.475.1	yes	40
91.20	even	12	inner	546.2.bx.a.475.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.223.5	✓	40	1.1	even	1	trivial
546.2.bx.a.475.5	yes	40	91.20	even	12	inner
546.2.bx.b.223.1	yes	40	7.6	odd	2
546.2.bx.b.475.1	yes	40	13.7	odd	12

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.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.53071 + 2.53071i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.06416 - 2.42231i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.53071 + 2.53071i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.06416 - 2.42231i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.78948 - 3.09948i) q^{10} +(1.24903 - 4.66145i) q^{11} +1.00000 q^{12} +(-3.47382 + 0.965682i) q^{13} +(0.400958 + 2.61519i) q^{14} +(3.45702 + 0.926305i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.64401 - 6.31161i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(5.46962 - 1.46558i) q^{19} +(0.926305 + 3.45702i) q^{20} +(-2.13274 - 1.56570i) q^{21} +(-2.41295 + 4.17934i) q^{22} +(-2.69208 + 1.55427i) q^{23} +(-0.965926 - 0.258819i) q^{24} +7.80902i q^{25} +(3.60539 - 0.0336851i) q^{26} -1.00000i q^{27} +(0.289566 - 2.62986i) q^{28} +(3.05124 + 5.28489i) q^{29} +(-3.09948 - 1.78948i) q^{30} +(6.07605 + 6.07605i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.24903 - 4.66145i) q^{33} +(-5.15340 + 5.15340i) q^{34} +(3.43708 - 8.82324i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-2.09834 + 7.83110i) q^{37} -5.66257 q^{38} +(-2.52558 + 2.57322i) q^{39} -3.57897i q^{40} +(0.957340 - 3.57284i) q^{41} +(1.65484 + 2.06434i) q^{42} +(-0.401200 - 0.231633i) q^{43} +(3.41242 - 3.41242i) q^{44} +(3.45702 - 0.926305i) q^{45} +(3.00263 - 0.804551i) q^{46} +(3.23615 - 3.23615i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-4.73514 + 5.15543i) q^{49} +(2.02112 - 7.54293i) q^{50} -7.28801i q^{51} +(-3.49126 - 0.900607i) q^{52} -5.63618 q^{53} +(-0.258819 + 0.965926i) q^{54} +(14.9577 - 8.63586i) q^{55} +(-0.960356 + 2.46530i) q^{56} +(4.00404 - 4.00404i) q^{57} +(-1.57944 - 5.89453i) q^{58} +(-2.29319 - 8.55829i) q^{59} +(2.53071 + 2.53071i) q^{60} +(-3.62054 - 2.09032i) q^{61} +(-4.29642 - 7.44161i) q^{62} +(-2.62986 - 0.289566i) q^{63} +1.00000i q^{64} +(-11.2351 - 6.34739i) q^{65} +4.82589i q^{66} +(4.63235 + 1.24124i) q^{67} +(6.31161 - 3.64401i) q^{68} +(-1.55427 + 2.69208i) q^{69} +(-5.60359 + 7.63301i) q^{70} +(1.02620 + 3.82981i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-0.575606 + 0.575606i) q^{73} +(4.05367 - 7.02117i) q^{74} +(3.90451 + 6.76281i) q^{75} +(5.46962 + 1.46558i) q^{76} +(-12.6206 + 1.93498i) q^{77} +(3.10552 - 1.83187i) q^{78} -13.0719 q^{79} +(-0.926305 + 3.45702i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.84944 + 3.20332i) q^{82} +(7.77258 + 7.77258i) q^{83} +(-1.06416 - 2.42231i) q^{84} +(25.1948 - 6.75093i) q^{85} +(0.327578 + 0.327578i) q^{86} +(5.28489 + 3.05124i) q^{87} +(-4.17934 + 2.41295i) q^{88} +(4.21399 + 1.12913i) q^{89} -3.57897 q^{90} +(6.03588 + 7.38703i) q^{91} -3.10855 q^{92} +(8.30004 + 2.22399i) q^{93} +(-3.96346 + 2.28830i) q^{94} +(17.5510 + 10.1331i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-14.8992 + 3.99223i) q^{97} +(5.90811 - 3.75422i) q^{98} +(-3.41242 - 3.41242i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 + 20 * q^9	\( 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

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