LMFDB - Embedded newform 546.2.bm.b.277.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 $ x^20 + 56x^18 + 1306x^16 + 16508x^14 + 123139x^12 + 552164x^10 + 1447090x^8 + 2035844x^6 + 1263505x^4 + 215520*x^2 + 576
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			277.10
Root			$3.79415i$ of defining polynomial
Character	$\chi$	$=$	546.277
Dual form			546.2.bm.b.205.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(3.28583 - 1.89707i) q^{5} +(0.866025 - 0.500000i) q^{6} +(2.13806 - 1.55842i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(3.28583 - 1.89707i) q^{5} +(0.866025 - 0.500000i) q^{6} +(2.13806 - 1.55842i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.89707 + 3.28583i) q^{10} +(0.483436 - 0.279112i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.73320 - 2.35152i) q^{13} +(1.55842 + 2.13806i) q^{14} +(-3.28583 - 1.89707i) q^{15} +1.00000 q^{16} -6.05364 q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.65134 - 2.10810i) q^{19} +(-3.28583 + 1.89707i) q^{20} +(-2.41867 - 1.07240i) q^{21} +(0.279112 + 0.483436i) q^{22} +5.66237 q^{23} +(-0.866025 + 0.500000i) q^{24} +(4.69778 - 8.13679i) q^{25} +(2.35152 - 2.73320i) q^{26} +1.00000 q^{27} +(-2.13806 + 1.55842i) q^{28} +(1.93411 - 3.34998i) q^{29} +(1.89707 - 3.28583i) q^{30} +(5.96291 + 3.44269i) q^{31} +1.00000i q^{32} +(-0.483436 - 0.279112i) q^{33} -6.05364i q^{34} +(4.06886 - 9.17678i) q^{35} +(0.500000 - 0.866025i) q^{36} +9.24963i q^{37} +(2.10810 - 3.65134i) q^{38} +(-0.669873 + 3.54278i) q^{39} +(-1.89707 - 3.28583i) q^{40} +(-3.99747 - 2.30794i) q^{41} +(1.07240 - 2.41867i) q^{42} +(6.47599 + 11.2167i) q^{43} +(-0.483436 + 0.279112i) q^{44} +3.79415i q^{45} +5.66237i q^{46} +(-5.18078 + 2.99112i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(2.14262 - 6.66402i) q^{49} +(8.13679 + 4.69778i) q^{50} +(3.02682 + 5.24261i) q^{51} +(2.73320 + 2.35152i) q^{52} +(6.70203 - 11.6083i) q^{53} +1.00000i q^{54} +(1.05899 - 1.83423i) q^{55} +(-1.55842 - 2.13806i) q^{56} +4.21620i q^{57} +(3.34998 + 1.93411i) q^{58} -2.64974i q^{59} +(3.28583 + 1.89707i) q^{60} +(-1.78557 + 3.09270i) q^{61} +(-3.44269 + 5.96291i) q^{62} +(0.280604 + 2.63083i) q^{63} -1.00000 q^{64} +(-13.4418 - 2.54160i) q^{65} +(0.279112 - 0.483436i) q^{66} +(10.2680 - 5.92821i) q^{67} +6.05364 q^{68} +(-2.83118 - 4.90375i) q^{69} +(9.17678 + 4.06886i) q^{70} +(-4.58090 + 2.64478i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-2.29627 - 1.32575i) q^{73} -9.24963 q^{74} -9.39555 q^{75} +(3.65134 + 2.10810i) q^{76} +(0.598641 - 1.35016i) q^{77} +(-3.54278 - 0.669873i) q^{78} +(4.38856 + 7.60121i) q^{79} +(3.28583 - 1.89707i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.30794 - 3.99747i) q^{82} +6.48635i q^{83} +(2.41867 + 1.07240i) q^{84} +(-19.8912 + 11.4842i) q^{85} +(-11.2167 + 6.47599i) q^{86} -3.86822 q^{87} +(-0.279112 - 0.483436i) q^{88} -5.45925i q^{89} -3.79415 q^{90} +(-9.50841 - 0.768204i) q^{91} -5.66237 q^{92} -6.88537i q^{93} +(-2.99112 - 5.18078i) q^{94} -15.9969 q^{95} +(0.866025 - 0.500000i) q^{96} +(4.64952 - 2.68440i) q^{97} +(6.66402 + 2.14262i) q^{98} +0.558224i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9	$ 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9} + 4 q^{10} + 6 q^{11} + 10 q^{12} + 8 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{21} - 10 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{26} + 20 q^{27} + 8 q^{29} + 4 q^{30} + 12 q^{31} - 6 q^{33} + 10 q^{35} + 10 q^{36} + 6 q^{38} - 10 q^{39} - 4 q^{40} - 18 q^{41} - 2 q^{42} + 18 q^{43} - 6 q^{44} - 6 q^{47} - 10 q^{48} - 20 q^{49} + 12 q^{50} + 4 q^{51} - 8 q^{52} + 18 q^{53} - 12 q^{55} - 4 q^{56} + 24 q^{58} - 6 q^{61} - 6 q^{63} - 20 q^{64} - 6 q^{65} - 10 q^{66} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 42 q^{70} - 6 q^{71} + 24 q^{73} + 36 q^{74} - 12 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} - 10 q^{81} + 18 q^{82} - 6 q^{84} - 36 q^{86} - 16 q^{87} + 10 q^{88} - 8 q^{90} - 10 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9 + 4 * q^10 + 6 * q^11 + 10 * q^12 + 8 * q^13 + 4 * q^14 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^21 - 10 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^26 + 20 * q^27 + 8 * q^29 + 4 * q^30 + 12 * q^31 - 6 * q^33 + 10 * q^35 + 10 * q^36 + 6 * q^38 - 10 * q^39 - 4 * q^40 - 18 * q^41 - 2 * q^42 + 18 * q^43 - 6 * q^44 - 6 * q^47 - 10 * q^48 - 20 * q^49 + 12 * q^50 + 4 * q^51 - 8 * q^52 + 18 * q^53 - 12 * q^55 - 4 * q^56 + 24 * q^58 - 6 * q^61 - 6 * q^63 - 20 * q^64 - 6 * q^65 - 10 * q^66 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 42 * q^70 - 6 * q^71 + 24 * q^73 + 36 * q^74 - 12 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 - 10 * q^81 + 18 * q^82 - 6 * q^84 - 36 * q^86 - 16 * q^87 + 10 * q^88 - 8 * q^90 - 10 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.00000			−0.500000
$5$	3.28583	−	1.89707i	1.46947	−	0.848397i	0.470053	−	0.882638i	$-0.344235\pi$
$5$	3.28583	−	1.89707i	1.46947	−	0.848397i	0.999414	+	0.0342410i	$0.0109014\pi$
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	2.13806	−	1.55842i	0.808112	−	0.589029i
$7$	2.13806	−	1.55842i	0.808112	−	0.589029i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.89707	+	3.28583i	0.599907	+	1.03907i
$11$	0.483436	−	0.279112i	0.145761	−	0.0841554i	−0.425346	−	0.905031i	$-0.639847\pi$
$11$	0.483436	−	0.279112i	0.145761	−	0.0841554i	0.571107	+	0.820876i	$0.306514\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−2.73320	−	2.35152i	−0.758053	−	0.652193i
$13$	−2.73320	−	2.35152i	−0.758053	−	0.652193i
$14$	1.55842	+	2.13806i	0.416507	+	0.571421i
$15$	−3.28583	−	1.89707i	−0.848397	−	0.489822i
$16$	1.00000			0.250000
$17$	−6.05364			−1.46822			−0.734112	−	0.679029i	$-0.762401\pi$
$17$	−6.05364			−1.46822			−0.734112	+	0.679029i	$0.762401\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−3.65134	−	2.10810i	−0.837674	−	0.483631i	0.0187989	−	0.999823i	$-0.494016\pi$
$19$	−3.65134	−	2.10810i	−0.837674	−	0.483631i	−0.856473	+	0.516192i	$0.827349\pi$
$20$	−3.28583	+	1.89707i	−0.734733	+	0.424199i
$21$	−2.41867	−	1.07240i	−0.527796	−	0.234018i
$22$	0.279112	+	0.483436i	0.0595068	+	0.103069i
$23$	5.66237			1.18069			0.590343	−	0.807153i	$-0.298993\pi$
$23$	5.66237			1.18069			0.590343	+	0.807153i	$0.298993\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	4.69778	−	8.13679i	0.939555	−	1.62736i
$26$	2.35152	−	2.73320i	0.461170	−	0.536024i
$27$	1.00000			0.192450
$28$	−2.13806	+	1.55842i	−0.404056	+	0.294515i
$29$	1.93411	−	3.34998i	0.359155	−	0.622075i	−0.628665	−	0.777677i	$-0.716398\pi$
$29$	1.93411	−	3.34998i	0.359155	−	0.622075i	0.987820	+	0.155601i	$0.0497315\pi$
$30$	1.89707	−	3.28583i	0.346357	−	0.599907i
$31$	5.96291	+	3.44269i	1.07097	+	0.618325i	0.928446	−	0.371467i	$-0.121145\pi$
$31$	5.96291	+	3.44269i	1.07097	+	0.618325i	0.142524	+	0.989791i	$0.454478\pi$
$32$			1.00000i			0.176777i
$33$	−0.483436	−	0.279112i	−0.0841554	−	0.0485871i
$34$		−	6.05364i		−	1.03819i
$35$	4.06886	−	9.17678i	0.687763	−	1.55116i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$			9.24963i			1.52063i	0.649555	+	0.760315i	$0.274955\pi$
$37$			9.24963i			1.52063i	−0.649555	+	0.760315i	$0.725045\pi$
$38$	2.10810	−	3.65134i	0.341979	−	0.592325i
$39$	−0.669873	+	3.54278i	−0.107266	+	0.567298i
$40$	−1.89707	−	3.28583i	−0.299954	−	0.519535i
$41$	−3.99747	−	2.30794i	−0.624300	−	0.360439i	0.154242	−	0.988033i	$-0.450707\pi$
$41$	−3.99747	−	2.30794i	−0.624300	−	0.360439i	−0.778541	+	0.627594i	$0.784040\pi$
$42$	1.07240	−	2.41867i	0.165476	−	0.373208i
$43$	6.47599	+	11.2167i	0.987580	+	1.71054i	0.629860	+	0.776709i	$0.283112\pi$
$43$	6.47599	+	11.2167i	0.987580	+	1.71054i	0.357720	+	0.933829i	$0.383554\pi$
$44$	−0.483436	+	0.279112i	−0.0728807	+	0.0420777i
$45$			3.79415i			0.565598i
$46$			5.66237i			0.834871i
$47$	−5.18078	+	2.99112i	−0.755694	+	0.436300i	−0.827748	−	0.561101i	$-0.810378\pi$
$47$	−5.18078	+	2.99112i	−0.755694	+	0.436300i	0.0720535	+	0.997401i	$0.477045\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	2.14262	−	6.66402i	0.306089	−	0.952003i
$50$	8.13679	+	4.69778i	1.15072	+	0.664366i
$51$	3.02682	+	5.24261i	0.423840	+	0.734112i
$52$	2.73320	+	2.35152i	0.379026	+	0.326097i
$53$	6.70203	−	11.6083i	0.920595	−	1.59452i	0.122099	−	0.992518i	$-0.461038\pi$
$53$	6.70203	−	11.6083i	0.920595	−	1.59452i	0.798496	−	0.601999i	$-0.205629\pi$
$54$			1.00000i			0.136083i
$55$	1.05899	−	1.83423i	0.142794	−	0.247327i
$56$	−1.55842	−	2.13806i	−0.208253	−	0.285711i
$57$			4.21620i			0.558449i
$58$	3.34998	+	1.93411i	0.439874	+	0.253961i
$59$		−	2.64974i		−	0.344967i	−0.985012	−	0.172484i	$-0.944821\pi$
$59$		−	2.64974i		−	0.344967i	0.985012	−	0.172484i	$-0.0551792\pi$
$60$	3.28583	+	1.89707i	0.424199	+	0.244911i
$61$	−1.78557	+	3.09270i	−0.228619	+	0.395980i	−0.957399	−	0.288768i	$-0.906754\pi$
$61$	−1.78557	+	3.09270i	−0.228619	+	0.395980i	0.728780	+	0.684748i	$0.240088\pi$
$62$	−3.44269	+	5.96291i	−0.437222	+	0.757290i
$63$	0.280604	+	2.63083i	0.0353528	+	0.331453i
$64$	−1.00000			−0.125000
$65$	−13.4418	−	2.54160i	−1.66725	−	0.315246i
$66$	0.279112	−	0.483436i	0.0343563	−	0.0595068i
$67$	10.2680	−	5.92821i	1.25443	−	0.724246i	0.282445	−	0.959283i	$-0.408854\pi$
$67$	10.2680	−	5.92821i	1.25443	−	0.724246i	0.971986	+	0.235037i	$0.0755212\pi$
$68$	6.05364			0.734112
$69$	−2.83118	−	4.90375i	−0.340835	−	0.590343i
$70$	9.17678	+	4.06886i	1.09683	+	0.486322i
$71$	−4.58090	+	2.64478i	−0.543652	+	0.313878i	−0.746558	−	0.665321i	$-0.768295\pi$
$71$	−4.58090	+	2.64478i	−0.543652	+	0.313878i	0.202906	+	0.979198i	$0.434962\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−2.29627	−	1.32575i	−0.268758	−	0.155168i	0.359565	−	0.933120i	$-0.382925\pi$
$73$	−2.29627	−	1.32575i	−0.268758	−	0.155168i	−0.628323	+	0.777952i	$0.716258\pi$
$74$	−9.24963			−1.07525
$75$	−9.39555			−1.08490
$76$	3.65134	+	2.10810i	0.418837	+	0.241816i
$77$	0.598641	−	1.35016i	0.0682215	−	0.153865i
$78$	−3.54278	−	0.669873i	−0.401141	−	0.0758482i
$79$	4.38856	+	7.60121i	0.493752	+	0.855203i	0.999974	−	0.00719982i	$-0.00229179\pi$
$79$	4.38856	+	7.60121i	0.493752	+	0.855203i	−0.506222	+	0.862403i	$0.668958\pi$
$80$	3.28583	−	1.89707i	0.367367	−	0.212099i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.30794	−	3.99747i	0.254869	−	0.441446i
$83$			6.48635i			0.711970i	0.934492	+	0.355985i	$0.115855\pi$
$83$			6.48635i			0.711970i	−0.934492	+	0.355985i	$0.884145\pi$
$84$	2.41867	+	1.07240i	0.263898	+	0.117009i
$85$	−19.8912	+	11.4842i	−2.15751	+	1.24564i
$86$	−11.2167	+	6.47599i	−1.20953	+	0.698324i
$87$	−3.86822			−0.414717
$88$	−0.279112	−	0.483436i	−0.0297534	−	0.0515344i
$89$		−	5.45925i		−	0.578679i	−0.957227	−	0.289340i	$-0.906564\pi$
$89$		−	5.45925i		−	0.578679i	0.957227	−	0.289340i	$-0.0934357\pi$
$90$	−3.79415			−0.399938
$91$	−9.50841	−	0.768204i	−0.996752	−	0.0805296i
$92$	−5.66237			−0.590343
$93$		−	6.88537i		−	0.713980i
$94$	−2.99112	−	5.18078i	−0.308511	−	0.534356i
$95$	−15.9969			−1.64125
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	4.64952	−	2.68440i	0.472088	−	0.272560i	−0.245026	−	0.969517i	$-0.578796\pi$
$97$	4.64952	−	2.68440i	0.472088	−	0.272560i	0.717113	+	0.696957i	$0.245463\pi$
$98$	6.66402	+	2.14262i	0.673168	+	0.216438i
$99$			0.558224i			0.0561036i
$100$	−4.69778	+	8.13679i	−0.469778	+	0.813679i
$101$	5.55150	+	9.61548i	0.552395	+	0.956776i	0.998101	+	0.0615968i	$0.0196193\pi$
$101$	5.55150	+	9.61548i	0.552395	+	0.956776i	−0.445706	+	0.895179i	$0.647047\pi$
$102$	−5.24261	+	3.02682i	−0.519095	+	0.299700i
$103$	7.78983	+	13.4924i	0.767554	+	1.32944i	0.938885	+	0.344230i	$0.111860\pi$
$103$	7.78983	+	13.4924i	0.767554	+	1.32944i	−0.171331	+	0.985214i	$0.554807\pi$
$104$	−2.35152	+	2.73320i	−0.230585	+	0.268012i
$105$	−9.98175	+	1.06465i	−0.974119	+	0.103900i
$106$	11.6083	+	6.70203i	1.12749	+	0.650959i
$107$	0.123141			0.0119045			0.00595225	−	0.999982i	$-0.498105\pi$
$107$	0.123141			0.0119045			0.00595225	+	0.999982i	$0.498105\pi$
$108$	−1.00000			−0.0962250
$109$	2.75562	+	1.59096i	0.263941	+	0.152386i	0.626131	−	0.779718i	$-0.284638\pi$
$109$	2.75562	+	1.59096i	0.263941	+	0.152386i	−0.362190	+	0.932104i	$0.617971\pi$
$110$	1.83423	+	1.05899i	0.174887	+	0.100971i
$111$	8.01041	−	4.62481i	0.760315	−	0.438968i
$112$	2.13806	−	1.55842i	0.202028	−	0.147257i
$113$	−5.41522	−	9.37943i	−0.509421	−	0.882343i	−0.999940	−	0.0109127i	$-0.996526\pi$
$113$	−5.41522	−	9.37943i	−0.509421	−	0.882343i	0.490520	−	0.871430i	$-0.336807\pi$
$114$	−4.21620			−0.394883
$115$	18.6056	−	10.7419i	1.73498	−	1.00169i
$116$	−1.93411	+	3.34998i	−0.179578	+	0.311038i
$117$	3.40307	−	1.19126i	0.314614	−	0.110132i
$118$	2.64974			0.243929
$119$	−12.9431	+	9.43414i	−1.18649	+	0.864826i
$120$	−1.89707	+	3.28583i	−0.173178	+	0.299954i
$121$	−5.34419	+	9.25641i	−0.485836	+	0.841492i
$122$	−3.09270	−	1.78557i	−0.280000	−	0.161658i
$123$			4.61588i			0.416200i
$124$	−5.96291	−	3.44269i	−0.535485	−	0.309162i
$125$		−	16.6774i		−	1.49167i
$126$	−2.63083	+	0.280604i	−0.234373	+	0.0249982i
$127$	−5.53819	+	9.59243i	−0.491435	+	0.851190i	−0.999951	−	0.00986189i	$-0.996861\pi$
$127$	−5.53819	+	9.59243i	−0.491435	+	0.851190i	0.508516	+	0.861052i	$0.330194\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	6.47599	−	11.2167i	0.570179	−	0.987580i
$130$	2.54160	−	13.4418i	0.222913	−	1.17893i
$131$	−2.75898	−	4.77869i	−0.241053	−	0.417516i	0.719962	−	0.694014i	$-0.244159\pi$
$131$	−2.75898	−	4.77869i	−0.241053	−	0.417516i	−0.961014	+	0.276498i	$0.910826\pi$
$132$	0.483436	+	0.279112i	0.0420777	+	0.0242936i
$133$	−11.0921	+	1.18308i	−0.961807	+	0.102586i
$134$	5.92821	+	10.2680i	0.512120	+	0.887017i
$135$	3.28583	−	1.89707i	0.282799	−	0.163274i
$136$			6.05364i			0.519095i
$137$			14.0832i			1.20321i	0.798795	+	0.601604i	$0.205471\pi$
$137$			14.0832i			1.20321i	−0.798795	+	0.601604i	$0.794529\pi$
$138$	4.90375	−	2.83118i	0.417435	−	0.241006i
$139$	−2.59129	−	4.48824i	−0.219790	−	0.380688i	0.734954	−	0.678117i	$-0.237204\pi$
$139$	−2.59129	−	4.48824i	−0.219790	−	0.380688i	−0.954744	+	0.297430i	$0.903871\pi$
$140$	−4.06886	+	9.17678i	−0.343881	+	0.775579i
$141$	5.18078	+	2.99112i	0.436300	+	0.251898i
$142$	−2.64478	−	4.58090i	−0.221945	−	0.384420i
$143$	−1.97766	−	0.373939i	−0.165380	−	0.0312704i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		−	14.6766i		−	1.21883i
$146$	1.32575	−	2.29627i	0.109720	−	0.190041i
$147$	−6.84252	+	1.47644i	−0.564362	+	0.121775i
$148$		−	9.24963i		−	0.760315i
$149$	−11.7144	−	6.76333i	−0.959684	−	0.554074i	−0.0636080	−	0.997975i	$-0.520261\pi$
$149$	−11.7144	−	6.76333i	−0.959684	−	0.554074i	−0.896076	+	0.443901i	$0.853594\pi$
$150$		−	9.39555i		−	0.767144i
$151$	8.86264	+	5.11685i	0.721232	+	0.416403i	0.815206	−	0.579171i	$-0.196624\pi$
$151$	8.86264	+	5.11685i	0.721232	+	0.416403i	−0.0939741	+	0.995575i	$0.529957\pi$
$152$	−2.10810	+	3.65134i	−0.170990	+	0.296163i
$153$	3.02682	−	5.24261i	0.244704	−	0.423840i
$154$	1.35016	+	0.598641i	0.108799	+	0.0482399i
$155$	26.1241			2.09834
$156$	0.669873	−	3.54278i	0.0536328	−	0.283649i
$157$	−6.19959	+	10.7380i	−0.494781	+	0.856986i	−0.999982	−	0.00601579i	$-0.998085\pi$
$157$	−6.19959	+	10.7380i	−0.494781	+	0.856986i	0.505201	+	0.863002i	$0.331418\pi$
$158$	−7.60121	+	4.38856i	−0.604720	+	0.349135i
$159$	−13.4041			−1.06301
$160$	1.89707	+	3.28583i	0.149977	+	0.259767i
$161$	12.1065	−	8.82438i	0.954126	−	0.695458i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−4.88449	−	2.82006i	−0.382583	−	0.220884i	0.296359	−	0.955077i	$-0.404228\pi$
$163$	−4.88449	−	2.82006i	−0.382583	−	0.220884i	−0.678941	+	0.734193i	$0.737561\pi$
$164$	3.99747	+	2.30794i	0.312150	+	0.180220i
$165$	−2.11798			−0.164885
$166$	−6.48635			−0.503439
$167$	12.7619	+	7.36806i	0.987542	+	0.570158i	0.904539	−	0.426391i	$-0.140215\pi$
$167$	12.7619	+	7.36806i	0.987542	+	0.570158i	0.0830035	+	0.996549i	$0.473549\pi$
$168$	−1.07240	+	2.41867i	−0.0827378	+	0.186604i
$169$	1.94075	+	12.8543i	0.149288	+	0.988794i
$170$	−11.4842	−	19.8912i	−0.880798	−	1.52559i
$171$	3.65134	−	2.10810i	0.279225	−	0.161210i
$172$	−6.47599	−	11.2167i	−0.493790	−	0.855269i
$173$	−2.97889	+	5.15958i	−0.226480	+	0.392276i	−0.956763	−	0.290870i	$-0.906055\pi$
$173$	−2.97889	+	5.15958i	−0.226480	+	0.392276i	0.730282	+	0.683146i	$0.239389\pi$
$174$		−	3.86822i		−	0.293249i
$175$	−2.63643	−	24.7181i	−0.199296	−	1.86851i
$176$	0.483436	−	0.279112i	0.0364404	−	0.0210388i
$177$	−2.29475	+	1.32487i	−0.172484	+	0.0995835i
$178$	5.45925			0.409188
$179$	−5.74012	−	9.94217i	−0.429036	−	0.743113i	0.567751	−	0.823200i	$-0.307813\pi$
$179$	−5.74012	−	9.94217i	−0.429036	−	0.743113i	−0.996788	+	0.0800871i	$0.974480\pi$
$180$		−	3.79415i		−	0.282799i
$181$	3.98113			0.295915			0.147958	−	0.988994i	$-0.452730\pi$
$181$	3.98113			0.295915			0.147958	+	0.988994i	$0.452730\pi$
$182$	0.768204	−	9.50841i	0.0569430	−	0.704810i
$183$	3.57114			0.263986
$184$		−	5.66237i		−	0.417435i
$185$	17.5472	+	30.3927i	1.29010	+	2.23451i
$186$	6.88537			0.504860
$187$	−2.92655	+	1.68964i	−0.214010	+	0.123559i
$188$	5.18078	−	2.99112i	0.377847	−	0.218150i
$189$	2.13806	−	1.55842i	0.155521	−	0.113359i
$190$		−	15.9969i		−	1.16054i
$191$	−4.79444	+	8.30421i	−0.346913	+	0.600872i	−0.985699	−	0.168513i	$-0.946104\pi$
$191$	−4.79444	+	8.30421i	−0.346913	+	0.600872i	0.638786	+	0.769384i	$0.279437\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−23.9040	+	13.8010i	−1.72065	+	0.993416i	−0.803045	+	0.595919i	$0.796788\pi$
$193$	−23.9040	+	13.8010i	−1.72065	+	0.993416i	−0.917603	+	0.397498i	$0.869879\pi$
$194$	2.68440	+	4.64952i	0.192729	+	0.333816i
$195$	4.51982	+	12.9118i	0.323671	+	0.924630i
$196$	−2.14262	+	6.66402i	−0.153045	+	0.476001i
$197$	5.55690	+	3.20828i	0.395913	+	0.228580i	0.684719	−	0.728807i	$-0.259925\pi$
$197$	5.55690	+	3.20828i	0.395913	+	0.228580i	−0.288806	+	0.957388i	$0.593258\pi$
$198$	−0.558224			−0.0396712
$199$	−0.723756			−0.0513057			−0.0256528	−	0.999671i	$-0.508166\pi$
$199$	−0.723756			−0.0513057			−0.0256528	+	0.999671i	$0.508166\pi$
$200$	−8.13679	−	4.69778i	−0.575358	−	0.332183i
$201$	−10.2680	−	5.92821i	−0.724246	−	0.418144i
$202$	−9.61548	+	5.55150i	−0.676543	+	0.390602i
$203$	−1.08544	−	10.1766i	−0.0761829	−	0.714259i
$204$	−3.02682	−	5.24261i	−0.211920	−	0.367056i
$205$	−17.5133			−1.22318
$206$	−13.4924	+	7.78983i	−0.940058	+	0.542743i
$207$	−2.83118	+	4.90375i	−0.196781	+	0.340835i
$208$	−2.73320	−	2.35152i	−0.189513	−	0.163048i
$209$	−2.35358			−0.162801
$210$	−1.06465	−	9.98175i	−0.0734681	−	0.688806i
$211$	5.19506	−	8.99811i	0.357643	−	0.619455i	−0.629924	−	0.776657i	$-0.716914\pi$
$211$	5.19506	−	8.99811i	0.357643	−	0.619455i	0.987567	+	0.157202i	$0.0502472\pi$
$212$	−6.70203	+	11.6083i	−0.460298	+	0.797259i
$213$	4.58090	+	2.64478i	0.313878	+	0.181217i
$214$			0.123141i			0.00841775i
$215$	42.5580	+	24.5709i	2.90243	+	1.67572i
$216$		−	1.00000i		−	0.0680414i
$217$	18.1142	−	1.93207i	1.22967	−	0.131157i
$218$	−1.59096	+	2.75562i	−0.107753	+	0.186634i
$219$			2.65150i			0.179172i
$220$	−1.05899	+	1.83423i	−0.0713972	+	0.123664i
$221$	16.5458	+	14.2352i	1.11299	+	0.957565i
$222$	4.62481	+	8.01041i	0.310397	+	0.537624i
$223$	−17.5088	−	10.1087i	−1.17248	−	0.676929i	−0.218213	−	0.975901i	$-0.570023\pi$
$223$	−17.5088	−	10.1087i	−1.17248	−	0.676929i	−0.954262	+	0.298972i	$0.903356\pi$
$224$	1.55842	+	2.13806i	0.104127	+	0.142855i
$225$	4.69778	+	8.13679i	0.313185	+	0.542452i
$226$	9.37943	−	5.41522i	0.623911	−	0.360215i
$227$			5.71303i			0.379187i	0.981863	+	0.189594i	$0.0607171\pi$
$227$			5.71303i			0.379187i	−0.981863	+	0.189594i	$0.939283\pi$
$228$		−	4.21620i		−	0.279225i
$229$	13.8628	−	8.00370i	0.916080	−	0.528899i	0.0336977	−	0.999432i	$-0.489272\pi$
$229$	13.8628	−	8.00370i	0.916080	−	0.528899i	0.882382	+	0.470533i	$0.155938\pi$
$230$	10.7419	+	18.6056i	0.708302	+	1.22681i
$231$	−1.46859	+	0.156640i	−0.0966262	+	0.0103062i
$232$	−3.34998	−	1.93411i	−0.219937	−	0.126981i
$233$	4.37032	+	7.56962i	0.286309	+	0.495902i	0.972926	−	0.231118i	$-0.0742382\pi$
$233$	4.37032	+	7.56962i	0.286309	+	0.495902i	−0.686617	+	0.727020i	$0.740905\pi$
$234$	1.19126	+	3.40307i	0.0778752	+	0.222466i
$235$	−11.3488	+	19.6566i	−0.740312	+	1.28226i
$236$			2.64974i			0.172484i
$237$	4.38856	−	7.60121i	0.285068	−	0.493752i
$238$	−9.43414	−	12.9431i	−0.611525	−	0.838974i
$239$		−	20.9144i		−	1.35284i	−0.736516	−	0.676421i	$-0.763530\pi$
$239$		−	20.9144i		−	1.35284i	0.736516	−	0.676421i	$-0.236470\pi$
$240$	−3.28583	−	1.89707i	−0.212099	−	0.122456i
$241$		−	5.04361i		−	0.324887i	−0.986718	−	0.162444i	$-0.948062\pi$
$241$		−	5.04361i		−	0.324887i	0.986718	−	0.162444i	$-0.0519376\pi$
$242$	−9.25641	−	5.34419i	−0.595025	−	0.343538i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.78557	−	3.09270i	0.114309	−	0.197990i
$245$	−5.60185	−	25.9615i	−0.357889	−	1.65862i
$246$	−4.61588			−0.294298
$247$	5.02260	+	14.3480i	0.319580	+	0.912943i
$248$	3.44269	−	5.96291i	0.218611	−	0.378645i
$249$	5.61735	−	3.24318i	0.355985	−	0.205528i
$250$	16.6774			1.05477
$251$	−1.92602	−	3.33596i	−0.121569	−	0.210564i	0.798818	−	0.601573i	$-0.205459\pi$
$251$	−1.92602	−	3.33596i	−0.121569	−	0.210564i	−0.920387	+	0.391010i	$0.872126\pi$
$252$	−0.280604	−	2.63083i	−0.0176764	−	0.165727i
$253$	2.73739	−	1.58043i	0.172098	−	0.0993610i
$254$	−9.59243	−	5.53819i	−0.601883	−	0.347497i
$255$	19.8912	+	11.4842i	1.24564	+	0.719168i
$256$	1.00000			0.0625000
$257$	−23.8615			−1.48844			−0.744219	−	0.667936i	$-0.767178\pi$
$257$	−23.8615			−1.48844			−0.744219	+	0.667936i	$0.767178\pi$
$258$	11.2167	+	6.47599i	0.698324	+	0.403178i
$259$	14.4149	+	19.7763i	0.895695	+	1.22884i
$260$	13.4418	+	2.54160i	0.833626	+	0.157623i
$261$	1.93411	+	3.34998i	0.119718	+	0.207358i
$262$	4.77869	−	2.75898i	0.295228	−	0.170450i
$263$	−4.59247	−	7.95439i	−0.283184	−	0.490489i	0.688983	−	0.724777i	$-0.258057\pi$
$263$	−4.59247	−	7.95439i	−0.283184	−	0.490489i	−0.972167	+	0.234288i	$0.924724\pi$
$264$	−0.279112	+	0.483436i	−0.0171781	+	0.0297534i
$265$		−	50.8570i		−	3.12412i
$266$	−1.18308	−	11.0921i	−0.0725395	−	0.680100i
$267$	−4.72785	+	2.72962i	−0.289340	+	0.167050i
$268$	−10.2680	+	5.92821i	−0.627216	+	0.362123i
$269$	2.78788			0.169980			0.0849899	−	0.996382i	$-0.472914\pi$
$269$	2.78788			0.169980			0.0849899	+	0.996382i	$0.472914\pi$
$270$	1.89707	+	3.28583i	0.115452	+	0.199969i
$271$		−	5.02576i		−	0.305293i	−0.988281	−	0.152647i	$-0.951220\pi$
$271$		−	5.02576i		−	0.305293i	0.988281	−	0.152647i	$-0.0487797\pi$
$272$	−6.05364			−0.367056
$273$	4.08892	+	8.61863i	0.247473	+	0.521623i
$274$	−14.0832			−0.850796
$275$		−	5.24482i		−	0.316275i
$276$	2.83118	+	4.90375i	0.170417	+	0.295171i
$277$	23.3990			1.40591			0.702953	−	0.711236i	$-0.251864\pi$
$277$	23.3990			1.40591			0.702953	+	0.711236i	$0.251864\pi$
$278$	4.48824	−	2.59129i	0.269187	−	0.155415i
$279$	−5.96291	+	3.44269i	−0.356990	+	0.206108i
$280$	−9.17678	−	4.06886i	−0.548417	−	0.243161i
$281$			9.57983i			0.571485i	0.958306	+	0.285742i	$0.0922401\pi$
$281$			9.57983i			0.571485i	−0.958306	+	0.285742i	$0.907760\pi$
$282$	−2.99112	+	5.18078i	−0.178119	+	0.308511i
$283$	4.98675	+	8.63731i	0.296432	+	0.513435i	0.975317	−	0.220810i	$-0.0708700\pi$
$283$	4.98675	+	8.63731i	0.296432	+	0.513435i	−0.678885	+	0.734244i	$0.737537\pi$
$284$	4.58090	−	2.64478i	0.271826	−	0.156939i
$285$	7.99844	+	13.8537i	0.473787	+	0.820623i
$286$	0.373939	−	1.97766i	0.0221115	−	0.116942i
$287$	−12.1436	+	1.29524i	−0.716813	+	0.0764553i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	19.6465			1.15568
$290$	14.6766			0.861840
$291$	−4.64952	−	2.68440i	−0.272560	−	0.157363i
$292$	2.29627	+	1.32575i	0.134379	+	0.0775838i
$293$	−5.93050	+	3.42398i	−0.346464	+	0.200031i	−0.663127	−	0.748507i	$-0.730771\pi$
$293$	−5.93050	+	3.42398i	−0.346464	+	0.200031i	0.316663	+	0.948538i	$0.397438\pi$
$294$	−1.47644	−	6.84252i	−0.0861080	−	0.399064i
$295$	−5.02676	−	8.70660i	−0.292669	−	0.506918i
$296$	9.24963			0.537624
$297$	0.483436	−	0.279112i	0.0280518	−	0.0161957i
$298$	6.76333	−	11.7144i	0.391789	−	0.678599i
$299$	−15.4764	−	13.3151i	−0.895022	−	0.770035i
$300$	9.39555			0.542452
$301$	31.3265	+	13.8898i	1.80563	+	0.800592i
$302$	−5.11685	+	8.86264i	−0.294442	+	0.509988i
$303$	5.55150	−	9.61548i	0.318925	−	0.552395i
$304$	−3.65134	−	2.10810i	−0.209419	−	0.120908i
$305$			13.5494i			0.775838i
$306$	5.24261	+	3.02682i	0.299700	+	0.173032i
$307$			14.7652i			0.842697i	0.906899	+	0.421348i	$0.138443\pi$
$307$			14.7652i			0.842697i	−0.906899	+	0.421348i	$0.861557\pi$
$308$	−0.598641	+	1.35016i	−0.0341108	+	0.0769323i
$309$	7.78983	−	13.4924i	0.443148	−	0.767554i
$310$			26.1241i			1.48375i
$311$	11.7514	−	20.3541i	0.666362	−	1.15417i	−0.312552	−	0.949901i	$-0.601184\pi$
$311$	11.7514	−	20.3541i	0.666362	−	1.15417i	0.978914	−	0.204273i	$-0.0654829\pi$
$312$	3.54278	+	0.669873i	0.200570	+	0.0379241i
$313$	−7.45703	−	12.9160i	−0.421497	−	0.730053i	0.574590	−	0.818442i	$-0.305162\pi$
$313$	−7.45703	−	12.9160i	−0.421497	−	0.730053i	−0.996086	+	0.0883883i	$0.971828\pi$
$314$	−10.7380	−	6.19959i	−0.605981	−	0.349863i
$315$	5.91289	+	8.11212i	0.333154	+	0.457066i
$316$	−4.38856	−	7.60121i	−0.246876	−	0.427602i
$317$	18.4005	−	10.6236i	1.03348	−	0.596679i	0.115499	−	0.993308i	$-0.463153\pi$
$317$	18.4005	−	10.6236i	1.03348	−	0.596679i	0.917979	+	0.396629i	$0.129820\pi$
$318$		−	13.4041i		−	0.751663i
$319$		−	2.15933i		−	0.120899i
$320$	−3.28583	+	1.89707i	−0.183683	+	0.106050i
$321$	−0.0615706	−	0.106643i	−0.00343653	−	0.00595225i
$322$	8.82438	+	12.1065i	0.491763	+	0.674669i
$323$	22.1039	+	12.7617i	1.22989	+	0.710079i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−31.9737	+	11.1926i	−1.77358	+	0.620851i
$326$	2.82006	−	4.88449i	0.156189	−	0.270527i
$327$		−	3.18192i		−	0.175961i
$328$	−2.30794	+	3.99747i	−0.127435	+	0.220723i
$329$	−6.41539	+	14.4691i	−0.353692	+	0.797705i
$330$		−	2.11798i		−	0.116591i
$331$	16.6242	+	9.59800i	0.913750	+	0.527554i	0.881636	−	0.471930i	$-0.156443\pi$
$331$	16.6242	+	9.59800i	0.913750	+	0.527554i	0.0321142	+	0.999484i	$0.489776\pi$
$332$		−	6.48635i		−	0.355985i
$333$	−8.01041	−	4.62481i	−0.438968	−	0.253438i
$334$	−7.36806	+	12.7619i	−0.403162	+	0.698298i
$335$	22.4925	−	38.9582i	1.22890	−	2.12851i
$336$	−2.41867	−	1.07240i	−0.131949	−	0.0585044i
$337$	−33.3743			−1.81801			−0.909007	−	0.416780i	$-0.863158\pi$
$337$	−33.3743			−1.81801			−0.909007	+	0.416780i	$0.863158\pi$
$338$	−12.8543	+	1.94075i	−0.699183	+	0.105563i
$339$	−5.41522	+	9.37943i	−0.294114	+	0.509421i
$340$	19.8912	−	11.4842i	1.07875	−	0.622818i
$341$	3.84358			0.208141
$342$	2.10810	+	3.65134i	0.113993	+	0.197442i
$343$	−5.80431	−	17.5872i	−0.313403	−	0.949620i
$344$	11.2167	−	6.47599i	0.604766	−	0.349162i
$345$	−18.6056	−	10.7419i	−1.00169	−	0.578326i
$346$	−5.15958	−	2.97889i	−0.277381	−	0.160146i
$347$	17.9443			0.963302			0.481651	−	0.876363i	$-0.340037\pi$
$347$	17.9443			0.963302			0.481651	+	0.876363i	$0.340037\pi$
$348$	3.86822			0.207358
$349$	4.49074	+	2.59273i	0.240384	+	0.138786i	0.615353	−	0.788252i	$-0.289013\pi$
$349$	4.49074	+	2.59273i	0.240384	+	0.138786i	−0.374969	+	0.927037i	$0.622347\pi$
$350$	24.7181	−	2.63643i	1.32124	−	0.140923i
$351$	−2.73320	−	2.35152i	−0.145887	−	0.125515i
$352$	0.279112	+	0.483436i	0.0148767	+	0.0257672i
$353$	−4.18422	+	2.41576i	−0.222704	+	0.128578i	−0.607202	−	0.794548i	$-0.707708\pi$
$353$	−4.18422	+	2.41576i	−0.222704	+	0.128578i	0.384498	+	0.923126i	$0.374375\pi$
$354$	−1.32487	−	2.29475i	−0.0704162	−	0.121964i
$355$	−10.0347	+	17.3806i	−0.532586	+	0.922466i
$356$			5.45925i			0.289340i
$357$	14.6417	+	6.49195i	0.774923	+	0.343590i
$358$	9.94217	−	5.74012i	0.525460	−	0.303375i
$359$	9.69017	−	5.59462i	0.511427	−	0.295273i	−0.221993	−	0.975048i	$-0.571256\pi$
$359$	9.69017	−	5.59462i	0.511427	−	0.295273i	0.733420	+	0.679776i	$0.237923\pi$
$360$	3.79415			0.199969
$361$	−0.611827	−	1.05972i	−0.0322014	−	0.0557745i
$362$			3.98113i			0.209244i
$363$	10.6884			0.560995
$364$	9.50841	+	0.768204i	0.498376	+	0.0402648i
$365$	−10.0602			−0.526575
$366$			3.57114i			0.186667i
$367$	7.41471	+	12.8427i	0.387045	+	0.670381i	0.992051	−	0.125840i	$-0.0401626\pi$
$367$	7.41471	+	12.8427i	0.387045	+	0.670381i	−0.605006	+	0.796221i	$0.706829\pi$
$368$	5.66237			0.295171
$369$	3.99747	−	2.30794i	0.208100	−	0.120146i
$370$	−30.3927	+	17.5472i	−1.58004	+	0.912237i
$371$	−3.76124	−	35.2638i	−0.195274	−	1.83081i
$372$			6.88537i			0.356990i
$373$	1.27292	−	2.20476i	0.0659093	−	0.114158i	−0.831188	−	0.555992i	$-0.812339\pi$
$373$	1.27292	−	2.20476i	0.0659093	−	0.114158i	0.897097	+	0.441834i	$0.145672\pi$
$374$	−1.68964	−	2.92655i	−0.0873693	−	0.151328i
$375$	−14.4430	+	8.33868i	−0.745835	+	0.430608i
$376$	2.99112	+	5.18078i	0.154255	+	0.267178i
$377$	−13.1638	+	4.60806i	−0.677972	+	0.237327i
$378$	1.55842	+	2.13806i	0.0801567	+	0.109970i
$379$	−10.1544	−	5.86266i	−0.521598	−	0.301145i	0.215990	−	0.976395i	$-0.430702\pi$
$379$	−10.1544	−	5.86266i	−0.521598	−	0.301145i	−0.737588	+	0.675251i	$0.764035\pi$
$380$	15.9969			0.820623
$381$	11.0764			0.567460
$382$	−8.30421	−	4.79444i	−0.424880	−	0.245305i
$383$	−18.1089	−	10.4552i	−0.925320	−	0.534234i	−0.0399914	−	0.999200i	$-0.512733\pi$
$383$	−18.1089	−	10.4552i	−0.925320	−	0.534234i	−0.885328	+	0.464966i	$0.846066\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	−0.594315	−	5.57205i	−0.0302891	−	0.283978i
$386$	−13.8010	−	23.9040i	−0.702452	−	1.21668i
$387$	−12.9520			−0.658386
$388$	−4.64952	+	2.68440i	−0.236044	+	0.136280i
$389$	−10.9119	+	18.9000i	−0.553258	+	0.958270i	0.444779	+	0.895640i	$0.353282\pi$
$389$	−10.9119	+	18.9000i	−0.553258	+	0.958270i	−0.998037	+	0.0626301i	$0.980051\pi$
$390$	−12.9118	+	4.51982i	−0.653812	+	0.228870i
$391$	−34.2779			−1.73351
$392$	−6.66402	−	2.14262i	−0.336584	−	0.108219i
$393$	−2.75898	+	4.77869i	−0.139172	+	0.241053i
$394$	−3.20828	+	5.55690i	−0.161631	+	0.279953i
$395$	28.8401	+	16.6508i	1.45110	+	0.837795i
$396$		−	0.558224i		−	0.0280518i
$397$	6.52750	+	3.76866i	0.327606	+	0.189143i	0.654778	−	0.755821i	$-0.272762\pi$
$397$	6.52750	+	3.76866i	0.327606	+	0.189143i	−0.327172	+	0.944965i	$0.606096\pi$
$398$		−	0.723756i		−	0.0362786i
$399$	6.57063	+	9.01450i	0.328943	+	0.451289i
$400$	4.69778	−	8.13679i	0.234889	−	0.406839i
$401$		−	30.1856i		−	1.50740i	−0.657220	−	0.753699i	$-0.728268\pi$
$401$		−	30.1856i		−	1.50740i	0.657220	−	0.753699i	$-0.271732\pi$
$402$	5.92821	−	10.2680i	0.295672	−	0.512120i
$403$	−8.20228	−	23.4314i	−0.408585	−	1.16720i
$404$	−5.55150	−	9.61548i	−0.276197	−	0.478388i
$405$	−3.28583	−	1.89707i	−0.163274	−	0.0942663i
$406$	10.1766	−	1.08544i	0.505058	−	0.0538695i
$407$	2.58168	+	4.47160i	0.127969	+	0.221649i
$408$	5.24261	−	3.02682i	0.259548	−	0.149850i
$409$		−	39.7944i		−	1.96771i	−0.178975	−	0.983854i	$-0.557278\pi$
$409$		−	39.7944i		−	1.96771i	0.178975	−	0.983854i	$-0.442722\pi$
$410$		−	17.5133i		−	0.864921i
$411$	12.1964	−	7.04159i	0.601604	−	0.347336i
$412$	−7.78983	−	13.4924i	−0.383777	−	0.664722i
$413$	−4.12943	−	5.66532i	−0.203196	−	0.278772i
$414$	−4.90375	−	2.83118i	−0.241006	−	0.139145i
$415$	12.3051	+	21.3130i	0.604033	+	1.04622i
$416$	2.35152	−	2.73320i	0.115293	−	0.134006i
$417$	−2.59129	+	4.48824i	−0.126896	+	0.219790i
$418$		−	2.35358i		−	0.115117i
$419$	−2.80736	+	4.86248i	−0.137148	+	0.237548i	−0.926416	−	0.376501i	$-0.877127\pi$
$419$	−2.80736	+	4.86248i	−0.137148	+	0.237548i	0.789268	+	0.614049i	$0.210460\pi$
$420$	9.98175	−	1.06465i	0.487060	−	0.0519498i
$421$		−	36.9373i		−	1.80021i	−0.435671	−	0.900106i	$-0.643489\pi$
$421$		−	36.9373i		−	1.80021i	0.435671	−	0.900106i	$-0.356511\pi$
$422$	8.99811	+	5.19506i	0.438021	+	0.252892i
$423$		−	5.98225i		−	0.290867i
$424$	−11.6083	−	6.70203i	−0.563747	−	0.325480i
$425$	−28.4386	+	49.2572i	−1.37948	+	2.38932i
$426$	−2.64478	+	4.58090i	−0.128140	+	0.221945i
$427$	1.00208	+	9.39506i	0.0484939	+	0.454659i
$428$	−0.123141			−0.00595225
$429$	0.664990	+	1.89968i	0.0321060	+	0.0917172i
$430$	−24.5709	+	42.5580i	−1.18491	+	2.05233i
$431$	−15.0587	+	8.69417i	−0.725354	+	0.418784i	−0.816720	−	0.577034i	$-0.804210\pi$
$431$	−15.0587	+	8.69417i	−0.725354	+	0.418784i	0.0913659	+	0.995817i	$0.470877\pi$
$432$	1.00000			0.0481125
$433$	−4.58677	−	7.94452i	−0.220426	−	0.381789i	0.734511	−	0.678596i	$-0.237411\pi$
$433$	−4.58677	−	7.94452i	−0.220426	−	0.381789i	−0.954937	+	0.296807i	$0.904078\pi$
$434$	1.93207	+	18.1142i	0.0927421	+	0.869511i
$435$	−12.7103	+	7.33830i	−0.609413	+	0.351845i
$436$	−2.75562	−	1.59096i	−0.131970	−	0.0761931i
$437$	−20.6752	−	11.9368i	−0.989030	−	0.571016i
$438$	−2.65150			−0.126694
$439$	−26.8841			−1.28311			−0.641555	−	0.767077i	$-0.721710\pi$
$439$	−26.8841			−1.28311			−0.641555	+	0.767077i	$0.721710\pi$
$440$	−1.83423	−	1.05899i	−0.0874433	−	0.0504854i
$441$	4.69990	+	5.18758i	0.223805	+	0.247027i
$442$	−14.2352	+	16.5458i	−0.677101	+	0.787003i
$443$	11.7004	+	20.2657i	0.555902	+	0.962850i	0.997833	+	0.0658012i	$0.0209603\pi$
$443$	11.7004	+	20.2657i	0.555902	+	0.962850i	−0.441931	+	0.897049i	$0.645706\pi$
$444$	−8.01041	+	4.62481i	−0.380157	+	0.219484i
$445$	−10.3566	−	17.9381i	−0.490950	−	0.850350i
$446$	10.1087	−	17.5088i	0.478661	−	0.829065i
$447$			13.5267i			0.639789i
$448$	−2.13806	+	1.55842i	−0.101014	+	0.0736287i
$449$	4.01243	−	2.31658i	0.189358	−	0.109326i	−0.402324	−	0.915497i	$-0.631797\pi$
$449$	4.01243	−	2.31658i	0.189358	−	0.109326i	0.591682	+	0.806171i	$0.298464\pi$
$450$	−8.13679	+	4.69778i	−0.383572	+	0.221455i
$451$	−2.57669			−0.121332
$452$	5.41522	+	9.37943i	0.254710	+	0.441171i
$453$		−	10.2337i		−	0.480821i
$454$	−5.71303			−0.268126
$455$	−32.7003	+	15.5140i	−1.53302	+	0.727306i
$456$	4.21620			0.197442
$457$			6.36150i			0.297578i	0.988869	+	0.148789i	$0.0475376\pi$
$457$			6.36150i			0.297578i	−0.988869	+	0.148789i	$0.952462\pi$
$458$	8.00370	+	13.8628i	0.373988	+	0.647766i
$459$	−6.05364			−0.282560
$460$	−18.6056	+	10.7419i	−0.867489	+	0.500845i
$461$	−0.349653	+	0.201872i	−0.0162850	+	0.00940212i	−0.508120	−	0.861286i	$-0.669659\pi$
$461$	−0.349653	+	0.201872i	−0.0162850	+	0.00940212i	0.491835	+	0.870688i	$0.336326\pi$
$462$	−0.156640	−	1.46859i	−0.00728755	−	0.0683250i
$463$			14.8936i			0.692165i	0.938204	+	0.346082i	$0.112488\pi$
$463$			14.8936i			0.692165i	−0.938204	+	0.346082i	$0.887512\pi$
$464$	1.93411	−	3.34998i	0.0897888	−	0.155519i
$465$	−13.0621	−	22.6242i	−0.605739	−	1.04917i
$466$	−7.56962	+	4.37032i	−0.350656	+	0.202451i
$467$	−3.68247	−	6.37822i	−0.170404	−	0.295149i	0.768157	−	0.640262i	$-0.221174\pi$
$467$	−3.68247	−	6.37822i	−0.170404	−	0.295149i	−0.938561	+	0.345113i	$0.887841\pi$
$468$	−3.40307	+	1.19126i	−0.157307	+	0.0550661i
$469$	12.7149	−	28.6767i	0.587118	−	1.32417i
$470$	−19.6566	−	11.3488i	−0.906693	−	0.523479i
$471$	12.3992			0.571324
$472$	−2.64974			−0.121964
$473$	6.26145	+	3.61505i	0.287902	+	0.166220i
$474$	7.60121	+	4.38856i	0.349135	+	0.201573i
$475$	−34.3063	+	19.8068i	−1.57408	+	0.908797i
$476$	12.9431	−	9.43414i	0.593244	−	0.432413i
$477$	6.70203	+	11.6083i	0.306865	+	0.531506i
$478$	20.9144			0.956603
$479$	3.80675	−	2.19783i	0.173935	−	0.100421i	−0.410505	−	0.911858i	$-0.634648\pi$
$479$	3.80675	−	2.19783i	0.173935	−	0.100421i	0.584440	+	0.811437i	$0.301314\pi$
$480$	1.89707	−	3.28583i	0.0865892	−	0.149977i
$481$	21.7507	−	25.2811i	0.991744	−	1.15272i
$482$	5.04361			0.229730
$483$	−13.6954	−	6.07235i	−0.623161	−	0.276301i
$484$	5.34419	−	9.25641i	0.242918	−	0.420746i
$485$	10.1850	−	17.6410i	0.462478	−	0.801035i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$		−	5.99995i		−	0.271883i	−0.990717	−	0.135942i	$-0.956594\pi$
$487$		−	5.99995i		−	0.271883i	0.990717	−	0.135942i	$-0.0434060\pi$
$488$	3.09270	+	1.78557i	0.140000	+	0.0808290i
$489$			5.64012i			0.255055i
$490$	25.9615	−	5.60185i	1.17282	−	0.253066i
$491$	−20.2497	+	35.0735i	−0.913855	+	1.58284i	−0.105287	+	0.994442i	$0.533576\pi$
$491$	−20.2497	+	35.0735i	−0.913855	+	1.58284i	−0.808569	+	0.588402i	$0.799757\pi$
$492$		−	4.61588i		−	0.208100i
$493$	−11.7084	+	20.2796i	−0.527320	+	0.913345i
$494$	−14.3480	+	5.02260i	−0.645548	+	0.225977i
$495$	1.05899	+	1.83423i	0.0475981	+	0.0824424i
$496$	5.96291	+	3.44269i	0.267742	+	0.154581i
$497$	−5.67255	+	12.7937i	−0.254449	+	0.573875i
$498$	3.24318	+	5.61735i	0.145330	+	0.251719i
$499$	−17.2985	+	9.98729i	−0.774387	+	0.447093i	−0.834437	−	0.551103i	$-0.814207\pi$
$499$	−17.2985	+	9.98729i	−0.774387	+	0.447093i	0.0600503	+	0.998195i	$0.480874\pi$
$500$			16.6774i			0.745835i
$501$		−	14.7361i		−	0.658362i
$502$	3.33596	−	1.92602i	0.148891	−	0.0859623i
$503$	9.61568	+	16.6548i	0.428742	+	0.742603i	0.996762	−	0.0804120i	$-0.0256236\pi$
$503$	9.61568	+	16.6548i	0.428742	+	0.742603i	−0.568020	+	0.823015i	$0.692290\pi$
$504$	2.63083	−	0.280604i	0.117186	−	0.0124991i
$505$	36.4825	+	21.0632i	1.62345	+	0.937300i
$506$	1.58043	+	2.73739i	0.0702589	+	0.121692i
$507$	10.1618	−	8.10789i	0.451301	−	0.360084i
$508$	5.53819	−	9.59243i	0.245718	−	0.425595i
$509$			22.2669i			0.986964i	0.869756	+	0.493482i	$0.164276\pi$
$509$			22.2669i			0.986964i	−0.869756	+	0.493482i	$0.835724\pi$
$510$	−11.4842	+	19.8912i	−0.508529	+	0.880798i
$511$	−6.97566	+	0.744024i	−0.308585	+	0.0329137i
$512$			1.00000i			0.0441942i
$513$	−3.65134	−	2.10810i	−0.161210	−	0.0930749i
$514$		−	23.8615i		−	1.05248i
$515$	51.1921	+	29.5557i	2.25579	+	1.30238i
$516$	−6.47599	+	11.2167i	−0.285090	+	0.493790i
$517$	−1.66972	+	2.89203i	−0.0734340	+	0.127191i
$518$	−19.7763	+	14.4149i	−0.868920	+	0.633352i
$519$	5.95777			0.261517
$520$	−2.54160	+	13.4418i	−0.111456	+	0.589463i
$521$	19.4060	−	33.6121i	0.850192	−	1.47257i	−0.0308437	−	0.999524i	$-0.509819\pi$
$521$	19.4060	−	33.6121i	0.850192	−	1.47257i	0.881035	−	0.473051i	$-0.156847\pi$
$522$	−3.34998	+	1.93411i	−0.146625	+	0.0846537i
$523$	6.42610			0.280994			0.140497	−	0.990081i	$-0.455130\pi$
$523$	6.42610			0.280994			0.140497	+	0.990081i	$0.455130\pi$
$524$	2.75898	+	4.77869i	0.120526	+	0.208758i
$525$	−20.0883	+	14.6423i	−0.876724	+	0.639041i
$526$	7.95439	−	4.59247i	0.346828	−	0.200241i
$527$	−36.0973	−	20.8408i	−1.57242	−	0.907839i
$528$	−0.483436	−	0.279112i	−0.0210388	−	0.0121468i
$529$	9.06241			0.394018
$530$	50.8570			2.20909
$531$	2.29475	+	1.32487i	0.0995835	+	0.0574945i
$532$	11.0921	−	1.18308i	0.480904	−	0.0512932i
$533$	5.49872	+	15.7082i	0.238176	+	0.680396i
$534$	−2.72962	−	4.72785i	−0.118122	−	0.204594i
$535$	0.404620	−	0.233608i	0.0174933	−	0.0100997i
$536$	−5.92821	−	10.2680i	−0.256060	−	0.443509i
$537$	−5.74012	+	9.94217i	−0.247704	+	0.429036i
$538$			2.78788i			0.120194i
$539$	−0.824186	−	3.81966i	−0.0355002	−	0.164524i
$540$	−3.28583	+	1.89707i	−0.141400	+	0.0816370i
$541$	−23.7062	+	13.6868i	−1.01921	+	0.588441i	−0.913875	−	0.405996i	$-0.866925\pi$
$541$	−23.7062	+	13.6868i	−1.01921	+	0.588441i	−0.105335	+	0.994437i	$0.533591\pi$
$542$	5.02576			0.215875
$543$	−1.99057	−	3.44776i	−0.0854234	−	0.147958i
$544$		−	6.05364i		−	0.259548i
$545$	12.0727			0.517136
$546$	−8.61863	+	4.08892i	−0.368843	+	0.174990i
$547$	7.91494			0.338418			0.169209	−	0.985580i	$-0.445879\pi$
$547$	7.91494			0.338418			0.169209	+	0.985580i	$0.445879\pi$
$548$		−	14.0832i		−	0.601604i
$549$	−1.78557	−	3.09270i	−0.0762063	−	0.131993i
$550$	5.24482			0.223640
$551$	−14.1242	+	8.15460i	−0.601710	+	0.347398i
$552$	−4.90375	+	2.83118i	−0.208718	+	0.120503i
$553$	21.2289	+	9.41262i	0.902746	+	0.400265i
$554$			23.3990i			0.994126i
$555$	17.5472	−	30.3927i	0.744838	−	1.29010i
$556$	2.59129	+	4.48824i	0.109895	+	0.190344i
$557$	4.32650	−	2.49791i	0.183320	−	0.105840i	−0.405532	−	0.914081i	$-0.632914\pi$
$557$	4.32650	−	2.49791i	0.183320	−	0.105840i	0.588852	+	0.808241i	$0.299580\pi$
$558$	−3.44269	−	5.96291i	−0.145741	−	0.252430i
$559$	8.67619	−	45.8860i	0.366964	−	1.94077i
$560$	4.06886	−	9.17678i	0.171941	−	0.387790i
$561$	2.92655	+	1.68964i	0.123559	+	0.0713368i
$562$	−9.57983			−0.404101
$563$	−12.2189			−0.514966			−0.257483	−	0.966283i	$-0.582893\pi$
$563$	−12.2189			−0.514966			−0.257483	+	0.966283i	$0.582893\pi$
$564$	−5.18078	−	2.99112i	−0.218150	−	0.125949i
$565$	−35.5870	−	20.5461i	−1.49715	−	0.864382i
$566$	−8.63731	+	4.98675i	−0.363053	+	0.209609i
$567$	−2.41867	−	1.07240i	−0.101574	−	0.0450367i
$568$	2.64478	+	4.58090i	0.110973	+	0.192210i
$569$	−4.53901			−0.190285			−0.0951425	−	0.995464i	$-0.530331\pi$
$569$	−4.53901			−0.190285			−0.0951425	+	0.995464i	$0.530331\pi$
$570$	−13.8537	+	7.99844i	−0.580268	+	0.335018i
$571$	−12.8965	+	22.3373i	−0.539700	+	0.934789i	0.459219	+	0.888323i	$0.348129\pi$
$571$	−12.8965	+	22.3373i	−0.539700	+	0.934789i	−0.998920	+	0.0464657i	$0.985204\pi$
$572$	1.97766	+	0.373939i	0.0826902	+	0.0156352i
$573$	9.58888			0.400581
$574$	−1.29524	−	12.1436i	−0.0540621	−	0.506863i
$575$	26.6005	−	46.0735i	1.10932	−	1.92140i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	23.0392	+	13.3017i	0.959134	+	0.553756i	0.895906	−	0.444243i	$-0.146527\pi$
$577$	23.0392	+	13.3017i	0.959134	+	0.553756i	0.0632275	+	0.997999i	$0.479861\pi$
$578$			19.6465i			0.817189i
$579$	23.9040	+	13.8010i	0.993416	+	0.573549i
$580$			14.6766i			0.609413i
$581$	10.1085	+	13.8682i	0.419371	+	0.575351i
$582$	2.68440	−	4.64952i	0.111272	−	0.192729i
$583$		−	7.48247i		−	0.309892i
$584$	−1.32575	+	2.29627i	−0.0548600	+	0.0950203i
$585$	8.92200	−	10.3702i	0.368879	−	0.428753i
$586$	−3.42398	−	5.93050i	−0.141443	−	0.244987i
$587$	19.6109	+	11.3223i	0.809427	+	0.467323i	0.846757	−	0.531980i	$-0.178552\pi$
$587$	19.6109	+	11.3223i	0.809427	+	0.467323i	−0.0373295	+	0.999303i	$0.511885\pi$
$588$	6.84252	−	1.47644i	0.282181	−	0.0608875i
$589$	−14.5151	−	25.1408i	−0.598083	−	1.03591i
$590$	8.70660	−	5.02676i	0.358445	−	0.206948i
$591$		−	6.41656i		−	0.263942i
$592$			9.24963i			0.380157i
$593$	−11.3158	+	6.53316i	−0.464682	+	0.268285i	−0.714011	−	0.700134i	$-0.753123\pi$
$593$	−11.3158	+	6.53316i	−0.464682	+	0.268285i	0.249329	+	0.968419i	$0.419790\pi$
$594$	0.279112	+	0.483436i	0.0114521	+	0.0198356i
$595$	−24.6314	+	55.5529i	−1.00979	+	2.27745i
$596$	11.7144	+	6.76333i	0.479842	+	0.277037i
$597$	0.361878	+	0.626791i	0.0148107	+	0.0256528i
$598$	13.3151	−	15.4764i	0.544497	−	0.632876i
$599$	15.1687	−	26.2730i	0.619777	−	1.07348i	−0.369749	−	0.929131i	$-0.620556\pi$
$599$	15.1687	−	26.2730i	0.619777	−	1.07348i	0.989526	−	0.144353i	$-0.0461102\pi$
$600$			9.39555i			0.383572i
$601$	−6.57930	+	11.3957i	−0.268375	+	0.464839i	−0.968442	−	0.249238i	$-0.919820\pi$
$601$	−6.57930	+	11.3957i	−0.268375	+	0.464839i	0.700067	+	0.714077i	$0.253153\pi$
$602$	−13.8898	+	31.3265i	−0.566104	+	1.27677i
$603$			11.8564i			0.482831i
$604$	−8.86264	−	5.11685i	−0.360616	−	0.208202i
$605$			40.5533i			1.64873i
$606$	9.61548	+	5.55150i	0.390602	+	0.225514i
$607$	−9.92834	+	17.1964i	−0.402979	+	0.697980i	−0.994084	−	0.108615i	$-0.965359\pi$
$607$	−9.92834	+	17.1964i	−0.402979	+	0.697980i	0.591105	+	0.806595i	$0.298692\pi$
$608$	2.10810	−	3.65134i	0.0854948	−	0.148081i
$609$	−8.27050	+	6.02833i	−0.335138	+	0.244280i
$610$	−13.5494			−0.548601
$611$	21.1938	+	4.00735i	0.857408	+	0.162120i
$612$	−3.02682	+	5.24261i	−0.122352	+	0.211920i
$613$	8.46072	−	4.88480i	0.341725	−	0.197295i	−0.319309	−	0.947651i	$-0.603451\pi$
$613$	8.46072	−	4.88480i	0.341725	−	0.197295i	0.661035	+	0.750355i	$0.270118\pi$
$614$	−14.7652			−0.595877
$615$	8.75666	+	15.1670i	0.353103	+	0.611592i
$616$	−1.35016	−	0.598641i	−0.0543994	−	0.0241199i
$617$	−24.8056	+	14.3215i	−0.998637	+	0.576563i	−0.907845	−	0.419306i	$-0.862273\pi$
$617$	−24.8056	+	14.3215i	−0.998637	+	0.576563i	−0.0907924	+	0.995870i	$0.528940\pi$
$618$	13.4924	+	7.78983i	0.542743	+	0.313353i
$619$	−1.25500	−	0.724575i	−0.0504427	−	0.0291231i	0.474567	−	0.880220i	$-0.342605\pi$
$619$	−1.25500	−	0.724575i	−0.0504427	−	0.0291231i	−0.525009	+	0.851097i	$0.675938\pi$
$620$	−26.1241			−1.04917
$621$	5.66237			0.227223
$622$	20.3541	+	11.7514i	0.816124	+	0.471189i
$623$	−8.50783	−	11.6722i	−0.340859	−	0.467637i
$624$	−0.669873	+	3.54278i	−0.0268164	+	0.141825i
$625$	−8.14932	−	14.1150i	−0.325973	−	0.564601i
$626$	12.9160	−	7.45703i	0.516226	−	0.298043i
$627$	1.17679	+	2.03826i	0.0469965	+	0.0814004i
$628$	6.19959	−	10.7380i	0.247391	−	0.428493i
$629$		−	55.9939i		−	2.23262i
$630$	−8.11212	+	5.91289i	−0.323195	+	0.235575i
$631$	−18.2911	+	10.5604i	−0.728159	+	0.420403i	−0.817748	−	0.575576i	$-0.804778\pi$
$631$	−18.2911	+	10.5604i	−0.728159	+	0.420403i	0.0895893	+	0.995979i	$0.471445\pi$
$632$	7.60121	−	4.38856i	0.302360	−	0.174568i
$633$	−10.3901			−0.412970
$634$	10.6236	+	18.4005i	0.421915	+	0.730779i
$635$			42.0254i			1.66773i
$636$	13.4041			0.531506
$637$	−21.5268	+	13.1757i	−0.852921	+	0.522039i
$638$	2.15933			0.0854888
$639$		−	5.28956i		−	0.209252i
$640$	−1.89707	−	3.28583i	−0.0749884	−	0.129884i
$641$	26.7729			1.05747			0.528734	−	0.848788i	$-0.322667\pi$
$641$	26.7729			1.05747			0.528734	+	0.848788i	$0.322667\pi$
$642$	0.106643	−	0.0615706i	0.00420888	−	0.00243000i
$643$	−5.15867	+	2.97836i	−0.203438	+	0.117455i	−0.598258	−	0.801303i	$-0.704140\pi$
$643$	−5.15867	+	2.97836i	−0.203438	+	0.117455i	0.394820	+	0.918759i	$0.370807\pi$
$644$	−12.1065	+	8.82438i	−0.477063	+	0.347729i
$645$		−	49.1417i		−	1.93495i
$646$	−12.7617	+	22.1039i	−0.502102	+	0.869665i
$647$	−10.2833	−	17.8112i	−0.404279	−	0.700232i	0.589958	−	0.807434i	$-0.299144\pi$
$647$	−10.2833	−	17.8112i	−0.404279	−	0.700232i	−0.994237	+	0.107202i	$0.965811\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−0.739575	−	1.28098i	−0.0290309	−	0.0502829i
$650$	−11.1926	−	31.9737i	−0.439008	−	1.25411i
$651$	−10.7303	−	14.7214i	−0.420555	−	0.576976i
$652$	4.88449	+	2.82006i	0.191291	+	0.110442i
$653$	−21.5768			−0.844366			−0.422183	−	0.906511i	$-0.638736\pi$
$653$	−21.5768			−0.844366			−0.422183	+	0.906511i	$0.638736\pi$
$654$	3.18192			0.124423
$655$	−18.1310	−	10.4680i	−0.708439	−	0.409017i
$656$	−3.99747	−	2.30794i	−0.156075	−	0.0901099i
$657$	2.29627	−	1.32575i	0.0895860	−	0.0517225i
$658$	−14.4691	−	6.41539i	−0.564063	−	0.250098i
$659$	−25.6135	−	44.3638i	−0.997759	−	1.72817i	−0.556830	−	0.830627i	$-0.687982\pi$
$659$	−25.6135	−	44.3638i	−0.997759	−	1.72817i	−0.440929	−	0.897542i	$-0.645351\pi$
$660$	2.11798			0.0824424
$661$	−0.243475	+	0.140570i	−0.00947006	+	0.00546754i	−0.504728	−	0.863279i	$-0.668407\pi$
$661$	−0.243475	+	0.140570i	−0.00947006	+	0.00546754i	0.495257	+	0.868746i	$0.335074\pi$
$662$	−9.59800	+	16.6242i	−0.373037	+	0.646119i
$663$	4.05517	−	21.4467i	0.157490	−	0.832921i
$664$	6.48635			0.251719
$665$	−34.2023	+	24.9299i	−1.32631	+	0.966742i
$666$	4.62481	−	8.01041i	0.179208	−	0.310397i
$667$	10.9516	−	18.9688i	0.424049	−	0.734475i
$668$	−12.7619	−	7.36806i	−0.493771	−	0.285079i
$669$			20.2174i			0.781650i
$670$	38.9582	+	22.4925i	1.50509	+	0.868961i
$671$			1.99350i			0.0769580i
$672$	1.07240	−	2.41867i	0.0413689	−	0.0933021i
$673$	−9.15181	+	15.8514i	−0.352777	+	0.611027i	−0.986735	−	0.162340i	$-0.948096\pi$
$673$	−9.15181	+	15.8514i	−0.352777	+	0.611027i	0.633958	+	0.773367i	$0.281429\pi$
$674$		−	33.3743i		−	1.28553i
$675$	4.69778	−	8.13679i	0.180817	−	0.313185i
$676$	−1.94075	−	12.8543i	−0.0746441	−	0.494397i
$677$	−8.16938	−	14.1498i	−0.313975	−	0.543820i	0.665244	−	0.746626i	$-0.268327\pi$
$677$	−8.16938	−	14.1498i	−0.313975	−	0.543820i	−0.979219	+	0.202806i	$0.934994\pi$
$678$	−9.37943	−	5.41522i	−0.360215	−	0.207970i
$679$	5.75753	−	12.9854i	0.220954	−	0.498332i
$680$	11.4842	+	19.8912i	0.440399	+	0.762793i
$681$	4.94763	−	2.85652i	0.189594	−	0.109462i
$682$			3.84358i			0.147178i
$683$			13.7001i			0.524219i	0.965038	+	0.262110i	$0.0844182\pi$
$683$			13.7001i			0.524219i	−0.965038	+	0.262110i	$0.915582\pi$
$684$	−3.65134	+	2.10810i	−0.139612	+	0.0806052i
$685$	26.7168	+	46.2749i	1.02080	+	1.76807i
$686$	17.5872	−	5.80431i	0.671483	−	0.221610i
$687$	−13.8628	−	8.00370i	−0.528899	−	0.305360i
$688$	6.47599	+	11.2167i	0.246895	+	0.427634i
$689$	−45.6150	+	15.9677i	−1.73779	+	0.608323i
$690$	10.7419	−	18.6056i	0.408938	−	0.708302i
$691$		−	21.1756i		−	0.805556i	−0.915298	−	0.402778i	$-0.868045\pi$
$691$		−	21.1756i		−	0.805556i	0.915298	−	0.402778i	$-0.131955\pi$
$692$	2.97889	−	5.15958i	0.113240	−	0.196138i
$693$	0.869950	+	1.19352i	0.0330467	+	0.0453380i
$694$			17.9443i			0.681157i
$695$	−17.0291	−	9.83173i	−0.645949	−	0.372939i
$696$			3.86822i			0.146625i
$697$	24.1992	+	13.9714i	0.916611	+	0.529206i
$698$	−2.59273	+	4.49074i	−0.0981362	+	0.169977i
$699$	4.37032	−	7.56962i	0.165301	−	0.286309i
$700$	2.63643	+	24.7181i	0.0996478	+	0.934256i
$701$	−15.2363			−0.575466			−0.287733	−	0.957711i	$-0.592902\pi$
$701$	−15.2363			−0.575466			−0.287733	+	0.957711i	$0.592902\pi$
$702$	2.35152	−	2.73320i	0.0887522	−	0.103158i
$703$	19.4991	−	33.7735i	0.735424	−	1.27379i
$704$	−0.483436	+	0.279112i	−0.0182202	+	0.0105194i
$705$	22.6975			0.854838
$706$	−2.41576	−	4.18422i	−0.0909184	−	0.157475i
$707$	26.8545	+	11.9069i	1.00997	+	0.447805i
$708$	2.29475	−	1.32487i	0.0862418	−	0.0497917i
$709$	19.5969	+	11.3143i	0.735976	+	0.424916i	0.820604	−	0.571497i	$-0.193637\pi$
$709$	19.5969	+	11.3143i	0.735976	+	0.424916i	−0.0846284	+	0.996413i	$0.526970\pi$
$710$	−17.3806	−	10.0347i	−0.652282	−	0.376595i
$711$	−8.77712			−0.329168
$712$	−5.45925			−0.204594
$713$	33.7642	+	19.4938i	1.26448	+	0.730047i
$714$	−6.49195	+	14.6417i	−0.242955	+	0.547953i
$715$	−7.20765	+	2.52307i	−0.269551	+	0.0943575i
$716$	5.74012	+	9.94217i	0.214518	+	0.371557i
$717$	−18.1124	+	10.4572i	−0.676421	+	0.390532i
$718$	5.59462	+	9.69017i	0.208789	+	0.361634i
$719$	6.85326	−	11.8702i	0.255583	−	0.442683i	−0.709470	−	0.704735i	$-0.751066\pi$
$719$	6.85326	−	11.8702i	0.255583	−	0.442683i	0.965054	+	0.262052i	$0.0843991\pi$
$720$			3.79415i			0.141400i
$721$	37.6820	+	16.7077i	1.40335	+	0.622227i
$722$	1.05972	−	0.611827i	0.0394385	−	0.0227698i
$723$	−4.36789	+	2.52180i	−0.162444	+	0.0937868i
$724$	−3.98113			−0.147958
$725$	−18.1720	−	31.4749i	−0.674892	−	1.16895i
$726$			10.6884i			0.396683i
$727$	−23.2975			−0.864057			−0.432028	−	0.901860i	$-0.642202\pi$
$727$	−23.2975			−0.864057			−0.432028	+	0.901860i	$0.642202\pi$
$728$	−0.768204	+	9.50841i	−0.0284715	+	0.352405i
$729$	1.00000			0.0370370
$730$		−	10.0602i		−	0.372345i
$731$	−39.2033	−	67.9021i	−1.44999	−	2.51145i
$732$	−3.57114			−0.131993
$733$	1.12669	−	0.650493i	0.0416152	−	0.0240265i	−0.479048	−	0.877789i	$-0.659018\pi$
$733$	1.12669	−	0.650493i	0.0416152	−	0.0240265i	0.520663	+	0.853762i	$0.325685\pi$
$734$	−12.8427	+	7.41471i	−0.474031	+	0.273682i
$735$	−19.6824	+	17.8321i	−0.725997	+	0.657747i
$736$			5.66237i			0.208718i
$737$	3.30927	−	5.73182i	0.121898	−	0.211134i
$738$	2.30794	+	3.99747i	0.0849564	+	0.147149i
$739$	38.2421	−	22.0791i	1.40676	−	0.812192i	0.411684	−	0.911327i	$-0.364941\pi$
$739$	38.2421	−	22.0791i	1.40676	−	0.812192i	0.995074	+	0.0991348i	$0.0316075\pi$
$740$	−17.5472	−	30.3927i	−0.645049	−	1.11726i
$741$	9.91446	−	11.5237i	0.364217	−	0.423334i
$742$	35.2638	−	3.76124i	1.29458	−	0.138079i
$743$	−29.9809	−	17.3095i	−1.09989	−	0.635024i	−0.163700	−	0.986510i	$-0.552343\pi$
$743$	−29.9809	−	17.3095i	−1.09989	−	0.635024i	−0.936193	+	0.351487i	$0.885676\pi$
$744$	−6.88537			−0.252430
$745$	−51.3221			−1.88030
$746$	2.20476	+	1.27292i	0.0807221	+	0.0466049i
$747$	−5.61735	−	3.24318i	−0.205528	−	0.118662i
$748$	2.92655	−	1.68964i	0.107005	−	0.0617794i
$749$	0.263283	−	0.191906i	0.00962017	−	0.00701210i
$750$	−8.33868	−	14.4430i	−0.304486	−	0.527385i
$751$	6.63143			0.241984			0.120992	−	0.992653i	$-0.461392\pi$
$751$	6.63143			0.241984			0.120992	+	0.992653i	$0.461392\pi$
$752$	−5.18078	+	2.99112i	−0.188924	+	0.109075i
$753$	−1.92602	+	3.33596i	−0.0701879	+	0.121569i
$754$	−4.60806	−	13.1638i	−0.167816	−	0.479399i
$755$	38.8282			1.41310
$756$	−2.13806	+	1.55842i	−0.0777606	+	0.0566794i
$757$	18.8551	−	32.6580i	0.685300	−	1.18697i	−0.288043	−	0.957617i	$-0.593005\pi$
$757$	18.8551	−	32.6580i	0.685300	−	1.18697i	0.973343	−	0.229356i	$-0.0736621\pi$
$758$	5.86266	−	10.1544i	0.212941	−	0.368825i
$759$	−2.73739	−	1.58043i	−0.0993610	−	0.0573661i
$760$			15.9969i			0.580268i
$761$	0.856887	+	0.494724i	0.0310621	+	0.0179337i	0.515451	−	0.856919i	$-0.327625\pi$
$761$	0.856887	+	0.494724i	0.0310621	+	0.0179337i	−0.484389	+	0.874853i	$0.660958\pi$
$762$			11.0764i			0.401255i
$763$	8.37108	−	0.892860i	0.303054	−	0.0323237i
$764$	4.79444	−	8.30421i	0.173457	−	0.300436i
$765$		−	22.9684i		−	0.830424i
$766$	10.4552	−	18.1089i	0.377760	−	0.654300i
$767$	−6.23092	+	7.24228i	−0.224985	+	0.261503i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	30.7190	+	17.7357i	1.10776	+	0.639564i	0.938248	−	0.345965i	$-0.112448\pi$
$769$	30.7190	+	17.7357i	1.10776	+	0.639564i	0.169510	+	0.985529i	$0.445782\pi$
$770$	5.57205	−	0.594315i	0.200803	−	0.0214176i
$771$	11.9307	+	20.6646i	0.429675	+	0.744219i
$772$	23.9040	−	13.8010i	0.860324	−	0.496708i
$773$			0.835263i			0.0300423i	0.999887	+	0.0150212i	$0.00478156\pi$
$773$			0.835263i			0.0300423i	−0.999887	+	0.0150212i	$0.995218\pi$
$774$		−	12.9520i		−	0.465549i
$775$	56.0248	−	32.3459i	2.01247	−	1.16190i
$776$	−2.68440	−	4.64952i	−0.0963645	−	0.166908i
$777$	9.91934	−	22.3718i	0.355854	−	0.802583i
$778$	−18.9000	−	10.9119i	−0.677600	−	0.391212i
$779$	9.73073	+	16.8541i	0.348640	+	0.603862i
$780$	−4.51982	−	12.9118i	−0.161836	−	0.462315i
$781$	−1.47638	+	2.55716i	−0.0528290	+	0.0915025i
$782$		−	34.2779i		−	1.22578i
$783$	1.93411	−	3.34998i	0.0691195	−	0.119718i
$784$	2.14262	−	6.66402i	0.0765223	−	0.238001i
$785$			47.0443i			1.67908i
$786$	−4.77869	−	2.75898i	−0.170450	−	0.0984095i
$787$		−	33.2200i		−	1.18416i	−0.805878	−	0.592082i	$-0.798306\pi$
$787$		−	33.2200i		−	1.18416i	0.805878	−	0.592082i	$-0.201694\pi$
$788$	−5.55690	−	3.20828i	−0.197957	−	0.114290i
$789$	−4.59247	+	7.95439i	−0.163496	+	0.283184i
$790$	−16.6508	+	28.8401i	−0.592411	+	1.02609i
$791$	−26.1952	−	11.6146i	−0.931395	−	0.412968i
$792$	0.558224			0.0198356
$793$	12.1529	−	4.25416i	0.431560	−	0.151070i
$794$	−3.76866	+	6.52750i	−0.133745	+	0.231652i
$795$	−44.0435	+	25.4285i	−1.56206	+	0.901856i
$796$	0.723756			0.0256528
$797$	23.0760	+	39.9688i	0.817393	+	1.41577i	0.907597	+	0.419843i	$0.137915\pi$
$797$	23.0760	+	39.9688i	0.817393	+	1.41577i	−0.0902041	+	0.995923i	$0.528752\pi$
$798$	−9.01450	+	6.57063i	−0.319110	+	0.232598i
$799$	31.3626	−	18.1072i	1.10953	−	0.640586i
$800$	8.13679	+	4.69778i	0.287679	+	0.166091i
$801$	4.72785	+	2.72962i	0.167050	+	0.0964465i
$802$	30.1856			1.06589
$803$	−1.48013			−0.0522327
$804$	10.2680	+	5.92821i	0.362123	+	0.209072i
$805$	23.0394	−	51.9623i	0.812031	−	1.83143i
$806$	23.4314	−	8.20228i	0.825337	−	0.288913i
$807$	−1.39394	−	2.41437i	−0.0490690	−	0.0849899i
$808$	9.61548	−	5.55150i	0.338271	−	0.195301i
$809$	−24.5265	−	42.4811i	−0.862306	−	1.49356i	−0.869698	−	0.493584i	$-0.835686\pi$
$809$	−24.5265	−	42.4811i	−0.862306	−	1.49356i	0.00739247	−	0.999973i	$-0.497647\pi$
$810$	1.89707	−	3.28583i	0.0666564	−	0.115452i
$811$			8.16725i			0.286791i	0.989665	+	0.143395i	$0.0458021\pi$
$811$			8.16725i			0.286791i	−0.989665	+	0.143395i	$0.954198\pi$
$812$	1.08544	+	10.1766i	0.0380915	+	0.357130i
$813$	−4.35244	+	2.51288i	−0.152647	+	0.0881306i
$814$	−4.47160	+	2.58168i	−0.156730	+	0.0904879i
$815$	−21.3994			−0.749590
$816$	3.02682	+	5.24261i	0.105960	+	0.183528i
$817$		−	54.6082i		−	1.91050i
$818$	39.7944			1.39138
$819$	5.41949	−	7.85042i	0.189372	−	0.274316i
$820$	17.5133			0.611592
$821$		−	18.5766i		−	0.648327i	−0.946001	−	0.324164i	$-0.894917\pi$
$821$		−	18.5766i		−	0.648327i	0.946001	−	0.324164i	$-0.105083\pi$
$822$	7.04159	+	12.1964i	0.245604	+	0.425398i
$823$	29.6669			1.03412			0.517062	−	0.855948i	$-0.327026\pi$
$823$	29.6669			1.03412			0.517062	+	0.855948i	$0.327026\pi$
$824$	13.4924	−	7.78983i	0.470029	−	0.271371i
$825$	−4.54215	+	2.62241i	−0.158137	+	0.0913006i
$826$	5.66532	−	4.12943i	0.197122	−	0.143681i
$827$		−	1.95284i		−	0.0679070i	−0.999423	−	0.0339535i	$-0.989190\pi$
$827$		−	1.95284i		−	0.0679070i	0.999423	−	0.0339535i	$-0.0108098\pi$
$828$	2.83118	−	4.90375i	0.0983904	−	0.170417i
$829$	14.8412	+	25.7058i	0.515457	+	0.892798i	0.999839	+	0.0179414i	$0.00571123\pi$
$829$	14.8412	+	25.7058i	0.515457	+	0.892798i	−0.484382	+	0.874857i	$0.660955\pi$
$830$	−21.3130	+	12.3051i	−0.739787	+	0.427116i
$831$	−11.6995	−	20.2641i	−0.405850	−	0.702953i
$832$	2.73320	+	2.35152i	0.0947566	+	0.0815241i
$833$	−12.9707	+	40.3416i	−0.449407	+	1.39775i
$834$	−4.48824	−	2.59129i	−0.155415	−	0.0897290i
$835$	55.9110			1.93488
$836$	2.35358			0.0814004
$837$	5.96291	+	3.44269i	0.206108	+	0.118997i
$838$	−4.86248	−	2.80736i	−0.167972	−	0.0969785i
$839$	48.0514	−	27.7425i	1.65892	−	0.957776i	0.685701	−	0.727883i	$-0.259496\pi$
$839$	48.0514	−	27.7425i	1.65892	−	0.957776i	0.973216	−	0.229893i	$-0.0738375\pi$
$840$	1.06465	+	9.98175i	0.0367341	+	0.344403i
$841$	7.01843	+	12.1563i	0.242015	+	0.419182i
$842$	36.9373			1.27294
$843$	8.29638	−	4.78991i	0.285742	−	0.164973i
$844$	−5.19506	+	8.99811i	−0.178821	+	0.309728i
$845$	30.7625	+	38.5553i	1.05826	+	1.32634i
$846$	5.98225			0.205674
$847$	2.99921	+	28.1193i	0.103054	+	0.966191i
$848$	6.70203	−	11.6083i	0.230149	−	0.398629i
$849$	4.98675	−	8.63731i	0.171145	−	0.296432i
$850$	−49.2572	−	28.4386i	−1.68951	−	0.975437i
$851$			52.3748i			1.79539i
$852$	−4.58090	−	2.64478i	−0.156939	−	0.0906087i
$853$		−	40.5339i		−	1.38785i	−0.720045	−	0.693927i	$-0.755879\pi$
$853$		−	40.5339i		−	1.38785i	0.720045	−	0.693927i	$-0.244121\pi$
$854$	−9.39506	+	1.00208i	−0.321492	+	0.0342904i
$855$	7.99844	−	13.8537i	0.273541	−	0.473787i
$856$		−	0.123141i		−	0.00420888i
$857$	−18.7340	+	32.4483i	−0.639943	+	1.10841i	0.345502	+	0.938418i	$0.387709\pi$
$857$	−18.7340	+	32.4483i	−0.639943	+	1.10841i	−0.985445	+	0.169995i	$0.945625\pi$
$858$	−1.89968	+	0.664990i	−0.0648538	+	0.0227024i
$859$	28.2816	+	48.9852i	0.964957	+	1.67135i	0.709730	+	0.704473i	$0.248817\pi$
$859$	28.2816	+	48.9852i	0.964957	+	1.67135i	0.255227	+	0.966881i	$0.417850\pi$
$860$	−42.5580	−	24.5709i	−1.45122	−	0.837860i
$861$	7.19350	+	9.86904i	0.245154	+	0.336336i
$862$	−8.69417	−	15.0587i	−0.296125	−	0.512903i
$863$	13.2208	−	7.63301i	0.450040	−	0.259831i	−0.257807	−	0.966196i	$-0.583000\pi$
$863$	13.2208	−	7.63301i	0.450040	−	0.259831i	0.707847	+	0.706366i	$0.249667\pi$
$864$			1.00000i			0.0340207i
$865$			22.6047i			0.768581i
$866$	7.94452	−	4.58677i	0.269966	−	0.155865i
$867$	−9.82327	−	17.0144i	−0.333616	−	0.577840i
$868$	−18.1142	+	1.93207i	−0.614837	+	0.0655786i
$869$	4.24318	+	2.44980i	0.143940	+	0.0831037i
$870$	−7.33830	−	12.7103i	−0.248792	−	0.430920i
$871$	−42.0047	−	7.94230i	−1.42327	−	0.269115i
$872$	1.59096	−	2.75562i	0.0538767	−	0.0933172i
$873$			5.36881i			0.181707i
$874$	11.9368	−	20.6752i	0.403770	−	0.699349i
$875$	−25.9904	−	35.6573i	−0.878637	−	1.20544i
$876$		−	2.65150i		−	0.0895860i
$877$	−14.2933	−	8.25226i	−0.482652	−	0.278659i	0.238869	−	0.971052i	$-0.423223\pi$
$877$	−14.2933	−	8.25226i	−0.482652	−	0.278659i	−0.721521	+	0.692393i	$0.756557\pi$
$878$		−	26.8841i		−	0.907295i
$879$	5.93050	+	3.42398i	0.200031	+	0.115488i
$880$	1.05899	−	1.83423i	0.0356986	−	0.0618318i
$881$	−11.4382	+	19.8116i	−0.385364	+	0.667469i	−0.991820	−	0.127648i	$-0.959257\pi$
$881$	−11.4382	+	19.8116i	−0.385364	+	0.667469i	0.606456	+	0.795117i	$0.292591\pi$
$882$	−5.18758	+	4.69990i	−0.174675	+	0.158254i
$883$	−11.7690			−0.396060			−0.198030	−	0.980196i	$-0.563454\pi$
$883$	−11.7690			−0.396060			−0.198030	+	0.980196i	$0.563454\pi$
$884$	−16.5458	−	14.2352i	−0.556495	−	0.478783i
$885$	−5.02676	+	8.70660i	−0.168973	+	0.292669i
$886$	−20.2657	+	11.7004i	−0.680838	+	0.393082i
$887$	13.1629			0.441967			0.220983	−	0.975278i	$-0.429073\pi$
$887$	13.1629			0.441967			0.220983	+	0.975278i	$0.429073\pi$
$888$	−4.62481	−	8.01041i	−0.155199	−	0.268812i
$889$	3.10808	+	29.1401i	0.104242	+	0.977327i
$890$	17.9381	−	10.3566i	0.601288	−	0.347154i
$891$	−0.483436	−	0.279112i	−0.0161957	−	0.00935060i
$892$	17.5088	+	10.1087i	0.586238	+	0.338464i
$893$	25.2224			0.844034
$894$	−13.5267			−0.452399
$895$	−37.7221	−	21.7788i	−1.26091	−	0.727987i
$896$	−1.55842	−	2.13806i	−0.0520633	−	0.0714277i
$897$	−3.79307	+	20.0605i	−0.126647	+	0.669801i
$898$	2.31658	+	4.01243i	0.0773052	+	0.133896i
$899$	23.0658	−	13.3171i	0.769289	−	0.444149i
$900$	−4.69778	−	8.13679i	−0.156593	−	0.271226i
$901$	−40.5717	+	70.2722i	−1.35164	+	2.34111i
$902$		−	2.57669i		−	0.0857945i
$903$	−3.63438	−	34.0745i	−0.120945	−	1.13393i
$904$	−9.37943	+	5.41522i	−0.311955	+	0.180107i
$905$	13.0813	−	7.55250i	0.434838	−	0.251054i
$906$	10.2337			0.339992
$907$	−1.26498	−	2.19101i	−0.0420029	−	0.0727512i	0.844260	−	0.535934i	$-0.180041\pi$
$907$	−1.26498	−	2.19101i	−0.0420029	−	0.0727512i	−0.886263	+	0.463183i	$0.846707\pi$
$908$		−	5.71303i		−	0.189594i
$909$	−11.1030			−0.368263
$910$	−15.5140	−	32.7003i	−0.514283	−	1.08401i
$911$	−42.9504			−1.42301			−0.711506	−	0.702680i	$-0.751986\pi$
$911$	−42.9504			−1.42301			−0.711506	+	0.702680i	$0.751986\pi$
$912$			4.21620i			0.139612i
$913$	1.81042	+	3.13574i	0.0599161	+	0.103778i
$914$	−6.36150			−0.210420
$915$	11.7342	−	6.77472i	0.387919	−	0.223965i
$916$	−13.8628	+	8.00370i	−0.458040	+	0.264450i
$917$	−13.3461	−	5.91748i	−0.440727	−	0.195412i
$918$		−	6.05364i		−	0.199800i
$919$	13.4747	−	23.3389i	0.444490	−	0.769879i	−0.553527	−	0.832831i	$-0.686718\pi$
$919$	13.4747	−	23.3389i	0.444490	−	0.769879i	0.998017	+	0.0629528i	$0.0200517\pi$
$920$	−10.7419	−	18.6056i	−0.354151	−	0.613407i
$921$	12.7871	−	7.38262i	0.421348	−	0.243266i
$922$	−0.201872	−	0.349653i	−0.00664831	−	0.0115152i
$923$	18.7397	+	3.54334i	0.616826	+	0.116630i
$924$	1.46859	−	0.156640i	0.0483131	−	0.00515308i
$925$	75.2623	+	43.4527i	2.47461	+	1.42872i
$926$	−14.8936			−0.489434
$927$	−15.5797			−0.511703
$928$	3.34998	+	1.93411i	0.109968	+	0.0634903i
$929$	33.5148	+	19.3498i	1.09958	+	0.634846i	0.936112	−	0.351702i	$-0.114397\pi$
$929$	33.5148	+	19.3498i	1.09958	+	0.634846i	0.163473	+	0.986548i	$0.447730\pi$
$930$	22.6242	−	13.0621i	0.741875	−	0.428322i
$931$	−21.8719	+	19.8157i	−0.716821	+	0.649434i
$932$	−4.37032	−	7.56962i	−0.143155	−	0.247951i
$933$	−23.5029			−0.769449
$934$	6.37822	−	3.68247i	0.208702	−	0.120494i
$935$	−6.41075	+	11.1037i	−0.209654	+	0.363131i
$936$	−1.19126	−	3.40307i	−0.0389376	−	0.111233i
$937$	20.8581			0.681405			0.340703	−	0.940171i	$-0.389335\pi$
$937$	20.8581			0.681405			0.340703	+	0.940171i	$0.389335\pi$
$938$	28.6767	+	12.7149i	0.936329	+	0.415155i
$939$	−7.45703	+	12.9160i	−0.243351	+	0.421497i
$940$	11.3488	−	19.6566i	0.370156	−	0.641129i
$941$	22.6264	+	13.0633i	0.737598	+	0.425853i	0.821195	−	0.570647i	$-0.193308\pi$
$941$	22.6264	+	13.0633i	0.737598	+	0.425853i	−0.0835971	+	0.996500i	$0.526641\pi$
$942$			12.3992i			0.403987i
$943$	−22.6351	−	13.0684i	−0.737101	−	0.425566i
$944$		−	2.64974i		−	0.0862418i
$945$	4.06886	−	9.17678i	0.132360	−	0.298521i
$946$	−3.61505	+	6.26145i	−0.117535	+	0.203577i
$947$			17.6950i			0.575010i	0.957779	+	0.287505i	$0.0928259\pi$
$947$			17.6950i			0.575010i	−0.957779	+	0.287505i	$0.907174\pi$
$948$	−4.38856	+	7.60121i	−0.142534	+	0.246876i
$949$	3.15863	+	9.02326i	0.102534	+	0.292907i
$950$	−19.8068	−	34.3063i	−0.642616	−	1.11304i
$951$	−18.4005	−	10.6236i	−0.596679	−	0.344493i
$952$	9.43414	+	12.9431i	0.305762	+	0.419487i
$953$	−11.5429	−	19.9928i	−0.373910	−	0.647631i	0.616253	−	0.787548i	$-0.288650\pi$
$953$	−11.5429	−	19.9928i	−0.373910	−	0.647631i	−0.990163	+	0.139917i	$0.955316\pi$
$954$	−11.6083	+	6.70203i	−0.375831	+	0.216986i
$955$			36.3816i			1.17728i
$956$			20.9144i			0.676421i
$957$	−1.87004	+	1.07967i	−0.0604497	+	0.0349007i
$958$	2.19783	+	3.80675i	0.0710086	+	0.122990i
$959$	21.9476	+	30.1107i	0.708725	+	0.972326i
$960$	3.28583	+	1.89707i	0.106050	+	0.0612278i
$961$	8.20419	+	14.2101i	0.264651	+	0.458389i
$962$	25.2811	+	21.7507i	0.815094	+	0.701269i
$963$	−0.0615706	+	0.106643i	−0.00198408	+	0.00343653i
$964$			5.04361i			0.162444i
$965$	−52.3630	+	90.6953i	−1.68562	+	2.91959i
$966$	6.07235	−	13.6954i	0.195375	−	0.440642i
$967$		−	10.1406i		−	0.326100i	−0.986618	−	0.163050i	$-0.947867\pi$
$967$		−	10.1406i		−	0.326100i	0.986618	−	0.163050i	$-0.0521332\pi$
$968$	9.25641	+	5.34419i	0.297512	+	0.171769i
$969$		−	25.5234i		−	0.819928i
$970$	17.6410	+	10.1850i	0.566418	+	0.327021i
$971$	26.3127	−	45.5749i	0.844414	−	1.46257i	−0.0417142	−	0.999130i	$-0.513282\pi$
$971$	26.3127	−	45.5749i	0.844414	−	1.46257i	0.886129	−	0.463439i	$-0.153385\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−12.5349	−	5.55782i	−0.401851	−	0.178175i
$974$	5.99995			0.192251
$975$	25.6799	+	22.0938i	0.822415	+	0.707568i
$976$	−1.78557	+	3.09270i	−0.0571547	+	0.0989949i
$977$	−8.36025	+	4.82679i	−0.267468	+	0.154423i	−0.627737	−	0.778426i	$-0.716018\pi$
$977$	−8.36025	+	4.82679i	−0.267468	+	0.154423i	0.360268	+	0.932849i	$0.382685\pi$
$978$	−5.64012			−0.180351
$979$	−1.52374	−	2.63920i	−0.0486990	−	0.0843491i
$980$	5.60185	+	25.9615i	0.178944	+	0.829311i
$981$	−2.75562	+	1.59096i	−0.0879803	+	0.0507954i
$982$	−35.0735	−	20.2497i	−1.11924	−	0.646193i
$983$	−53.6054	−	30.9491i	−1.70975	−	0.987122i	−0.934858	−	0.355023i	$-0.884473\pi$
$983$	−53.6054	−	30.9491i	−1.70975	−	0.987122i	−0.774888	−	0.632099i	$-0.782194\pi$
$984$	4.61588			0.147149
$985$	24.3454			0.775708
$986$	−20.2796	−	11.7084i	−0.645833	−	0.372872i
$987$	15.7383	−	1.67864i	0.500955	−	0.0534318i
$988$	−5.02260	−	14.3480i	−0.159790	−	0.456472i
$989$	36.6695	+	63.5134i	1.16602	+	2.01961i
$990$	−1.83423	+	1.05899i	−0.0582956	+	0.0336570i
$991$	−21.1536	−	36.6391i	−0.671967	−	1.16388i	−0.977346	−	0.211650i	$-0.932116\pi$
$991$	−21.1536	−	36.6391i	−0.671967	−	1.16388i	0.305379	−	0.952231i	$-0.401217\pi$
$992$	−3.44269	+	5.96291i	−0.109305	+	0.189323i
$993$		−	19.1960i		−	0.609167i
$994$	−12.7937	−	5.67255i	−0.405791	−	0.179922i
$995$	−2.37814	+	1.37302i	−0.0753920	+	0.0435276i
$996$	−5.61735	+	3.24318i	−0.177992	+	0.102764i
$997$	4.90544			0.155357			0.0776784	−	0.996978i	$-0.475249\pi$
$997$	4.90544			0.155357			0.0776784	+	0.996978i	$0.475249\pi$
$998$	−9.98729	−	17.2985i	−0.316142	−	0.547574i
$999$			9.24963i			0.292645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bm.b.277.10	yes	20
3.2	odd	2		1638.2.dt.b.1369.1		20
7.2	even	3		546.2.bd.b.121.6	✓	20
13.10	even	6		546.2.bd.b.361.6	yes	20
21.2	odd	6		1638.2.cr.b.667.5		20
39.23	odd	6		1638.2.cr.b.361.5		20
91.23	even	6	inner	546.2.bm.b.205.5	yes	20
273.23	odd	6		1638.2.dt.b.1297.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.6	✓	20	7.2	even	3
546.2.bd.b.361.6	yes	20	13.10	even	6
546.2.bm.b.205.5	yes	20	91.23	even	6	inner
546.2.bm.b.277.10	yes	20	1.1	even	1	trivial
1638.2.cr.b.361.5		20	39.23	odd	6
1638.2.cr.b.667.5		20	21.2	odd	6
1638.2.dt.b.1297.6		20	273.23	odd	6
1638.2.dt.b.1369.1		20	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(3.28583 - 1.89707i) q^{5} +(0.866025 - 0.500000i) q^{6} +(2.13806 - 1.55842i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(3.28583 - 1.89707i) q^{5} +(0.866025 - 0.500000i) q^{6} +(2.13806 - 1.55842i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.89707 + 3.28583i) q^{10} +(0.483436 - 0.279112i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.73320 - 2.35152i) q^{13} +(1.55842 + 2.13806i) q^{14} +(-3.28583 - 1.89707i) q^{15} +1.00000 q^{16} -6.05364 q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.65134 - 2.10810i) q^{19} +(-3.28583 + 1.89707i) q^{20} +(-2.41867 - 1.07240i) q^{21} +(0.279112 + 0.483436i) q^{22} +5.66237 q^{23} +(-0.866025 + 0.500000i) q^{24} +(4.69778 - 8.13679i) q^{25} +(2.35152 - 2.73320i) q^{26} +1.00000 q^{27} +(-2.13806 + 1.55842i) q^{28} +(1.93411 - 3.34998i) q^{29} +(1.89707 - 3.28583i) q^{30} +(5.96291 + 3.44269i) q^{31} +1.00000i q^{32} +(-0.483436 - 0.279112i) q^{33} -6.05364i q^{34} +(4.06886 - 9.17678i) q^{35} +(0.500000 - 0.866025i) q^{36} +9.24963i q^{37} +(2.10810 - 3.65134i) q^{38} +(-0.669873 + 3.54278i) q^{39} +(-1.89707 - 3.28583i) q^{40} +(-3.99747 - 2.30794i) q^{41} +(1.07240 - 2.41867i) q^{42} +(6.47599 + 11.2167i) q^{43} +(-0.483436 + 0.279112i) q^{44} +3.79415i q^{45} +5.66237i q^{46} +(-5.18078 + 2.99112i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(2.14262 - 6.66402i) q^{49} +(8.13679 + 4.69778i) q^{50} +(3.02682 + 5.24261i) q^{51} +(2.73320 + 2.35152i) q^{52} +(6.70203 - 11.6083i) q^{53} +1.00000i q^{54} +(1.05899 - 1.83423i) q^{55} +(-1.55842 - 2.13806i) q^{56} +4.21620i q^{57} +(3.34998 + 1.93411i) q^{58} -2.64974i q^{59} +(3.28583 + 1.89707i) q^{60} +(-1.78557 + 3.09270i) q^{61} +(-3.44269 + 5.96291i) q^{62} +(0.280604 + 2.63083i) q^{63} -1.00000 q^{64} +(-13.4418 - 2.54160i) q^{65} +(0.279112 - 0.483436i) q^{66} +(10.2680 - 5.92821i) q^{67} +6.05364 q^{68} +(-2.83118 - 4.90375i) q^{69} +(9.17678 + 4.06886i) q^{70} +(-4.58090 + 2.64478i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-2.29627 - 1.32575i) q^{73} -9.24963 q^{74} -9.39555 q^{75} +(3.65134 + 2.10810i) q^{76} +(0.598641 - 1.35016i) q^{77} +(-3.54278 - 0.669873i) q^{78} +(4.38856 + 7.60121i) q^{79} +(3.28583 - 1.89707i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.30794 - 3.99747i) q^{82} +6.48635i q^{83} +(2.41867 + 1.07240i) q^{84} +(-19.8912 + 11.4842i) q^{85} +(-11.2167 + 6.47599i) q^{86} -3.86822 q^{87} +(-0.279112 - 0.483436i) q^{88} -5.45925i q^{89} -3.79415 q^{90} +(-9.50841 - 0.768204i) q^{91} -5.66237 q^{92} -6.88537i q^{93} +(-2.99112 - 5.18078i) q^{94} -15.9969 q^{95} +(0.866025 - 0.500000i) q^{96} +(4.64952 - 2.68440i) q^{97} +(6.66402 + 2.14262i) q^{98} +0.558224i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9	\( 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9} + 4 q^{10} + 6 q^{11} + 10 q^{12} + 8 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{21} - 10 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{26} + 20 q^{27} + 8 q^{29} + 4 q^{30} + 12 q^{31} - 6 q^{33} + 10 q^{35} + 10 q^{36} + 6 q^{38} - 10 q^{39} - 4 q^{40} - 18 q^{41} - 2 q^{42} + 18 q^{43} - 6 q^{44} - 6 q^{47} - 10 q^{48} - 20 q^{49} + 12 q^{50} + 4 q^{51} - 8 q^{52} + 18 q^{53} - 12 q^{55} - 4 q^{56} + 24 q^{58} - 6 q^{61} - 6 q^{63} - 20 q^{64} - 6 q^{65} - 10 q^{66} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 42 q^{70} - 6 q^{71} + 24 q^{73} + 36 q^{74} - 12 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} - 10 q^{81} + 18 q^{82} - 6 q^{84} - 36 q^{86} - 16 q^{87} + 10 q^{88} - 8 q^{90} - 10 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9 + 4 * q^10 + 6 * q^11 + 10 * q^12 + 8 * q^13 + 4 * q^14 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^21 - 10 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^26 + 20 * q^27 + 8 * q^29 + 4 * q^30 + 12 * q^31 - 6 * q^33 + 10 * q^35 + 10 * q^36 + 6 * q^38 - 10 * q^39 - 4 * q^40 - 18 * q^41 - 2 * q^42 + 18 * q^43 - 6 * q^44 - 6 * q^47 - 10 * q^48 - 20 * q^49 + 12 * q^50 + 4 * q^51 - 8 * q^52 + 18 * q^53 - 12 * q^55 - 4 * q^56 + 24 * q^58 - 6 * q^61 - 6 * q^63 - 20 * q^64 - 6 * q^65 - 10 * q^66 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 42 * q^70 - 6 * q^71 + 24 * q^73 + 36 * q^74 - 12 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 - 10 * q^81 + 18 * q^82 - 6 * q^84 - 36 * q^86 - 16 * q^87 + 10 * q^88 - 8 * q^90 - 10 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95 - 96 * q^97 - 12 * q^98

Introduction

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