LMFDB - Embedded newform 218.2.c.c.45.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [218,2,Mod(45,218)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(218, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("218.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 218 = 2 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	218.c (of order $3$, 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:	$1.74073876406$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 14x^{8} + 6x^{7} + 95x^{6} + 2x^{5} + 231x^{4} + 53x^{3} + 389x^{2} - 76x + 16 $ x^10 - 2x^9 + 14x^8 + 6x^7 + 95x^6 + 2x^5 + 231x^4 + 53x^3 + 389x^2 - 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.5
Root			$-0.771434 - 1.33616i$ of defining polynomial
Character	$\chi$	$=$	218.45
Dual form			218.2.c.c.63.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.49167 - 2.58365i) q^{3} +1.00000 q^{4} +(-1.77143 + 3.06821i) q^{5} +(1.49167 - 2.58365i) q^{6} +(1.53001 - 2.65006i) q^{7} +1.00000 q^{8} +(-2.95015 - 5.10982i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.49167 - 2.58365i) q^{3} +1.00000 q^{4} +(-1.77143 + 3.06821i) q^{5} +(1.49167 - 2.58365i) q^{6} +(1.53001 - 2.65006i) q^{7} +1.00000 q^{8} +(-2.95015 - 5.10982i) q^{9} +(-1.77143 + 3.06821i) q^{10} +(0.758581 + 1.31390i) q^{11} +(1.49167 - 2.58365i) q^{12} +(-1.95015 + 3.37777i) q^{13} +(1.53001 - 2.65006i) q^{14} +(5.28479 + 9.15352i) q^{15} +1.00000 q^{16} -0.974294 q^{17} +(-2.95015 - 5.10982i) q^{18} -7.48384 q^{19} +(-1.77143 + 3.06821i) q^{20} +(-4.56455 - 7.90604i) q^{21} +(0.758581 + 1.31390i) q^{22} +9.42652 q^{23} +(1.49167 - 2.58365i) q^{24} +(-3.77596 - 6.54015i) q^{25} +(-1.95015 + 3.37777i) q^{26} -8.65260 q^{27} +(1.53001 - 2.65006i) q^{28} +(-4.79764 + 8.30976i) q^{29} +(5.28479 + 9.15352i) q^{30} +(-0.609875 - 1.05633i) q^{31} +1.00000 q^{32} +4.52621 q^{33} -0.974294 q^{34} +(5.42064 + 9.38882i) q^{35} +(-2.95015 - 5.10982i) q^{36} +(-0.258581 - 0.447875i) q^{37} -7.48384 q^{38} +(5.81797 + 10.0770i) q^{39} +(-1.77143 + 3.06821i) q^{40} +3.20309 q^{41} +(-4.56455 - 7.90604i) q^{42} +1.94268 q^{43} +(0.758581 + 1.31390i) q^{44} +20.9040 q^{45} +9.42652 q^{46} +(1.49167 - 2.58365i) q^{48} +(-1.18189 - 2.04709i) q^{49} +(-3.77596 - 6.54015i) q^{50} +(-1.45332 + 2.51723i) q^{51} +(-1.95015 + 3.37777i) q^{52} +(3.63657 - 6.29872i) q^{53} -8.65260 q^{54} -5.37510 q^{55} +(1.53001 - 2.65006i) q^{56} +(-11.1634 + 19.3356i) q^{57} +(-4.79764 + 8.30976i) q^{58} +(-4.35265 - 7.53901i) q^{59} +(5.28479 + 9.15352i) q^{60} +(-2.74192 + 4.74914i) q^{61} +(-0.609875 - 1.05633i) q^{62} -18.0551 q^{63} +1.00000 q^{64} +(-6.90914 - 11.9670i) q^{65} +4.52621 q^{66} +(-5.04151 - 8.73216i) q^{67} -0.974294 q^{68} +(14.0612 - 24.3548i) q^{69} +(5.42064 + 9.38882i) q^{70} -3.00904 q^{71} +(-2.95015 - 5.10982i) q^{72} +(2.92282 + 5.06248i) q^{73} +(-0.258581 - 0.447875i) q^{74} -22.5299 q^{75} -7.48384 q^{76} +4.64256 q^{77} +(5.81797 + 10.0770i) q^{78} +(-5.34480 - 9.25747i) q^{79} +(-1.77143 + 3.06821i) q^{80} +(-4.05636 + 7.02582i) q^{81} +3.20309 q^{82} +(2.07605 - 3.59583i) q^{83} +(-4.56455 - 7.90604i) q^{84} +(1.72590 - 2.98934i) q^{85} +1.94268 q^{86} +(14.3130 + 24.7908i) q^{87} +(0.758581 + 1.31390i) q^{88} +(0.725397 - 1.25642i) q^{89} +20.9040 q^{90} +(5.96753 + 10.3361i) q^{91} +9.42652 q^{92} -3.63893 q^{93} +(13.2571 - 22.9620i) q^{95} +(1.49167 - 2.58365i) q^{96} +(-1.65373 + 2.86434i) q^{97} +(-1.18189 - 2.04709i) q^{98} +(4.47586 - 7.75242i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + q^{6} - q^{7} + 10 q^{8} - 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + q^6 - q^7 + 10 * q^8 - 10 * q^9	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + q^{6} - q^{7} + 10 q^{8} - 10 q^{9} - 8 q^{10} + q^{11} + q^{12} - q^{14} - q^{15} + 10 q^{16} - 16 q^{17} - 10 q^{18} - 6 q^{19} - 8 q^{20} + 4 q^{21} + q^{22} + 8 q^{23} + q^{24} - 11 q^{25} + 10 q^{27} - q^{28} + 9 q^{29} - q^{30} + 7 q^{31} + 10 q^{32} - 2 q^{33} - 16 q^{34} + 10 q^{35} - 10 q^{36} + 4 q^{37} - 6 q^{38} - 4 q^{39} - 8 q^{40} - 22 q^{41} + 4 q^{42} + 2 q^{43} + q^{44} + 38 q^{45} + 8 q^{46} + q^{48} - 10 q^{49} - 11 q^{50} - 3 q^{51} - 2 q^{53} + 10 q^{54} + 20 q^{55} - q^{56} - 49 q^{57} + 9 q^{58} - 12 q^{59} - q^{60} + 7 q^{61} + 7 q^{62} - 36 q^{63} + 10 q^{64} - 3 q^{65} - 2 q^{66} - 56 q^{67} - 16 q^{68} + 19 q^{69} + 10 q^{70} + 4 q^{71} - 10 q^{72} + 12 q^{73} + 4 q^{74} - 46 q^{75} - 6 q^{76} + 66 q^{77} - 4 q^{78} - 30 q^{79} - 8 q^{80} - 41 q^{81} - 22 q^{82} - 7 q^{83} + 4 q^{84} - 22 q^{85} + 2 q^{86} + 40 q^{87} + q^{88} + 9 q^{89} + 38 q^{90} + 20 q^{91} + 8 q^{92} + 10 q^{93} - 12 q^{95} + q^{96} + 35 q^{97} - 10 q^{98} + 19 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + q^6 - q^7 + 10 * q^8 - 10 * q^9 - 8 * q^10 + q^11 + q^12 - q^14 - q^15 + 10 * q^16 - 16 * q^17 - 10 * q^18 - 6 * q^19 - 8 * q^20 + 4 * q^21 + q^22 + 8 * q^23 + q^24 - 11 * q^25 + 10 * q^27 - q^28 + 9 * q^29 - q^30 + 7 * q^31 + 10 * q^32 - 2 * q^33 - 16 * q^34 + 10 * q^35 - 10 * q^36 + 4 * q^37 - 6 * q^38 - 4 * q^39 - 8 * q^40 - 22 * q^41 + 4 * q^42 + 2 * q^43 + q^44 + 38 * q^45 + 8 * q^46 + q^48 - 10 * q^49 - 11 * q^50 - 3 * q^51 - 2 * q^53 + 10 * q^54 + 20 * q^55 - q^56 - 49 * q^57 + 9 * q^58 - 12 * q^59 - q^60 + 7 * q^61 + 7 * q^62 - 36 * q^63 + 10 * q^64 - 3 * q^65 - 2 * q^66 - 56 * q^67 - 16 * q^68 + 19 * q^69 + 10 * q^70 + 4 * q^71 - 10 * q^72 + 12 * q^73 + 4 * q^74 - 46 * q^75 - 6 * q^76 + 66 * q^77 - 4 * q^78 - 30 * q^79 - 8 * q^80 - 41 * q^81 - 22 * q^82 - 7 * q^83 + 4 * q^84 - 22 * q^85 + 2 * q^86 + 40 * q^87 + q^88 + 9 * q^89 + 38 * q^90 + 20 * q^91 + 8 * q^92 + 10 * q^93 - 12 * q^95 + q^96 + 35 * q^97 - 10 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/218\mathbb{Z}\right)^\times$.

$n$	$115$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.49167	−	2.58365i	0.861216	−	1.49167i	−0.00954065	−	0.999954i	$-0.503037\pi$
$3$	1.49167	−	2.58365i	0.861216	−	1.49167i	0.870756	−	0.491715i	$-0.163630\pi$
$4$	1.00000			0.500000
$5$	−1.77143	+	3.06821i	−0.792209	+	1.37215i	0.132387	+	0.991198i	$0.457736\pi$
$5$	−1.77143	+	3.06821i	−0.792209	+	1.37215i	−0.924596	+	0.380949i	$0.875597\pi$
$6$	1.49167	−	2.58365i	0.608971	−	1.05477i
$7$	1.53001	−	2.65006i	0.578291	−	1.00163i	−0.417384	−	0.908730i	$-0.637053\pi$
$7$	1.53001	−	2.65006i	0.578291	−	1.00163i	0.995675	−	0.0928997i	$-0.0296136\pi$
$8$	1.00000			0.353553
$9$	−2.95015	−	5.10982i	−0.983385	−	1.70327i
$10$	−1.77143	+	3.06821i	−0.560177	+	0.970254i
$11$	0.758581	+	1.31390i	0.228721	+	0.396156i	0.957429	−	0.288668i	$-0.0932124\pi$
$11$	0.758581	+	1.31390i	0.228721	+	0.396156i	−0.728709	+	0.684824i	$0.759879\pi$
$12$	1.49167	−	2.58365i	0.430608	−	0.745835i
$13$	−1.95015	+	3.37777i	−0.540876	+	0.936824i	0.457978	+	0.888963i	$0.348574\pi$
$13$	−1.95015	+	3.37777i	−0.540876	+	0.936824i	−0.998854	+	0.0478607i	$0.984760\pi$
$14$	1.53001	−	2.65006i	0.408914	−	0.708259i
$15$	5.28479	+	9.15352i	1.36453	+	2.36343i
$16$	1.00000			0.250000
$17$	−0.974294			−0.236301			−0.118150	−	0.992996i	$-0.537697\pi$
$17$	−0.974294			−0.236301			−0.118150	+	0.992996i	$0.537697\pi$
$18$	−2.95015	−	5.10982i	−0.695358	−	1.20440i
$19$	−7.48384			−1.71691			−0.858455	−	0.512889i	$-0.828575\pi$
$19$	−7.48384			−1.71691			−0.858455	+	0.512889i	$0.828575\pi$
$20$	−1.77143	+	3.06821i	−0.396105	+	0.686073i
$21$	−4.56455	−	7.90604i	−0.996067	−	1.72524i
$22$	0.758581	+	1.31390i	0.161730	+	0.280125i
$23$	9.42652			1.96556			0.982782	−	0.184768i	$-0.0591533\pi$
$23$	9.42652			1.96556			0.982782	+	0.184768i	$0.0591533\pi$
$24$	1.49167	−	2.58365i	0.304486	−	0.527385i
$25$	−3.77596	−	6.54015i	−0.755191	−	1.30803i
$26$	−1.95015	+	3.37777i	−0.382457	+	0.662435i
$27$	−8.65260			−1.66519
$28$	1.53001	−	2.65006i	0.289146	−	0.500815i
$29$	−4.79764	+	8.30976i	−0.890899	+	1.54308i	−0.0521005	+	0.998642i	$0.516592\pi$
$29$	−4.79764	+	8.30976i	−0.890899	+	1.54308i	−0.838799	+	0.544441i	$0.816742\pi$
$30$	5.28479	+	9.15352i	0.964866	+	1.67120i
$31$	−0.609875	−	1.05633i	−0.109537	−	0.189723i	0.806046	−	0.591853i	$-0.201603\pi$
$31$	−0.609875	−	1.05633i	−0.109537	−	0.189723i	−0.915583	+	0.402130i	$0.868270\pi$
$32$	1.00000			0.176777
$33$	4.52621			0.787911
$34$	−0.974294			−0.167090
$35$	5.42064	+	9.38882i	0.916255	+	1.58700i
$36$	−2.95015	−	5.10982i	−0.491692	−	0.851636i
$37$	−0.258581	−	0.447875i	−0.0425104	−	0.0736302i	0.843987	−	0.536363i	$-0.180202\pi$
$37$	−0.258581	−	0.447875i	−0.0425104	−	0.0736302i	−0.886498	+	0.462733i	$0.846869\pi$
$38$	−7.48384			−1.21404
$39$	5.81797	+	10.0770i	0.931621	+	1.61361i
$40$	−1.77143	+	3.06821i	−0.280088	+	0.485127i
$41$	3.20309			0.500238			0.250119	−	0.968215i	$-0.419530\pi$
$41$	3.20309			0.500238			0.250119	+	0.968215i	$0.419530\pi$
$42$	−4.56455	−	7.90604i	−0.704326	−	1.21993i
$43$	1.94268			0.296255			0.148128	−	0.988968i	$-0.452675\pi$
$43$	1.94268			0.296255			0.148128	+	0.988968i	$0.452675\pi$
$44$	0.758581	+	1.31390i	0.114360	+	0.198078i
$45$	20.9040			3.11619
$46$	9.42652			1.38986
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	1.49167	−	2.58365i	0.215304	−	0.372917i
$49$	−1.18189	−	2.04709i	−0.168841	−	0.292442i
$50$	−3.77596	−	6.54015i	−0.534001	−	0.924917i
$51$	−1.45332	+	2.51723i	−0.203506	+	0.352483i
$52$	−1.95015	+	3.37777i	−0.270438	+	0.468412i
$53$	3.63657	−	6.29872i	0.499521	−	0.865196i	−0.500479	−	0.865749i	$-0.666843\pi$
$53$	3.63657	−	6.29872i	0.499521	−	0.865196i	1.00000		0.000553143i	$0.000176071\pi$
$54$	−8.65260			−1.17747
$55$	−5.37510			−0.724779
$56$	1.53001	−	2.65006i	0.204457	−	0.354130i
$57$	−11.1634	+	19.3356i	−1.47863	+	2.56106i
$58$	−4.79764	+	8.30976i	−0.629961	+	1.09112i
$59$	−4.35265	−	7.53901i	−0.566666	−	0.981495i	−0.996893	−	0.0787738i	$-0.974900\pi$
$59$	−4.35265	−	7.53901i	−0.566666	−	0.981495i	0.430226	−	0.902721i	$-0.358434\pi$
$60$	5.28479	+	9.15352i	0.682263	+	1.18171i
$61$	−2.74192	+	4.74914i	−0.351067	+	0.608066i	−0.986437	−	0.164142i	$-0.947514\pi$
$61$	−2.74192	+	4.74914i	−0.351067	+	0.608066i	0.635370	+	0.772208i	$0.280848\pi$
$62$	−0.609875	−	1.05633i	−0.0774542	−	0.134155i
$63$	−18.0551			−2.27473
$64$	1.00000			0.125000
$65$	−6.90914	−	11.9670i	−0.856973	−	1.48432i
$66$	4.52621			0.557138
$67$	−5.04151	−	8.73216i	−0.615919	−	1.06680i	−0.990223	−	0.139497i	$-0.955451\pi$
$67$	−5.04151	−	8.73216i	−0.615919	−	1.06680i	0.374303	−	0.927306i	$-0.377882\pi$
$68$	−0.974294			−0.118150
$69$	14.0612	−	24.3548i	1.69277	−	2.93197i
$70$	5.42064	+	9.38882i	0.647890	+	1.12218i
$71$	−3.00904			−0.357108			−0.178554	−	0.983930i	$-0.557142\pi$
$71$	−3.00904			−0.357108			−0.178554	+	0.983930i	$0.557142\pi$
$72$	−2.95015	−	5.10982i	−0.347679	−	0.602198i
$73$	2.92282	+	5.06248i	0.342091	+	0.592518i	0.984821	−	0.173574i	$-0.0555317\pi$
$73$	2.92282	+	5.06248i	0.342091	+	0.592518i	−0.642730	+	0.766093i	$0.722198\pi$
$74$	−0.258581	−	0.447875i	−0.0300594	−	0.0520644i
$75$	−22.5299			−2.60153
$76$	−7.48384			−0.858455
$77$	4.64256			0.529069
$78$	5.81797	+	10.0770i	0.658756	+	1.14100i
$79$	−5.34480	−	9.25747i	−0.601337	−	1.04155i	−0.992619	−	0.121276i	$-0.961302\pi$
$79$	−5.34480	−	9.25747i	−0.601337	−	1.04155i	0.391282	−	0.920271i	$-0.372032\pi$
$80$	−1.77143	+	3.06821i	−0.198052	+	0.343037i
$81$	−4.05636	+	7.02582i	−0.450707	+	0.780647i
$82$	3.20309			0.353722
$83$	2.07605	−	3.59583i	0.227876	−	0.394693i	−0.729302	−	0.684192i	$-0.760155\pi$
$83$	2.07605	−	3.59583i	0.227876	−	0.394693i	0.957179	+	0.289498i	$0.0934885\pi$
$84$	−4.56455	−	7.90604i	−0.498033	−	0.862619i
$85$	1.72590	−	2.98934i	0.187200	−	0.324240i
$86$	1.94268			0.209484
$87$	14.3130	+	24.7908i	1.53451	+	2.65785i
$88$	0.758581	+	1.31390i	0.0808650	+	0.140062i
$89$	0.725397	−	1.25642i	0.0768919	−	0.133181i	−0.825016	−	0.565110i	$-0.808834\pi$
$89$	0.725397	−	1.25642i	0.0768919	−	0.133181i	0.901907	+	0.431929i	$0.142167\pi$
$90$	20.9040			2.20348
$91$	5.96753	+	10.3361i	0.625567	+	1.08351i
$92$	9.42652			0.982782
$93$	−3.63893			−0.377339
$94$		0			0
$95$	13.2571	−	22.9620i	1.36015	−	2.35585i
$96$	1.49167	−	2.58365i	0.152243	−	0.263692i
$97$	−1.65373	+	2.86434i	−0.167911	+	0.290830i	−0.937685	−	0.347486i	$-0.887035\pi$
$97$	−1.65373	+	2.86434i	−0.167911	+	0.290830i	0.769774	+	0.638316i	$0.220369\pi$
$98$	−1.18189	−	2.04709i	−0.119389	−	0.206788i
$99$	4.47586	−	7.75242i	0.449841	−	0.779147i
$100$	−3.77596	−	6.54015i	−0.377596	−	0.654015i
$101$	−0.711633			−0.0708101			−0.0354051	−	0.999373i	$-0.511272\pi$
$101$	−0.711633			−0.0708101			−0.0354051	+	0.999373i	$0.511272\pi$
$102$	−1.45332	+	2.51723i	−0.143901	+	0.249243i
$103$	5.83146	−	10.1004i	0.574591	−	0.995221i	−0.421495	−	0.906831i	$-0.638494\pi$
$103$	5.83146	−	10.1004i	0.574591	−	0.995221i	0.996086	−	0.0883902i	$-0.0281723\pi$
$104$	−1.95015	+	3.37777i	−0.191228	+	0.331217i
$105$	32.3432			3.15637
$106$	3.63657	−	6.29872i	0.353215	−	0.611786i
$107$	−13.9780			−1.35130			−0.675652	−	0.737221i	$-0.736138\pi$
$107$	−13.9780			−1.35130			−0.675652	+	0.737221i	$0.736138\pi$
$108$	−8.65260			−0.832597
$109$	8.11588	−	6.56753i	0.777361	−	0.629055i
$109$	8.11588	−	6.56753i	0.777361	−	0.629055i
$110$	−5.37510			−0.512496
$111$	−1.54287			−0.146443
$112$	1.53001	−	2.65006i	0.144573	−	0.250407i
$113$	0.194043			0.0182541			0.00912703	−	0.999958i	$-0.497095\pi$
$113$	0.194043			0.0182541			0.00912703	+	0.999958i	$0.497095\pi$
$114$	−11.1634	+	19.3356i	−1.04555	+	1.81094i
$115$	−16.6984	+	28.9226i	−1.55714	+	2.69704i
$116$	−4.79764	+	8.30976i	−0.445450	+	0.771542i
$117$	23.0130			2.12756
$118$	−4.35265	−	7.53901i	−0.400694	−	0.694022i
$119$	−1.49068	+	2.58194i	−0.136651	+	0.236686i
$120$	5.28479	+	9.15352i	0.482433	+	0.835598i
$121$	4.34911	−	7.53288i	0.395374	−	0.684807i
$122$	−2.74192	+	4.74914i	−0.248242	+	0.429967i
$123$	4.77795	−	8.27565i	0.430813	−	0.746190i
$124$	−0.609875	−	1.05633i	−0.0547684	−	0.0948616i
$125$	9.04109			0.808660
$126$	−18.0551			−1.60848
$127$	−1.59321	−	2.75953i	−0.141375	−	0.244868i	0.786640	−	0.617412i	$-0.211819\pi$
$127$	−1.59321	−	2.75953i	−0.141375	−	0.244868i	−0.928015	+	0.372544i	$0.878486\pi$
$128$	1.00000			0.0883883
$129$	2.89783	−	5.01919i	0.255140	−	0.441915i
$130$	−6.90914	−	11.9670i	−0.605972	−	1.04957i
$131$	4.63473	+	8.02758i	0.404938	+	0.701373i	0.994314	−	0.106485i	$-0.0339597\pi$
$131$	4.63473	+	8.02758i	0.404938	+	0.701373i	−0.589376	+	0.807859i	$0.700626\pi$
$132$	4.52621			0.393956
$133$	−11.4504	+	19.8326i	−0.992874	+	1.71971i
$134$	−5.04151	−	8.73216i	−0.435521	−	0.754344i
$135$	15.3275	−	26.5480i	1.31918	−	2.28489i
$136$	−0.974294			−0.0835450
$137$	−9.51090	+	16.4734i	−0.812571	+	1.40741i	0.0984882	+	0.995138i	$0.468599\pi$
$137$	−9.51090	+	16.4734i	−0.812571	+	1.40741i	−0.911059	+	0.412276i	$0.864734\pi$
$138$	14.0612	−	24.3548i	1.19697	−	2.07322i
$139$	−2.94499	−	5.10088i	−0.249791	−	0.432651i	0.713677	−	0.700475i	$-0.247029\pi$
$139$	−2.94499	−	5.10088i	−0.249791	−	0.432651i	−0.963468	+	0.267824i	$0.913695\pi$
$140$	5.42064	+	9.38882i	0.458128	+	0.793500i
$141$		0			0
$142$	−3.00904			−0.252513
$143$	−5.91740			−0.494838
$144$	−2.95015	−	5.10982i	−0.245846	−	0.425818i
$145$	−16.9974	−	29.4404i	−1.41156	−	2.44489i
$146$	2.92282	+	5.06248i	0.241895	+	0.418974i
$147$	−7.05196			−0.581636
$148$	−0.258581	−	0.447875i	−0.0212552	−	0.0368151i
$149$	4.00955	−	6.94474i	0.328475	−	0.568935i	−0.653735	−	0.756724i	$-0.726799\pi$
$149$	4.00955	−	6.94474i	0.328475	−	0.568935i	0.982209	+	0.187789i	$0.0601321\pi$
$150$	−22.5299			−1.83956
$151$	5.83146	+	10.1004i	0.474558	+	0.821958i	0.999576	−	0.0291331i	$-0.00927467\pi$
$151$	5.83146	+	10.1004i	0.474558	+	0.821958i	−0.525018	+	0.851091i	$0.675941\pi$
$152$	−7.48384			−0.607019
$153$	2.87432	+	4.97846i	0.232375	+	0.402485i
$154$	4.64256			0.374108
$155$	4.32141			0.347104
$156$	5.81797	+	10.0770i	0.465810	+	0.806807i
$157$	1.99521	−	3.45580i	0.159235	−	0.275803i	−0.775358	−	0.631522i	$-0.782431\pi$
$157$	1.99521	−	3.45580i	0.159235	−	0.275803i	0.934593	+	0.355719i	$0.115764\pi$
$158$	−5.34480	−	9.25747i	−0.425210	−	0.736485i
$159$	−10.8491	−	18.7912i	−0.860390	−	1.49024i
$160$	−1.77143	+	3.06821i	−0.140044	+	0.242564i
$161$	14.4227	−	24.9809i	1.13667	−	1.96877i
$162$	−4.05636	+	7.02582i	−0.318698	+	0.552001i
$163$	12.5375			0.982015			0.491008	−	0.871155i	$-0.336629\pi$
$163$	12.5375			0.982015			0.491008	+	0.871155i	$0.336629\pi$
$164$	3.20309			0.250119
$165$	−8.01788	+	13.8874i	−0.624191	+	1.08113i
$166$	2.07605	−	3.59583i	0.161133	−	0.279090i
$167$	−5.24057	+	9.07693i	−0.405527	+	0.702394i	−0.994383	−	0.105845i	$-0.966245\pi$
$167$	−5.24057	+	9.07693i	−0.405527	+	0.702394i	0.588855	+	0.808238i	$0.299579\pi$
$168$	−4.56455	−	7.90604i	−0.352163	−	0.609964i
$169$	−1.10621	−	1.91600i	−0.0850927	−	0.147385i
$170$	1.72590	−	2.98934i	0.132370	−	0.229272i
$171$	22.0785	+	38.2411i	1.68838	+	2.92437i
$172$	1.94268			0.148128
$173$	10.9094			0.829423			0.414711	−	0.909953i	$-0.363883\pi$
$173$	10.9094			0.829423			0.414711	+	0.909953i	$0.363883\pi$
$174$	14.3130	+	24.7908i	1.08506	+	1.87939i
$175$	−23.1091			−1.74688
$176$	0.758581	+	1.31390i	0.0571802	+	0.0990390i
$177$	−25.9708			−1.95209
$178$	0.725397	−	1.25642i	0.0543708	−	0.0941730i
$179$	5.14893	+	8.91822i	0.384849	+	0.666579i	0.991748	−	0.128200i	$-0.0409200\pi$
$179$	5.14893	+	8.91822i	0.384849	+	0.666579i	−0.606899	+	0.794779i	$0.707587\pi$
$180$	20.9040			1.55809
$181$	−12.2266	−	21.1771i	−0.908797	−	1.57408i	−0.815738	−	0.578422i	$-0.803669\pi$
$181$	−12.2266	−	21.1771i	−0.908797	−	1.57408i	−0.0930589	−	0.995661i	$-0.529664\pi$
$182$	5.96753	+	10.3361i	0.442343	+	0.766160i
$183$	8.18007	+	14.1683i	0.604688	+	1.04735i
$184$	9.42652			0.694932
$185$	1.83223			0.134709
$186$	−3.63893			−0.266819
$187$	−0.739080	−	1.28012i	−0.0540469	−	0.0936120i
$188$		0			0
$189$	−13.2386	+	22.9299i	−0.962967	+	1.66791i
$190$	13.2571	−	22.9620i	0.961773	−	1.66584i
$191$	20.6149			1.49164			0.745821	−	0.666146i	$-0.232057\pi$
$191$	20.6149			1.49164			0.745821	+	0.666146i	$0.232057\pi$
$192$	1.49167	−	2.58365i	0.107652	−	0.186459i
$193$	2.42331	+	4.19729i	0.174434	+	0.302128i	0.939965	−	0.341271i	$-0.110857\pi$
$193$	2.42331	+	4.19729i	0.174434	+	0.302128i	−0.765532	+	0.643398i	$0.777524\pi$
$194$	−1.65373	+	2.86434i	−0.118731	+	0.205648i
$195$	−41.2246			−2.95216
$196$	−1.18189	−	2.04709i	−0.0844207	−	0.146221i
$197$	9.84165	+	17.0462i	0.701188	+	1.21449i	0.968050	+	0.250759i	$0.0806801\pi$
$197$	9.84165	+	17.0462i	0.701188	+	1.21449i	−0.266861	+	0.963735i	$0.585987\pi$
$198$	4.47586	−	7.75242i	0.318086	−	0.550940i
$199$	−4.21441			−0.298752			−0.149376	−	0.988780i	$-0.547726\pi$
$199$	−4.21441			−0.298752			−0.149376	+	0.988780i	$0.547726\pi$
$200$	−3.77596	−	6.54015i	−0.267000	−	0.462458i
$201$	−30.0811			−2.12176
$202$	−0.711633			−0.0500703
$203$	14.6809	+	25.4281i	1.03040	+	1.78470i
$204$	−1.45332	+	2.51723i	−0.101753	+	0.176241i
$205$	−5.67406	+	9.82776i	−0.396293	+	0.686400i
$206$	5.83146	−	10.1004i	0.406297	−	0.703728i
$207$	−27.8097	−	48.1678i	−1.93291	−	3.34789i
$208$	−1.95015	+	3.37777i	−0.135219	+	0.234206i
$209$	−5.67710	−	9.83302i	−0.392693	−	0.680164i
$210$	32.3432			2.23189
$211$	4.17845	−	7.23729i	0.287656	−	0.498235i	−0.685594	−	0.727985i	$-0.740457\pi$
$211$	4.17845	−	7.23729i	0.287656	−	0.498235i	0.973250	+	0.229749i	$0.0737906\pi$
$212$	3.63657	−	6.29872i	0.249760	−	0.432598i
$213$	−4.48850	+	7.77431i	−0.307547	+	0.532687i
$214$	−13.9780			−0.955516
$215$	−3.44132	+	5.96055i	−0.234696	+	0.406506i
$216$	−8.65260			−0.588735
$217$	−3.73247			−0.253377
$218$	8.11588	−	6.56753i	0.549677	−	0.444809i
$219$	17.4395			1.17846
$220$	−5.37510			−0.362389
$221$	1.90002	−	3.29094i	0.127809	−	0.221372i
$222$	−1.54287			−0.103551
$223$	−9.27130	+	16.0584i	−0.620852	+	1.07535i	0.368476	+	0.929637i	$0.379880\pi$
$223$	−9.27130	+	16.0584i	−0.620852	+	1.07535i	−0.989327	+	0.145710i	$0.953454\pi$
$224$	1.53001	−	2.65006i	0.102228	−	0.177065i
$225$	−22.2793	+	38.5889i	−1.48529	+	2.57259i
$226$	0.194043			0.0129076
$227$	2.60290	+	4.50835i	0.172760	+	0.299230i	0.939384	−	0.342867i	$-0.111398\pi$
$227$	2.60290	+	4.50835i	0.172760	+	0.299230i	−0.766624	+	0.642097i	$0.778065\pi$
$228$	−11.1634	+	19.3356i	−0.739315	+	1.28053i
$229$	7.54557	+	13.0693i	0.498626	+	0.863645i	0.999999	−	0.00158632i	$-0.000504943\pi$
$229$	7.54557	+	13.0693i	0.498626	+	0.863645i	−0.501373	+	0.865231i	$0.667172\pi$
$230$	−16.6984	+	28.9226i	−1.10106	+	1.90710i
$231$	6.92516	−	11.9947i	0.455642	−	0.789195i
$232$	−4.79764	+	8.30976i	−0.314981	+	0.545562i
$233$	−9.56210	−	16.5620i	−0.626434	−	1.08502i	−0.988262	−	0.152770i	$-0.951181\pi$
$233$	−9.56210	−	16.5620i	−0.626434	−	1.08502i	0.361828	−	0.932245i	$-0.382153\pi$
$234$	23.0130			1.50441
$235$		0			0
$236$	−4.35265	−	7.53901i	−0.283333	−	0.490748i
$237$	−31.8907			−2.07152
$238$	−1.49068	+	2.58194i	−0.0966267	+	0.167362i
$239$	14.6167	+	25.3169i	0.945478	+	1.63762i	0.754791	+	0.655965i	$0.227738\pi$
$239$	14.6167	+	25.3169i	0.945478	+	1.63762i	0.190687	+	0.981651i	$0.438928\pi$
$240$	5.28479	+	9.15352i	0.341132	+	0.590857i
$241$	10.1794			0.655710			0.327855	−	0.944728i	$-0.393674\pi$
$241$	10.1794			0.655710			0.327855	+	0.944728i	$0.393674\pi$
$242$	4.34911	−	7.53288i	0.279571	−	0.484232i
$243$	−0.877411	−	1.51972i	−0.0562859	−	0.0974901i
$244$	−2.74192	+	4.74914i	−0.175533	+	0.304033i
$245$	8.37456			0.535031
$246$	4.77795	−	8.27565i	0.304631	−	0.527636i
$247$	14.5946	−	25.2787i	0.928635	−	1.60844i
$248$	−0.609875	−	1.05633i	−0.0387271	−	0.0670773i
$249$	−6.19357	−	10.7276i	−0.392501	−	0.679832i
$250$	9.04109			0.571809
$251$	−0.0771191			−0.00486772			−0.00243386	−	0.999997i	$-0.500775\pi$
$251$	−0.0771191			−0.00486772			−0.00243386	+	0.999997i	$0.500775\pi$
$252$	−18.0551			−1.13737
$253$	7.15077	+	12.3855i	0.449565	+	0.778670i
$254$	−1.59321	−	2.75953i	−0.0999671	−	0.173148i
$255$	−5.14893	−	8.91822i	−0.322439	−	0.558480i
$256$	1.00000			0.0625000
$257$	−5.58235	−	9.66892i	−0.348218	−	0.603131i	0.637715	−	0.770272i	$-0.279880\pi$
$257$	−5.58235	−	9.66892i	−0.348218	−	0.603131i	−0.985933	+	0.167142i	$0.946546\pi$
$258$	2.89783	−	5.01919i	0.180411	−	0.312481i
$259$	−1.58253			−0.0983336
$260$	−6.90914	−	11.9670i	−0.428487	−	0.742161i
$261$	56.6151			3.50439
$262$	4.63473	+	8.02758i	0.286334	+	0.495946i
$263$	−15.1235			−0.932552			−0.466276	−	0.884639i	$-0.654405\pi$
$263$	−15.1235			−0.932552			−0.466276	+	0.884639i	$0.654405\pi$
$264$	4.52621			0.278569
$265$	12.8839	+	22.3155i	0.791450	+	1.37083i
$266$	−11.4504	+	19.8326i	−0.702068	+	1.21602i
$267$	−2.16410	−	3.74834i	−0.132441	−	0.229395i
$268$	−5.04151	−	8.73216i	−0.307960	−	0.533402i
$269$	−14.0441	+	24.3251i	−0.856283	+	1.48313i	0.0191670	+	0.999816i	$0.493899\pi$
$269$	−14.0441	+	24.3251i	−0.856283	+	1.48313i	−0.875450	+	0.483309i	$0.839435\pi$
$270$	15.3275	−	26.5480i	0.932803	−	1.61566i
$271$	−5.65812	+	9.80015i	−0.343706	+	0.595317i	−0.985118	−	0.171880i	$-0.945016\pi$
$271$	−5.65812	+	9.80015i	−0.343706	+	0.595317i	0.641412	+	0.767197i	$0.278349\pi$
$272$	−0.974294			−0.0590752
$273$	35.6063			2.15499
$274$	−9.51090	+	16.4734i	−0.574574	+	0.995192i
$275$	5.72874	−	9.92246i	0.345456	−	0.598347i
$276$	14.0612	−	24.3548i	0.846387	−	1.46599i
$277$	9.51385	+	16.4785i	0.571632	+	0.990096i	0.996399	+	0.0847928i	$0.0270228\pi$
$277$	9.51385	+	16.4785i	0.571632	+	0.990096i	−0.424767	+	0.905303i	$0.639644\pi$
$278$	−2.94499	−	5.10088i	−0.176629	−	0.305930i
$279$	−3.59845	+	6.23270i	−0.215434	+	0.373142i
$280$	5.42064	+	9.38882i	0.323945	+	0.561090i
$281$	−10.4148			−0.621293			−0.310646	−	0.950526i	$-0.600545\pi$
$281$	−10.4148			−0.621293			−0.310646	+	0.950526i	$0.600545\pi$
$282$		0			0
$283$	−5.42588	−	9.39789i	−0.322535	−	0.558647i	0.658475	−	0.752602i	$-0.271202\pi$
$283$	−5.42588	−	9.39789i	−0.322535	−	0.558647i	−0.981010	+	0.193955i	$0.937868\pi$
$284$	−3.00904			−0.178554
$285$	−39.5505	−	68.5035i	−2.34277	−	4.05780i
$286$	−5.91740			−0.349903
$287$	4.90077	−	8.48839i	0.289283	−	0.501054i
$288$	−2.95015	−	5.10982i	−0.173840	−	0.301099i
$289$	−16.0508			−0.944162
$290$	−16.9974	−	29.4404i	−0.998122	−	1.72880i
$291$	4.93363	+	8.54530i	0.289215	+	0.500934i
$292$	2.92282	+	5.06248i	0.171045	+	0.296259i
$293$	14.4956			0.846841			0.423421	−	0.905933i	$-0.360829\pi$
$293$	14.4956			0.846841			0.423421	+	0.905933i	$0.360829\pi$
$294$	−7.05196			−0.411278
$295$	30.8417			1.79567
$296$	−0.258581	−	0.447875i	−0.0150297	−	0.0260322i
$297$	−6.56370	−	11.3687i	−0.380864	−	0.659677i
$298$	4.00955	−	6.94474i	0.232267	−	0.402298i
$299$	−18.3832	+	31.8406i	−1.06313	+	1.84139i
$300$	−22.5299			−1.30077
$301$	2.97232	−	5.14822i	0.171322	−	0.296738i
$302$	5.83146	+	10.1004i	0.335563	+	0.581212i
$303$	−1.06152	+	1.83861i	−0.0609828	+	0.105625i
$304$	−7.48384			−0.429228
$305$	−9.71426	−	16.8256i	−0.556237	−	0.963430i
$306$	2.87432	+	4.97846i	0.164314	+	0.284600i
$307$	−11.3825	+	19.7151i	−0.649634	+	1.12520i	0.333576	+	0.942723i	$0.391745\pi$
$307$	−11.3825	+	19.7151i	−0.649634	+	1.12520i	−0.983210	+	0.182476i	$0.941589\pi$
$308$	4.64256			0.264534
$309$	−17.3972	−	30.1329i	−0.989694	−	1.71420i
$310$	4.32141			0.245440
$311$	19.5083			1.10621			0.553106	−	0.833111i	$-0.313442\pi$
$311$	19.5083			1.10621			0.553106	+	0.833111i	$0.313442\pi$
$312$	5.81797	+	10.0770i	0.329378	+	0.570499i
$313$	−5.61418	+	9.72405i	−0.317332	+	0.549636i	−0.979931	−	0.199339i	$-0.936120\pi$
$313$	−5.61418	+	9.72405i	−0.317332	+	0.549636i	0.662598	+	0.748975i	$0.269454\pi$
$314$	1.99521	−	3.45580i	0.112596	−	0.195022i
$315$	31.9835	−	55.3970i	1.80206	−	3.12127i
$316$	−5.34480	−	9.25747i	−0.300669	−	0.520773i
$317$	−6.78713	+	11.7556i	−0.381203	+	0.660263i	−0.991234	−	0.132114i	$-0.957823\pi$
$317$	−6.78713	+	11.7556i	−0.381203	+	0.660263i	0.610032	+	0.792377i	$0.291157\pi$
$318$	−10.8491	−	18.7912i	−0.608388	−	1.05376i
$319$	−14.5576			−0.815069
$320$	−1.77143	+	3.06821i	−0.0990262	+	0.171518i
$321$	−20.8506	+	36.1142i	−1.16376	+	2.01570i
$322$	14.4227	−	24.9809i	0.803746	−	1.39213i
$323$	7.29146			0.405707
$324$	−4.05636	+	7.02582i	−0.225353	+	0.390323i
$325$	29.4548			1.63386
$326$	12.5375			0.694390
$327$	−4.86196	−	30.7652i	−0.268867	−	1.70132i
$328$	3.20309			0.176861
$329$		0			0
$330$	−8.01788	+	13.8874i	−0.441370	+	0.764474i
$331$	−23.3226			−1.28193			−0.640963	−	0.767572i	$-0.721465\pi$
$331$	−23.3226			−1.28193			−0.640963	+	0.767572i	$0.721465\pi$
$332$	2.07605	−	3.59583i	0.113938	−	0.197347i
$333$	−1.52571	+	2.64260i	−0.0836082	+	0.144814i
$334$	−5.24057	+	9.07693i	−0.286751	+	0.496667i
$335$	35.7228			1.95175
$336$	−4.56455	−	7.90604i	−0.249017	−	0.431310i
$337$	9.62323	−	16.6679i	0.524211	−	0.907959i	−0.475392	−	0.879774i	$-0.657694\pi$
$337$	9.62323	−	16.6679i	0.524211	−	0.907959i	0.999603	−	0.0281854i	$-0.00897288\pi$
$338$	−1.10621	−	1.91600i	−0.0601696	−	0.104217i
$339$	0.289448	−	0.501339i	0.0157207	−	0.0272290i
$340$	1.72590	−	2.98934i	0.0935999	−	0.162120i
$341$	0.925279	−	1.60263i	0.0501066	−	0.0867873i
$342$	22.0785	+	38.2411i	1.19387	+	2.06784i
$343$	14.1870			0.766024
$344$	1.94268			0.104742
$345$	49.8171	+	86.2858i	2.68206	+	4.64547i
$346$	10.9094			0.586491
$347$	7.36442	−	12.7555i	0.395343	−	0.684754i	−0.597802	−	0.801644i	$-0.703959\pi$
$347$	7.36442	−	12.7555i	0.395343	−	0.684754i	0.993145	+	0.116890i	$0.0372925\pi$
$348$	14.3130	+	24.7908i	0.767257	+	1.32893i
$349$	−2.72477	−	4.71944i	−0.145854	−	0.252626i	0.783837	−	0.620966i	$-0.213260\pi$
$349$	−2.72477	−	4.71944i	−0.145854	−	0.252626i	−0.929691	+	0.368340i	$0.879926\pi$
$350$	−23.1091			−1.23523
$351$	16.8739	−	29.2265i	0.900663	−	1.55999i
$352$	0.758581	+	1.31390i	0.0404325	+	0.0700311i
$353$	−0.777926	+	1.34741i	−0.0414048	+	0.0717152i	−0.885985	−	0.463714i	$-0.846517\pi$
$353$	−0.777926	+	1.34741i	−0.0414048	+	0.0717152i	0.844580	+	0.535429i	$0.179850\pi$
$354$	−25.9708			−1.38033
$355$	5.33032	−	9.23239i	0.282904	−	0.490005i
$356$	0.725397	−	1.25642i	0.0384459	−	0.0665903i
$357$	4.44721	+	7.70280i	0.235372	+	0.407675i
$358$	5.14893	+	8.91822i	0.272130	+	0.471342i
$359$	6.08260			0.321027			0.160514	−	0.987034i	$-0.448685\pi$
$359$	6.08260			0.321027			0.160514	+	0.987034i	$0.448685\pi$
$360$	20.9040			1.10174
$361$	37.0078			1.94778
$362$	−12.2266	−	21.1771i	−0.642616	−	1.11304i
$363$	−12.9749	−	22.4731i	−0.681004	−	1.17953i
$364$	5.96753	+	10.3361i	0.312784	+	0.541757i
$365$	−20.7104			−1.08403
$366$	8.18007	+	14.1683i	0.427579	+	0.740589i
$367$	13.6748	−	23.6855i	0.713819	−	1.23637i	−0.249594	−	0.968351i	$-0.580297\pi$
$367$	13.6748	−	23.6855i	0.713819	−	1.23637i	0.963413	−	0.268021i	$-0.0863696\pi$
$368$	9.42652			0.491391
$369$	−9.44961	−	16.3672i	−0.491927	−	0.852042i
$370$	1.83223			0.0952534
$371$	−11.1280	−	19.2743i	−0.577737	−	1.00067i
$372$	−3.63893			−0.188670
$373$	−24.1598			−1.25095			−0.625473	−	0.780246i	$-0.715094\pi$
$373$	−24.1598			−1.25095			−0.625473	+	0.780246i	$0.715094\pi$
$374$	−0.739080	−	1.28012i	−0.0382169	−	0.0661937i
$375$	13.4863	−	23.3590i	0.696430	−	1.20625i
$376$		0			0
$377$	−18.7123	−	32.4106i	−0.963731	−	1.66923i
$378$	−13.2386	+	22.9299i	−0.680921	+	1.17939i
$379$	5.32292	−	9.21957i	0.273420	−	0.473577i	−0.696315	−	0.717736i	$-0.745178\pi$
$379$	5.32292	−	9.21957i	0.273420	−	0.473577i	0.969735	+	0.244159i	$0.0785118\pi$
$380$	13.2571	−	22.9620i	0.680076	−	1.17793i
$381$	−9.50619			−0.487017
$382$	20.6149			1.05475
$383$	−17.5586	+	30.4123i	−0.897201	+	1.55400i	−0.0661448	+	0.997810i	$0.521070\pi$
$383$	−17.5586	+	30.4123i	−0.897201	+	1.55400i	−0.831056	+	0.556188i	$0.812263\pi$
$384$	1.49167	−	2.58365i	0.0761214	−	0.131846i
$385$	−8.22399	+	14.2444i	−0.419133	+	0.725960i
$386$	2.42331	+	4.19729i	0.123343	+	0.213637i
$387$	−5.73120	−	9.92672i	−0.291333	−	0.504604i
$388$	−1.65373	+	2.86434i	−0.0839553	+	0.145415i
$389$	−0.0602435	−	0.104345i	−0.00305447	−	0.00529050i	0.864494	−	0.502643i	$-0.167639\pi$
$389$	−0.0602435	−	0.104345i	−0.00305447	−	0.00529050i	−0.867549	+	0.497352i	$0.834306\pi$
$390$	−41.2246			−2.08749
$391$	−9.18419			−0.464465
$392$	−1.18189	−	2.04709i	−0.0596945	−	0.103394i
$393$	27.6539			1.39496
$394$	9.84165	+	17.0462i	0.495815	+	0.858777i
$395$	37.8719			1.90554
$396$	4.47586	−	7.75242i	0.224920	−	0.389574i
$397$	0.370272	+	0.641330i	0.0185834	+	0.0321874i	0.875168	−	0.483820i	$-0.160751\pi$
$397$	0.370272	+	0.641330i	0.0185834	+	0.0321874i	−0.856584	+	0.516007i	$0.827418\pi$
$398$	−4.21441			−0.211249
$399$	34.1604	+	59.1675i	1.71016	+	2.96208i
$400$	−3.77596	−	6.54015i	−0.188798	−	0.327007i
$401$	1.32192	+	2.28963i	0.0660134	+	0.114339i	0.897143	−	0.441740i	$-0.145639\pi$
$401$	1.32192	+	2.28963i	0.0660134	+	0.114339i	−0.831130	+	0.556079i	$0.812305\pi$
$402$	−30.0811			−1.50031
$403$	4.75740			0.236983
$404$	−0.711633			−0.0354051
$405$	−14.3711	−	24.8916i	−0.714108	−	1.23687i
$406$	14.6809	+	25.4281i	0.728602	+	1.26198i
$407$	0.392309	−	0.679499i	0.0194460	−	0.0336815i
$408$	−1.45332	+	2.51723i	−0.0719503	+	0.124621i
$409$	15.9601			0.789174			0.394587	−	0.918859i	$-0.370888\pi$
$409$	15.9601			0.789174			0.394587	+	0.918859i	$0.370888\pi$
$410$	−5.67406	+	9.82776i	−0.280222	+	0.485358i
$411$	28.3742	+	49.1456i	1.39960	+	2.42417i
$412$	5.83146	−	10.1004i	0.287296	−	0.497611i
$413$	−26.6385			−1.31079
$414$	−27.8097	−	48.1678i	−1.36677	−	2.36732i
$415$	7.35518	+	12.7395i	0.361051	+	0.625359i
$416$	−1.95015	+	3.37777i	−0.0956142	+	0.165609i
$417$	−17.5718			−0.860496
$418$	−5.67710	−	9.83302i	−0.277676	−	0.480949i
$419$	34.6031			1.69047			0.845237	−	0.534392i	$-0.179459\pi$
$419$	34.6031			1.69047			0.845237	+	0.534392i	$0.179459\pi$
$420$	32.3432			1.57819
$421$	−12.5597	−	21.7540i	−0.612122	−	1.06023i	−0.990882	−	0.134732i	$-0.956983\pi$
$421$	−12.5597	−	21.7540i	−0.612122	−	1.06023i	0.378760	−	0.925495i	$-0.376351\pi$
$422$	4.17845	−	7.23729i	0.203404	−	0.352306i
$423$		0			0
$424$	3.63657	−	6.29872i	0.176607	−	0.305893i
$425$	3.67889	+	6.37202i	0.178452	+	0.309089i
$426$	−4.48850	+	7.77431i	−0.217469	+	0.376667i
$427$	8.39035	+	14.5325i	0.406038	+	0.703278i
$428$	−13.9780			−0.675652
$429$	−8.82680	+	15.2885i	−0.426162	+	0.738134i
$430$	−3.44132	+	5.96055i	−0.165955	+	0.287443i
$431$	−19.8230	+	34.3344i	−0.954840	+	1.65383i	−0.220106	+	0.975476i	$0.570640\pi$
$431$	−19.8230	+	34.3344i	−0.954840	+	1.65383i	−0.734734	+	0.678355i	$0.762693\pi$
$432$	−8.65260			−0.416299
$433$	−0.0841685	+	0.145784i	−0.00404488	+	0.00700594i	−0.868041	−	0.496493i	$-0.834621\pi$
$433$	−0.0841685	+	0.145784i	−0.00404488	+	0.00700594i	0.863996	+	0.503499i	$0.167954\pi$
$434$	−3.73247			−0.179164
$435$	−101.418			−4.86262
$436$	8.11588	−	6.56753i	0.388680	−	0.314528i
$437$	−70.5465			−3.37470
$438$	17.4395			0.833294
$439$	−0.472677	+	0.818701i	−0.0225596	+	0.0390745i	−0.877085	−	0.480336i	$-0.840515\pi$
$439$	−0.472677	+	0.818701i	−0.0225596	+	0.0390745i	0.854525	+	0.519410i	$0.173848\pi$
$440$	−5.37510			−0.256248
$441$	−6.97352	+	12.0785i	−0.332072	+	0.575166i
$442$	1.90002	−	3.29094i	0.0903749	−	0.156534i
$443$	2.08086	−	3.60416i	0.0988647	−	0.171239i	−0.812350	−	0.583170i	$-0.801812\pi$
$443$	2.08086	−	3.60416i	0.0988647	−	0.171239i	0.911215	+	0.411931i	$0.135146\pi$
$444$	−1.54287			−0.0732213
$445$	2.56998	+	4.45134i	0.121829	+	0.211014i
$446$	−9.27130	+	16.0584i	−0.439009	+	0.760385i
$447$	−11.9618	−	20.7185i	−0.565775	−	0.979951i
$448$	1.53001	−	2.65006i	0.0722864	−	0.125204i
$449$	14.2468	−	24.6762i	0.672348	−	1.16454i	−0.304888	−	0.952388i	$-0.598619\pi$
$449$	14.2468	−	24.6762i	0.672348	−	1.16454i	0.977236	−	0.212153i	$-0.0680477\pi$
$450$	−22.2793	+	38.5889i	−1.05026	+	1.81910i
$451$	2.42980	+	4.20854i	0.114415	+	0.198172i
$452$	0.194043			0.00912703
$453$	34.7945			1.63479
$454$	2.60290	+	4.50835i	0.122160	+	0.211587i
$455$	−42.2843			−1.98232
$456$	−11.1634	+	19.3356i	−0.522775	+	0.905472i
$457$	7.53981	+	13.0593i	0.352697	+	0.610890i	0.986721	−	0.162424i	$-0.0519312\pi$
$457$	7.53981	+	13.0593i	0.352697	+	0.610890i	−0.634024	+	0.773314i	$0.718598\pi$
$458$	7.54557	+	13.0693i	0.352582	+	0.610689i
$459$	8.43018			0.393487
$460$	−16.6984	+	28.9226i	−0.778569	+	1.34852i
$461$	−10.4944	−	18.1768i	−0.488771	−	0.846576i	0.511146	−	0.859494i	$-0.329221\pi$
$461$	−10.4944	−	18.1768i	−0.488771	−	0.846576i	−0.999917	+	0.0129182i	$0.995888\pi$
$462$	6.92516	−	11.9947i	0.322188	−	0.558045i
$463$	−18.8040			−0.873897			−0.436948	−	0.899487i	$-0.643941\pi$
$463$	−18.8040			−0.873897			−0.436948	+	0.899487i	$0.643941\pi$
$464$	−4.79764	+	8.30976i	−0.222725	+	0.385771i
$465$	6.44612	−	11.1650i	0.298932	−	0.517765i
$466$	−9.56210	−	16.5620i	−0.442956	−	0.767222i
$467$	−9.52286	−	16.4941i	−0.440665	−	0.763255i	0.557074	−	0.830463i	$-0.311924\pi$
$467$	−9.52286	−	16.4941i	−0.440665	−	0.763255i	−0.997739	+	0.0672082i	$0.978591\pi$
$468$	23.0130			1.06378
$469$	−30.8544			−1.42472
$470$		0			0
$471$	−5.95238	−	10.3098i	−0.274271	−	0.475051i
$472$	−4.35265	−	7.53901i	−0.200347	−	0.347011i
$473$	1.47368	+	2.55248i	0.0677598	+	0.117363i
$474$	−31.8907			−1.46479
$475$	28.2586	+	48.9454i	1.29660	+	2.24577i
$476$	−1.49068	+	2.58194i	−0.0683254	+	0.118343i
$477$	−42.9137			−1.96489
$478$	14.6167	+	25.3169i	0.668554	+	1.15797i
$479$	−36.6083			−1.67268			−0.836339	−	0.548213i	$-0.815308\pi$
$479$	−36.6083			−1.67268			−0.836339	+	0.548213i	$0.815308\pi$
$480$	5.28479	+	9.15352i	0.241216	+	0.417799i
$481$	2.01709			0.0919714
$482$	10.1794			0.463657
$483$	−43.0278	−	74.5264i	−1.95783	−	3.39107i
$484$	4.34911	−	7.53288i	0.197687	−	0.342404i
$485$	−5.85894	−	10.1480i	−0.266041	−	0.460796i
$486$	−0.877411	−	1.51972i	−0.0398002	−	0.0689359i
$487$	9.96753	−	17.2643i	0.451672	−	0.782319i	−0.546818	−	0.837251i	$-0.684161\pi$
$487$	9.96753	−	17.2643i	0.451672	−	0.782319i	0.998490	+	0.0549327i	$0.0174944\pi$
$488$	−2.74192	+	4.74914i	−0.124121	+	0.214984i
$489$	18.7018	−	32.3926i	0.845727	−	1.46484i
$490$	8.37456			0.378324
$491$	23.0615			1.04075			0.520376	−	0.853938i	$-0.325792\pi$
$491$	23.0615			1.04075			0.520376	+	0.853938i	$0.325792\pi$
$492$	4.77795	−	8.27565i	0.215407	−	0.373095i
$493$	4.67431	−	8.09614i	0.210520	−	0.364632i
$494$	14.5946	−	25.2787i	0.656644	−	1.13734i
$495$	15.8574	+	27.4658i	0.712736	+	1.23450i
$496$	−0.609875	−	1.05633i	−0.0273842	−	0.0474308i
$497$	−4.60388	+	7.97416i	−0.206512	+	0.357690i
$498$	−6.19357	−	10.7276i	−0.277540	−	0.480714i
$499$	−6.03247			−0.270051			−0.135025	−	0.990842i	$-0.543112\pi$
$499$	−6.03247			−0.270051			−0.135025	+	0.990842i	$0.543112\pi$
$500$	9.04109			0.404330
$501$	15.6344	+	27.0795i	0.698493	+	1.20982i
$502$	−0.0771191			−0.00344199
$503$	10.3513	+	17.9290i	0.461543	+	0.799416i	0.999038	−	0.0438509i	$-0.0139627\pi$
$503$	10.3513	+	17.9290i	0.461543	+	0.799416i	−0.537495	+	0.843267i	$0.680629\pi$
$504$	−18.0551			−0.804239
$505$	1.26061	−	2.18344i	0.0560965	−	0.0971619i
$506$	7.15077	+	12.3855i	0.317891	+	0.550603i
$507$	−6.60037			−0.293133
$508$	−1.59321	−	2.75953i	−0.0706874	−	0.122434i
$509$	11.9180	+	20.6427i	0.528258	+	0.914970i	0.999457	+	0.0329430i	$0.0104880\pi$
$509$	11.9180	+	20.6427i	0.528258	+	0.914970i	−0.471199	+	0.882027i	$0.656179\pi$
$510$	−5.14893	−	8.91822i	−0.227999	−	0.394905i
$511$	17.8879			0.791312
$512$	1.00000			0.0441942
$513$	64.7547			2.85899
$514$	−5.58235	−	9.66892i	−0.246227	−	0.426478i
$515$	20.6601	+	35.7844i	0.910393	+	1.57685i
$516$	2.89783	−	5.01919i	0.127570	−	0.220958i
$517$		0			0
$518$	−1.58253			−0.0695324
$519$	16.2731	−	28.1859i	0.714312	−	1.23722i
$520$	−6.90914	−	11.9670i	−0.302986	−	0.524787i
$521$	−5.48421	+	9.49892i	−0.240267	+	0.416155i	−0.960790	−	0.277276i	$-0.910568\pi$
$521$	−5.48421	+	9.49892i	−0.240267	+	0.416155i	0.720523	+	0.693431i	$0.243902\pi$
$522$	56.6151			2.47798
$523$	4.01005	+	6.94560i	0.175347	+	0.303710i	0.940281	−	0.340398i	$-0.110562\pi$
$523$	4.01005	+	6.94560i	0.175347	+	0.303710i	−0.764934	+	0.644108i	$0.777229\pi$
$524$	4.63473	+	8.02758i	0.202469	+	0.350687i
$525$	−34.4711	+	59.7057i	−1.50444	+	2.60577i
$526$	−15.1235			−0.659414
$527$	0.594197	+	1.02918i	0.0258836	+	0.0448318i
$528$	4.52621			0.196978
$529$	65.8592			2.86344
$530$	12.8839	+	22.3155i	0.559640	+	0.969325i
$531$	−25.6820	+	44.4825i	−1.11450	+	1.93037i
$532$	−11.4504	+	19.8326i	−0.496437	+	0.859854i
$533$	−6.24652	+	10.8193i	−0.270567	+	0.468635i
$534$	−2.16410	−	3.74834i	−0.0936499	−	0.162206i
$535$	24.7611	−	42.8875i	1.07052	−	1.85419i
$536$	−5.04151	−	8.73216i	−0.217760	−	0.377172i
$537$	30.7220			1.32575
$538$	−14.0441	+	24.3251i	−0.605483	+	1.04873i
$539$	1.79312	−	3.10577i	0.0772351	−	0.133775i
$540$	15.3275	−	26.5480i	0.659591	−	1.14245i
$541$	43.8040			1.88328			0.941642	−	0.336617i	$-0.109283\pi$
$541$	43.8040			1.88328			0.941642	+	0.336617i	$0.109283\pi$
$542$	−5.65812	+	9.80015i	−0.243037	+	0.420952i
$543$	−72.9522			−3.13068
$544$	−0.974294			−0.0417725
$545$	5.77383	+	36.5352i	0.247324	+	1.56500i
$546$	35.6063			1.52381
$547$	22.2469			0.951208			0.475604	−	0.879659i	$-0.342230\pi$
$547$	22.2469			0.951208			0.475604	+	0.879659i	$0.342230\pi$
$548$	−9.51090	+	16.4734i	−0.406285	+	0.703707i
$549$	32.3563			1.38094
$550$	5.72874	−	9.92246i	0.244274	−	0.423095i
$551$	35.9048	−	62.1889i	1.52959	−	2.64934i
$552$	14.0612	−	24.3548i	0.598486	−	1.03661i
$553$	−32.7105			−1.39099
$554$	9.51385	+	16.4785i	0.404205	+	0.700103i
$555$	2.73309	−	4.73385i	0.116013	−	0.200941i
$556$	−2.94499	−	5.10088i	−0.124896	−	0.216325i
$557$	9.75048	−	16.8883i	0.413141	−	0.715581i	−0.582090	−	0.813124i	$-0.697765\pi$
$557$	9.75048	−	16.8883i	0.413141	−	0.715581i	0.995231	+	0.0975429i	$0.0310983\pi$
$558$	−3.59845	+	6.23270i	−0.152335	+	0.263851i
$559$	−3.78852	+	6.56191i	−0.160237	+	0.277539i
$560$	5.42064	+	9.38882i	0.229064	+	0.396750i
$561$	−4.40985			−0.186184
$562$	−10.4148			−0.439320
$563$	−10.5887	−	18.3402i	−0.446262	−	0.772948i	0.551877	−	0.833925i	$-0.313912\pi$
$563$	−10.5887	−	18.3402i	−0.446262	−	0.772948i	−0.998139	+	0.0609773i	$0.980578\pi$
$564$		0			0
$565$	−0.343735	+	0.595366i	−0.0144610	+	0.0250473i
$566$	−5.42588	−	9.39789i	−0.228067	−	0.395023i
$567$	12.4126	+	21.4992i	0.521279	+	0.902882i
$568$	−3.00904			−0.126257
$569$	−14.4885	+	25.0948i	−0.607389	+	1.05203i	0.384280	+	0.923217i	$0.374450\pi$
$569$	−14.4885	+	25.0948i	−0.607389	+	1.05203i	−0.991669	+	0.128812i	$0.958884\pi$
$570$	−39.5505	−	68.5035i	−1.65659	−	2.86929i
$571$	9.55015	−	16.5414i	0.399662	−	0.692234i	−0.594023	−	0.804448i	$-0.702461\pi$
$571$	9.55015	−	16.5414i	0.399662	−	0.692234i	0.993684	+	0.112214i	$0.0357943\pi$
$572$	−5.91740			−0.247419
$573$	30.7506	−	53.2617i	1.28463	−	2.22504i
$574$	4.90077	−	8.48839i	0.204554	−	0.354298i
$575$	−35.5941	−	61.6508i	−1.48438	−	2.57102i
$576$	−2.95015	−	5.10982i	−0.122923	−	0.212909i
$577$	−34.2512			−1.42589			−0.712947	−	0.701218i	$-0.752640\pi$
$577$	−34.2512			−1.42589			−0.712947	+	0.701218i	$0.752640\pi$
$578$	−16.0508			−0.667623
$579$	14.4591			0.600900
$580$	−16.9974	−	29.4404i	−0.705779	−	1.22244i
$581$	−6.35278	−	11.0033i	−0.263558	−	0.456495i
$582$	4.93363	+	8.54530i	0.204506	+	0.354214i
$583$	11.0345			0.457003
$584$	2.92282	+	5.06248i	0.120947	+	0.209487i
$585$	−40.7661	+	70.6089i	−1.68547	+	2.91932i
$586$	14.4956			0.598807
$587$	−19.7475	−	34.2036i	−0.815065	−	1.41173i	−0.909281	−	0.416182i	$-0.863368\pi$
$587$	−19.7475	−	34.2036i	−0.815065	−	1.41173i	0.0942161	−	0.995552i	$-0.469966\pi$
$588$	−7.05196			−0.290818
$589$	4.56421	+	7.90544i	0.188065	+	0.325738i
$590$	30.8417			1.26973
$591$	58.7219			2.41550
$592$	−0.258581	−	0.447875i	−0.0106276	−	0.0184075i
$593$	−8.05452	+	13.9508i	−0.330760	+	0.572892i	−0.982661	−	0.185411i	$-0.940638\pi$
$593$	−8.05452	+	13.9508i	−0.330760	+	0.572892i	0.651901	+	0.758304i	$0.273972\pi$
$594$	−6.56370	−	11.3687i	−0.269312	−	0.466462i
$595$	−5.28129	−	9.14747i	−0.216512	−	0.375010i
$596$	4.00955	−	6.94474i	0.164237	−	0.284467i
$597$	−6.28651	+	10.8886i	−0.257290	+	0.445639i
$598$	−18.3832	+	31.8406i	−0.751743	+	1.30206i
$599$	−19.4555			−0.794930			−0.397465	−	0.917617i	$-0.630110\pi$
$599$	−19.4555			−0.794930			−0.397465	+	0.917617i	$0.630110\pi$
$600$	−22.5299			−0.919780
$601$	10.7945	−	18.6966i	0.440316	−	0.762649i	−0.557397	−	0.830246i	$-0.688200\pi$
$601$	10.7945	−	18.6966i	0.440316	−	0.762649i	0.997713	+	0.0675970i	$0.0215332\pi$
$602$	2.97232	−	5.14822i	0.121143	−	0.209826i
$603$	−29.7465	+	51.5224i	−1.21137	+	2.09816i
$604$	5.83146	+	10.1004i	0.237279	+	0.410979i
$605$	15.4083	+	26.6880i	0.626437	+	1.08502i
$606$	−1.06152	+	1.83861i	−0.0431214	+	0.0746884i
$607$	−6.57949	−	11.3960i	−0.267053	−	0.462550i	0.701046	−	0.713116i	$-0.252717\pi$
$607$	−6.57949	−	11.3960i	−0.267053	−	0.462550i	−0.968100	+	0.250566i	$0.919383\pi$
$608$	−7.48384			−0.303510
$609$	87.5963			3.54958
$610$	−9.71426	−	16.8256i	−0.393319	−	0.681248i
$611$		0			0
$612$	2.87432	+	4.97846i	0.116187	+	0.201242i
$613$	2.52082			0.101815			0.0509075	−	0.998703i	$-0.483789\pi$
$613$	2.52082			0.101815			0.0509075	+	0.998703i	$0.483789\pi$
$614$	−11.3825	+	19.7151i	−0.459361	+	0.795636i
$615$	16.9276	+	29.3195i	0.682588	+	1.18228i
$616$	4.64256			0.187054
$617$	−7.81246	−	13.5316i	−0.314518	−	0.544761i	0.664817	−	0.747006i	$-0.268510\pi$
$617$	−7.81246	−	13.5316i	−0.314518	−	0.544761i	−0.979335	+	0.202245i	$0.935176\pi$
$618$	−17.3972	−	30.1329i	−0.699819	−	1.21212i
$619$	−21.4192	−	37.0992i	−0.860911	−	1.49114i	−0.871051	−	0.491192i	$-0.836561\pi$
$619$	−21.4192	−	37.0992i	−0.860911	−	1.49114i	0.0101405	−	0.999949i	$-0.496772\pi$
$620$	4.32141			0.173552
$621$	−81.5639			−3.27305
$622$	19.5083			0.782210
$623$	−2.21974	−	3.84469i	−0.0889318	−	0.154034i
$624$	5.81797	+	10.0770i	0.232905	+	0.403404i
$625$	2.86409	−	4.96075i	0.114564	−	0.198430i
$626$	−5.61418	+	9.72405i	−0.224388	+	0.388651i
$627$	−33.8734			−1.35277
$628$	1.99521	−	3.45580i	0.0796174	−	0.137901i
$629$	0.251934	+	0.436362i	0.0100452	+	0.0173989i
$630$	31.9835	−	55.3970i	1.27425	−	2.20707i
$631$	−33.2525			−1.32376			−0.661881	−	0.749609i	$-0.730242\pi$
$631$	−33.2525			−1.32376			−0.661881	+	0.749609i	$0.730242\pi$
$632$	−5.34480	−	9.25747i	−0.212605	−	0.368242i
$633$	−12.4657	−	21.5913i	−0.495468	−	0.858176i
$634$	−6.78713	+	11.7556i	−0.269551	+	0.466876i
$635$	11.2891			0.447994
$636$	−10.8491	−	18.7912i	−0.430195	−	0.745120i
$637$	9.21947			0.365289
$638$	−14.5576			−0.576341
$639$	8.87715	+	15.3757i	0.351175	+	0.608252i
$640$	−1.77143	+	3.06821i	−0.0700221	+	0.121282i
$641$	−0.449244	+	0.778114i	−0.0177441	+	0.0307336i	−0.874761	−	0.484554i	$-0.838982\pi$
$641$	−0.449244	+	0.778114i	−0.0177441	+	0.0307336i	0.857017	+	0.515288i	$0.172315\pi$
$642$	−20.8506	+	36.1142i	−0.822906	+	1.42531i
$643$	13.1353	+	22.7511i	0.518007	+	0.897214i	0.999781	+	0.0209187i	$0.00665911\pi$
$643$	13.1353	+	22.7511i	0.518007	+	0.897214i	−0.481774	+	0.876295i	$0.660008\pi$
$644$	14.4227	−	24.9809i	0.568334	−	0.984384i
$645$	10.2666	+	17.7823i	0.404248	+	0.700179i
$646$	7.29146			0.286879
$647$	11.0353	−	19.1137i	0.433843	−	0.751438i	−0.563358	−	0.826213i	$-0.690491\pi$
$647$	11.0353	−	19.1137i	0.433843	−	0.751438i	0.997200	+	0.0747755i	$0.0238240\pi$
$648$	−4.05636	+	7.02582i	−0.159349	+	0.276000i
$649$	6.60367	−	11.4379i	0.259217	−	0.448976i
$650$	29.4548			1.15531
$651$	−5.56761	+	9.64338i	−0.218212	+	0.377954i
$652$	12.5375			0.491008
$653$	−20.2535			−0.792581			−0.396290	−	0.918125i	$-0.629703\pi$
$653$	−20.2535			−0.792581			−0.396290	+	0.918125i	$0.629703\pi$
$654$	−4.86196	−	30.7652i	−0.190118	−	1.20301i
$655$	−32.8405			−1.28318
$656$	3.20309			0.125060
$657$	17.2456	−	29.8702i	0.672813	−	1.16535i
$658$		0			0
$659$	4.25110	−	7.36313i	0.165599	−	0.286827i	−0.771269	−	0.636510i	$-0.780377\pi$
$659$	4.25110	−	7.36313i	0.165599	−	0.286827i	0.936868	+	0.349683i	$0.113711\pi$
$660$	−8.01788	+	13.8874i	−0.312095	+	0.540565i
$661$	5.75360	−	9.96552i	0.223789	−	0.387614i	−0.732166	−	0.681126i	$-0.761491\pi$
$661$	5.75360	−	9.96552i	0.223789	−	0.387614i	0.955955	+	0.293512i	$0.0948240\pi$
$662$	−23.3226			−0.906459
$663$	−5.66841	−	9.81798i	−0.220143	−	0.381299i
$664$	2.07605	−	3.59583i	0.0805664	−	0.139545i
$665$	−40.5672	−	70.2644i	−1.57313	−	2.72474i
$666$	−1.52571	+	2.64260i	−0.0591199	+	0.102399i
$667$	−45.2250	+	78.3321i	−1.75112	+	3.03303i
$668$	−5.24057	+	9.07693i	−0.202764	+	0.351197i
$669$	27.6594	+	47.9075i	1.06937	+	1.85221i
$670$	35.7228			1.38009
$671$	−8.31987			−0.321185
$672$	−4.56455	−	7.90604i	−0.176081	−	0.304982i
$673$	20.1092			0.775154			0.387577	−	0.921837i	$-0.373312\pi$
$673$	20.1092			0.775154			0.387577	+	0.921837i	$0.373312\pi$
$674$	9.62323	−	16.6679i	0.370673	−	0.642024i
$675$	32.6719	+	56.5893i	1.25754	+	2.17812i
$676$	−1.10621	−	1.91600i	−0.0425464	−	0.0736925i
$677$	−10.9401			−0.420463			−0.210231	−	0.977652i	$-0.567422\pi$
$677$	−10.9401			−0.420463			−0.210231	+	0.977652i	$0.567422\pi$
$678$	0.289448	−	0.501339i	0.0111162	−	0.0192538i
$679$	5.06046	+	8.76497i	0.194203	+	0.336369i
$680$	1.72590	−	2.98934i	0.0661851	−	0.114636i
$681$	15.5306			0.595136
$682$	0.925279	−	1.60263i	0.0354308	−	0.0613679i
$683$	6.74509	−	11.6828i	0.258094	−	0.447031i	−0.707638	−	0.706576i	$-0.750239\pi$
$683$	6.74509	−	11.6828i	0.258094	−	0.447031i	0.965731	+	0.259544i	$0.0835724\pi$
$684$	22.0785	+	38.2411i	0.844192	+	1.46218i
$685$	−33.6959	−	58.3629i	−1.28745	−	2.22993i
$686$	14.1870			0.541661
$687$	45.0220			1.71770
$688$	1.94268			0.0740639
$689$	14.1837	+	24.5669i	0.540357	+	0.935926i
$690$	49.8171	+	86.2858i	1.89651	+	3.28484i
$691$	2.93434	+	5.08242i	0.111627	+	0.193344i	0.916427	−	0.400203i	$-0.131060\pi$
$691$	2.93434	+	5.08242i	0.111627	+	0.193344i	−0.804799	+	0.593547i	$0.797727\pi$
$692$	10.9094			0.414711
$693$	−13.6963	−	23.7226i	−0.520278	−	0.901148i
$694$	7.36442	−	12.7555i	0.279550	−	0.484194i
$695$	20.8674			0.791547
$696$	14.3130	+	24.7908i	0.542532	+	0.939694i
$697$	−3.12075			−0.118207
$698$	−2.72477	−	4.71944i	−0.103134	−	0.178634i
$699$	−57.0539			−2.15798
$700$	−23.1091			−0.873441
$701$	1.39921	+	2.42350i	0.0528473	+	0.0915342i	0.891239	−	0.453534i	$-0.149837\pi$
$701$	1.39921	+	2.42350i	0.0528473	+	0.0915342i	−0.838392	+	0.545068i	$0.816504\pi$
$702$	16.8739	−	29.2265i	0.636865	−	1.10308i
$703$	1.93518	+	3.35182i	0.0729866	+	0.126416i
$704$	0.758581	+	1.31390i	0.0285901	+	0.0495195i
$705$		0			0
$706$	−0.777926	+	1.34741i	−0.0292776	+	0.0507103i
$707$	−1.08881	+	1.88587i	−0.0409489	+	0.0709255i
$708$	−25.9708			−0.976044
$709$	−25.3417			−0.951726			−0.475863	−	0.879519i	$-0.657864\pi$
$709$	−25.3417			−0.951726			−0.475863	+	0.879519i	$0.657864\pi$
$710$	5.33032	−	9.23239i	0.200044	−	0.346486i
$711$	−31.5360	+	54.6219i	−1.18269	+	2.04848i
$712$	0.725397	−	1.25642i	0.0271854	−	0.0470865i
$713$	−5.74899	−	9.95755i	−0.215302	−	0.372913i
$714$	4.44721	+	7.70280i	0.166433	+	0.288270i
$715$	10.4823	−	18.1558i	0.392015	−	0.678990i
$716$	5.14893	+	8.91822i	0.192425	+	0.333289i
$717$	87.2133			3.25704
$718$	6.08260			0.227001
$719$	−3.99370	−	6.91729i	−0.148940	−	0.257971i	0.781896	−	0.623409i	$-0.214253\pi$
$719$	−3.99370	−	6.91729i	−0.148940	−	0.257971i	−0.930836	+	0.365437i	$0.880919\pi$
$720$	20.9040			0.779047
$721$	−17.8444	−	30.9075i	−0.664562	−	1.15106i
$722$	37.0078			1.37729
$723$	15.1842	−	26.2999i	0.564708	−	0.978102i
$724$	−12.2266	−	21.1771i	−0.454398	−	0.787041i
$725$	72.4627			2.69120
$726$	−12.9749	−	22.4731i	−0.481543	−	0.834056i
$727$	24.0083	+	41.5836i	0.890419	+	1.54225i	0.839374	+	0.543554i	$0.182922\pi$
$727$	24.0083	+	41.5836i	0.890419	+	1.54225i	0.0510446	+	0.998696i	$0.483745\pi$
$728$	5.96753	+	10.3361i	0.221171	+	0.383080i
$729$	−29.5734			−1.09531
$730$	−20.7104			−0.766525
$731$	−1.89274			−0.0700054
$732$	8.18007	+	14.1683i	0.302344	+	0.523676i
$733$	−19.5703	−	33.8968i	−0.722846	−	1.25201i	−0.959855	−	0.280498i	$-0.909500\pi$
$733$	−19.5703	−	33.8968i	−0.722846	−	1.25201i	0.237009	−	0.971507i	$-0.423833\pi$
$734$	13.6748	−	23.6855i	0.504746	−	0.874247i
$735$	12.4921	−	21.6369i	0.460777	−	0.798089i
$736$	9.42652			0.347466
$737$	7.64879	−	13.2481i	0.281747	−	0.488000i
$738$	−9.44961	−	16.3672i	−0.347845	−	0.602485i
$739$	1.22180	−	2.11622i	0.0449447	−	0.0778466i	−0.842678	−	0.538418i	$-0.819022\pi$
$739$	1.22180	−	2.11622i	0.0449447	−	0.0778466i	0.887623	+	0.460571i	$0.152355\pi$
$740$	1.83223			0.0673543
$741$	−43.5408	−	75.4148i	−1.59951	−	2.77043i
$742$	−11.1280	−	19.2743i	−0.408522	−	0.707581i
$743$	−25.3244	+	43.8631i	−0.929061	+	1.60918i	−0.144164	+	0.989554i	$0.546049\pi$
$743$	−25.3244	+	43.8631i	−0.929061	+	1.60918i	−0.784897	+	0.619627i	$0.787284\pi$
$744$	−3.63893			−0.133410
$745$	14.2053	+	24.6043i	0.520441	+	0.901431i
$746$	−24.1598			−0.884553
$747$	−24.4987			−0.896360
$748$	−0.739080	−	1.28012i	−0.0270235	−	0.0468060i
$749$	−21.3865	+	37.0426i	−0.781447	+	1.35351i
$750$	13.4863	−	23.3590i	0.492451	−	0.852950i
$751$	−21.3402	+	36.9623i	−0.778716	+	1.34877i	0.153967	+	0.988076i	$0.450795\pi$
$751$	−21.3402	+	36.9623i	−0.778716	+	1.34877i	−0.932682	+	0.360699i	$0.882538\pi$
$752$		0			0
$753$	−0.115036	+	0.199249i	−0.00419215	+	0.00726102i
$754$	−18.7123	−	32.4106i	−0.681461	−	1.18033i
$755$	−41.3202			−1.50380
$756$	−13.2386	+	22.9299i	−0.481484	+	0.833954i
$757$	−3.50248	+	6.06647i	−0.127300	+	0.220490i	−0.922630	−	0.385687i	$-0.873964\pi$
$757$	−3.50248	+	6.06647i	−0.127300	+	0.220490i	0.795330	+	0.606177i	$0.207298\pi$
$758$	5.32292	−	9.21957i	0.193337	−	0.334870i
$759$	42.6664			1.54869
$760$	13.2571	−	22.9620i	0.480886	−	0.832920i
$761$	−2.82051			−0.102244			−0.0511218	−	0.998692i	$-0.516280\pi$
$761$	−2.82051			−0.102244			−0.0511218	+	0.998692i	$0.516280\pi$
$762$	−9.50619			−0.344373
$763$	−4.98695	−	31.5560i	−0.180540	−	1.14240i
$764$	20.6149			0.745821
$765$	−20.3666			−0.736358
$766$	−17.5586	+	30.4123i	−0.634417	+	1.09884i
$767$	33.9533			1.22598
$768$	1.49167	−	2.58365i	0.0538260	−	0.0932293i
$769$	−5.52008	+	9.56106i	−0.199059	+	0.344781i	−0.948224	−	0.317603i	$-0.897122\pi$
$769$	−5.52008	+	9.56106i	−0.199059	+	0.344781i	0.749164	+	0.662384i	$0.230455\pi$
$770$	−8.22399	+	14.2444i	−0.296372	+	0.513331i
$771$	−33.3081			−1.19956
$772$	2.42331	+	4.19729i	0.0872168	+	0.151064i
$773$	10.8879	−	18.8584i	0.391610	−	0.678288i	−0.601052	−	0.799210i	$-0.705252\pi$
$773$	10.8879	−	18.8584i	0.391610	−	0.678288i	0.992662	+	0.120922i	$0.0385850\pi$
$774$	−5.73120	−	9.92672i	−0.206004	−	0.356809i
$775$	−4.60572	+	7.97734i	−0.165442	+	0.286555i
$776$	−1.65373	+	2.86434i	−0.0593654	+	0.102824i
$777$	−2.36061	+	4.08870i	−0.0846864	+	0.146681i
$778$	−0.0602435	−	0.104345i	−0.00215984	−	0.00374095i
$779$	−23.9714			−0.858864
$780$	−41.2246			−1.47608
$781$	−2.28260	−	3.95359i	−0.0816780	−	0.141470i
$782$	−9.18419			−0.328426
$783$	41.5121	−	71.9010i	1.48352	−	2.56953i
$784$	−1.18189	−	2.04709i	−0.0422104	−	0.0731105i
$785$	7.06875	+	12.2434i	0.252295	+	0.436987i
$786$	27.6539			0.986383
$787$	−8.73918	+	15.1367i	−0.311518	+	0.539565i	−0.978691	−	0.205338i	$-0.934171\pi$
$787$	−8.73918	+	15.1367i	−0.311518	+	0.539565i	0.667173	+	0.744903i	$0.267504\pi$
$788$	9.84165	+	17.0462i	0.350594	+	0.607247i
$789$	−22.5592	+	39.0737i	−0.803129	+	1.39106i
$790$	37.8719			1.34742
$791$	0.296889	−	0.514227i	0.0105562	−	0.0182838i
$792$	4.47586	−	7.75242i	0.159043	−	0.275470i
$793$	−10.6943	−	18.5231i	−0.379767	−	0.657776i
$794$	0.370272	+	0.641330i	0.0131405	+	0.0227599i
$795$	76.8739			2.72644
$796$	−4.21441			−0.149376
$797$	−0.997866			−0.0353462			−0.0176731	−	0.999844i	$-0.505626\pi$
$797$	−0.997866			−0.0353462			−0.0176731	+	0.999844i	$0.505626\pi$
$798$	34.1604	+	59.1675i	1.20926	+	2.09451i
$799$		0			0
$800$	−3.77596	−	6.54015i	−0.133500	−	0.231229i
$801$	−8.56013			−0.302457
$802$	1.32192	+	2.28963i	0.0466786	+	0.0808496i
$803$	−4.43440	+	7.68060i	−0.156486	+	0.271042i
$804$	−30.0811			−1.06088
$805$	51.0977	+	88.5039i	1.80096	+	3.11935i
$806$	4.75740			0.167572
$807$	41.8983	+	72.5699i	1.47489	+	2.55458i
$808$	−0.711633			−0.0250352
$809$	−36.3839			−1.27919			−0.639595	−	0.768712i	$-0.720898\pi$
$809$	−36.3839			−1.27919			−0.639595	+	0.768712i	$0.720898\pi$
$810$	−14.3711	−	24.8916i	−0.504951	−	0.874600i
$811$	8.08551	−	14.0045i	0.283921	−	0.491765i	−0.688426	−	0.725306i	$-0.741698\pi$
$811$	8.08551	−	14.0045i	0.283921	−	0.491765i	0.972347	+	0.233541i	$0.0750315\pi$
$812$	14.6809	+	25.4281i	0.515199	+	0.892351i
$813$	16.8801	+	29.2372i	0.592010	+	1.02539i
$814$	0.392309	−	0.679499i	0.0137504	−	0.0238164i
$815$	−22.2094	+	38.4678i	−0.777962	+	1.34747i
$816$	−1.45332	+	2.51723i	−0.0508765	+	0.0881207i
$817$	−14.5387			−0.508644
$818$	15.9601			0.558030
$819$	35.2103	−	60.9860i	1.23035	−	2.13102i
$820$	−5.67406	+	9.82776i	−0.198147	+	0.343200i
$821$	−14.3380	+	24.8341i	−0.500399	+	0.866717i	0.499601	+	0.866256i	$0.333480\pi$
$821$	−14.3380	+	24.8341i	−0.500399	+	0.866717i	−1.00000		0.000461227i	$0.999853\pi$
$822$	28.3742	+	49.1456i	0.989665	+	1.71415i
$823$	−3.34262	−	5.78958i	−0.116516	−	0.201812i	0.801869	−	0.597500i	$-0.203839\pi$
$823$	−3.34262	−	5.78958i	−0.116516	−	0.201812i	−0.918385	+	0.395688i	$0.870506\pi$
$824$	5.83146	−	10.1004i	0.203149	−	0.351864i
$825$	−17.0908	−	29.6021i	−0.595024	−	1.03061i
$826$	−26.6385			−0.926870
$827$	16.1112			0.560240			0.280120	−	0.959965i	$-0.409626\pi$
$827$	16.1112			0.560240			0.280120	+	0.959965i	$0.409626\pi$
$828$	−27.8097	−	48.1678i	−0.966453	−	1.67395i
$829$	28.4489			0.988071			0.494035	−	0.869442i	$-0.335521\pi$
$829$	28.4489			0.988071			0.494035	+	0.869442i	$0.335521\pi$
$830$	7.35518	+	12.7395i	0.255302	+	0.442196i
$831$	56.7661			1.96919
$832$	−1.95015	+	3.37777i	−0.0676094	+	0.117103i
$833$	1.15151	+	1.99447i	0.0398974	+	0.0691043i
$834$	−17.5718			−0.608462
$835$	−18.5666	−	32.1584i	−0.642525	−	1.11289i
$836$	−5.67710	−	9.83302i	−0.196346	−	0.340082i
$837$	5.27701	+	9.14004i	0.182400	+	0.315926i
$838$	34.6031			1.19535
$839$	8.16979			0.282053			0.141026	−	0.990006i	$-0.454960\pi$
$839$	8.16979			0.282053			0.141026	+	0.990006i	$0.454960\pi$
$840$	32.3432			1.11595
$841$	−31.5347	−	54.6197i	−1.08740	−	1.88344i
$842$	−12.5597	−	21.7540i	−0.432836	−	0.749694i
$843$	−15.5354	+	26.9081i	−0.535067	+	0.926763i
$844$	4.17845	−	7.23729i	0.143828	−	0.249118i
$845$	7.83828			0.269645
$846$		0			0
$847$	−13.3084	−	23.0508i	−0.457282	−	0.792036i
$848$	3.63657	−	6.29872i	0.124880	−	0.216299i
$849$	−32.3745			−1.11109
$850$	3.67889	+	6.37202i	0.126185	+	0.218559i
$851$	−2.43752	−	4.22190i	−0.0835570	−	0.144725i
$852$	−4.48850	+	7.77431i	−0.153773	+	0.266343i
$853$	27.4923			0.941317			0.470658	−	0.882316i	$-0.344016\pi$
$853$	27.4923			0.941317			0.470658	+	0.882316i	$0.344016\pi$
$854$	8.39035	+	14.5325i	0.287112	+	0.497293i
$855$	−156.442			−5.35021
$856$	−13.9780			−0.477758
$857$	−20.5545	−	35.6014i	−0.702127	−	1.21612i	−0.967718	−	0.252034i	$-0.918901\pi$
$857$	−20.5545	−	35.6014i	−0.702127	−	1.21612i	0.265591	−	0.964086i	$-0.414433\pi$
$858$	−8.82680	+	15.2885i	−0.301342	+	0.521940i
$859$	−5.78406	+	10.0183i	−0.197350	+	0.341819i	−0.947668	−	0.319257i	$-0.896567\pi$
$859$	−5.78406	+	10.0183i	−0.197350	+	0.341819i	0.750319	+	0.661076i	$0.229900\pi$
$860$	−3.44132	+	5.96055i	−0.117348	+	0.203253i
$861$	−14.6207	−	25.3237i	−0.498271	−	0.863030i
$862$	−19.8230	+	34.3344i	−0.675174	+	1.16944i
$863$	−1.87079	−	3.24031i	−0.0636826	−	0.110301i	0.832426	−	0.554136i	$-0.186951\pi$
$863$	−1.87079	−	3.24031i	−0.0636826	−	0.110301i	−0.896109	+	0.443834i	$0.853618\pi$
$864$	−8.65260			−0.294368
$865$	−19.3252	+	33.4722i	−0.657077	+	1.13809i
$866$	−0.0841685	+	0.145784i	−0.00286016	+	0.00495395i
$867$	−23.9424	+	41.4695i	−0.813127	+	1.40838i
$868$	−3.73247			−0.126688
$869$	8.10893	−	14.0451i	0.275077	−	0.476447i
$870$	−101.418			−3.43839
$871$	39.3269			1.33254
$872$	8.11588	−	6.56753i	0.274838	−	0.222405i
$873$	19.5150			0.660483
$874$	−70.5465			−2.38627
$875$	13.8330	−	23.9595i	0.467641	−	0.809978i
$876$	17.4395			0.589228
$877$	−7.61716	+	13.1933i	−0.257213	+	0.445506i	−0.965494	−	0.260424i	$-0.916138\pi$
$877$	−7.61716	+	13.1933i	−0.257213	+	0.445506i	0.708281	+	0.705931i	$0.249471\pi$
$878$	−0.472677	+	0.818701i	−0.0159521	+	0.0276298i
$879$	21.6226	−	37.4515i	0.729313	−	1.26321i
$880$	−5.37510			−0.181195
$881$	−20.4438	−	35.4097i	−0.688769	−	1.19298i	−0.972236	−	0.234002i	$-0.924818\pi$
$881$	−20.4438	−	35.4097i	−0.688769	−	1.19298i	0.283467	−	0.958982i	$-0.408515\pi$
$882$	−6.97352	+	12.0785i	−0.234810	+	0.406704i
$883$	−0.0371024	−	0.0642633i	−0.00124860	−	0.00216263i	0.865400	−	0.501081i	$-0.167064\pi$
$883$	−0.0371024	−	0.0642633i	−0.00124860	−	0.00216263i	−0.866649	+	0.498918i	$0.833731\pi$
$884$	1.90002	−	3.29094i	0.0639047	−	0.110686i
$885$	46.0056	−	79.6841i	1.54646	−	2.67855i
$886$	2.08086	−	3.60416i	0.0699079	−	0.121084i
$887$	8.68189	+	15.0375i	0.291509	+	0.504909i	0.974167	−	0.225830i	$-0.0725092\pi$
$887$	8.68189	+	15.0375i	0.291509	+	0.504909i	−0.682658	+	0.730738i	$0.739176\pi$
$888$	−1.54287			−0.0517753
$889$	−9.75056			−0.327023
$890$	2.56998	+	4.45134i	0.0861461	+	0.149209i
$891$	−12.3083			−0.412344
$892$	−9.27130	+	16.0584i	−0.310426	+	0.537673i
$893$		0			0
$894$	−11.9618	−	20.7185i	−0.400063	−	0.692930i
$895$	−36.4840			−1.21953
$896$	1.53001	−	2.65006i	0.0511142	−	0.0885324i
$897$	54.8432	+	94.9912i	1.83116	+	3.17166i
$898$	14.2468	−	24.6762i	0.475422	−	0.823455i
$899$	11.7038			0.390345
$900$	−22.2793	+	38.5889i	−0.742644	+	1.28630i
$901$	−3.54308	+	6.13680i	−0.118037	+	0.204447i
$902$	2.42980	+	4.20854i	0.0809035	+	0.140129i
$903$	−8.86745	−	15.3589i	−0.295090	−	0.511111i
$904$	0.194043			0.00645379
$905$	86.6345			2.87983
$906$	34.7945			1.15597
$907$	7.51260	+	13.0122i	0.249452	+	0.432063i	0.963374	−	0.268162i	$-0.0864163\pi$
$907$	7.51260	+	13.0122i	0.249452	+	0.432063i	−0.713922	+	0.700225i	$0.753083\pi$
$908$	2.60290	+	4.50835i	0.0863802	+	0.149615i
$909$	2.09943	+	3.63632i	0.0696336	+	0.120609i
$910$	−42.2843			−1.40171
$911$	−5.18063	−	8.97312i	−0.171642	−	0.297293i	0.767352	−	0.641226i	$-0.221574\pi$
$911$	−5.18063	−	8.97312i	−0.171642	−	0.297293i	−0.938994	+	0.343933i	$0.888241\pi$
$912$	−11.1634	+	19.3356i	−0.369658	+	0.640266i
$913$	6.29941			0.208480
$914$	7.53981	+	13.0593i	0.249395	+	0.431964i
$915$	−57.9618			−1.91616
$916$	7.54557	+	13.0693i	0.249313	+	0.431822i
$917$	28.3648			0.936689
$918$	8.43018			0.278237
$919$	−6.90052	−	11.9521i	−0.227627	−	0.394262i	0.729477	−	0.684005i	$-0.239763\pi$
$919$	−6.90052	−	11.9521i	−0.227627	−	0.394262i	−0.957104	+	0.289743i	$0.906430\pi$
$920$	−16.6984	+	28.9226i	−0.550532	+	0.953549i
$921$	33.9579	+	58.8168i	1.11895	+	1.93808i
$922$	−10.4944	−	18.1768i	−0.345613	−	0.598619i
$923$	5.86810	−	10.1639i	0.193151	−	0.334547i
$924$	6.92516	−	11.9947i	0.227821	−	0.394598i
$925$	−1.95278	+	3.38231i	−0.0642070	+	0.111210i
$926$	−18.8040			−0.617938
$927$	−68.8149			−2.26018
$928$	−4.79764	+	8.30976i	−0.157490	+	0.272781i
$929$	−12.7148	+	22.0227i	−0.417160	+	0.722542i	−0.995653	−	0.0931455i	$-0.970308\pi$
$929$	−12.7148	+	22.0227i	−0.417160	+	0.722542i	0.578493	+	0.815688i	$0.303641\pi$
$930$	6.44612	−	11.1650i	0.211377	−	0.366115i
$931$	8.84507	+	15.3201i	0.289886	+	0.502097i
$932$	−9.56210	−	16.5620i	−0.313217	−	0.542508i
$933$	29.0999	−	50.4025i	0.952687	−	1.65010i
$934$	−9.52286	−	16.4941i	−0.311598	−	0.539703i
$935$	5.23693			0.171266
$936$	23.0130			0.752204
$937$	12.8390	+	22.2378i	0.419432	+	0.726477i	0.995882	−	0.0906547i	$-0.0288960\pi$
$937$	12.8390	+	22.2378i	0.419432	+	0.726477i	−0.576450	+	0.817132i	$0.695563\pi$
$938$	−30.8544			−1.00743
$939$	16.7490	+	29.0101i	0.546583	+	0.946710i
$940$		0			0
$941$	−3.13254	+	5.42573i	−0.102118	+	0.176874i	−0.912557	−	0.408949i	$-0.865895\pi$
$941$	−3.13254	+	5.42573i	−0.102118	+	0.176874i	0.810439	+	0.585823i	$0.199229\pi$
$942$	−5.95238	−	10.3098i	−0.193939	−	0.335912i
$943$	30.1940			0.983251
$944$	−4.35265	−	7.53901i	−0.141667	−	0.245374i
$945$	−46.9027	−	81.2378i	−1.52574	−	2.64266i
$946$	1.47368	+	2.55248i	0.0479134	+	0.0829884i
$947$	46.1744			1.50047			0.750233	−	0.661174i	$-0.229942\pi$
$947$	46.1744			1.50047			0.750233	+	0.661174i	$0.229942\pi$
$948$	−31.8907			−1.03576
$949$	−22.7998			−0.740114
$950$	28.2586	+	48.9454i	0.916832	+	1.58800i
$951$	20.2483	+	35.0711i	0.656596	+	1.13726i
$952$	−1.49068	+	2.58194i	−0.0483133	+	0.0836811i
$953$	−5.76479	+	9.98490i	−0.186740	+	0.323443i	−0.944161	−	0.329483i	$-0.893125\pi$
$953$	−5.76479	+	9.98490i	−0.186740	+	0.323443i	0.757422	+	0.652926i	$0.226459\pi$
$954$	−42.9137			−1.38938
$955$	−36.5180	+	63.2510i	−1.18169	+	2.04675i
$956$	14.6167	+	25.3169i	0.472739	+	0.818808i
$957$	−21.7151	+	37.6117i	−0.701950	+	1.21581i
$958$	−36.6083			−1.18276
$959$	29.1036	+	50.4090i	0.939805	+	1.62779i
$960$	5.28479	+	9.15352i	0.170566	+	0.295429i
$961$	14.7561	−	25.5583i	0.476003	−	0.824462i
$962$	2.01709			0.0650336
$963$	41.2373	+	71.4250i	1.32885	+	2.30164i
$964$	10.1794			0.327855
$965$	−17.1709			−0.552752
$966$	−43.0278	−	74.5264i	−1.38440	−	2.39785i
$967$	11.0173	−	19.0826i	0.354293	−	0.613654i	−0.632704	−	0.774394i	$-0.718055\pi$
$967$	11.0173	−	19.0826i	0.354293	−	0.613654i	0.986997	+	0.160740i	$0.0513882\pi$
$968$	4.34911	−	7.53288i	0.139786	−	0.242116i
$969$	10.8764	−	18.8385i	0.349402	−	0.605181i
$970$	−5.85894	−	10.1480i	−0.188119	−	0.325832i
$971$	9.03552	−	15.6500i	0.289964	−	0.502232i	−0.683837	−	0.729635i	$-0.739690\pi$
$971$	9.03552	−	15.6500i	0.289964	−	0.502232i	0.973801	+	0.227403i	$0.0730234\pi$
$972$	−0.877411	−	1.51972i	−0.0281430	−	0.0487450i
$973$	−18.0235			−0.577808
$974$	9.96753	−	17.2643i	0.319380	−	0.553183i
$975$	43.9368	−	76.1008i	1.40710	−	2.43718i
$976$	−2.74192	+	4.74914i	−0.0877667	+	0.152016i
$977$	46.0765			1.47412			0.737058	−	0.675829i	$-0.236214\pi$
$977$	46.0765			1.47412			0.737058	+	0.675829i	$0.236214\pi$
$978$	18.7018	−	32.3926i	0.598019	−	1.03580i
$979$	2.20109			0.0703471
$980$	8.37456			0.267516
$981$	−57.5020	−	22.0955i	−1.83590	−	0.705454i
$982$	23.0615			0.735922
$983$	23.0295			0.734527			0.367263	−	0.930117i	$-0.380295\pi$
$983$	23.0295			0.734527			0.367263	+	0.930117i	$0.380295\pi$
$984$	4.77795	−	8.27565i	0.152315	−	0.263818i
$985$	−69.7353			−2.22195
$986$	4.67431	−	8.09614i	0.148860	−	0.257834i
$987$		0			0
$988$	14.5946	−	25.2787i	0.464317	−	0.804221i
$989$	18.3127			0.582309
$990$	15.8574	+	27.4658i	0.503981	+	0.872920i
$991$	25.9116	−	44.8803i	0.823111	−	1.42567i	−0.0802440	−	0.996775i	$-0.525570\pi$
$991$	25.9116	−	44.8803i	0.823111	−	1.42567i	0.903355	−	0.428894i	$-0.141097\pi$
$992$	−0.609875	−	1.05633i	−0.0193635	−	0.0335386i
$993$	−34.7896	+	60.2574i	−1.10401	+	1.91221i
$994$	−4.60388	+	7.97416i	−0.146026	+	0.252925i
$995$	7.46555	−	12.9307i	0.236674	−	0.409931i
$996$	−6.19357	−	10.7276i	−0.196251	−	0.339916i
$997$	61.2158			1.93872			0.969361	−	0.245640i	$-0.0789981\pi$
$997$	61.2158			1.93872			0.969361	+	0.245640i	$0.0789981\pi$
$998$	−6.03247			−0.190955
$999$	2.23740	+	3.87529i	0.0707881	+	0.122609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	218.2.c.c.45.5	✓	10
3.2	odd	2		1962.2.f.k.1135.4		10
109.63	even	3	inner	218.2.c.c.63.5	yes	10
327.281	odd	6		1962.2.f.k.1153.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
218.2.c.c.45.5	✓	10	1.1	even	1	trivial
218.2.c.c.63.5	yes	10	109.63	even	3	inner
1962.2.f.k.1135.4		10	3.2	odd	2
1962.2.f.k.1153.4		10	327.281	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 218 = 2 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	218.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.49167 - 2.58365i) q^{3} +1.00000 q^{4} +(-1.77143 + 3.06821i) q^{5} +(1.49167 - 2.58365i) q^{6} +(1.53001 - 2.65006i) q^{7} +1.00000 q^{8} +(-2.95015 - 5.10982i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.49167 - 2.58365i) q^{3} +1.00000 q^{4} +(-1.77143 + 3.06821i) q^{5} +(1.49167 - 2.58365i) q^{6} +(1.53001 - 2.65006i) q^{7} +1.00000 q^{8} +(-2.95015 - 5.10982i) q^{9} +(-1.77143 + 3.06821i) q^{10} +(0.758581 + 1.31390i) q^{11} +(1.49167 - 2.58365i) q^{12} +(-1.95015 + 3.37777i) q^{13} +(1.53001 - 2.65006i) q^{14} +(5.28479 + 9.15352i) q^{15} +1.00000 q^{16} -0.974294 q^{17} +(-2.95015 - 5.10982i) q^{18} -7.48384 q^{19} +(-1.77143 + 3.06821i) q^{20} +(-4.56455 - 7.90604i) q^{21} +(0.758581 + 1.31390i) q^{22} +9.42652 q^{23} +(1.49167 - 2.58365i) q^{24} +(-3.77596 - 6.54015i) q^{25} +(-1.95015 + 3.37777i) q^{26} -8.65260 q^{27} +(1.53001 - 2.65006i) q^{28} +(-4.79764 + 8.30976i) q^{29} +(5.28479 + 9.15352i) q^{30} +(-0.609875 - 1.05633i) q^{31} +1.00000 q^{32} +4.52621 q^{33} -0.974294 q^{34} +(5.42064 + 9.38882i) q^{35} +(-2.95015 - 5.10982i) q^{36} +(-0.258581 - 0.447875i) q^{37} -7.48384 q^{38} +(5.81797 + 10.0770i) q^{39} +(-1.77143 + 3.06821i) q^{40} +3.20309 q^{41} +(-4.56455 - 7.90604i) q^{42} +1.94268 q^{43} +(0.758581 + 1.31390i) q^{44} +20.9040 q^{45} +9.42652 q^{46} +(1.49167 - 2.58365i) q^{48} +(-1.18189 - 2.04709i) q^{49} +(-3.77596 - 6.54015i) q^{50} +(-1.45332 + 2.51723i) q^{51} +(-1.95015 + 3.37777i) q^{52} +(3.63657 - 6.29872i) q^{53} -8.65260 q^{54} -5.37510 q^{55} +(1.53001 - 2.65006i) q^{56} +(-11.1634 + 19.3356i) q^{57} +(-4.79764 + 8.30976i) q^{58} +(-4.35265 - 7.53901i) q^{59} +(5.28479 + 9.15352i) q^{60} +(-2.74192 + 4.74914i) q^{61} +(-0.609875 - 1.05633i) q^{62} -18.0551 q^{63} +1.00000 q^{64} +(-6.90914 - 11.9670i) q^{65} +4.52621 q^{66} +(-5.04151 - 8.73216i) q^{67} -0.974294 q^{68} +(14.0612 - 24.3548i) q^{69} +(5.42064 + 9.38882i) q^{70} -3.00904 q^{71} +(-2.95015 - 5.10982i) q^{72} +(2.92282 + 5.06248i) q^{73} +(-0.258581 - 0.447875i) q^{74} -22.5299 q^{75} -7.48384 q^{76} +4.64256 q^{77} +(5.81797 + 10.0770i) q^{78} +(-5.34480 - 9.25747i) q^{79} +(-1.77143 + 3.06821i) q^{80} +(-4.05636 + 7.02582i) q^{81} +3.20309 q^{82} +(2.07605 - 3.59583i) q^{83} +(-4.56455 - 7.90604i) q^{84} +(1.72590 - 2.98934i) q^{85} +1.94268 q^{86} +(14.3130 + 24.7908i) q^{87} +(0.758581 + 1.31390i) q^{88} +(0.725397 - 1.25642i) q^{89} +20.9040 q^{90} +(5.96753 + 10.3361i) q^{91} +9.42652 q^{92} -3.63893 q^{93} +(13.2571 - 22.9620i) q^{95} +(1.49167 - 2.58365i) q^{96} +(-1.65373 + 2.86434i) q^{97} +(-1.18189 - 2.04709i) q^{98} +(4.47586 - 7.75242i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + q^{6} - q^{7} + 10 q^{8} - 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + q^6 - q^7 + 10 * q^8 - 10 * q^9	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + q^{6} - q^{7} + 10 q^{8} - 10 q^{9} - 8 q^{10} + q^{11} + q^{12} - q^{14} - q^{15} + 10 q^{16} - 16 q^{17} - 10 q^{18} - 6 q^{19} - 8 q^{20} + 4 q^{21} + q^{22} + 8 q^{23} + q^{24} - 11 q^{25} + 10 q^{27} - q^{28} + 9 q^{29} - q^{30} + 7 q^{31} + 10 q^{32} - 2 q^{33} - 16 q^{34} + 10 q^{35} - 10 q^{36} + 4 q^{37} - 6 q^{38} - 4 q^{39} - 8 q^{40} - 22 q^{41} + 4 q^{42} + 2 q^{43} + q^{44} + 38 q^{45} + 8 q^{46} + q^{48} - 10 q^{49} - 11 q^{50} - 3 q^{51} - 2 q^{53} + 10 q^{54} + 20 q^{55} - q^{56} - 49 q^{57} + 9 q^{58} - 12 q^{59} - q^{60} + 7 q^{61} + 7 q^{62} - 36 q^{63} + 10 q^{64} - 3 q^{65} - 2 q^{66} - 56 q^{67} - 16 q^{68} + 19 q^{69} + 10 q^{70} + 4 q^{71} - 10 q^{72} + 12 q^{73} + 4 q^{74} - 46 q^{75} - 6 q^{76} + 66 q^{77} - 4 q^{78} - 30 q^{79} - 8 q^{80} - 41 q^{81} - 22 q^{82} - 7 q^{83} + 4 q^{84} - 22 q^{85} + 2 q^{86} + 40 q^{87} + q^{88} + 9 q^{89} + 38 q^{90} + 20 q^{91} + 8 q^{92} + 10 q^{93} - 12 q^{95} + q^{96} + 35 q^{97} - 10 q^{98} + 19 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + q^6 - q^7 + 10 * q^8 - 10 * q^9 - 8 * q^10 + q^11 + q^12 - q^14 - q^15 + 10 * q^16 - 16 * q^17 - 10 * q^18 - 6 * q^19 - 8 * q^20 + 4 * q^21 + q^22 + 8 * q^23 + q^24 - 11 * q^25 + 10 * q^27 - q^28 + 9 * q^29 - q^30 + 7 * q^31 + 10 * q^32 - 2 * q^33 - 16 * q^34 + 10 * q^35 - 10 * q^36 + 4 * q^37 - 6 * q^38 - 4 * q^39 - 8 * q^40 - 22 * q^41 + 4 * q^42 + 2 * q^43 + q^44 + 38 * q^45 + 8 * q^46 + q^48 - 10 * q^49 - 11 * q^50 - 3 * q^51 - 2 * q^53 + 10 * q^54 + 20 * q^55 - q^56 - 49 * q^57 + 9 * q^58 - 12 * q^59 - q^60 + 7 * q^61 + 7 * q^62 - 36 * q^63 + 10 * q^64 - 3 * q^65 - 2 * q^66 - 56 * q^67 - 16 * q^68 + 19 * q^69 + 10 * q^70 + 4 * q^71 - 10 * q^72 + 12 * q^73 + 4 * q^74 - 46 * q^75 - 6 * q^76 + 66 * q^77 - 4 * q^78 - 30 * q^79 - 8 * q^80 - 41 * q^81 - 22 * q^82 - 7 * q^83 + 4 * q^84 - 22 * q^85 + 2 * q^86 + 40 * q^87 + q^88 + 9 * q^89 + 38 * q^90 + 20 * q^91 + 8 * q^92 + 10 * q^93 - 12 * q^95 + q^96 + 35 * q^97 - 10 * q^98 + 19 * q^99

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