LMFDB - Embedded newform 273.2.bd.b.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(43,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("273.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bd (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} - 8 x^{13} - 3 x^{12} + 32 x^{11} - 5 x^{10} - 44 x^{9} + 214 x^{8} + \cdots + 6561 $ x^16 - 4x^15 + 10x^14 - 8x^13 - 3x^12 + 32x^11 - 5x^10 - 44x^9 + 214x^8 - 132x^7 - 45x^6 + 864x^5 - 243x^4 - 1944x^3 + 7290x^2 - 8748*x + 6561
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			127.2
Root			$1.35201 + 1.08262i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.b.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98604 + 1.14664i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.62956 - 2.82249i) q^{4} -0.692320i q^{5} +(-1.98604 - 1.14664i) q^{6} +(-0.866025 - 0.500000i) q^{7} +2.88753i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.98604 + 1.14664i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.62956 - 2.82249i) q^{4} -0.692320i q^{5} +(-1.98604 - 1.14664i) q^{6} +(-0.866025 - 0.500000i) q^{7} +2.88753i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.793841 + 1.37497i) q^{10} +(-5.20978 + 3.00787i) q^{11} +3.25913 q^{12} +(-3.26337 - 1.53311i) q^{13} +2.29328 q^{14} +(0.599567 - 0.346160i) q^{15} +(-0.0518251 - 0.0897638i) q^{16} +(-3.99752 + 6.92391i) q^{17} -2.29328i q^{18} +(-2.60603 - 1.50459i) q^{19} +(-1.95406 - 1.12818i) q^{20} -1.00000i q^{21} +(6.89788 - 11.9475i) q^{22} +(0.326773 + 0.565988i) q^{23} +(-2.50067 + 1.44376i) q^{24} +4.52069 q^{25} +(8.23910 - 0.697093i) q^{26} -1.00000 q^{27} +(-2.82249 + 1.62956i) q^{28} +(-4.64346 - 8.04271i) q^{29} +(-0.793841 + 1.37497i) q^{30} +1.47475i q^{31} +(-4.79549 - 2.76868i) q^{32} +(-5.20978 - 3.00787i) q^{33} -18.3348i q^{34} +(-0.346160 + 0.599567i) q^{35} +(1.62956 + 2.82249i) q^{36} +(-3.49559 + 2.01818i) q^{37} +6.90088 q^{38} +(-0.303972 - 3.59271i) q^{39} +1.99909 q^{40} +(7.95226 - 4.59124i) q^{41} +(1.14664 + 1.98604i) q^{42} +(-4.06494 + 7.04068i) q^{43} +19.6060i q^{44} +(0.599567 + 0.346160i) q^{45} +(-1.29797 - 0.749382i) q^{46} +0.664432i q^{47} +(0.0518251 - 0.0897638i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-8.97827 + 5.18360i) q^{50} -7.99504 q^{51} +(-9.64505 + 6.71251i) q^{52} +10.3300 q^{53} +(1.98604 - 1.14664i) q^{54} +(2.08241 + 3.60683i) q^{55} +(1.44376 - 2.50067i) q^{56} -3.00918i q^{57} +(18.4442 + 10.6488i) q^{58} +(-1.76761 - 1.02053i) q^{59} -2.25636i q^{60} +(-0.693979 + 1.20201i) q^{61} +(-1.69101 - 2.92891i) q^{62} +(0.866025 - 0.500000i) q^{63} +12.9060 q^{64} +(-1.06140 + 2.25930i) q^{65} +13.7958 q^{66} +(-6.39137 + 3.69006i) q^{67} +(13.0284 + 22.5659i) q^{68} +(-0.326773 + 0.565988i) q^{69} -1.58768i q^{70} +(0.867789 + 0.501018i) q^{71} +(-2.50067 - 1.44376i) q^{72} +10.6068i q^{73} +(4.62825 - 8.01636i) q^{74} +(2.26035 + 3.91503i) q^{75} +(-8.49336 + 4.90365i) q^{76} +6.01573 q^{77} +(4.72325 + 6.78672i) q^{78} +6.08603 q^{79} +(-0.0621453 + 0.0358796i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.5290 + 18.2367i) q^{82} -0.377468i q^{83} +(-2.82249 - 1.62956i) q^{84} +(4.79356 + 2.76756i) q^{85} -18.6441i q^{86} +(4.64346 - 8.04271i) q^{87} +(-8.68529 - 15.0434i) q^{88} +(-5.74801 + 3.31861i) q^{89} -1.58768 q^{90} +(2.05961 + 2.95940i) q^{91} +2.12999 q^{92} +(-1.27717 + 0.737375i) q^{93} +(-0.761864 - 1.31959i) q^{94} +(-1.04166 + 1.80420i) q^{95} -5.53735i q^{96} +(-0.299798 - 0.173089i) q^{97} +(-1.98604 - 1.14664i) q^{98} -6.01573i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.98604	+	1.14664i	−1.40434	+	0.810796i	−0.994834	−	0.101511i	$-0.967632\pi$
$2$	−1.98604	+	1.14664i	−1.40434	+	0.810796i	−0.409506	+	0.912307i	$0.634299\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.62956	−	2.82249i	0.814782	−	1.41124i
$5$		−	0.692320i		−	0.309615i	−0.987945	−	0.154807i	$-0.950524\pi$
$5$		−	0.692320i		−	0.309615i	0.987945	−	0.154807i	$-0.0494757\pi$
$6$	−1.98604	−	1.14664i	−0.810796	−	0.468114i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$			2.88753i			1.02089i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.793841	+	1.37497i	0.251035	+	0.434805i
$11$	−5.20978	+	3.00787i	−1.57081	+	0.906906i	−0.574737	+	0.818338i	$0.694896\pi$
$11$	−5.20978	+	3.00787i	−1.57081	+	0.906906i	−0.996070	+	0.0885675i	$0.971771\pi$
$12$	3.25913			0.940829
$13$	−3.26337	−	1.53311i	−0.905096	−	0.425208i
$13$	−3.26337	−	1.53311i	−0.905096	−	0.425208i
$14$	2.29328			0.612904
$15$	0.599567	−	0.346160i	0.154807	−	0.0893781i
$16$	−0.0518251	−	0.0897638i	−0.0129563	−	0.0224409i
$17$	−3.99752	+	6.92391i	−0.969541	+	1.67929i	−0.272655	+	0.962112i	$0.587902\pi$
$17$	−3.99752	+	6.92391i	−0.969541	+	1.67929i	−0.696886	+	0.717182i	$0.745432\pi$
$18$		−	2.29328i		−	0.540531i
$19$	−2.60603	−	1.50459i	−0.597863	−	0.345176i	0.170337	−	0.985386i	$-0.445514\pi$
$19$	−2.60603	−	1.50459i	−0.597863	−	0.345176i	−0.768200	+	0.640209i	$0.778848\pi$
$20$	−1.95406	−	1.12818i	−0.436942	−	0.252269i
$21$		−	1.00000i		−	0.218218i
$22$	6.89788	−	11.9475i	1.47063	−	2.54721i
$23$	0.326773	+	0.565988i	0.0681370	+	0.118017i	0.898081	−	0.439830i	$-0.144961\pi$
$23$	0.326773	+	0.565988i	0.0681370	+	0.118017i	−0.829944	+	0.557846i	$0.811628\pi$
$24$	−2.50067	+	1.44376i	−0.510447	+	0.294707i
$25$	4.52069			0.904139
$26$	8.23910	−	0.697093i	1.61582	−	0.136711i
$27$	−1.00000			−0.192450
$28$	−2.82249	+	1.62956i	−0.533400	+	0.307958i
$29$	−4.64346	−	8.04271i	−0.862269	−	1.49349i	−0.869733	−	0.493522i	$-0.835709\pi$
$29$	−4.64346	−	8.04271i	−0.862269	−	1.49349i	0.00746411	−	0.999972i	$-0.497624\pi$
$30$	−0.793841	+	1.37497i	−0.144935	+	0.251035i
$31$			1.47475i			0.264873i	0.991191	+	0.132437i	$0.0422801\pi$
$31$			1.47475i			0.264873i	−0.991191	+	0.132437i	$0.957720\pi$
$32$	−4.79549	−	2.76868i	−0.847731	−	0.489438i
$33$	−5.20978	−	3.00787i	−0.906906	−	0.523602i
$34$		−	18.3348i		−	3.14440i
$35$	−0.346160	+	0.599567i	−0.0585117	+	0.101345i
$36$	1.62956	+	2.82249i	0.271594	+	0.470414i
$37$	−3.49559	+	2.01818i	−0.574672	+	0.331787i	−0.759013	−	0.651075i	$-0.774318\pi$
$37$	−3.49559	+	2.01818i	−0.574672	+	0.331787i	0.184341	+	0.982862i	$0.440985\pi$
$38$	6.90088			1.11947
$39$	−0.303972	−	3.59271i	−0.0486745	−	0.575295i
$40$	1.99909			0.316084
$41$	7.95226	−	4.59124i	1.24193	−	0.717031i	0.272446	−	0.962171i	$-0.412167\pi$
$41$	7.95226	−	4.59124i	1.24193	−	0.717031i	0.969488	+	0.245140i	$0.0788340\pi$
$42$	1.14664	+	1.98604i	0.176930	+	0.306452i
$43$	−4.06494	+	7.04068i	−0.619897	+	1.07369i	0.369607	+	0.929188i	$0.379492\pi$
$43$	−4.06494	+	7.04068i	−0.619897	+	1.07369i	−0.989504	+	0.144505i	$0.953841\pi$
$44$			19.6060i			2.95572i
$45$	0.599567	+	0.346160i	0.0893781	+	0.0516025i
$46$	−1.29797	−	0.749382i	−0.191375	−	0.110490i
$47$			0.664432i			0.0969174i	0.998825	+	0.0484587i	$0.0154309\pi$
$47$			0.664432i			0.0969174i	−0.998825	+	0.0484587i	$0.984569\pi$
$48$	0.0518251	−	0.0897638i	0.00748032	−	0.0129563i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−8.97827	+	5.18360i	−1.26972	+	0.733072i
$51$	−7.99504			−1.11953
$52$	−9.64505	+	6.71251i	−1.33753	+	0.930858i
$53$	10.3300			1.41894			0.709470	−	0.704735i	$-0.248934\pi$
$53$	10.3300			1.41894			0.709470	+	0.704735i	$0.248934\pi$
$54$	1.98604	−	1.14664i	0.270265	−	0.156038i
$55$	2.08241	+	3.60683i	0.280792	+	0.486345i
$56$	1.44376	−	2.50067i	0.192931	−	0.334166i
$57$		−	3.00918i		−	0.398575i
$58$	18.4442	+	10.6488i	2.42184	+	1.39825i
$59$	−1.76761	−	1.02053i	−0.230123	−	0.132862i	0.380506	−	0.924779i	$-0.375750\pi$
$59$	−1.76761	−	1.02053i	−0.230123	−	0.132862i	−0.610629	+	0.791917i	$0.709083\pi$
$60$		−	2.25636i		−	0.291295i
$61$	−0.693979	+	1.20201i	−0.0888550	+	0.153901i	−0.907027	−	0.421072i	$-0.861654\pi$
$61$	−0.693979	+	1.20201i	−0.0888550	+	0.153901i	0.818172	+	0.574973i	$0.194987\pi$
$62$	−1.69101	−	2.92891i	−0.214758	−	0.371972i
$63$	0.866025	−	0.500000i	0.109109	−	0.0629941i
$64$	12.9060			1.61325
$65$	−1.06140	+	2.25930i	−0.131651	+	0.280231i
$66$	13.7958			1.69814
$67$	−6.39137	+	3.69006i	−0.780831	+	0.450813i	−0.836725	−	0.547624i	$-0.815532\pi$
$67$	−6.39137	+	3.69006i	−0.780831	+	0.450813i	0.0558940	+	0.998437i	$0.482199\pi$
$68$	13.0284	+	22.5659i	1.57993	+	2.73652i
$69$	−0.326773	+	0.565988i	−0.0393389	+	0.0681370i
$70$		−	1.58768i		−	0.189764i
$71$	0.867789	+	0.501018i	0.102988	+	0.0594599i	0.550609	−	0.834763i	$-0.314395\pi$
$71$	0.867789	+	0.501018i	0.102988	+	0.0594599i	−0.447622	+	0.894223i	$0.647729\pi$
$72$	−2.50067	−	1.44376i	−0.294707	−	0.170149i
$73$			10.6068i			1.24144i	0.784034	+	0.620718i	$0.213159\pi$
$73$			10.6068i			1.24144i	−0.784034	+	0.620718i	$0.786841\pi$
$74$	4.62825	−	8.01636i	0.538023	−	0.931883i
$75$	2.26035	+	3.91503i	0.261002	+	0.452069i
$76$	−8.49336	+	4.90365i	−0.974256	+	0.562487i
$77$	6.01573			0.685556
$78$	4.72325	+	6.78672i	0.534803	+	0.768445i
$79$	6.08603			0.684731			0.342366	−	0.939567i	$-0.388772\pi$
$79$	6.08603			0.684731			0.342366	+	0.939567i	$0.388772\pi$
$80$	−0.0621453	+	0.0358796i	−0.00694805	+	0.00401146i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.5290	+	18.2367i	−1.16273	+	2.01391i
$83$		−	0.377468i		−	0.0414325i	−0.999785	−	0.0207163i	$-0.993405\pi$
$83$		−	0.377468i		−	0.0414325i	0.999785	−	0.0207163i	$-0.00659466\pi$
$84$	−2.82249	−	1.62956i	−0.307958	−	0.177800i
$85$	4.79356	+	2.76756i	0.519935	+	0.300184i
$86$		−	18.6441i		−	2.01044i
$87$	4.64346	−	8.04271i	0.497831	−	0.862269i
$88$	−8.68529	−	15.0434i	−0.925855	−	1.60363i
$89$	−5.74801	+	3.31861i	−0.609287	+	0.351772i	−0.772687	−	0.634788i	$-0.781088\pi$
$89$	−5.74801	+	3.31861i	−0.609287	+	0.351772i	0.163399	+	0.986560i	$0.447754\pi$
$90$	−1.58768			−0.167356
$91$	2.05961	+	2.95940i	0.215905	+	0.310229i
$92$	2.12999			0.222067
$93$	−1.27717	+	0.737375i	−0.132437	+	0.0764623i
$94$	−0.761864	−	1.31959i	−0.0785803	−	0.136105i
$95$	−1.04166	+	1.80420i	−0.106872	+	0.185107i
$96$		−	5.53735i		−	0.565154i
$97$	−0.299798	−	0.173089i	−0.0304399	−	0.0175745i	0.484703	−	0.874679i	$-0.338928\pi$
$97$	−0.299798	−	0.173089i	−0.0304399	−	0.0175745i	−0.515143	+	0.857104i	$0.672261\pi$
$98$	−1.98604	−	1.14664i	−0.200620	−	0.115828i
$99$		−	6.01573i		−	0.604604i
$100$	7.36675	−	12.7596i	0.736675	−	1.27596i
$101$	−7.64733	−	13.2456i	−0.760938	−	1.31798i	−0.942368	−	0.334579i	$-0.891406\pi$
$101$	−7.64733	−	13.2456i	−0.760938	−	1.31798i	0.181430	−	0.983404i	$-0.441927\pi$
$102$	15.8784	−	9.16742i	1.57220	−	0.907710i
$103$	−10.6987			−1.05418			−0.527088	−	0.849811i	$-0.676716\pi$
$103$	−10.6987			−1.05418			−0.527088	+	0.849811i	$0.676716\pi$
$104$	4.42690	−	9.42306i	0.434093	−	0.924007i
$105$	−0.692320			−0.0675635
$106$	−20.5159	+	11.8448i	−1.99268	+	1.15047i
$107$	5.80692	+	10.0579i	0.561376	+	0.972331i	0.997377	+	0.0723852i	$0.0230611\pi$
$107$	5.80692	+	10.0579i	0.561376	+	0.972331i	−0.436001	+	0.899946i	$0.643606\pi$
$108$	−1.62956	+	2.82249i	−0.156805	+	0.271594i
$109$		−	7.98992i		−	0.765296i	−0.923894	−	0.382648i	$-0.875012\pi$
$109$		−	7.98992i		−	0.765296i	0.923894	−	0.382648i	$-0.124988\pi$
$110$	−8.27147	−	4.77554i	−0.788654	−	0.455330i
$111$	−3.49559	−	2.01818i	−0.331787	−	0.191557i
$112$			0.103650i			0.00979403i
$113$	−3.85183	+	6.67157i	−0.362350	+	0.627608i	−0.988347	−	0.152217i	$-0.951359\pi$
$113$	−3.85183	+	6.67157i	−0.362350	+	0.627608i	0.625997	+	0.779825i	$0.284692\pi$
$114$	3.45044	+	5.97634i	0.323164	+	0.559736i
$115$	0.391845	−	0.226232i	0.0365397	−	0.0210962i
$116$	−30.2673			−2.81024
$117$	2.95940	−	2.05961i	0.273596	−	0.190411i
$118$	4.68072			0.430896
$119$	6.92391	−	3.99752i	0.634713	−	0.366452i
$120$	0.999546	+	1.73127i	0.0912457	+	0.158042i
$121$	12.5945	−	21.8143i	1.14496	−	1.98312i
$122$		−	3.18298i		−	0.288173i
$123$	7.95226	+	4.59124i	0.717031	+	0.413978i
$124$	4.16246	+	2.40320i	0.373800	+	0.215814i
$125$		−	6.59137i		−	0.589550i
$126$	−1.14664	+	1.98604i	−0.102151	+	0.176930i
$127$	0.366697	+	0.635138i	0.0325391	+	0.0563594i	0.881836	−	0.471556i	$-0.156307\pi$
$127$	0.366697	+	0.635138i	0.0325391	+	0.0563594i	−0.849297	+	0.527915i	$0.822974\pi$
$128$	−16.0408	+	9.26117i	−1.41782	+	0.818579i
$129$	−8.12988			−0.715796
$130$	−0.482611	−	5.70409i	−0.0423278	−	0.500282i
$131$	−9.82604			−0.858505			−0.429253	−	0.903185i	$-0.641223\pi$
$131$	−9.82604			−0.858505			−0.429253	+	0.903185i	$0.641223\pi$
$132$	−16.9793	+	9.80302i	−1.47786	+	0.853243i
$133$	1.50459	+	2.60603i	0.130464	+	0.225971i
$134$	8.46234	−	14.6572i	0.731035	−	1.26619i
$135$			0.692320i			0.0595854i
$136$	−19.9930	−	11.5429i	−1.71438	−	0.989799i
$137$	4.93527	+	2.84938i	0.421648	+	0.243439i	0.695782	−	0.718253i	$-0.255058\pi$
$137$	4.93527	+	2.84938i	0.421648	+	0.243439i	−0.274134	+	0.961692i	$0.588391\pi$
$138$		−	1.49876i		−	0.127583i
$139$	4.92022	−	8.52207i	0.417328	−	0.722833i	−0.578342	−	0.815794i	$-0.696300\pi$
$139$	4.92022	−	8.52207i	0.417328	−	0.722833i	0.995670	+	0.0929616i	$0.0296334\pi$
$140$	1.12818	+	1.95406i	0.0953485	+	0.165149i
$141$	−0.575415	+	0.332216i	−0.0484587	+	0.0279777i
$142$	−2.29795			−0.192840
$143$	21.6128	−	1.82862i	1.80735	−	0.152917i
$144$	0.103650			0.00863752
$145$	−5.56813	+	3.21476i	−0.462408	+	0.266971i
$146$	−12.1622	−	21.0656i	−1.00655	−	1.74340i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$			13.1550i			1.08134i
$149$	11.8290	+	6.82947i	0.969069	+	0.559492i	0.898952	−	0.438047i	$-0.144329\pi$
$149$	11.8290	+	6.82947i	0.969069	+	0.559492i	0.0701167	+	0.997539i	$0.477663\pi$
$150$	−8.97827	−	5.18360i	−0.733072	−	0.423239i
$151$			11.4487i			0.931684i	0.884868	+	0.465842i	$0.154248\pi$
$151$			11.4487i			0.931684i	−0.884868	+	0.465842i	$0.845752\pi$
$152$	4.34454	−	7.52497i	0.352389	−	0.610355i
$153$	−3.99752	−	6.92391i	−0.323180	−	0.559765i
$154$	−11.9475	+	6.89788i	−0.962755	+	0.555847i
$155$	1.02100			0.0820086
$156$	−10.6357	−	4.99660i	−0.851540	−	0.400048i
$157$	−8.49845			−0.678250			−0.339125	−	0.940741i	$-0.610131\pi$
$157$	−8.49845			−0.678250			−0.339125	+	0.940741i	$0.610131\pi$
$158$	−12.0871	+	6.97848i	−0.961596	+	0.555178i
$159$	5.16502	+	8.94608i	0.409613	+	0.709470i
$160$	−1.91681	+	3.32001i	−0.151537	+	0.262470i
$161$		−	0.653547i		−	0.0515067i
$162$	1.98604	+	1.14664i	0.156038	+	0.0900885i
$163$	13.5765	+	7.83841i	1.06340	+	0.613951i	0.926369	−	0.376616i	$-0.122912\pi$
$163$	13.5765	+	7.83841i	1.06340	+	0.613951i	0.137026	+	0.990567i	$0.456246\pi$
$164$		−	29.9268i		−	2.33689i
$165$	−2.08241	+	3.60683i	−0.162115	+	0.280792i
$166$	0.432820	+	0.749666i	0.0335933	+	0.0581853i
$167$	−16.8245	+	9.71364i	−1.30192	+	0.751664i	−0.980733	−	0.195352i	$-0.937415\pi$
$167$	−16.8245	+	9.71364i	−1.30192	+	0.751664i	−0.321187	+	0.947016i	$0.604082\pi$
$168$	2.88753			0.222778
$169$	8.29915	+	10.0062i	0.638396	+	0.769708i
$170$	−12.6936			−0.973554
$171$	2.60603	−	1.50459i	0.199288	−	0.115059i
$172$	13.2481	+	22.9465i	1.01016	+	1.74965i
$173$	6.56552	−	11.3718i	0.499167	−	0.864583i	−0.500832	−	0.865544i	$-0.666973\pi$
$173$	6.56552	−	11.3718i	0.499167	−	0.864583i	1.00000		0.000961031i	$0.000305906\pi$
$174$			21.2975i			1.61456i
$175$	−3.91503	−	2.26035i	−0.295949	−	0.170866i
$176$	0.539995	+	0.311766i	0.0407037	+	0.0235003i
$177$		−	2.04106i		−	0.153416i
$178$	7.61050	−	13.1818i	0.570431	−	0.988016i
$179$	4.97228	+	8.61223i	0.371645	+	0.643709i	0.989819	−	0.142333i	$-0.0454604\pi$
$179$	4.97228	+	8.61223i	0.371645	+	0.643709i	−0.618173	+	0.786042i	$0.712127\pi$
$180$	1.95406	−	1.12818i	0.145647	−	0.0840895i
$181$	0.453624			0.0337176			0.0168588	−	0.999858i	$-0.494633\pi$
$181$	0.453624			0.0337176			0.0168588	+	0.999858i	$0.494633\pi$
$182$	−7.48381	−	3.51585i	−0.554737	−	0.260612i
$183$	−1.38796			−0.102601
$184$	−1.63431	+	0.943567i	−0.120483	+	0.0695607i
$185$	1.39723	+	2.42007i	0.102726	+	0.177927i
$186$	1.69101	−	2.92891i	0.123991	−	0.214758i
$187$		−	48.0960i		−	3.51713i
$188$	1.87535	+	1.08273i	0.136774	+	0.0789665i
$189$	0.866025	+	0.500000i	0.0629941	+	0.0363696i
$190$		−	4.77762i		−	0.346605i
$191$	−0.619944	+	1.07378i	−0.0448576	+	0.0776957i	−0.887582	−	0.460649i	$-0.847617\pi$
$191$	−0.619944	+	1.07378i	−0.0448576	+	0.0776957i	0.842725	+	0.538345i	$0.180950\pi$
$192$	6.45300	+	11.1769i	0.465705	+	0.806625i
$193$	−1.37797	+	0.795569i	−0.0991882	+	0.0572663i	−0.548774	−	0.835971i	$-0.684905\pi$
$193$	−1.37797	+	0.795569i	−0.0991882	+	0.0572663i	0.449585	+	0.893237i	$0.351572\pi$
$194$	0.793881			0.0569973
$195$	−2.48731	+	0.210446i	−0.178120	+	0.0150704i
$196$	3.25913			0.232795
$197$	9.89068	−	5.71039i	0.704682	−	0.406848i	−0.104407	−	0.994535i	$-0.533294\pi$
$197$	9.89068	−	5.71039i	0.704682	−	0.406848i	0.809089	+	0.587686i	$0.199961\pi$
$198$	6.89788	+	11.9475i	0.490211	+	0.849070i
$199$	−12.0540	+	20.8782i	−0.854487	+	1.48001i	0.0226337	+	0.999744i	$0.492795\pi$
$199$	−12.0540	+	20.8782i	−0.854487	+	1.48001i	−0.877120	+	0.480271i	$0.840538\pi$
$200$			13.0536i			0.923030i
$201$	−6.39137	−	3.69006i	−0.450813	−	0.260277i
$202$	30.3758	+	17.5375i	2.13723	+	1.23393i
$203$			9.28692i			0.651814i
$204$	−13.0284	+	22.5659i	−0.912172	+	1.57993i
$205$	−3.17861	−	5.50551i	−0.222003	−	0.384521i
$206$	21.2480	−	12.2676i	1.48042	−	0.854722i
$207$	−0.653547			−0.0454246
$208$	0.0315068	+	0.372386i	0.00218460	+	0.0258203i
$209$	18.1024			1.25217
$210$	1.37497	−	0.793841i	0.0948822	−	0.0547803i
$211$	−0.189741	−	0.328642i	−0.0130623	−	0.0226246i	0.859420	−	0.511270i	$-0.170825\pi$
$211$	−0.189741	−	0.328642i	−0.0130623	−	0.0226246i	−0.872483	+	0.488645i	$0.837491\pi$
$212$	16.8335	−	29.1564i	1.15613	−	2.00247i
$213$			1.00204i			0.0686584i
$214$	−23.0655	−	13.3169i	−1.57673	−	0.910323i
$215$	4.87440	+	2.81424i	0.332432	+	0.191929i
$216$		−	2.88753i		−	0.196471i
$217$	0.737375	−	1.27717i	0.0500563	−	0.0867000i
$218$	9.16156	+	15.8683i	0.620499	+	1.07474i
$219$	−9.18578	+	5.30341i	−0.620718	+	0.358371i
$220$	13.5736			0.915135
$221$	23.6605	−	16.4666i	1.59158	−	1.10766i
$222$	9.25650			0.621256
$223$	9.59507	−	5.53972i	0.642534	−	0.370967i	−0.143056	−	0.989715i	$-0.545693\pi$
$223$	9.59507	−	5.53972i	0.642534	−	0.370967i	0.785590	+	0.618748i	$0.212360\pi$
$224$	2.76868	+	4.79549i	0.184990	+	0.320412i
$225$	−2.26035	+	3.91503i	−0.150690	+	0.261002i
$226$		−	17.6666i		−	1.17517i
$227$	−14.0812	−	8.12977i	−0.934601	−	0.539592i	−0.0463370	−	0.998926i	$-0.514755\pi$
$227$	−14.0812	−	8.12977i	−0.934601	−	0.539592i	−0.888264	+	0.459334i	$0.848088\pi$
$228$	−8.49336	−	4.90365i	−0.562487	−	0.324752i
$229$			10.4004i			0.687278i	0.939102	+	0.343639i	$0.111660\pi$
$229$			10.4004i			0.687278i	−0.939102	+	0.343639i	$0.888340\pi$
$230$	−0.518812	+	0.898610i	−0.0342095	+	0.0592526i
$231$	3.00787	+	5.20978i	0.197903	+	0.342778i
$232$	23.2235	−	13.4081i	1.52470	−	0.880286i
$233$	−15.5960			−1.02173			−0.510863	−	0.859662i	$-0.670674\pi$
$233$	−15.5960			−1.02173			−0.510863	+	0.859662i	$0.670674\pi$
$234$	−3.51585	+	7.48381i	−0.229838	+	0.489232i
$235$	0.460000			0.0300071
$236$	−5.76087	+	3.32604i	−0.375001	+	0.216507i
$237$	3.04301	+	5.27065i	0.197665	+	0.342366i
$238$	−9.16742	+	15.8784i	−0.594236	+	1.02925i
$239$			23.1700i			1.49874i	0.662151	+	0.749370i	$0.269644\pi$
$239$			23.1700i			1.49874i	−0.662151	+	0.749370i	$0.730356\pi$
$240$	−0.0621453	−	0.0358796i	−0.00401146	−	0.00231602i
$241$	−8.94744	−	5.16581i	−0.576355	−	0.332759i	0.183328	−	0.983052i	$-0.441313\pi$
$241$	−8.94744	−	5.16581i	−0.576355	−	0.332759i	−0.759684	+	0.650293i	$0.774646\pi$
$242$			57.7655i			3.71331i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	2.26177	+	3.91749i	0.144795	+	0.250792i
$245$	0.599567	−	0.346160i	0.0383049	−	0.0221154i
$246$	−21.0580			−1.34261
$247$	6.19772	+	8.90535i	0.394351	+	0.566634i
$248$	−4.25838			−0.270407
$249$	0.326897	−	0.188734i	0.0207163	−	0.0119605i
$250$	7.55792	+	13.0907i	0.478005	+	0.827929i
$251$	−7.44016	+	12.8867i	−0.469619	+	0.813404i	−0.999397	−	0.0347328i	$-0.988942\pi$
$251$	−7.44016	+	12.8867i	−0.469619	+	0.813404i	0.529778	+	0.848136i	$0.322275\pi$
$252$		−	3.25913i		−	0.205306i
$253$	−3.40483	−	1.96578i	−0.214060	−	0.123588i
$254$	−1.45655	−	0.840939i	−0.0913920	−	0.0527652i
$255$			5.53513i			0.346623i
$256$	8.33244	−	14.4322i	0.520777	−	0.902013i
$257$	−12.0049	−	20.7931i	−0.748844	−	1.29704i	−0.948377	−	0.317145i	$-0.897276\pi$
$257$	−12.0049	−	20.7931i	−0.748844	−	1.29704i	0.199533	−	0.979891i	$-0.436057\pi$
$258$	16.1462	−	9.32204i	1.00522	−	0.580365i
$259$	4.03636			0.250807
$260$	4.64721	+	6.67746i	0.288208	+	0.414118i
$261$	9.28692			0.574846
$262$	19.5149	−	11.2669i	1.20563	−	0.696073i
$263$	3.93068	+	6.80814i	0.242376	+	0.419808i	0.961391	−	0.275187i	$-0.0887398\pi$
$263$	3.93068	+	6.80814i	0.242376	+	0.419808i	−0.719014	+	0.694995i	$0.755406\pi$
$264$	8.68529	−	15.0434i	0.534543	−	0.925855i
$265$		−	7.15170i		−	0.439325i
$266$	−5.97634	−	3.45044i	−0.366433	−	0.211560i
$267$	−5.74801	−	3.31861i	−0.351772	−	0.203096i
$268$			24.0527i			1.46926i
$269$	4.34172	−	7.52008i	0.264719	−	0.458508i	−0.702771	−	0.711417i	$-0.748054\pi$
$269$	4.34172	−	7.52008i	0.264719	−	0.458508i	0.967490	+	0.252909i	$0.0813873\pi$
$270$	−0.793841	−	1.37497i	−0.0483116	−	0.0836782i
$271$	2.42564	−	1.40044i	0.147347	−	0.0850710i	−0.424514	−	0.905421i	$-0.639555\pi$
$271$	2.42564	−	1.40044i	0.147347	−	0.0850710i	0.571861	+	0.820350i	$0.306222\pi$
$272$	0.828688			0.0502466
$273$	−1.53311	+	3.26337i	−0.0927880	+	0.197508i
$274$	−13.0688			−0.789517
$275$	−23.5518	+	13.5976i	−1.42023	+	0.819969i
$276$	1.06500	+	1.84463i	0.0641052	+	0.111033i
$277$	1.64248	−	2.84485i	0.0986868	−	0.170931i	−0.812455	−	0.583025i	$-0.801869\pi$
$277$	1.64248	−	2.84485i	0.0986868	−	0.170931i	0.911141	+	0.412094i	$0.135202\pi$
$278$			22.5669i			1.35347i
$279$	−1.27717	−	0.737375i	−0.0764623	−	0.0441455i
$280$	−1.73127	−	0.999546i	−0.103463	−	0.0597343i
$281$		−	13.9619i		−	0.832895i	−0.909160	−	0.416447i	$-0.863275\pi$
$281$		−	13.9619i		−	0.832895i	0.909160	−	0.416447i	$-0.136725\pi$
$282$	0.761864	−	1.31959i	0.0453684	−	0.0785803i
$283$	4.46031	+	7.72548i	0.265138	+	0.459232i	0.967600	−	0.252489i	$-0.0812492\pi$
$283$	4.46031	+	7.72548i	0.265138	+	0.459232i	−0.702462	+	0.711721i	$0.747916\pi$
$284$	2.82823	−	1.63288i	0.167825	−	0.0968937i
$285$	−2.08331			−0.123405
$286$	−40.8271	+	28.4138i	−2.41416	+	1.68014i
$287$	−9.18247			−0.542024
$288$	4.79549	−	2.76868i	0.282577	−	0.163146i
$289$	−23.4603	−	40.6345i	−1.38002	−	2.39026i
$290$	7.37234	−	12.7693i	0.432919	−	0.749838i
$291$		−	0.346177i		−	0.0202933i
$292$	29.9376	+	17.2845i	1.75197	+	1.01150i
$293$	5.11738	+	2.95452i	0.298961	+	0.172605i	0.641976	−	0.766725i	$-0.278115\pi$
$293$	5.11738	+	2.95452i	0.298961	+	0.172605i	−0.343015	+	0.939330i	$0.611448\pi$
$294$		−	2.29328i		−	0.133747i
$295$	−0.706534	+	1.22375i	−0.0411360	+	0.0712497i
$296$	−5.82755	−	10.0936i	−0.338719	−	0.586679i
$297$	5.20978	−	3.00787i	0.302302	−	0.174534i
$298$	−31.3238			−1.81454
$299$	−0.198660	−	2.34801i	−0.0114888	−	0.135789i
$300$	14.7335			0.850639
$301$	7.04068	−	4.06494i	0.405818	−	0.234299i
$302$	−13.1276	−	22.7376i	−0.755406	−	1.30840i
$303$	7.64733	−	13.2456i	0.439328	−	0.760938i
$304$			0.311902i			0.0178888i
$305$	0.832174	+	0.480456i	0.0476501	+	0.0275108i
$306$	15.8784	+	9.16742i	0.907710	+	0.524067i
$307$		−	17.9000i		−	1.02161i	−0.859697	−	0.510804i	$-0.829348\pi$
$307$		−	17.9000i		−	1.02161i	0.859697	−	0.510804i	$-0.170652\pi$
$308$	9.80302	−	16.9793i	0.558579	−	0.967487i
$309$	−5.34936	−	9.26536i	−0.304314	−	0.527088i
$310$	−2.02774	+	1.17072i	−0.115168	+	0.0664923i
$311$	−14.2495			−0.808014			−0.404007	−	0.914756i	$-0.632383\pi$
$311$	−14.2495			−0.808014			−0.404007	+	0.914756i	$0.632383\pi$
$312$	10.3741	−	0.877728i	0.587315	−	0.0496916i
$313$	−9.44689			−0.533970			−0.266985	−	0.963701i	$-0.586027\pi$
$313$	−9.44689			−0.533970			−0.266985	+	0.963701i	$0.586027\pi$
$314$	16.8782	−	9.74466i	0.952494	−	0.549923i
$315$	−0.346160	−	0.599567i	−0.0195039	−	0.0337818i
$316$	9.91756	−	17.1777i	0.557907	−	0.966323i
$317$			15.8830i			0.892076i	0.895014	+	0.446038i	$0.147165\pi$
$317$			15.8830i			0.892076i	−0.895014	+	0.446038i	$0.852835\pi$
$318$	−20.5159	−	11.8448i	−1.15047	−	0.664225i
$319$	48.3828	+	27.9338i	2.70892	+	1.56399i
$320$		−	8.93508i		−	0.499486i
$321$	−5.80692	+	10.0579i	−0.324110	+	0.561376i
$322$	0.749382	+	1.29797i	0.0417614	+	0.0723329i
$323$	20.8353	−	12.0293i	1.15931	−	0.669325i
$324$	−3.25913			−0.181063
$325$	−14.7527	−	6.93072i	−0.818332	−	0.384447i
$326$	−35.9513			−1.99116
$327$	6.91948	−	3.99496i	0.382648	−	0.220922i
$328$	13.2573	+	22.9623i	0.732013	+	1.26788i
$329$	0.332216	−	0.575415i	0.0183157	−	0.0317237i
$330$		−	9.55108i		−	0.525769i
$331$	1.66323	+	0.960265i	0.0914193	+	0.0527810i	0.545013	−	0.838428i	$-0.316525\pi$
$331$	1.66323	+	0.960265i	0.0914193	+	0.0527810i	−0.453593	+	0.891209i	$0.649858\pi$
$332$	−1.06540	−	0.615108i	−0.0584713	−	0.0337584i
$333$		−	4.03636i		−	0.221191i
$334$	22.2761	−	38.5833i	1.21889	−	2.11118i
$335$	2.55470	+	4.42488i	0.139578	+	0.241757i
$336$	−0.0897638	+	0.0518251i	−0.00489702	+	0.00282729i
$337$	−23.6637			−1.28904			−0.644522	−	0.764586i	$-0.722944\pi$
$337$	−23.6637			−1.28904			−0.644522	+	0.764586i	$0.722944\pi$
$338$	−27.9559	−	10.3566i	−1.52060	−	0.563323i
$339$	−7.70366			−0.418406
$340$	15.6228	−	9.01984i	0.847266	−	0.489169i
$341$	−4.43585	−	7.68312i	−0.240215	−	0.416064i
$342$	−3.45044	+	5.97634i	−0.186579	+	0.323164i
$343$		−	1.00000i		−	0.0539949i
$344$	−20.3301	−	11.7376i	−1.09613	−	0.632850i
$345$	0.391845	+	0.226232i	0.0210962	+	0.0121799i
$346$			30.1131i			1.61889i
$347$	−8.67517	+	15.0258i	−0.465708	+	0.806629i	−0.999233	−	0.0391547i	$-0.987533\pi$
$347$	−8.67517	+	15.0258i	−0.465708	+	0.806629i	0.533526	+	0.845784i	$0.320867\pi$
$348$	−15.1336	−	26.2122i	−0.811248	−	1.40512i
$349$	−21.3798	+	12.3437i	−1.14444	+	0.660740i	−0.947525	−	0.319681i	$-0.896424\pi$
$349$	−21.3798	+	12.3437i	−1.14444	+	0.660740i	−0.196911	+	0.980421i	$0.563091\pi$
$350$	10.3672			0.554151
$351$	3.26337	+	1.53311i	0.174186	+	0.0818313i
$352$	33.3112			1.77550
$353$	17.5947	−	10.1583i	0.936472	−	0.540673i	0.0476196	−	0.998866i	$-0.484836\pi$
$353$	17.5947	−	10.1583i	0.936472	−	0.540673i	0.888853	+	0.458193i	$0.151503\pi$
$354$	2.34036	+	4.05363i	0.124389	+	0.215448i
$355$	0.346865	−	0.600788i	0.0184097	−	0.0318865i
$356$			21.6316i			1.14647i
$357$	6.92391	+	3.99752i	0.366452	+	0.211571i
$358$	−19.7503	−	11.4028i	−1.04383	−	0.602657i
$359$		−	0.0752273i		−	0.00397035i	−0.999998	−	0.00198517i	$-0.999368\pi$
$359$		−	0.0752273i		−	0.00397035i	0.999998	−	0.00198517i	$-0.000631901\pi$
$360$	−0.999546	+	1.73127i	−0.0526807	+	0.0912457i
$361$	−4.97242	−	8.61249i	−0.261706	−	0.453289i
$362$	−0.900915	+	0.520143i	−0.0473510	+	0.0273381i
$363$	25.1890			1.32208
$364$	11.7091	−	0.990684i	0.613724	−	0.0519259i
$365$	7.34332			0.384367
$366$	2.75654	−	1.59149i	0.144087	−	0.0831884i
$367$	−18.2812	−	31.6639i	−0.954270	−	1.65284i	−0.736029	−	0.676950i	$-0.763301\pi$
$367$	−18.2812	−	31.6639i	−0.954270	−	1.65284i	−0.218241	−	0.975895i	$-0.570032\pi$
$368$	0.0338702	−	0.0586648i	0.00176560	−	0.00305812i
$369$			9.18247i			0.478021i
$370$	−5.54989	−	3.20423i	−0.288525	−	0.166580i
$371$	−8.94608	−	5.16502i	−0.464457	−	0.268155i
$372$			4.80640i			0.249200i
$373$	−8.77235	+	15.1941i	−0.454215	+	0.786723i	−0.998643	−	0.0520845i	$-0.983413\pi$
$373$	−8.77235	+	15.1941i	−0.454215	+	0.786723i	0.544428	+	0.838808i	$0.316747\pi$
$374$	55.1488	+	95.5205i	2.85168	+	4.93925i
$375$	5.70829	−	3.29568i	0.294775	−	0.170188i
$376$	−1.91857			−0.0989425
$377$	2.82297	+	33.3653i	0.145390	+	1.71840i
$378$	−2.29328			−0.117954
$379$	0.848119	−	0.489662i	0.0435649	−	0.0251522i	−0.478059	−	0.878328i	$-0.658660\pi$
$379$	0.848119	−	0.489662i	0.0435649	−	0.0251522i	0.521624	+	0.853175i	$0.325326\pi$
$380$	3.39489	+	5.88013i	0.174154	+	0.301644i
$381$	−0.366697	+	0.635138i	−0.0187865	+	0.0325391i
$382$		−	2.84341i		−	0.145482i
$383$	6.10082	+	3.52231i	0.311737	+	0.179982i	0.647704	−	0.761892i	$-0.275730\pi$
$383$	6.10082	+	3.52231i	0.311737	+	0.179982i	−0.335966	+	0.941874i	$0.609063\pi$
$384$	−16.0408	−	9.26117i	−0.818579	−	0.472607i
$385$		−	4.16481i		−	0.212259i
$386$	1.82446	−	3.16006i	0.0928627	−	0.160843i
$387$	−4.06494	−	7.04068i	−0.206632	−	0.357898i
$388$	−0.977081	+	0.564118i	−0.0496038	+	0.0286387i
$389$	−32.5771			−1.65172			−0.825862	−	0.563873i	$-0.809311\pi$
$389$	−32.5771			−1.65172			−0.825862	+	0.563873i	$0.809311\pi$
$390$	4.69858	−	3.27000i	0.237922	−	0.165583i
$391$	−5.22513			−0.264246
$392$	−2.50067	+	1.44376i	−0.126303	+	0.0729211i
$393$	−4.91302	−	8.50960i	−0.247829	−	0.429253i
$394$	−13.0955	+	22.6821i	−0.659742	+	1.14271i
$395$		−	4.21348i		−	0.212003i
$396$	−16.9793	−	9.80302i	−0.853243	−	0.492620i
$397$	−6.83593	−	3.94673i	−0.343086	−	0.198081i	0.318550	−	0.947906i	$-0.396804\pi$
$397$	−6.83593	−	3.94673i	−0.343086	−	0.198081i	−0.661636	+	0.749825i	$0.730137\pi$
$398$		−	55.2864i		−	2.77126i
$399$	−1.50459	+	2.60603i	−0.0753237	+	0.130464i
$400$	−0.234286	−	0.405795i	−0.0117143	−	0.0202897i
$401$	24.2448	−	13.9977i	1.21073	−	0.699014i	0.247810	−	0.968809i	$-0.420289\pi$
$401$	24.2448	−	13.9977i	1.21073	−	0.699014i	0.962918	+	0.269794i	$0.0869558\pi$
$402$	16.9247			0.844126
$403$	2.26095	−	4.81265i	0.112626	−	0.239735i
$404$	−49.8472			−2.47999
$405$	−0.599567	+	0.346160i	−0.0297927	+	0.0172008i
$406$	−10.6488	−	18.4442i	−0.528489	−	0.915369i
$407$	12.1408	−	21.0285i	0.601799	−	1.04235i
$408$		−	23.0859i		−	1.14292i
$409$	−1.99387	−	1.15116i	−0.0985907	−	0.0569214i	0.449894	−	0.893082i	$-0.351462\pi$
$409$	−1.99387	−	1.15116i	−0.0985907	−	0.0569214i	−0.548485	+	0.836161i	$0.684795\pi$
$410$	12.6257	+	7.28943i	0.623537	+	0.359999i
$411$			5.69875i			0.281099i
$412$	−17.4342	+	30.1970i	−0.858923	+	1.48770i
$413$	1.02053	+	1.76761i	0.0502170	+	0.0869785i
$414$	1.29797	−	0.749382i	0.0637917	−	0.0368301i
$415$	−0.261329			−0.0128281
$416$	11.4048	+	16.3872i	0.559165	+	0.803450i
$417$	9.84044			0.481889
$418$	−35.9521	+	20.7569i	−1.75847	+	1.01526i
$419$	−6.27850	−	10.8747i	−0.306725	−	0.531263i	0.670919	−	0.741531i	$-0.265900\pi$
$419$	−6.27850	−	10.8747i	−0.306725	−	0.531263i	−0.977644	+	0.210268i	$0.932566\pi$
$420$	−1.12818	+	1.95406i	−0.0550495	+	0.0953485i
$421$			5.65171i			0.275448i	0.990471	+	0.137724i	$0.0439786\pi$
$421$			5.65171i			0.275448i	−0.990471	+	0.137724i	$0.956021\pi$
$422$	0.753667	+	0.435130i	0.0366879	+	0.0211818i
$423$	−0.575415	−	0.332216i	−0.0279777	−	0.0161529i
$424$			29.8283i			1.44859i
$425$	−18.0716	+	31.3009i	−0.876599	+	1.51831i
$426$	−1.14897	−	1.99008i	−0.0556680	−	0.0964198i
$427$	1.20201	−	0.693979i	0.0581692	−	0.0335840i
$428$	37.8509			1.82959
$429$	12.3900	+	17.8029i	0.598196	+	0.859534i
$430$	−12.9077			−0.622463
$431$	25.7889	−	14.8892i	1.24221	−	0.717188i	0.272663	−	0.962110i	$-0.412096\pi$
$431$	25.7889	−	14.8892i	1.24221	−	0.717188i	0.969543	+	0.244922i	$0.0787622\pi$
$432$	0.0518251	+	0.0897638i	0.00249344	+	0.00431876i
$433$	10.9554	−	18.9752i	0.526481	−	0.911892i	−0.473043	−	0.881039i	$-0.656844\pi$
$433$	10.9554	−	18.9752i	0.526481	−	0.911892i	0.999524	−	0.0308527i	$-0.00982228\pi$
$434$			3.38201i			0.162342i
$435$	−5.56813	−	3.21476i	−0.266971	−	0.154136i
$436$	−22.5514	−	13.0201i	−1.08002	−	0.623549i
$437$		−	1.96664i		−	0.0940771i
$438$	12.1622	−	21.0656i	0.581133	−	1.00655i
$439$	16.3857	+	28.3808i	0.782045	+	1.35454i	0.930748	+	0.365661i	$0.119157\pi$
$439$	16.3857	+	28.3808i	0.782045	+	1.35454i	−0.148703	+	0.988882i	$0.547510\pi$
$440$	−10.4148	+	6.01300i	−0.496507	+	0.286659i
$441$	−1.00000			−0.0476190
$442$	−28.1093	+	59.8334i	−1.33702	+	2.84598i
$443$	7.38161			0.350711			0.175355	−	0.984505i	$-0.443893\pi$
$443$	7.38161			0.350711			0.175355	+	0.984505i	$0.443893\pi$
$444$	−11.3926	+	6.57751i	−0.540668	+	0.312155i
$445$	2.29754	+	3.97946i	0.108914	+	0.188644i
$446$	−12.7041	+	22.0042i	−0.601557	+	1.04193i
$447$			13.6589i			0.646046i
$448$	−11.1769	−	6.45300i	−0.528060	−	0.304875i
$449$	29.3164	+	16.9258i	1.38353	+	0.798779i	0.992575	−	0.121633i	$-0.0388131\pi$
$449$	29.3164	+	16.9258i	1.38353	+	0.798779i	0.390950	+	0.920412i	$0.372146\pi$
$450$		−	10.3672i		−	0.488715i
$451$	−27.6197	+	47.8386i	−1.30056	+	2.25263i
$452$	12.5536	+	21.7435i	0.590472	+	1.02273i
$453$	−9.91488	+	5.72436i	−0.465842	+	0.268954i
$454$	37.2877			1.75000
$455$	2.04885	−	1.42591i	0.0960515	−	0.0668475i
$456$	8.68908			0.406904
$457$	−24.0642	+	13.8935i	−1.12568	+	0.649910i	−0.942844	−	0.333234i	$-0.891860\pi$
$457$	−24.0642	+	13.8935i	−1.12568	+	0.649910i	−0.182833	+	0.983144i	$0.558527\pi$
$458$	−11.9255	−	20.6556i	−0.557242	−	0.965172i
$459$	3.99752	−	6.92391i	0.186588	−	0.323180i
$460$		−	1.47464i		−	0.0687553i
$461$	25.8743	+	14.9385i	1.20509	+	0.695757i	0.961682	−	0.274168i	$-0.0884025\pi$
$461$	25.8743	+	14.9385i	1.20509	+	0.695757i	0.243404	+	0.969925i	$0.421736\pi$
$462$	−11.9475	−	6.89788i	−0.555847	−	0.320918i
$463$		−	2.45788i		−	0.114228i	−0.998368	−	0.0571138i	$-0.981810\pi$
$463$		−	2.45788i		−	0.114228i	0.998368	−	0.0571138i	$-0.0181898\pi$
$464$	−0.481296	+	0.833629i	−0.0223436	+	0.0387003i
$465$	0.510500	+	0.884211i	0.0236739	+	0.0410043i
$466$	30.9742	−	17.8829i	1.43485	−	0.828411i
$467$	−5.12405			−0.237113			−0.118556	−	0.992947i	$-0.537827\pi$
$467$	−5.12405			−0.237113			−0.118556	+	0.992947i	$0.537827\pi$
$468$	−0.990684	−	11.7091i	−0.0457944	−	0.541254i
$469$	7.38012			0.340782
$470$	−0.913577	+	0.527454i	−0.0421402	+	0.0243296i
$471$	−4.24923	−	7.35988i	−0.195794	−	0.339125i
$472$	2.94681	−	5.10402i	0.135638	−	0.234932i
$473$		−	48.9072i		−	2.24875i
$474$	−12.0871	−	6.97848i	−0.555178	−	0.320532i
$475$	−11.7810	−	6.80179i	−0.540551	−	0.312087i
$476$		−	26.0568i		−	1.19431i
$477$	−5.16502	+	8.94608i	−0.236490	+	0.409613i
$478$	−26.5676	−	46.0164i	−1.21517	−	2.10474i
$479$	−26.1326	+	15.0876i	−1.19403	+	0.689372i	−0.959217	−	0.282670i	$-0.908780\pi$
$479$	−26.1326	+	15.0876i	−1.19403	+	0.689372i	−0.234810	+	0.972041i	$0.575447\pi$
$480$	−3.83362			−0.174980
$481$	14.5015	−	1.22694i	0.661211	−	0.0559437i
$482$	23.6933			1.07920
$483$	0.565988	−	0.326773i	0.0257534	−	0.0148687i
$484$	−41.0471	−	71.0957i	−1.86578	−	3.23162i
$485$	−0.119833	+	0.207556i	−0.00544133	+	0.00942465i
$486$			2.29328i			0.104025i
$487$	−6.48499	−	3.74411i	−0.293863	−	0.169662i	0.345820	−	0.938301i	$-0.387601\pi$
$487$	−6.48499	−	3.74411i	−0.293863	−	0.169662i	−0.639683	+	0.768639i	$0.720934\pi$
$488$	−3.47083	−	2.00388i	−0.157117	−	0.0907116i
$489$			15.6768i			0.708930i
$490$	−0.793841	+	1.37497i	−0.0358621	+	0.0621150i
$491$	−10.2310	−	17.7205i	−0.461717	−	0.799717i	0.537330	−	0.843372i	$-0.319433\pi$
$491$	−10.2310	−	17.7205i	−0.461717	−	0.799717i	−0.999047	+	0.0436554i	$0.986100\pi$
$492$	25.9174	−	14.9634i	1.16845	−	0.674603i
$493$	74.2493			3.34402
$494$	−22.5201	−	10.5798i	−1.01323	−	0.476008i
$495$	−4.16481			−0.187194
$496$	0.132379	−	0.0764292i	0.00594400	−	0.00343177i
$497$	−0.501018	−	0.867789i	−0.0224737	−	0.0389257i
$498$	−0.432820	+	0.749666i	−0.0193951	+	0.0335933i
$499$		−	4.96188i		−	0.222124i	−0.993813	−	0.111062i	$-0.964575\pi$
$499$		−	4.96188i		−	0.222124i	0.993813	−	0.111062i	$-0.0354252\pi$
$500$	−18.6040	−	10.7410i	−0.831998	−	0.480354i
$501$	−16.8245	−	9.71364i	−0.751664	−	0.433973i
$502$		−	34.1247i		−	1.52306i
$503$	2.94598	−	5.10259i	0.131355	−	0.227513i	−0.792844	−	0.609424i	$-0.791401\pi$
$503$	2.94598	−	5.10259i	0.131355	−	0.227513i	0.924199	+	0.381911i	$0.124734\pi$
$504$	1.44376	+	2.50067i	0.0643103	+	0.111389i
$505$	−9.17017	+	5.29440i	−0.408067	+	0.235598i
$506$	9.01617			0.400818
$507$	−4.51605	+	12.1904i	−0.200565	+	0.541394i
$508$	2.39022			0.106049
$509$	−10.7101	+	6.18348i	−0.474717	+	0.274078i	−0.718212	−	0.695824i	$-0.755039\pi$
$509$	−10.7101	+	6.18348i	−0.474717	+	0.274078i	0.243495	+	0.969902i	$0.421706\pi$
$510$	−6.34679	−	10.9930i	−0.281041	−	0.486777i
$511$	5.30341	−	9.18578i	0.234609	−	0.406355i
$512$			1.17253i			0.0518192i
$513$	2.60603	+	1.50459i	0.115059	+	0.0664292i
$514$	47.6843	+	27.5305i	2.10326	+	1.21432i
$515$			7.40693i			0.326389i
$516$	−13.2481	+	22.9465i	−0.583217	+	1.01016i
$517$	−1.99852	−	3.46155i	−0.0878950	−	0.152239i
$518$	−8.01636	+	4.62825i	−0.352219	+	0.203354i
$519$	13.1310			0.576389
$520$	−6.52378	−	3.06483i	−0.286087	−	0.134402i
$521$	1.39280			0.0610196			0.0305098	−	0.999534i	$-0.490287\pi$
$521$	1.39280			0.0610196			0.0305098	+	0.999534i	$0.490287\pi$
$522$	−18.4442	+	10.6488i	−0.807280	+	0.466083i
$523$	−9.99594	−	17.3135i	−0.437092	−	0.757066i	0.560372	−	0.828241i	$-0.310658\pi$
$523$	−9.99594	−	17.3135i	−0.437092	−	0.757066i	−0.997464	+	0.0711756i	$0.977325\pi$
$524$	−16.0122	+	27.7339i	−0.699494	+	1.21156i
$525$		−	4.52069i		−	0.197299i
$526$	−15.6130	−	9.01415i	−0.680758	−	0.393036i
$527$	−10.2110	−	5.89534i	−0.444800	−	0.256805i
$528$			0.623532i			0.0271358i
$529$	11.2864	−	19.5487i	0.490715	−	0.849943i
$530$	8.20042	+	14.2035i	0.356203	+	0.616962i
$531$	1.76761	−	1.02053i	0.0767078	−	0.0442873i
$532$	9.80729			0.425200
$533$	−32.9900	+	2.79122i	−1.42896	+	0.120901i
$534$	15.2210			0.658677
$535$	6.96327	−	4.02025i	0.301048	−	0.173810i
$536$	−10.6551	−	18.4553i	−0.460232	−	0.797146i
$537$	−4.97228	+	8.61223i	−0.214570	+	0.371645i
$538$			19.9136i			0.858534i
$539$	−5.20978	−	3.00787i	−0.224401	−	0.129558i
$540$	1.95406	+	1.12818i	0.0840895	+	0.0485491i
$541$		−	13.5238i		−	0.581434i	−0.956809	−	0.290717i	$-0.906106\pi$
$541$		−	13.5238i		−	0.581434i	0.956809	−	0.290717i	$-0.0938938\pi$
$542$	−3.21161	+	5.56267i	−0.137950	+	0.238937i
$543$	0.226812	+	0.392850i	0.00973344	+	0.0168588i
$544$	38.3401	−	22.1357i	1.64382	−	0.949059i
$545$	−5.53159			−0.236947
$546$	−0.697093	−	8.23910i	−0.0298328	−	0.352601i
$547$	23.9335			1.02332			0.511660	−	0.859188i	$-0.329031\pi$
$547$	23.9335			1.02332			0.511660	+	0.859188i	$0.329031\pi$
$548$	16.0847	−	9.28648i	0.687102	−	0.396699i
$549$	−0.693979	−	1.20201i	−0.0296183	−	0.0513004i
$550$	31.1832	−	54.0108i	1.32966	−	2.30303i
$551$			27.9460i			1.19054i
$552$	−1.63431	−	0.943567i	−0.0695607	−	0.0401609i
$553$	−5.27065	−	3.04301i	−0.224131	−	0.129402i
$554$			7.53331i			0.320060i
$555$	−1.39723	+	2.42007i	−0.0593090	+	0.102726i
$556$	−16.0356	−	27.7745i	−0.680062	−	1.17790i
$557$	11.7573	−	6.78806i	0.498171	−	0.287619i	−0.229787	−	0.973241i	$-0.573803\pi$
$557$	11.7573	−	6.78806i	0.498171	−	0.287619i	0.727958	+	0.685622i	$0.240470\pi$
$558$	3.38201			0.143172
$559$	24.0595	−	16.7443i	1.01761	−	0.708210i
$560$	0.0717592			0.00303238
$561$	41.6524	−	24.0480i	1.75856	−	1.01531i
$562$	16.0092	+	27.7288i	0.675308	+	1.16967i
$563$	−16.3479	+	28.3154i	−0.688983	+	1.19335i	0.283184	+	0.959065i	$0.408609\pi$
$563$	−16.3479	+	28.3154i	−0.688983	+	1.19335i	−0.972167	+	0.234288i	$0.924724\pi$
$564$			2.16547i			0.0911827i
$565$	4.61886	+	2.66670i	0.194317	+	0.112189i
$566$	−17.7167	−	10.2287i	−0.744687	−	0.429946i
$567$			1.00000i			0.0419961i
$568$	−1.44670	+	2.50576i	−0.0607023	+	0.105139i
$569$	15.2591	+	26.4296i	0.639696	+	1.10799i	0.985499	+	0.169679i	$0.0542732\pi$
$569$	15.2591	+	26.4296i	0.639696	+	1.10799i	−0.345803	+	0.938307i	$0.612393\pi$
$570$	4.13754	−	2.38881i	0.173303	−	0.100056i
$571$	−26.4381			−1.10640			−0.553201	−	0.833048i	$-0.686594\pi$
$571$	−26.4381			−1.10640			−0.553201	+	0.833048i	$0.686594\pi$
$572$	30.0582	−	63.9817i	1.25680	−	2.67521i
$573$	−1.23989			−0.0517971
$574$	18.2367	−	10.5290i	0.761187	−	0.439471i
$575$	1.47724	+	2.55866i	0.0616053	+	0.106703i
$576$	−6.45300	+	11.1769i	−0.268875	+	0.465705i
$577$			20.6254i			0.858648i	0.903151	+	0.429324i	$0.141248\pi$
$577$			20.6254i			0.858648i	−0.903151	+	0.429324i	$0.858752\pi$
$578$	93.1862	+	53.8011i	3.87603	+	2.23783i
$579$	−1.37797	−	0.795569i	−0.0572663	−	0.0330627i
$580$			20.9546i			0.870094i
$581$	−0.188734	+	0.326897i	−0.00783001	+	0.0135620i
$582$	0.396940	+	0.687521i	0.0164537	+	0.0284987i
$583$	−53.8172	+	31.0714i	−2.22888	+	1.28685i
$584$	−30.6275			−1.26737
$585$	−1.42591	−	2.04885i	−0.0589540	−	0.0847095i
$586$	−13.5511			−0.559790
$587$	−6.54569	+	3.77915i	−0.270169	+	0.155982i	−0.628965	−	0.777434i	$-0.716521\pi$
$587$	−6.54569	+	3.77915i	−0.270169	+	0.155982i	0.358795	+	0.933416i	$0.383188\pi$
$588$	1.62956	+	2.82249i	0.0672020	+	0.116397i
$589$	2.21889	−	3.84324i	0.0914279	−	0.158358i
$590$		−	3.24056i		−	0.133412i
$591$	9.89068	+	5.71039i	0.406848	+	0.234894i
$592$	0.362319	+	0.209185i	0.0148912	+	0.00859745i
$593$			27.0632i			1.11135i	0.831399	+	0.555676i	$0.187540\pi$
$593$			27.0632i			1.11135i	−0.831399	+	0.555676i	$0.812460\pi$
$594$	−6.89788	+	11.9475i	−0.283023	+	0.490211i
$595$	−2.76756	−	4.79356i	−0.113459	−	0.196517i
$596$	38.5522	−	22.2581i	1.57916	−	0.911728i
$597$	−24.1080			−0.986676
$598$	3.08686	+	4.43544i	0.126231	+	0.181379i
$599$	−46.2708			−1.89057			−0.945286	−	0.326242i	$-0.894218\pi$
$599$	−46.2708			−1.89057			−0.945286	+	0.326242i	$0.894218\pi$
$600$	−11.3048	+	6.52681i	−0.461515	+	0.266456i
$601$	9.46685	+	16.3971i	0.386161	+	0.668850i	0.991929	−	0.126791i	$-0.0404677\pi$
$601$	9.46685	+	16.3971i	0.386161	+	0.668850i	−0.605769	+	0.795641i	$0.707134\pi$
$602$	−9.32204	+	16.1462i	−0.379938	+	0.658072i
$603$		−	7.38012i		−	0.300542i
$604$	32.3138	+	18.6564i	1.31483	+	0.759119i
$605$	−15.1025	−	8.71944i	−0.614004	−	0.354496i
$606$			35.0749i			1.42482i
$607$	2.00295	−	3.46922i	0.0812974	−	0.140811i	−0.822510	−	0.568751i	$-0.807427\pi$
$607$	2.00295	−	3.46922i	0.0812974	−	0.140811i	0.903807	+	0.427939i	$0.140760\pi$
$608$	8.33144	+	14.4305i	0.337885	+	0.585233i
$609$	−8.04271	+	4.64346i	−0.325907	+	0.188163i
$610$	−2.20364			−0.0892227
$611$	1.01865	−	2.16829i	0.0412101	−	0.0877195i
$612$	−26.0568			−1.05329
$613$	−5.63182	+	3.25153i	−0.227467	+	0.131328i	−0.609403	−	0.792861i	$-0.708591\pi$
$613$	−5.63182	+	3.25153i	−0.227467	+	0.131328i	0.381936	+	0.924189i	$0.375257\pi$
$614$	20.5249	+	35.5501i	0.828317	+	1.43469i
$615$	3.17861	−	5.50551i	0.128174	−	0.222003i
$616$			17.3706i			0.699881i
$617$	−14.8281	−	8.56098i	−0.596955	−	0.344652i	0.170888	−	0.985291i	$-0.445337\pi$
$617$	−14.8281	−	8.56098i	−0.596955	−	0.344652i	−0.767843	+	0.640638i	$0.778670\pi$
$618$	21.2480	+	12.2676i	0.854722	+	0.493474i
$619$		−	23.5838i		−	0.947912i	−0.880548	−	0.473956i	$-0.842826\pi$
$619$		−	23.5838i		−	0.947912i	0.880548	−	0.473956i	$-0.157174\pi$
$620$	1.66378	−	2.88176i	0.0668191	−	0.115734i
$621$	−0.326773	−	0.565988i	−0.0131130	−	0.0227123i
$622$	28.3000	−	16.3390i	1.13473	−	0.655135i
$623$	6.63723			0.265915
$624$	−0.306742	+	0.213479i	−0.0122795	+	0.00854599i
$625$	18.0401			0.721605
$626$	18.7619	−	10.8322i	0.749876	−	0.432941i
$627$	9.05121	+	15.6772i	0.361470	+	0.626085i
$628$	−13.8488	+	23.9868i	−0.552626	+	0.957176i
$629$		−	32.2709i		−	1.28672i
$630$	1.37497	+	0.793841i	0.0547803	+	0.0316274i
$631$	33.6839	+	19.4474i	1.34093	+	0.774189i	0.986945	−	0.161061i	$-0.0514914\pi$
$631$	33.6839	+	19.4474i	1.34093	+	0.774189i	0.353990	+	0.935249i	$0.384825\pi$
$632$			17.5736i			0.699039i
$633$	0.189741	−	0.328642i	0.00754154	−	0.0130623i
$634$	−18.2120	−	31.5441i	−0.723292	−	1.25278i
$635$	0.439719	−	0.253872i	0.0174497	−	0.0100746i
$636$	33.6669			1.33498
$637$	−0.303972	−	3.59271i	−0.0120438	−	0.142349i
$638$	−128.120			−5.07232
$639$	−0.867789	+	0.501018i	−0.0343292	+	0.0198200i
$640$	6.41169	+	11.1054i	0.253444	+	0.438979i
$641$	−19.8343	+	34.3540i	−0.783406	+	1.35690i	0.146540	+	0.989205i	$0.453186\pi$
$641$	−19.8343	+	34.3540i	−0.783406	+	1.35690i	−0.929947	+	0.367695i	$0.880147\pi$
$642$		−	26.6338i		−	1.05115i
$643$	−22.4371	−	12.9541i	−0.884832	−	0.510858i	−0.0125835	−	0.999921i	$-0.504006\pi$
$643$	−22.4371	−	12.9541i	−0.884832	−	0.510858i	−0.872249	+	0.489063i	$0.837339\pi$
$644$	−1.84463	−	1.06500i	−0.0726885	−	0.0419667i
$645$			5.62848i			0.221621i
$646$	−27.5864	+	47.7811i	−1.08537	+	1.87992i
$647$	1.14806	+	1.98850i	0.0451350	+	0.0781761i	0.887710	−	0.460402i	$-0.152295\pi$
$647$	1.14806	+	1.98850i	0.0451350	+	0.0781761i	−0.842575	+	0.538579i	$0.818962\pi$
$648$	2.50067	−	1.44376i	0.0982356	−	0.0567164i
$649$	12.2785			0.481973
$650$	37.2464	−	3.15134i	1.46092	−	0.123606i
$651$	1.47475			0.0578000
$652$	44.2476	−	25.5464i	1.73287	−	1.00047i
$653$	11.8918	+	20.5973i	0.465363	+	0.806033i	0.999218	−	0.0395434i	$-0.0125903\pi$
$653$	11.8918	+	20.5973i	0.465363	+	0.806033i	−0.533855	+	0.845576i	$0.679257\pi$
$654$	−9.16156	+	15.8683i	−0.358245	+	0.620499i
$655$			6.80276i			0.265806i
$656$	−0.824254	−	0.475883i	−0.0321817	−	0.0185801i
$657$	−9.18578	−	5.30341i	−0.358371	−	0.206906i
$658$			1.52373i			0.0594011i
$659$	8.04212	−	13.9294i	0.313276	−	0.542611i	−0.665793	−	0.746136i	$-0.731907\pi$
$659$	8.04212	−	13.9294i	0.313276	−	0.542611i	0.979070	+	0.203526i	$0.0652400\pi$
$660$	6.78682	+	11.7551i	0.264177	+	0.457568i
$661$	−3.52181	+	2.03332i	−0.136982	+	0.0790868i	−0.566925	−	0.823769i	$-0.691867\pi$
$661$	−3.52181	+	2.03332i	−0.136982	+	0.0790868i	0.429943	+	0.902856i	$0.358534\pi$
$662$	−4.40431			−0.171178
$663$	26.0908	+	12.2573i	1.01328	+	0.476033i
$664$	1.08995			0.0422982
$665$	1.80420	−	1.04166i	0.0699640	−	0.0403937i
$666$	4.62825	+	8.01636i	0.179341	+	0.310628i
$667$	3.03472	−	5.25629i	0.117505	−	0.203524i
$668$			63.3159i			2.44977i
$669$	9.59507	+	5.53972i	0.370967	+	0.214178i
$670$	−10.1475	−	5.85865i	−0.392031	−	0.226339i
$671$		−	8.34959i		−	0.322332i
$672$	−2.76868	+	4.79549i	−0.106804	+	0.184990i
$673$	18.2254	+	31.5674i	0.702539	+	1.21683i	0.967572	+	0.252594i	$0.0812837\pi$
$673$	18.2254	+	31.5674i	0.702539	+	1.21683i	−0.265033	+	0.964239i	$0.585383\pi$
$674$	46.9970	−	27.1337i	1.81026	−	1.04515i
$675$	−4.52069			−0.174002
$676$	41.7664	−	7.11849i	1.60640	−	0.273788i
$677$	25.4552			0.978324			0.489162	−	0.872193i	$-0.337303\pi$
$677$	25.4552			0.978324			0.489162	+	0.872193i	$0.337303\pi$
$678$	15.2998	−	8.83332i	0.587584	−	0.339242i
$679$	0.173089	+	0.299798i	0.00664253	+	0.0115052i
$680$	−7.99141	+	13.8415i	−0.306457	+	0.530798i
$681$		−	16.2595i		−	0.623067i
$682$	17.6195	+	10.1726i	0.674687	+	0.389531i
$683$	1.84567	+	1.06560i	0.0706228	+	0.0407741i	0.534896	−	0.844918i	$-0.320351\pi$
$683$	1.84567	+	1.06560i	0.0706228	+	0.0407741i	−0.464273	+	0.885692i	$0.653684\pi$
$684$		−	9.80729i		−	0.374991i
$685$	1.97268	−	3.41678i	0.0753723	−	0.130549i
$686$	1.14664	+	1.98604i	0.0437789	+	0.0758273i
$687$	−9.00701	+	5.20020i	−0.343639	+	0.198400i
$688$	0.842664			0.0321263
$689$	−33.7107	−	15.8371i	−1.28428	−	0.603345i
$690$	−1.03762			−0.0395017
$691$	22.3230	−	12.8882i	0.849207	−	0.490290i	−0.0111759	−	0.999938i	$-0.503557\pi$
$691$	22.3230	−	12.8882i	0.849207	−	0.490290i	0.860383	+	0.509647i	$0.170224\pi$
$692$	−21.3979	−	37.0622i	−0.813425	−	1.40889i
$693$	−3.00787	+	5.20978i	−0.114259	+	0.197903i
$694$		−	39.7892i		−	1.51038i
$695$	−5.90000	−	3.40637i	−0.223800	−	0.129211i
$696$	23.2235	+	13.4081i	0.880286	+	0.508233i
$697$			73.4142i			2.78076i
$698$	28.3074	−	49.0299i	1.07145	−	1.85581i
$699$	−7.79798	−	13.5065i	−0.294947	−	0.510863i
$700$	−12.7596	+	7.36675i	−0.482267	+	0.278437i
$701$	8.75888			0.330819			0.165409	−	0.986225i	$-0.447106\pi$
$701$	8.75888			0.330819			0.165409	+	0.986225i	$0.447106\pi$
$702$	−8.23910	+	0.697093i	−0.310965	+	0.0263101i
$703$	12.1461			0.458100
$704$	−67.2374	+	38.8195i	−2.53410	+	1.46307i
$705$	0.230000	+	0.398372i	0.00866230	+	0.0150035i
$706$	−23.2958	+	40.3496i	−0.876751	+	1.51858i
$707$			15.2947i			0.575215i
$708$	−5.76087	−	3.32604i	−0.216507	−	0.125000i
$709$	−16.5858	−	9.57584i	−0.622895	−	0.359628i	0.155101	−	0.987899i	$-0.450430\pi$
$709$	−16.5858	−	9.57584i	−0.622895	−	0.359628i	−0.777995	+	0.628270i	$0.783763\pi$
$710$			1.59092i			0.0597060i
$711$	−3.04301	+	5.27065i	−0.114122	+	0.197665i
$712$	−9.58258	−	16.5975i	−0.359122	−	0.622018i
$713$	−0.834691	+	0.481909i	−0.0312594	+	0.0180476i
$714$	−18.3348			−0.686165
$715$	−1.26599	−	14.9630i	−0.0473452	−	0.559584i
$716$	32.4105			1.21124
$717$	−20.0658	+	11.5850i	−0.749370	+	0.432649i
$718$	0.0862586	+	0.149404i	0.00321914	+	0.00557572i
$719$	16.2428	−	28.1333i	0.605753	−	1.04919i	−0.386179	−	0.922424i	$-0.626205\pi$
$719$	16.2428	−	28.1333i	0.605753	−	1.04919i	0.991932	−	0.126771i	$-0.0404613\pi$
$720$		−	0.0717592i		−	0.00267431i
$721$	9.26536	+	5.34936i	0.345060	+	0.199220i
$722$	19.7508	+	11.4031i	0.735050	+	0.424381i
$723$		−	10.3316i		−	0.384237i
$724$	0.739209	−	1.28035i	0.0274725	−	0.0475838i
$725$	−20.9917	−	36.3586i	−0.779611	−	1.35033i
$726$	−50.0264	+	28.8827i	−1.85665	+	1.07194i
$727$	34.2511			1.27030			0.635151	−	0.772388i	$-0.280938\pi$
$727$	34.2511			1.27030			0.635151	+	0.772388i	$0.280938\pi$
$728$	−8.54534	+	5.94716i	−0.316711	+	0.220417i
$729$	1.00000			0.0370370
$730$	−14.5841	+	8.42014i	−0.539782	+	0.311643i
$731$	−32.4993	−	56.2905i	−1.20203	−	2.08198i
$732$	−2.26177	+	3.91749i	−0.0835973	+	0.144795i
$733$		−	10.0339i		−	0.370611i	−0.982681	−	0.185306i	$-0.940672\pi$
$733$		−	10.0339i		−	0.370611i	0.982681	−	0.185306i	$-0.0593275\pi$
$734$	72.6143	+	41.9239i	2.68024	+	1.54744i
$735$	0.599567	+	0.346160i	0.0221154	+	0.0127683i
$736$		−	3.61892i		−	0.133395i
$737$	22.1984	−	38.4488i	0.817689	−	1.41628i
$738$	−10.5290	−	18.2367i	−0.387577	−	0.671304i
$739$	−33.2440	+	19.1934i	−1.22290	+	0.706041i	−0.965535	−	0.260273i	$-0.916187\pi$
$739$	−33.2440	+	19.1934i	−1.22290	+	0.706041i	−0.257364	+	0.966314i	$0.582854\pi$
$740$	9.10748			0.334798
$741$	−4.61340	+	9.82006i	−0.169478	+	0.360749i
$742$	23.6897			0.869675
$743$	−6.70955	+	3.87376i	−0.246149	+	0.142114i	−0.618000	−	0.786178i	$-0.712057\pi$
$743$	−6.70955	+	3.87376i	−0.246149	+	0.142114i	0.371850	+	0.928293i	$0.378723\pi$
$744$	−2.12919	−	3.68787i	−0.0780599	−	0.135204i
$745$	4.72818	−	8.18945i	0.173227	−	0.300038i
$746$		−	40.2349i		−	1.47310i
$747$	0.326897	+	0.188734i	0.0119605	+	0.00690542i
$748$	−135.750	−	78.3755i	−4.96352	−	2.86569i
$749$		−	11.6138i		−	0.424360i
$750$	−7.55792	+	13.0907i	−0.275976	+	0.478005i
$751$	−14.0367	−	24.3122i	−0.512205	−	0.887165i	−0.999900	−	0.0141511i	$-0.995495\pi$
$751$	−14.0367	−	24.3122i	−0.512205	−	0.887165i	0.487695	−	0.873014i	$-0.337838\pi$
$752$	0.0596420	−	0.0344343i	0.00217492	−	0.00125569i
$753$	−14.8803			−0.542269
$754$	−43.8644	−	63.0277i	−1.59745	−	2.29534i
$755$	7.92618			0.288463
$756$	2.82249	−	1.62956i	0.102653	−	0.0592666i
$757$	26.3909	+	45.7103i	0.959192	+	1.66137i	0.724469	+	0.689307i	$0.242085\pi$
$757$	26.3909	+	45.7103i	0.959192	+	1.66137i	0.234723	+	0.972062i	$0.424582\pi$
$758$	−1.12293	+	1.94497i	−0.0407867	+	0.0706446i
$759$		−	3.93156i		−	0.142707i
$760$	−5.20969	−	3.00781i	−0.188975	−	0.109105i
$761$	−13.5423	−	7.81867i	−0.490909	−	0.283427i	0.234042	−	0.972226i	$-0.424805\pi$
$761$	−13.5423	−	7.81867i	−0.490909	−	0.283427i	−0.724952	+	0.688800i	$0.758138\pi$
$762$		−	1.68188i		−	0.0609280i
$763$	−3.99496	+	6.91948i	−0.144627	+	0.250502i
$764$	2.02048	+	3.49957i	0.0730983	+	0.126610i
$765$	−4.79356	+	2.76756i	−0.173312	+	0.100061i
$766$	−16.1553			−0.583714
$767$	4.20378	+	6.04031i	0.151790	+	0.218103i
$768$	16.6649			0.601342
$769$	−45.9494	+	26.5289i	−1.65698	+	0.956656i	−0.682879	+	0.730531i	$0.739273\pi$
$769$	−45.9494	+	26.5289i	−1.65698	+	0.956656i	−0.974098	+	0.226125i	$0.927394\pi$
$770$	4.77554	+	8.27147i	0.172098	+	0.298083i
$771$	12.0049	−	20.7931i	0.432345	−	0.748844i
$772$			5.18572i			0.186638i
$773$	−14.7200	−	8.49862i	−0.529443	−	0.305674i	0.211346	−	0.977411i	$-0.432215\pi$
$773$	−14.7200	−	8.49862i	−0.529443	−	0.305674i	−0.740790	+	0.671737i	$0.765548\pi$
$774$	16.1462	+	9.32204i	0.580365	+	0.335074i
$775$			6.66689i			0.239482i
$776$	0.499798	−	0.865676i	0.0179417	−	0.0310759i
$777$	2.01818	+	3.49559i	0.0724018	+	0.125404i
$778$	64.6993	−	37.3542i	2.31958	−	1.33921i
$779$	−27.6317			−0.990009
$780$	−3.45925	+	7.36333i	−0.123861	+	0.263649i
$781$	−6.02798			−0.215698
$782$	10.3773	−	5.99134i	0.371092	−	0.214250i
$783$	4.64346	+	8.04271i	0.165944	+	0.287423i
$784$	0.0518251	−	0.0897638i	0.00185090	−	0.00320585i
$785$			5.88365i			0.209996i
$786$	19.5149	+	11.2669i	0.696073	+	0.401878i
$787$	−18.8112	−	10.8607i	−0.670548	−	0.387141i	0.125736	−	0.992064i	$-0.459871\pi$
$787$	−18.8112	−	10.8607i	−0.670548	−	0.387141i	−0.796284	+	0.604923i	$0.793204\pi$
$788$		−	37.2217i		−	1.32597i
$789$	−3.93068	+	6.80814i	−0.139936	+	0.242376i
$790$	4.83134	+	8.36813i	0.171891	+	0.297725i
$791$	6.67157	−	3.85183i	0.237214	−	0.136955i
$792$	17.3706			0.617237
$793$	4.10752	−	2.85865i	0.145862	−	0.101514i
$794$	18.1019			0.642412
$795$	6.19355	−	3.57585i	0.219663	−	0.126822i
$796$	39.2856	+	68.0446i	1.39244	+	2.41178i
$797$	−8.25382	+	14.2960i	−0.292365	+	0.506392i	−0.974369	−	0.224958i	$-0.927776\pi$
$797$	−8.25382	+	14.2960i	−0.292365	+	0.506392i	0.682003	+	0.731349i	$0.261109\pi$
$798$		−	6.90088i		−	0.244289i
$799$	−4.60047	−	2.65608i	−0.162753	−	0.0939654i
$800$	−21.6789	−	12.5163i	−0.766466	−	0.442519i
$801$		−	6.63723i		−	0.234515i
$802$	−32.1007	+	55.6001i	−1.13352	+	1.96331i
$803$	−31.9039	−	55.2592i	−1.12586	−	1.95006i
$804$	−20.8303	+	12.0264i	−0.734628	+	0.424138i
$805$	−0.452464			−0.0159472
$806$	1.02804	+	12.1506i	0.0362111	+	0.427987i
$807$	8.68344			0.305672
$808$	38.2469	−	22.0819i	1.34552	−	0.776837i
$809$	−6.19787	−	10.7350i	−0.217905	−	0.377423i	0.736262	−	0.676697i	$-0.236589\pi$
$809$	−6.19787	−	10.7350i	−0.217905	−	0.377423i	−0.954167	+	0.299273i	$0.903256\pi$
$810$	0.793841	−	1.37497i	0.0278927	−	0.0483116i
$811$			42.7478i			1.50108i	0.660826	+	0.750539i	$0.270206\pi$
$811$			42.7478i			1.50108i	−0.660826	+	0.750539i	$0.729794\pi$
$812$	26.2122	+	15.1336i	0.919868	+	0.531086i
$813$	2.42564	+	1.40044i	0.0850710	+	0.0491157i
$814$			55.6846i			1.95175i
$815$	5.42669	−	9.39930i	0.190089	−	0.329243i
$816$	0.414344	+	0.717665i	0.0145049	+	0.0251233i
$817$	21.1867	−	12.2321i	0.741228	−	0.427948i
$818$	5.27988			0.184607
$819$	−3.59271	+	0.303972i	−0.125540	+	0.0106216i
$820$	−20.7190			−0.723537
$821$	19.9037	−	11.4914i	0.694643	−	0.401052i	−0.110706	−	0.993853i	$-0.535311\pi$
$821$	19.9037	−	11.4914i	0.694643	−	0.401052i	0.805349	+	0.592801i	$0.201978\pi$
$822$	−6.53442	−	11.3179i	−0.227914	−	0.394758i
$823$	27.8132	−	48.1739i	0.969508	−	1.67924i	0.272526	−	0.962148i	$-0.412141\pi$
$823$	27.8132	−	48.1739i	0.969508	−	1.67924i	0.696982	−	0.717089i	$-0.254526\pi$
$824$		−	30.8928i		−	1.07620i
$825$	−23.5518	−	13.5976i	−0.819969	−	0.473409i
$826$	−4.05363	−	2.34036i	−0.141044	−	0.0814316i
$827$		−	18.5823i		−	0.646170i	−0.946370	−	0.323085i	$-0.895280\pi$
$827$		−	18.5823i		−	0.646170i	0.946370	−	0.323085i	$-0.104720\pi$
$828$	−1.06500	+	1.84463i	−0.0370112	+	0.0641052i
$829$	−0.266321	−	0.461282i	−0.00924972	−	0.0160210i	0.861363	−	0.507989i	$-0.169611\pi$
$829$	−0.266321	−	0.461282i	−0.00924972	−	0.0160210i	−0.870613	+	0.491968i	$0.836278\pi$
$830$	0.519009	−	0.299650i	0.0180151	−	0.0104010i
$831$	3.28495			0.113954
$832$	−42.1170	−	19.7863i	−1.46014	−	0.685967i
$833$	−7.99504			−0.277012
$834$	−19.5435	+	11.2834i	−0.676736	+	0.390713i
$835$	6.72495	+	11.6479i	0.232726	+	0.403094i
$836$	29.4990	−	51.0938i	1.02025	−	1.76712i
$837$		−	1.47475i		−	0.0509748i
$838$	24.9387	+	14.3983i	0.861492	+	0.497383i
$839$	11.1858	+	6.45811i	0.386176	+	0.222959i	0.680502	−	0.732746i	$-0.261762\pi$
$839$	11.1858	+	6.45811i	0.386176	+	0.222959i	−0.294326	+	0.955705i	$0.595095\pi$
$840$		−	1.99909i		−	0.0689753i
$841$	−28.6235	+	49.5773i	−0.987016	+	1.70956i
$842$	−6.48048	−	11.2245i	−0.223332	−	0.386822i
$843$	12.0913	−	6.98093i	0.416447	−	0.240436i
$844$	−1.23678			−0.0425718
$845$	6.92750	−	5.74567i	0.238313	−	0.197657i
$846$	1.52373			0.0523869
$847$	−21.8143	+	12.5945i	−0.749550	+	0.432753i
$848$	−0.535356	−	0.927264i	−0.0183842	−	0.0318424i
$849$	−4.46031	+	7.72548i	−0.153077	+	0.265138i
$850$		−	82.8862i		−	2.84297i
$851$	−2.28453	−	1.31898i	−0.0783128	−	0.0452139i
$852$	2.82823	+	1.63288i	0.0968937	+	0.0559416i
$853$		−	9.35074i		−	0.320163i	−0.987104	−	0.160082i	$-0.948824\pi$
$853$		−	9.35074i		−	0.320163i	0.987104	−	0.160082i	$-0.0511758\pi$
$854$	−1.59149	+	2.75654i	−0.0544596	+	0.0943268i
$855$	−1.04166	−	1.80420i	−0.0356239	−	0.0617025i
$856$	−29.0424	+	16.7676i	−0.992648	+	0.573106i
$857$	9.28116			0.317038			0.158519	−	0.987356i	$-0.449328\pi$
$857$	9.28116			0.317038			0.158519	+	0.987356i	$0.449328\pi$
$858$	−45.0206	−	21.1504i	−1.53698	−	0.722063i
$859$	28.7220			0.979983			0.489991	−	0.871727i	$-0.337000\pi$
$859$	28.7220			0.979983			0.489991	+	0.871727i	$0.337000\pi$
$860$	15.8863	−	9.17196i	0.541718	−	0.312761i
$861$	−4.59124	−	7.95226i	−0.156469	−	0.271012i
$862$	−34.1451	+	59.1411i	−1.16299	+	2.01435i
$863$			34.3446i			1.16910i	0.811357	+	0.584551i	$0.198729\pi$
$863$			34.3446i			1.16910i	−0.811357	+	0.584551i	$0.801271\pi$
$864$	4.79549	+	2.76868i	0.163146	+	0.0941923i
$865$	−7.87294	−	4.54544i	−0.267688	−	0.154550i
$866$			50.2474i			1.70748i
$867$	23.4603	−	40.6345i	0.796754	−	1.38002i
$868$	−2.40320	−	4.16246i	−0.0815699	−	0.141283i
$869$	−31.7068	+	18.3060i	−1.07558	+	0.620987i
$870$	14.7447			0.499892
$871$	26.5147	−	2.24335i	0.898416	−	0.0760131i
$872$	23.0711			0.781287
$873$	0.299798	−	0.173089i	0.0101466	−	0.00585816i
$874$	2.25503	+	3.90582i	0.0762774	+	0.132116i
$875$	−3.29568	+	5.70829i	−0.111414	+	0.192975i
$876$			34.5690i			1.16798i
$877$	−45.0785	−	26.0261i	−1.52219	−	0.878839i	−0.999656	−	0.0262222i	$-0.991652\pi$
$877$	−45.0785	−	26.0261i	−1.52219	−	0.878839i	−0.522537	−	0.852617i	$-0.675014\pi$
$878$	−65.0851	−	37.5769i	−2.19652	−	1.26816i
$879$			5.90904i			0.199307i
$880$	0.215842	−	0.373849i	0.00727603	−	0.0126025i
$881$	11.7089	+	20.2805i	0.394484	+	0.683267i	0.993035	−	0.117818i	$-0.0375899\pi$
$881$	11.7089	+	20.2805i	0.394484	+	0.683267i	−0.598551	+	0.801085i	$0.704257\pi$
$882$	1.98604	−	1.14664i	0.0668734	−	0.0386094i
$883$	−21.6246			−0.727725			−0.363863	−	0.931453i	$-0.618542\pi$
$883$	−21.6246			−0.727725			−0.363863	+	0.931453i	$0.618542\pi$
$884$	−7.92056	−	93.6148i	−0.266397	−	3.14861i
$885$	−1.41307			−0.0474998
$886$	−14.6601	+	8.46404i	−0.492517	+	0.284355i
$887$	1.96781	+	3.40834i	0.0660726	+	0.114441i	0.897169	−	0.441687i	$-0.145620\pi$
$887$	1.96781	+	3.40834i	0.0660726	+	0.114441i	−0.831097	+	0.556128i	$0.812286\pi$
$888$	5.82755	−	10.0936i	0.195560	−	0.338719i
$889$		−	0.733394i		−	0.0245973i
$890$	−9.12601	−	5.26890i	−0.305905	−	0.176614i
$891$	5.20978	+	3.00787i	0.174534	+	0.100767i
$892$		−	36.1093i		−	1.20903i
$893$	0.999698	−	1.73153i	0.0334536	−	0.0579434i
$894$	−15.6619	−	27.1272i	−0.523812	−	0.907269i
$895$	5.96242	−	3.44241i	0.199302	−	0.115067i
$896$	18.5223			0.618788
$897$	1.93410	−	1.34605i	0.0645779	−	0.0449432i
$898$	−77.6312			−2.59059
$899$	11.8610	−	6.84795i	0.395586	−	0.228392i
$900$	7.36675	+	12.7596i	0.245558	+	0.425320i
$901$	−41.2946	+	71.5243i	−1.37572	+	2.38282i
$902$		−	126.679i		−	4.21795i
$903$	7.04068	+	4.06494i	0.234299	+	0.135273i
$904$	−19.2643	−	11.1223i	−0.640722	−	0.369921i
$905$		−	0.314053i		−	0.0104395i
$906$	13.1276	−	22.7376i	0.436134	−	0.755406i
$907$	−11.9467	−	20.6922i	−0.396683	−	0.687074i	0.596632	−	0.802515i	$-0.296505\pi$
$907$	−11.9467	−	20.6922i	−0.396683	−	0.687074i	−0.993314	+	0.115441i	$0.963172\pi$
$908$	−45.8923	+	26.4960i	−1.52299	+	0.879299i
$909$	15.2947			0.507292
$910$	−2.43409	+	5.18119i	−0.0806894	+	0.171755i
$911$	9.66281			0.320143			0.160072	−	0.987105i	$-0.448827\pi$
$911$	9.66281			0.320143			0.160072	+	0.987105i	$0.448827\pi$
$912$	−0.270115	+	0.155951i	−0.00894441	+	0.00516406i
$913$	1.13537	+	1.96652i	0.0375754	+	0.0650825i
$914$	31.8616	−	55.1860i	1.05389	−	1.82539i
$915$			0.960912i			0.0317668i
$916$	29.3550	+	16.9481i	0.969916	+	0.559981i
$917$	8.50960	+	4.91302i	0.281012	+	0.162242i
$918$			18.3348i			0.605140i
$919$	13.2920	−	23.0224i	0.438461	−	0.759438i	−0.559110	−	0.829094i	$-0.688857\pi$
$919$	13.2920	−	23.0224i	0.438461	−	0.759438i	0.997571	+	0.0696562i	$0.0221902\pi$
$920$	0.653250	+	1.13146i	0.0215370	+	0.0373032i
$921$	15.5019	−	8.95002i	0.510804	−	0.294913i
$922$	−68.5164			−2.25647
$923$	−2.06380	−	2.96542i	−0.0679308	−	0.0976081i
$924$	19.6060			0.644991
$925$	−15.8025	+	9.12357i	−0.519583	+	0.299981i
$926$	2.81831	+	4.88145i	0.0926153	+	0.160414i
$927$	5.34936	−	9.26536i	0.175696	−	0.304314i
$928$			51.4250i			1.68811i
$929$	38.0853	+	21.9886i	1.24954	+	0.721422i	0.971018	−	0.239008i	$-0.0768223\pi$
$929$	38.0853	+	21.9886i	1.24954	+	0.721422i	0.278522	+	0.960430i	$0.410156\pi$
$930$	−2.02774	−	1.17072i	−0.0664923	−	0.0383894i
$931$		−	3.00918i		−	0.0986219i
$932$	−25.4146	+	44.0194i	−0.832483	+	1.44190i
$933$	−7.12474	−	12.3404i	−0.233254	−	0.404007i
$934$	10.1766	−	5.87544i	0.332987	−	0.192250i
$935$	−33.2978			−1.08896
$936$	5.94716	+	8.54534i	0.194389	+	0.279313i
$937$	−4.79340			−0.156594			−0.0782968	−	0.996930i	$-0.524948\pi$
$937$	−4.79340			−0.156594			−0.0782968	+	0.996930i	$0.524948\pi$
$938$	−14.6572	+	8.46234i	−0.478575	+	0.276305i
$939$	−4.72345	−	8.18125i	−0.154144	−	0.266985i
$940$	0.749599	−	1.29834i	0.0244492	−	0.0423473i
$941$			2.57174i			0.0838362i	0.999121	+	0.0419181i	$0.0133469\pi$
$941$			2.57174i			0.0838362i	−0.999121	+	0.0419181i	$0.986653\pi$
$942$	16.8782	+	9.74466i	0.549923	+	0.317498i
$943$	5.19717	+	3.00059i	0.169243	+	0.0977126i
$944$			0.211557i			0.00688558i
$945$	0.346160	−	0.599567i	0.0112606	−	0.0195039i
$946$	56.0789	+	97.1315i	1.82328	+	3.15802i
$947$	−34.6150	+	19.9850i	−1.12484	+	0.649424i	−0.942631	−	0.333836i	$-0.891657\pi$
$947$	−34.6150	+	19.9850i	−1.12484	+	0.649424i	−0.182205	+	0.983261i	$0.558323\pi$
$948$	19.8351			0.644215
$949$	16.2614	−	34.6140i	0.527868	−	1.12362i
$950$	31.1968			1.01216
$951$	−13.7550	+	7.94148i	−0.446038	+	0.257520i
$952$	11.5429	+	19.9930i	0.374109	+	0.647976i
$953$	−1.70264	+	2.94906i	−0.0551540	+	0.0955295i	−0.892284	−	0.451474i	$-0.850898\pi$
$953$	−1.70264	+	2.94906i	−0.0551540	+	0.0955295i	0.837130	+	0.547004i	$0.184232\pi$
$954$		−	23.6897i		−	0.766981i
$955$	0.743396	+	0.429200i	0.0240557	+	0.0138886i
$956$	65.3969	+	37.7569i	2.11509	+	1.22115i
$957$			55.8677i			1.80594i
$958$	34.6002	−	59.9292i	1.11788	−	1.93623i
$959$	−2.84938	−	4.93527i	−0.0920112	−	0.159368i
$960$	7.73801	−	4.46754i	0.249743	−	0.144189i
$961$	28.8251			0.929842
$962$	−27.3937	+	19.0647i	−0.883207	+	0.614672i
$963$	−11.6138			−0.374251
$964$	−29.1608	+	16.8360i	−0.939207	+	0.542252i
$965$	0.550789	+	0.953994i	0.0177305	+	0.0307101i
$966$	−0.749382	+	1.29797i	−0.0241110	+	0.0417614i
$967$		−	16.2860i		−	0.523723i	−0.965105	−	0.261861i	$-0.915664\pi$
$967$		−	16.2860i		−	0.523723i	0.965105	−	0.261861i	$-0.0843364\pi$
$968$	62.9895	+	36.3670i	2.02456	+	1.16888i
$969$	20.8353	+	12.0293i	0.669325	+	0.386435i
$970$		−	0.549620i		−	0.0176472i
$971$	−0.0168695	+	0.0292189i	−0.000541369	+	0.000937679i	−0.866296	−	0.499531i	$-0.833506\pi$
$971$	−0.0168695	+	0.0292189i	−0.000541369	+	0.000937679i	0.865755	+	0.500469i	$0.166839\pi$
$972$	−1.62956	−	2.82249i	−0.0522683	−	0.0905313i
$973$	−8.52207	+	4.92022i	−0.273205	+	0.157735i
$974$	17.1726			0.550245
$975$	−1.37417	−	16.2416i	−0.0440085	−	0.520146i
$976$	0.143862			0.00460492
$977$	43.8750	−	25.3312i	1.40369	−	0.810418i	0.408917	−	0.912572i	$-0.365907\pi$
$977$	43.8750	−	25.3312i	1.40369	−	0.810418i	0.994769	+	0.102154i	$0.0325733\pi$
$978$	−17.9757	−	31.1347i	−0.574798	−	0.995579i
$979$	19.9639	−	34.5785i	0.638049	−	1.10513i
$980$		−	2.25636i		−	0.0720767i
$981$	6.91948	+	3.99496i	0.220922	+	0.127549i
$982$	40.6381	+	23.4624i	1.29681	+	0.748716i
$983$			3.36456i			0.107313i	0.998559	+	0.0536564i	$0.0170876\pi$
$983$			3.36456i			0.107313i	−0.998559	+	0.0536564i	$0.982912\pi$
$984$	−13.2573	+	22.9623i	−0.422628	+	0.732013i
$985$	−3.95342	−	6.84752i	−0.125966	−	0.218180i
$986$	−147.462	+	85.1372i	−4.69614	+	2.71132i
$987$	0.664432			0.0211491
$988$	35.2348	−	2.98114i	1.12097	−	0.0948428i
$989$	−5.31325			−0.168952
$990$	8.27147	−	4.77554i	0.262885	−	0.151777i
$991$	9.85700	+	17.0728i	0.313118	+	0.542336i	0.979036	−	0.203689i	$-0.0652931\pi$
$991$	9.85700	+	17.0728i	0.313118	+	0.542336i	−0.665918	+	0.746025i	$0.731960\pi$
$992$	4.08311	−	7.07215i	0.129639	−	0.224541i
$993$			1.92053i			0.0609462i
$994$	1.99008	+	1.14897i	0.0631216	+	0.0364432i
$995$	14.4544	+	8.34524i	0.458235	+	0.264562i
$996$		−	1.23022i		−	0.0389809i
$997$	−15.2716	+	26.4512i	−0.483657	+	0.837718i	−0.999824	−	0.0187699i	$-0.994025\pi$
$997$	−15.2716	+	26.4512i	−0.483657	+	0.837718i	0.516167	+	0.856488i	$0.327358\pi$
$998$	5.68948	+	9.85447i	0.180097	+	0.311938i
$999$	3.49559	−	2.01818i	0.110596	−	0.0638524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bd.b.127.2	yes	16
3.2	odd	2		819.2.ct.c.127.7		16
13.2	odd	12		3549.2.a.bc.1.1		8
13.4	even	6	inner	273.2.bd.b.43.2	✓	16
13.11	odd	12		3549.2.a.ba.1.8		8
39.17	odd	6		819.2.ct.c.316.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.b.43.2	✓	16	13.4	even	6	inner
273.2.bd.b.127.2	yes	16	1.1	even	1	trivial
819.2.ct.c.127.7		16	3.2	odd	2
819.2.ct.c.316.7		16	39.17	odd	6
3549.2.a.ba.1.8		8	13.11	odd	12
3549.2.a.bc.1.1		8	13.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98604 + 1.14664i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.62956 - 2.82249i) q^{4} -0.692320i q^{5} +(-1.98604 - 1.14664i) q^{6} +(-0.866025 - 0.500000i) q^{7} +2.88753i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.98604 + 1.14664i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.62956 - 2.82249i) q^{4} -0.692320i q^{5} +(-1.98604 - 1.14664i) q^{6} +(-0.866025 - 0.500000i) q^{7} +2.88753i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.793841 + 1.37497i) q^{10} +(-5.20978 + 3.00787i) q^{11} +3.25913 q^{12} +(-3.26337 - 1.53311i) q^{13} +2.29328 q^{14} +(0.599567 - 0.346160i) q^{15} +(-0.0518251 - 0.0897638i) q^{16} +(-3.99752 + 6.92391i) q^{17} -2.29328i q^{18} +(-2.60603 - 1.50459i) q^{19} +(-1.95406 - 1.12818i) q^{20} -1.00000i q^{21} +(6.89788 - 11.9475i) q^{22} +(0.326773 + 0.565988i) q^{23} +(-2.50067 + 1.44376i) q^{24} +4.52069 q^{25} +(8.23910 - 0.697093i) q^{26} -1.00000 q^{27} +(-2.82249 + 1.62956i) q^{28} +(-4.64346 - 8.04271i) q^{29} +(-0.793841 + 1.37497i) q^{30} +1.47475i q^{31} +(-4.79549 - 2.76868i) q^{32} +(-5.20978 - 3.00787i) q^{33} -18.3348i q^{34} +(-0.346160 + 0.599567i) q^{35} +(1.62956 + 2.82249i) q^{36} +(-3.49559 + 2.01818i) q^{37} +6.90088 q^{38} +(-0.303972 - 3.59271i) q^{39} +1.99909 q^{40} +(7.95226 - 4.59124i) q^{41} +(1.14664 + 1.98604i) q^{42} +(-4.06494 + 7.04068i) q^{43} +19.6060i q^{44} +(0.599567 + 0.346160i) q^{45} +(-1.29797 - 0.749382i) q^{46} +0.664432i q^{47} +(0.0518251 - 0.0897638i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-8.97827 + 5.18360i) q^{50} -7.99504 q^{51} +(-9.64505 + 6.71251i) q^{52} +10.3300 q^{53} +(1.98604 - 1.14664i) q^{54} +(2.08241 + 3.60683i) q^{55} +(1.44376 - 2.50067i) q^{56} -3.00918i q^{57} +(18.4442 + 10.6488i) q^{58} +(-1.76761 - 1.02053i) q^{59} -2.25636i q^{60} +(-0.693979 + 1.20201i) q^{61} +(-1.69101 - 2.92891i) q^{62} +(0.866025 - 0.500000i) q^{63} +12.9060 q^{64} +(-1.06140 + 2.25930i) q^{65} +13.7958 q^{66} +(-6.39137 + 3.69006i) q^{67} +(13.0284 + 22.5659i) q^{68} +(-0.326773 + 0.565988i) q^{69} -1.58768i q^{70} +(0.867789 + 0.501018i) q^{71} +(-2.50067 - 1.44376i) q^{72} +10.6068i q^{73} +(4.62825 - 8.01636i) q^{74} +(2.26035 + 3.91503i) q^{75} +(-8.49336 + 4.90365i) q^{76} +6.01573 q^{77} +(4.72325 + 6.78672i) q^{78} +6.08603 q^{79} +(-0.0621453 + 0.0358796i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.5290 + 18.2367i) q^{82} -0.377468i q^{83} +(-2.82249 - 1.62956i) q^{84} +(4.79356 + 2.76756i) q^{85} -18.6441i q^{86} +(4.64346 - 8.04271i) q^{87} +(-8.68529 - 15.0434i) q^{88} +(-5.74801 + 3.31861i) q^{89} -1.58768 q^{90} +(2.05961 + 2.95940i) q^{91} +2.12999 q^{92} +(-1.27717 + 0.737375i) q^{93} +(-0.761864 - 1.31959i) q^{94} +(-1.04166 + 1.80420i) q^{95} -5.53735i q^{96} +(-0.299798 - 0.173089i) q^{97} +(-1.98604 - 1.14664i) q^{98} -6.01573i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

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