LMFDB - Embedded newform 273.2.l.b.16.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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, 2, 2]))

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.5
Root			$-0.0340180 - 0.0589209i$ of defining polynomial
Character	$\chi$	$=$	273.16
Dual form			273.2.l.b.256.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0680360 q^{2} +(0.500000 - 0.866025i) q^{3} -1.99537 q^{4} +(1.52954 - 2.64923i) q^{5} +(0.0340180 - 0.0589209i) q^{6} +(0.910236 + 2.48424i) q^{7} -0.271829 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+0.0680360 q^{2} +(0.500000 - 0.866025i) q^{3} -1.99537 q^{4} +(1.52954 - 2.64923i) q^{5} +(0.0340180 - 0.0589209i) q^{6} +(0.910236 + 2.48424i) q^{7} -0.271829 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.104063 - 0.180243i) q^{10} +(2.17896 - 3.77408i) q^{11} +(-0.997686 + 1.72804i) q^{12} +(-1.79952 - 3.12437i) q^{13} +(0.0619288 + 0.169018i) q^{14} +(-1.52954 - 2.64923i) q^{15} +3.97225 q^{16} -3.52867 q^{17} +(-0.0340180 - 0.0589209i) q^{18} +(-3.45112 - 5.97751i) q^{19} +(-3.05199 + 5.28621i) q^{20} +(2.60654 + 0.453835i) q^{21} +(0.148248 - 0.256773i) q^{22} +3.33524 q^{23} +(-0.135914 + 0.235411i) q^{24} +(-2.17896 - 3.77408i) q^{25} +(-0.122432 - 0.212570i) q^{26} -1.00000 q^{27} +(-1.81626 - 4.95699i) q^{28} +(4.95991 + 8.59082i) q^{29} +(-0.104063 - 0.180243i) q^{30} +(4.62451 + 8.00989i) q^{31} +0.813913 q^{32} +(-2.17896 - 3.77408i) q^{33} -0.240077 q^{34} +(7.97359 + 1.38831i) q^{35} +(0.997686 + 1.72804i) q^{36} -0.109046 q^{37} +(-0.234800 - 0.406686i) q^{38} +(-3.60555 - 0.00375337i) q^{39} +(-0.415772 + 0.720139i) q^{40} +(1.76899 + 3.06399i) q^{41} +(0.177338 + 0.0308771i) q^{42} +(-0.844102 + 1.46203i) q^{43} +(-4.34784 + 7.53068i) q^{44} -3.05907 q^{45} +0.226916 q^{46} +(1.28133 - 2.21933i) q^{47} +(1.98612 - 3.44007i) q^{48} +(-5.34294 + 4.52250i) q^{49} +(-0.148248 - 0.256773i) q^{50} +(-1.76434 + 3.05592i) q^{51} +(3.59072 + 6.23429i) q^{52} +(2.65681 + 4.60173i) q^{53} -0.0680360 q^{54} +(-6.66561 - 11.5452i) q^{55} +(-0.247428 - 0.675289i) q^{56} -6.90224 q^{57} +(0.337453 + 0.584485i) q^{58} +7.55704 q^{59} +(3.05199 + 5.28621i) q^{60} +(-2.43658 - 4.22029i) q^{61} +(0.314633 + 0.544960i) q^{62} +(1.69630 - 2.03041i) q^{63} -7.88912 q^{64} +(-11.0296 - 0.0114818i) q^{65} +(-0.148248 - 0.256773i) q^{66} +(-0.340218 + 0.589274i) q^{67} +7.04101 q^{68} +(1.66762 - 2.88840i) q^{69} +(0.542491 + 0.0944552i) q^{70} +(-2.61572 + 4.53055i) q^{71} +(0.135914 + 0.235411i) q^{72} +(1.75956 + 3.04764i) q^{73} -0.00741905 q^{74} -4.35793 q^{75} +(6.88626 + 11.9274i) q^{76} +(11.3591 + 1.97778i) q^{77} +(-0.245307 - 0.000255364i) q^{78} +(4.85408 - 8.40751i) q^{79} +(6.07570 - 10.5234i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.120355 + 0.208461i) q^{82} +5.41662 q^{83} +(-5.20101 - 0.905568i) q^{84} +(-5.39723 + 9.34828i) q^{85} +(-0.0574293 + 0.0994705i) q^{86} +9.91983 q^{87} +(-0.592305 + 1.02590i) q^{88} -7.70414 q^{89} -0.208127 q^{90} +(6.12372 - 7.31438i) q^{91} -6.65503 q^{92} +9.24902 q^{93} +(0.0871768 - 0.150995i) q^{94} -21.1144 q^{95} +(0.406957 - 0.704870i) q^{96} +(-3.86359 + 6.69194i) q^{97} +(-0.363512 + 0.307692i) q^{98} -4.35793 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25} + 33 q^{26} - 16 q^{27} - q^{28} + 15 q^{29} + 4 q^{30} + 3 q^{31} - 6 q^{32} + 2 q^{33} - 68 q^{34} - 6 q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - 25 q^{40} + 19 q^{41} - 17 q^{42} + 11 q^{43} - 16 q^{44} - 4 q^{46} + 5 q^{47} + 6 q^{48} + 7 q^{49} - 7 q^{50} + 2 q^{51} - 18 q^{52} + 36 q^{53} - 15 q^{55} - 51 q^{56} - 22 q^{57} + 20 q^{58} + 34 q^{59} + 20 q^{60} - 22 q^{61} - 6 q^{62} - 2 q^{63} - 20 q^{64} - 24 q^{65} - 7 q^{66} + 26 q^{67} - 10 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} - 6 q^{72} - 6 q^{73} - 30 q^{74} + 4 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} - 28 q^{80} - 8 q^{81} - q^{82} + 36 q^{83} - 8 q^{84} - 4 q^{85} + 16 q^{86} + 30 q^{87} + 24 q^{88} - 40 q^{89} + 8 q^{90} - 10 q^{91} - 94 q^{92} + 6 q^{93} - 20 q^{94} - 3 q^{96} + 7 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.0680360			0.0481087			0.0240543	−	0.999711i	$-0.492343\pi$
$2$	0.0680360			0.0481087			0.0240543	+	0.999711i	$0.492343\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.99537			−0.997686
$5$	1.52954	−	2.64923i	0.684030	−	1.18477i	−0.289711	−	0.957114i	$-0.593559\pi$
$5$	1.52954	−	2.64923i	0.684030	−	1.18477i	0.973741	−	0.227660i	$-0.0731074\pi$
$6$	0.0340180	−	0.0589209i	0.0138878	−	0.0240543i
$7$	0.910236	+	2.48424i	0.344037	+	0.938956i
$7$	0.910236	+	2.48424i	0.344037	+	0.938956i
$8$	−0.271829			−0.0961060
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.104063	−	0.180243i	0.0329078	−	0.0569979i
$11$	2.17896	−	3.77408i	0.656982	−	1.13793i	−0.324411	−	0.945916i	$-0.605166\pi$
$11$	2.17896	−	3.77408i	0.656982	−	1.13793i	0.981393	−	0.192010i	$-0.0615007\pi$
$12$	−0.997686	+	1.72804i	−0.288007	+	0.498843i
$13$	−1.79952	−	3.12437i	−0.499098	−	0.866545i
$13$	−1.79952	−	3.12437i	−0.499098	−	0.866545i
$14$	0.0619288	+	0.169018i	0.0165512	+	0.0451719i
$15$	−1.52954	−	2.64923i	−0.394925	−	0.684030i
$16$	3.97225			0.993062
$17$	−3.52867			−0.855829			−0.427914	−	0.903819i	$-0.640752\pi$
$17$	−3.52867			−0.855829			−0.427914	+	0.903819i	$0.640752\pi$
$18$	−0.0340180	−	0.0589209i	−0.00801811	−	0.0138878i
$19$	−3.45112	−	5.97751i	−0.791741	−	1.37134i	−0.924888	−	0.380239i	$-0.875842\pi$
$19$	−3.45112	−	5.97751i	−0.791741	−	1.37134i	0.133147	−	0.991096i	$-0.457492\pi$
$20$	−3.05199	+	5.28621i	−0.682446	+	1.18203i
$21$	2.60654	+	0.453835i	0.568793	+	0.0990348i
$22$	0.148248	−	0.256773i	0.0316066	−	0.0547442i
$23$	3.33524			0.695445			0.347722	−	0.937598i	$-0.386955\pi$
$23$	3.33524			0.695445			0.347722	+	0.937598i	$0.386955\pi$
$24$	−0.135914	+	0.235411i	−0.0277434	+	0.0480530i
$25$	−2.17896	−	3.77408i	−0.435793	−	0.754815i
$26$	−0.122432	−	0.212570i	−0.0240110	−	0.0416884i
$27$	−1.00000			−0.192450
$28$	−1.81626	−	4.95699i	−0.343241	−	0.936783i
$29$	4.95991	+	8.59082i	0.921033	+	1.59528i	0.797820	+	0.602896i	$0.205987\pi$
$29$	4.95991	+	8.59082i	0.921033	+	1.59528i	0.123213	+	0.992380i	$0.460680\pi$
$30$	−0.104063	−	0.180243i	−0.0189993	−	0.0329078i
$31$	4.62451	+	8.00989i	0.830587	+	1.43862i	0.897574	+	0.440865i	$0.145328\pi$
$31$	4.62451	+	8.00989i	0.830587	+	1.43862i	−0.0669867	+	0.997754i	$0.521339\pi$
$32$	0.813913			0.143881
$33$	−2.17896	−	3.77408i	−0.379309	−	0.656982i
$34$	−0.240077			−0.0411728
$35$	7.97359	+	1.38831i	1.34778	+	0.234668i
$36$	0.997686	+	1.72804i	0.166281	+	0.288007i
$37$	−0.109046			−0.0179270			−0.00896352	−	0.999960i	$-0.502853\pi$
$37$	−0.109046			−0.0179270			−0.00896352	+	0.999960i	$0.502853\pi$
$38$	−0.234800	−	0.406686i	−0.0380896	−	0.0659731i
$39$	−3.60555	−	0.00375337i	−0.577350	−	0.000601021i
$40$	−0.415772	+	0.720139i	−0.0657394	+	0.113864i
$41$	1.76899	+	3.06399i	0.276270	+	0.478514i	0.970455	−	0.241283i	$-0.0775682\pi$
$41$	1.76899	+	3.06399i	0.276270	+	0.478514i	−0.694185	+	0.719797i	$0.744235\pi$
$42$	0.177338	+	0.0308771i	0.0273639	+	0.00476444i
$43$	−0.844102	+	1.46203i	−0.128724	+	0.222957i	−0.923183	−	0.384362i	$-0.874422\pi$
$43$	−0.844102	+	1.46203i	−0.128724	+	0.222957i	0.794458	+	0.607319i	$0.207755\pi$
$44$	−4.34784	+	7.53068i	−0.655462	+	1.13529i
$45$	−3.05907			−0.456020
$46$	0.226916			0.0334569
$47$	1.28133	−	2.21933i	0.186902	−	0.323723i	−0.757314	−	0.653051i	$-0.773489\pi$
$47$	1.28133	−	2.21933i	0.186902	−	0.323723i	0.944216	+	0.329328i	$0.106822\pi$
$48$	1.98612	−	3.44007i	0.286672	−	0.496531i
$49$	−5.34294	+	4.52250i	−0.763277	+	0.646071i
$50$	−0.148248	−	0.256773i	−0.0209654	−	0.0363132i
$51$	−1.76434	+	3.05592i	−0.247057	+	0.427914i
$52$	3.59072	+	6.23429i	0.497943	+	0.864540i
$53$	2.65681	+	4.60173i	0.364941	+	0.632097i	0.988767	−	0.149467i	$-0.0477557\pi$
$53$	2.65681	+	4.60173i	0.364941	+	0.632097i	−0.623825	+	0.781564i	$0.714422\pi$
$54$	−0.0680360			−0.00925852
$55$	−6.66561	−	11.5452i	−0.898791	−	1.55675i
$56$	−0.247428	−	0.675289i	−0.0330640	−	0.0902393i
$57$	−6.90224			−0.914224
$58$	0.337453	+	0.584485i	0.0443097	+	0.0767466i
$59$	7.55704			0.983843			0.491921	−	0.870640i	$-0.336295\pi$
$59$	7.55704			0.983843			0.491921	+	0.870640i	$0.336295\pi$
$60$	3.05199	+	5.28621i	0.394011	+	0.682446i
$61$	−2.43658	−	4.22029i	−0.311973	−	0.540352i	0.666817	−	0.745222i	$-0.267656\pi$
$61$	−2.43658	−	4.22029i	−0.311973	−	0.540352i	−0.978789	+	0.204869i	$0.934323\pi$
$62$	0.314633	+	0.544960i	0.0399584	+	0.0692101i
$63$	1.69630	−	2.03041i	0.213714	−	0.255808i
$64$	−7.88912			−0.986140
$65$	−11.0296	−	0.0114818i	−1.36806	−	0.00142415i
$66$	−0.148248	−	0.256773i	−0.0182481	−	0.0316066i
$67$	−0.340218	+	0.589274i	−0.0415642	+	0.0719913i	−0.886059	−	0.463572i	$-0.846567\pi$
$67$	−0.340218	+	0.589274i	−0.0415642	+	0.0719913i	0.844495	+	0.535564i	$0.179901\pi$
$68$	7.04101			0.853848
$69$	1.66762	−	2.88840i	0.200758	−	0.347722i
$70$	0.542491	+	0.0944552i	0.0648400	+	0.0112896i
$71$	−2.61572	+	4.53055i	−0.310428	+	0.537678i	−0.978455	−	0.206460i	$-0.933806\pi$
$71$	−2.61572	+	4.53055i	−0.310428	+	0.537678i	0.668027	+	0.744137i	$0.267139\pi$
$72$	0.135914	+	0.235411i	0.0160177	+	0.0277434i
$73$	1.75956	+	3.04764i	0.205941	+	0.356699i	0.950432	−	0.310933i	$-0.100641\pi$
$73$	1.75956	+	3.04764i	0.205941	+	0.356699i	−0.744491	+	0.667632i	$0.767308\pi$
$74$	−0.00741905			−0.000862447
$75$	−4.35793			−0.503210
$76$	6.88626	+	11.9274i	0.789908	+	1.36816i
$77$	11.3591	+	1.97778i	1.29449	+	0.225389i
$78$	−0.245307		0.000255364i	−0.0277755		2.89143e-5i
$79$	4.85408	−	8.40751i	0.546126	−	0.945919i	−0.452409	−	0.891811i	$-0.649435\pi$
$79$	4.85408	−	8.40751i	0.546126	−	0.945919i	0.998535	−	0.0541080i	$-0.0172315\pi$
$80$	6.07570	−	10.5234i	0.679284	−	1.17655i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.120355	+	0.208461i	0.0132910	+	0.0230207i
$83$	5.41662			0.594551			0.297275	−	0.954792i	$-0.403922\pi$
$83$	5.41662			0.594551			0.297275	+	0.954792i	$0.403922\pi$
$84$	−5.20101	−	0.905568i	−0.567477	−	0.0988056i
$85$	−5.39723	+	9.34828i	−0.585412	+	1.01396i
$86$	−0.0574293	+	0.0994705i	−0.00619276	+	0.0107262i
$87$	9.91983			1.06352
$88$	−0.592305	+	1.02590i	−0.0631400	+	0.109362i
$89$	−7.70414			−0.816638			−0.408319	−	0.912839i	$-0.633885\pi$
$89$	−7.70414			−0.816638			−0.408319	+	0.912839i	$0.633885\pi$
$90$	−0.208127			−0.0219385
$91$	6.12372	−	7.31438i	0.641940	−	0.766755i
$92$	−6.65503			−0.693835
$93$	9.24902			0.959079
$94$	0.0871768	−	0.150995i	0.00899160	−	0.0155739i
$95$	−21.1144			−2.16630
$96$	0.406957	−	0.704870i	0.0415348	−	0.0719405i
$97$	−3.86359	+	6.69194i	−0.392288	+	0.679463i	−0.992751	−	0.120189i	$-0.961650\pi$
$97$	−3.86359	+	6.69194i	−0.392288	+	0.679463i	0.600463	+	0.799653i	$0.294983\pi$
$98$	−0.363512	+	0.307692i	−0.0367203	+	0.0310816i
$99$	−4.35793			−0.437988
$100$	4.34784	+	7.53068i	0.434784	+	0.753068i
$101$	1.94016	−	3.36045i	0.193053	−	0.334377i	−0.753208	−	0.657783i	$-0.771495\pi$
$101$	1.94016	−	3.36045i	0.193053	−	0.334377i	0.946260	+	0.323406i	$0.104828\pi$
$102$	−0.120038	+	0.207912i	−0.0118856	+	0.0205864i
$103$	−4.29088	+	7.43202i	−0.422793	+	0.732299i	−0.996211	−	0.0869638i	$-0.972284\pi$
$103$	−4.29088	+	7.43202i	−0.422793	+	0.732299i	0.573419	+	0.819263i	$0.305617\pi$
$104$	0.489163	+	0.849295i	0.0479663	+	0.0832802i
$105$	5.18911	−	6.21117i	0.506405	−	0.606148i
$106$	0.180759	+	0.313083i	0.0175568	+	0.0304093i
$107$	−11.2032			−1.08305			−0.541525	−	0.840684i	$-0.682153\pi$
$107$	−11.2032			−1.08305			−0.541525	+	0.840684i	$0.682153\pi$
$108$	1.99537			0.192005
$109$	6.98282	+	12.0946i	0.668833	+	1.15845i	0.978231	+	0.207520i	$0.0665391\pi$
$109$	6.98282	+	12.0946i	0.668833	+	1.15845i	−0.309398	+	0.950933i	$0.600128\pi$
$110$	−0.453501	−	0.785487i	−0.0432396	−	0.0748932i
$111$	−0.0545230	+	0.0944366i	−0.00517509	+	0.00896352i
$112$	3.61568	+	9.86804i	0.341650	+	0.932442i
$113$	−3.38888	+	5.86972i	−0.318799	+	0.552176i	−0.980238	−	0.197823i	$-0.936613\pi$
$113$	−3.38888	+	5.86972i	−0.318799	+	0.552176i	0.661439	+	0.749999i	$0.269946\pi$
$114$	−0.469600			−0.0439821
$115$	5.10137	−	8.83582i	0.475705	−	0.823945i
$116$	−9.89687	−	17.1419i	−0.918901	−	1.59158i
$117$	−1.80603	+	3.12062i	−0.166967	+	0.288501i
$118$	0.514150			0.0473314
$119$	−3.21193	−	8.76609i	−0.294437	−	0.803586i
$120$	0.415772	+	0.720139i	0.0379546	+	0.0657394i
$121$	−3.99577	−	6.92087i	−0.363252	−	0.629170i
$122$	−0.165775	−	0.287131i	−0.0150086	−	0.0259956i
$123$	3.53799			0.319009
$124$	−9.22762	−	15.9827i	−0.828664	−	1.43529i
$125$	1.96415			0.175679
$126$	0.115409	−	0.138141i	0.0102815	−	0.0123066i
$127$	−6.68899	−	11.5857i	−0.593552	−	1.02806i	−0.993750	−	0.111633i	$-0.964392\pi$
$127$	−6.68899	−	11.5857i	−0.593552	−	1.02806i	0.400198	−	0.916429i	$-0.368941\pi$
$128$	−2.16457			−0.191323
$129$	0.844102	+	1.46203i	0.0743191	+	0.128724i
$130$	−0.750412		0.000781178i	−0.0658155		6.85139e-5i
$131$	9.06148	−	15.6949i	0.791705	−	1.37127i	−0.133205	−	0.991089i	$-0.542527\pi$
$131$	9.06148	−	15.6949i	0.791705	−	1.37127i	0.924910	−	0.380185i	$-0.124140\pi$
$132$	4.34784	+	7.53068i	0.378431	+	0.655462i
$133$	11.7083	−	14.0144i	1.01524	−	1.21520i
$134$	−0.0231470	+	0.0400918i	−0.00199960	+	0.00346341i
$135$	−1.52954	+	2.64923i	−0.131642	+	0.228010i
$136$	0.959195			0.0822503
$137$	21.3405			1.82324			0.911622	−	0.411030i	$-0.134831\pi$
$137$	21.3405			1.82324			0.911622	+	0.411030i	$0.134831\pi$
$138$	0.113458	−	0.196515i	0.00965818	−	0.0167285i
$139$	−0.0705287	+	0.122159i	−0.00598217	+	0.0103614i	−0.869001	−	0.494810i	$-0.835238\pi$
$139$	−0.0705287	+	0.122159i	−0.00598217	+	0.0103614i	0.863019	+	0.505172i	$0.168571\pi$
$140$	−15.9103	−	2.77020i	−1.34466	−	0.234125i
$141$	−1.28133	−	2.21933i	−0.107908	−	0.186902i
$142$	−0.177963	+	0.308240i	−0.0149343	+	0.0258670i
$143$	−15.7127	−	0.0163569i	−1.31396	−	0.00136784i
$144$	−1.98612	−	3.44007i	−0.165510	−	0.286672i
$145$	30.3455			2.52006
$146$	0.119713	+	0.207349i	0.00990753	+	0.0171603i
$147$	1.24513	+	6.88837i	0.102696	+	0.568143i
$148$	0.217587			0.0178856
$149$	7.17797	+	12.4326i	0.588043	+	1.01852i	0.994489	+	0.104845i	$0.0334346\pi$
$149$	7.17797	+	12.4326i	0.588043	+	1.01852i	−0.406446	+	0.913675i	$0.633232\pi$
$150$	−0.296496			−0.0242088
$151$	−7.83172	−	13.5649i	−0.637336	−	1.10390i	−0.986015	−	0.166657i	$-0.946703\pi$
$151$	−7.83172	−	13.5649i	−0.637336	−	1.10390i	0.348679	−	0.937242i	$-0.386631\pi$
$152$	0.938114	+	1.62486i	0.0760911	+	0.131794i
$153$	1.76434	+	3.05592i	0.142638	+	0.247057i
$154$	0.772827	+	0.134560i	0.0622762	+	0.0108432i
$155$	28.2934			2.27258
$156$	7.19441	+	0.00748937i	0.576014	+	0.000599630i
$157$	−6.75022	−	11.6917i	−0.538726	−	0.933101i	−0.998973	−	0.0453098i	$-0.985572\pi$
$157$	−6.75022	−	11.6917i	−0.538726	−	0.933101i	0.460247	−	0.887791i	$-0.347761\pi$
$158$	0.330252	−	0.572013i	0.0262734	−	0.0455069i
$159$	5.31362			0.421398
$160$	1.24491	−	2.15625i	0.0984188	−	0.170466i
$161$	3.03585	+	8.28554i	0.239259	+	0.652992i
$162$	−0.0340180	+	0.0589209i	−0.00267270	+	0.00462926i
$163$	1.32862	+	2.30124i	0.104066	+	0.180247i	0.913356	−	0.407162i	$-0.133481\pi$
$163$	1.32862	+	2.30124i	0.104066	+	0.180247i	−0.809291	+	0.587409i	$0.800148\pi$
$164$	−3.52980	−	6.11379i	−0.275631	−	0.477407i
$165$	−13.3312			−1.03783
$166$	0.368525			0.0286031
$167$	−10.9142	−	18.9040i	−0.844567	−	1.46283i	−0.885997	−	0.463692i	$-0.846525\pi$
$167$	−10.9142	−	18.9040i	−0.844567	−	1.46283i	0.0414294	−	0.999141i	$-0.486809\pi$
$168$	−0.708532	−	0.123365i	−0.0546644	−	0.00951784i
$169$	−6.52343	+	11.2448i	−0.501802	+	0.864983i
$170$	−0.367206	+	0.636019i	−0.0281634	+	0.0487805i
$171$	−3.45112	+	5.97751i	−0.263914	+	0.457112i
$172$	1.68430	−	2.91729i	0.128426	−	0.222441i
$173$	−8.84120	−	15.3134i	−0.672184	−	1.16426i	−0.977283	−	0.211936i	$-0.932023\pi$
$173$	−8.84120	−	15.3134i	−0.672184	−	1.16426i	0.305099	−	0.952321i	$-0.401310\pi$
$174$	0.674905			0.0511644
$175$	7.39236	−	8.84838i	0.558810	−	0.668875i
$176$	8.65539	−	14.9916i	0.652424	−	1.13003i
$177$	3.77852	−	6.54459i	0.284011	−	0.491921i
$178$	−0.524159			−0.0392874
$179$	−4.86499	+	8.42641i	−0.363626	+	0.629819i	−0.988555	−	0.150863i	$-0.951795\pi$
$179$	−4.86499	+	8.42641i	−0.363626	+	0.629819i	0.624928	+	0.780682i	$0.285128\pi$
$180$	6.10399			0.454964
$181$	4.01332			0.298308			0.149154	−	0.988814i	$-0.452345\pi$
$181$	4.01332			0.298308			0.149154	+	0.988814i	$0.452345\pi$
$182$	0.416633	−	0.497641i	0.0308829	−	0.0368876i
$183$	−4.87317			−0.360235
$184$	−0.906613			−0.0668364
$185$	−0.166790	+	0.288888i	−0.0122626	+	0.0212395i
$186$	0.629266			0.0461400
$187$	−7.68885	+	13.3175i	−0.562265	+	0.973871i
$188$	−2.55674	+	4.42840i	−0.186469	+	0.322974i
$189$	−0.910236	−	2.48424i	−0.0662099	−	0.180702i
$190$	−1.43654			−0.104218
$191$	7.39519	+	12.8088i	0.535097	+	0.926816i	0.999159	+	0.0410127i	$0.0130584\pi$
$191$	7.39519	+	12.8088i	0.535097	+	0.926816i	−0.464061	+	0.885803i	$0.653608\pi$
$192$	−3.94456	+	6.83218i	−0.284674	+	0.493070i
$193$	−11.1716	+	19.3497i	−0.804146	+	1.39282i	0.112720	+	0.993627i	$0.464044\pi$
$193$	−11.1716	+	19.3497i	−0.804146	+	1.39282i	−0.916866	+	0.399195i	$0.869290\pi$
$194$	−0.262863	+	0.455292i	−0.0188725	+	0.0326881i
$195$	−5.52476	+	9.54621i	−0.395636	+	0.683618i
$196$	10.6611	−	9.02406i	0.761511	−	0.644576i
$197$	−3.16282	−	5.47816i	−0.225342	−	0.390303i	0.731080	−	0.682291i	$-0.239016\pi$
$197$	−3.16282	−	5.47816i	−0.225342	−	0.390303i	−0.956422	+	0.291988i	$0.905683\pi$
$198$	−0.296496			−0.0210710
$199$	−6.03617			−0.427893			−0.213946	−	0.976845i	$-0.568632\pi$
$199$	−6.03617			−0.427893			−0.213946	+	0.976845i	$0.568632\pi$
$200$	0.592305	+	1.02590i	0.0418823	+	0.0725423i
$201$	0.340218	+	0.589274i	0.0239971	+	0.0415642i
$202$	0.132000	−	0.228631i	0.00928751	−	0.0160864i
$203$	−16.8270	+	20.1413i	−1.18102	+	1.41364i
$204$	3.52051	−	6.09770i	0.246485	−	0.426924i
$205$	10.8230			0.755908
$206$	−0.291934	+	0.505645i	−0.0203400	+	0.0352299i
$207$	−1.66762	−	2.88840i	−0.115907	−	0.200758i
$208$	−7.14816	−	12.4108i	−0.495635	−	0.860533i
$209$	−30.0795			−2.08064
$210$	0.353046	−	0.422583i	0.0243625	−	0.0291610i
$211$	0.646092	+	1.11906i	0.0444788	+	0.0770395i	0.887408	−	0.460985i	$-0.152504\pi$
$211$	0.646092	+	1.11906i	0.0444788	+	0.0770395i	−0.842929	+	0.538025i	$0.819171\pi$
$212$	−5.30133	−	9.18217i	−0.364097	−	0.630634i
$213$	2.61572	+	4.53055i	0.179226	+	0.310428i
$214$	−0.762218			−0.0521041
$215$	2.58217	+	4.47245i	0.176103	+	0.305019i
$216$	0.271829			0.0184956
$217$	−15.6891	+	18.7793i	−1.06505	+	1.27482i
$218$	0.475083	+	0.822868i	0.0321767	+	0.0557316i
$219$	3.51911			0.237800
$220$	13.3004	+	23.0369i	0.896710	+	1.55315i
$221$	6.34993	+	11.0249i	0.427143	+	0.741615i
$222$	−0.00370952	+	0.00642508i	−0.000248967	+	0.000431223i
$223$	5.79892	+	10.0440i	0.388324	+	0.672597i	0.992224	−	0.124463i	$-0.0397207\pi$
$223$	5.79892	+	10.0440i	0.388324	+	0.672597i	−0.603900	+	0.797060i	$0.706387\pi$
$224$	0.740853	+	2.02196i	0.0495004	+	0.135098i
$225$	−2.17896	+	3.77408i	−0.145264	+	0.251605i
$226$	−0.230566	+	0.399352i	−0.0153370	+	0.0265645i
$227$	−0.798498			−0.0529982			−0.0264991	−	0.999649i	$-0.508436\pi$
$227$	−0.798498			−0.0529982			−0.0264991	+	0.999649i	$0.508436\pi$
$228$	13.7725			0.912108
$229$	−11.6073	+	20.1044i	−0.767030	+	1.32854i	0.172136	+	0.985073i	$0.444933\pi$
$229$	−11.6073	+	20.1044i	−0.767030	+	1.32854i	−0.939166	+	0.343463i	$0.888400\pi$
$230$	0.347076	−	0.601154i	0.0228855	−	0.0396389i
$231$	7.39236	−	8.84838i	0.486381	−	0.582181i
$232$	−1.34825	−	2.33523i	−0.0885168	−	0.153316i
$233$	6.09388	−	10.5549i	0.399223	−	0.691475i	−0.594407	−	0.804164i	$-0.702613\pi$
$233$	6.09388	−	10.5549i	0.399223	−	0.691475i	0.993630	+	0.112689i	$0.0359465\pi$
$234$	−0.122875	+	0.212314i	−0.00803257	+	0.0138794i
$235$	−3.91969	−	6.78911i	−0.255693	−	0.442873i
$236$	−15.0791			−0.981565
$237$	−4.85408	−	8.40751i	−0.315306	−	0.546126i
$238$	−0.218526	−	0.596409i	−0.0141650	−	0.0386595i
$239$	−0.484332			−0.0313289			−0.0156644	−	0.999877i	$-0.504986\pi$
$239$	−0.484332			−0.0313289			−0.0156644	+	0.999877i	$0.504986\pi$
$240$	−6.07570	−	10.5234i	−0.392185	−	0.679284i
$241$	−2.32012			−0.149452			−0.0747261	−	0.997204i	$-0.523808\pi$
$241$	−2.32012			−0.149452			−0.0747261	+	0.997204i	$0.523808\pi$
$242$	−0.271856	−	0.470868i	−0.0174756	−	0.0302686i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	4.86189	+	8.42104i	0.311251	+	0.539102i
$245$	3.80894	+	21.0720i	0.243344	+	1.34624i
$246$	0.240710			0.0153471
$247$	−12.4656	+	21.5393i	−0.793168	+	1.37051i
$248$	−1.25708	−	2.17732i	−0.0798244	−	0.138260i
$249$	2.70831	−	4.69093i	0.171632	−	0.297275i
$250$	0.133633			0.00845166
$251$	13.7950	−	23.8936i	0.870732	−	1.50815i	0.00949135	−	0.999955i	$-0.496979\pi$
$251$	13.7950	−	23.8936i	0.870732	−	1.50815i	0.861241	−	0.508197i	$-0.169688\pi$
$252$	−3.38475	+	4.05142i	−0.213219	+	0.255216i
$253$	7.26736	−	12.5874i	0.456895	−	0.791365i
$254$	−0.455092	−	0.788242i	−0.0285550	−	0.0494587i
$255$	5.39723	+	9.34828i	0.337988	+	0.585412i
$256$	15.6310			0.976936
$257$	9.13005			0.569517			0.284758	−	0.958599i	$-0.408087\pi$
$257$	9.13005			0.569517			0.284758	+	0.958599i	$0.408087\pi$
$258$	0.0574293	+	0.0994705i	0.00357539	+	0.00619276i
$259$	−0.0992576	−	0.270897i	−0.00616757	−	0.0168327i
$260$	22.0082	+	0.0229105i	1.36489	+	0.00142085i
$261$	4.95991	−	8.59082i	0.307011	−	0.531759i
$262$	0.616507	−	1.06782i	0.0380879	−	0.0659702i
$263$	2.79485	−	4.84082i	0.172338	−	0.298498i	−0.766899	−	0.641768i	$-0.778201\pi$
$263$	2.79485	−	4.84082i	0.172338	−	0.298498i	0.939237	+	0.343270i	$0.111535\pi$
$264$	0.592305	+	1.02590i	0.0364539	+	0.0631400i
$265$	16.2548			0.998522
$266$	0.796583	−	0.953481i	0.0488417	−	0.0584617i
$267$	−3.85207	+	6.67198i	−0.235743	+	0.408319i
$268$	0.678860	−	1.17582i	0.0414680	−	0.0718247i
$269$	21.2921			1.29820			0.649102	−	0.760701i	$-0.275145\pi$
$269$	21.2921			1.29820			0.649102	+	0.760701i	$0.275145\pi$
$270$	−0.104063	+	0.180243i	−0.00633310	+	0.0109693i
$271$	11.3270			0.688064			0.344032	−	0.938958i	$-0.388207\pi$
$271$	11.3270			0.688064			0.344032	+	0.938958i	$0.388207\pi$
$272$	−14.0168			−0.849891
$273$	−3.27258	−	8.96048i	−0.198065	−	0.542313i
$274$	1.45192			0.0877139
$275$	−18.9915			−1.14523
$276$	−3.32752	+	5.76343i	−0.200293	+	0.346918i
$277$	−11.3623			−0.682696			−0.341348	−	0.939937i	$-0.610883\pi$
$277$	−11.3623			−0.682696			−0.341348	+	0.939937i	$0.610883\pi$
$278$	−0.00479849	+	0.00831123i	−0.000287794	+	0.000498474i
$279$	4.62451	−	8.00989i	0.276862	−	0.479540i
$280$	−2.16745	−	0.377384i	−0.129530	−	0.0225530i
$281$	7.98667			0.476445			0.238222	−	0.971211i	$-0.423435\pi$
$281$	7.98667			0.476445			0.238222	+	0.971211i	$0.423435\pi$
$282$	−0.0871768	−	0.150995i	−0.00519130	−	0.00899160i
$283$	−2.06937	+	3.58425i	−0.123011	+	0.213062i	−0.920954	−	0.389672i	$-0.872588\pi$
$283$	−2.06937	+	3.58425i	−0.123011	+	0.213062i	0.797943	+	0.602733i	$0.205922\pi$
$284$	5.21932	−	9.04013i	0.309710	−	0.536433i
$285$	−10.5572	+	18.2856i	−0.625356	+	1.08315i
$286$	−1.06903	−	0.00111286i	−0.0632131	−	6.58048e-5i
$287$	−6.00149	+	7.18356i	−0.354257	+	0.424032i
$288$	−0.406957	−	0.704870i	−0.0239802	−	0.0415348i
$289$	−4.54846			−0.267557
$290$	2.06458			0.121237
$291$	3.86359	+	6.69194i	0.226488	+	0.392288i
$292$	−3.51097	−	6.08118i	−0.205464	−	0.355874i
$293$	−14.1626	+	24.5303i	−0.827385	+	1.43307i	0.0726976	+	0.997354i	$0.476839\pi$
$293$	−14.1626	+	24.5303i	−0.827385	+	1.43307i	−0.900083	+	0.435719i	$0.856494\pi$
$294$	0.0847135	+	0.468657i	0.00494059	+	0.0273326i
$295$	11.5588	−	20.0204i	0.672977	−	1.16563i
$296$	0.0296418			0.00172290
$297$	−2.17896	+	3.77408i	−0.126436	+	0.218994i
$298$	0.488360	+	0.845865i	0.0282900	+	0.0489996i
$299$	−6.00184	−	10.4205i	−0.347095	−	0.602634i
$300$	8.69568			0.502046
$301$	−4.40037	−	0.766166i	−0.253633	−	0.0441611i
$302$	−0.532839	−	0.922904i	−0.0306614	−	0.0531071i
$303$	−1.94016	−	3.36045i	−0.111459	−	0.193053i
$304$	−13.7087	−	23.7442i	−0.786248	−	1.36182i
$305$	−14.9074			−0.853594
$306$	0.120038	+	0.207912i	0.00686213	+	0.0118856i
$307$	18.0617			1.03083			0.515417	−	0.856939i	$-0.327637\pi$
$307$	18.0617			1.03083			0.515417	+	0.856939i	$0.327637\pi$
$308$	−22.6656	−	3.94640i	−1.29149	−	0.224867i
$309$	4.29088	+	7.43202i	0.244100	+	0.422793i
$310$	1.92497			0.109331
$311$	−6.03959	−	10.4609i	−0.342474	−	0.593182i	0.642418	−	0.766355i	$-0.277931\pi$
$311$	−6.03959	−	10.4609i	−0.342474	−	0.593182i	−0.984891	+	0.173173i	$0.944598\pi$
$312$	0.980092	+	0.00102028i	0.0554868	+	5.77617e-5i
$313$	−10.3790	+	17.9769i	−0.586654	+	1.01611i	0.408013	+	0.912976i	$0.366222\pi$
$313$	−10.3790	+	17.9769i	−0.586654	+	1.01611i	−0.994667	+	0.103138i	$0.967112\pi$
$314$	−0.459257	−	0.795457i	−0.0259174	−	0.0448902i
$315$	−2.78448	−	7.59949i	−0.156888	−	0.428182i
$316$	−9.68569	+	16.7761i	−0.544862	+	0.943729i
$317$	−8.73476	+	15.1290i	−0.490593	+	0.849732i	−0.999941	−	0.0108284i	$-0.996553\pi$
$317$	−8.73476	+	15.1290i	−0.490593	+	0.849732i	0.509348	+	0.860560i	$0.329886\pi$
$318$	0.361518			0.0202729
$319$	43.2299			2.42041
$320$	−12.0667	+	20.9001i	−0.674549	+	1.16835i
$321$	−5.60158	+	9.70222i	−0.312650	+	0.541525i
$322$	0.206547	+	0.563715i	0.0115104	+	0.0314146i
$323$	12.1779	+	21.0927i	0.677595	+	1.17363i
$324$	0.997686	−	1.72804i	0.0554270	−	0.0960023i
$325$	−7.87053	+	13.5994i	−0.436578	+	0.754361i
$326$	0.0903939	+	0.156567i	0.00500646	+	0.00867144i
$327$	13.9656			0.772302
$328$	−0.480863	−	0.832880i	−0.0265512	−	0.0459881i
$329$	6.67969	+	1.16303i	0.368263	+	0.0641198i
$330$	−0.907002			−0.0499288
$331$	−3.56309	−	6.17145i	−0.195845	−	0.339213i	0.751332	−	0.659924i	$-0.229412\pi$
$331$	−3.56309	−	6.17145i	−0.195845	−	0.339213i	−0.947177	+	0.320711i	$0.896078\pi$
$332$	−10.8082			−0.593175
$333$	0.0545230	+	0.0944366i	0.00298784	+	0.00517509i
$334$	−0.742559	−	1.28615i	−0.0406310	−	0.0703750i
$335$	1.04075	+	1.80263i	0.0568623	+	0.0984883i
$336$	10.3538	+	1.80274i	0.564847	+	0.0983477i
$337$	−22.8396			−1.24415			−0.622077	−	0.782956i	$-0.713711\pi$
$337$	−22.8396			−1.24415			−0.622077	+	0.782956i	$0.713711\pi$
$338$	−0.443828	+	0.765049i	−0.0241410	+	0.0416132i
$339$	3.38888	+	5.86972i	0.184059	+	0.318799i
$340$	10.7695	−	18.6533i	0.584057	−	1.01162i
$341$	40.3066			2.18272
$342$	−0.234800	+	0.406686i	−0.0126965	+	0.0219910i
$343$	−16.0983	−	9.15663i	−0.869228	−	0.494412i
$344$	0.229451	−	0.397422i	0.0123712	−	0.0214275i
$345$	−5.10137	−	8.83582i	−0.274648	−	0.475705i
$346$	−0.601520	−	1.04186i	−0.0323379	−	0.0560109i
$347$	−17.2581			−0.926462			−0.463231	−	0.886238i	$-0.653310\pi$
$347$	−17.2581			−0.926462			−0.463231	+	0.886238i	$0.653310\pi$
$348$	−19.7937			−1.06106
$349$	−15.3687	−	26.6193i	−0.822665	−	1.42490i	−0.903691	−	0.428186i	$-0.859153\pi$
$349$	−15.3687	−	26.6193i	−0.822665	−	1.42490i	0.0810257	−	0.996712i	$-0.474180\pi$
$350$	0.502946	−	0.602008i	0.0268836	−	0.0321787i
$351$	1.79952	+	3.12437i	0.0960515	+	0.166767i
$352$	1.77349	−	3.07177i	0.0945272	−	0.163726i
$353$	0.480320	−	0.831939i	0.0255649	−	0.0442797i	−0.852960	−	0.521976i	$-0.825195\pi$
$353$	0.480320	−	0.831939i	0.0255649	−	0.0442797i	0.878525	+	0.477697i	$0.158528\pi$
$354$	0.257075	−	0.445267i	0.0136634	−	0.0236657i
$355$	8.00167	+	13.8593i	0.424684	+	0.735575i
$356$	15.3726			0.814748
$357$	−9.19762	−	1.60143i	−0.486790	−	0.0847569i
$358$	−0.330994	+	0.573299i	−0.0174936	+	0.0302998i
$359$	16.4526	−	28.4967i	0.868334	−	1.50400i	0.00463555	−	0.999989i	$-0.498524\pi$
$359$	16.4526	−	28.4967i	0.868334	−	1.50400i	0.863698	−	0.504009i	$-0.168142\pi$
$360$	0.831544			0.0438262
$361$	−14.3204	+	24.8037i	−0.753707	+	1.30546i
$362$	0.273050			0.0143512
$363$	−7.99154			−0.419447
$364$	−12.2191	+	14.5949i	−0.640454	+	0.764980i
$365$	10.7652			0.563478
$366$	−0.331551			−0.0173304
$367$	−11.0277	+	19.1006i	−0.575643	+	0.997042i	0.420329	+	0.907372i	$0.361915\pi$
$367$	−11.0277	+	19.1006i	−0.575643	+	0.997042i	−0.995972	+	0.0896703i	$0.971419\pi$
$368$	13.2484			0.690620
$369$	1.76899	−	3.06399i	0.0920901	−	0.159505i
$370$	−0.0113477	+	0.0196548i	−0.000589939	+	0.00102180i
$371$	−9.01351	+	10.7888i	−0.467958	+	0.560128i
$372$	−18.4552			−0.956859
$373$	−12.9560	−	22.4404i	−0.670835	−	1.16192i	−0.977668	−	0.210157i	$-0.932603\pi$
$373$	−12.9560	−	22.4404i	−0.670835	−	1.16192i	0.306833	−	0.951763i	$-0.400731\pi$
$374$	−0.523118	+	0.906068i	−0.0270498	+	0.0468516i
$375$	0.982073	−	1.70100i	0.0507140	−	0.0878393i
$376$	−0.348303	+	0.603279i	−0.0179624	+	0.0311118i
$377$	17.9155	−	30.9560i	0.922693	−	1.59432i
$378$	−0.0619288	−	0.169018i	−0.00318527	−	0.00869334i
$379$	−1.77121	−	3.06783i	−0.0909811	−	0.157584i	0.816943	−	0.576718i	$-0.195667\pi$
$379$	−1.77121	−	3.06783i	−0.0909811	−	0.157584i	−0.907924	+	0.419134i	$0.862334\pi$
$380$	42.1312			2.16128
$381$	−13.3780			−0.685374
$382$	0.503139	+	0.871462i	0.0257428	+	0.0445879i
$383$	14.6975	+	25.4569i	0.751008	+	1.30078i	0.947334	+	0.320246i	$0.103766\pi$
$383$	14.6975	+	25.4569i	0.751008	+	1.30078i	−0.196326	+	0.980539i	$0.562901\pi$
$384$	−1.08229	+	1.87457i	−0.0552301	+	0.0956614i
$385$	22.6138	−	27.0678i	1.15250	−	1.37950i
$386$	−0.760067	+	1.31648i	−0.0386864	+	0.0670068i
$387$	1.68820			0.0858163
$388$	7.70930	−	13.3529i	0.391380	−	0.677891i
$389$	1.32057	+	2.28730i	0.0669556	+	0.115971i	0.897560	−	0.440893i	$-0.145338\pi$
$389$	1.32057	+	2.28730i	0.0669556	+	0.115971i	−0.830604	+	0.556863i	$0.812005\pi$
$390$	−0.375883	+	0.649485i	−0.0190336	+	0.0328880i
$391$	−11.7690			−0.595182
$392$	1.45237	−	1.22935i	0.0733555	−	0.0620913i
$393$	−9.06148	−	15.6949i	−0.457091	−	0.791705i
$394$	−0.215185	−	0.372712i	−0.0108409	−	0.0187770i
$395$	−14.8490	−	25.7192i	−0.747133	−	1.29407i
$396$	8.69568			0.436975
$397$	−0.287989	−	0.498811i	−0.0144537	−	0.0250346i	0.858708	−	0.512465i	$-0.171268\pi$
$397$	−0.287989	−	0.498811i	−0.0144537	−	0.0250346i	−0.873162	+	0.487430i	$0.837934\pi$
$398$	−0.410677			−0.0205854
$399$	−6.28267	−	17.1468i	−0.314527	−	0.858416i
$400$	−8.65539	−	14.9916i	−0.432769	−	0.749578i
$401$	−9.51197			−0.475005			−0.237503	−	0.971387i	$-0.576329\pi$
$401$	−9.51197			−0.475005			−0.237503	+	0.971387i	$0.576329\pi$
$402$	0.0231470	+	0.0400918i	0.00115447	+	0.00199960i
$403$	16.7040	−	28.8627i	0.832084	−	1.43775i
$404$	−3.87133	+	6.70534i	−0.192606	+	0.333603i
$405$	1.52954	+	2.64923i	0.0760033	+	0.131642i
$406$	−1.14484	+	1.37033i	−0.0568176	+	0.0680085i
$407$	−0.237607	+	0.411548i	−0.0117778	+	0.0203997i
$408$	0.479598	−	0.830688i	0.0237436	−	0.0411252i
$409$	−0.186321			−0.00921299			−0.00460649	−	0.999989i	$-0.501466\pi$
$409$	−0.186321			−0.00921299			−0.00460649	+	0.999989i	$0.501466\pi$
$410$	0.736350			0.0363657
$411$	10.6703	−	18.4814i	0.526325	−	0.911622i
$412$	8.56190	−	14.8296i	0.421814	−	0.730604i
$413$	6.87869	+	18.7735i	0.338478	+	0.923785i
$414$	−0.113458	−	0.196515i	−0.00557616	−	0.00965818i
$415$	8.28491	−	14.3499i	0.406690	−	0.704408i
$416$	−1.46466	−	2.54297i	−0.0718107	−	0.124679i
$417$	0.0705287	+	0.122159i	0.00345381	+	0.00598217i
$418$	−2.04648			−0.100097
$419$	−0.448814	−	0.777369i	−0.0219260	−	0.0379769i	0.854854	−	0.518868i	$-0.173646\pi$
$419$	−0.448814	−	0.777369i	−0.0219260	−	0.0379769i	−0.876780	+	0.480891i	$0.840313\pi$
$420$	−10.3542	+	12.3936i	−0.505233	+	0.604745i
$421$	−4.34862			−0.211939			−0.105969	−	0.994369i	$-0.533795\pi$
$421$	−4.34862			−0.211939			−0.105969	+	0.994369i	$0.533795\pi$
$422$	0.0439575	+	0.0761366i	0.00213982	+	0.00370627i
$423$	−2.56267			−0.124601
$424$	−0.722198	−	1.25088i	−0.0350731	−	0.0607483i
$425$	7.68885	+	13.3175i	0.372964	+	0.645993i
$426$	0.177963	+	0.308240i	0.00862232	+	0.0149343i
$427$	8.26636	−	9.89453i	0.400037	−	0.478830i
$428$	22.3545			1.08054
$429$	−7.87053	+	13.5994i	−0.379993	+	0.656587i
$430$	0.175680	+	0.304287i	0.00847206	+	0.0146740i
$431$	5.36333	−	9.28956i	0.258342	−	0.447462i	−0.707456	−	0.706758i	$-0.750157\pi$
$431$	5.36333	−	9.28956i	0.258342	−	0.447462i	0.965798	+	0.259296i	$0.0834904\pi$
$432$	−3.97225			−0.191115
$433$	3.46111	−	5.99482i	0.166330	−	0.288093i	−0.770797	−	0.637081i	$-0.780142\pi$
$433$	3.46111	−	5.99482i	0.166330	−	0.288093i	0.937127	+	0.348989i	$0.113475\pi$
$434$	−1.06742	+	1.27767i	−0.0512380	+	0.0613300i
$435$	15.1727	−	26.2800i	0.727477	−	1.26003i
$436$	−13.9333	−	24.1332i	−0.667285	−	1.15577i
$437$	−11.5103	−	19.9364i	−0.550612	−	0.953688i
$438$	0.239426			0.0114402
$439$	25.2180			1.20359			0.601794	−	0.798652i	$-0.294453\pi$
$439$	25.2180			1.20359			0.601794	+	0.798652i	$0.294453\pi$
$440$	1.81191	+	3.13831i	0.0863792	+	0.149613i
$441$	6.58807	+	2.36587i	0.313718	+	0.112661i
$442$	0.432024	+	0.750089i	0.0205493	+	0.0356781i
$443$	−8.71266	+	15.0908i	−0.413951	+	0.716984i	−0.995318	−	0.0966574i	$-0.969185\pi$
$443$	−8.71266	+	15.0908i	−0.413951	+	0.716984i	0.581367	+	0.813642i	$0.302518\pi$
$444$	0.108794	−	0.188436i	0.00516312	−	0.00894278i
$445$	−11.7838	+	20.4101i	−0.558604	+	0.967531i
$446$	0.394535	+	0.683354i	0.0186818	+	0.0323578i
$447$	14.3559			0.679013
$448$	−7.18096	−	19.5985i	−0.339269	−	0.925942i
$449$	−5.91239	+	10.2406i	−0.279023	+	0.483282i	−0.971142	−	0.238501i	$-0.923344\pi$
$449$	−5.91239	+	10.2406i	−0.279023	+	0.483282i	0.692119	+	0.721783i	$0.256677\pi$
$450$	−0.148248	+	0.256773i	−0.00698847	+	0.0121044i
$451$	15.4183			0.726019
$452$	6.76208	−	11.7123i	0.318061	−	0.550898i
$453$	−15.6634			−0.735933
$454$	−0.0543266			−0.00254967
$455$	−10.0111	−	27.4108i	−0.469325	−	1.28504i
$456$	1.87623			0.0878624
$457$	−8.33251			−0.389779			−0.194889	−	0.980825i	$-0.562435\pi$
$457$	−8.33251			−0.389779			−0.194889	+	0.980825i	$0.562435\pi$
$458$	−0.789712	+	1.36782i	−0.0369008	+	0.0639141i
$459$	3.52867			0.164704
$460$	−10.1791	+	17.6307i	−0.474604	+	0.822038i
$461$	2.20305	−	3.81579i	0.102606	−	0.177719i	−0.810152	−	0.586221i	$-0.800615\pi$
$461$	2.20305	−	3.81579i	0.102606	−	0.177719i	0.912758	+	0.408502i	$0.133949\pi$
$462$	0.502946	−	0.602008i	0.0233992	−	0.0280079i
$463$	20.2243			0.939904			0.469952	−	0.882692i	$-0.344271\pi$
$463$	20.2243			0.939904			0.469952	+	0.882692i	$0.344271\pi$
$464$	19.7020	+	34.1249i	0.914643	+	1.58421i
$465$	14.1467	−	24.5028i	0.656038	−	1.13629i
$466$	0.414603	−	0.718113i	0.0192061	−	0.0332660i
$467$	−3.27010	+	5.66398i	−0.151322	+	0.262098i	−0.931714	−	0.363193i	$-0.881686\pi$
$467$	−3.27010	+	5.66398i	−0.151322	+	0.262098i	0.780392	+	0.625291i	$0.215020\pi$
$468$	3.60369	−	6.22680i	0.166581	−	0.287834i
$469$	−1.77358	−	0.308805i	−0.0818963	−	0.0142593i
$470$	−0.266680	−	0.461903i	−0.0123010	−	0.0213060i
$471$	−13.5004			−0.622067
$472$	−2.05422			−0.0945532
$473$	3.67854	+	6.37141i	0.169139	+	0.292958i
$474$	−0.330252	−	0.572013i	−0.0151690	−	0.0262734i
$475$	−15.0397	+	26.0496i	−0.690070	+	1.19524i
$476$	6.40898	+	17.4916i	0.293755	+	0.801726i
$477$	2.65681	−	4.60173i	0.121647	−	0.210699i
$478$	−0.0329520			−0.00150719
$479$	3.90667	−	6.76656i	0.178500	−	0.309172i	−0.762867	−	0.646556i	$-0.776209\pi$
$479$	3.90667	−	6.76656i	0.178500	−	0.309172i	0.941367	+	0.337384i	$0.109542\pi$
$480$	−1.24491	−	2.15625i	−0.0568221	−	0.0984188i
$481$	0.196231	+	0.340700i	0.00894736	+	0.0155346i
$482$	−0.157852			−0.00718995
$483$	8.69342	+	1.51365i	0.395564	+	0.0688733i
$484$	7.97304	+	13.8097i	0.362411	+	0.627714i
$485$	11.8190	+	20.4711i	0.536674	+	0.929546i
$486$	0.0340180	+	0.0589209i	0.00154309	+	0.00267270i
$487$	−21.0741			−0.954959			−0.477479	−	0.878643i	$-0.658449\pi$
$487$	−21.0741			−0.954959			−0.477479	+	0.878643i	$0.658449\pi$
$488$	0.662334	+	1.14720i	0.0299824	+	0.0519311i
$489$	2.65724			0.120165
$490$	0.259145	+	1.43366i	0.0117070	+	0.0647660i
$491$	−4.36913	−	7.56755i	−0.197176	−	0.341519i	0.750436	−	0.660943i	$-0.229844\pi$
$491$	−4.36913	−	7.56755i	−0.197176	−	0.341519i	−0.947612	+	0.319425i	$0.896510\pi$
$492$	−7.05959			−0.318271
$493$	−17.5019	−	30.3142i	−0.788247	−	1.36528i
$494$	−0.848110	+	1.46544i	−0.0381583	+	0.0659335i
$495$	−6.66561	+	11.5452i	−0.299597	+	0.518917i
$496$	18.3697	+	31.8173i	0.824824	+	1.42864i
$497$	−13.6359	−	2.37420i	−0.611655	−	0.106498i
$498$	0.184262	−	0.319152i	0.00825699	−	0.0143015i
$499$	−10.6426	+	18.4336i	−0.476430	+	0.825200i	−0.999635	−	0.0270062i	$-0.991403\pi$
$499$	−10.6426	+	18.4336i	−0.476430	+	0.825200i	0.523206	+	0.852206i	$0.324736\pi$
$500$	−3.91920			−0.175272
$501$	−21.8284			−0.975222
$502$	0.938555	−	1.62563i	0.0418898	−	0.0725552i
$503$	−2.29846	+	3.98105i	−0.102483	+	0.177506i	−0.912707	−	0.408614i	$-0.866012\pi$
$503$	−2.29846	+	3.98105i	−0.102483	+	0.177506i	0.810224	+	0.586120i	$0.199345\pi$
$504$	−0.461104	+	0.551924i	−0.0205392	+	0.0245847i
$505$	−5.93508	−	10.2799i	−0.264107	−	0.457448i
$506$	0.494442	−	0.856398i	0.0219806	−	0.0380715i
$507$	6.47655	+	11.2718i	0.287634	+	0.500600i
$508$	13.3470	+	23.1177i	0.592178	+	1.02568i
$509$	−13.7063			−0.607522			−0.303761	−	0.952748i	$-0.598242\pi$
$509$	−13.7063			−0.607522			−0.303761	+	0.952748i	$0.598242\pi$
$510$	0.367206	+	0.636019i	0.0162602	+	0.0281634i
$511$	−5.96947	+	7.14524i	−0.264074	+	0.316087i
$512$	5.39261			0.238322
$513$	3.45112	+	5.97751i	0.152371	+	0.263914i
$514$	0.621172			0.0273987
$515$	13.1261	+	22.7351i	0.578406	+	1.00183i
$516$	−1.68430	−	2.91729i	−0.0741471	−	0.128426i
$517$	−5.58396	−	9.67170i	−0.245582	−	0.425361i
$518$	−0.00675308	−	0.0184307i	−0.000296713	−	0.000809800i
$519$	−17.6824			−0.776171
$520$	2.99817	+	0.00312110i	0.131479	+	0.000136869i
$521$	−2.13457	−	3.69718i	−0.0935172	−	0.161977i	0.815472	−	0.578797i	$-0.196478\pi$
$521$	−2.13457	−	3.69718i	−0.0935172	−	0.161977i	−0.908989	+	0.416821i	$0.863144\pi$
$522$	0.337453	−	0.584485i	0.0147699	−	0.0255822i
$523$	−28.1706			−1.23181			−0.615907	−	0.787819i	$-0.711210\pi$
$523$	−28.1706			−1.23181			−0.615907	+	0.787819i	$0.711210\pi$
$524$	−18.0810	+	31.3172i	−0.789873	+	1.36810i
$525$	−3.96674	−	10.8262i	−0.173123	−	0.472492i
$526$	0.190150	−	0.329350i	0.00829094	−	0.0143603i
$527$	−16.3184	−	28.2643i	−0.710840	−	1.23121i
$528$	−8.65539	−	14.9916i	−0.376677	−	0.652424i
$529$	−11.8762			−0.516357
$530$	1.10591			0.0480376
$531$	−3.77852	−	6.54459i	−0.163974	−	0.284011i
$532$	−23.3623	+	27.9639i	−1.01289	+	1.21239i
$533$	6.38969	−	11.0407i	0.276768	−	0.478226i
$534$	−0.262079	+	0.453935i	−0.0113413	+	0.0196437i
$535$	−17.1356	+	29.6798i	−0.740839	+	1.28317i
$536$	0.0924810	−	0.160182i	0.00399457	−	0.00691880i
$537$	4.86499	+	8.42641i	0.209940	+	0.363626i
$538$	1.44863			0.0624549
$539$	5.42618	+	30.0190i	0.233722	+	1.29301i
$540$	3.05199	−	5.28621i	0.131337	−	0.227482i
$541$	9.24717	−	16.0166i	0.397567	−	0.688606i	−0.595858	−	0.803089i	$-0.703188\pi$
$541$	9.24717	−	16.0166i	0.397567	−	0.688606i	0.993425	+	0.114484i	$0.0365214\pi$
$542$	0.770641			0.0331019
$543$	2.00666	−	3.47564i	0.0861140	−	0.149154i
$544$	−2.87203			−0.123137
$545$	42.7219			1.83001
$546$	−0.222653	−	0.609635i	−0.00952866	−	0.0260900i
$547$	24.6951			1.05589			0.527943	−	0.849280i	$-0.322963\pi$
$547$	24.6951			1.05589			0.527943	+	0.849280i	$0.322963\pi$
$548$	−42.5823			−1.81902
$549$	−2.43658	+	4.22029i	−0.103991	+	0.180117i
$550$	−1.29211			−0.0550956
$551$	34.2345	−	59.2959i	1.45844	−	2.52609i
$552$	−0.453307	+	0.785150i	−0.0192940	+	0.0334182i
$553$	25.3047	+	4.40590i	1.07606	+	0.187358i
$554$	−0.773046			−0.0328436
$555$	0.166790	+	0.288888i	0.00707983	+	0.0122626i
$556$	0.140731	−	0.243753i	0.00596832	−	0.0103374i
$557$	1.48587	−	2.57361i	0.0629584	−	0.109047i	−0.832828	−	0.553532i	$-0.813280\pi$
$557$	1.48587	−	2.57361i	0.0629584	−	0.109047i	0.895787	+	0.444485i	$0.146613\pi$
$558$	0.314633	−	0.544960i	0.0133195	−	0.0230700i
$559$	6.08691	+	0.00633646i	0.257449	+	0.000268004i
$560$	31.6731	+	5.51472i	1.33843	+	0.233040i
$561$	7.68885	+	13.3175i	0.324624	+	0.562265i
$562$	0.543380			0.0229211
$563$	−3.20058			−0.134889			−0.0674443	−	0.997723i	$-0.521484\pi$
$563$	−3.20058			−0.134889			−0.0674443	+	0.997723i	$0.521484\pi$
$564$	2.55674	+	4.42840i	0.107658	+	0.186469i
$565$	10.3668	+	17.9559i	0.436136	+	0.755410i
$566$	−0.140791	+	0.243858i	−0.00591791	+	0.0102501i
$567$	−2.60654	−	0.453835i	−0.109464	−	0.0190593i
$568$	0.711027	−	1.23154i	0.0298340	−	0.0516741i
$569$	−12.5838			−0.527539			−0.263770	−	0.964586i	$-0.584966\pi$
$569$	−12.5838			−0.527539			−0.263770	+	0.964586i	$0.584966\pi$
$570$	−0.718271	+	1.24408i	−0.0300851	+	0.0521088i
$571$	11.8472	+	20.5200i	0.495792	+	0.858736i	0.999988	−	0.00485262i	$-0.00154464\pi$
$571$	11.8472	+	20.5200i	0.495792	+	0.858736i	−0.504197	+	0.863589i	$0.668211\pi$
$572$	31.3527	+	0.0326381i	1.31092	+	0.00136467i
$573$	14.7904			0.617877
$574$	−0.408317	+	0.488740i	−0.0170428	+	0.0203996i
$575$	−7.26736	−	12.5874i	−0.303070	−	0.524932i
$576$	3.94456	+	6.83218i	0.164357	+	0.284674i
$577$	−1.67873	−	2.90764i	−0.0698863	−	0.121047i	0.828965	−	0.559301i	$-0.188930\pi$
$577$	−1.67873	−	2.90764i	−0.0698863	−	0.121047i	−0.898851	+	0.438254i	$0.855597\pi$
$578$	−0.309459			−0.0128718
$579$	11.1716	+	19.3497i	0.464274	+	0.804146i
$580$	−60.5505			−2.51422
$581$	4.93040	+	13.4562i	0.204547	+	0.558257i
$582$	0.262863	+	0.455292i	0.0108960	+	0.0188725i
$583$	23.1564			0.959040
$584$	−0.478298	−	0.828437i	−0.0197921	−	0.0342810i
$585$	5.50488	+	9.55769i	0.227599	+	0.395162i
$586$	−0.963563	+	1.66894i	−0.0398044	+	0.0689433i
$587$	−4.99547	−	8.65242i	−0.206185	−	0.357123i	0.744324	−	0.667818i	$-0.232772\pi$
$587$	−4.99547	−	8.65242i	−0.206185	−	0.357123i	−0.950510	+	0.310695i	$0.899438\pi$
$588$	−2.48449	−	13.7449i	−0.102459	−	0.566828i
$589$	31.9195	−	55.2862i	1.31522	−	2.27803i
$590$	0.786412	−	1.36210i	0.0323761	−	0.0560770i
$591$	−6.32564			−0.260202
$592$	−0.433158			−0.0178027
$593$	−16.4331	+	28.4629i	−0.674825	+	1.16883i	0.301695	+	0.953404i	$0.402447\pi$
$593$	−16.4331	+	28.4629i	−0.674825	+	1.16883i	−0.976520	+	0.215426i	$0.930886\pi$
$594$	−0.148248	+	0.256773i	−0.00608268	+	0.0105355i
$595$	−28.1362	−	4.89890i	−1.15347	−	0.200835i
$596$	−14.3227	−	24.8077i	−0.586682	−	1.01616i
$597$	−3.01808	+	5.22748i	−0.123522	+	0.213946i
$598$	−0.408341	−	0.708970i	−0.0166983	−	0.0289920i
$599$	10.6138	+	18.3836i	0.433667	+	0.751133i	0.997186	−	0.0749700i	$-0.0238861\pi$
$599$	10.6138	+	18.3836i	0.433667	+	0.751133i	−0.563519	+	0.826103i	$0.690553\pi$
$600$	1.18461			0.0483615
$601$	0.776508	+	1.34495i	0.0316744	+	0.0548617i	0.881428	−	0.472318i	$-0.156583\pi$
$601$	0.776508	+	1.34495i	0.0316744	+	0.0548617i	−0.849754	+	0.527180i	$0.823249\pi$
$602$	−0.299383	−	0.0521268i	−0.0122020	−	0.00212453i
$603$	0.680435			0.0277095
$604$	15.6272	+	27.0671i	0.635861	+	1.10134i
$605$	−24.4467			−0.993899
$606$	−0.132000	−	0.228631i	−0.00536215	−	0.00928751i
$607$	−3.30552	−	5.72533i	−0.134167	−	0.232384i	0.791112	−	0.611671i	$-0.209502\pi$
$607$	−3.30552	−	5.72533i	−0.134167	−	0.232384i	−0.925279	+	0.379287i	$0.876169\pi$
$608$	−2.80891	−	4.86518i	−0.113916	−	0.197309i
$609$	9.02939	+	24.6433i	0.365889	+	0.998596i
$610$	−1.01424			−0.0410653
$611$	−9.23982	−	0.00961865i	−0.373803	−	0.000389129i
$612$	−3.52051	−	6.09770i	−0.142308	−	0.246485i
$613$	6.02920	−	10.4429i	0.243517	−	0.421784i	−0.718197	−	0.695840i	$-0.755032\pi$
$613$	6.02920	−	10.4429i	0.243517	−	0.421784i	0.961714	+	0.274056i	$0.0883655\pi$
$614$	1.22884			0.0495921
$615$	5.41148	−	9.37295i	0.218212	−	0.377954i
$616$	−3.08773	−	0.537617i	−0.124408	−	0.0216612i
$617$	−16.5723	+	28.7040i	−0.667175	+	1.15558i	0.311515	+	0.950241i	$0.399163\pi$
$617$	−16.5723	+	28.7040i	−0.667175	+	1.15558i	−0.978691	+	0.205340i	$0.934170\pi$
$618$	0.291934	+	0.505645i	0.0117433	+	0.0203400i
$619$	23.8269	+	41.2695i	0.957686	+	1.65876i	0.728099	+	0.685472i	$0.240404\pi$
$619$	23.8269	+	41.2695i	0.957686	+	1.65876i	0.229587	+	0.973288i	$0.426263\pi$
$620$	−56.4559			−2.26732
$621$	−3.33524			−0.133838
$622$	−0.410909	−	0.711716i	−0.0164760	−	0.0285372i
$623$	−7.01259	−	19.1390i	−0.280953	−	0.766787i
$624$	−14.3221	−	0.0149093i	−0.573344	−	0.000596851i
$625$	13.8991	−	24.0739i	0.555962	−	0.962955i
$626$	−0.706143	+	1.22308i	−0.0282231	+	0.0488839i
$627$	−15.0397	+	26.0496i	−0.600629	+	1.04032i
$628$	13.4692	+	23.3293i	0.537479	+	0.930941i
$629$	0.384788			0.0153425
$630$	−0.189445	−	0.517038i	−0.00754766	−	0.0205993i
$631$	1.28825	−	2.23132i	0.0512846	−	0.0888276i	−0.839243	−	0.543756i	$-0.817002\pi$
$631$	1.28825	−	2.23132i	0.0512846	−	0.0888276i	0.890528	+	0.454928i	$0.150335\pi$
$632$	−1.31948	+	2.28540i	−0.0524860	+	0.0909085i
$633$	1.29218			0.0513597
$634$	−0.594278	+	1.02932i	−0.0236018	+	0.0408795i
$635$	−40.9242			−1.62403
$636$	−10.6027			−0.420423
$637$	23.7447	+	8.55500i	0.940800	+	0.338961i
$638$	2.94119			0.116443
$639$	5.23143			0.206952
$640$	−3.31079	+	5.73446i	−0.130870	+	0.226674i
$641$	40.7526			1.60963			0.804815	−	0.593526i	$-0.202265\pi$
$641$	40.7526			1.60963			0.804815	+	0.593526i	$0.202265\pi$
$642$	−0.381109	+	0.660100i	−0.0150412	+	0.0260521i
$643$	−4.68006	+	8.10610i	−0.184564	+	0.319674i	−0.943429	−	0.331574i	$-0.892420\pi$
$643$	−4.68006	+	8.10610i	−0.184564	+	0.319674i	0.758866	+	0.651247i	$0.225754\pi$
$644$	−6.05765	−	16.5327i	−0.238705	−	0.651481i
$645$	5.16434			0.203346
$646$	0.828533	+	1.43506i	0.0325982	+	0.0564617i
$647$	−12.5098	+	21.6677i	−0.491812	+	0.851844i	−0.999956	−	0.00942863i	$-0.996999\pi$
$647$	−12.5098	+	21.6677i	−0.491812	+	0.851844i	0.508143	+	0.861273i	$0.330332\pi$
$648$	0.135914	−	0.235411i	0.00533922	−	0.00924781i
$649$	16.4665	−	28.5208i	0.646367	−	1.11954i
$650$	−0.535479	+	0.925251i	−0.0210032	+	0.0362913i
$651$	8.41880	+	22.9768i	0.329959	+	0.900533i
$652$	−2.65109	−	4.59182i	−0.103825	−	0.179830i
$653$	−18.5614			−0.726364			−0.363182	−	0.931718i	$-0.618310\pi$
$653$	−18.5614			−0.726364			−0.363182	+	0.931718i	$0.618310\pi$
$654$	0.950166			0.0371544
$655$	−27.7197	−	48.0120i	−1.08310	−	1.87598i
$656$	7.02688	+	12.1709i	0.274353	+	0.475194i
$657$	1.75956	−	3.04764i	0.0686468	−	0.118900i
$658$	0.454459	+	0.0791277i	0.0177167	+	0.00308472i
$659$	18.4907	−	32.0268i	0.720295	−	1.24759i	−0.240587	−	0.970628i	$-0.577340\pi$
$659$	18.4907	−	32.0268i	0.720295	−	1.24759i	0.960882	−	0.276960i	$-0.0893268\pi$
$660$	26.6007			1.03543
$661$	−7.96164	+	13.7900i	−0.309672	+	0.536368i	−0.978291	−	0.207238i	$-0.933553\pi$
$661$	−7.96164	+	13.7900i	−0.309672	+	0.536368i	0.668619	+	0.743606i	$0.266886\pi$
$662$	−0.242418	−	0.419880i	−0.00942184	−	0.0163191i
$663$	12.7228	+	0.0132444i	0.494113	+	0.000514371i
$664$	−1.47239			−0.0571399
$665$	−19.2191	−	52.4534i	−0.745286	−	2.03406i
$666$	0.00370952	+	0.00642508i	0.000143741	+	0.000248967i
$667$	16.5425	+	28.6524i	0.640528	+	1.10943i
$668$	21.7779	+	37.7204i	0.842612	+	1.45945i
$669$	11.5978			0.448398
$670$	0.0708085	+	0.122644i	0.00273557	+	0.00473814i
$671$	−21.2369			−0.819842
$672$	2.12150	+	0.369382i	0.0818385	+	0.0142492i
$673$	10.9624	+	18.9874i	0.422569	+	0.731910i	0.996190	−	0.0872103i	$-0.0277952\pi$
$673$	10.9624	+	18.9874i	0.422569	+	0.731910i	−0.573621	+	0.819121i	$0.694462\pi$
$674$	−1.55392			−0.0598546
$675$	2.17896	+	3.77408i	0.0838684	+	0.145264i
$676$	13.0167	−	22.4375i	0.500641	−	0.862981i
$677$	−16.0122	+	27.7339i	−0.615398	+	1.06590i	0.374917	+	0.927059i	$0.377671\pi$
$677$	−16.0122	+	27.7339i	−0.615398	+	1.06590i	−0.990315	+	0.138842i	$0.955662\pi$
$678$	0.230566	+	0.399352i	0.00885483	+	0.0153370i
$679$	−20.1412	−	3.50686i	−0.772948	−	0.134581i
$680$	1.46712	−	2.54113i	0.0562617	−	0.0974480i
$681$	−0.399249	+	0.691520i	−0.0152993	+	0.0264991i
$682$	2.74230			0.105008
$683$	−3.02269			−0.115660			−0.0578300	−	0.998326i	$-0.518418\pi$
$683$	−3.02269			−0.115660			−0.0578300	+	0.998326i	$0.518418\pi$
$684$	6.88626	−	11.9274i	0.263303	−	0.456054i
$685$	32.6411	−	56.5361i	1.24715	−	2.16013i
$686$	−1.09527	−	0.622980i	−0.0418174	−	0.0237855i
$687$	11.6073	+	20.1044i	0.442845	+	0.767030i
$688$	−3.35298	+	5.80754i	−0.127831	+	0.221410i
$689$	9.59654	−	16.5818i	0.365599	−	0.631717i
$690$	−0.347076	−	0.601154i	−0.0132130	−	0.0228855i
$691$	−11.8991			−0.452662			−0.226331	−	0.974050i	$-0.572673\pi$
$691$	−11.8991			−0.452662			−0.226331	+	0.974050i	$0.572673\pi$
$692$	17.6415	+	30.5559i	0.670628	+	1.16156i
$693$	−3.96674	−	10.8262i	−0.150684	−	0.411252i
$694$	−1.17417			−0.0445709
$695$	0.215752	+	0.373694i	0.00818396	+	0.0141750i
$696$	−2.69650			−0.102210
$697$	−6.24220	−	10.8118i	−0.236440	−	0.409526i
$698$	−1.04562	−	1.81107i	−0.0395773	−	0.0685500i
$699$	−6.09388	−	10.5549i	−0.230492	−	0.399223i
$700$	−14.7505	+	17.6558i	−0.557516	+	0.667327i
$701$	2.07215			0.0782642			0.0391321	−	0.999234i	$-0.487541\pi$
$701$	2.07215			0.0782642			0.0391321	+	0.999234i	$0.487541\pi$
$702$	0.122432	+	0.212570i	0.00462091	+	0.00802293i
$703$	0.376331	+	0.651824i	0.0141936	+	0.0245840i
$704$	−17.1901	+	29.7741i	−0.647877	+	1.12216i
$705$	−7.83939			−0.295248
$706$	0.0326791	−	0.0566018i	0.00122989	−	0.00213024i
$707$	10.1142	+	1.76102i	0.380383	+	0.0662300i
$708$	−7.53955	+	13.0589i	−0.283354	+	0.490783i
$709$	−3.61999	−	6.27001i	−0.135952	−	0.235475i	0.790009	−	0.613095i	$-0.210076\pi$
$709$	−3.61999	−	6.27001i	−0.135952	−	0.235475i	−0.925961	+	0.377620i	$0.876743\pi$
$710$	0.544401	+	0.942930i	0.0204310	+	0.0353875i
$711$	−9.70816			−0.364084
$712$	2.09421			0.0784838
$713$	15.4238	+	26.7149i	0.577627	+	1.00048i
$714$	−0.625769	−	0.108955i	−0.0234188	−	0.00407754i
$715$	−24.0765	+	41.6017i	−0.900411	+	1.55581i
$716$	9.70746	−	16.8138i	0.362785	−	0.628362i
$717$	−0.242166	+	0.419444i	−0.00904386	+	0.0156644i
$718$	1.11937	−	1.93880i	0.0417744	−	0.0723554i
$719$	−25.4653	−	44.1071i	−0.949694	−	1.64492i	−0.746068	−	0.665870i	$-0.768061\pi$
$719$	−25.4653	−	44.1071i	−0.949694	−	1.64492i	−0.203626	−	0.979049i	$-0.565273\pi$
$720$	−12.1514			−0.452856
$721$	−22.3687	−	3.89470i	−0.833053	−	0.145046i
$722$	−0.974305	+	1.68755i	−0.0362599	+	0.0628039i
$723$	−1.16006	+	2.00929i	−0.0431432	+	0.0747261i
$724$	−8.00806			−0.297617
$725$	21.6150	−	37.4382i	0.802759	−	1.39042i
$726$	−0.543712			−0.0201790
$727$	−21.6848			−0.804244			−0.402122	−	0.915586i	$-0.631727\pi$
$727$	−21.6848			−0.804244			−0.402122	+	0.915586i	$0.631727\pi$
$728$	−1.66460	+	1.98826i	−0.0616943	+	0.0736898i
$729$	1.00000			0.0370370
$730$	0.732422			0.0271082
$731$	2.97856	−	5.15902i	0.110166	−	0.190813i
$732$	9.72378			0.359401
$733$	10.8930	−	18.8673i	0.402343	−	0.696879i	−0.591665	−	0.806184i	$-0.701529\pi$
$733$	10.8930	−	18.8673i	0.402343	−	0.696879i	0.994008	+	0.109305i	$0.0348625\pi$
$734$	−0.750282	+	1.29953i	−0.0276934	+	0.0479664i
$735$	20.1534	+	7.23738i	0.743369	+	0.266955i
$736$	2.71459			0.100061
$737$	1.48264	+	2.56801i	0.0546139	+	0.0945940i
$738$	0.120355	−	0.208461i	0.00443033	−	0.00767356i
$739$	−17.9533	+	31.0960i	−0.660421	+	1.14388i	0.320084	+	0.947389i	$0.396289\pi$
$739$	−17.9533	+	31.0960i	−0.660421	+	1.14388i	−0.980505	+	0.196494i	$0.937044\pi$
$740$	0.332808	−	0.576440i	0.0122342	−	0.0211903i
$741$	12.4207	+	21.5652i	0.456287	+	0.792216i
$742$	−0.613242	+	0.734029i	−0.0225128	+	0.0269470i
$743$	25.6310	+	44.3942i	0.940310	+	1.62867i	0.764879	+	0.644174i	$0.222799\pi$
$743$	25.6310	+	44.3942i	0.940310	+	1.62867i	0.175431	+	0.984492i	$0.443868\pi$
$744$	−2.51415			−0.0921733
$745$	43.9159			1.60895
$746$	−0.881472	−	1.52675i	−0.0322730	−	0.0558984i
$747$	−2.70831	−	4.69093i	−0.0990918	−	0.171632i
$748$	15.3421	−	26.5733i	0.560963	−	0.971617i
$749$	−10.1975	−	27.8314i	−0.372609	−	1.01694i
$750$	0.0668163	−	0.115729i	0.00243978	−	0.00422583i
$751$	48.7540			1.77906			0.889530	−	0.456877i	$-0.151032\pi$
$751$	48.7540			1.77906			0.889530	+	0.456877i	$0.151032\pi$
$752$	5.08977	−	8.81575i	0.185605	−	0.321477i
$753$	−13.7950	−	23.8936i	−0.502717	−	0.870732i
$754$	1.21890	−	2.10612i	0.0443896	−	0.0767005i
$755$	−47.9156			−1.74383
$756$	1.81626	+	4.95699i	0.0660567	+	0.180284i
$757$	7.41023	+	12.8349i	0.269329	+	0.466492i	0.968689	−	0.248278i	$-0.0798647\pi$
$757$	7.41023	+	12.8349i	0.269329	+	0.466492i	−0.699360	+	0.714770i	$0.746531\pi$
$758$	−0.120506	−	0.208723i	−0.00437698	−	0.00758115i
$759$	−7.26736	−	12.5874i	−0.263788	−	0.456895i
$760$	5.73952			0.208194
$761$	−5.65515	−	9.79500i	−0.204999	−	0.355068i	0.745134	−	0.666915i	$-0.232386\pi$
$761$	−5.65515	−	9.79500i	−0.204999	−	0.355068i	−0.950132	+	0.311847i	$0.899052\pi$
$762$	−0.910183			−0.0329725
$763$	−23.6899	+	28.3560i	−0.857633	+	1.02656i
$764$	−14.7562	−	25.5584i	−0.533859	−	0.924671i
$765$	10.7945			0.390275
$766$	0.999960	+	1.73198i	0.0361300	+	0.0625790i
$767$	−13.5991	−	23.6110i	−0.491034	−	0.852544i
$768$	7.81549	−	13.5368i	0.282017	−	0.488468i
$769$	8.92963	+	15.4666i	0.322011	+	0.557739i	0.980903	−	0.194498i	$-0.0623079\pi$
$769$	8.92963	+	15.4666i	0.322011	+	0.557739i	−0.658892	+	0.752238i	$0.728975\pi$
$770$	1.53855	−	1.84159i	0.0554454	−	0.0663662i
$771$	4.56503	−	7.90686i	0.164405	−	0.284758i
$772$	22.2914	−	38.6098i	0.802285	−	1.38960i
$773$	2.86552			0.103066			0.0515329	−	0.998671i	$-0.483589\pi$
$773$	2.86552			0.103066			0.0515329	+	0.998671i	$0.483589\pi$
$774$	0.114859			0.00412851
$775$	20.1533	−	34.9065i	0.723928	−	1.25388i
$776$	1.05024	−	1.81906i	0.0377013	−	0.0653005i
$777$	−0.284232	−	0.0494888i	−0.0101968	−	0.00177540i
$778$	0.0898463	+	0.155618i	0.00322115	+	0.00557919i
$779$	12.2100	−	21.1484i	0.437469	−	0.757718i
$780$	11.0240	−	19.0482i	0.394721	−	0.682036i
$781$	11.3991	+	19.7438i	0.407892	+	0.706489i
$782$	−0.800712			−0.0286334
$783$	−4.95991	−	8.59082i	−0.177253	−	0.307011i
$784$	−21.2235	+	17.9645i	−0.757982	+	0.641589i
$785$	−41.2988			−1.47402
$786$	−0.616507	−	1.06782i	−0.0219901	−	0.0380879i
$787$	3.16514			0.112825			0.0564125	−	0.998408i	$-0.482034\pi$
$787$	3.16514			0.112825			0.0564125	+	0.998408i	$0.482034\pi$
$788$	6.31100	+	10.9310i	0.224820	+	0.389400i
$789$	−2.79485	−	4.84082i	−0.0994992	−	0.172338i
$790$	−1.01026	−	1.74983i	−0.0359436	−	0.0622561i
$791$	−17.6665	−	3.07598i	−0.628148	−	0.109369i
$792$	1.18461			0.0420933
$793$	−8.80106	+	15.2073i	−0.312535	+	0.540027i
$794$	−0.0195936	−	0.0339371i	−0.000695350	−	0.00120438i
$795$	8.12738	−	14.0770i	0.288249	−	0.499261i
$796$	12.0444			0.426902
$797$	12.0425	−	20.8583i	0.426568	−	0.738838i	−0.569997	−	0.821647i	$-0.693056\pi$
$797$	12.0425	−	20.8583i	0.426568	−	0.738838i	0.996565	+	0.0828085i	$0.0263890\pi$
$798$	−0.427447	−	1.16660i	−0.0151315	−	0.0412973i
$799$	−4.52141	+	7.83131i	−0.159956	+	0.277052i
$800$	−1.77349	−	3.07177i	−0.0627023	−	0.108604i
$801$	3.85207	+	6.67198i	0.136106	+	0.235743i
$802$	−0.647156			−0.0228519
$803$	15.3360			0.541197
$804$	−0.678860	−	1.17582i	−0.0239416	−	0.0414680i
$805$	26.5938	+	4.63035i	0.937308	+	0.163198i
$806$	1.13647	−	1.96370i	0.0400305	−	0.0691684i
$807$	10.6461	−	18.4395i	0.374759	−	0.649102i
$808$	−0.527390	+	0.913467i	−0.0185535	+	0.0321357i
$809$	19.1556	−	33.1784i	0.673474	−	1.16649i	−0.303438	−	0.952851i	$-0.598135\pi$
$809$	19.1556	−	33.1784i	0.673474	−	1.16649i	0.976912	−	0.213640i	$-0.0685320\pi$
$810$	0.104063	+	0.180243i	0.00365642	+	0.00633310i
$811$	2.79091			0.0980022			0.0490011	−	0.998799i	$-0.484396\pi$
$811$	2.79091			0.0980022			0.0490011	+	0.998799i	$0.484396\pi$
$812$	33.5761	−	40.1894i	1.17829	−	1.41037i
$813$	5.66348	−	9.80944i	0.198627	−	0.344032i
$814$	−0.0161658	+	0.0280000i	−0.000566612	+	0.000981401i
$815$	8.12869			0.284736
$816$	−7.00838	+	12.1389i	−0.245342	+	0.424946i
$817$	11.6524			0.407666
$818$	−0.0126765			−0.000443225
$819$	−9.39629	−	1.64611i	−0.328333	−	0.0575196i
$820$	−21.5958			−0.754158
$821$	−44.3710			−1.54856			−0.774279	−	0.632844i	$-0.781887\pi$
$821$	−44.3710			−1.54856			−0.774279	+	0.632844i	$0.781887\pi$
$822$	0.725961	−	1.25740i	0.0253208	−	0.0438569i
$823$	−8.21493			−0.286354			−0.143177	−	0.989697i	$-0.545732\pi$
$823$	−8.21493			−0.286354			−0.143177	+	0.989697i	$0.545732\pi$
$824$	1.16639	−	2.02024i	0.0406329	−	0.0703783i
$825$	−9.49577	+	16.4472i	−0.330600	+	0.572616i
$826$	0.467998	+	1.27728i	0.0162837	+	0.0444421i
$827$	−37.0687			−1.28900			−0.644502	−	0.764603i	$-0.722935\pi$
$827$	−37.0687			−1.28900			−0.644502	+	0.764603i	$0.722935\pi$
$828$	3.32752	+	5.76343i	0.115639	+	0.200293i
$829$	21.2293	−	36.7702i	0.737323	−	1.27708i	−0.216373	−	0.976311i	$-0.569423\pi$
$829$	21.2293	−	36.7702i	0.737323	−	1.27708i	0.953696	−	0.300771i	$-0.0972439\pi$
$830$	0.563672	−	0.976309i	0.0195653	−	0.0338882i
$831$	−5.68116	+	9.84006i	−0.197077	+	0.341348i
$832$	14.1967	+	24.6486i	0.492181	+	0.854535i
$833$	18.8535	−	15.9584i	0.653235	−	0.552926i
$834$	0.00479849	+	0.00831123i	0.000166158	+	0.000287794i
$835$	−66.7747			−2.31084
$836$	60.0197			2.07582
$837$	−4.62451	−	8.00989i	−0.159847	−	0.276862i
$838$	−0.0305355	−	0.0528890i	−0.00105483	−	0.00182702i
$839$	0.873903	−	1.51365i	0.0301705	−	0.0522568i	−0.850546	−	0.525901i	$-0.823728\pi$
$839$	0.873903	−	1.51365i	0.0301705	−	0.0522568i	0.880716	+	0.473644i	$0.157062\pi$
$840$	−1.41055	+	1.68838i	−0.0486686	+	0.0582545i
$841$	−34.7015	+	60.1048i	−1.19660	+	2.07258i
$842$	−0.295863			−0.0101961
$843$	3.99333	−	6.91666i	0.137538	−	0.238222i
$844$	−1.28919	−	2.23295i	−0.0443759	−	0.0768612i
$845$	19.8122	+	34.4814i	0.681561	+	1.18620i
$846$	−0.174354			−0.00599440
$847$	13.5560	−	16.2261i	0.465791	−	0.557535i
$848$	10.5535	+	18.2792i	0.362409	+	0.627711i
$849$	2.06937	+	3.58425i	0.0710205	+	0.123011i
$850$	0.523118	+	0.906068i	0.0179428	+	0.0310779i
$851$	−0.363694			−0.0124673
$852$	−5.21932	−	9.04013i	−0.178811	−	0.309710i
$853$	−55.5244			−1.90112			−0.950560	−	0.310540i	$-0.899490\pi$
$853$	−55.5244			−1.90112			−0.950560	+	0.310540i	$0.899490\pi$
$854$	0.562409	−	0.673184i	0.0192453	−	0.0230359i
$855$	10.5572	+	18.2856i	0.361049	+	0.625356i
$856$	3.04534			0.104088
$857$	14.8303	+	25.6869i	0.506595	+	0.877448i	0.999971	+	0.00763209i	$0.00242939\pi$
$857$	14.8303	+	25.6869i	0.506595	+	0.877448i	−0.493376	+	0.869816i	$0.664237\pi$
$858$	−0.535479	+	0.925251i	−0.0182809	+	0.0315875i
$859$	−10.6791	+	18.4967i	−0.364365	+	0.631098i	−0.988674	−	0.150079i	$-0.952047\pi$
$859$	−10.6791	+	18.4967i	−0.364365	+	0.631098i	0.624309	+	0.781177i	$0.285381\pi$
$860$	−5.15239	−	8.92420i	−0.175695	−	0.304313i
$861$	3.22040	+	8.78922i	0.109751	+	0.299536i
$862$	0.364899	−	0.632024i	0.0124285	−	0.0215268i
$863$	17.5615	−	30.4174i	0.597800	−	1.03542i	−0.395345	−	0.918533i	$-0.629375\pi$
$863$	17.5615	−	30.4174i	0.597800	−	1.03542i	0.993145	−	0.116887i	$-0.0372916\pi$
$864$	−0.813913			−0.0276899
$865$	−54.0918			−1.83917
$866$	0.235480	−	0.407863i	0.00800194	−	0.0138598i
$867$	−2.27423	+	3.93909i	−0.0772370	+	0.133778i
$868$	31.3056	−	37.4717i	1.06258	−	1.27187i
$869$	−21.1537	−	36.6393i	−0.717591	−	1.24290i
$870$	1.03229	−	1.78798i	0.0349980	−	0.0606183i
$871$	2.45334	+	0.00255393i	0.0831283	+	8.65365e-5i
$872$	−1.89813	−	3.28766i	−0.0642789	−	0.111334i
$873$	7.72719			0.261526
$874$	−0.783114	−	1.35639i	−0.0264892	−	0.0458807i
$875$	1.78784	+	4.87942i	0.0604399	+	0.164954i
$876$	−7.02194			−0.237249
$877$	−9.40278	−	16.2861i	−0.317509	−	0.549943i	0.662458	−	0.749099i	$-0.269513\pi$
$877$	−9.40278	−	16.2861i	−0.317509	−	0.549943i	−0.979968	+	0.199156i	$0.936180\pi$
$878$	1.71573			0.0579030
$879$	14.1626	+	24.5303i	0.477691	+	0.827385i
$880$	−26.4775	−	45.8603i	−0.892555	−	1.54595i
$881$	−22.3970	−	38.7927i	−0.754573	−	1.30696i	−0.945586	−	0.325371i	$-0.894511\pi$
$881$	−22.3970	−	38.7927i	−0.754573	−	1.30696i	0.191013	−	0.981587i	$-0.438823\pi$
$882$	0.448226	+	0.160964i	0.0150925	+	0.00541996i
$883$	−2.57264			−0.0865764			−0.0432882	−	0.999063i	$-0.513783\pi$
$883$	−2.57264			−0.0865764			−0.0432882	+	0.999063i	$0.513783\pi$
$884$	−12.6705	−	21.9988i	−0.426154	−	0.739898i
$885$	−11.5588	−	20.0204i	−0.388544	−	0.672977i
$886$	−0.592774	+	1.02672i	−0.0199146	+	0.0344932i
$887$	−36.8102			−1.23597			−0.617983	−	0.786191i	$-0.712050\pi$
$887$	−36.8102			−1.23597			−0.617983	+	0.786191i	$0.712050\pi$
$888$	0.0148209	−	0.0256706i	0.000497358	−	0.000861449i
$889$	22.6931	−	27.1628i	0.761101	−	0.911010i
$890$	−0.801720	+	1.38862i	−0.0268737	+	0.0465466i
$891$	2.17896	+	3.77408i	0.0729980	+	0.126436i
$892$	−11.5710	−	20.0415i	−0.387425	−	0.671041i
$893$	−17.6881			−0.591911
$894$	0.976721			0.0326664
$895$	14.8824	+	25.7770i	0.497462	+	0.861630i
$896$	−1.97027	−	5.37732i	−0.0658221	−	0.179644i
$897$	−12.0254	−	0.0125184i	−0.401515	−	0.000417977i
$898$	−0.402255	+	0.696726i	−0.0134234	+	0.0232501i
$899$	−45.8744	+	79.4567i	−1.53000	+	2.65003i
$900$	4.34784	−	7.53068i	0.144928	−	0.251023i
$901$	−9.37502	−	16.2380i	−0.312327	−	0.540967i
$902$	1.04900			0.0349278
$903$	−2.86370	+	3.42775i	−0.0952981	+	0.114068i
$904$	0.921196	−	1.59556i	0.0306385	−	0.0530675i
$905$	6.13852	−	10.6322i	0.204051	−	0.353427i
$906$	−1.06568			−0.0354048
$907$	−1.92469	+	3.33367i	−0.0639084	+	0.110693i	−0.896209	−	0.443632i	$-0.853690\pi$
$907$	−1.92469	+	3.33367i	−0.0639084	+	0.110693i	0.832301	+	0.554324i	$0.187023\pi$
$908$	1.59330			0.0528755
$909$	−3.88031			−0.128702
$910$	−0.681111	−	1.86492i	−0.0225786	−	0.0618214i
$911$	−47.0839			−1.55996			−0.779980	−	0.625804i	$-0.784771\pi$
$911$	−47.0839			−1.55996			−0.779980	+	0.625804i	$0.784771\pi$
$912$	−27.4174			−0.907881
$913$	11.8026	−	20.4427i	0.390609	−	0.676555i
$914$	−0.566911			−0.0187517
$915$	−7.45369	+	12.9102i	−0.246411	+	0.426797i
$916$	23.1608	−	40.1157i	0.765255	−	1.32546i
$917$	47.2382	+	8.22483i	1.55994	+	0.271608i
$918$	0.240077			0.00792371
$919$	27.8881	+	48.3036i	0.919943	+	1.59339i	0.799499	+	0.600667i	$0.205098\pi$
$919$	27.8881	+	48.3036i	0.919943	+	1.59339i	0.120443	+	0.992720i	$0.461568\pi$
$920$	−1.38670	+	2.40183i	−0.0457181	+	0.0791861i
$921$	9.03084	−	15.6419i	0.297576	−	0.515417i
$922$	0.149886	−	0.259611i	0.00493625	−	0.00854983i
$923$	18.8622	+	0.0196355i	0.620856	+	0.000646311i
$924$	−14.7505	+	17.6558i	−0.485256	+	0.580833i
$925$	0.237607	+	0.411548i	0.00781248	+	0.0135316i
$926$	1.37598			0.0452175
$927$	8.58176			0.281862
$928$	4.03694	+	6.99219i	0.132519	+	0.229530i
$929$	−19.4720	−	33.7264i	−0.638855	−	1.10653i	−0.985684	−	0.168601i	$-0.946075\pi$
$929$	−19.4720	−	33.7264i	−0.638855	−	1.10653i	0.346830	−	0.937928i	$-0.387258\pi$
$930$	0.962486	−	1.66707i	0.0315611	−	0.0546655i
$931$	45.4724	+	16.3298i	1.49030	+	0.535188i
$932$	−12.1596	+	21.0610i	−0.398299	+	0.689875i
$933$	−12.0792			−0.395455
$934$	−0.222484	+	0.385354i	−0.00727991	+	0.0126092i
$935$	23.5208	+	40.7392i	0.769211	+	1.33231i
$936$	0.490930	−	0.848275i	0.0160465	−	0.0277267i
$937$	19.5763			0.639531			0.319765	−	0.947497i	$-0.396396\pi$
$937$	19.5763			0.639531			0.319765	+	0.947497i	$0.396396\pi$
$938$	−0.120667	−	0.0210098i	−0.00393992	−	0.000685996i
$939$	10.3790	+	17.9769i	0.338705	+	0.586654i
$940$	7.82124	+	13.5468i	0.255101	+	0.441848i
$941$	3.84200	+	6.65455i	0.125246	+	0.216932i	0.921829	−	0.387597i	$-0.126695\pi$
$941$	3.84200	+	6.65455i	0.125246	+	0.216932i	−0.796583	+	0.604529i	$0.793361\pi$
$942$	−0.918515			−0.0299268
$943$	5.90001	+	10.2191i	0.192131	+	0.332780i
$944$	30.0184			0.977017
$945$	−7.97359	−	1.38831i	−0.259381	−	0.0451618i
$946$	0.250273	+	0.433485i	0.00813707	+	0.0140938i
$947$	34.3969			1.11775			0.558874	−	0.829253i	$-0.311234\pi$
$947$	34.3969			1.11775			0.558874	+	0.829253i	$0.311234\pi$
$948$	9.68569	+	16.7761i	0.314576	+	0.544862i
$949$	6.35561	−	10.9818i	0.206312	−	0.356485i
$950$	−1.02324	+	1.77231i	−0.0331984	+	0.0575012i
$951$	8.73476	+	15.1290i	0.283244	+	0.490593i
$952$	0.873094	+	2.38288i	0.0282971	+	0.0772294i
$953$	−23.8888	+	41.3766i	−0.773834	+	1.34032i	0.161613	+	0.986854i	$0.448330\pi$
$953$	−23.8888	+	41.3766i	−0.773834	+	1.34032i	−0.935447	+	0.353466i	$0.885003\pi$
$954$	0.180759	−	0.313083i	0.00585228	−	0.0101364i
$955$	45.2449			1.46409
$956$	0.966423			0.0312563
$957$	21.6150	−	37.4382i	0.698712	−	1.21020i
$958$	0.265794	−	0.460369i	0.00858742	−	0.0148739i
$959$	19.4249	+	53.0151i	0.627263	+	1.71195i
$960$	12.0667	+	20.9001i	0.389451	+	0.674549i
$961$	−27.2722	+	47.2369i	−0.879749	+	1.52377i
$962$	0.0133508	+	0.0231799i	0.000430446	+	0.000747349i
$963$	5.60158	+	9.70222i	0.180508	+	0.312650i
$964$	4.62951			0.149106
$965$	34.1746	+	59.1921i	1.10012	+	1.90546i
$966$	0.591465	+	0.102982i	0.0190301	+	0.00331340i
$967$	52.1099			1.67574			0.837871	−	0.545869i	$-0.183800\pi$
$967$	52.1099			1.67574			0.837871	+	0.545869i	$0.183800\pi$
$968$	1.08617	+	1.88129i	0.0349107	+	0.0604671i
$969$	24.3557			0.782419
$970$	0.804118	+	1.39277i	0.0258187	+	0.0447192i
$971$	−10.3147	−	17.8656i	−0.331014	−	0.573333i	0.651697	−	0.758479i	$-0.274057\pi$
$971$	−10.3147	−	17.8656i	−0.331014	−	0.573333i	−0.982711	+	0.185146i	$0.940724\pi$
$972$	−0.997686	−	1.72804i	−0.0320008	−	0.0554270i
$973$	−0.367671	−	0.0640167i	−0.0117870	−	0.00205228i
$974$	−1.43380			−0.0459418
$975$	7.84220	+	13.6158i	0.251151	+	0.436054i
$976$	−9.67871	−	16.7640i	−0.309808	−	0.536603i
$977$	12.9795	−	22.4811i	0.415251	−	0.719235i	−0.580204	−	0.814471i	$-0.697027\pi$
$977$	12.9795	−	22.4811i	0.415251	−	0.719235i	0.995455	+	0.0952360i	$0.0303606\pi$
$978$	0.180788			0.00578096
$979$	−16.7871	+	29.0760i	−0.536516	+	0.929274i
$980$	−7.60024	−	42.0465i	−0.242781	−	1.34313i
$981$	6.98282	−	12.0946i	0.222944	−	0.386151i
$982$	−0.297258	−	0.514866i	−0.00948588	−	0.0164300i
$983$	−19.0424	−	32.9825i	−0.607359	−	1.05198i	−0.991674	−	0.128775i	$-0.958896\pi$
$983$	−19.0424	−	32.9825i	−0.607359	−	1.05198i	0.384315	−	0.923202i	$-0.374438\pi$
$984$	−0.961727			−0.0306587
$985$	−19.3506			−0.616561
$986$	−1.19076	−	2.06246i	−0.0379215	−	0.0656820i
$987$	4.34705	−	5.20326i	0.138368	−	0.165622i
$988$	24.8735	−	42.9788i	0.791332	−	1.36734i
$989$	−2.81528	+	4.87621i	−0.0895207	+	0.155054i
$990$	−0.453501	+	0.785487i	−0.0144132	+	0.0249644i
$991$	30.6807	−	53.1406i	0.974605	−	1.68807i	0.293373	−	0.955998i	$-0.405222\pi$
$991$	30.6807	−	53.1406i	0.974605	−	1.68807i	0.681232	−	0.732068i	$-0.261445\pi$
$992$	3.76395	+	6.51936i	0.119506	+	0.206990i
$993$	−7.12617			−0.226142
$994$	−0.927733	−	0.161531i	−0.0294259	−	0.00512346i
$995$	−9.23254	+	15.9912i	−0.292691	+	0.506956i
$996$	−5.40408	+	9.36014i	−0.171235	+	0.296587i
$997$	−19.3317			−0.612240			−0.306120	−	0.951993i	$-0.599031\pi$
$997$	−19.3317			−0.612240			−0.306120	+	0.951993i	$0.599031\pi$
$998$	−0.724082	+	1.25415i	−0.0229204	+	0.0396993i
$999$	0.109046			0.00345006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.b.16.5	yes	16
3.2	odd	2		819.2.s.e.289.4		16
7.4	even	3		273.2.j.b.172.4	yes	16
13.9	even	3		273.2.j.b.100.4	✓	16
21.11	odd	6		819.2.n.e.172.5		16
39.35	odd	6		819.2.n.e.100.5		16
91.74	even	3	inner	273.2.l.b.256.5	yes	16
273.74	odd	6		819.2.s.e.802.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.4	✓	16	13.9	even	3
273.2.j.b.172.4	yes	16	7.4	even	3
273.2.l.b.16.5	yes	16	1.1	even	1	trivial
273.2.l.b.256.5	yes	16	91.74	even	3	inner
819.2.n.e.100.5		16	39.35	odd	6
819.2.n.e.172.5		16	21.11	odd	6
819.2.s.e.289.4		16	3.2	odd	2
819.2.s.e.802.4		16	273.74	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.0680360 q^{2} +(0.500000 - 0.866025i) q^{3} -1.99537 q^{4} +(1.52954 - 2.64923i) q^{5} +(0.0340180 - 0.0589209i) q^{6} +(0.910236 + 2.48424i) q^{7} -0.271829 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+0.0680360 q^{2} +(0.500000 - 0.866025i) q^{3} -1.99537 q^{4} +(1.52954 - 2.64923i) q^{5} +(0.0340180 - 0.0589209i) q^{6} +(0.910236 + 2.48424i) q^{7} -0.271829 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.104063 - 0.180243i) q^{10} +(2.17896 - 3.77408i) q^{11} +(-0.997686 + 1.72804i) q^{12} +(-1.79952 - 3.12437i) q^{13} +(0.0619288 + 0.169018i) q^{14} +(-1.52954 - 2.64923i) q^{15} +3.97225 q^{16} -3.52867 q^{17} +(-0.0340180 - 0.0589209i) q^{18} +(-3.45112 - 5.97751i) q^{19} +(-3.05199 + 5.28621i) q^{20} +(2.60654 + 0.453835i) q^{21} +(0.148248 - 0.256773i) q^{22} +3.33524 q^{23} +(-0.135914 + 0.235411i) q^{24} +(-2.17896 - 3.77408i) q^{25} +(-0.122432 - 0.212570i) q^{26} -1.00000 q^{27} +(-1.81626 - 4.95699i) q^{28} +(4.95991 + 8.59082i) q^{29} +(-0.104063 - 0.180243i) q^{30} +(4.62451 + 8.00989i) q^{31} +0.813913 q^{32} +(-2.17896 - 3.77408i) q^{33} -0.240077 q^{34} +(7.97359 + 1.38831i) q^{35} +(0.997686 + 1.72804i) q^{36} -0.109046 q^{37} +(-0.234800 - 0.406686i) q^{38} +(-3.60555 - 0.00375337i) q^{39} +(-0.415772 + 0.720139i) q^{40} +(1.76899 + 3.06399i) q^{41} +(0.177338 + 0.0308771i) q^{42} +(-0.844102 + 1.46203i) q^{43} +(-4.34784 + 7.53068i) q^{44} -3.05907 q^{45} +0.226916 q^{46} +(1.28133 - 2.21933i) q^{47} +(1.98612 - 3.44007i) q^{48} +(-5.34294 + 4.52250i) q^{49} +(-0.148248 - 0.256773i) q^{50} +(-1.76434 + 3.05592i) q^{51} +(3.59072 + 6.23429i) q^{52} +(2.65681 + 4.60173i) q^{53} -0.0680360 q^{54} +(-6.66561 - 11.5452i) q^{55} +(-0.247428 - 0.675289i) q^{56} -6.90224 q^{57} +(0.337453 + 0.584485i) q^{58} +7.55704 q^{59} +(3.05199 + 5.28621i) q^{60} +(-2.43658 - 4.22029i) q^{61} +(0.314633 + 0.544960i) q^{62} +(1.69630 - 2.03041i) q^{63} -7.88912 q^{64} +(-11.0296 - 0.0114818i) q^{65} +(-0.148248 - 0.256773i) q^{66} +(-0.340218 + 0.589274i) q^{67} +7.04101 q^{68} +(1.66762 - 2.88840i) q^{69} +(0.542491 + 0.0944552i) q^{70} +(-2.61572 + 4.53055i) q^{71} +(0.135914 + 0.235411i) q^{72} +(1.75956 + 3.04764i) q^{73} -0.00741905 q^{74} -4.35793 q^{75} +(6.88626 + 11.9274i) q^{76} +(11.3591 + 1.97778i) q^{77} +(-0.245307 - 0.000255364i) q^{78} +(4.85408 - 8.40751i) q^{79} +(6.07570 - 10.5234i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.120355 + 0.208461i) q^{82} +5.41662 q^{83} +(-5.20101 - 0.905568i) q^{84} +(-5.39723 + 9.34828i) q^{85} +(-0.0574293 + 0.0994705i) q^{86} +9.91983 q^{87} +(-0.592305 + 1.02590i) q^{88} -7.70414 q^{89} -0.208127 q^{90} +(6.12372 - 7.31438i) q^{91} -6.65503 q^{92} +9.24902 q^{93} +(0.0871768 - 0.150995i) q^{94} -21.1144 q^{95} +(0.406957 - 0.704870i) q^{96} +(-3.86359 + 6.69194i) q^{97} +(-0.363512 + 0.307692i) q^{98} -4.35793 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25} + 33 q^{26} - 16 q^{27} - q^{28} + 15 q^{29} + 4 q^{30} + 3 q^{31} - 6 q^{32} + 2 q^{33} - 68 q^{34} - 6 q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - 25 q^{40} + 19 q^{41} - 17 q^{42} + 11 q^{43} - 16 q^{44} - 4 q^{46} + 5 q^{47} + 6 q^{48} + 7 q^{49} - 7 q^{50} + 2 q^{51} - 18 q^{52} + 36 q^{53} - 15 q^{55} - 51 q^{56} - 22 q^{57} + 20 q^{58} + 34 q^{59} + 20 q^{60} - 22 q^{61} - 6 q^{62} - 2 q^{63} - 20 q^{64} - 24 q^{65} - 7 q^{66} + 26 q^{67} - 10 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} - 6 q^{72} - 6 q^{73} - 30 q^{74} + 4 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} - 28 q^{80} - 8 q^{81} - q^{82} + 36 q^{83} - 8 q^{84} - 4 q^{85} + 16 q^{86} + 30 q^{87} + 24 q^{88} - 40 q^{89} + 8 q^{90} - 10 q^{91} - 94 q^{92} + 6 q^{93} - 20 q^{94} - 3 q^{96} + 7 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

Introduction

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