LMFDB - Embedded newform 273.2.j.b.172.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(100,273)]

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, 4]))

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

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

chi := DirichletCharacter("273.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.j (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			172.4
Root			$-0.0340180 + 0.0589209i$ of defining polynomial
Character	$\chi$	$=$	273.172
Dual form			273.2.j.b.100.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0340180 + 0.0589209i) q^{2} -1.00000 q^{3} +(0.997686 + 1.72804i) q^{4} +(1.52954 + 2.64923i) q^{5} +(0.0340180 - 0.0589209i) q^{6} +(-2.60654 + 0.453835i) q^{7} -0.271829 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.0340180 + 0.0589209i) q^{2} -1.00000 q^{3} +(0.997686 + 1.72804i) q^{4} +(1.52954 + 2.64923i) q^{5} +(0.0340180 - 0.0589209i) q^{6} +(-2.60654 + 0.453835i) q^{7} -0.271829 q^{8} +1.00000 q^{9} -0.208127 q^{10} -4.35793 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} +(-1.98612 + 3.44007i) q^{16} +(1.76434 + 3.05592i) q^{17} +(-0.0340180 + 0.0589209i) q^{18} +6.90224 q^{19} +(-3.05199 + 5.28621i) q^{20} +(2.60654 - 0.453835i) q^{21} +(0.148248 - 0.256773i) q^{22} +(-1.66762 + 2.88840i) q^{23} +0.271829 q^{24} +(-2.17896 + 3.77408i) q^{25} +(0.245307 + 0.000255364i) q^{26} -1.00000 q^{27} +(-3.38475 - 4.05142i) q^{28} +(4.95991 + 8.59082i) q^{29} +0.208127 q^{30} +(4.62451 - 8.00989i) q^{31} +(-0.406957 - 0.704870i) q^{32} +4.35793 q^{33} -0.240077 q^{34} +(-5.18911 - 6.21117i) q^{35} +(0.997686 + 1.72804i) q^{36} +(0.0545230 - 0.0944366i) q^{37} +(-0.234800 + 0.406686i) q^{38} +(1.79952 + 3.12437i) q^{39} +(-0.415772 - 0.720139i) q^{40} +(1.76899 + 3.06399i) q^{41} +(-0.0619288 + 0.169018i) q^{42} +(-0.844102 + 1.46203i) q^{43} +(-4.34784 - 7.53068i) q^{44} +(1.52954 + 2.64923i) q^{45} +(-0.113458 - 0.196515i) q^{46} +(1.28133 + 2.21933i) q^{47} +(1.98612 - 3.44007i) q^{48} +(6.58807 - 2.36587i) q^{49} +(-0.148248 - 0.256773i) q^{50} +(-1.76434 - 3.05592i) q^{51} +(3.60369 - 6.22680i) q^{52} +(2.65681 - 4.60173i) q^{53} +(0.0340180 - 0.0589209i) q^{54} +(-6.66561 - 11.5452i) q^{55} +(0.708532 - 0.123365i) q^{56} -6.90224 q^{57} -0.674905 q^{58} +(-3.77852 - 6.54459i) q^{59} +(3.05199 - 5.28621i) q^{60} +4.87317 q^{61} +(0.314633 + 0.544960i) q^{62} +(-2.60654 + 0.453835i) q^{63} -7.88912 q^{64} +(5.52476 - 9.54621i) q^{65} +(-0.148248 + 0.256773i) q^{66} +0.680435 q^{67} +(-3.52051 + 6.09770i) q^{68} +(1.66762 - 2.88840i) q^{69} +(0.542491 - 0.0944552i) q^{70} +(-2.61572 + 4.53055i) q^{71} -0.271829 q^{72} +(1.75956 - 3.04764i) q^{73} +(0.00370952 + 0.00642508i) q^{74} +(2.17896 - 3.77408i) 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} -12.1514 q^{80} +1.00000 q^{81} -0.240710 q^{82} +5.41662 q^{83} +(3.38475 + 4.05142i) q^{84} +(-5.39723 + 9.34828i) q^{85} +(-0.0574293 - 0.0994705i) q^{86} +(-4.95991 - 8.59082i) q^{87} +1.18461 q^{88} +(3.85207 - 6.67198i) q^{89} -0.208127 q^{90} +(6.10848 + 7.32711i) q^{91} -6.65503 q^{92} +(-4.62451 + 8.00989i) q^{93} -0.174354 q^{94} +(10.5572 + 18.2856i) q^{95} +(0.406957 + 0.704870i) q^{96} +(-3.86359 + 6.69194i) q^{97} +(-0.0847135 + 0.468657i) q^{98} -4.35793 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9} + 8 q^{10} + 4 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} - 6 q^{16} - 2 q^{17} + 22 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} + 4 q^{23} - 12 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{27} - 7 q^{28} + 15 q^{29} - 8 q^{30} + 3 q^{31} + 3 q^{32} - 4 q^{33} - 68 q^{34} - 12 q^{35} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 5 q^{39} - 25 q^{40} + 19 q^{41} + 7 q^{42} + 11 q^{43} - 16 q^{44} + 2 q^{46} + 5 q^{47} + 6 q^{48} + 13 q^{49} - 7 q^{50} + 2 q^{51} + 36 q^{52} + 36 q^{53} - 15 q^{55} + 39 q^{56} - 22 q^{57} - 40 q^{58} - 17 q^{59} + 20 q^{60} + 44 q^{61} - 6 q^{62} + q^{63} - 20 q^{64} - 21 q^{65} - 7 q^{66} - 52 q^{67} + 5 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} + 12 q^{72} - 6 q^{73} + 15 q^{74} - 2 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} + 56 q^{80} + 16 q^{81} + 2 q^{82} + 36 q^{83} + 7 q^{84} - 4 q^{85} + 16 q^{86} - 15 q^{87} - 48 q^{88} + 20 q^{89} + 8 q^{90} - 7 q^{91} - 94 q^{92} - 3 q^{93} + 40 q^{94} - 3 q^{96} + 7 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9 + 8 * q^10 + 4 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 - 6 * q^16 - 2 * q^17 + 22 * q^19 - 20 * q^20 - q^21 + 7 * q^22 + 4 * q^23 - 12 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^27 - 7 * q^28 + 15 * q^29 - 8 * q^30 + 3 * q^31 + 3 * q^32 - 4 * q^33 - 68 * q^34 - 12 * q^35 - 6 * q^36 + 4 * q^37 + 2 * q^38 - 5 * q^39 - 25 * q^40 + 19 * q^41 + 7 * q^42 + 11 * q^43 - 16 * q^44 + 2 * q^46 + 5 * q^47 + 6 * q^48 + 13 * q^49 - 7 * q^50 + 2 * q^51 + 36 * q^52 + 36 * q^53 - 15 * q^55 + 39 * q^56 - 22 * q^57 - 40 * q^58 - 17 * q^59 + 20 * q^60 + 44 * q^61 - 6 * q^62 + q^63 - 20 * q^64 - 21 * q^65 - 7 * q^66 - 52 * q^67 + 5 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 + 12 * q^72 - 6 * q^73 + 15 * q^74 - 2 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 + 56 * q^80 + 16 * q^81 + 2 * q^82 + 36 * q^83 + 7 * q^84 - 4 * q^85 + 16 * q^86 - 15 * q^87 - 48 * q^88 + 20 * q^89 + 8 * q^90 - 7 * q^91 - 94 * q^92 - 3 * q^93 + 40 * q^94 - 3 * q^96 + 7 * q^97 - 3 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.0340180	+	0.0589209i	−0.0240543	+	0.0416633i	−0.877802	−	0.479024i	$-0.840991\pi$
$2$	−0.0340180	+	0.0589209i	−0.0240543	+	0.0416633i	0.853748	+	0.520687i	$0.174324\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.997686	+	1.72804i	0.498843	+	0.864021i
$5$	1.52954	+	2.64923i	0.684030	+	1.18477i	0.973741	+	0.227660i	$0.0731074\pi$
$5$	1.52954	+	2.64923i	0.684030	+	1.18477i	−0.289711	+	0.957114i	$0.593559\pi$
$6$	0.0340180	−	0.0589209i	0.0138878	−	0.0240543i
$7$	−2.60654	+	0.453835i	−0.985178	+	0.171533i
$7$	−2.60654	+	0.453835i	−0.985178	+	0.171533i
$8$	−0.271829			−0.0961060
$9$	1.00000			0.333333
$10$	−0.208127			−0.0658155
$11$	−4.35793			−1.31396			−0.656982	−	0.753906i	$-0.728167\pi$
$11$	−4.35793			−1.31396			−0.656982	+	0.753906i	$0.728167\pi$
$12$	−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
$16$	−1.98612	+	3.44007i	−0.496531	+	0.860017i
$17$	1.76434	+	3.05592i	0.427914	+	0.741170i	0.996688	−	0.0813248i	$-0.0259151\pi$
$17$	1.76434	+	3.05592i	0.427914	+	0.741170i	−0.568773	+	0.822494i	$0.692582\pi$
$18$	−0.0340180	+	0.0589209i	−0.00801811	+	0.0138878i
$19$	6.90224			1.58348			0.791741	−	0.610857i	$-0.209175\pi$
$19$	6.90224			1.58348			0.791741	+	0.610857i	$0.209175\pi$
$20$	−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
$23$	−1.66762	+	2.88840i	−0.347722	+	0.602273i	−0.985844	−	0.167662i	$-0.946378\pi$
$23$	−1.66762	+	2.88840i	−0.347722	+	0.602273i	0.638122	+	0.769935i	$0.279711\pi$
$24$	0.271829			0.0554868
$25$	−2.17896	+	3.77408i	−0.435793	+	0.754815i
$26$	0.245307		0.000255364i	0.0481087		5.00811e-5i
$27$	−1.00000			−0.192450
$28$	−3.38475	−	4.05142i	−0.639658	−	0.765647i
$29$	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	$0.460680\pi$
$30$	0.208127			0.0379986
$31$	4.62451	−	8.00989i	0.830587	−	1.43862i	−0.0669867	−	0.997754i	$-0.521339\pi$
$31$	4.62451	−	8.00989i	0.830587	−	1.43862i	0.897574	−	0.440865i	$-0.145328\pi$
$32$	−0.406957	−	0.704870i	−0.0719405	−	0.124605i
$33$	4.35793			0.758618
$34$	−0.240077			−0.0411728
$35$	−5.18911	−	6.21117i	−0.877119	−	1.04988i
$36$	0.997686	+	1.72804i	0.166281	+	0.288007i
$37$	0.0545230	−	0.0944366i	0.00896352	−	0.0155253i	−0.861509	−	0.507743i	$-0.830480\pi$
$37$	0.0545230	−	0.0944366i	0.00896352	−	0.0155253i	0.870472	+	0.492217i	$0.163813\pi$
$38$	−0.234800	+	0.406686i	−0.0380896	+	0.0659731i
$39$	1.79952	+	3.12437i	0.288154	+	0.500300i
$40$	−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	$0.744235\pi$
$42$	−0.0619288	+	0.169018i	−0.00955582	+	0.0260800i
$43$	−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
$45$	1.52954	+	2.64923i	0.228010	+	0.394925i
$46$	−0.113458	−	0.196515i	−0.0167285	−	0.0289746i
$47$	1.28133	+	2.21933i	0.186902	+	0.323723i	0.944216	−	0.329328i	$-0.106822\pi$
$47$	1.28133	+	2.21933i	0.186902	+	0.323723i	−0.757314	+	0.653051i	$0.773489\pi$
$48$	1.98612	−	3.44007i	0.286672	−	0.496531i
$49$	6.58807	−	2.36587i	0.941153	−	0.337982i
$50$	−0.148248	−	0.256773i	−0.0209654	−	0.0363132i
$51$	−1.76434	−	3.05592i	−0.247057	−	0.427914i
$52$	3.60369	−	6.22680i	0.499742	−	0.863501i
$53$	2.65681	−	4.60173i	0.364941	−	0.632097i	−0.623825	−	0.781564i	$-0.714422\pi$
$53$	2.65681	−	4.60173i	0.364941	−	0.632097i	0.988767	+	0.149467i	$0.0477557\pi$
$54$	0.0340180	−	0.0589209i	0.00462926	−	0.00801811i
$55$	−6.66561	−	11.5452i	−0.898791	−	1.55675i
$56$	0.708532	−	0.123365i	0.0946816	−	0.0164854i
$57$	−6.90224			−0.914224
$58$	−0.674905			−0.0886194
$59$	−3.77852	−	6.54459i	−0.491921	−	0.852033i	0.508035	−	0.861336i	$-0.330372\pi$
$59$	−3.77852	−	6.54459i	−0.491921	−	0.852033i	−0.999957	+	0.00930353i	$0.997039\pi$
$60$	3.05199	−	5.28621i	0.394011	−	0.682446i
$61$	4.87317			0.623945			0.311973	−	0.950091i	$-0.399010\pi$
$61$	4.87317			0.623945			0.311973	+	0.950091i	$0.399010\pi$
$62$	0.314633	+	0.544960i	0.0399584	+	0.0692101i
$63$	−2.60654	+	0.453835i	−0.328393	+	0.0571778i
$64$	−7.88912			−0.986140
$65$	5.52476	−	9.54621i	0.685263	−	1.18406i
$66$	−0.148248	+	0.256773i	−0.0182481	+	0.0316066i
$67$	0.680435			0.0831284			0.0415642	−	0.999136i	$-0.486766\pi$
$67$	0.680435			0.0831284			0.0415642	+	0.999136i	$0.486766\pi$
$68$	−3.52051	+	6.09770i	−0.426924	+	0.739454i
$69$	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	$0.267139\pi$
$72$	−0.271829			−0.0320353
$73$	1.75956	−	3.04764i	0.205941	−	0.356699i	−0.744491	−	0.667632i	$-0.767308\pi$
$73$	1.75956	−	3.04764i	0.205941	−	0.356699i	0.950432	+	0.310933i	$0.100641\pi$
$74$	0.00370952	+	0.00642508i	0.000431223	+	0.000746901i
$75$	2.17896	−	3.77408i	0.251605	−	0.435793i
$76$	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	0.998535	+	0.0541080i	$0.0172315\pi$
$79$	4.85408	+	8.40751i	0.546126	+	0.945919i	−0.452409	+	0.891811i	$0.649435\pi$
$80$	−12.1514			−1.35857
$81$	1.00000			0.111111
$82$	−0.240710			−0.0265820
$83$	5.41662			0.594551			0.297275	−	0.954792i	$-0.403922\pi$
$83$	5.41662			0.594551			0.297275	+	0.954792i	$0.403922\pi$
$84$	3.38475	+	4.05142i	0.369306	+	0.442046i
$85$	−5.39723	+	9.34828i	−0.585412	+	1.01396i
$86$	−0.0574293	−	0.0994705i	−0.00619276	−	0.0107262i
$87$	−4.95991	−	8.59082i	−0.531759	−	0.921033i
$88$	1.18461			0.126280
$89$	3.85207	−	6.67198i	0.408319	−	0.707229i	−0.586383	−	0.810034i	$-0.699449\pi$
$89$	3.85207	−	6.67198i	0.408319	−	0.707229i	0.994702	+	0.102805i	$0.0327818\pi$
$90$	−0.208127			−0.0219385
$91$	6.10848	+	7.32711i	0.640342	+	0.768090i
$92$	−6.65503			−0.693835
$93$	−4.62451	+	8.00989i	−0.479540	+	0.830587i
$94$	−0.174354			−0.0179832
$95$	10.5572	+	18.2856i	1.08315	+	1.87607i
$96$	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	$0.294983\pi$
$98$	−0.0847135	+	0.468657i	−0.00855735	+	0.0473415i
$99$	−4.35793			−0.437988
$100$	−8.69568			−0.869568
$101$	−3.88031			−0.386105			−0.193053	−	0.981188i	$-0.561839\pi$
$101$	−3.88031			−0.386105			−0.193053	+	0.981188i	$0.561839\pi$
$102$	0.240077			0.0237711
$103$	−4.29088	−	7.43202i	−0.422793	−	0.732299i	0.573419	−	0.819263i	$-0.305617\pi$
$103$	−4.29088	−	7.43202i	−0.422793	−	0.732299i	−0.996211	+	0.0869638i	$0.972284\pi$
$104$	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
$107$	5.60158	−	9.70222i	0.541525	−	0.937949i	−0.457291	−	0.889317i	$-0.651180\pi$
$107$	5.60158	−	9.70222i	0.541525	−	0.937949i	0.998817	−	0.0486324i	$-0.0154863\pi$
$108$	−0.997686	−	1.72804i	−0.0960023	−	0.166281i
$109$	6.98282	−	12.0946i	0.668833	−	1.15845i	−0.309398	−	0.950933i	$-0.600128\pi$
$109$	6.98282	−	12.0946i	0.668833	−	1.15845i	0.978231	−	0.207520i	$-0.0665391\pi$
$110$	0.907002			0.0864793
$111$	−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	$0.269946\pi$
$114$	0.234800	−	0.406686i	0.0219910	−	0.0380896i
$115$	−10.2027			−0.951410
$116$	−9.89687	+	17.1419i	−0.918901	+	1.59158i
$117$	−1.79952	−	3.12437i	−0.166366	−	0.288848i
$118$	0.514150			0.0473314
$119$	−5.98569	−	7.16465i	−0.548707	−	0.656783i
$120$	0.415772	+	0.720139i	0.0379546	+	0.0657394i
$121$	7.99154			0.726503
$122$	−0.165775	+	0.287131i	−0.0150086	+	0.0259956i
$123$	−1.76899	−	3.06399i	−0.159505	−	0.276270i
$124$	18.4552			1.65733
$125$	1.96415			0.175679
$126$	0.0619288	−	0.169018i	0.00551705	−	0.0150573i
$127$	−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	$-0.368941\pi$
$128$	1.08229	−	1.87457i	0.0956614	−	0.165690i
$129$	0.844102	−	1.46203i	0.0743191	−	0.128724i
$130$	0.374529	+	0.650266i	0.0328484	+	0.0570321i
$131$	9.06148	+	15.6949i	0.791705	+	1.37127i	0.924910	+	0.380185i	$0.124140\pi$
$131$	9.06148	+	15.6949i	0.791705	+	1.37127i	−0.133205	+	0.991089i	$0.542527\pi$
$132$	4.34784	+	7.53068i	0.378431	+	0.655462i
$133$	−17.9909	+	3.13247i	−1.56001	+	0.271620i
$134$	−0.0231470	+	0.0400918i	−0.00199960	+	0.00346341i
$135$	−1.52954	−	2.64923i	−0.131642	−	0.228010i
$136$	−0.479598	−	0.830688i	−0.0411252	−	0.0712309i
$137$	−10.6703	−	18.4814i	−0.911622	−	1.57898i	−0.811773	−	0.583973i	$-0.801497\pi$
$137$	−10.6703	−	18.4814i	−0.911622	−	1.57898i	−0.0998490	−	0.995003i	$-0.531836\pi$
$138$	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	$0.168571\pi$
$140$	5.55607	−	15.1638i	0.469573	−	1.28157i
$141$	−1.28133	−	2.21933i	−0.107908	−	0.186902i
$142$	−0.177963	−	0.308240i	−0.0149343	−	0.0258670i
$143$	7.84220	+	13.6158i	0.655797	+	1.13861i
$144$	−1.98612	+	3.44007i	−0.165510	+	0.286672i
$145$	−15.1727	+	26.2800i	−1.26003	+	2.18243i
$146$	0.119713	+	0.207349i	0.00990753	+	0.0171603i
$147$	−6.58807	+	2.36587i	−0.543375	+	0.195134i
$148$	0.217587			0.0178856
$149$	−14.3559			−1.17609			−0.588043	−	0.808830i	$-0.700101\pi$
$149$	−14.3559			−1.17609			−0.588043	+	0.808830i	$0.700101\pi$
$150$	0.148248	+	0.256773i	0.0121044	+	0.0209654i
$151$	−7.83172	+	13.5649i	−0.637336	+	1.10390i	0.348679	+	0.937242i	$0.386631\pi$
$151$	−7.83172	+	13.5649i	−0.637336	+	1.10390i	−0.986015	+	0.166657i	$0.946703\pi$
$152$	−1.87623			−0.152182
$153$	1.76434	+	3.05592i	0.142638	+	0.247057i
$154$	−0.269881	+	0.736568i	−0.0217476	+	0.0593543i
$155$	28.2934			2.27258
$156$	−3.60369	+	6.22680i	−0.288526	+	0.498543i
$157$	−6.75022	+	11.6917i	−0.538726	+	0.933101i	0.460247	+	0.887791i	$0.347761\pi$
$157$	−6.75022	+	11.6917i	−0.538726	+	0.933101i	−0.998973	+	0.0453098i	$0.985572\pi$
$158$	−0.660504			−0.0525469
$159$	−2.65681	+	4.60173i	−0.210699	+	0.364941i
$160$	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
$163$	−2.65724			−0.208131			−0.104066	−	0.994570i	$-0.533185\pi$
$163$	−2.65724			−0.208131			−0.104066	+	0.994570i	$0.533185\pi$
$164$	−3.52980	+	6.11379i	−0.275631	+	0.477407i
$165$	6.66561	+	11.5452i	0.518917	+	0.898791i
$166$	−0.184262	+	0.319152i	−0.0143015	+	0.0247710i
$167$	−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
$171$	6.90224			0.527827
$172$	−3.36860			−0.256853
$173$	17.6824			1.34437			0.672184	−	0.740384i	$-0.265356\pi$
$173$	17.6824			1.34437			0.672184	+	0.740384i	$0.265356\pi$
$174$	0.674905			0.0511644
$175$	3.96674	−	10.8262i	0.299858	−	0.818381i
$176$	8.65539	−	14.9916i	0.652424	−	1.13003i
$177$	3.77852	+	6.54459i	0.284011	+	0.491921i
$178$	0.262079	+	0.453935i	0.0196437	+	0.0340239i
$179$	9.72998			0.727253			0.363626	−	0.931545i	$-0.381538\pi$
$179$	9.72998			0.727253			0.363626	+	0.931545i	$0.381538\pi$
$180$	−3.05199	+	5.28621i	−0.227482	+	0.394011i
$181$	4.01332			0.298308			0.149154	−	0.988814i	$-0.452345\pi$
$181$	4.01332			0.298308			0.149154	+	0.988814i	$0.452345\pi$
$182$	−0.639518	+	0.110663i	−0.0474042	+	0.00820290i
$183$	−4.87317			−0.360235
$184$	0.453307	−	0.785150i	0.0334182	−	0.0578820i
$185$	0.333580			0.0245253
$186$	−0.314633	−	0.544960i	−0.0230700	−	0.0399584i
$187$	−7.68885	−	13.3175i	−0.562265	−	0.973871i
$188$	−2.55674	+	4.42840i	−0.186469	+	0.322974i
$189$	2.60654	−	0.453835i	0.189598	−	0.0330116i
$190$	−1.43654			−0.104218
$191$	−14.7904			−1.07019			−0.535097	−	0.844790i	$-0.679725\pi$
$191$	−14.7904			−1.07019			−0.535097	+	0.844790i	$0.679725\pi$
$192$	7.88912			0.569348
$193$	22.3431			1.60829			0.804146	−	0.594432i	$-0.202623\pi$
$193$	22.3431			1.60829			0.804146	+	0.594432i	$0.202623\pi$
$194$	−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	$0.905683\pi$
$198$	0.148248	−	0.256773i	0.0105355	−	0.0182481i
$199$	3.01808	+	5.22748i	0.213946	+	0.370566i	0.952946	−	0.303140i	$-0.0980349\pi$
$199$	3.01808	+	5.22748i	0.213946	+	0.370566i	−0.739000	+	0.673706i	$0.764702\pi$
$200$	0.592305	−	1.02590i	0.0418823	−	0.0725423i
$201$	−0.680435			−0.0479942
$202$	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
$205$	−5.41148	+	9.37295i	−0.377954	+	0.654636i
$206$	0.583868			0.0406800
$207$	−1.66762	+	2.88840i	−0.115907	+	0.200758i
$208$	14.3221	+	0.0149093i	0.993061	+	0.00103378i
$209$	−30.0795			−2.08064
$210$	−0.542491	+	0.0944552i	−0.0374354	+	0.00651803i
$211$	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	$0.819171\pi$
$212$	10.6027			0.728193
$213$	2.61572	−	4.53055i	0.179226	−	0.310428i
$214$	0.381109	+	0.660100i	0.0260521	+	0.0451235i
$215$	−5.16434			−0.352205
$216$	0.271829			0.0184956
$217$	−8.41880	+	22.9768i	−0.571505	+	1.55977i
$218$	0.475083	+	0.822868i	0.0321767	+	0.0557316i
$219$	−1.75956	+	3.04764i	−0.118900	+	0.205941i
$220$	13.3004	−	23.0369i	0.896710	−	1.55315i
$221$	6.37287	−	11.0117i	0.428686	−	0.740724i
$222$	−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	$0.706387\pi$
$224$	1.38064	+	1.65258i	0.0922480	+	0.110418i
$225$	−2.17896	+	3.77408i	−0.145264	+	0.251605i
$226$	−0.230566	−	0.399352i	−0.0153370	−	0.0265645i
$227$	0.399249	+	0.691520i	0.0264991	+	0.0458978i	0.878971	−	0.476876i	$-0.158231\pi$
$227$	0.399249	+	0.691520i	0.0264991	+	0.0458978i	−0.852472	+	0.522773i	$0.824897\pi$
$228$	−6.88626	−	11.9274i	−0.456054	−	0.789908i
$229$	−11.6073	−	20.1044i	−0.767030	−	1.32854i	−0.939166	−	0.343463i	$-0.888400\pi$
$229$	−11.6073	−	20.1044i	−0.767030	−	1.32854i	0.172136	−	0.985073i	$-0.444933\pi$
$230$	0.347076	−	0.601154i	0.0228855	−	0.0396389i
$231$	−11.3591	+	1.97778i	−0.747374	+	0.130128i
$232$	−1.34825	−	2.33523i	−0.0885168	−	0.153316i
$233$	6.09388	+	10.5549i	0.399223	+	0.691475i	0.993630	−	0.112689i	$-0.0359465\pi$
$233$	6.09388	+	10.5549i	0.399223	+	0.691475i	−0.594407	+	0.804164i	$0.702613\pi$
$234$	0.245307		0.000255364i	0.0160362		1.66937e-5i
$235$	−3.91969	+	6.78911i	−0.255693	+	0.442873i
$236$	7.53955	−	13.0589i	0.490783	−	0.850061i
$237$	−4.85408	−	8.40751i	−0.315306	−	0.546126i
$238$	0.625769	−	0.108955i	0.0405626	−	0.00706251i
$239$	−0.484332			−0.0313289			−0.0156644	−	0.999877i	$-0.504986\pi$
$239$	−0.484332			−0.0313289			−0.0156644	+	0.999877i	$0.504986\pi$
$240$	12.1514			0.784369
$241$	1.16006	+	2.00929i	0.0747261	+	0.129429i	0.900967	−	0.433887i	$-0.142858\pi$
$241$	1.16006	+	2.00929i	0.0747261	+	0.129429i	−0.826241	+	0.563317i	$0.809525\pi$
$242$	−0.271856	+	0.470868i	−0.0174756	+	0.0302686i
$243$	−1.00000			−0.0641500
$244$	4.86189	+	8.42104i	0.311251	+	0.539102i
$245$	16.3444	+	13.8347i	1.04421	+	0.883863i
$246$	0.240710			0.0153471
$247$	−12.4207	−	21.5652i	−0.790313	−	1.37216i
$248$	−1.25708	+	2.17732i	−0.0798244	+	0.138260i
$249$	−5.41662			−0.343264
$250$	−0.0668163	+	0.115729i	−0.00422583	+	0.00731935i
$251$	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
$254$	0.910183			0.0571100
$255$	5.39723	−	9.34828i	0.337988	−	0.585412i
$256$	−7.81549	−	13.5368i	−0.488468	−	0.846051i
$257$	−4.56503	+	7.90686i	−0.284758	+	0.493216i	−0.972551	−	0.232692i	$-0.925247\pi$
$257$	−4.56503	+	7.90686i	−0.284758	+	0.493216i	0.687792	+	0.725908i	$0.258580\pi$
$258$	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
$262$	−1.23301			−0.0761758
$263$	−5.58969			−0.344675			−0.172338	−	0.985038i	$-0.555132\pi$
$263$	−5.58969			−0.344675			−0.172338	+	0.985038i	$0.555132\pi$
$264$	−1.18461			−0.0729077
$265$	16.2548			0.998522
$266$	0.427447	−	1.16660i	0.0262085	−	0.0715290i
$267$	−3.85207	+	6.67198i	−0.235743	+	0.408319i
$268$	0.678860	+	1.17582i	0.0414680	+	0.0718247i
$269$	−10.6461	−	18.4395i	−0.649102	−	1.12428i	−0.983338	−	0.181789i	$-0.941811\pi$
$269$	−10.6461	−	18.4395i	−0.649102	−	1.12428i	0.334235	−	0.942490i	$-0.391522\pi$
$270$	0.208127			0.0126662
$271$	−5.66348	+	9.80944i	−0.344032	+	0.595881i	−0.985177	−	0.171539i	$-0.945126\pi$
$271$	−5.66348	+	9.80944i	−0.344032	+	0.595881i	0.641145	+	0.767419i	$0.278460\pi$
$272$	−14.0168			−0.849891
$273$	−6.10848	−	7.32711i	−0.369702	−	0.443457i
$274$	1.45192			0.0877139
$275$	9.49577	−	16.4472i	0.572616	−	0.991801i
$276$	6.65503			0.400586
$277$	5.68116	+	9.84006i	0.341348	+	0.591232i	0.984683	−	0.174353i	$-0.0557832\pi$
$277$	5.68116	+	9.84006i	0.341348	+	0.591232i	−0.643335	+	0.765584i	$0.722450\pi$
$278$	−0.00479849	−	0.00831123i	−0.000287794	−	0.000498474i
$279$	4.62451	−	8.00989i	0.276862	−	0.479540i
$280$	1.41055	+	1.68838i	0.0842965	+	0.100900i
$281$	7.98667			0.476445			0.238222	−	0.971211i	$-0.423435\pi$
$281$	7.98667			0.476445			0.238222	+	0.971211i	$0.423435\pi$
$282$	0.174354			0.0103826
$283$	4.13874			0.246022			0.123011	−	0.992405i	$-0.460745\pi$
$283$	4.13874			0.246022			0.123011	+	0.992405i	$0.460745\pi$
$284$	−10.4386			−0.619420
$285$	−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
$289$	2.27423	−	3.93909i	0.133778	−	0.231711i
$290$	−1.03229	−	1.78798i	−0.0606183	−	0.104994i
$291$	3.86359	−	6.69194i	0.226488	−	0.392288i
$292$	7.02194			0.410928
$293$	−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
$296$	−0.0148209	+	0.0256706i	−0.000861449	+	0.00149207i
$297$	4.35793			0.252873
$298$	0.488360	−	0.845865i	0.0282900	−	0.0489996i
$299$	12.0254	+	0.0125184i	0.695444	+	0.000723957i
$300$	8.69568			0.502046
$301$	1.53666	−	4.19391i	0.0885719	−	0.241733i
$302$	−0.532839	−	0.922904i	−0.0306614	−	0.0531071i
$303$	3.88031			0.222918
$304$	−13.7087	+	23.7442i	−0.786248	+	1.36182i
$305$	7.45369	+	12.9102i	0.426797	+	0.739234i
$306$	−0.240077			−0.0137243
$307$	18.0617			1.03083			0.515417	−	0.856939i	$-0.327637\pi$
$307$	18.0617			1.03083			0.515417	+	0.856939i	$0.327637\pi$
$308$	14.7505	+	17.6558i	0.840487	+	1.00603i
$309$	4.29088	+	7.43202i	0.244100	+	0.422793i
$310$	−0.962486	+	1.66707i	−0.0546655	+	0.0946834i
$311$	−6.03959	+	10.4609i	−0.342474	+	0.593182i	−0.984891	−	0.173173i	$-0.944598\pi$
$311$	−6.03959	+	10.4609i	−0.342474	+	0.593182i	0.642418	+	0.766355i	$0.277931\pi$
$312$	−0.489163	−	0.849295i	−0.0276934	−	0.0480819i
$313$	−10.3790	−	17.9769i	−0.586654	−	1.01611i	−0.994667	−	0.103138i	$-0.967112\pi$
$313$	−10.3790	−	17.9769i	−0.586654	−	1.01611i	0.408013	−	0.912976i	$-0.366222\pi$
$314$	−0.459257	−	0.795457i	−0.0259174	−	0.0448902i
$315$	−5.18911	−	6.21117i	−0.292373	−	0.349960i
$316$	−9.68569	+	16.7761i	−0.544862	+	0.943729i
$317$	−8.73476	−	15.1290i	−0.490593	−	0.849732i	0.509348	−	0.860560i	$-0.329886\pi$
$317$	−8.73476	−	15.1290i	−0.490593	−	0.849732i	−0.999941	+	0.0108284i	$0.996553\pi$
$318$	−0.180759	−	0.313083i	−0.0101364	−	0.0175568i
$319$	−21.6150	−	37.4382i	−1.21020	−	2.09614i
$320$	−12.0667	−	20.9001i	−0.674549	−	1.16835i
$321$	−5.60158	+	9.70222i	−0.312650	+	0.541525i
$322$	0.384918	+	0.460732i	0.0214506	+	0.0256756i
$323$	12.1779	+	21.0927i	0.677595	+	1.17363i
$324$	0.997686	+	1.72804i	0.0554270	+	0.0960023i
$325$	15.7127	+	0.0163569i	0.871585	+	0.000907319i
$326$	0.0903939	−	0.156567i	0.00500646	−	0.00867144i
$327$	−6.98282	+	12.0946i	−0.386151	+	0.668833i
$328$	−0.480863	−	0.832880i	−0.0265512	−	0.0459881i
$329$	−4.34705	−	5.20326i	−0.239661	−	0.286865i
$330$	−0.907002			−0.0499288
$331$	7.12617			0.391690			0.195845	−	0.980635i	$-0.437255\pi$
$331$	7.12617			0.391690			0.195845	+	0.980635i	$0.437255\pi$
$332$	5.40408	+	9.36014i	0.296587	+	0.513705i
$333$	0.0545230	−	0.0944366i	0.00298784	−	0.00517509i
$334$	1.48512			0.0812620
$335$	1.04075	+	1.80263i	0.0568623	+	0.0984883i
$336$	−3.61568	+	9.86804i	−0.197252	+	0.538345i
$337$	−22.8396			−1.24415			−0.622077	−	0.782956i	$-0.713711\pi$
$337$	−22.8396			−1.24415			−0.622077	+	0.782956i	$0.713711\pi$
$338$	−0.440638	−	0.766890i	−0.0239675	−	0.0417133i
$339$	3.38888	−	5.86972i	0.184059	−	0.318799i
$340$	−21.5390			−1.16811
$341$	−20.1533	+	34.9065i	−1.09136	+	1.89029i
$342$	−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
$345$	10.2027			0.549297
$346$	−0.601520	+	1.04186i	−0.0323379	+	0.0560109i
$347$	8.62904	+	14.9459i	0.463231	+	0.802340i	0.999120	−	0.0419489i	$-0.0133567\pi$
$347$	8.62904	+	14.9459i	0.463231	+	0.802340i	−0.535889	+	0.844289i	$0.680023\pi$
$348$	9.89687	−	17.1419i	0.530528	−	0.918901i
$349$	−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
$353$	−0.960641			−0.0511298			−0.0255649	−	0.999673i	$-0.508138\pi$
$353$	−0.960641			−0.0511298			−0.0255649	+	0.999673i	$0.508138\pi$
$354$	−0.514150			−0.0273268
$355$	−16.0033			−0.849369
$356$	15.3726			0.814748
$357$	5.98569	+	7.16465i	0.316796	+	0.379194i
$358$	−0.330994	+	0.573299i	−0.0174936	+	0.0302998i
$359$	16.4526	+	28.4967i	0.868334	+	1.50400i	0.863698	+	0.504009i	$0.168142\pi$
$359$	16.4526	+	28.4967i	0.868334	+	1.50400i	0.00463555	+	0.999989i	$0.498524\pi$
$360$	−0.415772	−	0.720139i	−0.0219131	−	0.0379546i
$361$	28.6409			1.50741
$362$	−0.136525	+	0.236468i	−0.00717559	+	0.0124285i
$363$	−7.99154			−0.419447
$364$	−6.56722	+	17.8659i	−0.344216	+	0.936425i
$365$	10.7652			0.563478
$366$	0.165775	−	0.287131i	0.00866521	−	0.0150086i
$367$	22.0554			1.15129			0.575643	−	0.817701i	$-0.304752\pi$
$367$	22.0554			1.15129			0.575643	+	0.817701i	$0.304752\pi$
$368$	−6.62419	−	11.4734i	−0.345310	−	0.598094i
$369$	1.76899	+	3.06399i	0.0920901	+	0.159505i
$370$	−0.0113477	+	0.0196548i	−0.000589939	+	0.00102180i
$371$	−4.83665	+	13.2003i	−0.251107	+	0.685328i
$372$	−18.4552			−0.956859
$373$	25.9119			1.34167			0.670835	−	0.741607i	$-0.265936\pi$
$373$	25.9119			1.34167			0.670835	+	0.741607i	$0.265936\pi$
$374$	1.04624			0.0540996
$375$	−1.96415			−0.101428
$376$	−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	$0.862334\pi$
$380$	−21.0656	+	36.4867i	−1.08064	+	1.87173i
$381$	6.68899	+	11.5857i	0.342687	+	0.593552i
$382$	0.503139	−	0.871462i	0.0257428	−	0.0445879i
$383$	−29.3950			−1.50202			−0.751008	−	0.660293i	$-0.770432\pi$
$383$	−29.3950			−1.50202			−0.751008	+	0.660293i	$0.770432\pi$
$384$	−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
$387$	−0.844102	+	1.46203i	−0.0429081	+	0.0743191i
$388$	−15.4186			−0.782761
$389$	1.32057	−	2.28730i	0.0669556	−	0.115971i	−0.830604	−	0.556863i	$-0.812005\pi$
$389$	1.32057	−	2.28730i	0.0669556	−	0.115971i	0.897560	+	0.440893i	$0.145338\pi$
$390$	−0.374529	−	0.650266i	−0.0189650	−	0.0329275i
$391$	−11.7690			−0.595182
$392$	−1.79083	+	0.643113i	−0.0904504	+	0.0324821i
$393$	−9.06148	−	15.6949i	−0.457091	−	0.791705i
$394$	0.430371			0.0216818
$395$	−14.8490	+	25.7192i	−0.747133	+	1.29407i
$396$	−4.34784	−	7.53068i	−0.218487	−	0.378431i
$397$	0.575977			0.0289075			0.0144537	−	0.999896i	$-0.495399\pi$
$397$	0.575977			0.0289075			0.0144537	+	0.999896i	$0.495399\pi$
$398$	−0.410677			−0.0205854
$399$	17.9909	−	3.13247i	0.900673	−	0.156820i
$400$	−8.65539	−	14.9916i	−0.432769	−	0.749578i
$401$	4.75598	−	8.23761i	0.237503	−	0.411366i	−0.722494	−	0.691377i	$-0.757005\pi$
$401$	4.75598	−	8.23761i	0.237503	−	0.411366i	0.959997	+	0.280010i	$0.0903379\pi$
$402$	0.0231470	−	0.0400918i	0.00115447	−	0.00199960i
$403$	−33.3478	−	0.0347150i	−1.66117	−	0.00172928i
$404$	−3.87133	−	6.70534i	−0.192606	−	0.333603i
$405$	1.52954	+	2.64923i	0.0760033	+	0.131642i
$406$	1.75916	−	0.306295i	0.0873059	−	0.0152012i
$407$	−0.237607	+	0.411548i	−0.0117778	+	0.0203997i
$408$	0.479598	+	0.830688i	0.0237436	+	0.0411252i
$409$	0.0931606	+	0.161359i	0.00460649	+	0.00797868i	0.868319	−	0.496005i	$-0.165200\pi$
$409$	0.0931606	+	0.161359i	0.00460649	+	0.00797868i	−0.863713	+	0.503984i	$0.831867\pi$
$410$	−0.368175	−	0.637698i	−0.0181829	−	0.0314937i
$411$	10.6703	+	18.4814i	0.526325	+	0.911622i
$412$	8.56190	−	14.8296i	0.421814	−	0.730604i
$413$	12.8190	+	15.3439i	0.630782	+	0.755023i
$414$	−0.113458	−	0.196515i	−0.00557616	−	0.00965818i
$415$	8.28491	+	14.3499i	0.406690	+	0.704408i
$416$	−1.46995	+	2.53992i	−0.0720701	+	0.124530i
$417$	0.0705287	−	0.122159i	0.00345381	−	0.00598217i
$418$	1.02324	−	1.77231i	0.0500484	−	0.0866864i
$419$	−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	$0.840313\pi$
$420$	−5.55607	+	15.1638i	−0.271108	+	0.739917i
$421$	−4.34862			−0.211939			−0.105969	−	0.994369i	$-0.533795\pi$
$421$	−4.34862			−0.211939			−0.105969	+	0.994369i	$0.533795\pi$
$422$	−0.0879150			−0.00427963
$423$	1.28133	+	2.21933i	0.0623006	+	0.107908i
$424$	−0.722198	+	1.25088i	−0.0350731	+	0.0607483i
$425$	−15.3777			−0.745928
$426$	0.177963	+	0.308240i	0.00862232	+	0.0149343i
$427$	−12.7021	+	2.21161i	−0.614697	+	0.107027i
$428$	22.3545			1.08054
$429$	−7.84220	−	13.6158i	−0.378625	−	0.657377i
$430$	0.175680	−	0.304287i	0.00847206	−	0.0146740i
$431$	−10.7267			−0.516685			−0.258342	−	0.966053i	$-0.583176\pi$
$431$	−10.7267			−0.516685			−0.258342	+	0.966053i	$0.583176\pi$
$432$	1.98612	−	3.44007i	0.0955574	−	0.165510i
$433$	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
$436$	27.8666			1.33457
$437$	−11.5103	+	19.9364i	−0.550612	+	0.953688i
$438$	−0.119713	−	0.207349i	−0.00572011	−	0.00990753i
$439$	−12.6090	+	21.8394i	−0.601794	+	1.04234i	0.390756	+	0.920494i	$0.372214\pi$
$439$	−12.6090	+	21.8394i	−0.601794	+	1.04234i	−0.992549	+	0.121843i	$0.961120\pi$
$440$	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	0.581367	−	0.813642i	$-0.302518\pi$
$443$	−8.71266	−	15.0908i	−0.413951	−	0.716984i	−0.995318	+	0.0966574i	$0.969185\pi$
$444$	−0.217587			−0.0103262
$445$	23.5675			1.11721
$446$	−0.789070			−0.0373635
$447$	14.3559			0.679013
$448$	20.5633	−	3.58036i	0.971524	−	0.169156i
$449$	−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
$451$	−7.70914	−	13.3526i	−0.363009	−	0.628751i
$452$	−13.5242			−0.636123
$453$	7.83172	−	13.5649i	0.367966	−	0.637336i
$454$	−0.0543266			−0.00254967
$455$	−10.0681	+	27.3899i	−0.472000	+	1.28406i
$456$	1.87623			0.0878624
$457$	4.16626	−	7.21617i	0.194889	−	0.337558i	−0.751975	−	0.659192i	$-0.770899\pi$
$457$	4.16626	−	7.21617i	0.194889	−	0.337558i	0.946864	+	0.321634i	$0.104232\pi$
$458$	1.57942			0.0738017
$459$	−1.76434	−	3.05592i	−0.0823522	−	0.142638i
$460$	−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	$0.133949\pi$
$462$	0.269881	−	0.736568i	0.0125560	−	0.0342682i
$463$	20.2243			0.939904			0.469952	−	0.882692i	$-0.344271\pi$
$463$	20.2243			0.939904			0.469952	+	0.882692i	$0.344271\pi$
$464$	−39.4040			−1.82929
$465$	−28.2934			−1.31208
$466$	−0.829206			−0.0384122
$467$	−3.27010	−	5.66398i	−0.151322	−	0.262098i	0.780392	−	0.625291i	$-0.215020\pi$
$467$	−3.27010	−	5.66398i	−0.151322	−	0.262098i	−0.931714	+	0.363193i	$0.881686\pi$
$468$	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
$471$	6.75022	−	11.6917i	0.311034	−	0.538726i
$472$	1.02711	+	1.77901i	0.0472766	+	0.0818855i
$473$	3.67854	−	6.37141i	0.169139	−	0.292958i
$474$	0.660504			0.0303379
$475$	−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
$478$	0.0164760	−	0.0285373i	0.000753595	−	0.00130527i
$479$	−7.81335			−0.357001			−0.178500	−	0.983940i	$-0.557125\pi$
$479$	−7.81335			−0.357001			−0.178500	+	0.983940i	$0.557125\pi$
$480$	−1.24491	+	2.15625i	−0.0568221	+	0.0984188i
$481$	−0.393171		0.000409290i	−0.0179270		1.86620e-5i
$482$	−0.157852			−0.00718995
$483$	−3.03585	+	8.28554i	−0.138136	+	0.377005i
$484$	7.97304	+	13.8097i	0.362411	+	0.627714i
$485$	−23.6380			−1.07335
$486$	0.0340180	−	0.0589209i	0.00154309	−	0.00267270i
$487$	10.5370	+	18.2507i	0.477479	+	0.827018i	0.999667	−	0.0258123i	$-0.00821724\pi$
$487$	10.5370	+	18.2507i	0.477479	+	0.827018i	−0.522188	+	0.852831i	$0.674884\pi$
$488$	−1.32467			−0.0599649
$489$	2.65724			0.120165
$490$	−1.37115	+	0.492402i	−0.0619425	+	0.0222445i
$491$	−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	$0.896510\pi$
$492$	3.52980	−	6.11379i	0.159136	−	0.275631i
$493$	−17.5019	+	30.3142i	−0.788247	+	1.36528i
$494$	1.69317	+	0.00176259i	0.0761792	+	7.93025e-5i
$495$	−6.66561	−	11.5452i	−0.299597	−	0.518917i
$496$	18.3697	+	31.8173i	0.824824	+	1.42864i
$497$	4.76184	−	12.9962i	0.213598	−	0.582957i
$498$	0.184262	−	0.319152i	0.00825699	−	0.0143015i
$499$	−10.6426	−	18.4336i	−0.476430	−	0.825200i	0.523206	−	0.852206i	$-0.324736\pi$
$499$	−10.6426	−	18.4336i	−0.476430	−	0.825200i	−0.999635	+	0.0270062i	$0.991403\pi$
$500$	1.95960	+	3.39413i	0.0876360	+	0.151790i
$501$	10.9142	+	18.9040i	0.487611	+	0.844567i
$502$	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	$0.199345\pi$
$504$	0.708532	−	0.123365i	0.0315605	−	0.00549513i
$505$	−5.93508	−	10.2799i	−0.264107	−	0.457448i
$506$	0.494442	+	0.856398i	0.0219806	+	0.0380715i
$507$	6.52343	−	11.2448i	0.289716	−	0.499398i
$508$	13.3470	−	23.1177i	0.592178	−	1.02568i
$509$	6.85316	−	11.8700i	0.303761	−	0.526129i	−0.673224	−	0.739439i	$-0.735091\pi$
$509$	6.85316	−	11.8700i	0.303761	−	0.526129i	0.976985	+	0.213309i	$0.0684242\pi$
$510$	0.367206	+	0.636019i	0.0162602	+	0.0281634i
$511$	−3.20322	+	8.74234i	−0.141702	+	0.386738i
$512$	5.39261			0.238322
$513$	−6.90224			−0.304741
$514$	−0.310586	−	0.537950i	−0.0136994	−	0.0237280i
$515$	13.1261	−	22.7351i	0.578406	−	1.00183i
$516$	3.36860			0.148294
$517$	−5.58396	−	9.67170i	−0.245582	−	0.425361i
$518$	−0.0125849	−	0.0150637i	−0.000552950	−	0.000661861i
$519$	−17.6824			−0.776171
$520$	−1.50179	+	2.59493i	−0.0658579	+	0.113795i
$521$	−2.13457	+	3.69718i	−0.0935172	+	0.161977i	−0.908989	−	0.416821i	$-0.863144\pi$
$521$	−2.13457	+	3.69718i	−0.0935172	+	0.161977i	0.815472	+	0.578797i	$0.196478\pi$
$522$	−0.674905			−0.0295398
$523$	14.0853	−	24.3964i	0.615907	−	1.06678i	−0.374318	−	0.927300i	$-0.622123\pi$
$523$	14.0853	−	24.3964i	0.615907	−	1.06678i	0.990225	−	0.139481i	$-0.0445436\pi$
$524$	−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
$527$	32.6368			1.42168
$528$	−8.65539	+	14.9916i	−0.376677	+	0.652424i
$529$	5.93810	+	10.2851i	0.258178	+	0.447178i
$530$	−0.552954	+	0.957745i	−0.0240188	+	0.0416018i
$531$	−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
$535$	34.2713			1.48168
$536$	−0.184962			−0.00798914
$537$	−9.72998			−0.419880
$538$	1.44863			0.0624549
$539$	−28.7103	+	10.3103i	−1.23664	+	0.444096i
$540$	3.05199	−	5.28621i	0.131337	−	0.227482i
$541$	9.24717	+	16.0166i	0.397567	+	0.688606i	0.993425	−	0.114484i	$-0.0365214\pi$
$541$	9.24717	+	16.0166i	0.397567	+	0.688606i	−0.595858	+	0.803089i	$0.703188\pi$
$542$	−0.385320	−	0.667394i	−0.0165509	−	0.0286670i
$543$	−4.01332			−0.172228
$544$	1.43602	−	2.48726i	0.0615687	−	0.106640i
$545$	42.7219			1.83001
$546$	0.639518	−	0.110663i	0.0273688	−	0.00473595i
$547$	24.6951			1.05589			0.527943	−	0.849280i	$-0.322963\pi$
$547$	24.6951			1.05589			0.527943	+	0.849280i	$0.322963\pi$
$548$	21.2911	−	36.8773i	0.909512	−	1.57532i
$549$	4.87317			0.207982
$550$	0.646054	+	1.11900i	0.0275478	+	0.0477142i
$551$	34.2345	+	59.2959i	1.45844	+	2.52609i
$552$	−0.453307	+	0.785150i	−0.0192940	+	0.0334182i
$553$	−16.4680	−	19.7115i	−0.700289	−	0.838220i
$554$	−0.773046			−0.0328436
$555$	−0.333580			−0.0141597
$556$	−0.281462			−0.0119366
$557$	−2.97174			−0.125917			−0.0629584	−	0.998016i	$-0.520054\pi$
$557$	−2.97174			−0.125917			−0.0629584	+	0.998016i	$0.520054\pi$
$558$	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
$562$	−0.271690	+	0.470581i	−0.0114606	+	0.0198503i
$563$	1.60029	+	2.77179i	0.0674443	+	0.116817i	0.897776	−	0.440453i	$-0.145182\pi$
$563$	1.60029	+	2.77179i	0.0674443	+	0.116817i	−0.830331	+	0.557270i	$0.811849\pi$
$564$	2.55674	−	4.42840i	0.107658	−	0.186469i
$565$	−20.7337			−0.872272
$566$	−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
$569$	6.29189	−	10.8979i	0.263770	−	0.456862i	−0.703471	−	0.710724i	$-0.748367\pi$
$569$	6.29189	−	10.8979i	0.263770	−	0.456862i	0.967241	+	0.253862i	$0.0817008\pi$
$570$	1.43654			0.0601701
$571$	11.8472	−	20.5200i	0.495792	−	0.858736i	−0.504197	−	0.863589i	$-0.668211\pi$
$571$	11.8472	−	20.5200i	0.495792	−	0.858736i	0.999988	+	0.00485262i	$0.00154464\pi$
$572$	−15.7046	+	27.1359i	−0.656643	+	1.13461i
$573$	14.7904			0.617877
$574$	0.627420	−	0.109243i	0.0261880	−	0.00455970i
$575$	−7.26736	−	12.5874i	−0.303070	−	0.524932i
$576$	−7.88912			−0.328713
$577$	−1.67873	+	2.90764i	−0.0698863	+	0.121047i	−0.898851	−	0.438254i	$-0.855597\pi$
$577$	−1.67873	+	2.90764i	−0.0698863	+	0.121047i	0.828965	+	0.559301i	$0.188930\pi$
$578$	0.154730	+	0.267999i	0.00643590	+	0.0111473i
$579$	−22.3431			−0.928548
$580$	−60.5505			−2.51422
$581$	−14.1186	+	2.45825i	−0.585739	+	0.101985i
$582$	0.262863	+	0.455292i	0.0108960	+	0.0188725i
$583$	−11.5782	+	20.0540i	−0.479520	+	0.830553i
$584$	−0.478298	+	0.828437i	−0.0197921	+	0.0342810i
$585$	5.52476	−	9.54621i	0.228421	−	0.394687i
$586$	−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	$0.899438\pi$
$588$	−10.6611	−	9.02406i	−0.439658	−	0.372146i
$589$	31.9195	−	55.2862i	1.31522	−	2.27803i
$590$	0.786412	+	1.36210i	0.0323761	+	0.0560770i
$591$	3.16282	+	5.47816i	0.130101	+	0.225342i
$592$	0.216579	+	0.375126i	0.00890133	+	0.0154176i
$593$	−16.4331	−	28.4629i	−0.674825	−	1.16883i	−0.976520	−	0.215426i	$-0.930886\pi$
$593$	−16.4331	−	28.4629i	−0.674825	−	1.16883i	0.301695	−	0.953404i	$-0.402447\pi$
$594$	−0.148248	+	0.256773i	−0.00608268	+	0.0105355i
$595$	9.82552	−	26.8161i	0.402807	−	1.09935i
$596$	−14.3227	−	24.8077i	−0.586682	−	1.01616i
$597$	−3.01808	−	5.22748i	−0.123522	−	0.213946i
$598$	−0.409816	+	0.708119i	−0.0167586	+	0.0289571i
$599$	10.6138	−	18.3836i	0.433667	−	0.751133i	−0.563519	−	0.826103i	$-0.690553\pi$
$599$	10.6138	−	18.3836i	0.433667	−	0.751133i	0.997186	+	0.0749700i	$0.0238861\pi$
$600$	−0.592305	+	1.02590i	−0.0241808	+	0.0418823i
$601$	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	$0.823249\pi$
$602$	0.194835	+	0.233210i	0.00794087	+	0.00950493i
$603$	0.680435			0.0277095
$604$	−31.2544			−1.27172
$605$	12.2233	+	21.1715i	0.496950	+	0.860742i
$606$	−0.132000	+	0.228631i	−0.00536215	+	0.00928751i
$607$	6.61104			0.268334			0.134167	−	0.990959i	$-0.457164\pi$
$607$	6.61104			0.268334			0.134167	+	0.990959i	$0.457164\pi$
$608$	−2.80891	−	4.86518i	−0.113916	−	0.197309i
$609$	16.8270	+	20.1413i	0.681865	+	0.816167i
$610$	−1.01424			−0.0410653
$611$	4.62824	−	7.99711i	0.187239	−	0.323529i
$612$	−3.52051	+	6.09770i	−0.142308	+	0.246485i
$613$	−12.0584			−0.487034			−0.243517	−	0.969897i	$-0.578301\pi$
$613$	−12.0584			−0.487034			−0.243517	+	0.969897i	$0.578301\pi$
$614$	−0.614422	+	1.06421i	−0.0247960	+	0.0429480i
$615$	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	$0.934170\pi$
$618$	−0.583868			−0.0234866
$619$	23.8269	−	41.2695i	0.957686	−	1.65876i	0.229587	−	0.973288i	$-0.426263\pi$
$619$	23.8269	−	41.2695i	0.957686	−	1.65876i	0.728099	−	0.685472i	$-0.240404\pi$
$620$	28.2280	+	48.8923i	1.13366	+	1.96356i
$621$	1.66762	−	2.88840i	0.0669192	−	0.115907i
$622$	−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
$626$	1.41229			0.0564463
$627$	30.0795			1.20126
$628$	−26.9384			−1.07496
$629$	0.384788			0.0153425
$630$	0.542491	−	0.0944552i	0.0216133	−	0.00376319i
$631$	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
$633$	−0.646092	−	1.11906i	−0.0256798	−	0.0444788i
$634$	1.18856			0.0472036
$635$	20.4621	−	35.4414i	0.812014	−	1.40645i
$636$	−10.6027			−0.420423
$637$	−19.2473	−	16.3261i	−0.762604	−	0.646865i
$638$	2.94119			0.116443
$639$	−2.61572	+	4.53055i	−0.103476	+	0.179226i
$640$	6.62158			0.261741
$641$	−20.3763	−	35.2928i	−0.804815	−	1.39398i	−0.916416	−	0.400227i	$-0.868931\pi$
$641$	−20.3763	−	35.2928i	−0.804815	−	1.39398i	0.111601	−	0.993753i	$-0.464402\pi$
$642$	−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	$0.225754\pi$
$644$	17.3466	−	3.02028i	0.683551	−	0.119016i
$645$	5.16434			0.203346
$646$	−1.65707			−0.0651964
$647$	25.0197			0.983625			0.491812	−	0.870701i	$-0.336335\pi$
$647$	25.0197			0.983625			0.491812	+	0.870701i	$0.336335\pi$
$648$	−0.271829			−0.0106784
$649$	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
$653$	9.28070	−	16.0746i	0.363182	−	0.629049i	−0.625301	−	0.780384i	$-0.715024\pi$
$653$	9.28070	−	16.0746i	0.363182	−	0.629049i	0.988483	+	0.151334i	$0.0483570\pi$
$654$	−0.475083	−	0.822868i	−0.0185772	−	0.0321767i
$655$	−27.7197	+	48.0120i	−1.08310	+	1.87598i
$656$	−14.0538			−0.548707
$657$	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	$-0.0893268\pi$
$660$	−13.3004	+	23.0369i	−0.517716	+	0.896710i
$661$	15.9233			0.619344			0.309672	−	0.950843i	$-0.399781\pi$
$661$	15.9233			0.619344			0.309672	+	0.950843i	$0.399781\pi$
$662$	−0.242418	+	0.419880i	−0.00942184	+	0.0163191i
$663$	−6.37287	+	11.0117i	−0.247502	+	0.427657i
$664$	−1.47239			−0.0571399
$665$	−35.8165	−	42.8710i	−1.38890	−	1.66247i
$666$	0.00370952	+	0.00642508i	0.000143741	+	0.000248967i
$667$	−33.0850			−1.28106
$668$	21.7779	−	37.7204i	0.842612	−	1.45945i
$669$	−5.79892	−	10.0440i	−0.224199	−	0.388324i
$670$	−0.141617			−0.00547114
$671$	−21.2369			−0.819842
$672$	−1.38064	−	1.65258i	−0.0532594	−	0.0637496i
$673$	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	$0.694462\pi$
$674$	0.776958	−	1.34573i	0.0299273	−	0.0518356i
$675$	2.17896	−	3.77408i	0.0838684	−	0.145264i
$676$	−25.9398	−	0.0540066i	−0.997683	−	0.00207718i
$677$	−16.0122	−	27.7339i	−0.615398	−	1.06590i	−0.990315	−	0.138842i	$-0.955662\pi$
$677$	−16.0122	−	27.7339i	−0.615398	−	1.06590i	0.374917	−	0.927059i	$-0.377671\pi$
$678$	0.230566	+	0.399352i	0.00885483	+	0.0153370i
$679$	7.03356	−	19.1962i	0.269923	−	0.736683i
$680$	1.46712	−	2.54113i	0.0562617	−	0.0974480i
$681$	−0.399249	−	0.691520i	−0.0152993	−	0.0264991i
$682$	−1.37115	−	2.37490i	−0.0525040	−	0.0909396i
$683$	1.51134	+	2.61772i	0.0578300	+	0.100164i	0.893491	−	0.449081i	$-0.148249\pi$
$683$	1.51134	+	2.61772i	0.0578300	+	0.100164i	−0.835661	+	0.549245i	$0.814915\pi$
$684$	6.88626	+	11.9274i	0.263303	+	0.456054i
$685$	32.6411	−	56.5361i	1.24715	−	2.16013i
$686$	0.00811601	−	1.26002i	0.000309871	−	0.0481077i
$687$	11.6073	+	20.1044i	0.442845	+	0.767030i
$688$	−3.35298	−	5.80754i	−0.127831	−	0.221410i
$689$	−19.1585	−	0.0199440i	−0.729882	−	0.000759807i
$690$	−0.347076	+	0.601154i	−0.0132130	+	0.0228855i
$691$	5.94954	−	10.3049i	0.226331	−	0.392017i	−0.730387	−	0.683034i	$-0.760660\pi$
$691$	5.94954	−	10.3049i	0.226331	−	0.392017i	0.956718	+	0.291017i	$0.0939936\pi$
$692$	17.6415	+	30.5559i	0.670628	+	1.16156i
$693$	11.3591	−	1.97778i	0.431497	−	0.0751296i
$694$	−1.17417			−0.0445709
$695$	−0.431505			−0.0163679
$696$	1.34825	+	2.33523i	0.0511052	+	0.0885168i
$697$	−6.24220	+	10.8118i	−0.236440	+	0.409526i
$698$	2.09124			0.0791547
$699$	−6.09388	−	10.5549i	−0.230492	−	0.399223i
$700$	22.6656	−	3.94640i	0.856680	−	0.149160i
$701$	2.07215			0.0782642			0.0391321	−	0.999234i	$-0.487541\pi$
$701$	2.07215			0.0782642			0.0391321	+	0.999234i	$0.487541\pi$
$702$	−0.245307		0.000255364i	−0.00925852		9.63811e-6i
$703$	0.376331	−	0.651824i	0.0141936	−	0.0245840i
$704$	34.3802			1.29575
$705$	3.91969	−	6.78911i	0.147624	−	0.255693i
$706$	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
$709$	7.23998			0.271903			0.135952	−	0.990715i	$-0.456591\pi$
$709$	7.23998			0.271903			0.135952	+	0.990715i	$0.456591\pi$
$710$	0.544401	−	0.942930i	0.0204310	−	0.0353875i
$711$	4.85408	+	8.40751i	0.182042	+	0.315306i
$712$	−1.04710	+	1.81364i	−0.0392419	+	0.0679690i
$713$	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
$717$	0.484332			0.0180877
$718$	−2.23873			−0.0835488
$719$	50.9305			1.89939			0.949694	−	0.313179i	$-0.101394\pi$
$719$	50.9305			1.89939			0.949694	+	0.313179i	$0.101394\pi$
$720$	−12.1514			−0.452856
$721$	14.5572	+	17.4245i	0.542140	+	0.648922i
$722$	−0.974305	+	1.68755i	−0.0362599	+	0.0628039i
$723$	−1.16006	−	2.00929i	−0.0431432	−	0.0747261i
$724$	4.00403	+	6.93518i	0.148809	+	0.257744i
$725$	−43.2299			−1.60552
$726$	0.271856	−	0.470868i	0.0100895	−	0.0174756i
$727$	−21.6848			−0.804244			−0.402122	−	0.915586i	$-0.631727\pi$
$727$	−21.6848			−0.804244			−0.402122	+	0.915586i	$0.631727\pi$
$728$	−1.66046	−	1.99172i	−0.0615407	−	0.0738181i
$729$	1.00000			0.0370370
$730$	−0.366211	+	0.634296i	−0.0135541	+	0.0234764i
$731$	−5.95712			−0.220332
$732$	−4.86189	−	8.42104i	−0.179701	−	0.311251i
$733$	10.8930	+	18.8673i	0.402343	+	0.696879i	0.994008	−	0.109305i	$-0.0348625\pi$
$733$	10.8930	+	18.8673i	0.402343	+	0.696879i	−0.591665	+	0.806184i	$0.701529\pi$
$734$	−0.750282	+	1.29953i	−0.0276934	+	0.0479664i
$735$	−16.3444	−	13.8347i	−0.602874	−	0.510299i
$736$	2.71459			0.100061
$737$	−2.96529			−0.109228
$738$	−0.240710			−0.00886066
$739$	35.9065			1.32084			0.660421	−	0.750895i	$-0.270378\pi$
$739$	35.9065			1.32084			0.660421	+	0.750895i	$0.270378\pi$
$740$	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	$0.443868\pi$
$744$	1.25708	−	2.17732i	0.0460866	−	0.0798244i
$745$	−21.9579	−	38.0323i	−0.804477	−	1.39339i
$746$	−0.881472	+	1.52675i	−0.0322730	+	0.0558984i
$747$	5.41662			0.198184
$748$	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
$751$	−24.3770	+	42.2222i	−0.889530	+	1.54071i	−0.0490976	+	0.998794i	$0.515635\pi$
$751$	−24.3770	+	42.2222i	−0.889530	+	1.54071i	−0.840432	+	0.541917i	$0.817699\pi$
$752$	−10.1795			−0.371210
$753$	−13.7950	+	23.8936i	−0.502717	+	0.870732i
$754$	1.21451	+	2.10866i	0.0442298	+	0.0767927i
$755$	−47.9156			−1.74383
$756$	3.38475	+	4.05142i	0.123102	+	0.147349i
$757$	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	$0.746531\pi$
$758$	0.241012			0.00875396
$759$	−7.26736	+	12.5874i	−0.263788	+	0.456895i
$760$	−2.86976	−	4.97057i	−0.104097	−	0.180301i
$761$	11.3103			0.409998			0.204999	−	0.978762i	$-0.434281\pi$
$761$	11.3103			0.409998			0.204999	+	0.978762i	$0.434281\pi$
$762$	−0.910183			−0.0329725
$763$	−12.7120	+	34.6941i	−0.460206	+	1.25601i
$764$	−14.7562	−	25.5584i	−0.533859	−	0.924671i
$765$	−5.39723	+	9.34828i	−0.195137	+	0.337988i
$766$	0.999960	−	1.73198i	0.0361300	−	0.0625790i
$767$	−13.6482	+	23.5826i	−0.492808	+	0.851520i
$768$	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	$0.728975\pi$
$770$	−2.36413	+	0.411629i	−0.0851975	+	0.0148341i
$771$	4.56503	−	7.90686i	0.164405	−	0.284758i
$772$	22.2914	+	38.6098i	0.802285	+	1.38960i
$773$	−1.43276	−	2.48162i	−0.0515329	−	0.0892575i	0.839108	−	0.543964i	$-0.183077\pi$
$773$	−1.43276	−	2.48162i	−0.0515329	−	0.0892575i	−0.890641	+	0.454707i	$0.849744\pi$
$774$	−0.0574293	−	0.0994705i	−0.00206425	−	0.00357539i
$775$	20.1533	+	34.9065i	0.723928	+	1.25388i
$776$	1.05024	−	1.81906i	0.0377013	−	0.0653005i
$777$	0.0992576	−	0.270897i	0.00356085	−	0.00971837i
$778$	0.0898463	+	0.155618i	0.00322115	+	0.00557919i
$779$	12.2100	+	21.1484i	0.437469	+	0.757718i
$780$	−22.0082	−	0.0229105i	−0.788021	−	0.000820329i
$781$	11.3991	−	19.7438i	0.407892	−	0.706489i
$782$	0.400356	−	0.693437i	0.0143167	−	0.0247973i
$783$	−4.95991	−	8.59082i	−0.177253	−	0.307011i
$784$	−4.94596	+	27.3623i	−0.176641	+	0.977226i
$785$	−41.2988			−1.47402
$786$	1.23301			0.0439801
$787$	−1.58257	−	2.74109i	−0.0564125	−	0.0977094i	0.836440	−	0.548058i	$-0.184633\pi$
$787$	−1.58257	−	2.74109i	−0.0564125	−	0.0977094i	−0.892853	+	0.450349i	$0.851300\pi$
$788$	6.31100	−	10.9310i	0.224820	−	0.389400i
$789$	5.58969			0.198998
$790$	−1.01026	−	1.74983i	−0.0359436	−	0.0622561i
$791$	6.16936	−	16.8376i	0.219357	−	0.598677i
$792$	1.18461			0.0420933
$793$	−8.76938	−	15.2256i	−0.311410	−	0.540677i
$794$	−0.0195936	+	0.0339371i	−0.000695350	+	0.00120438i
$795$	−16.2548			−0.576497
$796$	−6.02220	+	10.4308i	−0.213451	+	0.369708i
$797$	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
$800$	3.54698			0.125405
$801$	3.85207	−	6.67198i	0.136106	−	0.235743i
$802$	0.323578	+	0.560453i	0.0114259	+	0.0197903i
$803$	−7.66802	+	13.2814i	−0.270599	+	0.468690i
$804$	−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
$808$	1.05478			0.0371071
$809$	−38.3111			−1.34695			−0.673474	−	0.739211i	$-0.735199\pi$
$809$	−38.3111			−1.34695			−0.673474	+	0.739211i	$0.735199\pi$
$810$	−0.208127			−0.00731284
$811$	2.79091			0.0980022			0.0490011	−	0.998799i	$-0.484396\pi$
$811$	2.79091			0.0980022			0.0490011	+	0.998799i	$0.484396\pi$
$812$	18.0170	−	49.1725i	0.632272	−	1.72562i
$813$	5.66348	−	9.80944i	0.198627	−	0.344032i
$814$	−0.0161658	−	0.0280000i	−0.000566612	−	0.000981401i
$815$	−4.06434	−	7.03965i	−0.142368	−	0.246588i
$816$	14.0168			0.490685
$817$	−5.82620	+	10.0913i	−0.203833	+	0.353049i
$818$	−0.0126765			−0.000443225
$819$	6.10848	+	7.32711i	0.213447	+	0.256030i
$820$	−21.5958			−0.754158
$821$	22.1855	−	38.4264i	0.774279	−	1.34109i	−0.160919	−	0.986968i	$-0.551446\pi$
$821$	22.1855	−	38.4264i	0.774279	−	1.34109i	0.935199	−	0.354124i	$-0.115221\pi$
$822$	−1.45192			−0.0506416
$823$	4.10746	+	7.11433i	0.143177	+	0.247990i	0.928691	−	0.370853i	$-0.120935\pi$
$823$	4.10746	+	7.11433i	0.143177	+	0.247990i	−0.785514	+	0.618844i	$0.787601\pi$
$824$	1.16639	+	2.02024i	0.0406329	+	0.0703783i
$825$	−9.49577	+	16.4472i	−0.330600	+	0.572616i
$826$	−1.34015	+	0.233339i	−0.0466298	+	0.00811891i
$827$	−37.0687			−1.28900			−0.644502	−	0.764603i	$-0.722935\pi$
$827$	−37.0687			−1.28900			−0.644502	+	0.764603i	$0.722935\pi$
$828$	−6.65503			−0.231278
$829$	−42.4586			−1.47465			−0.737323	−	0.675540i	$-0.763911\pi$
$829$	−42.4586			−1.47465			−0.737323	+	0.675540i	$0.763911\pi$
$830$	−1.12734			−0.0391307
$831$	−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
$835$	33.3874	−	57.8286i	1.15542	−	2.00124i
$836$	−30.0098	−	51.9786i	−1.03791	−	1.79772i
$837$	−4.62451	+	8.00989i	−0.159847	+	0.276862i
$838$	0.0610710			0.00210966
$839$	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
$842$	0.147931	−	0.256225i	0.00509805	−	0.00883008i
$843$	−7.98667			−0.275075
$844$	−1.28919	+	2.23295i	−0.0443759	+	0.0768612i
$845$	−39.7679	−	0.0827967i	−1.36806	−	0.00284829i
$846$	−0.174354			−0.00599440
$847$	−20.8302	+	3.62684i	−0.715735	+	0.124620i
$848$	10.5535	+	18.2792i	0.362409	+	0.627711i
$849$	−4.13874			−0.142041
$850$	0.523118	−	0.906068i	0.0179428	−	0.0310779i
$851$	0.181847	+	0.314968i	0.00623364	+	0.0107970i
$852$	10.4386			0.357622
$853$	−55.5244			−1.90112			−0.950560	−	0.310540i	$-0.899490\pi$
$853$	−55.5244			−1.90112			−0.950560	+	0.310540i	$0.899490\pi$
$854$	0.301789	−	0.823653i	0.0103270	−	0.0281848i
$855$	10.5572	+	18.2856i	0.361049	+	0.625356i
$856$	−1.52267	+	2.63734i	−0.0520438	+	0.0901426i
$857$	14.8303	−	25.6869i	0.506595	−	0.877448i	−0.493376	−	0.869816i	$-0.664237\pi$
$857$	14.8303	−	25.6869i	0.506595	−	0.877448i	0.999971	−	0.00763209i	$-0.00242939\pi$
$858$	1.06903	+	0.00111286i	0.0364961	+	3.79924e-5i
$859$	−10.6791	−	18.4967i	−0.364365	−	0.631098i	0.624309	−	0.781177i	$-0.285381\pi$
$859$	−10.6791	−	18.4967i	−0.364365	−	0.631098i	−0.988674	+	0.150079i	$0.952047\pi$
$860$	−5.15239	−	8.92420i	−0.175695	−	0.304313i
$861$	6.00149	+	7.18356i	0.204530	+	0.244815i
$862$	0.364899	−	0.632024i	0.0124285	−	0.0215268i
$863$	17.5615	+	30.4174i	0.597800	+	1.03542i	0.993145	+	0.116887i	$0.0372916\pi$
$863$	17.5615	+	30.4174i	0.597800	+	1.03542i	−0.395345	+	0.918533i	$0.629375\pi$
$864$	0.406957	+	0.704870i	0.0138449	+	0.0239802i
$865$	27.0459	+	46.8448i	0.919587	+	1.59277i
$866$	0.235480	+	0.407863i	0.00800194	+	0.0138598i
$867$	−2.27423	+	3.93909i	−0.0772370	+	0.133778i
$868$	−48.1042	+	8.37562i	−1.63276	+	0.284287i
$869$	−21.1537	−	36.6393i	−0.717591	−	1.24290i
$870$	1.03229	+	1.78798i	0.0349980	+	0.0606183i
$871$	−1.22446	−	2.12593i	−0.0414892	−	0.0720345i
$872$	−1.89813	+	3.28766i	−0.0642789	+	0.111334i
$873$	−3.86359	+	6.69194i	−0.130763	+	0.226488i
$874$	−0.783114	−	1.35639i	−0.0264892	−	0.0458807i
$875$	−5.11962	+	0.891397i	−0.173075	+	0.0301347i
$876$	−7.02194			−0.237249
$877$	18.8056			0.635019			0.317509	−	0.948255i	$-0.397153\pi$
$877$	18.8056			0.635019			0.317509	+	0.948255i	$0.397153\pi$
$878$	−0.857864	−	1.48586i	−0.0289515	−	0.0501455i
$879$	14.1626	−	24.5303i	0.477691	−	0.827385i
$880$	52.9549			1.78511
$881$	−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	$-0.438823\pi$
$882$	−0.0847135	+	0.468657i	−0.00285245	+	0.0157805i
$883$	−2.57264			−0.0865764			−0.0432882	−	0.999063i	$-0.513783\pi$
$883$	−2.57264			−0.0865764			−0.0432882	+	0.999063i	$0.513783\pi$
$884$	25.3867	+	0.0264275i	0.853848	+	0.000888855i
$885$	−11.5588	+	20.0204i	−0.388544	+	0.672977i
$886$	1.18555			0.0398293
$887$	18.4051	−	31.8786i	0.617983	−	1.07038i	−0.371870	−	0.928285i	$-0.621283\pi$
$887$	18.4051	−	31.8786i	0.617983	−	1.07038i	0.989853	−	0.142093i	$-0.0453833\pi$
$888$	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
$891$	−4.35793			−0.145996
$892$	−11.5710	+	20.0415i	−0.387425	+	0.671041i
$893$	8.84407	+	15.3184i	0.295955	+	0.512610i
$894$	−0.488360	+	0.845865i	−0.0163332	+	0.0282900i
$895$	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
$899$	91.7487			3.05999
$900$	−8.69568			−0.289856
$901$	18.7500			0.624655
$902$	1.04900			0.0349278
$903$	−1.53666	+	4.19391i	−0.0511370	+	0.139565i
$904$	0.921196	−	1.59556i	0.0306385	−	0.0530675i
$905$	6.13852	+	10.6322i	0.204051	+	0.353427i
$906$	0.532839	+	0.922904i	0.0177024	+	0.0306614i
$907$	3.84939			0.127817			0.0639084	−	0.997956i	$-0.479643\pi$
$907$	3.84939			0.127817			0.0639084	+	0.997956i	$0.479643\pi$
$908$	−0.796650	+	1.37984i	−0.0264378	+	0.0457915i
$909$	−3.88031			−0.128702
$910$	−1.27134	−	1.52497i	−0.0421445	−	0.0505522i
$911$	−47.0839			−1.55996			−0.779980	−	0.625804i	$-0.784771\pi$
$911$	−47.0839			−1.55996			−0.779980	+	0.625804i	$0.784771\pi$
$912$	13.7087	−	23.7442i	0.453940	−	0.786248i
$913$	−23.6052			−0.781219
$914$	0.283455	+	0.490959i	0.00937587	+	0.0162395i
$915$	−7.45369	−	12.9102i	−0.246411	−	0.426797i
$916$	23.1608	−	40.1157i	0.765255	−	1.32546i
$917$	−30.7420	−	36.7970i	−1.01519	−	1.21515i
$918$	0.240077			0.00792371
$919$	−55.7761			−1.83989			−0.919943	−	0.392053i	$-0.871765\pi$
$919$	−55.7761			−1.83989			−0.919943	+	0.392053i	$0.871765\pi$
$920$	2.77340			0.0914362
$921$	−18.0617			−0.595152
$922$	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
$926$	−0.687990	+	1.19163i	−0.0226088	+	0.0391595i
$927$	−4.29088	−	7.43202i	−0.140931	−	0.244100i
$928$	4.03694	−	6.99219i	0.132519	−	0.229530i
$929$	38.9439			1.27771			0.638855	−	0.769327i	$-0.279409\pi$
$929$	38.9439			1.27771			0.638855	+	0.769327i	$0.279409\pi$
$930$	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
$933$	6.03959	−	10.4609i	0.197727	−	0.342474i
$934$	0.444969			0.0145598
$935$	23.5208	−	40.7392i	0.769211	−	1.33231i
$936$	0.489163	+	0.849295i	0.0159888	+	0.0277601i
$937$	19.5763			0.639531			0.319765	−	0.947497i	$-0.396396\pi$
$937$	19.5763			0.639531			0.319765	+	0.947497i	$0.396396\pi$
$938$	0.0421385	−	0.115006i	0.00137587	−	0.00375507i
$939$	10.3790	+	17.9769i	0.338705	+	0.586654i
$940$	−15.6425			−0.510202
$941$	3.84200	−	6.65455i	0.125246	−	0.216932i	−0.796583	−	0.604529i	$-0.793361\pi$
$941$	3.84200	−	6.65455i	0.125246	−	0.216932i	0.921829	+	0.387597i	$0.126695\pi$
$942$	0.459257	+	0.795457i	0.0149634	+	0.0259174i
$943$	−11.8000			−0.384261
$944$	30.0184			0.977017
$945$	5.18911	+	6.21117i	0.168802	+	0.202049i
$946$	0.250273	+	0.433485i	0.00813707	+	0.0140938i
$947$	−17.1984	+	29.7886i	−0.558874	+	0.967998i	0.438717	+	0.898625i	$0.355433\pi$
$947$	−17.1984	+	29.7886i	−0.558874	+	0.967998i	−0.997591	+	0.0693727i	$0.977900\pi$
$948$	9.68569	−	16.7761i	0.314576	−	0.544862i
$949$	−12.6883	−	0.0132085i	−0.411881	−	0.000428767i
$950$	−1.02324	−	1.77231i	−0.0331984	−	0.0575012i
$951$	8.73476	+	15.1290i	0.283244	+	0.490593i
$952$	1.62708	+	1.94756i	0.0527341	+	0.0631208i
$953$	−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
$955$	−22.6224	−	39.1832i	−0.732045	−	1.26794i
$956$	−0.483211	−	0.836947i	−0.0156282	−	0.0270688i
$957$	21.6150	+	37.4382i	0.698712	+	1.21020i
$958$	0.265794	−	0.460369i	0.00858742	−	0.0148739i
$959$	36.1999	+	43.3300i	1.16896	+	1.39920i
$960$	12.0667	+	20.9001i	0.389451	+	0.674549i
$961$	−27.2722	−	47.2369i	−0.879749	−	1.52377i
$962$	0.0133990	−	0.0231520i	0.000432001	−	0.000746451i
$963$	5.60158	−	9.70222i	0.180508	−	0.312650i
$964$	−2.31475	+	4.00927i	−0.0745532	+	0.129130i
$965$	34.1746	+	59.1921i	1.10012	+	1.90546i
$966$	−0.384918	−	0.460732i	−0.0123845	−	0.0148238i
$967$	52.1099			1.67574			0.837871	−	0.545869i	$-0.183800\pi$
$967$	52.1099			1.67574			0.837871	+	0.545869i	$0.183800\pi$
$968$	−2.17233			−0.0698213
$969$	−12.1779	−	21.0927i	−0.391210	−	0.677595i
$970$	0.804118	−	1.39277i	0.0258187	−	0.0447192i
$971$	20.6294			0.662028			0.331014	−	0.943626i	$-0.392609\pi$
$971$	20.6294			0.662028			0.331014	+	0.943626i	$0.392609\pi$
$972$	−0.997686	−	1.72804i	−0.0320008	−	0.0554270i
$973$	0.128396	−	0.350421i	0.00411617	−	0.0112340i
$974$	−1.43380			−0.0459418
$975$	−15.7127	−	0.0163569i	−0.503210	−	0.000523841i
$976$	−9.67871	+	16.7640i	−0.309808	+	0.536603i
$977$	−25.9590			−0.830501			−0.415251	−	0.909707i	$-0.636306\pi$
$977$	−25.9590			−0.830501			−0.415251	+	0.909707i	$0.636306\pi$
$978$	−0.0903939	+	0.156567i	−0.00289048	+	0.00500646i
$979$	−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
$982$	0.594516			0.0189718
$983$	−19.0424	+	32.9825i	−0.607359	+	1.05198i	0.384315	+	0.923202i	$0.374438\pi$
$983$	−19.0424	+	32.9825i	−0.607359	+	1.05198i	−0.991674	+	0.128775i	$0.958896\pi$
$984$	0.480863	+	0.832880i	0.0153294	+	0.0265512i
$985$	9.67529	−	16.7581i	0.308281	−	0.533958i
$986$	−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
$990$	0.907002			0.0288264
$991$	−61.3614			−1.94921			−0.974605	−	0.223930i	$-0.928111\pi$
$991$	−61.3614			−1.94921			−0.974605	+	0.223930i	$0.928111\pi$
$992$	−7.52791			−0.239011
$993$	−7.12617			−0.226142
$994$	0.603757	+	0.722675i	0.0191500	+	0.0229218i
$995$	−9.23254	+	15.9912i	−0.292691	+	0.506956i
$996$	−5.40408	−	9.36014i	−0.171235	−	0.296587i
$997$	9.66583	+	16.7417i	0.306120	+	0.530215i	0.977510	−	0.210889i	$-0.0676358\pi$
$997$	9.66583	+	16.7417i	0.306120	+	0.530215i	−0.671390	+	0.741104i	$0.734302\pi$
$998$	1.44816			0.0458408
$999$	−0.0545230	+	0.0944366i	−0.00172503	+	0.00298784i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.4	✓	16	91.9	even	3	inner
273.2.j.b.172.4	yes	16	1.1	even	1	trivial
273.2.l.b.16.5	yes	16	7.2	even	3
273.2.l.b.256.5	yes	16	13.9	even	3
819.2.n.e.100.5		16	273.191	odd	6
819.2.n.e.172.5		16	3.2	odd	2
819.2.s.e.289.4		16	21.2	odd	6
819.2.s.e.802.4		16	39.35	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0340180 + 0.0589209i) q^{2} -1.00000 q^{3} +(0.997686 + 1.72804i) q^{4} +(1.52954 + 2.64923i) q^{5} +(0.0340180 - 0.0589209i) q^{6} +(-2.60654 + 0.453835i) q^{7} -0.271829 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.0340180 + 0.0589209i) q^{2} -1.00000 q^{3} +(0.997686 + 1.72804i) q^{4} +(1.52954 + 2.64923i) q^{5} +(0.0340180 - 0.0589209i) q^{6} +(-2.60654 + 0.453835i) q^{7} -0.271829 q^{8} +1.00000 q^{9} -0.208127 q^{10} -4.35793 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} +(-1.98612 + 3.44007i) q^{16} +(1.76434 + 3.05592i) q^{17} +(-0.0340180 + 0.0589209i) q^{18} +6.90224 q^{19} +(-3.05199 + 5.28621i) q^{20} +(2.60654 - 0.453835i) q^{21} +(0.148248 - 0.256773i) q^{22} +(-1.66762 + 2.88840i) q^{23} +0.271829 q^{24} +(-2.17896 + 3.77408i) q^{25} +(0.245307 + 0.000255364i) q^{26} -1.00000 q^{27} +(-3.38475 - 4.05142i) q^{28} +(4.95991 + 8.59082i) q^{29} +0.208127 q^{30} +(4.62451 - 8.00989i) q^{31} +(-0.406957 - 0.704870i) q^{32} +4.35793 q^{33} -0.240077 q^{34} +(-5.18911 - 6.21117i) q^{35} +(0.997686 + 1.72804i) q^{36} +(0.0545230 - 0.0944366i) q^{37} +(-0.234800 + 0.406686i) q^{38} +(1.79952 + 3.12437i) q^{39} +(-0.415772 - 0.720139i) q^{40} +(1.76899 + 3.06399i) q^{41} +(-0.0619288 + 0.169018i) q^{42} +(-0.844102 + 1.46203i) q^{43} +(-4.34784 - 7.53068i) q^{44} +(1.52954 + 2.64923i) q^{45} +(-0.113458 - 0.196515i) q^{46} +(1.28133 + 2.21933i) q^{47} +(1.98612 - 3.44007i) q^{48} +(6.58807 - 2.36587i) q^{49} +(-0.148248 - 0.256773i) q^{50} +(-1.76434 - 3.05592i) q^{51} +(3.60369 - 6.22680i) q^{52} +(2.65681 - 4.60173i) q^{53} +(0.0340180 - 0.0589209i) q^{54} +(-6.66561 - 11.5452i) q^{55} +(0.708532 - 0.123365i) q^{56} -6.90224 q^{57} -0.674905 q^{58} +(-3.77852 - 6.54459i) q^{59} +(3.05199 - 5.28621i) q^{60} +4.87317 q^{61} +(0.314633 + 0.544960i) q^{62} +(-2.60654 + 0.453835i) q^{63} -7.88912 q^{64} +(5.52476 - 9.54621i) q^{65} +(-0.148248 + 0.256773i) q^{66} +0.680435 q^{67} +(-3.52051 + 6.09770i) q^{68} +(1.66762 - 2.88840i) q^{69} +(0.542491 - 0.0944552i) q^{70} +(-2.61572 + 4.53055i) q^{71} -0.271829 q^{72} +(1.75956 - 3.04764i) q^{73} +(0.00370952 + 0.00642508i) q^{74} +(2.17896 - 3.77408i) 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} -12.1514 q^{80} +1.00000 q^{81} -0.240710 q^{82} +5.41662 q^{83} +(3.38475 + 4.05142i) q^{84} +(-5.39723 + 9.34828i) q^{85} +(-0.0574293 - 0.0994705i) q^{86} +(-4.95991 - 8.59082i) q^{87} +1.18461 q^{88} +(3.85207 - 6.67198i) q^{89} -0.208127 q^{90} +(6.10848 + 7.32711i) q^{91} -6.65503 q^{92} +(-4.62451 + 8.00989i) q^{93} -0.174354 q^{94} +(10.5572 + 18.2856i) q^{95} +(0.406957 + 0.704870i) q^{96} +(-3.86359 + 6.69194i) q^{97} +(-0.0847135 + 0.468657i) q^{98} -4.35793 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9} + 8 q^{10} + 4 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} - 6 q^{16} - 2 q^{17} + 22 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} + 4 q^{23} - 12 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{27} - 7 q^{28} + 15 q^{29} - 8 q^{30} + 3 q^{31} + 3 q^{32} - 4 q^{33} - 68 q^{34} - 12 q^{35} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 5 q^{39} - 25 q^{40} + 19 q^{41} + 7 q^{42} + 11 q^{43} - 16 q^{44} + 2 q^{46} + 5 q^{47} + 6 q^{48} + 13 q^{49} - 7 q^{50} + 2 q^{51} + 36 q^{52} + 36 q^{53} - 15 q^{55} + 39 q^{56} - 22 q^{57} - 40 q^{58} - 17 q^{59} + 20 q^{60} + 44 q^{61} - 6 q^{62} + q^{63} - 20 q^{64} - 21 q^{65} - 7 q^{66} - 52 q^{67} + 5 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} + 12 q^{72} - 6 q^{73} + 15 q^{74} - 2 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} + 56 q^{80} + 16 q^{81} + 2 q^{82} + 36 q^{83} + 7 q^{84} - 4 q^{85} + 16 q^{86} - 15 q^{87} - 48 q^{88} + 20 q^{89} + 8 q^{90} - 7 q^{91} - 94 q^{92} - 3 q^{93} + 40 q^{94} - 3 q^{96} + 7 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9 + 8 * q^10 + 4 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 - 6 * q^16 - 2 * q^17 + 22 * q^19 - 20 * q^20 - q^21 + 7 * q^22 + 4 * q^23 - 12 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^27 - 7 * q^28 + 15 * q^29 - 8 * q^30 + 3 * q^31 + 3 * q^32 - 4 * q^33 - 68 * q^34 - 12 * q^35 - 6 * q^36 + 4 * q^37 + 2 * q^38 - 5 * q^39 - 25 * q^40 + 19 * q^41 + 7 * q^42 + 11 * q^43 - 16 * q^44 + 2 * q^46 + 5 * q^47 + 6 * q^48 + 13 * q^49 - 7 * q^50 + 2 * q^51 + 36 * q^52 + 36 * q^53 - 15 * q^55 + 39 * q^56 - 22 * q^57 - 40 * q^58 - 17 * q^59 + 20 * q^60 + 44 * q^61 - 6 * q^62 + q^63 - 20 * q^64 - 21 * q^65 - 7 * q^66 - 52 * q^67 + 5 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 + 12 * q^72 - 6 * q^73 + 15 * q^74 - 2 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 + 56 * q^80 + 16 * q^81 + 2 * q^82 + 36 * q^83 + 7 * q^84 - 4 * q^85 + 16 * q^86 - 15 * q^87 - 48 * q^88 + 20 * q^89 + 8 * q^90 - 7 * q^91 - 94 * q^92 - 3 * q^93 + 40 * q^94 - 3 * q^96 + 7 * q^97 - 3 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more