LMFDB - Embedded newform 273.2.j.c.100.8

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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.8
Root			$-0.828334 + 1.43472i$ of defining polynomial
Character	$\chi$	$=$	273.100
Dual form			273.2.j.c.172.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.828334 + 1.43472i) q^{2} +1.00000 q^{3} +(-0.372274 + 0.644798i) q^{4} +(1.05011 - 1.81885i) q^{5} +(0.828334 + 1.43472i) q^{6} +(-1.14598 - 2.38469i) q^{7} +2.07987 q^{8} +1.00000 q^{9} +3.47937 q^{10} -0.304241 q^{11} +(-0.372274 + 0.644798i) q^{12} +(-0.494423 + 3.57149i) q^{13} +(2.47210 - 3.61947i) q^{14} +(1.05011 - 1.81885i) q^{15} +(2.46737 + 4.27361i) q^{16} +(-2.90593 + 5.03321i) q^{17} +(0.828334 + 1.43472i) q^{18} -7.48756 q^{19} +(0.781858 + 1.35422i) q^{20} +(-1.14598 - 2.38469i) q^{21} +(-0.252013 - 0.436500i) q^{22} +(-3.00828 - 5.21049i) q^{23} +2.07987 q^{24} +(0.294535 + 0.510150i) q^{25} +(-5.53362 + 2.24903i) q^{26} +1.00000 q^{27} +(1.96426 + 0.148834i) q^{28} +(1.09353 - 1.89405i) q^{29} +3.47937 q^{30} +(3.51152 + 6.08213i) q^{31} +(-2.00775 + 3.47753i) q^{32} -0.304241 q^{33} -9.62831 q^{34} +(-5.54078 - 0.419832i) q^{35} +(-0.372274 + 0.644798i) q^{36} +(0.0524484 + 0.0908433i) q^{37} +(-6.20220 - 10.7425i) q^{38} +(-0.494423 + 3.57149i) q^{39} +(2.18409 - 3.78295i) q^{40} +(-1.00378 + 1.73860i) q^{41} +(2.47210 - 3.61947i) q^{42} +(4.03998 + 6.99746i) q^{43} +(0.113261 - 0.196174i) q^{44} +(1.05011 - 1.81885i) q^{45} +(4.98372 - 8.63206i) q^{46} +(4.30078 - 7.44916i) q^{47} +(2.46737 + 4.27361i) q^{48} +(-4.37347 + 5.46560i) q^{49} +(-0.487947 + 0.845149i) q^{50} +(-2.90593 + 5.03321i) q^{51} +(-2.11883 - 1.64838i) q^{52} +(-1.10014 - 1.90550i) q^{53} +(0.828334 + 1.43472i) q^{54} +(-0.319487 + 0.553367i) q^{55} +(-2.38348 - 4.95983i) q^{56} -7.48756 q^{57} +3.62323 q^{58} +(6.84210 - 11.8509i) q^{59} +(0.781858 + 1.35422i) q^{60} -11.0263 q^{61} +(-5.81742 + 10.0761i) q^{62} +(-1.14598 - 2.38469i) q^{63} +3.21714 q^{64} +(5.97679 + 4.64974i) q^{65} +(-0.252013 - 0.436500i) q^{66} +10.0815 q^{67} +(-2.16360 - 3.74747i) q^{68} +(-3.00828 - 5.21049i) q^{69} +(-3.98728 - 8.29721i) q^{70} +(-0.149636 - 0.259177i) q^{71} +2.07987 q^{72} +(-2.96778 - 5.14034i) q^{73} +(-0.0868896 + 0.150497i) q^{74} +(0.294535 + 0.510150i) q^{75} +(2.78743 - 4.82796i) q^{76} +(0.348653 + 0.725520i) q^{77} +(-5.53362 + 2.24903i) q^{78} +(6.54933 - 11.3438i) q^{79} +10.3641 q^{80} +1.00000 q^{81} -3.32586 q^{82} -9.33190 q^{83} +(1.96426 + 0.148834i) q^{84} +(6.10309 + 10.5709i) q^{85} +(-6.69291 + 11.5925i) q^{86} +(1.09353 - 1.89405i) q^{87} -0.632780 q^{88} +(-1.54769 - 2.68068i) q^{89} +3.47937 q^{90} +(9.08349 - 2.91380i) q^{91} +4.47962 q^{92} +(3.51152 + 6.08213i) q^{93} +14.2499 q^{94} +(-7.86277 + 13.6187i) q^{95} +(-2.00775 + 3.47753i) q^{96} +(-3.19711 - 5.53756i) q^{97} +(-11.4643 - 1.74736i) q^{98} -0.304241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) $ 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

Character values

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

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

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 $

$2$	0.828334	+	1.43472i	0.585721	+	1.01450i	0.994785	+	0.101992i	$0.0325217\pi$
$2$	0.828334	+	1.43472i	0.585721	+	1.01450i	−0.409065	+	0.912505i	$0.634145\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.372274	+	0.644798i	−0.186137	+	0.322399i
$5$	1.05011	−	1.81885i	0.469624	−	0.813412i	−0.529773	−	0.848139i	$-0.677723\pi$
$5$	1.05011	−	1.81885i	0.469624	−	0.813412i	0.999397	+	0.0347272i	$0.0110562\pi$
$6$	0.828334	+	1.43472i	0.338166	+	0.585721i
$7$	−1.14598	−	2.38469i	−0.433139	−	0.901327i
$7$	−1.14598	−	2.38469i	−0.433139	−	0.901327i
$8$	2.07987			0.735344
$9$	1.00000			0.333333
$10$	3.47937			1.10027
$11$	−0.304241			−0.0917321			−0.0458660	−	0.998948i	$-0.514605\pi$
$11$	−0.304241			−0.0917321			−0.0458660	+	0.998948i	$0.514605\pi$
$12$	−0.372274	+	0.644798i	−0.107466	+	0.186137i
$13$	−0.494423	+	3.57149i	−0.137128	+	0.990553i
$13$	−0.494423	+	3.57149i	−0.137128	+	0.990553i
$14$	2.47210	−	3.61947i	0.660696	−	0.967344i
$15$	1.05011	−	1.81885i	0.271137	−	0.469624i
$16$	2.46737	+	4.27361i	0.616843	+	1.06840i
$17$	−2.90593	+	5.03321i	−0.704791	+	1.22073i	0.261976	+	0.965074i	$0.415626\pi$
$17$	−2.90593	+	5.03321i	−0.704791	+	1.22073i	−0.966767	+	0.255659i	$0.917707\pi$
$18$	0.828334	+	1.43472i	0.195240	+	0.338166i
$19$	−7.48756			−1.71776			−0.858882	−	0.512173i	$-0.828841\pi$
$19$	−7.48756			−1.71776			−0.858882	+	0.512173i	$0.828841\pi$
$20$	0.781858	+	1.35422i	0.174829	+	0.302812i
$21$	−1.14598	−	2.38469i	−0.250073	−	0.520382i
$22$	−0.252013	−	0.436500i	−0.0537294	−	0.0930620i
$23$	−3.00828	−	5.21049i	−0.627270	−	1.08646i	−0.988097	−	0.153830i	$-0.950839\pi$
$23$	−3.00828	−	5.21049i	−0.627270	−	1.08646i	0.360828	−	0.932633i	$-0.382494\pi$
$24$	2.07987			0.424551
$25$	0.294535	+	0.510150i	0.0589070	+	0.102030i
$26$	−5.53362	+	2.24903i	−1.08523	+	0.441071i
$27$	1.00000			0.192450
$28$	1.96426	+	0.148834i	0.371210	+	0.0281270i
$29$	1.09353	−	1.89405i	0.203063	−	0.351716i	−0.746451	−	0.665441i	$-0.768244\pi$
$29$	1.09353	−	1.89405i	0.203063	−	0.351716i	0.949514	+	0.313725i	$0.101577\pi$
$30$	3.47937			0.635243
$31$	3.51152	+	6.08213i	0.630687	+	1.09238i	0.987411	+	0.158173i	$0.0505603\pi$
$31$	3.51152	+	6.08213i	0.630687	+	1.09238i	−0.356724	+	0.934210i	$0.616106\pi$
$32$	−2.00775	+	3.47753i	−0.354923	+	0.614745i
$33$	−0.304241			−0.0529616
$34$	−9.62831			−1.65124
$35$	−5.54078	−	0.419832i	−0.936563	−	0.0709645i
$36$	−0.372274	+	0.644798i	−0.0620457	+	0.107466i
$37$	0.0524484	+	0.0908433i	0.00862246	+	0.0149345i	0.870304	−	0.492514i	$-0.163922\pi$
$37$	0.0524484	+	0.0908433i	0.00862246	+	0.0149345i	−0.861682	+	0.507449i	$0.830589\pi$
$38$	−6.20220	−	10.7425i	−1.00613	−	1.74267i
$39$	−0.494423	+	3.57149i	−0.0791711	+	0.571896i
$40$	2.18409	−	3.78295i	0.345335	−	0.598138i
$41$	−1.00378	+	1.73860i	−0.156764	+	0.271524i	−0.933700	−	0.358056i	$-0.883440\pi$
$41$	−1.00378	+	1.73860i	−0.156764	+	0.271524i	0.776936	+	0.629580i	$0.216773\pi$
$42$	2.47210	−	3.61947i	0.381453	−	0.558496i
$43$	4.03998	+	6.99746i	0.616092	+	1.06710i	0.990192	+	0.139714i	$0.0446183\pi$
$43$	4.03998	+	6.99746i	0.616092	+	1.06710i	−0.374100	+	0.927388i	$0.622048\pi$
$44$	0.113261	−	0.196174i	0.0170747	−	0.0295743i
$45$	1.05011	−	1.81885i	0.156541	−	0.271137i
$46$	4.98372	−	8.63206i	0.734809	−	1.27273i
$47$	4.30078	−	7.44916i	0.627333	−	1.08657i	−0.360752	−	0.932662i	$-0.617480\pi$
$47$	4.30078	−	7.44916i	0.627333	−	1.08657i	0.988085	−	0.153910i	$-0.0491867\pi$
$48$	2.46737	+	4.27361i	0.356135	+	0.616843i
$49$	−4.37347	+	5.46560i	−0.624782	+	0.780799i
$50$	−0.487947	+	0.845149i	−0.0690061	+	0.119522i
$51$	−2.90593	+	5.03321i	−0.406911	+	0.704791i
$52$	−2.11883	−	1.64838i	−0.293829	−	0.228589i
$53$	−1.10014	−	1.90550i	−0.151116	−	0.261741i	0.780522	−	0.625128i	$-0.214953\pi$
$53$	−1.10014	−	1.90550i	−0.151116	−	0.261741i	−0.931638	+	0.363388i	$0.881620\pi$
$54$	0.828334	+	1.43472i	0.112722	+	0.195240i
$55$	−0.319487	+	0.553367i	−0.0430796	+	0.0746160i
$56$	−2.38348	−	4.95983i	−0.318506	−	0.662785i
$57$	−7.48756			−0.991752
$58$	3.62323			0.475753
$59$	6.84210	−	11.8509i	0.890766	−	1.54285i	0.0518074	−	0.998657i	$-0.483502\pi$
$59$	6.84210	−	11.8509i	0.890766	−	1.54285i	0.838959	−	0.544195i	$-0.183165\pi$
$60$	0.781858	+	1.35422i	0.100937	+	0.174829i
$61$	−11.0263			−1.41177			−0.705886	−	0.708325i	$-0.749451\pi$
$61$	−11.0263			−1.41177			−0.705886	+	0.708325i	$0.749451\pi$
$62$	−5.81742	+	10.0761i	−0.738813	+	1.27966i
$63$	−1.14598	−	2.38469i	−0.144380	−	0.300442i
$64$	3.21714			0.402142
$65$	5.97679	+	4.64974i	0.741329	+	0.576729i
$66$	−0.252013	−	0.436500i	−0.0310207	−	0.0537294i
$67$	10.0815			1.23165			0.615823	−	0.787885i	$-0.288824\pi$
$67$	10.0815			1.23165			0.615823	+	0.787885i	$0.288824\pi$
$68$	−2.16360	−	3.74747i	−0.262375	−	0.454448i
$69$	−3.00828	−	5.21049i	−0.362154	−	0.627270i
$70$	−3.98728	−	8.29721i	−0.476571	−	0.991706i
$71$	−0.149636	−	0.259177i	−0.0177585	−	0.0307587i	0.857010	−	0.515300i	$-0.172320\pi$
$71$	−0.149636	−	0.259177i	−0.0177585	−	0.0307587i	−0.874768	+	0.484542i	$0.838986\pi$
$72$	2.07987			0.245115
$73$	−2.96778	−	5.14034i	−0.347352	−	0.601631i	0.638426	−	0.769683i	$-0.279586\pi$
$73$	−2.96778	−	5.14034i	−0.347352	−	0.601631i	−0.985778	+	0.168052i	$0.946252\pi$
$74$	−0.0868896	+	0.150497i	−0.0101007	+	0.0174949i
$75$	0.294535	+	0.510150i	0.0340100	+	0.0589070i
$76$	2.78743	−	4.82796i	0.319740	−	0.553805i
$77$	0.348653	+	0.725520i	0.0397327	+	0.0826806i
$78$	−5.53362	+	2.24903i	−0.626560	+	0.254652i
$79$	6.54933	−	11.3438i	0.736857	−	1.27627i	−0.217047	−	0.976161i	$-0.569642\pi$
$79$	6.54933	−	11.3438i	0.736857	−	1.27627i	0.953904	−	0.300112i	$-0.0970242\pi$
$80$	10.3641			1.15874
$81$	1.00000			0.111111
$82$	−3.32586			−0.367280
$83$	−9.33190			−1.02431			−0.512155	−	0.858893i	$-0.671153\pi$
$83$	−9.33190			−1.02431			−0.512155	+	0.858893i	$0.671153\pi$
$84$	1.96426	+	0.148834i	0.214318	+	0.0162392i
$85$	6.10309	+	10.5709i	0.661973	+	1.14657i
$86$	−6.69291	+	11.5925i	−0.721715	+	1.25005i
$87$	1.09353	−	1.89405i	0.117239	−	0.203063i
$88$	−0.632780			−0.0674546
$89$	−1.54769	−	2.68068i	−0.164055	−	0.284152i	0.772264	−	0.635301i	$-0.219124\pi$
$89$	−1.54769	−	2.68068i	−0.164055	−	0.284152i	−0.936319	+	0.351150i	$0.885791\pi$
$90$	3.47937			0.366758
$91$	9.08349	−	2.91380i	0.952208	−	0.305449i
$92$	4.47962			0.467033
$93$	3.51152	+	6.08213i	0.364127	+	0.630687i
$94$	14.2499			1.46977
$95$	−7.86277	+	13.6187i	−0.806703	+	1.39725i
$96$	−2.00775	+	3.47753i	−0.204915	+	0.354923i
$97$	−3.19711	−	5.53756i	−0.324618	−	0.562254i	0.656817	−	0.754050i	$-0.271902\pi$
$97$	−3.19711	−	5.53756i	−0.324618	−	0.562254i	−0.981435	+	0.191795i	$0.938569\pi$
$98$	−11.4643	−	1.74736i	−1.15807	−	0.176510i
$99$	−0.304241			−0.0305774
$100$	−0.438591			−0.0438591
$101$	1.38002			0.137317			0.0686584	−	0.997640i	$-0.478128\pi$
$101$	1.38002			0.137317			0.0686584	+	0.997640i	$0.478128\pi$
$102$	−9.62831			−0.953345
$103$	−2.82628	+	4.89525i	−0.278481	+	0.482344i	−0.971008	−	0.239049i	$-0.923164\pi$
$103$	−2.82628	+	4.89525i	−0.278481	+	0.482344i	0.692526	+	0.721393i	$0.256498\pi$
$104$	−1.02833	+	7.42822i	−0.100837	+	0.728397i
$105$	−5.54078	−	0.419832i	−0.540725	−	0.0409714i
$106$	1.82257	−	3.15678i	0.177023	−	0.306614i
$107$	−7.06296	−	12.2334i	−0.682802	−	1.18265i	−0.974122	−	0.226022i	$-0.927428\pi$
$107$	−7.06296	−	12.2334i	−0.682802	−	1.18265i	0.291321	−	0.956626i	$-0.405905\pi$
$108$	−0.372274	+	0.644798i	−0.0358221	+	0.0620457i
$109$	−4.56805	−	7.91209i	−0.437539	−	0.757840i	0.559960	−	0.828520i	$-0.310817\pi$
$109$	−4.56805	−	7.91209i	−0.437539	−	0.757840i	−0.997499	+	0.0706794i	$0.977483\pi$
$110$	−1.05857			−0.100930
$111$	0.0524484	+	0.0908433i	0.00497818	+	0.00862246i
$112$	7.36368	−	10.7814i	0.695803	−	1.01874i
$113$	5.58957	+	9.68142i	0.525823	+	0.910751i	0.999548	+	0.0300785i	$0.00957573\pi$
$113$	5.58957	+	9.68142i	0.525823	+	0.910751i	−0.473725	+	0.880673i	$0.657091\pi$
$114$	−6.20220	−	10.7425i	−0.580889	−	1.00613i
$115$	−12.6361			−1.17832
$116$	0.814185	+	1.41021i	0.0755952	+	0.130935i
$117$	−0.494423	+	3.57149i	−0.0457095	+	0.330184i
$118$	22.6702			2.08696
$119$	15.3328	+	1.16178i	1.40555	+	0.106500i
$120$	2.18409	−	3.78295i	0.199379	−	0.345335i
$121$	−10.9074			−0.991585
$122$	−9.13346	−	15.8196i	−0.826904	−	1.43224i
$123$	−1.00378	+	1.73860i	−0.0905079	+	0.156764i
$124$	−5.22899			−0.469577
$125$	11.7383			1.04990
$126$	2.47210	−	3.61947i	0.220232	−	0.322448i
$127$	−8.41791	+	14.5802i	−0.746969	+	1.29379i	0.202300	+	0.979324i	$0.435158\pi$
$127$	−8.41791	+	14.5802i	−0.746969	+	1.29379i	−0.949269	+	0.314464i	$0.898175\pi$
$128$	6.68037	+	11.5707i	0.590466	+	1.02272i
$129$	4.03998	+	6.99746i	0.355701	+	0.616092i
$130$	−1.72028	+	12.4265i	−0.150879	+	1.08988i
$131$	−6.97748	+	12.0854i	−0.609625	+	1.05590i	0.381677	+	0.924296i	$0.375347\pi$
$131$	−6.97748	+	12.0854i	−0.609625	+	1.05590i	−0.991302	+	0.131606i	$0.957987\pi$
$132$	0.113261	−	0.196174i	0.00985811	−	0.0170747i
$133$	8.58057	+	17.8555i	0.744030	+	1.54827i
$134$	8.35081	+	14.4640i	0.721400	+	1.24950i
$135$	1.05011	−	1.81885i	0.0903791	−	0.156541i
$136$	−6.04394	+	10.4684i	−0.518264	+	0.897659i
$137$	0.304544	−	0.527486i	0.0260190	−	0.0450662i	−0.852723	−	0.522364i	$-0.825050\pi$
$137$	0.304544	−	0.527486i	0.0260190	−	0.0450662i	0.878742	+	0.477298i	$0.158384\pi$
$138$	4.98372	−	8.63206i	0.424242	−	0.734809i
$139$	−4.23753	−	7.33962i	−0.359423	−	0.622539i	0.628442	−	0.777857i	$-0.283693\pi$
$139$	−4.23753	−	7.33962i	−0.359423	−	0.622539i	−0.987865	+	0.155318i	$0.950360\pi$
$140$	2.33340	−	3.41639i	0.197208	−	0.288738i
$141$	4.30078	−	7.44916i	0.362191	−	0.627333i
$142$	0.247897	−	0.429371i	0.0208031	−	0.0360320i
$143$	0.150424	−	1.08659i	0.0125791	−	0.0908655i
$144$	2.46737	+	4.27361i	0.205614	+	0.356135i
$145$	−2.29665	−	3.97792i	−0.190727	−	0.330348i
$146$	4.91662	−	8.51583i	0.406902	−	0.704775i
$147$	−4.37347	+	5.46560i	−0.360718	+	0.450795i
$148$	−0.0781008			−0.00641984
$149$	6.62649			0.542863			0.271431	−	0.962458i	$-0.412503\pi$
$149$	6.62649			0.542863			0.271431	+	0.962458i	$0.412503\pi$
$150$	−0.487947	+	0.845149i	−0.0398407	+	0.0690061i
$151$	0.762113	+	1.32002i	0.0620199	+	0.107422i	0.895368	−	0.445327i	$-0.146912\pi$
$151$	0.762113	+	1.32002i	0.0620199	+	0.107422i	−0.833348	+	0.552748i	$0.813579\pi$
$152$	−15.5731			−1.26315
$153$	−2.90593	+	5.03321i	−0.234930	+	0.406911i
$154$	−0.752114	+	1.10119i	−0.0606071	+	0.0887365i
$155$	14.7499			1.18474
$156$	−2.11883	−	1.64838i	−0.169642	−	0.131976i
$157$	8.46505	+	14.6619i	0.675584	+	1.17015i	0.976298	+	0.216432i	$0.0694419\pi$
$157$	8.46505	+	14.6619i	0.675584	+	1.17015i	−0.300713	+	0.953715i	$0.597225\pi$
$158$	21.7001			1.72637
$159$	−1.10014	−	1.90550i	−0.0872468	−	0.151116i
$160$	4.21672	+	7.30357i	0.333361	+	0.577398i
$161$	−8.97798	+	13.1449i	−0.707564	+	1.03596i
$162$	0.828334	+	1.43472i	0.0650801	+	0.112722i
$163$	9.64163			0.755191			0.377595	−	0.925971i	$-0.376751\pi$
$163$	9.64163			0.755191			0.377595	+	0.925971i	$0.376751\pi$
$164$	−0.747364	−	1.29447i	−0.0583593	−	0.101081i
$165$	−0.319487	+	0.553367i	−0.0248720	+	0.0430796i
$166$	−7.72993	−	13.3886i	−0.599959	−	1.03916i
$167$	9.10684	−	15.7735i	0.704708	−	1.22059i	−0.262088	−	0.965044i	$-0.584411\pi$
$167$	9.10684	−	15.7735i	0.704708	−	1.22059i	0.966797	−	0.255547i	$-0.0822555\pi$
$168$	−2.38348	−	4.95983i	−0.183889	−	0.382659i
$169$	−12.5111	−	3.53166i	−0.962392	−	0.271666i
$170$	−10.1108	+	17.5124i	−0.775462	+	1.34314i
$171$	−7.48756			−0.572588
$172$	−6.01593			−0.458710
$173$	21.5144			1.63571			0.817853	−	0.575427i	$-0.195164\pi$
$173$	21.5144			1.63571			0.817853	+	0.575427i	$0.195164\pi$
$174$	3.62323			0.274676
$175$	0.879018	−	1.28699i	0.0664475	−	0.0972876i
$176$	−0.750676	−	1.30021i	−0.0565843	−	0.0980069i
$177$	6.84210	−	11.8509i	0.514284	−	0.890766i
$178$	2.56401	−	4.44100i	0.192181	−	0.332867i
$179$	−2.72518			−0.203689			−0.101845	−	0.994800i	$-0.532474\pi$
$179$	−2.72518			−0.203689			−0.101845	+	0.994800i	$0.532474\pi$
$180$	0.781858	+	1.35422i	0.0582763	+	0.100937i
$181$	−6.47170			−0.481038			−0.240519	−	0.970644i	$-0.577318\pi$
$181$	−6.47170			−0.481038			−0.240519	+	0.970644i	$0.577318\pi$
$182$	11.7046	+	10.6186i	0.867606	+	0.787105i
$183$	−11.0263			−0.815087
$184$	−6.25682	−	10.8371i	−0.461259	−	0.798924i
$185$	0.220307			0.0161973
$186$	−5.81742	+	10.0761i	−0.426554	+	0.738813i
$187$	0.884102	−	1.53131i	0.0646519	−	0.111980i
$188$	3.20214	+	5.54626i	0.233540	+	0.404503i
$189$	−1.14598	−	2.38469i	−0.0833576	−	0.173461i
$190$	−26.0520			−1.89001
$191$	12.7429			0.922042			0.461021	−	0.887389i	$-0.347483\pi$
$191$	12.7429			0.922042			0.461021	+	0.887389i	$0.347483\pi$
$192$	3.21714			0.232177
$193$	−0.652105			−0.0469395			−0.0234698	−	0.999725i	$-0.507471\pi$
$193$	−0.652105			−0.0469395			−0.0234698	+	0.999725i	$0.507471\pi$
$194$	5.29656	−	9.17390i	0.380271	−	0.658648i
$195$	5.97679	+	4.64974i	0.428007	+	0.332975i
$196$	−1.89607	−	4.85471i	−0.135434	−	0.346765i
$197$	3.03080	−	5.24950i	0.215936	−	0.374011i	−0.737626	−	0.675209i	$-0.764053\pi$
$197$	3.03080	−	5.24950i	0.215936	−	0.374011i	0.953562	+	0.301198i	$0.0973866\pi$
$198$	−0.252013	−	0.436500i	−0.0179098	−	0.0310207i
$199$	−1.02227	+	1.77062i	−0.0724666	+	0.125516i	−0.899982	−	0.435927i	$-0.856420\pi$
$199$	−1.02227	+	1.77062i	−0.0724666	+	0.125516i	0.827515	+	0.561443i	$0.189754\pi$
$200$	0.612594	+	1.06104i	0.0433169	+	0.0750271i
$201$	10.0815			0.711091
$202$	1.14311	+	1.97993i	0.0804293	+	0.139308i
$203$	−5.76987	−	0.437190i	−0.404966	−	0.0306847i
$204$	−2.16360	−	3.74747i	−0.151483	−	0.262375i
$205$	2.10816	+	3.65144i	0.147240	+	0.255028i
$206$	−9.36440			−0.652449
$207$	−3.00828	−	5.21049i	−0.209090	−	0.362154i
$208$	−16.4831	+	6.69922i	−1.14290	+	0.464507i
$209$	2.27802			0.157574
$210$	−3.98728	−	8.29721i	−0.275148	−	0.572562i
$211$	−2.27669	+	3.94334i	−0.156734	+	0.271471i	−0.933689	−	0.358085i	$-0.883430\pi$
$211$	−2.27669	+	3.94334i	−0.156734	+	0.271471i	0.776955	+	0.629556i	$0.216763\pi$
$212$	1.63822			0.112513
$213$	−0.149636	−	0.259177i	−0.0102529	−	0.0177585i
$214$	11.7010	−	20.2667i	0.799862	−	1.38540i
$215$	16.9697			1.15733
$216$	2.07987			0.141517
$217$	10.4799	−	15.3439i	0.711419	−	1.04161i
$218$	7.56773	−	13.1077i	0.512552	−	0.887765i
$219$	−2.96778	−	5.14034i	−0.200544	−	0.347352i
$220$	−0.237873	−	0.412009i	−0.0160374	−	0.0277776i
$221$	−16.5393	−	12.8670i	−1.11255	−	0.865530i
$222$	−0.0868896	+	0.150497i	−0.00583165	+	0.0101007i
$223$	7.85506	−	13.6054i	0.526014	−	0.911082i	−0.473527	−	0.880779i	$-0.657019\pi$
$223$	7.85506	−	13.6054i	0.526014	−	0.911082i	0.999541	−	0.0303029i	$-0.00964720\pi$
$224$	10.5936	+	0.802693i	0.707818	+	0.0536322i
$225$	0.294535	+	0.510150i	0.0196357	+	0.0340100i
$226$	−9.26006	+	16.0389i	−0.615970	+	1.06689i
$227$	6.27169	−	10.8629i	0.416267	−	0.720995i	−0.579294	−	0.815119i	$-0.696672\pi$
$227$	6.27169	−	10.8629i	0.416267	−	0.720995i	0.995561	+	0.0941238i	$0.0300049\pi$
$228$	2.78743	−	4.82796i	0.184602	−	0.319740i
$229$	−10.3182	+	17.8717i	−0.681849	+	1.18100i	0.292567	+	0.956245i	$0.405490\pi$
$229$	−10.3182	+	17.8717i	−0.681849	+	1.18100i	−0.974416	+	0.224752i	$0.927843\pi$
$230$	−10.4669	−	18.1292i	−0.690168	−	1.19541i
$231$	0.348653	+	0.725520i	0.0229397	+	0.0477357i
$232$	2.27439	−	3.93936i	0.149321	−	0.258632i
$233$	4.00908	−	6.94394i	0.262644	−	0.454912i	−0.704300	−	0.709903i	$-0.748739\pi$
$233$	4.00908	−	6.94394i	0.262644	−	0.454912i	0.966944	+	0.254990i	$0.0820723\pi$
$234$	−5.53362	+	2.24903i	−0.361744	+	0.147024i
$235$	−9.03258	−	15.6449i	−0.589221	−	1.02056i
$236$	5.09428	+	8.82355i	0.331609	+	0.574364i
$237$	6.54933	−	11.3438i	0.425425	−	0.736857i
$238$	11.0338	+	22.9605i	0.715217	+	1.48831i
$239$	−1.16836			−0.0755752			−0.0377876	−	0.999286i	$-0.512031\pi$
$239$	−1.16836			−0.0755752			−0.0377876	+	0.999286i	$0.512031\pi$
$240$	10.3641			0.668997
$241$	0.536076	−	0.928511i	0.0345317	−	0.0598107i	−0.848243	−	0.529607i	$-0.822339\pi$
$241$	0.536076	−	0.928511i	0.0345317	−	0.0598107i	0.882775	+	0.469796i	$0.155673\pi$
$242$	−9.03500	−	15.6491i	−0.580792	−	1.00596i
$243$	1.00000			0.0641500
$244$	4.10481	−	7.10973i	0.262783	−	0.455154i
$245$	5.34844	+	13.6941i	0.341699	+	0.874887i
$246$	−3.32586			−0.212049
$247$	3.70203	−	26.7418i	0.235554	−	1.70154i
$248$	7.30349	+	12.6500i	0.463772	+	0.803277i
$249$	−9.33190			−0.591385
$250$	9.72322	+	16.8411i	0.614950	+	1.06513i
$251$	−6.29717	−	10.9070i	−0.397474	−	0.688445i	0.595940	−	0.803029i	$-0.296780\pi$
$251$	−6.29717	−	10.9070i	−0.397474	−	0.688445i	−0.993414	+	0.114584i	$0.963446\pi$
$252$	1.96426	+	0.148834i	0.123737	+	0.00937568i
$253$	0.915242	+	1.58525i	0.0575408	+	0.0996635i
$254$	−27.8914			−1.75006
$255$	6.10309	+	10.5709i	0.382190	+	0.661973i
$256$	−7.85001	+	13.5966i	−0.490626	+	0.849788i
$257$	10.6490	+	18.4446i	0.664268	+	1.15055i	0.979483	+	0.201526i	$0.0645899\pi$
$257$	10.6490	+	18.4446i	0.664268	+	1.15055i	−0.315215	+	0.949020i	$0.602077\pi$
$258$	−6.69291	+	11.5925i	−0.416683	+	0.721715i
$259$	0.156528	−	0.229177i	0.00972619	−	0.0142404i
$260$	−5.22315	+	2.12284i	−0.323926	+	0.131653i
$261$	1.09353	−	1.89405i	0.0676877	−	0.117239i
$262$	−23.1187			−1.42828
$263$	−22.0285			−1.35833			−0.679167	−	0.733984i	$-0.737659\pi$
$263$	−22.0285			−1.35833			−0.679167	+	0.733984i	$0.737659\pi$
$264$	−0.632780			−0.0389449
$265$	−4.62108			−0.283871
$266$	−18.5100	+	27.1010i	−1.13492	+	1.66167i
$267$	−1.54769	−	2.68068i	−0.0947172	−	0.164055i
$268$	−3.75307	+	6.50050i	−0.229255	+	0.397081i
$269$	−8.92932	+	15.4660i	−0.544430	+	0.942981i	0.454212	+	0.890893i	$0.349921\pi$
$269$	−8.92932	+	15.4660i	−0.544430	+	0.942981i	−0.998643	+	0.0520871i	$0.983413\pi$
$270$	3.47937			0.211748
$271$	3.60531	+	6.24459i	0.219007	+	0.379332i	0.954505	−	0.298196i	$-0.0963848\pi$
$271$	3.60531	+	6.24459i	0.219007	+	0.379332i	−0.735497	+	0.677527i	$0.763051\pi$
$272$	−28.6800			−1.73898
$273$	9.08349	−	2.91380i	0.549758	−	0.176351i
$274$	1.00906			0.0609594
$275$	−0.0896097	−	0.155208i	−0.00540367	−	0.00935942i
$276$	4.47962			0.269641
$277$	2.19138	−	3.79558i	0.131667	−	0.228054i	−0.792652	−	0.609674i	$-0.791300\pi$
$277$	2.19138	−	3.79558i	0.131667	−	0.228054i	0.924319	+	0.381620i	$0.124634\pi$
$278$	7.02018	−	12.1593i	0.421043	−	0.729267i
$279$	3.51152	+	6.08213i	0.210229	+	0.364127i
$280$	−11.5241	−	0.873193i	−0.688696	−	0.0521833i
$281$	−0.474280			−0.0282932			−0.0141466	−	0.999900i	$-0.504503\pi$
$281$	−0.474280			−0.0282932			−0.0141466	+	0.999900i	$0.504503\pi$
$282$	14.2499			0.848570
$283$	−1.12693			−0.0669888			−0.0334944	−	0.999439i	$-0.510664\pi$
$283$	−1.12693			−0.0669888			−0.0334944	+	0.999439i	$0.510664\pi$
$284$	0.222823			0.0132221
$285$	−7.86277	+	13.6187i	−0.465750	+	0.806703i
$286$	1.68356	−	0.684247i	0.0995507	−	0.0404604i
$287$	5.29633	+	0.401309i	0.312632	+	0.0236885i
$288$	−2.00775	+	3.47753i	−0.118308	+	0.204915i
$289$	−8.38883	−	14.5299i	−0.493460	−	0.854698i
$290$	3.80479	−	6.59009i	0.223425	−	0.386983i
$291$	−3.19711	−	5.53756i	−0.187418	−	0.324618i
$292$	4.41931			0.258620
$293$	6.43732	+	11.1498i	0.376072	+	0.651376i	0.990487	−	0.137607i	$-0.0439411\pi$
$293$	6.43732	+	11.1498i	0.376072	+	0.651376i	−0.614415	+	0.788983i	$0.710608\pi$
$294$	−11.4643	−	1.74736i	−0.668610	−	0.101908i
$295$	−14.3699	−	24.8895i	−0.836650	−	1.44912i
$296$	0.109086	+	0.188942i	0.00634048	+	0.0109820i
$297$	−0.304241			−0.0176539
$298$	5.48894	+	9.50713i	0.317966	+	0.550733i
$299$	20.0966	−	8.16785i	1.16222	−	0.472359i
$300$	−0.438591			−0.0253221
$301$	12.0570	−	17.6530i	0.694955	−	1.01750i
$302$	−1.26257	+	2.18683i	−0.0726526	+	0.125838i
$303$	1.38002			0.0792799
$304$	−18.4746	−	31.9989i	−1.05959	−	1.83527i
$305$	−11.5788	+	20.0551i	−0.663002	+	1.14835i
$306$	−9.62831			−0.550414
$307$	−8.01524			−0.457454			−0.228727	−	0.973491i	$-0.573456\pi$
$307$	−8.01524			−0.457454			−0.228727	+	0.973491i	$0.573456\pi$
$308$	−0.597608	−	0.0452815i	−0.0340519	−	0.00258015i
$309$	−2.82628	+	4.89525i	−0.160781	+	0.278481i
$310$	12.2179	+	21.1620i	0.693928	+	1.20192i
$311$	−1.57684	−	2.73117i	−0.0894145	−	0.154871i	0.817849	−	0.575433i	$-0.195166\pi$
$311$	−1.57684	−	2.73117i	−0.0894145	−	0.154871i	−0.907264	+	0.420562i	$0.861833\pi$
$312$	−1.02833	+	7.42822i	−0.0582180	+	0.420540i
$313$	0.264591	−	0.458285i	0.0149556	−	0.0259038i	−0.858451	−	0.512896i	$-0.828573\pi$
$313$	0.264591	−	0.458285i	0.0149556	−	0.0259038i	0.873406	+	0.486992i	$0.161906\pi$
$314$	−14.0238	+	24.2899i	−0.791407	+	1.37076i
$315$	−5.54078	−	0.419832i	−0.312188	−	0.0236548i
$316$	4.87629	+	8.44599i	0.274313	+	0.475124i
$317$	−2.19029	+	3.79369i	−0.123019	+	0.213075i	−0.920957	−	0.389665i	$-0.872591\pi$
$317$	−2.19029	+	3.79369i	−0.123019	+	0.213075i	0.797938	+	0.602739i	$0.205924\pi$
$318$	1.82257	−	3.15678i	0.102205	−	0.177023i
$319$	−0.332696	+	0.576247i	−0.0186274	+	0.0322636i
$320$	3.37835	−	5.85148i	0.188856	−	0.327107i
$321$	−7.06296	−	12.2334i	−0.394216	−	0.682802i
$322$	−26.2960	−	1.99248i	−1.46542	−	0.111036i
$323$	21.7583	−	37.6865i	1.21066	−	2.09693i
$324$	−0.372274	+	0.644798i	−0.0206819	+	0.0358221i
$325$	−1.96762	+	0.799700i	−0.109144	+	0.0443593i
$326$	7.98649	+	13.8330i	0.442331	+	0.766139i
$327$	−4.56805	−	7.91209i	−0.252613	−	0.437539i
$328$	−2.08773	+	3.61605i	−0.115276	+	0.199663i
$329$	−22.6925	−	1.71944i	−1.25108	−	0.0947957i
$330$	−1.05857			−0.0582722
$331$	−26.9352			−1.48049			−0.740246	−	0.672336i	$-0.765291\pi$
$331$	−26.9352			−1.48049			−0.740246	+	0.672336i	$0.765291\pi$
$332$	3.47403	−	6.01719i	0.190662	−	0.330236i
$333$	0.0524484	+	0.0908433i	0.00287415	+	0.00497818i
$334$	30.1740			1.65105
$335$	10.5866	−	18.3366i	0.578410	−	1.00184i
$336$	7.36368	−	10.7814i	0.401722	−	0.588172i
$337$	20.8356			1.13498			0.567492	−	0.823379i	$-0.307914\pi$
$337$	20.8356			1.13498			0.567492	+	0.823379i	$0.307914\pi$
$338$	−5.29643	−	20.8753i	−0.288088	−	1.13546i
$339$	5.58957	+	9.68142i	0.303584	+	0.525823i
$340$	−9.08809			−0.492871
$341$	−1.06835	−	1.85043i	−0.0578543	−	0.100207i
$342$	−6.20220	−	10.7425i	−0.335377	−	0.580889i
$343$	18.0456	+	4.16592i	0.974373	+	0.224939i
$344$	8.40263	+	14.5538i	0.453039	+	0.784687i
$345$	−12.6361			−0.680305
$346$	17.8211	+	30.8670i	0.958067	+	1.65942i
$347$	6.66918	−	11.5514i	0.358021	−	0.620110i	−0.629610	−	0.776912i	$-0.716785\pi$
$347$	6.66918	−	11.5514i	0.358021	−	0.620110i	0.987630	+	0.156802i	$0.0501185\pi$
$348$	0.814185	+	1.41021i	0.0436449	+	0.0755952i
$349$	−10.2622	+	17.7746i	−0.549322	+	0.951453i	0.449000	+	0.893532i	$0.351780\pi$
$349$	−10.2622	+	17.7746i	−0.549322	+	0.951453i	−0.998321	+	0.0579208i	$0.981553\pi$
$350$	2.57459	+	0.195080i	0.137618	+	0.0104275i
$351$	−0.494423	+	3.57149i	−0.0263904	+	0.190632i
$352$	0.610840	−	1.05801i	0.0325579	−	0.0563919i
$353$	−6.44714			−0.343147			−0.171573	−	0.985171i	$-0.554885\pi$
$353$	−6.44714			−0.343147			−0.171573	+	0.985171i	$0.554885\pi$
$354$	22.6702			1.20491
$355$	−0.628538			−0.0333593
$356$	2.30466			0.122147
$357$	15.3328	+	1.16178i	0.811496	+	0.0614880i
$358$	−2.25736	−	3.90986i	−0.119305	−	0.206642i
$359$	−4.38549	+	7.59588i	−0.231457	+	0.400895i	−0.958237	−	0.285975i	$-0.907683\pi$
$359$	−4.38549	+	7.59588i	−0.231457	+	0.400895i	0.726780	+	0.686870i	$0.241016\pi$
$360$	2.18409	−	3.78295i	0.115112	−	0.199379i
$361$	37.0636			1.95071
$362$	−5.36073	−	9.28506i	−0.281754	−	0.488012i
$363$	−10.9074			−0.572492
$364$	−1.50274	+	6.94175i	−0.0787648	+	0.363846i
$365$	−12.4660			−0.652499
$366$	−9.13346	−	15.8196i	−0.477413	−	0.826904i
$367$	12.1796			0.635772			0.317886	−	0.948129i	$-0.397027\pi$
$367$	12.1796			0.635772			0.317886	+	0.948129i	$0.397027\pi$
$368$	14.8451	−	25.7125i	0.773854	−	1.34035i
$369$	−1.00378	+	1.73860i	−0.0522548	+	0.0905079i
$370$	0.182487	+	0.316077i	0.00948707	+	0.0164321i
$371$	−3.28329	+	4.80715i	−0.170460	+	0.249575i
$372$	−5.22899			−0.271111
$373$	30.5975			1.58428			0.792140	−	0.610339i	$-0.208967\pi$
$373$	30.5975			1.58428			0.792140	+	0.610339i	$0.208967\pi$
$374$	2.92933			0.151472
$375$	11.7383			0.606162
$376$	8.94504	−	15.4933i	0.461305	−	0.799004i
$377$	6.22391	+	4.84199i	0.320547	+	0.249375i
$378$	2.47210	−	3.61947i	0.127151	−	0.186165i
$379$	−2.54078	+	4.40075i	−0.130511	+	0.226052i	−0.923874	−	0.382698i	$-0.874995\pi$
$379$	−2.54078	+	4.40075i	−0.130511	+	0.226052i	0.793363	+	0.608749i	$0.208328\pi$
$380$	−5.85421	−	10.1398i	−0.300315	−	0.520160i
$381$	−8.41791	+	14.5802i	−0.431263	+	0.746969i
$382$	10.5554	+	18.2824i	0.540059	+	0.935410i
$383$	−24.6280			−1.25843			−0.629217	−	0.777230i	$-0.716624\pi$
$383$	−24.6280			−1.25843			−0.629217	+	0.777230i	$0.716624\pi$
$384$	6.68037	+	11.5707i	0.340906	+	0.590466i
$385$	1.68573	+	0.127730i	0.0859129	+	0.00650972i
$386$	−0.540161	−	0.935585i	−0.0274934	−	0.0476200i
$387$	4.03998	+	6.99746i	0.205364	+	0.355701i
$388$	4.76081			0.241694
$389$	−9.26991	−	16.0559i	−0.470003	−	0.814069i	0.529409	−	0.848367i	$-0.322414\pi$
$389$	−9.26991	−	16.0559i	−0.470003	−	0.814069i	−0.999412	+	0.0342980i	$0.989080\pi$
$390$	−1.72028	+	12.4265i	−0.0871099	+	0.629242i
$391$	34.9674			1.76838
$392$	−9.09624	+	11.3677i	−0.459429	+	0.574156i
$393$	−6.97748	+	12.0854i	−0.351967	+	0.609625i
$394$	10.0421			0.505912
$395$	−13.7550	−	23.8244i	−0.692091	−	1.19874i
$396$	0.113261	−	0.196174i	0.00569158	−	0.00985811i
$397$	31.2026			1.56601			0.783007	−	0.622013i	$-0.213685\pi$
$397$	31.2026			1.56601			0.783007	+	0.622013i	$0.213685\pi$
$398$	−3.38712			−0.169781
$399$	8.58057	+	17.8555i	0.429566	+	0.893893i
$400$	−1.45346	+	2.51746i	−0.0726728	+	0.125873i
$401$	17.1125	+	29.6396i	0.854555	+	1.48013i	0.877057	+	0.480386i	$0.159504\pi$
$401$	17.1125	+	29.6396i	0.854555	+	1.48013i	−0.0225016	+	0.999747i	$0.507163\pi$
$402$	8.35081	+	14.4640i	0.416501	+	0.721400i
$403$	−23.4584	+	9.53421i	−1.16855	+	0.474933i
$404$	−0.513745	+	0.889832i	−0.0255598	+	0.0442708i
$405$	1.05011	−	1.81885i	0.0521804	−	0.0903791i
$406$	−4.15214	−	8.64027i	−0.206067	−	0.428809i
$407$	−0.0159570	−	0.0276383i	−0.000790957	−	0.00136998i
$408$	−6.04394	+	10.4684i	−0.299220	+	0.518264i
$409$	4.97900	−	8.62389i	0.246196	−	0.426424i	−0.716271	−	0.697822i	$-0.754153\pi$
$409$	4.97900	−	8.62389i	0.246196	−	0.426424i	0.962467	+	0.271398i	$0.0874860\pi$
$410$	−3.49252	+	6.04923i	−0.172484	+	0.298750i
$411$	0.304544	−	0.527486i	0.0150221	−	0.0260190i
$412$	−2.10430	−	3.64475i	−0.103671	−	0.179564i
$413$	−36.1015	−	2.73546i	−1.77644	−	0.134603i
$414$	4.98372	−	8.63206i	0.244936	−	0.424242i
$415$	−9.79953	+	16.9733i	−0.481040	+	0.833186i
$416$	−11.4273	−	8.89003i	−0.560268	−	0.435870i
$417$	−4.23753	−	7.33962i	−0.207513	−	0.359423i
$418$	1.88696	+	3.26832i	0.0922944	+	0.159859i
$419$	0.586220	−	1.01536i	0.0286387	−	0.0496037i	−0.851351	−	0.524597i	$-0.824216\pi$
$419$	0.586220	−	1.01536i	0.0286387	−	0.0496037i	0.879990	+	0.474993i	$0.157549\pi$
$420$	2.33340	−	3.41639i	0.113858	−	0.166703i
$421$	−10.2374			−0.498938			−0.249469	−	0.968383i	$-0.580256\pi$
$421$	−10.2374			−0.498938			−0.249469	+	0.968383i	$0.580256\pi$
$422$	−7.54343			−0.367209
$423$	4.30078	−	7.44916i	0.209111	−	0.362191i
$424$	−2.28815	−	3.96318i	−0.111122	−	0.192469i
$425$	−3.42359			−0.166069
$426$	0.247897	−	0.429371i	0.0120107	−	0.0208031i
$427$	12.6359	+	26.2943i	0.611493	+	1.27247i
$428$	10.5174			0.508379
$429$	0.150424	−	1.08659i	0.00726253	−	0.0524612i
$430$	14.0566	+	24.3467i	0.677869	+	1.17410i
$431$	23.6395			1.13868			0.569338	−	0.822103i	$-0.307200\pi$
$431$	23.6395			1.13868			0.569338	+	0.822103i	$0.307200\pi$
$432$	2.46737	+	4.27361i	0.118712	+	0.205614i
$433$	−0.246165	−	0.426370i	−0.0118299	−	0.0204900i	0.860050	−	0.510210i	$-0.170432\pi$
$433$	−0.246165	−	0.426370i	−0.0118299	−	0.0204900i	−0.871880	+	0.489720i	$0.837099\pi$
$434$	30.6949	+	2.32579i	1.47340	+	0.111641i
$435$	−2.29665	−	3.97792i	−0.110116	−	0.190727i
$436$	6.80226			0.325769
$437$	22.5247	+	39.0139i	1.07750	+	1.86629i
$438$	4.91662	−	8.51583i	0.234925	−	0.406902i
$439$	7.53188	+	13.0456i	0.359477	+	0.622633i	0.987874	−	0.155261i	$-0.0496217\pi$
$439$	7.53188	+	13.0456i	0.359477	+	0.622633i	−0.628396	+	0.777893i	$0.716288\pi$
$440$	−0.664490	+	1.15093i	−0.0316783	+	0.0548684i
$441$	−4.37347	+	5.46560i	−0.208261	+	0.260266i
$442$	4.76046	−	34.3874i	0.226432	−	1.63564i
$443$	−13.3996	+	23.2088i	−0.636635	+	1.10268i	0.349531	+	0.936925i	$0.386341\pi$
$443$	−13.3996	+	23.2088i	−0.636635	+	1.10268i	−0.986166	+	0.165760i	$0.946992\pi$
$444$	−0.0781008			−0.00370650
$445$	−6.50099			−0.308177
$446$	26.0264			1.23239
$447$	6.62649			0.313422
$448$	−3.68677	−	7.67187i	−0.174183	−	0.362462i
$449$	2.26268	+	3.91908i	0.106783	+	0.184953i	0.914465	−	0.404665i	$-0.132612\pi$
$449$	2.26268	+	3.91908i	0.106783	+	0.184953i	−0.807683	+	0.589618i	$0.799278\pi$
$450$	−0.487947	+	0.845149i	−0.0230020	+	0.0398407i
$451$	0.305391	−	0.528953i	0.0143803	−	0.0249074i
$452$	−8.32341			−0.391500
$453$	0.762113	+	1.32002i	0.0358072	+	0.0620199i
$454$	20.7802			0.975264
$455$	4.23892	−	19.5813i	0.198723	−	0.917984i
$456$	−15.5731			−0.729278
$457$	−17.1770	−	29.7514i	−0.803505	−	1.39171i	−0.917296	−	0.398207i	$-0.869633\pi$
$457$	−17.1770	−	29.7514i	−0.803505	−	1.39171i	0.113790	−	0.993505i	$-0.463701\pi$
$458$	−34.1878			−1.59749
$459$	−2.90593	+	5.03321i	−0.135637	+	0.234930i
$460$	4.70410	−	8.14773i	0.219330	−	0.379890i
$461$	−0.499436	−	0.865049i	−0.0232611	−	0.0402893i	0.854161	−	0.520009i	$-0.174072\pi$
$461$	−0.499436	−	0.865049i	−0.0232611	−	0.0402893i	−0.877422	+	0.479720i	$0.840738\pi$
$462$	−0.752114	+	1.10119i	−0.0349915	+	0.0512320i
$463$	32.5538			1.51290			0.756452	−	0.654049i	$-0.226931\pi$
$463$	32.5538			1.51290			0.756452	+	0.654049i	$0.226931\pi$
$464$	10.7926			0.501032
$465$	14.7499			0.684012
$466$	13.2834			0.615343
$467$	12.1056	−	20.9675i	0.560180	−	0.970261i	−0.437300	−	0.899316i	$-0.644065\pi$
$467$	12.1056	−	20.9675i	0.560180	−	0.970261i	0.997480	−	0.0709451i	$-0.0226015\pi$
$468$	−2.11883	−	1.64838i	−0.0979429	−	0.0761963i
$469$	−11.5531	−	24.0411i	−0.533473	−	1.11012i
$470$	14.9640	−	25.9184i	0.690237	−	1.19553i
$471$	8.46505	+	14.6619i	0.390049	+	0.675584i
$472$	14.2307	−	24.6482i	0.655019	−	1.13453i
$473$	−1.22913	−	2.12891i	−0.0565154	−	0.0978875i
$474$	21.7001			0.996720
$475$	−2.20535	−	3.81978i	−0.101188	−	0.175263i
$476$	−6.45711	+	9.45404i	−0.295961	+	0.433325i
$477$	−1.10014	−	1.90550i	−0.0503720	−	0.0872468i
$478$	−0.967796	−	1.67627i	−0.0442660	−	0.0766709i
$479$	−30.3368			−1.38612			−0.693061	−	0.720879i	$-0.743738\pi$
$479$	−30.3368			−1.38612			−0.693061	+	0.720879i	$0.743738\pi$
$480$	4.21672	+	7.30357i	0.192466	+	0.333361i
$481$	−0.350378	+	0.142404i	−0.0159758	+	0.00649306i
$482$	1.77620			0.0809037
$483$	−8.97798	+	13.1449i	−0.408512	+	0.598114i
$484$	4.06056	−	7.03309i	0.184571	−	0.319686i
$485$	−13.4293			−0.609793
$486$	0.828334	+	1.43472i	0.0375740	+	0.0650801i
$487$	2.69224	−	4.66310i	0.121997	−	0.211305i	−0.798558	−	0.601918i	$-0.794403\pi$
$487$	2.69224	−	4.66310i	0.121997	−	0.211305i	0.920555	+	0.390613i	$0.127737\pi$
$488$	−22.9332			−1.03814
$489$	9.64163			0.436009
$490$	−15.2169	+	19.0168i	−0.687431	+	0.859093i
$491$	−17.4920	+	30.2970i	−0.789401	+	1.36728i	0.136933	+	0.990580i	$0.456275\pi$
$491$	−17.4920	+	30.2970i	−0.789401	+	1.36728i	−0.926334	+	0.376703i	$0.877058\pi$
$492$	−0.747364	−	1.29447i	−0.0336938	−	0.0583593i
$493$	6.35543	+	11.0079i	0.286234	+	0.495772i
$494$	41.4333	−	16.8397i	1.86417	−	0.757656i
$495$	−0.319487	+	0.553367i	−0.0143599	+	0.0248720i
$496$	−17.3284	+	30.0137i	−0.778070	+	1.34766i
$497$	−0.446577	+	0.653846i	−0.0200317	+	0.0293290i
$498$	−7.72993	−	13.3886i	−0.346386	−	0.599959i
$499$	−0.527303	+	0.913315i	−0.0236053	+	0.0408856i	−0.877587	−	0.479418i	$-0.840848\pi$
$499$	−0.527303	+	0.913315i	−0.0236053	+	0.0408856i	0.853981	+	0.520303i	$0.174181\pi$
$500$	−4.36986	+	7.56882i	−0.195426	+	0.338488i
$501$	9.10684	−	15.7735i	0.406864	−	0.704708i
$502$	10.4323	−	18.0693i	0.465617	−	0.806472i
$503$	6.93072	+	12.0044i	0.309026	+	0.535248i	0.978150	−	0.207903i	$-0.0666638\pi$
$503$	6.93072	+	12.0044i	0.309026	+	0.535248i	−0.669124	+	0.743151i	$0.733330\pi$
$504$	−2.38348	−	4.95983i	−0.106169	−	0.220928i
$505$	1.44917	−	2.51004i	0.0644872	−	0.111695i
$506$	−1.51625	+	2.62623i	−0.0674056	+	0.116750i
$507$	−12.5111	−	3.53166i	−0.555637	−	0.156846i
$508$	−6.26754	−	10.8557i	−0.278077	−	0.481644i
$509$	−14.6143	−	25.3127i	−0.647768	−	1.12197i	−0.983655	−	0.180064i	$-0.942369\pi$
$509$	−14.6143	−	25.3127i	−0.647768	−	1.12197i	0.335887	−	0.941902i	$-0.390964\pi$
$510$	−10.1108	+	17.5124i	−0.447713	+	0.775462i
$511$	−8.85710	+	12.9679i	−0.391815	+	0.573667i
$512$	0.711748			0.0314551
$513$	−7.48756			−0.330584
$514$	−17.6419	+	30.5567i	−0.778151	+	1.34780i
$515$	5.93581	+	10.2811i	0.261563	+	0.453040i
$516$	−6.01593			−0.264837
$517$	−1.30847	+	2.26634i	−0.0575465	+	0.0996735i
$518$	0.458462	+	0.0347382i	0.0201437	+	0.00152631i
$519$	21.5144			0.944376
$520$	12.4309	+	9.67084i	0.545132	+	0.424094i
$521$	−4.13001	−	7.15338i	−0.180939	−	0.313395i	0.761262	−	0.648445i	$-0.224580\pi$
$521$	−4.13001	−	7.15338i	−0.180939	−	0.313395i	−0.942201	+	0.335049i	$0.891247\pi$
$522$	3.62323			0.158584
$523$	0.228220	+	0.395289i	0.00997937	+	0.0172848i	0.870972	−	0.491333i	$-0.163490\pi$
$523$	0.228220	+	0.395289i	0.00997937	+	0.0172848i	−0.860993	+	0.508617i	$0.830157\pi$
$524$	−5.19507	−	8.99813i	−0.226948	−	0.393085i
$525$	0.879018	−	1.28699i	0.0383635	−	0.0561690i
$526$	−18.2469	−	31.6046i	−0.795604	−	1.37803i
$527$	−40.8169			−1.77801
$528$	−0.750676	−	1.30021i	−0.0326690	−	0.0565843i
$529$	−6.59949	+	11.4307i	−0.286934	+	0.496985i
$530$	−3.82780	−	6.62994i	−0.166269	−	0.287986i
$531$	6.84210	−	11.8509i	0.296922	−	0.514284i
$532$	−14.7075	−	1.11441i	−0.637651	−	0.0483156i
$533$	−5.71310	−	4.44460i	−0.247462	−	0.192517i
$534$	2.56401	−	4.44100i	0.110956	−	0.192181i
$535$	−29.6675			−1.28264
$536$	20.9681			0.905683
$537$	−2.72518			−0.117600
$538$	−29.5858			−1.27554
$539$	1.33059	−	1.66286i	0.0573126	−	0.0716244i
$540$	0.781858	+	1.35422i	0.0336458	+	0.0582763i
$541$	−10.6399	+	18.4289i	−0.457447	+	0.792321i	−0.998825	−	0.0484578i	$-0.984569\pi$
$541$	−10.6399	+	18.4289i	−0.457447	+	0.792321i	0.541378	+	0.840779i	$0.317903\pi$
$542$	−5.97281	+	10.3452i	−0.256554	+	0.444365i
$543$	−6.47170			−0.277727
$544$	−11.6688	−	20.2109i	−0.500294	−	0.866534i
$545$	−19.1878			−0.821916
$546$	11.7046	+	10.6186i	0.500912	+	0.454435i
$547$	−43.8895			−1.87658			−0.938290	−	0.345849i	$-0.887591\pi$
$547$	−43.8895			−1.87658			−0.938290	+	0.345849i	$0.887591\pi$
$548$	0.226748	+	0.392739i	0.00968619	+	0.0167770i
$549$	−11.0263			−0.470591
$550$	0.148453	−	0.257129i	0.00633008	−	0.0109640i
$551$	−8.18786	+	14.1818i	−0.348815	+	0.604165i
$552$	−6.25682	−	10.8371i	−0.266308	−	0.461259i
$553$	−34.5567	−	2.61840i	−1.46950	−	0.111346i
$554$	7.26077			0.308480
$555$	0.220307			0.00935149
$556$	6.31010			0.267608
$557$	−36.5882			−1.55029			−0.775145	−	0.631783i	$-0.782323\pi$
$557$	−36.5882			−1.55029			−0.775145	+	0.631783i	$0.782323\pi$
$558$	−5.81742	+	10.0761i	−0.246271	+	0.426554i
$559$	−26.9888	+	10.9691i	−1.14151	+	0.463942i
$560$	−11.8770	−	24.7150i	−0.501894	−	1.04440i
$561$	0.884102	−	1.53131i	0.0373268	−	0.0646519i
$562$	−0.392862	−	0.680457i	−0.0165719	−	0.0287033i
$563$	21.6405	−	37.4824i	0.912036	−	1.57969i	0.100853	−	0.994901i	$-0.467843\pi$
$563$	21.6405	−	37.4824i	0.912036	−	1.57969i	0.811183	−	0.584792i	$-0.198824\pi$
$564$	3.20214	+	5.54626i	0.134834	+	0.233540i
$565$	23.4787			0.987755
$566$	−0.933471	−	1.61682i	−0.0392367	−	0.0679600i
$567$	−1.14598	−	2.38469i	−0.0481265	−	0.100147i
$568$	−0.311223	−	0.539054i	−0.0130586	−	0.0226182i
$569$	7.76021	+	13.4411i	0.325325	+	0.563479i	0.981578	−	0.191062i	$-0.0611930\pi$
$569$	7.76021	+	13.4411i	0.325325	+	0.563479i	−0.656253	+	0.754541i	$0.727860\pi$
$570$	−26.0520			−1.09120
$571$	5.62473	+	9.74231i	0.235387	+	0.407703i	0.959385	−	0.282099i	$-0.0910308\pi$
$571$	5.62473	+	9.74231i	0.235387	+	0.407703i	−0.723998	+	0.689802i	$0.757697\pi$
$572$	0.644634	+	0.501504i	0.0269535	+	0.0209689i
$573$	12.7429			0.532341
$574$	3.81136	+	7.93115i	0.159083	+	0.331040i
$575$	1.77209	−	3.06935i	0.0739012	−	0.128001i
$576$	3.21714			0.134047
$577$	13.0442	+	22.5933i	0.543038	+	0.940570i	0.998728	+	0.0504308i	$0.0160594\pi$
$577$	13.0442	+	22.5933i	0.543038	+	0.940570i	−0.455689	+	0.890139i	$0.650607\pi$
$578$	13.8975	−	24.0712i	0.578060	−	1.00123i
$579$	−0.652105			−0.0271006
$580$	3.41994			0.142005
$581$	10.6941	+	22.2537i	0.443668	+	0.923238i
$582$	5.29656	−	9.17390i	0.219549	−	0.380271i
$583$	0.334708	+	0.579731i	0.0138622	+	0.0240100i
$584$	−6.17258	−	10.6912i	−0.255423	−	0.442406i
$585$	5.97679	+	4.64974i	0.247110	+	0.192243i
$586$	−10.6645	+	18.4715i	−0.440547	+	0.763049i
$587$	−20.9471	+	36.2815i	−0.864581	+	1.49750i	0.00288215	+	0.999996i	$0.499083\pi$
$587$	−20.9471	+	36.2815i	−0.864581	+	1.49750i	−0.867463	+	0.497502i	$0.834251\pi$
$588$	−1.89607	−	4.85471i	−0.0781927	−	0.200205i
$589$	−26.2927	−	45.5403i	−1.08337	−	1.87646i
$590$	23.8062	−	41.2336i	0.980086	−	1.69756i
$591$	3.03080	−	5.24950i	0.124670	−	0.215936i
$592$	−0.258819	+	0.448288i	−0.0106374	+	0.0184245i
$593$	0.0938527	−	0.162558i	0.00385407	−	0.00667544i	−0.864092	−	0.503334i	$-0.832107\pi$
$593$	0.0938527	−	0.162558i	0.00385407	−	0.00667544i	0.867946	+	0.496659i	$0.165440\pi$
$594$	−0.252013	−	0.436500i	−0.0103402	−	0.0179098i
$595$	18.2142	−	26.6679i	0.746710	−	1.09328i
$596$	−2.46687	+	4.27275i	−0.101047	+	0.175018i
$597$	−1.02227	+	1.77062i	−0.0418386	+	0.0724666i
$598$	28.3652	+	22.0672i	1.15994	+	0.902395i
$599$	11.9802	+	20.7503i	0.489498	+	0.847835i	0.999927	−	0.0120845i	$-0.00384672\pi$
$599$	11.9802	+	20.7503i	0.489498	+	0.847835i	−0.510429	+	0.859920i	$0.670513\pi$
$600$	0.612594	+	1.06104i	0.0250090	+	0.0433169i
$601$	−11.4417	+	19.8176i	−0.466717	+	0.808377i	−0.999277	−	0.0380151i	$-0.987896\pi$
$601$	−11.4417	+	19.8176i	−0.466717	+	0.808377i	0.532561	+	0.846392i	$0.321230\pi$
$602$	35.3143	+	2.67581i	1.43930	+	0.109058i
$603$	10.0815			0.410549
$604$	−1.13486			−0.0461768
$605$	−11.4540	+	19.8389i	−0.465672	+	0.806568i
$606$	1.14311	+	1.97993i	0.0464359	+	0.0804293i
$607$	1.97432			0.0801350			0.0400675	−	0.999197i	$-0.487243\pi$
$607$	1.97432			0.0801350			0.0400675	+	0.999197i	$0.487243\pi$
$608$	15.0332	−	26.0382i	0.609675	−	1.05599i
$609$	−5.76987	−	0.437190i	−0.233807	−	0.0177158i
$610$	−38.3646			−1.55334
$611$	24.4782	+	19.0432i	0.990282	+	0.770406i
$612$	−2.16360	−	3.74747i	−0.0874585	−	0.151483i
$613$	3.15262			0.127333			0.0636667	−	0.997971i	$-0.479721\pi$
$613$	3.15262			0.127333			0.0636667	+	0.997971i	$0.479721\pi$
$614$	−6.63930	−	11.4996i	−0.267940	−	0.464086i
$615$	2.10816	+	3.65144i	0.0850093	+	0.147240i
$616$	0.725152	+	1.50898i	0.0292172	+	0.0607987i
$617$	−6.03895	−	10.4598i	−0.243119	−	0.421094i	0.718482	−	0.695545i	$-0.244837\pi$
$617$	−6.03895	−	10.4598i	−0.243119	−	0.421094i	−0.961601	+	0.274451i	$0.911504\pi$
$618$	−9.36440			−0.376692
$619$	−20.4442	−	35.4104i	−0.821722	−	1.42327i	−0.904399	−	0.426689i	$-0.859680\pi$
$619$	−20.4442	−	35.4104i	−0.821722	−	1.42327i	0.0826762	−	0.996576i	$-0.473653\pi$
$620$	−5.49102	+	9.51072i	−0.220525	+	0.381960i
$621$	−3.00828	−	5.21049i	−0.120718	−	0.209090i
$622$	2.61230	−	4.52464i	0.104744	−	0.181422i
$623$	−4.61897	+	6.76276i	−0.185055	+	0.270944i
$624$	−16.4831	+	6.69922i	−0.659852	+	0.268184i
$625$	10.8538	−	18.7994i	0.434153	−	0.751975i
$626$	0.876680			0.0350392
$627$	2.27802			0.0909755
$628$	−12.6053			−0.503005
$629$	−0.609645			−0.0243081
$630$	−3.98728	−	8.29721i	−0.158857	−	0.330569i
$631$	17.6950	+	30.6486i	0.704427	+	1.22010i	0.966898	+	0.255163i	$0.0821293\pi$
$631$	17.6950	+	30.6486i	0.704427	+	1.22010i	−0.262471	+	0.964940i	$0.584537\pi$
$632$	13.6217	−	23.5935i	0.541843	−	0.938500i
$633$	−2.27669	+	3.94334i	−0.0904902	+	0.156734i
$634$	−7.25715			−0.288218
$635$	17.6795	+	30.6218i	0.701589	+	1.21519i
$636$	1.63822			0.0649595
$637$	−17.3580	−	18.3221i	−0.687748	−	0.725949i
$638$	−1.10233			−0.0436418
$639$	−0.149636	−	0.259177i	−0.00591951	−	0.0102529i
$640$	28.0605			1.10919
$641$	−13.9438	+	24.1513i	−0.550747	+	0.953921i	0.447474	+	0.894297i	$0.352324\pi$
$641$	−13.9438	+	24.1513i	−0.550747	+	0.953921i	−0.998221	+	0.0596242i	$0.981010\pi$
$642$	11.7010	−	20.2667i	0.461801	−	0.799862i
$643$	−3.37661	−	5.84847i	−0.133161	−	0.230641i	0.791733	−	0.610868i	$-0.209179\pi$
$643$	−3.37661	−	5.84847i	−0.133161	−	0.230641i	−0.924893	+	0.380227i	$0.875846\pi$
$644$	−5.13354	−	10.6825i	−0.202290	−	0.420949i
$645$	16.9697			0.668182
$646$	72.0926			2.83644
$647$	46.0687			1.81115			0.905574	−	0.424189i	$-0.139441\pi$
$647$	46.0687			1.81115			0.905574	+	0.424189i	$0.139441\pi$
$648$	2.07987			0.0817049
$649$	−2.08165	+	3.60552i	−0.0817118	+	0.141529i
$650$	−2.77719	−	2.16056i	−0.108930	−	0.0847441i
$651$	10.4799	−	15.3439i	0.410738	−	0.601373i
$652$	−3.58933	+	6.21690i	−0.140569	+	0.243473i
$653$	−17.9401	−	31.0732i	−0.702052	−	1.21599i	−0.967745	−	0.251932i	$-0.918934\pi$
$653$	−17.9401	−	31.0732i	−0.702052	−	1.21599i	0.265693	−	0.964058i	$-0.414399\pi$
$654$	7.56773	−	13.1077i	0.295922	−	0.512552i
$655$	14.6543	+	25.3819i	0.572589	+	0.991753i
$656$	−9.90681			−0.386796
$657$	−2.96778	−	5.14034i	−0.115784	−	0.200544i
$658$	−16.3301	−	33.9816i	−0.636613	−	1.32474i
$659$	−17.2510	−	29.8796i	−0.672004	−	1.16395i	−0.977335	−	0.211699i	$-0.932100\pi$
$659$	−17.2510	−	29.8796i	−0.672004	−	1.16395i	0.305331	−	0.952246i	$-0.401233\pi$
$660$	−0.237873	−	0.412009i	−0.00925921	−	0.0160374i
$661$	−40.5569			−1.57748			−0.788740	−	0.614727i	$-0.789266\pi$
$661$	−40.5569			−1.57748			−0.788740	+	0.614727i	$0.789266\pi$
$662$	−22.3113	−	38.6444i	−0.867155	−	1.50196i
$663$	−16.5393	−	12.8670i	−0.642334	−	0.499714i
$664$	−19.4091			−0.753219
$665$	41.4869	+	3.14351i	1.60879	+	0.121900i
$666$	−0.0868896	+	0.150497i	−0.00336690	+	0.00583165i
$667$	−13.1586			−0.509501
$668$	6.78048	+	11.7441i	0.262345	+	0.454395i
$669$	7.85506	−	13.6054i	0.303694	−	0.526014i
$670$	35.0771			1.35515
$671$	3.35465			0.129505
$672$	10.5936	+	0.802693i	0.408659	+	0.0309646i
$673$	−11.5572	+	20.0177i	−0.445498	+	0.771625i	−0.998087	−	0.0618288i	$-0.980307\pi$
$673$	−11.5572	+	20.0177i	−0.445498	+	0.771625i	0.552589	+	0.833454i	$0.313640\pi$
$674$	17.2588	+	29.8931i	0.664784	+	1.15144i
$675$	0.294535	+	0.510150i	0.0113367	+	0.0196357i
$676$	6.93476	−	6.75238i	0.266722	−	0.259707i
$677$	8.56573	−	14.8363i	0.329208	−	0.570205i	−0.653147	−	0.757231i	$-0.726552\pi$
$677$	8.56573	−	14.8363i	0.329208	−	0.570205i	0.982355	+	0.187026i	$0.0598850\pi$
$678$	−9.26006	+	16.0389i	−0.355631	+	0.615970i
$679$	−9.54154	+	13.9700i	−0.366171	+	0.536121i
$680$	12.6936	+	21.9860i	0.486778	+	0.843124i
$681$	6.27169	−	10.8629i	0.240332	−	0.416267i
$682$	1.76990	−	3.06555i	0.0677729	−	0.117386i
$683$	22.0922	−	38.2648i	0.845335	−	1.46416i	−0.0399956	−	0.999200i	$-0.512734\pi$
$683$	22.0922	−	38.2648i	0.845335	−	1.46416i	0.885330	−	0.464963i	$-0.153932\pi$
$684$	2.78743	−	4.82796i	0.106580	−	0.184602i
$685$	−0.639610	−	1.10784i	−0.0244382	−	0.0423283i
$686$	8.97090	+	29.3412i	0.342511	+	1.12025i
$687$	−10.3182	+	17.8717i	−0.393665	+	0.681849i
$688$	−19.9363	+	34.5307i	−0.760064	+	1.31647i
$689$	7.34941	−	2.98702i	0.279990	−	0.113796i
$690$	−10.4669	−	18.1292i	−0.398469	−	0.690168i
$691$	5.02584	+	8.70500i	0.191192	+	0.331154i	0.945645	−	0.325199i	$-0.105431\pi$
$691$	5.02584	+	8.70500i	0.191192	+	0.331154i	−0.754454	+	0.656353i	$0.772098\pi$
$692$	−8.00924	+	13.8724i	−0.304466	+	0.527350i
$693$	0.348653	+	0.725520i	0.0132442	+	0.0275602i
$694$	22.0972			0.838800
$695$	−17.7995			−0.675174
$696$	2.27439	−	3.93936i	0.0862107	−	0.149321i
$697$	−5.83383	−	10.1045i	−0.220972	−	0.382735i
$698$	−34.0020			−1.28700
$699$	4.00908	−	6.94394i	0.151637	−	0.262644i
$700$	0.502616	+	1.04590i	0.0189971	+	0.0395314i
$701$	11.0843			0.418647			0.209323	−	0.977846i	$-0.432874\pi$
$701$	11.0843			0.418647			0.209323	+	0.977846i	$0.432874\pi$
$702$	−5.53362	+	2.24903i	−0.208853	+	0.0848841i
$703$	−0.392711	−	0.680195i	−0.0148114	−	0.0256540i
$704$	−0.978785			−0.0368894
$705$	−9.03258	−	15.6449i	−0.340187	−	0.589221i
$706$	−5.34039	−	9.24982i	−0.200988	−	0.348122i
$707$	−1.58147	−	3.29091i	−0.0594772	−	0.123767i
$708$	5.09428	+	8.82355i	0.191455	+	0.331609i
$709$	−1.43514			−0.0538980			−0.0269490	−	0.999637i	$-0.508579\pi$
$709$	−1.43514			−0.0538980			−0.0269490	+	0.999637i	$0.508579\pi$
$710$	−0.520639	−	0.901773i	−0.0195392	−	0.0338430i
$711$	6.54933	−	11.3438i	0.245619	−	0.425425i
$712$	−3.21899	−	5.57546i	−0.120637	−	0.208949i
$713$	21.1273	−	36.5935i	0.791222	−	1.37044i
$714$	11.0338	+	22.9605i	0.412931	+	0.859276i
$715$	−1.81838	−	1.41464i	−0.0680037	−	0.0529046i
$716$	1.01451	−	1.75719i	0.0379141	−	0.0656692i
$717$	−1.16836			−0.0436334
$718$	−14.5306			−0.542277
$719$	−36.2706			−1.35267			−0.676333	−	0.736596i	$-0.736432\pi$
$719$	−36.2706			−1.35267			−0.676333	+	0.736596i	$0.736432\pi$
$720$	10.3641			0.386246
$721$	14.9125	+	1.12994i	0.555371	+	0.0420811i
$722$	30.7010	+	53.1757i	1.14257	+	1.97899i
$723$	0.536076	−	0.928511i	0.0199369	−	0.0345317i
$724$	2.40925	−	4.17294i	0.0895390	−	0.155086i
$725$	1.28833			0.0478474
$726$	−9.03500	−	15.6491i	−0.335320	−	0.580792i
$727$	45.0943			1.67245			0.836227	−	0.548384i	$-0.184757\pi$
$727$	45.0943			1.67245			0.836227	+	0.548384i	$0.184757\pi$
$728$	18.8924	−	6.06032i	0.700200	−	0.224610i
$729$	1.00000			0.0370370
$730$	−10.3260	−	17.8851i	−0.382182	−	0.661958i
$731$	−46.9596			−1.73686
$732$	4.10481	−	7.10973i	0.151718	−	0.262783i
$733$	−9.09554	+	15.7539i	−0.335952	+	0.581885i	−0.983667	−	0.179997i	$-0.942391\pi$
$733$	−9.09554	+	15.7539i	−0.335952	+	0.581885i	0.647716	+	0.761882i	$0.275725\pi$
$734$	10.0888	+	17.4743i	0.372385	+	0.644989i
$735$	5.34844	+	13.6941i	0.197280	+	0.505116i
$736$	24.1595			0.890531
$737$	−3.06719			−0.112981
$738$	−3.32586			−0.122427
$739$	−25.9042			−0.952902			−0.476451	−	0.879201i	$-0.658077\pi$
$739$	−25.9042			−0.952902			−0.476451	+	0.879201i	$0.658077\pi$
$740$	−0.0820144	+	0.142053i	−0.00301491	+	0.00522198i
$741$	3.70203	−	26.7418i	0.135997	−	0.982383i
$742$	−9.61656	−	0.728658i	−0.353035	−	0.0267499i
$743$	−22.0599	+	38.2089i	−0.809301	+	1.40175i	0.104049	+	0.994572i	$0.466820\pi$
$743$	−22.0599	+	38.2089i	−0.809301	+	1.40175i	−0.913349	+	0.407177i	$0.866513\pi$
$744$	7.30349	+	12.6500i	0.267759	+	0.463772i
$745$	6.95855	−	12.0526i	0.254941	−	0.441571i
$746$	25.3450	+	43.8988i	0.927946	+	1.60725i
$747$	−9.33190			−0.341436
$748$	0.658257	+	1.14013i	0.0240683	+	0.0416874i
$749$	−21.0789	+	30.8621i	−0.770204	+	1.12768i
$750$	9.72322	+	16.8411i	0.355042	+	0.614950i
$751$	2.06035	+	3.56863i	0.0751831	+	0.130221i	0.901166	−	0.433474i	$-0.142713\pi$
$751$	2.06035	+	3.56863i	0.0751831	+	0.130221i	−0.825983	+	0.563695i	$0.809379\pi$
$752$	42.4465			1.54786
$753$	−6.29717	−	10.9070i	−0.229482	−	0.397474i
$754$	−1.79141	+	12.9403i	−0.0652393	+	0.471259i
$755$	3.20121			0.116504
$756$	1.96426	+	0.148834i	0.0714394	+	0.00541305i
$757$	20.4854	−	35.4818i	0.744556	−	1.28961i	−0.205846	−	0.978584i	$-0.565995\pi$
$757$	20.4854	−	35.4818i	0.744556	−	1.28961i	0.950402	−	0.311024i	$-0.100672\pi$
$758$	−8.41845			−0.305772
$759$	0.915242	+	1.58525i	0.0332212	+	0.0575408i
$760$	−16.3535	+	28.3251i	−0.593204	+	1.02746i
$761$	44.3948			1.60931			0.804654	−	0.593743i	$-0.202351\pi$
$761$	44.3948			1.60931			0.804654	+	0.593743i	$0.202351\pi$
$762$	−27.8914			−1.01040
$763$	−13.6330	+	19.9604i	−0.493547	+	0.722616i
$764$	−4.74385	+	8.21658i	−0.171626	+	0.297266i
$765$	6.10309	+	10.5709i	0.220658	+	0.382190i
$766$	−20.4002	−	35.3342i	−0.737090	−	1.27668i
$767$	38.9424	+	30.2959i	1.40613	+	1.09392i
$768$	−7.85001	+	13.5966i	−0.283263	+	0.490626i
$769$	6.60276	−	11.4363i	0.238101	−	0.412404i	−0.722068	−	0.691822i	$-0.756808\pi$
$769$	6.60276	−	11.4363i	0.238101	−	0.412404i	0.960169	+	0.279418i	$0.0901416\pi$
$770$	1.21309	+	2.52435i	0.0437168	+	0.0909713i
$771$	10.6490	+	18.4446i	0.383515	+	0.664268i
$772$	0.242762	−	0.420476i	0.00873719	−	0.0151333i
$773$	8.68483	−	15.0426i	0.312372	−	0.541044i	−0.666504	−	0.745502i	$-0.732210\pi$
$773$	8.68483	−	15.0426i	0.312372	−	0.541044i	0.978875	+	0.204458i	$0.0655432\pi$
$774$	−6.69291	+	11.5925i	−0.240572	+	0.416683i
$775$	−2.06853	+	3.58280i	−0.0743038	+	0.128698i
$776$	−6.64957	−	11.5174i	−0.238706	−	0.413450i
$777$	0.156528	−	0.229177i	0.00561542	−	0.00822169i
$778$	15.3572	−	26.5994i	0.550581	−	0.953634i
$779$	7.51587	−	13.0179i	0.269284	−	0.466414i
$780$	−5.22315	+	2.12284i	−0.187019	+	0.0760099i
$781$	0.0455254	+	0.0788523i	0.00162903	+	0.00282156i
$782$	28.9647	+	50.1683i	1.03577	+	1.79401i
$783$	1.09353	−	1.89405i	0.0390795	−	0.0676877i
$784$	−34.1488	−	5.20488i	−1.21960	−	0.185888i
$785$	35.5569			1.26908
$786$	−23.1187			−0.824618
$787$	2.07480	−	3.59366i	0.0739587	−	0.128100i	−0.826674	−	0.562681i	$-0.809770\pi$
$787$	2.07480	−	3.59366i	0.0739587	−	0.128100i	0.900633	+	0.434581i	$0.143103\pi$
$788$	2.25658	+	3.90851i	0.0803872	+	0.139235i
$789$	−22.0285			−0.784235
$790$	22.7875	−	39.4692i	0.810744	−	1.40425i
$791$	16.6816	−	24.4241i	0.593131	−	0.868420i
$792$	−0.632780			−0.0224849
$793$	5.45166	−	39.3803i	0.193594	−	1.39844i
$794$	25.8462	+	44.7669i	0.917247	+	1.58872i
$795$	−4.62108			−0.163893
$796$	−0.761128	−	1.31831i	−0.0269775	−	0.0467263i
$797$	−10.4435	−	18.0887i	−0.369928	−	0.640735i	0.619626	−	0.784897i	$-0.287284\pi$
$797$	−10.4435	−	18.0887i	−0.369928	−	0.640735i	−0.989554	+	0.144163i	$0.953951\pi$
$798$	−18.5100	+	27.1010i	−0.655247	+	0.959365i
$799$	24.9955	+	43.2934i	0.884277	+	1.53161i
$800$	−2.36541			−0.0836300
$801$	−1.54769	−	2.68068i	−0.0546850	−	0.0947172i
$802$	−28.3497	+	49.1030i	−1.00106	+	1.73389i
$803$	0.902919	+	1.56390i	0.0318633	+	0.0551889i
$804$	−3.75307	+	6.50050i	−0.132360	+	0.229255i
$805$	14.4807	+	30.1332i	0.510377	+	1.06205i
$806$	−33.1103	−	25.7587i	−1.16626	−	0.907312i
$807$	−8.92932	+	15.4660i	−0.314327	+	0.544430i
$808$	2.87025			0.100975
$809$	3.58471			0.126032			0.0630158	−	0.998013i	$-0.479928\pi$
$809$	3.58471			0.126032			0.0630158	+	0.998013i	$0.479928\pi$
$810$	3.47937			0.122253
$811$	47.0892			1.65353			0.826763	−	0.562551i	$-0.190180\pi$
$811$	47.0892			1.65353			0.826763	+	0.562551i	$0.190180\pi$
$812$	2.42987	−	3.55765i	0.0852718	−	0.124849i
$813$	3.60531	+	6.24459i	0.126444	+	0.219007i
$814$	0.0264354	−	0.0457874i	0.000926559	−	0.00160485i
$815$	10.1248	−	17.5366i	0.354655	−	0.614281i
$816$	−28.6800			−1.00400
$817$	−30.2496	−	52.3939i	−1.05830	−	1.83303i
$818$	16.4971			0.576808
$819$	9.08349	−	2.91380i	0.317403	−	0.101816i
$820$	−3.13926			−0.109628
$821$	5.68240	+	9.84220i	0.198317	+	0.343495i	0.947983	−	0.318321i	$-0.103119\pi$
$821$	5.68240	+	9.84220i	0.198317	+	0.343495i	−0.749666	+	0.661816i	$0.769786\pi$
$822$	1.00906			0.0351949
$823$	−5.06585	+	8.77431i	−0.176584	+	0.305853i	−0.940708	−	0.339216i	$-0.889838\pi$
$823$	−5.06585	+	8.77431i	−0.176584	+	0.305853i	0.764124	+	0.645069i	$0.223172\pi$
$824$	−5.87828	+	10.1815i	−0.204779	+	0.354688i
$825$	−0.0896097	−	0.155208i	−0.00311981	−	0.00540367i
$826$	−25.9795	−	54.0613i	−0.903943	−	1.88103i
$827$	−47.6358			−1.65646			−0.828230	−	0.560388i	$-0.810652\pi$
$827$	−47.6358			−1.65646			−0.828230	+	0.560388i	$0.810652\pi$
$828$	4.47962			0.155678
$829$	19.7666			0.686521			0.343260	−	0.939240i	$-0.388469\pi$
$829$	19.7666			0.686521			0.343260	+	0.939240i	$0.388469\pi$
$830$	−32.4691			−1.12702
$831$	2.19138	−	3.79558i	0.0760180	−	0.131667i
$832$	−1.59063	+	11.4900i	−0.0551451	+	0.398343i
$833$	−14.8005	−	37.8952i	−0.512807	−	1.31299i
$834$	7.02018	−	12.1593i	0.243089	−	0.421043i
$835$	−19.1264	−	33.1279i	−0.661896	−	1.14644i
$836$	−0.848049	+	1.46886i	−0.0293304	+	0.0508017i
$837$	3.51152	+	6.08213i	0.121376	+	0.210229i
$838$	1.94234			0.0670972
$839$	−3.47420	−	6.01748i	−0.119943	−	0.207747i	0.799802	−	0.600264i	$-0.204938\pi$
$839$	−3.47420	−	6.01748i	−0.119943	−	0.207747i	−0.919745	+	0.392517i	$0.871604\pi$
$840$	−11.5241	−	0.873193i	−0.397619	−	0.0301280i
$841$	12.1084	+	20.9723i	0.417531	+	0.723184i
$842$	−8.47995	−	14.6877i	−0.292238	−	0.506172i
$843$	−0.474280			−0.0163351
$844$	−1.69511	−	2.93601i	−0.0583479	−	0.101062i
$845$	−19.5616	+	19.0471i	−0.672938	+	0.655240i
$846$	14.2499			0.489922
$847$	12.4997	+	26.0108i	0.429494	+	0.893743i
$848$	5.42891	−	9.40315i	0.186430	−	0.322906i
$849$	−1.12693			−0.0386760
$850$	−2.83588	−	4.91188i	−0.0972698	−	0.168476i
$851$	0.315559	−	0.546564i	0.0108172	−	0.0187360i
$852$	0.222823			0.00763378
$853$	40.0909			1.37269			0.686343	−	0.727278i	$-0.259215\pi$
$853$	40.0909			1.37269			0.686343	+	0.727278i	$0.259215\pi$
$854$	−27.2581	+	39.9094i	−0.932753	+	1.36567i
$855$	−7.86277	+	13.6187i	−0.268901	+	0.465750i
$856$	−14.6900	−	25.4438i	−0.502094	−	0.869652i
$857$	2.09069	+	3.62118i	0.0714166	+	0.123697i	0.899522	−	0.436875i	$-0.143915\pi$
$857$	2.09069	+	3.62118i	0.0714166	+	0.123697i	−0.828106	+	0.560572i	$0.810581\pi$
$858$	1.68356	−	0.684247i	0.0574756	−	0.0233598i
$859$	−2.22930	+	3.86127i	−0.0760629	+	0.131745i	−0.901548	−	0.432679i	$-0.857568\pi$
$859$	−2.22930	+	3.86127i	−0.0760629	+	0.131745i	0.825485	+	0.564424i	$0.190902\pi$
$860$	−6.31739	+	10.9420i	−0.215421	+	0.373121i
$861$	5.29633	+	0.401309i	0.180498	+	0.0136766i
$862$	19.5814	+	33.9160i	0.666946	+	1.15518i
$863$	−6.39008	+	11.0680i	−0.217521	+	0.376757i	−0.954049	−	0.299649i	$-0.903130\pi$
$863$	−6.39008	+	11.0680i	−0.217521	+	0.376757i	0.736528	+	0.676407i	$0.236464\pi$
$864$	−2.00775	+	3.47753i	−0.0683050	+	0.118308i
$865$	22.5925	−	39.1313i	0.768167	−	1.33050i
$866$	0.407813	−	0.706353i	0.0138581	−	0.0240029i
$867$	−8.38883	−	14.5299i	−0.284899	−	0.493460i
$868$	5.99230	+	12.4695i	0.203392	+	0.423243i
$869$	−1.99257	+	3.45124i	−0.0675934	+	0.117075i
$870$	3.80479	−	6.59009i	0.128994	−	0.223425i
$871$	−4.98451	+	36.0058i	−0.168894	+	1.22001i
$872$	−9.50092	−	16.4561i	−0.321742	−	0.557273i
$873$	−3.19711	−	5.53756i	−0.108206	−	0.187418i
$874$	−37.3159	+	64.6330i	−1.26223	+	2.18625i
$875$	−13.4518	−	27.9921i	−0.454754	−	0.946307i
$876$	4.41931			0.149314
$877$	46.1431			1.55814			0.779070	−	0.626937i	$-0.215692\pi$
$877$	46.1431			1.55814			0.779070	+	0.626937i	$0.215692\pi$
$878$	−12.4778	+	21.6122i	−0.421106	+	0.729377i
$879$	6.43732	+	11.1498i	0.217125	+	0.376072i
$880$	−3.15317			−0.106293
$881$	6.60175	−	11.4346i	0.222419	−	0.385240i	−0.733123	−	0.680096i	$-0.761938\pi$
$881$	6.60175	−	11.4346i	0.222419	−	0.385240i	0.955542	+	0.294855i	$0.0952715\pi$
$882$	−11.4643	−	1.74736i	−0.386022	−	0.0588365i
$883$	−23.5256			−0.791701			−0.395850	−	0.918315i	$-0.629550\pi$
$883$	−23.5256			−0.791701			−0.395850	+	0.918315i	$0.629550\pi$
$884$	14.4538	−	5.87445i	0.486134	−	0.197579i
$885$	−14.3699	−	24.8895i	−0.483040	−	0.836650i
$886$	−44.3974			−1.49156
$887$	18.9356	+	32.7975i	0.635796	+	1.10123i	0.986346	+	0.164687i	$0.0526613\pi$
$887$	18.9356	+	32.7975i	0.635796	+	1.10123i	−0.350550	+	0.936544i	$0.614005\pi$
$888$	0.109086	+	0.188942i	0.00366068	+	0.00634048i
$889$	44.4161	+	3.36546i	1.48967	+	0.112874i
$890$	−5.38499	−	9.32708i	−0.180505	−	0.312644i
$891$	−0.304241			−0.0101925
$892$	5.84847	+	10.1298i	0.195821	+	0.339172i
$893$	−32.2023	+	55.7761i	−1.07761	+	1.86647i
$894$	5.48894	+	9.50713i	0.183578	+	0.317966i
$895$	−2.86174	+	4.95667i	−0.0956573	+	0.165683i
$896$	19.9370	−	29.1904i	0.666050	−	0.975182i
$897$	20.0966	−	8.16785i	0.671006	−	0.272717i
$898$	−3.74851	+	6.49261i	−0.125089	+	0.216661i
$899$	15.3598			0.512277
$900$	−0.438591			−0.0146197
$901$	12.7877			0.426021
$902$	1.01186			0.0336914
$903$	12.0570	−	17.6530i	0.401233	−	0.587456i
$904$	11.6256	+	20.1361i	0.386660	+	0.669715i
$905$	−6.79600	+	11.7710i	−0.225907	+	0.391282i
$906$	−1.26257	+	2.18683i	−0.0419460	+	0.0726526i
$907$	−45.3930			−1.50725			−0.753625	−	0.657304i	$-0.771697\pi$
$907$	−45.3930			−1.50725			−0.753625	+	0.657304i	$0.771697\pi$
$908$	4.66958	+	8.08794i	0.154965	+	0.268408i
$909$	1.38002			0.0457723
$910$	31.6048	−	10.1382i	1.04769	−	0.336078i
$911$	−45.3167			−1.50141			−0.750704	−	0.660638i	$-0.770286\pi$
$911$	−45.3167			−1.50141			−0.750704	+	0.660638i	$0.770286\pi$
$912$	−18.4746	−	31.9989i	−0.611755	−	1.05959i
$913$	2.83915			0.0939620
$914$	28.4566	−	49.2882i	0.941259	−	1.63031i
$915$	−11.5788	+	20.0551i	−0.382784	+	0.663002i
$916$	−7.68243	−	13.3064i	−0.253835	−	0.439655i
$917$	36.8158	+	2.78958i	1.21577	+	0.0921200i
$918$	−9.62831			−0.317782
$919$	−37.5888			−1.23994			−0.619970	−	0.784626i	$-0.712855\pi$
$919$	−37.5888			−1.23994			−0.619970	+	0.784626i	$0.712855\pi$
$920$	−26.2814			−0.866472
$921$	−8.01524			−0.264111
$922$	0.827400	−	1.43310i	0.0272490	−	0.0471966i
$923$	0.999633	−	0.406280i	0.0329033	−	0.0133729i
$924$	−0.597608	−	0.0452815i	−0.0196599	−	0.00148965i
$925$	−0.0308958	+	0.0535131i	−0.00101585	+	0.00175950i
$926$	26.9654	+	46.7055i	0.886139	+	1.53484i
$927$	−2.82628	+	4.89525i	−0.0928271	+	0.160781i
$928$	4.39106	+	7.60555i	0.144144	+	0.249664i
$929$	−15.7982			−0.518321			−0.259160	−	0.965834i	$-0.583446\pi$
$929$	−15.7982			−0.518321			−0.259160	+	0.965834i	$0.583446\pi$
$930$	12.2179	+	21.1620i	0.400640	+	0.693928i
$931$	32.7466	−	40.9240i	1.07323	−	1.34123i
$932$	2.98496	+	5.17010i	0.0977755	+	0.169352i
$933$	−1.57684	−	2.73117i	−0.0516235	−	0.0894145i
$934$	40.1099			1.31244
$935$	−1.85681	−	3.21609i	−0.0607242	−	0.105177i
$936$	−1.02833	+	7.42822i	−0.0336122	+	0.242799i
$937$	3.77902			0.123455			0.0617276	−	0.998093i	$-0.480339\pi$
$937$	3.77902			0.123455			0.0617276	+	0.998093i	$0.480339\pi$
$938$	24.9224	−	36.4895i	0.813744	−	1.19142i
$939$	0.264591	−	0.458285i	0.00863461	−	0.0149556i
$940$	13.4504			0.438703
$941$	5.19282	+	8.99424i	0.169281	+	0.293204i	0.938167	−	0.346182i	$-0.112522\pi$
$941$	5.19282	+	8.99424i	0.169281	+	0.293204i	−0.768886	+	0.639386i	$0.779189\pi$
$942$	−14.0238	+	24.2899i	−0.456919	+	0.791407i
$943$	12.0786			0.393334
$944$	67.5281			2.19785
$945$	−5.54078	−	0.419832i	−0.180242	−	0.0136571i
$946$	2.03626	−	3.52690i	0.0662045	−	0.114669i
$947$	1.51945	+	2.63177i	0.0493755	+	0.0855209i	0.889657	−	0.456630i	$-0.150944\pi$
$947$	1.51945	+	2.63177i	0.0493755	+	0.0855209i	−0.840281	+	0.542151i	$0.817610\pi$
$948$	4.87629	+	8.44599i	0.158375	+	0.274313i
$949$	19.8260	−	8.05788i	0.643579	−	0.261570i
$950$	3.65353	−	6.32810i	0.118536	−	0.205311i
$951$	−2.19029	+	3.79369i	−0.0710249	+	0.123019i
$952$	31.8901	+	2.41635i	1.03356	+	0.0783144i
$953$	1.70817	+	2.95863i	0.0553329	+	0.0958394i	0.892365	−	0.451314i	$-0.149045\pi$
$953$	1.70817	+	2.95863i	0.0553329	+	0.0958394i	−0.837032	+	0.547154i	$0.815711\pi$
$954$	1.82257	−	3.15678i	0.0590078	−	0.102205i
$955$	13.3814	−	23.1773i	0.433013	−	0.750001i
$956$	0.434952	−	0.753359i	0.0140674	−	0.0243654i
$957$	−0.332696	+	0.576247i	−0.0107545	+	0.0186274i
$958$	−25.1290	−	43.5247i	−0.811880	−	1.40622i
$959$	−1.60689	−	0.121756i	−0.0518892	−	0.00393171i
$960$	3.37835	−	5.85148i	0.109036	−	0.188856i
$961$	−9.16152	+	15.8682i	−0.295533	+	0.511878i
$962$	−0.494539	−	0.384735i	−0.0159446	−	0.0124043i
$963$	−7.06296	−	12.2334i	−0.227601	−	0.394216i
$964$	0.399135	+	0.691322i	0.0128553	+	0.0222660i
$965$	−0.684782	+	1.18608i	−0.0220439	+	0.0381812i
$966$	−26.2960	−	1.99248i	−0.846060	−	0.0641069i
$967$	2.27084			0.0730254			0.0365127	−	0.999333i	$-0.488375\pi$
$967$	2.27084			0.0730254			0.0365127	+	0.999333i	$0.488375\pi$
$968$	−22.6860			−0.729156
$969$	21.7583	−	37.6865i	0.698977	−	1.21066i
$970$	−11.1239	−	19.2672i	−0.357168	−	0.618633i
$971$	−22.0727			−0.708347			−0.354174	−	0.935180i	$-0.615238\pi$
$971$	−22.0727			−0.708347			−0.354174	+	0.935180i	$0.615238\pi$
$972$	−0.372274	+	0.644798i	−0.0119407	+	0.0206819i
$973$	−12.6466	+	18.5162i	−0.405431	+	0.593603i
$974$	8.92030			0.285825
$975$	−1.96762	+	0.799700i	−0.0630143	+	0.0256109i
$976$	−27.2060	−	47.1221i	−0.870842	−	1.50834i
$977$	−4.29757			−0.137491			−0.0687457	−	0.997634i	$-0.521900\pi$
$977$	−4.29757			−0.137491			−0.0687457	+	0.997634i	$0.521900\pi$
$978$	7.98649	+	13.8330i	0.255380	+	0.442331i
$979$	0.470871	+	0.815573i	0.0150491	+	0.0260658i
$980$	−10.8210	−	1.64932i	−0.345666	−	0.0526855i
$981$	−4.56805	−	7.91209i	−0.145846	−	0.252613i
$982$	−57.9567			−1.84947
$983$	−1.81793	−	3.14875i	−0.0579831	−	0.100430i	0.835577	−	0.549374i	$-0.185134\pi$
$983$	−1.81793	−	3.14875i	−0.0579831	−	0.100430i	−0.893560	+	0.448944i	$0.851800\pi$
$984$	−2.08773	+	3.61605i	−0.0665544	+	0.115276i
$985$	−6.36535	−	11.0251i	−0.202817	−	0.351289i
$986$	−10.5288	+	18.2365i	−0.335306	+	0.580768i
$987$	−22.6925	−	1.71944i	−0.722311	−	0.0547303i
$988$	15.8649	+	12.3423i	0.504728	+	0.392662i
$989$	24.3068	−	42.1006i	0.772912	−	1.33872i
$990$	−1.05857			−0.0336435
$991$	2.14200			0.0680429			0.0340214	−	0.999421i	$-0.489169\pi$
$991$	2.14200			0.0680429			0.0340214	+	0.999421i	$0.489169\pi$
$992$	−28.2010			−0.895383
$993$	−26.9352			−0.854762
$994$	−1.30800	−	0.0991087i	−0.0414872	−	0.00314354i
$995$	2.14699	+	3.71869i	0.0680641	+	0.117890i
$996$	3.47403	−	6.01719i	0.110079	−	0.190662i
$997$	11.0526	−	19.1436i	0.350038	−	0.606284i	−0.636217	−	0.771510i	$-0.719502\pi$
$997$	11.0526	−	19.1436i	0.350038	−	0.606284i	0.986256	+	0.165225i	$0.0528352\pi$
$998$	−1.74713			−0.0553045
$999$	0.0524484	+	0.0908433i	0.00165939	+	0.00287415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.j.c.100.8	✓	20
3.2	odd	2		819.2.n.f.100.3		20
7.4	even	3		273.2.l.c.256.3	yes	20
13.3	even	3		273.2.l.c.16.3	yes	20
21.11	odd	6		819.2.s.f.802.8		20
39.29	odd	6		819.2.s.f.289.8		20
91.81	even	3	inner	273.2.j.c.172.8	yes	20
273.263	odd	6		819.2.n.f.172.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.8	✓	20	1.1	even	1	trivial
273.2.j.c.172.8	yes	20	91.81	even	3	inner
273.2.l.c.16.3	yes	20	13.3	even	3
273.2.l.c.256.3	yes	20	7.4	even	3
819.2.n.f.100.3		20	3.2	odd	2
819.2.n.f.172.3		20	273.263	odd	6
819.2.s.f.289.8		20	39.29	odd	6
819.2.s.f.802.8		20	21.11	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+(0.828334 + 1.43472i) q^{2} +1.00000 q^{3} +(-0.372274 + 0.644798i) q^{4} +(1.05011 - 1.81885i) q^{5} +(0.828334 + 1.43472i) q^{6} +(-1.14598 - 2.38469i) q^{7} +2.07987 q^{8} +1.00000 q^{9} +3.47937 q^{10} -0.304241 q^{11} +(-0.372274 + 0.644798i) q^{12} +(-0.494423 + 3.57149i) q^{13} +(2.47210 - 3.61947i) q^{14} +(1.05011 - 1.81885i) q^{15} +(2.46737 + 4.27361i) q^{16} +(-2.90593 + 5.03321i) q^{17} +(0.828334 + 1.43472i) q^{18} -7.48756 q^{19} +(0.781858 + 1.35422i) q^{20} +(-1.14598 - 2.38469i) q^{21} +(-0.252013 - 0.436500i) q^{22} +(-3.00828 - 5.21049i) q^{23} +2.07987 q^{24} +(0.294535 + 0.510150i) q^{25} +(-5.53362 + 2.24903i) q^{26} +1.00000 q^{27} +(1.96426 + 0.148834i) q^{28} +(1.09353 - 1.89405i) q^{29} +3.47937 q^{30} +(3.51152 + 6.08213i) q^{31} +(-2.00775 + 3.47753i) q^{32} -0.304241 q^{33} -9.62831 q^{34} +(-5.54078 - 0.419832i) q^{35} +(-0.372274 + 0.644798i) q^{36} +(0.0524484 + 0.0908433i) q^{37} +(-6.20220 - 10.7425i) q^{38} +(-0.494423 + 3.57149i) q^{39} +(2.18409 - 3.78295i) q^{40} +(-1.00378 + 1.73860i) q^{41} +(2.47210 - 3.61947i) q^{42} +(4.03998 + 6.99746i) q^{43} +(0.113261 - 0.196174i) q^{44} +(1.05011 - 1.81885i) q^{45} +(4.98372 - 8.63206i) q^{46} +(4.30078 - 7.44916i) q^{47} +(2.46737 + 4.27361i) q^{48} +(-4.37347 + 5.46560i) q^{49} +(-0.487947 + 0.845149i) q^{50} +(-2.90593 + 5.03321i) q^{51} +(-2.11883 - 1.64838i) q^{52} +(-1.10014 - 1.90550i) q^{53} +(0.828334 + 1.43472i) q^{54} +(-0.319487 + 0.553367i) q^{55} +(-2.38348 - 4.95983i) q^{56} -7.48756 q^{57} +3.62323 q^{58} +(6.84210 - 11.8509i) q^{59} +(0.781858 + 1.35422i) q^{60} -11.0263 q^{61} +(-5.81742 + 10.0761i) q^{62} +(-1.14598 - 2.38469i) q^{63} +3.21714 q^{64} +(5.97679 + 4.64974i) q^{65} +(-0.252013 - 0.436500i) q^{66} +10.0815 q^{67} +(-2.16360 - 3.74747i) q^{68} +(-3.00828 - 5.21049i) q^{69} +(-3.98728 - 8.29721i) q^{70} +(-0.149636 - 0.259177i) q^{71} +2.07987 q^{72} +(-2.96778 - 5.14034i) q^{73} +(-0.0868896 + 0.150497i) q^{74} +(0.294535 + 0.510150i) q^{75} +(2.78743 - 4.82796i) q^{76} +(0.348653 + 0.725520i) q^{77} +(-5.53362 + 2.24903i) q^{78} +(6.54933 - 11.3438i) q^{79} +10.3641 q^{80} +1.00000 q^{81} -3.32586 q^{82} -9.33190 q^{83} +(1.96426 + 0.148834i) q^{84} +(6.10309 + 10.5709i) q^{85} +(-6.69291 + 11.5925i) q^{86} +(1.09353 - 1.89405i) q^{87} -0.632780 q^{88} +(-1.54769 - 2.68068i) q^{89} +3.47937 q^{90} +(9.08349 - 2.91380i) q^{91} +4.47962 q^{92} +(3.51152 + 6.08213i) q^{93} +14.2499 q^{94} +(-7.86277 + 13.6187i) q^{95} +(-2.00775 + 3.47753i) q^{96} +(-3.19711 - 5.53756i) q^{97} +(-11.4643 - 1.74736i) q^{98} -0.304241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) \) 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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