LMFDB - Embedded newform 550.2.h.n.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(201,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("550.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.h (of order $5$, degree $4$, 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:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.20164000000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 76x^{4} + 781x^{2} + 5041 $ x^8 + 6x^6 + 76x^4 + 781*x^2 + 5041
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.2
Root			$-0.839592 - 2.58400i$ of defining polynomial
Character	$\chi$	$=$	550.201
Dual form			550.2.h.n.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 - 0.587785i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.30902 + 0.951057i) q^{6} +(1.16751 - 3.59321i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 - 0.224514i) q^{9} +(-2.64861 - 1.99621i) q^{11} +1.61803 q^{12} +(2.50710 - 1.82151i) q^{13} +(-1.16751 - 3.59321i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(2.66751 + 1.93806i) q^{17} +(0.118034 - 0.363271i) q^{18} +(0.400863 + 1.23373i) q^{19} +6.11314 q^{21} +(-3.31611 - 0.0581575i) q^{22} +0.556884 q^{23} +(1.30902 - 0.951057i) q^{24} +(0.957626 - 2.94727i) q^{26} +(4.42705 + 3.21644i) q^{27} +(-3.05657 - 2.22073i) q^{28} +(-2.95763 + 9.10264i) q^{29} +(-4.32760 + 3.14419i) q^{31} -1.00000 q^{32} +(1.74755 - 5.07390i) q^{33} +3.29722 q^{34} +(-0.118034 - 0.363271i) q^{36} +(2.44595 - 7.52785i) q^{37} +(1.04947 + 0.762486i) q^{38} +(4.05657 + 2.94727i) q^{39} +(1.94312 + 5.98030i) q^{41} +(4.94563 - 3.59321i) q^{42} +3.61803 q^{43} +(-2.71698 + 1.90211i) q^{44} +(0.450528 - 0.327328i) q^{46} +(-1.65300 - 5.08740i) q^{47} +(0.500000 - 1.53884i) q^{48} +(-5.88499 - 4.27570i) q^{49} +(-1.64861 + 5.07390i) q^{51} +(-0.957626 - 2.94727i) q^{52} +(-8.91067 + 6.47398i) q^{53} +5.47214 q^{54} -3.77813 q^{56} +(-1.69808 + 1.23373i) q^{57} +(2.95763 + 9.10264i) q^{58} +(1.63693 - 5.03795i) q^{59} +(-1.98801 - 1.44437i) q^{61} +(-1.65300 + 5.08740i) q^{62} +(-0.445947 - 1.37249i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.56856 - 5.13205i) q^{66} +9.21247 q^{67} +(2.66751 - 1.93806i) q^{68} +(0.278442 + 0.856956i) q^{69} +(-8.81173 - 6.40210i) q^{71} +(-0.309017 - 0.224514i) q^{72} +(-1.04947 + 3.22994i) q^{73} +(-2.44595 - 7.52785i) q^{74} +1.29722 q^{76} +(-10.2651 + 7.18643i) q^{77} +5.01420 q^{78} +(-13.2383 + 9.61817i) q^{79} +(-2.38197 + 7.33094i) q^{81} +(5.08714 + 3.69603i) q^{82} +(-0.148923 - 0.108199i) q^{83} +(1.88906 - 5.81394i) q^{84} +(2.92705 - 2.12663i) q^{86} -15.4863 q^{87} +(-1.08005 + 3.13584i) q^{88} +6.09017 q^{89} +(-3.61803 - 11.1352i) q^{91} +(0.172087 - 0.529628i) q^{92} +(-7.00220 - 5.08740i) q^{93} +(-4.32760 - 3.14419i) q^{94} +(-0.500000 - 1.53884i) q^{96} +(-9.99782 + 7.26384i) q^{97} -7.27425 q^{98} +(-1.26664 - 0.0222142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 6 q^{6} - 6 q^{7} + 2 q^{8} - 2 q^{9} - 10 q^{11} + 4 q^{12} - 2 q^{13} + 6 q^{14} - 2 q^{16} + 6 q^{17} - 8 q^{18} + 8 q^{19} - 8 q^{21} + 6 q^{24} - 8 q^{26} + 22 q^{27}+ \cdots + 10 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + 6 * q^6 - 6 * q^7 + 2 * q^8 - 2 * q^9 - 10 * q^11 + 4 * q^12 - 2 * q^13 + 6 * q^14 - 2 * q^16 + 6 * q^17 - 8 * q^18 + 8 * q^19 - 8 * q^21 + 6 * q^24 - 8 * q^26 + 22 * q^27 + 4 * q^28 - 8 * q^29 - 2 * q^31 - 8 * q^32 - 10 * q^33 + 4 * q^34 + 8 * q^36 + 2 * q^37 + 2 * q^38 + 4 * q^39 + 20 * q^41 - 2 * q^42 + 20 * q^43 + 10 * q^46 - 18 * q^47 + 4 * q^48 - 42 * q^49 - 2 * q^51 + 8 * q^52 - 16 * q^53 + 8 * q^54 - 4 * q^56 + 4 * q^57 + 8 * q^58 + 10 * q^61 - 18 * q^62 + 14 * q^63 - 2 * q^64 - 10 * q^66 + 20 * q^67 + 6 * q^68 - 28 * q^71 + 2 * q^72 - 2 * q^73 - 2 * q^74 - 12 * q^76 - 24 * q^77 - 4 * q^78 - 18 * q^79 - 28 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 + 10 * q^86 - 44 * q^87 + 4 * q^89 - 20 * q^91 + 10 * q^92 + 14 * q^93 - 2 * q^94 - 4 * q^96 + 6 * q^97 - 48 * q^98 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.500000	+	1.53884i	0.288675	+	0.888451i	0.985273	+	0.170989i	$0.0546962\pi$
$3$	0.500000	+	1.53884i	0.288675	+	0.888451i	−0.696598	+	0.717462i	$0.745304\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	1.30902	+	0.951057i	0.534404	+	0.388267i
$7$	1.16751	−	3.59321i	0.441276	−	1.35811i	−0.445241	−	0.895411i	$-0.646882\pi$
$7$	1.16751	−	3.59321i	0.441276	−	1.35811i	0.886517	−	0.462696i	$-0.153118\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.309017	−	0.224514i	0.103006	−	0.0748380i
$10$		0			0
$11$	−2.64861	−	1.99621i	−0.798586	−	0.601881i
$11$	−2.64861	−	1.99621i	−0.798586	−	0.601881i
$12$	1.61803			0.467086
$13$	2.50710	−	1.82151i	0.695344	−	0.505197i	−0.183069	−	0.983100i	$-0.558603\pi$
$13$	2.50710	−	1.82151i	0.695344	−	0.505197i	0.878412	+	0.477903i	$0.158603\pi$
$14$	−1.16751	−	3.59321i	−0.312029	−	0.960327i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.66751	+	1.93806i	0.646965	+	0.470048i	0.862236	−	0.506507i	$-0.169063\pi$
$17$	2.66751	+	1.93806i	0.646965	+	0.470048i	−0.215271	+	0.976554i	$0.569063\pi$
$18$	0.118034	−	0.363271i	0.0278209	−	0.0856239i
$19$	0.400863	+	1.23373i	0.0919642	+	0.283037i	0.986451	−	0.164058i	$-0.0524586\pi$
$19$	0.400863	+	1.23373i	0.0919642	+	0.283037i	−0.894486	+	0.447095i	$0.852459\pi$
$20$		0			0
$21$	6.11314			1.33400
$22$	−3.31611	−	0.0581575i	−0.706998	−	0.0123992i
$23$	0.556884			0.116118			0.0580591	−	0.998313i	$-0.481509\pi$
$23$	0.556884			0.116118			0.0580591	+	0.998313i	$0.481509\pi$
$24$	1.30902	−	0.951057i	0.267202	−	0.194134i
$25$		0			0
$26$	0.957626	−	2.94727i	0.187806	−	0.578007i
$27$	4.42705	+	3.21644i	0.851986	+	0.619004i
$28$	−3.05657	−	2.22073i	−0.577637	−	0.419678i
$29$	−2.95763	+	9.10264i	−0.549217	+	1.69032i	0.161528	+	0.986868i	$0.448358\pi$
$29$	−2.95763	+	9.10264i	−0.549217	+	1.69032i	−0.710746	+	0.703449i	$0.751642\pi$
$30$		0			0
$31$	−4.32760	+	3.14419i	−0.777260	+	0.564712i	−0.904155	−	0.427204i	$-0.859499\pi$
$31$	−4.32760	+	3.14419i	−0.777260	+	0.564712i	0.126896	+	0.991916i	$0.459499\pi$
$32$	−1.00000			−0.176777
$33$	1.74755	−	5.07390i	0.304210	−	0.883252i
$34$	3.29722			0.565468
$35$		0			0
$36$	−0.118034	−	0.363271i	−0.0196723	−	0.0605452i
$37$	2.44595	−	7.52785i	0.402111	−	1.23757i	−0.521172	−	0.853452i	$-0.674505\pi$
$37$	2.44595	−	7.52785i	0.402111	−	1.23757i	0.923283	−	0.384120i	$-0.125495\pi$
$38$	1.04947	+	0.762486i	0.170247	+	0.123692i
$39$	4.05657	+	2.94727i	0.649571	+	0.471941i
$40$		0			0
$41$	1.94312	+	5.98030i	0.303464	+	0.933966i	0.980246	+	0.197782i	$0.0633739\pi$
$41$	1.94312	+	5.98030i	0.303464	+	0.933966i	−0.676782	+	0.736183i	$0.736626\pi$
$42$	4.94563	−	3.59321i	0.763128	−	0.554445i
$43$	3.61803			0.551745			0.275873	−	0.961194i	$-0.411033\pi$
$43$	3.61803			0.551745			0.275873	+	0.961194i	$0.411033\pi$
$44$	−2.71698	+	1.90211i	−0.409600	+	0.286754i
$45$		0			0
$46$	0.450528	−	0.327328i	0.0664268	−	0.0482619i
$47$	−1.65300	−	5.08740i	−0.241114	−	0.742073i	−0.996251	−	0.0865064i	$-0.972430\pi$
$47$	−1.65300	−	5.08740i	−0.241114	−	0.742073i	0.755137	−	0.655567i	$-0.227570\pi$
$48$	0.500000	−	1.53884i	0.0721688	−	0.222113i
$49$	−5.88499	−	4.27570i	−0.840713	−	0.610814i
$50$		0			0
$51$	−1.64861	+	5.07390i	−0.230851	+	0.710488i
$52$	−0.957626	−	2.94727i	−0.132799	−	0.408713i
$53$	−8.91067	+	6.47398i	−1.22397	+	0.889270i	−0.996424	−	0.0844964i	$-0.973072\pi$
$53$	−8.91067	+	6.47398i	−1.22397	+	0.889270i	−0.227551	+	0.973766i	$0.573072\pi$
$54$	5.47214			0.744663
$55$		0			0
$56$	−3.77813			−0.504874
$57$	−1.69808	+	1.23373i	−0.224916	+	0.163411i
$58$	2.95763	+	9.10264i	0.388355	+	1.19523i
$59$	1.63693	−	5.03795i	0.213110	−	0.655886i	−0.786172	−	0.618008i	$-0.787940\pi$
$59$	1.63693	−	5.03795i	0.213110	−	0.655886i	0.999282	−	0.0378782i	$-0.0120599\pi$
$60$		0			0
$61$	−1.98801	−	1.44437i	−0.254538	−	0.184933i	0.453197	−	0.891410i	$-0.350283\pi$
$61$	−1.98801	−	1.44437i	−0.254538	−	0.184933i	−0.707736	+	0.706477i	$0.750283\pi$
$62$	−1.65300	+	5.08740i	−0.209931	+	0.646100i
$63$	−0.445947	−	1.37249i	−0.0561841	−	0.172917i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$		0			0
$66$	−1.56856	−	5.13205i	−0.193077	−	0.631712i
$67$	9.21247			1.12548			0.562741	−	0.826633i	$-0.309747\pi$
$67$	9.21247			1.12548			0.562741	+	0.826633i	$0.309747\pi$
$68$	2.66751	−	1.93806i	0.323483	−	0.235024i
$69$	0.278442	+	0.856956i	0.0335205	+	0.103165i
$70$		0			0
$71$	−8.81173	−	6.40210i	−1.04576	−	0.759789i	−0.0743582	−	0.997232i	$-0.523691\pi$
$71$	−8.81173	−	6.40210i	−1.04576	−	0.759789i	−0.971402	+	0.237443i	$0.923691\pi$
$72$	−0.309017	−	0.224514i	−0.0364180	−	0.0264592i
$73$	−1.04947	+	3.22994i	−0.122831	+	0.378036i	−0.993500	−	0.113834i	$-0.963687\pi$
$73$	−1.04947	+	3.22994i	−0.122831	+	0.378036i	0.870668	+	0.491871i	$0.163687\pi$
$74$	−2.44595	−	7.52785i	−0.284336	−	0.875095i
$75$		0			0
$76$	1.29722			0.148801
$77$	−10.2651	+	7.18643i	−1.16982	+	0.818969i
$78$	5.01420			0.567746
$79$	−13.2383	+	9.61817i	−1.48942	+	1.08213i	−0.515057	+	0.857156i	$0.672229\pi$
$79$	−13.2383	+	9.61817i	−1.48942	+	1.08213i	−0.974365	+	0.224972i	$0.927771\pi$
$80$		0			0
$81$	−2.38197	+	7.33094i	−0.264663	+	0.814549i
$82$	5.08714	+	3.69603i	0.561781	+	0.408158i
$83$	−0.148923	−	0.108199i	−0.0163464	−	0.0118764i	0.579582	−	0.814914i	$-0.303216\pi$
$83$	−0.148923	−	0.108199i	−0.0163464	−	0.0118764i	−0.595928	+	0.803038i	$0.703216\pi$
$84$	1.88906	−	5.81394i	0.206114	−	0.634353i
$85$		0			0
$86$	2.92705	−	2.12663i	0.315632	−	0.229320i
$87$	−15.4863			−1.66031
$88$	−1.08005	+	3.13584i	−0.115133	+	0.334282i
$89$	6.09017			0.645557			0.322778	−	0.946475i	$-0.395383\pi$
$89$	6.09017			0.645557			0.322778	+	0.946475i	$0.395383\pi$
$90$		0			0
$91$	−3.61803	−	11.1352i	−0.379273	−	1.16728i
$92$	0.172087	−	0.529628i	0.0179413	−	0.0552175i
$93$	−7.00220	−	5.08740i	−0.726095	−	0.527539i
$94$	−4.32760	−	3.14419i	−0.446358	−	0.324298i
$95$		0			0
$96$	−0.500000	−	1.53884i	−0.0510310	−	0.157057i
$97$	−9.99782	+	7.26384i	−1.01512	+	0.737531i	−0.965278	−	0.261226i	$-0.915873\pi$
$97$	−9.99782	+	7.26384i	−1.01512	+	0.737531i	−0.0498467	+	0.998757i	$0.515873\pi$
$98$	−7.27425			−0.734810
$99$	−1.26664	−	0.0222142i	−0.127302	−	0.00223261i
$100$		0			0
$101$	7.29264	−	5.29841i	0.725645	−	0.527212i	−0.162538	−	0.986702i	$-0.551968\pi$
$101$	7.29264	−	5.29841i	0.725645	−	0.527212i	0.888183	+	0.459491i	$0.151968\pi$
$102$	1.64861	+	5.07390i	0.163237	+	0.502391i
$103$	3.53329	−	10.8743i	0.348145	−	1.07148i	−0.611733	−	0.791064i	$-0.709527\pi$
$103$	3.53329	−	10.8743i	0.348145	−	1.07148i	0.959878	−	0.280416i	$-0.0904725\pi$
$104$	−2.50710	−	1.82151i	−0.245841	−	0.178614i
$105$		0			0
$106$	−3.40357	+	10.4751i	−0.330584	+	1.01743i
$107$	4.74484	+	14.6031i	0.458701	+	1.41174i	0.866734	+	0.498770i	$0.166215\pi$
$107$	4.74484	+	14.6031i	0.458701	+	1.41174i	−0.408033	+	0.912967i	$0.633785\pi$
$108$	4.42705	−	3.21644i	0.425993	−	0.309502i
$109$	2.42892			0.232648			0.116324	−	0.993211i	$-0.462889\pi$
$109$	2.42892			0.232648			0.116324	+	0.993211i	$0.462889\pi$
$110$		0			0
$111$	12.8071			1.21560
$112$	−3.05657	+	2.22073i	−0.288819	+	0.209839i
$113$	2.58998	+	7.97113i	0.243644	+	0.749860i	0.995856	+	0.0909393i	$0.0289869\pi$
$113$	2.58998	+	7.97113i	0.243644	+	0.749860i	−0.752212	+	0.658921i	$0.771013\pi$
$114$	−0.648609	+	1.99621i	−0.0607478	+	0.186963i
$115$		0			0
$116$	7.74317	+	5.62574i	0.718935	+	0.522337i
$117$	0.365781	−	1.12576i	0.0338164	−	0.104076i
$118$	−1.63693	−	5.03795i	−0.150692	−	0.463781i
$119$	10.0782	−	7.32222i	0.923865	−	0.671227i
$120$		0			0
$121$	3.03026	+	10.5744i	0.275478	+	0.961307i
$122$	−2.45731			−0.222475
$123$	−8.23117	+	5.98030i	−0.742180	+	0.539225i
$124$	1.65300	+	5.08740i	0.148443	+	0.456862i
$125$		0			0
$126$	−1.16751	−	0.848243i	−0.104010	−	0.0755675i
$127$	−5.62545	−	4.08713i	−0.499178	−	0.362674i	0.309525	−	0.950891i	$-0.399830\pi$
$127$	−5.62545	−	4.08713i	−0.499178	−	0.362674i	−0.808703	+	0.588217i	$0.799830\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	1.80902	+	5.56758i	0.159275	+	0.490198i
$130$		0			0
$131$	−5.61741			−0.490795			−0.245398	−	0.969423i	$-0.578918\pi$
$131$	−5.61741			−0.490795			−0.245398	+	0.969423i	$0.578918\pi$
$132$	−4.28554	−	3.22994i	−0.373008	−	0.281130i
$133$	4.90106			0.424976
$134$	7.45305	−	5.41495i	0.643845	−	0.467781i
$135$		0			0
$136$	1.01890	−	3.13584i	0.0873697	−	0.268896i
$137$	−6.21969	−	4.51887i	−0.531384	−	0.386073i	0.289491	−	0.957181i	$-0.406514\pi$
$137$	−6.21969	−	4.51887i	−0.531384	−	0.386073i	−0.820875	+	0.571108i	$0.806514\pi$
$138$	0.728970	+	0.529628i	0.0620541	+	0.0450849i
$139$	0.297218	−	0.914744i	0.0252097	−	0.0775876i	−0.937660	−	0.347554i	$-0.887012\pi$
$139$	0.297218	−	0.914744i	0.0252097	−	0.0775876i	0.962870	+	0.269966i	$0.0870125\pi$
$140$		0			0
$141$	7.00220	−	5.08740i	0.589692	−	0.428436i
$142$	−10.8919			−0.914028
$143$	−10.2765	−	0.180227i	−0.859360	−	0.0150713i
$144$	−0.381966			−0.0318305
$145$		0			0
$146$	1.04947	+	3.22994i	0.0868549	+	0.267312i
$147$	3.63712	−	11.1939i	0.299985	−	0.923259i
$148$	−6.40357	−	4.65247i	−0.526371	−	0.382431i
$149$	7.11314	+	5.16800i	0.582731	+	0.423379i	0.839708	−	0.543039i	$-0.182726\pi$
$149$	7.11314	+	5.16800i	0.582731	+	0.423379i	−0.256977	+	0.966418i	$0.582726\pi$
$150$		0			0
$151$	−2.76194	−	8.50038i	−0.224764	−	0.691751i	−0.998316	−	0.0580184i	$-0.981522\pi$
$151$	−2.76194	−	8.50038i	−0.224764	−	0.691751i	0.773552	−	0.633733i	$-0.218478\pi$
$152$	1.04947	−	0.762486i	0.0851234	−	0.0618458i
$153$	1.25943			0.101819
$154$	−4.08056	+	11.8476i	−0.328820	+	0.954707i
$155$		0			0
$156$	4.05657	−	2.94727i	0.324785	−	0.235970i
$157$	5.45137	+	16.7776i	0.435067	+	1.33900i	0.893018	+	0.450020i	$0.148583\pi$
$157$	5.45137	+	16.7776i	0.435067	+	1.33900i	−0.457952	+	0.888977i	$0.651417\pi$
$158$	−5.05657	+	15.5625i	−0.402279	+	1.23809i
$159$	−14.4178	−	10.4751i	−1.14340	−	0.830731i
$160$		0			0
$161$	0.650165	−	2.00100i	0.0512402	−	0.157701i
$162$	2.38197	+	7.33094i	0.187145	+	0.575973i
$163$	0.141003	−	0.102445i	0.0110442	−	0.00802409i	−0.582249	−	0.813010i	$-0.697827\pi$
$163$	0.141003	−	0.102445i	0.0110442	−	0.00802409i	0.593294	+	0.804986i	$0.297827\pi$
$164$	6.28806			0.491015
$165$		0			0
$166$	−0.184079			−0.0142873
$167$	4.43854	−	3.22478i	0.343464	−	0.249541i	−0.402658	−	0.915351i	$-0.631914\pi$
$167$	4.43854	−	3.22478i	0.343464	−	0.249541i	0.746122	+	0.665809i	$0.231914\pi$
$168$	−1.88906	−	5.81394i	−0.145744	−	0.448555i
$169$	−1.04959	+	3.23031i	−0.0807378	+	0.248485i
$170$		0			0
$171$	0.400863	+	0.291244i	0.0306547	+	0.0222720i
$172$	1.11803	−	3.44095i	0.0852493	−	0.262370i
$173$	7.41518	+	22.8216i	0.563766	+	1.73509i	0.671591	+	0.740922i	$0.265611\pi$
$173$	7.41518	+	22.8216i	0.563766	+	1.73509i	−0.107825	+	0.994170i	$0.534389\pi$
$174$	−12.5287	+	9.10264i	−0.949799	+	0.690069i
$175$		0			0
$176$	0.969425	+	3.17178i	0.0730731	+	0.239082i
$177$	8.57108			0.644242
$178$	4.92705	−	3.57971i	0.369298	−	0.268311i
$179$	−0.0658512	−	0.202669i	−0.00492195	−	0.0151482i	0.948565	−	0.316581i	$-0.102535\pi$
$179$	−0.0658512	−	0.202669i	−0.00492195	−	0.0151482i	−0.953487	+	0.301433i	$0.902535\pi$
$180$		0			0
$181$	−0.839906	−	0.610228i	−0.0624297	−	0.0453579i	0.556133	−	0.831094i	$-0.312285\pi$
$181$	−0.839906	−	0.610228i	−0.0624297	−	0.0453579i	−0.618562	+	0.785736i	$0.712285\pi$
$182$	−9.47214	−	6.88191i	−0.702121	−	0.510121i
$183$	1.22866	−	3.78141i	0.0908249	−	0.279530i
$184$	−0.172087	−	0.529628i	−0.0126864	−	0.0390447i
$185$		0			0
$186$	−8.65520			−0.634630
$187$	−3.19641	−	10.4581i	−0.233744	−	0.764769i
$188$	−5.34921			−0.390131
$189$	16.7260	−	12.1521i	1.21663	−	0.883937i
$190$		0			0
$191$	−5.54206	+	17.0567i	−0.401009	+	1.23418i	0.523172	+	0.852227i	$0.324748\pi$
$191$	−5.54206	+	17.0567i	−0.401009	+	1.23418i	−0.924182	+	0.381953i	$0.875252\pi$
$192$	−1.30902	−	0.951057i	−0.0944702	−	0.0686366i
$193$	−7.29722	−	5.30174i	−0.525265	−	0.381628i	0.293318	−	0.956015i	$-0.405240\pi$
$193$	−7.29722	−	5.30174i	−0.525265	−	0.381628i	−0.818584	+	0.574387i	$0.805240\pi$
$194$	−3.81883	+	11.7531i	−0.274176	+	0.843826i
$195$		0			0
$196$	−5.88499	+	4.27570i	−0.420357	+	0.305407i
$197$	3.68422			0.262490			0.131245	−	0.991350i	$-0.458103\pi$
$197$	3.68422			0.262490			0.131245	+	0.991350i	$0.458103\pi$
$198$	−1.03779	+	0.726543i	−0.0737527	+	0.0516331i
$199$	−4.23544			−0.300242			−0.150121	−	0.988668i	$-0.547966\pi$
$199$	−4.23544			−0.300242			−0.150121	+	0.988668i	$0.547966\pi$
$200$		0			0
$201$	4.60624	+	14.1765i	0.324899	+	0.999936i
$202$	2.78554	−	8.57301i	0.195990	−	0.603195i
$203$	29.2547	+	21.2548i	2.05328	+	1.49179i
$204$	4.31611	+	3.13584i	0.302188	+	0.219553i
$205$		0			0
$206$	−3.53329	−	10.8743i	−0.246176	−	0.757651i
$207$	0.172087	−	0.125028i	0.0119608	−	0.00869006i
$208$	−3.09894			−0.214873
$209$	1.40106	−	4.06787i	0.0969131	−	0.281380i
$210$		0			0
$211$	11.0596	−	8.03527i	0.761374	−	0.553171i	−0.137958	−	0.990438i	$-0.544054\pi$
$211$	11.0596	−	8.03527i	0.761374	−	0.553171i	0.899331	+	0.437268i	$0.144054\pi$
$212$	3.40357	+	10.4751i	0.233758	+	0.719434i
$213$	5.44595	−	16.7609i	0.373150	−	1.14844i
$214$	12.4222	+	9.02522i	0.849161	+	0.616952i
$215$		0			0
$216$	1.69098	−	5.20431i	0.115057	−	0.354108i
$217$	6.24523	+	19.2208i	0.423954	+	1.30480i
$218$	1.96504	−	1.42768i	0.133089	−	0.0966949i
$219$	−5.49511			−0.371325
$220$		0			0
$221$	10.2179			0.687330
$222$	10.3612	−	7.52785i	0.695398	−	0.505236i
$223$	−7.40777	−	22.7988i	−0.496061	−	1.52672i	−0.815297	−	0.579043i	$-0.803426\pi$
$223$	−7.40777	−	22.7988i	−0.496061	−	1.52672i	0.319236	−	0.947675i	$-0.396574\pi$
$224$	−1.16751	+	3.59321i	−0.0780073	+	0.240082i
$225$		0			0
$226$	6.78064	+	4.92643i	0.451042	+	0.327701i
$227$	−6.39803	+	19.6911i	−0.424652	+	1.30695i	0.478675	+	0.877992i	$0.341117\pi$
$227$	−6.39803	+	19.6911i	−0.424652	+	1.30695i	−0.903327	+	0.428953i	$0.858883\pi$
$228$	0.648609	+	1.99621i	0.0429552	+	0.132202i
$229$	13.2199	−	9.60481i	0.873594	−	0.634704i	−0.0579546	−	0.998319i	$-0.518458\pi$
$229$	13.2199	−	9.60481i	0.873594	−	0.634704i	0.931549	+	0.363616i	$0.118458\pi$
$230$		0			0
$231$	−16.1913	−	12.2031i	−1.06531	−	0.802907i
$232$	9.57108			0.628372
$233$	0.388556	−	0.282302i	0.0254551	−	0.0184942i	−0.574985	−	0.818164i	$-0.694992\pi$
$233$	0.388556	−	0.282302i	0.0254551	−	0.0184942i	0.600440	+	0.799670i	$0.294992\pi$
$234$	−0.365781	−	1.12576i	−0.0239118	−	0.0735930i
$235$		0			0
$236$	−4.28554	−	3.11363i	−0.278965	−	0.202680i
$237$	−21.4200	−	15.5625i	−1.39138	−	1.01089i
$238$	3.84952	−	11.8476i	0.249527	−	0.767966i
$239$	0.348754	+	1.07335i	0.0225590	+	0.0694295i	0.961702	−	0.274096i	$-0.0883787\pi$
$239$	0.348754	+	1.07335i	0.0225590	+	0.0694295i	−0.939143	+	0.343526i	$0.888379\pi$
$240$		0			0
$241$	−12.7220			−0.819497			−0.409748	−	0.912199i	$-0.634384\pi$
$241$	−12.7220			−0.819497			−0.409748	+	0.912199i	$0.634384\pi$
$242$	8.66700	+	6.77371i	0.557136	+	0.435431i
$243$	3.94427			0.253025
$244$	−1.98801	+	1.44437i	−0.127269	+	0.0924664i
$245$		0			0
$246$	−3.14403	+	9.67632i	−0.200456	+	0.616940i
$247$	3.25225	+	2.36290i	0.206936	+	0.150348i
$248$	4.32760	+	3.14419i	0.274803	+	0.199656i
$249$	0.0920396	−	0.283269i	0.00583277	−	0.0179514i
$250$		0			0
$251$	2.29722	−	1.66903i	0.144999	−	0.105348i	−0.512921	−	0.858436i	$-0.671437\pi$
$251$	2.29722	−	1.66903i	0.144999	−	0.105348i	0.657920	+	0.753088i	$0.271437\pi$
$252$	−1.44312			−0.0909078
$253$	−1.47497	−	1.11166i	−0.0927304	−	0.0698894i
$254$	−6.95343			−0.436297
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	9.53038	−	29.3315i	0.594489	−	1.82965i	0.0372347	−	0.999307i	$-0.488145\pi$
$257$	9.53038	−	29.3315i	0.594489	−	1.82965i	0.557254	−	0.830342i	$-0.311855\pi$
$258$	4.73607	+	3.44095i	0.294855	+	0.214224i
$259$	−24.1935	−	17.5776i	−1.50331	−	1.09222i
$260$		0			0
$261$	1.12971	+	3.47690i	0.0699275	+	0.215215i
$262$	−4.54458	+	3.30183i	−0.280765	+	0.203988i
$263$	−27.7069			−1.70848			−0.854242	−	0.519876i	$-0.825978\pi$
$263$	−27.7069			−1.70848			−0.854242	+	0.519876i	$0.825978\pi$
$264$	−5.36559	−	0.0941007i	−0.330229	−	0.00579150i
$265$		0			0
$266$	3.96504	−	2.88077i	0.243112	−	0.176631i
$267$	3.04508	+	9.37181i	0.186356	+	0.573545i
$268$	2.84681	−	8.76158i	0.173897	−	0.535199i
$269$	−10.3224	−	7.49966i	−0.629367	−	0.457262i	0.226814	−	0.973938i	$-0.427169\pi$
$269$	−10.3224	−	7.49966i	−0.629367	−	0.457262i	−0.856181	+	0.516676i	$0.827169\pi$
$270$		0			0
$271$	1.76218	−	5.42344i	0.107045	−	0.329450i	−0.883160	−	0.469072i	$-0.844589\pi$
$271$	1.76218	−	5.42344i	0.107045	−	0.329450i	0.990205	+	0.139621i	$0.0445885\pi$
$272$	−1.01890	−	3.13584i	−0.0617797	−	0.190138i
$273$	15.3262	−	11.1352i	0.927586	−	0.673931i
$274$	−7.68796			−0.464447
$275$		0			0
$276$	0.901057			0.0542372
$277$	25.6680	−	18.6489i	1.54224	−	1.12050i	0.593333	−	0.804957i	$-0.297812\pi$
$277$	25.6680	−	18.6489i	1.54224	−	1.12050i	0.948910	−	0.315548i	$-0.102188\pi$
$278$	−0.297218	−	0.914744i	−0.0178260	−	0.0548627i
$279$	−0.631388	+	1.94321i	−0.0378002	+	0.116337i
$280$		0			0
$281$	1.56805	+	1.13926i	0.0935423	+	0.0679624i	0.633573	−	0.773683i	$-0.281588\pi$
$281$	1.56805	+	1.13926i	0.0935423	+	0.0679624i	−0.540031	+	0.841645i	$0.681588\pi$
$282$	2.67460	−	8.23158i	0.159270	−	0.490184i
$283$	1.51909	+	4.67528i	0.0903006	+	0.277917i	0.986000	−	0.166742i	$-0.0533249\pi$
$283$	1.51909	+	4.67528i	0.0903006	+	0.277917i	−0.895700	+	0.444659i	$0.853325\pi$
$284$	−8.81173	+	6.40210i	−0.522880	+	0.379894i
$285$		0			0
$286$	−8.41976	+	5.89454i	−0.497871	+	0.348551i
$287$	23.7571			1.40234
$288$	−0.309017	+	0.224514i	−0.0182090	+	0.0132296i
$289$	−1.89376	−	5.82841i	−0.111398	−	0.342848i
$290$		0			0
$291$	−16.1768	−	11.7531i	−0.948301	−	0.688981i
$292$	2.74755	+	1.99621i	0.160788	+	0.116820i
$293$	−0.0583193	+	0.179488i	−0.00340705	+	0.0104858i	−0.952746	−	0.303769i	$-0.901755\pi$
$293$	−0.0583193	+	0.179488i	−0.00340705	+	0.0104858i	0.949339	+	0.314255i	$0.101755\pi$
$294$	−3.63712	−	11.1939i	−0.212121	−	0.652843i
$295$		0			0
$296$	−7.91525			−0.460065
$297$	−5.30482	−	17.3564i	−0.307817	−	1.00712i
$298$	8.79232			0.509326
$299$	1.39616	−	1.01437i	0.0807421	−	0.0586626i
$300$		0			0
$301$	4.22408	−	13.0004i	0.243472	−	0.749329i
$302$	−7.23086	−	5.25353i	−0.416089	−	0.302306i
$303$	11.7997	+	8.57301i	0.677877	+	0.492507i
$304$	0.400863	−	1.23373i	0.0229910	−	0.0707592i
$305$		0			0
$306$	1.01890	−	0.740272i	0.0582464	−	0.0423185i
$307$	−12.3820			−0.706676			−0.353338	−	0.935496i	$-0.614953\pi$
$307$	−12.3820			−0.706676			−0.353338	+	0.935496i	$0.614953\pi$
$308$	3.66261	+	11.9834i	0.208697	+	0.682818i
$309$	18.5005			1.05246
$310$		0			0
$311$	−6.52587	−	20.0846i	−0.370048	−	1.13889i	−0.946759	−	0.321943i	$-0.895664\pi$
$311$	−6.52587	−	20.0846i	−0.370048	−	1.13889i	0.576711	−	0.816949i	$-0.304336\pi$
$312$	1.54947	−	4.76878i	0.0877216	−	0.269979i
$313$	−13.4129	−	9.74502i	−0.758140	−	0.550821i	0.140199	−	0.990123i	$-0.455226\pi$
$313$	−13.4129	−	9.74502i	−0.758140	−	0.550821i	−0.898339	+	0.439302i	$0.855226\pi$
$314$	14.2719	+	10.3691i	0.805408	+	0.585163i
$315$		0			0
$316$	5.05657	+	15.5625i	0.284454	+	0.875460i
$317$	15.8867	−	11.5424i	0.892285	−	0.648283i	−0.0441877	−	0.999023i	$-0.514070\pi$
$317$	15.8867	−	11.5424i	0.892285	−	0.648283i	0.936473	+	0.350740i	$0.114070\pi$
$318$	−17.8213			−0.999371
$319$	26.0044	−	18.2053i	1.45597	−	1.01930i
$320$		0			0
$321$	−20.0995	+	14.6031i	−1.12184	+	0.815067i
$322$	−0.650165	−	2.00100i	−0.0362323	−	0.111511i
$323$	−1.32173	+	4.06787i	−0.0735431	+	0.226342i
$324$	6.23607	+	4.53077i	0.346448	+	0.251709i
$325$		0			0
$326$	0.0538584	−	0.165759i	0.00298294	−	0.00918055i
$327$	1.21446	+	3.73772i	0.0671598	+	0.206697i
$328$	5.08714	−	3.69603i	0.280891	−	0.204079i
$329$	−20.2100			−1.11421
$330$		0			0
$331$	−23.4826			−1.29072			−0.645360	−	0.763879i	$-0.723293\pi$
$331$	−23.4826			−1.29072			−0.645360	+	0.763879i	$0.723293\pi$
$332$	−0.148923	+	0.108199i	−0.00817322	+	0.00593820i
$333$	−0.934269	−	2.87538i	−0.0511976	−	0.157570i
$334$	1.69537	−	5.21781i	0.0927665	−	0.285506i
$335$		0			0
$336$	−4.94563	−	3.59321i	−0.269806	−	0.196026i
$337$	3.96317	−	12.1974i	0.215888	−	0.664434i	−0.783202	−	0.621768i	$-0.786415\pi$
$337$	3.96317	−	12.1974i	0.215888	−	0.664434i	0.999089	−	0.0426660i	$-0.0135851\pi$
$338$	1.04959	+	3.23031i	0.0570903	+	0.175706i
$339$	−10.9713	+	7.97113i	−0.595880	+	0.432932i
$340$		0			0
$341$	17.7386	+	0.311096i	0.960598	+	0.0168468i
$342$	0.495493			0.0267932
$343$	−0.838262	+	0.609033i	−0.0452619	+	0.0328847i
$344$	−1.11803	−	3.44095i	−0.0602804	−	0.185524i
$345$		0			0
$346$	19.4132	+	14.1045i	1.04366	+	0.758263i
$347$	−16.7415	−	12.1634i	−0.898730	−	0.652966i	0.0394093	−	0.999223i	$-0.487452\pi$
$347$	−16.7415	−	12.1634i	−0.898730	−	0.652966i	−0.938140	+	0.346257i	$0.887452\pi$
$348$	−4.78554	+	14.7284i	−0.256532	+	0.789524i
$349$	6.71104	+	20.6544i	0.359233	+	1.10561i	0.953514	+	0.301349i	$0.0974369\pi$
$349$	6.71104	+	20.6544i	0.359233	+	1.10561i	−0.594280	+	0.804258i	$0.702563\pi$
$350$		0			0
$351$	16.9578			0.905143
$352$	2.64861	+	1.99621i	0.141171	+	0.106399i
$353$	−0.260293			−0.0138540			−0.00692701	−	0.999976i	$-0.502205\pi$
$353$	−0.260293			−0.0138540			−0.00692701	+	0.999976i	$0.502205\pi$
$354$	6.93415	−	5.03795i	0.368546	−	0.267764i
$355$		0			0
$356$	1.88197	−	5.79210i	0.0997440	−	0.306980i
$357$	16.3068	+	11.8476i	0.863049	+	0.627042i
$358$	−0.172401	−	0.125256i	−0.00911165	−	0.00662000i
$359$	2.54070	−	7.81947i	0.134093	−	0.412696i	−0.861355	−	0.508004i	$-0.830384\pi$
$359$	2.54070	−	7.81947i	0.134093	−	0.412696i	0.995448	+	0.0953081i	$0.0303836\pi$
$360$		0			0
$361$	14.0099	−	10.1788i	0.737365	−	0.535727i
$362$	−1.03818			−0.0545656
$363$	−14.7572	+	9.95028i	−0.774550	+	0.522254i
$364$	−11.7082			−0.613677
$365$		0			0
$366$	−1.22866	−	3.78141i	−0.0642229	−	0.197658i
$367$	2.22904	−	6.86029i	0.116355	−	0.358104i	−0.875872	−	0.482543i	$-0.839713\pi$
$367$	2.22904	−	6.86029i	0.116355	−	0.358104i	0.992227	+	0.124439i	$0.0397131\pi$
$368$	−0.450528	−	0.327328i	−0.0234854	−	0.0170632i
$369$	1.94312	+	1.41176i	0.101155	+	0.0734931i
$370$		0			0
$371$	12.8591	+	39.5764i	0.667613	+	2.05470i
$372$	−7.00220	+	5.08740i	−0.363047	+	0.263769i
$373$	29.9629			1.55142			0.775709	−	0.631090i	$-0.217392\pi$
$373$	29.9629			1.55142			0.775709	+	0.631090i	$0.217392\pi$
$374$	−8.73304	−	6.58195i	−0.451575	−	0.340345i
$375$		0			0
$376$	−4.32760	+	3.14419i	−0.223179	+	0.162149i
$377$	9.16552	+	28.2086i	0.472048	+	1.45281i
$378$	6.38875	−	19.6626i	0.328602	−	1.01133i
$379$	29.6962	+	21.5756i	1.52539	+	1.10826i	0.958732	+	0.284312i	$0.0917651\pi$
$379$	29.6962	+	21.5756i	1.52539	+	1.10826i	0.566661	+	0.823951i	$0.308235\pi$
$380$		0			0
$381$	3.47672	−	10.7002i	0.178118	−	0.548190i
$382$	5.54206	+	17.0567i	0.283556	+	0.872697i
$383$	5.21666	−	3.79013i	0.266559	−	0.193666i	−0.446475	−	0.894796i	$-0.647321\pi$
$383$	5.21666	−	3.79013i	0.266559	−	0.193666i	0.713034	+	0.701130i	$0.247321\pi$
$384$	−1.61803			−0.0825700
$385$		0			0
$386$	−9.01986			−0.459099
$387$	1.11803	−	0.812299i	0.0568329	−	0.0412915i
$388$	3.81883	+	11.7531i	0.193872	+	0.596675i
$389$	−8.83792	+	27.2003i	−0.448100	+	1.37911i	0.430948	+	0.902377i	$0.358179\pi$
$389$	−8.83792	+	27.2003i	−0.448100	+	1.37911i	−0.879048	+	0.476734i	$0.841821\pi$
$390$		0			0
$391$	1.48549	+	1.07927i	0.0751245	+	0.0545811i
$392$	−2.24787	+	6.91822i	−0.113534	+	0.349423i
$393$	−2.80870	−	8.64430i	−0.141680	−	0.436047i
$394$	2.98060	−	2.16553i	0.150160	−	0.109098i
$395$		0			0
$396$	−0.412541	+	1.19778i	−0.0207310	+	0.0601909i
$397$	−24.5049			−1.22987			−0.614934	−	0.788579i	$-0.710817\pi$
$397$	−24.5049			−1.22987			−0.614934	+	0.788579i	$0.710817\pi$
$398$	−3.42654	+	2.48953i	−0.171757	+	0.124789i
$399$	2.45053	+	7.54195i	0.122680	+	0.377570i
$400$		0			0
$401$	24.8467	+	18.0522i	1.24079	+	0.901483i	0.997650	−	0.0685091i	$-0.0218242\pi$
$401$	24.8467	+	18.0522i	1.24079	+	0.901483i	0.243135	+	0.969992i	$0.421824\pi$
$402$	12.0593	+	8.76158i	0.601462	+	0.436988i
$403$	−5.12254	+	15.7656i	−0.255172	+	0.785338i
$404$	−2.78554	−	8.57301i	−0.138586	−	0.426523i
$405$		0			0
$406$	36.1608			1.79463
$407$	−21.5056	+	15.0557i	−1.06599	+	0.746284i
$408$	5.33501			0.264122
$409$	−17.6836	+	12.8479i	−0.874397	+	0.635287i	−0.931763	−	0.363066i	$-0.881730\pi$
$409$	−17.6836	+	12.8479i	−0.874397	+	0.635287i	0.0573660	+	0.998353i	$0.481730\pi$
$410$		0			0
$411$	3.84398	−	11.8306i	0.189609	−	0.583558i
$412$	−9.25026	−	6.72071i	−0.455728	−	0.331106i
$413$	−16.1913	−	11.7637i	−0.796723	−	0.578853i
$414$	0.0657312	−	0.202300i	0.00323051	−	0.00994249i
$415$		0			0
$416$	−2.50710	+	1.82151i	−0.122921	+	0.0893070i
$417$	1.55626			0.0762102
$418$	−1.25756	−	4.11450i	−0.0615091	−	0.201247i
$419$	4.17764			0.204091			0.102046	−	0.994780i	$-0.467461\pi$
$419$	4.17764			0.204091			0.102046	+	0.994780i	$0.467461\pi$
$420$		0			0
$421$	3.92266	+	12.0727i	0.191179	+	0.588388i	1.00000		0.000333393i	$0.000106122\pi$
$421$	3.92266	+	12.0727i	0.191179	+	0.588388i	−0.808821	+	0.588055i	$0.799894\pi$
$422$	4.22439	−	13.0013i	0.205640	−	0.632895i
$423$	−1.65300	−	1.20097i	−0.0803714	−	0.0583932i
$424$	8.91067	+	6.47398i	0.432740	+	0.314404i
$425$		0			0
$426$	−5.44595	−	16.7609i	−0.263857	−	0.812068i
$427$	−7.51095	+	5.45702i	−0.363480	+	0.264084i
$428$	15.3546			0.742194
$429$	−4.86089	−	15.9039i	−0.234686	−	0.767850i
$430$		0			0
$431$	0.591217	−	0.429545i	0.0284779	−	0.0206904i	−0.573455	−	0.819237i	$-0.694397\pi$
$431$	0.591217	−	0.429545i	0.0284779	−	0.0206904i	0.601933	+	0.798546i	$0.294397\pi$
$432$	−1.69098	−	5.20431i	−0.0813575	−	0.250393i
$433$	−1.74465	+	5.36947i	−0.0838424	+	0.258040i	−0.984186	−	0.177140i	$-0.943315\pi$
$433$	−1.74465	+	5.36947i	−0.0838424	+	0.258040i	0.900343	+	0.435180i	$0.143315\pi$
$434$	16.3502	+	11.8791i	0.784836	+	0.570217i
$435$		0			0
$436$	0.750578	−	2.31004i	0.0359462	−	0.110631i
$437$	0.223234	+	0.687043i	0.0106787	+	0.0328657i
$438$	−4.44563	+	3.22994i	−0.212421	+	0.154333i
$439$	13.7074			0.654220			0.327110	−	0.944986i	$-0.393925\pi$
$439$	13.7074			0.654220			0.327110	+	0.944986i	$0.393925\pi$
$440$		0			0
$441$	−2.77852			−0.132310
$442$	8.26645	−	6.00593i	0.393195	−	0.285673i
$443$	−4.33967	−	13.3561i	−0.206184	−	0.634568i	−0.999663	−	0.0259707i	$-0.991732\pi$
$443$	−4.33967	−	13.3561i	−0.206184	−	0.634568i	0.793479	−	0.608598i	$-0.208268\pi$
$444$	3.95763	−	12.1803i	0.187821	−	0.578052i
$445$		0			0
$446$	−19.3938	−	14.0904i	−0.918322	−	0.667200i
$447$	−4.39616	+	13.5300i	−0.207931	+	0.639947i
$448$	1.16751	+	3.59321i	0.0551595	+	0.169763i
$449$	−7.81141	+	5.67532i	−0.368643	+	0.267835i	−0.756648	−	0.653822i	$-0.773164\pi$
$449$	−7.81141	+	5.67532i	−0.368643	+	0.267835i	0.388005	+	0.921657i	$0.373164\pi$
$450$		0			0
$451$	6.79140	−	19.7183i	0.319794	−	0.928501i
$452$	8.38134			0.394225
$453$	11.6998	−	8.50038i	0.549703	−	0.399383i
$454$	6.39803	+	19.6911i	0.300274	+	0.924150i
$455$		0			0
$456$	1.69808	+	1.23373i	0.0795199	+	0.0577746i
$457$	−0.832300	−	0.604702i	−0.0389334	−	0.0282867i	0.568148	−	0.822926i	$-0.307660\pi$
$457$	−0.832300	−	0.604702i	−0.0389334	−	0.0282867i	−0.607082	+	0.794639i	$0.707660\pi$
$458$	5.04955	−	15.5409i	0.235950	−	0.726179i
$459$	5.57554	+	17.1597i	0.260244	+	0.800948i
$460$		0			0
$461$	−8.05882			−0.375336			−0.187668	−	0.982232i	$-0.560093\pi$
$461$	−8.05882			−0.375336			−0.187668	+	0.982232i	$0.560093\pi$
$462$	−20.2719	−	0.355525i	−0.943133	−	0.0165405i
$463$	7.46633			0.346990			0.173495	−	0.984835i	$-0.444494\pi$
$463$	7.46633			0.346990			0.173495	+	0.984835i	$0.444494\pi$
$464$	7.74317	−	5.62574i	0.359467	−	0.261168i
$465$		0			0
$466$	0.148415	−	0.456775i	0.00687520	−	0.0211597i
$467$	9.05238	+	6.57694i	0.418894	+	0.304344i	0.777193	−	0.629263i	$-0.216643\pi$
$467$	9.05238	+	6.57694i	0.418894	+	0.304344i	−0.358299	+	0.933607i	$0.616643\pi$
$468$	−0.957626	−	0.695756i	−0.0442663	−	0.0321613i
$469$	10.7556	−	33.1024i	0.496648	−	1.52853i
$470$		0			0
$471$	−23.0924	+	16.7776i	−1.06404	+	0.773071i
$472$	−5.29722			−0.243824
$473$	−9.58276	−	7.22237i	−0.440616	−	0.332085i
$474$	−26.4765			−1.21611
$475$		0			0
$476$	−3.84952	−	11.8476i	−0.176443	−	0.543034i
$477$	−1.30005	+	4.00114i	−0.0595252	+	0.183200i
$478$	0.913049	+	0.663369i	0.0417619	+	0.0303418i
$479$	−21.6571	−	15.7348i	−0.989536	−	0.718940i	−0.0297167	−	0.999558i	$-0.509461\pi$
$479$	−21.6571	−	15.7348i	−0.989536	−	0.718940i	−0.959819	+	0.280618i	$0.909461\pi$
$480$		0			0
$481$	−7.57985	−	23.3284i	−0.345612	−	1.06368i
$482$	−10.2923	+	7.47781i	−0.468802	+	0.340605i
$483$	3.40431			0.154901
$484$	10.9932	+	0.385714i	0.499693	+	0.0175324i
$485$		0			0
$486$	3.19098	−	2.31838i	0.144746	−	0.105164i
$487$	−5.67918	−	17.4787i	−0.257348	−	0.792037i	−0.993358	−	0.115066i	$-0.963292\pi$
$487$	−5.67918	−	17.4787i	−0.257348	−	0.792037i	0.736009	−	0.676971i	$-0.236708\pi$
$488$	−0.759351	+	2.33704i	−0.0343742	+	0.105793i
$489$	0.228148	+	0.165759i	0.0103172	+	0.00749589i
$490$		0			0
$491$	−8.02923	+	24.7114i	−0.362354	+	1.11521i	0.589268	+	0.807938i	$0.299416\pi$
$491$	−8.02923	+	24.7114i	−0.362354	+	1.11521i	−0.951622	+	0.307273i	$0.900584\pi$
$492$	3.14403	+	9.67632i	0.141744	+	0.436242i
$493$	−25.5309	+	18.5493i	−1.14985	+	0.835418i
$494$	4.02001			0.180869
$495$		0			0
$496$	5.34921			0.240186
$497$	−33.2918	+	24.1879i	−1.49334	+	1.08498i
$498$	−0.0920396	−	0.283269i	−0.00412439	−	0.0126936i
$499$	5.24736	−	16.1497i	0.234904	−	0.722960i	−0.762230	−	0.647306i	$-0.775896\pi$
$499$	5.24736	−	16.1497i	0.234904	−	0.722960i	0.997134	−	0.0756541i	$-0.0241045\pi$
$500$		0			0
$501$	7.18170	+	5.21781i	0.320855	+	0.233115i
$502$	0.877459	−	2.70054i	0.0391629	−	0.120531i
$503$	4.13825	+	12.7362i	0.184515	+	0.567880i	0.999940	−	0.0109840i	$-0.00349637\pi$
$503$	4.13825	+	12.7362i	0.184515	+	0.567880i	−0.815424	+	0.578864i	$0.803496\pi$
$504$	−1.16751	+	0.848243i	−0.0520048	+	0.0377837i
$505$		0			0
$506$	−1.84669	−	0.0323869i	−0.0820954	−	0.00143977i
$507$	−5.49573			−0.244074
$508$	−5.62545	+	4.08713i	−0.249589	+	0.181337i
$509$	−6.18963	−	19.0497i	−0.274351	−	0.844365i	−0.989390	−	0.145281i	$-0.953591\pi$
$509$	−6.18963	−	19.0497i	−0.274351	−	0.844365i	0.715040	−	0.699084i	$-0.246409\pi$
$510$		0			0
$511$	10.3806	+	7.54195i	0.459211	+	0.333636i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−2.19357	+	6.75113i	−0.0968487	+	0.298070i
$514$	−9.53038	−	29.3315i	−0.420367	−	1.29376i
$515$		0			0
$516$	5.85410			0.257712
$517$	−5.77739	+	16.7743i	−0.254090	+	0.737731i
$518$	−29.9048			−1.31394
$519$	−31.4112	+	22.8216i	−1.37880	+	1.00176i
$520$		0			0
$521$	0.718847	−	2.21238i	0.0314933	−	0.0969263i	−0.934074	−	0.357079i	$-0.883773\pi$
$521$	0.718847	−	2.21238i	0.0314933	−	0.0969263i	0.965568	+	0.260152i	$0.0837728\pi$
$522$	2.95763	+	2.14884i	0.129452	+	0.0940522i
$523$	−15.4672	−	11.2376i	−0.676335	−	0.491386i	0.195805	−	0.980643i	$-0.437268\pi$
$523$	−15.4672	−	11.2376i	−0.676335	−	0.491386i	−0.872140	+	0.489257i	$0.837268\pi$
$524$	−1.73587	+	5.34247i	−0.0758320	+	0.233387i
$525$		0			0
$526$	−22.4154	+	16.2857i	−0.977358	+	0.710092i
$527$	−17.6375			−0.768302
$528$	−4.39616	+	3.07768i	−0.191318	+	0.133939i
$529$	−22.6899			−0.986517
$530$		0			0
$531$	−0.625252	−	1.92433i	−0.0271336	−	0.0835087i
$532$	1.51451	−	4.66118i	0.0656623	−	0.202088i
$533$	15.7648	+	11.4538i	0.682848	+	0.496118i
$534$	7.97214	+	5.79210i	0.344988	+	0.250648i
$535$		0			0
$536$	−2.84681	−	8.76158i	−0.122963	−	0.378443i
$537$	0.278950	−	0.202669i	0.0120376	−	0.00874581i
$538$	−12.7592			−0.550087
$539$	7.05184	+	23.0723i	0.303744	+	0.993796i
$540$		0			0
$541$	−24.1108	+	17.5175i	−1.03660	+	0.753136i	−0.969619	−	0.244618i	$-0.921337\pi$
$541$	−24.1108	+	17.5175i	−1.03660	+	0.753136i	−0.0669831	+	0.997754i	$0.521337\pi$
$542$	−1.76218	−	5.42344i	−0.0756922	−	0.232957i
$543$	0.519091	−	1.59760i	0.0222763	−	0.0685594i
$544$	−2.66751	−	1.93806i	−0.114368	−	0.0830935i
$545$		0			0
$546$	5.85410	−	18.0171i	0.250532	−	0.771060i
$547$	−5.85573	−	18.0221i	−0.250373	−	0.770569i	−0.994706	−	0.102760i	$-0.967233\pi$
$547$	−5.85573	−	18.0221i	−0.250373	−	0.770569i	0.744333	−	0.667808i	$-0.232767\pi$
$548$	−6.21969	+	4.51887i	−0.265692	+	0.193036i
$549$	−0.938610			−0.0400589
$550$		0			0
$551$	−12.4158			−0.528930
$552$	0.728970	−	0.529628i	0.0310270	−	0.0225425i
$553$	19.1044	+	58.7972i	0.812400	+	2.50031i
$554$	9.80432	−	30.1746i	0.416545	−	1.28200i
$555$		0			0
$556$	−0.778128	−	0.565343i	−0.0330000	−	0.0239759i
$557$	−2.06534	+	6.35647i	−0.0875114	+	0.269332i	−0.985230	−	0.171237i	$-0.945224\pi$
$557$	−2.06534	+	6.35647i	−0.0875114	+	0.269332i	0.897718	+	0.440570i	$0.145224\pi$
$558$	0.631388	+	1.94321i	0.0267288	+	0.0822628i
$559$	9.07077	−	6.59030i	0.383652	−	0.278740i
$560$		0			0
$561$	14.4951	−	10.1478i	0.611984	−	0.428440i
$562$	1.93822			0.0817589
$563$	7.70518	−	5.59814i	0.324735	−	0.235933i	−0.413459	−	0.910523i	$-0.635679\pi$
$563$	7.70518	−	5.59814i	0.324735	−	0.235933i	0.738193	+	0.674589i	$0.235679\pi$
$564$	−2.67460	−	8.23158i	−0.112621	−	0.346612i
$565$		0			0
$566$	3.97703	+	2.88948i	0.167167	+	0.121454i
$567$	23.5607	+	17.1178i	0.989455	+	0.718881i
$568$	−3.36578	+	10.3588i	−0.141225	+	0.434646i
$569$	8.67150	+	26.6881i	0.363528	+	1.11883i	0.950897	+	0.309506i	$0.100164\pi$
$569$	8.67150	+	26.6881i	0.363528	+	1.11883i	−0.587369	+	0.809319i	$0.699836\pi$
$570$		0			0
$571$	−1.61429			−0.0675561			−0.0337781	−	0.999429i	$-0.510754\pi$
$571$	−1.61429			−0.0675561			−0.0337781	+	0.999429i	$0.510754\pi$
$572$	−3.34700	+	9.71779i	−0.139945	+	0.406321i
$573$	−29.0186			−1.21227
$574$	19.2199	−	13.9641i	0.802222	−	0.582849i
$575$		0			0
$576$	−0.118034	+	0.363271i	−0.00491808	+	0.0151363i
$577$	−2.64516	−	1.92182i	−0.110120	−	0.0800066i	0.531363	−	0.847145i	$-0.321680\pi$
$577$	−2.64516	−	1.92182i	−0.110120	−	0.0800066i	−0.641482	+	0.767138i	$0.721680\pi$
$578$	−4.95794	−	3.60215i	−0.206223	−	0.149830i
$579$	4.50993	−	13.8801i	0.187426	−	0.576839i
$580$		0			0
$581$	−0.562651	+	0.408790i	−0.0233427	+	0.0169595i
$582$	−19.9956			−0.828846
$583$	36.5243	+	0.640558i	1.51268	+	0.0265292i
$584$	3.39616			0.140534
$585$		0			0
$586$	0.0583193	+	0.179488i	0.00240915	+	0.00741459i
$587$	1.08288	−	3.33276i	0.0446952	−	0.137558i	−0.926219	−	0.376987i	$-0.876960\pi$
$587$	1.08288	−	3.33276i	0.0446952	−	0.137558i	0.970914	+	0.239429i	$0.0769603\pi$
$588$	−9.52212	−	6.91822i	−0.392685	−	0.285303i
$589$	−5.61384	−	4.07869i	−0.231314	−	0.168060i
$590$		0			0
$591$	1.84211	+	5.66943i	0.0757742	+	0.233209i
$592$	−6.40357	+	4.65247i	−0.263185	+	0.191215i
$593$	−27.6283			−1.13456			−0.567278	−	0.823526i	$-0.692004\pi$
$593$	−27.6283			−1.13456			−0.567278	+	0.823526i	$0.692004\pi$
$594$	−14.4935	−	10.9236i	−0.594678	−	0.448199i
$595$		0			0
$596$	7.11314	−	5.16800i	0.291366	−	0.211689i
$597$	−2.11772	−	6.51767i	−0.0866725	−	0.266751i
$598$	0.533286	−	1.64129i	0.0218077	−	0.0671172i
$599$	6.43434	+	4.67482i	0.262900	+	0.191008i	0.711425	−	0.702762i	$-0.248050\pi$
$599$	6.43434	+	4.67482i	0.262900	+	0.191008i	−0.448524	+	0.893771i	$0.648050\pi$
$600$		0			0
$601$	2.01909	−	6.21412i	0.0823604	−	0.253479i	−0.901394	−	0.433000i	$-0.857455\pi$
$601$	2.01909	−	6.21412i	0.0823604	−	0.253479i	0.983754	+	0.179521i	$0.0574548\pi$
$602$	−4.22408	−	13.0004i	−0.172160	−	0.529855i
$603$	2.84681	−	2.06833i	0.115931	−	0.0842288i
$604$	−8.93783			−0.363675
$605$		0			0
$606$	14.5853			0.592486
$607$	6.77813	−	4.92460i	0.275116	−	0.199883i	−0.441668	−	0.897178i	$-0.645613\pi$
$607$	6.77813	−	4.92460i	0.275116	−	0.199883i	0.716784	+	0.697295i	$0.245613\pi$
$608$	−0.400863	−	1.23373i	−0.0162571	−	0.0500343i
$609$	−18.0804	+	55.6457i	−0.732654	+	2.25488i
$610$		0			0
$611$	−13.4110	−	9.74365i	−0.542550	−	0.394186i
$612$	0.389184	−	1.19778i	0.0157318	−	0.0484176i
$613$	−5.53528	−	17.0358i	−0.223568	−	0.688071i	−0.998434	−	0.0559453i	$-0.982183\pi$
$613$	−5.53528	−	17.0358i	−0.223568	−	0.688071i	0.774866	−	0.632125i	$-0.217817\pi$
$614$	−10.0172	+	7.27794i	−0.404262	+	0.293714i
$615$		0			0
$616$	10.0068	+	7.54195i	0.403185	+	0.303874i
$617$	21.3999			0.861529			0.430765	−	0.902464i	$-0.358244\pi$
$617$	21.3999			0.861529			0.430765	+	0.902464i	$0.358244\pi$
$618$	14.9672	−	10.8743i	0.602071	−	0.437430i
$619$	−1.82954	−	5.63076i	−0.0735356	−	0.226319i	0.907533	−	0.419981i	$-0.137963\pi$
$619$	−1.82954	−	5.63076i	−0.0735356	−	0.226319i	−0.981068	+	0.193662i	$0.937963\pi$
$620$		0			0
$621$	2.46535	+	1.79118i	0.0989312	+	0.0718777i
$622$	−17.0850	−	12.4130i	−0.685045	−	0.497714i
$623$	7.11031	−	21.8833i	0.284868	−	0.876735i
$624$	−1.54947	−	4.76878i	−0.0620285	−	0.190904i
$625$		0			0
$626$	−16.5792			−0.662639
$627$	6.96034	+	0.122069i	0.277969	+	0.00487497i
$628$	17.6410			0.703953
$629$	21.1140	−	15.3402i	0.841870	−	0.611654i
$630$		0			0
$631$	5.62521	−	17.3126i	0.223936	−	0.689204i	−0.774462	−	0.632620i	$-0.781979\pi$
$631$	5.62521	−	17.3126i	0.223936	−	0.689204i	0.998398	−	0.0565834i	$-0.0180207\pi$
$632$	13.2383	+	9.61817i	0.526590	+	0.382590i
$633$	17.8948	+	13.0013i	0.711254	+	0.516757i
$634$	6.06817	−	18.6759i	0.240998	−	0.741716i
$635$		0			0
$636$	−14.4178	+	10.4751i	−0.571702	+	0.415366i
$637$	−22.5425			−0.893166
$638$	10.3372	−	30.0134i	0.409254	−	1.18824i
$639$	−4.16033			−0.164580
$640$		0			0
$641$	5.44931	+	16.7712i	0.215235	+	0.662424i	0.999137	+	0.0415398i	$0.0132263\pi$
$641$	5.44931	+	16.7712i	0.215235	+	0.662424i	−0.783902	+	0.620884i	$0.786774\pi$
$642$	−7.67731	+	23.6283i	−0.302999	+	0.932536i
$643$	−35.5559	−	25.8329i	−1.40219	−	1.01875i	−0.994401	−	0.105673i	$-0.966300\pi$
$643$	−35.5559	−	25.8329i	−1.40219	−	1.01875i	−0.407788	−	0.913077i	$-0.633700\pi$
$644$	−1.70215	−	1.23669i	−0.0670742	−	0.0487323i
$645$		0			0
$646$	1.32173	+	4.06787i	0.0520028	+	0.160048i
$647$	0.401371	−	0.291613i	0.0157795	−	0.0114645i	−0.579868	−	0.814711i	$-0.696896\pi$
$647$	0.401371	−	0.291613i	0.0157795	−	0.0114645i	0.595647	+	0.803246i	$0.296896\pi$
$648$	7.70820			0.302807
$649$	−14.3924	+	10.0759i	−0.564952	+	0.395514i
$650$		0			0
$651$	−26.4552	+	19.2208i	−1.03686	+	0.753324i
$652$	−0.0538584	−	0.165759i	−0.00210926	−	0.00649163i
$653$	−5.61086	+	17.2685i	−0.219570	+	0.675767i	0.779228	+	0.626741i	$0.215612\pi$
$653$	−5.61086	+	17.2685i	−0.219570	+	0.675767i	−0.998798	+	0.0490258i	$0.984388\pi$
$654$	3.17950	+	2.31004i	0.124328	+	0.0903297i
$655$		0			0
$656$	1.94312	−	5.98030i	0.0758659	−	0.233491i
$657$	0.400863	+	1.23373i	0.0156391	+	0.0481323i
$658$	−16.3502	+	11.8791i	−0.637398	+	0.463097i
$659$	−14.4974			−0.564739			−0.282370	−	0.959306i	$-0.591120\pi$
$659$	−14.4974			−0.564739			−0.282370	+	0.959306i	$0.591120\pi$
$660$		0			0
$661$	−11.6178			−0.451880			−0.225940	−	0.974141i	$-0.572545\pi$
$661$	−11.6178			−0.451880			−0.225940	+	0.974141i	$0.572545\pi$
$662$	−18.9978	+	13.8027i	−0.738371	+	0.536458i
$663$	5.10895	+	15.7237i	0.198415	+	0.610659i
$664$	−0.0568836	+	0.175070i	−0.00220751	+	0.00679402i
$665$		0			0
$666$	−2.44595	−	1.77708i	−0.0947785	−	0.0688606i
$667$	−1.64705	+	5.06911i	−0.0637742	+	0.196277i
$668$	−1.69537	−	5.21781i	−0.0655958	−	0.201883i
$669$	31.3798	−	22.7988i	1.21321	−	0.881451i
$670$		0			0
$671$	2.38218	+	7.79406i	0.0919630	+	0.300886i
$672$	−6.11314			−0.235819
$673$	28.8239	−	20.9418i	1.11108	−	0.807246i	0.128245	−	0.991743i	$-0.459066\pi$
$673$	28.8239	−	20.9418i	1.11108	−	0.807246i	0.982833	+	0.184497i	$0.0590656\pi$
$674$	−3.96317	−	12.1974i	−0.152656	−	0.469825i
$675$		0			0
$676$	2.74787	+	1.99644i	0.105687	+	0.0767862i
$677$	19.8288	+	14.4064i	0.762081	+	0.553684i	0.899548	−	0.436822i	$-0.143896\pi$
$677$	19.8288	+	14.4064i	0.762081	+	0.553684i	−0.137467	+	0.990506i	$0.543896\pi$
$678$	−4.19067	+	12.8976i	−0.160942	+	0.495328i
$679$	14.4280	+	44.4049i	0.553696	+	1.70410i
$680$		0			0
$681$	−33.5005			−1.28374
$682$	14.5337	−	10.1748i	0.556523	−	0.389613i
$683$	25.5212			0.976540			0.488270	−	0.872693i	$-0.337628\pi$
$683$	25.5212			0.976540			0.488270	+	0.872693i	$0.337628\pi$
$684$	0.400863	−	0.291244i	0.0153274	−	0.0111360i
$685$		0			0
$686$	−0.320187	+	0.985436i	−0.0122248	+	0.0376241i
$687$	21.3902	+	15.5409i	0.816088	+	0.592922i
$688$	−2.92705	−	2.12663i	−0.111593	−	0.0810769i
$689$	−10.5475	+	32.4618i	−0.401827	+	1.23670i
$690$		0			0
$691$	36.7992	−	26.7362i	1.39991	−	1.01709i	0.405215	−	0.914222i	$-0.367197\pi$
$691$	36.7992	−	26.7362i	1.39991	−	1.01709i	0.994695	−	0.102872i	$-0.0328032\pi$
$692$	23.9960			0.912192
$693$	−1.55863	+	4.52538i	−0.0592076	+	0.171905i
$694$	−20.6936			−0.785519
$695$		0			0
$696$	4.78554	+	14.7284i	0.181395	+	0.558278i
$697$	−6.40688	+	19.7183i	−0.242678	+	0.746886i
$698$	17.5697	+	12.7651i	0.665024	+	0.483168i
$699$	0.628696	+	0.456775i	0.0237795	+	0.0172768i
$700$		0			0
$701$	−9.00678	−	27.7200i	−0.340182	−	1.04697i	−0.964113	−	0.265492i	$-0.914466\pi$
$701$	−9.00678	−	27.7200i	−0.340182	−	1.04697i	0.623932	−	0.781479i	$-0.285534\pi$
$702$	13.7192	−	9.96757i	0.517797	−	0.376202i
$703$	10.2678			0.387258
$704$	3.31611	+	0.0581575i	0.124981	+	0.00219189i
$705$		0			0
$706$	−0.210582	+	0.152997i	−0.00792535	+	0.00575810i
$707$	−10.5241	−	32.3899i	−0.395800	−	1.21815i
$708$	2.64861	−	8.15158i	0.0995408	−	0.306355i
$709$	−25.0122	−	18.1724i	−0.939353	−	0.682480i	0.00891175	−	0.999960i	$-0.497163\pi$
$709$	−25.0122	−	18.1724i	−0.939353	−	0.682480i	−0.948265	+	0.317480i	$0.897163\pi$
$710$		0			0
$711$	−1.93144	+	5.94435i	−0.0724346	+	0.222931i
$712$	−1.88197	−	5.79210i	−0.0705297	−	0.217068i
$713$	−2.40997	+	1.75095i	−0.0902541	+	0.0655734i
$714$	20.1564			0.754333
$715$		0			0
$716$	−0.213099			−0.00796388
$717$	−1.47734	+	1.07335i	−0.0551725	+	0.0400851i
$718$	−2.54070	−	7.81947i	−0.0948180	−	0.291820i
$719$	−5.42235	+	16.6883i	−0.202220	+	0.622368i	0.797597	+	0.603191i	$0.206104\pi$
$719$	−5.42235	+	16.6883i	−0.202220	+	0.622368i	−0.999816	+	0.0191765i	$0.993896\pi$
$720$		0			0
$721$	−34.9487	−	25.3917i	−1.30156	−	0.945636i
$722$	5.35132	−	16.4697i	0.199155	−	0.612937i
$723$	−6.36101	−	19.5772i	−0.236568	−	0.728083i
$724$	−0.839906	+	0.610228i	−0.0312149	+	0.0226789i
$725$		0			0
$726$	−6.09017	+	16.7240i	−0.226027	+	0.620686i
$727$	16.7731			0.622080			0.311040	−	0.950397i	$-0.399323\pi$
$727$	16.7731			0.622080			0.311040	+	0.950397i	$0.399323\pi$
$728$	−9.47214	+	6.88191i	−0.351061	+	0.255061i
$729$	9.11803	+	28.0624i	0.337705	+	1.03935i
$730$		0			0
$731$	9.65113	+	7.01195i	0.356960	+	0.259346i
$732$	−3.21666	−	2.33704i	−0.118891	−	0.0863796i
$733$	2.85868	−	8.79812i	0.105588	−	0.324966i	−0.884280	−	0.466957i	$-0.845350\pi$
$733$	2.85868	−	8.79812i	0.105588	−	0.324966i	0.989868	+	0.141991i	$0.0453503\pi$
$734$	−2.22904	−	6.86029i	−0.0822755	−	0.253218i
$735$		0			0
$736$	−0.556884			−0.0205270
$737$	−24.4002	−	18.3901i	−0.898794	−	0.677407i
$738$	2.40182			0.0884124
$739$	−6.06468	+	4.40625i	−0.223093	+	0.162087i	−0.693718	−	0.720247i	$-0.744029\pi$
$739$	−6.06468	+	4.40625i	−0.223093	+	0.162087i	0.470625	+	0.882333i	$0.344029\pi$
$740$		0			0
$741$	−2.01000	+	6.18615i	−0.0738393	+	0.227254i
$742$	33.6657	+	24.4595i	1.23591	+	0.897938i
$743$	−5.26124	−	3.82251i	−0.193016	−	0.140234i	0.487080	−	0.873357i	$-0.338062\pi$
$743$	−5.26124	−	3.82251i	−0.193016	−	0.140234i	−0.680096	+	0.733123i	$0.738062\pi$
$744$	−2.67460	+	8.23158i	−0.0980557	+	0.301784i
$745$		0			0
$746$	24.2405	−	17.6117i	0.887507	−	0.644811i
$747$	−0.0703120			−0.00257258
$748$	−10.9340	−	0.191758i	−0.399785	−	0.00701136i
$749$	58.0118			2.11970
$750$		0			0
$751$	6.27064	+	19.2991i	0.228819	+	0.704232i	0.997881	+	0.0650587i	$0.0207235\pi$
$751$	6.27064	+	19.2991i	0.228819	+	0.704232i	−0.769062	+	0.639174i	$0.779277\pi$
$752$	−1.65300	+	5.08740i	−0.0602786	+	0.185518i
$753$	3.71698	+	2.70054i	0.135454	+	0.0984132i
$754$	23.9956	+	17.4338i	0.873869	+	0.634903i
$755$		0			0
$756$	−6.38875	−	19.6626i	−0.232357	−	0.715120i
$757$	14.9271	−	10.8452i	0.542534	−	0.394174i	−0.282492	−	0.959270i	$-0.591161\pi$
$757$	14.9271	−	10.8452i	0.542534	−	0.394174i	0.825025	+	0.565096i	$0.191161\pi$
$758$	36.7066			1.33324
$759$	0.973183	−	2.82557i	0.0353243	−	0.102562i
$760$		0			0
$761$	11.0383	−	8.01981i	0.400139	−	0.290718i	−0.369459	−	0.929247i	$-0.620457\pi$
$761$	11.0383	−	8.01981i	0.400139	−	0.290718i	0.769598	+	0.638529i	$0.220457\pi$
$762$	−3.47672	−	10.7002i	−0.125948	−	0.387629i
$763$	2.83578	−	8.72763i	0.102662	−	0.315961i
$764$	14.5093	+	10.5416i	0.524928	+	0.381383i
$765$		0			0
$766$	1.99259	−	6.13256i	0.0719951	−	0.221578i
$767$	−5.07275	−	15.6123i	−0.183167	−	0.563729i
$768$	−1.30902	+	0.951057i	−0.0472351	+	0.0343183i
$769$	−6.77400			−0.244277			−0.122138	−	0.992513i	$-0.538975\pi$
$769$	−6.77400			−0.244277			−0.122138	+	0.992513i	$0.538975\pi$
$770$		0			0
$771$	49.9017			1.79717
$772$	−7.29722	+	5.30174i	−0.262633	+	0.190814i
$773$	−5.80173	−	17.8559i	−0.208674	−	0.642231i	−0.999542	−	0.0302456i	$-0.990371\pi$
$773$	−5.80173	−	17.8559i	−0.208674	−	0.642231i	0.790869	−	0.611986i	$-0.209629\pi$
$774$	0.427051	−	1.31433i	0.0153500	−	0.0472425i
$775$		0			0
$776$	9.99782	+	7.26384i	0.358901	+	0.260757i
$777$	14.9524	−	46.0188i	0.536415	−	1.65092i
$778$	8.83792	+	27.2003i	0.316855	+	0.975178i
$779$	−6.59914	+	4.79455i	−0.236439	+	0.171783i
$780$		0			0
$781$	10.5589	+	34.5467i	0.377826	+	1.23618i
$782$	1.83617			0.0656612
$783$	−42.3717	+	30.7848i	−1.51424	+	1.10016i
$784$	2.24787	+	6.91822i	0.0802810	+	0.247079i
$785$		0			0
$786$	−7.35328	−	5.34247i	−0.262283	−	0.190560i
$787$	22.1990	+	16.1285i	0.791310	+	0.574921i	0.908352	−	0.418206i	$-0.137341\pi$
$787$	22.1990	+	16.1285i	0.791310	+	0.574921i	−0.117042	+	0.993127i	$0.537341\pi$
$788$	1.13849	−	3.50390i	0.0405569	−	0.124821i
$789$	−13.8535	−	42.6366i	−0.493197	−	1.51790i
$790$		0			0
$791$	31.6658			1.12590
$792$	0.370287	+	1.21151i	0.0131576	+	0.0430493i
$793$	−7.61507			−0.270419
$794$	−19.8249	+	14.4036i	−0.703560	+	0.511166i
$795$		0			0
$796$	−1.30882	+	4.02814i	−0.0463900	+	0.142774i
$797$	−43.5855	−	31.6667i	−1.54388	−	1.12169i	−0.947845	−	0.318732i	$-0.896743\pi$
$797$	−43.5855	−	31.6667i	−1.54388	−	1.12169i	−0.596032	−	0.802960i	$-0.703257\pi$
$798$	6.41557	+	4.66118i	0.227109	+	0.165004i
$799$	5.45029	−	16.7743i	0.192817	−	0.593431i
$800$		0			0
$801$	1.88197	−	1.36733i	0.0664960	−	0.0483122i
$802$	30.7122			1.08449
$803$	9.22729	−	6.45988i	0.325624	−	0.227964i
$804$	14.9061			0.525697
$805$		0			0
$806$	5.12254	+	15.7656i	0.180434	+	0.555318i
$807$	6.37959	−	19.6344i	0.224572	−	0.691162i
$808$	−7.29264	−	5.29841i	−0.256554	−	0.186397i
$809$	−26.1612	−	19.0073i	−0.919781	−	0.668260i	0.0236888	−	0.999719i	$-0.492459\pi$
$809$	−26.1612	−	19.0073i	−0.919781	−	0.668260i	−0.943469	+	0.331460i	$0.892459\pi$
$810$		0			0
$811$	14.1920	+	43.6785i	0.498349	+	1.53376i	0.811671	+	0.584114i	$0.198558\pi$
$811$	14.1920	+	43.6785i	0.498349	+	1.53376i	−0.313322	+	0.949647i	$0.601442\pi$
$812$	29.2547	−	21.2548i	1.02664	−	0.745896i
$813$	9.22691			0.323602
$814$	−8.54884	+	24.8210i	−0.299637	+	0.869975i
$815$		0			0
$816$	4.31611	−	3.13584i	0.151094	−	0.109776i
$817$	1.45033	+	4.46367i	0.0507408	+	0.156164i
$818$	−6.75453	+	20.7883i	−0.236167	+	0.726846i
$819$	−3.61803	−	2.62866i	−0.126424	−	0.0918527i
$820$		0			0
$821$	8.78690	−	27.0433i	0.306665	−	0.943818i	−0.672386	−	0.740201i	$-0.734730\pi$
$821$	8.78690	−	27.0433i	0.306665	−	0.943818i	0.979051	−	0.203617i	$-0.0652697\pi$
$822$	−3.84398	−	11.8306i	−0.134074	−	0.412638i
$823$	−8.38417	+	6.09146i	−0.292254	+	0.212335i	−0.724245	−	0.689543i	$-0.757811\pi$
$823$	−8.38417	+	6.09146i	−0.292254	+	0.212335i	0.431991	+	0.901878i	$0.357811\pi$
$824$	−11.4340			−0.398321
$825$		0			0
$826$	−20.0136			−0.696361
$827$	15.8634	−	11.5254i	0.551625	−	0.400779i	−0.276760	−	0.960939i	$-0.589261\pi$
$827$	15.8634	−	11.5254i	0.551625	−	0.400779i	0.828384	+	0.560161i	$0.189261\pi$
$828$	−0.0657312	−	0.202300i	−0.00228432	−	0.00703040i
$829$	15.4118	−	47.4327i	0.535275	−	1.64741i	−0.207780	−	0.978176i	$-0.566624\pi$
$829$	15.4118	−	47.4327i	0.535275	−	1.64741i	0.743054	−	0.669231i	$-0.233376\pi$
$830$		0			0
$831$	41.5317	+	30.1746i	1.44072	+	1.04674i
$832$	−0.957626	+	2.94727i	−0.0331997	+	0.102178i
$833$	−7.41171	−	22.8109i	−0.256800	−	0.790350i
$834$	1.25904	−	0.914744i	0.0435969	−	0.0316750i
$835$		0			0
$836$	−3.43582	−	2.58953i	−0.118830	−	0.0895606i
$837$	−29.2716			−1.01177
$838$	3.37978	−	2.45556i	0.116753	−	0.0848258i
$839$	−3.25249	−	10.0101i	−0.112289	−	0.345589i	0.879083	−	0.476668i	$-0.158156\pi$
$839$	−3.25249	−	10.0101i	−0.112289	−	0.345589i	−0.991372	+	0.131080i	$0.958156\pi$
$840$		0			0
$841$	−50.6490	−	36.7986i	−1.74652	−	1.26892i
$842$	10.2697	+	7.46135i	0.353916	+	0.257135i
$843$	−0.969111	+	2.98262i	−0.0333779	+	0.102727i
$844$	−4.22439	−	13.0013i	−0.145409	−	0.447524i
$845$		0			0
$846$	−2.04322			−0.0702472
$847$	41.5338	+	1.45728i	1.42712	+	0.0500726i
$848$	11.0142			0.378229
$849$	−6.43497	+	4.67528i	−0.220848	+	0.160455i
$850$		0			0
$851$	1.36211	−	4.19214i	0.0466925	−	0.143705i
$852$	−14.2577	−	10.3588i	−0.488460	−	0.354887i
$853$	−12.7180	−	9.24016i	−0.435456	−	0.316377i	0.348371	−	0.937357i	$-0.386735\pi$
$853$	−12.7180	−	9.24016i	−0.435456	−	0.316377i	−0.783827	+	0.620980i	$0.786735\pi$
$854$	−2.86893	+	8.82965i	−0.0981726	+	0.302144i
$855$		0			0
$856$	12.4222	−	9.02522i	0.424581	−	0.308476i
$857$	37.8967			1.29453			0.647263	−	0.762267i	$-0.275914\pi$
$857$	37.8967			1.29453			0.647263	+	0.762267i	$0.275914\pi$
$858$	−13.2806	−	10.0094i	−0.453394	−	0.341716i
$859$	20.5913			0.702567			0.351283	−	0.936269i	$-0.385745\pi$
$859$	20.5913			0.702567			0.351283	+	0.936269i	$0.385745\pi$
$860$		0			0
$861$	11.8785	+	36.5584i	0.404820	+	1.24591i
$862$	0.225825	−	0.695018i	0.00769163	−	0.0236724i
$863$	−6.95203	−	5.05094i	−0.236650	−	0.171936i	0.463140	−	0.886285i	$-0.346723\pi$
$863$	−6.95203	−	5.05094i	−0.236650	−	0.171936i	−0.699789	+	0.714349i	$0.746723\pi$
$864$	−4.42705	−	3.21644i	−0.150611	−	0.109426i
$865$		0			0
$866$	1.74465	+	5.36947i	0.0592855	+	0.182462i
$867$	8.02212	−	5.82841i	0.272445	−	0.197943i
$868$	20.2100			0.685972
$869$	54.2629	+	0.951654i	1.84074	+	0.0322826i
$870$		0			0
$871$	23.0966	−	16.7806i	0.782597	−	0.568590i
$872$	−0.750578	−	2.31004i	−0.0254178	−	0.0782279i
$873$	−1.45866	+	4.48930i	−0.0493682	+	0.151940i
$874$	0.584434	+	0.424616i	0.0197688	+	0.0143628i
$875$		0			0
$876$	−1.69808	+	5.22616i	−0.0573728	+	0.176575i
$877$	13.9519	+	42.9395i	0.471122	+	1.44996i	0.851117	+	0.524976i	$0.175926\pi$
$877$	13.9519	+	42.9395i	0.471122	+	1.44996i	−0.379995	+	0.924989i	$0.624074\pi$
$878$	11.0895	−	8.05702i	0.374254	−	0.271911i
$879$	−0.305364			−0.0102997
$880$		0			0
$881$	−38.4847			−1.29658			−0.648291	−	0.761393i	$-0.724516\pi$
$881$	−38.4847			−1.29658			−0.648291	+	0.761393i	$0.724516\pi$
$882$	−2.24787	+	1.63317i	−0.0756896	+	0.0549917i
$883$	12.1504	+	37.3951i	0.408894	+	1.25845i	0.917600	+	0.397505i	$0.130124\pi$
$883$	12.1504	+	37.3951i	0.408894	+	1.25845i	−0.508706	+	0.860940i	$0.669876\pi$
$884$	3.15750	−	9.71779i	0.106198	−	0.326845i
$885$		0			0
$886$	−11.3614	−	8.25454i	−0.381693	−	0.277317i
$887$	2.42395	−	7.46016i	0.0813883	−	0.250488i	−0.902080	−	0.431570i	$-0.857960\pi$
$887$	2.42395	−	7.46016i	0.0813883	−	0.250488i	0.983468	+	0.181082i	$0.0579600\pi$
$888$	−3.95763	−	12.1803i	−0.132809	−	0.408745i
$889$	−21.2537	+	15.4417i	−0.712825	+	0.517897i
$890$		0			0
$891$	20.9430	−	14.6619i	0.701617	−	0.491191i
$892$	−23.9720			−0.802643
$893$	5.61384	−	4.07869i	0.187860	−	0.136488i
$894$	4.39616	+	13.5300i	0.147030	+	0.452511i
$895$		0			0
$896$	3.05657	+	2.22073i	0.102113	+	0.0741893i
$897$	2.25904	+	1.64129i	0.0754271	+	0.0548010i
$898$	−2.98369	+	9.18287i	−0.0995672	+	0.306436i
$899$	−15.8210	−	48.6919i	−0.527658	−	1.62397i
$900$		0			0
$901$	−36.3162			−1.20987
$902$	−6.09580	−	19.9444i	−0.202968	−	0.664075i
$903$	22.1175			0.736026
$904$	6.78064	−	4.92643i	0.225521	−	0.163851i
$905$		0			0
$906$	4.46892	−	13.7539i	0.148470	−	0.456943i
$907$	−35.8908	−	26.0762i	−1.19173	−	0.865845i	−0.198287	−	0.980144i	$-0.563538\pi$
$907$	−35.8908	−	26.0762i	−1.19173	−	0.865845i	−0.993446	+	0.114299i	$0.963538\pi$
$908$	16.7503	+	12.1698i	0.555877	+	0.403868i
$909$	1.06398	−	3.27460i	0.0352900	−	0.108612i
$910$		0			0
$911$	−11.2063	+	8.14186i	−0.371282	+	0.269752i	−0.757742	−	0.652554i	$-0.773698\pi$
$911$	−11.2063	+	8.14186i	−0.371282	+	0.269752i	0.386460	+	0.922306i	$0.373698\pi$
$912$	2.09894			0.0695030
$913$	0.178451	+	0.583860i	0.00590587	+	0.0193229i
$914$	−1.02878			−0.0340290
$915$		0			0
$916$	−5.04955	−	15.5409i	−0.166842	−	0.513486i
$917$	−6.55835	+	20.1845i	−0.216576	+	0.666552i
$918$	14.5970	+	10.6053i	0.481771	+	0.350027i
$919$	12.3286	+	8.95726i	0.406684	+	0.295473i	0.772258	−	0.635309i	$-0.219127\pi$
$919$	12.3286	+	8.95726i	0.406684	+	0.295473i	−0.365574	+	0.930782i	$0.619127\pi$
$920$		0			0
$921$	−6.19098	−	19.0539i	−0.204000	−	0.627847i
$922$	−6.51972	+	4.73685i	−0.214716	+	0.156000i
$923$	−33.7534			−1.11101
$924$	−16.6093	+	11.6279i	−0.546405	+	0.382529i
$925$		0			0
$926$	6.04038	−	4.38860i	0.198499	−	0.144218i
$927$	−1.34960	−	4.15363i	−0.0443265	−	0.136423i
$928$	2.95763	−	9.10264i	0.0970888	−	0.298809i
$929$	−30.6793	−	22.2898i	−1.00656	−	0.731306i	−0.0430721	−	0.999072i	$-0.513715\pi$
$929$	−30.6793	−	22.2898i	−1.00656	−	0.731306i	−0.963484	+	0.267766i	$0.913715\pi$
$930$		0			0
$931$	2.91597	−	8.97444i	0.0955672	−	0.294126i
$932$	−0.148415	−	0.456775i	−0.00486150	−	0.0149621i
$933$	27.6440	−	20.0846i	0.905025	−	0.657540i
$934$	11.1894			0.366127
$935$		0			0
$936$	−1.18369			−0.0386902
$937$	−4.43144	+	3.21963i	−0.144769	+	0.105181i	−0.657812	−	0.753182i	$-0.728518\pi$
$937$	−4.43144	+	3.21963i	−0.144769	+	0.105181i	0.513043	+	0.858363i	$0.328518\pi$
$938$	−10.7556	−	33.1024i	−0.351183	−	1.08083i
$939$	8.28961	−	25.5128i	0.270521	−	0.832579i
$940$		0			0
$941$	−37.5713	−	27.2971i	−1.22479	−	0.889861i	−0.228301	−	0.973591i	$-0.573317\pi$
$941$	−37.5713	−	27.2971i	−1.22479	−	0.889861i	−0.996489	+	0.0837293i	$0.973317\pi$
$942$	−8.82050	+	27.1467i	−0.287387	+	0.884488i
$943$	1.08209	+	3.33033i	0.0352377	+	0.108450i
$944$	−4.28554	+	3.11363i	−0.139482	+	0.101340i
$945$		0			0
$946$	−11.9978	−	0.210416i	−0.390083	−	0.00684120i
$947$	22.7220			0.738366			0.369183	−	0.929357i	$-0.379638\pi$
$947$	22.7220			0.738366			0.369183	+	0.929357i	$0.379638\pi$
$948$	−21.4200	+	15.5625i	−0.695688	+	0.505447i
$949$	3.25225	+	10.0094i	0.105573	+	0.324919i
$950$		0			0
$951$	25.7052	+	18.6759i	0.833548	+	0.605608i
$952$	−10.0782	−	7.32222i	−0.326636	−	0.237315i
$953$	11.1302	−	34.2554i	0.360544	−	1.10964i	−0.592181	−	0.805805i	$-0.701733\pi$
$953$	11.1302	−	34.2554i	0.360544	−	1.10964i	0.952725	−	0.303835i	$-0.0982671\pi$
$954$	1.30005	+	4.00114i	0.0420907	+	0.129542i
$955$		0			0
$956$	1.12859			0.0365012
$957$	41.0172	+	30.9140i	1.32590	+	0.999309i
$958$	−26.7696			−0.864886
$959$	−23.4988	+	17.0729i	−0.758815	+	0.551311i
$960$		0			0
$961$	−0.737310	+	2.26921i	−0.0237842	+	0.0732002i
$962$	−19.8443	−	14.4177i	−0.639806	−	0.464846i
$963$	4.74484	+	3.44733i	0.152900	+	0.111089i
$964$	−3.93132	+	12.0994i	−0.126619	+	0.389694i
$965$		0			0
$966$	2.75414	−	2.00100i	0.0886131	−	0.0643812i
$967$	23.8349			0.766479			0.383240	−	0.923649i	$-0.374808\pi$
$967$	23.8349			0.766479			0.383240	+	0.923649i	$0.374808\pi$
$968$	9.12043	−	6.14961i	0.293142	−	0.197656i
$969$	−6.92067			−0.222324
$970$		0			0
$971$	−10.9297	−	33.6381i	−0.350750	−	1.07950i	−0.958433	−	0.285319i	$-0.907901\pi$
$971$	−10.9297	−	33.6381i	−0.350750	−	1.07950i	0.607682	−	0.794180i	$-0.292099\pi$
$972$	1.21885	−	3.75123i	0.0390945	−	0.120321i
$973$	−2.93987	−	2.13594i	−0.0942478	−	0.0684750i
$974$	−14.8683	−	10.8025i	−0.476411	−	0.346133i
$975$		0			0
$976$	0.759351	+	2.33704i	0.0243062	+	0.0748069i
$977$	−9.12632	+	6.63066i	−0.291977	+	0.212134i	−0.724124	−	0.689669i	$-0.757756\pi$
$977$	−9.12632	+	6.63066i	−0.291977	+	0.212134i	0.432148	+	0.901803i	$0.357756\pi$
$978$	0.282006			0.00901757
$979$	−16.1305	−	12.1573i	−0.515532	−	0.388548i
$980$		0			0
$981$	0.750578	−	0.545327i	0.0239641	−	0.0174109i
$982$	8.02923	+	24.7114i	0.256223	+	0.788573i
$983$	2.64643	−	8.14486i	0.0844079	−	0.259781i	−0.899941	−	0.436012i	$-0.856391\pi$
$983$	2.64643	−	8.14486i	0.0844079	−	0.259781i	0.984349	+	0.176231i	$0.0563906\pi$
$984$	8.23117	+	5.98030i	0.262400	+	0.190645i
$985$		0			0
$986$	−9.75194	+	30.0134i	−0.310565	+	0.955821i
$987$	−10.1050	−	31.1000i	−0.321645	−	0.989923i
$988$	3.25225	−	2.36290i	0.103468	−	0.0751739i
$989$	2.01482			0.0640677
$990$		0			0
$991$	−15.9978			−0.508185			−0.254093	−	0.967180i	$-0.581777\pi$
$991$	−15.9978			−0.508185			−0.254093	+	0.967180i	$0.581777\pi$
$992$	4.32760	−	3.14419i	0.137401	−	0.0998280i
$993$	−11.7413	−	36.1360i	−0.372599	−	1.14674i
$994$	−12.7163	+	39.1369i	−0.403338	+	1.24135i
$995$		0			0
$996$	−0.240963	−	0.175070i	−0.00763520	−	0.00554730i
$997$	8.77729	−	27.0137i	0.277979	−	0.855533i	−0.710436	−	0.703762i	$-0.751502\pi$
$997$	8.77729	−	27.0137i	0.277979	−	0.855533i	0.988416	−	0.151771i	$-0.0484977\pi$
$998$	−5.24736	−	16.1497i	−0.166102	−	0.511210i
$999$	35.0412	−	25.4589i	1.10866	−	0.805485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.h.n.201.2		8
5.2	odd	4		110.2.j.b.69.3	yes	16
5.3	odd	4		110.2.j.b.69.1	yes	16
5.4	even	2		550.2.h.j.201.1		8
11.2	odd	10		6050.2.a.dl.1.3		4
11.4	even	5	inner	550.2.h.n.301.2		8
11.9	even	5		6050.2.a.dd.1.4		4
15.2	even	4		990.2.ba.h.289.2		16
15.8	even	4		990.2.ba.h.289.4		16
20.3	even	4		880.2.cd.b.289.3		16
20.7	even	4		880.2.cd.b.289.1		16
55.2	even	20		1210.2.b.l.969.6		8
55.4	even	10		550.2.h.j.301.1		8
55.9	even	10		6050.2.a.di.1.1		4
55.13	even	20		1210.2.b.l.969.4		8
55.24	odd	10		6050.2.a.da.1.2		4
55.37	odd	20		110.2.j.b.59.1	✓	16
55.42	odd	20		1210.2.b.k.969.2		8
55.48	odd	20		110.2.j.b.59.3	yes	16
55.53	odd	20		1210.2.b.k.969.8		8
165.92	even	20		990.2.ba.h.829.4		16
165.158	even	20		990.2.ba.h.829.2		16
220.103	even	20		880.2.cd.b.609.1		16
220.147	even	20		880.2.cd.b.609.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.1	✓	16	55.37	odd	20
110.2.j.b.59.3	yes	16	55.48	odd	20
110.2.j.b.69.1	yes	16	5.3	odd	4
110.2.j.b.69.3	yes	16	5.2	odd	4
550.2.h.j.201.1		8	5.4	even	2
550.2.h.j.301.1		8	55.4	even	10
550.2.h.n.201.2		8	1.1	even	1	trivial
550.2.h.n.301.2		8	11.4	even	5	inner
880.2.cd.b.289.1		16	20.7	even	4
880.2.cd.b.289.3		16	20.3	even	4
880.2.cd.b.609.1		16	220.103	even	20
880.2.cd.b.609.3		16	220.147	even	20
990.2.ba.h.289.2		16	15.2	even	4
990.2.ba.h.289.4		16	15.8	even	4
990.2.ba.h.829.2		16	165.158	even	20
990.2.ba.h.829.4		16	165.92	even	20
1210.2.b.k.969.2		8	55.42	odd	20
1210.2.b.k.969.8		8	55.53	odd	20
1210.2.b.l.969.4		8	55.13	even	20
1210.2.b.l.969.6		8	55.2	even	20
6050.2.a.da.1.2		4	55.24	odd	10
6050.2.a.dd.1.4		4	11.9	even	5
6050.2.a.di.1.1		4	55.9	even	10
6050.2.a.dl.1.3		4	11.2	odd	10

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.30902 + 0.951057i) q^{6} +(1.16751 - 3.59321i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 - 0.224514i) q^{9} +(-2.64861 - 1.99621i) q^{11} +1.61803 q^{12} +(2.50710 - 1.82151i) q^{13} +(-1.16751 - 3.59321i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(2.66751 + 1.93806i) q^{17} +(0.118034 - 0.363271i) q^{18} +(0.400863 + 1.23373i) q^{19} +6.11314 q^{21} +(-3.31611 - 0.0581575i) q^{22} +0.556884 q^{23} +(1.30902 - 0.951057i) q^{24} +(0.957626 - 2.94727i) q^{26} +(4.42705 + 3.21644i) q^{27} +(-3.05657 - 2.22073i) q^{28} +(-2.95763 + 9.10264i) q^{29} +(-4.32760 + 3.14419i) q^{31} -1.00000 q^{32} +(1.74755 - 5.07390i) q^{33} +3.29722 q^{34} +(-0.118034 - 0.363271i) q^{36} +(2.44595 - 7.52785i) q^{37} +(1.04947 + 0.762486i) q^{38} +(4.05657 + 2.94727i) q^{39} +(1.94312 + 5.98030i) q^{41} +(4.94563 - 3.59321i) q^{42} +3.61803 q^{43} +(-2.71698 + 1.90211i) q^{44} +(0.450528 - 0.327328i) q^{46} +(-1.65300 - 5.08740i) q^{47} +(0.500000 - 1.53884i) q^{48} +(-5.88499 - 4.27570i) q^{49} +(-1.64861 + 5.07390i) q^{51} +(-0.957626 - 2.94727i) q^{52} +(-8.91067 + 6.47398i) q^{53} +5.47214 q^{54} -3.77813 q^{56} +(-1.69808 + 1.23373i) q^{57} +(2.95763 + 9.10264i) q^{58} +(1.63693 - 5.03795i) q^{59} +(-1.98801 - 1.44437i) q^{61} +(-1.65300 + 5.08740i) q^{62} +(-0.445947 - 1.37249i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.56856 - 5.13205i) q^{66} +9.21247 q^{67} +(2.66751 - 1.93806i) q^{68} +(0.278442 + 0.856956i) q^{69} +(-8.81173 - 6.40210i) q^{71} +(-0.309017 - 0.224514i) q^{72} +(-1.04947 + 3.22994i) q^{73} +(-2.44595 - 7.52785i) q^{74} +1.29722 q^{76} +(-10.2651 + 7.18643i) q^{77} +5.01420 q^{78} +(-13.2383 + 9.61817i) q^{79} +(-2.38197 + 7.33094i) q^{81} +(5.08714 + 3.69603i) q^{82} +(-0.148923 - 0.108199i) q^{83} +(1.88906 - 5.81394i) q^{84} +(2.92705 - 2.12663i) q^{86} -15.4863 q^{87} +(-1.08005 + 3.13584i) q^{88} +6.09017 q^{89} +(-3.61803 - 11.1352i) q^{91} +(0.172087 - 0.529628i) q^{92} +(-7.00220 - 5.08740i) q^{93} +(-4.32760 - 3.14419i) q^{94} +(-0.500000 - 1.53884i) q^{96} +(-9.99782 + 7.26384i) q^{97} -7.27425 q^{98} +(-1.26664 - 0.0222142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 6 q^{6} - 6 q^{7} + 2 q^{8} - 2 q^{9} - 10 q^{11} + 4 q^{12} - 2 q^{13} + 6 q^{14} - 2 q^{16} + 6 q^{17} - 8 q^{18} + 8 q^{19} - 8 q^{21} + 6 q^{24} - 8 q^{26} + 22 q^{27}+ \cdots + 10 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + 6 * q^6 - 6 * q^7 + 2 * q^8 - 2 * q^9 - 10 * q^11 + 4 * q^12 - 2 * q^13 + 6 * q^14 - 2 * q^16 + 6 * q^17 - 8 * q^18 + 8 * q^19 - 8 * q^21 + 6 * q^24 - 8 * q^26 + 22 * q^27 + 4 * q^28 - 8 * q^29 - 2 * q^31 - 8 * q^32 - 10 * q^33 + 4 * q^34 + 8 * q^36 + 2 * q^37 + 2 * q^38 + 4 * q^39 + 20 * q^41 - 2 * q^42 + 20 * q^43 + 10 * q^46 - 18 * q^47 + 4 * q^48 - 42 * q^49 - 2 * q^51 + 8 * q^52 - 16 * q^53 + 8 * q^54 - 4 * q^56 + 4 * q^57 + 8 * q^58 + 10 * q^61 - 18 * q^62 + 14 * q^63 - 2 * q^64 - 10 * q^66 + 20 * q^67 + 6 * q^68 - 28 * q^71 + 2 * q^72 - 2 * q^73 - 2 * q^74 - 12 * q^76 - 24 * q^77 - 4 * q^78 - 18 * q^79 - 28 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 + 10 * q^86 - 44 * q^87 + 4 * q^89 - 20 * q^91 + 10 * q^92 + 14 * q^93 - 2 * q^94 - 4 * q^96 + 6 * q^97 - 48 * q^98 + 10 * q^99

Introduction

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