LMFDB - Embedded newform 475.2.l.c.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			226.1
Root			$-0.566185 - 0.980662i$ of defining polynomial
Character	$\chi$	$=$	475.226
Dual form			475.2.l.c.351.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.370282 + 2.09998i) q^{2} +(-1.70859 - 1.43367i) q^{3} +(-2.39340 - 0.871127i) q^{4} +(3.64334 - 3.05712i) q^{6} +(0.742812 + 1.28659i) q^{7} +(0.583208 - 1.01015i) q^{8} +(0.342900 + 1.94468i) q^{9} +O(q^{10})$	\(q+(-0.370282 + 2.09998i) q^{2} +(-1.70859 - 1.43367i) q^{3} +(-2.39340 - 0.871127i) q^{4} +(3.64334 - 3.05712i) q^{6} +(0.742812 + 1.28659i) q^{7} +(0.583208 - 1.01015i) q^{8} +(0.342900 + 1.94468i) q^{9} +(-2.34068 + 4.05417i) q^{11} +(2.84042 + 4.91975i) q^{12} +(0.276562 - 0.232063i) q^{13} +(-2.97685 + 1.08349i) q^{14} +(-1.99691 - 1.67560i) q^{16} +(0.951255 - 5.39483i) q^{17} -4.21075 q^{18} +(-1.68540 - 4.01988i) q^{19} +(0.575390 - 3.26320i) q^{21} +(-7.64695 - 6.41655i) q^{22} +(-5.79545 - 2.10937i) q^{23} +(-2.44468 + 0.889790i) q^{24} +(0.384921 + 0.666703i) q^{26} +(-1.14343 + 1.98049i) q^{27} +(-0.657066 - 3.72641i) q^{28} +(-0.155581 - 0.882346i) q^{29} +(-2.40012 - 4.15713i) q^{31} +(6.04520 - 5.07252i) q^{32} +(9.81160 - 3.57113i) q^{33} +(10.9768 + 3.99522i) q^{34} +(0.873368 - 4.95311i) q^{36} -11.3982 q^{37} +(9.06572 - 2.05081i) q^{38} -0.805233 q^{39} +(-4.01104 - 3.36566i) q^{41} +(6.63958 + 2.41661i) q^{42} +(6.78295 - 2.46879i) q^{43} +(9.13387 - 7.66423i) q^{44} +(6.57558 - 11.3892i) q^{46} +(1.88678 + 10.7005i) q^{47} +(1.00962 + 5.72583i) q^{48} +(2.39646 - 4.15079i) q^{49} +(-9.35973 + 7.85374i) q^{51} +(-0.864081 + 0.314500i) q^{52} +(-6.12941 - 2.23092i) q^{53} +(-3.73558 - 3.13452i) q^{54} +1.73286 q^{56} +(-2.88354 + 9.28462i) q^{57} +1.91051 q^{58} +(-1.70300 + 9.65818i) q^{59} +(-2.20795 - 0.803626i) q^{61} +(9.61858 - 3.50088i) q^{62} +(-2.24730 + 1.88571i) q^{63} +(5.80697 + 10.0580i) q^{64} +(3.86622 + 21.9264i) q^{66} +(-1.53717 - 8.71774i) q^{67} +(-6.97632 + 12.0833i) q^{68} +(6.87787 + 11.9128i) q^{69} +(-6.02538 + 2.19306i) q^{71} +(2.16439 + 0.787775i) q^{72} +(-2.19219 - 1.83946i) q^{73} +(4.22054 - 23.9359i) q^{74} +(0.532020 + 11.0894i) q^{76} -6.95473 q^{77} +(0.298164 - 1.69097i) q^{78} +(1.58226 + 1.32767i) q^{79} +(10.3598 - 3.77066i) q^{81} +(8.55302 - 7.17684i) q^{82} +(3.08199 + 5.33816i) q^{83} +(-4.21980 + 7.30890i) q^{84} +(2.67280 + 15.1582i) q^{86} +(-0.999172 + 1.73062i) q^{87} +(2.73020 + 4.72885i) q^{88} +(-2.54338 + 2.13415i) q^{89} +(0.504004 + 0.183442i) q^{91} +(12.0333 + 10.0971i) q^{92} +(-1.85915 + 10.5438i) q^{93} -23.1693 q^{94} -17.6011 q^{96} +(-0.819060 + 4.64512i) q^{97} +(7.82919 + 6.56947i) q^{98} +(-8.68669 - 3.16170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.370282	+	2.09998i	−0.261829	+	1.48491i	0.516086	+	0.856537i	$0.327389\pi$
$2$	−0.370282	+	2.09998i	−0.261829	+	1.48491i	−0.777915	+	0.628370i	$0.783723\pi$
$3$	−1.70859	−	1.43367i	−0.986452	−	0.827732i	−0.00140187	−	0.999999i	$-0.500446\pi$
$3$	−1.70859	−	1.43367i	−0.986452	−	0.827732i	−0.985050	+	0.172267i	$0.944891\pi$
$4$	−2.39340	−	0.871127i	−1.19670	−	0.435563i
$5$		0			0
$5$		0			0
$6$	3.64334	−	3.05712i	1.48739	−	1.24807i
$7$	0.742812	+	1.28659i	0.280757	+	0.486285i	0.971571	−	0.236747i	$-0.0760813\pi$
$7$	0.742812	+	1.28659i	0.280757	+	0.486285i	−0.690815	+	0.723032i	$0.742748\pi$
$8$	0.583208	−	1.01015i	0.206195	−	0.357140i
$9$	0.342900	+	1.94468i	0.114300	+	0.648227i
$10$		0			0
$11$	−2.34068	+	4.05417i	−0.705741	+	1.22238i	0.260683	+	0.965424i	$0.416052\pi$
$11$	−2.34068	+	4.05417i	−0.705741	+	1.22238i	−0.966424	+	0.256954i	$0.917281\pi$
$12$	2.84042	+	4.91975i	0.819958	+	1.42021i
$13$	0.276562	−	0.232063i	0.0767046	−	0.0643628i	−0.603629	−	0.797265i	$-0.706279\pi$
$13$	0.276562	−	0.232063i	0.0767046	−	0.0643628i	0.680334	+	0.732902i	$0.261835\pi$
$14$	−2.97685	+	1.08349i	−0.795598	+	0.289574i
$15$		0			0
$16$	−1.99691	−	1.67560i	−0.499227	−	0.418901i
$17$	0.951255	−	5.39483i	0.230713	−	1.30844i	−0.620743	−	0.784014i	$-0.713169\pi$
$17$	0.951255	−	5.39483i	0.230713	−	1.30844i	0.851456	−	0.524425i	$-0.175720\pi$
$18$	−4.21075			−0.992484
$19$	−1.68540	−	4.01988i	−0.386658	−	0.922223i
$19$	−1.68540	−	4.01988i	−0.386658	−	0.922223i
$20$		0			0
$21$	0.575390	−	3.26320i	0.125560	−	0.712088i
$22$	−7.64695	−	6.41655i	−1.63033	−	1.36801i
$23$	−5.79545	−	2.10937i	−1.20843	−	0.439834i	−0.342274	−	0.939600i	$-0.611197\pi$
$23$	−5.79545	−	2.10937i	−1.20843	−	0.439834i	−0.866161	+	0.499766i	$0.833419\pi$
$24$	−2.44468	+	0.889790i	−0.499018	+	0.181628i
$25$		0			0
$26$	0.384921	+	0.666703i	0.0754892	+	0.130751i
$27$	−1.14343	+	1.98049i	−0.220054	+	0.381145i
$28$	−0.657066	−	3.72641i	−0.124174	−	0.704225i
$29$	−0.155581	−	0.882346i	−0.0288907	−	0.163848i	0.966949	−	0.254970i	$-0.0820656\pi$
$29$	−0.155581	−	0.882346i	−0.0288907	−	0.163848i	−0.995840	+	0.0911225i	$0.970955\pi$
$30$		0			0
$31$	−2.40012	−	4.15713i	−0.431074	−	0.746642i	0.565892	−	0.824479i	$-0.308532\pi$
$31$	−2.40012	−	4.15713i	−0.431074	−	0.746642i	−0.996966	+	0.0778374i	$0.975199\pi$
$32$	6.04520	−	5.07252i	1.06865	−	0.896704i
$33$	9.81160	−	3.57113i	1.70798	−	0.621654i
$34$	10.9768	+	3.99522i	1.88250	+	0.685175i
$35$		0			0
$36$	0.873368	−	4.95311i	0.145561	−	0.825519i
$37$	−11.3982			−1.87385			−0.936924	−	0.349534i	$-0.886340\pi$
$37$	−11.3982			−1.87385			−0.936924	+	0.349534i	$0.886340\pi$
$38$	9.06572	−	2.05081i	1.47065	−	0.332686i
$39$	−0.805233			−0.128941
$40$		0			0
$41$	−4.01104	−	3.36566i	−0.626419	−	0.525628i	0.273395	−	0.961902i	$-0.411853\pi$
$41$	−4.01104	−	3.36566i	−0.626419	−	0.525628i	−0.899814	+	0.436274i	$0.856298\pi$
$42$	6.63958	+	2.41661i	1.02451	+	0.372891i
$43$	6.78295	−	2.46879i	1.03439	−	0.376487i	0.231639	−	0.972802i	$-0.425591\pi$
$43$	6.78295	−	2.46879i	1.03439	−	0.376487i	0.802751	+	0.596314i	$0.203369\pi$
$44$	9.13387	−	7.66423i	1.37698	−	1.15543i
$45$		0			0
$46$	6.57558	−	11.3892i	0.969516	−	1.67925i
$47$	1.88678	+	10.7005i	0.275215	+	1.56082i	0.738278	+	0.674497i	$0.235639\pi$
$47$	1.88678	+	10.7005i	0.275215	+	1.56082i	−0.463062	+	0.886326i	$0.653249\pi$
$48$	1.00962	+	5.72583i	0.145726	+	0.826452i
$49$	2.39646	−	4.15079i	0.342351	−	0.592970i
$50$		0			0
$51$	−9.35973	+	7.85374i	−1.31062	+	1.09974i
$52$	−0.864081	+	0.314500i	−0.119827	+	0.0436133i
$53$	−6.12941	−	2.23092i	−0.841940	−	0.306441i	−0.115190	−	0.993343i	$-0.536748\pi$
$53$	−6.12941	−	2.23092i	−0.841940	−	0.306441i	−0.726750	+	0.686902i	$0.758970\pi$
$54$	−3.73558	−	3.13452i	−0.508348	−	0.426555i
$55$		0			0
$56$	1.73286			0.231563
$57$	−2.88354	+	9.28462i	−0.381934	+	1.22978i
$58$	1.91051			0.250863
$59$	−1.70300	+	9.65818i	−0.221711	+	1.25739i	0.647162	+	0.762353i	$0.275956\pi$
$59$	−1.70300	+	9.65818i	−0.221711	+	1.25739i	−0.868873	+	0.495035i	$0.835155\pi$
$60$		0			0
$61$	−2.20795	−	0.803626i	−0.282698	−	0.102894i	0.196779	−	0.980448i	$-0.436952\pi$
$61$	−2.20795	−	0.803626i	−0.282698	−	0.102894i	−0.479478	+	0.877554i	$0.659174\pi$
$62$	9.61858	−	3.50088i	1.22156	−	0.444612i
$63$	−2.24730	+	1.88571i	−0.283133	+	0.237577i
$64$	5.80697	+	10.0580i	0.725871	+	1.25725i
$65$		0			0
$66$	3.86622	+	21.9264i	0.475899	+	2.69896i
$67$	−1.53717	−	8.71774i	−0.187796	−	1.06504i	−0.922311	−	0.386449i	$-0.873701\pi$
$67$	−1.53717	−	8.71774i	−0.187796	−	1.06504i	0.734515	−	0.678592i	$-0.237410\pi$
$68$	−6.97632	+	12.0833i	−0.846003	+	1.46532i
$69$	6.87787	+	11.9128i	0.827998	+	1.43414i
$70$		0			0
$71$	−6.02538	+	2.19306i	−0.715081	+	0.260268i	−0.673836	−	0.738881i	$-0.735355\pi$
$71$	−6.02538	+	2.19306i	−0.715081	+	0.260268i	−0.0412447	+	0.999149i	$0.513132\pi$
$72$	2.16439	+	0.787775i	0.255076	+	0.0928402i
$73$	−2.19219	−	1.83946i	−0.256576	−	0.215293i	0.505422	−	0.862872i	$-0.331337\pi$
$73$	−2.19219	−	1.83946i	−0.256576	−	0.215293i	−0.761998	+	0.647580i	$0.775781\pi$
$74$	4.22054	−	23.9359i	0.490628	−	2.78249i
$75$		0			0
$76$	0.532020	+	11.0894i	0.0610268	+	1.27204i
$77$	−6.95473			−0.792566
$78$	0.298164	−	1.69097i	0.0337604	−	0.191465i
$79$	1.58226	+	1.32767i	0.178018	+	0.149375i	0.727443	−	0.686168i	$-0.240709\pi$
$79$	1.58226	+	1.32767i	0.178018	+	0.149375i	−0.549425	+	0.835543i	$0.685153\pi$
$80$		0			0
$81$	10.3598	−	3.77066i	1.15109	−	0.418962i
$82$	8.55302	−	7.17684i	0.944523	−	0.792549i
$83$	3.08199	+	5.33816i	0.338292	+	0.585939i	0.984112	−	0.177551i	$-0.0568176\pi$
$83$	3.08199	+	5.33816i	0.338292	+	0.585939i	−0.645820	+	0.763490i	$0.723484\pi$
$84$	−4.21980	+	7.30890i	−0.460418	+	0.797467i
$85$		0			0
$86$	2.67280	+	15.1582i	0.288215	+	1.63455i
$87$	−0.999172	+	1.73062i	−0.107122	+	0.185542i
$88$	2.73020	+	4.72885i	0.291040	+	0.504097i
$89$	−2.54338	+	2.13415i	−0.269598	+	0.226220i	−0.767556	−	0.640981i	$-0.778528\pi$
$89$	−2.54338	+	2.13415i	−0.269598	+	0.226220i	0.497959	+	0.867201i	$0.334083\pi$
$90$		0			0
$91$	0.504004	+	0.183442i	0.0528340	+	0.0192300i
$92$	12.0333	+	10.0971i	1.25456	+	1.05270i
$93$	−1.85915	+	10.5438i	−0.192785	+	1.09334i
$94$	−23.1693			−2.38974
$95$		0			0
$96$	−17.6011			−1.79640
$97$	−0.819060	+	4.64512i	−0.0831630	+	0.471641i	0.914575	+	0.404416i	$0.132525\pi$
$97$	−0.819060	+	4.64512i	−0.0831630	+	0.471641i	−0.997738	+	0.0672241i	$0.978586\pi$
$98$	7.82919	+	6.56947i	0.790867	+	0.663617i
$99$	−8.68669	−	3.16170i	−0.873045	−	0.317762i
$100$		0			0
$101$	6.92692	−	5.81237i	0.689254	−	0.578353i	−0.229440	−	0.973323i	$-0.573690\pi$
$101$	6.92692	−	5.81237i	0.689254	−	0.578353i	0.918694	+	0.394970i	$0.129245\pi$
$102$	−13.0269	−	22.5633i	−1.28986	−	2.23410i
$103$	3.89934	−	6.75385i	0.384213	−	0.665476i	−0.607447	−	0.794360i	$-0.707806\pi$
$103$	3.89934	−	6.75385i	0.384213	−	0.665476i	0.991660	+	0.128884i	$0.0411395\pi$
$104$	−0.0731245	−	0.414709i	−0.00717044	−	0.0406656i
$105$		0			0
$106$	6.95450	−	12.0455i	0.675481	−	1.16997i
$107$	0.259152	+	0.448864i	0.0250531	+	0.0433933i	0.878280	−	0.478146i	$-0.158691\pi$
$107$	0.259152	+	0.448864i	0.0250531	+	0.0433933i	−0.853227	+	0.521540i	$0.825358\pi$
$108$	4.46195	−	3.74402i	0.429352	−	0.360269i
$109$	2.59771	−	0.945488i	0.248815	−	0.0905614i	−0.214602	−	0.976702i	$-0.568845\pi$
$109$	2.59771	−	0.945488i	0.248815	−	0.0905614i	0.463417	+	0.886140i	$0.346623\pi$
$110$		0			0
$111$	19.4747	+	16.3413i	1.84846	+	1.55104i
$112$	0.672486	−	3.81386i	0.0635440	−	0.360376i
$113$	−12.4325			−1.16955			−0.584774	−	0.811197i	$-0.698817\pi$
$113$	−12.4325			−1.16955			−0.584774	+	0.811197i	$0.698817\pi$
$114$	−18.4297	−	9.49329i	−1.72610	−	0.889128i
$115$		0			0
$116$	−0.396266	+	2.24734i	−0.0367924	+	0.208660i
$117$	0.546123	+	0.458251i	0.0504891	+	0.0423654i
$118$	−19.6513	−	7.15250i	−1.80905	−	0.658441i
$119$	7.64754	−	2.78348i	0.701049	−	0.255161i
$120$		0			0
$121$	−5.45753	−	9.45272i	−0.496139	−	0.859339i
$122$	2.50516	−	4.33906i	0.226806	−	0.392840i
$123$	2.02794	+	11.5010i	0.182853	+	1.03701i
$124$	2.12306	+	12.0405i	0.190656	+	1.08127i
$125$		0			0
$126$	−3.12780	−	5.41751i	−0.278647	−	0.482630i
$127$	1.04258	−	0.874829i	0.0925141	−	0.0776285i	−0.595358	−	0.803461i	$-0.702990\pi$
$127$	1.04258	−	0.874829i	0.0925141	−	0.0776285i	0.687872	+	0.725832i	$0.258545\pi$
$128$	−8.44062	+	3.07213i	−0.746052	+	0.271541i
$129$	−15.1287	−	5.50639i	−1.33201	−	0.484811i
$130$		0			0
$131$	−3.39033	+	19.2275i	−0.296214	+	1.67991i	0.366011	+	0.930610i	$0.380723\pi$
$131$	−3.39033	+	19.2275i	−0.296214	+	1.67991i	−0.662226	+	0.749305i	$0.730388\pi$
$132$	−26.5940			−2.31471
$133$	3.91999	−	5.15444i	0.339907	−	0.446946i
$134$	18.8762			1.63066
$135$		0			0
$136$	−4.89479	−	4.10721i	−0.419725	−	0.352191i
$137$	10.0363	+	3.65291i	0.857458	+	0.312089i	0.733077	−	0.680145i	$-0.238083\pi$
$137$	10.0363	+	3.65291i	0.857458	+	0.312089i	0.124381	+	0.992235i	$0.460306\pi$
$138$	−27.5634	+	10.0323i	−2.34635	+	0.854002i
$139$	−5.50879	+	4.62243i	−0.467250	+	0.392069i	−0.845790	−	0.533516i	$-0.820871\pi$
$139$	−5.50879	+	4.62243i	−0.467250	+	0.392069i	0.378541	+	0.925585i	$0.376426\pi$
$140$		0			0
$141$	12.1172	−	20.9877i	1.02046	−	1.76748i
$142$	−2.37428	−	13.4652i	−0.199245	−	1.12997i
$143$	0.293481	+	1.66442i	0.0245422	+	0.139185i
$144$	2.57378	−	4.45792i	0.214482	−	0.371493i
$145$		0			0
$146$	4.67455	−	3.92241i	0.386869	−	0.324621i
$147$	−10.0454	+	3.65624i	−0.828533	+	0.301561i
$148$	27.2804	+	9.92925i	2.24243	+	0.816179i
$149$	3.25360	+	2.73009i	0.266545	+	0.223658i	0.766258	−	0.642533i	$-0.222117\pi$
$149$	3.25360	+	2.73009i	0.266545	+	0.223658i	−0.499713	+	0.866191i	$0.666561\pi$
$150$		0			0
$151$	−19.5373			−1.58992			−0.794961	−	0.606660i	$-0.792509\pi$
$151$	−19.5373			−1.58992			−0.794961	+	0.606660i	$0.792509\pi$
$152$	−5.04360	−	0.641923i	−0.409090	−	0.0520668i
$153$	10.8174			0.874537
$154$	2.57521	−	14.6048i	0.207517	−	1.17689i
$155$		0			0
$156$	1.92725	+	0.701460i	0.154303	+	0.0561618i
$157$	0.269149	−	0.0979622i	0.0214804	−	0.00781823i	−0.331258	−	0.943540i	$-0.607473\pi$
$157$	0.269149	−	0.0979622i	0.0214804	−	0.00781823i	0.352738	+	0.935722i	$0.385251\pi$
$158$	−3.37396	+	2.83109i	−0.268418	+	0.225230i
$159$	7.27421	+	12.5993i	0.576882	+	0.999190i
$160$		0			0
$161$	−1.59104	−	9.02323i	−0.125391	−	0.711130i
$162$	4.08224	+	23.1515i	0.320731	+	1.81896i
$163$	−10.3128	+	17.8622i	−0.807759	+	1.39908i	0.106654	+	0.994296i	$0.465986\pi$
$163$	−10.3128	+	17.8622i	−0.807759	+	1.39908i	−0.914413	+	0.404783i	$0.867347\pi$
$164$	6.66811	+	11.5495i	0.520692	+	0.901864i
$165$		0			0
$166$	−12.3512	+	4.49547i	−0.958639	+	0.348916i
$167$	10.1993	+	3.71223i	0.789243	+	0.287261i	0.705021	−	0.709186i	$-0.250937\pi$
$167$	10.1993	+	3.71223i	0.789243	+	0.287261i	0.0842218	+	0.996447i	$0.473160\pi$
$168$	−2.96073	−	2.48435i	−0.228425	−	0.191672i
$169$	−2.23479	+	12.6741i	−0.171907	+	0.974934i
$170$		0			0
$171$	7.23946	−	4.65599i	0.553615	−	0.356052i
$172$	−18.3850			−1.40184
$173$	3.04734	−	17.2823i	0.231685	−	1.31395i	−0.617798	−	0.786337i	$-0.711975\pi$
$173$	3.04734	−	17.2823i	0.231685	−	1.31395i	0.849483	−	0.527616i	$-0.176914\pi$
$174$	−3.26428	−	2.73905i	−0.247464	−	0.207647i
$175$		0			0
$176$	11.4673	−	4.17376i	0.864380	−	0.314609i
$177$	16.7564	−	14.0603i	1.25949	−	1.05684i
$178$	−3.53989	−	6.13128i	−0.265326	−	0.459559i
$179$	−7.53220	+	13.0462i	−0.562983	+	0.975116i	0.434251	+	0.900792i	$0.357013\pi$
$179$	−7.53220	+	13.0462i	−0.562983	+	0.975116i	−0.997234	+	0.0743239i	$0.976320\pi$
$180$		0			0
$181$	2.59091	+	14.6938i	0.192581	+	1.09218i	0.915822	+	0.401585i	$0.131541\pi$
$181$	2.59091	+	14.6938i	0.192581	+	1.09218i	−0.723241	+	0.690596i	$0.757348\pi$
$182$	−0.571848	+	0.990471i	−0.0423882	+	0.0734186i
$183$	2.62033	+	4.53854i	0.193700	+	0.335498i
$184$	−5.51072	+	4.62405i	−0.406256	+	0.340889i
$185$		0			0
$186$	−21.4533	−	7.80836i	−1.57303	−	0.572536i
$187$	19.6450	+	16.4841i	1.43658	+	1.20544i
$188$	4.80564	−	27.2541i	0.350487	−	1.98771i
$189$	−3.39743			−0.247127
$190$		0			0
$191$	−0.00677854			−0.000490478			−0.000245239	−	1.00000i	$-0.500078\pi$
$191$	−0.00677854			−0.000490478			−0.000245239		1.00000i	$0.500078\pi$
$192$	4.49813	−	25.5102i	0.324625	−	1.84104i
$193$	−10.5149	−	8.82305i	−0.756880	−	0.635097i	0.180433	−	0.983587i	$-0.442250\pi$
$193$	−10.5149	−	8.82305i	−0.756880	−	0.635097i	−0.937313	+	0.348490i	$0.886695\pi$
$194$	−9.45136	−	3.44001i	−0.678568	−	0.246978i
$195$		0			0
$196$	−9.35155	+	7.84688i	−0.667968	+	0.560492i
$197$	0.239890	+	0.415502i	0.0170915	+	0.0296033i	0.874445	−	0.485125i	$-0.161226\pi$
$197$	0.239890	+	0.415502i	0.0170915	+	0.0296033i	−0.857353	+	0.514729i	$0.827893\pi$
$198$	9.85601	−	17.0711i	0.700436	−	1.21319i
$199$	−4.65737	−	26.4133i	−0.330152	−	1.87239i	−0.470670	−	0.882309i	$-0.655988\pi$
$199$	−4.65737	−	26.4133i	−0.330152	−	1.87239i	0.140517	−	0.990078i	$-0.455123\pi$
$200$		0			0
$201$	−9.87200	+	17.0988i	−0.696317	+	1.20606i
$202$	9.64092	+	16.6986i	0.678333	+	1.17491i
$203$	1.01965	−	0.855587i	0.0715653	−	0.0600504i
$204$	29.2432	−	10.6436i	2.04743	−	0.745205i
$205$		0			0
$206$	12.7391	+	10.6893i	0.887572	+	0.744761i
$207$	2.11480	−	11.9936i	0.146989	−	0.833614i
$208$	−0.941116			−0.0652547
$209$	20.2423	+	2.57633i	1.40019	+	0.178208i
$210$		0			0
$211$	1.43107	−	8.11599i	0.0985188	−	0.558728i	−0.895093	−	0.445879i	$-0.852891\pi$
$211$	1.43107	−	8.11599i	0.0985188	−	0.558728i	0.993612	−	0.112849i	$-0.0359976\pi$
$212$	12.7267	+	10.6790i	0.874075	+	0.733436i
$213$	13.4390	+	4.89139i	0.920825	+	0.335153i
$214$	−1.03856	+	0.378006i	−0.0709946	+	0.0258399i
$215$		0			0
$216$	1.33372	+	2.31007i	0.0907481	+	0.157180i
$217$	3.56567	−	6.17593i	0.242054	−	0.419249i
$218$	1.02362	+	5.80522i	0.0693281	+	0.393179i
$219$	1.10835	+	6.28576i	0.0748952	+	0.424752i
$220$		0			0
$221$	−0.988862	−	1.71276i	−0.0665181	−	0.115213i
$222$	−41.5274	+	34.8456i	−2.78713	+	2.33868i
$223$	1.61443	−	0.587605i	0.108110	−	0.0393489i	−0.287399	−	0.957811i	$-0.592790\pi$
$223$	1.61443	−	0.587605i	0.108110	−	0.0393489i	0.395509	+	0.918462i	$0.370568\pi$
$224$	11.0167	+	4.00975i	0.736085	+	0.267913i
$225$		0			0
$226$	4.60352	−	26.1079i	0.306222	−	1.73667i
$227$	−4.22601			−0.280490			−0.140245	−	0.990117i	$-0.544789\pi$
$227$	−4.22601			−0.280490			−0.140245	+	0.990117i	$0.544789\pi$
$228$	14.9895	−	19.7099i	0.992707	−	1.30532i
$229$	5.52322			0.364985			0.182492	−	0.983207i	$-0.441583\pi$
$229$	5.52322			0.364985			0.182492	+	0.983207i	$0.441583\pi$
$230$		0			0
$231$	11.8828	+	9.97082i	0.781828	+	0.656032i
$232$	−0.982034	−	0.357431i	−0.0644737	−	0.0234665i
$233$	26.4955	−	9.64357i	1.73578	−	0.631771i	0.736762	−	0.676152i	$-0.236354\pi$
$233$	26.4955	−	9.64357i	1.73578	−	0.631771i	0.999015	+	0.0443807i	$0.0141315\pi$
$234$	−1.16454	+	0.977162i	−0.0761281	+	0.0638791i
$235$		0			0
$236$	12.4895	−	21.6324i	0.812994	−	1.40815i
$237$	−0.799976	−	4.53689i	−0.0519640	−	0.294702i
$238$	3.01348	+	17.0903i	0.195335	+	1.10780i
$239$	5.66020	−	9.80375i	0.366128	−	0.634152i	−0.622829	−	0.782358i	$-0.714017\pi$
$239$	5.66020	−	9.80375i	0.366128	−	0.634152i	0.988956	+	0.148206i	$0.0473499\pi$
$240$		0			0
$241$	12.5356	−	10.5186i	0.807488	−	0.677563i	−0.142519	−	0.989792i	$-0.545520\pi$
$241$	12.5356	−	10.5186i	0.807488	−	0.677563i	0.950007	+	0.312229i	$0.101076\pi$
$242$	21.8713	−	7.96051i	1.40594	−	0.511721i
$243$	−16.6596	−	6.06362i	−1.06872	−	0.388981i
$244$	4.58444	+	3.84680i	0.293489	+	0.246266i
$245$		0			0
$246$	−24.9028			−1.58774
$247$	−1.39899	−	0.720627i	−0.0890153	−	0.0458524i
$248$	−5.59907			−0.355541
$249$	2.38734	−	13.5393i	0.151291	−	0.858015i
$250$		0			0
$251$	6.90186	+	2.51207i	0.435641	+	0.158560i	0.550525	−	0.834818i	$-0.314427\pi$
$251$	6.90186	+	2.51207i	0.435641	+	0.158560i	−0.114884	+	0.993379i	$0.536650\pi$
$252$	7.02137	−	2.55557i	0.442305	−	0.160986i
$253$	22.1170	−	18.5584i	1.39049	−	1.16676i
$254$	1.45107	+	2.51333i	0.0910482	+	0.157700i
$255$		0			0
$256$	0.707484	+	4.01234i	0.0442178	+	0.250771i
$257$	1.04416	+	5.92171i	0.0651327	+	0.369386i	0.999900	+	0.0141259i	$0.00449655\pi$
$257$	1.04416	+	5.92171i	0.0651327	+	0.369386i	−0.934768	+	0.355260i	$0.884392\pi$
$258$	17.1652	−	29.7310i	1.06866	−	1.85097i
$259$	−8.46670	−	14.6648i	−0.526095	−	0.911224i
$260$		0			0
$261$	1.66253	−	0.605113i	0.102908	−	0.0374555i
$262$	−39.1219	−	14.2392i	−2.41696	−	0.879701i
$263$	−5.65251	−	4.74302i	−0.348549	−	0.292467i	0.451658	−	0.892191i	$-0.350833\pi$
$263$	−5.65251	−	4.74302i	−0.348549	−	0.292467i	−0.800207	+	0.599724i	$0.795277\pi$
$264$	2.11484	−	11.9939i	0.130159	−	0.738171i
$265$		0			0
$266$	9.37268	+	10.1405i	0.574676	+	0.621753i
$267$	7.40526			0.453194
$268$	−3.91519	+	22.2041i	−0.239158	+	1.35633i
$269$	−8.32148	−	6.98255i	−0.507370	−	0.425734i	0.352833	−	0.935686i	$-0.385218\pi$
$269$	−8.32148	−	6.98255i	−0.507370	−	0.425734i	−0.860203	+	0.509953i	$0.829663\pi$
$270$		0			0
$271$	−2.67693	+	0.974323i	−0.162612	+	0.0591859i	−0.422043	−	0.906576i	$-0.638687\pi$
$271$	−2.67693	+	0.974323i	−0.162612	+	0.0591859i	0.259432	+	0.965762i	$0.416465\pi$
$272$	−10.9392	+	9.17906i	−0.663285	+	0.556562i
$273$	−0.598137	−	1.03600i	−0.0362009	−	0.0627018i
$274$	−11.3873	+	19.7233i	−0.687931	+	1.19153i
$275$		0			0
$276$	−6.08393	−	34.5037i	−0.366209	−	2.07688i
$277$	−8.07213	+	13.9813i	−0.485008	+	0.840058i	−0.999852	−	0.0172261i	$-0.994516\pi$
$277$	−8.07213	+	13.9813i	−0.485008	+	0.840058i	0.514844	+	0.857284i	$0.327850\pi$
$278$	−7.66717	−	13.2799i	−0.459846	−	0.796477i
$279$	7.26129	−	6.09294i	0.434722	−	0.364775i
$280$		0			0
$281$	−3.02211	−	1.09996i	−0.180284	−	0.0656179i	0.250301	−	0.968168i	$-0.419470\pi$
$281$	−3.02211	−	1.09996i	−0.180284	−	0.0656179i	−0.430585	+	0.902550i	$0.641693\pi$
$282$	39.5868	+	33.2173i	2.35736	+	1.97806i
$283$	−2.23560	+	12.6787i	−0.132893	+	0.753671i	0.843412	+	0.537268i	$0.180544\pi$
$283$	−2.23560	+	12.6787i	−0.132893	+	0.753671i	−0.976304	+	0.216403i	$0.930568\pi$
$284$	16.3316			0.969101
$285$		0			0
$286$	−3.60390			−0.213103
$287$	1.35077	−	7.66061i	0.0797336	−	0.452192i
$288$	11.9373	+	10.0166i	0.703415	+	0.590235i
$289$	−12.2246	−	4.44938i	−0.719092	−	0.261728i
$290$		0			0
$291$	8.05902	−	6.76232i	0.472428	−	0.396414i
$292$	3.64437	+	6.31224i	0.213271	+	0.369396i
$293$	−15.4055	+	26.6831i	−0.899999	+	1.55884i	−0.0725066	+	0.997368i	$0.523100\pi$
$293$	−15.4055	+	26.6831i	−0.899999	+	1.55884i	−0.827493	+	0.561476i	$0.810234\pi$
$294$	−3.95836	−	22.4490i	−0.230856	−	1.30925i
$295$		0			0
$296$	−6.64750	+	11.5138i	−0.386378	+	0.669227i
$297$	−5.35282	−	9.27136i	−0.310602	−	0.537979i
$298$	−6.93788	+	5.82157i	−0.401900	+	0.337234i
$299$	−2.09231	+	0.761539i	−0.121001	+	0.0440409i
$300$		0			0
$301$	8.21478	+	6.89302i	0.473492	+	0.397307i
$302$	7.23432	−	41.0278i	0.416288	−	2.36089i
$303$	−20.1683			−1.15864
$304$	−3.37013	+	10.8514i	−0.193290	+	0.622370i
$305$		0			0
$306$	−4.00550	+	22.7163i	−0.228979	+	1.29861i
$307$	−12.5488	−	10.5297i	−0.716196	−	0.600959i	0.210134	−	0.977673i	$-0.432610\pi$
$307$	−12.5488	−	10.5297i	−0.716196	−	0.600959i	−0.926330	+	0.376713i	$0.877054\pi$
$308$	16.6455	+	6.05846i	0.948464	+	0.345213i
$309$	−16.3452	+	5.94915i	−0.929844	+	0.338435i
$310$		0			0
$311$	−12.3873	−	21.4555i	−0.702420	−	1.21663i	−0.967615	−	0.252432i	$-0.918770\pi$
$311$	−12.3873	−	21.4555i	−0.702420	−	1.21663i	0.265195	−	0.964195i	$-0.414564\pi$
$312$	−0.469618	+	0.813403i	−0.0265869	+	0.0460499i
$313$	−1.78395	−	10.1173i	−0.100835	−	0.571863i	−0.992802	−	0.119763i	$-0.961786\pi$
$313$	−1.78395	−	10.1173i	−0.100835	−	0.571863i	0.891968	−	0.452099i	$-0.149325\pi$
$314$	0.106057	+	0.601480i	0.00598515	+	0.0339435i
$315$		0			0
$316$	−2.63041	−	4.55600i	−0.147972	−	0.256295i
$317$	−4.65473	+	3.90578i	−0.261436	+	0.219371i	−0.764078	−	0.645124i	$-0.776806\pi$
$317$	−4.65473	+	3.90578i	−0.261436	+	0.219371i	0.502642	+	0.864495i	$0.332361\pi$
$318$	−29.1517	+	10.6104i	−1.63475	+	0.595000i
$319$	3.94135	+	1.43453i	0.220673	+	0.0803184i
$320$		0			0
$321$	0.200741	−	1.13846i	0.0112043	−	0.0635427i
$322$	19.5377			1.08879
$323$	−23.2898	+	5.26854i	−1.29588	+	0.293149i
$324$	−28.0799			−1.55999
$325$		0			0
$326$	−33.6916	−	28.2706i	−1.86601	−	1.56577i
$327$	−5.79393	−	2.10882i	−0.320405	−	0.116618i
$328$	−5.73908	+	2.08885i	−0.316888	+	0.115338i
$329$	−12.3656	+	10.3759i	−0.681736	+	0.572044i
$330$		0			0
$331$	−5.90549	+	10.2286i	−0.324595	+	0.562215i	−0.981430	−	0.191819i	$-0.938561\pi$
$331$	−5.90549	+	10.2286i	−0.324595	+	0.562215i	0.656835	+	0.754034i	$0.271895\pi$
$332$	−2.72622	−	15.4611i	−0.149621	−	0.848541i
$333$	−3.90843	−	22.1658i	−0.214181	−	1.21468i
$334$	−11.5722	+	20.0436i	−0.633203	+	1.09674i
$335$		0			0
$336$	−6.61683	+	5.55218i	−0.360978	+	0.302896i
$337$	14.3082	−	5.20776i	0.779417	−	0.283685i	0.0784877	−	0.996915i	$-0.474991\pi$
$337$	14.3082	−	5.20776i	0.779417	−	0.283685i	0.700930	+	0.713230i	$0.252769\pi$
$338$	−25.7879	−	9.38602i	−1.40268	−	0.510532i
$339$	21.2419	+	17.8241i	1.15370	+	0.968071i
$340$		0			0
$341$	22.4716			1.21691
$342$	7.09681	+	16.9267i	0.383752	+	0.915292i
$343$	17.5199			0.945983
$344$	1.46203	−	8.29159i	0.0788274	−	0.447052i
$345$		0			0
$346$	35.1641	+	12.7987i	1.89044	+	0.688062i
$347$	−28.3603	+	10.3223i	−1.52246	+	0.554131i	−0.961762	−	0.273888i	$-0.911690\pi$
$347$	−28.3603	+	10.3223i	−1.52246	+	0.554131i	−0.560700	+	0.828019i	$0.689468\pi$
$348$	3.89900	−	3.27165i	0.209009	−	0.175379i
$349$	1.36886	+	2.37093i	0.0732732	+	0.126913i	0.900334	−	0.435200i	$-0.143322\pi$
$349$	1.36886	+	2.37093i	0.0732732	+	0.126913i	−0.827061	+	0.562112i	$0.809989\pi$
$350$		0			0
$351$	0.143367	+	0.813077i	0.00765239	+	0.0433989i
$352$	6.41502	+	36.3814i	0.341922	+	1.93914i
$353$	−2.30462	+	3.99172i	−0.122663	+	0.212458i	−0.920817	−	0.389995i	$-0.872477\pi$
$353$	−2.30462	+	3.99172i	−0.122663	+	0.212458i	0.798154	+	0.602453i	$0.205810\pi$
$354$	23.3216	+	40.3943i	1.23953	+	2.14693i
$355$		0			0
$356$	7.94645	−	2.89227i	0.421161	−	0.153290i
$357$	−17.0571	−	6.20826i	−0.902755	−	0.328576i
$358$	−24.6076	−	20.6482i	−1.30055	−	1.09129i
$359$	2.14281	−	12.1525i	0.113093	−	0.641383i	−0.874584	−	0.484875i	$-0.838865\pi$
$359$	2.14281	−	12.1525i	0.113093	−	0.641383i	0.987677	−	0.156508i	$-0.0500237\pi$
$360$		0			0
$361$	−13.3188	+	13.5502i	−0.700992	+	0.713170i
$362$	−31.8160			−1.67221
$363$	−4.22746	+	23.9751i	−0.221884	+	1.25837i
$364$	−1.04648	−	0.878103i	−0.0548506	−	0.0460251i
$365$		0			0
$366$	−10.5011	+	3.82208i	−0.548900	+	0.199783i
$367$	1.25334	−	1.05168i	0.0654239	−	0.0548972i	−0.609489	−	0.792794i	$-0.708625\pi$
$367$	1.25334	−	1.05168i	0.0654239	−	0.0548972i	0.674913	+	0.737897i	$0.264181\pi$
$368$	8.03851	+	13.9231i	0.419036	+	0.725792i
$369$	5.16976	−	8.95428i	0.269127	−	0.466141i
$370$		0			0
$371$	−1.68272	−	9.54319i	−0.0873626	−	0.495458i
$372$	13.6347	−	23.6160i	0.706925	−	1.22443i
$373$	−7.37936	−	12.7814i	−0.382089	−	0.661797i	0.609272	−	0.792961i	$-0.291462\pi$
$373$	−7.37936	−	12.7814i	−0.382089	−	0.661797i	−0.991361	+	0.131164i	$0.958129\pi$
$374$	−41.8904	+	35.1502i	−2.16610	+	1.81758i
$375$		0			0
$376$	11.9094	+	4.33467i	0.614181	+	0.223544i
$377$	−0.247788	−	0.207919i	−0.0127617	−	0.0107084i
$378$	1.25801	−	7.13452i	0.0647049	−	0.366960i
$379$	−1.75865			−0.0903358			−0.0451679	−	0.998979i	$-0.514382\pi$
$379$	−1.75865			−0.0903358			−0.0451679	+	0.998979i	$0.514382\pi$
$380$		0			0
$381$	−3.03556			−0.155516
$382$	0.00250997	−	0.0142348i	0.000128421	−	0.000728314i
$383$	6.51031	+	5.46280i	0.332661	+	0.279136i	0.793783	−	0.608201i	$-0.208108\pi$
$383$	6.51031	+	5.46280i	0.332661	+	0.279136i	−0.461122	+	0.887337i	$0.652553\pi$
$384$	18.8259	+	6.85209i	0.960708	+	0.349669i
$385$		0			0
$386$	22.4217	−	18.8140i	1.14123	−	0.957609i
$387$	7.12689	+	12.3441i	0.362280	+	0.627488i
$388$	6.00683	−	10.4041i	0.304951	−	0.528190i
$389$	−5.89390	−	33.4260i	−0.298833	−	1.69476i	−0.651203	−	0.758904i	$-0.725735\pi$
$389$	−5.89390	−	33.4260i	−0.298833	−	1.69476i	0.352370	−	0.935861i	$-0.385376\pi$
$390$		0			0
$391$	−16.8927	+	29.2589i	−0.854298	+	1.47969i
$392$	−2.79527	−	4.84155i	−0.141182	−	0.244535i
$393$	33.3586	−	27.9912i	1.68272	−	1.41197i
$394$	−0.961370	+	0.349910i	−0.0484331	+	0.0176282i
$395$		0			0
$396$	18.0365	+	15.1344i	0.906368	+	0.760533i
$397$	−1.35048	+	7.65893i	−0.0677785	+	0.384391i	0.931982	+	0.362505i	$0.118078\pi$
$397$	−1.35048	+	7.65893i	−0.0677785	+	0.384391i	−0.999760	+	0.0218863i	$0.993033\pi$
$398$	57.1918			2.86676
$399$	−14.0874	+	3.18680i	−0.705253	+	0.159540i
$400$		0			0
$401$	5.41570	−	30.7140i	0.270447	−	1.53378i	−0.482615	−	0.875833i	$-0.660313\pi$
$401$	5.41570	−	30.7140i	0.270447	−	1.53378i	0.753062	−	0.657950i	$-0.228576\pi$
$402$	−32.2516	−	27.0623i	−1.60857	−	1.34975i
$403$	−1.62850	−	0.592725i	−0.0811213	−	0.0295257i
$404$	−21.6422	+	7.87712i	−1.07674	+	0.391901i
$405$		0			0
$406$	1.41915	+	2.45805i	0.0704314	+	0.121991i
$407$	26.6794	−	46.2101i	1.32245	−	2.29055i
$408$	2.47476	+	14.0351i	0.122519	+	0.694839i
$409$	−2.54836	−	14.4525i	−0.126008	−	0.714629i	−0.980704	−	0.195499i	$-0.937367\pi$
$409$	−2.54836	−	14.4525i	−0.126008	−	0.714629i	0.854695	−	0.519130i	$-0.173744\pi$
$410$		0			0
$411$	−11.9108	−	20.6301i	−0.587515	−	1.01761i
$412$	−15.2161	+	12.7679i	−0.749645	+	0.629027i
$413$	−13.6911	+	4.98316i	−0.673696	+	0.245205i
$414$	24.4032	+	8.88204i	1.19935	+	0.436529i
$415$		0			0
$416$	0.494727	−	2.80574i	0.0242560	−	0.137563i
$417$	16.0393			0.785447
$418$	−12.9056	+	41.5543i	−0.631232	+	2.03249i
$419$	−20.6063			−1.00668			−0.503341	−	0.864088i	$-0.667896\pi$
$419$	−20.6063			−1.00668			−0.503341	+	0.864088i	$0.667896\pi$
$420$		0			0
$421$	21.2034	+	17.7918i	1.03339	+	0.867119i	0.991251	−	0.131993i	$-0.0421375\pi$
$421$	21.2034	+	17.7918i	1.03339	+	0.867119i	0.0421416	+	0.999112i	$0.486582\pi$
$422$	16.5135	+	6.01041i	0.803864	+	0.292582i
$423$	−20.1620	+	7.33837i	−0.980311	+	0.356804i
$424$	−5.82828	+	4.89051i	−0.283046	+	0.237504i
$425$		0			0
$426$	−15.2480	+	26.4104i	−0.738769	+	1.27959i
$427$	−0.606153	−	3.43766i	−0.0293338	−	0.166360i
$428$	−0.229237	−	1.30007i	−0.0110806	−	0.0628410i
$429$	1.88479	−	3.26455i	0.0909986	−	0.157614i
$430$		0			0
$431$	−16.0072	+	13.4317i	−0.771042	+	0.646981i	−0.940976	−	0.338475i	$-0.890089\pi$
$431$	−16.0072	+	13.4317i	−0.771042	+	0.646981i	0.169934	+	0.985455i	$0.445645\pi$
$432$	5.60185	−	2.03891i	0.269519	−	0.0980969i
$433$	1.80980	+	0.658712i	0.0869732	+	0.0316557i	0.385140	−	0.922858i	$-0.374153\pi$
$433$	1.80980	+	0.658712i	0.0869732	+	0.0316557i	−0.298167	+	0.954514i	$0.596375\pi$
$434$	11.6490	+	9.77467i	0.559170	+	0.469199i
$435$		0			0
$436$	−7.04100			−0.337203
$437$	1.28825	+	26.8521i	0.0616252	+	1.28451i
$438$	−13.6103			−0.650327
$439$	6.02549	−	34.1723i	0.287581	−	1.63095i	−0.408337	−	0.912831i	$-0.633891\pi$
$439$	6.02549	−	34.1723i	0.287581	−	1.63095i	0.695918	−	0.718121i	$-0.254998\pi$
$440$		0			0
$441$	8.89371	+	3.23705i	0.423510	+	0.154145i
$442$	3.96291	−	1.44238i	0.188496	−	0.0686071i
$443$	−20.1629	+	16.9187i	−0.957970	+	0.803832i	−0.980622	−	0.195911i	$-0.937234\pi$
$443$	−20.1629	+	16.9187i	−0.957970	+	0.803832i	0.0226514	+	0.999743i	$0.492789\pi$
$444$	−32.3756	−	56.0761i	−1.53648	−	2.66126i
$445$		0			0
$446$	0.636160	+	3.60784i	0.0301231	+	0.170836i
$447$	−1.64499	−	9.32919i	−0.0778053	−	0.441256i
$448$	−8.62698	+	14.9424i	−0.407586	+	0.705960i
$449$	6.71581	+	11.6321i	0.316939	+	0.548954i	0.979848	−	0.199746i	$-0.0640117\pi$
$449$	6.71581	+	11.6321i	0.316939	+	0.548954i	−0.662909	+	0.748700i	$0.730678\pi$
$450$		0			0
$451$	23.0335	−	8.38351i	1.08461	−	0.394764i
$452$	29.7559	+	10.8302i	1.39960	+	0.509412i
$453$	33.3811	+	28.0101i	1.56838	+	1.31603i
$454$	1.56482	−	8.87452i	0.0734405	−	0.416502i
$455$		0			0
$456$	7.69712	+	8.32766i	0.360450	+	0.389978i
$457$	−0.205882			−0.00963073			−0.00481537	−	0.999988i	$-0.501533\pi$
$457$	−0.205882			−0.00963073			−0.00481537	+	0.999988i	$0.501533\pi$
$458$	−2.04515	+	11.5986i	−0.0955637	+	0.541969i
$459$	9.59670	+	8.05259i	0.447935	+	0.375863i
$460$		0			0
$461$	−36.6739	+	13.3482i	−1.70807	+	0.621688i	−0.996704	−	0.0811290i	$-0.974147\pi$
$461$	−36.6739	+	13.3482i	−1.70807	+	0.621688i	−0.711371	+	0.702817i	$0.751925\pi$
$462$	−25.3384	+	21.2615i	−1.17885	+	0.989173i
$463$	−3.71234	−	6.42997i	−0.172527	−	0.298826i	0.766776	−	0.641915i	$-0.221860\pi$
$463$	−3.71234	−	6.42997i	−0.172527	−	0.298826i	−0.939303	+	0.343089i	$0.888527\pi$
$464$	−1.16778	+	2.02266i	−0.0542129	+	0.0938995i
$465$		0			0
$466$	10.4404	+	59.2107i	0.483644	+	2.74288i
$467$	10.9627	−	18.9880i	0.507295	−	0.878660i	−0.492670	−	0.870216i	$-0.663979\pi$
$467$	10.9627	−	18.9880i	0.507295	−	0.878660i	0.999964	−	0.00844368i	$-0.00268774\pi$
$468$	−0.907896	−	1.57252i	−0.0419675	−	0.0726898i
$469$	10.0743	−	8.45336i	0.465189	−	0.390340i
$470$		0			0
$471$	−0.600309	−	0.218495i	−0.0276608	−	0.0100677i
$472$	8.76296	+	7.35300i	0.403348	+	0.338449i
$473$	−5.86779	+	33.2779i	−0.269801	+	1.53012i
$474$	9.82357			0.451211
$475$		0			0
$476$	−20.7284			−0.950084
$477$	2.23666	−	12.6847i	0.102410	−	0.580795i
$478$	18.4918	+	15.5164i	0.845794	+	0.709705i
$479$	26.3861	+	9.60376i	1.20561	+	0.438807i	0.865180	−	0.501462i	$-0.167204\pi$
$479$	26.3861	+	9.60376i	1.20561	+	0.438807i	0.340433	+	0.940269i	$0.389427\pi$
$480$		0			0
$481$	−3.15230	+	2.64510i	−0.143733	+	0.120606i
$482$	17.4471	+	30.2193i	0.794694	+	1.37645i
$483$	−10.2179	+	17.6980i	−0.464932	+	0.805286i
$484$	4.82754	+	27.3784i	0.219434	+	1.24447i
$485$		0			0
$486$	18.9022	−	32.7396i	0.857422	−	1.48510i
$487$	−7.06739	−	12.2411i	−0.320254	−	0.554697i	0.660286	−	0.751014i	$-0.270435\pi$
$487$	−7.06739	−	12.2411i	−0.320254	−	0.554697i	−0.980540	+	0.196318i	$0.937102\pi$
$488$	−2.09947	+	1.76167i	−0.0950386	+	0.0797468i
$489$	43.2289	−	15.7340i	1.95488	−	0.711517i
$490$		0			0
$491$	−17.7677	−	14.9089i	−0.801847	−	0.672830i	0.146800	−	0.989166i	$-0.453103\pi$
$491$	−17.7677	−	14.9089i	−0.801847	−	0.672830i	−0.948647	+	0.316337i	$0.897547\pi$
$492$	5.16518	−	29.2932i	0.232864	−	1.32064i
$493$	−4.90811			−0.221050
$494$	2.03132	−	2.67100i	0.0913933	−	0.120174i
$495$		0			0
$496$	−2.17289	+	12.3230i	−0.0975654	+	0.553321i
$497$	−7.29729	−	6.12315i	−0.327328	−	0.274661i
$498$	27.5481	+	10.0267i	1.23446	+	0.449307i
$499$	39.8744	−	14.5131i	1.78502	−	0.649695i	0.785497	−	0.618865i	$-0.212407\pi$
$499$	39.8744	−	14.5131i	1.78502	−	0.649695i	0.999525	−	0.0308294i	$-0.00981485\pi$
$500$		0			0
$501$	−12.1042	−	20.9651i	−0.540776	−	0.936651i
$502$	−7.83092	+	13.5635i	−0.349511	+	0.605371i
$503$	−1.01542	−	5.75873i	−0.0452753	−	0.256769i	0.953766	−	0.300551i	$-0.0971705\pi$
$503$	−1.01542	−	5.75873i	−0.0452753	−	0.256769i	−0.999041	+	0.0437817i	$0.986059\pi$
$504$	0.594196	+	3.36985i	0.0264676	+	0.150105i
$505$		0			0
$506$	30.7826	+	53.3170i	1.36845	+	2.37023i
$507$	21.9889	−	18.4509i	0.976562	−	0.819433i
$508$	−3.25740	+	1.18560i	−0.144524	+	0.0526023i
$509$	−7.84135	−	2.85402i	−0.347562	−	0.126502i	0.162340	−	0.986735i	$-0.448096\pi$
$509$	−7.84135	−	2.85402i	−0.347562	−	0.126502i	−0.509902	+	0.860233i	$0.670318\pi$
$510$		0			0
$511$	0.738249	−	4.18682i	0.0326582	−	0.185214i
$512$	−26.6524			−1.17788
$513$	9.88846	+	1.25855i	0.436586	+	0.0555664i
$514$	−12.8221			−0.565557
$515$		0			0
$516$	31.4123	+	26.3580i	1.38285	+	1.16035i
$517$	−47.7978	−	17.3970i	−2.10215	−	0.765119i
$518$	33.9307	−	12.3498i	1.49083	−	0.542618i
$519$	−29.9839	+	25.1595i	−1.31615	+	1.10438i
$520$		0			0
$521$	−15.4419	+	26.7461i	−0.676521	+	1.17177i	0.299501	+	0.954096i	$0.403180\pi$
$521$	−15.4419	+	26.7461i	−0.676521	+	1.17177i	−0.976022	+	0.217673i	$0.930154\pi$
$522$	0.655115	+	3.71534i	0.0286736	+	0.162616i
$523$	−3.97753	−	22.5577i	−0.173925	−	0.986380i	−0.939377	−	0.342886i	$-0.888595\pi$
$523$	−3.97753	−	22.5577i	−0.173925	−	0.986380i	0.765452	−	0.643494i	$-0.222516\pi$
$524$	24.8640	−	43.0657i	1.08619	−	1.88134i
$525$		0			0
$526$	12.0532	−	10.1139i	0.525547	−	0.440986i
$527$	−24.7101	+	8.99375i	−1.07639	+	0.391774i
$528$	−25.5767	−	9.30914i	−1.11308	−	0.405129i
$529$	11.5188	+	9.66540i	0.500816	+	0.420235i
$530$		0			0
$531$	−19.3660			−0.840415
$532$	−13.8723	+	8.92182i	−0.601440	+	0.386810i
$533$	−1.89035			−0.0818801
$534$	−2.74204	+	15.5509i	−0.118659	+	0.672951i
$535$		0			0
$536$	−9.70268	−	3.53149i	−0.419092	−	0.152537i
$537$	31.5733	−	11.4918i	1.36249	−	0.495906i
$538$	17.7445	−	14.8894i	0.765019	−	0.641927i
$539$	11.2187	+	19.4313i	0.483222	+	0.836966i
$540$		0			0
$541$	−0.695195	−	3.94265i	−0.0298888	−	0.169508i	0.966210	−	0.257758i	$-0.0829837\pi$
$541$	−0.695195	−	3.94265i	−0.0298888	−	0.169508i	−0.996098	+	0.0882501i	$0.971873\pi$
$542$	−1.05483	−	5.98226i	−0.0453090	−	0.256960i
$543$	16.6393	−	28.8201i	0.714061	−	1.23679i
$544$	−21.6149	−	37.4381i	−0.926731	−	1.60515i
$545$		0			0
$546$	2.39706	−	0.872460i	0.102585	−	0.0373378i
$547$	39.1590	+	14.2527i	1.67432	+	0.609402i	0.992514	−	0.122133i	$-0.0389735\pi$
$547$	39.1590	+	14.2527i	1.67432	+	0.609402i	0.681804	+	0.731535i	$0.261196\pi$
$548$	−20.8387	−	17.4858i	−0.890186	−	0.746954i
$549$	0.805694	−	4.56932i	0.0343862	−	0.195014i
$550$		0			0
$551$	−3.28471	+	2.11253i	−0.139933	+	0.0899966i
$552$	16.0449			0.682917
$553$	−0.532848	+	3.02193i	−0.0226590	+	0.128506i
$554$	−26.3715	−	22.1283i	−1.12042	−	0.940142i
$555$		0			0
$556$	17.2115	−	6.26446i	0.729929	−	0.265672i
$557$	2.43219	−	2.04085i	0.103055	−	0.0864735i	−0.589804	−	0.807546i	$-0.700795\pi$
$557$	2.43219	−	2.04085i	0.103055	−	0.0864735i	0.692859	+	0.721073i	$0.256351\pi$
$558$	10.1063	+	17.5046i	0.427834	+	0.741030i
$559$	1.30299	−	2.25685i	0.0551107	−	0.0954546i
$560$		0			0
$561$	−9.93232	−	56.3290i	−0.419343	−	2.37821i
$562$	3.42891	−	5.93905i	0.144640	−	0.250524i
$563$	7.20295	+	12.4759i	0.303568	+	0.525796i	0.976942	−	0.213507i	$-0.0684886\pi$
$563$	7.20295	+	12.4759i	0.303568	+	0.525796i	−0.673373	+	0.739303i	$0.735155\pi$
$564$	−47.2843	+	39.6763i	−1.99103	+	1.67067i
$565$		0			0
$566$	−25.7972	−	9.38940i	−1.08434	−	0.394666i
$567$	12.5467	+	10.5279i	0.526911	+	0.442131i
$568$	−1.29874	+	7.36552i	−0.0544939	+	0.309050i
$569$	24.9795			1.04719			0.523597	−	0.851966i	$-0.324590\pi$
$569$	24.9795			1.04719			0.523597	+	0.851966i	$0.324590\pi$
$570$		0			0
$571$	13.1086			0.548579			0.274289	−	0.961647i	$-0.411557\pi$
$571$	13.1086			0.548579			0.274289	+	0.961647i	$0.411557\pi$
$572$	0.747499	−	4.23928i	0.0312545	−	0.177253i
$573$	0.0115817	+	0.00971822i	0.000483833	+	0.000405984i
$574$	15.5869	+	5.67318i	0.650586	+	0.236794i
$575$		0			0
$576$	−17.5683	+	14.7416i	−0.732014	+	0.614233i
$577$	4.12748	+	7.14901i	0.171829	+	0.297617i	0.939059	−	0.343755i	$-0.111699\pi$
$577$	4.12748	+	7.14901i	0.171829	+	0.297617i	−0.767230	+	0.641372i	$0.778366\pi$
$578$	13.8701	−	24.0238i	0.576921	−	0.999257i
$579$	5.31624	+	30.1499i	0.220935	+	1.25299i
$580$		0			0
$581$	−4.57867	+	7.93050i	−0.189955	+	0.329012i
$582$	11.2166	+	19.4277i	0.464943	+	0.805304i
$583$	23.3915	−	19.6278i	0.968778	−	0.812901i
$584$	−3.13662	+	1.14164i	−0.129794	+	0.0472413i
$585$		0			0
$586$	−50.3295	−	42.2315i	−2.07909	−	1.74457i
$587$	1.37287	−	7.78595i	0.0566646	−	0.321361i	−0.943279	−	0.332002i	$-0.892276\pi$
$587$	1.37287	−	7.78595i	0.0566646	−	0.321361i	0.999943	+	0.0106409i	$0.00338717\pi$
$588$	27.2278			1.12286
$589$	−12.6660	+	16.6546i	−0.521892	+	0.686241i
$590$		0			0
$591$	0.185821	−	1.05384i	0.00764366	−	0.0433493i
$592$	22.7611	+	19.0988i	0.935475	+	0.784957i
$593$	−3.34124	−	1.21611i	−0.137208	−	0.0499398i	0.272503	−	0.962155i	$-0.412148\pi$
$593$	−3.34124	−	1.21611i	−0.137208	−	0.0499398i	−0.409712	+	0.912215i	$0.634371\pi$
$594$	21.4517	−	7.80777i	0.880173	−	0.320357i
$595$		0			0
$596$	−5.40891	−	9.36850i	−0.221557	−	0.383749i
$597$	−29.9105	+	51.8065i	−1.22415	+	2.12030i
$598$	−0.824467	−	4.67579i	−0.0337150	−	0.191207i
$599$	1.91987	+	10.8881i	0.0784437	+	0.444876i	0.998580	+	0.0532774i	$0.0169668\pi$
$599$	1.91987	+	10.8881i	0.0784437	+	0.444876i	−0.920136	+	0.391599i	$0.871922\pi$
$600$		0			0
$601$	22.7722	+	39.4426i	0.928898	+	1.60890i	0.785170	+	0.619281i	$0.212576\pi$
$601$	22.7722	+	39.4426i	0.928898	+	1.60890i	0.143728	+	0.989617i	$0.454091\pi$
$602$	−17.5170	+	14.6985i	−0.713938	+	0.599065i
$603$	16.4261	−	5.97863i	0.668924	−	0.243468i
$604$	46.7606	+	17.0195i	1.90266	+	0.692512i
$605$		0			0
$606$	7.46795	−	42.3529i	0.303365	−	1.72047i
$607$	−36.4498			−1.47945			−0.739727	−	0.672907i	$-0.765045\pi$
$607$	−36.4498			−1.47945			−0.739727	+	0.672907i	$0.765045\pi$
$608$	−30.5795	−	15.7517i	−1.24016	−	0.638817i
$609$	−2.96879			−0.120301
$610$		0			0
$611$	3.00500	+	2.52149i	0.121569	+	0.102009i
$612$	−25.8904	−	9.42334i	−1.04656	−	0.380916i
$613$	6.33713	−	2.30653i	0.255954	−	0.0931597i	−0.210856	−	0.977517i	$-0.567625\pi$
$613$	6.33713	−	2.30653i	0.255954	−	0.0931597i	0.466811	+	0.884357i	$0.345403\pi$
$614$	26.7586	−	22.4531i	1.07989	−	0.906135i
$615$		0			0
$616$	−4.05606	+	7.02529i	−0.163423	+	0.283057i
$617$	−4.38423	−	24.8642i	−0.176503	−	1.00100i	−0.936395	−	0.350947i	$-0.885860\pi$
$617$	−4.38423	−	24.8642i	−0.176503	−	1.00100i	0.759893	−	0.650049i	$-0.225252\pi$
$618$	−6.44075	−	36.5273i	−0.259085	−	1.46934i
$619$	−11.1611	+	19.3317i	−0.448604	+	0.777006i	−0.998295	−	0.0583624i	$-0.981412\pi$
$619$	−11.1611	+	19.3317i	−0.448604	+	0.777006i	0.549691	+	0.835368i	$0.314745\pi$
$620$		0			0
$621$	10.8043	−	9.06588i	0.433562	−	0.363801i
$622$	49.6427	−	18.0685i	1.99049	−	0.724480i
$623$	−4.63503	−	1.68701i	−0.185699	−	0.0675887i
$624$	1.60798	+	1.34925i	0.0643706	+	0.0540133i
$625$		0			0
$626$	21.9066			0.875564
$627$	−30.8920	−	33.4226i	−1.23371	−	1.33477i
$628$	−0.729519			−0.0291110
$629$	−10.8426	+	61.4912i	−0.432321	+	2.45182i
$630$		0			0
$631$	−3.32590	−	1.21053i	−0.132402	−	0.0481904i	0.274969	−	0.961453i	$-0.411332\pi$
$631$	−3.32590	−	1.21053i	−0.132402	−	0.0481904i	−0.407371	+	0.913263i	$0.633555\pi$
$632$	2.26393	−	0.824003i	0.0900543	−	0.0327771i
$633$	−14.0808	+	11.8152i	−0.559661	+	0.469611i
$634$	−6.47848	−	11.2211i	−0.257293	−	0.445645i
$635$		0			0
$636$	−6.43451	−	36.4919i	−0.255145	−	1.44700i
$637$	−0.300476	−	1.70408i	−0.0119053	−	0.0675182i
$638$	−4.47189	+	7.74555i	−0.177044	+	0.306649i
$639$	−6.33090	−	10.9654i	−0.250447	−	0.433786i
$640$		0			0
$641$	−24.7767	+	9.01799i	−0.978622	+	0.356189i	−0.781304	−	0.624150i	$-0.785445\pi$
$641$	−24.7767	+	9.01799i	−0.978622	+	0.356189i	−0.197318	+	0.980340i	$0.563223\pi$
$642$	2.31641	+	0.843104i	0.0914213	+	0.0332746i
$643$	11.2983	+	9.48043i	0.445563	+	0.373872i	0.837786	−	0.545998i	$-0.183850\pi$
$643$	11.2983	+	9.48043i	0.445563	+	0.373872i	−0.392223	+	0.919870i	$0.628294\pi$
$644$	−4.05238	+	22.9822i	−0.159686	+	0.905626i
$645$		0			0
$646$	−2.43999	−	50.8589i	−0.0960000	−	2.00102i
$647$	−5.04555			−0.198361			−0.0991804	−	0.995069i	$-0.531622\pi$
$647$	−5.04555			−0.198361			−0.0991804	+	0.995069i	$0.531622\pi$
$648$	2.23300	−	12.6640i	0.0877207	−	0.497489i
$649$	−35.1697	−	29.5109i	−1.38053	−	1.15840i
$650$		0			0
$651$	−14.9465	+	5.44009i	−0.585800	+	0.213214i
$652$	40.2429	−	33.7678i	1.57603	−	1.32245i
$653$	−22.3362	−	38.6875i	−0.874084	−	1.51396i	−0.857735	−	0.514092i	$-0.828129\pi$
$653$	−22.3362	−	38.6875i	−0.874084	−	1.51396i	−0.0163488	−	0.999866i	$-0.505204\pi$
$654$	6.57385	−	11.3862i	0.257058	−	0.445237i
$655$		0			0
$656$	2.37016	+	13.4418i	0.0925391	+	0.524815i
$657$	2.82547	−	4.89386i	0.110232	−	0.190927i
$658$	−17.2105	−	29.8094i	−0.670934	−	1.16209i
$659$	22.5147	−	18.8921i	0.877049	−	0.735931i	−0.0885212	−	0.996074i	$-0.528214\pi$
$659$	22.5147	−	18.8921i	0.877049	−	0.735931i	0.965570	+	0.260143i	$0.0837697\pi$
$660$		0			0
$661$	19.0049	+	6.91721i	0.739204	+	0.269048i	0.684056	−	0.729430i	$-0.260215\pi$
$661$	19.0049	+	6.91721i	0.739204	+	0.269048i	0.0551486	+	0.998478i	$0.482437\pi$
$662$	−19.2931	−	16.1889i	−0.749849	−	0.629198i
$663$	−0.765982	+	4.34410i	−0.0297483	+	0.168711i
$664$	7.18975			0.279016
$665$		0			0
$666$	47.9949			1.85976
$667$	−0.959531	+	5.44177i	−0.0371532	+	0.210706i
$668$	−21.1771	−	17.7697i	−0.819367	−	0.687531i
$669$	−3.60083	−	1.31059i	−0.139216	−	0.0506705i
$670$		0			0
$671$	8.42612	−	7.07036i	0.325287	−	0.272948i
$672$	−13.0743	−	22.6454i	−0.504352	−	0.873564i
$673$	−13.8331	+	23.9597i	−0.533227	+	0.923577i	0.466019	+	0.884774i	$0.345688\pi$
$673$	−13.8331	+	23.9597i	−0.533227	+	0.923577i	−0.999247	+	0.0388026i	$0.987646\pi$
$674$	5.63809	+	31.9752i	0.217171	+	1.23164i
$675$		0			0
$676$	16.3895	−	28.3875i	0.630367	−	1.09183i
$677$	15.8370	+	27.4305i	0.608665	+	1.05424i	0.991461	+	0.130405i	$0.0416279\pi$
$677$	15.8370	+	27.4305i	0.608665	+	1.05424i	−0.382796	+	0.923833i	$0.625039\pi$
$678$	−45.2956	+	38.0075i	−1.73957	+	1.45967i
$679$	−6.58477	+	2.39666i	−0.252700	+	0.0919754i
$680$		0			0
$681$	7.22050	+	6.05872i	0.276690	+	0.232171i
$682$	−8.32083	+	47.1898i	−0.318621	+	1.80699i
$683$	4.75181			0.181823			0.0909114	−	0.995859i	$-0.471022\pi$
$683$	4.75181			0.181823			0.0909114	+	0.995859i	$0.471022\pi$
$684$	−21.3829	+	4.83716i	−0.817595	+	0.184953i
$685$		0			0
$686$	−6.48729	+	36.7913i	−0.247686	+	1.40470i
$687$	−9.43690	−	7.91850i	−0.360040	−	0.302110i
$688$	−17.6816	−	6.43559i	−0.674106	−	0.245355i
$689$	−2.21288	+	0.805423i	−0.0843040	+	0.0306842i
$690$		0			0
$691$	0.211770	+	0.366797i	0.00805613	+	0.0139536i	0.870025	−	0.493007i	$-0.164102\pi$
$691$	0.211770	+	0.366797i	0.00805613	+	0.0139536i	−0.861969	+	0.506961i	$0.830769\pi$
$692$	−22.3486	+	38.7090i	−0.849568	+	1.47149i
$693$	−2.38478	−	13.5247i	−0.0905902	−	0.513763i
$694$	−11.1753	−	63.3781i	−0.424208	−	2.40580i
$695$		0			0
$696$	1.16545	+	2.01862i	0.0441762	+	0.0765155i
$697$	−21.9727	+	18.4373i	−0.832275	+	0.698362i
$698$	−5.48575	+	1.99665i	−0.207639	+	0.0755743i
$699$	−59.0955	−	21.5090i	−2.23520	−	0.813545i
$700$		0			0
$701$	1.37980	−	7.82526i	0.0521145	−	0.295556i	−0.947600	−	0.319460i	$-0.896499\pi$
$701$	1.37980	−	7.82526i	0.0521145	−	0.295556i	0.999714	+	0.0239040i	$0.00760962\pi$
$702$	−1.76053			−0.0664469
$703$	19.2105	+	45.8193i	0.724538	+	1.72811i
$704$	−54.3689			−2.04911
$705$		0			0
$706$	−7.52915	−	6.31771i	−0.283363	−	0.237770i
$707$	12.6235	+	4.59459i	0.474757	+	0.172797i
$708$	−52.3530	+	19.0549i	−1.96755	+	0.716129i
$709$	8.99170	−	7.54493i	0.337690	−	0.283356i	−0.458134	−	0.888883i	$-0.651482\pi$
$709$	8.99170	−	7.54493i	0.337690	−	0.283356i	0.795825	+	0.605527i	$0.207038\pi$
$710$		0			0
$711$	−2.03935	+	3.53225i	−0.0764815	+	0.132470i
$712$	0.672483	+	3.81384i	0.0252024	+	0.142930i
$713$	5.14084	+	29.1552i	0.192526	+	1.09187i
$714$	19.3531	−	33.5206i	0.724272	−	1.25448i
$715$		0			0
$716$	29.3924	−	24.6632i	1.09845	−	0.921707i
$717$	−23.7263	+	8.63567i	−0.886075	+	0.322505i
$718$	24.7264	+	8.99969i	0.922783	+	0.335865i
$719$	−38.6452	−	32.4272i	−1.44122	−	1.20933i	−0.938686	−	0.344773i	$-0.887956\pi$
$719$	−38.6452	−	32.4272i	−1.44122	−	1.20933i	−0.502536	−	0.864556i	$-0.667600\pi$
$720$		0			0
$721$	11.5859			0.431481
$722$	−23.5234	−	32.9866i	−0.875450	−	1.22764i
$723$	−36.4983			−1.35739
$724$	6.59907	−	37.4252i	0.245252	−	1.39090i
$725$		0			0
$726$	−48.7818	−	17.7551i	−1.81046	−	0.658954i
$727$	24.4935	−	8.91490i	0.908414	−	0.330636i	0.154794	−	0.987947i	$-0.450529\pi$
$727$	24.4935	−	8.91490i	0.908414	−	0.330636i	0.753619	+	0.657311i	$0.228306\pi$
$728$	0.479243	−	0.402132i	0.0177619	−	0.0149040i
$729$	3.23417	+	5.60174i	0.119784	+	0.207472i
$730$		0			0
$731$	−6.86641	−	38.9413i	−0.253963	−	1.44030i
$732$	−2.31785	−	13.1452i	−0.0856702	−	0.485860i
$733$	8.54306	−	14.7970i	0.315545	−	0.546540i	−0.664008	−	0.747725i	$-0.731146\pi$
$733$	8.54306	−	14.7970i	0.315545	−	0.546540i	0.979553	+	0.201185i	$0.0644793\pi$
$734$	1.74441	+	3.02141i	0.0643873	+	0.111522i
$735$		0			0
$736$	−45.7345	+	16.6460i	−1.68580	+	0.613580i
$737$	38.9412	+	14.1734i	1.43442	+	0.522086i
$738$	16.8895	+	14.1720i	0.621711	+	0.521677i
$739$	−4.27432	+	24.2409i	−0.157233	+	0.891715i	0.799482	+	0.600690i	$0.205107\pi$
$739$	−4.27432	+	24.2409i	−0.157233	+	0.891715i	−0.956715	+	0.291025i	$0.906004\pi$
$740$		0			0
$741$	1.35714	+	3.23694i	0.0498559	+	0.118912i
$742$	20.6636			0.758583
$743$	1.33186	−	7.55333i	0.0488610	−	0.277105i	−0.950582	−	0.310473i	$-0.899512\pi$
$743$	1.33186	−	7.55333i	0.0488610	−	0.277105i	0.999443	+	0.0333687i	$0.0106236\pi$
$744$	9.56649	+	8.02724i	0.350724	+	0.294293i
$745$		0			0
$746$	29.5731	−	10.7637i	1.08275	−	0.394089i
$747$	−9.32420	+	7.82393i	−0.341155	+	0.286263i
$748$	−32.6586	−	56.5664i	−1.19412	−	2.06827i
$749$	−0.385002	+	0.666843i	−0.0140677	+	0.0243659i
$750$		0			0
$751$	3.65755	+	20.7430i	0.133466	+	0.756923i	0.975916	+	0.218148i	$0.0700017\pi$
$751$	3.65755	+	20.7430i	0.133466	+	0.756923i	−0.842450	+	0.538775i	$0.818887\pi$
$752$	14.1620	−	24.5293i	0.516436	−	0.894493i
$753$	−8.19092	−	14.1871i	−0.298494	−	0.517006i
$754$	0.528376	−	0.443360i	0.0192423	−	0.0161462i
$755$		0			0
$756$	8.13141	+	2.95959i	0.295737	+	0.107639i
$757$	−3.29957	−	2.76867i	−0.119925	−	0.100629i	0.580853	−	0.814009i	$-0.302719\pi$
$757$	−3.29957	−	2.76867i	−0.119925	−	0.100629i	−0.700778	+	0.713379i	$0.747164\pi$
$758$	0.651197	−	3.69312i	0.0236525	−	0.134140i
$759$	−64.3955			−2.33741
$760$		0			0
$761$	−1.11318			−0.0403529			−0.0201764	−	0.999796i	$-0.506423\pi$
$761$	−1.11318			−0.0403529			−0.0201764	+	0.999796i	$0.506423\pi$
$762$	1.12401	−	6.37459i	0.0407187	−	0.230927i
$763$	3.14606	+	2.63986i	0.113895	+	0.0955694i
$764$	0.0162238	+	0.00590497i	0.000586956	+	0.000213634i
$765$		0			0
$766$	−13.8824	+	11.6487i	−0.501591	+	0.420885i
$767$	1.77032	+	3.06629i	0.0639227	+	0.110717i
$768$	4.54359	−	7.86973i	0.163953	−	0.283975i
$769$	1.71410	+	9.72113i	0.0618119	+	0.350553i	0.999990	+	0.00440066i	$0.00140078\pi$
$769$	1.71410	+	9.72113i	0.0618119	+	0.350553i	−0.938178	+	0.346152i	$0.887488\pi$
$770$		0			0
$771$	6.70576	−	11.6147i	0.241502	−	0.418294i
$772$	17.4804	+	30.2769i	0.629133	+	1.08969i
$773$	13.0788	−	10.9744i	0.470410	−	0.394721i	−0.376534	−	0.926403i	$-0.622884\pi$
$773$	13.0788	−	10.9744i	0.470410	−	0.394721i	0.846944	+	0.531682i	$0.178440\pi$
$774$	−28.5613	+	10.3955i	−1.02662	+	0.373658i
$775$		0			0
$776$	4.21457	+	3.53644i	0.151294	+	0.126951i
$777$	−6.55839	+	37.1945i	−0.235281	+	1.33434i
$778$	72.3761			2.59481
$779$	−6.76933	+	21.7964i	−0.242537	+	0.780936i
$780$		0			0
$781$	5.21243	−	29.5611i	0.186515	−	1.05778i
$782$	−55.1880	−	46.3082i	−1.97352	−	1.65598i
$783$	1.92537	+	0.700778i	0.0688072	+	0.0250438i
$784$	−11.7406	+	4.27323i	−0.419307	+	0.152615i
$785$		0			0
$786$	46.4287	+	80.4169i	1.65606	+	2.86838i
$787$	−5.82825	+	10.0948i	−0.207755	+	0.359842i	−0.951007	−	0.309170i	$-0.899949\pi$
$787$	−5.82825	+	10.0948i	−0.207755	+	0.359842i	0.743252	+	0.669011i	$0.233282\pi$
$788$	−0.212198	−	1.20344i	−0.00755925	−	0.0428707i
$789$	2.85786	+	16.2077i	0.101742	+	0.577010i
$790$		0			0
$791$	−9.23498	−	15.9955i	−0.328358	−	0.568733i
$792$	−8.25992	+	6.93090i	−0.293503	+	0.246279i
$793$	−0.797127	+	0.290130i	−0.0283068	+	0.0103028i
$794$	−15.5835	−	5.67194i	−0.553038	−	0.201289i
$795$		0			0
$796$	−11.8624	+	67.2747i	−0.420450	+	2.38449i
$797$	29.8609			1.05773			0.528864	−	0.848707i	$-0.322618\pi$
$797$	29.8609			1.05773			0.528864	+	0.848707i	$0.322618\pi$
$798$	−1.47589	−	30.7632i	−0.0522458	−	1.08901i
$799$	59.5220			2.10574
$800$		0			0
$801$	−5.02237	−	4.21427i	−0.177457	−	0.148904i
$802$	62.4932	+	22.7457i	2.20671	+	0.803178i
$803$	12.5887	−	4.58191i	0.444245	−	0.161692i
$804$	38.5229	−	32.3245i	1.35860	−	1.14000i
$805$		0			0
$806$	1.84771	−	3.20033i	0.0650829	−	0.112727i
$807$	4.20726	+	23.8606i	0.148103	+	0.839932i
$808$	−1.83151	−	10.3870i	−0.0644323	−	0.365414i
$809$	19.1756	−	33.2132i	0.674180	−	1.16771i	−0.302528	−	0.953140i	$-0.597831\pi$
$809$	19.1756	−	33.2132i	0.674180	−	1.16771i	0.976708	−	0.214573i	$-0.0688360\pi$
$810$		0			0
$811$	8.55127	−	7.17537i	0.300276	−	0.251961i	−0.480183	−	0.877168i	$-0.659430\pi$
$811$	8.55127	−	7.17537i	0.300276	−	0.251961i	0.780459	+	0.625207i	$0.214985\pi$
$812$	−3.18575	+	1.15952i	−0.111798	+	0.0406911i
$813$	5.97062	+	2.17313i	0.209399	+	0.0762150i
$814$	87.1612	+	73.1369i	3.05500	+	2.56345i
$815$		0			0
$816$	31.8503			1.11498
$817$	−21.3562	−	23.1057i	−0.747160	−	0.808367i
$818$	31.2935			1.09415
$819$	−0.183914	+	1.04303i	−0.00642649	+	0.0364464i
$820$		0			0
$821$	−7.18934	−	2.61671i	−0.250910	−	0.0913236i	0.213504	−	0.976942i	$-0.431513\pi$
$821$	−7.18934	−	2.61671i	−0.250910	−	0.0913236i	−0.464413	+	0.885619i	$0.653735\pi$
$822$	47.7330	−	17.3734i	1.66488	−	0.605966i
$823$	−25.4494	+	21.3546i	−0.887110	+	0.744373i	−0.967628	−	0.252380i	$-0.918787\pi$
$823$	−25.4494	+	21.3546i	−0.887110	+	0.744373i	0.0805185	+	0.996753i	$0.474342\pi$
$824$	−4.54825	−	7.87779i	−0.158446	−	0.274436i
$825$		0			0
$826$	−5.39493	−	30.5962i	−0.187714	−	1.06458i
$827$	0.591681	+	3.35559i	0.0205748	+	0.116685i	0.993365	−	0.115001i	$-0.0366870\pi$
$827$	0.591681	+	3.35559i	0.0205748	+	0.116685i	−0.972791	+	0.231686i	$0.925576\pi$
$828$	−15.5095	+	26.8633i	−0.538993	+	0.933563i
$829$	−2.21217	−	3.83160i	−0.0768320	−	0.133077i	0.825049	−	0.565060i	$-0.191147\pi$
$829$	−2.21217	−	3.83160i	−0.0768320	−	0.133077i	−0.901881	+	0.431984i	$0.857814\pi$
$830$		0			0
$831$	33.8366	−	12.3155i	1.17378	−	0.427221i
$832$	3.94007	+	1.43407i	0.136597	+	0.0497174i
$833$	−20.1132	−	16.8770i	−0.696880	−	0.584752i
$834$	−5.93906	+	33.6821i	−0.205653	+	1.16632i
$835$		0			0
$836$	−46.2035	−	23.7998i	−1.59798	−	0.823132i
$837$	10.9775			0.379438
$838$	7.63013	−	43.2726i	0.263579	−	1.49483i
$839$	−18.2406	−	15.3057i	−0.629736	−	0.528411i	0.271111	−	0.962548i	$-0.412609\pi$
$839$	−18.2406	−	15.3057i	−0.629736	−	0.528411i	−0.900847	+	0.434137i	$0.857053\pi$
$840$		0			0
$841$	26.4968	−	9.64403i	0.913681	−	0.332553i
$842$	−45.2136	+	37.9387i	−1.55816	+	1.30745i
$843$	3.58655	+	6.21208i	0.123527	+	0.213956i
$844$	−10.4952	+	18.1782i	−0.361259	+	0.625719i
$845$		0			0
$846$	−7.94477	−	45.0570i	−0.273147	−	1.54909i
$847$	8.10785	−	14.0432i	0.278589	−	0.482530i
$848$	8.50173	+	14.7254i	0.291951	+	0.505673i
$849$	21.9968	−	18.4575i	0.754929	−	0.633461i
$850$		0			0
$851$	66.0575	+	24.0430i	2.26442	+	0.824183i
$852$	−27.9039	−	23.4141i	−0.955971	−	0.802155i
$853$	0.769903	−	4.36634i	0.0263610	−	0.149501i	−0.968786	−	0.247898i	$-0.920260\pi$
$853$	0.769903	−	4.36634i	0.0263610	−	0.149501i	0.995147	+	0.0983970i	$0.0313715\pi$
$854$	7.44345			0.254710
$855$		0			0
$856$	0.604557			0.0206633
$857$	−4.68808	+	26.5874i	−0.160142	+	0.908208i	0.793792	+	0.608190i	$0.208104\pi$
$857$	−4.68808	+	26.5874i	−0.160142	+	0.908208i	−0.953933	+	0.300019i	$0.903007\pi$
$858$	6.15758	+	5.16682i	0.210216	+	0.176392i
$859$	12.8850	+	4.68976i	0.439631	+	0.160013i	0.552346	−	0.833615i	$-0.313733\pi$
$859$	12.8850	+	4.68976i	0.439631	+	0.160013i	−0.112715	+	0.993627i	$0.535955\pi$
$860$		0			0
$861$	−13.2907	+	11.1522i	−0.452947	+	0.380067i
$862$	−22.2790	−	38.5883i	−0.758825	−	1.31432i
$863$	26.2240	−	45.4213i	0.892676	−	1.54616i	0.0560208	−	0.998430i	$-0.482159\pi$
$863$	26.2240	−	45.4213i	0.892676	−	1.54616i	0.836655	−	0.547730i	$-0.184508\pi$
$864$	3.13378	+	17.7725i	0.106613	+	0.604634i
$865$		0			0
$866$	−2.05341	+	3.55662i	−0.0697778	+	0.120859i
$867$	14.5078	+	25.1282i	0.492709	+	0.853398i
$868$	−13.9141	+	11.6753i	−0.472276	+	0.396286i
$869$	−9.08617	+	3.30710i	−0.308227	+	0.112186i
$870$		0			0
$871$	−2.44819	−	2.05428i	−0.0829538	−	0.0696065i
$872$	0.559923	−	3.17548i	0.0189614	−	0.107535i
$873$	−9.31414			−0.315236
$874$	−56.8658	−	7.23758i	−1.92352	−	0.244815i
$875$		0			0
$876$	2.82297	−	16.0098i	0.0953792	−	0.540923i
$877$	31.2742	+	26.2422i	1.05606	+	0.886136i	0.993717	−	0.111919i	$-0.0356998\pi$
$877$	31.2742	+	26.2422i	1.05606	+	0.886136i	0.0623382	+	0.998055i	$0.480144\pi$
$878$	69.5298	+	25.3068i	2.34652	+	0.854062i
$879$	64.5765	−	23.5039i	2.17811	−	0.792768i
$880$		0			0
$881$	23.8807	+	41.3627i	0.804563	+	1.39354i	0.916586	+	0.399838i	$0.130934\pi$
$881$	23.8807	+	41.3627i	0.804563	+	1.39354i	−0.112023	+	0.993706i	$0.535733\pi$
$882$	−10.0909	+	17.4780i	−0.339778	+	0.588513i
$883$	−5.57488	−	31.6167i	−0.187610	−	1.06399i	−0.922556	−	0.385863i	$-0.873904\pi$
$883$	−5.57488	−	31.6167i	−0.187610	−	1.06399i	0.734946	−	0.678125i	$-0.237207\pi$
$884$	0.874713	+	4.96074i	0.0294198	+	0.166848i
$885$		0			0
$886$	−28.0629	−	48.6064i	−0.942792	−	1.63296i
$887$	6.75510	−	5.66820i	0.226814	−	0.190319i	−0.522298	−	0.852763i	$-0.674925\pi$
$887$	6.75510	−	5.66820i	0.226814	−	0.190319i	0.749112	+	0.662444i	$0.230481\pi$
$888$	27.8649	−	10.1420i	0.935084	−	0.340343i
$889$	1.89999	+	0.691539i	0.0637235	+	0.0231935i
$890$		0			0
$891$	−8.96205	+	50.8263i	−0.300240	+	1.70275i
$892$	−4.37586			−0.146515
$893$	39.8346	−	25.6192i	1.33301	−	0.857314i
$894$	20.2002			0.675595
$895$		0			0
$896$	−10.2224	−	8.57759i	−0.341505	−	0.286557i
$897$	4.66669	+	1.69854i	0.155816	+	0.0567125i
$898$	−26.9139	+	9.79587i	−0.898130	+	0.326892i
$899$	−3.29461	+	2.76451i	−0.109881	+	0.0922014i
$900$		0			0
$901$	−17.8661	+	30.9450i	−0.595206	+	1.03093i
$902$	9.07627	+	51.4741i	0.302207	+	1.71390i
$903$	−4.15332	−	23.5546i	−0.138214	−	0.783849i
$904$	−7.25071	+	12.5586i	−0.241155	+	0.417693i
$905$		0			0
$906$	−71.1810	+	59.7279i	−2.36483	+	1.98433i
$907$	9.71693	−	3.53667i	0.322645	−	0.117433i	−0.175620	−	0.984458i	$-0.556193\pi$
$907$	9.71693	−	3.53667i	0.322645	−	0.117433i	0.498265	+	0.867025i	$0.333971\pi$
$908$	10.1145	+	3.68139i	0.335663	+	0.122171i
$909$	13.6785	+	11.4776i	0.453686	+	0.380688i
$910$		0			0
$911$	5.25941			0.174252			0.0871260	−	0.996197i	$-0.472232\pi$
$911$	5.25941			0.174252			0.0871260	+	0.996197i	$0.472232\pi$
$912$	21.3155	−	13.7089i	0.705827	−	0.453946i
$913$	−28.8557			−0.954985
$914$	0.0762343	−	0.432346i	0.00252161	−	0.0143007i
$915$		0			0
$916$	−13.2193	−	4.81143i	−0.436778	−	0.158974i
$917$	−27.2563	+	9.92047i	−0.900081	+	0.327603i
$918$	−20.4637	+	17.1711i	−0.675403	+	0.566731i
$919$	−0.101184	−	0.175255i	−0.00333774	−	0.00578114i	0.864352	−	0.502888i	$-0.167729\pi$
$919$	−0.101184	−	0.175255i	−0.00333774	−	0.00578114i	−0.867689	+	0.497107i	$0.834396\pi$
$920$		0			0
$921$	6.34453	+	35.9816i	0.209060	+	1.18564i
$922$	−14.4512	−	81.9569i	−0.475925	−	2.69911i
$923$	−1.15746	+	2.00479i	−0.0380984	+	0.0659883i
$924$	−19.7544	−	34.2155i	−0.649871	−	1.12561i
$925$		0			0
$926$	14.8774	−	5.41492i	0.488901	−	0.177945i
$927$	14.4712	+	5.26707i	0.475296	+	0.172993i
$928$	−5.41624	−	4.54477i	−0.177797	−	0.149189i
$929$	3.23698	−	18.3578i	0.106202	−	0.602301i	−0.884532	−	0.466480i	$-0.845522\pi$
$929$	3.23698	−	18.3578i	0.106202	−	0.602301i	0.990733	−	0.135821i	$-0.0433671\pi$
$930$		0			0
$931$	−20.7247	−	2.63773i	−0.679223	−	0.0864480i
$932$	−71.8151			−2.35238
$933$	−9.59533	+	54.4178i	−0.314137	+	1.78156i
$934$	35.8150	+	30.0524i	1.17190	+	0.983344i
$935$		0			0
$936$	0.781404	−	0.284408i	0.0255410	−	0.00929615i
$937$	38.6935	−	32.4677i	1.26406	−	1.06067i	0.268824	−	0.963189i	$-0.413365\pi$
$937$	38.6935	−	32.4677i	1.26406	−	1.06067i	0.995237	−	0.0974836i	$-0.0310794\pi$
$938$	14.0215	+	24.2859i	0.457818	+	0.792964i
$939$	−11.4568	+	19.8438i	−0.373880	+	0.647579i
$940$		0			0
$941$	−2.87903	−	16.3278i	−0.0938538	−	0.532271i	−0.995093	−	0.0989484i	$-0.968452\pi$
$941$	−2.87903	−	16.3278i	−0.0938538	−	0.532271i	0.901239	−	0.433323i	$-0.142659\pi$
$942$	0.681118	−	1.17973i	0.0221920	−	0.0384377i
$943$	16.1463	+	27.9663i	0.525797	+	0.910708i
$944$	19.5840	−	16.4329i	0.637405	−	0.534847i
$945$		0			0
$946$	−67.7100	−	24.6444i	−2.20144	−	0.801259i
$947$	−28.6765	−	24.0625i	−0.931862	−	0.781925i	0.0442887	−	0.999019i	$-0.485898\pi$
$947$	−28.6765	−	24.0625i	−0.931862	−	0.781925i	−0.976151	+	0.217094i	$0.930342\pi$
$948$	−2.03754	+	11.5555i	−0.0661763	+	0.375304i
$949$	−1.03315			−0.0335374
$950$		0			0
$951$	13.5526			0.439474
$952$	1.64839	−	9.34847i	0.0534245	−	0.302986i
$953$	−32.5326	−	27.2981i	−1.05384	−	0.884273i	−0.0603438	−	0.998178i	$-0.519220\pi$
$953$	−32.5326	−	27.2981i	−1.05384	−	0.884273i	−0.993492	+	0.113905i	$0.963664\pi$
$954$	25.8095	+	9.39387i	0.835612	+	0.304138i
$955$		0			0
$956$	−22.0874	+	18.5336i	−0.714359	+	0.599418i
$957$	−4.67748	−	8.10162i	−0.151201	−	0.261888i
$958$	−29.9380	+	51.8541i	−0.967252	+	1.67533i
$959$	2.75529	+	15.6260i	0.0889728	+	0.504590i
$960$		0			0
$961$	3.97887	−	6.89160i	0.128351	−	0.222310i
$962$	−4.38740	−	7.59919i	−0.141455	−	0.245008i
$963$	−0.784034	+	0.657883i	−0.0252652	+	0.0212000i
$964$	−39.1657	+	14.2552i	−1.26144	+	0.459128i
$965$		0			0
$966$	−33.3818	−	28.0107i	−1.07404	−	0.901228i
$967$	−2.81797	+	15.9815i	−0.0906197	+	0.513930i	0.905382	+	0.424598i	$0.139584\pi$
$967$	−2.81797	+	15.9815i	−0.0906197	+	0.513930i	−0.996002	+	0.0893324i	$0.971527\pi$
$968$	−12.7315			−0.409206
$969$	47.3460	+	24.3882i	1.52097	+	0.783463i
$970$		0			0
$971$	−3.05833	+	17.3447i	−0.0981465	+	0.556617i	0.895591	+	0.444878i	$0.146753\pi$
$971$	−3.05833	+	17.3447i	−0.0981465	+	0.556617i	−0.993738	+	0.111738i	$0.964358\pi$
$972$	34.5910	+	29.0253i	1.10951	+	0.930988i
$973$	−10.0392	−	3.65396i	−0.321841	−	0.117140i
$974$	28.3229	−	10.3087i	0.907524	−	0.330312i
$975$		0			0
$976$	3.06250	+	5.30441i	0.0980283	+	0.169790i
$977$	0.0604375	−	0.104681i	0.00193357	−	0.00334903i	−0.865057	−	0.501674i	$-0.832718\pi$
$977$	0.0604375	−	0.104681i	0.00193357	−	0.00334903i	0.866991	+	0.498325i	$0.166051\pi$
$978$	17.0342	+	96.6056i	0.544693	+	3.08911i
$979$	−2.69898	−	15.3067i	−0.0862597	−	0.489203i
$980$		0			0
$981$	2.72943	+	4.72751i	0.0871439	+	0.150938i
$982$	37.8874	−	31.7913i	1.20904	−	1.01450i
$983$	21.3108	−	7.75648i	0.679708	−	0.247393i	0.0209857	−	0.999780i	$-0.493320\pi$
$983$	21.3108	−	7.75648i	0.679708	−	0.247393i	0.658722	+	0.752386i	$0.271097\pi$
$984$	12.8004	+	4.65898i	0.408063	+	0.148523i
$985$		0			0
$986$	1.81738	−	10.3069i	0.0578773	−	0.328239i
$987$	36.0033			1.14600
$988$	2.72058	+	2.94344i	0.0865530	+	0.0936434i
$989$	−44.5179			−1.41559
$990$		0			0
$991$	−41.1874	−	34.5603i	−1.30836	−	1.09784i	−0.988635	−	0.150334i	$-0.951965\pi$
$991$	−41.1874	−	34.5603i	−1.30836	−	1.09784i	−0.319725	−	0.947510i	$-0.603591\pi$
$992$	−35.5963	−	12.9560i	−1.13018	−	0.411353i
$993$	24.7545	−	9.00991i	0.785561	−	0.285921i
$994$	15.5605	−	13.0568i	0.493550	−	0.414137i
$995$		0			0
$996$	−17.5083	+	30.3252i	−0.554770	+	0.960890i
$997$	−6.38045	−	36.1853i	−0.202071	−	1.14600i	−0.901983	−	0.431772i	$-0.857889\pi$
$997$	−6.38045	−	36.1853i	−0.202071	−	1.14600i	0.699912	−	0.714229i	$-0.253223\pi$
$998$	15.7123	+	89.1091i	0.497365	+	2.82070i
$999$	13.0331	−	22.5739i	0.412348	−	0.714207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.c.226.1		18
5.2	odd	4		475.2.u.b.74.2		36
5.3	odd	4		475.2.u.b.74.5		36
5.4	even	2		95.2.k.a.36.3	✓	18
15.14	odd	2		855.2.bs.c.226.1		18
19.3	odd	18		9025.2.a.cf.1.7		9
19.9	even	9	inner	475.2.l.c.351.1		18
19.16	even	9		9025.2.a.cc.1.3		9
95.9	even	18		95.2.k.a.66.3	yes	18
95.28	odd	36		475.2.u.b.199.2		36
95.47	odd	36		475.2.u.b.199.5		36
95.54	even	18		1805.2.a.v.1.7		9
95.79	odd	18		1805.2.a.s.1.3		9
285.104	odd	18		855.2.bs.c.541.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.36.3	✓	18	5.4	even	2
95.2.k.a.66.3	yes	18	95.9	even	18
475.2.l.c.226.1		18	1.1	even	1	trivial
475.2.l.c.351.1		18	19.9	even	9	inner
475.2.u.b.74.2		36	5.2	odd	4
475.2.u.b.74.5		36	5.3	odd	4
475.2.u.b.199.2		36	95.28	odd	36
475.2.u.b.199.5		36	95.47	odd	36
855.2.bs.c.226.1		18	15.14	odd	2
855.2.bs.c.541.1		18	285.104	odd	18
1805.2.a.s.1.3		9	95.79	odd	18
1805.2.a.v.1.7		9	95.54	even	18
9025.2.a.cc.1.3		9	19.16	even	9
9025.2.a.cf.1.7		9	19.3	odd	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.370282 + 2.09998i) q^{2} +(-1.70859 - 1.43367i) q^{3} +(-2.39340 - 0.871127i) q^{4} +(3.64334 - 3.05712i) q^{6} +(0.742812 + 1.28659i) q^{7} +(0.583208 - 1.01015i) q^{8} +(0.342900 + 1.94468i) q^{9} +O(q^{10})\)	\(q+(-0.370282 + 2.09998i) q^{2} +(-1.70859 - 1.43367i) q^{3} +(-2.39340 - 0.871127i) q^{4} +(3.64334 - 3.05712i) q^{6} +(0.742812 + 1.28659i) q^{7} +(0.583208 - 1.01015i) q^{8} +(0.342900 + 1.94468i) q^{9} +(-2.34068 + 4.05417i) q^{11} +(2.84042 + 4.91975i) q^{12} +(0.276562 - 0.232063i) q^{13} +(-2.97685 + 1.08349i) q^{14} +(-1.99691 - 1.67560i) q^{16} +(0.951255 - 5.39483i) q^{17} -4.21075 q^{18} +(-1.68540 - 4.01988i) q^{19} +(0.575390 - 3.26320i) q^{21} +(-7.64695 - 6.41655i) q^{22} +(-5.79545 - 2.10937i) q^{23} +(-2.44468 + 0.889790i) q^{24} +(0.384921 + 0.666703i) q^{26} +(-1.14343 + 1.98049i) q^{27} +(-0.657066 - 3.72641i) q^{28} +(-0.155581 - 0.882346i) q^{29} +(-2.40012 - 4.15713i) q^{31} +(6.04520 - 5.07252i) q^{32} +(9.81160 - 3.57113i) q^{33} +(10.9768 + 3.99522i) q^{34} +(0.873368 - 4.95311i) q^{36} -11.3982 q^{37} +(9.06572 - 2.05081i) q^{38} -0.805233 q^{39} +(-4.01104 - 3.36566i) q^{41} +(6.63958 + 2.41661i) q^{42} +(6.78295 - 2.46879i) q^{43} +(9.13387 - 7.66423i) q^{44} +(6.57558 - 11.3892i) q^{46} +(1.88678 + 10.7005i) q^{47} +(1.00962 + 5.72583i) q^{48} +(2.39646 - 4.15079i) q^{49} +(-9.35973 + 7.85374i) q^{51} +(-0.864081 + 0.314500i) q^{52} +(-6.12941 - 2.23092i) q^{53} +(-3.73558 - 3.13452i) q^{54} +1.73286 q^{56} +(-2.88354 + 9.28462i) q^{57} +1.91051 q^{58} +(-1.70300 + 9.65818i) q^{59} +(-2.20795 - 0.803626i) q^{61} +(9.61858 - 3.50088i) q^{62} +(-2.24730 + 1.88571i) q^{63} +(5.80697 + 10.0580i) q^{64} +(3.86622 + 21.9264i) q^{66} +(-1.53717 - 8.71774i) q^{67} +(-6.97632 + 12.0833i) q^{68} +(6.87787 + 11.9128i) q^{69} +(-6.02538 + 2.19306i) q^{71} +(2.16439 + 0.787775i) q^{72} +(-2.19219 - 1.83946i) q^{73} +(4.22054 - 23.9359i) q^{74} +(0.532020 + 11.0894i) q^{76} -6.95473 q^{77} +(0.298164 - 1.69097i) q^{78} +(1.58226 + 1.32767i) q^{79} +(10.3598 - 3.77066i) q^{81} +(8.55302 - 7.17684i) q^{82} +(3.08199 + 5.33816i) q^{83} +(-4.21980 + 7.30890i) q^{84} +(2.67280 + 15.1582i) q^{86} +(-0.999172 + 1.73062i) q^{87} +(2.73020 + 4.72885i) q^{88} +(-2.54338 + 2.13415i) q^{89} +(0.504004 + 0.183442i) q^{91} +(12.0333 + 10.0971i) q^{92} +(-1.85915 + 10.5438i) q^{93} -23.1693 q^{94} -17.6011 q^{96} +(-0.819060 + 4.64512i) q^{97} +(7.82919 + 6.56947i) q^{98} +(-8.68669 - 3.16170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

Introduction

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