LMFDB - Embedded newform 475.2.u.b.74.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(24,475)]

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([9, 16]))

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

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

chi := DirichletCharacter("475.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.u (of order $18$, degree $6$, not 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:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			74.2
Character	$\chi$	$=$	475.74
Dual form			475.2.u.b.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.09998 - 0.370282i) q^{2} +(-1.43367 + 1.70859i) q^{3} +(2.39340 + 0.871127i) q^{4} +(3.64334 - 3.05712i) q^{6} +(-1.28659 + 0.742812i) q^{7} +(-1.01015 - 0.583208i) q^{8} +(-0.342900 - 1.94468i) q^{9} +O(q^{10})$	\(q+(-2.09998 - 0.370282i) q^{2} +(-1.43367 + 1.70859i) q^{3} +(2.39340 + 0.871127i) q^{4} +(3.64334 - 3.05712i) q^{6} +(-1.28659 + 0.742812i) q^{7} +(-1.01015 - 0.583208i) q^{8} +(-0.342900 - 1.94468i) q^{9} +(-2.34068 + 4.05417i) q^{11} +(-4.91975 + 2.84042i) q^{12} +(-0.232063 - 0.276562i) q^{13} +(2.97685 - 1.08349i) q^{14} +(-1.99691 - 1.67560i) q^{16} +(5.39483 + 0.951255i) q^{17} +4.21075i q^{18} +(1.68540 + 4.01988i) q^{19} +(0.575390 - 3.26320i) q^{21} +(6.41655 - 7.64695i) q^{22} +(-2.10937 + 5.79545i) q^{23} +(2.44468 - 0.889790i) q^{24} +(0.384921 + 0.666703i) q^{26} +(-1.98049 - 1.14343i) q^{27} +(-3.72641 + 0.657066i) q^{28} +(0.155581 + 0.882346i) q^{29} +(-2.40012 - 4.15713i) q^{31} +(5.07252 + 6.04520i) q^{32} +(-3.57113 - 9.81160i) q^{33} +(-10.9768 - 3.99522i) q^{34} +(0.873368 - 4.95311i) q^{36} -11.3982i q^{37} +(-2.05081 - 9.06572i) q^{38} +0.805233 q^{39} +(-4.01104 - 3.36566i) q^{41} +(-2.41661 + 6.63958i) q^{42} +(-2.46879 - 6.78295i) q^{43} +(-9.13387 + 7.66423i) q^{44} +(6.57558 - 11.3892i) q^{46} +(-10.7005 + 1.88678i) q^{47} +(5.72583 - 1.00962i) q^{48} +(-2.39646 + 4.15079i) q^{49} +(-9.35973 + 7.85374i) q^{51} +(-0.314500 - 0.864081i) q^{52} +(-2.23092 + 6.12941i) q^{53} +(3.73558 + 3.13452i) q^{54} +1.73286 q^{56} +(-9.28462 - 2.88354i) q^{57} -1.91051i q^{58} +(1.70300 - 9.65818i) q^{59} +(-2.20795 - 0.803626i) q^{61} +(3.50088 + 9.61858i) q^{62} +(1.88571 + 2.24730i) q^{63} +(-5.80697 - 10.0580i) q^{64} +(3.86622 + 21.9264i) q^{66} +(8.71774 - 1.53717i) q^{67} +(12.0833 + 6.97632i) q^{68} +(-6.87787 - 11.9128i) q^{69} +(-6.02538 + 2.19306i) q^{71} +(-0.787775 + 2.16439i) q^{72} +(-1.83946 + 2.19219i) q^{73} +(-4.22054 + 23.9359i) q^{74} +(0.532020 + 11.0894i) q^{76} -6.95473i q^{77} +(-1.69097 - 0.298164i) q^{78} +(-1.58226 - 1.32767i) q^{79} +(10.3598 - 3.77066i) q^{81} +(7.17684 + 8.55302i) q^{82} +(5.33816 - 3.08199i) q^{83} +(4.21980 - 7.30890i) q^{84} +(2.67280 + 15.1582i) q^{86} +(-1.73062 - 0.999172i) q^{87} +(4.72885 - 2.73020i) q^{88} +(2.54338 - 2.13415i) q^{89} +(0.504004 + 0.183442i) q^{91} +(-10.0971 + 12.0333i) q^{92} +(10.5438 + 1.85915i) q^{93} +23.1693 q^{94} -17.6011 q^{96} +(-4.64512 - 0.819060i) q^{97} +(6.56947 - 7.82919i) q^{98} +(8.68669 + 3.16170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9}+O(q^{10}) $ 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9	$ 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9} + 24 q^{14} - 6 q^{16} - 42 q^{21} + 30 q^{24} + 6 q^{26} - 30 q^{29} - 36 q^{31} + 24 q^{34} + 150 q^{36} - 72 q^{39} - 60 q^{41} - 84 q^{44} + 18 q^{46} - 18 q^{49} - 90 q^{51} + 132 q^{54} - 36 q^{59} - 60 q^{61} - 72 q^{64} + 78 q^{66} - 30 q^{69} - 24 q^{71} + 30 q^{74} - 66 q^{76} + 102 q^{79} + 54 q^{81} - 96 q^{84} + 126 q^{86} + 108 q^{89} + 60 q^{91} - 60 q^{94} - 132 q^{96} + 186 q^{99}+O(q^{100}) $ 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9 + 24 * q^14 - 6 * q^16 - 42 * q^21 + 30 * q^24 + 6 * q^26 - 30 * q^29 - 36 * q^31 + 24 * q^34 + 150 * q^36 - 72 * q^39 - 60 * q^41 - 84 * q^44 + 18 * q^46 - 18 * q^49 - 90 * q^51 + 132 * q^54 - 36 * q^59 - 60 * q^61 - 72 * q^64 + 78 * q^66 - 30 * q^69 - 24 * q^71 + 30 * q^74 - 66 * q^76 + 102 * q^79 + 54 * q^81 - 96 * q^84 + 126 * q^86 + 108 * q^89 + 60 * q^91 - 60 * q^94 - 132 * q^96 + 186 * 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 $

$2$	−2.09998	−	0.370282i	−1.48491	−	0.261829i	−0.628370	−	0.777915i	$-0.716277\pi$
$2$	−2.09998	−	0.370282i	−1.48491	−	0.261829i	−0.856537	+	0.516086i	$0.827389\pi$
$3$	−1.43367	+	1.70859i	−0.827732	+	0.986452i	0.172267	+	0.985050i	$0.444891\pi$
$3$	−1.43367	+	1.70859i	−0.827732	+	0.986452i	−0.999999	+	0.00140187i	$0.999554\pi$
$4$	2.39340	+	0.871127i	1.19670	+	0.435563i
$5$		0			0
$5$		0			0
$6$	3.64334	−	3.05712i	1.48739	−	1.24807i
$7$	−1.28659	+	0.742812i	−0.486285	+	0.280757i	−0.723032	−	0.690815i	$-0.757252\pi$
$7$	−1.28659	+	0.742812i	−0.486285	+	0.280757i	0.236747	+	0.971571i	$0.423919\pi$
$8$	−1.01015	−	0.583208i	−0.357140	−	0.206195i
$9$	−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	$0.917281\pi$
$12$	−4.91975	+	2.84042i	−1.42021	+	0.819958i
$13$	−0.232063	−	0.276562i	−0.0643628	−	0.0767046i	0.732902	−	0.680334i	$-0.238165\pi$
$13$	−0.232063	−	0.276562i	−0.0643628	−	0.0767046i	−0.797265	+	0.603629i	$0.793721\pi$
$14$	2.97685	−	1.08349i	0.795598	−	0.289574i
$15$		0			0
$16$	−1.99691	−	1.67560i	−0.499227	−	0.418901i
$17$	5.39483	+	0.951255i	1.30844	+	0.230713i	0.784014	−	0.620743i	$-0.213169\pi$
$17$	5.39483	+	0.951255i	1.30844	+	0.230713i	0.524425	+	0.851456i	$0.324280\pi$
$18$			4.21075i			0.992484i
$19$	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
$22$	6.41655	−	7.64695i	1.36801	−	1.63033i
$23$	−2.10937	+	5.79545i	−0.439834	+	1.20843i	0.499766	+	0.866161i	$0.333419\pi$
$23$	−2.10937	+	5.79545i	−0.439834	+	1.20843i	−0.939600	+	0.342274i	$0.888803\pi$
$24$	2.44468	−	0.889790i	0.499018	−	0.181628i
$25$		0			0
$26$	0.384921	+	0.666703i	0.0754892	+	0.130751i
$27$	−1.98049	−	1.14343i	−0.381145	−	0.220054i
$28$	−3.72641	+	0.657066i	−0.704225	+	0.124174i
$29$	0.155581	+	0.882346i	0.0288907	+	0.163848i	0.995840	−	0.0911225i	$-0.0290455\pi$
$29$	0.155581	+	0.882346i	0.0288907	+	0.163848i	−0.966949	+	0.254970i	$0.917934\pi$
$30$		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	$0.975199\pi$
$32$	5.07252	+	6.04520i	0.896704	+	1.06865i
$33$	−3.57113	−	9.81160i	−0.621654	−	1.70798i
$34$	−10.9768	−	3.99522i	−1.88250	−	0.685175i
$35$		0			0
$36$	0.873368	−	4.95311i	0.145561	−	0.825519i
$37$		−	11.3982i		−	1.87385i	−0.349534	−	0.936924i	$-0.613660\pi$
$37$		−	11.3982i		−	1.87385i	0.349534	−	0.936924i	$-0.386340\pi$
$38$	−2.05081	−	9.06572i	−0.332686	−	1.47065i
$39$	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	$0.856298\pi$
$42$	−2.41661	+	6.63958i	−0.372891	+	1.02451i
$43$	−2.46879	−	6.78295i	−0.376487	−	1.03439i	−0.972802	−	0.231639i	$-0.925591\pi$
$43$	−2.46879	−	6.78295i	−0.376487	−	1.03439i	0.596314	−	0.802751i	$-0.296631\pi$
$44$	−9.13387	+	7.66423i	−1.37698	+	1.15543i
$45$		0			0
$46$	6.57558	−	11.3892i	0.969516	−	1.67925i
$47$	−10.7005	+	1.88678i	−1.56082	+	0.275215i	−0.886326	−	0.463062i	$-0.846751\pi$
$47$	−10.7005	+	1.88678i	−1.56082	+	0.275215i	−0.674497	+	0.738278i	$0.735639\pi$
$48$	5.72583	−	1.00962i	0.826452	−	0.145726i
$49$	−2.39646	+	4.15079i	−0.342351	+	0.592970i
$50$		0			0
$51$	−9.35973	+	7.85374i	−1.31062	+	1.09974i
$52$	−0.314500	−	0.864081i	−0.0436133	−	0.119827i
$53$	−2.23092	+	6.12941i	−0.306441	+	0.841940i	0.686902	+	0.726750i	$0.258970\pi$
$53$	−2.23092	+	6.12941i	−0.306441	+	0.841940i	−0.993343	+	0.115190i	$0.963252\pi$
$54$	3.73558	+	3.13452i	0.508348	+	0.426555i
$55$		0			0
$56$	1.73286			0.231563
$57$	−9.28462	−	2.88354i	−1.22978	−	0.381934i
$58$		−	1.91051i		−	0.250863i
$59$	1.70300	−	9.65818i	0.221711	−	1.25739i	−0.647162	−	0.762353i	$-0.724044\pi$
$59$	1.70300	−	9.65818i	0.221711	−	1.25739i	0.868873	−	0.495035i	$-0.164845\pi$
$60$		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	$0.659174\pi$
$62$	3.50088	+	9.61858i	0.444612	+	1.22156i
$63$	1.88571	+	2.24730i	0.237577	+	0.283133i
$64$	−5.80697	−	10.0580i	−0.725871	−	1.25725i
$65$		0			0
$66$	3.86622	+	21.9264i	0.475899	+	2.69896i
$67$	8.71774	−	1.53717i	1.06504	−	0.187796i	0.386449	−	0.922311i	$-0.373701\pi$
$67$	8.71774	−	1.53717i	1.06504	−	0.187796i	0.678592	+	0.734515i	$0.262590\pi$
$68$	12.0833	+	6.97632i	1.46532	+	0.846003i
$69$	−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	$0.513132\pi$
$72$	−0.787775	+	2.16439i	−0.0928402	+	0.255076i
$73$	−1.83946	+	2.19219i	−0.215293	+	0.256576i	−0.862872	−	0.505422i	$-0.831337\pi$
$73$	−1.83946	+	2.19219i	−0.215293	+	0.256576i	0.647580	+	0.761998i	$0.275781\pi$
$74$	−4.22054	+	23.9359i	−0.490628	+	2.78249i
$75$		0			0
$76$	0.532020	+	11.0894i	0.0610268	+	1.27204i
$77$		−	6.95473i		−	0.792566i
$78$	−1.69097	−	0.298164i	−0.191465	−	0.0337604i
$79$	−1.58226	−	1.32767i	−0.178018	−	0.149375i	0.549425	−	0.835543i	$-0.314847\pi$
$79$	−1.58226	−	1.32767i	−0.178018	−	0.149375i	−0.727443	+	0.686168i	$0.759291\pi$
$80$		0			0
$81$	10.3598	−	3.77066i	1.15109	−	0.418962i
$82$	7.17684	+	8.55302i	0.792549	+	0.944523i
$83$	5.33816	−	3.08199i	0.585939	−	0.338292i	−0.177551	−	0.984112i	$-0.556818\pi$
$83$	5.33816	−	3.08199i	0.585939	−	0.338292i	0.763490	+	0.645820i	$0.223484\pi$
$84$	4.21980	−	7.30890i	0.460418	−	0.797467i
$85$		0			0
$86$	2.67280	+	15.1582i	0.288215	+	1.63455i
$87$	−1.73062	−	0.999172i	−0.185542	−	0.107122i
$88$	4.72885	−	2.73020i	0.504097	−	0.291040i
$89$	2.54338	−	2.13415i	0.269598	−	0.226220i	−0.497959	−	0.867201i	$-0.665917\pi$
$89$	2.54338	−	2.13415i	0.269598	−	0.226220i	0.767556	+	0.640981i	$0.221472\pi$
$90$		0			0
$91$	0.504004	+	0.183442i	0.0528340	+	0.0192300i
$92$	−10.0971	+	12.0333i	−1.05270	+	1.25456i
$93$	10.5438	+	1.85915i	1.09334	+	0.192785i
$94$	23.1693			2.38974
$95$		0			0
$96$	−17.6011			−1.79640
$97$	−4.64512	−	0.819060i	−0.471641	−	0.0831630i	−0.0672241	−	0.997738i	$-0.521414\pi$
$97$	−4.64512	−	0.819060i	−0.471641	−	0.0831630i	−0.404416	+	0.914575i	$0.632525\pi$
$98$	6.56947	−	7.82919i	0.663617	−	0.790867i
$99$	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	$0.129245\pi$
$102$	22.5633	−	13.0269i	2.23410	−	1.28986i
$103$	−6.75385	−	3.89934i	−0.665476	−	0.384213i	0.128884	−	0.991660i	$-0.458860\pi$
$103$	−6.75385	−	3.89934i	−0.665476	−	0.384213i	−0.794360	+	0.607447i	$0.792194\pi$
$104$	0.0731245	+	0.414709i	0.00717044	+	0.0406656i
$105$		0			0
$106$	6.95450	−	12.0455i	0.675481	−	1.16997i
$107$	−0.448864	+	0.259152i	−0.0433933	+	0.0250531i	−0.521540	−	0.853227i	$-0.674642\pi$
$107$	−0.448864	+	0.259152i	−0.0433933	+	0.0250531i	0.478146	+	0.878280i	$0.341309\pi$
$108$	−3.74402	−	4.46195i	−0.360269	−	0.429352i
$109$	−2.59771	+	0.945488i	−0.248815	+	0.0905614i	−0.463417	−	0.886140i	$-0.653377\pi$
$109$	−2.59771	+	0.945488i	−0.248815	+	0.0905614i	0.214602	+	0.976702i	$0.431155\pi$
$110$		0			0
$111$	19.4747	+	16.3413i	1.84846	+	1.55104i
$112$	3.81386	+	0.672486i	0.360376	+	0.0635440i
$113$			12.4325i			1.16955i	0.811197	+	0.584774i	$0.198817\pi$
$113$			12.4325i			1.16955i	−0.811197	+	0.584774i	$0.801183\pi$
$114$	18.4297	+	9.49329i	1.72610	+	0.889128i
$115$		0			0
$116$	−0.396266	+	2.24734i	−0.0367924	+	0.208660i
$117$	−0.458251	+	0.546123i	−0.0423654	+	0.0504891i
$118$	−7.15250	+	19.6513i	−0.658441	+	1.80905i
$119$	−7.64754	+	2.78348i	−0.701049	+	0.255161i
$120$		0			0
$121$	−5.45753	−	9.45272i	−0.496139	−	0.859339i
$122$	4.33906	+	2.50516i	0.392840	+	0.226806i
$123$	11.5010	−	2.02794i	1.03701	−	0.182853i
$124$	−2.12306	−	12.0405i	−0.190656	−	1.08127i
$125$		0			0
$126$	−3.12780	−	5.41751i	−0.278647	−	0.482630i
$127$	0.874829	+	1.04258i	0.0776285	+	0.0925141i	0.803461	−	0.595358i	$-0.202990\pi$
$127$	0.874829	+	1.04258i	0.0776285	+	0.0925141i	−0.725832	+	0.687872i	$0.758545\pi$
$128$	3.07213	+	8.44062i	0.271541	+	0.746052i
$129$	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	$0.730388\pi$
$132$		−	26.5940i		−	2.31471i
$133$	−5.15444	−	3.91999i	−0.446946	−	0.339907i
$134$	−18.8762			−1.63066
$135$		0			0
$136$	−4.89479	−	4.10721i	−0.419725	−	0.352191i
$137$	−3.65291	+	10.0363i	−0.312089	+	0.857458i	0.680145	+	0.733077i	$0.261917\pi$
$137$	−3.65291	+	10.0363i	−0.312089	+	0.857458i	−0.992235	+	0.124381i	$0.960306\pi$
$138$	10.0323	+	27.5634i	0.854002	+	2.34635i
$139$	5.50879	−	4.62243i	0.467250	−	0.392069i	−0.378541	−	0.925585i	$-0.623574\pi$
$139$	5.50879	−	4.62243i	0.467250	−	0.392069i	0.845790	+	0.533516i	$0.179129\pi$
$140$		0			0
$141$	12.1172	−	20.9877i	1.02046	−	1.76748i
$142$	13.4652	−	2.37428i	1.12997	−	0.199245i
$143$	1.66442	−	0.293481i	0.139185	−	0.0245422i
$144$	−2.57378	+	4.45792i	−0.214482	+	0.371493i
$145$		0			0
$146$	4.67455	−	3.92241i	0.386869	−	0.324621i
$147$	−3.65624	−	10.0454i	−0.301561	−	0.828533i
$148$	9.92925	−	27.2804i	0.816179	−	2.24243i
$149$	−3.25360	−	2.73009i	−0.266545	−	0.223658i	0.499713	−	0.866191i	$-0.333439\pi$
$149$	−3.25360	−	2.73009i	−0.266545	−	0.223658i	−0.766258	+	0.642533i	$0.777883\pi$
$150$		0			0
$151$	−19.5373			−1.58992			−0.794961	−	0.606660i	$-0.792509\pi$
$151$	−19.5373			−1.58992			−0.794961	+	0.606660i	$0.792509\pi$
$152$	0.641923	−	5.04360i	0.0520668	−	0.409090i
$153$		−	10.8174i		−	0.874537i
$154$	−2.57521	+	14.6048i	−0.207517	+	1.17689i
$155$		0			0
$156$	1.92725	+	0.701460i	0.154303	+	0.0561618i
$157$	0.0979622	+	0.269149i	0.00781823	+	0.0214804i	0.943540	−	0.331258i	$-0.107473\pi$
$157$	0.0979622	+	0.269149i	0.00781823	+	0.0214804i	−0.935722	+	0.352738i	$0.885251\pi$
$158$	2.83109	+	3.37396i	0.225230	+	0.268418i
$159$	−7.27421	−	12.5993i	−0.576882	−	0.999190i
$160$		0			0
$161$	−1.59104	−	9.02323i	−0.125391	−	0.711130i
$162$	−23.1515	+	4.08224i	−1.81896	+	0.320731i
$163$	17.8622	+	10.3128i	1.39908	+	0.807759i	0.994296	−	0.106654i	$-0.0340138\pi$
$163$	17.8622	+	10.3128i	1.39908	+	0.807759i	0.404783	+	0.914413i	$0.367347\pi$
$164$	−6.66811	−	11.5495i	−0.520692	−	0.901864i
$165$		0			0
$166$	−12.3512	+	4.49547i	−0.958639	+	0.348916i
$167$	−3.71223	+	10.1993i	−0.287261	+	0.789243i	0.709186	+	0.705021i	$0.249063\pi$
$167$	−3.71223	+	10.1993i	−0.287261	+	0.789243i	−0.996447	+	0.0842218i	$0.973160\pi$
$168$	−2.48435	+	2.96073i	−0.191672	+	0.228425i
$169$	2.23479	−	12.6741i	0.171907	−	0.974934i
$170$		0			0
$171$	7.23946	−	4.65599i	0.553615	−	0.356052i
$172$		−	18.3850i		−	1.40184i
$173$	−17.2823	−	3.04734i	−1.31395	−	0.231685i	−0.527616	−	0.849483i	$-0.676914\pi$
$173$	−17.2823	−	3.04734i	−1.31395	−	0.231685i	−0.786337	+	0.617798i	$0.788025\pi$
$174$	3.26428	+	2.73905i	0.247464	+	0.207647i
$175$		0			0
$176$	11.4673	−	4.17376i	0.864380	−	0.314609i
$177$	14.0603	+	16.7564i	1.05684	+	1.25949i
$178$	−6.13128	+	3.53989i	−0.459559	+	0.265326i
$179$	7.53220	−	13.0462i	0.562983	−	0.975116i	−0.434251	−	0.900792i	$-0.642987\pi$
$179$	7.53220	−	13.0462i	0.562983	−	0.975116i	0.997234	−	0.0743239i	$-0.0236799\pi$
$180$		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	$0.757348\pi$
$182$	−0.990471	−	0.571848i	−0.0734186	−	0.0423882i
$183$	4.53854	−	2.62033i	0.335498	−	0.193700i
$184$	5.51072	−	4.62405i	0.406256	−	0.340889i
$185$		0			0
$186$	−21.4533	−	7.80836i	−1.57303	−	0.572536i
$187$	−16.4841	+	19.6450i	−1.20544	+	1.43658i
$188$	−27.2541	−	4.80564i	−1.98771	−	0.350487i
$189$	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	$0.500078\pi$
$192$	25.5102	+	4.49813i	1.84104	+	0.324625i
$193$	−8.82305	+	10.5149i	−0.635097	+	0.756880i	−0.983587	−	0.180433i	$-0.942250\pi$
$193$	−8.82305	+	10.5149i	−0.635097	+	0.756880i	0.348490	+	0.937313i	$0.386695\pi$
$194$	9.45136	+	3.44001i	0.678568	+	0.246978i
$195$		0			0
$196$	−9.35155	+	7.84688i	−0.667968	+	0.560492i
$197$	−0.415502	+	0.239890i	−0.0296033	+	0.0170915i	−0.514729	−	0.857353i	$-0.672107\pi$
$197$	−0.415502	+	0.239890i	−0.0296033	+	0.0170915i	0.485125	+	0.874445i	$0.338774\pi$
$198$	−17.0711	−	9.85601i	−1.21319	−	0.700436i
$199$	4.65737	+	26.4133i	0.330152	+	1.87239i	0.470670	+	0.882309i	$0.344012\pi$
$199$	4.65737	+	26.4133i	0.330152	+	1.87239i	−0.140517	+	0.990078i	$0.544877\pi$
$200$		0			0
$201$	−9.87200	+	17.0988i	−0.696317	+	1.20606i
$202$	−16.6986	+	9.64092i	−1.17491	+	0.678333i
$203$	−0.855587	−	1.01965i	−0.0600504	−	0.0715653i
$204$	−29.2432	+	10.6436i	−2.04743	+	0.745205i
$205$		0			0
$206$	12.7391	+	10.6893i	0.887572	+	0.744761i
$207$	11.9936	+	2.11480i	0.833614	+	0.146989i
$208$			0.941116i			0.0652547i
$209$	−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	$-0.0359976\pi$
$212$	−10.6790	+	12.7267i	−0.733436	+	0.874075i
$213$	4.89139	−	13.4390i	0.335153	−	0.920825i
$214$	1.03856	−	0.378006i	0.0709946	−	0.0258399i
$215$		0			0
$216$	1.33372	+	2.31007i	0.0907481	+	0.157180i
$217$	6.17593	+	3.56567i	0.419249	+	0.242054i
$218$	5.80522	−	1.02362i	0.393179	−	0.0693281i
$219$	−1.10835	−	6.28576i	−0.0748952	−	0.424752i
$220$		0			0
$221$	−0.988862	−	1.71276i	−0.0665181	−	0.115213i
$222$	−34.8456	−	41.5274i	−2.33868	−	2.78713i
$223$	−0.587605	−	1.61443i	−0.0393489	−	0.108110i	0.918462	−	0.395509i	$-0.129432\pi$
$223$	−0.587605	−	1.61443i	−0.0393489	−	0.108110i	−0.957811	+	0.287399i	$0.907210\pi$
$224$	−11.0167	−	4.00975i	−0.736085	−	0.267913i
$225$		0			0
$226$	4.60352	−	26.1079i	0.306222	−	1.73667i
$227$		−	4.22601i		−	0.280490i	−0.990117	−	0.140245i	$-0.955211\pi$
$227$		−	4.22601i		−	0.280490i	0.990117	−	0.140245i	$-0.0447891\pi$
$228$	−19.7099	−	14.9895i	−1.30532	−	0.992707i
$229$	−5.52322			−0.364985			−0.182492	−	0.983207i	$-0.558417\pi$
$229$	−5.52322			−0.364985			−0.182492	+	0.983207i	$0.558417\pi$
$230$		0			0
$231$	11.8828	+	9.97082i	0.781828	+	0.656032i
$232$	0.357431	−	0.982034i	0.0234665	−	0.0644737i
$233$	−9.64357	−	26.4955i	−0.631771	−	1.73578i	−0.676152	−	0.736762i	$-0.736354\pi$
$233$	−9.64357	−	26.4955i	−0.631771	−	1.73578i	0.0443807	−	0.999015i	$-0.485869\pi$
$234$	1.16454	−	0.977162i	0.0761281	−	0.0638791i
$235$		0			0
$236$	12.4895	−	21.6324i	0.812994	−	1.40815i
$237$	4.53689	−	0.799976i	0.294702	−	0.0519640i
$238$	17.0903	−	3.01348i	1.10780	−	0.195335i
$239$	−5.66020	+	9.80375i	−0.366128	+	0.634152i	−0.988956	−	0.148206i	$-0.952650\pi$
$239$	−5.66020	+	9.80375i	−0.366128	+	0.634152i	0.622829	+	0.782358i	$0.285983\pi$
$240$		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	$0.101076\pi$
$242$	7.96051	+	21.8713i	0.511721	+	1.40594i
$243$	−6.06362	+	16.6596i	−0.388981	+	1.06872i
$244$	−4.58444	−	3.84680i	−0.293489	−	0.246266i
$245$		0			0
$246$	−24.9028			−1.58774
$247$	0.720627	−	1.39899i	0.0458524	−	0.0890153i
$248$			5.59907i			0.355541i
$249$	−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	$0.536650\pi$
$252$	2.55557	+	7.02137i	0.160986	+	0.442305i
$253$	−18.5584	−	22.1170i	−1.16676	−	1.39049i
$254$	−1.45107	−	2.51333i	−0.0910482	−	0.157700i
$255$		0			0
$256$	0.707484	+	4.01234i	0.0442178	+	0.250771i
$257$	−5.92171	+	1.04416i	−0.369386	+	0.0651327i	−0.355260	−	0.934768i	$-0.615608\pi$
$257$	−5.92171	+	1.04416i	−0.369386	+	0.0651327i	−0.0141259	+	0.999900i	$0.504497\pi$
$258$	−29.7310	−	17.1652i	−1.85097	−	1.06866i
$259$	8.46670	+	14.6648i	0.526095	+	0.911224i
$260$		0			0
$261$	1.66253	−	0.605113i	0.102908	−	0.0374555i
$262$	14.2392	−	39.1219i	0.879701	−	2.41696i
$263$	−4.74302	+	5.65251i	−0.292467	+	0.348549i	−0.892191	−	0.451658i	$-0.850833\pi$
$263$	−4.74302	+	5.65251i	−0.292467	+	0.348549i	0.599724	+	0.800207i	$0.295277\pi$
$264$	−2.11484	+	11.9939i	−0.130159	+	0.738171i
$265$		0			0
$266$	9.37268	+	10.1405i	0.574676	+	0.621753i
$267$			7.40526i			0.453194i
$268$	22.2041	+	3.91519i	1.35633	+	0.239158i
$269$	8.32148	+	6.98255i	0.507370	+	0.425734i	0.860203	−	0.509953i	$-0.170337\pi$
$269$	8.32148	+	6.98255i	0.507370	+	0.425734i	−0.352833	+	0.935686i	$0.614782\pi$
$270$		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	$0.416465\pi$
$272$	−9.17906	−	10.9392i	−0.556562	−	0.663285i
$273$	−1.03600	+	0.598137i	−0.0627018	+	0.0362009i
$274$	11.3873	−	19.7233i	0.687931	−	1.19153i
$275$		0			0
$276$	−6.08393	−	34.5037i	−0.366209	−	2.07688i
$277$	−13.9813	−	8.07213i	−0.840058	−	0.485008i	0.0172261	−	0.999852i	$-0.494516\pi$
$277$	−13.9813	−	8.07213i	−0.840058	−	0.485008i	−0.857284	+	0.514844i	$0.827850\pi$
$278$	−13.2799	+	7.66717i	−0.796477	+	0.459846i
$279$	−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	$0.641693\pi$
$282$	−33.2173	+	39.5868i	−1.97806	+	2.35736i
$283$	12.6787	+	2.23560i	0.753671	+	0.132893i	0.537268	−	0.843412i	$-0.319456\pi$
$283$	12.6787	+	2.23560i	0.753671	+	0.132893i	0.216403	+	0.976304i	$0.430568\pi$
$284$	−16.3316			−0.969101
$285$		0			0
$286$	−3.60390			−0.213103
$287$	7.66061	+	1.35077i	0.452192	+	0.0797336i
$288$	10.0166	−	11.9373i	0.590235	−	0.703415i
$289$	12.2246	+	4.44938i	0.719092	+	0.261728i
$290$		0			0
$291$	8.05902	−	6.76232i	0.472428	−	0.396414i
$292$	−6.31224	+	3.64437i	−0.369396	+	0.213271i
$293$	26.6831	+	15.4055i	1.55884	+	0.899999i	0.997368	+	0.0725066i	$0.0230998\pi$
$293$	26.6831	+	15.4055i	1.55884	+	0.899999i	0.561476	+	0.827493i	$0.310234\pi$
$294$	3.95836	+	22.4490i	0.230856	+	1.30925i
$295$		0			0
$296$	−6.64750	+	11.5138i	−0.386378	+	0.669227i
$297$	9.27136	−	5.35282i	0.537979	−	0.310602i
$298$	5.82157	+	6.93788i	0.337234	+	0.401900i
$299$	2.09231	−	0.761539i	0.121001	−	0.0440409i
$300$		0			0
$301$	8.21478	+	6.89302i	0.473492	+	0.397307i
$302$	41.0278	+	7.23432i	2.36089	+	0.416288i
$303$			20.1683i			1.15864i
$304$	3.37013	−	10.8514i	0.193290	−	0.622370i
$305$		0			0
$306$	−4.00550	+	22.7163i	−0.228979	+	1.29861i
$307$	10.5297	−	12.5488i	0.600959	−	0.716196i	−0.376713	−	0.926330i	$-0.622946\pi$
$307$	10.5297	−	12.5488i	0.600959	−	0.716196i	0.977673	+	0.210134i	$0.0673902\pi$
$308$	6.05846	−	16.6455i	0.345213	−	0.948464i
$309$	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	$-0.414564\pi$
$312$	−0.813403	−	0.469618i	−0.0460499	−	0.0265869i
$313$	−10.1173	+	1.78395i	−0.571863	+	0.100835i	−0.452099	−	0.891968i	$-0.649325\pi$
$313$	−10.1173	+	1.78395i	−0.571863	+	0.100835i	−0.119763	+	0.992802i	$0.538214\pi$
$314$	−0.106057	−	0.601480i	−0.00598515	−	0.0339435i
$315$		0			0
$316$	−2.63041	−	4.55600i	−0.147972	−	0.256295i
$317$	−3.90578	−	4.65473i	−0.219371	−	0.261436i	0.645124	−	0.764078i	$-0.276806\pi$
$317$	−3.90578	−	4.65473i	−0.219371	−	0.261436i	−0.864495	+	0.502642i	$0.832361\pi$
$318$	10.6104	+	29.1517i	0.595000	+	1.63475i
$319$	−3.94135	−	1.43453i	−0.220673	−	0.0803184i
$320$		0			0
$321$	0.200741	−	1.13846i	0.0112043	−	0.0635427i
$322$			19.5377i			1.08879i
$323$	5.26854	+	23.2898i	0.293149	+	1.29588i
$324$	28.0799			1.55999
$325$		0			0
$326$	−33.6916	−	28.2706i	−1.86601	−	1.56577i
$327$	2.10882	−	5.79393i	0.116618	−	0.320405i
$328$	2.08885	+	5.73908i	0.115338	+	0.316888i
$329$	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	$0.271895\pi$
$332$	15.4611	−	2.72622i	0.848541	−	0.149621i
$333$	−22.1658	+	3.90843i	−1.21468	+	0.214181i
$334$	11.5722	−	20.0436i	0.633203	−	1.09674i
$335$		0			0
$336$	−6.61683	+	5.55218i	−0.360978	+	0.302896i
$337$	5.20776	+	14.3082i	0.283685	+	0.779417i	0.996915	+	0.0784877i	$0.0250091\pi$
$337$	5.20776	+	14.3082i	0.283685	+	0.779417i	−0.713230	+	0.700930i	$0.752769\pi$
$338$	−9.38602	+	25.7879i	−0.510532	+	1.40268i
$339$	−21.2419	−	17.8241i	−1.15370	−	0.968071i
$340$		0			0
$341$	22.4716			1.21691
$342$	−16.9267	+	7.09681i	−0.915292	+	0.383752i
$343$		−	17.5199i		−	0.945983i
$344$	−1.46203	+	8.29159i	−0.0788274	+	0.447052i
$345$		0			0
$346$	35.1641	+	12.7987i	1.89044	+	0.688062i
$347$	−10.3223	−	28.3603i	−0.554131	−	1.52246i	−0.828019	−	0.560700i	$-0.810532\pi$
$347$	−10.3223	−	28.3603i	−0.554131	−	1.52246i	0.273888	−	0.961762i	$-0.411690\pi$
$348$	−3.27165	−	3.89900i	−0.175379	−	0.209009i
$349$	−1.36886	−	2.37093i	−0.0732732	−	0.126913i	0.827061	−	0.562112i	$-0.190011\pi$
$349$	−1.36886	−	2.37093i	−0.0732732	−	0.126913i	−0.900334	+	0.435200i	$0.856678\pi$
$350$		0			0
$351$	0.143367	+	0.813077i	0.00765239	+	0.0433989i
$352$	−36.3814	+	6.41502i	−1.93914	+	0.341922i
$353$	3.99172	+	2.30462i	0.212458	+	0.122663i	0.602453	−	0.798154i	$-0.294190\pi$
$353$	3.99172	+	2.30462i	0.212458	+	0.122663i	−0.389995	+	0.920817i	$0.627523\pi$
$354$	−23.3216	−	40.3943i	−1.23953	−	2.14693i
$355$		0			0
$356$	7.94645	−	2.89227i	0.421161	−	0.153290i
$357$	6.20826	−	17.0571i	0.328576	−	0.902755i
$358$	−20.6482	+	24.6076i	−1.09129	+	1.30055i
$359$	−2.14281	+	12.1525i	−0.113093	+	0.641383i	0.874584	+	0.484875i	$0.161135\pi$
$359$	−2.14281	+	12.1525i	−0.113093	+	0.641383i	−0.987677	+	0.156508i	$0.949976\pi$
$360$		0			0
$361$	−13.3188	+	13.5502i	−0.700992	+	0.713170i
$362$		−	31.8160i		−	1.67221i
$363$	23.9751	+	4.22746i	1.25837	+	0.221884i
$364$	1.04648	+	0.878103i	0.0548506	+	0.0460251i
$365$		0			0
$366$	−10.5011	+	3.82208i	−0.548900	+	0.199783i
$367$	1.05168	+	1.25334i	0.0548972	+	0.0654239i	0.792794	−	0.609489i	$-0.208625\pi$
$367$	1.05168	+	1.25334i	0.0548972	+	0.0654239i	−0.737897	+	0.674913i	$0.764181\pi$
$368$	13.9231	−	8.03851i	0.725792	−	0.419036i
$369$	−5.16976	+	8.95428i	−0.269127	+	0.466141i
$370$		0			0
$371$	−1.68272	−	9.54319i	−0.0873626	−	0.495458i
$372$	23.6160	+	13.6347i	1.22443	+	0.706925i
$373$	−12.7814	+	7.37936i	−0.661797	+	0.382089i	−0.792961	−	0.609272i	$-0.791462\pi$
$373$	−12.7814	+	7.37936i	−0.661797	+	0.382089i	0.131164	+	0.991361i	$0.458129\pi$
$374$	41.8904	−	35.1502i	2.16610	−	1.81758i
$375$		0			0
$376$	11.9094	+	4.33467i	0.614181	+	0.223544i
$377$	0.207919	−	0.247788i	0.0107084	−	0.0127617i
$378$	−7.13452	−	1.25801i	−0.366960	−	0.0647049i
$379$	1.75865			0.0903358			0.0451679	−	0.998979i	$-0.485618\pi$
$379$	1.75865			0.0903358			0.0451679	+	0.998979i	$0.485618\pi$
$380$		0			0
$381$	−3.03556			−0.155516
$382$	0.0142348	+	0.00250997i	0.000728314	+	0.000128421i
$383$	5.46280	−	6.51031i	0.279136	−	0.332661i	−0.608201	−	0.793783i	$-0.708108\pi$
$383$	5.46280	−	6.51031i	0.279136	−	0.332661i	0.887337	+	0.461122i	$0.152553\pi$
$384$	−18.8259	−	6.85209i	−0.960708	−	0.349669i
$385$		0			0
$386$	22.4217	−	18.8140i	1.14123	−	0.957609i
$387$	−12.3441	+	7.12689i	−0.627488	+	0.362280i
$388$	−10.4041	−	6.00683i	−0.528190	−	0.304951i
$389$	5.89390	+	33.4260i	0.298833	+	1.69476i	0.651203	+	0.758904i	$0.274265\pi$
$389$	5.89390	+	33.4260i	0.298833	+	1.69476i	−0.352370	+	0.935861i	$0.614624\pi$
$390$		0			0
$391$	−16.8927	+	29.2589i	−0.854298	+	1.47969i
$392$	4.84155	−	2.79527i	0.244535	−	0.141182i
$393$	−27.9912	−	33.3586i	−1.41197	−	1.68272i
$394$	0.961370	−	0.349910i	0.0484331	−	0.0176282i
$395$		0			0
$396$	18.0365	+	15.1344i	0.906368	+	0.760533i
$397$	−7.65893	−	1.35048i	−0.384391	−	0.0677785i	−0.0218863	−	0.999760i	$-0.506967\pi$
$397$	−7.65893	−	1.35048i	−0.384391	−	0.0677785i	−0.362505	+	0.931982i	$0.618078\pi$
$398$		−	57.1918i		−	2.86676i
$399$	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	$-0.228576\pi$
$402$	27.0623	−	32.2516i	1.34975	−	1.60857i
$403$	−0.592725	+	1.62850i	−0.0295257	+	0.0811213i
$404$	21.6422	−	7.87712i	1.07674	−	0.391901i
$405$		0			0
$406$	1.41915	+	2.45805i	0.0704314	+	0.121991i
$407$	46.2101	+	26.6794i	2.29055	+	1.32245i
$408$	14.0351	−	2.47476i	0.694839	−	0.122519i
$409$	2.54836	+	14.4525i	0.126008	+	0.714629i	0.980704	+	0.195499i	$0.0626328\pi$
$409$	2.54836	+	14.4525i	0.126008	+	0.714629i	−0.854695	+	0.519130i	$0.826256\pi$
$410$		0			0
$411$	−11.9108	−	20.6301i	−0.587515	−	1.01761i
$412$	−12.7679	−	15.2161i	−0.629027	−	0.749645i
$413$	4.98316	+	13.6911i	0.245205	+	0.673696i
$414$	−24.4032	−	8.88204i	−1.19935	−	0.436529i
$415$		0			0
$416$	0.494727	−	2.80574i	0.0242560	−	0.137563i
$417$			16.0393i			0.785447i
$418$	41.5543	+	12.9056i	2.03249	+	0.631232i
$419$	20.6063			1.00668			0.503341	−	0.864088i	$-0.332104\pi$
$419$	20.6063			1.00668			0.503341	+	0.864088i	$0.332104\pi$
$420$		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	$0.486582\pi$
$422$	−6.01041	+	16.5135i	−0.292582	+	0.803864i
$423$	7.33837	+	20.1620i	0.356804	+	0.980311i
$424$	5.82828	−	4.89051i	0.283046	−	0.237504i
$425$		0			0
$426$	−15.2480	+	26.4104i	−0.738769	+	1.27959i
$427$	3.43766	−	0.606153i	0.166360	−	0.0293338i
$428$	−1.30007	+	0.229237i	−0.0628410	+	0.0110806i
$429$	−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	$0.445645\pi$
$432$	2.03891	+	5.60185i	0.0980969	+	0.269519i
$433$	0.658712	−	1.80980i	0.0316557	−	0.0869732i	−0.922858	−	0.385140i	$-0.874153\pi$
$433$	0.658712	−	1.80980i	0.0316557	−	0.0869732i	0.954514	+	0.298167i	$0.0963753\pi$
$434$	−11.6490	−	9.77467i	−0.559170	−	0.469199i
$435$		0			0
$436$	−7.04100			−0.337203
$437$	−26.8521	+	1.28825i	−1.28451	+	0.0616252i
$438$			13.6103i			0.650327i
$439$	−6.02549	+	34.1723i	−0.287581	+	1.63095i	0.408337	+	0.912831i	$0.366109\pi$
$439$	−6.02549	+	34.1723i	−0.287581	+	1.63095i	−0.695918	+	0.718121i	$0.745002\pi$
$440$		0			0
$441$	8.89371	+	3.23705i	0.423510	+	0.154145i
$442$	1.44238	+	3.96291i	0.0686071	+	0.188496i
$443$	16.9187	+	20.1629i	0.803832	+	0.957970i	0.999743	−	0.0226514i	$-0.00721079\pi$
$443$	16.9187	+	20.1629i	0.803832	+	0.957970i	−0.195911	+	0.980622i	$0.562766\pi$
$444$	32.3756	+	56.0761i	1.53648	+	2.66126i
$445$		0			0
$446$	0.636160	+	3.60784i	0.0301231	+	0.170836i
$447$	9.32919	−	1.64499i	0.441256	−	0.0778053i
$448$	14.9424	+	8.62698i	0.705960	+	0.407586i
$449$	−6.71581	−	11.6321i	−0.316939	−	0.548954i	0.662909	−	0.748700i	$-0.269322\pi$
$449$	−6.71581	−	11.6321i	−0.316939	−	0.548954i	−0.979848	+	0.199746i	$0.935988\pi$
$450$		0			0
$451$	23.0335	−	8.38351i	1.08461	−	0.394764i
$452$	−10.8302	+	29.7559i	−0.509412	+	1.39960i
$453$	28.0101	−	33.3811i	1.31603	−	1.56838i
$454$	−1.56482	+	8.87452i	−0.0734405	+	0.416502i
$455$		0			0
$456$	7.69712	+	8.32766i	0.360450	+	0.389978i
$457$		−	0.205882i		−	0.00963073i	−0.999988	−	0.00481537i	$-0.998467\pi$
$457$		−	0.205882i		−	0.00963073i	0.999988	−	0.00481537i	$-0.00153278\pi$
$458$	11.5986	+	2.04515i	0.541969	+	0.0955637i
$459$	−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	$0.751925\pi$
$462$	−21.2615	−	25.3384i	−0.989173	−	1.17885i
$463$	−6.42997	+	3.71234i	−0.298826	+	0.172527i	−0.641915	−	0.766776i	$-0.721860\pi$
$463$	−6.42997	+	3.71234i	−0.298826	+	0.172527i	0.343089	+	0.939303i	$0.388527\pi$
$464$	1.16778	−	2.02266i	0.0542129	−	0.0938995i
$465$		0			0
$466$	10.4404	+	59.2107i	0.483644	+	2.74288i
$467$	18.9880	+	10.9627i	0.878660	+	0.507295i	0.870216	−	0.492670i	$-0.163979\pi$
$467$	18.9880	+	10.9627i	0.878660	+	0.507295i	0.00844368	+	0.999964i	$0.497312\pi$
$468$	−1.57252	+	0.907896i	−0.0726898	+	0.0419675i
$469$	−10.0743	+	8.45336i	−0.465189	+	0.390340i
$470$		0			0
$471$	−0.600309	−	0.218495i	−0.0276608	−	0.0100677i
$472$	−7.35300	+	8.76296i	−0.338449	+	0.403348i
$473$	33.2779	+	5.86779i	1.53012	+	0.269801i
$474$	−9.82357			−0.451211
$475$		0			0
$476$	−20.7284			−0.950084
$477$	12.6847	+	2.23666i	0.580795	+	0.102410i
$478$	15.5164	−	18.4918i	0.709705	−	0.845794i
$479$	−26.3861	−	9.60376i	−1.20561	−	0.438807i	−0.340433	−	0.940269i	$-0.610573\pi$
$479$	−26.3861	−	9.60376i	−1.20561	−	0.438807i	−0.865180	+	0.501462i	$0.832796\pi$
$480$		0			0
$481$	−3.15230	+	2.64510i	−0.143733	+	0.120606i
$482$	−30.2193	+	17.4471i	−1.37645	+	0.794694i
$483$	17.6980	+	10.2179i	0.805286	+	0.464932i
$484$	−4.82754	−	27.3784i	−0.219434	−	1.24447i
$485$		0			0
$486$	18.9022	−	32.7396i	0.857422	−	1.48510i
$487$	12.2411	−	7.06739i	0.554697	−	0.320254i	−0.196318	−	0.980540i	$-0.562898\pi$
$487$	12.2411	−	7.06739i	0.554697	−	0.320254i	0.751014	+	0.660286i	$0.229565\pi$
$488$	1.76167	+	2.09947i	0.0797468	+	0.0950386i
$489$	−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	$0.897547\pi$
$492$	29.2932	+	5.16518i	1.32064	+	0.232864i
$493$			4.90811i			0.221050i
$494$	−2.03132	+	2.67100i	−0.0913933	+	0.120174i
$495$		0			0
$496$	−2.17289	+	12.3230i	−0.0975654	+	0.553321i
$497$	6.12315	−	7.29729i	0.274661	−	0.327328i
$498$	10.0267	−	27.5481i	0.449307	−	1.23446i
$499$	−39.8744	+	14.5131i	−1.78502	+	0.649695i	−0.785497	+	0.618865i	$0.787593\pi$
$499$	−39.8744	+	14.5131i	−1.78502	+	0.649695i	−0.999525	+	0.0308294i	$0.990185\pi$
$500$		0			0
$501$	−12.1042	−	20.9651i	−0.540776	−	0.936651i
$502$	−13.5635	−	7.83092i	−0.605371	−	0.349511i
$503$	−5.75873	+	1.01542i	−0.256769	+	0.0452753i	−0.300551	−	0.953766i	$-0.597170\pi$
$503$	−5.75873	+	1.01542i	−0.256769	+	0.0452753i	0.0437817	+	0.999041i	$0.486059\pi$
$504$	−0.594196	−	3.36985i	−0.0264676	−	0.150105i
$505$		0			0
$506$	30.7826	+	53.3170i	1.36845	+	2.37023i
$507$	18.4509	+	21.9889i	0.819433	+	0.976562i
$508$	1.18560	+	3.25740i	0.0526023	+	0.144524i
$509$	7.84135	+	2.85402i	0.347562	+	0.126502i	0.509902	−	0.860233i	$-0.329682\pi$
$509$	7.84135	+	2.85402i	0.347562	+	0.126502i	−0.162340	+	0.986735i	$0.551904\pi$
$510$		0			0
$511$	0.738249	−	4.18682i	0.0326582	−	0.185214i
$512$		−	26.6524i		−	1.17788i
$513$	1.25855	−	9.88846i	0.0555664	−	0.436586i
$514$	12.8221			0.565557
$515$		0			0
$516$	31.4123	+	26.3580i	1.38285	+	1.16035i
$517$	17.3970	−	47.7978i	0.765119	−	2.10215i
$518$	−12.3498	−	33.9307i	−0.542618	−	1.49083i
$519$	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	$0.930154\pi$
$522$	−3.71534	+	0.655115i	−0.162616	+	0.0286736i
$523$	−22.5577	+	3.97753i	−0.986380	+	0.173925i	−0.643494	−	0.765452i	$-0.722516\pi$
$523$	−22.5577	+	3.97753i	−0.986380	+	0.173925i	−0.342886	+	0.939377i	$0.611405\pi$
$524$	−24.8640	+	43.0657i	−1.08619	+	1.88134i
$525$		0			0
$526$	12.0532	−	10.1139i	0.525547	−	0.440986i
$527$	−8.99375	−	24.7101i	−0.391774	−	1.07639i
$528$	−9.30914	+	25.5767i	−0.405129	+	1.11308i
$529$	−11.5188	−	9.66540i	−0.500816	−	0.420235i
$530$		0			0
$531$	−19.3660			−0.840415
$532$	−8.92182	−	13.8723i	−0.386810	−	0.601440i
$533$			1.89035i			0.0818801i
$534$	2.74204	−	15.5509i	0.118659	−	0.672951i
$535$		0			0
$536$	−9.70268	−	3.53149i	−0.419092	−	0.152537i
$537$	11.4918	+	31.5733i	0.495906	+	1.36249i
$538$	−14.8894	−	17.7445i	−0.641927	−	0.765019i
$539$	−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	$0.971873\pi$
$542$	5.98226	−	1.05483i	0.256960	−	0.0453090i
$543$	−28.8201	−	16.6393i	−1.23679	−	0.714061i
$544$	21.6149	+	37.4381i	0.926731	+	1.60515i
$545$		0			0
$546$	2.39706	−	0.872460i	0.102585	−	0.0373378i
$547$	−14.2527	+	39.1590i	−0.609402	+	1.67432i	0.122133	+	0.992514i	$0.461027\pi$
$547$	−14.2527	+	39.1590i	−0.609402	+	1.67432i	−0.731535	+	0.681804i	$0.761196\pi$
$548$	−17.4858	+	20.8387i	−0.746954	+	0.890186i
$549$	−0.805694	+	4.56932i	−0.0343862	+	0.195014i
$550$		0			0
$551$	−3.28471	+	2.11253i	−0.139933	+	0.0899966i
$552$			16.0449i			0.682917i
$553$	3.02193	+	0.532848i	0.128506	+	0.0226590i
$554$	26.3715	+	22.1283i	1.12042	+	0.940142i
$555$		0			0
$556$	17.2115	−	6.26446i	0.729929	−	0.265672i
$557$	2.04085	+	2.43219i	0.0864735	+	0.103055i	0.807546	−	0.589804i	$-0.200795\pi$
$557$	2.04085	+	2.43219i	0.0864735	+	0.103055i	−0.721073	+	0.692859i	$0.756351\pi$
$558$	17.5046	−	10.1063i	0.741030	−	0.427834i
$559$	−1.30299	+	2.25685i	−0.0551107	+	0.0954546i
$560$		0			0
$561$	−9.93232	−	56.3290i	−0.419343	−	2.37821i
$562$	5.93905	+	3.42891i	0.250524	+	0.144640i
$563$	12.4759	−	7.20295i	0.525796	−	0.303568i	−0.213507	−	0.976942i	$-0.568489\pi$
$563$	12.4759	−	7.20295i	0.525796	−	0.303568i	0.739303	+	0.673373i	$0.235155\pi$
$564$	47.2843	−	39.6763i	1.99103	−	1.67067i
$565$		0			0
$566$	−25.7972	−	9.38940i	−1.08434	−	0.394666i
$567$	−10.5279	+	12.5467i	−0.442131	+	0.526911i
$568$	7.36552	+	1.29874i	0.309050	+	0.0544939i
$569$	−24.9795			−1.04719			−0.523597	−	0.851966i	$-0.675410\pi$
$569$	−24.9795			−1.04719			−0.523597	+	0.851966i	$0.675410\pi$
$570$		0			0
$571$	13.1086			0.548579			0.274289	−	0.961647i	$-0.411557\pi$
$571$	13.1086			0.548579			0.274289	+	0.961647i	$0.411557\pi$
$572$	4.23928	+	0.747499i	0.177253	+	0.0312545i
$573$	0.00971822	−	0.0115817i	0.000405984	−	0.000483833i
$574$	−15.5869	−	5.67318i	−0.650586	−	0.236794i
$575$		0			0
$576$	−17.5683	+	14.7416i	−0.732014	+	0.614233i
$577$	−7.14901	+	4.12748i	−0.297617	+	0.171829i	−0.641372	−	0.767230i	$-0.721634\pi$
$577$	−7.14901	+	4.12748i	−0.297617	+	0.171829i	0.343755	+	0.939059i	$0.388301\pi$
$578$	−24.0238	−	13.8701i	−0.999257	−	0.576921i
$579$	−5.31624	−	30.1499i	−0.220935	−	1.25299i
$580$		0			0
$581$	−4.57867	+	7.93050i	−0.189955	+	0.329012i
$582$	−19.4277	+	11.2166i	−0.805304	+	0.464943i
$583$	−19.6278	−	23.3915i	−0.812901	−	0.968778i
$584$	3.13662	−	1.14164i	0.129794	−	0.0472413i
$585$		0			0
$586$	−50.3295	−	42.2315i	−2.07909	−	1.74457i
$587$	7.78595	+	1.37287i	0.321361	+	0.0566646i	0.332002	−	0.943279i	$-0.392276\pi$
$587$	7.78595	+	1.37287i	0.321361	+	0.0566646i	−0.0106409	+	0.999943i	$0.503387\pi$
$588$		−	27.2278i		−	1.12286i
$589$	12.6660	−	16.6546i	0.521892	−	0.686241i
$590$		0			0
$591$	0.185821	−	1.05384i	0.00764366	−	0.0433493i
$592$	−19.0988	+	22.7611i	−0.784957	+	0.935475i
$593$	−1.21611	+	3.34124i	−0.0499398	+	0.137208i	−0.962155	−	0.272503i	$-0.912148\pi$
$593$	−1.21611	+	3.34124i	−0.0499398	+	0.137208i	0.912215	+	0.409712i	$0.134371\pi$
$594$	−21.4517	+	7.80777i	−0.880173	+	0.320357i
$595$		0			0
$596$	−5.40891	−	9.36850i	−0.221557	−	0.383749i
$597$	−51.8065	−	29.9105i	−2.12030	−	1.22415i
$598$	−4.67579	+	0.824467i	−0.191207	+	0.0337150i
$599$	−1.91987	−	10.8881i	−0.0784437	−	0.444876i	−0.998580	−	0.0532774i	$-0.983033\pi$
$599$	−1.91987	−	10.8881i	−0.0784437	−	0.444876i	0.920136	−	0.391599i	$-0.128078\pi$
$600$		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	$0.454091\pi$
$602$	−14.6985	−	17.5170i	−0.599065	−	0.713938i
$603$	−5.97863	−	16.4261i	−0.243468	−	0.668924i
$604$	−46.7606	−	17.0195i	−1.90266	−	0.692512i
$605$		0			0
$606$	7.46795	−	42.3529i	0.303365	−	1.72047i
$607$		−	36.4498i		−	1.47945i	−0.672907	−	0.739727i	$-0.734955\pi$
$607$		−	36.4498i		−	1.47945i	0.672907	−	0.739727i	$-0.265045\pi$
$608$	−15.7517	+	30.5795i	−0.638817	+	1.24016i
$609$	2.96879			0.120301
$610$		0			0
$611$	3.00500	+	2.52149i	0.121569	+	0.102009i
$612$	9.42334	−	25.8904i	0.380916	−	1.04656i
$613$	−2.30653	−	6.33713i	−0.0931597	−	0.255954i	0.884357	−	0.466811i	$-0.154597\pi$
$613$	−2.30653	−	6.33713i	−0.0931597	−	0.255954i	−0.977517	+	0.210856i	$0.932375\pi$
$614$	−26.7586	+	22.4531i	−1.07989	+	0.906135i
$615$		0			0
$616$	−4.05606	+	7.02529i	−0.163423	+	0.283057i
$617$	24.8642	−	4.38423i	1.00100	−	0.176503i	0.350947	−	0.936395i	$-0.385860\pi$
$617$	24.8642	−	4.38423i	1.00100	−	0.176503i	0.650049	+	0.759893i	$0.274748\pi$
$618$	−36.5273	+	6.44075i	−1.46934	+	0.259085i
$619$	11.1611	−	19.3317i	0.448604	−	0.777006i	−0.549691	−	0.835368i	$-0.685255\pi$
$619$	11.1611	−	19.3317i	0.448604	−	0.777006i	0.998295	+	0.0583624i	$0.0185879\pi$
$620$		0			0
$621$	10.8043	−	9.06588i	0.433562	−	0.363801i
$622$	18.0685	+	49.6427i	0.724480	+	1.99049i
$623$	−1.68701	+	4.63503i	−0.0675887	+	0.185699i
$624$	−1.60798	−	1.34925i	−0.0643706	−	0.0540133i
$625$		0			0
$626$	21.9066			0.875564
$627$	33.4226	−	30.8920i	1.33477	−	1.23371i
$628$			0.729519i			0.0291110i
$629$	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	$0.633555\pi$
$632$	0.824003	+	2.26393i	0.0327771	+	0.0900543i
$633$	11.8152	+	14.0808i	0.469611	+	0.559661i
$634$	6.47848	+	11.2211i	0.257293	+	0.445645i
$635$		0			0
$636$	−6.43451	−	36.4919i	−0.255145	−	1.44700i
$637$	1.70408	−	0.300476i	0.0675182	−	0.0119053i
$638$	7.74555	+	4.47189i	0.306649	+	0.177044i
$639$	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	$0.563223\pi$
$642$	−0.843104	+	2.31641i	−0.0332746	+	0.0914213i
$643$	9.48043	−	11.2983i	0.373872	−	0.445563i	−0.545998	−	0.837786i	$-0.683850\pi$
$643$	9.48043	−	11.2983i	0.373872	−	0.445563i	0.919870	+	0.392223i	$0.128294\pi$
$644$	4.05238	−	22.9822i	0.159686	−	0.905626i
$645$		0			0
$646$	−2.43999	−	50.8589i	−0.0960000	−	2.00102i
$647$		−	5.04555i		−	0.198361i	−0.995069	−	0.0991804i	$-0.968378\pi$
$647$		−	5.04555i		−	0.198361i	0.995069	−	0.0991804i	$-0.0316221\pi$
$648$	−12.6640	−	2.23300i	−0.497489	−	0.0877207i
$649$	35.1697	+	29.5109i	1.38053	+	1.15840i
$650$		0			0
$651$	−14.9465	+	5.44009i	−0.585800	+	0.213214i
$652$	33.7678	+	40.2429i	1.32245	+	1.57603i
$653$	−38.6875	+	22.3362i	−1.51396	+	0.874084i	−0.514092	+	0.857735i	$0.671871\pi$
$653$	−38.6875	+	22.3362i	−1.51396	+	0.874084i	−0.999866	+	0.0163488i	$0.994796\pi$
$654$	−6.57385	+	11.3862i	−0.257058	+	0.445237i
$655$		0			0
$656$	2.37016	+	13.4418i	0.0925391	+	0.524815i
$657$	4.89386	+	2.82547i	0.190927	+	0.110232i
$658$	−29.8094	+	17.2105i	−1.16209	+	0.670934i
$659$	−22.5147	+	18.8921i	−0.877049	+	0.735931i	−0.965570	−	0.260143i	$-0.916230\pi$
$659$	−22.5147	+	18.8921i	−0.877049	+	0.735931i	0.0885212	+	0.996074i	$0.471786\pi$
$660$		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	$0.482437\pi$
$662$	16.1889	−	19.2931i	0.629198	−	0.749849i
$663$	4.34410	+	0.765982i	0.168711	+	0.0297483i
$664$	−7.18975			−0.279016
$665$		0			0
$666$	47.9949			1.85976
$667$	−5.44177	−	0.959531i	−0.210706	−	0.0371532i
$668$	−17.7697	+	21.1771i	−0.687531	+	0.819367i
$669$	3.60083	+	1.31059i	0.139216	+	0.0506705i
$670$		0			0
$671$	8.42612	−	7.07036i	0.325287	−	0.272948i
$672$	22.6454	−	13.0743i	0.873564	−	0.504352i
$673$	23.9597	+	13.8331i	0.923577	+	0.533227i	0.884774	−	0.466019i	$-0.154312\pi$
$673$	23.9597	+	13.8331i	0.923577	+	0.533227i	0.0388026	+	0.999247i	$0.487646\pi$
$674$	−5.63809	−	31.9752i	−0.217171	−	1.23164i
$675$		0			0
$676$	16.3895	−	28.3875i	0.630367	−	1.09183i
$677$	−27.4305	+	15.8370i	−1.05424	+	0.608665i	−0.923833	−	0.382796i	$-0.874961\pi$
$677$	−27.4305	+	15.8370i	−1.05424	+	0.608665i	−0.130405	+	0.991461i	$0.541628\pi$
$678$	38.0075	+	45.2956i	1.45967	+	1.73957i
$679$	6.58477	−	2.39666i	0.252700	−	0.0919754i
$680$		0			0
$681$	7.22050	+	6.05872i	0.276690	+	0.232171i
$682$	−47.1898	−	8.32083i	−1.80699	−	0.318621i
$683$		−	4.75181i		−	0.181823i	−0.995859	−	0.0909114i	$-0.971022\pi$
$683$		−	4.75181i		−	0.181823i	0.995859	−	0.0909114i	$-0.0289780\pi$
$684$	21.3829	−	4.83716i	0.817595	−	0.184953i
$685$		0			0
$686$	−6.48729	+	36.7913i	−0.247686	+	1.40470i
$687$	7.91850	−	9.43690i	0.302110	−	0.360040i
$688$	−6.43559	+	17.6816i	−0.245355	+	0.674106i
$689$	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	$0.830769\pi$
$692$	−38.7090	−	22.3486i	−1.47149	−	0.849568i
$693$	−13.5247	+	2.38478i	−0.513763	+	0.0905902i
$694$	11.1753	+	63.3781i	0.424208	+	2.40580i
$695$		0			0
$696$	1.16545	+	2.01862i	0.0441762	+	0.0765155i
$697$	−18.4373	−	21.9727i	−0.698362	−	0.832275i
$698$	1.99665	+	5.48575i	0.0755743	+	0.207639i
$699$	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	$0.00760962\pi$
$702$		−	1.76053i		−	0.0664469i
$703$	45.8193	−	19.2105i	1.72811	−	0.724538i
$704$	54.3689			2.04911
$705$		0			0
$706$	−7.52915	−	6.31771i	−0.283363	−	0.237770i
$707$	−4.59459	+	12.6235i	−0.172797	+	0.474757i
$708$	19.0549	+	52.3530i	0.716129	+	1.96755i
$709$	−8.99170	+	7.54493i	−0.337690	+	0.283356i	−0.795825	−	0.605527i	$-0.792962\pi$
$709$	−8.99170	+	7.54493i	−0.337690	+	0.283356i	0.458134	+	0.888883i	$0.348518\pi$
$710$		0			0
$711$	−2.03935	+	3.53225i	−0.0764815	+	0.132470i
$712$	−3.81384	+	0.672483i	−0.142930	+	0.0252024i
$713$	29.1552	−	5.14084i	1.09187	−	0.192526i
$714$	−19.3531	+	33.5206i	−0.724272	+	1.25448i
$715$		0			0
$716$	29.3924	−	24.6632i	1.09845	−	0.921707i
$717$	−8.63567	−	23.7263i	−0.322505	−	0.886075i
$718$	8.99969	−	24.7264i	0.335865	−	0.922783i
$719$	38.6452	+	32.4272i	1.44122	+	1.20933i	0.938686	+	0.344773i	$0.112044\pi$
$719$	38.6452	+	32.4272i	1.44122	+	1.20933i	0.502536	+	0.864556i	$0.332400\pi$
$720$		0			0
$721$	11.5859			0.431481
$722$	32.9866	−	23.5234i	1.22764	−	0.875450i
$723$			36.4983i			1.35739i
$724$	−6.59907	+	37.4252i	−0.245252	+	1.39090i
$725$		0			0
$726$	−48.7818	−	17.7551i	−1.81046	−	0.658954i
$727$	8.91490	+	24.4935i	0.330636	+	0.908414i	0.987947	+	0.154794i	$0.0494715\pi$
$727$	8.91490	+	24.4935i	0.330636	+	0.908414i	−0.657311	+	0.753619i	$0.728306\pi$
$728$	−0.402132	−	0.479243i	−0.0149040	−	0.0177619i
$729$	−3.23417	−	5.60174i	−0.119784	−	0.207472i
$730$		0			0
$731$	−6.86641	−	38.9413i	−0.253963	−	1.44030i
$732$	13.1452	−	2.31785i	0.485860	−	0.0856702i
$733$	−14.7970	−	8.54306i	−0.546540	−	0.315545i	0.201185	−	0.979553i	$-0.435521\pi$
$733$	−14.7970	−	8.54306i	−0.546540	−	0.315545i	−0.747725	+	0.664008i	$0.768854\pi$
$734$	−1.74441	−	3.02141i	−0.0643873	−	0.111522i
$735$		0			0
$736$	−45.7345	+	16.6460i	−1.68580	+	0.613580i
$737$	−14.1734	+	38.9412i	−0.522086	+	1.43442i
$738$	14.1720	−	16.8895i	0.521677	−	0.621711i
$739$	4.27432	−	24.2409i	0.157233	−	0.891715i	−0.799482	−	0.600690i	$-0.794893\pi$
$739$	4.27432	−	24.2409i	0.157233	−	0.891715i	0.956715	−	0.291025i	$-0.0939963\pi$
$740$		0			0
$741$	1.35714	+	3.23694i	0.0498559	+	0.118912i
$742$			20.6636i			0.758583i
$743$	−7.55333	−	1.33186i	−0.277105	−	0.0488610i	0.0333687	−	0.999443i	$-0.489376\pi$
$743$	−7.55333	−	1.33186i	−0.277105	−	0.0488610i	−0.310473	+	0.950582i	$0.600488\pi$
$744$	−9.56649	−	8.02724i	−0.350724	−	0.294293i
$745$		0			0
$746$	29.5731	−	10.7637i	1.08275	−	0.394089i
$747$	−7.82393	−	9.32420i	−0.286263	−	0.341155i
$748$	−56.5664	+	32.6586i	−2.06827	+	1.19412i
$749$	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	$0.818887\pi$
$752$	24.5293	+	14.1620i	0.894493	+	0.516436i
$753$	−14.1871	+	8.19092i	−0.517006	+	0.298494i
$754$	−0.528376	+	0.443360i	−0.0192423	+	0.0161462i
$755$		0			0
$756$	8.13141	+	2.95959i	0.295737	+	0.107639i
$757$	2.76867	−	3.29957i	0.100629	−	0.119925i	−0.713379	−	0.700778i	$-0.752836\pi$
$757$	2.76867	−	3.29957i	0.100629	−	0.119925i	0.814009	+	0.580853i	$0.197281\pi$
$758$	−3.69312	−	0.651197i	−0.134140	−	0.0236525i
$759$	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	$0.506423\pi$
$762$	6.37459	+	1.12401i	0.230927	+	0.0407187i
$763$	2.63986	−	3.14606i	0.0955694	−	0.113895i
$764$	−0.0162238	−	0.00590497i	−0.000586956	−	0.000213634i
$765$		0			0
$766$	−13.8824	+	11.6487i	−0.501591	+	0.420885i
$767$	−3.06629	+	1.77032i	−0.110717	+	0.0639227i
$768$	−7.86973	−	4.54359i	−0.283975	−	0.163953i
$769$	−1.71410	−	9.72113i	−0.0618119	−	0.350553i	−0.999990	−	0.00440066i	$-0.998599\pi$
$769$	−1.71410	−	9.72113i	−0.0618119	−	0.350553i	0.938178	−	0.346152i	$-0.112512\pi$
$770$		0			0
$771$	6.70576	−	11.6147i	0.241502	−	0.418294i
$772$	−30.2769	+	17.4804i	−1.08969	+	0.629133i
$773$	−10.9744	−	13.0788i	−0.394721	−	0.470410i	0.531682	−	0.846944i	$-0.321560\pi$
$773$	−10.9744	−	13.0788i	−0.394721	−	0.470410i	−0.926403	+	0.376534i	$0.877116\pi$
$774$	28.5613	−	10.3955i	1.02662	−	0.373658i
$775$		0			0
$776$	4.21457	+	3.53644i	0.151294	+	0.126951i
$777$	−37.1945	−	6.55839i	−1.33434	−	0.235281i
$778$		−	72.3761i		−	2.59481i
$779$	6.76933	−	21.7964i	0.242537	−	0.780936i
$780$		0			0
$781$	5.21243	−	29.5611i	0.186515	−	1.05778i
$782$	46.3082	−	55.1880i	1.65598	−	1.97352i
$783$	0.700778	−	1.92537i	0.0250438	−	0.0688072i
$784$	11.7406	−	4.27323i	0.419307	−	0.152615i
$785$		0			0
$786$	46.4287	+	80.4169i	1.65606	+	2.86838i
$787$	−10.0948	−	5.82825i	−0.359842	−	0.207755i	0.309170	−	0.951007i	$-0.399949\pi$
$787$	−10.0948	−	5.82825i	−0.359842	−	0.207755i	−0.669011	+	0.743252i	$0.733282\pi$
$788$	−1.20344	+	0.212198i	−0.0428707	+	0.00755925i
$789$	−2.85786	−	16.2077i	−0.101742	−	0.577010i
$790$		0			0
$791$	−9.23498	−	15.9955i	−0.328358	−	0.568733i
$792$	−6.93090	−	8.25992i	−0.246279	−	0.293503i
$793$	0.290130	+	0.797127i	0.0103028	+	0.0283068i
$794$	15.5835	+	5.67194i	0.553038	+	0.201289i
$795$		0			0
$796$	−11.8624	+	67.2747i	−0.420450	+	2.38449i
$797$			29.8609i			1.05773i	0.848707	+	0.528864i	$0.177382\pi$
$797$			29.8609i			1.05773i	−0.848707	+	0.528864i	$0.822618\pi$
$798$	−30.7632	+	1.47589i	−1.08901	+	0.0522458i
$799$	−59.5220			−2.10574
$800$		0			0
$801$	−5.02237	−	4.21427i	−0.177457	−	0.148904i
$802$	−22.7457	+	62.4932i	−0.803178	+	2.20671i
$803$	−4.58191	−	12.5887i	−0.161692	−	0.444245i
$804$	−38.5229	+	32.3245i	−1.35860	+	1.14000i
$805$		0			0
$806$	1.84771	−	3.20033i	0.0650829	−	0.112727i
$807$	−23.8606	+	4.20726i	−0.839932	+	0.148103i
$808$	−10.3870	+	1.83151i	−0.365414	+	0.0644323i
$809$	−19.1756	+	33.2132i	−0.674180	+	1.16771i	0.302528	+	0.953140i	$0.402169\pi$
$809$	−19.1756	+	33.2132i	−0.674180	+	1.16771i	−0.976708	+	0.214573i	$0.931164\pi$
$810$		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	$0.214985\pi$
$812$	−1.15952	−	3.18575i	−0.0406911	−	0.111798i
$813$	2.17313	−	5.97062i	0.0762150	−	0.209399i
$814$	−87.1612	−	73.1369i	−3.05500	−	2.56345i
$815$		0			0
$816$	31.8503			1.11498
$817$	23.1057	−	21.3562i	0.808367	−	0.747160i
$818$		−	31.2935i		−	1.09415i
$819$	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	$0.653735\pi$
$822$	17.3734	+	47.7330i	0.605966	+	1.66488i
$823$	21.3546	+	25.4494i	0.744373	+	0.887110i	0.996753	−	0.0805185i	$-0.0256576\pi$
$823$	21.3546	+	25.4494i	0.744373	+	0.887110i	−0.252380	+	0.967628i	$0.581213\pi$
$824$	4.54825	+	7.87779i	0.158446	+	0.274436i
$825$		0			0
$826$	−5.39493	−	30.5962i	−0.187714	−	1.06458i
$827$	−3.35559	+	0.591681i	−0.116685	+	0.0205748i	−0.231686	−	0.972791i	$-0.574424\pi$
$827$	−3.35559	+	0.591681i	−0.116685	+	0.0205748i	0.115001	+	0.993365i	$0.463313\pi$
$828$	26.8633	+	15.5095i	0.933563	+	0.538993i
$829$	2.21217	+	3.83160i	0.0768320	+	0.133077i	0.901881	−	0.431984i	$-0.142186\pi$
$829$	2.21217	+	3.83160i	0.0768320	+	0.133077i	−0.825049	+	0.565060i	$0.808853\pi$
$830$		0			0
$831$	33.8366	−	12.3155i	1.17378	−	0.427221i
$832$	−1.43407	+	3.94007i	−0.0497174	+	0.136597i
$833$	−16.8770	+	20.1132i	−0.584752	+	0.696880i
$834$	5.93906	−	33.6821i	0.205653	−	1.16632i
$835$		0			0
$836$	−46.2035	−	23.7998i	−1.59798	−	0.823132i
$837$			10.9775i			0.379438i
$838$	−43.2726	−	7.63013i	−1.49483	−	0.263579i
$839$	18.2406	+	15.3057i	0.629736	+	0.528411i	0.900847	−	0.434137i	$-0.142947\pi$
$839$	18.2406	+	15.3057i	0.629736	+	0.528411i	−0.271111	+	0.962548i	$0.587391\pi$
$840$		0			0
$841$	26.4968	−	9.64403i	0.913681	−	0.332553i
$842$	−37.9387	−	45.2136i	−1.30745	−	1.55816i
$843$	6.21208	−	3.58655i	0.213956	−	0.123527i
$844$	10.4952	−	18.1782i	0.361259	−	0.625719i
$845$		0			0
$846$	−7.94477	−	45.0570i	−0.273147	−	1.54909i
$847$	14.0432	+	8.10785i	0.482530	+	0.278589i
$848$	14.7254	−	8.50173i	0.505673	−	0.291951i
$849$	−21.9968	+	18.4575i	−0.754929	+	0.633461i
$850$		0			0
$851$	66.0575	+	24.0430i	2.26442	+	0.824183i
$852$	23.4141	−	27.9039i	0.802155	−	0.955971i
$853$	−4.36634	−	0.769903i	−0.149501	−	0.0263610i	0.0983970	−	0.995147i	$-0.468629\pi$
$853$	−4.36634	−	0.769903i	−0.149501	−	0.0263610i	−0.247898	+	0.968786i	$0.579740\pi$
$854$	−7.44345			−0.254710
$855$		0			0
$856$	0.604557			0.0206633
$857$	−26.5874	−	4.68808i	−0.908208	−	0.160142i	−0.300019	−	0.953933i	$-0.596993\pi$
$857$	−26.5874	−	4.68808i	−0.908208	−	0.160142i	−0.608190	+	0.793792i	$0.708104\pi$
$858$	5.16682	−	6.15758i	0.176392	−	0.210216i
$859$	−12.8850	−	4.68976i	−0.439631	−	0.160013i	0.112715	−	0.993627i	$-0.464045\pi$
$859$	−12.8850	−	4.68976i	−0.439631	−	0.160013i	−0.552346	+	0.833615i	$0.686267\pi$
$860$		0			0
$861$	−13.2907	+	11.1522i	−0.452947	+	0.380067i
$862$	38.5883	−	22.2790i	1.31432	−	0.758825i
$863$	−45.4213	−	26.2240i	−1.54616	−	0.892676i	−0.998430	−	0.0560208i	$-0.982159\pi$
$863$	−45.4213	−	26.2240i	−1.54616	−	0.892676i	−0.547730	−	0.836655i	$-0.684508\pi$
$864$	−3.13378	−	17.7725i	−0.106613	−	0.604634i
$865$		0			0
$866$	−2.05341	+	3.55662i	−0.0697778	+	0.120859i
$867$	−25.1282	+	14.5078i	−0.853398	+	0.492709i
$868$	11.6753	+	13.9141i	0.396286	+	0.472276i
$869$	9.08617	−	3.30710i	0.308227	−	0.112186i
$870$		0			0
$871$	−2.44819	−	2.05428i	−0.0829538	−	0.0696065i
$872$	3.17548	+	0.559923i	0.107535	+	0.0189614i
$873$			9.31414i			0.315236i
$874$	56.8658	+	7.23758i	1.92352	+	0.244815i
$875$		0			0
$876$	2.82297	−	16.0098i	0.0953792	−	0.540923i
$877$	−26.2422	+	31.2742i	−0.886136	+	1.05606i	0.111919	+	0.993717i	$0.464300\pi$
$877$	−26.2422	+	31.2742i	−0.886136	+	1.05606i	−0.998055	+	0.0623382i	$0.980144\pi$
$878$	25.3068	−	69.5298i	0.854062	−	2.34652i
$879$	−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	$0.535733\pi$
$882$	−17.4780	−	10.0909i	−0.588513	−	0.339778i
$883$	−31.6167	+	5.57488i	−1.06399	+	0.187610i	−0.678125	−	0.734946i	$-0.737207\pi$
$883$	−31.6167	+	5.57488i	−1.06399	+	0.187610i	−0.385863	+	0.922556i	$0.626096\pi$
$884$	−0.874713	−	4.96074i	−0.0294198	−	0.166848i
$885$		0			0
$886$	−28.0629	−	48.6064i	−0.942792	−	1.63296i
$887$	5.66820	+	6.75510i	0.190319	+	0.226814i	0.852763	−	0.522298i	$-0.174925\pi$
$887$	5.66820	+	6.75510i	0.190319	+	0.226814i	−0.662444	+	0.749112i	$0.730481\pi$
$888$	−10.1420	−	27.8649i	−0.340343	−	0.935084i
$889$	−1.89999	−	0.691539i	−0.0637235	−	0.0231935i
$890$		0			0
$891$	−8.96205	+	50.8263i	−0.300240	+	1.70275i
$892$		−	4.37586i		−	0.146515i
$893$	−25.6192	−	39.8346i	−0.857314	−	1.33301i
$894$	−20.2002			−0.675595
$895$		0			0
$896$	−10.2224	−	8.57759i	−0.341505	−	0.286557i
$897$	−1.69854	+	4.66669i	−0.0567125	+	0.155816i
$898$	9.79587	+	26.9139i	0.326892	+	0.898130i
$899$	3.29461	−	2.76451i	0.109881	−	0.0922014i
$900$		0			0
$901$	−17.8661	+	30.9450i	−0.595206	+	1.03093i
$902$	−51.4741	+	9.07627i	−1.71390	+	0.302207i
$903$	−23.5546	+	4.15332i	−0.783849	+	0.138214i
$904$	7.25071	−	12.5586i	0.241155	−	0.417693i
$905$		0			0
$906$	−71.1810	+	59.7279i	−2.36483	+	1.98433i
$907$	3.53667	+	9.71693i	0.117433	+	0.322645i	0.984458	−	0.175620i	$-0.0561929\pi$
$907$	3.53667	+	9.71693i	0.117433	+	0.322645i	−0.867025	+	0.498265i	$0.833971\pi$
$908$	3.68139	−	10.1145i	0.122171	−	0.335663i
$909$	−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	$0.472232\pi$
$912$	13.7089	+	21.3155i	0.453946	+	0.705827i
$913$			28.8557i			0.954985i
$914$	−0.0762343	+	0.432346i	−0.00252161	+	0.0143007i
$915$		0			0
$916$	−13.2193	−	4.81143i	−0.436778	−	0.158974i
$917$	−9.92047	−	27.2563i	−0.327603	−	0.900081i
$918$	17.1711	+	20.4637i	0.566731	+	0.675403i
$919$	0.101184	+	0.175255i	0.00333774	+	0.00578114i	0.867689	−	0.497107i	$-0.165604\pi$
$919$	0.101184	+	0.175255i	0.00333774	+	0.00578114i	−0.864352	+	0.502888i	$0.832271\pi$
$920$		0			0
$921$	6.34453	+	35.9816i	0.209060	+	1.18564i
$922$	81.9569	−	14.4512i	2.69911	−	0.475925i
$923$	2.00479	+	1.15746i	0.0659883	+	0.0380984i
$924$	19.7544	+	34.2155i	0.649871	+	1.12561i
$925$		0			0
$926$	14.8774	−	5.41492i	0.488901	−	0.177945i
$927$	−5.26707	+	14.4712i	−0.172993	+	0.475296i
$928$	−4.54477	+	5.41624i	−0.149189	+	0.177797i
$929$	−3.23698	+	18.3578i	−0.106202	+	0.602301i	0.884532	+	0.466480i	$0.154478\pi$
$929$	−3.23698	+	18.3578i	−0.106202	+	0.602301i	−0.990733	+	0.135821i	$0.956633\pi$
$930$		0			0
$931$	−20.7247	−	2.63773i	−0.679223	−	0.0864480i
$932$		−	71.8151i		−	2.35238i
$933$	54.4178	+	9.59533i	1.78156	+	0.314137i
$934$	−35.8150	−	30.0524i	−1.17190	−	0.983344i
$935$		0			0
$936$	0.781404	−	0.284408i	0.0255410	−	0.00929615i
$937$	32.4677	+	38.6935i	1.06067	+	1.26406i	0.963189	+	0.268824i	$0.0866349\pi$
$937$	32.4677	+	38.6935i	1.06067	+	1.26406i	0.0974836	+	0.995237i	$0.468921\pi$
$938$	24.2859	−	14.0215i	0.792964	−	0.457818i
$939$	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	$-0.142659\pi$
$942$	1.17973	+	0.681118i	0.0384377	+	0.0221920i
$943$	27.9663	−	16.1463i	0.910708	−	0.525797i
$944$	−19.5840	+	16.4329i	−0.637405	+	0.534847i
$945$		0			0
$946$	−67.7100	−	24.6444i	−2.20144	−	0.801259i
$947$	24.0625	−	28.6765i	0.781925	−	0.931862i	−0.217094	−	0.976151i	$-0.569658\pi$
$947$	24.0625	−	28.6765i	0.781925	−	0.931862i	0.999019	+	0.0442887i	$0.0141021\pi$
$948$	11.5555	+	2.03754i	0.375304	+	0.0661763i
$949$	1.03315			0.0335374
$950$		0			0
$951$	13.5526			0.439474
$952$	9.34847	+	1.64839i	0.302986	+	0.0534245i
$953$	−27.2981	+	32.5326i	−0.884273	+	1.05384i	0.113905	+	0.993492i	$0.463664\pi$
$953$	−27.2981	+	32.5326i	−0.884273	+	1.05384i	−0.998178	+	0.0603438i	$0.980780\pi$
$954$	−25.8095	−	9.39387i	−0.835612	−	0.304138i
$955$		0			0
$956$	−22.0874	+	18.5336i	−0.714359	+	0.599418i
$957$	8.10162	−	4.67748i	0.261888	−	0.151201i
$958$	51.8541	+	29.9380i	1.67533	+	0.967252i
$959$	−2.75529	−	15.6260i	−0.0889728	−	0.504590i
$960$		0			0
$961$	3.97887	−	6.89160i	0.128351	−	0.222310i
$962$	7.59919	−	4.38740i	0.245008	−	0.141455i
$963$	0.657883	+	0.784034i	0.0212000	+	0.0252652i
$964$	39.1657	−	14.2552i	1.26144	−	0.459128i
$965$		0			0
$966$	−33.3818	−	28.0107i	−1.07404	−	0.901228i
$967$	−15.9815	−	2.81797i	−0.513930	−	0.0906197i	−0.0893324	−	0.996002i	$-0.528473\pi$
$967$	−15.9815	−	2.81797i	−0.513930	−	0.0906197i	−0.424598	+	0.905382i	$0.639584\pi$
$968$			12.7315i			0.409206i
$969$	−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	$0.964358\pi$
$972$	−29.0253	+	34.5910i	−0.930988	+	1.10951i
$973$	−3.65396	+	10.0392i	−0.117140	+	0.321841i
$974$	−28.3229	+	10.3087i	−0.907524	+	0.330312i
$975$		0			0
$976$	3.06250	+	5.30441i	0.0980283	+	0.169790i
$977$	0.104681	+	0.0604375i	0.00334903	+	0.00193357i	0.501674	−	0.865057i	$-0.332718\pi$
$977$	0.104681	+	0.0604375i	0.00334903	+	0.00193357i	−0.498325	+	0.866991i	$0.666051\pi$
$978$	96.6056	−	17.0342i	3.08911	−	0.544693i
$979$	2.69898	+	15.3067i	0.0862597	+	0.489203i
$980$		0			0
$981$	2.72943	+	4.72751i	0.0871439	+	0.150938i
$982$	31.7913	+	37.8874i	1.01450	+	1.20904i
$983$	−7.75648	−	21.3108i	−0.247393	−	0.679708i	−0.999780	−	0.0209857i	$-0.993320\pi$
$983$	−7.75648	−	21.3108i	−0.247393	−	0.679708i	0.752386	−	0.658722i	$-0.228903\pi$
$984$	−12.8004	−	4.65898i	−0.408063	−	0.148523i
$985$		0			0
$986$	1.81738	−	10.3069i	0.0578773	−	0.328239i
$987$			36.0033i			1.14600i
$988$	2.94344	−	2.72058i	0.0936434	−	0.0865530i
$989$	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	$-0.603591\pi$
$992$	12.9560	−	35.5963i	0.411353	−	1.13018i
$993$	−9.00991	−	24.7545i	−0.285921	−	0.785561i
$994$	−15.5605	+	13.0568i	−0.493550	+	0.414137i
$995$		0			0
$996$	−17.5083	+	30.3252i	−0.554770	+	0.960890i
$997$	36.1853	−	6.38045i	1.14600	−	0.202071i	0.431772	−	0.901983i	$-0.357889\pi$
$997$	36.1853	−	6.38045i	1.14600	−	0.202071i	0.714229	+	0.699912i	$0.246777\pi$
$998$	89.1091	−	15.7123i	2.82070	−	0.497365i
$999$	−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.u.b.74.2		36
5.2	odd	4		95.2.k.a.36.3	✓	18
5.3	odd	4		475.2.l.c.226.1		18
5.4	even	2	inner	475.2.u.b.74.5		36
15.2	even	4		855.2.bs.c.226.1		18
19.9	even	9	inner	475.2.u.b.199.5		36
95.3	even	36		9025.2.a.cf.1.7		9
95.9	even	18	inner	475.2.u.b.199.2		36
95.22	even	36		1805.2.a.s.1.3		9
95.28	odd	36		475.2.l.c.351.1		18
95.47	odd	36		95.2.k.a.66.3	yes	18
95.73	odd	36		9025.2.a.cc.1.3		9
95.92	odd	36		1805.2.a.v.1.7		9
285.47	even	36		855.2.bs.c.541.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.36.3	✓	18	5.2	odd	4
95.2.k.a.66.3	yes	18	95.47	odd	36
475.2.l.c.226.1		18	5.3	odd	4
475.2.l.c.351.1		18	95.28	odd	36
475.2.u.b.74.2		36	1.1	even	1	trivial
475.2.u.b.74.5		36	5.4	even	2	inner
475.2.u.b.199.2		36	95.9	even	18	inner
475.2.u.b.199.5		36	19.9	even	9	inner
855.2.bs.c.226.1		18	15.2	even	4
855.2.bs.c.541.1		18	285.47	even	36
1805.2.a.s.1.3		9	95.22	even	36
1805.2.a.v.1.7		9	95.92	odd	36
9025.2.a.cc.1.3		9	95.73	odd	36
9025.2.a.cf.1.7		9	95.3	even	36

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.09998 - 0.370282i) q^{2} +(-1.43367 + 1.70859i) q^{3} +(2.39340 + 0.871127i) q^{4} +(3.64334 - 3.05712i) q^{6} +(-1.28659 + 0.742812i) q^{7} +(-1.01015 - 0.583208i) q^{8} +(-0.342900 - 1.94468i) q^{9} +O(q^{10})\)	\(q+(-2.09998 - 0.370282i) q^{2} +(-1.43367 + 1.70859i) q^{3} +(2.39340 + 0.871127i) q^{4} +(3.64334 - 3.05712i) q^{6} +(-1.28659 + 0.742812i) q^{7} +(-1.01015 - 0.583208i) q^{8} +(-0.342900 - 1.94468i) q^{9} +(-2.34068 + 4.05417i) q^{11} +(-4.91975 + 2.84042i) q^{12} +(-0.232063 - 0.276562i) q^{13} +(2.97685 - 1.08349i) q^{14} +(-1.99691 - 1.67560i) q^{16} +(5.39483 + 0.951255i) q^{17} +4.21075i q^{18} +(1.68540 + 4.01988i) q^{19} +(0.575390 - 3.26320i) q^{21} +(6.41655 - 7.64695i) q^{22} +(-2.10937 + 5.79545i) q^{23} +(2.44468 - 0.889790i) q^{24} +(0.384921 + 0.666703i) q^{26} +(-1.98049 - 1.14343i) q^{27} +(-3.72641 + 0.657066i) q^{28} +(0.155581 + 0.882346i) q^{29} +(-2.40012 - 4.15713i) q^{31} +(5.07252 + 6.04520i) q^{32} +(-3.57113 - 9.81160i) q^{33} +(-10.9768 - 3.99522i) q^{34} +(0.873368 - 4.95311i) q^{36} -11.3982i q^{37} +(-2.05081 - 9.06572i) q^{38} +0.805233 q^{39} +(-4.01104 - 3.36566i) q^{41} +(-2.41661 + 6.63958i) q^{42} +(-2.46879 - 6.78295i) q^{43} +(-9.13387 + 7.66423i) q^{44} +(6.57558 - 11.3892i) q^{46} +(-10.7005 + 1.88678i) q^{47} +(5.72583 - 1.00962i) q^{48} +(-2.39646 + 4.15079i) q^{49} +(-9.35973 + 7.85374i) q^{51} +(-0.314500 - 0.864081i) q^{52} +(-2.23092 + 6.12941i) q^{53} +(3.73558 + 3.13452i) q^{54} +1.73286 q^{56} +(-9.28462 - 2.88354i) q^{57} -1.91051i q^{58} +(1.70300 - 9.65818i) q^{59} +(-2.20795 - 0.803626i) q^{61} +(3.50088 + 9.61858i) q^{62} +(1.88571 + 2.24730i) q^{63} +(-5.80697 - 10.0580i) q^{64} +(3.86622 + 21.9264i) q^{66} +(8.71774 - 1.53717i) q^{67} +(12.0833 + 6.97632i) q^{68} +(-6.87787 - 11.9128i) q^{69} +(-6.02538 + 2.19306i) q^{71} +(-0.787775 + 2.16439i) q^{72} +(-1.83946 + 2.19219i) q^{73} +(-4.22054 + 23.9359i) q^{74} +(0.532020 + 11.0894i) q^{76} -6.95473i q^{77} +(-1.69097 - 0.298164i) q^{78} +(-1.58226 - 1.32767i) q^{79} +(10.3598 - 3.77066i) q^{81} +(7.17684 + 8.55302i) q^{82} +(5.33816 - 3.08199i) q^{83} +(4.21980 - 7.30890i) q^{84} +(2.67280 + 15.1582i) q^{86} +(-1.73062 - 0.999172i) q^{87} +(4.72885 - 2.73020i) q^{88} +(2.54338 - 2.13415i) q^{89} +(0.504004 + 0.183442i) q^{91} +(-10.0971 + 12.0333i) q^{92} +(10.5438 + 1.85915i) q^{93} +23.1693 q^{94} -17.6011 q^{96} +(-4.64512 - 0.819060i) q^{97} +(6.56947 - 7.82919i) q^{98} +(8.68669 + 3.16170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9}+O(q^{10}) \) 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9	\( 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9} + 24 q^{14} - 6 q^{16} - 42 q^{21} + 30 q^{24} + 6 q^{26} - 30 q^{29} - 36 q^{31} + 24 q^{34} + 150 q^{36} - 72 q^{39} - 60 q^{41} - 84 q^{44} + 18 q^{46} - 18 q^{49} - 90 q^{51} + 132 q^{54} - 36 q^{59} - 60 q^{61} - 72 q^{64} + 78 q^{66} - 30 q^{69} - 24 q^{71} + 30 q^{74} - 66 q^{76} + 102 q^{79} + 54 q^{81} - 96 q^{84} + 126 q^{86} + 108 q^{89} + 60 q^{91} - 60 q^{94} - 132 q^{96} + 186 q^{99}+O(q^{100}) \) 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9 + 24 * q^14 - 6 * q^16 - 42 * q^21 + 30 * q^24 + 6 * q^26 - 30 * q^29 - 36 * q^31 + 24 * q^34 + 150 * q^36 - 72 * q^39 - 60 * q^41 - 84 * q^44 + 18 * q^46 - 18 * q^49 - 90 * q^51 + 132 * q^54 - 36 * q^59 - 60 * q^61 - 72 * q^64 + 78 * q^66 - 30 * q^69 - 24 * q^71 + 30 * q^74 - 66 * q^76 + 102 * q^79 + 54 * q^81 - 96 * q^84 + 126 * q^86 + 108 * q^89 + 60 * q^91 - 60 * q^94 - 132 * q^96 + 186 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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