LMFDB - Embedded newform 722.2.e.n.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.186694177220038656.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 343x^{6} + 117649 $ x^12 + 343*x^6 + 117649
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			415.1
Root			$2.02676 + 1.70066i$ of defining polynomial
Character	$\chi$	$=$	722.415
Dual form			722.2.e.n.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-2.48619 + 0.904900i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.285782 + 1.62075i) q^{5} +(-2.48619 - 0.904900i) q^{6} +(-1.82288 - 3.15731i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(3.06418 - 2.57115i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-2.48619 + 0.904900i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.285782 + 1.62075i) q^{5} +(-2.48619 - 0.904900i) q^{6} +(-1.82288 - 3.15731i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(3.06418 - 2.57115i) q^{9} +(-1.26072 + 1.05787i) q^{10} +(2.32288 - 4.02334i) q^{11} +(-1.32288 - 2.29129i) q^{12} +(-1.87939 - 0.684040i) q^{13} +(0.633078 - 3.59036i) q^{14} +(-0.756107 - 4.28810i) q^{15} +(-0.939693 + 0.342020i) q^{16} +4.00000 q^{18} -1.64575 q^{20} +(7.38907 + 6.20017i) q^{21} +(4.36558 - 1.58894i) q^{22} +(-0.285782 - 1.62075i) q^{23} +(0.459430 - 2.60556i) q^{24} +(2.15331 + 0.783740i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(-1.32288 + 2.29129i) q^{27} +(2.79281 - 2.34344i) q^{28} +(1.26072 - 1.05787i) q^{29} +(2.17712 - 3.77089i) q^{30} +(2.82288 + 4.88936i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-2.13440 + 12.1048i) q^{33} +(5.63816 - 2.05212i) q^{35} +(3.06418 + 2.57115i) q^{36} +0.354249 q^{37} +5.29150 q^{39} +(-1.26072 - 1.05787i) q^{40} +(0.273923 - 0.0996998i) q^{41} +(1.67497 + 9.49921i) q^{42} +(1.96075 - 11.1200i) q^{43} +(4.36558 + 1.58894i) q^{44} +(3.29150 + 5.70105i) q^{45} +(0.822876 - 1.42526i) q^{46} +(3.33555 - 2.79886i) q^{47} +(2.02676 - 1.70066i) q^{48} +(-3.14575 + 5.44860i) q^{49} +(1.14575 + 1.98450i) q^{50} +(0.347296 - 1.96962i) q^{52} +(-2.18502 - 12.3918i) q^{53} +(-2.48619 + 0.904900i) q^{54} +(5.85699 + 4.91459i) q^{55} +3.64575 q^{56} +1.64575 q^{58} +(-6.08029 - 5.10197i) q^{59} +(4.09166 - 1.48924i) q^{60} +(0.162752 + 0.923015i) q^{61} +(-0.980374 + 5.55998i) q^{62} +(-13.7035 - 4.98768i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.64575 - 2.85052i) q^{65} +(-9.41584 + 7.90083i) q^{66} +(0.494674 - 0.415081i) q^{67} +(2.17712 + 3.77089i) q^{69} +(5.63816 + 2.05212i) q^{70} +(-0.470326 + 2.66735i) q^{71} +(0.694593 + 3.93923i) q^{72} +(-1.60546 + 0.584341i) q^{73} +(0.271370 + 0.227707i) q^{74} -6.06275 q^{75} -16.9373 q^{77} +(4.05353 + 3.40131i) q^{78} +(3.75877 - 1.36808i) q^{79} +(-0.285782 - 1.62075i) q^{80} +(-0.868241 + 4.92404i) q^{81} +(0.273923 + 0.0996998i) q^{82} +(-3.96863 - 6.87386i) q^{83} +(-4.82288 + 8.35347i) q^{84} +(8.64979 - 7.25804i) q^{86} +(-2.17712 + 3.77089i) q^{87} +(2.32288 + 4.02334i) q^{88} +(-1.14313 + 6.48299i) q^{90} +(1.26616 + 7.18073i) q^{91} +(1.54650 - 0.562880i) q^{92} +(-11.4426 - 9.60148i) q^{93} +4.35425 q^{94} +2.64575 q^{96} +(-2.84087 - 2.38378i) q^{97} +(-5.91208 + 2.15182i) q^{98} +(-3.22690 - 18.3007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^7 - 6 * q^8	$ 12 q - 6 q^{7} - 6 q^{8} + 12 q^{11} + 48 q^{18} + 12 q^{20} - 12 q^{26} + 42 q^{30} + 18 q^{31} + 36 q^{37} - 24 q^{45} - 6 q^{46} - 6 q^{49} - 18 q^{50} + 12 q^{56} - 12 q^{58} - 6 q^{64} - 12 q^{65} + 42 q^{69} - 168 q^{75} - 108 q^{77} - 42 q^{84} - 42 q^{87} + 12 q^{88} + 84 q^{94}+O(q^{100}) $ 12 * q - 6 * q^7 - 6 * q^8 + 12 * q^11 + 48 * q^18 + 12 * q^20 - 12 * q^26 + 42 * q^30 + 18 * q^31 + 36 * q^37 - 24 * q^45 - 6 * q^46 - 6 * q^49 - 18 * q^50 + 12 * q^56 - 12 * q^58 - 6 * q^64 - 12 * q^65 + 42 * q^69 - 168 * q^75 - 108 * q^77 - 42 * q^84 - 42 * q^87 + 12 * q^88 + 84 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−2.48619	+	0.904900i	−1.43540	+	0.522444i	−0.938475	−	0.345347i	$-0.887761\pi$
$3$	−2.48619	+	0.904900i	−1.43540	+	0.522444i	−0.496929	+	0.867791i	$0.665539\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.285782	+	1.62075i	−0.127805	+	0.724821i	0.851796	+	0.523873i	$0.175513\pi$
$5$	−0.285782	+	1.62075i	−0.127805	+	0.724821i	−0.979602	+	0.200948i	$0.935598\pi$
$6$	−2.48619	−	0.904900i	−1.01498	−	0.369424i
$7$	−1.82288	−	3.15731i	−0.688982	−	1.19335i	−0.972167	−	0.234287i	$-0.924724\pi$
$7$	−1.82288	−	3.15731i	−0.688982	−	1.19335i	0.283185	−	0.959065i	$-0.408609\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	3.06418	−	2.57115i	1.02139	−	0.857050i
$10$	−1.26072	+	1.05787i	−0.398674	+	0.334527i
$11$	2.32288	−	4.02334i	0.700373	−	1.21308i	−0.267962	−	0.963429i	$-0.586350\pi$
$11$	2.32288	−	4.02334i	0.700373	−	1.21308i	0.968335	−	0.249653i	$-0.0803165\pi$
$12$	−1.32288	−	2.29129i	−0.381881	−	0.661438i
$13$	−1.87939	−	0.684040i	−0.521248	−	0.189719i	0.0679785	−	0.997687i	$-0.478345\pi$
$13$	−1.87939	−	0.684040i	−0.521248	−	0.189719i	−0.589226	+	0.807968i	$0.700567\pi$
$14$	0.633078	−	3.59036i	0.169197	−	0.959565i
$15$	−0.756107	−	4.28810i	−0.195226	−	1.10718i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$17$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$18$	4.00000			0.942809
$19$		0			0
$19$		0			0
$20$	−1.64575			−0.368001
$21$	7.38907	+	6.20017i	1.61243	+	1.35299i
$22$	4.36558	−	1.58894i	0.930744	−	0.338763i
$23$	−0.285782	−	1.62075i	−0.0595896	−	0.337949i	0.940408	−	0.340048i	$-0.110443\pi$
$23$	−0.285782	−	1.62075i	−0.0595896	−	0.337949i	−0.999998	+	0.00209824i	$0.999332\pi$
$24$	0.459430	−	2.60556i	0.0937807	−	0.531857i
$25$	2.15331	+	0.783740i	0.430662	+	0.156748i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$	−1.32288	+	2.29129i	−0.254588	+	0.440959i
$28$	2.79281	−	2.34344i	0.527791	−	0.442869i
$29$	1.26072	−	1.05787i	0.234110	−	0.196441i	−0.518184	−	0.855269i	$-0.673392\pi$
$29$	1.26072	−	1.05787i	0.234110	−	0.196441i	0.752294	+	0.658828i	$0.228947\pi$
$30$	2.17712	−	3.77089i	0.397487	−	0.688467i
$31$	2.82288	+	4.88936i	0.507003	+	0.878156i	0.999967	+	0.00810584i	$0.00258020\pi$
$31$	2.82288	+	4.88936i	0.507003	+	0.878156i	−0.492964	+	0.870050i	$0.664086\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−2.13440	+	12.1048i	−0.371551	+	2.10717i
$34$		0			0
$35$	5.63816	−	2.05212i	0.953022	−	0.346872i
$36$	3.06418	+	2.57115i	0.510696	+	0.428525i
$37$	0.354249			0.0582381			0.0291191	−	0.999576i	$-0.490730\pi$
$37$	0.354249			0.0582381			0.0291191	+	0.999576i	$0.490730\pi$
$38$		0			0
$39$	5.29150			0.847319
$40$	−1.26072	−	1.05787i	−0.199337	−	0.167264i
$41$	0.273923	−	0.0996998i	0.0427796	−	0.0155705i	−0.320542	−	0.947234i	$-0.603865\pi$
$41$	0.273923	−	0.0996998i	0.0427796	−	0.0155705i	0.363321	+	0.931664i	$0.381643\pi$
$42$	1.67497	+	9.49921i	0.258453	+	1.46576i
$43$	1.96075	−	11.1200i	0.299011	−	1.69578i	−0.351424	−	0.936216i	$-0.614302\pi$
$43$	1.96075	−	11.1200i	0.299011	−	1.69578i	0.650435	−	0.759562i	$-0.274586\pi$
$44$	4.36558	+	1.58894i	0.658136	+	0.239542i
$45$	3.29150	+	5.70105i	0.490668	+	0.849862i
$46$	0.822876	−	1.42526i	0.121326	−	0.210143i
$47$	3.33555	−	2.79886i	0.486540	−	0.408255i	−0.366245	−	0.930519i	$-0.619357\pi$
$47$	3.33555	−	2.79886i	0.486540	−	0.408255i	0.852784	+	0.522263i	$0.174912\pi$
$48$	2.02676	−	1.70066i	0.292538	−	0.245469i
$49$	−3.14575	+	5.44860i	−0.449393	+	0.778372i
$50$	1.14575	+	1.98450i	0.162034	+	0.280651i
$51$		0			0
$52$	0.347296	−	1.96962i	0.0481613	−	0.273137i
$53$	−2.18502	−	12.3918i	−0.300135	−	1.70215i	−0.645565	−	0.763706i	$-0.723378\pi$
$53$	−2.18502	−	12.3918i	−0.300135	−	1.70215i	0.345430	−	0.938445i	$-0.387733\pi$
$54$	−2.48619	+	0.904900i	−0.338328	+	0.123141i
$55$	5.85699	+	4.91459i	0.789756	+	0.662684i
$56$	3.64575			0.487184
$57$		0			0
$58$	1.64575			0.216098
$59$	−6.08029	−	5.10197i	−0.791586	−	0.664220i	0.154551	−	0.987985i	$-0.450607\pi$
$59$	−6.08029	−	5.10197i	−0.791586	−	0.664220i	−0.946138	+	0.323765i	$0.895051\pi$
$60$	4.09166	−	1.48924i	0.528230	−	0.192260i
$61$	0.162752	+	0.923015i	0.0208383	+	0.118180i	0.993453	−	0.114245i	$-0.0364450\pi$
$61$	0.162752	+	0.923015i	0.0208383	+	0.118180i	−0.972614	+	0.232425i	$0.925334\pi$
$62$	−0.980374	+	5.55998i	−0.124508	+	0.706118i
$63$	−13.7035	−	4.98768i	−1.72648	−	0.628389i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.64575	−	2.85052i	0.204130	−	0.353564i
$66$	−9.41584	+	7.90083i	−1.15901	+	0.972524i
$67$	0.494674	−	0.415081i	0.0604341	−	0.0507102i	−0.612070	−	0.790803i	$-0.709663\pi$
$67$	0.494674	−	0.415081i	0.0604341	−	0.0507102i	0.672504	+	0.740093i	$0.265219\pi$
$68$		0			0
$69$	2.17712	+	3.77089i	0.262095	+	0.453962i
$70$	5.63816	+	2.05212i	0.673889	+	0.245275i
$71$	−0.470326	+	2.66735i	−0.0558174	+	0.316556i	−0.999914	−	0.0131127i	$-0.995826\pi$
$71$	−0.470326	+	2.66735i	−0.0558174	+	0.316556i	0.944097	+	0.329669i	$0.106937\pi$
$72$	0.694593	+	3.93923i	0.0818585	+	0.464243i
$73$	−1.60546	+	0.584341i	−0.187905	+	0.0683919i	−0.434259	−	0.900788i	$-0.642990\pi$
$73$	−1.60546	+	0.584341i	−0.187905	+	0.0683919i	0.246354	+	0.969180i	$0.420767\pi$
$74$	0.271370	+	0.227707i	0.0315461	+	0.0264704i
$75$	−6.06275			−0.700066
$76$		0			0
$77$	−16.9373			−1.93018
$78$	4.05353	+	3.40131i	0.458971	+	0.385123i
$79$	3.75877	−	1.36808i	0.422895	−	0.153921i	−0.121802	−	0.992554i	$-0.538867\pi$
$79$	3.75877	−	1.36808i	0.422895	−	0.153921i	0.544696	+	0.838633i	$0.316645\pi$
$80$	−0.285782	−	1.62075i	−0.0319514	−	0.181205i
$81$	−0.868241	+	4.92404i	−0.0964712	+	0.547115i
$82$	0.273923	+	0.0996998i	0.0302497	+	0.0110100i
$83$	−3.96863	−	6.87386i	−0.435613	−	0.754505i	0.561732	−	0.827319i	$-0.310135\pi$
$83$	−3.96863	−	6.87386i	−0.435613	−	0.754505i	−0.997345	+	0.0728147i	$0.976802\pi$
$84$	−4.82288	+	8.35347i	−0.526219	+	0.911438i
$85$		0			0
$86$	8.64979	−	7.25804i	0.932731	−	0.782654i
$87$	−2.17712	+	3.77089i	−0.233412	+	0.404282i
$88$	2.32288	+	4.02334i	0.247619	+	0.428889i
$89$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$89$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$90$	−1.14313	+	6.48299i	−0.120496	+	0.683368i
$91$	1.26616	+	7.18073i	0.132729	+	0.752745i
$92$	1.54650	−	0.562880i	0.161234	−	0.0586843i
$93$	−11.4426	−	9.60148i	−1.18654	−	0.995627i
$94$	4.35425			0.449106
$95$		0			0
$96$	2.64575			0.270031
$97$	−2.84087	−	2.38378i	−0.288447	−	0.242036i	0.487069	−	0.873363i	$-0.338066\pi$
$97$	−2.84087	−	2.38378i	−0.288447	−	0.242036i	−0.775516	+	0.631328i	$0.782510\pi$
$98$	−5.91208	+	2.15182i	−0.597210	+	0.217367i
$99$	−3.22690	−	18.3007i	−0.324316	−	1.83929i
$100$	−0.397915	+	2.25669i	−0.0397915	+	0.225669i
$101$	12.8228	+	4.66712i	1.27592	+	0.464396i	0.889080	−	0.457752i	$-0.151345\pi$
$101$	12.8228	+	4.66712i	1.27592	+	0.464396i	0.386838	+	0.922148i	$0.373567\pi$
$102$		0			0
$103$	6.64575	−	11.5108i	0.654825	−	1.13419i	−0.327112	−	0.944985i	$-0.606076\pi$
$103$	6.64575	−	11.5108i	0.654825	−	1.13419i	0.981938	−	0.189205i	$-0.0605912\pi$
$104$	1.53209	−	1.28558i	0.150234	−	0.126061i
$105$	−12.1606	+	10.2039i	−1.18675	+	0.995802i
$106$	6.29150	−	10.8972i	0.611085	−	1.05843i
$107$	−7.64575	−	13.2428i	−0.739143	−	1.28023i	−0.952882	−	0.303342i	$-0.901898\pi$
$107$	−7.64575	−	13.2428i	−0.739143	−	1.28023i	0.213739	−	0.976891i	$-0.431436\pi$
$108$	−2.48619	−	0.904900i	−0.239234	−	0.0870741i
$109$	2.53231	−	14.3615i	0.242552	−	1.37558i	−0.583559	−	0.812070i	$-0.698340\pi$
$109$	2.53231	−	14.3615i	0.242552	−	1.37558i	0.826111	−	0.563508i	$-0.190548\pi$
$110$	1.32767	+	7.52960i	0.126588	+	0.717919i
$111$	−0.880731	+	0.320560i	−0.0835952	+	0.0304262i
$112$	2.79281	+	2.34344i	0.263896	+	0.221435i
$113$	−15.5830			−1.46593			−0.732963	−	0.680269i	$-0.761863\pi$
$113$	−15.5830			−1.46593			−0.732963	+	0.680269i	$0.761863\pi$
$114$		0			0
$115$	2.70850			0.252569
$116$	1.26072	+	1.05787i	0.117055	+	0.0982206i
$117$	−7.51754	+	2.73616i	−0.694997	+	0.252958i
$118$	−1.37829	−	7.81667i	−0.126882	−	0.719583i
$119$		0			0
$120$	4.09166	+	1.48924i	0.373515	+	0.135948i
$121$	−5.29150	−	9.16515i	−0.481046	−	0.833196i
$122$	−0.468627	+	0.811686i	−0.0424275	+	0.0734866i
$123$	−0.590807	+	0.495746i	−0.0532713	+	0.0446999i
$124$	−4.32490	+	3.62902i	−0.388387	+	0.325896i
$125$	−6.00000	+	10.3923i	−0.536656	+	0.929516i
$126$	−7.29150	−	12.6293i	−0.649579	−	1.12510i
$127$	12.4899	+	4.54596i	1.10830	+	0.403389i	0.830370	−	0.557212i	$-0.188129\pi$
$127$	12.4899	+	4.54596i	1.10830	+	0.403389i	0.277932	+	0.960601i	$0.410351\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	5.18765	+	29.4206i	0.456747	+	2.59034i
$130$	3.09300	−	1.12576i	0.271274	−	0.0987357i
$131$	1.48402	+	1.24524i	0.129660	+	0.108797i	0.705311	−	0.708898i	$-0.250807\pi$
$131$	1.48402	+	1.24524i	0.129660	+	0.108797i	−0.575652	+	0.817695i	$0.695252\pi$
$132$	−12.2915			−1.06984
$133$		0			0
$134$	0.645751			0.0557844
$135$	−3.33555	−	2.79886i	−0.287078	−	0.240887i
$136$		0			0
$137$	2.70596	+	15.3463i	0.231186	+	1.31112i	0.850499	+	0.525976i	$0.176300\pi$
$137$	2.70596	+	15.3463i	0.231186	+	1.31112i	−0.619314	+	0.785144i	$0.712589\pi$
$138$	−0.756107	+	4.28810i	−0.0643641	+	0.365027i
$139$	−17.5213	−	6.37722i	−1.48614	−	0.540909i	−0.533706	−	0.845670i	$-0.679201\pi$
$139$	−17.5213	−	6.37722i	−1.48614	−	0.540909i	−0.952429	+	0.304761i	$0.901423\pi$
$140$	3.00000	+	5.19615i	0.253546	+	0.439155i
$141$	−5.76013	+	9.97684i	−0.485090	+	0.840201i
$142$	−2.07483	+	1.74099i	−0.174116	+	0.146101i
$143$	−7.11770	+	5.97246i	−0.595212	+	0.499442i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$	1.35425	+	2.34563i	0.112464	+	0.194794i
$146$	−1.60546	−	0.584341i	−0.132869	−	0.0483604i
$147$	2.89050	−	16.3929i	0.238405	−	1.35206i
$148$	0.0615146	+	0.348867i	0.00505647	+	0.0286767i
$149$	−10.2777	+	3.74076i	−0.841978	+	0.306455i	−0.726765	−	0.686886i	$-0.758977\pi$
$149$	−10.2777	+	3.74076i	−0.841978	+	0.306455i	−0.115213	+	0.993341i	$0.536755\pi$
$150$	−4.64433	−	3.89706i	−0.379208	−	0.318193i
$151$	12.9373			1.05282			0.526409	−	0.850231i	$-0.323538\pi$
$151$	12.9373			1.05282			0.526409	+	0.850231i	$0.323538\pi$
$152$		0			0
$153$		0			0
$154$	−12.9747	−	10.8871i	−1.04553	−	0.877304i
$155$	−8.73116	+	3.17788i	−0.701303	+	0.255254i
$156$	0.918860	+	5.21111i	0.0735677	+	0.417223i
$157$	−1.83772	+	10.4222i	−0.146666	+	0.831784i	0.819348	+	0.573296i	$0.194335\pi$
$157$	−1.83772	+	10.4222i	−0.146666	+	0.831784i	−0.966014	+	0.258488i	$0.916776\pi$
$158$	3.75877	+	1.36808i	0.299032	+	0.108839i
$159$	16.6458	+	28.8313i	1.32009	+	2.28647i
$160$	0.822876	−	1.42526i	0.0650540	−	0.112677i
$161$	−4.59627	+	3.85673i	−0.362237	+	0.303953i
$162$	−3.83022	+	3.21394i	−0.300931	+	0.252511i
$163$	−1.96863	+	3.40976i	−0.154195	+	0.267073i	−0.932766	−	0.360484i	$-0.882612\pi$
$163$	−1.96863	+	3.40976i	−0.154195	+	0.267073i	0.778571	+	0.627557i	$0.215945\pi$
$164$	0.145751	+	0.252449i	0.0113813	+	0.0197129i
$165$	−19.0088	−	6.91864i	−1.47983	−	0.538616i
$166$	1.37829	−	7.81667i	0.106976	−	0.606691i
$167$	−2.08378	−	11.8177i	−0.161248	−	0.914481i	−0.952849	−	0.303443i	$-0.901864\pi$
$167$	−2.08378	−	11.8177i	−0.161248	−	0.914481i	0.791602	−	0.611037i	$-0.209247\pi$
$168$	−9.06404	+	3.29904i	−0.699306	+	0.254527i
$169$	−6.89440	−	5.78509i	−0.530338	−	0.445007i
$170$		0			0
$171$		0			0
$172$	11.2915			0.860969
$173$	−4.59627	−	3.85673i	−0.349448	−	0.293221i	0.451121	−	0.892463i	$-0.351024\pi$
$173$	−4.59627	−	3.85673i	−0.349448	−	0.293221i	−0.800568	+	0.599242i	$0.795469\pi$
$174$	−4.09166	+	1.48924i	−0.310188	+	0.112899i
$175$	−1.45070	−	8.22733i	−0.109663	−	0.621928i
$176$	−0.806726	+	4.57517i	−0.0608093	+	0.344867i
$177$	19.7335	+	7.18242i	1.48326	+	0.539864i
$178$		0			0
$179$	−2.03137	+	3.51844i	−0.151832	+	0.262981i	−0.931901	−	0.362713i	$-0.881851\pi$
$179$	−2.03137	+	3.51844i	−0.151832	+	0.262981i	0.780069	+	0.625693i	$0.215184\pi$
$180$	−5.04287	+	4.23147i	−0.375874	+	0.315395i
$181$	17.0282	−	14.2884i	1.26570	−	1.06205i	0.270646	−	0.962679i	$-0.412763\pi$
$181$	17.0282	−	14.2884i	1.26570	−	1.06205i	0.995051	−	0.0993673i	$-0.0316819\pi$
$182$	−3.64575	+	6.31463i	−0.270241	+	0.468071i
$183$	−1.23987	−	2.14752i	−0.0916539	−	0.158749i
$184$	1.54650	+	0.562880i	0.114010	+	0.0414961i
$185$	−0.101238	+	0.574148i	−0.00744315	+	0.0422122i
$186$	−2.59383	−	14.7103i	−0.190189	−	1.07861i
$187$		0			0
$188$	3.33555	+	2.79886i	0.243270	+	0.204128i
$189$	9.64575			0.701625
$190$		0			0
$191$	6.58301			0.476330			0.238165	−	0.971225i	$-0.423454\pi$
$191$	6.58301			0.476330			0.238165	+	0.971225i	$0.423454\pi$
$192$	2.02676	+	1.70066i	0.146269	+	0.122734i
$193$	−13.7035	+	4.98768i	−0.986403	+	0.359021i	−0.784326	−	0.620349i	$-0.786991\pi$
$193$	−13.7035	+	4.98768i	−0.986403	+	0.359021i	−0.202076	+	0.979370i	$0.564769\pi$
$194$	−0.643974	−	3.65216i	−0.0462346	−	0.262210i
$195$	−1.51221	+	8.57620i	−0.108292	+	0.614154i
$196$	−5.91208	−	2.15182i	−0.422291	−	0.153701i
$197$	3.82288	+	6.62141i	0.272369	+	0.471756i	0.969468	−	0.245218i	$-0.0788597\pi$
$197$	3.82288	+	6.62141i	0.272369	+	0.471756i	−0.697099	+	0.716975i	$0.745526\pi$
$198$	9.29150	−	16.0934i	0.660318	−	1.14370i
$199$	−15.2248	+	12.7751i	−1.07925	+	0.905602i	−0.995859	−	0.0909146i	$-0.971021\pi$
$199$	−15.2248	+	12.7751i	−1.07925	+	0.905602i	−0.0833957	+	0.996517i	$0.526577\pi$
$200$	−1.75539	+	1.47295i	−0.124125	+	0.104153i
$201$	−0.854249	+	1.47960i	−0.0602541	+	0.104363i
$202$	6.82288	+	11.8176i	0.480056	+	0.831481i
$203$	−5.63816	−	2.05212i	−0.395721	−	0.144031i
$204$		0			0
$205$	0.0833061	+	0.472452i	0.00581835	+	0.0329975i
$206$	12.4899	−	4.54596i	0.870214	−	0.316732i
$207$	−5.04287	−	4.23147i	−0.350504	−	0.294108i
$208$	2.00000			0.138675
$209$		0			0
$210$	−15.8745			−1.09545
$211$	−10.1819	−	8.54361i	−0.700950	−	0.588167i	0.221094	−	0.975253i	$-0.429037\pi$
$211$	−10.1819	−	8.54361i	−0.700950	−	0.588167i	−0.922044	+	0.387086i	$0.873482\pi$
$212$	11.8242	−	4.30364i	0.812086	−	0.295575i
$213$	−1.24436	−	7.05714i	−0.0852625	−	0.483547i
$214$	2.65534	−	15.0592i	0.181515	−	1.02943i
$215$	17.4623	+	6.35576i	1.19092	+	0.433459i
$216$	−1.32288	−	2.29129i	−0.0900103	−	0.155902i
$217$	10.2915	−	17.8254i	0.698633	−	1.21007i
$218$	11.1712	−	9.37378i	0.756611	−	0.634872i
$219$	3.46272	−	2.90557i	0.233989	−	0.196340i
$220$	−3.82288	+	6.62141i	−0.257738	+	0.446416i
$221$		0			0
$222$	−0.880731	−	0.320560i	−0.0591108	−	0.0215146i
$223$	−3.26663	+	18.5260i	−0.218750	+	1.24059i	0.655530	+	0.755169i	$0.272445\pi$
$223$	−3.26663	+	18.5260i	−0.218750	+	1.24059i	−0.874280	+	0.485422i	$0.838666\pi$
$224$	0.633078	+	3.59036i	0.0422993	+	0.239891i
$225$	8.61323	−	3.13496i	0.574215	−	0.208997i
$226$	−11.9373	−	10.0166i	−0.794056	−	0.666292i
$227$	−7.35425			−0.488119			−0.244059	−	0.969760i	$-0.578479\pi$
$227$	−7.35425			−0.488119			−0.244059	+	0.969760i	$0.578479\pi$
$228$		0			0
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$	2.07483	+	1.74099i	0.136810	+	0.114797i
$231$	42.1093	−	15.3265i	2.77059	−	1.00841i
$232$	0.285782	+	1.62075i	0.0187625	+	0.106407i
$233$	3.27752	−	18.5878i	0.214718	−	1.21772i	−0.666678	−	0.745346i	$-0.732284\pi$
$233$	3.27752	−	18.5878i	0.214718	−	1.21772i	0.881396	−	0.472379i	$-0.156605\pi$
$234$	−7.51754	−	2.73616i	−0.491437	−	0.178868i
$235$	3.58301	+	6.20595i	0.233729	+	0.404831i
$236$	3.96863	−	6.87386i	0.258336	−	0.447450i
$237$	−8.10705	+	6.80262i	−0.526610	+	0.441878i
$238$		0			0
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	−0.604087	−	0.796918i	$-0.706462\pi$
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	0.992195	+	0.124696i	$0.0397955\pi$
$240$	2.17712	+	3.77089i	0.140533	+	0.243410i
$241$	7.12569	+	2.59354i	0.459006	+	0.167065i	0.561166	−	0.827703i	$-0.310353\pi$
$241$	7.12569	+	2.59354i	0.459006	+	0.167065i	−0.102160	+	0.994768i	$0.532575\pi$
$242$	1.83772	−	10.4222i	0.118133	−	0.669966i
$243$	−3.67544	−	20.8445i	−0.235780	−	1.33717i
$244$	−0.880731	+	0.320560i	−0.0563830	+	0.0205217i
$245$	−7.93181	−	6.65558i	−0.506745	−	0.425210i
$246$	−0.771243			−0.0491727
$247$		0			0
$248$	−5.64575			−0.358506
$249$	16.0869	+	13.4985i	1.01947	+	0.855435i
$250$	−11.2763	+	4.10424i	−0.713177	+	0.259575i
$251$	5.07552	+	28.7847i	0.320364	+	1.81687i	0.540429	+	0.841389i	$0.318262\pi$
$251$	5.07552	+	28.7847i	0.320364	+	1.81687i	−0.220065	+	0.975485i	$0.570627\pi$
$252$	2.53231	−	14.3615i	0.159521	−	0.904687i
$253$	−7.18466	−	2.61500i	−0.451695	−	0.164404i
$254$	6.64575	+	11.5108i	0.416992	+	0.722251i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	9.41584	−	7.90083i	0.587344	−	0.492840i	−0.300006	−	0.953937i	$-0.596989\pi$
$257$	9.41584	−	7.90083i	0.587344	−	0.492840i	0.887350	+	0.461097i	$0.152544\pi$
$258$	−14.9373	+	25.8721i	−0.929953	+	1.61073i
$259$	−0.645751	−	1.11847i	−0.0401250	−	0.0694986i
$260$	3.09300	+	1.12576i	0.191820	+	0.0698167i
$261$	1.14313	−	6.48299i	0.0707578	−	0.401287i
$262$	0.336401	+	1.90782i	0.0207829	+	0.117866i
$263$	10.2777	−	3.74076i	0.633747	−	0.230665i	−0.00511410	−	0.999987i	$-0.501628\pi$
$263$	10.2777	−	3.74076i	0.633747	−	0.230665i	0.638862	+	0.769322i	$0.279406\pi$
$264$	−9.41584	−	7.90083i	−0.579505	−	0.486262i
$265$	20.7085			1.27211
$266$		0			0
$267$		0			0
$268$	0.494674	+	0.415081i	0.0302170	+	0.0253551i
$269$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$269$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$270$	−0.756107	−	4.28810i	−0.0460152	−	0.260965i
$271$	2.14529	−	12.1666i	0.130317	−	0.739066i	−0.847690	−	0.530493i	$-0.822007\pi$
$271$	2.14529	−	12.1666i	0.130317	−	0.739066i	0.978007	−	0.208573i	$-0.0668819\pi$
$272$		0			0
$273$	−9.64575	−	16.7069i	−0.583787	−	1.01115i
$274$	−7.79150	+	13.4953i	−0.470702	+	0.815280i
$275$	8.15512	−	6.84296i	0.491772	−	0.412646i
$276$	−3.33555	+	2.79886i	−0.200776	+	0.168471i
$277$	13.7601	−	23.8332i	0.826766	−	1.43200i	−0.0737960	−	0.997273i	$-0.523511\pi$
$277$	13.7601	−	23.8332i	0.826766	−	1.43200i	0.900562	−	0.434727i	$-0.143155\pi$
$278$	−9.32288	−	16.1477i	−0.559149	−	0.968474i
$279$	21.2211	+	7.72384i	1.27047	+	0.462414i
$280$	−1.04189	+	5.90885i	−0.0622648	+	0.353121i
$281$	4.42065	+	25.0708i	0.263714	+	1.49560i	0.772672	+	0.634805i	$0.218920\pi$
$281$	4.42065	+	25.0708i	0.263714	+	1.49560i	−0.508959	+	0.860791i	$0.669969\pi$
$282$	−10.8255	+	3.94016i	−0.644649	+	0.234633i
$283$	23.4760	+	19.6987i	1.39550	+	1.17097i	0.963054	+	0.269309i	$0.0867952\pi$
$283$	23.4760	+	19.6987i	1.39550	+	1.17097i	0.432450	+	0.901658i	$0.357649\pi$
$284$	−2.70850			−0.160720
$285$		0			0
$286$	−9.29150			−0.549418
$287$	−0.814111	−	0.683120i	−0.0480554	−	0.0403233i
$288$	−3.75877	+	1.36808i	−0.221488	+	0.0806149i
$289$	−2.95202	−	16.7417i	−0.173648	−	0.984808i
$290$	−0.470326	+	2.66735i	−0.0276185	+	0.156632i
$291$	9.22004	+	3.35582i	0.540488	+	0.196722i
$292$	−0.854249	−	1.47960i	−0.0499911	−	0.0865872i
$293$	−14.4686	+	25.0604i	−0.845266	+	1.46404i	0.0401236	+	0.999195i	$0.487225\pi$
$293$	−14.4686	+	25.0604i	−0.845266	+	1.46404i	−0.885390	+	0.464849i	$0.846109\pi$
$294$	12.7514	−	10.6997i	0.743676	−	0.624018i
$295$	10.0066	−	8.39657i	0.582609	−	0.488867i
$296$	−0.177124	+	0.306788i	−0.0102951	+	0.0178317i
$297$	6.14575	+	10.6448i	0.356613	+	0.617671i
$298$	−10.2777	−	3.74076i	−0.595369	−	0.216696i
$299$	−0.571563	+	3.24150i	−0.0330544	+	0.187461i
$300$	−1.05278	−	5.97064i	−0.0607826	−	0.344715i
$301$	−38.6834	+	14.0796i	−2.22967	+	0.811535i
$302$	9.91051	+	8.31591i	0.570286	+	0.478527i
$303$	−36.1033			−2.07408
$304$		0			0
$305$	−1.54249			−0.0883225
$306$		0			0
$307$	−0.606808	+	0.220860i	−0.0346323	+	0.0126051i	−0.359278	−	0.933230i	$-0.616977\pi$
$307$	−0.606808	+	0.220860i	−0.0346323	+	0.0126051i	0.324646	+	0.945836i	$0.394755\pi$
$308$	−2.94112	−	16.6799i	−0.167586	−	0.950428i
$309$	−6.10651	+	34.6318i	−0.347387	+	1.97013i
$310$	−8.73116	−	3.17788i	−0.495896	−	0.180492i
$311$	−6.82288	−	11.8176i	−0.386890	−	0.670113i	0.605140	−	0.796119i	$-0.293117\pi$
$311$	−6.82288	−	11.8176i	−0.386890	−	0.670113i	−0.992029	+	0.126007i	$0.959784\pi$
$312$	−2.64575	+	4.58258i	−0.149786	+	0.259437i
$313$	6.79827	−	5.70442i	0.384261	−	0.322433i	−0.430112	−	0.902776i	$-0.641526\pi$
$313$	6.79827	−	5.70442i	0.384261	−	0.322433i	0.814372	+	0.580343i	$0.197081\pi$
$314$	−8.10705	+	6.80262i	−0.457507	+	0.383894i
$315$	12.0000	−	20.7846i	0.676123	−	1.17108i
$316$	2.00000	+	3.46410i	0.112509	+	0.194871i
$317$	5.63816	+	2.05212i	0.316670	+	0.115259i	0.495465	−	0.868628i	$-0.334998\pi$
$317$	5.63816	+	2.05212i	0.316670	+	0.115259i	−0.178795	+	0.983886i	$0.557220\pi$
$318$	−5.78101	+	32.7857i	−0.324183	+	1.83853i
$319$	−1.32767	−	7.52960i	−0.0743353	−	0.421576i
$320$	1.54650	−	0.562880i	0.0864520	−	0.0314660i
$321$	30.9923	+	26.0056i	1.72982	+	1.45149i
$322$	−6.00000			−0.334367
$323$		0			0
$324$	−5.00000			−0.277778
$325$	−3.51079	−	2.94590i	−0.194743	−	0.163409i
$326$	−3.69981	+	1.34662i	−0.204913	+	0.0745824i
$327$	6.69987	+	37.9968i	0.370504	+	2.10123i
$328$	−0.0506189	+	0.287074i	−0.00279496	+	0.0158510i
$329$	−14.9172	−	5.42940i	−0.822410	−	0.299333i
$330$	−10.1144	−	17.5186i	−0.556778	−	0.964368i
$331$	−9.90588	+	17.1575i	−0.544476	+	0.943061i	0.454163	+	0.890919i	$0.349938\pi$
$331$	−9.90588	+	17.1575i	−0.544476	+	0.943061i	−0.998640	+	0.0521424i	$0.983395\pi$
$332$	6.08029	−	5.10197i	0.333699	−	0.280007i
$333$	1.08548	−	0.910827i	0.0594840	−	0.0499130i
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$	0.531373	+	0.920365i	0.0290320	+	0.0502849i
$336$	−9.06404	−	3.29904i	−0.494484	−	0.179977i
$337$	−1.68586	+	9.56100i	−0.0918348	+	0.520821i	0.903837	+	0.427878i	$0.140739\pi$
$337$	−1.68586	+	9.56100i	−0.0918348	+	0.520821i	−0.995671	+	0.0929433i	$0.970372\pi$
$338$	−1.56283	−	8.86327i	−0.0850069	−	0.482098i
$339$	38.7424	−	14.1011i	2.10420	−	0.765865i
$340$		0			0
$341$	26.2288			1.42037
$342$		0			0
$343$	−2.58301			−0.139469
$344$	8.64979	+	7.25804i	0.466366	+	0.391327i
$345$	−6.73385	+	2.45092i	−0.362538	+	0.131953i
$346$	−1.04189	−	5.90885i	−0.0560123	−	0.317662i
$347$	−4.03363	+	22.8759i	−0.216537	+	1.22804i	0.661683	+	0.749783i	$0.269842\pi$
$347$	−4.03363	+	22.8759i	−0.216537	+	1.22804i	−0.878220	+	0.478257i	$0.841269\pi$
$348$	−4.09166	−	1.48924i	−0.219336	−	0.0798317i
$349$	−10.5830	−	18.3303i	−0.566495	−	0.981199i	−0.996909	−	0.0785668i	$-0.974966\pi$
$349$	−10.5830	−	18.3303i	−0.566495	−	0.981199i	0.430414	−	0.902632i	$-0.358368\pi$
$350$	4.17712	−	7.23499i	0.223277	−	0.386727i
$351$	4.05353	−	3.40131i	0.216361	−	0.181549i
$352$	−3.55885	+	2.98623i	−0.189687	+	0.159167i
$353$	−6.43725	+	11.1497i	−0.342620	+	0.593436i	−0.984918	−	0.173019i	$-0.944648\pi$
$353$	−6.43725	+	11.1497i	−0.342620	+	0.593436i	0.642298	+	0.766455i	$0.277981\pi$
$354$	10.5000	+	18.1865i	0.558069	+	0.966603i
$355$	−4.18869	−	1.52456i	−0.222313	−	0.0809152i
$356$		0			0
$357$		0			0
$358$	−3.81773	+	1.38954i	−0.201773	+	0.0734395i
$359$	−3.78216	−	3.17361i	−0.199615	−	0.167497i	0.537501	−	0.843263i	$-0.319368\pi$
$359$	−3.78216	−	3.17361i	−0.199615	−	0.167497i	−0.737116	+	0.675766i	$0.763813\pi$
$360$	−6.58301			−0.346955
$361$		0			0
$362$	22.2288			1.16832
$363$	21.4492	+	17.9981i	1.12579	+	0.944653i
$364$	−6.85177	+	2.49384i	−0.359130	+	0.130713i
$365$	−0.488257	−	2.76904i	−0.0255566	−	0.144938i
$366$	0.430602	−	2.44207i	0.0225080	−	0.127649i
$367$	−15.2500	−	5.55056i	−0.796046	−	0.289737i	−0.0881989	−	0.996103i	$-0.528111\pi$
$367$	−15.2500	−	5.55056i	−0.796046	−	0.289737i	−0.707847	+	0.706366i	$0.750333\pi$
$368$	0.822876	+	1.42526i	0.0428954	+	0.0742969i
$369$	0.583005	−	1.00979i	0.0303500	−	0.0525678i
$370$	−0.446608	+	0.374749i	−0.0232180	+	0.0194822i
$371$	−35.1419	+	29.4876i	−1.82448	+	1.53092i
$372$	7.46863	−	12.9360i	0.387230	−	0.670703i
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	5.51316	−	31.2667i	0.284698	−	1.61460i
$376$	0.756107	+	4.28810i	0.0389933	+	0.221142i
$377$	−3.09300	+	1.12576i	−0.159298	+	0.0579796i
$378$	7.38907	+	6.20017i	0.380053	+	0.318902i
$379$	10.7085			0.550059			0.275029	−	0.961436i	$-0.411312\pi$
$379$	10.7085			0.550059			0.275029	+	0.961436i	$0.411312\pi$
$380$		0			0
$381$	−35.1660			−1.80161
$382$	5.04287	+	4.23147i	0.258016	+	0.216501i
$383$	−5.18735	+	1.88804i	−0.265061	+	0.0964743i	−0.471132	−	0.882063i	$-0.656154\pi$
$383$	−5.18735	+	1.88804i	−0.265061	+	0.0964743i	0.206071	+	0.978537i	$0.433932\pi$
$384$	0.459430	+	2.60556i	0.0234452	+	0.132964i
$385$	4.84036	−	27.4510i	0.246687	−	1.39903i
$386$	−13.7035	−	4.98768i	−0.697492	−	0.253866i
$387$	−22.5830	−	39.1149i	−1.14796	−	1.98832i
$388$	1.85425	−	3.21165i	0.0941352	−	0.163047i
$389$	9.19253	−	7.71345i	0.466080	−	0.391088i	−0.379282	−	0.925281i	$-0.623829\pi$
$389$	9.19253	−	7.71345i	0.466080	−	0.391088i	0.845362	+	0.534194i	$0.179385\pi$
$390$	−6.67110	+	5.59771i	−0.337804	+	0.283451i
$391$		0			0
$392$	−3.14575	−	5.44860i	−0.158884	−	0.275196i
$393$	−4.81639	−	1.75302i	−0.242955	−	0.0884282i
$394$	−1.32767	+	7.52960i	−0.0668871	+	0.379336i
$395$	1.14313	+	6.48299i	0.0575170	+	0.326195i
$396$	17.4623	−	6.35576i	0.877514	−	0.319389i
$397$	16.1350	+	13.5389i	0.809792	+	0.679497i	0.950558	−	0.310546i	$-0.100512\pi$
$397$	16.1350	+	13.5389i	0.809792	+	0.679497i	−0.140766	+	0.990043i	$0.544956\pi$
$398$	−19.8745			−0.996219
$399$		0			0
$400$	−2.29150			−0.114575
$401$	21.1298	+	17.7300i	1.05517	+	0.885395i	0.993628	−	0.112710i	$-0.0359530\pi$
$401$	21.1298	+	17.7300i	1.05517	+	0.885395i	0.0615443	+	0.998104i	$0.480397\pi$
$402$	−1.60546	+	0.584341i	−0.0800732	+	0.0291443i
$403$	−1.96075	−	11.1200i	−0.0976719	−	0.553925i
$404$	−2.36956	+	13.4384i	−0.117890	+	0.668587i
$405$	−7.73250	−	2.81440i	−0.384231	−	0.139849i
$406$	−3.00000	−	5.19615i	−0.148888	−	0.257881i
$407$	0.822876	−	1.42526i	0.0407884	−	0.0706476i
$408$		0			0
$409$	−5.80892	+	4.87426i	−0.287233	+	0.241017i	−0.775007	−	0.631953i	$-0.782253\pi$
$409$	−5.80892	+	4.87426i	−0.287233	+	0.241017i	0.487774	+	0.872970i	$0.337809\pi$
$410$	−0.239870	+	0.415468i	−0.0118464	+	0.0205185i
$411$	−20.6144	−	35.7052i	−1.01683	−	1.76121i
$412$	12.4899	+	4.54596i	0.615335	+	0.223963i
$413$	−5.02490	+	28.4976i	−0.247259	+	1.40228i
$414$	−1.14313	−	6.48299i	−0.0561816	−	0.318622i
$415$	12.2750	−	4.46772i	0.602554	−	0.219312i
$416$	1.53209	+	1.28558i	0.0751168	+	0.0630305i
$417$	49.3320			2.41580
$418$		0			0
$419$	−31.7490			−1.55104			−0.775520	−	0.631322i	$-0.782512\pi$
$419$	−31.7490			−1.55104			−0.775520	+	0.631322i	$0.782512\pi$
$420$	−12.1606	−	10.2039i	−0.593375	−	0.497901i
$421$	23.3154	−	8.48612i	1.13632	−	0.413588i	0.295740	−	0.955269i	$-0.404434\pi$
$421$	23.3154	−	8.48612i	1.13632	−	0.413588i	0.840585	+	0.541680i	$0.182212\pi$
$422$	−2.30805	−	13.0896i	−0.112354	−	0.637191i
$423$	3.02443	−	17.1524i	0.147053	−	0.833978i
$424$	11.8242	+	4.30364i	0.574232	+	0.209003i
$425$		0			0
$426$	3.58301	−	6.20595i	0.173597	−	0.300679i
$427$	2.61757	−	2.19640i	0.126673	−	0.106291i
$428$	11.7140	−	9.82919i	0.566216	−	0.475112i
$429$	12.2915	−	21.2895i	0.593439	−	1.02787i
$430$	9.29150	+	16.0934i	0.448076	+	0.776090i
$431$	−26.1935	−	9.53364i	−1.26170	−	0.459219i	−0.377358	−	0.926068i	$-0.623167\pi$
$431$	−26.1935	−	9.53364i	−1.26170	−	0.459219i	−0.884337	+	0.466848i	$0.845389\pi$
$432$	0.459430	−	2.60556i	0.0221043	−	0.125360i
$433$	3.10388	+	17.6030i	0.149163	+	0.845944i	0.963930	+	0.266156i	$0.0857536\pi$
$433$	3.10388	+	17.6030i	0.149163	+	0.845944i	−0.814767	+	0.579788i	$0.803135\pi$
$434$	19.3417	−	7.03980i	0.928431	−	0.337921i
$435$	−5.48948	−	4.60622i	−0.263201	−	0.220851i
$436$	14.5830			0.698399
$437$		0			0
$438$	4.52026			0.215986
$439$	8.28229	+	6.94967i	0.395292	+	0.331689i	0.818671	−	0.574263i	$-0.194711\pi$
$439$	8.28229	+	6.94967i	0.395292	+	0.331689i	−0.423378	+	0.905953i	$0.639156\pi$
$440$	−7.18466	+	2.61500i	−0.342515	+	0.124665i
$441$	4.37003	+	24.7837i	0.208097	+	1.18018i
$442$		0			0
$443$	−10.0037	−	3.64106i	−0.475292	−	0.172992i	0.0932563	−	0.995642i	$-0.470272\pi$
$443$	−10.0037	−	3.64106i	−0.475292	−	0.172992i	−0.568548	+	0.822650i	$0.692495\pi$
$444$	−0.468627	−	0.811686i	−0.0222401	−	0.0385209i
$445$		0			0
$446$	−14.4106	+	12.0920i	−0.682364	+	0.572571i
$447$	22.1672	−	18.6005i	1.04847	−	0.879774i
$448$	−1.82288	+	3.15731i	−0.0861228	+	0.149169i
$449$	12.1458	+	21.0371i	0.573193	+	0.992800i	0.996235	+	0.0866900i	$0.0276290\pi$
$449$	12.1458	+	21.0371i	0.573193	+	0.992800i	−0.423042	+	0.906110i	$0.639038\pi$
$450$	8.61323	+	3.13496i	0.406032	+	0.147783i
$451$	0.235163	−	1.33367i	0.0110734	−	0.0628003i
$452$	−2.70596	−	15.3463i	−0.127278	−	0.721828i
$453$	−32.1645	+	11.7069i	−1.51122	+	0.550039i
$454$	−5.63368	−	4.72722i	−0.264402	−	0.221859i
$455$	−12.0000			−0.562569
$456$		0			0
$457$	32.8745			1.53780			0.768902	−	0.639366i	$-0.220803\pi$
$457$	32.8745			1.53780			0.768902	+	0.639366i	$0.220803\pi$
$458$	15.3209	+	12.8558i	0.715898	+	0.600710i
$459$		0			0
$460$	0.470326	+	2.66735i	0.0219290	+	0.124366i
$461$	3.32814	−	18.8748i	0.155007	−	0.879089i	−0.803772	−	0.594937i	$-0.797177\pi$
$461$	3.32814	−	18.8748i	0.155007	−	0.879089i	0.958779	−	0.284152i	$-0.0917119\pi$
$462$	42.1093	+	15.3265i	1.95910	+	0.713054i
$463$	19.2288	+	33.3052i	0.893636	+	1.54782i	0.835484	+	0.549515i	$0.185188\pi$
$463$	19.2288	+	33.3052i	0.893636	+	1.54782i	0.0581525	+	0.998308i	$0.481479\pi$
$464$	−0.822876	+	1.42526i	−0.0382010	+	0.0661661i
$465$	18.8317	−	15.8017i	0.873298	−	0.732784i
$466$	14.4587	−	12.1323i	0.669787	−	0.562018i
$467$	9.67712	−	16.7613i	0.447804	−	0.775619i	−0.550439	−	0.834875i	$-0.685540\pi$
$467$	9.67712	−	16.7613i	0.447804	−	0.775619i	0.998243	+	0.0592563i	$0.0188729\pi$
$468$	−4.00000	−	6.92820i	−0.184900	−	0.320256i
$469$	−2.21227	−	0.805200i	−0.102153	−	0.0371807i
$470$	−1.24436	+	7.05714i	−0.0573983	+	0.325522i
$471$	−4.86215	−	27.5746i	−0.224036	−	1.27057i
$472$	7.45858	−	2.71470i	0.343309	−	0.124954i
$473$	−40.1848	−	33.7190i	−1.84770	−	1.55040i
$474$	−10.5830			−0.486094
$475$		0			0
$476$		0			0
$477$	−38.5566	−	32.3528i	−1.76538	−	1.48133i
$478$	11.2763	−	4.10424i	0.515766	−	0.187724i
$479$	1.14313	+	6.48299i	0.0522308	+	0.296216i	0.999722	−	0.0235654i	$-0.00750179\pi$
$479$	1.14313	+	6.48299i	0.0522308	+	0.296216i	−0.947491	+	0.319781i	$0.896391\pi$
$480$	−0.756107	+	4.28810i	−0.0345114	+	0.195724i
$481$	−0.665770	−	0.242320i	−0.0303565	−	0.0110489i
$482$	3.79150	+	6.56708i	0.172698	+	0.299122i
$483$	7.93725	−	13.7477i	0.361158	−	0.625543i
$484$	8.10705	−	6.80262i	0.368502	−	0.309210i
$485$	4.67537	−	3.92310i	0.212298	−	0.178139i
$486$	10.5830	−	18.3303i	0.480055	−	0.831479i
$487$	−2.11438	−	3.66221i	−0.0958116	−	0.165951i	0.814135	−	0.580675i	$-0.197211\pi$
$487$	−2.11438	−	3.66221i	−0.0958116	−	0.165951i	−0.909947	+	0.414724i	$0.863878\pi$
$488$	−0.880731	−	0.320560i	−0.0398688	−	0.0145111i
$489$	1.80889	−	10.2587i	0.0818009	−	0.463916i
$490$	−1.79800	−	10.1969i	−0.0812252	−	0.460651i
$491$	−36.9219	+	13.4385i	−1.66626	+	0.606470i	−0.991329	−	0.131407i	$-0.958051\pi$
$491$	−36.9219	+	13.4385i	−1.66626	+	0.606470i	−0.674935	+	0.737877i	$0.735828\pi$
$492$	−0.590807	−	0.495746i	−0.0266356	−	0.0223499i
$493$		0			0
$494$		0			0
$495$	30.5830			1.37460
$496$	−4.32490	−	3.62902i	−0.194194	−	0.162948i
$497$	9.27900	−	3.37728i	0.416220	−	0.151492i
$498$	3.64661	+	20.6810i	0.163409	+	0.926736i
$499$	−0.828518	+	4.69876i	−0.0370895	+	0.210345i	−0.997720	−	0.0674825i	$-0.978503\pi$
$499$	−0.828518	+	4.69876i	−0.0370895	+	0.210345i	0.960631	+	0.277828i	$0.0896144\pi$
$500$	−11.2763	−	4.10424i	−0.504292	−	0.183547i
$501$	15.8745	+	27.4955i	0.709221	+	1.22841i
$502$	−14.6144	+	25.3128i	−0.652272	+	1.12977i
$503$	−31.3598	+	26.3140i	−1.39826	+	1.17328i	−0.436398	+	0.899754i	$0.643746\pi$
$503$	−31.3598	+	26.3140i	−1.39826	+	1.17328i	−0.961864	+	0.273528i	$0.911809\pi$
$504$	11.1712	−	9.37378i	0.497606	−	0.417541i
$505$	−11.2288	+	19.4488i	−0.499673	+	0.865459i
$506$	−3.82288	−	6.62141i	−0.169948	−	0.294358i
$507$	22.3757	+	8.14410i	0.993741	+	0.361692i
$508$	−2.30805	+	13.0896i	−0.102403	+	0.580756i
$509$	−5.51316	−	31.2667i	−0.244366	−	1.38587i	−0.821959	−	0.569546i	$-0.807119\pi$
$509$	−5.51316	−	31.2667i	−0.244366	−	1.38587i	0.577593	−	0.816325i	$-0.303992\pi$
$510$		0			0
$511$	4.77150	+	4.00377i	0.211079	+	0.177116i
$512$	1.00000			0.0441942
$513$		0			0
$514$	12.2915			0.542155
$515$	16.7568	+	14.0607i	0.738395	+	0.619587i
$516$	−28.0729	+	10.2177i	−1.23584	+	0.449808i
$517$	−3.51269	−	19.9214i	−0.154488	−	0.876144i
$518$	0.224267	−	1.27188i	0.00985373	−	0.0558833i
$519$	14.9172	+	5.42940i	0.654791	+	0.238324i
$520$	1.64575	+	2.85052i	0.0721710	+	0.125004i
$521$	5.85425	−	10.1399i	0.256479	−	0.444235i	−0.708817	−	0.705392i	$-0.750771\pi$
$521$	5.85425	−	10.1399i	0.256479	−	0.444235i	0.965296	+	0.261157i	$0.0841041\pi$
$522$	5.04287	−	4.23147i	0.220721	−	0.185207i
$523$	−1.43596	+	1.20491i	−0.0627900	+	0.0526871i	−0.673643	−	0.739057i	$-0.735271\pi$
$523$	−1.43596	+	1.20491i	−0.0627900	+	0.0526871i	0.610853	+	0.791744i	$0.290827\pi$
$524$	−0.968627	+	1.67771i	−0.0423147	+	0.0732912i
$525$	11.0516	+	19.1420i	0.482333	+	0.835425i
$526$	10.2777	+	3.74076i	0.448127	+	0.163105i
$527$		0			0
$528$	−2.13440	−	12.1048i	−0.0928877	−	0.526792i
$529$	19.0678	−	6.94010i	0.829034	−	0.301744i
$530$	15.8636	+	13.3112i	0.689072	+	0.578200i
$531$	−31.7490			−1.37779
$532$		0			0
$533$	−0.583005			−0.0252528
$534$		0			0
$535$	23.6483	−	8.60728i	1.02241	−	0.372125i
$536$	0.112134	+	0.635941i	0.00484343	+	0.0274685i
$537$	1.86655	−	10.5857i	0.0805474	−	0.456807i
$538$		0			0
$539$	14.6144	+	25.3128i	0.629486	+	1.09030i
$540$	2.17712	−	3.77089i	0.0936885	−	0.162273i
$541$	6.12836	−	5.14230i	0.263479	−	0.221085i	−0.501472	−	0.865174i	$-0.667208\pi$
$541$	6.12836	−	5.14230i	0.263479	−	0.221085i	0.764950	+	0.644089i	$0.222763\pi$
$542$	9.46390	−	7.94116i	0.406509	−	0.341102i
$543$	−29.4059	+	50.9325i	−1.26193	+	2.18572i
$544$		0			0
$545$	22.5526	+	8.20848i	0.966048	+	0.351613i
$546$	3.34993	−	18.9984i	0.143364	−	0.813057i
$547$	1.96075	+	11.1200i	0.0838356	+	0.475455i	0.997602	+	0.0692147i	$0.0220493\pi$
$547$	1.96075	+	11.1200i	0.0838356	+	0.475455i	−0.913766	+	0.406240i	$0.866840\pi$
$548$	−14.6432	+	5.32970i	−0.625528	+	0.227674i
$549$	2.87191	+	2.40982i	0.122570	+	0.102849i
$550$	10.6458			0.453936
$551$		0			0
$552$	−4.35425			−0.185329
$553$	−11.1712	−	9.37378i	−0.475049	−	0.398613i
$554$	25.8606	−	9.41248i	1.09871	−	0.399898i
$555$	−0.267850	−	1.51905i	−0.0113696	−	0.0644802i
$556$	3.23780	−	18.3625i	0.137313	−	0.778743i
$557$	5.09031	+	1.85272i	0.215683	+	0.0785023i	0.447602	−	0.894233i	$-0.352278\pi$
$557$	5.09031	+	1.85272i	0.215683	+	0.0785023i	−0.231919	+	0.972735i	$0.574500\pi$
$558$	11.2915	+	19.5575i	0.478007	+	0.827933i
$559$	−11.2915	+	19.5575i	−0.477580	+	0.827192i
$560$	−4.59627	+	3.85673i	−0.194228	+	0.162976i
$561$		0			0
$562$	−12.7288	+	22.0469i	−0.536930	+	0.929990i
$563$	−5.03137	−	8.71459i	−0.212047	−	0.367276i	0.740308	−	0.672268i	$-0.234680\pi$
$563$	−5.03137	−	8.71459i	−0.212047	−	0.367276i	−0.952355	+	0.304992i	$0.901346\pi$
$564$	−10.8255	−	3.94016i	−0.455836	−	0.165911i
$565$	4.45334	−	25.2561i	0.187353	−	1.06253i
$566$	5.32158	+	30.1802i	0.223683	+	1.26857i
$567$	17.1294	−	6.23460i	0.719368	−	0.261829i
$568$	−2.07483	−	1.74099i	−0.0870579	−	0.0730503i
$569$	6.58301			0.275974			0.137987	−	0.990434i	$-0.455937\pi$
$569$	6.58301			0.275974			0.137987	+	0.990434i	$0.455937\pi$
$570$		0			0
$571$	7.81176			0.326912			0.163456	−	0.986551i	$-0.447736\pi$
$571$	7.81176			0.326912			0.163456	+	0.986551i	$0.447736\pi$
$572$	−7.11770	−	5.97246i	−0.297606	−	0.249721i
$573$	−16.3666	+	5.95696i	−0.683725	+	0.248856i
$574$	−0.184544	−	1.04660i	−0.00770271	−	0.0436843i
$575$	0.654870	−	3.71395i	0.0273099	−	0.154882i
$576$	−3.75877	−	1.36808i	−0.156615	−	0.0570034i
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$	29.5563	−	24.8007i	1.22832	−	1.03068i
$580$	−2.07483	+	1.74099i	−0.0861526	+	0.0722906i
$581$	−14.4686	+	25.0604i	−0.600260	+	1.03968i
$582$	4.90588	+	8.49723i	0.203355	+	0.352222i
$583$	−54.9321	−	19.9936i	−2.27505	−	0.828052i
$584$	0.296677	−	1.68254i	0.0122766	−	0.0696241i
$585$	−2.28625	−	12.9660i	−0.0945250	−	0.536078i
$586$	−27.1921	+	9.89712i	−1.12330	+	0.408846i
$587$	−10.8208	−	9.07969i	−0.446620	−	0.374759i	0.391560	−	0.920153i	$-0.371936\pi$
$587$	−10.8208	−	9.07969i	−0.446620	−	0.374759i	−0.838180	+	0.545394i	$0.816380\pi$
$588$	16.6458			0.686459
$589$		0			0
$590$	13.0627			0.537785
$591$	−15.4961	−	13.0028i	−0.637425	−	0.534863i
$592$	−0.332885	+	0.121160i	−0.0136815	+	0.00497965i
$593$	5.15883	+	29.2572i	0.211848	+	1.20145i	0.886294	+	0.463123i	$0.153271\pi$
$593$	5.15883	+	29.2572i	0.211848	+	1.20145i	−0.674446	+	0.738324i	$0.735618\pi$
$594$	−2.13440	+	12.1048i	−0.0875754	+	0.496665i
$595$		0			0
$596$	−5.46863	−	9.47194i	−0.224004	−	0.387986i
$597$	26.2915	−	45.5382i	1.07604	−	1.86376i
$598$	−2.52144	+	2.11574i	−0.103109	+	0.0865189i
$599$	−12.9747	+	10.8871i	−0.530131	+	0.444833i	−0.868147	−	0.496308i	$-0.834689\pi$
$599$	−12.9747	+	10.8871i	−0.530131	+	0.444833i	0.338015	+	0.941141i	$0.390244\pi$
$600$	3.03137	−	5.25049i	0.123755	−	0.214350i
$601$	−5.20850	−	9.02138i	−0.212459	−	0.367990i	0.740025	−	0.672580i	$-0.234814\pi$
$601$	−5.20850	−	9.02138i	−0.212459	−	0.367990i	−0.952484	+	0.304590i	$0.901481\pi$
$602$	−38.6834	−	14.0796i	−1.57662	−	0.573842i
$603$	0.448534	−	2.54376i	0.0182657	−	0.103590i
$604$	2.24653	+	12.7407i	0.0914100	+	0.518412i
$605$	16.3666	−	5.95696i	0.665398	−	0.242185i
$606$	−27.6567	−	23.2067i	−1.12348	−	0.942709i
$607$	6.93725			0.281574			0.140787	−	0.990040i	$-0.455037\pi$
$607$	6.93725			0.281574			0.140787	+	0.990040i	$0.455037\pi$
$608$		0			0
$609$	15.8745			0.643268
$610$	−1.18161	−	0.991491i	−0.0478421	−	0.0401443i
$611$	−8.18331	+	2.97848i	−0.331061	+	0.120496i
$612$		0			0
$613$	1.28795	−	7.30431i	0.0520197	−	0.295018i	−0.947688	−	0.319198i	$-0.896586\pi$
$613$	1.28795	−	7.30431i	0.0520197	−	0.295018i	0.999708	+	0.0241800i	$0.00769747\pi$
$614$	−0.606808	−	0.220860i	−0.0244888	−	0.00891318i
$615$	−0.634637	−	1.09922i	−0.0255911	−	0.0443250i
$616$	8.46863	−	14.6681i	0.341211	−	0.590994i
$617$	−23.6512	+	19.8458i	−0.952163	+	0.798960i	−0.979661	−	0.200662i	$-0.935691\pi$
$617$	−23.6512	+	19.8458i	−0.952163	+	0.798960i	0.0274973	+	0.999622i	$0.491246\pi$
$618$	−26.9387	+	22.6043i	−1.08363	+	0.909277i
$619$	4.22876	−	7.32442i	0.169968	−	0.294393i	−0.768440	−	0.639921i	$-0.778967\pi$
$619$	4.22876	−	7.32442i	0.169968	−	0.294393i	0.938408	+	0.345528i	$0.112300\pi$
$620$	−4.64575	−	8.04668i	−0.186578	−	0.323162i
$621$	4.09166	+	1.48924i	0.164192	+	0.0597612i
$622$	2.36956	−	13.4384i	0.0950107	−	0.538832i
$623$		0			0
$624$	−4.97239	+	1.80980i	−0.199055	+	0.0724500i
$625$	−6.35166	−	5.32968i	−0.254066	−	0.213187i
$626$	8.87451			0.354697
$627$		0			0
$628$	−10.5830			−0.422308
$629$		0			0
$630$	22.5526	−	8.20848i	0.898518	−	0.327034i
$631$	−4.30852	−	24.4348i	−0.171519	−	0.972735i	−0.942085	−	0.335374i	$-0.891137\pi$
$631$	−4.30852	−	24.4348i	−0.171519	−	0.972735i	0.770566	−	0.637361i	$-0.219974\pi$
$632$	−0.694593	+	3.93923i	−0.0276294	+	0.156694i
$633$	33.0452	+	12.0275i	1.31343	+	0.478050i
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$	−10.9373	+	18.9439i	−0.434032	+	0.751765i
$636$	−25.5028	+	21.3994i	−1.01125	+	0.848540i
$637$	9.63914	−	8.08820i	0.381917	−	0.320466i
$638$	3.82288	−	6.62141i	0.151349	−	0.262144i
$639$	5.41699	+	9.38251i	0.214293	+	0.371166i
$640$	1.54650	+	0.562880i	0.0611308	+	0.0222498i
$641$	2.23563	−	12.6789i	0.0883023	−	0.500787i	−0.908293	−	0.418335i	$-0.862614\pi$
$641$	2.23563	−	12.6789i	0.0883023	−	0.500787i	0.996595	−	0.0824520i	$-0.0262751\pi$
$642$	7.02537	+	39.8429i	0.277269	+	1.57247i
$643$	6.12704	−	2.23006i	0.241627	−	0.0879450i	−0.218368	−	0.975866i	$-0.570073\pi$
$643$	6.12704	−	2.23006i	0.241627	−	0.0879450i	0.459995	+	0.887921i	$0.347851\pi$
$644$	−4.59627	−	3.85673i	−0.181118	−	0.151976i
$645$	−49.1660			−1.93591
$646$		0			0
$647$	−22.4575			−0.882896			−0.441448	−	0.897287i	$-0.645535\pi$
$647$	−22.4575			−0.882896			−0.441448	+	0.897287i	$0.645535\pi$
$648$	−3.83022	−	3.21394i	−0.150465	−	0.126255i
$649$	−34.6507	+	12.6118i	−1.36016	+	0.495057i
$650$	−0.795831	−	4.51338i	−0.0312150	−	0.177029i
$651$	−9.45645	+	53.6302i	−0.370627	+	2.10193i
$652$	−3.69981	−	1.34662i	−0.144896	−	0.0527377i
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	0.529799	−	0.848123i	$-0.322267\pi$
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	−0.999396	+	0.0347583i	$0.988934\pi$
$654$	−19.2915	+	33.4139i	−0.754357	+	1.30659i
$655$	−2.44233	+	2.04936i	−0.0954298	+	0.0800751i
$656$	−0.223304	+	0.187374i	−0.00871856	+	0.00731574i
$657$	−3.41699	+	5.91841i	−0.133310	+	0.230899i
$658$	−7.93725	−	13.7477i	−0.309426	−	0.535942i
$659$	17.4623	+	6.35576i	0.680235	+	0.247585i	0.658948	−	0.752188i	$-0.271002\pi$
$659$	17.4623	+	6.35576i	0.680235	+	0.247585i	0.0212867	+	0.999773i	$0.493224\pi$
$660$	3.51269	−	19.9214i	0.136731	−	0.775441i
$661$	2.81809	+	15.9822i	0.109611	+	0.621636i	0.989278	+	0.146045i	$0.0466545\pi$
$661$	2.81809	+	15.9822i	0.109611	+	0.621636i	−0.879667	+	0.475591i	$0.842234\pi$
$662$	−18.6170	+	6.77602i	−0.723569	+	0.263358i
$663$		0			0
$664$	7.93725			0.308025
$665$		0			0
$666$	1.41699			0.0549074
$667$	−2.07483	−	1.74099i	−0.0803377	−	0.0674113i
$668$	11.2763	−	4.10424i	0.436294	−	0.158798i
$669$	−8.64269	−	49.0151i	−0.334146	−	1.89503i
$670$	−0.184544	+	1.04660i	−0.00712955	+	0.0404337i
$671$	4.09166	+	1.48924i	0.157957	+	0.0574915i
$672$	−4.82288	−	8.35347i	−0.186046	−	0.322242i
$673$	6.93725	−	12.0157i	0.267411	−	0.463170i	−0.700781	−	0.713376i	$-0.747165\pi$
$673$	6.93725	−	12.0157i	0.267411	−	0.463170i	0.968193	+	0.250206i	$0.0804984\pi$
$674$	−7.43714	+	6.24050i	−0.286468	+	0.240375i
$675$	−4.64433	+	3.89706i	−0.178760	+	0.149998i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	5.70850	+	9.88741i	0.219395	+	0.380004i	0.954623	−	0.297816i	$-0.0962582\pi$
$677$	5.70850	+	9.88741i	0.219395	+	0.380004i	−0.735228	+	0.677820i	$0.762925\pi$
$678$	38.7424	+	14.1011i	1.48789	+	0.541548i
$679$	−2.34777	+	13.3149i	−0.0900991	+	0.510977i
$680$		0			0
$681$	18.2841	−	6.65486i	0.700648	−	0.255015i
$682$	20.0924	+	16.8595i	0.769377	+	0.645584i
$683$	−5.41699			−0.207276			−0.103638	−	0.994615i	$-0.533048\pi$
$683$	−5.41699			−0.207276			−0.103638	+	0.994615i	$0.533048\pi$
$684$		0			0
$685$	−25.6458			−0.979874
$686$	−1.97870	−	1.66032i	−0.0755470	−	0.0633915i
$687$	−49.7239	+	18.0980i	−1.89708	+	0.690482i
$688$	1.96075	+	11.1200i	0.0747528	+	0.423944i
$689$	−4.37003	+	24.7837i	−0.166485	+	0.944183i
$690$	−6.73385	−	2.45092i	−0.256353	−	0.0933049i
$691$	−1.29150	−	2.23695i	−0.0491311	−	0.0850975i	0.840414	−	0.541945i	$-0.182312\pi$
$691$	−1.29150	−	2.23695i	−0.0491311	−	0.0850975i	−0.889545	+	0.456847i	$0.848979\pi$
$692$	3.00000	−	5.19615i	0.114043	−	0.197528i
$693$	−51.8988	+	43.5482i	−1.97147	+	1.65426i
$694$	−17.7943	+	14.9312i	−0.675461	+	0.566779i
$695$	15.3431	−	26.5751i	0.581998	−	1.00805i
$696$	−2.17712	−	3.77089i	−0.0825237	−	0.142935i
$697$		0			0
$698$	3.67544	−	20.8445i	0.139117	−	0.788974i
$699$	8.67151	+	49.1786i	0.327987	+	1.86011i
$700$	7.85043	−	2.85732i	0.296718	−	0.107997i
$701$	7.93181	+	6.65558i	0.299581	+	0.251378i	0.780170	−	0.625568i	$-0.215133\pi$
$701$	7.93181	+	6.65558i	0.299581	+	0.251378i	−0.480589	+	0.876946i	$0.659577\pi$
$702$	5.29150			0.199715
$703$		0			0
$704$	−4.64575			−0.175093
$705$	−14.5238	−	12.1869i	−0.546998	−	0.458986i
$706$	−12.0981	+	4.40334i	−0.455317	+	0.165722i
$707$	−8.63883	−	48.9932i	−0.324896	−	1.84258i
$708$	−3.64661	+	20.6810i	−0.137048	+	0.777238i
$709$	−3.42589	−	1.24692i	−0.128662	−	0.0468291i	0.276887	−	0.960903i	$-0.410697\pi$
$709$	−3.42589	−	1.24692i	−0.128662	−	0.0468291i	−0.405549	+	0.914073i	$0.632920\pi$
$710$	−2.22876	−	3.86032i	−0.0836437	−	0.144875i
$711$	8.00000	−	13.8564i	0.300023	−	0.519656i
$712$		0			0
$713$	7.11770	−	5.97246i	0.266560	−	0.223670i
$714$		0			0
$715$	−7.64575	−	13.2428i	−0.285935	−	0.495254i
$716$	−3.81773	−	1.38954i	−0.142675	−	0.0519296i
$717$	−5.51316	+	31.2667i	−0.205893	+	1.16768i
$718$	−0.857345	−	4.86225i	−0.0319958	−	0.181457i
$719$	−2.54515	+	0.926361i	−0.0949183	+	0.0345474i	−0.389043	−	0.921220i	$-0.627194\pi$
$719$	−2.54515	+	0.926361i	−0.0949183	+	0.0345474i	0.294125	+	0.955767i	$0.404972\pi$
$720$	−5.04287	−	4.23147i	−0.187937	−	0.157698i
$721$	−48.4575			−1.80465
$722$		0			0
$723$	−20.0627			−0.746142
$724$	17.0282	+	14.2884i	0.632849	+	0.531023i
$725$	3.54381	−	1.28984i	0.131614	−	0.0479035i
$726$	4.86215	+	27.5746i	0.180451	+	1.02339i
$727$	0.246059	−	1.39547i	0.00912581	−	0.0517550i	−0.979905	−	0.199466i	$-0.936079\pi$
$727$	0.246059	−	1.39547i	0.00912581	−	0.0517550i	0.989031	+	0.147711i	$0.0471905\pi$
$728$	−6.85177	−	2.49384i	−0.253944	−	0.0924279i
$729$	20.5000	+	35.5070i	0.759259	+	1.31508i
$730$	1.40588	−	2.43506i	0.0520340	−	0.0901255i
$731$		0			0
$732$	1.89959	−	1.59395i	0.0702109	−	0.0589140i
$733$	8.05163	−	13.9458i	0.297394	−	0.515101i	−0.678145	−	0.734928i	$-0.737216\pi$
$733$	8.05163	−	13.9458i	0.297394	−	0.515101i	0.975539	+	0.219827i	$0.0705492\pi$
$734$	−8.11438	−	14.0545i	−0.299507	−	0.518762i
$735$	25.7427	+	9.36956i	0.949532	+	0.345602i
$736$	−0.285782	+	1.62075i	−0.0105341	+	0.0597416i
$737$	−0.520945	−	2.95442i	−0.0191892	−	0.108828i
$738$	1.09569	−	0.398799i	0.0403330	−	0.0146800i
$739$	−25.9013	−	21.7338i	−0.952795	−	0.799490i	0.0269709	−	0.999636i	$-0.491414\pi$
$739$	−25.9013	−	21.7338i	−0.952795	−	0.799490i	−0.979766	+	0.200146i	$0.935858\pi$
$740$	−0.583005			−0.0214317
$741$		0			0
$742$	−45.8745			−1.68411
$743$	−36.4026	−	30.5454i	−1.33548	−	1.12060i	−0.982762	−	0.184875i	$-0.940812\pi$
$743$	−36.4026	−	30.5454i	−1.33548	−	1.12060i	−0.352721	−	0.935729i	$-0.614743\pi$
$744$	14.0364	−	5.10884i	0.514600	−	0.187299i
$745$	−3.12567	−	17.7265i	−0.114516	−	0.649450i
$746$	−0.694593	+	3.93923i	−0.0254308	+	0.144225i
$747$	−29.8343	−	10.8588i	−1.09158	−	0.397303i
$748$		0			0
$749$	−27.8745	+	48.2801i	−1.01851	+	1.76412i
$750$	24.3212	−	20.4079i	0.888083	−	0.745190i
$751$	−6.03222	+	5.06164i	−0.220119	+	0.184702i	−0.746178	−	0.665746i	$-0.768113\pi$
$751$	−6.03222	+	5.06164i	−0.220119	+	0.184702i	0.526059	+	0.850448i	$0.323669\pi$
$752$	−2.17712	+	3.77089i	−0.0793916	+	0.137510i
$753$	−38.6660	−	66.9715i	−1.40907	−	2.44058i
$754$	−3.09300	−	1.12576i	−0.112640	−	0.0409978i
$755$	−3.69723	+	20.9680i	−0.134556	+	0.763105i
$756$	1.67497	+	9.49921i	0.0609180	+	0.345483i
$757$	4.30662	−	1.56748i	0.156527	−	0.0569710i	−0.262569	−	0.964913i	$-0.584570\pi$
$757$	4.30662	−	1.56748i	0.156527	−	0.0569710i	0.419095	+	0.907942i	$0.362347\pi$
$758$	8.20318	+	6.88329i	0.297953	+	0.250012i
$759$	20.2288			0.734257
$760$		0			0
$761$	42.8745			1.55420			0.777100	−	0.629377i	$-0.216690\pi$
$761$	42.8745			1.55420			0.777100	+	0.629377i	$0.216690\pi$
$762$	−26.9387	−	22.6043i	−0.975887	−	0.818867i
$763$	−49.9597	+	18.1838i	−1.80866	+	0.658299i
$764$	1.14313	+	6.48299i	0.0413569	+	0.234547i
$765$		0			0
$766$	−5.18735	−	1.88804i	−0.187426	−	0.0682177i
$767$	7.93725	+	13.7477i	0.286598	+	0.496402i
$768$	−1.32288	+	2.29129i	−0.0477352	+	0.0826797i
$769$	27.0349	−	22.6849i	0.974902	−	0.818040i	−0.00841049	−	0.999965i	$-0.502677\pi$
$769$	27.0349	−	22.6849i	0.974902	−	0.818040i	0.983312	+	0.181925i	$0.0582327\pi$
$770$	21.3531	−	17.9174i	0.769513	−	0.645698i
$771$	−16.2601	+	28.1634i	−0.585594	+	1.01428i
$772$	−7.29150	−	12.6293i	−0.262427	−	0.454537i
$773$	4.63950	+	1.68864i	0.166871	+	0.0607362i	0.424105	−	0.905613i	$-0.360589\pi$
$773$	4.63950	+	1.68864i	0.166871	+	0.0607362i	−0.257234	+	0.966349i	$0.582811\pi$
$774$	7.84300	−	44.4798i	0.281911	−	1.59879i
$775$	2.24653	+	12.7407i	0.0806978	+	0.457660i
$776$	3.48485	−	1.26838i	0.125099	−	0.0455322i
$777$	2.61757	+	2.19640i	0.0939048	+	0.0787955i
$778$	12.0000			0.430221
$779$		0			0
$780$	−8.70850			−0.311814
$781$	9.63914	+	8.08820i	0.344916	+	0.289419i
$782$		0			0
$783$	0.756107	+	4.28810i	0.0270211	+	0.153244i
$784$	1.09251	−	6.19592i	0.0390181	−	0.221283i
$785$	−16.3666	−	5.95696i	−0.584150	−	0.212613i
$786$	−2.56275	−	4.43881i	−0.0914101	−	0.158327i
$787$	21.2601	−	36.8236i	0.757842	−	1.31262i	−0.186107	−	0.982529i	$-0.559587\pi$
$787$	21.2601	−	36.8236i	0.757842	−	1.31262i	0.943949	−	0.330091i	$-0.107079\pi$
$788$	−5.85699	+	4.91459i	−0.208646	+	0.175075i
$789$	−22.1672	+	18.6005i	−0.789174	+	0.662196i
$790$	−3.29150	+	5.70105i	−0.117106	+	0.202834i
$791$	28.4059	+	49.2004i	1.01000	+	1.74937i
$792$	17.4623	+	6.35576i	0.620496	+	0.225842i
$793$	0.325505	−	1.84603i	0.0115590	−	0.0655544i
$794$	3.65751	+	20.7428i	0.129800	+	0.736133i
$795$	−51.4853	+	18.7391i	−1.82600	+	0.664608i
$796$	−15.2248	−	12.7751i	−0.539627	−	0.452801i
$797$	−44.8118			−1.58731			−0.793657	−	0.608365i	$-0.791826\pi$
$797$	−44.8118			−1.58731			−0.793657	+	0.608365i	$0.791826\pi$
$798$		0			0
$799$		0			0
$800$	−1.75539	−	1.47295i	−0.0620625	−	0.0520766i
$801$		0			0
$802$	4.78974	+	27.1640i	0.169132	+	0.959193i
$803$	−1.37829	+	7.81667i	−0.0486388	+	0.275844i
$804$	−1.60546	−	0.584341i	−0.0566203	−	0.0206081i
$805$	−4.93725	−	8.55157i	−0.174015	−	0.301403i
$806$	5.64575	−	9.77873i	0.198863	−	0.344441i
$807$		0			0
$808$	−10.4533	+	8.77132i	−0.367744	+	0.308574i
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$	−4.11438	−	7.12631i	−0.144565	−	0.250393i
$811$	29.4044	+	10.7023i	1.03253	+	0.375809i	0.802043	−	0.597266i	$-0.203747\pi$
$811$	29.4044	+	10.7023i	1.03253	+	0.375809i	0.230485	+	0.973076i	$0.425969\pi$
$812$	1.04189	−	5.90885i	0.0365631	−	0.207360i
$813$	5.67591	+	32.1897i	0.199063	+	1.12894i
$814$	1.54650	−	0.562880i	0.0542048	−	0.0197289i
$815$	−4.96377	−	4.16510i	−0.173873	−	0.145897i
$816$		0			0
$817$		0			0
$818$	−7.58301			−0.265134
$819$	22.3425	+	18.7476i	0.780709	+	0.655092i
$820$	−0.450809	+	0.164081i	−0.0157429	+	0.00572996i
$821$	−1.04189	−	5.90885i	−0.0363622	−	0.206220i	0.961214	−	0.275804i	$-0.0889440\pi$
$821$	−1.04189	−	5.90885i	−0.0363622	−	0.206220i	−0.997576	+	0.0695837i	$0.977833\pi$
$822$	7.15930	−	40.6024i	0.249709	−	1.41617i
$823$	29.9522	+	10.9017i	1.04407	+	0.380010i	0.806422	−	0.591341i	$-0.201401\pi$
$823$	29.9522	+	10.9017i	1.04407	+	0.380010i	0.237648	+	0.971351i	$0.423624\pi$
$824$	6.64575	+	11.5108i	0.231516	+	0.400997i
$825$	−14.0830	+	24.3925i	−0.490307	+	0.849237i
$826$	−22.1672	+	18.6005i	−0.771296	+	0.647194i
$827$	−40.3290	+	33.8400i	−1.40238	+	1.17673i	−0.442343	+	0.896846i	$0.645853\pi$
$827$	−40.3290	+	33.8400i	−1.40238	+	1.17673i	−0.960033	+	0.279888i	$0.909703\pi$
$828$	3.29150	−	5.70105i	0.114388	−	0.198125i
$829$	8.58301	+	14.8662i	0.298100	+	0.516325i	0.975701	−	0.219105i	$-0.0703137\pi$
$829$	8.58301	+	14.8662i	0.298100	+	0.516325i	−0.677601	+	0.735430i	$0.736980\pi$
$830$	12.2750	+	4.46772i	0.426070	+	0.155077i
$831$	−12.6436	+	71.7056i	−0.438603	+	2.48744i
$832$	0.347296	+	1.96962i	0.0120403	+	0.0682841i
$833$		0			0
$834$	37.7905	+	31.7100i	1.30858	+	1.09803i
$835$	19.7490			0.683443
$836$		0			0
$837$	−14.9373			−0.516307
$838$	−24.3212	−	20.4079i	−0.840160	−	0.704978i
$839$	39.0163	−	14.2008i	1.34699	−	0.490265i	0.434984	−	0.900438i	$-0.356754\pi$
$839$	39.0163	−	14.2008i	1.34699	−	0.490265i	0.912008	+	0.410173i	$0.134532\pi$
$840$	−2.75658	−	15.6333i	−0.0951110	−	0.539401i
$841$	−4.56547	+	25.8921i	−0.157430	+	0.892830i
$842$	23.3154	+	8.48612i	0.803503	+	0.292451i
$843$	−33.6771	−	58.3305i	−1.15990	−	2.00901i
$844$	6.64575	−	11.5108i	0.228756	−	0.396217i
$845$	11.3465	−	9.52082i	0.390330	−	0.327526i
$846$	13.3422	−	11.1954i	0.458714	−	0.384907i
$847$	−19.2915	+	33.4139i	−0.662864	+	1.14811i
$848$	6.29150	+	10.8972i	0.216051	+	0.374211i
$849$	−76.1913	−	27.7313i	−2.61488	−	0.951737i
$850$		0			0
$851$	−0.101238	−	0.574148i	−0.00347039	−	0.0196815i
$852$	6.73385	−	2.45092i	0.230698	−	0.0839671i
$853$	6.57496	+	5.51705i	0.225122	+	0.188900i	0.748372	−	0.663279i	$-0.230836\pi$
$853$	6.57496	+	5.51705i	0.225122	+	0.188900i	−0.523249	+	0.852180i	$0.675280\pi$
$854$	3.41699			0.116927
$855$		0			0
$856$	15.2915			0.522653
$857$	16.0869	+	13.4985i	0.549519	+	0.461101i	0.874778	−	0.484524i	$-0.161007\pi$
$857$	16.0869	+	13.4985i	0.549519	+	0.461101i	−0.325259	+	0.945625i	$0.605451\pi$
$858$	23.1005	−	8.40788i	0.788637	−	0.287040i
$859$	2.29715	+	13.0278i	0.0783777	+	0.444502i	0.998590	+	0.0530828i	$0.0169047\pi$
$859$	2.29715	+	13.0278i	0.0783777	+	0.444502i	−0.920212	+	0.391419i	$0.871984\pi$
$860$	−3.22690	+	18.3007i	−0.110037	+	0.624048i
$861$	2.64219	+	0.961679i	0.0900457	+	0.0327739i
$862$	−13.9373	−	24.1400i	−0.474705	−	0.822213i
$863$	15.5314	−	26.9011i	0.528694	−	0.915725i	−0.470746	−	0.882269i	$-0.656015\pi$
$863$	15.5314	−	26.9011i	0.528694	−	0.915725i	0.999440	−	0.0334563i	$-0.0106515\pi$
$864$	2.02676	−	1.70066i	0.0689519	−	0.0578575i
$865$	7.56431	−	6.34721i	0.257194	−	0.215812i
$866$	−8.93725	+	15.4798i	−0.303700	+	0.526024i
$867$	22.4889	+	38.9519i	0.763763	+	1.32288i
$868$	19.3417	+	7.03980i	0.656500	+	0.238946i
$869$	3.22690	−	18.3007i	0.109465	−	0.620808i
$870$	−1.24436	−	7.05714i	−0.0421879	−	0.239260i
$871$	−1.21362	+	0.441720i	−0.0411218	+	0.0149671i
$872$	11.1712	+	9.37378i	0.378306	+	0.317436i
$873$	−14.8340			−0.502054
$874$		0			0
$875$	43.7490			1.47899
$876$	3.46272	+	2.90557i	0.116994	+	0.0981700i
$877$	39.1342	−	14.2437i	1.32147	−	0.480975i	0.417540	−	0.908659i	$-0.362892\pi$
$877$	39.1342	−	14.2437i	1.32147	−	0.480975i	0.903929	+	0.427684i	$0.140670\pi$
$878$	1.87744	+	10.6475i	0.0633606	+	0.359336i
$879$	13.2946	−	75.3976i	0.448417	−	2.54310i
$880$	−7.18466	−	2.61500i	−0.242195	−	0.0881517i
$881$	18.4373	+	31.9343i	0.621167	+	1.07589i	0.989269	+	0.146107i	$0.0466744\pi$
$881$	18.4373	+	31.9343i	0.621167	+	1.07589i	−0.368102	+	0.929785i	$0.619992\pi$
$882$	−12.5830	+	21.7944i	−0.423692	+	0.733856i
$883$	−21.7517	+	18.2518i	−0.732001	+	0.614222i	−0.930676	−	0.365843i	$-0.880781\pi$
$883$	−21.7517	+	18.2518i	−0.732001	+	0.614222i	0.198675	+	0.980065i	$0.436336\pi$
$884$		0			0
$885$	−17.2804	+	29.9305i	−0.580874	+	1.00610i
$886$	−5.32288	−	9.21949i	−0.178826	−	0.309735i
$887$	16.3666	+	5.95696i	0.549537	+	0.200015i	0.601841	−	0.798616i	$-0.294434\pi$
$887$	16.3666	+	5.95696i	0.549537	+	0.200015i	−0.0523036	+	0.998631i	$0.516656\pi$
$888$	0.162752	−	0.923015i	0.00546161	−	0.0309744i
$889$	−8.41456	−	47.7213i	−0.282215	−	1.60052i
$890$		0			0
$891$	17.7943	+	14.9312i	0.596130	+	0.500213i
$892$	−18.8118			−0.629864
$893$		0			0
$894$	28.9373			0.967807
$895$	−5.12198	−	4.29785i	−0.171209	−	0.143661i
$896$	−3.42589	+	1.24692i	−0.114451	+	0.0416567i
$897$	−1.51221	−	8.57620i	−0.0504914	−	0.286351i
$898$	−4.21818	+	23.9225i	−0.140762	+	0.798303i
$899$	8.73116	+	3.17788i	0.291200	+	0.105988i
$900$	4.58301	+	7.93800i	0.152767	+	0.264600i
$901$		0			0
$902$	1.03741	−	0.870494i	0.0345421	−	0.0289843i
$903$	83.4338	−	70.0092i	2.77650	−	2.32976i
$904$	7.79150	−	13.4953i	0.259142	−	0.448846i
$905$	18.2915	+	31.6818i	0.608030	+	1.05314i
$906$	−32.1645	−	11.7069i	−1.06859	−	0.388937i
$907$	6.93503	−	39.3305i	0.230274	−	1.30595i	−0.622068	−	0.782963i	$-0.713707\pi$
$907$	6.93503	−	39.3305i	0.230274	−	1.30595i	0.852342	−	0.522985i	$-0.175182\pi$
$908$	−1.27705	−	7.24252i	−0.0423805	−	0.240352i
$909$	51.2912	−	18.6685i	1.70122	−	0.619195i
$910$	−9.19253	−	7.71345i	−0.304730	−	0.255698i
$911$	16.9373			0.561156			0.280578	−	0.959831i	$-0.409474\pi$
$911$	16.9373			0.561156			0.280578	+	0.959831i	$0.409474\pi$
$912$		0			0
$913$	−36.8745			−1.22037
$914$	25.1833	+	21.1313i	0.832991	+	0.698962i
$915$	3.83492	−	1.39580i	0.126779	−	0.0461436i
$916$	3.47296	+	19.6962i	0.114750	+	0.650779i
$917$	1.22643	−	6.95545i	0.0405004	−	0.229689i
$918$		0			0
$919$	9.93725	+	17.2118i	0.327800	+	0.567766i	0.982075	−	0.188491i	$-0.0603595\pi$
$919$	9.93725	+	17.2118i	0.327800	+	0.567766i	−0.654275	+	0.756257i	$0.727026\pi$
$920$	−1.35425	+	2.34563i	−0.0446483	+	0.0773330i
$921$	1.30878	−	1.09820i	0.0431259	−	0.0361870i
$922$	14.6820	−	12.3197i	0.483526	−	0.405727i
$923$	2.70850	−	4.69126i	0.0891513	−	0.154415i
$924$	22.4059	+	38.8081i	0.737099	+	1.27669i
$925$	0.762807	+	0.277639i	0.0250809	+	0.00912871i
$926$	−6.67808	+	37.8733i	−0.219455	+	1.24459i
$927$	−9.23218	−	52.3583i	−0.303225	−	1.71967i
$928$	−1.54650	+	0.562880i	−0.0507664	+	0.0184774i
$929$	−7.34101	−	6.15984i	−0.240851	−	0.202098i	0.514370	−	0.857568i	$-0.328026\pi$
$929$	−7.34101	−	6.15984i	−0.240851	−	0.202098i	−0.755221	+	0.655471i	$0.772470\pi$
$930$	24.5830			0.806108
$931$		0			0
$932$	18.8745			0.618255
$933$	27.6567	+	23.2067i	0.905440	+	0.759754i
$934$	18.1870	−	6.61954i	0.595098	−	0.216598i
$935$		0			0
$936$	1.38919	−	7.87846i	0.0454069	−	0.257516i
$937$	−6.69577	−	2.43706i	−0.218741	−	0.0796153i	0.230325	−	0.973114i	$-0.426021\pi$
$937$	−6.69577	−	2.43706i	−0.218741	−	0.0796153i	−0.449066	+	0.893498i	$0.648243\pi$
$938$	−1.17712	−	2.03884i	−0.0384345	−	0.0665705i
$939$	−11.7399	+	20.3341i	−0.383116	+	0.663577i
$940$	−5.48948	+	4.60622i	−0.179047	+	0.150238i
$941$	12.8956	−	10.8207i	0.420384	−	0.352744i	−0.407925	−	0.913015i	$-0.633748\pi$
$941$	12.8956	−	10.8207i	0.420384	−	0.352744i	0.828309	+	0.560271i	$0.189303\pi$
$942$	14.0000	−	24.2487i	0.456145	−	0.790066i
$943$	−0.239870	−	0.415468i	−0.00781126	−	0.0135295i
$944$	7.45858	+	2.71470i	0.242756	+	0.0883560i
$945$	−2.75658	+	15.6333i	−0.0896715	+	0.508553i
$946$	−9.10915	−	51.6606i	−0.296164	−	1.67963i
$947$	7.28169	−	2.65032i	0.236623	−	0.0861238i	−0.220987	−	0.975277i	$-0.570928\pi$
$947$	7.28169	−	2.65032i	0.236623	−	0.0861238i	0.457610	+	0.889153i	$0.348706\pi$
$948$	−8.10705	−	6.80262i	−0.263305	−	0.220939i
$949$	3.41699			0.110920
$950$		0			0
$951$	−15.8745			−0.514766
$952$		0			0
$953$	12.6459	−	4.60274i	0.409642	−	0.149097i	−0.128976	−	0.991648i	$-0.541169\pi$
$953$	12.6459	−	4.60274i	0.409642	−	0.149097i	0.538618	+	0.842550i	$0.318947\pi$
$954$	−8.74006	−	49.5674i	−0.282970	−	1.60480i
$955$	−1.88130	+	10.6694i	−0.0608775	+	0.345254i
$956$	11.2763	+	4.10424i	0.364702	+	0.132741i
$957$	10.1144	+	17.5186i	0.326951	+	0.566296i
$958$	−3.29150	+	5.70105i	−0.106344	+	0.184193i
$959$	43.5203	−	36.5179i	1.40534	−	1.17922i
$960$	−3.33555	+	2.79886i	−0.107654	+	0.0903327i
$961$	−0.437254	+	0.757346i	−0.0141050	+	0.0244305i
$962$	−0.354249	−	0.613577i	−0.0114214	−	0.0197825i
$963$	−57.4772	−	20.9200i	−1.85218	−	0.674138i
$964$	−1.31678	+	7.46780i	−0.0424105	+	0.240522i
$965$	−4.16756	−	23.6354i	−0.134158	−	0.760850i
$966$	14.9172	−	5.42940i	0.479952	−	0.174688i
$967$	−10.1819	−	8.54361i	−0.327427	−	0.274744i	0.464223	−	0.885718i	$-0.346334\pi$
$967$	−10.1819	−	8.54361i	−0.327427	−	0.274744i	−0.791651	+	0.610974i	$0.790778\pi$
$968$	10.5830			0.340151
$969$		0			0
$970$	6.10326			0.195964
$971$	−41.6688	−	34.9643i	−1.33722	−	1.12206i	−0.982332	−	0.187147i	$-0.940076\pi$
$971$	−41.6688	−	34.9643i	−1.33722	−	1.12206i	−0.354884	−	0.934910i	$-0.615480\pi$
$972$	19.8895	−	7.23920i	0.637957	−	0.232198i
$973$	11.8042	+	66.9450i	0.378426	+	2.14616i
$974$	0.734316	−	4.16451i	0.0235290	−	0.133440i
$975$	11.3942	+	4.14716i	0.364908	+	0.132815i
$976$	−0.468627	−	0.811686i	−0.0150004	−	0.0259814i
$977$	3.72876	−	6.45840i	0.119293	−	0.206622i	−0.800194	−	0.599741i	$-0.795270\pi$
$977$	3.72876	−	6.45840i	0.119293	−	0.206622i	0.919488	+	0.393118i	$0.128604\pi$
$978$	7.97988	−	6.69592i	0.255168	−	0.214112i
$979$		0			0
$980$	5.17712	−	8.96704i	0.165377	−	0.286442i
$981$	−29.1660	−	50.5170i	−0.931199	−	1.61288i
$982$	−36.9219	−	13.4385i	−1.17823	−	0.428839i
$983$	5.51316	−	31.2667i	0.175842	−	0.997252i	−0.761325	−	0.648371i	$-0.775451\pi$
$983$	5.51316	−	31.2667i	0.175842	−	0.997252i	0.937167	−	0.348881i	$-0.113438\pi$
$984$	−0.133925	−	0.759527i	−0.00426937	−	0.0242128i
$985$	−11.8242	+	4.30364i	−0.376749	+	0.137125i
$986$		0			0
$987$	42.0000			1.33687
$988$		0			0
$989$	−18.5830			−0.590905
$990$	23.4279	+	19.6584i	0.744589	+	0.624784i
$991$	2.66308	−	0.969281i	0.0845955	−	0.0307902i	−0.299376	−	0.954135i	$-0.596778\pi$
$991$	2.66308	−	0.969281i	0.0845955	−	0.0307902i	0.383971	+	0.923345i	$0.374556\pi$
$992$	−0.980374	−	5.55998i	−0.0311269	−	0.176530i
$993$	9.10212	−	51.6207i	0.288847	−	1.63813i
$994$	9.27900	+	3.37728i	0.294312	+	0.107121i
$995$	−16.3542	−	28.3264i	−0.518465	−	0.898007i
$996$	−10.5000	+	18.1865i	−0.332705	+	0.576262i
$997$	12.4319	−	10.4316i	0.393724	−	0.330373i	−0.424338	−	0.905504i	$-0.639493\pi$
$997$	12.4319	−	10.4316i	0.393724	−	0.330373i	0.818062	+	0.575130i	$0.195049\pi$
$998$	−3.65498	+	3.06690i	−0.115697	+	0.0970809i
$999$	−0.468627	+	0.811686i	−0.0148267	+	0.0256806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.n.415.1		12
19.2	odd	18		722.2.c.j.653.2		4
19.3	odd	18		722.2.c.j.429.2		4
19.4	even	9	inner	722.2.e.n.389.2		12
19.5	even	9		722.2.a.j.1.2		2
19.6	even	9	inner	722.2.e.n.595.1		12
19.7	even	3	inner	722.2.e.n.423.2		12
19.8	odd	6		722.2.e.o.245.1		12
19.9	even	9	inner	722.2.e.n.99.2		12
19.10	odd	18		722.2.e.o.99.1		12
19.11	even	3	inner	722.2.e.n.245.2		12
19.12	odd	6		722.2.e.o.423.1		12
19.13	odd	18		722.2.e.o.595.2		12
19.14	odd	18		722.2.a.g.1.1		2
19.15	odd	18		722.2.e.o.389.1		12
19.16	even	9		38.2.c.b.11.1	yes	4
19.17	even	9		38.2.c.b.7.1	✓	4
19.18	odd	2		722.2.e.o.415.2		12
57.5	odd	18		6498.2.a.ba.1.2		2
57.14	even	18		6498.2.a.bg.1.2		2
57.17	odd	18		342.2.g.f.235.1		4
57.35	odd	18		342.2.g.f.163.1		4
76.35	odd	18		304.2.i.e.49.2		4
76.43	odd	18		5776.2.a.ba.1.1		2
76.55	odd	18		304.2.i.e.273.2		4
76.71	even	18		5776.2.a.z.1.2		2
95.17	odd	36		950.2.j.g.349.3		8
95.54	even	18		950.2.e.k.201.2		4
95.73	odd	36		950.2.j.g.49.3		8
95.74	even	18		950.2.e.k.501.2		4
95.92	odd	36		950.2.j.g.49.2		8
95.93	odd	36		950.2.j.g.349.2		8
152.35	odd	18		1216.2.i.k.961.1		4
152.93	even	18		1216.2.i.l.577.2		4
152.131	odd	18		1216.2.i.k.577.1		4
152.149	even	18		1216.2.i.l.961.2		4
228.35	even	18		2736.2.s.v.1873.1		4
228.131	even	18		2736.2.s.v.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.1	✓	4	19.17	even	9
38.2.c.b.11.1	yes	4	19.16	even	9
304.2.i.e.49.2		4	76.35	odd	18
304.2.i.e.273.2		4	76.55	odd	18
342.2.g.f.163.1		4	57.35	odd	18
342.2.g.f.235.1		4	57.17	odd	18
722.2.a.g.1.1		2	19.14	odd	18
722.2.a.j.1.2		2	19.5	even	9
722.2.c.j.429.2		4	19.3	odd	18
722.2.c.j.653.2		4	19.2	odd	18
722.2.e.n.99.2		12	19.9	even	9	inner
722.2.e.n.245.2		12	19.11	even	3	inner
722.2.e.n.389.2		12	19.4	even	9	inner
722.2.e.n.415.1		12	1.1	even	1	trivial
722.2.e.n.423.2		12	19.7	even	3	inner
722.2.e.n.595.1		12	19.6	even	9	inner
722.2.e.o.99.1		12	19.10	odd	18
722.2.e.o.245.1		12	19.8	odd	6
722.2.e.o.389.1		12	19.15	odd	18
722.2.e.o.415.2		12	19.18	odd	2
722.2.e.o.423.1		12	19.12	odd	6
722.2.e.o.595.2		12	19.13	odd	18
950.2.e.k.201.2		4	95.54	even	18
950.2.e.k.501.2		4	95.74	even	18
950.2.j.g.49.2		8	95.92	odd	36
950.2.j.g.49.3		8	95.73	odd	36
950.2.j.g.349.2		8	95.93	odd	36
950.2.j.g.349.3		8	95.17	odd	36
1216.2.i.k.577.1		4	152.131	odd	18
1216.2.i.k.961.1		4	152.35	odd	18
1216.2.i.l.577.2		4	152.93	even	18
1216.2.i.l.961.2		4	152.149	even	18
2736.2.s.v.577.1		4	228.131	even	18
2736.2.s.v.1873.1		4	228.35	even	18
5776.2.a.z.1.2		2	76.71	even	18
5776.2.a.ba.1.1		2	76.43	odd	18
6498.2.a.ba.1.2		2	57.5	odd	18
6498.2.a.bg.1.2		2	57.14	even	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-2.48619 + 0.904900i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.285782 + 1.62075i) q^{5} +(-2.48619 - 0.904900i) q^{6} +(-1.82288 - 3.15731i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(3.06418 - 2.57115i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-2.48619 + 0.904900i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.285782 + 1.62075i) q^{5} +(-2.48619 - 0.904900i) q^{6} +(-1.82288 - 3.15731i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(3.06418 - 2.57115i) q^{9} +(-1.26072 + 1.05787i) q^{10} +(2.32288 - 4.02334i) q^{11} +(-1.32288 - 2.29129i) q^{12} +(-1.87939 - 0.684040i) q^{13} +(0.633078 - 3.59036i) q^{14} +(-0.756107 - 4.28810i) q^{15} +(-0.939693 + 0.342020i) q^{16} +4.00000 q^{18} -1.64575 q^{20} +(7.38907 + 6.20017i) q^{21} +(4.36558 - 1.58894i) q^{22} +(-0.285782 - 1.62075i) q^{23} +(0.459430 - 2.60556i) q^{24} +(2.15331 + 0.783740i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(-1.32288 + 2.29129i) q^{27} +(2.79281 - 2.34344i) q^{28} +(1.26072 - 1.05787i) q^{29} +(2.17712 - 3.77089i) q^{30} +(2.82288 + 4.88936i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-2.13440 + 12.1048i) q^{33} +(5.63816 - 2.05212i) q^{35} +(3.06418 + 2.57115i) q^{36} +0.354249 q^{37} +5.29150 q^{39} +(-1.26072 - 1.05787i) q^{40} +(0.273923 - 0.0996998i) q^{41} +(1.67497 + 9.49921i) q^{42} +(1.96075 - 11.1200i) q^{43} +(4.36558 + 1.58894i) q^{44} +(3.29150 + 5.70105i) q^{45} +(0.822876 - 1.42526i) q^{46} +(3.33555 - 2.79886i) q^{47} +(2.02676 - 1.70066i) q^{48} +(-3.14575 + 5.44860i) q^{49} +(1.14575 + 1.98450i) q^{50} +(0.347296 - 1.96962i) q^{52} +(-2.18502 - 12.3918i) q^{53} +(-2.48619 + 0.904900i) q^{54} +(5.85699 + 4.91459i) q^{55} +3.64575 q^{56} +1.64575 q^{58} +(-6.08029 - 5.10197i) q^{59} +(4.09166 - 1.48924i) q^{60} +(0.162752 + 0.923015i) q^{61} +(-0.980374 + 5.55998i) q^{62} +(-13.7035 - 4.98768i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.64575 - 2.85052i) q^{65} +(-9.41584 + 7.90083i) q^{66} +(0.494674 - 0.415081i) q^{67} +(2.17712 + 3.77089i) q^{69} +(5.63816 + 2.05212i) q^{70} +(-0.470326 + 2.66735i) q^{71} +(0.694593 + 3.93923i) q^{72} +(-1.60546 + 0.584341i) q^{73} +(0.271370 + 0.227707i) q^{74} -6.06275 q^{75} -16.9373 q^{77} +(4.05353 + 3.40131i) q^{78} +(3.75877 - 1.36808i) q^{79} +(-0.285782 - 1.62075i) q^{80} +(-0.868241 + 4.92404i) q^{81} +(0.273923 + 0.0996998i) q^{82} +(-3.96863 - 6.87386i) q^{83} +(-4.82288 + 8.35347i) q^{84} +(8.64979 - 7.25804i) q^{86} +(-2.17712 + 3.77089i) q^{87} +(2.32288 + 4.02334i) q^{88} +(-1.14313 + 6.48299i) q^{90} +(1.26616 + 7.18073i) q^{91} +(1.54650 - 0.562880i) q^{92} +(-11.4426 - 9.60148i) q^{93} +4.35425 q^{94} +2.64575 q^{96} +(-2.84087 - 2.38378i) q^{97} +(-5.91208 + 2.15182i) q^{98} +(-3.22690 - 18.3007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^7 - 6 * q^8	\( 12 q - 6 q^{7} - 6 q^{8} + 12 q^{11} + 48 q^{18} + 12 q^{20} - 12 q^{26} + 42 q^{30} + 18 q^{31} + 36 q^{37} - 24 q^{45} - 6 q^{46} - 6 q^{49} - 18 q^{50} + 12 q^{56} - 12 q^{58} - 6 q^{64} - 12 q^{65} + 42 q^{69} - 168 q^{75} - 108 q^{77} - 42 q^{84} - 42 q^{87} + 12 q^{88} + 84 q^{94}+O(q^{100}) \) 12 * q - 6 * q^7 - 6 * q^8 + 12 * q^11 + 48 * q^18 + 12 * q^20 - 12 * q^26 + 42 * q^30 + 18 * q^31 + 36 * q^37 - 24 * q^45 - 6 * q^46 - 6 * q^49 - 18 * q^50 + 12 * q^56 - 12 * q^58 - 6 * q^64 - 12 * q^65 + 42 * q^69 - 168 * q^75 - 108 * q^77 - 42 * q^84 - 42 * q^87 + 12 * q^88 + 84 * q^94

Introduction

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