LMFDB - Embedded newform 289.2.d.e.134.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(110,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("289.110");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.d (of order $8$, degree $4$, 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:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	16.0.229607785695641627262976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 799x^{8} + 6561 $ x^16 + 799*x^8 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			134.3
Root			$2.12749 + 0.881234i$ of defining polynomial
Character	$\chi$	$=$	289.134
Dual form			289.2.d.e.110.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62831 + 1.62831i) q^{2} +(-0.498551 - 1.20361i) q^{3} +3.30278i q^{4} +(2.12749 - 0.881234i) q^{5} +(1.14805 - 2.77164i) q^{6} +(-0.279728 - 0.115867i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(0.921201 - 0.921201i) q^{9} +O(q^{10})$	\(q+(1.62831 + 1.62831i) q^{2} +(-0.498551 - 1.20361i) q^{3} +3.30278i q^{4} +(2.12749 - 0.881234i) q^{5} +(1.14805 - 2.77164i) q^{6} +(-0.279728 - 0.115867i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(0.921201 - 0.921201i) q^{9} +(4.89913 + 2.02928i) q^{10} +(-1.14805 + 2.77164i) q^{11} +(3.97525 - 1.64660i) q^{12} +3.30278i q^{13} +(-0.266816 - 0.644151i) q^{14} +(-2.12132 - 2.12132i) q^{15} -0.302776 q^{16} +3.00000 q^{18} +(-4.17782 - 4.17782i) q^{19} +(2.91052 + 7.02661i) q^{20} +0.394449i q^{21} +(-6.38246 + 2.64370i) q^{22} +(0.881234 - 2.12749i) q^{23} +(3.61082 + 1.49565i) q^{24} +(0.214095 - 0.214095i) q^{25} +(-5.37794 + 5.37794i) q^{26} +(-5.17885 - 2.14515i) q^{27} +(0.382683 - 0.923880i) q^{28} +(-9.15410 + 3.79175i) q^{29} -6.90833i q^{30} +(-1.37978 - 3.33110i) q^{31} +(3.74963 + 3.74963i) q^{32} +3.90833 q^{33} -0.697224 q^{35} +(3.04252 + 3.04252i) q^{36} +(0.231734 + 0.559456i) q^{37} -13.6056i q^{38} +(3.97525 - 1.64660i) q^{39} +(-2.64370 + 6.38246i) q^{40} +(5.54328 + 2.29610i) q^{41} +(-0.642284 + 0.642284i) q^{42} +(1.69313 - 1.69313i) q^{43} +(-9.15410 - 3.79175i) q^{44} +(1.14805 - 2.77164i) q^{45} +(4.89913 - 2.02928i) q^{46} -3.00000i q^{47} +(0.150949 + 0.364423i) q^{48} +(-4.88492 - 4.88492i) q^{49} +0.697224 q^{50} -10.9083 q^{52} +(-1.47904 - 1.47904i) q^{53} +(-4.93980 - 11.9257i) q^{54} +6.90833i q^{55} +(0.839185 - 0.347602i) q^{56} +(-2.94560 + 7.11131i) q^{57} +(-21.0798 - 8.73156i) q^{58} +(4.24264 - 4.24264i) q^{59} +(7.00625 - 7.00625i) q^{60} +(8.14553 + 3.37399i) q^{61} +(3.17733 - 7.67076i) q^{62} +(-0.364423 + 0.150949i) q^{63} +12.8167i q^{64} +(2.91052 + 7.02661i) q^{65} +(6.36396 + 6.36396i) q^{66} -12.6056 q^{67} -3.00000 q^{69} +(-1.13530 - 1.13530i) q^{70} +(-1.22884 - 2.96667i) q^{71} +3.90833i q^{72} +(0.364423 - 0.150949i) q^{73} +(-0.533632 + 1.28830i) q^{74} +(-0.364423 - 0.150949i) q^{75} +(13.7984 - 13.7984i) q^{76} +(0.642284 - 0.642284i) q^{77} +(9.15410 + 3.79175i) q^{78} +(-4.29030 + 10.3577i) q^{79} +(-0.644151 + 0.266816i) q^{80} +3.39445i q^{81} +(5.28740 + 12.7649i) q^{82} +(1.77758 + 1.77758i) q^{83} -1.30278 q^{84} +5.51388 q^{86} +(9.12757 + 9.12757i) q^{87} +(-3.44415 - 8.31492i) q^{88} +3.21110i q^{89} +(6.38246 - 2.64370i) q^{90} +(0.382683 - 0.923880i) q^{91} +(7.02661 + 2.91052i) q^{92} +(-3.32144 + 3.32144i) q^{93} +(4.88492 - 4.88492i) q^{94} +(-12.5699 - 5.20662i) q^{95} +(2.64370 - 6.38246i) q^{96} +(10.0780 - 4.17444i) q^{97} -15.9083i q^{98} +(1.49565 + 3.61082i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 24 q^{16} + 48 q^{18} - 24 q^{33} - 40 q^{35} + 40 q^{50} - 88 q^{52} - 144 q^{67} - 48 q^{69} + 8 q^{84} - 56 q^{86}+O(q^{100}) $ 16 * q + 24 * q^16 + 48 * q^18 - 24 * q^33 - 40 * q^35 + 40 * q^50 - 88 * q^52 - 144 * q^67 - 48 * q^69 + 8 * q^84 - 56 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	1.62831	+	1.62831i	1.15139	+	1.15139i	0.986275	+	0.165113i	$0.0527989\pi$
$2$	1.62831	+	1.62831i	1.15139	+	1.15139i	0.165113	+	0.986275i	$0.447201\pi$
$3$	−0.498551	−	1.20361i	−0.287838	−	0.694903i	0.712136	−	0.702041i	$-0.247728\pi$
$3$	−0.498551	−	1.20361i	−0.287838	−	0.694903i	−0.999975	+	0.00713811i	$0.997728\pi$
$4$			3.30278i			1.65139i
$5$	2.12749	−	0.881234i	0.951441	−	0.394100i	0.147669	−	0.989037i	$-0.452823\pi$
$5$	2.12749	−	0.881234i	0.951441	−	0.394100i	0.803772	+	0.594937i	$0.202823\pi$
$6$	1.14805	−	2.77164i	0.468690	−	1.13152i
$7$	−0.279728	−	0.115867i	−0.105727	−	0.0437937i	0.329193	−	0.944263i	$-0.393223\pi$
$7$	−0.279728	−	0.115867i	−0.105727	−	0.0437937i	−0.434920	+	0.900469i	$0.643223\pi$
$8$	−2.12132	+	2.12132i	−0.750000	+	0.750000i
$9$	0.921201	−	0.921201i	0.307067	−	0.307067i
$10$	4.89913	+	2.02928i	1.54924	+	0.641716i
$11$	−1.14805	+	2.77164i	−0.346150	+	0.835680i	0.650917	+	0.759149i	$0.274385\pi$
$11$	−1.14805	+	2.77164i	−0.346150	+	0.835680i	−0.997067	+	0.0765316i	$0.975615\pi$
$12$	3.97525	−	1.64660i	1.14755	−	0.475333i
$13$			3.30278i			0.916025i	0.888946	+	0.458013i	$0.151439\pi$
$13$			3.30278i			0.916025i	−0.888946	+	0.458013i	$0.848561\pi$
$14$	−0.266816	−	0.644151i	−0.0713096	−	0.172157i
$15$	−2.12132	−	2.12132i	−0.547723	−	0.547723i
$16$	−0.302776			−0.0756939
$17$		0			0
$17$		0			0
$18$	3.00000			0.707107
$19$	−4.17782	−	4.17782i	−0.958457	−	0.958457i	0.0407137	−	0.999171i	$-0.487037\pi$
$19$	−4.17782	−	4.17782i	−0.958457	−	0.958457i	−0.999171	+	0.0407137i	$0.987037\pi$
$20$	2.91052	+	7.02661i	0.650812	+	1.57120i
$21$			0.394449i			0.0860758i
$22$	−6.38246	+	2.64370i	−1.36075	+	0.563639i
$23$	0.881234	−	2.12749i	0.183750	−	0.443612i	−0.804984	−	0.593297i	$-0.797826\pi$
$23$	0.881234	−	2.12749i	0.183750	−	0.443612i	0.988734	+	0.149685i	$0.0478260\pi$
$24$	3.61082	+	1.49565i	0.737056	+	0.305299i
$25$	0.214095	−	0.214095i	0.0428189	−	0.0428189i
$26$	−5.37794	+	5.37794i	−1.05470	+	1.05470i
$27$	−5.17885	−	2.14515i	−0.996671	−	0.412835i
$28$	0.382683	−	0.923880i	0.0723204	−	0.174597i
$29$	−9.15410	+	3.79175i	−1.69987	+	0.704111i	−0.999949	−	0.0101057i	$-0.996783\pi$
$29$	−9.15410	+	3.79175i	−1.69987	+	0.704111i	−0.699925	+	0.714217i	$0.746783\pi$
$30$		−	6.90833i		−	1.26128i
$31$	−1.37978	−	3.33110i	−0.247817	−	0.598282i	0.750201	−	0.661209i	$-0.229956\pi$
$31$	−1.37978	−	3.33110i	−0.247817	−	0.598282i	−0.998018	+	0.0629270i	$0.979956\pi$
$32$	3.74963	+	3.74963i	0.662847	+	0.662847i
$33$	3.90833			0.680352
$34$		0			0
$35$	−0.697224			−0.117852
$36$	3.04252	+	3.04252i	0.507087	+	0.507087i
$37$	0.231734	+	0.559456i	0.0380969	+	0.0919741i	0.941783	−	0.336222i	$-0.109149\pi$
$37$	0.231734	+	0.559456i	0.0380969	+	0.0919741i	−0.903686	+	0.428196i	$0.859149\pi$
$38$		−	13.6056i		−	2.20711i
$39$	3.97525	−	1.64660i	0.636549	−	0.263667i
$40$	−2.64370	+	6.38246i	−0.418006	+	1.00916i
$41$	5.54328	+	2.29610i	0.865714	+	0.358591i	0.770940	−	0.636908i	$-0.219787\pi$
$41$	5.54328	+	2.29610i	0.865714	+	0.358591i	0.0947747	+	0.995499i	$0.469787\pi$
$42$	−0.642284	+	0.642284i	−0.0991066	+	0.0991066i
$43$	1.69313	−	1.69313i	0.258200	−	0.258200i	−0.566122	−	0.824322i	$-0.691557\pi$
$43$	1.69313	−	1.69313i	0.258200	−	0.258200i	0.824322	+	0.566122i	$0.191557\pi$
$44$	−9.15410	−	3.79175i	−1.38003	−	0.571628i
$45$	1.14805	−	2.77164i	0.171141	−	0.413171i
$46$	4.89913	−	2.02928i	0.722337	−	0.299202i
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$	0.150949	+	0.364423i	0.0217876	+	0.0525999i
$49$	−4.88492	−	4.88492i	−0.697846	−	0.697846i
$50$	0.697224			0.0986024
$51$		0			0
$52$	−10.9083			−1.51271
$53$	−1.47904	−	1.47904i	−0.203161	−	0.203161i	0.598192	−	0.801353i	$-0.295886\pi$
$53$	−1.47904	−	1.47904i	−0.203161	−	0.203161i	−0.801353	+	0.598192i	$0.795886\pi$
$54$	−4.93980	−	11.9257i	−0.672222	−	1.62289i
$55$			6.90833i			0.931519i
$56$	0.839185	−	0.347602i	0.112141	−	0.0464502i
$57$	−2.94560	+	7.11131i	−0.390154	+	0.941916i
$58$	−21.0798	−	8.73156i	−2.76792	−	1.14651i
$59$	4.24264	−	4.24264i	0.552345	−	0.552345i	−0.374772	−	0.927117i	$-0.622279\pi$
$59$	4.24264	−	4.24264i	0.552345	−	0.552345i	0.927117	+	0.374772i	$0.122279\pi$
$60$	7.00625	−	7.00625i	0.904502	−	0.904502i
$61$	8.14553	+	3.37399i	1.04293	+	0.431995i	0.837362	−	0.546649i	$-0.184097\pi$
$61$	8.14553	+	3.37399i	1.04293	+	0.431995i	0.205566	+	0.978643i	$0.434097\pi$
$62$	3.17733	−	7.67076i	0.403522	−	0.974188i
$63$	−0.364423	+	0.150949i	−0.0459130	+	0.0190178i
$64$			12.8167i			1.60208i
$65$	2.91052	+	7.02661i	0.361005	+	0.871544i
$66$	6.36396	+	6.36396i	0.783349	+	0.783349i
$67$	−12.6056			−1.54001			−0.770007	−	0.638036i	$-0.779747\pi$
$67$	−12.6056			−1.54001			−0.770007	+	0.638036i	$0.779747\pi$
$68$		0			0
$69$	−3.00000			−0.361158
$70$	−1.13530	−	1.13530i	−0.135694	−	0.135694i
$71$	−1.22884	−	2.96667i	−0.145836	−	0.352079i	0.834035	−	0.551712i	$-0.186025\pi$
$71$	−1.22884	−	2.96667i	−0.145836	−	0.352079i	−0.979871	+	0.199633i	$0.936025\pi$
$72$			3.90833i			0.460601i
$73$	0.364423	−	0.150949i	0.0426525	−	0.0176672i	−0.361255	−	0.932467i	$-0.617652\pi$
$73$	0.364423	−	0.150949i	0.0426525	−	0.0176672i	0.403908	+	0.914800i	$0.367652\pi$
$74$	−0.533632	+	1.28830i	−0.0620335	+	0.149762i
$75$	−0.364423	−	0.150949i	−0.0420800	−	0.0174301i
$76$	13.7984	−	13.7984i	1.58278	−	1.58278i
$77$	0.642284	−	0.642284i	0.0731951	−	0.0731951i
$78$	9.15410	+	3.79175i	1.03650	+	0.429331i
$79$	−4.29030	+	10.3577i	−0.482697	+	1.16533i	0.475626	+	0.879647i	$0.342221\pi$
$79$	−4.29030	+	10.3577i	−0.482697	+	1.16533i	−0.958323	+	0.285686i	$0.907779\pi$
$80$	−0.644151	+	0.266816i	−0.0720183	+	0.0298310i
$81$			3.39445i			0.377161i
$82$	5.28740	+	12.7649i	0.583896	+	1.40965i
$83$	1.77758	+	1.77758i	0.195115	+	0.195115i	0.797902	−	0.602787i	$-0.205943\pi$
$83$	1.77758	+	1.77758i	0.195115	+	0.195115i	−0.602787	+	0.797902i	$0.705943\pi$
$84$	−1.30278			−0.142144
$85$		0			0
$86$	5.51388			0.594577
$87$	9.12757	+	9.12757i	0.978578	+	0.978578i
$88$	−3.44415	−	8.31492i	−0.367148	−	0.886373i
$89$			3.21110i			0.340376i	0.985412	+	0.170188i	$0.0544375\pi$
$89$			3.21110i			0.340376i	−0.985412	+	0.170188i	$0.945562\pi$
$90$	6.38246	−	2.64370i	0.672771	−	0.278671i
$91$	0.382683	−	0.923880i	0.0401161	−	0.0968489i
$92$	7.02661	+	2.91052i	0.732575	+	0.303443i
$93$	−3.32144	+	3.32144i	−0.344417	+	0.344417i
$94$	4.88492	−	4.88492i	0.503842	−	0.503842i
$95$	−12.5699	−	5.20662i	−1.28964	−	0.534188i
$96$	2.64370	−	6.38246i	0.269822	−	0.651407i
$97$	10.0780	−	4.17444i	1.02326	−	0.423850i	0.192987	−	0.981201i	$-0.438182\pi$
$97$	10.0780	−	4.17444i	1.02326	−	0.423850i	0.830277	+	0.557352i	$0.188182\pi$
$98$		−	15.9083i		−	1.60698i
$99$	1.49565	+	3.61082i	0.150319	+	0.362901i
$100$	0.707107	+	0.707107i	0.0707107	+	0.0707107i
$101$	4.39445			0.437264			0.218632	−	0.975807i	$-0.429841\pi$
$101$	4.39445			0.437264			0.218632	+	0.975807i	$0.429841\pi$
$102$		0			0
$103$	2.00000			0.197066			0.0985329	−	0.995134i	$-0.468585\pi$
$103$	2.00000			0.197066			0.0985329	+	0.995134i	$0.468585\pi$
$104$	−7.00625	−	7.00625i	−0.687019	−	0.687019i
$105$	0.347602	+	0.839185i	0.0339224	+	0.0818960i
$106$		−	4.81665i		−	0.467835i
$107$	−11.2816	+	4.67299i	−1.09063	+	0.451755i	−0.854227	−	0.519900i	$-0.825969\pi$
$107$	−11.2816	+	4.67299i	−1.09063	+	0.451755i	−0.236405	+	0.971655i	$0.575969\pi$
$108$	7.08495	−	17.1046i	0.681750	−	1.64589i
$109$	13.1293	+	5.43835i	1.25756	+	0.520900i	0.909161	−	0.416445i	$-0.136724\pi$
$109$	13.1293	+	5.43835i	1.25756	+	0.520900i	0.348403	+	0.937345i	$0.386724\pi$
$110$	−11.2489	+	11.2489i	−1.07254	+	1.07254i
$111$	0.557835	−	0.557835i	0.0529473	−	0.0529473i
$112$	0.0846949	+	0.0350818i	0.00800291	+	0.00331492i
$113$	4.40617	−	10.6374i	0.414498	−	1.00069i	−0.569417	−	0.822049i	$-0.692831\pi$
$113$	4.40617	−	10.6374i	0.414498	−	1.00069i	0.983915	−	0.178637i	$-0.0571689\pi$
$114$	−16.3757	+	6.78306i	−1.53373	+	0.635291i
$115$		−	5.30278i		−	0.494486i
$116$	−12.5233	−	30.2339i	−1.16276	−	2.80715i
$117$	3.04252	+	3.04252i	0.281281	+	0.281281i
$118$	13.8167			1.27193
$119$		0			0
$120$	9.00000			0.821584
$121$	1.41421	+	1.41421i	0.128565	+	0.128565i
$122$	7.76954	+	18.7573i	0.703421	+	1.69821i
$123$		−	7.81665i		−	0.704804i
$124$	11.0019	−	4.55712i	0.987996	−	0.409241i
$125$	−4.13935	+	9.99329i	−0.370235	+	0.893827i
$126$	−0.839185	−	0.347602i	−0.0747605	−	0.0309668i
$127$	−10.4770	+	10.4770i	−0.929680	+	0.929680i	−0.997685	−	0.0680054i	$-0.978336\pi$
$127$	−10.4770	+	10.4770i	−0.929680	+	0.929680i	0.0680054	+	0.997685i	$0.478336\pi$
$128$	−13.3702	+	13.3702i	−1.18177	+	1.18177i
$129$	−2.88198	−	1.19375i	−0.253744	−	0.105104i
$130$	−6.70227	+	16.1807i	−0.587828	+	1.41914i
$131$	4.25497	−	1.76247i	0.371759	−	0.153988i	−0.188979	−	0.981981i	$-0.560518\pi$
$131$	4.25497	−	1.76247i	0.371759	−	0.153988i	0.560737	+	0.827994i	$0.310518\pi$
$132$			12.9083i			1.12353i
$133$	0.684581	+	1.65273i	0.0593607	+	0.143309i
$134$	−20.5257	−	20.5257i	−1.77315	−	1.77315i
$135$	−12.9083			−1.11097
$136$		0			0
$137$	−1.81665			−0.155207			−0.0776036	−	0.996984i	$-0.524727\pi$
$137$	−1.81665			−0.155207			−0.0776036	+	0.996984i	$0.524727\pi$
$138$	−4.88492	−	4.88492i	−0.415832	−	0.415832i
$139$	7.46764	+	18.0285i	0.633397	+	1.52916i	0.835326	+	0.549755i	$0.185279\pi$
$139$	7.46764	+	18.0285i	0.633397	+	1.52916i	−0.201929	+	0.979400i	$0.564721\pi$
$140$		−	2.30278i		−	0.194620i
$141$	−3.61082	+	1.49565i	−0.304086	+	0.125957i
$142$	2.82973	−	6.83158i	0.237466	−	0.573293i
$143$	−9.15410	−	3.79175i	−0.765504	−	0.317082i
$144$	−0.278917	+	0.278917i	−0.0232431	+	0.0232431i
$145$	−16.1338	+	16.1338i	−1.33984	+	1.33984i
$146$	0.839185	+	0.347602i	0.0694514	+	0.0287677i
$147$	−3.44415	+	8.31492i	−0.284069	+	0.685803i
$148$	−1.84776	+	0.765367i	−0.151885	+	0.0629128i
$149$			1.39445i			0.114238i	0.998367	+	0.0571188i	$0.0181914\pi$
$149$			1.39445i			0.114238i	−0.998367	+	0.0571188i	$0.981809\pi$
$150$	−0.347602	−	0.839185i	−0.0283816	−	0.0685191i
$151$	3.53553	+	3.53553i	0.287718	+	0.287718i	0.836177	−	0.548459i	$-0.184786\pi$
$151$	3.53553	+	3.53553i	0.287718	+	0.287718i	−0.548459	+	0.836177i	$0.684786\pi$
$152$	17.7250			1.43769
$153$		0			0
$154$	2.09167			0.168552
$155$	−5.87095	−	5.87095i	−0.471566	−	0.471566i
$156$	5.43835	+	13.1293i	0.435417	+	1.05119i
$157$			5.69722i			0.454688i	0.973815	+	0.227344i	$0.0730042\pi$
$157$			5.69722i			0.454688i	−0.973815	+	0.227344i	$0.926996\pi$
$158$	−23.8515	+	9.87961i	−1.89752	+	0.785979i
$159$	−1.04280	+	2.51755i	−0.0826998	+	0.199655i
$160$	11.2816	+	4.67299i	0.891888	+	0.369432i
$161$	−0.493012	+	0.493012i	−0.0388548	+	0.0388548i
$162$	−5.52721	+	5.52721i	−0.434259	+	0.434259i
$163$	16.2654	+	6.73735i	1.27401	+	0.527710i	0.914180	−	0.405309i	$-0.132836\pi$
$163$	16.2654	+	6.73735i	1.27401	+	0.527710i	0.359826	+	0.933020i	$0.382836\pi$
$164$	−7.58351	+	18.3082i	−0.592172	+	1.42963i
$165$	8.31492	−	3.44415i	0.647315	−	0.268127i
$166$			5.78890i			0.449306i
$167$	−7.15512	−	17.2740i	−0.553680	−	1.33670i	−0.914696	−	0.404142i	$-0.867570\pi$
$167$	−7.15512	−	17.2740i	−0.553680	−	1.33670i	0.361017	−	0.932559i	$-0.382430\pi$
$168$	−0.836752	−	0.836752i	−0.0645568	−	0.0645568i
$169$	2.09167			0.160898
$170$		0			0
$171$	−7.69722			−0.588621
$172$	5.59203	+	5.59203i	0.426388	+	0.426388i
$173$	−2.91052	−	7.02661i	−0.221283	−	0.534224i	0.773782	−	0.633452i	$-0.218363\pi$
$173$	−2.91052	−	7.02661i	−0.221283	−	0.534224i	−0.995065	+	0.0992284i	$0.968363\pi$
$174$			29.7250i			2.25344i
$175$	−0.0846949	+	0.0350818i	−0.00640233	+	0.00265193i
$176$	0.347602	−	0.839185i	0.0262015	−	0.0632559i
$177$	−7.22165	−	2.99130i	−0.542812	−	0.224840i
$178$	−5.22866	+	5.22866i	−0.391905	+	0.391905i
$179$	14.6548	−	14.6548i	1.09535	−	1.09535i	0.100402	−	0.994947i	$-0.467987\pi$
$179$	14.6548	−	14.6548i	1.09535	−	1.09535i	0.994947	−	0.100402i	$-0.0320130\pi$
$180$	9.15410	+	3.79175i	0.682306	+	0.282621i
$181$	8.49982	−	20.5204i	0.631787	−	1.52527i	−0.205588	−	0.978639i	$-0.565911\pi$
$181$	8.49982	−	20.5204i	0.631787	−	1.52527i	0.837375	−	0.546629i	$-0.184089\pi$
$182$	2.12749	−	0.881234i	0.157700	−	0.0653214i
$183$		−	11.4861i		−	0.849079i
$184$	2.64370	+	6.38246i	0.194896	+	0.470521i
$185$	0.986024	+	0.986024i	0.0724939	+	0.0724939i
$186$	−10.8167			−0.793116
$187$		0			0
$188$	9.90833			0.722639
$189$	1.20012	+	1.20012i	0.0872958	+	0.0872958i
$190$	−11.9897	−	28.9456i	−0.869822	−	2.09994i
$191$		−	11.3028i		−	0.817840i	−0.912570	−	0.408920i	$-0.865905\pi$
$191$		−	11.3028i		−	0.817840i	0.912570	−	0.408920i	$-0.134095\pi$
$192$	15.4262	−	6.38975i	1.11329	−	0.461141i
$193$	7.89602	−	19.0627i	0.568368	−	1.37216i	−0.334561	−	0.942374i	$-0.608588\pi$
$193$	7.89602	−	19.0627i	0.568368	−	1.37216i	0.902930	−	0.429788i	$-0.141412\pi$
$194$	23.2073	+	9.61279i	1.66619	+	0.690158i
$195$	7.00625	−	7.00625i	0.501728	−	0.501728i
$196$	16.1338	−	16.1338i	1.15242	−	1.15242i
$197$	6.38246	+	2.64370i	0.454732	+	0.188356i	0.598280	−	0.801287i	$-0.295851\pi$
$197$	6.38246	+	2.64370i	0.454732	+	0.188356i	−0.143548	+	0.989643i	$0.545851\pi$
$198$	−3.44415	+	8.31492i	−0.244765	+	0.590915i
$199$	−3.33110	+	1.37978i	−0.236135	+	0.0978103i	−0.497613	−	0.867399i	$-0.665790\pi$
$199$	−3.33110	+	1.37978i	−0.236135	+	0.0978103i	0.261478	+	0.965209i	$0.415790\pi$
$200$			0.908327i			0.0642284i
$201$	6.28451	+	15.1721i	0.443275	+	1.07016i
$202$	7.15552	+	7.15552i	0.503460	+	0.503460i
$203$	3.00000			0.210559
$204$		0			0
$205$	13.8167			0.964997
$206$	3.25662	+	3.25662i	0.226899	+	0.226899i
$207$	−1.14805	−	2.77164i	−0.0797950	−	0.192642i
$208$		−	1.00000i		−	0.0693375i
$209$	16.3757	−	6.78306i	1.13273	−	0.469194i
$210$	−0.800449	+	1.93245i	−0.0552362	+	0.133352i
$211$	−8.39961	−	3.47923i	−0.578253	−	0.239520i	0.0743348	−	0.997233i	$-0.476317\pi$
$211$	−8.39961	−	3.47923i	−0.578253	−	0.239520i	−0.652588	+	0.757713i	$0.726317\pi$
$212$	4.88492	−	4.88492i	0.335498	−	0.335498i
$213$	−2.95807	+	2.95807i	−0.202684	+	0.202684i
$214$	−25.9790	−	10.7608i	−1.77589	−	0.735596i
$215$	2.11007	−	5.09416i	0.143906	−	0.347419i
$216$	15.5366	−	6.43545i	1.05713	−	0.437877i
$217$			1.09167i			0.0741076i
$218$	12.5233	+	30.2339i	0.848185	+	2.04770i
$219$	−0.363367	−	0.363367i	−0.0245540	−	0.0245540i
$220$	−22.8167			−1.53830
$221$		0			0
$222$	1.81665			0.121926
$223$	19.4552	+	19.4552i	1.30282	+	1.30282i	0.926483	+	0.376337i	$0.122817\pi$
$223$	19.4552	+	19.4552i	1.30282	+	1.30282i	0.376337	+	0.926483i	$0.377183\pi$
$224$	−0.614418	−	1.48334i	−0.0410525	−	0.0991096i
$225$		−	0.394449i		−	0.0262966i
$226$	24.4956	−	10.1464i	1.62943	−	0.674930i
$227$	6.43545	−	15.5366i	0.427136	−	1.03120i	−0.553055	−	0.833145i	$-0.686538\pi$
$227$	6.43545	−	15.5366i	0.427136	−	1.03120i	0.980191	−	0.198053i	$-0.0634619\pi$
$228$	−23.4871	−	9.72866i	−1.55547	−	0.644296i
$229$	−7.36961	+	7.36961i	−0.486998	+	0.486998i	−0.907357	−	0.420360i	$-0.861904\pi$
$229$	−7.36961	+	7.36961i	−0.486998	+	0.486998i	0.420360	+	0.907357i	$0.361904\pi$
$230$	8.63455	−	8.63455i	0.569346	−	0.569346i
$231$	−1.09327	−	0.452847i	−0.0719318	−	0.0297951i
$232$	11.3753	−	27.4623i	0.746822	−	1.80299i
$233$	−3.86491	+	1.60090i	−0.253199	+	0.104878i	−0.505673	−	0.862725i	$-0.668756\pi$
$233$	−3.86491	+	1.60090i	−0.253199	+	0.104878i	0.252474	+	0.967604i	$0.418756\pi$
$234$			9.90833i			0.647728i
$235$	−2.64370	−	6.38246i	−0.172456	−	0.416346i
$236$	14.0125	+	14.0125i	0.912135	+	0.912135i
$237$	14.6056			0.948733
$238$		0			0
$239$	−6.21110			−0.401763			−0.200881	−	0.979616i	$-0.564381\pi$
$239$	−6.21110			−0.401763			−0.200881	+	0.979616i	$0.564381\pi$
$240$	0.642284	+	0.642284i	0.0414593	+	0.0414593i
$241$	−3.64080	−	8.78968i	−0.234525	−	0.566193i	0.762175	−	0.647371i	$-0.224132\pi$
$241$	−3.64080	−	8.78968i	−0.234525	−	0.566193i	−0.996700	+	0.0811784i	$0.974132\pi$
$242$			4.60555i			0.296056i
$243$	−11.4510	+	4.74315i	−0.734581	+	0.304273i
$244$	−11.1435	+	26.9028i	−0.713391	+	1.72228i
$245$	−14.6974	−	6.08785i	−0.938981	−	0.388939i
$246$	12.7279	−	12.7279i	0.811503	−	0.811503i
$247$	13.7984	−	13.7984i	0.877971	−	0.877971i
$248$	9.99329	+	4.13935i	0.634574	+	0.262849i
$249$	1.25330	−	3.02572i	0.0794244	−	0.191747i
$250$	−23.0123	+	9.53200i	−1.45543	+	0.602857i
$251$			15.9083i			1.00412i	0.864831	+	0.502062i	$0.167425\pi$
$251$			15.9083i			1.00412i	−0.864831	+	0.502062i	$0.832575\pi$
$252$	−0.498551	−	1.20361i	−0.0314057	−	0.0758202i
$253$	4.88492	+	4.88492i	0.307113	+	0.307113i
$254$	−34.1194			−2.14084
$255$		0			0
$256$	−17.9083			−1.11927
$257$	−18.8974	−	18.8974i	−1.17879	−	1.17879i	−0.980053	−	0.198735i	$-0.936317\pi$
$257$	−18.8974	−	18.8974i	−1.17879	−	1.17879i	−0.198735	−	0.980053i	$-0.563683\pi$
$258$	−2.74895	−	6.63655i	−0.171142	−	0.413173i
$259$		−	0.183346i		−	0.0113926i
$260$	−23.2073	+	9.61279i	−1.43926	+	0.596160i
$261$	−4.93980	+	11.9257i	−0.305766	+	0.738185i
$262$	9.79825	+	4.05857i	0.605338	+	0.250739i
$263$	14.5055	−	14.5055i	0.894448	−	0.894448i	−0.100490	−	0.994938i	$-0.532041\pi$
$263$	14.5055	−	14.5055i	0.894448	−	0.894448i	0.994938	+	0.100490i	$0.0320412\pi$
$264$	−8.29081	+	8.29081i	−0.510264	+	0.510264i
$265$	−4.45001	−	1.84325i	−0.273362	−	0.113230i
$266$	−1.57644	+	3.80586i	−0.0966576	+	0.233352i
$267$	3.86491	−	1.60090i	0.236529	−	0.0979733i
$268$		−	41.6333i		−	2.54316i
$269$	−0.428387	−	1.03422i	−0.0261192	−	0.0630574i	0.910282	−	0.413989i	$-0.135865\pi$
$269$	−0.428387	−	1.03422i	−0.0261192	−	0.0630574i	−0.936401	+	0.350932i	$0.885865\pi$
$270$	−21.0187	−	21.0187i	−1.27916	−	1.27916i
$271$	26.5416			1.61229			0.806145	−	0.591718i	$-0.201550\pi$
$271$	26.5416			1.61229			0.806145	+	0.591718i	$0.201550\pi$
$272$		0			0
$273$	−1.30278			−0.0788476
$274$	−2.95807	−	2.95807i	−0.178704	−	0.178704i
$275$	0.347602	+	0.839185i	0.0209612	+	0.0506047i
$276$		−	9.90833i		−	0.596411i
$277$	−3.69552	+	1.53073i	−0.222042	+	0.0919729i	−0.490931	−	0.871198i	$-0.663343\pi$
$277$	−3.69552	+	1.53073i	−0.222042	+	0.0919729i	0.268889	+	0.963171i	$0.413343\pi$
$278$	−17.1963	+	41.5155i	−1.03137	+	2.48994i
$279$	−4.33967	−	1.79755i	−0.259809	−	0.107617i
$280$	1.47904	−	1.47904i	0.0883893	−	0.0883893i
$281$	−20.1820	+	20.1820i	−1.20396	+	1.20396i	−0.231003	+	0.972953i	$0.574201\pi$
$281$	−20.1820	+	20.1820i	−1.20396	+	1.20396i	−0.972953	+	0.231003i	$0.925799\pi$
$282$	−8.31492	−	3.44415i	−0.495146	−	0.205096i
$283$	−7.65367	+	18.4776i	−0.454963	+	1.09838i	0.515448	+	0.856921i	$0.327626\pi$
$283$	−7.65367	+	18.4776i	−0.454963	+	1.09838i	−0.970411	+	0.241458i	$0.922374\pi$
$284$	9.79825	−	4.05857i	0.581419	−	0.240832i
$285$			17.7250i			1.04994i
$286$	−8.73156	−	21.0798i	−0.516308	−	1.24648i
$287$	−1.28457	−	1.28457i	−0.0758257	−	0.0758257i
$288$	6.90833			0.407077
$289$		0			0
$290$	−52.5416			−3.08535
$291$	−10.0488	−	10.0488i	−0.589069	−	0.589069i
$292$	0.498551	+	1.20361i	0.0291755	+	0.0704358i
$293$		−	25.8167i		−	1.50823i	−0.656745	−	0.754113i	$-0.728067\pi$
$293$		−	25.8167i		−	1.50823i	0.656745	−	0.754113i	$-0.271933\pi$
$294$	−19.1474	+	7.93111i	−1.11670	+	0.462552i
$295$	5.28740	−	12.7649i	0.307845	−	0.743203i
$296$	−1.67837	−	0.695203i	−0.0975532	−	0.0404079i
$297$	11.8912	−	11.8912i	0.689996	−	0.689996i
$298$	−2.27059	+	2.27059i	−0.131532	+	0.131532i
$299$	7.02661	+	2.91052i	0.406360	+	0.168320i
$300$	0.498551	−	1.20361i	0.0287838	−	0.0694903i
$301$	−0.669795	+	0.277438i	−0.0386063	+	0.0159913i
$302$			11.5139i			0.662549i
$303$	−2.19086	−	5.28919i	−0.125861	−	0.303856i
$304$	1.26494	+	1.26494i	0.0725494	+	0.0725494i
$305$	20.3028			1.16253
$306$		0			0
$307$	12.1194			0.691692			0.345846	−	0.938291i	$-0.387592\pi$
$307$	12.1194			0.691692			0.345846	+	0.938291i	$0.387592\pi$
$308$	2.12132	+	2.12132i	0.120873	+	0.120873i
$309$	−0.997101	−	2.40722i	−0.0567231	−	0.136942i
$310$		−	19.1194i		−	1.08591i
$311$	14.3073	−	5.92628i	0.811293	−	0.336049i	0.0618233	−	0.998087i	$-0.480308\pi$
$311$	14.3073	−	5.92628i	0.811293	−	0.336049i	0.749470	+	0.662038i	$0.230308\pi$
$312$	−4.93980	+	11.9257i	−0.279661	+	0.675162i
$313$	9.06941	+	3.75667i	0.512633	+	0.212340i	0.623978	−	0.781442i	$-0.285516\pi$
$313$	9.06941	+	3.75667i	0.512633	+	0.212340i	−0.111344	+	0.993782i	$0.535516\pi$
$314$	−9.27684	+	9.27684i	−0.523522	+	0.523522i
$315$	−0.642284	+	0.642284i	−0.0361886	+	0.0361886i
$316$	−34.2092	−	14.1699i	−1.92442	−	0.797120i
$317$	−8.89313	+	21.4699i	−0.499488	+	1.20587i	0.450272	+	0.892891i	$0.351327\pi$
$317$	−8.89313	+	21.4699i	−0.499488	+	1.20587i	−0.949760	+	0.312979i	$0.898673\pi$
$318$	−5.79736	+	2.40135i	−0.325100	+	0.134661i
$319$		−	29.7250i		−	1.66428i
$320$	11.2945	+	27.2673i	0.631380	+	1.52429i
$321$	11.2489	+	11.2489i	0.627852	+	0.627852i
$322$	−1.60555			−0.0894739
$323$		0			0
$324$	−11.2111			−0.622839
$325$	0.707107	+	0.707107i	0.0392232	+	0.0392232i
$326$	15.5146	+	37.4556i	0.859275	+	2.07447i
$327$		−	18.5139i		−	1.02382i
$328$	−16.6298	+	6.88830i	−0.918229	+	0.380343i
$329$	−0.347602	+	0.839185i	−0.0191639	+	0.0462657i
$330$	19.1474	+	7.93111i	1.05403	+	0.436593i
$331$	−0.214095	+	0.214095i	−0.0117677	+	0.0117677i	−0.712966	−	0.701198i	$-0.752649\pi$
$331$	−0.214095	+	0.214095i	−0.0117677	+	0.0117677i	0.701198	+	0.712966i	$0.252649\pi$
$332$	−5.87095	+	5.87095i	−0.322210	+	0.322210i
$333$	0.728846	+	0.301898i	0.0399405	+	0.0165439i
$334$	16.4766	−	39.7781i	0.901561	−	2.17656i
$335$	−26.8181	+	11.1084i	−1.46523	+	0.606919i
$336$		−	0.119429i		−	0.00651541i
$337$	−8.61569	−	20.8001i	−0.469326	−	1.13305i	−0.964458	−	0.264236i	$-0.914880\pi$
$337$	−8.61569	−	20.8001i	−0.469326	−	1.13305i	0.495132	−	0.868818i	$-0.335120\pi$
$338$	3.40589	+	3.40589i	0.185256	+	0.185256i
$339$	−15.0000			−0.814688
$340$		0			0
$341$	10.8167			0.585755
$342$	−12.5335	−	12.5335i	−0.677732	−	0.677732i
$343$	1.61152	+	3.89055i	0.0870139	+	0.210070i
$344$			7.18335i			0.387300i
$345$	−6.38246	+	2.64370i	−0.343620	+	0.142332i
$346$	6.70227	−	16.1807i	0.360316	−	0.869881i
$347$	−15.9857	−	6.62149i	−0.858156	−	0.355460i	−0.0901701	−	0.995926i	$-0.528741\pi$
$347$	−15.9857	−	6.62149i	−0.858156	−	0.355460i	−0.767986	+	0.640466i	$0.778741\pi$
$348$	−30.1463	+	30.1463i	−1.61601	+	1.61601i
$349$	−4.52156	+	4.52156i	−0.242033	+	0.242033i	−0.817691	−	0.575657i	$-0.804746\pi$
$349$	−4.52156	+	4.52156i	−0.242033	+	0.242033i	0.575657	+	0.817691i	$0.304746\pi$
$350$	−0.195033	−	0.0807854i	−0.0104250	−	0.00431816i
$351$	7.08495	−	17.1046i	0.378167	−	0.912976i
$352$	−14.6974	+	6.08785i	−0.783373	+	0.324484i
$353$		−	3.00000i		−	0.159674i	−0.996808	−	0.0798369i	$-0.974560\pi$
$353$		−	3.00000i		−	0.159674i	0.996808	−	0.0798369i	$-0.0254400\pi$
$354$	−6.88830	−	16.6298i	−0.366109	−	0.883866i
$355$	−5.22866	−	5.22866i	−0.277509	−	0.277509i
$356$	−10.6056			−0.562093
$357$		0			0
$358$	47.7250			2.52234
$359$	7.84300	+	7.84300i	0.413938	+	0.413938i	0.883108	−	0.469170i	$-0.155447\pi$
$359$	7.84300	+	7.84300i	0.413938	+	0.413938i	−0.469170	+	0.883108i	$0.655447\pi$
$360$	3.44415	+	8.31492i	0.181523	+	0.438235i
$361$			15.9083i			0.837280i
$362$	47.2538	−	19.5732i	2.48361	−	1.02874i
$363$	0.997101	−	2.40722i	0.0523342	−	0.126346i
$364$	3.05137	+	1.26392i	0.159935	+	0.0662473i
$365$	0.642284	−	0.642284i	0.0336187	−	0.0336187i
$366$	18.7029	−	18.7029i	0.977619	−	0.977619i
$367$	−22.7326	−	9.41614i	−1.18663	−	0.491518i	−0.299974	−	0.953947i	$-0.596978\pi$
$367$	−22.7326	−	9.41614i	−1.18663	−	0.491518i	−0.886656	+	0.462429i	$0.846978\pi$
$368$	−0.266816	+	0.644151i	−0.0139088	+	0.0335787i
$369$	7.22165	−	2.99130i	0.375944	−	0.155721i
$370$			3.21110i			0.166937i
$371$	0.242356	+	0.585100i	0.0125825	+	0.0303769i
$372$	−10.9700	−	10.9700i	−0.568766	−	0.568766i
$373$	−8.21110			−0.425155			−0.212577	−	0.977144i	$-0.568186\pi$
$373$	−8.21110			−0.425155			−0.212577	+	0.977144i	$0.568186\pi$
$374$		0			0
$375$	14.0917			0.727691
$376$	6.36396	+	6.36396i	0.328196	+	0.328196i
$377$	−12.5233	−	30.2339i	−0.644983	−	1.55713i
$378$			3.90833i			0.201023i
$379$	−7.75546	+	3.21242i	−0.398371	+	0.165011i	−0.572869	−	0.819647i	$-0.694170\pi$
$379$	−7.75546	+	3.21242i	−0.398371	+	0.165011i	0.174498	+	0.984658i	$0.444170\pi$
$380$	17.1963	−	41.5155i	0.882151	−	2.12970i
$381$	17.8334	+	7.38685i	0.913635	+	0.378440i
$382$	18.4044	−	18.4044i	0.941651	−	0.941651i
$383$	−2.76360	+	2.76360i	−0.141214	+	0.141214i	−0.774180	−	0.632966i	$-0.781837\pi$
$383$	−2.76360	+	2.76360i	−0.141214	+	0.141214i	0.632966	+	0.774180i	$0.281837\pi$
$384$	22.7582	+	9.42676i	1.16137	+	0.481057i
$385$	0.800449	−	1.93245i	0.0407946	−	0.0984870i
$386$	43.8971	−	18.1828i	2.23430	−	0.925479i
$387$		−	3.11943i		−	0.158570i
$388$	13.7872	+	33.2853i	0.699940	+	1.68981i
$389$	8.93310	+	8.93310i	0.452926	+	0.452926i	0.896325	−	0.443399i	$-0.146227\pi$
$389$	8.93310	+	8.93310i	0.452926	+	0.452926i	−0.443399	+	0.896325i	$0.646227\pi$
$390$	22.8167			1.15537
$391$		0			0
$392$	20.7250			1.04677
$393$	−4.24264	−	4.24264i	−0.214013	−	0.214013i
$394$	6.08785	+	14.6974i	0.306702	+	0.740443i
$395$			25.8167i			1.29898i
$396$	−11.9257	+	4.93980i	−0.599291	+	0.248234i
$397$	0.150949	−	0.364423i	0.00757591	−	0.0182899i	−0.920046	−	0.391810i	$-0.871849\pi$
$397$	0.150949	−	0.364423i	0.00757591	−	0.0182899i	0.927622	+	0.373520i	$0.121849\pi$
$398$	−7.67076	−	3.17733i	−0.384501	−	0.159265i
$399$	1.64793	−	1.64793i	0.0824999	−	0.0824999i
$400$	−0.0648227	+	0.0648227i	−0.00324113	+	0.00324113i
$401$	14.5023	+	6.00707i	0.724213	+	0.299979i	0.714171	−	0.699971i	$-0.246804\pi$
$401$	14.5023	+	6.00707i	0.724213	+	0.299979i	0.0100412	+	0.999950i	$0.496804\pi$
$402$	−14.4718	+	34.9380i	−0.721788	+	1.74255i
$403$	11.0019	−	4.55712i	0.548042	−	0.227006i
$404$			14.5139i			0.722092i
$405$	2.99130	+	7.22165i	0.148639	+	0.358846i
$406$	4.88492	+	4.88492i	0.242435	+	0.242435i
$407$	−1.81665			−0.0900482
$408$		0			0
$409$	−11.1833			−0.552981			−0.276490	−	0.961017i	$-0.589171\pi$
$409$	−11.1833			−0.552981			−0.276490	+	0.961017i	$0.589171\pi$
$410$	22.4978	+	22.4978i	1.11109	+	1.11109i
$411$	0.905694	+	2.18654i	0.0446746	+	0.107854i
$412$			6.60555i			0.325432i
$413$	−1.67837	+	0.695203i	−0.0825872	+	0.0342087i
$414$	2.64370	−	6.38246i	0.129931	−	0.313681i
$415$	5.34824	+	2.21532i	0.262535	+	0.108746i
$416$	−12.3842	+	12.3842i	−0.607184	+	0.607184i
$417$	17.9762	−	17.9762i	0.880299	−	0.880299i
$418$	37.7097	+	15.6199i	1.84444	+	0.763992i
$419$	−4.51142	+	10.8915i	−0.220397	+	0.532086i	−0.994944	−	0.100431i	$-0.967978\pi$
$419$	−4.51142	+	10.8915i	−0.220397	+	0.532086i	0.774547	+	0.632516i	$0.217978\pi$
$420$	−2.77164	+	1.14805i	−0.135242	+	0.0560191i
$421$			27.9361i			1.36152i	0.732506	+	0.680761i	$0.238351\pi$
$421$			27.9361i			1.36152i	−0.732506	+	0.680761i	$0.761649\pi$
$422$	−8.01189	−	19.3424i	−0.390013	−	0.941574i
$423$	−2.76360	−	2.76360i	−0.134371	−	0.134371i
$424$	6.27502			0.304742
$425$		0			0
$426$	−9.63331			−0.466735
$427$	−1.88760	−	1.88760i	−0.0913473	−	0.0913473i
$428$	−15.4338	−	37.2606i	−0.746022	−	1.80106i
$429$			12.9083i			0.623220i
$430$	11.7307	−	4.85902i	0.565705	−	0.234323i
$431$	4.24460	−	10.2474i	0.204455	−	0.493598i	−0.788078	−	0.615576i	$-0.788924\pi$
$431$	4.24460	−	10.2474i	0.204455	−	0.493598i	0.992533	+	0.121977i	$0.0389235\pi$
$432$	1.56803	+	0.649500i	0.0754419	+	0.0312491i
$433$	−19.7990	+	19.7990i	−0.951479	+	0.951479i	−0.998876	−	0.0473974i	$-0.984907\pi$
$433$	−19.7990	+	19.7990i	−0.951479	+	0.951479i	0.0473974	+	0.998876i	$0.484907\pi$
$434$	−1.77758	+	1.77758i	−0.0853266	+	0.0853266i
$435$	27.4623	+	11.3753i	1.31672	+	0.545402i
$436$	−17.9617	+	43.3633i	−0.860208	+	2.07672i
$437$	−12.5699	+	5.20662i	−0.601299	+	0.249066i
$438$		−	1.18335i		−	0.0565425i
$439$	8.04697	+	19.4271i	0.384061	+	0.927206i	0.991171	+	0.132588i	$0.0423287\pi$
$439$	8.04697	+	19.4271i	0.384061	+	0.927206i	−0.607110	+	0.794618i	$0.707671\pi$
$440$	−14.6548	−	14.6548i	−0.698639	−	0.698639i
$441$	−9.00000			−0.428571
$442$		0			0
$443$	−35.2389			−1.67425			−0.837124	−	0.547013i	$-0.815765\pi$
$443$	−35.2389			−1.67425			−0.837124	+	0.547013i	$0.815765\pi$
$444$	1.84240	+	1.84240i	0.0874366	+	0.0874366i
$445$	2.82973	+	6.83158i	0.134142	+	0.323848i
$446$			63.3583i			3.00010i
$447$	1.67837	−	0.695203i	0.0793841	−	0.0328820i
$448$	1.48503	−	3.58518i	0.0701611	−	0.169384i
$449$	−7.86580	−	3.25812i	−0.371210	−	0.153760i	0.189276	−	0.981924i	$-0.439386\pi$
$449$	−7.86580	−	3.25812i	−0.371210	−	0.153760i	−0.560486	+	0.828164i	$0.689386\pi$
$450$	0.642284	−	0.642284i	0.0302776	−	0.0302776i
$451$	−12.7279	+	12.7279i	−0.599334	+	0.599334i
$452$	35.1331	+	14.5526i	1.65252	+	0.684496i
$453$	2.49275	−	6.01804i	0.117120	−	0.282752i
$454$	35.7772	−	14.8194i	1.67911	−	0.695509i
$455$		−	2.30278i		−	0.107956i
$456$	−8.83680	−	21.3339i	−0.413821	−	0.999053i
$457$	−6.72733	−	6.72733i	−0.314691	−	0.314691i	0.532033	−	0.846724i	$-0.321428\pi$
$457$	−6.72733	−	6.72733i	−0.314691	−	0.314691i	−0.846724	+	0.532033i	$0.821428\pi$
$458$	−24.0000			−1.12145
$459$		0			0
$460$	17.5139			0.816589
$461$	8.78383	+	8.78383i	0.409104	+	0.409104i	0.881426	−	0.472322i	$-0.156584\pi$
$461$	8.78383	+	8.78383i	0.409104	+	0.409104i	−0.472322	+	0.881426i	$0.656584\pi$
$462$	−1.04280	−	2.51755i	−0.0485157	−	0.117127i
$463$			15.8167i			0.735062i	0.930011	+	0.367531i	$0.119797\pi$
$463$			15.8167i			0.735062i	−0.930011	+	0.367531i	$0.880203\pi$
$464$	2.77164	−	1.14805i	0.128670	−	0.0532969i
$465$	−4.13935	+	9.99329i	−0.191958	+	0.463427i
$466$	−8.90002	−	3.68651i	−0.412285	−	0.170774i
$467$	17.6128	−	17.6128i	0.815025	−	0.815025i	−0.170357	−	0.985382i	$-0.554492\pi$
$467$	17.6128	−	17.6128i	0.815025	−	0.815025i	0.985382	+	0.170357i	$0.0544921\pi$
$468$	−10.0488	+	10.0488i	−0.464504	+	0.464504i
$469$	3.52613	+	1.46057i	0.162821	+	0.0674429i
$470$	6.08785	−	14.6974i	0.280812	−	0.677939i
$471$	6.85722	−	2.84035i	0.315964	−	0.130877i
$472$			18.0000i			0.828517i
$473$	2.74895	+	6.63655i	0.126397	+	0.305149i
$474$	23.7823	+	23.7823i	1.09236	+	1.09236i
$475$	−1.78890			−0.0820802
$476$		0			0
$477$	−2.72498			−0.124768
$478$	−10.1136	−	10.1136i	−0.462585	−	0.462585i
$479$	4.83456	+	11.6717i	0.220897	+	0.533292i	0.995012	−	0.0997526i	$-0.0318051\pi$
$479$	4.83456	+	11.6717i	0.220897	+	0.533292i	−0.774116	+	0.633044i	$0.781805\pi$
$480$		−	15.9083i		−	0.726112i
$481$	−1.84776	+	0.765367i	−0.0842506	+	0.0348977i
$482$	8.38395	−	20.2407i	0.381879	−	0.921937i
$483$	0.839185	+	0.347602i	0.0381842	+	0.0158164i
$484$	−4.67083	+	4.67083i	−0.212310	+	0.212310i
$485$	17.7621	−	17.7621i	0.806536	−	0.806536i
$486$	−26.3690	−	10.9224i	−1.19612	−	0.495451i
$487$	4.62728	−	11.1712i	0.209682	−	0.506218i	−0.783691	−	0.621151i	$-0.786665\pi$
$487$	4.62728	−	11.1712i	0.209682	−	0.506218i	0.993373	+	0.114933i	$0.0366654\pi$
$488$	−24.4366	+	10.1220i	−1.10619	+	0.458200i
$489$		−	22.9361i		−	1.03721i
$490$	−14.0190	−	33.8448i	−0.633312	−	1.52895i
$491$	−15.6408	−	15.6408i	−0.705859	−	0.705859i	0.259802	−	0.965662i	$-0.416343\pi$
$491$	−15.6408	−	15.6408i	−0.705859	−	0.705859i	−0.965662	+	0.259802i	$0.916343\pi$
$492$	25.8167			1.16390
$493$		0			0
$494$	44.9361			2.02177
$495$	6.36396	+	6.36396i	0.286039	+	0.286039i
$496$	0.417765	+	1.00857i	0.0187582	+	0.0452863i
$497$			0.972244i			0.0436111i
$498$	6.96756	−	2.88606i	0.312224	−	0.129327i
$499$	−8.76664	+	21.1645i	−0.392449	+	0.947455i	0.596957	+	0.802274i	$0.296376\pi$
$499$	−8.76664	+	21.1645i	−0.392449	+	0.947455i	−0.989405	+	0.145181i	$0.953624\pi$
$500$	−33.0056	−	13.6714i	−1.47605	−	0.611402i
$501$	−17.2239	+	17.2239i	−0.769508	+	0.769508i
$502$	−25.9037	+	25.9037i	−1.15614	+	1.15614i
$503$	−33.8448	−	14.0190i	−1.50906	−	0.625075i	−0.533699	−	0.845674i	$-0.679198\pi$
$503$	−33.8448	−	14.0190i	−1.50906	−	0.625075i	−0.975364	+	0.220600i	$0.929198\pi$
$504$	0.452847	−	1.09327i	0.0201714	−	0.0486981i
$505$	9.34913	−	3.87254i	0.416031	−	0.172326i
$506$			15.9083i			0.707211i
$507$	−1.04280	−	2.51755i	−0.0463126	−	0.111808i
$508$	−34.6030	−	34.6030i	−1.53526	−	1.53526i
$509$	−4.39445			−0.194781			−0.0973903	−	0.995246i	$-0.531049\pi$
$509$	−4.39445			−0.194781			−0.0973903	+	0.995246i	$0.531049\pi$
$510$		0			0
$511$	−0.119429			−0.00528325
$512$	−2.41986	−	2.41986i	−0.106944	−	0.106944i
$513$	12.6743	+	30.5984i	0.559582	+	1.35095i
$514$		−	61.5416i		−	2.71449i
$515$	4.25497	−	1.76247i	0.187497	−	0.0776636i
$516$	3.94270	−	9.51852i	0.173568	−	0.419030i
$517$	8.31492	+	3.44415i	0.365690	+	0.151474i
$518$	0.298544	−	0.298544i	0.0131173	−	0.0131173i
$519$	−7.00625	+	7.00625i	−0.307540	+	0.307540i
$520$	−21.0798	−	8.73156i	−0.924412	−	0.382904i
$521$	4.91534	−	11.8667i	0.215345	−	0.519889i	−0.778884	−	0.627168i	$-0.784214\pi$
$521$	4.91534	−	11.8667i	0.215345	−	0.519889i	0.994229	+	0.107279i	$0.0342139\pi$
$522$	−27.4623	+	11.3753i	−1.20199	+	0.497882i
$523$			13.4222i			0.586912i	0.955973	+	0.293456i	$0.0948054\pi$
$523$			13.4222i			0.586912i	−0.955973	+	0.293456i	$0.905195\pi$
$524$	5.82104	+	14.0532i	0.254293	+	0.613918i
$525$	0.0844494	+	0.0844494i	0.00368567	+	0.00368567i
$526$	47.2389			2.05971
$527$		0			0
$528$	−1.18335			−0.0514985
$529$	12.5138	+	12.5138i	0.544079	+	0.544079i
$530$	−4.24460	−	10.2474i	−0.184374	−	0.445117i
$531$		−	7.81665i		−	0.339214i
$532$	−5.45858	+	2.26102i	−0.236660	+	0.0980276i
$533$	−7.58351	+	18.3082i	−0.328478	+	0.793016i
$534$	8.90002	+	3.68651i	0.385141	+	0.159531i
$535$	−19.8834	+	19.8834i	−0.859636	+	0.859636i
$536$	26.7404	−	26.7404i	1.15501	−	1.15501i
$537$	−24.9447	−	10.3325i	−1.07645	−	0.445878i
$538$	0.986479	−	2.38157i	0.0425301	−	0.102677i
$539$	19.1474	−	7.93111i	0.824736	−	0.341617i
$540$		−	42.6333i		−	1.83465i
$541$	2.49275	+	6.01804i	0.107172	+	0.258736i	0.968363	−	0.249545i	$-0.0802811\pi$
$541$	2.49275	+	6.01804i	0.107172	+	0.258736i	−0.861191	+	0.508281i	$0.830281\pi$
$542$	43.2180	+	43.2180i	1.85637	+	1.85637i
$543$	−28.9361			−1.24177
$544$		0			0
$545$	32.7250			1.40178
$546$	−2.12132	−	2.12132i	−0.0907841	−	0.0907841i
$547$	9.65849	+	23.3177i	0.412967	+	0.996991i	0.984337	+	0.176298i	$0.0564124\pi$
$547$	9.65849	+	23.3177i	0.412967	+	0.996991i	−0.571369	+	0.820693i	$0.693588\pi$
$548$		−	6.00000i		−	0.256307i
$549$	10.6118	−	4.39555i	0.452900	−	0.187597i
$550$	−0.800449	+	1.93245i	−0.0341312	+	0.0824001i
$551$	54.0854	+	22.4029i	2.30412	+	0.954396i
$552$	6.36396	−	6.36396i	0.270868	−	0.270868i
$553$	2.40024	−	2.40024i	0.102068	−	0.102068i
$554$	−8.50995	−	3.52494i	−0.361553	−	0.149760i
$555$	0.695203	−	1.67837i	0.0295097	−	0.0712428i
$556$	−59.5440	+	24.6639i	−2.52523	+	1.04598i
$557$		−	27.6333i		−	1.17086i	−0.810723	−	0.585430i	$-0.800926\pi$
$557$		−	27.6333i		−	1.17086i	0.810723	−	0.585430i	$-0.199074\pi$
$558$	−4.13935	−	9.99329i	−0.175233	−	0.423049i
$559$	5.59203	+	5.59203i	0.236518	+	0.236518i
$560$	0.211103			0.00892071
$561$		0			0
$562$	−65.7250			−2.77244
$563$	−11.7419	−	11.7419i	−0.494862	−	0.494862i	0.414972	−	0.909834i	$-0.363791\pi$
$563$	−11.7419	−	11.7419i	−0.494862	−	0.494862i	−0.909834	+	0.414972i	$0.863791\pi$
$564$	−4.93980	−	11.9257i	−0.208003	−	0.502164i
$565$		−	26.5139i		−	1.11545i
$566$	−42.5497	+	17.6247i	−1.78850	+	0.740821i
$567$	0.393305	−	0.949523i	0.0165173	−	0.0398762i
$568$	8.90002	+	3.68651i	0.373436	+	0.154682i
$569$	7.34999	−	7.34999i	0.308127	−	0.308127i	−0.536055	−	0.844183i	$-0.680086\pi$
$569$	7.34999	−	7.34999i	0.308127	−	0.308127i	0.844183	+	0.536055i	$0.180086\pi$
$570$	−28.8617	+	28.8617i	−1.20888	+	1.20888i
$571$	6.91627	+	2.86481i	0.289437	+	0.119889i	0.522678	−	0.852530i	$-0.324933\pi$
$571$	6.91627	+	2.86481i	0.289437	+	0.119889i	−0.233241	+	0.972419i	$0.574933\pi$
$572$	12.5233	−	30.2339i	0.523626	−	1.26414i
$573$	−13.6041	+	5.63501i	−0.568320	+	0.235406i
$574$		−	4.18335i		−	0.174609i
$575$	−0.266816	−	0.644151i	−0.0111270	−	0.0268630i
$576$	11.8067	+	11.8067i	0.491947	+	0.491947i
$577$	−37.2389			−1.55027			−0.775137	−	0.631793i	$-0.782319\pi$
$577$	−37.2389			−1.55027			−0.775137	+	0.631793i	$0.782319\pi$
$578$		0			0
$579$	−26.8806			−1.11712
$580$	−53.2864	−	53.2864i	−2.21260	−	2.21260i
$581$	−0.291276	−	0.703203i	−0.0120842	−	0.0291738i
$582$		−	32.7250i		−	1.35649i
$583$	5.79736	−	2.40135i	0.240102	−	0.0994536i
$584$	−0.452847	+	1.09327i	−0.0187389	+	0.0452398i
$585$	9.15410	+	3.79175i	0.378475	+	0.156770i
$586$	42.0375	−	42.0375i	1.73655	−	1.73655i
$587$	3.45108	−	3.45108i	0.142442	−	0.142442i	−0.632290	−	0.774732i	$-0.717885\pi$
$587$	3.45108	−	3.45108i	0.142442	−	0.142442i	0.774732	+	0.632290i	$0.217885\pi$
$588$	−27.4623	−	11.3753i	−1.13253	−	0.469108i
$589$	−8.15222	+	19.6812i	−0.335906	+	0.810950i
$590$	29.3948	−	12.1757i	1.21016	−	0.501266i
$591$		−	9.00000i		−	0.370211i
$592$	−0.0701635	−	0.169390i	−0.00288370	−	0.00696188i
$593$	−25.9037	−	25.9037i	−1.06374	−	1.06374i	−0.997826	−	0.0659103i	$-0.979005\pi$
$593$	−25.9037	−	25.9037i	−1.06374	−	1.06374i	−0.0659103	−	0.997826i	$-0.520995\pi$
$594$	38.7250			1.58891
$595$		0			0
$596$	−4.60555			−0.188651
$597$	3.32144	+	3.32144i	0.135937	+	0.135937i
$598$	6.70227	+	16.1807i	0.274076	+	0.661679i
$599$		−	12.6333i		−	0.516183i	−0.966120	−	0.258091i	$-0.916906\pi$
$599$		−	12.6333i		−	0.516183i	0.966120	−	0.258091i	$-0.0830936\pi$
$600$	1.09327	−	0.452847i	0.0446325	−	0.0184874i
$601$	−10.4483	+	25.2245i	−0.426196	+	1.02893i	0.554287	+	0.832325i	$0.312991\pi$
$601$	−10.4483	+	25.2245i	−0.426196	+	1.02893i	−0.980483	+	0.196602i	$0.937009\pi$
$602$	−1.54239	−	0.638878i	−0.0628630	−	0.0260387i
$603$	−11.6123	+	11.6123i	−0.472887	+	0.472887i
$604$	−11.6771	+	11.6771i	−0.475133	+	0.475133i
$605$	4.25497	+	1.76247i	0.172989	+	0.0716545i
$606$	5.04505	−	12.1798i	0.204941	−	0.494772i
$607$	15.3672	−	6.36529i	0.623734	−	0.258359i	−0.0483540	−	0.998830i	$-0.515398\pi$
$607$	15.3672	−	6.36529i	0.623734	−	0.258359i	0.672088	+	0.740471i	$0.265398\pi$
$608$		−	31.3305i		−	1.27062i
$609$	−1.49565	−	3.61082i	−0.0606069	−	0.146318i
$610$	33.0592	+	33.0592i	1.33853	+	1.33853i
$611$	9.90833			0.400848
$612$		0			0
$613$	−27.0278			−1.09164			−0.545820	−	0.837902i	$-0.683782\pi$
$613$	−27.0278			−1.09164			−0.545820	+	0.837902i	$0.683782\pi$
$614$	19.7342	+	19.7342i	0.796406	+	0.796406i
$615$	−6.88830	−	16.6298i	−0.277763	−	0.670580i
$616$			2.72498i			0.109793i
$617$	−19.4015	+	8.03635i	−0.781074	+	0.323531i	−0.737349	−	0.675512i	$-0.763923\pi$
$617$	−19.4015	+	8.03635i	−0.781074	+	0.323531i	−0.0437250	+	0.999044i	$0.513923\pi$
$618$	2.29610	−	5.54328i	0.0923627	−	0.222983i
$619$	−32.3871	−	13.4152i	−1.30175	−	0.539201i	−0.379281	−	0.925281i	$-0.623829\pi$
$619$	−32.3871	−	13.4152i	−1.30175	−	0.539201i	−0.922465	+	0.386080i	$0.873829\pi$
$620$	19.3904	−	19.3904i	0.778738	−	0.778738i
$621$	−9.12757	+	9.12757i	−0.366277	+	0.366277i
$622$	32.9465	+	13.6469i	1.32104	+	0.547191i
$623$	0.372062	−	0.898236i	0.0149063	−	0.0359871i
$624$	−1.20361	+	0.498551i	−0.0481829	+	0.0199580i
$625$			26.4222i			1.05689i
$626$	8.65077	+	20.8848i	0.345754	+	0.834725i
$627$	−16.3283	−	16.3283i	−0.652089	−	0.652089i
$628$	−18.8167			−0.750866
$629$		0			0
$630$	−2.09167			−0.0833343
$631$	−18.4889	−	18.4889i	−0.736030	−	0.736030i	0.235777	−	0.971807i	$-0.424236\pi$
$631$	−18.4889	−	18.4889i	−0.736030	−	0.736030i	−0.971807	+	0.235777i	$0.924236\pi$
$632$	−12.8709	−	31.0731i	−0.511977	−	1.23602i
$633$			11.8444i			0.470773i
$634$	−49.4404	+	20.4789i	−1.96353	+	0.813320i
$635$	−13.0569	+	31.5222i	−0.518149	+	1.25092i
$636$	−8.31492	−	3.44415i	−0.329708	−	0.136569i
$637$	16.1338	−	16.1338i	0.639245	−	0.639245i
$638$	48.4014	−	48.4014i	1.91623	−	1.91623i
$639$	−3.86491	−	1.60090i	−0.152893	−	0.0633305i
$640$	−16.6627	+	40.2272i	−0.658650	+	1.59012i
$641$	−9.15410	+	3.79175i	−0.361565	+	0.149765i	−0.556068	−	0.831137i	$-0.687691\pi$
$641$	−9.15410	+	3.79175i	−0.361565	+	0.149765i	0.194503	+	0.980902i	$0.437691\pi$
$642$			36.6333i			1.44580i
$643$	11.4103	+	27.5470i	0.449980	+	1.08635i	0.972329	+	0.233616i	$0.0750558\pi$
$643$	11.4103	+	27.5470i	0.449980	+	1.08635i	−0.522349	+	0.852732i	$0.674944\pi$
$644$	−1.62831	−	1.62831i	−0.0641643	−	0.0641643i
$645$	−7.18335			−0.282844
$646$		0			0
$647$	43.0555			1.69269			0.846343	−	0.532638i	$-0.178799\pi$
$647$	43.0555			1.69269			0.846343	+	0.532638i	$0.178799\pi$
$648$	−7.20071	−	7.20071i	−0.282871	−	0.282871i
$649$	6.88830	+	16.6298i	0.270389	+	0.652778i
$650$			2.30278i			0.0903223i
$651$	1.31395	−	0.544254i	0.0514976	−	0.0213310i
$652$	−22.2520	+	53.7210i	−0.871454	+	2.10388i
$653$	−6.63655	−	2.74895i	−0.259708	−	0.107575i	0.249031	−	0.968496i	$-0.419888\pi$
$653$	−6.63655	−	2.74895i	−0.259708	−	0.107575i	−0.508739	+	0.860921i	$0.669888\pi$
$654$	30.1463	−	30.1463i	1.17881	−	1.17881i
$655$	7.49926	−	7.49926i	0.293020	−	0.293020i
$656$	−1.67837	−	0.695203i	−0.0655293	−	0.0271431i
$657$	0.196653	−	0.474762i	0.00767215	−	0.0185222i
$658$	−1.93245	+	0.800449i	−0.0753349	+	0.0312047i
$659$			43.6056i			1.69863i	0.527885	+	0.849316i	$0.322985\pi$
$659$			43.6056i			1.69863i	−0.527885	+	0.849316i	$0.677015\pi$
$660$	11.3753	+	27.4623i	0.442781	+	1.06897i
$661$	−0.512639	−	0.512639i	−0.0199393	−	0.0199393i	0.697067	−	0.717006i	$-0.254488\pi$
$661$	−0.512639	−	0.512639i	−0.0199393	−	0.0199393i	−0.717006	+	0.697067i	$0.754488\pi$
$662$	−0.697224			−0.0270984
$663$		0			0
$664$	−7.54163			−0.292672
$665$	2.91288	+	2.91288i	0.112957	+	0.112957i
$666$	0.695203	+	1.67837i	0.0269386	+	0.0650355i
$667$			22.8167i			0.883464i
$668$	57.0521	−	23.6317i	2.20741	−	0.914340i
$669$	13.7171	−	33.1159i	0.530332	−	1.28034i
$670$	−61.7562	−	25.5802i	−2.38585	−	0.988251i
$671$	−18.7029	+	18.7029i	−0.722019	+	0.722019i
$672$	−1.47904	+	1.47904i	−0.0570551	+	0.0570551i
$673$	−4.03430	−	1.67106i	−0.155511	−	0.0644147i	0.303570	−	0.952809i	$-0.401821\pi$
$673$	−4.03430	−	1.67106i	−0.155511	−	0.0644147i	−0.459081	+	0.888394i	$0.651821\pi$
$674$	19.8400	−	47.8980i	0.764208	−	1.84496i
$675$	−1.56803	+	0.649500i	−0.0603535	+	0.0249993i
$676$			6.90833i			0.265705i
$677$	−3.79175	−	9.15410i	−0.145729	−	0.351821i	0.834113	−	0.551593i	$-0.185980\pi$
$677$	−3.79175	−	9.15410i	−0.145729	−	0.351821i	−0.979842	+	0.199772i	$0.935980\pi$
$678$	−24.4246	−	24.4246i	−0.938022	−	0.938022i
$679$	−3.30278			−0.126749
$680$		0			0
$681$	−21.9083			−0.839529
$682$	17.6128	+	17.6128i	0.674431	+	0.674431i
$683$	−17.8915	−	43.1939i	−0.684599	−	1.65277i	−0.755388	−	0.655277i	$-0.772552\pi$
$683$	−17.8915	−	43.1939i	−0.684599	−	1.65277i	0.0707893	−	0.997491i	$-0.477448\pi$
$684$		−	25.4222i		−	0.972042i
$685$	−3.86491	+	1.60090i	−0.147671	+	0.0611671i
$686$	−3.71097	+	8.95907i	−0.141685	+	0.342059i
$687$	12.5442	+	5.19600i	0.478593	+	0.198240i
$688$	−0.512639	+	0.512639i	−0.0195442	+	0.0195442i
$689$	4.88492	−	4.88492i	0.186101	−	0.186101i
$690$	−14.6974	−	6.08785i	−0.559520	−	0.231761i
$691$	−0.926938	+	2.23783i	−0.0352624	+	0.0851309i	−0.940530	−	0.339712i	$-0.889671\pi$
$691$	−0.926938	+	2.23783i	−0.0352624	+	0.0851309i	0.905267	+	0.424843i	$0.139671\pi$
$692$	23.2073	−	9.61279i	0.882210	−	0.365423i
$693$		−	1.18335i		−	0.0449516i
$694$	−15.2478	−	36.8114i	−0.578798	−	1.39734i
$695$	31.7746	+	31.7746i	1.20528	+	1.20528i
$696$	−38.7250			−1.46787
$697$		0			0
$698$	−14.7250			−0.557349
$699$	3.85370	+	3.85370i	0.145760	+	0.145760i
$700$	−0.115867	−	0.279728i	−0.00437937	−	0.0105727i
$701$			36.6333i			1.38362i	0.722079	+	0.691810i	$0.243187\pi$
$701$			36.6333i			1.38362i	−0.722079	+	0.691810i	$0.756813\pi$
$702$	39.3880	−	16.3151i	1.48661	−	0.615772i
$703$	1.36916	−	3.30545i	0.0516390	−	0.124667i
$704$	−35.5231	−	14.7142i	−1.33883	−	0.554561i
$705$	−6.36396	+	6.36396i	−0.239681	+	0.239681i
$706$	4.88492	−	4.88492i	0.183847	−	0.183847i
$707$	−1.22925	−	0.509173i	−0.0462308	−	0.0191494i
$708$	9.87961	−	23.8515i	0.371298	−	0.896393i
$709$	−2.10184	+	0.870612i	−0.0789364	+	0.0326965i	−0.421802	−	0.906688i	$-0.638602\pi$
$709$	−2.10184	+	0.870612i	−0.0789364	+	0.0326965i	0.342866	+	0.939384i	$0.388602\pi$
$710$		−	17.0278i		−	0.639040i
$711$	5.58930	+	13.4938i	0.209615	+	0.506056i
$712$	−6.81178	−	6.81178i	−0.255282	−	0.255282i
$713$	−8.30278			−0.310941
$714$		0			0
$715$	−22.8167			−0.853294
$716$	48.4014	+	48.4014i	1.80885	+	1.80885i
$717$	3.09655	+	7.47573i	0.115643	+	0.279186i
$718$			25.5416i			0.953205i
$719$	31.7763	−	13.1622i	1.18506	−	0.490867i	0.298915	−	0.954280i	$-0.403375\pi$
$719$	31.7763	−	13.1622i	1.18506	−	0.490867i	0.886142	+	0.463413i	$0.153375\pi$
$720$	−0.347602	+	0.839185i	−0.0129543	+	0.0312746i
$721$	−0.559456	−	0.231734i	−0.0208352	−	0.00863024i
$722$	−25.9037	+	25.9037i	−0.964034	+	0.964034i
$723$	−8.76420	+	8.76420i	−0.325944	+	0.325944i
$724$	67.7742	+	28.0730i	2.51881	+	1.04332i
$725$	−1.14805	+	2.77164i	−0.0426375	+	0.102936i
$726$	5.54328	−	2.29610i	0.205730	−	0.0852163i
$727$		−	28.7889i		−	1.06772i	−0.845573	−	0.533861i	$-0.820741\pi$
$727$		−	28.7889i		−	1.06772i	0.845573	−	0.533861i	$-0.179259\pi$
$728$	1.14805	+	2.77164i	0.0425496	+	0.102724i
$729$	18.6185	+	18.6185i	0.689574	+	0.689574i
$730$	2.09167			0.0774163
$731$		0			0
$732$	37.9361			1.40216
$733$	−10.3925	−	10.3925i	−0.383856	−	0.383856i	0.488633	−	0.872489i	$-0.337496\pi$
$733$	−10.3925	−	10.3925i	−0.383856	−	0.383856i	−0.872489	+	0.488633i	$0.837496\pi$
$734$	−21.6833	−	52.3480i	−0.800343	−	1.93220i
$735$			20.7250i			0.764452i
$736$	11.2816	−	4.67299i	0.415845	−	0.172249i
$737$	14.4718	−	34.9380i	0.533076	−	1.28696i
$738$	16.6298	+	6.88830i	0.612153	+	0.253562i
$739$	3.83408	−	3.83408i	0.141039	−	0.141039i	−0.633062	−	0.774101i	$-0.718202\pi$
$739$	3.83408	−	3.83408i	0.141039	−	0.141039i	0.774101	+	0.633062i	$0.218202\pi$
$740$	−3.25662	+	3.25662i	−0.119716	+	0.119716i
$741$	−23.4871	−	9.72866i	−0.862819	−	0.357391i
$742$	−0.558092	+	1.34735i	−0.0204882	+	0.0494629i
$743$	−26.6231	+	11.0277i	−0.976707	+	0.404565i	−0.813205	−	0.581977i	$-0.802279\pi$
$743$	−26.6231	+	11.0277i	−0.976707	+	0.404565i	−0.163503	+	0.986543i	$0.552279\pi$
$744$		−	14.0917i		−	0.516626i
$745$	1.22884	+	2.96667i	0.0450211	+	0.108690i
$746$	−13.3702	−	13.3702i	−0.489518	−	0.489518i
$747$	3.27502			0.119827
$748$		0			0
$749$	3.69722			0.135094
$750$	22.9456	+	22.9456i	0.837854	+	0.837854i
$751$	−16.9401	−	40.8970i	−0.618153	−	1.49235i	−0.853846	−	0.520526i	$-0.825736\pi$
$751$	−16.9401	−	40.8970i	−0.618153	−	1.49235i	0.235693	−	0.971828i	$-0.424264\pi$
$752$			0.908327i			0.0331233i
$753$	19.1474	−	7.93111i	0.697770	−	0.289026i
$754$	28.8384	−	69.6220i	1.05023	−	2.53548i
$755$	10.6374	+	4.40617i	0.387136	+	0.160357i
$756$	−3.96372	+	3.96372i	−0.144159	+	0.144159i
$757$	28.4335	−	28.4335i	1.03343	−	1.03343i	0.0340133	−	0.999421i	$-0.489171\pi$
$757$	28.4335	−	28.4335i	1.03343	−	1.03343i	0.999421	−	0.0340133i	$-0.0108289\pi$
$758$	−17.8591	−	7.39747i	−0.648671	−	0.268688i
$759$	3.44415	−	8.31492i	0.125015	−	0.301812i
$760$	37.7097	−	15.6199i	1.36787	−	0.566592i
$761$		−	11.7889i		−	0.427347i	−0.976905	−	0.213674i	$-0.931457\pi$
$761$		−	11.7889i		−	0.427347i	0.976905	−	0.213674i	$-0.0685429\pi$
$762$	17.0103	+	41.0664i	0.616217	+	1.48768i
$763$	−3.04252	−	3.04252i	−0.110147	−	0.110147i
$764$	37.3305			1.35057
$765$		0			0
$766$	−9.00000			−0.325183
$767$	14.0125	+	14.0125i	0.505962	+	0.505962i
$768$	8.92821	+	21.5546i	0.322169	+	0.777785i
$769$		−	18.9361i		−	0.682853i	−0.939909	−	0.341426i	$-0.889090\pi$
$769$		−	18.9361i		−	0.682853i	0.939909	−	0.341426i	$-0.110910\pi$
$770$	4.45001	−	1.84325i	0.160367	−	0.0664262i
$771$	−13.3238	+	32.1664i	−0.479843	+	1.15844i
$772$	62.9598	+	26.0788i	2.26597	+	0.938597i
$773$	15.4463	−	15.4463i	0.555566	−	0.555566i	−0.372476	−	0.928042i	$-0.621491\pi$
$773$	15.4463	−	15.4463i	0.555566	−	0.555566i	0.928042	+	0.372476i	$0.121491\pi$
$774$	5.07939	−	5.07939i	0.182575	−	0.182575i
$775$	−1.00857	−	0.417765i	−0.0362291	−	0.0150066i
$776$	−12.5233	+	30.2339i	−0.449561	+	1.08534i
$777$	−0.220677	+	0.0914074i	−0.00791674	+	0.00327922i
$778$			29.0917i			1.04299i
$779$	−13.5661	−	32.7515i	−0.486056	−	1.17344i
$780$	23.1401	+	23.1401i	0.828547	+	0.828547i
$781$	9.63331			0.344707
$782$		0			0
$783$	55.5416			1.98490
$784$	1.47904	+	1.47904i	0.0528227	+	0.0528227i
$785$	5.02059	+	12.1208i	0.179192	+	0.432609i
$786$		−	13.8167i		−	0.492824i
$787$	−30.5137	+	12.6392i	−1.08769	+	0.450538i	−0.853202	−	0.521580i	$-0.825343\pi$
$787$	−30.5137	+	12.6392i	−1.08769	+	0.450538i	−0.234492	+	0.972118i	$0.575343\pi$
$788$	−8.73156	+	21.0798i	−0.311049	+	0.750938i
$789$	−24.6907	−	10.2272i	−0.879011	−	0.364098i
$790$	−42.0375	+	42.0375i	−1.49563	+	1.49563i
$791$	−2.46506	+	2.46506i	−0.0876475	+	0.0876475i
$792$	−10.8325	−	4.48696i	−0.384915	−	0.159437i
$793$	−11.1435	+	26.9028i	−0.395718	+	0.955348i
$794$	0.839185	−	0.347602i	0.0297815	−	0.0123359i
$795$			6.27502i			0.222552i
$796$	−4.55712	−	11.0019i	−0.161523	−	0.389951i
$797$	−32.1183	−	32.1183i	−1.13769	−	1.13769i	−0.988863	−	0.148827i	$-0.952450\pi$
$797$	−32.1183	−	32.1183i	−1.13769	−	1.13769i	−0.148827	−	0.988863i	$-0.547550\pi$
$798$	5.36669			0.189979
$799$		0			0
$800$	1.60555			0.0567648
$801$	2.95807	+	2.95807i	0.104518	+	0.104518i
$802$	13.8329	+	33.3956i	0.488458	+	1.17924i
$803$			1.18335i			0.0417594i
$804$	−50.1102	+	20.7563i	−1.76725	+	0.732019i
$805$	−0.614418	+	1.48334i	−0.0216554	+	0.0522807i
$806$	25.3348	+	10.4940i	0.892381	+	0.369636i
$807$	−1.03122	+	1.03122i	−0.0363007	+	0.0363007i
$808$	−9.32203	+	9.32203i	−0.327948	+	0.327948i
$809$	15.7316	+	6.51624i	0.553093	+	0.229099i	0.641684	−	0.766969i	$-0.278236\pi$
$809$	15.7316	+	6.51624i	0.553093	+	0.229099i	−0.0885903	+	0.996068i	$0.528236\pi$
$810$	−6.88830	+	16.6298i	−0.242030	+	0.584313i
$811$	−26.0893	+	10.8065i	−0.916119	+	0.379469i	−0.790396	−	0.612596i	$-0.790125\pi$
$811$	−26.0893	+	10.8065i	−0.916119	+	0.379469i	−0.125723	+	0.992065i	$0.540125\pi$
$812$			9.90833i			0.347714i
$813$	−13.2323	−	31.9457i	−0.464079	−	1.12039i
$814$	−2.95807	−	2.95807i	−0.103680	−	0.103680i
$815$	40.5416			1.42011
$816$		0			0
$817$	−14.1472			−0.494947
$818$	−18.2099	−	18.2099i	−0.636695	−	0.636695i
$819$	−0.498551	−	1.20361i	−0.0174208	−	0.0420575i
$820$			45.6333i			1.59358i
$821$	15.5366	−	6.43545i	0.542230	−	0.224599i	−0.0947204	−	0.995504i	$-0.530196\pi$
$821$	15.5366	−	6.43545i	0.542230	−	0.224599i	0.636950	+	0.770905i	$0.280196\pi$
$822$	−2.08561	+	5.03511i	−0.0727440	+	0.175620i
$823$	31.8276	+	13.1834i	1.10944	+	0.459545i	0.860745	−	0.509036i	$-0.169998\pi$
$823$	31.8276	+	13.1834i	1.10944	+	0.459545i	0.248696	+	0.968582i	$0.419998\pi$
$824$	−4.24264	+	4.24264i	−0.147799	+	0.147799i
$825$	0.836752	−	0.836752i	0.0291320	−	0.0291320i
$826$	−3.86491	−	1.60090i	−0.134477	−	0.0557023i
$827$	−5.52976	+	13.3500i	−0.192289	+	0.464226i	−0.990391	−	0.138296i	$-0.955837\pi$
$827$	−5.52976	+	13.3500i	−0.192289	+	0.464226i	0.798102	+	0.602522i	$0.205837\pi$
$828$	9.15410	−	3.79175i	0.318127	−	0.131773i
$829$		−	31.4500i		−	1.09230i	−0.837687	−	0.546151i	$-0.816092\pi$
$829$		−	31.4500i		−	1.09230i	0.837687	−	0.546151i	$-0.183908\pi$
$830$	5.10137	+	12.3158i	0.177071	+	0.427488i
$831$	3.68481	+	3.68481i	0.127825	+	0.127825i
$832$	−42.3305			−1.46755
$833$		0			0
$834$	58.5416			2.02713
$835$	−30.4448	−	30.4448i	−1.05359	−	1.05359i
$836$	22.4029	+	54.0854i	0.774821	+	1.87058i
$837$			20.2111i			0.698598i
$838$	−25.0807	+	10.3888i	−0.866399	+	0.358874i
$839$	19.2256	−	46.4147i	0.663741	−	1.60241i	−0.128154	−	0.991754i	$-0.540905\pi$
$839$	19.2256	−	46.4147i	0.663741	−	1.60241i	0.791895	−	0.610658i	$-0.209095\pi$
$840$	−2.51755	−	1.04280i	−0.0868639	−	0.0359802i
$841$	48.9141	−	48.9141i	1.68669	−	1.68669i
$842$	−45.4886	+	45.4886i	−1.56764	+	1.56764i
$843$	34.3529	+	14.2295i	1.18318	+	0.490088i
$844$	11.4911	−	27.7420i	0.395541	−	0.954920i
$845$	4.45001	−	1.84325i	0.153085	−	0.0634099i
$846$		−	9.00000i		−	0.309426i
$847$	−0.231734	−	0.559456i	−0.00796249	−	0.0192232i
$848$	0.447816	+	0.447816i	0.0153781	+	0.0153781i
$849$	26.0555			0.894223
$850$		0			0
$851$	1.39445			0.0478011
$852$	−9.76985	−	9.76985i	−0.334710	−	0.334710i
$853$	1.91342	+	4.61940i	0.0655142	+	0.158165i	0.953246	−	0.302196i	$-0.0977198\pi$
$853$	1.91342	+	4.61940i	0.0655142	+	0.158165i	−0.887732	+	0.460361i	$0.847720\pi$
$854$		−	6.14719i		−	0.210352i
$855$	−16.3757	+	6.78306i	−0.560039	+	0.231976i
$856$	14.0190	−	33.8448i	0.479158	−	1.15679i
$857$	−14.7564	−	6.11231i	−0.504070	−	0.208793i	0.116133	−	0.993234i	$-0.462950\pi$
$857$	−14.7564	−	6.11231i	−0.504070	−	0.208793i	−0.620203	+	0.784441i	$0.712950\pi$
$858$	−21.0187	+	21.0187i	−0.717568	+	0.717568i
$859$	−34.3693	+	34.3693i	−1.17267	+	1.17267i	−0.191094	+	0.981572i	$0.561204\pi$
$859$	−34.3693	+	34.3693i	−1.17267	+	1.17267i	−0.981572	+	0.191094i	$0.938796\pi$
$860$	16.8249	+	6.96909i	0.573723	+	0.237644i
$861$	−0.905694	+	2.18654i	−0.0308660	+	0.0745170i
$862$	23.5974	−	9.77436i	0.803730	−	0.332916i
$863$			49.3305i			1.67923i	0.543181	+	0.839615i	$0.317220\pi$
$863$			49.3305i			1.67923i	−0.543181	+	0.839615i	$0.682780\pi$
$864$	−11.3753	−	27.4623i	−0.386994	−	0.934286i
$865$	−12.3842	−	12.3842i	−0.421075	−	0.421075i
$866$	−64.4777			−2.19104
$867$		0			0
$868$	−3.60555			−0.122380
$869$	−23.7823	−	23.7823i	−0.806761	−	0.806761i
$870$	26.1947	+	63.2395i	0.888082	+	2.14402i
$871$		−	41.6333i		−	1.41069i
$872$	−39.3880	+	16.3151i	−1.33385	+	0.552498i
$873$	5.43835	−	13.1293i	0.184060	−	0.444361i
$874$	−28.9456	−	11.9897i	−0.979101	−	0.405557i
$875$	2.31579	−	2.31579i	0.0782879	−	0.0782879i
$876$	1.20012	−	1.20012i	0.0405483	−	0.0405483i
$877$	10.9762	+	4.54650i	0.370640	+	0.153524i	0.560226	−	0.828340i	$-0.310714\pi$
$877$	10.9762	+	4.54650i	0.370640	+	0.153524i	−0.189585	+	0.981864i	$0.560714\pi$
$878$	−18.5304	+	44.7363i	−0.625370	+	1.50978i
$879$	−31.0731	+	12.8709i	−1.04807	+	0.434125i
$880$		−	2.09167i		−	0.0705103i
$881$	7.31669	+	17.6640i	0.246506	+	0.595117i	0.997903	−	0.0647334i	$-0.0206197\pi$
$881$	7.31669	+	17.6640i	0.246506	+	0.595117i	−0.751397	+	0.659850i	$0.770620\pi$
$882$	−14.6548	−	14.6548i	−0.493452	−	0.493452i
$883$	10.6972			0.359990			0.179995	−	0.983668i	$-0.442392\pi$
$883$	10.6972			0.359990			0.179995	+	0.983668i	$0.442392\pi$
$884$		0			0
$885$	−18.0000			−0.605063
$886$	−57.3797	−	57.3797i	−1.92771	−	1.92771i
$887$	17.1155	+	41.3205i	0.574683	+	1.38741i	0.897529	+	0.440955i	$0.145360\pi$
$887$	17.1155	+	41.3205i	0.574683	+	1.38741i	−0.322847	+	0.946451i	$0.604640\pi$
$888$			2.36669i			0.0794210i
$889$	4.14464	−	1.71676i	0.139007	−	0.0575784i
$890$	−6.51624	+	15.7316i	−0.218425	+	0.527324i
$891$	−9.40819	−	3.89700i	−0.315186	−	0.130554i
$892$	−64.2563	+	64.2563i	−2.15146	+	2.15146i
$893$	−12.5335	+	12.5335i	−0.419416	+	0.419416i
$894$	3.86491	+	1.60090i	0.129262	+	0.0535420i
$895$	18.2636	−	44.0921i	0.610483	−	1.47384i
$896$	5.28919	−	2.19086i	0.176700	−	0.0731913i
$897$		−	9.90833i		−	0.330829i
$898$	−7.50272	−	18.1132i	−0.250369	−	0.604444i
$899$	25.2614	+	25.2614i	0.842514	+	0.842514i
$900$	1.30278			0.0434259
$901$		0			0
$902$	−41.4500			−1.38013
$903$	0.667853	+	0.667853i	0.0222248	+	0.0222248i
$904$	13.2185	+	31.9123i	0.439641	+	1.06139i
$905$		−	51.1472i		−	1.70019i
$906$	13.8582	−	5.74025i	0.460408	−	0.190707i
$907$	−18.1934	+	43.9227i	−0.604102	+	1.45843i	0.265222	+	0.964187i	$0.414555\pi$
$907$	−18.1934	+	43.9227i	−0.604102	+	1.45843i	−0.869324	+	0.494243i	$0.835445\pi$
$908$	51.3138	+	21.2549i	1.70291	+	0.705367i
$909$	4.04817	−	4.04817i	0.134269	−	0.134269i
$910$	3.74963	−	3.74963i	0.124299	−	0.124299i
$911$	−1.73742	−	0.719663i	−0.0575633	−	0.0238435i	0.353716	−	0.935353i	$-0.384918\pi$
$911$	−1.73742	−	0.719663i	−0.0575633	−	0.0238435i	−0.411279	+	0.911509i	$0.634918\pi$
$912$	0.891856	−	2.15313i	0.0295323	−	0.0712973i
$913$	−6.96756	+	2.88606i	−0.230593	+	0.0955146i
$914$		−	21.9083i		−	0.724663i
$915$	−10.1220	−	24.4366i	−0.334622	−	0.807848i
$916$	−24.3402	−	24.3402i	−0.804222	−	0.804222i
$917$	−1.39445			−0.0460488
$918$		0			0
$919$	25.3028			0.834662			0.417331	−	0.908755i	$-0.362966\pi$
$919$	25.3028			0.834662			0.417331	+	0.908755i	$0.362966\pi$
$920$	11.2489	+	11.2489i	0.370865	+	0.370865i
$921$	−6.04215	−	14.5870i	−0.199096	−	0.480659i
$922$			28.6056i			0.942074i
$923$	9.79825	−	4.05857i	0.322513	−	0.133589i
$924$	1.49565	−	3.61082i	0.0492033	−	0.118787i
$925$	0.169390	+	0.0701635i	0.00556950	+	0.00230696i
$926$	−25.7544	+	25.7544i	−0.846342	+	0.846342i
$927$	1.84240	−	1.84240i	0.0605125	−	0.0605125i
$928$	−48.5421	−	20.1068i	−1.59347	−	0.660038i
$929$	−22.8558	+	55.1787i	−0.749873	+	1.81035i	−0.189983	+	0.981787i	$0.560843\pi$
$929$	−22.8558	+	55.1787i	−0.749873	+	1.81035i	−0.559891	+	0.828567i	$0.689157\pi$
$930$	−23.0123	+	9.53200i	−0.754603	+	0.312567i
$931$			40.8167i			1.33771i
$932$	−5.28740	−	12.7649i	−0.173195	−	0.418129i
$933$	−14.2658	−	14.2658i	−0.467043	−	0.467043i
$934$	57.3583			1.87682
$935$		0			0
$936$	−12.9083			−0.421922
$937$	33.7663	+	33.7663i	1.10310	+	1.10310i	0.994035	+	0.109061i	$0.0347845\pi$
$937$	33.7663	+	33.7663i	1.10310	+	1.10310i	0.109061	+	0.994035i	$0.465215\pi$
$938$	3.36337	+	8.11988i	0.109818	+	0.265124i
$939$		−	12.7889i		−	0.417350i
$940$	21.0798	−	8.73156i	0.687549	−	0.284792i
$941$	18.7164	−	45.1854i	0.610137	−	1.47300i	−0.252712	−	0.967541i	$-0.581323\pi$
$941$	18.7164	−	45.1854i	0.610137	−	1.47300i	0.862850	−	0.505461i	$-0.168677\pi$
$942$	15.7906	+	6.54070i	0.514487	+	0.213108i
$943$	9.76985	−	9.76985i	0.318150	−	0.318150i
$944$	−1.28457	+	1.28457i	−0.0418091	+	0.0418091i
$945$	3.61082	+	1.49565i	0.117460	+	0.0486536i
$946$	−6.33021	+	15.2825i	−0.205813	+	0.496876i
$947$	24.5547	−	10.1709i	0.797920	−	0.330509i	0.0537969	−	0.998552i	$-0.482868\pi$
$947$	24.5547	−	10.1709i	0.797920	−	0.330509i	0.744123	+	0.668043i	$0.232868\pi$
$948$			48.2389i			1.56673i
$949$	0.498551	+	1.20361i	0.0161836	+	0.0390708i
$950$	−2.91288	−	2.91288i	−0.0945062	−	0.0945062i
$951$	30.2750			0.981735
$952$		0			0
$953$	−0.486122			−0.0157470			−0.00787352	−	0.999969i	$-0.502506\pi$
$953$	−0.486122			−0.0157470			−0.00787352	+	0.999969i	$0.502506\pi$
$954$	−4.43711	−	4.43711i	−0.143657	−	0.143657i
$955$	−9.96039	−	24.0465i	−0.322311	−	0.778127i
$956$		−	20.5139i		−	0.663466i
$957$	−35.7772	+	14.8194i	−1.15651	+	0.479043i
$958$	−11.1329	+	26.8772i	−0.359688	+	0.868363i
$959$	0.508169	+	0.210491i	0.0164096	+	0.00679710i
$960$	27.1882	−	27.1882i	0.877496	−	0.877496i
$961$	12.7279	−	12.7279i	0.410578	−	0.410578i
$962$	−4.25497	−	1.76247i	−0.137186	−	0.0568243i
$963$	−6.08785	+	14.6974i	−0.196178	+	0.473616i
$964$	29.0303	−	12.0248i	0.935004	−	0.387291i
$965$		−	47.5139i		−	1.52953i
$966$	0.800449	+	1.93245i	0.0257540	+	0.0621757i
$967$	1.36902	+	1.36902i	0.0440246	+	0.0440246i	0.728776	−	0.684752i	$-0.240089\pi$
$967$	1.36902	+	1.36902i	0.0440246	+	0.0440246i	−0.684752	+	0.728776i	$0.740089\pi$
$968$	−6.00000			−0.192847
$969$		0			0
$970$	57.8444			1.85727
$971$	−10.8011	−	10.8011i	−0.346623	−	0.346623i	0.512227	−	0.858850i	$-0.328821\pi$
$971$	−10.8011	−	10.8011i	−0.346623	−	0.346623i	−0.858850	+	0.512227i	$0.828821\pi$
$972$	−15.6656	−	37.8200i	−0.502473	−	1.21308i
$973$		−	5.90833i		−	0.189412i
$974$	25.7249	−	10.6556i	0.824278	−	0.341427i
$975$	0.498551	−	1.20361i	0.0159664	−	0.0385463i
$976$	−2.46627	−	1.02156i	−0.0789433	−	0.0326994i
$977$	−26.5459	+	26.5459i	−0.849280	+	0.849280i	−0.990043	−	0.140763i	$-0.955044\pi$
$977$	−26.5459	+	26.5459i	−0.849280	+	0.849280i	0.140763	+	0.990043i	$0.455044\pi$
$978$	37.3470	−	37.3470i	1.19423	−	1.19423i
$979$	−8.90002	−	3.68651i	−0.284446	−	0.117821i
$980$	20.1068	−	48.5421i	0.642289	−	1.55062i
$981$	17.1046	−	7.08495i	0.546108	−	0.226205i
$982$		−	50.9361i		−	1.62544i
$983$	12.8709	+	31.0731i	0.410518	+	0.991079i	0.984999	+	0.172561i	$0.0552041\pi$
$983$	12.8709	+	31.0731i	0.410518	+	0.991079i	−0.574481	+	0.818518i	$0.694796\pi$
$984$	16.5816	+	16.5816i	0.528603	+	0.528603i
$985$	15.9083			0.506881
$986$		0			0
$987$	1.18335			0.0376663
$988$	45.5730	+	45.5730i	1.44987	+	1.44987i
$989$	−2.11007	−	5.09416i	−0.0670963	−	0.161985i
$990$			20.7250i			0.658683i
$991$	28.4118	−	11.7686i	0.902531	−	0.373841i	0.117338	−	0.993092i	$-0.462564\pi$
$991$	28.4118	−	11.7686i	0.902531	−	0.373841i	0.785193	+	0.619251i	$0.212564\pi$
$992$	7.31669	−	17.6640i	0.232305	−	0.560834i
$993$	0.364423	+	0.150949i	0.0115646	+	0.00479022i
$994$	−1.58311	+	1.58311i	−0.0502133	+	0.0502133i
$995$	−5.87095	+	5.87095i	−0.186122	+	0.186122i
$996$	9.99329	+	4.13935i	0.316649	+	0.131160i
$997$	15.7357	−	37.9894i	0.498355	−	1.20314i	−0.452014	−	0.892011i	$-0.649294\pi$
$997$	15.7357	−	37.9894i	0.498355	−	1.20314i	0.950369	−	0.311125i	$-0.100706\pi$
$998$	−48.7372	+	20.1876i	−1.54275	+	0.639027i
$999$		−	3.39445i		−	0.107396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.d.e.134.3		16
17.2	even	8	inner	289.2.d.e.179.1		16
17.3	odd	16		289.2.b.c.288.3		4
17.4	even	4	inner	289.2.d.e.155.1		16
17.5	odd	16		289.2.a.b.1.1	✓	2
17.6	odd	16		289.2.c.b.251.3		8
17.7	odd	16		289.2.c.b.38.1		8
17.8	even	8	inner	289.2.d.e.110.3		16
17.9	even	8	inner	289.2.d.e.110.4		16
17.10	odd	16		289.2.c.b.38.2		8
17.11	odd	16		289.2.c.b.251.4		8
17.12	odd	16		289.2.a.c.1.1	yes	2
17.13	even	4	inner	289.2.d.e.155.2		16
17.14	odd	16		289.2.b.c.288.4		4
17.15	even	8	inner	289.2.d.e.179.2		16
17.16	even	2	inner	289.2.d.e.134.4		16
51.5	even	16		2601.2.a.s.1.2		2
51.29	even	16		2601.2.a.r.1.2		2
68.39	even	16		4624.2.a.v.1.1		2
68.63	even	16		4624.2.a.j.1.2		2
85.29	odd	16		7225.2.a.m.1.2		2
85.39	odd	16		7225.2.a.n.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.b.1.1	✓	2	17.5	odd	16
289.2.a.c.1.1	yes	2	17.12	odd	16
289.2.b.c.288.3		4	17.3	odd	16
289.2.b.c.288.4		4	17.14	odd	16
289.2.c.b.38.1		8	17.7	odd	16
289.2.c.b.38.2		8	17.10	odd	16
289.2.c.b.251.3		8	17.6	odd	16
289.2.c.b.251.4		8	17.11	odd	16
289.2.d.e.110.3		16	17.8	even	8	inner
289.2.d.e.110.4		16	17.9	even	8	inner
289.2.d.e.134.3		16	1.1	even	1	trivial
289.2.d.e.134.4		16	17.16	even	2	inner
289.2.d.e.155.1		16	17.4	even	4	inner
289.2.d.e.155.2		16	17.13	even	4	inner
289.2.d.e.179.1		16	17.2	even	8	inner
289.2.d.e.179.2		16	17.15	even	8	inner
2601.2.a.r.1.2		2	51.29	even	16
2601.2.a.s.1.2		2	51.5	even	16
4624.2.a.j.1.2		2	68.63	even	16
4624.2.a.v.1.1		2	68.39	even	16
7225.2.a.m.1.2		2	85.29	odd	16
7225.2.a.n.1.2		2	85.39	odd	16

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.d (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.62831 + 1.62831i) q^{2} +(-0.498551 - 1.20361i) q^{3} +3.30278i q^{4} +(2.12749 - 0.881234i) q^{5} +(1.14805 - 2.77164i) q^{6} +(-0.279728 - 0.115867i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(0.921201 - 0.921201i) q^{9} +O(q^{10})\)	\(q+(1.62831 + 1.62831i) q^{2} +(-0.498551 - 1.20361i) q^{3} +3.30278i q^{4} +(2.12749 - 0.881234i) q^{5} +(1.14805 - 2.77164i) q^{6} +(-0.279728 - 0.115867i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(0.921201 - 0.921201i) q^{9} +(4.89913 + 2.02928i) q^{10} +(-1.14805 + 2.77164i) q^{11} +(3.97525 - 1.64660i) q^{12} +3.30278i q^{13} +(-0.266816 - 0.644151i) q^{14} +(-2.12132 - 2.12132i) q^{15} -0.302776 q^{16} +3.00000 q^{18} +(-4.17782 - 4.17782i) q^{19} +(2.91052 + 7.02661i) q^{20} +0.394449i q^{21} +(-6.38246 + 2.64370i) q^{22} +(0.881234 - 2.12749i) q^{23} +(3.61082 + 1.49565i) q^{24} +(0.214095 - 0.214095i) q^{25} +(-5.37794 + 5.37794i) q^{26} +(-5.17885 - 2.14515i) q^{27} +(0.382683 - 0.923880i) q^{28} +(-9.15410 + 3.79175i) q^{29} -6.90833i q^{30} +(-1.37978 - 3.33110i) q^{31} +(3.74963 + 3.74963i) q^{32} +3.90833 q^{33} -0.697224 q^{35} +(3.04252 + 3.04252i) q^{36} +(0.231734 + 0.559456i) q^{37} -13.6056i q^{38} +(3.97525 - 1.64660i) q^{39} +(-2.64370 + 6.38246i) q^{40} +(5.54328 + 2.29610i) q^{41} +(-0.642284 + 0.642284i) q^{42} +(1.69313 - 1.69313i) q^{43} +(-9.15410 - 3.79175i) q^{44} +(1.14805 - 2.77164i) q^{45} +(4.89913 - 2.02928i) q^{46} -3.00000i q^{47} +(0.150949 + 0.364423i) q^{48} +(-4.88492 - 4.88492i) q^{49} +0.697224 q^{50} -10.9083 q^{52} +(-1.47904 - 1.47904i) q^{53} +(-4.93980 - 11.9257i) q^{54} +6.90833i q^{55} +(0.839185 - 0.347602i) q^{56} +(-2.94560 + 7.11131i) q^{57} +(-21.0798 - 8.73156i) q^{58} +(4.24264 - 4.24264i) q^{59} +(7.00625 - 7.00625i) q^{60} +(8.14553 + 3.37399i) q^{61} +(3.17733 - 7.67076i) q^{62} +(-0.364423 + 0.150949i) q^{63} +12.8167i q^{64} +(2.91052 + 7.02661i) q^{65} +(6.36396 + 6.36396i) q^{66} -12.6056 q^{67} -3.00000 q^{69} +(-1.13530 - 1.13530i) q^{70} +(-1.22884 - 2.96667i) q^{71} +3.90833i q^{72} +(0.364423 - 0.150949i) q^{73} +(-0.533632 + 1.28830i) q^{74} +(-0.364423 - 0.150949i) q^{75} +(13.7984 - 13.7984i) q^{76} +(0.642284 - 0.642284i) q^{77} +(9.15410 + 3.79175i) q^{78} +(-4.29030 + 10.3577i) q^{79} +(-0.644151 + 0.266816i) q^{80} +3.39445i q^{81} +(5.28740 + 12.7649i) q^{82} +(1.77758 + 1.77758i) q^{83} -1.30278 q^{84} +5.51388 q^{86} +(9.12757 + 9.12757i) q^{87} +(-3.44415 - 8.31492i) q^{88} +3.21110i q^{89} +(6.38246 - 2.64370i) q^{90} +(0.382683 - 0.923880i) q^{91} +(7.02661 + 2.91052i) q^{92} +(-3.32144 + 3.32144i) q^{93} +(4.88492 - 4.88492i) q^{94} +(-12.5699 - 5.20662i) q^{95} +(2.64370 - 6.38246i) q^{96} +(10.0780 - 4.17444i) q^{97} -15.9083i q^{98} +(1.49565 + 3.61082i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 24 q^{16} + 48 q^{18} - 24 q^{33} - 40 q^{35} + 40 q^{50} - 88 q^{52} - 144 q^{67} - 48 q^{69} + 8 q^{84} - 56 q^{86}+O(q^{100}) \) 16 * q + 24 * q^16 + 48 * q^18 - 24 * q^33 - 40 * q^35 + 40 * q^50 - 88 * q^52 - 144 * q^67 - 48 * q^69 + 8 * q^84 - 56 * q^86

Introduction

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Representations

Groups

Database

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