LMFDB - Embedded newform 1000.2.o.a.549.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1000,2,Mod(149,1000)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1000.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1000, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [112] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			549.21
Character	$\chi$	$=$	1000.549
Dual form			1000.2.o.a.949.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.950798 - 1.04689i) q^{2} +(-0.853735 - 2.62753i) q^{3} +(-0.191967 - 1.99077i) q^{4} +(-3.56247 - 1.60448i) q^{6} -2.67391i q^{7} +(-2.26664 - 1.69185i) q^{8} +(-3.74798 + 2.72307i) q^{9} +(0.305554 - 0.420559i) q^{11} +(-5.06690 + 2.20399i) q^{12} +(-4.26356 + 3.09766i) q^{13} +(-2.79930 - 2.54235i) q^{14} +(-3.92630 + 0.764324i) q^{16} +(6.80346 + 2.21058i) q^{17} +(-0.712813 + 6.51282i) q^{18} +(-3.74715 - 1.21752i) q^{19} +(-7.02577 + 2.28281i) q^{21} +(-0.149760 - 0.719749i) q^{22} +(2.11996 - 2.91788i) q^{23} +(-2.51026 + 7.40004i) q^{24} +(-0.810869 + 7.40873i) q^{26} +(3.64939 + 2.65144i) q^{27} +(-5.32313 + 0.513303i) q^{28} +(3.63988 - 1.18267i) q^{29} +(2.54168 - 7.82249i) q^{31} +(-2.93295 + 4.83713i) q^{32} +(-1.36589 - 0.443805i) q^{33} +(8.78295 - 5.02068i) q^{34} +(6.14048 + 6.93861i) q^{36} +(1.62286 - 1.17908i) q^{37} +(-4.83739 + 2.76524i) q^{38} +(11.7791 + 8.55804i) q^{39} +(-5.16753 + 3.75443i) q^{41} +(-4.29023 + 9.52572i) q^{42} -5.41659 q^{43} +(-0.895891 - 0.527553i) q^{44} +(-1.03905 - 4.99369i) q^{46} +(-0.748265 + 0.243126i) q^{47} +(5.36030 + 9.66392i) q^{48} -0.149804 q^{49} -19.7635i q^{51} +(6.98517 + 7.89310i) q^{52} +(-1.71792 - 5.28721i) q^{53} +(6.24561 - 1.29954i) q^{54} +(-4.52385 + 6.06079i) q^{56} +10.8852i q^{57} +(2.22267 - 4.93505i) q^{58} +(3.67423 + 5.05715i) q^{59} +(4.51387 - 6.21281i) q^{61} +(-5.77268 - 10.0985i) q^{62} +(7.28124 + 10.0218i) q^{63} +(2.27531 + 7.66961i) q^{64} +(-1.76330 + 1.00797i) q^{66} +(-1.98087 + 6.09648i) q^{67} +(3.09470 - 13.9685i) q^{68} +(-9.47669 - 3.07916i) q^{69} +(0.885245 + 2.72450i) q^{71} +(13.1023 + 0.168797i) q^{72} +(0.839035 - 1.15483i) q^{73} +(0.308646 - 2.82003i) q^{74} +(-1.70447 + 7.69341i) q^{76} +(-1.12454 - 0.817024i) q^{77} +(20.1589 - 4.19452i) q^{78} +(-2.10919 - 6.49143i) q^{79} +(-0.443692 + 1.36554i) q^{81} +(-0.982791 + 8.97955i) q^{82} +(-0.170500 + 0.524746i) q^{83} +(5.89326 + 13.5484i) q^{84} +(-5.15008 + 5.67058i) q^{86} +(-6.21499 - 8.55421i) q^{87} +(-1.40410 + 0.436305i) q^{88} +(-11.0001 - 7.99206i) q^{89} +(8.28286 + 11.4004i) q^{91} +(-6.21578 - 3.66021i) q^{92} -22.7237 q^{93} +(-0.456922 + 1.01452i) q^{94} +(15.2136 + 3.57678i) q^{96} +(-4.85400 + 1.57716i) q^{97} +(-0.142433 + 0.156829i) q^{98} +2.40829i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36}+ \cdots - 90 q^{98}+O(q^{100}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.950798	−	1.04689i	0.672316	−	0.740265i
$2$	0.950798	−	1.04689i	0.672316	−	0.740265i
$3$	−0.853735	−	2.62753i	−0.492904	−	1.51700i	−0.820198	−	0.572080i	$-0.806137\pi$
$3$	−0.853735	−	2.62753i	−0.492904	−	1.51700i	0.327293	−	0.944923i	$-0.393863\pi$
$4$	−0.191967	−	1.99077i	−0.0959836	−	0.995383i
$5$		0			0
$5$		0			0
$6$	−3.56247	−	1.60448i	−1.45437	−	0.655025i
$7$		−	2.67391i		−	1.01064i	−0.862931	−	0.505322i	$-0.831374\pi$
$7$		−	2.67391i		−	1.01064i	0.862931	−	0.505322i	$-0.168626\pi$
$8$	−2.26664	−	1.69185i	−0.801378	−	0.598158i
$9$	−3.74798	+	2.72307i	−1.24933	+	0.907689i
$10$		0			0
$11$	0.305554	−	0.420559i	0.0921280	−	0.126803i	−0.760465	−	0.649379i	$-0.775029\pi$
$11$	0.305554	−	0.420559i	0.0921280	−	0.126803i	0.852593	+	0.522576i	$0.175029\pi$
$12$	−5.06690	+	2.20399i	−1.46269	+	0.636236i
$13$	−4.26356	+	3.09766i	−1.18250	+	0.859136i	−0.992451	−	0.122639i	$-0.960864\pi$
$13$	−4.26356	+	3.09766i	−1.18250	+	0.859136i	−0.190047	+	0.981775i	$0.560864\pi$
$14$	−2.79930	−	2.54235i	−0.748144	−	0.679471i
$15$		0			0
$16$	−3.92630	+	0.764324i	−0.981574	+	0.191081i
$17$	6.80346	+	2.21058i	1.65008	+	0.536144i	0.978758	−	0.205020i	$-0.0657259\pi$
$17$	6.80346	+	2.21058i	1.65008	+	0.536144i	0.671324	+	0.741164i	$0.265726\pi$
$18$	−0.712813	+	6.51282i	−0.168012	+	1.53509i
$19$	−3.74715	−	1.21752i	−0.859654	−	0.279319i	−0.154170	−	0.988044i	$-0.549270\pi$
$19$	−3.74715	−	1.21752i	−0.859654	−	0.279319i	−0.705484	+	0.708726i	$0.749270\pi$
$20$		0			0
$21$	−7.02577	+	2.28281i	−1.53315	+	0.498151i
$22$	−0.149760	−	0.719749i	−0.0319289	−	0.153451i
$23$	2.11996	−	2.91788i	0.442043	−	0.608420i	−0.528622	−	0.848858i	$-0.677291\pi$
$23$	2.11996	−	2.91788i	0.442043	−	0.608420i	0.970665	+	0.240438i	$0.0772910\pi$
$24$	−2.51026	+	7.40004i	−0.512405	+	1.51053i
$25$		0			0
$26$	−0.810869	+	7.40873i	−0.159025	+	1.45297i
$27$	3.64939	+	2.65144i	0.702326	+	0.510270i
$28$	−5.32313	+	0.513303i	−1.00598	+	0.0970052i
$29$	3.63988	−	1.18267i	0.675910	−	0.219616i	0.0491059	−	0.998794i	$-0.484363\pi$
$29$	3.63988	−	1.18267i	0.675910	−	0.219616i	0.626804	+	0.779177i	$0.284363\pi$
$30$		0			0
$31$	2.54168	−	7.82249i	0.456499	−	1.40496i	−0.412867	−	0.910791i	$-0.635473\pi$
$31$	2.54168	−	7.82249i	0.456499	−	1.40496i	0.869366	−	0.494168i	$-0.164527\pi$
$32$	−2.93295	+	4.83713i	−0.518477	+	0.855091i
$33$	−1.36589	−	0.443805i	−0.237771	−	0.0772566i
$34$	8.78295	−	5.02068i	1.50626	−	0.861039i
$35$		0			0
$36$	6.14048	+	6.93861i	1.02341	+	1.15644i
$37$	1.62286	−	1.17908i	0.266797	−	0.193839i	−0.446341	−	0.894863i	$-0.647273\pi$
$37$	1.62286	−	1.17908i	0.266797	−	0.193839i	0.713138	+	0.701024i	$0.247273\pi$
$38$	−4.83739	+	2.76524i	−0.784729	+	0.448581i
$39$	11.7791	+	8.55804i	1.88617	+	1.37038i
$40$		0			0
$41$	−5.16753	+	3.75443i	−0.807032	+	0.586343i	−0.912969	−	0.408030i	$-0.866216\pi$
$41$	−5.16753	+	3.75443i	−0.807032	+	0.586343i	0.105936	+	0.994373i	$0.466216\pi$
$42$	−4.29023	+	9.52572i	−0.661997	+	1.46985i
$43$	−5.41659			−0.826022			−0.413011	−	0.910726i	$-0.635523\pi$
$43$	−5.41659			−0.826022			−0.413011	+	0.910726i	$0.635523\pi$
$44$	−0.895891	−	0.527553i	−0.135061	−	0.0795316i
$45$		0			0
$46$	−1.03905	−	4.99369i	−0.153199	−	0.736279i
$47$	−0.748265	+	0.243126i	−0.109146	+	0.0354636i	−0.363081	−	0.931758i	$-0.618275\pi$
$47$	−0.748265	+	0.243126i	−0.109146	+	0.0354636i	0.253935	+	0.967221i	$0.418275\pi$
$48$	5.36030	+	9.66392i	0.773692	+	1.39487i
$49$	−0.149804			−0.0214006
$50$		0			0
$51$		−	19.7635i		−	2.76745i
$52$	6.98517	+	7.89310i	0.968669	+	1.09458i
$53$	−1.71792	−	5.28721i	−0.235974	−	0.726254i	−0.996991	−	0.0775214i	$-0.975299\pi$
$53$	−1.71792	−	5.28721i	−0.235974	−	0.726254i	0.761016	−	0.648733i	$-0.224701\pi$
$54$	6.24561	−	1.29954i	0.849919	−	0.176845i
$55$		0			0
$56$	−4.52385	+	6.06079i	−0.604525	+	0.809908i
$57$			10.8852i			1.44178i
$58$	2.22267	−	4.93505i	0.291850	−	0.648003i
$59$	3.67423	+	5.05715i	0.478344	+	0.658385i	0.978186	−	0.207732i	$-0.0666083\pi$
$59$	3.67423	+	5.05715i	0.478344	+	0.658385i	−0.499841	+	0.866117i	$0.666608\pi$
$60$		0			0
$61$	4.51387	−	6.21281i	0.577941	−	0.795468i	−0.415526	−	0.909581i	$-0.636403\pi$
$61$	4.51387	−	6.21281i	0.577941	−	0.795468i	0.993468	+	0.114113i	$0.0364026\pi$
$62$	−5.77268	−	10.0985i	−0.733131	−	1.28251i
$63$	7.28124	+	10.0218i	0.917350	+	1.26262i
$64$	2.27531	+	7.66961i	0.284414	+	0.958702i
$65$		0			0
$66$	−1.76330	+	1.00797i	−0.217048	+	0.124073i
$67$	−1.98087	+	6.09648i	−0.242001	+	0.744804i	0.754114	+	0.656744i	$0.228067\pi$
$67$	−1.98087	+	6.09648i	−0.242001	+	0.744804i	−0.996115	+	0.0880600i	$0.971933\pi$
$68$	3.09470	−	13.9685i	0.375288	−	1.69392i
$69$	−9.47669	−	3.07916i	−1.14086	−	0.370688i
$70$		0			0
$71$	0.885245	+	2.72450i	0.105059	+	0.323339i	0.989744	−	0.142850i	$-0.0456266\pi$
$71$	0.885245	+	2.72450i	0.105059	+	0.323339i	−0.884685	+	0.466189i	$0.845627\pi$
$72$	13.1023	+	0.168797i	1.54413	+	0.0198929i
$73$	0.839035	−	1.15483i	0.0982017	−	0.135163i	−0.757089	−	0.653312i	$-0.773379\pi$
$73$	0.839035	−	1.15483i	0.0982017	−	0.135163i	0.855290	+	0.518149i	$0.173379\pi$
$74$	0.308646	−	2.82003i	0.0358793	−	0.327822i
$75$		0			0
$76$	−1.70447	+	7.69341i	−0.195516	+	0.882495i
$77$	−1.12454	−	0.817024i	−0.128153	−	0.0931086i
$78$	20.1589	−	4.19452i	2.28255	−	0.474935i
$79$	−2.10919	−	6.49143i	−0.237303	−	0.730342i	−0.996808	−	0.0798409i	$-0.974559\pi$
$79$	−2.10919	−	6.49143i	−0.237303	−	0.730342i	0.759505	−	0.650501i	$-0.225441\pi$
$80$		0			0
$81$	−0.443692	+	1.36554i	−0.0492991	+	0.151727i
$82$	−0.982791	+	8.97955i	−0.108531	+	0.991625i
$83$	−0.170500	+	0.524746i	−0.0187148	+	0.0575984i	−0.959978	−	0.280076i	$-0.909640\pi$
$83$	−0.170500	+	0.524746i	−0.0187148	+	0.0575984i	0.941263	+	0.337674i	$0.109640\pi$
$84$	5.89326	+	13.5484i	0.643008	+	1.47826i
$85$		0			0
$86$	−5.15008	+	5.67058i	−0.555347	+	0.611475i
$87$	−6.21499	−	8.55421i	−0.666317	−	0.917107i
$88$	−1.40410	+	0.436305i	−0.149678	+	0.0465103i
$89$	−11.0001	−	7.99206i	−1.16601	−	0.847156i	−0.175485	−	0.984482i	$-0.556149\pi$
$89$	−11.0001	−	7.99206i	−1.16601	−	0.847156i	−0.990526	+	0.137326i	$0.956149\pi$
$90$		0			0
$91$	8.28286	+	11.4004i	0.868280	+	1.19508i
$92$	−6.21578	−	3.66021i	−0.648040	−	0.381604i
$93$	−22.7237			−2.35634
$94$	−0.456922	+	1.01452i	−0.0471279	+	0.104639i
$95$		0			0
$96$	15.2136	+	3.57678i	1.55274	+	0.365053i
$97$	−4.85400	+	1.57716i	−0.492849	+	0.160136i	−0.544888	−	0.838509i	$-0.683428\pi$
$97$	−4.85400	+	1.57716i	−0.492849	+	0.160136i	0.0520390	+	0.998645i	$0.483428\pi$
$98$	−0.142433	+	0.156829i	−0.0143879	+	0.0158421i
$99$			2.40829i			0.242042i
$100$		0			0
$101$		−	1.77393i		−	0.176513i	−0.996098	−	0.0882565i	$-0.971870\pi$
$101$		−	1.77393i		−	0.176513i	0.996098	−	0.0882565i	$-0.0281295\pi$
$102$	−20.6903	−	18.7911i	−2.04864	−	1.86060i
$103$	0.666003	−	0.216398i	0.0656233	−	0.0213223i	−0.276021	−	0.961151i	$-0.589016\pi$
$103$	0.666003	−	0.216398i	0.0656233	−	0.0213223i	0.341645	+	0.939829i	$0.389016\pi$
$104$	14.9047	+	0.192017i	1.46153	+	0.0188288i
$105$		0			0
$106$	−7.16853	−	3.22859i	−0.696269	−	0.313588i
$107$	20.2036			1.95315			0.976576	−	0.215171i	$-0.0690310\pi$
$107$	20.2036			1.95315			0.976576	+	0.215171i	$0.0690310\pi$
$108$	4.57783	−	7.77408i	0.440502	−	0.748061i
$109$	−3.68500	−	5.07197i	−0.352959	−	0.485807i	0.595211	−	0.803569i	$-0.297068\pi$
$109$	−3.68500	−	5.07197i	−0.352959	−	0.485807i	−0.948170	+	0.317763i	$0.897068\pi$
$110$		0			0
$111$	−4.48355	−	3.25749i	−0.425560	−	0.309188i
$112$	2.04373	+	10.4986i	0.193115	+	0.992022i
$113$	2.03808	+	2.80517i	0.191726	+	0.263888i	0.894048	−	0.447971i	$-0.147853\pi$
$113$	2.03808	+	2.80517i	0.191726	+	0.263888i	−0.702322	+	0.711859i	$0.747853\pi$
$114$	11.3956	+	10.3496i	1.06730	+	0.969328i
$115$		0			0
$116$	−3.05316	−	7.01912i	−0.283479	−	0.651709i
$117$	7.54461	−	23.2199i	0.697499	−	2.14668i
$118$	8.78774	+	0.961798i	0.808977	+	0.0885407i
$119$	5.91089	−	18.1919i	0.541851	−	1.66764i
$120$		0			0
$121$	3.31568	+	10.2046i	0.301425	+	0.927692i
$122$	−2.21236	−	10.6327i	−0.200298	−	0.962635i
$123$	14.2766	+	10.3725i	1.28727	+	0.935260i
$124$	−16.0607	−	3.55823i	−1.44229	−	0.319538i
$125$		0			0
$126$	17.4147	+	1.90600i	1.55143	+	0.169800i
$127$	1.99694	−	2.74856i	0.177200	−	0.243895i	−0.711173	−	0.703017i	$-0.751836\pi$
$127$	1.99694	−	2.74856i	0.177200	−	0.243895i	0.888373	+	0.459122i	$0.151836\pi$
$128$	10.1926	+	4.91025i	0.900909	+	0.434009i
$129$	4.62433	+	14.2322i	0.407150	+	1.25308i
$130$		0			0
$131$	−6.90619	−	2.24396i	−0.603397	−	0.196055i	−0.00864194	−	0.999963i	$-0.502751\pi$
$131$	−6.90619	−	2.24396i	−0.603397	−	0.196055i	−0.594755	+	0.803907i	$0.702751\pi$
$132$	−0.621306	+	2.80437i	−0.0540777	+	0.244089i
$133$	−3.25555	+	10.0195i	−0.282292	+	0.868804i
$134$	4.49896	+	7.87028i	0.388651	+	0.679888i
$135$		0			0
$136$	−11.6810	−	16.5210i	−1.00164	−	1.41666i
$137$	−10.8418	−	14.9224i	−0.926276	−	1.27491i	−0.961295	−	0.275522i	$-0.911149\pi$
$137$	−10.8418	−	14.9224i	−0.926276	−	1.27491i	0.0350190	−	0.999387i	$-0.488851\pi$
$138$	−12.2340	+	6.99341i	−1.04142	+	0.595319i
$139$	−5.88707	+	8.10286i	−0.499335	+	0.687275i	−0.982076	−	0.188488i	$-0.939641\pi$
$139$	−5.88707	+	8.10286i	−0.499335	+	0.687275i	0.482741	+	0.875763i	$0.339641\pi$
$140$		0			0
$141$	1.27764	+	1.75852i	0.107597	+	0.148094i
$142$	3.69395	+	1.66370i	0.309990	+	0.139614i
$143$			2.73958i			0.229095i
$144$	12.6344	−	13.5562i	1.05287	−	1.12969i
$145$		0			0
$146$	−0.411233	−	1.97639i	−0.0340339	−	0.163567i
$147$	0.127893	+	0.393614i	0.0105484	+	0.0324647i
$148$	−2.65881	−	3.00439i	−0.218552	−	0.246960i
$149$		−	22.4904i		−	1.84249i	−0.388984	−	0.921245i	$-0.627174\pi$
$149$		−	22.4904i		−	1.84249i	0.388984	−	0.921245i	$-0.372826\pi$
$150$		0			0
$151$	−13.2680			−1.07974			−0.539869	−	0.841749i	$-0.681526\pi$
$151$	−13.2680			−1.07974			−0.539869	+	0.841749i	$0.681526\pi$
$152$	6.43357	+	9.09928i	0.521831	+	0.738049i
$153$	−31.5188	+	10.2411i	−2.54814	+	0.827942i
$154$	−1.92454	+	0.400445i	−0.155084	+	0.0322688i
$155$		0			0
$156$	14.7758	−	25.0923i	1.18301	−	2.00900i
$157$	−6.77950			−0.541063			−0.270531	−	0.962711i	$-0.587199\pi$
$157$	−6.77950			−0.541063			−0.270531	+	0.962711i	$0.587199\pi$
$158$	−8.80124	−	3.96394i	−0.700189	−	0.315354i
$159$	−12.4256	+	9.02775i	−0.985417	+	0.715947i
$160$		0			0
$161$	−7.80215	−	5.66859i	−0.614896	−	0.446748i
$162$	1.00772	+	1.76285i	0.0791736	+	0.138503i
$163$	11.6472	−	8.46217i	0.912277	−	0.662808i	−0.0293124	−	0.999570i	$-0.509332\pi$
$163$	11.6472	−	8.46217i	0.912277	−	0.662808i	0.941590	+	0.336762i	$0.109332\pi$
$164$	8.46619	+	9.56661i	0.661098	+	0.747027i
$165$		0			0
$166$	0.387241	+	0.677423i	0.0300558	+	0.0525782i
$167$	−3.69785	−	1.20150i	−0.286148	−	0.0929752i	0.162426	−	0.986721i	$-0.448068\pi$
$167$	−3.69785	−	1.20150i	−0.286148	−	0.0929752i	−0.448574	+	0.893746i	$0.648068\pi$
$168$	19.7871	+	6.71222i	1.52661	+	0.517859i
$169$	4.56524	−	14.0504i	0.351172	−	1.08080i
$170$		0			0
$171$	17.3596	−	5.64048i	1.32752	−	0.431339i
$172$	1.03981	+	10.7832i	0.0792846	+	0.822208i
$173$	1.77044	+	1.28630i	0.134604	+	0.0977957i	0.653050	−	0.757315i	$-0.273489\pi$
$173$	1.77044	+	1.28630i	0.134604	+	0.0977957i	−0.518446	+	0.855111i	$0.673489\pi$
$174$	−14.8645	−	1.62689i	−1.12688	−	0.123334i
$175$		0			0
$176$	−0.878253	+	1.88478i	−0.0662008	+	0.142071i
$177$	10.1510	−	13.9716i	0.762994	−	1.05017i
$178$	−18.8257	+	3.91712i	−1.41105	+	0.293600i
$179$	−8.52431	+	2.76971i	−0.637137	+	0.207018i	−0.609734	−	0.792606i	$-0.708724\pi$
$179$	−8.52431	+	2.76971i	−0.637137	+	0.207018i	−0.0274027	+	0.999624i	$0.508724\pi$
$180$		0			0
$181$	20.6836	+	6.72051i	1.53740	+	0.499531i	0.950657	−	0.310243i	$-0.100410\pi$
$181$	20.6836	+	6.72051i	1.53740	+	0.499531i	0.586742	+	0.809774i	$0.300410\pi$
$182$	19.8103	+	2.16819i	1.46844	+	0.160717i
$183$	−20.1780	−	6.55622i	−1.49160	−	0.484649i
$184$	−9.74180	+	3.02713i	−0.718175	+	0.223163i
$185$		0			0
$186$	−21.6057	+	23.7893i	−1.58420	+	1.74431i
$187$	3.00850	−	2.18581i	0.220004	−	0.159842i
$188$	0.627649	+	1.44295i	0.0457760	+	0.105238i
$189$	7.08972	−	9.75816i	0.515701	−	0.709801i
$190$		0			0
$191$	1.35201	−	0.982290i	0.0978277	−	0.0710760i	−0.537796	−	0.843075i	$-0.680743\pi$
$191$	1.35201	−	0.982290i	0.0978277	−	0.0710760i	0.635624	+	0.771999i	$0.280743\pi$
$192$	18.2096	−	12.5263i	1.31416	−	0.904005i
$193$		−	8.56535i		−	0.616548i	−0.951298	−	0.308274i	$-0.900249\pi$
$193$		−	8.56535i		−	0.616548i	0.951298	−	0.308274i	$-0.0997513\pi$
$194$	−2.96406	+	6.58118i	−0.212807	+	0.472501i
$195$		0			0
$196$	0.0287574	+	0.298225i	0.00205410	+	0.0213018i
$197$	−3.12786	−	9.62655i	−0.222851	−	0.685864i	−0.998503	−	0.0547029i	$-0.982579\pi$
$197$	−3.12786	−	9.62655i	−0.222851	−	0.685864i	0.775652	−	0.631161i	$-0.217421\pi$
$198$	2.52122	+	2.28980i	0.179175	+	0.162729i
$199$	−17.2203			−1.22071			−0.610356	−	0.792127i	$-0.708974\pi$
$199$	−17.2203			−1.22071			−0.610356	+	0.792127i	$0.708974\pi$
$200$		0			0
$201$	17.7098			1.24915
$202$	−1.85712	−	1.68665i	−0.130666	−	0.118672i
$203$	−3.16236	−	9.73273i	−0.221954	−	0.683104i
$204$	−39.3445	+	3.79395i	−2.75467	+	0.265630i
$205$		0			0
$206$	0.406690	−	0.902984i	0.0283354	−	0.0629139i
$207$			16.7090i			1.16135i
$208$	14.3724	−	15.4211i	0.996546	−	1.06926i
$209$	−1.65700	+	1.20388i	−0.114617	+	0.0832739i
$210$		0			0
$211$	10.5323	−	14.4965i	0.725075	−	0.997980i	−0.274265	−	0.961654i	$-0.588435\pi$
$211$	10.5323	−	14.4965i	0.725075	−	0.997980i	0.999340	−	0.0363260i	$-0.0115655\pi$
$212$	−10.1958	+	4.43494i	−0.700251	+	0.304593i
$213$	6.40294	−	4.65201i	0.438722	−	0.318751i
$214$	19.2095	−	21.1510i	1.31313	−	1.44585i
$215$		0			0
$216$	−3.78603	−	12.1841i	−0.257607	−	0.829021i
$217$	−20.9166	−	6.79623i	−1.41991	−	0.461358i
$218$	−8.81350	−	0.964618i	−0.596926	−	0.0653322i
$219$	−3.75067	−	1.21867i	−0.253447	−	0.0823498i
$220$		0			0
$221$	−35.8546	+	11.6499i	−2.41184	+	0.783654i
$222$	−7.67320	+	1.59658i	−0.514991	+	0.107156i
$223$	3.76665	−	5.18435i	0.252233	−	0.347170i	−0.664058	−	0.747681i	$-0.731167\pi$
$223$	3.76665	−	5.18435i	0.252233	−	0.347170i	0.916292	+	0.400511i	$0.131167\pi$
$224$	12.9341	+	7.84245i	0.864193	+	0.523996i
$225$		0			0
$226$	4.87451	+	0.533504i	0.324248	+	0.0354882i
$227$	−21.6339	−	15.7179i	−1.43589	−	1.04324i	−0.988881	−	0.148706i	$-0.952489\pi$
$227$	−21.6339	−	15.7179i	−1.43589	−	1.04324i	−0.447009	−	0.894529i	$-0.647511\pi$
$228$	21.6698	−	2.08960i	1.43512	−	0.138387i
$229$	−1.64026	+	0.532952i	−0.108391	+	0.0352185i	−0.362711	−	0.931902i	$-0.618149\pi$
$229$	−1.64026	+	0.532952i	−0.108391	+	0.0352185i	0.254319	+	0.967120i	$0.418149\pi$
$230$		0			0
$231$	−1.18670	+	3.65228i	−0.0780789	+	0.240302i
$232$	−10.2512	−	3.47744i	−0.673024	−	0.228305i
$233$	25.2733	+	8.21180i	1.65571	+	0.537973i	0.979966	−	0.199164i	$-0.0638228\pi$
$233$	25.2733	+	8.21180i	1.65571	+	0.537973i	0.675743	+	0.737137i	$0.263823\pi$
$234$	−17.1354	−	29.9758i	−1.12017	−	1.95958i
$235$		0			0
$236$	9.36226	−	8.28534i	0.609432	−	0.539330i
$237$	−15.2557	+	11.0839i	−0.990964	+	0.719978i
$238$	−13.4249	−	23.4848i	−0.870204	−	1.52230i
$239$	−10.8304	−	7.86871i	−0.700557	−	0.508985i	0.179556	−	0.983748i	$-0.442534\pi$
$239$	−10.8304	−	7.86871i	−0.700557	−	0.508985i	−0.880114	+	0.474763i	$0.842534\pi$
$240$		0			0
$241$	9.29368	−	6.75225i	0.598658	−	0.434951i	−0.246744	−	0.969081i	$-0.579361\pi$
$241$	9.29368	−	6.75225i	0.598658	−	0.434951i	0.845402	+	0.534130i	$0.179361\pi$
$242$	13.8357	+	6.23136i	0.889391	+	0.400567i
$243$	17.4995			1.12259
$244$	−13.2348	−	7.79340i	−0.847268	−	0.498921i
$245$		0			0
$246$	24.4330	−	5.08385i	1.55779	−	0.324134i
$247$	19.7476	−	6.41640i	1.25651	−	0.408266i
$248$	−18.9955	+	13.4306i	−1.20622	+	0.852845i
$249$	1.52435			0.0966015
$250$		0			0
$251$		−	10.3951i		−	0.656130i	−0.944655	−	0.328065i	$-0.893603\pi$
$251$		−	10.3951i		−	0.656130i	0.944655	−	0.328065i	$-0.106397\pi$
$252$	18.5532	−	16.4191i	1.16874	−	1.03431i
$253$	−0.579377	−	1.78314i	−0.0364251	−	0.112105i
$254$	−0.978753	−	4.70390i	−0.0614124	−	0.295149i
$255$		0			0
$256$	14.8316	−	6.00192i	0.926976	−	0.375120i
$257$			5.90778i			0.368517i	0.982878	+	0.184258i	$0.0589884\pi$
$257$			5.90778i			0.368517i	−0.982878	+	0.184258i	$0.941012\pi$
$258$	19.2964	+	8.69079i	1.20134	+	0.541065i
$259$	−3.15275	−	4.33939i	−0.195902	−	0.269637i
$260$		0			0
$261$	−10.4217	+	14.3443i	−0.645089	+	0.887889i
$262$	−8.91557	+	5.09649i	−0.550806	+	0.314862i
$263$	−3.28152	−	4.51662i	−0.202347	−	0.278507i	0.695769	−	0.718266i	$-0.255064\pi$
$263$	−3.28152	−	4.51662i	−0.202347	−	0.278507i	−0.898116	+	0.439759i	$0.855064\pi$
$264$	2.34513	+	3.31683i	0.144333	+	0.204137i
$265$		0			0
$266$	7.39401	+	12.9348i	0.453356	+	0.793081i
$267$	−11.6082	+	35.7262i	−0.710407	+	2.18641i
$268$	12.5169	+	2.77312i	0.764593	+	0.169395i
$269$	2.00902	+	0.652770i	0.122492	+	0.0398001i	0.369622	−	0.929182i	$-0.379487\pi$
$269$	2.00902	+	0.652770i	0.122492	+	0.0398001i	−0.247130	+	0.968982i	$0.579487\pi$
$270$		0			0
$271$	5.94944	+	18.3105i	0.361403	+	1.11228i	0.952203	+	0.305466i	$0.0988121\pi$
$271$	5.94944	+	18.3105i	0.361403	+	1.11228i	−0.590800	+	0.806818i	$0.701188\pi$
$272$	−28.4020	−	3.47934i	−1.72212	−	0.210966i
$273$	22.8834	−	31.4963i	1.38497	−	1.90625i
$274$	−25.9305	−	2.83804i	−1.56652	−	0.171452i
$275$		0			0
$276$	−4.31068	+	19.4570i	−0.259472	+	1.17117i
$277$	16.0691	+	11.6749i	0.965498	+	0.701476i	0.954421	−	0.298463i	$-0.0964739\pi$
$277$	16.0691	+	11.6749i	0.965498	+	0.701476i	0.0110772	+	0.999939i	$0.496474\pi$
$278$	2.88541	+	13.8673i	0.173055	+	0.831706i
$279$	11.7750	+	36.2397i	0.704950	+	2.16961i
$280$		0			0
$281$	−3.83866	+	11.8142i	−0.228995	+	0.704775i	0.768866	+	0.639410i	$0.220821\pi$
$281$	−3.83866	+	11.8142i	−0.228995	+	0.704775i	−0.997861	+	0.0653651i	$0.979179\pi$
$282$	3.05576	+	0.334446i	0.181968	+	0.0199160i
$283$	0.0965181	−	0.297052i	0.00573740	−	0.0176579i	−0.948147	−	0.317833i	$-0.897045\pi$
$283$	0.0965181	−	0.297052i	0.00573740	−	0.0176579i	0.953884	+	0.300175i	$0.0970450\pi$
$284$	5.25391	−	2.28533i	0.311762	−	0.135609i
$285$		0			0
$286$	2.86805	+	2.60479i	0.169591	+	0.154024i
$287$	10.0390	+	13.8175i	0.592584	+	0.815622i
$288$	−2.17918	−	26.1161i	−0.128410	−	1.53891i
$289$	27.6471	+	20.0868i	1.62630	+	1.18158i
$290$		0			0
$291$	8.28807	+	11.4075i	0.485855	+	0.668722i
$292$	−2.46007	−	1.44863i	−0.143965	−	0.0847748i
$293$	10.1550			0.593262			0.296631	−	0.954992i	$-0.404137\pi$
$293$	10.1550			0.593262			0.296631	+	0.954992i	$0.404137\pi$
$294$	0.533672	+	0.240357i	0.0311244	+	0.0140179i
$295$		0			0
$296$	−5.67326	−	0.0730883i	−0.329752	−	0.00424817i
$297$	2.23017	−	0.724627i	0.129408	−	0.0420471i
$298$	−23.5451	−	21.3839i	−1.36393	−	1.23873i
$299$			19.0075i			1.09923i
$300$		0			0
$301$			14.4835i			0.834814i
$302$	−12.6152	+	13.8902i	−0.725925	+	0.799292i
$303$	−4.66106	+	1.51447i	−0.267771	+	0.0870040i
$304$	15.6430	+	1.91632i	0.897187	+	0.109908i
$305$		0			0
$306$	−19.2467	+	42.7340i	−1.10026	+	2.44294i
$307$	30.2858			1.72850			0.864250	−	0.503062i	$-0.167793\pi$
$307$	30.2858			1.72850			0.864250	+	0.503062i	$0.167793\pi$
$308$	−1.41063	+	2.39553i	−0.0803781	+	0.136498i
$309$	−1.13718	−	1.56520i	−0.0646920	−	0.0890408i
$310$		0			0
$311$	20.4723	+	14.8740i	1.16088	+	0.843426i	0.989889	−	0.141847i	$-0.0453041\pi$
$311$	20.4723	+	14.8740i	1.16088	+	0.843426i	0.170988	+	0.985273i	$0.445304\pi$
$312$	−12.2201	−	39.3265i	−0.691830	−	2.22642i
$313$	15.0000	+	20.6458i	0.847852	+	1.16697i	0.984332	+	0.176325i	$0.0564211\pi$
$313$	15.0000	+	20.6458i	0.847852	+	1.16697i	−0.136480	+	0.990643i	$0.543579\pi$
$314$	−6.44593	+	7.09741i	−0.363765	+	0.400530i
$315$		0			0
$316$	−12.5180	+	5.44505i	−0.704193	+	0.306308i
$317$	8.30209	−	25.5512i	0.466292	−	1.43510i	−0.391059	−	0.920366i	$-0.627891\pi$
$317$	8.30209	−	25.5512i	0.466292	−	1.43510i	0.857351	−	0.514733i	$-0.172109\pi$
$318$	−2.36318	+	21.5919i	−0.132521	+	1.21081i
$319$	0.614799	−	1.89216i	0.0344221	−	0.105940i
$320$		0			0
$321$	−17.2485	−	53.0854i	−0.962717	−	2.96294i
$322$	−13.3527	+	2.77832i	−0.744115	+	0.154830i
$323$	−22.8021	−	16.5667i	−1.26874	−	0.921797i
$324$	2.80365	+	0.621147i	0.155758	+	0.0345082i
$325$		0			0
$326$	2.21513	−	20.2392i	0.122685	−	1.12094i
$327$	−10.1807	+	14.0126i	−0.562995	+	0.774897i
$328$	18.0648	+	0.232728i	0.997464	+	0.0128503i
$329$	0.650098	+	2.00079i	0.0358410	+	0.110307i
$330$		0			0
$331$	11.4630	+	3.72455i	0.630063	+	0.204720i	0.606603	−	0.795005i	$-0.292532\pi$
$331$	11.4630	+	3.72455i	0.630063	+	0.204720i	0.0234603	+	0.999725i	$0.492532\pi$
$332$	1.07738	+	0.238692i	0.0591288	+	0.0130999i
$333$	−2.87175	+	8.83833i	−0.157371	+	0.484337i
$334$	−4.77375	+	2.72886i	−0.261208	+	0.149317i
$335$		0			0
$336$	25.8405	−	14.3330i	1.40971	−	0.781927i
$337$	8.18324	+	11.2633i	0.445769	+	0.613549i	0.971482	−	0.237113i	$-0.0762013\pi$
$337$	8.18324	+	11.2633i	0.445769	+	0.613549i	−0.525713	+	0.850662i	$0.676201\pi$
$338$	−10.3686	−	18.1384i	−0.563977	−	0.986597i
$339$	5.63068	−	7.74997i	0.305817	−	0.420921i
$340$		0			0
$341$	−2.51320	−	3.45912i	−0.136097	−	0.187322i
$342$	10.6005	−	23.5366i	0.573210	−	1.27271i
$343$		−	18.3168i		−	0.989015i
$344$	12.2775	+	9.16404i	0.661956	+	0.494092i
$345$		0			0
$346$	3.02995	−	0.630450i	0.162891	−	0.0338932i
$347$	4.69862	+	14.4609i	0.252235	+	0.776300i	0.994362	+	0.106041i	$0.0338173\pi$
$347$	4.69862	+	14.4609i	0.252235	+	0.776300i	−0.742127	+	0.670260i	$0.766183\pi$
$348$	−15.8363	+	14.0147i	−0.848917	+	0.751268i
$349$			23.4212i			1.25371i	0.779136	+	0.626854i	$0.215658\pi$
$349$			23.4212i			1.25371i	−0.779136	+	0.626854i	$0.784342\pi$
$350$		0			0
$351$	−23.7727			−1.26889
$352$	1.13812	+	2.71148i	0.0606622	+	0.144522i
$353$	4.26001	−	1.38416i	0.226738	−	0.0736715i	−0.193445	−	0.981111i	$-0.561966\pi$
$353$	4.26001	−	1.38416i	0.226738	−	0.0736715i	0.420182	+	0.907440i	$0.361966\pi$
$354$	−4.97525	−	23.9111i	−0.264432	−	1.27086i
$355$		0			0
$356$	−13.7987	+	23.4329i	−0.731327	+	1.24194i
$357$	−52.8459			−2.79690
$358$	−5.20530	+	11.5575i	−0.275109	+	0.610831i
$359$	−7.45656	+	5.41751i	−0.393542	+	0.285925i	−0.766906	−	0.641760i	$-0.778205\pi$
$359$	−7.45656	+	5.41751i	−0.393542	+	0.285925i	0.373363	+	0.927685i	$0.378205\pi$
$360$		0			0
$361$	−2.81258	−	2.04346i	−0.148030	−	0.107550i
$362$	26.7016	−	15.2636i	1.40340	−	0.802240i
$363$	23.9822	−	17.4241i	1.25874	−	0.914527i
$364$	21.1055	−	18.6777i	1.10623	−	0.978979i
$365$		0			0
$366$	−26.0488	+	14.8905i	−1.36159	+	0.778340i
$367$	32.3311	+	10.5050i	1.68767	+	0.548357i	0.986375	−	0.164513i	$-0.0526053\pi$
$367$	32.3311	+	10.5050i	1.68767	+	0.548357i	0.701296	+	0.712871i	$0.252605\pi$
$368$	−6.09340	+	13.0768i	−0.317641	+	0.681675i
$369$	9.14424	−	28.1431i	0.476030	−	1.46507i
$370$		0			0
$371$	−14.1375	+	4.59356i	−0.733984	+	0.238486i
$372$	4.36221	+	45.2376i	0.226170	+	2.34546i
$373$	−20.7909	−	15.1054i	−1.07651	−	0.782130i	−0.0994385	−	0.995044i	$-0.531705\pi$
$373$	−20.7909	−	15.1054i	−1.07651	−	0.782130i	−0.977071	+	0.212914i	$0.931705\pi$
$374$	0.572175	−	5.22784i	0.0295865	−	0.270325i
$375$		0			0
$376$	2.10738	+	0.714871i	0.108680	+	0.0368666i
$377$	−11.8554	+	16.3175i	−0.610582	+	0.840394i
$378$	−3.47485	−	16.7002i	−0.178727	−	0.858966i
$379$	23.6500	−	7.68435i	1.21482	−	0.394719i	0.369627	−	0.929180i	$-0.379486\pi$
$379$	23.6500	−	7.68435i	1.21482	−	0.394719i	0.845193	+	0.534462i	$0.179486\pi$
$380$		0			0
$381$	−8.92676	−	2.90048i	−0.457332	−	0.148596i
$382$	0.257132	−	2.34936i	0.0131560	−	0.120204i
$383$	−5.06647	−	1.64620i	−0.258885	−	0.0841167i	0.176699	−	0.984265i	$-0.443458\pi$
$383$	−5.06647	−	1.64620i	−0.258885	−	0.0841167i	−0.435584	+	0.900148i	$0.643458\pi$
$384$	4.20001	−	30.9734i	0.214331	−	1.58061i
$385$		0			0
$386$	−8.96700	−	8.14392i	−0.456408	−	0.414515i
$387$	20.3013	−	14.7497i	1.03197	−	0.749771i
$388$	4.07157	+	9.36042i	0.206703	+	0.475203i
$389$	6.84259	−	9.41801i	0.346933	−	0.477512i	−0.599517	−	0.800362i	$-0.704641\pi$
$389$	6.84259	−	9.41801i	0.346933	−	0.477512i	0.946450	+	0.322850i	$0.104641\pi$
$390$		0			0
$391$	20.8733	−	15.1653i	1.05561	−	0.766944i
$392$	0.339552	+	0.253445i	0.0171499	+	0.0128009i
$393$			20.0619i			1.01199i
$394$	−13.0519	−	5.87838i	−0.657547	−	0.296148i
$395$		0			0
$396$	4.79434	−	0.462313i	0.240925	−	0.0232321i
$397$	1.22834	+	3.78044i	0.0616486	+	0.189735i	0.977137	−	0.212608i	$-0.0681958\pi$
$397$	1.22834	+	3.78044i	0.0616486	+	0.189735i	−0.915489	+	0.402343i	$0.868196\pi$
$398$	−16.3730	+	18.0278i	−0.820704	+	0.903650i
$399$	29.1060			1.45712
$400$		0			0
$401$	14.8970			0.743920			0.371960	−	0.928249i	$-0.378686\pi$
$401$	14.8970			0.743920			0.371960	+	0.928249i	$0.378686\pi$
$402$	16.8384	−	18.5403i	0.839825	−	0.924704i
$403$	13.3948	+	41.2249i	0.667241	+	2.05356i
$404$	−3.53149	+	0.340537i	−0.175698	+	0.0169424i
$405$		0			0
$406$	−13.1959	−	5.94321i	−0.654901	−	0.294957i
$407$		−	1.04278i		−	0.0516888i
$408$	−33.4369	+	44.7968i	−1.65537	+	2.21777i
$409$	−9.86001	+	7.16371i	−0.487546	+	0.354223i	−0.804240	−	0.594305i	$-0.797427\pi$
$409$	−9.86001	+	7.16371i	−0.487546	+	0.354223i	0.316694	+	0.948528i	$0.397427\pi$
$410$		0			0
$411$	−29.9531	+	41.2269i	−1.47748	+	2.03357i
$412$	−0.558648	−	1.28432i	−0.0275226	−	0.0632737i
$413$	13.5224	−	9.82457i	0.665392	−	0.483436i
$414$	17.4925	+	15.8868i	0.859709	+	0.780796i
$415$		0			0
$416$	−2.47896	−	29.7087i	−0.121541	−	1.45659i
$417$	26.3165	+	8.55074i	1.28872	+	0.418732i
$418$	−0.315137	+	2.87934i	−0.0154139	+	0.140833i
$419$	11.9484	+	3.88226i	0.583716	+	0.189661i	0.585965	−	0.810337i	$-0.300716\pi$
$419$	11.9484	+	3.88226i	0.583716	+	0.189661i	−0.00224856	+	0.999997i	$0.500716\pi$
$420$		0			0
$421$	6.83134	−	2.21964i	0.332939	−	0.108179i	−0.137777	−	0.990463i	$-0.543996\pi$
$421$	6.83134	−	2.21964i	0.332939	−	0.108179i	0.470716	+	0.882285i	$0.343996\pi$
$422$	−5.16216	−	24.8094i	−0.251290	−	1.20770i
$423$	2.14243	−	2.94881i	0.104169	−	0.143376i
$424$	−5.05125	+	14.8907i	−0.245310	+	0.723154i
$425$		0			0
$426$	1.21775	−	11.1263i	0.0590002	−	0.539072i
$427$	−16.6125	−	12.0697i	−0.803935	−	0.584093i
$428$	−3.87842	−	40.2206i	−0.187471	−	1.94413i
$429$	7.19832	−	2.33888i	0.347538	−	0.112922i
$430$		0			0
$431$	7.56243	−	23.2748i	0.364269	−	1.12111i	−0.586168	−	0.810190i	$-0.699364\pi$
$431$	7.56243	−	23.2748i	0.364269	−	1.12111i	0.950437	−	0.310916i	$-0.100636\pi$
$432$	−16.3552	−	7.62102i	−0.786888	−	0.366667i
$433$	0.422614	+	0.137316i	0.0203095	+	0.00659896i	0.319154	−	0.947703i	$-0.396601\pi$
$433$	0.422614	+	0.137316i	0.0203095	+	0.00659896i	−0.298845	+	0.954302i	$0.596601\pi$
$434$	−27.0024	+	15.4356i	−1.29616	+	0.740934i
$435$		0			0
$436$	−9.38971	+	8.30963i	−0.449686	+	0.397959i
$437$	−11.4964	+	8.35262i	−0.549947	+	0.399560i
$438$	−4.84194	+	2.76784i	−0.231357	+	0.132253i
$439$	−20.5740	−	14.9479i	−0.981941	−	0.713422i	−0.0237998	−	0.999717i	$-0.507576\pi$
$439$	−20.5740	−	14.9479i	−0.981941	−	0.713422i	−0.958142	+	0.286295i	$0.907576\pi$
$440$		0			0
$441$	0.561462	−	0.407926i	0.0267363	−	0.0194251i
$442$	−21.8943	+	48.6125i	−1.04141	+	2.31226i
$443$	1.21860			0.0578973			0.0289486	−	0.999581i	$-0.490784\pi$
$443$	1.21860			0.0578973			0.0289486	+	0.999581i	$0.490784\pi$
$444$	−5.62421	+	9.55104i	−0.266913	+	0.453272i
$445$		0			0
$446$	−1.84613	−	8.87254i	−0.0874169	−	0.420127i
$447$	−59.0943	+	19.2009i	−2.79506	+	0.908171i
$448$	20.5079	−	6.08398i	0.968906	−	0.287441i
$449$	5.21381			0.246055			0.123027	−	0.992403i	$-0.460740\pi$
$449$	5.21381			0.246055			0.123027	+	0.992403i	$0.460740\pi$
$450$		0			0
$451$			3.32043i			0.156353i
$452$	5.19319	−	4.59583i	0.244267	−	0.216170i
$453$	11.3274	+	34.8622i	0.532208	+	1.63797i
$454$	−37.0244	+	7.70377i	−1.73764	+	0.361556i
$455$		0			0
$456$	18.4160	−	24.6727i	0.862410	−	1.15541i
$457$		−	29.9606i		−	1.40150i	−0.713408	−	0.700749i	$-0.752849\pi$
$457$		−	29.9606i		−	1.40150i	0.713408	−	0.700749i	$-0.247151\pi$
$458$	−1.00161	+	2.22390i	−0.0468022	+	0.103916i
$459$	18.9673	+	26.1062i	0.885317	+	1.21853i
$460$		0			0
$461$	14.3867	−	19.8016i	0.670055	−	0.922251i	−0.329707	−	0.944083i	$-0.606950\pi$
$461$	14.3867	−	19.8016i	0.670055	−	0.922251i	0.999762	+	0.0218322i	$0.00694996\pi$
$462$	2.69523	+	4.71492i	0.125393	+	0.219358i
$463$	19.5394	+	26.8937i	0.908072	+	1.24985i	0.967821	+	0.251641i	$0.0809702\pi$
$463$	19.5394	+	26.8937i	0.908072	+	1.24985i	−0.0597482	+	0.998213i	$0.519030\pi$
$464$	−13.3873	+	7.42556i	−0.621491	+	0.344723i
$465$		0			0
$466$	32.6267	−	18.6507i	1.51140	−	0.863976i
$467$	−6.61921	+	20.3718i	−0.306301	+	0.942697i	0.672888	+	0.739744i	$0.265054\pi$
$467$	−6.61921	+	20.3718i	−0.306301	+	0.942697i	−0.979189	+	0.202952i	$0.934946\pi$
$468$	−47.6737	−	10.5621i	−2.20372	−	0.488233i
$469$	16.3015	+	5.29666i	0.752731	+	0.244577i
$470$		0			0
$471$	5.78790	+	17.8133i	0.266692	+	0.820794i
$472$	0.227757	−	17.6790i	0.0104834	−	0.813741i
$473$	−1.65506	+	2.27799i	−0.0760997	+	0.104742i
$474$	−2.90142	+	26.5096i	−0.133267	+	1.21763i
$475$		0			0
$476$	−37.3504	−	8.27496i	−1.71195	−	0.379282i
$477$	20.8362	+	15.1384i	0.954022	+	0.693138i
$478$	−18.5352	+	3.85666i	−0.847779	+	0.176400i
$479$	−2.03109	−	6.25104i	−0.0928026	−	0.285617i	0.893872	−	0.448322i	$-0.147978\pi$
$479$	−2.03109	−	6.25104i	−0.0928026	−	0.285617i	−0.986675	+	0.162705i	$0.947978\pi$
$480$		0			0
$481$	−3.26679	+	10.0541i	−0.148953	+	0.458429i
$482$	1.76753	−	16.1495i	0.0805086	−	0.735590i
$483$	−8.23341	+	25.3398i	−0.374633	+	1.15300i
$484$	19.6785	−	8.55969i	0.894477	−	0.389077i
$485$		0			0
$486$	16.6385	−	18.3201i	0.754737	−	0.831016i
$487$	−13.2598	−	18.2506i	−0.600860	−	0.827013i	0.394927	−	0.918713i	$-0.370770\pi$
$487$	−13.2598	−	18.2506i	−0.600860	−	0.827013i	−0.995787	+	0.0917000i	$0.970770\pi$
$488$	−20.7424	+	6.44542i	−0.938965	+	0.291770i
$489$	−32.1782	−	23.3788i	−1.45515	−	1.05723i
$490$		0			0
$491$	−16.2270	−	22.3345i	−0.732313	−	1.00794i	−0.999024	−	0.0441661i	$-0.985937\pi$
$491$	−16.2270	−	22.3345i	−0.732313	−	1.00794i	0.266711	−	0.963777i	$-0.414063\pi$
$492$	17.9086	−	30.4125i	0.807384	−	1.37110i
$493$	27.3782			1.23305
$494$	12.0587	−	26.7744i	0.542548	−	1.20464i
$495$		0			0
$496$	−4.00048	+	32.6561i	−0.179627	+	1.46630i
$497$	7.28509	−	2.36707i	0.326781	−	0.106177i
$498$	1.44935	−	1.59583i	0.0649467	−	0.0715107i
$499$			15.6614i			0.701101i	0.936544	+	0.350551i	$0.114006\pi$
$499$			15.6614i			0.701101i	−0.936544	+	0.350551i	$0.885994\pi$
$500$		0			0
$501$			10.7420i			0.479916i
$502$	−10.8825	−	9.88360i	−0.485710	−	0.441127i
$503$	−15.7968	+	5.13269i	−0.704344	+	0.228855i	−0.639222	−	0.769022i	$-0.720744\pi$
$503$	−15.7968	+	5.13269i	−0.704344	+	0.228855i	−0.0651216	+	0.997877i	$0.520744\pi$
$504$	0.451347	−	35.0345i	0.0201046	−	1.56056i
$505$		0			0
$506$	−2.41763	−	1.08886i	−0.107477	−	0.0484057i
$507$	−40.8152			−1.81267
$508$	−5.85508	−	3.44781i	−0.259777	−	0.152972i
$509$	7.12293	+	9.80387i	0.315718	+	0.434549i	0.937154	−	0.348916i	$-0.113450\pi$
$509$	7.12293	+	9.80387i	0.315718	+	0.434549i	−0.621436	+	0.783465i	$0.713450\pi$
$510$		0			0
$511$	−3.08792	−	2.24351i	−0.136602	−	0.0992469i
$512$	7.81850	−	21.2337i	0.345532	−	0.938407i
$513$	−10.4466	−	14.3785i	−0.461230	−	0.634828i
$514$	6.18481	+	5.61710i	0.272800	+	0.247760i
$515$		0			0
$516$	27.4453	−	11.9381i	1.20821	−	0.525545i
$517$	−0.126387	+	0.388978i	−0.00555847	+	0.0171072i
$518$	−7.54050	−	0.825291i	−0.331311	−	0.0362612i
$519$	1.86830	−	5.75005i	0.0820094	−	0.252399i
$520$		0			0
$521$	6.53479	+	20.1120i	0.286294	+	0.881123i	0.986008	+	0.166700i	$0.0533110\pi$
$521$	6.53479	+	20.1120i	0.286294	+	0.881123i	−0.699713	+	0.714424i	$0.746689\pi$
$522$	5.10796	+	24.5489i	0.223569	+	1.07448i
$523$	19.5338	+	14.1922i	0.854155	+	0.620580i	0.926289	−	0.376815i	$-0.122981\pi$
$523$	19.5338	+	14.1922i	0.854155	+	0.620580i	−0.0721334	+	0.997395i	$0.522981\pi$
$524$	−3.14143	+	14.1794i	−0.137234	+	0.619429i
$525$		0			0
$526$	−7.84848	−	0.858998i	−0.342210	−	0.0374541i
$527$	34.5844	−	47.6014i	1.50652	−	2.07355i
$528$	5.70211	+	0.698528i	0.248152	+	0.0303995i
$529$	3.08762	+	9.50271i	0.134244	+	0.413161i
$530$		0			0
$531$	−27.5419	−	8.94891i	−1.19522	−	0.388350i
$532$	20.5715	+	4.55761i	0.891888	+	0.197597i
$533$	10.4021	−	32.0145i	0.450566	−	1.38670i
$534$	26.3645	+	46.1209i	1.14090	+	1.99585i
$535$		0			0
$536$	14.8042	−	10.4672i	0.639445	−	0.452114i
$537$	14.5550	+	20.0332i	0.628095	+	0.864498i
$538$	2.59355	−	1.48257i	0.111816	−	0.0639183i
$539$	−0.0457732	+	0.0630014i	−0.00197159	+	0.00271366i
$540$		0			0
$541$	−4.93039	−	6.78610i	−0.211974	−	0.291757i	0.689769	−	0.724029i	$-0.257712\pi$
$541$	−4.93039	−	6.78610i	−0.211974	−	0.291757i	−0.901743	+	0.432272i	$0.857712\pi$
$542$	24.8258	+	11.1812i	1.06636	+	0.480272i
$543$		−	60.0842i		−	2.57846i
$544$	−30.6471	+	26.4257i	−1.31398	+	1.13299i
$545$		0			0
$546$	−11.2158	−	53.9031i	−0.479990	−	2.30684i
$547$	−6.01158	−	18.5017i	−0.257037	−	0.791077i	−0.993422	−	0.114514i	$-0.963469\pi$
$547$	−6.01158	−	18.5017i	−0.257037	−	0.791077i	0.736385	−	0.676563i	$-0.236531\pi$
$548$	−27.6258	+	24.4481i	−1.18012	+	1.04437i
$549$			35.5770i			1.51839i
$550$		0			0
$551$	−15.0791			−0.642391
$552$	16.2708	+	23.0125i	0.692530	+	0.979475i
$553$	−17.3575	+	5.63979i	−0.738116	+	0.239828i
$554$	27.5008	−	5.72216i	1.16840	−	0.243111i
$555$		0			0
$556$	17.2610	+	10.1643i	0.732030	+	0.431062i
$557$	16.0914			0.681815			0.340907	−	0.940097i	$-0.389266\pi$
$557$	16.0914			0.681815			0.340907	+	0.940097i	$0.389266\pi$
$558$	49.1347	+	22.1295i	2.08004	+	0.936815i
$559$	23.0939	−	16.7787i	0.976770	−	0.709665i
$560$		0			0
$561$	−8.31173	−	6.03882i	−0.350921	−	0.254959i
$562$	8.71838	+	15.2516i	0.367763	+	0.643348i
$563$	−21.5684	+	15.6704i	−0.909000	+	0.660427i	−0.940762	−	0.339068i	$-0.889888\pi$
$563$	−21.5684	+	15.6704i	−0.909000	+	0.660427i	0.0317617	+	0.999495i	$0.489888\pi$
$564$	3.25554	−	2.88106i	0.137083	−	0.121315i
$565$		0			0
$566$	−0.219212	−	0.383480i	−0.00921418	−	0.0161189i
$567$	3.65134	+	1.18639i	0.153342	+	0.0498238i
$568$	2.60291	−	7.67317i	0.109216	−	0.321959i
$569$	0.701887	−	2.16018i	0.0294246	−	0.0905597i	−0.935266	−	0.353946i	$-0.884840\pi$
$569$	0.701887	−	2.16018i	0.0294246	−	0.0905597i	0.964690	+	0.263387i	$0.0848395\pi$
$570$		0			0
$571$	26.3024	−	8.54617i	1.10072	−	0.357646i	0.298342	−	0.954459i	$-0.403567\pi$
$571$	26.3024	−	8.54617i	1.10072	−	0.357646i	0.802380	+	0.596813i	$0.203567\pi$
$572$	5.45386	−	0.525910i	0.228037	−	0.0219894i
$573$	−3.73525	−	2.71382i	−0.156042	−	0.113371i
$574$	24.0105	+	2.62790i	1.00218	+	0.109686i
$575$		0			0
$576$	−29.4127	−	22.5497i	−1.22553	−	0.939573i
$577$	7.01351	−	9.65326i	0.291976	−	0.401871i	−0.637679	−	0.770302i	$-0.720105\pi$
$577$	7.01351	−	9.65326i	0.291976	−	0.401871i	0.929655	+	0.368432i	$0.120105\pi$
$578$	47.3156	−	9.84507i	1.96807	−	0.409501i
$579$	−22.5057	+	7.31254i	−0.935305	+	0.303899i
$580$		0			0
$581$	1.40312	+	0.455903i	0.0582114	+	0.0189140i
$582$	19.8227	+	2.16955i	0.821679	+	0.0899309i
$583$	−2.74850	−	0.893042i	−0.113831	−	0.0369860i
$584$	−3.85559	+	1.19807i	−0.159545	+	0.0495765i
$585$		0			0
$586$	9.65535	−	10.6312i	0.398859	−	0.439171i
$587$	−32.6376	+	23.7126i	−1.34710	+	0.978723i	−0.347946	+	0.937515i	$0.613121\pi$
$587$	−32.6376	+	23.7126i	−1.34710	+	0.978723i	−0.999151	+	0.0412086i	$0.986879\pi$
$588$	0.759042	−	0.330166i	0.0313024	−	0.0136158i
$589$	−19.0481	+	26.2174i	−0.784863	+	1.08027i
$590$		0			0
$591$	−22.6237	+	16.4371i	−0.930613	+	0.676130i
$592$	−5.47064	+	5.86980i	−0.224842	+	0.241247i
$593$			5.46839i			0.224560i	0.993677	+	0.112280i	$0.0358153\pi$
$593$			5.46839i			0.224560i	−0.993677	+	0.112280i	$0.964185\pi$
$594$	1.36184	−	3.02373i	0.0558769	−	0.124065i
$595$		0			0
$596$	−44.7732	+	4.31743i	−1.83398	+	0.176849i
$597$	14.7015	+	45.2467i	0.601694	+	1.85182i
$598$	19.8988	+	18.0723i	0.813721	+	0.739030i
$599$	27.9052			1.14017			0.570087	−	0.821584i	$-0.306909\pi$
$599$	27.9052			1.14017			0.570087	+	0.821584i	$0.306909\pi$
$600$		0			0
$601$	13.3613			0.545018			0.272509	−	0.962153i	$-0.412146\pi$
$601$	13.3613			0.545018			0.272509	+	0.962153i	$0.412146\pi$
$602$	15.1626	+	13.7709i	0.617983	+	0.561258i
$603$	−9.17688	−	28.2435i	−0.373712	−	1.15017i
$604$	2.54703	+	26.4136i	0.103637	+	1.07475i
$605$		0			0
$606$	−2.84624	+	6.31958i	−0.115621	+	0.256716i
$607$		−	31.7630i		−	1.28922i	−0.764511	−	0.644611i	$-0.777019\pi$
$607$		−	31.7630i		−	1.28922i	0.764511	−	0.644611i	$-0.222981\pi$
$608$	16.8795	−	14.5545i	0.684554	−	0.590263i
$609$	−22.8732	+	16.6183i	−0.926869	+	0.673409i
$610$		0			0
$611$	2.43715	−	3.35445i	0.0985966	−	0.135707i
$612$	26.4382	+	60.7806i	1.06870	+	2.45691i
$613$	−31.8620	+	23.1491i	−1.28690	+	0.934985i	−0.999738	−	0.0228985i	$-0.992711\pi$
$613$	−31.8620	+	23.1491i	−1.28690	+	0.934985i	−0.287158	+	0.957883i	$0.592711\pi$
$614$	28.7956	−	31.7059i	1.16210	−	1.27955i
$615$		0			0
$616$	1.16664	+	3.75445i	0.0470053	+	0.151271i
$617$	−16.4548	−	5.34648i	−0.662445	−	0.215241i	−0.0415512	−	0.999136i	$-0.513230\pi$
$617$	−16.4548	−	5.34648i	−0.662445	−	0.215241i	−0.620893	+	0.783895i	$0.713230\pi$
$618$	−2.71982	−	0.297678i	−0.109407	−	0.0119744i
$619$	19.9635	+	6.48655i	0.802402	+	0.260716i	0.681377	−	0.731933i	$-0.261382\pi$
$619$	19.9635	+	6.48655i	0.802402	+	0.260716i	0.121026	+	0.992649i	$0.461382\pi$
$620$		0			0
$621$	15.4732	−	5.02753i	0.620916	−	0.201748i
$622$	35.0365	−	7.29012i	1.40483	−	0.292307i
$623$	−21.3701	+	29.4134i	−0.856173	+	1.17842i
$624$	−52.7895	−	24.5983i	−2.11327	−	0.984721i
$625$		0			0
$626$	35.8759	+	3.92654i	1.43389	+	0.156936i
$627$	4.57786	+	3.32601i	0.182822	+	0.132828i
$628$	1.30144	+	13.4964i	0.0519332	+	0.538565i
$629$	13.6475	−	4.43435i	0.544163	−	0.176809i
$630$		0			0
$631$	4.33588	−	13.3445i	0.172609	−	0.531235i	−0.826907	−	0.562338i	$-0.809902\pi$
$631$	4.33588	−	13.3445i	0.172609	−	0.531235i	0.999516	+	0.0311029i	$0.00990195\pi$
$632$	−6.20172	+	18.2822i	−0.246691	+	0.727225i
$633$	−47.0818	−	15.2978i	−1.87133	−	0.608032i
$634$	−18.8558	−	32.9854i	−0.748858	−	1.31002i
$635$		0			0
$636$	20.3575	+	23.0035i	0.807226	+	0.912148i
$637$	0.638698	−	0.464041i	0.0253061	−	0.0183860i
$638$	−1.39633	−	2.44269i	−0.0552814	−	0.0967069i
$639$	−10.7369	−	7.80081i	−0.424745	−	0.308595i
$640$		0			0
$641$	−38.2200	+	27.7684i	−1.50960	+	1.09679i	−0.543242	+	0.839576i	$0.682803\pi$
$641$	−38.2200	+	27.7684i	−1.50960	+	1.09679i	−0.966355	+	0.257210i	$0.917197\pi$
$642$	−71.9745	−	32.4162i	−2.84061	−	1.27936i
$643$	−35.9924			−1.41940			−0.709702	−	0.704502i	$-0.751170\pi$
$643$	−35.9924			−1.41940			−0.709702	+	0.704502i	$0.751170\pi$
$644$	−9.78709	+	16.6204i	−0.385665	+	0.654937i
$645$		0			0
$646$	−39.0238	+	8.11978i	−1.53537	+	0.319468i
$647$	0.591058	−	0.192046i	0.0232369	−	0.00755012i	−0.297375	−	0.954761i	$-0.596111\pi$
$647$	0.591058	−	0.192046i	0.0232369	−	0.00755012i	0.320612	+	0.947210i	$0.396111\pi$
$648$	3.31598	−	2.34454i	0.130264	−	0.0921020i
$649$	3.24951			0.127554
$650$		0			0
$651$			60.7612i			2.38142i
$652$	−19.0821	−	21.5623i	−0.747312	−	0.844447i
$653$	−2.23277	−	6.87175i	−0.0873749	−	0.268912i	0.897817	−	0.440369i	$-0.145152\pi$
$653$	−2.23277	−	6.87175i	−0.0873749	−	0.268912i	−0.985192	+	0.171457i	$0.945152\pi$
$654$	4.98984	+	23.9812i	0.195118	+	0.937741i
$655$		0			0
$656$	17.4197	−	18.6907i	0.680123	−	0.729748i
$657$			6.61304i			0.257999i
$658$	2.71273	+	1.22177i	0.105753	+	0.0476295i
$659$	−14.7715	−	20.3312i	−0.575415	−	0.791991i	0.417768	−	0.908554i	$-0.362812\pi$
$659$	−14.7715	−	20.3312i	−0.575415	−	0.791991i	−0.993183	+	0.116563i	$0.962812\pi$
$660$		0			0
$661$	−1.96163	+	2.69996i	−0.0762987	+	0.105016i	−0.845461	−	0.534038i	$-0.820674\pi$
$661$	−1.96163	+	2.69996i	−0.0762987	+	0.105016i	0.769162	+	0.639054i	$0.220674\pi$
$662$	14.7982	−	8.45923i	0.575149	−	0.328777i
$663$	61.2206	+	84.2630i	2.37761	+	3.27250i
$664$	1.27425	−	0.900950i	0.0494506	−	0.0349636i
$665$		0			0
$666$	6.52233	+	11.4099i	0.252735	+	0.442124i
$667$	4.26553	−	13.1280i	0.165162	−	0.508317i
$668$	−1.68205	+	7.59220i	−0.0650804	+	0.293751i
$669$	−16.8377	−	5.47091i	−0.650984	−	0.211518i
$670$		0			0
$671$	−1.23362	−	3.79670i	−0.0476234	−	0.146570i
$672$	9.56399	−	40.6799i	0.368939	−	1.56926i
$673$	19.4876	−	26.8224i	0.751191	−	1.03393i	−0.246705	−	0.969091i	$-0.579348\pi$
$673$	19.4876	−	26.8224i	0.751191	−	1.03393i	0.997896	−	0.0648353i	$-0.0206522\pi$
$674$	19.5720	+	2.14211i	0.753886	+	0.0825111i
$675$		0			0
$676$	−28.8473	−	6.39111i	−1.10951	−	0.245812i
$677$	−9.80817	−	7.12605i	−0.376959	−	0.273876i	0.383132	−	0.923694i	$-0.374845\pi$
$677$	−9.80817	−	7.12605i	−0.376959	−	0.273876i	−0.760091	+	0.649817i	$0.774845\pi$
$678$	−2.75974	−	13.2634i	−0.105987	−	0.509377i
$679$	4.21719	+	12.9792i	0.161841	+	0.498095i
$680$		0			0
$681$	−22.8297	+	70.2625i	−0.874835	+	2.69247i
$682$	−6.01087	−	0.657876i	−0.230168	−	0.0251914i
$683$	12.5862	−	38.7363i	0.481597	−	1.48220i	−0.355253	−	0.934770i	$-0.615605\pi$
$683$	12.5862	−	38.7363i	0.481597	−	1.48220i	0.836850	−	0.547432i	$-0.184395\pi$
$684$	−14.5614	−	33.4762i	−0.556768	−	1.27999i
$685$		0			0
$686$	−19.1757	−	17.4156i	−0.732133	−	0.664930i
$687$	2.80069	+	3.85482i	0.106853	+	0.147071i
$688$	21.2671	−	4.14003i	0.810802	−	0.157837i
$689$	23.7024	+	17.2208i	0.902990	+	0.656061i
$690$		0			0
$691$	4.49348	+	6.18474i	0.170940	+	0.235279i	0.885888	−	0.463899i	$-0.153550\pi$
$691$	4.49348	+	6.18474i	0.170940	+	0.235279i	−0.714948	+	0.699177i	$0.753550\pi$
$692$	2.22086	−	3.77146i	0.0844244	−	0.143370i
$693$	6.43956			0.244619
$694$	19.6064	+	8.83041i	0.744249	+	0.335198i
$695$		0			0
$696$	−0.385253	+	29.9041i	−0.0146030	+	1.13351i
$697$	−43.4565	+	14.1199i	−1.64603	+	0.534829i
$698$	24.5195	+	22.2688i	0.928076	+	0.842888i
$699$		−	73.4170i		−	2.77689i
$700$		0			0
$701$			41.0013i			1.54860i	0.632820	+	0.774299i	$0.281897\pi$
$701$			41.0013i			1.54860i	−0.632820	+	0.774299i	$0.718103\pi$
$702$	−22.6030	+	24.8874i	−0.853095	+	0.939315i
$703$	−7.51666	+	2.44231i	−0.283496	+	0.0921135i
$704$	3.92075	+	1.38658i	0.147769	+	0.0522587i
$705$		0			0
$706$	2.60134	−	5.77583i	0.0979028	−	0.217376i
$707$	−4.74334			−0.178392
$708$	−29.7629	−	17.5261i	−1.11856	−	0.658672i
$709$	18.4825	+	25.4390i	0.694125	+	0.955382i	0.999995	+	0.00330817i	$0.00105303\pi$
$709$	18.4825	+	25.4390i	0.694125	+	0.955382i	−0.305869	+	0.952074i	$0.598947\pi$
$710$		0			0
$711$	25.5818	+	18.5863i	0.959393	+	0.697040i
$712$	11.4120	+	36.7256i	0.427682	+	1.37635i
$713$	−17.4368	−	23.9997i	−0.653013	−	0.898796i
$714$	−50.2458	+	55.3240i	−1.88040	+	2.07045i
$715$		0			0
$716$	7.15024	+	16.4382i	0.267217	+	0.614324i
$717$	−11.4290	+	35.1748i	−0.426824	+	1.31363i
$718$	−1.41813	+	12.9572i	−0.0529243	+	0.483558i
$719$	−0.494184	+	1.52094i	−0.0184300	+	0.0567216i	−0.959849	−	0.280519i	$-0.909494\pi$
$719$	−0.494184	+	1.52094i	−0.0184300	+	0.0567216i	0.941419	+	0.337240i	$0.109494\pi$
$720$		0			0
$721$	−0.578628	−	1.78083i	−0.0215492	−	0.0663217i
$722$	−4.81347	+	1.00155i	−0.179139	+	0.0372739i
$723$	−25.6761	−	18.6548i	−0.954903	−	0.693778i
$724$	9.40838	−	42.4663i	0.349660	−	1.57825i
$725$		0			0
$726$	4.56107	−	41.6735i	0.169277	−	1.54665i
$727$	−29.8436	+	41.0762i	−1.10684	+	1.52343i	−0.280843	+	0.959754i	$0.590614\pi$
$727$	−29.8436	+	41.0762i	−1.10684	+	1.52343i	−0.825995	+	0.563678i	$0.809386\pi$
$728$	0.513435	−	39.8539i	0.0190292	−	1.47708i
$729$	−13.6089	−	41.8837i	−0.504032	−	1.55125i
$730$		0			0
$731$	−36.8515	−	11.9738i	−1.36300	−	0.442867i
$732$	−9.17838	+	41.4282i	−0.339243	+	1.53123i
$733$	−6.55606	+	20.1775i	−0.242154	+	0.745272i	0.753938	+	0.656946i	$0.228152\pi$
$733$	−6.55606	+	20.1775i	−0.242154	+	0.745272i	−0.996092	+	0.0883266i	$0.971848\pi$
$734$	41.7380	−	23.8591i	1.54058	−	0.880654i
$735$		0			0
$736$	7.89641	+	18.8125i	0.291065	+	0.693439i
$737$	1.95867	+	2.69588i	0.0721485	+	0.0993039i
$738$	−20.7684	−	36.3314i	−0.764497	−	1.33738i
$739$	−14.2869	+	19.6642i	−0.525551	+	0.723358i	−0.986444	−	0.164097i	$-0.947529\pi$
$739$	−14.2869	+	19.6642i	−0.525551	+	0.723358i	0.460894	+	0.887455i	$0.347529\pi$
$740$		0			0
$741$	−33.7185	−	46.4096i	−1.23868	−	1.70490i
$742$	−8.63297	+	19.1680i	−0.316926	+	0.703680i
$743$		−	11.2680i		−	0.413384i	−0.978406	−	0.206692i	$-0.933730\pi$
$743$		−	11.2680i		−	0.413384i	0.978406	−	0.206692i	$-0.0662698\pi$
$744$	51.5065	+	38.4450i	1.88832	+	1.40946i
$745$		0			0
$746$	−35.5817	+	7.40357i	−1.30274	+	0.271064i
$747$	−0.789887	−	2.43102i	−0.0289005	−	0.0889465i
$748$	−4.92896	−	5.56962i	−0.180221	−	0.203646i
$749$		−	54.0226i		−	1.97394i
$750$		0			0
$751$	−8.71647			−0.318068			−0.159034	−	0.987273i	$-0.550838\pi$
$751$	−8.71647			−0.318068			−0.159034	+	0.987273i	$0.550838\pi$
$752$	2.75208	−	1.52650i	0.100358	−	0.0556658i
$753$	−27.3133	+	8.87463i	−0.995352	+	0.323409i
$754$	5.81062	+	27.9259i	0.211610	+	1.01700i
$755$		0			0
$756$	−20.7872	−	12.2407i	−0.756023	−	0.445191i
$757$	38.5500			1.40112			0.700562	−	0.713592i	$-0.252933\pi$
$757$	38.5500			1.40112			0.700562	+	0.713592i	$0.252933\pi$
$758$	14.4417	−	32.0653i	0.524546	−	1.16466i
$759$	−4.19061	+	3.04466i	−0.152110	+	0.110514i
$760$		0			0
$761$	22.7571	+	16.5340i	0.824944	+	0.599357i	0.918124	−	0.396292i	$-0.129703\pi$
$761$	22.7571	+	16.5340i	0.824944	+	0.599357i	−0.0931801	+	0.995649i	$0.529703\pi$
$762$	−11.5240	+	6.58759i	−0.417472	+	0.238643i
$763$	−13.5620	+	9.85338i	−0.490978	+	0.356716i
$764$	−2.21505	−	2.50296i	−0.0801377	−	0.0905539i
$765$		0			0
$766$	−6.54058	+	3.73885i	−0.236321	+	0.135090i
$767$	−31.3306	−	10.1799i	−1.13128	−	0.367576i
$768$	−28.4325	−	33.8464i	−1.02597	−	1.22133i
$769$	−1.71576	+	5.28055i	−0.0618717	+	0.190422i	−0.977215	−	0.212254i	$-0.931920\pi$
$769$	−1.71576	+	5.28055i	−0.0618717	+	0.190422i	0.915343	+	0.402675i	$0.131920\pi$
$770$		0			0
$771$	15.5228	−	5.04368i	0.559041	−	0.181644i
$772$	−17.0516	+	1.64427i	−0.613701	+	0.0591785i
$773$	26.9230	+	19.5607i	0.968353	+	0.703549i	0.955076	−	0.296362i	$-0.0957736\pi$
$773$	26.9230	+	19.5607i	0.968353	+	0.703549i	0.0132772	+	0.999912i	$0.495774\pi$
$774$	3.86102	−	35.2773i	0.138781	−	1.26801i
$775$		0			0
$776$	13.6706	+	4.63737i	0.490746	+	0.166472i
$777$	−8.71025	+	11.9886i	−0.312478	+	0.430090i
$778$	−3.35373	−	16.1181i	−0.120237	−	0.577861i
$779$	23.9346	−	7.77682i	0.857545	−	0.278633i
$780$		0			0
$781$	1.41631	+	0.460185i	0.0506794	+	0.0164667i
$782$	3.96981	−	36.2712i	0.141960	−	1.29706i
$783$	16.4191	+	5.33491i	0.586773	+	0.190654i
$784$	0.588175	−	0.114499i	0.0210062	−	0.00408924i
$785$		0			0
$786$	21.0027	+	19.0749i	0.749141	+	0.680377i
$787$	17.2535	−	12.5354i	0.615021	−	0.446839i	−0.236158	−	0.971715i	$-0.575888\pi$
$787$	17.2535	−	12.5354i	0.615021	−	0.446839i	0.851179	+	0.524876i	$0.175888\pi$
$788$	−18.5638	+	8.07481i	−0.661307	+	0.287653i
$789$	−9.06600	+	12.4783i	−0.322758	+	0.444239i
$790$		0			0
$791$	7.50078	−	5.44963i	0.266697	−	0.193767i
$792$	4.07446	−	5.45873i	0.144780	−	0.193967i
$793$			40.4711i			1.43717i
$794$	5.12562	+	2.30850i	0.181901	+	0.0819254i
$795$		0			0
$796$	3.30573	+	34.2815i	0.117168	+	1.21508i
$797$	0.373055	+	1.14814i	0.0132143	+	0.0406694i	0.957446	−	0.288612i	$-0.0931937\pi$
$797$	0.373055	+	1.14814i	0.0132143	+	0.0406694i	−0.944232	+	0.329281i	$0.893194\pi$
$798$	27.6739	−	30.4708i	0.979645	−	1.07866i
$799$	−5.62824			−0.199113
$800$		0			0
$801$	62.9912			2.22568
$802$	14.1640	−	15.5955i	0.500149	−	0.550697i
$803$	−0.229305	−	0.705728i	−0.00809199	−	0.0249046i
$804$	−3.39970	−	35.2561i	−0.119898	−	1.24339i
$805$		0			0
$806$	55.8937	+	25.1736i	1.96877	+	0.886704i
$807$		−	5.83604i		−	0.205438i
$808$	−3.00123	+	4.02087i	−0.105583	+	0.141454i
$809$	−8.23313	+	5.98172i	−0.289462	+	0.210306i	−0.723034	−	0.690813i	$-0.757253\pi$
$809$	−8.23313	+	5.98172i	−0.289462	+	0.210306i	0.433572	+	0.901119i	$0.357253\pi$
$810$		0			0
$811$	−9.04159	+	12.4447i	−0.317493	+	0.436992i	−0.937700	−	0.347447i	$-0.887049\pi$
$811$	−9.04159	+	12.4447i	−0.317493	+	0.436992i	0.620206	+	0.784439i	$0.287049\pi$
$812$	−18.7685	+	8.16387i	−0.658646	+	0.286496i
$813$	43.0321	−	31.2646i	1.50920	−	1.09650i
$814$	−1.09168	−	0.991474i	−0.0382634	−	0.0347512i
$815$		0			0
$816$	15.1057	+	77.5975i	0.528806	+	2.71645i
$817$	20.2967	+	6.59481i	0.710093	+	0.230723i
$818$	−1.87523	+	17.1336i	−0.0655660	+	0.599063i
$819$	−62.0880	−	20.1736i	−2.16953	−	0.704923i
$820$		0			0
$821$	49.2854	−	16.0138i	1.72007	−	0.558885i	0.728115	−	0.685455i	$-0.240397\pi$
$821$	49.2854	−	16.0138i	1.72007	−	0.558885i	0.991958	+	0.126570i	$0.0403968\pi$
$822$	14.6808	+	70.5560i	0.512051	+	2.46092i
$823$	15.1546	−	20.8585i	0.528256	−	0.727082i	−0.458607	−	0.888639i	$-0.651651\pi$
$823$	15.1546	−	20.8585i	0.528256	−	0.727082i	0.986863	+	0.161557i	$0.0516515\pi$
$824$	−1.87570	−	0.636280i	−0.0653431	−	0.0221659i
$825$		0			0
$826$	2.57176	−	23.4976i	0.0894831	−	0.817588i
$827$	−2.88316	−	2.09474i	−0.100257	−	0.0728411i	0.536527	−	0.843883i	$-0.319736\pi$
$827$	−2.88316	−	2.09474i	−0.100257	−	0.0728411i	−0.636784	+	0.771042i	$0.719736\pi$
$828$	33.2636	−	3.20757i	1.15599	−	0.111471i
$829$	−25.3530	+	8.23770i	−0.880547	+	0.286107i	−0.714184	−	0.699958i	$-0.753202\pi$
$829$	−25.3530	+	8.23770i	−0.880547	+	0.286107i	−0.166362	+	0.986065i	$0.553202\pi$
$830$		0			0
$831$	16.9573	−	52.1892i	0.588243	−	1.81042i
$832$	−33.4588	−	25.6517i	−1.15997	−	0.889313i
$833$	−1.01919	−	0.331153i	−0.0353127	−	0.0114738i
$834$	33.9733	−	19.4205i	1.17640	−	0.672477i
$835$		0			0
$836$	2.71473	+	3.06758i	0.0938908	+	0.106095i
$837$	30.0164	−	21.8082i	1.03752	−	0.753802i
$838$	15.4248	−	8.81741i	0.532841	−	0.304592i
$839$	−2.07141	−	1.50497i	−0.0715131	−	0.0519573i	0.551454	−	0.834205i	$-0.314073\pi$
$839$	−2.07141	−	1.50497i	−0.0715131	−	0.0519573i	−0.622967	+	0.782248i	$0.714073\pi$
$840$		0			0
$841$	−11.6114	+	8.43621i	−0.400395	+	0.290904i
$842$	4.17150	−	9.26211i	0.143760	−	0.319193i
$843$	34.3193			1.18202
$844$	−30.8810	−	18.1845i	−1.06297	−	0.625938i
$845$		0			0
$846$	−1.05006	−	5.04662i	−0.0361019	−	0.173506i
$847$	27.2862	−	8.86584i	0.937566	−	0.304634i
$848$	10.7862	+	19.4461i	0.370399	+	0.667782i
$849$	−0.862913			−0.0296151
$850$		0			0
$851$		−	7.23492i		−	0.248010i
$852$	−10.4902	−	11.8537i	−0.359389	−	0.406102i
$853$	−0.926669	−	2.85199i	−0.0317285	−	0.0976504i	0.933938	−	0.357435i	$-0.116349\pi$
$853$	−0.926669	−	2.85199i	−0.0317285	−	0.0976504i	−0.965667	+	0.259784i	$0.916349\pi$
$854$	−28.4308	+	5.91566i	−0.972881	+	0.202430i
$855$		0			0
$856$	−45.7942	−	34.1813i	−1.56521	−	1.16829i
$857$		−	6.92518i		−	0.236560i	−0.992980	−	0.118280i	$-0.962262\pi$
$857$		−	6.92518i		−	0.236560i	0.992980	−	0.118280i	$-0.0377380\pi$
$858$	4.39559	−	9.75966i	0.150063	−	0.333189i
$859$	−15.0901	−	20.7697i	−0.514866	−	0.708653i	0.469864	−	0.882739i	$-0.344303\pi$
$859$	−15.0901	−	20.7697i	−0.514866	−	0.708653i	−0.984730	+	0.174086i	$0.944303\pi$
$860$		0			0
$861$	27.7352	−	38.1743i	0.945214	−	1.30098i
$862$	−17.1758	−	30.0466i	−0.585011	−	1.02339i
$863$	−8.57489	−	11.8023i	−0.291893	−	0.401756i	0.637735	−	0.770256i	$-0.279871\pi$
$863$	−8.57489	−	11.8023i	−0.291893	−	0.401756i	−0.929628	+	0.368500i	$0.879871\pi$
$864$	−23.5288	+	9.87604i	−0.800467	+	0.335990i
$865$		0			0
$866$	0.545575	−	0.311872i	0.0185394	−	0.0105978i
$867$	29.1753	−	89.7924i	0.990846	−	3.04951i
$868$	−9.51439	+	42.9448i	−0.322939	+	1.45764i
$869$	−3.37450	−	1.09644i	−0.114472	−	0.0371942i
$870$		0			0
$871$	−10.4393	−	32.1288i	−0.353721	−	1.08864i
$872$	−0.228425	+	17.7308i	−0.00773544	+	0.600440i
$873$	13.8980	−	19.1289i	0.470376	−	0.647417i
$874$	−2.18645	+	19.9771i	−0.0739578	+	0.675737i
$875$		0			0
$876$	−1.70607	+	7.70065i	−0.0576429	+	0.260181i
$877$	−29.6831	−	21.5661i	−1.00233	−	0.728234i	−0.0397424	−	0.999210i	$-0.512654\pi$
$877$	−29.6831	−	21.5661i	−1.00233	−	0.728234i	−0.962586	+	0.270976i	$0.912654\pi$
$878$	−35.2105	+	7.32633i	−1.18830	+	0.247252i
$879$	−8.66968	−	26.6825i	−0.292421	−	0.899980i
$880$		0			0
$881$	7.66494	−	23.5903i	0.258238	−	0.794776i	−0.734936	−	0.678137i	$-0.762788\pi$
$881$	7.66494	−	23.5903i	0.258238	−	0.794776i	0.993174	−	0.116639i	$-0.0372122\pi$
$882$	0.106782	−	0.975646i	0.00359555	−	0.0328517i
$883$	3.12800	−	9.62701i	0.105266	−	0.323975i	−0.884527	−	0.466489i	$-0.845519\pi$
$883$	3.12800	−	9.62701i	0.105266	−	0.323975i	0.989793	+	0.142514i	$0.0455187\pi$
$884$	30.0750	+	69.1417i	1.01153	+	2.32549i
$885$		0			0
$886$	1.15864	−	1.27574i	0.0389252	−	0.0428593i
$887$	6.68404	+	9.19979i	0.224428	+	0.308899i	0.906351	−	0.422525i	$-0.138856\pi$
$887$	6.68404	+	9.19979i	0.224428	+	0.308899i	−0.681923	+	0.731424i	$0.738856\pi$
$888$	4.65142	+	14.9691i	0.156092	+	0.502328i
$889$	−7.34939	−	5.33965i	−0.246491	−	0.179086i
$890$		0			0
$891$	0.438720	+	0.603846i	0.0146977	+	0.0202296i
$892$	−11.0439	−	6.50329i	−0.369777	−	0.217746i
$893$	3.09987			0.103733
$894$	−36.0854	+	80.1215i	−1.20688	+	2.67966i
$895$		0			0
$896$	13.1296	−	27.2542i	0.438628	−	0.910498i
$897$	49.9426	−	16.2273i	1.66754	−	0.541815i
$898$	4.95728	−	5.45830i	0.165426	−	0.182146i
$899$		−	31.4789i		−	1.04988i
$900$		0			0
$901$		−	39.7689i		−	1.32489i
$902$	3.47613	+	3.15706i	0.115743	+	0.105119i
$903$	38.0557	−	12.3651i	1.26642	−	0.411483i
$904$	0.126336	−	9.80642i	0.00420186	−	0.326157i
$905$		0			0
$906$	47.2670	+	21.2883i	1.57034	+	0.707256i
$907$	16.5101			0.548207			0.274104	−	0.961700i	$-0.411619\pi$
$907$	16.5101			0.548207			0.274104	+	0.961700i	$0.411619\pi$
$908$	−27.1377	+	46.0853i	−0.900597	+	1.52939i
$909$	4.83054	+	6.64867i	0.160219	+	0.220523i
$910$		0			0
$911$	−10.4321	−	7.57935i	−0.345630	−	0.251115i	0.401403	−	0.915901i	$-0.368523\pi$
$911$	−10.4321	−	7.57935i	−0.345630	−	0.251115i	−0.747033	+	0.664786i	$0.768523\pi$
$912$	−8.31979	−	42.7384i	−0.275496	−	1.41521i
$913$	0.168590	+	0.232044i	0.00557950	+	0.00767953i
$914$	−31.3655	−	28.4865i	−1.03748	−	0.942249i
$915$		0			0
$916$	1.37586	+	3.16306i	0.0454597	+	0.104510i
$917$	−6.00014	+	18.4665i	−0.198142	+	0.609819i
$918$	45.3645	+	4.96504i	1.49725	+	0.163871i
$919$	6.83471	−	21.0351i	0.225456	−	0.693883i	−0.772789	−	0.634663i	$-0.781139\pi$
$919$	6.83471	−	21.0351i	0.225456	−	0.693883i	0.998245	−	0.0592194i	$-0.0188612\pi$
$920$		0			0
$921$	−25.8560	−	79.5767i	−0.851985	−	2.62214i
$922$	−7.05129	−	33.8886i	−0.232222	−	1.11606i
$923$	−12.2139	−	8.87390i	−0.402025	−	0.292088i
$924$	7.49863	+	1.66132i	0.246687	+	0.0546533i
$925$		0			0
$926$	46.7328	+	5.11480i	1.53573	+	0.168083i
$927$	−1.90690	+	2.62463i	−0.0626309	+	0.0862040i
$928$	−4.95487	+	21.0753i	−0.162652	+	0.691831i
$929$	11.8169	+	36.3687i	0.387701	+	1.19322i	0.934502	+	0.355958i	$0.115845\pi$
$929$	11.8169	+	36.3687i	0.387701	+	1.19322i	−0.546801	+	0.837262i	$0.684155\pi$
$930$		0			0
$931$	0.561337	+	0.182390i	0.0183971	+	0.00597758i
$932$	11.4961	−	51.8896i	0.376568	−	1.69970i
$933$	21.6039	−	66.4899i	0.707279	−	2.17678i
$934$	15.0336	+	26.2991i	0.491914	+	0.860533i
$935$		0			0
$936$	−56.3855	+	39.8669i	−1.84302	+	1.30309i
$937$	8.14697	+	11.2133i	0.266150	+	0.366324i	0.921085	−	0.389361i	$-0.127304\pi$
$937$	8.14697	+	11.2133i	0.266150	+	0.366324i	−0.654935	+	0.755685i	$0.727304\pi$
$938$	21.0444	−	12.0298i	0.687125	−	0.392787i
$939$	41.4413	−	57.0390i	1.35238	−	1.86140i
$940$		0			0
$941$	23.3206	+	32.0981i	0.760230	+	1.04637i	0.997195	+	0.0748487i	$0.0238474\pi$
$941$	23.3206	+	32.0981i	0.760230	+	1.04637i	−0.236965	+	0.971518i	$0.576153\pi$
$942$	24.1517	+	10.8776i	0.786906	+	0.354410i
$943$			23.0375i			0.750203i
$944$	−18.2914	−	17.0476i	−0.595335	−	0.554851i
$945$		0			0
$946$	0.811188	+	3.89858i	0.0263740	+	0.126754i
$947$	−9.93611	−	30.5802i	−0.322880	−	0.993724i	−0.972388	−	0.233369i	$-0.925025\pi$
$947$	−9.93611	−	30.5802i	−0.322880	−	0.993724i	0.649508	−	0.760355i	$-0.274975\pi$
$948$	24.9941	+	28.2428i	0.811770	+	0.917283i
$949$			7.52274i			0.244199i
$950$		0			0
$951$	−74.2243			−2.40689
$952$	−44.1757	+	31.2341i	−1.43174	+	1.01230i
$953$	−2.59539	+	0.843293i	−0.0840729	+	0.0273169i	−0.350751	−	0.936469i	$-0.614074\pi$
$953$	−2.59539	+	0.843293i	−0.0840729	+	0.0273169i	0.266679	+	0.963786i	$0.414074\pi$
$954$	35.6592	−	7.41970i	1.15451	−	0.240222i
$955$		0			0
$956$	−13.5857	+	23.0712i	−0.439393	+	0.746177i
$957$	−5.49657			−0.177679
$958$	−8.47531	−	3.81714i	−0.273825	−	0.123326i
$959$	−39.9013	+	28.9900i	−1.28848	+	0.936135i
$960$		0			0
$961$	−29.6516	−	21.5432i	−0.956504	−	0.694941i
$962$	7.41955	+	12.9794i	0.239216	+	0.418474i
$963$	−75.7226	+	55.0157i	−2.44013	+	1.77286i
$964$	−15.2262	−	17.2053i	−0.490404	−	0.554146i
$965$		0			0
$966$	18.6998	+	32.7126i	0.601655	+	1.05251i
$967$	−18.5861	−	6.03899i	−0.597689	−	0.194201i	−0.00547963	−	0.999985i	$-0.501744\pi$
$967$	−18.5861	−	6.03899i	−0.597689	−	0.194201i	−0.592210	+	0.805784i	$0.701744\pi$
$968$	9.74919	−	28.7398i	0.313351	−	0.923732i
$969$	−24.0625	+	74.0568i	−0.772999	+	2.37905i
$970$		0			0
$971$	−5.24830	+	1.70528i	−0.168426	+	0.0547250i	−0.392016	−	0.919958i	$-0.628222\pi$
$971$	−5.24830	+	1.70528i	−0.168426	+	0.0547250i	0.223590	+	0.974683i	$0.428222\pi$
$972$	−3.35933	−	34.8374i	−0.107751	−	1.11741i
$973$	21.6663	+	15.7415i	0.694591	+	0.504650i
$974$	−31.7138	−	3.47100i	−1.01618	−	0.111218i
$975$		0			0
$976$	−12.9742	+	27.8434i	−0.415294	+	0.891245i
$977$	0.133245	−	0.183396i	0.00426289	−	0.00586736i	−0.806880	−	0.590715i	$-0.798846\pi$
$977$	0.133245	−	0.183396i	0.00426289	−	0.00586736i	0.811143	+	0.584848i	$0.198846\pi$
$978$	−55.0701	+	11.4586i	−1.76095	+	0.366405i
$979$	−6.72226	+	2.18420i	−0.214844	+	0.0698072i
$980$		0			0
$981$	27.6227	+	8.97514i	0.881923	+	0.286554i
$982$	−38.8104	−	4.24771i	−1.23849	−	0.135550i
$983$	−36.7510	−	11.9411i	−1.17217	−	0.380862i	−0.342720	−	0.939438i	$-0.611348\pi$
$983$	−36.7510	−	11.9411i	−1.17217	−	0.380862i	−0.829454	+	0.558575i	$0.811348\pi$
$984$	−14.8111	−	47.6645i	−0.472160	−	1.51949i
$985$		0			0
$986$	26.0311	−	28.6620i	0.829000	−	0.912785i
$987$	4.70213	−	3.41630i	0.149670	−	0.108742i
$988$	−16.5644	−	38.0812i	−0.526985	−	1.21152i
$989$	−11.4830	+	15.8049i	−0.365137	+	0.502568i
$990$		0			0
$991$	41.5262	−	30.1706i	1.31912	−	0.958400i	0.319181	−	0.947694i	$-0.396592\pi$
$991$	41.5262	−	30.1706i	1.31912	−	0.958400i	0.999943	−	0.0107060i	$-0.00340790\pi$
$992$	30.3837	+	35.2374i	0.964685	+	1.11879i
$993$		−	33.2991i		−	1.05672i
$994$	4.44858	−	9.87730i	0.141100	−	0.313289i
$995$		0			0
$996$	−0.292625	−	3.03462i	−0.00927216	−	0.0961555i
$997$	−6.00849	−	18.4922i	−0.190291	−	0.585655i	0.809709	−	0.586832i	$-0.199625\pi$
$997$	−6.00849	−	18.4922i	−0.190291	−	0.585655i	−0.999999	+	0.00117756i	$0.999625\pi$
$998$	16.3958	+	14.8908i	0.519001	+	0.471361i
$999$	9.04872			0.286289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.o.a.549.21		112
5.2	odd	4		1000.2.t.b.701.44		224
5.3	odd	4		1000.2.t.b.701.13		224
5.4	even	2		200.2.o.a.109.8	✓	112
8.5	even	2	inner	1000.2.o.a.549.18		112
20.19	odd	2		800.2.be.a.209.4		112
25.2	odd	20		1000.2.t.b.301.48		224
25.11	even	5		200.2.o.a.189.11	yes	112
25.14	even	10	inner	1000.2.o.a.949.18		112
25.23	odd	20		1000.2.t.b.301.9		224
40.13	odd	4		1000.2.t.b.701.9		224
40.19	odd	2		800.2.be.a.209.25		112
40.29	even	2		200.2.o.a.109.11	yes	112
40.37	odd	4		1000.2.t.b.701.48		224
100.11	odd	10		800.2.be.a.689.25		112
200.11	odd	10		800.2.be.a.689.4		112
200.61	even	10		200.2.o.a.189.8	yes	112
200.77	odd	20		1000.2.t.b.301.44		224
200.173	odd	20		1000.2.t.b.301.13		224
200.189	even	10	inner	1000.2.o.a.949.21		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.8	✓	112	5.4	even	2
200.2.o.a.109.11	yes	112	40.29	even	2
200.2.o.a.189.8	yes	112	200.61	even	10
200.2.o.a.189.11	yes	112	25.11	even	5
800.2.be.a.209.4		112	20.19	odd	2
800.2.be.a.209.25		112	40.19	odd	2
800.2.be.a.689.4		112	200.11	odd	10
800.2.be.a.689.25		112	100.11	odd	10
1000.2.o.a.549.18		112	8.5	even	2	inner
1000.2.o.a.549.21		112	1.1	even	1	trivial
1000.2.o.a.949.18		112	25.14	even	10	inner
1000.2.o.a.949.21		112	200.189	even	10	inner
1000.2.t.b.301.9		224	25.23	odd	20
1000.2.t.b.301.13		224	200.173	odd	20
1000.2.t.b.301.44		224	200.77	odd	20
1000.2.t.b.301.48		224	25.2	odd	20
1000.2.t.b.701.9		224	40.13	odd	4
1000.2.t.b.701.13		224	5.3	odd	4
1000.2.t.b.701.44		224	5.2	odd	4
1000.2.t.b.701.48		224	40.37	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.950798 - 1.04689i) q^{2} +(-0.853735 - 2.62753i) q^{3} +(-0.191967 - 1.99077i) q^{4} +(-3.56247 - 1.60448i) q^{6} -2.67391i q^{7} +(-2.26664 - 1.69185i) q^{8} +(-3.74798 + 2.72307i) q^{9} +(0.305554 - 0.420559i) q^{11} +(-5.06690 + 2.20399i) q^{12} +(-4.26356 + 3.09766i) q^{13} +(-2.79930 - 2.54235i) q^{14} +(-3.92630 + 0.764324i) q^{16} +(6.80346 + 2.21058i) q^{17} +(-0.712813 + 6.51282i) q^{18} +(-3.74715 - 1.21752i) q^{19} +(-7.02577 + 2.28281i) q^{21} +(-0.149760 - 0.719749i) q^{22} +(2.11996 - 2.91788i) q^{23} +(-2.51026 + 7.40004i) q^{24} +(-0.810869 + 7.40873i) q^{26} +(3.64939 + 2.65144i) q^{27} +(-5.32313 + 0.513303i) q^{28} +(3.63988 - 1.18267i) q^{29} +(2.54168 - 7.82249i) q^{31} +(-2.93295 + 4.83713i) q^{32} +(-1.36589 - 0.443805i) q^{33} +(8.78295 - 5.02068i) q^{34} +(6.14048 + 6.93861i) q^{36} +(1.62286 - 1.17908i) q^{37} +(-4.83739 + 2.76524i) q^{38} +(11.7791 + 8.55804i) q^{39} +(-5.16753 + 3.75443i) q^{41} +(-4.29023 + 9.52572i) q^{42} -5.41659 q^{43} +(-0.895891 - 0.527553i) q^{44} +(-1.03905 - 4.99369i) q^{46} +(-0.748265 + 0.243126i) q^{47} +(5.36030 + 9.66392i) q^{48} -0.149804 q^{49} -19.7635i q^{51} +(6.98517 + 7.89310i) q^{52} +(-1.71792 - 5.28721i) q^{53} +(6.24561 - 1.29954i) q^{54} +(-4.52385 + 6.06079i) q^{56} +10.8852i q^{57} +(2.22267 - 4.93505i) q^{58} +(3.67423 + 5.05715i) q^{59} +(4.51387 - 6.21281i) q^{61} +(-5.77268 - 10.0985i) q^{62} +(7.28124 + 10.0218i) q^{63} +(2.27531 + 7.66961i) q^{64} +(-1.76330 + 1.00797i) q^{66} +(-1.98087 + 6.09648i) q^{67} +(3.09470 - 13.9685i) q^{68} +(-9.47669 - 3.07916i) q^{69} +(0.885245 + 2.72450i) q^{71} +(13.1023 + 0.168797i) q^{72} +(0.839035 - 1.15483i) q^{73} +(0.308646 - 2.82003i) q^{74} +(-1.70447 + 7.69341i) q^{76} +(-1.12454 - 0.817024i) q^{77} +(20.1589 - 4.19452i) q^{78} +(-2.10919 - 6.49143i) q^{79} +(-0.443692 + 1.36554i) q^{81} +(-0.982791 + 8.97955i) q^{82} +(-0.170500 + 0.524746i) q^{83} +(5.89326 + 13.5484i) q^{84} +(-5.15008 + 5.67058i) q^{86} +(-6.21499 - 8.55421i) q^{87} +(-1.40410 + 0.436305i) q^{88} +(-11.0001 - 7.99206i) q^{89} +(8.28286 + 11.4004i) q^{91} +(-6.21578 - 3.66021i) q^{92} -22.7237 q^{93} +(-0.456922 + 1.01452i) q^{94} +(15.2136 + 3.57678i) q^{96} +(-4.85400 + 1.57716i) q^{97} +(-0.142433 + 0.156829i) q^{98} +2.40829i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36}+ \cdots - 90 q^{98}+O(q^{100}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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