LMFDB - Embedded newform 483.2.r.a.475.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			475.25
Character	$\chi$	$=$	483.475
Dual form			483.2.r.a.181.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.249170 - 1.73301i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-1.02227 - 0.300164i) q^{4} +(-0.949954 - 1.09631i) q^{5} +(0.493267 + 1.67991i) q^{6} +(2.24482 + 1.40028i) q^{7} +(0.679740 - 1.48842i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.249170 - 1.73301i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-1.02227 - 0.300164i) q^{4} +(-0.949954 - 1.09631i) q^{5} +(0.493267 + 1.67991i) q^{6} +(2.24482 + 1.40028i) q^{7} +(0.679740 - 1.48842i) q^{8} +(0.654861 - 0.755750i) q^{9} +(-2.13661 + 1.37312i) q^{10} +(4.23455 - 0.608836i) q^{11} +(1.05458 - 0.151625i) q^{12} +(0.348161 + 0.541750i) q^{13} +(2.98605 - 3.54139i) q^{14} +(1.31953 + 0.602609i) q^{15} +(-4.20267 - 2.70089i) q^{16} +(3.23495 - 0.949868i) q^{17} +(-1.14655 - 1.32319i) q^{18} +(-5.44140 - 1.59774i) q^{19} +(0.642033 + 1.40586i) q^{20} +(-2.62366 - 0.341213i) q^{21} -7.49023i q^{22} +(-3.94316 - 2.72975i) q^{23} +1.63629i q^{24} +(0.412101 - 2.86623i) q^{25} +(1.02561 - 0.468381i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(-1.87448 - 2.10528i) q^{28} +(0.971380 - 0.285223i) q^{29} +(1.37312 - 2.13661i) q^{30} +(-1.32538 - 0.605279i) q^{31} +(-3.58477 + 4.13705i) q^{32} +(-3.59896 + 2.31291i) q^{33} +(-0.840082 - 5.84290i) q^{34} +(-0.597334 - 3.79121i) q^{35} +(-0.896290 + 0.576011i) q^{36} +(4.12525 + 3.57455i) q^{37} +(-4.12473 + 9.03191i) q^{38} +(-0.541750 - 0.348161i) q^{39} +(-2.27749 + 0.668731i) q^{40} +(8.09702 - 7.01611i) q^{41} +(-1.24506 + 4.46181i) q^{42} +(0.221014 - 0.100934i) q^{43} +(-4.51158 - 0.648668i) q^{44} -1.45062 q^{45} +(-5.71320 + 6.15337i) q^{46} -9.53579i q^{47} +(4.94487 + 0.710965i) q^{48} +(3.07841 + 6.28676i) q^{49} +(-4.86453 - 1.42835i) q^{50} +(-2.54803 + 2.20788i) q^{51} +(-0.193299 - 0.658317i) q^{52} +(-3.23708 + 5.03700i) q^{53} +(1.59262 + 0.727323i) q^{54} +(-4.69010 - 4.06399i) q^{55} +(3.61011 - 2.38941i) q^{56} +(5.61339 - 0.807084i) q^{57} +(-0.252257 - 1.75448i) q^{58} +(2.73409 + 4.25433i) q^{59} +(-1.16803 - 1.01210i) q^{60} +(-3.29586 + 7.21692i) q^{61} +(-1.37920 + 2.14608i) q^{62} +(2.52831 - 0.779528i) q^{63} +(-0.266659 - 0.307740i) q^{64} +(0.263186 - 0.896329i) q^{65} +(3.11156 + 6.81336i) q^{66} +(3.82326 + 0.549702i) q^{67} -3.59210 q^{68} +(4.72080 + 0.845019i) q^{69} +(-6.71906 + 0.0905321i) q^{70} +(-2.33283 + 16.2252i) q^{71} +(-0.679740 - 1.48842i) q^{72} +(-1.52030 + 5.17765i) q^{73} +(7.22263 - 6.25845i) q^{74} +(0.815813 + 2.77841i) q^{75} +(5.08297 + 3.26662i) q^{76} +(10.3583 + 4.56285i) q^{77} +(-0.738356 + 0.852108i) q^{78} +(8.23381 + 12.8121i) q^{79} +(1.03134 + 7.17313i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-10.1415 - 15.7805i) q^{82} +(-0.871454 + 1.00571i) q^{83} +(2.57965 + 1.13634i) q^{84} +(-4.11440 - 2.64417i) q^{85} +(-0.119849 - 0.408170i) q^{86} +(-0.765112 + 0.662973i) q^{87} +(1.97219 - 6.71665i) q^{88} +(-2.86528 - 6.27410i) q^{89} +(-0.361451 + 2.51394i) q^{90} +(0.0229549 + 1.70365i) q^{91} +(3.21158 + 3.97412i) q^{92} +1.45705 q^{93} +(-16.5256 - 2.37603i) q^{94} +(3.41747 + 7.48321i) q^{95} +(1.54223 - 5.25236i) q^{96} +(4.37973 + 5.05447i) q^{97} +(11.6621 - 3.76845i) q^{98} +(2.31291 - 3.59896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{17}{22}\right)$

Coefficient data

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

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

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

$2$	0.249170	−	1.73301i	0.176190	−	1.22543i	−0.689291	−	0.724484i	$-0.742078\pi$
$2$	0.249170	−	1.73301i	0.176190	−	1.22543i	0.865481	−	0.500942i	$-0.167013\pi$
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$4$	−1.02227	−	0.300164i	−0.511133	−	0.150082i
$5$	−0.949954	−	1.09631i	−0.424832	−	0.490283i	0.502471	−	0.864594i	$-0.332425\pi$
$5$	−0.949954	−	1.09631i	−0.424832	−	0.490283i	−0.927303	+	0.374312i	$0.877879\pi$
$6$	0.493267	+	1.67991i	0.201375	+	0.685822i
$7$	2.24482	+	1.40028i	0.848461	+	0.529258i
$7$	2.24482	+	1.40028i	0.848461	+	0.529258i
$8$	0.679740	−	1.48842i	0.240324	−	0.526237i
$9$	0.654861	−	0.755750i	0.218287	−	0.251917i
$10$	−2.13661	+	1.37312i	−0.675656	+	0.434218i
$11$	4.23455	−	0.608836i	1.27676	−	0.183571i	0.529621	−	0.848234i	$-0.322334\pi$
$11$	4.23455	−	0.608836i	1.27676	−	0.183571i	0.747143	+	0.664663i	$0.231425\pi$
$12$	1.05458	−	0.151625i	0.304430	−	0.0437705i
$13$	0.348161	+	0.541750i	0.0965626	+	0.150254i	0.886174	−	0.463353i	$-0.153354\pi$
$13$	0.348161	+	0.541750i	0.0965626	+	0.150254i	−0.789611	+	0.613608i	$0.789718\pi$
$14$	2.98605	−	3.54139i	0.798056	−	0.946476i
$15$	1.31953	+	0.602609i	0.340701	+	0.155593i
$16$	−4.20267	−	2.70089i	−1.05067	−	0.675223i
$17$	3.23495	−	0.949868i	0.784592	−	0.230377i	0.135187	−	0.990820i	$-0.456836\pi$
$17$	3.23495	−	0.949868i	0.784592	−	0.230377i	0.649404	+	0.760443i	$0.275018\pi$
$18$	−1.14655	−	1.32319i	−0.270245	−	0.311879i
$19$	−5.44140	−	1.59774i	−1.24834	−	0.366546i	−0.410199	−	0.911996i	$-0.634541\pi$
$19$	−5.44140	−	1.59774i	−1.24834	−	0.366546i	−0.838143	+	0.545450i	$0.816359\pi$
$20$	0.642033	+	1.40586i	0.143563	+	0.314359i
$21$	−2.62366	−	0.341213i	−0.572529	−	0.0744588i
$22$		−	7.49023i		−	1.59692i
$23$	−3.94316	−	2.72975i	−0.822205	−	0.569192i
$23$	−3.94316	−	2.72975i	−0.822205	−	0.569192i
$24$			1.63629i			0.334007i
$25$	0.412101	−	2.86623i	0.0824203	−	0.573246i
$26$	1.02561	−	0.468381i	0.201139	−	0.0918570i
$27$	−0.281733	+	0.959493i	−0.0542195	+	0.184655i
$28$	−1.87448	−	2.10528i	−0.354244	−	0.397860i
$29$	0.971380	−	0.285223i	0.180381	−	0.0529645i	−0.190295	−	0.981727i	$-0.560944\pi$
$29$	0.971380	−	0.285223i	0.180381	−	0.0529645i	0.370675	+	0.928762i	$0.379126\pi$
$30$	1.37312	−	2.13661i	0.250696	−	0.390090i
$31$	−1.32538	−	0.605279i	−0.238044	−	0.108711i	0.292821	−	0.956167i	$-0.405406\pi$
$31$	−1.32538	−	0.605279i	−0.238044	−	0.108711i	−0.530866	+	0.847456i	$0.678133\pi$
$32$	−3.58477	+	4.13705i	−0.633704	+	0.731334i
$33$	−3.59896	+	2.31291i	−0.626499	+	0.402626i
$34$	−0.840082	−	5.84290i	−0.144073	−	1.00205i
$35$	−0.597334	−	3.79121i	−0.100968	−	0.640832i
$36$	−0.896290	+	0.576011i	−0.149382	+	0.0960018i
$37$	4.12525	+	3.57455i	0.678187	+	0.587653i	0.924336	−	0.381580i	$-0.124620\pi$
$37$	4.12525	+	3.57455i	0.678187	+	0.587653i	−0.246149	+	0.969232i	$0.579165\pi$
$38$	−4.12473	+	9.03191i	−0.669120	+	1.46517i
$39$	−0.541750	−	0.348161i	−0.0867494	−	0.0557504i
$40$	−2.27749	+	0.668731i	−0.360102	+	0.105736i
$41$	8.09702	−	7.01611i	1.26454	−	1.09573i	0.273544	−	0.961860i	$-0.411804\pi$
$41$	8.09702	−	7.01611i	1.26454	−	1.09573i	0.990999	−	0.133873i	$-0.0427414\pi$
$42$	−1.24506	+	4.46181i	−0.192117	+	0.688473i
$43$	0.221014	−	0.100934i	0.0337043	−	0.0153922i	−0.398492	−	0.917172i	$-0.630466\pi$
$43$	0.221014	−	0.100934i	0.0337043	−	0.0153922i	0.432196	+	0.901780i	$0.357739\pi$
$44$	−4.51158	−	0.648668i	−0.680147	−	0.0977903i
$45$	−1.45062			−0.216246
$46$	−5.71320	+	6.15337i	−0.842366	+	0.907266i
$47$		−	9.53579i		−	1.39094i	−0.718556	−	0.695469i	$-0.755197\pi$
$47$		−	9.53579i		−	1.39094i	0.718556	−	0.695469i	$-0.244803\pi$
$48$	4.94487	+	0.710965i	0.713731	+	0.102619i
$49$	3.07841	+	6.28676i	0.439772	+	0.898109i
$50$	−4.86453	−	1.42835i	−0.687948	−	0.202000i
$51$	−2.54803	+	2.20788i	−0.356795	+	0.309165i
$52$	−0.193299	−	0.658317i	−0.0268058	−	0.0912922i
$53$	−3.23708	+	5.03700i	−0.444648	+	0.691885i	−0.989156	−	0.146870i	$-0.953080\pi$
$53$	−3.23708	+	5.03700i	−0.444648	+	0.691885i	0.544508	+	0.838756i	$0.316716\pi$
$54$	1.59262	+	0.727323i	0.216727	+	0.0989761i
$55$	−4.69010	−	4.06399i	−0.632412	−	0.547988i
$56$	3.61011	−	2.38941i	0.482421	−	0.319298i
$57$	5.61339	−	0.807084i	0.743512	−	0.106901i
$58$	−0.252257	−	1.75448i	−0.0331229	−	0.230375i
$59$	2.73409	+	4.25433i	0.355948	+	0.553866i	0.972339	−	0.233574i	$-0.0750422\pi$
$59$	2.73409	+	4.25433i	0.355948	+	0.553866i	−0.616391	+	0.787440i	$0.711406\pi$
$60$	−1.16803	−	1.01210i	−0.150792	−	0.130662i
$61$	−3.29586	+	7.21692i	−0.421991	+	0.924032i	0.572568	+	0.819857i	$0.305947\pi$
$61$	−3.29586	+	7.21692i	−0.421991	+	0.924032i	−0.994559	+	0.104174i	$0.966780\pi$
$62$	−1.37920	+	2.14608i	−0.175159	+	0.272552i
$63$	2.52831	−	0.779528i	0.318537	−	0.0982113i
$64$	−0.266659	−	0.307740i	−0.0333323	−	0.0384676i
$65$	0.263186	−	0.896329i	0.0326442	−	0.111176i
$66$	3.11156	+	6.81336i	0.383006	+	0.838666i
$67$	3.82326	+	0.549702i	0.467086	+	0.0671568i	0.371840	−	0.928297i	$-0.378727\pi$
$67$	3.82326	+	0.549702i	0.467086	+	0.0671568i	0.0952461	+	0.995454i	$0.469636\pi$
$68$	−3.59210			−0.435606
$69$	4.72080	+	0.845019i	0.568317	+	0.101728i
$70$	−6.71906	+	0.0905321i	−0.803081	+	0.0108207i
$71$	−2.33283	+	16.2252i	−0.276856	+	1.92558i	0.0913169	+	0.995822i	$0.470892\pi$
$71$	−2.33283	+	16.2252i	−0.276856	+	1.92558i	−0.368173	+	0.929757i	$0.620017\pi$
$72$	−0.679740	−	1.48842i	−0.0801081	−	0.175412i
$73$	−1.52030	+	5.17765i	−0.177937	+	0.605998i	0.821426	+	0.570315i	$0.193179\pi$
$73$	−1.52030	+	5.17765i	−0.177937	+	0.605998i	−0.999363	+	0.0356831i	$0.988639\pi$
$74$	7.22263	−	6.25845i	0.839614	−	0.727530i
$75$	0.815813	+	2.77841i	0.0942020	+	0.320823i
$76$	5.08297	+	3.26662i	0.583056	+	0.374708i
$77$	10.3583	+	4.56285i	1.18044	+	0.519985i
$78$	−0.738356	+	0.852108i	−0.0836024	+	0.0964823i
$79$	8.23381	+	12.8121i	0.926375	+	1.44147i	0.897065	+	0.441898i	$0.145695\pi$
$79$	8.23381	+	12.8121i	0.926375	+	1.44147i	0.0293101	+	0.999570i	$0.490669\pi$
$80$	1.03134	+	7.17313i	0.115307	+	0.801980i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−10.1415	−	15.7805i	−1.11994	−	1.74266i
$83$	−0.871454	+	1.00571i	−0.0956545	+	0.110391i	−0.801559	−	0.597916i	$-0.795996\pi$
$83$	−0.871454	+	1.00571i	−0.0956545	+	0.110391i	0.705904	+	0.708307i	$0.250541\pi$
$84$	2.57965	+	1.13634i	0.281463	+	0.123985i
$85$	−4.11440	−	2.64417i	−0.446270	−	0.286800i
$86$	−0.119849	−	0.408170i	−0.0129237	−	0.0440141i
$87$	−0.765112	+	0.662973i	−0.0820286	+	0.0710782i
$88$	1.97219	−	6.71665i	0.210236	−	0.715997i
$89$	−2.86528	−	6.27410i	−0.303720	−	0.665053i	0.694814	−	0.719190i	$-0.255487\pi$
$89$	−2.86528	−	6.27410i	−0.303720	−	0.665053i	−0.998534	+	0.0541364i	$0.982759\pi$
$90$	−0.361451	+	2.51394i	−0.0381002	+	0.264993i
$91$	0.0229549	+	1.70365i	0.00240633	+	0.178591i
$92$	3.21158	+	3.97412i	0.334830	+	0.414331i
$93$	1.45705			0.151089
$94$	−16.5256	−	2.37603i	−1.70449	−	0.245069i
$95$	3.41747	+	7.48321i	0.350625	+	0.767761i
$96$	1.54223	−	5.25236i	0.157403	−	0.536067i
$97$	4.37973	+	5.05447i	0.444694	+	0.513204i	0.933201	−	0.359356i	$-0.117004\pi$
$97$	4.37973	+	5.05447i	0.444694	+	0.513204i	−0.488507	+	0.872560i	$0.662458\pi$
$98$	11.6621	−	3.76845i	1.17805	−	0.380671i
$99$	2.31291	−	3.59896i	0.232456	−	0.361709i
$100$	−1.28162	+	2.80635i	−0.128162	+	0.280635i
$101$	−1.08927	−	0.943854i	−0.108386	−	0.0939170i	0.598982	−	0.800763i	$-0.295572\pi$
$101$	−1.08927	−	0.943854i	−0.108386	−	0.0939170i	−0.707368	+	0.706846i	$0.750118\pi$
$102$	3.19139	+	4.96590i	0.315995	+	0.491698i
$103$	−1.95676	−	13.6096i	−0.192805	−	1.34099i	−0.824539	−	0.565805i	$-0.808566\pi$
$103$	−1.95676	−	13.6096i	−0.192805	−	1.34099i	0.631734	−	0.775185i	$-0.282343\pi$
$104$	1.04301	−	0.149962i	0.102276	−	0.0147050i
$105$	2.11828	+	3.20047i	0.206723	+	0.312333i
$106$	7.92261	+	6.86498i	0.769512	+	0.666786i
$107$	1.11810	+	0.510620i	0.108091	+	0.0493635i	0.468727	−	0.883343i	$-0.344713\pi$
$107$	1.11810	+	0.510620i	0.108091	+	0.0493635i	−0.360636	+	0.932707i	$0.617440\pi$
$108$	0.576011	−	0.896290i	0.0554267	−	0.0862456i
$109$	−1.00860	−	3.43499i	−0.0966067	−	0.329012i	0.896982	−	0.442067i	$-0.145755\pi$
$109$	−1.00860	−	3.43499i	−0.0966067	−	0.329012i	−0.993589	+	0.113055i	$0.963936\pi$
$110$	−8.21158	+	7.11538i	−0.782944	+	0.678425i
$111$	−5.23738	−	1.53783i	−0.497110	−	0.145965i
$112$	−5.65220	−	11.9479i	−0.534083	−	1.12897i
$113$	−3.65192	−	0.525067i	−0.343544	−	0.0493941i	−0.0316163	−	0.999500i	$-0.510065\pi$
$113$	−3.65192	−	0.525067i	−0.343544	−	0.0493941i	−0.311927	+	0.950106i	$0.600975\pi$
$114$		−	9.92919i		−	0.929954i
$115$	0.753181	+	6.91604i	0.0702345	+	0.644924i
$116$	−1.07862			−0.100147
$117$	0.637424	+	0.0916478i	0.0589299	+	0.00847284i
$118$	8.05406	−	3.67817i	0.741436	−	0.338603i
$119$	8.59196	+	2.39758i	0.787624	+	0.219785i
$120$	1.79387	−	1.55440i	0.163758	−	0.141897i
$121$	7.00629	−	2.05723i	0.636936	−	0.187021i
$122$	11.6858	+	7.51000i	1.05798	+	0.679924i
$123$	−4.45071	+	9.74570i	−0.401307	+	0.878740i
$124$	1.17320	+	1.01659i	0.105357	+	0.0912921i
$125$	−9.63543	+	6.19232i	−0.861819	+	0.553858i
$126$	−0.720955	−	4.57583i	−0.0642278	−	0.407647i
$127$	−0.951892	−	6.62056i	−0.0844668	−	0.587479i	−0.987465	−	0.157836i	$-0.949548\pi$
$127$	−0.951892	−	6.62056i	−0.0844668	−	0.587479i	0.902999	−	0.429644i	$-0.141361\pi$
$128$	−9.80997	+	6.30448i	−0.867087	+	0.557243i
$129$	−0.159112	+	0.183625i	−0.0140090	+	0.0161673i
$130$	−1.48777	−	0.679443i	−0.130486	−	0.0595911i
$131$	−4.88667	+	7.60380i	−0.426950	+	0.664347i	−0.986371	−	0.164537i	$-0.947387\pi$
$131$	−4.88667	+	7.60380i	−0.426950	+	0.664347i	0.559421	+	0.828884i	$0.311024\pi$
$132$	4.37335	−	1.28413i	0.380651	−	0.111769i
$133$	−9.97765	−	11.2061i	−0.865172	−	0.971695i
$134$	1.90528	−	6.48880i	0.164591	−	0.560547i
$135$	1.31953	−	0.602609i	0.113567	−	0.0518644i
$136$	0.785122	−	5.46064i	0.0673236	−	0.468246i
$137$		−	11.5105i		−	0.983405i	−0.870763	−	0.491703i	$-0.836375\pi$
$137$		−	11.5105i		−	0.983405i	0.870763	−	0.491703i	$-0.163625\pi$
$138$	2.64071	−	7.97066i	0.224792	−	0.678507i
$139$			18.7004i			1.58614i	0.609128	+	0.793072i	$0.291520\pi$
$139$			18.7004i			1.58614i	−0.609128	+	0.793072i	$0.708480\pi$
$140$	−0.527352	+	4.05492i	−0.0445694	+	0.342703i
$141$	3.96131	+	8.67406i	0.333602	+	0.730487i
$142$	27.5373	+	8.08567i	2.31087	+	0.678534i
$143$	1.80414	+	2.08209i	0.150870	+	0.174113i
$144$	−4.79336	+	1.40746i	−0.399447	+	0.117288i
$145$	−1.23546	−	0.793980i	−0.102599	−	0.0659365i
$146$	8.59413	+	3.92481i	0.711255	+	0.324819i
$147$	−5.41183	−	4.43983i	−0.446361	−	0.366191i
$148$	−3.14415	−	4.89239i	−0.258447	−	0.402152i
$149$	20.5609	−	2.95622i	1.68442	−	0.242183i	0.767440	−	0.641121i	$-0.221530\pi$
$149$	20.5609	−	2.95622i	1.68442	−	0.242183i	0.916978	+	0.398938i	$0.130621\pi$
$150$	5.01829	−	0.721521i	0.409742	−	0.0589120i
$151$	−18.9904	+	12.2044i	−1.54542	+	0.993178i	−0.558951	+	0.829201i	$0.688796\pi$
$151$	−18.9904	+	12.2044i	−1.54542	+	0.993178i	−0.986464	+	0.163977i	$0.947568\pi$
$152$	−6.07684	+	7.01305i	−0.492897	+	0.568834i
$153$	1.40058	−	3.06685i	0.113230	−	0.247940i
$154$	10.4885	−	16.8142i	0.845184	−	1.35493i
$155$	0.595475	+	2.02800i	0.0478297	+	0.162893i
$156$	0.449306	+	0.518527i	0.0359733	+	0.0415154i
$157$	17.6017	+	5.16833i	1.40477	+	0.412478i	0.894320	−	0.447429i	$-0.147660\pi$
$157$	17.6017	+	5.16833i	1.40477	+	0.412478i	0.510451	+	0.859907i	$0.329478\pi$
$158$	24.2551	−	11.0769i	1.92963	−	0.881233i
$159$	0.852109	−	5.92655i	0.0675767	−	0.470006i
$160$	7.94084			0.627778
$161$	−5.02924	−	11.6493i	−0.396360	−	0.918095i
$162$	−1.75083			−0.137559
$163$	−1.96677	+	13.6792i	−0.154050	+	1.07144i	0.755292	+	0.655389i	$0.227495\pi$
$163$	−1.96677	+	13.6792i	−0.154050	+	1.07144i	−0.909342	+	0.416050i	$0.863414\pi$
$164$	−10.3833	+	4.74189i	−0.810799	+	0.370279i
$165$	5.95450	+	1.74840i	0.463558	+	0.136113i
$166$	1.52577	+	1.76083i	0.118423	+	0.136667i
$167$	0.775195	+	2.64007i	0.0599864	+	0.204295i	0.984033	−	0.177984i	$-0.0569575\pi$
$167$	0.775195	+	2.64007i	0.0599864	+	0.204295i	−0.924047	+	0.382279i	$0.875139\pi$
$168$	−2.29127	+	3.67317i	−0.176776	+	0.283392i
$169$	5.22812	−	11.4480i	0.402163	−	0.880614i
$170$	−5.60756	+	6.47147i	−0.430080	+	0.496339i
$171$	−4.77085	+	3.06604i	−0.364836	+	0.234466i
$172$	−0.256232	+	0.0368405i	−0.0195375	+	0.00280906i
$173$	0.976571	−	0.140410i	0.0742474	−	0.0106752i	−0.105091	−	0.994463i	$-0.533513\pi$
$173$	0.976571	−	0.140410i	0.0742474	−	0.0106752i	0.179338	+	0.983787i	$0.442604\pi$
$174$	0.958299	+	1.49114i	0.0726485	+	0.113043i
$175$	4.93863	−	5.85710i	0.373325	−	0.442755i
$176$	−19.4408	−	8.87831i	−1.46540	−	0.669228i
$177$	−4.25433	−	2.73409i	−0.319775	−	0.205507i
$178$	−11.5870	+	3.40226i	−0.868486	+	0.255010i
$179$	0.839105	+	0.968379i	0.0627177	+	0.0723801i	0.786241	−	0.617919i	$-0.212024\pi$
$179$	0.839105	+	0.968379i	0.0627177	+	0.0723801i	−0.723524	+	0.690300i	$0.757479\pi$
$180$	1.48292	+	0.435424i	0.110530	+	0.0324546i
$181$	−4.35709	−	9.54069i	−0.323860	−	0.709154i	0.675749	−	0.737132i	$-0.263820\pi$
$181$	−4.35709	−	9.54069i	−0.323860	−	0.709154i	−0.999609	+	0.0279780i	$0.991093\pi$
$182$	2.95818	+	0.384718i	0.219275	+	0.0285172i
$183$		−	7.93389i		−	0.586490i
$184$	−6.74334	+	4.01357i	−0.497125	+	0.295884i
$185$		−	7.91819i		−	0.582157i
$186$	0.363052	−	2.52508i	0.0266202	−	0.185148i
$187$	13.1203	−	5.99182i	0.959448	−	0.438165i
$188$	−2.86230	+	9.74810i	−0.208755	+	0.710953i
$189$	−1.97600	+	1.75938i	−0.143733	+	0.127976i
$190$	13.8200	−	4.05793i	1.00261	−	0.294393i
$191$	−7.12396	+	11.0851i	−0.515472	+	0.802090i	−0.997243	−	0.0742075i	$-0.976357\pi$
$191$	−7.12396	+	11.0851i	−0.515472	+	0.802090i	0.481771	+	0.876297i	$0.339994\pi$
$192$	0.370401	+	0.169157i	0.0267314	+	0.0122078i
$193$	−2.56259	+	2.95739i	−0.184459	+	0.212877i	−0.840446	−	0.541895i	$-0.817707\pi$
$193$	−2.56259	+	2.95739i	−0.184459	+	0.212877i	0.655987	+	0.754772i	$0.272253\pi$
$194$	9.85077	−	6.33070i	0.707244	−	0.454518i
$195$	0.132946	+	0.924660i	0.00952047	+	0.0662163i
$196$	−1.25989	−	7.35077i	−0.0899919	−	0.525055i
$197$	−18.9842	+	12.2004i	−1.35257	+	0.869244i	−0.997838	−	0.0657247i	$-0.979064\pi$
$197$	−18.9842	+	12.2004i	−1.35257	+	0.869244i	−0.354732	+	0.934968i	$0.615428\pi$
$198$	−5.66074	−	4.90506i	−0.402291	−	0.348587i
$199$	−2.24844	+	4.92341i	−0.159388	+	0.349011i	−0.972430	−	0.233193i	$-0.925082\pi$
$199$	−2.24844	+	4.92341i	−0.159388	+	0.349011i	0.813042	+	0.582205i	$0.197810\pi$
$200$	−3.98604	−	2.56167i	−0.281855	−	0.181137i
$201$	−3.70612	+	1.08821i	−0.261409	+	0.0767567i
$202$	−1.90712	+	1.65253i	−0.134185	+	0.116272i
$203$	2.57996	+	0.719935i	0.181078	+	0.0505295i
$204$	3.26749	−	1.49221i	0.228770	−	0.104476i
$205$	−15.3836	−	2.21183i	−1.07444	−	0.154481i
$206$	−24.0731			−1.67725
$207$	−4.64522	+	1.19243i	−0.322865	+	0.0828800i
$208$		−	3.21714i		−	0.223068i
$209$	−24.0146	−	3.45278i	−1.66113	−	0.238834i
$210$	6.07426	−	2.87355i	0.419164	−	0.198294i
$211$	12.1292	+	3.56145i	0.835008	+	0.245180i	0.671167	−	0.741306i	$-0.265793\pi$
$211$	12.1292	+	3.56145i	0.835008	+	0.245180i	0.163841	+	0.986487i	$0.447612\pi$
$212$	4.82109	−	4.17749i	0.331114	−	0.286912i
$213$	−4.61818	−	15.7281i	−0.316432	−	1.07767i
$214$	1.16351	−	1.81045i	0.0795357	−	0.123760i
$215$	−0.320607	−	0.146416i	−0.0218652	−	0.00998552i
$216$	1.23663	+	1.07154i	0.0841418	+	0.0729093i
$217$	−2.12766	−	3.21464i	−0.144435	−	0.218224i
$218$	−6.20419	+	0.892028i	−0.420201	+	0.0604158i
$219$	−0.767965	−	5.34131i	−0.0518942	−	0.360932i
$220$	3.57466	+	5.56228i	0.241003	+	0.375009i
$221$	1.64088	+	1.42183i	0.110377	+	0.0956425i
$222$	−3.97009	+	8.69327i	−0.266455	+	0.583454i
$223$	−11.3708	+	17.6933i	−0.761443	+	1.18483i	0.216567	+	0.976268i	$0.430514\pi$
$223$	−11.3708	+	17.6933i	−0.761443	+	1.18483i	−0.978009	+	0.208560i	$0.933122\pi$
$224$	−13.8402	+	4.26721i	−0.924737	+	0.285115i
$225$	−1.89628	−	2.18843i	−0.126419	−	0.145895i
$226$	−1.81990	+	6.19800i	−0.121058	+	0.412285i
$227$	4.14413	+	9.07438i	0.275056	+	0.602288i	0.995865	−	0.0908455i	$-0.0289570\pi$
$227$	4.14413	+	9.07438i	0.275056	+	0.602288i	−0.720809	+	0.693133i	$0.756230\pi$
$228$	−5.98063	−	0.859885i	−0.396077	−	0.0569473i
$229$	7.24148			0.478531			0.239265	−	0.970954i	$-0.423093\pi$
$229$	7.24148			0.478531			0.239265	+	0.970954i	$0.423093\pi$
$230$	12.1733	+	0.417994i	0.802681	+	0.0275617i
$231$	−11.3177	+	0.152494i	−0.744653	+	0.0100334i
$232$	0.235753	−	1.63970i	0.0154780	−	0.107652i
$233$	−11.2999	−	24.7434i	−0.740283	−	1.62099i	−0.783088	−	0.621911i	$-0.786357\pi$
$233$	−11.2999	−	24.7434i	−0.740283	−	1.62099i	0.0428051	−	0.999083i	$-0.486371\pi$
$234$	0.317654	−	1.08183i	0.0207657	−	0.0707214i
$235$	−10.4541	+	9.05856i	−0.681952	+	0.590915i
$236$	−1.51797	−	5.16973i	−0.0988113	−	0.336521i
$237$	−12.8121	−	8.23381i	−0.832232	−	0.534843i
$238$	6.29589	−	14.2926i	0.408102	−	0.926451i
$239$	−16.3445	+	18.8626i	−1.05724	+	1.22012i	−0.0825432	+	0.996587i	$0.526304\pi$
$239$	−16.3445	+	18.8626i	−1.05724	+	1.22012i	−0.974697	+	0.223532i	$0.928241\pi$
$240$	−3.91797	−	6.09647i	−0.252904	−	0.393526i
$241$	2.65362	+	18.4564i	0.170935	+	1.18888i	0.876915	+	0.480646i	$0.159598\pi$
$241$	2.65362	+	18.4564i	0.170935	+	1.18888i	−0.705980	+	0.708232i	$0.749493\pi$
$242$	−1.81946	−	12.6546i	−0.116959	−	0.813468i
$243$	0.540641	+	0.841254i	0.0346821	+	0.0539664i
$244$	5.53550	−	6.38831i	0.354374	−	0.408969i
$245$	3.96787	−	9.34701i	0.253498	−	0.597159i
$246$	15.7805	+	10.1415i	1.00613	+	0.646597i
$247$	−1.02891	−	3.50415i	−0.0654680	−	0.222963i
$248$	−1.80182	+	1.56129i	−0.114416	+	0.0991418i
$249$	0.374915	−	1.27684i	0.0237593	−	0.0809166i
$250$	8.33051	+	18.2413i	0.526868	+	1.15368i
$251$	−2.08156	+	14.4776i	−0.131387	+	0.913818i	0.812362	+	0.583154i	$0.198182\pi$
$251$	−2.08156	+	14.4776i	−0.131387	+	0.913818i	−0.943749	+	0.330664i	$0.892727\pi$
$252$	−2.81859	+	0.0379774i	−0.177554	+	0.00239235i
$253$	−18.3595	−	9.15851i	−1.15425	−	0.575790i
$254$	−11.7107			−0.734795
$255$	4.84102	+	0.696033i	0.303156	+	0.0435873i
$256$	8.14310	+	17.8309i	0.508944	+	1.11443i
$257$	8.13365	−	27.7007i	0.507363	−	1.72792i	−0.163692	−	0.986512i	$-0.552340\pi$
$257$	8.13365	−	27.7007i	0.507363	−	1.72792i	0.671055	−	0.741408i	$-0.265842\pi$
$258$	0.278579	+	0.321497i	0.0173436	+	0.0200155i
$259$	4.25505	+	13.8007i	0.264396	+	0.857536i
$260$	−0.538091	+	0.837287i	−0.0333710	+	0.0519263i
$261$	0.420561	−	0.920901i	0.0260321	−	0.0570023i
$262$	11.9599	+	10.3633i	0.738884	+	0.640247i
$263$	−11.3145	−	17.6058i	−0.697685	−	1.08562i	−0.991544	−	0.129770i	$-0.958576\pi$
$263$	−11.3145	−	17.6058i	−0.697685	−	1.08562i	0.293860	−	0.955849i	$-0.405060\pi$
$264$	0.996233	+	6.92895i	0.0613139	+	0.426448i
$265$	8.59717	−	1.23609i	0.528120	−	0.0759322i
$266$	−21.9065	+	14.4992i	−1.34317	+	0.889002i
$267$	5.21271	+	4.51684i	0.319013	+	0.276426i
$268$	−3.74339	−	1.70955i	−0.228664	−	0.104427i
$269$	−4.10146	+	6.38200i	−0.250070	+	0.389117i	−0.943482	−	0.331425i	$-0.892471\pi$
$269$	−4.10146	+	6.38200i	−0.250070	+	0.389117i	0.693411	+	0.720542i	$0.256107\pi$
$270$	−0.715543	−	2.43692i	−0.0435466	−	0.148306i
$271$	8.25140	−	7.14987i	0.501237	−	0.434324i	−0.367187	−	0.930147i	$-0.619679\pi$
$271$	8.25140	−	7.14987i	0.501237	−	0.434324i	0.868423	+	0.495823i	$0.165134\pi$
$272$	−16.1609	−	4.74528i	−0.979900	−	0.287725i
$273$	−0.728604	−	1.54016i	−0.0440971	−	0.0932149i
$274$	−19.9478	−	2.86806i	−1.20509	−	0.173266i
$275$		−	12.3881i		−	0.747029i
$276$	−4.57226	−	2.28085i	−0.275218	−	0.137291i
$277$	7.36924			0.442774			0.221387	−	0.975186i	$-0.428942\pi$
$277$	7.36924			0.442774			0.221387	+	0.975186i	$0.428942\pi$
$278$	32.4080	+	4.65956i	1.94370	+	0.279462i
$279$	−1.32538	+	0.605279i	−0.0793481	+	0.0362371i
$280$	−6.04896	−	1.68795i	−0.361494	−	0.100874i
$281$	−2.23160	+	1.93369i	−0.133126	+	0.115354i	−0.718879	−	0.695135i	$-0.755344\pi$
$281$	−2.23160	+	1.93369i	−0.133126	+	0.115354i	0.585753	+	0.810490i	$0.300799\pi$
$282$	16.0193	−	4.70369i	0.953935	−	0.280101i
$283$	−11.9621	−	7.68757i	−0.711073	−	0.456979i	0.134448	−	0.990921i	$-0.457074\pi$
$283$	−11.9621	−	7.68757i	−0.711073	−	0.456979i	−0.845521	+	0.533942i	$0.820710\pi$
$284$	7.25500	−	15.8862i	0.430505	−	0.942675i
$285$	−6.21728	−	5.38730i	−0.368280	−	0.319116i
$286$	4.05783	−	2.60781i	0.239945	−	0.154203i
$287$	28.0009	−	4.41175i	1.65284	−	0.260417i
$288$	0.779045	+	5.41838i	0.0459057	+	0.319281i
$289$	−4.73863	+	3.04534i	−0.278743	+	0.179137i
$290$	−1.68382	+	1.94323i	−0.0988772	+	0.114110i
$291$	−6.08364	−	2.77831i	−0.356629	−	0.162867i
$292$	3.10829	−	4.83659i	0.181899	−	0.283040i
$293$	8.38257	−	2.46134i	0.489715	−	0.143793i	−0.0275468	−	0.999621i	$-0.508770\pi$
$293$	8.38257	−	2.46134i	0.489715	−	0.143793i	0.517262	+	0.855827i	$0.326951\pi$
$294$	−9.04275	+	8.27251i	−0.527384	+	0.482463i
$295$	2.06678	−	7.03881i	0.120333	−	0.409816i
$296$	8.12454	−	3.71035i	0.472229	−	0.215660i
$297$	−0.608836	+	4.23455i	−0.0353283	+	0.245713i
$298$		−	36.3690i		−	2.10680i
$299$	0.105985	−	3.08660i	0.00612925	−	0.178502i
$300$		−	3.08515i		−	0.178121i
$301$	0.637472	+	0.0829047i	0.0367433	+	0.00477855i
$302$	16.4185	+	35.9515i	0.944780	+	2.06878i
$303$	1.38292	+	0.406063i	0.0794468	+	0.0233277i
$304$	18.5531	+	21.4114i	1.06409	+	1.22803i
$305$	11.0429	−	3.24248i	0.632312	−	0.185664i
$306$	−4.96590	−	3.19139i	−0.283882	−	0.182440i
$307$	−14.0136	−	6.39978i	−0.799796	−	0.365254i	−0.0267800	−	0.999641i	$-0.508525\pi$
$307$	−14.0136	−	6.39978i	−0.799796	−	0.365254i	−0.773016	+	0.634387i	$0.781253\pi$
$308$	−9.21936	−	7.77364i	−0.525322	−	0.442944i
$309$	7.43355	+	11.5668i	0.422880	+	0.658014i
$310$	3.66293	−	0.526650i	0.208041	−	0.0299117i
$311$	25.9383	−	3.72936i	1.47082	−	0.211473i	0.640158	−	0.768243i	$-0.278869\pi$
$311$	25.9383	−	3.72936i	1.47082	−	0.211473i	0.830666	+	0.556770i	$0.187960\pi$
$312$	−0.886460	+	0.569693i	−0.0501859	+	0.0322525i
$313$	3.80853	−	4.39528i	0.215271	−	0.248436i	−0.637836	−	0.770172i	$-0.720170\pi$
$313$	3.80853	−	4.39528i	0.215271	−	0.248436i	0.853107	+	0.521737i	$0.174716\pi$
$314$	13.3426	−	29.2162i	0.752967	−	1.64877i
$315$	−3.25638	−	2.03128i	−0.183476	−	0.114450i
$316$	−4.57141	−	15.5688i	−0.257162	−	0.875814i
$317$	−7.73726	−	8.92928i	−0.434568	−	0.501518i	0.495652	−	0.868521i	$-0.334929\pi$
$317$	−7.73726	−	8.92928i	−0.434568	−	0.501518i	−0.930220	+	0.367003i	$0.880384\pi$
$318$	−10.0585	−	2.95343i	−0.564051	−	0.165620i
$319$	3.93970	−	1.79920i	0.220581	−	0.100736i
$320$	−0.0840641	+	0.584679i	−0.00469933	+	0.0326845i
$321$	−1.22918			−0.0686061
$322$	−21.4416	+	5.81309i	−1.19489	+	0.323951i
$323$	−19.1203			−1.06388
$324$	−0.151625	+	1.05458i	−0.00842363	+	0.0585877i
$325$	1.69626	−	0.774654i	0.0940913	−	0.0429701i
$326$	23.2162	+	6.81689i	1.28583	+	0.377553i
$327$	2.34440	+	2.70559i	0.129646	+	0.149619i
$328$	−4.93907	−	16.8209i	−0.272714	−	0.928780i
$329$	13.3528	−	21.4061i	0.736164	−	1.18016i
$330$	4.51368	−	9.88359i	0.248470	−	0.544074i
$331$	−8.30520	+	9.58472i	−0.456495	+	0.526824i	−0.936606	−	0.350384i	$-0.886051\pi$
$331$	−8.30520	+	9.58472i	−0.456495	+	0.526824i	0.480111	+	0.877208i	$0.340596\pi$
$332$	1.19274	−	0.766524i	0.0654599	−	0.0420685i
$333$	5.40293	−	0.776824i	0.296079	−	0.0425697i
$334$	4.76844	−	0.685598i	0.260917	−	0.0375142i
$335$	−3.02928	−	4.71365i	−0.165507	−	0.257534i
$336$	10.1048	+	8.52021i	0.551261	+	0.464816i
$337$	−0.976839	−	0.446108i	−0.0532118	−	0.0243010i	0.388631	−	0.921393i	$-0.372948\pi$
$337$	−0.976839	−	0.446108i	−0.0532118	−	0.0243010i	−0.441843	+	0.897092i	$0.645675\pi$
$338$	−18.5368	−	11.9129i	−1.00827	−	0.647976i
$339$	3.54002	−	1.03944i	0.192268	−	0.0564549i
$340$	3.41233	+	3.93804i	0.185059	+	0.213570i
$341$	−5.98088	−	1.75614i	−0.323883	−	0.0951006i
$342$	4.12473	+	9.03191i	0.223040	+	0.488390i
$343$	−1.89280	+	18.4233i	−0.102202	+	0.994764i
$344$		−	0.397571i		−	0.0214356i
$345$	−3.55814	−	5.97817i	−0.191564	−	0.321854i
$346$		−	1.72740i		−	0.0928655i
$347$	0.764596	−	5.31788i	0.0410456	−	0.285479i	−0.958953	−	0.283567i	$-0.908482\pi$
$347$	0.764596	−	5.31788i	0.0410456	−	0.285479i	0.999998	−	0.00191205i	$-0.000608626\pi$
$348$	0.981148	−	0.448075i	0.0525951	−	0.0240194i
$349$	−8.55513	+	29.1361i	−0.457946	+	1.55962i	0.330065	+	0.943958i	$0.392929\pi$
$349$	−8.55513	+	29.1361i	−0.457946	+	1.55962i	−0.788011	+	0.615661i	$0.788889\pi$
$350$	−8.91987	−	10.0181i	−0.476787	−	0.535491i
$351$	−0.617893	+	0.181430i	−0.0329807	+	0.00968401i
$352$	−12.6611	+	19.7011i	−0.674839	+	1.05007i
$353$	−0.709932	−	0.324215i	−0.0377859	−	0.0172562i	0.396432	−	0.918064i	$-0.370248\pi$
$353$	−0.709932	−	0.324215i	−0.0377859	−	0.0172562i	−0.434218	+	0.900808i	$0.642975\pi$
$354$	−5.79827	+	6.69156i	−0.308174	+	0.355652i
$355$	20.0039	−	12.8557i	1.06170	−	0.682310i
$356$	1.04582	+	7.27385i	0.0554284	+	0.385513i
$357$	−8.81151	+	1.38832i	−0.466355	+	0.0734777i
$358$	1.88729	−	1.21289i	0.0997466	−	0.0641033i
$359$	16.3227	+	14.1437i	0.861479	+	0.746476i	0.968825	−	0.247746i	$-0.0796898\pi$
$359$	16.3227	+	14.1437i	0.861479	+	0.746476i	−0.107346	+	0.994222i	$0.534235\pi$
$360$	−0.986044	+	2.15914i	−0.0519691	+	0.113796i
$361$	11.0722	+	7.11568i	0.582748	+	0.374509i
$362$	−17.6198	+	5.17364i	−0.926076	+	0.271921i
$363$	−5.51854	+	4.78184i	−0.289648	+	0.250982i
$364$	0.487910	−	1.74848i	0.0255734	−	0.0916451i
$365$	7.12050	−	3.25182i	0.372704	−	0.170208i
$366$	−13.7495	−	1.97689i	−0.718700	−	0.103333i
$367$	22.8047			1.19040			0.595198	−	0.803579i	$-0.297074\pi$
$367$	22.8047			1.19040			0.595198	+	0.803579i	$0.297074\pi$
$368$	9.19903	+	22.1222i	0.479532	+	1.15320i
$369$		−	10.7139i		−	0.557743i
$370$	−13.7223	−	1.97297i	−0.713390	−	0.102570i
$371$	−14.3199	+	6.77431i	−0.743452	+	0.351705i
$372$	−1.48949	−	0.437353i	−0.0772263	−	0.0226757i
$373$	21.0360	−	18.2278i	1.08920	−	0.943799i	0.0905602	−	0.995891i	$-0.471134\pi$
$373$	21.0360	−	18.2278i	1.08920	−	0.943799i	0.998642	+	0.0520916i	$0.0165888\pi$
$374$	−7.11473	−	24.2306i	−0.367894	−	1.25293i
$375$	6.19232	−	9.63543i	0.319770	−	0.497572i
$376$	−14.1933	−	6.48185i	−0.731963	−	0.334276i
$377$	0.492716	+	0.426941i	0.0253762	+	0.0219886i
$378$	2.55667	+	3.86282i	0.131501	+	0.198682i
$379$	33.8906	−	4.87273i	1.74084	−	0.250295i	0.802659	−	0.596438i	$-0.203418\pi$
$379$	33.8906	−	4.87273i	1.74084	−	0.250295i	0.938182	+	0.346143i	$0.112509\pi$
$380$	−1.24737	−	8.67563i	−0.0639886	−	0.445050i
$381$	3.61615	+	5.62684i	0.185261	+	0.288272i
$382$	17.4356	+	15.1080i	0.892081	+	0.772992i
$383$	10.5026	−	22.9974i	0.536656	−	1.17511i	−0.426083	−	0.904684i	$-0.640107\pi$
$383$	10.5026	−	22.9974i	0.536656	−	1.17511i	0.962740	−	0.270430i	$-0.0871657\pi$
$384$	6.30448	−	9.80997i	0.321724	−	0.500613i
$385$	−4.83766	−	15.6904i	−0.246550	−	0.799656i
$386$	4.48667	+	5.17789i	0.228365	+	0.263548i
$387$	0.0684528	−	0.233129i	0.00347965	−	0.0118506i
$388$	−2.96007	−	6.48165i	−0.150275	−	0.329056i
$389$	−16.7978	−	2.41516i	−0.851682	−	0.122453i	−0.297370	−	0.954762i	$-0.596110\pi$
$389$	−16.7978	−	2.41516i	−0.851682	−	0.122453i	−0.554312	+	0.832309i	$0.687019\pi$
$390$	1.63558			0.0828206
$391$	−15.3488	−	5.08513i	−0.776224	−	0.257166i
$392$	11.4499	−	0.308606i	0.578306	−	0.0155869i
$393$	1.28633	−	8.94665i	0.0648870	−	0.451299i
$394$	16.4132	+	35.9399i	0.826885	+	1.81063i
$395$	6.22418	−	21.1976i	0.313173	−	1.06657i
$396$	−3.44469	+	2.98484i	−0.173102	+	0.149994i
$397$	6.24256	+	21.2602i	0.313305	+	1.06702i	0.954145	+	0.299345i	$0.0967680\pi$
$397$	6.24256	+	21.2602i	0.313305	+	1.06702i	−0.640840	+	0.767674i	$0.721414\pi$
$398$	7.97209	+	5.12335i	0.399605	+	0.256810i
$399$	13.7312	+	6.04859i	0.687419	+	0.302808i
$400$	−9.47329	+	10.9328i	−0.473665	+	0.546638i
$401$	8.62873	+	13.4266i	0.430898	+	0.670491i	0.987018	−	0.160612i	$-0.0513467\pi$
$401$	8.62873	+	13.4266i	0.430898	+	0.670491i	−0.556120	+	0.831102i	$0.687710\pi$
$402$	0.962437	+	6.69390i	0.0480020	+	0.333861i
$403$	−0.133535	−	0.928756i	−0.00665185	−	0.0462646i
$404$	0.830207	+	1.29183i	0.0413044	+	0.0642708i
$405$	−0.949954	+	1.09631i	−0.0472036	+	0.0544759i
$406$	1.89051	−	4.29172i	0.0938242	−	0.212995i
$407$	19.6449	+	12.6250i	0.973761	+	0.625798i
$408$	1.55426	+	5.29333i	0.0769474	+	0.262059i
$409$	−13.8812	+	12.0282i	−0.686383	+	0.594754i	−0.926638	−	0.375956i	$-0.877314\pi$
$409$	−13.8812	+	12.0282i	−0.686383	+	0.594754i	0.240255	+	0.970710i	$0.422769\pi$
$410$	−7.66626	+	26.1089i	−0.378609	+	1.28943i
$411$	4.78162	+	10.4703i	0.235860	+	0.516461i
$412$	−2.08478	+	14.4999i	−0.102709	+	0.714360i
$413$	0.180264	+	13.3787i	0.00887019	+	0.658322i
$414$	0.909057	+	8.34735i	0.0446777	+	0.410250i
$415$	1.93041			0.0947600
$416$	−3.48932	−	0.501689i	−0.171078	−	0.0245973i
$417$	−7.76841	−	17.0104i	−0.380421	−	0.833005i
$418$	−11.9674	+	40.7573i	−0.585346	+	1.99351i
$419$	−25.2639	−	29.1561i	−1.23422	−	1.42437i	−0.869998	−	0.493055i	$-0.835880\pi$
$419$	−25.2639	−	29.1561i	−1.23422	−	1.42437i	−0.364223	−	0.931312i	$-0.618665\pi$
$420$	−1.20478	−	3.90756i	−0.0587872	−	0.190669i
$421$	8.11211	−	12.6227i	0.395360	−	0.615193i	−0.585322	−	0.810801i	$-0.699032\pi$
$421$	8.11211	−	12.6227i	0.395360	−	0.615193i	0.980682	+	0.195608i	$0.0626682\pi$
$422$	9.19427	−	20.1326i	0.447570	−	0.980042i
$423$	−7.20667	−	6.24461i	−0.350400	−	0.303623i
$424$	5.29681	+	8.24200i	0.257236	+	0.400267i
$425$	−1.38941	−	9.66356i	−0.0673963	−	0.468751i
$426$	−28.4077	+	4.08441i	−1.37636	+	0.197890i
$427$	−17.5043	+	11.5855i	−0.847094	+	0.560663i
$428$	−0.989726	−	0.857602i	−0.0478402	−	0.0414538i
$429$	−2.50604	−	1.14447i	−0.120993	−	0.0552555i
$430$	−0.333627	+	0.519134i	−0.0160889	+	0.0250349i
$431$	−4.87681	−	16.6089i	−0.234908	−	0.800022i	−0.989588	−	0.143929i	$-0.954026\pi$
$431$	−4.87681	−	16.6089i	−0.234908	−	0.800022i	0.754680	−	0.656093i	$-0.227792\pi$
$432$	3.77551	−	3.27150i	0.181649	−	0.157400i
$433$	6.84574	+	2.01009i	0.328985	+	0.0965988i	0.442054	−	0.896988i	$-0.354250\pi$
$433$	6.84574	+	2.01009i	0.328985	+	0.0965988i	−0.113069	+	0.993587i	$0.536068\pi$
$434$	−6.10117	+	2.88628i	−0.292865	+	0.138546i
$435$	1.45364	+	0.209002i	0.0696968	+	0.0100209i
$436$			3.81421i			0.182668i
$437$	17.0949	+	21.1538i	0.817758	+	1.01192i
$438$	−9.44792			−0.451439
$439$	31.8093	+	4.57348i	1.51817	+	0.218280i	0.850421	−	0.526103i	$-0.176347\pi$
$439$	31.8093	+	4.57348i	1.51817	+	0.218280i	0.667753	+	0.744383i	$0.267256\pi$
$440$	−9.23698	+	4.21839i	−0.440356	+	0.201104i
$441$	6.76715	+	1.79045i	0.322245	+	0.0852596i
$442$	2.87290	−	2.48939i	0.136650	−	0.118408i
$443$	−0.357814	+	0.105064i	−0.0170003	+	0.00499173i	−0.290222	−	0.956959i	$-0.593729\pi$
$443$	−0.357814	+	0.105064i	−0.0170003	+	0.00499173i	0.273221	+	0.961951i	$0.411911\pi$
$444$	4.89239	+	3.14415i	0.232183	+	0.149215i
$445$	−4.15644	+	9.10133i	−0.197034	+	0.431445i
$446$	27.8294	+	24.1143i	1.31776	+	1.14185i
$447$	−17.4748	+	11.2304i	−0.826531	+	0.531179i
$448$	−0.167676	−	1.06422i	−0.00792193	−	0.0502796i
$449$	−3.68759	−	25.6478i	−0.174028	−	1.21039i	−0.870266	−	0.492582i	$-0.836053\pi$
$449$	−3.68759	−	25.6478i	−0.174028	−	1.21039i	0.696238	−	0.717811i	$-0.254856\pi$
$450$	−4.26507	+	2.74099i	−0.201057	+	0.129212i
$451$	30.0156	−	34.6398i	1.41338	−	1.63113i
$452$	3.57562	+	1.63293i	0.168183	+	0.0768067i
$453$	12.2044	−	18.9904i	0.573412	−	0.892246i
$454$	16.7586	−	4.92077i	0.786521	−	0.230943i
$455$	1.84592	−	1.64356i	0.0865380	−	0.0770512i
$456$	2.61436	−	8.90371i	0.122429	−	0.416954i
$457$	14.4616	−	6.60440i	0.676486	−	0.308941i	−0.0473846	−	0.998877i	$-0.515089\pi$
$457$	14.4616	−	6.60440i	0.676486	−	0.308941i	0.723870	+	0.689936i	$0.242361\pi$
$458$	1.80436	−	12.5496i	0.0843121	−	0.586404i
$459$			3.37152i			0.157369i
$460$	1.30600	−	7.29610i	0.0608924	−	0.340183i
$461$			10.9991i			0.512277i	0.966640	+	0.256139i	$0.0824504\pi$
$461$			10.9991i			0.512277i	−0.966640	+	0.256139i	$0.917550\pi$
$462$	−2.55576	+	19.6518i	−0.118905	+	0.914284i
$463$	−10.3529	−	22.6696i	−0.481139	−	1.05355i	−0.982149	−	0.188106i	$-0.939765\pi$
$463$	−10.3529	−	22.6696i	−0.481139	−	1.05355i	0.501010	−	0.865442i	$-0.332962\pi$
$464$	−4.85274	−	1.42489i	−0.225283	−	0.0661490i
$465$	−1.38413	−	1.59737i	−0.0641873	−	0.0740761i
$466$	−45.6963	+	13.4176i	−2.11684	+	0.621560i
$467$	20.8776	+	13.4172i	0.966098	+	0.620874i	0.925679	−	0.378309i	$-0.123494\pi$
$467$	20.8776	+	13.4172i	0.966098	+	0.620874i	0.0404191	+	0.999183i	$0.487131\pi$
$468$	−0.624107	−	0.285020i	−0.0288494	−	0.0131751i
$469$	7.81278	+	6.58763i	0.360761	+	0.304189i
$470$	13.0938	+	20.3743i	0.603970	+	0.939795i
$471$	−18.1581	+	2.61074i	−0.836681	+	0.120297i
$472$	8.19071	−	1.17765i	0.377008	−	0.0542055i
$473$	0.874442	−	0.561970i	0.0402069	−	0.0258394i
$474$	−17.4617	+	20.1518i	−0.802041	+	0.925605i
$475$	−6.82189	+	14.9379i	−0.313010	+	0.685396i
$476$	−8.06360	−	5.02996i	−0.369595	−	0.230548i
$477$	1.68687	+	5.74496i	0.0772366	+	0.263044i
$478$	28.6166	+	33.0253i	1.30889	+	1.51054i
$479$	−31.7749	−	9.32994i	−1.45183	−	0.426296i	−0.541684	−	0.840582i	$-0.682213\pi$
$479$	−31.7749	−	9.32994i	−1.45183	−	0.426296i	−0.910146	+	0.414287i	$0.864031\pi$
$480$	−7.22324	+	3.29874i	−0.329694	+	0.150566i
$481$	−0.500259	+	3.47937i	−0.0228098	+	0.158646i
$482$	32.6463			1.48700
$483$	9.41406	+	8.50737i	0.428355	+	0.387099i
$484$	−7.77979			−0.353627
$485$	1.38071	−	9.60304i	0.0626947	−	0.436051i
$486$	1.59262	−	0.727323i	0.0722425	−	0.0329920i
$487$	23.8293	+	6.99693i	1.07981	+	0.317061i	0.772803	−	0.634646i	$-0.218854\pi$
$487$	23.8293	+	6.99693i	1.07981	+	0.317061i	0.307008	+	0.951707i	$0.400672\pi$
$488$	8.50150	+	9.81125i	0.384845	+	0.444135i
$489$	−3.89351	−	13.2601i	−0.176071	−	0.599642i
$490$	−15.2098	−	9.20537i	−0.687110	−	0.415856i
$491$	−6.82832	+	14.9519i	−0.308158	+	0.674771i	−0.998828	−	0.0483984i	$-0.984588\pi$
$491$	−6.82832	+	14.9519i	−0.308158	+	0.674771i	0.690670	+	0.723170i	$0.257316\pi$
$492$	7.47512	−	8.62675i	0.337004	−	0.388924i
$493$	2.87144	−	1.84537i	0.129323	−	0.0831111i
$494$	−6.32911	+	0.909988i	−0.284760	+	0.0409423i
$495$	−6.14272	+	0.883190i	−0.276095	+	0.0396964i
$496$	3.93532	+	6.12348i	0.176701	+	0.274952i
$497$	−27.9567	+	33.1560i	−1.25403	+	1.48725i
$498$	−2.11937	−	0.967883i	−0.0949711	−	0.0433719i
$499$	−9.42766	−	6.05879i	−0.422040	−	0.271229i	0.312336	−	0.949972i	$-0.398889\pi$
$499$	−9.42766	−	6.05879i	−0.422040	−	0.271229i	−0.734376	+	0.678743i	$0.762525\pi$
$500$	11.7087	−	3.43798i	0.523628	−	0.153751i
$501$	−1.80187	−	2.07947i	−0.0805015	−	0.0929037i
$502$	24.5712	+	7.21476i	1.09667	+	0.322010i
$503$	−3.44939	−	7.55311i	−0.153801	−	0.336777i	0.817010	−	0.576624i	$-0.195630\pi$
$503$	−3.44939	−	7.55311i	−0.153801	−	0.336777i	−0.970811	+	0.239847i	$0.922903\pi$
$504$	0.558324	−	4.29307i	0.0248697	−	0.191228i
$505$			2.09079i			0.0930388i
$506$	−20.4464	+	29.5352i	−0.908955	+	1.31300i
$507$			12.5853i			0.558932i
$508$	−1.01417	+	7.05369i	−0.0449964	+	0.312957i
$509$	−20.9577	+	9.57105i	−0.928933	+	0.424229i	−0.821646	−	0.569999i	$-0.806944\pi$
$509$	−20.9577	+	9.57105i	−0.928933	+	0.424229i	−0.107287	+	0.994228i	$0.534216\pi$
$510$	2.41247	−	8.21612i	0.106826	−	0.363816i
$511$	−10.6630	+	9.49403i	−0.471702	+	0.419991i
$512$	10.5527	−	3.09854i	0.466366	−	0.136937i
$513$	3.06604	−	4.77085i	0.135369	−	0.210638i
$514$	−45.9790	−	20.9979i	−2.02804	−	0.926177i
$515$	−13.0614	+	15.0737i	−0.575554	+	0.664225i
$516$	0.217772	−	0.139954i	0.00958689	−	0.00616112i
$517$	−5.80573	−	40.3797i	−0.255336	−	1.77590i
$518$	24.9771	−	3.93533i	1.09743	−	0.172908i
$519$	−0.829992	+	0.533404i	−0.0364326	+	0.0234138i
$520$	−1.15522	−	1.00100i	−0.0506597	−	0.0438968i
$521$	3.02606	−	6.62614i	0.132574	−	0.290297i	−0.831690	−	0.555241i	$-0.812626\pi$
$521$	3.02606	−	6.62614i	0.132574	−	0.290297i	0.964264	+	0.264944i	$0.0853535\pi$
$522$	−1.49114	−	0.958299i	−0.0652655	−	0.0419436i
$523$	−34.5271	+	10.1381i	−1.50977	+	0.443307i	−0.928788	−	0.370612i	$-0.879148\pi$
$523$	−34.5271	+	10.1381i	−1.50977	+	0.443307i	−0.580978	+	0.813919i	$0.697330\pi$
$524$	7.27786	−	6.30630i	0.317935	−	0.275492i
$525$	−2.05921	+	7.37938i	−0.0898711	+	0.322063i
$526$	−33.3303	+	15.2214i	−1.45327	+	0.663686i
$527$	−4.86246	−	0.699117i	−0.211812	−	0.0304540i
$528$	21.3722			0.930104
$529$	8.09697	+	21.5276i	0.352042	+	0.935984i
$530$		−	15.2070i		−	0.660551i
$531$	5.00565	+	0.719704i	0.217227	+	0.0312325i
$532$	6.83613	+	14.4506i	0.296384	+	0.626512i
$533$	6.62005	+	1.94382i	0.286746	+	0.0841962i
$534$	9.12659	−	7.90824i	0.394946	−	0.342223i
$535$	−0.502349	−	1.71085i	−0.0217185	−	0.0739663i
$536$	3.41701	−	5.31697i	0.147592	−	0.229658i
$537$	−1.16556	−	0.532292i	−0.0502975	−	0.0229701i
$538$	10.0381	+	8.69809i	0.432774	+	0.375001i
$539$	16.8633	+	24.7474i	0.726352	+	1.06594i
$540$	−1.52979	+	0.219951i	−0.0658318	+	0.00946518i
$541$	−2.70557	−	18.8177i	−0.116322	−	0.809034i	−0.961550	−	0.274629i	$-0.911445\pi$
$541$	−2.70557	−	18.8177i	−0.116322	−	0.809034i	0.845229	−	0.534405i	$-0.179464\pi$
$542$	−10.3348	−	16.0813i	−0.443919	−	0.690752i
$543$	7.92669	+	6.86852i	0.340167	+	0.294756i
$544$	−7.66692	+	16.7882i	−0.328717	+	0.719789i
$545$	−2.80767	+	4.36882i	−0.120267	+	0.187140i
$546$	−2.85067	+	0.878919i	−0.121997	+	0.0376143i
$547$	−0.516558	−	0.596140i	−0.0220864	−	0.0254891i	0.744599	−	0.667512i	$-0.232641\pi$
$547$	−0.516558	−	0.596140i	−0.0220864	−	0.0254891i	−0.766685	+	0.642023i	$0.778095\pi$
$548$	−3.45503	+	11.7667i	−0.147592	+	0.502651i
$549$	3.29586	+	7.21692i	0.140664	+	0.308011i
$550$	−21.4687	−	3.08674i	−0.915429	−	0.131619i
$551$	−5.74137			−0.244591
$552$	4.46666	−	6.45215i	0.190114	−	0.274622i
$553$	0.542870	+	40.2904i	0.0230852	+	1.71332i
$554$	1.83619	−	12.7710i	0.0780123	−	0.542587i
$555$	3.28934	+	7.20264i	0.139625	+	0.305735i
$556$	5.61318	−	19.1167i	0.238052	−	0.810730i
$557$	−1.34739	+	1.16752i	−0.0570906	+	0.0494693i	−0.682939	−	0.730476i	$-0.739298\pi$
$557$	−1.34739	+	1.16752i	−0.0570906	+	0.0494693i	0.625848	+	0.779945i	$0.284753\pi$
$558$	0.718713	+	2.44771i	0.0304255	+	0.103620i
$559$	0.131629	+	0.0845930i	0.00556733	+	0.00357790i
$560$	−7.72925	+	17.5465i	−0.326620	+	0.741476i
$561$	−9.44551	+	10.9007i	−0.398790	+	0.460228i
$562$	2.79507	+	4.34921i	0.117903	+	0.183460i
$563$	4.32521	+	30.0825i	0.182286	+	1.26783i	0.851341	+	0.524613i	$0.175790\pi$
$563$	4.32521	+	30.0825i	0.182286	+	1.26783i	−0.669055	+	0.743213i	$0.733301\pi$
$564$	−1.44587	−	10.0562i	−0.0608820	−	0.423444i
$565$	2.89352	+	4.50241i	0.121731	+	0.189418i
$566$	−16.3033	+	18.8150i	−0.685277	+	0.790852i
$567$	1.06656	−	2.42125i	0.0447913	−	0.101683i
$568$	22.5643	+	14.5012i	0.946775	+	0.608456i
$569$	−4.78037	−	16.2805i	−0.200404	−	0.682512i	−0.996958	−	0.0779449i	$-0.975164\pi$
$569$	−4.78037	−	16.2805i	−0.200404	−	0.682512i	0.796554	−	0.604567i	$-0.206654\pi$
$570$	−10.8854	+	9.43227i	−0.455940	+	0.395074i
$571$	2.57295	−	8.76265i	0.107674	−	0.366705i	−0.887974	−	0.459893i	$-0.847888\pi$
$571$	2.57295	−	8.76265i	0.107674	−	0.366705i	0.995649	+	0.0931881i	$0.0297058\pi$
$572$	−1.21934	−	2.66999i	−0.0509833	−	0.111638i
$573$	1.87527	−	13.0428i	0.0783404	−	0.544869i
$574$	−0.668646	−	49.6252i	−0.0279088	−	2.07132i
$575$	−9.44906	+	10.1771i	−0.394053	+	0.424412i
$576$	−0.407199			−0.0169666
$577$	−8.28649	−	1.19142i	−0.344971	−	0.0495994i	−0.0323481	−	0.999477i	$-0.510299\pi$
$577$	−8.28649	−	1.19142i	−0.344971	−	0.0495994i	−0.312623	+	0.949877i	$0.601208\pi$
$578$	4.09688	+	8.97092i	0.170408	+	0.373141i
$579$	1.10247	−	3.75467i	0.0458171	−	0.156039i
$580$	1.02464	+	1.18250i	0.0425459	+	0.0491006i
$581$	−3.36454	+	1.03735i	−0.139584	+	0.0430367i
$582$	−6.33070	+	9.85077i	−0.262416	+	0.408327i
$583$	−10.6409	+	23.3003i	−0.440700	+	0.964999i
$584$	6.67313	+	5.78230i	0.276136	+	0.239273i
$585$	−0.505050	−	0.785873i	−0.0208812	−	0.0324918i
$586$	−2.17686	−	15.1404i	−0.0899253	−	0.625444i
$587$	−28.6078	+	4.11318i	−1.18077	+	0.169769i	−0.704613	−	0.709591i	$-0.748880\pi$
$587$	−28.6078	+	4.11318i	−1.18077	+	0.169769i	−0.476157	+	0.879360i	$0.657971\pi$
$588$	4.19965	+	6.16312i	0.173191	+	0.254163i
$589$	6.24482	+	5.41116i	0.257313	+	0.222963i
$590$	−11.6834	−	5.33562i	−0.480997	−	0.219664i
$591$	12.2004	−	18.9842i	0.501858	−	0.780906i
$592$	−7.68259	−	26.1645i	−0.315752	−	1.07535i
$593$	17.2049	−	14.9081i	0.706519	−	0.612202i	−0.225658	−	0.974207i	$-0.572453\pi$
$593$	17.2049	−	14.9081i	0.706519	−	0.612202i	0.932176	+	0.362005i	$0.117908\pi$
$594$	7.18683	+	2.11024i	0.294879	+	0.0865843i
$595$	−5.53350	−	11.6970i	−0.226851	−	0.479530i
$596$	−21.9061	−	3.14962i	−0.897308	−	0.129013i
$597$		−	5.41253i		−	0.221520i
$598$	−5.32271	−	0.952759i	−0.217662	−	0.0389612i
$599$	−1.67618			−0.0684869			−0.0342434	−	0.999414i	$-0.510902\pi$
$599$	−1.67618			−0.0684869			−0.0342434	+	0.999414i	$0.510902\pi$
$600$	4.68998	+	0.674318i	0.191468	+	0.0275289i
$601$	−1.18356	+	0.540514i	−0.0482784	+	0.0220480i	−0.439408	−	0.898288i	$-0.644812\pi$
$601$	−1.18356	+	0.540514i	−0.0482784	+	0.0220480i	0.391129	+	0.920336i	$0.372084\pi$
$602$	0.302514	−	1.08409i	0.0123295	−	0.0441842i
$603$	2.91914	−	2.52945i	0.118877	−	0.103007i
$604$	23.0765	−	6.77588i	0.938970	−	0.275707i
$605$	−8.91101	−	5.72676i	−0.362284	−	0.232826i
$606$	1.04829	−	2.29545i	0.0425841	−	0.0932461i
$607$	−19.5103	−	16.9058i	−0.791900	−	0.686185i	0.161840	−	0.986817i	$-0.448257\pi$
$607$	−19.5103	−	16.9058i	−0.791900	−	0.686185i	−0.953740	+	0.300632i	$0.902802\pi$
$608$	26.1161	−	16.7838i	1.05915	−	0.680672i
$609$	−2.64589	+	0.416879i	−0.107217	+	0.0168928i
$610$	−2.86771	−	19.9454i	−0.116110	−	0.807564i
$611$	5.16601	−	3.31999i	0.208994	−	0.134313i
$612$	−2.35232	+	2.71473i	−0.0950870	+	0.109736i
$613$	−6.60590	−	3.01681i	−0.266810	−	0.121848i	0.277518	−	0.960720i	$-0.410488\pi$
$613$	−6.60590	−	3.01681i	−0.266810	−	0.121848i	−0.544328	+	0.838872i	$0.683215\pi$
$614$	−14.5827	+	22.6911i	−0.588508	+	0.915736i
$615$	14.9122	−	4.37863i	0.601320	−	0.176563i
$616$	13.8324	−	12.3160i	0.557324	−	0.496227i
$617$	13.5051	−	45.9940i	0.543693	−	1.85165i	0.0199010	−	0.999802i	$-0.493665\pi$
$617$	13.5051	−	45.9940i	0.543693	−	1.85165i	0.523792	−	0.851846i	$-0.324517\pi$
$618$	21.8977	−	10.0003i	0.880854	−	0.402273i
$619$	3.61778	−	25.1622i	0.145411	−	1.01136i	−0.778198	−	0.628019i	$-0.783866\pi$
$619$	3.61778	−	25.1622i	0.145411	−	1.01136i	0.923609	−	0.383337i	$-0.125225\pi$
$620$		−	2.25190i		−	0.0904384i
$621$	3.73009	−	3.01437i	0.149683	−	0.120963i
$622$		−	45.8806i		−	1.83965i
$623$	2.35348	−	18.0964i	0.0942903	−	0.725018i
$624$	1.33645	+	2.92641i	0.0535007	+	0.117150i
$625$	2.04986	+	0.601894i	0.0819945	+	0.0240758i
$626$	−6.66811	−	7.69541i	−0.266511	−	0.307570i
$627$	23.2788	−	6.83527i	0.929666	−	0.272974i
$628$	−16.4423	−	10.5668i	−0.656119	−	0.421662i
$629$	16.7403	+	7.64506i	0.667481	+	0.304829i
$630$	−4.33163	+	5.13721i	−0.172576	+	0.204671i
$631$	−16.5871	−	25.8100i	−0.660320	−	1.02748i	−0.996328	−	0.0856191i	$-0.972713\pi$
$631$	−16.5871	−	25.8100i	−0.660320	−	1.02748i	0.336008	−	0.941859i	$-0.390923\pi$
$632$	24.6666	−	3.54652i	0.981184	−	0.141073i
$633$	−12.5126	+	1.79904i	−0.497330	+	0.0715053i
$634$	−17.4025	+	11.1839i	−0.691140	+	0.444169i
$635$	−6.35390	+	7.33279i	−0.252147	+	0.290993i
$636$	−2.65002	+	5.80273i	−0.105080	+	0.230093i
$637$	−2.33407	+	3.85653i	−0.0924792	+	0.152801i
$638$	−2.13639	−	7.27586i	−0.0845803	−	0.288054i
$639$	10.7345	+	12.3883i	0.424651	+	0.490073i
$640$	16.2307	+	4.76575i	0.641573	+	0.188383i
$641$	−24.0599	+	10.9878i	−0.950308	+	0.433991i	−0.829389	−	0.558671i	$-0.811311\pi$
$641$	−24.0599	+	10.9878i	−0.950308	+	0.433991i	−0.120919	+	0.992662i	$0.538584\pi$
$642$	−0.306274	+	2.13018i	−0.0120877	+	0.0840717i
$643$	−7.35411			−0.290018			−0.145009	−	0.989430i	$-0.546321\pi$
$643$	−7.35411			−0.290018			−0.145009	+	0.989430i	$0.546321\pi$
$644$	1.64451	+	13.4183i	0.0648028	+	0.528755i
$645$	0.352458			0.0138780
$646$	−4.76420	+	33.1358i	−0.187445	+	1.30371i
$647$	0.612007	−	0.279494i	0.0240605	−	0.0109880i	−0.403348	−	0.915046i	$-0.632154\pi$
$647$	0.612007	−	0.279494i	0.0240605	−	0.0109880i	0.427409	+	0.904058i	$0.359426\pi$
$648$	−1.57001	−	0.460996i	−0.0616758	−	0.0181097i
$649$	14.1678	+	16.3505i	0.556136	+	0.641815i
$650$	−0.919831	−	3.13266i	−0.0360787	−	0.122873i
$651$	3.27080	+	2.04028i	0.128193	+	0.0799648i
$652$	6.11658	−	13.3934i	0.239544	−	0.524527i
$653$	3.35217	−	3.86861i	0.131181	−	0.151391i	−0.686359	−	0.727263i	$-0.740792\pi$
$653$	3.35217	−	3.86861i	0.131181	−	0.151391i	0.817540	+	0.575872i	$0.195338\pi$
$654$	5.27297	−	3.38873i	0.206189	−	0.132510i
$655$	12.9782	−	1.86598i	0.507100	−	0.0729100i
$656$	−52.9788	+	7.61721i	−2.06848	+	0.297402i
$657$	2.91743	+	4.53960i	0.113820	+	0.177107i
$658$	−33.7699	−	28.4744i	−1.31649	−	1.11005i
$659$	12.0470	+	5.50166i	0.469283	+	0.214314i	0.635998	−	0.771691i	$-0.280589\pi$
$659$	12.0470	+	5.50166i	0.469283	+	0.214314i	−0.166715	+	0.986005i	$0.553316\pi$
$660$	−5.56228	−	3.57466i	−0.216511	−	0.139143i
$661$	40.0187	−	11.7506i	1.55655	−	0.457044i	0.613499	−	0.789696i	$-0.289762\pi$
$661$	40.0187	−	11.7506i	1.55655	−	0.457044i	0.943050	+	0.332652i	$0.107943\pi$
$662$	14.5410	+	16.7813i	0.565154	+	0.652222i
$663$	−2.08324	−	0.611695i	−0.0809064	−	0.0237563i
$664$	0.904562	+	1.98071i	0.0351038	+	0.0768666i
$665$	−2.80703	+	21.5839i	−0.108852	+	0.836986i
$666$		−	9.55691i		−	0.370323i
$667$	−4.60889	−	1.52694i	−0.178457	−	0.0591234i
$668$		−	2.93154i		−	0.113425i
$669$	2.99317	−	20.8179i	0.115723	−	0.804868i
$670$	−8.92363	+	4.07529i	−0.344750	+	0.157442i
$671$	−9.56254	+	32.5670i	−0.369158	+	1.25724i
$672$	10.8168	−	9.63102i	0.417268	−	0.371525i
$673$	32.0631	−	9.41457i	1.23594	−	0.362905i	0.402452	−	0.915441i	$-0.368158\pi$
$673$	32.0631	−	9.41457i	1.23594	−	0.362905i	0.833489	+	0.552536i	$0.186340\pi$
$674$	−1.01651	+	1.58172i	−0.0391545	+	0.0609256i
$675$	2.63402	+	1.20292i	0.101384	+	0.0463003i
$676$	−8.78080	+	10.1336i	−0.337723	+	0.389753i
$677$	−22.9860	+	14.7722i	−0.883423	+	0.567741i	−0.901831	−	0.432089i	$-0.857777\pi$
$677$	−22.9860	+	14.7722i	−0.883423	+	0.567741i	0.0184079	+	0.999831i	$0.494140\pi$
$678$	−0.919305	−	6.39391i	−0.0353057	−	0.245557i
$679$	2.75398	+	17.4792i	0.105688	+	0.670791i
$680$	−6.73236	+	4.32663i	−0.258174	+	0.165919i
$681$	−7.53927	−	6.53281i	−0.288905	−	0.250338i
$682$	−4.53368	+	9.92737i	−0.173603	+	0.380139i
$683$	−9.37917	−	6.02763i	−0.358884	−	0.230641i	0.348756	−	0.937213i	$-0.386604\pi$
$683$	−9.37917	−	6.02763i	−0.358884	−	0.230641i	−0.707641	+	0.706573i	$0.750240\pi$
$684$	5.79739	−	1.70227i	0.221669	−	0.0650878i
$685$	−12.6190	+	10.9344i	−0.482147	+	0.417782i
$686$	31.4562	+	7.87077i	1.20100	+	0.300507i
$687$	−6.58708	+	3.00822i	−0.251313	+	0.114771i
$688$	−1.20146	−	0.172744i	−0.0458052	−	0.00658579i
$689$	−3.85582			−0.146895
$690$	−11.2468	+	4.67673i	−0.428159	+	0.178040i
$691$		−	30.1286i		−	1.14615i	−0.819505	−	0.573073i	$-0.805751\pi$
$691$		−	30.1286i		−	1.14615i	0.819505	−	0.573073i	$-0.194249\pi$
$692$	−1.04046	−	0.149596i	−0.0395524	−	0.00568678i
$693$	10.2316	−	4.84027i	0.388668	−	0.183867i
$694$	−9.02544	−	2.65011i	−0.342601	−	0.100597i
$695$	20.5013	−	17.7645i	0.777659	−	0.673845i
$696$	0.466708	+	1.58946i	0.0176905	+	0.0602483i
$697$	19.5291	−	30.3879i	0.739718	−	1.15102i
$698$	48.3616	+	22.0860i	1.83051	+	0.835967i
$699$	20.5576	+	17.8132i	0.777558	+	0.673758i
$700$	−6.80668	+	4.50511i	−0.257268	+	0.170277i
$701$	−26.7322	+	3.84352i	−1.00966	+	0.145168i	−0.627245	−	0.778822i	$-0.715818\pi$
$701$	−26.7322	+	3.84352i	−1.00966	+	0.145168i	−0.382418	+	0.923990i	$0.624908\pi$
$702$	0.160460	+	1.11602i	0.00605618	+	0.0421216i
$703$	−16.7359	−	26.0416i	−0.631208	−	0.982178i
$704$	−1.31654	−	1.14079i	−0.0496191	−	0.0429952i
$705$	5.74635	−	12.5828i	0.216420	−	0.473894i
$706$	−0.738763	+	1.14954i	−0.0278037	+	0.0432634i
$707$	−1.12354	−	3.64406i	−0.0422550	−	0.137049i
$708$	3.52838	+	4.07196i	0.132604	+	0.153034i
$709$	−8.90032	+	30.3117i	−0.334259	+	1.13838i	0.605302	+	0.795996i	$0.293053\pi$
$709$	−8.90032	+	30.3117i	−0.334259	+	1.13838i	−0.939560	+	0.342384i	$0.888766\pi$
$710$	−17.2948	−	37.8703i	−0.649061	−	1.42125i
$711$	15.0747	+	2.16741i	0.565345	+	0.0812844i
$712$	−11.2862			−0.422967
$713$	3.57390	+	6.00465i	0.133844	+	0.224876i
$714$	0.210414	+	15.6164i	0.00787456	+	0.584429i
$715$	0.568756	−	3.95578i	0.0212703	−	0.147938i
$716$	−0.567116	−	1.24181i	−0.0211941	−	0.0464086i
$717$	7.03170	−	23.9478i	0.262604	−	0.894346i
$718$	28.5784	−	24.7633i	1.06653	−	0.924157i
$719$	7.98611	+	27.1982i	0.297832	+	1.01432i	0.963419	+	0.268001i	$0.0863632\pi$
$719$	7.98611	+	27.1982i	0.297832	+	1.01432i	−0.665587	+	0.746320i	$0.731819\pi$
$720$	6.09647	+	3.91797i	0.227202	+	0.146014i
$721$	14.6647	−	33.2910i	0.546142	−	1.23982i
$722$	15.0904	−	17.4153i	0.561608	−	0.648130i
$723$	−10.0809	−	15.6861i	−0.374911	−	0.583374i
$724$	1.59033	+	11.0610i	0.0591040	+	0.411077i
$725$	−0.417207	−	2.90174i	−0.0154947	−	0.107768i
$726$	6.91195	+	10.7552i	0.256526	+	0.399163i
$727$	30.0121	−	34.6358i	1.11309	−	1.28457i	0.158263	−	0.987397i	$-0.449410\pi$
$727$	30.0121	−	34.6358i	1.11309	−	1.28457i	0.954823	−	0.297174i	$-0.0960441\pi$
$728$	2.55136	+	1.12387i	0.0945597	+	0.0416536i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	−3.86124	−	13.1502i	−0.142911	−	0.486710i
$731$	0.619096	−	0.536450i	0.0228981	−	0.0198413i
$732$	−2.38147	+	8.11054i	−0.0880216	+	0.299774i
$733$	−5.13364	−	11.2411i	−0.189615	−	0.415199i	0.790818	−	0.612051i	$-0.209655\pi$
$733$	−5.13364	−	11.2411i	−0.189615	−	0.415199i	−0.980433	+	0.196852i	$0.936928\pi$
$734$	5.68224	−	39.5209i	0.209735	−	1.45874i
$735$	0.273588	+	10.1507i	0.0100914	+	0.374412i
$736$	25.4284	−	6.52751i	0.937304	−	0.240607i
$737$	16.5245			0.608686
$738$	−18.5673	−	2.66958i	−0.683473	−	0.0982686i
$739$	−7.30753	−	16.0013i	−0.268812	−	0.588616i	0.726299	−	0.687379i	$-0.241239\pi$
$739$	−7.30753	−	16.0013i	−0.268812	−	0.588616i	−0.995111	+	0.0987629i	$0.968511\pi$
$740$	−2.37676	+	8.09449i	−0.0873714	+	0.297560i
$741$	2.39160	+	2.76006i	0.0878578	+	0.101393i
$742$	8.17188	+	26.5045i	0.299999	+	0.973012i
$743$	11.3653	−	17.6848i	0.416954	−	0.648793i	−0.567715	−	0.823225i	$-0.692173\pi$
$743$	11.3653	−	17.6848i	0.416954	−	0.648793i	0.984669	+	0.174432i	$0.0558089\pi$
$744$	0.990412	−	2.16870i	0.0363103	−	0.0795084i
$745$	−22.7729	−	19.7328i	−0.834333	−	0.722954i
$746$	−26.3475	−	40.9975i	−0.964650	−	1.50102i
$747$	0.189385	+	1.31720i	0.00692923	+	0.0481939i
$748$	−15.2109	+	2.18700i	−0.556166	+	0.0799646i
$749$	1.79492	+	2.71191i	0.0655849	+	0.0990909i
$750$	−15.1554	−	13.1322i	−0.553397	−	0.479521i
$751$	−19.0553	−	8.70224i	−0.695336	−	0.317549i	0.0362072	−	0.999344i	$-0.488472\pi$
$751$	−19.0553	−	8.70224i	−0.695336	−	0.317549i	−0.731543	+	0.681795i	$0.761200\pi$
$752$	−25.7551	+	40.0757i	−0.939192	+	1.46141i
$753$	−4.12075	−	14.0340i	−0.150169	−	0.511427i
$754$	0.862665	−	0.747503i	0.0314164	−	0.0272225i
$755$	31.4197	+	9.22566i	1.14348	+	0.335756i
$756$	2.54810	−	1.20543i	0.0926735	−	0.0438410i
$757$	−24.6354	−	3.54203i	−0.895388	−	0.128737i	−0.320768	−	0.947158i	$-0.603941\pi$
$757$	−24.6354	−	3.54203i	−0.895388	−	0.128737i	−0.574620	+	0.818420i	$0.694850\pi$
$758$		−	59.9469i		−	2.17737i
$759$	20.5049	+	0.704079i	0.744282	+	0.0255564i
$760$	13.4612			0.488288
$761$	5.17784	+	0.744461i	0.187697	+	0.0269867i	0.235522	−	0.971869i	$-0.424320\pi$
$761$	5.17784	+	0.744461i	0.187697	+	0.0269867i	−0.0478254	+	0.998856i	$0.515229\pi$
$762$	10.6524	−	4.86480i	0.385897	−	0.176233i
$763$	2.54583	−	9.12325i	0.0921652	−	0.330284i
$764$	10.6099	−	9.19355i	0.383854	−	0.332611i
$765$	−4.69269	+	1.37790i	−0.169665	+	0.0498180i
$766$	−37.2379	−	23.9314i	−1.34546	−	0.864675i
$767$	−1.35288	+	2.96239i	−0.0488495	+	0.106966i
$768$	−14.8144	−	12.8368i	−0.534570	−	0.463208i
$769$	20.5975	−	13.2372i	0.742764	−	0.477346i	−0.113724	−	0.993512i	$-0.536278\pi$
$769$	20.5975	−	13.2372i	0.742764	−	0.477346i	0.856488	+	0.516167i	$0.172642\pi$
$770$	−28.3971	+	4.47417i	−1.02336	+	0.161238i
$771$	4.10864	+	28.5762i	0.147969	+	1.02915i
$772$	3.50735	−	2.25403i	0.126232	−	0.0811245i
$773$	−4.49022	+	5.18199i	−0.161502	+	0.186383i	−0.830733	−	0.556671i	$-0.812078\pi$
$773$	−4.49022	+	5.18199i	−0.161502	+	0.186383i	0.669231	+	0.743055i	$0.266624\pi$
$774$	−0.386959	−	0.176718i	−0.0139090	−	0.00635201i
$775$	−2.28106	+	3.54939i	−0.0819379	+	0.127498i
$776$	10.5003	−	3.08316i	0.376938	−	0.110679i
$777$	−9.60356	−	10.7860i	−0.344526	−	0.386945i
$778$	−8.37101	+	28.5090i	−0.300115	+	1.02210i
$779$	−55.2690	+	25.2405i	−1.98022	+	0.904335i
$780$	0.141644	−	0.985154i	0.00507166	−	0.0352742i
$781$			70.1268i			2.50933i
$782$	−12.6371	+	25.3327i	−0.451900	+	0.905894i
$783$			1.01239i			0.0361798i
$784$	4.04234	−	34.7356i	0.144369	−	1.24056i
$785$	−11.0548	−	24.2066i	−0.394561	−	0.863969i
$786$	−15.1842	−	4.45847i	−0.541601	−	0.159028i
$787$	−35.9371	−	41.4737i	−1.28102	−	1.47838i	−0.797858	−	0.602846i	$-0.794033\pi$
$787$	−35.9371	−	41.4737i	−1.28102	−	1.47838i	−0.483163	−	0.875530i	$-0.660512\pi$
$788$	23.0690	−	6.77368i	0.821800	−	0.241302i
$789$	17.6058	+	11.3145i	0.626782	+	0.402808i
$790$	−35.1849	−	16.0684i	−1.25182	−	0.571688i
$791$	−7.46265	−	6.29240i	−0.265341	−	0.223732i
$792$	−3.78460	−	5.88895i	−0.134480	−	0.209255i
$793$	−5.05725	+	0.727123i	−0.179588	+	0.0258209i
$794$	38.3997	−	5.52104i	1.36275	−	0.195934i
$795$	−7.30677	+	4.69578i	−0.259145	+	0.166542i
$796$	3.77634	−	4.35813i	0.133849	−	0.154470i
$797$	−3.30049	+	7.22706i	−0.116909	+	0.255995i	−0.959036	−	0.283284i	$-0.908576\pi$
$797$	−3.30049	+	7.22706i	−0.116909	+	0.255995i	0.842127	+	0.539280i	$0.181303\pi$
$798$	13.9037	−	22.2892i	0.492185	−	0.789029i
$799$	−9.05774	−	30.8478i	−0.320440	−	1.09132i
$800$	10.3804	+	11.9797i	0.367004	+	0.423545i
$801$	−6.61801	−	1.94322i	−0.233836	−	0.0686604i
$802$	25.4184	−	11.6082i	0.897556	−	0.409900i
$803$	−3.28542	+	22.8506i	−0.115940	+	0.806381i
$804$	4.11528			0.145135
$805$	−7.99367	+	16.5799i	−0.281740	+	0.584365i
$806$	−1.64282			−0.0578659
$807$	1.07964	−	7.50908i	0.0380052	−	0.264332i
$808$	−2.14527	+	0.979713i	−0.0754704	+	0.0344662i
$809$	2.13112	+	0.625753i	0.0749262	+	0.0220003i	0.318981	−	0.947761i	$-0.396659\pi$
$809$	2.13112	+	0.625753i	0.0749262	+	0.0220003i	−0.244055	+	0.969761i	$0.578478\pi$
$810$	1.66321	+	1.91945i	0.0584393	+	0.0674426i
$811$	9.73660	+	33.1598i	0.341898	+	1.16440i	0.933623	+	0.358258i	$0.116629\pi$
$811$	9.73660	+	33.1598i	0.341898	+	1.16440i	−0.591724	+	0.806140i	$0.701553\pi$
$812$	−2.42131	−	1.51038i	−0.0849712	−	0.0530038i
$813$	−4.53557	+	9.93151i	−0.159069	+	0.348313i
$814$	26.7742	−	30.8991i	0.938436	−	1.08301i
$815$	16.8649	−	10.8384i	0.590753	−	0.379654i
$816$	16.6718	−	2.39704i	0.583628	−	0.0839130i
$817$	−1.36389	+	0.196098i	−0.0477165	+	0.00686059i
$818$	17.3862	+	27.0534i	0.607894	+	0.945901i
$819$	1.30257	+	1.09831i	0.0455154	+	0.0383780i
$820$	15.0622	+	6.87868i	0.525995	+	0.240214i
$821$	31.0618	+	19.9622i	1.08406	+	0.696686i	0.955493	−	0.295014i	$-0.0953245\pi$
$821$	31.0618	+	19.9622i	1.08406	+	0.696686i	0.128571	+	0.991700i	$0.458961\pi$
$822$	19.3366	−	5.67773i	0.674441	−	0.198034i
$823$	18.7576	+	21.6475i	0.653850	+	0.754583i	0.981760	−	0.190126i	$-0.0608897\pi$
$823$	18.7576	+	21.6475i	0.653850	+	0.754583i	−0.327910	+	0.944709i	$0.606344\pi$
$824$	−21.5869	−	6.33848i	−0.752014	−	0.220811i
$825$	5.14619	+	11.2686i	0.179167	+	0.392322i
$826$	23.2304	+	3.02117i	0.808288	+	0.105120i
$827$		−	20.1465i		−	0.700561i	−0.936645	−	0.350281i	$-0.886086\pi$
$827$		−	20.1465i		−	0.700561i	0.936645	−	0.350281i	$-0.113914\pi$
$828$	5.10658	+	0.175345i	0.177466	+	0.00609365i
$829$			46.7925i			1.62517i	0.582842	+	0.812585i	$0.301940\pi$
$829$			46.7925i			1.62517i	−0.582842	+	0.812585i	$0.698060\pi$
$830$	0.480999	−	3.34542i	0.0166957	−	0.116121i
$831$	−6.70329	+	3.06129i	−0.232535	+	0.106195i
$832$	0.0738781	−	0.251606i	0.00256126	−	0.00872285i
$833$	15.9301	+	17.4133i	0.551945	+	0.603336i
$834$	−31.4150	+	9.22427i	−1.08781	+	0.319410i
$835$	2.15793	−	3.35780i	0.0746781	−	0.116201i
$836$	23.5129	+	10.7380i	0.813211	+	0.371381i
$837$	0.954162	−	1.10116i	0.0329807	−	0.0380617i
$838$	−56.8229	+	36.5178i	−1.96291	+	1.26149i
$839$	5.50143	+	38.2633i	0.189931	+	1.32100i	0.832182	+	0.554502i	$0.187091\pi$
$839$	5.50143	+	38.2633i	0.189931	+	1.32100i	−0.642252	+	0.766494i	$0.722000\pi$
$840$	6.20352	−	0.977412i	0.214042	−	0.0337239i
$841$	−23.5341	+	15.1245i	−0.811522	+	0.521533i
$842$	−19.8540	−	17.2036i	−0.684214	−	0.592875i
$843$	1.22665	−	2.68599i	0.0422480	−	0.0925103i
$844$	−11.3302	−	7.28150i	−0.390003	−	0.250639i
$845$	−17.5170	+	5.14344i	−0.602602	+	0.176940i
$846$	−12.6177	+	10.9333i	−0.433805	+	0.375894i
$847$	18.6086	+	5.19269i	0.639397	+	0.178423i
$848$	27.2088	−	12.4258i	0.934353	−	0.426705i
$849$	14.0746	+	2.02363i	0.483040	+	0.0694507i
$850$	−17.0933			−0.586294
$851$	−6.50889	−	25.3559i	−0.223122	−	0.869189i
$852$			17.4645i			0.598323i
$853$	−20.5946	−	2.96106i	−0.705146	−	0.101385i	−0.219593	−	0.975592i	$-0.570473\pi$
$853$	−20.5946	−	2.96106i	−0.705146	−	0.101385i	−0.485554	+	0.874207i	$0.661382\pi$
$854$	15.7163	+	33.2220i	0.537802	+	1.13683i
$855$	7.89340	+	2.31771i	0.269949	+	0.0792640i
$856$	1.52004	−	1.31712i	0.0519537	−	0.0450182i
$857$	−3.99073	−	13.5912i	−0.136321	−	0.464266i	0.862829	−	0.505496i	$-0.168691\pi$
$857$	−3.99073	−	13.5912i	−0.136321	−	0.464266i	−0.999150	+	0.0412300i	$0.986872\pi$
$858$	−2.60781	+	4.05783i	−0.0890292	+	0.138532i
$859$	−52.9894	−	24.1995i	−1.80798	−	0.825675i	−0.950192	−	0.311664i	$-0.899114\pi$
$859$	−52.9894	−	24.1995i	−1.80798	−	0.825675i	−0.857784	−	0.514011i	$-0.828159\pi$
$860$	0.283797	+	0.245911i	0.00967739	+	0.00838550i
$861$	−23.6378	+	15.6451i	−0.805574	+	0.533182i
$862$	−29.9986	+	4.31314i	−1.02176	+	0.146906i
$863$	5.29662	+	36.8388i	0.180299	+	1.25401i	0.856056	+	0.516883i	$0.172908\pi$
$863$	5.29662	+	36.8388i	0.180299	+	1.25401i	−0.675757	+	0.737125i	$0.736183\pi$
$864$	−2.95952	−	4.60510i	−0.100685	−	0.156669i
$865$	−1.08163	−	0.937238i	−0.0367765	−	0.0318670i
$866$	5.18927	−	11.3629i	0.176338	−	0.386127i
$867$	3.04534	−	4.73863i	0.103425	−	0.160932i
$868$	1.21012	+	3.92486i	0.0410740	+	0.133219i
$869$	42.6669	+	49.2402i	1.44737	+	1.67036i
$870$	0.724408	−	2.46711i	0.0245597	−	0.0836427i
$871$	1.03331	+	2.26264i	0.0350124	+	0.0766665i
$872$	−5.79830	−	0.833670i	−0.196355	−	0.0282316i
$873$	6.68803			0.226355
$874$	40.9193	−	24.3547i	1.38412	−	0.823812i
$875$	−30.3008	+	0.408271i	−1.02435	+	0.0138021i
$876$	−0.818207	+	5.69075i	−0.0276446	+	0.192273i
$877$	−16.0741	−	35.1973i	−0.542783	−	1.18853i	−0.960071	−	0.279755i	$-0.909747\pi$
$877$	−16.0741	−	35.1973i	−0.542783	−	1.18853i	0.417288	−	0.908774i	$-0.362981\pi$
$878$	15.8518	−	53.9863i	0.534973	−	1.82195i
$879$	−6.60257	+	5.72116i	−0.222699	+	0.192970i
$880$	8.73452	+	29.7470i	0.294441	+	1.00277i
$881$	30.2326	+	19.4293i	1.01856	+	0.654589i	0.939595	−	0.342288i	$-0.111202\pi$
$881$	30.2326	+	19.4293i	1.01856	+	0.654589i	0.0789656	+	0.996877i	$0.474838\pi$
$882$	4.78904	−	11.2814i	0.161256	−	0.379866i
$883$	−22.5942	+	26.0751i	−0.760356	+	0.877497i	−0.995529	−	0.0944562i	$-0.969889\pi$
$883$	−22.5942	+	26.0751i	−0.760356	+	0.877497i	0.235173	+	0.971953i	$0.424434\pi$
$884$	−1.25063	−	1.94602i	−0.0420632	−	0.0654517i
$885$	1.04402	+	7.26130i	0.0350943	+	0.244086i
$886$	0.0929204	+	0.646275i	0.00312172	+	0.0217120i
$887$	12.2123	+	19.0027i	0.410048	+	0.638047i	0.983440	−	0.181234i	$-0.0580092\pi$
$887$	12.2123	+	19.0027i	0.410048	+	0.638047i	−0.573392	+	0.819281i	$0.694373\pi$
$888$	−5.84901	+	6.75011i	−0.196280	+	0.226519i
$889$	7.13384	−	16.1949i	0.239261	−	0.543158i
$890$	14.7371	+	9.47094i	0.493988	+	0.317467i
$891$	−1.20528	−	4.10480i	−0.0403783	−	0.137516i
$892$	16.9348	−	14.6741i	0.567020	−	0.491325i
$893$	−15.2357	+	51.8880i	−0.509843	+	1.73637i
$894$	15.1082	+	33.0824i	0.505295	+	1.10644i
$895$	0.264528	−	1.83983i	0.00884219	−	0.0614988i
$896$	−30.8497	+	0.415666i	−1.03061	+	0.0138864i
$897$	1.18581	+	2.85169i	0.0395931	+	0.0952153i
$898$	−45.3668			−1.51391
$899$	−1.46008	−	0.209928i	−0.0486965	−	0.00700149i
$900$	1.28162	+	2.80635i	0.0427205	+	0.0935449i
$901$	−5.68733	+	19.3693i	−0.189472	+	0.645284i
$902$	−52.5523	−	60.6486i	−1.74980	−	2.01938i
$903$	−0.614305	+	0.189403i	−0.0204428	+	0.00630292i
$904$	−3.26388	+	5.07869i	−0.108555	+	0.168915i
$905$	−6.32048	+	13.8399i	−0.210100	+	0.460054i
$906$	−29.8696	−	25.8822i	−0.992352	−	0.859878i
$907$	14.2934	+	22.2410i	0.474606	+	0.738501i	0.993187	−	0.116527i	$-0.0371762\pi$
$907$	14.2934	+	22.2410i	0.474606	+	0.738501i	−0.518582	+	0.855028i	$0.673540\pi$
$908$	−1.51260	−	10.5203i	−0.0501973	−	0.349130i
$909$	−1.42663	+	0.205119i	−0.0473185	+	0.00680337i
$910$	−2.38836	−	3.60853i	−0.0791734	−	0.119622i
$911$	20.7863	+	18.0114i	0.688682	+	0.596746i	0.927278	−	0.374373i	$-0.122142\pi$
$911$	20.7863	+	18.0114i	0.688682	+	0.596746i	−0.238597	+	0.971119i	$0.576687\pi$
$912$	−25.7711	−	11.7693i	−0.853365	−	0.389719i
$913$	−3.07790	+	4.78930i	−0.101864	+	0.158503i
$914$	−7.84211	−	26.7078i	−0.259394	−	0.883415i
$915$	−8.69796	+	7.53683i	−0.287546	+	0.249160i
$916$	−7.40272	−	2.17363i	−0.244593	−	0.0718189i
$917$	−21.6172	+	10.2264i	−0.713861	+	0.337706i
$918$	5.84290	+	0.840082i	0.192844	+	0.0277268i
$919$			41.7559i			1.37740i	0.725047	+	0.688700i	$0.241818\pi$
$919$			41.7559i			1.37740i	−0.725047	+	0.688700i	$0.758182\pi$
$920$	10.8060	+	3.58005i	0.356262	+	0.118031i
$921$	15.4057			0.507636
$922$	19.0615	+	2.74063i	0.627758	+	0.0902580i
$923$	−9.60221	+	4.38518i	−0.316061	+	0.144340i
$924$	11.6155	+	3.24129i	0.382122	+	0.106631i
$925$	11.9455	−	10.3508i	0.392766	−	0.340333i
$926$	−41.8664	+	12.2931i	−1.37582	+	0.403976i
$927$	−11.5668	−	7.43355i	−0.379904	−	0.244150i
$928$	−2.30219	+	5.04110i	−0.0755732	+	0.165482i
$929$	−27.3349	−	23.6858i	−0.896828	−	0.777106i	0.0787192	−	0.996897i	$-0.474917\pi$
$929$	−27.3349	−	23.6858i	−0.896828	−	0.777106i	−0.975547	+	0.219791i	$0.929462\pi$
$930$	−3.11314	+	2.00069i	−0.102084	+	0.0656054i
$931$	−6.70623	−	39.1273i	−0.219788	−	1.28234i
$932$	4.12445	+	28.6862i	0.135101	+	0.939646i
$933$	−22.0451	+	14.1675i	−0.721723	+	0.463823i
$934$	28.4542	−	32.8379i	0.931051	−	1.07449i
$935$	−19.0325	−	8.69185i	−0.622429	−	0.284254i
$936$	0.569693	−	0.886460i	0.0186210	−	0.0289749i
$937$	31.6066	−	9.28053i	1.03254	−	0.303182i	0.278798	−	0.960350i	$-0.410064\pi$
$937$	31.6066	−	9.28053i	1.03254	−	0.303182i	0.753744	+	0.657168i	$0.228246\pi$
$938$	13.3632	−	11.8982i	0.436323	−	0.388491i
$939$	−1.63850	+	5.58021i	−0.0534703	+	0.182103i
$940$	13.4060	−	6.12229i	0.437254	−	0.199687i
$941$	5.65794	−	39.3519i	0.184444	−	1.28283i	−0.661655	−	0.749808i	$-0.730146\pi$
$941$	5.65794	−	39.3519i	0.184444	−	1.28283i	0.846099	−	0.533026i	$-0.178945\pi$
$942$			32.1188i			1.04649i
$943$	−51.0800	+	5.56280i	−1.66339	+	0.181150i
$944$		−	25.2640i		−	0.822273i
$945$	3.80593	+	0.494970i	0.123807	+	0.0161014i
$946$	−0.756017	−	1.65545i	−0.0245802	−	0.0538232i
$947$	17.0927	+	5.01886i	0.555437	+	0.163091i	0.547392	−	0.836877i	$-0.315621\pi$
$947$	17.0927	+	5.01886i	0.555437	+	0.163091i	0.00804536	+	0.999968i	$0.497439\pi$
$948$	10.6258	+	12.2629i	0.345111	+	0.398279i
$949$	−3.33430	+	0.979039i	−0.108236	+	0.0317809i
$950$	24.1877	+	15.5445i	0.784752	+	0.504330i
$951$	10.7474	+	4.90818i	0.348509	+	0.159159i
$952$	9.40891	−	11.1587i	0.304944	−	0.361657i
$953$	24.7280	+	38.4775i	0.801017	+	1.24641i	0.965597	+	0.260043i	$0.0837369\pi$
$953$	24.7280	+	38.4775i	0.801017	+	1.24641i	−0.164580	+	0.986364i	$0.552627\pi$
$954$	10.3764	−	1.49190i	0.335949	−	0.0483021i
$955$	18.9201	−	2.72030i	0.612240	−	0.0880268i
$956$	22.3703	−	14.3765i	0.723508	−	0.464970i
$957$	−2.83626	+	3.27322i	−0.0916833	+	0.105808i
$958$	−24.0862	+	52.7415i	−0.778191	+	1.70400i
$959$	16.1179	−	25.8389i	0.520475	−	0.834381i
$960$	−0.166417	−	0.566764i	−0.00537108	−	0.0182922i
$961$	−18.9104	−	21.8238i	−0.610014	−	0.703993i
$962$	5.90515	+	1.73391i	0.190390	+	0.0559035i
$963$	1.11810	−	0.510620i	0.0360303	−	0.0164545i
$964$	2.82723	−	19.6638i	0.0910589	−	0.633329i
$965$	5.67654			0.182734
$966$	17.0891	−	14.1949i	0.549833	−	0.456714i
$967$	−16.1316			−0.518756			−0.259378	−	0.965776i	$-0.583518\pi$
$967$	−16.1316			−0.518756			−0.259378	+	0.965776i	$0.583518\pi$
$968$	1.70042	−	11.8267i	0.0546537	−	0.380125i
$969$	17.3924	−	7.94286i	0.558726	−	0.255161i
$970$	−16.2982	−	4.78557i	−0.523302	−	0.153655i
$971$	−9.84366	−	11.3602i	−0.315898	−	0.364566i	0.575488	−	0.817810i	$-0.304812\pi$
$971$	−9.84366	−	11.3602i	−0.315898	−	0.364566i	−0.891386	+	0.453244i	$0.850267\pi$
$972$	−0.300164	−	1.02227i	−0.00962777	−	0.0327892i
$973$	−26.1858	+	41.9789i	−0.839479	+	1.34578i
$974$	18.0633	−	39.5532i	0.578786	−	1.26736i
$975$	−1.22117	+	1.40930i	−0.0391086	+	0.0451337i
$976$	33.3435	−	21.4286i	1.06730	−	0.685912i
$977$	−22.0998	+	3.17748i	−0.707036	+	0.101656i	−0.486447	−	0.873710i	$-0.661707\pi$
$977$	−22.0998	+	3.17748i	−0.707036	+	0.101656i	−0.220589	+	0.975367i	$0.570798\pi$
$978$	−23.9500	+	3.44350i	−0.765838	+	0.110111i
$979$	−15.9531	−	24.8235i	−0.509863	−	0.793362i
$980$	−6.86185	+	8.36411i	−0.219194	+	0.267182i
$981$	−3.25648	−	1.48719i	−0.103972	−	0.0474822i
$982$	24.2105	+	15.5591i	0.772588	+	0.496512i
$983$	−15.3459	+	4.50597i	−0.489459	+	0.143718i	−0.517144	−	0.855899i	$-0.673005\pi$
$983$	−15.3459	+	4.50597i	−0.489459	+	0.143718i	0.0276849	+	0.999617i	$0.491186\pi$
$984$	11.4804	+	13.2491i	0.365982	+	0.422365i
$985$	31.4095	+	9.22267i	1.00079	+	0.293859i
$986$	−2.48257	−	5.43606i	−0.0790610	−	0.173119i
$987$	−3.25373	+	25.0186i	−0.103567	+	0.796352i
$988$			3.89101i			0.123789i
$989$	−1.14702	−	0.205315i	−0.0364730	−	0.00652863i
$990$			10.8655i			0.345328i
$991$	4.38746	−	30.5154i	0.139372	−	0.969355i	−0.793352	−	0.608763i	$-0.791666\pi$
$991$	4.38746	−	30.5154i	0.139372	−	0.969355i	0.932724	−	0.360591i	$-0.117425\pi$
$992$	7.25523	−	3.31335i	0.230354	−	0.105199i
$993$	3.57304	−	12.1687i	0.113387	−	0.386161i
$994$	50.4939	+	56.7108i	1.60157	+	1.79876i
$995$	7.53348	−	2.21203i	0.238827	−	0.0701260i
$996$	−0.766524	+	1.19274i	−0.0242883	+	0.0377933i
$997$	−25.9821	−	11.8656i	−0.822861	−	0.375788i	−0.0409367	−	0.999162i	$-0.513034\pi$
$997$	−25.9821	−	11.8656i	−0.822861	−	0.375788i	−0.781924	+	0.623374i	$0.785761\pi$
$998$	−12.8490	+	14.8286i	−0.406730	+	0.469391i
$999$	−4.59197	+	2.95108i	−0.145284	+	0.0933681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.475.25	yes	320
7.6	odd	2	inner	483.2.r.a.475.26	yes	320
23.20	odd	22	inner	483.2.r.a.181.26	yes	320
161.20	even	22	inner	483.2.r.a.181.25	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.181.25	✓	320	161.20	even	22	inner
483.2.r.a.181.26	yes	320	23.20	odd	22	inner
483.2.r.a.475.25	yes	320	1.1	even	1	trivial
483.2.r.a.475.26	yes	320	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.249170 - 1.73301i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-1.02227 - 0.300164i) q^{4} +(-0.949954 - 1.09631i) q^{5} +(0.493267 + 1.67991i) q^{6} +(2.24482 + 1.40028i) q^{7} +(0.679740 - 1.48842i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.249170 - 1.73301i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-1.02227 - 0.300164i) q^{4} +(-0.949954 - 1.09631i) q^{5} +(0.493267 + 1.67991i) q^{6} +(2.24482 + 1.40028i) q^{7} +(0.679740 - 1.48842i) q^{8} +(0.654861 - 0.755750i) q^{9} +(-2.13661 + 1.37312i) q^{10} +(4.23455 - 0.608836i) q^{11} +(1.05458 - 0.151625i) q^{12} +(0.348161 + 0.541750i) q^{13} +(2.98605 - 3.54139i) q^{14} +(1.31953 + 0.602609i) q^{15} +(-4.20267 - 2.70089i) q^{16} +(3.23495 - 0.949868i) q^{17} +(-1.14655 - 1.32319i) q^{18} +(-5.44140 - 1.59774i) q^{19} +(0.642033 + 1.40586i) q^{20} +(-2.62366 - 0.341213i) q^{21} -7.49023i q^{22} +(-3.94316 - 2.72975i) q^{23} +1.63629i q^{24} +(0.412101 - 2.86623i) q^{25} +(1.02561 - 0.468381i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(-1.87448 - 2.10528i) q^{28} +(0.971380 - 0.285223i) q^{29} +(1.37312 - 2.13661i) q^{30} +(-1.32538 - 0.605279i) q^{31} +(-3.58477 + 4.13705i) q^{32} +(-3.59896 + 2.31291i) q^{33} +(-0.840082 - 5.84290i) q^{34} +(-0.597334 - 3.79121i) q^{35} +(-0.896290 + 0.576011i) q^{36} +(4.12525 + 3.57455i) q^{37} +(-4.12473 + 9.03191i) q^{38} +(-0.541750 - 0.348161i) q^{39} +(-2.27749 + 0.668731i) q^{40} +(8.09702 - 7.01611i) q^{41} +(-1.24506 + 4.46181i) q^{42} +(0.221014 - 0.100934i) q^{43} +(-4.51158 - 0.648668i) q^{44} -1.45062 q^{45} +(-5.71320 + 6.15337i) q^{46} -9.53579i q^{47} +(4.94487 + 0.710965i) q^{48} +(3.07841 + 6.28676i) q^{49} +(-4.86453 - 1.42835i) q^{50} +(-2.54803 + 2.20788i) q^{51} +(-0.193299 - 0.658317i) q^{52} +(-3.23708 + 5.03700i) q^{53} +(1.59262 + 0.727323i) q^{54} +(-4.69010 - 4.06399i) q^{55} +(3.61011 - 2.38941i) q^{56} +(5.61339 - 0.807084i) q^{57} +(-0.252257 - 1.75448i) q^{58} +(2.73409 + 4.25433i) q^{59} +(-1.16803 - 1.01210i) q^{60} +(-3.29586 + 7.21692i) q^{61} +(-1.37920 + 2.14608i) q^{62} +(2.52831 - 0.779528i) q^{63} +(-0.266659 - 0.307740i) q^{64} +(0.263186 - 0.896329i) q^{65} +(3.11156 + 6.81336i) q^{66} +(3.82326 + 0.549702i) q^{67} -3.59210 q^{68} +(4.72080 + 0.845019i) q^{69} +(-6.71906 + 0.0905321i) q^{70} +(-2.33283 + 16.2252i) q^{71} +(-0.679740 - 1.48842i) q^{72} +(-1.52030 + 5.17765i) q^{73} +(7.22263 - 6.25845i) q^{74} +(0.815813 + 2.77841i) q^{75} +(5.08297 + 3.26662i) q^{76} +(10.3583 + 4.56285i) q^{77} +(-0.738356 + 0.852108i) q^{78} +(8.23381 + 12.8121i) q^{79} +(1.03134 + 7.17313i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-10.1415 - 15.7805i) q^{82} +(-0.871454 + 1.00571i) q^{83} +(2.57965 + 1.13634i) q^{84} +(-4.11440 - 2.64417i) q^{85} +(-0.119849 - 0.408170i) q^{86} +(-0.765112 + 0.662973i) q^{87} +(1.97219 - 6.71665i) q^{88} +(-2.86528 - 6.27410i) q^{89} +(-0.361451 + 2.51394i) q^{90} +(0.0229549 + 1.70365i) q^{91} +(3.21158 + 3.97412i) q^{92} +1.45705 q^{93} +(-16.5256 - 2.37603i) q^{94} +(3.41747 + 7.48321i) q^{95} +(1.54223 - 5.25236i) q^{96} +(4.37973 + 5.05447i) q^{97} +(11.6621 - 3.76845i) q^{98} +(2.31291 - 3.59896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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