LMFDB - Embedded newform 483.2.m.a.137.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(137,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 3]))

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

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

chi := DirichletCharacter("483.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.m (of order $6$, degree $2$, 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:	$120$
Relative dimension:	$60$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.7
Character	$\chi$	$=$	483.137
Dual form			483.2.m.a.275.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05926 + 1.18892i) q^{2} +(1.51759 - 0.834823i) q^{3} +(1.82704 - 3.16453i) q^{4} +(-0.178457 - 0.309097i) q^{5} +(-2.13257 + 3.52340i) q^{6} +(2.62376 + 0.340385i) q^{7} +3.93312i q^{8} +(1.60614 - 2.53383i) q^{9} +O(q^{10})$	\(q+(-2.05926 + 1.18892i) q^{2} +(1.51759 - 0.834823i) q^{3} +(1.82704 - 3.16453i) q^{4} +(-0.178457 - 0.309097i) q^{5} +(-2.13257 + 3.52340i) q^{6} +(2.62376 + 0.340385i) q^{7} +3.93312i q^{8} +(1.60614 - 2.53383i) q^{9} +(0.734981 + 0.424342i) q^{10} +(-0.555687 + 0.962478i) q^{11} +(0.130872 - 6.32770i) q^{12} +1.48361 q^{13} +(-5.80771 + 2.41849i) q^{14} +(-0.528866 - 0.320102i) q^{15} +(-1.02207 - 1.77028i) q^{16} +(2.58471 - 4.47685i) q^{17} +(-0.294950 + 7.12739i) q^{18} +(-6.74705 + 3.89541i) q^{19} -1.30420 q^{20} +(4.26595 - 1.67382i) q^{21} -2.64266i q^{22} +(3.39383 + 3.38850i) q^{23} +(3.28346 + 5.96886i) q^{24} +(2.43631 - 4.21981i) q^{25} +(-3.05514 + 1.76389i) q^{26} +(0.322154 - 5.18616i) q^{27} +(5.87088 - 7.68107i) q^{28} -6.21811i q^{29} +(1.46965 + 0.0303959i) q^{30} +(1.10408 - 1.91233i) q^{31} +(-2.60294 - 1.50281i) q^{32} +(-0.0398042 + 1.92454i) q^{33} +12.2920i q^{34} +(-0.363018 - 0.871743i) q^{35} +(-5.08390 - 9.71209i) q^{36} +(3.98917 - 2.30315i) q^{37} +(9.26263 - 16.0433i) q^{38} +(2.25151 - 1.23855i) q^{39} +(1.21572 - 0.701895i) q^{40} -0.798529i q^{41} +(-6.79469 + 8.51868i) q^{42} +5.09766i q^{43} +(2.03052 + 3.51697i) q^{44} +(-1.06983 - 0.0442722i) q^{45} +(-11.0174 - 2.94282i) q^{46} +(2.10281 - 1.21406i) q^{47} +(-3.02895 - 1.83330i) q^{48} +(6.76828 + 1.78618i) q^{49} +11.5862i q^{50} +(0.185145 - 8.95179i) q^{51} +(2.71061 - 4.69492i) q^{52} +(-4.27812 + 7.40992i) q^{53} +(5.50250 + 11.0627i) q^{54} +0.396666 q^{55} +(-1.33878 + 10.3196i) q^{56} +(-6.98725 + 11.5442i) q^{57} +(7.39281 + 12.8047i) q^{58} +(9.79854 + 5.65719i) q^{59} +(-1.97923 + 1.08877i) q^{60} +(4.54113 - 2.62182i) q^{61} +5.25065i q^{62} +(5.07661 - 6.10148i) q^{63} +11.2351 q^{64} +(-0.264761 - 0.458580i) q^{65} +(-2.20615 - 4.01046i) q^{66} +(-6.41222 - 3.70209i) q^{67} +(-9.44474 - 16.3588i) q^{68} +(7.97923 + 2.30909i) q^{69} +(1.78398 + 1.36355i) q^{70} +3.16085i q^{71} +(9.96588 + 6.31715i) q^{72} +(-4.98817 + 8.63977i) q^{73} +(-5.47649 + 9.48556i) q^{74} +(0.174514 - 8.43781i) q^{75} +28.4683i q^{76} +(-1.78560 + 2.33617i) q^{77} +(-3.16391 + 5.22735i) q^{78} +(11.1686 - 6.44819i) q^{79} +(-0.364792 + 0.631839i) q^{80} +(-3.84063 - 8.13938i) q^{81} +(0.949384 + 1.64438i) q^{82} -6.78799 q^{83} +(2.49723 - 16.5578i) q^{84} -1.84504 q^{85} +(-6.06068 - 10.4974i) q^{86} +(-5.19103 - 9.43653i) q^{87} +(-3.78554 - 2.18558i) q^{88} +(5.78893 + 10.0267i) q^{89} +(2.25569 - 1.18077i) q^{90} +(3.89264 + 0.504998i) q^{91} +(16.9237 - 4.54895i) q^{92} +(0.0790862 - 3.82384i) q^{93} +(-2.88683 + 5.00013i) q^{94} +(2.40812 + 1.39033i) q^{95} +(-5.20478 - 0.107647i) q^{96} +0.191290i q^{97} +(-16.0613 + 4.36870i) q^{98} +(1.54625 + 2.95389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9}+O(q^{10}) $ 120 * q - 2 * q^3 + 52 * q^4 - 24 * q^6 + 2 * q^9	$ 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9} + 14 q^{12} - 16 q^{13} - 60 q^{16} - 10 q^{18} - 24 q^{24} - 40 q^{25} - 20 q^{27} - 4 q^{31} + 64 q^{36} - 12 q^{39} - 20 q^{46} + 140 q^{48} - 48 q^{49} - 76 q^{52} - 2 q^{54} + 72 q^{55} - 28 q^{58} - 128 q^{64} - 20 q^{69} - 68 q^{70} + 6 q^{72} + 20 q^{73} + 20 q^{75} - 156 q^{78} - 62 q^{81} + 80 q^{82} + 112 q^{85} + 46 q^{87} - 38 q^{93} + 36 q^{94} + 72 q^{96}+O(q^{100}) $ 120 * q - 2 * q^3 + 52 * q^4 - 24 * q^6 + 2 * q^9 + 14 * q^12 - 16 * q^13 - 60 * q^16 - 10 * q^18 - 24 * q^24 - 40 * q^25 - 20 * q^27 - 4 * q^31 + 64 * q^36 - 12 * q^39 - 20 * q^46 + 140 * q^48 - 48 * q^49 - 76 * q^52 - 2 * q^54 + 72 * q^55 - 28 * q^58 - 128 * q^64 - 20 * q^69 - 68 * q^70 + 6 * q^72 + 20 * q^73 + 20 * q^75 - 156 * q^78 - 62 * q^81 + 80 * q^82 + 112 * q^85 + 46 * q^87 - 38 * q^93 + 36 * q^94 + 72 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−2.05926	+	1.18892i	−1.45612	+	0.840690i	−0.998817	−	0.0486218i	$-0.984517\pi$
$2$	−2.05926	+	1.18892i	−1.45612	+	0.840690i	−0.457301	+	0.889312i	$0.651184\pi$
$3$	1.51759	−	0.834823i	0.876179	−	0.481985i
$3$	1.51759	−	0.834823i	0.876179	−	0.481985i
$4$	1.82704	−	3.16453i	0.913520	−	1.58226i
$5$	−0.178457	−	0.309097i	−0.0798086	−	0.138233i	0.823359	−	0.567521i	$-0.192098\pi$
$5$	−0.178457	−	0.309097i	−0.0798086	−	0.138233i	−0.903167	+	0.429289i	$0.858764\pi$
$6$	−2.13257	+	3.52340i	−0.870620	+	1.43842i
$7$	2.62376	+	0.340385i	0.991690	+	0.128653i
$7$	2.62376	+	0.340385i	0.991690	+	0.128653i
$8$			3.93312i			1.39057i
$9$	1.60614	−	2.53383i	0.535380	−	0.844611i
$10$	0.734981	+	0.424342i	0.232422	+	0.134189i
$11$	−0.555687	+	0.962478i	−0.167546	+	0.290198i	−0.937556	−	0.347833i	$-0.886918\pi$
$11$	−0.555687	+	0.962478i	−0.167546	+	0.290198i	0.770011	+	0.638031i	$0.220251\pi$
$12$	0.130872	−	6.32770i	0.0377795	−	1.82665i
$13$	1.48361			0.411479			0.205740	−	0.978607i	$-0.434040\pi$
$13$	1.48361			0.411479			0.205740	+	0.978607i	$0.434040\pi$
$14$	−5.80771	+	2.41849i	−1.55217	+	0.646369i
$15$	−0.528866	−	0.320102i	−0.136553	−	0.0826499i
$16$	−1.02207	−	1.77028i	−0.255518	−	0.442570i
$17$	2.58471	−	4.47685i	0.626885	−	1.08580i	−0.361288	−	0.932454i	$-0.617663\pi$
$17$	2.58471	−	4.47685i	0.626885	−	1.08580i	0.988173	−	0.153342i	$-0.0490036\pi$
$18$	−0.294950	+	7.12739i	−0.0695203	+	1.67994i
$19$	−6.74705	+	3.89541i	−1.54788	+	0.893669i	−0.549576	+	0.835444i	$0.685211\pi$
$19$	−6.74705	+	3.89541i	−1.54788	+	0.893669i	−0.998304	+	0.0582247i	$0.981456\pi$
$20$	−1.30420			−0.291627
$21$	4.26595	−	1.67382i	0.930907	−	0.365257i
$22$		−	2.64266i		−	0.563417i
$23$	3.39383	+	3.38850i	0.707663	+	0.706550i
$23$	3.39383	+	3.38850i	0.707663	+	0.706550i
$24$	3.28346	+	5.96886i	0.670234	+	1.21839i
$25$	2.43631	−	4.21981i	0.487261	−	0.843961i
$26$	−3.05514	+	1.76389i	−0.599162	+	0.345926i
$27$	0.322154	−	5.18616i	0.0619986	−	0.998076i
$28$	5.87088	−	7.68107i	1.10949	−	1.45159i
$29$		−	6.21811i		−	1.15467i	−0.816506	−	0.577337i	$-0.804092\pi$
$29$		−	6.21811i		−	1.15467i	0.816506	−	0.577337i	$-0.195908\pi$
$30$	1.46965	+	0.0303959i	0.268320	+	0.00554950i
$31$	1.10408	−	1.91233i	0.198299	−	0.343464i	−0.749678	−	0.661803i	$-0.769792\pi$
$31$	1.10408	−	1.91233i	0.198299	−	0.343464i	0.947977	+	0.318339i	$0.103125\pi$
$32$	−2.60294	−	1.50281i	−0.460140	−	0.265662i
$33$	−0.0398042	+	1.92454i	−0.00692902	+	0.335020i
$34$			12.2920i			2.10806i
$35$	−0.363018	−	0.871743i	−0.0613613	−	0.147351i
$36$	−5.08390	−	9.71209i	−0.847317	−	1.61868i
$37$	3.98917	−	2.30315i	0.655815	−	0.378635i	−0.134866	−	0.990864i	$-0.543060\pi$
$37$	3.98917	−	2.30315i	0.655815	−	0.378635i	0.790681	+	0.612229i	$0.209727\pi$
$38$	9.26263	−	16.0433i	1.50260	−	2.60257i
$39$	2.25151	−	1.23855i	0.360529	−	0.198327i
$40$	1.21572	−	0.701895i	0.192222	−	0.110979i
$41$		−	0.798529i		−	0.124709i	−0.998054	−	0.0623547i	$-0.980139\pi$
$41$		−	0.798529i		−	0.124709i	0.998054	−	0.0623547i	$-0.0198610\pi$
$42$	−6.79469	+	8.51868i	−1.04844	+	1.31446i
$43$			5.09766i			0.777385i	0.921367	+	0.388693i	$0.127073\pi$
$43$			5.09766i			0.777385i	−0.921367	+	0.388693i	$0.872927\pi$
$44$	2.03052	+	3.51697i	0.306113	+	0.530203i
$45$	−1.06983	−	0.0442722i	−0.159481	−	0.00659972i
$46$	−11.0174	−	2.94282i	−1.62443	−	0.433895i
$47$	2.10281	−	1.21406i	0.306727	−	0.177089i	−0.338734	−	0.940882i	$-0.609999\pi$
$47$	2.10281	−	1.21406i	0.306727	−	0.177089i	0.645461	+	0.763793i	$0.276665\pi$
$48$	−3.02895	−	1.83330i	−0.437192	−	0.264615i
$49$	6.76828	+	1.78618i	0.966897	+	0.255168i
$50$			11.5862i			1.63854i
$51$	0.185145	−	8.95179i	0.0259254	−	1.25350i
$52$	2.71061	−	4.69492i	0.375894	−	0.651068i
$53$	−4.27812	+	7.40992i	−0.587645	+	1.01783i	0.406895	+	0.913475i	$0.366611\pi$
$53$	−4.27812	+	7.40992i	−0.587645	+	1.01783i	−0.994540	+	0.104356i	$0.966722\pi$
$54$	5.50250	+	11.0627i	0.748796	+	1.50544i
$55$	0.396666			0.0534864
$56$	−1.33878	+	10.3196i	−0.178901	+	1.37901i
$57$	−6.98725	+	11.5442i	−0.925484	+	1.52907i
$58$	7.39281	+	12.8047i	0.970724	+	1.68134i
$59$	9.79854	+	5.65719i	1.27566	+	0.736503i	0.976047	−	0.217558i	$-0.0698090\pi$
$59$	9.79854	+	5.65719i	1.27566	+	0.736503i	0.299613	+	0.954061i	$0.403142\pi$
$60$	−1.97923	+	1.08877i	−0.255518	+	0.140560i
$61$	4.54113	−	2.62182i	0.581433	−	0.335690i	−0.180270	−	0.983617i	$-0.557697\pi$
$61$	4.54113	−	2.62182i	0.581433	−	0.335690i	0.761703	+	0.647927i	$0.224364\pi$
$62$			5.25065i			0.666833i
$63$	5.07661	−	6.10148i	0.639593	−	0.768714i
$64$	11.2351			1.40439
$65$	−0.264761	−	0.458580i	−0.0328396	−	0.0568798i
$66$	−2.20615	−	4.01046i	−0.271559	−	0.493654i
$67$	−6.41222	−	3.70209i	−0.783377	−	0.452283i	0.0542489	−	0.998527i	$-0.482724\pi$
$67$	−6.41222	−	3.70209i	−0.783377	−	0.452283i	−0.837626	+	0.546245i	$0.816057\pi$
$68$	−9.44474	−	16.3588i	−1.14534	−	1.98379i
$69$	7.97923	+	2.30909i	0.960586	+	0.277981i
$70$	1.78398	+	1.36355i	0.213226	+	0.162975i
$71$			3.16085i			0.375124i	0.982253	+	0.187562i	$0.0600586\pi$
$71$			3.16085i			0.375124i	−0.982253	+	0.187562i	$0.939941\pi$
$72$	9.96588	+	6.31715i	1.17449	+	0.744483i
$73$	−4.98817	+	8.63977i	−0.583822	+	1.01121i	0.411200	+	0.911545i	$0.365110\pi$
$73$	−4.98817	+	8.63977i	−0.583822	+	1.01121i	−0.995021	+	0.0996633i	$0.968223\pi$
$74$	−5.47649	+	9.48556i	−0.636629	+	1.10267i
$75$	0.174514	−	8.43781i	0.0201512	−	0.974314i
$76$			28.4683i			3.26554i
$77$	−1.78560	+	2.33617i	−0.203488	+	0.266231i
$78$	−3.16391	+	5.22735i	−0.358242	+	0.591881i
$79$	11.1686	−	6.44819i	1.25656	−	0.725478i	0.284159	−	0.958777i	$-0.408286\pi$
$79$	11.1686	−	6.44819i	1.25656	−	0.725478i	0.972405	+	0.233299i	$0.0749522\pi$
$80$	−0.364792	+	0.631839i	−0.0407850	+	0.0706418i
$81$	−3.84063	−	8.13938i	−0.426736	−	0.904376i
$82$	0.949384	+	1.64438i	0.104842	+	0.181592i
$83$	−6.78799			−0.745079			−0.372539	−	0.928016i	$-0.621513\pi$
$83$	−6.78799			−0.745079			−0.372539	+	0.928016i	$0.621513\pi$
$84$	2.49723	−	16.5578i	0.272470	−	1.80661i
$85$	−1.84504			−0.200123
$86$	−6.06068	−	10.4974i	−0.653540	−	1.13196i
$87$	−5.19103	−	9.43653i	−0.556536	−	1.01170i
$88$	−3.78554	−	2.18558i	−0.403540	−	0.232984i
$89$	5.78893	+	10.0267i	0.613626	+	1.06283i	0.990624	+	0.136617i	$0.0436229\pi$
$89$	5.78893	+	10.0267i	0.613626	+	1.06283i	−0.376998	+	0.926214i	$0.623044\pi$
$90$	2.25569	−	1.18077i	0.237771	−	0.124464i
$91$	3.89264	+	0.504998i	0.408059	+	0.0529382i
$92$	16.9237	−	4.54895i	1.76441	−	0.474261i
$93$	0.0790862	−	3.82384i	0.00820086	−	0.396514i
$94$	−2.88683	+	5.00013i	−0.297753	+	0.515724i
$95$	2.40812	+	1.39033i	0.247068	+	0.142645i
$96$	−5.20478	−	0.107647i	−0.531210	−	0.0109867i
$97$			0.191290i			0.0194226i	0.999953	+	0.00971130i	$0.00309125\pi$
$97$			0.191290i			0.0194226i	−0.999953	+	0.00971130i	$0.996909\pi$
$98$	−16.0613	+	4.36870i	−1.62243	+	0.441305i
$99$	1.54625	+	2.95389i	0.155404	+	0.296877i
$100$	−8.90246	−	15.4195i	−0.890246	−	1.54195i
$101$	−8.68182	−	5.01245i	−0.863873	−	0.498757i	0.00143441	−	0.999999i	$-0.499543\pi$
$101$	−8.68182	−	5.01245i	−0.863873	−	0.498757i	−0.865307	+	0.501242i	$0.832877\pi$
$102$	10.2617	+	18.6542i	1.01606	+	1.84704i
$103$	−7.96694	+	4.59972i	−0.785006	+	0.453223i	−0.838202	−	0.545361i	$-0.816393\pi$
$103$	−7.96694	+	4.59972i	−0.785006	+	0.453223i	0.0531954	+	0.998584i	$0.483059\pi$
$104$			5.83522i			0.572190i
$105$	−1.27866	−	1.01989i	−0.124785	−	0.0995310i
$106$		−	20.3453i		−	1.97611i
$107$	−5.03584	−	8.72233i	−0.486833	−	0.843220i	0.513052	−	0.858357i	$-0.328515\pi$
$107$	−5.03584	−	8.72233i	−0.486833	−	0.843220i	−0.999885	+	0.0151377i	$0.995181\pi$
$108$	−15.8231	−	10.4948i	−1.52258	−	1.00986i
$109$	−13.4727	−	7.77847i	−1.29045	−	0.745042i	−0.311717	−	0.950175i	$-0.600904\pi$
$109$	−13.4727	−	7.77847i	−1.29045	−	0.745042i	−0.978734	+	0.205133i	$0.934237\pi$
$110$	−0.816839	+	0.471602i	−0.0778825	+	0.0449655i
$111$	4.13119	−	6.82547i	0.392115	−	0.647845i
$112$	−2.07910	−	4.99269i	−0.196456	−	0.471765i
$113$	7.37382			0.693670			0.346835	−	0.937926i	$-0.387256\pi$
$113$	7.37382			0.693670			0.346835	+	0.937926i	$0.387256\pi$
$114$	0.663488	−	32.0798i	0.0621414	−	3.00455i
$115$	0.441721	−	1.65373i	0.0411907	−	0.154211i
$116$	−19.6774	−	11.3607i	−1.82700	−	1.05482i
$117$	2.38288	−	3.75922i	0.220298	−	0.347540i
$118$	−26.9037			−2.47668
$119$	8.30553	−	10.8664i	0.761366	−	0.996122i
$120$	1.25900	−	2.08010i	0.114930	−	0.189886i
$121$	4.88242	+	8.45661i	0.443857	+	0.768783i
$122$	−6.23426	+	10.7980i	−0.564423	+	0.977609i
$123$	−0.666631	−	1.21184i	−0.0601081	−	0.109268i
$124$	−4.03441	−	6.98780i	−0.362301	−	0.627523i
$125$	−3.52368			−0.315168
$126$	−3.19993	+	18.6002i	−0.285073	+	1.65704i
$127$	−13.8089			−1.22534			−0.612671	−	0.790338i	$-0.709905\pi$
$127$	−13.8089			−1.22534			−0.612671	+	0.790338i	$0.709905\pi$
$128$	−17.9302	+	10.3520i	−1.58482	+	0.914998i
$129$	4.25564	+	7.73614i	0.374688	+	0.681129i
$130$	1.09042	+	0.629557i	0.0956366	+	0.0552158i
$131$	−5.86216	+	3.38452i	−0.512180	+	0.295707i	−0.733729	−	0.679442i	$-0.762222\pi$
$131$	−5.86216	+	3.38452i	−0.512180	+	0.295707i	0.221550	+	0.975149i	$0.428889\pi$
$132$	6.01754	+	3.64218i	0.523760	+	0.317011i
$133$	−19.0286	+	7.92405i	−1.64999	+	0.687102i
$134$	17.6059			1.52092
$135$	−1.66052	+	0.825931i	−0.142915	+	0.0710849i
$136$	17.6080	+	10.1660i	1.50987	+	0.871726i
$137$	6.95654	−	12.0491i	0.594337	−	1.02942i	−0.399303	−	0.916819i	$-0.630748\pi$
$137$	6.95654	−	12.0491i	0.594337	−	1.02942i	0.993640	−	0.112603i	$-0.0359188\pi$
$138$	−19.1766	+	4.73162i	−1.63242	+	0.402782i
$139$	−5.27070			−0.447055			−0.223527	−	0.974698i	$-0.571757\pi$
$139$	−5.27070			−0.447055			−0.223527	+	0.974698i	$0.571757\pi$
$140$	−3.42190	−	0.443928i	−0.289204	−	0.0375188i
$141$	2.17767	−	3.59792i	0.183393	−	0.302999i
$142$	−3.75799	−	6.50902i	−0.315363	−	0.546225i
$143$	−0.824422	+	1.42794i	−0.0689416	+	0.119410i
$144$	−6.12718	−	0.253558i	−0.510599	−	0.0211299i
$145$	−1.92200	+	1.10967i	−0.159614	+	0.0921530i
$146$		−	23.7221i		−	1.96325i
$147$	11.7626	−	2.93963i	0.970162	−	0.242457i
$148$		−	16.8318i		−	1.38356i
$149$	−2.74340	−	4.75170i	−0.224748	−	0.389275i	0.731496	−	0.681846i	$-0.238822\pi$
$149$	−2.74340	−	4.75170i	−0.224748	−	0.389275i	−0.956244	+	0.292571i	$0.905489\pi$
$150$	9.67247	+	17.5831i	0.789754	+	1.43566i
$151$	−2.12367	+	3.67831i	−0.172822	+	0.299337i	−0.939405	−	0.342808i	$-0.888622\pi$
$151$	−2.12367	+	3.67831i	−0.172822	+	0.299337i	0.766583	+	0.642145i	$0.221955\pi$
$152$	−15.3211	−	26.5370i	−1.24271	−	2.15243i
$153$	−7.19219	−	13.7397i	−0.581454	−	1.11079i
$154$	0.899521	−	6.93371i	0.0724854	−	0.558734i
$155$	−0.788128			−0.0633039
$156$	0.194163	−	9.38783i	0.0155455	−	0.751628i
$157$	−5.62939	−	3.25013i	−0.449274	−	0.259389i	0.258249	−	0.966078i	$-0.416854\pi$
$157$	−5.62939	−	3.25013i	−0.449274	−	0.259389i	−0.707524	+	0.706690i	$0.750188\pi$
$158$	−15.3327	+	26.5570i	−1.21980	+	2.11276i
$159$	−0.306444	+	14.8167i	−0.0243026	+	1.17504i
$160$			1.07275i			0.0848084i
$161$	7.75122	+	10.0458i	0.610882	+	0.791722i
$162$	17.5859	+	12.1949i	1.38168	+	0.958125i
$163$	−3.41851	−	5.92103i	−0.267758	−	0.463770i	0.700525	−	0.713628i	$-0.252949\pi$
$163$	−3.41851	−	5.92103i	−0.267758	−	0.463770i	−0.968283	+	0.249858i	$0.919616\pi$
$164$	−2.52697	−	1.45895i	−0.197323	−	0.113924i
$165$	0.601975	−	0.331146i	0.0468637	−	0.0257797i
$166$	13.9783	−	8.07035i	1.08492	−	0.626381i
$167$			18.6039i			1.43962i	0.694174	+	0.719808i	$0.255770\pi$
$167$			18.6039i			1.43962i	−0.694174	+	0.719808i	$0.744230\pi$
$168$	6.58332	+	16.7785i	0.507914	+	1.29449i
$169$	−10.7989			−0.830685
$170$	3.79943	−	2.19360i	0.291403	−	0.168242i
$171$	−0.966385	+	23.3525i	−0.0739013	+	1.78581i
$172$	16.1317	+	9.31362i	1.23003	+	0.710157i
$173$	1.19172	−	0.688042i	0.0906051	−	0.0523109i	−0.454013	−	0.890995i	$-0.650008\pi$
$173$	1.19172	−	0.688042i	0.0906051	−	0.0523109i	0.544618	+	0.838684i	$0.316675\pi$
$174$	21.9089	+	13.2606i	1.66091	+	1.00528i
$175$	7.82865	−	10.2425i	0.591790	−	0.774260i
$176$	2.27181			0.171244
$177$	19.5929	+	0.405228i	1.47269	+	0.0304588i
$178$	−23.8419	−	13.7651i	−1.78702	−	1.03174i
$179$	9.53476	+	5.50490i	0.712662	+	0.411455i	0.812046	−	0.583594i	$-0.198354\pi$
$179$	9.53476	+	5.50490i	0.712662	+	0.411455i	−0.0993842	+	0.995049i	$0.531687\pi$
$180$	−2.09472	+	3.30462i	−0.156131	+	0.246312i
$181$			19.4077i			1.44257i	0.692641	+	0.721283i	$0.256447\pi$
$181$			19.4077i			1.44257i	−0.692641	+	0.721283i	$0.743553\pi$
$182$	−8.61636	+	3.58810i	−0.638687	+	0.265967i
$183$	4.70281	−	7.76989i	0.347641	−	0.574367i
$184$	−13.3274	+	13.3484i	−0.982507	+	0.984054i
$185$	−1.42379	−	0.822027i	−0.104679	−	0.0604367i
$186$	4.38336	+	7.96831i	0.321404	+	0.584265i
$187$	2.87258	+	4.97545i	0.210064	+	0.363841i
$188$		−	8.87254i		−	0.647096i
$189$	2.61055	−	13.4976i	0.189889	−	0.981806i
$190$	−6.61194			−0.479681
$191$	4.26072	+	7.37979i	0.308295	+	0.533983i	0.977990	−	0.208654i	$-0.0669082\pi$
$191$	4.26072	+	7.37979i	0.308295	+	0.533983i	−0.669694	+	0.742637i	$0.733575\pi$
$192$	17.0503	−	9.37936i	1.23050	−	0.676897i
$193$	−12.4836	+	21.6222i	−0.898589	+	1.55640i	−0.0692910	+	0.997596i	$0.522074\pi$
$193$	−12.4836	+	21.6222i	−0.898589	+	1.55640i	−0.829298	+	0.558806i	$0.811260\pi$
$194$	−0.227428	−	0.393917i	−0.0163284	−	0.0282816i
$195$	−0.784631	−	0.474906i	−0.0561886	−	0.0340087i
$196$	18.0183	−	18.1550i	1.28702	−	1.29678i
$197$			0.818313i			0.0583024i	0.999575	+	0.0291512i	$0.00928043\pi$
$197$			0.818313i			0.0583024i	−0.999575	+	0.0291512i	$0.990720\pi$
$198$	−6.69606	−	4.24448i	−0.475868	−	0.301642i
$199$	4.08520	+	2.35859i	0.289592	+	0.167196i	0.637758	−	0.770237i	$-0.279862\pi$
$199$	4.08520	+	2.35859i	0.289592	+	0.167196i	−0.348166	+	0.937433i	$0.613195\pi$
$200$	16.5970	+	9.58229i	1.17359	+	0.677570i
$201$	−12.8217	−	0.265183i	−0.904372	−	0.0187046i
$202$	23.8375			1.67720
$203$	2.11655	−	16.3149i	0.148553	−	1.14508i
$204$	−27.9899	−	16.9412i	−1.95969	−	1.18612i
$205$	−0.246823	+	0.142504i	−0.0172389	+	0.00995288i
$206$	10.9373	−	18.9440i	0.762041	−	1.31989i
$207$	14.0369	−	3.15701i	0.975629	−	0.219427i
$208$	−1.51635	−	2.62640i	−0.105140	−	0.182108i
$209$		−	8.65851i		−	0.598922i
$210$	3.84566	+	0.579998i	0.265376	+	0.0400236i
$211$	21.5073			1.48062			0.740311	−	0.672265i	$-0.234678\pi$
$211$	21.5073			1.48062			0.740311	+	0.672265i	$0.234678\pi$
$212$	15.6326	+	27.0764i	1.07365	+	1.85962i
$213$	2.63875	+	4.79687i	0.180804	+	0.328676i
$214$	20.7402	+	11.9744i	1.41777	+	0.818552i
$215$	1.57567	−	0.909715i	0.107460	−	0.0620420i
$216$	20.3978	+	1.26707i	1.38789	+	0.0862134i
$217$	3.54778	−	4.64168i	0.240839	−	0.315098i
$218$	36.9918			2.50540
$219$	−0.357306	+	17.2758i	−0.0241445	+	1.16739i
$220$	0.724724	−	1.25526i	0.0488609	−	0.0846296i
$221$	3.83470	−	6.64190i	0.257950	−	0.446782i
$222$	−0.392285	+	18.9671i	−0.0263284	+	1.27299i
$223$	−24.1040			−1.61412			−0.807062	−	0.590467i	$-0.798944\pi$
$223$	−24.1040			−1.61412			−0.807062	+	0.590467i	$0.798944\pi$
$224$	−6.31798	−	4.82902i	−0.422138	−	0.322653i
$225$	−6.77924	−	12.9508i	−0.451949	−	0.863386i
$226$	−15.1846	+	8.76684i	−1.01007	+	0.583162i
$227$	−12.3280	+	21.3528i	−0.818241	+	1.41723i	0.0887365	+	0.996055i	$0.471717\pi$
$227$	−12.3280	+	21.3528i	−0.818241	+	1.41723i	−0.906977	+	0.421180i	$0.861616\pi$
$228$	23.7660	+	43.2031i	1.57394	+	2.86120i
$229$	3.30248	−	1.90669i	0.218234	−	0.125998i	−0.386898	−	0.922122i	$-0.626454\pi$
$229$	3.30248	−	1.90669i	0.218234	−	0.125998i	0.605132	+	0.796125i	$0.293120\pi$
$230$	1.05652	+	3.93063i	0.0696651	+	0.259178i
$231$	−0.759522	+	5.03600i	−0.0499729	+	0.331344i
$232$	24.4566			1.60566
$233$	6.40597	−	3.69849i	0.419669	−	0.242296i	−0.275267	−	0.961368i	$-0.588766\pi$
$233$	6.40597	−	3.69849i	0.419669	−	0.242296i	0.694936	+	0.719072i	$0.255433\pi$
$234$	−0.437590	+	10.5743i	−0.0286061	+	0.691261i
$235$	−0.750525	−	0.433316i	−0.0489588	−	0.0282664i
$236$	35.8046	−	20.6718i	2.33068	−	1.34562i
$237$	11.5662	−	19.1095i	0.751306	−	1.24129i
$238$	−4.18401	+	32.2513i	−0.271209	+	2.09054i
$239$			13.0214i			0.842283i	0.906995	+	0.421142i	$0.138370\pi$
$239$			13.0214i			0.842283i	−0.906995	+	0.421142i	$0.861630\pi$
$240$	−0.0261303	+	1.26341i	−0.00168671	+	0.0815526i
$241$	−18.1150	−	10.4587i	−1.16689	−	0.673706i	−0.213946	−	0.976845i	$-0.568632\pi$
$241$	−18.1150	−	10.4587i	−1.16689	−	0.673706i	−0.952946	+	0.303140i	$0.901965\pi$
$242$	−20.1084	−	11.6096i	−1.29262	−	0.746292i
$243$	−12.6234	−	9.14598i	−0.809794	−	0.586715i
$244$		−	19.1607i		−	1.22664i
$245$	−0.655746	−	2.41081i	−0.0418941	−	0.154021i
$246$	2.81354	+	1.70292i	0.179385	+	0.108574i
$247$	−10.0100	+	5.77927i	−0.636920	+	0.367726i
$248$	7.52142	+	4.34249i	0.477611	+	0.275749i
$249$	−10.3014	+	5.66677i	−0.652823	+	0.359117i
$250$	7.25619	−	4.18936i	0.458922	−	0.264958i
$251$	−21.9034			−1.38253			−0.691266	−	0.722600i	$-0.742947\pi$
$251$	−21.9034			−1.38253			−0.691266	+	0.722600i	$0.742947\pi$
$252$	−10.0331	−	27.2127i	−0.632026	−	1.71424i
$253$	−5.14726	+	1.38355i	−0.323605	+	0.0869827i
$254$	28.4361	−	16.4176i	1.78424	−	1.03013i
$255$	−2.80002	+	1.54029i	−0.175344	+	0.0964565i
$256$	13.3802	−	23.1752i	0.836263	−	1.44845i
$257$	−10.8306	+	6.25305i	−0.675594	+	0.390055i	−0.798193	−	0.602402i	$-0.794211\pi$
$257$	−10.8306	+	6.25305i	−0.675594	+	0.390055i	0.122599	+	0.992456i	$0.460877\pi$
$258$	−17.9611	−	10.8711i	−1.11821	−	0.676807i
$259$	11.2506	−	4.68506i	0.699078	−	0.291116i
$260$	−1.93492			−0.119998
$261$	−15.7557	−	9.98716i	−0.975251	−	0.618190i
$262$	8.04782	−	13.9392i	0.497196	−	0.861169i
$263$	−5.55585	+	9.62301i	−0.342588	+	0.593380i	−0.984913	−	0.173053i	$-0.944637\pi$
$263$	−5.55585	+	9.62301i	−0.342588	+	0.593380i	0.642324	+	0.766433i	$0.277970\pi$
$264$	−7.56947	−	0.156555i	−0.465869	−	0.00963529i
$265$	3.05385			0.187596
$266$	29.7639	−	38.9411i	1.82494	−	2.38763i
$267$	17.1557	+	10.3837i	1.04991	+	0.635472i
$268$	−23.4307	+	13.5277i	−1.43126	+	0.826339i
$269$	−16.3711	−	9.45186i	−0.998164	−	0.576290i	−0.0904592	−	0.995900i	$-0.528833\pi$
$269$	−16.3711	−	9.45186i	−0.998164	−	0.576290i	−0.907704	+	0.419610i	$0.862167\pi$
$270$	2.43748	−	3.67503i	0.148340	−	0.223655i
$271$	0.943008	+	1.63334i	0.0572837	+	0.0992182i	0.893245	−	0.449570i	$-0.148423\pi$
$271$	0.943008	+	1.63334i	0.0572837	+	0.0992182i	−0.835962	+	0.548788i	$0.815089\pi$
$272$	−10.5670			−0.640721
$273$	6.32900	−	2.48329i	0.383049	−	0.150295i
$274$			33.0829i			1.99861i
$275$	2.70765	+	4.68978i	0.163277	+	0.282804i
$276$	21.8855	−	21.0317i	1.31735	−	1.26596i
$277$	−0.617211	+	1.06904i	−0.0370846	+	0.0642324i	−0.883972	−	0.467540i	$-0.845140\pi$
$277$	−0.617211	+	1.06904i	−0.0370846	+	0.0642324i	0.846887	+	0.531772i	$0.178474\pi$
$278$	10.8537	−	6.26641i	0.650964	−	0.375834i
$279$	−3.07221	−	5.86903i	−0.183928	−	0.351370i
$280$	3.42867	−	1.42780i	0.204902	−	0.0853271i
$281$	2.26786			0.135289			0.0676446	−	0.997709i	$-0.478452\pi$
$281$	2.26786			0.135289			0.0676446	+	0.997709i	$0.478452\pi$
$282$	−0.206785	+	9.99812i	−0.0123139	+	0.595380i
$283$	7.63262	+	4.40669i	0.453712	+	0.261951i	0.709397	−	0.704809i	$-0.248968\pi$
$283$	7.63262	+	4.40669i	0.453712	+	0.261951i	−0.255685	+	0.966760i	$0.582301\pi$
$284$	10.0026	+	5.77500i	0.593545	+	0.342683i
$285$	4.81522	+	0.0995903i	0.285229	+	0.00589922i
$286$		−	3.92067i		−	0.231834i
$287$	0.271807	−	2.09515i	0.0160443	−	0.123673i
$288$	−7.98857	+	4.18170i	−0.470731	+	0.246409i
$289$	−4.86147	−	8.42031i	−0.285969	−	0.495312i
$290$	2.63861	−	4.57020i	0.154944	−	0.268371i
$291$	0.159694	+	0.290300i	0.00936141	+	0.0170177i
$292$	18.2272	+	31.5704i	1.06667	+	1.84752i
$293$	−19.4950			−1.13891			−0.569456	−	0.822022i	$-0.692846\pi$
$293$	−19.4950			−1.13891			−0.569456	+	0.822022i	$0.692846\pi$
$294$	−20.7273	+	20.0382i	−1.20884	+	1.16865i
$295$		−	4.03827i		−	0.235117i
$296$	9.05856	+	15.6899i	0.526518	+	0.911956i
$297$	4.81254	+	3.19194i	0.279252	+	0.185215i
$298$	11.2987	+	6.52333i	0.654519	+	0.377887i
$299$	5.03512	+	5.02720i	0.291188	+	0.290731i
$300$	−26.3828	−	15.9685i	−1.52321	−	0.921940i
$301$	−1.73516	+	13.3750i	−0.100013	+	0.770925i
$302$		−	10.0995i		−	0.581160i
$303$	−17.3599	−	0.359045i	−0.997301	−	0.0206266i
$304$	13.7919	+	7.96277i	0.791021	+	0.456696i
$305$	−1.62080	−	0.935768i	−0.0928067	−	0.0535819i
$306$	31.1459	+	19.7427i	1.78049	+	1.12862i
$307$	20.5386			1.17220			0.586101	−	0.810238i	$-0.300662\pi$
$307$	20.5386			1.17220			0.586101	+	0.810238i	$0.300662\pi$
$308$	4.13049	+	9.91886i	0.235357	+	0.565179i
$309$	−8.25058	+	13.6315i	−0.469359	+	0.775467i
$310$	1.62296	−	0.937017i	0.0921780	−	0.0532190i
$311$	22.1844	+	12.8082i	1.25796	+	0.726285i	0.972678	−	0.232158i	$-0.0745786\pi$
$311$	22.1844	+	12.8082i	1.25796	+	0.726285i	0.285285	+	0.958443i	$0.407912\pi$
$312$	4.87137	+	8.85545i	0.275787	+	0.501341i
$313$	18.3014	−	10.5663i	1.03445	−	0.597242i	0.116196	−	0.993226i	$-0.462930\pi$
$313$	18.3014	−	10.5663i	1.03445	−	0.597242i	0.918257	+	0.395984i	$0.129596\pi$
$314$	15.4565			0.872262
$315$	−2.79191	−	0.480313i	−0.157306	−	0.0270626i
$316$		−	47.1244i		−	2.65095i
$317$	−20.6498	+	11.9222i	−1.15981	+	0.669615i	−0.951258	−	0.308397i	$-0.900207\pi$
$317$	−20.6498	+	11.9222i	−1.15981	+	0.669615i	−0.208549	+	0.978012i	$0.566874\pi$
$318$	−16.9847	−	30.8757i	−0.952455	−	1.73142i
$319$	5.98480	+	3.45532i	0.335084	+	0.193461i
$320$	−2.00500	−	3.47275i	−0.112083	−	0.194133i
$321$	−14.9239	−	9.03286i	−0.832973	−	0.504165i
$322$	−27.9054	−	11.4714i	−1.55511	−	0.639278i
$323$			40.2741i			2.24091i
$324$	−32.7743	−	2.71722i	−1.82079	−	0.150957i
$325$	3.61452	−	6.26054i	0.200498	−	0.347272i
$326$	14.0792	+	8.12863i	0.779775	+	0.450203i
$327$	−26.9396	−	0.557177i	−1.48977	−	0.0308120i
$328$	3.14071			0.173417
$329$	5.93053	−	2.46964i	0.326961	−	0.136156i
$330$	−0.845919	+	1.39761i	−0.0465663	+	0.0769361i
$331$	−1.01261	−	1.75388i	−0.0556578	−	0.0964021i	0.836854	−	0.547426i	$-0.184392\pi$
$331$	−1.01261	−	1.75388i	−0.0556578	−	0.0964021i	−0.892512	+	0.451024i	$0.851059\pi$
$332$	−12.4019	+	21.4808i	−0.680645	+	1.17891i
$333$	0.571371	−	13.8071i	0.0313109	−	0.756622i
$334$	−22.1185	−	38.3104i	−1.21027	−	2.09625i
$335$			2.64267i			0.144384i
$336$	−7.32323	−	5.84117i	−0.399515	−	0.318662i
$337$			32.4125i			1.76562i	0.469731	+	0.882810i	$0.344351\pi$
$337$			32.4125i			1.76562i	−0.469731	+	0.882810i	$0.655649\pi$
$338$	22.2378	−	12.8390i	1.20958	−	0.698349i
$339$	11.1904	−	6.15583i	0.607779	−	0.334339i
$340$	−3.37097	+	5.83869i	−0.182817	+	0.316648i
$341$	1.22705	+	2.12531i	0.0664484	+	0.115092i
$342$	−25.7741	−	49.2378i	−1.39370	−	2.66248i
$343$	17.1504	+	6.99033i	0.926033	+	0.377442i
$344$	−20.0497			−1.08101
$345$	−0.710220	−	2.87843i	−0.0382370	−	0.154970i
$346$	−1.63605	+	2.83372i	−0.0879545	+	0.152342i
$347$	4.44473	+	2.56617i	0.238606	+	0.137759i	0.614536	−	0.788889i	$-0.289343\pi$
$347$	4.44473	+	2.56617i	0.238606	+	0.137759i	−0.375930	+	0.926648i	$0.622677\pi$
$348$	−39.3464	−	0.813778i	−2.10919	−	0.0436231i
$349$	−8.39696			−0.449479			−0.224739	−	0.974419i	$-0.572153\pi$
$349$	−8.39696			−0.449479			−0.224739	+	0.974419i	$0.572153\pi$
$350$	−3.94378	+	30.3996i	−0.210804	+	1.62493i
$351$	0.477951	−	7.69423i	0.0255111	−	0.410687i
$352$	2.89284	−	1.67018i	0.154189	−	0.0890211i
$353$	24.8159	+	14.3275i	1.32082	+	0.762574i	0.983859	−	0.178946i	$-0.0572689\pi$
$353$	24.8159	+	14.3275i	1.32082	+	0.762574i	0.336957	+	0.941520i	$0.390602\pi$
$354$	−40.8287	+	22.4598i	−2.17002	+	1.19373i
$355$	0.977011	−	0.564078i	0.0518544	−	0.0299381i
$356$	42.3064			2.24224
$357$	3.53283	−	23.4244i	0.186977	−	1.23975i
$358$	−26.1794			−1.38363
$359$	3.00486	+	5.20457i	0.158590	+	0.274686i	0.934361	−	0.356329i	$-0.115972\pi$
$359$	3.00486	+	5.20457i	0.158590	+	0.274686i	−0.775770	+	0.631015i	$0.782638\pi$
$360$	0.174128	−	4.20777i	0.00917736	−	0.221769i
$361$	20.8485	−	36.1106i	1.09729	−	1.90056i
$362$	−23.0742	−	39.9656i	−1.21275	−	2.10055i
$363$	14.4693	+	8.75768i	0.759440	+	0.459659i
$364$	8.71009	−	11.3957i	0.456533	−	0.597297i
$365$	3.56071			0.186376
$366$	−0.446564	+	21.5915i	−0.0233423	+	1.12860i
$367$	−25.6979	−	14.8367i	−1.34142	−	0.774468i	−0.354402	−	0.935093i	$-0.615316\pi$
$367$	−25.6979	−	14.8367i	−1.34142	−	0.774468i	−0.987016	+	0.160625i	$0.948649\pi$
$368$	2.52985	−	9.47131i	0.131877	−	0.493726i
$369$	−2.02334	−	1.28255i	−0.105331	−	0.0667669i
$370$	3.90928			0.203234
$371$	−13.7470	+	17.9857i	−0.713708	+	0.933769i
$372$	−11.9561	−	7.23658i	−0.619897	−	0.375199i
$373$	3.99722	−	2.30780i	0.206968	−	0.119493i	−0.392933	−	0.919567i	$-0.628540\pi$
$373$	3.99722	−	2.30780i	0.206968	−	0.119493i	0.599902	+	0.800074i	$0.295206\pi$
$374$	−11.8308	−	6.83051i	−0.611756	−	0.353197i
$375$	−5.34749	+	2.94165i	−0.276143	+	0.151906i
$376$	4.77504	+	8.27062i	0.246254	+	0.426525i
$377$		−	9.22525i		−	0.475124i
$378$	10.6717	+	30.8988i	0.548893	+	1.58926i
$379$		−	21.1201i		−	1.08487i	−0.840099	−	0.542433i	$-0.817503\pi$
$379$		−	21.1201i		−	1.08487i	0.840099	−	0.542433i	$-0.182497\pi$
$380$	8.79947	−	5.08038i	0.451404	−	0.260618i
$381$	−20.9562	+	11.5280i	−1.07362	+	0.590597i
$382$	−17.5479	−	10.1313i	−0.897828	−	0.518361i
$383$	−17.8644	−	30.9420i	−0.912826	−	1.58106i	−0.810053	−	0.586357i	$-0.800562\pi$
$383$	−17.8644	−	30.9420i	−0.912826	−	1.58106i	−0.102773	−	0.994705i	$-0.532772\pi$
$384$	−18.5686	+	30.6786i	−0.947573	+	1.56556i
$385$	1.04076	+	0.135019i	0.0530419	+	0.00688120i
$386$		−	59.3678i		−	3.02174i
$387$	12.9166	+	8.18755i	0.656588	+	0.416197i
$388$	0.605344	+	0.349495i	0.0307317	+	0.0177429i
$389$	−1.62293	+	2.81100i	−0.0822858	+	0.142523i	−0.904231	−	0.427043i	$-0.859555\pi$
$389$	−1.62293	+	2.81100i	−0.0822858	+	0.142523i	0.821946	+	0.569566i	$0.192889\pi$
$390$	2.18038	+	0.0450956i	0.110408	+	0.00228350i
$391$	23.9419	−	6.43540i	1.21079	−	0.325452i
$392$	−7.02526	+	26.6205i	−0.354829	+	1.34454i
$393$	−6.07087	+	10.0302i	−0.306235	+	0.505955i
$394$	−0.972906	−	1.68512i	−0.0490143	−	0.0848952i
$395$	−3.98624	−	2.30145i	−0.200569	−	0.115799i
$396$	12.1727	+	0.503738i	0.611702	+	0.0253138i
$397$	−2.42368	−	4.19795i	−0.121641	−	0.210689i	0.798774	−	0.601631i	$-0.205482\pi$
$397$	−2.42368	−	4.19795i	−0.121641	−	0.210689i	−0.920415	+	0.390943i	$0.872149\pi$
$398$	−11.2167			−0.562240
$399$	−22.2624	+	27.9110i	−1.11451	+	1.39730i
$400$	−9.96031			−0.498016
$401$	11.6124	+	20.1133i	0.579898	+	1.00441i	0.995490	+	0.0948617i	$0.0302409\pi$
$401$	11.6124	+	20.1133i	0.579898	+	1.00441i	−0.415593	+	0.909551i	$0.636426\pi$
$402$	26.7185	−	14.6978i	1.33260	−	0.733061i
$403$	1.63803	−	2.83715i	0.0815959	−	0.141328i
$404$	−31.7240	+	18.3159i	−1.57833	+	0.911250i
$405$	−1.83047	+	2.63966i	−0.0909570	+	0.131166i
$406$	15.0385	+	36.1130i	0.746346	+	1.79226i
$407$			5.11931i			0.253755i
$408$	35.2085	+	0.728197i	1.74308	+	0.0360511i
$409$	9.43221	−	16.3371i	0.466393	−	0.807816i	−0.532871	−	0.846197i	$-0.678887\pi$
$409$	9.43221	−	16.3371i	0.466393	−	0.807816i	0.999263	+	0.0383811i	$0.0122201\pi$
$410$	0.338849	−	0.586904i	0.0167346	−	0.0289851i
$411$	0.498301	−	24.0930i	0.0245794	−	1.18842i
$412$			33.6155i			1.65612i
$413$	23.7834	+	18.1784i	1.17031	+	0.894501i
$414$	−25.1521	+	23.1897i	−1.23616	+	1.13971i
$415$	1.21137	+	2.09815i	0.0594637	+	0.102994i
$416$	−3.86175	−	2.22958i	−0.189338	−	0.109314i
$417$	−7.99874	+	4.40010i	−0.391700	+	0.215474i
$418$	10.2942	+	17.8301i	0.503508	+	0.872101i
$419$	22.7529			1.11155			0.555776	−	0.831332i	$-0.312421\pi$
$419$	22.7529			1.11155			0.555776	+	0.831332i	$0.312421\pi$
$420$	−5.56364	+	2.18298i	−0.271478	+	0.106519i
$421$			23.6961i			1.15488i	0.816435	+	0.577438i	$0.195947\pi$
$421$			23.6961i			1.15488i	−0.816435	+	0.577438i	$0.804053\pi$
$422$	−44.2891	+	25.5703i	−2.15596	+	1.24474i
$423$	0.301187	−	7.27812i	0.0146442	−	0.353874i
$424$	−29.1441	−	16.8264i	−1.41536	−	0.817160i
$425$	−12.5943	−	21.8140i	−0.610913	−	1.05813i
$426$	−11.1370	−	6.74075i	−0.539587	−	0.326591i
$427$	12.8073	−	5.33332i	0.619788	−	0.258097i
$428$	−36.8027			−1.77893
$429$	−0.0590539	+	2.85527i	−0.00285115	+	0.137854i
$430$	−2.16315	+	3.74668i	−0.104316	+	0.180681i
$431$	20.3474	−	35.2428i	0.980101	−	1.69759i	0.318147	−	0.948041i	$-0.396939\pi$
$431$	20.3474	−	35.2428i	0.980101	−	1.69759i	0.661954	−	0.749544i	$-0.269727\pi$
$432$	−9.51021	+	4.73032i	−0.457560	+	0.227588i
$433$		−	21.8918i		−	1.05205i	−0.850468	−	0.526027i	$-0.823681\pi$
$433$		−	21.8918i		−	1.05205i	0.850468	−	0.526027i	$-0.176319\pi$
$434$	−1.78724	+	13.7765i	−0.0857903	+	0.661291i
$435$	−1.99043	+	3.28855i	−0.0954338	+	0.157674i
$436$	−49.2303	+	28.4231i	−2.35771	+	1.36122i
$437$	−36.0979	−	9.64198i	−1.72680	−	0.461238i
$438$	−19.8037	−	36.0003i	−0.946259	−	1.72016i
$439$	11.2093	+	19.4151i	0.534991	+	0.926632i	0.999164	+	0.0408869i	$0.0130183\pi$
$439$	11.2093	+	19.4151i	0.534991	+	0.926632i	−0.464173	+	0.885745i	$0.653648\pi$
$440$			1.56014i			0.0743765i
$441$	15.3967	−	14.2808i	0.733175	−	0.680040i
$442$			18.2365i			0.867424i
$443$	4.48683	−	2.59047i	0.213176	−	0.123077i	−0.389611	−	0.920980i	$-0.627390\pi$
$443$	4.48683	−	2.59047i	0.213176	−	0.123077i	0.602786	+	0.797903i	$0.294057\pi$
$444$	−14.0515	−	25.5437i	−0.666857	−	1.21225i
$445$	2.06616	−	3.57869i	0.0979452	−	0.169646i
$446$	49.6365	−	28.6576i	2.35035	−	1.35698i
$447$	−8.13017	−	4.92087i	−0.384544	−	0.232749i
$448$	29.4784	+	3.82427i	1.39272	+	0.180680i
$449$		−	27.4074i		−	1.29344i	−0.762729	−	0.646719i	$-0.776141\pi$
$449$		−	27.4074i		−	1.29344i	0.762729	−	0.646719i	$-0.223859\pi$
$450$	29.3576	+	18.6091i	1.38393	+	0.877243i
$451$	0.768567	+	0.443732i	0.0361904	+	0.0208945i
$452$	13.4723	−	23.3346i	0.633682	−	1.09757i
$453$	−0.152120	+	7.35505i	−0.00714723	+	0.345570i
$454$		−	58.6280i		−	2.75155i
$455$	−0.538577	−	1.29333i	−0.0252489	−	0.0606320i
$456$	−45.4048	−	27.4817i	−2.12628	−	1.28695i
$457$	25.5483	−	14.7503i	1.19510	−	0.689990i	0.235640	−	0.971840i	$-0.424281\pi$
$457$	25.5483	−	14.7503i	1.19510	−	0.689990i	0.959458	+	0.281850i	$0.0909481\pi$
$458$	−4.53378	+	7.85275i	−0.211850	+	0.366935i
$459$	−22.3850	−	14.8470i	−1.04484	−	0.692997i
$460$	−4.42622	−	4.41926i	−0.206374	−	0.206049i
$461$		−	24.4755i		−	1.13994i	−0.821667	−	0.569968i	$-0.806956\pi$
$461$		−	24.4755i		−	1.13994i	0.821667	−	0.569968i	$-0.193044\pi$
$462$	−4.42332	−	11.2735i	−0.205792	−	0.524488i
$463$	18.3799			0.854187			0.427093	−	0.904207i	$-0.359538\pi$
$463$	18.3799			0.854187			0.427093	+	0.904207i	$0.359538\pi$
$464$	−11.0078	+	6.35536i	−0.511024	+	0.295040i
$465$	−1.19605	+	0.657947i	−0.0554656	+	0.0305116i
$466$	−8.79438	+	15.2323i	−0.407392	+	0.705623i
$467$	−5.12130	−	8.87035i	−0.236985	−	0.410471i	0.722862	−	0.690992i	$-0.242826\pi$
$467$	−5.12130	−	8.87035i	−0.236985	−	0.410471i	−0.959848	+	0.280521i	$0.909493\pi$
$468$	−7.54252	−	14.4089i	−0.348653	−	0.666053i
$469$	−15.5640	−	11.8960i	−0.718679	−	0.549308i
$470$	2.06070			0.0950532
$471$	−11.2564	−	0.232809i	−0.518666	−	0.0107273i
$472$	−22.2504	+	38.5389i	−1.02416	+	1.77389i
$473$	−4.90638	−	2.83270i	−0.225596	−	0.130248i
$474$	−1.09829	+	53.1027i	−0.0504462	+	2.43909i
$475$			37.9616i			1.74180i
$476$	−19.2125	−	46.1364i	−0.880604	−	2.11466i
$477$	11.9042	+	22.7414i	0.545058	+	1.04126i
$478$	−15.4813	−	26.8144i	−0.708099	−	1.22646i
$479$	−11.2599	+	19.5027i	−0.514478	+	0.891101i	0.485381	+	0.874303i	$0.338681\pi$
$479$	−11.2599	+	19.5027i	−0.514478	+	0.891101i	−0.999859	+	0.0167987i	$0.994653\pi$
$480$	0.895558	+	1.62799i	0.0408764	+	0.0743074i
$481$	5.91836	−	3.41697i	0.269854	−	0.155800i
$482$	49.7382			2.26551
$483$	20.1496	+	8.77451i	0.916840	+	0.399254i
$484$	35.6815			1.62189
$485$	0.0591274	−	0.0341372i	0.00268484	−	0.00155009i
$486$	36.8688	+	3.82577i	1.67240	+	0.173541i
$487$	5.24103	−	9.07773i	0.237494	−	0.411351i	−0.722501	−	0.691370i	$-0.757007\pi$
$487$	5.24103	−	9.07773i	0.237494	−	0.411351i	0.959994	+	0.280019i	$0.0903408\pi$
$488$	10.3120	+	17.8608i	0.466801	+	0.808522i
$489$	−10.1309	−	6.13182i	−0.458135	−	0.277291i
$490$	4.21661	+	4.18487i	0.190487	+	0.189053i
$491$		−	7.74756i		−	0.349643i	−0.984600	−	0.174821i	$-0.944065\pi$
$491$		−	7.74756i		−	0.349643i	0.984600	−	0.174821i	$-0.0559348\pi$
$492$	−5.05285	−	0.104505i	−0.227800	−	0.00471146i
$493$	−27.8376	−	16.0720i	−1.25374	−	0.723848i
$494$	13.7421	−	23.8020i	0.618287	−	1.07090i
$495$	0.637101	−	1.00509i	0.0286356	−	0.0451752i
$496$	−4.51381			−0.202676
$497$	−1.07591	+	8.29333i	−0.0482610	+	0.372007i
$498$	14.4759	−	23.9168i	0.648681	−	1.07174i
$499$	21.0714	+	36.4967i	0.943286	+	1.63382i	0.759148	+	0.650918i	$0.225616\pi$
$499$	21.0714	+	36.4967i	0.943286	+	1.63382i	0.184138	+	0.982900i	$0.441051\pi$
$500$	−6.43791	+	11.1508i	−0.287912	+	0.498678i
$501$	15.5310	+	28.2331i	0.693874	+	1.26136i
$502$	45.1049	−	26.0413i	2.01313	−	1.16228i
$503$	−23.3264			−1.04007			−0.520037	−	0.854144i	$-0.674082\pi$
$503$	−23.3264			−1.04007			−0.520037	+	0.854144i	$0.674082\pi$
$504$	23.9979	+	19.9669i	1.06895	+	0.889398i
$505$			3.57804i			0.159220i
$506$	8.95464	−	8.96874i	0.398082	−	0.398709i
$507$	−16.3883	+	9.01518i	−0.727829	+	0.400378i
$508$	−25.2294	+	43.6986i	−1.11937	+	1.93881i
$509$	11.9873	−	6.92087i	0.531328	−	0.306762i	−0.210229	−	0.977652i	$-0.567421\pi$
$509$	11.9873	−	6.92087i	0.531328	−	0.306762i	0.741557	+	0.670890i	$0.234088\pi$
$510$	3.93470	−	6.50083i	0.174231	−	0.287862i
$511$	−16.0286	+	20.9708i	−0.709065	+	0.927694i
$512$			22.2236i			0.982156i
$513$	18.0286	+	36.2462i	0.795983	+	1.60031i
$514$	14.8687	−	25.7533i	0.655830	−	1.13593i
$515$	2.84352	+	1.64171i	0.125300	+	0.0723423i
$516$	32.2564	+	0.667141i	1.42001	+	0.0293692i
$517$			2.69855i			0.118682i
$518$	−17.5978	+	23.0238i	−0.773202	+	1.01161i
$519$	1.23415	−	2.03904i	0.0541732	−	0.0895041i
$520$	1.80365	−	1.04134i	0.0790953	−	0.0456657i
$521$	−3.50081	+	6.06358i	−0.153373	+	0.265650i	−0.932465	−	0.361259i	$-0.882347\pi$
$521$	−3.50081	+	6.06358i	−0.153373	+	0.265650i	0.779092	+	0.626909i	$0.215680\pi$
$522$	44.3189	+	1.83403i	1.93979	+	0.0802733i
$523$	−24.5619	+	14.1808i	−1.07402	+	0.620083i	−0.929276	−	0.369387i	$-0.879568\pi$
$523$	−24.5619	+	14.1808i	−1.07402	+	0.620083i	−0.144740	+	0.989470i	$0.546235\pi$
$524$			24.7346i			1.08054i
$525$	3.32998	−	22.0794i	0.145332	−	0.963625i
$526$		−	26.4217i		−	1.15204i
$527$	−5.70747	−	9.88563i	−0.248621	−	0.430625i
$528$	3.44766	−	1.89656i	0.150040	−	0.0825370i
$529$	0.0361920	+	23.0000i	0.00157357	+	0.999999i
$530$	−6.28867	+	3.63077i	−0.273163	+	0.157710i
$531$	30.0722	−	15.7416i	1.30502	−	0.683128i
$532$	−9.69017	+	74.6941i	−0.420122	+	3.23840i
$533$		−	1.18471i		−	0.0513153i
$534$	−47.6735	−	0.986003i	−2.06303	−	0.0426685i
$535$	−1.79737	+	3.11313i	−0.0777069	+	0.134592i
$536$	14.5608	−	25.2200i	0.628931	−	1.08934i
$537$	19.0654	+	0.394319i	0.822735	+	0.0170161i
$538$	44.9498			1.93793
$539$	−5.48020	+	5.52176i	−0.236049	+	0.237839i
$540$	−0.420152	+	6.76376i	−0.0180805	+	0.291066i
$541$	22.6020	+	39.1478i	0.971735	+	1.68309i	0.690315	+	0.723509i	$0.257472\pi$
$541$	22.6020	+	39.1478i	0.971735	+	1.68309i	0.281419	+	0.959585i	$0.409195\pi$
$542$	−3.88380	−	2.24231i	−0.166824	−	0.0963156i
$543$	16.2020	+	29.4529i	0.695296	+	1.26395i
$544$	−13.4557	+	7.76867i	−0.576909	+	0.333079i
$545$			5.55250i			0.237843i
$546$	−10.0807	+	12.6384i	−0.431412	+	0.540873i
$547$	0.668545			0.0285849			0.0142925	−	0.999898i	$-0.495450\pi$
$547$	0.668545			0.0285849			0.0142925	+	0.999898i	$0.495450\pi$
$548$	−25.4197	−	44.0283i	−1.08588	−	1.88080i
$549$	0.650430	−	15.7175i	0.0277597	−	0.670806i
$550$	−11.1515	−	6.43832i	−0.475502	−	0.274531i
$551$	24.2221	+	41.9539i	1.03190	+	1.78730i
$552$	−9.08192	+	31.3833i	−0.386552	+	1.33576i
$553$	31.4986	−	13.1169i	1.33946	−	0.557787i
$554$		−	2.93525i		−	0.124707i
$555$	−2.84698	−	0.0588824i	−0.120847	−	0.00249942i
$556$	−9.62977	+	16.6793i	−0.408393	+	0.707358i
$557$	13.7213	−	23.7660i	0.581390	−	1.00700i	−0.413925	−	0.910311i	$-0.635842\pi$
$557$	13.7213	−	23.7660i	0.581390	−	1.00700i	0.995315	−	0.0966864i	$-0.0308244\pi$
$558$	13.3043	+	8.43327i	0.563214	+	0.357009i
$559$			7.56293i			0.319878i
$560$	−1.17220	+	1.53363i	−0.0495344	+	0.0648076i
$561$	8.51301	+	5.15259i	0.359420	+	0.217542i
$562$	−4.67012	+	2.69629i	−0.196997	+	0.113736i
$563$	−11.8874	+	20.5895i	−0.500992	+	0.867744i	0.499007	+	0.866598i	$0.333698\pi$
$563$	−11.8874	+	20.5895i	−0.500992	+	0.867744i	−0.999999	+	0.00114606i	$0.999635\pi$
$564$	−7.40700	−	13.4648i	−0.311891	−	0.566972i
$565$	−1.31591	−	2.27923i	−0.0553609	−	0.0958878i
$566$	−20.9567			−0.880878
$567$	−7.30638	−	22.6631i	−0.306839	−	0.951761i
$568$	−12.4320			−0.521636
$569$	−13.7733	−	23.8561i	−0.577409	−	1.00010i	−0.995775	−	0.0918231i	$-0.970731\pi$
$569$	−13.7733	−	23.8561i	−0.577409	−	1.00010i	0.418366	−	0.908278i	$-0.362603\pi$
$570$	−10.0342	+	5.51980i	−0.420286	+	0.231199i
$571$	−2.01789	−	1.16503i	−0.0844462	−	0.0487550i	0.457182	−	0.889373i	$-0.348859\pi$
$571$	−2.01789	−	1.16503i	−0.0844462	−	0.0487550i	−0.541628	+	0.840618i	$0.682192\pi$
$572$	3.01250	+	5.21781i	0.125959	+	0.218167i
$573$	12.6268	+	7.64252i	0.527494	+	0.319271i
$574$	1.93124	+	4.63762i	0.0806083	+	0.193571i
$575$	22.5672	−	6.06590i	0.941118	−	0.252965i
$576$	18.0452	−	28.4680i	0.751884	−	1.18617i
$577$	20.0639	−	34.7516i	0.835269	−	1.44673i	−0.0585414	−	0.998285i	$-0.518645\pi$
$577$	20.0639	−	34.7516i	0.835269	−	1.44673i	0.893811	−	0.448444i	$-0.148022\pi$
$578$	20.0221	+	11.5598i	0.832809	+	0.480822i
$579$	−0.894209	+	43.2352i	−0.0371620	+	1.79679i
$580$			8.10964i			0.336734i
$581$	−17.8101	−	2.31053i	−0.738887	−	0.0958569i
$582$	−0.673993	−	0.407941i	−0.0279379	−	0.0169097i
$583$	−4.75459	−	8.23518i	−0.196915	−	0.341066i
$584$	−33.9813	−	19.6191i	−1.40616	−	0.811844i
$585$	−1.58721	−	0.0656827i	−0.0656230	−	0.00271564i
$586$	40.1454	−	23.1780i	1.65839	−	0.957473i
$587$			39.6883i			1.63811i	0.573714	+	0.819056i	$0.305502\pi$
$587$			39.6883i			1.63811i	−0.573714	+	0.819056i	$0.694498\pi$
$588$	12.1882	−	42.5939i	0.502632	−	1.75654i
$589$			17.2034i			0.708855i
$590$	4.80116	+	8.31586i	0.197661	+	0.342358i
$591$	0.683147	+	1.24186i	0.0281009	+	0.0510834i
$592$	−8.15443	−	4.70796i	−0.335145	−	0.193496i
$593$	−14.4180	+	8.32423i	−0.592076	+	0.341835i	−0.765918	−	0.642938i	$-0.777715\pi$
$593$	−14.4180	+	8.32423i	−0.592076	+	0.341835i	0.173842	+	0.984774i	$0.444382\pi$
$594$	−13.7052	−	0.851343i	−0.562333	−	0.0349310i
$595$	−4.84096	−	0.628025i	−0.198460	−	0.0257465i
$596$	−20.0492			−0.821246
$597$	8.16864	+	0.168947i	0.334320	+	0.00691455i
$598$	−16.3455	−	4.36600i	−0.668419	−	0.178539i
$599$	−28.1753	−	16.2670i	−1.15121	−	0.664652i	−0.202029	−	0.979380i	$-0.564754\pi$
$599$	−28.1753	−	16.2670i	−1.15121	−	0.664652i	−0.949182	+	0.314727i	$0.898087\pi$
$600$	33.1869	+	0.686386i	1.35485	+	0.0280216i
$601$	−30.8136			−1.25691			−0.628456	−	0.777845i	$-0.716313\pi$
$601$	−30.8136			−1.25691			−0.628456	+	0.777845i	$0.716313\pi$
$602$	−12.3286	−	29.6057i	−0.502478	−	1.20664i
$603$	−19.6794	+	10.3014i	−0.801407	+	0.419506i
$604$	7.76008	+	13.4408i	0.315753	+	0.546900i
$605$	1.74261	−	3.01829i	0.0708472	−	0.122711i
$606$	36.1755	−	19.9001i	1.46953	−	0.808387i
$607$	−11.8728	−	20.5643i	−0.481903	−	0.834680i	0.517881	−	0.855453i	$-0.326721\pi$
$607$	−11.8728	−	20.5643i	−0.481903	−	0.834680i	−0.999784	+	0.0207721i	$0.993388\pi$
$608$	23.4163			0.949655
$609$	−10.4080	−	26.5262i	−0.421753	−	1.07489i
$610$	4.45020			0.180183
$611$	3.11975	−	1.80119i	0.126212	−	0.0728683i
$612$	−56.6200	−	2.34308i	−2.28873	−	0.0947134i
$613$	5.69374	+	3.28728i	0.229968	+	0.132772i	0.610557	−	0.791972i	$-0.290945\pi$
$613$	5.69374	+	3.28728i	0.229968	+	0.132772i	−0.380589	+	0.924744i	$0.624279\pi$
$614$	−42.2945	+	24.4187i	−1.70687	+	0.985459i
$615$	−0.255611	+	0.422315i	−0.0103072	+	0.0170294i
$616$	−9.18843	−	7.02300i	−0.370212	−	0.282965i
$617$	−25.8416			−1.04034			−0.520172	−	0.854061i	$-0.674132\pi$
$617$	−25.8416			−1.04034			−0.520172	+	0.854061i	$0.674132\pi$
$618$	0.783449	−	37.8800i	0.0315150	−	1.52376i
$619$	11.7443	+	6.78057i	0.472043	+	0.272534i	0.717094	−	0.696976i	$-0.245472\pi$
$619$	11.7443	+	6.78057i	0.472043	+	0.272534i	−0.245052	+	0.969510i	$0.578805\pi$
$620$	−1.43994	+	2.49405i	−0.0578294	+	0.100163i
$621$	18.6666	−	16.5093i	0.749065	−	0.662496i
$622$	−60.9114			−2.44232
$623$	11.7758	+	28.2782i	0.471789	+	1.13294i
$624$	−4.49378	−	2.71991i	−0.179895	−	0.108883i
$625$	−11.5527	−	20.0099i	−0.462108	−	0.800395i
$626$	−25.1249	+	43.5175i	−1.00419	+	1.73931i
$627$	−7.22833	−	13.1400i	−0.288672	−	0.524763i
$628$	−20.5702	+	11.8762i	−0.820842	+	0.473913i
$629$		−	23.8119i		−	0.949442i
$630$	6.32033	−	2.33025i	0.251808	−	0.0928395i
$631$		−	19.0453i		−	0.758181i	−0.925360	−	0.379090i	$-0.876237\pi$
$631$		−	19.0453i		−	0.758181i	0.925360	−	0.379090i	$-0.123763\pi$
$632$	25.3615	+	43.9274i	1.00883	+	1.74734i
$633$	32.6392	−	17.9548i	1.29729	−	0.713638i
$634$	28.3489	−	49.1017i	1.12588	−	1.95008i
$635$	2.46430	+	4.26829i	0.0977928	+	0.169382i
$636$	46.3278	+	28.0404i	1.83702	+	1.11187i
$637$	10.0415	+	2.64999i	0.397858	+	0.104996i
$638$	−16.4323			−0.650563
$639$	8.00907	+	5.07677i	0.316834	+	0.200834i
$640$	6.39956	+	3.69479i	0.252965	+	0.146049i
$641$	17.0552	−	29.5404i	0.673638	−	1.16678i	−0.303227	−	0.952919i	$-0.598064\pi$
$641$	17.0552	−	29.5404i	0.673638	−	1.16678i	0.976865	−	0.213857i	$-0.0686028\pi$
$642$	41.4716	+	0.857733i	1.63675	+	0.0338520i
$643$			14.3846i			0.567274i	0.958932	+	0.283637i	$0.0915410\pi$
$643$			14.3846i			0.567274i	−0.958932	+	0.283637i	$0.908459\pi$
$644$	45.9521	−	6.17483i	1.81077	−	0.243322i
$645$	1.63177	−	2.69598i	0.0642508	−	0.106154i
$646$	−47.8824	−	82.9348i	−1.88391	−	3.26303i
$647$	−29.8091	−	17.2103i	−1.17192	−	0.676607i	−0.217787	−	0.975996i	$-0.569884\pi$
$647$	−29.8091	−	17.2103i	−1.17192	−	0.676607i	−0.954131	+	0.299390i	$0.903217\pi$
$648$	32.0132	−	15.1057i	1.25760	−	0.593406i
$649$	−10.8898	+	6.28725i	−0.427463	+	0.246796i
$650$			17.1895i			0.674226i
$651$	1.50908	−	10.0059i	0.0591455	−	0.392163i
$652$	−24.9830			−0.978409
$653$	−23.5463	+	13.5945i	−0.921438	+	0.531993i	−0.884094	−	0.467310i	$-0.845223\pi$
$653$	−23.5463	+	13.5945i	−0.921438	+	0.531993i	−0.0373447	+	0.999302i	$0.511890\pi$
$654$	56.1382	−	30.8816i	2.19518	−	1.20757i
$655$	2.09229	+	1.20799i	0.0817527	+	0.0471999i
$656$	−1.41362	+	0.816154i	−0.0551926	+	0.0318655i
$657$	13.8800	+	26.5159i	0.541512	+	1.03448i
$658$	−9.27632	+	12.1365i	−0.361629	+	0.473131i
$659$	8.55210			0.333142			0.166571	−	0.986029i	$-0.446730\pi$
$659$	8.55210			0.333142			0.166571	+	0.986029i	$0.446730\pi$
$660$	0.0519125	−	2.50998i	0.00202069	−	0.0977009i
$661$	−14.9577	−	8.63583i	−0.581787	−	0.335895i	0.180056	−	0.983656i	$-0.442372\pi$
$661$	−14.9577	−	8.63583i	−0.581787	−	0.335895i	−0.761843	+	0.647761i	$0.775705\pi$
$662$	4.17044	+	2.40780i	0.162089	+	0.0935819i
$663$	0.274682	−	13.2810i	0.0106678	−	0.515789i
$664$		−	26.6980i		−	1.03608i
$665$	5.84510	+	4.46759i	0.226663	+	0.173246i
$666$	15.2388	+	29.1117i	0.590493	+	1.12805i
$667$	21.0701	−	21.1032i	0.815836	−	0.817121i
$668$	58.8726	+	33.9901i	2.27785	+	1.31512i
$669$	−36.5799	+	20.1226i	−1.41426	+	0.777984i
$670$	−3.14191	−	5.44194i	−0.121382	−	0.210241i
$671$			5.82765i			0.224974i
$672$	−13.6195	−	2.05407i	−0.525382	−	0.0792374i
$673$	−27.1396			−1.04615			−0.523077	−	0.852285i	$-0.675216\pi$
$673$	−27.1396			−1.04615			−0.523077	+	0.852285i	$0.675216\pi$
$674$	−38.5357	−	66.7457i	−1.48434	−	2.57095i
$675$	−21.0997	−	13.9945i	−0.812128	−	0.538648i
$676$	−19.7300	+	34.1734i	−0.758847	+	1.31436i
$677$	1.81271	+	3.13970i	0.0696680	+	0.120669i	0.898755	−	0.438451i	$-0.144473\pi$
$677$	1.81271	+	3.13970i	0.0696680	+	0.120669i	−0.829087	+	0.559119i	$0.811139\pi$
$678$	−15.7252	+	25.9809i	−0.603923	+	0.997791i
$679$	−0.0651124	+	0.501901i	−0.00249878	+	0.0192612i
$680$		−	7.25679i		−	0.278285i
$681$	−0.883066	+	42.6965i	−0.0338392	+	1.63613i
$682$	−5.05363	−	2.91771i	−0.193513	−	0.111725i
$683$	29.8773	+	17.2497i	1.14322	+	0.660041i	0.947227	−	0.320564i	$-0.103872\pi$
$683$	29.8773	+	17.2497i	1.14322	+	0.660041i	0.195997	+	0.980604i	$0.437206\pi$
$684$	72.1339	+	45.7241i	2.75811	+	1.74830i
$685$	−4.96578			−0.189733
$686$	−43.6280	+	5.99542i	−1.66573	+	0.228906i
$687$	3.42006	−	5.65056i	0.130483	−	0.215582i
$688$	9.02427	−	5.21017i	0.344047	−	0.198636i
$689$	−6.34705	+	10.9934i	−0.241803	+	0.418816i
$690$	4.88474	+	5.08306i	0.185959	+	0.193509i
$691$	−10.2077	−	17.6803i	−0.388321	−	0.672591i	0.603903	−	0.797058i	$-0.293611\pi$
$691$	−10.2077	−	17.6803i	−0.388321	−	0.672591i	−0.992224	+	0.124467i	$0.960278\pi$
$692$		−	5.02832i		−	0.191148i
$693$	3.05153	+	8.27663i	0.115918	+	0.314403i
$694$	−12.2038			−0.463251
$695$	0.940595	+	1.62916i	0.0356788	+	0.0617975i
$696$	37.1150	−	20.4169i	1.40684	−	0.773902i
$697$	−3.57490	−	2.06397i	−0.135409	−	0.0781784i
$698$	17.2915	−	9.98327i	0.654494	−	0.377872i
$699$	6.63403	−	10.9606i	0.250922	−	0.414569i
$700$	−18.1094	−	43.4874i	−0.684470	−	1.64367i
$701$	−25.6159			−0.967498			−0.483749	−	0.875207i	$-0.660725\pi$
$701$	−25.6159			−0.967498			−0.483749	+	0.875207i	$0.660725\pi$
$702$	8.16356	+	16.4127i	0.308114	+	0.619456i
$703$	−17.9434	+	31.0789i	−0.676748	+	1.17216i
$704$	−6.24322	+	10.8136i	−0.235300	+	0.407552i
$705$	−1.50073	−	0.0310387i	−0.0565207	−	0.00116898i
$706$	−68.1365			−2.56435
$707$	−21.0729	−	16.1066i	−0.792527	−	0.605753i
$708$	37.0793	−	61.2618i	1.39353	−	2.30236i
$709$	36.0499	−	20.8134i	1.35388	−	0.781665i	0.365092	−	0.930971i	$-0.381037\pi$
$709$	36.0499	−	20.8134i	1.35388	−	0.781665i	0.988791	+	0.149306i	$0.0477041\pi$
$710$	−1.34128	+	2.32317i	−0.0503374	+	0.0871869i
$711$	1.59968	−	38.6560i	0.0599929	−	1.44971i
$712$	−39.4363	+	22.7686i	−1.47794	+	0.853289i
$713$	10.2270	−	2.74894i	0.383004	−	0.102949i
$714$	20.5746	+	52.4371i	0.769984	+	1.96241i
$715$	0.588497			0.0220085
$716$	34.8408	−	20.1153i	1.30206	−	0.751745i
$717$	10.8706	+	19.7611i	0.405968	+	0.737991i
$718$	−12.3756	−	7.14504i	−0.461852	−	0.266651i
$719$	7.99498	−	4.61590i	0.298162	−	0.172144i	−0.343455	−	0.939169i	$-0.611597\pi$
$719$	7.99498	−	4.61590i	0.298162	−	0.172144i	0.641617	+	0.767025i	$0.278264\pi$
$720$	1.01507	+	1.93915i	0.0378293	+	0.0722677i
$721$	−22.4690	+	9.35674i	−0.836791	+	0.348463i
$722$			99.1482i			3.68991i
$723$	−36.2223	−	0.749165i	−1.34712	−	0.0278618i
$724$	61.4163	+	35.4587i	2.28252	+	1.31781i
$725$	−26.2392	−	15.1492i	−0.974501	−	0.562628i
$726$	−40.2082	−	0.831602i	−1.49227	−	0.0308636i
$727$		−	2.96802i		−	0.110078i	−0.998484	−	0.0550389i	$-0.982472\pi$
$727$		−	2.96802i		−	0.110078i	0.998484	−	0.0550389i	$-0.0175283\pi$
$728$	−1.98622	+	15.3102i	−0.0736142	+	0.567435i
$729$	−26.7924	−	3.34148i	−0.992312	−	0.123759i
$730$	−7.33243	+	4.23338i	−0.271385	+	0.156684i
$731$	22.8215	+	13.1760i	0.844082	+	0.487331i
$732$	−15.9958	−	29.0781i	−0.591222	−	1.07476i
$733$	6.41386	−	3.70305i	0.236901	−	0.136775i	−0.376850	−	0.926274i	$-0.622993\pi$
$733$	6.41386	−	3.70305i	0.236901	−	0.136775i	0.613752	+	0.789499i	$0.289660\pi$
$734$	70.5582			2.60435
$735$	−3.00776	−	3.11119i	−0.110943	−	0.114758i
$736$	−3.74169	−	13.9204i	−0.137920	−	0.513111i
$737$	7.12637	−	4.11441i	0.262503	−	0.151556i
$738$	5.69143	+	0.235526i	0.209505	+	0.00866983i
$739$	15.0189	−	26.0135i	0.552479	−	0.956921i	−0.445616	−	0.895224i	$-0.647015\pi$
$739$	15.0189	−	26.0135i	0.552479	−	0.956921i	0.998095	−	0.0616970i	$-0.0196512\pi$
$740$	−5.20266	+	3.00375i	−0.191253	+	0.110420i
$741$	−10.3664	+	17.1271i	−0.380817	+	0.629180i
$742$	6.92522	−	53.3812i	0.254233	−	1.95969i
$743$	21.1202			0.774826			0.387413	−	0.921906i	$-0.373369\pi$
$743$	21.1202			0.774826			0.387413	+	0.921906i	$0.373369\pi$
$744$	15.0396	+	0.311056i	0.551379	+	0.0114039i
$745$	−0.979159	+	1.69595i	−0.0358736	+	0.0621349i
$746$	−5.48756	+	9.50472i	−0.200914	+	0.347993i
$747$	−10.9025	+	17.1996i	−0.398900	+	0.629302i
$748$	20.9933			0.767590
$749$	−10.2439	−	24.5995i	−0.374304	−	0.898845i
$750$	7.51452	−	12.4154i	0.274391	−	0.453345i
$751$	13.9987	−	8.08215i	0.510820	−	0.294922i	−0.222351	−	0.974967i	$-0.571373\pi$
$751$	13.9987	−	8.08215i	0.510820	−	0.294922i	0.733170	+	0.680045i	$0.238040\pi$
$752$	−4.29845	−	2.48171i	−0.156748	−	0.0904986i
$753$	−33.2404	+	18.2855i	−1.21135	+	0.666361i
$754$	10.9680	+	18.9972i	0.399432	+	0.691837i
$755$	1.51594			0.0551708
$756$	−37.9439	−	32.9218i	−1.38001	−	1.19735i
$757$		−	34.1445i		−	1.24100i	−0.784205	−	0.620502i	$-0.786929\pi$
$757$		−	34.1445i		−	1.24100i	0.784205	−	0.620502i	$-0.213071\pi$
$758$	25.1100	+	43.4918i	0.912037	+	1.57969i
$759$	−6.65640	+	6.39670i	−0.241612	+	0.232186i
$760$	−5.46834	+	9.47144i	−0.198358	+	0.343565i
$761$	8.65292	−	4.99577i	0.313668	−	0.181096i	−0.334899	−	0.942254i	$-0.608702\pi$
$761$	8.65292	−	4.99577i	0.313668	−	0.181096i	0.648567	+	0.761158i	$0.275369\pi$
$762$	29.4485	−	48.6543i	1.06681	−	1.76256i
$763$	−32.7015	−	24.9948i	−1.18387	−	0.904871i
$764$	31.1381			1.12654
$765$	−2.96340	+	4.67504i	−0.107142	+	0.169026i
$766$	73.5748	+	42.4784i	2.65837	+	1.53481i
$767$	14.5372	+	8.39305i	0.524908	+	0.303056i
$768$	0.958433	−	46.3405i	0.0345845	−	1.67217i
$769$			13.5856i			0.489908i	0.969535	+	0.244954i	$0.0787728\pi$
$769$			13.5856i			0.489908i	−0.969535	+	0.244954i	$0.921227\pi$
$770$	−2.30372	+	0.959333i	−0.0830202	+	0.0345720i
$771$	−11.2162	+	18.5312i	−0.403941	+	0.667384i
$772$	45.6161	+	79.0094i	1.64176	+	2.84361i
$773$	−3.21311	+	5.56527i	−0.115568	+	0.200169i	−0.918006	−	0.396565i	$-0.870202\pi$
$773$	−3.21311	+	5.56527i	−0.115568	+	0.200169i	0.802439	+	0.596734i	$0.203535\pi$
$774$	−36.3330	−	1.50355i	−1.30596	−	0.0540440i
$775$	−5.37977	−	9.31803i	−0.193247	−	0.334714i
$776$	−0.752369			−0.0270085
$777$	13.1625	−	16.5022i	0.472204	−	0.592015i
$778$		−	7.71810i		−	0.276707i
$779$	3.11060	+	5.38772i	0.111449	+	0.193035i
$780$	−2.93640	+	1.61531i	−0.105140	+	0.0578375i
$781$	−3.04225	−	1.75644i	−0.108860	−	0.0628505i
$782$	−41.6514	+	41.7170i	−1.48945	+	1.49180i
$783$	−32.2481	−	2.00319i	−1.15245	−	0.0715882i
$784$	−3.75563	−	13.8073i	−0.134129	−	0.493119i
$785$			2.32004i			0.0828058i
$786$	0.576471	−	27.8725i	0.0205620	−	0.994179i
$787$	6.00288	+	3.46576i	0.213980	+	0.123541i	0.603160	−	0.797621i	$-0.293908\pi$
$787$	6.00288	+	3.46576i	0.213980	+	0.123541i	−0.389180	+	0.921162i	$0.627242\pi$
$788$	2.58957	+	1.49509i	0.0922498	+	0.0532604i
$789$	−0.397969	+	19.2419i	−0.0141681	+	0.685030i
$790$	10.9449			0.389403
$791$	19.3472	+	2.50993i	0.687906	+	0.0892430i
$792$	−11.6180	+	6.08158i	−0.412828	+	0.216100i
$793$	6.73727	−	3.88976i	0.239247	−	0.138129i
$794$	9.98200	+	5.76311i	0.354248	+	0.204525i
$795$	4.63448	−	2.54942i	0.164368	−	0.0904187i
$796$	14.9276	−	8.61847i	0.529096	−	0.305474i
$797$	−32.5033			−1.15133			−0.575663	−	0.817687i	$-0.695256\pi$
$797$	−32.5033			−1.15133			−0.575663	+	0.817687i	$0.695256\pi$
$798$	12.6603	−	83.9441i	0.448170	−	2.97159i
$799$		−	12.5520i		−	0.444057i
$800$	−12.6831	+	7.32261i	−0.448417	+	0.258894i
$801$	34.7039	+	1.43613i	1.22620	+	0.0507433i
$802$	−47.8261	−	27.6124i	−1.68880	−	0.975029i
$803$	−5.54372	−	9.60201i	−0.195634	−	0.338848i
$804$	−24.2649	+	40.0901i	−0.855758	+	1.41387i
$805$	1.72187	−	4.18864i	0.0606881	−	0.147630i
$806$			7.78990i			0.274388i
$807$	−32.7352	−	0.677043i	−1.15233	−	0.0238330i
$808$	19.7146	−	34.1467i	0.693556	−	1.20127i
$809$	30.5038	+	17.6114i	1.07246	+	0.619183i	0.928851	−	0.370452i	$-0.120797\pi$
$809$	30.5038	+	17.6114i	1.07246	+	0.619183i	0.143605	+	0.989635i	$0.454131\pi$
$810$	0.631091	−	7.61203i	0.0221743	−	0.267460i
$811$	16.1570			0.567349			0.283675	−	0.958921i	$-0.408446\pi$
$811$	16.1570			0.567349			0.283675	+	0.958921i	$0.408446\pi$
$812$	−47.7618	−	36.5058i	−1.67611	−	1.28110i
$813$	2.79464	+	1.69149i	0.0980125	+	0.0593230i
$814$	−6.08643	−	10.5420i	−0.213329	−	0.369497i
$815$	−1.22012	+	2.11330i	−0.0427388	+	0.0740258i
$816$	−16.0364	+	8.82161i	−0.561386	+	0.308818i
$817$	−19.8575	−	34.3941i	−0.694725	−	1.20330i
$818$			44.8564i			1.56837i
$819$	7.53170	−	9.05220i	0.263179	−	0.316310i
$820$			1.04144i			0.0363686i
$821$	−6.82135	+	3.93831i	−0.238067	+	0.137448i	−0.614288	−	0.789082i	$-0.710557\pi$
$821$	−6.82135	+	3.93831i	−0.238067	+	0.137448i	0.376221	+	0.926530i	$0.377223\pi$
$822$	27.6184	+	50.2062i	0.963303	+	1.75114i
$823$	6.22226	−	10.7773i	0.216894	−	0.375672i	−0.736963	−	0.675934i	$-0.763741\pi$
$823$	6.22226	−	10.7773i	0.216894	−	0.375672i	0.953857	+	0.300262i	$0.0970740\pi$
$824$	−18.0913	−	31.3350i	−0.630239	−	1.09161i
$825$	8.02422	+	4.85674i	0.279368	+	0.169090i
$826$	−70.5889	−	9.15760i	−2.45610	−	0.318634i
$827$	53.3129			1.85387			0.926936	−	0.375219i	$-0.122433\pi$
$827$	53.3129			1.85387			0.926936	+	0.375219i	$0.122433\pi$
$828$	15.6555	−	50.1880i	0.544065	−	1.74415i
$829$	−14.7529	+	25.5528i	−0.512390	+	0.887485i	0.487507	+	0.873119i	$0.337906\pi$
$829$	−14.7529	+	25.5528i	−0.512390	+	0.887485i	−0.999897	+	0.0143660i	$0.995427\pi$
$830$	−4.98905	−	2.88043i	−0.173172	−	0.0999811i
$831$	−0.0442112	+	2.13762i	−0.00153367	+	0.0741534i
$832$	16.6686			0.577878
$833$	25.4905	−	25.6838i	0.883194	−	0.889891i
$834$	11.2402	−	18.5708i	0.389215	−	0.643054i
$835$	5.75043	−	3.32001i	0.199002	−	0.114894i
$836$	−27.4001	−	15.8194i	−0.947652	−	0.547127i
$837$	−9.56195	−	6.34201i	−0.330509	−	0.219212i
$838$	−46.8542	+	27.0513i	−1.61855	+	0.934471i
$839$	−50.5166			−1.74403			−0.872014	−	0.489481i	$-0.837186\pi$
$839$	−50.5166			−1.74403			−0.872014	+	0.489481i	$0.837186\pi$
$840$	4.01135	−	5.02914i	0.138405	−	0.173522i
$841$	−9.66494			−0.333274
$842$	−28.1726	−	48.7964i	−0.970893	−	1.68164i
$843$	3.44168	−	1.89326i	0.118538	−	0.0652074i
$844$	39.2946	−	68.0603i	1.35258	−	2.34273i
$845$	1.92715	+	3.33791i	0.0662958	+	0.114828i
$846$	8.03285	+	15.3457i	0.276175	+	0.527594i
$847$	9.93183	+	23.8500i	0.341262	+	0.819497i
$848$	17.4902			0.600615
$849$	15.2620	+	0.315654i	0.523790	+	0.0108332i
$850$	51.8699	+	29.9471i	1.77912	+	1.02718i
$851$	21.3428	+	5.70078i	0.731621	+	0.195420i
$852$	20.0009	+	0.413667i	0.685220	+	0.0141720i
$853$	−4.61147			−0.157894			−0.0789469	−	0.996879i	$-0.525156\pi$
$853$	−4.61147			−0.157894			−0.0789469	+	0.996879i	$0.525156\pi$
$854$	−20.0327	+	26.2095i	−0.685505	+	0.896870i
$855$	7.39065	−	3.86872i	0.252755	−	0.132307i
$856$	34.3060	−	19.8066i	1.17256	−	0.676975i
$857$	10.8421	+	6.25967i	0.370358	+	0.213826i	0.673615	−	0.739083i	$-0.264741\pi$
$857$	10.8421	+	6.25967i	0.370358	+	0.213826i	−0.303257	+	0.952909i	$0.598074\pi$
$858$	−3.27307	−	5.94996i	−0.111741	−	0.203128i
$859$	−1.37306	−	2.37821i	−0.0468483	−	0.0811436i	0.841650	−	0.540023i	$-0.181584\pi$
$859$	−1.37306	−	2.37821i	−0.0468483	−	0.0811436i	−0.888499	+	0.458879i	$0.848251\pi$
$860$		−	6.64834i		−	0.226707i
$861$	−1.33659	−	3.40649i	−0.0455509	−	0.116093i
$862$			96.7655i			3.29585i
$863$	46.0073	−	26.5623i	1.56611	−	0.904191i	0.569489	−	0.821999i	$-0.307141\pi$
$863$	46.0073	−	26.5623i	1.56611	−	0.904191i	0.996616	−	0.0821924i	$-0.0261922\pi$
$864$	−8.63236	+	13.0151i	−0.293679	+	0.442784i
$865$	−0.425344	−	0.245573i	−0.0144621	−	0.00834972i
$866$	26.0275	+	45.0810i	0.884452	+	1.53192i
$867$	−14.4072	−	8.72009i	−0.489293	−	0.296150i
$868$	−8.20679	−	19.7076i	−0.278557	−	0.668919i
$869$			14.3327i			0.486203i
$870$	0.189005	−	9.13844i	0.00640787	−	0.309822i
$871$	−9.51322	−	5.49246i	−0.322343	−	0.186105i
$872$	30.5937	−	52.9898i	1.03603	−	1.79446i
$873$	0.484698	+	0.307239i	0.0164045	+	0.0103985i
$874$	85.7986	−	23.0620i	2.90218	−	0.780085i
$875$	−9.24531	−	1.19941i	−0.312549	−	0.0405474i
$876$	54.0171	+	32.6944i	1.82507	+	1.10464i
$877$	−12.5572	−	21.7496i	−0.424025	−	0.734433i	0.572304	−	0.820042i	$-0.306050\pi$
$877$	−12.5572	−	21.7496i	−0.424025	−	0.734433i	−0.996329	+	0.0856090i	$0.972716\pi$
$878$	−46.1658	−	26.6538i	−1.55802	−	0.899523i
$879$	−29.5854	+	16.2749i	−0.997891	+	0.548939i
$880$	−0.405421	−	0.702209i	−0.0136667	−	0.0236715i
$881$	−3.51125			−0.118297			−0.0591486	−	0.998249i	$-0.518839\pi$
$881$	−3.51125			−0.118297			−0.0591486	+	0.998249i	$0.518839\pi$
$882$	−14.7271	+	47.7133i	−0.495887	+	1.60659i
$883$	38.7803			1.30506			0.652531	−	0.757762i	$-0.273707\pi$
$883$	38.7803			1.30506			0.652531	+	0.757762i	$0.273707\pi$
$884$	−14.0123	−	24.2700i	−0.471285	−	0.816289i
$885$	−3.37124	−	6.12843i	−0.113323	−	0.206005i
$886$	−6.15970	+	10.6689i	−0.206939	+	0.358429i
$887$	−2.48143	+	1.43266i	−0.0833183	+	0.0481039i	−0.541080	−	0.840971i	$-0.681985\pi$
$887$	−2.48143	+	1.43266i	−0.0833183	+	0.0481039i	0.457762	+	0.889075i	$0.348651\pi$
$888$	26.8454	+	16.2485i	0.900874	+	0.545263i
$889$	−36.2313	−	4.70034i	−1.21516	−	0.157644i
$890$			9.82594i			0.329366i
$891$	9.96816	+	0.826431i	0.333946	+	0.0276865i
$892$	−44.0390	+	76.2778i	−1.47453	+	2.55397i
$893$	−9.45852	+	16.3826i	−0.316517	+	0.548224i
$894$	22.5927	+	0.467271i	0.755611	+	0.0156279i
$895$		−	3.92956i		−	0.131351i
$896$	−50.5683	+	21.0581i	−1.68937	+	0.703501i
$897$	11.8381	+	3.42578i	0.395261	+	0.114384i
$898$	32.5851	+	56.4391i	1.08738	+	1.88340i
$899$	−11.8911	−	6.86531i	−0.396590	−	0.228971i
$900$	−53.3691	−	2.20855i	−1.77897	−	0.0736182i
$901$	22.1154	+	38.3050i	0.736771	+	1.27612i
$902$	−2.11024			−0.0702633
$903$	8.53254	+	21.7464i	0.283945	+	0.723673i
$904$			29.0021i			0.964596i
$905$	5.99888	−	3.46346i	0.199410	−	0.115129i
$906$	−8.43128	−	15.3268i	−0.280110	−	0.509200i
$907$	−22.2535	−	12.8480i	−0.738914	−	0.426612i	0.0827601	−	0.996569i	$-0.473626\pi$
$907$	−22.2535	−	12.8480i	−0.738914	−	0.426612i	−0.821674	+	0.569957i	$0.806960\pi$
$908$	45.0477	+	78.0248i	1.49496	+	2.58934i
$909$	−26.6449	+	13.9476i	−0.883756	+	0.462612i
$910$	2.64673	+	2.02297i	0.0877381	+	0.0670609i
$911$	4.81062			0.159383			0.0796915	−	0.996820i	$-0.474606\pi$
$911$	4.81062			0.159383			0.0796915	+	0.996820i	$0.474606\pi$
$912$	27.5780	+	0.570379i	0.913198	+	0.0188871i
$913$	3.77200	−	6.53329i	0.124835	−	0.216220i
$914$	−35.0737	+	60.7495i	−1.16014	+	2.00941i
$915$	−3.24090	−	0.0670297i	−0.107141	−	0.00221593i
$916$		−	13.9344i		−	0.460405i
$917$	−16.5330	+	6.88480i	−0.545967	+	0.227356i
$918$	63.7483	+	3.95992i	2.10401	+	0.130697i
$919$	13.0698	−	7.54584i	0.431132	−	0.248914i	−0.268697	−	0.963225i	$-0.586593\pi$
$919$	13.0698	−	7.54584i	0.431132	−	0.248914i	0.699829	+	0.714310i	$0.253260\pi$
$920$	6.50431	+	1.73734i	0.214441	+	0.0572785i
$921$	31.1692	−	17.1461i	1.02706	−	0.564985i
$922$	29.0993	+	50.4014i	0.958333	+	1.65988i
$923$			4.68947i			0.154356i
$924$	14.5489	+	11.6045i	0.478623	+	0.381760i
$925$		−	22.4447i		−	0.737976i
$926$	−37.8491	+	21.8522i	−1.24380	+	0.718107i
$927$	−1.14111	+	27.5747i	−0.0374790	+	0.905672i
$928$	−9.34465	+	16.1854i	−0.306753	+	0.531312i
$929$	34.3636	−	19.8398i	1.12743	−	0.650924i	0.184145	−	0.982899i	$-0.441048\pi$
$929$	34.3636	−	19.8398i	1.12743	−	0.650924i	0.943288	+	0.331975i	$0.107715\pi$
$930$	1.68074	−	2.77689i	0.0551137	−	0.0910578i
$931$	−52.6238	+	14.3138i	−1.72468	+	0.469115i
$932$		−	27.0291i		−	0.885369i
$933$	44.3593	+	0.917458i	1.45226	+	0.0300362i
$934$	21.0922	+	12.1776i	0.690158	+	0.398463i
$935$	1.02527	−	1.77581i	0.0335298	−	0.0580753i
$936$	14.7855	+	9.37218i	0.483278	+	0.306339i
$937$			33.4387i			1.09239i	0.837657	+	0.546197i	$0.183925\pi$
$937$			33.4387i			1.09239i	−0.837657	+	0.546197i	$0.816075\pi$
$938$	46.1938	+	5.99278i	1.50828	+	0.195671i
$939$	18.9529	−	31.3137i	0.618505	−	1.02188i
$940$	−2.74248	+	1.58337i	−0.0894498	+	0.0516439i
$941$	26.6324	−	46.1287i	0.868191	−	1.50375i	0.00434813	−	0.999991i	$-0.498616\pi$
$941$	26.6324	−	46.1287i	0.868191	−	1.50375i	0.863843	−	0.503761i	$-0.168051\pi$
$942$	23.4566	−	12.9035i	0.764258	−	0.420417i
$943$	2.70581	−	2.71007i	0.0881134	−	0.0882522i
$944$		−	23.1282i		−	0.752759i
$945$	−4.63794	+	1.60183i	−0.150872	+	0.0521077i
$946$	13.4714			0.437992
$947$	0.625192	−	0.360955i	0.0203160	−	0.0117295i	−0.489808	−	0.871831i	$-0.662933\pi$
$947$	0.625192	−	0.360955i	0.0203160	−	0.0117295i	0.510124	+	0.860101i	$0.329600\pi$
$948$	−39.3405	−	71.5153i	−1.27772	−	2.32271i
$949$	−7.40050	+	12.8180i	−0.240230	+	0.416091i
$950$	−45.1332	−	78.1730i	−1.46431	−	2.53627i
$951$	−21.3849	+	35.3318i	−0.693454	+	1.14571i
$952$	42.7389	+	32.6667i	1.38518	+	1.05873i
$953$	2.92082			0.0946146			0.0473073	−	0.998880i	$-0.484936\pi$
$953$	2.92082			0.0946146			0.0473073	+	0.998880i	$0.484936\pi$
$954$	−51.5516	−	32.6774i	−1.66904	−	1.05797i
$955$	1.52072	−	2.63396i	0.0492092	−	0.0852329i
$956$	41.2065	+	23.7906i	1.33271	+	0.769443i
$957$	11.9670	+	0.247507i	0.386839	+	0.00800077i
$958$		−	53.5482i		−	1.73007i
$959$	22.3536	−	29.2460i	0.721837	−	0.944404i
$960$	−5.94189	−	3.59639i	−0.191774	−	0.116073i
$961$	13.0620	+	22.6240i	0.421355	+	0.729808i
$962$	−8.12497	+	14.0729i	−0.261960	+	0.453727i
$963$	−30.1892	−	1.24931i	−0.972833	−	0.0402583i
$964$	−66.1938	+	38.2170i	−2.13196	+	1.23089i
$965$	8.91117			0.286861
$966$	−51.9255	+	5.88721i	−1.67068	+	0.189418i
$967$	2.21989			0.0713867			0.0356933	−	0.999363i	$-0.488636\pi$
$967$	2.21989			0.0713867			0.0356933	+	0.999363i	$0.488636\pi$
$968$	−33.2609	+	19.2032i	−1.06905	+	0.617214i
$969$	33.6217	+	61.1194i	1.08009	+	1.96344i
$970$	−0.0811725	+	0.140595i	−0.00260629	+	0.00451423i
$971$	13.8124	+	23.9238i	0.443261	+	0.767750i	0.997929	−	0.0643212i	$-0.0204882\pi$
$971$	13.8124	+	23.9238i	0.443261	+	0.767750i	−0.554668	+	0.832071i	$0.687155\pi$
$972$	−52.0062	+	23.2371i	−1.66810	+	0.745331i
$973$	−13.8291	−	1.79406i	−0.443339	−	0.0575151i
$974$			24.9246i			0.798634i
$975$	0.258911	−	12.5184i	0.00829178	−	0.400910i
$976$	−9.28272	−	5.35938i	−0.297133	−	0.171550i
$977$	−24.6888	+	42.7622i	−0.789864	+	1.36809i	0.136185	+	0.990683i	$0.456516\pi$
$977$	−24.6888	+	42.7622i	−0.789864	+	1.36809i	−0.926050	+	0.377402i	$0.876818\pi$
$978$	28.1524	+	0.582259i	0.900214	+	0.0186186i
$979$	−12.8673			−0.411242
$980$	−8.82716	−	2.32953i	−0.281973	−	0.0744140i
$981$	−41.3484	+	21.6443i	−1.32015	+	0.691049i
$982$	9.21120	+	15.9543i	0.293941	+	0.509121i
$983$	9.84946	−	17.0598i	0.314149	−	0.544122i	−0.665107	−	0.746748i	$-0.731614\pi$
$983$	9.84946	−	17.0598i	0.314149	−	0.544122i	0.979256	+	0.202626i	$0.0649476\pi$
$984$	4.76631	−	2.62194i	0.151944	−	0.0835845i
$985$	0.252939	−	0.146034i	0.00805929	−	0.00465303i
$986$	76.4332			2.43413
$987$	6.93838	−	8.69884i	0.220851	−	0.276887i
$988$			42.2358i			1.34370i
$989$	−17.2734	+	17.3006i	−0.549262	+	0.550127i
$990$	−0.116996	+	2.82719i	−0.00371839	+	0.0898541i
$991$	−21.7203	+	37.6207i	−0.689969	+	1.19506i	0.281879	+	0.959450i	$0.409042\pi$
$991$	−21.7203	+	37.6207i	−0.689969	+	1.19506i	−0.971848	+	0.235611i	$0.924291\pi$
$992$	−5.74773	+	3.31846i	−0.182491	+	0.105361i
$993$	−3.00090	−	1.81632i	−0.0952306	−	0.0576393i
$994$	−7.64450	−	18.3573i	−0.242469	−	0.582258i
$995$		−	1.68363i		−	0.0533747i
$996$	−0.888359	+	42.9524i	−0.0281487	+	1.36100i
$997$	17.6614	−	30.5904i	0.559342	−	0.968809i	−0.438210	−	0.898873i	$-0.644387\pi$
$997$	17.6614	−	30.5904i	0.559342	−	0.968809i	0.997551	−	0.0699359i	$-0.0222795\pi$
$998$	−86.7831	−	50.1042i	−2.74707	−	1.58602i
$999$	−10.6594	−	21.4304i	−0.337247	−	0.678028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.m.a.137.7	✓	120
3.2	odd	2	inner	483.2.m.a.137.54	yes	120
7.2	even	3	inner	483.2.m.a.275.53	yes	120
21.2	odd	6	inner	483.2.m.a.275.8	yes	120
23.22	odd	2	inner	483.2.m.a.137.8	yes	120
69.68	even	2	inner	483.2.m.a.137.53	yes	120
161.114	odd	6	inner	483.2.m.a.275.54	yes	120
483.275	even	6	inner	483.2.m.a.275.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.m.a.137.7	✓	120	1.1	even	1	trivial
483.2.m.a.137.8	yes	120	23.22	odd	2	inner
483.2.m.a.137.53	yes	120	69.68	even	2	inner
483.2.m.a.137.54	yes	120	3.2	odd	2	inner
483.2.m.a.275.7	yes	120	483.275	even	6	inner
483.2.m.a.275.8	yes	120	21.2	odd	6	inner
483.2.m.a.275.53	yes	120	7.2	even	3	inner
483.2.m.a.275.54	yes	120	161.114	odd	6	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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.05926 + 1.18892i) q^{2} +(1.51759 - 0.834823i) q^{3} +(1.82704 - 3.16453i) q^{4} +(-0.178457 - 0.309097i) q^{5} +(-2.13257 + 3.52340i) q^{6} +(2.62376 + 0.340385i) q^{7} +3.93312i q^{8} +(1.60614 - 2.53383i) q^{9} +O(q^{10})\)	\(q+(-2.05926 + 1.18892i) q^{2} +(1.51759 - 0.834823i) q^{3} +(1.82704 - 3.16453i) q^{4} +(-0.178457 - 0.309097i) q^{5} +(-2.13257 + 3.52340i) q^{6} +(2.62376 + 0.340385i) q^{7} +3.93312i q^{8} +(1.60614 - 2.53383i) q^{9} +(0.734981 + 0.424342i) q^{10} +(-0.555687 + 0.962478i) q^{11} +(0.130872 - 6.32770i) q^{12} +1.48361 q^{13} +(-5.80771 + 2.41849i) q^{14} +(-0.528866 - 0.320102i) q^{15} +(-1.02207 - 1.77028i) q^{16} +(2.58471 - 4.47685i) q^{17} +(-0.294950 + 7.12739i) q^{18} +(-6.74705 + 3.89541i) q^{19} -1.30420 q^{20} +(4.26595 - 1.67382i) q^{21} -2.64266i q^{22} +(3.39383 + 3.38850i) q^{23} +(3.28346 + 5.96886i) q^{24} +(2.43631 - 4.21981i) q^{25} +(-3.05514 + 1.76389i) q^{26} +(0.322154 - 5.18616i) q^{27} +(5.87088 - 7.68107i) q^{28} -6.21811i q^{29} +(1.46965 + 0.0303959i) q^{30} +(1.10408 - 1.91233i) q^{31} +(-2.60294 - 1.50281i) q^{32} +(-0.0398042 + 1.92454i) q^{33} +12.2920i q^{34} +(-0.363018 - 0.871743i) q^{35} +(-5.08390 - 9.71209i) q^{36} +(3.98917 - 2.30315i) q^{37} +(9.26263 - 16.0433i) q^{38} +(2.25151 - 1.23855i) q^{39} +(1.21572 - 0.701895i) q^{40} -0.798529i q^{41} +(-6.79469 + 8.51868i) q^{42} +5.09766i q^{43} +(2.03052 + 3.51697i) q^{44} +(-1.06983 - 0.0442722i) q^{45} +(-11.0174 - 2.94282i) q^{46} +(2.10281 - 1.21406i) q^{47} +(-3.02895 - 1.83330i) q^{48} +(6.76828 + 1.78618i) q^{49} +11.5862i q^{50} +(0.185145 - 8.95179i) q^{51} +(2.71061 - 4.69492i) q^{52} +(-4.27812 + 7.40992i) q^{53} +(5.50250 + 11.0627i) q^{54} +0.396666 q^{55} +(-1.33878 + 10.3196i) q^{56} +(-6.98725 + 11.5442i) q^{57} +(7.39281 + 12.8047i) q^{58} +(9.79854 + 5.65719i) q^{59} +(-1.97923 + 1.08877i) q^{60} +(4.54113 - 2.62182i) q^{61} +5.25065i q^{62} +(5.07661 - 6.10148i) q^{63} +11.2351 q^{64} +(-0.264761 - 0.458580i) q^{65} +(-2.20615 - 4.01046i) q^{66} +(-6.41222 - 3.70209i) q^{67} +(-9.44474 - 16.3588i) q^{68} +(7.97923 + 2.30909i) q^{69} +(1.78398 + 1.36355i) q^{70} +3.16085i q^{71} +(9.96588 + 6.31715i) q^{72} +(-4.98817 + 8.63977i) q^{73} +(-5.47649 + 9.48556i) q^{74} +(0.174514 - 8.43781i) q^{75} +28.4683i q^{76} +(-1.78560 + 2.33617i) q^{77} +(-3.16391 + 5.22735i) q^{78} +(11.1686 - 6.44819i) q^{79} +(-0.364792 + 0.631839i) q^{80} +(-3.84063 - 8.13938i) q^{81} +(0.949384 + 1.64438i) q^{82} -6.78799 q^{83} +(2.49723 - 16.5578i) q^{84} -1.84504 q^{85} +(-6.06068 - 10.4974i) q^{86} +(-5.19103 - 9.43653i) q^{87} +(-3.78554 - 2.18558i) q^{88} +(5.78893 + 10.0267i) q^{89} +(2.25569 - 1.18077i) q^{90} +(3.89264 + 0.504998i) q^{91} +(16.9237 - 4.54895i) q^{92} +(0.0790862 - 3.82384i) q^{93} +(-2.88683 + 5.00013i) q^{94} +(2.40812 + 1.39033i) q^{95} +(-5.20478 - 0.107647i) q^{96} +0.191290i q^{97} +(-16.0613 + 4.36870i) q^{98} +(1.54625 + 2.95389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9}+O(q^{10}) \) 120 * q - 2 * q^3 + 52 * q^4 - 24 * q^6 + 2 * q^9	\( 120 q - 2 q^{3} + 52 q^{4} - 24 q^{6} + 2 q^{9} + 14 q^{12} - 16 q^{13} - 60 q^{16} - 10 q^{18} - 24 q^{24} - 40 q^{25} - 20 q^{27} - 4 q^{31} + 64 q^{36} - 12 q^{39} - 20 q^{46} + 140 q^{48} - 48 q^{49} - 76 q^{52} - 2 q^{54} + 72 q^{55} - 28 q^{58} - 128 q^{64} - 20 q^{69} - 68 q^{70} + 6 q^{72} + 20 q^{73} + 20 q^{75} - 156 q^{78} - 62 q^{81} + 80 q^{82} + 112 q^{85} + 46 q^{87} - 38 q^{93} + 36 q^{94} + 72 q^{96}+O(q^{100}) \) 120 * q - 2 * q^3 + 52 * q^4 - 24 * q^6 + 2 * q^9 + 14 * q^12 - 16 * q^13 - 60 * q^16 - 10 * q^18 - 24 * q^24 - 40 * q^25 - 20 * q^27 - 4 * q^31 + 64 * q^36 - 12 * q^39 - 20 * q^46 + 140 * q^48 - 48 * q^49 - 76 * q^52 - 2 * q^54 + 72 * q^55 - 28 * q^58 - 128 * q^64 - 20 * q^69 - 68 * q^70 + 6 * q^72 + 20 * q^73 + 20 * q^75 - 156 * q^78 - 62 * q^81 + 80 * q^82 + 112 * q^85 + 46 * q^87 - 38 * q^93 + 36 * q^94 + 72 * q^96

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