LMFDB - Embedded newform 48.4.k.a.11.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [48,4,Mod(11,48)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("48.11"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(48, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.17
Character	$\chi$	$=$	48.11
Dual form			48.4.k.a.35.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.97996 - 2.01984i) q^{2} +(-0.0749974 - 5.19561i) q^{3} +(-0.159526 - 7.99841i) q^{4} +(-5.37662 + 5.37662i) q^{5} +(-10.6428 - 10.1356i) q^{6} +14.8575 q^{7} +(-16.4714 - 15.5143i) q^{8} +(-26.9888 + 0.779314i) q^{9} +(0.214439 + 21.5054i) q^{10} +(30.0526 + 30.0526i) q^{11} +(-41.5447 + 1.42870i) q^{12} +(61.5437 - 61.5437i) q^{13} +(29.4173 - 30.0098i) q^{14} +(28.3380 + 27.5316i) q^{15} +(-63.9491 + 2.55192i) q^{16} +48.8426i q^{17} +(-51.8625 + 56.0560i) q^{18} +(7.45581 + 7.45581i) q^{19} +(43.8621 + 42.1467i) q^{20} +(-1.11427 - 77.1939i) q^{21} +(120.205 - 1.19861i) q^{22} +43.0756i q^{23} +(-79.3710 + 86.7424i) q^{24} +67.1840i q^{25} +(-2.45458 - 246.162i) q^{26} +(6.07310 + 140.165i) q^{27} +(-2.37017 - 118.837i) q^{28} +(-32.9665 - 32.9665i) q^{29} +(111.718 - 2.72699i) q^{30} +173.357i q^{31} +(-121.462 + 134.220i) q^{32} +(153.888 - 158.396i) q^{33} +(98.6543 + 96.7063i) q^{34} +(-79.8832 + 79.8832i) q^{35} +(10.5387 + 215.743i) q^{36} +(-177.539 - 177.539i) q^{37} +(29.8218 - 0.297365i) q^{38} +(-324.373 - 315.141i) q^{39} +(171.975 - 5.14585i) q^{40} -454.458 q^{41} +(-158.126 - 150.590i) q^{42} +(239.150 - 239.150i) q^{43} +(235.579 - 245.167i) q^{44} +(140.918 - 149.298i) q^{45} +(87.0058 + 85.2878i) q^{46} +30.4238 q^{47} +(18.0548 + 332.063i) q^{48} -122.254 q^{49} +(135.701 + 133.022i) q^{50} +(253.767 - 3.66306i) q^{51} +(-502.069 - 482.433i) q^{52} +(235.743 - 235.743i) q^{53} +(295.135 + 265.253i) q^{54} -323.163 q^{55} +(-244.724 - 230.504i) q^{56} +(38.1783 - 39.2967i) q^{57} +(-131.860 + 1.31482i) q^{58} +(260.222 + 260.222i) q^{59} +(215.688 - 231.051i) q^{60} +(-388.869 + 388.869i) q^{61} +(350.153 + 343.239i) q^{62} +(-400.986 + 11.5787i) q^{63} +(30.6128 + 511.084i) q^{64} +661.793i q^{65} +(-15.2425 - 624.446i) q^{66} +(334.013 + 334.013i) q^{67} +(390.663 - 7.79168i) q^{68} +(223.804 - 3.23055i) q^{69} +(3.18603 + 319.517i) q^{70} -522.443i q^{71} +(456.633 + 405.875i) q^{72} +689.751i q^{73} +(-710.119 + 7.08088i) q^{74} +(349.062 - 5.03862i) q^{75} +(58.4453 - 60.8241i) q^{76} +(446.508 + 446.508i) q^{77} +(-1278.78 + 31.2146i) q^{78} -692.930i q^{79} +(330.109 - 357.550i) q^{80} +(727.785 - 42.0654i) q^{81} +(-899.808 + 917.934i) q^{82} +(-677.176 + 677.176i) q^{83} +(-617.251 + 21.2269i) q^{84} +(-262.608 - 262.608i) q^{85} +(-9.53815 - 956.551i) q^{86} +(-168.809 + 173.754i) q^{87} +(-28.7628 - 961.254i) q^{88} +261.949 q^{89} +(-22.5469 - 580.237i) q^{90} +(914.386 - 914.386i) q^{91} +(344.536 - 6.87169i) q^{92} +(900.694 - 13.0013i) q^{93} +(60.2378 - 61.4512i) q^{94} -80.1741 q^{95} +(706.463 + 621.004i) q^{96} -641.755 q^{97} +(-242.058 + 246.934i) q^{98} +(-834.504 - 787.663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33}+ \cdots + 1196 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7 + 56 * q^10 - 80 * q^12 - 4 * q^13 - 112 * q^16 + 52 * q^18 + 20 * q^19 - 56 * q^21 - 40 * q^22 - 120 * q^24 - 134 * q^27 - 296 * q^28 - 332 * q^30 - 4 * q^33 + 520 * q^34 - 604 * q^36 - 4 * q^37 + 596 * q^39 + 632 * q^40 + 696 * q^42 - 436 * q^43 - 252 * q^45 + 664 * q^46 + 1200 * q^48 + 972 * q^49 - 648 * q^51 + 320 * q^52 + 1592 * q^54 + 280 * q^55 - 424 * q^58 + 800 * q^60 - 916 * q^61 - 2056 * q^64 - 668 * q^66 - 1636 * q^67 + 52 * q^69 - 5192 * q^70 - 3704 * q^72 + 1454 * q^75 - 568 * q^76 - 4932 * q^78 - 4 * q^81 + 768 * q^82 - 2096 * q^84 + 736 * q^85 + 1284 * q^87 + 8864 * q^88 + 2672 * q^90 + 424 * q^91 - 2084 * q^93 + 5616 * q^94 + 8008 * q^96 - 8 * q^97 + 1196 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.97996	−	2.01984i	0.700021	−	0.714122i
$2$	1.97996	−	2.01984i	0.700021	−	0.714122i
$3$	−0.0749974	−	5.19561i	−0.0144332	−	0.999896i
$3$	−0.0749974	−	5.19561i	−0.0144332	−	0.999896i
$4$	−0.159526	−	7.99841i	−0.0199408	−	0.999801i
$5$	−5.37662	+	5.37662i	−0.480899	+	0.480899i	−0.905419	−	0.424520i	$-0.860443\pi$
$5$	−5.37662	+	5.37662i	−0.480899	+	0.480899i	0.424520	+	0.905419i	$0.360443\pi$
$6$	−10.6428	−	10.1356i	−0.724151	−	0.689641i
$7$	14.8575			0.802231			0.401115	−	0.916028i	$-0.368623\pi$
$7$	14.8575			0.802231			0.401115	+	0.916028i	$0.368623\pi$
$8$	−16.4714	−	15.5143i	−0.727939	−	0.685642i
$9$	−26.9888	+	0.779314i	−0.999583	+	0.0288635i
$10$	0.214439	+	21.5054i	0.00678115	+	0.680060i
$11$	30.0526	+	30.0526i	0.823746	+	0.823746i	0.986643	−	0.162897i	$-0.0520837\pi$
$11$	30.0526	+	30.0526i	0.823746	+	0.823746i	−0.162897	+	0.986643i	$0.552084\pi$
$12$	−41.5447	+	1.42870i	−0.999409	+	0.0343691i
$13$	61.5437	−	61.5437i	1.31301	−	1.31301i	0.393825	−	0.919185i	$-0.371151\pi$
$13$	61.5437	−	61.5437i	1.31301	−	1.31301i	0.919185	−	0.393825i	$-0.128849\pi$
$14$	29.4173	−	30.0098i	0.561578	−	0.572891i
$15$	28.3380	+	27.5316i	0.487790	+	0.473908i
$16$	−63.9491	+	2.55192i	−0.999205	+	0.0398737i
$17$			48.8426i			0.696827i	0.937341	+	0.348414i	$0.113280\pi$
$17$			48.8426i			0.696827i	−0.937341	+	0.348414i	$0.886720\pi$
$18$	−51.8625	+	56.0560i	−0.679117	+	0.734030i
$19$	7.45581	+	7.45581i	0.0900253	+	0.0900253i	0.750685	−	0.660660i	$-0.229723\pi$
$19$	7.45581	+	7.45581i	0.0900253	+	0.0900253i	−0.660660	+	0.750685i	$0.729723\pi$
$20$	43.8621	+	42.1467i	0.490393	+	0.471214i
$21$	−1.11427	−	77.1939i	−0.0115788	−	0.802147i
$22$	120.205	−	1.19861i	1.16490	−	0.0116156i
$23$			43.0756i			0.390516i	0.980752	+	0.195258i	$0.0625545\pi$
$23$			43.0756i			0.390516i	−0.980752	+	0.195258i	$0.937446\pi$
$24$	−79.3710	+	86.7424i	−0.675064	+	0.737759i
$25$			67.1840i			0.537472i
$26$	−2.45458	−	246.162i	−0.0185147	−	1.85679i
$27$	6.07310	+	140.165i	0.0432877	+	0.999063i
$28$	−2.37017	−	118.837i	−0.0159971	−	0.802071i
$29$	−32.9665	−	32.9665i	−0.211094	−	0.211094i	0.593638	−	0.804732i	$-0.297691\pi$
$29$	−32.9665	−	32.9665i	−0.211094	−	0.211094i	−0.804732	+	0.593638i	$0.797691\pi$
$30$	111.718	−	2.72699i	0.679891	−	0.0165959i
$31$			173.357i			1.00438i	0.864757	+	0.502190i	$0.167472\pi$
$31$			173.357i			1.00438i	−0.864757	+	0.502190i	$0.832528\pi$
$32$	−121.462	+	134.220i	−0.670990	+	0.741467i
$33$	153.888	−	158.396i	0.811771	−	0.835550i
$34$	98.6543	+	96.7063i	0.497620	+	0.487794i
$35$	−79.8832	+	79.8832i	−0.385792	+	0.385792i
$36$	10.5387	+	215.743i	0.0487903	+	0.998809i
$37$	−177.539	−	177.539i	−0.788842	−	0.788842i	0.192462	−	0.981304i	$-0.438353\pi$
$37$	−177.539	−	177.539i	−0.788842	−	0.788842i	−0.981304	+	0.192462i	$0.938353\pi$
$38$	29.8218	−	0.297365i	0.127309	−	0.00126945i
$39$	−324.373	−	315.141i	−1.33182	−	1.29392i
$40$	171.975	−	5.14585i	0.679790	−	0.0203407i
$41$	−454.458			−1.73108			−0.865542	−	0.500837i	$-0.833026\pi$
$41$	−454.458			−1.73108			−0.865542	+	0.500837i	$0.833026\pi$
$42$	−158.126	−	150.590i	−0.580936	−	0.553251i
$43$	239.150	−	239.150i	0.848139	−	0.848139i	−0.141762	−	0.989901i	$-0.545277\pi$
$43$	239.150	−	239.150i	0.848139	−	0.848139i	0.989901	+	0.141762i	$0.0452766\pi$
$44$	235.579	−	245.167i	0.807156	−	0.840009i
$45$	140.918	−	149.298i	0.466818	−	0.494579i
$46$	87.0058	+	85.2878i	0.278876	+	0.273370i
$47$	30.4238			0.0944205			0.0472102	−	0.998885i	$-0.484967\pi$
$47$	30.4238			0.0944205			0.0472102	+	0.998885i	$0.484967\pi$
$48$	18.0548	+	332.063i	0.0542913	+	0.998525i
$49$	−122.254			−0.356426
$50$	135.701	+	133.022i	0.383821	+	0.376242i
$51$	253.767	−	3.66306i	0.696755	−	0.0100575i
$52$	−502.069	−	482.433i	−1.33893	−	1.28657i
$53$	235.743	−	235.743i	0.610976	−	0.610976i	−0.332224	−	0.943200i	$-0.607799\pi$
$53$	235.743	−	235.743i	0.610976	−	0.610976i	0.943200	+	0.332224i	$0.107799\pi$
$54$	295.135	+	265.253i	0.743755	+	0.668452i
$55$	−323.163			−0.792278
$56$	−244.724	−	230.504i	−0.583975	−	0.550043i
$57$	38.1783	−	39.2967i	0.0887166	−	0.0913153i
$58$	−131.860	+	1.31482i	−0.298517	+	0.00297663i
$59$	260.222	+	260.222i	0.574204	+	0.574204i	0.933300	−	0.359096i	$-0.116915\pi$
$59$	260.222	+	260.222i	0.574204	+	0.574204i	−0.359096	+	0.933300i	$0.616915\pi$
$60$	215.688	−	231.051i	0.464087	−	0.497143i
$61$	−388.869	+	388.869i	−0.816222	+	0.816222i	−0.985558	−	0.169336i	$-0.945838\pi$
$61$	−388.869	+	388.869i	−0.816222	+	0.816222i	0.169336	+	0.985558i	$0.445838\pi$
$62$	350.153	+	343.239i	0.717250	+	0.703087i
$63$	−400.986	+	11.5787i	−0.801896	+	0.0231552i
$64$	30.6128	+	511.084i	0.0597907	+	0.998211i
$65$			661.793i			1.26285i
$66$	−15.2425	−	624.446i	−0.0284276	−	1.16461i
$67$	334.013	+	334.013i	0.609047	+	0.609047i	0.942697	−	0.333650i	$-0.108280\pi$
$67$	334.013	+	334.013i	0.609047	+	0.609047i	−0.333650	+	0.942697i	$0.608280\pi$
$68$	390.663	−	7.79168i	0.696689	−	0.0138953i
$69$	223.804	−	3.23055i	0.390476	−	0.00563642i
$70$	3.18603	+	319.517i	0.00544005	+	0.545565i
$71$		−	522.443i		−	0.873275i	−0.899637	−	0.436638i	$-0.856169\pi$
$71$		−	522.443i		−	0.873275i	0.899637	−	0.436638i	$-0.143831\pi$
$72$	456.633	+	405.875i	0.747426	+	0.664345i
$73$			689.751i			1.10588i	0.833221	+	0.552940i	$0.186494\pi$
$73$			689.751i			1.10588i	−0.833221	+	0.552940i	$0.813506\pi$
$74$	−710.119	+	7.08088i	−1.11554	+	0.0111235i
$75$	349.062	−	5.03862i	0.537416	−	0.00775747i
$76$	58.4453	−	60.8241i	0.0882122	−	0.0918026i
$77$	446.508	+	446.508i	0.660835	+	0.660835i
$78$	−1278.78	+	31.2146i	−1.85632	+	0.0453123i
$79$		−	692.930i		−	0.986844i	−0.869790	−	0.493422i	$-0.835746\pi$
$79$		−	692.930i		−	0.986844i	0.869790	−	0.493422i	$-0.164254\pi$
$80$	330.109	−	357.550i	0.461341	−	0.499692i
$81$	727.785	−	42.0654i	0.998334	−	0.0577029i
$82$	−899.808	+	917.934i	−1.21180	+	1.23621i
$83$	−677.176	+	677.176i	−0.895539	+	0.895539i	−0.995038	−	0.0994989i	$-0.968276\pi$
$83$	−677.176	+	677.176i	−0.895539	+	0.895539i	0.0994989	+	0.995038i	$0.468276\pi$
$84$	−617.251	+	21.2269i	−0.801757	+	0.0275720i
$85$	−262.608	−	262.608i	−0.335104	−	0.335104i
$86$	−9.53815	−	956.551i	−0.0119596	−	1.19939i
$87$	−168.809	+	173.754i	−0.208025	+	0.214119i
$88$	−28.7628	−	961.254i	−0.0348423	−	1.16443i
$89$	261.949			0.311983			0.155992	−	0.987758i	$-0.450143\pi$
$89$	261.949			0.311983			0.155992	+	0.987758i	$0.450143\pi$
$90$	−22.5469	−	580.237i	−0.0264072	−	0.679581i
$91$	914.386	−	914.386i	1.05334	−	1.05334i
$92$	344.536	−	6.87169i	0.390439	−	0.00778721i
$93$	900.694	−	13.0013i	1.00428	−	0.0144965i
$94$	60.2378	−	61.4512i	0.0660963	−	0.0674277i
$95$	−80.1741			−0.0865862
$96$	706.463	+	621.004i	0.751074	+	0.660218i
$97$	−641.755			−0.671757			−0.335878	−	0.941905i	$-0.609033\pi$
$97$	−641.755			−0.671757			−0.335878	+	0.941905i	$0.609033\pi$
$98$	−242.058	+	246.934i	−0.249506	+	0.254532i
$99$	−834.504	−	787.663i	−0.847179	−	0.799627i
$100$	537.365	−	10.7176i	0.537365	−	0.0107176i
$101$	962.520	−	962.520i	0.948260	−	0.948260i	−0.0504657	−	0.998726i	$-0.516071\pi$
$101$	962.520	−	962.520i	0.948260	−	0.948260i	0.998726	+	0.0504657i	$0.0160705\pi$
$102$	495.049	−	519.822i	0.480561	−	0.504608i
$103$	1478.65			1.41452			0.707262	−	0.706951i	$-0.249930\pi$
$103$	1478.65			1.41452			0.707262	+	0.706951i	$0.249930\pi$
$104$	−1968.52	+	58.9022i	−1.85605	+	0.0555368i
$105$	421.033	+	409.051i	0.391320	+	0.380184i
$106$	−9.40227	−	942.924i	−0.00861537	−	0.864008i
$107$	−1484.78	−	1484.78i	−1.34149	−	1.34149i	−0.894580	−	0.446908i	$-0.852525\pi$
$107$	−1484.78	−	1484.78i	−1.34149	−	1.34149i	−0.446908	−	0.894580i	$-0.647475\pi$
$108$	1120.13	−	70.9351i	0.998001	−	0.0632012i
$109$	−103.806	+	103.806i	−0.0912181	+	0.0912181i	−0.751243	−	0.660025i	$-0.770546\pi$
$109$	−103.806	+	103.806i	−0.0912181	+	0.0912181i	0.660025	+	0.751243i	$0.270546\pi$
$110$	−639.849	+	652.738i	−0.554611	+	0.565783i
$111$	−909.107	+	935.736i	−0.777375	+	0.800146i
$112$	−950.125	+	37.9151i	−0.801593	+	0.0319879i
$113$			54.5390i			0.0454035i	0.999742	+	0.0227017i	$0.00722681\pi$
$113$			54.5390i			0.0454035i	−0.999742	+	0.0227017i	$0.992773\pi$
$114$	−3.78155	−	154.920i	−0.00310679	−	0.127277i
$115$	−231.601	−	231.601i	−0.187799	−	0.187799i
$116$	−258.421	+	268.939i	−0.206843	+	0.215262i
$117$	−1613.02	+	1708.95i	−1.27457	+	1.35036i
$118$	1040.84	−	10.3786i	0.812007	−	0.00809684i
$119$			725.680i			0.559016i
$120$	−39.6335	−	893.128i	−0.0301502	−	0.679425i
$121$			475.322i			0.357116i
$122$	15.5095	+	1555.40i	0.0115095	+	1.15426i
$123$	34.0832	+	2361.19i	0.0249852	+	1.73090i
$124$	1386.58	−	27.6550i	1.00418	−	0.0200281i
$125$	−1033.30	−	1033.30i	−0.739369	−	0.739369i
$126$	−770.548	+	832.854i	−0.544809	+	0.588861i
$127$		−	31.6817i		−	0.0221362i	−0.999939	−	0.0110681i	$-0.996477\pi$
$127$		−	31.6817i		−	0.0221362i	0.999939	−	0.0110681i	$-0.00352315\pi$
$128$	1092.92	+	950.092i	0.754699	+	0.656071i
$129$	−1260.46	−	1224.59i	−0.860292	−	0.835810i
$130$	1336.72	+	1310.32i	0.901830	+	0.884023i
$131$	1687.23	−	1687.23i	1.12530	−	1.12530i	0.134364	−	0.990932i	$-0.457101\pi$
$131$	1687.23	−	1687.23i	1.12530	−	1.12530i	0.990932	−	0.134364i	$-0.0428990\pi$
$132$	−1291.46	−	1205.59i	−0.851571	−	0.794948i
$133$	110.775	+	110.775i	0.0722211	+	0.0722211i
$134$	1335.98	−	13.3216i	0.861279	−	0.00858816i
$135$	−786.264	−	720.958i	−0.501265	−	0.459631i
$136$	757.759	−	804.505i	0.477774	−	0.507248i
$137$	−453.548			−0.282841			−0.141420	−	0.989950i	$-0.545167\pi$
$137$	−453.548			−0.282841			−0.141420	+	0.989950i	$0.545167\pi$
$138$	436.597	−	458.445i	0.269316	−	0.282793i
$139$	−1392.05	+	1392.05i	−0.849439	+	0.849439i	−0.990063	−	0.140624i	$-0.955089\pi$
$139$	−1392.05	+	1392.05i	−0.849439	+	0.849439i	0.140624	+	0.990063i	$0.455089\pi$
$140$	651.682	+	626.195i	0.393408	+	0.378022i
$141$	−2.28170	−	158.070i	−0.00136279	−	0.0944106i
$142$	−1055.25	−	1034.42i	−0.623625	−	0.611311i
$143$	3699.10			2.16318
$144$	1723.92	−	118.709i	0.997638	−	0.0686976i
$145$	354.497			0.203030
$146$	1393.19	+	1365.68i	0.789734	+	0.774140i
$147$	9.16874	+	635.185i	0.00514438	+	0.356389i
$148$	−1391.70	+	1448.35i	−0.772955	+	0.804416i
$149$	118.909	−	118.909i	0.0653785	−	0.0653785i	−0.673662	−	0.739040i	$-0.735279\pi$
$149$	118.909	−	118.909i	0.0653785	−	0.0653785i	0.739040	+	0.673662i	$0.235279\pi$
$150$	680.951	−	715.027i	0.370663	−	0.389211i
$151$	289.153			0.155834			0.0779170	−	0.996960i	$-0.475173\pi$
$151$	289.153			0.155834			0.0779170	+	0.996960i	$0.475173\pi$
$152$	−7.13581	−	238.479i	−0.00380783	−	0.127258i
$153$	−38.0637	−	1318.20i	−0.0201129	−	0.696537i
$154$	1785.94	−	17.8083i	0.934515	−	0.00931842i
$155$	−932.072	−	932.072i	−0.483005	−	0.483005i
$156$	−2468.88	+	2644.74i	−1.26711	+	1.35736i
$157$	−683.842	+	683.842i	−0.347621	+	0.347621i	−0.859223	−	0.511602i	$-0.829052\pi$
$157$	−683.842	+	683.842i	−0.347621	+	0.347621i	0.511602	+	0.859223i	$0.329052\pi$
$158$	−1399.61	−	1371.97i	−0.704727	−	0.690812i
$159$	−1242.51	−	1207.15i	−0.619731	−	0.602094i
$160$	−68.5931	−	1374.70i	−0.0338923	−	0.679249i
$161$			639.996i			0.313284i
$162$	1356.02	−	1553.30i	0.657648	−	0.753326i
$163$	35.4216	+	35.4216i	0.0170210	+	0.0170210i	0.715566	−	0.698545i	$-0.246169\pi$
$163$	35.4216	+	35.4216i	0.0170210	+	0.0170210i	−0.698545	+	0.715566i	$0.746169\pi$
$164$	72.4981	+	3634.94i	0.0345192	+	1.73074i
$165$	24.2364	+	1679.03i	0.0114351	+	0.792195i
$166$	27.0082	+	2708.57i	0.0126280	+	1.26642i
$167$			2091.54i			0.969150i	0.874750	+	0.484575i	$0.161026\pi$
$167$			2091.54i			0.969150i	−0.874750	+	0.484575i	$0.838974\pi$
$168$	−1179.26	+	1288.78i	−0.541557	+	0.591853i
$169$		−	5378.24i		−	2.44799i
$170$	−1050.38	+	10.4737i	−0.473885	+	0.00472529i
$171$	−207.034	−	195.413i	−0.0925863	−	0.0873894i
$172$	−1950.97	−	1874.67i	−0.864883	−	0.831058i
$173$	−2566.01	−	2566.01i	−1.12769	−	1.12769i	−0.990552	−	0.137137i	$-0.956210\pi$
$173$	−2566.01	−	2566.01i	−1.12769	−	1.12769i	−0.137137	−	0.990552i	$-0.543790\pi$
$174$	16.7204	+	684.992i	0.00728490	+	0.298443i
$175$			998.188i			0.431177i
$176$	−1998.53	−	1845.15i	−0.855937	−	0.790246i
$177$	1332.50	−	1371.53i	0.565857	−	0.582432i
$178$	518.648	−	529.095i	0.218395	−	0.222794i
$179$	−1252.13	+	1252.13i	−0.522841	+	0.522841i	−0.918429	−	0.395587i	$-0.870541\pi$
$179$	−1252.13	+	1252.13i	−0.522841	+	0.522841i	0.395587	+	0.918429i	$0.370541\pi$
$180$	−1216.63	−	1103.30i	−0.503790	−	0.456863i
$181$	1732.51	+	1732.51i	0.711474	+	0.711474i	0.966844	−	0.255370i	$-0.0821971\pi$
$181$	1732.51	+	1732.51i	0.711474	+	0.711474i	−0.255370	+	0.966844i	$0.582197\pi$
$182$	−36.4690	−	3657.36i	−0.0148531	−	1.48957i
$183$	2049.58	+	1991.25i	0.827918	+	0.804357i
$184$	668.287	−	709.514i	0.267754	−	0.284272i
$185$	1909.11			0.758707
$186$	1757.08	−	1845.00i	0.692662	−	0.727323i
$187$	−1467.85	+	1467.85i	−0.574009	+	0.574009i
$188$	−4.85339	−	243.342i	−0.00188282	−	0.0944017i
$189$	90.2312	+	2082.50i	0.0347267	+	0.801479i
$190$	−158.741	+	161.939i	−0.0606122	+	0.0618331i
$191$	188.463			0.0713965			0.0356983	−	0.999363i	$-0.488634\pi$
$191$	188.463			0.0713965			0.0356983	+	0.999363i	$0.488634\pi$
$192$	2653.10	−	197.382i	0.997244	−	0.0741919i
$193$	−84.5839			−0.0315465			−0.0157733	−	0.999876i	$-0.505021\pi$
$193$	−84.5839			−0.0315465			−0.0157733	+	0.999876i	$0.505021\pi$
$194$	−1270.65	+	1296.24i	−0.470244	+	0.479716i
$195$	3438.42	−	49.6327i	1.26272	−	0.0182270i
$196$	19.5028	+	977.838i	0.00710742	+	0.356355i
$197$	−780.741	+	780.741i	−0.282363	+	0.282363i	−0.834051	−	0.551688i	$-0.813984\pi$
$197$	−780.741	+	780.741i	−0.282363	+	0.282363i	0.551688	+	0.834051i	$0.313984\pi$
$198$	−3243.24	+	126.026i	−1.16407	+	0.0452337i
$199$	−1640.08			−0.584233			−0.292116	−	0.956383i	$-0.594360\pi$
$199$	−1640.08			−0.584233			−0.292116	+	0.956383i	$0.594360\pi$
$200$	1042.31	−	1106.61i	0.368513	−	0.391247i
$201$	1710.35	−	1760.45i	0.600193	−	0.617774i
$202$	−38.3887	−	3849.89i	−0.0133714	−	1.34098i
$203$	−489.801	−	489.801i	−0.169346	−	0.169346i
$204$	−69.7812	−	2029.15i	−0.0239493	−	0.696416i
$205$	2443.45	−	2443.45i	0.832477	−	0.832477i
$206$	2927.67	−	2986.65i	0.990197	−	1.01014i
$207$	−33.5694	−	1162.56i	−0.0112717	−	0.390354i
$208$	−3778.61	+	4092.72i	−1.25961	+	1.36432i
$209$			448.134i			0.148316i
$210$	1659.85	−	40.5163i	0.545430	−	0.0133138i
$211$	−436.919	−	436.919i	−0.142553	−	0.142553i	0.632229	−	0.774782i	$-0.282140\pi$
$211$	−436.919	−	436.919i	−0.142553	−	0.142553i	−0.774782	+	0.632229i	$0.782140\pi$
$212$	−1923.17	−	1847.96i	−0.623038	−	0.598672i
$213$	−2714.41	+	39.1818i	−0.873185	+	0.0126042i
$214$	−5938.83	+	59.2184i	−1.89706	+	0.0189163i
$215$			2571.63i			0.815739i
$216$	2074.52	−	2402.92i	0.653488	−	0.756937i
$217$			2575.65i			0.805745i
$218$	4.14014	+	415.202i	0.00128626	+	0.128995i
$219$	3583.68	−	51.7295i	1.10577	−	0.0159614i
$220$	51.5530	+	2584.79i	0.0157987	+	0.792120i
$221$	3005.95	+	3005.95i	0.914942	+	0.914942i
$222$	90.0465	+	3688.97i	0.0272231	+	1.11526i
$223$		−	450.388i		−	0.135248i	−0.997711	−	0.0676239i	$-0.978458\pi$
$223$		−	450.388i		−	0.135248i	0.997711	−	0.0676239i	$-0.0215418\pi$
$224$	−1804.63	+	1994.17i	−0.538289	+	0.594827i
$225$	−52.3575	−	1813.21i	−0.0155133	−	0.537248i
$226$	110.160	+	107.985i	0.0324236	+	0.0317834i
$227$	−1039.61	+	1039.61i	−0.303972	+	0.303972i	−0.842566	−	0.538594i	$-0.818956\pi$
$227$	−1039.61	+	1039.61i	−0.303972	+	0.303972i	0.538594	+	0.842566i	$0.318956\pi$
$228$	−320.401	−	299.097i	−0.0930662	−	0.0868780i
$229$	1142.20	+	1142.20i	0.329601	+	0.329601i	0.852435	−	0.522834i	$-0.175125\pi$
$229$	1142.20	+	1142.20i	0.329601	+	0.329601i	−0.522834	+	0.852435i	$0.675125\pi$
$230$	−926.357	+	9.23707i	−0.265575	+	0.00264815i
$231$	2286.39	−	2353.37i	0.651228	−	0.670304i
$232$	31.5516	+	1054.46i	0.00892872	+	0.298399i
$233$	−3480.39			−0.978575			−0.489287	−	0.872123i	$-0.662743\pi$
$233$	−3480.39			−0.978575			−0.489287	+	0.872123i	$0.662743\pi$
$234$	258.084	+	6641.70i	0.0721003	+	1.85548i
$235$	−163.577	+	163.577i	−0.0454067	+	0.0454067i
$236$	2039.85	−	2122.88i	0.562640	−	0.585540i
$237$	−3600.19	+	51.9679i	−0.986742	+	0.0142434i
$238$	1465.76	+	1436.82i	0.399206	+	0.391323i
$239$	3195.92			0.864966			0.432483	−	0.901642i	$-0.357637\pi$
$239$	3195.92			0.864966			0.432483	+	0.901642i	$0.357637\pi$
$240$	−1882.45	−	1688.30i	−0.506298	−	0.454081i
$241$	−255.355			−0.0682525			−0.0341262	−	0.999418i	$-0.510865\pi$
$241$	−255.355			−0.0682525			−0.0341262	+	0.999418i	$0.510865\pi$
$242$	960.075	+	941.118i	0.255025	+	0.249989i
$243$	−273.138	−	3778.13i	−0.0721061	−	0.997397i
$244$	3172.37	+	3048.30i	0.832336	+	0.799784i
$245$	657.313	−	657.313i	0.171405	−	0.171405i
$246$	4836.71	+	4606.21i	1.25357	+	1.19383i
$247$	917.716			0.236408
$248$	2689.51	−	2855.42i	0.688645	−	0.731128i
$249$	3569.13	+	3467.56i	0.908371	+	0.882520i
$250$	−4132.99	+	41.2117i	−1.04557	+	0.0104258i
$251$	−3550.34	−	3550.34i	−0.892811	−	0.892811i	0.101976	−	0.994787i	$-0.467484\pi$
$251$	−3550.34	−	3550.34i	−0.892811	−	0.892811i	−0.994787	+	0.101976i	$0.967484\pi$
$252$	156.579	+	3205.40i	0.0391410	+	0.801275i
$253$	−1294.53	+	1294.53i	−0.321686	+	0.321686i
$254$	−63.9920	−	62.7284i	−0.0158079	−	0.0154958i
$255$	−1344.71	+	1384.10i	−0.330232	+	0.339905i
$256$	4082.98	−	326.385i	0.996820	−	0.0796839i
$257$			7256.80i			1.76135i	0.473721	+	0.880675i	$0.342911\pi$
$257$			7256.80i			1.76135i	−0.473721	+	0.880675i	$0.657089\pi$
$258$	−4969.15	+	121.295i	−1.19909	+	0.0292695i
$259$	−2637.78	−	2637.78i	−0.632834	−	0.632834i
$260$	5293.29	−	105.573i	1.26260	−	0.0251823i
$261$	915.417	+	864.034i	0.217099	+	0.204913i
$262$	−67.2927	−	6748.57i	−0.0158678	−	1.59133i
$263$		−	2114.79i		−	0.495832i	−0.968782	−	0.247916i	$-0.920254\pi$
$263$		−	2114.79i		−	0.495832i	0.968782	−	0.247916i	$-0.0797457\pi$
$264$	−4992.15	+	221.532i	−1.16381	+	0.0516452i
$265$			2535.00i			0.587636i
$266$	443.078	−	4.41810i	0.102131	−	0.00101839i
$267$	−19.6455	−	1360.98i	−0.00450293	−	0.311951i
$268$	2618.29	−	2724.85i	0.596781	−	0.621070i
$269$	120.142	+	120.142i	0.0272312	+	0.0272312i	0.720591	−	0.693360i	$-0.243870\pi$
$269$	120.142	+	120.142i	0.0272312	+	0.0272312i	−0.693360	+	0.720591i	$0.743870\pi$
$270$	−3012.99	+	160.661i	−0.679129	+	0.0362130i
$271$			924.962i			0.207334i	0.994612	+	0.103667i	$0.0330576\pi$
$271$			924.962i			0.207334i	−0.994612	+	0.103667i	$0.966942\pi$
$272$	−124.642	−	3123.44i	−0.0277851	−	0.696273i
$273$	−4819.37	−	4682.22i	−1.06843	−	1.03802i
$274$	−898.006	+	916.095i	−0.197995	+	0.201983i
$275$	−2019.06	+	2019.06i	−0.442741	+	0.442741i
$276$	−61.5419	−	1789.56i	−0.0134217	−	0.390286i
$277$	−3882.29	−	3882.29i	−0.842110	−	0.842110i	0.147023	−	0.989133i	$-0.453031\pi$
$277$	−3882.29	−	3882.29i	−0.842110	−	0.842110i	−0.989133	+	0.147023i	$0.953031\pi$
$278$	55.5199	+	5567.92i	0.0119779	+	1.20123i
$279$	−135.099	−	4678.68i	−0.0289899	−	1.00396i
$280$	2555.12	−	76.4545i	0.545348	−	0.0163180i
$281$	−175.744			−0.0373097			−0.0186548	−	0.999826i	$-0.505938\pi$
$281$	−175.744			−0.0373097			−0.0186548	+	0.999826i	$0.505938\pi$
$282$	−323.794	−	308.363i	−0.0683747	−	0.0651162i
$283$	−563.080	+	563.080i	−0.118274	+	0.118274i	−0.763767	−	0.645492i	$-0.776652\pi$
$283$	−563.080	+	563.080i	−0.118274	+	0.118274i	0.645492	+	0.763767i	$0.276652\pi$
$284$	−4178.71	+	83.3435i	−0.873102	+	0.0174138i
$285$	6.01285	+	416.553i	0.00124972	+	0.0865772i
$286$	7324.06	−	7471.59i	1.51427	−	1.54477i
$287$	−6752.12			−1.38873
$288$	3173.51	−	3717.08i	0.649309	−	0.760525i
$289$	2527.40			0.514432
$290$	701.889	−	716.027i	0.142125	−	0.144988i
$291$	48.1300	+	3334.31i	0.00969563	+	0.671687i
$292$	5516.91	−	110.034i	1.10566	−	0.0220521i
$293$	5718.53	−	5718.53i	1.14020	−	1.14020i	0.151792	−	0.988412i	$-0.451496\pi$
$293$	5718.53	−	5718.53i	1.14020	−	1.14020i	0.988412	−	0.151792i	$-0.0485045\pi$
$294$	1301.13	+	1239.12i	0.258106	+	0.245806i
$295$	−2798.23			−0.552268
$296$	169.919	+	5678.69i	0.0333659	+	1.11509i
$297$	−4029.80	+	4394.83i	−0.787316	+	0.858632i
$298$	−4.74251	−	475.612i	−0.000921901	−	0.0924545i
$299$	2651.03	+	2651.03i	0.512752	+	0.512752i
$300$	−95.9856	−	2791.14i	−0.0184724	−	0.537155i
$301$	3553.17	−	3553.17i	0.680403	−	0.680403i
$302$	572.511	−	584.043i	0.109087	−	0.111284i
$303$	−5073.06	−	4928.69i	−0.961848	−	0.934475i
$304$	−495.819	−	457.766i	−0.0935434	−	0.0863641i
$305$		−	4181.60i		−	0.785041i
$306$	−2737.92	−	2533.10i	−0.511492	−	0.473228i
$307$	1027.09	+	1027.09i	0.190942	+	0.190942i	0.796103	−	0.605161i	$-0.206891\pi$
$307$	1027.09	+	1027.09i	0.190942	+	0.190942i	−0.605161	+	0.796103i	$0.706891\pi$
$308$	3500.12	−	3642.58i	0.647526	−	0.673881i
$309$	−110.895	−	7682.51i	−0.0204162	−	1.41438i
$310$	−3728.10	+	37.1744i	−0.683039	+	0.00681085i
$311$		−	3479.04i		−	0.634335i	−0.948370	−	0.317168i	$-0.897268\pi$
$311$		−	3479.04i		−	0.634335i	0.948370	−	0.317168i	$-0.102732\pi$
$312$	453.666	+	10223.2i	0.0823198	+	1.85505i
$313$			3308.25i			0.597424i	0.954343	+	0.298712i	$0.0965569\pi$
$313$			3308.25i			0.597424i	−0.954343	+	0.298712i	$0.903443\pi$
$314$	27.2741	+	2735.23i	0.00490180	+	0.491586i
$315$	2093.69	−	2218.20i	0.374496	−	0.396767i
$316$	−5542.34	+	110.541i	−0.986648	+	0.0196785i
$317$	1297.15	+	1297.15i	0.229826	+	0.229826i	0.812620	−	0.582794i	$-0.198040\pi$
$317$	1297.15	+	1297.15i	0.229826	+	0.229826i	−0.582794	+	0.812620i	$0.698040\pi$
$318$	−4898.36	+	119.567i	−0.863794	+	0.0210849i
$319$		−	1981.46i		−	0.347776i
$320$	−2912.50	−	2583.31i	−0.508792	−	0.451285i
$321$	−7602.99	+	7825.70i	−1.32199	+	1.36071i
$322$	1292.69	+	1267.17i	0.223723	+	0.219306i
$323$	−364.161	+	364.161i	−0.0627321	+	0.0627321i
$324$	−452.558	−	5814.41i	−0.0775990	−	0.996985i
$325$	4134.75	+	4134.75i	0.705707	+	0.705707i
$326$	141.679	−	1.41274i	0.0240702	−	0.000240013i
$327$	547.119	+	531.548i	0.0925252	+	0.0898920i
$328$	7485.55	+	7050.60i	1.26012	+	1.18690i
$329$	452.022			0.0757470
$330$	3439.36	+	3275.45i	0.573729	+	0.546387i
$331$	4319.83	−	4319.83i	0.717339	−	0.717339i	−0.250721	−	0.968059i	$-0.580668\pi$
$331$	4319.83	−	4319.83i	0.717339	−	0.717339i	0.968059	+	0.250721i	$0.0806676\pi$
$332$	5524.36	+	5308.30i	0.913218	+	0.877503i
$333$	4929.90	+	4653.19i	0.811282	+	0.765745i
$334$	4224.58	+	4141.16i	0.692092	+	0.678426i
$335$	−3591.71			−0.585780
$336$	268.249	+	4933.64i	0.0435541	+	0.801047i
$337$	9925.19			1.60433			0.802165	−	0.597102i	$-0.203681\pi$
$337$	9925.19			1.60433			0.802165	+	0.597102i	$0.203681\pi$
$338$	−10863.2	−	10648.7i	−1.74817	−	1.71365i
$339$	283.363	−	4.09028i	0.0453988	−	0.000655320i
$340$	−2058.55	+	2142.34i	−0.328355	+	0.341719i
$341$	−5209.83	+	5209.83i	−0.827355	+	0.827355i
$342$	−804.621	+	31.2660i	−0.127219	+	0.00494349i
$343$	−6912.52			−1.08817
$344$	−7649.37	+	228.885i	−1.19891	+	0.0358740i
$345$	−1185.94	+	1220.68i	−0.185069	+	0.190490i
$346$	−10263.5	+	102.342i	−1.59471	+	0.0159015i
$347$	6188.11	+	6188.11i	0.957335	+	0.957335i	0.999126	−	0.0417910i	$-0.0133063\pi$
$347$	6188.11	+	6188.11i	0.957335	+	0.957335i	−0.0417910	+	0.999126i	$0.513306\pi$
$348$	1416.68	+	1322.48i	0.218225	+	0.203714i
$349$	−1274.05	+	1274.05i	−0.195411	+	0.195411i	−0.798030	−	0.602618i	$-0.794124\pi$
$349$	−1274.05	+	1274.05i	−0.195411	+	0.195411i	0.602618	+	0.798030i	$0.294124\pi$
$350$	2016.18	+	1976.37i	0.307913	+	0.301833i
$351$	9000.00	+	8252.48i	1.36862	+	1.25494i
$352$	−7683.92	+	383.402i	−1.16351	+	0.0580551i
$353$			1359.26i			0.204947i	0.994736	+	0.102473i	$0.0326756\pi$
$353$			1359.26i			0.204947i	−0.994736	+	0.102473i	$0.967324\pi$
$354$	−131.983	−	5407.00i	−0.0198159	−	0.811805i
$355$	2808.97	+	2808.97i	0.419957	+	0.419957i
$356$	−41.7877	−	2095.17i	−0.00622120	−	0.311921i
$357$	3770.35	−	54.4241i	0.558958	−	0.00806842i
$358$	49.9395	+	5008.27i	0.00737258	+	0.739373i
$359$			479.331i			0.0704683i	0.999379	+	0.0352342i	$0.0112177\pi$
$359$			479.331i			0.0704683i	−0.999379	+	0.0352342i	$0.988782\pi$
$360$	−4637.37	+	272.902i	−0.678919	+	0.0399534i
$361$		−	6747.82i		−	0.983791i
$362$	6929.71	−	69.0989i	1.00613	−	0.0100325i
$363$	2469.59	−	35.6479i	0.357079	−	0.00515435i
$364$	−7459.50	−	7167.77i	−1.07413	−	1.03212i
$365$	−3708.53	−	3708.53i	−0.531817	−	0.531817i
$366$	8080.08	−	197.232i	1.15397	−	0.0281680i
$367$			6512.69i			0.926320i	0.886275	+	0.463160i	$0.153285\pi$
$367$			6512.69i			0.926320i	−0.886275	+	0.463160i	$0.846715\pi$
$368$	−109.925	−	2754.64i	−0.0155713	−	0.390206i
$369$	12265.3	−	354.166i	1.73036	−	0.0499651i
$370$	3779.97	−	3856.11i	0.531111	−	0.541810i
$371$	3502.55	−	3502.55i	0.490144	−	0.490144i
$372$	−247.674	−	7202.05i	−0.0345196	−	1.00379i
$373$	−8069.28	−	8069.28i	−1.12014	−	1.12014i	−0.991720	−	0.128418i	$-0.959010\pi$
$373$	−8069.28	−	8069.28i	−1.12014	−	1.12014i	−0.128418	−	0.991720i	$-0.540990\pi$
$374$	58.5431	+	5871.10i	0.00809409	+	0.811731i
$375$	−5291.13	+	5446.12i	−0.728620	+	0.749963i
$376$	−501.121	−	472.003i	−0.0687323	−	0.0647386i
$377$	−4057.76			−0.554338
$378$	4384.97	+	3941.01i	0.596663	+	0.536253i
$379$	1799.74	−	1799.74i	0.243922	−	0.243922i	−0.574548	−	0.818471i	$-0.694822\pi$
$379$	1799.74	−	1799.74i	0.243922	−	0.243922i	0.818471	+	0.574548i	$0.194822\pi$
$380$	12.7899	+	641.265i	0.00172660	+	0.0865690i
$381$	−164.606	+	2.37604i	−0.0221339	+	0.000319497i
$382$	373.150	−	380.666i	0.0499791	−	0.0509858i
$383$	12267.5			1.63666			0.818332	−	0.574746i	$-0.194899\pi$
$383$	12267.5			1.63666			0.818332	+	0.574746i	$0.194899\pi$
$384$	4854.34	−	5749.65i	0.645110	−	0.764090i
$385$	−4801.40			−0.635590
$386$	−167.473	+	170.846i	−0.0220832	+	0.0225281i
$387$	−6267.98	+	6640.73i	−0.823306	+	0.872266i
$388$	102.377	+	5133.02i	0.0133954	+	0.671623i
$389$	1661.54	−	1661.54i	0.216564	−	0.216564i	−0.590485	−	0.807049i	$-0.701064\pi$
$389$	1661.54	−	1661.54i	0.216564	−	0.216564i	0.807049	+	0.590485i	$0.201064\pi$
$390$	6707.68	−	7043.34i	0.870914	−	0.914495i
$391$	−2103.92			−0.272122
$392$	2013.69	+	1896.69i	0.259456	+	0.244381i
$393$	−8892.71	−	8639.64i	−1.14142	−	1.10894i
$394$	31.1388	+	3122.81i	0.00398159	+	0.399302i
$395$	3725.62	+	3725.62i	0.474573	+	0.474573i
$396$	−6166.92	+	6800.35i	−0.782575	+	0.862956i
$397$	−259.031	+	259.031i	−0.0327465	+	0.0327465i	−0.723290	−	0.690544i	$-0.757371\pi$
$397$	−259.031	+	259.031i	−0.0327465	+	0.0327465i	0.690544	+	0.723290i	$0.257371\pi$
$398$	−3247.30	+	3312.71i	−0.408975	+	0.417214i
$399$	567.236	−	583.851i	0.0711712	−	0.0732559i
$400$	−171.448	−	4296.36i	−0.0214310	−	0.537045i
$401$		−	5120.78i		−	0.637705i	−0.947804	−	0.318852i	$-0.896703\pi$
$401$		−	5120.78i		−	0.637705i	0.947804	−	0.318852i	$-0.103297\pi$
$402$	−169.409	−	6940.25i	−0.0210183	−	0.861066i
$403$	10669.0	+	10669.0i	1.31876	+	1.31876i
$404$	−7852.17	−	7545.08i	−0.966981	−	0.929163i
$405$	−3686.85	+	4139.19i	−0.452349	+	0.507847i
$406$	−1959.11	+	19.5350i	−0.239480	+	0.00238795i
$407$		−	10671.0i		−	1.29961i
$408$	−4236.72	−	3876.68i	−0.514091	−	0.470403i
$409$			4138.32i			0.500311i	0.968206	+	0.250155i	$0.0804817\pi$
$409$			4138.32i			0.500311i	−0.968206	+	0.250155i	$0.919518\pi$
$410$	−97.4534	−	9773.30i	−0.0117387	−	1.17724i
$411$	34.0149	+	2356.46i	0.00408231	+	0.282811i
$412$	−235.884	−	11826.9i	−0.0282068	−	1.41424i
$413$	3866.26	+	3866.26i	0.460644	+	0.460644i
$414$	−2414.64	−	2234.01i	−0.286651	−	0.265206i
$415$		−	7281.83i		−	0.861327i
$416$	785.154	+	15735.6i	0.0925369	+	1.85457i
$417$	7336.94	+	7128.14i	0.861610	+	0.837090i
$418$	905.160	+	887.286i	0.105916	+	0.103824i
$419$	2623.85	−	2623.85i	0.305927	−	0.305927i	−0.537401	−	0.843327i	$-0.680594\pi$
$419$	2623.85	−	2623.85i	0.305927	−	0.305927i	0.843327	+	0.537401i	$0.180594\pi$
$420$	3204.59	−	3432.85i	0.372305	−	0.398823i
$421$	−207.548	−	207.548i	−0.0240268	−	0.0240268i	0.694991	−	0.719018i	$-0.255408\pi$
$421$	−207.548	−	207.548i	−0.0240268	−	0.0240268i	−0.719018	+	0.694991i	$0.755408\pi$
$422$	−1747.59	+	17.4259i	−0.201591	+	0.00201014i
$423$	−821.099	+	23.7097i	−0.0943811	+	0.00272530i
$424$	−7540.39	+	225.624i	−0.863665	+	0.0258427i
$425$	−3281.44			−0.374525
$426$	−5295.28	+	5560.26i	−0.602247	+	0.632384i
$427$	−5777.63	+	5777.63i	−0.654799	+	0.654799i
$428$	−11639.0	+	12112.7i	−1.31447	+	1.36797i
$429$	−277.423	−	19219.1i	−0.0312217	−	2.16295i
$430$	5194.29	+	5091.73i	0.582537	+	0.571034i
$431$	−11772.7			−1.31571			−0.657855	−	0.753145i	$-0.728536\pi$
$431$	−11772.7			−1.31571			−0.657855	+	0.753145i	$0.728536\pi$
$432$	−746.057	−	8947.90i	−0.0830896	−	0.996542i
$433$	−4268.67			−0.473763			−0.236881	−	0.971539i	$-0.576125\pi$
$433$	−4268.67			−0.473763			−0.236881	+	0.971539i	$0.576125\pi$
$434$	5202.41	+	5099.68i	0.575400	+	0.564038i
$435$	−26.5863	−	1841.83i	−0.00293038	−	0.203009i
$436$	846.839	+	813.720i	0.0930189	+	0.0893810i
$437$	−321.163	+	321.163i	−0.0351564	+	0.0351564i
$438$	6991.05	−	7340.89i	0.762661	−	0.800825i
$439$	1006.82			0.109459			0.0547297	−	0.998501i	$-0.482570\pi$
$439$	1006.82			0.109459			0.0547297	+	0.998501i	$0.482570\pi$
$440$	5322.94	+	5013.65i	0.576730	+	0.543219i
$441$	3299.49	−	95.2744i	0.356277	−	0.0102877i
$442$	12023.2	−	119.888i	1.29386	−	0.0129016i
$443$	−3697.94	−	3697.94i	−0.396601	−	0.396601i	0.480431	−	0.877032i	$-0.340480\pi$
$443$	−3697.94	−	3697.94i	−0.396601	−	0.396601i	−0.877032	+	0.480431i	$0.840480\pi$
$444$	7629.43	+	7122.13i	0.815488	+	0.761264i
$445$	−1408.40	+	1408.40i	−0.150032	+	0.150032i
$446$	−909.714	−	891.751i	−0.0965834	−	0.0946763i
$447$	−626.722	−	608.886i	−0.0663153	−	0.0644281i
$448$	454.831	+	7593.44i	0.0479659	+	0.800795i
$449$		−	11582.4i		−	1.21738i	−0.793407	−	0.608692i	$-0.791695\pi$
$449$		−	11582.4i		−	1.21738i	0.793407	−	0.608692i	$-0.208305\pi$
$450$	−3766.07	−	3484.33i	−0.394520	−	0.365007i
$451$	−13657.7	−	13657.7i	−1.42597	−	1.42597i
$452$	436.225	−	8.70041i	0.0453945	−	0.000905382i
$453$	−21.6857	−	1502.33i	−0.00224919	−	0.155818i
$454$	41.4636	+	4158.25i	0.00428630	+	0.429860i
$455$			9832.60i			1.01310i
$456$	−1238.51	+	54.9602i	−0.127190	+	0.00564418i
$457$		−	1710.35i		−	0.175070i	−0.996161	−	0.0875349i	$-0.972101\pi$
$457$		−	1710.35i		−	0.175070i	0.996161	−	0.0875349i	$-0.0278989\pi$
$458$	4568.57	−	45.5550i	0.466103	−	0.00464770i
$459$	−6846.00	+	296.626i	−0.696174	+	0.0301641i
$460$	−1815.49	+	1889.38i	−0.184017	+	0.191506i
$461$	−4945.52	−	4945.52i	−0.499644	−	0.499644i	0.411683	−	0.911327i	$-0.364941\pi$
$461$	−4945.52	−	4945.52i	−0.499644	−	0.499644i	−0.911327	+	0.411683i	$0.864941\pi$
$462$	−226.466	−	9277.72i	−0.0228055	−	0.934283i
$463$			5550.67i			0.557152i	0.960414	+	0.278576i	$0.0898624\pi$
$463$			5550.67i			0.557152i	−0.960414	+	0.278576i	$0.910138\pi$
$464$	2192.31	+	2024.05i	0.219343	+	0.202509i
$465$	−4772.78	+	4912.59i	−0.475984	+	0.489926i
$466$	−6891.03	+	7029.84i	−0.685023	+	0.698822i
$467$	5335.45	−	5335.45i	0.528683	−	0.528683i	−0.391497	−	0.920180i	$-0.628043\pi$
$467$	5335.45	−	5335.45i	0.528683	−	0.528683i	0.920180	+	0.391497i	$0.128043\pi$
$468$	13926.2	+	12629.0i	1.37551	+	1.24738i
$469$	4962.60	+	4962.60i	0.488596	+	0.488596i
$470$	6.52403	+	654.275i	0.000640279	+	0.0642116i
$471$	3604.26	+	3501.69i	0.352602	+	0.342568i
$472$	−249.053	−	8323.38i	−0.0242873	−	0.811684i
$473$	14374.2			1.39730
$474$	−7023.27	+	7374.72i	−0.680568	+	0.714625i
$475$	−500.912	+	500.912i	−0.0483861	+	0.0483861i
$476$	5804.28	−	115.765i	0.558905	−	0.0111472i
$477$	−6178.68	+	6546.12i	−0.593087	+	0.628357i
$478$	6327.79	−	6455.26i	0.605495	−	0.617692i
$479$	−3196.65			−0.304924			−0.152462	−	0.988309i	$-0.548720\pi$
$479$	−3196.65			−0.304924			−0.152462	+	0.988309i	$0.548720\pi$
$480$	−7137.28	+	459.482i	−0.678689	+	0.0436925i
$481$	−21852.7			−2.07152
$482$	−505.592	+	515.776i	−0.0477782	+	0.0487406i
$483$	3325.17	−	47.9980i	0.313251	−	0.00452171i
$484$	3801.82	−	75.8264i	0.357045	−	0.00712119i
$485$	3450.47	−	3450.47i	0.323047	−	0.323047i
$486$	−8172.04	−	6928.86i	−0.762739	−	0.646706i
$487$	18653.5			1.73567			0.867833	−	0.496856i	$-0.165512\pi$
$487$	18653.5			1.73567			0.867833	+	0.496856i	$0.165512\pi$
$488$	12438.2	−	372.178i	1.15380	−	0.0345240i
$489$	181.380	−	186.693i	0.0167736	−	0.0172649i
$490$	−26.2160	−	2629.12i	−0.00241698	−	0.242391i
$491$	4162.67	+	4162.67i	0.382604	+	0.382604i	0.872039	−	0.489436i	$-0.162797\pi$
$491$	4162.67	+	4162.67i	0.382604	+	0.382604i	−0.489436	+	0.872039i	$0.662797\pi$
$492$	18880.3	−	649.283i	1.73006	−	0.0594958i
$493$	1610.17	−	1610.17i	0.147096	−	0.147096i
$494$	1817.04	−	1853.64i	0.165491	−	0.168824i
$495$	8721.76	−	251.845i	0.791948	−	0.0228679i
$496$	−442.392	−	11086.0i	−0.0400483	−	1.00358i
$497$		−	7762.20i		−	0.700568i
$498$	14070.6	−	343.460i	1.26611	−	0.0309052i
$499$	−7570.74	−	7570.74i	−0.679184	−	0.679184i	0.280631	−	0.959816i	$-0.409456\pi$
$499$	−7570.74	−	7570.74i	−0.679184	−	0.679184i	−0.959816	+	0.280631i	$0.909456\pi$
$500$	−8099.91	+	8429.59i	−0.724478	+	0.753966i
$501$	10866.8	−	156.860i	0.969049	−	0.0139880i
$502$	−14200.7	+	141.600i	−1.26256	+	0.0125895i
$503$		−	10216.7i		−	0.905647i	−0.891600	−	0.452823i	$-0.850417\pi$
$503$		−	10216.7i		−	0.905647i	0.891600	−	0.452823i	$-0.149583\pi$
$504$	6784.43	+	6030.30i	0.599608	+	0.532958i
$505$			10350.2i			0.912035i
$506$	51.6307	+	5177.88i	0.00453609	+	0.454911i
$507$	−27943.3	+	403.354i	−2.44774	+	0.0353325i
$508$	−253.403	+	5.05406i	−0.0221318	+	0.000441413i
$509$	12175.7	+	12175.7i	1.06027	+	1.06027i	0.998063	+	0.0622119i	$0.0198155\pi$
$509$	12175.7	+	12175.7i	1.06027	+	1.06027i	0.0622119	+	0.998063i	$0.480185\pi$
$510$	133.193	+	5456.57i	0.0115645	+	0.473767i
$511$			10248.0i			0.887171i
$512$	7424.88	−	8893.20i	0.640891	−	0.767632i
$513$	−999.761	+	1090.32i	−0.0860439	+	0.0938379i
$514$	14657.6	+	14368.2i	1.25782	+	1.23298i
$515$	−7950.15	+	7950.15i	−0.680244	+	0.680244i
$516$	−9593.72	+	10277.1i	−0.818488	+	0.876788i
$517$	914.314	+	914.314i	0.0777785	+	0.0777785i
$518$	−10550.6	+	105.204i	−0.894917	+	0.00892357i
$519$	−13139.5	+	13524.4i	−1.11130	+	1.14385i
$520$	10267.3	−	10900.6i	0.865864	−	0.919279i
$521$	−734.120			−0.0617320			−0.0308660	−	0.999524i	$-0.509827\pi$
$521$	−734.120			−0.0617320			−0.0308660	+	0.999524i	$0.509827\pi$
$522$	3557.70	−	138.245i	0.298307	−	0.0115916i
$523$	4289.83	−	4289.83i	0.358664	−	0.358664i	−0.504656	−	0.863320i	$-0.668381\pi$
$523$	4289.83	−	4289.83i	0.358664	−	0.358664i	0.863320	+	0.504656i	$0.168381\pi$
$524$	−13764.3	−	13226.0i	−1.14751	−	1.10263i
$525$	5186.20	−	74.8615i	0.431132	−	0.00622328i
$526$	−4271.55	−	4187.21i	−0.354085	−	0.347093i
$527$	−8467.19			−0.699880
$528$	−9436.78	+	10522.0i	−0.777809	+	0.867254i
$529$	10311.5			0.847497
$530$	5120.29	+	5019.19i	0.419644	+	0.411358i
$531$	−7225.86	−	6820.27i	−0.590538	−	0.557391i
$532$	868.352	−	903.695i	0.0707666	−	0.0736469i
$533$	−27969.0	+	27969.0i	−2.27293	+	2.27293i
$534$	−2787.87	−	2655.01i	−0.225923	−	0.215156i
$535$	15966.2			1.29024
$536$	−319.677	−	10683.6i	−0.0257611	−	0.860937i
$537$	6599.49	+	6411.68i	0.530333	+	0.515241i
$538$	480.545	−	4.79171i	0.0385089	−	0.000383987i
$539$	−3674.06	−	3674.06i	−0.293605	−	0.293605i
$540$	−5641.09	+	6403.87i	−0.449544	+	0.510331i
$541$	−11785.3	+	11785.3i	−0.936583	+	0.936583i	−0.998106	−	0.0615231i	$-0.980404\pi$
$541$	−11785.3	+	11785.3i	−0.936583	+	0.936583i	0.0615231	+	0.998106i	$0.480404\pi$
$542$	1868.28	+	1831.39i	0.148062	+	0.145138i
$543$	8871.54	−	9131.41i	0.701131	−	0.721669i
$544$	−6555.64	−	5932.52i	−0.516674	−	0.467564i
$545$		−	1116.25i		−	0.0877334i
$546$	−18999.5	+	463.771i	−1.48920	+	0.0363509i
$547$	10084.5	+	10084.5i	0.788268	+	0.788268i	0.981210	−	0.192942i	$-0.0618029\pi$
$547$	10084.5	+	10084.5i	0.788268	+	0.788268i	−0.192942	+	0.981210i	$0.561803\pi$
$548$	72.3529	+	3627.66i	0.00564007	+	0.282785i
$549$	10192.0	−	10798.1i	0.792323	−	0.839441i
$550$	80.5272	+	8075.83i	0.00624308	+	0.626099i
$551$		−	491.585i		−	0.0380076i
$552$	−3736.48	−	3418.95i	−0.288107	−	0.263623i
$553$		−	10295.2i		−	0.791677i
$554$	−15528.4	+	154.840i	−1.19086	+	0.0118746i
$555$	−143.178	−	9919.01i	−0.0109506	−	0.758628i
$556$	11356.2	+	10912.1i	0.866208	+	0.832331i
$557$	−6502.22	−	6502.22i	−0.494628	−	0.494628i	0.415133	−	0.909761i	$-0.363735\pi$
$557$	−6502.22	−	6502.22i	−0.494628	−	0.494628i	−0.909761	+	0.415133i	$0.863735\pi$
$558$	−9717.69	−	8990.72i	−0.737245	−	0.682092i
$559$		−	29436.3i		−	2.22723i
$560$	4904.60	−	5312.31i	0.370102	−	0.400868i
$561$	7736.45	+	7516.28i	0.582234	+	0.565664i
$562$	−347.966	+	354.976i	−0.0261176	+	0.0266437i
$563$	6184.95	−	6184.95i	0.462992	−	0.462992i	−0.436643	−	0.899635i	$-0.643833\pi$
$563$	6184.95	−	6184.95i	0.462992	−	0.462992i	0.899635	+	0.436643i	$0.143833\pi$
$564$	−1263.94	+	43.4663i	−0.0943647	+	0.00324515i
$565$	−293.235	−	293.235i	−0.0218345	−	0.0218345i
$566$	22.4576	+	2252.21i	0.00166778	+	0.167257i
$567$	10813.1	−	624.988i	0.800894	−	0.0462911i
$568$	−8105.34	+	8605.36i	−0.598754	+	0.635691i
$569$	25063.0			1.84657			0.923284	−	0.384119i	$-0.125495\pi$
$569$	25063.0			1.84657			0.923284	+	0.384119i	$0.125495\pi$
$570$	853.277	+	812.614i	0.0627015	+	0.0597134i
$571$	15682.4	−	15682.4i	1.14937	−	1.14937i	0.162692	−	0.986677i	$-0.447982\pi$
$571$	15682.4	−	15682.4i	1.14937	−	1.14937i	0.986677	−	0.162692i	$-0.0520177\pi$
$572$	−590.104	−	29586.9i	−0.0431355	−	2.16275i
$573$	−14.1343	−	979.183i	−0.00103048	−	0.0713891i
$574$	−13368.9	+	13638.2i	−0.972139	+	0.991722i
$575$	−2893.99			−0.209892
$576$	−1224.50	−	13769.7i	−0.0885776	−	0.996069i
$577$	−1972.54			−0.142319			−0.0711593	−	0.997465i	$-0.522670\pi$
$577$	−1972.54			−0.142319			−0.0711593	+	0.997465i	$0.522670\pi$
$578$	5004.15	−	5104.95i	0.360113	−	0.367367i
$579$	6.34357	+	439.465i	0.000455319	+	0.0315432i
$580$	−56.5516	−	2835.41i	−0.00404858	−	0.202990i
$581$	−10061.2	+	10061.2i	−0.718429	+	0.718429i
$582$	6830.08	+	6504.58i	0.486453	+	0.463271i
$583$	14169.4			1.00658
$584$	10701.0	−	11361.2i	0.758238	−	0.805014i
$585$	−515.745	−	17861.0i	−0.0364503	−	1.26233i
$586$	−228.075	−	22873.0i	−0.0160780	−	1.61241i
$587$	3171.66	+	3171.66i	0.223013	+	0.223013i	0.809766	−	0.586753i	$-0.199594\pi$
$587$	3171.66	+	3171.66i	0.223013	+	0.223013i	−0.586753	+	0.809766i	$0.699594\pi$
$588$	5079.01	−	174.664i	0.356215	−	0.0122500i
$589$	−1292.52	+	1292.52i	−0.0904196	+	0.0904196i
$590$	−5540.38	+	5651.98i	−0.386599	+	0.394387i
$591$	4114.98	+	3997.87i	0.286409	+	0.278258i
$592$	11806.5	+	10900.4i	0.819669	+	0.756761i
$593$			2763.19i			0.191350i	0.995413	+	0.0956752i	$0.0305010\pi$
$593$			2763.19i			0.191350i	−0.995413	+	0.0956752i	$0.969499\pi$
$594$	898.017	+	16841.1i	0.0620304	+	1.16330i
$595$	−3901.70	−	3901.70i	−0.268830	−	0.268830i
$596$	−970.051	−	932.113i	−0.0666692	−	0.0640618i
$597$	123.002	+	8521.23i	0.00843238	+	0.584172i
$598$	10603.6	−	105.732i	0.725105	−	0.00723031i
$599$			27598.5i			1.88255i	0.337647	+	0.941273i	$0.390369\pi$
$599$			27598.5i			1.88255i	−0.337647	+	0.941273i	$0.609631\pi$
$600$	−5827.70	−	5332.46i	−0.396525	−	0.362828i
$601$		−	12432.1i		−	0.843789i	−0.906645	−	0.421894i	$-0.861365\pi$
$601$		−	12432.1i		−	0.843789i	0.906645	−	0.421894i	$-0.138635\pi$
$602$	−141.713	−	14212.0i	−0.00959435	−	0.962188i
$603$	−9274.88	−	8754.28i	−0.626372	−	0.591214i
$604$	−46.1275	−	2312.76i	−0.00310745	−	0.155803i
$605$	−2555.62	−	2555.62i	−0.171737	−	0.171737i
$606$	−19999.6	+	488.184i	−1.34064	+	0.0327246i
$607$		−	13691.9i		−	0.915545i	−0.889069	−	0.457772i	$-0.848647\pi$
$607$		−	13691.9i		−	0.915545i	0.889069	−	0.457772i	$-0.151353\pi$
$608$	−1906.32	+	95.1189i	−0.127157	+	0.00634470i
$609$	−2508.08	+	2581.55i	−0.166884	+	0.171773i
$610$	−8446.17	−	8279.39i	−0.560615	−	0.549545i
$611$	1872.39	−	1872.39i	0.123975	−	0.123975i
$612$	−10537.4	+	514.737i	−0.695997	+	0.0339984i
$613$	17418.7	+	17418.7i	1.14769	+	1.14769i	0.987006	+	0.160686i	$0.0513706\pi$
$613$	17418.7	+	17418.7i	1.14769	+	1.14769i	0.160686	+	0.987006i	$0.448629\pi$
$614$	4108.17	−	40.9642i	0.270020	−	0.00269248i
$615$	−12878.4	−	12511.9i	−0.844405	−	0.820375i
$616$	−427.343	−	14281.9i	−0.0279515	−	0.934143i
$617$	−6194.64			−0.404193			−0.202096	−	0.979366i	$-0.564775\pi$
$617$	−6194.64			−0.404193			−0.202096	+	0.979366i	$0.564775\pi$
$618$	−15737.0	−	14987.1i	−1.02433	−	0.975514i
$619$	−15342.7	+	15342.7i	−0.996247	+	0.996247i	−0.999993	−	0.00374578i	$-0.998808\pi$
$619$	−15342.7	+	15342.7i	−0.996247	+	0.996247i	0.00374578	+	0.999993i	$0.498808\pi$
$620$	−7306.41	+	7603.79i	−0.473278	+	0.492541i
$621$	−6037.67	+	261.602i	−0.390150	+	0.0169046i
$622$	−7027.11	−	6888.35i	−0.452993	−	0.444048i
$623$	3891.91			0.250282
$624$	21547.5	+	19325.2i	1.38236	+	1.23979i
$625$	2713.31			0.173652
$626$	6682.15	+	6550.21i	0.426633	+	0.418209i
$627$	2328.33	−	33.6088i	0.148301	−	0.00214068i
$628$	5578.74	+	5360.56i	0.354484	+	0.340620i
$629$	8671.44	−	8671.44i	0.549687	−	0.549687i
$630$	−334.991	−	8620.88i	−0.0211847	−	0.545181i
$631$	−24841.9			−1.56726			−0.783631	−	0.621227i	$-0.786635\pi$
$631$	−24841.9			−1.56726			−0.783631	+	0.621227i	$0.786635\pi$
$632$	−10750.3	+	11413.5i	−0.676622	+	0.718363i
$633$	−2237.30	+	2302.83i	−0.140481	+	0.144596i
$634$	5188.32	−	51.7348i	0.325007	−	0.00324078i
$635$	170.340	+	170.340i	0.0106453	+	0.0106453i
$636$	−9457.04	+	10130.7i	−0.589617	+	0.631614i
$637$	−7523.96	+	7523.96i	−0.467991	+	0.467991i
$638$	−4002.24	−	3923.21i	−0.248355	−	0.243451i
$639$	407.147	+	14100.1i	0.0252058	+	0.872912i
$640$	−10984.5	+	767.937i	−0.678438	+	0.0474303i
$641$			13544.6i			0.834600i	0.908769	+	0.417300i	$0.137024\pi$
$641$			13544.6i			0.834600i	−0.908769	+	0.417300i	$0.862976\pi$
$642$	753.072	+	30851.4i	0.0462950	+	1.89659i
$643$	12655.0	+	12655.0i	0.776152	+	0.776152i	0.979174	−	0.203022i	$-0.0650764\pi$
$643$	12655.0	+	12655.0i	0.776152	+	0.776152i	−0.203022	+	0.979174i	$0.565076\pi$
$644$	5118.95	−	102.096i	0.313222	−	0.00624714i
$645$	13361.2	−	192.866i	0.815654	−	0.0117738i
$646$	14.5241	+	1456.57i	0.000884584	+	0.0887122i
$647$			8771.04i			0.532960i	0.963840	+	0.266480i	$0.0858607\pi$
$647$			8771.04i			0.532960i	−0.963840	+	0.266480i	$0.914139\pi$
$648$	−12640.2	−	10598.2i	−0.766290	−	0.642495i
$649$			15640.7i			0.945997i
$650$	16538.2	−	164.909i	0.997970	−	0.00995116i
$651$	13382.1	−	193.167i	0.805661	−	0.0116295i
$652$	277.665	−	288.967i	0.0166782	−	0.0173571i
$653$	21658.4	+	21658.4i	1.29794	+	1.29794i	0.929748	+	0.368197i	$0.120025\pi$
$653$	21658.4	+	21658.4i	1.29794	+	1.29794i	0.368197	+	0.929748i	$0.379975\pi$
$654$	2156.92	−	52.6496i	0.128963	−	0.00314795i
$655$			18143.1i			1.08231i
$656$	29062.2	−	1159.74i	1.72971	−	0.0690247i
$657$	−537.533	−	18615.5i	−0.0319196	−	1.10542i
$658$	894.984	−	913.012i	0.0530245	−	0.0540926i
$659$	−9280.25	+	9280.25i	−0.548569	+	0.548569i	−0.926027	−	0.377457i	$-0.876798\pi$
$659$	−9280.25	+	9280.25i	−0.548569	+	0.548569i	0.377457	+	0.926027i	$0.376798\pi$
$660$	13425.7	−	461.702i	0.791810	−	0.0272299i
$661$	−13336.7	−	13336.7i	−0.784776	−	0.784776i	0.195857	−	0.980632i	$-0.437251\pi$
$661$	−13336.7	−	13336.7i	−0.784776	−	0.784776i	−0.980632	+	0.195857i	$0.937251\pi$
$662$	−172.290	−	17278.4i	−0.0101152	−	1.01442i
$663$	15392.3	−	15843.2i	0.901641	−	0.928052i
$664$	21659.9	−	648.111i	1.26592	−	0.0378789i
$665$	−1191.19			−0.0694621
$666$	19159.7	−	744.510i	1.11475	−	0.0433171i
$667$	1420.05	−	1420.05i	0.0824357	−	0.0824357i
$668$	16729.0	−	333.656i	0.968958	−	0.0193256i
$669$	−2340.04	+	33.7779i	−0.135234	+	0.00195206i
$670$	−7111.45	+	7254.70i	−0.410058	+	0.418318i
$671$	−23373.1			−1.34472
$672$	10496.3	+	9226.58i	0.602535	+	0.529647i
$673$	−15820.7			−0.906156			−0.453078	−	0.891471i	$-0.649674\pi$
$673$	−15820.7			−0.906156			−0.453078	+	0.891471i	$0.649674\pi$
$674$	19651.5	−	20047.3i	1.12307	−	1.14569i
$675$	−9416.82	+	408.015i	−0.536968	+	0.0232659i
$676$	−43017.4	+	857.972i	−2.44751	+	0.0488150i
$677$	3185.15	−	3185.15i	0.180820	−	0.180820i	−0.610893	−	0.791713i	$-0.709189\pi$
$677$	3185.15	−	3185.15i	0.180820	−	0.180820i	0.791713	+	0.610893i	$0.209189\pi$
$678$	552.786	−	580.448i	0.0313121	−	0.0328790i
$679$	−9534.89			−0.538904
$680$	251.336	+	8399.69i	0.0141740	+	0.473696i
$681$	5479.40	+	5323.46i	0.308328	+	0.299553i
$682$	207.787	+	20838.3i	0.0116665	+	1.17000i
$683$	−423.850	−	423.850i	−0.0237455	−	0.0237455i	0.695134	−	0.718880i	$-0.255345\pi$
$683$	−423.850	−	423.850i	−0.0237455	−	0.0237455i	−0.718880	+	0.695134i	$0.755345\pi$
$684$	−1529.96	+	1687.11i	−0.0855257	+	0.0943105i
$685$	2438.55	−	2438.55i	0.136018	−	0.136018i
$686$	−13686.5	+	13962.2i	−0.761740	+	0.777084i
$687$	5848.76	−	6020.08i	0.324810	−	0.334324i
$688$	−14683.1	+	15903.7i	−0.813646	+	0.881283i
$689$		−	29016.9i		−	1.60444i
$690$	117.467	+	4812.30i	0.00648098	+	0.265509i
$691$	5607.03	+	5607.03i	0.308685	+	0.308685i	0.844399	−	0.535714i	$-0.179958\pi$
$691$	5607.03	+	5607.03i	0.308685	+	0.308685i	−0.535714	+	0.844399i	$0.679958\pi$
$692$	−20114.7	+	20933.3i	−1.10498	+	1.14995i
$693$	−12398.7	−	11702.7i	−0.679633	−	0.641485i
$694$	24751.2	−	246.804i	1.35381	−	0.0134994i
$695$		−	14969.0i		−	0.816989i
$696$	5476.18	−	243.011i	0.298239	−	0.0132347i
$697$		−	22196.9i		−	1.20627i
$698$	50.8139	+	5095.96i	0.00275549	+	0.276340i
$699$	261.020	+	18082.7i	0.0141240	+	0.978473i
$700$	7983.92	−	159.237i	0.431091	−	0.00859801i
$701$	−15985.1	−	15985.1i	−0.861267	−	0.861267i	0.130218	−	0.991485i	$-0.458432\pi$
$701$	−15985.1	−	15985.1i	−0.861267	−	0.861267i	−0.991485	+	0.130218i	$0.958432\pi$
$702$	34488.3	−	1839.01i	1.85424	−	0.0988734i
$703$		−	2647.39i		−	0.142032i
$704$	−14439.4	+	16279.4i	−0.773020	+	0.871525i
$705$	862.150	+	837.614i	0.0460574	+	0.0447466i
$706$	2745.49	+	2691.28i	0.146357	+	0.143467i
$707$	14300.7	−	14300.7i	0.760723	−	0.760723i
$708$	−11182.6	−	10439.1i	−0.593600	−	0.554130i
$709$	−3590.05	−	3590.05i	−0.190165	−	0.190165i	0.605602	−	0.795768i	$-0.292932\pi$
$709$	−3590.05	−	3590.05i	−0.190165	−	0.190165i	−0.795768	+	0.605602i	$0.792932\pi$
$710$	11235.3	−	112.032i	0.593880	−	0.00592181i
$711$	540.010	+	18701.3i	0.0284838	+	0.986433i
$712$	−4314.66	−	4063.95i	−0.227105	−	0.213909i
$713$	−7467.44			−0.392227
$714$	7355.21	−	7723.27i	0.385521	−	0.404812i
$715$	−19888.6	+	19888.6i	−1.04027	+	1.04027i
$716$	10214.8	+	9815.30i	0.533163	+	0.512312i
$717$	−239.686	−	16604.8i	−0.0124843	−	0.864876i
$718$	968.173	+	949.056i	0.0503230	+	0.0493293i
$719$	5996.91			0.311053			0.155526	−	0.987832i	$-0.450293\pi$
$719$	5996.91			0.311053			0.155526	+	0.987832i	$0.450293\pi$
$720$	−8630.59	+	9907.10i	−0.446726	+	0.512800i
$721$	21969.1			1.13477
$722$	−13629.5	−	13360.4i	−0.702547	−	0.688674i
$723$	19.1509	+	1326.72i	0.000985105	+	0.0682454i
$724$	13581.0	−	14133.7i	0.697145	−	0.725520i
$725$	2214.82	−	2214.82i	0.113457	−	0.113457i
$726$	4817.68	−	5058.76i	0.246282	−	0.258606i
$727$	−15850.3			−0.808606			−0.404303	−	0.914625i	$-0.632486\pi$
$727$	−15850.3			−0.808606			−0.404303	+	0.914625i	$0.632486\pi$
$728$	−29247.3	+	875.140i	−1.48898	+	0.0445534i
$729$	−19609.2	+	1702.47i	−0.996252	+	0.0864943i
$730$	−14833.4	+	147.909i	−0.752065	+	0.00749914i
$731$	11680.7	+	11680.7i	0.591007	+	0.591007i
$732$	15599.9	−	16711.0i	0.787687	−	0.843793i
$733$	15633.8	−	15633.8i	0.787784	−	0.787784i	−0.193346	−	0.981131i	$-0.561934\pi$
$733$	15633.8	−	15633.8i	0.787784	−	0.787784i	0.981131	+	0.193346i	$0.0619341\pi$
$734$	13154.6	+	12894.9i	0.661506	+	0.648444i
$735$	−3464.44	−	3365.85i	−0.173861	−	0.168913i
$736$	−5781.59	−	5232.05i	−0.289555	−	0.262032i
$737$			20075.9i			1.00340i
$738$	23569.3	−	25475.1i	1.17561	−	1.27067i
$739$	−22820.0	−	22820.0i	−1.13592	−	1.13592i	−0.989174	−	0.146747i	$-0.953120\pi$
$739$	−22820.0	−	22820.0i	−1.13592	−	1.13592i	−0.146747	−	0.989174i	$-0.546880\pi$
$740$	−304.554	−	15269.9i	−0.0151292	−	0.758556i
$741$	−68.8263	−	4768.10i	−0.00341214	−	0.236384i
$742$	−139.694	−	14009.5i	−0.00691151	−	0.693134i
$743$		−	34196.9i		−	1.68851i	−0.535941	−	0.844255i	$-0.680043\pi$
$743$		−	34196.9i		−	1.68851i	0.535941	−	0.844255i	$-0.319957\pi$
$744$	−15037.4	−	13759.5i	−0.740991	−	0.678021i
$745$			1278.65i			0.0628809i
$746$	−32275.5	+	321.832i	−1.58404	+	0.0157950i
$747$	17748.4	−	18803.9i	0.869317	−	0.921014i
$748$	11974.6	+	11506.3i	0.585341	+	0.562449i
$749$	−22060.2	−	22060.2i	−1.07618	−	1.07618i
$750$	524.084	+	21470.3i	0.0255158	+	1.04531i
$751$			36702.6i			1.78335i	0.452675	+	0.891676i	$0.350470\pi$
$751$			36702.6i			1.78335i	−0.452675	+	0.891676i	$0.649530\pi$
$752$	−1945.57	+	77.6389i	−0.0943454	+	0.00376489i
$753$	−18179.9	+	18712.5i	−0.879832	+	0.905604i
$754$	−8034.20	+	8196.04i	−0.388048	+	0.395865i
$755$	−1554.66	+	1554.66i	−0.0749404	+	0.0749404i
$756$	16642.3	−	1053.92i	0.800627	−	0.0507020i
$757$	−12194.0	−	12194.0i	−0.585468	−	0.585468i	0.350933	−	0.936401i	$-0.385865\pi$
$757$	−12194.0	−	12194.0i	−0.585468	−	0.585468i	−0.936401	+	0.350933i	$0.885865\pi$
$758$	−71.7801	−	7198.60i	−0.00343954	−	0.344941i
$759$	6822.98	+	6628.81i	0.326296	+	0.317010i
$760$	1320.58	+	1243.85i	0.0630295	+	0.0593671i
$761$	−33960.5			−1.61770			−0.808848	−	0.588018i	$-0.799909\pi$
$761$	−33960.5			−1.61770			−0.808848	+	0.588018i	$0.799909\pi$
$762$	−321.113	+	337.182i	−0.0152660	+	0.0160299i
$763$	−1542.29	+	1542.29i	−0.0731780	+	0.0731780i
$764$	−30.0649	−	1507.41i	−0.00142370	−	0.0713823i
$765$	7292.11	+	6882.80i	0.344636	+	0.325292i
$766$	24289.2	−	24778.5i	1.14570	−	1.16878i
$767$	32030.0			1.50787
$768$	−2001.98	−	21189.1i	−0.0940630	−	0.995566i
$769$	21884.2			1.02622			0.513112	−	0.858322i	$-0.328493\pi$
$769$	21884.2			1.02622			0.513112	+	0.858322i	$0.328493\pi$
$770$	−9506.57	+	9698.07i	−0.444926	+	0.453889i
$771$	37703.5	−	544.241i	1.76117	−	0.0254220i
$772$	13.4934	+	676.536i	0.000629063	+	0.0315403i
$773$	−2736.24	+	2736.24i	−0.127316	+	0.127316i	−0.767894	−	0.640577i	$-0.778695\pi$
$773$	−2736.24	+	2736.24i	−0.127316	+	0.127316i	0.640577	+	0.767894i	$0.278695\pi$
$774$	1002.88	+	25808.7i	0.0465732	+	1.19855i
$775$	−11646.8			−0.539826
$776$	10570.6	+	9956.39i	0.488998	+	0.460584i
$777$	−13507.1	+	13902.7i	−0.623634	+	0.641901i
$778$	−66.2681	−	6645.82i	−0.00305376	−	0.306252i
$779$	−3388.36	−	3388.36i	−0.155841	−	0.155841i
$780$	−945.502	−	27494.0i	−0.0434031	−	1.26211i
$781$	15700.8	−	15700.8i	0.719358	−	0.719358i
$782$	−4165.68	+	4249.59i	−0.190491	+	0.194329i
$783$	4420.53	−	4820.95i	0.201759	−	0.220034i
$784$	7818.04	−	311.982i	0.356142	−	0.0142120i
$785$		−	7353.51i		−	0.334341i
$786$	−35057.9	+	855.752i	−1.59093	+	0.0388342i
$787$	4548.50	+	4548.50i	0.206018	+	0.206018i	0.802573	−	0.596554i	$-0.203464\pi$
$787$	4548.50	+	4548.50i	0.206018	+	0.206018i	−0.596554	+	0.802573i	$0.703464\pi$
$788$	6369.24	+	6120.14i	0.287937	+	0.276676i
$789$	−10987.6	+	158.604i	−0.495780	+	0.00715647i
$790$	14901.7	−	148.591i	0.671114	−	0.00669194i
$791$			810.314i			0.0364241i
$792$	1525.39	+	25920.6i	0.0684373	+	1.16294i
$793$			47864.8i			2.14342i
$794$	10.3311	+	1036.07i	0.000461758	+	0.0463083i
$795$	13170.9	−	190.118i	0.587575	−	0.00848150i
$796$	261.637	+	13118.1i	0.0116501	+	0.584117i
$797$	10333.6	+	10333.6i	0.459265	+	0.459265i	0.898414	−	0.439149i	$-0.144720\pi$
$797$	10333.6	+	10333.6i	0.459265	+	0.459265i	−0.439149	+	0.898414i	$0.644720\pi$
$798$	−56.1844	−	2301.73i	−0.00249236	−	0.102106i
$799$			1485.97i			0.0657948i
$800$	−9017.43	−	8160.31i	−0.398518	−	0.360638i
$801$	−7069.67	+	204.140i	−0.311853	+	0.00900492i
$802$	−10343.2	−	10138.9i	−0.455399	−	0.446407i
$803$	−20728.8	+	20728.8i	−0.910965	+	0.910965i
$804$	−14353.6	−	13399.2i	−0.629619	−	0.587754i
$805$	−3441.01	−	3441.01i	−0.150658	−	0.150658i
$806$	42673.9	−	425.518i	1.86492	−	0.0185958i
$807$	615.202	−	633.223i	0.0268354	−	0.0276214i
$808$	−30786.8	+	921.208i	−1.34044	+	0.0401089i
$809$	−12937.6			−0.562252			−0.281126	−	0.959671i	$-0.590708\pi$
$809$	−12937.6			−0.562252			−0.281126	+	0.959671i	$0.590708\pi$
$810$	1060.70	+	15642.3i	0.0460113	+	0.678536i
$811$	13303.5	−	13303.5i	0.576015	−	0.576015i	−0.357788	−	0.933803i	$-0.616469\pi$
$811$	13303.5	−	13303.5i	0.576015	−	0.576015i	0.933803	+	0.357788i	$0.116469\pi$
$812$	−3839.49	+	3995.76i	−0.165936	+	0.172689i
$813$	4805.74	−	69.3697i	0.207312	−	0.00299250i
$814$	−21553.8	−	21128.2i	−0.928082	−	0.909756i
$815$	−380.896			−0.0163708
$816$	−16218.8	+	881.842i	−0.695800	+	0.0378317i
$817$	3566.11			0.152708
$818$	8358.76	+	8193.71i	0.357283	+	0.350228i
$819$	−23965.5	+	25390.7i	−1.02250	+	1.08330i
$820$	−19933.5	−	19153.9i	−0.848911	−	0.815711i
$821$	23606.7	−	23606.7i	1.00351	−	1.00351i	0.00351227	−	0.999994i	$-0.498882\pi$
$821$	23606.7	−	23606.7i	1.00351	−	1.00351i	0.999994	−	0.00351227i	$-0.00111799\pi$
$822$	4827.02	+	4596.98i	0.204820	+	0.195059i
$823$	−13577.6			−0.575071			−0.287536	−	0.957770i	$-0.592836\pi$
$823$	−13577.6			−0.575071			−0.287536	+	0.957770i	$0.592836\pi$
$824$	−24355.5	−	22940.3i	−1.02969	−	0.969857i
$825$	10641.7	+	10338.8i	0.449085	+	0.436304i
$826$	15464.3	−	154.200i	0.651417	−	0.00649553i
$827$	28241.2	+	28241.2i	1.18747	+	1.18747i	0.977763	+	0.209711i	$0.0672523\pi$
$827$	28241.2	+	28241.2i	1.18747	+	1.18747i	0.209711	+	0.977763i	$0.432748\pi$
$828$	−9293.24	+	453.960i	−0.390051	+	0.0190534i
$829$	13869.8	−	13869.8i	0.581082	−	0.581082i	−0.354118	−	0.935201i	$-0.615219\pi$
$829$	13869.8	−	13869.8i	0.581082	−	0.581082i	0.935201	+	0.354118i	$0.115219\pi$
$830$	−14708.1	−	14417.7i	−0.615093	−	0.602947i
$831$	−19879.7	+	20462.1i	−0.829868	+	0.854177i
$832$	33338.0	+	29570.0i	1.38917	+	1.23216i
$833$		−	5971.21i		−	0.248367i
$834$	28924.6	−	706.039i	1.20093	−	0.0293143i
$835$	−11245.4	−	11245.4i	−0.466064	−	0.466064i
$836$	3584.36	−	71.4892i	0.148287	−	0.00295754i
$837$	−24298.5	+	1052.81i	−1.00344	+	0.0434773i
$838$	−104.648	−	10494.9i	−0.00431387	−	0.432624i
$839$		−	15874.8i		−	0.653229i	−0.945158	−	0.326615i	$-0.894092\pi$
$839$		−	15874.8i		−	0.653229i	0.945158	−	0.326615i	$-0.105908\pi$
$840$	−588.855	−	13269.7i	−0.0241874	−	0.545056i
$841$		−	22215.4i		−	0.910878i
$842$	−830.152	+	8.27778i	−0.0339774	+	0.000338802i
$843$	13.1804	+	913.099i	0.000538500	+	0.0373058i
$844$	−3424.96	+	3564.36i	−0.139682	+	0.145368i
$845$	28916.7	+	28916.7i	1.17724	+	1.17724i
$846$	−1577.85	+	1705.44i	−0.0641226	+	0.0693074i
$847$			7062.10i			0.286490i
$848$	−14473.9	+	15677.1i	−0.586129	+	0.634852i
$849$	2967.77	+	2883.31i	0.119969	+	0.116555i
$850$	−6497.12	+	6627.99i	−0.262176	+	0.267457i
$851$	7647.57	−	7647.57i	0.308056	−	0.308056i
$852$	746.413	+	21704.7i	0.0300137	+	0.872760i
$853$	−2526.73	−	2526.73i	−0.101423	−	0.101423i	0.654575	−	0.755997i	$-0.272848\pi$
$853$	−2526.73	−	2526.73i	−0.101423	−	0.101423i	−0.755997	+	0.654575i	$0.772848\pi$
$854$	230.433	+	23109.4i	0.00923330	+	0.925979i
$855$	2163.80	−	62.4808i	0.0865501	−	0.00249918i
$856$	1421.05	+	47491.7i	0.0567414	+	1.89630i
$857$	35121.3			1.39991			0.699954	−	0.714188i	$-0.253204\pi$
$857$	35121.3			1.39991			0.699954	+	0.714188i	$0.253204\pi$
$858$	−39368.8	−	37492.6i	−1.56647	−	1.49181i
$859$	14337.3	−	14337.3i	0.569480	−	0.569480i	−0.362503	−	0.931983i	$-0.618078\pi$
$859$	14337.3	−	14337.3i	0.569480	−	0.569480i	0.931983	+	0.362503i	$0.118078\pi$
$860$	20569.0	−	410.243i	0.815577	−	0.0162665i
$861$	506.391	+	35081.4i	0.0200439	+	1.38858i
$862$	−23309.4	+	23779.0i	−0.921024	+	0.939577i
$863$	−4109.05			−0.162079			−0.0810393	−	0.996711i	$-0.525824\pi$
$863$	−4109.05			−0.162079			−0.0810393	+	0.996711i	$0.525824\pi$
$864$	−19550.5	−	16209.6i	−0.769817	−	0.638264i
$865$	27592.9			1.08461
$866$	−8451.79	+	8622.04i	−0.331644	+	0.338324i
$867$	−189.549	−	13131.4i	−0.00742492	−	0.514378i
$868$	20601.1	−	410.884i	0.805584	−	0.0160672i
$869$	20824.4	−	20824.4i	0.812910	−	0.812910i
$870$	−3772.84	−	3593.04i	−0.147024	−	0.140018i
$871$	41112.7			1.59937
$872$	3320.29	−	99.3502i	0.128944	−	0.00385828i
$873$	17320.2	−	500.129i	0.671477	−	0.0193892i
$874$	12.8091	+	1284.59i	0.000495739	+	0.0497161i
$875$	−15352.3	−	15352.3i	−0.593144	−	0.593144i
$876$	−985.446	−	28655.5i	−0.0380081	−	1.10523i
$877$	−2839.24	+	2839.24i	−0.109321	+	0.109321i	−0.759651	−	0.650331i	$-0.774630\pi$
$877$	−2839.24	+	2839.24i	−0.109321	+	0.109321i	0.650331	+	0.759651i	$0.274630\pi$
$878$	1993.45	−	2033.61i	0.0766239	−	0.0781674i
$879$	−30140.1	−	29282.4i	−1.15654	−	1.12363i
$880$	20666.0	−	824.685i	0.791648	−	0.0315910i
$881$			25816.2i			0.987254i	0.869674	+	0.493627i	$0.164329\pi$
$881$			25816.2i			0.987254i	−0.869674	+	0.493627i	$0.835671\pi$
$882$	6340.41	−	6853.08i	0.242055	−	0.261627i
$883$	21733.3	+	21733.3i	0.828294	+	0.828294i	0.987281	−	0.158986i	$-0.0508226\pi$
$883$	21733.3	+	21733.3i	0.828294	+	0.828294i	−0.158986	+	0.987281i	$0.550823\pi$
$884$	23563.3	−	24522.4i	0.896515	−	0.933004i
$885$	209.860	+	14538.5i	0.00797103	+	0.552211i
$886$	−14791.0	+	147.487i	−0.560851	+	0.00559247i
$887$			32216.9i			1.21955i	0.792575	+	0.609774i	$0.208740\pi$
$887$			32216.9i			1.21955i	−0.792575	+	0.609774i	$0.791260\pi$
$888$	29491.5	−	1308.72i	1.11449	−	0.0494569i
$889$		−	470.711i		−	0.0177583i
$890$	56.1719	+	5633.31i	0.00211560	+	0.212167i
$891$	23136.0	+	20607.7i	0.869906	+	0.774841i
$892$	−3602.39	+	71.8489i	−0.135221	+	0.00269695i
$893$	226.834	+	226.834i	0.00850023	+	0.00850023i
$894$	−2470.74	+	60.3099i	−0.0924316	+	0.00225622i
$895$		−	13464.4i		−	0.502868i
$896$	16238.1	+	14116.0i	0.605443	+	0.526320i
$897$	13574.9	−	13972.5i	0.505298	−	0.520099i
$898$	−23394.5	−	22932.6i	−0.869360	−	0.852194i
$899$	5714.97	−	5714.97i	0.212019	−	0.212019i
$900$	−14494.5	+	708.032i	−0.536832	+	0.0262234i
$901$	11514.3	+	11514.3i	0.425745	+	0.425745i
$902$	−54627.9	+	544.717i	−2.01653	+	0.0201076i
$903$	−18727.4	−	18194.4i	−0.690153	−	0.670512i
$904$	846.134	−	898.332i	0.0311305	−	0.0330510i
$905$	−18630.1			−0.684294
$906$	−3077.40	−	2930.74i	−0.112847	−	0.107469i
$907$	6623.37	−	6623.37i	0.242476	−	0.242476i	−0.575398	−	0.817874i	$-0.695153\pi$
$907$	6623.37	−	6623.37i	0.242476	−	0.242476i	0.817874	+	0.575398i	$0.195153\pi$
$908$	8481.11	+	8149.42i	0.309973	+	0.297850i
$909$	−25227.1	+	26727.3i	−0.920495	+	0.975235i
$910$	19860.3	+	19468.2i	0.723476	+	0.709190i
$911$	13826.3			0.502838			0.251419	−	0.967878i	$-0.419103\pi$
$911$	13826.3			0.502838			0.251419	+	0.967878i	$0.419103\pi$
$912$	−2341.19	+	2610.42i	−0.0850050	+	0.0947801i
$913$	−40701.8			−1.47539
$914$	−3454.64	−	3386.43i	−0.125021	−	0.122553i
$915$	−21726.0	+	313.609i	−0.784959	+	0.0113307i
$916$	8953.57	−	9317.99i	0.322963	−	0.336108i
$917$	25068.0	−	25068.0i	0.902747	−	0.902747i
$918$	−12955.7	+	14415.1i	−0.465796	+	0.518269i
$919$	−32283.9			−1.15881			−0.579407	−	0.815039i	$-0.696716\pi$
$919$	−32283.9			−1.15881			−0.579407	+	0.815039i	$0.696716\pi$
$920$	221.660	+	7407.91i	0.00794339	+	0.265469i
$921$	5259.35	−	5413.41i	0.188167	−	0.193678i
$922$	−19781.1	+	197.245i	−0.706568	+	0.00704547i
$923$	−32153.0	−	32153.0i	−1.14662	−	1.14662i
$924$	−19187.9	−	17912.1i	−0.683157	−	0.637732i
$925$	11927.8	−	11927.8i	0.423981	−	0.423981i
$926$	11211.5	+	10990.1i	0.397875	+	0.390018i
$927$	−39907.0	+	1152.34i	−1.41394	+	0.0408281i
$928$	8428.95	−	420.576i	0.298161	−	0.0148773i
$929$			19418.8i			0.685801i	0.939372	+	0.342901i	$0.111409\pi$
$929$			19418.8i			0.685801i	−0.939372	+	0.342901i	$0.888591\pi$
$930$	472.742	+	19367.0i	0.0166686	+	0.682869i
$931$	−911.504	−	911.504i	−0.0320874	−	0.0320874i
$932$	555.214	+	27837.6i	0.0195136	+	0.978380i
$933$	−18075.7	+	260.919i	−0.634269	+	0.00915552i
$934$	−212.797	−	21340.7i	−0.00745495	−	0.747633i
$935$		−	15784.1i		−	0.552081i
$936$	53081.9	−	3123.79i	1.85367	−	0.109086i
$937$			13947.1i			0.486266i	0.969993	+	0.243133i	$0.0781751\pi$
$937$			13947.1i			0.486266i	−0.969993	+	0.243133i	$0.921825\pi$
$938$	19849.4	−	197.926i	0.690945	−	0.00688968i
$939$	17188.4	−	248.110i	0.597361	−	0.00862276i
$940$	1334.45	+	1282.26i	0.0463031	+	0.0444922i
$941$	−32438.8	−	32438.8i	−1.12378	−	1.12378i	−0.991169	−	0.132608i	$-0.957665\pi$
$941$	−32438.8	−	32438.8i	−1.12378	−	1.12378i	−0.132608	−	0.991169i	$-0.542335\pi$
$942$	14209.2	−	346.841i	0.491464	−	0.0119965i
$943$		−	19576.0i		−	0.676016i
$944$	−17305.0	−	15976.9i	−0.596643	−	0.550852i
$945$	−11681.9	−	10711.7i	−0.402130	−	0.368730i
$946$	28460.2	−	29033.5i	0.978142	−	0.997845i
$947$	−14766.0	+	14766.0i	−0.506685	+	0.506685i	−0.913507	−	0.406823i	$-0.866637\pi$
$947$	−14766.0	+	14766.0i	−0.506685	+	0.506685i	0.406823	+	0.913507i	$0.366637\pi$
$948$	989.987	+	28787.5i	0.0339170	+	0.986261i
$949$	42449.8	+	42449.8i	1.45203	+	1.45203i
$950$	19.9782	+	2003.55i	0.000682291	+	0.0684249i
$951$	6642.18	−	6836.75i	0.226485	−	0.233120i
$952$	11258.4	−	11952.9i	0.383285	−	0.406930i
$953$	−27736.7			−0.942791			−0.471395	−	0.881922i	$-0.656250\pi$
$953$	−27736.7			−0.942791			−0.471395	+	0.881922i	$0.656250\pi$
$954$	988.589	+	25441.0i	0.0335501	+	0.863399i
$955$	−1013.30	+	1013.30i	−0.0343345	+	0.0343345i
$956$	−509.834	−	25562.3i	−0.0172481	−	0.864794i
$957$	−10294.9	+	148.604i	−0.347740	+	0.00501954i
$958$	−6329.23	+	6456.73i	−0.213453	+	0.217753i
$959$	−6738.59			−0.226904
$960$	−13203.4	+	15325.9i	−0.443895	+	0.515253i
$961$	−261.548			−0.00877942
$962$	−43267.5	+	44139.1i	−1.45011	+	1.47932i
$963$	41229.5	+	38915.3i	1.37965	+	1.30221i
$964$	40.7358	+	2042.43i	0.00136101	+	0.0682389i
$965$	454.775	−	454.775i	0.0151707	−	0.0151707i
$966$	6486.75	−	6811.35i	0.216054	−	0.226865i
$967$	−38161.5			−1.26907			−0.634535	−	0.772894i	$-0.718809\pi$
$967$	−38161.5			−1.26907			−0.634535	+	0.772894i	$0.718809\pi$
$968$	7374.29	−	7829.21i	0.244854	−	0.259959i
$969$	1919.35	+	1864.73i	0.0636310	+	0.0618201i
$970$	−137.617	−	13801.2i	−0.00455528	−	0.456835i
$971$	−40351.2	−	40351.2i	−1.33361	−	1.33361i	−0.902119	−	0.431488i	$-0.857989\pi$
$971$	−40351.2	−	40351.2i	−1.33361	−	1.33361i	−0.431488	−	0.902119i	$-0.642011\pi$
$972$	−30175.5	+	2787.38i	−0.995761	+	0.0919807i
$973$	−20682.4	+	20682.4i	−0.681446	+	0.681446i
$974$	36933.1	−	37677.1i	1.21500	−	1.23948i
$975$	21172.5	−	21792.6i	0.695447	−	0.715819i
$976$	23875.5	−	25860.2i	0.783027	−	0.848119i
$977$			37478.8i			1.22728i	0.789586	+	0.613640i	$0.210296\pi$
$977$			37478.8i			1.22728i	−0.789586	+	0.613640i	$0.789704\pi$
$978$	−17.9656	−	736.004i	−0.000587400	−	0.0240642i
$979$	7872.25	+	7872.25i	0.256995	+	0.256995i
$980$	−5362.32	−	5152.60i	−0.174789	−	0.167953i
$981$	2720.69	−	2882.48i	0.0885472	−	0.0938130i
$982$	16649.8	−	166.022i	0.541057	−	0.00539509i
$983$		−	11135.5i		−	0.361310i	−0.983547	−	0.180655i	$-0.942178\pi$
$983$		−	11135.5i		−	0.361310i	0.983547	−	0.180655i	$-0.0578217\pi$
$984$	36070.8	−	39420.8i	1.16859	−	1.27712i
$985$		−	8395.49i		−	0.271576i
$986$	−64.2194	−	6440.36i	−0.00207420	−	0.208015i
$987$	−33.9004	−	2348.53i	−0.00109328	−	0.0757391i
$988$	−146.400	−	7340.27i	−0.00471417	−	0.236361i
$989$	10301.5	+	10301.5i	0.331212	+	0.331212i
$990$	16760.0	−	18115.2i	0.538050	−	0.581555i
$991$		−	39321.0i		−	1.26042i	−0.776427	−	0.630208i	$-0.782970\pi$
$991$		−	39321.0i		−	1.26042i	0.776427	−	0.630208i	$-0.217030\pi$
$992$	−23267.9	−	21056.3i	−0.744714	−	0.673929i
$993$	−22768.1	−	22120.2i	−0.727617	−	0.706910i
$994$	−15678.4	−	15368.8i	−0.500291	−	0.490413i
$995$	8818.09	−	8818.09i	0.280957	−	0.280957i
$996$	27165.6	−	29100.5i	0.864231	−	0.925789i
$997$	−33341.7	−	33341.7i	−1.05912	−	1.05912i	−0.998139	−	0.0609797i	$-0.980578\pi$
$997$	−33341.7	−	33341.7i	−1.05912	−	1.05912i	−0.0609797	−	0.998139i	$-0.519422\pi$
$998$	−30281.5	+	301.948i	−0.960464	+	0.00957716i
$999$	23806.4	−	25962.8i	0.753956	−	0.822250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.k.a.11.17	yes	44
3.2	odd	2	inner	48.4.k.a.11.6	✓	44
4.3	odd	2		192.4.k.a.143.11		44
8.3	odd	2		384.4.k.a.287.12		44
8.5	even	2		384.4.k.b.287.11		44
12.11	even	2		192.4.k.a.143.22		44
16.3	odd	4	inner	48.4.k.a.35.6	yes	44
16.5	even	4		384.4.k.a.95.1		44
16.11	odd	4		384.4.k.b.95.22		44
16.13	even	4		192.4.k.a.47.22		44
24.5	odd	2		384.4.k.b.287.22		44
24.11	even	2		384.4.k.a.287.1		44
48.5	odd	4		384.4.k.a.95.12		44
48.11	even	4		384.4.k.b.95.11		44
48.29	odd	4		192.4.k.a.47.11		44
48.35	even	4	inner	48.4.k.a.35.17	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.6	✓	44	3.2	odd	2	inner
48.4.k.a.11.17	yes	44	1.1	even	1	trivial
48.4.k.a.35.6	yes	44	16.3	odd	4	inner
48.4.k.a.35.17	yes	44	48.35	even	4	inner
192.4.k.a.47.11		44	48.29	odd	4
192.4.k.a.47.22		44	16.13	even	4
192.4.k.a.143.11		44	4.3	odd	2
192.4.k.a.143.22		44	12.11	even	2
384.4.k.a.95.1		44	16.5	even	4
384.4.k.a.95.12		44	48.5	odd	4
384.4.k.a.287.1		44	24.11	even	2
384.4.k.a.287.12		44	8.3	odd	2
384.4.k.b.95.11		44	48.11	even	4
384.4.k.b.95.22		44	16.11	odd	4
384.4.k.b.287.11		44	8.5	even	2
384.4.k.b.287.22		44	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.97996 - 2.01984i) q^{2} +(-0.0749974 - 5.19561i) q^{3} +(-0.159526 - 7.99841i) q^{4} +(-5.37662 + 5.37662i) q^{5} +(-10.6428 - 10.1356i) q^{6} +14.8575 q^{7} +(-16.4714 - 15.5143i) q^{8} +(-26.9888 + 0.779314i) q^{9} +(0.214439 + 21.5054i) q^{10} +(30.0526 + 30.0526i) q^{11} +(-41.5447 + 1.42870i) q^{12} +(61.5437 - 61.5437i) q^{13} +(29.4173 - 30.0098i) q^{14} +(28.3380 + 27.5316i) q^{15} +(-63.9491 + 2.55192i) q^{16} +48.8426i q^{17} +(-51.8625 + 56.0560i) q^{18} +(7.45581 + 7.45581i) q^{19} +(43.8621 + 42.1467i) q^{20} +(-1.11427 - 77.1939i) q^{21} +(120.205 - 1.19861i) q^{22} +43.0756i q^{23} +(-79.3710 + 86.7424i) q^{24} +67.1840i q^{25} +(-2.45458 - 246.162i) q^{26} +(6.07310 + 140.165i) q^{27} +(-2.37017 - 118.837i) q^{28} +(-32.9665 - 32.9665i) q^{29} +(111.718 - 2.72699i) q^{30} +173.357i q^{31} +(-121.462 + 134.220i) q^{32} +(153.888 - 158.396i) q^{33} +(98.6543 + 96.7063i) q^{34} +(-79.8832 + 79.8832i) q^{35} +(10.5387 + 215.743i) q^{36} +(-177.539 - 177.539i) q^{37} +(29.8218 - 0.297365i) q^{38} +(-324.373 - 315.141i) q^{39} +(171.975 - 5.14585i) q^{40} -454.458 q^{41} +(-158.126 - 150.590i) q^{42} +(239.150 - 239.150i) q^{43} +(235.579 - 245.167i) q^{44} +(140.918 - 149.298i) q^{45} +(87.0058 + 85.2878i) q^{46} +30.4238 q^{47} +(18.0548 + 332.063i) q^{48} -122.254 q^{49} +(135.701 + 133.022i) q^{50} +(253.767 - 3.66306i) q^{51} +(-502.069 - 482.433i) q^{52} +(235.743 - 235.743i) q^{53} +(295.135 + 265.253i) q^{54} -323.163 q^{55} +(-244.724 - 230.504i) q^{56} +(38.1783 - 39.2967i) q^{57} +(-131.860 + 1.31482i) q^{58} +(260.222 + 260.222i) q^{59} +(215.688 - 231.051i) q^{60} +(-388.869 + 388.869i) q^{61} +(350.153 + 343.239i) q^{62} +(-400.986 + 11.5787i) q^{63} +(30.6128 + 511.084i) q^{64} +661.793i q^{65} +(-15.2425 - 624.446i) q^{66} +(334.013 + 334.013i) q^{67} +(390.663 - 7.79168i) q^{68} +(223.804 - 3.23055i) q^{69} +(3.18603 + 319.517i) q^{70} -522.443i q^{71} +(456.633 + 405.875i) q^{72} +689.751i q^{73} +(-710.119 + 7.08088i) q^{74} +(349.062 - 5.03862i) q^{75} +(58.4453 - 60.8241i) q^{76} +(446.508 + 446.508i) q^{77} +(-1278.78 + 31.2146i) q^{78} -692.930i q^{79} +(330.109 - 357.550i) q^{80} +(727.785 - 42.0654i) q^{81} +(-899.808 + 917.934i) q^{82} +(-677.176 + 677.176i) q^{83} +(-617.251 + 21.2269i) q^{84} +(-262.608 - 262.608i) q^{85} +(-9.53815 - 956.551i) q^{86} +(-168.809 + 173.754i) q^{87} +(-28.7628 - 961.254i) q^{88} +261.949 q^{89} +(-22.5469 - 580.237i) q^{90} +(914.386 - 914.386i) q^{91} +(344.536 - 6.87169i) q^{92} +(900.694 - 13.0013i) q^{93} +(60.2378 - 61.4512i) q^{94} -80.1741 q^{95} +(706.463 + 621.004i) q^{96} -641.755 q^{97} +(-242.058 + 246.934i) q^{98} +(-834.504 - 787.663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33}+ \cdots + 1196 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7 + 56 * q^10 - 80 * q^12 - 4 * q^13 - 112 * q^16 + 52 * q^18 + 20 * q^19 - 56 * q^21 - 40 * q^22 - 120 * q^24 - 134 * q^27 - 296 * q^28 - 332 * q^30 - 4 * q^33 + 520 * q^34 - 604 * q^36 - 4 * q^37 + 596 * q^39 + 632 * q^40 + 696 * q^42 - 436 * q^43 - 252 * q^45 + 664 * q^46 + 1200 * q^48 + 972 * q^49 - 648 * q^51 + 320 * q^52 + 1592 * q^54 + 280 * q^55 - 424 * q^58 + 800 * q^60 - 916 * q^61 - 2056 * q^64 - 668 * q^66 - 1636 * q^67 + 52 * q^69 - 5192 * q^70 - 3704 * q^72 + 1454 * q^75 - 568 * q^76 - 4932 * q^78 - 4 * q^81 + 768 * q^82 - 2096 * q^84 + 736 * q^85 + 1284 * q^87 + 8864 * q^88 + 2672 * q^90 + 424 * q^91 - 2084 * q^93 + 5616 * q^94 + 8008 * q^96 - 8 * q^97 + 1196 * q^99

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