LMFDB - Embedded newform 48.4.k.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,4,Mod(11,48)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$2.83209168028$
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			11.6
Character	$\chi$	$=$	48.11
Dual form			48.4.k.a.35.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97996 + 2.01984i) q^{2} +(-5.19561 - 0.0749974i) q^{3} +(-0.159526 - 7.99841i) q^{4} +(5.37662 - 5.37662i) q^{5} +(10.4386 - 10.3458i) q^{6} +14.8575 q^{7} +(16.4714 + 15.5143i) q^{8} +(26.9888 + 0.779314i) q^{9} +O(q^{10})$	\(q+(-1.97996 + 2.01984i) q^{2} +(-5.19561 - 0.0749974i) q^{3} +(-0.159526 - 7.99841i) q^{4} +(5.37662 - 5.37662i) q^{5} +(10.4386 - 10.3458i) 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} +(0.228978 + 41.5686i) 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} +(-55.0107 + 52.9700i) q^{18} +(7.45581 + 7.45581i) q^{19} +(-43.8621 - 42.1467i) q^{20} +(-77.1939 - 1.11427i) q^{21} +(120.205 - 1.19861i) q^{22} -43.0756i q^{23} +(-84.4154 - 81.8416i) q^{24} +67.1840i q^{25} +(2.45458 + 246.162i) q^{26} +(-140.165 - 6.07310i) q^{27} +(-2.37017 - 118.837i) q^{28} +(32.9665 + 32.9665i) q^{29} +(0.498707 - 111.750i) 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} +(1.92785 - 215.991i) 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} +(155.091 - 153.713i) q^{42} +(239.150 - 239.150i) q^{43} +(-235.579 + 245.167i) q^{44} +(149.298 - 140.918i) q^{45} +(87.0058 + 85.2878i) q^{46} -30.4238 q^{47} +(332.446 - 8.46275i) q^{48} -122.254 q^{49} +(-135.701 - 133.022i) q^{50} +(-3.66306 + 253.767i) q^{51} +(-502.069 - 482.433i) q^{52} +(-235.743 + 235.743i) q^{53} +(289.787 - 271.086i) 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} +(224.729 + 222.267i) 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} +(-624.626 - 2.78753i) q^{66} +(334.013 + 334.013i) q^{67} +(-390.663 + 7.79168i) q^{68} +(-3.23055 + 223.804i) q^{69} +(3.18603 + 319.517i) q^{70} +522.443i q^{71} +(432.452 + 431.548i) q^{72} +689.751i q^{73} +(710.119 - 7.08088i) q^{74} +(5.03862 - 349.062i) q^{75} +(58.4453 - 60.8241i) q^{76} +(-446.508 - 446.508i) q^{77} +(5.70847 - 1279.15i) 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} +(3.40204 + 617.606i) 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} +(-10.9720 + 580.571i) q^{90} +(914.386 - 914.386i) q^{91} +(-344.536 + 6.87169i) q^{92} +(13.0013 - 900.694i) q^{93} +(60.2378 - 61.4512i) q^{94} +80.1741 q^{95} +(-641.136 + 688.245i) q^{96} -641.755 q^{97} +(242.058 - 246.934i) q^{98} +(-787.663 - 834.504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7}+O(q^{10}) $ 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

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
$3$	−5.19561	−	0.0749974i	−0.999896	−	0.0144332i
$3$	−5.19561	−	0.0749974i	−0.999896	−	0.0144332i
$4$	−0.159526	−	7.99841i	−0.0199408	−	0.999801i
$5$	5.37662	−	5.37662i	0.480899	−	0.480899i	−0.424520	−	0.905419i	$-0.639557\pi$
$5$	5.37662	−	5.37662i	0.480899	−	0.480899i	0.905419	+	0.424520i	$0.139557\pi$
$6$	10.4386	−	10.3458i	0.710255	−	0.703944i
$7$	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	0.162897	−	0.986643i	$-0.447916\pi$
$11$	−30.0526	−	30.0526i	−0.823746	−	0.823746i	−0.986643	+	0.162897i	$0.947916\pi$
$12$	0.228978	+	41.5686i	0.00550835	+	0.999985i
$13$	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	$-0.886720\pi$
$17$		−	48.8426i		−	0.696827i	0.937341	−	0.348414i	$-0.113280\pi$
$18$	−55.0107	+	52.9700i	−0.720342	+	0.693620i
$19$	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
$21$	−77.1939	−	1.11427i	−0.802147	−	0.0115788i
$22$	120.205	−	1.19861i	1.16490	−	0.0116156i
$23$		−	43.0756i		−	0.390516i	−0.980752	−	0.195258i	$-0.937446\pi$
$23$		−	43.0756i		−	0.390516i	0.980752	−	0.195258i	$-0.0625545\pi$
$24$	−84.4154	−	81.8416i	−0.717967	−	0.696077i
$25$			67.1840i			0.537472i
$26$	2.45458	+	246.162i	0.0185147	+	1.85679i
$27$	−140.165	−	6.07310i	−0.999063	−	0.0432877i
$28$	−2.37017	−	118.837i	−0.0159971	−	0.802071i
$29$	32.9665	+	32.9665i	0.211094	+	0.211094i	0.804732	−	0.593638i	$-0.202309\pi$
$29$	32.9665	+	32.9665i	0.211094	+	0.211094i	−0.593638	+	0.804732i	$0.702309\pi$
$30$	0.498707	−	111.750i	0.00303504	−	0.680087i
$31$			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
$36$	1.92785	−	215.991i	0.00892525	−	0.999960i
$37$	−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	$-0.166974\pi$
$41$	454.458			1.73108			0.865542	+	0.500837i	$0.166974\pi$
$42$	155.091	−	153.713i	0.569789	−	0.564726i
$43$	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
$45$	149.298	−	140.918i	0.494579	−	0.466818i
$46$	87.0058	+	85.2878i	0.278876	+	0.273370i
$47$	−30.4238			−0.0944205			−0.0472102	−	0.998885i	$-0.515033\pi$
$47$	−30.4238			−0.0944205			−0.0472102	+	0.998885i	$0.515033\pi$
$48$	332.446	−	8.46275i	0.999676	−	0.0254478i
$49$	−122.254			−0.356426
$50$	−135.701	−	133.022i	−0.383821	−	0.376242i
$51$	−3.66306	+	253.767i	−0.0100575	+	0.696755i
$52$	−502.069	−	482.433i	−1.33893	−	1.28657i
$53$	−235.743	+	235.743i	−0.610976	+	0.610976i	−0.943200	−	0.332224i	$-0.892201\pi$
$53$	−235.743	+	235.743i	−0.610976	+	0.610976i	0.332224	+	0.943200i	$0.392201\pi$
$54$	289.787	−	271.086i	0.730278	−	0.683150i
$55$	−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	0.359096	−	0.933300i	$-0.383085\pi$
$59$	−260.222	−	260.222i	−0.574204	−	0.574204i	−0.933300	+	0.359096i	$0.883085\pi$
$60$	224.729	+	222.267i	0.483541	+	0.478243i
$61$	−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
$66$	−624.626	−	2.78753i	−1.16494	−	0.00519880i
$67$	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
$69$	−3.23055	+	223.804i	−0.00563642	+	0.390476i
$70$	3.18603	+	319.517i	0.00544005	+	0.545565i
$71$			522.443i			0.873275i	0.899637	+	0.436638i	$0.143831\pi$
$71$			522.443i			0.873275i	−0.899637	+	0.436638i	$0.856169\pi$
$72$	432.452	+	431.548i	0.707846	+	0.706367i
$73$			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
$75$	5.03862	−	349.062i	0.00775747	−	0.537416i
$76$	58.4453	−	60.8241i	0.0882122	−	0.0918026i
$77$	−446.508	−	446.508i	−0.660835	−	0.660835i
$78$	5.70847	−	1279.15i	0.00828663	−	1.85686i
$79$		−	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	−0.0994989	−	0.995038i	$-0.531724\pi$
$83$	677.176	−	677.176i	0.895539	−	0.895539i	0.995038	+	0.0994989i	$0.0317240\pi$
$84$	3.40204	+	617.606i	0.00441897	+	0.802219i
$85$	−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	$-0.549857\pi$
$89$	−261.949			−0.311983			−0.155992	+	0.987758i	$0.549857\pi$
$90$	−10.9720	+	580.571i	−0.0128506	+	0.679973i
$91$	914.386	−	914.386i	1.05334	−	1.05334i
$92$	−344.536	+	6.87169i	−0.390439	+	0.00778721i
$93$	13.0013	−	900.694i	0.0144965	−	1.00428i
$94$	60.2378	−	61.4512i	0.0660963	−	0.0674277i
$95$	80.1741			0.0865862
$96$	−641.136	+	688.245i	−0.681622	+	0.731705i
$97$	−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
$99$	−787.663	−	834.504i	−0.799627	−	0.847179i
$100$	537.365	−	10.7176i	0.537365	−	0.0107176i
$101$	−962.520	+	962.520i	−0.948260	+	0.948260i	−0.998726	−	0.0504657i	$-0.983929\pi$
$101$	−962.520	+	962.520i	−0.948260	+	0.948260i	0.0504657	+	0.998726i	$0.483929\pi$
$102$	−505.317	−	509.847i	−0.490528	−	0.494925i
$103$	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	$0.147475\pi$
$107$	1484.78	+	1484.78i	1.34149	+	1.34149i	0.446908	+	0.894580i	$0.352525\pi$
$108$	−26.2152	+	1122.06i	−0.0233570	+	0.999727i
$109$	−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	$-0.992773\pi$
$113$		−	54.5390i		−	0.0454035i	0.999742	−	0.0227017i	$-0.00722681\pi$
$114$	154.965	+	0.691563i	0.127314	+	0.000568165i
$115$	−231.601	−	231.601i	−0.187799	−	0.187799i
$116$	258.421	−	268.939i	0.206843	−	0.215262i
$117$	1708.95	−	1613.02i	1.35036	−	1.27457i
$118$	1040.84	−	10.3786i	0.812007	−	0.00809684i
$119$		−	725.680i		−	0.559016i
$120$	−893.900	+	13.8382i	−0.680013	+	0.0105271i
$121$			475.322i			0.357116i
$122$	−15.5095	−	1555.40i	−0.0115095	−	1.15426i
$123$	−2361.19	−	34.0832i	−1.73090	−	0.0249852i
$124$	1386.58	−	27.6550i	1.00418	−	0.0200281i
$125$	1033.30	+	1033.30i	0.739369	+	0.739369i
$126$	−817.323	+	787.003i	−0.577880	+	0.556443i
$127$		−	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	$0.542899\pi$
$131$	−1687.23	+	1687.23i	−1.12530	+	1.12530i	−0.990932	+	0.134364i	$0.957101\pi$
$132$	1242.36	−	1256.13i	0.819196	−	0.828271i
$133$	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	$-0.454833\pi$
$137$	453.548			0.282841			0.141420	+	0.989950i	$0.454833\pi$
$138$	−445.652	−	449.648i	−0.274902	−	0.277366i
$139$	−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
$141$	158.070	+	2.28170i	0.0944106	+	0.00136279i
$142$	−1055.25	−	1034.42i	−0.623625	−	0.611311i
$143$	−3699.10			−2.16318
$144$	−1727.90	+	19.0366i	−0.999939	+	0.0110165i
$145$	354.497			0.203030
$146$	−1393.19	−	1365.68i	−0.789734	−	0.774140i
$147$	635.185	+	9.16874i	0.356389	+	0.00514438i
$148$	−1391.70	+	1448.35i	−0.772955	+	0.804416i
$149$	−118.909	+	118.909i	−0.0653785	+	0.0653785i	−0.739040	−	0.673662i	$-0.764721\pi$
$149$	−118.909	+	118.909i	−0.0653785	+	0.0653785i	0.673662	+	0.739040i	$0.264721\pi$
$150$	695.074	+	701.306i	0.378350	+	0.381742i
$151$	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
$156$	2572.37	+	2544.19i	1.32022	+	1.30576i
$157$	−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
$162$	−1525.95	+	1386.72i	−0.740062	+	0.672539i
$163$	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
$165$	1679.03	+	24.2364i	0.792195	+	0.0114351i
$166$	27.0082	+	2708.57i	0.0126280	+	1.26642i
$167$		−	2091.54i		−	0.969150i	−0.874750	−	0.484575i	$-0.838974\pi$
$167$		−	2091.54i		−	0.969150i	0.874750	−	0.484575i	$-0.161026\pi$
$168$	−1254.20	−	1215.96i	−0.575975	−	0.558414i
$169$		−	5378.24i		−	2.44799i
$170$	1050.38	−	10.4737i	0.473885	−	0.00472529i
$171$	195.413	+	207.034i	0.0873894	+	0.0925863i
$172$	−1950.97	−	1874.67i	−0.864883	−	0.831058i
$173$	2566.01	+	2566.01i	1.12769	+	1.12769i	0.990552	+	0.137137i	$0.0437899\pi$
$173$	2566.01	+	2566.01i	1.12769	+	1.12769i	0.137137	+	0.990552i	$0.456210\pi$
$174$	685.190	+	3.05781i	0.298529	+	0.00133225i
$175$			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	−0.395587	−	0.918429i	$-0.629459\pi$
$179$	1252.13	−	1252.13i	0.522841	−	0.522841i	0.918429	+	0.395587i	$0.129459\pi$
$180$	−1150.94	−	1171.67i	−0.476588	−	0.485172i
$181$	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
$186$	1793.52	+	1809.60i	0.707028	+	0.713366i
$187$	−1467.85	+	1467.85i	−0.574009	+	0.574009i
$188$	4.85339	+	243.342i	0.00188282	+	0.0944017i
$189$	−2082.50	−	90.2312i	−0.801479	−	0.0347267i
$190$	−158.741	+	161.939i	−0.0606122	+	0.0618331i
$191$	−188.463			−0.0713965			−0.0356983	−	0.999363i	$-0.511366\pi$
$191$	−188.463			−0.0713965			−0.0356983	+	0.999363i	$0.511366\pi$
$192$	−120.722	−	2657.69i	−0.0453770	−	0.998970i
$193$	−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
$195$	−49.6327	+	3438.42i	−0.0182270	+	1.26272i
$196$	19.5028	+	977.838i	0.00710742	+	0.356355i
$197$	780.741	−	780.741i	0.282363	−	0.282363i	−0.551688	−	0.834051i	$-0.686016\pi$
$197$	780.741	−	780.741i	0.282363	−	0.282363i	0.834051	+	0.551688i	$0.186016\pi$
$198$	3245.11	+	61.3282i	1.16475	+	0.0220122i
$199$	−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
$204$	2030.32	−	11.1839i	0.696817	−	0.00383837i
$205$	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
$210$	7.40955	−	1660.32i	0.00243480	−	0.545587i
$211$	−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
$213$	39.1818	−	2714.41i	0.0126042	−	0.873185i
$214$	−5938.83	+	59.2184i	−1.89706	+	0.0189163i
$215$		−	2571.63i		−	0.815739i
$216$	−2214.48	−	2274.59i	−0.697577	−	0.716510i
$217$			2575.65i			0.805745i
$218$	−4.14014	−	415.202i	−0.00128626	−	0.128995i
$219$	51.7295	−	3583.68i	0.0159614	−	1.10577i
$220$	51.5530	+	2584.79i	0.0157987	+	0.792120i
$221$	−3005.95	−	3005.95i	−0.914942	−	0.914942i
$222$	−3690.03	−	16.4676i	−1.11558	−	0.00497852i
$223$		−	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	−0.538594	−	0.842566i	$-0.681044\pi$
$227$	1039.61	−	1039.61i	0.303972	−	0.303972i	0.842566	+	0.538594i	$0.181044\pi$
$228$	−308.220	+	311.635i	−0.0895281	+	0.0905198i
$229$	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	$-0.337257\pi$
$233$	3480.39			0.978575			0.489287	+	0.872123i	$0.337257\pi$
$234$	−125.592	+	6645.53i	−0.0350863	+	1.85655i
$235$	−163.577	+	163.577i	−0.0454067	+	0.0454067i
$236$	−2039.85	+	2122.88i	−0.562640	+	0.585540i
$237$	−51.9679	+	3600.19i	−0.0142434	+	0.986742i
$238$	1465.76	+	1436.82i	0.399206	+	0.391323i
$239$	−3195.92			−0.864966			−0.432483	−	0.901642i	$-0.642363\pi$
$239$	−3195.92			−0.864966			−0.432483	+	0.901642i	$0.642363\pi$
$240$	1741.93	−	1832.94i	0.468506	−	0.492981i
$241$	−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
$243$	−3778.13	−	273.138i	−0.997397	−	0.0721061i
$244$	3172.37	+	3048.30i	0.832336	+	0.799784i
$245$	−657.313	+	657.313i	−0.171405	+	0.171405i
$246$	4743.90	−	4701.74i	1.22951	−	1.21859i
$247$	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	0.994787	−	0.101976i	$-0.0325164\pi$
$251$	3550.34	+	3550.34i	0.892811	+	0.892811i	−0.101976	+	0.994787i	$0.532516\pi$
$252$	28.6431	−	3209.10i	0.00716011	−	0.802199i
$253$	−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	$-0.657089\pi$
$257$		−	7256.80i		−	1.76135i	0.473721	−	0.880675i	$-0.342911\pi$
$258$	22.1823	−	4970.58i	0.00535275	−	1.19944i
$259$	−2637.78	−	2637.78i	−0.632834	−	0.632834i
$260$	−5293.29	+	105.573i	−1.26260	+	0.0251823i
$261$	864.034	+	915.417i	0.204913	+	0.217099i
$262$	−67.2927	−	6748.57i	−0.0158678	−	1.59133i
$263$			2114.79i			0.495832i	0.968782	+	0.247916i	$0.0797457\pi$
$263$			2114.79i			0.495832i	−0.968782	+	0.247916i	$0.920254\pi$
$264$	77.3486	+	4996.46i	0.0180321	+	1.16481i
$265$			2535.00i			0.587636i
$266$	−443.078	+	4.41810i	−0.102131	+	0.00101839i
$267$	1360.98	+	19.6455i	0.311951	+	0.00450293i
$268$	2618.29	−	2724.85i	0.596781	−	0.621070i
$269$	−120.142	−	120.142i	−0.0272312	−	0.0272312i	0.693360	−	0.720591i	$-0.256130\pi$
$269$	−120.142	−	120.142i	−0.0272312	−	0.0272312i	−0.720591	+	0.693360i	$0.756130\pi$
$270$	100.548	−	3015.60i	0.0226635	−	0.679716i
$271$			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
$276$	1790.59	−	9.86335i	0.390510	−	0.00215110i
$277$	−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	$-0.494062\pi$
$281$	175.744			0.0373097			0.0186548	+	0.999826i	$0.494062\pi$
$282$	−317.581	+	314.759i	−0.0670626	+	0.0664667i
$283$	−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
$285$	−416.553	−	6.01285i	−0.0865772	−	0.00124972i
$286$	7324.06	−	7471.59i	1.51427	−	1.54477i
$287$	6752.12			1.38873
$288$	3382.71	−	3527.77i	0.692112	−	0.721791i
$289$	2527.40			0.514432
$290$	−701.889	+	716.027i	−0.142125	+	0.144988i
$291$	3334.31	+	48.1300i	0.671687	+	0.00969563i
$292$	5516.91	−	110.034i	1.10566	−	0.0220521i
$293$	−5718.53	+	5718.53i	−1.14020	+	1.14020i	−0.151792	+	0.988412i	$0.548504\pi$
$293$	−5718.53	+	5718.53i	−1.14020	+	1.14020i	−0.988412	+	0.151792i	$0.951496\pi$
$294$	−1276.16	+	1264.82i	−0.253153	+	0.250904i
$295$	−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
$300$	−2792.74	+	15.3836i	−0.537464	+	0.00296058i
$301$	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
$306$	2587.19	+	2686.86i	0.483333	+	0.501954i
$307$	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
$309$	−7682.51	−	110.895i	−1.41438	−	0.0204162i
$310$	−3728.10	+	37.1744i	−0.683039	+	0.00681085i
$311$			3479.04i			0.634335i	0.948370	+	0.317168i	$0.102732\pi$
$311$			3479.04i			0.634335i	−0.948370	+	0.317168i	$0.897268\pi$
$312$	−10232.1	+	158.399i	−1.85665	+	0.0287423i
$313$			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
$315$	2218.20	−	2093.69i	0.396767	−	0.374496i
$316$	−5542.34	+	110.541i	−0.986648	+	0.0196785i
$317$	−1297.15	−	1297.15i	−0.229826	−	0.229826i	0.582794	−	0.812620i	$-0.301960\pi$
$317$	−1297.15	−	1297.15i	−0.229826	−	0.229826i	−0.812620	+	0.582794i	$0.801960\pi$
$318$	−21.8663	+	4899.77i	−0.00385598	+	0.864042i
$319$		−	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
$324$	220.356	−	5827.84i	0.0377839	−	0.999286i
$325$	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
$330$	−3373.36	+	3343.39i	−0.562720	+	0.557719i
$331$	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
$333$	−4653.19	−	4929.90i	−0.765745	−	0.811282i
$334$	4224.58	+	4141.16i	0.692092	+	0.678426i
$335$	3591.71			0.585780
$336$	4939.32	−	125.735i	0.801971	−	0.0204150i
$337$	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
$339$	−4.09028	+	283.363i	−0.000655320	+	0.0453988i
$340$	−2058.55	+	2142.34i	−0.328355	+	0.341719i
$341$	5209.83	−	5209.83i	0.827355	−	0.827355i
$342$	−805.084	−	15.2150i	−0.127292	−	0.00240566i
$343$	−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	0.0417910	−	0.999126i	$-0.486694\pi$
$347$	−6188.11	−	6188.11i	−0.957335	−	0.957335i	−0.999126	+	0.0417910i	$0.986694\pi$
$348$	−1362.82	+	1377.92i	−0.209928	+	0.212254i
$349$	−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	$-0.967324\pi$
$353$		−	1359.26i		−	0.204947i	0.994736	−	0.102473i	$-0.0326756\pi$
$354$	−5408.56	−	24.1369i	−0.812039	−	0.00362390i
$355$	2808.97	+	2808.97i	0.419957	+	0.419957i
$356$	41.7877	+	2095.17i	0.00622120	+	0.311921i
$357$	−54.4241	+	3770.35i	−0.00806842	+	0.558958i
$358$	49.9395	+	5008.27i	0.00737258	+	0.739373i
$359$		−	479.331i		−	0.0704683i	−0.999379	−	0.0352342i	$-0.988782\pi$
$359$		−	479.331i		−	0.0704683i	0.999379	−	0.0352342i	$-0.0112177\pi$
$360$	4645.39	−	4.85765i	0.680094	−	0.000711168i
$361$		−	6747.82i		−	0.983791i
$362$	−6929.71	+	69.0989i	−1.00613	+	0.0100325i
$363$	35.6479	−	2469.59i	0.00515435	−	0.357079i
$364$	−7459.50	−	7167.77i	−1.07413	−	1.03212i
$365$	3708.53	+	3708.53i	0.531817	+	0.531817i
$366$	−36.0695	+	8082.41i	−0.00515132	+	1.15430i
$367$			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
$372$	−7206.19	+	39.6948i	−1.00436	+	0.00553248i
$373$	−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
$378$	4305.51	−	4027.66i	0.585851	−	0.548044i
$379$	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
$381$	−2.37604	+	164.606i	−0.000319497	+	0.0221339i
$382$	373.150	−	380.666i	0.0499791	−	0.0509858i
$383$	−12267.5			−1.63666			−0.818332	−	0.574746i	$-0.805101\pi$
$383$	−12267.5			−1.63666			−0.818332	+	0.574746i	$0.805101\pi$
$384$	5607.14	+	5018.28i	0.745151	+	0.666895i
$385$	−4801.40			−0.635590
$386$	167.473	−	170.846i	0.0220832	−	0.0225281i
$387$	6640.73	−	6267.98i	0.872266	−	0.823306i
$388$	102.377	+	5133.02i	0.0133954	+	0.671623i
$389$	−1661.54	+	1661.54i	−0.216564	+	0.216564i	−0.807049	−	0.590485i	$-0.798936\pi$
$389$	−1661.54	+	1661.54i	−0.216564	+	0.216564i	0.590485	+	0.807049i	$0.298936\pi$
$390$	−6846.79	−	6908.18i	−0.888977	−	0.896947i
$391$	−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
$396$	−6549.05	+	6433.17i	−0.831066	+	0.816361i
$397$	−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	$0.103297\pi$
$401$			5120.78i			0.637705i	−0.947804	+	0.318852i	$0.896703\pi$
$402$	6942.25	+	30.9813i	0.861313	+	0.00384380i
$403$	10669.0	+	10669.0i	1.31876	+	1.31876i
$404$	7852.17	+	7545.08i	0.966981	+	0.929163i
$405$	4139.19	−	3686.85i	0.507847	−	0.452349i
$406$	−1959.11	+	19.5350i	−0.239480	+	0.00238795i
$407$			10671.0i			1.29961i
$408$	−3997.35	+	4123.06i	−0.485045	+	0.500299i
$409$			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
$411$	−2356.46	−	34.0149i	−0.282811	−	0.00408231i
$412$	−235.884	−	11826.9i	−0.0282068	−	1.41424i
$413$	−3866.26	−	3866.26i	−0.460644	−	0.460644i
$414$	2281.71	+	2369.62i	0.270870	+	0.281305i
$415$		−	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	−0.843327	−	0.537401i	$-0.819406\pi$
$419$	−2623.85	+	2623.85i	−0.305927	+	0.305927i	0.537401	+	0.843327i	$0.319406\pi$
$420$	3338.92	+	3302.34i	0.387911	+	0.383661i
$421$	−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
$426$	5405.10	+	5453.56i	0.614737	+	0.620249i
$427$	−5777.63	+	5777.63i	−0.654799	+	0.654799i
$428$	11639.0	−	12112.7i	1.31447	−	1.36797i
$429$	19219.1	+	277.423i	2.16295	+	0.0312217i
$430$	5194.29	+	5091.73i	0.582537	+	0.571034i
$431$	11772.7			1.31571			0.657855	−	0.753145i	$-0.271464\pi$
$431$	11772.7			1.31571			0.657855	+	0.753145i	$0.271464\pi$
$432$	8978.90	+	30.6810i	0.999994	+	0.00341699i
$433$	−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
$435$	−1841.83	−	26.5863i	−0.203009	−	0.00293038i
$436$	846.839	+	813.720i	0.0930189	+	0.0893810i
$437$	321.163	−	321.163i	0.0351564	−	0.0351564i
$438$	7136.05	+	7200.02i	0.778478	+	0.785458i
$439$	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	0.877032	−	0.480431i	$-0.159520\pi$
$443$	3697.94	+	3697.94i	0.396601	+	0.396601i	−0.480431	+	0.877032i	$0.659520\pi$
$444$	7339.38	−	7420.68i	0.784485	−	0.793176i
$445$	−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	$0.208305\pi$
$449$			11582.4i			1.21738i	−0.793407	+	0.608692i	$0.791695\pi$
$450$	−3558.74	−	3695.84i	−0.372801	−	0.387164i
$451$	−13657.7	−	13657.7i	−1.42597	−	1.42597i
$452$	−436.225	+	8.70041i	−0.0453945	+	0.000905382i
$453$	−1502.33	−	21.6857i	−0.155818	−	0.00224919i
$454$	41.4636	+	4158.25i	0.00428630	+	0.429860i
$455$		−	9832.60i		−	1.01310i
$456$	−19.1896	−	1239.58i	−0.00197069	−	0.127300i
$457$		−	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
$459$	−296.626	+	6846.00i	−0.0301641	+	0.696174i
$460$	−1815.49	+	1889.38i	−0.184017	+	0.191506i
$461$	4945.52	+	4945.52i	0.499644	+	0.499644i	0.911327	−	0.411683i	$-0.135059\pi$
$461$	4945.52	+	4945.52i	0.499644	+	0.499644i	−0.411683	+	0.911327i	$0.635059\pi$
$462$	−9280.39	−	41.4158i	−0.934552	−	0.00417064i
$463$			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	−0.920180	−	0.391497i	$-0.871957\pi$
$467$	−5335.45	+	5335.45i	−0.528683	+	0.528683i	0.391497	+	0.920180i	$0.371957\pi$
$468$	−13174.3	−	13411.5i	−1.30124	−	1.32468i
$469$	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
$474$	−7168.93	−	7233.20i	−0.694683	−	0.700912i
$475$	−500.912	+	500.912i	−0.0483861	+	0.0483861i
$476$	−5804.28	+	115.765i	−0.558905	+	0.0111472i
$477$	−6546.12	+	6178.68i	−0.628357	+	0.593087i
$478$	6327.79	−	6455.26i	0.605495	−	0.617692i
$479$	3196.65			0.304924			0.152462	−	0.988309i	$-0.451280\pi$
$479$	3196.65			0.304924			0.152462	+	0.988309i	$0.451280\pi$
$480$	253.284	+	7147.57i	0.0240850	+	0.679667i
$481$	−21852.7			−2.07152
$482$	505.592	−	515.776i	0.0477782	−	0.0487406i
$483$	−47.9980	+	3325.17i	−0.00452171	+	0.313251i
$484$	3801.82	−	75.8264i	0.357045	−	0.00712119i
$485$	−3450.47	+	3450.47i	−0.323047	+	0.323047i
$486$	8032.25	−	7090.44i	0.749692	−	0.661787i
$487$	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	0.489436	−	0.872039i	$-0.337203\pi$
$491$	−4162.67	−	4162.67i	−0.382604	−	0.382604i	−0.872039	+	0.489436i	$0.837203\pi$
$492$	104.061	+	18891.2i	0.00953541	+	1.73106i
$493$	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
$498$	62.8114	−	14074.7i	0.00565190	−	1.26647i
$499$	−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
$501$	−156.860	+	10866.8i	−0.0139880	+	0.969049i
$502$	−14200.7	+	141.600i	−1.26256	+	0.0125895i
$503$			10216.7i			0.905647i	0.891600	+	0.452823i	$0.149583\pi$
$503$			10216.7i			0.905647i	−0.891600	+	0.452823i	$0.850417\pi$
$504$	6425.16	+	6411.73i	0.567856	+	0.566669i
$505$			10350.2i			0.912035i
$506$	−51.6307	−	5177.88i	−0.00453609	−	0.454911i
$507$	−403.354	+	27943.3i	−0.0353325	+	2.44774i
$508$	−253.403	+	5.05406i	−0.0221318	+	0.000441413i
$509$	−12175.7	−	12175.7i	−1.06027	−	1.06027i	−0.998063	−	0.0622119i	$-0.980185\pi$
$509$	−12175.7	−	12175.7i	−1.06027	−	1.06027i	−0.0622119	−	0.998063i	$-0.519815\pi$
$510$	−5458.15	−	24.3582i	−0.473903	−	0.00211490i
$511$			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
$516$	9995.88	+	9886.36i	0.852798	+	0.843455i
$517$	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	$-0.490173\pi$
$521$	734.120			0.0617320			0.0308660	+	0.999524i	$0.490173\pi$
$522$	−3559.75	−	67.2746i	−0.298479	−	0.00564086i
$523$	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
$525$	74.8615	−	5186.20i	0.00622328	−	0.431132i
$526$	−4271.55	−	4187.21i	−0.354085	−	0.347093i
$527$	8467.19			0.699880
$528$	−10245.2	−	9736.55i	−0.844442	−	0.802517i
$529$	10311.5			0.847497
$530$	−5120.29	−	5019.19i	−0.419644	−	0.411358i
$531$	−6820.27	−	7225.86i	−0.557391	−	0.590538i
$532$	868.352	−	903.695i	0.0707666	−	0.0736469i
$533$	27969.0	−	27969.0i	2.27293	−	2.27293i
$534$	−2734.37	+	2710.07i	−0.221588	+	0.219619i
$535$	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
$540$	5891.95	+	6173.85i	0.469536	+	0.492000i
$541$	−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
$546$	84.8138	−	19005.0i	0.00664779	−	1.48963i
$547$	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
$549$	−10798.1	+	10192.0i	−0.839441	+	0.792323i
$550$	80.5272	+	8075.83i	0.00624308	+	0.626099i
$551$			491.585i			0.0380076i
$552$	−3525.37	+	3636.24i	−0.271829	+	0.280378i
$553$		−	10295.2i		−	0.791677i
$554$	15528.4	−	154.840i	1.19086	−	0.0118746i
$555$	9919.01	+	143.178i	0.758628	+	0.0109506i
$556$	11356.2	+	10912.1i	0.866208	+	0.832331i
$557$	6502.22	+	6502.22i	0.494628	+	0.494628i	0.909761	−	0.415133i	$-0.136265\pi$
$557$	6502.22	+	6502.22i	0.494628	+	0.494628i	−0.415133	+	0.909761i	$0.636265\pi$
$558$	−9182.71	−	9536.47i	−0.696658	−	0.723497i
$559$		−	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	−0.899635	−	0.436643i	$-0.856167\pi$
$563$	−6184.95	+	6184.95i	−0.462992	+	0.462992i	0.436643	+	0.899635i	$0.356167\pi$
$564$	−6.96637	−	1264.67i	−0.000520101	−	0.0944190i
$565$	−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	$-0.874505\pi$
$569$	−25063.0			−1.84657			−0.923284	+	0.384119i	$0.874505\pi$
$570$	836.904	−	829.467i	0.0614983	−	0.0609518i
$571$	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
$573$	979.183	+	14.1343i	0.0713891	+	0.00103048i
$574$	−13368.9	+	13638.2i	−0.972139	+	0.991722i
$575$	2893.99			0.209892
$576$	427.907	+	13817.4i	0.0309539	+	0.999521i
$577$	−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
$579$	439.465	+	6.34357i	0.0315432	+	0.000455319i
$580$	−56.5516	−	2835.41i	−0.00404858	−	0.202990i
$581$	10061.2	−	10061.2i	0.718429	−	0.718429i
$582$	−6699.01	+	6639.49i	−0.477119	+	0.472879i
$583$	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	0.586753	−	0.809766i	$-0.300406\pi$
$587$	−3171.66	−	3171.66i	−0.223013	−	0.223013i	−0.809766	+	0.586753i	$0.800406\pi$
$588$	−27.9935	−	5081.93i	−0.00196332	−	0.356421i
$589$	−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	$-0.969499\pi$
$593$		−	2763.19i		−	0.191350i	0.995413	−	0.0956752i	$-0.0305010\pi$
$594$	−16855.7	−	562.012i	−1.16431	−	0.0388209i
$595$	−3901.70	−	3901.70i	−0.268830	−	0.268830i
$596$	970.051	+	932.113i	0.0666692	+	0.0640618i
$597$	8521.23	+	123.002i	0.584172	+	0.00843238i
$598$	10603.6	−	105.732i	0.725105	−	0.00723031i
$599$		−	27598.5i		−	1.88255i	−0.337647	−	0.941273i	$-0.609631\pi$
$599$		−	27598.5i		−	1.88255i	0.337647	−	0.941273i	$-0.390369\pi$
$600$	5498.45	−	5671.36i	0.374122	−	0.385887i
$601$		−	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
$603$	8754.28	+	9274.88i	0.591214	+	0.626372i
$604$	−46.1275	−	2312.76i	−0.00310745	−	0.155803i
$605$	2555.62	+	2555.62i	0.171737	+	0.171737i
$606$	−89.2784	+	20005.4i	−0.00598463	+	1.34103i
$607$		−	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
$612$	−10549.6	−	94.1614i	−0.696800	−	0.00621936i
$613$	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	$-0.435225\pi$
$617$	6194.64			0.404193			0.202096	+	0.979366i	$0.435225\pi$
$618$	15435.0	−	15297.9i	1.00467	−	0.995746i
$619$	−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
$621$	−261.602	+	6037.67i	−0.0169046	+	0.390150i
$622$	−7027.11	−	6888.35i	−0.452993	−	0.444048i
$623$	−3891.91			−0.250282
$624$	19939.1	−	20980.8i	1.27917	−	1.34600i
$625$	2713.31			0.173652
$626$	−6682.15	−	6550.21i	−0.426633	−	0.418209i
$627$	−33.6088	+	2328.33i	−0.00214068	+	0.148301i
$628$	5578.74	+	5360.56i	0.354484	+	0.340620i
$629$	−8671.44	+	8671.44i	−0.549687	+	0.549687i
$630$	−163.017	+	8625.84i	−0.0103091	+	0.545495i
$631$	−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
$636$	−9853.47	−	9745.51i	−0.614333	−	0.607602i
$637$	−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	$-0.862976\pi$
$641$		−	13544.6i		−	0.834600i	0.908769	−	0.417300i	$-0.137024\pi$
$642$	30860.3	+	137.721i	1.89713	+	0.00846636i
$643$	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
$645$	−192.866	+	13361.2i	−0.0117738	+	0.815654i
$646$	14.5241	+	1456.57i	0.000884584	+	0.0887122i
$647$		−	8771.04i		−	0.532960i	−0.963840	−	0.266480i	$-0.914139\pi$
$647$		−	8771.04i		−	0.532960i	0.963840	−	0.266480i	$-0.0858607\pi$
$648$	11335.0	+	11984.0i	0.687163	+	0.726504i
$649$			15640.7i			0.945997i
$650$	−16538.2	+	164.909i	−0.997970	+	0.00995116i
$651$	193.167	−	13382.1i	0.0116295	−	0.805661i
$652$	277.665	−	288.967i	0.0166782	−	0.0173571i
$653$	−21658.4	−	21658.4i	−1.29794	−	1.29794i	−0.929748	−	0.368197i	$-0.879975\pi$
$653$	−21658.4	−	21658.4i	−1.29794	−	1.29794i	−0.368197	−	0.929748i	$-0.620025\pi$
$654$	−9.62848	+	2157.54i	−0.000575693	+	0.129001i
$655$			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	−0.377457	−	0.926027i	$-0.623202\pi$
$659$	9280.25	−	9280.25i	0.548569	−	0.548569i	0.926027	+	0.377457i	$0.123202\pi$
$660$	−73.9971	−	13433.4i	−0.00436414	−	0.792266i
$661$	−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
$666$	19170.7	+	362.302i	1.11539	+	0.0210795i
$667$	1420.05	−	1420.05i	0.0824357	−	0.0824357i
$668$	−16729.0	+	333.656i	−0.968958	+	0.0193256i
$669$	−33.7779	+	2340.04i	−0.00195206	+	0.135234i
$670$	−7111.45	+	7254.70i	−0.410058	+	0.418318i
$671$	23373.1			1.34472
$672$	−9525.69	+	10225.6i	−0.546818	+	0.586996i
$673$	−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
$675$	408.015	−	9416.82i	0.0232659	−	0.536968i
$676$	−43017.4	+	857.972i	−2.44751	+	0.0488150i
$677$	−3185.15	+	3185.15i	−0.180820	+	0.180820i	−0.791713	−	0.610893i	$-0.790811\pi$
$677$	−3185.15	+	3185.15i	−0.180820	+	0.180820i	0.610893	+	0.791713i	$0.290811\pi$
$678$	−564.251	−	569.309i	−0.0319615	−	0.0322481i
$679$	−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	0.718880	−	0.695134i	$-0.244655\pi$
$683$	423.850	+	423.850i	0.0237455	+	0.0237455i	−0.695134	+	0.718880i	$0.744655\pi$
$684$	1624.77	−	1596.02i	0.0908252	−	0.0892182i
$685$	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
$690$	−4813.68	−	21.4821i	−0.265585	−	0.00118523i
$691$	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
$693$	−11702.7	−	12398.7i	−0.641485	−	0.679633i
$694$	24751.2	−	246.804i	1.35381	−	0.0134994i
$695$			14969.0i			0.816989i
$696$	−84.8483	−	5480.92i	−0.00462093	−	0.298496i
$697$		−	22196.9i		−	1.20627i
$698$	−50.8139	−	5095.96i	−0.00275549	−	0.276340i
$699$	−18082.7	−	261.020i	−0.978473	−	0.0141240i
$700$	7983.92	−	159.237i	0.431091	−	0.00859801i
$701$	15985.1	+	15985.1i	0.861267	+	0.861267i	0.991485	−	0.130218i	$-0.0415677\pi$
$701$	15985.1	+	15985.1i	0.861267	+	0.861267i	−0.130218	+	0.991485i	$0.541568\pi$
$702$	1150.92	−	34518.2i	0.0618786	−	1.85585i
$703$		−	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
$708$	10757.5	−	10876.7i	0.571032	−	0.577358i
$709$	−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
$714$	−7507.75	−	7575.06i	−0.393516	−	0.397044i
$715$	−19888.6	+	19888.6i	−1.04027	+	1.04027i
$716$	−10214.8	−	9815.30i	−0.533163	−	0.512312i
$717$	16604.8	+	239.686i	0.864876	+	0.0124843i
$718$	968.173	+	949.056i	0.0503230	+	0.0493293i
$719$	−5996.91			−0.311053			−0.155526	−	0.987832i	$-0.549707\pi$
$719$	−5996.91			−0.311053			−0.155526	+	0.987832i	$0.549707\pi$
$720$	−9187.87	+	9392.58i	−0.475572	+	0.486168i
$721$	21969.1			1.13477
$722$	13629.5	+	13360.4i	0.702547	+	0.688674i
$723$	1326.72	+	19.1509i	0.0682454	+	0.000985105i
$724$	13581.0	−	14133.7i	0.697145	−	0.725520i
$725$	−2214.82	+	2214.82i	−0.113457	+	0.113457i
$726$	4917.60	+	4961.68i	0.251390	+	0.253644i
$727$	−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
$732$	−16253.8	−	16075.7i	−0.820706	−	0.811714i
$733$	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
$738$	−25000.1	+	24072.7i	−1.24697	+	1.20071i
$739$	−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
$741$	−4768.10	−	68.8263i	−0.236384	−	0.00341214i
$742$	−139.694	−	14009.5i	−0.00691151	−	0.693134i
$743$			34196.9i			1.68851i	0.535941	+	0.844255i	$0.319957\pi$
$743$			34196.9i			1.68851i	−0.535941	+	0.844255i	$0.680043\pi$
$744$	14187.8	−	14634.0i	0.699126	−	0.721112i
$745$			1278.65i			0.0628809i
$746$	32275.5	−	321.832i	1.58404	−	0.0157950i
$747$	18803.9	−	17748.4i	0.921014	−	0.869317i
$748$	11974.6	+	11506.3i	0.585341	+	0.562449i
$749$	22060.2	+	22060.2i	1.07618	+	1.07618i
$750$	21476.5	+	95.8436i	1.04562	+	0.00466628i
$751$			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
$756$	−389.492	+	16671.1i	−0.0187377	+	0.802012i
$757$	−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	$-0.200091\pi$
$761$	33960.5			1.61770			0.808848	+	0.588018i	$0.200091\pi$
$762$	−327.773	−	330.712i	−0.0155826	−	0.0157223i
$763$	−1542.29	+	1542.29i	−0.0731780	+	0.0731780i
$764$	30.0649	+	1507.41i	0.00142370	+	0.0713823i
$765$	−6882.80	−	7292.11i	−0.325292	−	0.344636i
$766$	24289.2	−	24778.5i	1.14570	−	1.16878i
$767$	−32030.0			−1.50787
$768$	−21238.0	+	1389.56i	−0.997866	+	0.0652883i
$769$	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
$771$	−544.241	+	37703.5i	−0.0254220	+	1.76117i
$772$	13.4934	+	676.536i	0.000629063	+	0.0315403i
$773$	2736.24	−	2736.24i	0.127316	−	0.127316i	−0.640577	−	0.767894i	$-0.721305\pi$
$773$	2736.24	−	2736.24i	0.127316	−	0.127316i	0.767894	+	0.640577i	$0.221305\pi$
$774$	−488.031	+	25823.6i	−0.0226640	+	1.19924i
$775$	−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
$780$	27509.8	−	151.536i	1.26283	−	0.00695623i
$781$	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
$786$	−156.499	+	35068.0i	−0.00710193	+	1.59139i
$787$	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
$789$	158.604	−	10987.6i	0.00715647	−	0.495780i
$790$	14901.7	−	148.591i	0.671114	−	0.00669194i
$791$		−	810.314i		−	0.0364241i
$792$	−27.1519	−	25965.5i	−0.00121818	−	1.16495i
$793$			47864.8i			2.14342i
$794$	−10.3311	−	1036.07i	−0.000461758	−	0.0463083i
$795$	190.118	−	13170.9i	0.00848150	−	0.587575i
$796$	261.637	+	13118.1i	0.0116501	+	0.584117i
$797$	−10333.6	−	10333.6i	−0.459265	−	0.459265i	0.439149	−	0.898414i	$-0.355280\pi$
$797$	−10333.6	−	10333.6i	−0.459265	−	0.459265i	−0.898414	+	0.439149i	$0.855280\pi$
$798$	2302.39	+	10.2749i	0.102135	+	0.000455800i
$799$			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
$804$	−13807.9	+	13960.9i	−0.605683	+	0.612392i
$805$	−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	$-0.409292\pi$
$809$	12937.6			0.562252			0.281126	+	0.959671i	$0.409292\pi$
$810$	−748.568	+	15660.3i	−0.0324716	+	0.679318i
$811$	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
$813$	69.3697	−	4805.74i	0.00299250	−	0.207312i
$814$	−21553.8	−	21128.2i	−0.928082	−	0.909756i
$815$	380.896			0.0163708
$816$	−413.342	−	16237.5i	−0.0177327	−	0.696602i
$817$	3566.11			0.152708
$818$	−8358.76	−	8193.71i	−0.357283	−	0.350228i
$819$	25390.7	−	23965.5i	1.08330	−	1.02250i
$820$	−19933.5	−	19153.9i	−0.848911	−	0.815711i
$821$	−23606.7	+	23606.7i	−1.00351	+	1.00351i	−0.00351227	+	0.999994i	$0.501118\pi$
$821$	−23606.7	+	23606.7i	−1.00351	+	1.00351i	−0.999994	+	0.00351227i	$0.998882\pi$
$822$	4734.39	−	4692.33i	0.200889	−	0.199104i
$823$	−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	$-0.932748\pi$
$827$	−28241.2	−	28241.2i	−1.18747	−	1.18747i	−0.209711	−	0.977763i	$-0.567252\pi$
$828$	−9303.95	−	83.0434i	−0.390501	−	0.00348546i
$829$	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
$834$	−129.119	+	28932.9i	−0.00536095	+	1.20128i
$835$	−11245.4	−	11245.4i	−0.466064	−	0.466064i
$836$	−3584.36	+	71.4892i	−0.148287	+	0.00295754i
$837$	1052.81	−	24298.5i	0.0434773	−	1.00344i
$838$	−104.648	−	10494.9i	−0.00431387	−	0.432624i
$839$			15874.8i			0.653229i	0.945158	+	0.326615i	$0.105908\pi$
$839$			15874.8i			0.653229i	−0.945158	+	0.326615i	$0.894092\pi$
$840$	−13281.1	+	205.601i	−0.545527	+	0.00844513i
$841$		−	22215.4i		−	0.910878i
$842$	830.152	−	8.27778i	0.0339774	−	0.000338802i
$843$	−913.099	−	13.1804i	−0.0373058	−	0.000538500i
$844$	−3424.96	+	3564.36i	−0.139682	+	0.145368i
$845$	−28916.7	−	28916.7i	−1.17724	−	1.17724i
$846$	1673.63	−	1611.55i	0.0680150	−	0.0654919i
$847$			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
$852$	−21717.2	+	119.628i	−0.873262	+	0.00481031i
$853$	−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	$-0.746796\pi$
$857$	−35121.3			−1.39991			−0.699954	+	0.714188i	$0.746796\pi$
$858$	−38613.3	+	38270.2i	−1.53641	+	1.52275i
$859$	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
$861$	−35081.4	−	506.391i	−1.38858	−	0.0200439i
$862$	−23309.4	+	23779.0i	−0.921024	+	0.939577i
$863$	4109.05			0.162079			0.0810393	−	0.996711i	$-0.474176\pi$
$863$	4109.05			0.162079			0.0810393	+	0.996711i	$0.474176\pi$
$864$	−17839.8	+	18075.2i	−0.702457	+	0.711726i
$865$	27592.9			1.08461
$866$	8451.79	−	8622.04i	0.331644	−	0.338324i
$867$	−13131.4	−	189.549i	−0.514378	−	0.00742492i
$868$	20601.1	−	410.884i	0.805584	−	0.0160672i
$869$	−20824.4	+	20824.4i	−0.812910	+	0.812910i
$870$	3700.44	−	3667.56i	0.144203	−	0.142922i
$871$	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
$876$	−28672.0	+	157.938i	−1.10586	+	0.00609158i
$877$	−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	$-0.835671\pi$
$881$		−	25816.2i		−	0.987254i	0.869674	−	0.493627i	$-0.164329\pi$
$882$	6725.28	−	6475.80i	0.256748	−	0.247224i
$883$	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
$885$	14538.5	+	209.860i	0.552211	+	0.00797103i
$886$	−14791.0	+	147.487i	−0.560851	+	0.00559247i
$887$		−	32216.9i		−	1.21955i	−0.792575	−	0.609774i	$-0.791260\pi$
$887$		−	32216.9i		−	1.21955i	0.792575	−	0.609774i	$-0.208740\pi$
$888$	456.944	+	29517.0i	0.0172680	+	1.11546i
$889$		−	470.711i		−	0.0177583i
$890$	−56.1719	−	5633.31i	−0.00211560	−	0.212167i
$891$	−20607.7	−	23136.0i	−0.774841	−	0.869906i
$892$	−3602.39	+	71.8489i	−0.135221	+	0.00269695i
$893$	−226.834	−	226.834i	−0.00850023	−	0.00850023i
$894$	−11.0294	+	2471.45i	−0.000412615	+	0.0924582i
$895$		−	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
$900$	14511.2	+	129.521i	0.537451	+	0.00479708i
$901$	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
$906$	3018.34	−	2991.52i	0.110682	−	0.109698i
$907$	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
$909$	−26727.3	+	25227.1i	−0.975235	+	0.920495i
$910$	19860.3	+	19468.2i	0.723476	+	0.709190i
$911$	−13826.3			−0.502838			−0.251419	−	0.967878i	$-0.580897\pi$
$911$	−13826.3			−0.502838			−0.251419	+	0.967878i	$0.580897\pi$
$912$	2541.75	+	2415.56i	0.0922871	+	0.0877052i
$913$	−40701.8			−1.47539
$914$	3454.64	+	3386.43i	0.125021	+	0.122553i
$915$	313.609	−	21726.0i	0.0113307	−	0.784959i
$916$	8953.57	−	9317.99i	0.322963	−	0.336108i
$917$	−25068.0	+	25068.0i	−0.902747	+	0.902747i
$918$	−13240.5	−	14153.9i	−0.476038	−	0.508877i
$919$	−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
$924$	18458.5	−	18662.9i	0.657185	−	0.664465i
$925$	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	$-0.888591\pi$
$929$		−	19418.8i		−	0.685801i	0.939372	−	0.342901i	$-0.111409\pi$
$930$	19372.6	+	86.4543i	0.683066	+	0.00304833i
$931$	−911.504	−	911.504i	−0.0320874	−	0.0320874i
$932$	−555.214	−	27837.6i	−0.0195136	−	0.978380i
$933$	260.919	−	18075.7i	0.00915552	−	0.634269i
$934$	−212.797	−	21340.7i	−0.00745495	−	0.747633i
$935$			15784.1i			0.552081i
$936$	53173.7	−	55.6033i	1.85688	−	0.00194172i
$937$			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
$939$	248.110	−	17188.4i	0.00862276	−	0.597361i
$940$	1334.45	+	1282.26i	0.0463031	+	0.0444922i
$941$	32438.8	+	32438.8i	1.12378	+	1.12378i	0.991169	+	0.132608i	$0.0423351\pi$
$941$	32438.8	+	32438.8i	1.12378	+	1.12378i	0.132608	+	0.991169i	$0.457665\pi$
$942$	−63.4297	+	14213.2i	−0.00219390	+	0.491606i
$943$		−	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	−0.406823	−	0.913507i	$-0.633363\pi$
$947$	14766.0	−	14766.0i	0.506685	−	0.506685i	0.913507	+	0.406823i	$0.133363\pi$
$948$	28804.1	−	158.666i	0.986829	−	0.00543588i
$949$	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	$-0.343750\pi$
$953$	27736.7			0.942791			0.471395	+	0.881922i	$0.343750\pi$
$954$	481.079	−	25455.7i	0.0163265	−	0.863897i
$955$	−1013.30	+	1013.30i	−0.0343345	+	0.0343345i
$956$	509.834	+	25562.3i	0.0172481	+	0.864794i
$957$	−148.604	+	10294.9i	−0.00501954	+	0.347740i
$958$	−6329.23	+	6456.73i	−0.213453	+	0.217753i
$959$	6738.59			0.226904
$960$	−14938.5	−	13640.3i	−0.502225	−	0.458582i
$961$	−261.548			−0.00877942
$962$	43267.5	−	44139.1i	1.45011	−	1.47932i
$963$	38915.3	+	41229.5i	1.30221	+	1.37965i
$964$	40.7358	+	2042.43i	0.00136101	+	0.0682389i
$965$	−454.775	+	454.775i	−0.0151707	+	0.0151707i
$966$	−6621.29	−	6680.65i	−0.220535	−	0.222512i
$967$	−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	$0.142011\pi$
$971$	40351.2	+	40351.2i	1.33361	+	1.33361i	0.431488	+	0.902119i	$0.357989\pi$
$972$	−1581.95	+	30262.6i	−0.0522029	+	0.998636i
$973$	−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	$-0.789704\pi$
$977$		−	37478.8i		−	1.22728i	0.789586	−	0.613640i	$-0.210296\pi$
$978$	736.216	+	3.28552i	0.0240712	+	0.000107423i
$979$	7872.25	+	7872.25i	0.256995	+	0.256995i
$980$	5362.32	+	5152.60i	0.174789	+	0.167953i
$981$	−2882.48	+	2720.69i	−0.0938130	+	0.0885472i
$982$	16649.8	−	166.022i	0.541057	−	0.00539509i
$983$			11135.5i			0.361310i	0.983547	+	0.180655i	$0.0578217\pi$
$983$			11135.5i			0.361310i	−0.983547	+	0.180655i	$0.942178\pi$
$984$	−38363.2	−	37193.6i	−1.24286	−	1.20497i
$985$		−	8395.49i		−	0.271576i
$986$	64.2194	+	6440.36i	0.00207420	+	0.208015i
$987$	2348.53	+	33.9004i	0.0757391	+	0.00109328i
$988$	−146.400	−	7340.27i	−0.00471417	−	0.236361i
$989$	−10301.5	−	10301.5i	−0.331212	−	0.331212i
$990$	17777.4	−	17117.9i	0.570711	−	0.549539i
$991$		−	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
$996$	28304.3	+	27994.2i	0.900458	+	0.890592i
$997$	−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.11.6	✓	44
3.2	odd	2	inner	48.4.k.a.11.17	yes	44
4.3	odd	2		192.4.k.a.143.22		44
8.3	odd	2		384.4.k.a.287.1		44
8.5	even	2		384.4.k.b.287.22		44
12.11	even	2		192.4.k.a.143.11		44
16.3	odd	4	inner	48.4.k.a.35.17	yes	44
16.5	even	4		384.4.k.a.95.12		44
16.11	odd	4		384.4.k.b.95.11		44
16.13	even	4		192.4.k.a.47.11		44
24.5	odd	2		384.4.k.b.287.11		44
24.11	even	2		384.4.k.a.287.12		44
48.5	odd	4		384.4.k.a.95.1		44
48.11	even	4		384.4.k.b.95.22		44
48.29	odd	4		192.4.k.a.47.22		44
48.35	even	4	inner	48.4.k.a.35.6	yes	44

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

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

\(f(q)\)	\(=\)	\(q+(-1.97996 + 2.01984i) q^{2} +(-5.19561 - 0.0749974i) q^{3} +(-0.159526 - 7.99841i) q^{4} +(5.37662 - 5.37662i) q^{5} +(10.4386 - 10.3458i) q^{6} +14.8575 q^{7} +(16.4714 + 15.5143i) q^{8} +(26.9888 + 0.779314i) q^{9} +O(q^{10})\)	\(q+(-1.97996 + 2.01984i) q^{2} +(-5.19561 - 0.0749974i) q^{3} +(-0.159526 - 7.99841i) q^{4} +(5.37662 - 5.37662i) q^{5} +(10.4386 - 10.3458i) 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} +(0.228978 + 41.5686i) 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} +(-55.0107 + 52.9700i) q^{18} +(7.45581 + 7.45581i) q^{19} +(-43.8621 - 42.1467i) q^{20} +(-77.1939 - 1.11427i) q^{21} +(120.205 - 1.19861i) q^{22} -43.0756i q^{23} +(-84.4154 - 81.8416i) q^{24} +67.1840i q^{25} +(2.45458 + 246.162i) q^{26} +(-140.165 - 6.07310i) q^{27} +(-2.37017 - 118.837i) q^{28} +(32.9665 + 32.9665i) q^{29} +(0.498707 - 111.750i) 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} +(1.92785 - 215.991i) 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} +(155.091 - 153.713i) q^{42} +(239.150 - 239.150i) q^{43} +(-235.579 + 245.167i) q^{44} +(149.298 - 140.918i) q^{45} +(87.0058 + 85.2878i) q^{46} -30.4238 q^{47} +(332.446 - 8.46275i) q^{48} -122.254 q^{49} +(-135.701 - 133.022i) q^{50} +(-3.66306 + 253.767i) q^{51} +(-502.069 - 482.433i) q^{52} +(-235.743 + 235.743i) q^{53} +(289.787 - 271.086i) 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} +(224.729 + 222.267i) 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} +(-624.626 - 2.78753i) q^{66} +(334.013 + 334.013i) q^{67} +(-390.663 + 7.79168i) q^{68} +(-3.23055 + 223.804i) q^{69} +(3.18603 + 319.517i) q^{70} +522.443i q^{71} +(432.452 + 431.548i) q^{72} +689.751i q^{73} +(710.119 - 7.08088i) q^{74} +(5.03862 - 349.062i) q^{75} +(58.4453 - 60.8241i) q^{76} +(-446.508 - 446.508i) q^{77} +(5.70847 - 1279.15i) 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} +(3.40204 + 617.606i) 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} +(-10.9720 + 580.571i) q^{90} +(914.386 - 914.386i) q^{91} +(-344.536 + 6.87169i) q^{92} +(13.0013 - 900.694i) q^{93} +(60.2378 - 61.4512i) q^{94} +80.1741 q^{95} +(-641.136 + 688.245i) q^{96} -641.755 q^{97} +(242.058 - 246.934i) q^{98} +(-787.663 - 834.504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7}+O(q^{10}) \) 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7	\( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33} + 520 q^{34} - 604 q^{36} - 4 q^{37} + 596 q^{39} + 632 q^{40} + 696 q^{42} - 436 q^{43} - 252 q^{45} + 664 q^{46} + 1200 q^{48} + 972 q^{49} - 648 q^{51} + 320 q^{52} + 1592 q^{54} + 280 q^{55} - 424 q^{58} + 800 q^{60} - 916 q^{61} - 2056 q^{64} - 668 q^{66} - 1636 q^{67} + 52 q^{69} - 5192 q^{70} - 3704 q^{72} + 1454 q^{75} - 568 q^{76} - 4932 q^{78} - 4 q^{81} + 768 q^{82} - 2096 q^{84} + 736 q^{85} + 1284 q^{87} + 8864 q^{88} + 2672 q^{90} + 424 q^{91} - 2084 q^{93} + 5616 q^{94} + 8008 q^{96} - 8 q^{97} + 1196 q^{99}+O(q^{100}) \) 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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