LMFDB - Embedded newform 48.4.k.a.11.16

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			11.16
Character	$\chi$	$=$	48.11
Dual form			48.4.k.a.35.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70353 + 2.25788i) q^{2} +(3.47813 + 3.86039i) q^{3} +(-2.19600 + 7.69270i) q^{4} +(13.5794 - 13.5794i) q^{5} +(-2.79119 + 14.4295i) q^{6} -19.7355 q^{7} +(-21.1101 + 8.14640i) q^{8} +(-2.80518 + 26.8539i) q^{9} +O(q^{10})$	\(q+(1.70353 + 2.25788i) q^{2} +(3.47813 + 3.86039i) q^{3} +(-2.19600 + 7.69270i) q^{4} +(13.5794 - 13.5794i) q^{5} +(-2.79119 + 14.4295i) q^{6} -19.7355 q^{7} +(-21.1101 + 8.14640i) q^{8} +(-2.80518 + 26.8539i) q^{9} +(53.7934 + 7.52774i) q^{10} +(-20.5372 - 20.5372i) q^{11} +(-37.3348 + 18.2788i) q^{12} +(36.7137 - 36.7137i) q^{13} +(-33.6199 - 44.5603i) q^{14} +(99.6526 + 5.19077i) q^{15} +(-54.3551 - 33.7864i) q^{16} +4.20201i q^{17} +(-65.4114 + 39.4125i) q^{18} +(38.6629 + 38.6629i) q^{19} +(74.6417 + 134.283i) q^{20} +(-68.6426 - 76.1866i) q^{21} +(11.3848 - 81.3563i) q^{22} -69.4323i q^{23} +(-104.872 - 53.1589i) q^{24} -243.800i q^{25} +(145.437 + 20.3522i) q^{26} +(-113.423 + 82.5723i) q^{27} +(43.3392 - 151.819i) q^{28} +(23.0218 + 23.0218i) q^{29} +(158.041 + 233.846i) q^{30} +219.983i q^{31} +(-16.3099 - 180.283i) q^{32} +(7.85044 - 150.713i) q^{33} +(-9.48762 + 7.15823i) q^{34} +(-267.996 + 267.996i) q^{35} +(-200.419 - 80.5506i) q^{36} +(68.0025 + 68.0025i) q^{37} +(-21.4328 + 153.159i) q^{38} +(269.424 + 14.0339i) q^{39} +(-176.039 + 397.285i) q^{40} -325.789 q^{41} +(55.0854 - 284.772i) q^{42} +(-36.9411 + 36.9411i) q^{43} +(203.087 - 112.887i) q^{44} +(326.567 + 402.752i) q^{45} +(156.769 - 118.280i) q^{46} +192.724 q^{47} +(-58.6259 - 327.345i) q^{48} +46.4894 q^{49} +(550.469 - 415.319i) q^{50} +(-16.2214 + 14.6152i) q^{51} +(201.804 + 363.050i) q^{52} +(-461.968 + 461.968i) q^{53} +(-379.657 - 115.431i) q^{54} -557.767 q^{55} +(416.618 - 160.773i) q^{56} +(-14.7791 + 283.729i) q^{57} +(-12.7621 + 91.1985i) q^{58} +(0.977987 + 0.977987i) q^{59} +(-258.769 + 755.198i) q^{60} +(216.498 - 216.498i) q^{61} +(-496.695 + 374.747i) q^{62} +(55.3615 - 529.974i) q^{63} +(379.272 - 343.942i) q^{64} -997.098i q^{65} +(353.665 - 239.018i) q^{66} +(-27.8307 - 27.8307i) q^{67} +(-32.3248 - 9.22763i) q^{68} +(268.036 - 241.495i) q^{69} +(-1061.64 - 148.564i) q^{70} -786.600i q^{71} +(-159.545 - 589.740i) q^{72} +510.757i q^{73} +(-37.6972 + 269.385i) q^{74} +(941.161 - 847.968i) q^{75} +(-382.326 + 212.518i) q^{76} +(405.313 + 405.313i) q^{77} +(427.284 + 632.233i) q^{78} -230.706i q^{79} +(-1196.91 + 279.311i) q^{80} +(-713.262 - 150.660i) q^{81} +(-554.990 - 735.592i) q^{82} +(-593.835 + 593.835i) q^{83} +(736.820 - 360.741i) q^{84} +(57.0607 + 57.0607i) q^{85} +(-146.339 - 20.4783i) q^{86} +(-8.80017 + 168.946i) q^{87} +(600.848 + 266.239i) q^{88} +1015.01 q^{89} +(-353.049 + 1423.45i) q^{90} +(-724.562 + 724.562i) q^{91} +(534.122 + 152.474i) q^{92} +(-849.221 + 765.131i) q^{93} +(328.309 + 435.146i) q^{94} +1050.04 q^{95} +(639.234 - 690.011i) q^{96} +805.334 q^{97} +(79.1958 + 104.967i) q^{98} +(609.115 - 493.894i) 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 $

$2$	1.70353	+	2.25788i	0.602287	+	0.798280i
$2$	1.70353	+	2.25788i	0.602287	+	0.798280i
$3$	3.47813	+	3.86039i	0.669367	+	0.742932i
$3$	3.47813	+	3.86039i	0.669367	+	0.742932i
$4$	−2.19600	+	7.69270i	−0.274501	+	0.961587i
$5$	13.5794	−	13.5794i	1.21458	−	1.21458i	0.245073	−	0.969505i	$-0.421188\pi$
$5$	13.5794	−	13.5794i	1.21458	−	1.21458i	0.969505	−	0.245073i	$-0.0788119\pi$
$6$	−2.79119	+	14.4295i	−0.189916	+	0.981800i
$7$	−19.7355			−1.06562			−0.532808	−	0.846236i	$-0.678863\pi$
$7$	−19.7355			−1.06562			−0.532808	+	0.846236i	$0.678863\pi$
$8$	−21.1101	+	8.14640i	−0.932943	+	0.360023i
$9$	−2.80518	+	26.8539i	−0.103895	+	0.994588i
$10$	53.7934	+	7.52774i	1.70110	+	0.238048i
$11$	−20.5372	−	20.5372i	−0.562928	−	0.562928i	0.367210	−	0.930138i	$-0.380313\pi$
$11$	−20.5372	−	20.5372i	−0.562928	−	0.562928i	−0.930138	+	0.367210i	$0.880313\pi$
$12$	−37.3348	+	18.2788i	−0.898135	+	0.439719i
$13$	36.7137	−	36.7137i	0.783272	−	0.783272i	−0.197110	−	0.980381i	$-0.563155\pi$
$13$	36.7137	−	36.7137i	0.783272	−	0.783272i	0.980381	+	0.197110i	$0.0631555\pi$
$14$	−33.6199	−	44.5603i	−0.641807	−	0.850660i
$15$	99.6526	+	5.19077i	1.71535	+	0.0893501i
$16$	−54.3551	−	33.7864i	−0.849299	−	0.527912i
$17$			4.20201i			0.0599493i	0.999551	+	0.0299746i	$0.00954265\pi$
$17$			4.20201i			0.0599493i	−0.999551	+	0.0299746i	$0.990457\pi$
$18$	−65.4114	+	39.4125i	−0.856534	+	0.516090i
$19$	38.6629	+	38.6629i	0.466836	+	0.466836i	0.900888	−	0.434052i	$-0.142917\pi$
$19$	38.6629	+	38.6629i	0.466836	+	0.466836i	−0.434052	+	0.900888i	$0.642917\pi$
$20$	74.6417	+	134.283i	0.834520	+	1.50132i
$21$	−68.6426	−	76.1866i	−0.713288	−	0.791680i
$22$	11.3848	−	81.3563i	0.110330	−	0.788419i
$23$		−	69.4323i		−	0.629462i	−0.949181	−	0.314731i	$-0.898086\pi$
$23$		−	69.4323i		−	0.629462i	0.949181	−	0.314731i	$-0.101914\pi$
$24$	−104.872	−	53.1589i	−0.891954	−	0.452126i
$25$		−	243.800i		−	1.95040i
$26$	145.437	+	20.3522i	1.09702	+	0.153515i
$27$	−113.423	+	82.5723i	−0.808455	+	0.588557i
$28$	43.3392	−	151.819i	0.292512	−	1.02468i
$29$	23.0218	+	23.0218i	0.147415	+	0.147415i	0.776962	−	0.629547i	$-0.216760\pi$
$29$	23.0218	+	23.0218i	0.147415	+	0.147415i	−0.629547	+	0.776962i	$0.716760\pi$
$30$	158.041	+	233.846i	0.961805	+	1.42314i
$31$			219.983i			1.27452i	0.770648	+	0.637261i	$0.219933\pi$
$31$			219.983i			1.27452i	−0.770648	+	0.637261i	$0.780067\pi$
$32$	−16.3099	−	180.283i	−0.0901003	−	0.995933i
$33$	7.85044	−	150.713i	0.0414117	−	0.795023i
$34$	−9.48762	+	7.15823i	−0.0478563	+	0.0361067i
$35$	−267.996	+	267.996i	−1.29427	+	1.29427i
$36$	−200.419	−	80.5506i	−0.927864	−	0.372919i
$37$	68.0025	+	68.0025i	0.302150	+	0.302150i	0.841854	−	0.539705i	$-0.181464\pi$
$37$	68.0025	+	68.0025i	0.302150	+	0.302150i	−0.539705	+	0.841854i	$0.681464\pi$
$38$	−21.4328	+	153.159i	−0.0914964	+	0.653835i
$39$	269.424	+	14.0339i	1.10621	+	0.0576212i
$40$	−176.039	+	397.285i	−0.695856	+	1.57041i
$41$	−325.789			−1.24097			−0.620485	−	0.784219i	$-0.713064\pi$
$41$	−325.789			−1.24097			−0.620485	+	0.784219i	$0.713064\pi$
$42$	55.0854	−	284.772i	0.202378	−	1.04622i
$43$	−36.9411	+	36.9411i	−0.131011	+	0.131011i	−0.769572	−	0.638561i	$-0.779530\pi$
$43$	−36.9411	+	36.9411i	−0.131011	+	0.131011i	0.638561	+	0.769572i	$0.279530\pi$
$44$	203.087	−	112.887i	0.695829	−	0.386781i
$45$	326.567	+	402.752i	1.08182	+	1.33419i
$46$	156.769	−	118.280i	0.502487	−	0.379117i
$47$	192.724			0.598120			0.299060	−	0.954234i	$-0.403327\pi$
$47$	192.724			0.598120			0.299060	+	0.954234i	$0.403327\pi$
$48$	−58.6259	−	327.345i	−0.176290	−	0.984338i
$49$	46.4894			0.135538
$50$	550.469	−	415.319i	1.55696	−	1.17470i
$51$	−16.2214	+	14.6152i	−0.0445382	+	0.0401281i
$52$	201.804	+	363.050i	0.538176	+	0.968193i
$53$	−461.968	+	461.968i	−1.19729	+	1.19729i	−0.222312	+	0.974976i	$0.571360\pi$
$53$	−461.968	+	461.968i	−1.19729	+	1.19729i	−0.974976	+	0.222312i	$0.928640\pi$
$54$	−379.657	−	115.431i	−0.956756	−	0.290893i
$55$	−557.767			−1.36744
$56$	416.618	−	160.773i	0.994159	−	0.383647i
$57$	−14.7791	+	283.729i	−0.0343427	+	0.659312i
$58$	−12.7621	+	91.1985i	−0.0288923	+	0.206465i
$59$	0.977987	+	0.977987i	0.00215802	+	0.00215802i	0.708185	−	0.706027i	$-0.249514\pi$
$59$	0.977987	+	0.977987i	0.00215802	+	0.00215802i	−0.706027	+	0.708185i	$0.749514\pi$
$60$	−258.769	+	755.198i	−0.556781	+	1.62493i
$61$	216.498	−	216.498i	0.454421	−	0.454421i	−0.442398	−	0.896819i	$-0.645872\pi$
$61$	216.498	−	216.498i	0.454421	−	0.454421i	0.896819	+	0.442398i	$0.145872\pi$
$62$	−496.695	+	374.747i	−1.01742	+	0.767628i
$63$	55.3615	−	529.974i	0.110713	−	1.05985i
$64$	379.272	−	343.942i	0.740766	−	0.671763i
$65$		−	997.098i		−	1.90269i
$66$	353.665	−	239.018i	0.659593	−	0.445774i
$67$	−27.8307	−	27.8307i	−0.0507472	−	0.0507472i	0.681278	−	0.732025i	$-0.261425\pi$
$67$	−27.8307	−	27.8307i	−0.0507472	−	0.0507472i	−0.732025	+	0.681278i	$0.761425\pi$
$68$	−32.3248	−	9.22763i	−0.0576464	−	0.0164561i
$69$	268.036	−	241.495i	0.467648	−	0.421341i
$70$	−1061.64	−	148.564i	−1.81272	−	0.253668i
$71$		−	786.600i		−	1.31482i	−0.753533	−	0.657411i	$-0.771652\pi$
$71$		−	786.600i		−	1.31482i	0.753533	−	0.657411i	$-0.228348\pi$
$72$	−159.545	−	589.740i	−0.261146	−	0.965299i
$73$			510.757i			0.818898i	0.912333	+	0.409449i	$0.134279\pi$
$73$			510.757i			0.818898i	−0.912333	+	0.409449i	$0.865721\pi$
$74$	−37.6972	+	269.385i	−0.0592191	+	0.423181i
$75$	941.161	−	847.968i	1.44901	−	1.30553i
$76$	−382.326	+	212.518i	−0.577050	+	0.320757i
$77$	405.313	+	405.313i	0.599866	+	0.599866i
$78$	427.284	+	632.233i	0.620261	+	0.917773i
$79$		−	230.706i		−	0.328562i	−0.986414	−	0.164281i	$-0.947470\pi$
$79$		−	230.706i		−	0.328562i	0.986414	−	0.164281i	$-0.0525304\pi$
$80$	−1196.91	+	279.311i	−1.67273	+	0.390349i
$81$	−713.262	−	150.660i	−0.978411	−	0.206666i
$82$	−554.990	−	735.592i	−0.747420	−	0.990641i
$83$	−593.835	+	593.835i	−0.785323	+	0.785323i	−0.980724	−	0.195400i	$-0.937399\pi$
$83$	−593.835	+	593.835i	−0.785323	+	0.785323i	0.195400	+	0.980724i	$0.437399\pi$
$84$	736.820	−	360.741i	0.957067	−	0.468572i
$85$	57.0607	+	57.0607i	0.0728130	+	0.0728130i
$86$	−146.339	−	20.4783i	−0.183490	−	0.0256772i
$87$	−8.80017	+	168.946i	−0.0108446	+	0.208194i
$88$	600.848	+	266.239i	0.727848	+	0.322513i
$89$	1015.01			1.20889			0.604443	−	0.796648i	$-0.293396\pi$
$89$	1015.01			1.20889			0.604443	+	0.796648i	$0.293396\pi$
$90$	−353.049	+	1423.45i	−0.413496	+	1.66716i
$91$	−724.562	+	724.562i	−0.834667	+	0.834667i
$92$	534.122	+	152.474i	0.605283	+	0.172788i
$93$	−849.221	+	765.131i	−0.946883	+	0.853123i
$94$	328.309	+	435.146i	0.360240	+	0.477467i
$95$	1050.04			1.13402
$96$	639.234	−	690.011i	0.679600	−	0.733583i
$97$	805.334			0.842982			0.421491	−	0.906833i	$-0.361507\pi$
$97$	805.334			0.842982			0.421491	+	0.906833i	$0.361507\pi$
$98$	79.1958	+	104.967i	0.0816325	+	0.108197i
$99$	609.115	−	493.894i	0.618368	−	0.501396i
$100$	1875.48	+	535.385i	1.87548	+	0.535385i
$101$	611.231	−	611.231i	0.602176	−	0.602176i	−0.338714	−	0.940889i	$-0.609992\pi$
$101$	611.231	−	611.231i	0.602176	−	0.602176i	0.940889	+	0.338714i	$0.109992\pi$
$102$	−60.6327	−	11.7286i	−0.0588582	−	0.0113853i
$103$	1268.38			1.21337			0.606685	−	0.794942i	$-0.292499\pi$
$103$	1268.38			1.21337			0.606685	+	0.794942i	$0.292499\pi$
$104$	−475.945	+	1074.11i	−0.448752	+	1.01274i
$105$	−1966.69	−	102.442i	−1.82790	−	0.0952129i
$106$	−1830.04	−	256.092i	−1.67688	−	0.234659i
$107$	−153.071	−	153.071i	−0.138298	−	0.138298i	0.634568	−	0.772867i	$-0.281178\pi$
$107$	−153.071	−	153.071i	−0.138298	−	0.138298i	−0.772867	+	0.634568i	$0.781178\pi$
$108$	−386.126	−	1053.86i	−0.344028	−	0.938960i
$109$	−119.589	+	119.589i	−0.105088	+	0.105088i	−0.757696	−	0.652608i	$-0.773675\pi$
$109$	−119.589	+	119.589i	−0.105088	+	0.105088i	0.652608	+	0.757696i	$0.273675\pi$
$110$	−950.169	−	1259.37i	−0.823592	−	1.09160i
$111$	−25.9942	+	499.038i	−0.0222276	+	0.426726i
$112$	1072.72	+	666.791i	0.905027	+	0.562552i
$113$			2097.44i			1.74611i	0.487622	+	0.873055i	$0.337865\pi$
$113$			2097.44i			1.74611i	−0.487622	+	0.873055i	$0.662135\pi$
$114$	−665.801	+	449.970i	−0.547000	+	0.369680i
$115$	−942.848	−	942.848i	−0.764531	−	0.764531i
$116$	−227.656	+	126.544i	−0.182218	+	0.101287i
$117$	882.916	+	1088.89i	0.697655	+	0.860411i
$118$	−0.542147	+	3.87420i	−0.000422955	+	0.00302245i
$119$		−	82.9287i		−	0.0638829i
$120$	−2145.96	+	702.232i	−1.63249	+	0.534206i
$121$		−	487.443i		−	0.366223i
$122$	857.633	+	120.015i	0.636447	+	0.0890631i
$123$	−1133.14	−	1257.67i	−0.830664	−	0.921956i
$124$	−1692.26	−	483.084i	−1.22556	−	0.349857i
$125$	−1613.23	−	1613.23i	−1.15433	−	1.15433i
$126$	1290.93	−	777.825i	0.912737	−	0.549954i
$127$		−	781.522i		−	0.546054i	−0.962006	−	0.273027i	$-0.911975\pi$
$127$		−	781.522i		−	0.546054i	0.962006	−	0.273027i	$-0.0880249\pi$
$128$	1422.68	+	270.435i	0.982408	+	0.186745i
$129$	−271.093	−	14.1209i	−0.185027	−	0.00963779i
$130$	2251.32	−	1698.58i	1.51888	−	1.14597i
$131$	−150.465	+	150.465i	−0.100353	+	0.100353i	−0.755501	−	0.655148i	$-0.772606\pi$
$131$	−150.465	+	150.465i	−0.100353	+	0.100353i	0.655148	+	0.755501i	$0.272606\pi$
$132$	1142.15	+	391.357i	0.753116	+	0.258055i
$133$	−763.032	−	763.032i	−0.497468	−	0.497468i
$134$	15.4280	−	110.249i	0.00994606	−	0.0710748i
$135$	−418.936	+	2661.50i	−0.267083	+	1.69678i
$136$	−34.2312	−	88.7049i	−0.0215831	−	0.0559293i
$137$	1912.58			1.19272			0.596361	−	0.802716i	$-0.296613\pi$
$137$	1912.58			1.19272			0.596361	+	0.802716i	$0.296613\pi$
$138$	1001.87	+	193.798i	0.618006	+	0.119545i
$139$	112.824	−	112.824i	0.0688461	−	0.0688461i	−0.671845	−	0.740691i	$-0.734498\pi$
$139$	112.824	−	112.824i	0.0688461	−	0.0688461i	0.740691	+	0.671845i	$0.234498\pi$
$140$	−1473.09	−	2650.13i	−0.889278	−	1.59984i
$141$	670.318	+	743.988i	0.400362	+	0.444362i
$142$	1776.05	−	1339.99i	1.04959	−	0.791900i
$143$	−1507.99			−0.881852
$144$	1059.77	−	1364.87i	0.613294	−	0.789855i
$145$	625.244			0.358094
$146$	−1153.23	+	870.087i	−0.653710	+	0.493212i
$147$	161.696	+	179.467i	0.0907244	+	0.100695i
$148$	−672.456	+	373.789i	−0.373484	+	0.207603i
$149$	−597.206	+	597.206i	−0.328356	+	0.328356i	−0.851961	−	0.523605i	$-0.824587\pi$
$149$	−597.206	+	597.206i	−0.328356	+	0.328356i	0.523605	+	0.851961i	$0.324587\pi$
$150$	3517.90	+	680.490i	1.91490	+	0.370412i
$151$	−2256.11			−1.21589			−0.607946	−	0.793978i	$-0.708006\pi$
$151$	−2256.11			−1.21589			−0.607946	+	0.793978i	$0.708006\pi$
$152$	−1131.14	−	501.215i	−0.603604	−	0.267460i
$153$	−112.840	−	11.7874i	−0.0596248	−	0.00622845i
$154$	−224.685	+	1605.61i	−0.117569	+	0.840152i
$155$	2987.24	+	2987.24i	1.54801	+	1.54801i
$156$	−699.615	+	2041.78i	−0.359064	+	1.04790i
$157$	2287.02	−	2287.02i	1.16258	−	1.16258i	0.178666	−	0.983910i	$-0.442822\pi$
$157$	2287.02	−	2287.02i	1.16258	−	1.16258i	0.983910	−	0.178666i	$-0.0571782\pi$
$158$	520.904	−	393.013i	0.262284	−	0.197889i
$159$	−3390.16	−	176.589i	−1.69093	−	0.0880782i
$160$	−2669.61	−	2226.66i	−1.31907	−	1.10020i
$161$			1370.28i			0.670765i
$162$	−874.889	−	1867.11i	−0.424307	−	0.905518i
$163$	2602.79	+	2602.79i	1.25071	+	1.25071i	0.955400	+	0.295313i	$0.0954241\pi$
$163$	2602.79	+	2602.79i	1.25071	+	1.25071i	0.295313	+	0.955400i	$0.404576\pi$
$164$	715.435	−	2506.20i	0.340647	−	1.19330i
$165$	−1939.99	−	2153.19i	−0.915320	−	1.01592i
$166$	−2352.42	−	329.193i	−1.09990	−	0.153917i
$167$		−	1654.83i		−	0.766795i	−0.923583	−	0.383397i	$-0.874754\pi$
$167$		−	1654.83i		−	0.766795i	0.923583	−	0.383397i	$-0.125246\pi$
$168$	2069.70	+	1049.12i	0.950481	+	0.481792i
$169$		−	498.785i		−	0.227030i
$170$	−31.6316	+	226.040i	−0.0142708	+	0.101979i
$171$	−1146.71	+	929.794i	−0.512812	+	0.415808i
$172$	−203.054	−	365.300i	−0.0900158	−	0.161941i
$173$	−2534.53	−	2534.53i	−1.11385	−	1.11385i	−0.992625	−	0.121229i	$-0.961317\pi$
$173$	−2534.53	−	2534.53i	−1.11385	−	1.11385i	−0.121229	−	0.992625i	$-0.538683\pi$
$174$	−396.450	+	267.934i	−0.172729	+	0.116736i
$175$			4811.50i			2.07837i
$176$	422.426	+	1810.18i	0.180918	+	0.775271i
$177$	−0.373839	+	7.17697i	−0.000158754	+	0.00304777i
$178$	1729.10	+	2291.77i	0.728097	+	0.965029i
$179$	3012.01	−	3012.01i	1.25770	−	1.25770i	0.305508	−	0.952190i	$-0.401174\pi$
$179$	3012.01	−	3012.01i	1.25770	−	1.25770i	0.952190	−	0.305508i	$-0.0988262\pi$
$180$	−3815.39	+	1627.73i	−1.57990	+	0.674023i
$181$	432.978	+	432.978i	0.177807	+	0.177807i	0.790399	−	0.612592i	$-0.209873\pi$
$181$	432.978	+	432.978i	0.177807	+	0.177807i	−0.612592	+	0.790399i	$0.709873\pi$
$182$	−2870.28	−	401.661i	−1.16901	−	0.163588i
$183$	1588.77	+	82.7570i	0.641778	+	0.0334294i
$184$	565.623	+	1465.72i	0.226621	+	0.587253i
$185$	1846.87			0.733969
$186$	−3174.24	−	614.014i	−1.25133	−	0.242052i
$187$	86.2977	−	86.2977i	0.0337471	−	0.0337471i
$188$	−423.222	+	1482.56i	−0.164184	+	0.575144i
$189$	2238.46	−	1629.60i	0.861503	−	0.627176i
$190$	1788.77	+	2370.86i	0.683004	+	0.905263i
$191$	−888.400			−0.336557			−0.168278	−	0.985740i	$-0.553821\pi$
$191$	−888.400			−0.336557			−0.168278	+	0.985740i	$0.553821\pi$
$192$	2646.91	+	267.861i	0.994919	+	0.100683i
$193$	−2530.09			−0.943627			−0.471813	−	0.881698i	$-0.656400\pi$
$193$	−2530.09			−0.943627			−0.471813	+	0.881698i	$0.656400\pi$
$194$	1371.91	+	1818.34i	0.507717	+	0.672936i
$195$	3849.18	−	3468.04i	1.41357	−	1.27360i
$196$	−102.091	+	357.629i	−0.0372051	+	0.130331i
$197$	−1032.98	+	1032.98i	−0.373587	+	0.373587i	−0.868782	−	0.495195i	$-0.835097\pi$
$197$	−1032.98	+	1032.98i	−0.373587	+	0.373587i	0.495195	+	0.868782i	$0.335097\pi$
$198$	2152.80	+	533.946i	0.772689	+	0.191646i
$199$	641.440			0.228495			0.114247	−	0.993452i	$-0.463554\pi$
$199$	641.440			0.228495			0.114247	+	0.993452i	$0.463554\pi$
$200$	1986.09	+	5146.63i	0.702188	+	1.81961i
$201$	10.6384	−	204.236i	0.00373320	−	0.0716702i
$202$	2421.33	+	338.836i	0.843387	+	0.118022i
$203$	−454.346	−	454.346i	−0.157088	−	0.157088i
$204$	−76.8077	−	156.881i	−0.0263609	−	0.0538425i
$205$	−4424.02	+	4424.02i	−1.50725	+	1.50725i
$206$	2160.72	+	2863.84i	0.730797	+	0.968609i
$207$	1864.53	+	194.770i	0.626056	+	0.0653983i
$208$	−3236.00	+	755.154i	−1.07873	+	0.251733i
$209$		−	1588.06i		−	0.525591i
$210$	−3119.01	−	4615.06i	−1.02491	−	1.51652i
$211$	−2040.63	−	2040.63i	−0.665796	−	0.665796i	0.290944	−	0.956740i	$-0.406031\pi$
$211$	−2040.63	−	2040.63i	−0.665796	−	0.665796i	−0.956740	+	0.290944i	$0.906031\pi$
$212$	−2539.30	−	4568.27i	−0.822640	−	1.47995i
$213$	3036.58	−	2735.90i	0.976822	−	0.880098i
$214$	84.8548	−	606.374i	0.0271054	−	0.193696i
$215$			1003.28i			0.318246i
$216$	1721.71	−	2667.10i	0.542349	−	0.840153i
$217$		−	4341.48i		−	1.35815i
$218$	−473.740	−	66.2942i	−0.147182	−	0.0205964i
$219$	−1971.72	+	1776.48i	−0.608386	+	0.548144i
$220$	1224.86	−	4290.73i	0.375363	−	1.31491i
$221$	154.271	+	154.271i	0.0469566	+	0.0469566i
$222$	−1171.05	+	791.432i	−0.354034	+	0.239268i
$223$		−	4220.28i		−	1.26731i	−0.773614	−	0.633657i	$-0.781553\pi$
$223$		−	4220.28i		−	1.26731i	0.773614	−	0.633657i	$-0.218447\pi$
$224$	321.884	+	3557.97i	0.0960123	+	1.06128i
$225$	6546.97	+	683.901i	1.93984	+	0.202637i
$226$	−4735.76	+	3573.04i	−1.39388	+	1.05166i
$227$	−4171.11	+	4171.11i	−1.21959	+	1.21959i	−0.251810	+	0.967777i	$0.581026\pi$
$227$	−4171.11	+	4171.11i	−1.21959	+	1.21959i	−0.967777	+	0.251810i	$0.918974\pi$
$228$	−2150.18	−	736.760i	−0.624559	−	0.214005i
$229$	2178.48	+	2178.48i	0.628638	+	0.628638i	0.947725	−	0.319087i	$-0.103376\pi$
$229$	2178.48	+	2178.48i	0.628638	+	0.628638i	−0.319087	+	0.947725i	$0.603376\pi$
$230$	522.668	−	3735.00i	0.149842	−	1.07078i
$231$	−154.932	+	2974.39i	−0.0441290	+	0.847190i
$232$	−673.537	−	298.448i	−0.190603	−	0.0844571i
$233$	3707.90			1.04254			0.521272	−	0.853391i	$-0.325458\pi$
$233$	3707.90			1.04254			0.521272	+	0.853391i	$0.325458\pi$
$234$	−954.514	+	3848.47i	−0.266660	+	1.07514i
$235$	2617.07	−	2617.07i	0.726463	−	0.726463i
$236$	−9.67102	+	5.37569i	−0.00266750	+	0.00148274i
$237$	890.613	−	802.425i	0.244099	−	0.219929i
$238$	187.243	−	141.271i	0.0509964	−	0.0384758i
$239$	−1721.72			−0.465979			−0.232990	−	0.972479i	$-0.574851\pi$
$239$	−1721.72			−0.465979			−0.232990	+	0.972479i	$0.574851\pi$
$240$	−5241.25	−	3649.05i	−1.40967	−	0.981437i
$241$	−3133.35			−0.837497			−0.418748	−	0.908102i	$-0.637531\pi$
$241$	−3133.35			−0.837497			−0.418748	+	0.908102i	$0.637531\pi$
$242$	1100.59	−	830.371i	0.292348	−	0.220571i
$243$	−1899.22	−	3277.48i	−0.501377	−	0.865229i
$244$	1190.02	+	2140.88i	0.312226	+	0.561704i
$245$	631.297	−	631.297i	0.164621	−	0.164621i
$246$	909.339	−	4700.96i	0.235680	−	1.21838i
$247$	2838.92			0.731319
$248$	−1792.07	−	4643.87i	−0.458857	−	1.18906i
$249$	−4357.87	−	226.996i	−1.10911	−	0.0577721i
$250$	894.293	−	6390.64i	0.226240	−	1.61672i
$251$	−2709.36	−	2709.36i	−0.681327	−	0.681327i	0.278972	−	0.960299i	$-0.410006\pi$
$251$	−2709.36	−	2709.36i	−0.681327	−	0.681327i	−0.960299	+	0.278972i	$0.910006\pi$
$252$	3955.36	+	1589.71i	0.988746	+	0.397389i
$253$	−1425.95	+	1425.95i	−0.354342	+	0.354342i
$254$	1764.58	−	1331.34i	0.435904	−	0.328882i
$255$	−21.8117	+	418.741i	−0.00535647	+	0.102834i
$256$	1812.96	+	3672.93i	0.442617	+	0.896711i
$257$			4861.83i			1.18005i	0.807385	+	0.590025i	$0.200882\pi$
$257$			4861.83i			1.18005i	−0.807385	+	0.590025i	$0.799118\pi$
$258$	−429.931	−	636.150i	−0.103745	−	0.153508i
$259$	−1342.06	−	1342.06i	−0.321976	−	0.321976i
$260$	7670.37	+	2189.63i	1.82960	+	0.522289i
$261$	−682.805	+	553.644i	−0.161933	+	0.131302i
$262$	−596.053	−	83.4104i	−0.140551	−	0.0196684i
$263$		−	5128.25i		−	1.20236i	−0.799113	−	0.601181i	$-0.794697\pi$
$263$		−	5128.25i		−	1.20236i	0.799113	−	0.601181i	$-0.205303\pi$
$264$	1062.04	+	3245.52i	0.247592	+	0.756621i
$265$			12546.5i			2.90840i
$266$	422.987	−	3022.68i	0.0975000	−	0.696737i
$267$	3530.34	+	3918.33i	0.809189	+	0.898120i
$268$	275.209	−	152.977i	0.0627279	−	0.0348677i
$269$	−2562.79	−	2562.79i	−0.580877	−	0.580877i	0.354267	−	0.935144i	$-0.384730\pi$
$269$	−2562.79	−	2562.79i	−0.580877	−	0.580877i	−0.935144	+	0.354267i	$0.884730\pi$
$270$	−6723.00	+	3588.03i	−1.51537	+	0.808742i
$271$		−	4786.88i		−	1.07300i	−0.843901	−	0.536499i	$-0.819747\pi$
$271$		−	4786.88i		−	1.07300i	0.843901	−	0.536499i	$-0.180253\pi$
$272$	141.971	−	228.401i	0.0316479	−	0.0509148i
$273$	−5317.21	−	276.966i	−1.17880	−	0.0614021i
$274$	3258.13	+	4318.37i	0.718361	+	0.952126i
$275$	−5006.97	+	5006.97i	−1.09793	+	1.09793i
$276$	1269.14	+	2592.24i	0.276787	+	0.565342i
$277$	288.977	+	288.977i	0.0626821	+	0.0626821i	0.737753	−	0.675071i	$-0.235887\pi$
$277$	288.977	+	288.977i	0.0626821	+	0.0626821i	−0.675071	+	0.737753i	$0.735887\pi$
$278$	446.941	+	62.5440i	0.0964236	+	0.0134933i
$279$	−5907.41	−	617.092i	−1.26762	−	0.132417i
$280$	3474.22	−	7840.62i	0.741515	−	1.67345i
$281$	−6854.61			−1.45520			−0.727601	−	0.686001i	$-0.759365\pi$
$281$	−6854.61			−1.45520			−0.727601	+	0.686001i	$0.759365\pi$
$282$	−537.927	+	2780.90i	−0.113593	+	0.587234i
$283$	3730.40	−	3730.40i	0.783566	−	0.783566i	−0.196865	−	0.980431i	$-0.563076\pi$
$283$	3730.40	−	3730.40i	0.783566	−	0.783566i	0.980431	+	0.196865i	$0.0630760\pi$
$284$	6051.08	+	1727.38i	1.26431	+	0.360919i
$285$	3652.17	+	4053.55i	0.759074	+	0.842498i
$286$	−2568.91	−	3404.86i	−0.531128	−	0.703965i
$287$	6429.61			1.32240
$288$	4887.05	+	67.7420i	0.999904	+	0.0138602i
$289$	4895.34			0.996406
$290$	1065.12	+	1411.72i	0.215676	+	0.285859i
$291$	2801.06	+	3108.90i	0.564265	+	0.626278i
$292$	−3929.10	−	1121.62i	−0.787442	−	0.224788i
$293$	−4295.66	+	4295.66i	−0.856502	+	0.856502i	−0.990924	−	0.134422i	$-0.957082\pi$
$293$	−4295.66	+	4295.66i	−0.856502	+	0.856502i	0.134422	+	0.990924i	$0.457082\pi$
$294$	−129.761	+	670.817i	−0.0257408	+	0.133071i
$295$	26.5609			0.00524216
$296$	−1989.52	−	881.564i	−0.390670	−	0.173108i
$297$	4025.21	+	633.591i	0.786418	+	0.123787i
$298$	−2365.77	−	331.062i	−0.459885	−	0.0643553i
$299$	−2549.11	−	2549.11i	−0.493040	−	0.493040i
$300$	4456.36	+	9102.21i	0.857628	+	1.75172i
$301$	729.051	−	729.051i	0.139607	−	0.139607i
$302$	−3843.34	−	5094.02i	−0.732316	−	0.970622i
$303$	4485.53	+	233.645i	0.850452	+	0.0442989i
$304$	−795.248	−	3407.81i	−0.150035	−	0.642932i
$305$		−	5879.81i		−	1.10386i
$306$	−165.612	−	274.859i	−0.0309392	−	0.0513486i
$307$	5854.72	+	5854.72i	1.08843	+	1.08843i	0.995691	+	0.0927348i	$0.0295609\pi$
$307$	5854.72	+	5854.72i	1.08843	+	1.08843i	0.0927348	+	0.995691i	$0.470439\pi$
$308$	−4008.01	+	2227.88i	−0.741486	+	0.412160i
$309$	4411.59	+	4896.44i	0.812190	+	0.901451i
$310$	−1655.98	+	11833.7i	−0.303397	+	2.16808i
$311$			4251.57i			0.775190i	0.921830	+	0.387595i	$0.126694\pi$
$311$			4251.57i			0.775190i	−0.921830	+	0.387595i	$0.873306\pi$
$312$	−5801.89	+	1898.58i	−1.05278	+	0.344505i
$313$		−	468.690i		−	0.0846388i	−0.999104	−	0.0423194i	$-0.986525\pi$
$313$		−	468.690i		−	0.0846388i	0.999104	−	0.0423194i	$-0.0134747\pi$
$314$	9059.82	+	1267.81i	1.62826	+	0.227856i
$315$	−6444.95	−	7948.50i	−1.15280	−	1.42174i
$316$	1774.75	+	506.630i	0.315941	+	0.0901905i
$317$	4956.33	+	4956.33i	0.878155	+	0.878155i	0.993344	−	0.115188i	$-0.0367472\pi$
$317$	4956.33	+	4956.33i	0.878155	+	0.878155i	−0.115188	+	0.993344i	$0.536747\pi$
$318$	−5376.51	−	7955.39i	−0.948113	−	1.40288i
$319$		−	945.608i		−	0.165968i
$320$	479.759	−	9820.82i	0.0838105	−	1.71563i
$321$	58.5118	−	1123.31i	0.0101739	−	0.195318i
$322$	−3093.92	+	2334.31i	−0.535458	+	0.403993i
$323$	−162.462	+	162.462i	−0.0279865	+	0.0279865i
$324$	2725.31	−	5156.06i	0.467302	−	0.884098i
$325$	−8950.78	−	8950.78i	−1.52769	−	1.52769i
$326$	−1442.86	+	10310.7i	−0.245130	+	1.75171i
$327$	−877.607	−	45.7134i	−0.148415	−	0.00773075i
$328$	6877.44	−	2654.01i	1.15775	−	0.446778i
$329$	−3803.49			−0.637366
$330$	1556.83	−	8048.27i	0.259699	−	1.34255i
$331$	−3112.74	+	3112.74i	−0.516894	+	0.516894i	−0.916630	−	0.399736i	$-0.869102\pi$
$331$	−3112.74	+	3112.74i	−0.516894	+	0.516894i	0.399736	+	0.916630i	$0.369102\pi$
$332$	−3264.13	−	5872.25i	−0.539585	−	0.970728i
$333$	−2016.89	+	1635.37i	−0.331907	+	0.269123i
$334$	3736.40	−	2819.05i	0.612117	−	0.461831i
$335$	−755.848			−0.123273
$336$	1157.01	+	6460.32i	0.187857	+	1.04893i
$337$	−6448.09			−1.04228			−0.521142	−	0.853470i	$-0.674494\pi$
$337$	−6448.09			−1.04228			−0.521142	+	0.853470i	$0.674494\pi$
$338$	1126.19	−	849.692i	0.181233	−	0.136737i
$339$	−8096.92	+	7295.17i	−1.29724	+	1.16879i
$340$	−564.257	+	313.645i	−0.0900033	+	0.0500288i
$341$	4517.85	−	4517.85i	0.717464	−	0.717464i
$342$	−4052.80	−	1005.19i	−0.640791	−	0.158932i
$343$	5851.78			0.921185
$344$	478.894	−	1080.77i	0.0750588	−	0.169393i
$345$	360.407	−	6919.11i	0.0562425	−	1.07975i
$346$	1405.02	−	10040.3i	0.218307	−	1.56003i
$347$	9064.25	+	9064.25i	1.40229	+	1.40229i	0.792774	+	0.609516i	$0.208636\pi$
$347$	9064.25	+	9064.25i	1.40229	+	1.40229i	0.609516	+	0.792774i	$0.291364\pi$
$348$	−1280.32	−	438.703i	−0.197220	−	0.0675774i
$349$	4033.73	−	4033.73i	0.618684	−	0.618684i	−0.326510	−	0.945194i	$-0.605873\pi$
$349$	4033.73	−	4033.73i	0.618684	−	0.618684i	0.945194	+	0.326510i	$0.105873\pi$
$350$	−10863.8	+	8196.52i	−1.65912	+	1.25178i
$351$	−1132.65	+	7195.71i	−0.172240	+	1.09424i
$352$	−3367.56	+	4037.48i	−0.509919	+	0.611359i
$353$		−	7626.45i		−	1.14990i	−0.818188	−	0.574950i	$-0.805021\pi$
$353$		−	7626.45i		−	1.14990i	0.818188	−	0.574950i	$-0.194979\pi$
$354$	−16.8416	+	11.3821i	−0.00252858	+	0.00170890i
$355$	−10681.6	−	10681.6i	−1.59695	−	1.59695i
$356$	−2228.97	+	7808.17i	−0.331840	+	1.16245i
$357$	320.137	−	288.437i	0.0474606	−	0.0427611i
$358$	11931.8	+	1669.71i	1.76149	+	0.246499i
$359$		−	5750.40i		−	0.845389i	−0.906272	−	0.422694i	$-0.861084\pi$
$359$		−	5750.40i		−	0.845389i	0.906272	−	0.422694i	$-0.138916\pi$
$360$	−10174.8	−	5841.79i	−1.48961	−	0.855248i
$361$		−	3869.35i		−	0.564128i
$362$	−240.022	+	1715.20i	−0.0348488	+	0.249030i
$363$	1881.72	−	1695.39i	0.272079	−	0.245138i
$364$	−3982.69	−	7164.97i	−0.573488	−	1.03172i
$365$	6935.77	+	6935.77i	0.994616	+	0.994616i
$366$	2519.66	+	3728.23i	0.359849	+	0.532452i
$367$		−	1897.35i		−	0.269866i	−0.990855	−	0.134933i	$-0.956918\pi$
$367$		−	1897.35i		−	0.269866i	0.990855	−	0.134933i	$-0.0430820\pi$
$368$	−2345.87	+	3774.00i	−0.332301	+	0.534602i
$369$	913.897	−	8748.71i	0.128931	−	1.23425i
$370$	3146.18	+	4169.99i	0.442060	+	0.585912i
$371$	9117.17	−	9117.17i	1.27585	−	1.27585i
$372$	−4021.03	−	8213.03i	−0.560432	−	1.14469i
$373$	7007.64	+	7007.64i	0.972766	+	0.972766i	0.999639	−	0.0268725i	$-0.00855481\pi$
$373$	7007.64	+	7007.64i	0.972766	+	0.972766i	−0.0268725	+	0.999639i	$0.508555\pi$
$374$	341.860	+	47.8392i	0.0472651	+	0.00661419i
$375$	616.662	−	11838.7i	0.0849181	−	1.63026i
$376$	−4068.41	+	1570.00i	−0.558012	+	0.215337i
$377$	1690.43			0.230932
$378$	7492.72	+	2278.09i	1.01953	+	0.309980i
$379$	−6022.88	+	6022.88i	−0.816292	+	0.816292i	−0.985569	−	0.169277i	$-0.945857\pi$
$379$	−6022.88	+	6022.88i	−0.816292	+	0.816292i	0.169277	+	0.985569i	$0.445857\pi$
$380$	−2305.89	+	8077.63i	−0.311288	+	1.09046i
$381$	3016.98	−	2718.24i	0.405681	−	0.365511i
$382$	−1513.41	−	2005.90i	−0.202704	−	0.268666i
$383$	5812.46			0.775464			0.387732	−	0.921772i	$-0.373259\pi$
$383$	5812.46			0.775464			0.387732	+	0.921772i	$0.373259\pi$
$384$	3904.28	+	6432.70i	0.518853	+	0.854863i
$385$	11007.8			1.45717
$386$	−4310.07	−	5712.63i	−0.568334	−	0.753278i
$387$	−888.386	−	1095.64i	−0.116690	−	0.143913i
$388$	−1768.52	+	6195.19i	−0.231399	+	0.810601i
$389$	−1335.20	+	1335.20i	−0.174030	+	0.174030i	−0.788747	−	0.614718i	$-0.789270\pi$
$389$	−1335.20	+	1335.20i	−0.174030	+	0.174030i	0.614718	+	0.788747i	$0.289270\pi$
$390$	14387.6	+	2783.09i	1.86806	+	0.361351i
$391$	291.755			0.0377358
$392$	−981.395	+	378.721i	−0.126449	+	0.0487967i
$393$	−1104.19	−	57.5158i	−0.141728	−	0.00738242i
$394$	−4092.04	−	572.632i	−0.523234	−	0.0732202i
$395$	−3132.84	−	3132.84i	−0.399064	−	0.399064i
$396$	2461.76	+	5770.33i	0.312394	+	0.732248i
$397$	−7841.95	+	7841.95i	−0.991375	+	0.991375i	−0.999963	−	0.00858791i	$-0.997266\pi$
$397$	−7841.95	+	7841.95i	−0.991375	+	0.991375i	0.00858791	+	0.999963i	$0.497266\pi$
$398$	1092.71	+	1448.29i	0.137619	+	0.182403i
$399$	291.672	−	5599.53i	0.0365961	−	0.702574i
$400$	−8237.11	+	13251.8i	−1.02964	+	1.65647i
$401$		−	1006.91i		−	0.125393i	−0.998033	−	0.0626965i	$-0.980030\pi$
$401$		−	1006.91i		−	0.125393i	0.998033	−	0.0626965i	$-0.0199700\pi$
$402$	479.262	−	323.901i	0.0594613	−	0.0401859i
$403$	8076.39	+	8076.39i	0.998297	+	0.998297i
$404$	3359.75	+	6044.28i	0.413747	+	0.744342i
$405$	−11731.5	+	7639.79i	−1.43937	+	0.937344i
$406$	251.867	−	1799.85i	0.0307881	−	0.220012i
$407$		−	2793.17i		−	0.340178i
$408$	223.374	−	440.673i	0.0271046	−	0.0534720i
$409$		−	7577.54i		−	0.916100i	−0.888926	−	0.458050i	$-0.848548\pi$
$409$		−	7577.54i		−	0.916100i	0.888926	−	0.458050i	$-0.151452\pi$
$410$	−17525.3	−	2452.46i	−2.11101	−	0.295410i
$411$	6652.22	+	7383.31i	0.798369	+	0.886111i
$412$	−2785.37	+	9757.26i	−0.333071	+	1.16676i
$413$	−19.3010	−	19.3010i	−0.00229962	−	0.00229962i
$414$	2736.50	+	4541.66i	0.324859	+	0.539156i
$415$			16127.8i			1.90767i
$416$	−7217.65	−	6020.05i	−0.850659	−	0.709513i
$417$	827.961	+	43.1274i	0.0972313	+	0.00506465i
$418$	3585.64	−	2705.30i	0.419568	−	0.316557i
$419$	−5402.94	+	5402.94i	−0.629954	+	0.629954i	−0.948056	−	0.318102i	$-0.896955\pi$
$419$	−5402.94	+	5402.94i	−0.629954	+	0.629954i	0.318102	+	0.948056i	$0.396955\pi$
$420$	5106.92	−	14904.2i	0.593315	−	1.73155i
$421$	−1089.62	−	1089.62i	−0.126139	−	0.126139i	0.641219	−	0.767358i	$-0.278429\pi$
$421$	−1089.62	−	1089.62i	−0.126139	−	0.126139i	−0.767358	+	0.641219i	$0.778429\pi$
$422$	1131.22	−	8083.76i	0.130491	−	0.932491i
$423$	−540.624	+	5175.38i	−0.0621419	+	0.594883i
$424$	5988.82	−	13515.6i	0.685950	−	1.54805i
$425$	1024.45			0.116925
$426$	11350.2	+	2195.55i	1.29089	+	0.249706i
$427$	−4272.68	+	4272.68i	−0.484238	+	0.484238i
$428$	1513.67	−	841.382i	0.170949	−	0.0950228i
$429$	−5245.01	−	5821.44i	−0.590283	−	0.655156i
$430$	−2265.27	+	1709.11i	−0.254049	+	0.191675i
$431$	−2457.25			−0.274621			−0.137310	−	0.990528i	$-0.543846\pi$
$431$	−2457.25			−0.274621			−0.137310	+	0.990528i	$0.543846\pi$
$432$	8954.95	−	656.071i	0.997327	−	0.0730677i
$433$	−10663.1			−1.18346			−0.591728	−	0.806138i	$-0.701554\pi$
$433$	−10663.1			−1.18346			−0.591728	+	0.806138i	$0.701554\pi$
$434$	9802.52	−	7395.82i	1.08418	−	0.817997i
$435$	2174.68	+	2413.68i	0.239696	+	0.266040i
$436$	−657.344	−	1182.58i	−0.0722043	−	0.129898i
$437$	2684.46	−	2684.46i	0.293856	−	0.293856i
$438$	−7369.95	−	1425.62i	−0.803995	−	0.155522i
$439$	−12250.0			−1.33180			−0.665900	−	0.746041i	$-0.731952\pi$
$439$	−12250.0			−1.33180			−0.665900	+	0.746041i	$0.731952\pi$
$440$	11774.5	−	4543.79i	1.27574	−	0.492310i
$441$	−130.411	+	1248.42i	−0.0140817	+	0.134804i
$442$	−85.5203	+	611.130i	−0.00920313	+	0.0657658i
$443$	−7482.50	−	7482.50i	−0.802492	−	0.802492i	0.180992	−	0.983485i	$-0.442069\pi$
$443$	−7482.50	−	7482.50i	−0.802492	−	0.802492i	−0.983485	+	0.180992i	$0.942069\pi$
$444$	−3781.86	−	1295.85i	−0.404233	−	0.138510i
$445$	13783.2	−	13783.2i	1.46829	−	1.46829i
$446$	9528.87	−	7189.35i	1.01167	−	0.763287i
$447$	−4382.61	−	228.284i	−0.463737	−	0.0241554i
$448$	−7485.13	+	6787.87i	−0.789373	+	0.715841i
$449$			461.956i			0.0485547i	0.999705	+	0.0242773i	$0.00772848\pi$
$449$			461.956i			0.0485547i	−0.999705	+	0.0242773i	$0.992272\pi$
$450$	9608.76	+	15947.3i	1.00658	+	1.67058i
$451$	6690.82	+	6690.82i	0.698577	+	0.698577i
$452$	−16135.0	−	4605.98i	−1.67904	−	0.479308i
$453$	−7847.05	−	8709.46i	−0.813878	−	0.903325i
$454$	−16523.4	−	2312.25i	−1.70811	−	0.239030i
$455$			19678.2i			2.02754i
$456$	−1999.38	−	6109.94i	−0.205328	−	0.627465i
$457$			4766.75i			0.487919i	0.969785	+	0.243960i	$0.0784464\pi$
$457$			4766.75i			0.487919i	−0.969785	+	0.243960i	$0.921554\pi$
$458$	−1207.64	+	8629.84i	−0.123208	+	0.880449i
$459$	−346.970	−	476.605i	−0.0352836	−	0.0484663i
$460$	9323.54	−	5182.55i	0.945027	−	0.525299i
$461$	6786.71	+	6786.71i	0.685658	+	0.685658i	0.961269	−	0.275611i	$-0.0888801\pi$
$461$	6786.71	+	6786.71i	0.685658	+	0.685658i	−0.275611	+	0.961269i	$0.588880\pi$
$462$	−6979.74	+	4717.14i	−0.702872	+	0.475024i
$463$			4659.31i			0.467681i	0.972275	+	0.233841i	$0.0751294\pi$
$463$			4659.31i			0.467681i	−0.972275	+	0.233841i	$0.924871\pi$
$464$	−473.529	−	2029.18i	−0.0473773	−	0.203022i
$465$	−1141.88	+	21921.9i	−0.113879	+	2.18625i
$466$	6316.51	+	8371.98i	0.627911	+	0.832242i
$467$	−77.7107	+	77.7107i	−0.00770026	+	0.00770026i	−0.710946	−	0.703246i	$-0.751733\pi$
$467$	−77.7107	+	77.7107i	−0.00770026	+	0.00770026i	0.703246	+	0.710946i	$0.251733\pi$
$468$	−10315.4	+	4400.79i	−1.01887	+	0.434672i
$469$	549.252	+	549.252i	0.0540770	+	0.0540770i
$470$	10367.3	+	1450.77i	1.01746	+	0.142381i
$471$	16783.4	+	874.224i	1.64190	+	0.0855246i
$472$	−28.6125	−	12.6783i	−0.00279024	−	0.00123637i
$473$	1517.34			0.147500
$474$	3328.96	+	643.942i	0.322582	+	0.0623992i
$475$	9426.01	−	9426.01i	0.910516	−	0.910516i
$476$	637.945	+	182.112i	0.0614290	+	0.0175359i
$477$	−11109.7	−	13701.5i	−1.06642	−	1.31520i
$478$	−2933.00	−	3887.44i	−0.280653	−	0.371982i
$479$	−4315.85			−0.411683			−0.205842	−	0.978585i	$-0.565993\pi$
$479$	−4315.85			−0.411683			−0.205842	+	0.978585i	$0.565993\pi$
$480$	−689.515	−	18050.3i	−0.0655665	−	1.71642i
$481$	4993.24			0.473331
$482$	−5337.74	−	7074.71i	−0.504413	−	0.668556i
$483$	−5289.81	+	4766.02i	−0.498333	+	0.448988i
$484$	3749.75	+	1070.43i	0.352155	+	0.100528i
$485$	10935.9	−	10935.9i	1.02387	−	1.02387i
$486$	4164.79	−	9871.46i	0.388721	−	0.921355i
$487$	−11571.8			−1.07673			−0.538367	−	0.842711i	$-0.680958\pi$
$487$	−11571.8			−1.07673			−0.538367	+	0.842711i	$0.680958\pi$
$488$	−2806.61	+	6333.96i	−0.260347	+	0.587551i
$489$	−994.927	+	19100.6i	−0.0920085	+	1.76638i
$490$	2500.82	+	349.960i	0.230563	+	0.0322645i
$491$	−3134.09	−	3134.09i	−0.288064	−	0.288064i	0.548250	−	0.836314i	$-0.315294\pi$
$491$	−3134.09	−	3134.09i	−0.288064	−	0.288064i	−0.836314	+	0.548250i	$0.815294\pi$
$492$	12163.3	−	5955.04i	1.11456	−	0.545678i
$493$	−96.7378	+	96.7378i	−0.00883743	+	0.00883743i
$494$	4836.16	+	6409.92i	0.440464	+	0.583797i
$495$	1564.63	−	14978.2i	0.142071	−	1.36004i
$496$	7432.44	−	11957.2i	0.672835	−	1.08245i
$497$			15523.9i			1.40109i
$498$	−6911.21	−	10226.2i	−0.621885	−	0.920176i
$499$	−4382.81	−	4382.81i	−0.393190	−	0.393190i	0.482633	−	0.875823i	$-0.339680\pi$
$499$	−4382.81	−	4382.81i	−0.393190	−	0.393190i	−0.875823	+	0.482633i	$0.839680\pi$
$500$	15952.7	−	8867.41i	1.42685	−	0.793125i
$501$	6388.29	−	5755.73i	0.569676	−	0.513267i
$502$	1501.93	−	10732.8i	0.133535	−	0.954243i
$503$			11741.7i			1.04082i	0.853915	+	0.520412i	$0.174222\pi$
$503$			11741.7i			1.04082i	−0.853915	+	0.520412i	$0.825778\pi$
$504$	3148.69	+	11638.8i	0.278282	+	1.02864i
$505$		−	16600.3i		−	1.46278i
$506$	−5648.75	−	790.475i	−0.496280	−	0.0694484i
$507$	1925.50	−	1734.84i	0.168668	−	0.151966i
$508$	6012.01	+	1716.23i	0.525079	+	0.149892i
$509$	−9177.29	−	9177.29i	−0.799167	−	0.799167i	0.183797	−	0.982964i	$-0.441161\pi$
$509$	−9177.29	−	9177.29i	−0.799167	−	0.799167i	−0.982964	+	0.183797i	$0.941161\pi$
$510$	−982.623	+	664.089i	−0.0853162	+	0.0576595i
$511$		−	10080.0i		−	0.872631i
$512$	−5204.59	+	10350.4i	−0.449243	+	0.893410i
$513$	−7577.76	−	1192.78i	−0.652176	−	0.102656i
$514$	−10977.4	+	8282.26i	−0.942010	+	0.710729i
$515$	17223.8	−	17223.8i	1.47373	−	1.47373i
$516$	703.950	−	2054.43i	0.0600575	−	0.175274i
$517$	−3958.01	−	3958.01i	−0.336699	−	0.336699i
$518$	743.973	−	5316.45i	0.0631048	−	0.450948i
$519$	968.833	−	18599.7i	0.0819404	−	1.57309i
$520$	8122.76	+	21048.8i	0.685012	+	1.77510i
$521$	−21786.3			−1.83200			−0.916001	−	0.401176i	$-0.868602\pi$
$521$	−21786.3			−1.83200			−0.916001	+	0.401176i	$0.868602\pi$
$522$	−2413.23	−	598.541i	−0.202346	−	0.0501866i
$523$	−3381.21	+	3381.21i	−0.282696	+	0.282696i	−0.834183	−	0.551487i	$-0.814061\pi$
$523$	−3381.21	+	3381.21i	−0.282696	+	0.282696i	0.551487	+	0.834183i	$0.314061\pi$
$524$	−827.060	−	1487.90i	−0.0689509	−	0.124045i
$525$	−18574.3	+	16735.1i	−1.54409	+	1.39120i
$526$	11579.0	−	8736.10i	0.959822	−	0.724168i
$527$	−924.372			−0.0764066
$528$	−5518.76	+	7926.79i	−0.454873	+	0.653351i
$529$	7346.16			0.603777
$530$	−28328.4	+	21373.3i	−2.32171	+	1.75169i
$531$	−29.0062	+	23.5193i	−0.00237055	+	0.00192213i
$532$	7545.39	−	4194.15i	0.614914	−	0.341804i
$533$	−11960.9	+	11960.9i	−0.972017	+	0.972017i
$534$	−2833.08	+	14646.1i	−0.229587	+	1.18689i
$535$	−4157.21			−0.335948
$536$	814.228	+	360.789i	0.0656144	+	0.0290741i
$537$	22103.7	+	1151.35i	1.77624	+	0.0925222i
$538$	1420.68	−	10152.2i	0.113847	−	0.813557i
$539$	−954.764	−	954.764i	−0.0762979	−	0.0762979i
$540$	−19554.1	−	9067.41i	−1.55829	−	0.722591i
$541$	−2531.45	+	2531.45i	−0.201175	+	0.201175i	−0.800503	−	0.599328i	$-0.795434\pi$
$541$	−2531.45	+	2531.45i	−0.201175	+	0.201175i	0.599328	+	0.800503i	$0.295434\pi$
$542$	10808.2	−	8154.57i	0.856552	−	0.646253i
$543$	−165.508	+	3177.42i	−0.0130803	+	0.251116i
$544$	757.551	−	68.5343i	0.0597054	−	0.00540144i
$545$			3247.89i			0.255274i
$546$	−8432.65	−	12477.4i	−0.660960	−	0.977993i
$547$	−13220.9	−	13220.9i	−1.03343	−	1.03343i	−0.999422	−	0.0340067i	$-0.989173\pi$
$547$	−13220.9	−	13220.9i	−1.03343	−	1.03343i	−0.0340067	−	0.999422i	$-0.510827\pi$
$548$	−4200.04	+	14712.9i	−0.327403	+	1.14691i
$549$	5206.49	+	6421.11i	0.404749	+	0.499174i
$550$	−19834.6	−	2775.62i	−1.53773	−	0.215187i
$551$			1780.18i			0.137637i
$552$	−3690.94	+	7281.50i	−0.284596	+	0.561452i
$553$			4553.09i			0.350121i
$554$	−160.194	+	1144.75i	−0.0122852	+	0.0877904i
$555$	6423.64	+	7129.62i	0.491295	+	0.545289i
$556$	620.159	+	1115.68i	0.0473032	+	0.0850998i
$557$	−1799.67	−	1799.67i	−0.136902	−	0.136902i	0.635335	−	0.772237i	$-0.280862\pi$
$557$	−1799.67	−	1799.67i	−0.136902	−	0.136902i	−0.772237	+	0.635335i	$0.780862\pi$
$558$	−8670.10	−	14389.4i	−0.657768	−	1.09167i
$559$			2712.49i			0.205234i
$560$	23621.6	−	5512.34i	1.78249	−	0.415962i
$561$	633.298	+	32.9876i	0.0476611	+	0.00248260i
$562$	−11677.0	−	15476.9i	−0.876449	−	1.16166i
$563$	9770.30	−	9770.30i	0.731384	−	0.731384i	−0.239510	−	0.970894i	$-0.576987\pi$
$563$	9770.30	−	9770.30i	0.731384	−	0.731384i	0.970894	+	0.239510i	$0.0769869\pi$
$564$	−7195.29	+	3522.76i	−0.537192	+	0.263005i
$565$	28481.9	+	28481.9i	2.12079	+	2.12079i
$566$	14777.6	+	2067.95i	1.09744	+	0.153573i
$567$	14076.6	+	2973.34i	1.04261	+	0.220227i
$568$	6407.96	+	16605.2i	0.473366	+	1.22665i
$569$	10828.4			0.797804			0.398902	−	0.916994i	$-0.369391\pi$
$569$	10828.4			0.797804			0.398902	+	0.916994i	$0.369391\pi$
$570$	−2930.85	+	15151.5i	−0.215368	+	1.11338i
$571$	7393.50	−	7393.50i	0.541871	−	0.541871i	−0.382206	−	0.924077i	$-0.624836\pi$
$571$	7393.50	−	7393.50i	0.541871	−	0.541871i	0.924077	+	0.382206i	$0.124836\pi$
$572$	3311.56	−	11600.5i	0.242069	−	0.847977i
$573$	−3089.97	−	3429.57i	−0.225280	−	0.250039i
$574$	10953.0	+	14517.3i	0.796463	+	1.05564i
$575$	−16927.6			−1.22770
$576$	8172.26	+	11149.8i	0.591165	+	0.806551i
$577$	9184.00			0.662625			0.331313	−	0.943521i	$-0.392508\pi$
$577$	9184.00			0.662625			0.331313	+	0.943521i	$0.392508\pi$
$578$	8339.34	+	11053.1i	0.600123	+	0.795411i
$579$	−8799.99	−	9767.13i	−0.631633	−	0.701050i
$580$	−1373.04	+	4809.81i	−0.0982970	+	0.344339i
$581$	11719.6	−	11719.6i	0.836853	−	0.836853i
$582$	−2247.84	+	11620.5i	−0.160096	+	0.827640i
$583$	18975.1			1.34797
$584$	−4160.83	−	10782.1i	−0.294823	−	0.763986i
$585$	26776.0	+	2797.04i	1.89239	+	0.197681i
$586$	−17016.8	−	2381.30i	−1.19959	−	0.167868i
$587$	13196.5	+	13196.5i	0.927903	+	0.927903i	0.997570	−	0.0696672i	$-0.0221937\pi$
$587$	13196.5	+	13196.5i	0.927903	+	0.927903i	−0.0696672	+	0.997570i	$0.522194\pi$
$588$	−1735.67	+	849.770i	−0.121731	+	0.0595985i
$589$	−8505.20	+	8505.20i	−0.594993	+	0.594993i
$590$	45.2472	+	59.9713i	0.00315728	+	0.00418471i
$591$	−7580.53	−	394.860i	−0.527617	−	0.0274828i
$592$	−1398.73	−	5993.84i	−0.0971070	−	0.416124i
$593$		−	6984.22i		−	0.483655i	−0.970319	−	0.241828i	$-0.922253\pi$
$593$		−	6984.22i		−	0.483655i	0.970319	−	0.241828i	$-0.0777469\pi$
$594$	5426.47	+	10167.8i	0.374833	+	0.702337i
$595$	−1126.12	−	1126.12i	−0.0775907	−	0.0775907i
$596$	−3282.66	−	5905.59i	−0.225609	−	0.405877i
$597$	2231.01	+	2476.21i	0.152947	+	0.169756i
$598$	1413.10	−	10098.1i	0.0966322	−	0.690536i
$599$			6684.31i			0.455949i	0.973667	+	0.227975i	$0.0732104\pi$
$599$			6684.31i			0.455949i	−0.973667	+	0.227975i	$0.926790\pi$
$600$	−12960.1	+	25567.8i	−0.881825	+	1.73967i
$601$			14533.0i			0.986377i	0.869923	+	0.493188i	$0.164169\pi$
$601$			14533.0i			0.986377i	−0.869923	+	0.493188i	$0.835831\pi$
$602$	2888.06	+	404.150i	0.195529	+	0.0273620i
$603$	825.432	−	669.292i	0.0557449	−	0.0452001i
$604$	4954.43	−	17355.6i	0.333763	−	1.16919i
$605$	−6619.18	−	6619.18i	−0.444806	−	0.444806i
$606$	7113.67	+	10525.8i	0.476853	+	0.705579i
$607$		−	12378.6i		−	0.827733i	−0.910338	−	0.413866i	$-0.864178\pi$
$607$		−	12378.6i		−	0.827733i	0.910338	−	0.413866i	$-0.135822\pi$
$608$	6339.69	−	7600.86i	0.422875	−	0.506999i
$609$	173.676	−	3334.23i	0.0115561	−	0.221855i
$610$	13275.9	−	10016.4i	0.881188	−	0.664840i
$611$	7075.59	−	7075.59i	0.468490	−	0.468490i
$612$	338.475	−	842.161i	0.0223562	−	0.0556247i
$613$	−18856.7	−	18856.7i	−1.24244	−	1.24244i	−0.958986	−	0.283455i	$-0.908519\pi$
$613$	−18856.7	−	18856.7i	−1.24244	−	1.24244i	−0.283455	−	0.958986i	$-0.591481\pi$
$614$	−3245.57	+	23192.9i	−0.213323	+	1.52441i
$615$	−32465.8	−	1691.10i	−2.12869	−	0.110881i
$616$	−11858.0	−	5254.35i	−0.775606	−	0.343675i
$617$	−4117.09			−0.268635			−0.134317	−	0.990938i	$-0.542884\pi$
$617$	−4117.09			−0.268635			−0.134317	+	0.990938i	$0.542884\pi$
$618$	−3540.28	+	18302.0i	−0.230439	+	1.19129i
$619$	−11488.2	+	11488.2i	−0.745958	+	0.745958i	−0.973717	−	0.227759i	$-0.926860\pi$
$619$	−11488.2	+	11488.2i	−0.745958	+	0.745958i	0.227759	+	0.973717i	$0.426860\pi$
$620$	−29539.9	+	16419.9i	−1.91347	+	1.06361i
$621$	5733.19	+	7875.23i	0.370475	+	0.508892i
$622$	−9599.51	+	7242.65i	−0.618818	+	0.466887i
$623$	−20031.7			−1.28821
$624$	−14170.4	−	9865.67i	−0.909088	−	0.632922i
$625$	−13338.3			−0.853652
$626$	1058.24	−	798.425i	0.0675654	−	0.0509768i
$627$	6130.53	−	5523.49i	0.390478	−	0.351813i
$628$	12571.1	+	22615.7i	0.798790	+	1.43705i
$629$	−285.747	+	285.747i	−0.0181137	+	0.0181137i
$630$	6967.59	−	28092.4i	0.440628	−	1.77655i
$631$	12047.6			0.760077			0.380039	−	0.924971i	$-0.375911\pi$
$631$	12047.6			0.760077			0.380039	+	0.924971i	$0.375911\pi$
$632$	1879.42	+	4870.22i	0.118290	+	0.306530i
$633$	780.039	−	14975.2i	0.0489791	−	0.940302i
$634$	−2747.54	+	19634.0i	−0.172112	+	1.22991i
$635$	−10612.6	−	10612.6i	−0.663225	−	0.663225i
$636$	8803.26	−	25691.7i	0.548855	−	1.60180i
$637$	1706.80	−	1706.80i	0.106163	−	0.106163i
$638$	2135.07	−	1610.87i	0.132489	−	0.0999606i
$639$	21123.3	+	2206.55i	1.30771	+	0.136604i
$640$	22991.5	−	15646.8i	1.42003	−	0.966395i
$641$		−	15280.3i		−	0.941550i	−0.882253	−	0.470775i	$-0.843974\pi$
$641$		−	15280.3i		−	0.941550i	0.882253	−	0.470775i	$-0.156026\pi$
$642$	2635.98	−	1781.48i	0.162046	−	0.109516i
$643$	10573.2	+	10573.2i	0.648468	+	0.648468i	0.952623	−	0.304155i	$-0.0983740\pi$
$643$	10573.2	+	10573.2i	0.648468	+	0.648468i	−0.304155	+	0.952623i	$0.598374\pi$
$644$	−10541.1	−	3009.14i	−0.644999	−	0.184125i
$645$	−3873.03	+	3489.53i	−0.236435	+	0.213023i
$646$	−643.578	−	90.0609i	−0.0391969	−	0.00548514i
$647$		−	4804.62i		−	0.291946i	−0.989289	−	0.145973i	$-0.953369\pi$
$647$		−	4804.62i		−	0.291946i	0.989289	−	0.145973i	$-0.0466312\pi$
$648$	16284.4	−	2630.07i	0.987207	−	0.159443i
$649$		−	40.1703i		−	0.00242962i
$650$	4961.87	−	35457.6i	0.299416	−	2.13963i
$651$	16759.8	−	15100.2i	1.00901	−	0.909101i
$652$	−25738.2	+	14306.7i	−1.54599	+	0.859349i
$653$	1034.28	+	1034.28i	0.0619823	+	0.0619823i	0.737418	−	0.675436i	$-0.236045\pi$
$653$	1034.28	+	1034.28i	0.0619823	+	0.0619823i	−0.675436	+	0.737418i	$0.736045\pi$
$654$	−1391.81	−	2059.40i	−0.0832172	−	0.123133i
$655$			4086.45i			0.243772i
$656$	17708.3	+	11007.2i	1.05395	+	0.655123i
$657$	−13715.8	−	1432.76i	−0.814467	−	0.0850798i
$658$	−6479.35	−	8587.82i	−0.383877	−	0.508796i
$659$	−3161.81	+	3161.81i	−0.186899	+	0.186899i	−0.794354	−	0.607455i	$-0.792191\pi$
$659$	−3161.81	+	3161.81i	−0.186899	+	0.186899i	0.607455	+	0.794354i	$0.292191\pi$
$660$	20824.1	−	10195.3i	1.22815	−	0.601290i
$661$	−17535.7	−	17535.7i	−1.03186	−	1.03186i	−0.999475	−	0.0323858i	$-0.989689\pi$
$661$	−17535.7	−	17535.7i	−1.03186	−	1.03186i	−0.0323858	−	0.999475i	$-0.510311\pi$
$662$	−12330.8	−	1725.55i	−0.723944	−	0.101307i
$663$	−58.9707	+	1132.12i	−0.00345435	+	0.0663167i
$664$	7698.30	−	17373.5i	0.449927	−	1.01540i
$665$	−20723.0			−1.20843
$666$	−7128.29	−	1767.99i	−0.414738	−	0.102865i
$667$	1598.46	−	1598.46i	0.0927923	−	0.0927923i
$668$	12730.1	+	3634.02i	0.737340	+	0.210486i
$669$	16291.9	−	14678.7i	0.941528	−	0.848298i
$670$	−1287.61	−	1706.61i	−0.0742456	−	0.0984061i
$671$	−8892.53			−0.511613
$672$	−12615.6	+	13617.7i	−0.724193	+	0.781718i
$673$	10046.4			0.575426			0.287713	−	0.957717i	$-0.407105\pi$
$673$	10046.4			0.575426			0.287713	+	0.957717i	$0.407105\pi$
$674$	−10984.5	−	14559.0i	−0.627755	−	0.832035i
$675$	20131.1	+	27652.5i	1.14792	+	1.57681i
$676$	3837.00	+	1095.33i	0.218309	+	0.0623198i
$677$	−7587.41	+	7587.41i	−0.430735	+	0.430735i	−0.888878	−	0.458143i	$-0.848515\pi$
$677$	−7587.41	+	7587.41i	−0.430735	+	0.430735i	0.458143	+	0.888878i	$0.348515\pi$
$678$	−30264.9	−	5854.34i	−1.71433	−	0.331614i
$679$	−15893.7			−0.898295
$680$	−1669.40	−	739.718i	−0.0941448	−	0.0417160i
$681$	−30609.8	−	1594.42i	−1.72242	−	0.0897186i
$682$	17897.0	+	2504.47i	1.00486	+	0.140618i
$683$	−2298.94	−	2298.94i	−0.128795	−	0.128795i	0.639771	−	0.768566i	$-0.279029\pi$
$683$	−2298.94	−	2298.94i	−0.128795	−	0.128795i	−0.768566	+	0.639771i	$0.779029\pi$
$684$	−4634.45	−	10863.1i	−0.259068	−	0.607253i
$685$	25971.7	−	25971.7i	1.44865	−	1.44865i
$686$	9968.66	+	13212.6i	0.554818	+	0.735363i
$687$	−832.733	+	15986.8i	−0.0462456	+	0.887825i
$688$	3256.05	−	759.833i	0.180430	−	0.0421052i
$689$			33921.1i			1.87560i
$690$	16236.5	−	10973.1i	0.895813	−	0.605420i
$691$	1119.72	+	1119.72i	0.0616442	+	0.0616442i	0.737257	−	0.675613i	$-0.236121\pi$
$691$	1119.72	+	1119.72i	0.0616442	+	0.0616442i	−0.675613	+	0.737257i	$0.736121\pi$
$692$	25063.2	−	13931.5i	1.37682	−	0.765314i
$693$	−12021.2	+	9747.24i	−0.658943	+	0.534296i
$694$	−5024.77	+	35907.1i	−0.274838	+	1.96400i
$695$		−	3064.16i		−	0.167238i
$696$	−1190.53	−	3638.15i	−0.0648374	−	0.198138i
$697$		−	1368.97i		−	0.0743952i
$698$	15979.2	+	2236.10i	0.866508	+	0.121257i
$699$	12896.6	+	14313.9i	0.697845	+	0.774539i
$700$	−37013.4	−	10566.1i	−1.99854	−	0.570515i
$701$	15121.9	+	15121.9i	0.814760	+	0.814760i	0.985343	−	0.170583i	$-0.0545652\pi$
$701$	15121.9	+	15121.9i	0.814760	+	0.814760i	−0.170583	+	0.985343i	$0.554565\pi$
$702$	−18176.5	+	9700.70i	−0.977248	+	0.521552i
$703$			5258.35i			0.282109i
$704$	−14852.8	−	725.580i	−0.795153	−	0.0388442i
$705$	19205.4	+	1000.38i	1.02598	+	0.0534421i
$706$	17219.6	−	12991.8i	0.917942	−	0.692570i
$707$	−12062.9	+	12062.9i	−0.641688	+	0.641688i
$708$	−54.3893	−	18.6365i	−0.00288711	−	0.000989269i
$709$	−2222.19	−	2222.19i	−0.117710	−	0.117710i	0.645798	−	0.763508i	$-0.276525\pi$
$709$	−2222.19	−	2222.19i	−0.117710	−	0.117710i	−0.763508	+	0.645798i	$0.776525\pi$
$710$	5921.32	−	42313.9i	0.312991	−	2.23664i
$711$	6195.34	+	647.170i	0.326784	+	0.0341361i
$712$	−21427.0	+	8268.68i	−1.12782	+	0.435227i
$713$	15273.9			0.802263
$714$	1196.62	+	231.469i	0.0627202	+	0.0121324i
$715$	−20477.6	+	20477.6i	−1.07108	+	1.07108i
$716$	16556.1	+	29784.8i	0.864147	+	1.55462i
$717$	−5988.38	−	6646.52i	−0.311911	−	0.346191i
$718$	12983.7	−	9795.95i	0.674857	−	0.509167i
$719$	27781.8			1.44101			0.720505	−	0.693450i	$-0.243910\pi$
$719$	27781.8			1.44101			0.720505	+	0.693450i	$0.243910\pi$
$720$	−4143.05	−	32925.1i	−0.214448	−	1.70423i
$721$	−25032.1			−1.29299
$722$	8736.52	−	6591.54i	0.450332	−	0.339767i
$723$	−10898.2	−	12095.9i	−0.560593	−	0.622203i
$724$	−4281.59	+	2379.95i	−0.219785	+	0.122169i
$725$	5612.70	−	5612.70i	0.287518	−	0.287518i
$726$	7033.54	+	1360.54i	0.359558	+	0.0695517i
$727$	−16679.8			−0.850921			−0.425460	−	0.904977i	$-0.639888\pi$
$727$	−16679.8			−0.850921			−0.425460	+	0.904977i	$0.639888\pi$
$728$	9393.00	−	21198.1i	0.478198	−	1.07920i
$729$	6046.63	−	18731.2i	0.307200	−	0.951645i
$730$	−3844.85	+	27475.4i	−0.194937	+	1.39303i
$731$	−155.227	−	155.227i	−0.00785401	−	0.00785401i
$732$	−4125.57	+	12040.2i	−0.208314	+	0.607949i
$733$	−17838.8	+	17838.8i	−0.898898	+	0.898898i	−0.995339	−	0.0964409i	$-0.969254\pi$
$733$	−17838.8	+	17838.8i	−0.898898	+	0.898898i	0.0964409	+	0.995339i	$0.469254\pi$
$734$	4283.98	−	3232.19i	0.215429	−	0.162537i
$735$	4632.79	+	241.316i	0.232494	+	0.0121103i
$736$	−12517.5	+	1132.43i	−0.626902	+	0.0567147i
$737$			1143.13i			0.0571340i
$738$	21310.3	−	12840.2i	1.06293	−	0.640452i
$739$	3174.87	+	3174.87i	0.158037	+	0.158037i	0.781696	−	0.623659i	$-0.214355\pi$
$739$	3174.87	+	3174.87i	0.158037	+	0.158037i	−0.623659	+	0.781696i	$0.714355\pi$
$740$	−4055.72	+	14207.4i	−0.201475	+	0.705775i
$741$	9874.13	+	10959.3i	0.489521	+	0.543320i
$742$	36116.8	+	5054.11i	1.78691	+	0.250057i
$743$			20203.2i			0.997555i	0.866730	+	0.498777i	$0.166218\pi$
$743$			20203.2i			0.997555i	−0.866730	+	0.498777i	$0.833782\pi$
$744$	11694.1	−	23070.1i	0.576244	−	1.13682i
$745$			16219.4i			0.797628i
$746$	−3884.69	+	27760.1i	−0.190655	+	1.36242i
$747$	−14281.0	−	17612.6i	−0.699482	−	0.862665i
$748$	474.352	+	853.372i	0.0231872	+	0.0417144i
$749$	3020.92	+	3020.92i	0.147373	+	0.147373i
$750$	27780.8	−	18775.2i	1.35255	−	0.914097i
$751$			7584.16i			0.368508i	0.982879	+	0.184254i	$0.0589870\pi$
$751$			7584.16i			0.368508i	−0.982879	+	0.184254i	$0.941013\pi$
$752$	−10475.5	−	6511.43i	−0.507982	−	0.315755i
$753$	1035.66	−	19882.7i	0.0501216	−	0.962237i
$754$	2879.69	+	3816.78i	0.139088	+	0.184349i
$755$	−30636.6	+	30636.6i	−1.47680	+	1.47680i
$756$	7620.38	+	20798.4i	0.366601	+	1.00057i
$757$	−1287.51	−	1287.51i	−0.0618169	−	0.0618169i	0.675522	−	0.737339i	$-0.263918\pi$
$757$	−1287.51	−	1287.51i	−0.0618169	−	0.0618169i	−0.737339	+	0.675522i	$0.763918\pi$
$758$	−23859.0	−	3338.79i	−1.14327	−	0.159987i
$759$	−10464.4	−	545.074i	−0.500437	−	0.0260671i
$760$	−22166.4	+	8554.03i	−1.05797	+	0.408273i
$761$	−8175.32			−0.389428			−0.194714	−	0.980860i	$-0.562378\pi$
$761$	−8175.32			−0.389428			−0.194714	+	0.980860i	$0.562378\pi$
$762$	11276.9	+	2181.37i	0.536116	+	0.103705i
$763$	2360.15	−	2360.15i	0.111983	−	0.111983i
$764$	1950.93	−	6834.19i	0.0923850	−	0.323629i
$765$	−1692.37	+	1372.24i	−0.0799839	+	0.0648540i
$766$	9901.67	+	13123.8i	0.467052	+	0.619037i
$767$	71.8109			0.00338063
$768$	−7873.20	+	19773.7i	−0.369921	+	0.929063i
$769$	30704.5			1.43984			0.719918	−	0.694060i	$-0.244180\pi$
$769$	30704.5			1.43984			0.719918	+	0.694060i	$0.244180\pi$
$770$	18752.1	+	24854.2i	0.877633	+	1.16323i
$771$	−18768.6	+	16910.1i	−0.876697	+	0.789887i
$772$	5556.09	−	19463.2i	0.259026	−	0.907379i
$773$	−9803.75	+	9803.75i	−0.456166	+	0.456166i	−0.897395	−	0.441229i	$-0.854543\pi$
$773$	−9803.75	+	9803.75i	−0.456166	+	0.456166i	0.441229	+	0.897395i	$0.354543\pi$
$774$	960.428	−	3872.31i	0.0446019	−	0.179829i
$775$	53631.9			2.48582
$776$	−17000.7	+	6560.57i	−0.786455	+	0.303493i
$777$	513.009	−	9848.75i	0.0236861	−	0.454726i
$778$	−5289.28	−	740.171i	−0.243740	−	0.0341085i
$779$	−12596.0	−	12596.0i	−0.579329	−	0.579329i
$780$	18225.8	+	37226.4i	0.836649	+	1.70887i
$781$	−16154.6	+	16154.6i	−0.740150	+	0.740150i
$782$	497.012	+	658.747i	0.0227278	+	0.0301237i
$783$	−4512.17	−	710.242i	−0.205941	−	0.0324163i
$784$	−2526.94	−	1570.71i	−0.115112	−	0.0715519i
$785$		−	62112.8i		−	2.82408i
$786$	−1751.15	−	2591.11i	−0.0794677	−	0.117585i
$787$	6207.55	+	6207.55i	0.281163	+	0.281163i	0.833573	−	0.552410i	$-0.186292\pi$
$787$	6207.55	+	6207.55i	0.281163	+	0.281163i	−0.552410	+	0.833573i	$0.686292\pi$
$788$	−5677.96	−	10214.8i	−0.256687	−	0.461786i
$789$	19797.0	−	17836.7i	0.893274	−	0.804822i
$790$	1736.69	−	12410.4i	0.0782136	−	0.558916i
$791$		−	41394.0i		−	1.86068i
$792$	−8835.03	+	15388.3i	−0.396388	+	0.690401i
$793$		−	15896.8i		−	0.711870i
$794$	−31065.1	−	4347.19i	−1.38849	−	0.194302i
$795$	−48434.3	+	43638.4i	−2.16074	+	1.94678i
$796$	−1408.60	+	4934.40i	−0.0627219	+	0.219718i
$797$	16268.2	+	16268.2i	0.723025	+	0.723025i	0.969220	−	0.246196i	$-0.0791805\pi$
$797$	16268.2	+	16268.2i	0.723025	+	0.723025i	−0.246196	+	0.969220i	$0.579181\pi$
$798$	13139.9	−	8880.37i	0.582892	−	0.393937i
$799$			809.827i			0.0358568i
$800$	−43953.0	+	3976.35i	−1.94246	+	0.175731i
$801$	−2847.28	+	27257.0i	−0.125598	+	1.20234i
$802$	2273.47	−	1715.29i	0.100099	−	0.0755226i
$803$	10489.5	−	10489.5i	0.460981	−	0.460981i
$804$	1547.76	+	530.341i	0.0678923	+	0.0232633i
$805$	18607.6	+	18607.6i	0.814696	+	0.814696i
$806$	−4477.15	+	31993.8i	−0.195659	+	1.39818i
$807$	979.635	−	18807.1i	0.0427321	−	0.820372i
$808$	−7923.81	+	17882.5i	−0.344999	+	0.778593i
$809$	22495.3			0.977616			0.488808	−	0.872391i	$-0.337432\pi$
$809$	22495.3			0.977616			0.488808	+	0.872391i	$0.337432\pi$
$810$	−37234.7	−	13473.8i	−1.61518	−	0.584468i
$811$	24289.2	−	24289.2i	1.05168	−	1.05168i	0.0530865	−	0.998590i	$-0.483094\pi$
$811$	24289.2	−	24289.2i	1.05168	−	1.05168i	0.998590	−	0.0530865i	$-0.0169059\pi$
$812$	4492.89	−	2497.40i	0.194174	−	0.107933i
$813$	18479.2	−	16649.4i	0.797164	−	0.718229i
$814$	6306.63	−	4758.23i	0.271557	−	0.204885i
$815$	70688.6			3.03818
$816$	1375.51	−	246.347i	0.0590103	−	0.0105685i
$817$	−2856.51			−0.122321
$818$	17109.1	−	12908.5i	0.731304	−	0.551755i
$819$	−17424.8	−	21489.8i	−0.743432	−	0.916868i
$820$	−24317.5	−	43747.8i	−1.03561	−	1.86310i
$821$	8033.40	−	8033.40i	0.341495	−	0.341495i	−0.515434	−	0.856929i	$-0.672369\pi$
$821$	8033.40	−	8033.40i	0.341495	−	0.341495i	0.856929	+	0.515434i	$0.172369\pi$
$822$	−5338.37	+	27597.5i	−0.226517	+	1.17102i
$823$	−14074.4			−0.596114			−0.298057	−	0.954548i	$-0.596339\pi$
$823$	−14074.4			−0.596114			−0.298057	+	0.954548i	$0.596339\pi$
$824$	−26775.6	+	10332.7i	−1.13201	+	0.436842i
$825$	−36743.8	−	1913.93i	−1.55061	−	0.0807693i
$826$	10.6995	−	76.4592i	0.000450708	−	0.00322077i
$827$	6382.42	+	6382.42i	0.268366	+	0.268366i	0.828441	−	0.560076i	$-0.189228\pi$
$827$	6382.42	+	6382.42i	0.268366	+	0.268366i	−0.560076	+	0.828441i	$0.689228\pi$
$828$	−5592.81	+	13915.5i	−0.234739	+	0.584055i
$829$	8468.39	−	8468.39i	0.354788	−	0.354788i	−0.507099	−	0.861888i	$-0.669282\pi$
$829$	8468.39	−	8468.39i	0.354788	−	0.354788i	0.861888	+	0.507099i	$0.169282\pi$
$830$	−36414.6	+	27474.2i	−1.52286	+	1.14897i
$831$	−110.462	+	2120.66i	−0.00461119	+	0.0885258i
$832$	1297.09	−	26551.9i	0.0540488	−	1.10639i
$833$			195.349i			0.00812538i
$834$	1313.08	+	1942.90i	0.0545181	+	0.0806681i
$835$	−22471.6	−	22471.6i	−0.931332	−	0.931332i
$836$	12216.5	+	3487.39i	0.505401	+	0.144275i
$837$	−18164.5	−	24951.2i	−0.750129	−	1.03039i
$838$	−21403.2	−	2995.12i	−0.882293	−	0.123466i
$839$			4878.66i			0.200751i	0.994950	+	0.100375i	$0.0320044\pi$
$839$			4878.66i			0.200751i	−0.994950	+	0.100375i	$0.967996\pi$
$840$	42351.6	−	13858.9i	1.73961	−	0.569259i
$841$		−	23329.0i		−	0.956538i
$842$	604.030	−	4316.41i	0.0247224	−	0.176667i
$843$	−23841.2	−	26461.4i	−0.974064	−	1.08112i
$844$	20179.2	−	11216.7i	0.822982	−	0.457459i
$845$	−6773.19	−	6773.19i	−0.275745	−	0.275745i
$846$	−12606.3	+	7595.72i	−0.512310	+	0.308684i
$847$			9619.92i			0.390253i
$848$	40718.6	−	9502.11i	1.64892	−	0.384792i
$849$	27375.6	+	1425.96i	1.10663	+	0.0576429i
$850$	1745.17	+	2313.08i	0.0704223	+	0.0933387i
$851$	4721.57	−	4721.57i	0.190192	−	0.190192i
$852$	14378.1	+	29367.6i	0.578152	+	1.18089i
$853$	−3062.44	−	3062.44i	−0.122926	−	0.122926i	0.642967	−	0.765894i	$-0.277703\pi$
$853$	−3062.44	−	3062.44i	−0.122926	−	0.122926i	−0.765894	+	0.642967i	$0.777703\pi$
$854$	−16925.8	−	2368.56i	−0.678208	−	0.0949070i
$855$	−2945.54	+	28197.6i	−0.117819	+	1.12788i
$856$	4478.31	+	1984.36i	0.178815	+	0.0792338i
$857$	−22998.9			−0.916716			−0.458358	−	0.888768i	$-0.651562\pi$
$857$	−22998.9			−0.916716			−0.458358	+	0.888768i	$0.651562\pi$
$858$	4209.09	−	21759.5i	0.167478	−	0.865803i
$859$	20152.0	−	20152.0i	0.800441	−	0.800441i	−0.182723	−	0.983164i	$-0.558491\pi$
$859$	20152.0	−	20152.0i	0.800441	−	0.800441i	0.983164	+	0.182723i	$0.0584912\pi$
$860$	−7717.90	−	2203.20i	−0.306021	−	0.0873586i
$861$	22363.0	+	24820.8i	0.885169	+	0.982451i
$862$	−4185.99	−	5548.16i	−0.165401	−	0.219224i
$863$	39922.6			1.57472			0.787359	−	0.616495i	$-0.211448\pi$
$863$	39922.6			1.57472			0.787359	+	0.616495i	$0.211448\pi$
$864$	16736.3	+	19101.5i	0.659006	+	0.752138i
$865$	−68834.7			−2.70572
$866$	−18164.9	−	24076.0i	−0.712780	−	0.944728i
$867$	17026.7	+	18897.9i	0.666961	+	0.740262i
$868$	33397.7	+	9533.90i	1.30598	+	0.372813i
$869$	−4738.06	+	4738.06i	−0.184957	+	0.184957i
$870$	−1745.17	+	9021.93i	−0.0680079	+	0.351577i
$871$	−2043.53			−0.0794977
$872$	1550.32	−	3498.76i	0.0602068	−	0.135875i
$873$	−2259.10	+	21626.3i	−0.0875820	+	0.838420i
$874$	10634.2	+	1488.13i	0.411565	+	0.0575935i
$875$	31837.8	+	31837.8i	1.23007	+	1.23007i
$876$	−9336.02	−	19069.0i	−0.360086	−	0.735482i
$877$	−24622.0	+	24622.0i	−0.948035	+	0.948035i	−0.998715	−	0.0506799i	$-0.983861\pi$
$877$	−24622.0	+	24622.0i	−0.948035	+	0.948035i	0.0506799	+	0.998715i	$0.483861\pi$
$878$	−20868.2	−	27659.0i	−0.802126	−	1.06315i
$879$	−31523.8	−	1642.03i	−1.20964	−	0.0630084i
$880$	30317.5	+	18844.9i	1.16137	+	0.721889i
$881$			10455.7i			0.399843i	0.979812	+	0.199921i	$0.0640686\pi$
$881$			10455.7i			0.399843i	−0.979812	+	0.199921i	$0.935931\pi$
$882$	−3040.94	+	1832.26i	−0.116093	+	0.0699496i
$883$	25017.7	+	25017.7i	0.953468	+	0.953468i	0.998964	−	0.0454970i	$-0.0144871\pi$
$883$	25017.7	+	25017.7i	0.953468	+	0.953468i	−0.0454970	+	0.998964i	$0.514487\pi$
$884$	−1525.54	+	847.981i	−0.0580424	+	0.0322632i
$885$	92.3824	+	102.535i	0.00350893	+	0.00389457i
$886$	4147.92	−	29641.2i	0.157282	−	1.12394i
$887$		−	47236.6i		−	1.78811i	−0.447960	−	0.894054i	$-0.647849\pi$
$887$		−	47236.6i		−	1.78811i	0.447960	−	0.894054i	$-0.352151\pi$
$888$	−3516.62	−	10746.5i	−0.132894	−	0.406114i
$889$			15423.7i			0.581884i
$890$	54600.9	+	7640.73i	2.05643	+	0.287773i
$891$	11554.3	+	17742.6i	0.434437	+	0.667114i
$892$	32465.3	+	9267.75i	1.21863	+	0.347878i
$893$	7451.26	+	7451.26i	0.279224	+	0.279224i
$894$	−6950.45	−	10284.3i	−0.260020	−	0.384740i
$895$		−	81802.4i		−	3.05514i
$896$	−28077.3	−	5337.17i	−1.04687	−	0.198998i
$897$	974.408	−	18706.7i	0.0362704	−	0.696320i
$898$	−1043.04	+	786.954i	−0.0387602	+	0.0292439i
$899$	−5064.41	+	5064.41i	−0.187884	+	0.187884i
$900$	−19638.2	+	48862.0i	−0.727341	+	1.80970i
$901$	−1941.20	−	1941.20i	−0.0717765	−	0.0717765i
$902$	−3709.06	+	26505.0i	−0.136916	+	0.978404i
$903$	5350.16	+	278.683i	0.197167	+	0.0102702i
$904$	−17086.6	−	44277.1i	−0.628640	−	1.62902i
$905$	11759.2			0.431920
$906$	6297.22	−	32554.5i	0.230918	−	1.19376i
$907$	31025.7	−	31025.7i	1.13582	−	1.13582i	0.146634	−	0.989191i	$-0.453156\pi$
$907$	31025.7	−	31025.7i	1.13582	−	1.13582i	0.989191	−	0.146634i	$-0.0468440\pi$
$908$	−22927.3	−	41246.8i	−0.837961	−	1.50752i
$909$	14699.3	+	18128.5i	0.536354	+	0.661480i
$910$	−44431.0	+	33522.3i	−1.61854	+	1.22116i
$911$	−37779.4			−1.37397			−0.686985	−	0.726672i	$-0.741066\pi$
$911$	−37779.4			−1.37397			−0.686985	+	0.726672i	$0.741066\pi$
$912$	10389.5	−	14922.8i	0.377226	−	0.541823i
$913$	24391.5			0.884162
$914$	−10762.7	+	8120.27i	−0.389496	+	0.293867i
$915$	22698.3	−	20450.8i	0.820092	−	0.738887i
$916$	−21542.3	+	11974.4i	−0.777051	+	0.431929i
$917$	2969.50	−	2969.50i	0.106937	−	0.106937i
$918$	485.044	−	1595.32i	0.0174388	−	0.0573568i
$919$	−29840.1			−1.07109			−0.535547	−	0.844505i	$-0.679894\pi$
$919$	−29840.1			−1.07109			−0.535547	+	0.844505i	$0.679894\pi$
$920$	27584.4	+	12222.8i	0.988513	+	0.438015i
$921$	−2237.99	+	42965.0i	−0.0800698	+	1.53718i
$922$	−3762.21	+	26884.9i	−0.134384	+	0.960310i
$923$	−28879.0	−	28879.0i	−1.02986	−	1.02986i
$924$	−22540.9	−	7723.63i	−0.802533	−	0.274988i
$925$	16579.0	−	16579.0i	0.589312	−	0.589312i
$926$	−10520.1	+	7937.25i	−0.373340	+	0.281678i
$927$	−3558.03	+	34060.9i	−0.126064	+	1.20680i
$928$	3774.96	−	4525.92i	0.133533	−	0.160098i
$929$		−	5194.44i		−	0.183449i	−0.995784	−	0.0917244i	$-0.970762\pi$
$929$		−	5194.44i		−	0.183449i	0.995784	−	0.0917244i	$-0.0292379\pi$
$930$	−51442.2	+	34766.3i	−1.81382	+	1.22584i
$931$	1797.42	+	1797.42i	0.0632738	+	0.0632738i
$932$	−8142.57	+	28523.8i	−0.286179	+	1.00250i
$933$	−16412.7	+	14787.5i	−0.575913	+	0.518887i
$934$	−307.843	−	43.0789i	−0.0107847	−	0.00150919i
$935$		−	2343.74i		−	0.0819770i
$936$	−27509.0	−	15794.0i	−0.960640	−	0.551543i
$937$			22506.4i			0.784687i	0.919819	+	0.392344i	$0.128336\pi$
$937$			22506.4i			0.784687i	−0.919819	+	0.392344i	$0.871664\pi$
$938$	−304.478	+	2175.81i	−0.0105987	+	0.0757384i
$939$	1809.33	−	1630.17i	0.0628808	−	0.0566544i
$940$	14385.2	+	25879.4i	0.499143	+	0.897971i
$941$	−32342.6	−	32342.6i	−1.12045	−	1.12045i	−0.991674	−	0.128771i	$-0.958897\pi$
$941$	−32342.6	−	32342.6i	−1.12045	−	1.12045i	−0.128771	−	0.991674i	$-0.541103\pi$
$942$	26617.0	+	39384.0i	0.920625	+	1.36221i
$943$			22620.3i			0.781144i
$944$	−20.1160	−	86.2012i	−0.000693558	−	0.00297205i
$945$	8267.90	−	52526.0i	0.284608	−	1.80812i
$946$	2584.82	+	3425.96i	0.0888371	+	0.117746i
$947$	−35064.2	+	35064.2i	−1.20320	+	1.20320i	−0.230018	+	0.973186i	$0.573878\pi$
$947$	−35064.2	+	35064.2i	−1.20320	+	1.20320i	−0.973186	+	0.230018i	$0.926122\pi$
$948$	4217.02	+	8613.34i	0.144475	+	0.295093i
$949$	18751.8	+	18751.8i	0.641420	+	0.641420i
$950$	37340.2	+	5225.31i	1.27524	+	0.178454i
$951$	−1894.58	+	36372.1i	−0.0646013	+	1.24022i
$952$	675.570	+	1750.63i	0.0229993	+	0.0595991i
$953$	54026.3			1.83640			0.918198	−	0.396122i	$-0.129644\pi$
$953$	54026.3			1.83640			0.918198	+	0.396122i	$0.129644\pi$
$954$	12010.7	−	48425.3i	0.407610	−	1.64343i
$955$	−12063.9	+	12063.9i	−0.408774	+	0.408774i
$956$	3780.91	−	13244.7i	0.127911	−	0.448079i
$957$	3650.41	−	3288.95i	0.123303	−	0.111094i
$958$	−7352.16	−	9744.66i	−0.247952	−	0.328638i
$959$	−37745.7			−1.27098
$960$	39580.8	−	32306.1i	1.33069	−	1.08612i
$961$	−18601.7			−0.624405
$962$	8506.11	+	11274.1i	0.285081	+	0.377850i
$963$	4539.93	−	3681.15i	0.151918	−	0.123181i
$964$	6880.85	−	24103.9i	0.229893	−	0.805326i
$965$	−34357.1	+	34357.1i	−1.14611	+	1.14611i
$966$	−19772.4	−	3824.71i	−0.658558	−	0.127389i
$967$	20637.1			0.686291			0.343145	−	0.939282i	$-0.388508\pi$
$967$	20637.1			0.686291			0.343145	+	0.939282i	$0.388508\pi$
$968$	3970.90	+	10290.0i	0.131849	+	0.341665i
$969$	−1192.23	−	62.1018i	−0.0395253	−	0.00205882i
$970$	43321.7	+	6062.35i	1.43399	+	0.200670i
$971$	23101.0	+	23101.0i	0.763487	+	0.763487i	0.976951	−	0.213464i	$-0.0684746\pi$
$971$	23101.0	+	23101.0i	0.763487	+	0.763487i	−0.213464	+	0.976951i	$0.568475\pi$
$972$	29383.4	−	7412.72i	0.969621	−	0.244612i
$973$	−2226.64	+	2226.64i	−0.0733635	+	0.0733635i
$974$	−19712.9	−	26127.7i	−0.648503	−	0.859534i
$975$	3421.47	−	65685.5i	0.112384	−	2.15756i
$976$	−19082.4	+	4453.08i	−0.625833	+	0.146045i
$977$		−	2329.22i		−	0.0762725i	−0.999273	−	0.0381362i	$-0.987858\pi$
$977$		−	2329.22i		−	0.0762725i	0.999273	−	0.0381362i	$-0.0121421\pi$
$978$	−44821.7	+	30292.0i	−1.46548	+	0.990421i
$979$	−20845.5	−	20845.5i	−0.680517	−	0.680517i
$980$	3470.05	+	6242.71i	0.113109	+	0.203486i
$981$	−2875.96	−	3546.90i	−0.0936008	−	0.115437i
$982$	1737.39	−	12415.4i	0.0564585	−	0.403454i
$983$			32246.0i			1.04628i	0.852248	+	0.523138i	$0.175239\pi$
$983$			32246.0i			1.04628i	−0.852248	+	0.523138i	$0.824761\pi$
$984$	34166.2	+	17318.6i	1.10689	+	0.561074i
$985$			28054.4i			0.907501i
$986$	−383.217	−	53.6266i	−0.0123774	−	0.00173207i
$987$	−13229.1	−	14683.0i	−0.426632	−	0.473519i
$988$	−6234.27	+	21838.9i	−0.200748	+	0.703227i
$989$	2564.91	+	2564.91i	0.0824664	+	0.0824664i
$990$	36484.3	−	21983.0i	1.17126	−	0.705722i
$991$			37641.1i			1.20657i	0.797526	+	0.603284i	$0.206142\pi$
$991$			37641.1i			1.20657i	−0.797526	+	0.603284i	$0.793858\pi$
$992$	39659.3	−	3587.90i	1.26934	−	0.114835i
$993$	−22842.9	−	1189.86i	−0.730009	−	0.0380252i
$994$	−35051.1	+	26445.4i	−1.11847	+	0.843861i
$995$	8710.36	−	8710.36i	0.277525	−	0.277525i
$996$	11316.1	−	33025.3i	0.360005	−	1.05065i
$997$	23110.9	+	23110.9i	0.734131	+	0.734131i	0.971435	−	0.237304i	$-0.0762638\pi$
$997$	23110.9	+	23110.9i	0.734131	+	0.734131i	−0.237304	+	0.971435i	$0.576264\pi$
$998$	2429.61	−	17362.1i	0.0770622	−	0.550688i
$999$	−13328.2	−	2097.94i	−0.422107	−	0.0664422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.k.a.11.16	yes	44
3.2	odd	2	inner	48.4.k.a.11.7	✓	44
4.3	odd	2		192.4.k.a.143.7		44
8.3	odd	2		384.4.k.a.287.16		44
8.5	even	2		384.4.k.b.287.7		44
12.11	even	2		192.4.k.a.143.5		44
16.3	odd	4	inner	48.4.k.a.35.7	yes	44
16.5	even	4		384.4.k.a.95.18		44
16.11	odd	4		384.4.k.b.95.5		44
16.13	even	4		192.4.k.a.47.5		44
24.5	odd	2		384.4.k.b.287.5		44
24.11	even	2		384.4.k.a.287.18		44
48.5	odd	4		384.4.k.a.95.16		44
48.11	even	4		384.4.k.b.95.7		44
48.29	odd	4		192.4.k.a.47.7		44
48.35	even	4	inner	48.4.k.a.35.16	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.7	✓	44	3.2	odd	2	inner
48.4.k.a.11.16	yes	44	1.1	even	1	trivial
48.4.k.a.35.7	yes	44	16.3	odd	4	inner
48.4.k.a.35.16	yes	44	48.35	even	4	inner
192.4.k.a.47.5		44	16.13	even	4
192.4.k.a.47.7		44	48.29	odd	4
192.4.k.a.143.5		44	12.11	even	2
192.4.k.a.143.7		44	4.3	odd	2
384.4.k.a.95.16		44	48.5	odd	4
384.4.k.a.95.18		44	16.5	even	4
384.4.k.a.287.16		44	8.3	odd	2
384.4.k.a.287.18		44	24.11	even	2
384.4.k.b.95.5		44	16.11	odd	4
384.4.k.b.95.7		44	48.11	even	4
384.4.k.b.287.5		44	24.5	odd	2
384.4.k.b.287.7		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)

\(f(q)\)	\(=\)	\(q+(1.70353 + 2.25788i) q^{2} +(3.47813 + 3.86039i) q^{3} +(-2.19600 + 7.69270i) q^{4} +(13.5794 - 13.5794i) q^{5} +(-2.79119 + 14.4295i) q^{6} -19.7355 q^{7} +(-21.1101 + 8.14640i) q^{8} +(-2.80518 + 26.8539i) q^{9} +O(q^{10})\)	\(q+(1.70353 + 2.25788i) q^{2} +(3.47813 + 3.86039i) q^{3} +(-2.19600 + 7.69270i) q^{4} +(13.5794 - 13.5794i) q^{5} +(-2.79119 + 14.4295i) q^{6} -19.7355 q^{7} +(-21.1101 + 8.14640i) q^{8} +(-2.80518 + 26.8539i) q^{9} +(53.7934 + 7.52774i) q^{10} +(-20.5372 - 20.5372i) q^{11} +(-37.3348 + 18.2788i) q^{12} +(36.7137 - 36.7137i) q^{13} +(-33.6199 - 44.5603i) q^{14} +(99.6526 + 5.19077i) q^{15} +(-54.3551 - 33.7864i) q^{16} +4.20201i q^{17} +(-65.4114 + 39.4125i) q^{18} +(38.6629 + 38.6629i) q^{19} +(74.6417 + 134.283i) q^{20} +(-68.6426 - 76.1866i) q^{21} +(11.3848 - 81.3563i) q^{22} -69.4323i q^{23} +(-104.872 - 53.1589i) q^{24} -243.800i q^{25} +(145.437 + 20.3522i) q^{26} +(-113.423 + 82.5723i) q^{27} +(43.3392 - 151.819i) q^{28} +(23.0218 + 23.0218i) q^{29} +(158.041 + 233.846i) q^{30} +219.983i q^{31} +(-16.3099 - 180.283i) q^{32} +(7.85044 - 150.713i) q^{33} +(-9.48762 + 7.15823i) q^{34} +(-267.996 + 267.996i) q^{35} +(-200.419 - 80.5506i) q^{36} +(68.0025 + 68.0025i) q^{37} +(-21.4328 + 153.159i) q^{38} +(269.424 + 14.0339i) q^{39} +(-176.039 + 397.285i) q^{40} -325.789 q^{41} +(55.0854 - 284.772i) q^{42} +(-36.9411 + 36.9411i) q^{43} +(203.087 - 112.887i) q^{44} +(326.567 + 402.752i) q^{45} +(156.769 - 118.280i) q^{46} +192.724 q^{47} +(-58.6259 - 327.345i) q^{48} +46.4894 q^{49} +(550.469 - 415.319i) q^{50} +(-16.2214 + 14.6152i) q^{51} +(201.804 + 363.050i) q^{52} +(-461.968 + 461.968i) q^{53} +(-379.657 - 115.431i) q^{54} -557.767 q^{55} +(416.618 - 160.773i) q^{56} +(-14.7791 + 283.729i) q^{57} +(-12.7621 + 91.1985i) q^{58} +(0.977987 + 0.977987i) q^{59} +(-258.769 + 755.198i) q^{60} +(216.498 - 216.498i) q^{61} +(-496.695 + 374.747i) q^{62} +(55.3615 - 529.974i) q^{63} +(379.272 - 343.942i) q^{64} -997.098i q^{65} +(353.665 - 239.018i) q^{66} +(-27.8307 - 27.8307i) q^{67} +(-32.3248 - 9.22763i) q^{68} +(268.036 - 241.495i) q^{69} +(-1061.64 - 148.564i) q^{70} -786.600i q^{71} +(-159.545 - 589.740i) q^{72} +510.757i q^{73} +(-37.6972 + 269.385i) q^{74} +(941.161 - 847.968i) q^{75} +(-382.326 + 212.518i) q^{76} +(405.313 + 405.313i) q^{77} +(427.284 + 632.233i) q^{78} -230.706i q^{79} +(-1196.91 + 279.311i) q^{80} +(-713.262 - 150.660i) q^{81} +(-554.990 - 735.592i) q^{82} +(-593.835 + 593.835i) q^{83} +(736.820 - 360.741i) q^{84} +(57.0607 + 57.0607i) q^{85} +(-146.339 - 20.4783i) q^{86} +(-8.80017 + 168.946i) q^{87} +(600.848 + 266.239i) q^{88} +1015.01 q^{89} +(-353.049 + 1423.45i) q^{90} +(-724.562 + 724.562i) q^{91} +(534.122 + 152.474i) q^{92} +(-849.221 + 765.131i) q^{93} +(328.309 + 435.146i) q^{94} +1050.04 q^{95} +(639.234 - 690.011i) q^{96} +805.334 q^{97} +(79.1958 + 104.967i) q^{98} +(609.115 - 493.894i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more