LMFDB - Embedded newform 80.3.k.a.19.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,3,Mod(19,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("80.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	80.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:	$2.17984211488$
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			19.20
Character	$\chi$	$=$	80.19
Dual form			80.3.k.a.59.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85180 + 0.755534i) q^{2} +(1.37405 + 1.37405i) q^{3} +(2.85834 + 2.79820i) q^{4} +(-1.48609 - 4.77405i) q^{5} +(1.50632 + 3.58260i) q^{6} +5.00956i q^{7} +(3.17893 + 7.34128i) q^{8} -5.22398i q^{9} +O(q^{10})$	\(q+(1.85180 + 0.755534i) q^{2} +(1.37405 + 1.37405i) q^{3} +(2.85834 + 2.79820i) q^{4} +(-1.48609 - 4.77405i) q^{5} +(1.50632 + 3.58260i) q^{6} +5.00956i q^{7} +(3.17893 + 7.34128i) q^{8} -5.22398i q^{9} +(0.855008 - 9.96338i) q^{10} +(-6.42909 - 6.42909i) q^{11} +(0.0826298 + 7.77235i) q^{12} +(-11.0519 + 11.0519i) q^{13} +(-3.78490 + 9.27672i) q^{14} +(4.51781 - 8.60173i) q^{15} +(0.340161 + 15.9964i) q^{16} -14.8302i q^{17} +(3.94690 - 9.67378i) q^{18} +(17.5407 - 17.5407i) q^{19} +(9.11098 - 17.8042i) q^{20} +(-6.88338 + 6.88338i) q^{21} +(-7.04800 - 16.7628i) q^{22} +4.37435i q^{23} +(-5.71926 + 14.4553i) q^{24} +(-20.5831 + 14.1894i) q^{25} +(-28.8160 + 12.1158i) q^{26} +(19.5444 - 19.5444i) q^{27} +(-14.0178 + 14.3190i) q^{28} +(-18.8676 - 18.8676i) q^{29} +(14.8650 - 12.5153i) q^{30} +32.9924i q^{31} +(-11.4559 + 29.8791i) q^{32} -17.6678i q^{33} +(11.2048 - 27.4627i) q^{34} +(23.9159 - 7.44468i) q^{35} +(14.6177 - 14.9319i) q^{36} +(-18.0984 - 18.0984i) q^{37} +(45.7346 - 19.2293i) q^{38} -30.3717 q^{39} +(30.3234 - 26.0862i) q^{40} +76.1027i q^{41} +(-17.9473 + 7.54602i) q^{42} +(-19.1807 + 19.1807i) q^{43} +(-0.386620 - 36.3664i) q^{44} +(-24.9395 + 7.76333i) q^{45} +(-3.30497 + 8.10042i) q^{46} +59.1180 q^{47} +(-21.5124 + 22.4472i) q^{48} +23.9043 q^{49} +(-48.8363 + 10.7247i) q^{50} +(20.3775 - 20.3775i) q^{51} +(-62.5155 + 0.664617i) q^{52} +(21.5406 + 21.5406i) q^{53} +(50.9589 - 21.4259i) q^{54} +(-21.1385 + 40.2470i) q^{55} +(-36.7766 + 15.9251i) q^{56} +48.2036 q^{57} +(-20.6839 - 49.1941i) q^{58} +(53.6021 + 53.6021i) q^{59} +(36.9828 - 11.9449i) q^{60} +(-25.4876 - 25.4876i) q^{61} +(-24.9269 + 61.0955i) q^{62} +26.1699 q^{63} +(-43.7888 + 46.6749i) q^{64} +(69.1865 + 36.3381i) q^{65} +(13.3486 - 32.7172i) q^{66} +(-5.92820 - 5.92820i) q^{67} +(41.4980 - 42.3898i) q^{68} +(-6.01056 + 6.01056i) q^{69} +(49.9122 + 4.28322i) q^{70} -25.9177 q^{71} +(38.3507 - 16.6067i) q^{72} +31.2154 q^{73} +(-19.8407 - 47.1886i) q^{74} +(-47.7790 - 8.78525i) q^{75} +(99.2197 - 1.05483i) q^{76} +(32.2069 - 32.2069i) q^{77} +(-56.2423 - 22.9469i) q^{78} +122.054i q^{79} +(75.8620 - 25.3961i) q^{80} +6.69413 q^{81} +(-57.4982 + 140.927i) q^{82} +(-115.988 - 115.988i) q^{83} +(-38.9361 + 0.413939i) q^{84} +(-70.8003 + 22.0391i) q^{85} +(-50.0105 + 21.0271i) q^{86} -51.8499i q^{87} +(26.7601 - 67.6354i) q^{88} -85.3925i q^{89} +(-52.0485 - 4.46655i) q^{90} +(-55.3652 - 55.3652i) q^{91} +(-12.2403 + 12.5033i) q^{92} +(-45.3332 + 45.3332i) q^{93} +(109.475 + 44.6657i) q^{94} +(-109.807 - 57.6731i) q^{95} +(-56.7963 + 25.3144i) q^{96} -16.3915i q^{97} +(44.2659 + 18.0605i) q^{98} +(-33.5855 + 33.5855i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) $ 44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	$ 44 q - 4 q^{4} - 2 q^{5} - 4 q^{6} - 20 q^{10} - 4 q^{11} + 4 q^{14} - 32 q^{16} - 36 q^{19} + 40 q^{20} + 32 q^{21} + 16 q^{24} - 56 q^{26} - 4 q^{29} - 160 q^{30} - 192 q^{34} + 212 q^{36} - 8 q^{39} - 184 q^{40} + 224 q^{44} + 30 q^{45} + 124 q^{46} - 148 q^{49} + 100 q^{50} + 128 q^{51} + 24 q^{54} - 260 q^{55} + 360 q^{56} - 68 q^{59} - 80 q^{60} + 28 q^{61} - 16 q^{64} - 20 q^{65} + 448 q^{66} + 128 q^{69} + 396 q^{70} - 264 q^{71} + 480 q^{74} + 60 q^{75} - 464 q^{76} + 504 q^{80} - 116 q^{81} - 496 q^{84} + 48 q^{85} - 852 q^{86} + 144 q^{90} + 384 q^{91} - 340 q^{94} - 1128 q^{96} + 484 q^{99}+O(q^{100}) $ 44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 - 20 * q^10 - 4 * q^11 + 4 * q^14 - 32 * q^16 - 36 * q^19 + 40 * q^20 + 32 * q^21 + 16 * q^24 - 56 * q^26 - 4 * q^29 - 160 * q^30 - 192 * q^34 + 212 * q^36 - 8 * q^39 - 184 * q^40 + 224 * q^44 + 30 * q^45 + 124 * q^46 - 148 * q^49 + 100 * q^50 + 128 * q^51 + 24 * q^54 - 260 * q^55 + 360 * q^56 - 68 * q^59 - 80 * q^60 + 28 * q^61 - 16 * q^64 - 20 * q^65 + 448 * q^66 + 128 * q^69 + 396 * q^70 - 264 * q^71 + 480 * q^74 + 60 * q^75 - 464 * q^76 + 504 * q^80 - 116 * q^81 - 496 * q^84 + 48 * q^85 - 852 * q^86 + 144 * q^90 + 384 * q^91 - 340 * q^94 - 1128 * q^96 + 484 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.85180	+	0.755534i	0.925901	+	0.377767i
$2$	1.85180	+	0.755534i	0.925901	+	0.377767i
$3$	1.37405	+	1.37405i	0.458016	+	0.458016i	0.898004	−	0.439988i	$-0.145017\pi$
$3$	1.37405	+	1.37405i	0.458016	+	0.458016i	−0.439988	+	0.898004i	$0.645017\pi$
$4$	2.85834	+	2.79820i	0.714584	+	0.699550i
$5$	−1.48609	−	4.77405i	−0.297219	−	0.954809i
$5$	−1.48609	−	4.77405i	−0.297219	−	0.954809i
$6$	1.50632	+	3.58260i	0.251054	+	0.597101i
$7$			5.00956i			0.715652i	0.933788	+	0.357826i	$0.116482\pi$
$7$			5.00956i			0.715652i	−0.933788	+	0.357826i	$0.883518\pi$
$8$	3.17893	+	7.34128i	0.397367	+	0.917660i
$9$		−	5.22398i		−	0.580443i
$10$	0.855008	−	9.96338i	0.0855008	−	0.996338i
$11$	−6.42909	−	6.42909i	−0.584463	−	0.584463i	0.351664	−	0.936126i	$-0.385616\pi$
$11$	−6.42909	−	6.42909i	−0.584463	−	0.584463i	−0.936126	+	0.351664i	$0.885616\pi$
$12$	0.0826298	+	7.77235i	0.00688581	+	0.647696i
$13$	−11.0519	+	11.0519i	−0.850146	+	0.850146i	−0.990151	−	0.140005i	$-0.955288\pi$
$13$	−11.0519	+	11.0519i	−0.850146	+	0.850146i	0.140005	+	0.990151i	$0.455288\pi$
$14$	−3.78490	+	9.27672i	−0.270350	+	0.662623i
$15$	4.51781	−	8.60173i	0.301187	−	0.573449i
$16$	0.340161	+	15.9964i	0.0212601	+	0.999774i
$17$		−	14.8302i		−	0.872367i	−0.899858	−	0.436184i	$-0.856330\pi$
$17$		−	14.8302i		−	0.872367i	0.899858	−	0.436184i	$-0.143670\pi$
$18$	3.94690	−	9.67378i	0.219272	−	0.537432i
$19$	17.5407	−	17.5407i	0.923196	−	0.923196i	−0.0740578	−	0.997254i	$-0.523595\pi$
$19$	17.5407	−	17.5407i	0.923196	−	0.923196i	0.997254	+	0.0740578i	$0.0235949\pi$
$20$	9.11098	−	17.8042i	0.455549	−	0.890211i
$21$	−6.88338	+	6.88338i	−0.327780	+	0.327780i
$22$	−7.04800	−	16.7628i	−0.320363	−	0.761945i
$23$			4.37435i			0.190189i	0.995468	+	0.0950945i	$0.0303153\pi$
$23$			4.37435i			0.190189i	−0.995468	+	0.0950945i	$0.969685\pi$
$24$	−5.71926	+	14.4553i	−0.238303	+	0.602303i
$25$	−20.5831	+	14.1894i	−0.823322	+	0.567574i
$26$	−28.8160	+	12.1158i	−1.10831	+	0.465994i
$27$	19.5444	−	19.5444i	0.723868	−	0.723868i
$28$	−14.0178	+	14.3190i	−0.500634	+	0.511393i
$29$	−18.8676	−	18.8676i	−0.650605	−	0.650605i	0.302533	−	0.953139i	$-0.402168\pi$
$29$	−18.8676	−	18.8676i	−0.650605	−	0.650605i	−0.953139	+	0.302533i	$0.902168\pi$
$30$	14.8650	−	12.5153i	0.495500	−	0.417178i
$31$			32.9924i			1.06427i	0.846659	+	0.532136i	$0.178611\pi$
$31$			32.9924i			1.06427i	−0.846659	+	0.532136i	$0.821389\pi$
$32$	−11.4559	+	29.8791i	−0.357997	+	0.933723i
$33$		−	17.6678i		−	0.535386i
$34$	11.2048	−	27.4627i	0.329552	−	0.807726i
$35$	23.9159	−	7.44468i	0.683311	−	0.212705i
$36$	14.6177	−	14.9319i	0.406049	−	0.414775i
$37$	−18.0984	−	18.0984i	−0.489146	−	0.489146i	0.418891	−	0.908037i	$-0.362419\pi$
$37$	−18.0984	−	18.0984i	−0.489146	−	0.489146i	−0.908037	+	0.418891i	$0.862419\pi$
$38$	45.7346	−	19.2293i	1.20354	−	0.506035i
$39$	−30.3717			−0.778761
$40$	30.3234	−	26.0862i	0.758086	−	0.652155i
$41$			76.1027i			1.85616i	0.372376	+	0.928082i	$0.378543\pi$
$41$			76.1027i			1.85616i	−0.372376	+	0.928082i	$0.621457\pi$
$42$	−17.9473	+	7.54602i	−0.427316	+	0.179667i
$43$	−19.1807	+	19.1807i	−0.446062	+	0.446062i	−0.894043	−	0.447981i	$-0.852143\pi$
$43$	−19.1807	+	19.1807i	−0.446062	+	0.446062i	0.447981	+	0.894043i	$0.352143\pi$
$44$	−0.386620	−	36.3664i	−0.00878681	−	0.826508i
$45$	−24.9395	+	7.76333i	−0.554212	+	0.172518i
$46$	−3.30497	+	8.10042i	−0.0718471	+	0.176096i
$47$	59.1180			1.25783			0.628915	−	0.777474i	$-0.283499\pi$
$47$	59.1180			1.25783			0.628915	+	0.777474i	$0.283499\pi$
$48$	−21.5124	+	22.4472i	−0.448175	+	0.467650i
$49$	23.9043			0.487842
$50$	−48.8363	+	10.7247i	−0.976725	+	0.214493i
$51$	20.3775	−	20.3775i	0.399558	−	0.399558i
$52$	−62.5155	+	0.664617i	−1.20222	+	0.0127811i
$53$	21.5406	+	21.5406i	0.406427	+	0.406427i	0.880491	−	0.474064i	$-0.157213\pi$
$53$	21.5406	+	21.5406i	0.406427	+	0.406427i	−0.474064	+	0.880491i	$0.657213\pi$
$54$	50.9589	−	21.4259i	0.943683	−	0.396776i
$55$	−21.1385	+	40.2470i	−0.384337	+	0.731764i
$56$	−36.7766	+	15.9251i	−0.656725	+	0.284376i
$57$	48.2036			0.845677
$58$	−20.6839	−	49.1941i	−0.356619	−	0.848173i
$59$	53.6021	+	53.6021i	0.908511	+	0.908511i	0.996152	−	0.0876411i	$-0.0279329\pi$
$59$	53.6021	+	53.6021i	0.908511	+	0.908511i	−0.0876411	+	0.996152i	$0.527933\pi$
$60$	36.9828	−	11.9449i	0.616380	−	0.199082i
$61$	−25.4876	−	25.4876i	−0.417830	−	0.417830i	0.466625	−	0.884455i	$-0.345470\pi$
$61$	−25.4876	−	25.4876i	−0.417830	−	0.417830i	−0.884455	+	0.466625i	$0.845470\pi$
$62$	−24.9269	+	61.0955i	−0.402047	+	0.985411i
$63$	26.1699			0.415395
$64$	−43.7888	+	46.6749i	−0.684200	+	0.729295i
$65$	69.1865	+	36.3381i	1.06441	+	0.559048i
$66$	13.3486	−	32.7172i	0.202251	−	0.495715i
$67$	−5.92820	−	5.92820i	−0.0884806	−	0.0884806i	0.661481	−	0.749962i	$-0.269928\pi$
$67$	−5.92820	−	5.92820i	−0.0884806	−	0.0884806i	−0.749962	+	0.661481i	$0.769928\pi$
$68$	41.4980	−	42.3898i	0.610264	−	0.623380i
$69$	−6.01056	+	6.01056i	−0.0871096	+	0.0871096i
$70$	49.9122	+	4.28322i	0.713031	+	0.0611889i
$71$	−25.9177			−0.365038			−0.182519	−	0.983202i	$-0.558425\pi$
$71$	−25.9177			−0.365038			−0.182519	+	0.983202i	$0.558425\pi$
$72$	38.3507	−	16.6067i	0.532649	−	0.230649i
$73$	31.2154			0.427608			0.213804	−	0.976877i	$-0.431415\pi$
$73$	31.2154			0.427608			0.213804	+	0.976877i	$0.431415\pi$
$74$	−19.8407	−	47.1886i	−0.268117	−	0.637684i
$75$	−47.7790	−	8.78525i	−0.637053	−	0.117137i
$76$	99.2197	−	1.05483i	1.30552	−	0.0138793i
$77$	32.2069	−	32.2069i	0.418272	−	0.418272i
$78$	−56.2423	−	22.9469i	−0.721055	−	0.294190i
$79$			122.054i			1.54499i	0.635019	+	0.772497i	$0.280992\pi$
$79$			122.054i			1.54499i	−0.635019	+	0.772497i	$0.719008\pi$
$80$	75.8620	−	25.3961i	0.948275	−	0.317451i
$81$	6.69413			0.0826436
$82$	−57.4982	+	140.927i	−0.701198	+	1.71862i
$83$	−115.988	−	115.988i	−1.39745	−	1.39745i	−0.807280	−	0.590169i	$-0.799061\pi$
$83$	−115.988	−	115.988i	−1.39745	−	1.39745i	−0.590169	−	0.807280i	$-0.700939\pi$
$84$	−38.9361	+	0.413939i	−0.463525	+	0.00492785i
$85$	−70.8003	+	22.0391i	−0.832945	+	0.259284i
$86$	−50.0105	+	21.0271i	−0.581517	+	0.244502i
$87$		−	51.8499i		−	0.595975i
$88$	26.7601	−	67.6354i	0.304092	−	0.768584i
$89$		−	85.3925i		−	0.959466i	−0.877415	−	0.479733i	$-0.840734\pi$
$89$		−	85.3925i		−	0.959466i	0.877415	−	0.479733i	$-0.159266\pi$
$90$	−52.0485	−	4.46655i	−0.578317	−	0.0496283i
$91$	−55.3652	−	55.3652i	−0.608409	−	0.608409i
$92$	−12.2403	+	12.5033i	−0.133047	+	0.135906i
$93$	−45.3332	+	45.3332i	−0.487454	+	0.487454i
$94$	109.475	+	44.6657i	1.16463	+	0.475167i
$95$	−109.807	−	57.6731i	−1.15587	−	0.607085i
$96$	−56.7963	+	25.3144i	−0.591628	+	0.263692i
$97$		−	16.3915i		−	0.168984i	−0.996424	−	0.0844921i	$-0.973073\pi$
$97$		−	16.3915i		−	0.168984i	0.996424	−	0.0844921i	$-0.0269268\pi$
$98$	44.2659	+	18.0605i	0.451693	+	0.184291i
$99$	−33.5855	+	33.5855i	−0.339247	+	0.339247i
$100$	−98.5379	−	17.0375i	−0.985379	−	0.170375i
$101$	105.008	−	105.008i	1.03969	−	1.03969i	0.0405066	−	0.999179i	$-0.487103\pi$
$101$	105.008	−	105.008i	1.03969	−	1.03969i	0.999179	−	0.0405066i	$-0.0128972\pi$
$102$	53.1309	−	22.3391i	0.520891	−	0.219011i
$103$			47.2447i			0.458687i	0.973346	+	0.229343i	$0.0736579\pi$
$103$			47.2447i			0.458687i	−0.973346	+	0.229343i	$0.926342\pi$
$104$	−116.268	−	46.0018i	−1.11796	−	0.442325i
$105$	43.0909	+	22.6322i	0.410390	+	0.215545i
$106$	23.6143	+	56.1637i	0.222776	+	0.529846i
$107$	55.7447	−	55.7447i	0.520979	−	0.520979i	−0.396888	−	0.917867i	$-0.629910\pi$
$107$	55.7447	−	55.7447i	0.520979	−	0.520979i	0.917867	+	0.396888i	$0.129910\pi$
$108$	110.554	−	1.17532i	1.02365	−	0.0108826i
$109$	−129.985	−	129.985i	−1.19253	−	1.19253i	−0.976356	−	0.216169i	$-0.930644\pi$
$109$	−129.985	−	129.985i	−1.19253	−	1.19253i	−0.216169	−	0.976356i	$-0.569356\pi$
$110$	−69.5524	+	58.5585i	−0.632294	+	0.532350i
$111$		−	49.7362i		−	0.448074i
$112$	−80.1349	+	1.70406i	−0.715490	+	0.0152148i
$113$		−	47.6474i		−	0.421658i	−0.977523	−	0.210829i	$-0.932384\pi$
$113$		−	47.6474i		−	0.421658i	0.977523	−	0.210829i	$-0.0676164\pi$
$114$	89.2635	+	36.4195i	0.783013	+	0.319469i
$115$	20.8833	−	6.50068i	0.181594	−	0.0565277i
$116$	−1.13462	−	106.725i	−0.00978120	−	0.920043i
$117$	57.7350	+	57.7350i	0.493461	+	0.493461i
$118$	58.7623	+	139.759i	0.497985	+	1.18440i
$119$	74.2931			0.624312
$120$	77.5095	+	5.82215i	0.645913	+	0.0485179i
$121$		−	38.3336i		−	0.316807i
$122$	−27.9412	−	66.4548i	−0.229027	−	0.544711i
$123$	−104.569	+	104.569i	−0.850153	+	0.850153i
$124$	−92.3194	+	94.3035i	−0.744512	+	0.760512i
$125$	98.3290	+	77.1778i	0.786632	+	0.617422i
$126$	48.4614	+	19.7723i	0.384614	+	0.156923i
$127$	−178.817			−1.40801			−0.704005	−	0.710195i	$-0.748607\pi$
$127$	−178.817			−1.40801			−0.704005	+	0.710195i	$0.748607\pi$
$128$	−116.353	+	53.3486i	−0.909004	+	0.416786i
$129$	−52.7103			−0.408607
$130$	100.665	+	119.564i	0.774345	+	0.919721i
$131$	50.1661	−	50.1661i	0.382948	−	0.382948i	−0.489215	−	0.872163i	$-0.662717\pi$
$131$	50.1661	−	50.1661i	0.382948	−	0.382948i	0.872163	+	0.489215i	$0.162717\pi$
$132$	49.4379	−	50.5004i	0.374530	−	0.382579i
$133$	87.8714	+	87.8714i	0.660687	+	0.660687i
$134$	−6.49889	−	15.4568i	−0.0484992	−	0.115349i
$135$	−122.351	−	64.2612i	−0.906303	−	0.476009i
$136$	108.873	−	47.1444i	0.800537	−	0.346650i
$137$	4.72138			0.0344626			0.0172313	−	0.999852i	$-0.494515\pi$
$137$	4.72138			0.0344626			0.0172313	+	0.999852i	$0.494515\pi$
$138$	−15.6715	+	6.58918i	−0.113562	+	0.0477477i
$139$	72.2925	+	72.2925i	0.520090	+	0.520090i	0.917598	−	0.397509i	$-0.130125\pi$
$139$	72.2925	+	72.2925i	0.520090	+	0.520090i	−0.397509	+	0.917598i	$0.630125\pi$
$140$	89.1914	+	45.6421i	0.637081	+	0.326015i
$141$	81.2310	+	81.2310i	0.576106	+	0.576106i
$142$	−47.9945	−	19.5817i	−0.337989	−	0.137899i
$143$	142.107			0.993757
$144$	83.5649	−	1.77700i	0.580311	−	0.0123403i
$145$	−62.0357	+	118.114i	−0.427832	+	0.814576i
$146$	57.8047	+	23.5843i	0.395922	+	0.161536i
$147$	32.8456	+	32.8456i	0.223439	+	0.223439i
$148$	−1.08837	−	102.374i	−0.00735383	−	0.691718i
$149$	82.5656	−	82.5656i	0.554131	−	0.554131i	−0.373499	−	0.927631i	$-0.621842\pi$
$149$	82.5656	−	82.5656i	0.554131	−	0.554131i	0.927631	+	0.373499i	$0.121842\pi$
$150$	−81.8396	−	52.3672i	−0.545597	−	0.349115i
$151$	95.3210			0.631265			0.315632	−	0.948882i	$-0.397783\pi$
$151$	95.3210			0.631265			0.315632	+	0.948882i	$0.397783\pi$
$152$	184.532	+	73.0106i	1.21403	+	0.480333i
$153$	−77.4730			−0.506359
$154$	83.9743	−	35.3074i	0.545288	−	0.229269i
$155$	157.508	−	49.0298i	1.01618	−	0.316322i
$156$	−86.8125	−	84.9860i	−0.556490	−	0.544782i
$157$	103.454	−	103.454i	0.658941	−	0.658941i	−0.296188	−	0.955130i	$-0.595716\pi$
$157$	103.454	−	103.454i	0.658941	−	0.658941i	0.955130	+	0.296188i	$0.0957156\pi$
$158$	−92.2164	+	226.021i	−0.583648	+	1.43051i
$159$			59.1957i			0.372300i
$160$	159.669	+	10.2879i	0.997931	+	0.0642993i
$161$	−21.9136			−0.136109
$162$	12.3962	+	5.05765i	0.0765198	+	0.0312200i
$163$	129.670	+	129.670i	0.795524	+	0.795524i	0.982386	−	0.186862i	$-0.0598318\pi$
$163$	129.670	+	129.670i	0.795524	+	0.795524i	−0.186862	+	0.982386i	$0.559832\pi$
$164$	−212.951	+	217.527i	−1.29848	+	1.32638i
$165$	−84.3467	+	26.2559i	−0.511192	+	0.159127i
$166$	−127.154	−	302.420i	−0.765988	−	1.82181i
$167$		−	50.8326i		−	0.304387i	−0.988351	−	0.152193i	$-0.951366\pi$
$167$		−	50.8326i		−	0.304387i	0.988351	−	0.152193i	$-0.0486337\pi$
$168$	−72.4146	−	28.6510i	−0.431040	−	0.170542i
$169$		−	75.2890i		−	0.445497i
$170$	−147.759	−	12.6800i	−0.869173	−	0.0745881i
$171$	−91.6325	−	91.6325i	−0.535862	−	0.535862i
$172$	−108.496	+	1.15345i	−0.630792	+	0.00670610i
$173$	−118.979	+	118.979i	−0.687738	+	0.687738i	−0.961732	−	0.273993i	$-0.911655\pi$
$173$	−118.979	+	118.979i	−0.687738	+	0.687738i	0.273993	+	0.961732i	$0.411655\pi$
$174$	39.1744	−	96.0156i	0.225140	−	0.551814i
$175$	−71.0825	−	103.112i	−0.406186	−	0.589212i
$176$	100.655	−	105.029i	0.571905	−	0.596756i
$177$			147.304i			0.832225i
$178$	64.5170	−	158.130i	0.362455	−	0.888370i
$179$	−171.651	+	171.651i	−0.958946	+	0.958946i	−0.999190	−	0.0402443i	$-0.987186\pi$
$179$	−171.651	+	171.651i	−0.958946	+	0.958946i	0.0402443	+	0.999190i	$0.487186\pi$
$180$	−93.0089	−	47.5956i	−0.516716	−	0.264420i
$181$	−144.176	+	144.176i	−0.796550	+	0.796550i	−0.982550	−	0.186000i	$-0.940448\pi$
$181$	−144.176	+	144.176i	−0.796550	+	0.796550i	0.186000	+	0.982550i	$0.440448\pi$
$182$	−60.6950	−	144.356i	−0.333489	−	0.793163i
$183$		−	70.0424i		−	0.382746i
$184$	−32.1133	+	13.9058i	−0.174529	+	0.0755747i
$185$	−59.5067	+	113.299i	−0.321658	+	0.612425i
$186$	−118.199	+	49.6973i	−0.635478	+	0.267190i
$187$	−95.3450	+	95.3450i	−0.509866	+	0.509866i
$188$	168.979	+	165.424i	0.898825	+	0.879915i
$189$	97.9091	+	97.9091i	0.518038	+	0.518038i
$190$	−159.767	−	189.762i	−0.840881	−	0.998750i
$191$		−	49.0166i		−	0.256631i	−0.991733	−	0.128316i	$-0.959043\pi$
$191$		−	49.0166i		−	0.256631i	0.991733	−	0.128316i	$-0.0409571\pi$
$192$	−124.301	+	3.96563i	−0.647403	+	0.0206543i
$193$		−	371.977i		−	1.92734i	−0.267094	−	0.963671i	$-0.586063\pi$
$193$		−	371.977i		−	1.92734i	0.267094	−	0.963671i	$-0.413937\pi$
$194$	12.3843	−	30.3537i	0.0638367	−	0.156463i
$195$	45.1352	+	144.996i	0.231462	+	0.743569i
$196$	68.3264	+	66.8889i	0.348604	+	0.341270i
$197$	−164.712	−	164.712i	−0.836102	−	0.836102i	0.152241	−	0.988343i	$-0.451351\pi$
$197$	−164.712	−	164.712i	−0.836102	−	0.836102i	−0.988343	+	0.152241i	$0.951351\pi$
$198$	−87.5686	+	36.8186i	−0.442265	+	0.185953i
$199$	141.117			0.709130			0.354565	−	0.935031i	$-0.384629\pi$
$199$	141.117			0.709130			0.354565	+	0.935031i	$0.384629\pi$
$200$	−169.600	−	105.999i	−0.848001	−	0.529995i
$201$		−	16.2913i		−	0.0810511i
$202$	273.792	−	115.117i	1.35541	−	0.569887i
$203$	94.5182	−	94.5182i	0.465607	−	0.465607i
$204$	115.266	−	1.22542i	0.565029	−	0.00600696i
$205$	363.318	−	113.096i	1.77228	−	0.551686i
$206$	−35.6950	+	87.4879i	−0.173277	+	0.424698i
$207$	22.8515			0.110394
$208$	−180.550	−	173.031i	−0.868028	−	0.831880i
$209$	−225.542			−1.07915
$210$	62.6964	+	74.4671i	0.298554	+	0.354605i
$211$	−167.007	+	167.007i	−0.791502	+	0.791502i	−0.981738	−	0.190236i	$-0.939075\pi$
$211$	−167.007	+	167.007i	−0.791502	+	0.791502i	0.190236	+	0.981738i	$0.439075\pi$
$212$	1.29537	+	121.845i	0.00611023	+	0.574742i
$213$	−35.6122	−	35.6122i	−0.167193	−	0.167193i
$214$	145.345	−	61.1111i	0.679183	−	0.285566i
$215$	120.074	+	63.0652i	0.558482	+	0.293326i
$216$	205.612	+	81.3507i	0.951906	+	0.376624i
$217$	−165.278			−0.761649
$218$	−142.498	−	338.915i	−0.653663	−	1.55466i
$219$	42.8914	+	42.8914i	0.195851	+	0.195851i
$220$	−173.040	+	55.8895i	−0.786546	+	0.254043i
$221$	163.902	+	163.902i	0.741640	+	0.741640i
$222$	37.5774	−	92.1015i	0.169268	−	0.414872i
$223$	360.595			1.61702			0.808508	−	0.588485i	$-0.200275\pi$
$223$	360.595			1.61702			0.808508	+	0.588485i	$0.200275\pi$
$224$	−149.681	−	57.3891i	−0.668221	−	0.256201i
$225$	74.1250	+	107.526i	0.329444	+	0.477891i
$226$	35.9992	−	88.2335i	0.159289	−	0.390414i
$227$	162.621	+	162.621i	0.716392	+	0.716392i	0.967865	−	0.251472i	$-0.0809147\pi$
$227$	162.621	+	162.621i	0.716392	+	0.716392i	−0.251472	+	0.967865i	$0.580915\pi$
$228$	137.782	+	134.883i	0.604307	+	0.591593i
$229$	−6.11249	+	6.11249i	−0.0266921	+	0.0266921i	−0.720327	−	0.693635i	$-0.756008\pi$
$229$	−6.11249	+	6.11249i	−0.0266921	+	0.0266921i	0.693635	+	0.720327i	$0.256008\pi$
$230$	43.5833	+	3.74010i	0.189492	+	0.0162613i
$231$	88.5078			0.383150
$232$	78.5333	−	198.491i	0.338506	−	0.855563i
$233$	−121.619			−0.521968			−0.260984	−	0.965343i	$-0.584047\pi$
$233$	−121.619			−0.521968			−0.260984	+	0.965343i	$0.584047\pi$
$234$	63.2929	+	150.534i	0.270483	+	0.643309i
$235$	−87.8549	−	282.232i	−0.373850	−	1.20099i
$236$	3.22342	+	303.202i	0.0136586	+	1.28476i
$237$	−167.709	+	167.709i	−0.707632	+	0.707632i
$238$	137.576	+	56.1310i	0.578050	+	0.235844i
$239$		−	224.468i		−	0.939196i	−0.882880	−	0.469598i	$-0.844399\pi$
$239$		−	224.468i		−	0.939196i	0.882880	−	0.469598i	$-0.155601\pi$
$240$	139.133	+	69.3426i	0.579723	+	0.288927i
$241$	−128.007			−0.531150			−0.265575	−	0.964090i	$-0.585562\pi$
$241$	−128.007			−0.531150			−0.265575	+	0.964090i	$0.585562\pi$
$242$	28.9624	−	70.9863i	0.119679	−	0.293332i
$243$	−166.702	−	166.702i	−0.686016	−	0.686016i
$244$	−1.53272	−	144.172i	−0.00628166	−	0.590867i
$245$	−35.5240	−	114.120i	−0.144996	−	0.465796i
$246$	−272.646	+	114.635i	−1.10832	+	0.465997i
$247$			387.717i			1.56970i
$248$	−242.207	+	104.881i	−0.976640	+	0.422906i
$249$		−	318.747i		−	1.28011i
$250$	123.775	+	217.209i	0.495101	+	0.868835i
$251$	145.552	+	145.552i	0.579888	+	0.579888i	0.934872	−	0.354984i	$-0.115514\pi$
$251$	145.552	+	145.552i	0.579888	+	0.579888i	−0.354984	+	0.934872i	$0.615514\pi$
$252$	74.8023	+	73.2286i	0.296835	+	0.290590i
$253$	28.1231	−	28.1231i	0.111158	−	0.111158i
$254$	−331.134	−	135.103i	−1.30368	−	0.531900i
$255$	−127.566	−	67.0002i	−0.500258	−	0.262746i
$256$	−255.769	+	10.8827i	−0.999096	+	0.0425106i
$257$			450.082i			1.75129i	0.482953	+	0.875646i	$0.339564\pi$
$257$			450.082i			1.75129i	−0.482953	+	0.875646i	$0.660436\pi$
$258$	−97.6091	−	39.8245i	−0.378330	−	0.154358i
$259$	90.6652	−	90.6652i	0.350059	−	0.350059i
$260$	96.0767	+	297.464i	0.369526	+	1.14409i
$261$	−98.5638	+	98.5638i	−0.377639	+	0.377639i
$262$	130.800	−	54.9955i	0.499236	−	0.209906i
$263$		−	199.203i		−	0.757427i	−0.925514	−	0.378713i	$-0.876367\pi$
$263$		−	199.203i		−	0.757427i	0.925514	−	0.378713i	$-0.123633\pi$
$264$	129.704	−	56.1646i	0.491303	−	0.212745i
$265$	70.8246	−	134.847i	0.267263	−	0.508858i
$266$	96.3305	+	229.110i	0.362145	+	0.861317i
$267$	117.333	−	117.333i	0.439451	−	0.439451i
$268$	−0.356498	−	33.5331i	−0.00133022	−	0.125123i
$269$	−48.1424	−	48.1424i	−0.178968	−	0.178968i	0.611938	−	0.790906i	$-0.290390\pi$
$269$	−48.1424	−	48.1424i	−0.178968	−	0.178968i	−0.790906	+	0.611938i	$0.790390\pi$
$270$	−178.018	−	211.439i	−0.659326	−	0.783109i
$271$		−	317.904i		−	1.17308i	−0.809921	−	0.586538i	$-0.800490\pi$
$271$		−	317.904i		−	1.17308i	0.809921	−	0.586538i	$-0.199510\pi$
$272$	237.230	−	5.04468i	0.872170	−	0.0185466i
$273$		−	152.149i		−	0.557322i
$274$	8.74305	+	3.56716i	0.0319089	+	0.0130188i
$275$	223.555	+	41.1056i	0.812927	+	0.149475i
$276$	−33.9989	+	0.361451i	−0.123185	+	0.00130961i
$277$	−68.3059	−	68.3059i	−0.246592	−	0.246592i	0.572979	−	0.819570i	$-0.305788\pi$
$277$	−68.3059	−	68.3059i	−0.246592	−	0.246592i	−0.819570	+	0.572979i	$0.805788\pi$
$278$	79.2518	+	188.491i	0.285079	+	0.678024i
$279$	172.352			0.617749
$280$	130.681	+	151.907i	0.466716	+	0.542526i
$281$			131.237i			0.467035i	0.972353	+	0.233517i	$0.0750236\pi$
$281$			131.237i			0.467035i	−0.972353	+	0.233517i	$0.924976\pi$
$282$	89.0508	+	211.796i	0.315783	+	0.751051i
$283$	−386.539	+	386.539i	−1.36586	+	1.36586i	−0.499618	+	0.866246i	$0.666526\pi$
$283$	−386.539	+	386.539i	−1.36586	+	1.36586i	−0.866246	+	0.499618i	$0.833474\pi$
$284$	−74.0815	−	72.5229i	−0.260850	−	0.255362i
$285$	−71.6350	−	230.126i	−0.251351	−	0.807461i
$286$	263.154	+	107.367i	0.920121	+	0.375409i
$287$	−381.241			−1.32837
$288$	156.088	+	59.8455i	0.541973	+	0.207797i
$289$	69.0638			0.238975
$290$	−204.117	+	171.853i	−0.703850	+	0.592596i
$291$	22.5227	−	22.5227i	0.0773975	−	0.0773975i
$292$	89.2240	+	87.3468i	0.305562	+	0.299133i
$293$	221.104	+	221.104i	0.754620	+	0.754620i	0.975338	−	0.220718i	$-0.0708400\pi$
$293$	221.104	+	221.104i	0.754620	+	0.754620i	−0.220718	+	0.975338i	$0.570840\pi$
$294$	36.0075	+	85.6395i	0.122475	+	0.291291i
$295$	176.241	−	335.557i	0.597428	−	1.13748i
$296$	75.3319	−	190.399i	0.254500	−	0.643240i
$297$	−251.306			−0.846148
$298$	215.276	−	90.5139i	0.722403	−	0.303738i
$299$	−48.3448	−	48.3448i	−0.161688	−	0.161688i
$300$	−111.985	−	158.806i	−0.373285	−	0.529354i
$301$	−96.0868	−	96.0868i	−0.319225	−	0.319225i
$302$	176.515	+	72.0183i	0.584488	+	0.238471i
$303$	288.573			0.952386
$304$	286.555	+	274.622i	0.942615	+	0.903360i
$305$	−83.8021	+	159.556i	−0.274761	+	0.523135i
$306$	−143.465	−	58.5335i	−0.468838	−	0.191286i
$307$	−80.4368	−	80.4368i	−0.262009	−	0.262009i	0.563861	−	0.825870i	$-0.309315\pi$
$307$	−80.4368	−	80.4368i	−0.262009	−	0.262009i	−0.825870	+	0.563861i	$0.809315\pi$
$308$	182.180	−	1.93680i	0.591492	−	0.00628830i
$309$	−64.9165	+	64.9165i	−0.210086	+	0.210086i
$310$	328.716	+	28.2088i	1.06038	+	0.0909962i
$311$	−433.169			−1.39283			−0.696413	−	0.717641i	$-0.745222\pi$
$311$	−433.169			−1.39283			−0.696413	+	0.717641i	$0.745222\pi$
$312$	−96.5495	−	222.967i	−0.309454	−	0.714638i
$313$	269.601			0.861346			0.430673	−	0.902508i	$-0.358276\pi$
$313$	269.601			0.861346			0.430673	+	0.902508i	$0.358276\pi$
$314$	269.739	−	113.413i	0.859040	−	0.361188i
$315$	−38.8909	−	124.936i	−0.123463	−	0.396623i
$316$	−341.533	+	348.873i	−1.08080	+	1.10403i
$317$	20.0627	−	20.0627i	0.0632894	−	0.0632894i	−0.674754	−	0.738043i	$-0.735750\pi$
$317$	20.0627	−	20.0627i	0.0632894	−	0.0632894i	0.738043	+	0.674754i	$0.235750\pi$
$318$	−44.7244	+	109.619i	−0.140643	+	0.344713i
$319$			242.602i			0.760509i
$320$	287.902	+	139.686i	0.899694	+	0.436520i
$321$	153.192			0.477233
$322$	−40.5796	−	16.5565i	−0.126024	−	0.0514176i
$323$	−260.133	−	260.133i	−0.805366	−	0.805366i
$324$	19.1341	+	18.7315i	0.0590558	+	0.0578133i
$325$	70.6625	−	384.301i	0.217423	−	1.18247i
$326$	142.153	+	338.094i	0.436053	+	1.03710i
$327$		−	357.212i		−	1.09239i
$328$	−558.691	+	241.925i	−1.70333	+	0.737577i
$329$			296.155i			0.900169i
$330$	−176.031	−	15.1061i	−0.533426	−	0.0457760i
$331$	162.499	+	162.499i	0.490933	+	0.490933i	0.908600	−	0.417667i	$-0.137152\pi$
$331$	162.499	+	162.499i	0.490933	+	0.490933i	−0.417667	+	0.908600i	$0.637152\pi$
$332$	−6.97507	−	656.091i	−0.0210092	−	1.97618i
$333$	−94.5458	+	94.5458i	−0.283921	+	0.283921i
$334$	38.4058	−	94.1319i	0.114987	−	0.281832i
$335$	−19.4917	+	37.1114i	−0.0581840	+	0.110780i
$336$	−112.451	−	107.768i	−0.334675	−	0.320737i
$337$		−	331.372i		−	0.983301i	−0.870793	−	0.491650i	$-0.836394\pi$
$337$		−	331.372i		−	0.983301i	0.870793	−	0.491650i	$-0.163606\pi$
$338$	56.8835	−	139.420i	0.168294	−	0.412486i
$339$	65.4698	−	65.4698i	0.193126	−	0.193126i
$340$	−264.041	−	135.118i	−0.776591	−	0.397406i
$341$	212.111	−	212.111i	0.622028	−	0.622028i
$342$	−100.454	−	238.917i	−0.293724	−	0.698587i
$343$			365.219i			1.06478i
$344$	−201.785	−	79.8366i	−0.586584	−	0.232083i
$345$	37.6270	+	19.7624i	0.109064	+	0.0572825i
$346$	−310.217	+	130.432i	−0.896582	+	0.376972i
$347$	−140.935	+	140.935i	−0.406154	+	0.406154i	−0.880395	−	0.474241i	$-0.842722\pi$
$347$	−140.935	+	140.935i	−0.406154	+	0.406154i	0.474241	+	0.880395i	$0.342722\pi$
$348$	145.086	−	148.204i	0.416914	−	0.425874i
$349$	94.5429	+	94.5429i	0.270897	+	0.270897i	0.829461	−	0.558564i	$-0.188648\pi$
$349$	94.5429	+	94.5429i	0.270897	+	0.270897i	−0.558564	+	0.829461i	$0.688648\pi$
$350$	−53.7259	−	244.648i	−0.153503	−	0.698996i
$351$			432.006i			1.23079i
$352$	265.747	−	118.445i	0.754962	−	0.336490i
$353$		−	232.200i		−	0.657791i	−0.944366	−	0.328896i	$-0.893324\pi$
$353$		−	232.200i		−	0.657791i	0.944366	−	0.328896i	$-0.106676\pi$
$354$	−111.293	+	272.777i	−0.314387	+	0.770558i
$355$	38.5161	+	123.732i	0.108496	+	0.348542i
$356$	238.945	−	244.080i	0.671194	−	0.685619i
$357$	102.082	+	102.082i	0.285945	+	0.285945i
$358$	−447.552	+	188.176i	−1.25015	+	0.525630i
$359$	−701.851			−1.95502			−0.977508	−	0.210899i	$-0.932361\pi$
$359$	−701.851			−1.95502			−0.977508	+	0.210899i	$0.932361\pi$
$360$	−136.274	−	158.409i	−0.378539	−	0.440025i
$361$		−	254.354i		−	0.704582i
$362$	−375.914	+	158.055i	−1.03844	+	0.436616i
$363$	52.6722	−	52.6722i	0.145103	−	0.145103i
$364$	−3.32944	−	313.175i	−0.00914682	−	0.860372i
$365$	−46.3889	−	149.024i	−0.127093	−	0.408284i
$366$	52.9195	−	129.705i	0.144589	−	0.354384i
$367$	−126.106			−0.343612			−0.171806	−	0.985131i	$-0.554960\pi$
$367$	−126.106			−0.343612			−0.171806	+	0.985131i	$0.554960\pi$
$368$	−69.9737	+	1.48798i	−0.190146	+	0.00404343i
$369$	397.559			1.07740
$370$	−195.796	+	164.847i	−0.529177	+	0.445533i
$371$	−107.909	+	107.909i	−0.290860	+	0.290860i
$372$	−256.429	+	2.72616i	−0.689325	+	0.00732838i
$373$	414.853	+	414.853i	1.11221	+	1.11221i	0.992852	+	0.119356i	$0.0380829\pi$
$373$	414.853	+	414.853i	1.11221	+	1.11221i	0.119356	+	0.992852i	$0.461917\pi$
$374$	−248.596	+	104.524i	−0.664696	+	0.279475i
$375$	29.0628	+	241.155i	0.0775008	+	0.643079i
$376$	187.932	+	434.002i	0.499820	+	1.15426i
$377$	417.045			1.10622
$378$	107.335	+	255.282i	0.283954	+	0.675349i
$379$	−117.567	−	117.567i	−0.310204	−	0.310204i	0.534784	−	0.844989i	$-0.320393\pi$
$379$	−117.567	−	117.567i	−0.310204	−	0.310204i	−0.844989	+	0.534784i	$0.820393\pi$
$380$	−152.486	−	472.112i	−0.401278	−	1.24240i
$381$	−245.703	−	245.703i	−0.644891	−	0.644891i
$382$	37.0337	−	90.7690i	0.0969469	−	0.237615i
$383$	−254.533			−0.664577			−0.332289	−	0.943178i	$-0.607821\pi$
$383$	−254.533			−0.664577			−0.332289	+	0.943178i	$0.607821\pi$
$384$	−233.178	−	86.5704i	−0.607233	−	0.225444i
$385$	−201.620	−	105.895i	−0.523688	−	0.275052i
$386$	281.041	−	688.827i	0.728086	−	1.78453i
$387$	100.200	+	100.200i	0.258914	+	0.258914i
$388$	45.8666	−	46.8523i	0.118213	−	0.120753i
$389$	32.2185	−	32.2185i	0.0828240	−	0.0828240i	−0.664481	−	0.747305i	$-0.731347\pi$
$389$	32.2185	−	32.2185i	0.0828240	−	0.0828240i	0.747305	+	0.664481i	$0.231347\pi$
$390$	−25.9680	+	302.605i	−0.0665847	+	0.775909i
$391$	64.8726			0.165915
$392$	75.9900	+	175.488i	0.193852	+	0.447673i
$393$	137.861			0.350792
$394$	−180.568	−	429.460i	−0.458296	−	1.09000i
$395$	582.694	−	181.384i	1.47517	−	0.459201i
$396$	−189.977	+	2.01970i	−0.479741	+	0.00510024i
$397$	105.079	−	105.079i	0.264682	−	0.264682i	−0.562271	−	0.826953i	$-0.690072\pi$
$397$	105.079	−	105.079i	0.264682	−	0.264682i	0.826953	+	0.562271i	$0.190072\pi$
$398$	261.320	+	106.619i	0.656584	+	0.267886i
$399$			241.479i			0.605211i
$400$	−233.980	−	324.428i	−0.584950	−	0.811069i
$401$	248.416			0.619492			0.309746	−	0.950819i	$-0.399756\pi$
$401$	248.416			0.619492			0.309746	+	0.950819i	$0.399756\pi$
$402$	12.3086	−	30.1682i	0.0306184	−	0.0750452i
$403$	−364.629	−	364.629i	−0.904787	−	0.904787i
$404$	593.983	−	6.31478i	1.47025	−	0.0156306i
$405$	−9.94810	−	31.9581i	−0.0245632	−	0.0789089i
$406$	246.441	−	103.617i	0.606997	−	0.255215i
$407$			232.713i			0.571775i
$408$	214.375	+	84.8181i	0.525430	+	0.207888i
$409$			455.293i			1.11318i	0.830786	+	0.556592i	$0.187891\pi$
$409$			455.293i			1.11318i	−0.830786	+	0.556592i	$0.812109\pi$
$410$	758.240	+	65.0685i	1.84937	+	0.158704i
$411$	6.48740	+	6.48740i	0.0157844	+	0.0157844i
$412$	−132.200	+	135.041i	−0.320874	+	0.327770i
$413$	−268.523	+	268.523i	−0.650178	+	0.650178i
$414$	42.3165	+	17.2651i	0.102214	+	0.0417032i
$415$	−381.364	+	726.103i	−0.918949	+	1.74964i
$416$	−203.612	−	456.831i	−0.489451	−	1.09815i
$417$			198.667i			0.476419i
$418$	−417.659	−	170.405i	−0.999183	−	0.407666i
$419$	296.148	−	296.148i	0.706797	−	0.706797i	−0.259063	−	0.965860i	$-0.583414\pi$
$419$	296.148	−	296.148i	0.706797	−	0.706797i	0.965860	+	0.259063i	$0.0834139\pi$
$420$	59.8388	+	185.268i	0.142473	+	0.441113i
$421$	−354.858	+	354.858i	−0.842893	+	0.842893i	−0.989234	−	0.146341i	$-0.953250\pi$
$421$	−354.858	+	354.858i	−0.842893	+	0.842893i	0.146341	+	0.989234i	$0.453250\pi$
$422$	−435.443	+	183.084i	−1.03186	+	0.433849i
$423$		−	308.832i		−	0.730098i
$424$	−89.6596	+	226.612i	−0.211461	+	0.534462i
$425$	210.432	+	305.252i	0.495133	+	0.718239i
$426$	−39.0405	−	92.8529i	−0.0916443	−	0.217965i
$427$	127.682	−	127.682i	0.299021	−	0.299021i
$428$	315.322	−	3.35227i	0.736734	−	0.00783240i
$429$	195.262	+	195.262i	0.455157	+	0.455157i
$430$	174.705	+	207.504i	0.406290	+	0.482567i
$431$			79.8832i			0.185344i	0.995697	+	0.0926719i	$0.0295408\pi$
$431$			79.8832i			0.185344i	−0.995697	+	0.0926719i	$0.970459\pi$
$432$	319.289	+	305.992i	0.739094	+	0.708315i
$433$		−	1.57519i		−	0.00363785i	−0.999998	−	0.00181892i	$-0.999421\pi$
$433$		−	1.57519i		−	0.00363785i	0.999998	−	0.00181892i	$-0.000578982\pi$
$434$	−306.062	−	124.873i	−0.705211	−	0.287726i
$435$	−247.534	+	77.0537i	−0.569043	+	0.177135i
$436$	−7.81679	−	735.266i	−0.0179284	−	1.68639i
$437$	76.7292	+	76.7292i	0.175582	+	0.175582i
$438$	47.0204	+	111.832i	0.107353	+	0.255325i
$439$	249.750			0.568907			0.284453	−	0.958690i	$-0.408188\pi$
$439$	249.750			0.568907			0.284453	+	0.958690i	$0.408188\pi$
$440$	−362.663	−	27.2415i	−0.824233	−	0.0619125i
$441$		−	124.875i		−	0.283164i
$442$	179.681	+	427.349i	0.406518	+	0.966852i
$443$	−121.031	+	121.031i	−0.273208	+	0.273208i	−0.830390	−	0.557182i	$-0.811882\pi$
$443$	−121.031	+	121.031i	−0.273208	+	0.273208i	0.557182	+	0.830390i	$0.311882\pi$
$444$	139.172	−	142.163i	0.313450	−	0.320186i
$445$	−407.668	+	126.901i	−0.916107	+	0.285171i
$446$	667.750	+	272.442i	1.49720	+	0.610856i
$447$	226.898			0.507602
$448$	−233.821	−	219.363i	−0.521921	−	0.489649i
$449$	−297.105			−0.661703			−0.330852	−	0.943683i	$-0.607336\pi$
$449$	−297.105			−0.661703			−0.330852	+	0.943683i	$0.607336\pi$
$450$	56.0255	+	255.120i	0.124501	+	0.566933i
$451$	489.271	−	489.271i	1.08486	−	1.08486i
$452$	133.327	−	136.192i	0.294971	−	0.301310i
$453$	130.976	+	130.976i	0.289129	+	0.289129i
$454$	178.276	+	424.008i	0.392679	+	0.933938i
$455$	−182.038	+	346.594i	−0.400084	+	0.761745i
$456$	153.236	+	353.876i	0.336044	+	0.776044i
$457$	361.107			0.790169			0.395085	−	0.918645i	$-0.370715\pi$
$457$	361.107			0.790169			0.395085	+	0.918645i	$0.370715\pi$
$458$	−15.9373	+	6.70092i	−0.0347976	+	0.0146308i
$459$	−289.849	−	289.849i	−0.631479	−	0.631479i
$460$	77.8818	+	39.8546i	0.169308	+	0.0866404i
$461$	−166.498	−	166.498i	−0.361167	−	0.361167i	0.503075	−	0.864243i	$-0.332202\pi$
$461$	−166.498	−	166.498i	−0.361167	−	0.361167i	−0.864243	+	0.503075i	$0.832202\pi$
$462$	163.899	+	66.8707i	0.354759	+	0.144742i
$463$	712.425			1.53871			0.769357	−	0.638819i	$-0.220577\pi$
$463$	712.425			1.53871			0.769357	+	0.638819i	$0.220577\pi$
$464$	295.395	−	308.231i	0.636626	−	0.664290i
$465$	283.792	+	149.054i	0.610306	+	0.320545i
$466$	−225.213	−	91.8871i	−0.483291	−	0.197183i
$467$	−205.618	−	205.618i	−0.440295	−	0.440295i	0.451816	−	0.892111i	$-0.350776\pi$
$467$	−205.618	−	205.618i	−0.440295	−	0.440295i	−0.892111	+	0.451816i	$0.850776\pi$
$468$	3.47195	+	326.580i	0.00741870	+	0.697820i
$469$	29.6977	−	29.6977i	0.0633213	−	0.0633213i
$470$	50.5464	−	589.015i	0.107546	−	1.25322i
$471$	284.301			0.603611
$472$	−223.111	+	563.906i	−0.472692	+	1.19472i
$473$	246.629			0.521413
$474$	−437.273	+	183.853i	−0.922517	+	0.387877i
$475$	−112.150	+	609.933i	−0.236105	+	1.28407i
$476$	212.355	+	207.887i	0.446123	+	0.436737i
$477$	112.528	−	112.528i	0.235908	−	0.235908i
$478$	169.593	−	415.670i	0.354798	−	0.869602i
$479$		−	775.000i		−	1.61795i	−0.587841	−	0.808977i	$-0.700022\pi$
$479$		−	775.000i		−	1.61795i	0.587841	−	0.808977i	$-0.299978\pi$
$480$	205.257	+	233.529i	0.427618	+	0.486518i
$481$	400.044			0.831692
$482$	−237.044	−	96.7139i	−0.491793	−	0.200651i
$483$	−30.1103	−	30.1103i	−0.0623401	−	0.0623401i
$484$	107.265	−	109.570i	0.221622	−	0.226385i
$485$	−78.2537	+	24.3593i	−0.161348	+	0.0502253i
$486$	−182.750	−	434.648i	−0.376028	−	0.894337i
$487$		−	267.618i		−	0.549523i	−0.961512	−	0.274762i	$-0.911401\pi$
$487$		−	267.618i		−	0.549523i	0.961512	−	0.274762i	$-0.0885989\pi$
$488$	106.088	−	268.135i	0.217394	−	0.549457i
$489$			356.347i			0.728725i
$490$	20.4383	−	238.167i	0.0417109	−	0.486056i
$491$	−41.1597	−	41.1597i	−0.0838283	−	0.0838283i	0.663949	−	0.747778i	$-0.268879\pi$
$491$	−41.1597	−	41.1597i	−0.0838283	−	0.0838283i	−0.747778	+	0.663949i	$0.768879\pi$
$492$	−591.497	+	6.28835i	−1.20223	+	0.0127812i
$493$	−279.810	+	279.810i	−0.567567	+	0.567567i
$494$	−292.933	+	717.974i	−0.592983	+	1.45339i
$495$	210.250	+	110.427i	0.424747	+	0.223086i
$496$	−527.760	+	11.2228i	−1.06403	+	0.0226265i
$497$		−	129.836i		−	0.261240i
$498$	240.824	−	590.256i	0.483583	−	1.18525i
$499$	−165.335	+	165.335i	−0.331332	+	0.331332i	−0.853092	−	0.521760i	$-0.825276\pi$
$499$	−165.335	+	165.335i	−0.331332	+	0.331332i	0.521760	+	0.853092i	$0.325276\pi$
$500$	65.0985	+	495.744i	0.130197	+	0.991488i
$501$	69.8464	−	69.8464i	0.139414	−	0.139414i
$502$	159.564	+	379.503i	0.317856	+	0.755982i
$503$			427.936i			0.850767i	0.905013	+	0.425384i	$0.139861\pi$
$503$			427.936i			0.850767i	−0.905013	+	0.425384i	$0.860139\pi$
$504$	83.1923	+	192.120i	0.165064	+	0.381191i
$505$	−657.367	−	345.262i	−1.30172	−	0.683688i
$506$	73.3262	−	30.8304i	0.144914	−	0.0609296i
$507$	103.451	−	103.451i	0.204045	−	0.204045i
$508$	−511.120	−	500.366i	−1.00614	−	0.984973i
$509$	−465.764	−	465.764i	−0.915056	−	0.915056i	0.0816082	−	0.996664i	$-0.473994\pi$
$509$	−465.764	−	465.764i	−0.915056	−	0.915056i	−0.996664	+	0.0816082i	$0.973994\pi$
$510$	−185.606	−	220.451i	−0.363933	−	0.432258i
$511$			156.375i			0.306018i
$512$	−481.855	−	173.089i	−0.941123	−	0.338065i
$513$		−	685.647i		−	1.33654i
$514$	−340.053	+	833.462i	−0.661581	+	1.62152i
$515$	225.549	−	70.2101i	0.437958	−	0.136330i
$516$	−150.664	−	147.494i	−0.291984	−	0.285841i
$517$	−380.075	−	380.075i	−0.735155	−	0.735155i
$518$	236.395	−	99.3932i	0.456360	−	0.191879i
$519$	−326.965			−0.629990
$520$	−46.8294	+	623.434i	−0.0900566	+	1.19891i
$521$		−	262.979i		−	0.504758i	−0.967628	−	0.252379i	$-0.918787\pi$
$521$		−	262.979i		−	0.504758i	0.967628	−	0.252379i	$-0.0812129\pi$
$522$	−256.989	+	108.052i	−0.492316	+	0.206997i
$523$	−142.934	+	142.934i	−0.273296	+	0.273296i	−0.830426	−	0.557129i	$-0.811903\pi$
$523$	−142.934	+	142.934i	−0.273296	+	0.273296i	0.557129	+	0.830426i	$0.311903\pi$
$524$	283.766	−	3.01679i	0.541539	−	0.00575723i
$525$	44.0103	−	239.352i	0.0838291	−	0.455908i
$526$	150.505	−	368.885i	0.286131	−	0.701302i
$527$	489.286			0.928437
$528$	282.620	−	6.00989i	0.535265	−	0.0113824i
$529$	509.865			0.963828
$530$	233.035	−	196.200i	0.439689	−	0.370189i
$531$	280.017	−	280.017i	0.527339	−	0.527339i
$532$	5.28424	+	497.048i	0.00993277	+	0.934300i
$533$	−841.080	−	841.080i	−1.57801	−	1.57801i
$534$	305.927	−	128.629i	0.572898	−	0.240878i
$535$	−348.970	−	183.286i	−0.652280	−	0.342591i
$536$	24.6752	−	62.3659i	0.0460359	−	0.116354i
$537$	−471.714			−0.878425
$538$	−52.7769	−	125.523i	−0.0980983	−	0.233315i
$539$	−153.683	−	153.683i	−0.285125	−	0.285125i
$540$	−169.904	−	526.042i	−0.314638	−	0.974153i
$541$	−214.719	−	214.719i	−0.396892	−	0.396892i	0.480243	−	0.877135i	$-0.340548\pi$
$541$	−214.719	−	214.719i	−0.396892	−	0.396892i	−0.877135	+	0.480243i	$0.840548\pi$
$542$	240.187	−	588.695i	0.443150	−	1.08615i
$543$	−396.208			−0.729665
$544$	443.115	+	169.894i	0.814549	+	0.312305i
$545$	−427.386	+	813.726i	−0.784194	+	1.49307i
$546$	114.954	−	281.750i	0.210538	−	0.516025i
$547$	247.657	+	247.657i	0.452754	+	0.452754i	0.896268	−	0.443513i	$-0.146268\pi$
$547$	247.657	+	247.657i	0.452754	+	0.452754i	−0.443513	+	0.896268i	$0.646268\pi$
$548$	13.4953	+	13.2114i	0.0246264	+	0.0241083i
$549$	−133.147	+	133.147i	−0.242526	+	0.242526i
$550$	382.923	+	245.023i	0.696223	+	0.445496i
$551$	−661.901			−1.20127
$552$	−63.2324	−	25.0180i	−0.114551	−	0.0453225i
$553$	−611.440			−1.10568
$554$	−74.8815	−	178.096i	−0.135165	−	0.321474i
$555$	−237.443	+	73.9126i	−0.427825	+	0.133176i
$556$	4.34738	+	408.925i	0.00781903	+	0.735476i
$557$	252.575	−	252.575i	0.453456	−	0.453456i	−0.443044	−	0.896500i	$-0.646101\pi$
$557$	252.575	−	252.575i	0.453456	−	0.453456i	0.896500	+	0.443044i	$0.146101\pi$
$558$	319.162	+	130.218i	0.571974	+	0.233365i
$559$		−	423.966i		−	0.758436i
$560$	127.223	+	380.035i	0.227184	+	0.678635i
$561$	−262.017			−0.467054
$562$	−99.1539	+	243.024i	−0.176430	+	0.432428i
$563$	274.938	+	274.938i	0.488345	+	0.488345i	0.907784	−	0.419439i	$-0.137773\pi$
$563$	274.938	+	274.938i	0.488345	+	0.488345i	−0.419439	+	0.907784i	$0.637773\pi$
$564$	4.88491	+	459.486i	0.00866118	+	0.814691i
$565$	−227.471	+	70.8084i	−0.402603	+	0.125325i
$566$	−1007.84	+	423.750i	−1.78063	+	0.748676i
$567$			33.5347i			0.0591441i
$568$	−82.3907	−	190.269i	−0.145054	−	0.334981i
$569$			985.556i			1.73208i	0.499971	+	0.866042i	$0.333344\pi$
$569$			985.556i			1.73208i	−0.499971	+	0.866042i	$0.666656\pi$
$570$	41.2145	−	480.271i	0.0723061	−	0.842580i
$571$	246.409	+	246.409i	0.431539	+	0.431539i	0.889152	−	0.457613i	$-0.151295\pi$
$571$	246.409	+	246.409i	0.431539	+	0.431539i	−0.457613	+	0.889152i	$0.651295\pi$
$572$	406.190	+	397.645i	0.710123	+	0.695183i
$573$	67.3511	−	67.3511i	0.117541	−	0.117541i
$574$	−705.983	−	288.041i	−1.22994	−	0.501814i
$575$	−62.0692	−	90.0374i	−0.107946	−	0.156587i
$576$	243.829	+	228.752i	0.423314	+	0.397139i
$577$		−	374.750i		−	0.649481i	−0.945803	−	0.324740i	$-0.894723\pi$
$577$		−	374.750i		−	0.649481i	0.945803	−	0.324740i	$-0.105277\pi$
$578$	127.892	+	52.1801i	0.221267	+	0.0902770i
$579$	511.114	−	511.114i	0.882753	−	0.882753i
$580$	−507.824	+	164.020i	−0.875559	+	0.282793i
$581$	581.051	−	581.051i	1.00009	−	1.00009i
$582$	58.7242	−	24.6909i	0.100901	−	0.0424241i
$583$		−	276.973i		−	0.475083i
$584$	99.2316	+	229.161i	0.169917	+	0.392399i
$585$	189.830	−	361.429i	0.324496	−	0.617827i
$586$	242.388	+	576.491i	0.413632	+	0.983773i
$587$	558.540	−	558.540i	0.951517	−	0.951517i	−0.0473610	−	0.998878i	$-0.515081\pi$
$587$	558.540	−	558.540i	0.951517	−	0.951517i	0.998878	+	0.0473610i	$0.0150811\pi$
$588$	1.97520	+	185.792i	0.00335919	+	0.315973i
$589$	578.712	+	578.712i	0.982532	+	0.982532i
$590$	579.889	−	488.228i	0.982863	−	0.827506i
$591$		−	452.645i		−	0.765897i
$592$	283.353	−	295.666i	0.478636	−	0.499435i
$593$			217.889i			0.367435i	0.982979	+	0.183717i	$0.0588131\pi$
$593$			217.889i			0.367435i	−0.982979	+	0.183717i	$0.941187\pi$
$594$	−465.368	−	189.870i	−0.783449	−	0.319647i
$595$	−110.406	−	354.679i	−0.185557	−	0.596099i
$596$	467.035	−	4.96516i	0.783616	−	0.00833081i
$597$	193.901	+	193.901i	0.324793	+	0.324793i
$598$	−52.9988	−	126.051i	−0.0886268	−	0.210788i
$599$	238.766			0.398607			0.199304	−	0.979938i	$-0.436132\pi$
$599$	238.766			0.398607			0.199304	+	0.979938i	$0.436132\pi$
$600$	−87.3912	−	378.686i	−0.145652	−	0.631144i
$601$			307.946i			0.512390i	0.966625	+	0.256195i	$0.0824688\pi$
$601$			307.946i			0.512390i	−0.966625	+	0.256195i	$0.917531\pi$
$602$	−105.337	−	250.531i	−0.174978	−	0.416164i
$603$	−30.9688	+	30.9688i	−0.0513579	+	0.0513579i
$604$	272.459	+	266.727i	0.451091	+	0.441601i
$605$	−183.007	+	56.9673i	−0.302490	+	0.0941609i
$606$	534.379	+	218.027i	0.881814	+	0.359780i
$607$	257.142			0.423627			0.211814	−	0.977310i	$-0.432063\pi$
$607$	257.142			0.423627			0.211814	+	0.977310i	$0.432063\pi$
$608$	323.157	+	725.047i	0.531508	+	1.19251i
$609$	259.745			0.426511
$610$	−275.735	+	232.151i	−0.452025	+	0.380575i
$611$	−653.366	+	653.366i	−1.06934	+	1.06934i
$612$	−221.444	−	216.785i	−0.361836	−	0.354224i
$613$	352.976	+	352.976i	0.575817	+	0.575817i	0.933748	−	0.357931i	$-0.116518\pi$
$613$	352.976	+	352.976i	0.575817	+	0.575817i	−0.357931	+	0.933748i	$0.616518\pi$
$614$	−88.1801	−	209.726i	−0.143616	−	0.341573i
$615$	654.615	+	343.817i	1.06442	+	0.559053i
$616$	338.824	+	134.056i	0.550039	+	0.217624i
$617$	−188.628			−0.305719			−0.152859	−	0.988248i	$-0.548848\pi$
$617$	−188.628			−0.305719			−0.152859	+	0.988248i	$0.548848\pi$
$618$	−169.259	+	71.1658i	−0.273882	+	0.115155i
$619$	−387.137	−	387.137i	−0.625424	−	0.625424i	0.321490	−	0.946913i	$-0.395817\pi$
$619$	−387.137	−	387.137i	−0.625424	−	0.625424i	−0.946913	+	0.321490i	$0.895817\pi$
$620$	587.405	+	300.594i	0.947427	+	0.484828i
$621$	85.4941	+	85.4941i	0.137672	+	0.137672i
$622$	−802.143	−	327.274i	−1.28962	−	0.526164i
$623$	427.779			0.686644
$624$	−10.3313	−	485.837i	−0.0165565	−	0.778585i
$625$	222.324	−	584.121i	0.355719	−	0.934593i
$626$	499.248	+	203.693i	0.797521	+	0.325388i
$627$	−309.905	−	309.905i	−0.494267	−	0.494267i
$628$	585.190	−	6.22130i	0.931831	−	0.00990652i
$629$	−268.404	+	268.404i	−0.426715	+	0.426715i
$630$	22.3755	−	260.741i	0.0355166	−	0.413874i
$631$	561.749			0.890252			0.445126	−	0.895468i	$-0.353159\pi$
$631$	561.749			0.890252			0.445126	+	0.895468i	$0.353159\pi$
$632$	−896.036	+	388.003i	−1.41778	+	0.613929i
$633$	−458.951			−0.725041
$634$	52.3103	−	21.9941i	0.0825083	−	0.0346910i
$635$	265.739	+	853.682i	0.418487	+	1.34438i
$636$	−165.641	+	169.201i	−0.260443	+	0.266040i
$637$	−264.188	+	264.188i	−0.414737	+	0.414737i
$638$	−183.294	+	449.251i	−0.287295	+	0.704156i
$639$			135.394i			0.211884i
$640$	427.600	+	476.192i	0.668125	+	0.744049i
$641$	−1009.43			−1.57477			−0.787387	−	0.616459i	$-0.788567\pi$
$641$	−1009.43			−1.57477			−0.787387	+	0.616459i	$0.788567\pi$
$642$	283.681	+	115.742i	0.441870	+	0.180283i
$643$	775.300	+	775.300i	1.20575	+	1.20575i	0.972389	+	0.233364i	$0.0749735\pi$
$643$	775.300	+	775.300i	1.20575	+	1.20575i	0.233364	+	0.972389i	$0.425027\pi$
$644$	−62.6363	−	61.3185i	−0.0972614	−	0.0952151i
$645$	78.3325	+	251.642i	0.121446	+	0.390142i
$646$	−285.175	−	678.255i	−0.441448	−	1.04993i
$647$			5.25109i			0.00811606i	0.999992	+	0.00405803i	$0.00129171\pi$
$647$			5.25109i			0.00811606i	−0.999992	+	0.00405803i	$0.998708\pi$
$648$	21.2802	+	49.1435i	0.0328398	+	0.0758387i
$649$		−	689.226i		−	1.06198i
$650$	421.206	−	658.262i	0.648009	−	1.01271i
$651$	−227.100	−	227.100i	−0.348847	−	0.348847i
$652$	7.79786	+	733.485i	0.0119599	+	1.12498i
$653$	−15.2963	+	15.2963i	−0.0234247	+	0.0234247i	−0.718722	−	0.695297i	$-0.755273\pi$
$653$	−15.2963	+	15.2963i	−0.0234247	+	0.0234247i	0.695297	+	0.718722i	$0.255273\pi$
$654$	269.886	−	661.485i	0.412670	−	1.01145i
$655$	−314.047	−	164.944i	−0.479461	−	0.251823i
$656$	−1217.37	+	25.8872i	−1.85574	+	0.0394622i
$657$		−	163.069i		−	0.248202i
$658$	−223.756	+	548.421i	−0.340054	+	0.833467i
$659$	−378.187	+	378.187i	−0.573880	+	0.573880i	−0.933211	−	0.359330i	$-0.883005\pi$
$659$	−378.187	+	378.187i	−0.573880	+	0.573880i	0.359330	+	0.933211i	$0.383005\pi$
$660$	−314.560	−	160.971i	−0.476607	−	0.243895i
$661$	−42.5546	+	42.5546i	−0.0643791	+	0.0643791i	−0.738563	−	0.674184i	$-0.764495\pi$
$661$	−42.5546	+	42.5546i	−0.0643791	+	0.0643791i	0.674184	+	0.738563i	$0.264495\pi$
$662$	178.142	+	423.689i	0.269097	+	0.640013i
$663$			450.420i			0.679366i
$664$	482.783	−	1220.22i	0.727083	−	1.83768i
$665$	288.917	−	550.087i	0.434462	−	0.827199i
$666$	−246.513	+	103.647i	−0.370139	+	0.155627i
$667$	82.5332	−	82.5332i	0.123738	−	0.123738i
$668$	142.240	−	145.297i	0.212934	−	0.217510i
$669$	495.475	+	495.475i	0.740620	+	0.740620i
$670$	−64.1336	+	53.9963i	−0.0957218	+	0.0805914i
$671$			327.724i			0.488412i
$672$	−126.814	−	284.525i	−0.188711	−	0.423400i
$673$			1181.74i			1.75593i	0.478727	+	0.877964i	$0.341098\pi$
$673$			1181.74i			1.75593i	−0.478727	+	0.877964i	$0.658902\pi$
$674$	250.363	−	613.636i	0.371459	−	0.910439i
$675$	−124.961	+	679.607i	−0.185128	+	1.00683i
$676$	210.674	−	215.201i	0.311648	−	0.318345i
$677$	−71.0492	−	71.0492i	−0.104947	−	0.104947i	0.652684	−	0.757631i	$-0.273643\pi$
$677$	−71.0492	−	71.0492i	−0.104947	−	0.104947i	−0.757631	+	0.652684i	$0.773643\pi$
$678$	170.702	−	71.7724i	0.251772	−	0.105859i
$679$	82.1141			0.120934
$680$	−386.865	−	449.704i	−0.568919	−	0.661329i
$681$			446.898i			0.656238i
$682$	553.046	−	232.531i	0.810917	−	0.340954i
$683$	246.349	−	246.349i	0.360687	−	0.360687i	−0.503379	−	0.864066i	$-0.667910\pi$
$683$	246.349	−	246.349i	0.360687	−	0.360687i	0.864066	+	0.503379i	$0.167910\pi$
$684$	−5.51041	−	518.322i	−0.00805616	−	0.757781i
$685$	−7.01641	−	22.5401i	−0.0102429	−	0.0329052i
$686$	−275.935	+	676.312i	−0.402238	+	0.985878i
$687$	−16.7977			−0.0244508
$688$	−313.346	−	300.297i	−0.455445	−	0.436478i
$689$	−476.130			−0.691045
$690$	54.7464	+	65.0246i	0.0793426	+	0.0942385i
$691$	−176.426	+	176.426i	−0.255320	+	0.255320i	−0.823148	−	0.567827i	$-0.807784\pi$
$691$	−176.426	+	176.426i	−0.255320	+	0.255320i	0.567827	+	0.823148i	$0.307784\pi$
$692$	−673.007	+	7.15491i	−0.972554	+	0.0103395i
$693$	−168.249	−	168.249i	−0.242783	−	0.242783i
$694$	−367.466	+	154.503i	−0.529489	+	0.222626i
$695$	237.694	−	452.561i	0.342006	−	0.651167i
$696$	380.644	−	164.827i	0.546903	−	0.236821i
$697$	1128.62			1.61926
$698$	103.644	+	246.505i	0.148487	+	0.353159i
$699$	−167.110	−	167.110i	−0.239070	−	0.239070i
$700$	85.3507	−	493.632i	0.121930	−	0.705189i
$701$	715.573	+	715.573i	1.02079	+	1.02079i	0.999779	+	0.0210094i	$0.00668799\pi$
$701$	715.573	+	715.573i	1.02079	+	1.02079i	0.0210094	+	0.999779i	$0.493312\pi$
$702$	−326.396	+	799.990i	−0.464951	+	1.13959i
$703$	−634.919			−0.903156
$704$	581.599	−	18.5550i	0.826135	−	0.0263565i
$705$	267.084	−	508.517i	0.378842	−	0.721301i
$706$	175.435	−	429.989i	0.248492	−	0.609049i
$707$	526.046	+	526.046i	0.744053	+	0.744053i
$708$	−412.186	+	421.044i	−0.582183	+	0.594695i
$709$	−306.482	+	306.482i	−0.432273	+	0.432273i	−0.889401	−	0.457128i	$-0.848878\pi$
$709$	−306.482	+	306.482i	−0.432273	+	0.432273i	0.457128	+	0.889401i	$0.348878\pi$
$710$	−22.1599	+	258.228i	−0.0312111	+	0.363702i
$711$	637.611			0.896780
$712$	626.890	−	271.457i	0.880464	−	0.381260i
$713$	−144.320			−0.202413
$714$	111.909	+	266.163i	0.156736	+	0.372777i
$715$	−211.185	−	678.427i	−0.295363	−	0.948849i
$716$	−970.951	+	10.3224i	−1.35608	+	0.0144168i
$717$	308.430	−	308.430i	0.430167	−	0.430167i
$718$	−1299.69	−	530.272i	−1.81015	−	0.738541i
$719$		−	87.8746i		−	0.122218i	−0.998131	−	0.0611089i	$-0.980536\pi$
$719$		−	87.8746i		−	0.122218i	0.998131	−	0.0611089i	$-0.0194637\pi$
$720$	−132.669	−	396.302i	−0.184262	−	0.550419i
$721$	−236.676			−0.328260
$722$	192.173	−	471.013i	0.266168	−	0.652373i
$723$	−175.888	−	175.888i	−0.243275	−	0.243275i
$724$	−815.534	+	8.67014i	−1.12643	+	0.0119753i
$725$	656.070	+	120.633i	0.904925	+	0.166391i
$726$	137.334	−	57.7428i	0.189166	−	0.0795356i
$727$		−	370.209i		−	0.509228i	−0.967043	−	0.254614i	$-0.918052\pi$
$727$		−	370.209i		−	0.509228i	0.967043	−	0.254614i	$-0.0819484\pi$
$728$	230.449	−	582.454i	0.316551	−	0.800074i
$729$		−	518.360i		−	0.711056i
$730$	26.6894	−	311.011i	0.0365608	−	0.426042i
$731$	284.454	+	284.454i	0.389130	+	0.389130i
$732$	195.993	−	200.205i	0.267750	−	0.273504i
$733$	626.686	−	626.686i	0.854960	−	0.854960i	−0.135779	−	0.990739i	$-0.543354\pi$
$733$	626.686	−	626.686i	0.854960	−	0.854960i	0.990739	+	0.135779i	$0.0433536\pi$
$734$	−233.523	−	95.2772i	−0.318151	−	0.129805i
$735$	107.995	−	205.618i	0.146932	−	0.279753i
$736$	−130.702	−	50.1121i	−0.177584	−	0.0680871i
$737$			76.2259i			0.103427i
$738$	736.201	+	300.370i	0.997562	+	0.407005i
$739$	−388.772	+	388.772i	−0.526078	+	0.526078i	−0.919401	−	0.393322i	$-0.871326\pi$
$739$	−388.772	+	388.772i	−0.526078	+	0.526078i	0.393322	+	0.919401i	$0.371326\pi$
$740$	−487.122	+	157.334i	−0.658273	+	0.212613i
$741$	−532.741	+	532.741i	−0.718949	+	0.718949i
$742$	−281.356	+	118.297i	−0.379185	+	0.159430i
$743$		−	121.878i		−	0.164035i	−0.996631	−	0.0820173i	$-0.973864\pi$
$743$		−	121.878i		−	0.164035i	0.996631	−	0.0820173i	$-0.0261363\pi$
$744$	−476.915	−	188.693i	−0.641015	−	0.253619i
$745$	−516.872	−	271.472i	−0.693788	−	0.364392i
$746$	454.790	+	1081.66i	0.609638	+	1.44995i
$747$	−605.921	+	605.921i	−0.811139	+	0.811139i
$748$	−539.322	+	5.73367i	−0.721019	+	0.00766533i
$749$	279.257	+	279.257i	0.372840	+	0.372840i
$750$	−128.382	+	468.529i	−0.171176	+	0.624705i
$751$			914.610i			1.21786i	0.793225	+	0.608928i	$0.208400\pi$
$751$			914.610i			1.21786i	−0.793225	+	0.608928i	$0.791600\pi$
$752$	20.1097	+	945.674i	0.0267416	+	1.25755i
$753$			399.991i			0.531196i
$754$	772.284	+	315.092i	1.02425	+	0.417893i
$755$	−141.656	−	455.067i	−0.187624	−	0.602737i
$756$	5.88786	+	553.826i	0.00778818	+	0.732574i
$757$	129.143	+	129.143i	0.170599	+	0.170599i	0.787242	−	0.616644i	$-0.211508\pi$
$757$	129.143	+	129.143i	0.170599	+	0.170599i	−0.616644	+	0.787242i	$0.711508\pi$
$758$	−128.885	−	306.538i	−0.170033	−	0.404403i
$759$	77.2849			0.101825
$760$	74.3240	−	989.466i	0.0977948	−	1.30193i
$761$		−	352.217i		−	0.462835i	−0.972855	−	0.231417i	$-0.925664\pi$
$761$		−	352.217i		−	0.462835i	0.972855	−	0.231417i	$-0.0743363\pi$
$762$	−269.356	−	640.631i	−0.353486	−	0.840723i
$763$	651.169	−	651.169i	0.853433	−	0.853433i
$764$	137.158	−	140.106i	0.179526	−	0.183385i
$765$	115.132	+	369.860i	0.150499	+	0.483477i
$766$	−471.345	−	192.308i	−0.615332	−	0.251055i
$767$	−1184.81			−1.54473
$768$	−366.392	−	336.485i	−0.477072	−	0.438131i
$769$	105.447			0.137122			0.0685611	−	0.997647i	$-0.478159\pi$
$769$	105.447			0.137122			0.0685611	+	0.997647i	$0.478159\pi$
$770$	−293.353	−	348.427i	−0.380978	−	0.452503i
$771$	−618.434	+	618.434i	−0.802120	+	0.802120i
$772$	1040.87	−	1063.23i	1.34827	−	1.37725i
$773$	−124.080	−	124.080i	−0.160518	−	0.160518i	0.622278	−	0.782796i	$-0.286207\pi$
$773$	−124.080	−	124.080i	−0.160518	−	0.160518i	−0.782796	+	0.622278i	$0.786207\pi$
$774$	109.845	+	261.254i	0.141919	+	0.337537i
$775$	−468.142	−	679.085i	−0.604054	−	0.876239i
$776$	120.334	−	52.1074i	0.155070	−	0.0671487i
$777$	249.157			0.320665
$778$	84.0045	−	35.3201i	0.107975	−	0.0453986i
$779$	1334.90	+	1334.90i	1.71360	+	1.71360i
$780$	−276.716	+	540.744i	−0.354764	+	0.693261i
$781$	166.627	+	166.627i	0.213351	+	0.213351i
$782$	120.131	+	49.0135i	0.153620	+	0.0626771i
$783$	−737.512			−0.941905
$784$	8.13131	+	382.382i	0.0103716	+	0.487732i
$785$	−647.635	−	340.151i	−0.825013	−	0.433314i
$786$	255.292	+	104.159i	0.324799	+	0.132518i
$787$	−615.831	−	615.831i	−0.782505	−	0.782505i	0.197748	−	0.980253i	$-0.436637\pi$
$787$	−615.831	−	615.831i	−0.782505	−	0.782505i	−0.980253	+	0.197748i	$0.936637\pi$
$788$	−9.90513	−	931.700i	−0.0125700	−	1.18236i
$789$	273.715	−	273.715i	0.346914	−	0.346914i
$790$	1216.08	+	104.358i	1.53934	+	0.132098i
$791$	238.693			0.301761
$792$	−353.326	−	139.794i	−0.446119	−	0.176508i
$793$	563.373			0.710433
$794$	273.976	−	115.195i	0.345058	−	0.145081i
$795$	282.603	−	87.9704i	0.355476	−	0.110655i
$796$	403.359	+	394.873i	0.506733	+	0.496072i
$797$	−56.7101	+	56.7101i	−0.0711545	+	0.0711545i	−0.741788	−	0.670634i	$-0.766022\pi$
$797$	−56.7101	+	56.7101i	−0.0711545	+	0.0711545i	0.670634	+	0.741788i	$0.266022\pi$
$798$	−182.446	+	447.171i	−0.228629	+	0.560365i
$799$		−	876.735i		−	1.09729i
$800$	−188.168	−	777.556i	−0.235210	−	0.971945i
$801$	−446.089			−0.556915
$802$	460.017	+	187.687i	0.573588	+	0.234024i
$803$	−200.686	−	200.686i	−0.249921	−	0.249921i
$804$	45.5862	−	46.5659i	0.0566993	−	0.0579178i
$805$	32.5656	+	104.616i	0.0404542	+	0.129958i
$806$	−399.731	−	950.711i	−0.495944	−	1.17954i
$807$		−	132.300i		−	0.163940i
$808$	1104.71	+	437.081i	1.36721	+	0.540942i
$809$		−	556.339i		−	0.687688i	−0.939027	−	0.343844i	$-0.888271\pi$
$809$		−	556.339i		−	0.687688i	0.939027	−	0.343844i	$-0.111729\pi$
$810$	5.72354	−	66.6962i	0.00706610	−	0.0823410i
$811$	−993.474	−	993.474i	−1.22500	−	1.22500i	−0.965833	−	0.259166i	$-0.916552\pi$
$811$	−993.474	−	993.474i	−1.22500	−	1.22500i	−0.259166	−	0.965833i	$-0.583448\pi$
$812$	534.646	−	5.68395i	0.658431	−	0.00699994i
$813$	436.815	−	436.815i	0.537288	−	0.537288i
$814$	−175.822	+	430.937i	−0.215998	+	0.529407i
$815$	426.350	−	811.755i	0.523129	−	0.996018i
$816$	332.897	+	319.034i	0.407963	+	0.390973i
$817$			672.886i			0.823606i
$818$	−343.989	+	843.111i	−0.420525	+	1.03070i
$819$	−289.227	+	289.227i	−0.353147	+	0.353147i
$820$	1354.95	+	693.371i	1.65238	+	0.845574i
$821$	620.009	−	620.009i	0.755188	−	0.755188i	−0.220255	−	0.975442i	$-0.570689\pi$
$821$	620.009	−	620.009i	0.755188	−	0.755188i	0.975442	+	0.220255i	$0.0706889\pi$
$822$	7.11192	+	16.9148i	0.00865197	+	0.0205776i
$823$		−	646.223i		−	0.785204i	−0.919708	−	0.392602i	$-0.871575\pi$
$823$		−	646.223i		−	0.785204i	0.919708	−	0.392602i	$-0.128425\pi$
$824$	−346.837	+	150.188i	−0.420918	+	0.182267i
$825$	250.694	+	363.656i	0.303872	+	0.440796i
$826$	−700.131	+	294.373i	−0.847616	+	0.356384i
$827$	−836.004	+	836.004i	−1.01089	+	1.01089i	−0.0109471	+	0.999940i	$0.503485\pi$
$827$	−836.004	+	836.004i	−1.01089	+	1.01089i	−0.999940	+	0.0109471i	$0.996515\pi$
$828$	65.3173	+	63.9431i	0.0788856	+	0.0772259i
$829$	−234.984	−	234.984i	−0.283454	−	0.283454i	0.551031	−	0.834485i	$-0.314235\pi$
$829$	−234.984	−	234.984i	−0.283454	−	0.283454i	−0.834485	+	0.551031i	$0.814235\pi$
$830$	−1254.81	+	1056.46i	−1.51181	+	1.27285i
$831$		−	187.711i		−	0.225886i
$832$	−31.8968	−	999.795i	−0.0383375	−	1.20168i
$833$		−	354.506i		−	0.425578i
$834$	−150.100	+	367.891i	−0.179975	+	0.441116i
$835$	−242.677	+	75.5420i	−0.290631	+	0.0904694i
$836$	−644.674	−	631.111i	−0.771141	−	0.754917i
$837$	644.819	+	644.819i	0.770393	+	0.770393i
$838$	772.157	−	324.657i	0.921428	−	0.387419i
$839$	−219.575			−0.261711			−0.130855	−	0.991401i	$-0.541772\pi$
$839$	−219.575			−0.261711			−0.130855	+	0.991401i	$0.541772\pi$
$840$	−29.1664	+	388.289i	−0.0347220	+	0.462249i
$841$		−	129.031i		−	0.153425i
$842$	−925.234	+	389.019i	−1.09885	+	0.462018i
$843$	−180.326	+	180.326i	−0.213909	+	0.213909i
$844$	−944.681	+	10.0431i	−1.11929	+	0.0118994i
$845$	−359.433	+	111.887i	−0.425365	+	0.132410i
$846$	233.333	−	571.895i	0.275807	−	0.675998i
$847$	192.035			0.226723
$848$	−337.245	+	351.900i	−0.397695	+	0.414976i
$849$	−1062.25			−1.25117
$850$	159.049	+	724.254i	0.187117	+	0.852063i
$851$	79.1687	−	79.1687i	0.0930302	−	0.0930302i
$852$	−2.14158	−	201.442i	−0.00251359	−	0.236434i
$853$	47.0723	+	47.0723i	0.0551844	+	0.0551844i	0.734160	−	0.678976i	$-0.237576\pi$
$853$	47.0723	+	47.0723i	0.0551844	+	0.0551844i	−0.678976	+	0.734160i	$0.737576\pi$
$854$	332.910	−	139.973i	0.389824	−	0.163903i
$855$	−301.283	+	573.632i	−0.352378	+	0.670915i
$856$	586.446	+	232.029i	0.685101	+	0.271062i
$857$	−1620.86			−1.89132			−0.945661	−	0.325154i	$-0.894584\pi$
$857$	−1620.86			−1.89132			−0.945661	+	0.325154i	$0.894584\pi$
$858$	214.060	+	509.114i	0.249487	+	0.593373i
$859$	−317.610	−	317.610i	−0.369744	−	0.369744i	0.497640	−	0.867384i	$-0.334200\pi$
$859$	−317.610	−	317.610i	−0.369744	−	0.369744i	−0.867384	+	0.497640i	$0.834200\pi$
$860$	166.742	+	516.252i	0.193886	+	0.600293i
$861$	−523.844	−	523.844i	−0.608414	−	0.608414i
$862$	−60.3545	+	147.928i	−0.0700168	+	0.171610i
$863$	−1407.45			−1.63088			−0.815439	−	0.578842i	$-0.803505\pi$
$863$	−1407.45			−1.63088			−0.815439	+	0.578842i	$0.803505\pi$
$864$	360.071	+	807.870i	0.416749	+	0.935035i
$865$	744.823	+	391.197i	0.861068	+	0.452250i
$866$	1.19011	−	2.91693i	0.00137426	−	0.00336828i
$867$	94.8970	+	94.8970i	0.109454	+	0.109454i
$868$	−472.419	−	462.480i	−0.544262	−	0.532811i
$869$	784.699	−	784.699i	0.902991	−	0.902991i
$870$	−516.600	−	44.3321i	−0.593793	−	0.0509564i
$871$	131.036			0.150443
$872$	541.044	−	1367.47i	0.620463	−	1.56820i
$873$	−85.6288			−0.0980857
$874$	84.1157	+	200.059i	0.0962422	+	0.228900i
$875$	−386.627	+	492.585i	−0.441859	+	0.562955i
$876$	2.57932	+	242.617i	0.00294443	+	0.276960i
$877$	−507.991	+	507.991i	−0.579237	+	0.579237i	−0.934693	−	0.355456i	$-0.884326\pi$
$877$	−507.991	+	507.991i	−0.579237	+	0.579237i	0.355456	+	0.934693i	$0.384326\pi$
$878$	462.487	+	188.695i	0.526751	+	0.214914i
$879$			607.614i			0.691256i
$880$	−650.997	−	324.450i	−0.739769	−	0.368693i
$881$	1167.86			1.32561			0.662803	−	0.748793i	$-0.269367\pi$
$881$	1167.86			1.32561			0.662803	+	0.748793i	$0.269367\pi$
$882$	94.3477	−	231.245i	0.106970	−	0.262182i
$883$	641.739	+	641.739i	0.726771	+	0.726771i	0.969975	−	0.243204i	$-0.0781984\pi$
$883$	641.739	+	641.739i	0.726771	+	0.726771i	−0.243204	+	0.969975i	$0.578198\pi$
$884$	9.85644	+	927.120i	0.0111498	+	1.04878i
$885$	703.236	−	218.907i	0.794616	−	0.247353i
$886$	−315.569	+	132.682i	−0.356172	+	0.149754i
$887$			172.729i			0.194734i	0.995249	+	0.0973670i	$0.0310420\pi$
$887$			172.729i			0.194734i	−0.995249	+	0.0973670i	$0.968958\pi$
$888$	365.127	−	158.108i	0.411179	−	0.178049i
$889$		−	895.796i		−	1.00764i
$890$	−850.798	−	73.0113i	−0.955953	−	0.0820351i
$891$	−43.0372	−	43.0372i	−0.0483021	−	0.0483021i
$892$	1030.70	+	1009.02i	1.15549	+	1.13118i
$893$	1036.97	−	1036.97i	1.16122	−	1.16122i
$894$	420.170	+	171.429i	0.469989	+	0.191755i
$895$	1074.56	+	564.381i	1.20063	+	0.630594i
$896$	−267.253	−	582.876i	−0.298274	−	0.650531i
$897$		−	132.856i		−	0.148112i
$898$	−550.179	−	224.473i	−0.612671	−	0.249970i
$899$	622.487	−	622.487i	0.692421	−	0.692421i
$900$	−89.0039	+	514.761i	−0.0988932	+	0.571956i
$901$	319.453	−	319.453i	0.354554	−	0.354554i
$902$	1275.69	−	536.372i	1.41430	−	0.594647i
$903$		−	264.056i		−	0.292421i
$904$	349.793	−	151.468i	0.386939	−	0.167553i
$905$	902.559	+	474.043i	0.997303	+	0.523804i
$906$	143.584	+	341.497i	0.158481	+	0.376929i
$907$	83.4405	−	83.4405i	0.0919962	−	0.0919962i	−0.659611	−	0.751607i	$-0.729279\pi$
$907$	83.4405	−	83.4405i	0.0919962	−	0.0919962i	0.751607	+	0.659611i	$0.229279\pi$
$908$	9.77938	+	919.872i	0.0107702	+	1.01307i
$909$	−548.562	−	548.562i	−0.603478	−	0.603478i
$910$	−598.962	+	504.287i	−0.658200	+	0.554162i
$911$		−	692.752i		−	0.760430i	−0.924898	−	0.380215i	$-0.875850\pi$
$911$		−	692.752i		−	0.760430i	0.924898	−	0.380215i	$-0.124150\pi$
$912$	16.3970	+	771.083i	0.0179792	+	0.845486i
$913$			1491.40i			1.63351i
$914$	668.699	+	272.829i	0.731618	+	0.298500i
$915$	−334.386	+	104.090i	−0.365449	+	0.113759i
$916$	−34.5755	+	0.367581i	−0.0377462	+	0.000401289i
$917$	251.310	+	251.310i	0.274057	+	0.274057i
$918$	−317.752	−	755.733i	−0.346135	−	0.823239i
$919$	−23.1013			−0.0251374			−0.0125687	−	0.999921i	$-0.504001\pi$
$919$	−23.1013			−0.0251374			−0.0125687	+	0.999921i	$0.504001\pi$
$920$	114.110	+	132.645i	0.124033	+	0.144180i
$921$		−	221.048i		−	0.240009i
$922$	−182.526	−	434.116i	−0.197968	−	0.470842i
$923$	286.440	−	286.440i	0.310336	−	0.310336i
$924$	252.985	+	247.662i	0.273793	+	0.268033i
$925$	629.325	+	115.716i	0.680352	+	0.125098i
$926$	1319.27	+	538.261i	1.42470	+	0.581276i
$927$	246.806			0.266241
$928$	779.891	−	347.601i	0.840400	−	0.374570i
$929$	862.326			0.928231			0.464115	−	0.885775i	$-0.346372\pi$
$929$	862.326			0.928231			0.464115	+	0.885775i	$0.346372\pi$
$930$	412.912	+	490.432i	0.443991	+	0.527347i
$931$	419.298	−	419.298i	0.450374	−	0.450374i
$932$	−347.627	−	340.313i	−0.372990	−	0.365143i
$933$	−595.195	−	595.195i	−0.637937	−	0.637937i
$934$	−225.412	−	536.115i	−0.241340	−	0.573998i
$935$	596.873	+	313.490i	0.638367	+	0.335283i
$936$	−240.313	+	607.384i	−0.256745	+	0.648915i
$937$	−968.975			−1.03412			−0.517062	−	0.855948i	$-0.672974\pi$
$937$	−968.975			−1.03412			−0.517062	+	0.855948i	$0.672974\pi$
$938$	77.4319	−	32.5566i	0.0825500	−	0.0347085i
$939$	370.445	+	370.445i	0.394510	+	0.394510i
$940$	538.623	−	1052.55i	0.573003	−	1.11973i
$941$	165.112	+	165.112i	0.175465	+	0.175465i	0.789375	−	0.613911i	$-0.210405\pi$
$941$	165.112	+	165.112i	0.175465	+	0.175465i	−0.613911	+	0.789375i	$0.710405\pi$
$942$	526.469	+	214.799i	0.558884	+	0.228025i
$943$	−332.900			−0.353022
$944$	−839.207	+	875.674i	−0.888991	+	0.927621i
$945$	321.921	−	612.925i	0.340657	−	0.648598i
$946$	456.707	+	186.336i	0.482777	+	0.196973i
$947$	347.438	+	347.438i	0.366883	+	0.366883i	0.866339	−	0.499456i	$-0.166467\pi$
$947$	347.438	+	347.438i	0.366883	+	0.366883i	−0.499456	+	0.866339i	$0.666467\pi$
$948$	−948.650	+	10.0853i	−1.00069	+	0.0106385i
$949$	−344.989	+	344.989i	−0.363529	+	0.363529i
$950$	−668.505	+	1044.74i	−0.703690	+	1.09973i
$951$	55.1343			0.0579751
$952$	236.173	+	545.406i	0.248081	+	0.572906i
$953$	1222.59			1.28288			0.641442	−	0.767171i	$-0.278336\pi$
$953$	1222.59			1.28288			0.641442	+	0.767171i	$0.278336\pi$
$954$	293.398	−	123.361i	0.307545	−	0.129309i
$955$	−234.008	+	72.8432i	−0.245034	+	0.0762756i
$956$	628.106	−	641.604i	0.657014	−	0.671134i
$957$	−333.347	+	333.347i	−0.348325	+	0.348325i
$958$	585.539	−	1435.15i	0.611210	−	1.49806i
$959$			23.6520i			0.0246632i
$960$	203.656	+	587.527i	0.212141	+	0.612008i
$961$	−127.502			−0.132676
$962$	740.801	+	302.247i	0.770064	+	0.314186i
$963$	−291.210	−	291.210i	−0.302398	−	0.302398i
$964$	−365.888	−	358.190i	−0.379552	−	0.371566i
$965$	−1775.84	+	552.792i	−1.84024	+	0.572842i
$966$	−33.0089	−	78.5076i	−0.0341707	−	0.0812708i
$967$			967.881i			1.00091i	0.865762	+	0.500455i	$0.166834\pi$
$967$			967.881i			1.00091i	−0.865762	+	0.500455i	$0.833166\pi$
$968$	281.418	−	121.860i	0.290721	−	0.125888i
$969$		−	714.871i		−	0.737741i
$970$	−163.314	−	14.0148i	−0.168365	−	0.0144483i
$971$	−84.0735	−	84.0735i	−0.0865844	−	0.0865844i	0.662488	−	0.749072i	$-0.269501\pi$
$971$	−84.0735	−	84.0735i	−0.0865844	−	0.0865844i	−0.749072	+	0.662488i	$0.769501\pi$
$972$	−10.0248	−	942.955i	−0.0103136	−	0.970118i
$973$	−362.154	+	362.154i	−0.372203	+	0.372203i
$974$	202.195	−	495.575i	0.207592	−	0.508804i
$975$	625.142	−	430.955i	0.641171	−	0.442005i
$976$	399.040	−	416.380i	0.408852	−	0.426619i
$977$		−	759.084i		−	0.776954i	−0.921458	−	0.388477i	$-0.873001\pi$
$977$		−	759.084i		−	0.776954i	0.921458	−	0.388477i	$-0.126999\pi$
$978$	−269.232	+	659.883i	−0.275289	+	0.674727i
$979$	−548.996	+	548.996i	−0.560772	+	0.560772i
$980$	217.791	−	425.597i	0.222236	−	0.434282i
$981$	−679.041	+	679.041i	−0.692192	+	0.692192i
$982$	−45.1220	−	107.317i	−0.0459491	−	0.109284i
$983$		−	278.089i		−	0.282899i	−0.989945	−	0.141449i	$-0.954824\pi$
$983$		−	278.089i		−	0.282899i	0.989945	−	0.141449i	$-0.0451762\pi$
$984$	−1100.09	−	435.252i	−1.11797	−	0.442329i
$985$	−541.566	+	1031.12i	−0.549813	+	1.04682i
$986$	−729.560	+	306.747i	−0.739919	+	0.311102i
$987$	−406.932	+	406.932i	−0.412292	+	0.412292i
$988$	−1084.91	+	1108.22i	−1.09809	+	1.12168i
$989$	−83.9029	−	83.9029i	−0.0848361	−	0.0848361i
$990$	305.909	+	363.341i	0.308999	+	0.367011i
$991$		−	722.074i		−	0.728632i	−0.931275	−	0.364316i	$-0.881303\pi$
$991$		−	722.074i		−	0.728632i	0.931275	−	0.364316i	$-0.118697\pi$
$992$	−985.786	−	377.958i	−0.993735	−	0.381006i
$993$			446.562i			0.449710i
$994$	98.0959	−	240.431i	0.0986881	−	0.241883i
$995$	−209.713	−	673.698i	−0.210767	−	0.677084i
$996$	891.917	−	911.085i	0.895499	−	0.914744i
$997$	−388.829	−	388.829i	−0.389999	−	0.389999i	0.484688	−	0.874687i	$-0.338933\pi$
$997$	−388.829	−	388.829i	−0.389999	−	0.389999i	−0.874687	+	0.484688i	$0.838933\pi$
$998$	−431.083	+	181.251i	−0.431946	+	0.181614i
$999$	−707.447			−0.708155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.k.a.19.20	yes	44
4.3	odd	2		320.3.k.a.239.7		44
5.2	odd	4		400.3.r.g.51.9		44
5.3	odd	4		400.3.r.g.51.14		44
5.4	even	2	inner	80.3.k.a.19.3	✓	44
8.3	odd	2		640.3.k.a.479.16		44
8.5	even	2		640.3.k.b.479.7		44
16.3	odd	4		640.3.k.b.159.16		44
16.5	even	4		320.3.k.a.79.16		44
16.11	odd	4	inner	80.3.k.a.59.3	yes	44
16.13	even	4		640.3.k.a.159.7		44
20.19	odd	2		320.3.k.a.239.16		44
40.19	odd	2		640.3.k.a.479.7		44
40.29	even	2		640.3.k.b.479.16		44
80.19	odd	4		640.3.k.b.159.7		44
80.27	even	4		400.3.r.g.251.9		44
80.29	even	4		640.3.k.a.159.16		44
80.43	even	4		400.3.r.g.251.14		44
80.59	odd	4	inner	80.3.k.a.59.20	yes	44
80.69	even	4		320.3.k.a.79.7		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.k.a.19.3	✓	44	5.4	even	2	inner
80.3.k.a.19.20	yes	44	1.1	even	1	trivial
80.3.k.a.59.3	yes	44	16.11	odd	4	inner
80.3.k.a.59.20	yes	44	80.59	odd	4	inner
320.3.k.a.79.7		44	80.69	even	4
320.3.k.a.79.16		44	16.5	even	4
320.3.k.a.239.7		44	4.3	odd	2
320.3.k.a.239.16		44	20.19	odd	2
400.3.r.g.51.9		44	5.2	odd	4
400.3.r.g.51.14		44	5.3	odd	4
400.3.r.g.251.9		44	80.27	even	4
400.3.r.g.251.14		44	80.43	even	4
640.3.k.a.159.7		44	16.13	even	4
640.3.k.a.159.16		44	80.29	even	4
640.3.k.a.479.7		44	40.19	odd	2
640.3.k.a.479.16		44	8.3	odd	2
640.3.k.b.159.7		44	80.19	odd	4
640.3.k.b.159.16		44	16.3	odd	4
640.3.k.b.479.7		44	8.5	even	2
640.3.k.b.479.16		44	40.29	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	80.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.85180 + 0.755534i) q^{2} +(1.37405 + 1.37405i) q^{3} +(2.85834 + 2.79820i) q^{4} +(-1.48609 - 4.77405i) q^{5} +(1.50632 + 3.58260i) q^{6} +5.00956i q^{7} +(3.17893 + 7.34128i) q^{8} -5.22398i q^{9} +O(q^{10})\)	\(q+(1.85180 + 0.755534i) q^{2} +(1.37405 + 1.37405i) q^{3} +(2.85834 + 2.79820i) q^{4} +(-1.48609 - 4.77405i) q^{5} +(1.50632 + 3.58260i) q^{6} +5.00956i q^{7} +(3.17893 + 7.34128i) q^{8} -5.22398i q^{9} +(0.855008 - 9.96338i) q^{10} +(-6.42909 - 6.42909i) q^{11} +(0.0826298 + 7.77235i) q^{12} +(-11.0519 + 11.0519i) q^{13} +(-3.78490 + 9.27672i) q^{14} +(4.51781 - 8.60173i) q^{15} +(0.340161 + 15.9964i) q^{16} -14.8302i q^{17} +(3.94690 - 9.67378i) q^{18} +(17.5407 - 17.5407i) q^{19} +(9.11098 - 17.8042i) q^{20} +(-6.88338 + 6.88338i) q^{21} +(-7.04800 - 16.7628i) q^{22} +4.37435i q^{23} +(-5.71926 + 14.4553i) q^{24} +(-20.5831 + 14.1894i) q^{25} +(-28.8160 + 12.1158i) q^{26} +(19.5444 - 19.5444i) q^{27} +(-14.0178 + 14.3190i) q^{28} +(-18.8676 - 18.8676i) q^{29} +(14.8650 - 12.5153i) q^{30} +32.9924i q^{31} +(-11.4559 + 29.8791i) q^{32} -17.6678i q^{33} +(11.2048 - 27.4627i) q^{34} +(23.9159 - 7.44468i) q^{35} +(14.6177 - 14.9319i) q^{36} +(-18.0984 - 18.0984i) q^{37} +(45.7346 - 19.2293i) q^{38} -30.3717 q^{39} +(30.3234 - 26.0862i) q^{40} +76.1027i q^{41} +(-17.9473 + 7.54602i) q^{42} +(-19.1807 + 19.1807i) q^{43} +(-0.386620 - 36.3664i) q^{44} +(-24.9395 + 7.76333i) q^{45} +(-3.30497 + 8.10042i) q^{46} +59.1180 q^{47} +(-21.5124 + 22.4472i) q^{48} +23.9043 q^{49} +(-48.8363 + 10.7247i) q^{50} +(20.3775 - 20.3775i) q^{51} +(-62.5155 + 0.664617i) q^{52} +(21.5406 + 21.5406i) q^{53} +(50.9589 - 21.4259i) q^{54} +(-21.1385 + 40.2470i) q^{55} +(-36.7766 + 15.9251i) q^{56} +48.2036 q^{57} +(-20.6839 - 49.1941i) q^{58} +(53.6021 + 53.6021i) q^{59} +(36.9828 - 11.9449i) q^{60} +(-25.4876 - 25.4876i) q^{61} +(-24.9269 + 61.0955i) q^{62} +26.1699 q^{63} +(-43.7888 + 46.6749i) q^{64} +(69.1865 + 36.3381i) q^{65} +(13.3486 - 32.7172i) q^{66} +(-5.92820 - 5.92820i) q^{67} +(41.4980 - 42.3898i) q^{68} +(-6.01056 + 6.01056i) q^{69} +(49.9122 + 4.28322i) q^{70} -25.9177 q^{71} +(38.3507 - 16.6067i) q^{72} +31.2154 q^{73} +(-19.8407 - 47.1886i) q^{74} +(-47.7790 - 8.78525i) q^{75} +(99.2197 - 1.05483i) q^{76} +(32.2069 - 32.2069i) q^{77} +(-56.2423 - 22.9469i) q^{78} +122.054i q^{79} +(75.8620 - 25.3961i) q^{80} +6.69413 q^{81} +(-57.4982 + 140.927i) q^{82} +(-115.988 - 115.988i) q^{83} +(-38.9361 + 0.413939i) q^{84} +(-70.8003 + 22.0391i) q^{85} +(-50.0105 + 21.0271i) q^{86} -51.8499i q^{87} +(26.7601 - 67.6354i) q^{88} -85.3925i q^{89} +(-52.0485 - 4.46655i) q^{90} +(-55.3652 - 55.3652i) q^{91} +(-12.2403 + 12.5033i) q^{92} +(-45.3332 + 45.3332i) q^{93} +(109.475 + 44.6657i) q^{94} +(-109.807 - 57.6731i) q^{95} +(-56.7963 + 25.3144i) q^{96} -16.3915i q^{97} +(44.2659 + 18.0605i) q^{98} +(-33.5855 + 33.5855i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 44 q - 4 q^{4} - 2 q^{5} - 4 q^{6} - 20 q^{10} - 4 q^{11} + 4 q^{14} - 32 q^{16} - 36 q^{19} + 40 q^{20} + 32 q^{21} + 16 q^{24} - 56 q^{26} - 4 q^{29} - 160 q^{30} - 192 q^{34} + 212 q^{36} - 8 q^{39} - 184 q^{40} + 224 q^{44} + 30 q^{45} + 124 q^{46} - 148 q^{49} + 100 q^{50} + 128 q^{51} + 24 q^{54} - 260 q^{55} + 360 q^{56} - 68 q^{59} - 80 q^{60} + 28 q^{61} - 16 q^{64} - 20 q^{65} + 448 q^{66} + 128 q^{69} + 396 q^{70} - 264 q^{71} + 480 q^{74} + 60 q^{75} - 464 q^{76} + 504 q^{80} - 116 q^{81} - 496 q^{84} + 48 q^{85} - 852 q^{86} + 144 q^{90} + 384 q^{91} - 340 q^{94} - 1128 q^{96} + 484 q^{99}+O(q^{100}) \) 44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 - 20 * q^10 - 4 * q^11 + 4 * q^14 - 32 * q^16 - 36 * q^19 + 40 * q^20 + 32 * q^21 + 16 * q^24 - 56 * q^26 - 4 * q^29 - 160 * q^30 - 192 * q^34 + 212 * q^36 - 8 * q^39 - 184 * q^40 + 224 * q^44 + 30 * q^45 + 124 * q^46 - 148 * q^49 + 100 * q^50 + 128 * q^51 + 24 * q^54 - 260 * q^55 + 360 * q^56 - 68 * q^59 - 80 * q^60 + 28 * q^61 - 16 * q^64 - 20 * q^65 + 448 * q^66 + 128 * q^69 + 396 * q^70 - 264 * q^71 + 480 * q^74 + 60 * q^75 - 464 * q^76 + 504 * q^80 - 116 * q^81 - 496 * q^84 + 48 * q^85 - 852 * q^86 + 144 * q^90 + 384 * q^91 - 340 * q^94 - 1128 * q^96 + 484 * q^99

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