LMFDB - Embedded newform 80.3.k.a.19.3

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			19.3
Character	$\chi$	$=$	80.19
Dual form			80.3.k.a.59.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85180 - 0.755534i) q^{2} +(-1.37405 - 1.37405i) q^{3} +(2.85834 + 2.79820i) q^{4} +(4.77405 + 1.48609i) q^{5} +(1.50632 + 3.58260i) q^{6} -5.00956i q^{7} +(-3.17893 - 7.34128i) q^{8} -5.22398i q^{9} +O(q^{10})$	\(q+(-1.85180 - 0.755534i) q^{2} +(-1.37405 - 1.37405i) q^{3} +(2.85834 + 2.79820i) q^{4} +(4.77405 + 1.48609i) q^{5} +(1.50632 + 3.58260i) q^{6} -5.00956i q^{7} +(-3.17893 - 7.34128i) q^{8} -5.22398i q^{9} +(-7.71779 - 6.35891i) 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} +(9.48744 + 17.6065i) 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} +(1.86717 + 19.3421i) q^{30} +32.9924i q^{31} +(11.4559 - 29.8791i) q^{32} +17.6678i q^{33} +(11.2048 - 27.4627i) q^{34} +(7.44468 - 23.9159i) q^{35} +(14.6177 - 14.9319i) q^{36} +(18.0984 + 18.0984i) q^{37} +(-45.7346 + 19.2293i) q^{38} -30.3717 q^{39} +(-4.26655 - 39.7718i) q^{40} +76.1027i q^{41} +(17.9473 - 7.54602i) q^{42} +(19.1807 - 19.1807i) q^{43} +(-0.386620 - 36.3664i) q^{44} +(7.76333 - 24.9395i) q^{45} +(-3.30497 + 8.10042i) q^{46} -59.1180 q^{47} +(21.5124 - 22.4472i) q^{48} +23.9043 q^{49} +(-27.3952 - 41.8271i) 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} +(11.1560 - 37.2284i) 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} +(-31.8554 + 38.6628i) q^{70} -25.9177 q^{71} +(-38.3507 + 16.6067i) q^{72} -31.2154 q^{73} +(-19.8407 - 47.1886i) q^{74} +(-8.78525 - 47.7790i) q^{75} +(99.2197 - 1.05483i) q^{76} +(-32.2069 + 32.2069i) q^{77} +(56.2423 + 22.9469i) q^{78} +122.054i q^{79} +(-22.1482 + 76.8730i) q^{80} +6.69413 q^{81} +(57.4982 - 140.927i) q^{82} +(115.988 + 115.988i) q^{83} +(-38.9361 + 0.413939i) q^{84} +(-22.0391 + 70.8003i) q^{85} +(-50.0105 + 21.0271i) q^{86} +51.8499i q^{87} +(-26.7601 + 67.6354i) q^{88} -85.3925i q^{89} +(-33.2188 + 40.3176i) 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	0.439988	−	0.898004i	$-0.354983\pi$
$3$	−1.37405	−	1.37405i	−0.458016	−	0.458016i	−0.898004	+	0.439988i	$0.854983\pi$
$4$	2.85834	+	2.79820i	0.714584	+	0.699550i
$5$	4.77405	+	1.48609i	0.954809	+	0.297219i
$5$	4.77405	+	1.48609i	0.954809	+	0.297219i
$6$	1.50632	+	3.58260i	0.251054	+	0.597101i
$7$		−	5.00956i		−	0.715652i	−0.933788	−	0.357826i	$-0.883518\pi$
$7$		−	5.00956i		−	0.715652i	0.933788	−	0.357826i	$-0.116482\pi$
$8$	−3.17893	−	7.34128i	−0.397367	−	0.917660i
$9$		−	5.22398i		−	0.580443i
$10$	−7.71779	−	6.35891i	−0.771779	−	0.635891i
$11$	−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	−0.140005	−	0.990151i	$-0.544712\pi$
$13$	11.0519	−	11.0519i	0.850146	−	0.850146i	0.990151	+	0.140005i	$0.0447117\pi$
$14$	−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	$0.143670\pi$
$17$			14.8302i			0.872367i	−0.899858	+	0.436184i	$0.856330\pi$
$18$	−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	$0.0235949\pi$
$20$	9.48744	+	17.6065i	0.474372	+	0.880324i
$21$	−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	$-0.969685\pi$
$23$		−	4.37435i		−	0.190189i	0.995468	−	0.0950945i	$-0.0303153\pi$
$24$	−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	$0.902168\pi$
$30$	1.86717	+	19.3421i	0.0622391	+	0.644735i
$31$			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
$35$	7.44468	−	23.9159i	0.212705	−	0.683311i
$36$	14.6177	−	14.9319i	0.406049	−	0.414775i
$37$	18.0984	+	18.0984i	0.489146	+	0.489146i	0.908037	−	0.418891i	$-0.137581\pi$
$37$	18.0984	+	18.0984i	0.489146	+	0.489146i	−0.418891	+	0.908037i	$0.637581\pi$
$38$	−45.7346	+	19.2293i	−1.20354	+	0.506035i
$39$	−30.3717			−0.778761
$40$	−4.26655	−	39.7718i	−0.106664	−	0.994295i
$41$			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	−0.447981	−	0.894043i	$-0.647857\pi$
$43$	19.1807	−	19.1807i	0.446062	−	0.446062i	0.894043	+	0.447981i	$0.147857\pi$
$44$	−0.386620	−	36.3664i	−0.00878681	−	0.826508i
$45$	7.76333	−	24.9395i	0.172518	−	0.554212i
$46$	−3.30497	+	8.10042i	−0.0718471	+	0.176096i
$47$	−59.1180			−1.25783			−0.628915	−	0.777474i	$-0.716501\pi$
$47$	−59.1180			−1.25783			−0.628915	+	0.777474i	$0.716501\pi$
$48$	21.5124	−	22.4472i	0.448175	−	0.467650i
$49$	23.9043			0.487842
$50$	−27.3952	−	41.8271i	−0.547904	−	0.836542i
$51$	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	0.474064	−	0.880491i	$-0.342787\pi$
$53$	−21.5406	−	21.5406i	−0.406427	−	0.406427i	−0.880491	+	0.474064i	$0.842787\pi$
$54$	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	$0.527933\pi$
$60$	11.1560	−	37.2284i	0.185933	−	0.620473i
$61$	−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	0.749962	−	0.661481i	$-0.230072\pi$
$67$	5.92820	+	5.92820i	0.0884806	+	0.0884806i	−0.661481	+	0.749962i	$0.730072\pi$
$68$	−41.4980	+	42.3898i	−0.610264	+	0.623380i
$69$	−6.01056	+	6.01056i	−0.0871096	+	0.0871096i
$70$	−31.8554	+	38.6628i	−0.455076	+	0.552325i
$71$	−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	$-0.568585\pi$
$73$	−31.2154			−0.427608			−0.213804	+	0.976877i	$0.568585\pi$
$74$	−19.8407	−	47.1886i	−0.268117	−	0.637684i
$75$	−8.78525	−	47.7790i	−0.117137	−	0.637053i
$76$	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	$0.719008\pi$
$80$	−22.1482	+	76.8730i	−0.276852	+	0.960913i
$81$	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	$0.200939\pi$
$83$	115.988	+	115.988i	1.39745	+	1.39745i	0.590169	+	0.807280i	$0.299061\pi$
$84$	−38.9361	+	0.413939i	−0.463525	+	0.00492785i
$85$	−22.0391	+	70.8003i	−0.259284	+	0.832945i
$86$	−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	$-0.159266\pi$
$90$	−33.2188	+	40.3176i	−0.369098	+	0.447974i
$91$	−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	$0.0269268\pi$
$97$			16.3915i			0.168984i	−0.996424	+	0.0844921i	$0.973073\pi$
$98$	−44.2659	−	18.0605i	−0.451693	−	0.184291i
$99$	−33.5855	+	33.5855i	−0.339247	+	0.339247i
$100$	19.1286	+	98.1534i	0.191286	+	0.981534i
$101$	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	$-0.926342\pi$
$103$		−	47.2447i		−	0.458687i	0.973346	−	0.229343i	$-0.0736579\pi$
$104$	−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	−0.917867	−	0.396888i	$-0.870090\pi$
$107$	−55.7447	+	55.7447i	−0.520979	+	0.520979i	0.396888	+	0.917867i	$0.370090\pi$
$108$	−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	$-0.569356\pi$
$110$	8.73640	+	90.5003i	0.0794218	+	0.822730i
$111$		−	49.7362i		−	0.448074i
$112$	80.1349	−	1.70406i	0.715490	−	0.0152148i
$113$			47.6474i			0.421658i	0.977523	+	0.210829i	$0.0676164\pi$
$113$			47.6474i			0.421658i	−0.977523	+	0.210829i	$0.932384\pi$
$114$	89.2635	+	36.4195i	0.783013	+	0.319469i
$115$	6.50068	−	20.8833i	0.0565277	−	0.181594i
$116$	−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
$120$	−48.7859	+	60.5108i	−0.406549	+	0.504257i
$121$		−	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
$125$	77.1778	+	98.3290i	0.617422	+	0.786632i
$126$	48.4614	+	19.7723i	0.384614	+	0.156923i
$127$	178.817			1.40801			0.704005	−	0.710195i	$-0.251393\pi$
$127$	178.817			1.40801			0.704005	+	0.710195i	$0.251393\pi$
$128$	116.353	−	53.3486i	0.909004	−	0.416786i
$129$	−52.7103			−0.408607
$130$	−155.574	+	15.0183i	−1.19673	+	0.115525i
$131$	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	$-0.505485\pi$
$137$	−4.72138			−0.0344626			−0.0172313	+	0.999852i	$0.505485\pi$
$138$	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	$0.630125\pi$
$140$	88.2008	−	47.5280i	0.630006	−	0.339485i
$141$	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	$0.121842\pi$
$150$	−19.8301	+	95.1147i	−0.132201	+	0.634098i
$151$	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
$155$	−49.0298	+	157.508i	−0.316322	+	1.01618i
$156$	−86.8125	−	84.9860i	−0.556490	−	0.544782i
$157$	−103.454	+	103.454i	−0.658941	+	0.658941i	−0.955130	−	0.296188i	$-0.904284\pi$
$157$	−103.454	+	103.454i	−0.658941	+	0.658941i	0.296188	+	0.955130i	$0.404284\pi$
$158$	92.2164	−	226.021i	0.583648	−	1.43051i
$159$			59.1957i			0.372300i
$160$	99.0942	−	125.620i	0.619339	−	0.785124i
$161$	−21.9136			−0.136109
$162$	−12.3962	−	5.05765i	−0.0765198	−	0.0312200i
$163$	−129.670	−	129.670i	−0.795524	−	0.795524i	0.186862	−	0.982386i	$-0.440168\pi$
$163$	−129.670	−	129.670i	−0.795524	−	0.795524i	−0.982386	+	0.186862i	$0.940168\pi$
$164$	−212.951	+	217.527i	−1.29848	+	1.32638i
$165$	−26.2559	+	84.3467i	−0.159127	+	0.511192i
$166$	−127.154	−	302.420i	−0.765988	−	1.82181i
$167$			50.8326i			0.304387i	0.988351	+	0.152193i	$0.0486337\pi$
$167$			50.8326i			0.304387i	−0.988351	+	0.152193i	$0.951366\pi$
$168$	72.4146	+	28.6510i	0.431040	+	0.170542i
$169$		−	75.2890i		−	0.445497i
$170$	94.3041	−	114.457i	0.554730	−	0.673275i
$171$	−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	−0.273993	−	0.961732i	$-0.588345\pi$
$173$	118.979	−	118.979i	0.687738	−	0.687738i	0.961732	+	0.273993i	$0.0883446\pi$
$174$	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	$0.487186\pi$
$180$	91.9760	−	49.5623i	0.510978	−	0.275346i
$181$	−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
$190$	−246.916	+	23.8358i	−1.29956	+	0.125452i
$191$		−	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	$0.413937\pi$
$193$			371.977i			1.92734i	−0.267094	+	0.963671i	$0.586063\pi$
$194$	12.3843	−	30.3537i	0.0638367	−	0.156463i
$195$	−144.996	−	45.1352i	−0.743569	−	0.231462i
$196$	68.3264	+	66.8889i	0.348604	+	0.341270i
$197$	164.712	+	164.712i	0.836102	+	0.836102i	0.988343	−	0.152241i	$-0.0486490\pi$
$197$	164.712	+	164.712i	0.836102	+	0.836102i	−0.152241	+	0.988343i	$0.548649\pi$
$198$	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	$0.384629\pi$
$200$	38.7359	−	196.213i	0.193679	−	0.981065i
$201$		−	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
$205$	−113.096	+	363.318i	−0.551686	+	1.77228i
$206$	−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
$210$	96.8953	−	9.35373i	0.461406	−	0.0445416i
$211$	−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
$220$	52.1981	−	174.189i	0.237264	−	0.791770i
$221$	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	$-0.799725\pi$
$223$	−360.595			−1.61702			−0.808508	+	0.588485i	$0.799725\pi$
$224$	−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	0.251472	−	0.967865i	$-0.419085\pi$
$227$	−162.621	−	162.621i	−0.716392	−	0.716392i	−0.967865	+	0.251472i	$0.919085\pi$
$228$	−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	$0.256008\pi$
$230$	−27.8161	+	33.7603i	−0.120939	+	0.146784i
$231$	88.5078			0.383150
$232$	−78.5333	+	198.491i	−0.338506	+	0.855563i
$233$	121.619			0.521968			0.260984	−	0.965343i	$-0.415953\pi$
$233$	121.619			0.521968			0.260984	+	0.965343i	$0.415953\pi$
$234$	63.2929	+	150.534i	0.270483	+	0.643309i
$235$	−282.232	−	87.8549i	−1.20099	−	0.373850i
$236$	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	$-0.155601\pi$
$240$	136.060	−	75.1946i	0.566916	−	0.313311i
$241$	−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
$245$	114.120	+	35.5240i	0.465796	+	0.144996i
$246$	−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
$250$	−68.6269	−	240.396i	−0.274508	−	0.961585i
$251$	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	$-0.660436\pi$
$257$		−	450.082i		−	1.75129i	0.482953	−	0.875646i	$-0.339564\pi$
$258$	97.6091	+	39.8245i	0.378330	+	0.154358i
$259$	90.6652	−	90.6652i	0.350059	−	0.350059i
$260$	299.439	+	89.7309i	1.15169	+	0.345119i
$261$	−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	$0.123633\pi$
$263$			199.203i			0.757427i	−0.925514	+	0.378713i	$0.876367\pi$
$264$	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	$0.790390\pi$
$270$	275.121	−	26.5587i	1.01897	−	0.0983654i
$271$		−	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
$275$	−41.1056	−	223.555i	−0.149475	−	0.812927i
$276$	−33.9989	+	0.361451i	−0.123185	+	0.00130961i
$277$	68.3059	+	68.3059i	0.246592	+	0.246592i	0.819570	−	0.572979i	$-0.194212\pi$
$277$	68.3059	+	68.3059i	0.246592	+	0.246592i	−0.572979	+	0.819570i	$0.694212\pi$
$278$	−79.2518	−	188.491i	−0.285079	−	0.678024i
$279$	172.352			0.617749
$280$	−199.239	+	21.3736i	−0.711569	+	0.0763341i
$281$			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	$-0.333474\pi$
$283$	386.539	−	386.539i	1.36586	−	1.36586i	0.866246	−	0.499618i	$-0.166526\pi$
$284$	−74.0815	−	72.5229i	−0.260850	−	0.255362i
$285$	−230.126	−	71.6350i	−0.807461	−	0.251351i
$286$	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
$290$	25.6388	+	265.593i	0.0884098	+	0.915838i
$291$	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	0.220718	−	0.975338i	$-0.429160\pi$
$293$	−221.104	−	221.104i	−0.754620	−	0.754620i	−0.975338	+	0.220718i	$0.929160\pi$
$294$	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
$300$	108.584	−	161.151i	0.361946	−	0.537171i
$301$	−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	0.825870	−	0.563861i	$-0.190685\pi$
$307$	80.4368	+	80.4368i	0.262009	+	0.262009i	−0.563861	+	0.825870i	$0.690685\pi$
$308$	−182.180	+	1.93680i	−0.591492	+	0.00628830i
$309$	−64.9165	+	64.9165i	−0.210086	+	0.210086i
$310$	209.796	−	254.629i	0.676761	−	0.821383i
$311$	−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	$-0.641724\pi$
$313$	−269.601			−0.861346			−0.430673	+	0.902508i	$0.641724\pi$
$314$	269.739	−	113.413i	0.859040	−	0.361188i
$315$	−124.936	−	38.8909i	−0.396623	−	0.123463i
$316$	−341.533	+	348.873i	−1.08080	+	1.10403i
$317$	−20.0627	+	20.0627i	−0.0632894	+	0.0632894i	−0.738043	−	0.674754i	$-0.764250\pi$
$317$	−20.0627	+	20.0627i	−0.0632894	+	0.0632894i	0.674754	+	0.738043i	$0.264250\pi$
$318$	44.7244	−	109.619i	0.140643	−	0.344713i
$319$			242.602i			0.760509i
$320$	−278.413	+	157.754i	−0.870040	+	0.492981i
$321$	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
$325$	384.301	−	70.6625i	1.18247	−	0.217423i
$326$	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
$330$	112.348	−	136.356i	0.340447	−	0.413200i
$331$	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	$0.163606\pi$
$337$			331.372i			0.983301i	−0.870793	+	0.491650i	$0.836394\pi$
$338$	−56.8835	+	139.420i	−0.168294	+	0.412486i
$339$	65.4698	−	65.4698i	0.193126	−	0.193126i
$340$	−261.109	+	140.701i	−0.767966	+	0.413827i
$341$	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	−0.474241	−	0.880395i	$-0.657278\pi$
$347$	140.935	−	140.935i	0.406154	−	0.406154i	0.880395	+	0.474241i	$0.157278\pi$
$348$	−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	$0.688648\pi$
$350$	−209.535	+	137.238i	−0.598673	+	0.392108i
$351$			432.006i			1.23079i
$352$	−265.747	+	118.445i	−0.754962	+	0.336490i
$353$			232.200i			0.657791i	0.944366	+	0.328896i	$0.106676\pi$
$353$			232.200i			0.657791i	−0.944366	+	0.328896i	$0.893324\pi$
$354$	−111.293	+	272.777i	−0.314387	+	0.770558i
$355$	−123.732	−	38.5161i	−0.348542	−	0.108496i
$356$	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	$0.932361\pi$
$360$	−207.767	+	22.2884i	−0.577131	+	0.0619122i
$361$		−	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
$365$	−149.024	−	46.3889i	−0.408284	−	0.127093i
$366$	52.9195	−	129.705i	0.144589	−	0.354384i
$367$	126.106			0.343612			0.171806	−	0.985131i	$-0.445040\pi$
$367$	126.106			0.343612			0.171806	+	0.985131i	$0.445040\pi$
$368$	69.9737	−	1.48798i	0.190146	−	0.00404343i
$369$	397.559			1.07740
$370$	−24.5937	−	254.766i	−0.0664694	−	0.688556i
$371$	−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	$-0.961917\pi$
$373$	−414.853	−	414.853i	−1.11221	−	1.11221i	−0.119356	−	0.992852i	$-0.538083\pi$
$374$	−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	$0.820393\pi$
$380$	475.247	+	142.414i	1.25065	+	0.374774i
$381$	−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	$-0.392179\pi$
$383$	254.533			0.664577			0.332289	+	0.943178i	$0.392179\pi$
$384$	−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	$0.231347\pi$
$390$	234.402	+	193.131i	0.601032	+	0.495207i
$391$	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
$395$	−181.384	+	582.694i	−0.459201	+	1.47517i
$396$	−189.977	+	2.01970i	−0.479741	+	0.00510024i
$397$	−105.079	+	105.079i	−0.264682	+	0.264682i	−0.826953	−	0.562271i	$-0.809928\pi$
$397$	−105.079	+	105.079i	−0.264682	+	0.264682i	0.562271	+	0.826953i	$0.309928\pi$
$398$	−261.320	−	106.619i	−0.656584	−	0.267886i
$399$			241.479i			0.605211i
$400$	−219.977	+	334.081i	−0.549942	+	0.835203i
$401$	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
$405$	31.9581	+	9.94810i	0.0789089	+	0.0245632i
$406$	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	$0.812109\pi$
$410$	483.930	−	587.345i	1.18032	−	1.43255i
$411$	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	$0.0834139\pi$
$420$	−186.498	−	55.8865i	−0.444043	−	0.133063i
$421$	−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
$430$	−270.001	+	26.0643i	−0.627908	+	0.0606148i
$431$			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	$0.000578982\pi$
$433$			1.57519i			0.00363785i	−0.999998	+	0.00181892i	$0.999421\pi$
$434$	−306.062	−	124.873i	−0.705211	−	0.287726i
$435$	−77.0537	+	247.534i	−0.177135	+	0.569043i
$436$	−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	$0.408188\pi$
$440$	−228.266	+	283.127i	−0.518787	+	0.643469i
$441$		−	124.875i		−	0.283164i
$442$	−179.681	−	427.349i	−0.406518	−	0.966852i
$443$	121.031	−	121.031i	0.273208	−	0.273208i	−0.557182	−	0.830390i	$-0.688118\pi$
$443$	121.031	−	121.031i	0.273208	−	0.273208i	0.830390	+	0.557182i	$0.188118\pi$
$444$	139.172	−	142.163i	0.313450	−	0.320186i
$445$	126.901	−	407.668i	0.285171	−	0.916107i
$446$	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	$0.607336\pi$
$450$	−218.504	+	143.112i	−0.485564	+	0.318027i
$451$	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	$-0.629285\pi$
$457$	−361.107			−0.790169			−0.395085	+	0.918645i	$0.629285\pi$
$458$	15.9373	−	6.70092i	0.0347976	−	0.0146308i
$459$	−289.849	−	289.849i	−0.631479	−	0.631479i
$460$	77.0169	−	41.5014i	0.167428	−	0.0902203i
$461$	−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	$-0.779423\pi$
$463$	−712.425			−1.53871			−0.769357	+	0.638819i	$0.779423\pi$
$464$	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	0.892111	−	0.451816i	$-0.149224\pi$
$467$	205.618	+	205.618i	0.440295	+	0.440295i	−0.451816	+	0.892111i	$0.649224\pi$
$468$	−3.47195	−	326.580i	−0.00741870	−	0.697820i
$469$	29.6977	−	29.6977i	0.0633213	−	0.0633213i
$470$	456.260	+	375.926i	0.970767	+	0.799842i
$471$	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
$475$	609.933	−	112.150i	1.28407	−	0.236105i
$476$	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	$-0.299978\pi$
$480$	−308.768	+	36.4475i	−0.643266	+	0.0759322i
$481$	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
$485$	−24.3593	+	78.2537i	−0.0502253	+	0.161348i
$486$	−182.750	−	434.648i	−0.376028	−	0.894337i
$487$			267.618i			0.549523i	0.961512	+	0.274762i	$0.0885989\pi$
$487$			267.618i			0.549523i	−0.961512	+	0.274762i	$0.911401\pi$
$488$	−106.088	+	268.135i	−0.217394	+	0.549457i
$489$			356.347i			0.728725i
$490$	−184.488	−	152.005i	−0.376506	−	0.310214i
$491$	−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	$0.325276\pi$
$500$	−54.5442	+	497.016i	−0.109088	+	0.994032i
$501$	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	$-0.860139\pi$
$503$		−	427.936i		−	0.850767i	0.905013	−	0.425384i	$-0.139861\pi$
$504$	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	$0.973994\pi$
$510$	−286.847	+	27.6907i	−0.562446	+	0.0542954i
$511$			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
$515$	70.2101	−	225.549i	0.136330	−	0.437958i
$516$	−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
$520$	−486.708	−	392.401i	−0.935976	−	0.754617i
$521$		−	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	−0.557129	−	0.830426i	$-0.688097\pi$
$523$	142.934	−	142.934i	0.273296	−	0.273296i	0.830426	+	0.557129i	$0.188097\pi$
$524$	283.766	−	3.01679i	0.541539	−	0.00575723i
$525$	−239.352	+	44.0103i	−0.455908	+	0.0838291i
$526$	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
$530$	29.2713	+	303.221i	0.0552288	+	0.572115i
$531$	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
$540$	−529.536	−	158.682i	−0.980622	−	0.293856i
$541$	−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	0.443513	−	0.896268i	$-0.353732\pi$
$547$	−247.657	−	247.657i	−0.452754	−	0.452754i	−0.896268	+	0.443513i	$0.853732\pi$
$548$	−13.4953	−	13.2114i	−0.0246264	−	0.0241083i
$549$	−133.147	+	133.147i	−0.242526	+	0.242526i
$550$	−92.7840	+	445.036i	−0.168698	+	0.809156i
$551$	−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
$555$	73.9126	−	237.443i	0.133176	−	0.427825i
$556$	4.34738	+	408.925i	0.00781903	+	0.735476i
$557$	−252.575	+	252.575i	−0.453456	+	0.453456i	−0.896500	−	0.443044i	$-0.853899\pi$
$557$	−252.575	+	252.575i	−0.453456	+	0.453456i	0.443044	+	0.896500i	$0.353899\pi$
$558$	−319.162	−	130.218i	−0.571974	−	0.233365i
$559$		−	423.966i		−	0.758436i
$560$	385.100	+	110.953i	0.687679	+	0.198130i
$561$	−262.017			−0.467054
$562$	99.1539	−	243.024i	0.176430	−	0.432428i
$563$	−274.938	−	274.938i	−0.488345	−	0.488345i	0.419439	−	0.907784i	$-0.362227\pi$
$563$	−274.938	−	274.938i	−0.488345	−	0.488345i	−0.907784	+	0.419439i	$0.862227\pi$
$564$	4.88491	+	459.486i	0.00866118	+	0.814691i
$565$	−70.8084	+	227.471i	−0.125325	+	0.402603i
$566$	−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	$0.666656\pi$
$570$	372.025	+	306.522i	0.652676	+	0.537758i
$571$	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	$0.105277\pi$
$577$			374.750i			0.649481i	−0.945803	+	0.324740i	$0.894723\pi$
$578$	−127.892	−	52.1801i	−0.221267	−	0.0902770i
$579$	511.114	−	511.114i	0.882753	−	0.882753i
$580$	153.187	−	511.196i	0.264115	−	0.881373i
$581$	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	−0.998878	−	0.0473610i	$-0.984919\pi$
$587$	−558.540	+	558.540i	−0.951517	+	0.951517i	0.0473610	+	0.998878i	$0.484919\pi$
$588$	−1.97520	−	185.792i	−0.00335919	−	0.315973i
$589$	578.712	+	578.712i	0.982532	+	0.982532i
$590$	−72.8392	−	754.541i	−0.123456	−	1.27888i
$591$		−	452.645i		−	0.765897i
$592$	−283.353	+	295.666i	−0.478636	+	0.499435i
$593$		−	217.889i		−	0.367435i	−0.982979	−	0.183717i	$-0.941187\pi$
$593$		−	217.889i		−	0.367435i	0.982979	−	0.183717i	$-0.0588131\pi$
$594$	−465.368	−	189.870i	−0.783449	−	0.319647i
$595$	354.679	+	110.406i	0.596099	+	0.185557i
$596$	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	$0.436132\pi$
$600$	−322.831	+	216.381i	−0.538052	+	0.360635i
$601$			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
$605$	56.9673	−	183.007i	0.0941609	−	0.302490i
$606$	534.379	+	218.027i	0.881814	+	0.359780i
$607$	−257.142			−0.423627			−0.211814	−	0.977310i	$-0.567937\pi$
$607$	−257.142			−0.423627			−0.211814	+	0.977310i	$0.567937\pi$
$608$	−323.157	−	725.047i	−0.531508	−	1.19251i
$609$	259.745			0.426511
$610$	34.6348	+	358.782i	0.0567783	+	0.588167i
$611$	−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	0.357931	−	0.933748i	$-0.383482\pi$
$613$	−352.976	−	352.976i	−0.575817	−	0.575817i	−0.933748	+	0.357931i	$0.883482\pi$
$614$	−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	$-0.451152\pi$
$617$	188.628			0.305719			0.152859	+	0.988248i	$0.451152\pi$
$618$	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	$0.895817\pi$
$620$	−580.881	+	313.014i	−0.936905	+	0.504861i
$621$	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
$630$	201.974	+	166.412i	0.320593	+	0.264146i
$631$	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
$635$	853.682	+	265.739i	1.34438	+	0.418487i
$636$	−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
$640$	634.754	−	81.7782i	0.991803	−	0.127778i
$641$	−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	$-0.925027\pi$
$643$	−775.300	−	775.300i	−1.20575	−	1.20575i	−0.233364	−	0.972389i	$-0.574973\pi$
$644$	−62.6363	−	61.3185i	−0.0972614	−	0.0952151i
$645$	−251.642	−	78.3325i	−0.390142	−	0.121446i
$646$	−285.175	−	678.255i	−0.441448	−	1.04993i
$647$		−	5.25109i		−	0.00811606i	−0.999992	−	0.00405803i	$-0.998708\pi$
$647$		−	5.25109i		−	0.00811606i	0.999992	−	0.00405803i	$-0.00129171\pi$
$648$	−21.2802	−	49.1435i	−0.0328398	−	0.0758387i
$649$		−	689.226i		−	1.06198i
$650$	−765.038	−	159.500i	−1.17698	−	0.245385i
$651$	−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	−0.695297	−	0.718722i	$-0.744727\pi$
$653$	15.2963	−	15.2963i	0.0234247	−	0.0234247i	0.718722	+	0.695297i	$0.244727\pi$
$654$	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	$0.383005\pi$
$660$	−311.067	+	167.622i	−0.471314	+	0.253972i
$661$	−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
$670$	−8.05575	−	83.4495i	−0.0120235	−	0.124551i
$671$			327.724i			0.488412i
$672$	126.814	+	284.525i	0.188711	+	0.423400i
$673$		−	1181.74i		−	1.75593i	−0.478727	−	0.877964i	$-0.658902\pi$
$673$		−	1181.74i		−	1.75593i	0.478727	−	0.877964i	$-0.341098\pi$
$674$	250.363	−	613.636i	0.371459	−	0.910439i
$675$	−679.607	+	124.961i	−1.00683	+	0.185128i
$676$	210.674	−	215.201i	0.311648	−	0.318345i
$677$	71.0492	+	71.0492i	0.104947	+	0.104947i	0.757631	−	0.652684i	$-0.226357\pi$
$677$	71.0492	+	71.0492i	0.104947	+	0.104947i	−0.652684	+	0.757631i	$0.726357\pi$
$678$	−170.702	+	71.7724i	−0.251772	+	0.105859i
$679$	82.1141			0.120934
$680$	589.826	−	63.2740i	0.867391	−	0.0930500i
$681$			446.898i			0.656238i
$682$	−553.046	+	232.531i	−0.810917	+	0.340954i
$683$	−246.349	+	246.349i	−0.360687	+	0.360687i	−0.864066	−	0.503379i	$-0.832090\pi$
$683$	−246.349	+	246.349i	−0.360687	+	0.360687i	0.503379	+	0.864066i	$0.332090\pi$
$684$	−5.51041	−	518.322i	−0.00805616	−	0.757781i
$685$	−22.5401	−	7.01641i	−0.0329052	−	0.0102429i
$686$	−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
$690$	84.6088	−	8.16766i	0.122622	−	0.0118372i
$691$	−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
$700$	491.706	−	95.8261i	0.702437	−	0.136894i
$701$	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	$0.348878\pi$
$710$	200.028	+	164.808i	0.281729	+	0.232124i
$711$	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
$715$	−678.427	−	211.185i	−0.948849	−	0.295363i
$716$	−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	$-0.0194637\pi$
$720$	401.583	+	115.702i	0.557755	+	0.160697i
$721$	−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
$725$	−120.633	−	656.070i	−0.166391	−	0.904925i
$726$	137.334	−	57.7428i	0.189166	−	0.0795356i
$727$			370.209i			0.509228i	0.967043	+	0.254614i	$0.0819484\pi$
$727$			370.209i			0.509228i	−0.967043	+	0.254614i	$0.918052\pi$
$728$	−230.449	+	582.454i	−0.316551	+	0.800074i
$729$		−	518.360i		−	0.711056i
$730$	240.914	+	198.496i	0.330019	+	0.271912i
$731$	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	−0.990739	−	0.135779i	$-0.956646\pi$
$733$	−626.686	+	626.686i	−0.854960	+	0.854960i	0.135779	+	0.990739i	$0.456646\pi$
$734$	−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	$0.371326\pi$
$740$	−146.942	+	490.357i	−0.198570	+	0.662645i
$741$	−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	$0.0261363\pi$
$743$			121.878i			0.164035i	−0.996631	+	0.0820173i	$0.973864\pi$
$744$	−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
$750$	−236.019	+	424.613i	−0.314692	+	0.566150i
$751$			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
$755$	455.067	+	141.656i	0.602737	+	0.187624i
$756$	5.88786	+	553.826i	0.00778818	+	0.732574i
$757$	−129.143	−	129.143i	−0.170599	−	0.170599i	0.616644	−	0.787242i	$-0.288492\pi$
$757$	−129.143	−	129.143i	−0.170599	−	0.170599i	−0.787242	+	0.616644i	$0.788492\pi$
$758$	128.885	+	306.538i	0.170033	+	0.404403i
$759$	77.2849			0.101825
$760$	−772.465	−	622.788i	−1.01640	−	0.819458i
$761$		−	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
$765$	369.860	+	115.132i	0.483477	+	0.150499i
$766$	−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	$0.478159\pi$
$770$	453.367	−	43.7655i	0.588789	−	0.0568384i
$771$	−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	0.782796	−	0.622278i	$-0.213793\pi$
$773$	124.080	+	124.080i	0.160518	+	0.160518i	−0.622278	+	0.782796i	$0.713793\pi$
$774$	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
$780$	−288.150	−	534.739i	−0.369423	−	0.685562i
$781$	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	0.980253	−	0.197748i	$-0.0633628\pi$
$787$	615.831	+	615.831i	0.782505	+	0.782505i	−0.197748	+	0.980253i	$0.563363\pi$
$788$	9.90513	+	931.700i	0.0125700	+	1.18236i
$789$	273.715	−	273.715i	0.346914	−	0.346914i
$790$	776.133	−	941.991i	0.982447	−	1.19239i
$791$	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
$795$	−87.9704	+	282.603i	−0.110655	+	0.355476i
$796$	403.359	+	394.873i	0.506733	+	0.496072i
$797$	56.7101	−	56.7101i	0.0711545	−	0.0711545i	−0.670634	−	0.741788i	$-0.733978\pi$
$797$	56.7101	−	56.7101i	0.0711545	−	0.0711545i	0.741788	+	0.670634i	$0.233978\pi$
$798$	182.446	−	447.171i	0.228629	−	0.560365i
$799$		−	876.735i		−	1.09729i
$800$	659.763	−	452.452i	0.824704	−	0.565565i
$801$	−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
$805$	−104.616	−	32.5656i	−0.129958	−	0.0404542i
$806$	−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	$-0.111729\pi$
$810$	−51.6639	−	42.5674i	−0.0637826	−	0.0525523i
$811$	−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
$820$	−1339.90	+	722.020i	−1.63403	+	0.880512i
$821$	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	$0.128425\pi$
$823$			646.223i			0.785204i	−0.919708	+	0.392602i	$0.871575\pi$
$824$	−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	$-0.496515\pi$
$827$	836.004	−	836.004i	1.01089	−	1.01089i	0.999940	−	0.0109471i	$-0.00348464\pi$
$828$	−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	$0.814235\pi$
$830$	−157.615	−	1632.73i	−0.189897	−	1.96715i
$831$		−	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
$835$	−75.5420	+	242.677i	−0.0904694	+	0.290631i
$836$	−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	$0.541772\pi$
$840$	303.133	+	244.396i	0.360872	+	0.290948i
$841$		−	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
$845$	111.887	−	359.433i	0.132410	−	0.425365i
$846$	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
$850$	620.306	−	406.277i	0.729772	−	0.477973i
$851$	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	0.678976	−	0.734160i	$-0.262424\pi$
$853$	−47.0723	−	47.0723i	−0.0551844	−	0.0551844i	−0.734160	+	0.678976i	$0.762424\pi$
$854$	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	$-0.105416\pi$
$857$	1620.86			1.89132			0.945661	+	0.325154i	$0.105416\pi$
$858$	−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	$0.834200\pi$
$860$	519.680	+	155.729i	0.604279	+	0.181080i
$861$	−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	$-0.196495\pi$
$863$	1407.45			1.63088			0.815439	+	0.578842i	$0.196495\pi$
$864$	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
$870$	329.708	−	400.166i	0.378975	−	0.459961i
$871$	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
$875$	492.585	−	386.627i	0.562955	−	0.441859i
$876$	2.57932	+	242.617i	0.00294443	+	0.276960i
$877$	507.991	−	507.991i	0.579237	−	0.579237i	−0.355456	−	0.934693i	$-0.615674\pi$
$877$	507.991	−	507.991i	0.579237	−	0.579237i	0.934693	+	0.355456i	$0.115674\pi$
$878$	−462.487	−	188.695i	−0.526751	−	0.214914i
$879$			607.614i			0.691256i
$880$	636.616	−	351.831i	0.723427	−	0.399808i
$881$	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	0.243204	−	0.969975i	$-0.421802\pi$
$883$	−641.739	−	641.739i	−0.726771	−	0.726771i	−0.969975	+	0.243204i	$0.921802\pi$
$884$	9.85644	+	927.120i	0.0111498	+	1.04878i
$885$	218.907	−	703.236i	0.247353	−	0.794616i
$886$	−315.569	+	132.682i	−0.356172	+	0.149754i
$887$		−	172.729i		−	0.194734i	−0.995249	−	0.0973670i	$-0.968958\pi$
$887$		−	172.729i		−	0.194734i	0.995249	−	0.0973670i	$-0.0310420\pi$
$888$	−365.127	+	158.108i	−0.411179	+	0.178049i
$889$		−	895.796i		−	1.00764i
$890$	−543.003	+	659.041i	−0.610115	+	0.740496i
$891$	−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
$900$	512.752	−	99.9276i	0.569724	−	0.111031i
$901$	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	−0.751607	−	0.659611i	$-0.770721\pi$
$907$	−83.4405	+	83.4405i	−0.0919962	+	0.0919962i	0.659611	+	0.751607i	$0.270721\pi$
$908$	−9.77938	−	919.872i	−0.0107702	−	1.01307i
$909$	−548.562	−	548.562i	−0.603478	−	0.603478i
$910$	75.2350	+	779.359i	0.0826758	+	0.856439i
$911$		−	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
$915$	−104.090	+	334.386i	−0.113759	+	0.365449i
$916$	−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	$0.504001\pi$
$920$	−173.976	+	18.6634i	−0.189104	+	0.0202863i
$921$		−	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
$925$	115.716	+	629.325i	0.125098	+	0.680352i
$926$	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	$0.346372\pi$
$930$	−638.142	+	61.6026i	−0.686174	+	0.0662394i
$931$	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	$-0.327026\pi$
$937$	968.975			1.03412			0.517062	+	0.855948i	$0.327026\pi$
$938$	−77.4319	+	32.5566i	−0.0825500	+	0.0347085i
$939$	370.445	+	370.445i	0.394510	+	0.394510i
$940$	−560.879	−	1040.86i	−0.596679	−	1.10730i
$941$	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	0.499456	−	0.866339i	$-0.333533\pi$
$947$	−347.438	−	347.438i	−0.366883	−	0.366883i	−0.866339	+	0.499456i	$0.833533\pi$
$948$	948.650	−	10.0853i	1.00069	−	0.0106385i
$949$	−344.989	+	344.989i	−0.363529	+	0.363529i
$950$	−1214.21	−	253.146i	−1.27811	−	0.266469i
$951$	55.1343			0.0579751
$952$	−236.173	−	545.406i	−0.248081	−	0.572906i
$953$	−1222.59			−1.28288			−0.641442	−	0.767171i	$-0.721664\pi$
$953$	−1222.59			−1.28288			−0.641442	+	0.767171i	$0.721664\pi$
$954$	293.398	−	123.361i	0.307545	−	0.129309i
$955$	72.8432	−	234.008i	0.0762756	−	0.245034i
$956$	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
$960$	599.314	+	165.791i	0.624285	+	0.172699i
$961$	−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
$965$	−552.792	+	1775.84i	−0.572842	+	1.84024i
$966$	−33.0089	−	78.5076i	−0.0341707	−	0.0812708i
$967$		−	967.881i		−	1.00091i	−0.865762	−	0.500455i	$-0.833166\pi$
$967$		−	967.881i		−	1.00091i	0.865762	−	0.500455i	$-0.166834\pi$
$968$	−281.418	+	121.860i	−0.290721	+	0.125888i
$969$		−	714.871i		−	0.737741i
$970$	104.232	−	126.506i	0.107455	−	0.130419i
$971$	−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	$0.126999\pi$
$977$			759.084i			0.776954i	−0.921458	+	0.388477i	$0.873001\pi$
$978$	269.232	−	659.883i	0.275289	−	0.674727i
$979$	−548.996	+	548.996i	−0.560772	+	0.560772i
$980$	226.790	+	420.870i	0.231419	+	0.429459i
$981$	−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	$0.0451762\pi$
$983$			278.089i			0.282899i	−0.989945	+	0.141449i	$0.954824\pi$
$984$	−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
$990$	472.772	−	45.6388i	0.477548	−	0.0460998i
$991$		−	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
$995$	673.698	+	209.713i	0.677084	+	0.210767i
$996$	891.917	−	911.085i	0.895499	−	0.914744i
$997$	388.829	+	388.829i	0.389999	+	0.389999i	0.874687	−	0.484688i	$-0.161067\pi$
$997$	388.829	+	388.829i	0.389999	+	0.389999i	−0.484688	+	0.874687i	$0.661067\pi$
$998$	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.19.3	✓	44
4.3	odd	2		320.3.k.a.239.16		44
5.2	odd	4		400.3.r.g.51.14		44
5.3	odd	4		400.3.r.g.51.9		44
5.4	even	2	inner	80.3.k.a.19.20	yes	44
8.3	odd	2		640.3.k.a.479.7		44
8.5	even	2		640.3.k.b.479.16		44
16.3	odd	4		640.3.k.b.159.7		44
16.5	even	4		320.3.k.a.79.7		44
16.11	odd	4	inner	80.3.k.a.59.20	yes	44
16.13	even	4		640.3.k.a.159.16		44
20.19	odd	2		320.3.k.a.239.7		44
40.19	odd	2		640.3.k.a.479.16		44
40.29	even	2		640.3.k.b.479.7		44
80.19	odd	4		640.3.k.b.159.16		44
80.27	even	4		400.3.r.g.251.14		44
80.29	even	4		640.3.k.a.159.7		44
80.43	even	4		400.3.r.g.251.9		44
80.59	odd	4	inner	80.3.k.a.59.3	yes	44
80.69	even	4		320.3.k.a.79.16		44

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

\(f(q)\)	\(=\)	\(q+(-1.85180 - 0.755534i) q^{2} +(-1.37405 - 1.37405i) q^{3} +(2.85834 + 2.79820i) q^{4} +(4.77405 + 1.48609i) q^{5} +(1.50632 + 3.58260i) q^{6} -5.00956i q^{7} +(-3.17893 - 7.34128i) q^{8} -5.22398i q^{9} +O(q^{10})\)	\(q+(-1.85180 - 0.755534i) q^{2} +(-1.37405 - 1.37405i) q^{3} +(2.85834 + 2.79820i) q^{4} +(4.77405 + 1.48609i) q^{5} +(1.50632 + 3.58260i) q^{6} -5.00956i q^{7} +(-3.17893 - 7.34128i) q^{8} -5.22398i q^{9} +(-7.71779 - 6.35891i) 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} +(9.48744 + 17.6065i) 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} +(1.86717 + 19.3421i) q^{30} +32.9924i q^{31} +(11.4559 - 29.8791i) q^{32} +17.6678i q^{33} +(11.2048 - 27.4627i) q^{34} +(7.44468 - 23.9159i) q^{35} +(14.6177 - 14.9319i) q^{36} +(18.0984 + 18.0984i) q^{37} +(-45.7346 + 19.2293i) q^{38} -30.3717 q^{39} +(-4.26655 - 39.7718i) q^{40} +76.1027i q^{41} +(17.9473 - 7.54602i) q^{42} +(19.1807 - 19.1807i) q^{43} +(-0.386620 - 36.3664i) q^{44} +(7.76333 - 24.9395i) q^{45} +(-3.30497 + 8.10042i) q^{46} -59.1180 q^{47} +(21.5124 - 22.4472i) q^{48} +23.9043 q^{49} +(-27.3952 - 41.8271i) 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} +(11.1560 - 37.2284i) 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} +(-31.8554 + 38.6628i) q^{70} -25.9177 q^{71} +(-38.3507 + 16.6067i) q^{72} -31.2154 q^{73} +(-19.8407 - 47.1886i) q^{74} +(-8.78525 - 47.7790i) q^{75} +(99.2197 - 1.05483i) q^{76} +(-32.2069 + 32.2069i) q^{77} +(56.2423 + 22.9469i) q^{78} +122.054i q^{79} +(-22.1482 + 76.8730i) q^{80} +6.69413 q^{81} +(57.4982 - 140.927i) q^{82} +(115.988 + 115.988i) q^{83} +(-38.9361 + 0.413939i) q^{84} +(-22.0391 + 70.8003i) q^{85} +(-50.0105 + 21.0271i) q^{86} +51.8499i q^{87} +(-26.7601 + 67.6354i) q^{88} -85.3925i q^{89} +(-33.2188 + 40.3176i) 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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