LMFDB - Embedded newform 80.3.k.a.59.19

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			59.19
Character	$\chi$	$=$	80.59
Dual form			80.3.k.a.19.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82198 + 0.824856i) q^{2} +(-2.39041 + 2.39041i) q^{3} +(2.63923 + 3.00574i) q^{4} +(-3.54593 + 3.52510i) q^{5} +(-6.32702 + 2.38354i) q^{6} -5.08144i q^{7} +(2.32932 + 7.65338i) q^{8} -2.42812i q^{9} +O(q^{10})$	\(q+(1.82198 + 0.824856i) q^{2} +(-2.39041 + 2.39041i) q^{3} +(2.63923 + 3.00574i) q^{4} +(-3.54593 + 3.52510i) q^{5} +(-6.32702 + 2.38354i) q^{6} -5.08144i q^{7} +(2.32932 + 7.65338i) q^{8} -2.42812i q^{9} +(-9.36832 + 3.49778i) q^{10} +(9.77953 - 9.77953i) q^{11} +(-13.4938 - 0.876121i) q^{12} +(16.0002 + 16.0002i) q^{13} +(4.19145 - 9.25828i) q^{14} +(0.0497986 - 16.9027i) q^{15} +(-2.06896 + 15.8657i) q^{16} -9.82261i q^{17} +(2.00285 - 4.42399i) q^{18} +(2.54131 + 2.54131i) q^{19} +(-19.9541 - 1.35462i) q^{20} +(12.1467 + 12.1467i) q^{21} +(25.8848 - 9.75141i) q^{22} -32.5737i q^{23} +(-23.8627 - 12.7267i) q^{24} +(0.147309 - 24.9996i) q^{25} +(15.9542 + 42.3499i) q^{26} +(-15.7095 - 15.7095i) q^{27} +(15.2735 - 13.4111i) q^{28} +(-8.31667 + 8.31667i) q^{29} +(14.0330 - 30.7553i) q^{30} +38.6552i q^{31} +(-16.8565 + 27.2003i) q^{32} +46.7542i q^{33} +(8.10223 - 17.8966i) q^{34} +(17.9126 + 18.0185i) q^{35} +(7.29830 - 6.40836i) q^{36} +(12.8743 - 12.8743i) q^{37} +(2.53400 + 6.72643i) q^{38} -76.4941 q^{39} +(-35.2386 - 18.9273i) q^{40} -30.0736i q^{41} +(12.1118 + 32.1504i) q^{42} +(-17.9578 - 17.9578i) q^{43} +(55.2051 + 3.58434i) q^{44} +(8.55937 + 8.60995i) q^{45} +(26.8686 - 59.3486i) q^{46} -5.99252 q^{47} +(-32.9798 - 42.8711i) q^{48} +23.1790 q^{49} +(20.8894 - 45.4272i) q^{50} +(23.4801 + 23.4801i) q^{51} +(-5.86432 + 90.3207i) q^{52} +(-18.6201 + 18.6201i) q^{53} +(-15.6643 - 41.5804i) q^{54} +(-0.203734 + 69.1514i) q^{55} +(38.8902 - 11.8363i) q^{56} -12.1495 q^{57} +(-22.0129 + 8.29276i) q^{58} +(21.8610 - 21.8610i) q^{59} +(50.9365 - 44.4603i) q^{60} +(-80.6491 + 80.6491i) q^{61} +(-31.8850 + 70.4290i) q^{62} -12.3383 q^{63} +(-53.1486 + 35.6543i) q^{64} +(-113.138 - 0.333327i) q^{65} +(-38.5654 + 85.1852i) q^{66} +(51.4930 - 51.4930i) q^{67} +(29.5242 - 25.9241i) q^{68} +(77.8645 + 77.8645i) q^{69} +(17.7738 + 47.6046i) q^{70} -33.5962 q^{71} +(18.5833 - 5.65586i) q^{72} +80.6663 q^{73} +(34.0761 - 12.8373i) q^{74} +(59.4071 + 60.1113i) q^{75} +(-0.931428 + 14.3456i) q^{76} +(-49.6941 - 49.6941i) q^{77} +(-139.371 - 63.0966i) q^{78} -59.9317i q^{79} +(-48.5917 - 63.5519i) q^{80} +96.9573 q^{81} +(24.8064 - 54.7936i) q^{82} +(-34.7533 + 34.7533i) q^{83} +(-4.45195 + 68.5679i) q^{84} +(34.6257 + 34.8303i) q^{85} +(-17.9061 - 47.5313i) q^{86} -39.7605i q^{87} +(97.6261 + 52.0668i) q^{88} -64.5309i q^{89} +(8.49304 + 22.7474i) q^{90} +(81.3041 - 81.3041i) q^{91} +(97.9081 - 85.9694i) q^{92} +(-92.4018 - 92.4018i) q^{93} +(-10.9182 - 4.94296i) q^{94} +(-17.9697 - 0.0529423i) q^{95} +(-24.7260 - 105.314i) q^{96} -137.264i q^{97} +(42.2316 + 19.1193i) q^{98} +(-23.7459 - 23.7459i) 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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.82198	+	0.824856i	0.910990	+	0.412428i
$2$	1.82198	+	0.824856i	0.910990	+	0.412428i
$3$	−2.39041	+	2.39041i	−0.796803	+	0.796803i	−0.982590	−	0.185787i	$-0.940517\pi$
$3$	−2.39041	+	2.39041i	−0.796803	+	0.796803i	0.185787	+	0.982590i	$0.440517\pi$
$4$	2.63923	+	3.00574i	0.659807	+	0.751435i
$5$	−3.54593	+	3.52510i	−0.709187	+	0.705020i
$5$	−3.54593	+	3.52510i	−0.709187	+	0.705020i
$6$	−6.32702	+	2.38354i	−1.05450	+	0.397256i
$7$		−	5.08144i		−	0.725920i	−0.931805	−	0.362960i	$-0.881766\pi$
$7$		−	5.08144i		−	0.725920i	0.931805	−	0.362960i	$-0.118234\pi$
$8$	2.32932	+	7.65338i	0.291165	+	0.956673i
$9$		−	2.42812i		−	0.269791i
$10$	−9.36832	+	3.49778i	−0.936832	+	0.349778i
$11$	9.77953	−	9.77953i	0.889048	−	0.889048i	−0.105384	−	0.994432i	$-0.533607\pi$
$11$	9.77953	−	9.77953i	0.889048	−	0.889048i	0.994432	+	0.105384i	$0.0336071\pi$
$12$	−13.4938	−	0.876121i	−1.12448	−	0.0730101i
$13$	16.0002	+	16.0002i	1.23079	+	1.23079i	0.963662	+	0.267123i	$0.0860732\pi$
$13$	16.0002	+	16.0002i	1.23079	+	1.23079i	0.267123	+	0.963662i	$0.413927\pi$
$14$	4.19145	−	9.25828i	0.299390	−	0.661306i
$15$	0.0497986	−	16.9027i	0.00331991	−	1.12685i
$16$	−2.06896	+	15.8657i	−0.129310	+	0.991604i
$17$		−	9.82261i		−	0.577800i	−0.957359	−	0.288900i	$-0.906710\pi$
$17$		−	9.82261i		−	0.577800i	0.957359	−	0.288900i	$-0.0932896\pi$
$18$	2.00285	−	4.42399i	0.111269	−	0.245777i
$19$	2.54131	+	2.54131i	0.133753	+	0.133753i	0.770814	−	0.637061i	$-0.219850\pi$
$19$	2.54131	+	2.54131i	0.133753	+	0.133753i	−0.637061	+	0.770814i	$0.719850\pi$
$20$	−19.9541	−	1.35462i	−0.997704	−	0.0677310i
$21$	12.1467	+	12.1467i	0.578415	+	0.578415i
$22$	25.8848	−	9.75141i	1.17658	−	0.443246i
$23$		−	32.5737i		−	1.41625i	−0.706088	−	0.708124i	$-0.749542\pi$
$23$		−	32.5737i		−	1.41625i	0.706088	−	0.708124i	$-0.250458\pi$
$24$	−23.8627	−	12.7267i	−0.994281	−	0.530279i
$25$	0.147309	−	24.9996i	0.00589234	−	0.999983i
$26$	15.9542	+	42.3499i	0.613624	+	1.62884i
$27$	−15.7095	−	15.7095i	−0.581833	−	0.581833i
$28$	15.2735	−	13.4111i	0.545482	−	0.478967i
$29$	−8.31667	+	8.31667i	−0.286782	+	0.286782i	−0.835806	−	0.549025i	$-0.814999\pi$
$29$	−8.31667	+	8.31667i	−0.286782	+	0.286782i	0.549025	+	0.835806i	$0.314999\pi$
$30$	14.0330	−	30.7553i	0.467767	−	1.02518i
$31$			38.6552i			1.24694i	0.781847	+	0.623471i	$0.214278\pi$
$31$			38.6552i			1.24694i	−0.781847	+	0.623471i	$0.785722\pi$
$32$	−16.8565	+	27.2003i	−0.526766	+	0.850011i
$33$			46.7542i			1.41679i
$34$	8.10223	−	17.8966i	0.238301	−	0.526371i
$35$	17.9126	+	18.0185i	0.511788	+	0.514813i
$36$	7.29830	−	6.40836i	0.202731	−	0.178010i
$37$	12.8743	−	12.8743i	0.347954	−	0.347954i	−0.511393	−	0.859347i	$-0.670870\pi$
$37$	12.8743	−	12.8743i	0.347954	−	0.347954i	0.859347	+	0.511393i	$0.170870\pi$
$38$	2.53400	+	6.72643i	0.0666843	+	0.177011i
$39$	−76.4941			−1.96139
$40$	−35.2386	−	18.9273i	−0.880964	−	0.473183i
$41$		−	30.0736i		−	0.733503i	−0.930319	−	0.366752i	$-0.880470\pi$
$41$		−	30.0736i		−	0.733503i	0.930319	−	0.366752i	$-0.119530\pi$
$42$	12.1118	+	32.1504i	0.288376	+	0.765485i
$43$	−17.9578	−	17.9578i	−0.417623	−	0.417623i	0.466761	−	0.884384i	$-0.345421\pi$
$43$	−17.9578	−	17.9578i	−0.417623	−	0.417623i	−0.884384	+	0.466761i	$0.845421\pi$
$44$	55.2051	+	3.58434i	1.25466	+	0.0814623i
$45$	8.55937	+	8.60995i	0.190208	+	0.191332i
$46$	26.8686	−	59.3486i	0.584100	−	1.29019i
$47$	−5.99252			−0.127500			−0.0637502	−	0.997966i	$-0.520306\pi$
$47$	−5.99252			−0.127500			−0.0637502	+	0.997966i	$0.520306\pi$
$48$	−32.9798	−	42.8711i	−0.687079	−	0.893148i
$49$	23.1790			0.473040
$50$	20.8894	−	45.4272i	0.417788	−	0.908544i
$51$	23.4801	+	23.4801i	0.460393	+	0.460393i
$52$	−5.86432	+	90.3207i	−0.112775	+	1.73694i
$53$	−18.6201	+	18.6201i	−0.351323	+	0.351323i	−0.860602	−	0.509279i	$-0.829912\pi$
$53$	−18.6201	+	18.6201i	−0.351323	+	0.351323i	0.509279	+	0.860602i	$0.329912\pi$
$54$	−15.6643	−	41.5804i	−0.290080	−	0.770008i
$55$	−0.203734	+	69.1514i	−0.00370425	+	1.25730i
$56$	38.8902	−	11.8363i	0.694468	−	0.211362i
$57$	−12.1495			−0.213150
$58$	−22.0129	+	8.29276i	−0.379532	+	0.142979i
$59$	21.8610	−	21.8610i	0.370525	−	0.370525i	−0.497143	−	0.867668i	$-0.665618\pi$
$59$	21.8610	−	21.8610i	0.370525	−	0.370525i	0.867668	+	0.497143i	$0.165618\pi$
$60$	50.9365	−	44.4603i	0.848942	−	0.741005i
$61$	−80.6491	+	80.6491i	−1.32212	+	1.32212i	−0.410055	+	0.912061i	$0.634491\pi$
$61$	−80.6491	+	80.6491i	−1.32212	+	1.32212i	−0.912061	+	0.410055i	$0.865509\pi$
$62$	−31.8850	+	70.4290i	−0.514273	+	1.13595i
$63$	−12.3383			−0.195847
$64$	−53.1486	+	35.6543i	−0.830446	+	0.557099i
$65$	−113.138	−	0.333327i	−1.74059	−	0.00512811i
$66$	−38.5654	+	85.1852i	−0.584325	+	1.29068i
$67$	51.4930	−	51.4930i	0.768552	−	0.768552i	−0.209300	−	0.977852i	$-0.567118\pi$
$67$	51.4930	−	51.4930i	0.768552	−	0.768552i	0.977852	+	0.209300i	$0.0671184\pi$
$68$	29.5242	−	25.9241i	0.434180	−	0.381237i
$69$	77.8645	+	77.8645i	1.12847	+	1.12847i
$70$	17.7738	+	47.6046i	0.253911	+	0.680065i
$71$	−33.5962			−0.473186			−0.236593	−	0.971609i	$-0.576031\pi$
$71$	−33.5962			−0.473186			−0.236593	+	0.971609i	$0.576031\pi$
$72$	18.5833	−	5.65586i	0.258102	−	0.0785536i
$73$	80.6663			1.10502			0.552509	−	0.833507i	$-0.313670\pi$
$73$	80.6663			1.10502			0.552509	+	0.833507i	$0.313670\pi$
$74$	34.0761	−	12.8373i	0.460488	−	0.173477i
$75$	59.4071	+	60.1113i	0.792094	+	0.801485i
$76$	−0.931428	+	14.3456i	−0.0122556	+	0.188758i
$77$	−49.6941	−	49.6941i	−0.645377	−	0.645377i
$78$	−139.371	−	63.0966i	−1.78681	−	0.808931i
$79$		−	59.9317i		−	0.758629i	−0.925268	−	0.379315i	$-0.876160\pi$
$79$		−	59.9317i		−	0.758629i	0.925268	−	0.379315i	$-0.123840\pi$
$80$	−48.5917	−	63.5519i	−0.607396	−	0.794399i
$81$	96.9573			1.19700
$82$	24.8064	−	54.7936i	0.302517	−	0.668214i
$83$	−34.7533	+	34.7533i	−0.418715	+	0.418715i	−0.884761	−	0.466046i	$-0.845678\pi$
$83$	−34.7533	+	34.7533i	−0.418715	+	0.418715i	0.466046	+	0.884761i	$0.345678\pi$
$84$	−4.45195	+	68.5679i	−0.0529995	+	0.816284i
$85$	34.6257	+	34.8303i	0.407361	+	0.409769i
$86$	−17.9061	−	47.5313i	−0.208211	−	0.552689i
$87$		−	39.7605i		−	0.457017i
$88$	97.6261	+	52.0668i	1.10939	+	0.591669i
$89$		−	64.5309i		−	0.725067i	−0.931971	−	0.362533i	$-0.881912\pi$
$89$		−	64.5309i		−	0.725067i	0.931971	−	0.362533i	$-0.118088\pi$
$90$	8.49304	+	22.7474i	0.0943671	+	0.252749i
$91$	81.3041	−	81.3041i	0.893452	−	0.893452i
$92$	97.9081	−	85.9694i	1.06422	−	0.934449i
$93$	−92.4018	−	92.4018i	−0.993567	−	0.993567i
$94$	−10.9182	−	4.94296i	−0.116152	−	0.0525847i
$95$	−17.9697	−	0.0529423i	−0.189155	−	0.000557287i
$96$	−24.7260	−	105.314i	−0.257563	−	1.09702i
$97$		−	137.264i		−	1.41509i	−0.706669	−	0.707544i	$-0.749803\pi$
$97$		−	137.264i		−	1.41509i	0.706669	−	0.707544i	$-0.250197\pi$
$98$	42.2316	+	19.1193i	0.430935	+	0.195095i
$99$	−23.7459	−	23.7459i	−0.239857	−	0.239857i
$100$	75.5310	−	65.5368i	0.755310	−	0.655368i
$101$	−115.953	−	115.953i	−1.14805	−	1.14805i	−0.986937	−	0.161109i	$-0.948493\pi$
$101$	−115.953	−	115.953i	−1.14805	−	1.14805i	−0.161109	−	0.986937i	$-0.551507\pi$
$102$	23.4126	+	62.1479i	0.229535	+	0.609293i
$103$			87.5329i			0.849834i	0.905232	+	0.424917i	$0.139697\pi$
$103$			87.5329i			0.849834i	−0.905232	+	0.424917i	$0.860303\pi$
$104$	−85.1862	+	159.725i	−0.819098	+	1.53582i
$105$	−85.8899	−	0.253049i	−0.817999	−	0.00240999i
$106$	−49.2844	+	18.5666i	−0.464947	+	0.175156i
$107$	25.2243	+	25.2243i	0.235741	+	0.235741i	0.815084	−	0.579343i	$-0.196691\pi$
$107$	25.2243	+	25.2243i	0.235741	+	0.235741i	−0.579343	+	0.815084i	$0.696691\pi$
$108$	5.75776	−	88.6796i	0.0533126	−	0.821107i
$109$	104.801	−	104.801i	0.961474	−	0.961474i	−0.0378105	−	0.999285i	$-0.512038\pi$
$109$	104.801	−	104.801i	0.961474	−	0.961474i	0.999285	+	0.0378105i	$0.0120383\pi$
$110$	−57.4111	+	125.824i	−0.521919	+	1.14386i
$111$			61.5496i			0.554501i
$112$	80.6204	+	10.5133i	0.719825	+	0.0938689i
$113$			27.4328i			0.242769i	0.992606	+	0.121384i	$0.0387333\pi$
$113$			27.4328i			0.242769i	−0.992606	+	0.121384i	$0.961267\pi$
$114$	−22.1362	−	10.0216i	−0.194178	−	0.0879090i
$115$	114.826	+	115.504i	0.998483	+	1.00438i
$116$	−46.9473	−	3.04818i	−0.404718	−	0.0262774i
$117$	38.8504	−	38.8504i	0.332055	−	0.332055i
$118$	57.8624	−	21.7981i	0.490359	−	0.184730i
$119$	−49.9130			−0.419437
$120$	129.479	−	38.9906i	1.07899	−	0.324921i
$121$		−	70.2782i		−	0.580812i
$122$	−213.465	+	80.4172i	−1.74971	+	0.659158i
$123$	71.8883	+	71.8883i	0.584458	+	0.584458i
$124$	−116.188	+	102.020i	−0.936996	+	0.822741i
$125$	87.6037	+	89.1661i	0.700829	+	0.713329i
$126$	−22.4802	−	10.1773i	−0.178414	−	0.0807726i
$127$	−33.5455			−0.264138			−0.132069	−	0.991241i	$-0.542162\pi$
$127$	−33.5455			−0.264138			−0.132069	+	0.991241i	$0.542162\pi$
$128$	−126.245	+	21.1216i	−0.986291	+	0.165012i
$129$	85.8529			0.665526
$130$	−205.861	−	93.9299i	−1.58354	−	0.722538i
$131$	−105.904	−	105.904i	−0.808428	−	0.808428i	0.175968	−	0.984396i	$-0.443695\pi$
$131$	−105.904	−	105.904i	−0.808428	−	0.808428i	−0.984396	+	0.175968i	$0.943695\pi$
$132$	−140.531	+	123.395i	−1.06463	+	0.934809i
$133$	12.9135	−	12.9135i	0.0970941	−	0.0970941i
$134$	136.293	−	51.3449i	1.01712	−	0.383171i
$135$	111.082	+	0.327271i	0.822832	+	0.00242423i
$136$	75.1762	−	22.8800i	0.552766	−	0.168235i
$137$	−102.458			−0.747868			−0.373934	−	0.927455i	$-0.621991\pi$
$137$	−102.458			−0.747868			−0.373934	+	0.927455i	$0.621991\pi$
$138$	77.6406	+	206.094i	0.562613	+	1.49344i
$139$	−153.879	+	153.879i	−1.10704	+	1.10704i	−0.113502	+	0.993538i	$0.536207\pi$
$139$	−153.879	+	153.879i	−1.10704	+	1.10704i	−0.993538	+	0.113502i	$0.963793\pi$
$140$	−6.88342	+	101.395i	−0.0491673	+	0.724253i
$141$	14.3246	−	14.3246i	0.101593	−	0.101593i
$142$	−61.2116	−	27.7120i	−0.431067	−	0.195155i
$143$	312.949			2.18845
$144$	38.5237	+	5.02369i	0.267526	+	0.0348868i
$145$	0.173258	−	58.8075i	0.00119489	−	0.405569i
$146$	146.972	+	66.5381i	1.00666	+	0.455740i
$147$	−55.4073	+	55.4073i	−0.376920	+	0.376920i
$148$	72.6749	+	4.71861i	0.491047	+	0.0318825i
$149$	121.007	+	121.007i	0.812126	+	0.812126i	0.984952	−	0.172826i	$-0.0552898\pi$
$149$	121.007	+	121.007i	0.812126	+	0.812126i	−0.172826	+	0.984952i	$0.555290\pi$
$150$	58.6554	+	158.524i	0.391036	+	1.05683i
$151$	120.496			0.797990			0.398995	−	0.916953i	$-0.369359\pi$
$151$	120.496			0.797990			0.398995	+	0.916953i	$0.369359\pi$
$152$	−13.5301	+	25.3691i	−0.0890139	+	0.166902i
$153$	−23.8505			−0.155885
$154$	−49.5512	−	131.532i	−0.321761	−	0.854104i
$155$	−136.264	−	137.069i	−0.879119	−	0.884315i
$156$	−201.885	−	229.922i	−1.29414	−	1.47386i
$157$	146.326	+	146.326i	0.932012	+	0.932012i	0.997832	−	0.0658192i	$-0.0209660\pi$
$157$	146.326	+	146.326i	0.932012	+	0.932012i	−0.0658192	+	0.997832i	$0.520966\pi$
$158$	49.4350	−	109.194i	0.312880	−	0.691104i
$159$		−	89.0194i		−	0.559870i
$160$	−36.1119	−	155.872i	−0.225700	−	0.974197i
$161$	−165.521			−1.02808
$162$	176.654	+	79.9758i	1.09046	+	0.493678i
$163$	−208.182	+	208.182i	−1.27719	+	1.27719i	−0.334954	+	0.942235i	$0.608721\pi$
$163$	−208.182	+	208.182i	−1.27719	+	1.27719i	−0.942235	+	0.334954i	$0.891279\pi$
$164$	90.3936	−	79.3712i	0.551180	−	0.483970i
$165$	−164.813	−	165.787i	−0.998868	−	1.00477i
$166$	−91.9863	+	34.6534i	−0.554134	+	0.208755i
$167$			114.093i			0.683193i	0.939847	+	0.341597i	$0.110968\pi$
$167$			114.093i			0.683193i	−0.939847	+	0.341597i	$0.889032\pi$
$168$	−64.6700	+	121.257i	−0.384940	+	0.721768i
$169$			343.014i			2.02967i
$170$	34.3574	+	92.0214i	0.202102	+	0.541302i
$171$	6.17061	−	6.17061i	0.0360854	−	0.0360854i
$172$	6.58179	−	101.371i	0.0382662	−	0.589366i
$173$	−107.166	−	107.166i	−0.619456	−	0.619456i	0.325936	−	0.945392i	$-0.394321\pi$
$173$	−107.166	−	107.166i	−0.619456	−	0.619456i	−0.945392	+	0.325936i	$0.894321\pi$
$174$	32.7967	−	72.4428i	0.188487	−	0.416338i
$175$	−127.034	−	0.748540i	−0.725907	−	0.00427737i
$176$	134.925	+	175.392i	0.766620	+	0.996547i
$177$			104.513i			0.590471i
$178$	53.2287	−	117.574i	0.299038	−	0.660529i
$179$	−158.081	−	158.081i	−0.883132	−	0.883132i	0.110719	−	0.993852i	$-0.464685\pi$
$179$	−158.081	−	158.081i	−0.883132	−	0.883132i	−0.993852	+	0.110719i	$0.964685\pi$
$180$	−3.28918	+	48.4509i	−0.0182732	+	0.269172i
$181$	−57.5726	−	57.5726i	−0.318081	−	0.318081i	0.529949	−	0.848030i	$-0.322211\pi$
$181$	−57.5726	−	57.5726i	−0.318081	−	0.318081i	−0.848030	+	0.529949i	$0.822211\pi$
$182$	215.199	−	81.0704i	1.18241	−	0.445442i
$183$		−	385.569i		−	2.10693i
$184$	249.299	−	75.8745i	1.35489	−	0.412361i
$185$	−0.268206	+	91.0345i	−0.00144976	+	0.492079i
$186$	−92.1361	−	244.572i	−0.495355	−	1.31490i
$187$	−96.0604	−	96.0604i	−0.513692	−	0.513692i
$188$	−15.8156	−	18.0120i	−0.0841256	−	0.0958083i
$189$	−79.8268	+	79.8268i	−0.422364	+	0.422364i
$190$	−32.6968	−	14.9189i	−0.172088	−	0.0785204i
$191$			116.104i			0.607875i	0.952692	+	0.303937i	$0.0983013\pi$
$191$			116.104i			0.607875i	−0.952692	+	0.303937i	$0.901699\pi$
$192$	41.8184	−	212.275i	0.217804	−	1.10560i
$193$			28.9615i			0.150059i	0.997181	+	0.0750297i	$0.0239052\pi$
$193$			28.9615i			0.150059i	−0.997181	+	0.0750297i	$0.976095\pi$
$194$	113.223	−	250.092i	0.583622	−	1.28913i
$195$	271.243	−	269.650i	1.39099	−	1.38282i
$196$	61.1746	+	69.6700i	0.312115	+	0.355459i
$197$	−118.620	+	118.620i	−0.602131	+	0.602131i	−0.940878	−	0.338746i	$-0.889997\pi$
$197$	−118.620	+	118.620i	−0.602131	+	0.602131i	0.338746	+	0.940878i	$0.389997\pi$
$198$	−23.6776	−	62.8514i	−0.119584	−	0.317431i
$199$	−11.1379			−0.0559694			−0.0279847	−	0.999608i	$-0.508909\pi$
$199$	−11.1379			−0.0559694			−0.0279847	+	0.999608i	$0.508909\pi$
$200$	191.674	−	57.1045i	0.958372	−	0.285523i
$201$			246.179i			1.22477i
$202$	−115.619	−	306.908i	−0.572372	−	1.51934i
$203$	42.2606	+	42.2606i	0.208180	+	0.208180i
$204$	−8.60579	+	132.544i	−0.0421852	+	0.649726i
$205$	106.013	+	106.639i	0.517135	+	0.520191i
$206$	−72.2020	+	159.483i	−0.350495	+	0.774191i
$207$	−79.0928			−0.382091
$208$	−286.958	+	220.750i	−1.37961	+	1.06130i
$209$	49.7056			0.237826
$210$	−156.281	−	71.3078i	−0.744196	−	0.339561i
$211$	−0.884244	−	0.884244i	−0.00419073	−	0.00419073i	0.705008	−	0.709199i	$-0.250943\pi$
$211$	−0.884244	−	0.884244i	−0.00419073	−	0.00419073i	−0.709199	+	0.705008i	$0.750943\pi$
$212$	−105.110	−	6.82454i	−0.495801	−	0.0321912i
$213$	80.3086	−	80.3086i	0.377036	−	0.377036i
$214$	25.1518	+	66.7646i	0.117532	+	0.311984i
$215$	126.980	+	0.374108i	0.590605	+	0.00174004i
$216$	83.6384	−	156.823i	0.387215	−	0.726033i
$217$	196.424			0.905180
$218$	277.390	−	104.499i	1.27243	−	0.479355i
$219$	−192.826	+	192.826i	−0.880482	+	0.880482i
$220$	−208.389	+	181.894i	−0.947222	+	0.826790i
$221$	157.164	−	157.164i	0.711149	−	0.711149i
$222$	−50.7695	+	112.142i	−0.228692	+	0.505145i
$223$	−241.623			−1.08351			−0.541755	−	0.840536i	$-0.682240\pi$
$223$	−241.623			−1.08351			−0.541755	+	0.840536i	$0.682240\pi$
$224$	138.217	+	85.6553i	0.617040	+	0.382390i
$225$	−60.7019	−	0.357683i	−0.269786	−	0.00158970i
$226$	−22.6281	+	49.9821i	−0.100125	+	0.221160i
$227$	240.523	−	240.523i	1.05957	−	1.05957i	0.0614631	−	0.998109i	$-0.480423\pi$
$227$	240.523	−	240.523i	1.05957	−	1.05957i	0.998109	−	0.0614631i	$-0.0195767\pi$
$228$	−32.0654	−	36.5184i	−0.140638	−	0.160168i
$229$	−121.946	−	121.946i	−0.532514	−	0.532514i	0.388806	−	0.921320i	$-0.372888\pi$
$229$	−121.946	−	121.946i	−0.532514	−	0.532514i	−0.921320	+	0.388806i	$0.872888\pi$
$230$	113.936	+	305.161i	0.495373	+	1.32679i
$231$	237.578			1.02848
$232$	−83.0228	−	44.2785i	−0.357857	−	0.190856i
$233$	292.240			1.25425			0.627125	−	0.778918i	$-0.284231\pi$
$233$	292.240			1.25425			0.627125	+	0.778918i	$0.284231\pi$
$234$	102.831	−	38.7387i	0.439448	−	0.165550i
$235$	21.2491	−	21.1242i	0.0904216	−	0.0898903i
$236$	123.404	+	8.01237i	0.522900	+	0.0339507i
$237$	143.261	+	143.261i	0.604478	+	0.604478i
$238$	−90.9405	−	41.1710i	−0.382103	−	0.172987i
$239$			60.9550i			0.255042i	0.991836	+	0.127521i	$0.0407020\pi$
$239$			60.9550i			0.255042i	−0.991836	+	0.127521i	$0.959298\pi$
$240$	268.069	+	35.7611i	1.11696	+	0.149005i
$241$	83.2832			0.345573			0.172787	−	0.984959i	$-0.444723\pi$
$241$	83.2832			0.345573			0.172787	+	0.984959i	$0.444723\pi$
$242$	57.9694	−	128.046i	0.239543	−	0.529114i
$243$	−90.3823	+	90.3823i	−0.371944	+	0.371944i
$244$	−455.261	−	29.5591i	−1.86583	−	0.121144i
$245$	−82.1911	+	81.7083i	−0.335474	+	0.333503i
$246$	71.6817	+	190.277i	0.291389	+	0.773482i
$247$			81.3230i			0.329243i
$248$	−295.843	+	90.0402i	−1.19292	+	0.363065i
$249$		−	166.149i		−	0.667266i
$250$	86.0630	+	234.719i	0.344252	+	0.938877i
$251$	−195.109	+	195.109i	−0.777326	+	0.777326i	−0.979375	−	0.202049i	$-0.935240\pi$
$251$	−195.109	+	195.109i	−0.777326	+	0.777326i	0.202049	+	0.979375i	$0.435240\pi$
$252$	−32.5637	−	37.0859i	−0.129221	−	0.147166i
$253$	−318.555	−	318.555i	−1.25911	−	1.25911i
$254$	−61.1193	−	27.6702i	−0.240627	−	0.108938i
$255$	−166.028	−	0.489152i	−0.651092	−	0.00191824i
$256$	−247.439	−	65.6510i	−0.966558	−	0.256449i
$257$			329.631i			1.28261i	0.767286	+	0.641305i	$0.221607\pi$
$257$			329.631i			1.28261i	−0.767286	+	0.641305i	$0.778393\pi$
$258$	156.422	+	70.8162i	0.606288	+	0.274481i
$259$	−65.4199	−	65.4199i	−0.252586	−	0.252586i
$260$	−297.595	−	340.944i	−1.14460	−	1.31132i
$261$	20.1939	+	20.1939i	0.0773711	+	0.0773711i
$262$	−105.600	−	280.311i	−0.403052	−	1.06989i
$263$		−	56.1771i		−	0.213601i	−0.994280	−	0.106801i	$-0.965939\pi$
$263$		−	56.1771i		−	0.213601i	0.994280	−	0.106801i	$-0.0340607\pi$
$264$	−357.827	+	108.905i	−1.35541	+	0.412520i
$265$	0.387906	−	131.663i	0.00146380	−	0.496843i
$266$	34.1800	−	12.8764i	0.128496	−	0.0484075i
$267$	154.255	+	154.255i	0.577736	+	0.577736i
$268$	290.676	+	18.8729i	1.08461	+	0.0704214i
$269$	287.851	−	287.851i	1.07008	−	1.07008i	0.0727268	−	0.997352i	$-0.476830\pi$
$269$	287.851	−	287.851i	1.07008	−	1.07008i	0.997352	−	0.0727268i	$-0.0231701\pi$
$270$	202.120	+	92.2232i	0.748593	+	0.341567i
$271$		−	287.492i		−	1.06086i	−0.847730	−	0.530428i	$-0.822031\pi$
$271$		−	287.492i		−	1.06086i	0.847730	−	0.530428i	$-0.177969\pi$
$272$	155.842	+	20.3226i	0.572949	+	0.0747155i
$273$			388.700i			1.42381i
$274$	−186.676	−	84.5130i	−0.681300	−	0.308441i
$275$	−243.043	−	245.925i	−0.883794	−	0.894271i
$276$	−28.5385	+	439.542i	−0.103400	+	1.59255i
$277$	−50.1607	+	50.1607i	−0.181085	+	0.181085i	−0.791829	−	0.610743i	$-0.790871\pi$
$277$	−50.1607	+	50.1607i	−0.181085	+	0.181085i	0.610743	+	0.791829i	$0.290871\pi$
$278$	−407.291	+	153.436i	−1.46508	+	0.551929i
$279$	93.8594			0.336414
$280$	−96.1780	+	179.063i	−0.343493	+	0.639509i
$281$			105.191i			0.374347i	0.982327	+	0.187173i	$0.0599326\pi$
$281$			105.191i			0.374347i	−0.982327	+	0.187173i	$0.940067\pi$
$282$	37.9148	−	14.2834i	0.134450	−	0.0506503i
$283$	−267.270	−	267.270i	−0.944417	−	0.944417i	0.0541177	−	0.998535i	$-0.482765\pi$
$283$	−267.270	−	267.270i	−0.944417	−	0.944417i	−0.998535	+	0.0541177i	$0.982765\pi$
$284$	−88.6679	−	100.981i	−0.312211	−	0.355568i
$285$	43.0815	−	42.8284i	0.151163	−	0.150275i
$286$	570.187	+	258.138i	1.99366	+	0.902580i
$287$	−152.817			−0.532465
$288$	66.0457	+	40.9296i	0.229325	+	0.142117i
$289$	192.516			0.666147
$290$	48.8233	−	107.003i	0.168356	−	0.368976i
$291$	328.116	+	328.116i	1.12755	+	1.12755i
$292$	212.897	+	242.462i	0.729098	+	0.830350i
$293$	−134.928	+	134.928i	−0.460507	+	0.460507i	−0.898822	−	0.438315i	$-0.855576\pi$
$293$	−134.928	+	134.928i	−0.460507	+	0.460507i	0.438315	+	0.898822i	$0.355576\pi$
$294$	−146.654	+	55.2480i	−0.498823	+	0.187918i
$295$	−0.455422	+	154.580i	−0.00154380	+	0.523999i
$296$	128.520	+	68.5435i	0.434190	+	0.231566i
$297$	−307.263			−1.03455
$298$	120.659	+	320.285i	0.404896	+	1.07478i
$299$	521.186	−	521.186i	1.74310	−	1.74310i
$300$	−23.8904	+	337.210i	−0.0796346	+	1.12403i
$301$	−91.2513	+	91.2513i	−0.303160	+	0.303160i
$302$	219.542	+	99.3921i	0.726961	+	0.329113i
$303$	554.348			1.82953
$304$	−45.5775	+	35.0617i	−0.149926	+	0.115335i
$305$	1.68014	−	570.273i	0.00550864	−	1.86975i
$306$	−43.4551	−	19.6732i	−0.142010	−	0.0642915i
$307$	−198.450	+	198.450i	−0.646415	+	0.646415i	−0.952125	−	0.305709i	$-0.901106\pi$
$307$	−198.450	+	198.450i	−0.646415	+	0.646415i	0.305709	+	0.952125i	$0.401106\pi$
$308$	18.2136	−	280.521i	0.0591351	−	0.910784i
$309$	−209.240	−	209.240i	−0.677151	−	0.677151i
$310$	−135.208	−	362.134i	−0.436153	−	1.16818i
$311$	−97.0520			−0.312064			−0.156032	−	0.987752i	$-0.549870\pi$
$311$	−97.0520			−0.312064			−0.156032	+	0.987752i	$0.549870\pi$
$312$	−178.179	−	585.439i	−0.571087	−	1.87641i
$313$	175.107			0.559446			0.279723	−	0.960081i	$-0.409757\pi$
$313$	175.107			0.559446			0.279723	+	0.960081i	$0.409757\pi$
$314$	145.905	+	387.301i	0.464666	+	1.23344i
$315$	43.7510	−	43.4939i	0.138892	−	0.138076i
$316$	180.139	−	158.173i	0.570061	−	0.500549i
$317$	111.108	+	111.108i	0.350498	+	0.350498i	0.860295	−	0.509797i	$-0.170279\pi$
$317$	111.108	+	111.108i	0.350498	+	0.350498i	−0.509797	+	0.860295i	$0.670279\pi$
$318$	73.4281	−	162.192i	0.230906	−	0.510036i
$319$			162.666i			0.509925i
$320$	62.7762	−	313.782i	0.196176	−	0.980569i
$321$	−120.593			−0.375679
$322$	−301.576	−	136.531i	−0.936573	−	0.424010i
$323$	24.9623	−	24.9623i	0.0772826	−	0.0772826i
$324$	255.892	+	291.429i	0.789791	+	0.899471i
$325$	402.355	−	397.641i	1.23802	−	1.22351i
$326$	−551.023	+	207.583i	−1.69025	+	0.636758i
$327$			501.033i			1.53221i
$328$	230.165	−	70.0511i	0.701723	−	0.213570i
$329$			30.4506i			0.0925550i
$330$	−163.536	−	438.008i	−0.495563	−	1.32730i
$331$	−244.119	+	244.119i	−0.737521	+	0.737521i	−0.972098	−	0.234577i	$-0.924630\pi$
$331$	−244.119	+	244.119i	−0.737521	+	0.737521i	0.234577	+	0.972098i	$0.424630\pi$
$332$	−196.181	−	12.7376i	−0.590908	−	0.0383663i
$333$	−31.2603	−	31.2603i	−0.0938748	−	0.0938748i
$334$	−94.1104	+	207.876i	−0.281768	+	0.622382i
$335$	−1.07274	+	364.109i	−0.00320220	+	1.08689i
$336$	−217.847	+	167.585i	−0.648354	+	0.498764i
$337$		−	333.980i		−	0.991037i	−0.868597	−	0.495519i	$-0.834978\pi$
$337$		−	333.980i		−	0.991037i	0.868597	−	0.495519i	$-0.165022\pi$
$338$	−282.937	+	624.964i	−0.837091	+	1.84901i
$339$	−65.5758	−	65.5758i	−0.193439	−	0.193439i
$340$	−13.3059	+	196.001i	−0.0391350	+	0.576474i
$341$	378.029	+	378.029i	1.10859	+	1.10859i
$342$	16.3326	−	6.15287i	0.0477561	−	0.0179908i
$343$		−	366.773i		−	1.06931i
$344$	95.6083	−	179.267i	0.277931	−	0.521125i
$345$	−550.583	−	1.62212i	−1.59589	−	0.00470181i
$346$	−106.858	−	283.650i	−0.308837	−	0.819799i
$347$	43.0694	+	43.0694i	0.124119	+	0.124119i	0.766438	−	0.642319i	$-0.222027\pi$
$347$	43.0694	+	43.0694i	0.124119	+	0.124119i	−0.642319	+	0.766438i	$0.722027\pi$
$348$	119.510	−	104.937i	0.343419	−	0.301543i
$349$	−206.400	+	206.400i	−0.591404	+	0.591404i	−0.938011	−	0.346607i	$-0.887334\pi$
$349$	−206.400	+	206.400i	−0.591404	+	0.591404i	0.346607	+	0.938011i	$0.387334\pi$
$350$	−230.836	−	106.148i	−0.659530	−	0.303281i
$351$		−	502.710i		−	1.43222i
$352$	101.158	+	430.855i	0.287380	+	1.22402i
$353$		−	86.0684i		−	0.243820i	−0.992541	−	0.121910i	$-0.961098\pi$
$353$		−	86.0684i		−	0.243820i	0.992541	−	0.121910i	$-0.0389019\pi$
$354$	−86.2084	+	190.421i	−0.243527	+	0.537913i
$355$	119.130	−	118.430i	0.335577	−	0.333605i
$356$	193.963	−	170.312i	0.544841	−	0.478404i
$357$	119.312	−	119.312i	0.334209	−	0.334209i
$358$	−157.626	−	418.414i	−0.440297	−	1.16875i
$359$	−26.9476			−0.0750629			−0.0375314	−	0.999295i	$-0.511949\pi$
$359$	−26.9476			−0.0750629			−0.0375314	+	0.999295i	$0.511949\pi$
$360$	−45.9578	+	85.5635i	−0.127661	+	0.237676i
$361$		−	348.083i		−	0.964220i
$362$	−57.4071	−	152.385i	−0.158583	−	0.420954i
$363$	167.994	+	167.994i	0.462793	+	0.462793i
$364$	458.959	+	29.7992i	1.26088	+	0.0818658i
$365$	−286.038	+	284.357i	−0.783664	+	0.779060i
$366$	318.038	−	702.499i	0.868958	−	1.91940i
$367$	388.947			1.05980			0.529900	−	0.848060i	$-0.322229\pi$
$367$	388.947			1.05980			0.529900	+	0.848060i	$0.322229\pi$
$368$	516.803	+	67.3938i	1.40436	+	0.183135i
$369$	−73.0224			−0.197893
$370$	−75.5790	+	165.642i	−0.204268	+	0.447681i
$371$	94.6169	+	94.6169i	0.255032	+	0.255032i
$372$	33.8666	−	521.605i	0.0910393	−	1.40216i
$373$	93.7772	−	93.7772i	0.251413	−	0.251413i	−0.570137	−	0.821550i	$-0.693110\pi$
$373$	93.7772	−	93.7772i	0.251413	−	0.251413i	0.821550	+	0.570137i	$0.193110\pi$
$374$	−95.7843	−	254.256i	−0.256108	−	0.679829i
$375$	−422.552	−	3.73485i	−1.12681	−	0.00995961i
$376$	−13.9585	−	45.8630i	−0.0371236	−	0.121976i
$377$	−266.137			−0.705933
$378$	−211.288	+	79.5973i	−0.558964	+	0.210575i
$379$	37.2892	−	37.2892i	0.0983885	−	0.0983885i	−0.656199	−	0.754588i	$-0.727837\pi$
$379$	37.2892	−	37.2892i	0.0983885	−	0.0983885i	0.754588	+	0.656199i	$0.227837\pi$
$380$	−47.2670	−	54.1520i	−0.124387	−	0.142505i
$381$	80.1875	−	80.1875i	0.210466	−	0.210466i
$382$	−95.7691	+	211.539i	−0.250704	+	0.553768i
$383$	97.1930			0.253768			0.126884	−	0.991918i	$-0.459502\pi$
$383$	97.1930			0.253768			0.126884	+	0.991918i	$0.459502\pi$
$384$	251.289	−	352.267i	0.654398	−	0.917363i
$385$	351.389	+	1.03526i	0.912698	+	0.00268899i
$386$	−23.8890	+	52.7672i	−0.0618887	+	0.136703i
$387$	−43.6036	+	43.6036i	−0.112671	+	0.112671i
$388$	412.579	−	362.270i	1.06335	−	0.933685i
$389$	148.407	+	148.407i	0.381509	+	0.381509i	0.871646	−	0.490137i	$-0.163053\pi$
$389$	148.407	+	148.407i	0.381509	+	0.381509i	−0.490137	+	0.871646i	$0.663053\pi$
$390$	716.622	−	267.560i	1.83749	−	0.686051i
$391$	−319.959			−0.818308
$392$	53.9912	+	177.398i	0.137733	+	0.452545i
$393$	506.308			1.28832
$394$	−313.967	+	118.279i	−0.796871	+	0.300200i
$395$	211.265	+	212.514i	0.534849	+	0.538010i
$396$	8.70321	−	134.045i	0.0219778	−	0.338497i
$397$	−188.053	−	188.053i	−0.473685	−	0.473685i	0.429420	−	0.903105i	$-0.358718\pi$
$397$	−188.053	−	188.053i	−0.473685	−	0.473685i	−0.903105	+	0.429420i	$0.858718\pi$
$398$	−20.2931	−	9.18717i	−0.0509876	−	0.0230833i
$399$			61.7372i			0.154730i
$400$	396.330	+	54.0604i	0.990825	+	0.135151i
$401$	−692.545			−1.72705			−0.863523	−	0.504310i	$-0.831747\pi$
$401$	−692.545			−1.72705			−0.863523	+	0.504310i	$0.831747\pi$
$402$	−203.062	+	448.533i	−0.505129	+	1.11575i
$403$	−618.491	+	618.491i	−1.53472	+	1.53472i
$404$	42.4983	−	654.549i	0.105194	−	1.62017i
$405$	−343.804	+	341.784i	−0.848900	+	0.843912i
$406$	42.1391	+	111.857i	0.103791	+	0.275510i
$407$		−	251.809i		−	0.618695i
$408$	−125.009	+	234.394i	−0.306396	+	0.574496i
$409$		−	107.152i		−	0.261985i	−0.991383	−	0.130993i	$-0.958184\pi$
$409$		−	107.152i		−	0.261985i	0.991383	−	0.130993i	$-0.0418164\pi$
$410$	105.191	+	281.740i	0.256564	+	0.687170i
$411$	244.916	−	244.916i	0.595904	−	0.595904i
$412$	−263.101	+	231.019i	−0.638595	+	0.560726i
$413$	−111.085	−	111.085i	−0.268971	−	0.268971i
$414$	−144.106	−	65.2401i	−0.348081	−	0.157585i
$415$	0.724004	−	245.742i	0.00174459	−	0.592149i
$416$	−704.919	+	165.504i	−1.69452	+	0.397846i
$417$		−	735.666i		−	1.76419i
$418$	90.5627	+	41.0000i	0.216657	+	0.0980860i
$419$	475.736	+	475.736i	1.13541	+	1.13541i	0.989263	+	0.146146i	$0.0466869\pi$
$419$	475.736	+	475.736i	1.13541	+	1.13541i	0.146146	+	0.989263i	$0.453313\pi$
$420$	−225.922	−	258.831i	−0.537910	−	0.616264i
$421$	264.190	+	264.190i	0.627530	+	0.627530i	0.947446	−	0.319916i	$-0.103655\pi$
$421$	264.190	+	264.190i	0.627530	+	0.627530i	−0.319916	+	0.947446i	$0.603655\pi$
$422$	−0.881702	−	2.34045i	−0.00208934	−	0.00554609i
$423$			14.5505i			0.0343984i
$424$	−185.879	−	99.1347i	−0.438394	−	0.233808i
$425$	−245.561	−	1.44695i	−0.577790	−	0.00340460i
$426$	212.564	−	80.0777i	0.498976	−	0.187976i
$427$	409.813	+	409.813i	0.959750	+	0.959750i
$428$	−9.24508	+	142.390i	−0.0216007	+	0.332688i
$429$	−748.076	+	748.076i	−1.74377	+	1.74377i
$430$	231.047	+	105.422i	0.537318	+	0.245167i
$431$			507.341i			1.17713i	0.808451	+	0.588563i	$0.200306\pi$
$431$			507.341i			1.17713i	−0.808451	+	0.588563i	$0.799694\pi$
$432$	281.744	−	216.739i	0.652185	−	0.501711i
$433$			495.619i			1.14462i	0.820039	+	0.572308i	$0.193952\pi$
$433$			495.619i			1.14462i	−0.820039	+	0.572308i	$0.806048\pi$
$434$	357.881	+	162.021i	0.824610	+	0.373321i
$435$	140.160	+	140.988i	0.322206	+	0.324111i
$436$	591.597	+	38.4110i	1.35687	+	0.0880987i
$437$	82.7799	−	82.7799i	0.189428	−	0.189428i
$438$	−510.378	+	192.271i	−1.16525	+	0.438975i
$439$	−228.193			−0.519801			−0.259901	−	0.965635i	$-0.583690\pi$
$439$	−228.193			−0.519801			−0.259901	+	0.965635i	$0.583690\pi$
$440$	−529.717	+	159.516i	−1.20390	+	0.362537i
$441$		−	56.2813i		−	0.127622i
$442$	415.987	−	156.712i	0.941147	−	0.354552i
$443$	−113.426	−	113.426i	−0.256041	−	0.256041i	0.567401	−	0.823442i	$-0.307949\pi$
$443$	−113.426	−	113.426i	−0.256041	−	0.256041i	−0.823442	+	0.567401i	$0.807949\pi$
$444$	−185.002	+	162.443i	−0.416672	+	0.365864i
$445$	227.478	+	228.823i	0.511187	+	0.514208i
$446$	−440.232	−	199.304i	−0.987068	−	0.446870i
$447$	−578.512			−1.29421
$448$	181.175	+	270.071i	0.404409	+	0.602837i
$449$	−385.638			−0.858881			−0.429441	−	0.903095i	$-0.641289\pi$
$449$	−385.638			−0.858881			−0.429441	+	0.903095i	$0.641289\pi$
$450$	−110.303	−	50.7220i	−0.245117	−	0.112716i
$451$	−294.106	−	294.106i	−0.652120	−	0.652120i
$452$	−82.4561	+	72.4015i	−0.182425	+	0.160180i
$453$	−288.036	+	288.036i	−0.635841	+	0.635841i
$454$	636.625	−	239.831i	1.40226	−	0.528263i
$455$	−1.69378	+	574.904i	−0.00372260	+	1.26353i
$456$	−28.3002	−	92.9852i	−0.0620617	−	0.203915i
$457$	29.4858			0.0645203			0.0322601	−	0.999480i	$-0.489729\pi$
$457$	29.4858			0.0645203			0.0322601	+	0.999480i	$0.489729\pi$
$458$	−121.595	−	322.770i	−0.265491	−	0.704738i
$459$	−154.308	+	154.308i	−0.336183	+	0.336183i
$460$	−44.1250	+	649.978i	−0.0959238	+	1.41300i
$461$	334.283	−	334.283i	0.725126	−	0.725126i	−0.244519	−	0.969645i	$-0.578630\pi$
$461$	334.283	−	334.283i	0.725126	−	0.725126i	0.969645	+	0.244519i	$0.0786300\pi$
$462$	432.863	+	195.968i	0.936933	+	0.424173i
$463$	−218.319			−0.471531			−0.235765	−	0.971810i	$-0.575760\pi$
$463$	−218.319			−0.471531			−0.235765	+	0.971810i	$0.575760\pi$
$464$	−114.743	−	149.156i	−0.247290	−	0.321458i
$465$	653.376	+	1.92498i	1.40511	+	0.00413973i
$466$	532.456	+	241.056i	1.14261	+	0.517288i
$467$	205.296	−	205.296i	0.439607	−	0.439607i	−0.452273	−	0.891880i	$-0.649387\pi$
$467$	205.296	−	205.296i	0.439607	−	0.439607i	0.891880	+	0.452273i	$0.149387\pi$
$468$	219.309	+	14.2393i	0.468610	+	0.0304258i
$469$	−261.658	−	261.658i	−0.557907	−	0.557907i
$470$	56.1398	−	20.9605i	0.119446	−	0.0445969i
$471$	−699.558			−1.48526
$472$	218.232	+	116.389i	0.462355	+	0.246587i
$473$	−351.237			−0.742573
$474$	142.849	+	379.189i	0.301370	+	0.799977i
$475$	63.9060	−	63.1573i	0.134539	−	0.132963i
$476$	−131.732	−	150.026i	−0.276747	−	0.315180i
$477$	45.2118	+	45.2118i	0.0947837	+	0.0947837i
$478$	−50.2790	+	111.059i	−0.105186	+	0.232340i
$479$			498.778i			1.04129i	0.853773	+	0.520645i	$0.174308\pi$
$479$			498.778i			1.04129i	−0.853773	+	0.520645i	$0.825692\pi$
$480$	458.919	+	286.274i	0.956082	+	0.596405i
$481$	411.983			0.856513
$482$	151.740	+	68.6966i	0.314814	+	0.142524i
$483$	395.664	−	395.664i	0.819179	−	0.819179i
$484$	211.238	−	185.480i	0.436443	−	0.383224i
$485$	483.868	+	486.728i	0.997666	+	1.00356i
$486$	−239.227	+	90.1225i	−0.492237	+	0.185437i
$487$		−	79.5802i		−	0.163409i	−0.996657	−	0.0817045i	$-0.973964\pi$
$487$		−	79.5802i		−	0.163409i	0.996657	−	0.0817045i	$-0.0260364\pi$
$488$	−805.096	−	429.381i	−1.64979	−	0.879879i
$489$		−	995.279i		−	2.03534i
$490$	−217.148	+	81.0750i	−0.443160	+	0.165459i
$491$	310.801	−	310.801i	0.632996	−	0.632996i	−0.315823	−	0.948818i	$-0.602280\pi$
$491$	310.801	−	310.801i	0.632996	−	0.632996i	0.948818	+	0.315823i	$0.102280\pi$
$492$	−26.3481	+	405.807i	−0.0535531	+	0.824812i
$493$	81.6913	+	81.6913i	0.165703	+	0.165703i
$494$	−67.0798	+	148.169i	−0.135789	+	0.299937i
$495$	167.908	+	0.494690i	0.339208	+	0.000999373i
$496$	−613.290	−	79.9762i	−1.23647	−	0.161242i
$497$			170.717i			0.343495i
$498$	137.049	−	302.721i	0.275199	−	0.607873i
$499$	607.980	+	607.980i	1.21840	+	1.21840i	0.968193	+	0.250204i	$0.0804977\pi$
$499$	607.980	+	607.980i	1.21840	+	1.21840i	0.250204	+	0.968193i	$0.419502\pi$
$500$	−36.8043	+	498.644i	−0.0736086	+	0.997287i
$501$	−272.730	−	272.730i	−0.544370	−	0.544370i
$502$	−516.421	+	194.548i	−1.02873	+	0.387546i
$503$		−	325.228i		−	0.646576i	−0.946301	−	0.323288i	$-0.895212\pi$
$503$		−	325.228i		−	0.646576i	0.946301	−	0.323288i	$-0.104788\pi$
$504$	−28.7399	−	94.4301i	−0.0570236	−	0.187361i
$505$	819.905	+	2.41560i	1.62357	+	0.00478337i
$506$	−317.639	−	843.163i	−0.627746	−	1.66633i
$507$	−819.944	−	819.944i	−1.61725	−	1.61725i
$508$	−88.5342	−	100.829i	−0.174280	−	0.198483i
$509$	269.365	−	269.365i	0.529205	−	0.529205i	−0.391130	−	0.920335i	$-0.627916\pi$
$509$	269.365	−	269.365i	0.529205	−	0.529205i	0.920335	+	0.391130i	$0.127916\pi$
$510$	−302.097	−	137.841i	−0.592347	−	0.270276i
$511$		−	409.901i		−	0.802155i
$512$	−396.676	−	323.716i	−0.774758	−	0.632258i
$513$		−	79.8454i		−	0.155644i
$514$	−271.898	+	600.581i	−0.528984	+	1.16845i
$515$	−308.562	−	310.386i	−0.599150	−	0.602691i
$516$	226.585	+	258.051i	0.439119	+	0.500100i
$517$	−58.6040	+	58.6040i	−0.113354	+	0.113354i
$518$	−65.2318	−	173.156i	−0.125930	−	0.334277i
$519$	512.341			0.987169
$520$	−260.984	−	866.666i	−0.501891	−	1.66667i
$521$		−	667.589i		−	1.28136i	−0.767807	−	0.640681i	$-0.778652\pi$
$521$		−	667.589i		−	1.28136i	0.767807	−	0.640681i	$-0.221348\pi$
$522$	20.1358	+	53.4498i	0.0385743	+	0.102394i
$523$	188.149	+	188.149i	0.359749	+	0.359749i	0.863720	−	0.503972i	$-0.168128\pi$
$523$	188.149	+	188.149i	0.359749	+	0.359749i	−0.503972	+	0.863720i	$0.668128\pi$
$524$	38.8154	−	597.825i	0.0740752	−	1.14089i
$525$	305.452	−	301.873i	0.581814	−	0.574997i
$526$	46.3380	−	102.354i	0.0880951	−	0.194589i
$527$	379.695			0.720483
$528$	−741.786	−	96.7327i	−1.40490	−	0.183206i
$529$	−532.045			−1.00576
$530$	109.310	−	239.568i	0.206245	−	0.452016i
$531$	−53.0811	−	53.0811i	−0.0999643	−	0.0999643i
$532$	72.8964	+	4.73299i	0.137023	+	0.00889661i
$533$	481.185	−	481.185i	0.902786	−	0.902786i
$534$	153.812	+	408.289i	0.288037	+	0.764586i
$535$	−178.362	−	0.525490i	−0.333387	−	0.000982224i
$536$	514.039	+	274.152i	0.959028	+	0.511478i
$537$	755.755			1.40737
$538$	761.895	−	287.024i	1.41616	−	0.533501i
$539$	226.679	−	226.679i	0.420555	−	0.420555i
$540$	292.188	+	334.749i	0.541089	+	0.619905i
$541$	−249.000	+	249.000i	−0.460259	+	0.460259i	−0.898740	−	0.438481i	$-0.855517\pi$
$541$	−249.000	+	249.000i	−0.460259	+	0.460259i	0.438481	+	0.898740i	$0.355517\pi$
$542$	237.139	−	523.805i	0.437527	−	0.966430i
$543$	275.244			0.506896
$544$	267.178	+	165.575i	0.491136	+	0.304365i
$545$	−2.18328	+	741.050i	−0.00400602	+	1.35972i
$546$	−320.622	+	708.205i	−0.587219	+	1.29708i
$547$	621.267	−	621.267i	1.13577	−	1.13577i	0.146571	−	0.989200i	$-0.453176\pi$
$547$	621.267	−	621.267i	1.13577	−	1.13577i	0.989200	−	0.146571i	$-0.0468237\pi$
$548$	−270.410	−	307.962i	−0.493448	−	0.561974i
$549$	195.826	+	195.826i	0.356695	+	0.356695i
$550$	−239.968	−	648.545i	−0.436305	−	1.17917i
$551$	−42.2705			−0.0767159
$552$	−414.556	+	777.298i	−0.751007	+	1.40815i
$553$	−304.539			−0.550704
$554$	−132.767	+	50.0165i	−0.239652	+	0.0902824i
$555$	−216.969	−	218.251i	−0.390935	−	0.393245i
$556$	−868.639	−	56.3988i	−1.56230	−	0.101437i
$557$	−269.024	−	269.024i	−0.482987	−	0.482987i	0.423097	−	0.906084i	$-0.360943\pi$
$557$	−269.024	−	269.024i	−0.482987	−	0.482987i	−0.906084	+	0.423097i	$0.860943\pi$
$558$	171.010	+	77.4205i	0.306470	+	0.138746i
$559$		−	574.656i		−	1.02801i
$560$	−322.935	+	246.916i	−0.576670	+	0.440921i
$561$	459.248			0.818623
$562$	−86.7678	+	191.657i	−0.154391	+	0.341026i
$563$	−366.055	+	366.055i	−0.650186	+	0.650186i	−0.953038	−	0.302852i	$-0.902061\pi$
$563$	−366.055	+	366.055i	−0.650186	+	0.650186i	0.302852	+	0.953038i	$0.402061\pi$
$564$	80.8617	+	5.25017i	0.143372	+	0.00930881i
$565$	−96.7036	−	97.2751i	−0.171157	−	0.172168i
$566$	−266.502	−	707.420i	−0.470851	−	1.24986i
$567$		−	492.683i		−	0.868929i
$568$	−78.2561	−	257.124i	−0.137775	−	0.452684i
$569$			761.087i			1.33759i	0.743448	+	0.668794i	$0.233189\pi$
$569$			761.087i			1.33759i	−0.743448	+	0.668794i	$0.766811\pi$
$570$	113.821	−	42.4965i	0.199686	−	0.0745553i
$571$	−18.9101	+	18.9101i	−0.0331175	+	0.0331175i	−0.723472	−	0.690354i	$-0.757455\pi$
$571$	−18.9101	+	18.9101i	−0.0331175	+	0.0331175i	0.690354	+	0.723472i	$0.257455\pi$
$572$	825.943	+	940.644i	1.44396	+	1.64448i
$573$	−277.536	−	277.536i	−0.484357	−	0.484357i
$574$	−278.430	−	126.052i	−0.485070	−	0.219603i
$575$	−814.328	−	4.79838i	−1.41622	−	0.00834502i
$576$	86.5730	+	129.051i	0.150300	+	0.224047i
$577$			770.887i			1.33603i	0.744150	+	0.668013i	$0.232855\pi$
$577$			770.887i			1.33603i	−0.744150	+	0.668013i	$0.767145\pi$
$578$	350.761	+	158.798i	0.606853	+	0.274737i
$579$	−69.2298	−	69.2298i	−0.119568	−	0.119568i
$580$	177.217	−	154.685i	0.305547	−	0.266699i
$581$	176.597	+	176.597i	0.303953	+	0.303953i
$582$	327.173	+	868.470i	0.562153	+	1.49222i
$583$			364.192i			0.624685i
$584$	187.897	+	617.370i	0.321742	+	1.05714i
$585$	−0.809358	+	274.713i	−0.00138352	+	0.469595i
$586$	−357.134	+	134.541i	−0.609443	+	0.229591i
$587$	−396.570	−	396.570i	−0.675587	−	0.675587i	0.283411	−	0.958998i	$-0.408534\pi$
$587$	−396.570	−	396.570i	−0.675587	−	0.675587i	−0.958998	+	0.283411i	$0.908534\pi$
$588$	−312.772	−	20.3076i	−0.531925	−	0.0345367i
$589$	−98.2349	+	98.2349i	−0.166782	+	0.166782i
$590$	−128.336	+	281.266i	−0.217518	+	0.476721i
$591$		−	567.100i		−	0.959560i
$592$	177.623	+	230.895i	0.300038	+	0.390026i
$593$			344.909i			0.581634i	0.956779	+	0.290817i	$0.0939272\pi$
$593$			344.909i			0.581634i	−0.956779	+	0.290817i	$0.906073\pi$
$594$	−559.827	−	253.447i	−0.942469	−	0.426679i
$595$	176.988	−	175.948i	0.297459	−	0.295712i
$596$	−44.3508	+	683.080i	−0.0744141	+	1.14611i
$597$	26.6242	−	26.6242i	0.0445966	−	0.0445966i
$598$	1379.49	−	519.688i	2.30685	−	0.869043i
$599$	970.796			1.62069			0.810347	−	0.585950i	$-0.199279\pi$
$599$	970.796			1.62069			0.810347	+	0.585950i	$0.199279\pi$
$600$	−321.677	+	594.684i	−0.536129	+	0.991139i
$601$			588.278i			0.978832i	0.872051	+	0.489416i	$0.162790\pi$
$601$			588.278i			0.978832i	−0.872051	+	0.489416i	$0.837210\pi$
$602$	−241.527	+	90.9890i	−0.401208	+	0.151144i
$603$	−125.031	−	125.031i	−0.207348	−	0.207348i
$604$	318.017	+	362.181i	0.526519	+	0.599638i
$605$	247.738	+	249.202i	0.409484	+	0.411904i
$606$	1010.01	+	457.257i	1.66669	+	0.754550i
$607$	−742.181			−1.22270			−0.611351	−	0.791359i	$-0.709374\pi$
$607$	−742.181			−1.22270			−0.611351	+	0.791359i	$0.709374\pi$
$608$	−111.962	+	26.2869i	−0.184148	+	0.0432351i
$609$	−202.040			−0.331758
$610$	473.454	−	1037.64i	0.776154	−	1.70105i
$611$	−95.8815	−	95.8815i	−0.156926	−	0.156926i
$612$	−62.9468	−	71.6883i	−0.102854	−	0.117138i
$613$	−282.998	+	282.998i	−0.461660	+	0.461660i	−0.899199	−	0.437539i	$-0.855850\pi$
$613$	−282.998	+	282.998i	−0.461660	+	0.461660i	0.437539	+	0.899199i	$0.355850\pi$
$614$	−525.263	+	197.879i	−0.855478	+	0.322278i
$615$	−508.325	−	1.49763i	−0.826545	−	0.00243516i
$616$	264.574	−	496.081i	0.429504	−	0.805326i
$617$	−521.001			−0.844411			−0.422205	−	0.906500i	$-0.638744\pi$
$617$	−521.001			−0.844411			−0.422205	+	0.906500i	$0.638744\pi$
$618$	−208.638	−	553.823i	−0.337602	−	0.896153i
$619$	249.150	−	249.150i	0.402505	−	0.402505i	−0.476610	−	0.879115i	$-0.658135\pi$
$619$	249.150	−	249.150i	0.402505	−	0.402505i	0.879115	+	0.476610i	$0.158135\pi$
$620$	52.3631	−	771.329i	0.0844566	−	1.24408i
$621$	−511.716	+	511.716i	−0.824019	+	0.824019i
$622$	−176.827	−	80.0539i	−0.284288	−	0.128704i
$623$	−327.910			−0.526340
$624$	158.264	−	1213.63i	0.253628	−	1.94492i
$625$	−624.957	−	7.36530i	−0.999931	−	0.0117845i
$626$	319.041	+	144.438i	0.509650	+	0.230731i
$627$	−118.817	+	118.817i	−0.189501	+	0.189501i
$628$	−53.6306	+	826.005i	−0.0853991	+	1.31530i
$629$	−126.459	−	126.459i	−0.201048	−	0.201048i
$630$	115.590	−	43.1569i	0.183476	−	0.0685029i
$631$	815.349			1.29215			0.646077	−	0.763272i	$-0.276408\pi$
$631$	815.349			1.29215			0.646077	+	0.763272i	$0.276408\pi$
$632$	458.680	−	139.600i	0.725760	−	0.220886i
$633$	4.22741			0.00667838
$634$	110.788	+	294.084i	0.174745	+	0.463855i
$635$	118.950	−	118.251i	0.187323	−	0.186223i
$636$	267.569	−	234.942i	0.420706	−	0.369406i
$637$	370.869	+	370.869i	0.582211	+	0.582211i
$638$	−134.176	+	296.374i	−0.210307	+	0.464537i
$639$			81.5755i			0.127661i
$640$	373.202	−	519.923i	0.583128	−	0.812380i
$641$	778.586			1.21464			0.607321	−	0.794456i	$-0.292244\pi$
$641$	778.586			1.21464			0.607321	+	0.794456i	$0.292244\pi$
$642$	−219.718	−	99.4717i	−0.342240	−	0.154940i
$643$	338.184	−	338.184i	0.525947	−	0.525947i	−0.393415	−	0.919361i	$-0.628706\pi$
$643$	338.184	−	338.184i	0.525947	−	0.525947i	0.919361	+	0.393415i	$0.128706\pi$
$644$	−436.848	−	497.514i	−0.678335	−	0.772537i
$645$	−304.429	+	302.640i	−0.471982	+	0.469209i
$646$	66.0711	−	24.8905i	0.102277	−	0.0385302i
$647$		−	251.550i		−	0.388794i	−0.980923	−	0.194397i	$-0.937725\pi$
$647$		−	251.550i		−	0.388794i	0.980923	−	0.194397i	$-0.0622750\pi$
$648$	225.844	+	742.051i	0.348525	+	1.14514i
$649$		−	427.580i		−	0.658829i
$650$	1061.08	−	392.610i	1.63243	−	0.604015i
$651$	−469.534	+	469.534i	−0.721250	+	0.721250i
$652$	−1175.18	−	76.3017i	−1.80242	−	0.117027i
$653$	658.816	+	658.816i	1.00891	+	1.00891i	0.999960	+	0.00894710i	$0.00284799\pi$
$653$	658.816	+	658.816i	1.00891	+	1.00891i	0.00894710	+	0.999960i	$0.497152\pi$
$654$	−413.280	+	912.873i	−0.631927	+	1.39583i
$655$	748.852	+	2.20626i	1.14329	+	0.00336834i
$656$	477.138	+	62.2213i	0.727345	+	0.0948495i
$657$		−	195.867i		−	0.298124i
$658$	−25.1173	+	55.4804i	−0.0381723	+	0.0843167i
$659$	−693.169	−	693.169i	−1.05185	−	1.05185i	−0.998580	−	0.0532691i	$-0.983036\pi$
$659$	−693.169	−	693.169i	−1.05185	−	1.05185i	−0.0532691	−	0.998580i	$-0.516964\pi$
$660$	63.3341	−	932.936i	0.0959608	−	1.41354i
$661$	−517.616	−	517.616i	−0.783080	−	0.783080i	0.197269	−	0.980349i	$-0.436793\pi$
$661$	−517.616	−	517.616i	−0.783080	−	0.783080i	−0.980349	+	0.197269i	$0.936793\pi$
$662$	−646.144	+	243.417i	−0.976048	+	0.367700i
$663$			751.372i			1.13329i
$664$	−346.932	−	185.029i	−0.522488	−	0.278658i
$665$	−0.269023	+	91.3119i	−0.000404546	+	0.137311i
$666$	−31.1704	−	82.7409i	−0.0468024	−	0.124236i
$667$	270.904	+	270.904i	0.406154	+	0.406154i
$668$	−342.935	+	301.118i	−0.513375	+	0.450775i
$669$	577.578	−	577.578i	0.863345	−	0.863345i
$670$	−302.292	+	662.514i	−0.451181	+	0.988827i
$671$			1577.42i			2.35085i
$672$	−535.146	+	125.644i	−0.796349	+	0.186970i
$673$		−	821.981i		−	1.22137i	−0.791874	−	0.610684i	$-0.790895\pi$
$673$		−	821.981i		−	1.22137i	0.791874	−	0.610684i	$-0.209105\pi$
$674$	275.485	−	608.504i	0.408731	−	0.902825i
$675$	−395.045	+	390.416i	−0.585251	+	0.578394i
$676$	−1031.01	+	905.291i	−1.52516	+	1.33919i
$677$	256.582	−	256.582i	0.378998	−	0.378998i	−0.491743	−	0.870741i	$-0.663640\pi$
$677$	256.582	−	256.582i	0.378998	−	0.378998i	0.870741	+	0.491743i	$0.163640\pi$
$678$	−65.3872	−	173.568i	−0.0964413	−	0.256000i
$679$	−697.497			−1.02724
$680$	−185.916	+	346.135i	−0.273405	+	0.509021i
$681$			1149.90i			1.68854i
$682$	376.943	+	1000.58i	0.552702	+	1.46713i
$683$	841.969	+	841.969i	1.23275	+	1.23275i	0.962903	+	0.269849i	$0.0869738\pi$
$683$	841.969	+	841.969i	1.23275	+	1.23275i	0.269849	+	0.962903i	$0.413026\pi$
$684$	34.8329	+	2.26162i	0.0509253	+	0.00330646i
$685$	363.309	−	361.175i	0.530378	−	0.527262i
$686$	302.535	−	668.253i	0.441013	−	0.974130i
$687$	583.000			0.848617
$688$	322.066	−	247.758i	0.468119	−	0.360113i
$689$	−595.851			−0.864806
$690$	−1001.81	−	457.107i	−1.45190	−	0.662473i
$691$	79.9699	+	79.9699i	0.115731	+	0.115731i	0.762600	−	0.646870i	$-0.223922\pi$
$691$	79.9699	+	79.9699i	0.115731	+	0.115731i	−0.646870	+	0.762600i	$0.723922\pi$
$692$	39.2779	−	604.948i	0.0567599	−	0.874202i
$693$	−120.663	+	120.663i	−0.174117	+	0.174117i
$694$	42.9456	+	113.998i	0.0618812	+	0.164262i
$695$	3.20570	−	1088.08i	0.00461252	−	1.56558i
$696$	304.302	−	92.6148i	0.437216	−	0.133067i
$697$	−295.402			−0.423819
$698$	−546.307	+	205.807i	−0.782675	+	0.294852i
$699$	−698.574	+	698.574i	−0.999391	+	0.999391i
$700$	−333.021	−	383.806i	−0.475744	−	0.548295i
$701$	282.604	−	282.604i	0.403144	−	0.403144i	−0.476196	−	0.879339i	$-0.657985\pi$
$701$	282.604	−	282.604i	0.403144	−	0.403144i	0.879339	+	0.476196i	$0.157985\pi$
$702$	414.663	−	915.929i	0.590689	−	1.30474i
$703$	65.4351			0.0930798
$704$	−171.085	+	868.450i	−0.243019	+	1.23359i
$705$	−0.298419	+	101.290i	−0.000423289	+	0.143673i
$706$	70.9940	−	156.815i	0.100558	−	0.222117i
$707$	−589.206	+	589.206i	−0.833389	+	0.833389i
$708$	−314.140	+	275.834i	−0.443701	+	0.389597i
$709$	−656.306	−	656.306i	−0.925678	−	0.925678i	0.0717452	−	0.997423i	$-0.477143\pi$
$709$	−656.306	−	656.306i	−0.925678	−	0.925678i	−0.997423	+	0.0717452i	$0.977143\pi$
$710$	314.740	−	117.512i	0.443296	−	0.165510i
$711$	−145.521			−0.204671
$712$	493.880	−	150.313i	0.693652	−	0.211114i
$713$	1259.14			1.76598
$714$	315.801	−	118.969i	0.442298	−	0.166624i
$715$	−1109.70	+	1103.18i	−1.55202	+	1.54291i
$716$	57.9389	−	892.361i	0.0809203	−	1.24631i
$717$	−145.707	−	145.707i	−0.203218	−	0.203218i
$718$	−49.0980	−	22.2279i	−0.0683815	−	0.0309580i
$719$		−	214.819i		−	0.298775i	−0.988779	−	0.149387i	$-0.952270\pi$
$719$		−	214.819i		−	0.298775i	0.988779	−	0.149387i	$-0.0477301\pi$
$720$	−154.312	+	117.986i	−0.214322	+	0.163870i
$721$	444.793			0.616912
$722$	287.119	−	634.201i	0.397671	−	0.878395i
$723$	−199.081	+	199.081i	−0.275354	+	0.275354i
$724$	21.1012	−	324.996i	0.0291453	−	0.448889i
$725$	206.688	+	209.138i	0.285087	+	0.288466i
$726$	167.511	+	444.652i	0.230731	+	0.612468i
$727$		−	939.330i		−	1.29206i	−0.763311	−	0.646031i	$-0.776428\pi$
$727$		−	939.330i		−	1.29206i	0.763311	−	0.646031i	$-0.223572\pi$
$728$	811.635	+	432.869i	1.11488	+	0.594600i
$729$			440.514i			0.604272i
$730$	−755.708	+	282.153i	−1.03522	+	0.386511i
$731$	−176.392	+	176.392i	−0.241302	+	0.241302i
$732$	1158.92	−	1017.60i	1.58322	−	1.39017i
$733$	−479.564	−	479.564i	−0.654248	−	0.654248i	0.299765	−	0.954013i	$-0.403092\pi$
$733$	−479.564	−	479.564i	−0.654248	−	0.654248i	−0.954013	+	0.299765i	$0.903092\pi$
$734$	708.653	+	320.825i	0.965468	+	0.437091i
$735$	1.15428	−	391.787i	0.00157045	−	0.533043i
$736$	886.015	+	549.078i	1.20383	+	0.746030i
$737$		−	1007.15i		−	1.36656i
$738$	−133.045	−	60.2329i	−0.180278	−	0.0816164i
$739$	618.066	+	618.066i	0.836355	+	0.836355i	0.988377	−	0.152022i	$-0.0485786\pi$
$739$	618.066	+	618.066i	0.836355	+	0.836355i	−0.152022	+	0.988377i	$0.548579\pi$
$740$	−274.334	+	239.455i	−0.370722	+	0.323587i
$741$	−194.395	−	194.395i	−0.262342	−	0.262342i
$742$	94.3449	+	250.435i	0.127149	+	0.337514i
$743$			305.455i			0.411110i	0.978646	+	0.205555i	$0.0659000\pi$
$743$			305.455i			0.411110i	−0.978646	+	0.205555i	$0.934100\pi$
$744$	491.953	−	922.419i	0.661227	−	1.23981i
$745$	−855.644	−	2.52090i	−1.14852	−	0.00338375i
$746$	248.213	−	93.5076i	0.332725	−	0.125345i
$747$	84.3852	+	84.3852i	0.112965	+	0.112965i
$748$	35.2076	−	542.258i	0.0470689	−	0.724944i
$749$	128.176	−	128.176i	0.171129	−	0.171129i
$750$	−766.801	−	355.349i	−1.02240	−	0.473799i
$751$			853.156i			1.13603i	0.823019	+	0.568013i	$0.192288\pi$
$751$			853.156i			1.13603i	−0.823019	+	0.568013i	$0.807712\pi$
$752$	12.3983	−	95.0753i	0.0164871	−	0.126430i
$753$		−	932.780i		−	1.23875i
$754$	−484.896	−	219.524i	−0.643099	−	0.291147i
$755$	−427.273	+	424.762i	−0.565924	+	0.562599i
$756$	−450.620	−	29.2577i	−0.596058	−	0.0387007i
$757$	−360.656	+	360.656i	−0.476428	+	0.476428i	−0.903987	−	0.427559i	$-0.859373\pi$
$757$	−360.656	+	360.656i	−0.476428	+	0.476428i	0.427559	+	0.903987i	$0.359373\pi$
$758$	98.6985	−	37.1820i	0.130209	−	0.0490528i
$759$	1522.96			2.00653
$760$	−41.4520	−	137.652i	−0.0545420	−	0.181121i
$761$		−	241.725i		−	0.317641i	−0.987307	−	0.158821i	$-0.949231\pi$
$761$		−	241.725i		−	0.317641i	0.987307	−	0.158821i	$-0.0507691\pi$
$762$	212.243	−	79.9570i	0.278534	−	0.104930i
$763$	−532.538	−	532.538i	−0.697953	−	0.697953i
$764$	−348.979	+	306.425i	−0.456779	+	0.401080i
$765$	84.5722	−	84.0753i	0.110552	−	0.109902i
$766$	177.084	+	80.1702i	0.231180	+	0.104661i
$767$	699.561			0.912074
$768$	748.413	−	434.547i	0.974496	−	0.565817i
$769$	295.013			0.383632			0.191816	−	0.981431i	$-0.438562\pi$
$769$	295.013			0.383632			0.191816	+	0.981431i	$0.438562\pi$
$770$	639.369	+	291.731i	0.830350	+	0.378871i
$771$	−787.953	−	787.953i	−1.02199	−	1.02199i
$772$	−87.0507	+	76.4359i	−0.112760	+	0.0990102i
$773$	55.1851	−	55.1851i	0.0713908	−	0.0713908i	−0.670510	−	0.741901i	$-0.733925\pi$
$773$	55.1851	−	55.1851i	0.0713908	−	0.0713908i	0.741901	+	0.670510i	$0.233925\pi$
$774$	−115.412	+	43.4783i	−0.149111	+	0.0561735i
$775$	966.363	+	5.69424i	1.24692	+	0.00734741i
$776$	1050.53	−	319.730i	1.35378	−	0.412024i
$777$	312.761			0.402523
$778$	147.980	+	392.809i	0.190206	+	0.504896i
$779$	76.4265	−	76.4265i	0.0981084	−	0.0981084i
$780$	1526.37	+	103.620i	1.95688	+	0.132847i
$781$	−328.555	+	328.555i	−0.420685	+	0.420685i
$782$	−582.958	−	263.920i	−0.745471	−	0.337493i
$783$	261.301			0.333718
$784$	−47.9565	+	367.750i	−0.0611690	+	0.469069i
$785$	−1034.68	−	3.04836i	−1.31806	−	0.00388326i
$786$	922.484	+	417.631i	1.17364	+	0.531337i
$787$	−236.729	+	236.729i	−0.300800	+	0.300800i	−0.841327	−	0.540527i	$-0.818225\pi$
$787$	−236.729	+	236.729i	−0.300800	+	0.300800i	0.540527	+	0.841327i	$0.318225\pi$
$788$	−669.605	−	43.4759i	−0.849753	−	0.0551725i
$789$	134.286	+	134.286i	0.170198	+	0.170198i
$790$	209.628	+	561.460i	0.265352	+	0.710708i
$791$	139.398			0.176231
$792$	126.425	−	237.048i	0.159627	−	0.299303i
$793$	−2580.81			−3.25448
$794$	−187.512	−	497.745i	−0.236161	−	0.626883i
$795$	313.802	+	315.657i	0.394720	+	0.397053i
$796$	−29.3955	−	33.4777i	−0.0369290	−	0.0420574i
$797$	−190.629	−	190.629i	−0.239183	−	0.239183i	0.577329	−	0.816512i	$-0.304095\pi$
$797$	−190.629	−	190.629i	−0.239183	−	0.239183i	−0.816512	+	0.577329i	$0.804095\pi$
$798$	−50.9243	+	112.484i	−0.0638149	+	0.140957i
$799$			58.8621i			0.0736697i
$800$	677.514	+	425.412i	0.846892	+	0.531765i
$801$	−156.689			−0.195617
$802$	−1261.80	−	571.250i	−1.57332	−	0.712282i
$803$	788.878	−	788.878i	0.982414	−	0.982414i
$804$	−739.949	+	649.721i	−0.920335	+	0.808111i
$805$	586.927	−	583.479i	0.729102	−	0.724819i
$806$	−1637.05	+	616.713i	−2.03107	+	0.765153i
$807$			1376.16i			1.70528i
$808$	617.339	−	1157.52i	0.764034	−	1.43257i
$809$			844.246i			1.04357i	0.853078	+	0.521784i	$0.174733\pi$
$809$			844.246i			1.04357i	−0.853078	+	0.521784i	$0.825267\pi$
$810$	−908.328	+	339.136i	−1.12139	+	0.418686i
$811$	443.406	−	443.406i	0.546740	−	0.546740i	−0.378756	−	0.925496i	$-0.623648\pi$
$811$	443.406	−	443.406i	0.546740	−	0.546740i	0.925496	+	0.378756i	$0.123648\pi$
$812$	−15.4891	+	238.560i	−0.0190753	+	0.293793i
$813$	687.224	+	687.224i	0.845294	+	0.845294i
$814$	207.706	−	458.791i	0.255167	−	0.563625i
$815$	4.33698	−	1472.06i	0.00532145	−	1.80621i
$816$	−421.106	+	323.947i	−0.516061	+	0.396994i
$817$		−	91.2725i		−	0.111717i
$818$	88.3849	−	195.229i	0.108050	−	0.238666i
$819$	−197.416	−	197.416i	−0.241045	−	0.241045i
$820$	−40.7383	+	600.092i	−0.0496809	+	0.731819i
$821$	−64.3891	−	64.3891i	−0.0784277	−	0.0784277i	0.666805	−	0.745232i	$-0.267661\pi$
$821$	−64.3891	−	64.3891i	−0.0784277	−	0.0784277i	−0.745232	+	0.666805i	$0.767661\pi$
$822$	648.254	−	244.212i	0.788630	−	0.297095i
$823$			659.199i			0.800971i	0.916303	+	0.400486i	$0.131159\pi$
$823$			659.199i			0.800971i	−0.916303	+	0.400486i	$0.868841\pi$
$824$	−669.923	+	203.892i	−0.813013	+	0.247442i
$825$	1168.83	+	6.88729i	1.41677	+	0.00834823i
$826$	−110.766	−	294.024i	−0.134099	−	0.355962i
$827$	565.628	+	565.628i	0.683951	+	0.683951i	0.960888	−	0.276937i	$-0.0893193\pi$
$827$	565.628	+	565.628i	0.683951	+	0.683951i	−0.276937	+	0.960888i	$0.589319\pi$
$828$	−208.744	−	237.733i	−0.252106	−	0.287117i
$829$	271.351	−	271.351i	0.327323	−	0.327323i	−0.524245	−	0.851568i	$-0.675652\pi$
$829$	271.351	−	271.351i	0.327323	−	0.327323i	0.851568	+	0.524245i	$0.175652\pi$
$830$	204.021	−	447.140i	0.245808	−	0.538723i
$831$		−	239.809i		−	0.288579i
$832$	−1420.87	−	279.912i	−1.70777	−	0.336432i
$833$		−	227.678i		−	0.273323i
$834$	606.818	−	1340.37i	0.727599	−	1.60716i
$835$	−402.190	−	404.567i	−0.481665	−	0.484512i
$836$	131.184	+	149.402i	0.156919	+	0.178711i
$837$	607.253	−	607.253i	0.725512	−	0.725512i
$838$	474.369	+	1259.20i	0.566072	+	1.50262i
$839$	−1187.06			−1.41485			−0.707425	−	0.706789i	$-0.750143\pi$
$839$	−1187.06			−1.41485			−0.707425	+	0.706789i	$0.750143\pi$
$840$	−198.128	−	657.938i	−0.235867	−	0.783260i
$841$			702.666i			0.835513i
$842$	263.431	+	699.268i	0.312863	+	0.830485i
$843$	−251.451	−	251.451i	−0.298281	−	0.298281i
$844$	0.324089	−	4.99153i	0.000383991	−	0.00591414i
$845$	−1209.16	−	1216.30i	−1.43096	−	1.43941i
$846$	−12.0021	+	26.5108i	−0.0141869	+	0.0313367i
$847$	−357.115			−0.421623
$848$	−256.896	−	333.945i	−0.302943	−	0.393803i
$849$	1277.77			1.50503
$850$	−446.214	−	205.189i	−0.524957	−	0.241398i
$851$	−419.363	−	419.363i	−0.492788	−	0.492788i
$852$	453.340	+	29.4343i	0.532089	+	0.0345473i
$853$	84.9264	−	84.9264i	0.0995620	−	0.0995620i	−0.655571	−	0.755133i	$-0.727572\pi$
$853$	84.9264	−	84.9264i	0.0995620	−	0.0995620i	0.755133	+	0.655571i	$0.227572\pi$
$854$	408.635	+	1084.71i	0.478496	+	1.27015i
$855$	−0.128550	+	43.6326i	−0.000150351	+	0.0510323i
$856$	−134.296	+	251.807i	−0.156888	+	0.294167i
$857$	222.414			0.259526			0.129763	−	0.991545i	$-0.458578\pi$
$857$	222.414			0.259526			0.129763	+	0.991545i	$0.458578\pi$
$858$	−1980.04	+	745.926i	−2.30773	+	0.869377i
$859$	2.04685	−	2.04685i	0.00238283	−	0.00238283i	−0.705914	−	0.708297i	$-0.749464\pi$
$859$	2.04685	−	2.04685i	0.00238283	−	0.00238283i	0.708297	+	0.705914i	$0.249464\pi$
$860$	334.005	+	382.657i	0.388378	+	0.444949i
$861$	365.296	−	365.296i	0.424270	−	0.424270i
$862$	−418.483	+	924.366i	−0.485479	+	1.07235i
$863$	−905.739			−1.04952			−0.524762	−	0.851249i	$-0.675846\pi$
$863$	−905.739			−1.04952			−0.524762	+	0.851249i	$0.675846\pi$
$864$	692.110	−	162.497i	0.801054	−	0.188075i
$865$	757.774	+	2.23255i	0.876039	+	0.00258098i
$866$	−408.814	+	903.008i	−0.472072	+	1.04273i
$867$	−460.193	+	460.193i	−0.530788	+	0.530788i
$868$	518.408	+	590.400i	0.597244	+	0.680184i
$869$	−586.104	−	586.104i	−0.674458	−	0.674458i
$870$	139.074	+	372.489i	0.159855	+	0.428148i
$871$	1647.80			1.89185
$872$	1046.19	+	557.966i	1.19976	+	0.639869i
$873$	−333.292			−0.381778
$874$	219.105	−	82.5419i	0.250692	−	0.0944415i
$875$	453.092	−	445.153i	0.517820	−	0.508746i
$876$	−1088.49	−	70.6734i	−1.24257	−	0.0806774i
$877$	−349.241	−	349.241i	−0.398222	−	0.398222i	0.479383	−	0.877606i	$-0.340860\pi$
$877$	−349.241	−	349.241i	−0.398222	−	0.398222i	−0.877606	+	0.479383i	$0.840860\pi$
$878$	−415.763	−	188.226i	−0.473534	−	0.214381i
$879$		−	645.069i		−	0.733867i
$880$	−1096.71	−	146.304i	−1.24626	−	0.166255i
$881$	−319.778			−0.362972			−0.181486	−	0.983394i	$-0.558091\pi$
$881$	−319.778			−0.362972			−0.181486	+	0.983394i	$0.558091\pi$
$882$	46.4240	−	102.543i	0.0526349	−	0.116262i
$883$	1037.87	−	1037.87i	1.17539	−	1.17539i	0.194481	−	0.980906i	$-0.437698\pi$
$883$	1037.87	−	1037.87i	1.17539	−	1.17539i	0.980906	−	0.194481i	$-0.0623022\pi$
$884$	887.185	+	57.6029i	1.00360	+	0.0651616i
$885$	−368.420	−	370.598i	−0.416294	−	0.418754i
$886$	−113.100	−	300.221i	−0.127653	−	0.338850i
$887$			1514.15i			1.70704i	0.521057	+	0.853522i	$0.325538\pi$
$887$			1514.15i			1.70704i	−0.521057	+	0.853522i	$0.674462\pi$
$888$	−471.063	+	143.369i	−0.530476	+	0.161451i
$889$			170.460i			0.191743i
$890$	225.715	+	604.547i	0.253613	+	0.679266i
$891$	948.197	−	948.197i	1.06419	−	1.06419i
$892$	−637.697	−	726.256i	−0.714907	−	0.814188i
$893$	−15.2288	−	15.2288i	−0.0170536	−	0.0170536i
$894$	−1054.04	−	477.189i	−1.17901	−	0.533768i
$895$	1117.79	+	3.29324i	1.24893	+	0.00367960i
$896$	107.328	+	641.508i	0.119786	+	0.715969i
$897$			2491.70i			2.77781i
$898$	−702.624	−	318.095i	−0.782432	−	0.354226i
$899$	−321.482	−	321.482i	−0.357600	−	0.357600i
$900$	−159.131	−	183.398i	−0.176812	−	0.203776i
$901$	182.898	+	182.898i	0.202994	+	0.202994i
$902$	−293.260	−	778.450i	−0.325122	−	0.863027i
$903$		−	436.256i		−	0.483119i
$904$	−209.954	+	63.8998i	−0.232250	+	0.0706856i
$905$	407.098	+	1.19939i	0.449832	+	0.00132529i
$906$	−762.384	+	287.208i	−0.841483	+	0.317006i
$907$	822.168	+	822.168i	0.906469	+	0.906469i	0.995985	−	0.0895162i	$-0.0285321\pi$
$907$	822.168	+	822.168i	0.906469	+	0.906469i	−0.0895162	+	0.995985i	$0.528532\pi$
$908$	1357.74	+	88.1552i	1.49531	+	0.0970873i
$909$	−281.547	+	281.547i	−0.309732	+	0.309732i
$910$	−477.299	+	1046.07i	−0.524505	+	1.14952i
$911$			331.730i			0.364139i	0.983286	+	0.182069i	$0.0582795\pi$
$911$			331.730i			0.364139i	−0.983286	+	0.182069i	$0.941720\pi$
$912$	25.1370	−	192.761i	0.0275625	−	0.211360i
$913$			679.742i			0.744515i
$914$	53.7225	+	24.3215i	0.0587774	+	0.0266100i
$915$	1359.17	+	1367.20i	1.48543	+	1.49421i
$916$	44.6949	−	688.379i	0.0487935	−	0.751506i
$917$	−538.145	+	538.145i	−0.586854	+	0.586854i
$918$	−408.428	+	153.865i	−0.444911	+	0.167608i
$919$	−820.793			−0.893137			−0.446568	−	0.894749i	$-0.647354\pi$
$919$	−820.793			−0.893137			−0.446568	+	0.894749i	$0.647354\pi$
$920$	−616.533	+	1147.85i	−0.670144	+	1.24766i
$921$		−	948.751i		−	1.03013i
$922$	884.792	−	333.322i	0.959644	−	0.361520i
$923$	−537.546	−	537.546i	−0.582390	−	0.582390i
$924$	627.023	+	714.099i	0.678597	+	0.772835i
$925$	−319.955	−	323.748i	−0.345897	−	0.349998i
$926$	−397.772	−	180.081i	−0.429560	−	0.194472i
$927$	212.540			0.229278
$928$	−86.0263	−	366.406i	−0.0927008	−	0.394834i
$929$	−724.971			−0.780378			−0.390189	−	0.920735i	$-0.627590\pi$
$929$	−724.971			−0.780378			−0.390189	+	0.920735i	$0.627590\pi$
$930$	1188.85	+	542.448i	1.27833	+	0.583278i
$931$	58.9050	+	58.9050i	0.0632706	+	0.0632706i
$932$	771.289	+	878.399i	0.827563	+	0.942488i
$933$	231.994	−	231.994i	0.248654	−	0.248654i
$934$	543.386	−	204.706i	0.581784	−	0.219172i
$935$	679.247	+	2.00120i	0.726467	+	0.00214032i
$936$	387.832	+	206.842i	0.414351	+	0.220985i
$937$	605.697			0.646422			0.323211	−	0.946327i	$-0.395238\pi$
$937$	605.697			0.646422			0.323211	+	0.946327i	$0.395238\pi$
$938$	−260.906	−	692.567i	−0.278152	−	0.738344i
$939$	−418.576	+	418.576i	−0.445768	+	0.445768i
$940$	119.575	+	8.11758i	0.127208	+	0.00863572i
$941$	934.190	−	934.190i	0.992763	−	0.992763i	−0.00721133	−	0.999974i	$-0.502295\pi$
$941$	934.190	−	934.190i	0.992763	−	0.992763i	0.999974	+	0.00721133i	$0.00229546\pi$
$942$	−1274.58	−	577.034i	−1.35306	−	0.612563i
$943$	−979.609			−1.03882
$944$	301.609	+	392.068i	0.319501	+	0.415327i
$945$	1.66301	−	564.458i	0.00175979	−	0.597310i
$946$	−639.947	−	289.720i	−0.676477	−	0.306258i
$947$	−328.488	+	328.488i	−0.346872	+	0.346872i	−0.858943	−	0.512071i	$-0.828879\pi$
$947$	−328.488	+	328.488i	−0.346872	+	0.346872i	0.512071	+	0.858943i	$0.328879\pi$
$948$	−52.5074	+	808.706i	−0.0553876	+	0.853065i
$949$	1290.68	+	1290.68i	1.36004	+	1.36004i
$950$	168.531	−	62.3582i	0.177401	−	0.0656402i
$951$	−531.187			−0.558556
$952$	−116.263	−	382.003i	−0.122125	−	0.401264i
$953$	605.174			0.635020			0.317510	−	0.948255i	$-0.397153\pi$
$953$	605.174			0.635020			0.317510	+	0.948255i	$0.397153\pi$
$954$	45.0819	+	119.668i	0.0472556	+	0.125438i
$955$	−409.279	−	411.697i	−0.428564	−	0.431097i
$956$	−183.215	+	160.874i	−0.191647	+	0.168278i
$957$	−388.839	−	388.839i	−0.406310	−	0.406310i
$958$	−411.420	+	908.763i	−0.429457	+	0.948605i
$959$			520.634i			0.542892i
$960$	600.007	+	900.129i	0.625007	+	0.937634i
$961$	−533.224			−0.554864
$962$	750.624	+	339.826i	0.780275	+	0.353250i
$963$	61.2476	−	61.2476i	0.0636009	−	0.0636009i
$964$	219.803	+	250.328i	0.228012	+	0.259676i
$965$	−102.092	−	102.695i	−0.105795	−	0.106420i
$966$	1047.26	−	394.526i	1.08412	−	0.408412i
$967$		−	587.364i		−	0.607408i	−0.952766	−	0.303704i	$-0.901777\pi$
$967$		−	587.364i		−	0.607408i	0.952766	−	0.303704i	$-0.0982234\pi$
$968$	537.866	−	163.700i	0.555647	−	0.169112i
$969$			119.340i			0.123158i
$970$	480.118	+	1285.93i	0.494967	+	1.32570i
$971$	−780.030	+	780.030i	−0.803326	+	0.803326i	−0.983614	−	0.180288i	$-0.942297\pi$
$971$	−780.030	+	780.030i	−0.803326	+	0.803326i	0.180288	+	0.983614i	$0.442297\pi$
$972$	−510.205	−	33.1265i	−0.524903	−	0.0340807i
$973$	781.924	+	781.924i	0.803622	+	0.803622i
$974$	65.6421	−	144.993i	0.0673944	−	0.148864i
$975$	−11.2682	+	1912.32i	−0.0115572	+	1.96135i
$976$	−1112.69	−	1446.41i	−1.14005	−	1.48198i
$977$			182.727i			0.187028i	0.995618	+	0.0935142i	$0.0298101\pi$
$977$			182.727i			0.187028i	−0.995618	+	0.0935142i	$0.970190\pi$
$978$	820.961	−	1813.38i	0.839429	−	1.85417i
$979$	−631.082	−	631.082i	−0.644619	−	0.644619i
$980$	−462.515	−	31.3987i	−0.471954	−	0.0320395i
$981$	−254.469	−	254.469i	−0.259397	−	0.259397i
$982$	822.639	−	309.907i	0.837718	−	0.315588i
$983$		−	213.302i		−	0.216991i	−0.994097	−	0.108495i	$-0.965397\pi$
$983$		−	213.302i		−	0.216991i	0.994097	−	0.108495i	$-0.0346033\pi$
$984$	−382.738	+	717.640i	−0.388962	+	0.729309i
$985$	2.47117	−	838.765i	0.00250880	−	0.851538i
$986$	81.4565	+	216.224i	0.0826131	+	0.219294i
$987$	−72.7894	−	72.7894i	−0.0737482	−	0.0737482i
$988$	−244.436	+	214.630i	−0.247405	+	0.217237i
$989$	−584.951	+	584.951i	−0.591457	+	0.591457i
$990$	305.517	+	139.401i	0.308603	+	0.140809i
$991$		−	1722.88i		−	1.73853i	−0.494345	−	0.869266i	$-0.664592\pi$
$991$		−	1722.88i		−	1.73853i	0.494345	−	0.869266i	$-0.335408\pi$
$992$	−1051.43	−	651.591i	−1.05991	−	0.656846i
$993$		−	1167.09i		−	1.17532i
$994$	−140.817	+	311.043i	−0.141667	+	0.312920i
$995$	39.4943	−	39.2623i	0.0396928	−	0.0394596i
$996$	499.402	−	438.506i	0.501408	−	0.440267i
$997$	−1133.95	+	1133.95i	−1.13737	+	1.13737i	−0.148445	+	0.988921i	$0.547427\pi$
$997$	−1133.95	+	1133.95i	−1.13737	+	1.13737i	−0.988921	+	0.148445i	$0.952573\pi$
$998$	606.232	+	1609.22i	0.607447	+	1.61245i
$999$	−404.497			−0.404902

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.k.a.59.19	yes	44
4.3	odd	2		320.3.k.a.79.18		44
5.2	odd	4		400.3.r.g.251.8		44
5.3	odd	4		400.3.r.g.251.15		44
5.4	even	2	inner	80.3.k.a.59.4	yes	44
8.3	odd	2		640.3.k.a.159.5		44
8.5	even	2		640.3.k.b.159.18		44
16.3	odd	4	inner	80.3.k.a.19.4	✓	44
16.5	even	4		640.3.k.a.479.18		44
16.11	odd	4		640.3.k.b.479.5		44
16.13	even	4		320.3.k.a.239.5		44
20.19	odd	2		320.3.k.a.79.5		44
40.19	odd	2		640.3.k.a.159.18		44
40.29	even	2		640.3.k.b.159.5		44
80.3	even	4		400.3.r.g.51.15		44
80.19	odd	4	inner	80.3.k.a.19.19	yes	44
80.29	even	4		320.3.k.a.239.18		44
80.59	odd	4		640.3.k.b.479.18		44
80.67	even	4		400.3.r.g.51.8		44
80.69	even	4		640.3.k.a.479.5		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.k.a.19.4	✓	44	16.3	odd	4	inner
80.3.k.a.19.19	yes	44	80.19	odd	4	inner
80.3.k.a.59.4	yes	44	5.4	even	2	inner
80.3.k.a.59.19	yes	44	1.1	even	1	trivial
320.3.k.a.79.5		44	20.19	odd	2
320.3.k.a.79.18		44	4.3	odd	2
320.3.k.a.239.5		44	16.13	even	4
320.3.k.a.239.18		44	80.29	even	4
400.3.r.g.51.8		44	80.67	even	4
400.3.r.g.51.15		44	80.3	even	4
400.3.r.g.251.8		44	5.2	odd	4
400.3.r.g.251.15		44	5.3	odd	4
640.3.k.a.159.5		44	8.3	odd	2
640.3.k.a.159.18		44	40.19	odd	2
640.3.k.a.479.5		44	80.69	even	4
640.3.k.a.479.18		44	16.5	even	4
640.3.k.b.159.5		44	40.29	even	2
640.3.k.b.159.18		44	8.5	even	2
640.3.k.b.479.5		44	16.11	odd	4
640.3.k.b.479.18		44	80.59	odd	4

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)

\(f(q)\)	\(=\)	\(q+(1.82198 + 0.824856i) q^{2} +(-2.39041 + 2.39041i) q^{3} +(2.63923 + 3.00574i) q^{4} +(-3.54593 + 3.52510i) q^{5} +(-6.32702 + 2.38354i) q^{6} -5.08144i q^{7} +(2.32932 + 7.65338i) q^{8} -2.42812i q^{9} +O(q^{10})\)	\(q+(1.82198 + 0.824856i) q^{2} +(-2.39041 + 2.39041i) q^{3} +(2.63923 + 3.00574i) q^{4} +(-3.54593 + 3.52510i) q^{5} +(-6.32702 + 2.38354i) q^{6} -5.08144i q^{7} +(2.32932 + 7.65338i) q^{8} -2.42812i q^{9} +(-9.36832 + 3.49778i) q^{10} +(9.77953 - 9.77953i) q^{11} +(-13.4938 - 0.876121i) q^{12} +(16.0002 + 16.0002i) q^{13} +(4.19145 - 9.25828i) q^{14} +(0.0497986 - 16.9027i) q^{15} +(-2.06896 + 15.8657i) q^{16} -9.82261i q^{17} +(2.00285 - 4.42399i) q^{18} +(2.54131 + 2.54131i) q^{19} +(-19.9541 - 1.35462i) q^{20} +(12.1467 + 12.1467i) q^{21} +(25.8848 - 9.75141i) q^{22} -32.5737i q^{23} +(-23.8627 - 12.7267i) q^{24} +(0.147309 - 24.9996i) q^{25} +(15.9542 + 42.3499i) q^{26} +(-15.7095 - 15.7095i) q^{27} +(15.2735 - 13.4111i) q^{28} +(-8.31667 + 8.31667i) q^{29} +(14.0330 - 30.7553i) q^{30} +38.6552i q^{31} +(-16.8565 + 27.2003i) q^{32} +46.7542i q^{33} +(8.10223 - 17.8966i) q^{34} +(17.9126 + 18.0185i) q^{35} +(7.29830 - 6.40836i) q^{36} +(12.8743 - 12.8743i) q^{37} +(2.53400 + 6.72643i) q^{38} -76.4941 q^{39} +(-35.2386 - 18.9273i) q^{40} -30.0736i q^{41} +(12.1118 + 32.1504i) q^{42} +(-17.9578 - 17.9578i) q^{43} +(55.2051 + 3.58434i) q^{44} +(8.55937 + 8.60995i) q^{45} +(26.8686 - 59.3486i) q^{46} -5.99252 q^{47} +(-32.9798 - 42.8711i) q^{48} +23.1790 q^{49} +(20.8894 - 45.4272i) q^{50} +(23.4801 + 23.4801i) q^{51} +(-5.86432 + 90.3207i) q^{52} +(-18.6201 + 18.6201i) q^{53} +(-15.6643 - 41.5804i) q^{54} +(-0.203734 + 69.1514i) q^{55} +(38.8902 - 11.8363i) q^{56} -12.1495 q^{57} +(-22.0129 + 8.29276i) q^{58} +(21.8610 - 21.8610i) q^{59} +(50.9365 - 44.4603i) q^{60} +(-80.6491 + 80.6491i) q^{61} +(-31.8850 + 70.4290i) q^{62} -12.3383 q^{63} +(-53.1486 + 35.6543i) q^{64} +(-113.138 - 0.333327i) q^{65} +(-38.5654 + 85.1852i) q^{66} +(51.4930 - 51.4930i) q^{67} +(29.5242 - 25.9241i) q^{68} +(77.8645 + 77.8645i) q^{69} +(17.7738 + 47.6046i) q^{70} -33.5962 q^{71} +(18.5833 - 5.65586i) q^{72} +80.6663 q^{73} +(34.0761 - 12.8373i) q^{74} +(59.4071 + 60.1113i) q^{75} +(-0.931428 + 14.3456i) q^{76} +(-49.6941 - 49.6941i) q^{77} +(-139.371 - 63.0966i) q^{78} -59.9317i q^{79} +(-48.5917 - 63.5519i) q^{80} +96.9573 q^{81} +(24.8064 - 54.7936i) q^{82} +(-34.7533 + 34.7533i) q^{83} +(-4.45195 + 68.5679i) q^{84} +(34.6257 + 34.8303i) q^{85} +(-17.9061 - 47.5313i) q^{86} -39.7605i q^{87} +(97.6261 + 52.0668i) q^{88} -64.5309i q^{89} +(8.49304 + 22.7474i) q^{90} +(81.3041 - 81.3041i) q^{91} +(97.9081 - 85.9694i) q^{92} +(-92.4018 - 92.4018i) q^{93} +(-10.9182 - 4.94296i) q^{94} +(-17.9697 - 0.0529423i) q^{95} +(-24.7260 - 105.314i) q^{96} -137.264i q^{97} +(42.2316 + 19.1193i) q^{98} +(-23.7459 - 23.7459i) 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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