LMFDB - Embedded newform 80.3.k.a.19.19

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			19.19
Character	$\chi$	$=$	80.19
Dual form			80.3.k.a.59.19

$q$-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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.82198	−	0.824856i	0.910990	−	0.412428i
$2$	1.82198	−	0.824856i	0.910990	−	0.412428i
$3$	−2.39041	−	2.39041i	−0.796803	−	0.796803i	0.185787	−	0.982590i	$-0.440517\pi$
$3$	−2.39041	−	2.39041i	−0.796803	−	0.796803i	−0.982590	+	0.185787i	$0.940517\pi$
$4$	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	$0.118234\pi$
$7$			5.08144i			0.725920i	−0.931805	+	0.362960i	$0.881766\pi$
$8$	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	0.994432	−	0.105384i	$-0.0336071\pi$
$11$	9.77953	+	9.77953i	0.889048	+	0.889048i	−0.105384	+	0.994432i	$0.533607\pi$
$12$	−13.4938	+	0.876121i	−1.12448	+	0.0730101i
$13$	16.0002	−	16.0002i	1.23079	−	1.23079i	0.267123	−	0.963662i	$-0.413927\pi$
$13$	16.0002	−	16.0002i	1.23079	−	1.23079i	0.963662	−	0.267123i	$-0.0860732\pi$
$14$	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	$0.0932896\pi$
$17$			9.82261i			0.577800i	−0.957359	+	0.288900i	$0.906710\pi$
$18$	2.00285	+	4.42399i	0.111269	+	0.245777i
$19$	2.54131	−	2.54131i	0.133753	−	0.133753i	−0.637061	−	0.770814i	$-0.719850\pi$
$19$	2.54131	−	2.54131i	0.133753	−	0.133753i	0.770814	+	0.637061i	$0.219850\pi$
$20$	−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	$0.250458\pi$
$23$			32.5737i			1.41625i	−0.706088	+	0.708124i	$0.749542\pi$
$24$	−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	0.549025	−	0.835806i	$-0.314999\pi$
$29$	−8.31667	−	8.31667i	−0.286782	−	0.286782i	−0.835806	+	0.549025i	$0.814999\pi$
$30$	14.0330	+	30.7553i	0.467767	+	1.02518i
$31$		−	38.6552i		−	1.24694i	−0.781847	−	0.623471i	$-0.785722\pi$
$31$		−	38.6552i		−	1.24694i	0.781847	−	0.623471i	$-0.214278\pi$
$32$	−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	0.859347	−	0.511393i	$-0.170870\pi$
$37$	12.8743	+	12.8743i	0.347954	+	0.347954i	−0.511393	+	0.859347i	$0.670870\pi$
$38$	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	$0.119530\pi$
$41$			30.0736i			0.733503i	−0.930319	+	0.366752i	$0.880470\pi$
$42$	12.1118	−	32.1504i	0.288376	−	0.765485i
$43$	−17.9578	+	17.9578i	−0.417623	+	0.417623i	−0.884384	−	0.466761i	$-0.845421\pi$
$43$	−17.9578	+	17.9578i	−0.417623	+	0.417623i	0.466761	+	0.884384i	$0.345421\pi$
$44$	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	0.509279	−	0.860602i	$-0.329912\pi$
$53$	−18.6201	−	18.6201i	−0.351323	−	0.351323i	−0.860602	+	0.509279i	$0.829912\pi$
$54$	−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	0.867668	−	0.497143i	$-0.165618\pi$
$59$	21.8610	+	21.8610i	0.370525	+	0.370525i	−0.497143	+	0.867668i	$0.665618\pi$
$60$	50.9365	+	44.4603i	0.848942	+	0.741005i
$61$	−80.6491	−	80.6491i	−1.32212	−	1.32212i	−0.912061	−	0.410055i	$-0.865509\pi$
$61$	−80.6491	−	80.6491i	−1.32212	−	1.32212i	−0.410055	−	0.912061i	$-0.634491\pi$
$62$	−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	0.977852	−	0.209300i	$-0.0671184\pi$
$67$	51.4930	+	51.4930i	0.768552	+	0.768552i	−0.209300	+	0.977852i	$0.567118\pi$
$68$	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	$0.123840\pi$
$79$			59.9317i			0.758629i	−0.925268	+	0.379315i	$0.876160\pi$
$80$	−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	0.466046	−	0.884761i	$-0.345678\pi$
$83$	−34.7533	−	34.7533i	−0.418715	−	0.418715i	−0.884761	+	0.466046i	$0.845678\pi$
$84$	−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	$0.118088\pi$
$89$			64.5309i			0.725067i	−0.931971	+	0.362533i	$0.881912\pi$
$90$	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	$0.250197\pi$
$97$			137.264i			1.41509i	−0.706669	+	0.707544i	$0.749803\pi$
$98$	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	−0.161109	+	0.986937i	$0.551507\pi$
$101$	−115.953	+	115.953i	−1.14805	+	1.14805i	−0.986937	+	0.161109i	$0.948493\pi$
$102$	23.4126	−	62.1479i	0.229535	−	0.609293i
$103$		−	87.5329i		−	0.849834i	−0.905232	−	0.424917i	$-0.860303\pi$
$103$		−	87.5329i		−	0.849834i	0.905232	−	0.424917i	$-0.139697\pi$
$104$	−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	−0.579343	−	0.815084i	$-0.696691\pi$
$107$	25.2243	−	25.2243i	0.235741	−	0.235741i	0.815084	+	0.579343i	$0.196691\pi$
$108$	5.75776	+	88.6796i	0.0533126	+	0.821107i
$109$	104.801	+	104.801i	0.961474	+	0.961474i	0.999285	−	0.0378105i	$-0.0120383\pi$
$109$	104.801	+	104.801i	0.961474	+	0.961474i	−0.0378105	+	0.999285i	$0.512038\pi$
$110$	−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	$-0.961267\pi$
$113$		−	27.4328i		−	0.242769i	0.992606	−	0.121384i	$-0.0387333\pi$
$114$	−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	−0.984396	−	0.175968i	$-0.943695\pi$
$131$	−105.904	+	105.904i	−0.808428	+	0.808428i	0.175968	+	0.984396i	$0.443695\pi$
$132$	−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	−0.993538	−	0.113502i	$-0.963793\pi$
$139$	−153.879	−	153.879i	−1.10704	−	1.10704i	−0.113502	−	0.993538i	$-0.536207\pi$
$140$	−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	−0.172826	−	0.984952i	$-0.555290\pi$
$149$	121.007	−	121.007i	0.812126	−	0.812126i	0.984952	+	0.172826i	$0.0552898\pi$
$150$	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	−0.0658192	−	0.997832i	$-0.520966\pi$
$157$	146.326	−	146.326i	0.932012	−	0.932012i	0.997832	+	0.0658192i	$0.0209660\pi$
$158$	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	−0.942235	−	0.334954i	$-0.891279\pi$
$163$	−208.182	−	208.182i	−1.27719	−	1.27719i	−0.334954	−	0.942235i	$-0.608721\pi$
$164$	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	$-0.889032\pi$
$167$		−	114.093i		−	0.683193i	0.939847	−	0.341597i	$-0.110968\pi$
$168$	−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	−0.945392	−	0.325936i	$-0.894321\pi$
$173$	−107.166	+	107.166i	−0.619456	+	0.619456i	0.325936	+	0.945392i	$0.394321\pi$
$174$	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	−0.993852	−	0.110719i	$-0.964685\pi$
$179$	−158.081	+	158.081i	−0.883132	+	0.883132i	0.110719	+	0.993852i	$0.464685\pi$
$180$	−3.28918	−	48.4509i	−0.0182732	−	0.269172i
$181$	−57.5726	+	57.5726i	−0.318081	+	0.318081i	−0.848030	−	0.529949i	$-0.822211\pi$
$181$	−57.5726	+	57.5726i	−0.318081	+	0.318081i	0.529949	+	0.848030i	$0.322211\pi$
$182$	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	$-0.901699\pi$
$191$		−	116.104i		−	0.607875i	0.952692	−	0.303937i	$-0.0983013\pi$
$192$	41.8184	+	212.275i	0.217804	+	1.10560i
$193$		−	28.9615i		−	0.150059i	−0.997181	−	0.0750297i	$-0.976095\pi$
$193$		−	28.9615i		−	0.150059i	0.997181	−	0.0750297i	$-0.0239052\pi$
$194$	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	0.338746	−	0.940878i	$-0.389997\pi$
$197$	−118.620	−	118.620i	−0.602131	−	0.602131i	−0.940878	+	0.338746i	$0.889997\pi$
$198$	−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	−0.709199	−	0.705008i	$-0.750943\pi$
$211$	−0.884244	+	0.884244i	−0.00419073	+	0.00419073i	0.705008	+	0.709199i	$0.250943\pi$
$212$	−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	0.998109	+	0.0614631i	$0.0195767\pi$
$227$	240.523	+	240.523i	1.05957	+	1.05957i	0.0614631	+	0.998109i	$0.480423\pi$
$228$	−32.0654	+	36.5184i	−0.140638	+	0.160168i
$229$	−121.946	+	121.946i	−0.532514	+	0.532514i	−0.921320	−	0.388806i	$-0.872888\pi$
$229$	−121.946	+	121.946i	−0.532514	+	0.532514i	0.388806	+	0.921320i	$0.372888\pi$
$230$	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	$-0.959298\pi$
$239$		−	60.9550i		−	0.255042i	0.991836	−	0.127521i	$-0.0407020\pi$
$240$	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	0.202049	−	0.979375i	$-0.435240\pi$
$251$	−195.109	−	195.109i	−0.777326	−	0.777326i	−0.979375	+	0.202049i	$0.935240\pi$
$252$	−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	$-0.778393\pi$
$257$		−	329.631i		−	1.28261i	0.767286	−	0.641305i	$-0.221607\pi$
$258$	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	$0.0340607\pi$
$263$			56.1771i			0.213601i	−0.994280	+	0.106801i	$0.965939\pi$
$264$	−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	0.997352	+	0.0727268i	$0.0231701\pi$
$269$	287.851	+	287.851i	1.07008	+	1.07008i	0.0727268	+	0.997352i	$0.476830\pi$
$270$	202.120	−	92.2232i	0.748593	−	0.341567i
$271$			287.492i			1.06086i	0.847730	+	0.530428i	$0.177969\pi$
$271$			287.492i			1.06086i	−0.847730	+	0.530428i	$0.822031\pi$
$272$	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	0.610743	−	0.791829i	$-0.290871\pi$
$277$	−50.1607	−	50.1607i	−0.181085	−	0.181085i	−0.791829	+	0.610743i	$0.790871\pi$
$278$	−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	$-0.940067\pi$
$281$		−	105.191i		−	0.374347i	0.982327	−	0.187173i	$-0.0599326\pi$
$282$	37.9148	+	14.2834i	0.134450	+	0.0506503i
$283$	−267.270	+	267.270i	−0.944417	+	0.944417i	−0.998535	−	0.0541177i	$-0.982765\pi$
$283$	−267.270	+	267.270i	−0.944417	+	0.944417i	0.0541177	+	0.998535i	$0.482765\pi$
$284$	−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	0.438315	−	0.898822i	$-0.355576\pi$
$293$	−134.928	−	134.928i	−0.460507	−	0.460507i	−0.898822	+	0.438315i	$0.855576\pi$
$294$	−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	0.305709	−	0.952125i	$-0.401106\pi$
$307$	−198.450	−	198.450i	−0.646415	−	0.646415i	−0.952125	+	0.305709i	$0.901106\pi$
$308$	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	−0.509797	−	0.860295i	$-0.670279\pi$
$317$	111.108	−	111.108i	0.350498	−	0.350498i	0.860295	+	0.509797i	$0.170279\pi$
$318$	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	0.234577	−	0.972098i	$-0.424630\pi$
$331$	−244.119	−	244.119i	−0.737521	−	0.737521i	−0.972098	+	0.234577i	$0.924630\pi$
$332$	−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	$0.165022\pi$
$337$			333.980i			0.991037i	−0.868597	+	0.495519i	$0.834978\pi$
$338$	−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	−0.642319	−	0.766438i	$-0.722027\pi$
$347$	43.0694	−	43.0694i	0.124119	−	0.124119i	0.766438	+	0.642319i	$0.222027\pi$
$348$	119.510	+	104.937i	0.343419	+	0.301543i
$349$	−206.400	−	206.400i	−0.591404	−	0.591404i	0.346607	−	0.938011i	$-0.387334\pi$
$349$	−206.400	−	206.400i	−0.591404	−	0.591404i	−0.938011	+	0.346607i	$0.887334\pi$
$350$	−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	$0.0389019\pi$
$353$			86.0684i			0.243820i	−0.992541	+	0.121910i	$0.961098\pi$
$354$	−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	0.821550	−	0.570137i	$-0.193110\pi$
$373$	93.7772	+	93.7772i	0.251413	+	0.251413i	−0.570137	+	0.821550i	$0.693110\pi$
$374$	−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	0.754588	−	0.656199i	$-0.227837\pi$
$379$	37.2892	+	37.2892i	0.0983885	+	0.0983885i	−0.656199	+	0.754588i	$0.727837\pi$
$380$	−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	−0.490137	−	0.871646i	$-0.663053\pi$
$389$	148.407	−	148.407i	0.381509	−	0.381509i	0.871646	+	0.490137i	$0.163053\pi$
$390$	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	−0.903105	−	0.429420i	$-0.858718\pi$
$397$	−188.053	+	188.053i	−0.473685	+	0.473685i	0.429420	+	0.903105i	$0.358718\pi$
$398$	−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	$0.0418164\pi$
$409$			107.152i			0.261985i	−0.991383	+	0.130993i	$0.958184\pi$
$410$	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	0.146146	−	0.989263i	$-0.453313\pi$
$419$	475.736	−	475.736i	1.13541	−	1.13541i	0.989263	−	0.146146i	$-0.0466869\pi$
$420$	−225.922	+	258.831i	−0.537910	+	0.616264i
$421$	264.190	−	264.190i	0.627530	−	0.627530i	−0.319916	−	0.947446i	$-0.603655\pi$
$421$	264.190	−	264.190i	0.627530	−	0.627530i	0.947446	+	0.319916i	$0.103655\pi$
$422$	−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	$-0.799694\pi$
$431$		−	507.341i		−	1.17713i	0.808451	−	0.588563i	$-0.200306\pi$
$432$	281.744	+	216.739i	0.652185	+	0.501711i
$433$		−	495.619i		−	1.14462i	−0.820039	−	0.572308i	$-0.806048\pi$
$433$		−	495.619i		−	1.14462i	0.820039	−	0.572308i	$-0.193952\pi$
$434$	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	−0.823442	−	0.567401i	$-0.807949\pi$
$443$	−113.426	+	113.426i	−0.256041	+	0.256041i	0.567401	+	0.823442i	$0.307949\pi$
$444$	−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	0.969645	−	0.244519i	$-0.0786300\pi$
$461$	334.283	+	334.283i	0.725126	+	0.725126i	−0.244519	+	0.969645i	$0.578630\pi$
$462$	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	0.891880	−	0.452273i	$-0.149387\pi$
$467$	205.296	+	205.296i	0.439607	+	0.439607i	−0.452273	+	0.891880i	$0.649387\pi$
$468$	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	$-0.825692\pi$
$479$		−	498.778i		−	1.04129i	0.853773	−	0.520645i	$-0.174308\pi$
$480$	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	$0.0260364\pi$
$487$			79.5802i			0.163409i	−0.996657	+	0.0817045i	$0.973964\pi$
$488$	−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	0.948818	−	0.315823i	$-0.102280\pi$
$491$	310.801	+	310.801i	0.632996	+	0.632996i	−0.315823	+	0.948818i	$0.602280\pi$
$492$	−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	0.250204	−	0.968193i	$-0.419502\pi$
$499$	607.980	−	607.980i	1.21840	−	1.21840i	0.968193	−	0.250204i	$-0.0804977\pi$
$500$	−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	$0.104788\pi$
$503$			325.228i			0.646576i	−0.946301	+	0.323288i	$0.895212\pi$
$504$	−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	0.920335	−	0.391130i	$-0.127916\pi$
$509$	269.365	+	269.365i	0.529205	+	0.529205i	−0.391130	+	0.920335i	$0.627916\pi$
$510$	−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	$0.221348\pi$
$521$			667.589i			1.28136i	−0.767807	+	0.640681i	$0.778652\pi$
$522$	20.1358	−	53.4498i	0.0385743	−	0.102394i
$523$	188.149	−	188.149i	0.359749	−	0.359749i	−0.503972	−	0.863720i	$-0.668128\pi$
$523$	188.149	−	188.149i	0.359749	−	0.359749i	0.863720	+	0.503972i	$0.168128\pi$
$524$	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	0.438481	−	0.898740i	$-0.355517\pi$
$541$	−249.000	−	249.000i	−0.460259	−	0.460259i	−0.898740	+	0.438481i	$0.855517\pi$
$542$	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	0.989200	+	0.146571i	$0.0468237\pi$
$547$	621.267	+	621.267i	1.13577	+	1.13577i	0.146571	+	0.989200i	$0.453176\pi$
$548$	−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	−0.906084	−	0.423097i	$-0.860943\pi$
$557$	−269.024	+	269.024i	−0.482987	+	0.482987i	0.423097	+	0.906084i	$0.360943\pi$
$558$	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	0.302852	−	0.953038i	$-0.402061\pi$
$563$	−366.055	−	366.055i	−0.650186	−	0.650186i	−0.953038	+	0.302852i	$0.902061\pi$
$564$	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	$-0.766811\pi$
$569$		−	761.087i		−	1.33759i	0.743448	−	0.668794i	$-0.233189\pi$
$570$	113.821	+	42.4965i	0.199686	+	0.0745553i
$571$	−18.9101	−	18.9101i	−0.0331175	−	0.0331175i	0.690354	−	0.723472i	$-0.257455\pi$
$571$	−18.9101	−	18.9101i	−0.0331175	−	0.0331175i	−0.723472	+	0.690354i	$0.757455\pi$
$572$	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	$-0.767145\pi$
$577$		−	770.887i		−	1.33603i	0.744150	−	0.668013i	$-0.232855\pi$
$578$	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	−0.958998	−	0.283411i	$-0.908534\pi$
$587$	−396.570	+	396.570i	−0.675587	+	0.675587i	0.283411	+	0.958998i	$0.408534\pi$
$588$	−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	$-0.906073\pi$
$593$		−	344.909i		−	0.581634i	0.956779	−	0.290817i	$-0.0939272\pi$
$594$	−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	$-0.837210\pi$
$601$		−	588.278i		−	0.978832i	0.872051	−	0.489416i	$-0.162790\pi$
$602$	−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	0.437539	−	0.899199i	$-0.355850\pi$
$613$	−282.998	−	282.998i	−0.461660	−	0.461660i	−0.899199	+	0.437539i	$0.855850\pi$
$614$	−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	0.879115	−	0.476610i	$-0.158135\pi$
$619$	249.150	+	249.150i	0.402505	+	0.402505i	−0.476610	+	0.879115i	$0.658135\pi$
$620$	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	0.919361	−	0.393415i	$-0.128706\pi$
$643$	338.184	+	338.184i	0.525947	+	0.525947i	−0.393415	+	0.919361i	$0.628706\pi$
$644$	−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	$0.0622750\pi$
$647$			251.550i			0.388794i	−0.980923	+	0.194397i	$0.937725\pi$
$648$	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	0.00894710	−	0.999960i	$-0.497152\pi$
$653$	658.816	−	658.816i	1.00891	−	1.00891i	0.999960	−	0.00894710i	$-0.00284799\pi$
$654$	−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	−0.0532691	+	0.998580i	$0.516964\pi$
$659$	−693.169	+	693.169i	−1.05185	+	1.05185i	−0.998580	+	0.0532691i	$0.983036\pi$
$660$	63.3341	+	932.936i	0.0959608	+	1.41354i
$661$	−517.616	+	517.616i	−0.783080	+	0.783080i	−0.980349	−	0.197269i	$-0.936793\pi$
$661$	−517.616	+	517.616i	−0.783080	+	0.783080i	0.197269	+	0.980349i	$0.436793\pi$
$662$	−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	$0.209105\pi$
$673$			821.981i			1.22137i	−0.791874	+	0.610684i	$0.790895\pi$
$674$	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	0.870741	−	0.491743i	$-0.163640\pi$
$677$	256.582	+	256.582i	0.378998	+	0.378998i	−0.491743	+	0.870741i	$0.663640\pi$
$678$	−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	0.269849	−	0.962903i	$-0.413026\pi$
$683$	841.969	−	841.969i	1.23275	−	1.23275i	0.962903	−	0.269849i	$-0.0869738\pi$
$684$	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	−0.646870	−	0.762600i	$-0.723922\pi$
$691$	79.9699	−	79.9699i	0.115731	−	0.115731i	0.762600	+	0.646870i	$0.223922\pi$
$692$	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	0.879339	−	0.476196i	$-0.157985\pi$
$701$	282.604	+	282.604i	0.403144	+	0.403144i	−0.476196	+	0.879339i	$0.657985\pi$
$702$	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	−0.997423	−	0.0717452i	$-0.977143\pi$
$709$	−656.306	+	656.306i	−0.925678	+	0.925678i	0.0717452	+	0.997423i	$0.477143\pi$
$710$	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	$0.0477301\pi$
$719$			214.819i			0.298775i	−0.988779	+	0.149387i	$0.952270\pi$
$720$	−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	$0.223572\pi$
$727$			939.330i			1.29206i	−0.763311	+	0.646031i	$0.776428\pi$
$728$	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	−0.954013	−	0.299765i	$-0.903092\pi$
$733$	−479.564	+	479.564i	−0.654248	+	0.654248i	0.299765	+	0.954013i	$0.403092\pi$
$734$	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	−0.152022	−	0.988377i	$-0.548579\pi$
$739$	618.066	−	618.066i	0.836355	−	0.836355i	0.988377	+	0.152022i	$0.0485786\pi$
$740$	−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	$-0.934100\pi$
$743$		−	305.455i		−	0.411110i	0.978646	−	0.205555i	$-0.0659000\pi$
$744$	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	$-0.807712\pi$
$751$		−	853.156i		−	1.13603i	0.823019	−	0.568013i	$-0.192288\pi$
$752$	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	0.427559	−	0.903987i	$-0.359373\pi$
$757$	−360.656	−	360.656i	−0.476428	−	0.476428i	−0.903987	+	0.427559i	$0.859373\pi$
$758$	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	$0.0507691\pi$
$761$			241.725i			0.317641i	−0.987307	+	0.158821i	$0.949231\pi$
$762$	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	0.741901	−	0.670510i	$-0.233925\pi$
$773$	55.1851	+	55.1851i	0.0713908	+	0.0713908i	−0.670510	+	0.741901i	$0.733925\pi$
$774$	−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	0.540527	−	0.841327i	$-0.318225\pi$
$787$	−236.729	−	236.729i	−0.300800	−	0.300800i	−0.841327	+	0.540527i	$0.818225\pi$
$788$	−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	−0.816512	−	0.577329i	$-0.804095\pi$
$797$	−190.629	+	190.629i	−0.239183	+	0.239183i	0.577329	+	0.816512i	$0.304095\pi$
$798$	−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	$-0.825267\pi$
$809$		−	844.246i		−	1.04357i	0.853078	−	0.521784i	$-0.174733\pi$
$810$	−908.328	−	339.136i	−1.12139	−	0.418686i
$811$	443.406	+	443.406i	0.546740	+	0.546740i	0.925496	−	0.378756i	$-0.123648\pi$
$811$	443.406	+	443.406i	0.546740	+	0.546740i	−0.378756	+	0.925496i	$0.623648\pi$
$812$	−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	−0.745232	−	0.666805i	$-0.767661\pi$
$821$	−64.3891	+	64.3891i	−0.0784277	+	0.0784277i	0.666805	+	0.745232i	$0.267661\pi$
$822$	648.254	+	244.212i	0.788630	+	0.297095i
$823$		−	659.199i		−	0.800971i	−0.916303	−	0.400486i	$-0.868841\pi$
$823$		−	659.199i		−	0.800971i	0.916303	−	0.400486i	$-0.131159\pi$
$824$	−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	−0.276937	−	0.960888i	$-0.589319\pi$
$827$	565.628	−	565.628i	0.683951	−	0.683951i	0.960888	+	0.276937i	$0.0893193\pi$
$828$	−208.744	+	237.733i	−0.252106	+	0.287117i
$829$	271.351	+	271.351i	0.327323	+	0.327323i	0.851568	−	0.524245i	$-0.175652\pi$
$829$	271.351	+	271.351i	0.327323	+	0.327323i	−0.524245	+	0.851568i	$0.675652\pi$
$830$	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	0.755133	−	0.655571i	$-0.227572\pi$
$853$	84.9264	+	84.9264i	0.0995620	+	0.0995620i	−0.655571	+	0.755133i	$0.727572\pi$
$854$	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	0.708297	−	0.705914i	$-0.249464\pi$
$859$	2.04685	+	2.04685i	0.00238283	+	0.00238283i	−0.705914	+	0.708297i	$0.749464\pi$
$860$	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	−0.877606	−	0.479383i	$-0.840860\pi$
$877$	−349.241	+	349.241i	−0.398222	+	0.398222i	0.479383	+	0.877606i	$0.340860\pi$
$878$	−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	0.980906	+	0.194481i	$0.0623022\pi$
$883$	1037.87	+	1037.87i	1.17539	+	1.17539i	0.194481	+	0.980906i	$0.437698\pi$
$884$	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	$-0.674462\pi$
$887$		−	1514.15i		−	1.70704i	0.521057	−	0.853522i	$-0.325538\pi$
$888$	−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	−0.0895162	−	0.995985i	$-0.528532\pi$
$907$	822.168	−	822.168i	0.906469	−	0.906469i	0.995985	+	0.0895162i	$0.0285321\pi$
$908$	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	$-0.941720\pi$
$911$		−	331.730i		−	0.364139i	0.983286	−	0.182069i	$-0.0582795\pi$
$912$	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	0.999974	−	0.00721133i	$-0.00229546\pi$
$941$	934.190	+	934.190i	0.992763	+	0.992763i	−0.00721133	+	0.999974i	$0.502295\pi$
$942$	−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	0.512071	−	0.858943i	$-0.328879\pi$
$947$	−328.488	−	328.488i	−0.346872	−	0.346872i	−0.858943	+	0.512071i	$0.828879\pi$
$948$	−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	$0.0982234\pi$
$967$			587.364i			0.607408i	−0.952766	+	0.303704i	$0.901777\pi$
$968$	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	0.180288	−	0.983614i	$-0.442297\pi$
$971$	−780.030	−	780.030i	−0.803326	−	0.803326i	−0.983614	+	0.180288i	$0.942297\pi$
$972$	−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	$-0.970190\pi$
$977$		−	182.727i		−	0.187028i	0.995618	−	0.0935142i	$-0.0298101\pi$
$978$	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	$0.0346033\pi$
$983$			213.302i			0.216991i	−0.994097	+	0.108495i	$0.965397\pi$
$984$	−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	$0.335408\pi$
$991$			1722.88i			1.73853i	−0.494345	+	0.869266i	$0.664592\pi$
$992$	−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	−0.988921	−	0.148445i	$-0.952573\pi$
$997$	−1133.95	−	1133.95i	−1.13737	−	1.13737i	−0.148445	−	0.988921i	$-0.547427\pi$
$998$	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.19.19	yes	44
4.3	odd	2		320.3.k.a.239.18		44
5.2	odd	4		400.3.r.g.51.15		44
5.3	odd	4		400.3.r.g.51.8		44
5.4	even	2	inner	80.3.k.a.19.4	✓	44
8.3	odd	2		640.3.k.a.479.5		44
8.5	even	2		640.3.k.b.479.18		44
16.3	odd	4		640.3.k.b.159.5		44
16.5	even	4		320.3.k.a.79.5		44
16.11	odd	4	inner	80.3.k.a.59.4	yes	44
16.13	even	4		640.3.k.a.159.18		44
20.19	odd	2		320.3.k.a.239.5		44
40.19	odd	2		640.3.k.a.479.18		44
40.29	even	2		640.3.k.b.479.5		44
80.19	odd	4		640.3.k.b.159.18		44
80.27	even	4		400.3.r.g.251.15		44
80.29	even	4		640.3.k.a.159.5		44
80.43	even	4		400.3.r.g.251.8		44
80.59	odd	4	inner	80.3.k.a.59.19	yes	44
80.69	even	4		320.3.k.a.79.18		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.k.a.19.4	✓	44	5.4	even	2	inner
80.3.k.a.19.19	yes	44	1.1	even	1	trivial
80.3.k.a.59.4	yes	44	16.11	odd	4	inner
80.3.k.a.59.19	yes	44	80.59	odd	4	inner
320.3.k.a.79.5		44	16.5	even	4
320.3.k.a.79.18		44	80.69	even	4
320.3.k.a.239.5		44	20.19	odd	2
320.3.k.a.239.18		44	4.3	odd	2
400.3.r.g.51.8		44	5.3	odd	4
400.3.r.g.51.15		44	5.2	odd	4
400.3.r.g.251.8		44	80.43	even	4
400.3.r.g.251.15		44	80.27	even	4
640.3.k.a.159.5		44	80.29	even	4
640.3.k.a.159.18		44	16.13	even	4
640.3.k.a.479.5		44	8.3	odd	2
640.3.k.a.479.18		44	40.19	odd	2
640.3.k.b.159.5		44	16.3	odd	4
640.3.k.b.159.18		44	80.19	odd	4
640.3.k.b.479.5		44	40.29	even	2
640.3.k.b.479.18		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)

\(f(q)\)	\(=\)	\(q+(1.82198 - 0.824856i) q^{2} +(-2.39041 - 2.39041i) q^{3} +(2.63923 - 3.00574i) q^{4} +(-3.54593 - 3.52510i) q^{5} +(-6.32702 - 2.38354i) q^{6} +5.08144i q^{7} +(2.32932 - 7.65338i) q^{8} +2.42812i q^{9} +O(q^{10})\)	\(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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