LMFDB - Embedded newform 80.3.i.a.13.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,3,Mod(13,80)]

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([0, 3, 3]))

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

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

chi := DirichletCharacter("80.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	80.i (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			13.16
Character	$\chi$	$=$	80.13
Dual form			80.3.i.a.37.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25977 + 1.55338i) q^{2} -0.119786i q^{3} +(-0.825960 + 3.91379i) q^{4} +(-3.85807 + 3.18046i) q^{5} +(0.186072 - 0.150902i) q^{6} +(4.73972 + 4.73972i) q^{7} +(-7.12012 + 3.64745i) q^{8} +8.98565 q^{9} +O(q^{10})$	\(q+(1.25977 + 1.55338i) q^{2} -0.119786i q^{3} +(-0.825960 + 3.91379i) q^{4} +(-3.85807 + 3.18046i) q^{5} +(0.186072 - 0.150902i) q^{6} +(4.73972 + 4.73972i) q^{7} +(-7.12012 + 3.64745i) q^{8} +8.98565 q^{9} +(-9.80073 - 1.98640i) q^{10} +(2.49487 - 2.49487i) q^{11} +(0.468816 + 0.0989381i) q^{12} -18.4567i q^{13} +(-1.39162 + 13.3335i) q^{14} +(0.380972 + 0.462141i) q^{15} +(-14.6356 - 6.46528i) q^{16} +(10.7165 - 10.7165i) q^{17} +(11.3199 + 13.9581i) q^{18} +(0.469722 - 0.469722i) q^{19} +(-9.26104 - 17.7266i) q^{20} +(0.567750 - 0.567750i) q^{21} +(7.01842 + 0.732510i) q^{22} +(-27.9445 + 27.9445i) q^{23} +(0.436912 + 0.852887i) q^{24} +(4.76941 - 24.5408i) q^{25} +(28.6701 - 23.2511i) q^{26} -2.15442i q^{27} +(-22.4651 + 14.6355i) q^{28} +(15.6079 - 15.6079i) q^{29} +(-0.237942 + 1.17399i) q^{30} +49.2667 q^{31} +(-8.39445 - 30.8793i) q^{32} +(-0.298849 - 0.298849i) q^{33} +(30.1472 + 3.14645i) q^{34} +(-33.3606 - 3.21171i) q^{35} +(-7.42179 + 35.1680i) q^{36} +29.1310i q^{37} +(1.32140 + 0.137914i) q^{38} -2.21084 q^{39} +(15.8694 - 36.7173i) q^{40} -16.4684i q^{41} +(1.59716 + 0.166695i) q^{42} -4.48974 q^{43} +(7.70373 + 11.8251i) q^{44} +(-34.6673 + 28.5785i) q^{45} +(-78.6119 - 8.20470i) q^{46} +(-40.6666 + 40.6666i) q^{47} +(-0.774447 + 1.75313i) q^{48} -4.07009i q^{49} +(44.1295 - 23.5071i) q^{50} +(-1.28369 - 1.28369i) q^{51} +(72.2356 + 15.2445i) q^{52} -78.7038 q^{53} +(3.34663 - 2.71407i) q^{54} +(-1.69056 + 17.5602i) q^{55} +(-51.0353 - 16.4595i) q^{56} +(-0.0562658 - 0.0562658i) q^{57} +(43.9073 + 4.58259i) q^{58} +(3.26583 + 3.26583i) q^{59} +(-2.12339 + 1.10934i) q^{60} +(-23.0393 - 23.0393i) q^{61} +(62.0647 + 76.5297i) q^{62} +(42.5895 + 42.5895i) q^{63} +(37.3922 - 51.9406i) q^{64} +(58.7006 + 71.2071i) q^{65} +(0.0877441 - 0.840705i) q^{66} -58.9247 q^{67} +(33.0909 + 50.7938i) q^{68} +(3.34734 + 3.34734i) q^{69} +(-37.0377 - 55.8677i) q^{70} +76.8059i q^{71} +(-63.9789 + 32.7747i) q^{72} +(18.7472 - 18.7472i) q^{73} +(-45.2514 + 36.6984i) q^{74} +(-2.93964 - 0.571306i) q^{75} +(1.45042 + 2.22637i) q^{76} +23.6499 q^{77} +(-2.78515 - 3.43427i) q^{78} -141.697i q^{79} +(77.0276 - 21.6043i) q^{80} +80.6128 q^{81} +(25.5817 - 20.7464i) q^{82} -120.053i q^{83} +(1.75312 + 2.69100i) q^{84} +(-7.26169 + 75.4286i) q^{85} +(-5.65604 - 6.97426i) q^{86} +(-1.86960 - 1.86960i) q^{87} +(-8.66383 + 26.8636i) q^{88} -87.7260 q^{89} +(-88.0659 - 17.8491i) q^{90} +(87.4794 - 87.4794i) q^{91} +(-86.2879 - 132.450i) q^{92} -5.90143i q^{93} +(-114.401 - 11.9400i) q^{94} +(-0.318290 + 3.30615i) q^{95} +(-3.69890 + 1.00553i) q^{96} +(34.6438 - 34.6438i) q^{97} +(6.32239 - 5.12738i) q^{98} +(22.4180 - 22.4180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9	$ 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9} + 6 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{15} + 24 q^{16} - 4 q^{17} + 22 q^{18} + 32 q^{19} + 40 q^{20} - 4 q^{21} + 92 q^{22} + 36 q^{24} - 52 q^{26} + 36 q^{28} - 28 q^{30} - 8 q^{31} - 132 q^{32} - 4 q^{33} - 88 q^{34} + 96 q^{35} - 116 q^{36} - 216 q^{38} + 72 q^{39} + 16 q^{40} + 16 q^{42} + 124 q^{43} - 168 q^{44} - 34 q^{45} + 108 q^{46} - 4 q^{47} + 340 q^{48} + 10 q^{50} - 100 q^{51} + 48 q^{52} - 4 q^{53} + 228 q^{54} - 172 q^{56} + 36 q^{57} + 16 q^{58} + 64 q^{59} + 136 q^{60} - 36 q^{61} - 356 q^{62} - 200 q^{63} - 176 q^{64} - 4 q^{65} + 276 q^{66} - 292 q^{67} - 72 q^{68} - 60 q^{69} - 92 q^{70} + 448 q^{72} + 48 q^{73} + 284 q^{74} + 96 q^{75} + 252 q^{76} + 192 q^{77} + 620 q^{78} + 4 q^{80} + 100 q^{81} - 240 q^{82} + 288 q^{84} + 48 q^{85} + 20 q^{86} + 36 q^{87} - 624 q^{88} - 578 q^{90} + 188 q^{91} - 412 q^{92} - 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 78 q^{98} - 92 q^{99}+O(q^{100}) $ 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9 + 6 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^15 + 24 * q^16 - 4 * q^17 + 22 * q^18 + 32 * q^19 + 40 * q^20 - 4 * q^21 + 92 * q^22 + 36 * q^24 - 52 * q^26 + 36 * q^28 - 28 * q^30 - 8 * q^31 - 132 * q^32 - 4 * q^33 - 88 * q^34 + 96 * q^35 - 116 * q^36 - 216 * q^38 + 72 * q^39 + 16 * q^40 + 16 * q^42 + 124 * q^43 - 168 * q^44 - 34 * q^45 + 108 * q^46 - 4 * q^47 + 340 * q^48 + 10 * q^50 - 100 * q^51 + 48 * q^52 - 4 * q^53 + 228 * q^54 - 172 * q^56 + 36 * q^57 + 16 * q^58 + 64 * q^59 + 136 * q^60 - 36 * q^61 - 356 * q^62 - 200 * q^63 - 176 * q^64 - 4 * q^65 + 276 * q^66 - 292 * q^67 - 72 * q^68 - 60 * q^69 - 92 * q^70 + 448 * q^72 + 48 * q^73 + 284 * q^74 + 96 * q^75 + 252 * q^76 + 192 * q^77 + 620 * q^78 + 4 * q^80 + 100 * q^81 - 240 * q^82 + 288 * q^84 + 48 * q^85 + 20 * q^86 + 36 * q^87 - 624 * q^88 - 578 * q^90 + 188 * q^91 - 412 * q^92 - 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 78 * q^98 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.25977	+	1.55338i	0.629885	+	0.776688i
$2$	1.25977	+	1.55338i	0.629885	+	0.776688i
$3$		−	0.119786i		−	0.0399285i	−0.999801	−	0.0199643i	$-0.993645\pi$
$3$		−	0.119786i		−	0.0399285i	0.999801	−	0.0199643i	$-0.00635524\pi$
$4$	−0.825960	+	3.91379i	−0.206490	+	0.978449i
$5$	−3.85807	+	3.18046i	−0.771614	+	0.636091i
$5$	−3.85807	+	3.18046i	−0.771614	+	0.636091i
$6$	0.186072	−	0.150902i	0.0310120	−	0.0251504i
$7$	4.73972	+	4.73972i	0.677103	+	0.677103i	0.959344	−	0.282241i	$-0.0910777\pi$
$7$	4.73972	+	4.73972i	0.677103	+	0.677103i	−0.282241	+	0.959344i	$0.591078\pi$
$8$	−7.12012	+	3.64745i	−0.890015	+	0.455932i
$9$	8.98565			0.998406
$10$	−9.80073	−	1.98640i	−0.980073	−	0.198640i
$11$	2.49487	−	2.49487i	0.226806	−	0.226806i	−0.584551	−	0.811357i	$-0.698729\pi$
$11$	2.49487	−	2.49487i	0.226806	−	0.226806i	0.811357	+	0.584551i	$0.198729\pi$
$12$	0.468816	+	0.0989381i	0.0390680	+	0.00824484i
$13$		−	18.4567i		−	1.41974i	−0.704331	−	0.709871i	$-0.748753\pi$
$13$		−	18.4567i		−	1.41974i	0.704331	−	0.709871i	$-0.251247\pi$
$14$	−1.39162	+	13.3335i	−0.0994012	+	0.952395i
$15$	0.380972	+	0.462141i	0.0253982	+	0.0308094i
$16$	−14.6356	−	6.46528i	−0.914724	−	0.404080i
$17$	10.7165	−	10.7165i	0.630385	−	0.630385i	−0.317780	−	0.948165i	$-0.602937\pi$
$17$	10.7165	−	10.7165i	0.630385	−	0.630385i	0.948165	+	0.317780i	$0.102937\pi$
$18$	11.3199	+	13.9581i	0.628881	+	0.775450i
$19$	0.469722	−	0.469722i	0.0247222	−	0.0247222i	−0.694638	−	0.719360i	$-0.744435\pi$
$19$	0.469722	−	0.469722i	0.0247222	−	0.0247222i	0.719360	+	0.694638i	$0.244435\pi$
$20$	−9.26104	−	17.7266i	−0.463052	−	0.886331i
$21$	0.567750	−	0.567750i	0.0270357	−	0.0270357i
$22$	7.01842	+	0.732510i	0.319019	+	0.0332959i
$23$	−27.9445	+	27.9445i	−1.21498	+	1.21498i	−0.245608	+	0.969369i	$0.578988\pi$
$23$	−27.9445	+	27.9445i	−1.21498	+	1.21498i	−0.969369	+	0.245608i	$0.921012\pi$
$24$	0.436912	+	0.852887i	0.0182047	+	0.0355370i
$25$	4.76941	−	24.5408i	0.190776	−	0.981634i
$26$	28.6701	−	23.2511i	1.10270	−	0.894275i
$27$		−	2.15442i		−	0.0797934i
$28$	−22.4651	+	14.6355i	−0.802326	+	0.522695i
$29$	15.6079	−	15.6079i	0.538203	−	0.538203i	−0.384798	−	0.923001i	$-0.625729\pi$
$29$	15.6079	−	15.6079i	0.538203	−	0.538203i	0.923001	+	0.384798i	$0.125729\pi$
$30$	−0.237942	+	1.17399i	−0.00793138	+	0.0391328i
$31$	49.2667			1.58925			0.794624	−	0.607102i	$-0.207668\pi$
$31$	49.2667			1.58925			0.794624	+	0.607102i	$0.207668\pi$
$32$	−8.39445	−	30.8793i	−0.262327	−	0.964979i
$33$	−0.298849	−	0.298849i	−0.00905602	−	0.00905602i
$34$	30.1472	+	3.14645i	0.886682	+	0.0925427i
$35$	−33.3606	−	3.21171i	−0.953161	−	0.0917630i
$36$	−7.42179	+	35.1680i	−0.206161	+	0.976889i
$37$			29.1310i			0.787325i	0.919255	+	0.393662i	$0.128792\pi$
$37$			29.1310i			0.787325i	−0.919255	+	0.393662i	$0.871208\pi$
$38$	1.32140	+	0.137914i	0.0347736	+	0.00362931i
$39$	−2.21084			−0.0566882
$40$	15.8694	−	36.7173i	0.396734	−	0.917934i
$41$		−	16.4684i		−	0.401669i	−0.979625	−	0.200834i	$-0.935635\pi$
$41$		−	16.4684i		−	0.401669i	0.979625	−	0.200834i	$-0.0643653\pi$
$42$	1.59716	+	0.166695i	0.0380277	+	0.00396894i
$43$	−4.48974			−0.104413			−0.0522063	−	0.998636i	$-0.516625\pi$
$43$	−4.48974			−0.104413			−0.0522063	+	0.998636i	$0.516625\pi$
$44$	7.70373	+	11.8251i	0.175085	+	0.268751i
$45$	−34.6673	+	28.5785i	−0.770384	+	0.635077i
$46$	−78.6119	−	8.20470i	−1.70895	−	0.178363i
$47$	−40.6666	+	40.6666i	−0.865246	+	0.865246i	−0.991942	−	0.126695i	$-0.959563\pi$
$47$	−40.6666	+	40.6666i	−0.865246	+	0.865246i	0.126695	+	0.991942i	$0.459563\pi$
$48$	−0.774447	+	1.75313i	−0.0161343	+	0.0365236i
$49$		−	4.07009i		−	0.0830632i
$50$	44.1295	−	23.5071i	0.882591	−	0.470142i
$51$	−1.28369	−	1.28369i	−0.0251703	−	0.0251703i
$52$	72.2356	+	15.2445i	1.38915	+	0.293163i
$53$	−78.7038			−1.48498			−0.742488	−	0.669859i	$-0.766354\pi$
$53$	−78.7038			−1.48498			−0.742488	+	0.669859i	$0.766354\pi$
$54$	3.34663	−	2.71407i	0.0619746	−	0.0502606i
$55$	−1.69056	+	17.5602i	−0.0307374	+	0.319276i
$56$	−51.0353	−	16.4595i	−0.911344	−	0.293919i
$57$	−0.0562658	−	0.0562658i	−0.000987120	−	0.000987120i
$58$	43.9073	+	4.58259i	0.757022	+	0.0790102i
$59$	3.26583	+	3.26583i	0.0553530	+	0.0553530i	0.734241	−	0.678888i	$-0.237538\pi$
$59$	3.26583	+	3.26583i	0.0553530	+	0.0553530i	−0.678888	+	0.734241i	$0.737538\pi$
$60$	−2.12339	+	1.10934i	−0.0353899	+	0.0184890i
$61$	−23.0393	−	23.0393i	−0.377694	−	0.377694i	0.492576	−	0.870269i	$-0.336055\pi$
$61$	−23.0393	−	23.0393i	−0.377694	−	0.377694i	−0.870269	+	0.492576i	$0.836055\pi$
$62$	62.0647	+	76.5297i	1.00104	+	1.23435i
$63$	42.5895	+	42.5895i	0.676023	+	0.676023i
$64$	37.3922	−	51.9406i	0.584253	−	0.811572i
$65$	58.7006	+	71.2071i	0.903086	+	1.09549i
$66$	0.0877441	−	0.840705i	0.00132946	−	0.0127380i
$67$	−58.9247			−0.879474			−0.439737	−	0.898127i	$-0.644928\pi$
$67$	−58.9247			−0.879474			−0.439737	+	0.898127i	$0.644928\pi$
$68$	33.0909	+	50.7938i	0.486631	+	0.746967i
$69$	3.34734	+	3.34734i	0.0485122	+	0.0485122i
$70$	−37.0377	−	55.8677i	−0.529111	−	0.798110i
$71$			76.8059i			1.08177i	0.841096	+	0.540886i	$0.181911\pi$
$71$			76.8059i			1.08177i	−0.841096	+	0.540886i	$0.818089\pi$
$72$	−63.9789	+	32.7747i	−0.888596	+	0.455205i
$73$	18.7472	−	18.7472i	0.256811	−	0.256811i	−0.566945	−	0.823756i	$-0.691875\pi$
$73$	18.7472	−	18.7472i	0.256811	−	0.256811i	0.823756	+	0.566945i	$0.191875\pi$
$74$	−45.2514	+	36.6984i	−0.611506	+	0.495924i
$75$	−2.93964	−	0.571306i	−0.0391952	−	0.00761742i
$76$	1.45042	+	2.22637i	0.0190845	+	0.0292943i
$77$	23.6499			0.307142
$78$	−2.78515	−	3.43427i	−0.0357070	−	0.0440291i
$79$		−	141.697i		−	1.79363i	−0.442407	−	0.896815i	$-0.645875\pi$
$79$		−	141.697i		−	1.79363i	0.442407	−	0.896815i	$-0.354125\pi$
$80$	77.0276	−	21.6043i	0.962845	−	0.270054i
$81$	80.6128			0.995220
$82$	25.5817	−	20.7464i	0.311972	−	0.253005i
$83$		−	120.053i		−	1.44642i	−0.690628	−	0.723210i	$-0.742666\pi$
$83$		−	120.053i		−	1.44642i	0.690628	−	0.723210i	$-0.257334\pi$
$84$	1.75312	+	2.69100i	0.0208705	+	0.0320357i
$85$	−7.26169	+	75.4286i	−0.0854316	+	0.887396i
$86$	−5.65604	−	6.97426i	−0.0657679	−	0.0810961i
$87$	−1.86960	−	1.86960i	−0.0214897	−	0.0214897i
$88$	−8.66383	+	26.8636i	−0.0984526	+	0.305269i
$89$	−87.7260			−0.985686			−0.492843	−	0.870118i	$-0.664042\pi$
$89$	−87.7260			−0.985686			−0.492843	+	0.870118i	$0.664042\pi$
$90$	−88.0659	−	17.8491i	−0.978510	−	0.198323i
$91$	87.4794	−	87.4794i	0.961312	−	0.961312i
$92$	−86.2879	−	132.450i	−0.937912	−	1.43967i
$93$		−	5.90143i		−	0.0634563i
$94$	−114.401	−	11.9400i	−1.21703	−	0.127021i
$95$	−0.318290	+	3.30615i	−0.00335043	+	0.0348015i
$96$	−3.69890	+	1.00553i	−0.0385302	+	0.0104743i
$97$	34.6438	−	34.6438i	0.357153	−	0.357153i	−0.505609	−	0.862762i	$-0.668732\pi$
$97$	34.6438	−	34.6438i	0.357153	−	0.357153i	0.862762	+	0.505609i	$0.168732\pi$
$98$	6.32239	−	5.12738i	0.0645142	−	0.0523202i
$99$	22.4180	−	22.4180i	0.226444	−	0.226444i
$100$	92.1085	+	38.9363i	0.921085	+	0.389363i
$101$	−29.5707	+	29.5707i	−0.292780	+	0.292780i	−0.838177	−	0.545398i	$-0.816379\pi$
$101$	−29.5707	+	29.5707i	−0.292780	+	0.292780i	0.545398	+	0.838177i	$0.316379\pi$
$102$	0.376900	−	3.61120i	0.00369509	−	0.0354039i
$103$	48.5504	−	48.5504i	0.471363	−	0.471363i	−0.430992	−	0.902356i	$-0.641836\pi$
$103$	48.5504	−	48.5504i	0.471363	−	0.471363i	0.902356	+	0.430992i	$0.141836\pi$
$104$	67.3198	+	131.414i	0.647306	+	1.26359i
$105$	−0.384716	+	3.99612i	−0.00366396	+	0.0380583i
$106$	−99.1486	−	122.257i	−0.935364	−	1.15336i
$107$			62.1016i			0.580389i	0.956968	+	0.290194i	$0.0937200\pi$
$107$			62.1016i			0.580389i	−0.956968	+	0.290194i	$0.906280\pi$
$108$	8.43196	+	1.77947i	0.0780737	+	0.0164765i
$109$	−31.6457	+	31.6457i	−0.290327	+	0.290327i	−0.837209	−	0.546882i	$-0.815814\pi$
$109$	−31.6457	+	31.6457i	−0.290327	+	0.290327i	0.546882	+	0.837209i	$0.315814\pi$
$110$	−29.4073	+	19.4957i	−0.267339	+	0.177234i
$111$	3.48947			0.0314367
$112$	−38.7250	−	100.012i	−0.345758	−	0.892966i
$113$	−56.1211	−	56.1211i	−0.496647	−	0.496647i	0.413745	−	0.910393i	$-0.364220\pi$
$113$	−56.1211	−	56.1211i	−0.496647	−	0.496647i	−0.910393	+	0.413745i	$0.864220\pi$
$114$	0.0165201	−	0.158284i	0.000144913	−	0.00138846i
$115$	18.9356	−	196.688i	0.164657	−	1.71033i
$116$	48.1946	+	73.9776i	0.415471	+	0.637738i
$117$		−	165.845i		−	1.41748i
$118$	−0.958871	+	9.18725i	−0.00812602	+	0.0778581i
$119$	101.587			0.853671
$120$	−4.39821	−	1.90092i	−0.0366517	−	0.0158410i
$121$			108.551i			0.897118i
$122$	6.76451	−	64.8130i	0.0554468	−	0.531254i
$123$	−1.97268			−0.0160380
$124$	−40.6923	+	192.820i	−0.328164	+	1.55500i
$125$	59.6503	+	109.849i	0.477202	+	0.878793i
$126$	−12.5046	+	119.810i	−0.0992427	+	0.950877i
$127$	−60.1440	+	60.1440i	−0.473575	+	0.473575i	−0.903069	−	0.429495i	$-0.858692\pi$
$127$	−60.1440	+	60.1440i	−0.473575	+	0.473575i	0.429495	+	0.903069i	$0.358692\pi$
$128$	127.789	−	7.34905i	0.998350	−	0.0574144i
$129$			0.537806i			0.00416904i
$130$	−36.6622	+	180.889i	−0.282017	+	1.39145i
$131$	129.876	+	129.876i	0.991422	+	0.991422i	0.999964	−	0.00854147i	$-0.00271887\pi$
$131$	129.876	+	129.876i	0.991422	+	0.991422i	−0.00854147	+	0.999964i	$0.502719\pi$
$132$	1.41647	−	0.922796i	0.0107308	−	0.00699088i
$133$	4.45270			0.0334789
$134$	−74.2316	−	91.5323i	−0.553967	−	0.683077i
$135$	6.85204	+	8.31191i	0.0507558	+	0.0615697i
$136$	−37.2150	+	115.391i	−0.273639	+	0.848464i
$137$	69.8267	+	69.8267i	0.509684	+	0.509684i	0.914429	−	0.404745i	$-0.132640\pi$
$137$	69.8267	+	69.8267i	0.509684	+	0.509684i	−0.404745	+	0.914429i	$0.632640\pi$
$138$	−0.982804	+	9.41657i	−0.00712177	+	0.0682360i
$139$	−16.8371	−	16.8371i	−0.121130	−	0.121130i	0.643943	−	0.765073i	$-0.277297\pi$
$139$	−16.8371	−	16.8371i	−0.121130	−	0.121130i	−0.765073	+	0.643943i	$0.777297\pi$
$140$	40.1245	−	127.914i	0.286604	−	0.913671i
$141$	4.87127	+	4.87127i	0.0345480	+	0.0345480i
$142$	−119.308	+	96.7577i	−0.840201	+	0.681392i
$143$	−46.0469	−	46.0469i	−0.322006	−	0.322006i
$144$	−131.510	−	58.0947i	−0.913265	−	0.403436i
$145$	−10.5761	+	109.857i	−0.0729389	+	0.757631i
$146$	52.7386	+	5.50431i	0.361223	+	0.0377008i
$147$	−0.487538			−0.00331659
$148$	−114.013	−	24.0611i	−0.770357	−	0.162575i
$149$	126.048	+	126.048i	0.845963	+	0.845963i	0.989627	−	0.143664i	$-0.0458883\pi$
$149$	126.048	+	126.048i	0.845963	+	0.845963i	−0.143664	+	0.989627i	$0.545888\pi$
$150$	−2.81581	−	5.28608i	−0.0187721	−	0.0352405i
$151$		−	170.000i		−	1.12583i	−0.826516	−	0.562914i	$-0.809680\pi$
$151$		−	170.000i		−	1.12583i	0.826516	−	0.562914i	$-0.190320\pi$
$152$	−1.63119	+	5.05776i	−0.0107315	+	0.0332747i
$153$	96.2951	−	96.2951i	0.629380	−	0.629380i
$154$	29.7935	+	36.7373i	0.193464	+	0.238554i
$155$	−190.074	+	156.690i	−1.22629	+	1.01091i
$156$	1.82607	−	8.65278i	0.0117056	−	0.0554665i
$157$	12.1854			0.0776137			0.0388069	−	0.999247i	$-0.487644\pi$
$157$	12.1854			0.0776137			0.0388069	+	0.999247i	$0.487644\pi$
$158$	220.108	−	178.505i	1.39309	−	1.12978i
$159$			9.42757i			0.0592929i
$160$	130.597	+	92.4365i	0.816229	+	0.577728i
$161$	−264.898			−1.64533
$162$	101.554	+	125.222i	0.626874	+	0.772976i
$163$			285.780i			1.75325i	0.481170	+	0.876627i	$0.340212\pi$
$163$			285.780i			1.75325i	−0.481170	+	0.876627i	$0.659788\pi$
$164$	64.4540	+	13.6023i	0.393012	+	0.0829406i
$165$	2.10345	+	0.202504i	0.0127482	+	0.00122730i
$166$	186.487	−	151.239i	1.12342	−	0.911078i
$167$	−102.579	−	102.579i	−0.614248	−	0.614248i	0.329802	−	0.944050i	$-0.393018\pi$
$167$	−102.579	−	102.579i	−0.614248	−	0.614248i	−0.944050	+	0.329802i	$0.893018\pi$
$168$	−1.97161	+	6.11329i	−0.0117357	+	0.0363886i
$169$	−171.648			−1.01567
$170$	−126.317	+	83.7426i	−0.743042	+	0.492603i
$171$	4.22075	−	4.22075i	0.0246828	−	0.0246828i
$172$	3.70835	−	17.5719i	0.0215602	−	0.102162i
$173$		−	68.3056i		−	0.394830i	−0.980320	−	0.197415i	$-0.936745\pi$
$173$		−	68.3056i		−	0.394830i	0.980320	−	0.197415i	$-0.0632546\pi$
$174$	0.548928	−	5.25946i	0.00315476	−	0.0302268i
$175$	138.922	−	93.7110i	0.793842	−	0.535492i
$176$	−52.6438	+	20.3838i	−0.299112	+	0.115817i
$177$	0.391199	−	0.391199i	0.00221016	−	0.00221016i
$178$	−110.515	−	136.272i	−0.620869	−	0.765571i
$179$	−165.892	+	165.892i	−0.926773	+	0.926773i	−0.997496	−	0.0707227i	$-0.977469\pi$
$179$	−165.892	+	165.892i	−0.926773	+	0.926773i	0.0707227	+	0.997496i	$0.477469\pi$
$180$	−83.2164	−	159.285i	−0.462314	−	0.884918i
$181$	101.633	−	101.633i	0.561506	−	0.561506i	−0.368229	−	0.929735i	$-0.620036\pi$
$181$	101.633	−	101.633i	0.561506	−	0.561506i	0.929735	+	0.368229i	$0.120036\pi$
$182$	246.092	+	25.6846i	1.35216	+	0.141124i
$183$	−2.75978	+	2.75978i	−0.0150807	+	0.0150807i
$184$	97.0418	−	300.894i	0.527401	−	1.63529i
$185$	−92.6499	−	112.389i	−0.500810	−	0.607511i
$186$	9.16715	−	7.43445i	0.0492858	−	0.0399701i
$187$		−	53.4726i		−	0.285950i
$188$	−125.572	−	192.750i	−0.667934	−	1.02526i
$189$	10.2114	−	10.2114i	0.0540283	−	0.0540283i
$190$	−5.53667	+	3.67056i	−0.0291403	+	0.0193187i
$191$	−144.454			−0.756301			−0.378151	−	0.925744i	$-0.623440\pi$
$191$	−144.454			−0.756301			−0.378151	+	0.925744i	$0.623440\pi$
$192$	−6.22173	−	4.47904i	−0.0324049	−	0.0233283i
$193$	−32.7772	−	32.7772i	−0.169830	−	0.169830i	0.617075	−	0.786905i	$-0.288318\pi$
$193$	−32.7772	−	32.7772i	−0.169830	−	0.169830i	−0.786905	+	0.617075i	$0.788318\pi$
$194$	97.4582	+	10.1717i	0.502362	+	0.0524313i
$195$	8.52958	−	7.03148i	0.0437414	−	0.0360589i
$196$	15.9295	+	3.36174i	0.0812730	+	0.0171517i
$197$		−	335.205i		−	1.70155i	−0.525530	−	0.850775i	$-0.676133\pi$
$197$		−	335.205i		−	1.70155i	0.525530	−	0.850775i	$-0.323867\pi$
$198$	63.0651	+	6.58208i	0.318511	+	0.0332428i
$199$	−184.734			−0.928313			−0.464156	−	0.885753i	$-0.653642\pi$
$199$	−184.734			−0.928313			−0.464156	+	0.885753i	$0.653642\pi$
$200$	55.5528	+	192.130i	0.277764	+	0.960649i
$201$			7.05833i			0.0351161i
$202$	−83.1869	−	8.68218i	−0.411816	−	0.0429811i
$203$	147.954			0.728838
$204$	6.08436	−	3.96381i	0.0298253	−	0.0194304i
$205$	52.3771	+	63.5363i	0.255498	+	0.309933i
$206$	136.579	+	14.2548i	0.663007	+	0.0691978i
$207$	−251.099	+	251.099i	−1.21304	+	1.21304i
$208$	−119.327	+	270.124i	−0.573689	+	1.29867i
$209$		−	2.34378i		−	0.0112143i
$210$	−6.69214	+	4.43659i	−0.0318673	+	0.0211266i
$211$	187.999	+	187.999i	0.890989	+	0.890989i	0.994616	−	0.103627i	$-0.0330448\pi$
$211$	187.999	+	187.999i	0.890989	+	0.890989i	−0.103627	+	0.994616i	$0.533045\pi$
$212$	65.0062	−	308.030i	0.306633	−	1.45297i
$213$	9.20023			0.0431936
$214$	−96.4672	+	78.2337i	−0.450781	+	0.365578i
$215$	17.3217	−	14.2794i	0.0805662	−	0.0664159i
$216$	7.85815	+	15.3397i	0.0363803	+	0.0710173i
$217$	233.510	+	233.510i	1.07608	+	1.07608i
$218$	−89.0239	−	9.29139i	−0.408366	−	0.0426211i
$219$	−2.24564	−	2.24564i	−0.0102541	−	0.0102541i
$220$	−67.3306	−	21.1205i	−0.306048	−	0.0960023i
$221$	−197.791	−	197.791i	−0.894984	−	0.894984i
$222$	4.39593	+	5.42047i	0.0198015	+	0.0244165i
$223$	282.322	+	282.322i	1.26602	+	1.26602i	0.948128	+	0.317889i	$0.102974\pi$
$223$	282.322	+	282.322i	1.26602	+	1.26602i	0.317889	+	0.948128i	$0.397026\pi$
$224$	106.572	−	186.147i	0.475768	−	0.831012i
$225$	42.8563	−	220.515i	0.190472	−	0.980069i
$226$	16.4776	−	157.877i	0.0729096	−	0.698571i
$227$	146.872			0.647015			0.323507	−	0.946226i	$-0.395138\pi$
$227$	146.872			0.647015			0.323507	+	0.946226i	$0.395138\pi$
$228$	0.266686	−	0.173740i	0.00116968	−	0.000762016i
$229$	194.697	+	194.697i	0.850205	+	0.850205i	0.990158	−	0.139953i	$-0.0446953\pi$
$229$	194.697	+	194.697i	0.850205	+	0.850205i	−0.139953	+	0.990158i	$0.544695\pi$
$230$	329.385	−	218.367i	1.43211	−	0.949423i
$231$		−	2.83292i		−	0.0122637i
$232$	−54.2010	+	168.059i	−0.233625	+	0.724393i
$233$	−87.0218	+	87.0218i	−0.373484	+	0.373484i	−0.868745	−	0.495260i	$-0.835073\pi$
$233$	−87.0218	+	87.0218i	−0.373484	+	0.373484i	0.495260	+	0.868745i	$0.335073\pi$
$234$	257.620	−	208.927i	1.10094	−	0.892849i
$235$	27.5563	−	286.233i	0.117261	−	1.21801i
$236$	−15.4792	+	10.0843i	−0.0655899	+	0.0427302i
$237$	−16.9732			−0.0716169
$238$	127.976	+	157.803i	0.537714	+	0.663036i
$239$		−	334.837i		−	1.40099i	−0.713657	−	0.700495i	$-0.752963\pi$
$239$		−	334.837i		−	1.40099i	0.713657	−	0.700495i	$-0.247037\pi$
$240$	−2.58788	−	9.22679i	−0.0107828	−	0.0384450i
$241$	−378.876			−1.57210			−0.786049	−	0.618164i	$-0.787877\pi$
$241$	−378.876			−1.57210			−0.786049	+	0.618164i	$0.787877\pi$
$242$	−168.621	+	136.750i	−0.696781	+	0.565081i
$243$		−	29.0460i		−	0.119531i
$244$	109.201	−	71.1416i	0.447544	−	0.291564i
$245$	12.9448	+	15.7027i	0.0528357	+	0.0640927i
$246$	−2.48512	−	3.06431i	−0.0101021	−	0.0124566i
$247$	−8.66949	−	8.66949i	−0.0350991	−	0.0350991i
$248$	−350.784	+	179.698i	−1.41445	+	0.724588i
$249$	−14.3806			−0.0577534
$250$	−95.4915	+	231.044i	−0.381966	+	0.924176i
$251$	−181.937	+	181.937i	−0.724849	+	0.724849i	−0.969589	−	0.244740i	$-0.921297\pi$
$251$	−181.937	+	181.937i	−0.724849	+	0.724849i	0.244740	+	0.969589i	$0.421297\pi$
$252$	−201.864	+	131.509i	−0.801046	+	0.521862i
$253$			139.435i			0.551128i
$254$	−169.194	−	17.6587i	−0.666118	−	0.0695225i
$255$	9.03526	+	0.869845i	0.0354324	+	0.00341116i
$256$	172.400	+	189.246i	0.673439	+	0.739243i
$257$	38.2528	−	38.2528i	0.148843	−	0.148843i	−0.628758	−	0.777601i	$-0.716436\pi$
$257$	38.2528	−	38.2528i	0.148843	−	0.148843i	0.777601	+	0.628758i	$0.216436\pi$
$258$	−0.835416	+	0.677512i	−0.00323804	+	0.00262601i
$259$	−138.073	+	138.073i	−0.533100	+	0.533100i
$260$	−327.174	+	170.928i	−1.25836	+	0.657414i
$261$	140.247	−	140.247i	0.537345	−	0.537345i
$262$	−38.1326	+	365.361i	−0.145544	+	1.39451i
$263$	−165.962	+	165.962i	−0.631034	+	0.631034i	−0.948327	−	0.317294i	$-0.897226\pi$
$263$	−165.962	+	165.962i	−0.631034	+	0.631034i	0.317294	+	0.948327i	$0.397226\pi$
$264$	3.21788	+	1.03780i	0.0121889	+	0.00393107i
$265$	303.645	−	250.314i	1.14583	−	0.944580i
$266$	5.60937	+	6.91672i	0.0210879	+	0.0260027i
$267$			10.5083i			0.0393570i
$268$	48.6695	−	230.619i	0.181603	−	0.860520i
$269$	310.294	−	310.294i	1.15351	−	1.15351i	0.167665	−	0.985844i	$-0.446377\pi$
$269$	310.294	−	310.294i	1.15351	−	1.15351i	0.985844	−	0.167665i	$-0.0536228\pi$
$270$	−4.27953	+	21.1149i	−0.0158501	+	0.0782033i
$271$	−272.486			−1.00548			−0.502741	−	0.864437i	$-0.667675\pi$
$271$	−272.486			−1.00548			−0.502741	+	0.864437i	$0.667675\pi$
$272$	−226.128	+	87.5574i	−0.831354	+	0.321902i
$273$	−10.4788	−	10.4788i	−0.0383838	−	0.0383838i
$274$	−20.5016	+	196.433i	−0.0748235	+	0.716908i
$275$	−49.3270	−	73.1251i	−0.179371	−	0.265910i
$276$	−15.8656	+	10.3360i	−0.0574840	+	0.0374494i
$277$			143.172i			0.516868i	0.966029	+	0.258434i	$0.0832064\pi$
$277$			143.172i			0.516868i	−0.966029	+	0.258434i	$0.916794\pi$
$278$	4.94350	−	47.3653i	0.0177824	−	0.170379i
$279$	442.693			1.58671
$280$	249.246	−	98.8137i	0.890165	−	0.352906i
$281$			139.408i			0.496115i	0.968745	+	0.248057i	$0.0797921\pi$
$281$			139.408i			0.496115i	−0.968745	+	0.248057i	$0.920208\pi$
$282$	−1.43024	+	13.7036i	−0.00507177	+	0.0485943i
$283$	−336.283			−1.18828			−0.594140	−	0.804362i	$-0.702507\pi$
$283$	−336.283			−1.18828			−0.594140	+	0.804362i	$0.702507\pi$
$284$	−300.602	−	63.4386i	−1.05846	−	0.223375i
$285$	0.396029	+	0.0381266i	0.00138957	+	0.000133777i
$286$	13.5197	−	129.537i	0.0472717	−	0.452925i
$287$	78.0557	−	78.0557i	0.271971	−	0.271971i
$288$	−75.4296	−	277.471i	−0.261908	−	0.963441i
$289$			59.3116i			0.205230i
$290$	−183.972	+	121.965i	−0.634387	+	0.420570i
$291$	−4.14983	−	4.14983i	−0.0142606	−	0.0142606i
$292$	57.8883	+	88.8571i	0.198247	+	0.304305i
$293$	−33.1195			−0.113036			−0.0565179	−	0.998402i	$-0.518000\pi$
$293$	−33.1195			−0.113036			−0.0565179	+	0.998402i	$0.518000\pi$
$294$	−0.614186	−	0.757331i	−0.00208907	−	0.00257596i
$295$	−22.9866	−	2.21297i	−0.0779207	−	0.00750161i
$296$	−106.254	−	207.416i	−0.358966	−	0.700731i
$297$	−5.37499	−	5.37499i	−0.0180976	−	0.0180976i
$298$	−37.0087	+	354.593i	−0.124190	+	1.18991i
$299$	515.762	+	515.762i	1.72496	+	1.72496i
$300$	4.66400	−	11.0333i	0.0155467	−	0.0367775i
$301$	−21.2801	−	21.2801i	−0.0706981	−	0.0706981i
$302$	264.074	−	214.161i	0.874417	−	0.709142i
$303$	3.54215	+	3.54215i	0.0116903	+	0.0116903i
$304$	−9.91153	+	3.83777i	−0.0326037	+	0.0126242i
$305$	162.163	+	15.6118i	0.531681	+	0.0511862i
$306$	270.892	+	28.2729i	0.885269	+	0.0923952i
$307$	479.642			1.56235			0.781176	−	0.624310i	$-0.214620\pi$
$307$	479.642			1.56235			0.781176	+	0.624310i	$0.214620\pi$
$308$	−19.5339	+	92.5610i	−0.0634218	+	0.300523i
$309$	−5.81564	−	5.81564i	−0.0188208	−	0.0188208i
$310$	−482.849	−	97.8631i	−1.55758	−	0.315687i
$311$		−	328.043i		−	1.05480i	−0.849617	−	0.527401i	$-0.823167\pi$
$311$		−	328.043i		−	1.05480i	0.849617	−	0.527401i	$-0.176833\pi$
$312$	15.7414	−	8.06394i	0.0504533	−	0.0258459i
$313$	90.2171	−	90.2171i	0.288233	−	0.288233i	−0.548148	−	0.836381i	$-0.684667\pi$
$313$	90.2171	−	90.2171i	0.288233	−	0.288233i	0.836381	+	0.548148i	$0.184667\pi$
$314$	15.3507	+	18.9284i	0.0488877	+	0.0602817i
$315$	−299.767	−	28.8593i	−0.951642	−	0.0916167i
$316$	554.572	+	117.036i	1.75497	+	0.370367i
$317$	324.328			1.02312			0.511558	−	0.859249i	$-0.329068\pi$
$317$	324.328			1.02312			0.511558	+	0.859249i	$0.329068\pi$
$318$	−14.6446	+	11.8766i	−0.0460521	+	0.0373477i
$319$		−	77.8792i		−	0.244135i
$320$	20.9331	+	319.315i	0.0654159	+	0.997858i
$321$	7.43887			0.0231741
$322$	−333.711	−	411.487i	−1.03637	−	1.27791i
$323$		−	10.0676i		−	0.0311690i
$324$	−66.5830	+	315.502i	−0.205503	+	0.973771i
$325$	−452.942	−	88.0274i	−1.39367	−	0.270853i
$326$	−443.925	+	360.018i	−1.36173	+	1.10435i
$327$	3.79069	+	3.79069i	0.0115923	+	0.0115923i
$328$	60.0678	+	117.257i	0.183134	+	0.357491i
$329$	−385.496			−1.17172
$330$	2.33530	+	3.52257i	0.00707667	+	0.0106744i
$331$	248.635	−	248.635i	0.751162	−	0.751162i	−0.223534	−	0.974696i	$-0.571759\pi$
$331$	248.635	−	248.635i	0.751162	−	0.751162i	0.974696	+	0.223534i	$0.0717594\pi$
$332$	469.862	+	99.1589i	1.41525	+	0.298671i
$333$			261.761i			0.786069i
$334$	30.1181	−	288.571i	0.0901739	−	0.863985i
$335$	227.336	−	187.407i	0.678614	−	0.559425i
$336$	−11.9800	+	4.63869i	−0.0356548	+	0.0138056i
$337$	−82.9415	+	82.9415i	−0.246117	+	0.246117i	−0.819375	−	0.573258i	$-0.805679\pi$
$337$	−82.9415	+	82.9415i	−0.246117	+	0.246117i	0.573258	+	0.819375i	$0.305679\pi$
$338$	−216.237	−	266.634i	−0.639755	−	0.788859i
$339$	−6.72250	+	6.72250i	−0.0198304	+	0.0198304i
$340$	−289.214	−	90.7218i	−0.850630	−	0.266829i
$341$	122.914	−	122.914i	0.360451	−	0.360451i
$342$	11.8736	+	1.23924i	0.0347181	+	0.00362352i
$343$	251.537	−	251.537i	0.733345	−	0.733345i
$344$	31.9675	−	16.3761i	0.0929288	−	0.0476050i
$345$	−23.5604	−	2.26821i	−0.0682909	−	0.00657452i
$346$	106.104	−	86.0493i	0.306660	−	0.248697i
$347$		−	288.892i		−	0.832540i	−0.909241	−	0.416270i	$-0.863337\pi$
$347$		−	288.892i		−	0.832540i	0.909241	−	0.416270i	$-0.136663\pi$
$348$	8.86144	−	5.77301i	0.0254639	−	0.0165891i
$349$	−345.135	+	345.135i	−0.988927	+	0.988927i	−0.999939	−	0.0110128i	$-0.996494\pi$
$349$	−345.135	+	345.135i	−0.988927	+	0.988927i	0.0110128	+	0.999939i	$0.496494\pi$
$350$	320.579	+	97.7445i	0.915939	+	0.279270i
$351$	−39.7634			−0.113286
$352$	−97.9828	−	56.0968i	−0.278360	−	0.159366i
$353$	242.242	+	242.242i	0.686239	+	0.686239i	0.961399	−	0.275159i	$-0.0887306\pi$
$353$	242.242	+	242.242i	0.686239	+	0.686239i	−0.275159	+	0.961399i	$0.588731\pi$
$354$	1.10050	+	0.114859i	0.00310876	+	0.000324460i
$355$	−244.278	−	296.322i	−0.688106	−	0.834711i
$356$	72.4582	−	343.342i	0.203534	−	0.964443i
$357$		−	12.1686i		−	0.0340858i
$358$	−466.680	−	48.7072i	−1.30357	−	0.136054i
$359$	−221.083			−0.615831			−0.307916	−	0.951414i	$-0.599631\pi$
$359$	−221.083			−0.615831			−0.307916	+	0.951414i	$0.599631\pi$
$360$	142.597	−	329.929i	0.396101	−	0.916470i
$361$			360.559i			0.998778i
$362$	285.907	+	29.8401i	0.789799	+	0.0824311i
$363$	13.0029			0.0358206
$364$	270.122	+	414.631i	0.742093	+	1.13910i
$365$	−12.7034	+	131.953i	−0.0348038	+	0.361514i
$366$	−7.76365	−	0.810290i	−0.0212122	−	0.00221391i
$367$	−71.5971	+	71.5971i	−0.195087	+	0.195087i	−0.797890	−	0.602803i	$-0.794051\pi$
$367$	−71.5971	+	71.5971i	−0.195087	+	0.195087i	0.602803	+	0.797890i	$0.294051\pi$
$368$	589.652	−	228.315i	1.60232	−	0.620421i
$369$		−	147.980i		−	0.401028i
$370$	57.8657	−	285.505i	0.156394	−	0.771635i
$371$	−373.034	−	373.034i	−1.00548	−	1.00548i
$372$	23.0970	+	4.87435i	0.0620887	+	0.0131031i
$373$	−174.847			−0.468758			−0.234379	−	0.972145i	$-0.575306\pi$
$373$	−174.847			−0.468758			−0.234379	+	0.972145i	$0.575306\pi$
$374$	83.0632	−	67.3632i	0.222094	−	0.180116i
$375$	13.1583	−	7.14524i	0.0350889	−	0.0190540i
$376$	141.221	−	437.880i	0.375589	−	1.16458i
$377$	−288.070	−	288.070i	−0.764110	−	0.764110i
$378$	28.7260	+	2.99813i	0.0759948	+	0.00793155i
$379$	−329.561	−	329.561i	−0.869553	−	0.869553i	0.122870	−	0.992423i	$-0.460790\pi$
$379$	−329.561	−	329.561i	−0.869553	−	0.869553i	−0.992423	+	0.122870i	$0.960790\pi$
$380$	−12.6767	−	3.97647i	−0.0333597	−	0.0104644i
$381$	7.20438	+	7.20438i	0.0189091	+	0.0189091i
$382$	−181.978	−	224.391i	−0.476383	−	0.587411i
$383$	−1.40406	−	1.40406i	−0.00366594	−	0.00366594i	0.705271	−	0.708937i	$-0.250825\pi$
$383$	−1.40406	−	1.40406i	−0.00366594	−	0.00366594i	−0.708937	+	0.705271i	$0.750825\pi$
$384$	−0.880310	−	15.3073i	−0.00229247	−	0.0398626i
$385$	−91.2431	+	75.2175i	−0.236995	+	0.195370i
$386$	9.62363	−	92.2072i	0.0249317	−	0.238879i
$387$	−40.3433			−0.104246
$388$	106.974	+	164.203i	0.275707	+	0.423204i
$389$	276.184	+	276.184i	0.709984	+	0.709984i	0.966532	−	0.256548i	$-0.0825851\pi$
$389$	276.184	+	276.184i	0.709984	+	0.709984i	−0.256548	+	0.966532i	$0.582585\pi$
$390$	21.6678	+	4.39160i	0.0555586	+	0.0112605i
$391$			598.936i			1.53181i
$392$	14.8455	+	28.9796i	0.0378711	+	0.0739274i
$393$	15.5573	−	15.5573i	0.0395860	−	0.0395860i
$394$	520.701	−	422.282i	1.32157	−	1.07178i
$395$	450.660	+	546.676i	1.14091	+	1.38399i
$396$	69.2230	+	106.256i	0.174806	+	0.268323i
$397$	−692.870			−1.74526			−0.872632	−	0.488378i	$-0.837589\pi$
$397$	−692.870			−1.74526			−0.872632	+	0.488378i	$0.837589\pi$
$398$	−232.723	−	286.962i	−0.584730	−	0.721010i
$399$		−	0.533369i		−	0.00133676i
$400$	−228.466	+	328.334i	−0.571166	+	0.820835i
$401$	755.828			1.88486			0.942429	−	0.334407i	$-0.108536\pi$
$401$	755.828			1.88486			0.942429	+	0.334407i	$0.108536\pi$
$402$	−10.9642	+	8.89187i	−0.0272742	+	0.0221191i
$403$		−	909.298i		−	2.25632i
$404$	−91.3096	−	140.158i	−0.226014	−	0.346926i
$405$	−311.010	+	256.385i	−0.767925	+	0.633050i
$406$	186.388	+	229.829i	0.459084	+	0.566080i
$407$	72.6780	+	72.6780i	0.178570	+	0.178570i
$408$	13.8222	+	4.45781i	0.0338779	+	0.0109260i
$409$	−43.3293			−0.105940			−0.0529698	−	0.998596i	$-0.516869\pi$
$409$	−43.3293			−0.105940			−0.0529698	+	0.998596i	$0.516869\pi$
$410$	−32.7128	+	161.402i	−0.0797873	+	0.393665i
$411$	8.36423	−	8.36423i	0.0203509	−	0.0203509i
$412$	149.916	+	230.117i	0.363873	+	0.558537i
$413$			30.9582i			0.0749594i
$414$	−706.379	−	73.7246i	−1.70623	−	0.178079i
$415$	381.823	+	463.172i	0.920055	+	1.11608i
$416$	−569.929	+	154.933i	−1.37002	+	0.372436i
$417$	−2.01684	+	2.01684i	−0.00483655	+	0.00483655i
$418$	3.64078	−	2.95263i	0.00871000	−	0.00706370i
$419$	−345.453	+	345.453i	−0.824471	+	0.824471i	−0.986746	−	0.162274i	$-0.948117\pi$
$419$	−345.453	+	345.453i	−0.824471	+	0.824471i	0.162274	+	0.986746i	$0.448117\pi$
$420$	−15.3222	−	4.80634i	−0.0364815	−	0.0114437i
$421$	−371.173	+	371.173i	−0.881645	+	0.881645i	−0.993702	−	0.112056i	$-0.964256\pi$
$421$	−371.173	+	371.173i	−0.881645	+	0.881645i	0.112056	+	0.993702i	$0.464256\pi$
$422$	−55.1978	+	528.868i	−0.130800	+	1.25324i
$423$	−365.416	+	365.416i	−0.863867	+	0.863867i
$424$	560.380	−	287.068i	1.32165	−	0.677048i
$425$	−211.881	−	314.104i	−0.498544	−	0.739069i
$426$	11.5902	+	14.2914i	0.0272070	+	0.0335480i
$427$		−	218.400i		−	0.511475i
$428$	−243.053	−	51.2935i	−0.567881	−	0.119845i
$429$	−5.51575	+	5.51575i	−0.0128572	+	0.0128572i
$430$	44.0027	+	8.91841i	0.102332	+	0.0207405i
$431$	−150.726			−0.349712			−0.174856	−	0.984594i	$-0.555946\pi$
$431$	−150.726			−0.349712			−0.174856	+	0.984594i	$0.555946\pi$
$432$	−13.9289	+	31.5312i	−0.0322429	+	0.0729889i
$433$	249.306	+	249.306i	0.575765	+	0.575765i	0.933734	−	0.357969i	$-0.116531\pi$
$433$	249.306	+	249.306i	0.575765	+	0.575765i	−0.357969	+	0.933734i	$0.616531\pi$
$434$	−68.5603	+	656.899i	−0.157973	+	1.51359i
$435$	13.1592	+	1.26687i	0.0302511	+	0.00291234i
$436$	−97.7165	−	149.993i	−0.224121	−	0.344020i
$437$			26.2522i			0.0600738i
$438$	0.659337	−	6.31732i	0.00150534	−	0.0144231i
$439$	106.380			0.242324			0.121162	−	0.992633i	$-0.461338\pi$
$439$	106.380			0.242324			0.121162	+	0.992633i	$0.461338\pi$
$440$	−52.0129	−	131.197i	−0.118211	−	0.298174i
$441$		−	36.5725i		−	0.0829307i
$442$	58.0730	−	556.416i	0.131387	−	1.25886i
$443$	235.281			0.531108			0.265554	−	0.964096i	$-0.414445\pi$
$443$	235.281			0.531108			0.265554	+	0.964096i	$0.414445\pi$
$444$	−2.88217	+	13.6571i	−0.00649137	+	0.0307592i
$445$	338.453	−	279.009i	0.760569	−	0.626986i
$446$	−82.8917	+	794.213i	−0.185856	+	1.78075i
$447$	15.0988	−	15.0988i	0.0337780	−	0.0337780i
$448$	423.412	−	68.9554i	0.945117	−	0.153918i
$449$			78.1899i			0.174142i	0.996202	+	0.0870712i	$0.0277508\pi$
$449$			78.1899i			0.174142i	−0.996202	+	0.0870712i	$0.972249\pi$
$450$	396.533	−	211.227i	0.881184	−	0.469393i
$451$	−41.0865	−	41.0865i	−0.0911009	−	0.0911009i
$452$	266.000	−	173.293i	0.588496	−	0.383391i
$453$	−20.3635			−0.0449526
$454$	185.025	+	228.148i	0.407545	+	0.502529i
$455$	−59.2774	+	615.726i	−0.130280	+	1.35324i
$456$	0.605847	+	0.195392i	0.00132861	+	0.000428492i
$457$	401.924	+	401.924i	0.879483	+	0.879483i	0.993481	−	0.113998i	$-0.0363659\pi$
$457$	401.924	+	401.924i	0.879483	+	0.879483i	−0.113998	+	0.993481i	$0.536366\pi$
$458$	−57.1644	+	547.711i	−0.124813	+	1.19588i
$459$	−23.0879	−	23.0879i	−0.0503005	−	0.0503005i
$460$	754.156	+	236.566i	1.63947	+	0.514275i
$461$	158.945	+	158.945i	0.344783	+	0.344783i	0.858162	−	0.513379i	$-0.171606\pi$
$461$	158.945	+	158.945i	0.344783	+	0.344783i	−0.513379	+	0.858162i	$0.671606\pi$
$462$	4.40059	−	3.56883i	0.00952509	−	0.00772473i
$463$	−200.675	−	200.675i	−0.433422	−	0.433422i	0.456369	−	0.889791i	$-0.349150\pi$
$463$	−200.675	−	200.675i	−0.433422	−	0.433422i	−0.889791	+	0.456369i	$0.849150\pi$
$464$	−329.340	+	127.521i	−0.709784	+	0.274830i
$465$	18.7692	+	22.7681i	0.0403640	+	0.0489638i
$466$	−244.805	−	25.5502i	−0.525333	−	0.0548288i
$467$	−188.298			−0.403208			−0.201604	−	0.979467i	$-0.564615\pi$
$467$	−188.298			−0.403208			−0.201604	+	0.979467i	$0.564615\pi$
$468$	649.084	+	136.981i	1.38693	+	0.292695i
$469$	−279.287	−	279.287i	−0.595494	−	0.595494i
$470$	479.342	−	317.782i	1.01988	−	0.676132i
$471$		−	1.45963i		−	0.00309900i
$472$	−35.1650	−	11.3411i	−0.0745022	−	0.0240278i
$473$	−11.2013	+	11.2013i	−0.0236814	+	0.0236814i
$474$	−21.3823	−	26.3658i	−0.0451104	−	0.0556241i
$475$	−9.28707	−	13.7677i	−0.0195517	−	0.0289845i
$476$	−83.9067	+	397.590i	−0.176274	+	0.835273i
$477$	−707.204			−1.48261
$478$	520.127	−	421.817i	1.08813	−	0.882462i
$479$		−	175.422i		−	0.366225i	−0.983092	−	0.183112i	$-0.941383\pi$
$479$		−	175.422i		−	0.366225i	0.983092	−	0.183112i	$-0.0586172\pi$
$480$	11.0726	−	15.6436i	0.0230678	−	0.0325908i
$481$	537.661			1.11780
$482$	−477.296	−	588.537i	−0.990241	−	1.22103i
$483$			31.7309i			0.0656955i
$484$	−424.847	−	89.6590i	−0.877784	−	0.185246i
$485$	−23.4752	+	243.842i	−0.0484025	+	0.502766i
$486$	45.1194	−	36.5913i	0.0928383	−	0.0752908i
$487$	−53.3922	−	53.3922i	−0.109635	−	0.109635i	0.650161	−	0.759796i	$-0.274701\pi$
$487$	−53.3922	−	53.3922i	−0.109635	−	0.109635i	−0.759796	+	0.650161i	$0.774701\pi$
$488$	248.077	+	80.0078i	0.508355	+	0.163950i
$489$	34.2324			0.0700048
$490$	−8.08482	+	39.8899i	−0.0164996	+	0.0814079i
$491$	96.7903	−	96.7903i	0.197129	−	0.197129i	−0.601639	−	0.798768i	$-0.705485\pi$
$491$	96.7903	−	96.7903i	0.197129	−	0.197129i	0.798768	+	0.601639i	$0.205485\pi$
$492$	1.62935	−	7.72066i	0.00331170	−	0.0156924i
$493$		−	334.525i		−	0.678550i
$494$	2.54542	−	24.3885i	0.00515268	−	0.0493695i
$495$	−15.1908	+	157.790i	−0.0306884	+	0.318767i
$496$	−721.046	−	318.523i	−1.45372	−	0.642183i
$497$	−364.038	+	364.038i	−0.732472	+	0.732472i
$498$	−18.1162	−	22.3385i	−0.0363780	−	0.0448564i
$499$	139.686	−	139.686i	0.279931	−	0.279931i	−0.553150	−	0.833081i	$-0.686574\pi$
$499$	139.686	−	139.686i	0.279931	−	0.279931i	0.833081	+	0.553150i	$0.186574\pi$
$500$	−479.196	+	142.728i	−0.958392	+	0.285456i
$501$	−12.2875	+	12.2875i	−0.0245260	+	0.0245260i
$502$	−511.815	−	53.4180i	−1.01955	−	0.106410i
$503$	319.688	−	319.688i	0.635562	−	0.635562i	−0.313895	−	0.949458i	$-0.601634\pi$
$503$	319.688	−	319.688i	0.635562	−	0.635562i	0.949458	+	0.313895i	$0.101634\pi$
$504$	−458.585	−	147.899i	−0.909891	−	0.293450i
$505$	20.0376	−	208.134i	0.0396784	−	0.412147i
$506$	−216.596	+	175.657i	−0.428055	+	0.347147i
$507$			20.5610i			0.0405542i
$508$	−185.715	−	285.068i	−0.365580	−	0.561157i
$509$	702.440	−	702.440i	1.38004	−	1.38004i	0.535510	−	0.844529i	$-0.320119\pi$
$509$	702.440	−	702.440i	1.38004	−	1.38004i	0.844529	−	0.535510i	$-0.179881\pi$
$510$	10.0311	+	15.1310i	0.0196689	+	0.0296686i
$511$	177.713			0.347775
$512$	−76.7858	+	506.209i	−0.149972	+	0.988690i
$513$	−1.01198	−	1.01198i	−0.00197267	−	0.00197267i
$514$	107.611	+	11.2313i	0.209359	+	0.0218508i
$515$	−32.8985	+	341.723i	−0.0638806	+	0.663541i
$516$	−2.10486	−	0.444206i	−0.00407919	−	0.000860865i
$517$			202.915i			0.392486i
$518$	−388.419	−	40.5392i	−0.749844	−	0.0782610i
$519$	−8.18202			−0.0157650
$520$	−677.679	−	292.895i	−1.30323	−	0.563260i
$521$		−	614.419i		−	1.17931i	−0.807656	−	0.589654i	$-0.799264\pi$
$521$		−	614.419i		−	1.17931i	0.807656	−	0.589654i	$-0.200736\pi$
$522$	394.536	+	41.1776i	0.755815	+	0.0788842i
$523$	−178.970			−0.342199			−0.171100	−	0.985254i	$-0.554732\pi$
$523$	−178.970			−0.342199			−0.171100	+	0.985254i	$0.554732\pi$
$524$	−615.582	+	401.037i	−1.17477	+	0.765337i
$525$	−11.2252	−	16.6409i	−0.0213814	−	0.0316969i
$526$	−466.875	−	48.7276i	−0.887595	−	0.0926380i
$527$	527.968	−	527.968i	1.00184	−	1.00184i
$528$	2.44168	+	6.30596i	0.00462440	+	0.0119431i
$529$		−	1032.79i		−	1.95234i
$530$	771.354	+	156.337i	1.45538	+	0.294975i
$531$	29.3456	+	29.3456i	0.0552648	+	0.0552648i
$532$	−3.67775	+	17.4269i	−0.00691307	+	0.0327574i
$533$	−303.952			−0.570266
$534$	−16.3234	+	13.2381i	−0.0305681	+	0.0247904i
$535$	−197.511	−	239.592i	−0.369180	−	0.447836i
$536$	419.551	−	214.925i	0.782745	−	0.400980i
$537$	19.8715	+	19.8715i	0.0370047	+	0.0370047i
$538$	872.903	+	91.1046i	1.62250	+	0.169339i
$539$	−10.1543	−	10.1543i	−0.0188392	−	0.0188392i
$540$	−38.1906	+	19.9522i	−0.0707233	+	0.0369485i
$541$	216.557	+	216.557i	0.400291	+	0.400291i	0.878336	−	0.478045i	$-0.158654\pi$
$541$	216.557	+	216.557i	0.400291	+	0.400291i	−0.478045	+	0.878336i	$0.658654\pi$
$542$	−343.269	−	423.273i	−0.633338	−	0.780947i
$543$	−12.1741	−	12.1741i	−0.0224201	−	0.0224201i
$544$	−420.879	−	240.960i	−0.773675	−	0.442941i
$545$	21.4436	−	222.739i	0.0393460	−	0.408695i
$546$	3.07664	−	29.4783i	0.00563487	−	0.0539896i
$547$	204.888			0.374567			0.187284	−	0.982306i	$-0.440032\pi$
$547$	204.888			0.374567			0.187284	+	0.982306i	$0.440032\pi$
$548$	−330.962	+	215.613i	−0.603945	+	0.393455i
$549$	−207.023	−	207.023i	−0.377091	−	0.377091i
$550$	51.4502	−	168.744i	0.0935457	−	0.306808i
$551$		−	14.6627i		−	0.0266111i
$552$	−36.0428	−	11.6242i	−0.0652949	−	0.0210583i
$553$	671.603	−	671.603i	1.21447	−	1.21447i
$554$	−222.401	+	180.364i	−0.401445	+	0.325567i
$555$	−13.4626	+	11.0981i	−0.0242570	+	0.0199966i
$556$	79.8038	−	51.9902i	0.143532	−	0.0935076i
$557$	345.777			0.620784			0.310392	−	0.950609i	$-0.399540\pi$
$557$	345.777			0.620784			0.310392	+	0.950609i	$0.399540\pi$
$558$	557.691	+	687.669i	0.999447	+	1.23238i
$559$			82.8656i			0.148239i
$560$	467.488	+	262.691i	0.834800	+	0.469091i
$561$	−6.40525			−0.0114176
$562$	−216.553	+	175.622i	−0.385326	+	0.312495i
$563$		−	319.750i		−	0.567940i	−0.958833	−	0.283970i	$-0.908348\pi$
$563$		−	319.750i		−	0.567940i	0.958833	−	0.283970i	$-0.0916516\pi$
$564$	−23.0886	+	15.0417i	−0.0409373	+	0.0266696i
$565$	395.010	+	38.0285i	0.699133	+	0.0673071i
$566$	−423.639	−	522.374i	−0.748479	−	0.922923i
$567$	382.082	+	382.082i	0.673866	+	0.673866i
$568$	−280.146	−	546.867i	−0.493214	−	0.962794i
$569$	−146.472			−0.257420			−0.128710	−	0.991682i	$-0.541084\pi$
$569$	−146.472			−0.257420			−0.128710	+	0.991682i	$0.541084\pi$
$570$	0.439680	+	0.663212i	0.000771368	+	0.00116353i
$571$	−221.670	+	221.670i	−0.388214	+	0.388214i	−0.874050	−	0.485836i	$-0.838515\pi$
$571$	−221.670	+	221.670i	−0.388214	+	0.388214i	0.485836	+	0.874050i	$0.338515\pi$
$572$	218.251	−	142.185i	0.381558	−	0.248575i
$573$			17.3034i			0.0301980i
$574$	219.582	+	22.9177i	0.382547	+	0.0399263i
$575$	552.502	+	819.060i	0.960873	+	1.42445i
$576$	335.993	−	466.720i	0.583321	−	0.810278i
$577$	−293.131	+	293.131i	−0.508026	+	0.508026i	−0.913920	−	0.405894i	$-0.866960\pi$
$577$	−293.131	+	293.131i	−0.508026	+	0.508026i	0.405894	+	0.913920i	$0.366960\pi$
$578$	−92.1332	+	74.7189i	−0.159400	+	0.129272i
$579$	−3.92624	+	3.92624i	−0.00678107	+	0.00678107i
$580$	−421.221	−	132.130i	−0.726242	−	0.227810i
$581$	569.017	−	569.017i	0.979375	−	0.979375i
$582$	1.21842	−	11.6741i	0.00209351	−	0.0200586i
$583$	−196.355	+	196.355i	−0.336801	+	0.336801i
$584$	−65.1028	+	201.862i	−0.111477	+	0.345654i
$585$	527.463	+	639.842i	0.901646	+	1.09375i
$586$	−41.7229	−	51.4470i	−0.0711995	−	0.0877936i
$587$		−	176.460i		−	0.300614i	−0.988639	−	0.150307i	$-0.951974\pi$
$587$		−	176.460i		−	0.300614i	0.988639	−	0.150307i	$-0.0480262\pi$
$588$	0.402687	−	1.90813i	0.000684842	−	0.00324511i
$589$	23.1416	−	23.1416i	0.0392897	−	0.0392897i
$590$	−25.5203	−	38.4947i	−0.0432547	−	0.0652453i
$591$	−40.1528			−0.0679404
$592$	188.340	−	426.349i	0.318142	−	0.720185i
$593$	−311.192	−	311.192i	−0.524776	−	0.524776i	0.394234	−	0.919010i	$-0.371010\pi$
$593$	−311.192	−	311.192i	−0.524776	−	0.524776i	−0.919010	+	0.394234i	$0.871010\pi$
$594$	1.57814	−	15.1206i	0.00265679	−	0.0254556i
$595$	−391.929	+	323.092i	−0.658704	+	0.543012i
$596$	−597.439	+	389.217i	−1.00241	+	0.653048i
$597$			22.1285i			0.0370661i
$598$	−151.431	+	1450.91i	−0.253230	+	2.42628i
$599$	−550.344			−0.918771			−0.459386	−	0.888237i	$-0.651930\pi$
$599$	−550.344			−0.918771			−0.459386	+	0.888237i	$0.651930\pi$
$600$	23.0144	−	6.65442i	0.0383573	−	0.0110907i
$601$			440.349i			0.732693i	0.930478	+	0.366347i	$0.119392\pi$
$601$			440.349i			0.732693i	−0.930478	+	0.366347i	$0.880608\pi$
$602$	6.24800	−	59.8641i	0.0103787	−	0.0994420i
$603$	−529.477			−0.878071
$604$	665.345	+	140.413i	1.10156	+	0.232472i
$605$	−345.243	−	418.799i	−0.570649	−	0.692229i
$606$	−1.04000	+	9.96458i	−0.00171617	+	0.0164432i
$607$	−12.8864	+	12.8864i	−0.0212296	+	0.0212296i	−0.717642	−	0.696412i	$-0.754779\pi$
$607$	−12.8864	+	12.8864i	−0.0212296	+	0.0212296i	0.696412	+	0.717642i	$0.254779\pi$
$608$	−18.4477	−	10.5616i	−0.0303417	−	0.0173711i
$609$		−	17.7228i		−	0.0291014i
$610$	180.037	+	271.567i	0.295142	+	0.445192i
$611$	750.569	+	750.569i	1.22843	+	1.22843i
$612$	297.343	+	456.415i	0.485855	+	0.745776i
$613$	228.861			0.373346			0.186673	−	0.982422i	$-0.440229\pi$
$613$	228.861			0.373346			0.186673	+	0.982422i	$0.440229\pi$
$614$	604.239	+	745.065i	0.984102	+	1.21346i
$615$	7.61073	−	6.27402i	0.0123752	−	0.0102017i
$616$	−168.390	+	86.2620i	−0.273361	+	0.140036i
$617$	−236.901	−	236.901i	−0.383957	−	0.383957i	0.488569	−	0.872525i	$-0.337519\pi$
$617$	−236.901	−	236.901i	−0.383957	−	0.383957i	−0.872525	+	0.488569i	$0.837519\pi$
$618$	1.70751	−	16.3602i	0.00276297	−	0.0264729i
$619$	204.389	+	204.389i	0.330192	+	0.330192i	0.852659	−	0.522468i	$-0.174988\pi$
$619$	204.389	+	204.389i	0.330192	+	0.330192i	−0.522468	+	0.852659i	$0.674988\pi$
$620$	−456.260	−	873.332i	−0.735904	−	1.40860i
$621$	60.2042	+	60.2042i	0.0969471	+	0.0969471i
$622$	509.575	−	413.259i	0.819252	−	0.664403i
$623$	−415.797	−	415.797i	−0.667411	−	0.667411i
$624$	32.3569	+	14.2937i	0.0518541	+	0.0229066i
$625$	−579.505	−	234.091i	−0.927209	−	0.374545i
$626$	253.794	+	26.4884i	0.405421	+	0.0423137i
$627$	−0.280751			−0.000447769
$628$	−10.0646	+	47.6910i	−0.0160265	+	0.0759410i
$629$	312.184	+	312.184i	0.496317	+	0.496317i
$630$	−332.808	−	502.007i	−0.528267	−	0.796837i
$631$			219.606i			0.348029i	0.984743	+	0.174014i	$0.0556739\pi$
$631$			219.606i			0.348029i	−0.984743	+	0.174014i	$0.944326\pi$
$632$	516.832	+	1008.90i	0.817772	+	1.59636i
$633$	22.5195	−	22.5195i	0.0355759	−	0.0355759i
$634$	408.579	+	503.804i	0.644446	+	0.794643i
$635$	40.7545	−	423.325i	0.0641803	−	0.666654i
$636$	−36.8976	−	7.78680i	−0.0580151	−	0.0122434i
$637$	−75.1203			−0.117928
$638$	120.976	−	98.1098i	0.189617	−	0.153777i
$639$			690.151i			1.08005i
$640$	−469.645	+	434.780i	−0.733820	+	0.679344i
$641$	−399.195			−0.622770			−0.311385	−	0.950284i	$-0.600793\pi$
$641$	−399.195			−0.622770			−0.311385	+	0.950284i	$0.600793\pi$
$642$	9.37127	+	11.5554i	0.0145970	+	0.0179990i
$643$			864.637i			1.34469i	0.740237	+	0.672346i	$0.234713\pi$
$643$			864.637i			1.34469i	−0.740237	+	0.672346i	$0.765287\pi$
$644$	218.795	−	1036.76i	0.339744	−	1.60987i
$645$	−1.71047	−	2.07489i	−0.00265189	−	0.00321689i
$646$	15.6387	−	12.6828i	0.0242086	−	0.0196329i
$647$	−569.775	−	569.775i	−0.880641	−	0.880641i	0.112959	−	0.993600i	$-0.463967\pi$
$647$	−569.775	−	569.775i	−0.880641	−	0.880641i	−0.993600	+	0.112959i	$0.963967\pi$
$648$	−573.973	+	294.031i	−0.885760	+	0.453752i
$649$	16.2956			0.0251088
$650$	−433.863	−	814.484i	−0.667481	−	1.25305i
$651$	27.9711	−	27.9711i	0.0429664	−	0.0429664i
$652$	−1118.49	−	236.043i	−1.71547	−	0.362030i
$653$			139.259i			0.213261i	0.994299	+	0.106630i	$0.0340062\pi$
$653$			139.259i			0.213261i	−0.994299	+	0.106630i	$0.965994\pi$
$654$	−1.11297	+	10.6638i	−0.00170180	+	0.0163055i
$655$	−914.138	−	88.0061i	−1.39563	−	0.134361i
$656$	−106.473	+	241.025i	−0.162306	+	0.367416i
$657$	168.456	−	168.456i	0.256402	−	0.256402i
$658$	−485.637	−	598.821i	−0.738050	−	0.910063i
$659$	348.410	−	348.410i	0.528695	−	0.528695i	−0.391488	−	0.920183i	$-0.628040\pi$
$659$	348.410	−	348.410i	0.528695	−	0.528695i	0.920183	+	0.391488i	$0.128040\pi$
$660$	−2.52993	+	8.06523i	−0.00383323	+	0.0122200i
$661$	270.659	−	270.659i	0.409469	−	0.409469i	−0.472084	−	0.881553i	$-0.656498\pi$
$661$	270.659	−	270.659i	0.409469	−	0.409469i	0.881553	+	0.472084i	$0.156498\pi$
$662$	699.446	+	73.0009i	1.05656	+	0.110273i
$663$	−23.6926	+	23.6926i	−0.0357354	+	0.0357354i
$664$	437.887	+	854.791i	0.659469	+	1.28734i
$665$	−17.1788	+	14.1616i	−0.0258328	+	0.0212956i
$666$	−406.614	+	329.759i	−0.610531	+	0.495133i
$667$			872.309i			1.30781i
$668$	486.202	−	316.748i	0.727847	−	0.474174i
$669$	33.8181	−	33.8181i	0.0505502	−	0.0505502i
$670$	577.505	+	117.048i	0.861948	+	0.174698i
$671$	−114.960			−0.171326
$672$	−22.2977	−	12.7658i	−0.0331811	−	0.0189967i
$673$	−29.4792	−	29.4792i	−0.0438027	−	0.0438027i	0.684866	−	0.728669i	$-0.259861\pi$
$673$	−29.4792	−	29.4792i	−0.0438027	−	0.0438027i	−0.728669	+	0.684866i	$0.759861\pi$
$674$	−233.327	−	24.3522i	−0.346182	−	0.0361309i
$675$	−52.8713	−	10.2753i	−0.0783278	−	0.0152227i
$676$	141.775	−	671.796i	0.209726	−	0.993781i
$677$			519.409i			0.767221i	0.923495	+	0.383611i	$0.125319\pi$
$677$			519.409i			0.767221i	−0.923495	+	0.383611i	$0.874681\pi$
$678$	−18.9114	−	1.97377i	−0.0278929	−	0.00291117i
$679$	328.404			0.483659
$680$	−223.418	−	563.547i	−0.328556	−	0.828746i
$681$		−	17.5932i		−	0.0258343i
$682$	345.774	+	36.0883i	0.507000	+	0.0529155i
$683$	254.873			0.373167			0.186583	−	0.982439i	$-0.440259\pi$
$683$	254.873			0.373167			0.186583	+	0.982439i	$0.440259\pi$
$684$	13.0330	+	20.0053i	0.0190541	+	0.0292476i
$685$	−491.477	−	47.3157i	−0.717485	−	0.0690739i
$686$	707.612	+	73.8532i	1.03150	+	0.107658i
$687$	23.3219	−	23.3219i	0.0339474	−	0.0339474i
$688$	65.7100	+	29.0274i	0.0955087	+	0.0421910i
$689$			1452.61i			2.10828i
$690$	−26.1572	−	39.4555i	−0.0379091	−	0.0571820i
$691$	−422.293	−	422.293i	−0.611133	−	0.611133i	0.332108	−	0.943241i	$-0.392240\pi$
$691$	−422.293	−	422.293i	−0.611133	−	0.611133i	−0.943241	+	0.332108i	$0.892240\pi$
$692$	267.334	+	56.4177i	0.386321	+	0.0815285i
$693$	212.510			0.306652
$694$	448.757	−	363.937i	0.646625	−	0.524405i
$695$	118.508	+	11.4091i	0.170516	+	0.0164160i
$696$	20.1310	+	6.49249i	0.0289239	+	0.00932830i
$697$	−176.484	−	176.484i	−0.253206	−	0.253206i
$698$	−970.916	−	101.334i	−1.39100	−	0.145178i
$699$	10.4240	+	10.4240i	0.0149127	+	0.0149127i
$700$	252.021	+	621.115i	0.360031	+	0.887308i
$701$	203.994	+	203.994i	0.291004	+	0.291004i	0.837477	−	0.546473i	$-0.184030\pi$
$701$	203.994	+	203.994i	0.291004	+	0.291004i	−0.546473	+	0.837477i	$0.684030\pi$
$702$	−50.0927	−	61.7676i	−0.0713572	−	0.0879880i
$703$	13.6835	+	13.6835i	0.0194644	+	0.0194644i
$704$	−36.2963	−	222.873i	−0.0515573	−	0.316581i
$705$	−34.2865	−	3.30084i	−0.0486334	−	0.00468205i
$706$	−71.1241	+	681.464i	−0.100742	+	0.965246i
$707$	−280.314			−0.396484
$708$	1.20796	+	1.85419i	0.00170615	+	0.00261891i
$709$	−407.106	−	407.106i	−0.574197	−	0.574197i	0.359101	−	0.933299i	$-0.383083\pi$
$709$	−407.106	−	407.106i	−0.574197	−	0.574197i	−0.933299	+	0.359101i	$0.883083\pi$
$710$	152.567	−	752.753i	0.214883	−	1.06022i
$711$		−	1273.24i		−	1.79077i
$712$	624.620	−	319.977i	0.877275	−	0.449405i
$713$	−1376.73	+	1376.73i	−1.93090	+	1.93090i
$714$	18.9025	−	15.3297i	0.0264740	−	0.0214701i
$715$	324.102	+	31.2021i	0.453290	+	0.0436392i
$716$	−512.248	−	786.289i	−0.715431	−	1.09817i
$717$	−40.1086			−0.0559394
$718$	−278.514	−	343.426i	−0.387903	−	0.478309i
$719$		−	725.464i		−	1.00899i	−0.863415	−	0.504495i	$-0.831679\pi$
$719$		−	725.464i		−	1.00899i	0.863415	−	0.504495i	$-0.168321\pi$
$720$	692.143	−	194.129i	0.961310	−	0.269623i
$721$	460.231			0.638323
$722$	−560.084	+	454.221i	−0.775739	+	0.629115i
$723$			45.3838i			0.0627716i
$724$	313.825	+	481.714i	0.433459	+	0.665350i
$725$	−308.590	−	457.471i	−0.425642	−	0.630995i
$726$	16.3806	+	20.1984i	0.0225628	+	0.0278214i
$727$	442.782	+	442.782i	0.609054	+	0.609054i	0.942699	−	0.333645i	$-0.108279\pi$
$727$	442.782	+	442.782i	0.609054	+	0.609054i	−0.333645	+	0.942699i	$0.608279\pi$
$728$	−303.787	+	941.941i	−0.417289	+	1.29387i
$729$	722.036			0.990447
$730$	−220.976	+	146.497i	−0.302706	+	0.200681i
$731$	−48.1145	+	48.1145i	−0.0658201	+	0.0658201i
$732$	−8.52173	−	13.0807i	−0.0116417	−	0.0178698i
$733$			358.600i			0.489222i	0.969621	+	0.244611i	$0.0786603\pi$
$733$			358.600i			0.489222i	−0.969621	+	0.244611i	$0.921340\pi$
$734$	−201.413	−	21.0214i	−0.274405	−	0.0286395i
$735$	1.88096	−	1.55059i	0.00255913	−	0.00210965i
$736$	1097.49	+	628.328i	1.49115	+	0.853707i
$737$	−147.009	+	147.009i	−0.199470	+	0.199470i
$738$	229.868	−	186.420i	0.311474	−	0.252602i
$739$	−575.294	+	575.294i	−0.778477	+	0.778477i	−0.979572	−	0.201095i	$-0.935550\pi$
$739$	−575.294	+	575.294i	−0.778477	+	0.778477i	0.201095	+	0.979572i	$0.435550\pi$
$740$	516.395	−	269.783i	0.697830	−	0.364572i
$741$	−1.03848	+	1.03848i	−0.00140146	+	0.00140146i
$742$	109.525	−	1049.40i	0.147608	−	1.41428i
$743$	−55.8927	+	55.8927i	−0.0752258	+	0.0752258i	−0.743719	−	0.668493i	$-0.766940\pi$
$743$	−55.8927	+	55.8927i	−0.0752258	+	0.0752258i	0.668493	+	0.743719i	$0.266940\pi$
$744$	21.5252	+	42.0189i	0.0289317	+	0.0564770i
$745$	−887.195	−	85.4124i	−1.19087	−	0.114647i
$746$	−220.266	−	271.603i	−0.295263	−	0.364079i
$747$		−	1078.75i		−	1.44411i
$748$	209.281	+	44.1663i	0.279787	+	0.0590458i
$749$	−294.344	+	294.344i	−0.392983	+	0.392983i
$750$	27.6757	+	11.4385i	0.0369010	+	0.0152513i
$751$	−63.5053			−0.0845610			−0.0422805	−	0.999106i	$-0.513462\pi$
$751$	−63.5053			−0.0845610			−0.0422805	+	0.999106i	$0.513462\pi$
$752$	858.100	−	332.258i	1.14109	−	0.441833i
$753$	21.7934	+	21.7934i	0.0289421	+	0.0289421i
$754$	84.5793	−	810.382i	0.112174	−	1.07478i
$755$	540.677	+	655.872i	0.716129	+	0.868704i
$756$	31.5310	+	48.3993i	0.0417076	+	0.0640202i
$757$		−	495.675i		−	0.654789i	−0.944888	−	0.327395i	$-0.893829\pi$
$757$		−	495.675i		−	0.654789i	0.944888	−	0.327395i	$-0.106171\pi$
$758$	96.7614	−	927.102i	0.127653	−	1.22309i
$759$	16.7023			0.0220057
$760$	−9.79275	−	24.7011i	−0.0128852	−	0.0325015i
$761$		−	228.669i		−	0.300485i	−0.988649	−	0.150243i	$-0.951995\pi$
$761$		−	228.669i		−	0.300485i	0.988649	−	0.150243i	$-0.0480055\pi$
$762$	−2.11526	+	20.2670i	−0.00277593	+	0.0265971i
$763$	−299.983			−0.393163
$764$	119.313	−	565.362i	0.156169	−	0.740002i
$765$	−65.2510	+	677.775i	−0.0852954	+	0.885981i
$766$	0.412241	−	3.94982i	0.000538174	−	0.00515642i
$767$	60.2763	−	60.2763i	0.0785871	−	0.0785871i
$768$	22.6690	−	20.6511i	0.0295169	−	0.0268894i
$769$		−	804.229i		−	1.04581i	−0.852391	−	0.522906i	$-0.824848\pi$
$769$		−	804.229i		−	1.04581i	0.852391	−	0.522906i	$-0.175152\pi$
$770$	−231.786	−	46.9781i	−0.301021	−	0.0610106i
$771$	−4.58213	−	4.58213i	−0.00594310	−	0.00594310i
$772$	155.356	−	101.211i	0.201238	−	0.131102i
$773$	186.546			0.241328			0.120664	−	0.992693i	$-0.461498\pi$
$773$	186.546			0.241328			0.120664	+	0.992693i	$0.461498\pi$
$774$	−50.8232	−	62.6683i	−0.0656631	−	0.0809668i
$775$	234.973	−	1209.05i	0.303191	−	1.56006i
$776$	−120.306	+	373.030i	−0.155034	+	0.480709i
$777$	16.5391	+	16.5391i	0.0212859	+	0.0212859i
$778$	−81.0895	+	776.945i	−0.104228	+	0.998644i
$779$	−7.73557	−	7.73557i	−0.00993013	−	0.00993013i
$780$	20.4747	+	39.1907i	0.0262496	+	0.0502445i
$781$	191.620	+	191.620i	0.245353	+	0.245353i
$782$	−930.374	+	754.522i	−1.18974	+	0.964861i
$783$	−33.6260	−	33.6260i	−0.0429450	−	0.0429450i
$784$	−26.3143	+	59.5682i	−0.0335641	+	0.0759798i
$785$	−47.0120	+	38.7550i	−0.0598878	+	0.0493694i
$786$	43.7650	+	4.56774i	0.0556806	+	0.00581137i
$787$	1134.28			1.44127			0.720635	−	0.693315i	$-0.243850\pi$
$787$	1134.28			1.44127			0.720635	+	0.693315i	$0.243850\pi$
$788$	1311.93	+	276.866i	1.66488	+	0.351353i
$789$	19.8798	+	19.8798i	0.0251962	+	0.0251962i
$790$	−281.466	+	1388.73i	−0.356286	+	1.75789i
$791$		−	531.997i		−	0.672563i
$792$	−77.8502	+	241.387i	−0.0982957	+	0.304782i
$793$	−425.229	+	425.229i	−0.536228	+	0.536228i
$794$	−872.856	−	1076.29i	−1.09932	−	1.35553i
$795$	−29.9840	−	36.3722i	−0.0377157	−	0.0457512i
$796$	152.583	−	723.012i	0.191687	−	0.908306i
$797$	250.905			0.314812			0.157406	−	0.987534i	$-0.449687\pi$
$797$	250.905			0.314812			0.157406	+	0.987534i	$0.449687\pi$
$798$	0.828523	−	0.671922i	0.00103825	−	0.000842007i
$799$			871.610i			1.09088i
$800$	−797.841	+	58.7306i	−0.997302	+	0.0734132i
$801$	−788.276			−0.984114
$802$	952.169	+	1174.09i	1.18724	+	1.46395i
$803$		−	93.5435i		−	0.116493i
$804$	−27.6249	−	5.82990i	−0.0343593	−	0.00725112i
$805$	1022.00	−	842.496i	1.26956	−	1.04658i
$806$	1412.48	−	1145.51i	1.75246	−	1.42122i
$807$	−37.1687	−	37.1687i	−0.0460579	−	0.0460579i
$808$	102.689	−	318.405i	0.127091	−	0.394066i
$809$	1099.77			1.35942			0.679712	−	0.733479i	$-0.262105\pi$
$809$	1099.77			1.35942			0.679712	+	0.733479i	$0.262105\pi$
$810$	−790.064	−	160.129i	−0.975388	−	0.197690i
$811$	−376.722	+	376.722i	−0.464515	+	0.464515i	−0.900132	−	0.435617i	$-0.856530\pi$
$811$	−376.722	+	376.722i	−0.464515	+	0.464515i	0.435617	+	0.900132i	$0.356530\pi$
$812$	−122.204	+	579.062i	−0.150498	+	0.713131i
$813$			32.6399i			0.0401474i
$814$	−21.3388	+	204.454i	−0.0262147	+	0.251172i
$815$	−908.912	−	1102.56i	−1.11523	−	1.35284i
$816$	10.4881	+	27.0869i	0.0128531	+	0.0331947i
$817$	−2.10893	+	2.10893i	−0.00258131	+	0.00258131i
$818$	−54.5849	−	67.3067i	−0.0667298	−	0.0822821i
$819$	786.059	−	786.059i	0.959779	−	0.959779i
$820$	−291.930	+	152.515i	−0.356012	+	0.185993i
$821$	−164.380	+	164.380i	−0.200220	+	0.200220i	−0.800094	−	0.599874i	$-0.795217\pi$
$821$	−164.380	+	164.380i	−0.200220	+	0.200220i	0.599874	+	0.800094i	$0.295217\pi$
$822$	23.5298	+	2.45580i	0.0286251	+	0.00298759i
$823$	794.892	−	794.892i	0.965847	−	0.965847i	−0.0335887	−	0.999436i	$-0.510694\pi$
$823$	794.892	−	794.892i	0.965847	−	0.965847i	0.999436	+	0.0335887i	$0.0106936\pi$
$824$	−168.599	+	522.770i	−0.204611	+	0.634430i
$825$	−8.75933	+	5.90867i	−0.0106174	+	0.00716202i
$826$	−48.0898	+	39.0002i	−0.0582201	+	0.0472158i
$827$			696.994i			0.842798i	0.906875	+	0.421399i	$0.138461\pi$
$827$			696.994i			0.842798i	−0.906875	+	0.421399i	$0.861539\pi$
$828$	−775.353	−	1190.15i	−0.936417	−	1.43738i
$829$	−857.248	+	857.248i	−1.03407	+	1.03407i	−0.0346759	+	0.999399i	$0.511040\pi$
$829$	−857.248	+	857.248i	−1.03407	+	1.03407i	−0.999399	+	0.0346759i	$0.988960\pi$
$830$	−238.473	+	1176.61i	−0.287316	+	1.41760i
$831$	17.1500			0.0206378
$832$	−958.650	−	690.134i	−1.15222	−	0.829489i
$833$	−43.6173	−	43.6173i	−0.0523617	−	0.0523617i
$834$	−5.67368	−	0.592160i	−0.00680297	−	0.000710024i
$835$	722.008	+	69.5094i	0.864681	+	0.0832448i
$836$	9.17309	+	1.93587i	0.0109726	+	0.00231564i
$837$		−	106.141i		−	0.126811i
$838$	−971.811	−	101.428i	−1.15968	−	0.121035i
$839$	428.122			0.510277			0.255139	−	0.966905i	$-0.417879\pi$
$839$	428.122			0.510277			0.255139	+	0.966905i	$0.417879\pi$
$840$	−11.8364	−	29.8561i	−0.0140910	−	0.0355430i
$841$			353.787i			0.420675i
$842$	−1044.16	−	108.979i	−1.24010	−	0.129429i
$843$	16.6991			0.0198091
$844$	−891.068	+	580.509i	−1.05577	+	0.687807i
$845$	662.231	−	545.919i	0.783705	−	0.646058i
$846$	−1027.97	−	107.289i	−1.21509	−	0.126819i
$847$	−514.503	+	514.503i	−0.607441	+	0.607441i
$848$	1151.88	+	508.842i	1.35834	+	0.600049i
$849$			40.2818i			0.0474462i
$850$	221.001	−	724.831i	0.260001	−	0.852742i
$851$	−814.051	−	814.051i	−0.956582	−	0.956582i
$852$	−7.59903	+	36.0078i	−0.00891904	+	0.0422627i
$853$	1569.13			1.83955			0.919773	−	0.392451i	$-0.128373\pi$
$853$	1569.13			1.83955			0.919773	+	0.392451i	$0.128373\pi$
$854$	339.257	−	275.133i	0.397257	−	0.322170i
$855$	−2.86005	+	29.7079i	−0.00334508	+	0.0347461i
$856$	−226.513	−	442.171i	−0.264618	−	0.516555i
$857$	454.985	+	454.985i	0.530904	+	0.530904i	0.920841	−	0.389937i	$-0.127503\pi$
$857$	454.985	+	454.985i	0.530904	+	0.530904i	−0.389937	+	0.920841i	$0.627503\pi$
$858$	−15.5166	−	1.61946i	−0.0180846	−	0.00188749i
$859$	−620.538	−	620.538i	−0.722396	−	0.722396i	0.246697	−	0.969093i	$-0.420655\pi$
$859$	−620.538	−	620.538i	−0.722396	−	0.722396i	−0.969093	+	0.246697i	$0.920655\pi$
$860$	41.5797	+	79.5880i	0.0483484	+	0.0925441i
$861$	−9.34995	−	9.34995i	−0.0108594	−	0.0108594i
$862$	−189.880	−	234.134i	−0.220278	−	0.271617i
$863$	−234.305	−	234.305i	−0.271500	−	0.271500i	0.558204	−	0.829704i	$-0.311491\pi$
$863$	−234.305	−	234.305i	−0.271500	−	0.271500i	−0.829704	+	0.558204i	$0.811491\pi$
$864$	−66.5271	+	18.0852i	−0.0769989	+	0.0209319i
$865$	217.243	+	263.528i	0.251148	+	0.304656i
$866$	−73.1981	+	701.335i	−0.0845243	+	0.809855i
$867$	7.10467			0.00819454
$868$	−1106.78	+	721.041i	−1.27509	+	0.830692i
$869$	−353.514	−	353.514i	−0.406806	−	0.406806i
$870$	14.6097	+	22.0372i	0.0167927	+	0.0253301i
$871$			1087.55i			1.24863i
$872$	109.895	−	340.747i	0.126026	−	0.390765i
$873$	311.297	−	311.297i	0.356584	−	0.356584i
$874$	−40.7796	+	33.0718i	−0.0466586	+	0.0378396i
$875$	−237.929	+	803.380i	−0.271918	+	0.918149i
$876$	10.6438	−	6.93417i	0.0121505	−	0.00791572i
$877$	1505.10			1.71620			0.858098	−	0.513485i	$-0.171646\pi$
$877$	1505.10			1.71620			0.858098	+	0.513485i	$0.171646\pi$
$878$	134.015	+	165.249i	0.152637	+	0.188211i
$879$			3.96723i			0.00451335i
$880$	138.274	−	246.073i	0.157129	−	0.279629i
$881$	−1589.76			−1.80450			−0.902250	−	0.431213i	$-0.858086\pi$
$881$	−1589.76			−1.80450			−0.902250	+	0.431213i	$0.858086\pi$
$882$	56.8108	−	46.0729i	0.0644113	−	0.0522368i
$883$			512.240i			0.580114i	0.957009	+	0.290057i	$0.0936742\pi$
$883$			512.240i			0.580114i	−0.957009	+	0.290057i	$0.906326\pi$
$884$	937.483	−	610.747i	1.06050	−	0.690891i
$885$	−0.265082	+	2.75346i	−0.000299528	+	0.00311126i
$886$	296.400	+	365.480i	0.334537	+	0.412505i
$887$	−495.921	−	495.921i	−0.559099	−	0.559099i	0.369952	−	0.929051i	$-0.379374\pi$
$887$	−495.921	−	495.921i	−0.559099	−	0.559099i	−0.929051	+	0.369952i	$0.879374\pi$
$888$	−24.8455	+	12.7277i	−0.0279791	+	0.0143330i
$889$	−570.132			−0.641318
$890$	859.779	+	174.259i	0.966044	+	0.195796i
$891$	201.118	−	201.118i	0.225722	−	0.225722i
$892$	−1338.14	+	871.763i	−1.50015	+	0.977313i
$893$			38.2039i			0.0427816i
$894$	42.4751	+	4.43311i	0.0475113	+	0.00495874i
$895$	112.411	−	1167.64i	0.125599	−	1.30462i
$896$	640.516	+	570.851i	0.714862	+	0.637111i
$897$	61.7808	−	61.7808i	0.0688749	−	0.0688749i
$898$	−121.458	+	98.5013i	−0.135254	+	0.109690i
$899$	768.949	−	768.949i	0.855338	−	0.855338i
$900$	827.655	+	349.868i	0.919616	+	0.388742i
$901$	−843.432	+	843.432i	−0.936106	+	0.936106i
$902$	12.0633	−	115.582i	0.0133739	−	0.128140i
$903$	−2.54905	+	2.54905i	−0.00282287	+	0.00282287i
$904$	604.288	+	194.890i	0.668460	+	0.215586i
$905$	−68.8678	+	715.344i	−0.0760970	+	0.790435i
$906$	−25.6534	−	31.6322i	−0.0283150	−	0.0349142i
$907$			530.597i			0.585002i	0.956265	+	0.292501i	$0.0944875\pi$
$907$			530.597i			0.585002i	−0.956265	+	0.292501i	$0.905512\pi$
$908$	−121.311	+	574.828i	−0.133602	+	0.633071i
$909$	−265.712	+	265.712i	−0.292313	+	0.292313i
$910$	−1031.13	+	683.593i	−1.13311	+	0.751201i
$911$	964.958			1.05923			0.529615	−	0.848238i	$-0.322337\pi$
$911$	964.958			1.05923			0.529615	+	0.848238i	$0.322337\pi$
$912$	0.459709	+	1.18726i	0.000504067	+	0.00130182i
$913$	−299.516	−	299.516i	−0.328057	−	0.328057i
$914$	−118.008	+	1130.67i	−0.129111	+	1.23706i
$915$	1.87007	−	19.4248i	0.00204379	−	0.0212292i
$916$	−922.815	+	601.192i	−1.00744	+	0.656323i
$917$			1231.15i			1.34259i
$918$	6.77878	−	64.9497i	0.00738430	−	0.0707514i
$919$	0.377866			0.000411171			0.000205586	−	1.00000i	$-0.499935\pi$
$919$	0.377866			0.000411171			0.000205586		1.00000i	$0.499935\pi$
$920$	582.586	+	1469.51i	0.633246	+	1.59729i
$921$		−	57.4542i		−	0.0623824i
$922$	−46.6674	+	447.136i	−0.0506154	+	0.484963i
$923$	1417.58			1.53584
$924$	11.0875	+	2.33988i	0.0119994	+	0.00253234i
$925$	714.899	+	138.938i	0.772864	+	0.150203i
$926$	58.9195	−	564.527i	0.0636280	−	0.609640i
$927$	436.257	−	436.257i	0.470612	−	0.470612i
$928$	−612.981	−	350.942i	−0.660540	−	0.378170i
$929$			170.314i			0.183330i	0.995790	+	0.0916650i	$0.0292189\pi$
$929$			170.314i			0.183330i	−0.995790	+	0.0916650i	$0.970781\pi$
$930$	−11.7226	+	57.8383i	−0.0126049	+	0.0621918i
$931$	−1.91181	−	1.91181i	−0.00205350	−	0.00205350i
$932$	−268.709	−	412.462i	−0.288314	−	0.442556i
$933$	−39.2948			−0.0421166
$934$	−237.212	−	292.498i	−0.253974	−	0.313167i
$935$	170.067	+	206.301i	0.181890	+	0.220643i
$936$	604.912	+	1180.84i	0.646274	+	1.26158i
$937$	−1277.81	−	1277.81i	−1.36372	−	1.36372i	−0.869119	−	0.494603i	$-0.835314\pi$
$937$	−1277.81	−	1277.81i	−1.36372	−	1.36372i	−0.494603	−	0.869119i	$-0.664686\pi$
$938$	82.0006	−	785.675i	0.0874207	−	0.837606i
$939$	−10.8067	−	10.8067i	−0.0115087	−	0.0115087i
$940$	1097.50	+	344.267i	1.16755	+	0.366241i
$941$	−557.710	−	557.710i	−0.592678	−	0.592678i	0.345676	−	0.938354i	$-0.387650\pi$
$941$	−557.710	−	557.710i	−0.592678	−	0.592678i	−0.938354	+	0.345676i	$0.887650\pi$
$942$	2.26735	−	1.83880i	0.00240696	−	0.00195201i
$943$	460.201	+	460.201i	0.488018	+	0.488018i
$944$	−26.6828	−	68.9118i	−0.0282657	−	0.0729998i
$945$	−6.91937	+	71.8729i	−0.00732208	+	0.0760559i
$946$	−31.5109	−	3.28878i	−0.0333096	−	0.00347651i
$947$	−978.575			−1.03334			−0.516671	−	0.856184i	$-0.672829\pi$
$947$	−978.575			−1.03334			−0.516671	+	0.856184i	$0.672829\pi$
$948$	14.0192	−	66.4297i	0.0147882	−	0.0700735i
$949$	−346.011	−	346.011i	−0.364606	−	0.364606i
$950$	9.68680	−	31.7704i	0.0101966	−	0.0334425i
$951$		−	38.8498i		−	0.0408515i
$952$	−723.310	+	370.533i	−0.759779	+	0.389215i
$953$	82.0352	−	82.0352i	0.0860810	−	0.0860810i	−0.662755	−	0.748836i	$-0.730613\pi$
$953$	82.0352	−	82.0352i	0.0860810	−	0.0860810i	0.748836	+	0.662755i	$0.230613\pi$
$954$	−890.915	−	1098.56i	−0.933873	−	1.15153i
$955$	557.312	−	459.428i	0.583573	−	0.481077i
$956$	1310.48	+	276.562i	1.37080	+	0.289290i
$957$	−9.32880			−0.00974796
$958$	272.496	−	220.991i	0.284443	−	0.230679i
$959$			661.919i			0.690217i
$960$	38.2493	−	2.50748i	0.0398430	−	0.00261196i
$961$	1466.20			1.52571
$962$	677.329	+	835.190i	0.704084	+	0.868181i
$963$			558.024i			0.579464i
$964$	312.936	−	1482.84i	0.324623	−	1.53822i
$965$	230.703	+	22.2103i	0.239071	+	0.0230159i
$966$	−49.2901	+	39.9737i	−0.0510250	+	0.0413806i
$967$	241.731	+	241.731i	0.249980	+	0.249980i	0.820962	−	0.570982i	$-0.193438\pi$
$967$	241.731	+	241.731i	0.249980	+	0.249980i	−0.570982	+	0.820962i	$0.693438\pi$
$968$	−395.936	−	772.898i	−0.409025	−	0.798448i
$969$	−1.20595			−0.00124453
$970$	−408.351	+	270.718i	−0.420981	+	0.279091i
$971$	−970.962	+	970.962i	−0.999961	+	0.999961i	−1.00000		3.91262e-5i	$-0.999988\pi$
$971$	−970.962	+	970.962i	−0.999961	+	0.999961i	3.91262e−5		1.00000i	$0.499988\pi$
$972$	113.680	+	23.9909i	0.116955	+	0.0246820i
$973$		−	159.606i		−	0.164035i
$974$	15.6763	−	150.200i	0.0160948	−	0.154210i
$975$	−10.5444	+	54.2559i	−0.0108148	+	0.0556470i
$976$	188.238	+	486.149i	0.192867	+	0.498104i
$977$	1199.24	−	1199.24i	1.22747	−	1.22747i	0.262558	−	0.964916i	$-0.415434\pi$
$977$	1199.24	−	1199.24i	1.22747	−	1.22747i	0.964916	−	0.262558i	$-0.0845662\pi$
$978$	43.1249	+	53.1758i	0.0440950	+	0.0543720i
$979$	−218.865	+	218.865i	−0.223559	+	0.223559i
$980$	−72.1490	+	37.6933i	−0.0736215	+	0.0384625i
$981$	−284.357	+	284.357i	−0.289864	+	0.289864i
$982$	272.285	+	28.4183i	0.277276	+	0.0289392i
$983$	269.570	−	269.570i	0.274232	−	0.274232i	−0.556569	−	0.830801i	$-0.687883\pi$
$983$	269.570	−	269.570i	0.274232	−	0.274232i	0.830801	+	0.556569i	$0.187883\pi$
$984$	14.0457	−	7.19525i	0.0142741	−	0.00731225i
$985$	1066.11	+	1293.25i	1.08234	+	1.31294i
$986$	519.644	−	421.425i	0.527022	−	0.427408i
$987$			46.1769i			0.0467851i
$988$	41.0913	−	26.7700i	0.0415903	−	0.0270951i
$989$	125.463	−	125.463i	0.126859	−	0.126859i
$990$	−264.244	+	175.182i	−0.266913	+	0.176951i
$991$	−514.885			−0.519561			−0.259781	−	0.965668i	$-0.583650\pi$
$991$	−514.885			−0.519561			−0.259781	+	0.965668i	$0.583650\pi$
$992$	−413.566	−	1521.32i	−0.416902	−	1.53359i
$993$	−29.7828	−	29.7828i	−0.0299928	−	0.0299928i
$994$	−1024.09	−	106.884i	−1.03028	−	0.107529i
$995$	712.718	−	587.539i	0.716299	−	0.590491i
$996$	11.8778	−	56.2827i	0.0119255	−	0.0565087i
$997$		−	1154.22i		−	1.15769i	−0.815437	−	0.578845i	$-0.803504\pi$
$997$		−	1154.22i		−	1.15769i	0.815437	−	0.578845i	$-0.196496\pi$
$998$	392.956	+	41.0127i	0.393744	+	0.0410949i
$999$	62.7605			0.0628233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.i.a.13.16	✓	44
4.3	odd	2		320.3.i.a.273.11		44
5.2	odd	4		80.3.t.a.77.5	yes	44
5.3	odd	4		400.3.t.b.157.18		44
5.4	even	2		400.3.i.b.93.7		44
8.3	odd	2		640.3.i.a.33.12		44
8.5	even	2		640.3.i.b.33.11		44
16.3	odd	4		640.3.t.a.353.12		44
16.5	even	4		80.3.t.a.53.5	yes	44
16.11	odd	4		320.3.t.a.113.11		44
16.13	even	4		640.3.t.b.353.11		44
20.7	even	4		320.3.t.a.17.11		44
40.27	even	4		640.3.t.a.417.12		44
40.37	odd	4		640.3.t.b.417.11		44
80.27	even	4		320.3.i.a.177.12		44
80.37	odd	4	inner	80.3.i.a.37.16	yes	44
80.53	odd	4		400.3.i.b.357.7		44
80.67	even	4		640.3.i.a.97.11		44
80.69	even	4		400.3.t.b.293.18		44
80.77	odd	4		640.3.i.b.97.12		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.16	✓	44	1.1	even	1	trivial
80.3.i.a.37.16	yes	44	80.37	odd	4	inner
80.3.t.a.53.5	yes	44	16.5	even	4
80.3.t.a.77.5	yes	44	5.2	odd	4
320.3.i.a.177.12		44	80.27	even	4
320.3.i.a.273.11		44	4.3	odd	2
320.3.t.a.17.11		44	20.7	even	4
320.3.t.a.113.11		44	16.11	odd	4
400.3.i.b.93.7		44	5.4	even	2
400.3.i.b.357.7		44	80.53	odd	4
400.3.t.b.157.18		44	5.3	odd	4
400.3.t.b.293.18		44	80.69	even	4
640.3.i.a.33.12		44	8.3	odd	2
640.3.i.a.97.11		44	80.67	even	4
640.3.i.b.33.11		44	8.5	even	2
640.3.i.b.97.12		44	80.77	odd	4
640.3.t.a.353.12		44	16.3	odd	4
640.3.t.a.417.12		44	40.27	even	4
640.3.t.b.353.11		44	16.13	even	4
640.3.t.b.417.11		44	40.37	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.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25977 + 1.55338i) q^{2} -0.119786i q^{3} +(-0.825960 + 3.91379i) q^{4} +(-3.85807 + 3.18046i) q^{5} +(0.186072 - 0.150902i) q^{6} +(4.73972 + 4.73972i) q^{7} +(-7.12012 + 3.64745i) q^{8} +8.98565 q^{9} +O(q^{10})\)	\(q+(1.25977 + 1.55338i) q^{2} -0.119786i q^{3} +(-0.825960 + 3.91379i) q^{4} +(-3.85807 + 3.18046i) q^{5} +(0.186072 - 0.150902i) q^{6} +(4.73972 + 4.73972i) q^{7} +(-7.12012 + 3.64745i) q^{8} +8.98565 q^{9} +(-9.80073 - 1.98640i) q^{10} +(2.49487 - 2.49487i) q^{11} +(0.468816 + 0.0989381i) q^{12} -18.4567i q^{13} +(-1.39162 + 13.3335i) q^{14} +(0.380972 + 0.462141i) q^{15} +(-14.6356 - 6.46528i) q^{16} +(10.7165 - 10.7165i) q^{17} +(11.3199 + 13.9581i) q^{18} +(0.469722 - 0.469722i) q^{19} +(-9.26104 - 17.7266i) q^{20} +(0.567750 - 0.567750i) q^{21} +(7.01842 + 0.732510i) q^{22} +(-27.9445 + 27.9445i) q^{23} +(0.436912 + 0.852887i) q^{24} +(4.76941 - 24.5408i) q^{25} +(28.6701 - 23.2511i) q^{26} -2.15442i q^{27} +(-22.4651 + 14.6355i) q^{28} +(15.6079 - 15.6079i) q^{29} +(-0.237942 + 1.17399i) q^{30} +49.2667 q^{31} +(-8.39445 - 30.8793i) q^{32} +(-0.298849 - 0.298849i) q^{33} +(30.1472 + 3.14645i) q^{34} +(-33.3606 - 3.21171i) q^{35} +(-7.42179 + 35.1680i) q^{36} +29.1310i q^{37} +(1.32140 + 0.137914i) q^{38} -2.21084 q^{39} +(15.8694 - 36.7173i) q^{40} -16.4684i q^{41} +(1.59716 + 0.166695i) q^{42} -4.48974 q^{43} +(7.70373 + 11.8251i) q^{44} +(-34.6673 + 28.5785i) q^{45} +(-78.6119 - 8.20470i) q^{46} +(-40.6666 + 40.6666i) q^{47} +(-0.774447 + 1.75313i) q^{48} -4.07009i q^{49} +(44.1295 - 23.5071i) q^{50} +(-1.28369 - 1.28369i) q^{51} +(72.2356 + 15.2445i) q^{52} -78.7038 q^{53} +(3.34663 - 2.71407i) q^{54} +(-1.69056 + 17.5602i) q^{55} +(-51.0353 - 16.4595i) q^{56} +(-0.0562658 - 0.0562658i) q^{57} +(43.9073 + 4.58259i) q^{58} +(3.26583 + 3.26583i) q^{59} +(-2.12339 + 1.10934i) q^{60} +(-23.0393 - 23.0393i) q^{61} +(62.0647 + 76.5297i) q^{62} +(42.5895 + 42.5895i) q^{63} +(37.3922 - 51.9406i) q^{64} +(58.7006 + 71.2071i) q^{65} +(0.0877441 - 0.840705i) q^{66} -58.9247 q^{67} +(33.0909 + 50.7938i) q^{68} +(3.34734 + 3.34734i) q^{69} +(-37.0377 - 55.8677i) q^{70} +76.8059i q^{71} +(-63.9789 + 32.7747i) q^{72} +(18.7472 - 18.7472i) q^{73} +(-45.2514 + 36.6984i) q^{74} +(-2.93964 - 0.571306i) q^{75} +(1.45042 + 2.22637i) q^{76} +23.6499 q^{77} +(-2.78515 - 3.43427i) q^{78} -141.697i q^{79} +(77.0276 - 21.6043i) q^{80} +80.6128 q^{81} +(25.5817 - 20.7464i) q^{82} -120.053i q^{83} +(1.75312 + 2.69100i) q^{84} +(-7.26169 + 75.4286i) q^{85} +(-5.65604 - 6.97426i) q^{86} +(-1.86960 - 1.86960i) q^{87} +(-8.66383 + 26.8636i) q^{88} -87.7260 q^{89} +(-88.0659 - 17.8491i) q^{90} +(87.4794 - 87.4794i) q^{91} +(-86.2879 - 132.450i) q^{92} -5.90143i q^{93} +(-114.401 - 11.9400i) q^{94} +(-0.318290 + 3.30615i) q^{95} +(-3.69890 + 1.00553i) q^{96} +(34.6438 - 34.6438i) q^{97} +(6.32239 - 5.12738i) q^{98} +(22.4180 - 22.4180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9	\( 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9} + 6 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{15} + 24 q^{16} - 4 q^{17} + 22 q^{18} + 32 q^{19} + 40 q^{20} - 4 q^{21} + 92 q^{22} + 36 q^{24} - 52 q^{26} + 36 q^{28} - 28 q^{30} - 8 q^{31} - 132 q^{32} - 4 q^{33} - 88 q^{34} + 96 q^{35} - 116 q^{36} - 216 q^{38} + 72 q^{39} + 16 q^{40} + 16 q^{42} + 124 q^{43} - 168 q^{44} - 34 q^{45} + 108 q^{46} - 4 q^{47} + 340 q^{48} + 10 q^{50} - 100 q^{51} + 48 q^{52} - 4 q^{53} + 228 q^{54} - 172 q^{56} + 36 q^{57} + 16 q^{58} + 64 q^{59} + 136 q^{60} - 36 q^{61} - 356 q^{62} - 200 q^{63} - 176 q^{64} - 4 q^{65} + 276 q^{66} - 292 q^{67} - 72 q^{68} - 60 q^{69} - 92 q^{70} + 448 q^{72} + 48 q^{73} + 284 q^{74} + 96 q^{75} + 252 q^{76} + 192 q^{77} + 620 q^{78} + 4 q^{80} + 100 q^{81} - 240 q^{82} + 288 q^{84} + 48 q^{85} + 20 q^{86} + 36 q^{87} - 624 q^{88} - 578 q^{90} + 188 q^{91} - 412 q^{92} - 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 78 q^{98} - 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9 + 6 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^15 + 24 * q^16 - 4 * q^17 + 22 * q^18 + 32 * q^19 + 40 * q^20 - 4 * q^21 + 92 * q^22 + 36 * q^24 - 52 * q^26 + 36 * q^28 - 28 * q^30 - 8 * q^31 - 132 * q^32 - 4 * q^33 - 88 * q^34 + 96 * q^35 - 116 * q^36 - 216 * q^38 + 72 * q^39 + 16 * q^40 + 16 * q^42 + 124 * q^43 - 168 * q^44 - 34 * q^45 + 108 * q^46 - 4 * q^47 + 340 * q^48 + 10 * q^50 - 100 * q^51 + 48 * q^52 - 4 * q^53 + 228 * q^54 - 172 * q^56 + 36 * q^57 + 16 * q^58 + 64 * q^59 + 136 * q^60 - 36 * q^61 - 356 * q^62 - 200 * q^63 - 176 * q^64 - 4 * q^65 + 276 * q^66 - 292 * q^67 - 72 * q^68 - 60 * q^69 - 92 * q^70 + 448 * q^72 + 48 * q^73 + 284 * q^74 + 96 * q^75 + 252 * q^76 + 192 * q^77 + 620 * q^78 + 4 * q^80 + 100 * q^81 - 240 * q^82 + 288 * q^84 + 48 * q^85 + 20 * q^86 + 36 * q^87 - 624 * q^88 - 578 * q^90 + 188 * q^91 - 412 * q^92 - 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 78 * q^98 - 92 * q^99

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