LMFDB - Embedded newform 80.3.i.a.13.14

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			13.14
Character	$\chi$	$=$	80.13
Dual form			80.3.i.a.37.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.634321 + 1.89674i) q^{2} +2.77329i q^{3} +(-3.19527 + 2.40629i) q^{4} +(4.55712 + 2.05735i) q^{5} +(-5.26021 + 1.75915i) q^{6} +(-5.39242 - 5.39242i) q^{7} +(-6.59094 - 4.53426i) q^{8} +1.30888 q^{9} +O(q^{10})$	\(q+(0.634321 + 1.89674i) q^{2} +2.77329i q^{3} +(-3.19527 + 2.40629i) q^{4} +(4.55712 + 2.05735i) q^{5} +(-5.26021 + 1.75915i) q^{6} +(-5.39242 - 5.39242i) q^{7} +(-6.59094 - 4.53426i) q^{8} +1.30888 q^{9} +(-1.01159 + 9.94870i) q^{10} +(2.98007 - 2.98007i) q^{11} +(-6.67333 - 8.86141i) q^{12} +21.2000i q^{13} +(6.80752 - 13.6486i) q^{14} +(-5.70562 + 12.6382i) q^{15} +(4.41955 - 15.3775i) q^{16} +(6.66924 - 6.66924i) q^{17} +(0.830250 + 2.48261i) q^{18} +(14.3102 - 14.3102i) q^{19} +(-19.5118 + 4.39195i) q^{20} +(14.9547 - 14.9547i) q^{21} +(7.54275 + 3.76211i) q^{22} +(2.07267 - 2.07267i) q^{23} +(12.5748 - 18.2786i) q^{24} +(16.5346 + 18.7512i) q^{25} +(-40.2109 + 13.4476i) q^{26} +28.5895i q^{27} +(30.2060 + 4.25454i) q^{28} +(17.5413 - 17.5413i) q^{29} +(-27.5906 - 2.80542i) q^{30} -23.6474 q^{31} +(31.9706 - 1.37153i) q^{32} +(8.26459 + 8.26459i) q^{33} +(16.8803 + 8.41940i) q^{34} +(-13.4798 - 35.6680i) q^{35} +(-4.18223 + 3.14954i) q^{36} -65.3234i q^{37} +(36.2201 + 18.0655i) q^{38} -58.7936 q^{39} +(-20.7072 - 34.2230i) q^{40} -1.18249i q^{41} +(37.8514 + 18.8792i) q^{42} +9.57434 q^{43} +(-2.35123 + 16.6930i) q^{44} +(5.96472 + 2.69282i) q^{45} +(5.24607 + 2.61659i) q^{46} +(-47.2286 + 47.2286i) q^{47} +(42.6462 + 12.2567i) q^{48} +9.15649i q^{49} +(-25.0779 + 43.2562i) q^{50} +(18.4957 + 18.4957i) q^{51} +(-51.0133 - 67.7397i) q^{52} -99.2178 q^{53} +(-54.2269 + 18.1349i) q^{54} +(19.7116 - 7.44949i) q^{55} +(11.0905 + 59.9918i) q^{56} +(39.6863 + 39.6863i) q^{57} +(44.3981 + 22.1445i) q^{58} +(-54.7400 - 54.7400i) q^{59} +(-12.1801 - 54.1119i) q^{60} +(-12.1054 - 12.1054i) q^{61} +(-15.0000 - 44.8531i) q^{62} +(-7.05803 - 7.05803i) q^{63} +(22.8811 + 59.7700i) q^{64} +(-43.6157 + 96.6108i) q^{65} +(-10.4334 + 20.9182i) q^{66} +109.074 q^{67} +(-5.26193 + 37.3582i) q^{68} +(5.74812 + 5.74812i) q^{69} +(59.1025 - 48.1927i) q^{70} -73.1674i q^{71} +(-8.62675 - 5.93479i) q^{72} +(17.0166 - 17.0166i) q^{73} +(123.902 - 41.4360i) q^{74} +(-52.0023 + 45.8553i) q^{75} +(-11.2905 + 80.1595i) q^{76} -32.1396 q^{77} +(-37.2940 - 111.516i) q^{78} -2.15129i q^{79} +(51.7773 - 60.9846i) q^{80} -67.5069 q^{81} +(2.24289 - 0.750081i) q^{82} +76.4850i q^{83} +(-11.7991 + 83.7699i) q^{84} +(44.1134 - 16.6716i) q^{85} +(6.07320 + 18.1601i) q^{86} +(48.6470 + 48.6470i) q^{87} +(-33.1539 + 6.12907i) q^{88} -38.7296 q^{89} +(-1.32404 + 13.0217i) q^{90} +(114.319 - 114.319i) q^{91} +(-1.63531 + 11.6102i) q^{92} -65.5810i q^{93} +(-119.539 - 59.6224i) q^{94} +(94.6543 - 35.7722i) q^{95} +(3.80365 + 88.6636i) q^{96} +(8.53929 - 8.53929i) q^{97} +(-17.3675 + 5.80816i) q^{98} +(3.90055 - 3.90055i) 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 $

$2$	0.634321	+	1.89674i	0.317161	+	0.948372i
$2$	0.634321	+	1.89674i	0.317161	+	0.948372i
$3$			2.77329i			0.924429i	0.886768	+	0.462215i	$0.152945\pi$
$3$			2.77329i			0.924429i	−0.886768	+	0.462215i	$0.847055\pi$
$4$	−3.19527	+	2.40629i	−0.798818	+	0.601572i
$5$	4.55712	+	2.05735i	0.911424	+	0.411470i
$5$	4.55712	+	2.05735i	0.911424	+	0.411470i
$6$	−5.26021	+	1.75915i	−0.876702	+	0.293192i
$7$	−5.39242	−	5.39242i	−0.770346	−	0.770346i	0.207821	−	0.978167i	$-0.433363\pi$
$7$	−5.39242	−	5.39242i	−0.770346	−	0.770346i	−0.978167	+	0.207821i	$0.933363\pi$
$8$	−6.59094	−	4.53426i	−0.823868	−	0.566782i
$9$	1.30888			0.145431
$10$	−1.01159	+	9.94870i	−0.101159	+	0.994870i
$11$	2.98007	−	2.98007i	0.270915	−	0.270915i	−0.558553	−	0.829469i	$-0.688643\pi$
$11$	2.98007	−	2.98007i	0.270915	−	0.270915i	0.829469	+	0.558553i	$0.188643\pi$
$12$	−6.67333	−	8.86141i	−0.556111	−	0.738451i
$13$			21.2000i			1.63077i	0.578921	+	0.815383i	$0.303474\pi$
$13$			21.2000i			1.63077i	−0.578921	+	0.815383i	$0.696526\pi$
$14$	6.80752	−	13.6486i	0.486251	−	0.974898i
$15$	−5.70562	+	12.6382i	−0.380374	+	0.842546i
$16$	4.41955	−	15.3775i	0.276222	−	0.961094i
$17$	6.66924	−	6.66924i	0.392308	−	0.392308i	−0.483201	−	0.875509i	$-0.660526\pi$
$17$	6.66924	−	6.66924i	0.392308	−	0.392308i	0.875509	+	0.483201i	$0.160526\pi$
$18$	0.830250	+	2.48261i	0.0461250	+	0.137923i
$19$	14.3102	−	14.3102i	0.753169	−	0.753169i	−0.221901	−	0.975069i	$-0.571226\pi$
$19$	14.3102	−	14.3102i	0.753169	−	0.753169i	0.975069	+	0.221901i	$0.0712261\pi$
$20$	−19.5118	+	4.39195i	−0.975591	+	0.219598i
$21$	14.9547	−	14.9547i	0.712131	−	0.712131i
$22$	7.54275	+	3.76211i	0.342852	+	0.171005i
$23$	2.07267	−	2.07267i	0.0901163	−	0.0901163i	−0.660612	−	0.750728i	$-0.729703\pi$
$23$	2.07267	−	2.07267i	0.0901163	−	0.0901163i	0.750728	+	0.660612i	$0.229703\pi$
$24$	12.5748	−	18.2786i	0.523950	−	0.761607i
$25$	16.5346	+	18.7512i	0.661386	+	0.750046i
$26$	−40.2109	+	13.4476i	−1.54657	+	0.517215i
$27$			28.5895i			1.05887i
$28$	30.2060	+	4.25454i	1.07879	+	0.151948i
$29$	17.5413	−	17.5413i	0.604872	−	0.604872i	−0.336730	−	0.941601i	$-0.609321\pi$
$29$	17.5413	−	17.5413i	0.604872	−	0.604872i	0.941601	+	0.336730i	$0.109321\pi$
$30$	−27.5906	−	2.80542i	−0.919687	−	0.0935139i
$31$	−23.6474			−0.762819			−0.381410	−	0.924406i	$-0.624561\pi$
$31$	−23.6474			−0.762819			−0.381410	+	0.924406i	$0.624561\pi$
$32$	31.9706	−	1.37153i	0.999081	−	0.0428603i
$33$	8.26459	+	8.26459i	0.250442	+	0.250442i
$34$	16.8803	+	8.41940i	0.496479	+	0.247629i
$35$	−13.4798	−	35.6680i	−0.385138	−	1.01909i
$36$	−4.18223	+	3.14954i	−0.116173	+	0.0874873i
$37$		−	65.3234i		−	1.76550i	−0.469845	−	0.882749i	$-0.655690\pi$
$37$		−	65.3234i		−	1.76550i	0.469845	−	0.882749i	$-0.344310\pi$
$38$	36.2201	+	18.0655i	0.953159	+	0.475409i
$39$	−58.7936			−1.50753
$40$	−20.7072	−	34.2230i	−0.517679	−	0.855575i
$41$		−	1.18249i		−	0.0288413i	−0.999896	−	0.0144207i	$-0.995410\pi$
$41$		−	1.18249i		−	0.0288413i	0.999896	−	0.0144207i	$-0.00459040\pi$
$42$	37.8514	+	18.8792i	0.901224	+	0.449505i
$43$	9.57434			0.222659			0.111330	−	0.993784i	$-0.464489\pi$
$43$	9.57434			0.222659			0.111330	+	0.993784i	$0.464489\pi$
$44$	−2.35123	+	16.6930i	−0.0534370	+	0.379387i
$45$	5.96472	+	2.69282i	0.132549	+	0.0598404i
$46$	5.24607	+	2.61659i	0.114045	+	0.0568824i
$47$	−47.2286	+	47.2286i	−1.00486	+	1.00486i	−0.00487524	+	0.999988i	$0.501552\pi$
$47$	−47.2286	+	47.2286i	−1.00486	+	1.00486i	−0.999988	+	0.00487524i	$0.998448\pi$
$48$	42.6462	+	12.2567i	0.888463	+	0.255347i
$49$			9.15649i			0.186867i
$50$	−25.0779	+	43.2562i	−0.501557	+	0.865125i
$51$	18.4957	+	18.4957i	0.362661	+	0.362661i
$52$	−51.0133	−	67.7397i	−0.981024	−	1.30269i
$53$	−99.2178			−1.87203			−0.936017	−	0.351955i	$-0.885517\pi$
$53$	−99.2178			−1.87203			−0.936017	+	0.351955i	$0.885517\pi$
$54$	−54.2269	+	18.1349i	−1.00420	+	0.335832i
$55$	19.7116	−	7.44949i	0.358392	−	0.135445i
$56$	11.0905	+	59.9918i	0.198045	+	1.07128i
$57$	39.6863	+	39.6863i	0.696251	+	0.696251i
$58$	44.3981	+	22.1445i	0.765485	+	0.381802i
$59$	−54.7400	−	54.7400i	−0.927796	−	0.927796i	0.0697673	−	0.997563i	$-0.477774\pi$
$59$	−54.7400	−	54.7400i	−0.927796	−	0.927796i	−0.997563	+	0.0697673i	$0.977774\pi$
$60$	−12.1801	−	54.1119i	−0.203002	−	0.901864i
$61$	−12.1054	−	12.1054i	−0.198449	−	0.198449i	0.600886	−	0.799335i	$-0.294815\pi$
$61$	−12.1054	−	12.1054i	−0.198449	−	0.198449i	−0.799335	+	0.600886i	$0.794815\pi$
$62$	−15.0000	−	44.8531i	−0.241936	−	0.723436i
$63$	−7.05803	−	7.05803i	−0.112032	−	0.112032i
$64$	22.8811	+	59.7700i	0.357517	+	0.933907i
$65$	−43.6157	+	96.6108i	−0.671011	+	1.48632i
$66$	−10.4334	+	20.9182i	−0.158082	+	0.316942i
$67$	109.074			1.62798			0.813988	−	0.580882i	$-0.197292\pi$
$67$	109.074			1.62798			0.813988	+	0.580882i	$0.197292\pi$
$68$	−5.26193	+	37.3582i	−0.0773813	+	0.549385i
$69$	5.74812	+	5.74812i	0.0833061	+	0.0833061i
$70$	59.1025	−	48.1927i	0.844322	−	0.688468i
$71$		−	73.1674i		−	1.03053i	−0.857032	−	0.515263i	$-0.827694\pi$
$71$		−	73.1674i		−	1.03053i	0.857032	−	0.515263i	$-0.172306\pi$
$72$	−8.62675	−	5.93479i	−0.119816	−	0.0824277i
$73$	17.0166	−	17.0166i	0.233103	−	0.233103i	−0.580883	−	0.813987i	$-0.697293\pi$
$73$	17.0166	−	17.0166i	0.233103	−	0.233103i	0.813987	+	0.580883i	$0.197293\pi$
$74$	123.902	−	41.4360i	1.67435	−	0.559946i
$75$	−52.0023	+	45.8553i	−0.693364	+	0.611404i
$76$	−11.2905	+	80.1595i	−0.148560	+	1.05473i
$77$	−32.1396			−0.417397
$78$	−37.2940	−	111.516i	−0.478129	−	1.42970i
$79$		−	2.15129i		−	0.0272315i	−0.999907	−	0.0136157i	$-0.995666\pi$
$79$		−	2.15129i		−	0.0272315i	0.999907	−	0.0136157i	$-0.00433416\pi$
$80$	51.7773	−	60.9846i	0.647216	−	0.762307i
$81$	−67.5069			−0.833419
$82$	2.24289	−	0.750081i	0.0273523	−	0.00914732i
$83$			76.4850i			0.921506i	0.887528	+	0.460753i	$0.152421\pi$
$83$			76.4850i			0.921506i	−0.887528	+	0.460753i	$0.847579\pi$
$84$	−11.7991	+	83.7699i	−0.140465	+	0.997261i
$85$	44.1134	−	16.6716i	0.518982	−	0.196136i
$86$	6.07320	+	18.1601i	0.0706187	+	0.211164i
$87$	48.6470	+	48.6470i	0.559161	+	0.559161i
$88$	−33.1539	+	6.12907i	−0.376748	+	0.0696485i
$89$	−38.7296			−0.435164			−0.217582	−	0.976042i	$-0.569817\pi$
$89$	−38.7296			−0.435164			−0.217582	+	0.976042i	$0.569817\pi$
$90$	−1.32404	+	13.0217i	−0.0147116	+	0.144685i
$91$	114.319	−	114.319i	1.25626	−	1.25626i
$92$	−1.63531	+	11.6102i	−0.0177751	+	0.126198i
$93$		−	65.5810i		−	0.705172i
$94$	−119.539	−	59.6224i	−1.27169	−	0.634281i
$95$	94.6543	−	35.7722i	0.996361	−	0.376550i
$96$	3.80365	+	88.6636i	0.0396213	+	0.923580i
$97$	8.53929	−	8.53929i	0.0880339	−	0.0880339i	−0.661718	−	0.749752i	$-0.730173\pi$
$97$	8.53929	−	8.53929i	0.0880339	−	0.0880339i	0.749752	+	0.661718i	$0.230173\pi$
$98$	−17.3675	+	5.80816i	−0.177220	+	0.0592669i
$99$	3.90055	−	3.90055i	0.0393995	−	0.0393995i
$100$	−97.9534	−	20.1279i	−0.979534	−	0.201279i
$101$	65.0118	−	65.0118i	0.643681	−	0.643681i	−0.307777	−	0.951458i	$-0.599585\pi$
$101$	65.0118	−	65.0118i	0.643681	−	0.643681i	0.951458	+	0.307777i	$0.0995852\pi$
$102$	−23.3494	+	46.8138i	−0.228916	+	0.458959i
$103$	32.9039	−	32.9039i	0.319456	−	0.319456i	−0.529102	−	0.848558i	$-0.677471\pi$
$103$	32.9039	−	32.9039i	0.319456	−	0.319456i	0.848558	+	0.529102i	$0.177471\pi$
$104$	96.1261	−	139.728i	0.924289	−	1.34354i
$105$	98.9176	−	37.3834i	0.942073	−	0.356033i
$106$	−62.9359	−	188.191i	−0.593735	−	1.77538i
$107$			19.9537i			0.186484i	0.995643	+	0.0932418i	$0.0297230\pi$
$107$			19.9537i			0.186484i	−0.995643	+	0.0932418i	$0.970277\pi$
$108$	−68.7946	−	91.3512i	−0.636987	−	0.845845i
$109$	−31.4162	+	31.4162i	−0.288222	+	0.288222i	−0.836377	−	0.548155i	$-0.815330\pi$
$109$	−31.4162	+	31.4162i	−0.288222	+	0.288222i	0.548155	+	0.836377i	$0.315330\pi$
$110$	26.6332	+	32.6624i	0.242120	+	0.296931i
$111$	181.161			1.63208
$112$	−106.754	+	59.0900i	−0.953162	+	0.527589i
$113$	−48.1807	−	48.1807i	−0.426378	−	0.426378i	0.461014	−	0.887393i	$-0.347486\pi$
$113$	−48.1807	−	48.1807i	−0.426378	−	0.426378i	−0.887393	+	0.461014i	$0.847486\pi$
$114$	−50.1009	+	100.449i	−0.439481	+	0.881128i
$115$	13.7096	−	5.18121i	0.119214	−	0.0450540i
$116$	−13.8398	+	98.2586i	−0.119309	+	0.847057i
$117$			27.7482i			0.237164i
$118$	69.1050	−	138.550i	0.585635	−	1.17416i
$119$	−71.9267			−0.604426
$120$	94.9102	−	57.4269i	0.790918	−	0.478558i
$121$			103.238i			0.853210i
$122$	15.2821	−	30.6395i	0.125263	−	0.251144i
$123$	3.27939			0.0266617
$124$	75.5599	−	56.9025i	0.609354	−	0.458891i
$125$	36.7727	+	119.469i	0.294181	+	0.955750i
$126$	8.91022	−	17.8643i	0.0707160	−	0.141780i
$127$	−165.164	+	165.164i	−1.30051	+	1.30051i	−0.372456	+	0.928050i	$0.621484\pi$
$127$	−165.164	+	165.164i	−1.30051	+	1.30051i	−0.928050	+	0.372456i	$0.878516\pi$
$128$	−98.8545	+	81.3129i	−0.772301	+	0.635257i
$129$			26.5524i			0.205832i
$130$	−210.912	−	21.4456i	−1.62240	−	0.164966i
$131$	10.9705	+	10.9705i	0.0837444	+	0.0837444i	0.747738	−	0.663994i	$-0.231140\pi$
$131$	10.9705	+	10.9705i	0.0837444	+	0.0837444i	−0.663994	+	0.747738i	$0.731140\pi$
$132$	−46.2946	−	6.52063i	−0.350717	−	0.0493987i
$133$	−154.333			−1.16040
$134$	69.1882	+	206.886i	0.516330	+	1.54393i
$135$	−58.8185	+	130.286i	−0.435693	+	0.965079i
$136$	−74.1966	+	13.7165i	−0.545563	+	0.100857i
$137$	−122.401	−	122.401i	−0.893436	−	0.893436i	0.101408	−	0.994845i	$-0.467665\pi$
$137$	−122.401	−	122.401i	−0.893436	−	0.893436i	−0.994845	+	0.101408i	$0.967665\pi$
$138$	−7.25656	+	14.5489i	−0.0525837	+	0.105427i
$139$	163.514	+	163.514i	1.17636	+	1.17636i	0.980665	+	0.195693i	$0.0626955\pi$
$139$	163.514	+	163.514i	1.17636	+	1.17636i	0.195693	+	0.980665i	$0.437305\pi$
$140$	128.899	+	81.5327i	0.920709	+	0.582376i
$141$	−130.978	−	130.978i	−0.928925	−	0.928925i
$142$	138.780	−	46.4116i	0.977322	−	0.326842i
$143$	63.1774	+	63.1774i	0.441800	+	0.441800i
$144$	5.78465	−	20.1273i	0.0401712	−	0.139773i
$145$	116.026	−	43.8492i	0.800181	−	0.302408i
$146$	43.0700	+	21.4821i	0.295000	+	0.147138i
$147$	−25.3936			−0.172745
$148$	157.187	+	208.726i	1.06207	+	1.41031i
$149$	182.956	+	182.956i	1.22789	+	1.22789i	0.964759	+	0.263134i	$0.0847562\pi$
$149$	182.956	+	182.956i	1.22789	+	1.22789i	0.263134	+	0.964759i	$0.415244\pi$
$150$	−119.962	−	69.5481i	−0.799746	−	0.463654i
$151$			100.104i			0.662938i	0.943466	+	0.331469i	$0.107544\pi$
$151$			100.104i			0.662938i	−0.943466	+	0.331469i	$0.892456\pi$
$152$	−159.204	+	29.4316i	−1.04739	+	0.193629i
$153$	8.72923	−	8.72923i	0.0570538	−	0.0570538i
$154$	−20.3868	−	60.9606i	−0.132382	−	0.395848i
$155$	−107.764	−	48.6509i	−0.695251	−	0.313877i
$156$	187.862	−	141.474i	1.20424	−	0.906887i
$157$	27.8875			0.177627			0.0888136	−	0.996048i	$-0.471692\pi$
$157$	27.8875			0.177627			0.0888136	+	0.996048i	$0.471692\pi$
$158$	4.08044	−	1.36461i	0.0258256	−	0.00863675i
$159$		−	275.159i		−	1.73056i
$160$	148.515	+	59.5244i	0.928222	+	0.372028i
$161$	−22.3535			−0.138841
$162$	−42.8211	−	128.043i	−0.264328	−	0.790391i
$163$		−	122.177i		−	0.749552i	−0.927115	−	0.374776i	$-0.877720\pi$
$163$		−	122.177i		−	0.749552i	0.927115	−	0.374776i	$-0.122280\pi$
$164$	2.84542	+	3.77839i	0.0173501	+	0.0230390i
$165$	20.6596	+	54.6658i	0.125209	+	0.331308i
$166$	−145.072	+	48.5160i	−0.873930	+	0.292265i
$167$	−102.217	−	102.217i	−0.612078	−	0.612078i	0.331409	−	0.943487i	$-0.392476\pi$
$167$	−102.217	−	102.217i	−0.612078	−	0.612078i	−0.943487	+	0.331409i	$0.892476\pi$
$168$	−166.374	+	30.7572i	−0.990324	+	0.183079i
$169$	−280.439			−1.65940
$170$	59.6038	+	73.0968i	0.350610	+	0.429981i
$171$	18.7303	−	18.7303i	0.109534	−	0.109534i
$172$	−30.5926	+	23.0386i	−0.177864	+	0.133945i
$173$			144.968i			0.837968i	0.907994	+	0.418984i	$0.137614\pi$
$173$			144.968i			0.837968i	−0.907994	+	0.418984i	$0.862386\pi$
$174$	−61.4131	+	123.129i	−0.352949	+	0.707636i
$175$	11.9524	−	190.276i	0.0682992	−	1.08729i
$176$	−32.6555	−	58.9966i	−0.185542	−	0.335208i
$177$	151.810	−	151.810i	0.857682	−	0.857682i
$178$	−24.5670	−	73.4602i	−0.138017	−	0.412698i
$179$	−71.1438	+	71.1438i	−0.397451	+	0.397451i	−0.877333	−	0.479882i	$-0.840680\pi$
$179$	−71.1438	+	71.1438i	−0.397451	+	0.397451i	0.479882	+	0.877333i	$0.340680\pi$
$180$	−25.5386	+	5.74854i	−0.141881	+	0.0319363i
$181$	−192.954	+	192.954i	−1.06604	+	1.06604i	−0.0683832	+	0.997659i	$0.521784\pi$
$181$	−192.954	+	192.954i	−1.06604	+	1.06604i	−0.997659	+	0.0683832i	$0.978216\pi$
$182$	289.349	+	144.319i	1.58983	+	0.792963i
$183$	33.5717	−	33.5717i	0.183452	−	0.183452i
$184$	−23.0589	+	4.26284i	−0.125320	+	0.0231676i
$185$	134.393	−	297.687i	0.726449	−	1.60912i
$186$	124.390	−	41.5994i	0.668765	−	0.223653i
$187$		−	39.7496i		−	0.212565i
$188$	37.2626	−	264.554i	0.198205	−	1.40720i
$189$	154.167	−	154.167i	0.815696	−	0.815696i
$190$	127.892	+	156.844i	0.673116	+	0.825495i
$191$	−209.558			−1.09716			−0.548581	−	0.836097i	$-0.684832\pi$
$191$	−209.558			−1.09716			−0.548581	+	0.836097i	$0.684832\pi$
$192$	−165.759	+	63.4558i	−0.863331	+	0.330499i
$193$	−90.2693	−	90.2693i	−0.467717	−	0.467717i	0.433457	−	0.901174i	$-0.357293\pi$
$193$	−90.2693	−	90.2693i	−0.467717	−	0.467717i	−0.901174	+	0.433457i	$0.857293\pi$
$194$	21.6135	+	10.7802i	0.111410	+	0.0555680i
$195$	−267.929	−	120.959i	−1.37400	−	0.620302i
$196$	−22.0332	−	29.2575i	−0.112414	−	0.149273i
$197$		−	67.8338i		−	0.344334i	−0.985068	−	0.172167i	$-0.944923\pi$
$197$		−	67.8338i		−	0.344334i	0.985068	−	0.172167i	$-0.0550768\pi$
$198$	9.87254	+	4.92414i	0.0498613	+	0.0248694i
$199$	278.771			1.40086			0.700430	−	0.713721i	$-0.252991\pi$
$199$	278.771			1.40086			0.700430	+	0.713721i	$0.252991\pi$
$200$	−23.9564	−	198.560i	−0.119782	−	0.992800i
$201$			302.495i			1.50495i
$202$	164.549	+	82.0723i	0.814599	+	0.406299i
$203$	−189.180			−0.931922
$204$	−103.605	−	14.5928i	−0.507867	−	0.0715335i
$205$	2.43280	−	5.38876i	0.0118673	−	0.0262866i
$206$	83.2820	+	41.5387i	0.404281	+	0.201644i
$207$	2.71288	−	2.71288i	0.0131057	−	0.0131057i
$208$	326.003	+	93.6942i	1.56732	+	0.450453i
$209$		−	85.2908i		−	0.408090i
$210$	133.652	+	163.908i	0.636439	+	0.780516i
$211$	−26.5489	−	26.5489i	−0.125824	−	0.125824i	0.641391	−	0.767215i	$-0.278358\pi$
$211$	−26.5489	−	26.5489i	−0.125824	−	0.125824i	−0.767215	+	0.641391i	$0.778358\pi$
$212$	317.028	−	238.747i	1.49542	−	1.12616i
$213$	202.914			0.952648
$214$	−37.8471	+	12.6571i	−0.176856	+	0.0591452i
$215$	43.6314	+	19.6977i	0.202937	+	0.0916174i
$216$	129.632	−	188.432i	0.600148	−	0.872369i
$217$	127.517	+	127.517i	0.587635	+	0.587635i
$218$	−79.5164	−	39.6605i	−0.364754	−	0.181929i
$219$	47.1918	+	47.1918i	0.215488	+	0.215488i
$220$	−45.0582	+	71.2349i	−0.204810	+	0.323795i
$221$	141.388	+	141.388i	0.639763	+	0.639763i
$222$	114.914	+	343.615i	0.517631	+	1.54782i
$223$	90.1705	+	90.1705i	0.404352	+	0.404352i	0.879764	−	0.475412i	$-0.157701\pi$
$223$	90.1705	+	90.1705i	0.404352	+	0.404352i	−0.475412	+	0.879764i	$0.657701\pi$
$224$	−179.795	−	165.003i	−0.802656	−	0.736621i
$225$	21.6418	+	24.5430i	0.0961860	+	0.109080i
$226$	60.8244	−	121.949i	0.269135	−	0.539595i
$227$	−346.057			−1.52448			−0.762240	−	0.647294i	$-0.775900\pi$
$227$	−346.057			−1.52448			−0.762240	+	0.647294i	$0.775900\pi$
$228$	−222.305	−	31.3119i	−0.975023	−	0.137333i
$229$	73.4761	+	73.4761i	0.320856	+	0.320856i	0.849096	−	0.528239i	$-0.177148\pi$
$229$	73.4761	+	73.4761i	0.320856	+	0.320856i	−0.528239	+	0.849096i	$0.677148\pi$
$230$	18.5237	+	22.7171i	0.0805380	+	0.0987700i
$231$		−	89.1323i		−	0.385854i
$232$	−195.150	+	36.0770i	−0.841165	+	0.155504i
$233$	86.7985	−	86.7985i	0.372526	−	0.372526i	−0.495871	−	0.868396i	$-0.665151\pi$
$233$	86.7985	−	86.7985i	0.372526	−	0.372526i	0.868396	+	0.495871i	$0.165151\pi$
$234$	−52.6312	+	17.6013i	−0.224920	+	0.0752191i
$235$	−312.392	+	118.061i	−1.32933	+	0.502385i
$236$	306.629	+	43.1890i	1.29928	+	0.183004i
$237$	5.96613			0.0251736
$238$	−45.6246	−	136.427i	−0.191700	−	0.573221i
$239$		−	204.791i		−	0.856868i	−0.903573	−	0.428434i	$-0.859065\pi$
$239$		−	204.791i		−	0.856868i	0.903573	−	0.428434i	$-0.140935\pi$
$240$	169.128	+	143.593i	0.704699	+	0.598305i
$241$	98.8804			0.410292			0.205146	−	0.978731i	$-0.434233\pi$
$241$	98.8804			0.410292			0.205146	+	0.978731i	$0.434233\pi$
$242$	−195.817	+	65.4863i	−0.809160	+	0.270604i
$243$			70.0893i			0.288433i
$244$	67.8091	+	9.55097i	0.277906	+	0.0391433i
$245$	−18.8381	+	41.7272i	−0.0768902	+	0.170315i
$246$	2.08019	+	6.22017i	0.00845605	+	0.0252852i
$247$	303.376	+	303.376i	1.22824	+	1.22824i
$248$	155.859	+	107.223i	0.628462	+	0.432352i
$249$	−212.115			−0.851867
$250$	−203.276	+	145.530i	−0.813103	+	0.582119i
$251$	−38.3371	+	38.3371i	−0.152737	+	0.152737i	−0.779339	−	0.626602i	$-0.784445\pi$
$251$	−38.3371	+	38.3371i	−0.152737	+	0.152737i	0.626602	+	0.779339i	$0.284445\pi$
$252$	39.5360	+	5.56868i	0.156889	+	0.0220979i
$253$		−	12.3534i		−	0.0488277i
$254$	−418.041	−	208.507i	−1.64583	−	0.820894i
$255$	46.2350	+	122.339i	0.181314	+	0.479762i
$256$	−216.935	−	135.923i	−0.847403	−	0.530950i
$257$	166.481	−	166.481i	0.647785	−	0.647785i	−0.304672	−	0.952457i	$-0.598547\pi$
$257$	166.481	−	166.481i	0.647785	−	0.647785i	0.952457	+	0.304672i	$0.0985468\pi$
$258$	−50.3631	+	16.8427i	−0.195206	+	0.0652819i
$259$	−352.252	+	352.252i	−1.36005	+	1.36005i
$260$	−93.1093	−	413.650i	−0.358113	−	1.59096i
$261$	22.9594	−	22.9594i	0.0879671	−	0.0879671i
$262$	−13.8494	+	27.7671i	−0.0528604	+	0.105981i
$263$	78.7097	−	78.7097i	0.299276	−	0.299276i	−0.541454	−	0.840730i	$-0.682126\pi$
$263$	78.7097	−	78.7097i	0.299276	−	0.299276i	0.840730	+	0.541454i	$0.182126\pi$
$264$	−16.9977	−	91.9452i	−0.0643851	−	0.348277i
$265$	−452.147	−	204.126i	−1.70622	−	0.770285i
$266$	−97.8969	−	292.731i	−0.368034	−	1.10049i
$267$		−	107.408i		−	0.402279i
$268$	−348.522	+	262.464i	−1.30046	+	0.979345i
$269$	98.2650	−	98.2650i	0.365297	−	0.365297i	−0.500461	−	0.865759i	$-0.666836\pi$
$269$	98.2650	−	98.2650i	0.365297	−	0.365297i	0.865759	+	0.500461i	$0.166836\pi$
$270$	−284.428	−	28.9207i	−1.05344	−	0.107114i
$271$	−115.967			−0.427922			−0.213961	−	0.976842i	$-0.568637\pi$
$271$	−115.967			−0.427922			−0.213961	+	0.976842i	$0.568637\pi$
$272$	−73.0812	−	132.031i	−0.268681	−	0.485409i
$273$	317.040	+	317.040i	1.16132	+	1.16132i
$274$	154.522	−	309.804i	0.563947	−	1.13067i
$275$	105.154	+	6.60535i	0.382378	+	0.0240195i
$276$	−32.1984	−	4.53518i	−0.116661	−	0.0164318i
$277$		−	340.610i		−	1.22964i	−0.788668	−	0.614819i	$-0.789229\pi$
$277$		−	340.610i		−	1.22964i	0.788668	−	0.614819i	$-0.210771\pi$
$278$	−206.423	+	413.864i	−0.742530	+	1.48872i
$279$	−30.9516			−0.110938
$280$	−72.8831	+	296.207i	−0.260297	+	1.05788i
$281$		−	103.541i		−	0.368474i	−0.982882	−	0.184237i	$-0.941019\pi$
$281$		−	103.541i		−	0.368474i	0.982882	−	0.184237i	$-0.0589814\pi$
$282$	165.350	−	331.515i	0.586348	−	1.17558i
$283$	561.986			1.98582			0.992908	−	0.118887i	$-0.0379325\pi$
$283$	561.986			1.98582			0.992908	+	0.118887i	$0.0379325\pi$
$284$	176.062	+	233.790i	0.619936	+	0.823203i
$285$	99.2066	+	262.504i	0.348093	+	0.921065i
$286$	−79.7565	+	159.906i	−0.278869	+	0.559112i
$287$	−6.37651	+	6.37651i	−0.0222178	+	0.0222178i
$288$	41.8456	−	1.79517i	0.145297	−	0.00623322i
$289$			200.043i			0.692189i
$290$	156.769	+	192.258i	0.540581	+	0.662957i
$291$	23.6819	+	23.6819i	0.0813811	+	0.0813811i
$292$	−13.4258	+	95.3193i	−0.0459787	+	0.326436i
$293$	1.90920			0.00651604			0.00325802	−	0.999995i	$-0.498963\pi$
$293$	1.90920			0.00651604			0.00325802	+	0.999995i	$0.498963\pi$
$294$	−16.1077	−	48.1651i	−0.0547880	−	0.163827i
$295$	−136.837	−	362.076i	−0.463855	−	1.22737i
$296$	−296.193	+	430.543i	−1.00065	+	1.45454i
$297$	85.1986	+	85.1986i	0.286864	+	0.286864i
$298$	−230.968	+	463.074i	−0.775060	+	1.55394i
$299$	43.9406	+	43.9406i	0.146959	+	0.146959i
$300$	55.8205	−	271.653i	0.186068	−	0.905510i
$301$	−51.6289	−	51.6289i	−0.171525	−	0.171525i
$302$	−189.871	+	63.4978i	−0.628712	+	0.210258i
$303$	180.296	+	180.296i	0.595037	+	0.595037i
$304$	−156.811	−	283.300i	−0.515824	−	0.931907i
$305$	−30.2607	−	80.0707i	−0.0992154	−	0.262527i
$306$	22.0942	+	11.0200i	0.0722034	+	0.0360130i
$307$	465.516			1.51634			0.758169	−	0.652058i	$-0.226094\pi$
$307$	465.516			1.51634			0.758169	+	0.652058i	$0.226094\pi$
$308$	102.695	−	77.3372i	0.333425	−	0.251095i
$309$	91.2520	+	91.2520i	0.295314	+	0.295314i
$310$	23.9214	−	235.261i	0.0771657	−	0.758906i
$311$			212.375i			0.682879i	0.939904	+	0.341439i	$0.110914\pi$
$311$			212.375i			0.682879i	−0.939904	+	0.341439i	$0.889086\pi$
$312$	387.505	+	266.585i	1.24200	+	0.854440i
$313$	46.0307	−	46.0307i	0.147063	−	0.147063i	−0.629742	−	0.776805i	$-0.716839\pi$
$313$	46.0307	−	46.0307i	0.147063	−	0.147063i	0.776805	+	0.629742i	$0.216839\pi$
$314$	17.6896	+	52.8954i	0.0563364	+	0.168457i
$315$	−17.6435	−	46.6851i	−0.0560110	−	0.148207i
$316$	5.17661	+	6.87395i	0.0163817	+	0.0217530i
$317$	−430.649			−1.35851			−0.679257	−	0.733901i	$-0.737698\pi$
$317$	−430.649			−1.35851			−0.679257	+	0.733901i	$0.737698\pi$
$318$	521.907	−	174.539i	1.64122	−	0.548866i
$319$		−	104.548i		−	0.327738i
$320$	−18.6960	+	319.453i	−0.0584251	+	0.998292i
$321$	−55.3375			−0.172391
$322$	−14.1793	−	42.3988i	−0.0440350	−	0.131673i
$323$		−	190.876i		−	0.590948i
$324$	215.703	−	162.441i	0.665750	−	0.501362i
$325$	−397.524	+	350.534i	−1.22315	+	1.07857i
$326$	231.738	−	77.4994i	0.710854	−	0.237728i
$327$	−87.1261	−	87.1261i	−0.266441	−	0.266441i
$328$	−5.36173	+	7.79375i	−0.0163467	+	0.0237614i
$329$	509.353			1.54819
$330$	−90.5822	+	73.8616i	−0.274492	+	0.223823i
$331$	3.70469	−	3.70469i	0.0111924	−	0.0111924i	−0.701488	−	0.712681i	$-0.747481\pi$
$331$	3.70469	−	3.70469i	0.0111924	−	0.0111924i	0.712681	+	0.701488i	$0.247481\pi$
$332$	−184.045	−	244.390i	−0.554352	−	0.736116i
$333$		−	85.5005i		−	0.256758i
$334$	129.041	−	258.718i	0.386351	−	0.774605i
$335$	497.065	+	224.404i	1.48378	+	0.669862i
$336$	−163.873	−	296.060i	−0.487719	−	0.881130i
$337$	−226.237	+	226.237i	−0.671327	+	0.671327i	−0.958022	−	0.286695i	$-0.907443\pi$
$337$	−226.237	+	226.237i	−0.671327	+	0.671327i	0.286695	+	0.958022i	$0.407443\pi$
$338$	−177.888	−	531.920i	−0.526297	−	1.57373i
$339$	133.619	−	133.619i	0.394156	−	0.394156i
$340$	−100.838	+	159.420i	−0.296582	+	0.468882i
$341$	−70.4709	+	70.4709i	−0.206659	+	0.206659i
$342$	47.4077	+	23.6456i	0.138619	+	0.0691391i
$343$	−214.853	+	214.853i	−0.626394	+	0.626394i
$344$	−63.1039	−	43.4125i	−0.183442	−	0.126199i
$345$	14.3690	+	38.0207i	0.0416492	+	0.110205i
$346$	−274.968	+	91.9566i	−0.794705	+	0.265770i
$347$		−	231.886i		−	0.668259i	−0.942527	−	0.334130i	$-0.891558\pi$
$347$		−	231.886i		−	0.668259i	0.942527	−	0.334130i	$-0.108442\pi$
$348$	−272.499	−	38.3817i	−0.783044	−	0.110292i
$349$	205.898	−	205.898i	0.589965	−	0.589965i	−0.347657	−	0.937622i	$-0.613022\pi$
$349$	205.898	−	205.898i	0.589965	−	0.589965i	0.937622	+	0.347657i	$0.113022\pi$
$350$	368.486	−	98.0255i	1.05282	−	0.280073i
$351$	−606.096			−1.72677
$352$	91.1873	−	99.3618i	0.259055	−	0.282278i
$353$	−299.539	−	299.539i	−0.848551	−	0.848551i	0.141401	−	0.989952i	$-0.454839\pi$
$353$	−299.539	−	299.539i	−0.848551	−	0.848551i	−0.989952	+	0.141401i	$0.954839\pi$
$354$	384.240	+	191.648i	1.08542	+	0.541378i
$355$	150.531	−	333.432i	0.424030	−	0.939246i
$356$	123.752	−	93.1947i	0.347617	−	0.261783i
$357$		−	199.473i		−	0.558749i
$358$	−180.070	−	89.8135i	−0.502987	−	0.250876i
$359$	−108.844			−0.303187			−0.151593	−	0.988443i	$-0.548440\pi$
$359$	−108.844			−0.303187			−0.151593	+	0.988443i	$0.548440\pi$
$360$	−27.1032	−	44.7938i	−0.0752866	−	0.124427i
$361$		−	48.5638i		−	0.134526i
$362$	−488.378	−	243.589i	−1.34911	−	0.672898i
$363$	−286.310			−0.788732
$364$	−90.1961	+	640.366i	−0.247791	+	1.75925i
$365$	112.555	−	42.5375i	0.308371	−	0.116541i
$366$	84.9722	+	42.3817i	0.232165	+	0.115797i
$367$	271.565	−	271.565i	0.739960	−	0.739960i	−0.232610	−	0.972570i	$-0.574726\pi$
$367$	271.565	−	271.565i	0.739960	−	0.739960i	0.972570	+	0.232610i	$0.0747265\pi$
$368$	−22.7123	−	41.0328i	−0.0617181	−	0.111502i
$369$		−	1.54774i		−	0.00419442i
$370$	649.883	+	66.0802i	1.75644	+	0.178595i
$371$	535.025	+	535.025i	1.44211	+	1.44211i
$372$	157.807	+	209.549i	0.424212	+	0.563305i
$373$	205.735			0.551569			0.275784	−	0.961220i	$-0.411062\pi$
$373$	205.735			0.551569			0.275784	+	0.961220i	$0.411062\pi$
$374$	75.3948	−	25.2140i	0.201590	−	0.0674171i
$375$	−331.321	+	101.981i	−0.883523	+	0.271950i
$376$	525.427	−	97.1345i	1.39741	−	0.258336i
$377$	371.875	+	371.875i	0.986405	+	0.986405i
$378$	390.206	+	194.623i	1.03229	+	0.514877i
$379$	146.474	+	146.474i	0.386475	+	0.386475i	0.873428	−	0.486953i	$-0.161892\pi$
$379$	146.474	+	146.474i	0.386475	+	0.386475i	−0.486953	+	0.873428i	$0.661892\pi$
$380$	−216.368	+	342.068i	−0.569390	+	0.900178i
$381$	−458.048	−	458.048i	−1.20223	−	1.20223i
$382$	−132.927	−	397.478i	−0.347977	−	1.04052i
$383$	77.8502	+	77.8502i	0.203264	+	0.203264i	0.801397	−	0.598133i	$-0.204090\pi$
$383$	77.8502	+	77.8502i	0.203264	+	0.203264i	−0.598133	+	0.801397i	$0.704090\pi$
$384$	−225.504	−	274.152i	−0.587250	−	0.713937i
$385$	−146.464	−	66.1223i	−0.380426	−	0.171746i
$386$	113.958	−	228.477i	0.295228	−	0.591910i
$387$	12.5317			0.0323815
$388$	−6.73737	+	47.8334i	−0.0173643	+	0.123282i
$389$	91.3251	+	91.3251i	0.234769	+	0.234769i	0.814680	−	0.579911i	$-0.196913\pi$
$389$	91.3251	+	91.3251i	0.234769	+	0.234769i	−0.579911	+	0.814680i	$0.696913\pi$
$390$	59.4748	−	584.920i	0.152499	−	1.49980i
$391$		−	27.6463i		−	0.0707067i
$392$	41.5179	−	60.3499i	0.105913	−	0.153954i
$393$	−30.4244	+	30.4244i	−0.0774158	+	0.0774158i
$394$	128.663	−	43.0284i	0.326557	−	0.109209i
$395$	4.42594	−	9.80366i	0.0112049	−	0.0248194i
$396$	−3.07747	+	21.8492i	−0.00777140	+	0.0551747i
$397$	−181.720			−0.457732			−0.228866	−	0.973458i	$-0.573502\pi$
$397$	−181.720			−0.457732			−0.228866	+	0.973458i	$0.573502\pi$
$398$	176.831	+	528.758i	0.444298	+	1.32854i
$399$		−	428.011i		−	1.07271i
$400$	361.421	−	171.390i	0.903554	−	0.428475i
$401$	−559.201			−1.39452			−0.697258	−	0.716821i	$-0.745597\pi$
$401$	−559.201			−1.39452			−0.697258	+	0.716821i	$0.745597\pi$
$402$	−573.755	+	191.879i	−1.42725	+	0.477310i
$403$		−	501.324i		−	1.24398i
$404$	−51.2933	+	364.167i	−0.126964	+	0.901405i
$405$	−307.637	−	138.885i	−0.759597	−	0.342926i
$406$	−120.001	−	358.826i	−0.295569	−	0.883808i
$407$	−194.668	−	194.668i	−0.478301	−	0.478301i
$408$	−38.0399	−	205.768i	−0.0932351	−	0.504334i
$409$	−724.291			−1.77088			−0.885441	−	0.464752i	$-0.846144\pi$
$409$	−724.291			−1.77088			−0.885441	+	0.464752i	$0.846144\pi$
$410$	11.7643	+	1.19619i	0.0286934	+	0.00291754i
$411$	339.453	−	339.453i	0.825919	−	0.825919i
$412$	−25.9607	+	184.313i	−0.0630114	+	0.447363i
$413$			590.362i			1.42945i
$414$	6.86647	+	3.42480i	0.0165857	+	0.00827246i
$415$	−157.356	+	348.551i	−0.379172	+	0.839882i
$416$	29.0764	+	677.776i	0.0698952	+	1.62927i
$417$	−453.471	+	453.471i	−1.08746	+	1.08746i
$418$	161.775	−	54.1017i	0.387021	−	0.129430i
$419$	76.4657	−	76.4657i	0.182496	−	0.182496i	−0.609947	−	0.792442i	$-0.708809\pi$
$419$	76.4657	−	76.4657i	0.182496	−	0.182496i	0.792442	+	0.609947i	$0.208809\pi$
$420$	−226.114	+	357.475i	−0.538366	+	0.851130i
$421$	470.702	−	470.702i	1.11806	−	1.11806i	0.126030	−	0.992026i	$-0.459776\pi$
$421$	470.702	−	470.702i	1.11806	−	1.11806i	0.992026	−	0.126030i	$-0.0402236\pi$
$422$	33.5159	−	67.1969i	0.0794215	−	0.159234i
$423$	−61.8165	+	61.8165i	−0.146138	+	0.146138i
$424$	653.939	+	449.879i	1.54231	+	1.06103i
$425$	235.329	+	14.7824i	0.553716	+	0.0347822i
$426$	128.713	+	384.876i	0.302143	+	0.903465i
$427$			130.555i			0.305749i
$428$	−48.0145	−	63.7577i	−0.112183	−	0.148967i
$429$	−175.209	+	175.209i	−0.408413	+	0.408413i
$430$	−9.68526	+	95.2522i	−0.0225239	+	0.221517i
$431$	185.108			0.429485			0.214742	−	0.976671i	$-0.431109\pi$
$431$	185.108			0.429485			0.214742	+	0.976671i	$0.431109\pi$
$432$	439.635	+	126.353i	1.01767	+	0.292483i
$433$	−354.954	−	354.954i	−0.819756	−	0.819756i	0.166317	−	0.986072i	$-0.446813\pi$
$433$	−354.954	−	354.954i	−0.819756	−	0.819756i	−0.986072	+	0.166317i	$0.946813\pi$
$434$	−160.980	+	322.753i	−0.370922	+	0.743671i
$435$	121.606	+	321.774i	0.279555	+	0.739710i
$436$	24.7869	−	175.980i	0.0568507	−	0.403623i
$437$		−	59.3208i		−	0.135745i
$438$	−59.5760	+	119.445i	−0.136018	+	0.272707i
$439$	−155.719			−0.354714			−0.177357	−	0.984147i	$-0.556755\pi$
$439$	−155.719			−0.354714			−0.177357	+	0.984147i	$0.556755\pi$
$440$	−163.696	−	40.2781i	−0.372036	−	0.0915411i
$441$			11.9847i			0.0271763i
$442$	−178.491	+	357.861i	−0.403826	+	0.809641i
$443$	−728.951			−1.64549			−0.822744	−	0.568412i	$-0.807558\pi$
$443$	−728.951			−1.64549			−0.822744	+	0.568412i	$0.807558\pi$
$444$	−578.858	+	435.925i	−1.30373	+	0.981813i
$445$	−176.496	−	79.6803i	−0.396619	−	0.179057i
$446$	−113.833	+	228.227i	−0.255232	+	0.511721i
$447$	−507.390	+	507.390i	−1.13510	+	1.13510i
$448$	198.921	−	445.690i	0.444020	−	0.994843i
$449$			46.9465i			0.104558i	0.998633	+	0.0522790i	$0.0166485\pi$
$449$			46.9465i			0.104558i	−0.998633	+	0.0522790i	$0.983351\pi$
$450$	−32.8239	+	56.6172i	−0.0729420	+	0.125816i
$451$	−3.52391	−	3.52391i	−0.00781355	−	0.00781355i
$452$	269.887	+	38.0138i	0.597096	+	0.0841014i
$453$	−277.616			−0.612839
$454$	−219.511	−	656.381i	−0.483505	−	1.44577i
$455$	756.161	−	285.772i	1.66189	−	0.628070i
$456$	−81.6223	−	441.518i	−0.178996	−	0.968241i
$457$	227.434	+	227.434i	0.497667	+	0.497667i	0.910711	−	0.413044i	$-0.135534\pi$
$457$	227.434	+	227.434i	0.497667	+	0.497667i	−0.413044	+	0.910711i	$0.635534\pi$
$458$	−92.7579	+	185.973i	−0.202528	+	0.406054i
$459$	190.670	+	190.670i	0.415403	+	0.415403i
$460$	−31.3385	+	49.5447i	−0.0681272	+	0.107706i
$461$	265.869	+	265.869i	0.576722	+	0.576722i	0.933999	−	0.357277i	$-0.116295\pi$
$461$	265.869	+	265.869i	0.576722	+	0.576722i	−0.357277	+	0.933999i	$0.616295\pi$
$462$	169.061	−	56.5385i	0.365933	−	0.122378i
$463$	1.16661	+	1.16661i	0.00251968	+	0.00251968i	0.708366	−	0.705846i	$-0.249433\pi$
$463$	1.16661	+	1.16661i	0.00251968	+	0.00251968i	−0.705846	+	0.708366i	$0.749433\pi$
$464$	−192.217	−	347.266i	−0.414260	−	0.748417i
$465$	134.923	−	298.860i	0.290157	−	0.642711i
$466$	219.693	+	109.576i	0.471444	+	0.235143i
$467$	632.343			1.35405			0.677027	−	0.735958i	$-0.263268\pi$
$467$	632.343			1.35405			0.677027	+	0.735958i	$0.263268\pi$
$468$	−66.7702	−	88.6631i	−0.142671	−	0.189451i
$469$	−588.175	−	588.175i	−1.25411	−	1.25411i
$470$	−422.087	−	517.639i	−0.898058	−	1.10136i
$471$			77.3400i			0.164204i
$472$	112.583	+	608.993i	0.238523	+	1.29024i
$473$	28.5322	−	28.5322i	0.0603217	−	0.0603217i
$474$	3.78444	+	11.3162i	0.00798406	+	0.0238739i
$475$	504.947	+	31.7187i	1.06305	+	0.0667762i
$476$	229.826	−	173.077i	0.482827	−	0.363606i
$477$	−129.864			−0.272252
$478$	388.437	−	129.904i	0.812630	−	0.271765i
$479$			552.415i			1.15327i	0.817003	+	0.576633i	$0.195634\pi$
$479$			552.415i			1.15327i	−0.817003	+	0.576633i	$0.804366\pi$
$480$	−165.078	+	411.876i	−0.343913	+	0.858075i
$481$	1384.85			2.87912
$482$	62.7219	+	187.551i	0.130128	+	0.389110i
$483$		−	61.9926i		−	0.128349i
$484$	−248.421	−	329.875i	−0.513267	−	0.681560i
$485$	56.4828	−	21.3463i	0.116459	−	0.0440129i
$486$	−132.941	+	44.4591i	−0.273542	+	0.0914796i
$487$	−285.326	−	285.326i	−0.585886	−	0.585886i	0.350629	−	0.936515i	$-0.385968\pi$
$487$	−285.326	−	285.326i	−0.585886	−	0.585886i	−0.936515	+	0.350629i	$0.885968\pi$
$488$	24.8970	+	134.675i	0.0510185	+	0.275973i
$489$	338.832			0.692908
$490$	−91.0952	−	9.26258i	−0.185909	−	0.0189032i
$491$	−617.833	+	617.833i	−1.25831	+	1.25831i	−0.306418	+	0.951897i	$0.599130\pi$
$491$	−617.833	+	617.833i	−1.25831	+	1.25831i	−0.951897	+	0.306418i	$0.900870\pi$
$492$	−10.4786	+	7.89117i	−0.0212979	+	0.0160390i
$493$		−	233.974i		−	0.474592i
$494$	−382.989	+	767.864i	−0.775281	+	1.55438i
$495$	25.8001	−	9.75048i	0.0521213	−	0.0196979i
$496$	−104.511	+	363.638i	−0.210707	+	0.733141i
$497$	−394.550	+	394.550i	−0.793862	+	0.793862i
$498$	−134.549	−	402.327i	−0.270179	−	0.807886i
$499$	−430.585	+	430.585i	−0.862895	+	0.862895i	−0.991673	−	0.128778i	$-0.958894\pi$
$499$	−430.585	+	430.585i	−0.862895	+	0.862895i	0.128778	+	0.991673i	$0.458894\pi$
$500$	−404.975	−	293.250i	−0.809950	−	0.586499i
$501$	283.477	−	283.477i	0.565823	−	0.565823i
$502$	−97.0337	−	48.3976i	−0.193294	−	0.0964096i
$503$	102.108	−	102.108i	0.202998	−	0.202998i	−0.598285	−	0.801283i	$-0.704151\pi$
$503$	102.108	−	102.108i	0.202998	−	0.202998i	0.801283	+	0.598285i	$0.204151\pi$
$504$	14.5162	+	78.5220i	0.0288019	+	0.155798i
$505$	430.018	−	162.514i	0.851521	−	0.321811i
$506$	23.4313	−	7.83604i	0.0463069	−	0.0154862i
$507$		−	777.737i		−	1.53400i
$508$	130.312	−	925.178i	0.256520	−	1.82122i
$509$	350.381	−	350.381i	0.688372	−	0.688372i	−0.273500	−	0.961872i	$-0.588181\pi$
$509$	350.381	−	350.381i	0.688372	−	0.688372i	0.961872	+	0.273500i	$0.0881813\pi$
$510$	−202.718	+	165.298i	−0.397487	+	0.324114i
$511$	−183.521			−0.359141
$512$	120.205	−	497.689i	0.234775	−	0.972050i
$513$	409.121	+	409.121i	0.797507	+	0.797507i
$514$	421.374	+	210.169i	0.819793	+	0.408889i
$515$	217.642	−	82.2523i	0.422606	−	0.159713i
$516$	−63.8927	−	84.8421i	−0.123823	−	0.164423i
$517$			281.489i			0.544466i
$518$	−891.572	−	444.691i	−1.72118	−	0.858476i
$519$	−402.039			−0.774642
$520$	725.526	−	438.991i	1.39524	−	0.844214i
$521$			89.0292i			0.170881i	0.996343	+	0.0854407i	$0.0272298\pi$
$521$			89.0292i			0.170881i	−0.996343	+	0.0854407i	$0.972770\pi$
$522$	58.1118	+	28.9845i	0.111325	+	0.0555258i
$523$	−399.222			−0.763331			−0.381666	−	0.924300i	$-0.624649\pi$
$523$	−399.222			−0.763331			−0.381666	+	0.924300i	$0.624649\pi$
$524$	−61.4521	−	8.65557i	−0.117275	−	0.0165183i
$525$	527.690	+	33.1473i	1.00512	+	0.0631378i
$526$	199.219	+	99.3649i	0.378744	+	0.188907i
$527$	−157.710	+	157.710i	−0.299260	+	0.299260i
$528$	163.614	−	90.5630i	0.309876	−	0.171521i
$529$			520.408i			0.983758i
$530$	100.367	−	987.088i	0.189372	−	1.86243i
$531$	−71.6480	−	71.6480i	−0.134930	−	0.134930i
$532$	493.137	−	371.371i	0.926950	−	0.698065i
$533$	25.0688			0.0470334
$534$	203.726	−	68.1314i	0.381510	−	0.127587i
$535$	−41.0518	+	90.9316i	−0.0767323	+	0.169966i
$536$	−718.903	−	494.571i	−1.34124	−	0.922707i
$537$	−197.302	−	197.302i	−0.367415	−	0.367415i
$538$	248.715	+	124.052i	0.462296	+	0.230580i
$539$	27.2870	+	27.2870i	0.0506252	+	0.0506252i
$540$	−125.564	−	557.833i	−0.232525	−	1.03302i
$541$	151.552	+	151.552i	0.280133	+	0.280133i	0.833162	−	0.553029i	$-0.186528\pi$
$541$	151.552	+	151.552i	0.280133	+	0.280133i	−0.553029	+	0.833162i	$0.686528\pi$
$542$	−73.5603	−	219.960i	−0.135720	−	0.405830i
$543$	−535.116	−	535.116i	−0.985480	−	0.985480i
$544$	204.072	−	222.367i	0.375133	−	0.408762i
$545$	−207.801	+	78.5333i	−0.381287	+	0.144098i
$546$	−400.239	+	802.449i	−0.733038	+	1.46969i
$547$	−327.523			−0.598762			−0.299381	−	0.954134i	$-0.596780\pi$
$547$	−327.523			−0.598762			−0.299381	+	0.954134i	$0.596780\pi$
$548$	685.636	+	96.5723i	1.25116	+	0.176227i
$549$	−15.8445	−	15.8445i	−0.0288607	−	0.0288607i
$550$	54.1728	+	203.640i	0.0984960	+	0.370255i
$551$		−	502.039i		−	0.911141i
$552$	−11.8221	−	63.9490i	−0.0214168	−	0.115850i
$553$	−11.6006	+	11.6006i	−0.0209777	+	0.0209777i
$554$	646.049	−	216.056i	1.16615	−	0.389993i
$555$	825.570	+	372.710i	1.48751	+	0.671550i
$556$	−915.933	−	129.010i	−1.64736	−	0.232032i
$557$	609.704			1.09462			0.547311	−	0.836930i	$-0.315652\pi$
$557$	609.704			1.09462			0.547311	+	0.836930i	$0.315652\pi$
$558$	−19.6332	−	58.7072i	−0.0351850	−	0.105210i
$559$			202.976i			0.363105i
$560$	−608.060	+	49.6496i	−1.08582	+	0.0886600i
$561$	110.237			0.196501
$562$	196.391	−	65.6784i	0.349451	−	0.116865i
$563$			104.576i			0.185748i	0.995678	+	0.0928738i	$0.0296053\pi$
$563$			104.576i			0.185748i	−0.995678	+	0.0928738i	$0.970395\pi$
$564$	733.684	+	103.340i	1.30086	+	0.183227i
$565$	−120.441	−	318.690i	−0.213169	−	0.564053i
$566$	356.479	+	1065.94i	0.629822	+	1.88329i
$567$	364.026	+	364.026i	0.642021	+	0.642021i
$568$	−331.760	+	482.242i	−0.584084	+	0.849018i
$569$	−153.954			−0.270569			−0.135284	−	0.990807i	$-0.543195\pi$
$569$	−153.954			−0.270569			−0.135284	+	0.990807i	$0.543195\pi$
$570$	−434.973	+	354.681i	−0.763111	+	0.622248i
$571$	475.501	−	475.501i	0.832751	−	0.832751i	−0.155141	−	0.987892i	$-0.549583\pi$
$571$	475.501	−	475.501i	0.832751	−	0.832751i	0.987892	+	0.155141i	$0.0495832\pi$
$572$	−353.892	−	49.8460i	−0.618692	−	0.0871433i
$573$		−	581.164i		−	1.01425i
$574$	−16.1394	−	8.04985i	−0.0281173	−	0.0140241i
$575$	73.1359	+	4.59410i	0.127193	+	0.00798974i
$576$	29.9485	+	78.2318i	0.0519940	+	0.135819i
$577$	430.563	−	430.563i	0.746210	−	0.746210i	−0.227555	−	0.973765i	$-0.573073\pi$
$577$	430.563	−	430.563i	0.746210	−	0.746210i	0.973765	+	0.227555i	$0.0730731\pi$
$578$	−379.429	+	126.891i	−0.656452	+	0.219535i
$579$	250.343	−	250.343i	0.432371	−	0.432371i
$580$	−265.222	+	419.303i	−0.457279	+	0.722936i
$581$	412.440	−	412.440i	0.709879	−	0.709879i
$582$	−29.8966	+	59.9404i	−0.0513687	+	0.102990i
$583$	−295.676	+	295.676i	−0.507163	+	0.507163i
$584$	−189.313	+	34.9977i	−0.324165	+	0.0599276i
$585$	−57.0877	+	126.452i	−0.0975858	+	0.216157i
$586$	1.21105	+	3.62126i	0.00206663	+	0.00617963i
$587$			24.8014i			0.0422512i	0.999777	+	0.0211256i	$0.00672498\pi$
$587$			24.8014i			0.0422512i	−0.999777	+	0.0211256i	$0.993275\pi$
$588$	81.1394	−	61.1043i	0.137992	−	0.103919i
$589$	−338.399	+	338.399i	−0.574531	+	0.574531i
$590$	599.966	−	489.217i	1.01689	−	0.829182i
$591$	188.123			0.318312
$592$	−1004.51	−	288.700i	−1.69681	−	0.487669i
$593$	714.962	+	714.962i	1.20567	+	1.20567i	0.972416	+	0.233255i	$0.0749375\pi$
$593$	714.962	+	714.962i	1.20567	+	1.20567i	0.233255	+	0.972416i	$0.425062\pi$
$594$	−107.557	+	215.643i	−0.181072	+	0.363036i
$595$	−327.779	−	147.978i	−0.550888	−	0.248703i
$596$	−1024.84	−	144.350i	−1.71953	−	0.242197i
$597$			773.113i			1.29500i
$598$	−55.4716	+	111.217i	−0.0927619	+	0.185981i
$599$	898.559			1.50010			0.750049	−	0.661382i	$-0.230030\pi$
$599$	898.559			1.50010			0.750049	+	0.661382i	$0.230030\pi$
$600$	550.664	−	66.4379i	0.917773	−	0.110730i
$601$			498.405i			0.829293i	0.909983	+	0.414646i	$0.136095\pi$
$601$			498.405i			0.829293i	−0.909983	+	0.414646i	$0.863905\pi$
$602$	65.1775	−	130.676i	0.108268	−	0.217070i
$603$	142.765			0.236758
$604$	−240.878	−	319.858i	−0.398805	−	0.529567i
$605$	−212.397	+	470.469i	−0.351070	+	0.777635i
$606$	−227.610	+	456.342i	−0.375594	+	0.753039i
$607$	476.327	−	476.327i	0.784723	−	0.784723i	−0.195900	−	0.980624i	$-0.562763\pi$
$607$	476.327	−	476.327i	0.784723	−	0.784723i	0.980624	+	0.195900i	$0.0627629\pi$
$608$	437.879	−	477.133i	0.720195	−	0.784758i
$609$		−	524.651i		−	0.861495i
$610$	132.679	−	108.187i	0.217506	−	0.177356i
$611$	−1001.24	−	1001.24i	−1.63870	−	1.63870i
$612$	−6.88722	+	48.8973i	−0.0112536	+	0.0798976i
$613$	294.722			0.480787			0.240393	−	0.970676i	$-0.422724\pi$
$613$	294.722			0.480787			0.240393	+	0.970676i	$0.422724\pi$
$614$	295.286	+	882.964i	0.480923	+	1.43805i
$615$	14.9446	+	6.74685i	0.0243001	+	0.0109705i
$616$	211.830	+	145.729i	0.343880	+	0.236573i
$617$	248.885	+	248.885i	0.403379	+	0.403379i	0.879422	−	0.476043i	$-0.157929\pi$
$617$	248.885	+	248.885i	0.403379	+	0.403379i	−0.476043	+	0.879422i	$0.657929\pi$
$618$	−115.199	+	230.965i	−0.186406	+	0.373730i
$619$	−320.358	−	320.358i	−0.517541	−	0.517541i	0.399286	−	0.916826i	$-0.369258\pi$
$619$	−320.358	−	320.358i	−0.517541	−	0.517541i	−0.916826	+	0.399286i	$0.869258\pi$
$620$	461.404	−	103.858i	0.744199	−	0.167513i
$621$	59.2567	+	59.2567i	0.0954214	+	0.0954214i
$622$	−402.822	+	134.714i	−0.647623	+	0.216582i
$623$	208.847	+	208.847i	0.335227	+	0.335227i
$624$	−259.841	+	904.099i	−0.416412	+	1.44888i
$625$	−78.2113	+	620.087i	−0.125138	+	0.992139i
$626$	116.507	+	58.1103i	0.186113	+	0.0928279i
$627$	236.536			0.377250
$628$	−89.1081	+	67.1053i	−0.141892	+	0.106856i
$629$	−435.658	−	435.658i	−0.692619	−	0.692619i
$630$	77.3581	−	63.0785i	0.122791	−	0.100125i
$631$		−	110.857i		−	0.175685i	−0.996134	−	0.0878423i	$-0.972003\pi$
$631$		−	110.857i		−	0.175685i	0.996134	−	0.0878423i	$-0.0279972\pi$
$632$	−9.75448	+	14.1790i	−0.0154343	+	0.0224351i
$633$	73.6276	−	73.6276i	0.116315	−	0.116315i
$634$	−273.170	−	816.830i	−0.430867	−	1.28838i
$635$	−1092.47	+	412.873i	−1.72043	+	0.650193i
$636$	662.113	+	879.210i	1.04106	+	1.38241i
$637$	−194.117			−0.304737
$638$	198.302	−	66.3173i	0.310818	−	0.103946i
$639$		−	95.7673i		−	0.149871i
$640$	−617.780	+	167.174i	−0.965282	+	0.261210i
$641$	−370.450			−0.577926			−0.288963	−	0.957340i	$-0.593310\pi$
$641$	−370.450			−0.577926			−0.288963	+	0.957340i	$0.593310\pi$
$642$	−35.1017	−	104.961i	−0.0546756	−	0.163491i
$643$			686.295i			1.06733i	0.845695	+	0.533667i	$0.179186\pi$
$643$			686.295i			1.06733i	−0.845695	+	0.533667i	$0.820814\pi$
$644$	71.4255	−	53.7889i	0.110909	−	0.0835232i
$645$	−54.6275	+	121.002i	−0.0846938	+	0.187601i
$646$	362.043	−	121.077i	0.560439	−	0.187426i
$647$	−499.985	−	499.985i	−0.772774	−	0.772774i	0.205817	−	0.978591i	$-0.434015\pi$
$647$	−499.985	−	499.985i	−0.772774	−	0.772774i	−0.978591	+	0.205817i	$0.934015\pi$
$648$	444.934	+	306.094i	0.686627	+	0.472367i
$649$	−326.258			−0.502708
$650$	−917.031	−	531.650i	−1.41082	−	0.817923i
$651$	−353.641	+	353.641i	−0.543227	+	0.543227i
$652$	293.993	+	390.389i	0.450910	+	0.598756i
$653$			599.129i			0.917502i	0.888565	+	0.458751i	$0.151703\pi$
$653$			599.129i			0.917502i	−0.888565	+	0.458751i	$0.848297\pi$
$654$	109.990	−	220.522i	0.168180	−	0.337189i
$655$	27.4238	+	72.5641i	0.0418684	+	0.110785i
$656$	−18.1838	−	5.22608i	−0.0277192	−	0.00796659i
$657$	22.2726	−	22.2726i	0.0339005	−	0.0339005i
$658$	323.093	+	966.112i	0.491023	+	1.46826i
$659$	−55.5691	+	55.5691i	−0.0843233	+	0.0843233i	−0.748010	−	0.663687i	$-0.768991\pi$
$659$	−55.5691	+	55.5691i	−0.0843233	+	0.0843233i	0.663687	+	0.748010i	$0.268991\pi$
$660$	−197.555	−	124.959i	−0.299325	−	0.189332i
$661$	24.3517	−	24.3517i	0.0368407	−	0.0368407i	−0.688446	−	0.725287i	$-0.741707\pi$
$661$	24.3517	−	24.3517i	0.0368407	−	0.0368407i	0.725287	+	0.688446i	$0.241707\pi$
$662$	9.37681	+	4.67689i	0.0141644	+	0.00706478i
$663$	−392.109	+	392.109i	−0.591416	+	0.591416i
$664$	346.802	−	504.108i	0.522293	−	0.759199i
$665$	−703.315	−	317.517i	−1.05762	−	0.477470i
$666$	162.173	−	54.2348i	0.243502	−	0.0814336i
$667$		−	72.7147i		−	0.109018i
$668$	572.575	+	80.6477i	0.857149	+	0.120730i
$669$	−250.069	+	250.069i	−0.373795	+	0.373795i
$670$	−110.338	+	1085.15i	−0.164684	+	1.61962i
$671$	−72.1498			−0.107526
$672$	457.601	−	498.623i	0.680954	−	0.741998i
$673$	−348.271	−	348.271i	−0.517490	−	0.517490i	0.399321	−	0.916811i	$-0.369246\pi$
$673$	−348.271	−	348.271i	−0.517490	−	0.517490i	−0.916811	+	0.399321i	$0.869246\pi$
$674$	−572.621	−	285.607i	−0.849586	−	0.423749i
$675$	−536.086	+	472.717i	−0.794201	+	0.700321i
$676$	896.079	−	674.817i	1.32556	−	0.998250i
$677$			780.155i			1.15237i	0.817319	+	0.576185i	$0.195459\pi$
$677$			780.155i			1.15237i	−0.817319	+	0.576185i	$0.804541\pi$
$678$	338.198	+	168.684i	0.498818	+	0.248796i
$679$	−92.0950			−0.135633
$680$	−366.342	−	90.1403i	−0.538739	−	0.132559i
$681$		−	959.715i		−	1.40927i
$682$	−178.366	−	88.9640i	−0.261534	−	0.130446i
$683$	170.375			0.249451			0.124725	−	0.992191i	$-0.460195\pi$
$683$	170.375			0.249451			0.124725	+	0.992191i	$0.460195\pi$
$684$	−14.7779	+	104.919i	−0.0216052	+	0.153390i
$685$	−305.974	−	809.616i	−0.446677	−	1.18192i
$686$	−543.807	−	271.235i	−0.792722	−	0.395387i
$687$	−203.770	+	203.770i	−0.296609	+	0.296609i
$688$	42.3142	−	147.229i	0.0615032	−	0.213996i
$689$		−	2103.41i		−	3.05285i
$690$	−63.0010	+	51.3716i	−0.0913059	+	0.0744516i
$691$	−51.2626	−	51.2626i	−0.0741861	−	0.0741861i	0.669040	−	0.743226i	$-0.266705\pi$
$691$	−51.2626	−	51.2626i	−0.0741861	−	0.0741861i	−0.743226	+	0.669040i	$0.766705\pi$
$692$	−348.836	−	463.214i	−0.504098	−	0.669384i
$693$	−42.0668			−0.0607025
$694$	439.828	−	147.090i	0.633758	−	0.211946i
$695$	408.747	+	1081.56i	0.588125	+	1.55620i
$696$	−100.052	−	541.208i	−0.143752	−	0.777597i
$697$	−7.88633	−	7.88633i	−0.0113147	−	0.0113147i
$698$	521.141	+	259.930i	0.746620	+	0.372393i
$699$	240.717	+	240.717i	0.344374	+	0.344374i
$700$	419.668	+	636.745i	0.599526	+	0.909635i
$701$	68.3903	+	68.3903i	0.0975610	+	0.0975610i	0.754203	−	0.656642i	$-0.228024\pi$
$701$	68.3903	+	68.3903i	0.0975610	+	0.0975610i	−0.656642	+	0.754203i	$0.728024\pi$
$702$	−384.460	−	1149.61i	−0.547663	−	1.63762i
$703$	−934.792	−	934.792i	−1.32972	−	1.32972i
$704$	246.306	+	109.932i	0.349866	+	0.156153i
$705$	−327.416	−	866.352i	−0.464420	−	1.22887i
$706$	378.144	−	758.152i	0.535615	−	1.07387i
$707$	−701.142			−0.991714
$708$	−119.775	+	850.371i	−0.169174	+	1.20109i
$709$	815.622	+	815.622i	1.15038	+	1.15038i	0.986476	+	0.163908i	$0.0524101\pi$
$709$	815.622	+	815.622i	1.15038	+	1.15038i	0.163908	+	0.986476i	$0.447590\pi$
$710$	727.920	+	74.0151i	1.02524	+	0.104247i
$711$		−	2.81577i		−	0.00396030i
$712$	255.265	+	175.610i	0.358518	+	0.246643i
$713$	−49.0133	+	49.0133i	−0.0687424	+	0.0687424i
$714$	378.350	−	126.530i	0.529902	−	0.177213i
$715$	157.929	+	417.885i	0.220880	+	0.584454i
$716$	56.1313	−	398.516i	0.0783957	−	0.556587i
$717$	567.946			0.792114
$718$	−69.0420	−	206.449i	−0.0961588	−	0.287534i
$719$		−	125.050i		−	0.173922i	−0.996212	−	0.0869612i	$-0.972284\pi$
$719$		−	125.050i		−	0.173922i	0.996212	−	0.0869612i	$-0.0277156\pi$
$720$	67.7702	−	79.8214i	0.0941252	−	0.110863i
$721$	−354.864			−0.492183
$722$	92.1131	−	30.8051i	0.127581	−	0.0426663i
$723$			274.224i			0.379286i
$724$	152.237	−	1080.84i	0.210273	−	1.49288i
$725$	618.958	+	38.8804i	0.853735	+	0.0536282i
$726$	−181.612	−	543.056i	−0.250155	−	0.748011i
$727$	307.763	+	307.763i	0.423333	+	0.423333i	0.886350	−	0.463016i	$-0.153233\pi$
$727$	307.763	+	307.763i	0.423333	+	0.423333i	−0.463016	+	0.886350i	$0.653233\pi$
$728$	−1271.82	+	235.119i	−1.74701	+	0.322966i
$729$	−801.940			−1.10005
$730$	152.079	+	186.506i	0.208327	+	0.255488i
$731$	63.8535	−	63.8535i	0.0873510	−	0.0873510i
$732$	−26.4876	+	188.054i	−0.0361852	+	0.256905i
$733$		−	94.8581i		−	0.129411i	−0.997904	−	0.0647054i	$-0.979389\pi$
$733$		−	94.8581i		−	0.129411i	0.997904	−	0.0647054i	$-0.0206108\pi$
$734$	687.350	+	342.830i	0.936444	+	0.467071i
$735$	−115.722	−	52.2434i	−0.157444	−	0.0710795i
$736$	63.4219	−	69.1073i	0.0861710	−	0.0938959i
$737$	325.049	−	325.049i	0.441044	−	0.441044i
$738$	2.93567	−	0.981765i	0.00397787	−	0.00133030i
$739$	761.284	−	761.284i	1.03015	−	1.03015i	0.0306228	−	0.999531i	$-0.490251\pi$
$739$	761.284	−	761.284i	1.03015	−	1.03015i	0.999531	−	0.0306228i	$-0.00974907\pi$
$740$	286.898	+	1274.58i	0.387699	+	1.72240i
$741$	−841.348	+	841.348i	−1.13542	+	1.13542i
$742$	−675.427	+	1354.18i	−0.910279	+	1.82504i
$743$	700.467	−	700.467i	0.942754	−	0.942754i	−0.0556935	−	0.998448i	$-0.517737\pi$
$743$	700.467	−	700.467i	0.942754	−	0.942754i	0.998448	+	0.0556935i	$0.0177370\pi$
$744$	−297.361	+	432.241i	−0.399679	+	0.580969i
$745$	457.348	+	1210.16i	0.613890	+	1.62437i
$746$	130.502	+	390.227i	0.174936	+	0.523092i
$747$			100.110i			0.134016i
$748$	95.6490	+	127.011i	0.127873	+	0.169800i
$749$	107.599	−	107.599i	0.143657	−	0.143657i
$750$	−403.596	−	563.742i	−0.538128	−	0.751656i
$751$	268.325			0.357291			0.178645	−	0.983914i	$-0.442829\pi$
$751$	268.325			0.357291			0.178645	+	0.983914i	$0.442829\pi$
$752$	517.529	+	934.986i	0.688203	+	1.24333i
$753$	−106.320	−	106.320i	−0.141195	−	0.141195i
$754$	−469.463	+	941.239i	−0.622630	+	1.24833i
$755$	−205.948	+	456.184i	−0.272779	+	0.604217i
$756$	−121.635	+	863.574i	−0.160893	+	1.14229i
$757$			777.969i			1.02770i	0.857880	+	0.513850i	$0.171781\pi$
$757$			777.969i			1.02770i	−0.857880	+	0.513850i	$0.828219\pi$
$758$	−184.912	+	370.736i	−0.243948	+	0.489097i
$759$	34.2596			0.0451378
$760$	−786.062	−	193.414i	−1.03429	−	0.254492i
$761$		−	1058.98i		−	1.39156i	−0.718254	−	0.695781i	$-0.755058\pi$
$761$		−	1058.98i		−	1.39156i	0.718254	−	0.695781i	$-0.244942\pi$
$762$	578.250	−	1159.35i	0.758858	−	1.52146i
$763$	338.819			0.444062
$764$	669.595	−	504.257i	0.876433	−	0.660022i
$765$	57.7392	−	21.8211i	0.0754760	−	0.0285243i
$766$	−98.2799	+	197.044i	−0.128303	+	0.257238i
$767$	1160.49	−	1160.49i	1.51302	−	1.51302i
$768$	376.954	−	601.624i	0.490825	−	0.783364i
$769$			262.583i			0.341461i	0.985318	+	0.170730i	$0.0546127\pi$
$769$			262.583i			0.341461i	−0.985318	+	0.170730i	$0.945387\pi$
$770$	32.5119	−	319.747i	0.0422233	−	0.415256i
$771$	461.699	+	461.699i	0.598832	+	0.598832i
$772$	505.649	+	71.2211i	0.654986	+	0.0922553i
$773$	−405.962			−0.525177			−0.262588	−	0.964908i	$-0.584576\pi$
$773$	−405.962			−0.525177			−0.262588	+	0.964908i	$0.584576\pi$
$774$	7.94909	+	23.7693i	0.0102701	+	0.0307097i
$775$	−391.001	−	443.416i	−0.504518	−	0.572150i
$776$	−95.0013	+	17.5627i	−0.122424	+	0.0226323i
$777$	−976.895	−	976.895i	−1.25727	−	1.25727i
$778$	−115.291	+	231.150i	−0.148189	+	0.297108i
$779$	−16.9217	−	16.9217i	−0.0217224	−	0.0217224i
$780$	1147.17	−	258.219i	1.47073	−	0.331050i
$781$	−218.044	−	218.044i	−0.279185	−	0.279185i
$782$	52.4380	−	17.5366i	0.0670562	−	0.0224254i
$783$	501.496	+	501.496i	0.640480	+	0.640480i
$784$	140.804	+	40.4675i	0.179597	+	0.0516168i
$785$	127.087	+	57.3742i	0.161894	+	0.0730882i
$786$	−77.0061	−	38.4085i	−0.0979722	−	0.0488657i
$787$	107.060			0.136036			0.0680181	−	0.997684i	$-0.478332\pi$
$787$	107.060			0.136036			0.0680181	+	0.997684i	$0.478332\pi$
$788$	163.228	+	216.747i	0.207142	+	0.275060i
$789$	218.285	+	218.285i	0.276660	+	0.276660i
$790$	21.4025	+	2.17621i	0.0270918	+	0.00275470i
$791$			519.622i			0.656918i
$792$	−43.3944	+	8.02221i	−0.0547909	+	0.0101291i
$793$	256.634	−	256.634i	0.323624	−	0.323624i
$794$	−115.269	−	344.675i	−0.145174	−	0.434100i
$795$	566.099	−	1253.93i	0.712074	−	1.57728i
$796$	−890.751	+	670.804i	−1.11903	+	0.842719i
$797$	−615.958			−0.772846			−0.386423	−	0.922322i	$-0.626289\pi$
$797$	−615.958			−0.772846			−0.386423	+	0.922322i	$0.626289\pi$
$798$	811.827	−	271.496i	1.01733	−	0.340221i
$799$			629.957i			0.788432i
$800$	554.340	+	576.808i	0.692925	+	0.721010i
$801$	−50.6924			−0.0632864
$802$	−354.713	−	1060.66i	−0.442285	−	1.32252i
$803$		−	101.421i		−	0.126303i
$804$	−727.889	−	966.553i	−0.905335	−	1.20218i
$805$	−101.867	−	45.9889i	−0.126543	−	0.0571290i
$806$	950.883	−	318.000i	1.17976	−	0.394542i
$807$	272.517	+	272.517i	0.337692	+	0.337692i
$808$	−723.269	+	133.709i	−0.895135	+	0.165481i
$809$	304.293			0.376135			0.188067	−	0.982156i	$-0.439778\pi$
$809$	304.293			0.376135			0.188067	+	0.982156i	$0.439778\pi$
$810$	68.2890	−	671.606i	0.0843074	−	0.829144i
$811$	−20.2059	+	20.2059i	−0.0249148	+	0.0249148i	−0.719454	−	0.694540i	$-0.755608\pi$
$811$	−20.2059	+	20.2059i	−0.0249148	+	0.0249148i	0.694540	+	0.719454i	$0.255608\pi$
$812$	604.482	−	455.222i	0.744436	−	0.560618i
$813$		−	321.610i		−	0.395584i
$814$	245.754	−	492.718i	0.301909	−	0.605305i
$815$	251.360	−	556.775i	0.308418	−	0.683159i
$816$	366.161	−	202.675i	0.448726	−	0.248377i
$817$	137.011	−	137.011i	0.167700	−	0.167700i
$818$	−459.433	−	1373.79i	−0.561654	−	1.67945i
$819$	149.630	−	149.630i	0.182699	−	0.182699i
$820$	5.19346	+	23.0726i	0.00633348	+	0.0281373i
$821$	−381.316	+	381.316i	−0.464453	+	0.464453i	−0.900112	−	0.435659i	$-0.856515\pi$
$821$	−381.316	+	381.316i	−0.464453	+	0.464453i	0.435659	+	0.900112i	$0.356515\pi$
$822$	859.176	+	428.533i	1.04523	+	0.521329i
$823$	420.324	−	420.324i	0.510721	−	0.510721i	−0.404026	−	0.914747i	$-0.632390\pi$
$823$	420.324	−	420.324i	0.510721	−	0.510721i	0.914747	+	0.404026i	$0.132390\pi$
$824$	−366.063	+	67.6731i	−0.444251	+	0.0821276i
$825$	−18.3185	+	291.622i	−0.0222043	+	0.353482i
$826$	−1119.77	+	374.479i	−1.35565	+	0.453365i
$827$			844.006i			1.02056i	0.860007	+	0.510281i	$0.170459\pi$
$827$			844.006i			1.02056i	−0.860007	+	0.510281i	$0.829541\pi$
$828$	−2.14042	+	15.1964i	−0.00258505	+	0.0183531i
$829$	−222.833	+	222.833i	−0.268798	+	0.268798i	−0.828616	−	0.559818i	$-0.810871\pi$
$829$	−222.833	+	222.833i	−0.268798	+	0.268798i	0.559818	+	0.828616i	$0.310871\pi$
$830$	−760.926	−	77.3711i	−0.916779	−	0.0932182i
$831$	944.609			1.13671
$832$	−1267.12	+	485.078i	−1.52298	+	0.583026i
$833$	61.0668	+	61.0668i	0.0733095	+	0.0733095i
$834$	−1147.76	−	572.471i	−1.37622	−	0.686417i
$835$	−255.519	−	676.111i	−0.306011	−	0.809714i
$836$	205.234	+	272.527i	0.245496	+	0.325990i
$837$		−	676.067i		−	0.807726i
$838$	193.540	+	96.5320i	0.230954	+	0.115193i
$839$	−554.445			−0.660841			−0.330420	−	0.943834i	$-0.607191\pi$
$839$	−554.445			−0.660841			−0.330420	+	0.943834i	$0.607191\pi$
$840$	−821.466	−	202.126i	−0.977936	−	0.240626i
$841$			225.607i			0.268260i
$842$	1191.38	+	594.225i	1.41494	+	0.705730i
$843$	287.150			0.340628
$844$	148.715	+	20.9466i	0.176203	+	0.0248183i
$845$	−1277.99	−	576.960i	−1.51242	−	0.682793i
$846$	−156.462	−	78.0386i	−0.184943	−	0.0922442i
$847$	556.705	−	556.705i	0.657267	−	0.657267i
$848$	−438.498	+	1525.72i	−0.517096	+	1.79920i
$849$			1558.55i			1.83575i
$850$	121.236	+	455.736i	0.142630	+	0.536160i
$851$	−135.394	−	135.394i	−0.159100	−	0.159100i
$852$	−648.366	+	488.270i	−0.760993	+	0.573087i
$853$	431.993			0.506440			0.253220	−	0.967409i	$-0.418510\pi$
$853$	431.993			0.506440			0.253220	+	0.967409i	$0.418510\pi$
$854$	−247.629	+	82.8137i	−0.289964	+	0.0969715i
$855$	123.891	−	46.8215i	0.144902	−	0.0547620i
$856$	90.4754	−	131.514i	0.105696	−	0.153638i
$857$	−457.844	−	457.844i	−0.534241	−	0.534241i	0.387591	−	0.921831i	$-0.373307\pi$
$857$	−457.844	−	457.844i	−0.534241	−	0.534241i	−0.921831	+	0.387591i	$0.873307\pi$
$858$	−443.465	−	221.188i	−0.516859	−	0.257795i
$859$	−822.277	−	822.277i	−0.957249	−	0.957249i	0.0418737	−	0.999123i	$-0.486667\pi$
$859$	−822.277	−	822.277i	−0.957249	−	0.957249i	−0.999123	+	0.0418737i	$0.986667\pi$
$860$	−186.813	+	42.0501i	−0.217224	+	0.0488954i
$861$	−17.6839	−	17.6839i	−0.0205388	−	0.0205388i
$862$	117.418	+	351.102i	0.136216	+	0.407311i
$863$	132.089	+	132.089i	0.153058	+	0.153058i	0.779482	−	0.626424i	$-0.215482\pi$
$863$	132.089	+	132.089i	0.153058	+	0.153058i	−0.626424	+	0.779482i	$0.715482\pi$
$864$	39.2113	+	914.023i	0.0453835	+	1.05790i
$865$	−298.251	+	660.638i	−0.344798	+	0.763744i
$866$	448.102	−	898.412i	0.517439	−	1.03743i
$867$	−554.775			−0.639879
$868$	−714.293	−	100.609i	−0.822919	−	0.115909i
$869$	−6.41098	−	6.41098i	−0.00737742	−	0.00737742i
$870$	−533.185	+	434.764i	−0.612857	+	0.499729i
$871$			2312.37i			2.65485i
$872$	349.511	−	64.6133i	0.400816	−	0.0740978i
$873$	11.1769	−	11.1769i	0.0128029	−	0.0128029i
$874$	112.516	−	37.6284i	0.128737	−	0.0430531i
$875$	445.932	−	842.520i	0.509637	−	0.962880i
$876$	−264.348	−	37.2336i	−0.301767	−	0.0425041i
$877$	363.488			0.414468			0.207234	−	0.978291i	$-0.433554\pi$
$877$	363.488			0.414468			0.207234	+	0.978291i	$0.433554\pi$
$878$	−98.7761	−	295.360i	−0.112501	−	0.336401i
$879$			5.29476i			0.00602362i
$880$	−27.4384	−	336.038i	−0.0311800	−	0.381861i
$881$	−242.827			−0.275627			−0.137813	−	0.990458i	$-0.544007\pi$
$881$	−242.827			−0.275627			−0.137813	+	0.990458i	$0.544007\pi$
$882$	−22.7320	+	7.60218i	−0.0257732	+	0.00861925i
$883$			1629.94i			1.84592i	0.384899	+	0.922959i	$0.374236\pi$
$883$			1629.94i			1.84592i	−0.384899	+	0.922959i	$0.625764\pi$
$884$	−791.992	−	111.553i	−0.895918	−	0.126191i
$885$	1004.14	−	379.489i	1.13462	−	0.428801i
$886$	−462.389	−	1382.63i	−0.521884	−	1.56053i
$887$	−196.533	−	196.533i	−0.221570	−	0.221570i	0.587589	−	0.809160i	$-0.300077\pi$
$887$	−196.533	−	196.533i	−0.221570	−	0.221570i	−0.809160	+	0.587589i	$0.800077\pi$
$888$	−1194.02	−	821.429i	−1.34462	−	0.925032i
$889$	1781.27			2.00368
$890$	39.1783	−	385.310i	0.0440206	−	0.432932i
$891$	−201.175	+	201.175i	−0.225786	+	0.225786i
$892$	−505.096	−	71.1431i	−0.566251	−	0.0797569i
$893$			1351.70i			1.51366i
$894$	−1284.24	−	640.540i	−1.43651	−	0.716488i
$895$	−470.578	+	177.843i	−0.525786	+	0.198707i
$896$	971.539	+	94.5917i	1.08431	+	0.105571i
$897$	−121.860	+	121.860i	−0.135853	+	0.135853i
$898$	−89.0455	+	29.7792i	−0.0991598	+	0.0331617i
$899$	−414.806	+	414.806i	−0.461408	+	0.461408i
$900$	−128.209	−	26.3450i	−0.142455	−	0.0292723i
$901$	−661.707	+	661.707i	−0.734414	+	0.734414i
$902$	4.44867	−	8.91925i	0.00493200	−	0.00988830i
$903$	143.182	−	143.182i	0.158562	−	0.158562i
$904$	99.0927	+	536.020i	0.109616	+	0.592943i
$905$	−1276.29	+	482.340i	−1.41026	+	0.532972i
$906$	−176.098	−	526.567i	−0.194368	−	0.581199i
$907$			188.488i			0.207814i	0.994587	+	0.103907i	$0.0331345\pi$
$907$			188.488i			0.207814i	−0.994587	+	0.103907i	$0.966866\pi$
$908$	1105.75	−	832.713i	1.21778	−	0.917085i
$909$	85.0925	−	85.0925i	0.0936112	−	0.0936112i
$910$	1021.68	+	1252.97i	1.12273	+	1.37689i
$911$	1051.06			1.15374			0.576870	−	0.816836i	$-0.304274\pi$
$911$	1051.06			1.15374			0.576870	+	0.816836i	$0.304274\pi$
$912$	785.672	−	434.881i	0.861482	−	0.476843i
$913$	227.930	+	227.930i	0.249650	+	0.249650i
$914$	−287.118	+	575.650i	−0.314133	+	0.629814i
$915$	222.059	−	83.9216i	0.242687	−	0.0917176i
$916$	−411.581	−	57.9715i	−0.449324	−	0.0632877i
$917$		−	118.315i		−	0.129024i
$918$	−240.706	+	482.598i	−0.262207	+	0.525706i
$919$	−158.471			−0.172439			−0.0862195	−	0.996276i	$-0.527479\pi$
$919$	−158.471			−0.172439			−0.0862195	+	0.996276i	$0.527479\pi$
$920$	−113.852	−	28.0139i	−0.123752	−	0.0304499i
$921$			1291.01i			1.40175i
$922$	−335.639	+	672.931i	−0.364033	+	0.729860i
$923$	1551.15			1.68055
$924$	214.478	+	284.802i	0.232119	+	0.308227i
$925$	1224.89	−	1080.10i	1.32420	−	1.16768i
$926$	−1.47276	+	2.95277i	−0.00159045	+	0.00318874i
$927$	43.0673	−	43.0673i	0.0464588	−	0.0464588i
$928$	536.747	−	584.864i	0.578391	−	0.630241i
$929$			1081.59i			1.16425i	0.813100	+	0.582124i	$0.197778\pi$
$929$			1081.59i			1.16425i	−0.813100	+	0.582124i	$0.802222\pi$
$930$	652.446	+	66.3408i	0.701555	+	0.0713342i
$931$	131.031	+	131.031i	0.140743	+	0.140743i
$932$	−68.4827	+	486.207i	−0.0734793	+	0.521682i
$933$	−588.978			−0.631273
$934$	401.109	+	1199.39i	0.429453	+	1.28415i
$935$	81.7787	−	181.144i	0.0874639	−	0.193736i
$936$	125.817	−	182.887i	0.134420	−	0.195392i
$937$	−484.345	−	484.345i	−0.516910	−	0.516910i	0.399725	−	0.916635i	$-0.369106\pi$
$937$	−484.345	−	484.345i	−0.516910	−	0.516910i	−0.916635	+	0.399725i	$0.869106\pi$
$938$	742.526	−	1488.71i	0.791605	−	1.58711i
$939$	127.656	+	127.656i	0.135949	+	0.135949i
$940$	714.089	−	1128.94i	0.759669	−	1.20100i
$941$	555.577	+	555.577i	0.590411	+	0.590411i	0.937742	−	0.347331i	$-0.112912\pi$
$941$	555.577	+	555.577i	0.590411	+	0.590411i	−0.347331	+	0.937742i	$0.612912\pi$
$942$	−146.694	+	49.0584i	−0.155726	+	0.0520790i
$943$	−2.45092	−	2.45092i	−0.00259907	−	0.00259907i
$944$	−1083.69	+	599.838i	−1.14798	+	0.635422i
$945$	1019.73	−	385.381i	1.07908	−	0.407811i
$946$	72.2168	+	36.0197i	0.0763391	+	0.0380758i
$947$	−476.289			−0.502945			−0.251473	−	0.967864i	$-0.580915\pi$
$947$	−476.289			−0.502945			−0.251473	+	0.967864i	$0.580915\pi$
$948$	−19.0634	+	14.3562i	−0.0201091	+	0.0151437i
$949$	360.750	+	360.750i	0.380137	+	0.380137i
$950$	260.136	+	977.875i	0.273828	+	1.02934i
$951$		−	1194.31i		−	1.25585i
$952$	474.065	+	326.134i	0.497967	+	0.342578i
$953$	80.9782	−	80.9782i	0.0849719	−	0.0849719i	−0.663343	−	0.748315i	$-0.730863\pi$
$953$	80.9782	−	80.9782i	0.0849719	−	0.0849719i	0.748315	+	0.663343i	$0.230863\pi$
$954$	−82.3755	−	246.319i	−0.0863475	−	0.258196i
$955$	−954.980	−	431.134i	−0.999979	−	0.451449i
$956$	492.788	+	654.365i	0.515468	+	0.684482i
$957$	289.943			0.302971
$958$	−1047.79	+	350.408i	−1.09373	+	0.365771i
$959$			1320.07i			1.37651i
$960$	−885.936	−	51.8495i	−0.922850	−	0.0540099i
$961$	−401.801			−0.418107
$962$	878.443	+	2626.71i	0.913142	+	2.73047i
$963$			26.1170i			0.0271205i
$964$	−315.950	+	237.935i	−0.327749	+	0.246820i
$965$	−225.652	−	597.083i	−0.233837	−	0.618739i
$966$	117.584	−	39.3232i	0.121723	−	0.0407073i
$967$	−226.347	−	226.347i	−0.234072	−	0.234072i	0.580318	−	0.814390i	$-0.302928\pi$
$967$	−226.347	−	226.347i	−0.234072	−	0.234072i	−0.814390	+	0.580318i	$0.802928\pi$
$968$	468.109	−	680.438i	0.483584	−	0.702932i
$969$	529.355			0.546290
$970$	76.3166	+	93.5931i	0.0786769	+	0.0964877i
$971$	−375.576	+	375.576i	−0.386793	+	0.386793i	−0.873542	−	0.486749i	$-0.838183\pi$
$971$	−375.576	+	375.576i	−0.386793	+	0.386793i	0.486749	+	0.873542i	$0.338183\pi$
$972$	−168.655	−	223.954i	−0.173513	−	0.230406i
$973$		−	1763.47i		−	1.81241i
$974$	360.203	−	722.180i	0.369818	−	0.741458i
$975$	−972.131	−	1102.45i	−0.997058	−	1.13072i
$976$	−239.651	+	132.650i	−0.245544	+	0.135912i
$977$	201.023	−	201.023i	0.205756	−	0.205756i	−0.596705	−	0.802461i	$-0.703524\pi$
$977$	201.023	−	201.023i	0.205756	−	0.205756i	0.802461	+	0.596705i	$0.203524\pi$
$978$	214.928	+	642.677i	0.219763	+	0.657134i
$979$	−115.417	+	115.417i	−0.117893	+	0.117893i
$980$	−40.2149	−	178.660i	−0.0410356	−	0.182306i
$981$	−41.1200	+	41.1200i	−0.0419164	+	0.0419164i
$982$	−1563.77	−	779.966i	−1.59244	−	0.794263i
$983$	536.933	−	536.933i	0.546218	−	0.546218i	−0.379126	−	0.925345i	$-0.623775\pi$
$983$	536.933	−	536.933i	0.546218	−	0.546218i	0.925345	+	0.379126i	$0.123775\pi$
$984$	−21.6143	−	14.8696i	−0.0219658	−	0.0151114i
$985$	139.558	−	309.126i	0.141683	−	0.313834i
$986$	443.789	−	148.415i	0.450090	−	0.150522i
$987$			1412.58i			1.43119i
$988$	−1699.38	−	239.359i	−1.72002	−	0.242266i
$989$	19.8445	−	19.8445i	0.0200652	−	0.0200652i
$990$	34.8597	+	42.7512i	0.0352118	+	0.0431830i
$991$	−1164.95			−1.17553			−0.587764	−	0.809032i	$-0.699992\pi$
$991$	−1164.95			−1.17553			−0.587764	+	0.809032i	$0.699992\pi$
$992$	−756.021	+	32.4331i	−0.762118	+	0.0326947i
$993$	10.2742	+	10.2742i	0.0103466	+	0.0103466i
$994$	−998.631	−	498.088i	−1.00466	−	0.501095i
$995$	1270.39	+	573.530i	1.27678	+	0.576412i
$996$	677.765	−	510.410i	0.680487	−	0.512459i
$997$		−	1493.41i		−	1.49790i	−0.662627	−	0.748950i	$-0.730558\pi$
$997$		−	1493.41i		−	1.49790i	0.662627	−	0.748950i	$-0.269442\pi$
$998$	−1089.84	−	543.580i	−1.09202	−	0.544669i
$999$	1867.56			1.86943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.i.a.13.14	✓	44
4.3	odd	2		320.3.i.a.273.7		44
5.2	odd	4		80.3.t.a.77.4	yes	44
5.3	odd	4		400.3.t.b.157.19		44
5.4	even	2		400.3.i.b.93.9		44
8.3	odd	2		640.3.i.a.33.16		44
8.5	even	2		640.3.i.b.33.7		44
16.3	odd	4		640.3.t.a.353.16		44
16.5	even	4		80.3.t.a.53.4	yes	44
16.11	odd	4		320.3.t.a.113.7		44
16.13	even	4		640.3.t.b.353.7		44
20.7	even	4		320.3.t.a.17.7		44
40.27	even	4		640.3.t.a.417.16		44
40.37	odd	4		640.3.t.b.417.7		44
80.27	even	4		320.3.i.a.177.16		44
80.37	odd	4	inner	80.3.i.a.37.14	yes	44
80.53	odd	4		400.3.i.b.357.9		44
80.67	even	4		640.3.i.a.97.7		44
80.69	even	4		400.3.t.b.293.19		44
80.77	odd	4		640.3.i.b.97.16		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.14	✓	44	1.1	even	1	trivial
80.3.i.a.37.14	yes	44	80.37	odd	4	inner
80.3.t.a.53.4	yes	44	16.5	even	4
80.3.t.a.77.4	yes	44	5.2	odd	4
320.3.i.a.177.16		44	80.27	even	4
320.3.i.a.273.7		44	4.3	odd	2
320.3.t.a.17.7		44	20.7	even	4
320.3.t.a.113.7		44	16.11	odd	4
400.3.i.b.93.9		44	5.4	even	2
400.3.i.b.357.9		44	80.53	odd	4
400.3.t.b.157.19		44	5.3	odd	4
400.3.t.b.293.19		44	80.69	even	4
640.3.i.a.33.16		44	8.3	odd	2
640.3.i.a.97.7		44	80.67	even	4
640.3.i.b.33.7		44	8.5	even	2
640.3.i.b.97.16		44	80.77	odd	4
640.3.t.a.353.16		44	16.3	odd	4
640.3.t.a.417.16		44	40.27	even	4
640.3.t.b.353.7		44	16.13	even	4
640.3.t.b.417.7		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)

\(f(q)\)	\(=\)	\(q+(0.634321 + 1.89674i) q^{2} +2.77329i q^{3} +(-3.19527 + 2.40629i) q^{4} +(4.55712 + 2.05735i) q^{5} +(-5.26021 + 1.75915i) q^{6} +(-5.39242 - 5.39242i) q^{7} +(-6.59094 - 4.53426i) q^{8} +1.30888 q^{9} +O(q^{10})\)	\(q+(0.634321 + 1.89674i) q^{2} +2.77329i q^{3} +(-3.19527 + 2.40629i) q^{4} +(4.55712 + 2.05735i) q^{5} +(-5.26021 + 1.75915i) q^{6} +(-5.39242 - 5.39242i) q^{7} +(-6.59094 - 4.53426i) q^{8} +1.30888 q^{9} +(-1.01159 + 9.94870i) q^{10} +(2.98007 - 2.98007i) q^{11} +(-6.67333 - 8.86141i) q^{12} +21.2000i q^{13} +(6.80752 - 13.6486i) q^{14} +(-5.70562 + 12.6382i) q^{15} +(4.41955 - 15.3775i) q^{16} +(6.66924 - 6.66924i) q^{17} +(0.830250 + 2.48261i) q^{18} +(14.3102 - 14.3102i) q^{19} +(-19.5118 + 4.39195i) q^{20} +(14.9547 - 14.9547i) q^{21} +(7.54275 + 3.76211i) q^{22} +(2.07267 - 2.07267i) q^{23} +(12.5748 - 18.2786i) q^{24} +(16.5346 + 18.7512i) q^{25} +(-40.2109 + 13.4476i) q^{26} +28.5895i q^{27} +(30.2060 + 4.25454i) q^{28} +(17.5413 - 17.5413i) q^{29} +(-27.5906 - 2.80542i) q^{30} -23.6474 q^{31} +(31.9706 - 1.37153i) q^{32} +(8.26459 + 8.26459i) q^{33} +(16.8803 + 8.41940i) q^{34} +(-13.4798 - 35.6680i) q^{35} +(-4.18223 + 3.14954i) q^{36} -65.3234i q^{37} +(36.2201 + 18.0655i) q^{38} -58.7936 q^{39} +(-20.7072 - 34.2230i) q^{40} -1.18249i q^{41} +(37.8514 + 18.8792i) q^{42} +9.57434 q^{43} +(-2.35123 + 16.6930i) q^{44} +(5.96472 + 2.69282i) q^{45} +(5.24607 + 2.61659i) q^{46} +(-47.2286 + 47.2286i) q^{47} +(42.6462 + 12.2567i) q^{48} +9.15649i q^{49} +(-25.0779 + 43.2562i) q^{50} +(18.4957 + 18.4957i) q^{51} +(-51.0133 - 67.7397i) q^{52} -99.2178 q^{53} +(-54.2269 + 18.1349i) q^{54} +(19.7116 - 7.44949i) q^{55} +(11.0905 + 59.9918i) q^{56} +(39.6863 + 39.6863i) q^{57} +(44.3981 + 22.1445i) q^{58} +(-54.7400 - 54.7400i) q^{59} +(-12.1801 - 54.1119i) q^{60} +(-12.1054 - 12.1054i) q^{61} +(-15.0000 - 44.8531i) q^{62} +(-7.05803 - 7.05803i) q^{63} +(22.8811 + 59.7700i) q^{64} +(-43.6157 + 96.6108i) q^{65} +(-10.4334 + 20.9182i) q^{66} +109.074 q^{67} +(-5.26193 + 37.3582i) q^{68} +(5.74812 + 5.74812i) q^{69} +(59.1025 - 48.1927i) q^{70} -73.1674i q^{71} +(-8.62675 - 5.93479i) q^{72} +(17.0166 - 17.0166i) q^{73} +(123.902 - 41.4360i) q^{74} +(-52.0023 + 45.8553i) q^{75} +(-11.2905 + 80.1595i) q^{76} -32.1396 q^{77} +(-37.2940 - 111.516i) q^{78} -2.15129i q^{79} +(51.7773 - 60.9846i) q^{80} -67.5069 q^{81} +(2.24289 - 0.750081i) q^{82} +76.4850i q^{83} +(-11.7991 + 83.7699i) q^{84} +(44.1134 - 16.6716i) q^{85} +(6.07320 + 18.1601i) q^{86} +(48.6470 + 48.6470i) q^{87} +(-33.1539 + 6.12907i) q^{88} -38.7296 q^{89} +(-1.32404 + 13.0217i) q^{90} +(114.319 - 114.319i) q^{91} +(-1.63531 + 11.6102i) q^{92} -65.5810i q^{93} +(-119.539 - 59.6224i) q^{94} +(94.6543 - 35.7722i) q^{95} +(3.80365 + 88.6636i) q^{96} +(8.53929 - 8.53929i) q^{97} +(-17.3675 + 5.80816i) q^{98} +(3.90055 - 3.90055i) 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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