LMFDB - Embedded newform 80.3.t.a.77.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,3,Mod(53,80)]

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, 1, 3]))

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

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

chi := DirichletCharacter("80.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	80.t (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			77.4
Character	$\chi$	$=$	80.77
Dual form			80.3.t.a.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.89674 + 0.634321i) q^{2} +2.77329 q^{3} +(3.19527 - 2.40629i) q^{4} +(-2.05735 - 4.55712i) q^{5} +(-5.26021 + 1.75915i) q^{6} +(5.39242 - 5.39242i) q^{7} +(-4.53426 + 6.59094i) q^{8} -1.30888 q^{9} +O(q^{10})$	\(q+(-1.89674 + 0.634321i) q^{2} +2.77329 q^{3} +(3.19527 - 2.40629i) q^{4} +(-2.05735 - 4.55712i) q^{5} +(-5.26021 + 1.75915i) q^{6} +(5.39242 - 5.39242i) q^{7} +(-4.53426 + 6.59094i) q^{8} -1.30888 q^{9} +(6.79294 + 7.33867i) q^{10} +(2.98007 - 2.98007i) q^{11} +(8.86141 - 6.67333i) q^{12} +21.2000 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} +(2.48261 - 0.830250i) q^{18} +(-14.3102 + 14.3102i) q^{19} +(-17.5395 - 9.61066i) q^{20} +(14.9547 - 14.9547i) q^{21} +(-3.76211 + 7.54275i) 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} -28.5895 q^{27} +(4.25454 - 30.2060i) q^{28} +(-17.5413 + 17.5413i) q^{29} +(18.8388 + 20.3522i) q^{30} -23.6474 q^{31} +(1.37153 + 31.9706i) q^{32} +(8.26459 - 8.26459i) q^{33} +(-16.8803 - 8.41940i) q^{34} +(-35.6680 - 13.4798i) q^{35} +(-4.18223 + 3.14954i) q^{36} +65.3234 q^{37} +(18.0655 - 36.2201i) q^{38} +58.7936 q^{39} +(39.3642 + 7.10327i) q^{40} -1.18249i q^{41} +(-18.8792 + 37.8514i) q^{42} -9.57434i q^{43} +(2.35123 - 16.6930i) q^{44} +(2.69282 + 5.96472i) q^{45} +(5.24607 + 2.61659i) q^{46} +(-47.2286 - 47.2286i) q^{47} +(12.2567 - 42.6462i) q^{48} -9.15649i q^{49} +(19.4677 - 46.0544i) q^{50} +(18.4957 + 18.4957i) q^{51} +(67.7397 - 51.0133i) q^{52} +99.2178i 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} +(22.1445 - 44.3981i) q^{58} +(54.7400 + 54.7400i) q^{59} +(-48.6422 - 26.6531i) q^{60} +(-12.1054 - 12.1054i) q^{61} +(44.8531 - 15.0000i) 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} +109.074i q^{67} +(37.3582 + 5.26193i) q^{68} +(-5.74812 - 5.74812i) q^{69} +(76.2036 + 2.94280i) q^{70} -73.1674i q^{71} +(5.93479 - 8.62675i) q^{72} +(-17.0166 - 17.0166i) q^{73} +(-123.902 + 41.4360i) q^{74} +(-45.8553 + 52.0023i) q^{75} +(-11.2905 + 80.1595i) q^{76} -32.1396i q^{77} +(-111.516 + 37.2940i) q^{78} +2.15129i q^{79} +(-79.1696 + 11.4965i) q^{80} -67.5069 q^{81} +(0.750081 + 2.24289i) q^{82} +76.4850 q^{83} +(11.7991 - 83.7699i) q^{84} +(16.6716 - 44.1134i) q^{85} +(6.07320 + 18.1601i) q^{86} +(-48.6470 + 48.6470i) q^{87} +(6.12907 + 33.1539i) q^{88} +38.7296 q^{89} +(-8.89113 - 9.60543i) q^{90} +(114.319 - 114.319i) q^{91} +(-11.6102 - 1.63531i) q^{92} -65.5810 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} +(5.80816 + 17.3675i) q^{98} +(-3.90055 + 3.90055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} - 4 q^{3} - 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^3 - 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 + 108 * q^9	\( 44 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} + 108 q^{9} - 10 q^{10} - 4 q^{11} - 44 q^{12} - 4 q^{13} - 4 q^{15} + 24 q^{16} - 4 q^{17} - 42 q^{18} - 32 q^{19} - 44 q^{20} - 4 q^{21} + 16 q^{22} - 36 q^{24} - 52 q^{26} - 40 q^{27} - 104 q^{28} - 160 q^{30} - 8 q^{31} - 12 q^{32} - 4 q^{33} + 88 q^{34} - 4 q^{35} - 116 q^{36} - 4 q^{37} - 68 q^{38} - 72 q^{39} + 200 q^{40} + 244 q^{42} + 168 q^{44} - 70 q^{45} + 108 q^{46} - 4 q^{47} - 4 q^{48} + 206 q^{50} - 100 q^{51} + 264 q^{52} - 228 q^{54} - 172 q^{56} - 36 q^{57} + 332 q^{58} - 64 q^{59} + 364 q^{60} - 36 q^{61} + 84 q^{62} - 200 q^{63} + 176 q^{64} - 4 q^{65} + 276 q^{66} + 440 q^{68} + 60 q^{69} + 472 q^{70} - 288 q^{72} - 48 q^{73} - 284 q^{74} - 324 q^{75} + 252 q^{76} - 132 q^{78} - 588 q^{80} + 100 q^{81} - 388 q^{82} + 156 q^{83} - 288 q^{84} - 52 q^{85} + 20 q^{86} - 36 q^{87} + 160 q^{88} - 554 q^{90} + 188 q^{91} - 352 q^{92} - 40 q^{93} + 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 818 q^{98} + 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 + 108 * q^9 - 10 * q^10 - 4 * q^11 - 44 * q^12 - 4 * q^13 - 4 * q^15 + 24 * q^16 - 4 * q^17 - 42 * q^18 - 32 * q^19 - 44 * q^20 - 4 * q^21 + 16 * q^22 - 36 * q^24 - 52 * q^26 - 40 * q^27 - 104 * q^28 - 160 * q^30 - 8 * q^31 - 12 * q^32 - 4 * q^33 + 88 * q^34 - 4 * q^35 - 116 * q^36 - 4 * q^37 - 68 * q^38 - 72 * q^39 + 200 * q^40 + 244 * q^42 + 168 * q^44 - 70 * q^45 + 108 * q^46 - 4 * q^47 - 4 * q^48 + 206 * q^50 - 100 * q^51 + 264 * q^52 - 228 * q^54 - 172 * q^56 - 36 * q^57 + 332 * q^58 - 64 * q^59 + 364 * q^60 - 36 * q^61 + 84 * q^62 - 200 * q^63 + 176 * q^64 - 4 * q^65 + 276 * q^66 + 440 * q^68 + 60 * q^69 + 472 * q^70 - 288 * q^72 - 48 * q^73 - 284 * q^74 - 324 * q^75 + 252 * q^76 - 132 * q^78 - 588 * q^80 + 100 * q^81 - 388 * q^82 + 156 * q^83 - 288 * q^84 - 52 * q^85 + 20 * q^86 - 36 * q^87 + 160 * q^88 - 554 * q^90 + 188 * q^91 - 352 * q^92 - 40 * q^93 + 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 818 * q^98 + 92 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.89674	+	0.634321i	−0.948372	+	0.317161i
$2$	−1.89674	+	0.634321i	−0.948372	+	0.317161i
$3$	2.77329			0.924429			0.462215	−	0.886768i	$-0.347055\pi$
$3$	2.77329			0.924429			0.462215	+	0.886768i	$0.347055\pi$
$4$	3.19527	−	2.40629i	0.798818	−	0.601572i
$5$	−2.05735	−	4.55712i	−0.411470	−	0.911424i
$5$	−2.05735	−	4.55712i	−0.411470	−	0.911424i
$6$	−5.26021	+	1.75915i	−0.876702	+	0.293192i
$7$	5.39242	−	5.39242i	0.770346	−	0.770346i	−0.207821	−	0.978167i	$-0.566637\pi$
$7$	5.39242	−	5.39242i	0.770346	−	0.770346i	0.978167	+	0.207821i	$0.0666370\pi$
$8$	−4.53426	+	6.59094i	−0.566782	+	0.823868i
$9$	−1.30888			−0.145431
$10$	6.79294	+	7.33867i	0.679294	+	0.733867i
$11$	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	$0.188643\pi$
$12$	8.86141	−	6.67333i	0.738451	−	0.556111i
$13$	21.2000			1.63077			0.815383	−	0.578921i	$-0.196526\pi$
$13$	21.2000			1.63077			0.815383	+	0.578921i	$0.196526\pi$
$14$	−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	0.875509	−	0.483201i	$-0.160526\pi$
$17$	6.66924	+	6.66924i	0.392308	+	0.392308i	−0.483201	+	0.875509i	$0.660526\pi$
$18$	2.48261	−	0.830250i	0.137923	−	0.0461250i
$19$	−14.3102	+	14.3102i	−0.753169	+	0.753169i	−0.975069	−	0.221901i	$-0.928774\pi$
$19$	−14.3102	+	14.3102i	−0.753169	+	0.753169i	0.221901	+	0.975069i	$0.428774\pi$
$20$	−17.5395	−	9.61066i	−0.876977	−	0.480533i
$21$	14.9547	−	14.9547i	0.712131	−	0.712131i
$22$	−3.76211	+	7.54275i	−0.171005	+	0.342852i
$23$	−2.07267	−	2.07267i	−0.0901163	−	0.0901163i	0.660612	−	0.750728i	$-0.270297\pi$
$23$	−2.07267	−	2.07267i	−0.0901163	−	0.0901163i	−0.750728	+	0.660612i	$0.770297\pi$
$24$	−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
$27$	−28.5895			−1.05887
$28$	4.25454	−	30.2060i	0.151948	−	1.07879i
$29$	−17.5413	+	17.5413i	−0.604872	+	0.604872i	−0.941601	−	0.336730i	$-0.890679\pi$
$29$	−17.5413	+	17.5413i	−0.604872	+	0.604872i	0.336730	+	0.941601i	$0.390679\pi$
$30$	18.8388	+	20.3522i	0.627959	+	0.678407i
$31$	−23.6474			−0.762819			−0.381410	−	0.924406i	$-0.624561\pi$
$31$	−23.6474			−0.762819			−0.381410	+	0.924406i	$0.624561\pi$
$32$	1.37153	+	31.9706i	0.0428603	+	0.999081i
$33$	8.26459	−	8.26459i	0.250442	−	0.250442i
$34$	−16.8803	−	8.41940i	−0.496479	−	0.247629i
$35$	−35.6680	−	13.4798i	−1.01909	−	0.385138i
$36$	−4.18223	+	3.14954i	−0.116173	+	0.0874873i
$37$	65.3234			1.76550			0.882749	−	0.469845i	$-0.155690\pi$
$37$	65.3234			1.76550			0.882749	+	0.469845i	$0.155690\pi$
$38$	18.0655	−	36.2201i	0.475409	−	0.953159i
$39$	58.7936			1.50753
$40$	39.3642	+	7.10327i	0.984106	+	0.177582i
$41$		−	1.18249i		−	0.0288413i	−0.999896	−	0.0144207i	$-0.995410\pi$
$41$		−	1.18249i		−	0.0288413i	0.999896	−	0.0144207i	$-0.00459040\pi$
$42$	−18.8792	+	37.8514i	−0.449505	+	0.901224i
$43$		−	9.57434i		−	0.222659i	−0.993784	−	0.111330i	$-0.964489\pi$
$43$		−	9.57434i		−	0.222659i	0.993784	−	0.111330i	$-0.0355109\pi$
$44$	2.35123	−	16.6930i	0.0534370	−	0.379387i
$45$	2.69282	+	5.96472i	0.0598404	+	0.132549i
$46$	5.24607	+	2.61659i	0.114045	+	0.0568824i
$47$	−47.2286	−	47.2286i	−1.00486	−	1.00486i	−0.999988	−	0.00487524i	$-0.998448\pi$
$47$	−47.2286	−	47.2286i	−1.00486	−	1.00486i	−0.00487524	−	0.999988i	$-0.501552\pi$
$48$	12.2567	−	42.6462i	0.255347	−	0.888463i
$49$		−	9.15649i		−	0.186867i
$50$	19.4677	−	46.0544i	0.389355	−	0.921088i
$51$	18.4957	+	18.4957i	0.362661	+	0.362661i
$52$	67.7397	−	51.0133i	1.30269	−	0.981024i
$53$			99.2178i			1.87203i	0.351955	+	0.936017i	$0.385517\pi$
$53$			99.2178i			1.87203i	−0.351955	+	0.936017i	$0.614483\pi$
$54$	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
$58$	22.1445	−	44.3981i	0.381802	−	0.765485i
$59$	54.7400	+	54.7400i	0.927796	+	0.927796i	0.997563	−	0.0697673i	$-0.0222257\pi$
$59$	54.7400	+	54.7400i	0.927796	+	0.927796i	−0.0697673	+	0.997563i	$0.522226\pi$
$60$	−48.6422	−	26.6531i	−0.810703	−	0.444219i
$61$	−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	$0.794815\pi$
$62$	44.8531	−	15.0000i	0.723436	−	0.241936i
$63$	−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
$67$			109.074i			1.62798i	0.580882	+	0.813988i	$0.302708\pi$
$67$			109.074i			1.62798i	−0.580882	+	0.813988i	$0.697292\pi$
$68$	37.3582	+	5.26193i	0.549385	+	0.0773813i
$69$	−5.74812	−	5.74812i	−0.0833061	−	0.0833061i
$70$	76.2036	+	2.94280i	1.08862	+	0.0420400i
$71$		−	73.1674i		−	1.03053i	−0.857032	−	0.515263i	$-0.827694\pi$
$71$		−	73.1674i		−	1.03053i	0.857032	−	0.515263i	$-0.172306\pi$
$72$	5.93479	−	8.62675i	0.0824277	−	0.119816i
$73$	−17.0166	−	17.0166i	−0.233103	−	0.233103i	0.580883	−	0.813987i	$-0.302707\pi$
$73$	−17.0166	−	17.0166i	−0.233103	−	0.233103i	−0.813987	+	0.580883i	$0.802707\pi$
$74$	−123.902	+	41.4360i	−1.67435	+	0.559946i
$75$	−45.8553	+	52.0023i	−0.611404	+	0.693364i
$76$	−11.2905	+	80.1595i	−0.148560	+	1.05473i
$77$		−	32.1396i		−	0.417397i
$78$	−111.516	+	37.2940i	−1.42970	+	0.478129i
$79$			2.15129i			0.0272315i	0.999907	+	0.0136157i	$0.00433416\pi$
$79$			2.15129i			0.0272315i	−0.999907	+	0.0136157i	$0.995666\pi$
$80$	−79.1696	+	11.4965i	−0.989620	+	0.143706i
$81$	−67.5069			−0.833419
$82$	0.750081	+	2.24289i	0.00914732	+	0.0273523i
$83$	76.4850			0.921506			0.460753	−	0.887528i	$-0.347579\pi$
$83$	76.4850			0.921506			0.460753	+	0.887528i	$0.347579\pi$
$84$	11.7991	−	83.7699i	0.140465	−	0.997261i
$85$	16.6716	−	44.1134i	0.196136	−	0.518982i
$86$	6.07320	+	18.1601i	0.0706187	+	0.211164i
$87$	−48.6470	+	48.6470i	−0.559161	+	0.559161i
$88$	6.12907	+	33.1539i	0.0696485	+	0.376748i
$89$	38.7296			0.435164			0.217582	−	0.976042i	$-0.430183\pi$
$89$	38.7296			0.435164			0.217582	+	0.976042i	$0.430183\pi$
$90$	−8.89113	−	9.60543i	−0.0987904	−	0.106727i
$91$	114.319	−	114.319i	1.25626	−	1.25626i
$92$	−11.6102	−	1.63531i	−0.126198	−	0.0177751i
$93$	−65.5810			−0.705172
$94$	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	0.749752	−	0.661718i	$-0.230173\pi$
$97$	8.53929	+	8.53929i	0.0880339	+	0.0880339i	−0.661718	+	0.749752i	$0.730173\pi$
$98$	5.80816	+	17.3675i	0.0592669	+	0.177220i
$99$	−3.90055	+	3.90055i	−0.0393995	+	0.0393995i
$100$	−7.71201	+	99.7022i	−0.0771201	+	0.997022i
$101$	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	$0.0995852\pi$
$102$	−46.8138	−	23.3494i	−0.458959	−	0.228916i
$103$	−32.9039	−	32.9039i	−0.319456	−	0.319456i	0.529102	−	0.848558i	$-0.322529\pi$
$103$	−32.9039	−	32.9039i	−0.319456	−	0.319456i	−0.848558	+	0.529102i	$0.822529\pi$
$104$	−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
$107$	−19.9537			−0.186484			−0.0932418	−	0.995643i	$-0.529723\pi$
$107$	−19.9537			−0.186484			−0.0932418	+	0.995643i	$0.529723\pi$
$108$	−91.3512	+	68.7946i	−0.845845	+	0.636987i
$109$	31.4162	−	31.4162i	0.288222	−	0.288222i	−0.548155	−	0.836377i	$-0.684670\pi$
$109$	31.4162	−	31.4162i	0.288222	−	0.288222i	0.836377	+	0.548155i	$0.184670\pi$
$110$	42.1131	+	1.62631i	0.382847	+	0.0147846i
$111$	181.161			1.63208
$112$	−59.0900	−	106.754i	−0.527589	−	0.953162i
$113$	−48.1807	+	48.1807i	−0.426378	+	0.426378i	−0.887393	−	0.461014i	$-0.847486\pi$
$113$	−48.1807	+	48.1807i	−0.426378	+	0.426378i	0.461014	+	0.887393i	$0.347486\pi$
$114$	50.1009	−	100.449i	0.439481	−	0.881128i
$115$	−5.18121	+	13.7096i	−0.0450540	+	0.119214i
$116$	−13.8398	+	98.2586i	−0.119309	+	0.847057i
$117$	−27.7482			−0.237164
$118$	−138.550	−	69.1050i	−1.17416	−	0.585635i
$119$	71.9267			0.604426
$120$	109.168	+	19.6994i	0.909736	+	0.164162i
$121$			103.238i			0.853210i
$122$	30.6395	+	15.2821i	0.251144	+	0.125263i
$123$		−	3.27939i		−	0.0266617i
$124$	−75.5599	+	56.9025i	−0.609354	+	0.458891i
$125$	119.469	+	36.7727i	0.955750	+	0.294181i
$126$	8.91022	−	17.8643i	0.0707160	−	0.141780i
$127$	−165.164	−	165.164i	−1.30051	−	1.30051i	−0.928050	−	0.372456i	$-0.878516\pi$
$127$	−165.164	−	165.164i	−1.30051	−	1.30051i	−0.372456	−	0.928050i	$-0.621484\pi$
$128$	81.3129	+	98.8545i	0.635257	+	0.772301i
$129$		−	26.5524i		−	0.205832i
$130$	144.010	+	155.579i	1.10777	+	1.19677i
$131$	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	$0.731140\pi$
$132$	6.52063	−	46.2946i	0.0493987	−	0.350717i
$133$			154.333i			1.16040i
$134$	−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	$-0.532335\pi$
$137$	122.401	−	122.401i	0.893436	−	0.893436i	0.994845	+	0.101408i	$0.0323349\pi$
$138$	14.5489	+	7.25656i	0.105427	+	0.0525837i
$139$	−163.514	−	163.514i	−1.17636	−	1.17636i	−0.980665	−	0.195693i	$-0.937305\pi$
$139$	−163.514	−	163.514i	−1.17636	−	1.17636i	−0.195693	−	0.980665i	$-0.562695\pi$
$140$	−146.405	+	42.7558i	−1.04575	+	0.305399i
$141$	−130.978	−	130.978i	−0.928925	−	0.928925i
$142$	46.4116	+	138.780i	0.326842	+	0.977322i
$143$	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
$147$		−	25.3936i		−	0.172745i
$148$	208.726	−	157.187i	1.41031	−	1.06207i
$149$	−182.956	−	182.956i	−1.22789	−	1.22789i	−0.964759	−	0.263134i	$-0.915244\pi$
$149$	−182.956	−	182.956i	−1.22789	−	1.22789i	−0.263134	−	0.964759i	$-0.584756\pi$
$150$	53.9896	−	127.722i	0.359931	−	0.851480i
$151$			100.104i			0.662938i	0.943466	+	0.331469i	$0.107544\pi$
$151$			100.104i			0.662938i	−0.943466	+	0.331469i	$0.892456\pi$
$152$	−29.4316	−	159.204i	−0.193629	−	1.04739i
$153$	−8.72923	−	8.72923i	−0.0570538	−	0.0570538i
$154$	20.3868	+	60.9606i	0.132382	+	0.395848i
$155$	48.6509	+	107.764i	0.313877	+	0.695251i
$156$	187.862	−	141.474i	1.20424	−	0.906887i
$157$			27.8875i			0.177627i	0.996048	+	0.0888136i	$0.0283076\pi$
$157$			27.8875i			0.177627i	−0.996048	+	0.0888136i	$0.971692\pi$
$158$	−1.36461	−	4.08044i	−0.00863675	−	0.0258256i
$159$			275.159i			1.73056i
$160$	142.872	−	72.0249i	0.892950	−	0.450155i
$161$	−22.3535			−0.138841
$162$	128.043	−	42.8211i	0.790391	−	0.264328i
$163$	−122.177			−0.749552			−0.374776	−	0.927115i	$-0.622280\pi$
$163$	−122.177			−0.749552			−0.374776	+	0.927115i	$0.622280\pi$
$164$	−2.84542	−	3.77839i	−0.0173501	−	0.0230390i
$165$	−54.6658	−	20.6596i	−0.331308	−	0.125209i
$166$	−145.072	+	48.5160i	−0.873930	+	0.292265i
$167$	102.217	−	102.217i	0.612078	−	0.612078i	−0.331409	−	0.943487i	$-0.607524\pi$
$167$	102.217	−	102.217i	0.612078	−	0.612078i	0.943487	+	0.331409i	$0.107524\pi$
$168$	30.7572	+	166.374i	0.183079	+	0.990324i
$169$	280.439			1.65940
$170$	−3.63959	+	94.2470i	−0.0214094	+	0.554394i
$171$	18.7303	−	18.7303i	0.109534	−	0.109534i
$172$	−23.0386	−	30.5926i	−0.133945	−	0.177864i
$173$	144.968			0.837968			0.418984	−	0.907994i	$-0.362386\pi$
$173$	144.968			0.837968			0.418984	+	0.907994i	$0.362386\pi$
$174$	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
$178$	−73.4602	+	24.5670i	−0.412698	+	0.138017i
$179$	71.1438	−	71.1438i	0.397451	−	0.397451i	−0.479882	−	0.877333i	$-0.659320\pi$
$179$	71.1438	−	71.1438i	0.397451	−	0.397451i	0.877333	+	0.479882i	$0.159320\pi$
$180$	22.9571	+	12.5792i	0.127540	+	0.0698844i
$181$	−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	$0.978216\pi$
$182$	−144.319	+	289.349i	−0.792963	+	1.58983i
$183$	−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
$187$	39.7496			0.212565
$188$	−264.554	−	37.2626i	−1.40720	−	0.198205i
$189$	−154.167	+	154.167i	−0.815696	+	0.815696i
$190$	−202.226	−	7.80948i	−1.06435	−	0.0411025i
$191$	−209.558			−1.09716			−0.548581	−	0.836097i	$-0.684832\pi$
$191$	−209.558			−1.09716			−0.548581	+	0.836097i	$0.684832\pi$
$192$	−63.4558	−	165.759i	−0.330499	−	0.863331i
$193$	−90.2693	+	90.2693i	−0.467717	+	0.467717i	−0.901174	−	0.433457i	$-0.857293\pi$
$193$	−90.2693	+	90.2693i	−0.467717	+	0.467717i	0.433457	+	0.901174i	$0.357293\pi$
$194$	−21.6135	−	10.7802i	−0.111410	−	0.0555680i
$195$	−120.959	−	267.929i	−0.620302	−	1.37400i
$196$	−22.0332	−	29.2575i	−0.112414	−	0.149273i
$197$	67.8338			0.344334			0.172167	−	0.985068i	$-0.444923\pi$
$197$	67.8338			0.344334			0.172167	+	0.985068i	$0.444923\pi$
$198$	4.92414	−	9.87254i	0.0248694	−	0.0498613i
$199$	−278.771			−1.40086			−0.700430	−	0.713721i	$-0.747009\pi$
$199$	−278.771			−1.40086			−0.700430	+	0.713721i	$0.747009\pi$
$200$	−48.6155	−	194.001i	−0.243077	−	0.970007i
$201$			302.495i			1.50495i
$202$	−82.0723	+	164.549i	−0.406299	+	0.814599i
$203$			189.180i			0.931922i
$204$	103.605	+	14.5928i	0.507867	+	0.0715335i
$205$	−5.38876	+	2.43280i	−0.0262866	+	0.0118673i
$206$	83.2820	+	41.5387i	0.404281	+	0.201644i
$207$	2.71288	+	2.71288i	0.0131057	+	0.0131057i
$208$	93.6942	−	326.003i	0.450453	−	1.56732i
$209$			85.2908i			0.408090i
$210$	211.334	+	8.16122i	1.00635	+	0.0388630i
$211$	−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	$0.778358\pi$
$212$	238.747	+	317.028i	1.12616	+	1.49542i
$213$		−	202.914i		−	0.952648i
$214$	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
$218$	−39.6605	+	79.5164i	−0.181929	+	0.364754i
$219$	−47.1918	−	47.1918i	−0.215488	−	0.215488i
$220$	−80.9094	+	23.6286i	−0.367770	+	0.107403i
$221$	141.388	+	141.388i	0.639763	+	0.639763i
$222$	−343.615	+	114.914i	−1.54782	+	0.517631i
$223$	90.1705	−	90.1705i	0.404352	−	0.404352i	−0.475412	−	0.879764i	$-0.657701\pi$
$223$	90.1705	−	90.1705i	0.404352	−	0.404352i	0.879764	+	0.475412i	$0.157701\pi$
$224$	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
$227$		−	346.057i		−	1.52448i	−0.647294	−	0.762240i	$-0.724100\pi$
$227$		−	346.057i		−	1.52448i	0.647294	−	0.762240i	$-0.275900\pi$
$228$	−31.3119	+	222.305i	−0.137333	+	0.975023i
$229$	−73.4761	−	73.4761i	−0.320856	−	0.320856i	0.528239	−	0.849096i	$-0.322852\pi$
$229$	−73.4761	−	73.4761i	−0.320856	−	0.320856i	−0.849096	+	0.528239i	$0.822852\pi$
$230$	1.13112	−	29.2902i	0.00491790	−	0.127349i
$231$		−	89.1323i		−	0.385854i
$232$	−36.0770	−	195.150i	−0.155504	−	0.841165i
$233$	−86.7985	−	86.7985i	−0.372526	−	0.372526i	0.495871	−	0.868396i	$-0.334849\pi$
$233$	−86.7985	−	86.7985i	−0.372526	−	0.372526i	−0.868396	+	0.495871i	$0.834849\pi$
$234$	52.6312	−	17.6013i	0.224920	−	0.0752191i
$235$	−118.061	+	312.392i	−0.502385	+	1.32933i
$236$	306.629	+	43.1890i	1.29928	+	0.183004i
$237$			5.96613i			0.0251736i
$238$	−136.427	+	45.6246i	−0.573221	+	0.191700i
$239$			204.791i			0.856868i	0.903573	+	0.428434i	$0.140935\pi$
$239$			204.791i			0.856868i	−0.903573	+	0.428434i	$0.859065\pi$
$240$	−219.560	+	31.8830i	−0.914834	+	0.132846i
$241$	98.8804			0.410292			0.205146	−	0.978731i	$-0.434233\pi$
$241$	98.8804			0.410292			0.205146	+	0.978731i	$0.434233\pi$
$242$	−65.4863	−	195.817i	−0.270604	−	0.809160i
$243$	70.0893			0.288433
$244$	−67.8091	−	9.55097i	−0.277906	−	0.0391433i
$245$	−41.7272	+	18.8381i	−0.170315	+	0.0768902i
$246$	2.08019	+	6.22017i	0.00845605	+	0.0252852i
$247$	−303.376	+	303.376i	−1.22824	+	1.22824i
$248$	107.223	−	155.859i	0.432352	−	0.628462i
$249$	212.115			0.851867
$250$	−249.927	+	6.03320i	−0.999709	+	0.0241328i
$251$	−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	$0.284445\pi$
$252$	−5.56868	+	39.5360i	−0.0220979	+	0.156889i
$253$	−12.3534			−0.0488277
$254$	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	0.952457	−	0.304672i	$-0.0985468\pi$
$257$	166.481	+	166.481i	0.647785	+	0.647785i	−0.304672	+	0.952457i	$0.598547\pi$
$258$	16.8427	+	50.3631i	0.0652819	+	0.195206i
$259$	352.252	−	352.252i	1.36005	−	1.36005i
$260$	−371.838	−	203.746i	−1.43014	−	0.783638i
$261$	22.9594	−	22.9594i	0.0879671	−	0.0879671i
$262$	−27.7671	−	13.8494i	−0.105981	−	0.0528604i
$263$	−78.7097	−	78.7097i	−0.299276	−	0.299276i	0.541454	−	0.840730i	$-0.317874\pi$
$263$	−78.7097	−	78.7097i	−0.299276	−	0.299276i	−0.840730	+	0.541454i	$0.817874\pi$
$264$	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
$267$	107.408			0.402279
$268$	262.464	+	348.522i	0.979345	+	1.30046i
$269$	−98.2650	+	98.2650i	−0.365297	+	0.365297i	−0.865759	−	0.500461i	$-0.833164\pi$
$269$	−98.2650	+	98.2650i	−0.365297	+	0.365297i	0.500461	+	0.865759i	$0.333164\pi$
$270$	−194.207	−	209.809i	−0.719283	−	0.777069i
$271$	−115.967			−0.427922			−0.213961	−	0.976842i	$-0.568637\pi$
$271$	−115.967			−0.427922			−0.213961	+	0.976842i	$0.568637\pi$
$272$	132.031	−	73.0812i	0.485409	−	0.268681i
$273$	317.040	−	317.040i	1.16132	−	1.16132i
$274$	−154.522	+	309.804i	−0.563947	+	1.13067i
$275$	6.60535	+	105.154i	0.0240195	+	0.382378i
$276$	−32.1984	−	4.53518i	−0.116661	−	0.0164318i
$277$	340.610			1.22964			0.614819	−	0.788668i	$-0.289229\pi$
$277$	340.610			1.22964			0.614819	+	0.788668i	$0.289229\pi$
$278$	413.864	+	206.423i	1.48872	+	0.742530i
$279$	30.9516			0.110938
$280$	250.573	−	173.965i	0.894902	−	0.621303i
$281$		−	103.541i		−	0.368474i	−0.982882	−	0.184237i	$-0.941019\pi$
$281$		−	103.541i		−	0.368474i	0.982882	−	0.184237i	$-0.0589814\pi$
$282$	331.515	+	165.350i	1.17558	+	0.586348i
$283$		−	561.986i		−	1.98582i	−0.118887	−	0.992908i	$-0.537932\pi$
$283$		−	561.986i		−	1.98582i	0.118887	−	0.992908i	$-0.462068\pi$
$284$	−176.062	−	233.790i	−0.619936	−	0.823203i
$285$	262.504	+	99.2066i	0.921065	+	0.348093i
$286$	−79.7565	+	159.906i	−0.278869	+	0.559112i
$287$	−6.37651	−	6.37651i	−0.0222178	−	0.0222178i
$288$	−1.79517	−	41.8456i	−0.00623322	−	0.145297i
$289$		−	200.043i		−	0.692189i
$290$	−247.886	−	9.57277i	−0.854781	−	0.0330095i
$291$	23.6819	+	23.6819i	0.0813811	+	0.0813811i
$292$	−95.3193	−	13.4258i	−0.326436	−	0.0459787i
$293$		−	1.90920i		−	0.00651604i	−0.999995	−	0.00325802i	$-0.998963\pi$
$293$		−	1.90920i		−	0.00651604i	0.999995	−	0.00325802i	$-0.00103706\pi$
$294$	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
$298$	463.074	+	230.968i	1.55394	+	0.775060i
$299$	−43.9406	−	43.9406i	−0.146959	−	0.146959i
$300$	−21.3876	+	276.503i	−0.0712921	+	0.921676i
$301$	−51.6289	−	51.6289i	−0.171525	−	0.171525i
$302$	−63.4978	−	189.871i	−0.210258	−	0.628712i
$303$	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
$307$			465.516i			1.51634i	0.652058	+	0.758169i	$0.273906\pi$
$307$			465.516i			1.51634i	−0.652058	+	0.758169i	$0.726094\pi$
$308$	−77.3372	−	102.695i	−0.251095	−	0.333425i
$309$	−91.2520	−	91.2520i	−0.295314	−	0.295314i
$310$	−160.635	−	173.540i	−0.518178	−	0.559807i
$311$			212.375i			0.682879i	0.939904	+	0.341439i	$0.110914\pi$
$311$			212.375i			0.682879i	−0.939904	+	0.341439i	$0.889086\pi$
$312$	−266.585	+	387.505i	−0.854440	+	1.24200i
$313$	−46.0307	−	46.0307i	−0.147063	−	0.147063i	0.629742	−	0.776805i	$-0.283161\pi$
$313$	−46.0307	−	46.0307i	−0.147063	−	0.147063i	−0.776805	+	0.629742i	$0.783161\pi$
$314$	−17.6896	−	52.8954i	−0.0563364	−	0.168457i
$315$	46.6851	+	17.6435i	0.148207	+	0.0560110i
$316$	5.17661	+	6.87395i	0.0163817	+	0.0217530i
$317$		−	430.649i		−	1.35851i	−0.733901	−	0.679257i	$-0.762302\pi$
$317$		−	430.649i		−	1.35851i	0.733901	−	0.679257i	$-0.237698\pi$
$318$	−174.539	−	521.907i	−0.548866	−	1.64122i
$319$			104.548i			0.327738i
$320$	−225.305	+	227.239i	−0.704077	+	0.710123i
$321$	−55.3375			−0.172391
$322$	42.3988	−	14.1793i	0.131673	−	0.0440350i
$323$	−190.876			−0.590948
$324$	−215.703	+	162.441i	−0.665750	+	0.501362i
$325$	−350.534	+	397.524i	−1.07857	+	1.22315i
$326$	231.738	−	77.4994i	0.710854	−	0.237728i
$327$	87.1261	−	87.1261i	0.266441	−	0.266441i
$328$	7.79375	+	5.36173i	0.0237614	+	0.0163467i
$329$	−509.353			−1.54819
$330$	116.792	+	4.51022i	0.353915	+	0.0136673i
$331$	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	$0.247481\pi$
$332$	244.390	−	184.045i	0.736116	−	0.554352i
$333$	−85.5005			−0.256758
$334$	−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	0.286695	−	0.958022i	$-0.407443\pi$
$337$	−226.237	−	226.237i	−0.671327	−	0.671327i	−0.958022	+	0.286695i	$0.907443\pi$
$338$	−531.920	+	177.888i	−1.57373	+	0.526297i
$339$	−133.619	+	133.619i	−0.394156	+	0.394156i
$340$	−52.8795	−	181.071i	−0.155528	−	0.532562i
$341$	−70.4709	+	70.4709i	−0.206659	+	0.206659i
$342$	−23.6456	+	47.4077i	−0.0691391	+	0.138619i
$343$	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
$347$	231.886			0.668259			0.334130	−	0.942527i	$-0.391558\pi$
$347$	231.886			0.668259			0.334130	+	0.942527i	$0.391558\pi$
$348$	−38.3817	+	272.499i	−0.110292	+	0.783044i
$349$	−205.898	+	205.898i	−0.589965	+	0.589965i	−0.937622	−	0.347657i	$-0.886978\pi$
$349$	−205.898	+	205.898i	−0.589965	+	0.589965i	0.347657	+	0.937622i	$0.386978\pi$
$350$	−143.367	−	353.323i	−0.409619	−	1.00949i
$351$	−606.096			−1.72677
$352$	99.3618	+	91.1873i	0.282278	+	0.259055i
$353$	−299.539	+	299.539i	−0.848551	+	0.848551i	−0.989952	−	0.141401i	$-0.954839\pi$
$353$	−299.539	+	299.539i	−0.848551	+	0.848551i	0.141401	+	0.989952i	$0.454839\pi$
$354$	−384.240	−	191.648i	−1.08542	−	0.541378i
$355$	−333.432	+	150.531i	−0.939246	+	0.424030i
$356$	123.752	−	93.1947i	0.347617	−	0.261783i
$357$	199.473			0.558749
$358$	−89.8135	+	180.070i	−0.250876	+	0.502987i
$359$	108.844			0.303187			0.151593	−	0.988443i	$-0.451560\pi$
$359$	108.844			0.303187			0.151593	+	0.988443i	$0.451560\pi$
$360$	−51.5230	−	9.29732i	−0.143120	−	0.0258259i
$361$		−	48.5638i		−	0.134526i
$362$	243.589	−	488.378i	0.672898	−	1.34911i
$363$			286.310i			0.788732i
$364$	90.1961	−	640.366i	0.247791	−	1.75925i
$365$	−42.5375	+	112.555i	−0.116541	+	0.308371i
$366$	84.9722	+	42.3817i	0.232165	+	0.115797i
$367$	271.565	+	271.565i	0.739960	+	0.739960i	0.972570	−	0.232610i	$-0.0747265\pi$
$367$	271.565	+	271.565i	0.739960	+	0.739960i	−0.232610	+	0.972570i	$0.574726\pi$
$368$	−41.0328	+	22.7123i	−0.111502	+	0.0617181i
$369$			1.54774i			0.00419442i
$370$	443.738	+	479.387i	1.19929	+	1.29564i
$371$	535.025	+	535.025i	1.44211	+	1.44211i
$372$	−209.549	+	157.807i	−0.563305	+	0.424212i
$373$		−	205.735i		−	0.551569i	−0.961220	−	0.275784i	$-0.911062\pi$
$373$		−	205.735i		−	0.551569i	0.961220	−	0.275784i	$-0.0889376\pi$
$374$	−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
$378$	194.623	−	390.206i	0.514877	−	1.03229i
$379$	−146.474	−	146.474i	−0.386475	−	0.386475i	0.486953	−	0.873428i	$-0.338108\pi$
$379$	−146.474	−	146.474i	−0.386475	−	0.386475i	−0.873428	+	0.486953i	$0.838108\pi$
$380$	388.525	−	113.464i	1.02243	−	0.298589i
$381$	−458.048	−	458.048i	−1.20223	−	1.20223i
$382$	397.478	−	132.927i	1.04052	−	0.347977i
$383$	77.8502	−	77.8502i	0.203264	−	0.203264i	−0.598133	−	0.801397i	$-0.704090\pi$
$383$	77.8502	−	77.8502i	0.203264	−	0.203264i	0.801397	+	0.598133i	$0.204090\pi$
$384$	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
$387$			12.5317i			0.0323815i
$388$	47.8334	+	6.73737i	0.123282	+	0.0173643i
$389$	−91.3251	−	91.3251i	−0.234769	−	0.234769i	0.579911	−	0.814680i	$-0.303087\pi$
$389$	−91.3251	−	91.3251i	−0.234769	−	0.234769i	−0.814680	+	0.579911i	$0.803087\pi$
$390$	399.381	+	431.467i	1.02405	+	1.10632i
$391$		−	27.6463i		−	0.0707067i
$392$	60.3499	+	41.5179i	0.153954	+	0.105913i
$393$	30.4244	+	30.4244i	0.0774158	+	0.0774158i
$394$	−128.663	+	43.0284i	−0.326557	+	0.109209i
$395$	9.80366	−	4.42594i	0.0248194	−	0.0112049i
$396$	−3.07747	+	21.8492i	−0.00777140	+	0.0551747i
$397$		−	181.720i		−	0.457732i	−0.973458	−	0.228866i	$-0.926498\pi$
$397$		−	181.720i		−	0.457732i	0.973458	−	0.228866i	$-0.0735017\pi$
$398$	528.758	−	176.831i	1.32854	−	0.444298i
$399$			428.011i			1.07271i
$400$	215.270	+	337.133i	0.538176	+	0.842833i
$401$	−559.201			−1.39452			−0.697258	−	0.716821i	$-0.745597\pi$
$401$	−559.201			−1.39452			−0.697258	+	0.716821i	$0.745597\pi$
$402$	−191.879	−	573.755i	−0.477310	−	1.42725i
$403$	−501.324			−1.24398
$404$	51.2933	−	364.167i	0.126964	−	0.901405i
$405$	138.885	+	307.637i	0.342926	+	0.759597i
$406$	−120.001	−	358.826i	−0.295569	−	0.883808i
$407$	194.668	−	194.668i	0.478301	−	0.478301i
$408$	−205.768	+	38.0399i	−0.504334	+	0.0932351i
$409$	724.291			1.77088			0.885441	−	0.464752i	$-0.153856\pi$
$409$	724.291			1.77088			0.885441	+	0.464752i	$0.153856\pi$
$410$	8.67792	−	8.03260i	0.0211657	−	0.0195917i
$411$	339.453	−	339.453i	0.825919	−	0.825919i
$412$	−184.313	−	25.9607i	−0.447363	−	0.0630114i
$413$	590.362			1.42945
$414$	−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
$418$	−54.1017	−	161.775i	−0.129430	−	0.387021i
$419$	−76.4657	+	76.4657i	−0.182496	+	0.182496i	−0.792442	−	0.609947i	$-0.791191\pi$
$419$	−76.4657	+	76.4657i	−0.182496	+	0.182496i	0.609947	+	0.792442i	$0.291191\pi$
$420$	−406.024	+	118.574i	−0.966724	+	0.282319i
$421$	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	$-0.0402236\pi$
$422$	67.1969	+	33.5159i	0.159234	+	0.0794215i
$423$	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
$427$	−130.555			−0.305749
$428$	−63.7577	+	48.0145i	−0.148967	+	0.112183i
$429$	175.209	−	175.209i	0.408413	−	0.408413i
$430$	70.2629	−	65.0379i	0.163402	−	0.151251i
$431$	185.108			0.429485			0.214742	−	0.976671i	$-0.431109\pi$
$431$	185.108			0.429485			0.214742	+	0.976671i	$0.431109\pi$
$432$	−126.353	+	439.635i	−0.292483	+	1.01767i
$433$	−354.954	+	354.954i	−0.819756	+	0.819756i	−0.986072	−	0.166317i	$-0.946813\pi$
$433$	−354.954	+	354.954i	−0.819756	+	0.819756i	0.166317	+	0.986072i	$0.446813\pi$
$434$	160.980	−	322.753i	0.370922	−	0.743671i
$435$	321.774	+	121.606i	0.739710	+	0.279555i
$436$	24.7869	−	175.980i	0.0568507	−	0.403623i
$437$	59.3208			0.135745
$438$	119.445	+	59.5760i	0.272707	+	0.136018i
$439$	155.719			0.354714			0.177357	−	0.984147i	$-0.443245\pi$
$439$	155.719			0.354714			0.177357	+	0.984147i	$0.443245\pi$
$440$	138.476	−	96.1399i	0.314719	−	0.218500i
$441$			11.9847i			0.0271763i
$442$	−357.861	−	178.491i	−0.809641	−	0.403826i
$443$			728.951i			1.64549i	0.568412	+	0.822744i	$0.307558\pi$
$443$			728.951i			1.64549i	−0.568412	+	0.822744i	$0.692442\pi$
$444$	578.858	−	435.925i	1.30373	−	0.981813i
$445$	−79.6803	−	176.496i	−0.179057	−	0.396619i
$446$	−113.833	+	228.227i	−0.255232	+	0.511721i
$447$	−507.390	−	507.390i	−1.13510	−	1.13510i
$448$	−445.690	−	198.921i	−0.994843	−	0.444020i
$449$		−	46.9465i		−	0.104558i	−0.998633	−	0.0522790i	$-0.983351\pi$
$449$		−	46.9465i		−	0.104558i	0.998633	−	0.0522790i	$-0.0166485\pi$
$450$	−25.4809	+	60.2796i	−0.0566242	+	0.133955i
$451$	−3.52391	−	3.52391i	−0.00781355	−	0.00781355i
$452$	−38.0138	+	269.887i	−0.0841014	+	0.597096i
$453$			277.616i			0.612839i
$454$	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	$-0.864466\pi$
$457$	−227.434	+	227.434i	−0.497667	+	0.497667i	0.413044	+	0.910711i	$0.364466\pi$
$458$	185.973	+	92.7579i	0.406054	+	0.202528i
$459$	−190.670	−	190.670i	−0.415403	−	0.415403i
$460$	16.4340	+	56.2735i	0.0357260	+	0.122334i
$461$	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	$0.616295\pi$
$462$	56.5385	+	169.061i	0.122378	+	0.365933i
$463$	1.16661	−	1.16661i	0.00251968	−	0.00251968i	−0.705846	−	0.708366i	$-0.749433\pi$
$463$	1.16661	−	1.16661i	0.00251968	−	0.00251968i	0.708366	+	0.705846i	$0.249433\pi$
$464$	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
$467$			632.343i			1.35405i	0.735958	+	0.677027i	$0.236732\pi$
$467$			632.343i			1.35405i	−0.735958	+	0.677027i	$0.763268\pi$
$468$	−88.6631	+	66.7702i	−0.189451	+	0.142671i
$469$	588.175	+	588.175i	1.25411	+	1.25411i
$470$	25.7740	−	667.415i	0.0548382	−	1.42003i
$471$			77.3400i			0.164204i
$472$	−608.993	+	112.583i	−1.29024	+	0.238523i
$473$	−28.5322	−	28.5322i	−0.0603217	−	0.0603217i
$474$	−3.78444	−	11.3162i	−0.00798406	−	0.0238739i
$475$	−31.7187	−	504.947i	−0.0667762	−	1.06305i
$476$	229.826	−	173.077i	0.482827	−	0.363606i
$477$		−	129.864i		−	0.272252i
$478$	−129.904	−	388.437i	−0.271765	−	0.812630i
$479$		−	552.415i		−	1.15327i	−0.817003	−	0.576633i	$-0.804366\pi$
$479$		−	552.415i		−	1.15327i	0.817003	−	0.576633i	$-0.195634\pi$
$480$	396.225	−	199.746i	0.825469	−	0.416137i
$481$	1384.85			2.87912
$482$	−187.551	+	62.7219i	−0.389110	+	0.130128i
$483$	−61.9926			−0.128349
$484$	248.421	+	329.875i	0.513267	+	0.681560i
$485$	21.3463	−	56.4828i	0.0440129	−	0.116459i
$486$	−132.941	+	44.4591i	−0.273542	+	0.0914796i
$487$	285.326	−	285.326i	0.585886	−	0.585886i	−0.350629	−	0.936515i	$-0.614032\pi$
$487$	285.326	−	285.326i	0.585886	−	0.585886i	0.936515	+	0.350629i	$0.114032\pi$
$488$	134.675	−	24.8970i	0.275973	−	0.0510185i
$489$	−338.832			−0.692908
$490$	67.1964	−	62.1995i	0.137136	−	0.126938i
$491$	−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	$0.900870\pi$
$492$	−7.89117	−	10.4786i	−0.0160390	−	0.0212979i
$493$	−233.974			−0.474592
$494$	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
$498$	−402.327	+	134.549i	−0.807886	+	0.270179i
$499$	430.585	−	430.585i	0.862895	−	0.862895i	−0.128778	−	0.991673i	$-0.541106\pi$
$499$	430.585	−	430.585i	0.862895	−	0.862895i	0.991673	+	0.128778i	$0.0411056\pi$
$500$	470.221	−	169.978i	0.940442	−	0.339955i
$501$	283.477	−	283.477i	0.565823	−	0.565823i
$502$	48.3976	−	97.0337i	0.0964096	−	0.193294i
$503$	−102.108	−	102.108i	−0.202998	−	0.202998i	0.598285	−	0.801283i	$-0.295849\pi$
$503$	−102.108	−	102.108i	−0.202998	−	0.202998i	−0.801283	+	0.598285i	$0.795849\pi$
$504$	−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
$507$	777.737			1.53400
$508$	−925.178	−	130.312i	−1.82122	−	0.256520i
$509$	−350.381	+	350.381i	−0.688372	+	0.688372i	−0.961872	−	0.273500i	$-0.911819\pi$
$509$	−350.381	+	350.381i	−0.688372	+	0.688372i	0.273500	+	0.961872i	$0.411819\pi$
$510$	−10.0936	+	261.374i	−0.0197914	+	0.512498i
$511$	−183.521			−0.359141
$512$	497.689	+	120.205i	0.972050	+	0.234775i
$513$	409.121	−	409.121i	0.797507	−	0.797507i
$514$	−421.374	−	210.169i	−0.819793	−	0.408889i
$515$	−82.2523	+	217.642i	−0.159713	+	0.422606i
$516$	−63.8927	−	84.8421i	−0.123823	−	0.164423i
$517$	−281.489			−0.544466
$518$	−444.691	+	891.572i	−0.858476	+	1.72118i
$519$	402.039			0.774642
$520$	834.521	+	150.589i	1.60485	+	0.289595i
$521$			89.0292i			0.170881i	0.996343	+	0.0854407i	$0.0272298\pi$
$521$			89.0292i			0.170881i	−0.996343	+	0.0854407i	$0.972770\pi$
$522$	−28.9845	+	58.1118i	−0.0555258	+	0.111325i
$523$			399.222i			0.763331i	0.924300	+	0.381666i	$0.124649\pi$
$523$			399.222i			0.763331i	−0.924300	+	0.381666i	$0.875351\pi$
$524$	61.4521	+	8.65557i	0.117275	+	0.0165183i
$525$	33.1473	+	527.690i	0.0631378	+	1.00512i
$526$	199.219	+	99.3649i	0.378744	+	0.188907i
$527$	−157.710	−	157.710i	−0.299260	−	0.299260i
$528$	−90.5630	−	163.614i	−0.171521	−	0.309876i
$529$		−	520.408i		−	0.983758i
$530$	−728.126	+	673.980i	−1.37382	+	1.27166i
$531$	−71.6480	−	71.6480i	−0.134930	−	0.134930i
$532$	371.371	+	493.137i	0.698065	+	0.926950i
$533$		−	25.0688i		−	0.0470334i
$534$	−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
$538$	124.052	−	248.715i	0.230580	−	0.462296i
$539$	−27.2870	−	27.2870i	−0.0506252	−	0.0506252i
$540$	501.446	+	274.764i	0.928604	+	0.508822i
$541$	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	$0.686528\pi$
$542$	219.960	−	73.5603i	0.405830	−	0.135720i
$543$	−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
$547$		−	327.523i		−	0.598762i	−0.954134	−	0.299381i	$-0.903220\pi$
$547$		−	327.523i		−	0.598762i	0.954134	−	0.299381i	$-0.0967802\pi$
$548$	96.5723	−	685.636i	0.176227	−	1.25116i
$549$	15.8445	+	15.8445i	0.0288607	+	0.0288607i
$550$	−79.2301	−	195.260i	−0.144055	−	0.355019i
$551$		−	502.039i		−	0.911141i
$552$	63.9490	−	11.8221i	0.115850	−	0.0214168i
$553$	11.6006	+	11.6006i	0.0209777	+	0.0209777i
$554$	−646.049	+	216.056i	−1.16615	+	0.389993i
$555$	−372.710	−	825.570i	−0.671550	−	1.48751i
$556$	−915.933	−	129.010i	−1.64736	−	0.232032i
$557$			609.704i			1.09462i	0.836930	+	0.547311i	$0.184348\pi$
$557$			609.704i			1.09462i	−0.836930	+	0.547311i	$0.815652\pi$
$558$	−58.7072	+	19.6332i	−0.105210	+	0.0351850i
$559$		−	202.976i		−	0.363105i
$560$	−364.922	+	488.910i	−0.651647	+	0.873054i
$561$	110.237			0.196501
$562$	65.6784	+	196.391i	0.116865	+	0.349451i
$563$	104.576			0.185748			0.0928738	−	0.995678i	$-0.470395\pi$
$563$	104.576			0.185748			0.0928738	+	0.995678i	$0.470395\pi$
$564$	−733.684	−	103.340i	−1.30086	−	0.183227i
$565$	318.690	+	120.441i	0.564053	+	0.213169i
$566$	356.479	+	1065.94i	0.629822	+	1.88329i
$567$	−364.026	+	364.026i	−0.642021	+	0.642021i
$568$	482.242	+	331.760i	0.849018	+	0.584084i
$569$	153.954			0.270569			0.135284	−	0.990807i	$-0.456805\pi$
$569$	153.954			0.270569			0.135284	+	0.990807i	$0.456805\pi$
$570$	−560.831	−	21.6579i	−0.983914	−	0.0379964i
$571$	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	$0.0495832\pi$
$572$	49.8460	−	353.892i	0.0871433	−	0.618692i
$573$	−581.164			−1.01425
$574$	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	0.973765	−	0.227555i	$-0.0730731\pi$
$577$	430.563	+	430.563i	0.746210	+	0.746210i	−0.227555	+	0.973765i	$0.573073\pi$
$578$	126.891	+	379.429i	0.219535	+	0.656452i
$579$	−250.343	+	250.343i	−0.432371	+	0.432371i
$580$	476.249	−	139.083i	0.821119	−	0.239797i
$581$	412.440	−	412.440i	0.709879	−	0.709879i
$582$	−59.9404	−	29.8966i	−0.102990	−	0.0513687i
$583$	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
$587$	−24.8014			−0.0422512			−0.0211256	−	0.999777i	$-0.506725\pi$
$587$	−24.8014			−0.0422512			−0.0211256	+	0.999777i	$0.506725\pi$
$588$	−61.1043	−	81.1394i	−0.103919	−	0.137992i
$589$	338.399	−	338.399i	0.574531	−	0.574531i
$590$	−29.8731	+	773.563i	−0.0506324	+	1.31112i
$591$	188.123			0.318312
$592$	288.700	−	1004.51i	0.487669	−	1.69681i
$593$	714.962	−	714.962i	1.20567	−	1.20567i	0.233255	−	0.972416i	$-0.425062\pi$
$593$	714.962	−	714.962i	1.20567	−	1.20567i	0.972416	−	0.233255i	$-0.0749375\pi$
$594$	107.557	−	215.643i	0.181072	−	0.363036i
$595$	−147.978	−	327.779i	−0.248703	−	0.550888i
$596$	−1024.84	−	144.350i	−1.71953	−	0.242197i
$597$	−773.113			−1.29500
$598$	111.217	+	55.4716i	0.185981	+	0.0927619i
$599$	−898.559			−1.50010			−0.750049	−	0.661382i	$-0.769970\pi$
$599$	−898.559			−1.50010			−0.750049	+	0.661382i	$0.769970\pi$
$600$	−134.825	−	538.021i	−0.224708	−	0.896702i
$601$			498.405i			0.829293i	0.909983	+	0.414646i	$0.136095\pi$
$601$			498.405i			0.829293i	−0.909983	+	0.414646i	$0.863905\pi$
$602$	130.676	+	65.1775i	0.217070	+	0.108268i
$603$		−	142.765i		−	0.236758i
$604$	240.878	+	319.858i	0.398805	+	0.529567i
$605$	470.469	−	212.397i	0.777635	−	0.351070i
$606$	−227.610	+	456.342i	−0.375594	+	0.753039i
$607$	476.327	+	476.327i	0.784723	+	0.784723i	0.980624	−	0.195900i	$-0.0627629\pi$
$607$	476.327	+	476.327i	0.784723	+	0.784723i	−0.195900	+	0.980624i	$0.562763\pi$
$608$	−477.133	−	437.879i	−0.784758	−	0.720195i
$609$			524.651i			0.861495i
$610$	6.60625	−	171.069i	0.0108299	−	0.280440i
$611$	−1001.24	−	1001.24i	−1.63870	−	1.63870i
$612$	−48.8973	−	6.88722i	−0.0798976	−	0.0112536i
$613$		−	294.722i		−	0.480787i	−0.970676	−	0.240393i	$-0.922724\pi$
$613$		−	294.722i		−	0.480787i	0.970676	−	0.240393i	$-0.0772764\pi$
$614$	−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	$-0.842071\pi$
$617$	−248.885	+	248.885i	−0.403379	+	0.403379i	0.476043	+	0.879422i	$0.342071\pi$
$618$	230.965	+	115.199i	0.373730	+	0.186406i
$619$	320.358	+	320.358i	0.517541	+	0.517541i	0.916826	−	0.399286i	$-0.130742\pi$
$619$	320.358	+	320.358i	0.517541	+	0.517541i	−0.399286	+	0.916826i	$0.630742\pi$
$620$	414.764	+	227.267i	0.668975	+	0.366560i
$621$	59.2567	+	59.2567i	0.0954214	+	0.0954214i
$622$	−134.714	−	402.822i	−0.216582	−	0.647623i
$623$	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
$627$			236.536i			0.377250i
$628$	67.1053	+	89.1081i	0.106856	+	0.141892i
$629$	435.658	+	435.658i	0.692619	+	0.692619i
$630$	−99.7413	−	3.85177i	−0.158320	−	0.00611391i
$631$		−	110.857i		−	0.175685i	−0.996134	−	0.0878423i	$-0.972003\pi$
$631$		−	110.857i		−	0.175685i	0.996134	−	0.0878423i	$-0.0279972\pi$
$632$	−14.1790	−	9.75448i	−0.0224351	−	0.0154343i
$633$	−73.6276	−	73.6276i	−0.116315	−	0.116315i
$634$	273.170	+	816.830i	0.430867	+	1.28838i
$635$	−412.873	+	1092.47i	−0.650193	+	1.72043i
$636$	662.113	+	879.210i	1.04106	+	1.38241i
$637$		−	194.117i		−	0.304737i
$638$	−66.3173	−	198.302i	−0.103946	−	0.310818i
$639$			95.7673i			0.149871i
$640$	283.203	−	573.931i	0.442504	−	0.896766i
$641$	−370.450			−0.577926			−0.288963	−	0.957340i	$-0.593310\pi$
$641$	−370.450			−0.577926			−0.288963	+	0.957340i	$0.593310\pi$
$642$	104.961	−	35.1017i	0.163491	−	0.0546756i
$643$	686.295			1.06733			0.533667	−	0.845695i	$-0.320814\pi$
$643$	686.295			1.06733			0.533667	+	0.845695i	$0.320814\pi$
$644$	−71.4255	+	53.7889i	−0.110909	+	0.0835232i
$645$	−121.002	+	54.6275i	−0.187601	+	0.0846938i
$646$	362.043	−	121.077i	0.560439	−	0.187426i
$647$	499.985	−	499.985i	0.772774	−	0.772774i	−0.205817	−	0.978591i	$-0.565985\pi$
$647$	499.985	−	499.985i	0.772774	−	0.772774i	0.978591	+	0.205817i	$0.0659851\pi$
$648$	306.094	−	444.934i	0.472367	−	0.686627i
$649$	326.258			0.502708
$650$	412.715	−	976.352i	0.634947	−	1.50208i
$651$	−353.641	+	353.641i	−0.543227	+	0.543227i
$652$	−390.389	+	293.993i	−0.598756	+	0.450910i
$653$	599.129			0.917502			0.458751	−	0.888565i	$-0.348297\pi$
$653$	599.129			0.917502			0.458751	+	0.888565i	$0.348297\pi$
$654$	−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
$658$	966.112	−	323.093i	1.46826	−	0.491023i
$659$	55.5691	−	55.5691i	0.0843233	−	0.0843233i	−0.663687	−	0.748010i	$-0.731009\pi$
$659$	55.5691	−	55.5691i	0.0843233	−	0.0843233i	0.748010	+	0.663687i	$0.231009\pi$
$660$	−224.385	+	65.5288i	−0.339977	+	0.0992861i
$661$	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	$0.241707\pi$
$662$	−4.67689	+	9.37681i	−0.00706478	+	0.0141644i
$663$	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
$667$	72.7147			0.109018
$668$	80.6477	−	572.575i	0.120730	−	0.857149i
$669$	250.069	−	250.069i	0.373795	−	0.373795i
$670$	−800.460	+	740.935i	−1.19472	+	1.10587i
$671$	−72.1498			−0.107526
$672$	498.623	+	457.601i	0.741998	+	0.680954i
$673$	−348.271	+	348.271i	−0.517490	+	0.517490i	−0.916811	−	0.399321i	$-0.869246\pi$
$673$	−348.271	+	348.271i	−0.517490	+	0.517490i	0.399321	+	0.916811i	$0.369246\pi$
$674$	572.621	+	285.607i	0.849586	+	0.423749i
$675$	472.717	−	536.086i	0.700321	−	0.794201i
$676$	896.079	−	674.817i	1.32556	−	0.998250i
$677$	−780.155			−1.15237			−0.576185	−	0.817319i	$-0.695459\pi$
$677$	−780.155			−1.15237			−0.576185	+	0.817319i	$0.695459\pi$
$678$	168.684	−	338.198i	0.248796	−	0.498818i
$679$	92.0950			0.135633
$680$	215.156	+	309.903i	0.316406	+	0.455740i
$681$		−	959.715i		−	1.40927i
$682$	88.9640	−	178.366i	0.130446	−	0.261534i
$683$		−	170.375i		−	0.249451i	−0.992191	−	0.124725i	$-0.960195\pi$
$683$		−	170.375i		−	0.249451i	0.992191	−	0.124725i	$-0.0398050\pi$
$684$	14.7779	−	104.919i	0.0216052	−	0.153390i
$685$	−809.616	−	305.974i	−1.18192	−	0.446677i
$686$	−543.807	−	271.235i	−0.792722	−	0.395387i
$687$	−203.770	−	203.770i	−0.296609	−	0.296609i
$688$	−147.229	−	42.3142i	−0.213996	−	0.0615032i
$689$			2103.41i			3.05285i
$690$	3.13691	−	81.2301i	0.00454625	−	0.117725i
$691$	−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	$0.766705\pi$
$692$	463.214	−	348.836i	0.669384	−	0.504098i
$693$			42.0668i			0.0607025i
$694$	−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
$698$	259.930	−	521.141i	0.372393	−	0.746620i
$699$	−240.717	−	240.717i	−0.344374	−	0.344374i
$700$	496.050	+	579.223i	0.708643	+	0.827461i
$701$	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	$0.728024\pi$
$702$	1149.61	−	384.460i	1.63762	−	0.547663i
$703$	−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
$707$		−	701.142i		−	0.991714i
$708$	850.371	+	119.775i	1.20109	+	0.169174i
$709$	−815.622	−	815.622i	−1.15038	−	1.15038i	−0.986476	−	0.163908i	$-0.947590\pi$
$709$	−815.622	−	815.622i	−1.15038	−	1.15038i	−0.163908	−	0.986476i	$-0.552410\pi$
$710$	536.951	−	497.021i	0.756269	−	0.700030i
$711$		−	2.81577i		−	0.00396030i
$712$	−175.610	+	255.265i	−0.246643	+	0.358518i
$713$	49.0133	+	49.0133i	0.0687424	+	0.0687424i
$714$	−378.350	+	126.530i	−0.529902	+	0.177213i
$715$	−417.885	−	157.929i	−0.584454	−	0.220880i
$716$	56.1313	−	398.516i	0.0783957	−	0.556587i
$717$			567.946i			0.792114i
$718$	−206.449	+	69.0420i	−0.287534	+	0.0961588i
$719$			125.050i			0.173922i	0.996212	+	0.0869612i	$0.0277156\pi$
$719$			125.050i			0.173922i	−0.996212	+	0.0869612i	$0.972284\pi$
$720$	103.623	−	15.0475i	0.143922	−	0.0208993i
$721$	−354.864			−0.492183
$722$	30.8051	+	92.1131i	0.0426663	+	0.127581i
$723$	274.224			0.379286
$724$	−152.237	+	1080.84i	−0.210273	+	1.49288i
$725$	−38.8804	−	618.958i	−0.0536282	−	0.853735i
$726$	−181.612	−	543.056i	−0.250155	−	0.748011i
$727$	−307.763	+	307.763i	−0.423333	+	0.423333i	−0.886350	−	0.463016i	$-0.846767\pi$
$727$	−307.763	+	307.763i	−0.423333	+	0.423333i	0.463016	+	0.886350i	$0.346767\pi$
$728$	235.119	+	1271.82i	0.322966	+	1.74701i
$729$	801.940			1.10005
$730$	9.28641	−	240.471i	0.0127211	−	0.329413i
$731$	63.8535	−	63.8535i	0.0873510	−	0.0873510i
$732$	−188.054	−	26.4876i	−0.256905	−	0.0361852i
$733$	−94.8581			−0.129411			−0.0647054	−	0.997904i	$-0.520611\pi$
$733$	−94.8581			−0.129411			−0.0647054	+	0.997904i	$0.520611\pi$
$734$	−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
$738$	−0.981765	−	2.93567i	−0.00133030	−	0.00397787i
$739$	−761.284	+	761.284i	−1.03015	+	1.03015i	−0.0306228	+	0.999531i	$0.509749\pi$
$739$	−761.284	+	761.284i	−1.03015	+	1.03015i	−0.999531	+	0.0306228i	$0.990251\pi$
$740$	−1145.74	−	627.802i	−1.54830	−	0.848381i
$741$	−841.348	+	841.348i	−1.13542	+	1.13542i
$742$	−1354.18	−	675.427i	−1.82504	−	0.910279i
$743$	−700.467	−	700.467i	−0.942754	−	0.942754i	0.0556935	−	0.998448i	$-0.482263\pi$
$743$	−700.467	−	700.467i	−0.942754	−	0.942754i	−0.998448	+	0.0556935i	$0.982263\pi$
$744$	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
$747$	−100.110			−0.134016
$748$	127.011	−	95.6490i	0.169800	−	0.127873i
$749$	−107.599	+	107.599i	−0.143657	+	0.143657i
$750$	−693.120	+	16.7318i	−0.924160	+	0.0223090i
$751$	268.325			0.357291			0.178645	−	0.983914i	$-0.442829\pi$
$751$	268.325			0.357291			0.178645	+	0.983914i	$0.442829\pi$
$752$	−934.986	+	517.529i	−1.24333	+	0.688203i
$753$	−106.320	+	106.320i	−0.141195	+	0.141195i
$754$	469.463	−	941.239i	0.622630	−	1.24833i
$755$	456.184	−	205.948i	0.604217	−	0.272779i
$756$	−121.635	+	863.574i	−0.160893	+	1.14229i
$757$	−777.969			−1.02770			−0.513850	−	0.857880i	$-0.671781\pi$
$757$	−777.969			−1.02770			−0.513850	+	0.857880i	$0.671781\pi$
$758$	370.736	+	184.912i	0.489097	+	0.243948i
$759$	−34.2596			−0.0451378
$760$	−664.960	+	461.661i	−0.874947	+	0.607449i
$761$		−	1058.98i		−	1.39156i	−0.718254	−	0.695781i	$-0.755058\pi$
$761$		−	1058.98i		−	1.39156i	0.718254	−	0.695781i	$-0.244942\pi$
$762$	1159.35	+	578.250i	1.52146	+	0.758858i
$763$		−	338.819i		−	0.444062i
$764$	−669.595	+	504.257i	−0.876433	+	0.660022i
$765$	−21.8211	+	57.7392i	−0.0285243	+	0.0754760i
$766$	−98.2799	+	197.044i	−0.128303	+	0.257238i
$767$	1160.49	+	1160.49i	1.51302	+	1.51302i
$768$	−601.624	−	376.954i	−0.783364	−	0.490825i
$769$		−	262.583i		−	0.341461i	−0.985318	−	0.170730i	$-0.945387\pi$
$769$		−	262.583i		−	0.341461i	0.985318	−	0.170730i	$-0.0546127\pi$
$770$	235.862	−	218.322i	0.306314	−	0.283535i
$771$	461.699	+	461.699i	0.598832	+	0.598832i
$772$	−71.2211	+	505.649i	−0.0922553	+	0.654986i
$773$			405.962i			0.525177i	0.964908	+	0.262588i	$0.0845761\pi$
$773$			405.962i			0.525177i	−0.964908	+	0.262588i	$0.915424\pi$
$774$	−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
$778$	231.150	+	115.291i	0.297108	+	0.148189i
$779$	16.9217	+	16.9217i	0.0217224	+	0.0217224i
$780$	−1031.21	−	565.046i	−1.32207	−	0.724417i
$781$	−218.044	−	218.044i	−0.279185	−	0.279185i
$782$	17.5366	+	52.4380i	0.0224254	+	0.0670562i
$783$	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
$787$			107.060i			0.136036i	0.997684	+	0.0680181i	$0.0216676\pi$
$787$			107.060i			0.136036i	−0.997684	+	0.0680181i	$0.978332\pi$
$788$	216.747	−	163.228i	0.275060	−	0.207142i
$789$	−218.285	−	218.285i	−0.276660	−	0.276660i
$790$	−15.7876	+	14.6135i	−0.0199843	+	0.0184982i
$791$			519.622i			0.656918i
$792$	−8.02221	−	43.3944i	−0.0101291	−	0.0547909i
$793$	−256.634	−	256.634i	−0.323624	−	0.323624i
$794$	115.269	+	344.675i	0.145174	+	0.434100i
$795$	1253.93	−	566.099i	1.57728	−	0.712074i
$796$	−890.751	+	670.804i	−1.11903	+	0.842719i
$797$		−	615.958i		−	0.772846i	−0.922322	−	0.386423i	$-0.873711\pi$
$797$		−	615.958i		−	0.772846i	0.922322	−	0.386423i	$-0.126289\pi$
$798$	−271.496	−	811.827i	−0.340221	−	1.01733i
$799$		−	629.957i		−	0.788432i
$800$	−622.163	−	502.905i	−0.777704	−	0.628631i
$801$	−50.6924			−0.0632864
$802$	1060.66	−	354.713i	1.32252	−	0.442285i
$803$	−101.421			−0.126303
$804$	727.889	+	966.553i	0.905335	+	1.20218i
$805$	45.9889	+	101.867i	0.0571290	+	0.126543i
$806$	950.883	−	318.000i	1.17976	−	0.394542i
$807$	−272.517	+	272.517i	−0.337692	+	0.337692i
$808$	133.709	+	723.269i	0.165481	+	0.895135i
$809$	−304.293			−0.376135			−0.188067	−	0.982156i	$-0.560222\pi$
$809$	−304.293			−0.376135			−0.188067	+	0.982156i	$0.560222\pi$
$810$	−458.570	−	495.411i	−0.566136	−	0.611618i
$811$	−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	$0.255608\pi$
$812$	455.222	+	604.482i	0.560618	+	0.744436i
$813$	−321.610			−0.395584
$814$	−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
$818$	−1373.79	+	459.433i	−1.67945	+	0.561654i
$819$	−149.630	+	149.630i	−0.182699	+	0.182699i
$820$	−11.3645	+	20.7404i	−0.0138592	+	0.0252931i
$821$	−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	$0.356515\pi$
$822$	−428.533	+	859.176i	−0.521329	+	1.04523i
$823$	−420.324	−	420.324i	−0.510721	−	0.510721i	0.404026	−	0.914747i	$-0.367610\pi$
$823$	−420.324	−	420.324i	−0.510721	−	0.510721i	−0.914747	+	0.404026i	$0.867610\pi$
$824$	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
$827$	−844.006			−1.02056			−0.510281	−	0.860007i	$-0.670459\pi$
$827$	−844.006			−1.02056			−0.510281	+	0.860007i	$0.670459\pi$
$828$	15.1964	+	2.14042i	0.0183531	+	0.00258505i
$829$	222.833	−	222.833i	0.268798	−	0.268798i	−0.559818	−	0.828616i	$-0.689129\pi$
$829$	222.833	−	222.833i	0.268798	−	0.268798i	0.828616	+	0.559818i	$0.189129\pi$
$830$	519.558	+	561.298i	0.625973	+	0.676262i
$831$	944.609			1.13671
$832$	−485.078	−	1267.12i	−0.583026	−	1.52298i
$833$	61.0668	−	61.0668i	0.0733095	−	0.0733095i
$834$	1147.76	+	572.471i	1.37622	+	0.686417i
$835$	−676.111	−	255.519i	−0.809714	−	0.306011i
$836$	205.234	+	272.527i	0.245496	+	0.325990i
$837$	676.067			0.807726
$838$	96.5320	−	193.540i	0.115193	−	0.230954i
$839$	554.445			0.660841			0.330420	−	0.943834i	$-0.392809\pi$
$839$	554.445			0.660841			0.330420	+	0.943834i	$0.392809\pi$
$840$	694.910	−	482.454i	0.827273	−	0.574351i
$841$			225.607i			0.268260i
$842$	−594.225	+	1191.38i	−0.705730	+	1.41494i
$843$		−	287.150i		−	0.340628i
$844$	−148.715	−	20.9466i	−0.176203	−	0.0248183i
$845$	−576.960	−	1277.99i	−0.682793	−	1.51242i
$846$	−156.462	−	78.0386i	−0.184943	−	0.0922442i
$847$	556.705	+	556.705i	0.657267	+	0.657267i
$848$	1525.72	+	438.498i	1.79920	+	0.517096i
$849$		−	1558.55i		−	1.83575i
$850$	436.983	−	177.313i	0.514097	−	0.208603i
$851$	−135.394	−	135.394i	−0.159100	−	0.159100i
$852$	−488.270	−	648.366i	−0.573087	−	0.760993i
$853$		−	431.993i		−	0.506440i	−0.967409	−	0.253220i	$-0.918510\pi$
$853$		−	431.993i		−	0.506440i	0.967409	−	0.253220i	$-0.0814896\pi$
$854$	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	$-0.626693\pi$
$857$	457.844	−	457.844i	0.534241	−	0.534241i	0.921831	+	0.387591i	$0.126693\pi$
$858$	−221.188	+	443.465i	−0.257795	+	0.516859i
$859$	822.277	+	822.277i	0.957249	+	0.957249i	0.999123	−	0.0418737i	$-0.0133327\pi$
$859$	822.277	+	822.277i	0.957249	+	0.957249i	−0.0418737	+	0.999123i	$0.513333\pi$
$860$	−92.0157	+	167.929i	−0.106995	+	0.195267i
$861$	−17.6839	−	17.6839i	−0.0205388	−	0.0205388i
$862$	−351.102	+	117.418i	−0.407311	+	0.136216i
$863$	132.089	−	132.089i	0.153058	−	0.153058i	−0.626424	−	0.779482i	$-0.715482\pi$
$863$	132.089	−	132.089i	0.153058	−	0.153058i	0.779482	+	0.626424i	$0.215482\pi$
$864$	−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
$867$		−	554.775i		−	0.639879i
$868$	−100.609	+	714.293i	−0.115909	+	0.822919i
$869$	6.41098	+	6.41098i	0.00737742	+	0.00737742i
$870$	−687.460	−	26.5480i	−0.790184	−	0.0305150i
$871$			2312.37i			2.65485i
$872$	64.6133	+	349.511i	0.0740978	+	0.400816i
$873$	−11.1769	−	11.1769i	−0.0128029	−	0.0128029i
$874$	−112.516	+	37.6284i	−0.128737	+	0.0430531i
$875$	842.520	−	445.932i	0.962880	−	0.509637i
$876$	−264.348	−	37.2336i	−0.301767	−	0.0425041i
$877$			363.488i			0.414468i	0.978291	+	0.207234i	$0.0664461\pi$
$877$			363.488i			0.414468i	−0.978291	+	0.207234i	$0.933554\pi$
$878$	−295.360	+	98.7761i	−0.336401	+	0.112501i
$879$		−	5.29476i		−	0.00602362i
$880$	−201.671	+	270.191i	−0.229171	+	0.307036i
$881$	−242.827			−0.275627			−0.137813	−	0.990458i	$-0.544007\pi$
$881$	−242.827			−0.275627			−0.137813	+	0.990458i	$0.544007\pi$
$882$	−7.60218	−	22.7320i	−0.00861925	−	0.0257732i
$883$	1629.94			1.84592			0.922959	−	0.384899i	$-0.125764\pi$
$883$	1629.94			1.84592			0.922959	+	0.384899i	$0.125764\pi$
$884$	791.992	+	111.553i	0.895918	+	0.126191i
$885$	379.489	−	1004.14i	0.428801	−	1.13462i
$886$	−462.389	−	1382.63i	−0.521884	−	1.56053i
$887$	196.533	−	196.533i	0.221570	−	0.221570i	−0.587589	−	0.809160i	$-0.699923\pi$
$887$	196.533	−	196.533i	0.221570	−	0.221570i	0.809160	+	0.587589i	$0.199923\pi$
$888$	−821.429	+	1194.02i	−0.925032	+	1.34462i
$889$	−1781.27			−2.00368
$890$	263.088	+	284.224i	0.295604	+	0.319353i
$891$	−201.175	+	201.175i	−0.225786	+	0.225786i
$892$	71.1431	−	505.096i	0.0797569	−	0.566251i
$893$	1351.70			1.51366
$894$	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
$898$	29.7792	+	89.0455i	0.0331617	+	0.0991598i
$899$	414.806	−	414.806i	0.461408	−	0.461408i
$900$	10.0941	−	130.498i	0.0112157	−	0.144998i
$901$	−661.707	+	661.707i	−0.734414	+	0.734414i
$902$	8.91925	+	4.44867i	0.00988830	+	0.00493200i
$903$	−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
$907$	−188.488			−0.207814			−0.103907	−	0.994587i	$-0.533134\pi$
$907$	−188.488			−0.207814			−0.103907	+	0.994587i	$0.533134\pi$
$908$	−832.713	−	1105.75i	−0.917085	−	1.21778i
$909$	−85.0925	+	85.0925i	−0.0936112	+	0.0936112i
$910$	1615.51	+	62.3872i	1.77529	+	0.0685574i
$911$	1051.06			1.15374			0.576870	−	0.816836i	$-0.304274\pi$
$911$	1051.06			1.15374			0.576870	+	0.816836i	$0.304274\pi$
$912$	434.881	+	785.672i	0.476843	+	0.861482i
$913$	227.930	−	227.930i	0.249650	−	0.249650i
$914$	287.118	−	575.650i	0.314133	−	0.629814i
$915$	−83.9216	+	222.059i	−0.0917176	+	0.242687i
$916$	−411.581	−	57.9715i	−0.449324	−	0.0632877i
$917$	118.315			0.129024
$918$	482.598	+	240.706i	0.525706	+	0.262207i
$919$	158.471			0.172439			0.0862195	−	0.996276i	$-0.472521\pi$
$919$	158.471			0.172439			0.0862195	+	0.996276i	$0.472521\pi$
$920$	−66.8665	−	96.3120i	−0.0726809	−	0.104687i
$921$			1291.01i			1.40175i
$922$	−672.931	−	335.639i	−0.729860	−	0.364033i
$923$		−	1551.15i		−	1.68055i
$924$	−214.478	−	284.802i	−0.232119	−	0.308227i
$925$	−1080.10	+	1224.89i	−1.16768	+	1.32420i
$926$	−1.47276	+	2.95277i	−0.00159045	+	0.00318874i
$927$	43.0673	+	43.0673i	0.0464588	+	0.0464588i
$928$	−584.864	−	536.747i	−0.630241	−	0.578391i
$929$		−	1081.59i		−	1.16425i	−0.813100	−	0.582124i	$-0.802222\pi$
$929$		−	1081.59i		−	1.16425i	0.813100	−	0.582124i	$-0.197778\pi$
$930$	−445.488	−	481.277i	−0.479019	−	0.517502i
$931$	131.031	+	131.031i	0.140743	+	0.140743i
$932$	−486.207	−	68.4827i	−0.521682	−	0.0734793i
$933$			588.978i			0.631273i
$934$	−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	$-0.630894\pi$
$937$	484.345	−	484.345i	0.516910	−	0.516910i	0.916635	+	0.399725i	$0.130894\pi$
$938$	−1488.71	−	742.526i	−1.58711	−	0.791605i
$939$	−127.656	−	127.656i	−0.135949	−	0.135949i
$940$	374.469	+	1282.27i	0.398371	+	1.36411i
$941$	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	$0.612912\pi$
$942$	−49.0584	−	146.694i	−0.0520790	−	0.155726i
$943$	−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
$947$		−	476.289i		−	0.502945i	−0.967864	−	0.251473i	$-0.919085\pi$
$947$		−	476.289i		−	0.502945i	0.967864	−	0.251473i	$-0.0809149\pi$
$948$	14.3562	+	19.0634i	0.0151437	+	0.0201091i
$949$	−360.750	−	360.750i	−0.380137	−	0.380137i
$950$	380.461	+	937.635i	0.400485	+	0.986984i
$951$		−	1194.31i		−	1.25585i
$952$	−326.134	+	474.065i	−0.342578	+	0.497967i
$953$	−80.9782	−	80.9782i	−0.0849719	−	0.0849719i	0.663343	−	0.748315i	$-0.269137\pi$
$953$	−80.9782	−	80.9782i	−0.0849719	−	0.0849719i	−0.748315	+	0.663343i	$0.769137\pi$
$954$	82.3755	+	246.319i	0.0863475	+	0.258196i
$955$	431.134	+	954.980i	0.451449	+	0.999979i
$956$	492.788	+	654.365i	0.515468	+	0.684482i
$957$			289.943i			0.302971i
$958$	350.408	+	1047.79i	0.365771	+	1.09373i
$959$		−	1320.07i		−	1.37651i
$960$	−624.835	+	630.200i	−0.650870	+	0.656459i
$961$	−401.801			−0.418107
$962$	−2626.71	+	878.443i	−2.73047	+	0.913142i
$963$	26.1170			0.0271205
$964$	315.950	−	237.935i	0.327749	−	0.246820i
$965$	597.083	+	225.652i	0.618739	+	0.233837i
$966$	117.584	−	39.3232i	0.121723	−	0.0407073i
$967$	226.347	−	226.347i	0.234072	−	0.234072i	−0.580318	−	0.814390i	$-0.697072\pi$
$967$	226.347	−	226.347i	0.234072	−	0.234072i	0.814390	+	0.580318i	$0.197072\pi$
$968$	−680.438	−	468.109i	−0.702932	−	0.483584i
$969$	−529.355			−0.546290
$970$	−4.66013	+	120.674i	−0.00480426	+	0.124406i
$971$	−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	$0.338183\pi$
$972$	223.954	−	168.655i	0.230406	−	0.173513i
$973$	−1763.47			−1.81241
$974$	−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	0.802461	−	0.596705i	$-0.203524\pi$
$977$	201.023	+	201.023i	0.205756	+	0.205756i	−0.596705	+	0.802461i	$0.703524\pi$
$978$	642.677	−	214.928i	0.657134	−	0.219763i
$979$	115.417	−	115.417i	0.117893	−	0.117893i
$980$	−88.0000	+	160.601i	−0.0897959	+	0.163878i
$981$	−41.1200	+	41.1200i	−0.0419164	+	0.0419164i
$982$	779.966	−	1563.77i	0.794263	−	1.59244i
$983$	−536.933	−	536.933i	−0.546218	−	0.546218i	0.379126	−	0.925345i	$-0.376225\pi$
$983$	−536.933	−	536.933i	−0.546218	−	0.546218i	−0.925345	+	0.379126i	$0.876225\pi$
$984$	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
$987$	−1412.58			−1.43119
$988$	−239.359	+	1699.38i	−0.242266	+	1.72002i
$989$	−19.8445	+	19.8445i	−0.0200652	+	0.0200652i
$990$	−55.1210	−	2.12864i	−0.0556778	−	0.00215014i
$991$	−1164.95			−1.17553			−0.587764	−	0.809032i	$-0.699992\pi$
$991$	−1164.95			−1.17553			−0.587764	+	0.809032i	$0.699992\pi$
$992$	−32.4331	−	756.021i	−0.0326947	−	0.762118i
$993$	10.2742	−	10.2742i	0.0103466	−	0.0103466i
$994$	998.631	+	498.088i	1.00466	+	0.501095i
$995$	573.530	+	1270.39i	0.576412	+	1.27678i
$996$	677.765	−	510.410i	0.680487	−	0.512459i
$997$	1493.41			1.49790			0.748950	−	0.662627i	$-0.230558\pi$
$997$	1493.41			1.49790			0.748950	+	0.662627i	$0.230558\pi$
$998$	−543.580	+	1089.84i	−0.544669	+	1.09202i
$999$	−1867.56			−1.86943

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.14	✓	44	5.3	odd	4
80.3.i.a.37.14	yes	44	16.5	even	4
80.3.t.a.53.4	yes	44	80.53	odd	4	inner
80.3.t.a.77.4	yes	44	1.1	even	1	trivial
320.3.i.a.177.16		44	16.11	odd	4
320.3.i.a.273.7		44	20.3	even	4
320.3.t.a.17.7		44	4.3	odd	2
320.3.t.a.113.7		44	80.43	even	4
400.3.i.b.93.9		44	5.2	odd	4
400.3.i.b.357.9		44	80.69	even	4
400.3.t.b.157.19		44	5.4	even	2
400.3.t.b.293.19		44	80.37	odd	4
640.3.i.a.33.16		44	40.3	even	4
640.3.i.a.97.7		44	16.3	odd	4
640.3.i.b.33.7		44	40.13	odd	4
640.3.i.b.97.16		44	16.13	even	4
640.3.t.a.353.16		44	80.3	even	4
640.3.t.a.417.16		44	8.3	odd	2
640.3.t.b.353.7		44	80.13	odd	4
640.3.t.b.417.7		44	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	80.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89674 + 0.634321i) q^{2} +2.77329 q^{3} +(3.19527 - 2.40629i) q^{4} +(-2.05735 - 4.55712i) q^{5} +(-5.26021 + 1.75915i) q^{6} +(5.39242 - 5.39242i) q^{7} +(-4.53426 + 6.59094i) q^{8} -1.30888 q^{9} +O(q^{10})\)	\(q+(-1.89674 + 0.634321i) q^{2} +2.77329 q^{3} +(3.19527 - 2.40629i) q^{4} +(-2.05735 - 4.55712i) q^{5} +(-5.26021 + 1.75915i) q^{6} +(5.39242 - 5.39242i) q^{7} +(-4.53426 + 6.59094i) q^{8} -1.30888 q^{9} +(6.79294 + 7.33867i) q^{10} +(2.98007 - 2.98007i) q^{11} +(8.86141 - 6.67333i) q^{12} +21.2000 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} +(2.48261 - 0.830250i) q^{18} +(-14.3102 + 14.3102i) q^{19} +(-17.5395 - 9.61066i) q^{20} +(14.9547 - 14.9547i) q^{21} +(-3.76211 + 7.54275i) 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} -28.5895 q^{27} +(4.25454 - 30.2060i) q^{28} +(-17.5413 + 17.5413i) q^{29} +(18.8388 + 20.3522i) q^{30} -23.6474 q^{31} +(1.37153 + 31.9706i) q^{32} +(8.26459 - 8.26459i) q^{33} +(-16.8803 - 8.41940i) q^{34} +(-35.6680 - 13.4798i) q^{35} +(-4.18223 + 3.14954i) q^{36} +65.3234 q^{37} +(18.0655 - 36.2201i) q^{38} +58.7936 q^{39} +(39.3642 + 7.10327i) q^{40} -1.18249i q^{41} +(-18.8792 + 37.8514i) q^{42} -9.57434i q^{43} +(2.35123 - 16.6930i) q^{44} +(2.69282 + 5.96472i) q^{45} +(5.24607 + 2.61659i) q^{46} +(-47.2286 - 47.2286i) q^{47} +(12.2567 - 42.6462i) q^{48} -9.15649i q^{49} +(19.4677 - 46.0544i) q^{50} +(18.4957 + 18.4957i) q^{51} +(67.7397 - 51.0133i) q^{52} +99.2178i 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} +(22.1445 - 44.3981i) q^{58} +(54.7400 + 54.7400i) q^{59} +(-48.6422 - 26.6531i) q^{60} +(-12.1054 - 12.1054i) q^{61} +(44.8531 - 15.0000i) 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} +109.074i q^{67} +(37.3582 + 5.26193i) q^{68} +(-5.74812 - 5.74812i) q^{69} +(76.2036 + 2.94280i) q^{70} -73.1674i q^{71} +(5.93479 - 8.62675i) q^{72} +(-17.0166 - 17.0166i) q^{73} +(-123.902 + 41.4360i) q^{74} +(-45.8553 + 52.0023i) q^{75} +(-11.2905 + 80.1595i) q^{76} -32.1396i q^{77} +(-111.516 + 37.2940i) q^{78} +2.15129i q^{79} +(-79.1696 + 11.4965i) q^{80} -67.5069 q^{81} +(0.750081 + 2.24289i) q^{82} +76.4850 q^{83} +(11.7991 - 83.7699i) q^{84} +(16.6716 - 44.1134i) q^{85} +(6.07320 + 18.1601i) q^{86} +(-48.6470 + 48.6470i) q^{87} +(6.12907 + 33.1539i) q^{88} +38.7296 q^{89} +(-8.89113 - 9.60543i) q^{90} +(114.319 - 114.319i) q^{91} +(-11.6102 - 1.63531i) q^{92} -65.5810 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} +(5.80816 + 17.3675i) q^{98} +(-3.90055 + 3.90055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} + 108 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 + 108 * q^9	\( 44 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} + 108 q^{9} - 10 q^{10} - 4 q^{11} - 44 q^{12} - 4 q^{13} - 4 q^{15} + 24 q^{16} - 4 q^{17} - 42 q^{18} - 32 q^{19} - 44 q^{20} - 4 q^{21} + 16 q^{22} - 36 q^{24} - 52 q^{26} - 40 q^{27} - 104 q^{28} - 160 q^{30} - 8 q^{31} - 12 q^{32} - 4 q^{33} + 88 q^{34} - 4 q^{35} - 116 q^{36} - 4 q^{37} - 68 q^{38} - 72 q^{39} + 200 q^{40} + 244 q^{42} + 168 q^{44} - 70 q^{45} + 108 q^{46} - 4 q^{47} - 4 q^{48} + 206 q^{50} - 100 q^{51} + 264 q^{52} - 228 q^{54} - 172 q^{56} - 36 q^{57} + 332 q^{58} - 64 q^{59} + 364 q^{60} - 36 q^{61} + 84 q^{62} - 200 q^{63} + 176 q^{64} - 4 q^{65} + 276 q^{66} + 440 q^{68} + 60 q^{69} + 472 q^{70} - 288 q^{72} - 48 q^{73} - 284 q^{74} - 324 q^{75} + 252 q^{76} - 132 q^{78} - 588 q^{80} + 100 q^{81} - 388 q^{82} + 156 q^{83} - 288 q^{84} - 52 q^{85} + 20 q^{86} - 36 q^{87} + 160 q^{88} - 554 q^{90} + 188 q^{91} - 352 q^{92} - 40 q^{93} + 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 818 q^{98} + 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 + 108 * q^9 - 10 * q^10 - 4 * q^11 - 44 * q^12 - 4 * q^13 - 4 * q^15 + 24 * q^16 - 4 * q^17 - 42 * q^18 - 32 * q^19 - 44 * q^20 - 4 * q^21 + 16 * q^22 - 36 * q^24 - 52 * q^26 - 40 * q^27 - 104 * q^28 - 160 * q^30 - 8 * q^31 - 12 * q^32 - 4 * q^33 + 88 * q^34 - 4 * q^35 - 116 * q^36 - 4 * q^37 - 68 * q^38 - 72 * q^39 + 200 * q^40 + 244 * q^42 + 168 * q^44 - 70 * q^45 + 108 * q^46 - 4 * q^47 - 4 * q^48 + 206 * q^50 - 100 * q^51 + 264 * q^52 - 228 * q^54 - 172 * q^56 - 36 * q^57 + 332 * q^58 - 64 * q^59 + 364 * q^60 - 36 * q^61 + 84 * q^62 - 200 * q^63 + 176 * q^64 - 4 * q^65 + 276 * q^66 + 440 * q^68 + 60 * q^69 + 472 * q^70 - 288 * q^72 - 48 * q^73 - 284 * q^74 - 324 * q^75 + 252 * q^76 - 132 * q^78 - 588 * q^80 + 100 * q^81 - 388 * q^82 + 156 * q^83 - 288 * q^84 - 52 * q^85 + 20 * q^86 - 36 * q^87 + 160 * q^88 - 554 * q^90 + 188 * q^91 - 352 * q^92 - 40 * q^93 + 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 818 * q^98 + 92 * q^99

Introduction

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