LMFDB - Embedded newform 80.3.t.a.77.11

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			77.11
Character	$\chi$	$=$	80.77
Dual form			80.3.t.a.53.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.284962 + 1.97960i) q^{2} -2.50699 q^{3} +(-3.83759 - 1.12822i) q^{4} +(-4.36488 - 2.43881i) q^{5} +(0.714398 - 4.96283i) q^{6} +(7.18571 - 7.18571i) q^{7} +(3.32699 - 7.27538i) q^{8} -2.71500 q^{9} +O(q^{10})$	\(q+(-0.284962 + 1.97960i) q^{2} -2.50699 q^{3} +(-3.83759 - 1.12822i) q^{4} +(-4.36488 - 2.43881i) q^{5} +(0.714398 - 4.96283i) q^{6} +(7.18571 - 7.18571i) q^{7} +(3.32699 - 7.27538i) q^{8} -2.71500 q^{9} +(6.07168 - 7.94573i) q^{10} +(-8.38398 + 8.38398i) q^{11} +(9.62081 + 2.82844i) q^{12} -12.9652 q^{13} +(12.1771 + 16.2724i) q^{14} +(10.9427 + 6.11407i) q^{15} +(13.4542 + 8.65930i) q^{16} +(-22.8157 - 22.8157i) q^{17} +(0.773673 - 5.37460i) q^{18} +(3.16584 - 3.16584i) q^{19} +(13.9991 + 14.2837i) q^{20} +(-18.0145 + 18.0145i) q^{21} +(-14.2078 - 18.9860i) q^{22} +(3.81600 + 3.81600i) q^{23} +(-8.34073 + 18.2393i) q^{24} +(13.1044 + 21.2902i) q^{25} +(3.69459 - 25.6658i) q^{26} +29.3694 q^{27} +(-35.6829 + 19.4688i) q^{28} +(-18.3544 + 18.3544i) q^{29} +(-15.2217 + 19.9199i) q^{30} -8.78531 q^{31} +(-20.9759 + 24.1664i) q^{32} +(21.0186 - 21.0186i) q^{33} +(51.6674 - 38.6642i) q^{34} +(-48.8893 + 13.8402i) q^{35} +(10.4191 + 3.06312i) q^{36} +32.4039 q^{37} +(5.36494 + 7.16923i) q^{38} +32.5036 q^{39} +(-32.2652 + 23.6423i) q^{40} +0.937574i q^{41} +(-30.5280 - 40.7949i) q^{42} -57.8364i q^{43} +(41.6333 - 22.7153i) q^{44} +(11.8506 + 6.62136i) q^{45} +(-8.64156 + 6.46672i) q^{46} +(27.9276 + 27.9276i) q^{47} +(-33.7296 - 21.7088i) q^{48} -54.2688i q^{49} +(-45.8803 + 19.8745i) q^{50} +(57.1987 + 57.1987i) q^{51} +(49.7550 + 14.6276i) q^{52} -20.6425i q^{53} +(-8.36917 + 58.1395i) q^{54} +(57.0420 - 16.1482i) q^{55} +(-28.3720 - 76.1855i) q^{56} +(-7.93674 + 7.93674i) q^{57} +(-31.1040 - 41.5647i) q^{58} +(-40.1490 - 40.1490i) q^{59} +(-35.0957 - 35.8091i) q^{60} +(-25.3893 - 25.3893i) q^{61} +(2.50348 - 17.3913i) q^{62} +(-19.5092 + 19.5092i) q^{63} +(-41.8623 - 48.4102i) q^{64} +(56.5915 + 31.6196i) q^{65} +(35.6187 + 47.5978i) q^{66} -29.3419i q^{67} +(61.8162 + 113.298i) q^{68} +(-9.56668 - 9.56668i) q^{69} +(-13.4664 - 100.725i) q^{70} +34.7686i q^{71} +(-9.03277 + 19.7526i) q^{72} +(-76.2777 - 76.2777i) q^{73} +(-9.23390 + 64.1466i) q^{74} +(-32.8527 - 53.3744i) q^{75} +(-15.7210 + 8.57745i) q^{76} +120.490i q^{77} +(-9.26230 + 64.3439i) q^{78} -17.2292i q^{79} +(-37.6078 - 70.6092i) q^{80} -49.1938 q^{81} +(-1.85602 - 0.267173i) q^{82} -73.3919 q^{83} +(89.4566 - 48.8080i) q^{84} +(43.9447 + 155.231i) q^{85} +(114.493 + 16.4812i) q^{86} +(46.0144 - 46.0144i) q^{87} +(33.1032 + 88.8901i) q^{88} +96.9216 q^{89} +(-16.4846 + 21.5726i) q^{90} +(-93.1639 + 93.1639i) q^{91} +(-10.3390 - 18.9496i) q^{92} +22.0247 q^{93} +(-63.2437 + 47.3270i) q^{94} +(-21.5394 + 6.09765i) q^{95} +(52.5863 - 60.5848i) q^{96} +(-53.4378 - 53.4378i) q^{97} +(107.430 + 15.4646i) q^{98} +(22.7625 - 22.7625i) 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 $

$2$	−0.284962	+	1.97960i	−0.142481	+	0.989798i
$2$	−0.284962	+	1.97960i	−0.142481	+	0.989798i
$3$	−2.50699			−0.835664			−0.417832	−	0.908524i	$-0.637210\pi$
$3$	−2.50699			−0.835664			−0.417832	+	0.908524i	$0.637210\pi$
$4$	−3.83759	−	1.12822i	−0.959398	−	0.282055i
$5$	−4.36488	−	2.43881i	−0.872977	−	0.487762i
$5$	−4.36488	−	2.43881i	−0.872977	−	0.487762i
$6$	0.714398	−	4.96283i	0.119066	−	0.827138i
$7$	7.18571	−	7.18571i	1.02653	−	1.02653i	0.0268912	−	0.999638i	$-0.491439\pi$
$7$	7.18571	−	7.18571i	1.02653	−	1.02653i	0.999638	−	0.0268912i	$-0.00856076\pi$
$8$	3.32699	−	7.27538i	0.415874	−	0.909422i
$9$	−2.71500			−0.301666
$10$	6.07168	−	7.94573i	0.607168	−	0.794573i
$11$	−8.38398	+	8.38398i	−0.762180	+	0.762180i	−0.976716	−	0.214536i	$-0.931176\pi$
$11$	−8.38398	+	8.38398i	−0.762180	+	0.762180i	0.214536	+	0.976716i	$0.431176\pi$
$12$	9.62081	+	2.82844i	0.801734	+	0.235703i
$13$	−12.9652			−0.997321			−0.498660	−	0.866797i	$-0.666175\pi$
$13$	−12.9652			−0.997321			−0.498660	+	0.866797i	$0.666175\pi$
$14$	12.1771	+	16.2724i	0.869795	+	1.16232i
$15$	10.9427	+	6.11407i	0.729515	+	0.407605i
$16$	13.4542	+	8.65930i	0.840890	+	0.541206i
$17$	−22.8157	−	22.8157i	−1.34210	−	1.34210i	−0.893967	−	0.448132i	$-0.852089\pi$
$17$	−22.8157	−	22.8157i	−1.34210	−	1.34210i	−0.448132	−	0.893967i	$-0.647911\pi$
$18$	0.773673	−	5.37460i	0.0429818	−	0.298589i
$19$	3.16584	−	3.16584i	0.166623	−	0.166623i	−0.618870	−	0.785493i	$-0.712409\pi$
$19$	3.16584	−	3.16584i	0.166623	−	0.166623i	0.785493	+	0.618870i	$0.212409\pi$
$20$	13.9991	+	14.2837i	0.699957	+	0.714185i
$21$	−18.0145	+	18.0145i	−0.857833	+	0.857833i
$22$	−14.2078	−	18.9860i	−0.645808	−	0.863000i
$23$	3.81600	+	3.81600i	0.165913	+	0.165913i	0.785180	−	0.619267i	$-0.212570\pi$
$23$	3.81600	+	3.81600i	0.165913	+	0.165913i	−0.619267	+	0.785180i	$0.712570\pi$
$24$	−8.34073	+	18.2393i	−0.347531	+	0.759971i
$25$	13.1044	+	21.2902i	0.524177	+	0.851610i
$26$	3.69459	−	25.6658i	0.142100	−	0.987146i
$27$	29.3694			1.08776
$28$	−35.6829	+	19.4688i	−1.27439	+	0.695313i
$29$	−18.3544	+	18.3544i	−0.632911	+	0.632911i	−0.948797	−	0.315886i	$-0.897698\pi$
$29$	−18.3544	+	18.3544i	−0.632911	+	0.632911i	0.315886	+	0.948797i	$0.397698\pi$
$30$	−15.2217	+	19.9199i	−0.507388	+	0.663996i
$31$	−8.78531			−0.283397			−0.141698	−	0.989910i	$-0.545256\pi$
$31$	−8.78531			−0.283397			−0.141698	+	0.989910i	$0.545256\pi$
$32$	−20.9759	+	24.1664i	−0.655496	+	0.755199i
$33$	21.0186	−	21.0186i	0.636926	−	0.636926i
$34$	51.6674	−	38.6642i	1.51963	−	1.13718i
$35$	−48.8893	+	13.8402i	−1.39684	+	0.395434i
$36$	10.4191	+	3.06312i	0.289418	+	0.0850866i
$37$	32.4039			0.875781			0.437891	−	0.899028i	$-0.355726\pi$
$37$	32.4039			0.875781			0.437891	+	0.899028i	$0.355726\pi$
$38$	5.36494	+	7.16923i	0.141183	+	0.188664i
$39$	32.5036			0.833425
$40$	−32.2652	+	23.6423i	−0.806630	+	0.591057i
$41$			0.937574i			0.0228677i	0.999935	+	0.0114338i	$0.00363958\pi$
$41$			0.937574i			0.0228677i	−0.999935	+	0.0114338i	$0.996360\pi$
$42$	−30.5280	−	40.7949i	−0.726856	−	0.971306i
$43$		−	57.8364i		−	1.34503i	−0.740083	−	0.672516i	$-0.765214\pi$
$43$		−	57.8364i		−	1.34503i	0.740083	−	0.672516i	$-0.234786\pi$
$44$	41.6333	−	22.7153i	0.946211	−	0.516257i
$45$	11.8506	+	6.62136i	0.263348	+	0.147141i
$46$	−8.64156	+	6.46672i	−0.187860	+	0.140581i
$47$	27.9276	+	27.9276i	0.594205	+	0.594205i	0.938764	−	0.344560i	$-0.111972\pi$
$47$	27.9276	+	27.9276i	0.594205	+	0.594205i	−0.344560	+	0.938764i	$0.611972\pi$
$48$	−33.7296	−	21.7088i	−0.702701	−	0.452266i
$49$		−	54.2688i		−	1.10753i
$50$	−45.8803	+	19.8745i	−0.917606	+	0.397490i
$51$	57.1987	+	57.1987i	1.12154	+	1.12154i
$52$	49.7550	+	14.6276i	0.956828	+	0.281300i
$53$		−	20.6425i		−	0.389482i	−0.980855	−	0.194741i	$-0.937613\pi$
$53$		−	20.6425i		−	0.389482i	0.980855	−	0.194741i	$-0.0623866\pi$
$54$	−8.36917	+	58.1395i	−0.154985	+	1.07666i
$55$	57.0420	−	16.1482i	1.03713	−	0.293603i
$56$	−28.3720	−	76.1855i	−0.506642	−	1.36046i
$57$	−7.93674	+	7.93674i	−0.139241	+	0.139241i
$58$	−31.1040	−	41.5647i	−0.536276	−	0.716632i
$59$	−40.1490	−	40.1490i	−0.680492	−	0.680492i	0.279619	−	0.960111i	$-0.409792\pi$
$59$	−40.1490	−	40.1490i	−0.680492	−	0.680492i	−0.960111	+	0.279619i	$0.909792\pi$
$60$	−35.0957	−	35.8091i	−0.584928	−	0.596819i
$61$	−25.3893	−	25.3893i	−0.416217	−	0.416217i	0.467680	−	0.883898i	$-0.345090\pi$
$61$	−25.3893	−	25.3893i	−0.416217	−	0.416217i	−0.883898	+	0.467680i	$0.845090\pi$
$62$	2.50348	−	17.3913i	0.0403788	−	0.280506i
$63$	−19.5092	+	19.5092i	−0.309669	+	0.309669i
$64$	−41.8623	−	48.4102i	−0.654098	−	0.756410i
$65$	56.5915	+	31.6196i	0.870638	+	0.486455i
$66$	35.6187	+	47.5978i	0.539678	+	0.721178i
$67$		−	29.3419i		−	0.437938i	−0.975732	−	0.218969i	$-0.929731\pi$
$67$		−	29.3419i		−	0.437938i	0.975732	−	0.218969i	$-0.0702694\pi$
$68$	61.8162	+	113.298i	0.909062	+	1.66615i
$69$	−9.56668	−	9.56668i	−0.138648	−	0.138648i
$70$	−13.4664	−	100.725i	−0.192377	−	1.43893i
$71$			34.7686i			0.489698i	0.969561	+	0.244849i	$0.0787385\pi$
$71$			34.7686i			0.489698i	−0.969561	+	0.244849i	$0.921262\pi$
$72$	−9.03277	+	19.7526i	−0.125455	+	0.274342i
$73$	−76.2777	−	76.2777i	−1.04490	−	1.04490i	−0.998943	−	0.0459567i	$-0.985366\pi$
$73$	−76.2777	−	76.2777i	−1.04490	−	1.04490i	−0.0459567	−	0.998943i	$-0.514634\pi$
$74$	−9.23390	+	64.1466i	−0.124782	+	0.866846i
$75$	−32.8527	−	53.3744i	−0.438035	−	0.711659i
$76$	−15.7210	+	8.57745i	−0.206855	+	0.112861i
$77$			120.490i			1.56480i
$78$	−9.26230	+	64.3439i	−0.118747	+	0.824922i
$79$		−	17.2292i		−	0.218092i	−0.994037	−	0.109046i	$-0.965220\pi$
$79$		−	17.2292i		−	0.218092i	0.994037	−	0.109046i	$-0.0347795\pi$
$80$	−37.6078	−	70.6092i	−0.470097	−	0.882615i
$81$	−49.1938			−0.607331
$82$	−1.85602	−	0.267173i	−0.0226344	−	0.00325821i
$83$	−73.3919			−0.884239			−0.442120	−	0.896956i	$-0.645773\pi$
$83$	−73.3919			−0.884239			−0.442120	+	0.896956i	$0.645773\pi$
$84$	89.4566	−	48.8080i	1.06496	−	0.581047i
$85$	43.9447	+	155.231i	0.516997	+	1.82625i
$86$	114.493	+	16.4812i	1.33131	+	0.191642i
$87$	46.0144	−	46.0144i	0.528901	−	0.528901i
$88$	33.1032	+	88.8901i	0.376173	+	1.01011i
$89$	96.9216			1.08901			0.544503	−	0.838759i	$-0.316718\pi$
$89$	96.9216			1.08901			0.544503	+	0.838759i	$0.316718\pi$
$90$	−16.4846	+	21.5726i	−0.183162	+	0.239696i
$91$	−93.1639	+	93.1639i	−1.02378	+	1.02378i
$92$	−10.3390	−	18.9496i	−0.112380	−	0.205973i
$93$	22.0247			0.236825
$94$	−63.2437	+	47.3270i	−0.672805	+	0.503479i
$95$	−21.5394	+	6.09765i	−0.226731	+	0.0641858i
$96$	52.5863	−	60.5848i	0.547774	−	0.631092i
$97$	−53.4378	−	53.4378i	−0.550905	−	0.550905i	0.375797	−	0.926702i	$-0.377369\pi$
$97$	−53.4378	−	53.4378i	−0.550905	−	0.550905i	−0.926702	+	0.375797i	$0.877369\pi$
$98$	107.430	+	15.4646i	1.09623	+	0.157802i
$99$	22.7625	−	22.7625i	0.229924	−	0.229924i
$100$	−26.2693	−	96.4879i	−0.262693	−	0.964879i
$101$	67.9450	−	67.9450i	0.672723	−	0.672723i	−0.285620	−	0.958343i	$-0.592200\pi$
$101$	67.9450	−	67.9450i	0.672723	−	0.672723i	0.958343	+	0.285620i	$0.0921995\pi$
$102$	−129.530	+	96.9308i	−1.26990	+	0.950302i
$103$	132.887	+	132.887i	1.29017	+	1.29017i	0.934681	+	0.355486i	$0.115685\pi$
$103$	132.887	+	132.887i	1.29017	+	1.29017i	0.355486	+	0.934681i	$0.384315\pi$
$104$	−43.1350	+	94.3265i	−0.414760	+	0.906986i
$105$	122.565	−	34.6973i	1.16729	−	0.330450i
$106$	40.8639	+	5.88235i	0.385508	+	0.0554939i
$107$	−44.9125			−0.419743			−0.209872	−	0.977729i	$-0.567305\pi$
$107$	−44.9125			−0.419743			−0.209872	+	0.977729i	$0.567305\pi$
$108$	−112.708	−	33.1352i	−1.04359	−	0.306807i
$109$	−31.7568	+	31.7568i	−0.291346	+	0.291346i	−0.837612	−	0.546266i	$-0.816049\pi$
$109$	−31.7568	+	31.7568i	−0.291346	+	0.291346i	0.546266	+	0.837612i	$0.316049\pi$
$110$	15.7120	+	117.522i	0.142836	+	1.06838i
$111$	−81.2363			−0.731859
$112$	158.901	−	34.4550i	1.41876	−	0.307634i
$113$	5.56976	−	5.56976i	0.0492899	−	0.0492899i	−0.682032	−	0.731322i	$-0.738904\pi$
$113$	5.56976	−	5.56976i	0.0492899	−	0.0492899i	0.731322	+	0.682032i	$0.238904\pi$
$114$	−13.4499	−	17.9732i	−0.117981	−	0.157660i
$115$	−7.34990	−	25.9629i	−0.0639122	−	0.225764i
$116$	91.1447	−	49.7290i	0.785730	−	0.428698i
$117$	35.2004			0.300858
$118$	90.9198	−	68.0379i	0.770507	−	0.576592i
$119$	−327.894			−2.75541
$120$	80.8885	−	59.2710i	0.674071	−	0.493925i
$121$		−	19.5823i		−	0.161837i
$122$	57.4954	−	43.0255i	0.471274	−	0.352668i
$123$		−	2.35049i		−	0.0191097i
$124$	33.7144	+	9.91176i	0.271891	+	0.0799336i
$125$	−5.27642	−	124.889i	−0.0422114	−	0.999109i
$126$	−33.0609	−	44.1797i	−0.262388	−	0.350632i
$127$	−106.254	−	106.254i	−0.836645	−	0.836645i	0.151771	−	0.988416i	$-0.451502\pi$
$127$	−106.254	−	106.254i	−0.836645	−	0.836645i	−0.988416	+	0.151771i	$0.951502\pi$
$128$	107.762	−	69.0753i	0.841889	−	0.539650i
$129$			144.995i			1.12399i
$130$	−78.7204	+	103.018i	−0.605542	+	0.792445i
$131$	−59.7795	−	59.7795i	−0.456332	−	0.456332i	0.441117	−	0.897449i	$-0.354582\pi$
$131$	−59.7795	−	59.7795i	−0.456332	−	0.456332i	−0.897449	+	0.441117i	$0.854582\pi$
$132$	−104.374	+	56.9471i	−0.790714	+	0.431418i
$133$		−	45.4976i		−	0.342088i
$134$	58.0850	+	8.36133i	0.433470	+	0.0623980i
$135$	−128.194	−	71.6263i	−0.949585	−	0.530566i
$136$	−241.900	+	90.0852i	−1.77868	+	0.662391i
$137$	−126.441	+	126.441i	−0.922925	+	0.922925i	−0.997235	−	0.0743099i	$-0.976325\pi$
$137$	−126.441	+	126.441i	−0.922925	+	0.922925i	0.0743099	+	0.997235i	$0.476325\pi$
$138$	21.6643	−	16.2120i	0.156988	−	0.117478i
$139$	41.3857	+	41.3857i	0.297739	+	0.297739i	0.840128	−	0.542389i	$-0.182480\pi$
$139$	41.3857	+	41.3857i	0.297739	+	0.297739i	−0.542389	+	0.840128i	$0.682480\pi$
$140$	203.232	+	2.04490i	1.45166	+	0.0146064i
$141$	−70.0143	−	70.0143i	−0.496555	−	0.496555i
$142$	−68.8277	−	9.90774i	−0.484702	−	0.0697728i
$143$	108.700	−	108.700i	0.760138	−	0.760138i
$144$	−36.5282	−	23.5100i	−0.253668	−	0.163264i
$145$	124.878	−	35.3520i	0.861227	−	0.243807i
$146$	172.735	−	129.263i	1.18312	−	0.885361i
$147$			136.051i			0.925519i
$148$	−124.353	−	36.5588i	−0.840223	−	0.247019i
$149$	−30.0503	−	30.0503i	−0.201680	−	0.201680i	0.599040	−	0.800719i	$-0.295549\pi$
$149$	−30.0503	−	30.0503i	−0.201680	−	0.201680i	−0.800719	+	0.599040i	$0.795549\pi$
$150$	115.022	−	49.8252i	0.766810	−	0.332168i
$151$			26.0891i			0.172776i	0.996262	+	0.0863878i	$0.0275324\pi$
$151$			26.0891i			0.172776i	−0.996262	+	0.0863878i	$0.972468\pi$
$152$	−12.5000	−	33.5654i	−0.0822367	−	0.220825i
$153$	61.9445	+	61.9445i	0.404866	+	0.404866i
$154$	−238.521	−	34.3350i	−1.54884	−	0.222955i
$155$	38.3468	+	21.4257i	0.247399	+	0.138230i
$156$	−124.735	−	36.6712i	−0.799586	−	0.235072i
$157$		−	2.64846i		−	0.0168691i	−0.999964	−	0.00843457i	$-0.997315\pi$
$157$		−	2.64846i		−	0.0168691i	0.999964	−	0.00843457i	$-0.00268484\pi$
$158$	34.1069	+	4.90969i	0.215866	+	0.0310740i
$159$			51.7507i			0.325476i
$160$	150.494	−	54.3272i	0.940590	−	0.339545i
$161$	54.8413			0.340629
$162$	14.0184	−	97.3838i	0.0865333	−	0.601135i
$163$	143.714			0.881682			0.440841	−	0.897585i	$-0.354680\pi$
$163$	143.714			0.881682			0.440841	+	0.897585i	$0.354680\pi$
$164$	1.05779	−	3.59803i	0.00644994	−	0.0219392i
$165$	−143.004	+	40.4833i	−0.866690	+	0.245353i
$166$	20.9139	−	145.286i	0.125987	−	0.875218i
$167$	192.906	−	192.906i	1.15513	−	1.15513i	0.169619	−	0.985510i	$-0.445746\pi$
$167$	192.906	−	192.906i	1.15513	−	1.15513i	0.985510	−	0.169619i	$-0.0542536\pi$
$168$	71.1283	+	190.996i	0.423382	+	1.13688i
$169$	−0.904324			−0.00535103
$170$	−319.817	+	42.7577i	−1.88128	+	0.251516i
$171$	−8.59526	+	8.59526i	−0.0502647	+	0.0502647i
$172$	−65.2522	+	221.952i	−0.379373	+	1.29042i
$173$	−2.04705			−0.0118326			−0.00591632	−	0.999982i	$-0.501883\pi$
$173$	−2.04705			−0.0118326			−0.00591632	+	0.999982i	$0.501883\pi$
$174$	77.9775	+	104.202i	0.448146	+	0.598863i
$175$	247.150	+	58.8209i	1.41229	+	0.336119i
$176$	−185.400	+	40.2006i	−1.05341	+	0.228413i
$177$	100.653	+	100.653i	0.568663	+	0.568663i
$178$	−27.6190	+	191.865i	−0.155163	+	1.07790i
$179$	101.208	−	101.208i	0.565405	−	0.565405i	−0.365432	−	0.930838i	$-0.619079\pi$
$179$	101.208	−	101.208i	0.565405	−	0.565405i	0.930838	+	0.365432i	$0.119079\pi$
$180$	−38.0076	−	38.7802i	−0.211153	−	0.215446i
$181$	154.013	−	154.013i	0.850901	−	0.850901i	−0.139343	−	0.990244i	$-0.544499\pi$
$181$	154.013	−	154.013i	0.850901	−	0.850901i	0.990244	+	0.139343i	$0.0444991\pi$
$182$	−157.879	−	210.975i	−0.867465	−	1.15920i
$183$	63.6506	+	63.6506i	0.347818	+	0.347818i
$184$	40.4587	−	15.0671i	0.219884	−	0.0818862i
$185$	−141.439	−	79.0270i	−0.764537	−	0.427173i
$186$	−6.27621	+	43.6000i	−0.0337431	+	0.234408i
$187$	382.573			2.04584
$188$	−75.6663	−	138.683i	−0.402480	−	0.737677i
$189$	211.040	−	211.040i	1.11661	−	1.11661i
$190$	−5.93295	−	44.3769i	−0.0312260	−	0.233563i
$191$	45.3049			0.237198			0.118599	−	0.992942i	$-0.462160\pi$
$191$	45.3049			0.237198			0.118599	+	0.992942i	$0.462160\pi$
$192$	104.948	+	121.364i	0.546606	+	0.632104i
$193$	−176.113	+	176.113i	−0.912503	+	0.912503i	−0.996469	−	0.0839658i	$-0.973241\pi$
$193$	−176.113	+	176.113i	−0.912503	+	0.912503i	0.0839658	+	0.996469i	$0.473241\pi$
$194$	121.013	−	90.5575i	0.623778	−	0.466791i
$195$	−141.874	−	79.2700i	−0.727560	−	0.406513i
$196$	−61.2271	+	208.261i	−0.312383	+	1.06256i
$197$	−308.173			−1.56433			−0.782164	−	0.623072i	$-0.785884\pi$
$197$	−308.173			−1.56433			−0.782164	+	0.623072i	$0.785884\pi$
$198$	38.5741	+	51.5470i	0.194818	+	0.260338i
$199$	−190.912			−0.959358			−0.479679	−	0.877444i	$-0.659247\pi$
$199$	−190.912			−0.959358			−0.479679	+	0.877444i	$0.659247\pi$
$200$	198.493	−	24.5072i	0.992464	−	0.122536i
$201$			73.5598i			0.365969i
$202$	115.142	+	153.865i	0.570009	+	0.761710i
$203$			263.779i			1.29940i
$204$	−154.973	−	284.038i	−0.759670	−	1.39234i
$205$	2.28656	−	4.09240i	0.0111540	−	0.0199629i
$206$	−300.931	+	225.195i	−1.46083	+	1.09318i
$207$	−10.3604	−	10.3604i	−0.0500504	−	0.0500504i
$208$	−174.436	−	112.269i	−0.838637	−	0.539756i
$209$			53.0847i			0.253994i
$210$	33.7601	+	252.517i	0.160762	+	1.20246i
$211$	230.999	+	230.999i	1.09478	+	1.09478i	0.995011	+	0.0997692i	$0.0318104\pi$
$211$	230.999	+	230.999i	1.09478	+	1.09478i	0.0997692	+	0.995011i	$0.468190\pi$
$212$	−23.2893	+	79.2177i	−0.109855	+	0.373668i
$213$		−	87.1645i		−	0.409223i
$214$	12.7984	−	88.9086i	0.0598055	−	0.415461i
$215$	−141.052	+	252.449i	−0.656055	+	1.17418i
$216$	97.7117	−	213.673i	0.452369	−	0.989229i
$217$	−63.1286	+	63.1286i	−0.290915	+	0.290915i
$218$	−53.8160	−	71.9150i	−0.246863	−	0.329885i
$219$	191.228	+	191.228i	0.873185	+	0.873185i
$220$	−237.123	−	2.38590i	−1.07783	−	0.0108450i
$221$	295.809	+	295.809i	1.33850	+	1.33850i
$222$	23.1493	−	160.815i	0.104276	−	0.724392i
$223$	−60.6724	+	60.6724i	−0.272073	+	0.272073i	−0.829934	−	0.557861i	$-0.811622\pi$
$223$	−60.6724	+	60.6724i	−0.272073	+	0.272073i	0.557861	+	0.829934i	$0.311622\pi$
$224$	22.9260	+	324.379i	0.102348	+	1.44812i
$225$	−35.5785	−	57.8030i	−0.158127	−	0.256902i
$226$	9.43869	+	12.6130i	0.0417641	+	0.0558099i
$227$		−	202.529i		−	0.892199i	−0.894983	−	0.446099i	$-0.852813\pi$
$227$		−	202.529i		−	0.892199i	0.894983	−	0.446099i	$-0.147187\pi$
$228$	39.4124	−	21.5036i	0.172861	−	0.0943139i
$229$	−137.361	−	137.361i	−0.599829	−	0.599829i	0.340438	−	0.940267i	$-0.389425\pi$
$229$	−137.361	−	137.361i	−0.599829	−	0.599829i	−0.940267	+	0.340438i	$0.889425\pi$
$230$	53.4905	−	7.15138i	0.232567	−	0.0310929i
$231$		−	302.067i		−	1.30765i
$232$	72.4704	+	194.600i	0.312372	+	0.838795i
$233$	−197.272	−	197.272i	−0.846660	−	0.846660i	0.143055	−	0.989715i	$-0.454308\pi$
$233$	−197.272	−	197.272i	−0.846660	−	0.846660i	−0.989715	+	0.143055i	$0.954308\pi$
$234$	−10.0308	+	69.6826i	−0.0428667	+	0.297789i
$235$	−53.7907	−	190.011i	−0.228896	−	0.808557i
$236$	108.779	+	199.373i	0.460927	+	0.844799i
$237$			43.1935i			0.182251i
$238$	93.4374	−	649.097i	0.392594	−	2.72730i
$239$			411.923i			1.72353i	0.507310	+	0.861763i	$0.330640\pi$
$239$			411.923i			1.72353i	−0.507310	+	0.861763i	$0.669360\pi$
$240$	94.2824	+	177.017i	0.392843	+	0.737569i
$241$	−293.936			−1.21965			−0.609826	−	0.792535i	$-0.708761\pi$
$241$	−293.936			−1.21965			−0.609826	+	0.792535i	$0.708761\pi$
$242$	38.7651	+	5.58023i	0.160186	+	0.0230588i
$243$	−140.996			−0.580231
$244$	68.7890	+	126.078i	0.281922	+	0.516714i
$245$	−132.351	+	236.877i	−0.540209	+	0.966844i
$246$	4.65302	+	0.669801i	0.0189147	+	0.00272277i
$247$	−41.0457	+	41.0457i	−0.166177	+	0.166177i
$248$	−29.2286	+	63.9164i	−0.117857	+	0.257728i
$249$	183.993			0.738926
$250$	248.732	+	25.1434i	0.994930	+	0.100574i
$251$	198.365	−	198.365i	0.790298	−	0.790298i	−0.191244	−	0.981542i	$-0.561252\pi$
$251$	198.365	−	198.365i	0.790298	−	0.790298i	0.981542	+	0.191244i	$0.0612523\pi$
$252$	96.8789	−	52.8576i	0.384440	−	0.209752i
$253$	−63.9866			−0.252911
$254$	240.618	−	180.061i	0.947315	−	0.708902i
$255$	−110.169	−	389.163i	−0.432035	−	1.52613i
$256$	106.033	+	233.009i	0.414191	+	0.910190i
$257$	−239.646	−	239.646i	−0.932473	−	0.932473i	0.0653871	−	0.997860i	$-0.479172\pi$
$257$	−239.646	−	239.646i	−0.932473	−	0.932473i	−0.997860	+	0.0653871i	$0.979172\pi$
$258$	−287.032	−	41.3182i	−1.11253	−	0.160148i
$259$	232.845	−	232.845i	0.899015	−	0.899015i
$260$	−181.501	−	185.191i	−0.698081	−	0.712272i
$261$	49.8322	−	49.8322i	0.190928	−	0.190928i
$262$	135.374	−	101.304i	0.516695	−	0.386658i
$263$	−142.437	−	142.437i	−0.541585	−	0.541585i	0.382408	−	0.923993i	$-0.375095\pi$
$263$	−142.437	−	142.437i	−0.541585	−	0.541585i	−0.923993	+	0.382408i	$0.875095\pi$
$264$	−82.9895	−	222.847i	−0.314354	−	0.844116i
$265$	−50.3432	+	90.1023i	−0.189974	+	0.340009i
$266$	90.0669	+	12.9651i	0.338597	+	0.0487411i
$267$	−242.981			−0.910043
$268$	−33.1041	+	112.602i	−0.123523	+	0.420157i
$269$	269.805	−	269.805i	1.00299	−	1.00299i	0.00299625	−	0.999996i	$-0.499046\pi$
$269$	269.805	−	269.805i	1.00299	−	1.00299i	0.999996	−	0.00299625i	$-0.000953737\pi$
$270$	178.322	−	233.361i	0.660450	−	0.864301i
$271$	71.4599			0.263690			0.131845	−	0.991270i	$-0.457910\pi$
$271$	71.4599			0.263690			0.131845	+	0.991270i	$0.457910\pi$
$272$	−109.400	−	504.536i	−0.402205	−	1.85491i
$273$	233.561	−	233.561i	0.855535	−	0.855535i
$274$	−214.271	−	286.332i	−0.782010	−	1.04501i
$275$	−288.364	−	68.6298i	−1.04860	−	0.249563i
$276$	25.9197	+	47.5064i	0.0939120	+	0.172124i
$277$	256.078			0.924470			0.462235	−	0.886758i	$-0.347048\pi$
$277$	256.078			0.924470			0.462235	+	0.886758i	$0.347048\pi$
$278$	−93.7202	+	70.1335i	−0.337123	+	0.252279i
$279$	23.8521			0.0854914
$280$	−61.9616	+	401.735i	−0.221292	+	1.43477i
$281$		−	315.882i		−	1.12413i	−0.827092	−	0.562067i	$-0.810006\pi$
$281$		−	315.882i		−	1.12413i	0.827092	−	0.562067i	$-0.189994\pi$
$282$	158.551	−	118.648i	0.562239	−	0.420739i
$283$			8.65428i			0.0305805i	0.999883	+	0.0152903i	$0.00486723\pi$
$283$			8.65428i			0.0305805i	−0.999883	+	0.0152903i	$0.995133\pi$
$284$	39.2266	−	133.428i	0.138122	−	0.469816i
$285$	53.9991	−	15.2867i	0.189471	−	0.0536377i
$286$	184.206	+	246.157i	0.644078	+	0.860688i
$287$	6.73713	+	6.73713i	0.0234743	+	0.0234743i
$288$	56.9494	−	65.6116i	0.197741	−	0.227818i
$289$			752.111i			2.60246i
$290$	34.3971	+	257.282i	0.118611	+	0.887178i
$291$	133.968	+	133.968i	0.460372	+	0.460372i
$292$	206.665	+	378.781i	0.707756	+	1.29719i
$293$			533.382i			1.82042i	0.414151	+	0.910208i	$0.364079\pi$
$293$			533.382i			1.82042i	−0.414151	+	0.910208i	$0.635921\pi$
$294$	−269.326	−	38.7695i	−0.916076	−	0.131869i
$295$	77.3300	+	273.162i	0.262136	+	0.925972i
$296$	107.807	−	235.751i	0.364215	−	0.796455i
$297$	−246.232	+	246.232i	−0.829066	+	0.829066i
$298$	68.0505	−	50.9241i	0.228357	−	0.170886i
$299$	−49.4751	−	49.4751i	−0.165469	−	0.165469i
$300$	65.8570	+	241.894i	0.219523	+	0.806315i
$301$	−415.595	−	415.595i	−1.38072	−	1.38072i
$302$	−51.6459	−	7.43442i	−0.171013	−	0.0246173i
$303$	−170.338	+	170.338i	−0.562170	+	0.562170i
$304$	70.0080	−	15.1800i	0.230289	−	0.0499342i
$305$	48.9016	+	172.741i	0.160333	+	0.566363i
$306$	−140.277	+	104.973i	−0.458422	+	0.343050i
$307$			322.054i			1.04903i	0.851400	+	0.524517i	$0.175754\pi$
$307$			322.054i			1.04903i	−0.851400	+	0.524517i	$0.824246\pi$
$308$	135.939	−	462.390i	0.441360	−	1.50127i
$309$	−333.147	−	333.147i	−1.07815	−	1.07815i
$310$	−53.3416	+	69.8057i	−0.172070	+	0.225180i
$311$			10.0499i			0.0323149i	0.999869	+	0.0161575i	$0.00514331\pi$
$311$			10.0499i			0.0323149i	−0.999869	+	0.0161575i	$0.994857\pi$
$312$	108.139	−	236.476i	0.346599	−	0.757935i
$313$	13.4351	+	13.4351i	0.0429237	+	0.0429237i	0.728243	−	0.685319i	$-0.240337\pi$
$313$	13.4351	+	13.4351i	0.0429237	+	0.0429237i	−0.685319	+	0.728243i	$0.740337\pi$
$314$	5.24287	+	0.754711i	0.0166970	+	0.00240354i
$315$	132.734	−	37.5761i	0.421379	−	0.119289i
$316$	−19.4384	+	66.1188i	−0.0615139	+	0.209237i
$317$		−	182.394i		−	0.575377i	−0.957724	−	0.287688i	$-0.907113\pi$
$317$		−	182.394i		−	0.575377i	0.957724	−	0.287688i	$-0.0928867\pi$
$318$	−102.445	−	14.7470i	−0.322155	−	0.0463742i
$319$		−	307.766i		−	0.964785i
$320$	64.6606	+	313.399i	0.202065	+	0.979372i
$321$	112.595			0.350764
$322$	−15.6277	+	108.564i	−0.0485333	+	0.337154i
$323$	−144.462			−0.447250
$324$	188.786	+	55.5015i	0.582672	+	0.171301i
$325$	−169.901	−	276.032i	−0.522772	−	0.849328i
$326$	−40.9532	+	284.496i	−0.125623	+	0.872687i
$327$	79.6139	−	79.6139i	0.243468	−	0.243468i
$328$	6.82121	+	3.11930i	0.0207964	+	0.00951006i
$329$	401.359			1.21994
$330$	−39.3898	−	294.626i	−0.119363	−	0.892806i
$331$	−213.565	+	213.565i	−0.645211	+	0.645211i	−0.951832	−	0.306621i	$-0.900802\pi$
$331$	−213.565	+	213.565i	−0.645211	+	0.645211i	0.306621	+	0.951832i	$0.400802\pi$
$332$	281.648	+	82.8022i	0.848337	+	0.249404i
$333$	−87.9766			−0.264194
$334$	326.906	+	436.848i	0.978759	+	1.30793i
$335$	−71.5592	+	128.074i	−0.213610	+	0.382310i
$336$	−398.364	+	86.3783i	−1.18561	+	0.257078i
$337$	−99.5263	−	99.5263i	−0.295330	−	0.295330i	0.543851	−	0.839182i	$-0.316966\pi$
$337$	−99.5263	−	99.5263i	−0.295330	−	0.295330i	−0.839182	+	0.543851i	$0.816966\pi$
$338$	0.257699	−	1.79020i	0.000762422	−	0.00529644i
$339$	−13.9633	+	13.9633i	−0.0411898	+	0.0411898i
$340$	6.49286	−	645.293i	0.0190967	−	1.89792i
$341$	73.6559	−	73.6559i	0.216000	−	0.216000i
$342$	−14.5658	−	19.4645i	−0.0425901	−	0.0569136i
$343$	−37.8598	−	37.8598i	−0.110378	−	0.110378i
$344$	−420.782	−	192.421i	−1.22320	−	0.559364i
$345$	18.4261	+	65.0888i	0.0534091	+	0.188663i
$346$	0.583332	−	4.05232i	0.00168593	−	0.0117119i
$347$	−481.819			−1.38853			−0.694264	−	0.719721i	$-0.744270\pi$
$347$	−481.819			−1.38853			−0.694264	+	0.719721i	$0.744270\pi$
$348$	−228.499	+	124.670i	−0.656606	+	0.358247i
$349$	−398.473	+	398.473i	−1.14176	+	1.14176i	−0.153628	+	0.988129i	$0.549096\pi$
$349$	−398.473	+	398.473i	−1.14176	+	1.14176i	−0.988129	+	0.153628i	$0.950904\pi$
$350$	−186.870	+	472.495i	−0.533914	+	1.34999i
$351$	−380.779			−1.08484
$352$	−26.7491	−	378.472i	−0.0759917	−	1.07520i
$353$	356.849	−	356.849i	1.01090	−	1.01090i	0.0109648	−	0.999940i	$-0.496510\pi$
$353$	356.849	−	356.849i	1.01090	−	1.01090i	0.999940	−	0.0109648i	$-0.00349027\pi$
$354$	−227.935	+	170.570i	−0.643884	+	0.481837i
$355$	84.7940	−	151.761i	0.238856	−	0.427495i
$356$	−371.946	−	109.349i	−1.04479	−	0.307160i
$357$	822.027			2.30260
$358$	171.510	+	229.190i	0.479077	+	0.640197i
$359$	417.857			1.16395			0.581974	−	0.813207i	$-0.302281\pi$
$359$	417.857			1.16395			0.581974	+	0.813207i	$0.302281\pi$
$360$	87.5999	−	64.1888i	0.243333	−	0.178302i
$361$			340.955i			0.944473i
$362$	260.996	+	348.772i	0.720982	+	0.963457i
$363$			49.0927i			0.135242i
$364$	462.635	−	252.416i	1.27097	−	0.693450i
$365$	146.917	+	518.970i	0.402511	+	1.42184i
$366$	−144.141	+	107.864i	−0.393827	+	0.294712i
$367$	−109.049	−	109.049i	−0.297136	−	0.297136i	0.542755	−	0.839891i	$-0.317381\pi$
$367$	−109.049	−	109.049i	−0.297136	−	0.297136i	−0.839891	+	0.542755i	$0.817381\pi$
$368$	18.2975	+	84.3853i	0.0497214	+	0.229308i
$369$		−	2.54551i		−	0.00689841i
$370$	196.746	−	257.473i	0.531747	−	0.695872i
$371$	−148.331	−	148.331i	−0.399815	−	0.399815i
$372$	−84.5218	−	24.8487i	−0.227209	−	0.0667976i
$373$			308.832i			0.827968i	0.910284	+	0.413984i	$0.135863\pi$
$373$			308.832i			0.827968i	−0.910284	+	0.413984i	$0.864137\pi$
$374$	−109.019	+	757.339i	−0.291494	+	2.02497i
$375$	13.2279	+	313.095i	0.0352745	+	0.834919i
$376$	296.099	−	110.269i	0.787497	−	0.293269i
$377$	237.968	−	237.968i	0.631216	−	0.631216i
$378$	357.635	+	477.912i	0.946124	+	1.26432i
$379$	28.3677	+	28.3677i	0.0748489	+	0.0748489i	0.743540	−	0.668691i	$-0.233145\pi$
$379$	28.3677	+	28.3677i	0.0748489	+	0.0748489i	−0.668691	+	0.743540i	$0.733145\pi$
$380$	89.5390	+	0.900932i	0.235629	+	0.00237087i
$381$	266.377	+	266.377i	0.699153	+	0.699153i
$382$	−12.9102	+	89.6853i	−0.0337963	+	0.234778i
$383$	422.953	−	422.953i	1.10432	−	1.10432i	0.110433	−	0.993884i	$-0.464776\pi$
$383$	422.953	−	422.953i	1.10432	−	1.10432i	0.993884	−	0.110433i	$-0.0352237\pi$
$384$	−270.158	+	173.171i	−0.703536	+	0.450966i
$385$	293.851	−	525.923i	0.763250	−	1.36603i
$386$	−298.447	−	398.818i	−0.773179	−	1.03321i
$387$			157.026i			0.405751i
$388$	144.783	+	265.362i	0.373152	+	0.683923i
$389$	178.975	+	178.975i	0.460089	+	0.460089i	0.898685	−	0.438595i	$-0.144524\pi$
$389$	178.975	+	178.975i	0.460089	+	0.460089i	−0.438595	+	0.898685i	$0.644524\pi$
$390$	197.351	−	258.265i	0.506029	−	0.662217i
$391$		−	174.129i		−	0.445344i
$392$	−394.826	−	180.552i	−1.00721	−	0.460591i
$393$	149.867	+	149.867i	0.381340	+	0.381340i
$394$	87.8177	−	610.057i	0.222888	−	1.54837i
$395$	−42.0188	+	75.2036i	−0.106377	+	0.190389i
$396$	−113.034	+	61.6721i	−0.285440	+	0.155738i
$397$			20.4646i			0.0515480i	0.999668	+	0.0257740i	$0.00820503\pi$
$397$			20.4646i			0.0515480i	−0.999668	+	0.0257740i	$0.991795\pi$
$398$	54.4028	−	377.929i	0.136690	−	0.949570i
$399$			114.062i			0.285870i
$400$	−8.04870	+	399.919i	−0.0201217	+	0.999798i
$401$	97.7306			0.243717			0.121859	−	0.992547i	$-0.461115\pi$
$401$	97.7306			0.243717			0.121859	+	0.992547i	$0.461115\pi$
$402$	−145.619	−	20.9618i	−0.362235	−	0.0521437i
$403$	113.903			0.282638
$404$	−337.402	+	184.088i	−0.835154	+	0.455664i
$405$	214.725	+	119.974i	0.530186	+	0.296233i
$406$	−522.176	−	75.1671i	−1.28615	−	0.185141i
$407$	−271.674	+	271.674i	−0.667503	+	0.667503i
$408$	606.442	−	225.843i	1.48638	−	0.553536i
$409$	−346.930			−0.848239			−0.424120	−	0.905606i	$-0.639416\pi$
$409$	−346.930			−0.848239			−0.424120	+	0.905606i	$0.639416\pi$
$410$	7.44971	+	5.69265i	0.0181700	+	0.0138845i
$411$	316.986	−	316.986i	0.771255	−	0.771255i
$412$	−360.041	−	659.893i	−0.873886	−	1.60168i
$413$	−576.998			−1.39709
$414$	23.4618	−	17.5571i	0.0566710	−	0.0424085i
$415$	320.347	+	178.989i	0.771920	+	0.431298i
$416$	271.956	−	313.321i	0.653740	−	0.753176i
$417$	−103.753	−	103.753i	−0.248809	−	0.248809i
$418$	−105.086	−	15.1272i	−0.251403	−	0.0361894i
$419$	94.6547	−	94.6547i	0.225906	−	0.225906i	−0.585074	−	0.810980i	$-0.698935\pi$
$419$	94.6547	−	94.6547i	0.225906	−	0.225906i	0.810980	+	0.585074i	$0.198935\pi$
$420$	−509.501	−	5.12655i	−1.21310	−	0.0122061i
$421$	303.154	−	303.154i	0.720080	−	0.720080i	−0.248541	−	0.968621i	$-0.579951\pi$
$421$	303.154	−	303.154i	0.720080	−	0.720080i	0.968621	+	0.248541i	$0.0799512\pi$
$422$	−523.109	+	391.458i	−1.23960	+	0.927625i
$423$	−75.8234	−	75.8234i	−0.179252	−	0.179252i
$424$	−150.182	−	68.6775i	−0.354204	−	0.161975i
$425$	186.765	−	784.738i	0.439447	−	1.84644i
$426$	172.550	+	24.8386i	0.405048	+	0.0583066i
$427$	−364.880			−0.854519
$428$	172.356	+	50.6712i	0.402701	+	0.118391i
$429$	−272.509	+	272.509i	−0.635220	+	0.635220i
$430$	−459.552	−	351.164i	−1.06873	−	0.816661i
$431$	505.491			1.17283			0.586416	−	0.810010i	$-0.300538\pi$
$431$	505.491			1.17283			0.586416	+	0.810010i	$0.300538\pi$
$432$	395.143	+	254.318i	0.914682	+	0.588700i
$433$	8.23935	−	8.23935i	0.0190285	−	0.0190285i	−0.697529	−	0.716557i	$-0.745717\pi$
$433$	8.23935	−	8.23935i	0.0190285	−	0.0190285i	0.716557	+	0.697529i	$0.245717\pi$
$434$	−106.980	−	142.958i	−0.246497	−	0.329397i
$435$	−313.068	+	88.6271i	−0.719696	+	0.203740i
$436$	157.698	−	86.0409i	0.361693	−	0.197341i
$437$	24.1617			0.0552900
$438$	−433.046	+	324.060i	−0.988689	+	0.739864i
$439$	−195.298			−0.444870			−0.222435	−	0.974948i	$-0.571400\pi$
$439$	−195.298			−0.444870			−0.222435	+	0.974948i	$0.571400\pi$
$440$	72.2942	−	468.727i	0.164305	−	1.06529i
$441$			147.340i			0.334103i
$442$	−669.877	+	501.288i	−1.51556	+	1.13414i
$443$		−	401.681i		−	0.906729i	−0.891325	−	0.453365i	$-0.850224\pi$
$443$		−	401.681i		−	0.906729i	0.891325	−	0.453365i	$-0.149776\pi$
$444$	311.752	+	91.6525i	0.702144	+	0.206425i
$445$	−423.051	−	236.373i	−0.950677	−	0.531176i
$446$	−102.817	−	137.396i	−0.230532	−	0.308063i
$447$	75.3357	+	75.3357i	0.168536	+	0.168536i
$448$	−648.672	−	47.0517i	−1.44793	−	0.105026i
$449$		−	189.448i		−	0.421934i	−0.977493	−	0.210967i	$-0.932339\pi$
$449$		−	189.448i		−	0.421934i	0.977493	−	0.210967i	$-0.0676613\pi$
$450$	124.565	−	53.9593i	0.276811	−	0.119910i
$451$	−7.86061	−	7.86061i	−0.0174293	−	0.0174293i
$452$	−27.6584	+	15.0905i	−0.0611911	+	0.0333862i
$453$		−	65.4052i		−	0.144382i
$454$	400.926	+	57.7132i	0.883096	+	0.127122i
$455$	633.859	−	179.441i	1.39310	−	0.394375i
$456$	31.3373	+	84.1482i	0.0687222	+	0.184536i
$457$	488.804	−	488.804i	1.06959	−	1.06959i	0.0722037	−	0.997390i	$-0.476997\pi$
$457$	488.804	−	488.804i	1.06959	−	1.06959i	0.997390	−	0.0722037i	$-0.0230032\pi$
$458$	311.062	−	232.776i	0.679174	−	0.508245i
$459$	−670.083	−	670.083i	−1.45988	−	1.45988i
$460$	−1.08595	+	107.927i	−0.00236077	+	0.234625i
$461$	392.290	+	392.290i	0.850954	+	0.850954i	0.990251	−	0.139297i	$-0.0444842\pi$
$461$	392.290	+	392.290i	0.850954	+	0.850954i	−0.139297	+	0.990251i	$0.544484\pi$
$462$	597.969	+	86.0776i	1.29431	+	0.186315i
$463$	−70.7053	+	70.7053i	−0.152711	+	0.152711i	−0.779328	−	0.626616i	$-0.784439\pi$
$463$	−70.7053	+	70.7053i	−0.152711	+	0.152711i	0.626616	+	0.779328i	$0.284439\pi$
$464$	−405.881	+	88.0083i	−0.874744	+	0.189673i
$465$	−96.1352	−	53.7140i	−0.206742	−	0.115514i
$466$	446.733	−	334.303i	0.958655	−	0.717389i
$467$			918.293i			1.96637i	0.182623	+	0.983183i	$0.441541\pi$
$467$			918.293i			1.96637i	−0.182623	+	0.983183i	$0.558459\pi$
$468$	−135.085	−	39.7138i	−0.288643	−	0.0848586i
$469$	−210.842	−	210.842i	−0.449557	−	0.449557i
$470$	391.473	−	52.3377i	0.832921	−	0.111357i
$471$			6.63965i			0.0140969i
$472$	−425.675	+	158.524i	−0.901854	+	0.335856i
$473$	484.899	+	484.899i	1.02516	+	1.02516i
$474$	−85.5057	−	12.3085i	−0.180392	−	0.0259674i
$475$	108.888	+	25.9150i	0.229238	+	0.0545579i
$476$	1258.32	+	369.936i	2.64353	+	0.777177i
$477$			56.0445i			0.117494i
$478$	−815.441	−	117.383i	−1.70594	−	0.245570i
$479$		−	49.5880i		−	0.103524i	−0.998659	−	0.0517620i	$-0.983516\pi$
$479$		−	49.5880i		−	0.103524i	0.998659	−	0.0517620i	$-0.0164837\pi$
$480$	−377.288	+	136.198i	−0.786017	+	0.283745i
$481$	−420.122			−0.873435
$482$	83.7608	−	581.875i	0.173778	−	1.20721i
$483$	−137.487			−0.284652
$484$	−22.0932	+	75.1490i	−0.0456471	+	0.155267i
$485$	102.925	+	363.575i	0.212217	+	0.749638i
$486$	40.1786	−	279.115i	0.0826720	−	0.574311i
$487$	644.145	−	644.145i	1.32268	−	1.32268i	0.411081	−	0.911599i	$-0.365151\pi$
$487$	644.145	−	644.145i	1.32268	−	1.32268i	0.911599	−	0.411081i	$-0.134849\pi$
$488$	−269.186	+	100.247i	−0.551611	+	0.205424i
$489$	−360.290			−0.736790
$490$	−431.205	−	329.503i	−0.880010	−	0.672455i
$491$	−541.213	+	541.213i	−1.10227	+	1.10227i	−0.108130	+	0.994137i	$0.534486\pi$
$491$	−541.213	+	541.213i	−1.10227	+	1.10227i	−0.994137	+	0.108130i	$0.965514\pi$
$492$	−2.65187	+	9.02022i	−0.00538998	+	0.0183338i
$493$	837.538			1.69886
$494$	−69.5574	−	92.9503i	−0.140804	−	0.188159i
$495$	−154.869	+	43.8423i	−0.312867	+	0.0885702i
$496$	−118.200	−	76.0746i	−0.238306	−	0.153376i
$497$	249.837	+	249.837i	0.502690	+	0.502690i
$498$	−52.4310	+	364.231i	−0.105283	+	0.731388i
$499$	−142.483	+	142.483i	−0.285537	+	0.285537i	−0.835313	−	0.549775i	$-0.814713\pi$
$499$	−142.483	+	142.483i	−0.285537	+	0.285537i	0.549775	+	0.835313i	$0.314713\pi$
$500$	−120.653	+	485.225i	−0.241306	+	0.970449i
$501$	−483.615	+	483.615i	−0.965299	+	0.965299i
$502$	336.156	+	449.209i	0.669633	+	0.894838i
$503$	307.222	+	307.222i	0.610780	+	0.610780i	0.943149	−	0.332370i	$-0.107848\pi$
$503$	307.222	+	307.222i	0.610780	+	0.610780i	−0.332370	+	0.943149i	$0.607848\pi$
$504$	77.0298	+	206.844i	0.152837	+	0.410404i
$505$	−462.277	+	130.867i	−0.915400	+	0.259143i
$506$	18.2338	−	126.668i	0.0360351	−	0.250331i
$507$	2.26713			0.00447166
$508$	287.881	+	527.637i	0.566695	+	1.03866i
$509$	268.080	−	268.080i	0.526681	−	0.526681i	−0.392900	−	0.919581i	$-0.628528\pi$
$509$	268.080	−	268.080i	0.526681	−	0.526681i	0.919581	+	0.392900i	$0.128528\pi$
$510$	801.778	−	107.193i	1.57211	−	0.210183i
$511$	−1096.22			−2.14524
$512$	−491.478	+	143.504i	−0.959918	+	0.280280i
$513$	92.9789	−	92.9789i	0.181245	−	0.181245i
$514$	542.691	−	406.111i	1.05582	−	0.790099i
$515$	−255.951	−	904.124i	−0.496992	−	1.75558i
$516$	163.587	−	556.433i	0.317028	−	1.07836i
$517$	−468.289			−0.905782
$518$	394.587	+	527.291i	0.761750	+	1.01794i
$519$	5.13193			0.00988811
$520$	418.324	−	306.526i	0.804469	−	0.589474i
$521$			364.737i			0.700071i	0.936736	+	0.350036i	$0.113831\pi$
$521$			364.737i			0.700071i	−0.936736	+	0.350036i	$0.886169\pi$
$522$	84.4473	+	112.848i	0.161776	+	0.216184i
$523$		−	434.085i		−	0.829991i	−0.909823	−	0.414996i	$-0.863783\pi$
$523$		−	434.085i		−	0.829991i	0.909823	−	0.414996i	$-0.136217\pi$
$524$	161.965	+	296.854i	0.309093	+	0.566515i
$525$	−619.603	−	147.463i	−1.18020	−	0.280883i
$526$	322.557	−	241.378i	0.613225	−	0.458894i
$527$	200.443	+	200.443i	0.380347	+	0.380347i
$528$	464.795	−	100.783i	0.880293	−	0.190876i
$529$		−	499.876i		−	0.944946i
$530$	−164.020	−	125.335i	−0.309472	−	0.236481i
$531$	109.005	+	109.005i	0.205282	+	0.205282i
$532$	−51.3314	+	174.601i	−0.0964875	+	0.328198i
$533$		−	12.1558i		−	0.0228064i
$534$	69.2406	−	481.005i	0.129664	−	0.900758i
$535$	196.038	+	109.533i	0.366426	+	0.204735i
$536$	−213.473	−	97.6201i	−0.398271	−	0.182127i
$537$	−253.726	+	253.726i	−0.472489	+	0.472489i
$538$	457.220	+	610.988i	0.849851	+	1.13567i
$539$	454.988	+	454.988i	0.844134	+	0.844134i
$540$	411.146	+	419.504i	0.761381	+	0.776859i
$541$	−299.573	−	299.573i	−0.553739	−	0.553739i	0.373779	−	0.927518i	$-0.378062\pi$
$541$	−299.573	−	299.573i	−0.553739	−	0.553739i	−0.927518	+	0.373779i	$0.878062\pi$
$542$	−20.3634	+	141.462i	−0.0375709	+	0.261000i
$543$	−386.109	+	386.109i	−0.711067	+	0.711067i
$544$	1029.95	−	72.7934i	1.89329	−	0.133811i
$545$	216.063	−	61.1659i	0.396446	−	0.112231i
$546$	395.800	+	528.913i	0.724909	+	0.968704i
$547$		−	9.98799i		−	0.0182596i	−0.999958	−	0.00912979i	$-0.997094\pi$
$547$		−	9.98799i		−	0.0182596i	0.999958	−	0.00912979i	$-0.00290614\pi$
$548$	627.881	−	342.575i	1.14577	−	0.625137i
$549$	68.9318	+	68.9318i	0.125559	+	0.125559i
$550$	218.032	−	551.287i	0.396422	−	1.00234i
$551$			116.214i			0.210916i
$552$	−101.429	+	37.7730i	−0.183749	+	0.0684293i
$553$	−123.804	−	123.804i	−0.223877	−	0.223877i
$554$	−72.9727	+	506.931i	−0.131720	+	0.915038i
$555$	354.587	+	198.120i	0.638896	+	0.356973i
$556$	−112.129	−	205.513i	−0.201671	−	0.369629i
$557$		−	360.011i		−	0.646339i	−0.946341	−	0.323170i	$-0.895252\pi$
$557$		−	360.011i		−	0.646339i	0.946341	−	0.323170i	$-0.104748\pi$
$558$	−6.79695	+	47.2175i	−0.0121809	+	0.0846191i
$559$			749.859i			1.34143i
$560$	−777.615	−	237.138i	−1.38860	−	0.423461i
$561$	−959.106			−1.70964
$562$	625.318	+	90.0144i	1.11267	+	0.160168i
$563$	−524.373			−0.931392			−0.465696	−	0.884945i	$-0.654196\pi$
$563$	−524.373			−0.931392			−0.465696	+	0.884945i	$0.654196\pi$
$564$	189.695	+	347.678i	0.336338	+	0.616450i
$565$	−37.8949	+	10.7278i	−0.0670707	+	0.0189872i
$566$	−17.1320	−	2.46615i	−0.0302685	−	0.00435715i
$567$	−353.492	+	353.492i	−0.623443	+	0.623443i
$568$	252.955	+	115.675i	0.445343	+	0.203653i
$569$	−606.955			−1.06670			−0.533352	−	0.845893i	$-0.679068\pi$
$569$	−606.955			−1.06670			−0.533352	+	0.845893i	$0.679068\pi$
$570$	14.8738	+	111.253i	0.0260945	+	0.195180i
$571$	763.721	−	763.721i	1.33752	−	1.33752i	0.439056	−	0.898460i	$-0.355313\pi$
$571$	763.721	−	763.721i	1.33752	−	1.33752i	0.898460	−	0.439056i	$-0.144687\pi$
$572$	−539.783	+	294.508i	−0.943676	+	0.514874i
$573$	−113.579			−0.198218
$574$	−15.2566	+	11.4170i	−0.0265795	+	0.0198902i
$575$	−31.2371	+	131.250i	−0.0543254	+	0.228261i
$576$	113.656	+	131.434i	0.197319	+	0.228183i
$577$	−95.1565	−	95.1565i	−0.164916	−	0.164916i	0.619824	−	0.784740i	$-0.287204\pi$
$577$	−95.1565	−	95.1565i	−0.164916	−	0.164916i	−0.784740	+	0.619824i	$0.787204\pi$
$578$	−1488.88	−	214.324i	−2.57591	−	0.370802i
$579$	441.514	−	441.514i	0.762545	−	0.762545i
$580$	−519.115	−	5.22328i	−0.895026	−	0.00900566i
$581$	−527.372	+	527.372i	−0.907698	+	0.907698i
$582$	−303.378	+	227.027i	−0.521269	+	0.390080i
$583$	173.067	+	173.067i	0.296855	+	0.296855i
$584$	−808.724	+	301.174i	−1.38480	+	0.515709i
$585$	−153.646	−	85.8471i	−0.262642	−	0.146747i
$586$	−1055.88	−	151.994i	−1.80184	−	0.259375i
$587$	445.447			0.758853			0.379427	−	0.925222i	$-0.376121\pi$
$587$	445.447			0.758853			0.379427	+	0.925222i	$0.376121\pi$
$588$	153.496	−	522.109i	0.261047	−	0.887941i
$589$	−27.8129	+	27.8129i	−0.0472205	+	0.0472205i
$590$	−562.786	+	75.2413i	−0.953874	+	0.127528i
$591$	772.586			1.30725
$592$	435.970	+	280.595i	0.736436	+	0.473979i
$593$	−359.016	+	359.016i	−0.605424	+	0.605424i	−0.941747	−	0.336323i	$-0.890817\pi$
$593$	−359.016	+	359.016i	−0.605424	+	0.605424i	0.336323	+	0.941747i	$0.390817\pi$
$594$	−417.274	−	557.608i	−0.702481	−	0.938733i
$595$	1431.22	+	799.670i	2.40541	+	1.34398i
$596$	81.4173	+	149.224i	0.136606	+	0.250376i
$597$	478.615			0.801700
$598$	112.039	−	83.8422i	0.187357	−	0.140204i
$599$	66.3175			0.110714			0.0553568	−	0.998467i	$-0.482370\pi$
$599$	66.3175			0.110714			0.0553568	+	0.998467i	$0.482370\pi$
$600$	−497.620	+	61.4393i	−0.829366	+	0.102399i
$601$			512.825i			0.853287i	0.904420	+	0.426643i	$0.140304\pi$
$601$			512.825i			0.853287i	−0.904420	+	0.426643i	$0.859696\pi$
$602$	941.139	−	704.281i	1.56335	−	1.16990i
$603$			79.6631i			0.132111i
$604$	29.4343	−	100.119i	0.0487322	−	0.165761i
$605$	−47.7576	+	85.4746i	−0.0789381	+	0.141280i
$606$	−288.659	−	385.739i	−0.476336	−	0.636533i
$607$	−700.017	−	700.017i	−1.15324	−	1.15324i	−0.985899	−	0.167341i	$-0.946482\pi$
$607$	−700.017	−	700.017i	−1.15324	−	1.15324i	−0.167341	−	0.985899i	$-0.553518\pi$
$608$	10.1006	+	142.913i	0.0166128	+	0.235055i
$609$		−	661.292i		−	1.08586i
$610$	−355.892	+	47.5807i	−0.583429	+	0.0780012i
$611$	−362.086	−	362.086i	−0.592613	−	0.592613i
$612$	−167.831	−	307.605i	−0.274233	−	0.502623i
$613$		−	402.030i		−	0.655840i	−0.944705	−	0.327920i	$-0.893652\pi$
$613$		−	402.030i		−	0.655840i	0.944705	−	0.327920i	$-0.106348\pi$
$614$	−637.536	−	91.7732i	−1.03833	−	0.149468i
$615$	−5.73240	+	10.2596i	−0.00932097	+	0.0166823i
$616$	876.608	+	400.868i	1.42307	+	0.650760i
$617$	451.281	−	451.281i	0.731412	−	0.731412i	−0.239488	−	0.970899i	$-0.576979\pi$
$617$	451.281	−	451.281i	0.731412	−	0.731412i	0.970899	+	0.239488i	$0.0769794\pi$
$618$	754.431	−	564.562i	1.22076	−	0.913531i
$619$	141.521	+	141.521i	0.228629	+	0.228629i	0.812120	−	0.583491i	$-0.198314\pi$
$619$	141.521	+	141.521i	0.228629	+	0.228629i	−0.583491	+	0.812120i	$0.698314\pi$
$620$	−122.987	−	125.487i	−0.198366	−	0.202398i
$621$	112.074	+	112.074i	0.180473	+	0.180473i
$622$	−19.8948	−	2.86386i	−0.0319853	−	0.00460427i
$623$	696.450	−	696.450i	1.11790	−	1.11790i
$624$	437.311	+	281.458i	0.700818	+	0.451055i
$625$	−281.549	+	557.992i	−0.450478	+	0.892788i
$626$	−30.4246	+	22.7676i	−0.0486016	+	0.0363700i
$627$		−	133.083i		−	0.212254i
$628$	−2.98804	+	10.1637i	−0.00475803	+	0.0161842i
$629$	−739.318	−	739.318i	−1.17539	−	1.17539i
$630$	36.5612	+	273.468i	0.0580336	+	0.434077i
$631$		−	430.554i		−	0.682335i	−0.940002	−	0.341168i	$-0.889178\pi$
$631$		−	430.554i		−	0.682335i	0.940002	−	0.341168i	$-0.110822\pi$
$632$	−125.349	−	57.3215i	−0.198337	−	0.0906986i
$633$	−579.111	−	579.111i	−0.914868	−	0.914868i
$634$	361.067	+	51.9756i	0.569506	+	0.0819804i
$635$	204.653	+	722.919i	0.322288	+	1.13845i
$636$	58.3862	−	198.598i	0.0918021	−	0.312261i
$637$			703.604i			1.10456i
$638$	609.253	+	87.7019i	0.954942	+	0.137464i
$639$		−	94.3966i		−	0.147726i
$640$	−638.829	+	38.6949i	−0.998171	+	0.0604608i
$641$	244.316			0.381147			0.190574	−	0.981673i	$-0.438965\pi$
$641$	244.316			0.381147			0.190574	+	0.981673i	$0.438965\pi$
$642$	−32.0854	+	222.893i	−0.0499773	+	0.347185i
$643$	−521.720			−0.811384			−0.405692	−	0.914010i	$-0.632969\pi$
$643$	−521.720			−0.811384			−0.405692	+	0.914010i	$0.632969\pi$
$644$	−210.459	−	61.8731i	−0.326799	−	0.0960763i
$645$	353.616	−	632.887i	0.548242	−	0.981221i
$646$	41.1662	−	285.976i	0.0637248	−	0.442687i
$647$	−7.36567	+	7.36567i	−0.0113843	+	0.0113843i	−0.712776	−	0.701392i	$-0.752562\pi$
$647$	−7.36567	+	7.36567i	−0.0113843	+	0.0113843i	0.701392	+	0.712776i	$0.252562\pi$
$648$	−163.667	+	357.904i	−0.252573	+	0.552320i
$649$	673.218			1.03732
$650$	594.846	−	257.677i	0.915148	−	0.396425i
$651$	158.263	−	158.263i	0.243107	−	0.243107i
$652$	−551.517	−	162.141i	−0.845885	−	0.248683i
$653$	171.839			0.263154			0.131577	−	0.991306i	$-0.457996\pi$
$653$	171.839			0.263154			0.131577	+	0.991306i	$0.457996\pi$
$654$	134.916	+	180.290i	0.206294	+	0.275673i
$655$	115.140	+	406.721i	0.175786	+	0.620949i
$656$	−8.11874	+	12.6143i	−0.0123761	+	0.0192292i
$657$	207.094	+	207.094i	0.315211	+	0.315211i
$658$	−114.372	+	794.529i	−0.173818	+	1.20749i
$659$	−66.3827	+	66.3827i	−0.100732	+	0.100732i	−0.755677	−	0.654945i	$-0.772692\pi$
$659$	−66.3827	+	66.3827i	−0.100732	+	0.100732i	0.654945	+	0.755677i	$0.272692\pi$
$660$	594.465	+	5.98144i	0.900704	+	0.00906279i
$661$	−38.9121	+	38.9121i	−0.0588685	+	0.0588685i	−0.735928	−	0.677060i	$-0.763254\pi$
$661$	−38.9121	+	38.9121i	−0.0588685	+	0.0588685i	0.677060	+	0.735928i	$0.263254\pi$
$662$	−361.914	−	483.630i	−0.546698	−	0.730559i
$663$	−741.591	−	741.591i	−1.11854	−	1.11854i
$664$	−244.174	+	533.954i	−0.367732	+	0.804147i
$665$	−110.960	+	198.592i	−0.166857	+	0.298634i
$666$	25.0700	−	174.158i	0.0376427	−	0.261498i
$667$	−140.081			−0.210017
$668$	−957.937	+	522.655i	−1.43404	+	0.782418i
$669$	152.105	−	152.105i	0.227362	−	0.227362i
$670$	−233.143	−	178.155i	−0.347974	−	0.265902i
$671$	425.726			0.634465
$672$	−57.4752	−	813.215i	−0.0855286	−	1.21014i
$673$	58.7394	−	58.7394i	0.0872799	−	0.0872799i	−0.662119	−	0.749399i	$-0.730343\pi$
$673$	58.7394	−	58.7394i	0.0872799	−	0.0872799i	0.749399	+	0.662119i	$0.230343\pi$
$674$	225.383	−	168.661i	0.334396	−	0.250238i
$675$	384.869	+	625.281i	0.570176	+	0.926343i
$676$	3.47043	+	1.02028i	0.00513377	+	0.00150929i
$677$	−408.523			−0.603431			−0.301716	−	0.953398i	$-0.597559\pi$
$677$	−408.523			−0.603431			−0.301716	+	0.953398i	$0.597559\pi$
$678$	−23.6627	−	31.6208i	−0.0349008	−	0.0466383i
$679$	−767.977			−1.13104
$680$	1275.57	+	196.737i	1.87583	+	0.289320i
$681$			507.738i			0.745578i
$682$	124.820	+	166.798i	0.183020	+	0.244572i
$683$		−	611.720i		−	0.895636i	−0.894125	−	0.447818i	$-0.852201\pi$
$683$		−	611.720i		−	0.895636i	0.894125	−	0.447818i	$-0.147799\pi$
$684$	42.6824	−	23.2877i	0.0624012	−	0.0340464i
$685$	860.264	−	243.534i	1.25586	−	0.355524i
$686$	85.7357	−	64.1585i	0.124979	−	0.0935254i
$687$	344.363	+	344.363i	0.501256	+	0.501256i
$688$	500.823	−	778.144i	0.727940	−	1.13102i
$689$			267.634i			0.388438i
$690$	−134.100	+	17.9284i	−0.194348	+	0.0259832i
$691$	−528.007	−	528.007i	−0.764120	−	0.764120i	0.212944	−	0.977064i	$-0.431695\pi$
$691$	−528.007	−	528.007i	−0.764120	−	0.764120i	−0.977064	+	0.212944i	$0.931695\pi$
$692$	7.85573	+	2.30952i	0.0113522	+	0.00333746i
$693$		−	327.129i		−	0.472048i
$694$	137.300	−	953.806i	0.197839	−	1.37436i
$695$	−79.7119	−	281.575i	−0.114693	−	0.405144i
$696$	−181.683	−	487.861i	−0.261038	−	0.700950i
$697$	21.3914	−	21.3914i	0.0306907	−	0.0306907i
$698$	−675.265	−	902.365i	−0.967429	−	1.29279i
$699$	494.559	+	494.559i	0.707523	+	0.707523i
$700$	−882.098	−	504.570i	−1.26014	−	0.720815i
$701$	163.932	+	163.932i	0.233855	+	0.233855i	0.814300	−	0.580445i	$-0.197121\pi$
$701$	163.932	+	163.932i	0.233855	+	0.233855i	−0.580445	+	0.814300i	$0.697121\pi$
$702$	108.508	−	753.789i	0.154569	−	1.07377i
$703$	102.586	−	102.586i	0.145926	−	0.145926i
$704$	756.843	+	54.8979i	1.07506	+	0.0779800i
$705$	134.853	+	476.356i	0.191280	+	0.675682i
$706$	604.729	+	808.106i	0.856556	+	1.14463i
$707$		−	976.466i		−	1.38114i
$708$	−272.707	−	499.825i	−0.385180	−	0.705968i
$709$	820.614	+	820.614i	1.15742	+	1.15742i	0.985027	+	0.172397i	$0.0551513\pi$
$709$	820.614	+	820.614i	1.15742	+	1.15742i	0.172397	+	0.985027i	$0.444849\pi$
$710$	276.262	+	211.104i	0.389101	+	0.297329i
$711$			46.7773i			0.0657909i
$712$	322.457	−	705.141i	0.452889	−	0.990367i
$713$	−33.5248	−	33.5248i	−0.0470193	−	0.0470193i
$714$	−234.247	+	1627.28i	−0.328077	+	2.27910i
$715$	−739.560	+	209.364i	−1.03435	+	0.292817i
$716$	−502.578	+	274.209i	−0.701924	+	0.382973i
$717$		−	1032.69i		−	1.44029i
$718$	−119.074	+	827.188i	−0.165841	+	1.15207i
$719$		−	578.830i		−	0.805048i	−0.915409	−	0.402524i	$-0.868133\pi$
$719$		−	578.830i		−	0.805048i	0.915409	−	0.402524i	$-0.131867\pi$
$720$	102.105	+	191.704i	0.141813	+	0.266255i
$721$	1909.78			2.64879
$722$	−674.953	−	97.1594i	−0.934837	−	0.134570i
$723$	736.896			1.01922
$724$	−764.800	+	417.279i	−1.05635	+	0.576352i
$725$	−631.294	−	150.246i	−0.870751	−	0.207236i
$726$	−97.1837	−	13.9896i	−0.133862	−	0.0192694i
$727$	−771.845	+	771.845i	−1.06168	+	1.06168i	−0.0637163	+	0.997968i	$0.520295\pi$
$727$	−771.845	+	771.845i	−1.06168	+	1.06168i	−0.997968	+	0.0637163i	$0.979705\pi$
$728$	367.847	+	987.758i	0.505285	+	1.35681i
$729$	796.220			1.09221
$730$	−1069.22	+	142.948i	−1.46468	+	0.195819i
$731$	−1319.58	+	1319.58i	−1.80517	+	1.80517i
$732$	−172.453	−	316.077i	−0.235592	−	0.431799i
$733$	455.036			0.620785			0.310393	−	0.950608i	$-0.399539\pi$
$733$	455.036			0.620785			0.310393	+	0.950608i	$0.399539\pi$
$734$	246.948	−	184.798i	0.336441	−	0.251769i
$735$	331.803	−	593.848i	0.451433	−	0.807957i
$736$	−172.263	+	12.1749i	−0.234053	+	0.0165420i
$737$	246.002	+	246.002i	0.333788	+	0.333788i
$738$	5.03908	+	0.725375i	0.00682803	+	0.000982893i
$739$	−723.106	+	723.106i	−0.978493	+	0.978493i	−0.999774	−	0.0212803i	$-0.993226\pi$
$739$	−723.106	+	723.106i	−0.978493	+	0.978493i	0.0212803	+	0.999774i	$0.493226\pi$
$740$	453.627	+	462.848i	0.613009	+	0.625470i
$741$	102.901	−	102.901i	0.138868	−	0.138868i
$742$	335.905	−	251.367i	0.452702	−	0.338770i
$743$	−134.068	−	134.068i	−0.180442	−	0.180442i	0.611107	−	0.791548i	$-0.290725\pi$
$743$	−134.068	−	134.068i	−0.180442	−	0.180442i	−0.791548	+	0.611107i	$0.790725\pi$
$744$	73.2759	−	160.238i	0.0984891	−	0.215374i
$745$	57.8790	+	204.453i	0.0776900	+	0.274433i
$746$	−611.362	−	88.0056i	−0.819521	−	0.117970i
$747$	199.259			0.266745
$748$	−1468.16	−	431.626i	−1.96278	−	0.577041i
$749$	−322.728	+	322.728i	−0.430879	+	0.430879i
$750$	−623.570	−	63.0342i	−0.831426	−	0.0840456i
$751$	−216.822			−0.288711			−0.144356	−	0.989526i	$-0.546111\pi$
$751$	−216.822			−0.288711			−0.144356	+	0.989526i	$0.546111\pi$
$752$	133.911	+	617.578i	0.178073	+	0.821248i
$753$	−497.299	+	497.299i	−0.660423	+	0.660423i
$754$	403.269	+	538.893i	0.534839	+	0.714712i
$755$	63.6264	−	113.876i	0.0842733	−	0.150829i
$756$	−1047.98	+	571.785i	−1.38622	+	0.756330i
$757$	747.764			0.987800			0.493900	−	0.869519i	$-0.335571\pi$
$757$	747.764			0.987800			0.493900	+	0.869519i	$0.335571\pi$
$758$	−64.2403	+	48.0729i	−0.0847498	+	0.0634207i
$759$	160.414			0.211349
$760$	−27.2987	+	176.994i	−0.0359194	+	0.232887i
$761$		−	1410.33i		−	1.85326i	−0.375978	−	0.926629i	$-0.622693\pi$
$761$		−	1410.33i		−	1.85326i	0.375978	−	0.926629i	$-0.377307\pi$
$762$	−603.227	+	451.412i	−0.791636	+	0.592404i
$763$			456.390i			0.598152i
$764$	−173.862	−	51.1139i	−0.227568	−	0.0669030i
$765$	−119.310	−	421.452i	−0.155961	−	0.550917i
$766$	716.750	+	957.802i	0.935705	+	1.25039i
$767$	520.539	+	520.539i	0.678669	+	0.678669i
$768$	−265.824	−	584.150i	−0.346124	−	0.760613i
$769$			925.036i			1.20291i	0.798907	+	0.601454i	$0.205412\pi$
$769$			925.036i			1.20291i	−0.798907	+	0.601454i	$0.794588\pi$
$770$	957.379	+	731.575i	1.24335	+	0.950098i
$771$	600.789	+	600.789i	0.779234	+	0.779234i
$772$	874.545	−	477.156i	1.13283	−	0.618077i
$773$		−	146.591i		−	0.189639i	−0.995494	−	0.0948196i	$-0.969773\pi$
$773$		−	146.591i		−	0.189639i	0.995494	−	0.0948196i	$-0.0302274\pi$
$774$	−310.847	−	44.7464i	−0.401611	−	0.0578119i
$775$	−115.126	−	187.041i	−0.148550	−	0.241344i
$776$	−566.567	+	210.993i	−0.730113	+	0.271899i
$777$	−583.740	+	583.740i	−0.751274	+	0.751274i
$778$	−405.298	+	303.296i	−0.520949	+	0.389841i
$779$	2.96821	+	2.96821i	0.00381029	+	0.00381029i
$780$	455.022	+	464.271i	0.583361	+	0.595220i
$781$	−291.499	−	291.499i	−0.373238	−	0.373238i
$782$	344.706	+	49.6204i	0.440800	+	0.0634532i
$783$	−539.058	+	539.058i	−0.688453	+	0.688453i
$784$	469.930	−	730.145i	0.599400	−	0.931307i
$785$	−6.45908	+	11.5602i	−0.00822813	+	0.0147264i
$786$	−339.382	+	253.969i	−0.431783	+	0.323116i
$787$		−	389.164i		−	0.494491i	−0.968953	−	0.247245i	$-0.920475\pi$
$787$		−	389.164i		−	0.494491i	0.968953	−	0.247245i	$-0.0795254\pi$
$788$	1182.64	+	347.687i	1.50081	+	0.441227i
$789$	357.088	+	357.088i	0.452583	+	0.452583i
$790$	−136.899	−	104.610i	−0.173290	−	0.132418i
$791$		−	80.0453i		−	0.101195i
$792$	−89.8752	−	241.336i	−0.113479	−	0.304718i
$793$	329.176	+	329.176i	0.415102	+	0.415102i
$794$	−40.5115	−	5.83163i	−0.0510221	−	0.00734463i
$795$	126.210	−	225.886i	0.158755	−	0.284133i
$796$	732.643	+	215.391i	0.920406	+	0.270592i
$797$			225.230i			0.282597i	0.989967	+	0.141298i	$0.0451277\pi$
$797$			225.230i			0.282597i	−0.989967	+	0.141298i	$0.954872\pi$
$798$	−225.797	−	32.5034i	−0.282953	−	0.0407311i
$799$		−	1274.38i		−	1.59496i
$800$	−789.384	−	129.895i	−0.986730	−	0.162369i
$801$	−263.142			−0.328517
$802$	−27.8496	+	193.467i	−0.0347251	+	0.241231i
$803$	1279.02			1.59280
$804$	82.9917	−	282.293i	0.103223	−	0.351110i
$805$	−239.376	−	133.748i	−0.297362	−	0.166146i
$806$	−32.4581	+	225.482i	−0.0402706	+	0.279754i
$807$	−676.398	+	676.398i	−0.838164	+	0.838164i
$808$	−268.273	−	720.378i	−0.332021	−	0.891557i
$809$	−389.024			−0.480870			−0.240435	−	0.970665i	$-0.577290\pi$
$809$	−389.024			−0.480870			−0.240435	+	0.970665i	$0.577290\pi$
$810$	−298.689	+	390.881i	−0.368752	+	0.482569i
$811$	235.660	−	235.660i	0.290580	−	0.290580i	−0.546730	−	0.837309i	$-0.684127\pi$
$811$	235.660	−	235.660i	0.290580	−	0.290580i	0.837309	+	0.546730i	$0.184127\pi$
$812$	297.601	−	1012.28i	0.366504	−	1.24665i
$813$	−179.149			−0.220356
$814$	−460.387	−	615.221i	−0.565586	−	0.755800i
$815$	−627.296	−	350.492i	−0.769688	−	0.430051i
$816$	274.264	+	1264.87i	0.336108	+	1.55008i
$817$	−183.101	−	183.101i	−0.224114	−	0.224114i
$818$	98.8620	−	686.781i	0.120858	−	0.839585i
$819$	252.940	−	252.940i	0.308840	−	0.308840i
$820$	−13.3920	+	13.1252i	−0.0163318	+	0.0160064i
$821$	423.452	−	423.452i	0.515775	−	0.515775i	−0.400515	−	0.916290i	$-0.631169\pi$
$821$	423.452	−	423.452i	0.515775	−	0.515775i	0.916290	+	0.400515i	$0.131169\pi$
$822$	537.174	+	717.833i	0.653497	+	0.873276i
$823$	−543.405	−	543.405i	−0.660274	−	0.660274i	0.295171	−	0.955445i	$-0.404623\pi$
$823$	−543.405	−	543.405i	−0.660274	−	0.660274i	−0.955445	+	0.295171i	$0.904623\pi$
$824$	1408.92	−	524.691i	1.70985	−	0.636761i
$825$	722.926	+	172.054i	0.876274	+	0.208551i
$826$	164.423	−	1142.22i	0.199059	−	1.38284i
$827$	912.383			1.10324			0.551622	−	0.834094i	$-0.314009\pi$
$827$	912.383			1.10324			0.551622	+	0.834094i	$0.314009\pi$
$828$	28.0703	+	51.4480i	0.0339013	+	0.0621353i
$829$	401.447	−	401.447i	0.484254	−	0.484254i	−0.422233	−	0.906487i	$-0.638754\pi$
$829$	401.447	−	401.447i	0.484254	−	0.484254i	0.906487	+	0.422233i	$0.138754\pi$
$830$	−445.612	+	583.152i	−0.536882	+	0.702593i
$831$	−641.985			−0.772546
$832$	542.752	+	627.647i	0.652346	+	0.754383i
$833$	−1238.18	+	1238.18i	−1.48641	+	1.48641i
$834$	234.956	−	175.824i	0.281721	−	0.210820i
$835$	−1312.48	+	371.552i	−1.57183	+	0.444973i
$836$	59.8913	−	203.718i	0.0716403	−	0.243681i
$837$	−258.019			−0.308267
$838$	160.405	+	214.351i	0.191414	+	0.255789i
$839$	355.908			0.424205			0.212102	−	0.977247i	$-0.431969\pi$
$839$	355.908			0.424205			0.212102	+	0.977247i	$0.431969\pi$
$840$	155.337	−	1007.15i	0.184925	−	1.19898i
$841$			167.230i			0.198847i
$842$	513.734	+	686.509i	0.610135	+	0.815331i
$843$			791.912i			0.939398i
$844$	−625.861	−	1147.10i	−0.741541	−	1.35912i
$845$	3.94727	+	2.20547i	0.00467133	+	0.00261003i
$846$	171.706	−	128.493i	0.202963	−	0.151883i
$847$	−140.713	−	140.713i	−0.166131	−	0.166131i
$848$	178.750	−	277.730i	0.210790	−	0.327511i
$849$		−	21.6962i		−	0.0255550i
$850$	1500.24	+	593.340i	1.76499	+	0.698047i
$851$	123.653	+	123.653i	0.145304	+	0.145304i
$852$	−98.3408	+	334.502i	−0.115423	+	0.392608i
$853$		−	184.144i		−	0.215878i	−0.994158	−	0.107939i	$-0.965575\pi$
$853$		−	184.144i		−	0.215878i	0.994158	−	0.107939i	$-0.0344252\pi$
$854$	103.977	−	722.314i	0.121753	−	0.845801i
$855$	58.4795	−	16.5551i	0.0683971	−	0.0193627i
$856$	−149.423	+	326.756i	−0.174560	+	0.381724i
$857$	503.631	−	503.631i	0.587667	−	0.587667i	−0.349332	−	0.936999i	$-0.613591\pi$
$857$	503.631	−	503.631i	0.587667	−	0.587667i	0.936999	+	0.349332i	$0.113591\pi$
$858$	−461.803	−	617.113i	−0.538232	−	0.719246i
$859$	136.193	+	136.193i	0.158548	+	0.158548i	0.781923	−	0.623375i	$-0.214239\pi$
$859$	136.193	+	136.193i	0.158548	+	0.158548i	−0.623375	+	0.781923i	$0.714239\pi$
$860$	826.118	−	809.659i	0.960602	−	0.941464i
$861$	−16.8899	−	16.8899i	−0.0196166	−	0.0196166i
$862$	−144.046	+	1000.67i	−0.167107	+	1.16087i
$863$	−778.037	+	778.037i	−0.901550	+	0.901550i	−0.995570	−	0.0940206i	$-0.970028\pi$
$863$	−778.037	+	778.037i	−0.901550	+	0.901550i	0.0940206	+	0.995570i	$0.470028\pi$
$864$	−616.048	+	709.751i	−0.713019	+	0.821471i
$865$	8.93512	+	4.99236i	0.0103296	+	0.00577151i
$866$	13.9627	+	18.6585i	0.0161232	+	0.0215456i
$867$		−	1885.54i		−	2.17478i
$868$	313.485	−	171.039i	0.361158	−	0.197050i
$869$	144.450	+	144.450i	0.166225	+	0.166225i
$870$	−86.2332	−	645.003i	−0.0991186	−	0.741382i
$871$			380.422i			0.436765i
$872$	125.388	+	336.697i	0.143794	+	0.386120i
$873$	145.084	+	145.084i	0.166190	+	0.166190i
$874$	−6.88519	+	47.8304i	−0.00787779	+	0.0547259i
$875$	−935.328	−	859.498i	−1.06895	−	0.982283i
$876$	−518.106	−	949.600i	−0.591446	−	1.08402i
$877$		−	450.954i		−	0.514201i	−0.966385	−	0.257101i	$-0.917233\pi$
$877$		−	450.954i		−	0.514201i	0.966385	−	0.257101i	$-0.0827672\pi$
$878$	55.6525	−	386.610i	0.0633856	−	0.440331i
$879$		−	1337.18i		−	1.52126i
$880$	907.289	+	276.683i	1.03101	+	0.314413i
$881$	929.171			1.05468			0.527339	−	0.849655i	$-0.323190\pi$
$881$	929.171			1.05468			0.527339	+	0.849655i	$0.323190\pi$
$882$	−291.673	−	41.9863i	−0.330695	−	0.0476035i
$883$	−244.738			−0.277166			−0.138583	−	0.990351i	$-0.544255\pi$
$883$	−244.738			−0.277166			−0.138583	+	0.990351i	$0.544255\pi$
$884$	−801.458	−	1468.93i	−0.906626	−	1.66169i
$885$	−193.866	−	684.814i	−0.219057	−	0.773801i
$886$	795.166	+	114.464i	0.897478	+	0.129192i
$887$	−987.070	+	987.070i	−1.11282	+	1.11282i	−0.120050	+	0.992768i	$0.538306\pi$
$887$	−987.070	+	987.070i	−1.11282	+	1.11282i	−0.992768	+	0.120050i	$0.961694\pi$
$888$	−270.272	+	591.025i	−0.304361	+	0.665569i
$889$	−1527.02			−1.71768
$890$	588.477	−	770.113i	0.661210	−	0.865295i
$891$	412.440	−	412.440i	0.462896	−	0.462896i
$892$	301.288	−	164.384i	0.337766	−	0.184287i
$893$	176.829			0.198017
$894$	−170.602	+	127.666i	−0.190830	+	0.142804i
$895$	−688.585	+	194.933i	−0.769369	+	0.217803i
$896$	277.990	−	1270.70i	0.310257	−	1.41819i
$897$	124.034	+	124.034i	0.138276	+	0.138276i
$898$	375.031	+	53.9857i	0.417629	+	0.0601177i
$899$	161.249	−	161.249i	0.179365	−	0.179365i
$900$	71.3212	+	261.965i	0.0792457	+	0.291072i
$901$	−470.974	+	470.974i	−0.522723	+	0.522723i
$902$	17.8008	−	13.3208i	0.0197348	−	0.0147681i
$903$	1041.89	+	1041.89i	1.15381	+	1.15381i
$904$	−21.9916	−	59.0526i	−0.0243270	−	0.0653237i
$905$	−1047.86	+	296.641i	−1.15785	+	0.327780i
$906$	129.476	+	18.6380i	0.142909	+	0.0205718i
$907$	160.752			0.177235			0.0886177	−	0.996066i	$-0.471755\pi$
$907$	160.752			0.177235			0.0886177	+	0.996066i	$0.471755\pi$
$908$	−228.497	+	777.224i	−0.251649	+	0.855974i
$909$	−184.471	+	184.471i	−0.202938	+	0.202938i
$910$	174.594	+	1305.92i	0.191861	+	1.43507i
$911$	36.8062			0.0404020			0.0202010	−	0.999796i	$-0.493569\pi$
$911$	36.8062			0.0404020			0.0202010	+	0.999796i	$0.493569\pi$
$912$	−175.509	+	38.0561i	−0.192444	+	0.0417282i
$913$	615.316	−	615.316i	0.673950	−	0.673950i
$914$	828.344	+	1106.93i	0.906284	+	1.21108i
$915$	−122.596	−	433.059i	−0.133985	−	0.473289i
$916$	372.162	+	682.109i	0.406290	+	0.744660i
$917$	−859.116			−0.936877
$918$	1517.44	−	1135.54i	1.65299	−	1.23698i
$919$	502.632			0.546934			0.273467	−	0.961881i	$-0.411830\pi$
$919$	502.632			0.546934			0.273467	+	0.961881i	$0.411830\pi$
$920$	−213.343	−	32.9050i	−0.231895	−	0.0357663i
$921$		−	807.386i		−	0.876640i
$922$	−888.363	+	664.787i	−0.963517	+	0.721027i
$923$		−	450.781i		−	0.488386i
$924$	−340.798	+	1159.21i	−0.368829	+	1.25455i
$925$	424.634	+	689.887i	0.459064	+	0.745824i
$926$	−119.820	−	160.116i	−0.129395	−	0.172912i
$927$	−360.789	−	360.789i	−0.389200	−	0.389200i
$928$	−58.5597	−	828.560i	−0.0631032	−	0.892845i
$929$		−	1098.03i		−	1.18195i	−0.806690	−	0.590975i	$-0.798743\pi$
$929$		−	1098.03i		−	1.18195i	0.806690	−	0.590975i	$-0.201257\pi$
$930$	133.727	−	175.002i	0.143792	−	0.188174i
$931$	−171.806	−	171.806i	−0.184540	−	0.184540i
$932$	534.483	+	979.615i	0.573479	+	1.05109i
$933$		−	25.1951i		−	0.0270044i
$934$	−1817.85	−	261.679i	−1.94630	−	0.280170i
$935$	−1669.89	−	933.022i	−1.78597	−	0.997884i
$936$	117.111	−	256.096i	0.125119	−	0.273607i
$937$	−68.4855	+	68.4855i	−0.0730902	+	0.0730902i	−0.742707	−	0.669617i	$-0.766458\pi$
$937$	−68.4855	+	68.4855i	−0.0730902	+	0.0730902i	0.669617	+	0.742707i	$0.266458\pi$
$938$	477.464	−	357.300i	0.509024	−	0.380917i
$939$	−33.6817	−	33.6817i	−0.0358698	−	0.0358698i
$940$	−7.94761	+	789.872i	−0.00845490	+	0.840290i
$941$	−517.439	−	517.439i	−0.549882	−	0.549882i	0.376525	−	0.926407i	$-0.377119\pi$
$941$	−517.439	−	517.439i	−0.549882	−	0.549882i	−0.926407	+	0.376525i	$0.877119\pi$
$942$	−13.1438	−	1.89205i	−0.0139531	−	0.00200855i
$943$	−3.57779	+	3.57779i	−0.00379405	+	0.00379405i
$944$	−192.512	−	887.837i	−0.203932	−	0.940506i
$945$	−1435.85	+	406.478i	−1.51942	+	0.430136i
$946$	−1098.08	+	821.726i	−1.16076	+	0.868632i
$947$			1065.70i			1.12534i	0.826680	+	0.562672i	$0.190227\pi$
$947$			1065.70i			1.12534i	−0.826680	+	0.562672i	$0.809773\pi$
$948$	48.7318	−	165.759i	0.0514049	−	0.174851i
$949$	988.954	+	988.954i	1.04210	+	1.04210i
$950$	−82.3303	+	208.169i	−0.0866634	+	0.219126i
$951$			457.261i			0.480821i
$952$	−1090.90	+	2385.55i	−1.14590	+	2.50583i
$953$	−620.695	−	620.695i	−0.651306	−	0.651306i	0.302001	−	0.953307i	$-0.402345\pi$
$953$	−620.695	−	620.695i	−0.651306	−	0.651306i	−0.953307	+	0.302001i	$0.902345\pi$
$954$	−110.945	−	15.9706i	−0.116295	−	0.0167406i
$955$	−197.751	−	110.490i	−0.207069	−	0.115696i
$956$	464.740	−	1580.79i	0.486130	−	1.65355i
$957$			771.567i			0.806236i
$958$	98.1641	+	14.1307i	0.102468	+	0.0147502i
$959$			1817.13i			1.89482i
$960$	−162.104	−	785.689i	−0.168858	−	0.818426i
$961$	−883.818			−0.919686
$962$	119.719	−	831.672i	0.124448	−	0.864524i
$963$	121.937			0.126622
$964$	1128.01	+	331.625i	1.17013	+	0.344009i
$965$	1198.22	−	339.207i	1.24168	−	0.351510i
$966$	39.1786	−	272.168i	0.0405575	−	0.281747i
$967$	1139.87	−	1139.87i	1.17877	−	1.17877i	0.198709	−	0.980059i	$-0.436325\pi$
$967$	1139.87	−	1139.87i	1.17877	−	1.17877i	0.980059	−	0.198709i	$-0.0636748\pi$
$968$	−142.469	−	65.1502i	−0.147179	−	0.0673039i
$969$	362.164			0.373751
$970$	−749.060	+	100.145i	−0.772227	+	0.103242i
$971$	470.641	−	470.641i	0.484697	−	0.484697i	−0.421931	−	0.906628i	$-0.638648\pi$
$971$	470.641	−	470.641i	0.484697	−	0.484697i	0.906628	+	0.421931i	$0.138648\pi$
$972$	541.086	+	159.075i	0.556672	+	0.163657i
$973$	594.771			0.611275
$974$	1091.59	+	1458.70i	1.12073	+	1.49764i
$975$	425.940	+	692.009i	0.436862	+	0.709752i
$976$	−121.740	−	561.446i	−0.124733	−	0.575252i
$977$	−2.84469	−	2.84469i	−0.00291165	−	0.00291165i	0.705649	−	0.708561i	$-0.250655\pi$
$977$	−2.84469	−	2.84469i	−0.00291165	−	0.00291165i	−0.708561	+	0.705649i	$0.750655\pi$
$978$	102.669	−	713.229i	0.104979	−	0.729273i
$979$	−812.589	+	812.589i	−0.830019	+	0.830019i
$980$	775.159	−	759.716i	0.790979	−	0.775220i
$981$	86.2195	−	86.2195i	0.0878894	−	0.0878894i
$982$	−917.157	−	1225.61i	−0.933968	−	1.24807i
$983$	177.652	+	177.652i	0.180724	+	0.180724i	0.791671	−	0.610947i	$-0.209211\pi$
$983$	177.652	+	177.652i	0.180724	+	0.180724i	−0.610947	+	0.791671i	$0.709211\pi$
$984$	−17.1007	−	7.82006i	−0.0173788	−	0.00794721i
$985$	1345.14	+	751.575i	1.36562	+	0.763020i
$986$	−238.667	+	1657.99i	−0.242056	+	1.68153i
$987$	−1006.20			−1.01946
$988$	203.825	−	111.208i	0.206301	−	0.112559i
$989$	220.704	−	220.704i	0.223158	−	0.223158i
$990$	−42.6580	−	319.071i	−0.0430889	−	0.322294i
$991$	1697.53			1.71295			0.856474	−	0.516190i	$-0.172650\pi$
$991$	1697.53			1.71295			0.856474	+	0.516190i	$0.172650\pi$
$992$	184.279	−	212.309i	0.185766	−	0.214021i
$993$	535.405	−	535.405i	0.539179	−	0.539179i
$994$	−565.770	+	423.382i	−0.569185	+	0.425937i
$995$	833.309	+	465.598i	0.837497	+	0.467938i
$996$	−706.089	−	207.584i	−0.708925	−	0.208418i
$997$	−1315.01			−1.31897			−0.659483	−	0.751720i	$-0.729225\pi$
$997$	−1315.01			−1.31897			−0.659483	+	0.751720i	$0.729225\pi$
$998$	−241.457	−	322.661i	−0.241941	−	0.323308i
$999$	951.683			0.952636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.t.a.77.11	yes	44
4.3	odd	2		320.3.t.a.17.17		44
5.2	odd	4		400.3.i.b.93.1		44
5.3	odd	4		80.3.i.a.13.22	✓	44
5.4	even	2		400.3.t.b.157.12		44
8.3	odd	2		640.3.t.a.417.6		44
8.5	even	2		640.3.t.b.417.17		44
16.3	odd	4		640.3.i.a.97.17		44
16.5	even	4		80.3.i.a.37.22	yes	44
16.11	odd	4		320.3.i.a.177.6		44
16.13	even	4		640.3.i.b.97.6		44
20.3	even	4		320.3.i.a.273.17		44
40.3	even	4		640.3.i.a.33.6		44
40.13	odd	4		640.3.i.b.33.17		44
80.3	even	4		640.3.t.a.353.6		44
80.13	odd	4		640.3.t.b.353.17		44
80.37	odd	4		400.3.t.b.293.12		44
80.43	even	4		320.3.t.a.113.17		44
80.53	odd	4	inner	80.3.t.a.53.11	yes	44
80.69	even	4		400.3.i.b.357.1		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.22	✓	44	5.3	odd	4
80.3.i.a.37.22	yes	44	16.5	even	4
80.3.t.a.53.11	yes	44	80.53	odd	4	inner
80.3.t.a.77.11	yes	44	1.1	even	1	trivial
320.3.i.a.177.6		44	16.11	odd	4
320.3.i.a.273.17		44	20.3	even	4
320.3.t.a.17.17		44	4.3	odd	2
320.3.t.a.113.17		44	80.43	even	4
400.3.i.b.93.1		44	5.2	odd	4
400.3.i.b.357.1		44	80.69	even	4
400.3.t.b.157.12		44	5.4	even	2
400.3.t.b.293.12		44	80.37	odd	4
640.3.i.a.33.6		44	40.3	even	4
640.3.i.a.97.17		44	16.3	odd	4
640.3.i.b.33.17		44	40.13	odd	4
640.3.i.b.97.6		44	16.13	even	4
640.3.t.a.353.6		44	80.3	even	4
640.3.t.a.417.6		44	8.3	odd	2
640.3.t.b.353.17		44	80.13	odd	4
640.3.t.b.417.17		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)

\(f(q)\)	\(=\)	\(q+(-0.284962 + 1.97960i) q^{2} -2.50699 q^{3} +(-3.83759 - 1.12822i) q^{4} +(-4.36488 - 2.43881i) q^{5} +(0.714398 - 4.96283i) q^{6} +(7.18571 - 7.18571i) q^{7} +(3.32699 - 7.27538i) q^{8} -2.71500 q^{9} +O(q^{10})\)	\(q+(-0.284962 + 1.97960i) q^{2} -2.50699 q^{3} +(-3.83759 - 1.12822i) q^{4} +(-4.36488 - 2.43881i) q^{5} +(0.714398 - 4.96283i) q^{6} +(7.18571 - 7.18571i) q^{7} +(3.32699 - 7.27538i) q^{8} -2.71500 q^{9} +(6.07168 - 7.94573i) q^{10} +(-8.38398 + 8.38398i) q^{11} +(9.62081 + 2.82844i) q^{12} -12.9652 q^{13} +(12.1771 + 16.2724i) q^{14} +(10.9427 + 6.11407i) q^{15} +(13.4542 + 8.65930i) q^{16} +(-22.8157 - 22.8157i) q^{17} +(0.773673 - 5.37460i) q^{18} +(3.16584 - 3.16584i) q^{19} +(13.9991 + 14.2837i) q^{20} +(-18.0145 + 18.0145i) q^{21} +(-14.2078 - 18.9860i) q^{22} +(3.81600 + 3.81600i) q^{23} +(-8.34073 + 18.2393i) q^{24} +(13.1044 + 21.2902i) q^{25} +(3.69459 - 25.6658i) q^{26} +29.3694 q^{27} +(-35.6829 + 19.4688i) q^{28} +(-18.3544 + 18.3544i) q^{29} +(-15.2217 + 19.9199i) q^{30} -8.78531 q^{31} +(-20.9759 + 24.1664i) q^{32} +(21.0186 - 21.0186i) q^{33} +(51.6674 - 38.6642i) q^{34} +(-48.8893 + 13.8402i) q^{35} +(10.4191 + 3.06312i) q^{36} +32.4039 q^{37} +(5.36494 + 7.16923i) q^{38} +32.5036 q^{39} +(-32.2652 + 23.6423i) q^{40} +0.937574i q^{41} +(-30.5280 - 40.7949i) q^{42} -57.8364i q^{43} +(41.6333 - 22.7153i) q^{44} +(11.8506 + 6.62136i) q^{45} +(-8.64156 + 6.46672i) q^{46} +(27.9276 + 27.9276i) q^{47} +(-33.7296 - 21.7088i) q^{48} -54.2688i q^{49} +(-45.8803 + 19.8745i) q^{50} +(57.1987 + 57.1987i) q^{51} +(49.7550 + 14.6276i) q^{52} -20.6425i q^{53} +(-8.36917 + 58.1395i) q^{54} +(57.0420 - 16.1482i) q^{55} +(-28.3720 - 76.1855i) q^{56} +(-7.93674 + 7.93674i) q^{57} +(-31.1040 - 41.5647i) q^{58} +(-40.1490 - 40.1490i) q^{59} +(-35.0957 - 35.8091i) q^{60} +(-25.3893 - 25.3893i) q^{61} +(2.50348 - 17.3913i) q^{62} +(-19.5092 + 19.5092i) q^{63} +(-41.8623 - 48.4102i) q^{64} +(56.5915 + 31.6196i) q^{65} +(35.6187 + 47.5978i) q^{66} -29.3419i q^{67} +(61.8162 + 113.298i) q^{68} +(-9.56668 - 9.56668i) q^{69} +(-13.4664 - 100.725i) q^{70} +34.7686i q^{71} +(-9.03277 + 19.7526i) q^{72} +(-76.2777 - 76.2777i) q^{73} +(-9.23390 + 64.1466i) q^{74} +(-32.8527 - 53.3744i) q^{75} +(-15.7210 + 8.57745i) q^{76} +120.490i q^{77} +(-9.26230 + 64.3439i) q^{78} -17.2292i q^{79} +(-37.6078 - 70.6092i) q^{80} -49.1938 q^{81} +(-1.85602 - 0.267173i) q^{82} -73.3919 q^{83} +(89.4566 - 48.8080i) q^{84} +(43.9447 + 155.231i) q^{85} +(114.493 + 16.4812i) q^{86} +(46.0144 - 46.0144i) q^{87} +(33.1032 + 88.8901i) q^{88} +96.9216 q^{89} +(-16.4846 + 21.5726i) q^{90} +(-93.1639 + 93.1639i) q^{91} +(-10.3390 - 18.9496i) q^{92} +22.0247 q^{93} +(-63.2437 + 47.3270i) q^{94} +(-21.5394 + 6.09765i) q^{95} +(52.5863 - 60.5848i) q^{96} +(-53.4378 - 53.4378i) q^{97} +(107.430 + 15.4646i) q^{98} +(22.7625 - 22.7625i) 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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