LMFDB - Embedded newform 80.3.i.a.13.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 3]))

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

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

chi := DirichletCharacter("80.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17984211488$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.22
Character	$\chi$	$=$	80.13
Dual form			80.3.i.a.37.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.97960 + 0.284962i) q^{2} -2.50699i q^{3} +(3.83759 + 1.12822i) q^{4} +(2.43881 + 4.36488i) q^{5} +(0.714398 - 4.96283i) q^{6} +(-7.18571 - 7.18571i) q^{7} +(7.27538 + 3.32699i) q^{8} +2.71500 q^{9} +O(q^{10})$	\(q+(1.97960 + 0.284962i) q^{2} -2.50699i q^{3} +(3.83759 + 1.12822i) q^{4} +(2.43881 + 4.36488i) q^{5} +(0.714398 - 4.96283i) q^{6} +(-7.18571 - 7.18571i) q^{7} +(7.27538 + 3.32699i) q^{8} +2.71500 q^{9} +(3.58403 + 9.33567i) q^{10} +(-8.38398 + 8.38398i) q^{11} +(2.82844 - 9.62081i) q^{12} -12.9652i 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} +(5.37460 + 0.773673i) q^{18} +(-3.16584 + 3.16584i) q^{19} +(4.43461 + 19.5022i) q^{20} +(-18.0145 + 18.0145i) q^{21} +(-18.9860 + 14.2078i) 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} -29.3694i q^{27} +(-19.4688 - 35.6829i) q^{28} +(18.3544 - 18.3544i) q^{29} +(23.4044 - 8.98512i) q^{30} -8.78531 q^{31} +(24.1664 + 20.9759i) q^{32} +(21.0186 + 21.0186i) q^{33} +(-51.6674 + 38.6642i) q^{34} +(13.8402 - 48.8893i) q^{35} +(10.4191 + 3.06312i) q^{36} -32.4039i q^{37} +(-7.16923 + 5.36494i) q^{38} -32.5036 q^{39} +(3.22134 + 39.8701i) q^{40} +0.937574i q^{41} +(-40.7949 + 30.5280i) q^{42} +57.8364 q^{43} +(-41.6333 + 22.7153i) q^{44} +(6.62136 + 11.8506i) q^{45} +(-8.64156 + 6.46672i) q^{46} +(27.9276 - 27.9276i) q^{47} +(21.7088 - 33.7296i) q^{48} +54.2688i q^{49} +(-32.0084 + 38.4118i) q^{50} +(57.1987 + 57.1987i) q^{51} +(14.6276 - 49.7550i) q^{52} +20.6425 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} +(41.5647 - 31.1040i) q^{58} +(40.1490 + 40.1490i) q^{59} +(48.8917 - 11.1175i) q^{60} +(-25.3893 - 25.3893i) q^{61} +(-17.3913 - 2.50348i) 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} -29.3419 q^{67} +(-113.298 + 61.8162i) q^{68} +(9.56668 + 9.56668i) q^{69} +(41.3296 - 92.8372i) q^{70} +34.7686i q^{71} +(19.7526 + 9.03277i) q^{72} +(76.2777 - 76.2777i) q^{73} +(9.23390 - 64.1466i) q^{74} +(53.3744 + 32.8527i) q^{75} +(-15.7210 + 8.57745i) q^{76} +120.490 q^{77} +(-64.3439 - 9.26230i) q^{78} +17.2292i q^{79} +(-4.98453 + 79.8446i) q^{80} -49.1938 q^{81} +(-0.267173 + 1.85602i) q^{82} -73.3919i q^{83} +(-89.4566 + 48.8080i) q^{84} +(-155.231 - 43.9447i) q^{85} +(114.493 + 16.4812i) q^{86} +(-46.0144 - 46.0144i) q^{87} +(-88.8901 + 33.1032i) q^{88} -96.9216 q^{89} +(9.73062 + 25.3463i) q^{90} +(-93.1639 + 93.1639i) q^{91} +(-18.9496 + 10.3390i) q^{92} +22.0247i 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} +(-15.4646 + 107.430i) q^{98} +(-22.7625 + 22.7625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9	$ 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9} + 6 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{15} + 24 q^{16} - 4 q^{17} + 22 q^{18} + 32 q^{19} + 40 q^{20} - 4 q^{21} + 92 q^{22} + 36 q^{24} - 52 q^{26} + 36 q^{28} - 28 q^{30} - 8 q^{31} - 132 q^{32} - 4 q^{33} - 88 q^{34} + 96 q^{35} - 116 q^{36} - 216 q^{38} + 72 q^{39} + 16 q^{40} + 16 q^{42} + 124 q^{43} - 168 q^{44} - 34 q^{45} + 108 q^{46} - 4 q^{47} + 340 q^{48} + 10 q^{50} - 100 q^{51} + 48 q^{52} - 4 q^{53} + 228 q^{54} - 172 q^{56} + 36 q^{57} + 16 q^{58} + 64 q^{59} + 136 q^{60} - 36 q^{61} - 356 q^{62} - 200 q^{63} - 176 q^{64} - 4 q^{65} + 276 q^{66} - 292 q^{67} - 72 q^{68} - 60 q^{69} - 92 q^{70} + 448 q^{72} + 48 q^{73} + 284 q^{74} + 96 q^{75} + 252 q^{76} + 192 q^{77} + 620 q^{78} + 4 q^{80} + 100 q^{81} - 240 q^{82} + 288 q^{84} + 48 q^{85} + 20 q^{86} + 36 q^{87} - 624 q^{88} - 578 q^{90} + 188 q^{91} - 412 q^{92} - 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 78 q^{98} - 92 q^{99}+O(q^{100}) $ 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9 + 6 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^15 + 24 * q^16 - 4 * q^17 + 22 * q^18 + 32 * q^19 + 40 * q^20 - 4 * q^21 + 92 * q^22 + 36 * q^24 - 52 * q^26 + 36 * q^28 - 28 * q^30 - 8 * q^31 - 132 * q^32 - 4 * q^33 - 88 * q^34 + 96 * q^35 - 116 * q^36 - 216 * q^38 + 72 * q^39 + 16 * q^40 + 16 * q^42 + 124 * q^43 - 168 * q^44 - 34 * q^45 + 108 * q^46 - 4 * q^47 + 340 * q^48 + 10 * q^50 - 100 * q^51 + 48 * q^52 - 4 * q^53 + 228 * q^54 - 172 * q^56 + 36 * q^57 + 16 * q^58 + 64 * q^59 + 136 * q^60 - 36 * q^61 - 356 * q^62 - 200 * q^63 - 176 * q^64 - 4 * q^65 + 276 * q^66 - 292 * q^67 - 72 * q^68 - 60 * q^69 - 92 * q^70 + 448 * q^72 + 48 * q^73 + 284 * q^74 + 96 * q^75 + 252 * q^76 + 192 * q^77 + 620 * q^78 + 4 * q^80 + 100 * q^81 - 240 * q^82 + 288 * q^84 + 48 * q^85 + 20 * q^86 + 36 * q^87 - 624 * q^88 - 578 * q^90 + 188 * q^91 - 412 * q^92 - 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 78 * q^98 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.97960	+	0.284962i	0.989798	+	0.142481i
$2$	1.97960	+	0.284962i	0.989798	+	0.142481i
$3$		−	2.50699i		−	0.835664i	−0.908524	−	0.417832i	$-0.862790\pi$
$3$		−	2.50699i		−	0.835664i	0.908524	−	0.417832i	$-0.137210\pi$
$4$	3.83759	+	1.12822i	0.959398	+	0.282055i
$5$	2.43881	+	4.36488i	0.487762	+	0.872977i
$5$	2.43881	+	4.36488i	0.487762	+	0.872977i
$6$	0.714398	−	4.96283i	0.119066	−	0.827138i
$7$	−7.18571	−	7.18571i	−1.02653	−	1.02653i	−0.999638	−	0.0268912i	$-0.991439\pi$
$7$	−7.18571	−	7.18571i	−1.02653	−	1.02653i	−0.0268912	−	0.999638i	$-0.508561\pi$
$8$	7.27538	+	3.32699i	0.909422	+	0.415874i
$9$	2.71500			0.301666
$10$	3.58403	+	9.33567i	0.358403	+	0.933567i
$11$	−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	$0.431176\pi$
$12$	2.82844	−	9.62081i	0.235703	−	0.801734i
$13$		−	12.9652i		−	0.997321i	−0.866797	−	0.498660i	$-0.833825\pi$
$13$		−	12.9652i		−	0.997321i	0.866797	−	0.498660i	$-0.166175\pi$
$14$	−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	−0.448132	+	0.893967i	$0.647911\pi$
$17$	−22.8157	+	22.8157i	−1.34210	+	1.34210i	−0.893967	+	0.448132i	$0.852089\pi$
$18$	5.37460	+	0.773673i	0.298589	+	0.0429818i
$19$	−3.16584	+	3.16584i	−0.166623	+	0.166623i	−0.785493	−	0.618870i	$-0.787591\pi$
$19$	−3.16584	+	3.16584i	−0.166623	+	0.166623i	0.618870	+	0.785493i	$0.287591\pi$
$20$	4.43461	+	19.5022i	0.221730	+	0.975108i
$21$	−18.0145	+	18.0145i	−0.857833	+	0.857833i
$22$	−18.9860	+	14.2078i	−0.863000	+	0.645808i
$23$	−3.81600	+	3.81600i	−0.165913	+	0.165913i	−0.785180	−	0.619267i	$-0.787430\pi$
$23$	−3.81600	+	3.81600i	−0.165913	+	0.165913i	0.619267	+	0.785180i	$0.287430\pi$
$24$	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
$27$		−	29.3694i		−	1.08776i
$28$	−19.4688	−	35.6829i	−0.695313	−	1.27439i
$29$	18.3544	−	18.3544i	0.632911	−	0.632911i	−0.315886	−	0.948797i	$-0.602302\pi$
$29$	18.3544	−	18.3544i	0.632911	−	0.632911i	0.948797	+	0.315886i	$0.102302\pi$
$30$	23.4044	−	8.98512i	0.780148	−	0.299504i
$31$	−8.78531			−0.283397			−0.141698	−	0.989910i	$-0.545256\pi$
$31$	−8.78531			−0.283397			−0.141698	+	0.989910i	$0.545256\pi$
$32$	24.1664	+	20.9759i	0.755199	+	0.655496i
$33$	21.0186	+	21.0186i	0.636926	+	0.636926i
$34$	−51.6674	+	38.6642i	−1.51963	+	1.13718i
$35$	13.8402	−	48.8893i	0.395434	−	1.39684i
$36$	10.4191	+	3.06312i	0.289418	+	0.0850866i
$37$		−	32.4039i		−	0.875781i	−0.899028	−	0.437891i	$-0.855726\pi$
$37$		−	32.4039i		−	0.875781i	0.899028	−	0.437891i	$-0.144274\pi$
$38$	−7.16923	+	5.36494i	−0.188664	+	0.141183i
$39$	−32.5036			−0.833425
$40$	3.22134	+	39.8701i	0.0805335	+	0.996752i
$41$			0.937574i			0.0228677i	0.999935	+	0.0114338i	$0.00363958\pi$
$41$			0.937574i			0.0228677i	−0.999935	+	0.0114338i	$0.996360\pi$
$42$	−40.7949	+	30.5280i	−0.971306	+	0.726856i
$43$	57.8364			1.34503			0.672516	−	0.740083i	$-0.265214\pi$
$43$	57.8364			1.34503			0.672516	+	0.740083i	$0.265214\pi$
$44$	−41.6333	+	22.7153i	−0.946211	+	0.516257i
$45$	6.62136	+	11.8506i	0.147141	+	0.263348i
$46$	−8.64156	+	6.46672i	−0.187860	+	0.140581i
$47$	27.9276	−	27.9276i	0.594205	−	0.594205i	−0.344560	−	0.938764i	$-0.611972\pi$
$47$	27.9276	−	27.9276i	0.594205	−	0.594205i	0.938764	+	0.344560i	$0.111972\pi$
$48$	21.7088	−	33.7296i	0.452266	−	0.702701i
$49$			54.2688i			1.10753i
$50$	−32.0084	+	38.4118i	−0.640167	+	0.768236i
$51$	57.1987	+	57.1987i	1.12154	+	1.12154i
$52$	14.6276	−	49.7550i	0.281300	−	0.956828i
$53$	20.6425			0.389482			0.194741	−	0.980855i	$-0.437613\pi$
$53$	20.6425			0.389482			0.194741	+	0.980855i	$0.437613\pi$
$54$	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
$58$	41.5647	−	31.1040i	0.716632	−	0.536276i
$59$	40.1490	+	40.1490i	0.680492	+	0.680492i	0.960111	−	0.279619i	$-0.0902081\pi$
$59$	40.1490	+	40.1490i	0.680492	+	0.680492i	−0.279619	+	0.960111i	$0.590208\pi$
$60$	48.8917	−	11.1175i	0.814862	−	0.185292i
$61$	−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	$0.845090\pi$
$62$	−17.3913	−	2.50348i	−0.280506	−	0.0403788i
$63$	−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
$67$	−29.3419			−0.437938			−0.218969	−	0.975732i	$-0.570269\pi$
$67$	−29.3419			−0.437938			−0.218969	+	0.975732i	$0.570269\pi$
$68$	−113.298	+	61.8162i	−1.66615	+	0.909062i
$69$	9.56668	+	9.56668i	0.138648	+	0.138648i
$70$	41.3296	−	92.8372i	0.590423	−	1.32625i
$71$			34.7686i			0.489698i	0.969561	+	0.244849i	$0.0787385\pi$
$71$			34.7686i			0.489698i	−0.969561	+	0.244849i	$0.921262\pi$
$72$	19.7526	+	9.03277i	0.274342	+	0.125455i
$73$	76.2777	−	76.2777i	1.04490	−	1.04490i	0.0459567	−	0.998943i	$-0.485366\pi$
$73$	76.2777	−	76.2777i	1.04490	−	1.04490i	0.998943	−	0.0459567i	$-0.0146336\pi$
$74$	9.23390	−	64.1466i	0.124782	−	0.866846i
$75$	53.3744	+	32.8527i	0.711659	+	0.438035i
$76$	−15.7210	+	8.57745i	−0.206855	+	0.112861i
$77$	120.490			1.56480
$78$	−64.3439	−	9.26230i	−0.824922	−	0.118747i
$79$			17.2292i			0.218092i	0.994037	+	0.109046i	$0.0347795\pi$
$79$			17.2292i			0.218092i	−0.994037	+	0.109046i	$0.965220\pi$
$80$	−4.98453	+	79.8446i	−0.0623066	+	0.998057i
$81$	−49.1938			−0.607331
$82$	−0.267173	+	1.85602i	−0.00325821	+	0.0226344i
$83$		−	73.3919i		−	0.884239i	−0.896956	−	0.442120i	$-0.854227\pi$
$83$		−	73.3919i		−	0.884239i	0.896956	−	0.442120i	$-0.145773\pi$
$84$	−89.4566	+	48.8080i	−1.06496	+	0.581047i
$85$	−155.231	−	43.9447i	−1.82625	−	0.516997i
$86$	114.493	+	16.4812i	1.33131	+	0.191642i
$87$	−46.0144	−	46.0144i	−0.528901	−	0.528901i
$88$	−88.8901	+	33.1032i	−1.01011	+	0.376173i
$89$	−96.9216			−1.08901			−0.544503	−	0.838759i	$-0.683282\pi$
$89$	−96.9216			−1.08901			−0.544503	+	0.838759i	$0.683282\pi$
$90$	9.73062	+	25.3463i	0.108118	+	0.281626i
$91$	−93.1639	+	93.1639i	−1.02378	+	1.02378i
$92$	−18.9496	+	10.3390i	−0.205973	+	0.112380i
$93$			22.0247i			0.236825i
$94$	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	−0.926702	−	0.375797i	$-0.877369\pi$
$97$	−53.4378	+	53.4378i	−0.550905	+	0.550905i	0.375797	+	0.926702i	$0.377369\pi$
$98$	−15.4646	+	107.430i	−0.157802	+	1.09623i
$99$	−22.7625	+	22.7625i	−0.229924	+	0.229924i
$100$	−74.3095	+	66.9186i	−0.743095	+	0.669186i
$101$	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	$0.0921995\pi$
$102$	96.9308	+	129.530i	0.950302	+	1.26990i
$103$	−132.887	+	132.887i	−1.29017	+	1.29017i	−0.355486	+	0.934681i	$0.615685\pi$
$103$	−132.887	+	132.887i	−1.29017	+	1.29017i	−0.934681	+	0.355486i	$0.884315\pi$
$104$	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
$107$			44.9125i			0.419743i	0.977729	+	0.209872i	$0.0673046\pi$
$107$			44.9125i			0.419743i	−0.977729	+	0.209872i	$0.932695\pi$
$108$	33.1352	−	112.708i	0.306807	−	1.04359i
$109$	31.7568	−	31.7568i	0.291346	−	0.291346i	−0.546266	−	0.837612i	$-0.683951\pi$
$109$	31.7568	−	31.7568i	0.291346	−	0.291346i	0.837612	+	0.546266i	$0.183951\pi$
$110$	−108.319	−	48.2217i	−0.984714	−	0.438379i
$111$	−81.2363			−0.731859
$112$	−34.4550	−	158.901i	−0.307634	−	1.41876i
$113$	5.56976	+	5.56976i	0.0492899	+	0.0492899i	0.731322	−	0.682032i	$-0.238904\pi$
$113$	5.56976	+	5.56976i	0.0492899	+	0.0492899i	−0.682032	+	0.731322i	$0.738904\pi$
$114$	13.4499	+	17.9732i	0.117981	+	0.157660i
$115$	−25.9629	−	7.34990i	−0.225764	−	0.0639122i
$116$	91.1447	−	49.7290i	0.785730	−	0.428698i
$117$		−	35.2004i		−	0.300858i
$118$	68.0379	+	90.9198i	0.576592	+	0.770507i
$119$	327.894			2.75541
$120$	99.9539	−	8.07587i	0.832949	−	0.0672989i
$121$		−	19.5823i		−	0.161837i
$122$	−43.0255	−	57.4954i	−0.352668	−	0.471274i
$123$	2.35049			0.0191097
$124$	−33.7144	−	9.91176i	−0.271891	−	0.0799336i
$125$	−124.889	−	5.27642i	−0.999109	−	0.0422114i
$126$	−33.0609	−	44.1797i	−0.262388	−	0.350632i
$127$	−106.254	+	106.254i	−0.836645	+	0.836645i	−0.988416	−	0.151771i	$-0.951502\pi$
$127$	−106.254	+	106.254i	−0.836645	+	0.836645i	0.151771	+	0.988416i	$0.451502\pi$
$128$	69.0753	+	107.762i	0.539650	+	0.841889i
$129$		−	144.995i		−	1.12399i
$130$	121.039	−	46.4675i	0.931066	−	0.357442i
$131$	−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	$0.854582\pi$
$132$	56.9471	+	104.374i	0.431418	+	0.790714i
$133$	45.4976			0.342088
$134$	−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	$-0.0236754\pi$
$137$	126.441	+	126.441i	0.922925	+	0.922925i	−0.0743099	+	0.997235i	$0.523675\pi$
$138$	16.2120	+	21.6643i	0.117478	+	0.156988i
$139$	−41.3857	−	41.3857i	−0.297739	−	0.297739i	0.542389	−	0.840128i	$-0.317520\pi$
$139$	−41.3857	−	41.3857i	−0.297739	−	0.297739i	−0.840128	+	0.542389i	$0.817520\pi$
$140$	108.271	−	172.003i	0.773365	−	1.22859i
$141$	−70.0143	−	70.0143i	−0.496555	−	0.496555i
$142$	−9.90774	+	68.8277i	−0.0697728	+	0.484702i
$143$	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
$147$	136.051			0.925519
$148$	36.5588	−	124.353i	0.247019	−	0.840223i
$149$	30.0503	+	30.0503i	0.201680	+	0.201680i	0.800719	−	0.599040i	$-0.204451\pi$
$149$	30.0503	+	30.0503i	0.201680	+	0.201680i	−0.599040	+	0.800719i	$0.704451\pi$
$150$	96.2980	+	80.2447i	0.641987	+	0.534964i
$151$			26.0891i			0.172776i	0.996262	+	0.0863878i	$0.0275324\pi$
$151$			26.0891i			0.172776i	−0.996262	+	0.0863878i	$0.972468\pi$
$152$	−33.5654	+	12.5000i	−0.220825	+	0.0822367i
$153$	−61.9445	+	61.9445i	−0.404866	+	0.404866i
$154$	238.521	+	34.3350i	1.54884	+	0.222955i
$155$	−21.4257	−	38.3468i	−0.138230	−	0.247399i
$156$	−124.735	−	36.6712i	−0.799586	−	0.235072i
$157$	−2.64846			−0.0168691			−0.00843457	−	0.999964i	$-0.502685\pi$
$157$	−2.64846			−0.0168691			−0.00843457	+	0.999964i	$0.502685\pi$
$158$	−4.90969	+	34.1069i	−0.0310740	+	0.215866i
$159$		−	51.7507i		−	0.325476i
$160$	−32.6201	+	156.639i	−0.203875	+	0.978997i
$161$	54.8413			0.340629
$162$	−97.3838	−	14.0184i	−0.601135	−	0.0865333i
$163$			143.714i			0.881682i	0.897585	+	0.440841i	$0.145320\pi$
$163$			143.714i			0.881682i	−0.897585	+	0.440841i	$0.854680\pi$
$164$	−1.05779	+	3.59803i	−0.00644994	+	0.0219392i
$165$	−40.4833	+	143.004i	−0.245353	+	0.866690i
$166$	20.9139	−	145.286i	0.125987	−	0.875218i
$167$	−192.906	−	192.906i	−1.15513	−	1.15513i	−0.985510	−	0.169619i	$-0.945746\pi$
$167$	−192.906	−	192.906i	−1.15513	−	1.15513i	−0.169619	−	0.985510i	$-0.554254\pi$
$168$	−190.996	+	71.1283i	−1.13688	+	0.423382i
$169$	0.904324			0.00535103
$170$	−294.772	−	131.228i	−1.73395	−	0.771928i
$171$	−8.59526	+	8.59526i	−0.0502647	+	0.0502647i
$172$	221.952	+	65.2522i	1.29042	+	0.379373i
$173$		−	2.04705i		−	0.0118326i	−0.999982	−	0.00591632i	$-0.998117\pi$
$173$		−	2.04705i		−	0.0118326i	0.999982	−	0.00591632i	$-0.00188323\pi$
$174$	−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
$178$	−191.865	−	27.6190i	−1.07790	−	0.155163i
$179$	−101.208	+	101.208i	−0.565405	+	0.565405i	−0.930838	−	0.365432i	$-0.880921\pi$
$179$	−101.208	+	101.208i	−0.565405	+	0.565405i	0.365432	+	0.930838i	$0.380921\pi$
$180$	12.0399	+	52.9483i	0.0668886	+	0.294157i
$181$	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	$0.0444991\pi$
$182$	−210.975	+	157.879i	−1.15920	+	0.867465i
$183$	−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
$187$		−	382.573i		−	2.04584i
$188$	138.683	−	75.6663i	0.737677	−	0.402480i
$189$	−211.040	+	211.040i	−1.11661	+	1.11661i
$190$	−40.9017	−	18.2088i	−0.215272	−	0.0958358i
$191$	45.3049			0.237198			0.118599	−	0.992942i	$-0.462160\pi$
$191$	45.3049			0.237198			0.118599	+	0.992942i	$0.462160\pi$
$192$	121.364	−	104.948i	0.632104	−	0.546606i
$193$	−176.113	−	176.113i	−0.912503	−	0.912503i	0.0839658	−	0.996469i	$-0.473241\pi$
$193$	−176.113	−	176.113i	−0.912503	−	0.912503i	−0.996469	+	0.0839658i	$0.973241\pi$
$194$	−121.013	+	90.5575i	−0.623778	+	0.466791i
$195$	−79.2700	−	141.874i	−0.406513	−	0.727560i
$196$	−61.2271	+	208.261i	−0.312383	+	1.06256i
$197$			308.173i			1.56433i	0.623072	+	0.782164i	$0.285884\pi$
$197$			308.173i			1.56433i	−0.623072	+	0.782164i	$0.714116\pi$
$198$	−51.5470	+	38.5741i	−0.260338	+	0.194818i
$199$	190.912			0.959358			0.479679	−	0.877444i	$-0.340753\pi$
$199$	190.912			0.959358			0.479679	+	0.877444i	$0.340753\pi$
$200$	−166.172	+	111.296i	−0.830860	+	0.556481i
$201$			73.5598i			0.365969i
$202$	153.865	−	115.142i	0.761710	−	0.570009i
$203$	−263.779			−1.29940
$204$	154.973	+	284.038i	0.759670	+	1.39234i
$205$	−4.09240	+	2.28656i	−0.0199629	+	0.0111540i
$206$	−300.931	+	225.195i	−1.46083	+	1.09318i
$207$	−10.3604	+	10.3604i	−0.0500504	+	0.0500504i
$208$	112.269	−	174.436i	0.539756	−	0.838637i
$209$		−	53.0847i		−	0.253994i
$210$	−232.742	−	103.613i	−1.10829	−	0.493395i
$211$	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	$0.468190\pi$
$212$	79.2177	+	23.2893i	0.373668	+	0.109855i
$213$	87.1645			0.409223
$214$	−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
$218$	71.9150	−	53.8160i	0.329885	−	0.246863i
$219$	−191.228	−	191.228i	−0.873185	−	0.873185i
$220$	−200.685	−	126.326i	−0.912207	−	0.574210i
$221$	295.809	+	295.809i	1.33850	+	1.33850i
$222$	−160.815	−	23.1493i	−0.724392	−	0.104276i
$223$	−60.6724	−	60.6724i	−0.272073	−	0.272073i	0.557861	−	0.829934i	$-0.311622\pi$
$223$	−60.6724	−	60.6724i	−0.272073	−	0.272073i	−0.829934	+	0.557861i	$0.811622\pi$
$224$	−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
$227$	−202.529			−0.892199			−0.446099	−	0.894983i	$-0.647187\pi$
$227$	−202.529			−0.892199			−0.446099	+	0.894983i	$0.647187\pi$
$228$	21.5036	+	39.4124i	0.0943139	+	0.172861i
$229$	137.361	+	137.361i	0.599829	+	0.599829i	0.940267	−	0.340438i	$-0.110575\pi$
$229$	137.361	+	137.361i	0.599829	+	0.599829i	−0.340438	+	0.940267i	$0.610575\pi$
$230$	−49.3016	−	21.9483i	−0.214355	−	0.0954273i
$231$		−	302.067i		−	1.30765i
$232$	194.600	−	72.4704i	0.838795	−	0.312372i
$233$	197.272	−	197.272i	0.846660	−	0.846660i	−0.143055	−	0.989715i	$-0.545692\pi$
$233$	197.272	−	197.272i	0.846660	−	0.846660i	0.989715	+	0.143055i	$0.0456925\pi$
$234$	10.0308	−	69.6826i	0.0428667	−	0.297789i
$235$	190.011	+	53.7907i	0.808557	+	0.228896i
$236$	108.779	+	199.373i	0.460927	+	0.844799i
$237$	43.1935			0.182251
$238$	649.097	+	93.4374i	2.72730	+	0.392594i
$239$		−	411.923i		−	1.72353i	−0.507310	−	0.861763i	$-0.669360\pi$
$239$		−	411.923i		−	1.72353i	0.507310	−	0.861763i	$-0.330640\pi$
$240$	200.170	+	12.4962i	0.834040	+	0.0520674i
$241$	−293.936			−1.21965			−0.609826	−	0.792535i	$-0.708761\pi$
$241$	−293.936			−1.21965			−0.609826	+	0.792535i	$0.708761\pi$
$242$	5.58023	−	38.7651i	0.0230588	−	0.160186i
$243$		−	140.996i		−	0.580231i
$244$	−68.7890	−	126.078i	−0.281922	−	0.516714i
$245$	−236.877	+	132.351i	−0.966844	+	0.540209i
$246$	4.65302	+	0.669801i	0.0189147	+	0.00272277i
$247$	41.0457	+	41.0457i	0.166177	+	0.166177i
$248$	−63.9164	−	29.2286i	−0.257728	−	0.117857i
$249$	−183.993			−0.738926
$250$	−245.725	−	46.0337i	−0.982901	−	0.184135i
$251$	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	$0.0612523\pi$
$252$	−52.8576	−	96.8789i	−0.209752	−	0.384440i
$253$		−	63.9866i		−	0.252911i
$254$	−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	−0.997860	−	0.0653871i	$-0.979172\pi$
$257$	−239.646	+	239.646i	−0.932473	+	0.932473i	0.0653871	+	0.997860i	$0.479172\pi$
$258$	41.3182	−	287.032i	0.160148	−	1.11253i
$259$	−232.845	+	232.845i	−0.899015	+	0.899015i
$260$	252.849	−	57.4954i	0.972496	−	0.221136i
$261$	49.8322	−	49.8322i	0.190928	−	0.190928i
$262$	−101.304	−	135.374i	−0.386658	−	0.516695i
$263$	142.437	−	142.437i	0.541585	−	0.541585i	−0.382408	−	0.923993i	$-0.624905\pi$
$263$	142.437	−	142.437i	0.541585	−	0.541585i	0.923993	+	0.382408i	$0.124905\pi$
$264$	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
$267$			242.981i			0.910043i
$268$	−112.602	−	33.1041i	−0.420157	−	0.123523i
$269$	−269.805	+	269.805i	−1.00299	+	1.00299i	−0.00299625	+	0.999996i	$0.500954\pi$
$269$	−269.805	+	269.805i	−1.00299	+	1.00299i	−0.999996	+	0.00299625i	$0.999046\pi$
$270$	274.183	−	105.261i	1.01549	−	0.389854i
$271$	71.4599			0.263690			0.131845	−	0.991270i	$-0.457910\pi$
$271$	71.4599			0.263690			0.131845	+	0.991270i	$0.457910\pi$
$272$	−504.536	+	109.400i	−1.85491	+	0.402205i
$273$	233.561	+	233.561i	0.855535	+	0.855535i
$274$	214.271	+	286.332i	0.782010	+	1.04501i
$275$	−68.6298	−	288.364i	−0.249563	−	1.04860i
$276$	25.9197	+	47.5064i	0.0939120	+	0.172124i
$277$		−	256.078i		−	0.924470i	−0.886758	−	0.462235i	$-0.847048\pi$
$277$		−	256.078i		−	0.924470i	0.886758	−	0.462235i	$-0.152952\pi$
$278$	−70.1335	−	93.7202i	−0.252279	−	0.337123i
$279$	−23.8521			−0.0854914
$280$	263.347	−	309.642i	0.940525	−	1.10587i
$281$		−	315.882i		−	1.12413i	−0.827092	−	0.562067i	$-0.810006\pi$
$281$		−	315.882i		−	1.12413i	0.827092	−	0.562067i	$-0.189994\pi$
$282$	−118.648	−	158.551i	−0.420739	−	0.562239i
$283$	−8.65428			−0.0305805			−0.0152903	−	0.999883i	$-0.504867\pi$
$283$	−8.65428			−0.0305805			−0.0152903	+	0.999883i	$0.504867\pi$
$284$	−39.2266	+	133.428i	−0.138122	+	0.469816i
$285$	−15.2867	+	53.9991i	−0.0536377	+	0.189471i
$286$	184.206	+	246.157i	0.644078	+	0.860688i
$287$	6.73713	−	6.73713i	0.0234743	−	0.0234743i
$288$	65.6116	+	56.9494i	0.227818	+	0.197741i
$289$		−	752.111i		−	2.60246i
$290$	237.134	+	105.568i	0.817702	+	0.364028i
$291$	133.968	+	133.968i	0.460372	+	0.460372i
$292$	378.781	−	206.665i	1.29719	−	0.707756i
$293$	−533.382			−1.82042			−0.910208	−	0.414151i	$-0.864079\pi$
$293$	−533.382			−1.82042			−0.910208	+	0.414151i	$0.864079\pi$
$294$	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
$298$	50.9241	+	68.0505i	0.170886	+	0.228357i
$299$	49.4751	+	49.4751i	0.165469	+	0.165469i
$300$	167.764	+	186.293i	0.559214	+	0.620977i
$301$	−415.595	−	415.595i	−1.38072	−	1.38072i
$302$	−7.43442	+	51.6459i	−0.0246173	+	0.171013i
$303$	−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
$307$	322.054			1.04903			0.524517	−	0.851400i	$-0.324246\pi$
$307$	322.054			1.04903			0.524517	+	0.851400i	$0.324246\pi$
$308$	462.390	+	135.939i	1.50127	+	0.441360i
$309$	333.147	+	333.147i	1.07815	+	1.07815i
$310$	−31.4868	−	82.0167i	−0.101570	−	0.264570i
$311$			10.0499i			0.0323149i	0.999869	+	0.0161575i	$0.00514331\pi$
$311$			10.0499i			0.0323149i	−0.999869	+	0.0161575i	$0.994857\pi$
$312$	−236.476	−	108.139i	−0.757935	−	0.346599i
$313$	−13.4351	+	13.4351i	−0.0429237	+	0.0429237i	−0.728243	−	0.685319i	$-0.759663\pi$
$313$	−13.4351	+	13.4351i	−0.0429237	+	0.0429237i	0.685319	+	0.728243i	$0.259663\pi$
$314$	−5.24287	−	0.754711i	−0.0166970	−	0.00240354i
$315$	37.5761	−	132.734i	0.119289	−	0.421379i
$316$	−19.4384	+	66.1188i	−0.0615139	+	0.209237i
$317$	−182.394			−0.575377			−0.287688	−	0.957724i	$-0.592887\pi$
$317$	−182.394			−0.575377			−0.287688	+	0.957724i	$0.592887\pi$
$318$	14.7470	−	102.445i	0.0463742	−	0.322155i
$319$			307.766i			0.964785i
$320$	−109.211	+	300.787i	−0.341284	+	0.939960i
$321$	112.595			0.350764
$322$	108.564	+	15.6277i	0.337154	+	0.0485333i
$323$		−	144.462i		−	0.447250i
$324$	−188.786	−	55.5015i	−0.582672	−	0.171301i
$325$	276.032	+	169.901i	0.849328	+	0.522772i
$326$	−40.9532	+	284.496i	−0.125623	+	0.872687i
$327$	−79.6139	−	79.6139i	−0.243468	−	0.243468i
$328$	−3.11930	+	6.82121i	−0.00951006	+	0.0207964i
$329$	−401.359			−1.21994
$330$	−120.891	+	271.554i	−0.366337	+	0.822889i
$331$	−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	$0.400802\pi$
$332$	82.8022	−	281.648i	0.249404	−	0.848337i
$333$		−	87.9766i		−	0.264194i
$334$	−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	−0.839182	−	0.543851i	$-0.816966\pi$
$337$	−99.5263	+	99.5263i	−0.295330	+	0.295330i	0.543851	+	0.839182i	$0.316966\pi$
$338$	1.79020	+	0.257699i	0.00529644	+	0.000762422i
$339$	13.9633	−	13.9633i	0.0411898	−	0.0411898i
$340$	−546.134	−	343.777i	−1.60628	−	1.01111i
$341$	73.6559	−	73.6559i	0.216000	−	0.216000i
$342$	−19.4645	+	14.5658i	−0.0569136	+	0.0425901i
$343$	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
$347$			481.819i			1.38853i	0.719721	+	0.694264i	$0.244270\pi$
$347$			481.819i			1.38853i	−0.719721	+	0.694264i	$0.755730\pi$
$348$	−124.670	−	228.499i	−0.358247	−	0.656606i
$349$	398.473	−	398.473i	1.14176	−	1.14176i	0.153628	−	0.988129i	$-0.450904\pi$
$349$	398.473	−	398.473i	1.14176	−	1.14176i	0.988129	−	0.153628i	$-0.0490957\pi$
$350$	506.018	−	46.0131i	1.44577	−	0.131466i
$351$	−380.779			−1.08484
$352$	−378.472	+	26.7491i	−1.07520	+	0.0759917i
$353$	356.849	+	356.849i	1.01090	+	1.01090i	0.999940	+	0.0109648i	$0.00349027\pi$
$353$	356.849	+	356.849i	1.01090	+	1.01090i	0.0109648	+	0.999940i	$0.496510\pi$
$354$	227.935	−	170.570i	0.643884	−	0.481837i
$355$	−151.761	+	84.7940i	−0.427495	+	0.238856i
$356$	−371.946	−	109.349i	−1.04479	−	0.307160i
$357$		−	822.027i		−	2.30260i
$358$	−229.190	+	171.510i	−0.640197	+	0.479077i
$359$	−417.857			−1.16395			−0.581974	−	0.813207i	$-0.697719\pi$
$359$	−417.857			−1.16395			−0.581974	+	0.813207i	$0.697719\pi$
$360$	8.74593	+	108.247i	0.0242942	+	0.300687i
$361$			340.955i			0.944473i
$362$	348.772	−	260.996i	0.963457	−	0.720982i
$363$	−49.0927			−0.135242
$364$	−462.635	+	252.416i	−1.27097	+	0.693450i
$365$	518.970	+	146.917i	1.42184	+	0.402511i
$366$	−144.141	+	107.864i	−0.393827	+	0.294712i
$367$	−109.049	+	109.049i	−0.297136	+	0.297136i	−0.839891	−	0.542755i	$-0.817381\pi$
$367$	−109.049	+	109.049i	−0.297136	+	0.297136i	0.542755	+	0.839891i	$0.317381\pi$
$368$	−84.3853	+	18.2975i	−0.229308	+	0.0497214i
$369$			2.54551i			0.00689841i
$370$	302.512	−	116.136i	0.817601	−	0.313882i
$371$	−148.331	−	148.331i	−0.399815	−	0.399815i
$372$	−24.8487	+	84.5218i	−0.0667976	+	0.227209i
$373$	−308.832			−0.827968			−0.413984	−	0.910284i	$-0.635863\pi$
$373$	−308.832			−0.827968			−0.413984	+	0.910284i	$0.635863\pi$
$374$	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
$378$	−477.912	+	357.635i	−1.26432	+	0.946124i
$379$	−28.3677	−	28.3677i	−0.0748489	−	0.0748489i	0.668691	−	0.743540i	$-0.266855\pi$
$379$	−28.3677	−	28.3677i	−0.0748489	−	0.0748489i	−0.743540	+	0.668691i	$0.766855\pi$
$380$	−75.7800	−	47.7015i	−0.199421	−	0.125530i
$381$	266.377	+	266.377i	0.699153	+	0.699153i
$382$	89.6853	+	12.9102i	0.234778	+	0.0337963i
$383$	422.953	+	422.953i	1.10432	+	1.10432i	0.993884	+	0.110433i	$0.0352237\pi$
$383$	422.953	+	422.953i	1.10432	+	1.10432i	0.110433	+	0.993884i	$0.464776\pi$
$384$	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
$387$	157.026			0.405751
$388$	−265.362	+	144.783i	−0.683923	+	0.373152i
$389$	−178.975	−	178.975i	−0.460089	−	0.460089i	0.438595	−	0.898685i	$-0.355476\pi$
$389$	−178.975	−	178.975i	−0.460089	−	0.460089i	−0.898685	+	0.438595i	$0.855476\pi$
$390$	−116.494	−	303.443i	−0.298702	−	0.778058i
$391$		−	174.129i		−	0.445344i
$392$	−180.552	+	394.826i	−0.460591	+	1.00721i
$393$	−149.867	+	149.867i	−0.381340	+	0.381340i
$394$	−87.8177	+	610.057i	−0.222888	+	1.54837i
$395$	−75.2036	+	42.0188i	−0.190389	+	0.106377i
$396$	−113.034	+	61.6721i	−0.285440	+	0.155738i
$397$	20.4646			0.0515480			0.0257740	−	0.999668i	$-0.491795\pi$
$397$	20.4646			0.0515480			0.0257740	+	0.999668i	$0.491795\pi$
$398$	377.929	+	54.4028i	0.949570	+	0.136690i
$399$		−	114.062i		−	0.285870i
$400$	−360.669	+	172.969i	−0.901671	+	0.432422i
$401$	97.7306			0.243717			0.121859	−	0.992547i	$-0.461115\pi$
$401$	97.7306			0.243717			0.121859	+	0.992547i	$0.461115\pi$
$402$	−20.9618	+	145.619i	−0.0521437	+	0.362235i
$403$			113.903i			0.282638i
$404$	337.402	−	184.088i	0.835154	−	0.455664i
$405$	−119.974	−	214.725i	−0.296233	−	0.530186i
$406$	−522.176	−	75.1671i	−1.28615	−	0.185141i
$407$	271.674	+	271.674i	0.667503	+	0.667503i
$408$	225.843	+	606.442i	0.553536	+	1.48638i
$409$	346.930			0.848239			0.424120	−	0.905606i	$-0.360584\pi$
$409$	346.930			0.848239			0.424120	+	0.905606i	$0.360584\pi$
$410$	−8.75288	+	3.36029i	−0.0213485	+	0.00819583i
$411$	316.986	−	316.986i	0.771255	−	0.771255i
$412$	−659.893	+	360.041i	−1.60168	+	0.873886i
$413$		−	576.998i		−	1.39709i
$414$	−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
$418$	15.1272	−	105.086i	0.0361894	−	0.251403i
$419$	−94.6547	+	94.6547i	−0.225906	+	0.225906i	−0.810980	−	0.585074i	$-0.801065\pi$
$419$	−94.6547	+	94.6547i	−0.225906	+	0.225906i	0.585074	+	0.810980i	$0.301065\pi$
$420$	−431.209	−	271.434i	−1.02669	−	0.646273i
$421$	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	$0.0799512\pi$
$422$	391.458	+	523.109i	0.927625	+	1.23960i
$423$	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
$427$			364.880i			0.854519i
$428$	−50.6712	+	172.356i	−0.118391	+	0.402701i
$429$	272.509	−	272.509i	0.635220	−	0.635220i
$430$	207.287	+	539.941i	0.482063	+	1.25568i
$431$	505.491			1.17283			0.586416	−	0.810010i	$-0.300538\pi$
$431$	505.491			1.17283			0.586416	+	0.810010i	$0.300538\pi$
$432$	254.318	−	395.143i	0.588700	−	0.914682i
$433$	8.23935	+	8.23935i	0.0190285	+	0.0190285i	0.716557	−	0.697529i	$-0.245717\pi$
$433$	8.23935	+	8.23935i	0.0190285	+	0.0190285i	−0.697529	+	0.716557i	$0.745717\pi$
$434$	106.980	+	142.958i	0.246497	+	0.329397i
$435$	88.6271	−	313.068i	0.203740	−	0.719696i
$436$	157.698	−	86.0409i	0.361693	−	0.197341i
$437$		−	24.1617i		−	0.0552900i
$438$	−324.060	−	433.046i	−0.739864	−	0.988689i
$439$	195.298			0.444870			0.222435	−	0.974948i	$-0.428600\pi$
$439$	195.298			0.444870			0.222435	+	0.974948i	$0.428600\pi$
$440$	−361.278	−	307.262i	−0.821086	−	0.698324i
$441$			147.340i			0.334103i
$442$	501.288	+	669.877i	1.13414	+	1.51556i
$443$	401.681			0.906729			0.453365	−	0.891325i	$-0.350224\pi$
$443$	401.681			0.906729			0.453365	+	0.891325i	$0.350224\pi$
$444$	−311.752	−	91.6525i	−0.702144	−	0.206425i
$445$	−236.373	−	423.051i	−0.531176	−	0.950677i
$446$	−102.817	−	137.396i	−0.230532	−	0.308063i
$447$	75.3357	−	75.3357i	0.168536	−	0.168536i
$448$	47.0517	−	648.672i	0.105026	−	1.44793i
$449$			189.448i			0.421934i	0.977493	+	0.210967i	$0.0676613\pi$
$449$			189.448i			0.421934i	−0.977493	+	0.210967i	$0.932339\pi$
$450$	−86.9026	+	104.288i	−0.193117	+	0.231751i
$451$	−7.86061	−	7.86061i	−0.0174293	−	0.0174293i
$452$	15.0905	+	27.6584i	0.0333862	+	0.0611911i
$453$	65.4052			0.144382
$454$	−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	−0.997390	−	0.0722037i	$-0.976997\pi$
$457$	−488.804	−	488.804i	−1.06959	−	1.06959i	−0.0722037	−	0.997390i	$-0.523003\pi$
$458$	232.776	+	311.062i	0.508245	+	0.679174i
$459$	670.083	+	670.083i	1.45988	+	1.45988i
$460$	−91.3428	−	57.4978i	−0.198571	−	0.124995i
$461$	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	$0.544484\pi$
$462$	86.0776	−	597.969i	0.186315	−	1.29431i
$463$	−70.7053	−	70.7053i	−0.152711	−	0.152711i	0.626616	−	0.779328i	$-0.284439\pi$
$463$	−70.7053	−	70.7053i	−0.152711	−	0.152711i	−0.779328	+	0.626616i	$0.784439\pi$
$464$	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
$467$	918.293			1.96637			0.983183	−	0.182623i	$-0.0584589\pi$
$467$	918.293			1.96637			0.983183	+	0.182623i	$0.0584589\pi$
$468$	39.7138	−	135.085i	0.0848586	−	0.288643i
$469$	210.842	+	210.842i	0.449557	+	0.449557i
$470$	360.816	+	160.630i	0.767694	+	0.341765i
$471$			6.63965i			0.0140969i
$472$	158.524	+	425.675i	0.335856	+	0.901854i
$473$	−484.899	+	484.899i	−1.02516	+	1.02516i
$474$	85.5057	+	12.3085i	0.180392	+	0.0259674i
$475$	−25.9150	−	108.888i	−0.0545579	−	0.229238i
$476$	1258.32	+	369.936i	2.64353	+	0.777177i
$477$	56.0445			0.117494
$478$	117.383	−	815.441i	0.245570	−	1.70594i
$479$			49.5880i			0.103524i	0.998659	+	0.0517620i	$0.0164837\pi$
$479$			49.5880i			0.103524i	−0.998659	+	0.0517620i	$0.983516\pi$
$480$	392.694	+	81.7782i	0.818112	+	0.170371i
$481$	−420.122			−0.873435
$482$	−581.875	−	83.7608i	−1.20721	−	0.173778i
$483$		−	137.487i		−	0.284652i
$484$	22.0932	−	75.1490i	0.0456471	−	0.155267i
$485$	−363.575	−	102.925i	−0.749638	−	0.212217i
$486$	40.1786	−	279.115i	0.0826720	−	0.574311i
$487$	−644.145	−	644.145i	−1.32268	−	1.32268i	−0.911599	−	0.411081i	$-0.865151\pi$
$487$	−644.145	−	644.145i	−1.32268	−	1.32268i	−0.411081	−	0.911599i	$-0.634849\pi$
$488$	−100.247	−	269.186i	−0.205424	−	0.551611i
$489$	360.290			0.736790
$490$	−506.635	+	194.501i	−1.03395	+	0.396940i
$491$	−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	$0.965514\pi$
$492$	9.02022	+	2.65187i	0.0183338	+	0.00538998i
$493$			837.538i			1.69886i
$494$	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
$498$	−364.231	−	52.4310i	−0.731388	−	0.105283i
$499$	142.483	−	142.483i	0.285537	−	0.285537i	−0.549775	−	0.835313i	$-0.685287\pi$
$499$	142.483	−	142.483i	0.285537	−	0.285537i	0.835313	+	0.549775i	$0.185287\pi$
$500$	−473.319	−	161.151i	−0.946637	−	0.322301i
$501$	−483.615	+	483.615i	−0.965299	+	0.965299i
$502$	449.209	−	336.156i	0.894838	−	0.669633i
$503$	−307.222	+	307.222i	−0.610780	+	0.610780i	−0.943149	−	0.332370i	$-0.892152\pi$
$503$	−307.222	+	307.222i	−0.610780	+	0.610780i	0.332370	+	0.943149i	$0.392152\pi$
$504$	−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
$507$		−	2.26713i		−	0.00447166i
$508$	−527.637	+	287.881i	−1.03866	+	0.566695i
$509$	−268.080	+	268.080i	−0.526681	+	0.526681i	−0.919581	−	0.392900i	$-0.871472\pi$
$509$	−268.080	+	268.080i	−0.526681	+	0.526681i	0.392900	+	0.919581i	$0.371472\pi$
$510$	−328.987	+	738.990i	−0.645072	+	1.44900i
$511$	−1096.22			−2.14524
$512$	143.504	+	491.478i	0.280280	+	0.959918i
$513$	92.9789	+	92.9789i	0.181245	+	0.181245i
$514$	−542.691	+	406.111i	−1.05582	+	0.790099i
$515$	−904.124	−	255.951i	−1.75558	−	0.496992i
$516$	163.587	−	556.433i	0.317028	−	1.07836i
$517$			468.289i			0.905782i
$518$	−527.291	+	394.587i	−1.01794	+	0.761750i
$519$	−5.13193			−0.00988811
$520$	516.922	−	41.7652i	0.994082	−	0.0803177i
$521$			364.737i			0.700071i	0.936736	+	0.350036i	$0.113831\pi$
$521$			364.737i			0.700071i	−0.936736	+	0.350036i	$0.886169\pi$
$522$	112.848	−	84.4473i	0.216184	−	0.161776i
$523$	434.085			0.829991			0.414996	−	0.909823i	$-0.363783\pi$
$523$	434.085			0.829991			0.414996	+	0.909823i	$0.363783\pi$
$524$	−161.965	−	296.854i	−0.309093	−	0.566515i
$525$	−147.463	−	619.603i	−0.280883	−	1.18020i
$526$	322.557	−	241.378i	0.613225	−	0.458894i
$527$	200.443	−	200.443i	0.380347	−	0.380347i
$528$	100.783	+	464.795i	0.190876	+	0.880293i
$529$			499.876i			0.944946i
$530$	73.9834	+	192.712i	0.139591	+	0.363608i
$531$	109.005	+	109.005i	0.205282	+	0.205282i
$532$	174.601	+	51.3314i	0.328198	+	0.0964875i
$533$	12.1558			0.0228064
$534$	−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
$538$	−610.988	+	457.220i	−1.13567	+	0.849851i
$539$	−454.988	−	454.988i	−0.844134	−	0.844134i
$540$	572.767	−	130.242i	1.06068	−	0.241188i
$541$	−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	$0.878062\pi$
$542$	141.462	+	20.3634i	0.261000	+	0.0375709i
$543$	−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
$547$	−9.98799			−0.0182596			−0.00912979	−	0.999958i	$-0.502906\pi$
$547$	−9.98799			−0.0182596			−0.00912979	+	0.999958i	$0.502906\pi$
$548$	342.575	+	627.881i	0.625137	+	1.14577i
$549$	−68.9318	−	68.9318i	−0.125559	−	0.125559i
$550$	−53.6862	−	590.401i	−0.0976113	−	1.07346i
$551$			116.214i			0.210916i
$552$	37.7730	+	101.429i	0.0684293	+	0.183749i
$553$	123.804	−	123.804i	0.223877	−	0.223877i
$554$	72.9727	−	506.931i	0.131720	−	0.915038i
$555$	−198.120	−	354.587i	−0.356973	−	0.638896i
$556$	−112.129	−	205.513i	−0.201671	−	0.369629i
$557$	−360.011			−0.646339			−0.323170	−	0.946341i	$-0.604748\pi$
$557$	−360.011			−0.646339			−0.323170	+	0.946341i	$0.604748\pi$
$558$	−47.2175	−	6.79695i	−0.0846191	−	0.0121809i
$559$		−	749.859i		−	1.34143i
$560$	609.557	−	537.922i	1.08849	−	0.960575i
$561$	−959.106			−1.70964
$562$	90.0144	−	625.318i	0.160168	−	1.11267i
$563$		−	524.373i		−	0.931392i	−0.884945	−	0.465696i	$-0.845804\pi$
$563$		−	524.373i		−	0.931392i	0.884945	−	0.465696i	$-0.154196\pi$
$564$	−189.695	−	347.678i	−0.336338	−	0.616450i
$565$	−10.7278	+	37.8949i	−0.0189872	+	0.0670707i
$566$	−17.1320	−	2.46615i	−0.0302685	−	0.00435715i
$567$	353.492	+	353.492i	0.623443	+	0.623443i
$568$	−115.675	+	252.955i	−0.203653	+	0.445343i
$569$	606.955			1.06670			0.533352	−	0.845893i	$-0.320932\pi$
$569$	606.955			1.06670			0.533352	+	0.845893i	$0.320932\pi$
$570$	−45.6493	+	102.540i	−0.0800865	+	0.179895i
$571$	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	$-0.144687\pi$
$572$	294.508	+	539.783i	0.514874	+	0.943676i
$573$		−	113.579i		−	0.198218i
$574$	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	−0.784740	−	0.619824i	$-0.787204\pi$
$577$	−95.1565	+	95.1565i	−0.164916	+	0.164916i	0.619824	+	0.784740i	$0.287204\pi$
$578$	214.324	−	1488.88i	0.370802	−	2.57591i
$579$	−441.514	+	441.514i	−0.762545	+	0.762545i
$580$	439.346	+	276.556i	0.757492	+	0.476821i
$581$	−527.372	+	527.372i	−0.907698	+	0.907698i
$582$	227.027	+	303.378i	0.390080	+	0.521269i
$583$	−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
$587$		−	445.447i		−	0.758853i	−0.925222	−	0.379427i	$-0.876121\pi$
$587$		−	445.447i		−	0.758853i	0.925222	−	0.379427i	$-0.123879\pi$
$588$	522.109	+	153.496i	0.887941	+	0.261047i
$589$	27.8129	−	27.8129i	0.0472205	−	0.0472205i
$590$	−230.923	+	518.713i	−0.391395	+	0.879175i
$591$	772.586			1.30725
$592$	280.595	−	435.970i	0.473979	−	0.736436i
$593$	−359.016	−	359.016i	−0.605424	−	0.605424i	0.336323	−	0.941747i	$-0.390817\pi$
$593$	−359.016	−	359.016i	−0.605424	−	0.605424i	−0.941747	+	0.336323i	$0.890817\pi$
$594$	417.274	+	557.608i	0.702481	+	0.938733i
$595$	799.670	+	1431.22i	1.34398	+	2.40541i
$596$	81.4173	+	149.224i	0.136606	+	0.250376i
$597$		−	478.615i		−	0.801700i
$598$	83.8422	+	112.039i	0.140204	+	0.187357i
$599$	−66.3175			−0.110714			−0.0553568	−	0.998467i	$-0.517630\pi$
$599$	−66.3175			−0.110714			−0.0553568	+	0.998467i	$0.517630\pi$
$600$	279.019	+	416.592i	0.465031	+	0.694319i
$601$			512.825i			0.853287i	0.904420	+	0.426643i	$0.140304\pi$
$601$			512.825i			0.853287i	−0.904420	+	0.426643i	$0.859696\pi$
$602$	−704.281	−	941.139i	−1.16990	−	1.56335i
$603$	−79.6631			−0.132111
$604$	−29.4343	+	100.119i	−0.0487322	+	0.165761i
$605$	85.4746	−	47.7576i	0.141280	−	0.0789381i
$606$	−288.659	−	385.739i	−0.476336	−	0.636533i
$607$	−700.017	+	700.017i	−1.15324	+	1.15324i	−0.167341	+	0.985899i	$0.553518\pi$
$607$	−700.017	+	700.017i	−1.15324	+	1.15324i	−0.985899	+	0.167341i	$0.946482\pi$
$608$	−142.913	+	10.1006i	−0.235055	+	0.0166128i
$609$			661.292i			1.08586i
$610$	146.030	−	328.022i	0.239393	−	0.537740i
$611$	−362.086	−	362.086i	−0.592613	−	0.592613i
$612$	−307.605	+	167.831i	−0.502623	+	0.274233i
$613$	402.030			0.655840			0.327920	−	0.944705i	$-0.393652\pi$
$613$	402.030			0.655840			0.327920	+	0.944705i	$0.393652\pi$
$614$	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	$-0.423021\pi$
$617$	−451.281	−	451.281i	−0.731412	−	0.731412i	−0.970899	+	0.239488i	$0.923021\pi$
$618$	564.562	+	754.431i	0.913531	+	1.22076i
$619$	−141.521	−	141.521i	−0.228629	−	0.228629i	0.583491	−	0.812120i	$-0.301686\pi$
$619$	−141.521	−	141.521i	−0.228629	−	0.228629i	−0.812120	+	0.583491i	$0.801686\pi$
$620$	−38.9594	−	171.332i	−0.0628377	−	0.276343i
$621$	112.074	+	112.074i	0.180473	+	0.180473i
$622$	−2.86386	+	19.8948i	−0.00460427	+	0.0319853i
$623$	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
$627$	−133.083			−0.212254
$628$	−10.1637	−	2.98804i	−0.0161842	−	0.00475803i
$629$	739.318	+	739.318i	1.17539	+	1.17539i
$630$	112.210	−	252.053i	0.178111	−	0.400084i
$631$		−	430.554i		−	0.682335i	−0.940002	−	0.341168i	$-0.889178\pi$
$631$		−	430.554i		−	0.682335i	0.940002	−	0.341168i	$-0.110822\pi$
$632$	−57.3215	+	125.349i	−0.0906986	+	0.198337i
$633$	579.111	−	579.111i	0.914868	−	0.914868i
$634$	−361.067	−	51.9756i	−0.569506	−	0.0819804i
$635$	−722.919	−	204.653i	−1.13845	−	0.322288i
$636$	58.3862	−	198.598i	0.0918021	−	0.312261i
$637$	703.604			1.10456
$638$	−87.7019	+	609.253i	−0.137464	+	0.954942i
$639$			94.3966i			0.147726i
$640$	−301.906	+	564.316i	−0.471729	+	0.881744i
$641$	244.316			0.381147			0.190574	−	0.981673i	$-0.438965\pi$
$641$	244.316			0.381147			0.190574	+	0.981673i	$0.438965\pi$
$642$	222.893	+	32.0854i	0.347185	+	0.0499773i
$643$		−	521.720i		−	0.811384i	−0.914010	−	0.405692i	$-0.867031\pi$
$643$		−	521.720i		−	0.811384i	0.914010	−	0.405692i	$-0.132969\pi$
$644$	210.459	+	61.8731i	0.326799	+	0.0960763i
$645$	632.887	−	353.616i	0.981221	−	0.548242i
$646$	41.1662	−	285.976i	0.0637248	−	0.442687i
$647$	7.36567	+	7.36567i	0.0113843	+	0.0113843i	0.712776	−	0.701392i	$-0.247438\pi$
$647$	7.36567	+	7.36567i	0.0113843	+	0.0113843i	−0.701392	+	0.712776i	$0.747438\pi$
$648$	−357.904	−	163.667i	−0.552320	−	0.252573i
$649$	−673.218			−1.03732
$650$	498.015	+	414.994i	0.766177	+	0.638452i
$651$	158.263	−	158.263i	0.243107	−	0.243107i
$652$	−162.141	+	551.517i	−0.248683	+	0.845885i
$653$			171.839i			0.263154i	0.991306	+	0.131577i	$0.0420040\pi$
$653$			171.839i			0.263154i	−0.991306	+	0.131577i	$0.957996\pi$
$654$	−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
$658$	−794.529	−	114.372i	−1.20749	−	0.173818i
$659$	66.3827	−	66.3827i	0.100732	−	0.100732i	−0.654945	−	0.755677i	$-0.727308\pi$
$659$	66.3827	−	66.3827i	0.100732	−	0.100732i	0.755677	+	0.654945i	$0.227308\pi$
$660$	−316.698	+	503.117i	−0.479846	+	0.762298i
$661$	−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	$0.263254\pi$
$662$	−483.630	+	361.914i	−0.730559	+	0.546698i
$663$	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
$667$			140.081i			0.210017i
$668$	−522.655	−	957.937i	−0.782418	−	1.43404i
$669$	−152.105	+	152.105i	−0.227362	+	0.227362i
$670$	−105.162	−	273.926i	−0.156958	−	0.408845i
$671$	425.726			0.634465
$672$	−813.215	+	57.4752i	−1.21014	+	0.0855286i
$673$	58.7394	+	58.7394i	0.0872799	+	0.0872799i	0.749399	−	0.662119i	$-0.230343\pi$
$673$	58.7394	+	58.7394i	0.0872799	+	0.0872799i	−0.662119	+	0.749399i	$0.730343\pi$
$674$	−225.383	+	168.661i	−0.334396	+	0.250238i
$675$	625.281	+	384.869i	0.926343	+	0.570176i
$676$	3.47043	+	1.02028i	0.00513377	+	0.00150929i
$677$			408.523i			0.603431i	0.953398	+	0.301716i	$0.0975593\pi$
$677$			408.523i			0.603431i	−0.953398	+	0.301716i	$0.902441\pi$
$678$	31.6208	−	23.6627i	0.0466383	−	0.0349008i
$679$	767.977			1.13104
$680$	−983.160	−	836.166i	−1.44582	−	1.22966i
$681$			507.738i			0.745578i
$682$	166.798	−	124.820i	0.244572	−	0.183020i
$683$	611.720			0.895636			0.447818	−	0.894125i	$-0.352201\pi$
$683$	611.720			0.895636			0.447818	+	0.894125i	$0.352201\pi$
$684$	−42.6824	+	23.2877i	−0.0624012	+	0.0340464i
$685$	−243.534	+	860.264i	−0.355524	+	1.25586i
$686$	85.7357	−	64.1585i	0.124979	−	0.0935254i
$687$	344.363	−	344.363i	0.501256	−	0.501256i
$688$	778.144	+	500.823i	1.13102	+	0.727940i
$689$		−	267.634i		−	0.388438i
$690$	−55.0242	+	123.599i	−0.0797451	+	0.179128i
$691$	−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	$0.931695\pi$
$692$	2.30952	−	7.85573i	0.00333746	−	0.0113522i
$693$	327.129			0.472048
$694$	−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
$698$	902.365	−	675.265i	1.29279	−	0.967429i
$699$	−494.559	−	494.559i	−0.707523	−	0.707523i
$700$	1014.82	+	53.1089i	1.44975	+	0.0758699i
$701$	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	$0.697121\pi$
$702$	−753.789	−	108.508i	−1.07377	−	0.154569i
$703$	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
$707$	−976.466			−1.38114
$708$	499.825	−	272.707i	0.705968	−	0.385180i
$709$	−820.614	−	820.614i	−1.15742	−	1.15742i	−0.985027	−	0.172397i	$-0.944849\pi$
$709$	−820.614	−	820.614i	−1.15742	−	1.15742i	−0.172397	−	0.985027i	$-0.555151\pi$
$710$	−324.588	+	124.612i	−0.457166	+	0.175509i
$711$			46.7773i			0.0657909i
$712$	−705.141	−	322.457i	−0.990367	−	0.452889i
$713$	33.5248	−	33.5248i	0.0470193	−	0.0470193i
$714$	234.247	−	1627.28i	0.328077	−	2.27910i
$715$	−209.364	+	739.560i	−0.292817	+	1.03435i
$716$	−502.578	+	274.209i	−0.701924	+	0.382973i
$717$	−1032.69			−1.44029
$718$	−827.188	−	119.074i	−1.15207	−	0.165841i
$719$			578.830i			0.805048i	0.915409	+	0.402524i	$0.131867\pi$
$719$			578.830i			0.805048i	−0.915409	+	0.402524i	$0.868133\pi$
$720$	−13.5330	+	216.778i	−0.0187958	+	0.301080i
$721$	1909.78			2.64879
$722$	−97.1594	+	674.953i	−0.134570	+	0.934837i
$723$			736.896i			1.01922i
$724$	764.800	−	417.279i	1.05635	−	0.576352i
$725$	150.246	+	631.294i	0.207236	+	0.870751i
$726$	−97.1837	−	13.9896i	−0.133862	−	0.0192694i
$727$	771.845	+	771.845i	1.06168	+	1.06168i	0.997968	+	0.0637163i	$0.0202953\pi$
$727$	771.845	+	771.845i	1.06168	+	1.06168i	0.0637163	+	0.997968i	$0.479705\pi$
$728$	−987.758	+	367.847i	−1.35681	+	0.505285i
$729$	−796.220			−1.09221
$730$	985.485	+	438.722i	1.34998	+	0.600989i
$731$	−1319.58	+	1319.58i	−1.80517	+	1.80517i
$732$	−316.077	+	172.453i	−0.431799	+	0.235592i
$733$			455.036i			0.620785i	0.950608	+	0.310393i	$0.100461\pi$
$733$			455.036i			0.620785i	−0.950608	+	0.310393i	$0.899539\pi$
$734$	−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
$738$	−0.725375	+	5.03908i	−0.000982893	+	0.00682803i
$739$	723.106	−	723.106i	0.978493	−	0.978493i	−0.0212803	−	0.999774i	$-0.506774\pi$
$739$	723.106	−	723.106i	0.978493	−	0.978493i	0.999774	+	0.0212803i	$0.00677425\pi$
$740$	631.946	−	143.699i	0.853981	−	0.194187i
$741$	102.901	−	102.901i	0.138868	−	0.138868i
$742$	−251.367	−	335.905i	−0.338770	−	0.452702i
$743$	134.068	−	134.068i	0.180442	−	0.180442i	−0.611107	−	0.791548i	$-0.709275\pi$
$743$	134.068	−	134.068i	0.180442	−	0.180442i	0.791548	+	0.611107i	$0.209275\pi$
$744$	−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
$747$		−	199.259i		−	0.266745i
$748$	431.626	−	1468.16i	0.577041	−	1.96278i
$749$	322.728	−	322.728i	0.430879	−	0.430879i
$750$	−115.406	+	616.031i	−0.153875	+	0.821375i
$751$	−216.822			−0.288711			−0.144356	−	0.989526i	$-0.546111\pi$
$751$	−216.822			−0.288711			−0.144356	+	0.989526i	$0.546111\pi$
$752$	617.578	−	133.911i	0.821248	−	0.178073i
$753$	−497.299	−	497.299i	−0.660423	−	0.660423i
$754$	−403.269	−	538.893i	−0.534839	−	0.714712i
$755$	−113.876	+	63.6264i	−0.150829	+	0.0842733i
$756$	−1047.98	+	571.785i	−1.38622	+	0.756330i
$757$		−	747.764i		−	0.987800i	−0.869519	−	0.493900i	$-0.835571\pi$
$757$		−	747.764i		−	0.987800i	0.869519	−	0.493900i	$-0.164429\pi$
$758$	−48.0729	−	64.2403i	−0.0634207	−	0.0847498i
$759$	−160.414			−0.211349
$760$	−136.421	−	116.024i	−0.179501	−	0.152663i
$761$		−	1410.33i		−	1.85326i	−0.375978	−	0.926629i	$-0.622693\pi$
$761$		−	1410.33i		−	1.85326i	0.375978	−	0.926629i	$-0.377307\pi$
$762$	451.412	+	603.227i	0.592404	+	0.791636i
$763$	−456.390			−0.598152
$764$	173.862	+	51.1139i	0.227568	+	0.0669030i
$765$	−421.452	−	119.310i	−0.550917	−	0.155961i
$766$	716.750	+	957.802i	0.935705	+	1.25039i
$767$	520.539	−	520.539i	0.678669	−	0.678669i
$768$	584.150	−	265.824i	0.760613	−	0.346124i
$769$		−	925.036i		−	1.20291i	−0.798907	−	0.601454i	$-0.794588\pi$
$769$		−	925.036i		−	1.20291i	0.798907	−	0.601454i	$-0.205412\pi$
$770$	431.838	+	1124.85i	0.560829	+	1.46085i
$771$	600.789	+	600.789i	0.779234	+	0.779234i
$772$	−477.156	−	874.545i	−0.618077	−	1.13283i
$773$	146.591			0.189639			0.0948196	−	0.995494i	$-0.469773\pi$
$773$	146.591			0.189639			0.0948196	+	0.995494i	$0.469773\pi$
$774$	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
$778$	−303.296	−	405.298i	−0.389841	−	0.520949i
$779$	−2.96821	−	2.96821i	−0.00381029	−	0.00381029i
$780$	−144.140	−	633.890i	−0.184795	−	0.812679i
$781$	−291.499	−	291.499i	−0.373238	−	0.373238i
$782$	49.6204	−	344.706i	0.0634532	−	0.440800i
$783$	−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
$787$	−389.164			−0.494491			−0.247245	−	0.968953i	$-0.579525\pi$
$787$	−389.164			−0.494491			−0.247245	+	0.968953i	$0.579525\pi$
$788$	−347.687	+	1182.64i	−0.441227	+	1.50081i
$789$	−357.088	−	357.088i	−0.452583	−	0.452583i
$790$	−160.846	+	61.7500i	−0.203603	+	0.0781646i
$791$		−	80.0453i		−	0.101195i
$792$	−241.336	+	89.8752i	−0.304718	+	0.113479i
$793$	−329.176	+	329.176i	−0.415102	+	0.415102i
$794$	40.5115	+	5.83163i	0.0510221	+	0.00734463i
$795$	225.886	−	126.210i	0.284133	−	0.158755i
$796$	732.643	+	215.391i	0.920406	+	0.270592i
$797$	225.230			0.282597			0.141298	−	0.989967i	$-0.454872\pi$
$797$	225.230			0.282597			0.141298	+	0.989967i	$0.454872\pi$
$798$	32.5034	−	225.797i	0.0407311	−	0.282953i
$799$			1274.38i			1.59496i
$800$	−763.267	+	239.631i	−0.954084	+	0.299539i
$801$	−263.142			−0.328517
$802$	193.467	+	27.8496i	0.241231	+	0.0347251i
$803$			1279.02i			1.59280i
$804$	−82.9917	+	282.293i	−0.103223	+	0.351110i
$805$	133.748	+	239.376i	0.166146	+	0.297362i
$806$	−32.4581	+	225.482i	−0.0402706	+	0.279754i
$807$	676.398	+	676.398i	0.838164	+	0.838164i
$808$	720.378	−	268.273i	0.891557	−	0.332021i
$809$	389.024			0.480870			0.240435	−	0.970665i	$-0.422710\pi$
$809$	389.024			0.480870			0.240435	+	0.970665i	$0.422710\pi$
$810$	−176.312	−	459.257i	−0.217669	−	0.566984i
$811$	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	$0.184127\pi$
$812$	−1012.28	−	297.601i	−1.24665	−	0.366504i
$813$		−	179.149i		−	0.220356i
$814$	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
$818$	686.781	+	98.8620i	0.839585	+	0.120858i
$819$	−252.940	+	252.940i	−0.308840	+	0.308840i
$820$	−18.2847	+	4.15777i	−0.0222984	+	0.00507045i
$821$	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	$0.131169\pi$
$822$	717.833	−	537.174i	0.873276	−	0.653497i
$823$	543.405	−	543.405i	0.660274	−	0.660274i	−0.295171	−	0.955445i	$-0.595377\pi$
$823$	543.405	−	543.405i	0.660274	−	0.660274i	0.955445	+	0.295171i	$0.0953765\pi$
$824$	−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
$827$		−	912.383i		−	1.10324i	−0.834094	−	0.551622i	$-0.814009\pi$
$827$		−	912.383i		−	1.10324i	0.834094	−	0.551622i	$-0.185991\pi$
$828$	−51.4480	+	28.0703i	−0.0621353	+	0.0339013i
$829$	−401.447	+	401.447i	−0.484254	+	0.484254i	−0.906487	−	0.422233i	$-0.861246\pi$
$829$	−401.447	+	401.447i	−0.484254	+	0.484254i	0.422233	+	0.906487i	$0.361246\pi$
$830$	685.162	−	263.038i	0.825497	−	0.316914i
$831$	−641.985			−0.772546
$832$	627.647	−	542.752i	0.754383	−	0.652346i
$833$	−1238.18	−	1238.18i	−1.48641	−	1.48641i
$834$	−234.956	+	175.824i	−0.281721	+	0.210820i
$835$	371.552	−	1312.48i	0.444973	−	1.57183i
$836$	59.8913	−	203.718i	0.0716403	−	0.243681i
$837$			258.019i			0.308267i
$838$	−214.351	+	160.405i	−0.255789	+	0.191414i
$839$	−355.908			−0.424205			−0.212102	−	0.977247i	$-0.568031\pi$
$839$	−355.908			−0.424205			−0.212102	+	0.977247i	$0.568031\pi$
$840$	−776.270	−	660.209i	−0.924131	−	0.785963i
$841$			167.230i			0.198847i
$842$	686.509	−	513.734i	0.815331	−	0.610135i
$843$	−791.912			−0.939398
$844$	625.861	+	1147.10i	0.741541	+	1.35912i
$845$	2.20547	+	3.94727i	0.00261003	+	0.00467133i
$846$	171.706	−	128.493i	0.202963	−	0.151883i
$847$	−140.713	+	140.713i	−0.166131	+	0.166131i
$848$	277.730	+	178.750i	0.327511	+	0.210790i
$849$			21.6962i			0.0255550i
$850$	−146.099	−	1606.68i	−0.171881	−	1.89022i
$851$	123.653	+	123.653i	0.145304	+	0.145304i
$852$	334.502	+	98.3408i	0.392608	+	0.115423i
$853$	184.144			0.215878			0.107939	−	0.994158i	$-0.465575\pi$
$853$	184.144			0.215878			0.107939	+	0.994158i	$0.465575\pi$
$854$	−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	$-0.386409\pi$
$857$	−503.631	−	503.631i	−0.587667	−	0.587667i	−0.936999	+	0.349332i	$0.886409\pi$
$858$	617.113	−	461.803i	0.719246	−	0.538232i
$859$	−136.193	−	136.193i	−0.158548	−	0.158548i	0.623375	−	0.781923i	$-0.285761\pi$
$859$	−136.193	−	136.193i	−0.158548	−	0.158548i	−0.781923	+	0.623375i	$0.785761\pi$
$860$	256.482	+	1127.93i	0.298234	+	1.31155i
$861$	−16.8899	−	16.8899i	−0.0196166	−	0.0196166i
$862$	1000.67	+	144.046i	1.16087	+	0.167107i
$863$	−778.037	−	778.037i	−0.901550	−	0.901550i	0.0940206	−	0.995570i	$-0.470028\pi$
$863$	−778.037	−	778.037i	−0.901550	−	0.901550i	−0.995570	+	0.0940206i	$0.970028\pi$
$864$	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
$867$	−1885.54			−2.17478
$868$	171.039	+	313.485i	0.197050	+	0.361158i
$869$	−144.450	−	144.450i	−0.166225	−	0.166225i
$870$	264.658	−	594.492i	0.304205	−	0.683324i
$871$			380.422i			0.436765i
$872$	336.697	−	125.388i	0.386120	−	0.143794i
$873$	−145.084	+	145.084i	−0.166190	+	0.166190i
$874$	6.88519	−	47.8304i	0.00787779	−	0.0547259i
$875$	859.498	+	935.328i	0.982283	+	1.06895i
$876$	−518.106	−	949.600i	−0.591446	−	1.08402i
$877$	−450.954			−0.514201			−0.257101	−	0.966385i	$-0.582767\pi$
$877$	−450.954			−0.514201			−0.257101	+	0.966385i	$0.582767\pi$
$878$	386.610	+	55.6525i	0.440331	+	0.0633856i
$879$			1337.18i			1.52126i
$880$	−627.625	−	711.206i	−0.713210	−	0.808188i
$881$	929.171			1.05468			0.527339	−	0.849655i	$-0.323190\pi$
$881$	929.171			1.05468			0.527339	+	0.849655i	$0.323190\pi$
$882$	−41.9863	+	291.673i	−0.0476035	+	0.330695i
$883$		−	244.738i		−	0.277166i	−0.990351	−	0.138583i	$-0.955745\pi$
$883$		−	244.738i		−	0.277166i	0.990351	−	0.138583i	$-0.0442548\pi$
$884$	801.458	+	1468.93i	0.906626	+	1.66169i
$885$	684.814	+	193.866i	0.773801	+	0.219057i
$886$	795.166	+	114.464i	0.897478	+	0.129192i
$887$	987.070	+	987.070i	1.11282	+	1.11282i	0.992768	+	0.120050i	$0.0383056\pi$
$887$	987.070	+	987.070i	1.11282	+	1.11282i	0.120050	+	0.992768i	$0.461694\pi$
$888$	−591.025	−	270.272i	−0.665569	−	0.304361i
$889$	1527.02			1.71768
$890$	−347.369	−	904.828i	−0.390303	−	1.01666i
$891$	412.440	−	412.440i	0.462896	−	0.462896i
$892$	−164.384	−	301.288i	−0.184287	−	0.337766i
$893$			176.829i			0.198017i
$894$	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
$898$	−53.9857	+	375.031i	−0.0601177	+	0.417629i
$899$	−161.249	+	161.249i	−0.179365	+	0.179365i
$900$	−201.750	+	181.684i	−0.224167	+	0.201871i
$901$	−470.974	+	470.974i	−0.522723	+	0.522723i
$902$	−13.3208	−	17.8008i	−0.0147681	−	0.0197348i
$903$	−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
$907$		−	160.752i		−	0.177235i	−0.996066	−	0.0886177i	$-0.971755\pi$
$907$		−	160.752i		−	0.177235i	0.996066	−	0.0886177i	$-0.0282449\pi$
$908$	−777.224	−	228.497i	−0.855974	−	0.251649i
$909$	184.471	−	184.471i	0.202938	−	0.202938i
$910$	−1203.65	−	535.846i	−1.32269	−	0.588841i
$911$	36.8062			0.0404020			0.0202010	−	0.999796i	$-0.493569\pi$
$911$	36.8062			0.0404020			0.0202010	+	0.999796i	$0.493569\pi$
$912$	38.0561	+	175.509i	0.0417282	+	0.192444i
$913$	615.316	+	615.316i	0.673950	+	0.673950i
$914$	−828.344	−	1106.93i	−0.906284	−	1.21108i
$915$	−433.059	−	122.596i	−0.473289	−	0.133985i
$916$	372.162	+	682.109i	0.406290	+	0.744660i
$917$			859.116i			0.936877i
$918$	1135.54	+	1517.44i	1.23698	+	1.65299i
$919$	−502.632			−0.546934			−0.273467	−	0.961881i	$-0.588170\pi$
$919$	−502.632			−0.546934			−0.273467	+	0.961881i	$0.588170\pi$
$920$	−164.437	−	139.852i	−0.178736	−	0.152013i
$921$		−	807.386i		−	0.876640i
$922$	664.787	+	888.363i	0.721027	+	0.963517i
$923$	450.781			0.488386
$924$	340.798	−	1159.21i	0.368829	−	1.25455i
$925$	689.887	+	424.634i	0.745824	+	0.459064i
$926$	−119.820	−	160.116i	−0.129395	−	0.172912i
$927$	−360.789	+	360.789i	−0.389200	+	0.389200i
$928$	828.560	−	58.5597i	0.892845	−	0.0631032i
$929$			1098.03i			1.18195i	0.806690	+	0.590975i	$0.201257\pi$
$929$			1098.03i			1.18195i	−0.806690	+	0.590975i	$0.798743\pi$
$930$	−205.615	+	78.9371i	−0.221092	+	0.0848785i
$931$	−171.806	−	171.806i	−0.184540	−	0.184540i
$932$	979.615	−	534.483i	1.05109	−	0.573479i
$933$	25.1951			0.0270044
$934$	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	$-0.233542\pi$
$937$	68.4855	+	68.4855i	0.0730902	+	0.0730902i	−0.669617	+	0.742707i	$0.733542\pi$
$938$	357.300	+	477.464i	0.380917	+	0.509024i
$939$	33.6817	+	33.6817i	0.0358698	+	0.0358698i
$940$	668.497	+	420.801i	0.711167	+	0.447661i
$941$	−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	$0.877119\pi$
$942$	−1.89205	+	13.1438i	−0.00200855	+	0.0139531i
$943$	−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
$947$	1065.70			1.12534			0.562672	−	0.826680i	$-0.309773\pi$
$947$	1065.70			1.12534			0.562672	+	0.826680i	$0.309773\pi$
$948$	165.759	+	48.7318i	0.174851	+	0.0514049i
$949$	−988.954	−	988.954i	−1.04210	−	1.04210i
$950$	−20.2722	−	222.939i	−0.0213392	−	0.234673i
$951$			457.261i			0.480821i
$952$	2385.55	+	1090.90i	2.50583	+	1.14590i
$953$	620.695	−	620.695i	0.651306	−	0.651306i	−0.302001	−	0.953307i	$-0.597655\pi$
$953$	620.695	−	620.695i	0.651306	−	0.651306i	0.953307	+	0.302001i	$0.0976547\pi$
$954$	110.945	+	15.9706i	0.116295	+	0.0167406i
$955$	110.490	+	197.751i	0.115696	+	0.207069i
$956$	464.740	−	1580.79i	0.486130	−	1.65355i
$957$	771.567			0.806236
$958$	−14.1307	+	98.1641i	−0.0147502	+	0.102468i
$959$		−	1817.13i		−	1.89482i
$960$	754.071	+	273.791i	0.785491	+	0.285199i
$961$	−883.818			−0.919686
$962$	−831.672	−	119.719i	−0.864524	−	0.124448i
$963$			121.937i			0.126622i
$964$	−1128.01	−	331.625i	−1.17013	−	0.344009i
$965$	339.207	−	1198.22i	0.351510	−	1.24168i
$966$	39.1786	−	272.168i	0.0405575	−	0.281747i
$967$	−1139.87	−	1139.87i	−1.17877	−	1.17877i	−0.980059	−	0.198709i	$-0.936325\pi$
$967$	−1139.87	−	1139.87i	−1.17877	−	1.17877i	−0.198709	−	0.980059i	$-0.563675\pi$
$968$	65.1502	−	142.469i	0.0673039	−	0.147179i
$969$	−362.164			−0.373751
$970$	−690.400	−	307.355i	−0.711753	−	0.316861i
$971$	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	$0.138648\pi$
$972$	159.075	−	541.086i	0.163657	−	0.556672i
$973$			594.771i			0.611275i
$974$	−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	−0.708561	−	0.705649i	$-0.750655\pi$
$977$	−2.84469	+	2.84469i	−0.00291165	+	0.00291165i	0.705649	+	0.708561i	$0.250655\pi$
$978$	713.229	+	102.669i	0.729273	+	0.104979i
$979$	812.589	−	812.589i	0.830019	−	0.830019i
$980$	−1058.36	+	240.661i	−1.07996	+	0.245572i
$981$	86.2195	−	86.2195i	0.0878894	−	0.0878894i
$982$	−1225.61	+	917.157i	−1.24807	+	0.933968i
$983$	−177.652	+	177.652i	−0.180724	+	0.180724i	−0.791671	−	0.610947i	$-0.790789\pi$
$983$	−177.652	+	177.652i	−0.180724	+	0.180724i	0.610947	+	0.791671i	$0.290789\pi$
$984$	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
$987$			1006.20i			1.01946i
$988$	111.208	+	203.825i	0.112559	+	0.206301i
$989$	−220.704	+	220.704i	−0.223158	+	0.223158i
$990$	−294.085	−	130.922i	−0.297055	−	0.132244i
$991$	1697.53			1.71295			0.856474	−	0.516190i	$-0.172650\pi$
$991$	1697.53			1.71295			0.856474	+	0.516190i	$0.172650\pi$
$992$	−212.309	−	184.279i	−0.214021	−	0.185766i
$993$	535.405	+	535.405i	0.539179	+	0.539179i
$994$	565.770	−	423.382i	0.569185	−	0.425937i
$995$	465.598	+	833.309i	0.467938	+	0.837497i
$996$	−706.089	−	207.584i	−0.708925	−	0.208418i
$997$			1315.01i			1.31897i	0.751720	+	0.659483i	$0.229225\pi$
$997$			1315.01i			1.31897i	−0.751720	+	0.659483i	$0.770775\pi$
$998$	322.661	−	241.457i	0.323308	−	0.241941i
$999$	−951.683			−0.952636

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.22	✓	44	1.1	even	1	trivial
80.3.i.a.37.22	yes	44	80.37	odd	4	inner
80.3.t.a.53.11	yes	44	16.5	even	4
80.3.t.a.77.11	yes	44	5.2	odd	4
320.3.i.a.177.6		44	80.27	even	4
320.3.i.a.273.17		44	4.3	odd	2
320.3.t.a.17.17		44	20.7	even	4
320.3.t.a.113.17		44	16.11	odd	4
400.3.i.b.93.1		44	5.4	even	2
400.3.i.b.357.1		44	80.53	odd	4
400.3.t.b.157.12		44	5.3	odd	4
400.3.t.b.293.12		44	80.69	even	4
640.3.i.a.33.6		44	8.3	odd	2
640.3.i.a.97.17		44	80.67	even	4
640.3.i.b.33.17		44	8.5	even	2
640.3.i.b.97.6		44	80.77	odd	4
640.3.t.a.353.6		44	16.3	odd	4
640.3.t.a.417.6		44	40.27	even	4
640.3.t.b.353.17		44	16.13	even	4
640.3.t.b.417.17		44	40.37	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.97960 + 0.284962i) q^{2} -2.50699i q^{3} +(3.83759 + 1.12822i) q^{4} +(2.43881 + 4.36488i) q^{5} +(0.714398 - 4.96283i) q^{6} +(-7.18571 - 7.18571i) q^{7} +(7.27538 + 3.32699i) q^{8} +2.71500 q^{9} +O(q^{10})\)	\(q+(1.97960 + 0.284962i) q^{2} -2.50699i q^{3} +(3.83759 + 1.12822i) q^{4} +(2.43881 + 4.36488i) q^{5} +(0.714398 - 4.96283i) q^{6} +(-7.18571 - 7.18571i) q^{7} +(7.27538 + 3.32699i) q^{8} +2.71500 q^{9} +(3.58403 + 9.33567i) q^{10} +(-8.38398 + 8.38398i) q^{11} +(2.82844 - 9.62081i) q^{12} -12.9652i 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} +(5.37460 + 0.773673i) q^{18} +(-3.16584 + 3.16584i) q^{19} +(4.43461 + 19.5022i) q^{20} +(-18.0145 + 18.0145i) q^{21} +(-18.9860 + 14.2078i) 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} -29.3694i q^{27} +(-19.4688 - 35.6829i) q^{28} +(18.3544 - 18.3544i) q^{29} +(23.4044 - 8.98512i) q^{30} -8.78531 q^{31} +(24.1664 + 20.9759i) q^{32} +(21.0186 + 21.0186i) q^{33} +(-51.6674 + 38.6642i) q^{34} +(13.8402 - 48.8893i) q^{35} +(10.4191 + 3.06312i) q^{36} -32.4039i q^{37} +(-7.16923 + 5.36494i) q^{38} -32.5036 q^{39} +(3.22134 + 39.8701i) q^{40} +0.937574i q^{41} +(-40.7949 + 30.5280i) q^{42} +57.8364 q^{43} +(-41.6333 + 22.7153i) q^{44} +(6.62136 + 11.8506i) q^{45} +(-8.64156 + 6.46672i) q^{46} +(27.9276 - 27.9276i) q^{47} +(21.7088 - 33.7296i) q^{48} +54.2688i q^{49} +(-32.0084 + 38.4118i) q^{50} +(57.1987 + 57.1987i) q^{51} +(14.6276 - 49.7550i) q^{52} +20.6425 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} +(41.5647 - 31.1040i) q^{58} +(40.1490 + 40.1490i) q^{59} +(48.8917 - 11.1175i) q^{60} +(-25.3893 - 25.3893i) q^{61} +(-17.3913 - 2.50348i) 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} -29.3419 q^{67} +(-113.298 + 61.8162i) q^{68} +(9.56668 + 9.56668i) q^{69} +(41.3296 - 92.8372i) q^{70} +34.7686i q^{71} +(19.7526 + 9.03277i) q^{72} +(76.2777 - 76.2777i) q^{73} +(9.23390 - 64.1466i) q^{74} +(53.3744 + 32.8527i) q^{75} +(-15.7210 + 8.57745i) q^{76} +120.490 q^{77} +(-64.3439 - 9.26230i) q^{78} +17.2292i q^{79} +(-4.98453 + 79.8446i) q^{80} -49.1938 q^{81} +(-0.267173 + 1.85602i) q^{82} -73.3919i q^{83} +(-89.4566 + 48.8080i) q^{84} +(-155.231 - 43.9447i) q^{85} +(114.493 + 16.4812i) q^{86} +(-46.0144 - 46.0144i) q^{87} +(-88.8901 + 33.1032i) q^{88} -96.9216 q^{89} +(9.73062 + 25.3463i) q^{90} +(-93.1639 + 93.1639i) q^{91} +(-18.9496 + 10.3390i) q^{92} +22.0247i 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} +(-15.4646 + 107.430i) q^{98} +(-22.7625 + 22.7625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9	\( 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9} + 6 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{15} + 24 q^{16} - 4 q^{17} + 22 q^{18} + 32 q^{19} + 40 q^{20} - 4 q^{21} + 92 q^{22} + 36 q^{24} - 52 q^{26} + 36 q^{28} - 28 q^{30} - 8 q^{31} - 132 q^{32} - 4 q^{33} - 88 q^{34} + 96 q^{35} - 116 q^{36} - 216 q^{38} + 72 q^{39} + 16 q^{40} + 16 q^{42} + 124 q^{43} - 168 q^{44} - 34 q^{45} + 108 q^{46} - 4 q^{47} + 340 q^{48} + 10 q^{50} - 100 q^{51} + 48 q^{52} - 4 q^{53} + 228 q^{54} - 172 q^{56} + 36 q^{57} + 16 q^{58} + 64 q^{59} + 136 q^{60} - 36 q^{61} - 356 q^{62} - 200 q^{63} - 176 q^{64} - 4 q^{65} + 276 q^{66} - 292 q^{67} - 72 q^{68} - 60 q^{69} - 92 q^{70} + 448 q^{72} + 48 q^{73} + 284 q^{74} + 96 q^{75} + 252 q^{76} + 192 q^{77} + 620 q^{78} + 4 q^{80} + 100 q^{81} - 240 q^{82} + 288 q^{84} + 48 q^{85} + 20 q^{86} + 36 q^{87} - 624 q^{88} - 578 q^{90} + 188 q^{91} - 412 q^{92} - 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 78 q^{98} - 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9 + 6 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^15 + 24 * q^16 - 4 * q^17 + 22 * q^18 + 32 * q^19 + 40 * q^20 - 4 * q^21 + 92 * q^22 + 36 * q^24 - 52 * q^26 + 36 * q^28 - 28 * q^30 - 8 * q^31 - 132 * q^32 - 4 * q^33 - 88 * q^34 + 96 * q^35 - 116 * q^36 - 216 * q^38 + 72 * q^39 + 16 * q^40 + 16 * q^42 + 124 * q^43 - 168 * q^44 - 34 * q^45 + 108 * q^46 - 4 * q^47 + 340 * q^48 + 10 * q^50 - 100 * q^51 + 48 * q^52 - 4 * q^53 + 228 * q^54 - 172 * q^56 + 36 * q^57 + 16 * q^58 + 64 * q^59 + 136 * q^60 - 36 * q^61 - 356 * q^62 - 200 * q^63 - 176 * q^64 - 4 * q^65 + 276 * q^66 - 292 * q^67 - 72 * q^68 - 60 * q^69 - 92 * q^70 + 448 * q^72 + 48 * q^73 + 284 * q^74 + 96 * q^75 + 252 * q^76 + 192 * q^77 + 620 * q^78 + 4 * q^80 + 100 * q^81 - 240 * q^82 + 288 * q^84 + 48 * q^85 + 20 * q^86 + 36 * q^87 - 624 * q^88 - 578 * q^90 + 188 * q^91 - 412 * q^92 - 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 78 * q^98 - 92 * q^99

Introduction

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