LMFDB - Embedded newform 570.4.i.f.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,4,Mod(121,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("570.121");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	570.i (of order $3$, 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:	$33.6310887033$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	570.121
Dual form			570.4.i.f.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-3.00000 + 5.19615i) q^{6} -19.0000 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-3.00000 + 5.19615i) q^{6} -19.0000 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-5.00000 + 8.66025i) q^{10} +15.0000 q^{11} -12.0000 q^{12} +(-25.0000 + 43.3013i) q^{13} +(-19.0000 - 32.9090i) q^{14} +(-7.50000 + 12.9904i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(21.0000 + 36.3731i) q^{17} -18.0000 q^{18} +(-66.5000 - 49.3634i) q^{19} -20.0000 q^{20} +(-28.5000 - 49.3634i) q^{21} +(15.0000 + 25.9808i) q^{22} +(22.5000 - 38.9711i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} -100.000 q^{26} -27.0000 q^{27} +(38.0000 - 65.8179i) q^{28} +(54.0000 - 93.5307i) q^{29} -30.0000 q^{30} -196.000 q^{31} +(16.0000 - 27.7128i) q^{32} +(22.5000 + 38.9711i) q^{33} +(-42.0000 + 72.7461i) q^{34} +(-47.5000 - 82.2724i) q^{35} +(-18.0000 - 31.1769i) q^{36} -43.0000 q^{37} +(19.0000 - 164.545i) q^{38} -150.000 q^{39} +(-20.0000 - 34.6410i) q^{40} +(-106.500 - 184.463i) q^{41} +(57.0000 - 98.7269i) q^{42} +(-169.000 - 292.717i) q^{43} +(-30.0000 + 51.9615i) q^{44} -45.0000 q^{45} +90.0000 q^{46} +(-120.000 + 207.846i) q^{47} +(24.0000 - 41.5692i) q^{48} +18.0000 q^{49} -50.0000 q^{50} +(-63.0000 + 109.119i) q^{51} +(-100.000 - 173.205i) q^{52} +(226.500 - 392.310i) q^{53} +(-27.0000 - 46.7654i) q^{54} +(37.5000 + 64.9519i) q^{55} +152.000 q^{56} +(28.5000 - 246.817i) q^{57} +216.000 q^{58} +(90.0000 + 155.885i) q^{59} +(-30.0000 - 51.9615i) q^{60} +(-49.0000 + 84.8705i) q^{61} +(-196.000 - 339.482i) q^{62} +(85.5000 - 148.090i) q^{63} +64.0000 q^{64} -250.000 q^{65} +(-45.0000 + 77.9423i) q^{66} +(-55.0000 + 95.2628i) q^{67} -168.000 q^{68} +135.000 q^{69} +(95.0000 - 164.545i) q^{70} +(-102.000 - 176.669i) q^{71} +(36.0000 - 62.3538i) q^{72} +(380.000 + 658.179i) q^{73} +(-43.0000 - 74.4782i) q^{74} -75.0000 q^{75} +(304.000 - 131.636i) q^{76} -285.000 q^{77} +(-150.000 - 259.808i) q^{78} +(107.000 + 185.329i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(213.000 - 368.927i) q^{82} -198.000 q^{83} +228.000 q^{84} +(-105.000 + 181.865i) q^{85} +(338.000 - 585.433i) q^{86} +324.000 q^{87} -120.000 q^{88} +(-307.500 + 532.606i) q^{89} +(-45.0000 - 77.9423i) q^{90} +(475.000 - 822.724i) q^{91} +(90.0000 + 155.885i) q^{92} +(-294.000 - 509.223i) q^{93} -480.000 q^{94} +(47.5000 - 411.362i) q^{95} +96.0000 q^{96} +(26.0000 + 45.0333i) q^{97} +(18.0000 + 31.1769i) q^{98} +(-67.5000 + 116.913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 5 q^{5} - 6 q^{6} - 38 q^{7} - 16 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 + 5 * q^5 - 6 * q^6 - 38 * q^7 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 5 q^{5} - 6 q^{6} - 38 q^{7} - 16 q^{8} - 9 q^{9} - 10 q^{10} + 30 q^{11} - 24 q^{12} - 50 q^{13} - 38 q^{14} - 15 q^{15} - 16 q^{16} + 42 q^{17} - 36 q^{18} - 133 q^{19} - 40 q^{20} - 57 q^{21} + 30 q^{22} + 45 q^{23} - 24 q^{24} - 25 q^{25} - 200 q^{26} - 54 q^{27} + 76 q^{28} + 108 q^{29} - 60 q^{30} - 392 q^{31} + 32 q^{32} + 45 q^{33} - 84 q^{34} - 95 q^{35} - 36 q^{36} - 86 q^{37} + 38 q^{38} - 300 q^{39} - 40 q^{40} - 213 q^{41} + 114 q^{42} - 338 q^{43} - 60 q^{44} - 90 q^{45} + 180 q^{46} - 240 q^{47} + 48 q^{48} + 36 q^{49} - 100 q^{50} - 126 q^{51} - 200 q^{52} + 453 q^{53} - 54 q^{54} + 75 q^{55} + 304 q^{56} + 57 q^{57} + 432 q^{58} + 180 q^{59} - 60 q^{60} - 98 q^{61} - 392 q^{62} + 171 q^{63} + 128 q^{64} - 500 q^{65} - 90 q^{66} - 110 q^{67} - 336 q^{68} + 270 q^{69} + 190 q^{70} - 204 q^{71} + 72 q^{72} + 760 q^{73} - 86 q^{74} - 150 q^{75} + 608 q^{76} - 570 q^{77} - 300 q^{78} + 214 q^{79} + 80 q^{80} - 81 q^{81} + 426 q^{82} - 396 q^{83} + 456 q^{84} - 210 q^{85} + 676 q^{86} + 648 q^{87} - 240 q^{88} - 615 q^{89} - 90 q^{90} + 950 q^{91} + 180 q^{92} - 588 q^{93} - 960 q^{94} + 95 q^{95} + 192 q^{96} + 52 q^{97} + 36 q^{98} - 135 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 + 5 * q^5 - 6 * q^6 - 38 * q^7 - 16 * q^8 - 9 * q^9 - 10 * q^10 + 30 * q^11 - 24 * q^12 - 50 * q^13 - 38 * q^14 - 15 * q^15 - 16 * q^16 + 42 * q^17 - 36 * q^18 - 133 * q^19 - 40 * q^20 - 57 * q^21 + 30 * q^22 + 45 * q^23 - 24 * q^24 - 25 * q^25 - 200 * q^26 - 54 * q^27 + 76 * q^28 + 108 * q^29 - 60 * q^30 - 392 * q^31 + 32 * q^32 + 45 * q^33 - 84 * q^34 - 95 * q^35 - 36 * q^36 - 86 * q^37 + 38 * q^38 - 300 * q^39 - 40 * q^40 - 213 * q^41 + 114 * q^42 - 338 * q^43 - 60 * q^44 - 90 * q^45 + 180 * q^46 - 240 * q^47 + 48 * q^48 + 36 * q^49 - 100 * q^50 - 126 * q^51 - 200 * q^52 + 453 * q^53 - 54 * q^54 + 75 * q^55 + 304 * q^56 + 57 * q^57 + 432 * q^58 + 180 * q^59 - 60 * q^60 - 98 * q^61 - 392 * q^62 + 171 * q^63 + 128 * q^64 - 500 * q^65 - 90 * q^66 - 110 * q^67 - 336 * q^68 + 270 * q^69 + 190 * q^70 - 204 * q^71 + 72 * q^72 + 760 * q^73 - 86 * q^74 - 150 * q^75 + 608 * q^76 - 570 * q^77 - 300 * q^78 + 214 * q^79 + 80 * q^80 - 81 * q^81 + 426 * q^82 - 396 * q^83 + 456 * q^84 - 210 * q^85 + 676 * q^86 + 648 * q^87 - 240 * q^88 - 615 * q^89 - 90 * q^90 + 950 * q^91 + 180 * q^92 - 588 * q^93 - 960 * q^94 + 95 * q^95 + 192 * q^96 + 52 * q^97 + 36 * q^98 - 135 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	−3.00000	+	5.19615i	−0.204124	+	0.353553i
$7$	−19.0000			−1.02590			−0.512952	−	0.858417i	$-0.671448\pi$
$7$	−19.0000			−1.02590			−0.512952	+	0.858417i	$0.671448\pi$
$8$	−8.00000			−0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−5.00000	+	8.66025i	−0.158114	+	0.273861i
$11$	15.0000			0.411152			0.205576	−	0.978641i	$-0.434093\pi$
$11$	15.0000			0.411152			0.205576	+	0.978641i	$0.434093\pi$
$12$	−12.0000			−0.288675
$13$	−25.0000	+	43.3013i	−0.533366	+	0.923816i	0.465875	+	0.884851i	$0.345740\pi$
$13$	−25.0000	+	43.3013i	−0.533366	+	0.923816i	−0.999241	+	0.0389657i	$0.987594\pi$
$14$	−19.0000	−	32.9090i	−0.362712	−	0.628235i
$15$	−7.50000	+	12.9904i	−0.129099	+	0.223607i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	21.0000	+	36.3731i	0.299603	+	0.518927i	0.976045	−	0.217568i	$-0.0698125\pi$
$17$	21.0000	+	36.3731i	0.299603	+	0.518927i	−0.676442	+	0.736496i	$0.736479\pi$
$18$	−18.0000			−0.235702
$19$	−66.5000	−	49.3634i	−0.802955	−	0.596040i
$19$	−66.5000	−	49.3634i	−0.802955	−	0.596040i
$20$	−20.0000			−0.223607
$21$	−28.5000	−	49.3634i	−0.296153	−	0.512952i
$22$	15.0000	+	25.9808i	0.145364	+	0.251778i
$23$	22.5000	−	38.9711i	0.203981	−	0.353306i	−0.745826	−	0.666141i	$-0.767945\pi$
$23$	22.5000	−	38.9711i	0.203981	−	0.353306i	0.949808	+	0.312834i	$0.101278\pi$
$24$	−12.0000	−	20.7846i	−0.102062	−	0.176777i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−100.000			−0.754293
$27$	−27.0000			−0.192450
$28$	38.0000	−	65.8179i	0.256476	−	0.444229i
$29$	54.0000	−	93.5307i	0.345778	−	0.598904i	−0.639717	−	0.768610i	$-0.720949\pi$
$29$	54.0000	−	93.5307i	0.345778	−	0.598904i	0.985495	+	0.169706i	$0.0542819\pi$
$30$	−30.0000			−0.182574
$31$	−196.000			−1.13557			−0.567785	−	0.823177i	$-0.692199\pi$
$31$	−196.000			−1.13557			−0.567785	+	0.823177i	$0.692199\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	22.5000	+	38.9711i	0.118689	+	0.205576i
$34$	−42.0000	+	72.7461i	−0.211851	+	0.366937i
$35$	−47.5000	−	82.2724i	−0.229399	−	0.397331i
$36$	−18.0000	−	31.1769i	−0.0833333	−	0.144338i
$37$	−43.0000			−0.191058			−0.0955291	−	0.995427i	$-0.530454\pi$
$37$	−43.0000			−0.191058			−0.0955291	+	0.995427i	$0.530454\pi$
$38$	19.0000	−	164.545i	0.0811107	−	0.702439i
$39$	−150.000			−0.615878
$40$	−20.0000	−	34.6410i	−0.0790569	−	0.136931i
$41$	−106.500	−	184.463i	−0.405671	−	0.702643i	0.588728	−	0.808331i	$-0.299629\pi$
$41$	−106.500	−	184.463i	−0.405671	−	0.702643i	−0.994399	+	0.105688i	$0.966295\pi$
$42$	57.0000	−	98.7269i	0.209412	−	0.362712i
$43$	−169.000	−	292.717i	−0.599355	−	1.03811i	−0.992916	−	0.118815i	$-0.962091\pi$
$43$	−169.000	−	292.717i	−0.599355	−	1.03811i	0.393562	−	0.919298i	$-0.371243\pi$
$44$	−30.0000	+	51.9615i	−0.102788	+	0.178034i
$45$	−45.0000			−0.149071
$46$	90.0000			0.288473
$47$	−120.000	+	207.846i	−0.372421	+	0.645053i	−0.989937	−	0.141506i	$-0.954806\pi$
$47$	−120.000	+	207.846i	−0.372421	+	0.645053i	0.617516	+	0.786558i	$0.288139\pi$
$48$	24.0000	−	41.5692i	0.0721688	−	0.125000i
$49$	18.0000			0.0524781
$50$	−50.0000			−0.141421
$51$	−63.0000	+	109.119i	−0.172976	+	0.299603i
$52$	−100.000	−	173.205i	−0.266683	−	0.461908i
$53$	226.500	−	392.310i	0.587022	−	1.01675i	−0.407598	−	0.913161i	$-0.633634\pi$
$53$	226.500	−	392.310i	0.587022	−	1.01675i	0.994620	−	0.103591i	$-0.0330331\pi$
$54$	−27.0000	−	46.7654i	−0.0680414	−	0.117851i
$55$	37.5000	+	64.9519i	0.0919363	+	0.159238i
$56$	152.000			0.362712
$57$	28.5000	−	246.817i	0.0662266	−	0.573539i
$58$	216.000			0.489003
$59$	90.0000	+	155.885i	0.198593	+	0.343974i	0.948073	−	0.318054i	$-0.103029\pi$
$59$	90.0000	+	155.885i	0.198593	+	0.343974i	−0.749479	+	0.662028i	$0.769696\pi$
$60$	−30.0000	−	51.9615i	−0.0645497	−	0.111803i
$61$	−49.0000	+	84.8705i	−0.102849	+	0.178140i	−0.912857	−	0.408278i	$-0.866129\pi$
$61$	−49.0000	+	84.8705i	−0.102849	+	0.178140i	0.810008	+	0.586419i	$0.199463\pi$
$62$	−196.000	−	339.482i	−0.401484	−	0.695391i
$63$	85.5000	−	148.090i	0.170984	−	0.296153i
$64$	64.0000			0.125000
$65$	−250.000			−0.477057
$66$	−45.0000	+	77.9423i	−0.0839260	+	0.145364i
$67$	−55.0000	+	95.2628i	−0.100288	+	0.173705i	−0.911803	−	0.410627i	$-0.865310\pi$
$67$	−55.0000	+	95.2628i	−0.100288	+	0.173705i	0.811515	+	0.584331i	$0.198643\pi$
$68$	−168.000			−0.299603
$69$	135.000			0.235538
$70$	95.0000	−	164.545i	0.162210	−	0.280955i
$71$	−102.000	−	176.669i	−0.170495	−	0.295307i	0.768098	−	0.640333i	$-0.221203\pi$
$71$	−102.000	−	176.669i	−0.170495	−	0.295307i	−0.938593	+	0.345026i	$0.887870\pi$
$72$	36.0000	−	62.3538i	0.0589256	−	0.102062i
$73$	380.000	+	658.179i	0.609255	+	1.05526i	0.991363	+	0.131143i	$0.0418649\pi$
$73$	380.000	+	658.179i	0.609255	+	1.05526i	−0.382108	+	0.924118i	$0.624802\pi$
$74$	−43.0000	−	74.4782i	−0.0675493	−	0.116999i
$75$	−75.0000			−0.115470
$76$	304.000	−	131.636i	0.458831	−	0.198680i
$77$	−285.000			−0.421802
$78$	−150.000	−	259.808i	−0.217746	−	0.377146i
$79$	107.000	+	185.329i	0.152385	+	0.263939i	0.932104	−	0.362191i	$-0.117971\pi$
$79$	107.000	+	185.329i	0.152385	+	0.263939i	−0.779719	+	0.626130i	$0.784638\pi$
$80$	40.0000	−	69.2820i	0.0559017	−	0.0968246i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	213.000	−	368.927i	0.286853	−	0.496843i
$83$	−198.000			−0.261847			−0.130924	−	0.991392i	$-0.541794\pi$
$83$	−198.000			−0.261847			−0.130924	+	0.991392i	$0.541794\pi$
$84$	228.000			0.296153
$85$	−105.000	+	181.865i	−0.133986	+	0.232071i
$86$	338.000	−	585.433i	0.423808	−	0.734057i
$87$	324.000			0.399269
$88$	−120.000			−0.145364
$89$	−307.500	+	532.606i	−0.366235	+	0.634338i	−0.988974	−	0.148092i	$-0.952687\pi$
$89$	−307.500	+	532.606i	−0.366235	+	0.634338i	0.622738	+	0.782430i	$0.286020\pi$
$90$	−45.0000	−	77.9423i	−0.0527046	−	0.0912871i
$91$	475.000	−	822.724i	0.547182	−	0.947746i
$92$	90.0000	+	155.885i	0.101991	+	0.176653i
$93$	−294.000	−	509.223i	−0.327811	−	0.567785i
$94$	−480.000			−0.526683
$95$	47.5000	−	411.362i	0.0512989	−	0.444262i
$96$	96.0000			0.102062
$97$	26.0000	+	45.0333i	0.0272155	+	0.0471386i	0.879312	−	0.476246i	$-0.158003\pi$
$97$	26.0000	+	45.0333i	0.0272155	+	0.0471386i	−0.852097	+	0.523384i	$0.824669\pi$
$98$	18.0000	+	31.1769i	0.0185538	+	0.0321362i
$99$	−67.5000	+	116.913i	−0.0685253	+	0.118689i
$100$	−50.0000	−	86.6025i	−0.0500000	−	0.0866025i
$101$	−159.000	+	275.396i	−0.156644	+	0.271316i	−0.933657	−	0.358169i	$-0.883401\pi$
$101$	−159.000	+	275.396i	−0.156644	+	0.271316i	0.777012	+	0.629486i	$0.216734\pi$
$102$	−252.000			−0.244625
$103$	−1003.00			−0.959500			−0.479750	−	0.877405i	$-0.659273\pi$
$103$	−1003.00			−0.959500			−0.479750	+	0.877405i	$0.659273\pi$
$104$	200.000	−	346.410i	0.188573	−	0.326618i
$105$	142.500	−	246.817i	0.132444	−	0.229399i
$106$	906.000			0.830175
$107$	−1122.00			−1.01372			−0.506859	−	0.862029i	$-0.669194\pi$
$107$	−1122.00			−1.01372			−0.506859	+	0.862029i	$0.669194\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	−523.000	−	905.863i	−0.459581	−	0.796017i	0.539358	−	0.842077i	$-0.318667\pi$
$109$	−523.000	−	905.863i	−0.459581	−	0.796017i	−0.998939	+	0.0460593i	$0.985334\pi$
$110$	−75.0000	+	129.904i	−0.0650088	+	0.112599i
$111$	−64.5000	−	111.717i	−0.0551538	−	0.0955291i
$112$	152.000	+	263.272i	0.128238	+	0.222115i
$113$	1590.00			1.32367			0.661835	−	0.749650i	$-0.269778\pi$
$113$	1590.00			1.32367			0.661835	+	0.749650i	$0.269778\pi$
$114$	456.000	−	197.454i	0.374634	−	0.162221i
$115$	225.000			0.182447
$116$	216.000	+	374.123i	0.172889	+	0.299452i
$117$	−225.000	−	389.711i	−0.177789	−	0.307939i
$118$	−180.000	+	311.769i	−0.140427	+	0.243226i
$119$	−399.000	−	691.088i	−0.307364	−	0.532369i
$120$	60.0000	−	103.923i	0.0456435	−	0.0790569i
$121$	−1106.00			−0.830954
$122$	−196.000			−0.145451
$123$	319.500	−	553.390i	0.234214	−	0.405671i
$124$	392.000	−	678.964i	0.283892	−	0.491716i
$125$	−125.000			−0.0894427
$126$	342.000			0.241808
$127$	399.500	−	691.954i	0.279133	−	0.483473i	−0.692037	−	0.721863i	$-0.743286\pi$
$127$	399.500	−	691.954i	0.279133	−	0.483473i	0.971170	+	0.238390i	$0.0766196\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	507.000	−	878.150i	0.346038	−	0.599355i
$130$	−250.000	−	433.013i	−0.168665	−	0.292136i
$131$	−109.500	−	189.660i	−0.0730310	−	0.126493i	0.827197	−	0.561912i	$-0.189934\pi$
$131$	−109.500	−	189.660i	−0.0730310	−	0.126493i	−0.900228	+	0.435418i	$0.856601\pi$
$132$	−180.000			−0.118689
$133$	1263.50	+	937.906i	0.823754	+	0.611479i
$134$	−220.000			−0.141829
$135$	−67.5000	−	116.913i	−0.0430331	−	0.0745356i
$136$	−168.000	−	290.985i	−0.105926	−	0.183469i
$137$	−1254.00	+	2171.99i	−0.782018	+	1.35449i	0.148747	+	0.988875i	$0.452476\pi$
$137$	−1254.00	+	2171.99i	−0.782018	+	1.35449i	−0.930764	+	0.365619i	$0.880857\pi$
$138$	135.000	+	233.827i	0.0832751	+	0.144237i
$139$	182.000	−	315.233i	0.111058	−	0.192358i	−0.805139	−	0.593086i	$-0.797909\pi$
$139$	182.000	−	315.233i	0.111058	−	0.192358i	0.916197	+	0.400728i	$0.131243\pi$
$140$	380.000			0.229399
$141$	−720.000			−0.430035
$142$	204.000	−	353.338i	0.120558	−	0.208813i
$143$	−375.000	+	649.519i	−0.219294	+	0.379829i
$144$	144.000			0.0833333
$145$	540.000			0.309273
$146$	−760.000	+	1316.36i	−0.430809	+	0.746182i
$147$	27.0000	+	46.7654i	0.0151491	+	0.0262391i
$148$	86.0000	−	148.956i	0.0477646	−	0.0827307i
$149$	−651.000	−	1127.57i	−0.357933	−	0.619958i	0.629682	−	0.776853i	$-0.283185\pi$
$149$	−651.000	−	1127.57i	−0.357933	−	0.619958i	−0.987615	+	0.156895i	$0.949852\pi$
$150$	−75.0000	−	129.904i	−0.0408248	−	0.0707107i
$151$	−682.000			−0.367552			−0.183776	−	0.982968i	$-0.558832\pi$
$151$	−682.000			−0.367552			−0.183776	+	0.982968i	$0.558832\pi$
$152$	532.000	+	394.908i	0.283887	+	0.210732i
$153$	−378.000			−0.199735
$154$	−285.000	−	493.634i	−0.149130	−	0.258300i
$155$	−490.000	−	848.705i	−0.253921	−	0.439804i
$156$	300.000	−	519.615i	0.153969	−	0.266683i
$157$	1266.50	+	2193.64i	0.643807	+	1.11511i	0.984576	+	0.174959i	$0.0559794\pi$
$157$	1266.50	+	2193.64i	0.643807	+	1.11511i	−0.340769	+	0.940147i	$0.610687\pi$
$158$	−214.000	+	370.659i	−0.107753	+	0.186633i
$159$	1359.00			0.677835
$160$	160.000			0.0790569
$161$	−427.500	+	740.452i	−0.209265	+	0.362458i
$162$	81.0000	−	140.296i	0.0392837	−	0.0680414i
$163$	3470.00			1.66743			0.833716	−	0.552194i	$-0.186209\pi$
$163$	3470.00			1.66743			0.833716	+	0.552194i	$0.186209\pi$
$164$	852.000			0.405671
$165$	−112.500	+	194.856i	−0.0530795	+	0.0919363i
$166$	−198.000	−	342.946i	−0.0925770	−	0.160348i
$167$	−964.500	+	1670.56i	−0.446918	+	0.774084i	−0.998184	−	0.0602455i	$-0.980812\pi$
$167$	−964.500	+	1670.56i	−0.446918	+	0.774084i	0.551266	+	0.834330i	$0.314145\pi$
$168$	228.000	+	394.908i	0.104706	+	0.181356i
$169$	−151.500	−	262.406i	−0.0689577	−	0.119438i
$170$	−420.000			−0.189485
$171$	684.000	−	296.181i	0.305888	−	0.132453i
$172$	1352.00			0.599355
$173$	718.500	+	1244.48i	0.315760	+	0.546913i	0.979599	−	0.200963i	$-0.0644071\pi$
$173$	718.500	+	1244.48i	0.315760	+	0.546913i	−0.663838	+	0.747876i	$0.731074\pi$
$174$	324.000	+	561.184i	0.141163	+	0.244502i
$175$	237.500	−	411.362i	0.102590	−	0.177692i
$176$	−120.000	−	207.846i	−0.0513940	−	0.0890170i
$177$	−270.000	+	467.654i	−0.114658	+	0.198593i
$178$	−1230.00			−0.517935
$179$	909.000			0.379563			0.189782	−	0.981826i	$-0.439222\pi$
$179$	909.000			0.379563			0.189782	+	0.981826i	$0.439222\pi$
$180$	90.0000	−	155.885i	0.0372678	−	0.0645497i
$181$	−1918.00	+	3322.07i	−0.787645	+	1.36424i	0.139761	+	0.990185i	$0.455367\pi$
$181$	−1918.00	+	3322.07i	−0.787645	+	1.36424i	−0.927406	+	0.374057i	$0.877967\pi$
$182$	1900.00			0.773832
$183$	−294.000			−0.118760
$184$	−180.000	+	311.769i	−0.0721183	+	0.124913i
$185$	−107.500	−	186.195i	−0.0427219	−	0.0739966i
$186$	588.000	−	1018.45i	0.231797	−	0.401484i
$187$	315.000	+	545.596i	0.123182	+	0.213358i
$188$	−480.000	−	831.384i	−0.186211	−	0.322526i
$189$	513.000			0.197435
$190$	760.000	−	329.090i	0.290191	−	0.125656i
$191$	−2334.00			−0.884201			−0.442100	−	0.896966i	$-0.645766\pi$
$191$	−2334.00			−0.884201			−0.442100	+	0.896966i	$0.645766\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	59.0000	+	102.191i	0.0220047	+	0.0381133i	0.876818	−	0.480822i	$-0.159662\pi$
$193$	59.0000	+	102.191i	0.0220047	+	0.0381133i	−0.854813	+	0.518936i	$0.826328\pi$
$194$	−52.0000	+	90.0666i	−0.0192442	+	0.0333320i
$195$	−375.000	−	649.519i	−0.137714	−	0.238528i
$196$	−36.0000	+	62.3538i	−0.0131195	+	0.0227237i
$197$	−4299.00			−1.55478			−0.777388	−	0.629021i	$-0.783456\pi$
$197$	−4299.00			−1.55478			−0.777388	+	0.629021i	$0.783456\pi$
$198$	−270.000			−0.0969094
$199$	−523.000	+	905.863i	−0.186304	+	0.322688i	−0.944015	−	0.329902i	$-0.892984\pi$
$199$	−523.000	+	905.863i	−0.186304	+	0.322688i	0.757711	+	0.652590i	$0.226318\pi$
$200$	100.000	−	173.205i	0.0353553	−	0.0612372i
$201$	−330.000			−0.115803
$202$	−636.000			−0.221529
$203$	−1026.00	+	1777.08i	−0.354734	+	0.614418i
$204$	−252.000	−	436.477i	−0.0864879	−	0.149801i
$205$	532.500	−	922.317i	0.181422	−	0.314231i
$206$	−1003.00	−	1737.25i	−0.339235	−	0.587572i
$207$	202.500	+	350.740i	0.0679938	+	0.117769i
$208$	800.000			0.266683
$209$	−997.500	−	740.452i	−0.330136	−	0.245063i
$210$	570.000			0.187304
$211$	381.500	+	660.777i	0.124472	+	0.215591i	0.921526	−	0.388316i	$-0.126943\pi$
$211$	381.500	+	660.777i	0.124472	+	0.215591i	−0.797055	+	0.603907i	$0.793610\pi$
$212$	906.000	+	1569.24i	0.293511	+	0.508376i
$213$	306.000	−	530.008i	0.0984356	−	0.170495i
$214$	−1122.00	−	1943.36i	−0.358403	−	0.620773i
$215$	845.000	−	1463.58i	0.268040	−	0.464258i
$216$	216.000			0.0680414
$217$	3724.00			1.16498
$218$	1046.00	−	1811.73i	0.324973	−	0.562869i
$219$	−1140.00	+	1974.54i	−0.351754	+	0.609255i
$220$	−300.000			−0.0919363
$221$	−2100.00			−0.639191
$222$	129.000	−	223.435i	0.0389996	−	0.0675493i
$223$	−950.500	−	1646.31i	−0.285427	−	0.494374i	0.687286	−	0.726387i	$-0.258802\pi$
$223$	−950.500	−	1646.31i	−0.285427	−	0.494374i	−0.972713	+	0.232013i	$0.925469\pi$
$224$	−304.000	+	526.543i	−0.0906779	+	0.157059i
$225$	−112.500	−	194.856i	−0.0333333	−	0.0577350i
$226$	1590.00	+	2753.96i	0.467988	+	0.810579i
$227$	−1176.00			−0.343850			−0.171925	−	0.985110i	$-0.554999\pi$
$227$	−1176.00			−0.343850			−0.171925	+	0.985110i	$0.554999\pi$
$228$	798.000	+	592.361i	0.231793	+	0.172062i
$229$	518.000			0.149478			0.0747389	−	0.997203i	$-0.476188\pi$
$229$	518.000			0.149478			0.0747389	+	0.997203i	$0.476188\pi$
$230$	225.000	+	389.711i	0.0645046	+	0.111725i
$231$	−427.500	−	740.452i	−0.121764	−	0.210901i
$232$	−432.000	+	748.246i	−0.122251	+	0.211745i
$233$	897.000	+	1553.65i	0.252208	+	0.436837i	0.964133	−	0.265418i	$-0.0855100\pi$
$233$	897.000	+	1553.65i	0.252208	+	0.436837i	−0.711926	+	0.702255i	$0.752177\pi$
$234$	450.000	−	779.423i	0.125715	−	0.217746i
$235$	−1200.00			−0.333104
$236$	−720.000			−0.198593
$237$	−321.000	+	555.988i	−0.0879797	+	0.152385i
$238$	798.000	−	1382.18i	0.217339	−	0.376442i
$239$	−3780.00			−1.02305			−0.511523	−	0.859270i	$-0.670918\pi$
$239$	−3780.00			−1.02305			−0.511523	+	0.859270i	$0.670918\pi$
$240$	240.000			0.0645497
$241$	−1279.00	+	2215.29i	−0.341857	+	0.592114i	−0.984778	−	0.173819i	$-0.944389\pi$
$241$	−1279.00	+	2215.29i	−0.341857	+	0.592114i	0.642920	+	0.765933i	$0.277723\pi$
$242$	−1106.00	−	1915.65i	−0.293787	−	0.508853i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−196.000	−	339.482i	−0.0514246	−	0.0890701i
$245$	45.0000	+	77.9423i	0.0117345	+	0.0203247i
$246$	1278.00			0.331229
$247$	3800.00	−	1645.45i	0.978900	−	0.423876i
$248$	1568.00			0.401484
$249$	−297.000	−	514.419i	−0.0755888	−	0.130924i
$250$	−125.000	−	216.506i	−0.0316228	−	0.0547723i
$251$	−2646.00	+	4583.01i	−0.665395	+	1.15250i	0.313784	+	0.949495i	$0.398403\pi$
$251$	−2646.00	+	4583.01i	−0.665395	+	1.15250i	−0.979178	+	0.203003i	$0.934930\pi$
$252$	342.000	+	592.361i	0.0854920	+	0.148076i
$253$	337.500	−	584.567i	0.0838674	−	0.145263i
$254$	1598.00			0.394754
$255$	−630.000			−0.154714
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−3093.00	+	5357.23i	−0.750724	+	1.30029i	0.196748	+	0.980454i	$0.436962\pi$
$257$	−3093.00	+	5357.23i	−0.750724	+	1.30029i	−0.947472	+	0.319838i	$0.896372\pi$
$258$	2028.00			0.489371
$259$	817.000			0.196007
$260$	500.000	−	866.025i	0.119264	−	0.206572i
$261$	486.000	+	841.777i	0.115259	+	0.199635i
$262$	219.000	−	379.319i	0.0516407	−	0.0894443i
$263$	3097.50	+	5365.03i	0.726236	+	1.25788i	0.958463	+	0.285216i	$0.0920653\pi$
$263$	3097.50	+	5365.03i	0.726236	+	1.25788i	−0.232227	+	0.972662i	$0.574601\pi$
$264$	−180.000	−	311.769i	−0.0419630	−	0.0726821i
$265$	2265.00			0.525048
$266$	−361.000	+	3126.35i	−0.0832118	+	0.720635i
$267$	−1845.00			−0.422892
$268$	−220.000	−	381.051i	−0.0501442	−	0.0868523i
$269$	2925.00	+	5066.25i	0.662975	+	1.14831i	0.979830	+	0.199833i	$0.0640400\pi$
$269$	2925.00	+	5066.25i	0.662975	+	1.14831i	−0.316855	+	0.948474i	$0.602627\pi$
$270$	135.000	−	233.827i	0.0304290	−	0.0527046i
$271$	881.000	+	1525.94i	0.197479	+	0.342044i	0.947711	−	0.319131i	$-0.103391\pi$
$271$	881.000	+	1525.94i	0.197479	+	0.342044i	−0.750231	+	0.661176i	$0.770058\pi$
$272$	336.000	−	581.969i	0.0749007	−	0.129732i
$273$	2850.00			0.631831
$274$	−5016.00			−1.10594
$275$	−187.500	+	324.760i	−0.0411152	+	0.0712136i
$276$	−270.000	+	467.654i	−0.0588844	+	0.101991i
$277$	−5722.00			−1.24116			−0.620581	−	0.784143i	$-0.713103\pi$
$277$	−5722.00			−1.24116			−0.620581	+	0.784143i	$0.713103\pi$
$278$	728.000			0.157059
$279$	882.000	−	1527.67i	0.189262	−	0.327811i
$280$	380.000	+	658.179i	0.0811048	+	0.140478i
$281$	−1483.50	+	2569.50i	−0.314940	+	0.545492i	−0.979425	−	0.201810i	$-0.935318\pi$
$281$	−1483.50	+	2569.50i	−0.314940	+	0.545492i	0.664485	+	0.747302i	$0.268651\pi$
$282$	−720.000	−	1247.08i	−0.152040	−	0.263342i
$283$	269.000	+	465.922i	0.0565031	+	0.0978663i	0.892893	−	0.450268i	$-0.148672\pi$
$283$	269.000	+	465.922i	0.0565031	+	0.0978663i	−0.836390	+	0.548134i	$0.815338\pi$
$284$	816.000			0.170495
$285$	1140.00	−	493.634i	0.236940	−	0.102598i
$286$	−1500.00			−0.310129
$287$	2023.50	+	3504.80i	0.416179	+	0.720844i
$288$	144.000	+	249.415i	0.0294628	+	0.0510310i
$289$	1574.50	−	2727.11i	0.320476	−	0.555081i
$290$	540.000	+	935.307i	0.109344	+	0.189390i
$291$	−78.0000	+	135.100i	−0.0157129	+	0.0272155i
$292$	−3040.00			−0.609255
$293$	−1215.00			−0.242256			−0.121128	−	0.992637i	$-0.538651\pi$
$293$	−1215.00			−0.242256			−0.121128	+	0.992637i	$0.538651\pi$
$294$	−54.0000	+	93.5307i	−0.0107121	+	0.0185538i
$295$	−450.000	+	779.423i	−0.0888136	+	0.153830i
$296$	344.000			0.0675493
$297$	−405.000			−0.0791262
$298$	1302.00	−	2255.13i	0.253097	−	0.438376i
$299$	1125.00	+	1948.56i	0.217593	+	0.376883i
$300$	150.000	−	259.808i	0.0288675	−	0.0500000i
$301$	3211.00	+	5561.62i	0.614880	+	1.06500i
$302$	−682.000	−	1181.26i	−0.129949	−	0.225079i
$303$	−954.000			−0.180877
$304$	−152.000	+	1316.36i	−0.0286770	+	0.248350i
$305$	−490.000			−0.0919912
$306$	−378.000	−	654.715i	−0.0706171	−	0.122312i
$307$	854.000	+	1479.17i	0.158763	+	0.274986i	0.934423	−	0.356165i	$-0.115916\pi$
$307$	854.000	+	1479.17i	0.158763	+	0.274986i	−0.775660	+	0.631151i	$0.782583\pi$
$308$	570.000	−	987.269i	0.105451	−	0.182646i
$309$	−1504.50	−	2605.87i	−0.276984	−	0.479750i
$310$	980.000	−	1697.41i	0.179549	−	0.310988i
$311$	−1272.00			−0.231924			−0.115962	−	0.993254i	$-0.536995\pi$
$311$	−1272.00			−0.231924			−0.115962	+	0.993254i	$0.536995\pi$
$312$	1200.00			0.217746
$313$	3572.00	−	6186.89i	0.645052	−	1.11726i	−0.339237	−	0.940701i	$-0.610169\pi$
$313$	3572.00	−	6186.89i	0.645052	−	1.11726i	0.984289	−	0.176562i	$-0.0564978\pi$
$314$	−2533.00	+	4387.28i	−0.455240	+	0.788499i
$315$	855.000			0.152933
$316$	−856.000			−0.152385
$317$	−439.500	+	761.236i	−0.0778700	+	0.134875i	−0.902331	−	0.431044i	$-0.858145\pi$
$317$	−439.500	+	761.236i	−0.0778700	+	0.134875i	0.824461	+	0.565919i	$0.191479\pi$
$318$	1359.00	+	2353.86i	0.239651	+	0.415087i
$319$	810.000	−	1402.96i	0.142167	−	0.246241i
$320$	160.000	+	277.128i	0.0279508	+	0.0484123i
$321$	−1683.00	−	2915.04i	−0.292635	−	0.506859i
$322$	−1710.00			−0.295946
$323$	399.000	−	3455.44i	0.0687336	−	0.595250i
$324$	324.000			0.0555556
$325$	−625.000	−	1082.53i	−0.106673	−	0.184763i
$326$	3470.00	+	6010.22i	0.589526	+	1.02109i
$327$	1569.00	−	2717.59i	0.265339	−	0.459581i
$328$	852.000	+	1475.71i	0.143426	+	0.248422i
$329$	2280.00	−	3949.08i	0.382068	−	0.661762i
$330$	−450.000			−0.0750657
$331$	5951.00			0.988207			0.494104	−	0.869403i	$-0.335496\pi$
$331$	5951.00			0.988207			0.494104	+	0.869403i	$0.335496\pi$
$332$	396.000	−	685.892i	0.0654618	−	0.113383i
$333$	193.500	−	335.152i	0.0318430	−	0.0551538i
$334$	−3858.00			−0.632037
$335$	−550.000			−0.0897006
$336$	−456.000	+	789.815i	−0.0740382	+	0.128238i
$337$	4211.00	+	7293.67i	0.680676	+	1.17897i	0.974775	+	0.223190i	$0.0716471\pi$
$337$	4211.00	+	7293.67i	0.680676	+	1.17897i	−0.294099	+	0.955775i	$0.595020\pi$
$338$	303.000	−	524.811i	0.0487604	−	0.0844556i
$339$	2385.00	+	4130.94i	0.382110	+	0.661835i
$340$	−420.000	−	727.461i	−0.0669932	−	0.116036i
$341$	−2940.00			−0.466891
$342$	1197.00	+	888.542i	0.189258	+	0.140488i
$343$	6175.00			0.972066
$344$	1352.00	+	2341.73i	0.211904	+	0.367028i
$345$	337.500	+	584.567i	0.0526678	+	0.0912233i
$346$	−1437.00	+	2488.96i	−0.223276	+	0.386726i
$347$	3273.00	+	5669.00i	0.506351	+	0.877026i	0.999973	+	0.00734926i	$0.00233936\pi$
$347$	3273.00	+	5669.00i	0.506351	+	0.877026i	−0.493622	+	0.869677i	$0.664327\pi$
$348$	−648.000	+	1122.37i	−0.0998174	+	0.172889i
$349$	−11194.0			−1.71691			−0.858454	−	0.512890i	$-0.828575\pi$
$349$	−11194.0			−1.71691			−0.858454	+	0.512890i	$0.828575\pi$
$350$	950.000			0.145085
$351$	675.000	−	1169.13i	0.102646	−	0.177789i
$352$	240.000	−	415.692i	0.0363410	−	0.0629445i
$353$	−114.000			−0.0171887			−0.00859435	−	0.999963i	$-0.502736\pi$
$353$	−114.000			−0.0171887			−0.00859435	+	0.999963i	$0.502736\pi$
$354$	−1080.00			−0.162151
$355$	510.000	−	883.346i	0.0762479	−	0.132065i
$356$	−1230.00	−	2130.42i	−0.183118	−	0.317169i
$357$	1197.00	−	2073.26i	0.177456	−	0.307364i
$358$	909.000	+	1574.43i	0.134196	+	0.232434i
$359$	−3036.00	−	5258.51i	−0.446334	−	0.773073i	0.551810	−	0.833970i	$-0.313937\pi$
$359$	−3036.00	−	5258.51i	−0.446334	−	0.773073i	−0.998144	+	0.0608965i	$0.980604\pi$
$360$	360.000			0.0527046
$361$	1985.50	+	6565.34i	0.289474	+	0.957186i
$362$	−7672.00			−1.11390
$363$	−1659.00	−	2873.47i	−0.239876	−	0.415477i
$364$	1900.00	+	3290.90i	0.273591	+	0.473873i
$365$	−1900.00	+	3290.90i	−0.272467	+	0.471927i
$366$	−294.000	−	509.223i	−0.0419880	−	0.0727254i
$367$	4448.00	−	7704.16i	0.632653	−	1.09579i	−0.354354	−	0.935111i	$-0.615299\pi$
$367$	4448.00	−	7704.16i	0.632653	−	1.09579i	0.987007	−	0.160676i	$-0.0513674\pi$
$368$	−720.000			−0.101991
$369$	1917.00			0.270447
$370$	215.000	−	372.391i	0.0302090	−	0.0523235i
$371$	−4303.50	+	7453.88i	−0.602228	+	1.04309i
$372$	2352.00			0.327811
$373$	−529.000			−0.0734332			−0.0367166	−	0.999326i	$-0.511690\pi$
$373$	−529.000			−0.0734332			−0.0367166	+	0.999326i	$0.511690\pi$
$374$	−630.000	+	1091.19i	−0.0871030	+	0.150867i
$375$	−187.500	−	324.760i	−0.0258199	−	0.0447214i
$376$	960.000	−	1662.77i	0.131671	−	0.228061i
$377$	2700.00	+	4676.54i	0.368852	+	0.638870i
$378$	513.000	+	888.542i	0.0698039	+	0.120904i
$379$	−1888.00			−0.255884			−0.127942	−	0.991782i	$-0.540837\pi$
$379$	−1888.00			−0.255884			−0.127942	+	0.991782i	$0.540837\pi$
$380$	1330.00	+	987.269i	0.179546	+	0.133278i
$381$	2397.00			0.322315
$382$	−2334.00	−	4042.61i	−0.312612	−	0.541460i
$383$	−3564.00	−	6173.03i	−0.475488	−	0.823569i	0.524118	−	0.851646i	$-0.324395\pi$
$383$	−3564.00	−	6173.03i	−0.475488	−	0.823569i	−0.999606	+	0.0280764i	$0.991062\pi$
$384$	−192.000	+	332.554i	−0.0255155	+	0.0441942i
$385$	−712.500	−	1234.09i	−0.0943178	−	0.163363i
$386$	−118.000	+	204.382i	−0.0155597	+	0.0269502i
$387$	3042.00			0.399570
$388$	−208.000			−0.0272155
$389$	4782.00	−	8282.67i	0.623283	−	1.07956i	−0.365587	−	0.930777i	$-0.619132\pi$
$389$	4782.00	−	8282.67i	0.623283	−	1.07956i	0.988870	−	0.148781i	$-0.0475348\pi$
$390$	750.000	−	1299.04i	0.0973788	−	0.168665i
$391$	1890.00			0.244454
$392$	−144.000			−0.0185538
$393$	328.500	−	568.979i	0.0421645	−	0.0730310i
$394$	−4299.00	−	7446.09i	−0.549697	−	0.952103i
$395$	−535.000	+	926.647i	−0.0681488	+	0.118037i
$396$	−270.000	−	467.654i	−0.0342627	−	0.0593447i
$397$	−3686.50	−	6385.21i	−0.466046	−	0.807215i	0.533202	−	0.845988i	$-0.320988\pi$
$397$	−3686.50	−	6385.21i	−0.466046	−	0.807215i	−0.999248	+	0.0387729i	$0.987655\pi$
$398$	−2092.00			−0.263474
$399$	−541.500	+	4689.53i	−0.0679421	+	0.588396i
$400$	400.000			0.0500000
$401$	969.000	+	1678.36i	0.120672	+	0.209010i	0.920033	−	0.391841i	$-0.128162\pi$
$401$	969.000	+	1678.36i	0.120672	+	0.209010i	−0.799361	+	0.600851i	$0.794828\pi$
$402$	−330.000	−	571.577i	−0.0409425	−	0.0709146i
$403$	4900.00	−	8487.05i	0.605673	−	1.04906i
$404$	−636.000	−	1101.58i	−0.0783222	−	0.135658i
$405$	202.500	−	350.740i	0.0248452	−	0.0430331i
$406$	−4104.00			−0.501670
$407$	−645.000			−0.0785540
$408$	504.000	−	872.954i	0.0611562	−	0.105926i
$409$	−374.500	+	648.653i	−0.0452759	+	0.0784201i	−0.887775	−	0.460277i	$-0.847750\pi$
$409$	−374.500	+	648.653i	−0.0452759	+	0.0784201i	0.842499	+	0.538697i	$0.181083\pi$
$410$	2130.00			0.256569
$411$	−7524.00			−0.902996
$412$	2006.00	−	3474.49i	0.239875	−	0.415476i
$413$	−1710.00	−	2961.81i	−0.203738	−	0.352884i
$414$	−405.000	+	701.481i	−0.0480789	+	0.0832751i
$415$	−495.000	−	857.365i	−0.0585508	−	0.101413i
$416$	800.000	+	1385.64i	0.0942866	+	0.163309i
$417$	1092.00			0.128239
$418$	285.000	−	2468.17i	0.0333488	−	0.288809i
$419$	−10641.0			−1.24068			−0.620342	−	0.784331i	$-0.713006\pi$
$419$	−10641.0			−1.24068			−0.620342	+	0.784331i	$0.713006\pi$
$420$	570.000	+	987.269i	0.0662218	+	0.114700i
$421$	−4015.00	−	6954.18i	−0.464796	−	0.805050i	0.534396	−	0.845234i	$-0.320539\pi$
$421$	−4015.00	−	6954.18i	−0.464796	−	0.805050i	−0.999192	+	0.0401837i	$0.987206\pi$
$422$	−763.000	+	1321.55i	−0.0880148	+	0.152446i
$423$	−1080.00	−	1870.61i	−0.124140	−	0.215018i
$424$	−1812.00	+	3138.48i	−0.207544	+	0.359476i
$425$	−1050.00			−0.119841
$426$	1224.00			0.139209
$427$	931.000	−	1612.54i	0.105513	−	0.182755i
$428$	2244.00	−	3886.72i	0.253430	−	0.438953i
$429$	−2250.00			−0.253219
$430$	3380.00			0.379065
$431$	−1815.00	+	3143.67i	−0.202843	+	0.351335i	−0.949443	−	0.313938i	$-0.898352\pi$
$431$	−1815.00	+	3143.67i	−0.202843	+	0.351335i	0.746600	+	0.665273i	$0.231685\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	6734.00	−	11663.6i	0.747380	−	1.29450i	−0.201695	−	0.979448i	$-0.564645\pi$
$433$	6734.00	−	11663.6i	0.747380	−	1.29450i	0.949075	−	0.315051i	$-0.102022\pi$
$434$	3724.00	+	6450.16i	0.411884	+	0.713404i
$435$	810.000	+	1402.96i	0.0892794	+	0.154636i
$436$	4184.00			0.459581
$437$	−3420.00	+	1480.90i	−0.374373	+	0.162108i
$438$	−4560.00			−0.497455
$439$	677.000	+	1172.60i	0.0736024	+	0.127483i	0.900478	−	0.434902i	$-0.143217\pi$
$439$	677.000	+	1172.60i	0.0736024	+	0.127483i	−0.826875	+	0.562385i	$0.809884\pi$
$440$	−300.000	−	519.615i	−0.0325044	−	0.0562993i
$441$	−81.0000	+	140.296i	−0.00874636	+	0.0151491i
$442$	−2100.00	−	3637.31i	−0.225988	−	0.391423i
$443$	2577.00	−	4463.49i	0.276381	−	0.478707i	−0.694101	−	0.719877i	$-0.744198\pi$
$443$	2577.00	−	4463.49i	0.276381	−	0.478707i	0.970483	+	0.241171i	$0.0775314\pi$
$444$	516.000			0.0551538
$445$	−3075.00			−0.327571
$446$	1901.00	−	3292.63i	0.201827	−	0.349575i
$447$	1953.00	−	3382.70i	0.206653	−	0.357933i
$448$	−1216.00			−0.128238
$449$	12099.0			1.27169			0.635843	−	0.771818i	$-0.280653\pi$
$449$	12099.0			1.27169			0.635843	+	0.771818i	$0.280653\pi$
$450$	225.000	−	389.711i	0.0235702	−	0.0408248i
$451$	−1597.50	−	2766.95i	−0.166792	−	0.288893i
$452$	−3180.00	+	5507.92i	−0.330917	+	0.573166i
$453$	−1023.00	−	1771.89i	−0.106103	−	0.183776i
$454$	−1176.00	−	2036.89i	−0.121569	−	0.210564i
$455$	4750.00			0.489414
$456$	−228.000	+	1974.54i	−0.0234146	+	0.202777i
$457$	−1126.00			−0.115256			−0.0576281	−	0.998338i	$-0.518354\pi$
$457$	−1126.00			−0.115256			−0.0576281	+	0.998338i	$0.518354\pi$
$458$	518.000	+	897.202i	0.0528484	+	0.0915361i
$459$	−567.000	−	982.073i	−0.0576586	−	0.0998676i
$460$	−450.000	+	779.423i	−0.0456116	+	0.0790017i
$461$	3321.00	+	5752.14i	0.335519	+	0.581136i	0.983584	−	0.180448i	$-0.0577549\pi$
$461$	3321.00	+	5752.14i	0.335519	+	0.581136i	−0.648065	+	0.761585i	$0.724422\pi$
$462$	855.000	−	1480.90i	0.0861000	−	0.149130i
$463$	7985.00			0.801500			0.400750	−	0.916187i	$-0.368750\pi$
$463$	7985.00			0.801500			0.400750	+	0.916187i	$0.368750\pi$
$464$	−1728.00			−0.172889
$465$	1470.00	−	2546.11i	0.146601	−	0.253921i
$466$	−1794.00	+	3107.30i	−0.178338	+	0.308890i
$467$	10860.0			1.07610			0.538052	−	0.842911i	$-0.319160\pi$
$467$	10860.0			1.07610			0.538052	+	0.842911i	$0.319160\pi$
$468$	1800.00			0.177789
$469$	1045.00	−	1809.99i	0.102886	−	0.178204i
$470$	−1200.00	−	2078.46i	−0.117770	−	0.203984i
$471$	−3799.50	+	6580.93i	−0.371702	+	0.643807i
$472$	−720.000	−	1247.08i	−0.0702133	−	0.121613i
$473$	−2535.00	−	4390.75i	−0.246426	−	0.426822i
$474$	−1284.00			−0.124422
$475$	1900.00	−	822.724i	0.183533	−	0.0794719i
$476$	3192.00			0.307364
$477$	2038.50	+	3530.79i	0.195674	+	0.338917i
$478$	−3780.00	−	6547.15i	−0.361701	−	0.626485i
$479$	7032.00	−	12179.8i	0.670773	−	1.16181i	−0.306912	−	0.951738i	$-0.599296\pi$
$479$	7032.00	−	12179.8i	0.670773	−	1.16181i	0.977685	−	0.210075i	$-0.0673709\pi$
$480$	240.000	+	415.692i	0.0228218	+	0.0395285i
$481$	1075.00	−	1861.95i	0.101904	−	0.176503i
$482$	−5116.00			−0.483459
$483$	−2565.00			−0.241639
$484$	2212.00	−	3831.30i	0.207739	−	0.359814i
$485$	−130.000	+	225.167i	−0.0121711	+	0.0210810i
$486$	486.000			0.0453609
$487$	−6415.00			−0.596902			−0.298451	−	0.954425i	$-0.596470\pi$
$487$	−6415.00			−0.596902			−0.298451	+	0.954425i	$0.596470\pi$
$488$	392.000	−	678.964i	0.0363627	−	0.0629821i
$489$	5205.00	+	9015.32i	0.481346	+	0.833716i
$490$	−90.0000	+	155.885i	−0.00829752	+	0.0143717i
$491$	−7996.50	−	13850.3i	−0.734984	−	1.27303i	−0.954730	−	0.297472i	$-0.903856\pi$
$491$	−7996.50	−	13850.3i	−0.734984	−	1.27303i	0.219747	−	0.975557i	$-0.429477\pi$
$492$	1278.00	+	2213.56i	0.117107	+	0.202835i
$493$	4536.00			0.414384
$494$	6650.00	+	4936.34i	0.605663	+	0.449588i
$495$	−675.000			−0.0612909
$496$	1568.00	+	2715.86i	0.141946	+	0.245858i
$497$	1938.00	+	3356.71i	0.174912	+	0.302956i
$498$	594.000	−	1028.84i	0.0534494	−	0.0925770i
$499$	−4790.50	−	8297.39i	−0.429764	−	0.744373i	0.567088	−	0.823657i	$-0.308070\pi$
$499$	−4790.50	−	8297.39i	−0.429764	−	0.744373i	−0.996852	+	0.0792841i	$0.974737\pi$
$500$	250.000	−	433.013i	0.0223607	−	0.0387298i
$501$	−5787.00			−0.516056
$502$	−10584.0			−0.941010
$503$	9433.50	−	16339.3i	0.836221	−	1.44838i	−0.0568121	−	0.998385i	$-0.518094\pi$
$503$	9433.50	−	16339.3i	0.836221	−	1.44838i	0.893033	−	0.449992i	$-0.148573\pi$
$504$	−684.000	+	1184.72i	−0.0604519	+	0.104706i
$505$	−1590.00			−0.140107
$506$	1350.00			0.118606
$507$	454.500	−	787.217i	0.0398127	−	0.0689577i
$508$	1598.00	+	2767.82i	0.139567	+	0.241736i
$509$	−6315.00	+	10937.9i	−0.549916	+	0.952483i	0.448363	+	0.893851i	$0.352007\pi$
$509$	−6315.00	+	10937.9i	−0.549916	+	0.952483i	−0.998280	+	0.0586317i	$0.981326\pi$
$510$	−630.000	−	1091.19i	−0.0546997	−	0.0947427i
$511$	−7220.00	−	12505.4i	−0.625037	−	1.08260i
$512$	−512.000			−0.0441942
$513$	1795.50	+	1332.81i	0.154529	+	0.114708i
$514$	−12372.0			−1.06168
$515$	−2507.50	−	4343.12i	−0.214551	−	0.371613i
$516$	2028.00	+	3512.60i	0.173019	+	0.299677i
$517$	−1800.00	+	3117.69i	−0.153122	+	0.265215i
$518$	817.000	+	1415.09i	0.0692991	+	0.120030i
$519$	−2155.50	+	3733.44i	−0.182304	+	0.315760i
$520$	2000.00			0.168665
$521$	−882.000			−0.0741672			−0.0370836	−	0.999312i	$-0.511807\pi$
$521$	−882.000			−0.0741672			−0.0370836	+	0.999312i	$0.511807\pi$
$522$	−972.000	+	1683.55i	−0.0815005	+	0.141163i
$523$	2426.00	−	4201.96i	0.202833	−	0.351317i	−0.746607	−	0.665265i	$-0.768319\pi$
$523$	2426.00	−	4201.96i	0.202833	−	0.351317i	0.949440	+	0.313948i	$0.101652\pi$
$524$	876.000			0.0730310
$525$	1425.00			0.118461
$526$	−6195.00	+	10730.1i	−0.513526	+	0.889454i
$527$	−4116.00	−	7129.12i	−0.340220	−	0.589278i
$528$	360.000	−	623.538i	0.0296723	−	0.0513940i
$529$	5071.00	+	8783.23i	0.416783	+	0.721890i
$530$	2265.00	+	3923.10i	0.185633	+	0.321525i
$531$	−1620.00			−0.132396
$532$	−5776.00	+	2501.08i	−0.470717	+	0.203826i
$533$	10650.0			0.865484
$534$	−1845.00	−	3195.63i	−0.149515	−	0.258967i
$535$	−2805.00	−	4858.40i	−0.226674	−	0.392611i
$536$	440.000	−	762.102i	0.0354573	−	0.0614138i
$537$	1363.50	+	2361.65i	0.109571	+	0.189782i
$538$	−5850.00	+	10132.5i	−0.468794	+	0.811976i
$539$	270.000			0.0215765
$540$	540.000			0.0430331
$541$	−8194.00	+	14192.4i	−0.651179	+	1.12787i	0.331659	+	0.943399i	$0.392392\pi$
$541$	−8194.00	+	14192.4i	−0.651179	+	1.12787i	−0.982837	+	0.184475i	$0.940942\pi$
$542$	−1762.00	+	3051.87i	−0.139639	+	0.241862i
$543$	−11508.0			−0.909495
$544$	1344.00			0.105926
$545$	2615.00	−	4529.31i	0.205531	−	0.355990i
$546$	2850.00	+	4936.34i	0.223386	+	0.386916i
$547$	11609.0	−	20107.4i	0.907431	−	1.57172i	0.0898117	−	0.995959i	$-0.471373\pi$
$547$	11609.0	−	20107.4i	0.907431	−	1.57172i	0.817620	−	0.575759i	$-0.195293\pi$
$548$	−5016.00	−	8687.97i	−0.391009	−	0.677247i
$549$	−441.000	−	763.834i	−0.0342831	−	0.0593801i
$550$	−750.000			−0.0581456
$551$	−8208.00	+	3554.17i	−0.634614	+	0.274796i
$552$	−1080.00			−0.0832751
$553$	−2033.00	−	3521.26i	−0.156333	−	0.270776i
$554$	−5722.00	−	9910.79i	−0.438817	−	0.760053i
$555$	322.500	−	558.586i	0.0246655	−	0.0427219i
$556$	728.000	+	1260.93i	0.0555289	+	0.0961789i
$557$	−6796.50	+	11771.9i	−0.517014	+	0.895495i	0.482791	+	0.875736i	$0.339623\pi$
$557$	−6796.50	+	11771.9i	−0.517014	+	0.895495i	−0.999805	+	0.0197591i	$0.993710\pi$
$558$	3528.00			0.267656
$559$	16900.0			1.27870
$560$	−760.000	+	1316.36i	−0.0573498	+	0.0993327i
$561$	−945.000	+	1636.79i	−0.0711193	+	0.123182i
$562$	−5934.00			−0.445393
$563$	−16284.0			−1.21899			−0.609493	−	0.792792i	$-0.708627\pi$
$563$	−16284.0			−1.21899			−0.609493	+	0.792792i	$0.708627\pi$
$564$	1440.00	−	2494.15i	0.107509	−	0.186211i
$565$	3975.00	+	6884.90i	0.295981	+	0.512655i
$566$	−538.000	+	931.843i	−0.0399538	+	0.0692019i
$567$	769.500	+	1332.81i	0.0569946	+	0.0987176i
$568$	816.000	+	1413.35i	0.0602792	+	0.104407i
$569$	10755.0			0.792396			0.396198	−	0.918165i	$-0.370329\pi$
$569$	10755.0			0.792396			0.396198	+	0.918165i	$0.370329\pi$
$570$	1995.00	+	1480.90i	0.146599	+	0.108821i
$571$	−3052.00			−0.223682			−0.111841	−	0.993726i	$-0.535675\pi$
$571$	−3052.00			−0.223682			−0.111841	+	0.993726i	$0.535675\pi$
$572$	−1500.00	−	2598.08i	−0.109647	−	0.189914i
$573$	−3501.00	−	6063.91i	−0.255247	−	0.442100i
$574$	−4047.00	+	7009.61i	−0.294283	+	0.509713i
$575$	562.500	+	974.279i	0.0407963	+	0.0706613i
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	9110.00			0.657286			0.328643	−	0.944454i	$-0.393409\pi$
$577$	9110.00			0.657286			0.328643	+	0.944454i	$0.393409\pi$
$578$	6298.00			0.453222
$579$	−177.000	+	306.573i	−0.0127044	+	0.0220047i
$580$	−1080.00	+	1870.61i	−0.0773182	+	0.133919i
$581$	3762.00			0.268630
$582$	−312.000			−0.0222213
$583$	3397.50	−	5884.64i	0.241355	−	0.418039i
$584$	−3040.00	−	5265.43i	−0.215404	−	0.373091i
$585$	1125.00	−	1948.56i	0.0795094	−	0.137714i
$586$	−1215.00	−	2104.44i	−0.0856505	−	0.148351i
$587$	−10590.0	−	18342.4i	−0.744627	−	1.28973i	−0.950369	−	0.311126i	$-0.899294\pi$
$587$	−10590.0	−	18342.4i	−0.744627	−	1.28973i	0.205742	−	0.978606i	$-0.434039\pi$
$588$	−216.000			−0.0151491
$589$	13034.0	+	9675.24i	0.911811	+	0.676844i
$590$	−1800.00			−0.125601
$591$	−6448.50	−	11169.1i	−0.448825	−	0.777388i
$592$	344.000	+	595.825i	0.0238823	+	0.0413653i
$593$	10212.0	−	17687.7i	0.707178	−	1.22487i	−0.258722	−	0.965952i	$-0.583301\pi$
$593$	10212.0	−	17687.7i	0.707178	−	1.22487i	0.965900	−	0.258916i	$-0.0833654\pi$
$594$	−405.000	−	701.481i	−0.0279753	−	0.0484547i
$595$	1995.00	−	3455.44i	0.137457	−	0.238083i
$596$	5208.00			0.357933
$597$	−3138.00			−0.215125
$598$	−2250.00	+	3897.11i	−0.153862	+	0.266496i
$599$	6603.00	−	11436.7i	0.450403	−	0.780121i	−0.548008	−	0.836473i	$-0.684614\pi$
$599$	6603.00	−	11436.7i	0.450403	−	0.780121i	0.998411	+	0.0563525i	$0.0179471\pi$
$600$	600.000			0.0408248
$601$	1985.00			0.134725			0.0673626	−	0.997729i	$-0.478542\pi$
$601$	1985.00			0.134725			0.0673626	+	0.997729i	$0.478542\pi$
$602$	−6422.00	+	11123.2i	−0.434786	+	0.753071i
$603$	−495.000	−	857.365i	−0.0334294	−	0.0579015i
$604$	1364.00	−	2362.52i	0.0918880	−	0.159155i
$605$	−2765.00	−	4789.12i	−0.185807	−	0.321827i
$606$	−954.000	−	1652.38i	−0.0639498	−	0.110764i
$607$	−20875.0			−1.39587			−0.697933	−	0.716164i	$-0.745896\pi$
$607$	−20875.0			−1.39587			−0.697933	+	0.716164i	$0.745896\pi$
$608$	−2432.00	+	1053.09i	−0.162221	+	0.0702439i
$609$	−6156.00			−0.409612
$610$	−490.000	−	848.705i	−0.0325238	−	0.0563329i
$611$	−6000.00	−	10392.3i	−0.397273	−	0.688098i
$612$	756.000	−	1309.43i	0.0499338	−	0.0864879i
$613$	7923.50	+	13723.9i	0.522067	+	0.904247i	0.999670	+	0.0256712i	$0.00817229\pi$
$613$	7923.50	+	13723.9i	0.522067	+	0.904247i	−0.477603	+	0.878576i	$0.658494\pi$
$614$	−1708.00	+	2958.34i	−0.112263	+	0.194445i
$615$	3195.00			0.209488
$616$	2280.00			0.149130
$617$	−336.000	+	581.969i	−0.0219236	+	0.0379728i	−0.876779	−	0.480893i	$-0.840312\pi$
$617$	−336.000	+	581.969i	−0.0219236	+	0.0379728i	0.854855	+	0.518866i	$0.173646\pi$
$618$	3009.00	−	5211.74i	0.195857	−	0.339235i
$619$	−8713.00			−0.565759			−0.282880	−	0.959155i	$-0.591290\pi$
$619$	−8713.00			−0.565759			−0.282880	+	0.959155i	$0.591290\pi$
$620$	3920.00			0.253921
$621$	−607.500	+	1052.22i	−0.0392563	+	0.0679938i
$622$	−1272.00	−	2203.17i	−0.0819977	−	0.142024i
$623$	5842.50	−	10119.5i	0.375722	−	0.650770i
$624$	1200.00	+	2078.46i	0.0769847	+	0.133341i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	14288.0			0.912242
$627$	427.500	−	3702.26i	0.0272292	−	0.235812i
$628$	−10132.0			−0.643807
$629$	−903.000	−	1564.04i	−0.0572416	−	0.0991454i
$630$	855.000	+	1480.90i	0.0540699	+	0.0936518i
$631$	−4210.00	+	7291.93i	−0.265606	+	0.460043i	−0.967722	−	0.252019i	$-0.918905\pi$
$631$	−4210.00	+	7291.93i	−0.265606	+	0.460043i	0.702116	+	0.712062i	$0.252239\pi$
$632$	−856.000	−	1482.64i	−0.0538763	−	0.0933166i
$633$	−1144.50	+	1982.33i	−0.0718638	+	0.124472i
$634$	−1758.00			−0.110125
$635$	3995.00			0.249664
$636$	−2718.00	+	4707.71i	−0.169459	+	0.293511i
$637$	−450.000	+	779.423i	−0.0279900	+	0.0484802i
$638$	3240.00			0.201055
$639$	1836.00			0.113664
$640$	−320.000	+	554.256i	−0.0197642	+	0.0342327i
$641$	−10881.0	−	18846.4i	−0.670474	−	1.16129i	−0.977770	−	0.209681i	$-0.932758\pi$
$641$	−10881.0	−	18846.4i	−0.670474	−	1.16129i	0.307296	−	0.951614i	$-0.400576\pi$
$642$	3366.00	−	5830.08i	0.206924	−	0.358403i
$643$	3785.00	+	6555.81i	0.232140	+	0.402078i	0.958438	−	0.285302i	$-0.0920940\pi$
$643$	3785.00	+	6555.81i	0.232140	+	0.402078i	−0.726298	+	0.687380i	$0.758761\pi$
$644$	−1710.00	−	2961.81i	−0.104633	−	0.181229i
$645$	5070.00			0.309506
$646$	6384.00	−	2764.35i	0.388816	−	0.168362i
$647$	−21261.0			−1.29190			−0.645948	−	0.763382i	$-0.723538\pi$
$647$	−21261.0			−1.29190			−0.645948	+	0.763382i	$0.723538\pi$
$648$	324.000	+	561.184i	0.0196419	+	0.0340207i
$649$	1350.00	+	2338.27i	0.0816520	+	0.141425i
$650$	1250.00	−	2165.06i	0.0754293	−	0.130647i
$651$	5586.00	+	9675.24i	0.336302	+	0.582492i
$652$	−6940.00	+	12020.4i	−0.416858	+	0.722019i
$653$	−11535.0			−0.691270			−0.345635	−	0.938369i	$-0.612336\pi$
$653$	−11535.0			−0.691270			−0.345635	+	0.938369i	$0.612336\pi$
$654$	6276.00			0.375246
$655$	547.500	−	948.298i	0.0326605	−	0.0565696i
$656$	−1704.00	+	2951.41i	−0.101418	+	0.175661i
$657$	−6840.00			−0.406170
$658$	9120.00			0.540326
$659$	9772.50	−	16926.5i	0.577667	−	1.00055i	−0.418079	−	0.908411i	$-0.637297\pi$
$659$	9772.50	−	16926.5i	0.577667	−	1.00055i	0.995746	−	0.0921380i	$-0.0293701\pi$
$660$	−450.000	−	779.423i	−0.0265397	−	0.0459682i
$661$	−9442.00	+	16354.0i	−0.555599	+	0.962326i	0.442257	+	0.896888i	$0.354178\pi$
$661$	−9442.00	+	16354.0i	−0.555599	+	0.962326i	−0.997857	+	0.0654382i	$0.979155\pi$
$662$	5951.00	+	10307.4i	0.349384	+	0.605151i
$663$	−3150.00	−	5455.96i	−0.184519	−	0.319596i
$664$	1584.00			0.0925770
$665$	−902.500	+	7815.88i	−0.0526277	+	0.455770i
$666$	774.000			0.0450329
$667$	−2430.00	−	4208.88i	−0.141064	−	0.244331i
$668$	−3858.00	−	6682.25i	−0.223459	−	0.387042i
$669$	2851.50	−	4938.94i	0.164791	−	0.285427i
$670$	−550.000	−	952.628i	−0.0317140	−	0.0549302i
$671$	−735.000	+	1273.06i	−0.0422867	+	0.0732427i
$672$	−1824.00			−0.104706
$673$	14792.0			0.847236			0.423618	−	0.905841i	$-0.360760\pi$
$673$	14792.0			0.847236			0.423618	+	0.905841i	$0.360760\pi$
$674$	−8422.00	+	14587.3i	−0.481311	+	0.833654i
$675$	337.500	−	584.567i	0.0192450	−	0.0333333i
$676$	1212.00			0.0689577
$677$	14529.0			0.824808			0.412404	−	0.911001i	$-0.364689\pi$
$677$	14529.0			0.824808			0.412404	+	0.911001i	$0.364689\pi$
$678$	−4770.00	+	8261.88i	−0.270193	+	0.467988i
$679$	−494.000	−	855.633i	−0.0279204	−	0.0483596i
$680$	840.000	−	1454.92i	0.0473714	−	0.0820496i
$681$	−1764.00	−	3055.34i	−0.0992608	−	0.171925i
$682$	−2940.00	−	5092.23i	−0.165071	−	0.285911i
$683$	−2778.00			−0.155633			−0.0778164	−	0.996968i	$-0.524795\pi$
$683$	−2778.00			−0.155633			−0.0778164	+	0.996968i	$0.524795\pi$
$684$	−342.000	+	2961.81i	−0.0191180	+	0.165567i
$685$	−12540.0			−0.699458
$686$	6175.00	+	10695.4i	0.343677	+	0.595266i
$687$	777.000	+	1345.80i	0.0431505	+	0.0747389i
$688$	−2704.00	+	4683.47i	−0.149839	+	0.259528i
$689$	11325.0	+	19615.5i	0.626195	+	1.08460i
$690$	−675.000	+	1169.13i	−0.0372418	+	0.0645046i
$691$	−16315.0			−0.898194			−0.449097	−	0.893483i	$-0.648254\pi$
$691$	−16315.0			−0.898194			−0.449097	+	0.893483i	$0.648254\pi$
$692$	−5748.00			−0.315760
$693$	1282.50	−	2221.36i	0.0703004	−	0.121764i
$694$	−6546.00	+	11338.0i	−0.358044	+	0.620151i
$695$	1820.00			0.0993331
$696$	−2592.00			−0.141163
$697$	4473.00	−	7747.46i	0.243080	−	0.421027i
$698$	−11194.0	−	19388.6i	−0.607019	−	1.05139i
$699$	−2691.00	+	4660.95i	−0.145612	+	0.252208i
$700$	950.000	+	1645.45i	0.0512952	+	0.0888459i
$701$	−1515.00	−	2624.06i	−0.0816273	−	0.141383i	0.822322	−	0.569023i	$-0.192678\pi$
$701$	−1515.00	−	2624.06i	−0.0816273	−	0.141383i	−0.903949	+	0.427640i	$0.859345\pi$
$702$	2700.00			0.145164
$703$	2859.50	+	2122.63i	0.153411	+	0.113878i
$704$	960.000			0.0513940
$705$	−1800.00	−	3117.69i	−0.0961588	−	0.166552i
$706$	−114.000	−	197.454i	−0.00607712	−	0.0105259i
$707$	3021.00	−	5232.53i	0.160702	−	0.278344i
$708$	−1080.00	−	1870.61i	−0.0573289	−	0.0992966i
$709$	−13189.0	+	22844.0i	−0.698622	+	1.21005i	0.270322	+	0.962770i	$0.412870\pi$
$709$	−13189.0	+	22844.0i	−0.698622	+	1.21005i	−0.968944	+	0.247279i	$0.920463\pi$
$710$	2040.00			0.107831
$711$	−1926.00			−0.101590
$712$	2460.00	−	4260.84i	0.129484	−	0.224272i
$713$	−4410.00	+	7638.34i	−0.231635	+	0.401204i
$714$	4788.00			0.250961
$715$	−3750.00			−0.196143
$716$	−1818.00	+	3148.87i	−0.0948909	+	0.164356i
$717$	−5670.00	−	9820.73i	−0.295328	−	0.511523i
$718$	6072.00	−	10517.0i	0.315606	−	0.546645i
$719$	−906.000	−	1569.24i	−0.0469932	−	0.0813946i	0.841572	−	0.540145i	$-0.181631\pi$
$719$	−906.000	−	1569.24i	−0.0469932	−	0.0813946i	−0.888565	+	0.458750i	$0.848297\pi$
$720$	360.000	+	623.538i	0.0186339	+	0.0322749i
$721$	19057.0			0.984355
$722$	−9386.00	+	10004.3i	−0.483810	+	0.515682i
$723$	−7674.00			−0.394743
$724$	−7672.00	−	13288.3i	−0.393823	−	0.682121i
$725$	1350.00	+	2338.27i	0.0691555	+	0.119781i
$726$	3318.00	−	5746.94i	0.169618	−	0.293787i
$727$	12824.0	+	22211.8i	0.654217	+	1.13314i	0.982089	+	0.188415i	$0.0603351\pi$
$727$	12824.0	+	22211.8i	0.654217	+	1.13314i	−0.327872	+	0.944722i	$0.606332\pi$
$728$	−3800.00	+	6581.79i	−0.193458	+	0.335079i
$729$	729.000			0.0370370
$730$	−7600.00			−0.385327
$731$	7098.00	−	12294.1i	0.359137	−	0.622043i
$732$	588.000	−	1018.45i	0.0296900	−	0.0514246i
$733$	32393.0			1.63228			0.816141	−	0.577853i	$-0.196109\pi$
$733$	32393.0			1.63228			0.816141	+	0.577853i	$0.196109\pi$
$734$	17792.0			0.894707
$735$	−135.000	+	233.827i	−0.00677490	+	0.0117345i
$736$	−720.000	−	1247.08i	−0.0360592	−	0.0624563i
$737$	−825.000	+	1428.94i	−0.0412337	+	0.0714189i
$738$	1917.00	+	3320.34i	0.0956175	+	0.165614i
$739$	5049.50	+	8745.99i	0.251352	+	0.435354i	0.963898	−	0.266271i	$-0.0857916\pi$
$739$	5049.50	+	8745.99i	0.251352	+	0.435354i	−0.712547	+	0.701625i	$0.752458\pi$
$740$	860.000			0.0427219
$741$	9975.00	+	7404.52i	0.494522	+	0.367087i
$742$	−17214.0			−0.851679
$743$	12922.5	+	22382.4i	0.638063	+	1.10516i	0.985857	+	0.167586i	$0.0535973\pi$
$743$	12922.5	+	22382.4i	0.638063	+	1.10516i	−0.347795	+	0.937571i	$0.613069\pi$
$744$	2352.00	+	4073.78i	0.115899	+	0.200742i
$745$	3255.00	−	5637.83i	0.160072	−	0.277254i
$746$	−529.000	−	916.255i	−0.0259626	−	0.0449685i
$747$	891.000	−	1543.26i	0.0436412	−	0.0755888i
$748$	−2520.00			−0.123182
$749$	21318.0			1.03998
$750$	375.000	−	649.519i	0.0182574	−	0.0316228i
$751$	944.000	−	1635.06i	0.0458682	−	0.0794461i	−0.842180	−	0.539197i	$-0.818728\pi$
$751$	944.000	−	1635.06i	0.0458682	−	0.0794461i	0.888048	+	0.459751i	$0.152061\pi$
$752$	3840.00			0.186211
$753$	−15876.0			−0.768331
$754$	−5400.00	+	9353.07i	−0.260818	+	0.451749i
$755$	−1705.00	−	2953.15i	−0.0821872	−	0.142352i
$756$	−1026.00	+	1777.08i	−0.0493588	+	0.0854920i
$757$	12807.5	+	22183.2i	0.614923	+	1.06508i	0.990398	+	0.138245i	$0.0441461\pi$
$757$	12807.5	+	22183.2i	0.614923	+	1.06508i	−0.375475	+	0.926832i	$0.622521\pi$
$758$	−1888.00	−	3270.11i	−0.0904687	−	0.156696i
$759$	2025.00			0.0968417
$760$	−380.000	+	3290.90i	−0.0181369	+	0.157070i
$761$	−20505.0			−0.976749			−0.488374	−	0.872634i	$-0.662410\pi$
$761$	−20505.0			−0.976749			−0.488374	+	0.872634i	$0.662410\pi$
$762$	2397.00	+	4151.73i	0.113956	+	0.197377i
$763$	9937.00	+	17211.4i	0.471486	+	0.816637i
$764$	4668.00	−	8085.21i	0.221050	−	0.382870i
$765$	−945.000	−	1636.79i	−0.0446622	−	0.0773571i
$766$	7128.00	−	12346.1i	0.336221	−	0.582351i
$767$	−9000.00			−0.423691
$768$	−768.000			−0.0360844
$769$	−9673.00	+	16754.1i	−0.453599	+	0.785656i	−0.998606	−	0.0527752i	$-0.983193\pi$
$769$	−9673.00	+	16754.1i	−0.453599	+	0.785656i	0.545008	+	0.838431i	$0.316527\pi$
$770$	1425.00	−	2468.17i	0.0666928	−	0.115515i
$771$	−18558.0			−0.866861
$772$	−472.000			−0.0220047
$773$	6382.50	−	11054.8i	0.296976	−	0.514378i	−0.678466	−	0.734631i	$-0.737355\pi$
$773$	6382.50	−	11054.8i	0.296976	−	0.514378i	0.975443	+	0.220254i	$0.0706885\pi$
$774$	3042.00	+	5268.90i	0.141269	+	0.244686i
$775$	2450.00	−	4243.52i	0.113557	−	0.196686i
$776$	−208.000	−	360.267i	−0.00962212	−	0.0166660i
$777$	1225.50	+	2122.63i	0.0565825	+	0.0980037i
$778$	19128.0			0.881455
$779$	−2023.50	+	17524.0i	−0.0930673	+	0.805986i
$780$	3000.00			0.137714
$781$	−1530.00	−	2650.04i	−0.0700995	−	0.121416i
$782$	1890.00	+	3273.58i	0.0864274	+	0.149697i
$783$	−1458.00	+	2525.33i	−0.0665449	+	0.115259i
$784$	−144.000	−	249.415i	−0.00655977	−	0.0113618i
$785$	−6332.50	+	10968.2i	−0.287919	+	0.498691i
$786$	1314.00			0.0596296
$787$	28484.0			1.29015			0.645073	−	0.764121i	$-0.276827\pi$
$787$	28484.0			1.29015			0.645073	+	0.764121i	$0.276827\pi$
$788$	8598.00	−	14892.2i	0.388694	−	0.673238i
$789$	−9292.50	+	16095.1i	−0.419292	+	0.726236i
$790$	−2140.00			−0.0963769
$791$	−30210.0			−1.35796
$792$	540.000	−	935.307i	0.0242274	−	0.0419630i
$793$	−2450.00	−	4243.52i	−0.109713	−	0.190028i
$794$	7373.00	−	12770.4i	0.329544	−	0.570787i
$795$	3397.50	+	5884.64i	0.151568	+	0.262524i
$796$	−2092.00	−	3623.45i	−0.0931520	−	0.161344i
$797$	33399.0			1.48438			0.742192	−	0.670188i	$-0.233786\pi$
$797$	33399.0			1.48438			0.742192	+	0.670188i	$0.233786\pi$
$798$	−8664.00	+	3751.62i	−0.384339	+	0.166424i
$799$	−10080.0			−0.446314
$800$	400.000	+	692.820i	0.0176777	+	0.0306186i
$801$	−2767.50	−	4793.45i	−0.122078	−	0.211446i
$802$	−1938.00	+	3356.71i	−0.0853281	+	0.147793i
$803$	5700.00	+	9872.69i	0.250496	+	0.433873i
$804$	660.000	−	1143.15i	0.0289508	−	0.0501442i
$805$	−4275.00			−0.187173
$806$	19600.0			0.856552
$807$	−8775.00	+	15198.7i	−0.382769	+	0.662975i
$808$	1272.00	−	2203.17i	0.0553822	−	0.0959248i
$809$	21954.0			0.954093			0.477047	−	0.878878i	$-0.341707\pi$
$809$	21954.0			0.954093			0.477047	+	0.878878i	$0.341707\pi$
$810$	810.000			0.0351364
$811$	−1139.50	+	1973.67i	−0.0493382	+	0.0854562i	−0.889640	−	0.456663i	$-0.849045\pi$
$811$	−1139.50	+	1973.67i	−0.0493382	+	0.0854562i	0.840302	+	0.542119i	$0.182378\pi$
$812$	−4104.00	−	7108.34i	−0.177367	−	0.307209i
$813$	−2643.00	+	4577.81i	−0.114015	+	0.197479i
$814$	−645.000	−	1117.17i	−0.0277730	−	0.0481043i
$815$	8675.00	+	15025.5i	0.372849	+	0.645794i
$816$	2016.00			0.0864879
$817$	−3211.00	+	27808.1i	−0.137501	+	1.19080i
$818$	−1498.00			−0.0640298
$819$	4275.00	+	7404.52i	0.182394	+	0.315915i
$820$	2130.00	+	3689.27i	0.0907108	+	0.157116i
$821$	3177.00	−	5502.73i	0.135052	−	0.233918i	−0.790565	−	0.612378i	$-0.790213\pi$
$821$	3177.00	−	5502.73i	0.135052	−	0.233918i	0.925617	+	0.378460i	$0.123546\pi$
$822$	−7524.00	−	13032.0i	−0.319257	−	0.552970i
$823$	−9869.50	+	17094.5i	−0.418018	+	0.724029i	−0.995740	−	0.0922047i	$-0.970609\pi$
$823$	−9869.50	+	17094.5i	−0.418018	+	0.724029i	0.577722	+	0.816234i	$0.303942\pi$
$824$	8024.00			0.339235
$825$	−1125.00			−0.0474757
$826$	3420.00	−	5923.61i	0.144064	−	0.249526i
$827$	14970.0	−	25928.8i	0.629453	−	1.09025i	−0.358208	−	0.933642i	$-0.616612\pi$
$827$	14970.0	−	25928.8i	0.629453	−	1.09025i	0.987662	−	0.156603i	$-0.0500545\pi$
$828$	−1620.00			−0.0679938
$829$	1976.00			0.0827857			0.0413928	−	0.999143i	$-0.486820\pi$
$829$	1976.00			0.0827857			0.0413928	+	0.999143i	$0.486820\pi$
$830$	990.000	−	1714.73i	0.0414017	−	0.0717098i
$831$	−8583.00	−	14866.2i	−0.358292	−	0.620581i
$832$	−1600.00	+	2771.28i	−0.0666707	+	0.115477i
$833$	378.000	+	654.715i	0.0157226	+	0.0272323i
$834$	1092.00	+	1891.40i	0.0453392	+	0.0785297i
$835$	−9645.00			−0.399735
$836$	4560.00	−	1974.54i	0.188649	−	0.0816876i
$837$	5292.00			0.218540
$838$	−10641.0	−	18430.8i	−0.438648	−	0.759761i
$839$	−6375.00	−	11041.8i	−0.262324	−	0.454358i	0.704535	−	0.709669i	$-0.251155\pi$
$839$	−6375.00	−	11041.8i	−0.262324	−	0.454358i	−0.966859	+	0.255311i	$0.917822\pi$
$840$	−1140.00	+	1974.54i	−0.0468259	+	0.0811048i
$841$	6362.50	+	11020.2i	0.260876	+	0.451850i
$842$	8030.00	−	13908.4i	0.328660	−	0.569257i
$843$	−8901.00			−0.363662
$844$	−3052.00			−0.124472
$845$	757.500	−	1312.03i	0.0308388	−	0.0534144i
$846$	2160.00	−	3741.23i	0.0877805	−	0.152040i
$847$	21014.0			0.852479
$848$	−7248.00			−0.293511
$849$	−807.000	+	1397.77i	−0.0326221	+	0.0565031i
$850$	−1050.00	−	1818.65i	−0.0423702	−	0.0733874i
$851$	−967.500	+	1675.76i	−0.0389724	+	0.0675021i
$852$	1224.00	+	2120.03i	0.0492178	+	0.0852477i
$853$	−2215.00	−	3836.49i	−0.0889099	−	0.153996i	0.818141	−	0.575018i	$-0.195005\pi$
$853$	−2215.00	−	3836.49i	−0.0889099	−	0.153996i	−0.907051	+	0.421022i	$0.861672\pi$
$854$	3724.00			0.149219
$855$	2992.50	+	2221.36i	0.119697	+	0.0888523i
$856$	8976.00			0.358403
$857$	5232.00	+	9062.09i	0.208543	+	0.361208i	0.951256	−	0.308403i	$-0.0997944\pi$
$857$	5232.00	+	9062.09i	0.208543	+	0.361208i	−0.742712	+	0.669610i	$0.766461\pi$
$858$	−2250.00	−	3897.11i	−0.0895265	−	0.155064i
$859$	−18797.5	+	32558.2i	−0.746638	+	1.29322i	0.202787	+	0.979223i	$0.435000\pi$
$859$	−18797.5	+	32558.2i	−0.746638	+	1.29322i	−0.949425	+	0.313993i	$0.898333\pi$
$860$	3380.00	+	5854.33i	0.134020	+	0.232129i
$861$	−6070.50	+	10514.4i	−0.240281	+	0.416179i
$862$	−7260.00			−0.286864
$863$	14331.0			0.565276			0.282638	−	0.959227i	$-0.408791\pi$
$863$	14331.0			0.565276			0.282638	+	0.959227i	$0.408791\pi$
$864$	−432.000	+	748.246i	−0.0170103	+	0.0294628i
$865$	−3592.50	+	6222.39i	−0.141212	+	0.244587i
$866$	26936.0			1.05695
$867$	9447.00			0.370054
$868$	−7448.00	+	12900.3i	−0.291246	+	0.504453i
$869$	1605.00	+	2779.94i	0.0626535	+	0.108519i
$870$	−1620.00	+	2805.92i	−0.0631301	+	0.109344i
$871$	−2750.00	−	4763.14i	−0.106981	−	0.185296i
$872$	4184.00	+	7246.90i	0.162486	+	0.281435i
$873$	−468.000			−0.0181436
$874$	−5985.00	−	4442.71i	−0.231631	−	0.171942i
$875$	2375.00			0.0917596
$876$	−4560.00	−	7898.15i	−0.175877	−	0.304628i
$877$	24066.5	+	41684.4i	0.926645	+	1.60500i	0.788893	+	0.614530i	$0.210654\pi$
$877$	24066.5	+	41684.4i	0.926645	+	1.60500i	0.137752	+	0.990467i	$0.456012\pi$
$878$	−1354.00	+	2345.20i	−0.0520447	+	0.0901441i
$879$	−1822.50	−	3156.66i	−0.0699333	−	0.121128i
$880$	600.000	−	1039.23i	0.0229841	−	0.0398096i
$881$	1263.00			0.0482992			0.0241496	−	0.999708i	$-0.492312\pi$
$881$	1263.00			0.0482992			0.0241496	+	0.999708i	$0.492312\pi$
$882$	−324.000			−0.0123692
$883$	2399.00	−	4155.19i	0.0914301	−	0.158362i	−0.816683	−	0.577087i	$-0.804190\pi$
$883$	2399.00	−	4155.19i	0.0914301	−	0.158362i	0.908113	+	0.418725i	$0.137523\pi$
$884$	4200.00	−	7274.61i	0.159798	−	0.276778i
$885$	−2700.00			−0.102553
$886$	10308.0			0.390862
$887$	294.000	−	509.223i	0.0111291	−	0.0192762i	−0.860407	−	0.509607i	$-0.829791\pi$
$887$	294.000	−	509.223i	0.0111291	−	0.0192762i	0.871536	+	0.490331i	$0.163124\pi$
$888$	516.000	+	893.738i	0.0194998	+	0.0337747i
$889$	−7590.50	+	13147.1i	−0.286364	+	0.495996i
$890$	−3075.00	−	5326.06i	−0.115814	−	0.200595i
$891$	−607.500	−	1052.22i	−0.0228418	−	0.0395631i
$892$	7604.00			0.285427
$893$	18240.0	−	7898.15i	0.683514	−	0.295970i
$894$	7812.00			0.292251
$895$	2272.50	+	3936.09i	0.0848730	+	0.147004i
$896$	−1216.00	−	2106.17i	−0.0453390	−	0.0785294i
$897$	−3375.00	+	5845.67i	−0.125628	+	0.217593i
$898$	12099.0	+	20956.1i	0.449609	+	0.778746i
$899$	−10584.0	+	18332.0i	−0.392654	+	0.680097i
$900$	900.000			0.0333333
$901$	19026.0			0.703494
$902$	3195.00	−	5533.90i	0.117940	−	0.204278i
$903$	−9633.00	+	16684.8i	−0.355001	+	0.614880i
$904$	−12720.0			−0.467988
$905$	−19180.0			−0.704491
$906$	2046.00	−	3543.78i	0.0750263	−	0.129949i
$907$	12707.0	+	22009.2i	0.465192	+	0.805736i	0.999210	−	0.0397370i	$-0.0126520\pi$
$907$	12707.0	+	22009.2i	0.465192	+	0.805736i	−0.534018	+	0.845473i	$0.679319\pi$
$908$	2352.00	−	4073.78i	0.0859624	−	0.148891i
$909$	−1431.00	−	2478.56i	−0.0522148	−	0.0904387i
$910$	4750.00	+	8227.24i	0.173034	+	0.299704i
$911$	3138.00			0.114124			0.0570618	−	0.998371i	$-0.481827\pi$
$911$	3138.00			0.114124			0.0570618	+	0.998371i	$0.481827\pi$
$912$	−3648.00	+	1579.63i	−0.132453	+	0.0573539i
$913$	−2970.00			−0.107659
$914$	−1126.00	−	1950.29i	−0.0407492	−	0.0705797i
$915$	−735.000	−	1273.06i	−0.0265556	−	0.0459956i
$916$	−1036.00	+	1794.40i	−0.0373694	+	0.0647258i
$917$	2080.50	+	3603.53i	0.0749228	+	0.129770i
$918$	1134.00	−	1964.15i	0.0407708	−	0.0706171i
$919$	−35692.0			−1.28114			−0.640572	−	0.767899i	$-0.721302\pi$
$919$	−35692.0			−1.28114			−0.640572	+	0.767899i	$0.721302\pi$
$920$	−1800.00			−0.0645046
$921$	−2562.00	+	4437.51i	−0.0916621	+	0.158763i
$922$	−6642.00	+	11504.3i	−0.237248	+	0.410926i
$923$	10200.0			0.363745
$924$	3420.00			0.121764
$925$	537.500	−	930.977i	0.0191058	−	0.0330923i
$926$	7985.00	+	13830.4i	0.283373	+	0.490816i
$927$	4513.50	−	7817.61i	0.159917	−	0.276984i
$928$	−1728.00	−	2992.98i	−0.0611254	−	0.105872i
$929$	20518.5	+	35539.1i	0.724640	+	1.25511i	0.959122	+	0.282992i	$0.0913271\pi$
$929$	20518.5	+	35539.1i	0.724640	+	1.25511i	−0.234483	+	0.972120i	$0.575340\pi$
$930$	5880.00			0.207326
$931$	−1197.00	−	888.542i	−0.0421376	−	0.0312790i
$932$	−7176.00			−0.252208
$933$	−1908.00	−	3304.75i	−0.0669508	−	0.115962i
$934$	10860.0	+	18810.1i	0.380460	+	0.658977i
$935$	−1575.00	+	2727.98i	−0.0550888	+	0.0954166i
$936$	1800.00	+	3117.69i	0.0628577	+	0.108873i
$937$	−6340.00	+	10981.2i	−0.221045	+	0.382860i	−0.955125	−	0.296202i	$-0.904280\pi$
$937$	−6340.00	+	10981.2i	−0.221045	+	0.382860i	0.734081	+	0.679062i	$0.237613\pi$
$938$	4180.00			0.145503
$939$	21432.0			0.744842
$940$	2400.00	−	4156.92i	0.0832759	−	0.144238i
$941$	−8106.00	+	14040.0i	−0.280816	+	0.486388i	−0.971586	−	0.236687i	$-0.923938\pi$
$941$	−8106.00	+	14040.0i	−0.280816	+	0.486388i	0.690770	+	0.723075i	$0.257272\pi$
$942$	−15198.0			−0.525666
$943$	−9585.00			−0.330997
$944$	1440.00	−	2494.15i	0.0496483	−	0.0859934i
$945$	1282.50	+	2221.36i	0.0441479	+	0.0764663i
$946$	5070.00	−	8781.50i	0.174249	−	0.301809i
$947$	12087.0	+	20935.3i	0.414757	+	0.718380i	0.995403	−	0.0957762i	$-0.0305333\pi$
$947$	12087.0	+	20935.3i	0.414757	+	0.718380i	−0.580646	+	0.814156i	$0.697200\pi$
$948$	−1284.00	−	2223.95i	−0.0439899	−	0.0761927i
$949$	−38000.0			−1.29982
$950$	3325.00	+	2468.17i	0.113555	+	0.0842927i
$951$	−2637.00			−0.0899165
$952$	3192.00	+	5528.71i	0.108669	+	0.188221i
$953$	−22860.0	−	39594.7i	−0.777028	−	1.34585i	−0.933647	−	0.358194i	$-0.883393\pi$
$953$	−22860.0	−	39594.7i	−0.777028	−	1.34585i	0.156619	−	0.987659i	$-0.449941\pi$
$954$	−4077.00	+	7061.57i	−0.138362	+	0.239651i
$955$	−5835.00	−	10106.5i	−0.197713	−	0.342449i
$956$	7560.00	−	13094.3i	0.255761	−	0.442992i
$957$	4860.00			0.164160
$958$	28128.0			0.948616
$959$	23826.0	−	41267.8i	0.802275	−	1.38958i
$960$	−480.000	+	831.384i	−0.0161374	+	0.0279508i
$961$	8625.00			0.289517
$962$	4300.00			0.144114
$963$	5049.00	−	8745.12i	0.168953	−	0.292635i
$964$	−5116.00	−	8861.17i	−0.170929	−	0.296057i
$965$	−295.000	+	510.955i	−0.00984081	+	0.0170448i
$966$	−2565.00	−	4442.71i	−0.0854322	−	0.147973i
$967$	−7270.00	−	12592.0i	−0.241766	−	0.418750i	0.719452	−	0.694543i	$-0.244393\pi$
$967$	−7270.00	−	12592.0i	−0.241766	−	0.418750i	−0.961217	+	0.275792i	$0.911060\pi$
$968$	8848.00			0.293787
$969$	9576.00	−	4146.53i	0.317467	−	0.137467i
$970$	−520.000			−0.0172126
$971$	−14790.0	−	25617.0i	−0.488809	−	0.846642i	0.511108	−	0.859517i	$-0.329235\pi$
$971$	−14790.0	−	25617.0i	−0.488809	−	0.846642i	−0.999917	+	0.0128742i	$0.995902\pi$
$972$	486.000	+	841.777i	0.0160375	+	0.0277778i
$973$	−3458.00	+	5989.43i	−0.113935	+	0.197341i
$974$	−6415.00	−	11111.1i	−0.211037	−	0.365526i
$975$	1875.00	−	3247.60i	0.0615878	−	0.106673i
$976$	1568.00			0.0514246
$977$	23820.0			0.780010			0.390005	−	0.920813i	$-0.372473\pi$
$977$	23820.0			0.780010			0.390005	+	0.920813i	$0.372473\pi$
$978$	−10410.0	+	18030.6i	−0.340363	+	0.589526i
$979$	−4612.50	+	7989.08i	−0.150578	+	0.260809i
$980$	−360.000			−0.0117345
$981$	9414.00			0.306387
$982$	15993.0	−	27700.7i	0.519712	−	0.900168i
$983$	8686.50	+	15045.5i	0.281848	+	0.488175i	0.971840	−	0.235642i	$-0.0757194\pi$
$983$	8686.50	+	15045.5i	0.281848	+	0.488175i	−0.689992	+	0.723817i	$0.742386\pi$
$984$	−2556.00	+	4427.12i	−0.0828072	+	0.143426i
$985$	−10747.5	−	18615.2i	−0.347659	−	0.602163i
$986$	4536.00	+	7856.58i	0.146507	+	0.253757i
$987$	13680.0			0.441174
$988$	−1900.00	+	16454.5i	−0.0611812	+	0.529845i
$989$	−15210.0			−0.489029
$990$	−675.000	−	1169.13i	−0.0216696	−	0.0375329i
$991$	−23836.0	−	41285.2i	−0.764052	−	1.32338i	−0.940746	−	0.339111i	$-0.889874\pi$
$991$	−23836.0	−	41285.2i	−0.764052	−	1.32338i	0.176694	−	0.984266i	$-0.443460\pi$
$992$	−3136.00	+	5431.71i	−0.100371	+	0.173848i
$993$	8926.50	+	15461.2i	0.285271	+	0.494104i
$994$	−3876.00	+	6713.43i	−0.123681	+	0.214222i
$995$	−5230.00			−0.166635
$996$	2376.00			0.0755888
$997$	28764.5	−	49821.6i	0.913722	−	1.58261i	0.104960	−	0.994476i	$-0.466528\pi$
$997$	28764.5	−	49821.6i	0.913722	−	1.58261i	0.808762	−	0.588137i	$-0.200138\pi$
$998$	9581.00	−	16594.8i	0.303889	−	0.526351i
$999$	1161.00			0.0367692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.4.i.f.121.1	✓	2
19.11	even	3	inner	570.4.i.f.391.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.4.i.f.121.1	✓	2	1.1	even	1	trivial
570.4.i.f.391.1	yes	2	19.11	even	3	inner

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	570.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-3.00000 + 5.19615i) q^{6} -19.0000 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-3.00000 + 5.19615i) q^{6} -19.0000 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-5.00000 + 8.66025i) q^{10} +15.0000 q^{11} -12.0000 q^{12} +(-25.0000 + 43.3013i) q^{13} +(-19.0000 - 32.9090i) q^{14} +(-7.50000 + 12.9904i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(21.0000 + 36.3731i) q^{17} -18.0000 q^{18} +(-66.5000 - 49.3634i) q^{19} -20.0000 q^{20} +(-28.5000 - 49.3634i) q^{21} +(15.0000 + 25.9808i) q^{22} +(22.5000 - 38.9711i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} -100.000 q^{26} -27.0000 q^{27} +(38.0000 - 65.8179i) q^{28} +(54.0000 - 93.5307i) q^{29} -30.0000 q^{30} -196.000 q^{31} +(16.0000 - 27.7128i) q^{32} +(22.5000 + 38.9711i) q^{33} +(-42.0000 + 72.7461i) q^{34} +(-47.5000 - 82.2724i) q^{35} +(-18.0000 - 31.1769i) q^{36} -43.0000 q^{37} +(19.0000 - 164.545i) q^{38} -150.000 q^{39} +(-20.0000 - 34.6410i) q^{40} +(-106.500 - 184.463i) q^{41} +(57.0000 - 98.7269i) q^{42} +(-169.000 - 292.717i) q^{43} +(-30.0000 + 51.9615i) q^{44} -45.0000 q^{45} +90.0000 q^{46} +(-120.000 + 207.846i) q^{47} +(24.0000 - 41.5692i) q^{48} +18.0000 q^{49} -50.0000 q^{50} +(-63.0000 + 109.119i) q^{51} +(-100.000 - 173.205i) q^{52} +(226.500 - 392.310i) q^{53} +(-27.0000 - 46.7654i) q^{54} +(37.5000 + 64.9519i) q^{55} +152.000 q^{56} +(28.5000 - 246.817i) q^{57} +216.000 q^{58} +(90.0000 + 155.885i) q^{59} +(-30.0000 - 51.9615i) q^{60} +(-49.0000 + 84.8705i) q^{61} +(-196.000 - 339.482i) q^{62} +(85.5000 - 148.090i) q^{63} +64.0000 q^{64} -250.000 q^{65} +(-45.0000 + 77.9423i) q^{66} +(-55.0000 + 95.2628i) q^{67} -168.000 q^{68} +135.000 q^{69} +(95.0000 - 164.545i) q^{70} +(-102.000 - 176.669i) q^{71} +(36.0000 - 62.3538i) q^{72} +(380.000 + 658.179i) q^{73} +(-43.0000 - 74.4782i) q^{74} -75.0000 q^{75} +(304.000 - 131.636i) q^{76} -285.000 q^{77} +(-150.000 - 259.808i) q^{78} +(107.000 + 185.329i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(213.000 - 368.927i) q^{82} -198.000 q^{83} +228.000 q^{84} +(-105.000 + 181.865i) q^{85} +(338.000 - 585.433i) q^{86} +324.000 q^{87} -120.000 q^{88} +(-307.500 + 532.606i) q^{89} +(-45.0000 - 77.9423i) q^{90} +(475.000 - 822.724i) q^{91} +(90.0000 + 155.885i) q^{92} +(-294.000 - 509.223i) q^{93} -480.000 q^{94} +(47.5000 - 411.362i) q^{95} +96.0000 q^{96} +(26.0000 + 45.0333i) q^{97} +(18.0000 + 31.1769i) q^{98} +(-67.5000 + 116.913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 5 q^{5} - 6 q^{6} - 38 q^{7} - 16 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 + 5 * q^5 - 6 * q^6 - 38 * q^7 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 5 q^{5} - 6 q^{6} - 38 q^{7} - 16 q^{8} - 9 q^{9} - 10 q^{10} + 30 q^{11} - 24 q^{12} - 50 q^{13} - 38 q^{14} - 15 q^{15} - 16 q^{16} + 42 q^{17} - 36 q^{18} - 133 q^{19} - 40 q^{20} - 57 q^{21} + 30 q^{22} + 45 q^{23} - 24 q^{24} - 25 q^{25} - 200 q^{26} - 54 q^{27} + 76 q^{28} + 108 q^{29} - 60 q^{30} - 392 q^{31} + 32 q^{32} + 45 q^{33} - 84 q^{34} - 95 q^{35} - 36 q^{36} - 86 q^{37} + 38 q^{38} - 300 q^{39} - 40 q^{40} - 213 q^{41} + 114 q^{42} - 338 q^{43} - 60 q^{44} - 90 q^{45} + 180 q^{46} - 240 q^{47} + 48 q^{48} + 36 q^{49} - 100 q^{50} - 126 q^{51} - 200 q^{52} + 453 q^{53} - 54 q^{54} + 75 q^{55} + 304 q^{56} + 57 q^{57} + 432 q^{58} + 180 q^{59} - 60 q^{60} - 98 q^{61} - 392 q^{62} + 171 q^{63} + 128 q^{64} - 500 q^{65} - 90 q^{66} - 110 q^{67} - 336 q^{68} + 270 q^{69} + 190 q^{70} - 204 q^{71} + 72 q^{72} + 760 q^{73} - 86 q^{74} - 150 q^{75} + 608 q^{76} - 570 q^{77} - 300 q^{78} + 214 q^{79} + 80 q^{80} - 81 q^{81} + 426 q^{82} - 396 q^{83} + 456 q^{84} - 210 q^{85} + 676 q^{86} + 648 q^{87} - 240 q^{88} - 615 q^{89} - 90 q^{90} + 950 q^{91} + 180 q^{92} - 588 q^{93} - 960 q^{94} + 95 q^{95} + 192 q^{96} + 52 q^{97} + 36 q^{98} - 135 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 + 5 * q^5 - 6 * q^6 - 38 * q^7 - 16 * q^8 - 9 * q^9 - 10 * q^10 + 30 * q^11 - 24 * q^12 - 50 * q^13 - 38 * q^14 - 15 * q^15 - 16 * q^16 + 42 * q^17 - 36 * q^18 - 133 * q^19 - 40 * q^20 - 57 * q^21 + 30 * q^22 + 45 * q^23 - 24 * q^24 - 25 * q^25 - 200 * q^26 - 54 * q^27 + 76 * q^28 + 108 * q^29 - 60 * q^30 - 392 * q^31 + 32 * q^32 + 45 * q^33 - 84 * q^34 - 95 * q^35 - 36 * q^36 - 86 * q^37 + 38 * q^38 - 300 * q^39 - 40 * q^40 - 213 * q^41 + 114 * q^42 - 338 * q^43 - 60 * q^44 - 90 * q^45 + 180 * q^46 - 240 * q^47 + 48 * q^48 + 36 * q^49 - 100 * q^50 - 126 * q^51 - 200 * q^52 + 453 * q^53 - 54 * q^54 + 75 * q^55 + 304 * q^56 + 57 * q^57 + 432 * q^58 + 180 * q^59 - 60 * q^60 - 98 * q^61 - 392 * q^62 + 171 * q^63 + 128 * q^64 - 500 * q^65 - 90 * q^66 - 110 * q^67 - 336 * q^68 + 270 * q^69 + 190 * q^70 - 204 * q^71 + 72 * q^72 + 760 * q^73 - 86 * q^74 - 150 * q^75 + 608 * q^76 - 570 * q^77 - 300 * q^78 + 214 * q^79 + 80 * q^80 - 81 * q^81 + 426 * q^82 - 396 * q^83 + 456 * q^84 - 210 * q^85 + 676 * q^86 + 648 * q^87 - 240 * q^88 - 615 * q^89 - 90 * q^90 + 950 * q^91 + 180 * q^92 - 588 * q^93 - 960 * q^94 + 95 * q^95 + 192 * q^96 + 52 * q^97 + 36 * q^98 - 135 * q^99

Introduction

L-functions

Modular forms

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