LMFDB - Embedded newform 570.4.i.i.121.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{481})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 121x^{2} + 120x + 14400 $ x^4 - x^3 + 121x^2 + 120x + 14400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Root			$5.73293 + 9.92972i$ of defining polynomial
Character	$\chi$	$=$	570.121
Dual form			570.4.i.i.391.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-3.00000 + 5.19615i) q^{6} +12.4659 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(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} +12.4659 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-5.00000 + 8.66025i) q^{10} +34.3976 q^{11} -12.0000 q^{12} +(21.7671 - 37.7017i) q^{13} +(12.4659 + 21.5915i) q^{14} +(-7.50000 + 12.9904i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(53.3293 + 92.3690i) q^{17} -18.0000 q^{18} +(81.9939 - 11.6618i) q^{19} -20.0000 q^{20} +(18.6988 + 32.3872i) q^{21} +(34.3976 + 59.5783i) q^{22} +(3.53414 - 6.12132i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} +87.0683 q^{26} -27.0000 q^{27} +(-24.9317 + 43.1830i) q^{28} +(-93.1988 + 161.425i) q^{29} -30.0000 q^{30} +166.068 q^{31} +(16.0000 - 27.7128i) q^{32} +(51.5964 + 89.3675i) q^{33} +(-106.659 + 184.738i) q^{34} +(31.1646 + 53.9787i) q^{35} +(-18.0000 - 31.1769i) q^{36} -98.6024 q^{37} +(102.193 + 130.356i) q^{38} +130.602 q^{39} +(-20.0000 - 34.6410i) q^{40} +(-138.398 - 239.712i) q^{41} +(-37.3976 + 64.7745i) q^{42} +(47.1646 + 81.6916i) q^{43} +(-68.7951 + 119.157i) q^{44} -45.0000 q^{45} +14.1366 q^{46} +(-66.9878 + 116.026i) q^{47} +(24.0000 - 41.5692i) q^{48} -187.602 q^{49} -50.0000 q^{50} +(-159.988 + 277.107i) q^{51} +(87.0683 + 150.807i) q^{52} +(116.590 - 201.940i) q^{53} +(-27.0000 - 46.7654i) q^{54} +(85.9939 + 148.946i) q^{55} -99.7268 q^{56} +(153.289 + 195.534i) q^{57} -372.795 q^{58} +(-101.596 - 175.970i) q^{59} +(-30.0000 - 51.9615i) q^{60} +(-115.376 + 199.836i) q^{61} +(166.068 + 287.639i) q^{62} +(-56.0964 + 97.1617i) q^{63} +64.0000 q^{64} +217.671 q^{65} +(-103.193 + 178.735i) q^{66} +(16.7671 - 29.0414i) q^{67} -426.634 q^{68} +21.2049 q^{69} +(-62.3293 + 107.957i) q^{70} +(380.982 + 659.880i) q^{71} +(36.0000 - 62.3538i) q^{72} +(294.016 + 509.250i) q^{73} +(-98.6024 - 170.784i) q^{74} -75.0000 q^{75} +(-123.590 + 307.359i) q^{76} +428.795 q^{77} +(130.602 + 226.210i) q^{78} +(-678.351 - 1174.94i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(276.795 - 479.423i) q^{82} -773.020 q^{83} -149.590 q^{84} +(-266.646 + 461.845i) q^{85} +(-94.3293 + 163.383i) q^{86} -559.193 q^{87} -275.181 q^{88} +(-498.243 + 862.982i) q^{89} +(-45.0000 - 77.9423i) q^{90} +(271.345 - 469.984i) q^{91} +(14.1366 + 24.4853i) q^{92} +(249.102 + 431.458i) q^{93} -267.951 q^{94} +(255.482 + 325.890i) q^{95} +96.0000 q^{96} +(-28.7390 - 49.7774i) q^{97} +(-187.602 - 324.937i) q^{98} +(-154.789 + 268.103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} - 12 q^{6} + 6 q^{7} - 32 q^{8} - 18 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 - 12 * q^6 + 6 * q^7 - 32 * q^8 - 18 * q^9	\( 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} - 12 q^{6} + 6 q^{7} - 32 q^{8} - 18 q^{9} - 20 q^{10} + 6 q^{11} - 48 q^{12} + 109 q^{13} + 6 q^{14} - 30 q^{15} - 32 q^{16} - 6 q^{17} - 72 q^{18} - q^{19} - 80 q^{20} + 9 q^{21} + 6 q^{22} + 58 q^{23} - 48 q^{24} - 50 q^{25} + 436 q^{26} - 108 q^{27} - 12 q^{28} - 307 q^{29} - 120 q^{30} + 752 q^{31} + 64 q^{32} + 9 q^{33} + 12 q^{34} + 15 q^{35} - 72 q^{36} - 526 q^{37} + 14 q^{38} + 654 q^{39} - 80 q^{40} - 422 q^{41} - 18 q^{42} + 79 q^{43} - 12 q^{44} - 180 q^{45} + 232 q^{46} + 390 q^{47} + 96 q^{48} - 882 q^{49} - 200 q^{50} + 18 q^{51} + 436 q^{52} - 60 q^{53} - 108 q^{54} + 15 q^{55} - 48 q^{56} + 21 q^{57} - 1228 q^{58} - 209 q^{59} - 120 q^{60} - 944 q^{61} + 752 q^{62} - 27 q^{63} + 256 q^{64} + 1090 q^{65} - 18 q^{66} + 89 q^{67} + 48 q^{68} + 348 q^{69} - 30 q^{70} + 537 q^{71} + 144 q^{72} + 233 q^{73} - 526 q^{74} - 300 q^{75} + 32 q^{76} + 1452 q^{77} + 654 q^{78} - 1880 q^{79} + 160 q^{80} - 162 q^{81} + 844 q^{82} - 548 q^{83} - 72 q^{84} + 30 q^{85} - 158 q^{86} - 1842 q^{87} - 48 q^{88} - 699 q^{89} - 180 q^{90} - 77 q^{91} + 232 q^{92} + 1128 q^{93} + 1560 q^{94} + 35 q^{95} + 384 q^{96} - 422 q^{97} - 882 q^{98} - 27 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 - 12 * q^6 + 6 * q^7 - 32 * q^8 - 18 * q^9 - 20 * q^10 + 6 * q^11 - 48 * q^12 + 109 * q^13 + 6 * q^14 - 30 * q^15 - 32 * q^16 - 6 * q^17 - 72 * q^18 - q^19 - 80 * q^20 + 9 * q^21 + 6 * q^22 + 58 * q^23 - 48 * q^24 - 50 * q^25 + 436 * q^26 - 108 * q^27 - 12 * q^28 - 307 * q^29 - 120 * q^30 + 752 * q^31 + 64 * q^32 + 9 * q^33 + 12 * q^34 + 15 * q^35 - 72 * q^36 - 526 * q^37 + 14 * q^38 + 654 * q^39 - 80 * q^40 - 422 * q^41 - 18 * q^42 + 79 * q^43 - 12 * q^44 - 180 * q^45 + 232 * q^46 + 390 * q^47 + 96 * q^48 - 882 * q^49 - 200 * q^50 + 18 * q^51 + 436 * q^52 - 60 * q^53 - 108 * q^54 + 15 * q^55 - 48 * q^56 + 21 * q^57 - 1228 * q^58 - 209 * q^59 - 120 * q^60 - 944 * q^61 + 752 * q^62 - 27 * q^63 + 256 * q^64 + 1090 * q^65 - 18 * q^66 + 89 * q^67 + 48 * q^68 + 348 * q^69 - 30 * q^70 + 537 * q^71 + 144 * q^72 + 233 * q^73 - 526 * q^74 - 300 * q^75 + 32 * q^76 + 1452 * q^77 + 654 * q^78 - 1880 * q^79 + 160 * q^80 - 162 * q^81 + 844 * q^82 - 548 * q^83 - 72 * q^84 + 30 * q^85 - 158 * q^86 - 1842 * q^87 - 48 * q^88 - 699 * q^89 - 180 * q^90 - 77 * q^91 + 232 * q^92 + 1128 * q^93 + 1560 * q^94 + 35 * q^95 + 384 * q^96 - 422 * q^97 - 882 * q^98 - 27 * 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
$7$	12.4659			0.673093			0.336546	−	0.941667i	$-0.390741\pi$
$7$	12.4659			0.673093			0.336546	+	0.941667i	$0.390741\pi$
$8$	−8.00000			−0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−5.00000	+	8.66025i	−0.158114	+	0.273861i
$11$	34.3976			0.942842			0.471421	−	0.881908i	$-0.343741\pi$
$11$	34.3976			0.942842			0.471421	+	0.881908i	$0.343741\pi$
$12$	−12.0000			−0.288675
$13$	21.7671	−	37.7017i	0.464392	−	0.804351i	−0.534782	−	0.844990i	$-0.679606\pi$
$13$	21.7671	−	37.7017i	0.464392	−	0.804351i	0.999174	+	0.0406393i	$0.0129395\pi$
$14$	12.4659	+	21.5915i	0.237974	+	0.412184i
$15$	−7.50000	+	12.9904i	−0.129099	+	0.223607i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	53.3293	+	92.3690i	0.760838	+	1.31781i	0.942419	+	0.334434i	$0.108545\pi$
$17$	53.3293	+	92.3690i	0.760838	+	1.31781i	−0.181581	+	0.983376i	$0.558121\pi$
$18$	−18.0000			−0.235702
$19$	81.9939	−	11.6618i	0.990037	−	0.140810i
$19$	81.9939	−	11.6618i	0.990037	−	0.140810i
$20$	−20.0000			−0.223607
$21$	18.6988	+	32.3872i	0.194305	+	0.336546i
$22$	34.3976	+	59.5783i	0.333345	+	0.577370i
$23$	3.53414	−	6.12132i	0.0320400	−	0.0554949i	−0.849561	−	0.527491i	$-0.823133\pi$
$23$	3.53414	−	6.12132i	0.0320400	−	0.0554949i	0.881601	+	0.471996i	$0.156466\pi$
$24$	−12.0000	−	20.7846i	−0.102062	−	0.176777i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	87.0683			0.656750
$27$	−27.0000			−0.192450
$28$	−24.9317	+	43.1830i	−0.168273	+	0.291458i
$29$	−93.1988	+	161.425i	−0.596779	+	1.03365i	0.396515	+	0.918028i	$0.370220\pi$
$29$	−93.1988	+	161.425i	−0.596779	+	1.03365i	−0.993293	+	0.115622i	$0.963114\pi$
$30$	−30.0000			−0.182574
$31$	166.068			0.962153			0.481077	−	0.876679i	$-0.340246\pi$
$31$	166.068			0.962153			0.481077	+	0.876679i	$0.340246\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	51.5964	+	89.3675i	0.272175	+	0.471421i
$34$	−106.659	+	184.738i	−0.537994	+	0.931833i
$35$	31.1646	+	53.9787i	0.150508	+	0.260688i
$36$	−18.0000	−	31.1769i	−0.0833333	−	0.144338i
$37$	−98.6024			−0.438112			−0.219056	−	0.975712i	$-0.570298\pi$
$37$	−98.6024			−0.438112			−0.219056	+	0.975712i	$0.570298\pi$
$38$	102.193	+	130.356i	0.436259	+	0.556487i
$39$	130.602			0.536234
$40$	−20.0000	−	34.6410i	−0.0790569	−	0.136931i
$41$	−138.398	−	239.712i	−0.527172	−	0.913089i	−0.999499	−	0.0316655i	$-0.989919\pi$
$41$	−138.398	−	239.712i	−0.527172	−	0.913089i	0.472326	−	0.881424i	$-0.343414\pi$
$42$	−37.3976	+	64.7745i	−0.137395	+	0.237974i
$43$	47.1646	+	81.6916i	0.167268	+	0.289717i	0.937459	−	0.348097i	$-0.113172\pi$
$43$	47.1646	+	81.6916i	0.167268	+	0.289717i	−0.770190	+	0.637814i	$0.779839\pi$
$44$	−68.7951	+	119.157i	−0.235710	+	0.408262i
$45$	−45.0000			−0.149071
$46$	14.1366			0.0453114
$47$	−66.9878	+	116.026i	−0.207897	+	0.360089i	−0.951052	−	0.309031i	$-0.899995\pi$
$47$	−66.9878	+	116.026i	−0.207897	+	0.360089i	0.743155	+	0.669120i	$0.233329\pi$
$48$	24.0000	−	41.5692i	0.0721688	−	0.125000i
$49$	−187.602			−0.546946
$50$	−50.0000			−0.141421
$51$	−159.988	+	277.107i	−0.439270	+	0.760838i
$52$	87.0683	+	150.807i	0.232196	+	0.402176i
$53$	116.590	−	201.940i	0.302168	−	0.523370i	−0.674459	−	0.738313i	$-0.735623\pi$
$53$	116.590	−	201.940i	0.302168	−	0.523370i	0.976627	+	0.214942i	$0.0689563\pi$
$54$	−27.0000	−	46.7654i	−0.0680414	−	0.117851i
$55$	85.9939	+	148.946i	0.210826	+	0.365161i
$56$	−99.7268			−0.237974
$57$	153.289	+	195.534i	0.356204	+	0.454370i
$58$	−372.795			−0.843972
$59$	−101.596	−	175.970i	−0.224182	−	0.388294i	0.731892	−	0.681421i	$-0.238638\pi$
$59$	−101.596	−	175.970i	−0.224182	−	0.388294i	−0.956074	+	0.293127i	$0.905304\pi$
$60$	−30.0000	−	51.9615i	−0.0645497	−	0.111803i
$61$	−115.376	+	199.836i	−0.242169	+	0.419450i	−0.961332	−	0.275392i	$-0.911192\pi$
$61$	−115.376	+	199.836i	−0.242169	+	0.419450i	0.719163	+	0.694842i	$0.244526\pi$
$62$	166.068	+	287.639i	0.340172	+	0.589196i
$63$	−56.0964	+	97.1617i	−0.112182	+	0.194305i
$64$	64.0000			0.125000
$65$	217.671			0.415365
$66$	−103.193	+	178.735i	−0.192457	+	0.333345i
$67$	16.7671	−	29.0414i	0.0305735	−	0.0529548i	−0.850334	−	0.526244i	$-0.823600\pi$
$67$	16.7671	−	29.0414i	0.0305735	−	0.0529548i	0.880907	+	0.473289i	$0.156933\pi$
$68$	−426.634			−0.760838
$69$	21.2049			0.0369966
$70$	−62.3293	+	107.957i	−0.106425	+	0.184334i
$71$	380.982	+	659.880i	0.636820	+	1.10300i	0.986126	+	0.165996i	$0.0530839\pi$
$71$	380.982	+	659.880i	0.636820	+	1.10300i	−0.349306	+	0.937009i	$0.613583\pi$
$72$	36.0000	−	62.3538i	0.0589256	−	0.102062i
$73$	294.016	+	509.250i	0.471397	+	0.816483i	0.999465	−	0.0327191i	$-0.0104167\pi$
$73$	294.016	+	509.250i	0.471397	+	0.816483i	−0.528068	+	0.849202i	$0.677083\pi$
$74$	−98.6024	−	170.784i	−0.154896	−	0.268288i
$75$	−75.0000			−0.115470
$76$	−123.590	+	307.359i	−0.186537	+	0.463901i
$77$	428.795			0.634620
$78$	130.602	+	226.210i	0.189587	+	0.328375i
$79$	−678.351	−	1174.94i	−0.966082	−	1.67330i	−0.706679	−	0.707534i	$-0.749808\pi$
$79$	−678.351	−	1174.94i	−0.966082	−	1.67330i	−0.259403	−	0.965769i	$-0.583526\pi$
$80$	40.0000	−	69.2820i	0.0559017	−	0.0968246i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	276.795	−	479.423i	0.372767	−	0.645652i
$83$	−773.020			−1.02229			−0.511144	−	0.859495i	$-0.670778\pi$
$83$	−773.020			−1.02229			−0.511144	+	0.859495i	$0.670778\pi$
$84$	−149.590			−0.194305
$85$	−266.646	+	461.845i	−0.340257	+	0.589343i
$86$	−94.3293	+	163.383i	−0.118277	+	0.204861i
$87$	−559.193			−0.689101
$88$	−275.181			−0.333345
$89$	−498.243	+	862.982i	−0.593412	+	1.02782i	0.400357	+	0.916359i	$0.368886\pi$
$89$	−498.243	+	862.982i	−0.593412	+	1.02782i	−0.993769	+	0.111460i	$0.964447\pi$
$90$	−45.0000	−	77.9423i	−0.0527046	−	0.0912871i
$91$	271.345	−	469.984i	0.312579	−	0.541403i
$92$	14.1366	+	24.4853i	0.0160200	+	0.0277475i
$93$	249.102	+	431.458i	0.277750	+	0.481077i
$94$	−267.951			−0.294011
$95$	255.482	+	325.890i	0.275914	+	0.351953i
$96$	96.0000			0.102062
$97$	−28.7390	−	49.7774i	−0.0300825	−	0.0521044i	0.850592	−	0.525826i	$-0.176244\pi$
$97$	−28.7390	−	49.7774i	−0.0300825	−	0.0521044i	−0.880675	+	0.473721i	$0.842910\pi$
$98$	−187.602	−	324.937i	−0.193375	−	0.334935i
$99$	−154.789	+	268.103i	−0.157140	+	0.272175i
$100$	−50.0000	−	86.6025i	−0.0500000	−	0.0866025i
$101$	−198.448	+	343.721i	−0.195508	+	0.338629i	−0.947067	−	0.321036i	$-0.895969\pi$
$101$	−198.448	+	343.721i	−0.195508	+	0.338629i	0.751559	+	0.659666i	$0.229302\pi$
$102$	−639.951			−0.621222
$103$	477.583			0.456870			0.228435	−	0.973559i	$-0.426639\pi$
$103$	477.583			0.456870			0.228435	+	0.973559i	$0.426639\pi$
$104$	−174.137	+	301.613i	−0.164187	+	0.284381i
$105$	−93.4939	+	161.936i	−0.0868959	+	0.150508i
$106$	466.361			0.427330
$107$	258.200			0.233282			0.116641	−	0.993174i	$-0.462787\pi$
$107$	258.200			0.233282			0.116641	+	0.993174i	$0.462787\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	−130.982	−	226.867i	−0.115099	−	0.199357i	0.802720	−	0.596356i	$-0.203385\pi$
$109$	−130.982	−	226.867i	−0.115099	−	0.199357i	−0.917819	+	0.396998i	$0.870052\pi$
$110$	−171.988	+	297.892i	−0.149076	+	0.258208i
$111$	−147.904	−	256.177i	−0.126472	−	0.219056i
$112$	−99.7268	−	172.732i	−0.0841366	−	0.145729i
$113$	−186.707			−0.155433			−0.0777165	−	0.996975i	$-0.524763\pi$
$113$	−186.707			−0.155433			−0.0777165	+	0.996975i	$0.524763\pi$
$114$	−185.385	+	461.038i	−0.152306	+	0.378774i
$115$	35.3414			0.0286574
$116$	−372.795	−	645.700i	−0.298389	−	0.516825i
$117$	195.904	+	339.315i	0.154797	+	0.268117i
$118$	203.193	−	351.940i	0.158520	−	0.274565i
$119$	664.795	+	1151.46i	0.512115	+	0.887009i
$120$	60.0000	−	103.923i	0.0456435	−	0.0790569i
$121$	−147.807			−0.111050
$122$	−461.502			−0.342479
$123$	415.193	−	719.135i	0.304363	−	0.527172i
$124$	−332.137	+	575.277i	−0.240538	+	0.416624i
$125$	−125.000			−0.0894427
$126$	−224.385			−0.158650
$127$	424.088	−	734.542i	0.296313	−	0.513229i	−0.678977	−	0.734160i	$-0.737576\pi$
$127$	424.088	−	734.542i	0.296313	−	0.513229i	0.975289	+	0.220931i	$0.0709096\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	−141.494	+	245.075i	−0.0965724	+	0.167268i
$130$	217.671	+	377.017i	0.146854	+	0.254358i
$131$	642.256	+	1112.42i	0.428353	+	0.741929i	0.996727	−	0.0808416i	$-0.0257608\pi$
$131$	642.256	+	1112.42i	0.428353	+	0.741929i	−0.568374	+	0.822770i	$0.692427\pi$
$132$	−412.771			−0.272175
$133$	1022.12	−	145.374i	0.666387	−	0.0947784i
$134$	67.0683			0.0432374
$135$	−67.5000	−	116.913i	−0.0430331	−	0.0745356i
$136$	−426.634	−	738.952i	−0.268997	−	0.465916i
$137$	1458.95	−	2526.98i	0.909829	−	1.57587i	0.0955293	−	0.995427i	$-0.469546\pi$
$137$	1458.95	−	2526.98i	0.909829	−	1.57587i	0.814300	−	0.580444i	$-0.197121\pi$
$138$	21.2049	+	36.7279i	0.0130803	+	0.0226557i
$139$	228.326	−	395.471i	0.139326	−	0.241320i	−0.787916	−	0.615783i	$-0.788840\pi$
$139$	228.326	−	395.471i	0.139326	−	0.241320i	0.927242	+	0.374463i	$0.122173\pi$
$140$	−249.317			−0.150508
$141$	−401.927			−0.240059
$142$	−761.964	+	1319.76i	−0.450300	+	0.779942i
$143$	748.734	−	1296.85i	0.437848	−	0.758376i
$144$	144.000			0.0833333
$145$	−931.988			−0.533775
$146$	−588.032	+	1018.50i	−0.333328	+	0.577341i
$147$	−281.404	−	487.405i	−0.157890	−	0.273473i
$148$	197.205	−	341.569i	0.109528	−	0.189708i
$149$	145.335	+	251.728i	0.0799083	+	0.138405i	0.903210	−	0.429198i	$-0.141204\pi$
$149$	145.335	+	251.728i	0.0799083	+	0.138405i	−0.823302	+	0.567604i	$0.807871\pi$
$150$	−75.0000	−	129.904i	−0.0408248	−	0.0707107i
$151$	688.261			0.370926			0.185463	−	0.982651i	$-0.440621\pi$
$151$	688.261			0.370926			0.185463	+	0.982651i	$0.440621\pi$
$152$	−655.951	+	93.2942i	−0.350031	+	0.0497839i
$153$	−959.927			−0.507226
$154$	428.795	+	742.695i	0.224372	+	0.388624i
$155$	415.171	+	719.097i	0.215144	+	0.372640i
$156$	−261.205	+	452.420i	−0.134059	+	0.232196i
$157$	150.767	+	261.136i	0.0766403	+	0.132745i	0.901798	−	0.432157i	$-0.142247\pi$
$157$	150.767	+	261.136i	0.0766403	+	0.132745i	−0.825158	+	0.564902i	$0.808914\pi$
$158$	1356.70	−	2349.88i	0.683123	−	1.18320i
$159$	699.542			0.348914
$160$	160.000			0.0790569
$161$	44.0561	−	76.3075i	0.0215659	−	0.0373532i
$162$	81.0000	−	140.296i	0.0392837	−	0.0680414i
$163$	−2798.55			−1.34478			−0.672392	−	0.740196i	$-0.734733\pi$
$163$	−2798.55			−1.34478			−0.672392	+	0.740196i	$0.734733\pi$
$164$	1107.18			0.527172
$165$	−257.982	+	446.838i	−0.121720	+	0.210826i
$166$	−773.020	−	1338.91i	−0.361434	−	0.626021i
$167$	−285.193	+	493.968i	−0.132149	+	0.228889i	−0.924505	−	0.381171i	$-0.875521\pi$
$167$	−285.193	+	493.968i	−0.132149	+	0.228889i	0.792356	+	0.610059i	$0.208854\pi$
$168$	−149.590	−	259.098i	−0.0686973	−	0.118987i
$169$	150.889	+	261.348i	0.0686796	+	0.118957i
$170$	−1066.59			−0.481196
$171$	−278.078	+	691.557i	−0.124358	+	0.309267i
$172$	−377.317			−0.167268
$173$	298.671	+	517.313i	0.131257	+	0.227344i	0.924161	−	0.382002i	$-0.124765\pi$
$173$	298.671	+	517.313i	0.131257	+	0.227344i	−0.792904	+	0.609346i	$0.791432\pi$
$174$	−559.193	−	968.550i	−0.243634	−	0.421986i
$175$	−155.823	+	269.894i	−0.0673093	+	0.116583i
$176$	−275.181	−	476.627i	−0.117855	−	0.204131i
$177$	304.789	−	527.910i	0.129431	−	0.224182i
$178$	−1992.97			−0.839211
$179$	−643.129			−0.268546			−0.134273	−	0.990944i	$-0.542870\pi$
$179$	−643.129			−0.268546			−0.134273	+	0.990944i	$0.542870\pi$
$180$	90.0000	−	155.885i	0.0372678	−	0.0645497i
$181$	−221.434	+	383.535i	−0.0909340	+	0.157502i	−0.907904	−	0.419177i	$-0.862319\pi$
$181$	−221.434	+	383.535i	−0.0909340	+	0.157502i	0.816970	+	0.576680i	$0.195652\pi$
$182$	1085.38			0.442054
$183$	−692.253			−0.279633
$184$	−28.2732	+	48.9705i	−0.0113278	+	0.0196204i
$185$	−246.506	−	426.961i	−0.0979648	−	0.169680i
$186$	−498.205	+	862.916i	−0.196399	+	0.340172i
$187$	1834.40	+	3177.27i	0.717350	+	1.24249i
$188$	−267.951	−	464.105i	−0.103949	−	0.180044i
$189$	−336.578			−0.129537
$190$	−308.976	+	768.397i	−0.117976	+	0.293397i
$191$	4222.56			1.59965			0.799827	−	0.600230i	$-0.204924\pi$
$191$	4222.56			1.59965			0.799827	+	0.600230i	$0.204924\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	−1363.67	−	2361.95i	−0.508596	−	0.880915i	−0.999950	−	0.00995485i	$-0.996831\pi$
$193$	−1363.67	−	2361.95i	−0.508596	−	0.880915i	0.491354	−	0.870960i	$-0.336502\pi$
$194$	57.4780	−	99.5548i	0.0212716	−	0.0368434i
$195$	326.506	+	565.525i	0.119906	+	0.207683i
$196$	375.205	−	649.874i	0.136736	−	0.236835i
$197$	3677.00			1.32982			0.664912	−	0.746921i	$-0.268469\pi$
$197$	3677.00			1.32982			0.664912	+	0.746921i	$0.268469\pi$
$198$	−619.156			−0.222230
$199$	−239.395	+	414.645i	−0.0852778	+	0.147705i	−0.905510	−	0.424326i	$-0.860511\pi$
$199$	−239.395	+	414.645i	−0.0852778	+	0.147705i	0.820232	+	0.572031i	$0.193844\pi$
$200$	100.000	−	173.205i	0.0353553	−	0.0612372i
$201$	100.602			0.0353032
$202$	−793.790			−0.276490
$203$	−1161.80	+	2012.30i	−0.401687	+	0.695743i
$204$	−639.951	−	1108.43i	−0.219635	−	0.380419i
$205$	691.988	−	1198.56i	0.235759	−	0.408346i
$206$	477.583	+	827.198i	0.161528	+	0.279775i
$207$	31.8073	+	55.0919i	0.0106800	+	0.0184983i
$208$	−696.546			−0.232196
$209$	2820.39	−	401.137i	0.933448	−	0.132762i
$210$	−373.976			−0.122889
$211$	−1445.67	−	2503.97i	−0.471677	−	0.816969i	0.527798	−	0.849370i	$-0.323018\pi$
$211$	−1445.67	−	2503.97i	−0.471677	−	0.816969i	−0.999475	+	0.0324011i	$0.989685\pi$
$212$	466.361	+	807.761i	0.151084	+	0.261685i
$213$	−1142.95	+	1979.64i	−0.367668	+	0.636820i
$214$	258.200	+	447.216i	0.0824776	+	0.142855i
$215$	−235.823	+	408.458i	−0.0748047	+	0.129566i
$216$	216.000			0.0680414
$217$	2070.18			0.647618
$218$	261.964	−	453.734i	0.0813872	−	0.140967i
$219$	−882.048	+	1527.75i	−0.272161	+	0.471397i
$220$	−687.951			−0.210826
$221$	4643.29			1.41331
$222$	295.807	−	512.353i	0.0894292	−	0.154896i
$223$	−2137.42	−	3702.11i	−0.641847	−	1.11171i	−0.985020	−	0.172440i	$-0.944835\pi$
$223$	−2137.42	−	3702.11i	−0.641847	−	1.11171i	0.343173	−	0.939272i	$-0.388498\pi$
$224$	199.454	−	345.464i	0.0594936	−	0.103046i
$225$	−112.500	−	194.856i	−0.0333333	−	0.0577350i
$226$	−186.707	−	323.386i	−0.0549539	−	0.0951829i
$227$	3667.25			1.07226			0.536132	−	0.844134i	$-0.319885\pi$
$227$	3667.25			1.07226			0.536132	+	0.844134i	$0.319885\pi$
$228$	−983.927	+	139.941i	−0.285799	+	0.0406484i
$229$	220.630			0.0636664			0.0318332	−	0.999493i	$-0.489865\pi$
$229$	220.630			0.0636664			0.0318332	+	0.999493i	$0.489865\pi$
$230$	35.3414	+	61.2132i	0.0101319	+	0.0175490i
$231$	643.193	+	1114.04i	0.183199	+	0.317310i
$232$	745.590	−	1291.40i	0.210993	−	0.365451i
$233$	472.442	+	818.293i	0.132836	+	0.230078i	0.924769	−	0.380530i	$-0.124258\pi$
$233$	472.442	+	818.293i	0.132836	+	0.230078i	−0.791933	+	0.610608i	$0.790925\pi$
$234$	−391.807	+	678.630i	−0.109458	+	0.189587i
$235$	−669.878			−0.185949
$236$	812.771			0.224182
$237$	2035.05	−	3524.82i	0.557768	−	0.966082i
$238$	−1329.59	+	2302.92i	−0.362120	+	0.627210i
$239$	5260.94			1.42386			0.711929	−	0.702251i	$-0.247822\pi$
$239$	5260.94			1.42386			0.711929	+	0.702251i	$0.247822\pi$
$240$	240.000			0.0645497
$241$	2764.58	−	4788.40i	0.738931	−	1.27987i	−0.214045	−	0.976824i	$-0.568664\pi$
$241$	2764.58	−	4788.40i	0.738931	−	1.27987i	0.952977	−	0.303043i	$-0.0980026\pi$
$242$	−147.807	−	256.010i	−0.0392620	−	0.0680038i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−461.502	−	799.345i	−0.121085	−	0.209725i
$245$	−469.006	−	812.342i	−0.122301	−	0.211831i
$246$	1660.77			0.430434
$247$	1345.10	−	3345.15i	0.346505	−	0.861728i
$248$	−1328.55			−0.340172
$249$	−1159.53	−	2008.36i	−0.295109	−	0.511144i
$250$	−125.000	−	216.506i	−0.0316228	−	0.0547723i
$251$	−415.628	+	719.889i	−0.104519	+	0.181032i	−0.913542	−	0.406746i	$-0.866664\pi$
$251$	−415.628	+	719.889i	−0.104519	+	0.181032i	0.809023	+	0.587777i	$0.199997\pi$
$252$	−224.385	−	388.647i	−0.0560911	−	0.0971526i
$253$	121.566	−	210.558i	0.0302086	−	0.0523229i
$254$	1696.35			0.419050
$255$	−1599.88			−0.392895
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	130.293	−	225.674i	0.0316243	−	0.0547749i	−0.849780	−	0.527137i	$-0.823265\pi$
$257$	130.293	−	225.674i	0.0316243	−	0.0547749i	0.881404	+	0.472362i	$0.156599\pi$
$258$	−565.976			−0.136574
$259$	−1229.16			−0.294890
$260$	−435.341	+	754.033i	−0.103841	+	0.179858i
$261$	−838.789	−	1452.83i	−0.198926	−	0.344550i
$262$	−1284.51	+	2224.84i	−0.302891	+	0.524623i
$263$	−2881.85	−	4991.50i	−0.675674	−	1.17030i	−0.976271	−	0.216551i	$-0.930519\pi$
$263$	−2881.85	−	4991.50i	−0.675674	−	1.17030i	0.300597	−	0.953751i	$-0.402814\pi$
$264$	−412.771	−	714.940i	−0.0962284	−	0.166672i
$265$	1165.90			0.270267
$266$	1273.92	+	1625.00i	0.293643	+	0.374568i
$267$	−2989.46			−0.685213
$268$	67.0683	+	116.166i	0.0152867	+	0.0264774i
$269$	323.985	+	561.158i	0.0734338	+	0.127191i	0.900404	−	0.435055i	$-0.143271\pi$
$269$	323.985	+	561.158i	0.0734338	+	0.127191i	−0.826970	+	0.562246i	$0.809938\pi$
$270$	135.000	−	233.827i	0.0304290	−	0.0527046i
$271$	2048.90	+	3548.80i	0.459269	+	0.795477i	0.998922	−	0.0464100i	$-0.0147781\pi$
$271$	2048.90	+	3548.80i	0.459269	+	0.795477i	−0.539654	+	0.841887i	$0.681445\pi$
$272$	853.268	−	1477.90i	0.190210	−	0.329453i
$273$	1628.07			0.360935
$274$	5835.81			1.28669
$275$	−429.970	+	744.729i	−0.0942842	+	0.163305i
$276$	−42.4097	+	73.4558i	−0.00924915	+	0.0160200i
$277$	−3141.96			−0.681523			−0.340762	−	0.940150i	$-0.610685\pi$
$277$	−3141.96			−0.681523			−0.340762	+	0.940150i	$0.610685\pi$
$278$	913.302			0.197037
$279$	−747.307	+	1294.37i	−0.160359	+	0.277750i
$280$	−249.317	−	431.830i	−0.0532127	−	0.0921670i
$281$	2404.10	−	4164.02i	0.510379	−	0.884002i	−0.489549	−	0.871976i	$-0.662838\pi$
$281$	2404.10	−	4164.02i	0.510379	−	0.884002i	0.999928	−	0.0120263i	$-0.00382818\pi$
$282$	−401.927	−	696.158i	−0.0848738	−	0.147006i
$283$	−2941.00	−	5093.96i	−0.617753	−	1.06998i	−0.989895	−	0.141804i	$-0.954710\pi$
$283$	−2941.00	−	5093.96i	−0.617753	−	1.06998i	0.372141	−	0.928176i	$-0.378624\pi$
$284$	−3047.85			−0.636820
$285$	−463.464	+	1152.60i	−0.0963271	+	0.239557i
$286$	2994.94			0.619211
$287$	−1725.24	−	2988.21i	−0.354836	−	0.614594i
$288$	144.000	+	249.415i	0.0294628	+	0.0510310i
$289$	−3231.52	+	5597.16i	−0.657750	+	1.13926i
$290$	−931.988	−	1614.25i	−0.188718	−	0.326869i
$291$	86.2170	−	149.332i	0.0173681	−	0.0300825i
$292$	−2352.13			−0.471397
$293$	2778.15			0.553930			0.276965	−	0.960880i	$-0.410671\pi$
$293$	2778.15			0.553930			0.276965	+	0.960880i	$0.410671\pi$
$294$	562.807	−	974.811i	0.111645	−	0.193375i
$295$	507.982	−	879.850i	0.100257	−	0.173650i
$296$	788.819			0.154896
$297$	−928.734			−0.181450
$298$	−290.671	+	503.456i	−0.0565037	+	0.0978673i
$299$	−153.856	−	266.486i	−0.0297583	−	0.0515428i
$300$	150.000	−	259.808i	0.0288675	−	0.0500000i
$301$	587.948	+	1018.36i	0.112587	+	0.195007i
$302$	688.261	+	1192.10i	0.131142	+	0.227145i
$303$	−1190.69			−0.225753
$304$	−817.542	−	1042.85i	−0.154241	−	0.196748i
$305$	−1153.76			−0.216603
$306$	−959.927	−	1662.64i	−0.179331	−	0.310611i
$307$	1232.43	+	2134.64i	0.229116	+	0.396841i	0.957546	−	0.288279i	$-0.0930830\pi$
$307$	1232.43	+	2134.64i	0.229116	+	0.396841i	−0.728430	+	0.685120i	$0.759750\pi$
$308$	−857.590	+	1485.39i	−0.158655	+	0.274799i
$309$	716.374	+	1240.80i	0.131887	+	0.228435i
$310$	−830.341	+	1438.19i	−0.152130	+	0.263496i
$311$	6131.69			1.11799			0.558997	−	0.829170i	$-0.311186\pi$
$311$	6131.69			1.11799			0.558997	+	0.829170i	$0.311186\pi$
$312$	−1044.82			−0.189587
$313$	3618.14	−	6266.81i	0.653385	−	1.13170i	−0.328911	−	0.944361i	$-0.606682\pi$
$313$	3618.14	−	6266.81i	0.653385	−	1.13170i	0.982296	−	0.187335i	$-0.0599851\pi$
$314$	−301.534	+	522.272i	−0.0541929	+	0.0938648i
$315$	−560.964			−0.100339
$316$	5426.81			0.966082
$317$	5110.65	−	8851.90i	0.905497	−	1.56837i	0.0852484	−	0.996360i	$-0.472832\pi$
$317$	5110.65	−	8851.90i	0.905497	−	1.56837i	0.820249	−	0.572007i	$-0.193835\pi$
$318$	699.542	+	1211.64i	0.123360	+	0.213665i
$319$	−3205.81	+	5552.63i	−0.562668	+	0.974569i
$320$	160.000	+	277.128i	0.0279508	+	0.0484123i
$321$	387.300	+	670.824i	0.0673427	+	0.116641i
$322$	176.225			0.0304988
$323$	5449.86	+	6951.78i	0.938819	+	1.19755i
$324$	324.000			0.0555556
$325$	544.177	+	942.542i	0.0928785	+	0.160870i
$326$	−2798.55	−	4847.24i	−0.475453	−	0.823508i
$327$	392.945	−	680.601i	0.0664524	−	0.115099i
$328$	1107.18	+	1917.69i	0.186384	+	0.322826i
$329$	−835.061	+	1446.37i	−0.139934	+	0.242373i
$330$	−1031.93			−0.172139
$331$	−1291.51			−0.214465			−0.107233	−	0.994234i	$-0.534199\pi$
$331$	−1291.51			−0.214465			−0.107233	+	0.994234i	$0.534199\pi$
$332$	1546.04	−	2677.82i	0.255572	−	0.442664i
$333$	443.711	−	768.530i	0.0730186	−	0.126472i
$334$	−1140.77			−0.186887
$335$	167.671			0.0273458
$336$	299.181	−	518.196i	0.0485763	−	0.0841366i
$337$	−1822.82	−	3157.21i	−0.294644	−	0.510339i	0.680258	−	0.732973i	$-0.261868\pi$
$337$	−1822.82	−	3157.21i	−0.294644	−	0.510339i	−0.974902	+	0.222634i	$0.928534\pi$
$338$	−301.778	+	522.695i	−0.0485638	+	0.0841150i
$339$	−280.061	−	485.080i	−0.0448697	−	0.0777165i
$340$	−1066.59	−	1847.38i	−0.170129	−	0.294671i
$341$	5712.35			0.907158
$342$	−1475.89	+	209.912i	−0.233354	+	0.0331893i
$343$	−6614.41			−1.04124
$344$	−377.317	−	653.532i	−0.0591383	−	0.102431i
$345$	53.0122	+	91.8198i	0.00827269	+	0.0143287i
$346$	−597.341	+	1034.63i	−0.0928129	+	0.160757i
$347$	1760.99	+	3050.13i	0.272435	+	0.471871i	0.969485	−	0.245152i	$-0.0788377\pi$
$347$	1760.99	+	3050.13i	0.272435	+	0.471871i	−0.697050	+	0.717023i	$0.745504\pi$
$348$	1118.39	−	1937.10i	0.172275	−	0.298389i
$349$	−1097.09			−0.168269			−0.0841346	−	0.996454i	$-0.526813\pi$
$349$	−1097.09			−0.168269			−0.0841346	+	0.996454i	$0.526813\pi$
$350$	−623.293			−0.0951897
$351$	−587.711	+	1017.95i	−0.0893723	+	0.154797i
$352$	550.361	−	953.253i	0.0833362	−	0.144343i
$353$	−5183.15			−0.781505			−0.390753	−	0.920496i	$-0.627785\pi$
$353$	−5183.15			−0.781505			−0.390753	+	0.920496i	$0.627785\pi$
$354$	1219.16			0.183044
$355$	−1904.91	+	3299.40i	−0.284795	+	0.493279i
$356$	−1992.97	−	3451.93i	−0.296706	−	0.513909i
$357$	−1994.39	+	3454.38i	−0.295670	+	0.512115i
$358$	−643.129	−	1113.93i	−0.0949453	−	0.164450i
$359$	−6088.69	−	10545.9i	−0.895122	−	1.55040i	−0.833654	−	0.552287i	$-0.813755\pi$
$359$	−6088.69	−	10545.9i	−0.895122	−	1.55040i	−0.0614678	−	0.998109i	$-0.519578\pi$
$360$	360.000			0.0527046
$361$	6587.01	−	1912.39i	0.960345	−	0.278815i
$362$	−885.736			−0.128600
$363$	−221.711	−	384.015i	−0.0320573	−	0.0555249i
$364$	1085.38	+	1879.93i	0.156290	+	0.270702i
$365$	−1470.08	+	2546.25i	−0.210815	+	0.365142i
$366$	−692.253	−	1199.02i	−0.0988652	−	0.171240i
$367$	−1905.35	+	3300.16i	−0.271004	+	0.469393i	−0.969119	−	0.246593i	$-0.920689\pi$
$367$	−1905.35	+	3300.16i	−0.271004	+	0.469393i	0.698115	+	0.715986i	$0.254022\pi$
$368$	−113.093			−0.0160200
$369$	2491.16			0.351448
$370$	493.012	−	853.922i	0.0692716	−	0.119982i
$371$	1453.40	−	2517.36i	0.203387	−	0.352277i
$372$	−1992.82			−0.277750
$373$	−1177.41			−0.163442			−0.0817212	−	0.996655i	$-0.526042\pi$
$373$	−1177.41			−0.163442			−0.0817212	+	0.996655i	$0.526042\pi$
$374$	−3668.80	+	6354.54i	−0.507243	+	0.878571i
$375$	−187.500	−	324.760i	−0.0258199	−	0.0447214i
$376$	535.903	−	928.211i	0.0735029	−	0.127311i
$377$	4057.33	+	7027.50i	0.554279	+	0.960039i
$378$	−336.578	−	582.970i	−0.0457982	−	0.0793248i
$379$	−4069.18			−0.551503			−0.275752	−	0.961229i	$-0.588927\pi$
$379$	−4069.18			−0.551503			−0.275752	+	0.961229i	$0.588927\pi$
$380$	−1639.88	+	233.235i	−0.221379	+	0.0314861i
$381$	2544.53			0.342152
$382$	4222.56	+	7313.70i	0.565563	+	0.979584i
$383$	−2657.55	−	4603.02i	−0.354555	−	0.614108i	0.632487	−	0.774571i	$-0.282034\pi$
$383$	−2657.55	−	4603.02i	−0.354555	−	0.614108i	−0.987042	+	0.160464i	$0.948701\pi$
$384$	−192.000	+	332.554i	−0.0255155	+	0.0441942i
$385$	1071.99	+	1856.74i	0.141905	+	0.245787i
$386$	2727.34	−	4723.89i	0.359632	−	0.622901i
$387$	−848.964			−0.111512
$388$	229.912			0.0300825
$389$	1690.88	−	2928.70i	0.220389	−	0.381725i	−0.734537	−	0.678568i	$-0.762601\pi$
$389$	1690.88	−	2928.70i	0.220389	−	0.381725i	0.954926	+	0.296844i	$0.0959341\pi$
$390$	−653.012	+	1131.05i	−0.0847860	+	0.146854i
$391$	753.893			0.0975090
$392$	1500.82			0.193375
$393$	−1926.77	+	3337.26i	−0.247310	+	0.428353i
$394$	3677.00	+	6368.75i	0.470164	+	0.814348i
$395$	3391.76	−	5874.69i	0.432045	−	0.748324i
$396$	−619.156	−	1072.41i	−0.0785701	−	0.136087i
$397$	−5757.47	−	9972.23i	−0.727857	−	1.26069i	−0.957787	−	0.287478i	$-0.907183\pi$
$397$	−5757.47	−	9972.23i	−0.727857	−	1.26069i	0.229930	−	0.973207i	$-0.426150\pi$
$398$	−957.581			−0.120601
$399$	1910.88	+	2437.50i	0.239758	+	0.305833i
$400$	400.000			0.0500000
$401$	4013.61	+	6951.77i	0.499826	+	0.865723i	1.00000		0.000201429i	$-6.41169e-5\pi$
$401$	4013.61	+	6951.77i	0.499826	+	0.865723i	−0.500174	+	0.865925i	$0.666731\pi$
$402$	100.602	+	174.249i	0.0124816	+	0.0216187i
$403$	3614.82	−	6261.05i	0.446816	−	0.773909i
$404$	−793.790	−	1374.89i	−0.0977538	−	0.169315i
$405$	202.500	−	350.740i	0.0248452	−	0.0430331i
$406$	−4647.21			−0.568072
$407$	−3391.68			−0.413070
$408$	1279.90	−	2216.86i	0.155305	−	0.268997i
$409$	4696.46	−	8134.51i	0.567788	−	0.983437i	−0.428997	−	0.903306i	$-0.641133\pi$
$409$	4696.46	−	8134.51i	0.567788	−	0.983437i	0.996784	−	0.0801309i	$-0.0255338\pi$
$410$	2767.95			0.333413
$411$	8753.71			1.05058
$412$	−955.166	+	1654.40i	−0.114218	+	0.197831i
$413$	−1266.49	−	2193.62i	−0.150895	−	0.261358i
$414$	−63.6146	+	110.184i	−0.00755190	+	0.0130803i
$415$	−1932.55	−	3347.27i	−0.228591	−	0.395931i
$416$	−696.546	−	1206.45i	−0.0820937	−	0.142191i
$417$	1369.95			0.160880
$418$	3515.18	+	4483.92i	0.411323	+	0.524679i
$419$	−13226.2			−1.54211			−0.771054	−	0.636770i	$-0.780270\pi$
$419$	−13226.2			−1.54211			−0.771054	+	0.636770i	$0.780270\pi$
$420$	−373.976	−	647.745i	−0.0434480	−	0.0752541i
$421$	964.469	+	1670.51i	0.111652	+	0.193386i	0.916436	−	0.400181i	$-0.131053\pi$
$421$	964.469	+	1670.51i	0.111652	+	0.193386i	−0.804785	+	0.593567i	$0.797719\pi$
$422$	2891.34	−	5007.94i	0.333526	−	0.577684i
$423$	−602.891	−	1044.24i	−0.0692992	−	0.120030i
$424$	−932.722	+	1615.52i	−0.106833	+	0.185039i
$425$	−2666.46			−0.304335
$426$	−4571.78			−0.519961
$427$	−1438.26	+	2491.13i	−0.163002	+	0.282329i
$428$	−516.400	+	894.432i	−0.0583205	+	0.101014i
$429$	4492.41			0.505584
$430$	−943.293			−0.105790
$431$	−7613.24	+	13186.5i	−0.850851	+	1.47372i	0.0295902	+	0.999562i	$0.490580\pi$
$431$	−7613.24	+	13186.5i	−0.850851	+	1.47372i	−0.880441	+	0.474155i	$0.842754\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	−8092.22	+	14016.1i	−0.898123	+	1.55560i	−0.0682323	+	0.997669i	$0.521736\pi$
$433$	−8092.22	+	14016.1i	−0.898123	+	1.55560i	−0.829891	+	0.557926i	$0.811597\pi$
$434$	2070.18	+	3585.66i	0.228968	+	0.396584i
$435$	−1397.98	−	2421.38i	−0.154088	−	0.266888i
$436$	1047.85			0.115099
$437$	218.393	−	543.125i	0.0239065	−	0.0594535i
$438$	−3528.19			−0.384894
$439$	5942.71	+	10293.1i	0.646082	+	1.11905i	0.984050	+	0.177889i	$0.0569269\pi$
$439$	5942.71	+	10293.1i	0.646082	+	1.11905i	−0.337968	+	0.941157i	$0.609740\pi$
$440$	−687.951	−	1191.57i	−0.0745382	−	0.129104i
$441$	844.211	−	1462.22i	0.0911576	−	0.157890i
$442$	4643.29	+	8042.41i	0.499680	+	0.865472i
$443$	−5795.51	+	10038.1i	−0.621564	+	1.07658i	0.367630	+	0.929972i	$0.380169\pi$
$443$	−5795.51	+	10038.1i	−0.621564	+	1.07658i	−0.989195	+	0.146609i	$0.953164\pi$
$444$	1183.23			0.126472
$445$	−4982.43			−0.530763
$446$	4274.83	−	7404.23i	0.453855	−	0.786099i
$447$	−436.006	+	755.185i	−0.0461351	+	0.0799083i
$448$	797.815			0.0841366
$449$	−13617.0			−1.43124			−0.715618	−	0.698492i	$-0.753855\pi$
$449$	−13617.0			−1.43124			−0.715618	+	0.698492i	$0.753855\pi$
$450$	225.000	−	389.711i	0.0235702	−	0.0408248i
$451$	−4760.54	−	8245.50i	−0.497040	−	0.860899i
$452$	373.414	−	646.773i	0.0388583	−	0.0673045i
$453$	1032.39	+	1788.15i	0.107077	+	0.185463i
$454$	3667.25	+	6351.86i	0.379103	+	0.656625i
$455$	2713.45			0.279579
$456$	−1226.31	−	1564.27i	−0.125937	−	0.160644i
$457$	−17906.9			−1.83293			−0.916464	−	0.400116i	$-0.868970\pi$
$457$	−17906.9			−1.83293			−0.916464	+	0.400116i	$0.868970\pi$
$458$	220.630	+	382.142i	0.0225095	+	0.0389876i
$459$	−1439.89	−	2493.96i	−0.146423	−	0.253613i
$460$	−70.6829	+	122.426i	−0.00716436	+	0.0124090i
$461$	−3352.50	−	5806.71i	−0.338702	−	0.586649i	0.645487	−	0.763771i	$-0.276655\pi$
$461$	−3352.50	−	5806.71i	−0.338702	−	0.586649i	−0.984189	+	0.177122i	$0.943321\pi$
$462$	−1286.39	+	2228.08i	−0.129541	+	0.224372i
$463$	−18791.5			−1.88621			−0.943104	−	0.332498i	$-0.892108\pi$
$463$	−18791.5			−1.88621			−0.943104	+	0.332498i	$0.892108\pi$
$464$	2982.36			0.298389
$465$	−1245.51	+	2157.29i	−0.124213	+	0.215144i
$466$	−944.883	+	1636.59i	−0.0939289	+	0.162690i
$467$	18466.5			1.82982			0.914910	−	0.403658i	$-0.132262\pi$
$467$	18466.5			1.82982			0.914910	+	0.403658i	$0.132262\pi$
$468$	−1567.23			−0.154797
$469$	209.016	−	362.026i	0.0205788	−	0.0356435i
$470$	−669.878	−	1160.26i	−0.0657430	−	0.113870i
$471$	−452.301	+	783.409i	−0.0442483	+	0.0766403i
$472$	812.771	+	1407.76i	0.0792602	+	0.137283i
$473$	1622.35	+	2809.99i	0.157708	+	0.273158i
$474$	8140.22			0.788803
$475$	−772.439	+	1920.99i	−0.0746146	+	0.185560i
$476$	−5318.36			−0.512115
$477$	1049.31	+	1817.46i	0.100723	+	0.174457i
$478$	5260.94	+	9112.22i	0.503410	+	0.871932i
$479$	3613.72	−	6259.14i	0.344708	−	0.597051i	−0.640593	−	0.767881i	$-0.721311\pi$
$479$	3613.72	−	6259.14i	0.344708	−	0.597051i	0.985301	+	0.170830i	$0.0546448\pi$
$480$	240.000	+	415.692i	0.0228218	+	0.0395285i
$481$	−2146.29	+	3717.48i	−0.203456	+	0.352396i
$482$	11058.3			1.04501
$483$	264.337			0.0249022
$484$	295.615	−	512.019i	0.0277625	−	0.0480860i
$485$	143.695	−	248.887i	0.0134533	−	0.0233018i
$486$	486.000			0.0453609
$487$	−12581.0			−1.17063			−0.585317	−	0.810804i	$-0.699030\pi$
$487$	−12581.0			−1.17063			−0.585317	+	0.810804i	$0.699030\pi$
$488$	923.005	−	1598.69i	0.0856198	−	0.148298i
$489$	−4197.83	−	7270.86i	−0.388205	−	0.672392i
$490$	938.012	−	1624.68i	0.0864797	−	0.149787i
$491$	4038.70	+	6995.23i	0.371210	+	0.642954i	0.989752	−	0.142798i	$-0.0456098\pi$
$491$	4038.70	+	6995.23i	0.371210	+	0.642954i	−0.618542	+	0.785752i	$0.712276\pi$
$492$	1660.77	+	2876.54i	0.152182	+	0.263586i
$493$	−19880.9			−1.81621
$494$	7139.07	−	1015.37i	0.650206	−	0.0924771i
$495$	−1547.89			−0.140551
$496$	−1328.55	−	2301.11i	−0.120269	−	0.208312i
$497$	4749.26	+	8225.97i	0.428639	+	0.742425i
$498$	2319.06	−	4016.73i	0.208674	−	0.361434i
$499$	3757.96	+	6508.99i	0.337133	+	0.583932i	0.983892	−	0.178762i	$-0.0572093\pi$
$499$	3757.96	+	6508.99i	0.337133	+	0.583932i	−0.646759	+	0.762695i	$0.723876\pi$
$500$	250.000	−	433.013i	0.0223607	−	0.0387298i
$501$	−1711.16			−0.152592
$502$	−1662.51			−0.147812
$503$	−10132.7	+	17550.4i	−0.898201	+	1.55573i	−0.0684090	+	0.997657i	$0.521792\pi$
$503$	−10132.7	+	17550.4i	−0.898201	+	1.55573i	−0.829792	+	0.558073i	$0.811541\pi$
$504$	448.771	−	777.294i	0.0396624	−	0.0686973i
$505$	−1984.48			−0.174867
$506$	486.264			0.0427215
$507$	−452.667	+	784.043i	−0.0396522	+	0.0686796i
$508$	1696.35	+	2938.17i	0.148156	+	0.256614i
$509$	5434.92	−	9413.56i	0.473278	−	0.819742i	−0.526254	−	0.850328i	$-0.676404\pi$
$509$	5434.92	−	9413.56i	0.473278	−	0.819742i	0.999532	+	0.0305855i	$0.00973717\pi$
$510$	−1599.88	−	2771.07i	−0.138909	−	0.240598i
$511$	3665.16	+	6348.24i	0.317294	+	0.549569i
$512$	−512.000			−0.0441942
$513$	−2213.84	+	314.868i	−0.190533	+	0.0270989i
$514$	521.171			0.0447235
$515$	1193.96	+	2067.99i	0.102159	+	0.176945i
$516$	−565.976	−	980.299i	−0.0482862	−	0.0836342i
$517$	−2304.22	+	3991.02i	−0.196014	+	0.339507i
$518$	−1229.16	−	2128.97i	−0.104259	−	0.180583i
$519$	−896.012	+	1551.94i	−0.0757814	+	0.131257i
$520$	−1741.37			−0.146854
$521$	11583.8			0.974080			0.487040	−	0.873380i	$-0.338077\pi$
$521$	11583.8			0.974080			0.487040	+	0.873380i	$0.338077\pi$
$522$	1677.58	−	2905.65i	0.140662	−	0.243634i
$523$	−9767.93	+	16918.6i	−0.816677	+	1.41453i	0.0914412	+	0.995810i	$0.470853\pi$
$523$	−9767.93	+	16918.6i	−0.816677	+	1.41453i	−0.908118	+	0.418715i	$0.862481\pi$
$524$	−5138.05			−0.428353
$525$	−934.939			−0.0777221
$526$	5763.69	−	9983.01i	0.477774	−	0.827528i
$527$	8856.30	+	15339.6i	0.732043	+	1.26794i
$528$	825.542	−	1429.88i	0.0680437	−	0.117855i
$529$	6058.52	+	10493.7i	0.497947	+	0.862469i
$530$	1165.90	+	2019.40i	0.0955539	+	0.165504i
$531$	1828.73			0.149454
$532$	−1540.66	+	3831.49i	−0.125556	+	0.312248i
$533$	−12050.0			−0.979259
$534$	−2989.46	−	5177.89i	−0.242259	−	0.419605i
$535$	645.501	+	1118.04i	0.0521634	+	0.0903497i
$536$	−134.137	+	232.331i	−0.0108094	+	0.0187224i
$537$	−964.694	−	1670.90i	−0.0775225	−	0.134273i
$538$	−647.969	+	1122.32i	−0.0519255	+	0.0899377i
$539$	−6453.07			−0.515683
$540$	540.000			0.0430331
$541$	8969.79	−	15536.1i	0.712830	−	1.23466i	−0.250960	−	0.967997i	$-0.580746\pi$
$541$	8969.79	−	15536.1i	0.712830	−	1.23466i	0.963790	−	0.266661i	$-0.0859204\pi$
$542$	−4097.80	+	7097.60i	−0.324752	+	0.562487i
$543$	−1328.60			−0.105002
$544$	3413.07			0.268997
$545$	654.909	−	1134.34i	0.0514738	−	0.0891552i
$546$	1628.07	+	2819.90i	0.127610	+	0.221027i
$547$	8687.71	−	15047.6i	0.679086	−	1.17621i	−0.296171	−	0.955135i	$-0.595710\pi$
$547$	8687.71	−	15047.6i	0.679086	−	1.17621i	0.975257	−	0.221076i	$-0.0709568\pi$
$548$	5835.81	+	10107.9i	0.454915	+	0.787935i
$549$	−1038.38	−	1798.53i	−0.0807231	−	0.139817i
$550$	−1719.88			−0.133338
$551$	−5759.23	+	14322.7i	−0.445284	+	1.10738i
$552$	−169.639			−0.0130803
$553$	−8456.23	−	14646.6i	−0.650263	−	1.12629i
$554$	−3141.96	−	5442.03i	−0.240955	−	0.417346i
$555$	739.518	−	1280.88i	0.0565600	−	0.0979648i
$556$	913.302	+	1581.89i	0.0696630	+	0.120660i
$557$	1521.62	−	2635.53i	0.115751	−	0.200486i	−0.802329	−	0.596882i	$-0.796406\pi$
$557$	1521.62	−	2635.53i	0.115751	−	0.200486i	0.918080	+	0.396396i	$0.129739\pi$
$558$	−2989.23			−0.226782
$559$	4106.54			0.310713
$560$	498.634	−	863.660i	0.0376270	−	0.0651719i
$561$	−5503.19	+	9531.81i	−0.414162	+	0.717350i
$562$	9616.39			0.721785
$563$	−13706.8			−1.02606			−0.513032	−	0.858369i	$-0.671478\pi$
$563$	−13706.8			−1.02606			−0.513032	+	0.858369i	$0.671478\pi$
$564$	803.854	−	1392.32i	0.0600148	−	0.103949i
$565$	−466.768	−	808.466i	−0.0347559	−	0.0601990i
$566$	5882.00	−	10187.9i	0.436818	−	0.756590i
$567$	−504.867	−	874.456i	−0.0373941	−	0.0647684i
$568$	−3047.85	−	5279.04i	−0.225150	−	0.389971i
$569$	4221.51			0.311028			0.155514	−	0.987834i	$-0.450297\pi$
$569$	4221.51			0.311028			0.155514	+	0.987834i	$0.450297\pi$
$570$	−2459.82	+	349.853i	−0.180755	+	0.0257083i
$571$	13657.1			1.00093			0.500467	−	0.865756i	$-0.333162\pi$
$571$	13657.1			1.00093			0.500467	+	0.865756i	$0.333162\pi$
$572$	2994.94	+	5187.38i	0.218924	+	0.379188i
$573$	6333.85	+	10970.5i	0.461780	+	0.799827i
$574$	3450.49	−	5976.42i	0.250907	−	0.434584i
$575$	88.3536	+	153.033i	0.00640800	+	0.0110990i
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	−5552.77			−0.400633			−0.200316	−	0.979731i	$-0.564197\pi$
$577$	−5552.77			−0.400633			−0.200316	+	0.979731i	$0.564197\pi$
$578$	−12926.1			−0.930199
$579$	4091.01	−	7085.84i	0.293638	−	0.508596i
$580$	1863.98	−	3228.50i	0.133444	−	0.231131i
$581$	−9636.35			−0.688095
$582$	344.868			0.0245623
$583$	4010.42	−	6946.25i	0.284897	−	0.493455i
$584$	−2352.13	−	4074.00i	−0.166664	−	0.288670i
$585$	−979.518	+	1696.58i	−0.0692275	+	0.119906i
$586$	2778.15	+	4811.90i	0.195844	+	0.339211i
$587$	−11911.3	−	20631.0i	−0.837533	−	1.45065i	−0.891951	−	0.452132i	$-0.850664\pi$
$587$	−11911.3	−	20631.0i	−0.837533	−	1.45065i	0.0544178	−	0.998518i	$-0.482670\pi$
$588$	2251.23			0.157890
$589$	13616.6	−	1936.65i	0.952567	−	0.135481i
$590$	2031.93			0.141785
$591$	5515.50	+	9553.13i	0.383887	+	0.664912i
$592$	788.819	+	1366.28i	0.0547640	+	0.0948540i
$593$	6474.43	−	11214.0i	0.448352	−	0.776569i	−0.549926	−	0.835213i	$-0.685344\pi$
$593$	6474.43	−	11214.0i	0.448352	−	0.776569i	0.998279	+	0.0586438i	$0.0186776\pi$
$594$	−928.734	−	1608.62i	−0.0641522	−	0.111115i
$595$	−3323.98	+	5757.29i	−0.229025	+	0.396682i
$596$	−1162.68			−0.0799083
$597$	−1436.37			−0.0984703
$598$	307.712	−	532.973i	0.0210423	−	0.0364463i
$599$	−5843.53	+	10121.3i	−0.398598	+	0.690391i	−0.993553	−	0.113367i	$-0.963836\pi$
$599$	−5843.53	+	10121.3i	−0.398598	+	0.690391i	0.594955	+	0.803759i	$0.297170\pi$
$600$	600.000			0.0408248
$601$	13601.9			0.923186			0.461593	−	0.887092i	$-0.347278\pi$
$601$	13601.9			0.923186			0.461593	+	0.887092i	$0.347278\pi$
$602$	−1175.90	+	2036.71i	−0.0796111	+	0.137891i
$603$	150.904	+	261.373i	0.0101912	+	0.0176516i
$604$	−1376.52	+	2384.21i	−0.0927316	+	0.160616i
$605$	−369.518	−	640.024i	−0.0248315	−	0.0430094i
$606$	−1190.69	−	2062.33i	−0.0798157	−	0.138245i
$607$	11383.9			0.761219			0.380609	−	0.924736i	$-0.375714\pi$
$607$	11383.9			0.761219			0.380609	+	0.924736i	$0.375714\pi$
$608$	988.722	−	2458.87i	0.0659506	−	0.164014i
$609$	−6970.82			−0.463829
$610$	−1153.76	−	1998.36i	−0.0765807	−	0.132642i
$611$	2916.26	+	5051.11i	0.193092	+	0.334445i
$612$	1919.85	−	3325.28i	0.126806	−	0.219635i
$613$	−7038.35	−	12190.8i	−0.463746	−	0.803232i	0.535398	−	0.844600i	$-0.320162\pi$
$613$	−7038.35	−	12190.8i	−0.463746	−	0.803232i	−0.999144	+	0.0413681i	$0.986828\pi$
$614$	−2464.87	+	4269.28i	−0.162010	+	0.280609i
$615$	4151.93			0.272231
$616$	−3430.36			−0.224372
$617$	−3400.74	+	5890.25i	−0.221894	+	0.384331i	−0.955383	−	0.295370i	$-0.904557\pi$
$617$	−3400.74	+	5890.25i	−0.221894	+	0.384331i	0.733489	+	0.679701i	$0.237891\pi$
$618$	−1432.75	+	2481.59i	−0.0932582	+	0.161528i
$619$	11693.4			0.759285			0.379643	−	0.925133i	$-0.376047\pi$
$619$	11693.4			0.759285			0.379643	+	0.925133i	$0.376047\pi$
$620$	−3321.37			−0.215144
$621$	−95.4219	+	165.276i	−0.00616610	+	0.0106800i
$622$	6131.69	+	10620.4i	0.395271	+	0.684629i
$623$	−6211.02	+	10757.8i	−0.399421	+	0.691818i
$624$	−1044.82	−	1809.68i	−0.0670293	−	0.116098i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	14472.6			0.924026
$627$	5272.77	+	6725.89i	0.335844	+	0.428399i
$628$	−1206.14			−0.0766403
$629$	−5258.40	−	9107.81i	−0.333332	−	0.577348i
$630$	−560.964	−	971.617i	−0.0354751	−	0.0614447i
$631$	−6132.68	+	10622.1i	−0.386906	+	0.670142i	−0.992032	−	0.125989i	$-0.959790\pi$
$631$	−6132.68	+	10622.1i	−0.386906	+	0.670142i	0.605125	+	0.796130i	$0.293123\pi$
$632$	5426.81	+	9399.51i	0.341562	+	0.591602i
$633$	4337.01	−	7511.91i	0.272323	−	0.471677i
$634$	20442.6			1.28057
$635$	4240.88			0.265030
$636$	−1399.08	+	2423.28i	−0.0872284	+	0.151084i
$637$	−4083.56	+	7072.93i	−0.253997	+	0.439936i
$638$	−12823.2			−0.795732
$639$	−6857.67			−0.424547
$640$	−320.000	+	554.256i	−0.0197642	+	0.0342327i
$641$	5638.65	+	9766.42i	0.347446	+	0.601795i	0.985795	−	0.167952i	$-0.0537155\pi$
$641$	5638.65	+	9766.42i	0.347446	+	0.601795i	−0.638349	+	0.769747i	$0.720382\pi$
$642$	−774.601	+	1341.65i	−0.0476185	+	0.0824776i
$643$	5917.41	+	10249.3i	0.362924	+	0.628602i	0.988441	−	0.151608i	$-0.0484452\pi$
$643$	5917.41	+	10249.3i	0.362924	+	0.628602i	−0.625517	+	0.780211i	$0.715112\pi$
$644$	176.225	+	305.230i	0.0107829	+	0.0186766i
$645$	−1414.94			−0.0863770
$646$	−6590.98	+	16391.2i	−0.401422	+	0.998304i
$647$	−16797.6			−1.02068			−0.510340	−	0.859973i	$-0.670481\pi$
$647$	−16797.6			−1.02068			−0.510340	+	0.859973i	$0.670481\pi$
$648$	324.000	+	561.184i	0.0196419	+	0.0340207i
$649$	−3494.67	−	6052.94i	−0.211368	−	0.366100i
$650$	−1088.35	+	1885.08i	−0.0656750	+	0.113752i
$651$	3105.28	+	5378.49i	0.186951	+	0.323809i
$652$	5597.11	−	9694.47i	0.336196	−	0.582308i
$653$	−12913.8			−0.773902			−0.386951	−	0.922100i	$-0.626472\pi$
$653$	−12913.8			−0.773902			−0.386951	+	0.922100i	$0.626472\pi$
$654$	1571.78			0.0939778
$655$	−3211.28	+	5562.10i	−0.191565	+	0.331801i
$656$	−2214.36	+	3835.39i	−0.131793	+	0.228272i
$657$	−5292.29			−0.314264
$658$	−3340.24			−0.197897
$659$	−8710.76	+	15087.5i	−0.514906	+	0.891843i	0.484944	+	0.874545i	$0.338840\pi$
$659$	−8710.76	+	15087.5i	−0.514906	+	0.891843i	−0.999850	+	0.0172984i	$0.994493\pi$
$660$	−1031.93	−	1787.35i	−0.0608602	−	0.105413i
$661$	13268.8	−	22982.2i	0.780780	−	1.35235i	−0.150709	−	0.988578i	$-0.548156\pi$
$661$	13268.8	−	22982.2i	0.780780	−	1.35235i	0.931488	−	0.363772i	$-0.118511\pi$
$662$	−1291.51	−	2236.97i	−0.0758249	−	0.131333i
$663$	6964.93	+	12063.6i	0.407987	+	0.706655i
$664$	6184.16			0.361434
$665$	3184.80	+	4062.49i	0.185716	+	0.236897i
$666$	1774.84			0.103264
$667$	658.756	+	1141.00i	0.0382416	+	0.0662363i
$668$	−1140.77	−	1975.87i	−0.0660745	−	0.114444i
$669$	6412.25	−	11106.3i	0.370571	−	0.641847i
$670$	167.671	+	290.414i	0.00966819	+	0.0167458i
$671$	−3968.64	+	6873.89i	−0.228327	+	0.395475i
$672$	1196.72			0.0686973
$673$	10962.1			0.627871			0.313936	−	0.949444i	$-0.398352\pi$
$673$	10962.1			0.627871			0.313936	+	0.949444i	$0.398352\pi$
$674$	3645.63	−	6314.42i	0.208345	−	0.360864i
$675$	337.500	−	584.567i	0.0192450	−	0.0333333i
$676$	−1207.11			−0.0686796
$677$	−7102.95			−0.403233			−0.201616	−	0.979465i	$-0.564619\pi$
$677$	−7102.95			−0.403233			−0.201616	+	0.979465i	$0.564619\pi$
$678$	560.122	−	970.159i	0.0317276	−	0.0549539i
$679$	−358.256	−	620.518i	−0.0202483	−	0.0350711i
$680$	2133.17	−	3694.76i	0.120299	−	0.208364i
$681$	5500.87	+	9527.79i	0.309536	+	0.536132i
$682$	5712.35	+	9894.07i	0.320729	+	0.555518i
$683$	−8458.51			−0.473874			−0.236937	−	0.971525i	$-0.576144\pi$
$683$	−8458.51			−0.473874			−0.236937	+	0.971525i	$0.576144\pi$
$684$	−1839.47	−	2346.41i	−0.102827	−	0.131165i
$685$	14589.5			0.813776
$686$	−6614.41	−	11456.5i	−0.368133	−	0.637626i
$687$	330.944	+	573.212i	0.0183789	+	0.0318332i
$688$	754.634	−	1307.06i	0.0418171	−	0.0724293i
$689$	−5075.66	−	8791.30i	−0.280649	−	0.486098i
$690$	−106.024	+	183.640i	−0.00584968	+	0.0101319i
$691$	−35252.0			−1.94074			−0.970368	−	0.241632i	$-0.922317\pi$
$691$	−35252.0			−1.94074			−0.970368	+	0.241632i	$0.922317\pi$
$692$	−2389.37			−0.131257
$693$	−1929.58	+	3342.13i	−0.105770	+	0.183199i
$694$	−3521.98	+	6100.25i	−0.192641	+	0.333663i
$695$	2283.26			0.124617
$696$	4473.54			0.243634
$697$	14761.3	−	25567.3i	0.802186	−	1.38943i
$698$	−1097.09	−	1900.22i	−0.0594921	−	0.103043i
$699$	−1417.32	+	2454.88i	−0.0766926	+	0.132836i
$700$	−623.293	−	1079.57i	−0.0336546	−	0.0582916i
$701$	3280.06	+	5681.22i	0.176728	+	0.306101i	0.940758	−	0.339079i	$-0.110116\pi$
$701$	3280.06	+	5681.22i	0.176728	+	0.306101i	−0.764030	+	0.645180i	$0.776782\pi$
$702$	−2350.84			−0.126392
$703$	−8084.80	+	1149.88i	−0.433747	+	0.0616906i
$704$	2201.44			0.117855
$705$	−1004.82	−	1740.40i	−0.0536789	−	0.0929746i
$706$	−5183.15	−	8977.48i	−0.276304	−	0.478572i
$707$	−2473.82	+	4284.78i	−0.131595	+	0.227929i
$708$	1219.16	+	2111.64i	0.0647157	+	0.112091i
$709$	−922.850	+	1598.42i	−0.0488834	+	0.0846686i	−0.889432	−	0.457068i	$-0.848900\pi$
$709$	−922.850	+	1598.42i	−0.0488834	+	0.0846686i	0.840548	+	0.541737i	$0.182233\pi$
$710$	−7619.64			−0.402760
$711$	12210.3			0.644055
$712$	3985.94	−	6903.85i	0.209803	−	0.363389i
$713$	586.909	−	1016.56i	0.0308274	−	0.0533946i
$714$	−7977.54			−0.418140
$715$	7487.34			0.391623
$716$	1286.26	−	2227.86i	0.0671365	−	0.116284i
$717$	7891.42	+	13668.3i	0.411033	+	0.711929i
$718$	12177.4	−	21091.8i	0.632947	−	1.09630i
$719$	−68.2596	−	118.229i	−0.00354055	−	0.00613241i	0.864250	−	0.503063i	$-0.167794\pi$
$719$	−68.2596	−	118.229i	−0.00354055	−	0.00613241i	−0.867790	+	0.496931i	$0.834460\pi$
$720$	360.000	+	623.538i	0.0186339	+	0.0322749i
$721$	5953.48			0.307516
$722$	9899.36	+	9496.64i	0.510272	+	0.489513i
$723$	16587.5			0.853244
$724$	−885.736	−	1534.14i	−0.0454670	−	0.0787512i
$725$	−2329.97	−	4035.63i	−0.119356	−	0.206730i
$726$	443.422	−	768.029i	0.0226679	−	0.0392620i
$727$	−1938.89	−	3358.25i	−0.0989125	−	0.171321i	0.812322	−	0.583209i	$-0.198203\pi$
$727$	−1938.89	−	3358.25i	−0.0989125	−	0.171321i	−0.911235	+	0.411887i	$0.864870\pi$
$728$	−2170.76	+	3759.87i	−0.110513	+	0.191415i
$729$	729.000			0.0370370
$730$	−5880.32			−0.298137
$731$	−5030.51	+	8713.10i	−0.254528	+	0.440856i
$732$	1384.51	−	2398.04i	0.0699083	−	0.121085i
$733$	12182.5			0.613875			0.306937	−	0.951730i	$-0.400696\pi$
$733$	12182.5			0.613875			0.306937	+	0.951730i	$0.400696\pi$
$734$	−7621.40			−0.383258
$735$	1407.02	−	2437.03i	0.0706104	−	0.122301i
$736$	−113.093	−	195.882i	−0.00566392	−	0.00981021i
$737$	576.747	−	998.954i	0.0288260	−	0.0499280i
$738$	2491.16	+	4314.81i	0.124256	+	0.215217i
$739$	−12872.5	−	22295.8i	−0.640760	−	1.10983i	−0.985263	−	0.171043i	$-0.945286\pi$
$739$	−12872.5	−	22295.8i	−0.640760	−	1.10983i	0.344504	−	0.938785i	$-0.388047\pi$
$740$	1972.05			0.0979648
$741$	10708.6	−	1523.06i	0.530891	−	0.0755072i
$742$	5813.59			0.287633
$743$	−4175.57	−	7232.29i	−0.206173	−	0.357102i	0.744333	−	0.667809i	$-0.232768\pi$
$743$	−4175.57	−	7232.29i	−0.206173	−	0.357102i	−0.950506	+	0.310707i	$0.899434\pi$
$744$	−1992.82	−	3451.66i	−0.0981993	−	0.170086i
$745$	−726.677	+	1258.64i	−0.0357361	+	0.0618967i
$746$	−1177.41	−	2039.34i	−0.0577856	−	0.100088i
$747$	3478.59	−	6025.09i	0.170381	−	0.295109i
$748$	−14675.2			−0.717350
$749$	3218.69			0.157020
$750$	375.000	−	649.519i	0.0182574	−	0.0316228i
$751$	−6847.24	+	11859.8i	−0.332702	+	0.576257i	−0.983041	−	0.183388i	$-0.941294\pi$
$751$	−6847.24	+	11859.8i	−0.332702	+	0.576257i	0.650339	+	0.759644i	$0.274627\pi$
$752$	2143.61			0.103949
$753$	−2493.77			−0.120688
$754$	−8114.66	+	14055.0i	−0.391934	+	0.678850i
$755$	1720.65	+	2980.26i	0.0829417	+	0.143659i
$756$	673.156	−	1165.94i	0.0323842	−	0.0560911i
$757$	−17147.5	−	29700.3i	−0.823296	−	1.42599i	−0.903215	−	0.429189i	$-0.858799\pi$
$757$	−17147.5	−	29700.3i	−0.823296	−	1.42599i	0.0799187	−	0.996801i	$-0.474534\pi$
$758$	−4069.18	−	7048.03i	−0.194986	−	0.337726i
$759$	729.396			0.0348819
$760$	−2043.85	−	2607.12i	−0.0975505	−	0.124434i
$761$	−33906.9			−1.61514			−0.807571	−	0.589771i	$-0.799218\pi$
$761$	−33906.9			−1.61514			−0.807571	+	0.589771i	$0.799218\pi$
$762$	2544.53	+	4407.25i	0.120969	+	0.209525i
$763$	−1632.80	−	2828.09i	−0.0774722	−	0.134186i
$764$	−8445.13	+	14627.4i	−0.399914	+	0.692671i
$765$	−2399.82	−	4156.61i	−0.113419	−	0.196448i
$766$	5315.11	−	9206.04i	0.250708	−	0.434240i
$767$	−8845.82			−0.416433
$768$	−768.000			−0.0360844
$769$	19640.5	−	34018.3i	0.921005	−	1.59523i	0.123142	−	0.992389i	$-0.460703\pi$
$769$	19640.5	−	34018.3i	0.921005	−	1.59523i	0.797863	−	0.602838i	$-0.205964\pi$
$770$	−2143.98	+	3713.47i	−0.100342	+	0.173798i
$771$	781.757			0.0365166
$772$	10909.4			0.508596
$773$	9430.92	−	16334.8i	0.438818	−	0.760056i	−0.558780	−	0.829316i	$-0.688730\pi$
$773$	9430.92	−	16334.8i	0.438818	−	0.760056i	0.997599	+	0.0692600i	$0.0220638\pi$
$774$	−848.964	−	1470.45i	−0.0394255	−	0.0682870i
$775$	−2075.85	+	3595.48i	−0.0962153	+	0.166650i
$776$	229.912	+	398.219i	0.0106358	+	0.0184217i
$777$	−1843.75	−	3193.46i	−0.0851274	−	0.147445i
$778$	6763.54			0.311677
$779$	−14143.2	−	18040.9i	−0.650492	−	0.829761i
$780$	−2612.05			−0.119906
$781$	13104.8	+	22698.3i	0.600420	+	1.03996i
$782$	753.893	+	1305.78i	0.0344746	+	0.0597118i
$783$	2516.37	−	4358.48i	0.114850	−	0.198926i
$784$	1500.82	+	2599.50i	0.0683682	+	0.118417i
$785$	−753.835	+	1305.68i	−0.0342746	+	0.0593653i
$786$	−7707.08			−0.349748
$787$	13130.9			0.594746			0.297373	−	0.954761i	$-0.403890\pi$
$787$	13130.9			0.594746			0.297373	+	0.954761i	$0.403890\pi$
$788$	−7354.00	+	12737.5i	−0.332456	+	0.575831i
$789$	8645.54	−	14974.5i	0.390101	−	0.675674i
$790$	13567.0			0.611004
$791$	−2327.47			−0.104621
$792$	1238.31	−	2144.82i	0.0555575	−	0.0962284i
$793$	5022.78	+	8699.71i	0.224923	+	0.389578i
$794$	11514.9	−	19944.5i	0.514673	−	0.891439i
$795$	1748.85	+	3029.10i	0.0780195	+	0.135134i
$796$	−957.581	−	1658.58i	−0.0426389	−	0.0738527i
$797$	30204.4			1.34240			0.671202	−	0.741275i	$-0.265778\pi$
$797$	30204.4			1.34240			0.671202	+	0.741275i	$0.265778\pi$
$798$	−2310.99	+	5747.24i	−0.102516	+	0.254950i
$799$	−14289.7			−0.632705
$800$	400.000	+	692.820i	0.0176777	+	0.0306186i
$801$	−4484.18	−	7766.84i	−0.197804	−	0.342606i
$802$	−8027.22	+	13903.5i	−0.353430	+	0.612159i
$803$	10113.4	+	17517.0i	0.444452	+	0.769814i
$804$	−201.205	+	348.497i	−0.00882581	+	0.0152867i
$805$	440.561			0.0192891
$806$	14459.3			0.631894
$807$	−971.954	+	1683.47i	−0.0423970	+	0.0734338i
$808$	1587.58	−	2749.77i	0.0691224	−	0.119724i
$809$	17368.2			0.754800			0.377400	−	0.926050i	$-0.376818\pi$
$809$	17368.2			0.754800			0.377400	+	0.926050i	$0.376818\pi$
$810$	810.000			0.0351364
$811$	11810.2	−	20455.9i	0.511359	−	0.885700i	−0.488554	−	0.872534i	$-0.662476\pi$
$811$	11810.2	−	20455.9i	0.511359	−	0.885700i	0.999913	−	0.0131664i	$-0.00419112\pi$
$812$	−4647.21	−	8049.20i	−0.200844	−	0.347872i
$813$	−6146.70	+	10646.4i	−0.265159	+	0.459269i
$814$	−3391.68	−	5874.57i	−0.146042	−	0.252953i
$815$	−6996.38	−	12118.1i	−0.300703	−	0.520832i
$816$	5119.61			0.219635
$817$	4819.88	+	6148.19i	0.206397	+	0.263278i
$818$	18785.9			0.802973
$819$	2442.11	+	4229.85i	0.104193	+	0.180468i
$820$	2767.95	+	4794.23i	0.117879	+	0.204173i
$821$	10379.2	−	17977.3i	0.441214	−	0.764206i	−0.556565	−	0.830804i	$-0.687881\pi$
$821$	10379.2	−	17977.3i	0.441214	−	0.764206i	0.997780	+	0.0665980i	$0.0212145\pi$
$822$	8753.71	+	15161.9i	0.371436	+	0.643347i
$823$	11681.3	−	20232.6i	0.494756	−	0.856942i	−0.505226	−	0.862987i	$-0.668591\pi$
$823$	11681.3	−	20232.6i	0.494756	−	0.856942i	0.999982	+	0.00604494i	$0.00192418\pi$
$824$	−3820.66			−0.161528
$825$	−2579.82			−0.108870
$826$	2532.97	−	4387.23i	0.106699	−	0.184808i
$827$	−1585.87	+	2746.80i	−0.0666820	+	0.115497i	−0.897439	−	0.441139i	$-0.854575\pi$
$827$	−1585.87	+	2746.80i	−0.0666820	+	0.115497i	0.830757	+	0.556635i	$0.187908\pi$
$828$	−254.458			−0.0106800
$829$	39709.3			1.66364			0.831822	−	0.555042i	$-0.187298\pi$
$829$	39709.3			1.66364			0.831822	+	0.555042i	$0.187298\pi$
$830$	3865.10	−	6694.55i	0.161638	−	0.279965i
$831$	−4712.94	−	8163.04i	−0.196739	−	0.340762i
$832$	1393.09	−	2412.91i	0.0580490	−	0.100544i
$833$	−10004.7	−	17328.7i	−0.416137	−	0.720771i
$834$	1369.95	+	2372.83i	0.0568796	+	0.0985184i
$835$	−2851.93			−0.118198
$836$	−4251.20	+	10572.4i	−0.175874	+	0.437385i
$837$	−4483.84			−0.185166
$838$	−13226.2	−	22908.5i	−0.545217	−	0.944344i
$839$	−1838.59	−	3184.53i	−0.0756557	−	0.131040i	0.825716	−	0.564087i	$-0.190772\pi$
$839$	−1838.59	−	3184.53i	−0.0756557	−	0.131040i	−0.901371	+	0.433047i	$0.857438\pi$
$840$	747.951	−	1295.49i	0.0307223	−	0.0532127i
$841$	−5177.53	−	8967.74i	−0.212289	−	0.367696i
$842$	−1928.94	+	3341.02i	−0.0789496	+	0.136745i
$843$	14424.6			0.589335
$844$	11565.3			0.471677
$845$	−754.446	+	1306.74i	−0.0307145	+	0.0531990i
$846$	1205.78	−	2088.47i	0.0490019	−	0.0848738i
$847$	−1842.54			−0.0747468
$848$	−3730.89			−0.151084
$849$	8822.99	−	15281.9i	0.356660	−	0.617753i
$850$	−2666.46	−	4618.45i	−0.107599	−	0.186367i
$851$	−348.475	+	603.577i	−0.0140371	+	0.0243130i
$852$	−4571.78	−	7918.56i	−0.183834	−	0.318410i
$853$	4492.45	+	7781.15i	0.180327	+	0.312335i	0.941992	−	0.335636i	$-0.108951\pi$
$853$	4492.45	+	7781.15i	0.180327	+	0.312335i	−0.761665	+	0.647971i	$0.775618\pi$
$854$	−5753.02			−0.230520
$855$	−3689.73	+	524.780i	−0.147586	+	0.0209907i
$856$	−2065.60			−0.0824776
$857$	−22533.3	−	39028.8i	−0.898160	−	1.55566i	−0.829844	−	0.557995i	$-0.811571\pi$
$857$	−22533.3	−	39028.8i	−0.898160	−	1.55566i	−0.0683157	−	0.997664i	$-0.521762\pi$
$858$	4492.41	+	7781.08i	0.178751	+	0.309606i
$859$	4237.68	−	7339.88i	0.168321	−	0.291541i	−0.769509	−	0.638637i	$-0.779499\pi$
$859$	4237.68	−	7339.88i	0.168321	−	0.291541i	0.937830	+	0.347096i	$0.112832\pi$
$860$	−943.293	−	1633.83i	−0.0374023	−	0.0647828i
$861$	5175.73	−	8964.63i	0.204865	−	0.354836i
$862$	−30453.0			−1.20329
$863$	47267.0			1.86441			0.932205	−	0.361931i	$-0.117882\pi$
$863$	47267.0			1.86441			0.932205	+	0.361931i	$0.117882\pi$
$864$	−432.000	+	748.246i	−0.0170103	+	0.0294628i
$865$	−1493.35	+	2586.56i	−0.0587001	+	0.101671i
$866$	−32368.9			−1.27014
$867$	−19389.1			−0.759504
$868$	−4140.37	+	7171.33i	−0.161905	+	0.280427i
$869$	−23333.6	−	40415.0i	−0.910862	−	1.57766i
$870$	2795.96	−	4842.75i	0.108956	−	0.188718i
$871$	−729.940	−	1264.29i	−0.0283962	−	0.0491836i
$872$	1047.85	+	1814.94i	0.0406936	+	0.0704834i
$873$	517.302			0.0200550
$874$	1159.11	−	164.858i	0.0448599	−	0.00638031i
$875$	−1558.23			−0.0602033
$876$	−3528.19	−	6111.01i	−0.136081	−	0.235698i
$877$	−15143.2	−	26228.9i	−0.583069	−	1.00990i	−0.995113	−	0.0987407i	$-0.968519\pi$
$877$	−15143.2	−	26228.9i	−0.583069	−	1.00990i	0.412045	−	0.911164i	$-0.364815\pi$
$878$	−11885.4	+	20586.1i	−0.456849	+	0.791286i
$879$	4167.23	+	7217.85i	0.159906	+	0.276965i
$880$	1375.90	−	2383.13i	0.0527064	−	0.0912902i
$881$	−34096.3			−1.30390			−0.651949	−	0.758263i	$-0.726048\pi$
$881$	−34096.3			−1.30390			−0.651949	+	0.758263i	$0.726048\pi$
$882$	3376.84			0.128916
$883$	21032.6	−	36429.5i	0.801589	−	1.38839i	−0.116980	−	0.993134i	$-0.537321\pi$
$883$	21032.6	−	36429.5i	0.801589	−	1.38839i	0.918570	−	0.395259i	$-0.129345\pi$
$884$	−9286.58	+	16084.8i	−0.353327	+	0.611981i
$885$	3047.89			0.115767
$886$	−23182.0			−0.879024
$887$	5072.24	−	8785.37i	0.192006	−	0.332564i	−0.753909	−	0.656979i	$-0.771834\pi$
$887$	5072.24	−	8785.37i	0.192006	−	0.332564i	0.945915	+	0.324415i	$0.105167\pi$
$888$	1183.23	+	2049.41i	0.0447146	+	0.0774480i
$889$	5286.62	−	9156.69i	0.199446	−	0.345451i
$890$	−4982.43	−	8629.82i	−0.187653	−	0.325025i
$891$	−1393.10	−	2412.92i	−0.0523801	−	0.0907250i
$892$	17099.3			0.641847
$893$	−4139.52	+	10294.7i	−0.155122	+	0.385775i
$894$	−1744.02			−0.0652449
$895$	−1607.82	−	2784.83i	−0.0600487	−	0.104007i
$896$	797.815	+	1381.86i	0.0297468	+	0.0515229i
$897$	461.568	−	799.459i	0.0171809	−	0.0297583i
$898$	−13617.0	−	23585.3i	−0.506019	−	0.876450i
$899$	−15477.4	+	26807.6i	−0.574192	+	0.994530i
$900$	900.000			0.0333333
$901$	24870.7			0.919604
$902$	9521.08	−	16491.0i	0.351460	−	0.608747i
$903$	−1763.84	+	3055.07i	−0.0650022	+	0.112587i
$904$	1493.66			0.0549539
$905$	−2214.34			−0.0813339
$906$	−2064.78	+	3576.31i	−0.0757150	+	0.131142i
$907$	−10745.9	−	18612.4i	−0.393396	−	0.681383i	0.599499	−	0.800376i	$-0.295367\pi$
$907$	−10745.9	−	18612.4i	−0.393396	−	0.681383i	−0.992895	+	0.118993i	$0.962033\pi$
$908$	−7334.50	+	12703.7i	−0.268066	+	0.464304i
$909$	−1786.03	−	3093.49i	−0.0651692	−	0.112876i
$910$	2713.45	+	4699.84i	0.0988462	+	0.171207i
$911$	35902.0			1.30569			0.652847	−	0.757490i	$-0.273574\pi$
$911$	35902.0			1.30569			0.652847	+	0.757490i	$0.273574\pi$
$912$	1483.08	−	3688.31i	0.0538485	−	0.133917i
$913$	−26590.0			−0.963856
$914$	−17906.9	−	31015.6i	−0.648038	−	1.12243i
$915$	−1730.63	−	2997.55i	−0.0625279	−	0.108301i
$916$	−441.259	+	764.283i	−0.0159166	+	0.0275684i
$917$	8006.27	+	13867.3i	0.288321	+	0.499387i
$918$	2879.78	−	4987.93i	0.103537	−	0.179331i
$919$	7330.36			0.263119			0.131559	−	0.991308i	$-0.458002\pi$
$919$	7330.36			0.263119			0.131559	+	0.991308i	$0.458002\pi$
$920$	−282.732			−0.0101319
$921$	−3697.30	+	6403.92i	−0.132280	+	0.229116i
$922$	6705.01	−	11613.4i	0.239499	−	0.414824i
$923$	33171.4			1.18294
$924$	−5145.54			−0.183199
$925$	1232.53	−	2134.81i	0.0438112	−	0.0758832i
$926$	−18791.5	−	32547.8i	−0.666875	−	1.15506i
$927$	−2149.12	+	3722.39i	−0.0761450	+	0.131887i
$928$	2982.36	+	5165.60i	0.105497	+	0.182725i
$929$	5853.84	+	10139.1i	0.206736	+	0.358078i	0.950685	−	0.310159i	$-0.100382\pi$
$929$	5853.84	+	10139.1i	0.206736	+	0.358078i	−0.743948	+	0.668237i	$0.767049\pi$
$930$	−4982.05			−0.175664
$931$	−15382.3	+	2187.78i	−0.541496	+	0.0770156i
$932$	−3779.53			−0.132836
$933$	9197.53	+	15930.6i	0.322737	+	0.558997i
$934$	18466.5	+	31984.8i	0.646939	+	1.12053i
$935$	−9171.99	+	15886.3i	−0.320809	+	0.555657i
$936$	−1567.23	−	2714.52i	−0.0547292	−	0.0947937i
$937$	23280.1	−	40322.3i	0.811661	−	1.40584i	−0.100039	−	0.994984i	$-0.531897\pi$
$937$	23280.1	−	40322.3i	0.811661	−	1.40584i	0.911701	−	0.410855i	$-0.134770\pi$
$938$	836.064			0.0291028
$939$	21708.9			0.754464
$940$	1339.76	−	2320.53i	0.0464873	−	0.0805183i
$941$	−5081.37	+	8801.19i	−0.176034	+	0.304900i	−0.940519	−	0.339742i	$-0.889660\pi$
$941$	−5081.37	+	8801.19i	−0.176034	+	0.304900i	0.764485	+	0.644642i	$0.222993\pi$
$942$	−1809.20			−0.0625765
$943$	−1956.47			−0.0675624
$944$	−1625.54	+	2815.52i	−0.0560454	+	0.0970735i
$945$	−841.445	−	1457.43i	−0.0289653	−	0.0501694i
$946$	−3244.70	+	5619.98i	−0.111516	+	0.193152i
$947$	−7493.70	−	12979.5i	−0.257141	−	0.445381i	0.708334	−	0.705878i	$-0.249447\pi$
$947$	−7493.70	−	12979.5i	−0.257141	−	0.445381i	−0.965475	+	0.260496i	$0.916114\pi$
$948$	8140.22	+	14099.3i	0.278884	+	0.483041i
$949$	25599.5			0.875652
$950$	−4099.70	+	583.089i	−0.140012	+	0.0199136i
$951$	30663.9			1.04558
$952$	−5318.36	−	9211.67i	−0.181060	−	0.313605i
$953$	−18730.1	−	32441.4i	−0.636649	−	1.10271i	−0.986163	−	0.165778i	$-0.946987\pi$
$953$	−18730.1	−	32441.4i	−0.636649	−	1.10271i	0.349514	−	0.936931i	$-0.386347\pi$
$954$	−2098.62	+	3634.92i	−0.0712217	+	0.123360i
$955$	10556.4	+	18284.2i	0.357694	+	0.619544i
$956$	−10521.9	+	18224.4i	−0.355965	+	0.616549i
$957$	−19234.9			−0.649713
$958$	14454.9			0.487490
$959$	18187.1	−	31500.9i	0.612400	−	1.06071i
$960$	−480.000	+	831.384i	−0.0161374	+	0.0279508i
$961$	−2212.32			−0.0742615
$962$	−8585.14			−0.287730
$963$	−1161.90	+	2012.47i	−0.0388803	+	0.0673427i
$964$	11058.3	+	19153.6i	0.369466	+	0.639933i
$965$	6818.35	−	11809.7i	0.227451	−	0.393957i
$966$	264.337	+	457.845i	0.00880424	+	0.0152494i
$967$	16018.8	+	27745.4i	0.532710	+	0.922681i	0.999270	+	0.0381914i	$0.0121597\pi$
$967$	16018.8	+	27745.4i	0.532710	+	0.922681i	−0.466561	+	0.884489i	$0.654507\pi$
$968$	1182.46			0.0392620
$969$	−9886.47	+	24586.8i	−0.327760	+	0.815111i
$970$	574.780			0.0190259
$971$	11690.8	+	20249.1i	0.386381	+	0.669231i	0.991960	−	0.126554i	$-0.0403918\pi$
$971$	11690.8	+	20249.1i	0.386381	+	0.669231i	−0.605579	+	0.795785i	$0.707058\pi$
$972$	486.000	+	841.777i	0.0160375	+	0.0277778i
$973$	2846.27	−	4929.89i	0.0937794	−	0.162431i
$974$	−12581.0	−	21790.9i	−0.413882	−	0.716865i
$975$	−1632.53	+	2827.63i	−0.0536234	+	0.0928785i
$976$	3692.02			0.121085
$977$	19186.7			0.628288			0.314144	−	0.949375i	$-0.398283\pi$
$977$	19186.7			0.628288			0.314144	+	0.949375i	$0.398283\pi$
$978$	8395.66	−	14541.7i	0.274503	−	0.475453i
$979$	−17138.3	+	29684.5i	−0.559493	+	0.969070i
$980$	3752.05			0.122301
$981$	2357.67			0.0767326
$982$	−8077.40	+	13990.5i	−0.262485	+	0.454637i
$983$	−1356.23	−	2349.06i	−0.0440051	−	0.0762190i	0.843184	−	0.537625i	$-0.180678\pi$
$983$	−1356.23	−	2349.06i	−0.0440051	−	0.0762190i	−0.887189	+	0.461406i	$0.847345\pi$
$984$	−3321.54	+	5753.08i	−0.107609	+	0.186384i
$985$	9192.50	+	15921.9i	0.297358	+	0.515039i
$986$	−19880.9	−	34434.7i	−0.642126	−	1.11220i
$987$	−5010.36			−0.161582
$988$	8897.74	+	11349.9i	0.286513	+	0.365473i
$989$	666.747			0.0214371
$990$	−1547.89	−	2681.03i	−0.0496921	−	0.0860693i
$991$	11463.4	+	19855.2i	0.367453	+	0.636448i	0.989167	−	0.146797i	$-0.0468965\pi$
$991$	11463.4	+	19855.2i	0.367453	+	0.636448i	−0.621713	+	0.783245i	$0.713563\pi$
$992$	2657.09	−	4602.22i	0.0850431	−	0.147299i
$993$	−1937.27	−	3355.45i	−0.0619108	−	0.107233i
$994$	−9498.53	+	16451.9i	−0.303094	+	0.524973i
$995$	−2393.95			−0.0762748
$996$	9276.24			0.295109
$997$	−12263.3	+	21240.6i	−0.389551	+	0.674722i	−0.992389	−	0.123142i	$-0.960703\pi$
$997$	−12263.3	+	21240.6i	−0.389551	+	0.674722i	0.602838	+	0.797863i	$0.294036\pi$
$998$	−7515.93	+	13018.0i	−0.238389	+	0.412902i
$999$	2662.27			0.0843147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.4.i.i.121.2	✓	4
19.11	even	3	inner	570.4.i.i.391.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.4.i.i.121.2	✓	4	1.1	even	1	trivial
570.4.i.i.391.2	yes	4	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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-3.00000 + 5.19615i) q^{6} +12.4659 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(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} +12.4659 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-5.00000 + 8.66025i) q^{10} +34.3976 q^{11} -12.0000 q^{12} +(21.7671 - 37.7017i) q^{13} +(12.4659 + 21.5915i) q^{14} +(-7.50000 + 12.9904i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(53.3293 + 92.3690i) q^{17} -18.0000 q^{18} +(81.9939 - 11.6618i) q^{19} -20.0000 q^{20} +(18.6988 + 32.3872i) q^{21} +(34.3976 + 59.5783i) q^{22} +(3.53414 - 6.12132i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} +87.0683 q^{26} -27.0000 q^{27} +(-24.9317 + 43.1830i) q^{28} +(-93.1988 + 161.425i) q^{29} -30.0000 q^{30} +166.068 q^{31} +(16.0000 - 27.7128i) q^{32} +(51.5964 + 89.3675i) q^{33} +(-106.659 + 184.738i) q^{34} +(31.1646 + 53.9787i) q^{35} +(-18.0000 - 31.1769i) q^{36} -98.6024 q^{37} +(102.193 + 130.356i) q^{38} +130.602 q^{39} +(-20.0000 - 34.6410i) q^{40} +(-138.398 - 239.712i) q^{41} +(-37.3976 + 64.7745i) q^{42} +(47.1646 + 81.6916i) q^{43} +(-68.7951 + 119.157i) q^{44} -45.0000 q^{45} +14.1366 q^{46} +(-66.9878 + 116.026i) q^{47} +(24.0000 - 41.5692i) q^{48} -187.602 q^{49} -50.0000 q^{50} +(-159.988 + 277.107i) q^{51} +(87.0683 + 150.807i) q^{52} +(116.590 - 201.940i) q^{53} +(-27.0000 - 46.7654i) q^{54} +(85.9939 + 148.946i) q^{55} -99.7268 q^{56} +(153.289 + 195.534i) q^{57} -372.795 q^{58} +(-101.596 - 175.970i) q^{59} +(-30.0000 - 51.9615i) q^{60} +(-115.376 + 199.836i) q^{61} +(166.068 + 287.639i) q^{62} +(-56.0964 + 97.1617i) q^{63} +64.0000 q^{64} +217.671 q^{65} +(-103.193 + 178.735i) q^{66} +(16.7671 - 29.0414i) q^{67} -426.634 q^{68} +21.2049 q^{69} +(-62.3293 + 107.957i) q^{70} +(380.982 + 659.880i) q^{71} +(36.0000 - 62.3538i) q^{72} +(294.016 + 509.250i) q^{73} +(-98.6024 - 170.784i) q^{74} -75.0000 q^{75} +(-123.590 + 307.359i) q^{76} +428.795 q^{77} +(130.602 + 226.210i) q^{78} +(-678.351 - 1174.94i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(276.795 - 479.423i) q^{82} -773.020 q^{83} -149.590 q^{84} +(-266.646 + 461.845i) q^{85} +(-94.3293 + 163.383i) q^{86} -559.193 q^{87} -275.181 q^{88} +(-498.243 + 862.982i) q^{89} +(-45.0000 - 77.9423i) q^{90} +(271.345 - 469.984i) q^{91} +(14.1366 + 24.4853i) q^{92} +(249.102 + 431.458i) q^{93} -267.951 q^{94} +(255.482 + 325.890i) q^{95} +96.0000 q^{96} +(-28.7390 - 49.7774i) q^{97} +(-187.602 - 324.937i) q^{98} +(-154.789 + 268.103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} - 12 q^{6} + 6 q^{7} - 32 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 - 12 * q^6 + 6 * q^7 - 32 * q^8 - 18 * q^9	\( 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} - 12 q^{6} + 6 q^{7} - 32 q^{8} - 18 q^{9} - 20 q^{10} + 6 q^{11} - 48 q^{12} + 109 q^{13} + 6 q^{14} - 30 q^{15} - 32 q^{16} - 6 q^{17} - 72 q^{18} - q^{19} - 80 q^{20} + 9 q^{21} + 6 q^{22} + 58 q^{23} - 48 q^{24} - 50 q^{25} + 436 q^{26} - 108 q^{27} - 12 q^{28} - 307 q^{29} - 120 q^{30} + 752 q^{31} + 64 q^{32} + 9 q^{33} + 12 q^{34} + 15 q^{35} - 72 q^{36} - 526 q^{37} + 14 q^{38} + 654 q^{39} - 80 q^{40} - 422 q^{41} - 18 q^{42} + 79 q^{43} - 12 q^{44} - 180 q^{45} + 232 q^{46} + 390 q^{47} + 96 q^{48} - 882 q^{49} - 200 q^{50} + 18 q^{51} + 436 q^{52} - 60 q^{53} - 108 q^{54} + 15 q^{55} - 48 q^{56} + 21 q^{57} - 1228 q^{58} - 209 q^{59} - 120 q^{60} - 944 q^{61} + 752 q^{62} - 27 q^{63} + 256 q^{64} + 1090 q^{65} - 18 q^{66} + 89 q^{67} + 48 q^{68} + 348 q^{69} - 30 q^{70} + 537 q^{71} + 144 q^{72} + 233 q^{73} - 526 q^{74} - 300 q^{75} + 32 q^{76} + 1452 q^{77} + 654 q^{78} - 1880 q^{79} + 160 q^{80} - 162 q^{81} + 844 q^{82} - 548 q^{83} - 72 q^{84} + 30 q^{85} - 158 q^{86} - 1842 q^{87} - 48 q^{88} - 699 q^{89} - 180 q^{90} - 77 q^{91} + 232 q^{92} + 1128 q^{93} + 1560 q^{94} + 35 q^{95} + 384 q^{96} - 422 q^{97} - 882 q^{98} - 27 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 - 12 * q^6 + 6 * q^7 - 32 * q^8 - 18 * q^9 - 20 * q^10 + 6 * q^11 - 48 * q^12 + 109 * q^13 + 6 * q^14 - 30 * q^15 - 32 * q^16 - 6 * q^17 - 72 * q^18 - q^19 - 80 * q^20 + 9 * q^21 + 6 * q^22 + 58 * q^23 - 48 * q^24 - 50 * q^25 + 436 * q^26 - 108 * q^27 - 12 * q^28 - 307 * q^29 - 120 * q^30 + 752 * q^31 + 64 * q^32 + 9 * q^33 + 12 * q^34 + 15 * q^35 - 72 * q^36 - 526 * q^37 + 14 * q^38 + 654 * q^39 - 80 * q^40 - 422 * q^41 - 18 * q^42 + 79 * q^43 - 12 * q^44 - 180 * q^45 + 232 * q^46 + 390 * q^47 + 96 * q^48 - 882 * q^49 - 200 * q^50 + 18 * q^51 + 436 * q^52 - 60 * q^53 - 108 * q^54 + 15 * q^55 - 48 * q^56 + 21 * q^57 - 1228 * q^58 - 209 * q^59 - 120 * q^60 - 944 * q^61 + 752 * q^62 - 27 * q^63 + 256 * q^64 + 1090 * q^65 - 18 * q^66 + 89 * q^67 + 48 * q^68 + 348 * q^69 - 30 * q^70 + 537 * q^71 + 144 * q^72 + 233 * q^73 - 526 * q^74 - 300 * q^75 + 32 * q^76 + 1452 * q^77 + 654 * q^78 - 1880 * q^79 + 160 * q^80 - 162 * q^81 + 844 * q^82 - 548 * q^83 - 72 * q^84 + 30 * q^85 - 158 * q^86 - 1842 * q^87 - 48 * q^88 - 699 * q^89 - 180 * q^90 - 77 * q^91 + 232 * q^92 + 1128 * q^93 + 1560 * q^94 + 35 * q^95 + 384 * q^96 - 422 * q^97 - 882 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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