LMFDB - Embedded newform 143.4.e.b.100.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(100,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("143.100");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.e (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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.9
Character	$\chi$	$=$	143.100
Dual form			143.4.e.b.133.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.315613 - 0.546657i) q^{2} +(-4.62136 + 8.00442i) q^{3} +(3.80078 + 6.58314i) q^{4} -19.0524 q^{5} +(2.91712 + 5.05260i) q^{6} +(12.7218 + 22.0348i) q^{7} +9.84810 q^{8} +(-29.2139 - 50.5999i) q^{9} +O(q^{10})$	\(q+(0.315613 - 0.546657i) q^{2} +(-4.62136 + 8.00442i) q^{3} +(3.80078 + 6.58314i) q^{4} -19.0524 q^{5} +(2.91712 + 5.05260i) q^{6} +(12.7218 + 22.0348i) q^{7} +9.84810 q^{8} +(-29.2139 - 50.5999i) q^{9} +(-6.01317 + 10.4151i) q^{10} +(-5.50000 + 9.52628i) q^{11} -70.2590 q^{12} +(46.6514 + 4.54358i) q^{13} +16.0607 q^{14} +(88.0477 - 152.503i) q^{15} +(-27.2980 + 47.2816i) q^{16} +(-15.5350 - 26.9073i) q^{17} -36.8811 q^{18} +(-36.6443 - 63.4698i) q^{19} +(-72.4137 - 125.424i) q^{20} -235.168 q^{21} +(3.47174 + 6.01323i) q^{22} +(47.9061 - 82.9758i) q^{23} +(-45.5116 + 78.8284i) q^{24} +237.992 q^{25} +(17.2076 - 24.0683i) q^{26} +290.478 q^{27} +(-96.7056 + 167.499i) q^{28} +(-113.502 + 196.592i) q^{29} +(-55.5780 - 96.2639i) q^{30} -5.28086 q^{31} +(56.6236 + 98.0750i) q^{32} +(-50.8349 - 88.0487i) q^{33} -19.6121 q^{34} +(-242.381 - 419.816i) q^{35} +(222.071 - 384.638i) q^{36} +(-152.373 + 263.918i) q^{37} -46.2617 q^{38} +(-251.962 + 352.420i) q^{39} -187.630 q^{40} +(75.3137 - 130.447i) q^{41} +(-74.2221 + 128.557i) q^{42} +(86.0343 + 149.016i) q^{43} -83.6171 q^{44} +(556.593 + 964.048i) q^{45} +(-30.2396 - 52.3765i) q^{46} -411.411 q^{47} +(-252.308 - 437.010i) q^{48} +(-152.189 + 263.600i) q^{49} +(75.1134 - 130.100i) q^{50} +287.170 q^{51} +(147.401 + 324.382i) q^{52} +185.777 q^{53} +(91.6785 - 158.792i) q^{54} +(104.788 - 181.498i) q^{55} +(125.286 + 217.001i) q^{56} +677.386 q^{57} +(71.6457 + 124.094i) q^{58} +(-219.804 - 380.711i) q^{59} +1338.60 q^{60} +(253.525 + 439.117i) q^{61} +(-1.66671 + 2.88682i) q^{62} +(743.307 - 1287.45i) q^{63} -365.284 q^{64} +(-888.820 - 86.5658i) q^{65} -64.1766 q^{66} +(351.703 - 609.167i) q^{67} +(118.090 - 204.538i) q^{68} +(442.782 + 766.922i) q^{69} -305.994 q^{70} +(259.555 + 449.563i) q^{71} +(-287.701 - 498.313i) q^{72} -669.636 q^{73} +(96.1817 + 166.592i) q^{74} +(-1099.85 + 1904.99i) q^{75} +(278.554 - 482.469i) q^{76} -279.880 q^{77} +(113.131 + 248.965i) q^{78} -42.5996 q^{79} +(520.092 - 900.825i) q^{80} +(-553.627 + 958.910i) q^{81} +(-47.5399 - 82.3416i) q^{82} +57.1927 q^{83} +(-893.822 - 1548.15i) q^{84} +(295.978 + 512.648i) q^{85} +108.614 q^{86} +(-1049.07 - 1817.04i) q^{87} +(-54.1646 + 93.8158i) q^{88} +(-260.707 + 451.558i) q^{89} +702.672 q^{90} +(493.374 + 1085.76i) q^{91} +728.322 q^{92} +(24.4047 - 42.2702i) q^{93} +(-129.846 + 224.901i) q^{94} +(698.161 + 1209.25i) q^{95} -1046.71 q^{96} +(-848.970 - 1470.46i) q^{97} +(96.0659 + 166.391i) q^{98} +642.705 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) $ 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20} - 368 q^{21} + 215 q^{23} - 214 q^{24} + 190 q^{25} + 123 q^{26} - 384 q^{27} + 358 q^{28} + 157 q^{29} - 829 q^{30} - 788 q^{31} + 553 q^{32} + 66 q^{33} - 1404 q^{34} - 58 q^{35} + 700 q^{36} - 88 q^{37} - 2636 q^{38} + 798 q^{39} + 1466 q^{40} + 512 q^{41} - 337 q^{42} - 927 q^{43} + 1100 q^{44} + 1482 q^{45} + 1361 q^{46} - 286 q^{47} + 178 q^{48} - 1835 q^{49} + 583 q^{50} - 1136 q^{51} + 2306 q^{52} + 212 q^{53} + 67 q^{54} + 264 q^{55} - 2059 q^{56} + 2596 q^{57} + 1690 q^{58} + 266 q^{59} + 74 q^{60} + 624 q^{61} - 643 q^{62} + 2360 q^{63} - 3178 q^{64} + 470 q^{65} + 352 q^{66} + 676 q^{67} + 413 q^{68} - 764 q^{69} - 2122 q^{70} + 763 q^{71} + 1366 q^{72} - 4748 q^{73} + 1649 q^{74} - 2420 q^{75} + 2101 q^{76} - 1364 q^{77} - 5848 q^{78} + 4328 q^{79} + 1013 q^{80} - 537 q^{81} - 3152 q^{82} + 1554 q^{83} + 3381 q^{84} + 1690 q^{85} + 5788 q^{86} + 4200 q^{87} + 231 q^{88} + 1687 q^{89} - 10798 q^{90} - 3380 q^{91} + 11084 q^{92} + 4310 q^{93} - 1777 q^{94} - 1124 q^{95} - 6930 q^{96} + 2047 q^{97} - 1553 q^{98} + 2970 q^{99}+O(q^{100}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9 - 2 * q^10 - 187 * q^11 - 254 * q^12 + 76 * q^13 + 148 * q^15 - 126 * q^16 + 74 * q^17 + 180 * q^18 + 159 * q^19 + 222 * q^20 - 368 * q^21 + 215 * q^23 - 214 * q^24 + 190 * q^25 + 123 * q^26 - 384 * q^27 + 358 * q^28 + 157 * q^29 - 829 * q^30 - 788 * q^31 + 553 * q^32 + 66 * q^33 - 1404 * q^34 - 58 * q^35 + 700 * q^36 - 88 * q^37 - 2636 * q^38 + 798 * q^39 + 1466 * q^40 + 512 * q^41 - 337 * q^42 - 927 * q^43 + 1100 * q^44 + 1482 * q^45 + 1361 * q^46 - 286 * q^47 + 178 * q^48 - 1835 * q^49 + 583 * q^50 - 1136 * q^51 + 2306 * q^52 + 212 * q^53 + 67 * q^54 + 264 * q^55 - 2059 * q^56 + 2596 * q^57 + 1690 * q^58 + 266 * q^59 + 74 * q^60 + 624 * q^61 - 643 * q^62 + 2360 * q^63 - 3178 * q^64 + 470 * q^65 + 352 * q^66 + 676 * q^67 + 413 * q^68 - 764 * q^69 - 2122 * q^70 + 763 * q^71 + 1366 * q^72 - 4748 * q^73 + 1649 * q^74 - 2420 * q^75 + 2101 * q^76 - 1364 * q^77 - 5848 * q^78 + 4328 * q^79 + 1013 * q^80 - 537 * q^81 - 3152 * q^82 + 1554 * q^83 + 3381 * q^84 + 1690 * q^85 + 5788 * q^86 + 4200 * q^87 + 231 * q^88 + 1687 * q^89 - 10798 * q^90 - 3380 * q^91 + 11084 * q^92 + 4310 * q^93 - 1777 * q^94 - 1124 * q^95 - 6930 * q^96 + 2047 * q^97 - 1553 * q^98 + 2970 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.315613	−	0.546657i	0.111586	−	0.193273i	−0.804824	−	0.593514i	$-0.797740\pi$
$2$	0.315613	−	0.546657i	0.111586	−	0.193273i	0.916410	+	0.400241i	$0.131074\pi$
$3$	−4.62136	+	8.00442i	−0.889381	+	1.54045i	−0.0487715	+	0.998810i	$0.515531\pi$
$3$	−4.62136	+	8.00442i	−0.889381	+	1.54045i	−0.840609	+	0.541642i	$0.817803\pi$
$4$	3.80078	+	6.58314i	0.475097	+	0.822892i
$5$	−19.0524			−1.70409			−0.852047	−	0.523465i	$-0.824639\pi$
$5$	−19.0524			−1.70409			−0.852047	+	0.523465i	$0.824639\pi$
$6$	2.91712	+	5.05260i	0.198485	+	0.343786i
$7$	12.7218	+	22.0348i	0.686914	+	1.18977i	0.972831	+	0.231515i	$0.0743683\pi$
$7$	12.7218	+	22.0348i	0.686914	+	1.18977i	−0.285917	+	0.958254i	$0.592298\pi$
$8$	9.84810			0.435229
$9$	−29.2139	−	50.5999i	−1.08200	−	1.87407i
$10$	−6.01317	+	10.4151i	−0.190153	+	0.329355i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$12$	−70.2590			−1.69017
$13$	46.6514	+	4.54358i	0.995291	+	0.0969355i
$13$	46.6514	+	4.54358i	0.995291	+	0.0969355i
$14$	16.0607			0.306600
$15$	88.0477	−	152.503i	1.51559	−	2.62508i
$16$	−27.2980	+	47.2816i	−0.426532	+	0.738775i
$17$	−15.5350	−	26.9073i	−0.221634	−	0.383882i	0.733670	−	0.679506i	$-0.237806\pi$
$17$	−15.5350	−	26.9073i	−0.221634	−	0.383882i	−0.955304	+	0.295624i	$0.904472\pi$
$18$	−36.8811			−0.482942
$19$	−36.6443	−	63.4698i	−0.442462	−	0.766367i	0.555409	−	0.831577i	$-0.312562\pi$
$19$	−36.6443	−	63.4698i	−0.442462	−	0.766367i	−0.997872	+	0.0652099i	$0.979228\pi$
$20$	−72.4137	−	125.424i	−0.809610	−	1.40229i
$21$	−235.168			−2.44371
$22$	3.47174	+	6.01323i	0.0336444	+	0.0582739i
$23$	47.9061	−	82.9758i	0.434309	−	0.752246i	−0.562930	−	0.826505i	$-0.690326\pi$
$23$	47.9061	−	82.9758i	0.434309	−	0.752246i	0.997239	+	0.0742590i	$0.0236592\pi$
$24$	−45.5116	+	78.8284i	−0.387084	+	0.670449i
$25$	237.992			1.90394
$26$	17.2076	−	24.0683i	0.129795	−	0.181546i
$27$	290.478			2.07046
$28$	−96.7056	+	167.499i	−0.652702	+	1.13051i
$29$	−113.502	+	196.592i	−0.726789	+	1.25884i	0.231444	+	0.972848i	$0.425655\pi$
$29$	−113.502	+	196.592i	−0.726789	+	1.25884i	−0.958233	+	0.285987i	$0.907678\pi$
$30$	−55.5780	−	96.2639i	−0.338237	−	0.585843i
$31$	−5.28086			−0.0305958			−0.0152979	−	0.999883i	$-0.504870\pi$
$31$	−5.28086			−0.0305958			−0.0152979	+	0.999883i	$0.504870\pi$
$32$	56.6236	+	98.0750i	0.312804	+	0.541793i
$33$	−50.8349	−	88.0487i	−0.268158	−	0.464464i
$34$	−19.6121			−0.0989251
$35$	−242.381	−	419.816i	−1.17057	−	2.02748i
$36$	222.071	−	384.638i	1.02811	−	1.78073i
$37$	−152.373	+	263.918i	−0.677026	+	1.17264i	0.298847	+	0.954301i	$0.403398\pi$
$37$	−152.373	+	263.918i	−0.677026	+	1.17264i	−0.975872	+	0.218342i	$0.929935\pi$
$38$	−46.2617			−0.197490
$39$	−251.962	+	352.420i	−1.03452	+	1.44699i
$40$	−187.630			−0.741671
$41$	75.3137	−	130.447i	0.286879	−	0.496888i	−0.686184	−	0.727428i	$-0.740716\pi$
$41$	75.3137	−	130.447i	0.286879	−	0.496888i	0.973063	+	0.230539i	$0.0740491\pi$
$42$	−74.2221	+	128.557i	−0.272684	+	0.472302i
$43$	86.0343	+	149.016i	0.305119	+	0.528481i	0.977288	−	0.211916i	$-0.0679705\pi$
$43$	86.0343	+	149.016i	0.305119	+	0.528481i	−0.672169	+	0.740398i	$0.734637\pi$
$44$	−83.6171			−0.286494
$45$	556.593	+	964.048i	1.84382	+	3.19359i
$46$	−30.2396	−	52.3765i	−0.0969257	−	0.167880i
$47$	−411.411			−1.27682			−0.638408	−	0.769698i	$-0.720407\pi$
$47$	−411.411			−1.27682			−0.638408	+	0.769698i	$0.720407\pi$
$48$	−252.308	−	437.010i	−0.758698	−	1.31410i
$49$	−152.189	+	263.600i	−0.443701	+	0.768513i
$50$	75.1134	−	130.100i	0.212453	−	0.367979i
$51$	287.170			0.788469
$52$	147.401	+	324.382i	0.393092	+	0.865071i
$53$	185.777			0.481481			0.240740	−	0.970590i	$-0.422610\pi$
$53$	185.777			0.481481			0.240740	+	0.970590i	$0.422610\pi$
$54$	91.6785	−	158.792i	0.231035	−	0.400164i
$55$	104.788	−	181.498i	0.256902	−	0.444967i
$56$	125.286	+	217.001i	0.298965	+	0.517822i
$57$	677.386			1.57407
$58$	71.6457	+	124.094i	0.162199	+	0.280937i
$59$	−219.804	−	380.711i	−0.485017	−	0.840074i	0.514835	−	0.857289i	$-0.327853\pi$
$59$	−219.804	−	380.711i	−0.485017	−	0.840074i	−0.999852	+	0.0172151i	$0.994520\pi$
$60$	1338.60			2.88021
$61$	253.525	+	439.117i	0.532139	+	0.921692i	0.999296	+	0.0375178i	$0.0119451\pi$
$61$	253.525	+	439.117i	0.532139	+	0.921692i	−0.467157	+	0.884175i	$0.654722\pi$
$62$	−1.66671	+	2.88682i	−0.00341406	+	0.00591333i
$63$	743.307	−	1287.45i	1.48648	−	2.57465i
$64$	−365.284			−0.713445
$65$	−888.820	−	86.5658i	−1.69607	−	0.165187i
$66$	−64.1766			−0.119691
$67$	351.703	−	609.167i	0.641303	−	1.11077i	−0.343839	−	0.939029i	$-0.611727\pi$
$67$	351.703	−	609.167i	0.641303	−	1.11077i	0.985142	−	0.171741i	$-0.0549392\pi$
$68$	118.090	−	204.538i	0.210596	−	0.364762i
$69$	442.782	+	766.922i	0.772532	+	1.33807i
$70$	−305.994			−0.522475
$71$	259.555	+	449.563i	0.433853	+	0.751455i	0.997201	−	0.0747643i	$-0.0238204\pi$
$71$	259.555	+	449.563i	0.433853	+	0.751455i	−0.563348	+	0.826219i	$0.690487\pi$
$72$	−287.701	−	498.313i	−0.470916	−	0.815650i
$73$	−669.636			−1.07363			−0.536815	−	0.843700i	$-0.680373\pi$
$73$	−669.636			−1.07363			−0.536815	+	0.843700i	$0.680373\pi$
$74$	96.1817	+	166.592i	0.151093	+	0.261701i
$75$	−1099.85	+	1904.99i	−1.69332	+	2.93292i
$76$	278.554	−	482.469i	0.420425	−	0.728198i
$77$	−279.880			−0.414225
$78$	113.131	+	248.965i	0.164225	+	0.361407i
$79$	−42.5996			−0.0606688			−0.0303344	−	0.999540i	$-0.509657\pi$
$79$	−42.5996			−0.0606688			−0.0303344	+	0.999540i	$0.509657\pi$
$80$	520.092	−	900.825i	0.726850	−	1.25894i
$81$	−553.627	+	958.910i	−0.759433	+	1.31538i
$82$	−47.5399	−	82.3416i	−0.0640233	−	0.110892i
$83$	57.1927			0.0756351			0.0378176	−	0.999285i	$-0.487959\pi$
$83$	57.1927			0.0756351			0.0378176	+	0.999285i	$0.487959\pi$
$84$	−893.822	−	1548.15i	−1.16100	−	2.01091i
$85$	295.978	+	512.648i	0.377686	+	0.654171i
$86$	108.614			0.136188
$87$	−1049.07	−	1817.04i	−1.29278	−	2.23917i
$88$	−54.1646	+	93.8158i	−0.0656132	+	0.113645i
$89$	−260.707	+	451.558i	−0.310504	+	0.537809i	−0.978472	−	0.206381i	$-0.933831\pi$
$89$	−260.707	+	451.558i	−0.310504	+	0.537809i	0.667967	+	0.744191i	$0.267165\pi$
$90$	702.672			0.822979
$91$	493.374	+	1085.76i	0.568348	+	1.25075i
$92$	728.322			0.825356
$93$	24.4047	−	42.2702i	0.0272113	−	0.0471314i
$94$	−129.846	+	224.901i	−0.142475	+	0.246774i
$95$	698.161	+	1209.25i	0.753998	+	1.30596i
$96$	−1046.71			−1.11281
$97$	−848.970	−	1470.46i	−0.888658	−	1.53920i	−0.841462	−	0.540316i	$-0.818305\pi$
$97$	−848.970	−	1470.46i	−0.888658	−	1.53920i	−0.0471961	−	0.998886i	$-0.515029\pi$
$98$	96.0659	+	166.391i	0.0990216	+	0.171511i
$99$	642.705			0.652468
$100$	904.555	+	1566.74i	0.904555	+	1.56674i
$101$	−373.262	+	646.509i	−0.367732	+	0.636931i	−0.989211	−	0.146500i	$-0.953199\pi$
$101$	−373.262	+	646.509i	−0.367732	+	0.636931i	0.621478	+	0.783431i	$0.286532\pi$
$102$	90.6347	−	156.984i	0.0879821	−	0.152389i
$103$	−888.476			−0.849943			−0.424971	−	0.905207i	$-0.639716\pi$
$103$	−888.476			−0.849943			−0.424971	+	0.905207i	$0.639716\pi$
$104$	459.428	+	44.7456i	0.433179	+	0.0421891i
$105$	4480.51			4.16431
$106$	58.6337	−	101.557i	0.0537265	−	0.0930571i
$107$	−525.786	+	910.688i	−0.475044	+	0.822800i	−0.999591	−	0.0285814i	$-0.990901\pi$
$107$	−525.786	+	910.688i	−0.475044	+	0.822800i	0.524548	+	0.851381i	$0.324234\pi$
$108$	1104.04	+	1912.26i	0.983671	+	1.70377i
$109$	−538.332			−0.473054			−0.236527	−	0.971625i	$-0.576009\pi$
$109$	−538.332			−0.473054			−0.236527	+	0.971625i	$0.576009\pi$
$110$	−66.1448	−	114.566i	−0.0573333	−	0.0993042i
$111$	−1408.34	−	2439.31i	−1.20427	−	2.08585i
$112$	−1389.12			−1.17196
$113$	299.156	+	518.154i	0.249046	+	0.431361i	0.963261	−	0.268565i	$-0.0865495\pi$
$113$	299.156	+	518.154i	0.249046	+	0.431361i	−0.714215	+	0.699926i	$0.753216\pi$
$114$	213.792	−	370.298i	0.175644	−	0.304225i
$115$	−912.724	+	1580.88i	−0.740104	+	1.28190i
$116$	−1725.59			−1.38118
$117$	−1132.96	−	2493.29i	−0.895236	−	1.97013i
$118$	−277.492			−0.216484
$119$	395.266	−	684.621i	0.304487	−	0.527387i
$120$	867.103	−	1501.87i	0.659628	−	1.14251i
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$	320.062			0.237517
$123$	696.103	+	1205.69i	0.510288	+	0.883845i
$124$	−20.0714	−	34.7646i	−0.0145360	−	0.0251771i
$125$	−2152.77			−1.54039
$126$	−469.195	−	812.669i	−0.331740	−	0.574590i
$127$	424.192	−	734.723i	0.296386	−	0.513355i	−0.678921	−	0.734212i	$-0.737552\pi$
$127$	424.192	−	734.723i	0.296386	−	0.513355i	0.975306	+	0.220857i	$0.0708853\pi$
$128$	−568.277	+	984.285i	−0.392415	+	0.679682i
$129$	−1590.38			−1.08547
$130$	−327.845	+	458.559i	−0.221184	+	0.309371i
$131$	−1687.43			−1.12543			−0.562715	−	0.826651i	$-0.690243\pi$
$131$	−1687.43			−1.12543			−0.562715	+	0.826651i	$0.690243\pi$
$132$	386.424	−	669.307i	0.254803	−	0.441331i
$133$	932.365	−	1614.90i	0.607867	−	1.05286i
$134$	−222.004	−	384.522i	−0.143121	−	0.247893i
$135$	−5534.29			−3.52826
$136$	−152.990	−	264.986i	−0.0964616	−	0.167076i
$137$	654.115	+	1132.96i	0.407919	+	0.706536i	0.994656	−	0.103241i	$-0.0329214\pi$
$137$	654.115	+	1132.96i	0.407919	+	0.706536i	−0.586738	+	0.809777i	$0.699588\pi$
$138$	558.991			0.344815
$139$	1234.62	+	2138.42i	0.753373	+	1.30488i	0.946179	+	0.323644i	$0.104908\pi$
$139$	1234.62	+	2138.42i	0.753373	+	1.30488i	−0.192806	+	0.981237i	$0.561759\pi$
$140$	1842.47	−	3191.25i	1.11226	−	1.92650i
$141$	1901.27	−	3293.10i	1.13558	−	1.96688i
$142$	327.676			0.193648
$143$	−299.866	+	419.425i	−0.175357	+	0.245273i
$144$	3189.93			1.84602
$145$	2162.49	−	3745.54i	1.23852	−	2.14517i
$146$	−211.346	+	366.062i	−0.119802	+	0.207503i
$147$	−1406.64	−	2436.38i	−0.789238	−	1.36700i
$148$	−2316.54			−1.28661
$149$	−66.9997	−	116.047i	−0.0368378	−	0.0638049i	0.847019	−	0.531563i	$-0.178395\pi$
$149$	−66.9997	−	116.047i	−0.0368378	−	0.0638049i	−0.883856	+	0.467758i	$0.845062\pi$
$150$	694.252	+	1202.48i	0.377903	+	0.654547i
$151$	2031.76			1.09498			0.547491	−	0.836811i	$-0.315583\pi$
$151$	2031.76			1.09498			0.547491	+	0.836811i	$0.315583\pi$
$152$	−360.877	−	625.057i	−0.192572	−	0.333545i
$153$	−907.673	+	1572.14i	−0.479614	+	0.830717i
$154$	−88.3337	+	152.999i	−0.0462217	+	0.0800583i
$155$	100.613			0.0521381
$156$	−3277.68	−	319.227i	−1.68221	−	0.163837i
$157$	−2957.38			−1.50334			−0.751672	−	0.659537i	$-0.770752\pi$
$157$	−2957.38			−1.50334			−0.751672	+	0.659537i	$0.770752\pi$
$158$	−13.4450	+	23.2874i	−0.00676979	+	0.0117256i
$159$	−858.544	+	1487.04i	−0.428220	+	0.741698i
$160$	−1078.81	−	1868.56i	−0.533048	−	0.923266i
$161$	2437.81			1.19333
$162$	349.463	+	605.288i	0.169484	+	0.293555i
$163$	488.415	+	845.959i	0.234697	+	0.406507i	0.959185	−	0.282781i	$-0.0912569\pi$
$163$	488.415	+	845.959i	0.234697	+	0.406507i	−0.724488	+	0.689288i	$0.757924\pi$
$164$	1145.00			0.545181
$165$	968.525	+	1677.53i	0.456967	+	0.791490i
$166$	18.0508	−	31.2648i	0.00843982	−	0.0146182i
$167$	1468.22	−	2543.04i	0.680327	−	1.17836i	−0.294555	−	0.955635i	$-0.595171\pi$
$167$	1468.22	−	2543.04i	0.680327	−	1.17836i	0.974881	−	0.222726i	$-0.0714954\pi$
$168$	−2315.96			−1.06357
$169$	2155.71	+	423.929i	0.981207	+	0.192958i
$170$	373.657			0.168578
$171$	−2141.05	+	3708.40i	−0.957485	+	1.65841i
$172$	−653.995	+	1132.75i	−0.289922	+	0.502160i
$173$	1741.71	+	3016.74i	0.765434	+	1.32577i	0.940017	+	0.341128i	$0.110809\pi$
$173$	1741.71	+	3016.74i	0.765434	+	1.32577i	−0.174583	+	0.984643i	$0.555858\pi$
$174$	−1324.40			−0.577026
$175$	3027.69	+	5244.12i	1.30784	+	2.26525i
$176$	−300.278	−	520.097i	−0.128604	−	0.222749i
$177$	4063.17			1.72546
$178$	164.565	+	285.035i	0.0692958	+	0.120024i
$179$	545.429	−	944.711i	0.227750	−	0.394475i	−0.729391	−	0.684097i	$-0.760196\pi$
$179$	545.429	−	944.711i	0.227750	−	0.394475i	0.957141	+	0.289622i	$0.0935297\pi$
$180$	−4230.97	+	7328.26i	−1.75199	+	3.03453i
$181$	3742.90			1.53706			0.768529	−	0.639815i	$-0.220989\pi$
$181$	3742.90			1.53706			0.768529	+	0.639815i	$0.220989\pi$
$182$	749.254	+	72.9729i	0.305156	+	0.0297204i
$183$	−4686.51			−1.89310
$184$	471.784	−	817.154i	0.189024	−	0.327399i
$185$	2903.06	−	5028.25i	1.15372	−	1.99829i
$186$	−15.4049	−	26.6821i	−0.00607280	−	0.0105184i
$187$	341.769			0.133650
$188$	−1563.68	−	2708.37i	−0.606612	−	1.05068i
$189$	3695.41	+	6400.63i	1.42223	+	2.46337i
$190$	881.394			0.336542
$191$	1016.19	+	1760.10i	0.384969	+	0.666786i	0.991765	−	0.128072i	$-0.0408788\pi$
$191$	1016.19	+	1760.10i	0.384969	+	0.666786i	−0.606796	+	0.794858i	$0.707545\pi$
$192$	1688.11	−	2923.89i	0.634524	−	1.09903i
$193$	−532.343	+	922.045i	−0.198543	+	0.343887i	−0.948056	−	0.318102i	$-0.896954\pi$
$193$	−532.343	+	922.045i	−0.198543	+	0.343887i	0.749513	+	0.661990i	$0.230288\pi$
$194$	−1071.78			−0.396647
$195$	4800.46	−	6714.44i	1.76291	−	2.46580i
$196$	−2313.75			−0.843204
$197$	944.907	−	1636.63i	0.341735	−	0.591903i	−0.643020	−	0.765849i	$-0.722319\pi$
$197$	944.907	−	1636.63i	0.341735	−	0.591903i	0.984755	+	0.173947i	$0.0556521\pi$
$198$	202.846	−	351.340i	0.0728063	−	0.126104i
$199$	−154.894	−	268.285i	−0.0551767	−	0.0955688i	0.837118	−	0.547023i	$-0.184239\pi$
$199$	−154.894	−	268.285i	−0.0551767	−	0.0955688i	−0.892294	+	0.451454i	$0.850906\pi$
$200$	2343.77			0.828648
$201$	3250.69	+	5630.35i	1.14072	+	1.97579i
$202$	235.613	+	408.093i	0.0820676	+	0.142145i
$203$	−5775.83			−1.99697
$204$	1091.47	+	1890.48i	0.374599	+	0.648825i
$205$	−1434.90	+	2485.32i	−0.488868	+	0.846744i
$206$	−280.414	+	485.692i	−0.0948417	+	0.164271i
$207$	−5598.09			−1.87968
$208$	−1488.32	+	2081.72i	−0.496137	+	0.693949i
$209$	806.175			0.266815
$210$	1414.11	−	2449.30i	0.464679	−	0.804848i
$211$	−2029.00	+	3514.33i	−0.662000	+	1.14662i	0.318089	+	0.948061i	$0.396959\pi$
$211$	−2029.00	+	3514.33i	−0.662000	+	1.14662i	−0.980089	+	0.198557i	$0.936375\pi$
$212$	706.098	+	1223.00i	0.228750	+	0.396207i
$213$	−4797.99			−1.54344
$214$	331.890	+	574.850i	0.106016	+	0.183626i
$215$	−1639.16	−	2839.10i	−0.519951	−	0.900582i
$216$	2860.65			0.901125
$217$	−67.1821	−	116.363i	−0.0210167	−	0.0364020i
$218$	−169.905	+	294.283i	−0.0527862	+	0.0914284i
$219$	3094.63	−	5360.05i	0.954866	−	1.65388i
$220$	1593.10			0.488213
$221$	−602.473	−	1325.85i	−0.183379	−	0.403558i
$222$	−1777.96			−0.537517
$223$	−1420.33	+	2460.09i	−0.426514	+	0.738743i	−0.996560	−	0.0828689i	$-0.973592\pi$
$223$	−1420.33	+	2460.09i	−0.426514	+	0.738743i	0.570047	+	0.821612i	$0.306925\pi$
$224$	−1440.71	+	2495.39i	−0.429739	+	0.744330i
$225$	−6952.67	−	12042.4i	−2.06005	−	3.56811i
$226$	377.670			0.111160
$227$	−2634.60	−	4563.25i	−0.770327	−	1.33425i	−0.937384	−	0.348298i	$-0.886760\pi$
$227$	−2634.60	−	4563.25i	−0.770327	−	1.33425i	0.167057	−	0.985947i	$-0.446574\pi$
$228$	2574.59	+	4459.33i	0.747836	+	1.29529i
$229$	−2708.47			−0.781576			−0.390788	−	0.920481i	$-0.627797\pi$
$229$	−2708.47			−0.781576			−0.390788	+	0.920481i	$0.627797\pi$
$230$	576.135	+	997.895i	0.165170	+	0.286084i
$231$	1293.43	−	2240.28i	0.368403	−	0.638093i
$232$	−1117.78	+	1936.06i	−0.316319	+	0.547881i
$233$	6366.14			1.78996			0.894978	−	0.446110i	$-0.147191\pi$
$233$	6366.14			1.78996			0.894978	+	0.446110i	$0.147191\pi$
$234$	−1720.56	−	167.572i	−0.480668	−	0.0468142i
$235$	7838.34			2.17582
$236$	1670.85	−	2894.00i	0.460861	−	0.798234i
$237$	196.868	−	340.986i	0.0539576	−	0.0934574i
$238$	−249.502	−	432.150i	−0.0679530	−	0.117698i
$239$	1601.70			0.433495			0.216748	−	0.976228i	$-0.430455\pi$
$239$	1601.70			0.433495			0.216748	+	0.976228i	$0.430455\pi$
$240$	4807.06	+	8326.07i	1.29289	+	2.23936i
$241$	2521.24	+	4366.91i	0.673889	+	1.16721i	0.976792	+	0.214188i	$0.0687106\pi$
$241$	2521.24	+	4366.91i	0.673889	+	1.16721i	−0.302904	+	0.953021i	$0.597956\pi$
$242$	−76.3783			−0.0202884
$243$	−1195.56	−	2070.78i	−0.315619	−	0.546668i
$244$	−1927.18	+	3337.98i	−0.505636	+	0.875787i
$245$	2899.57	−	5022.20i	0.756108	−	1.30962i
$246$	878.796			0.227764
$247$	−1421.13	−	3127.45i	−0.366090	−	0.805649i
$248$	−52.0064			−0.0133162
$249$	−264.308	+	457.795i	−0.0672684	+	0.116512i
$250$	−679.441	+	1176.83i	−0.171886	+	0.297716i
$251$	464.753	+	804.975i	0.116872	+	0.202429i	0.918527	−	0.395359i	$-0.129380\pi$
$251$	464.753	+	804.975i	0.116872	+	0.202429i	−0.801654	+	0.597788i	$0.796047\pi$
$252$	11300.6			2.82488
$253$	526.967	+	912.734i	0.130949	+	0.226811i
$254$	−267.761	−	463.776i	−0.0661450	−	0.114566i
$255$	−5471.27			−1.34362
$256$	−1102.42	−	1909.46i	−0.269147	−	0.466176i
$257$	667.647	−	1156.40i	0.162049	−	0.280678i	−0.773554	−	0.633730i	$-0.781523\pi$
$257$	667.647	−	1156.40i	0.162049	−	0.280678i	0.935604	+	0.353052i	$0.114856\pi$
$258$	−501.945	+	869.394i	−0.121123	+	0.209791i
$259$	−7753.84			−1.86023
$260$	−2808.33	−	6180.24i	−0.669866	−	1.47416i
$261$	13263.4			3.14553
$262$	−532.574	+	922.446i	−0.125582	+	0.217515i
$263$	−641.931	+	1111.86i	−0.150506	+	0.260684i	−0.931414	−	0.363962i	$-0.881424\pi$
$263$	−641.931	+	1111.86i	−0.150506	+	0.260684i	0.780907	+	0.624647i	$0.214757\pi$
$264$	−500.628	−	867.112i	−0.116710	−	0.202148i
$265$	−3539.50			−0.820489
$266$	−588.533	−	1019.37i	−0.135659	−	0.234968i
$267$	−2409.64	−	4173.62i	−0.552313	−	0.956634i
$268$	5346.97			1.21873
$269$	3959.03	+	6857.24i	0.897347	+	1.55425i	0.830873	+	0.556462i	$0.187842\pi$
$269$	3959.03	+	6857.24i	0.897347	+	1.55425i	0.0664739	+	0.997788i	$0.478825\pi$
$270$	−1746.69	+	3025.36i	−0.393705	+	0.681916i
$271$	737.461	−	1277.32i	0.165305	−	0.286316i	−0.771459	−	0.636279i	$-0.780473\pi$
$271$	737.461	−	1277.32i	0.165305	−	0.286316i	0.936763	+	0.349963i	$0.113806\pi$
$272$	1696.30			0.378136
$273$	−10970.9	−	1068.51i	−2.43220	−	0.236882i
$274$	825.789			0.182072
$275$	−1308.96	+	2267.18i	−0.287029	+	0.497149i
$276$	−3365.83	+	5829.80i	−0.734056	+	1.27142i
$277$	−2265.55	−	3924.05i	−0.491422	−	0.851168i	0.508529	−	0.861045i	$-0.330189\pi$
$277$	−2265.55	−	3924.05i	−0.491422	−	0.851168i	−0.999951	+	0.00987688i	$0.996856\pi$
$278$	1558.64			0.336264
$279$	154.274	+	267.211i	0.0331045	+	0.0573387i
$280$	−2386.99	−	4134.39i	−0.509464	−	0.882417i
$281$	−7496.75			−1.59152			−0.795762	−	0.605609i	$-0.792929\pi$
$281$	−7496.75			−1.59152			−0.795762	+	0.605609i	$0.792929\pi$
$282$	−1200.13	−	2078.69i	−0.253429	−	0.438952i
$283$	−1671.16	+	2894.53i	−0.351025	+	0.607993i	−0.986429	−	0.164186i	$-0.947500\pi$
$283$	−1671.16	+	2894.53i	−0.351025	+	0.607993i	0.635404	+	0.772180i	$0.280833\pi$
$284$	−1973.02	+	3417.38i	−0.412244	+	0.714028i
$285$	−12905.8			−2.68236
$286$	134.640	+	296.300i	0.0278372	+	0.0612608i
$287$	3832.51			0.788243
$288$	3308.39	−	5730.30i	0.676906	−	1.17244i
$289$	1973.83	−	3418.77i	0.401757	−	0.695863i
$290$	−1365.02	−	2364.28i	−0.276402	−	0.478743i
$291$	15693.6			3.16142
$292$	−2545.14	−	4408.31i	−0.510079	−	0.883482i
$293$	3331.69	+	5770.65i	0.664298	+	1.15060i	0.979475	+	0.201565i	$0.0646027\pi$
$293$	3331.69	+	5770.65i	0.664298	+	1.15060i	−0.315177	+	0.949033i	$0.602064\pi$
$294$	−1775.82			−0.352272
$295$	4187.78	+	7253.45i	0.826515	+	1.43157i
$296$	−1500.58	+	2599.09i	−0.294661	+	0.510368i
$297$	−1597.63	+	2767.17i	−0.312134	+	0.540632i
$298$	−84.5838			−0.0164423
$299$	2611.90	−	3653.28i	0.505183	−	0.706603i
$300$	−16721.1			−3.21798
$301$	−2189.03	+	3791.50i	−0.419181	+	0.726042i
$302$	641.250	−	1110.68i	0.122185	−	0.211630i
$303$	−3449.96	−	5975.50i	−0.654108	−	1.13295i
$304$	4001.27			0.754897
$305$	−4830.24	−	8366.22i	−0.906816	−	1.57065i
$306$	572.947	+	992.372i	0.107037	+	0.185393i
$307$	8345.10			1.55140			0.775701	−	0.631101i	$-0.217397\pi$
$307$	8345.10			1.55140			0.775701	+	0.631101i	$0.217397\pi$
$308$	−1063.76	−	1842.49i	−0.196797	−	0.340862i
$309$	4105.96	−	7111.74i	0.755923	−	1.30930i
$310$	31.7547	−	55.0007i	0.00581789	−	0.0100769i
$311$	−2835.06			−0.516917			−0.258459	−	0.966022i	$-0.583215\pi$
$311$	−2835.06			−0.516917			−0.258459	+	0.966022i	$0.583215\pi$
$312$	−2481.34	+	3470.67i	−0.450251	+	0.629770i
$313$	−3565.35			−0.643852			−0.321926	−	0.946765i	$-0.604330\pi$
$313$	−3565.35			−0.643852			−0.321926	+	0.946765i	$0.604330\pi$
$314$	−933.389	+	1616.68i	−0.167752	+	0.290555i
$315$	−14161.8	+	24528.9i	−2.53309	+	4.38745i
$316$	−161.912	−	280.439i	−0.0288236	−	0.0499239i
$317$	−3594.01			−0.636782			−0.318391	−	0.947959i	$-0.603142\pi$
$317$	−3594.01			−0.636782			−0.318391	+	0.947959i	$0.603142\pi$
$318$	541.935	+	938.658i	0.0955666	+	0.165526i
$319$	−1248.53	−	2162.51i	−0.219135	−	0.379553i
$320$	6959.52			1.21578
$321$	−4859.69	−	8417.23i	−0.844989	−	1.46356i
$322$	769.405	−	1332.65i	0.133159	−	0.230638i
$323$	−1138.54	+	1972.00i	−0.196130	+	0.339706i
$324$	−8416.85			−1.44322
$325$	11102.7	+	1081.34i	1.89497	+	0.184559i
$326$	616.600			0.104756
$327$	2487.83	−	4309.04i	0.420725	−	0.728717i
$328$	741.697	−	1284.66i	0.124858	−	0.216260i
$329$	−5233.89	−	9065.37i	−0.877063	−	1.51912i
$330$	1222.72			0.203964
$331$	740.444	+	1282.49i	0.122956	+	0.212966i	0.920932	−	0.389723i	$-0.127429\pi$
$331$	740.444	+	1282.49i	0.122956	+	0.212966i	−0.797976	+	0.602689i	$0.794096\pi$
$332$	217.377	+	376.508i	0.0359340	+	0.0622396i
$333$	17805.6			2.93015
$334$	−926.780	−	1605.23i	−0.151830	−	0.262977i
$335$	−6700.76	+	11606.1i	−1.09284	+	1.89286i
$336$	6419.63	−	11119.1i	1.04232	−	1.80535i
$337$	−3115.02			−0.503519			−0.251759	−	0.967790i	$-0.581009\pi$
$337$	−3115.02			−0.503519			−0.251759	+	0.967790i	$0.581009\pi$
$338$	912.114	−	1044.64i	0.146782	−	0.168109i
$339$	−5530.03			−0.885988
$340$	−2249.89	+	3896.92i	−0.358875	+	0.621589i
$341$	29.0447	−	50.3069i	0.00461249	−	0.00798907i
$342$	1351.48	+	2340.84i	0.213684	+	0.370111i
$343$	982.661			0.154690
$344$	847.275	+	1467.52i	0.132796	+	0.230010i
$345$	−8436.05	−	14611.7i	−1.31647	−	2.28019i
$346$	2198.83			0.341647
$347$	1678.64	+	2907.49i	0.259695	+	0.449804i	0.966160	−	0.257943i	$-0.0830447\pi$
$347$	1678.64	+	2907.49i	0.259695	+	0.449804i	−0.706465	+	0.707748i	$0.749711\pi$
$348$	7974.57	−	13812.4i	1.22840	−	2.12764i
$349$	−369.823	+	640.552i	−0.0567225	+	0.0982463i	−0.892992	−	0.450072i	$-0.851398\pi$
$349$	−369.823	+	640.552i	−0.0567225	+	0.0982463i	0.836270	+	0.548318i	$0.184732\pi$
$350$	3822.32			0.583747
$351$	13551.2	+	1319.81i	2.06071	+	0.200701i
$352$	−1245.72			−0.188628
$353$	−1196.65	+	2072.65i	−0.180428	+	0.312510i	−0.942026	−	0.335539i	$-0.891082\pi$
$353$	−1196.65	+	2072.65i	−0.180428	+	0.312510i	0.761599	+	0.648049i	$0.224415\pi$
$354$	1282.39	−	2221.16i	0.192537	−	0.333484i
$355$	−4945.14	−	8565.23i	−0.739326	−	1.28055i
$356$	−3963.56			−0.590079
$357$	3653.33	+	6327.75i	0.541610	+	0.938096i
$358$	−344.289	−	596.326i	−0.0508275	−	0.0880358i
$359$	−2111.90			−0.310478			−0.155239	−	0.987877i	$-0.549615\pi$
$359$	−2111.90			−0.310478			−0.155239	+	0.987877i	$0.549615\pi$
$360$	5481.39	+	9494.04i	0.802484	+	1.38994i
$361$	743.887	−	1288.45i	0.108454	−	0.187848i
$362$	1181.31	−	2046.08i	0.171514	−	0.297071i
$363$	1118.37			0.161706
$364$	−5272.50	+	7374.68i	−0.759215	+	1.06192i
$365$	12758.1			1.82957
$366$	−1479.12	+	2561.92i	−0.211243	+	0.365884i
$367$	−1086.14	+	1881.25i	−0.154485	+	0.267576i	−0.932871	−	0.360209i	$-0.882705\pi$
$367$	−1086.14	+	1881.25i	−0.154485	+	0.267576i	0.778386	+	0.627786i	$0.216039\pi$
$368$	2615.48	+	4530.15i	0.370493	+	0.641713i
$369$	−8800.82			−1.24161
$370$	−1832.49	−	3173.96i	−0.257477	−	0.445963i
$371$	2363.43	+	4093.57i	0.330736	+	0.572851i
$372$	371.028			0.0517121
$373$	2869.95	+	4970.90i	0.398392	+	0.690036i	0.993528	−	0.113590i	$-0.0362349\pi$
$373$	2869.95	+	4970.90i	0.398392	+	0.690036i	−0.595135	+	0.803626i	$0.702902\pi$
$374$	107.867	−	186.831i	0.0149135	−	0.0258310i
$375$	9948.70	−	17231.7i	1.37000	−	2.37290i
$376$	−4051.61			−0.555707
$377$	−6188.28	+	8655.59i	−0.845392	+	1.18246i
$378$	4665.27			0.634803
$379$	−3248.69	+	5626.90i	−0.440301	+	0.762624i	−0.997712	−	0.0676131i	$-0.978462\pi$
$379$	−3248.69	+	5626.90i	−0.440301	+	0.762624i	0.557410	+	0.830237i	$0.311795\pi$
$380$	−5307.11	+	9192.18i	−0.716444	+	1.24092i
$381$	3920.69	+	6790.83i	0.527199	+	0.913136i
$382$	1282.89			0.171829
$383$	−363.052	−	628.824i	−0.0484363	−	0.0838941i	0.840791	−	0.541360i	$-0.182090\pi$
$383$	−363.052	−	628.824i	−0.0484363	−	0.0838941i	−0.889227	+	0.457466i	$0.848757\pi$
$384$	−5252.42	−	9097.47i	−0.698012	−	1.20899i
$385$	5332.37			0.705878
$386$	336.029	+	582.019i	0.0443093	+	0.0767460i
$387$	5026.79	−	8706.66i	0.660274	−	1.14363i
$388$	6453.49	−	11177.8i	0.844398	−	1.46254i
$389$	−8016.40			−1.04485			−0.522426	−	0.852684i	$-0.674973\pi$
$389$	−8016.40			−1.04485			−0.522426	+	0.852684i	$0.674973\pi$
$390$	−2155.41	−	4743.37i	−0.279855	−	0.615872i
$391$	−2976.88			−0.385031
$392$	−1498.78	+	2595.96i	−0.193111	+	0.334479i
$393$	7798.21	−	13506.9i	1.00094	−	1.73367i
$394$	−596.449	−	1033.08i	−0.0762657	−	0.132096i
$395$	811.623			0.103385
$396$	2442.78	+	4231.02i	0.309986	+	0.536911i
$397$	−4015.72	−	6955.43i	−0.507665	−	0.879302i	−0.999961	−	0.00887363i	$-0.997175\pi$
$397$	−4015.72	−	6955.43i	−0.507665	−	0.879302i	0.492296	−	0.870428i	$-0.336158\pi$
$398$	−195.546			−0.0246278
$399$	8617.58	+	14926.1i	1.08125	+	1.87278i
$400$	−6496.72	+	11252.6i	−0.812090	+	1.40658i
$401$	−3127.41	+	5416.82i	−0.389464	+	0.674572i	−0.992378	−	0.123235i	$-0.960673\pi$
$401$	−3127.41	+	5416.82i	−0.389464	+	0.674572i	0.602913	+	0.797807i	$0.294006\pi$
$402$	4103.83			0.509156
$403$	−246.360	−	23.9940i	−0.0304517	−	0.00296582i
$404$	−5674.75			−0.698835
$405$	10547.9	−	18269.5i	1.29415	−	2.24153i
$406$	−1822.93	+	3157.40i	−0.222833	+	0.385959i
$407$	−1676.10	−	2903.09i	−0.204131	−	0.353565i
$408$	2828.08			0.343164
$409$	3222.09	+	5580.82i	0.389540	+	0.674703i	0.992388	−	0.123153i	$-0.0393007\pi$
$409$	3222.09	+	5580.82i	0.389540	+	0.674703i	−0.602848	+	0.797856i	$0.705967\pi$
$410$	905.748	+	1568.80i	0.109102	+	0.188970i
$411$	−12091.6			−1.45118
$412$	−3376.90	−	5848.96i	−0.403805	−	0.699412i
$413$	5592.61	−	9686.68i	0.666330	−	1.15412i
$414$	−1766.83	+	3060.24i	−0.209746	+	0.363291i
$415$	−1089.66			−0.128889
$416$	2195.96	+	4832.61i	0.258812	+	0.569563i
$417$	−22822.4			−2.68014
$418$	254.439	−	440.702i	0.0297728	−	0.0515680i
$419$	−6818.02	+	11809.2i	−0.794946	+	1.37689i	0.127928	+	0.991783i	$0.459167\pi$
$419$	−6818.02	+	11809.2i	−0.794946	+	1.37689i	−0.922874	+	0.385103i	$0.874166\pi$
$420$	17029.4	+	29495.8i	1.97845	+	3.42678i
$421$	−2844.00			−0.329236			−0.164618	−	0.986357i	$-0.552639\pi$
$421$	−2844.00			−0.329236			−0.164618	+	0.986357i	$0.552639\pi$
$422$	1280.76	+	2218.33i	0.147740	+	0.255893i
$423$	12018.9	+	20817.3i	1.38151	+	2.39285i
$424$	1829.55			0.209554
$425$	−3697.20	−	6403.74i	−0.421978	−	0.730887i
$426$	−1514.31	+	2622.86i	−0.172226	+	0.298305i
$427$	−6450.59	+	11172.7i	−0.731068	+	1.26625i
$428$	−7993.58			−0.902767
$429$	−1971.47	−	4338.57i	−0.221872	−	0.488271i
$430$	−2069.35			−0.232077
$431$	3804.83	−	6590.15i	0.425225	−	0.736511i	−0.571216	−	0.820800i	$-0.693528\pi$
$431$	3804.83	−	6590.15i	0.425225	−	0.736511i	0.996441	+	0.0842881i	$0.0268616\pi$
$432$	−7929.47	+	13734.2i	−0.883118	+	1.52960i
$433$	6412.18	+	11106.2i	0.711662	+	1.23263i	0.964233	+	0.265056i	$0.0853905\pi$
$433$	6412.18	+	11106.2i	0.711662	+	1.23263i	−0.252571	+	0.967578i	$0.581276\pi$
$434$	−84.8142			−0.00938067
$435$	19987.3	+	34619.0i	2.20303	+	3.81575i
$436$	−2046.08	−	3543.92i	−0.224747	−	0.389272i
$437$	−7021.95			−0.768662
$438$	−1953.41	−	3383.40i	−0.213099	−	0.369099i
$439$	2997.83	−	5192.39i	0.325919	−	0.564509i	−0.655779	−	0.754953i	$-0.727660\pi$
$439$	2997.83	−	5192.39i	0.325919	−	0.564509i	0.981698	+	0.190444i	$0.0609928\pi$
$440$	1031.96	−	1787.41i	0.111811	−	0.193662i
$441$	17784.2			1.92033
$442$	−914.934	−	89.1092i	−0.0984592	−	0.00958935i
$443$	5507.23			0.590646			0.295323	−	0.955397i	$-0.404573\pi$
$443$	5507.23			0.590646			0.295323	+	0.955397i	$0.404573\pi$
$444$	10705.6	−	18542.6i	1.14429	−	1.98196i
$445$	4967.08	−	8603.24i	0.529129	−	0.916477i
$446$	896.551	+	1552.87i	0.0951859	+	0.164867i
$447$	1238.52			0.131051
$448$	−4647.08	−	8048.97i	−0.490075	−	0.848835i
$449$	6599.68	+	11431.0i	0.693671	+	1.20147i	0.970627	+	0.240590i	$0.0773410\pi$
$449$	6599.68	+	11431.0i	0.693671	+	1.20147i	−0.276956	+	0.960883i	$0.589326\pi$
$450$	−8777.41			−0.919492
$451$	828.450	+	1434.92i	0.0864971	+	0.149817i
$452$	−2274.05	+	3938.77i	−0.236642	+	0.409877i
$453$	−9389.50	+	16263.1i	−0.973857	+	1.68677i
$454$	−3326.05			−0.343831
$455$	−9399.94	−	20686.3i	−0.968519	−	2.13140i
$456$	6670.97			0.685080
$457$	4238.49	−	7341.28i	0.433847	−	0.751446i	−0.563353	−	0.826216i	$-0.690489\pi$
$457$	4238.49	−	7341.28i	0.433847	−	0.751446i	0.997201	+	0.0747703i	$0.0238224\pi$
$458$	−854.828	+	1480.61i	−0.0872129	+	0.151057i
$459$	−4512.56	−	7815.99i	−0.458885	−	0.794813i
$460$	−13876.2			−1.40649
$461$	1723.35	+	2984.93i	0.174110	+	0.301567i	0.939853	−	0.341580i	$-0.110962\pi$
$461$	1723.35	+	2984.93i	0.174110	+	0.301567i	−0.765743	+	0.643146i	$0.777629\pi$
$462$	−816.443	−	1414.12i	−0.0822173	−	0.142405i
$463$	−125.734			−0.0126206			−0.00631032	−	0.999980i	$-0.502009\pi$
$463$	−125.734			−0.0126206			−0.00631032	+	0.999980i	$0.502009\pi$
$464$	−6196.79	−	10733.2i	−0.619997	−	1.07387i
$465$	−464.967	+	805.347i	−0.0463706	+	0.0803163i
$466$	2009.24	−	3480.10i	0.199734	−	0.345949i
$467$	11041.8			1.09412			0.547058	−	0.837095i	$-0.315748\pi$
$467$	11041.8			1.09412			0.547058	+	0.837095i	$0.315748\pi$
$468$	12107.6	−	16934.9i	1.19588	−	1.67269i
$469$	17897.2			1.76208
$470$	2473.88	−	4284.89i	0.242791	−	0.420526i
$471$	13667.1	−	23672.2i	1.33704	−	2.31583i
$472$	−2164.65	−	3749.28i	−0.211093	−	0.365624i
$473$	−1892.75			−0.183994
$474$	−124.268	−	215.239i	−0.0120418	−	0.0208571i
$475$	−8721.06	−	15105.3i	−0.842421	−	1.45912i
$476$	6009.27			0.578644
$477$	−5427.28	−	9400.32i	−0.520960	−	0.902329i
$478$	505.517	−	875.582i	0.0483720	−	0.0837828i
$479$	4156.27	−	7198.88i	0.396461	−	0.686691i	−0.596825	−	0.802371i	$-0.703571\pi$
$479$	4156.27	−	7198.88i	0.396461	−	0.686691i	0.993287	+	0.115680i	$0.0369048\pi$
$480$	19942.3			1.89633
$481$	−8307.54	+	11619.8i	−0.787508	+	1.10149i
$482$	3182.94			0.300786
$483$	−11266.0	+	19513.3i	−1.06133	+	1.83827i
$484$	459.894	−	796.560i	0.0431906	−	0.0748084i
$485$	16174.9	+	28015.7i	1.51436	+	2.62294i
$486$	−1509.34			−0.140875
$487$	−5807.74	−	10059.3i	−0.540398	−	0.935997i	−0.998881	−	0.0472941i	$-0.984940\pi$
$487$	−5807.74	−	10059.3i	−0.540398	−	0.935997i	0.458483	−	0.888703i	$-0.348393\pi$
$488$	2496.74	+	4324.47i	0.231602	+	0.401147i
$489$	−9028.56			−0.834939
$490$	−1830.28	−	3170.14i	−0.168742	−	0.292270i
$491$	587.823	−	1018.14i	0.0540287	−	0.0935804i	−0.837746	−	0.546060i	$-0.816127\pi$
$491$	587.823	−	1018.14i	0.0540287	−	0.0935804i	0.891775	+	0.452479i	$0.149460\pi$
$492$	−5291.46	+	9165.08i	−0.484873	+	0.839825i
$493$	7053.03			0.644325
$494$	−2158.17	−	210.193i	−0.196560	−	0.0191438i
$495$	−12245.0			−1.11187
$496$	144.157	−	249.687i	0.0130501	−	0.0226034i
$497$	−6604.03	+	11438.5i	−0.596039	+	1.03237i
$498$	166.838	+	288.972i	0.0150124	+	0.0260023i
$499$	−3882.10			−0.348270			−0.174135	−	0.984722i	$-0.555713\pi$
$499$	−3882.10			−0.348270			−0.174135	+	0.984722i	$0.555713\pi$
$500$	−8182.19	−	14172.0i	−0.731837	−	1.26758i
$501$	13570.4	+	23504.6i	1.21014	+	2.09602i
$502$	586.727			0.0521652
$503$	−3804.14	−	6588.97i	−0.337213	−	0.584071i	0.646694	−	0.762750i	$-0.276151\pi$
$503$	−3804.14	−	6588.97i	−0.337213	−	0.584071i	−0.983907	+	0.178679i	$0.942818\pi$
$504$	7320.17	−	12678.9i	0.646957	−	1.12056i
$505$	7111.52	−	12317.5i	0.626651	−	1.08539i
$506$	665.270			0.0584484
$507$	−13355.6	+	15296.1i	−1.16991	+	1.33989i
$508$	6449.04			0.563248
$509$	1482.67	−	2568.06i	0.129112	−	0.223629i	−0.794221	−	0.607630i	$-0.792121\pi$
$509$	1482.67	−	2568.06i	0.129112	−	0.223629i	0.923333	+	0.384000i	$0.125454\pi$
$510$	−1726.80	+	2990.91i	−0.149930	+	0.259686i
$511$	−8518.99	−	14755.3i	−0.737491	−	1.27737i
$512$	−10484.2			−0.904961
$513$	−10644.4	−	18436.6i	−0.916102	−	1.58673i
$514$	−421.436	−	729.949i	−0.0361649	−	0.0626394i
$515$	16927.6			1.44838
$516$	−6044.68	−	10469.7i	−0.515702	−	0.893223i
$517$	2262.76	−	3919.21i	0.192487	−	0.333398i
$518$	−2447.21	+	4238.70i	−0.207576	+	0.359532i
$519$	−32196.3			−2.72305
$520$	−8753.19	−	852.509i	−0.738178	−	0.0718942i
$521$	6092.91			0.512352			0.256176	−	0.966630i	$-0.417537\pi$
$521$	6092.91			0.512352			0.256176	+	0.966630i	$0.417537\pi$
$522$	4186.10	−	7250.53i	0.350997	−	0.607945i
$523$	9541.18	−	16525.8i	0.797718	−	1.38169i	−0.123381	−	0.992359i	$-0.539374\pi$
$523$	9541.18	−	16525.8i	0.797718	−	1.38169i	0.921099	−	0.389329i	$-0.127293\pi$
$524$	−6413.54	−	11108.6i	−0.534689	−	0.926108i
$525$	−55968.2			−4.65267
$526$	405.203	+	701.832i	0.0335888	+	0.0581775i
$527$	82.0379	+	142.094i	0.00678108	+	0.0117452i
$528$	5550.77			0.457512
$529$	1493.51	+	2586.84i	0.122751	+	0.212611i
$530$	−1117.11	+	1934.89i	−0.0915550	+	0.158578i
$531$	−12842.6	+	22244.1i	−1.04957	+	1.81791i
$532$	14174.8			1.15518
$533$	4106.19	−	5743.35i	0.333694	−	0.466739i
$534$	−3042.05			−0.246522
$535$	10017.5	−	17350.8i	0.809519	−	1.40213i
$536$	3463.60	−	5999.14i	0.279114	−	0.483439i
$537$	5041.25	+	8731.70i	0.405113	+	0.701677i
$538$	4998.08			0.400525
$539$	−1674.08	−	2899.60i	−0.133781	−	0.231715i
$540$	−21034.6	−	36433.0i	−1.67627	−	2.90338i
$541$	−1841.80			−0.146368			−0.0731839	−	0.997318i	$-0.523316\pi$
$541$	−1841.80			−0.146368			−0.0731839	+	0.997318i	$0.523316\pi$
$542$	−465.504	−	806.277i	−0.0368914	−	0.0638977i
$543$	−17297.3	+	29959.7i	−1.36703	+	2.36776i
$544$	1759.29	−	3047.18i	0.138656	−	0.240160i
$545$	10256.5			0.806128
$546$	−4046.68	+	5660.11i	−0.317183	+	0.443645i
$547$	9482.75			0.741230			0.370615	−	0.928787i	$-0.379147\pi$
$547$	9482.75			0.741230			0.370615	+	0.928787i	$0.379147\pi$
$548$	−4972.29	+	8612.26i	−0.387602	+	0.671346i
$549$	14812.9	−	25656.6i	1.15154	−	1.99453i
$550$	826.247	+	1431.10i	0.0640569	+	0.110950i
$551$	16636.9			1.28631
$552$	4360.57	+	7552.72i	0.336228	+	0.582365i
$553$	−541.945	−	938.676i	−0.0416742	−	0.0721819i
$554$	−2860.15			−0.219343
$555$	26832.2	+	46474.7i	2.05218	+	3.55449i
$556$	−9385.01	+	16255.3i	−0.715851	+	1.23989i
$557$	−10360.9	+	17945.6i	−0.788162	+	1.36514i	0.138929	+	0.990302i	$0.455634\pi$
$557$	−10360.9	+	17945.6i	−0.788162	+	1.36514i	−0.927092	+	0.374835i	$0.877699\pi$
$558$	194.764			0.0147760
$559$	3336.56	+	7342.70i	0.252453	+	0.555569i
$560$	26466.1			1.99713
$561$	−1579.44	+	2735.67i	−0.118866	+	0.205882i
$562$	−2366.07	+	4098.15i	−0.177592	+	0.307598i
$563$	−9675.74	−	16758.9i	−0.724305	−	1.25453i	−0.959260	−	0.282526i	$-0.908828\pi$
$563$	−9675.74	−	16758.9i	−0.724305	−	1.25453i	0.234955	−	0.972006i	$-0.424506\pi$
$564$	28905.3			2.15804
$565$	−5699.63	−	9872.05i	−0.424399	−	0.735080i
$566$	1054.88	+	1827.10i	0.0783390	+	0.135687i
$567$	−28172.6			−2.08666
$568$	2556.13	+	4427.34i	0.188825	+	0.327055i
$569$	−7366.97	+	12760.0i	−0.542776	+	0.940115i	0.455968	+	0.889996i	$0.349293\pi$
$569$	−7366.97	+	12760.0i	−0.542776	+	0.940115i	−0.998743	+	0.0501185i	$0.984040\pi$
$570$	−4073.24	+	7055.05i	−0.299314	+	0.518427i
$571$	−19934.2			−1.46098			−0.730491	−	0.682922i	$-0.760709\pi$
$571$	−19934.2			−1.46098			−0.730491	+	0.682922i	$0.760709\pi$
$572$	−3900.86	−	379.921i	−0.285145	−	0.0277715i
$573$	−18784.7			−1.36954
$574$	1209.59	−	2095.07i	0.0879569	−	0.152346i
$575$	11401.3	−	19747.6i	0.826898	−	1.43223i
$576$	10671.4	+	18483.3i	0.771944	+	1.33705i
$577$	−15550.5			−1.12197			−0.560985	−	0.827826i	$-0.689577\pi$
$577$	−15550.5			−1.12197			−0.560985	+	0.827826i	$0.689577\pi$
$578$	−1245.93	−	2158.02i	−0.0896608	−	0.155297i
$579$	−4920.29	−	8522.20i	−0.353161	−	0.611693i
$580$	32876.6			2.35366
$581$	727.596	+	1260.23i	0.0519548	+	0.0899884i
$582$	4953.09	−	8579.01i	0.352770	−	0.611016i
$583$	−1021.78	+	1769.77i	−0.0725860	+	0.125723i
$584$	−6594.65			−0.467275
$585$	21585.6	+	47503.1i	1.52557	+	3.35729i
$586$	4206.09			0.296505
$587$	2628.05	−	4551.92i	0.184789	−	0.320064i	−0.758716	−	0.651421i	$-0.774173\pi$
$587$	2628.05	−	4551.92i	0.184789	−	0.320064i	0.943506	+	0.331357i	$0.107506\pi$
$588$	10692.7	−	18520.3i	0.749930	−	1.29892i
$589$	193.513	+	335.175i	0.0135375	+	0.0234476i
$590$	5286.87			0.368910
$591$	8733.50	+	15126.9i	0.607865	+	1.05285i
$592$	−8318.96	−	14408.9i	−0.577546	−	1.00034i
$593$	−17164.4			−1.18863			−0.594314	−	0.804233i	$-0.702576\pi$
$593$	−17164.4			−1.18863			−0.594314	+	0.804233i	$0.702576\pi$
$594$	1008.46	+	1746.71i	0.0696595	+	0.120654i
$595$	−7530.75	+	13043.6i	−0.518875	+	0.898718i
$596$	509.302	−	882.136i	0.0350030	−	0.0606270i
$597$	2863.29			0.196292
$598$	−1172.74	−	2580.83i	−0.0801957	−	0.176485i
$599$	−7917.54			−0.540070			−0.270035	−	0.962851i	$-0.587035\pi$
$599$	−7917.54			−0.540070			−0.270035	+	0.962851i	$0.587035\pi$
$600$	−10831.4	+	18760.5i	−0.736984	+	1.27649i
$601$	1935.43	−	3352.26i	0.131361	−	0.227524i	−0.792841	−	0.609429i	$-0.791399\pi$
$601$	1935.43	−	3352.26i	0.131361	−	0.227524i	0.924201	+	0.381905i	$0.124732\pi$
$602$	1381.77	+	2393.30i	0.0935494	+	0.162032i
$603$	−41098.4			−2.77555
$604$	7722.27	+	13375.4i	0.520223	+	0.901053i
$605$	1152.67	+	1996.48i	0.0774588	+	0.134163i
$606$	−4355.40			−0.291957
$607$	4746.95	+	8221.95i	0.317418	+	0.549784i	0.979948	−	0.199251i	$-0.0638509\pi$
$607$	4746.95	+	8221.95i	0.317418	+	0.549784i	−0.662531	+	0.749035i	$0.730518\pi$
$608$	4149.87	−	7187.78i	0.276808	−	0.479446i
$609$	26692.2	−	46232.2i	1.77606	−	3.07623i
$610$	−6097.94			−0.404752
$611$	−19192.9	−	1869.28i	−1.27080	−	0.123769i
$612$	−13799.5			−0.911454
$613$	−6848.09	+	11861.2i	−0.451210	+	0.781519i	−0.998461	−	0.0554495i	$-0.982341\pi$
$613$	−6848.09	+	11861.2i	−0.451210	+	0.781519i	0.547251	+	0.836968i	$0.315674\pi$
$614$	2633.82	−	4561.91i	0.173115	−	0.299843i
$615$	−13262.4	−	22971.1i	−0.869580	−	1.50616i
$616$	−2756.29			−0.180282
$617$	3092.10	+	5355.68i	0.201756	+	0.349451i	0.949094	−	0.314992i	$-0.102002\pi$
$617$	3092.10	+	5355.68i	0.201756	+	0.349451i	−0.747338	+	0.664444i	$0.768669\pi$
$618$	−2591.79	−	4489.11i	−0.168701	−	0.292198i
$619$	1128.65			0.0732866			0.0366433	−	0.999328i	$-0.488333\pi$
$619$	1128.65			0.0732866			0.0366433	+	0.999328i	$0.488333\pi$
$620$	382.407	+	662.348i	0.0247707	+	0.0429041i
$621$	13915.7	−	24102.6i	0.899221	−	1.55750i
$622$	−894.780	+	1549.80i	−0.0576807	+	0.0999059i
$623$	−13266.7			−0.853159
$624$	−9784.93	−	21533.5i	−0.627742	−	1.38146i
$625$	11266.3			0.721040
$626$	−1125.27	+	1949.03i	−0.0718448	+	0.124439i
$627$	−3725.62	+	6452.97i	−0.237300	+	0.411016i
$628$	−11240.4	−	19468.9i	−0.714234	−	1.23709i
$629$	9468.43			0.600208
$630$	8939.26	+	15483.3i	0.565316	+	0.979155i
$631$	1855.93	+	3214.57i	0.117090	+	0.202805i	0.918613	−	0.395158i	$-0.129310\pi$
$631$	1855.93	+	3214.57i	0.117090	+	0.202805i	−0.801524	+	0.597963i	$0.795977\pi$
$632$	−419.526			−0.0264048
$633$	−18753.4	−	32481.9i	−1.17754	−	2.03956i
$634$	−1134.32	+	1964.69i	−0.0710559	+	0.123073i
$635$	−8081.86	+	13998.2i	−0.505069	+	0.874805i
$636$	−13052.5			−0.813784
$637$	−8297.54	+	11605.8i	−0.516108	+	0.721883i
$638$	−1576.20			−0.0978096
$639$	15165.2	−	26267.0i	0.938854	−	1.62614i
$640$	10827.0	−	18752.9i	0.668712	−	1.15824i
$641$	9792.35	+	16960.9i	0.603393	+	1.04511i	0.992303	+	0.123831i	$0.0395182\pi$
$641$	9792.35	+	16960.9i	0.603393	+	1.04511i	−0.388911	+	0.921276i	$0.627148\pi$
$642$	−6135.12			−0.377156
$643$	−8664.85	−	15008.0i	−0.531428	−	0.920461i	−0.999327	−	0.0366786i	$-0.988322\pi$
$643$	−8664.85	−	15008.0i	−0.531428	−	0.920461i	0.467899	−	0.883782i	$-0.345011\pi$
$644$	9265.58	+	16048.5i	0.566949	+	0.981984i
$645$	30300.5			1.84974
$646$	718.673	+	1244.78i	0.0437706	+	0.0758130i
$647$	8342.17	−	14449.1i	0.506900	−	0.877977i	−0.493068	−	0.869991i	$-0.664125\pi$
$647$	8342.17	−	14449.1i	0.506900	−	0.877977i	0.999968	−	0.00798625i	$-0.00254213\pi$
$648$	−5452.17	+	9443.44i	−0.330527	+	0.572490i
$649$	4835.68			0.292476
$650$	4095.27	−	5728.08i	0.247122	−	0.345652i
$651$	1241.89			0.0747673
$652$	−3712.71	+	6430.60i	−0.223008	+	0.386261i
$653$	2316.73	−	4012.69i	0.138837	−	0.240473i	−0.788220	−	0.615394i	$-0.788997\pi$
$653$	2316.73	−	4012.69i	0.138837	−	0.240473i	0.927057	+	0.374921i	$0.122330\pi$
$654$	−1570.38	−	2719.98i	−0.0938940	−	0.162629i
$655$	32149.5			1.91784
$656$	4111.83	+	7121.90i	0.244726	+	0.423877i
$657$	19562.7	+	33883.5i	1.16166	+	2.01206i
$658$	−6607.53			−0.391472
$659$	−5084.41	−	8806.46i	−0.300547	−	0.520563i	0.675713	−	0.737165i	$-0.263836\pi$
$659$	−5084.41	−	8806.46i	−0.300547	−	0.520563i	−0.976260	+	0.216602i	$0.930503\pi$
$660$	−7362.30	+	12751.9i	−0.434207	+	0.752069i
$661$	10402.0	−	18016.7i	0.612087	−	1.06017i	−0.378801	−	0.925478i	$-0.623664\pi$
$661$	10402.0	−	18016.7i	0.612087	−	1.06017i	0.990888	−	0.134688i	$-0.0430031\pi$
$662$	934.774			0.0548807
$663$	13396.9	+	1304.78i	0.784755	+	0.0764306i
$664$	563.240			0.0329186
$665$	−17763.7	+	30767.7i	−1.03586	+	1.79417i
$666$	5619.68	−	9733.57i	0.326964	−	0.566319i
$667$	10874.9	+	18835.9i	0.631302	+	1.09345i
$668$	22321.6			1.29288
$669$	−13127.7	−	22737.9i	−0.758666	−	1.31405i
$670$	4229.69	+	7326.04i	0.243891	+	0.422432i
$671$	−5577.54			−0.320892
$672$	−13316.1	−	23064.1i	−0.764403	−	1.32399i
$673$	14609.4	−	25304.3i	0.836779	−	1.44934i	−0.0557941	−	0.998442i	$-0.517769\pi$
$673$	14609.4	−	25304.3i	0.836779	−	1.44934i	0.892573	−	0.450902i	$-0.148898\pi$
$674$	−983.140	+	1702.85i	−0.0561856	+	0.0973164i
$675$	69131.4			3.94203
$676$	5402.60	+	15802.6i	0.307385	+	0.899102i
$677$	31195.5			1.77096			0.885480	−	0.464678i	$-0.153830\pi$
$677$	31195.5			1.77096			0.885480	+	0.464678i	$0.153830\pi$
$678$	−1745.35	+	3023.03i	−0.0988639	+	0.171237i
$679$	21600.9	−	37413.8i	1.22086	−	2.11460i
$680$	2914.82	+	5048.61i	0.164380	+	0.284714i
$681$	48701.6			2.74046
$682$	−18.3338	−	31.7550i	−0.00102938	−	0.00178294i
$683$	−13373.3	−	23163.3i	−0.749219	−	1.29769i	−0.948197	−	0.317682i	$-0.897096\pi$
$683$	−13373.3	−	23163.3i	−0.749219	−	1.29769i	0.198978	−	0.980004i	$-0.436238\pi$
$684$	−32550.6			−1.81959
$685$	−12462.4	−	21585.6i	−0.695132	−	1.20400i
$686$	310.140	−	537.179i	0.0172612	−	0.0298974i
$687$	12516.8	−	21679.8i	0.695118	−	1.20398i
$688$	−9394.27			−0.520571
$689$	8666.78	+	844.094i	0.479213	+	0.0466726i
$690$	−10650.1			−0.587598
$691$	−53.1356	+	92.0335i	−0.00292529	+	0.00506675i	−0.867484	−	0.497464i	$-0.834264\pi$
$691$	−53.1356	+	92.0335i	−0.00292529	+	0.00506675i	0.864559	+	0.502531i	$0.167598\pi$
$692$	−13239.7	+	22931.9i	−0.727311	+	1.25974i
$693$	8176.38	+	14161.9i	0.448189	+	0.776286i
$694$	2119.20			0.115913
$695$	−23522.4	−	40741.9i	−1.28382	−	2.22364i
$696$	−10331.4	−	17894.4i	−0.562657	−	0.974550i
$697$	−4679.98			−0.254328
$698$	233.442	+	404.333i	0.0126589	+	0.0219258i
$699$	−29420.2	+	50957.3i	−1.59195	+	2.75734i
$700$	−23015.2	+	39863.5i	−1.24270	+	2.15242i
$701$	−1225.85			−0.0660482			−0.0330241	−	0.999455i	$-0.510514\pi$
$701$	−1225.85			−0.0660482			−0.0330241	+	0.999455i	$0.510514\pi$
$702$	4998.42	−	6991.32i	0.268737	−	0.375884i
$703$	22334.4			1.19823
$704$	2009.06	−	3479.80i	0.107556	−	0.186292i
$705$	−36223.8	+	62741.4i	−1.93513	+	3.35174i
$706$	755.353	+	1308.31i	0.0402664	+	0.0697435i
$707$	−18994.3			−1.01040
$708$	15443.2	+	26748.4i	0.819761	+	1.41987i
$709$	16550.9	+	28666.9i	0.876701	+	1.51849i	0.854940	+	0.518727i	$0.173594\pi$
$709$	16550.9	+	28666.9i	0.876701	+	1.51849i	0.0217603	+	0.999763i	$0.493073\pi$
$710$	−6243.00			−0.329994
$711$	1244.50	+	2155.54i	0.0656433	+	0.113698i
$712$	−2567.47	+	4446.99i	−0.135140	+	0.234070i
$713$	−252.985	+	438.183i	−0.0132880	+	0.0230156i
$714$	4612.15			0.241744
$715$	5713.16	−	7991.03i	0.298825	−	0.417969i
$716$	8292.22			0.432814
$717$	−7402.03	+	12820.7i	−0.385542	+	0.667779i
$718$	−666.542	+	1154.49i	−0.0346450	+	0.0600070i
$719$	15907.2	+	27552.1i	0.825088	+	1.42909i	0.901852	+	0.432044i	$0.142208\pi$
$719$	15907.2	+	27552.1i	0.825088	+	1.42909i	−0.0767648	+	0.997049i	$0.524459\pi$
$720$	−60775.6			−3.14579
$721$	−11303.0	−	19577.4i	−0.583838	−	1.01124i
$722$	−469.560	−	813.302i	−0.0242039	−	0.0419224i
$723$	−46606.2			−2.39737
$724$	14225.9	+	24640.0i	0.730252	+	1.26483i
$725$	−27012.7	+	46787.4i	−1.38376	+	2.39674i
$726$	352.971	−	611.364i	0.0180441	−	0.0312533i
$727$	7991.52			0.407688			0.203844	−	0.979003i	$-0.434656\pi$
$727$	7991.52			0.407688			0.203844	+	0.979003i	$0.434656\pi$
$728$	4858.80	+	10692.7i	0.247361	+	0.544364i
$729$	−7795.34			−0.396044
$730$	4026.63	−	6974.34i	0.204154	−	0.353605i
$731$	2673.08	−	4629.91i	0.135250	−	0.234259i
$732$	−17812.4	−	30852.0i	−0.899405	−	1.55782i
$733$	31915.2			1.60820			0.804102	−	0.594492i	$-0.202647\pi$
$733$	31915.2			1.60820			0.804102	+	0.594492i	$0.202647\pi$
$734$	685.600	+	1187.49i	0.0344768	+	0.0597155i
$735$	26799.9	+	46418.7i	1.34494	+	2.32950i
$736$	10850.5			0.543415
$737$	3868.73	+	6700.83i	0.193360	+	0.334910i
$738$	−2777.65	+	4811.03i	−0.138546	+	0.239968i
$739$	2603.37	−	4509.17i	0.129589	−	0.224455i	−0.793928	−	0.608012i	$-0.791967\pi$
$739$	2603.37	−	4509.17i	0.129589	−	0.224455i	0.923518	+	0.383556i	$0.125301\pi$
$740$	44135.6			2.19251
$741$	31601.0	+	3077.76i	1.56666	+	0.152583i
$742$	2983.71			0.147622
$743$	−11537.0	+	19982.6i	−0.569650	+	0.986663i	0.426950	+	0.904275i	$0.359588\pi$
$743$	−11537.0	+	19982.6i	−0.569650	+	0.986663i	−0.996600	+	0.0823879i	$0.973745\pi$
$744$	240.340	−	416.281i	0.0118431	−	0.0205129i
$745$	1276.50	+	2210.97i	0.0627750	+	0.108730i
$746$	3623.17			0.177820
$747$	−1670.82	−	2893.95i	−0.0818369	−	0.141746i
$748$	1298.99	+	2249.91i	0.0634970	+	0.109980i
$749$	−26755.8			−1.30526
$750$	−6279.88	−	10877.1i	−0.305745	−	0.529566i
$751$	16202.6	−	28063.7i	0.787272	−	1.36360i	−0.140360	−	0.990101i	$-0.544826\pi$
$751$	16202.6	−	28063.7i	0.787272	−	1.36360i	0.927632	−	0.373495i	$-0.121841\pi$
$752$	11230.7	−	19452.1i	0.544603	−	0.943280i
$753$	−8591.15			−0.415775
$754$	2778.54	+	6114.69i	0.134202	+	0.295337i
$755$	−38709.8			−1.86595
$756$	−28090.8	+	48654.7i	−1.35139	+	2.34068i
$757$	4127.85	−	7149.64i	0.198189	−	0.343274i	−0.749752	−	0.661719i	$-0.769827\pi$
$757$	4127.85	−	7149.64i	0.198189	−	0.343274i	0.947941	+	0.318445i	$0.103161\pi$
$758$	2050.66	+	3551.84i	0.0982629	+	0.170196i
$759$	−9741.21			−0.465855
$760$	6875.56	+	11908.8i	0.328161	+	0.568392i
$761$	−5110.62	−	8851.85i	−0.243443	−	0.421655i	0.718250	−	0.695785i	$-0.244943\pi$
$761$	−5110.62	−	8851.85i	−0.243443	−	0.421655i	−0.961693	+	0.274130i	$0.911610\pi$
$762$	4949.68			0.235312
$763$	−6848.57	−	11862.1i	−0.324947	−	0.562825i
$764$	−7724.64	+	13379.5i	−0.365795	+	0.633576i
$765$	17293.3	−	29952.9i	0.817308	−	1.41562i
$766$	−458.335			−0.0216192
$767$	−8524.37	−	18759.4i	−0.401300	−	0.883134i
$768$	20378.8			0.957495
$769$	18398.4	−	31867.0i	0.862763	−	1.49435i	−0.00648873	−	0.999979i	$-0.502065\pi$
$769$	18398.4	−	31867.0i	0.862763	−	1.49435i	0.869252	−	0.494370i	$-0.164601\pi$
$770$	1682.97	−	2914.98i	0.0787661	−	0.136427i
$771$	6170.87	+	10688.3i	0.288247	+	0.499259i
$772$	−8093.27			−0.377310
$773$	−8711.47	−	15088.7i	−0.405343	−	0.702074i	0.589019	−	0.808119i	$-0.299514\pi$
$773$	−8711.47	−	15088.7i	−0.405343	−	0.702074i	−0.994361	+	0.106045i	$0.966181\pi$
$774$	−3173.04	−	5495.87i	−0.147355	−	0.255226i
$775$	−1256.80			−0.0582525
$776$	−8360.74	−	14481.2i	−0.386770	−	0.669905i
$777$	35833.3	−	62065.1i	1.65446	−	2.86560i
$778$	−2530.08	+	4382.23i	−0.116591	+	0.201941i
$779$	−11039.3			−0.507732
$780$	62447.6	+	6082.03i	2.86664	+	0.279194i
$781$	−5710.22			−0.261623
$782$	−939.541	+	1627.33i	−0.0429641	+	0.0744160i
$783$	−32969.9	+	57105.6i	−1.50479	+	2.60637i
$784$	−8308.94	−	14391.5i	−0.378505	−	0.655590i
$785$	56345.1			2.56184
$786$	−4922.43	−	8525.90i	−0.223381	−	0.386907i
$787$	−16900.0	−	29271.6i	−0.765463	−	1.32582i	−0.940001	−	0.341171i	$-0.889177\pi$
$787$	−16900.0	−	29271.6i	−0.765463	−	1.32582i	0.174538	−	0.984650i	$-0.444157\pi$
$788$	14365.5			0.649429
$789$	−5933.18	−	10276.6i	−0.267715	−	0.463695i
$790$	256.159	−	443.680i	0.0115364	−	0.0199816i
$791$	−7611.62	+	13183.7i	−0.342147	+	0.592616i
$792$	6329.43			0.283973
$793$	9832.12	+	21637.4i	0.440289	+	0.968935i
$794$	−5069.65			−0.226593
$795$	16357.3	−	28331.6i	0.729727	−	1.26392i
$796$	1177.44	−	2039.38i	0.0524286	−	0.0908089i
$797$	4934.67	+	8547.10i	0.219316	+	0.379867i	0.954599	−	0.297893i	$-0.0962840\pi$
$797$	4934.67	+	8547.10i	0.219316	+	0.379867i	−0.735283	+	0.677760i	$0.762951\pi$
$798$	10879.3			0.482609
$799$	6391.25	+	11070.0i	0.282986	+	0.490147i
$800$	13476.0	+	23341.1i	0.595560	+	1.03154i
$801$	30465.0			1.34386
$802$	1974.10	+	3419.24i	0.0869175	+	0.150546i
$803$	3683.00	−	6379.14i	0.161856	−	0.280343i
$804$	−24710.3	+	42799.4i	−1.08391	+	1.87739i
$805$	−46446.0			−2.03355
$806$	−90.8707	+	127.101i	−0.00397120	+	0.00555454i
$807$	−73184.4			−3.19233
$808$	−3675.92	+	6366.89i	−0.160048	+	0.277211i
$809$	4647.02	−	8048.88i	0.201954	−	0.349794i	−0.747204	−	0.664595i	$-0.768604\pi$
$809$	4647.02	−	8048.88i	0.201954	−	0.349794i	0.949158	+	0.314800i	$0.101938\pi$
$810$	−6658.10	−	11532.2i	−0.288817	−	0.500246i
$811$	−38657.3			−1.67379			−0.836894	−	0.547364i	$-0.815631\pi$
$811$	−38657.3			−1.67379			−0.836894	+	0.547364i	$0.815631\pi$
$812$	−21952.7	−	38023.1i	−0.948753	−	1.64329i
$813$	6816.14	+	11805.9i	0.294037	+	0.509288i
$814$	−2116.00			−0.0911126
$815$	−9305.45	−	16117.5i	−0.399946	−	0.692726i
$816$	−7839.19	+	13577.9i	−0.336307	+	0.582501i
$817$	6305.34	−	10921.2i	0.270007	−	0.467666i
$818$	4067.73			0.173869
$819$	40526.0	−	56683.9i	1.72905	−	2.41843i
$820$	−21815.0			−0.929039
$821$	−9124.54	+	15804.2i	−0.387879	+	0.671826i	−0.992164	−	0.124942i	$-0.960126\pi$
$821$	−9124.54	+	15804.2i	−0.387879	+	0.671826i	0.604285	+	0.796768i	$0.293459\pi$
$822$	−3816.26	+	6609.96i	−0.161931	+	0.280473i
$823$	11990.3	+	20767.8i	0.507844	+	0.879612i	0.999959	+	0.00908151i	$0.00289077\pi$
$823$	11990.3	+	20767.8i	0.507844	+	0.879612i	−0.492115	+	0.870530i	$0.663776\pi$
$824$	−8749.80			−0.369920
$825$	−12098.3	−	20954.9i	−0.510557	−	0.884310i
$826$	−3530.20	−	6114.48i	−0.148706	−	0.257567i
$827$	26899.1			1.13104			0.565521	−	0.824734i	$-0.308675\pi$
$827$	26899.1			1.13104			0.565521	+	0.824734i	$0.308675\pi$
$828$	−21277.1	−	36853.0i	−0.893032	−	1.54678i
$829$	308.778	−	534.819i	0.0129364	−	0.0224065i	−0.859485	−	0.511161i	$-0.829215\pi$
$829$	308.778	−	534.819i	0.0129364	−	0.0224065i	0.872421	+	0.488755i	$0.162549\pi$
$830$	−343.909	+	595.669i	−0.0143823	+	0.0249108i
$831$	41879.7			1.74824
$832$	−17041.0	−	1659.70i	−0.710085	−	0.0691582i
$833$	9457.03			0.393357
$834$	−7203.05	+	12476.1i	−0.299066	+	0.517998i
$835$	−27973.1	+	48450.9i	−1.15934	+	2.00804i
$836$	3064.09	+	5307.16i	0.126763	+	0.219560i
$837$	−1533.97			−0.0633475
$838$	4303.71	+	7454.25i	0.177410	+	0.307282i
$839$	10676.1	+	18491.6i	0.439309	+	0.760906i	0.997636	−	0.0687151i	$-0.0218900\pi$
$839$	10676.1	+	18491.6i	0.439309	+	0.760906i	−0.558327	+	0.829621i	$0.688557\pi$
$840$	44124.5			1.81243
$841$	−13571.1	−	23505.9i	−0.556444	−	0.963790i
$842$	−897.604	+	1554.70i	−0.0367381	+	0.0636323i
$843$	34645.1	−	60007.1i	1.41547	−	2.45167i
$844$	−30847.1			−1.25806
$845$	−41071.4	−	8076.84i	−1.67207	−	0.328819i
$846$	15173.3			0.616629
$847$	1539.34	−	2666.22i	0.0624467	−	0.108161i
$848$	−5071.36	+	8783.85i	−0.205367	+	0.355706i
$849$	−15446.0	−	26753.3i	−0.624390	−	1.08147i
$850$	−4667.53			−0.188347
$851$	14599.2	+	25286.5i	0.588077	+	1.01858i
$852$	−18236.1	−	31585.8i	−0.733284	−	1.27009i
$853$	−13702.1			−0.549999			−0.275000	−	0.961444i	$-0.588678\pi$
$853$	−13702.1			−0.549999			−0.275000	+	0.961444i	$0.588678\pi$
$854$	4071.78	+	7052.53i	0.163154	+	0.282591i
$855$	40792.0	−	70653.8i	1.63164	−	2.82609i
$856$	−5177.99	+	8968.55i	−0.206753	+	0.358106i
$857$	1574.39			0.0627541			0.0313771	−	0.999508i	$-0.490011\pi$
$857$	1574.39			0.0627541			0.0313771	+	0.999508i	$0.490011\pi$
$858$	−2993.93	−	291.591i	−0.119127	−	0.0116023i
$859$	−17197.3			−0.683077			−0.341539	−	0.939868i	$-0.610948\pi$
$859$	−17197.3			−0.683077			−0.341539	+	0.939868i	$0.610948\pi$
$860$	12460.1	−	21581.6i	0.494055	−	0.855728i
$861$	−17711.4	+	30677.0i	−0.701048	+	1.21425i
$862$	−2401.70	−	4159.87i	−0.0948983	−	0.164369i
$863$	31821.0			1.25515			0.627577	−	0.778554i	$-0.284047\pi$
$863$	31821.0			1.25515			0.627577	+	0.778554i	$0.284047\pi$
$864$	16447.9	+	28488.6i	0.647649	+	1.12176i
$865$	−33183.8	−	57476.0i	−1.30437	−	2.25924i
$866$	8095.06			0.317646
$867$	18243.5	+	31598.7i	0.714629	+	1.23777i
$868$	510.689	−	884.538i	0.0199699	−	0.0345889i
$869$	234.298	−	405.816i	0.00914616	−	0.0158416i
$870$	25233.0			0.983307
$871$	19175.2	−	26820.5i	0.745956	−	1.04337i
$872$	−5301.55			−0.205887
$873$	−49603.4	+	85915.7i	−1.92305	+	3.33082i
$874$	−2216.22	+	3838.60i	−0.0857719	+	0.148561i
$875$	−27387.1	−	47435.9i	−1.05812	−	1.83271i
$876$	47048.0			1.81462
$877$	3801.75	+	6584.82i	0.146381	+	0.253539i	0.929887	−	0.367845i	$-0.119904\pi$
$877$	3801.75	+	6584.82i	0.146381	+	0.253539i	−0.783506	+	0.621384i	$0.786571\pi$
$878$	−1892.31	−	3277.57i	−0.0727361	−	0.125983i
$879$	−61587.7			−2.36325
$880$	5721.01	+	9909.08i	0.219154	+	0.379585i
$881$	−6942.42	+	12024.6i	−0.265489	+	0.459841i	−0.967692	−	0.252136i	$-0.918867\pi$
$881$	−6942.42	+	12024.6i	−0.265489	+	0.459841i	0.702202	+	0.711977i	$0.252200\pi$
$882$	5612.92	−	9721.85i	0.214282	−	0.371147i
$883$	24979.6			0.952018			0.476009	−	0.879440i	$-0.342083\pi$
$883$	24979.6			0.952018			0.476009	+	0.879440i	$0.342083\pi$
$884$	6438.39	−	9005.42i	0.244962	−	0.342630i
$885$	−77412.9			−2.94035
$886$	1738.15	−	3010.57i	0.0659078	−	0.114156i
$887$	−6.73075	+	11.6580i	−0.000254787	+	0.000441305i	−0.866153	−	0.499779i	$-0.833414\pi$
$887$	−6.73075	+	11.6580i	−0.000254787	+	0.000441305i	0.865898	+	0.500221i	$0.166748\pi$
$888$	−13869.5	−	24022.6i	−0.524132	−	0.907822i
$889$	21586.0			0.814366
$890$	−3135.35	−	5430.58i	−0.118087	−	0.204532i
$891$	−6089.89	−	10548.0i	−0.228978	−	0.396601i
$892$	−21593.5			−0.810542
$893$	15075.9	+	26112.2i	0.564943	+	0.978511i
$894$	390.892	−	677.045i	0.0146235	−	0.0253286i
$895$	−10391.7	+	17999.0i	−0.388108	+	0.672223i
$896$	−28918.1			−1.07822
$897$	17171.9	+	37789.8i	0.639188	+	1.40665i
$898$	8331.77			0.309616
$899$	599.390	−	1038.17i	0.0222367	−	0.0385151i
$900$	52851.1	−	91540.8i	1.95745	−	3.39040i
$901$	−2886.04	−	4998.78i	−0.106713	−	0.184832i
$902$	1045.88			0.0386075
$903$	−20232.5	−	35043.8i	−0.745622	−	1.29146i
$904$	2946.12	+	5102.83i	0.108392	+	0.187741i
$905$	−71311.0			−2.61929
$906$	5926.89	+	10265.7i	0.217337	+	0.376440i
$907$	6779.14	−	11741.8i	0.248178	−	0.429857i	−0.714842	−	0.699286i	$-0.753501\pi$
$907$	6779.14	−	11741.8i	0.248178	−	0.429857i	0.963020	+	0.269429i	$0.0868348\pi$
$908$	20027.0	−	34687.8i	0.731960	−	1.26779i
$909$	43617.7			1.59154
$910$	−14275.0	−	1390.31i	−0.520014	−	0.0506464i
$911$	−38444.8			−1.39817			−0.699085	−	0.715039i	$-0.746409\pi$
$911$	−38444.8			−1.39817			−0.699085	+	0.715039i	$0.746409\pi$
$912$	−18491.3	+	32027.9i	−0.671391	+	1.16288i
$913$	−314.560	+	544.834i	−0.0114024	+	0.0197496i
$914$	−2675.44	−	4634.01i	−0.0968226	−	0.167702i
$915$	89289.1			3.22602
$916$	−10294.3	−	17830.2i	−0.371324	−	0.643153i
$917$	−21467.2	−	37182.2i	−0.773074	−	1.33900i
$918$	−5696.89			−0.204821
$919$	27697.5	+	47973.4i	0.994184	+	1.72198i	0.590358	+	0.807142i	$0.298987\pi$
$919$	27697.5	+	47973.4i	0.994184	+	1.72198i	0.403827	+	0.914836i	$0.367680\pi$
$920$	−8988.60	+	15568.7i	−0.322115	+	0.557919i
$921$	−38565.7	+	66797.7i	−1.37979	+	2.38986i
$922$	2175.65			0.0777128
$923$	10066.0	+	22152.1i	0.358967	+	0.789972i
$924$	19664.1			0.700109
$925$	−36263.6	+	62810.3i	−1.28901	+	2.23264i
$926$	−39.6833	+	68.7335i	−0.00140829	+	0.00243923i
$927$	25955.8	+	44956.8i	0.919634	+	1.59285i
$928$	−25707.7			−0.909371
$929$	3940.29	+	6824.78i	0.139157	+	0.241027i	0.927178	−	0.374622i	$-0.122227\pi$
$929$	3940.29	+	6824.78i	0.139157	+	0.241027i	−0.788021	+	0.615649i	$0.788894\pi$
$930$	293.499	+	508.356i	0.0103486	+	0.0179244i
$931$	22307.5			0.785284
$932$	24196.3	+	41909.2i	0.850403	+	1.47294i
$933$	13101.8	−	22693.0i	0.459736	−	0.796286i
$934$	3484.92	−	6036.07i	0.122088	−	0.211463i
$935$	−6511.51			−0.227753
$936$	−11157.6	−	24554.2i	−0.389632	−	0.857457i
$937$	−39342.0			−1.37166			−0.685832	−	0.727760i	$-0.740561\pi$
$937$	−39342.0			−1.37166			−0.685832	+	0.727760i	$0.740561\pi$
$938$	5648.58	−	9783.63i	0.196623	−	0.340562i
$939$	16476.8	−	28538.6i	0.572629	−	0.991823i
$940$	29791.8	+	51600.9i	1.03372	+	1.79046i
$941$	18205.4			0.630691			0.315345	−	0.948977i	$-0.397880\pi$
$941$	18205.4			0.630691			0.315345	+	0.948977i	$0.397880\pi$
$942$	−8627.04	−	14942.5i	−0.298391	−	0.516828i
$943$	−7215.97	−	12498.4i	−0.249188	−	0.431606i
$944$	24000.8			0.827501
$945$	−70406.2	−	121947.i	−2.42361	−	4.19782i
$946$	−597.378	+	1034.69i	−0.0205311	+	0.0355609i
$947$	2856.22	−	4947.12i	0.0980091	−	0.169757i	−0.812851	−	0.582471i	$-0.802086\pi$
$947$	2856.22	−	4947.12i	0.0980091	−	0.169757i	0.910861	+	0.412714i	$0.135419\pi$
$948$	2993.01			0.102540
$949$	−31239.5	−	3042.54i	−1.06857	−	0.104073i
$950$	−11009.9			−0.376009
$951$	16609.2	−	28768.0i	0.566342	−	0.980932i
$952$	3892.62	−	6742.22i	0.132522	−	0.229534i
$953$	−12820.7	−	22206.1i	−0.435785	−	0.754802i	0.561574	−	0.827426i	$-0.310196\pi$
$953$	−12820.7	−	22206.1i	−0.435785	−	0.754802i	−0.997359	+	0.0726247i	$0.976862\pi$
$954$	−6851.67			−0.232527
$955$	−19360.8	−	33534.0i	−0.656023	−	1.13627i
$956$	6087.71	+	10544.2i	0.205952	+	0.356720i
$957$	23079.6			0.779578
$958$	−2623.55	−	4544.12i	−0.0884791	−	0.153250i
$959$	−16643.1	+	28826.7i	−0.560410	+	0.970658i
$960$	−32162.4	+	55706.9i	−1.08129	+	1.87285i
$961$	−29763.1			−0.999064
$962$	3730.09	+	8208.74i	0.125013	+	0.275115i
$963$	61441.0			2.05598
$964$	−19165.3	+	33195.3i	−0.640325	+	1.10908i
$965$	10142.4	−	17567.1i	0.338337	−	0.586016i
$966$	7111.39	+	12317.3i	0.236858	+	0.410251i
$967$	34099.1			1.13398			0.566988	−	0.823726i	$-0.308109\pi$
$967$	34099.1			1.13398			0.566988	+	0.823726i	$0.308109\pi$
$968$	−595.810	−	1031.97i	−0.0197831	−	0.0342654i
$969$	−10523.2	−	18226.7i	−0.348868	−	0.604257i
$970$	20420.0			0.675924
$971$	23061.9	+	39944.4i	0.762195	+	1.32016i	0.941717	+	0.336407i	$0.109212\pi$
$971$	23061.9	+	39944.4i	0.762195	+	1.32016i	−0.179522	+	0.983754i	$0.557455\pi$
$972$	9088.14	−	15741.1i	0.299899	−	0.519441i
$973$	−31413.2	+	54409.2i	−1.03501	+	1.79268i
$974$	−7331.99			−0.241204
$975$	−59964.9	+	83873.3i	−1.96965	+	2.75497i
$976$	−27682.9			−0.907897
$977$	2966.33	−	5137.84i	0.0971354	−	0.168244i	−0.813362	−	0.581757i	$-0.802365\pi$
$977$	2966.33	−	5137.84i	0.0971354	−	0.168244i	0.910498	+	0.413514i	$0.135699\pi$
$978$	−2849.53	+	4935.53i	−0.0931675	+	0.161371i
$979$	−2867.78	−	4967.13i	−0.0936206	−	0.162156i
$980$	44082.4			1.43690
$981$	15726.8	+	27239.6i	0.511842	+	0.886537i
$982$	−371.049	−	642.676i	−0.0120577	−	0.0208845i
$983$	32666.1			1.05990			0.529952	−	0.848028i	$-0.322210\pi$
$983$	32666.1			1.05990			0.529952	+	0.848028i	$0.322210\pi$
$984$	6855.29	+	11873.7i	0.222092	+	0.384675i
$985$	−18002.7	+	31181.6i	−0.582349	+	1.00866i
$986$	2226.03	−	3855.59i	0.0718977	−	0.124530i
$987$	96750.7			3.12017
$988$	15187.1	−	21242.3i	0.489034	−	0.684014i
$989$	16486.3			0.530064
$990$	−3864.69	+	6693.85i	−0.124069	+	0.214893i
$991$	1549.15	−	2683.21i	0.0496573	−	0.0860090i	−0.840128	−	0.542388i	$-0.817520\pi$
$991$	1549.15	−	2683.21i	0.0496573	−	0.0860090i	0.889786	+	0.456379i	$0.150854\pi$
$992$	−299.021	−	517.920i	−0.00957050	−	0.0165766i
$993$	−13687.4			−0.437419
$994$	4168.64	+	7220.29i	0.133019	+	0.230396i
$995$	2951.10	+	5111.45i	0.0940263	+	0.162858i
$996$	−4018.30			−0.127836
$997$	5637.11	+	9763.76i	0.179066	+	0.310152i	0.941561	−	0.336843i	$-0.109359\pi$
$997$	5637.11	+	9763.76i	0.179066	+	0.310152i	−0.762495	+	0.646994i	$0.776026\pi$
$998$	−1225.24	+	2122.18i	−0.0388621	+	0.0673111i
$999$	−44260.9	+	76662.2i	−1.40176	+	2.42791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.b.100.9	✓	34
13.3	even	3	inner	143.4.e.b.133.9	yes	34
13.4	even	6		1859.4.a.h.1.9		17
13.9	even	3		1859.4.a.g.1.9		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.9	✓	34	1.1	even	1	trivial
143.4.e.b.133.9	yes	34	13.3	even	3	inner
1859.4.a.g.1.9		17	13.9	even	3
1859.4.a.h.1.9		17	13.4	even	6

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.315613 - 0.546657i) q^{2} +(-4.62136 + 8.00442i) q^{3} +(3.80078 + 6.58314i) q^{4} -19.0524 q^{5} +(2.91712 + 5.05260i) q^{6} +(12.7218 + 22.0348i) q^{7} +9.84810 q^{8} +(-29.2139 - 50.5999i) q^{9} +O(q^{10})\)	\(q+(0.315613 - 0.546657i) q^{2} +(-4.62136 + 8.00442i) q^{3} +(3.80078 + 6.58314i) q^{4} -19.0524 q^{5} +(2.91712 + 5.05260i) q^{6} +(12.7218 + 22.0348i) q^{7} +9.84810 q^{8} +(-29.2139 - 50.5999i) q^{9} +(-6.01317 + 10.4151i) q^{10} +(-5.50000 + 9.52628i) q^{11} -70.2590 q^{12} +(46.6514 + 4.54358i) q^{13} +16.0607 q^{14} +(88.0477 - 152.503i) q^{15} +(-27.2980 + 47.2816i) q^{16} +(-15.5350 - 26.9073i) q^{17} -36.8811 q^{18} +(-36.6443 - 63.4698i) q^{19} +(-72.4137 - 125.424i) q^{20} -235.168 q^{21} +(3.47174 + 6.01323i) q^{22} +(47.9061 - 82.9758i) q^{23} +(-45.5116 + 78.8284i) q^{24} +237.992 q^{25} +(17.2076 - 24.0683i) q^{26} +290.478 q^{27} +(-96.7056 + 167.499i) q^{28} +(-113.502 + 196.592i) q^{29} +(-55.5780 - 96.2639i) q^{30} -5.28086 q^{31} +(56.6236 + 98.0750i) q^{32} +(-50.8349 - 88.0487i) q^{33} -19.6121 q^{34} +(-242.381 - 419.816i) q^{35} +(222.071 - 384.638i) q^{36} +(-152.373 + 263.918i) q^{37} -46.2617 q^{38} +(-251.962 + 352.420i) q^{39} -187.630 q^{40} +(75.3137 - 130.447i) q^{41} +(-74.2221 + 128.557i) q^{42} +(86.0343 + 149.016i) q^{43} -83.6171 q^{44} +(556.593 + 964.048i) q^{45} +(-30.2396 - 52.3765i) q^{46} -411.411 q^{47} +(-252.308 - 437.010i) q^{48} +(-152.189 + 263.600i) q^{49} +(75.1134 - 130.100i) q^{50} +287.170 q^{51} +(147.401 + 324.382i) q^{52} +185.777 q^{53} +(91.6785 - 158.792i) q^{54} +(104.788 - 181.498i) q^{55} +(125.286 + 217.001i) q^{56} +677.386 q^{57} +(71.6457 + 124.094i) q^{58} +(-219.804 - 380.711i) q^{59} +1338.60 q^{60} +(253.525 + 439.117i) q^{61} +(-1.66671 + 2.88682i) q^{62} +(743.307 - 1287.45i) q^{63} -365.284 q^{64} +(-888.820 - 86.5658i) q^{65} -64.1766 q^{66} +(351.703 - 609.167i) q^{67} +(118.090 - 204.538i) q^{68} +(442.782 + 766.922i) q^{69} -305.994 q^{70} +(259.555 + 449.563i) q^{71} +(-287.701 - 498.313i) q^{72} -669.636 q^{73} +(96.1817 + 166.592i) q^{74} +(-1099.85 + 1904.99i) q^{75} +(278.554 - 482.469i) q^{76} -279.880 q^{77} +(113.131 + 248.965i) q^{78} -42.5996 q^{79} +(520.092 - 900.825i) q^{80} +(-553.627 + 958.910i) q^{81} +(-47.5399 - 82.3416i) q^{82} +57.1927 q^{83} +(-893.822 - 1548.15i) q^{84} +(295.978 + 512.648i) q^{85} +108.614 q^{86} +(-1049.07 - 1817.04i) q^{87} +(-54.1646 + 93.8158i) q^{88} +(-260.707 + 451.558i) q^{89} +702.672 q^{90} +(493.374 + 1085.76i) q^{91} +728.322 q^{92} +(24.4047 - 42.2702i) q^{93} +(-129.846 + 224.901i) q^{94} +(698.161 + 1209.25i) q^{95} -1046.71 q^{96} +(-848.970 - 1470.46i) q^{97} +(96.0659 + 166.391i) q^{98} +642.705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20} - 368 q^{21} + 215 q^{23} - 214 q^{24} + 190 q^{25} + 123 q^{26} - 384 q^{27} + 358 q^{28} + 157 q^{29} - 829 q^{30} - 788 q^{31} + 553 q^{32} + 66 q^{33} - 1404 q^{34} - 58 q^{35} + 700 q^{36} - 88 q^{37} - 2636 q^{38} + 798 q^{39} + 1466 q^{40} + 512 q^{41} - 337 q^{42} - 927 q^{43} + 1100 q^{44} + 1482 q^{45} + 1361 q^{46} - 286 q^{47} + 178 q^{48} - 1835 q^{49} + 583 q^{50} - 1136 q^{51} + 2306 q^{52} + 212 q^{53} + 67 q^{54} + 264 q^{55} - 2059 q^{56} + 2596 q^{57} + 1690 q^{58} + 266 q^{59} + 74 q^{60} + 624 q^{61} - 643 q^{62} + 2360 q^{63} - 3178 q^{64} + 470 q^{65} + 352 q^{66} + 676 q^{67} + 413 q^{68} - 764 q^{69} - 2122 q^{70} + 763 q^{71} + 1366 q^{72} - 4748 q^{73} + 1649 q^{74} - 2420 q^{75} + 2101 q^{76} - 1364 q^{77} - 5848 q^{78} + 4328 q^{79} + 1013 q^{80} - 537 q^{81} - 3152 q^{82} + 1554 q^{83} + 3381 q^{84} + 1690 q^{85} + 5788 q^{86} + 4200 q^{87} + 231 q^{88} + 1687 q^{89} - 10798 q^{90} - 3380 q^{91} + 11084 q^{92} + 4310 q^{93} - 1777 q^{94} - 1124 q^{95} - 6930 q^{96} + 2047 q^{97} - 1553 q^{98} + 2970 q^{99}+O(q^{100}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9 - 2 * q^10 - 187 * q^11 - 254 * q^12 + 76 * q^13 + 148 * q^15 - 126 * q^16 + 74 * q^17 + 180 * q^18 + 159 * q^19 + 222 * q^20 - 368 * q^21 + 215 * q^23 - 214 * q^24 + 190 * q^25 + 123 * q^26 - 384 * q^27 + 358 * q^28 + 157 * q^29 - 829 * q^30 - 788 * q^31 + 553 * q^32 + 66 * q^33 - 1404 * q^34 - 58 * q^35 + 700 * q^36 - 88 * q^37 - 2636 * q^38 + 798 * q^39 + 1466 * q^40 + 512 * q^41 - 337 * q^42 - 927 * q^43 + 1100 * q^44 + 1482 * q^45 + 1361 * q^46 - 286 * q^47 + 178 * q^48 - 1835 * q^49 + 583 * q^50 - 1136 * q^51 + 2306 * q^52 + 212 * q^53 + 67 * q^54 + 264 * q^55 - 2059 * q^56 + 2596 * q^57 + 1690 * q^58 + 266 * q^59 + 74 * q^60 + 624 * q^61 - 643 * q^62 + 2360 * q^63 - 3178 * q^64 + 470 * q^65 + 352 * q^66 + 676 * q^67 + 413 * q^68 - 764 * q^69 - 2122 * q^70 + 763 * q^71 + 1366 * q^72 - 4748 * q^73 + 1649 * q^74 - 2420 * q^75 + 2101 * q^76 - 1364 * q^77 - 5848 * q^78 + 4328 * q^79 + 1013 * q^80 - 537 * q^81 - 3152 * q^82 + 1554 * q^83 + 3381 * q^84 + 1690 * q^85 + 5788 * q^86 + 4200 * q^87 + 231 * q^88 + 1687 * q^89 - 10798 * q^90 - 3380 * q^91 + 11084 * q^92 + 4310 * q^93 - 1777 * q^94 - 1124 * q^95 - 6930 * q^96 + 2047 * q^97 - 1553 * q^98 + 2970 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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