LMFDB - Embedded newform 143.4.e.b.100.15

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			100.15
Character	$\chi$	$=$	143.100
Dual form			143.4.e.b.133.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05606 - 3.56120i) q^{2} +(2.00775 - 3.47753i) q^{3} +(-4.45478 - 7.71591i) q^{4} -12.3424 q^{5} +(-8.25614 - 14.3001i) q^{6} +(-14.8185 - 25.6664i) q^{7} -3.74025 q^{8} +(5.43784 + 9.41862i) q^{9} +O(q^{10})$	\(q+(2.05606 - 3.56120i) q^{2} +(2.00775 - 3.47753i) q^{3} +(-4.45478 - 7.71591i) q^{4} -12.3424 q^{5} +(-8.25614 - 14.3001i) q^{6} +(-14.8185 - 25.6664i) q^{7} -3.74025 q^{8} +(5.43784 + 9.41862i) q^{9} +(-25.3768 + 43.9540i) q^{10} +(-5.50000 + 9.52628i) q^{11} -35.7765 q^{12} +(18.7978 + 42.9377i) q^{13} -121.871 q^{14} +(-24.7806 + 42.9213i) q^{15} +(27.9481 - 48.4075i) q^{16} +(-50.0334 - 86.6604i) q^{17} +44.7221 q^{18} +(-19.3960 - 33.5948i) q^{19} +(54.9829 + 95.2332i) q^{20} -119.008 q^{21} +(22.6167 + 39.1732i) q^{22} +(53.9126 - 93.3794i) q^{23} +(-7.50951 + 13.0069i) q^{24} +27.3360 q^{25} +(191.559 + 21.3398i) q^{26} +152.090 q^{27} +(-132.027 + 228.677i) q^{28} +(-68.0303 + 117.832i) q^{29} +(101.901 + 176.498i) q^{30} -7.90141 q^{31} +(-129.887 - 224.971i) q^{32} +(22.0853 + 38.2529i) q^{33} -411.487 q^{34} +(182.897 + 316.787i) q^{35} +(48.4488 - 83.9158i) q^{36} +(207.793 - 359.907i) q^{37} -159.517 q^{38} +(187.059 + 20.8384i) q^{39} +46.1639 q^{40} +(128.633 - 222.798i) q^{41} +(-244.687 + 423.811i) q^{42} +(9.52117 + 16.4912i) q^{43} +98.0052 q^{44} +(-67.1163 - 116.249i) q^{45} +(-221.695 - 383.988i) q^{46} +167.428 q^{47} +(-112.226 - 194.381i) q^{48} +(-267.677 + 463.630i) q^{49} +(56.2046 - 97.3491i) q^{50} -401.819 q^{51} +(247.563 - 336.320i) q^{52} +96.3042 q^{53} +(312.707 - 541.624i) q^{54} +(67.8835 - 117.578i) q^{55} +(55.4250 + 95.9989i) q^{56} -155.769 q^{57} +(279.749 + 484.540i) q^{58} +(260.418 + 451.057i) q^{59} +441.569 q^{60} +(351.143 + 608.197i) q^{61} +(-16.2458 + 28.1385i) q^{62} +(161.161 - 279.140i) q^{63} -621.054 q^{64} +(-232.011 - 529.956i) q^{65} +181.635 q^{66} +(334.798 - 579.887i) q^{67} +(-445.776 + 772.107i) q^{68} +(-216.487 - 374.966i) q^{69} +1504.19 q^{70} +(-258.979 - 448.566i) q^{71} +(-20.3389 - 35.2280i) q^{72} -1154.37 q^{73} +(-854.469 - 1479.98i) q^{74} +(54.8840 - 95.0619i) q^{75} +(-172.810 + 299.315i) q^{76} +326.007 q^{77} +(458.814 - 623.309i) q^{78} +1197.20 q^{79} +(-344.948 + 597.467i) q^{80} +(158.538 - 274.596i) q^{81} +(-528.954 - 916.174i) q^{82} +77.3667 q^{83} +(530.154 + 918.254i) q^{84} +(617.535 + 1069.60i) q^{85} +78.3045 q^{86} +(273.176 + 473.155i) q^{87} +(20.5714 - 35.6307i) q^{88} +(-272.561 + 472.089i) q^{89} -551.981 q^{90} +(823.501 - 1118.74i) q^{91} -960.676 q^{92} +(-15.8641 + 27.4774i) q^{93} +(344.242 - 596.245i) q^{94} +(239.394 + 414.642i) q^{95} -1043.12 q^{96} +(-331.683 - 574.492i) q^{97} +(1100.72 + 1906.50i) q^{98} -119.632 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 $

$2$	2.05606	−	3.56120i	0.726928	−	1.25908i	−0.231248	−	0.972895i	$-0.574281\pi$
$2$	2.05606	−	3.56120i	0.726928	−	1.25908i	0.958176	−	0.286181i	$-0.0923858\pi$
$3$	2.00775	−	3.47753i	0.386393	−	0.669252i	−0.605569	−	0.795793i	$-0.707054\pi$
$3$	2.00775	−	3.47753i	0.386393	−	0.669252i	0.991961	+	0.126541i	$0.0403876\pi$
$4$	−4.45478	−	7.71591i	−0.556848	−	0.964489i
$5$	−12.3424			−1.10394			−0.551971	−	0.833863i	$-0.686124\pi$
$5$	−12.3424			−1.10394			−0.551971	+	0.833863i	$0.686124\pi$
$6$	−8.25614	−	14.3001i	−0.561759	−	0.972995i
$7$	−14.8185	−	25.6664i	−0.800125	−	1.38586i	−0.919534	−	0.393012i	$-0.871433\pi$
$7$	−14.8185	−	25.6664i	−0.800125	−	1.38586i	0.119409	−	0.992845i	$-0.461900\pi$
$8$	−3.74025			−0.165297
$9$	5.43784	+	9.41862i	0.201401	+	0.348838i
$10$	−25.3768	+	43.9540i	−0.802486	+	1.38995i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$12$	−35.7765			−0.860648
$13$	18.7978	+	42.9377i	0.401044	+	0.916059i
$13$	18.7978	+	42.9377i	0.401044	+	0.916059i
$14$	−121.871			−2.32653
$15$	−24.7806	+	42.9213i	−0.426555	+	0.738815i
$16$	27.9481	−	48.4075i	0.436689	−	0.756367i
$17$	−50.0334	−	86.6604i	−0.713817	−	1.23637i	−0.963414	−	0.268017i	$-0.913632\pi$
$17$	−50.0334	−	86.6604i	−0.713817	−	1.23637i	0.249598	−	0.968350i	$-0.419702\pi$
$18$	44.7221			0.585617
$19$	−19.3960	−	33.5948i	−0.234197	−	0.405641i	0.724842	−	0.688915i	$-0.241913\pi$
$19$	−19.3960	−	33.5948i	−0.234197	−	0.405641i	−0.959039	+	0.283274i	$0.908579\pi$
$20$	54.9829	+	95.2332i	0.614728	+	1.06474i
$21$	−119.008			−1.23665
$22$	22.6167	+	39.1732i	0.219177	+	0.379626i
$23$	53.9126	−	93.3794i	0.488763	−	0.846563i	−0.511153	−	0.859490i	$-0.670781\pi$
$23$	53.9126	−	93.3794i	0.488763	−	0.846563i	0.999916	+	0.0129268i	$0.00411483\pi$
$24$	−7.50951	+	13.0069i	−0.0638697	+	0.110626i
$25$	27.3360			0.218688
$26$	191.559	+	21.3398i	1.44492	+	0.160964i
$27$	152.090			1.08407
$28$	−132.027	+	228.677i	−0.891096	+	1.54342i
$29$	−68.0303	+	117.832i	−0.435618	+	0.754512i	−0.997346	−	0.0728101i	$-0.976803\pi$
$29$	−68.0303	+	117.832i	−0.435618	+	0.754512i	0.561728	+	0.827322i	$0.310137\pi$
$30$	101.901	+	176.498i	0.620149	+	1.07413i
$31$	−7.90141			−0.0457785			−0.0228893	−	0.999738i	$-0.507287\pi$
$31$	−7.90141			−0.0457785			−0.0228893	+	0.999738i	$0.507287\pi$
$32$	−129.887	−	224.971i	−0.717531	−	1.24280i
$33$	22.0853	+	38.2529i	0.116502	+	0.201787i
$34$	−411.487			−2.07557
$35$	182.897	+	316.787i	0.883291	+	1.52991i
$36$	48.4488	−	83.9158i	0.224300	−	0.388499i
$37$	207.793	−	359.907i	0.923267	−	1.59915i	0.128943	−	0.991652i	$-0.458842\pi$
$37$	207.793	−	359.907i	0.923267	−	1.59915i	0.794324	−	0.607494i	$-0.207825\pi$
$38$	−159.517			−0.680977
$39$	187.059	+	20.8384i	0.768034	+	0.0855593i
$40$	46.1639			0.182479
$41$	128.633	−	222.798i	0.489977	−	0.848665i	−0.509957	−	0.860200i	$-0.670339\pi$
$41$	128.633	−	222.798i	0.489977	−	0.848665i	0.999933	+	0.0115354i	$0.00367192\pi$
$42$	−244.687	+	423.811i	−0.898955	+	1.55704i
$43$	9.52117	+	16.4912i	0.0337666	+	0.0584855i	0.882415	−	0.470472i	$-0.155916\pi$
$43$	9.52117	+	16.4912i	0.0337666	+	0.0584855i	−0.848648	+	0.528958i	$0.822583\pi$
$44$	98.0052			0.335792
$45$	−67.1163	−	116.249i	−0.222336	−	0.385097i
$46$	−221.695	−	383.988i	−0.710591	−	1.23078i
$47$	167.428			0.519615			0.259807	−	0.965660i	$-0.416341\pi$
$47$	167.428			0.519615			0.259807	+	0.965660i	$0.416341\pi$
$48$	−112.226	−	194.381i	−0.337467	−	0.584509i
$49$	−267.677	+	463.630i	−0.780399	+	1.35169i
$50$	56.2046	−	97.3491i	0.158970	−	0.275345i
$51$	−401.819			−1.10325
$52$	247.563	−	336.320i	0.660208	−	0.896908i
$53$	96.3042			0.249592			0.124796	−	0.992182i	$-0.460172\pi$
$53$	96.3042			0.249592			0.124796	+	0.992182i	$0.460172\pi$
$54$	312.707	−	541.624i	0.788037	−	1.36492i
$55$	67.8835	−	117.578i	0.166426	−	0.288257i
$56$	55.4250	+	95.9989i	0.132258	+	0.229078i
$57$	−155.769			−0.361968
$58$	279.749	+	484.540i	0.633325	+	1.09695i
$59$	260.418	+	451.057i	0.574636	+	0.995298i	0.996081	+	0.0884443i	$0.0281895\pi$
$59$	260.418	+	451.057i	0.574636	+	0.995298i	−0.421446	+	0.906854i	$0.638477\pi$
$60$	441.569			0.950105
$61$	351.143	+	608.197i	0.737036	+	1.27658i	0.953824	+	0.300365i	$0.0971085\pi$
$61$	351.143	+	608.197i	0.737036	+	1.27658i	−0.216788	+	0.976219i	$0.569558\pi$
$62$	−16.2458	+	28.1385i	−0.0332777	+	0.0576386i
$63$	161.161	−	279.140i	0.322293	−	0.558227i
$64$	−621.054			−1.21300
$65$	−232.011	−	529.956i	−0.442729	−	1.01128i
$66$	181.635			0.338753
$67$	334.798	−	579.887i	0.610479	−	1.05738i	−0.380680	−	0.924707i	$-0.624310\pi$
$67$	334.798	−	579.887i	0.610479	−	1.05738i	0.991160	−	0.132674i	$-0.0423565\pi$
$68$	−445.776	+	772.107i	−0.794975	+	1.37694i
$69$	−216.487	−	374.966i	−0.377709	−	0.654211i
$70$	1504.19			2.56836
$71$	−258.979	−	448.566i	−0.432890	−	0.749788i	0.564231	−	0.825617i	$-0.309173\pi$
$71$	−258.979	−	448.566i	−0.432890	−	0.749788i	−0.997121	+	0.0758294i	$0.975840\pi$
$72$	−20.3389	−	35.2280i	−0.0332911	−	0.0576619i
$73$	−1154.37			−1.85081			−0.925406	−	0.378976i	$-0.876276\pi$
$73$	−1154.37			−1.85081			−0.925406	+	0.378976i	$0.876276\pi$
$74$	−854.469	−	1479.98i	−1.34230	−	2.32493i
$75$	54.8840	−	95.0619i	0.0844995	−	0.146357i
$76$	−172.810	+	299.315i	−0.260824	+	0.451761i
$77$	326.007			0.482493
$78$	458.814	−	623.309i	0.666031	−	0.904818i
$79$	1197.20			1.70500			0.852502	−	0.522723i	$-0.175084\pi$
$79$	1197.20			1.70500			0.852502	+	0.522723i	$0.175084\pi$
$80$	−344.948	+	597.467i	−0.482079	+	0.834985i
$81$	158.538	−	274.596i	0.217473	−	0.376675i
$82$	−528.954	−	916.174i	−0.712355	−	1.23384i
$83$	77.3667			0.102314			0.0511572	−	0.998691i	$-0.483709\pi$
$83$	77.3667			0.102314			0.0511572	+	0.998691i	$0.483709\pi$
$84$	530.154	+	918.254i	0.688626	+	1.19273i
$85$	617.535	+	1069.60i	0.788012	+	1.36488i
$86$	78.3045			0.0981836
$87$	273.176	+	473.155i	0.336639	+	0.583076i
$88$	20.5714	−	35.6307i	0.0249195	−	0.0431619i
$89$	−272.561	+	472.089i	−0.324622	+	0.562262i	−0.981436	−	0.191791i	$-0.938570\pi$
$89$	−272.561	+	472.089i	−0.324622	+	0.562262i	0.656814	+	0.754053i	$0.271904\pi$
$90$	−551.981			−0.646488
$91$	823.501	−	1118.74i	0.948642	−	1.28875i
$92$	−960.676			−1.08867
$93$	−15.8641	+	27.4774i	−0.0176885	+	0.0306374i
$94$	344.242	−	596.245i	0.377722	−	0.654234i
$95$	239.394	+	414.642i	0.258540	+	0.447804i
$96$	−1043.12			−1.10899
$97$	−331.683	−	574.492i	−0.347189	−	0.601348i	0.638560	−	0.769572i	$-0.279530\pi$
$97$	−331.683	−	574.492i	−0.347189	−	0.601348i	−0.985749	+	0.168223i	$0.946197\pi$
$98$	1100.72	+	1906.50i	1.13459	+	1.96516i
$99$	−119.632			−0.121450
$100$	−121.776	−	210.922i	−0.121776	−	0.210922i
$101$	−878.501	+	1521.61i	−0.865487	+	1.49907i	0.00107652	+	0.999999i	$0.499657\pi$
$101$	−878.501	+	1521.61i	−0.865487	+	1.49907i	−0.866563	+	0.499067i	$0.833676\pi$
$102$	−826.165	+	1430.96i	−0.801986	+	1.38908i
$103$	1224.64			1.17153			0.585765	−	0.810481i	$-0.300794\pi$
$103$	1224.64			1.17153			0.585765	+	0.810481i	$0.300794\pi$
$104$	−70.3084	−	160.598i	−0.0662914	−	0.151422i
$105$	1468.85			1.36519
$106$	198.007	−	342.959i	0.181436	−	0.314256i
$107$	−583.359	+	1010.41i	−0.527060	+	0.912895i	0.472443	+	0.881361i	$0.343372\pi$
$107$	−583.359	+	1010.41i	−0.527060	+	0.912895i	−0.999503	+	0.0315333i	$0.989961\pi$
$108$	−677.529	−	1173.51i	−0.603660	−	1.04557i
$109$	678.659			0.596365			0.298182	−	0.954509i	$-0.403620\pi$
$109$	678.659			0.596365			0.298182	+	0.954509i	$0.403620\pi$
$110$	−279.145	−	483.494i	−0.241959	−	0.419085i
$111$	−834.393	−	1445.21i	−0.713487	−	1.23580i
$112$	−1656.60			−1.39762
$113$	262.087	+	453.949i	0.218187	+	0.377911i	0.954254	−	0.298998i	$-0.0966525\pi$
$113$	262.087	+	453.949i	0.218187	+	0.377911i	−0.736067	+	0.676909i	$0.763319\pi$
$114$	−320.272	+	554.727i	−0.263124	+	0.455745i
$115$	−665.414	+	1152.53i	−0.539566	+	0.934556i
$116$	1212.24			0.970291
$117$	−302.194	+	410.537i	−0.238785	+	0.324395i
$118$	2141.74			1.67087
$119$	−1482.84	+	2568.36i	−1.14228	+	1.97850i
$120$	92.6857	−	160.536i	0.0705084	−	0.122124i
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$	2887.88			2.14309
$123$	−516.526	−	894.649i	−0.378647	−	0.655836i
$124$	35.1991	+	60.9665i	0.0254917	+	0.0441529i
$125$	1205.41			0.862523
$126$	−662.716	−	1147.86i	−0.468567	−	0.811582i
$127$	839.218	−	1453.57i	0.586366	−	1.01562i	−0.408337	−	0.912831i	$-0.633891\pi$
$127$	839.218	−	1453.57i	0.586366	−	1.01562i	0.994704	−	0.102785i	$-0.0327754\pi$
$128$	−237.829	+	411.932i	−0.164229	+	0.284453i
$129$	76.4647			0.0521887
$130$	−2364.31	−	263.385i	−1.59511	−	0.177695i
$131$	−2327.92			−1.55261			−0.776304	−	0.630359i	$-0.782908\pi$
$131$	−2327.92			−1.55261			−0.776304	+	0.630359i	$0.782908\pi$
$132$	196.770	−	340.816i	0.129748	−	0.224729i
$133$	−574.839	+	995.650i	−0.374773	+	0.649127i
$134$	−1376.73	−	2384.57i	−0.887549	−	1.53728i
$135$	−1877.16			−1.19675
$136$	187.138	+	324.132i	0.117992	+	0.204368i
$137$	733.707	+	1270.82i	0.457554	+	0.792506i	0.998831	−	0.0483379i	$-0.0153924\pi$
$137$	733.707	+	1270.82i	0.457554	+	0.792506i	−0.541277	+	0.840844i	$0.682059\pi$
$138$	−1780.44			−1.09827
$139$	499.645	+	865.411i	0.304887	+	0.528081i	0.977236	−	0.212154i	$-0.0680478\pi$
$139$	499.645	+	865.411i	0.304887	+	0.528081i	−0.672349	+	0.740234i	$0.734714\pi$
$140$	1629.53	−	2822.43i	0.983718	−	1.70385i
$141$	336.154	−	582.237i	0.200775	−	0.347753i
$142$	−2129.91			−1.25872
$143$	−512.424	−	57.0843i	−0.299658	−	0.0333820i
$144$	607.909			0.351799
$145$	839.660	−	1454.33i	0.480897	−	0.832937i
$146$	−2373.47	+	4110.96i	−1.34541	+	2.33031i
$147$	1074.86	+	1861.71i	0.603081	+	1.04457i
$148$	−3702.68			−2.05648
$149$	−361.475	−	626.093i	−0.198746	−	0.344238i	0.749376	−	0.662145i	$-0.230354\pi$
$149$	−361.475	−	626.093i	−0.198746	−	0.344238i	−0.948122	+	0.317906i	$0.897020\pi$
$150$	−225.690	−	390.906i	−0.122850	−	0.212783i
$151$	933.009			0.502829			0.251415	−	0.967879i	$-0.419104\pi$
$151$	933.009			0.502829			0.251415	+	0.967879i	$0.419104\pi$
$152$	72.5458	+	125.653i	0.0387121	+	0.0670514i
$153$	544.147	−	942.491i	0.287527	−	0.498012i
$154$	670.291	−	1160.98i	0.350738	−	0.607496i
$155$	97.5227			0.0505368
$156$	−672.518	−	1536.16i	−0.345157	−	0.788404i
$157$	763.894			0.388314			0.194157	−	0.980970i	$-0.437803\pi$
$157$	763.894			0.388314			0.194157	+	0.980970i	$0.437803\pi$
$158$	2461.51	−	4263.47i	1.23942	−	2.14673i
$159$	193.355	−	334.901i	0.0964406	−	0.167040i
$160$	1603.12	+	2776.69i	0.792113	+	1.37198i
$161$	−3195.62			−1.56429
$162$	−651.928	−	1129.17i	−0.316175	−	0.547631i
$163$	1285.63	+	2226.77i	0.617780	+	1.07003i	0.989890	+	0.141838i	$0.0453011\pi$
$163$	1285.63	+	2226.77i	0.617780	+	1.07003i	−0.372110	+	0.928189i	$0.621366\pi$
$164$	−2292.12			−1.09137
$165$	−272.587	−	472.134i	−0.128611	−	0.222761i
$166$	159.071	−	275.519i	0.0743752	−	0.128822i
$167$	−1444.11	+	2501.27i	−0.669154	+	1.15901i	0.308987	+	0.951066i	$0.400010\pi$
$167$	−1444.11	+	2501.27i	−0.669154	+	1.15901i	−0.978141	+	0.207943i	$0.933323\pi$
$168$	445.119			0.204415
$169$	−1490.29	+	1614.27i	−0.678328	+	0.734759i
$170$	5078.76			2.29131
$171$	210.944	−	365.366i	0.0943352	−	0.163393i
$172$	84.8295	−	146.929i	0.0376058	−	0.0651351i
$173$	−1120.22	−	1940.28i	−0.492306	−	0.852699i	0.507655	−	0.861561i	$-0.330513\pi$
$173$	−1120.22	−	1940.28i	−0.492306	−	0.852699i	−0.999961	+	0.00886164i	$0.997179\pi$
$174$	2246.67			0.978848
$175$	−405.079	−	701.618i	−0.174978	−	0.303070i
$176$	307.429	+	532.482i	0.131667	+	0.228053i
$177$	2091.42			0.888140
$178$	1120.80	+	1941.29i	0.471954	+	0.817448i
$179$	−815.573	+	1412.61i	−0.340552	+	0.589853i	−0.984535	−	0.175186i	$-0.943947\pi$
$179$	−815.573	+	1412.61i	−0.340552	+	0.589853i	0.643984	+	0.765039i	$0.277281\pi$
$180$	−597.977	+	1035.73i	−0.247614	+	0.428880i
$181$	2150.28			0.883032			0.441516	−	0.897253i	$-0.354441\pi$
$181$	2150.28			0.883032			0.441516	+	0.897253i	$0.354441\pi$
$182$	−2290.91	−	5232.86i	−0.933041	−	2.13124i
$183$	2820.03			1.13914
$184$	−201.647	+	349.262i	−0.0807913	+	0.139935i
$185$	−2564.67	+	4442.14i	−1.01923	+	1.76536i
$186$	65.2351	+	112.991i	0.0257165	+	0.0445423i
$187$	1100.73			0.430448
$188$	−745.856	−	1291.86i	−0.289346	−	0.501163i
$189$	−2253.75	−	3903.61i	−0.867388	−	1.50236i
$190$	1968.83			0.751759
$191$	381.382	+	660.573i	0.144481	+	0.250248i	0.929179	−	0.369630i	$-0.120515\pi$
$191$	381.382	+	660.573i	0.144481	+	0.250248i	−0.784698	+	0.619878i	$0.787182\pi$
$192$	−1246.92	+	2159.73i	−0.468692	+	0.811799i
$193$	835.443	−	1447.03i	0.311588	−	0.539687i	−0.667118	−	0.744952i	$-0.732472\pi$
$193$	835.443	−	1447.03i	0.311588	−	0.539687i	0.978706	+	0.205265i	$0.0658057\pi$
$194$	−2727.84			−1.00952
$195$	−2308.76	−	257.197i	−0.847865	−	0.0944526i
$196$	4769.77			1.73825
$197$	2101.27	−	3639.51i	0.759947	−	1.31627i	−0.182930	−	0.983126i	$-0.558558\pi$
$197$	2101.27	−	3639.51i	0.759947	−	1.31627i	0.942877	−	0.333141i	$-0.108109\pi$
$198$	−245.972	+	426.036i	−0.0882851	+	0.152914i
$199$	−345.926	−	599.162i	−0.123226	−	0.213434i	0.797812	−	0.602906i	$-0.205991\pi$
$199$	−345.926	−	599.162i	−0.123226	−	0.213434i	−0.921038	+	0.389472i	$0.872657\pi$
$200$	−102.244			−0.0361486
$201$	−1344.39	−	2328.54i	−0.471769	−	0.817128i
$202$	3612.51	+	6257.05i	1.25829	+	2.17943i
$203$	4032.43			1.39419
$204$	1790.02	+	3100.40i	0.614345	+	1.06408i
$205$	−1587.64	+	2749.88i	−0.540906	+	0.936877i
$206$	2517.94	−	4361.20i	0.851617	−	1.47504i
$207$	1172.67			0.393751
$208$	2603.87	+	290.072i	0.868008	+	0.0966965i
$209$	426.711			0.141226
$210$	3020.04	−	5230.87i	0.992394	−	1.71888i
$211$	540.931	−	936.920i	0.176489	−	0.305688i	−0.764186	−	0.644995i	$-0.776859\pi$
$211$	540.931	−	936.920i	0.176489	−	0.305688i	0.940676	+	0.339307i	$0.110193\pi$
$212$	−429.014	−	743.074i	−0.138985	−	0.240729i
$213$	−2079.87			−0.669062
$214$	2398.84	+	4154.92i	0.766269	+	1.32722i
$215$	−117.515	−	203.541i	−0.0372764	−	0.0645646i
$216$	−568.856			−0.179193
$217$	117.087	+	202.801i	0.0366285	+	0.0634425i
$218$	1395.36	−	2416.84i	0.433514	−	0.750868i
$219$	−2317.70	+	4014.38i	−0.715140	+	1.23866i
$220$	−1209.62			−0.370695
$221$	2780.48	−	3777.34i	0.846313	−	1.14974i
$222$	−6862.26			−2.07462
$223$	535.589	−	927.667i	0.160833	−	0.278570i	−0.774335	−	0.632776i	$-0.781915\pi$
$223$	535.589	−	927.667i	0.160833	−	0.278570i	0.935168	+	0.354206i	$0.115249\pi$
$224$	−3849.46	+	6667.47i	−1.14823	+	1.98879i
$225$	148.649	+	257.467i	0.0440441	+	0.0762866i
$226$	2155.47			0.634424
$227$	−938.038	−	1624.73i	−0.274272	−	0.475053i	0.695679	−	0.718353i	$-0.255104\pi$
$227$	−938.038	−	1624.73i	−0.274272	−	0.475053i	−0.969951	+	0.243299i	$0.921770\pi$
$228$	693.919	+	1201.90i	0.201561	+	0.349114i
$229$	851.152			0.245614			0.122807	−	0.992431i	$-0.460810\pi$
$229$	851.152			0.245614			0.122807	+	0.992431i	$0.460810\pi$
$230$	2736.26	+	4739.35i	0.784452	+	1.35871i
$231$	654.543	−	1133.70i	0.186432	−	0.322910i
$232$	254.450	−	440.721i	0.0720064	−	0.124719i
$233$	3288.70			0.924679			0.462339	−	0.886703i	$-0.347010\pi$
$233$	3288.70			0.924679			0.462339	+	0.886703i	$0.347010\pi$
$234$	840.677	+	1920.26i	0.234858	+	0.536460i
$235$	−2066.47			−0.573625
$236$	2320.21	−	4018.72i	0.639969	−	1.10846i
$237$	2403.68	−	4163.30i	0.658801	−	1.14108i
$238$	6097.63	+	10561.4i	1.66072	+	2.87645i
$239$	−3945.13			−1.06774			−0.533869	−	0.845567i	$-0.679262\pi$
$239$	−3945.13			−1.06774			−0.533869	+	0.845567i	$0.679262\pi$
$240$	1385.14	+	2399.13i	0.372544	+	0.645264i
$241$	−2637.69	−	4568.61i	−0.705015	−	1.22112i	−0.966686	−	0.255964i	$-0.917607\pi$
$241$	−2637.69	−	4568.61i	−0.705015	−	1.22112i	0.261672	−	0.965157i	$-0.415726\pi$
$242$	−497.567			−0.132169
$243$	1416.61	+	2453.63i	0.373972	+	0.647739i
$244$	3128.53	−	5418.77i	0.820834	−	1.42173i
$245$	3303.79	−	5722.33i	0.861516	−	1.49219i
$246$	−4248.04			−1.10100
$247$	1077.88	−	1464.33i	0.277668	−	0.377218i
$248$	29.5532			0.00756707
$249$	155.333	−	269.045i	0.0395335	−	0.0684741i
$250$	2478.40	−	4292.72i	0.626992	−	1.08598i
$251$	1646.98	+	2852.65i	0.414168	+	0.717361i	0.995341	−	0.0964197i	$-0.0307391\pi$
$251$	1646.98	+	2852.65i	0.414168	+	0.717361i	−0.581172	+	0.813781i	$0.697406\pi$
$252$	−2871.76			−0.717872
$253$	593.039	+	1027.17i	0.147368	+	0.255248i
$254$	−3450.97	−	5977.25i	−0.852492	−	1.47656i
$255$	4959.43			1.21793
$256$	−1506.23	−	2608.87i	−0.367732	−	0.636931i
$257$	43.2086	−	74.8395i	0.0104875	−	0.0181648i	−0.860734	−	0.509055i	$-0.829995\pi$
$257$	43.2086	−	74.8395i	0.0104875	−	0.0181648i	0.871222	+	0.490890i	$0.163328\pi$
$258$	157.216	−	272.307i	0.0379374	−	0.0657096i
$259$	−12316.7			−2.95492
$260$	−3055.54	+	4151.01i	−0.728832	+	0.990134i
$261$	−1479.75			−0.350936
$262$	−4786.36	+	8290.21i	−1.12863	+	1.95485i
$263$	−510.388	+	884.018i	−0.119665	+	0.207266i	−0.919635	−	0.392774i	$-0.871515\pi$
$263$	−510.388	+	884.018i	−0.119665	+	0.207266i	0.799970	+	0.600040i	$0.204849\pi$
$264$	−82.6046	−	143.075i	−0.0192574	−	0.0333548i
$265$	−1188.63			−0.275535
$266$	2363.81	+	4094.24i	0.544866	+	0.943736i
$267$	1094.47	+	1895.68i	0.250863	+	0.434508i
$268$	−5965.81			−1.35978
$269$	−3064.08	−	5307.13i	−0.694498	−	1.20291i	−0.970350	−	0.241706i	$-0.922293\pi$
$269$	−3064.08	−	5307.13i	−0.694498	−	1.20291i	0.275852	−	0.961200i	$-0.411040\pi$
$270$	−3859.57	+	6684.97i	−0.869947	+	1.50679i
$271$	2535.98	−	4392.45i	0.568450	−	0.984583i	−0.428270	−	0.903651i	$-0.640877\pi$
$271$	2535.98	−	4392.45i	0.568450	−	0.984583i	0.996720	−	0.0809327i	$-0.0257899\pi$
$272$	−5593.35			−1.24686
$273$	−2237.08	−	5109.92i	−0.495950	−	1.13284i
$274$	6034.19			1.33043
$275$	−150.348	+	260.411i	−0.0329685	+	0.0571031i
$276$	−1928.80	+	3340.78i	−0.420653	+	0.728592i
$277$	712.458	+	1234.01i	0.154540	+	0.267671i	0.932891	−	0.360158i	$-0.117277\pi$
$277$	712.458	+	1234.01i	0.154540	+	0.267671i	−0.778352	+	0.627829i	$0.783944\pi$
$278$	4109.21			0.886525
$279$	−42.9666	−	74.4203i	−0.00921986	−	0.0159693i
$280$	−684.080	−	1184.86i	−0.146006	−	0.252889i
$281$	−4430.28			−0.940529			−0.470264	−	0.882526i	$-0.655841\pi$
$281$	−4430.28			−0.940529			−0.470264	+	0.882526i	$0.655841\pi$
$282$	−1382.31	−	2394.23i	−0.291898	−	0.505583i
$283$	706.548	−	1223.78i	0.148410	−	0.257053i	−0.782230	−	0.622989i	$-0.785918\pi$
$283$	706.548	−	1223.78i	0.148410	−	0.257053i	0.930640	+	0.365937i	$0.119251\pi$
$284$	−2307.39	+	3996.52i	−0.482108	+	0.835036i
$285$	1922.58			0.399591
$286$	−1256.86	+	1707.48i	−0.259860	+	0.353025i
$287$	−7624.58			−1.56817
$288$	1412.61	−	2446.71i	0.289024	−	0.500604i
$289$	−2550.18	+	4417.05i	−0.519068	+	0.899053i
$290$	−3452.79	−	5980.40i	−0.699154	−	1.21097i
$291$	−2663.75			−0.536605
$292$	5142.49	+	8907.05i	1.03062	+	1.78509i
$293$	−3538.63	−	6129.08i	−0.705559	−	1.22206i	−0.966489	−	0.256707i	$-0.917362\pi$
$293$	−3538.63	−	6129.08i	−0.705559	−	1.22206i	0.260930	−	0.965358i	$-0.415971\pi$
$294$	8839.91			1.75359
$295$	−3214.19	−	5567.14i	−0.634364	−	1.09875i
$296$	−777.197	+	1346.14i	−0.152614	+	0.264335i
$297$	−836.496	+	1448.85i	−0.163429	+	0.283067i
$298$	−2972.86			−0.577896
$299$	5022.93	+	559.557i	0.971517	+	0.108227i
$300$	−977.986			−0.188213
$301$	282.179	−	488.749i	0.0540350	−	0.0935914i
$302$	1918.32	−	3322.64i	0.365520	−	0.633100i
$303$	3527.63	+	6110.04i	0.668835	+	1.15846i
$304$	−2168.32			−0.409084
$305$	−4333.96	−	7506.64i	−0.813645	−	1.40927i
$306$	−2237.60	−	3875.64i	−0.418023	−	0.724038i
$307$	−7728.94			−1.43685			−0.718426	−	0.695603i	$-0.755137\pi$
$307$	−7728.94			−1.43685			−0.718426	+	0.695603i	$0.755137\pi$
$308$	−1452.29	−	2515.44i	−0.268675	−	0.465360i
$309$	2458.78	−	4258.73i	0.452670	−	0.784048i
$310$	200.513	−	347.298i	0.0367366	−	0.0636297i
$311$	721.632			0.131576			0.0657878	−	0.997834i	$-0.479044\pi$
$311$	721.632			0.131576			0.0657878	+	0.997834i	$0.479044\pi$
$312$	−699.646	−	77.9409i	−0.126954	−	0.0141427i
$313$	−3856.16			−0.696367			−0.348184	−	0.937426i	$-0.613201\pi$
$313$	−3856.16			−0.696367			−0.348184	+	0.937426i	$0.613201\pi$
$314$	1570.61	−	2720.38i	0.282277	−	0.488917i
$315$	−1989.13	+	3445.27i	−0.355792	+	0.616251i
$316$	−5333.26	−	9237.48i	−0.949428	−	1.64446i
$317$	1180.38			0.209138			0.104569	−	0.994518i	$-0.466654\pi$
$317$	1180.38			0.209138			0.104569	+	0.994518i	$0.466654\pi$
$318$	−795.100	−	1377.15i	−0.140211	−	0.242852i
$319$	−748.333	−	1296.15i	−0.131344	−	0.227494i
$320$	7665.32			1.33908
$321$	2342.48	+	4057.30i	0.407304	+	0.705472i
$322$	−6570.39	+	11380.3i	−1.13712	+	1.96956i
$323$	−1940.89	+	3361.72i	−0.334347	+	0.579106i
$324$	−2825.01			−0.484398
$325$	513.857	+	1173.74i	0.0877035	+	0.200331i
$326$	10573.3			1.79633
$327$	1362.58	−	2360.06i	0.230431	−	0.399118i
$328$	−481.119	+	833.322i	−0.0809919	+	0.140282i
$329$	−2481.04	−	4297.28i	−0.415757	−	0.720111i
$330$	−2241.82			−0.373964
$331$	3169.59	+	5489.88i	0.526333	+	0.911635i	0.999529	+	0.0306785i	$0.00976680\pi$
$331$	3169.59	+	5489.88i	0.526333	+	0.911635i	−0.473196	+	0.880957i	$0.656900\pi$
$332$	−344.652	−	596.954i	−0.0569736	−	0.0986811i
$333$	4519.77			0.743790
$334$	5938.37	+	10285.6i	0.972853	+	1.68503i
$335$	−4132.23	+	7157.23i	−0.673934	+	1.16729i
$336$	−3326.04	+	5760.87i	−0.540031	+	0.935361i
$337$	3552.56			0.574244			0.287122	−	0.957894i	$-0.407302\pi$
$337$	3552.56			0.574244			0.287122	+	0.957894i	$0.407302\pi$
$338$	2684.61	+	8626.25i	0.432022	+	1.38818i
$339$	2104.83			0.337223
$340$	5501.97	−	9529.69i	0.877606	−	1.52006i
$341$	43.4577	−	75.2710i	0.00690137	−	0.0119535i
$342$	−867.429	−	1502.43i	−0.137150	−	0.237550i
$343$	5700.80			0.897418
$344$	−35.6116	−	61.6811i	−0.00558154	−	0.00966750i
$345$	2671.97	+	4628.00i	0.416969	+	0.722211i
$346$	−9212.99			−1.43148
$347$	342.429	+	593.104i	0.0529756	+	0.0917564i	0.891297	−	0.453420i	$-0.149796\pi$
$347$	342.429	+	593.104i	0.0529756	+	0.0917564i	−0.838322	+	0.545176i	$0.816463\pi$
$348$	2433.88	−	4215.61i	0.374913	−	0.649369i
$349$	4123.53	−	7142.16i	0.632457	−	1.09545i	−0.354591	−	0.935022i	$-0.615380\pi$
$349$	4123.53	−	7142.16i	0.632457	−	1.09545i	0.987048	−	0.160426i	$-0.0512868\pi$
$350$	−3331.47			−0.508785
$351$	2858.96	+	6530.40i	0.434757	+	0.993068i
$352$	2857.51			0.432687
$353$	−4090.96	+	7085.75i	−0.616827	+	1.06838i	0.373234	+	0.927737i	$0.378249\pi$
$353$	−4090.96	+	7085.75i	−0.616827	+	1.06838i	−0.990061	+	0.140638i	$0.955085\pi$
$354$	4300.09	−	7447.97i	0.645613	−	1.11824i
$355$	3196.44	+	5536.40i	0.477886	+	0.827722i
$356$	4856.79			0.723061
$357$	5954.37	+	10313.3i	0.882741	+	1.52895i
$358$	3353.74	+	5808.84i	0.495113	+	0.857561i
$359$	1224.23			0.179979			0.0899894	−	0.995943i	$-0.471317\pi$
$359$	1224.23			0.179979			0.0899894	+	0.995943i	$0.471317\pi$
$360$	251.032	+	434.800i	0.0367515	+	0.0636554i
$361$	2677.09	−	4636.86i	0.390304	−	0.676026i
$362$	4421.10	−	7657.57i	0.641901	−	1.11180i
$363$	−485.877			−0.0702532
$364$	−12300.7	−	1370.30i	−1.77123	−	0.197316i
$365$	14247.8			2.04319
$366$	5798.16	−	10042.7i	0.828073	−	1.43426i
$367$	−3736.81	+	6472.35i	−0.531499	+	0.920583i	0.467825	+	0.883821i	$0.345038\pi$
$367$	−3736.81	+	6472.35i	−0.531499	+	0.920583i	−0.999324	+	0.0367621i	$0.988296\pi$
$368$	−3013.51	−	5219.55i	−0.426875	−	0.739369i
$369$	2797.94			0.394728
$370$	10546.2	+	18266.6i	1.48182	+	2.56658i
$371$	−1427.09	−	2471.78i	−0.199705	−	0.345899i
$372$	282.684			0.0393992
$373$	6228.20	+	10787.6i	0.864569	+	1.49748i	0.867475	+	0.497481i	$0.165742\pi$
$373$	6228.20	+	10787.6i	0.864569	+	1.49748i	−0.00290589	+	0.999996i	$0.500925\pi$
$374$	2263.18	−	3919.94i	0.312904	−	0.541966i
$375$	2420.17	−	4191.86i	0.333273	−	0.577245i
$376$	−626.223			−0.0858909
$377$	−6338.25	−	706.083i	−0.865879	−	0.0964593i
$378$	−18535.4			−2.52211
$379$	5052.38	−	8750.97i	0.684758	−	1.18604i	−0.288755	−	0.957403i	$-0.593241\pi$
$379$	5052.38	−	8750.97i	0.684758	−	1.18604i	0.973513	−	0.228632i	$-0.0734253\pi$
$380$	2132.89	−	3694.28i	0.287935	−	0.498717i
$381$	−3369.89	−	5836.82i	−0.453135	−	0.784853i
$382$	3136.58			0.420108
$383$	6474.06	+	11213.4i	0.863730	+	1.49603i	0.868302	+	0.496036i	$0.165211\pi$
$383$	6474.06	+	11213.4i	0.863730	+	1.49603i	−0.00457171	+	0.999990i	$0.501455\pi$
$384$	955.004	+	1654.12i	0.126914	+	0.219821i
$385$	−4023.73			−0.532645
$386$	−3435.45	−	5950.37i	−0.453004	−	0.784626i
$387$	−103.549	+	179.353i	−0.0136013	+	0.0235581i
$388$	−2955.15	+	5118.47i	−0.386663	+	0.669719i
$389$	−3176.64			−0.414041			−0.207020	−	0.978337i	$-0.566377\pi$
$389$	−3176.64			−0.414041			−0.207020	+	0.978337i	$0.566377\pi$
$390$	−5662.88	+	7693.15i	−0.735260	+	0.998867i
$391$	−10789.7			−1.39555
$392$	1001.18	−	1734.09i	0.128998	−	0.223431i
$393$	−4673.90	+	8095.43i	−0.599916	+	1.03909i
$394$	−8640.70	−	14966.1i	−1.10485	−	1.91366i
$395$	−14776.4			−1.88223
$396$	532.937	+	923.074i	0.0676290	+	0.117137i
$397$	−394.234	−	682.834i	−0.0498389	−	0.0863235i	0.840030	−	0.542540i	$-0.182537\pi$
$397$	−394.234	−	682.834i	−0.0498389	−	0.0863235i	−0.889869	+	0.456217i	$0.849204\pi$
$398$	−2844.98			−0.358307
$399$	2308.27	+	3998.04i	0.289619	+	0.501635i
$400$	763.989	−	1323.27i	0.0954986	−	0.165409i
$401$	3894.57	−	6745.59i	0.485001	−	0.840047i	−0.514850	−	0.857280i	$-0.672152\pi$
$401$	3894.57	−	6745.59i	0.485001	−	0.840047i	0.999851	+	0.0172331i	$0.00548573\pi$
$402$	−11056.6			−1.37177
$403$	−148.529	−	339.268i	−0.0183592	−	0.0419358i
$404$	15654.1			1.92778
$405$	−1956.75	+	3389.19i	−0.240078	+	0.415827i
$406$	8290.93	−	14360.3i	1.01348	−	1.75540i
$407$	2285.72	+	3958.98i	0.278376	+	0.482161i
$408$	1502.91			0.182365
$409$	1789.76	+	3099.95i	0.216376	+	0.374774i	0.953697	−	0.300768i	$-0.0972429\pi$
$409$	1789.76	+	3099.95i	0.216376	+	0.374774i	−0.737321	+	0.675542i	$0.763910\pi$
$410$	6528.58	+	11307.8i	0.786399	+	1.36208i
$411$	5892.42			0.707181
$412$	−5455.51	−	9449.22i	−0.652364	−	1.12993i
$413$	7718.01	−	13368.0i	0.919560	−	1.59273i
$414$	2411.09	−	4176.13i	0.286228	−	0.495762i
$415$	−954.894			−0.112949
$416$	7218.14	−	9806.00i	0.850717	−	1.15572i
$417$	4012.66			0.471225
$418$	877.345	−	1519.61i	0.102661	−	0.177814i
$419$	2550.31	−	4417.27i	0.297353	−	0.515030i	−0.678177	−	0.734899i	$-0.737230\pi$
$419$	2550.31	−	4417.27i	0.297353	−	0.515030i	0.975529	+	0.219869i	$0.0705629\pi$
$420$	−6543.40	−	11333.5i	−0.760203	−	1.31671i
$421$	−9575.43			−1.10850			−0.554250	−	0.832351i	$-0.686995\pi$
$421$	−9575.43			−1.10850			−0.554250	+	0.832351i	$0.686995\pi$
$422$	−2224.37	−	3852.73i	−0.256590	−	0.444426i
$423$	910.447	+	1576.94i	0.104651	+	0.181261i
$424$	−360.202			−0.0412570
$425$	−1367.71	−	2368.95i	−0.156103	−	0.270379i
$426$	−4276.34	+	7406.84i	−0.486360	+	0.842400i
$427$	10406.8	−	18025.1i	1.17944	−	2.04285i
$428$	10394.9			1.17397
$429$	−1227.33	+	1667.36i	−0.138126	+	0.187648i
$430$	−966.469			−0.108389
$431$	−4379.00	+	7584.66i	−0.489395	+	0.847657i	−0.999926	−	0.0122027i	$-0.996116\pi$
$431$	−4379.00	+	7584.66i	−0.489395	+	0.847657i	0.510531	+	0.859860i	$0.329449\pi$
$432$	4250.63	−	7362.30i	0.473399	−	0.819951i
$433$	−4593.47	−	7956.12i	−0.509810	−	0.883018i	−0.999935	−	0.0113654i	$-0.996382\pi$
$433$	−4593.47	−	7956.12i	−0.509810	−	0.883018i	0.490125	−	0.871652i	$-0.336951\pi$
$434$	962.954			0.106505
$435$	−3371.66	−	5839.89i	−0.371630	−	0.643682i
$436$	−3023.28	−	5236.47i	−0.332084	−	0.575187i
$437$	−4182.75			−0.457867
$438$	9530.68	+	16507.6i	1.03971	+	1.80083i
$439$	1454.48	−	2519.24i	0.158129	−	0.273888i	−0.776065	−	0.630653i	$-0.782787\pi$
$439$	1454.48	−	2519.24i	0.158129	−	0.273888i	0.934194	+	0.356765i	$0.116120\pi$
$440$	−253.901	+	439.770i	−0.0275097	+	0.0476482i
$441$	−5822.34			−0.628694
$442$	−7735.05	−	17668.3i	−0.832395	−	1.90135i
$443$	6073.14			0.651340			0.325670	−	0.945484i	$-0.394410\pi$
$443$	6073.14			0.651340			0.325670	+	0.945484i	$0.394410\pi$
$444$	−7434.08	+	12876.2i	−0.794608	+	1.37630i
$445$	3364.07	−	5826.73i	0.358364	−	0.620705i
$446$	−2202.41	−	3814.68i	−0.233827	−	0.405001i
$447$	−2903.01			−0.307176
$448$	9203.09	+	15940.2i	0.970548	+	1.68104i
$449$	6615.34	+	11458.1i	0.695316	+	1.20432i	0.970074	+	0.242810i	$0.0780691\pi$
$449$	6615.34	+	11458.1i	0.695316	+	1.20432i	−0.274757	+	0.961514i	$0.588598\pi$
$450$	1222.53			0.128068
$451$	1414.96	+	2450.78i	0.147734	+	0.255882i
$452$	2335.09	−	4044.49i	0.242994	−	0.420878i
$453$	1873.25	−	3244.57i	0.194289	−	0.336519i
$454$	−7714.66			−0.797504
$455$	−10164.0	+	13808.0i	−1.04725	+	1.42271i
$456$	582.617			0.0598323
$457$	−5595.00	+	9690.82i	−0.572698	+	0.991942i	0.423590	+	0.905854i	$0.360770\pi$
$457$	−5595.00	+	9690.82i	−0.572698	+	0.991942i	−0.996288	+	0.0860875i	$0.972564\pi$
$458$	1750.02	−	3031.13i	0.178544	−	0.309247i
$459$	−7609.59	−	13180.2i	−0.773824	−	1.34030i
$460$	11857.1			1.20183
$461$	6809.59	+	11794.5i	0.687970	+	1.19160i	0.972494	+	0.232930i	$0.0748312\pi$
$461$	6809.59	+	11794.5i	0.687970	+	1.19160i	−0.284524	+	0.958669i	$0.591836\pi$
$462$	−2691.56	−	4661.92i	−0.271045	−	0.469464i
$463$	4389.01			0.440550			0.220275	−	0.975438i	$-0.429305\pi$
$463$	4389.01			0.440550			0.220275	+	0.975438i	$0.429305\pi$
$464$	3802.63	+	6586.35i	0.380459	+	0.658974i
$465$	195.802	−	339.138i	0.0195271	−	0.0338219i
$466$	6761.78	−	11711.7i	0.672175	−	1.16424i
$467$	−17910.3			−1.77471			−0.887356	−	0.461086i	$-0.847460\pi$
$467$	−17910.3			−1.77471			−0.887356	+	0.461086i	$0.847460\pi$
$468$	4513.88	+	502.848i	0.445842	+	0.0496670i
$469$	−19844.9			−1.95384
$470$	−4248.79	+	7359.13i	−0.416984	+	0.722237i
$471$	1533.71	−	2656.47i	0.150042	−	0.259880i
$472$	−974.028	−	1687.07i	−0.0949857	−	0.164520i
$473$	−209.466			−0.0203620
$474$	−9884.24	−	17120.0i	−0.957802	−	1.65896i
$475$	−530.209	−	918.348i	−0.0512161	−	0.0887088i
$476$	26423.0			2.54432
$477$	523.687	+	907.052i	0.0502683	+	0.0870672i
$478$	−8111.43	+	14049.4i	−0.776168	+	1.34436i
$479$	−472.560	+	818.499i	−0.0450769	+	0.0780755i	−0.887684	−	0.460454i	$-0.847687\pi$
$479$	−472.560	+	818.499i	−0.0450769	+	0.0780755i	0.842607	+	0.538530i	$0.181020\pi$
$480$	12874.7			1.22427
$481$	19359.6	+	2156.67i	1.83518	+	0.204440i
$482$	−21693.0			−2.04998
$483$	−6416.02	+	11112.9i	−0.604429	+	1.04690i
$484$	−539.029	+	933.625i	−0.0506225	+	0.0876808i
$485$	4093.78	+	7090.63i	0.383276	+	0.663854i
$486$	11650.5			1.08740
$487$	−3704.25	−	6415.94i	−0.344672	−	0.596990i	0.640622	−	0.767857i	$-0.278677\pi$
$487$	−3704.25	−	6415.94i	−0.344672	−	0.596990i	−0.985294	+	0.170866i	$0.945343\pi$
$488$	−1313.36	−	2274.81i	−0.121830	−	0.211016i
$489$	10324.9			0.954823
$490$	−13585.6	−	23530.9i	−1.25252	−	2.16943i
$491$	−2018.66	+	3496.42i	−0.185541	+	0.321367i	−0.943759	−	0.330635i	$-0.892737\pi$
$491$	−2018.66	+	3496.42i	−0.185541	+	0.321367i	0.758218	+	0.652002i	$0.226070\pi$
$492$	−4602.02	+	7970.93i	−0.421697	+	0.730401i
$493$	13615.1			1.24380
$494$	−2998.57	−	6849.30i	−0.273101	−	0.623815i
$495$	1476.56			0.134073
$496$	−220.829	+	382.487i	−0.0199910	+	0.0346254i
$497$	−7675.38	+	13294.2i	−0.692732	+	1.19985i
$498$	−638.750	−	1106.35i	−0.0574760	−	0.0995514i
$499$	14317.5			1.28445			0.642225	−	0.766516i	$-0.278011\pi$
$499$	14317.5			1.28445			0.642225	+	0.766516i	$0.278011\pi$
$500$	−5369.85	−	9300.86i	−0.480294	−	0.831894i
$501$	5798.85	+	10043.9i	0.517112	+	0.895665i
$502$	13545.2			1.20428
$503$	3571.83	+	6186.59i	0.316621	+	0.548403i	0.979781	−	0.200075i	$-0.0641185\pi$
$503$	3571.83	+	6186.59i	0.316621	+	0.548403i	−0.663160	+	0.748478i	$0.730785\pi$
$504$	−602.784	+	1044.05i	−0.0532741	+	0.0922735i
$505$	10842.9	−	18780.4i	0.955447	−	1.65488i
$506$	4877.30			0.428503
$507$	2621.53	+	8423.57i	0.229638	+	0.737878i
$508$	−14954.1			−1.30607
$509$	−5998.17	+	10389.1i	−0.522327	+	0.904697i	0.477336	+	0.878721i	$0.341603\pi$
$509$	−5998.17	+	10389.1i	−0.522327	+	0.904697i	−0.999663	+	0.0259757i	$0.991731\pi$
$510$	10196.9	−	17661.6i	0.885346	−	1.53346i
$511$	17106.1	+	29628.7i	1.48088	+	2.56496i
$512$	−16192.9			−1.39772
$513$	−2949.94	−	5109.44i	−0.253885	−	0.439741i
$514$	−177.679	−	307.749i	−0.0152473	−	0.0264090i
$515$	−15115.1			−1.29330
$516$	−340.634	−	589.995i	−0.0290612	−	0.0503354i
$517$	−920.854	+	1594.97i	−0.0783349	+	0.135680i
$518$	−25323.9	+	43862.3i	−2.14801	+	3.72046i
$519$	−8996.53			−0.760894
$520$	867.778	+	1982.17i	0.0731819	+	0.167161i
$521$	−5399.30			−0.454027			−0.227013	−	0.973892i	$-0.572896\pi$
$521$	−5399.30			−0.454027			−0.227013	+	0.973892i	$0.572896\pi$
$522$	−3042.46	+	5269.70i	−0.255105	+	0.441855i
$523$	4967.10	−	8603.26i	0.415289	−	0.719301i	−0.580170	−	0.814495i	$-0.697014\pi$
$523$	4967.10	−	8603.26i	0.415289	−	0.719301i	0.995459	+	0.0951944i	$0.0303473\pi$
$524$	10370.4	+	17962.1i	0.864567	+	1.49747i
$525$	−3253.20			−0.270441
$526$	2098.78	+	3635.19i	0.173976	+	0.301335i
$527$	395.334	+	684.739i	0.0326775	+	0.0565991i
$528$	2468.97			0.203500
$529$	270.361	+	468.279i	0.0222208	+	0.0384876i
$530$	−2443.90	+	4232.95i	−0.200294	+	0.346920i
$531$	−2832.22	+	4905.55i	−0.231465	+	0.400909i
$532$	10243.1			0.834767
$533$	11984.4	+	1335.07i	0.973929	+	0.108496i
$534$	9001.19			0.729438
$535$	7200.07	−	12470.9i	0.581844	−	1.00778i
$536$	−1252.23	+	2168.93i	−0.100911	+	0.174782i
$537$	3274.94	+	5672.36i	0.263173	+	0.455830i
$538$	−25199.7			−2.01940
$539$	−2944.45	−	5099.93i	−0.235299	−	0.407550i
$540$	8362.36	+	14484.0i	0.666405	+	1.15425i
$541$	21273.8			1.69063			0.845316	−	0.534267i	$-0.179412\pi$
$541$	21273.8			1.69063			0.845316	+	0.534267i	$0.179412\pi$
$542$	−10428.3	−	18062.3i	−0.826443	−	1.43144i
$543$	4317.23	−	7477.66i	0.341197	−	0.590971i
$544$	−12997.4	+	22512.1i	−1.02437	+	1.77426i
$545$	−8376.31			−0.658352
$546$	−22797.0	−	2539.60i	−1.78686	−	0.199057i
$547$	−18476.4			−1.44423			−0.722114	−	0.691774i	$-0.756829\pi$
$547$	−18476.4			−1.44423			−0.722114	+	0.691774i	$0.756829\pi$
$548$	6537.01	−	11322.4i	0.509576	−	0.882611i
$549$	−3818.91	+	6614.55i	−0.296880	+	0.514212i
$550$	618.250	+	1070.84i	0.0479314	+	0.0830196i
$551$	5278.05			0.408081
$552$	809.714	+	1402.47i	0.0624343	+	0.108139i
$553$	−17740.7	−	30727.8i	−1.36422	−	2.36289i
$554$	5859.44			0.449357
$555$	10298.5	+	17837.4i	0.787649	+	1.36425i
$556$	4451.62	−	7710.44i	0.339552	−	0.588121i
$557$	7670.18	−	13285.1i	0.583476	−	1.01061i	−0.411588	−	0.911370i	$-0.635026\pi$
$557$	7670.18	−	13285.1i	0.583476	−	1.01061i	0.995064	−	0.0992393i	$-0.0316409\pi$
$558$	−353.368			−0.0268087
$559$	−529.115	+	718.814i	−0.0400343	+	0.0543875i
$560$	20446.5			1.54289
$561$	2210.01	−	3827.84i	0.166322	−	0.288078i
$562$	−9108.94	+	15777.1i	−0.683696	+	1.18420i
$563$	−8588.73	−	14876.1i	−0.642934	−	1.11359i	−0.984775	−	0.173836i	$-0.944384\pi$
$563$	−8588.73	−	14876.1i	−0.642934	−	1.11359i	0.341841	−	0.939758i	$-0.388950\pi$
$564$	−5989.98			−0.447205
$565$	−3234.80	−	5602.84i	−0.240866	−	0.417191i
$566$	−2905.41	−	5032.32i	−0.215766	−	0.373718i
$567$	−9397.20			−0.696023
$568$	968.648	+	1677.75i	0.0715556	+	0.123938i
$569$	3580.86	−	6202.23i	0.263827	−	0.456961i	−0.703429	−	0.710766i	$-0.748349\pi$
$569$	3580.86	−	6202.23i	0.263827	−	0.456961i	0.967256	+	0.253805i	$0.0816820\pi$
$570$	3952.94	−	6846.68i	0.290474	−	0.503116i
$571$	7125.27			0.522212			0.261106	−	0.965310i	$-0.415913\pi$
$571$	7125.27			0.522212			0.261106	+	0.965310i	$0.415913\pi$
$572$	1842.28	+	4208.12i	0.134667	+	0.307605i
$573$	3062.89			0.223305
$574$	−15676.6	+	27152.7i	−1.13995	+	1.97445i
$575$	1473.76	−	2552.62i	0.106887	−	0.185133i
$576$	−3377.19	−	5849.46i	−0.244299	−	0.423138i
$577$	24023.6			1.73330			0.866651	−	0.498914i	$-0.166268\pi$
$577$	24023.6			1.73330			0.866651	+	0.498914i	$0.166268\pi$
$578$	10486.7	+	18163.4i	0.754650	+	1.30709i
$579$	−3354.73	−	5810.56i	−0.240791	−	0.417062i
$580$	−14962.0			−1.07115
$581$	−1146.46	−	1985.73i	−0.0818643	−	0.141793i
$582$	−5476.84	+	9486.17i	−0.390073	+	0.675626i
$583$	−529.673	+	917.420i	−0.0376275	+	0.0651727i
$584$	4317.65			0.305934
$585$	3729.81	−	5067.03i	0.263605	−	0.358113i
$586$	−29102.6			−2.05156
$587$	4418.75	−	7653.49i	0.310700	−	0.538149i	−0.667814	−	0.744328i	$-0.732770\pi$
$587$	4418.75	−	7653.49i	0.310700	−	0.538149i	0.978514	+	0.206179i	$0.0661031\pi$
$588$	9576.53	−	16587.0i	0.671649	−	1.16333i
$589$	153.255	+	265.446i	0.0107212	+	0.0185696i
$590$	−26434.3			−1.84455
$591$	−8437.69	−	14614.5i	−0.587276	−	1.01719i
$592$	−11614.8	−	20117.4i	−0.806361	−	1.39666i
$593$	−3054.42			−0.211518			−0.105759	−	0.994392i	$-0.533727\pi$
$593$	−3054.42			−0.211518			−0.105759	+	0.994392i	$0.533727\pi$
$594$	3439.78	+	5957.87i	0.237602	+	0.411539i
$595$	18301.9	−	31699.8i	1.26102	−	2.18414i
$596$	−3220.58	+	5578.22i	−0.221343	+	0.383377i
$597$	−2778.14			−0.190455
$598$	12320.2	−	16737.2i	0.842489	−	1.14454i
$599$	21193.1			1.44562			0.722812	−	0.691045i	$-0.242849\pi$
$599$	21193.1			1.44562			0.722812	+	0.691045i	$0.242849\pi$
$600$	−205.280	+	355.556i	−0.0139675	+	0.0241925i
$601$	−2407.74	+	4170.32i	−0.163417	+	0.283047i	−0.936092	−	0.351755i	$-0.885585\pi$
$601$	−2407.74	+	4170.32i	−0.163417	+	0.283047i	0.772675	+	0.634802i	$0.218918\pi$
$602$	−1160.36	−	2009.80i	−0.0785592	−	0.136068i
$603$	7282.32			0.491806
$604$	−4156.35	−	7199.02i	−0.279999	−	0.484973i
$605$	746.718	+	1293.35i	0.0501792	+	0.0869129i
$606$	29012.1			1.94478
$607$	8025.17	+	13900.0i	0.536626	+	0.929463i	0.999083	+	0.0428211i	$0.0136345\pi$
$607$	8025.17	+	13900.0i	0.536626	+	0.929463i	−0.462457	+	0.886642i	$0.653032\pi$
$608$	−5038.57	+	8727.05i	−0.336087	+	0.582120i
$609$	8096.14	−	14022.9i	0.538706	−	0.933066i
$610$	−35643.6			−2.36584
$611$	3147.28	+	7188.97i	0.208388	+	0.475998i
$612$	−9696.23			−0.640436
$613$	−424.259	+	734.837i	−0.0279537	+	0.0484173i	−0.879664	−	0.475596i	$-0.842232\pi$
$613$	−424.259	+	734.837i	−0.0279537	+	0.0484173i	0.851710	+	0.524013i	$0.175566\pi$
$614$	−15891.2	+	27524.3i	−1.04449	+	1.80911i
$615$	6375.19	+	11042.2i	0.418004	+	0.724004i
$616$	−1219.35			−0.0797549
$617$	−3140.16	−	5438.91i	−0.204891	−	0.354882i	0.745207	−	0.666834i	$-0.232351\pi$
$617$	−3140.16	−	5438.91i	−0.204891	−	0.354882i	−0.950098	+	0.311951i	$0.899017\pi$
$618$	−10110.8	−	17512.4i	−0.658117	−	1.13989i
$619$	−13573.1			−0.881338			−0.440669	−	0.897670i	$-0.645259\pi$
$619$	−13573.1			−0.881338			−0.440669	+	0.897670i	$0.645259\pi$
$620$	−434.442	−	752.476i	−0.0281413	−	0.0487422i
$621$	8199.58	−	14202.1i	0.529851	−	0.917730i
$622$	1483.72	−	2569.88i	0.0956459	−	0.165664i
$623$	16155.8			1.03895
$624$	6236.66	−	8472.64i	0.400106	−	0.543553i
$625$	−18294.7			−1.17086
$626$	−7928.50	+	13732.6i	−0.506209	+	0.876779i
$627$	856.732	−	1483.90i	0.0545687	−	0.0945157i
$628$	−3402.98	−	5894.14i	−0.216232	−	0.374525i
$629$	−41586.3			−2.63617
$630$	8179.54	+	14167.4i	0.517271	+	0.895939i
$631$	13254.4	+	22957.3i	0.836212	+	1.44836i	0.893040	+	0.449977i	$0.148568\pi$
$631$	13254.4	+	22957.3i	0.836212	+	1.44836i	−0.0568281	+	0.998384i	$0.518099\pi$
$632$	−4477.82			−0.281833
$633$	−2172.11	−	3762.21i	−0.136388	−	0.236231i
$634$	2426.93	−	4203.57i	0.152028	−	0.263320i
$635$	−10358.0	+	17940.6i	−0.647314	+	1.12118i
$636$	−3445.42			−0.214811
$637$	−24938.9	−	2778.21i	−1.55120	−	0.172805i
$638$	−6154.48			−0.381909
$639$	2816.58	−	4878.46i	0.174369	−	0.302017i
$640$	2935.39	−	5084.25i	0.181299	−	0.314020i
$641$	3520.90	+	6098.38i	0.216953	+	0.375774i	0.953875	−	0.300204i	$-0.0970547\pi$
$641$	3520.90	+	6098.38i	0.216953	+	0.375774i	−0.736922	+	0.675978i	$0.763721\pi$
$642$	19265.2			1.18432
$643$	−10268.6	−	17785.8i	−0.629789	−	1.09083i	−0.987594	−	0.157030i	$-0.949808\pi$
$643$	−10268.6	−	17785.8i	−0.629789	−	1.09083i	0.357804	−	0.933797i	$-0.383525\pi$
$644$	14235.8	+	24657.1i	0.871070	+	1.50874i
$645$	−943.762			−0.0576133
$646$	7981.19	+	13823.8i	0.486093	+	0.841937i
$647$	−12218.6	+	21163.3i	−0.742449	+	1.28596i	0.208928	+	0.977931i	$0.433002\pi$
$647$	−12218.6	+	21163.3i	−0.742449	+	1.28596i	−0.951377	+	0.308028i	$0.900331\pi$
$648$	−592.972	+	1027.06i	−0.0359478	+	0.0622634i
$649$	−5729.19			−0.346518
$650$	5236.47	+	583.345i	0.315986	+	0.0352010i
$651$	940.329			0.0566120
$652$	11454.4	−	19839.6i	0.688019	−	1.19168i
$653$	−335.433	+	580.987i	−0.0201019	+	0.0348174i	−0.875901	−	0.482490i	$-0.839732\pi$
$653$	−335.433	+	580.987i	−0.0201019	+	0.0348174i	0.855799	+	0.517308i	$0.173066\pi$
$654$	−5603.10	−	9704.86i	−0.335013	−	0.580260i
$655$	28732.3			1.71399
$656$	−7190.07	−	12453.6i	−0.427935	−	0.741205i
$657$	−6277.30	−	10872.6i	−0.372756	−	0.645633i
$658$	−20404.7			−1.20890
$659$	−576.259	−	998.110i	−0.0340635	−	0.0589998i	0.848491	−	0.529210i	$-0.177512\pi$
$659$	−576.259	−	998.110i	−0.0340635	−	0.0589998i	−0.882555	+	0.470210i	$0.844178\pi$
$660$	−2428.63	+	4206.51i	−0.143234	+	0.248088i
$661$	−8034.92	+	13916.9i	−0.472802	+	0.818918i	−0.999515	−	0.0311254i	$-0.990091\pi$
$661$	−8034.92	+	13916.9i	−0.472802	+	0.818918i	0.526713	+	0.850043i	$0.323424\pi$
$662$	26067.5			1.53042
$663$	−7553.31	−	17253.2i	−0.442453	−	1.01065i
$664$	−289.371			−0.0169123
$665$	7094.92	−	12288.8i	0.413728	−	0.716598i
$666$	9292.93	−	16095.8i	0.540681	−	0.936488i
$667$	7335.38	+	12705.3i	0.425828	+	0.737555i
$668$	25732.8			1.49047
$669$	−2150.66	−	3725.05i	−0.124289	−	0.215275i
$670$	16992.2	+	29431.4i	0.979802	+	1.69707i
$671$	−7725.14			−0.444449
$672$	15457.6	+	26773.3i	0.887334	+	1.53691i
$673$	−10985.9	+	19028.1i	−0.629233	+	1.08986i	0.358473	+	0.933540i	$0.383297\pi$
$673$	−10985.9	+	19028.1i	−0.629233	+	1.08986i	−0.987706	+	0.156323i	$0.950036\pi$
$674$	7304.28	−	12651.4i	0.417434	−	0.723016i
$675$	4157.54			0.237072
$676$	19094.4	+	4307.72i	1.08639	+	0.245091i
$677$	27156.2			1.54165			0.770826	−	0.637046i	$-0.219844\pi$
$677$	27156.2			1.54165			0.770826	+	0.637046i	$0.219844\pi$
$678$	4327.66	−	7495.73i	0.245137	−	0.424589i
$679$	−9830.10	+	17026.2i	−0.555589	+	0.962308i
$680$	−2309.74	−	4000.58i	−0.130256	−	0.225611i
$681$	−7533.41			−0.423907
$682$	−178.704	−	309.524i	−0.0100336	−	0.0173787i
$683$	1314.94	+	2277.55i	0.0736675	+	0.127596i	0.900506	−	0.434843i	$-0.143196\pi$
$683$	1314.94	+	2277.55i	0.0736675	+	0.127596i	−0.826839	+	0.562439i	$0.809863\pi$
$684$	−3758.85			−0.210121
$685$	−9055.74	−	15685.0i	−0.505113	−	0.874881i
$686$	11721.2	−	20301.7i	0.652358	−	1.12992i
$687$	1708.90	−	2959.91i	0.0949036	−	0.164378i
$688$	1064.39			0.0589820
$689$	1810.30	+	4135.08i	0.100097	+	0.228641i
$690$	21975.0			1.21243
$691$	1633.12	−	2828.65i	0.0899087	−	0.155726i	−0.817564	−	0.575838i	$-0.804676\pi$
$691$	1633.12	−	2828.65i	0.0899087	−	0.155726i	0.907472	+	0.420112i	$0.138009\pi$
$692$	−9980.70	+	17287.1i	−0.548279	+	0.949647i
$693$	1772.78	+	3070.54i	0.0971749	+	0.168312i
$694$	2816.22			0.154038
$695$	−6166.84	−	10681.3i	−0.336578	−	0.582970i
$696$	−1021.75	−	1769.72i	−0.0556455	−	0.0963808i
$697$	−25743.7			−1.39901
$698$	−16956.5	−	29369.5i	−0.919501	−	1.59262i
$699$	6602.91	−	11436.6i	0.357289	−	0.618843i
$700$	−3609.08	+	6251.11i	−0.194872	+	0.337528i
$701$	−6866.07			−0.369940			−0.184970	−	0.982744i	$-0.559219\pi$
$701$	−6866.07			−0.369940			−0.184970	+	0.982744i	$0.559219\pi$
$702$	29134.3	+	3245.57i	1.56639	+	0.174496i
$703$	−16121.4			−0.864905
$704$	3415.79	−	5916.33i	0.182866	−	0.316733i
$705$	−4148.97	+	7186.23i	−0.221644	+	0.383899i
$706$	16822.5	+	29137.5i	0.896777	+	1.55326i
$707$	52072.4			2.76999
$708$	−9316.82	−	16137.2i	−0.494559	−	0.856601i
$709$	−9958.30	−	17248.3i	−0.527492	−	0.913643i	−0.999487	−	0.0320414i	$-0.989799\pi$
$709$	−9958.30	−	17248.3i	−0.527492	−	0.913643i	0.471995	−	0.881601i	$-0.343534\pi$
$710$	26288.3			1.38955
$711$	6510.17	+	11276.0i	0.343390	+	0.594770i
$712$	1019.45	−	1765.73i	0.0536592	−	0.0929404i
$713$	−425.985	+	737.828i	−0.0223749	+	0.0387544i
$714$	48970.2			2.56676
$715$	6324.57	+	704.559i	0.330805	+	0.0368518i
$716$	14532.8			0.758542
$717$	−7920.85	+	13719.3i	−0.412566	+	0.714585i
$718$	2517.09	−	4359.73i	0.130832	−	0.226607i
$719$	13986.8	+	24225.8i	0.725479	+	1.25657i	0.958777	+	0.284161i	$0.0917149\pi$
$719$	13986.8	+	24225.8i	0.725479	+	1.25657i	−0.233298	+	0.972405i	$0.574952\pi$
$720$	−7503.08			−0.388366
$721$	−18147.4	−	31432.2i	−0.937369	−	1.62357i
$722$	−11008.5	−	19067.3i	−0.567445	−	0.982844i
$723$	−21183.3			−1.08965
$724$	−9579.02	−	16591.3i	−0.491715	−	0.851675i
$725$	−1859.68	+	3221.06i	−0.0952644	+	0.165003i
$726$	−998.993	+	1730.31i	−0.0510690	+	0.0884541i
$727$	−2847.88			−0.145285			−0.0726424	−	0.997358i	$-0.523143\pi$
$727$	−2847.88			−0.145285			−0.0726424	+	0.997358i	$0.523143\pi$
$728$	−3080.10	+	4184.39i	−0.156808	+	0.213027i
$729$	19937.8			1.01295
$730$	29294.4	−	50739.4i	1.48525	−	2.57253i
$731$	952.754	−	1650.22i	0.0482064	−	0.0834959i
$732$	−12562.6	−	21759.1i	−0.634328	−	1.09869i
$733$	−18147.3			−0.914443			−0.457221	−	0.889353i	$-0.651155\pi$
$733$	−18147.3			−0.914443			−0.457221	+	0.889353i	$0.651155\pi$
$734$	15366.2	+	26615.1i	0.772723	+	1.33839i
$735$	−13266.4	−	22978.1i	−0.665767	−	1.15314i
$736$	−28010.2			−1.40281
$737$	3682.78	+	6378.76i	0.184066	+	0.318812i
$738$	5752.73	−	9964.02i	0.286939	−	0.496993i
$739$	−4075.17	+	7058.41i	−0.202852	+	0.351350i	−0.949446	−	0.313930i	$-0.898354\pi$
$739$	−4075.17	+	7058.41i	−0.202852	+	0.351350i	0.746594	+	0.665280i	$0.231688\pi$
$740$	45700.2			2.27023
$741$	−2928.12	−	6688.37i	−0.145165	−	0.331584i
$742$	−11736.7			−0.580684
$743$	913.232	−	1581.76i	0.0450918	−	0.0781013i	−0.842599	−	0.538542i	$-0.818975\pi$
$743$	913.232	−	1581.76i	0.0450918	−	0.0781013i	0.887690	+	0.460441i	$0.152309\pi$
$744$	59.3357	−	102.772i	0.00292386	−	0.00506427i
$745$	4461.48	+	7727.52i	0.219404	+	0.380019i
$746$	51222.3			2.51392
$747$	420.708	+	728.687i	0.0206063	+	0.0356911i
$748$	−4903.54	−	8493.17i	−0.239694	−	0.415162i
$749$	34578.0			1.68685
$750$	−9952.05	−	17237.5i	−0.484530	−	0.839231i
$751$	14616.9	−	25317.2i	0.710223	−	1.23014i	−0.254550	−	0.967060i	$-0.581927\pi$
$751$	14616.9	−	25317.2i	0.710223	−	1.23014i	0.964773	−	0.263083i	$-0.0847394\pi$
$752$	4679.29	−	8104.77i	0.226910	−	0.393019i
$753$	13226.9			0.640127
$754$	−15546.3	+	21120.0i	−0.750881	+	1.02009i
$755$	−11515.6			−0.555094
$756$	−20079.9	+	34779.5i	−0.966006	+	1.67317i
$757$	7191.87	−	12456.7i	0.345301	−	0.598079i	−0.640107	−	0.768286i	$-0.721110\pi$
$757$	7191.87	−	12456.7i	0.345301	−	0.598079i	0.985408	+	0.170206i	$0.0544434\pi$
$758$	−20776.0	−	35985.1i	−0.995539	−	1.72432i
$759$	4762.71			0.227767
$760$	−895.393	−	1550.87i	−0.0427359	−	0.0740208i
$761$	6937.07	+	12015.4i	0.330445	+	0.572347i	0.982599	−	0.185739i	$-0.0594679\pi$
$761$	6937.07	+	12015.4i	0.330445	+	0.572347i	−0.652154	+	0.758086i	$0.726135\pi$
$762$	−27714.8			−1.31759
$763$	−10056.7	−	17418.7i	−0.477166	−	0.826476i
$764$	3397.95	−	5885.42i	0.160908	−	0.278700i
$765$	−6716.11	+	11632.6i	−0.317414	+	0.549777i
$766$	53244.2			2.51148
$767$	−14472.0	+	19660.6i	−0.681298	+	0.925558i
$768$	−12096.6			−0.568356
$769$	−16880.4	+	29237.7i	−0.791576	+	1.37105i	0.133416	+	0.991060i	$0.457405\pi$
$769$	−16880.4	+	29237.7i	−0.791576	+	1.37105i	−0.924991	+	0.379989i	$0.875928\pi$
$770$	−8273.04	+	14329.3i	−0.387194	+	0.670640i
$771$	−173.505	−	300.519i	−0.00810456	−	0.0140375i
$772$	−14886.9			−0.694029
$773$	−2551.09	−	4418.61i	−0.118701	−	0.205597i	0.800552	−	0.599263i	$-0.204540\pi$
$773$	−2551.09	−	4418.61i	−0.118701	−	0.205597i	−0.919253	+	0.393667i	$0.871206\pi$
$774$	425.807	+	737.520i	0.0197743	+	0.0342501i
$775$	−215.993			−0.0100112
$776$	1240.58	+	2148.74i	0.0573894	+	0.0994013i
$777$	−24728.9	+	42831.8i	−1.14176	+	1.97758i
$778$	−6531.36	+	11312.7i	−0.300978	+	0.521309i
$779$	−9979.82			−0.459004
$780$	8300.52	+	18959.9i	0.381034	+	0.870352i
$781$	5697.55			0.261043
$782$	−22184.3	+	38424.4i	−1.01446	+	1.75710i
$783$	−10346.7	+	17921.1i	−0.472238	+	0.817940i
$784$	14962.1	+	25915.1i	0.681583	+	1.18054i
$785$	−9428.32			−0.428677
$786$	19219.7	+	33289.4i	0.872192	+	1.51068i
$787$	18513.2	+	32065.8i	0.838532	+	1.45238i	0.891122	+	0.453764i	$0.149919\pi$
$787$	18513.2	+	32065.8i	0.838532	+	1.45238i	−0.0525901	+	0.998616i	$0.516748\pi$
$788$	−37442.9			−1.69270
$789$	2049.47	+	3549.78i	0.0924753	+	0.160172i
$790$	−30381.1	+	52621.6i	−1.36824	+	2.36987i
$791$	7767.49	−	13453.7i	0.349153	−	0.604751i
$792$	447.456			0.0200753
$793$	−19513.8	+	26510.0i	−0.873842	+	1.18713i
$794$	−3242.28			−0.144917
$795$	−2386.48	+	4133.50i	−0.106465	+	0.184403i
$796$	−3082.05	+	5338.27i	−0.137237	+	0.237701i
$797$	5757.41	+	9972.13i	0.255882	+	0.443201i	0.965135	−	0.261754i	$-0.0843008\pi$
$797$	5757.41	+	9972.13i	0.255882	+	0.443201i	−0.709253	+	0.704954i	$0.750967\pi$
$798$	18983.8			0.842129
$799$	−8376.99	−	14509.4i	−0.370910	−	0.642434i
$800$	−3550.59	−	6149.81i	−0.156916	−	0.271786i
$801$	−5928.57			−0.261518
$802$	−16015.0	−	27738.7i	−0.705122	−	1.22131i
$803$	6349.06	−	10996.9i	0.279021	−	0.483278i
$804$	−11977.9	+	20746.3i	−0.525408	+	0.910033i
$805$	39441.8			1.72688
$806$	−1513.59	−	168.614i	−0.0661462	−	0.00736871i
$807$	−24607.7			−1.07340
$808$	3285.82	−	5691.20i	0.143063	−	0.247792i
$809$	2728.47	−	4725.85i	0.118576	−	0.205380i	−0.800628	−	0.599162i	$-0.795500\pi$
$809$	2728.47	−	4725.85i	0.118576	−	0.205380i	0.919204	+	0.393783i	$0.128834\pi$
$810$	8046.39	+	13936.8i	0.349039	+	0.604553i
$811$	−4694.61			−0.203268			−0.101634	−	0.994822i	$-0.532407\pi$
$811$	−4694.61			−0.203268			−0.101634	+	0.994822i	$0.532407\pi$
$812$	−17963.6	−	31113.9i	−0.776354	−	1.34468i
$813$	−10183.3	−	17637.9i	−0.439289	−	0.760872i
$814$	18798.3			0.809436
$815$	−15867.8	−	27483.8i	−0.681993	−	1.18125i
$816$	−11230.1	+	19451.1i	−0.481779	+	0.834465i
$817$	369.345	−	639.724i	0.0158161	−	0.0273943i
$818$	14719.4			0.629159
$819$	15015.1	+	1672.69i	0.640622	+	0.0713656i
$820$	28290.4			1.20481
$821$	939.467	−	1627.20i	0.0399362	−	0.0691715i	−0.845366	−	0.534187i	$-0.820618\pi$
$821$	939.467	−	1627.20i	0.0399362	−	0.0691715i	0.885303	+	0.465015i	$0.153951\pi$
$822$	12115.2	−	20984.1i	0.514070	−	0.890395i
$823$	−8054.24	−	13950.4i	−0.341134	−	0.590861i	0.643510	−	0.765438i	$-0.277478\pi$
$823$	−8054.24	−	13950.4i	−0.341134	−	0.590861i	−0.984644	+	0.174577i	$0.944144\pi$
$824$	−4580.47			−0.193651
$825$	603.724	+	1045.68i	0.0254776	+	0.0441284i
$826$	−31737.4	−	54970.8i	−1.33691	−	2.31559i
$827$	−24298.9			−1.02171			−0.510857	−	0.859666i	$-0.670672\pi$
$827$	−24298.9			−1.02171			−0.510857	+	0.859666i	$0.670672\pi$
$828$	−5224.00	−	9048.24i	−0.219259	−	0.379768i
$829$	4773.01	−	8267.09i	0.199968	−	0.346355i	−0.748550	−	0.663078i	$-0.769250\pi$
$829$	4773.01	−	8267.09i	0.199968	−	0.346355i	0.948518	+	0.316724i	$0.102583\pi$
$830$	−1963.32	+	3400.57i	−0.0821059	+	0.142212i
$831$	5721.77			0.238852
$832$	−11674.4	−	26666.6i	−0.486464	−	1.11118i
$833$	53571.2			2.22825
$834$	8250.28	−	14289.9i	0.342547	−	0.593308i
$835$	17823.9	−	30871.9i	0.738707	−	1.27948i
$836$	−1900.91	−	3292.47i	−0.0786414	−	0.136211i
$837$	−1201.73			−0.0496269
$838$	−10487.2	−	18164.4i	−0.432308	−	0.748780i
$839$	13461.2	+	23315.5i	0.553912	+	0.959404i	0.997987	+	0.0634145i	$0.0201990\pi$
$839$	13461.2	+	23315.5i	0.553912	+	0.959404i	−0.444075	+	0.895990i	$0.646468\pi$
$840$	−5493.86			−0.225662
$841$	2938.26	+	5089.21i	0.120475	+	0.208668i
$842$	−19687.7	+	34100.1i	−0.805799	+	1.39568i
$843$	−8894.92	+	15406.5i	−0.363413	+	0.629450i
$844$	−9638.92			−0.393110
$845$	18393.8	−	19924.0i	0.748835	−	0.811132i
$846$	7487.74			0.304295
$847$	−1793.04	+	3105.64i	−0.0727386	+	0.125987i
$848$	2691.52	−	4661.84i	0.108994	−	0.188783i
$849$	−2837.15	−	4914.09i	−0.114689	−	0.198647i
$850$	−11248.4			−0.453903
$851$	−22405.3	−	38807.1i	−0.902518	−	1.56321i
$852$	9265.37	+	16048.1i	0.372566	+	0.645303i
$853$	35519.2			1.42574			0.712868	−	0.701298i	$-0.247396\pi$
$853$	35519.2			1.42574			0.712868	+	0.701298i	$0.247396\pi$
$854$	−42794.2	−	74121.7i	−1.71474	−	2.97001i
$855$	−2603.57	+	4509.51i	−0.104141	+	0.180377i
$856$	2181.91	−	3779.18i	0.0871216	−	0.150899i
$857$	−35440.1			−1.41262			−0.706308	−	0.707905i	$-0.749641\pi$
$857$	−35440.1			−1.41262			−0.706308	+	0.707905i	$0.749641\pi$
$858$	3414.34	+	7798.99i	0.135855	+	0.310318i
$859$	5211.30			0.206993			0.103497	−	0.994630i	$-0.466997\pi$
$859$	5211.30			0.206993			0.103497	+	0.994630i	$0.466997\pi$
$860$	−1047.00	+	1813.46i	−0.0415146	+	0.0719054i
$861$	−15308.3	+	26514.7i	−0.605929	+	1.04950i
$862$	18007.0	+	31189.1i	0.711510	+	1.23237i
$863$	−23920.1			−0.943512			−0.471756	−	0.881729i	$-0.656380\pi$
$863$	−23920.1			−0.943512			−0.471756	+	0.881729i	$0.656380\pi$
$864$	−19754.5	−	34215.9i	−0.777850	−	1.34728i
$865$	13826.3	+	23947.8i	0.543477	+	0.941330i
$866$	−37777.8			−1.48238
$867$	10240.3	+	17736.7i	0.401128	+	0.694775i
$868$	1043.20	−	1806.87i	0.0407930	−	0.0706556i
$869$	−6584.59	+	11404.8i	−0.257039	+	0.445205i
$870$	−27729.4			−1.08059
$871$	31192.5	+	3474.86i	1.21345	+	0.135179i
$872$	−2538.36			−0.0985775
$873$	3607.28	−	6247.99i	0.139849	−	0.242225i
$874$	−8599.99	+	14895.6i	−0.332836	+	0.576490i
$875$	−17862.4	−	30938.6i	−0.690126	−	1.19533i
$876$	41299.4			1.59290
$877$	15854.8	+	27461.2i	0.610464	+	1.05736i	0.991162	+	0.132656i	$0.0423505\pi$
$877$	15854.8	+	27461.2i	0.610464	+	1.05736i	−0.380698	+	0.924699i	$0.624316\pi$
$878$	−5981.02	−	10359.4i	−0.229897	−	0.398193i
$879$	−28418.8			−1.09049
$880$	−3794.42	−	6572.14i	−0.145352	−	0.251758i
$881$	9152.03	−	15851.8i	0.349988	−	0.606197i	−0.636259	−	0.771476i	$-0.719519\pi$
$881$	9152.03	−	15851.8i	0.349988	−	0.606197i	0.986247	+	0.165278i	$0.0528523\pi$
$882$	−11971.1	+	20734.5i	−0.457015	+	0.791574i
$883$	9723.16			0.370567			0.185283	−	0.982685i	$-0.440680\pi$
$883$	9723.16			0.370567			0.185283	+	0.982685i	$0.440680\pi$
$884$	−41532.1	−	4626.69i	−1.58017	−	0.176032i
$885$	−25813.2			−0.980455
$886$	12486.7	−	21627.7i	0.473477	−	0.820086i
$887$	13026.3	−	22562.3i	0.493103	−	0.854079i	−0.506866	−	0.862025i	$-0.669196\pi$
$887$	13026.3	−	22562.3i	0.493103	−	0.854079i	0.999968	+	0.00794631i	$0.00252942\pi$
$888$	3120.84	+	5405.45i	0.117938	+	0.204274i
$889$	−49743.8			−1.87666
$890$	−13833.5	−	23960.3i	−0.521010	−	0.902415i
$891$	1743.92	+	3020.56i	0.0655707	+	0.113572i
$892$	−9543.73			−0.358237
$893$	−3247.43	−	5624.71i	−0.121692	−	0.210777i
$894$	−5968.77	+	10338.2i	−0.223295	+	0.386758i
$895$	10066.2	−	17435.1i	0.375949	−	0.651163i
$896$	14097.1			0.525615
$897$	12030.7	−	16344.0i	0.447818	−	0.608371i
$898$	54406.2			2.02178
$899$	537.535	−	931.038i	0.0199419	−	0.0345404i
$900$	1324.40	−	2293.92i	0.0490517	−	0.0849601i
$901$	−4818.43	−	8345.76i	−0.178163	−	0.308588i
$902$	11637.0			0.429566
$903$	−1133.09	−	1962.58i	−0.0417575	−	0.0723261i
$904$	−980.273	−	1697.88i	−0.0360657	−	0.0624676i
$905$	−26539.7			−0.974816
$906$	−7703.05	−	13342.1i	−0.282469	−	0.489250i
$907$	−10931.7	+	18934.3i	−0.400201	+	0.693168i	−0.993750	−	0.111630i	$-0.964393\pi$
$907$	−10931.7	+	18934.3i	−0.400201	+	0.693168i	0.593549	+	0.804798i	$0.297726\pi$
$908$	−8357.52	+	14475.6i	−0.305456	+	0.529065i
$909$	−19108.6			−0.697241
$910$	28275.4	+	64586.4i	1.03002	+	2.35277i
$911$	16925.2			0.615539			0.307769	−	0.951461i	$-0.400417\pi$
$911$	16925.2			0.615539			0.307769	+	0.951461i	$0.400417\pi$
$912$	−4353.46	+	7540.41i	−0.158067	+	0.273780i
$913$	−425.517	+	737.017i	−0.0154245	+	0.0267160i
$914$	23007.3	+	39849.8i	0.832620	+	1.44214i
$915$	−34806.1			−1.25755
$916$	−3791.70	−	6567.41i	−0.136770	−	0.236892i
$917$	34496.4	+	59749.5i	1.24228	+	2.15169i
$918$	−62583.2			−2.25006
$919$	−22017.2	−	38134.9i	−0.790294	−	1.36883i	−0.925785	−	0.378051i	$-0.876594\pi$
$919$	−22017.2	−	38134.9i	−0.790294	−	1.36883i	0.135490	−	0.990779i	$-0.456739\pi$
$920$	2488.81	−	4310.75i	0.0891889	−	0.154480i
$921$	−15517.8	+	26877.6i	−0.555189	+	0.961616i
$922$	56003.7			2.00042
$923$	14392.1	−	19552.0i	0.513242	−	0.697251i
$924$	−11663.4			−0.415257
$925$	5680.22	−	9838.43i	0.201908	−	0.349714i
$926$	9024.08	−	15630.2i	0.320248	−	0.554686i
$927$	6659.40	+	11534.4i	0.235948	+	0.408673i
$928$	35345.0			1.25028
$929$	10121.8	+	17531.4i	0.357464	+	0.619146i	0.987536	−	0.157391i	$-0.0503082\pi$
$929$	10121.8	+	17531.4i	0.357464	+	0.619146i	−0.630072	+	0.776536i	$0.716975\pi$
$930$	−805.161	−	1394.58i	−0.0283895	−	0.0491721i
$931$	20767.4			0.731068
$932$	−14650.5	−	25375.3i	−0.514905	−	0.891842i
$933$	1448.86	−	2509.50i	0.0508398	−	0.0880571i
$934$	−36824.7	+	63782.3i	−1.29009	+	2.23450i
$935$	−13585.8			−0.475189
$936$	1130.28	−	1535.51i	0.0394705	−	0.0536216i
$937$	42402.7			1.47837			0.739187	−	0.673500i	$-0.235210\pi$
$937$	42402.7			1.47837			0.739187	+	0.673500i	$0.235210\pi$
$938$	−40802.2	+	70671.6i	−1.42030	+	2.46003i
$939$	−7742.22	+	13409.9i	−0.269071	+	0.466045i
$940$	9205.68	+	15944.7i	0.319422	+	0.553254i
$941$	−32336.2			−1.12022			−0.560111	−	0.828418i	$-0.689242\pi$
$941$	−32336.2			−1.12022			−0.560111	+	0.828418i	$0.689242\pi$
$942$	−6306.81	−	10923.7i	−0.218139	−	0.377828i
$943$	−13869.8	−	24023.3i	−0.478965	−	0.829592i
$944$	29112.7			1.00375
$945$	27816.8	+	48180.1i	0.957546	+	1.65852i
$946$	−430.675	+	745.951i	−0.0148017	+	0.0256374i
$947$	−2263.28	+	3920.12i	−0.0776628	+	0.134516i	−0.902241	−	0.431232i	$-0.858079\pi$
$947$	−2263.28	+	3920.12i	−0.0776628	+	0.134516i	0.824578	+	0.565748i	$0.191412\pi$
$948$	−42831.5			−1.46741
$949$	−21699.7	−	49566.2i	−0.742257	−	1.69545i
$950$	−4360.57			−0.148922
$951$	2369.91	−	4104.81i	0.0808093	−	0.139966i
$952$	5546.20	−	9606.30i	0.188817	−	0.327040i
$953$	−18260.7	−	31628.4i	−0.620694	−	1.07507i	−0.989357	−	0.145511i	$-0.953517\pi$
$953$	−18260.7	−	31628.4i	−0.620694	−	1.07507i	0.368662	−	0.929563i	$-0.379816\pi$
$954$	4306.93			0.146166
$955$	−4707.19	−	8153.09i	−0.159498	−	0.276259i
$956$	17574.7	+	30440.3i	0.594567	+	1.02982i
$957$	−6009.88			−0.203001
$958$	1943.23	+	3365.77i	0.0655353	+	0.113510i
$959$	21744.9	−	37663.3i	0.732200	−	1.26821i
$960$	15390.1	−	26656.4i	0.517409	−	0.896179i
$961$	−29728.6			−0.997904
$962$	47484.9	−	64509.3i	1.59145	−	2.16202i
$963$	−12688.8			−0.424603
$964$	−23500.7	+	40704.4i	−0.785172	+	1.35996i
$965$	−10311.4	+	17859.9i	−0.343975	+	0.595783i
$966$	26383.5	+	45697.5i	0.878752	+	1.52204i
$967$	−53292.3			−1.77225			−0.886125	−	0.463446i	$-0.846613\pi$
$967$	−53292.3			−1.77225			−0.886125	+	0.463446i	$0.846613\pi$
$968$	226.285	+	391.938i	0.00751352	+	0.0130138i
$969$	7793.67	+	13499.0i	0.258379	+	0.447525i
$970$	33668.3			1.11446
$971$	20859.1	+	36129.1i	0.689394	+	1.19407i	0.972034	+	0.234840i	$0.0754565\pi$
$971$	20859.1	+	36129.1i	0.689394	+	1.19407i	−0.282640	+	0.959226i	$0.591210\pi$
$972$	12621.3	−	21860.8i	0.416492	−	0.721385i
$973$	14808.0	−	25648.2i	0.487896	−	0.845061i
$974$	−30464.7			−1.00221
$975$	5113.44	+	569.639i	0.167960	+	0.0187108i
$976$	39255.0			1.28742
$977$	−21481.4	+	37206.9i	−0.703429	+	1.21838i	0.263826	+	0.964570i	$0.415016\pi$
$977$	−21481.4	+	37206.9i	−0.703429	+	1.21838i	−0.967255	+	0.253805i	$0.918318\pi$
$978$	21228.6	−	36769.1i	0.694087	−	1.20219i
$979$	−2998.17	−	5192.98i	−0.0978773	−	0.169528i
$980$	−58870.7			−1.91893
$981$	3690.44	+	6392.03i	0.120109	+	0.208034i
$982$	8300.97	+	14377.7i	0.269750	+	0.467221i
$983$	−30376.8			−0.985626			−0.492813	−	0.870135i	$-0.664031\pi$
$983$	−30376.8			−0.985626			−0.492813	+	0.870135i	$0.664031\pi$
$984$	1931.94	+	3346.21i	0.0625893	+	0.108408i
$985$	−25934.9	+	44920.5i	−0.838938	+	1.45308i
$986$	27993.6	−	48486.3i	0.904156	−	1.56604i
$987$	−19925.2			−0.642581
$988$	−16100.3	−	1793.58i	−0.518441	−	0.0577546i
$989$	2053.25			0.0660156
$990$	3035.89	−	5258.32i	0.0974617	−	0.168809i
$991$	15522.3	−	26885.4i	0.497560	−	0.861800i	−0.502436	−	0.864615i	$-0.667563\pi$
$991$	15522.3	−	26885.4i	0.497560	−	0.861800i	0.999996	+	0.00281493i	$0.000896022\pi$
$992$	1026.29	+	1777.59i	0.0328475	+	0.0568936i
$993$	25455.0			0.813485
$994$	31562.1	+	54667.2i	1.00713	+	1.74441i
$995$	4269.57	+	7395.12i	0.136035	+	0.235619i
$996$	−2767.91			−0.0880567
$997$	11197.5	+	19394.7i	0.355697	+	0.616085i	0.987237	−	0.159258i	$-0.0509102\pi$
$997$	11197.5	+	19394.7i	0.355697	+	0.616085i	−0.631540	+	0.775343i	$0.717577\pi$
$998$	29437.7	−	50987.7i	0.933703	−	1.61722i
$999$	31603.2	−	54738.4i	1.00088	−	1.73358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.b.100.15	✓	34
13.3	even	3	inner	143.4.e.b.133.15	yes	34
13.4	even	6		1859.4.a.h.1.15		17
13.9	even	3		1859.4.a.g.1.3		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.15	✓	34	1.1	even	1	trivial
143.4.e.b.133.15	yes	34	13.3	even	3	inner
1859.4.a.g.1.3		17	13.9	even	3
1859.4.a.h.1.15		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)

\(f(q)\)	\(=\)	\(q+(2.05606 - 3.56120i) q^{2} +(2.00775 - 3.47753i) q^{3} +(-4.45478 - 7.71591i) q^{4} -12.3424 q^{5} +(-8.25614 - 14.3001i) q^{6} +(-14.8185 - 25.6664i) q^{7} -3.74025 q^{8} +(5.43784 + 9.41862i) q^{9} +O(q^{10})\)	\(q+(2.05606 - 3.56120i) q^{2} +(2.00775 - 3.47753i) q^{3} +(-4.45478 - 7.71591i) q^{4} -12.3424 q^{5} +(-8.25614 - 14.3001i) q^{6} +(-14.8185 - 25.6664i) q^{7} -3.74025 q^{8} +(5.43784 + 9.41862i) q^{9} +(-25.3768 + 43.9540i) q^{10} +(-5.50000 + 9.52628i) q^{11} -35.7765 q^{12} +(18.7978 + 42.9377i) q^{13} -121.871 q^{14} +(-24.7806 + 42.9213i) q^{15} +(27.9481 - 48.4075i) q^{16} +(-50.0334 - 86.6604i) q^{17} +44.7221 q^{18} +(-19.3960 - 33.5948i) q^{19} +(54.9829 + 95.2332i) q^{20} -119.008 q^{21} +(22.6167 + 39.1732i) q^{22} +(53.9126 - 93.3794i) q^{23} +(-7.50951 + 13.0069i) q^{24} +27.3360 q^{25} +(191.559 + 21.3398i) q^{26} +152.090 q^{27} +(-132.027 + 228.677i) q^{28} +(-68.0303 + 117.832i) q^{29} +(101.901 + 176.498i) q^{30} -7.90141 q^{31} +(-129.887 - 224.971i) q^{32} +(22.0853 + 38.2529i) q^{33} -411.487 q^{34} +(182.897 + 316.787i) q^{35} +(48.4488 - 83.9158i) q^{36} +(207.793 - 359.907i) q^{37} -159.517 q^{38} +(187.059 + 20.8384i) q^{39} +46.1639 q^{40} +(128.633 - 222.798i) q^{41} +(-244.687 + 423.811i) q^{42} +(9.52117 + 16.4912i) q^{43} +98.0052 q^{44} +(-67.1163 - 116.249i) q^{45} +(-221.695 - 383.988i) q^{46} +167.428 q^{47} +(-112.226 - 194.381i) q^{48} +(-267.677 + 463.630i) q^{49} +(56.2046 - 97.3491i) q^{50} -401.819 q^{51} +(247.563 - 336.320i) q^{52} +96.3042 q^{53} +(312.707 - 541.624i) q^{54} +(67.8835 - 117.578i) q^{55} +(55.4250 + 95.9989i) q^{56} -155.769 q^{57} +(279.749 + 484.540i) q^{58} +(260.418 + 451.057i) q^{59} +441.569 q^{60} +(351.143 + 608.197i) q^{61} +(-16.2458 + 28.1385i) q^{62} +(161.161 - 279.140i) q^{63} -621.054 q^{64} +(-232.011 - 529.956i) q^{65} +181.635 q^{66} +(334.798 - 579.887i) q^{67} +(-445.776 + 772.107i) q^{68} +(-216.487 - 374.966i) q^{69} +1504.19 q^{70} +(-258.979 - 448.566i) q^{71} +(-20.3389 - 35.2280i) q^{72} -1154.37 q^{73} +(-854.469 - 1479.98i) q^{74} +(54.8840 - 95.0619i) q^{75} +(-172.810 + 299.315i) q^{76} +326.007 q^{77} +(458.814 - 623.309i) q^{78} +1197.20 q^{79} +(-344.948 + 597.467i) q^{80} +(158.538 - 274.596i) q^{81} +(-528.954 - 916.174i) q^{82} +77.3667 q^{83} +(530.154 + 918.254i) q^{84} +(617.535 + 1069.60i) q^{85} +78.3045 q^{86} +(273.176 + 473.155i) q^{87} +(20.5714 - 35.6307i) q^{88} +(-272.561 + 472.089i) q^{89} -551.981 q^{90} +(823.501 - 1118.74i) q^{91} -960.676 q^{92} +(-15.8641 + 27.4774i) q^{93} +(344.242 - 596.245i) q^{94} +(239.394 + 414.642i) q^{95} -1043.12 q^{96} +(-331.683 - 574.492i) q^{97} +(1100.72 + 1906.50i) q^{98} -119.632 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

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Database

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