LMFDB - Embedded newform 14.5.d.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,5,Mod(3,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("14.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	14.d (of order $6$, 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:	$1.44717948317$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	14.5
Dual form			14.5.d.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41421 - 2.44949i) q^{2} +(3.98528 - 2.30090i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(5.01472 + 2.89525i) q^{5} -13.0159i q^{6} +(-7.00000 + 48.4974i) q^{7} -22.6274 q^{8} +(-29.9117 + 51.8086i) q^{9} +O(q^{10})$	\(q+(1.41421 - 2.44949i) q^{2} +(3.98528 - 2.30090i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(5.01472 + 2.89525i) q^{5} -13.0159i q^{6} +(-7.00000 + 48.4974i) q^{7} -22.6274 q^{8} +(-29.9117 + 51.8086i) q^{9} +(14.1838 - 8.18900i) q^{10} +(-5.01472 - 8.68575i) q^{11} +(-31.8823 - 18.4072i) q^{12} -190.220i q^{13} +(108.894 + 85.7321i) q^{14} +26.6468 q^{15} +(-32.0000 + 55.4256i) q^{16} +(365.265 - 210.886i) q^{17} +(84.6030 + 146.537i) q^{18} +(-374.338 - 216.124i) q^{19} -46.3240i q^{20} +(83.6909 + 209.382i) q^{21} -28.3675 q^{22} +(-460.911 + 798.322i) q^{23} +(-90.1766 + 52.0635i) q^{24} +(-295.735 - 512.228i) q^{25} +(-465.941 - 269.011i) q^{26} +648.042i q^{27} +(364.000 - 145.492i) q^{28} +877.882 q^{29} +(37.6842 - 65.2709i) q^{30} +(627.175 - 362.100i) q^{31} +(90.5097 + 156.767i) q^{32} +(-39.9701 - 23.0768i) q^{33} -1192.95i q^{34} +(-175.515 + 222.934i) q^{35} +478.587 q^{36} +(270.338 - 468.239i) q^{37} +(-1058.79 + 611.291i) q^{38} +(-437.677 - 758.079i) q^{39} +(-113.470 - 65.5120i) q^{40} +894.280i q^{41} +(631.236 + 91.1111i) q^{42} -1246.82 q^{43} +(-40.1177 + 69.4860i) q^{44} +(-299.997 + 173.204i) q^{45} +(1303.65 + 2257.99i) q^{46} +(1516.17 + 875.364i) q^{47} +294.516i q^{48} +(-2303.00 - 678.964i) q^{49} -1672.93 q^{50} +(970.455 - 1680.88i) q^{51} +(-1317.88 + 760.879i) q^{52} +(-406.101 - 703.388i) q^{53} +(1587.37 + 916.470i) q^{54} -58.0754i q^{55} +(158.392 - 1097.37i) q^{56} -1989.12 q^{57} +(1241.51 - 2150.36i) q^{58} +(2472.07 - 1427.25i) q^{59} +(-106.587 - 184.614i) q^{60} +(5052.57 + 2917.10i) q^{61} -2048.35i q^{62} +(-2303.20 - 1813.30i) q^{63} +512.000 q^{64} +(550.733 - 953.898i) q^{65} +(-113.053 + 65.2709i) q^{66} +(1101.89 + 1908.54i) q^{67} +(-2922.12 - 1687.08i) q^{68} +4242.05i q^{69} +(297.859 + 745.199i) q^{70} +3408.24 q^{71} +(676.824 - 1172.29i) q^{72} +(-8136.88 + 4697.83i) q^{73} +(-764.630 - 1324.38i) q^{74} +(-2357.17 - 1360.92i) q^{75} +3457.98i q^{76} +(456.339 - 182.401i) q^{77} -2475.88 q^{78} +(-1176.12 + 2037.09i) q^{79} +(-320.942 + 185.296i) q^{80} +(-931.765 - 1613.86i) q^{81} +(2190.53 + 1264.70i) q^{82} -3750.16i q^{83} +(1115.88 - 1417.36i) q^{84} +2442.26 q^{85} +(-1763.27 + 3054.07i) q^{86} +(3498.61 - 2019.92i) q^{87} +(113.470 + 196.536i) q^{88} +(-5511.35 - 3181.98i) q^{89} +979.787i q^{90} +(9225.16 + 1331.54i) q^{91} +7374.58 q^{92} +(1666.31 - 2886.14i) q^{93} +(4288.39 - 2475.90i) q^{94} +(-1251.47 - 2167.60i) q^{95} +(721.413 + 416.508i) q^{96} -6370.47i q^{97} +(-4920.05 + 4680.97i) q^{98} +599.995 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 18 q^{3} - 16 q^{4} + 54 q^{5} - 28 q^{7} + 84 q^{9}+O(q^{10}) $ 4 * q - 18 * q^3 - 16 * q^4 + 54 * q^5 - 28 * q^7 + 84 * q^9	\( 4 q - 18 q^{3} - 16 q^{4} + 54 q^{5} - 28 q^{7} + 84 q^{9} - 96 q^{10} - 54 q^{11} + 144 q^{12} - 708 q^{15} - 128 q^{16} + 918 q^{17} + 576 q^{18} + 30 q^{19} - 378 q^{21} + 192 q^{22} - 486 q^{23} - 768 q^{24} - 572 q^{25} - 1728 q^{26} + 1456 q^{28} + 3240 q^{29} + 1152 q^{30} - 546 q^{31} + 1062 q^{33} - 1890 q^{35} - 1344 q^{36} - 446 q^{37} - 4320 q^{38} - 3312 q^{39} + 768 q^{40} + 5376 q^{42} + 2344 q^{43} - 432 q^{44} + 5724 q^{45} + 3840 q^{46} + 702 q^{47} - 9212 q^{49} - 3456 q^{50} + 318 q^{51} - 384 q^{52} + 2754 q^{53} - 1440 q^{54} - 17460 q^{57} + 384 q^{58} + 12366 q^{59} + 2832 q^{60} + 7686 q^{61} + 6468 q^{63} + 2048 q^{64} - 3024 q^{65} - 3456 q^{66} - 5062 q^{67} - 7344 q^{68} - 2016 q^{70} + 18792 q^{71} + 4608 q^{72} - 17274 q^{73} - 4320 q^{74} - 5220 q^{75} + 4914 q^{77} + 8832 q^{78} + 794 q^{79} - 3456 q^{80} - 4338 q^{81} + 9984 q^{82} - 5040 q^{84} + 10380 q^{85} - 10368 q^{86} - 12276 q^{87} - 768 q^{88} - 12474 q^{89} + 2688 q^{91} + 7776 q^{92} + 18918 q^{93} + 15168 q^{94} + 8910 q^{95} + 6144 q^{96} - 11448 q^{99}+O(q^{100}) \) 4 * q - 18 * q^3 - 16 * q^4 + 54 * q^5 - 28 * q^7 + 84 * q^9 - 96 * q^10 - 54 * q^11 + 144 * q^12 - 708 * q^15 - 128 * q^16 + 918 * q^17 + 576 * q^18 + 30 * q^19 - 378 * q^21 + 192 * q^22 - 486 * q^23 - 768 * q^24 - 572 * q^25 - 1728 * q^26 + 1456 * q^28 + 3240 * q^29 + 1152 * q^30 - 546 * q^31 + 1062 * q^33 - 1890 * q^35 - 1344 * q^36 - 446 * q^37 - 4320 * q^38 - 3312 * q^39 + 768 * q^40 + 5376 * q^42 + 2344 * q^43 - 432 * q^44 + 5724 * q^45 + 3840 * q^46 + 702 * q^47 - 9212 * q^49 - 3456 * q^50 + 318 * q^51 - 384 * q^52 + 2754 * q^53 - 1440 * q^54 - 17460 * q^57 + 384 * q^58 + 12366 * q^59 + 2832 * q^60 + 7686 * q^61 + 6468 * q^63 + 2048 * q^64 - 3024 * q^65 - 3456 * q^66 - 5062 * q^67 - 7344 * q^68 - 2016 * q^70 + 18792 * q^71 + 4608 * q^72 - 17274 * q^73 - 4320 * q^74 - 5220 * q^75 + 4914 * q^77 + 8832 * q^78 + 794 * q^79 - 3456 * q^80 - 4338 * q^81 + 9984 * q^82 - 5040 * q^84 + 10380 * q^85 - 10368 * q^86 - 12276 * q^87 - 768 * q^88 - 12474 * q^89 + 2688 * q^91 + 7776 * q^92 + 18918 * q^93 + 15168 * q^94 + 8910 * q^95 + 6144 * q^96 - 11448 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.41421	−	2.44949i	0.353553	−	0.612372i
$2$	1.41421	−	2.44949i	0.353553	−	0.612372i
$3$	3.98528	−	2.30090i	0.442809	−	0.255656i	−0.261979	−	0.965073i	$-0.584375\pi$
$3$	3.98528	−	2.30090i	0.442809	−	0.255656i	0.704788	+	0.709418i	$0.251042\pi$
$4$	−4.00000	−	6.92820i	−0.250000	−	0.433013i
$5$	5.01472	+	2.89525i	0.200589	+	0.115810i	0.596930	−	0.802293i	$-0.296387\pi$
$5$	5.01472	+	2.89525i	0.200589	+	0.115810i	−0.396341	+	0.918103i	$0.629720\pi$
$6$		−	13.0159i		−	0.361552i
$7$	−7.00000	+	48.4974i	−0.142857	+	0.989743i
$7$	−7.00000	+	48.4974i	−0.142857	+	0.989743i
$8$	−22.6274			−0.353553
$9$	−29.9117	+	51.8086i	−0.369280	+	0.639612i
$10$	14.1838	−	8.18900i	0.141838	−	0.0818900i
$11$	−5.01472	−	8.68575i	−0.0414440	−	0.0717830i	0.844559	−	0.535462i	$-0.179862\pi$
$11$	−5.01472	−	8.68575i	−0.0414440	−	0.0717830i	−0.886003	+	0.463679i	$0.846529\pi$
$12$	−31.8823	−	18.4072i	−0.221405	−	0.127828i
$13$		−	190.220i		−	1.12556i	−0.826607	−	0.562780i	$-0.809732\pi$
$13$		−	190.220i		−	1.12556i	0.826607	−	0.562780i	$-0.190268\pi$
$14$	108.894	+	85.7321i	0.555584	+	0.437409i
$15$	26.6468			0.118430
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$	365.265	−	210.886i	1.26389	−	0.729708i	0.290066	−	0.957007i	$-0.406323\pi$
$17$	365.265	−	210.886i	1.26389	−	0.729708i	0.973825	+	0.227299i	$0.0729894\pi$
$18$	84.6030	+	146.537i	0.261120	+	0.452274i
$19$	−374.338	−	216.124i	−1.03695	−	0.598681i	−0.117980	−	0.993016i	$-0.537642\pi$
$19$	−374.338	−	216.124i	−1.03695	−	0.598681i	−0.918967	+	0.394335i	$0.870975\pi$
$20$		−	46.3240i		−	0.115810i
$21$	83.6909	+	209.382i	0.189775	+	0.474790i
$22$	−28.3675			−0.0586106
$23$	−460.911	+	798.322i	−0.871288	+	1.50911i	−0.0106225	+	0.999944i	$0.503381\pi$
$23$	−460.911	+	798.322i	−0.871288	+	1.50911i	−0.860665	+	0.509171i	$0.829952\pi$
$24$	−90.1766	+	52.0635i	−0.156557	+	0.0903880i
$25$	−295.735	−	512.228i	−0.473176	−	0.819565i
$26$	−465.941	−	269.011i	−0.689262	−	0.397946i
$27$			648.042i			0.888946i
$28$	364.000	−	145.492i	0.464286	−	0.185577i
$29$	877.882			1.04386			0.521928	−	0.852990i	$-0.325213\pi$
$29$	877.882			1.04386			0.521928	+	0.852990i	$0.325213\pi$
$30$	37.6842	−	65.2709i	0.0418713	−	0.0725233i
$31$	627.175	−	362.100i	0.652628	−	0.376795i	−0.136834	−	0.990594i	$-0.543693\pi$
$31$	627.175	−	362.100i	0.652628	−	0.376795i	0.789462	+	0.613799i	$0.210360\pi$
$32$	90.5097	+	156.767i	0.0883883	+	0.153093i
$33$	−39.9701	−	23.0768i	−0.0367035	−	0.0211908i
$34$		−	1192.95i		−	1.03196i
$35$	−175.515	+	222.934i	−0.143278	+	0.181987i
$36$	478.587			0.369280
$37$	270.338	−	468.239i	0.197471	−	0.342030i	−0.750237	−	0.661169i	$-0.770061\pi$
$37$	270.338	−	468.239i	0.197471	−	0.342030i	0.947708	+	0.319140i	$0.103394\pi$
$38$	−1058.79	+	611.291i	−0.733232	+	0.423332i
$39$	−437.677	−	758.079i	−0.287756	−	0.498408i
$40$	−113.470	−	65.5120i	−0.0709188	−	0.0409450i
$41$			894.280i			0.531993i	0.963974	+	0.265996i	$0.0857009\pi$
$41$			894.280i			0.531993i	−0.963974	+	0.265996i	$0.914299\pi$
$42$	631.236	+	91.1111i	0.357844	+	0.0516503i
$43$	−1246.82			−0.674322			−0.337161	−	0.941447i	$-0.609467\pi$
$43$	−1246.82			−0.674322			−0.337161	+	0.941447i	$0.609467\pi$
$44$	−40.1177	+	69.4860i	−0.0207220	+	0.0358915i
$45$	−299.997	+	173.204i	−0.148147	+	0.0855326i
$46$	1303.65	+	2257.99i	0.616094	+	1.06711i
$47$	1516.17	+	875.364i	0.686362	+	0.396271i	0.802248	−	0.596991i	$-0.203637\pi$
$47$	1516.17	+	875.364i	0.686362	+	0.396271i	−0.115886	+	0.993263i	$0.536971\pi$
$48$			294.516i			0.127828i
$49$	−2303.00	−	678.964i	−0.959184	−	0.282784i
$50$	−1672.93			−0.669172
$51$	970.455	−	1680.88i	0.373108	−	0.646242i
$52$	−1317.88	+	760.879i	−0.487382	+	0.281390i
$53$	−406.101	−	703.388i	−0.144571	−	0.250405i	0.784642	−	0.619950i	$-0.212847\pi$
$53$	−406.101	−	703.388i	−0.144571	−	0.250405i	−0.929213	+	0.369545i	$0.879514\pi$
$54$	1587.37	+	916.470i	0.544366	+	0.314290i
$55$		−	58.0754i		−	0.0191985i
$56$	158.392	−	1097.37i	0.0505076	−	0.349927i
$57$	−1989.12			−0.612226
$58$	1241.51	−	2150.36i	0.369059	−	0.639228i
$59$	2472.07	−	1427.25i	0.710162	−	0.410012i	−0.100959	−	0.994891i	$-0.532191\pi$
$59$	2472.07	−	1427.25i	0.710162	−	0.410012i	0.811121	+	0.584878i	$0.198858\pi$
$60$	−106.587	−	184.614i	−0.0296075	−	0.0512817i
$61$	5052.57	+	2917.10i	1.35785	+	0.783956i	0.989334	−	0.145664i	$-0.0465319\pi$
$61$	5052.57	+	2917.10i	1.35785	+	0.783956i	0.368518	+	0.929620i	$0.379865\pi$
$62$		−	2048.35i		−	0.532868i
$63$	−2303.20	−	1813.30i	−0.580297	−	0.456866i
$64$	512.000			0.125000
$65$	550.733	−	953.898i	0.130351	−	0.225775i
$66$	−113.053	+	65.2709i	−0.0259533	+	0.0149841i
$67$	1101.89	+	1908.54i	0.245465	+	0.425158i	0.962262	−	0.272124i	$-0.0877259\pi$
$67$	1101.89	+	1908.54i	0.245465	+	0.425158i	−0.716797	+	0.697282i	$0.754393\pi$
$68$	−2922.12	−	1687.08i	−0.631946	−	0.364854i
$69$			4242.05i			0.891000i
$70$	297.859	+	745.199i	0.0607876	+	0.152081i
$71$	3408.24			0.676103			0.338052	−	0.941128i	$-0.390232\pi$
$71$	3408.24			0.676103			0.338052	+	0.941128i	$0.390232\pi$
$72$	676.824	−	1172.29i	0.130560	−	0.226137i
$73$	−8136.88	+	4697.83i	−1.52690	+	0.881559i	−0.527416	+	0.849607i	$0.676839\pi$
$73$	−8136.88	+	4697.83i	−1.52690	+	0.881559i	−0.999489	+	0.0319515i	$0.989828\pi$
$74$	−764.630	−	1324.38i	−0.139633	−	0.241851i
$75$	−2357.17	−	1360.92i	−0.419053	−	0.241941i
$76$			3457.98i			0.598681i
$77$	456.339	−	182.401i	0.0769673	−	0.0307642i
$78$	−2475.88			−0.406949
$79$	−1176.12	+	2037.09i	−0.188450	+	0.326405i	−0.944734	−	0.327839i	$-0.893680\pi$
$79$	−1176.12	+	2037.09i	−0.188450	+	0.326405i	0.756284	+	0.654244i	$0.227013\pi$
$80$	−320.942	+	185.296i	−0.0501472	+	0.0289525i
$81$	−931.765	−	1613.86i	−0.142016	−	0.245978i
$82$	2190.53	+	1264.70i	0.325778	+	0.188088i
$83$		−	3750.16i		−	0.544370i	−0.962245	−	0.272185i	$-0.912254\pi$
$83$		−	3750.16i		−	0.544370i	0.962245	−	0.272185i	$-0.0877462\pi$
$84$	1115.88	−	1417.36i	0.158146	−	0.200873i
$85$	2442.26			0.338030
$86$	−1763.27	+	3054.07i	−0.238409	+	0.412936i
$87$	3498.61	−	2019.92i	0.462229	−	0.266868i
$88$	113.470	+	196.536i	0.0146527	+	0.0253791i
$89$	−5511.35	−	3181.98i	−0.695790	−	0.401714i	0.109988	−	0.993933i	$-0.464919\pi$
$89$	−5511.35	−	3181.98i	−0.695790	−	0.401714i	−0.805777	+	0.592219i	$0.798252\pi$
$90$			979.787i			0.120961i
$91$	9225.16	+	1331.54i	1.11402	+	0.160794i
$92$	7374.58			0.871288
$93$	1666.31	−	2886.14i	0.192660	−	0.333696i
$94$	4288.39	−	2475.90i	0.485331	−	0.280206i
$95$	−1251.47	−	2167.60i	−0.138667	−	0.240177i
$96$	721.413	+	416.508i	0.0782783	+	0.0451940i
$97$		−	6370.47i		−	0.677062i	−0.940955	−	0.338531i	$-0.890070\pi$
$97$		−	6370.47i		−	0.677062i	0.940955	−	0.338531i	$-0.109930\pi$
$98$	−4920.05	+	4680.97i	−0.512292	+	0.487398i
$99$	599.995			0.0612177
$100$	−2365.88	+	4097.83i	−0.236588	+	0.409783i
$101$	7890.21	−	4555.42i	0.773474	−	0.446566i	−0.0606384	−	0.998160i	$-0.519314\pi$
$101$	7890.21	−	4555.42i	0.773474	−	0.446566i	0.834113	+	0.551594i	$0.185980\pi$
$102$	−2744.86	−	4754.24i	−0.263827	−	0.456962i
$103$	−13953.3	−	8055.91i	−1.31523	−	0.759347i	−0.332271	−	0.943184i	$-0.607815\pi$
$103$	−13953.3	−	8055.91i	−1.31523	−	0.759347i	−0.982957	+	0.183837i	$0.941148\pi$
$104$			4304.18i			0.397946i
$105$	−186.527	+	1292.30i	−0.0169186	+	0.117215i
$106$	−2297.26			−0.204455
$107$	−10275.7	+	17798.0i	−0.897518	+	1.55455i	−0.0668618	+	0.997762i	$0.521299\pi$
$107$	−10275.7	+	17798.0i	−0.897518	+	1.55455i	−0.830657	+	0.556785i	$0.812035\pi$
$108$	4489.77	−	2592.17i	0.384925	−	0.222237i
$109$	7128.87	+	12347.6i	0.600023	+	1.03927i	0.992817	+	0.119643i	$0.0381751\pi$
$109$	7128.87	+	12347.6i	0.600023	+	1.03927i	−0.392794	+	0.919626i	$0.628492\pi$
$110$	−142.255	−	82.1311i	−0.0117566	−	0.00678769i
$111$		−	2488.08i		−	0.201938i
$112$	−2464.00	−	1939.90i	−0.196429	−	0.154647i
$113$	−10304.7			−0.807010			−0.403505	−	0.914978i	$-0.632208\pi$
$113$	−10304.7			−0.807010			−0.403505	+	0.914978i	$0.632208\pi$
$114$	−2813.04	+	4872.33i	−0.216454	+	0.374910i
$115$	−4622.68	+	2668.91i	−0.349541	+	0.201808i
$116$	−3511.53	−	6082.15i	−0.260964	−	0.452003i
$117$	9855.01	+	5689.79i	0.719922	+	0.415647i
$118$		−	8073.76i		−	0.579845i
$119$	7670.55	+	19190.6i	0.541668	+	1.35517i
$120$	−602.947			−0.0418713
$121$	7270.21	−	12592.4i	0.496565	−	0.860075i
$122$	14290.8	−	8250.81i	0.960147	−	0.554341i
$123$	2057.65	+	3563.96i	0.136007	+	0.235571i
$124$	−5017.40	−	2896.80i	−0.326314	−	0.188397i
$125$		−	7043.97i		−	0.450814i
$126$	−7698.88	+	3077.27i	−0.484938	+	0.193832i
$127$	−2116.70			−0.131236			−0.0656179	−	0.997845i	$-0.520902\pi$
$127$	−2116.70			−0.131236			−0.0656179	+	0.997845i	$0.520902\pi$
$128$	724.077	−	1254.14i	0.0441942	−	0.0765466i
$129$	−4968.93	+	2868.81i	−0.298596	+	0.172394i
$130$	−1557.71	−	2698.03i	−0.0921721	−	0.159647i
$131$	−5245.64	−	3028.57i	−0.305672	−	0.176480i	0.339316	−	0.940672i	$-0.389804\pi$
$131$	−5245.64	−	3028.57i	−0.305672	−	0.176480i	−0.644988	+	0.764192i	$0.723138\pi$
$132$			369.228i			0.0211908i
$133$	13101.8	−	16641.5i	0.740676	−	0.940785i
$134$	6233.25			0.347140
$135$	−1876.24	+	3249.75i	−0.102949	+	0.178313i
$136$	−8264.99	+	4771.80i	−0.446853	+	0.257991i
$137$	−1430.13	−	2477.05i	−0.0761962	−	0.131976i	0.825410	−	0.564534i	$-0.190944\pi$
$137$	−1430.13	−	2477.05i	−0.0761962	−	0.131976i	−0.901606	+	0.432559i	$0.857611\pi$
$138$	10390.9	+	5999.16i	0.545624	+	0.315016i
$139$		−	16966.2i		−	0.878124i	−0.898457	−	0.439062i	$-0.855311\pi$
$139$		−	16966.2i		−	0.878124i	0.898457	−	0.439062i	$-0.144689\pi$
$140$	2246.59	+	324.268i	0.114622	+	0.0165443i
$141$	8056.51			0.405237
$142$	4819.98	−	8348.44i	0.239039	−	0.414027i
$143$	−1652.20	+	953.898i	−0.0807961	+	0.0466477i
$144$	−1914.35	−	3315.75i	−0.0923200	−	0.159903i
$145$	4402.33	+	2541.69i	0.209386	+	0.120889i
$146$			26574.9i			1.24671i
$147$	−10740.3	+	2593.12i	−0.497031	+	0.120002i
$148$	−4325.40			−0.197471
$149$	7455.05	−	12912.5i	0.335798	−	0.581619i	−0.647840	−	0.761777i	$-0.724327\pi$
$149$	7455.05	−	12912.5i	0.335798	−	0.581619i	0.983638	+	0.180157i	$0.0576607\pi$
$150$	−6667.10	+	3849.25i	−0.296315	+	0.171078i
$151$	1080.72	+	1871.87i	0.0473981	+	0.0820959i	0.888751	−	0.458390i	$-0.151574\pi$
$151$	1080.72	+	1871.87i	0.0473981	+	0.0820959i	−0.841353	+	0.540486i	$0.818240\pi$
$152$	8470.29	+	4890.33i	0.366616	+	0.211666i
$153$			25231.8i			1.07787i
$154$	198.573	−	1375.75i	0.00837294	−	0.0580095i
$155$	4193.48			0.174546
$156$	−3501.42	+	6064.63i	−0.143878	+	0.249204i
$157$	−35986.6	+	20776.9i	−1.45996	+	0.842909i	−0.999009	−	0.0445152i	$-0.985826\pi$
$157$	−35986.6	+	20776.9i	−1.45996	+	0.842909i	−0.460953	+	0.887425i	$0.652492\pi$
$158$	3326.56	+	5761.77i	0.133254	+	0.230803i
$159$	−3236.86	−	1868.80i	−0.128035	−	0.0739211i
$160$			1048.19i			0.0409450i
$161$	−35490.2	−	27941.3i	−1.36917	−	1.07794i
$162$	−5270.86			−0.200841
$163$	5882.56	−	10188.9i	0.221407	−	0.383488i	−0.733828	−	0.679335i	$-0.762268\pi$
$163$	5882.56	−	10188.9i	0.221407	−	0.383488i	0.955235	+	0.295847i	$0.0956018\pi$
$164$	6195.75	−	3577.12i	0.230360	−	0.132998i
$165$	−133.626	−	231.447i	−0.00490821	−	0.00850127i
$166$	−9185.98	−	5303.53i	−0.333357	−	0.192464i
$167$			13600.3i			0.487660i	0.969818	+	0.243830i	$0.0784038\pi$
$167$			13600.3i			0.487660i	−0.969818	+	0.243830i	$0.921596\pi$
$168$	−1893.71	−	4737.78i	−0.0670957	−	0.167863i
$169$	−7622.52			−0.266886
$170$	3453.88	−	5982.30i	0.119512	−	0.207000i
$171$	22394.1	−	12929.3i	0.765847	−	0.442162i
$172$	4987.28	+	8638.23i	0.168580	+	0.291990i
$173$	39103.8	+	22576.6i	1.30655	+	0.754337i	0.981519	−	0.191366i	$-0.0612917\pi$
$173$	39103.8	+	22576.6i	1.30655	+	0.754337i	0.325032	+	0.945703i	$0.394625\pi$
$174$		−	11426.4i		−	0.377408i
$175$	26911.9	−	10756.8i	0.878756	−	0.351242i
$176$	641.884			0.0207220
$177$	6567.94	−	11376.0i	0.209644	−	0.363114i
$178$	−15588.4	+	9000.00i	−0.491998	+	0.284055i
$179$	−9926.19	−	17192.7i	−0.309797	−	0.536583i	0.668521	−	0.743693i	$-0.266928\pi$
$179$	−9926.19	−	17192.7i	−0.309797	−	0.536583i	−0.978318	+	0.207110i	$0.933594\pi$
$180$	2399.98	+	1385.63i	0.0740734	+	0.0427663i
$181$			21398.5i			0.653170i	0.945168	+	0.326585i	$0.105898\pi$
$181$			21398.5i			0.653170i	−0.945168	+	0.326585i	$0.894102\pi$
$182$	16307.9	−	20713.9i	0.492330	−	0.625343i
$183$	26847.9			0.801692
$184$	10429.2	−	18064.0i	0.308047	−	0.533553i
$185$	2711.33	−	1565.39i	0.0792209	−	0.0457382i
$186$	−4713.05	−	8163.24i	−0.136231	−	0.235959i
$187$	−3663.40	−	2115.06i	−0.104761	−	0.0604840i
$188$		−	14005.8i		−	0.396271i
$189$	−31428.4	−	4536.29i	−0.879829	−	0.126992i
$190$	−7079.36			−0.196104
$191$	−5812.94	+	10068.3i	−0.159341	+	0.275988i	−0.934631	−	0.355618i	$-0.884270\pi$
$191$	−5812.94	+	10068.3i	−0.159341	+	0.275988i	0.775290	+	0.631606i	$0.217604\pi$
$192$	2040.46	−	1178.06i	0.0553511	−	0.0319570i
$193$	26273.5	+	45507.0i	0.705347	+	1.22170i	0.966566	+	0.256417i	$0.0825420\pi$
$193$	26273.5	+	45507.0i	0.705347	+	1.22170i	−0.261220	+	0.965279i	$0.584125\pi$
$194$	−15604.4	−	9009.21i	−0.414614	−	0.239377i
$195$		−	5068.74i		−	0.133300i
$196$	4508.00	+	18671.5i	0.117347	+	0.486035i
$197$	−54811.7			−1.41235			−0.706173	−	0.708039i	$-0.749580\pi$
$197$	−54811.7			−1.41235			−0.706173	+	0.708039i	$0.749580\pi$
$198$	848.521	−	1469.68i	0.0216437	−	0.0374880i
$199$	5172.66	−	2986.44i	0.130619	−	0.0754131i	−0.433266	−	0.901266i	$-0.642639\pi$
$199$	5172.66	−	2986.44i	0.130619	−	0.0754131i	0.563886	+	0.825853i	$0.309306\pi$
$200$	6691.72	+	11590.4i	0.167293	+	0.289760i
$201$	8782.71	+	5070.70i	0.217388	+	0.125509i
$202$		−	25769.3i		−	0.631539i
$203$	−6145.18	+	42575.0i	−0.149122	+	1.03315i
$204$	−15527.3			−0.373108
$205$	−2589.16	+	4484.56i	−0.0616101	+	0.106712i
$206$	−39465.8	+	22785.6i	−0.930007	+	0.536940i
$207$	−27573.3	−	47758.3i	−0.643499	−	1.11457i
$208$	10543.0	+	6087.03i	0.243691	+	0.140695i
$209$			4335.20i			0.0992469i
$210$	2901.68	+	2284.48i	0.0657978	+	0.0518023i
$211$	3042.82			0.0683457			0.0341729	−	0.999416i	$-0.489120\pi$
$211$	3042.82			0.0683457			0.0341729	+	0.999416i	$0.489120\pi$
$212$	−3248.81	+	5627.10i	−0.0722857	+	0.125203i
$213$	13582.8	−	7842.02i	0.299385	−	0.172850i
$214$	29064.0	+	50340.4i	0.634641	+	1.09923i
$215$	−6252.46	−	3609.86i	−0.135261	−	0.0780932i
$216$		−	14663.5i		−	0.314290i
$217$	13170.7	+	32951.1i	0.279698	+	0.699762i
$218$	40327.0			0.848560
$219$	−21618.5	+	37444.3i	−0.450752	+	0.780725i
$220$	−402.358	+	232.302i	−0.00831319	+	0.00479962i
$221$	−40114.6	−	69480.5i	−0.821330	−	1.42259i
$222$	−6094.53	−	3518.68i	−0.123662	−	0.0713960i
$223$		−	42104.7i		−	0.846683i	−0.905970	−	0.423341i	$-0.860857\pi$
$223$		−	42104.7i		−	0.846683i	0.905970	−	0.423341i	$-0.139143\pi$
$224$	−8236.38	+	3292.11i	−0.164150	+	0.0656113i
$225$	35383.7			0.698938
$226$	−14573.1	+	25241.3i	−0.285321	+	0.494190i
$227$	79838.4	−	46094.7i	1.54939	−	0.894540i	0.551200	−	0.834373i	$-0.314170\pi$
$227$	79838.4	−	46094.7i	1.54939	−	0.894540i	0.998188	−	0.0601663i	$-0.0191631\pi$
$228$	7956.48	+	13781.0i	0.153056	+	0.265101i
$229$	−20752.6	−	11981.5i	−0.395733	−	0.228477i	0.288908	−	0.957357i	$-0.406708\pi$
$229$	−20752.6	−	11981.5i	−0.395733	−	0.228477i	−0.684641	+	0.728880i	$0.740041\pi$
$230$			15097.6i			0.285399i
$231$	1398.95	−	1776.91i	0.0262168	−	0.0332998i
$232$	−19864.2			−0.369059
$233$	17674.1	−	30612.4i	0.325555	−	0.563878i	−0.656069	−	0.754701i	$-0.727782\pi$
$233$	17674.1	−	30612.4i	0.325555	−	0.563878i	0.981625	+	0.190822i	$0.0611155\pi$
$234$	27874.2	−	16093.2i	0.509061	−	0.293907i
$235$	5068.79	+	8779.41i	0.0917844	+	0.158975i
$236$	−19776.6	−	11418.0i	−0.355081	−	0.205006i
$237$			10824.5i			0.192713i
$238$	57854.9	+	8350.64i	1.02138	+	0.147423i
$239$	14393.5			0.251983			0.125992	−	0.992031i	$-0.459789\pi$
$239$	14393.5			0.251983			0.125992	+	0.992031i	$0.459789\pi$
$240$	−852.696	+	1476.91i	−0.0148038	+	0.0256409i
$241$	6495.14	−	3749.97i	0.111829	−	0.0645645i	−0.443042	−	0.896501i	$-0.646101\pi$
$241$	6495.14	−	3749.97i	0.111829	−	0.0645645i	0.554871	+	0.831936i	$0.312768\pi$
$242$	−20563.2	−	35616.6i	−0.351124	−	0.608165i
$243$	−52885.6	−	30533.5i	−0.895622	−	0.517088i
$244$		−	46673.6i		−	0.783956i
$245$	−9583.13	−	10072.6i	−0.159652	−	0.167806i
$246$	11639.8			0.192343
$247$	−41111.0	+	71206.4i	−0.673852	+	1.16715i
$248$	−14191.4	+	8193.38i	−0.230739	+	0.133217i
$249$	−8628.76	−	14945.5i	−0.139171	−	0.241052i
$250$	−17254.1	−	9961.68i	−0.276066	−	0.159387i
$251$			45414.9i			0.720860i	0.932786	+	0.360430i	$0.117370\pi$
$251$			45414.9i			0.720860i	−0.932786	+	0.360430i	$0.882630\pi$
$252$	−3350.11	+	23210.2i	−0.0527543	+	0.365493i
$253$	9245.36			0.144438
$254$	−2993.47	+	5184.84i	−0.0463988	+	0.0803652i
$255$	9733.11	−	5619.42i	0.149683	−	0.0864193i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	44797.7	+	25864.0i	0.678250	+	0.391588i	0.799195	−	0.601072i	$-0.205259\pi$
$257$	44797.7	+	25864.0i	0.678250	+	0.391588i	−0.120946	+	0.992659i	$0.538593\pi$
$258$			16228.5i			0.243802i
$259$	20816.0	+	16388.3i	0.310311	+	0.244307i
$260$	−8811.73			−0.130351
$261$	−26258.9	+	45481.8i	−0.385475	+	0.667662i
$262$	−14836.9	+	8566.10i	−0.216143	+	0.124790i
$263$	44917.0	+	77798.4i	0.649380	+	1.12476i	0.983271	+	0.182147i	$0.0583048\pi$
$263$	44917.0	+	77798.4i	0.649380	+	1.12476i	−0.333891	+	0.942612i	$0.608362\pi$
$264$	904.421	+	522.168i	0.0129767	+	0.00749207i
$265$		−	4703.06i		−	0.0669713i
$266$	−22234.5	−	55627.5i	−0.314242	−	0.786187i
$267$	−29285.7			−0.410803
$268$	8815.15	−	15268.3i	0.122733	−	0.212579i
$269$	−20580.0	+	11881.9i	−0.284408	+	0.164203i	−0.635417	−	0.772169i	$-0.719172\pi$
$269$	−20580.0	+	11881.9i	−0.284408	+	0.164203i	0.351009	+	0.936372i	$0.385838\pi$
$270$	5306.82	+	9191.68i	0.0727958	+	0.126086i
$271$	−95971.7	−	55409.3i	−1.30679	−	0.754473i	−0.325228	−	0.945636i	$-0.605441\pi$
$271$	−95971.7	−	55409.3i	−1.30679	−	0.754473i	−0.981558	+	0.191162i	$0.938774\pi$
$272$			26993.4i			0.364854i
$273$	39828.6	−	15919.7i	0.534404	−	0.213604i
$274$	−8090.01			−0.107758
$275$	−2966.06	+	5137.36i	−0.0392206	+	0.0679320i
$276$	29389.8	−	16968.2i	0.385814	−	0.222750i
$277$	3561.19	+	6168.17i	0.0464126	+	0.0803890i	0.888298	−	0.459267i	$-0.151888\pi$
$277$	3561.19	+	6168.17i	0.0464126	+	0.0803890i	−0.841886	+	0.539656i	$0.818554\pi$
$278$	−41558.6	−	23993.9i	−0.537739	−	0.310464i
$279$			43324.1i			0.556571i
$280$	3971.45	−	5044.42i	0.0506563	−	0.0643422i
$281$	90209.2			1.14245			0.571226	−	0.820792i	$-0.306468\pi$
$281$	90209.2			1.14245			0.571226	+	0.820792i	$0.306468\pi$
$282$	11393.6	−	19734.3i	0.143273	−	0.248156i
$283$	−62743.0	+	36224.7i	−0.783415	+	0.452305i	−0.837639	−	0.546224i	$-0.816065\pi$
$283$	−62743.0	+	36224.7i	−0.783415	+	0.452305i	0.0542240	+	0.998529i	$0.482732\pi$
$284$	−13632.9	−	23613.0i	−0.169026	−	0.292761i
$285$	−9974.88	−	5759.00i	−0.122806	−	0.0709018i
$286$			5396.06i			0.0659698i
$287$	−43370.3	−	6259.96i	−0.526536	−	0.0759990i
$288$	−10829.2			−0.130560
$289$	47184.9	−	81726.7i	0.564947	−	0.978517i
$290$	12451.7	−	7188.98i	0.148058	−	0.0854813i
$291$	−14657.8	−	25388.1i	−0.173095	−	0.299809i
$292$	65095.0	+	37582.6i	0.763452	+	0.440779i
$293$		−	89167.8i		−	1.03866i	−0.854574	−	0.519329i	$-0.826182\pi$
$293$		−	89167.8i		−	1.03866i	0.854574	−	0.519329i	$-0.173818\pi$
$294$	−8837.31	+	29975.6i	−0.102241	+	0.346795i
$295$	16529.0			0.189934
$296$	−6117.04	+	10595.0i	−0.0698165	+	0.120926i
$297$	5628.73	−	3249.75i	0.0638113	−	0.0368415i
$298$	−21086.1	−	36522.2i	−0.237445	−	0.411267i
$299$	151856.	+	87674.4i	1.69860	+	0.980687i
$300$			21774.6i			0.241941i
$301$	8727.75	−	60467.6i	0.0963317	−	0.667405i
$302$	6113.49			0.0670310
$303$	20963.1	−	36309.2i	0.228334	−	0.395487i
$304$	23957.6	−	13831.9i	0.259237	−	0.149670i
$305$	16891.5	+	29256.9i	0.181580	+	0.314506i
$306$	61805.0	+	35683.1i	0.660056	+	0.381083i
$307$		−	113110.i		−	1.20012i	−0.799954	−	0.600061i	$-0.795143\pi$
$307$		−	113110.i		−	1.20012i	0.799954	−	0.600061i	$-0.204857\pi$
$308$	−3089.07	−	2432.01i	−0.0325631	−	0.0256368i
$309$	−74143.5			−0.776526
$310$	5930.47	−	10271.9i	0.0617115	−	0.106887i
$311$	−56589.7	+	32672.1i	−0.585082	+	0.337797i	−0.763151	−	0.646221i	$-0.776349\pi$
$311$	−56589.7	+	32672.1i	−0.585082	+	0.337797i	0.178068	+	0.984018i	$0.443015\pi$
$312$	9903.50	+	17153.4i	0.101737	+	0.176214i
$313$	1696.42	+	979.430i	0.0173159	+	0.00999734i	0.508633	−	0.860983i	$-0.330151\pi$
$313$	1696.42	+	979.430i	0.0173159	+	0.00999734i	−0.491317	+	0.870981i	$0.663484\pi$
$314$			117532.i			1.19205i
$315$	−6299.95	−	15761.5i	−0.0634915	−	0.158846i
$316$	18817.8			0.188450
$317$	43075.6	−	74609.1i	0.428660	−	0.742461i	−0.568095	−	0.822963i	$-0.692319\pi$
$317$	43075.6	−	74609.1i	0.428660	−	0.742461i	0.996754	+	0.0805027i	$0.0256526\pi$
$318$	−9155.21	+	5285.76i	−0.0905345	+	0.0522701i
$319$	−4402.33	−	7625.06i	−0.0432615	−	0.0749311i
$320$	2567.54	+	1482.37i	0.0250736	+	0.0144762i
$321$			94573.5i			0.917824i
$322$	−118633.	+	47417.9i	−1.14417	+	0.457331i
$323$	−182310.			−1.74745
$324$	−7454.12	+	12910.9i	−0.0710078	+	0.122989i
$325$	−97435.9	+	56254.6i	−0.922470	+	0.532588i
$326$	−16638.4	−	28818.5i	−0.156558	−	0.271167i
$327$	56821.1	+	32805.7i	0.531391	+	0.306799i
$328$		−	20235.2i		−	0.188088i
$329$	−53066.1	+	67403.0i	−0.490259	+	0.622712i
$330$	−755.903			−0.00694125
$331$	45311.1	−	78481.2i	0.413570	−	0.716324i	−0.581707	−	0.813398i	$-0.697615\pi$
$331$	45311.1	−	78481.2i	0.413570	−	0.716324i	0.995277	+	0.0970742i	$0.0309484\pi$
$332$	−25981.9	+	15000.6i	−0.235719	+	0.136092i
$333$	16172.5	+	28011.6i	0.145844	+	0.252609i
$334$	33313.9	+	19233.8i	0.298629	+	0.172414i
$335$			12761.0i			0.113709i
$336$	−14283.2	−	2061.61i	−0.126517	−	0.0182611i
$337$	−26197.5			−0.230675			−0.115338	−	0.993326i	$-0.536795\pi$
$337$	−26197.5			−0.230675			−0.115338	+	0.993326i	$0.536795\pi$
$338$	−10779.9	+	18671.3i	−0.0943583	+	0.163433i
$339$	−41067.1	+	23710.1i	−0.357351	+	0.206317i
$340$	−9769.06	−	16920.5i	−0.0845074	−	0.146371i
$341$	−6290.22	−	3631.66i	−0.0540950	−	0.0312317i
$342$		−	73139.0i		−	0.625312i
$343$	49049.0	−	106937.i	0.416910	−	0.908948i
$344$	28212.3			0.238409
$345$	−12281.8	+	21272.7i	−0.103187	+	0.178724i
$346$	110602.	−	63856.2i	0.923871	−	0.533397i
$347$	80330.4	+	139136.i	0.667146	+	1.15553i	0.978699	+	0.205302i	$0.0658175\pi$
$347$	80330.4	+	139136.i	0.667146	+	1.15553i	−0.311553	+	0.950229i	$0.600849\pi$
$348$	−27988.9	−	16159.4i	−0.231114	−	0.133434i
$349$			18120.2i			0.148769i	0.997230	+	0.0743845i	$0.0236992\pi$
$349$			18120.2i			0.148769i	−0.997230	+	0.0743845i	$0.976301\pi$
$350$	11710.5	−	81132.8i	0.0955960	−	0.662309i
$351$	123270.			1.00056
$352$	907.761	−	1572.29i	0.00732633	−	0.0126896i
$353$	−11457.1	+	6614.74i	−0.0919441	+	0.0530839i	−0.545267	−	0.838262i	$-0.683572\pi$
$353$	−11457.1	+	6614.74i	−0.0919441	+	0.0530839i	0.453323	+	0.891346i	$0.350238\pi$
$354$	−18576.9	−	32176.2i	−0.148241	−	0.256761i
$355$	17091.4	+	9867.70i	0.135619	+	0.0782995i
$356$			50911.7i			0.401714i
$357$	74725.0	+	58830.7i	0.586313	+	0.461602i
$358$	−56151.0			−0.438119
$359$	53867.4	−	93301.1i	0.417962	−	0.723932i	−0.577772	−	0.816198i	$-0.696078\pi$
$359$	53867.4	−	93301.1i	0.417962	−	0.723932i	0.995734	+	0.0922663i	$0.0294111\pi$
$360$	6788.17	−	3919.15i	0.0523778	−	0.0302404i
$361$	28258.6	+	48945.4i	0.216839	+	0.375575i
$362$	52415.4	+	30262.0i	0.399983	+	0.230930i
$363$		−	66912.2i		−	0.507799i
$364$	−27675.5	−	69240.0i	−0.208878	−	0.522582i
$365$	−54405.5			−0.408373
$366$	37968.6	−	65763.6i	0.283441	−	0.490934i
$367$	60991.7	−	35213.6i	0.452834	−	0.261444i	−0.256192	−	0.966626i	$-0.582468\pi$
$367$	60991.7	−	35213.6i	0.452834	−	0.261444i	0.709026	+	0.705182i	$0.249135\pi$
$368$	−29498.3	−	51092.6i	−0.217822	−	0.377279i
$369$	−46331.4	−	26749.4i	−0.340269	−	0.196454i
$370$		−	8855.18i		−	0.0646836i
$371$	36955.2	−	14771.1i	0.268490	−	0.107316i
$372$	−26661.0			−0.192660
$373$	−95526.7	+	165457.i	−0.686605	+	1.18924i	0.286324	+	0.958133i	$0.407567\pi$
$373$	−95526.7	+	165457.i	−0.686605	+	1.18924i	−0.972929	+	0.231102i	$0.925767\pi$
$374$	−10361.7	+	5982.30i	−0.0740774	+	0.0427686i
$375$	−16207.5	−	28072.2i	−0.115253	−	0.199625i
$376$	−34307.1	−	19807.2i	−0.242666	−	0.140103i
$377$		−	166990.i		−	1.17492i
$378$	−55558.0	+	70568.2i	−0.388833	+	0.493884i
$379$	74979.5			0.521992			0.260996	−	0.965340i	$-0.415949\pi$
$379$	74979.5			0.521992			0.260996	+	0.965340i	$0.415949\pi$
$380$	−10011.7	+	17340.8i	−0.0693333	+	0.120089i
$381$	−8435.65	+	4870.32i	−0.0581124	+	0.0335512i
$382$	16441.5	+	28477.5i	0.112671	+	0.195153i
$383$	−111403.	−	64318.4i	−0.759449	−	0.438468i	0.0696492	−	0.997572i	$-0.477812\pi$
$383$	−111403.	−	64318.4i	−0.759449	−	0.438468i	−0.829098	+	0.559104i	$0.811145\pi$
$384$		−	6664.13i		−	0.0451940i
$385$	2816.51	+	406.528i	0.0190016	+	0.00274264i
$386$	148625.			0.997511
$387$	37294.5	−	64596.0i	0.249014	−	0.431304i
$388$	−44135.9	+	25481.9i	−0.293176	+	0.169265i
$389$	−13154.0	−	22783.4i	−0.0869278	−	0.150563i	0.819283	−	0.573389i	$-0.194372\pi$
$389$	−13154.0	−	22783.4i	−0.0869278	−	0.150563i	−0.906211	+	0.422826i	$0.861038\pi$
$390$	−12415.8	−	7168.28i	−0.0816293	−	0.0471287i
$391$			388798.i			2.54314i
$392$	52110.9	+	15363.2i	0.339123	+	0.0999792i
$393$	−27873.8			−0.180473
$394$	−77515.5	+	134261.i	−0.499340	+	0.864882i
$395$	−11795.8	+	6810.30i	−0.0756018	+	0.0436487i
$396$	−2399.98	−	4156.89i	−0.0153044	−	0.0265080i
$397$	−76233.0	−	44013.1i	−0.483684	−	0.279255i	0.238266	−	0.971200i	$-0.423421\pi$
$397$	−76233.0	−	44013.1i	−0.483684	−	0.279255i	−0.721951	+	0.691945i	$0.756754\pi$
$398$		−	16893.8i		−	0.106650i
$399$	13923.8	−	96467.3i	0.0874608	−	0.605946i
$400$	37854.1			0.236588
$401$	−132300.	+	229150.i	−0.822755	+	1.42505i	0.0808687	+	0.996725i	$0.474231\pi$
$401$	−132300.	+	229150.i	−0.822755	+	1.42505i	−0.903623	+	0.428328i	$0.859103\pi$
$402$	24841.3	−	14342.1i	0.153717	−	0.0887485i
$403$	−68878.5	−	119301.i	−0.424105	−	0.734572i
$404$	−63121.7	−	36443.3i	−0.386737	−	0.223283i
$405$		−	10790.8i		−	0.0657873i
$406$	95596.5	+	75262.7i	0.579949	+	0.456592i
$407$	−5422.67			−0.0327359
$408$	−21958.9	+	38033.9i	−0.131914	+	0.228481i
$409$	121392.	−	70085.4i	0.725674	−	0.418968i	−0.0911633	−	0.995836i	$-0.529059\pi$
$409$	121392.	−	70085.4i	0.725674	−	0.418968i	0.816838	+	0.576868i	$0.195725\pi$
$410$	7323.26	+	12684.3i	0.0435649	+	0.0754566i
$411$	−11398.9	−	6581.16i	−0.0674807	−	0.0389600i
$412$			128895.i			0.759347i
$413$	51913.6	+	129880.i	0.304355	+	0.761451i
$414$	−155978.			−0.910044
$415$	10857.7	−	18806.0i	0.0630434	−	0.109194i
$416$	29820.2	−	17216.7i	0.172316	−	0.0994864i
$417$	−39037.6	−	67615.2i	−0.224497	−	0.388841i
$418$	10619.0	+	6130.90i	0.0607761	+	0.0350891i
$419$		−	319409.i		−	1.81936i	−0.415306	−	0.909682i	$-0.636325\pi$
$419$		−	319409.i		−	1.81936i	0.415306	−	0.909682i	$-0.363675\pi$
$420$	9699.42	−	3876.90i	0.0549854	−	0.0219779i
$421$	315726.			1.78134			0.890670	−	0.454651i	$-0.150236\pi$
$421$	315726.			1.78134			0.890670	+	0.454651i	$0.150236\pi$
$422$	4303.20	−	7453.36i	0.0241639	−	0.0418530i
$423$	−90702.7	+	52367.2i	−0.506920	+	0.292670i
$424$	9189.02	+	15915.9i	0.0511137	+	0.0885316i
$425$	−216043.	−	124733.i	−1.19609	−	0.690561i
$426$		−	44361.2i		−	0.244447i
$427$	−176840.	+	224617.i	−0.969895	+	1.23193i
$428$	164411.			0.897518
$429$	−4389.65	+	7603.10i	−0.0238515	+	0.0413120i
$430$	−17684.6	+	10210.2i	−0.0956442	+	0.0552202i
$431$	−84265.4	−	145952.i	−0.453623	−	0.785698i	0.544985	−	0.838446i	$-0.316535\pi$
$431$	−84265.4	−	145952.i	−0.453623	−	0.785698i	−0.998608	+	0.0527481i	$0.983202\pi$
$432$	−35918.1	−	20737.3i	−0.192463	−	0.111118i
$433$		−	17104.3i		−	0.0912284i	−0.998959	−	0.0456142i	$-0.985476\pi$
$433$		−	17104.3i		−	0.0912284i	0.998959	−	0.0456142i	$-0.0145245\pi$
$434$	99339.5	+	14338.4i	0.527403	+	0.0761241i
$435$	23392.7			0.123624
$436$	57030.9	−	98780.5i	0.300011	−	0.519635i
$437$	345073.	−	199228.i	1.80696	−	1.04325i
$438$	61146.3	+	105909.i	0.318729	+	0.552056i
$439$	192241.	+	110991.i	0.997511	+	0.575913i	0.907511	−	0.420029i	$-0.137980\pi$
$439$	192241.	+	110991.i	0.997511	+	0.575913i	0.0899998	+	0.995942i	$0.471313\pi$
$440$			1314.10i			0.00678769i
$441$	104063.	−	99006.2i	0.535079	−	0.509079i
$442$	−226922.			−1.16154
$443$	−17115.4	+	29644.7i	−0.0872124	+	0.151056i	−0.906332	−	0.422567i	$-0.861129\pi$
$443$	−17115.4	+	29644.7i	−0.0872124	+	0.151056i	0.819119	+	0.573623i	$0.194463\pi$
$444$	−17237.9	+	9952.33i	−0.0874419	+	0.0504846i
$445$	−18425.2	−	31913.5i	−0.0930450	−	0.161159i
$446$	−103135.	−	59545.0i	−0.518485	−	0.299348i
$447$		−	68613.4i		−	0.343395i
$448$	−3584.00	+	24830.7i	−0.0178571	+	0.123718i
$449$	−187206.			−0.928598			−0.464299	−	0.885679i	$-0.653694\pi$
$449$	−187206.			−0.928598			−0.464299	+	0.885679i	$0.653694\pi$
$450$	50040.2	−	86672.1i	0.247112	−	0.428010i
$451$	7767.49	−	4484.56i	0.0381881	−	0.0220479i
$452$	41218.8	+	71393.1i	0.201752	+	0.349445i
$453$	8613.97	+	4973.28i	0.0419766	+	0.0242352i
$454$		−	260751.i		−	1.26507i
$455$	42406.5	+	33386.4i	0.204837	+	0.161268i
$456$	45008.7			0.216454
$457$	−73922.5	+	128038.i	−0.353952	+	0.613063i	−0.986938	−	0.161100i	$-0.948496\pi$
$457$	−73922.5	+	128038.i	−0.353952	+	0.613063i	0.632986	+	0.774163i	$0.281829\pi$
$458$	−58697.3	+	33888.9i	−0.279826	+	0.161557i
$459$	136663.	+	236707.i	0.648671	+	1.12353i
$460$	36981.4	+	21351.2i	0.174771	+	0.100904i
$461$			73979.5i			0.348105i	0.984736	+	0.174052i	$0.0556862\pi$
$461$			73979.5i			0.348105i	−0.984736	+	0.174052i	$0.944314\pi$
$462$	−2374.10	−	5939.66i	−0.0111228	−	0.0278277i
$463$	−66987.3			−0.312486			−0.156243	−	0.987719i	$-0.549938\pi$
$463$	−66987.3			−0.312486			−0.156243	+	0.987719i	$0.549938\pi$
$464$	−28092.2	+	48657.2i	−0.130482	+	0.226001i
$465$	16712.2	−	9648.79i	0.0772907	−	0.0446238i
$466$	−49989.8	−	86584.9i	−0.230202	−	0.398722i
$467$	200947.	+	116017.i	0.921399	+	0.531970i	0.884081	−	0.467333i	$-0.154785\pi$
$467$	200947.	+	116017.i	0.921399	+	0.531970i	0.0373181	+	0.999303i	$0.488119\pi$
$468$		−	91036.7i		−	0.415647i
$469$	−100272.	+	40079.2i	−0.455864	+	0.182211i
$470$	28673.4			0.129803
$471$	−95611.1	+	165603.i	−0.430990	+	0.746496i
$472$	−55936.7	+	32295.0i	−0.251080	+	0.144961i
$473$	6252.46	+	10829.6i	0.0279466	+	0.0484049i
$474$	26514.5	+	15308.2i	0.118012	+	0.0681344i
$475$			255662.i			1.13313i
$476$	102274.	−	129906.i	0.451390	−	0.573342i
$477$	48588.7			0.213549
$478$	20355.5	−	35256.8i	0.0890895	−	0.154308i
$479$	−190568.	+	110024.i	−0.830575	+	0.479532i	−0.854049	−	0.520192i	$-0.825860\pi$
$479$	−190568.	+	110024.i	−0.830575	+	0.479532i	0.0234748	+	0.999724i	$0.492527\pi$
$480$	2411.79	+	4177.34i	0.0104678	+	0.0181308i
$481$	−89068.2	−	51423.5i	−0.384975	−	0.222265i
$482$		−	21213.0i		−	0.0913079i
$483$	−205728.	−	29694.3i	−0.881861	−	0.127286i
$484$	−116323.			−0.496565
$485$	18444.1	−	31946.1i	0.0784105	−	0.135811i
$486$	−149583.	+	86361.8i	−0.633300	+	0.365636i
$487$	−69828.1	−	120946.i	−0.294423	−	0.509956i	0.680427	−	0.732816i	$-0.261794\pi$
$487$	−69828.1	−	120946.i	−0.294423	−	0.509956i	−0.974851	+	0.222859i	$0.928461\pi$
$488$	−114327.	−	66006.5i	−0.480073	−	0.277170i
$489$		−	54140.8i		−	0.226416i
$490$	−38225.2	+	9229.00i	−0.159206	+	0.0384382i
$491$	−284872.			−1.18164			−0.590821	−	0.806802i	$-0.701196\pi$
$491$	−284872.			−1.18164			−0.590821	+	0.806802i	$0.701196\pi$
$492$	16461.2	−	28511.7i	0.0680036	−	0.117786i
$493$	320659.	−	185133.i	1.31932	−	0.761709i
$494$	116280.	+	201402.i	0.476485	+	0.825297i
$495$	3008.81	+	1737.13i	0.0122796	+	0.00708962i
$496$			46348.8i			0.188397i
$497$	−23857.7	+	165291.i	−0.0965862	+	0.669169i
$498$	−48811.6			−0.196818
$499$	156787.	−	271562.i	0.629663	−	1.09061i	−0.357957	−	0.933738i	$-0.616526\pi$
$499$	156787.	−	271562.i	0.629663	−	1.09061i	0.987619	−	0.156869i	$-0.0501402\pi$
$500$	−48802.0	+	28175.9i	−0.195208	+	0.112703i
$501$	31293.1	+	54201.2i	0.124673	+	0.215940i
$502$	111243.	+	64226.4i	0.441435	+	0.254862i
$503$			192865.i			0.762285i	0.924516	+	0.381143i	$0.124469\pi$
$503$			192865.i			0.762285i	−0.924516	+	0.381143i	$0.875531\pi$
$504$	52115.5	+	41030.3i	0.205166	+	0.161526i
$505$	52756.2			0.206867
$506$	13074.9	−	22646.4i	0.0510667	−	0.0884501i
$507$	−30377.9	+	17538.7i	−0.118179	+	0.0682309i
$508$	8466.81	+	14664.9i	0.0328089	+	0.0568267i
$509$	150044.	+	86628.1i	0.579141	+	0.334367i	0.760792	−	0.648996i	$-0.224811\pi$
$509$	150044.	+	86628.1i	0.579141	+	0.334367i	−0.181651	+	0.983363i	$0.558144\pi$
$510$		−	31788.2i		−	0.122215i
$511$	−170874.	−	427502.i	−0.654388	−	1.63718i
$512$	−11585.2			−0.0441942
$513$	140057.	−	242587.i	0.532196	−	0.921790i
$514$	126707.	−	73154.4i	0.479595	−	0.276894i
$515$	−46647.8	−	80796.3i	−0.175880	−	0.304633i
$516$	39751.5	+	22950.5i	0.149298	+	0.0861972i
$517$		−	17558.8i		−	0.0656922i
$518$	69581.4	−	27812.0i	0.259318	−	0.103651i
$519$	207786.			0.771403
$520$	−12461.7	+	21584.3i	−0.0460861	+	0.0798234i
$521$	−145761.	+	84155.4i	−0.536991	+	0.310032i	−0.743859	−	0.668337i	$-0.767006\pi$
$521$	−145761.	+	84155.4i	−0.536991	+	0.310032i	0.206868	+	0.978369i	$0.433673\pi$
$522$	74271.5	+	128642.i	0.272572	+	0.472108i
$523$	392069.	+	226361.i	1.43337	+	0.827558i	0.997376	−	0.0723902i	$-0.0230627\pi$
$523$	392069.	+	226361.i	1.43337	+	0.827558i	0.435996	+	0.899948i	$0.356396\pi$
$524$			48457.2i			0.176480i
$525$	82501.1	−	104790.i	0.299324	−	0.380192i
$526$	254089.			0.918362
$527$	152723.	−	264524.i	0.549900	−	0.952455i
$528$	2558.09	−	1476.91i	0.00917588	−	0.00529770i
$529$	−284958.	−	493562.i	−1.01828	−	1.76372i
$530$	−11520.1	−	6651.13i	−0.0410114	−	0.0236779i
$531$			170766.i			0.605638i
$532$	−167703.	−	24205.9i	−0.592541	−	0.0855259i
$533$	170110.			0.598790
$534$	−41416.2	+	71735.0i	−0.145241	+	0.251564i
$535$	−103059.	+	59501.4i	−0.360064	+	0.207883i
$536$	−24933.0	−	43185.2i	−0.0867851	−	0.150316i
$537$	−79117.3	−	45678.4i	−0.274361	−	0.158403i
$538$			67214.1i			0.232218i
$539$	5651.59	+	23408.1i	0.0194533	+	0.0805728i
$540$	30019.9			0.102949
$541$	7236.20	−	12533.5i	0.0247238	−	0.0428230i	−0.853399	−	0.521259i	$-0.825463\pi$
$541$	7236.20	−	12533.5i	0.0247238	−	0.0428230i	0.878123	+	0.478436i	$0.158796\pi$
$542$	−271449.	+	156721.i	−0.924038	+	0.533493i
$543$	49235.9	+	85279.0i	0.166987	+	0.289229i
$544$	66119.9	+	38174.4i	0.223426	+	0.128995i
$545$			82559.4i			0.277954i
$546$	17331.1	−	120074.i	0.0581355	−	0.402775i
$547$	−370524.			−1.23835			−0.619173	−	0.785255i	$-0.712532\pi$
$547$	−370524.			−1.23835			−0.619173	+	0.785255i	$0.712532\pi$
$548$	−11441.0	+	19816.4i	−0.0380981	+	0.0659878i
$549$	−302262.	+	174511.i	−1.00286	+	0.578999i
$550$	8389.27	+	14530.6i	0.0277331	+	0.0480352i
$551$	−328624.	−	189731.i	−1.08242	−	0.624937i
$552$		−	95986.6i		−	0.315016i
$553$	−90560.9	−	71298.2i	−0.296135	−	0.233146i
$554$	20145.1			0.0656373
$555$	7203.62	−	12477.0i	0.0233865	−	0.0405066i
$556$	−117545.	+	67864.9i	−0.380239	+	0.219531i
$557$	218641.	+	378697.i	0.704727	+	1.22062i	0.966790	+	0.255572i	$0.0822636\pi$
$557$	218641.	+	378697.i	0.704727	+	1.22062i	−0.262064	+	0.965051i	$0.584403\pi$
$558$	106122.	+	61269.5i	0.340829	+	0.196778i
$559$			237170.i			0.758990i
$560$	−6739.78	−	16861.9i	−0.0214917	−	0.0537689i
$561$	−19466.2			−0.0618523
$562$	127575.	−	220967.i	0.403918	−	0.699607i
$563$	−3518.41	+	2031.36i	−0.0111002	+	0.00640869i	−0.505540	−	0.862803i	$-0.668707\pi$
$563$	−3518.41	+	2031.36i	−0.0111002	+	0.00640869i	0.494440	+	0.869212i	$0.335373\pi$
$564$	−32226.0	−	55817.1i	−0.101309	−	0.175473i
$565$	−51675.2	−	29834.7i	−0.161877	−	0.0934597i
$566$			204918.i			0.639656i
$567$	84790.6	−	33891.1i	0.263743	−	0.105419i
$568$	−77119.6			−0.239039
$569$	−216682.	+	375304.i	−0.669266	+	1.15920i	0.308844	+	0.951113i	$0.400058\pi$
$569$	−216682.	+	375304.i	−0.669266	+	1.15920i	−0.978110	+	0.208089i	$0.933276\pi$
$570$	−28213.2	+	16288.9i	−0.0868367	+	0.0501352i
$571$	−23818.3	−	41254.5i	−0.0730530	−	0.126532i	0.827185	−	0.561930i	$-0.189941\pi$
$571$	−23818.3	−	41254.5i	−0.0730530	−	0.126532i	−0.900238	+	0.435398i	$0.856608\pi$
$572$	13217.6	+	7631.18i	0.0403981	+	0.0233238i
$573$			53500.0i			0.162946i
$574$	−76668.5	+	97382.1i	−0.232698	+	0.295567i
$575$	545230.			1.64909
$576$	−15314.8	+	26526.0i	−0.0461600	+	0.0799515i
$577$	20898.1	−	12065.5i	0.0627703	−	0.0362404i	−0.468286	−	0.883577i	$-0.655128\pi$
$577$	20898.1	−	12065.5i	0.0627703	−	0.0362404i	0.531057	+	0.847336i	$0.321795\pi$
$578$	−133459.	−	231158.i	−0.399478	−	0.691916i
$579$	209414.	+	120905.i	0.624668	+	0.360652i
$580$		−	40667.0i		−	0.120889i
$581$	181873.	+	26251.1i	0.538786	+	0.0777671i
$582$	−82917.3			−0.244793
$583$	−4072.97	+	7054.59i	−0.0119832	+	0.0207556i
$584$	184117.	−	106300.i	0.539842	−	0.311678i
$585$	32946.7	+	57065.4i	0.0962721	+	0.166748i
$586$	−218416.	−	126102.i	−0.636046	−	0.367221i
$587$		−	680260.i		−	1.97423i	−0.160003	−	0.987117i	$-0.551150\pi$
$587$		−	680260.i		−	1.97423i	0.160003	−	0.987117i	$-0.448850\pi$
$588$	60927.0	+	64038.7i	0.176220	+	0.185220i
$589$	−313034.			−0.902320
$590$	23375.6	−	40487.6i	0.0671518	−	0.116310i
$591$	−218440.	+	126116.i	−0.625399	+	0.361075i
$592$	17301.6	+	29967.3i	0.0493677	+	0.0855074i
$593$	305380.	+	176311.i	0.868422	+	0.501383i	0.866823	−	0.498615i	$-0.166158\pi$
$593$	305380.	+	176311.i	0.868422	+	0.501383i	0.00159823	+	0.999999i	$0.499491\pi$
$594$		−	18383.4i		−	0.0521017i
$595$	−17095.9	+	118444.i	−0.0482900	+	0.334563i
$596$	−119281.			−0.335798
$597$	13743.0	−	23803.6i	0.0385596	−	0.0667872i
$598$	429515.	−	247981.i	1.20109	−	0.693450i
$599$	191298.	+	331338.i	0.533159	+	0.923458i	0.999250	+	0.0387216i	$0.0123285\pi$
$599$	191298.	+	331338.i	0.533159	+	0.923458i	−0.466091	+	0.884737i	$0.654338\pi$
$600$	53336.8	+	30794.0i	0.148158	+	0.0855389i
$601$		−	8474.87i		−	0.0234630i	−0.999931	−	0.0117315i	$-0.996266\pi$
$601$		−	8474.87i		−	0.0234630i	0.999931	−	0.0117315i	$-0.00373434\pi$
$602$	−135772.	−	106893.i	−0.374642	−	0.294954i
$603$	−131838.			−0.362582
$604$	8645.79	−	14974.9i	0.0236990	−	0.0410479i
$605$	72916.1	−	42098.1i	0.199211	−	0.115014i
$606$	−59292.7	−	102698.i	−0.161457	−	0.279651i
$607$	−192303.	−	111026.i	−0.521926	−	0.301334i	0.215796	−	0.976438i	$-0.430765\pi$
$607$	−192303.	−	111026.i	−0.521926	−	0.301334i	−0.737722	+	0.675104i	$0.764099\pi$
$608$		−	78245.2i		−	0.211666i
$609$	73470.8	+	183813.i	0.198098	+	0.495612i
$610$	95552.6			0.256793
$611$	166511.	−	288406.i	0.446027	−	0.772542i
$612$	174811.	−	100927.i	0.466730	−	0.269467i
$613$	−6570.21	−	11379.9i	−0.0174847	−	0.0302844i	0.857151	−	0.515066i	$-0.172233\pi$
$613$	−6570.21	−	11379.9i	−0.0174847	−	0.0302844i	−0.874635	+	0.484781i	$0.838899\pi$
$614$	−277063.	−	159962.i	−0.734922	−	0.424307i
$615$			23829.7i			0.0630039i
$616$	−10325.8	+	4127.26i	−0.0272121	+	0.0108768i
$617$	−235797.			−0.619394			−0.309697	−	0.950835i	$-0.600228\pi$
$617$	−235797.			−0.619394			−0.309697	+	0.950835i	$0.600228\pi$
$618$	−104855.	+	181614.i	−0.274544	+	0.475523i
$619$	535169.	−	308980.i	1.39672	−	0.806397i	0.402673	−	0.915344i	$-0.368081\pi$
$619$	535169.	−	308980.i	1.39672	−	0.806397i	0.994048	+	0.108947i	$0.0347478\pi$
$620$	−16773.9	−	29053.3i	−0.0436366	−	0.0755808i
$621$	−517346.	−	298690.i	−1.34152	−	0.774528i
$622$			184821.i			0.477718i
$623$	192897.	−	245012.i	0.496993	−	0.631265i
$624$	56022.7			0.143878
$625$	−164440.	+	284819.i	−0.420967	+	0.729137i
$626$	4798.21	−	2770.25i	0.0122442	−	0.00706919i
$627$	9974.88	+	17277.0i	0.0253731	+	0.0439474i
$628$	287893.	+	166215.i	0.729981	+	0.421455i
$629$		−	228041.i		−	0.576384i
$630$	−47517.2	−	6858.51i	−0.119721	−	0.0172802i
$631$	453628.			1.13931			0.569653	−	0.821885i	$-0.307077\pi$
$631$	453628.			1.13931			0.569653	+	0.821885i	$0.307077\pi$
$632$	26612.5	−	46094.1i	0.0666271	−	0.115402i
$633$	12126.5	−	7001.24i	0.0302641	−	0.0174730i
$634$	−121836.	−	211026.i	−0.303108	−	0.524999i
$635$	−10614.7	−	6128.38i	−0.0263244	−	0.0151984i
$636$			29900.8i			0.0739211i
$637$	−129152.	+	438076.i	−0.318290	+	1.07962i
$638$	−24903.4			−0.0611810
$639$	−101946.	+	176576.i	−0.249672	+	0.432444i
$640$	7262.09	−	4192.77i	0.0177297	−	0.0102363i
$641$	72469.1	+	125520.i	0.176375	+	0.305490i	0.940636	−	0.339416i	$-0.110230\pi$
$641$	72469.1	+	125520.i	0.176375	+	0.305490i	−0.764261	+	0.644907i	$0.776896\pi$
$642$	231657.	+	133747.i	0.562050	+	0.324500i
$643$		−	238775.i		−	0.577520i	−0.957401	−	0.288760i	$-0.906757\pi$
$643$		−	238775.i		−	0.577520i	0.957401	−	0.288760i	$-0.0932430\pi$
$644$	−51622.1	+	357648.i	−0.124470	+	0.862351i
$645$	−33223.7			−0.0798599
$646$	−257825.	+	446566.i	−0.617817	+	1.07009i
$647$	28818.4	−	16638.3i	0.0688432	−	0.0397466i	−0.465183	−	0.885214i	$-0.654012\pi$
$647$	28818.4	−	16638.3i	0.0688432	−	0.0397466i	0.534026	+	0.845468i	$0.320678\pi$
$648$	21083.4	+	36517.6i	0.0502101	+	0.0869665i
$649$	−24793.5	−	14314.5i	−0.0588639	−	0.0339851i
$650$			318224.i			0.753193i
$651$	128306.	+	101015.i	0.302751	+	0.238355i
$652$	−94121.0			−0.221407
$653$	−38782.2	+	67172.7i	−0.0909507	+	0.157531i	−0.907911	−	0.419162i	$-0.862324\pi$
$653$	−38782.2	+	67172.7i	−0.0909507	+	0.157531i	0.816961	+	0.576693i	$0.195657\pi$
$654$	160714.	−	92788.4i	0.375750	−	0.216939i
$655$	−17536.9	−	30374.9i	−0.0408763	−	0.0707998i
$656$	−49566.0	−	28617.0i	−0.115180	−	0.0664991i
$657$		−	562080.i		−	1.30217i
$658$	90056.2	+	225307.i	0.207999	+	0.520383i
$659$	−762599.			−1.75600			−0.878001	−	0.478658i	$-0.841123\pi$
$659$	−762599.			−1.75600			−0.878001	+	0.478658i	$0.841123\pi$
$660$	−1069.01	+	1851.58i	−0.00245410	+	0.00425063i
$661$	−432725.	+	249834.i	−0.990396	+	0.571805i	−0.905393	−	0.424575i	$-0.860423\pi$
$661$	−432725.	+	249834.i	−0.990396	+	0.571805i	−0.0850035	+	0.996381i	$0.527090\pi$
$662$	−128159.	−	221978.i	−0.292438	−	0.506518i
$663$	−319736.	−	184600.i	−0.727385	−	0.419956i
$664$			84856.5i			0.192464i
$665$	113883.	−	45519.6i	0.257524	−	0.102933i
$666$	91485.5			0.206255
$667$	−404626.	+	700832.i	−0.909498	+	1.57530i
$668$	94225.9	−	54401.3i	0.211163	−	0.121915i
$669$	−96878.8	−	167799.i	−0.216459	−	0.374919i
$670$	31258.0	+	18046.8i	0.0696324	+	0.0402023i
$671$		−	58513.8i		−	0.129961i
$672$	−25249.5	+	32071.1i	−0.0559131	+	0.0710192i
$673$	601790.			1.32866			0.664332	−	0.747438i	$-0.268716\pi$
$673$	601790.			1.32866			0.664332	+	0.747438i	$0.268716\pi$
$674$	−37048.9	+	64170.6i	−0.0815559	+	0.141259i
$675$	331945.	−	191649.i	0.728549	−	0.420628i
$676$	30490.1	+	52810.4i	0.0667214	+	0.115565i
$677$	−140213.	−	80951.9i	−0.305922	−	0.176624i	0.339178	−	0.940722i	$-0.389851\pi$
$677$	−140213.	−	80951.9i	−0.305922	−	0.176624i	−0.645100	+	0.764098i	$0.723184\pi$
$678$			134125.i			0.291776i
$679$	308952.	+	44593.3i	0.670117	+	0.0967231i
$680$	−55262.1			−0.119512
$681$	212119.	−	367401.i	0.457389	−	0.792220i
$682$	−17791.4	+	10271.9i	−0.0382509	+	0.0220842i
$683$	6717.15	+	11634.4i	0.0143994	+	0.0249404i	0.873135	−	0.487478i	$-0.162083\pi$
$683$	6717.15	+	11634.4i	0.0143994	+	0.0249404i	−0.858736	+	0.512418i	$0.828750\pi$
$684$	−179153.	−	103434.i	−0.382924	−	0.221081i
$685$		−	16562.3i		−	0.0352971i
$686$	−192575.	−	271377.i	−0.409215	−	0.576666i
$687$	−110274.			−0.233646
$688$	39898.3	−	69105.8i	0.0842902	−	0.145995i
$689$	−133798.	+	77248.5i	−0.281846	+	0.162724i
$690$	34738.1	+	60168.2i	0.0729640	+	0.126377i
$691$	−213194.	−	123088.i	−0.446497	−	0.257785i	0.259853	−	0.965648i	$-0.416326\pi$
$691$	−213194.	−	123088.i	−0.446497	−	0.257785i	−0.706350	+	0.707863i	$0.749659\pi$
$692$		−	361225.i		−	0.754337i
$693$	−4199.96	+	29098.2i	−0.00874539	+	0.0605898i
$694$	454417.			0.943487
$695$	49121.4	−	85080.8i	0.101695	−	0.176142i
$696$	−79164.5	+	45705.6i	−0.163422	+	0.0943520i
$697$	188591.	+	326649.i	0.388199	+	0.672381i
$698$	44385.3	+	25625.8i	0.0911020	+	0.0525978i
$699$		−	162665.i		−	0.332920i
$700$	−182173.	−	143424.i	−0.371781	−	0.292702i
$701$	750473.			1.52721			0.763605	−	0.645683i	$-0.223427\pi$
$701$	750473.			1.52721			0.763605	+	0.645683i	$0.223427\pi$
$702$	174331.	−	301949.i	0.353752	−	0.612717i
$703$	−202395.	+	116853.i	−0.409533	+	0.236444i
$704$	−2567.54	−	4447.10i	−0.00518049	−	0.00897288i
$705$	40401.1	+	23325.6i	0.0812859	+	0.0469304i
$706$			37418.6i			0.0750720i
$707$	165694.	+	414543.i	0.331489	+	0.829336i
$708$	−105087.			−0.209644
$709$	297668.	−	515576.i	0.592161	−	1.02565i	−0.401780	−	0.915736i	$-0.631608\pi$
$709$	297668.	−	515576.i	0.592161	−	1.02565i	0.993941	−	0.109916i	$-0.0350583\pi$
$710$	48341.6	−	27910.1i	0.0958969	−	0.0553661i
$711$	−70359.2	−	121866.i	−0.139182	−	0.241070i
$712$	124708.	+	72000.0i	0.245999	+	0.142027i
$713$			667584.i			1.31319i
$714$	249782.	−	99839.0i	0.489965	−	0.195841i
$715$	−11047.1			−0.0216091
$716$	−79409.5	+	137541.i	−0.154898	+	0.268292i
$717$	57362.3	−	33118.1i	0.111580	−	0.0644210i
$718$	−152360.	−	263895.i	−0.295544	−	0.511897i
$719$	−23147.3	−	13364.1i	−0.0447757	−	0.0258513i	0.477445	−	0.878662i	$-0.341563\pi$
$719$	−23147.3	−	13364.1i	−0.0447757	−	0.0258513i	−0.522221	+	0.852810i	$0.674896\pi$
$720$		−	22170.1i		−	0.0427663i
$721$	488364.	−	620305.i	0.939449	−	1.19326i
$722$	159855.			0.306656
$723$	17256.6	−	29889.4i	0.0330126	−	0.0571795i
$724$	148253.	−	85594.0i	0.282831	−	0.163292i
$725$	−259621.	−	449676.i	−0.493927	−	0.855507i
$726$	−163901.	−	94628.1i	−0.310962	−	0.179534i
$727$			514869.i			0.974154i	0.873359	+	0.487077i	$0.161937\pi$
$727$			514869.i			0.974154i	−0.873359	+	0.487077i	$0.838063\pi$
$728$	−208742.	−	30129.3i	−0.393864	−	0.0568494i
$729$	−130073.			−0.244755
$730$	−76941.0	+	133266.i	−0.144382	+	0.250077i
$731$	−455419.	+	262936.i	−0.852269	+	0.492058i
$732$	−107392.	−	186008.i	−0.200423	−	0.347143i
$733$	209395.	+	120894.i	0.389725	+	0.225008i	0.682041	−	0.731314i	$-0.261092\pi$
$733$	209395.	+	120894.i	0.389725	+	0.225008i	−0.292316	+	0.956322i	$0.594426\pi$
$734$		−	199198.i		−	0.369737i
$735$	−61367.5	−	18092.2i	−0.113596	−	0.0334901i
$736$	−166868.			−0.308047
$737$	11051.4	−	19141.5i	0.0203461	−	0.0352405i
$738$	−131045.	+	75658.8i	−0.240607	+	0.138914i
$739$	335761.	+	581555.i	0.614811	+	1.06488i	0.990418	+	0.138105i	$0.0441010\pi$
$739$	335761.	+	581555.i	0.614811	+	1.06488i	−0.375607	+	0.926779i	$0.622566\pi$
$740$	−21690.7	−	12523.1i	−0.0396104	−	0.0228691i
$741$			378370.i			0.689097i
$742$	16080.8	−	111411.i	0.0292079	−	0.202358i
$743$	−134542.			−0.243714			−0.121857	−	0.992548i	$-0.538885\pi$
$743$	−134542.			−0.243714			−0.121857	+	0.992548i	$0.538885\pi$
$744$	−37704.4	+	65305.9i	−0.0681155	+	0.117979i
$745$	74770.0	−	43168.5i	0.134715	−	0.0777775i
$746$	270190.	+	467983.i	0.485503	+	0.840916i
$747$	194291.	+	112174.i	0.348185	+	0.201025i
$748$			33841.0i			0.0604840i
$749$	−791228.	−	622930.i	−1.41039	−	1.11039i
$750$	−91683.4			−0.162993
$751$	−223281.	+	386733.i	−0.395887	+	0.685696i	−0.993214	−	0.116302i	$-0.962896\pi$
$751$	−223281.	+	386733.i	−0.395887	+	0.685696i	0.597327	+	0.801998i	$0.296229\pi$
$752$	−97035.2	+	56023.3i	−0.171591	+	0.0990679i
$753$	104495.	+	180991.i	0.184292	+	0.319203i
$754$	−409041.	−	236160.i	−0.719490	−	0.415398i
$755$			12515.9i			0.0219567i
$756$	94285.1	+	235887.i	0.164968	+	0.412725i
$757$	−939360.			−1.63923			−0.819616	−	0.572913i	$-0.805813\pi$
$757$	−939360.			−1.63923			−0.819616	+	0.572913i	$0.805813\pi$
$758$	106037.	−	183662.i	0.184552	−	0.319654i
$759$	36845.4	−	21272.7i	0.0639587	−	0.0369265i
$760$	28317.4	+	49047.2i	0.0490260	+	0.0849156i
$761$	858619.	+	495724.i	1.48262	+	0.855994i	0.999805	−	0.0197266i	$-0.00627957\pi$
$761$	858619.	+	495724.i	1.48262	+	0.855994i	0.482819	+	0.875720i	$0.339613\pi$
$762$			27550.7i			0.0474486i
$763$	−648727.	+	259299.i	−1.11433	+	0.445401i
$764$	93007.0			0.159341
$765$	−73052.3	+	126530.i	−0.124828	+	0.216208i
$766$	−315095.	+	181920.i	−0.537011	+	0.310044i
$767$	−271492.	−	470237.i	−0.461494	−	0.799330i
$768$	−16323.7	−	9424.50i	−0.0276756	−	0.0159785i
$769$		−	180922.i		−	0.305942i	−0.988231	−	0.152971i	$-0.951116\pi$
$769$		−	180922.i		−	0.305942i	0.988231	−	0.152971i	$-0.0488841\pi$
$770$	4978.93	−	6324.09i	0.00839759	−	0.0106664i
$771$	238042.			0.400447
$772$	210188.	−	364056.i	0.352673	−	0.610848i
$773$	−16688.7	+	9635.20i	−0.0279295	+	0.0161251i	−0.513900	−	0.857850i	$-0.671800\pi$
$773$	−16688.7	+	9635.20i	−0.0279295	+	0.0161251i	0.485970	+	0.873975i	$0.338466\pi$
$774$	−105485.	−	182705.i	−0.176079	−	0.304978i
$775$	−370955.	−	214171.i	−0.617616	−	0.356581i
$776$			144147.i			0.239377i
$777$	120666.	+	17416.6i	0.199867	+	0.0288483i
$778$	−74410.3			−0.122935
$779$	193275.	−	334763.i	0.318494	−	0.551648i
$780$	−35117.2	+	20274.9i	−0.0577206	+	0.0333250i
$781$	−17091.4	−	29603.1i	−0.0280204	−	0.0485328i
$782$	952357.	+	549844.i	1.55735	+	0.899137i
$783$			568905.i			0.927931i
$784$	111328.	−	105918.i	0.181122	−	0.172321i
$785$	−240617.			−0.390469
$786$	−39419.5	+	68276.6i	−0.0638067	+	0.110516i
$787$	240896.	−	139081.i	0.388938	−	0.224553i	−0.292762	−	0.956185i	$-0.594574\pi$
$787$	240896.	−	139081.i	0.388938	−	0.224553i	0.681700	+	0.731632i	$0.261241\pi$
$788$	219247.	+	379747.i	0.353086	+	0.611564i
$789$	358013.	+	206699.i	0.575103	+	0.332036i
$790$			38524.8i			0.0617286i
$791$	72132.9	−	499752.i	0.115287	−	0.798732i
$792$	−13576.3			−0.0216437
$793$	554890.	−	961098.i	0.882390	−	1.52834i
$794$	−215619.	+	124488.i	−0.342016	+	0.197463i
$795$	−10821.3	−	18743.0i	−0.0171216	−	0.0296555i
$796$	−41381.3	−	23891.5i	−0.0653097	−	0.0377066i
$797$		−	60214.6i		−	0.0947950i	−0.998876	−	0.0473975i	$-0.984907\pi$
$797$		−	60214.6i		−	0.0947950i	0.998876	−	0.0473975i	$-0.0150927\pi$
$798$	−216604.	−	170532.i	−0.340143	−	0.267793i
$799$	738406.			1.15665
$800$	53533.8	−	92723.2i	0.0836465	−	0.144880i
$801$	329708.	−	190357.i	0.513883	−	0.296690i
$802$	374200.	+	648134.i	0.581775	+	1.00766i
$803$	81608.3	+	47116.6i	0.126562	+	0.0730706i
$804$		−	81131.2i		−	0.125509i
$805$	−97076.3	−	242870.i	−0.149803	−	0.374786i
$806$	−389636.			−0.599775
$807$	−54678.1	+	94705.3i	−0.0839588	+	0.145421i
$808$	−178535.	+	103077.i	−0.273464	+	0.157885i
$809$	−35236.9	−	61032.2i	−0.0538395	−	0.0932528i	0.837850	−	0.545901i	$-0.183813\pi$
$809$	−35236.9	−	61032.2i	−0.0538395	−	0.0932528i	−0.891689	+	0.452648i	$0.850479\pi$
$810$	−26431.9	−	15260.4i	−0.0402863	−	0.0232593i
$811$		−	1.08434e6i		−	1.64863i	−0.566133	−	0.824314i	$-0.691561\pi$
$811$		−	1.08434e6i		−	1.64863i	0.566133	−	0.824314i	$-0.308439\pi$
$812$	319549.	−	127725.i	0.484647	−	0.193715i
$813$	−509966.			−0.771542
$814$	−7668.81	+	13282.8i	−0.0115739	+	0.0200466i
$815$	58998.8	−	34063.0i	0.0888235	−	0.0512823i
$816$	62109.1	+	107576.i	0.0932771	+	0.161561i
$817$	466732.	+	269468.i	0.699235	+	0.403704i
$818$		−	396463.i		−	0.592511i
$819$	−344925.	+	438114.i	−0.514230	+	0.653160i
$820$	41426.6			0.0616101
$821$	323845.	−	560916.i	0.480453	−	0.832169i	−0.519295	−	0.854595i	$-0.673806\pi$
$821$	323845.	−	560916.i	0.480453	−	0.832169i	0.999749	+	0.0224257i	$0.00713892\pi$
$822$	−32241.0	+	18614.3i	−0.0477161	+	0.0275489i
$823$	−539512.	−	934463.i	−0.796529	−	1.37963i	−0.921863	−	0.387515i	$-0.873334\pi$
$823$	−539512.	−	934463.i	−0.796529	−	1.37963i	0.125334	−	0.992115i	$-0.460000\pi$
$824$	315726.	+	182285.i	0.465003	+	0.268470i
$825$			27298.4i			0.0401079i
$826$	391557.	+	56516.3i	0.573898	+	0.0828350i
$827$	9026.16			0.0131975			0.00659875	−	0.999978i	$-0.497900\pi$
$827$	9026.16			0.0131975			0.00659875	+	0.999978i	$0.497900\pi$
$828$	−220586.	+	382066.i	−0.321749	+	0.557286i
$829$	−654736.	+	378012.i	−0.952702	+	0.550043i	−0.893919	−	0.448228i	$-0.852055\pi$
$829$	−654736.	+	378012.i	−0.952702	+	0.550043i	−0.0587830	+	0.998271i	$0.518722\pi$
$830$	−30710.1	−	53191.4i	−0.0445784	−	0.0772121i
$831$	28384.7	+	16387.9i	0.0411038	+	0.0237313i
$832$		−	97392.5i		−	0.140695i
$833$	−984388.	+	237668.i	−1.41865	+	0.342516i
$834$	−220830.			−0.317487
$835$	−39376.4	+	68201.9i	−0.0564758	+	0.0978190i
$836$	30035.2	−	17340.8i	0.0429752	−	0.0248117i
$837$	234656.	+	406436.i	0.334950	+	0.580151i
$838$	−782390.	−	451713.i	−1.11413	−	0.643242i
$839$			654438.i			0.929704i	0.885388	+	0.464852i	$0.153893\pi$
$839$			654438.i			0.929704i	−0.885388	+	0.464852i	$0.846107\pi$
$840$	4220.63	−	29241.4i	0.00598162	−	0.0414419i
$841$	63396.2			0.0896337
$842$	446504.	−	773368.i	0.629798	−	1.09084i
$843$	359509.	−	207563.i	0.505888	−	0.292075i
$844$	−12171.3	−	21081.3i	−0.0170864	−	0.0295946i
$845$	−38224.8	−	22069.1i	−0.0535343	−	0.0309080i
$846$			296234.i			0.413898i
$847$	559806.	+	440733.i	0.780316	+	0.614340i
$848$	51981.0			0.0722857
$849$	−166699.	+	288731.i	−0.231269	+	0.400570i
$850$	−611062.	+	352797.i	−0.845761	+	0.488300i
$851$	249203.	+	431633.i	0.344108	+	0.596013i
$852$	−108662.	−	62736.2i	−0.149692	−	0.0864249i
$853$		−	123790.i		−	0.170133i	−0.996375	−	0.0850664i	$-0.972890\pi$
$853$		−	123790.i		−	0.170133i	0.996375	−	0.0850664i	$-0.0271102\pi$
$854$	300107.	+	750824.i	0.411491	+	1.02949i
$855$	149734.			0.204827
$856$	232512.	−	402723.i	0.317321	−	0.549615i
$857$	−150023.	+	86615.8i	−0.204266	+	0.117933i	−0.598644	−	0.801015i	$-0.704293\pi$
$857$	−150023.	+	86615.8i	−0.204266	+	0.117933i	0.394378	+	0.918948i	$0.370960\pi$
$858$	12415.8	+	21504.8i	0.0168656	+	0.0292120i
$859$	231499.	+	133656.i	0.313735	+	0.181135i	0.648597	−	0.761132i	$-0.275356\pi$
$859$	231499.	+	133656.i	0.313735	+	0.181135i	−0.334862	+	0.942267i	$0.608690\pi$
$860$			57757.7i			0.0780932i
$861$	−187246.	+	74843.1i	−0.252585	+	0.100959i
$862$	−476677.			−0.641519
$863$	−619521.	+	1.07304e6i	−0.831830	+	1.44077i	0.0647550	+	0.997901i	$0.479373\pi$
$863$	−619521.	+	1.07304e6i	−0.831830	+	1.44077i	−0.896585	+	0.442871i	$0.853960\pi$
$864$	−101592.	+	58654.1i	−0.136092	+	0.0785725i
$865$	130730.	+	226430.i	0.174720	+	0.302623i
$866$	−41896.9	−	24189.2i	−0.0558658	−	0.0322541i
$867$		−	434272.i		−	0.577728i
$868$	175609.	−	223054.i	0.233081	−	0.296053i
$869$	23591.6			0.0312404
$870$	33082.3	−	57300.2i	0.0437076	−	0.0757038i
$871$	363041.	−	209602.i	0.478541	−	0.276286i
$872$	−161308.	−	279393.i	−0.212140	−	0.367437i
$873$	330045.	+	190552.i	0.433057	+	0.250025i
$874$		−	1.12700e6i		−	1.47537i
$875$	341614.	+	49307.8i	0.446190	+	0.0644020i
$876$	345896.			0.450752
$877$	−348961.	+	604419.i	−0.453710	+	0.785848i	−0.998613	−	0.0526507i	$-0.983233\pi$
$877$	−348961.	+	604419.i	−0.453710	+	0.785848i	0.544903	+	0.838499i	$0.316566\pi$
$878$	543740.	−	313929.i	0.705347	−	0.407232i
$879$	−205166.	−	355359.i	−0.265539	−	0.459927i
$880$	3218.87	+	1858.41i	0.00415660	+	0.00239981i
$881$			1.44660e6i			1.86378i	0.362735	+	0.931892i	$0.381843\pi$
$881$			1.44660e6i			1.86378i	−0.362735	+	0.931892i	$0.618157\pi$
$882$	−95347.6	−	394917.i	−0.122567	−	0.507654i
$883$	−539049.			−0.691364			−0.345682	−	0.938352i	$-0.612352\pi$
$883$	−539049.			−0.691364			−0.345682	+	0.938352i	$0.612352\pi$
$884$	−320917.	+	555844.i	−0.410665	+	0.711293i
$885$	65872.8	−	38031.7i	0.0841045	−	0.0485578i
$886$	48409.5	+	83847.8i	0.0616685	+	0.106813i
$887$	−851540.	−	491637.i	−1.08233	−	0.624881i	−0.150803	−	0.988564i	$-0.548186\pi$
$887$	−851540.	−	491637.i	−1.08233	−	0.624881i	−0.931523	+	0.363683i	$0.881519\pi$
$888$			56298.9i			0.0713960i
$889$	14816.9	−	102655.i	0.0187480	−	0.129890i
$890$	−104229.			−0.131586
$891$	−9345.08	+	16186.1i	−0.0117714	+	0.0203886i
$892$	−291710.	+	168419.i	−0.366624	+	0.211671i
$893$	−378374.	−	655363.i	−0.474481	−	0.821825i
$894$	−168068.	−	97034.1i	−0.210286	−	0.121409i
$895$		−	114955.i		−	0.143510i
$896$	55754.0	+	43894.9i	0.0694480	+	0.0546761i
$897$	806921.			1.00287
$898$	−264750.	+	458560.i	−0.328309	+	0.568648i
$899$	550586.	−	317881.i	0.681249	−	0.393319i
$900$	−141535.	−	245146.i	−0.174735	−	0.302649i
$901$	−296669.	−	171282.i	−0.365445	−	0.210990i
$902$		−	25368.5i		−	0.0311804i
$903$	−104348.	−	261062.i	−0.127970	−	0.320161i
$904$	233169.			0.285321
$905$	−61954.0	+	107307.i	−0.0756436	+	0.131018i
$906$	24364.0	−	14066.6i	0.0296819	−	0.0171369i
$907$	−146541.	−	253816.i	−0.178133	−	0.308535i	0.763108	−	0.646271i	$-0.223672\pi$
$907$	−146541.	−	253816.i	−0.178133	−	0.308535i	−0.941241	+	0.337736i	$0.890339\pi$
$908$	−638707.	−	368758.i	−0.774694	−	0.447270i
$909$			545041.i			0.659631i
$910$	141752.	−	56658.7i	0.171177	−	0.0684201i
$911$	1.39546e6			1.68143			0.840716	−	0.541477i	$-0.182135\pi$
$911$	1.39546e6			1.68143			0.840716	+	0.541477i	$0.182135\pi$
$912$	63651.9	−	110248.i	0.0765282	−	0.132551i
$913$	−32573.0	+	18806.0i	−0.0390765	+	0.0225608i
$914$	209084.	+	362145.i	0.250282	+	0.433501i
$915$	134635.	+	77731.3i	0.160810	+	0.0928440i
$916$			191705.i			0.228477i
$917$	183597.	−	233200.i	0.218337	−	0.277326i
$918$	773081.			0.917360
$919$	430159.	−	745057.i	0.509328	−	0.882182i	−0.490613	−	0.871377i	$-0.663227\pi$
$919$	430159.	−	745057.i	0.509328	−	0.882182i	0.999942	−	0.0108051i	$-0.00343942\pi$
$920$	104599.	−	60390.4i	0.123581	−	0.0713498i
$921$	−260256.	−	450777.i	−0.306819	−	0.531425i
$922$	181212.	+	104623.i	0.213170	+	0.123074i
$923$		−	648314.i		−	0.760995i
$924$	−17906.6	−	2584.60i	−0.0209734	−	0.00302726i
$925$	−319793.			−0.373754
$926$	−94734.3	+	164085.i	−0.110480	+	0.191358i
$927$	834731.	−	481932.i	0.971375	−	0.560824i
$928$	79456.8	+	137623.i	0.0922646	+	0.159807i
$929$	−935631.	−	540187.i	−1.08411	−	0.625911i	−0.152108	−	0.988364i	$-0.548606\pi$
$929$	−935631.	−	540187.i	−1.08411	−	0.625911i	−0.932002	+	0.362453i	$0.881939\pi$
$930$		−	54581.8i		−	0.0631076i
$931$	715359.	+	751895.i	0.825325	+	0.867477i
$932$	−282785.			−0.325555
$933$	−150351.	+	260415.i	−0.172720	+	0.299160i
$934$	568364.	−	328145.i	0.651528	−	0.376160i
$935$	−12247.3	−	21212.9i	−0.0140093	−	0.0242648i
$936$	−222993.	−	128745.i	−0.254531	−	0.146953i
$937$		−	659462.i		−	0.751122i	−0.926798	−	0.375561i	$-0.877450\pi$
$937$		−	659462.i		−	0.751122i	0.926798	−	0.375561i	$-0.122550\pi$
$938$	−43632.8	+	302297.i	−0.0495915	+	0.343580i
$939$	9014.29			0.0102235
$940$	40550.3	−	70235.2i	0.0458922	−	0.0794876i
$941$	771364.	−	445347.i	0.871124	−	0.502944i	0.00340238	−	0.999994i	$-0.498917\pi$
$941$	771364.	−	445347.i	0.871124	−	0.502944i	0.867722	+	0.497051i	$0.165584\pi$
$942$	270429.	+	468397.i	0.304756	+	0.527852i
$943$	−713923.	−	412184.i	−0.802838	−	0.463519i
$944$			182688.i			0.205006i
$945$	−144471.	−	113741.i	−0.161777	−	0.127366i
$946$	35369.2			0.0395224
$947$	−761268.	+	1.31855e6i	−0.848863	+	1.47027i	0.0333612	+	0.999443i	$0.489379\pi$
$947$	−761268.	+	1.31855e6i	−0.848863	+	1.47027i	−0.882224	+	0.470830i	$0.843954\pi$
$948$	74994.4	−	43298.1i	0.0834473	−	0.0481783i
$949$	893619.	+	1.54779e6i	0.992248	+	1.71862i
$950$	626241.	+	361560.i	0.693896	+	0.400621i
$951$		−	396451.i		−	0.438358i
$952$	−173565.	−	434233.i	−0.191508	−	0.479126i
$953$	−464150.			−0.511061			−0.255530	−	0.966801i	$-0.582250\pi$
$953$	−464150.			−0.511061			−0.255530	+	0.966801i	$0.582250\pi$
$954$	68714.8	−	119018.i	0.0755011	−	0.130772i
$955$	−58300.5	+	33659.8i	−0.0639242	+	0.0369067i
$956$	−57574.1	−	99721.3i	−0.0629958	−	0.109112i
$957$	−35089.1	−	20258.7i	−0.0383132	−	0.0221201i
$958$			622392.i			0.678161i
$959$	130141.	−	52018.1i	0.141507	−	0.0565610i
$960$	13643.1			0.0148038
$961$	−199528.	+	345592.i	−0.216051	+	0.374212i
$962$	−251923.	+	145448.i	−0.272218	+	0.157165i
$963$	−614726.	−	1.06474e6i	−0.662871	−	1.14813i
$964$	−51961.1	−	29999.8i	−0.0559145	−	0.0322822i
$965$			304273.i			0.326745i
$966$	−363680.	+	461936.i	−0.389731	+	0.495025i
$967$	61596.4			0.0658723			0.0329361	−	0.999457i	$-0.489514\pi$
$967$	61596.4			0.0658723			0.0329361	+	0.999457i	$0.489514\pi$
$968$	−164506.	+	284933.i	−0.175562	+	0.304083i
$969$	−726555.	+	419477.i	−0.773787	+	0.446746i
$970$	−52167.8	−	90357.3i	−0.0554446	−	0.0960329i
$971$	−668830.	−	386149.i	−0.709377	−	0.409559i	0.101453	−	0.994840i	$-0.467651\pi$
$971$	−668830.	−	386149.i	−0.709377	−	0.409559i	−0.810830	+	0.585281i	$0.800984\pi$
$972$			488536.i			0.517088i
$973$	822818.	+	118764.i	0.869117	+	0.125446i
$974$	−395007.			−0.416378
$975$	−258873.	+	448381.i	−0.272319	+	0.471670i
$976$	−323364.	+	186695.i	−0.339463	+	0.195989i
$977$	−501672.	−	868921.i	−0.525570	−	0.910314i	−0.999556	−	0.0297817i	$-0.990519\pi$
$977$	−501672.	−	868921.i	−0.525570	−	0.910314i	0.473987	−	0.880532i	$-0.342815\pi$
$978$	−132617.	−	76566.7i	−0.138651	−	0.0800501i
$979$			63826.9i			0.0665945i
$980$	−31452.3	+	106684.i	−0.0327492	+	0.111083i
$981$	−852946.			−0.886306
$982$	−402869.	+	697790.i	−0.417774	+	0.723606i
$983$	−453001.	+	261540.i	−0.468805	+	0.270665i	−0.715739	−	0.698367i	$-0.753910\pi$
$983$	−453001.	+	261540.i	−0.468805	+	0.270665i	0.246934	+	0.969032i	$0.420577\pi$
$984$	−46559.3	−	80643.2i	−0.0480858	−	0.0832870i
$985$	−274865.	−	158694.i	−0.283301	−	0.163564i
$986$		−	1.04727e6i		−	1.07722i
$987$	−56395.6	+	390720.i	−0.0578909	+	0.401080i
$988$	657776.			0.673852
$989$	574674.	−	995364.i	0.587528	−	1.01763i
$990$	8510.19	−	4913.36i	0.00868298	−	0.00501312i
$991$	837744.	+	1.45102e6i	0.853029	+	1.47749i	0.878461	+	0.477814i	$0.158571\pi$
$991$	837744.	+	1.45102e6i	0.853029	+	1.47749i	−0.0254316	+	0.999677i	$0.508096\pi$
$992$	113531.	+	65547.1i	0.115369	+	0.0666085i
$993$		−	417026.i		−	0.422926i
$994$	371138.	+	292195.i	0.375632	+	0.295734i
$995$	34585.9			0.0349344
$996$	−69030.1	+	119564.i	−0.0695857	+	0.120526i
$997$	−568548.	+	328251.i	−0.571975	+	0.330230i	−0.757938	−	0.652327i	$-0.773793\pi$
$997$	−568548.	+	328251.i	−0.571975	+	0.330230i	0.185963	+	0.982557i	$0.440460\pi$
$998$	−443460.	−	768094.i	−0.445239	−	0.771176i
$999$	303438.	+	175190.i	0.304046	+	0.175541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.5.d.a.5.2	yes	4
3.2	odd	2		126.5.n.a.19.1		4
4.3	odd	2		112.5.s.b.33.1		4
5.2	odd	4		350.5.i.a.299.4		8
5.3	odd	4		350.5.i.a.299.1		8
5.4	even	2		350.5.k.a.201.1		4
7.2	even	3		98.5.b.b.97.2		4
7.3	odd	6	inner	14.5.d.a.3.2	✓	4
7.4	even	3		98.5.d.a.31.2		4
7.5	odd	6		98.5.b.b.97.1		4
7.6	odd	2		98.5.d.a.19.2		4
21.2	odd	6		882.5.c.b.685.4		4
21.5	even	6		882.5.c.b.685.3		4
21.17	even	6		126.5.n.a.73.1		4
28.3	even	6		112.5.s.b.17.1		4
28.19	even	6		784.5.c.b.97.3		4
28.23	odd	6		784.5.c.b.97.2		4
35.3	even	12		350.5.i.a.199.4		8
35.17	even	12		350.5.i.a.199.1		8
35.24	odd	6		350.5.k.a.101.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.d.a.3.2	✓	4	7.3	odd	6	inner
14.5.d.a.5.2	yes	4	1.1	even	1	trivial
98.5.b.b.97.1		4	7.5	odd	6
98.5.b.b.97.2		4	7.2	even	3
98.5.d.a.19.2		4	7.6	odd	2
98.5.d.a.31.2		4	7.4	even	3
112.5.s.b.17.1		4	28.3	even	6
112.5.s.b.33.1		4	4.3	odd	2
126.5.n.a.19.1		4	3.2	odd	2
126.5.n.a.73.1		4	21.17	even	6
350.5.i.a.199.1		8	35.17	even	12
350.5.i.a.199.4		8	35.3	even	12
350.5.i.a.299.1		8	5.3	odd	4
350.5.i.a.299.4		8	5.2	odd	4
350.5.k.a.101.1		4	35.24	odd	6
350.5.k.a.201.1		4	5.4	even	2
784.5.c.b.97.2		4	28.23	odd	6
784.5.c.b.97.3		4	28.19	even	6
882.5.c.b.685.3		4	21.5	even	6
882.5.c.b.685.4		4	21.2	odd	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	14.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 - 2.44949i) q^{2} +(3.98528 - 2.30090i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(5.01472 + 2.89525i) q^{5} -13.0159i q^{6} +(-7.00000 + 48.4974i) q^{7} -22.6274 q^{8} +(-29.9117 + 51.8086i) q^{9} +O(q^{10})\)	\(q+(1.41421 - 2.44949i) q^{2} +(3.98528 - 2.30090i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(5.01472 + 2.89525i) q^{5} -13.0159i q^{6} +(-7.00000 + 48.4974i) q^{7} -22.6274 q^{8} +(-29.9117 + 51.8086i) q^{9} +(14.1838 - 8.18900i) q^{10} +(-5.01472 - 8.68575i) q^{11} +(-31.8823 - 18.4072i) q^{12} -190.220i q^{13} +(108.894 + 85.7321i) q^{14} +26.6468 q^{15} +(-32.0000 + 55.4256i) q^{16} +(365.265 - 210.886i) q^{17} +(84.6030 + 146.537i) q^{18} +(-374.338 - 216.124i) q^{19} -46.3240i q^{20} +(83.6909 + 209.382i) q^{21} -28.3675 q^{22} +(-460.911 + 798.322i) q^{23} +(-90.1766 + 52.0635i) q^{24} +(-295.735 - 512.228i) q^{25} +(-465.941 - 269.011i) q^{26} +648.042i q^{27} +(364.000 - 145.492i) q^{28} +877.882 q^{29} +(37.6842 - 65.2709i) q^{30} +(627.175 - 362.100i) q^{31} +(90.5097 + 156.767i) q^{32} +(-39.9701 - 23.0768i) q^{33} -1192.95i q^{34} +(-175.515 + 222.934i) q^{35} +478.587 q^{36} +(270.338 - 468.239i) q^{37} +(-1058.79 + 611.291i) q^{38} +(-437.677 - 758.079i) q^{39} +(-113.470 - 65.5120i) q^{40} +894.280i q^{41} +(631.236 + 91.1111i) q^{42} -1246.82 q^{43} +(-40.1177 + 69.4860i) q^{44} +(-299.997 + 173.204i) q^{45} +(1303.65 + 2257.99i) q^{46} +(1516.17 + 875.364i) q^{47} +294.516i q^{48} +(-2303.00 - 678.964i) q^{49} -1672.93 q^{50} +(970.455 - 1680.88i) q^{51} +(-1317.88 + 760.879i) q^{52} +(-406.101 - 703.388i) q^{53} +(1587.37 + 916.470i) q^{54} -58.0754i q^{55} +(158.392 - 1097.37i) q^{56} -1989.12 q^{57} +(1241.51 - 2150.36i) q^{58} +(2472.07 - 1427.25i) q^{59} +(-106.587 - 184.614i) q^{60} +(5052.57 + 2917.10i) q^{61} -2048.35i q^{62} +(-2303.20 - 1813.30i) q^{63} +512.000 q^{64} +(550.733 - 953.898i) q^{65} +(-113.053 + 65.2709i) q^{66} +(1101.89 + 1908.54i) q^{67} +(-2922.12 - 1687.08i) q^{68} +4242.05i q^{69} +(297.859 + 745.199i) q^{70} +3408.24 q^{71} +(676.824 - 1172.29i) q^{72} +(-8136.88 + 4697.83i) q^{73} +(-764.630 - 1324.38i) q^{74} +(-2357.17 - 1360.92i) q^{75} +3457.98i q^{76} +(456.339 - 182.401i) q^{77} -2475.88 q^{78} +(-1176.12 + 2037.09i) q^{79} +(-320.942 + 185.296i) q^{80} +(-931.765 - 1613.86i) q^{81} +(2190.53 + 1264.70i) q^{82} -3750.16i q^{83} +(1115.88 - 1417.36i) q^{84} +2442.26 q^{85} +(-1763.27 + 3054.07i) q^{86} +(3498.61 - 2019.92i) q^{87} +(113.470 + 196.536i) q^{88} +(-5511.35 - 3181.98i) q^{89} +979.787i q^{90} +(9225.16 + 1331.54i) q^{91} +7374.58 q^{92} +(1666.31 - 2886.14i) q^{93} +(4288.39 - 2475.90i) q^{94} +(-1251.47 - 2167.60i) q^{95} +(721.413 + 416.508i) q^{96} -6370.47i q^{97} +(-4920.05 + 4680.97i) q^{98} +599.995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 18 q^{3} - 16 q^{4} + 54 q^{5} - 28 q^{7} + 84 q^{9}+O(q^{10}) \) 4 * q - 18 * q^3 - 16 * q^4 + 54 * q^5 - 28 * q^7 + 84 * q^9	\( 4 q - 18 q^{3} - 16 q^{4} + 54 q^{5} - 28 q^{7} + 84 q^{9} - 96 q^{10} - 54 q^{11} + 144 q^{12} - 708 q^{15} - 128 q^{16} + 918 q^{17} + 576 q^{18} + 30 q^{19} - 378 q^{21} + 192 q^{22} - 486 q^{23} - 768 q^{24} - 572 q^{25} - 1728 q^{26} + 1456 q^{28} + 3240 q^{29} + 1152 q^{30} - 546 q^{31} + 1062 q^{33} - 1890 q^{35} - 1344 q^{36} - 446 q^{37} - 4320 q^{38} - 3312 q^{39} + 768 q^{40} + 5376 q^{42} + 2344 q^{43} - 432 q^{44} + 5724 q^{45} + 3840 q^{46} + 702 q^{47} - 9212 q^{49} - 3456 q^{50} + 318 q^{51} - 384 q^{52} + 2754 q^{53} - 1440 q^{54} - 17460 q^{57} + 384 q^{58} + 12366 q^{59} + 2832 q^{60} + 7686 q^{61} + 6468 q^{63} + 2048 q^{64} - 3024 q^{65} - 3456 q^{66} - 5062 q^{67} - 7344 q^{68} - 2016 q^{70} + 18792 q^{71} + 4608 q^{72} - 17274 q^{73} - 4320 q^{74} - 5220 q^{75} + 4914 q^{77} + 8832 q^{78} + 794 q^{79} - 3456 q^{80} - 4338 q^{81} + 9984 q^{82} - 5040 q^{84} + 10380 q^{85} - 10368 q^{86} - 12276 q^{87} - 768 q^{88} - 12474 q^{89} + 2688 q^{91} + 7776 q^{92} + 18918 q^{93} + 15168 q^{94} + 8910 q^{95} + 6144 q^{96} - 11448 q^{99}+O(q^{100}) \) 4 * q - 18 * q^3 - 16 * q^4 + 54 * q^5 - 28 * q^7 + 84 * q^9 - 96 * q^10 - 54 * q^11 + 144 * q^12 - 708 * q^15 - 128 * q^16 + 918 * q^17 + 576 * q^18 + 30 * q^19 - 378 * q^21 + 192 * q^22 - 486 * q^23 - 768 * q^24 - 572 * q^25 - 1728 * q^26 + 1456 * q^28 + 3240 * q^29 + 1152 * q^30 - 546 * q^31 + 1062 * q^33 - 1890 * q^35 - 1344 * q^36 - 446 * q^37 - 4320 * q^38 - 3312 * q^39 + 768 * q^40 + 5376 * q^42 + 2344 * q^43 - 432 * q^44 + 5724 * q^45 + 3840 * q^46 + 702 * q^47 - 9212 * q^49 - 3456 * q^50 + 318 * q^51 - 384 * q^52 + 2754 * q^53 - 1440 * q^54 - 17460 * q^57 + 384 * q^58 + 12366 * q^59 + 2832 * q^60 + 7686 * q^61 + 6468 * q^63 + 2048 * q^64 - 3024 * q^65 - 3456 * q^66 - 5062 * q^67 - 7344 * q^68 - 2016 * q^70 + 18792 * q^71 + 4608 * q^72 - 17274 * q^73 - 4320 * q^74 - 5220 * q^75 + 4914 * q^77 + 8832 * q^78 + 794 * q^79 - 3456 * q^80 - 4338 * q^81 + 9984 * q^82 - 5040 * q^84 + 10380 * q^85 - 10368 * q^86 - 12276 * q^87 - 768 * q^88 - 12474 * q^89 + 2688 * q^91 + 7776 * q^92 + 18918 * q^93 + 15168 * q^94 + 8910 * q^95 + 6144 * q^96 - 11448 * q^99

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