LMFDB - Embedded newform 21.5.f.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,5,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	21.f (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:	$2.17076922476$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	21.19
Dual form			21.5.f.b.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.50000 - 4.33013i) q^{2} +(4.50000 - 2.59808i) q^{3} +(-4.50000 - 7.79423i) q^{4} +(-1.50000 - 0.866025i) q^{5} -25.9808i q^{6} +(-45.5000 + 18.1865i) q^{7} +35.0000 q^{8} +(13.5000 - 23.3827i) q^{9} +O(q^{10})$	\(q+(2.50000 - 4.33013i) q^{2} +(4.50000 - 2.59808i) q^{3} +(-4.50000 - 7.79423i) q^{4} +(-1.50000 - 0.866025i) q^{5} -25.9808i q^{6} +(-45.5000 + 18.1865i) q^{7} +35.0000 q^{8} +(13.5000 - 23.3827i) q^{9} +(-7.50000 + 4.33013i) q^{10} +(74.5000 + 129.038i) q^{11} +(-40.5000 - 23.3827i) q^{12} +41.5692i q^{13} +(-35.0000 + 242.487i) q^{14} -9.00000 q^{15} +(159.500 - 276.262i) q^{16} +(-231.000 + 133.368i) q^{17} +(-67.5000 - 116.913i) q^{18} +(-309.000 - 178.401i) q^{19} +15.5885i q^{20} +(-157.500 + 200.052i) q^{21} +745.000 q^{22} +(280.000 - 484.974i) q^{23} +(157.500 - 90.9327i) q^{24} +(-311.000 - 538.668i) q^{25} +(180.000 + 103.923i) q^{26} -140.296i q^{27} +(346.500 + 272.798i) q^{28} +235.000 q^{29} +(-22.5000 + 38.9711i) q^{30} +(-1114.50 + 643.457i) q^{31} +(-517.500 - 896.336i) q^{32} +(670.500 + 387.113i) q^{33} +1333.68i q^{34} +(84.0000 + 12.1244i) q^{35} -243.000 q^{36} +(-985.000 + 1706.07i) q^{37} +(-1545.00 + 892.006i) q^{38} +(108.000 + 187.061i) q^{39} +(-52.5000 - 30.3109i) q^{40} -2816.31i q^{41} +(472.500 + 1182.12i) q^{42} +2798.00 q^{43} +(670.500 - 1161.34i) q^{44} +(-40.5000 + 23.3827i) q^{45} +(-1400.00 - 2424.87i) q^{46} +(3576.00 + 2064.60i) q^{47} -1657.57i q^{48} +(1739.50 - 1654.97i) q^{49} -3110.00 q^{50} +(-693.000 + 1200.31i) q^{51} +(324.000 - 187.061i) q^{52} +(-450.500 - 780.289i) q^{53} +(-607.500 - 350.740i) q^{54} -258.076i q^{55} +(-1592.50 + 636.529i) q^{56} -1854.00 q^{57} +(587.500 - 1017.58i) q^{58} +(1195.50 - 690.222i) q^{59} +(40.5000 + 70.1481i) q^{60} +(-3090.00 - 1784.01i) q^{61} +6434.57i q^{62} +(-189.000 + 1309.43i) q^{63} -71.0000 q^{64} +(36.0000 - 62.3538i) q^{65} +(3352.50 - 1935.57i) q^{66} +(2078.00 + 3599.20i) q^{67} +(2079.00 + 1200.31i) q^{68} -2909.85i q^{69} +(262.500 - 333.420i) q^{70} +484.000 q^{71} +(472.500 - 818.394i) q^{72} +(-822.000 + 474.582i) q^{73} +(4925.00 + 8530.35i) q^{74} +(-2799.00 - 1616.00i) q^{75} +3211.22i q^{76} +(-5736.50 - 4516.32i) q^{77} +1080.00 q^{78} +(-2162.50 + 3745.56i) q^{79} +(-478.500 + 276.262i) q^{80} +(-364.500 - 631.333i) q^{81} +(-12195.0 - 7040.79i) q^{82} +1304.23i q^{83} +(2268.00 + 327.358i) q^{84} +462.000 q^{85} +(6995.00 - 12115.7i) q^{86} +(1057.50 - 610.548i) q^{87} +(2607.50 + 4516.32i) q^{88} +(1713.00 + 989.001i) q^{89} +233.827i q^{90} +(-756.000 - 1891.40i) q^{91} -5040.00 q^{92} +(-3343.50 + 5791.11i) q^{93} +(17880.0 - 10323.0i) q^{94} +(309.000 + 535.204i) q^{95} +(-4657.50 - 2689.01i) q^{96} -5450.76i q^{97} +(-2817.50 - 11669.7i) q^{98} +4023.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 5 q^{2} + 9 q^{3} - 9 q^{4} - 3 q^{5} - 91 q^{7} + 70 q^{8} + 27 q^{9}+O(q^{10}) $ 2 * q + 5 * q^2 + 9 * q^3 - 9 * q^4 - 3 * q^5 - 91 * q^7 + 70 * q^8 + 27 * q^9	\( 2 q + 5 q^{2} + 9 q^{3} - 9 q^{4} - 3 q^{5} - 91 q^{7} + 70 q^{8} + 27 q^{9} - 15 q^{10} + 149 q^{11} - 81 q^{12} - 70 q^{14} - 18 q^{15} + 319 q^{16} - 462 q^{17} - 135 q^{18} - 618 q^{19} - 315 q^{21} + 1490 q^{22} + 560 q^{23} + 315 q^{24} - 622 q^{25} + 360 q^{26} + 693 q^{28} + 470 q^{29} - 45 q^{30} - 2229 q^{31} - 1035 q^{32} + 1341 q^{33} + 168 q^{35} - 486 q^{36} - 1970 q^{37} - 3090 q^{38} + 216 q^{39} - 105 q^{40} + 945 q^{42} + 5596 q^{43} + 1341 q^{44} - 81 q^{45} - 2800 q^{46} + 7152 q^{47} + 3479 q^{49} - 6220 q^{50} - 1386 q^{51} + 648 q^{52} - 901 q^{53} - 1215 q^{54} - 3185 q^{56} - 3708 q^{57} + 1175 q^{58} + 2391 q^{59} + 81 q^{60} - 6180 q^{61} - 378 q^{63} - 142 q^{64} + 72 q^{65} + 6705 q^{66} + 4156 q^{67} + 4158 q^{68} + 525 q^{70} + 968 q^{71} + 945 q^{72} - 1644 q^{73} + 9850 q^{74} - 5598 q^{75} - 11473 q^{77} + 2160 q^{78} - 4325 q^{79} - 957 q^{80} - 729 q^{81} - 24390 q^{82} + 4536 q^{84} + 924 q^{85} + 13990 q^{86} + 2115 q^{87} + 5215 q^{88} + 3426 q^{89} - 1512 q^{91} - 10080 q^{92} - 6687 q^{93} + 35760 q^{94} + 618 q^{95} - 9315 q^{96} - 5635 q^{98} + 8046 q^{99}+O(q^{100}) \) 2 * q + 5 * q^2 + 9 * q^3 - 9 * q^4 - 3 * q^5 - 91 * q^7 + 70 * q^8 + 27 * q^9 - 15 * q^10 + 149 * q^11 - 81 * q^12 - 70 * q^14 - 18 * q^15 + 319 * q^16 - 462 * q^17 - 135 * q^18 - 618 * q^19 - 315 * q^21 + 1490 * q^22 + 560 * q^23 + 315 * q^24 - 622 * q^25 + 360 * q^26 + 693 * q^28 + 470 * q^29 - 45 * q^30 - 2229 * q^31 - 1035 * q^32 + 1341 * q^33 + 168 * q^35 - 486 * q^36 - 1970 * q^37 - 3090 * q^38 + 216 * q^39 - 105 * q^40 + 945 * q^42 + 5596 * q^43 + 1341 * q^44 - 81 * q^45 - 2800 * q^46 + 7152 * q^47 + 3479 * q^49 - 6220 * q^50 - 1386 * q^51 + 648 * q^52 - 901 * q^53 - 1215 * q^54 - 3185 * q^56 - 3708 * q^57 + 1175 * q^58 + 2391 * q^59 + 81 * q^60 - 6180 * q^61 - 378 * q^63 - 142 * q^64 + 72 * q^65 + 6705 * q^66 + 4156 * q^67 + 4158 * q^68 + 525 * q^70 + 968 * q^71 + 945 * q^72 - 1644 * q^73 + 9850 * q^74 - 5598 * q^75 - 11473 * q^77 + 2160 * q^78 - 4325 * q^79 - 957 * q^80 - 729 * q^81 - 24390 * q^82 + 4536 * q^84 + 924 * q^85 + 13990 * q^86 + 2115 * q^87 + 5215 * q^88 + 3426 * q^89 - 1512 * q^91 - 10080 * q^92 - 6687 * q^93 + 35760 * q^94 + 618 * q^95 - 9315 * q^96 - 5635 * q^98 + 8046 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.50000	−	4.33013i	0.625000	−	1.08253i	−0.363541	−	0.931578i	$-0.618432\pi$
$2$	2.50000	−	4.33013i	0.625000	−	1.08253i	0.988541	−	0.150954i	$-0.0482344\pi$
$3$	4.50000	−	2.59808i	0.500000	−	0.288675i
$3$	4.50000	−	2.59808i	0.500000	−	0.288675i
$4$	−4.50000	−	7.79423i	−0.281250	−	0.487139i
$5$	−1.50000	−	0.866025i	−0.0600000	−	0.0346410i	0.469700	−	0.882826i	$-0.344362\pi$
$5$	−1.50000	−	0.866025i	−0.0600000	−	0.0346410i	−0.529700	+	0.848185i	$0.677695\pi$
$6$		−	25.9808i		−	0.721688i
$7$	−45.5000	+	18.1865i	−0.928571	+	0.371154i
$7$	−45.5000	+	18.1865i	−0.928571	+	0.371154i
$8$	35.0000			0.546875
$9$	13.5000	−	23.3827i	0.166667	−	0.288675i
$10$	−7.50000	+	4.33013i	−0.0750000	+	0.0433013i
$11$	74.5000	+	129.038i	0.615702	+	1.06643i	0.990261	+	0.139225i	$0.0444610\pi$
$11$	74.5000	+	129.038i	0.615702	+	1.06643i	−0.374558	+	0.927203i	$0.622206\pi$
$12$	−40.5000	−	23.3827i	−0.281250	−	0.162380i
$13$			41.5692i			0.245972i	0.992408	+	0.122986i	$0.0392470\pi$
$13$			41.5692i			0.245972i	−0.992408	+	0.122986i	$0.960753\pi$
$14$	−35.0000	+	242.487i	−0.178571	+	1.23718i
$15$	−9.00000			−0.0400000
$16$	159.500	−	276.262i	0.623047	−	1.07915i
$17$	−231.000	+	133.368i	−0.799308	+	0.461481i	−0.843229	−	0.537554i	$-0.819348\pi$
$17$	−231.000	+	133.368i	−0.799308	+	0.461481i	0.0439212	+	0.999035i	$0.486015\pi$
$18$	−67.5000	−	116.913i	−0.208333	−	0.360844i
$19$	−309.000	−	178.401i	−0.855956	−	0.494186i	0.00670019	−	0.999978i	$-0.497867\pi$
$19$	−309.000	−	178.401i	−0.855956	−	0.494186i	−0.862656	+	0.505791i	$0.831201\pi$
$20$			15.5885i			0.0389711i
$21$	−157.500	+	200.052i	−0.357143	+	0.453632i
$22$	745.000			1.53926
$23$	280.000	−	484.974i	0.529301	−	0.916775i	−0.470115	−	0.882605i	$-0.655788\pi$
$23$	280.000	−	484.974i	0.529301	−	0.916775i	0.999416	−	0.0341705i	$-0.0108789\pi$
$24$	157.500	−	90.9327i	0.273438	−	0.157869i
$25$	−311.000	−	538.668i	−0.497600	−	0.861868i
$26$	180.000	+	103.923i	0.266272	+	0.153732i
$27$		−	140.296i		−	0.192450i
$28$	346.500	+	272.798i	0.441964	+	0.347957i
$29$	235.000			0.279429			0.139715	−	0.990192i	$-0.455381\pi$
$29$	235.000			0.279429			0.139715	+	0.990192i	$0.455381\pi$
$30$	−22.5000	+	38.9711i	−0.0250000	+	0.0433013i
$31$	−1114.50	+	643.457i	−1.15973	+	0.669570i	−0.951239	−	0.308454i	$-0.900188\pi$
$31$	−1114.50	+	643.457i	−1.15973	+	0.669570i	−0.208490	+	0.978024i	$0.566855\pi$
$32$	−517.500	−	896.336i	−0.505371	−	0.875328i
$33$	670.500	+	387.113i	0.615702	+	0.355476i
$34$			1333.68i			1.15370i
$35$	84.0000	+	12.1244i	0.0685714	+	0.00989743i
$36$	−243.000			−0.187500
$37$	−985.000	+	1706.07i	−0.719503	+	1.24622i	0.241694	+	0.970353i	$0.422297\pi$
$37$	−985.000	+	1706.07i	−0.719503	+	1.24622i	−0.961197	+	0.275864i	$0.911036\pi$
$38$	−1545.00	+	892.006i	−1.06994	+	0.617733i
$39$	108.000	+	187.061i	0.0710059	+	0.122986i
$40$	−52.5000	−	30.3109i	−0.0328125	−	0.0189443i
$41$		−	2816.31i		−	1.67538i	−0.546146	−	0.837690i	$-0.683905\pi$
$41$		−	2816.31i		−	1.67538i	0.546146	−	0.837690i	$-0.316095\pi$
$42$	472.500	+	1182.12i	0.267857	+	0.670139i
$43$	2798.00			1.51325			0.756625	−	0.653849i	$-0.226847\pi$
$43$	2798.00			1.51325			0.756625	+	0.653849i	$0.226847\pi$
$44$	670.500	−	1161.34i	0.346333	−	0.599866i
$45$	−40.5000	+	23.3827i	−0.0200000	+	0.0115470i
$46$	−1400.00	−	2424.87i	−0.661626	−	1.14597i
$47$	3576.00	+	2064.60i	1.61883	+	0.934633i	0.987223	+	0.159346i	$0.0509386\pi$
$47$	3576.00	+	2064.60i	1.61883	+	0.934633i	0.631609	+	0.775287i	$0.282395\pi$
$48$		−	1657.57i		−	0.719433i
$49$	1739.50	−	1654.97i	0.724490	−	0.689286i
$50$	−3110.00			−1.24400
$51$	−693.000	+	1200.31i	−0.266436	+	0.461481i
$52$	324.000	−	187.061i	0.119822	−	0.0691795i
$53$	−450.500	−	780.289i	−0.160377	−	0.277782i	0.774627	−	0.632419i	$-0.217938\pi$
$53$	−450.500	−	780.289i	−0.160377	−	0.277782i	−0.935004	+	0.354637i	$0.884604\pi$
$54$	−607.500	−	350.740i	−0.208333	−	0.120281i
$55$		−	258.076i		−	0.0853142i
$56$	−1592.50	+	636.529i	−0.507812	+	0.202975i
$57$	−1854.00			−0.570637
$58$	587.500	−	1017.58i	0.174643	−	0.302491i
$59$	1195.50	−	690.222i	0.343436	−	0.198283i	−0.318355	−	0.947972i	$-0.603130\pi$
$59$	1195.50	−	690.222i	0.343436	−	0.198283i	0.661790	+	0.749689i	$0.269797\pi$
$60$	40.5000	+	70.1481i	0.0112500	+	0.0194856i
$61$	−3090.00	−	1784.01i	−0.830422	−	0.479444i	0.0235752	−	0.999722i	$-0.492495\pi$
$61$	−3090.00	−	1784.01i	−0.830422	−	0.479444i	−0.853997	+	0.520278i	$0.825828\pi$
$62$			6434.57i			1.67393i
$63$	−189.000	+	1309.43i	−0.0476190	+	0.329914i
$64$	−71.0000			−0.0173340
$65$	36.0000	−	62.3538i	0.00852071	−	0.0147583i
$66$	3352.50	−	1935.57i	0.769628	−	0.444345i
$67$	2078.00	+	3599.20i	0.462909	+	0.801782i	0.999104	−	0.0423116i	$-0.0134722\pi$
$67$	2078.00	+	3599.20i	0.462909	+	0.801782i	−0.536195	+	0.844094i	$0.680139\pi$
$68$	2079.00	+	1200.31i	0.449611	+	0.259583i
$69$		−	2909.85i		−	0.611184i
$70$	262.500	−	333.420i	0.0535714	−	0.0680449i
$71$	484.000			0.0960127			0.0480063	−	0.998847i	$-0.484713\pi$
$71$	484.000			0.0960127			0.0480063	+	0.998847i	$0.484713\pi$
$72$	472.500	−	818.394i	0.0911458	−	0.157869i
$73$	−822.000	+	474.582i	−0.154250	+	0.0890565i	−0.575138	−	0.818056i	$-0.695052\pi$
$73$	−822.000	+	474.582i	−0.154250	+	0.0890565i	0.420888	+	0.907113i	$0.361718\pi$
$74$	4925.00	+	8530.35i	0.899379	+	1.55777i
$75$	−2799.00	−	1616.00i	−0.497600	−	0.287289i
$76$			3211.22i			0.555960i
$77$	−5736.50	−	4516.32i	−0.967532	−	0.761734i
$78$	1080.00			0.177515
$79$	−2162.50	+	3745.56i	−0.346499	+	0.600154i	−0.985625	−	0.168948i	$-0.945963\pi$
$79$	−2162.50	+	3745.56i	−0.346499	+	0.600154i	0.639126	+	0.769102i	$0.279296\pi$
$80$	−478.500	+	276.262i	−0.0747656	+	0.0431660i
$81$	−364.500	−	631.333i	−0.0555556	−	0.0962250i
$82$	−12195.0	−	7040.79i	−1.81365	−	1.04711i
$83$			1304.23i			0.189321i	0.995510	+	0.0946606i	$0.0301766\pi$
$83$			1304.23i			0.189321i	−0.995510	+	0.0946606i	$0.969823\pi$
$84$	2268.00	+	327.358i	0.321429	+	0.0463942i
$85$	462.000			0.0639446
$86$	6995.00	−	12115.7i	0.945782	−	1.63814i
$87$	1057.50	−	610.548i	0.139715	−	0.0806643i
$88$	2607.50	+	4516.32i	0.336712	+	0.583203i
$89$	1713.00	+	989.001i	0.216261	+	0.124858i	0.604218	−	0.796819i	$-0.293486\pi$
$89$	1713.00	+	989.001i	0.216261	+	0.124858i	−0.387957	+	0.921677i	$0.626819\pi$
$90$			233.827i			0.0288675i
$91$	−756.000	−	1891.40i	−0.0912933	−	0.228402i
$92$	−5040.00			−0.595463
$93$	−3343.50	+	5791.11i	−0.386576	+	0.669570i
$94$	17880.0	−	10323.0i	2.02354	−	1.16829i
$95$	309.000	+	535.204i	0.0342382	+	0.0593023i
$96$	−4657.50	−	2689.01i	−0.505371	−	0.291776i
$97$		−	5450.76i		−	0.579314i	−0.957131	−	0.289657i	$-0.906459\pi$
$97$		−	5450.76i		−	0.579314i	0.957131	−	0.289657i	$-0.0935412\pi$
$98$	−2817.50	−	11669.7i	−0.293367	−	1.21509i
$99$	4023.00			0.410468
$100$	−2799.00	+	4848.01i	−0.279900	+	0.484801i
$101$	−3750.00	+	2165.06i	−0.367611	+	0.212240i	−0.672414	−	0.740175i	$-0.734743\pi$
$101$	−3750.00	+	2165.06i	−0.367611	+	0.212240i	0.304803	+	0.952415i	$0.401409\pi$
$102$	3465.00	+	6001.56i	0.333045	+	0.576851i
$103$	12516.0	+	7226.12i	1.17975	+	0.681131i	0.955957	−	0.293505i	$-0.0948219\pi$
$103$	12516.0	+	7226.12i	1.17975	+	0.681131i	0.223796	+	0.974636i	$0.428155\pi$
$104$			1454.92i			0.134516i
$105$	409.500	−	163.679i	0.0371429	−	0.0148461i
$106$	−4505.00			−0.400943
$107$	−2232.50	+	3866.80i	−0.194995	+	0.337742i	−0.946899	−	0.321531i	$-0.895802\pi$
$107$	−2232.50	+	3866.80i	−0.194995	+	0.337742i	0.751904	+	0.659273i	$0.229136\pi$
$108$	−1093.50	+	631.333i	−0.0937500	+	0.0541266i
$109$	−1660.00	−	2875.20i	−0.139719	−	0.242000i	0.787671	−	0.616096i	$-0.211287\pi$
$109$	−1660.00	−	2875.20i	−0.139719	−	0.242000i	−0.927390	+	0.374096i	$0.877953\pi$
$110$	−1117.50	−	645.189i	−0.0923554	−	0.0533214i
$111$			10236.4i			0.830811i
$112$	−2233.00	+	15470.7i	−0.178013	+	1.23331i
$113$	−9734.00			−0.762315			−0.381157	−	0.924510i	$-0.624474\pi$
$113$	−9734.00			−0.762315			−0.381157	+	0.924510i	$0.624474\pi$
$114$	−4635.00	+	8028.06i	−0.356648	+	0.617733i
$115$	−840.000	+	484.974i	−0.0635161	+	0.0366710i
$116$	−1057.50	−	1831.64i	−0.0785895	−	0.136121i
$117$	972.000	+	561.184i	0.0710059	+	0.0409953i
$118$		−	6902.22i		−	0.495707i
$119$	8085.00	−	10269.3i	0.570934	−	0.725184i
$120$	−315.000			−0.0218750
$121$	−3780.00	+	6547.15i	−0.258179	+	0.447179i
$122$	−15450.0	+	8920.06i	−1.03803	+	0.599305i
$123$	−7317.00	−	12673.4i	−0.483641	−	0.837690i
$124$	10030.5	+	5791.11i	0.652348	+	0.376633i
$125$			2159.87i			0.138232i
$126$	5197.50	+	4091.97i	0.327381	+	0.257746i
$127$	−29149.0			−1.80724			−0.903621	−	0.428333i	$-0.859101\pi$
$127$	−29149.0			−1.80724			−0.903621	+	0.428333i	$0.859101\pi$
$128$	8102.50	−	14033.9i	0.494537	−	0.856564i
$129$	12591.0	−	7269.42i	0.756625	−	0.436838i
$130$	−180.000	−	311.769i	−0.0106509	−	0.0184479i
$131$	23866.5	+	13779.3i	1.39074	+	0.802944i	0.993397	−	0.114726i	$-0.0365989\pi$
$131$	23866.5	+	13779.3i	1.39074	+	0.802944i	0.397343	+	0.917670i	$0.369932\pi$
$132$		−	6968.04i		−	0.399910i
$133$	17304.0	+	2497.62i	0.978235	+	0.141196i
$134$	20780.0			1.15727
$135$	−121.500	+	210.444i	−0.00666667	+	0.0115470i
$136$	−8085.00	+	4667.88i	−0.437122	+	0.252372i
$137$	−8912.00	−	15436.0i	−0.474826	−	0.822422i	0.524759	−	0.851251i	$-0.324155\pi$
$137$	−8912.00	−	15436.0i	−0.474826	−	0.822422i	−0.999584	+	0.0288290i	$0.990822\pi$
$138$	−12600.0	−	7274.61i	−0.661626	−	0.381990i
$139$		−	27986.5i		−	1.44850i	−0.689537	−	0.724250i	$-0.742186\pi$
$139$		−	27986.5i		−	1.44850i	0.689537	−	0.724250i	$-0.257814\pi$
$140$	−283.500	−	709.275i	−0.0144643	−	0.0361875i
$141$	21456.0			1.07922
$142$	1210.00	−	2095.78i	0.0600079	−	0.103937i
$143$	−5364.00	+	3096.91i	−0.262311	+	0.151445i
$144$	−4306.50	−	7459.08i	−0.207682	−	0.359716i
$145$	−352.500	−	203.516i	−0.0167658	−	0.00967971i
$146$			4745.82i			0.222641i
$147$	3528.00	−	11966.7i	0.163265	−	0.553785i
$148$	17730.0			0.809441
$149$	−4607.00	+	7979.56i	−0.207513	+	0.359423i	−0.950931	−	0.309404i	$-0.899870\pi$
$149$	−4607.00	+	7979.56i	−0.207513	+	0.359423i	0.743417	+	0.668828i	$0.233204\pi$
$150$	−13995.0	+	8080.02i	−0.622000	+	0.359112i
$151$	−5987.50	−	10370.7i	−0.262598	−	0.454833i	0.704333	−	0.709869i	$-0.251246\pi$
$151$	−5987.50	−	10370.7i	−0.262598	−	0.454833i	−0.966932	+	0.255036i	$0.917913\pi$
$152$	−10815.0	−	6244.04i	−0.468101	−	0.270258i
$153$			7201.87i			0.307654i
$154$	−33897.5	+	13549.0i	−1.42931	+	0.571301i
$155$	2229.00			0.0927784
$156$	972.000	−	1683.55i	0.0399408	−	0.0691795i
$157$	−1722.00	+	994.197i	−0.0698608	+	0.0403342i	−0.534524	−	0.845154i	$-0.679509\pi$
$157$	−1722.00	+	994.197i	−0.0698608	+	0.0403342i	0.464663	+	0.885488i	$0.346176\pi$
$158$	10812.5	+	18727.8i	0.433124	+	0.750192i
$159$	−4054.50	−	2340.87i	−0.160377	−	0.0925939i
$160$			1792.67i			0.0700263i
$161$	−3920.00	+	27158.6i	−0.151229	+	1.04774i
$162$	−3645.00			−0.138889
$163$	10400.0	−	18013.3i	0.391434	−	0.677983i	−0.601205	−	0.799095i	$-0.705313\pi$
$163$	10400.0	−	18013.3i	0.391434	−	0.677983i	0.992639	+	0.121112i	$0.0386459\pi$
$164$	−21951.0	+	12673.4i	−0.816144	+	0.471201i
$165$	−670.500	−	1161.34i	−0.0246281	−	0.0426571i
$166$	5647.50	+	3260.59i	0.204946	+	0.118326i
$167$			42483.7i			1.52332i	0.647980	+	0.761658i	$0.275614\pi$
$167$			42483.7i			1.52332i	−0.647980	+	0.761658i	$0.724386\pi$
$168$	−5512.50	+	7001.82i	−0.195312	+	0.248080i
$169$	26833.0			0.939498
$170$	1155.00	−	2000.52i	0.0399654	−	0.0692221i
$171$	−8343.00	+	4816.83i	−0.285319	+	0.164729i
$172$	−12591.0	−	21808.3i	−0.425602	−	0.737164i
$173$	−2094.00	−	1208.97i	−0.0699656	−	0.0403946i	0.464609	−	0.885516i	$-0.346195\pi$
$173$	−2094.00	−	1208.97i	−0.0699656	−	0.0403946i	−0.534575	+	0.845121i	$0.679528\pi$
$174$		−	6105.48i		−	0.201661i
$175$	23947.0	+	18853.4i	0.781943	+	0.615620i
$176$	47531.0			1.53445
$177$	3586.50	−	6212.00i	0.114479	−	0.198283i
$178$	8565.00	−	4945.01i	0.270326	−	0.156073i
$179$	−9689.00	−	16781.8i	−0.302394	−	0.523761i	0.674284	−	0.738472i	$-0.264452\pi$
$179$	−9689.00	−	16781.8i	−0.302394	−	0.523761i	−0.976678	+	0.214711i	$0.931119\pi$
$180$	364.500	+	210.444i	0.0112500	+	0.00649519i
$181$			7451.28i			0.227444i	0.993513	+	0.113722i	$0.0362773\pi$
$181$			7451.28i			0.227444i	−0.993513	+	0.113722i	$0.963723\pi$
$182$	−10080.0	−	1454.92i	−0.304311	−	0.0439235i
$183$	−18540.0			−0.553615
$184$	9800.00	−	16974.1i	0.289461	−	0.501362i
$185$	2955.00	−	1706.07i	0.0863404	−	0.0498486i
$186$	16717.5	+	28955.6i	0.483221	+	0.836963i
$187$	−34419.0	−	19871.8i	−0.984272	−	0.568270i
$188$		−	37162.9i		−	1.05146i
$189$	2551.50	+	6383.47i	0.0714286	+	0.178704i
$190$	3090.00			0.0855956
$191$	14380.0	−	24906.9i	0.394178	−	0.682736i	−0.598818	−	0.800885i	$-0.704363\pi$
$191$	14380.0	−	24906.9i	0.394178	−	0.682736i	0.992996	+	0.118149i	$0.0376961\pi$
$192$	−319.500	+	184.463i	−0.00866699	+	0.00500389i
$193$	22044.5	+	38182.2i	0.591815	+	1.02505i	0.993988	+	0.109489i	$0.0349216\pi$
$193$	22044.5	+	38182.2i	0.591815	+	1.02505i	−0.402173	+	0.915564i	$0.631745\pi$
$194$	−23602.5	−	13626.9i	−0.627126	−	0.362071i
$195$		−	374.123i		−	0.00983887i
$196$	−20727.0	−	6110.68i	−0.539541	−	0.159066i
$197$	−46478.0			−1.19761			−0.598804	−	0.800895i	$-0.704357\pi$
$197$	−46478.0			−1.19761			−0.598804	+	0.800895i	$0.704357\pi$
$198$	10057.5	−	17420.1i	0.256543	−	0.444345i
$199$	−33978.0	+	19617.2i	−0.858009	+	0.495372i	−0.863345	−	0.504614i	$-0.831635\pi$
$199$	−33978.0	+	19617.2i	−0.858009	+	0.495372i	0.00533629	+	0.999986i	$0.498301\pi$
$200$	−10885.0	−	18853.4i	−0.272125	−	0.471334i
$201$	18702.0	+	10797.6i	0.462909	+	0.267261i
$202$			21650.6i			0.530601i
$203$	−10692.5	+	4273.84i	−0.259470	+	0.103711i
$204$	12474.0			0.299740
$205$	−2439.00	+	4224.47i	−0.0580369	+	0.100523i
$206$	62580.0	−	36130.6i	1.47469	−	0.851413i
$207$	−7560.00	−	13094.3i	−0.176434	−	0.305592i
$208$	11484.0	+	6630.29i	0.265440	+	0.153252i
$209$		−	53163.6i		−	1.21709i
$210$	315.000	−	2182.38i	0.00714286	−	0.0494872i
$211$	−27688.0			−0.621909			−0.310954	−	0.950425i	$-0.600649\pi$
$211$	−27688.0			−0.621909			−0.310954	+	0.950425i	$0.600649\pi$
$212$	−4054.50	+	7022.60i	−0.0902123	+	0.156252i
$213$	2178.00	−	1257.47i	0.0480063	−	0.0277165i
$214$	11162.5	+	19334.0i	0.243744	+	0.422177i
$215$	−4197.00	−	2423.14i	−0.0907950	−	0.0524205i
$216$		−	4910.36i		−	0.105246i
$217$	39007.5	−	49546.2i	0.828378	−	1.05218i
$218$	−16600.0			−0.349297
$219$	−2466.00	+	4271.24i	−0.0514168	+	0.0890565i
$220$	−2011.50	+	1161.34i	−0.0415599	+	0.0239946i
$221$	−5544.00	−	9602.49i	−0.113511	−	0.196607i
$222$	44325.0	+	25591.1i	0.899379	+	0.519257i
$223$			49077.7i			0.986902i	0.869774	+	0.493451i	$0.164265\pi$
$223$			49077.7i			0.986902i	−0.869774	+	0.493451i	$0.835735\pi$
$224$	39847.5	+	31371.8i	0.794155	+	0.625235i
$225$	−16794.0			−0.331733
$226$	−24335.0	+	42149.5i	−0.476447	+	0.825230i
$227$	64141.5	−	37032.1i	1.24477	−	0.718665i	0.274705	−	0.961529i	$-0.411420\pi$
$227$	64141.5	−	37032.1i	1.24477	−	0.718665i	0.970061	+	0.242863i	$0.0780866\pi$
$228$	8343.00	+	14450.5i	0.160492	+	0.277980i
$229$	20697.0	+	11949.4i	0.394672	+	0.227864i	0.684183	−	0.729311i	$-0.260159\pi$
$229$	20697.0	+	11949.4i	0.394672	+	0.227864i	−0.289510	+	0.957175i	$0.593492\pi$
$230$			4849.74i			0.0916775i
$231$	−37548.0	−	5419.59i	−0.703660	−	0.101565i
$232$	8225.00			0.152813
$233$	−48191.0	+	83469.3i	−0.887675	+	1.53750i	−0.0450588	+	0.998984i	$0.514348\pi$
$233$	−48191.0	+	83469.3i	−0.887675	+	1.53750i	−0.842616	+	0.538514i	$0.818986\pi$
$234$	4860.00	−	2805.92i	0.0887574	−	0.0512441i
$235$	−3576.00	−	6193.81i	−0.0647533	−	0.112156i
$236$	−10759.5	−	6212.00i	−0.193183	−	0.111534i
$237$			22473.4i			0.400103i
$238$	−24255.0	−	60682.4i	−0.428201	−	1.07129i
$239$	−44276.0			−0.775126			−0.387563	−	0.921843i	$-0.626683\pi$
$239$	−44276.0			−0.775126			−0.387563	+	0.921843i	$0.626683\pi$
$240$	−1435.50	+	2486.36i	−0.0249219	+	0.0431660i
$241$	−49318.5	+	28474.0i	−0.849133	+	0.490247i	−0.860358	−	0.509690i	$-0.829760\pi$
$241$	−49318.5	+	28474.0i	−0.849133	+	0.490247i	0.0112252	+	0.999937i	$0.496427\pi$
$242$	18900.0	+	32735.8i	0.322724	+	0.558974i
$243$	−3280.50	−	1894.00i	−0.0555556	−	0.0320750i
$244$			32112.2i			0.539375i
$245$	−4042.50	+	976.011i	−0.0673469	+	0.0162601i
$246$	−73170.0			−1.20910
$247$	7416.00	−	12844.9i	0.121556	−	0.210541i
$248$	−39007.5	+	22521.0i	−0.634227	+	0.366171i
$249$	3388.50	+	5869.05i	0.0546523	+	0.0946606i
$250$	9352.50	+	5399.67i	0.149640	+	0.0863947i
$251$		−	74715.5i		−	1.18594i	−0.805224	−	0.592971i	$-0.797955\pi$
$251$		−	74715.5i		−	1.18594i	0.805224	−	0.592971i	$-0.202045\pi$
$252$	11056.5	−	4419.33i	0.174107	−	0.0695913i
$253$	83440.0			1.30357
$254$	−72872.5	+	126219.i	−1.12953	+	1.95640i
$255$	2079.00	−	1200.31i	0.0319723	−	0.0184592i
$256$	−41080.5	−	71153.5i	−0.626839	−	1.08572i
$257$	25419.0	+	14675.7i	0.384851	+	0.222194i	0.679927	−	0.733280i	$-0.262012\pi$
$257$	25419.0	+	14675.7i	0.384851	+	0.222194i	−0.295076	+	0.955474i	$0.595345\pi$
$258$		−	72694.2i		−	1.09209i
$259$	13790.0	−	95539.9i	0.205572	−	1.42425i
$260$	−648.000			−0.00958580
$261$	3172.50	−	5494.93i	0.0465715	−	0.0806643i
$262$	119332.	−	68896.7i	1.73843	−	1.00368i
$263$	44539.0	+	77143.8i	0.643916	+	1.11529i	0.984551	+	0.175099i	$0.0560246\pi$
$263$	44539.0	+	77143.8i	0.643916	+	1.11529i	−0.340635	+	0.940196i	$0.610642\pi$
$264$	23467.5	+	13549.0i	0.336712	+	0.194401i
$265$			1560.58i			0.0222225i
$266$	54075.0	−	68684.5i	0.764246	−	0.970723i
$267$	10278.0			0.144174
$268$	18702.0	−	32392.8i	0.260387	−	0.451003i
$269$	61693.5	−	35618.8i	0.852579	−	0.492237i	−0.00894091	−	0.999960i	$-0.502846\pi$
$269$	61693.5	−	35618.8i	0.852579	−	0.492237i	0.861520	+	0.507723i	$0.169513\pi$
$270$	607.500	+	1052.22i	0.00833333	+	0.0144338i
$271$	−36664.5	−	21168.3i	−0.499237	−	0.288235i	0.229161	−	0.973389i	$-0.426402\pi$
$271$	−36664.5	−	21168.3i	−0.499237	−	0.288235i	−0.728399	+	0.685154i	$0.759735\pi$
$272$			85088.7i			1.15010i
$273$	−8316.00	−	6547.15i	−0.111581	−	0.0878470i
$274$	−89120.0			−1.18706
$275$	46339.0	−	80261.5i	0.612747	−	1.06131i
$276$	−22680.0	+	13094.3i	−0.297732	+	0.171895i
$277$	23258.0	+	40284.0i	0.303119	+	0.525017i	0.976841	−	0.213968i	$-0.0686388\pi$
$277$	23258.0	+	40284.0i	0.303119	+	0.525017i	−0.673722	+	0.738985i	$0.735305\pi$
$278$	−121185.	−	69966.2i	−1.56805	−	0.905313i
$279$			34746.7i			0.446380i
$280$	2940.00	+	424.352i	0.0375000	+	0.00541266i
$281$	50284.0			0.636821			0.318410	−	0.947953i	$-0.396851\pi$
$281$	50284.0			0.636821			0.318410	+	0.947953i	$0.396851\pi$
$282$	53640.0	−	92907.2i	0.674513	−	1.16829i
$283$	−32043.0	+	18500.0i	−0.400092	+	0.230993i	−0.686524	−	0.727107i	$-0.740864\pi$
$283$	−32043.0	+	18500.0i	−0.400092	+	0.230993i	0.286431	+	0.958101i	$0.407531\pi$
$284$	−2178.00	−	3772.41i	−0.0270036	−	0.0467716i
$285$	2781.00	+	1605.61i	0.0342382	+	0.0197674i
$286$			30969.1i			0.378613i
$287$	51219.0	+	128142.i	0.621824	+	1.55571i
$288$	−27945.0			−0.336914
$289$	−6186.50	+	10715.3i	−0.0740712	+	0.128295i
$290$	−1762.50	+	1017.58i	−0.0209572	+	0.0120996i
$291$	−14161.5	−	24528.4i	−0.167233	−	0.289657i
$292$	7398.00	+	4271.24i	0.0867658	+	0.0500943i
$293$		−	66994.0i		−	0.780370i	−0.920736	−	0.390185i	$-0.872411\pi$
$293$		−	66994.0i		−	0.780370i	0.920736	−	0.390185i	$-0.127589\pi$
$294$	−42997.5	−	45193.5i	−0.497449	−	0.522855i
$295$	−2391.00			−0.0274749
$296$	−34475.0	+	59712.5i	−0.393478	+	0.681525i
$297$	18103.5	−	10452.1i	0.205234	−	0.118492i
$298$	23035.0	+	39897.8i	0.259391	+	0.449279i
$299$	20160.0	+	11639.4i	0.225501	+	0.130193i
$300$			29088.1i			0.323201i
$301$	−127309.	+	50885.9i	−1.40516	+	0.561649i
$302$	−59875.0			−0.656495
$303$	−11250.0	+	19485.6i	−0.122537	+	0.212240i
$304$	−98571.0	+	56910.0i	−1.06660	+	0.615802i
$305$	3090.00	+	5352.04i	0.0332169	+	0.0575333i
$306$	31185.0	+	18004.7i	0.333045	+	0.192284i
$307$			76258.7i			0.809120i	0.914511	+	0.404560i	$0.132575\pi$
$307$			76258.7i			0.809120i	−0.914511	+	0.404560i	$0.867425\pi$
$308$	−9387.00	+	65035.0i	−0.0989522	+	0.685561i
$309$	75096.0			0.786502
$310$	5572.50	−	9651.85i	0.0579865	−	0.100436i
$311$	45543.0	−	26294.3i	0.470870	−	0.271857i	−0.245734	−	0.969337i	$-0.579029\pi$
$311$	45543.0	−	26294.3i	0.470870	−	0.271857i	0.716604	+	0.697480i	$0.245696\pi$
$312$	3780.00	+	6547.15i	0.0388314	+	0.0672579i
$313$	−80404.5	−	46421.6i	−0.820714	−	0.473839i	0.0299488	−	0.999551i	$-0.490466\pi$
$313$	−80404.5	−	46421.6i	−0.820714	−	0.473839i	−0.850663	+	0.525712i	$0.823799\pi$
$314$			9941.97i			0.100835i
$315$	1417.50	−	1800.47i	0.0142857	−	0.0181453i
$316$	38925.0			0.389811
$317$	30791.5	−	53332.4i	0.306417	−	0.530729i	−0.671159	−	0.741313i	$-0.734203\pi$
$317$	30791.5	−	53332.4i	0.306417	−	0.530729i	0.977576	+	0.210584i	$0.0675366\pi$
$318$	−20272.5	+	11704.3i	−0.200472	+	0.115742i
$319$	17507.5	+	30323.9i	0.172045	+	0.297991i
$320$	106.500	+	61.4878i	0.00104004	+	0.000600467i
$321$			23200.8i			0.225161i
$322$	107800.	+	84870.5i	1.03970	+	0.818550i
$323$	95172.0			0.912230
$324$	−3280.50	+	5681.99i	−0.0312500	+	0.0541266i
$325$	22392.0	−	12928.0i	0.211995	−	0.122396i
$326$	−52000.0	−	90066.6i	−0.489292	−	0.847479i
$327$	−14940.0	−	8625.61i	−0.139719	−	0.0806667i
$328$		−	98571.0i		−	0.916224i
$329$	−200256.	−	28904.5i	−1.85009	−	0.267038i
$330$	−6705.00			−0.0615702
$331$	45740.0	−	79224.0i	0.417484	−	0.723104i	−0.578201	−	0.815894i	$-0.696245\pi$
$331$	45740.0	−	79224.0i	0.417484	−	0.723104i	0.995686	+	0.0927900i	$0.0295785\pi$
$332$	10165.5	−	5869.05i	0.0922258	−	0.0532466i
$333$	26595.0	+	46063.9i	0.239834	+	0.415405i
$334$	183960.	+	106209.i	1.64904	+	0.952072i
$335$		−	7198.40i		−	0.0641426i
$336$	30145.5	+	75419.6i	0.267020	+	0.668045i
$337$	9995.00			0.0880082			0.0440041	−	0.999031i	$-0.485989\pi$
$337$	9995.00			0.0880082			0.0440041	+	0.999031i	$0.485989\pi$
$338$	67082.5	−	116190.i	0.587186	−	1.01704i
$339$	−43803.0	+	25289.7i	−0.381157	+	0.220061i
$340$	−2079.00	−	3600.93i	−0.0179844	−	0.0311499i
$341$	−166060.	−	95875.1i	−1.42810	−	0.824512i
$342$			48168.3i			0.411822i
$343$	−49049.0	+	106937.i	−0.416910	+	0.908948i
$344$	97930.0			0.827559
$345$	−2520.00	+	4364.77i	−0.0211720	+	0.0366710i
$346$	−10470.0	+	6044.86i	−0.0874570	+	0.0504933i
$347$	−31229.0	−	54090.2i	−0.259358	−	0.449221i	0.706712	−	0.707501i	$-0.250178\pi$
$347$	−31229.0	−	54090.2i	−0.259358	−	0.449221i	−0.966070	+	0.258280i	$0.916844\pi$
$348$	−9517.50	−	5494.93i	−0.0785895	−	0.0453737i
$349$		−	233370.i		−	1.91599i	−0.286784	−	0.957995i	$-0.592586\pi$
$349$		−	233370.i		−	1.91599i	0.286784	−	0.957995i	$-0.407414\pi$
$350$	141505.	−	56560.1i	1.15514	−	0.461715i
$351$	5832.00			0.0473373
$352$	77107.5	−	133554.i	0.622316	−	1.07788i
$353$	−71898.0	+	41510.3i	−0.576989	+	0.333125i	−0.759936	−	0.649998i	$-0.774770\pi$
$353$	−71898.0	+	41510.3i	−0.576989	+	0.333125i	0.182947	+	0.983123i	$0.441436\pi$
$354$	−17932.5	−	31060.0i	−0.143098	−	0.247853i
$355$	−726.000	−	419.156i	−0.00576076	−	0.00332598i
$356$		−	17802.0i		−	0.140465i
$357$	9702.00	−	67217.4i	0.0761246	−	0.527406i
$358$	−96890.0			−0.755985
$359$	−82022.0	+	142066.i	−0.636417	+	1.10231i	0.349797	+	0.936826i	$0.386251\pi$
$359$	−82022.0	+	142066.i	−0.636417	+	1.10231i	−0.986213	+	0.165480i	$0.947083\pi$
$360$	−1417.50	+	818.394i	−0.0109375	+	0.00631477i
$361$	−1506.50	−	2609.33i	−0.0115599	−	0.0200224i
$362$	32265.0	+	18628.2i	0.246215	+	0.142152i
$363$			39282.9i			0.298120i
$364$	−11340.0	+	14403.7i	−0.0855875	+	0.108711i
$365$	1644.00			0.0123400
$366$	−46350.0	+	80280.6i	−0.346009	+	0.599305i
$367$	−3715.50	+	2145.14i	−0.0275858	+	0.0159267i	−0.513729	−	0.857952i	$-0.671736\pi$
$367$	−3715.50	+	2145.14i	−0.0275858	+	0.0159267i	0.486144	+	0.873879i	$0.338403\pi$
$368$	−89320.0	−	154707.i	−0.659558	−	1.14239i
$369$	−65853.0	−	38020.2i	−0.483641	−	0.279230i
$370$		−	17060.7i		−	0.124622i
$371$	34688.5	+	27310.1i	0.252022	+	0.198416i
$372$	60183.0			0.434899
$373$	−39313.0	+	68092.1i	−0.282565	+	0.489417i	−0.972016	−	0.234916i	$-0.924519\pi$
$373$	−39313.0	+	68092.1i	−0.282565	+	0.489417i	0.689451	+	0.724333i	$0.257852\pi$
$374$	−172095.	+	99359.1i	−1.23034	+	0.710337i
$375$	5611.50	+	9719.40i	0.0399040	+	0.0691158i
$376$	125160.	+	72261.2i	0.885299	+	0.511127i
$377$			9768.77i			0.0687317i
$378$	34020.0	+	4910.36i	0.238095	+	0.0343661i
$379$	56234.0			0.391490			0.195745	−	0.980655i	$-0.437288\pi$
$379$	56234.0			0.391490			0.195745	+	0.980655i	$0.437288\pi$
$380$	2781.00	−	4816.83i	0.0192590	−	0.0333576i
$381$	−131170.	+	75731.3i	−0.903621	+	0.521706i
$382$	−71900.0	−	124534.i	−0.492722	−	0.853420i
$383$	189957.	+	109672.i	1.29496	+	0.747648i	0.979530	−	0.201299i	$-0.0645164\pi$
$383$	189957.	+	109672.i	1.29496	+	0.747648i	0.315434	+	0.948947i	$0.397850\pi$
$384$		−	84203.7i		−	0.571043i
$385$	4693.50	+	11742.4i	0.0316647	+	0.0792204i
$386$	220445.			1.47954
$387$	37773.0	−	65424.8i	0.252208	−	0.436838i
$388$	−42484.5	+	24528.4i	−0.282207	+	0.162932i
$389$	2131.00	+	3691.00i	0.0140826	+	0.0243919i	0.872981	−	0.487754i	$-0.162184\pi$
$389$	2131.00	+	3691.00i	0.0140826	+	0.0243919i	−0.858898	+	0.512146i	$0.828851\pi$
$390$	−1620.00	−	935.307i	−0.0106509	−	0.00614929i
$391$			149372.i			0.977048i
$392$	60882.5	−	57924.1i	0.396205	−	0.376953i
$393$	143199.			0.927160
$394$	−116195.	+	201256.i	−0.748506	+	1.29645i
$395$	6487.50	−	3745.56i	0.0415799	−	0.0240062i
$396$	−18103.5	−	31356.2i	−0.115444	−	0.199955i
$397$	126618.	+	73102.9i	0.803368	+	0.463825i	0.844647	−	0.535323i	$-0.179810\pi$
$397$	126618.	+	73102.9i	0.803368	+	0.463825i	−0.0412796	+	0.999148i	$0.513143\pi$
$398$			196172.i			1.23843i
$399$	84357.0	−	33717.8i	0.529877	−	0.211794i
$400$	−198418.			−1.24011
$401$	45406.0	−	78645.5i	0.282374	−	0.489086i	−0.689595	−	0.724195i	$-0.742211\pi$
$401$	45406.0	−	78645.5i	0.282374	−	0.489086i	0.971969	+	0.235109i	$0.0755448\pi$
$402$	93510.0	−	53988.0i	0.578637	−	0.334076i
$403$	−26748.0	−	46328.9i	−0.164695	−	0.285261i
$404$	33750.0	+	19485.6i	0.206781	+	0.119385i
$405$			1262.67i			0.00769800i
$406$	−8225.00	+	56984.5i	−0.0498981	+	0.345704i
$407$	−293530.			−1.77200
$408$	−24255.0	+	42010.9i	−0.145707	+	0.252372i
$409$	39250.5	−	22661.3i	0.234638	−	0.135468i	−0.378072	−	0.925776i	$-0.623413\pi$
$409$	39250.5	−	22661.3i	0.234638	−	0.135468i	0.612710	+	0.790308i	$0.290079\pi$
$410$	12195.0	+	21122.4i	0.0725461	+	0.125654i
$411$	−80208.0	−	46308.1i	−0.474826	−	0.274141i
$412$		−	130070.i		−	0.766272i
$413$	−41842.5	+	53147.1i	−0.245311	+	0.311587i
$414$	−75600.0			−0.441084
$415$	1129.50	−	1956.35i	0.00655828	−	0.0113593i
$416$	37260.0	−	21512.1i	0.215306	−	0.124307i
$417$	−72711.0	−	125939.i	−0.418146	−	0.724250i
$418$	−230205.	−	132909.i	−1.31754	−	0.760679i
$419$			148922.i			0.848262i	0.905601	+	0.424131i	$0.139420\pi$
$419$			148922.i			0.848262i	−0.905601	+	0.424131i	$0.860580\pi$
$420$	−3118.50	−	2455.18i	−0.0176786	−	0.0139183i
$421$	4256.00			0.0240125			0.0120063	−	0.999928i	$-0.496178\pi$
$421$	4256.00			0.0240125			0.0120063	+	0.999928i	$0.496178\pi$
$422$	−69220.0	+	119893.i	−0.388693	+	0.673236i
$423$	96552.0	−	55744.3i	0.539611	−	0.311544i
$424$	−15767.5	−	27310.1i	−0.0877064	−	0.151912i
$425$	143682.	+	82954.8i	0.795471	+	0.459266i
$426$		−	12574.7i		−	0.0692912i
$427$	173040.	+	24976.2i	0.949054	+	0.136984i
$428$	40185.0			0.219370
$429$	−16092.0	+	27872.2i	−0.0874370	+	0.151445i
$430$	−20985.0	+	12115.7i	−0.113494	+	0.0655257i
$431$	73831.0	+	127879.i	0.397452	+	0.688406i	0.993411	−	0.114608i	$-0.0365613\pi$
$431$	73831.0	+	127879.i	0.397452	+	0.688406i	−0.595959	+	0.803015i	$0.703228\pi$
$432$	−38758.5	−	22377.2i	−0.207682	−	0.119905i
$433$		−	58799.7i		−	0.313617i	−0.987629	−	0.156808i	$-0.949880\pi$
$433$		−	58799.7i		−	0.313617i	0.987629	−	0.156808i	$-0.0501205\pi$
$434$	−117022.	−	292773.i	−0.621284	−	1.55436i
$435$	−2115.00			−0.0111772
$436$	−14940.0	+	25876.8i	−0.0785919	+	0.136125i
$437$	−173040.	+	99904.7i	−0.906116	+	0.523146i
$438$	12330.0	+	21356.2i	0.0642710	+	0.111321i
$439$	−88882.5	−	51316.3i	−0.461198	−	0.266273i	0.251350	−	0.967896i	$-0.419125\pi$
$439$	−88882.5	−	51316.3i	−0.461198	−	0.266273i	−0.712548	+	0.701624i	$0.752459\pi$
$440$		−	9032.64i		−	0.0466562i
$441$	−15214.5	−	63016.3i	−0.0782313	−	0.324023i
$442$	−55440.0			−0.283778
$443$	146990.	−	254595.i	0.749000	−	1.29731i	−0.199302	−	0.979938i	$-0.563868\pi$
$443$	146990.	−	254595.i	0.749000	−	1.29731i	0.948302	−	0.317368i	$-0.102799\pi$
$444$	79785.0	−	46063.9i	0.404721	−	0.233666i
$445$	−1713.00	−	2967.00i	−0.00865042	−	0.0149830i
$446$	212512.	+	122694.i	1.06835	+	0.616814i
$447$			47877.3i			0.239616i
$448$	3230.50	−	1291.24i	0.0160958	−	0.00643357i
$449$	21220.0			0.105257			0.0526287	−	0.998614i	$-0.483240\pi$
$449$	21220.0			0.105257			0.0526287	+	0.998614i	$0.483240\pi$
$450$	−41985.0	+	72720.2i	−0.207333	+	0.359112i
$451$	363411.	−	209815.i	1.78667	−	1.03154i
$452$	43803.0	+	75869.0i	0.214401	+	0.371354i
$453$	−53887.5	−	31112.0i	−0.262598	−	0.151611i
$454$		−	370321.i		−	1.79666i
$455$	−504.000	+	3491.81i	−0.00243449	+	0.0168666i
$456$	−64890.0			−0.312067
$457$	88233.5	−	152825.i	0.422475	−	0.731748i	−0.573706	−	0.819061i	$-0.694495\pi$
$457$	88233.5	−	152825.i	0.422475	−	0.731748i	0.996181	+	0.0873131i	$0.0278281\pi$
$458$	103485.	−	59747.1i	0.493340	−	0.284830i
$459$	18711.0	+	32408.4i	0.0888120	+	0.153827i
$460$	7560.00	+	4364.77i	0.0357278	+	0.0206274i
$461$		−	222063.i		−	1.04490i	−0.852671	−	0.522449i	$-0.825019\pi$
$461$		−	222063.i		−	1.04490i	0.852671	−	0.522449i	$-0.174981\pi$
$462$	−117337.	+	149039.i	−0.549734	+	0.698256i
$463$	142286.			0.663743			0.331872	−	0.943325i	$-0.392320\pi$
$463$	142286.			0.663743			0.331872	+	0.943325i	$0.392320\pi$
$464$	37482.5	−	64921.6i	0.174098	−	0.301546i
$465$	10030.5	−	5791.11i	0.0463892	−	0.0267828i
$466$	240955.	+	417346.i	1.10959	+	1.92187i
$467$	−338190.	−	195254.i	−1.55070	−	0.895295i	−0.998085	−	0.0618569i	$-0.980298\pi$
$467$	−338190.	−	195254.i	−1.55070	−	0.895295i	−0.552612	−	0.833439i	$-0.686369\pi$
$468$		−	10101.3i		−	0.0461197i
$469$	−160006.	−	125972.i	−0.727429	−	0.572702i
$470$	−35760.0			−0.161883
$471$	−5166.00	+	8947.77i	−0.0232869	+	0.0403342i
$472$	41842.5	−	24157.8i	0.187816	−	0.108436i
$473$	208451.	+	361048.i	0.931712	+	1.61377i
$474$	97312.5	+	56183.4i	0.433124	+	0.250064i
$475$			221931.i			0.983628i
$476$	−116424.	−	16804.4i	−0.513841	−	0.0741665i
$477$	−24327.0			−0.106918
$478$	−110690.	+	191721.i	−0.484454	+	0.839099i
$479$	−131271.	+	75789.3i	−0.572134	+	0.330322i	−0.758001	−	0.652253i	$-0.773824\pi$
$479$	−131271.	+	75789.3i	−0.572134	+	0.330322i	0.185867	+	0.982575i	$0.440491\pi$
$480$	4657.50	+	8067.03i	0.0202148	+	0.0350131i
$481$	−70920.0	−	40945.7i	−0.306534	−	0.176977i
$482$			284740.i			1.22562i
$483$	52920.0	+	132398.i	0.226843	+	0.567528i
$484$	68040.0			0.290451
$485$	−4720.50	+	8176.15i	−0.0200680	+	0.0347588i
$486$	−16402.5	+	9469.99i	−0.0694444	+	0.0400938i
$487$	−103014.	−	178425.i	−0.434346	−	0.752310i	0.562896	−	0.826528i	$-0.309687\pi$
$487$	−103014.	−	178425.i	−0.434346	−	0.752310i	−0.997242	+	0.0742179i	$0.976354\pi$
$488$	−108150.	−	62440.4i	−0.454137	−	0.262196i
$489$		−	108080.i		−	0.451989i
$490$	−5880.00	+	19944.6i	−0.0244898	+	0.0830677i
$491$	−477113.			−1.97906			−0.989528	−	0.144338i	$-0.953895\pi$
$491$	−477113.			−1.97906			−0.989528	+	0.144338i	$0.953895\pi$
$492$	−65853.0	+	114061.i	−0.272048	+	0.471201i
$493$	−54285.0	+	31341.5i	−0.223350	+	0.128951i
$494$	−37080.0	−	64224.4i	−0.151945	−	0.263176i
$495$	−6034.50	−	3484.02i	−0.0246281	−	0.0142190i
$496$			410525.i			1.66869i
$497$	−22022.0	+	8802.28i	−0.0891546	+	0.0356355i
$498$	33885.0			0.136631
$499$	−82405.0	+	142730.i	−0.330942	+	0.573209i	−0.982697	−	0.185221i	$-0.940700\pi$
$499$	−82405.0	+	142730.i	−0.330942	+	0.573209i	0.651754	+	0.758430i	$0.274033\pi$
$500$	16834.5	−	9719.40i	0.0673380	−	0.0388776i
$501$	110376.	+	191177.i	0.439743	+	0.761658i
$502$	−323528.	−	186789.i	−1.28382	−	0.741213i
$503$		−	203616.i		−	0.804779i	−0.915468	−	0.402390i	$-0.868180\pi$
$503$		−	203616.i		−	0.804779i	0.915468	−	0.402390i	$-0.131820\pi$
$504$	−6615.00	+	45830.1i	−0.0260417	+	0.180422i
$505$	7500.00			0.0294089
$506$	208600.	−	361306.i	0.814729	−	1.41115i
$507$	120748.	−	69714.2i	0.469749	−	0.271210i
$508$	131170.	+	227194.i	0.508287	+	0.880378i
$509$	408536.	+	235868.i	1.57686	+	0.910403i	0.995293	+	0.0969069i	$0.0308949\pi$
$509$	408536.	+	235868.i	1.57686	+	0.910403i	0.581571	+	0.813496i	$0.302438\pi$
$510$		−	12003.1i		−	0.0461481i
$511$	28770.0	−	36542.8i	0.110179	−	0.139946i
$512$	−151525.			−0.578022
$513$	−25029.0	+	43351.5i	−0.0951062	+	0.164729i
$514$	127095.	−	73378.3i	0.481063	−	0.277742i
$515$	−12516.0	−	21678.3i	−0.0471901	−	0.0817357i
$516$	−113319.	−	65424.8i	−0.425602	−	0.245721i
$517$			615252.i			2.30182i
$518$	−379225.	−	298562.i	−1.41331	−	1.11269i
$519$	−12564.0			−0.0466437
$520$	1260.00	−	2182.38i	0.00465976	−	0.00807095i
$521$	363081.	−	209625.i	1.33761	−	0.772267i	0.351154	−	0.936318i	$-0.385789\pi$
$521$	363081.	−	209625.i	1.33761	−	0.772267i	0.986452	+	0.164051i	$0.0524561\pi$
$522$	−15862.5	−	27474.7i	−0.0582144	−	0.100830i
$523$	−259374.	−	149750.i	−0.948250	−	0.547473i	−0.0557134	−	0.998447i	$-0.517743\pi$
$523$	−259374.	−	149750.i	−0.948250	−	0.547473i	−0.892537	+	0.450974i	$0.851077\pi$
$524$		−	248028.i		−	0.903313i
$525$	156744.	+	22624.0i	0.568686	+	0.0820827i
$526$	445390.			1.60979
$527$	171633.	−	297277.i	0.617987	−	1.07039i
$528$	213890.	−	123489.i	0.767223	−	0.442956i
$529$	−16879.5	−	29236.2i	−0.0603182	−	0.104474i
$530$	6757.50	+	3901.44i	0.0240566	+	0.0138891i
$531$		−	37272.0i		−	0.132188i
$532$	−58401.0	−	146111.i	−0.206346	−	0.516248i
$533$	117072.			0.412096
$534$	25695.0	−	44505.0i	0.0901086	−	0.156073i
$535$	6697.50	−	3866.80i	0.0233994	−	0.0135097i
$536$	72730.0	+	125972.i	0.253154	+	0.438475i
$537$	−87201.0	−	50345.5i	−0.302394	−	0.174587i
$538$		−	356188.i		−	1.23059i
$539$	343147.	+	101166.i	1.18114	+	0.348221i
$540$	2187.00			0.00750000
$541$	−152545.	+	264216.i	−0.521199	+	0.902743i	0.478497	+	0.878089i	$0.341182\pi$
$541$	−152545.	+	264216.i	−0.521199	+	0.902743i	−0.999696	+	0.0246538i	$0.992152\pi$
$542$	−183322.	+	105841.i	−0.624047	+	0.360294i
$543$	19359.0	+	33530.8i	0.0656573	+	0.113722i
$544$	239085.	+	138036.i	0.807894	+	0.466438i
$545$			5750.41i			0.0193600i
$546$	−49140.0	+	19641.5i	−0.164835	+	0.0658853i
$547$	−260974.			−0.872213			−0.436107	−	0.899895i	$-0.643643\pi$
$547$	−260974.			−0.872213			−0.436107	+	0.899895i	$0.643643\pi$
$548$	−80208.0	+	138924.i	−0.267089	+	0.462612i
$549$	−83430.0	+	48168.3i	−0.276807	+	0.159815i
$550$	−231695.	−	401308.i	−0.765934	−	1.32664i
$551$	−72615.0	−	41924.3i	−0.239179	−	0.138090i
$552$		−	101845.i		−	0.334241i
$553$	30275.0	−	209751.i	0.0989997	−	0.685890i
$554$	232580.			0.757797
$555$	8865.00	−	15354.6i	0.0287801	−	0.0498486i
$556$	−218133.	+	125939.i	−0.705621	+	0.407391i
$557$	−125632.	−	217600.i	−0.404938	−	0.701373i	0.589377	−	0.807858i	$-0.299373\pi$
$557$	−125632.	−	217600.i	−0.404938	−	0.701373i	−0.994314	+	0.106486i	$0.966040\pi$
$558$	150458.	+	86866.7i	0.483221	+	0.278988i
$559$			116311.i			0.372217i
$560$	16747.5	−	21272.2i	0.0534040	−	0.0678322i
$561$	−206514.			−0.656181
$562$	125710.	−	217736.i	0.398013	−	0.689379i
$563$	−179111.	+	103409.i	−0.565073	+	0.326245i	−0.755179	−	0.655519i	$-0.772450\pi$
$563$	−179111.	+	103409.i	−0.565073	+	0.326245i	0.190106	+	0.981764i	$0.439117\pi$
$564$	−96552.0	−	167233.i	−0.303531	−	0.525731i
$565$	14601.0	+	8429.89i	0.0457389	+	0.0264074i
$566$			185000.i			0.577484i
$567$	28066.5	+	22096.6i	0.0873016	+	0.0687322i
$568$	16940.0			0.0525069
$569$	−255431.	+	442419.i	−0.788949	+	1.36650i	0.137662	+	0.990479i	$0.456041\pi$
$569$	−255431.	+	442419.i	−0.788949	+	1.36650i	−0.926611	+	0.376021i	$0.877292\pi$
$570$	13905.0	−	8028.06i	0.0427978	−	0.0247093i
$571$	−187300.	−	324413.i	−0.574468	−	0.995007i	−0.996099	−	0.0882399i	$-0.971876\pi$
$571$	−187300.	−	324413.i	−0.574468	−	0.995007i	0.421632	−	0.906767i	$-0.361458\pi$
$572$	48276.0	+	27872.2i	0.147550	+	0.0851880i
$573$		−	149441.i		−	0.455157i
$574$	682920.	+	98571.0i	2.07275	+	0.299175i
$575$	−348320.			−1.05352
$576$	−958.500	+	1660.17i	−0.00288900	+	0.00500389i
$577$	−339416.	+	195962.i	−1.01948	+	0.588599i	−0.913954	−	0.405817i	$-0.866987\pi$
$577$	−339416.	+	195962.i	−1.01948	+	0.588599i	−0.105529	+	0.994416i	$0.533654\pi$
$578$	30932.5	+	53576.7i	0.0925890	+	0.160369i
$579$	198400.	+	114547.i	0.591815	+	0.341684i
$580$			3663.29i			0.0108897i
$581$	−23719.5	−	59342.7i	−0.0702673	−	0.175798i
$582$	−141615.			−0.418084
$583$	67124.5	−	116263.i	0.197489	−	0.342062i
$584$	−28770.0	+	16610.4i	−0.0843556	+	0.0487028i
$585$	−972.000	−	1683.55i	−0.00284024	−	0.00491943i
$586$	−290092.	−	167485.i	−0.844775	−	0.487731i
$587$			202645.i			0.588111i	0.955788	+	0.294055i	$0.0950050\pi$
$587$			202645.i			0.588111i	−0.955788	+	0.294055i	$0.904995\pi$
$588$	−109148.	+	26352.3i	−0.315689	+	0.0762191i
$589$	459174.			1.32357
$590$	−5977.50	+	10353.3i	−0.0171718	+	0.0297424i
$591$	−209151.	+	120753.i	−0.598804	+	0.345720i
$592$	314215.	+	544236.i	0.896569	+	1.55290i
$593$	554700.	+	320256.i	1.57743	+	0.910727i	0.995217	+	0.0976870i	$0.0311444\pi$
$593$	554700.	+	320256.i	1.57743	+	0.910727i	0.582208	+	0.813040i	$0.302189\pi$
$594$		−	104521.i		−	0.296230i
$595$	−21021.0	+	8402.18i	−0.0593772	+	0.0237333i
$596$	82926.0			0.233452
$597$	−101934.	+	176555.i	−0.286003	+	0.495372i
$598$	100800.	−	58196.9i	0.281876	−	0.162741i
$599$	−230642.	−	399484.i	−0.642813	−	1.11339i	−0.984802	−	0.173681i	$-0.944434\pi$
$599$	−230642.	−	399484.i	−0.642813	−	1.11339i	0.341989	−	0.939704i	$-0.388900\pi$
$600$	−97965.0	−	56560.1i	−0.272125	−	0.157111i
$601$		−	603767.i		−	1.67155i	−0.549069	−	0.835777i	$-0.685018\pi$
$601$		−	603767.i		−	1.67155i	0.549069	−	0.835777i	$-0.314982\pi$
$602$	−97930.0	+	678479.i	−0.270223	+	1.87216i
$603$	112212.			0.308606
$604$	−53887.5	+	93335.9i	−0.147711	+	0.255844i
$605$	11340.0	−	6547.15i	0.0309815	−	0.0178872i
$606$	56250.0	+	97427.9i	0.153171	+	0.265300i
$607$	340958.	+	196852.i	0.925386	+	0.534272i	0.885349	−	0.464926i	$-0.153919\pi$
$607$	340958.	+	196852.i	0.925386	+	0.534272i	0.0400366	+	0.999198i	$0.487253\pi$
$608$			369291.i			0.998990i
$609$	−37012.5	+	47012.2i	−0.0997962	+	0.126758i
$610$	30900.0			0.0830422
$611$	−85824.0	+	148652.i	−0.229893	+	0.398187i
$612$	56133.0	−	32408.4i	0.149870	−	0.0865276i
$613$	−202450.	−	350654.i	−0.538762	−	0.933163i	−0.998971	−	0.0453524i	$-0.985559\pi$
$613$	−202450.	−	350654.i	−0.538762	−	0.933163i	0.460209	−	0.887811i	$-0.347774\pi$
$614$	330210.	+	190647.i	0.875898	+	0.505700i
$615$			25346.8i			0.0670152i
$616$	−200778.	−	158071.i	−0.529119	−	0.416573i
$617$	258952.			0.680219			0.340110	−	0.940386i	$-0.389536\pi$
$617$	258952.			0.680219			0.340110	+	0.940386i	$0.389536\pi$
$618$	187740.	−	325175.i	0.491564	−	0.851413i
$619$	−110244.	+	63649.4i	−0.287722	+	0.166117i	−0.636914	−	0.770935i	$-0.719789\pi$
$619$	−110244.	+	63649.4i	−0.287722	+	0.166117i	0.349192	+	0.937051i	$0.386456\pi$
$620$	−10030.5	−	17373.3i	−0.0260939	−	0.0451960i
$621$	−68040.0	−	39282.9i	−0.176434	−	0.101864i
$622$		−	262943.i		−	0.679642i
$623$	−95928.0	−	13846.0i	−0.247155	−	0.0356737i
$624$	68904.0			0.176960
$625$	−192504.	+	333428.i	−0.492812	+	0.853575i
$626$	−402022.	+	232108.i	−1.02589	+	0.592299i
$627$	−138123.	−	239236.i	−0.351343	−	0.608543i
$628$	15498.0	+	8947.77i	0.0392967	+	0.0226880i
$629$		−	525470.i		−	1.32815i
$630$	−4252.50	−	10639.1i	−0.0107143	−	0.0268055i
$631$	−211021.			−0.529989			−0.264995	−	0.964250i	$-0.585370\pi$
$631$	−211021.			−0.529989			−0.264995	+	0.964250i	$0.585370\pi$
$632$	−75687.5	+	131095.i	−0.189492	+	0.328209i
$633$	−124596.	+	71935.5i	−0.310954	+	0.179530i
$634$	−153958.	−	266662.i	−0.383021	−	0.663411i
$635$	43723.5	+	25243.8i	0.108434	+	0.0626047i
$636$			42135.6i			0.104168i
$637$	68796.0	+	72309.7i	0.169545	+	0.178204i
$638$	175075.			0.430113
$639$	6534.00	−	11317.2i	0.0160021	−	0.0277165i
$640$	−24307.5	+	14033.9i	−0.0593445	+	0.0342626i
$641$	80584.0	+	139576.i	0.196125	+	0.339698i	0.947269	−	0.320440i	$-0.103831\pi$
$641$	80584.0	+	139576.i	0.196125	+	0.339698i	−0.751144	+	0.660139i	$0.770498\pi$
$642$	100462.	+	58002.1i	0.243744	+	0.140726i
$643$			427976.i			1.03514i	0.855642	+	0.517568i	$0.173163\pi$
$643$			427976.i			1.03514i	−0.855642	+	0.517568i	$0.826837\pi$
$644$	229320.	−	91660.1i	0.552930	−	0.221008i
$645$	−25182.0			−0.0605300
$646$	237930.	−	412107.i	0.570143	−	0.987517i
$647$	276222.	−	159477.i	0.659857	−	0.380969i	−0.132366	−	0.991201i	$-0.542257\pi$
$647$	276222.	−	159477.i	0.659857	−	0.380969i	0.792222	+	0.610232i	$0.208924\pi$
$648$	−12757.5	−	22096.6i	−0.0303819	−	0.0526231i
$649$	178130.	+	102843.i	0.422909	+	0.244166i
$650$		−	129280.i		−	0.305989i
$651$	46809.0	−	324302.i	0.110450	−	0.765223i
$652$	−187200.			−0.440363
$653$	233024.	−	403610.i	0.546481	−	0.946533i	−0.452031	−	0.892002i	$-0.649300\pi$
$653$	233024.	−	403610.i	0.546481	−	0.946533i	0.998512	−	0.0545309i	$-0.0173663\pi$
$654$	−74700.0	+	43128.1i	−0.174649	+	0.100833i
$655$	−23866.5	−	41338.0i	−0.0556296	−	0.0963533i
$656$	−778041.	−	449202.i	−1.80798	−	1.04384i
$657$			25627.4i			0.0593710i
$658$	−625800.	+	794873.i	−1.44539	+	1.83589i
$659$	103258.			0.237768			0.118884	−	0.992908i	$-0.462068\pi$
$659$	103258.			0.237768			0.118884	+	0.992908i	$0.462068\pi$
$660$	−6034.50	+	10452.1i	−0.0138533	+	0.0239946i
$661$	173265.	−	100035.i	0.396559	−	0.228954i	−0.288439	−	0.957498i	$-0.593136\pi$
$661$	173265.	−	100035.i	0.396559	−	0.228954i	0.684998	+	0.728545i	$0.259803\pi$
$662$	−228700.	−	396120.i	−0.521855	−	0.903880i
$663$	−49896.0	−	28807.5i	−0.113511	−	0.0655357i
$664$			45648.2i			0.103535i
$665$	−23793.0	−	18732.1i	−0.0538029	−	0.0423588i
$666$	265950.			0.599586
$667$	65800.0	−	113969.i	0.147902	−	0.256174i
$668$	331128.	−	191177.i	0.742067	−	0.428432i
$669$	127508.	+	220849.i	0.284894	+	0.493451i
$670$	−31170.0	−	17996.0i	−0.0694364	−	0.0400891i
$671$		−	531636.i		−	1.18078i
$672$	260820.	+	37646.1i	0.577567	+	0.0833646i
$673$	160973.			0.355404			0.177702	−	0.984084i	$-0.443134\pi$
$673$	160973.			0.355404			0.177702	+	0.984084i	$0.443134\pi$
$674$	24987.5	−	43279.6i	0.0550051	−	0.0952716i
$675$	−75573.0	+	43632.1i	−0.165867	+	0.0957632i
$676$	−120748.	−	209143.i	−0.264234	−	0.457666i
$677$	−186356.	−	107592.i	−0.406598	−	0.234749i	0.282729	−	0.959200i	$-0.408760\pi$
$677$	−186356.	−	107592.i	−0.406598	−	0.234749i	−0.689327	+	0.724451i	$0.742094\pi$
$678$			252897.i			0.550153i
$679$	99130.5	+	248010.i	0.215014	+	0.537934i
$680$	16170.0			0.0349697
$681$	192424.	−	333289.i	0.414922	−	0.718665i
$682$	−830302.	+	479375.i	−1.78512	+	1.03064i
$683$	72998.5	+	126437.i	0.156485	+	0.271040i	0.933599	−	0.358320i	$-0.116650\pi$
$683$	72998.5	+	126437.i	0.156485	+	0.271040i	−0.777114	+	0.629360i	$0.783317\pi$
$684$	75087.0	+	43351.5i	0.160492	+	0.0926599i
$685$			30872.1i			0.0657938i
$686$	340428.	+	479730.i	0.723397	+	1.01941i
$687$	124182.			0.263115
$688$	446281.	−	772981.i	0.942826	−	1.63302i
$689$	32436.0	−	18726.9i	0.0683264	−	0.0394483i
$690$	12600.0	+	21823.8i	0.0264650	+	0.0458388i
$691$	537693.	+	310437.i	1.12610	+	0.650156i	0.942952	−	0.332929i	$-0.108037\pi$
$691$	537693.	+	310437.i	1.12610	+	0.650156i	0.183151	+	0.983085i	$0.441370\pi$
$692$			21761.5i			0.0454440i
$693$	−183046.	+	73164.4i	−0.381149	+	0.152347i
$694$	−312290.			−0.648394
$695$	−24237.0	+	41979.7i	−0.0501775	+	0.0869100i
$696$	37012.5	−	21369.2i	0.0764064	−	0.0441133i
$697$	375606.	+	650569.i	0.773156	+	1.33914i
$698$	−1.01052e6	−	583424.i	−2.07412	−	1.19749i
$699$			500816.i			1.02500i
$700$	39186.0	−	271489.i	0.0799714	−	0.554058i
$701$	626353.			1.27463			0.637314	−	0.770605i	$-0.280046\pi$
$701$	626353.			1.27463			0.637314	+	0.770605i	$0.280046\pi$
$702$	14580.0	−	25253.3i	0.0295858	−	0.0512441i
$703$	608730.	−	351450.i	1.23173	−	0.711137i
$704$	−5289.50	−	9161.68i	−0.0106726	−	0.0184854i
$705$	−32184.0	−	18581.4i	−0.0647533	−	0.0373853i
$706$			415103.i			0.832812i
$707$	131250.	−	166710.i	0.262579	−	0.333521i
$708$	−64557.0			−0.128788
$709$	−155149.	+	268726.i	−0.308643	+	0.534585i	−0.978066	−	0.208296i	$-0.933208\pi$
$709$	−155149.	+	268726.i	−0.308643	+	0.534585i	0.669423	+	0.742882i	$0.266542\pi$
$710$	−3630.00	+	2095.78i	−0.00720095	+	0.00415747i
$711$	58387.5	+	101130.i	0.115500	+	0.200051i
$712$	59955.0	+	34615.0i	0.118268	+	0.0682818i
$713$			720672.i			1.41762i
$714$	−266805.	−	210054.i	−0.523356	−	0.412036i
$715$	10728.0			0.0209849
$716$	−87201.0	+	151037.i	−0.170097	+	0.294616i
$717$	−199242.	+	115032.i	−0.387563	+	0.223760i
$718$	410110.	+	710331.i	0.795521	+	1.37788i
$719$	−507615.	−	293072.i	−0.981921	−	0.566913i	−0.0790716	−	0.996869i	$-0.525196\pi$
$719$	−507615.	−	293072.i	−0.981921	−	0.566913i	−0.902850	+	0.429956i	$0.858529\pi$
$720$			14918.2i			0.0287773i
$721$	−700896.	−	101166.i	−1.34829	−	0.194609i
$722$	−15065.0			−0.0288998
$723$	−147956.	+	256266.i	−0.283044	+	0.490247i
$724$	58077.0	−	33530.8i	0.110797	−	0.0639685i
$725$	−73085.0	−	126587.i	−0.139044	−	0.240831i
$726$	170100.	+	98207.3i	0.322724	+	0.186325i
$727$		−	756846.i		−	1.43198i	−0.698108	−	0.715992i	$-0.745974\pi$
$727$		−	756846.i		−	1.43198i	0.698108	−	0.715992i	$-0.254026\pi$
$728$	−26460.0	−	66199.0i	−0.0499260	−	0.124908i
$729$	−19683.0			−0.0370370
$730$	4110.00	−	7118.73i	0.00771252	−	0.0133585i
$731$	−646338.	+	373163.i	−1.20955	+	0.698336i
$732$	83430.0	+	144505.i	0.155704	+	0.269687i
$733$	−95619.0	−	55205.7i	−0.177966	−	0.102749i	0.408371	−	0.912816i	$-0.366097\pi$
$733$	−95619.0	−	55205.7i	−0.177966	−	0.102749i	−0.586337	+	0.810068i	$0.699430\pi$
$734$			21451.4i			0.0398166i
$735$	−15655.5	+	14894.8i	−0.0289796	+	0.0275714i
$736$	−579600.			−1.06997
$737$	−309622.	+	536281.i	−0.570029	+	0.987319i
$738$	−329265.	+	190101.i	−0.604551	+	0.349038i
$739$	−53581.0	−	92805.0i	−0.0981120	−	0.169935i	0.812791	−	0.582555i	$-0.197947\pi$
$739$	−53581.0	−	92805.0i	−0.0981120	−	0.169935i	−0.910903	+	0.412620i	$0.864614\pi$
$740$	−26595.0	−	15354.6i	−0.0485665	−	0.0280399i
$741$		−	77069.3i		−	0.140361i
$742$	204978.	−	81930.3i	0.372305	−	0.148812i
$743$	90580.0			0.164080			0.0820398	−	0.996629i	$-0.473857\pi$
$743$	90580.0			0.164080			0.0820398	+	0.996629i	$0.473857\pi$
$744$	−117022.	+	202689.i	−0.211409	+	0.366171i
$745$	13821.0	−	7979.56i	0.0249016	−	0.0143769i
$746$	196565.	+	340461.i	0.353206	+	0.611771i
$747$	30496.5	+	17607.2i	0.0546523	+	0.0315535i
$748$			357693.i			0.639303i
$749$	31255.0	−	216541.i	0.0557129	−	0.385990i
$750$	56115.0			0.0997600
$751$	62139.5	−	107629.i	0.110176	−	0.190831i	−0.805665	−	0.592371i	$-0.798192\pi$
$751$	62139.5	−	107629.i	0.110176	−	0.190831i	0.915841	+	0.401541i	$0.131525\pi$
$752$	1.14074e6	−	658609.i	2.01722	−	1.16464i
$753$	−194116.	−	336220.i	−0.342352	−	0.592971i
$754$	42300.0	+	24421.9i	0.0744042	+	0.0429573i
$755$			20741.3i			0.0363867i
$756$	38272.5	−	48612.6i	0.0669643	−	0.0850561i
$757$	−147904.			−0.258100			−0.129050	−	0.991638i	$-0.541193\pi$
$757$	−147904.			−0.258100			−0.129050	+	0.991638i	$0.541193\pi$
$758$	140585.	−	243500.i	0.244681	−	0.423800i
$759$	375480.	−	216783.i	0.651783	−	0.376307i
$760$	10815.0	+	18732.1i	0.0187240	+	0.0324310i
$761$	−345318.	−	199369.i	−0.596280	−	0.344262i	0.171297	−	0.985219i	$-0.445204\pi$
$761$	−345318.	−	199369.i	−0.596280	−	0.344262i	−0.767577	+	0.640957i	$0.778538\pi$
$762$			757313.i			1.30426i
$763$	127820.	+	100632.i	0.219558	+	0.172857i
$764$	−258840.			−0.443450
$765$	6237.00	−	10802.8i	0.0106574	−	0.0184592i
$766$	949785.	−	548359.i	1.61871	−	0.934560i
$767$	28692.0	+	49696.0i	0.0487719	+	0.0844755i
$768$	−369724.	−	213461.i	−0.626839	−	0.361905i
$769$		−	1.07770e6i		−	1.82240i	−0.411962	−	0.911201i	$-0.635156\pi$
$769$		−	1.07770e6i		−	1.82240i	0.411962	−	0.911201i	$-0.364844\pi$
$770$	62580.0	+	9032.64i	0.105549	+	0.0152347i
$771$	152514.			0.256567
$772$	198400.	−	343640.i	0.332896	−	0.576592i
$773$	33762.0	−	19492.5i	0.0565027	−	0.0326218i	−0.471483	−	0.881875i	$-0.656281\pi$
$773$	33762.0	−	19492.5i	0.0565027	−	0.0326218i	0.527985	+	0.849254i	$0.322948\pi$
$774$	−188865.	−	327124.i	−0.315261	−	0.546047i
$775$	693219.	+	400230.i	1.15416	+	0.666356i
$776$		−	190777.i		−	0.316812i
$777$	−186165.	−	465757.i	−0.308359	−	0.771467i
$778$	21310.0			0.0352066
$779$	−502434.	+	870241.i	−0.827950	+	1.43405i
$780$	−2916.00	+	1683.55i	−0.00479290	+	0.00276718i
$781$	36058.0	+	62454.3i	0.0591153	+	0.102391i
$782$	646800.	+	373430.i	1.05769	+	0.610655i
$783$		−	32969.6i		−	0.0537762i
$784$	−179756.	−	744526.i	−0.292451	−	1.21129i
$785$	3444.00			0.00558887
$786$	357998.	−	620070.i	0.579475	−	1.00368i
$787$	−393276.	+	227058.i	−0.634962	+	0.366596i	−0.782671	−	0.622435i	$-0.786143\pi$
$787$	−393276.	+	227058.i	−0.634962	+	0.366596i	0.147709	+	0.989031i	$0.452810\pi$
$788$	209151.	+	362260.i	0.336827	+	0.583402i
$789$	400851.	+	231431.i	0.643916	+	0.371765i
$790$		−	37455.6i		−	0.0600154i
$791$	442897.	−	177028.i	0.707864	−	0.282936i
$792$	140805.			0.224475
$793$	74160.0	−	128449.i	0.117930	−	0.204260i
$794$	633090.	−	365515.i	1.00421	−	0.579781i
$795$	4054.50	+	7022.60i	0.00641509	+	0.0111113i
$796$	305802.	+	176555.i	0.482630	+	0.278646i
$797$		−	639589.i		−	1.00690i	−0.864026	−	0.503448i	$-0.832065\pi$
$797$		−	639589.i		−	1.00690i	0.864026	−	0.503448i	$-0.167935\pi$
$798$	64890.0	−	449571.i	0.101899	−	0.705980i
$799$	−1.10141e6			−1.72526
$800$	−321885.	+	557521.i	−0.502945	+	0.871127i
$801$	46251.0	−	26703.0i	0.0720869	−	0.0416194i
$802$	−227030.	−	393227.i	−0.352967	−	0.611357i
$803$	−122478.	−	70712.7i	−0.189945	−	0.109665i
$804$		−	194357.i		−	0.300668i
$805$	29400.0	−	37343.0i	0.0453686	−	0.0576259i
$806$	−267480.			−0.411738
$807$	185080.	−	320569.i	0.284193	−	0.492237i
$808$	−131250.	+	75777.2i	−0.201037	+	0.116069i
$809$	−152636.	−	264373.i	−0.233217	−	0.403943i	0.725536	−	0.688184i	$-0.241592\pi$
$809$	−152636.	−	264373.i	−0.233217	−	0.403943i	−0.958753	+	0.284241i	$0.908259\pi$
$810$	5467.50	+	3156.66i	0.00833333	+	0.00481125i
$811$			644552.i			0.979977i	0.871729	+	0.489989i	$0.162999\pi$
$811$			644552.i			0.979977i	−0.871729	+	0.489989i	$0.837001\pi$
$812$	81427.5	+	64107.5i	0.123498	+	0.0972293i
$813$	−219987.			−0.332825
$814$	−733825.	+	1.27102e6i	−1.10750	+	1.91825i
$815$	−31200.0	+	18013.3i	−0.0469720	+	0.0271193i
$816$	221067.	+	382899.i	0.332004	+	0.575048i
$817$	−864582.	−	499167.i	−1.29528	−	0.747828i
$818$		−	226613.i		−	0.338671i
$819$	−54432.0	−	7856.58i	−0.0811496	−	0.0117129i
$820$	43902.0			0.0652915
$821$	−459960.	+	796675.i	−0.682392	+	1.18194i	0.291856	+	0.956462i	$0.405727\pi$
$821$	−459960.	+	796675.i	−0.682392	+	1.18194i	−0.974249	+	0.225476i	$0.927606\pi$
$822$	−401040.	+	231541.i	−0.593532	+	0.342676i
$823$	107009.	+	185345.i	0.157987	+	0.273641i	0.934143	−	0.356900i	$-0.116166\pi$
$823$	107009.	+	185345.i	0.157987	+	0.273641i	−0.776156	+	0.630541i	$0.782833\pi$
$824$	438060.	+	252914.i	0.645177	+	0.372493i
$825$		−	481569.i		−	0.707539i
$826$	125528.	+	314051.i	0.183983	+	0.460299i
$827$	129841.			0.189846			0.0949229	−	0.995485i	$-0.469740\pi$
$827$	129841.			0.189846			0.0949229	+	0.995485i	$0.469740\pi$
$828$	−68040.0	+	117849.i	−0.0992439	+	0.171895i
$829$	−528375.	+	305057.i	−0.768835	+	0.443887i	−0.832459	−	0.554087i	$-0.813068\pi$
$829$	−528375.	+	305057.i	−0.768835	+	0.443887i	0.0636238	+	0.997974i	$0.479734\pi$
$830$	−5647.50	−	9781.76i	−0.00819785	−	0.0141991i
$831$	209322.	+	120852.i	0.303119	+	0.175006i
$832$		−	2951.41i		−	0.00426367i
$833$	−181104.	+	614293.i	−0.260999	+	0.885289i
$834$	−727110.			−1.04537
$835$	36792.0	−	63725.6i	0.0527692	−	0.0913989i
$836$	−414369.	+	239236.i	−0.592891	+	0.342306i
$837$	90274.5	+	156360.i	0.128859	+	0.223190i
$838$	644850.	+	372304.i	0.918271	+	0.530164i
$839$			903206.i			1.28311i	0.767079	+	0.641553i	$0.221710\pi$
$839$			903206.i			1.28311i	−0.767079	+	0.641553i	$0.778290\pi$
$840$	14332.5	−	5728.76i	0.0203125	−	0.00811899i
$841$	−652056.			−0.921919
$842$	10640.0	−	18429.0i	0.0150078	−	0.0259943i
$843$	226278.	−	130642.i	0.318410	−	0.183834i
$844$	124596.	+	215807.i	0.174912	+	0.302956i
$845$	−40249.5	−	23238.1i	−0.0563699	−	0.0325452i
$846$		−	557443.i		−	0.778861i
$847$	52920.0	−	366641.i	0.0737655	−	0.511062i
$848$	−287419.			−0.399690
$849$	−96129.0	+	166500.i	−0.133364	+	0.230993i
$850$	718410.	−	414774.i	0.994339	−	0.574082i
$851$	551600.	+	955399.i	0.761667	+	1.31925i
$852$	−19602.0	−	11317.2i	−0.0270036	−	0.0155905i
$853$		−	266542.i		−	0.366326i	−0.983083	−	0.183163i	$-0.941366\pi$
$853$		−	266542.i		−	0.366326i	0.983083	−	0.183163i	$-0.0586336\pi$
$854$	540750.	−	686845.i	0.741448	−	0.941766i
$855$	16686.0			0.0228255
$856$	−78137.5	+	135338.i	−0.106638	+	0.184702i
$857$	993954.	−	573860.i	1.35333	−	0.781347i	0.364618	−	0.931157i	$-0.381200\pi$
$857$	993954.	−	573860.i	1.35333	−	0.781347i	0.988715	+	0.149810i	$0.0478662\pi$
$858$	80460.0	+	139361.i	0.109296	+	0.189307i
$859$	−229917.	−	132743.i	−0.311591	−	0.179897i	0.336047	−	0.941845i	$-0.390910\pi$
$859$	−229917.	−	132743.i	−0.311591	−	0.179897i	−0.647638	+	0.761948i	$0.724243\pi$
$860$			43616.5i			0.0589731i
$861$	563409.	+	443570.i	0.760007	+	0.598350i
$862$	738310.			0.993629
$863$	528331.	−	915096.i	0.709389	−	1.22870i	−0.255695	−	0.966758i	$-0.582304\pi$
$863$	528331.	−	915096.i	0.709389	−	1.22870i	0.965084	−	0.261940i	$-0.0843624\pi$
$864$	−125752.	+	72603.2i	−0.168457	+	0.0972587i
$865$	2094.00	+	3626.91i	0.00279862	+	0.00484736i
$866$	−254610.	−	146999.i	−0.339500	−	0.196010i
$867$			64292.0i			0.0855300i
$868$	−561708.	−	81075.6i	−0.745540	−	0.107609i
$869$	−644425.			−0.853361
$870$	−5287.50	+	9158.22i	−0.00698573	+	0.0120996i
$871$	−149616.	+	86380.8i	−0.197216	+	0.113863i
$872$	−58100.0	−	100632.i	−0.0764088	−	0.132344i
$873$	−127454.	−	73585.3i	−0.167233	−	0.0965523i
$874$			999047.i			1.30787i
$875$	−39280.5	−	98274.0i	−0.0513051	−	0.128358i
$876$	44388.0			0.0578439
$877$	261728.	−	453326.i	0.340291	−	0.589402i	−0.644195	−	0.764861i	$-0.722808\pi$
$877$	261728.	−	453326.i	0.340291	−	0.589402i	0.984487	+	0.175459i	$0.0561409\pi$
$878$	−444412.	+	256582.i	−0.576497	+	0.332841i
$879$	−174056.	−	301473.i	−0.225273	−	0.390185i
$880$	−71296.5	−	41163.1i	−0.0920668	−	0.0531548i
$881$			1.20087e6i			1.54719i	0.633677	+	0.773597i	$0.281545\pi$
$881$			1.20087e6i			1.54719i	−0.633677	+	0.773597i	$0.718455\pi$
$882$	−310905.	−	91660.1i	−0.399660	−	0.117827i
$883$	872138.			1.11857			0.559286	−	0.828975i	$-0.311075\pi$
$883$	872138.			1.11857			0.559286	+	0.828975i	$0.311075\pi$
$884$	−49896.0	+	86422.4i	−0.0638500	+	0.110592i
$885$	−10759.5	+	6212.00i	−0.0137374	+	0.00793131i
$886$	−734952.	−	1.27298e6i	−0.936250	−	1.62163i
$887$	367212.	+	212010.i	0.466734	+	0.269469i	0.714872	−	0.699256i	$-0.246485\pi$
$887$	367212.	+	212010.i	0.466734	+	0.269469i	−0.248137	+	0.968725i	$0.579818\pi$
$888$			358275.i			0.454350i
$889$	1.32628e6	−	530119.i	1.67815	−	0.670764i
$890$	−17130.0			−0.0216261
$891$	54310.5	−	94068.5i	0.0684114	−	0.118492i
$892$	382522.	−	220849.i	0.480759	−	0.277566i
$893$	−736656.	−	1.27593e6i	−0.923766	−	1.60001i
$894$	207315.	+	119693.i	0.259391	+	0.149760i
$895$			33563.7i			0.0419009i
$896$	−113435.	+	785901.i	−0.141296	+	0.978930i
$897$	120960.			0.150334
$898$	53050.0	−	91885.3i	0.0657859	−	0.113944i
$899$	−261908.	+	151212.i	−0.324062	+	0.187097i
$900$	75573.0	+	130896.i	0.0933000	+	0.161600i
$901$	208131.	+	120164.i	0.256382	+	0.148022i
$902$		−	2.09815e6i		−	2.57884i
$903$	−440685.	+	559745.i	−0.540447	+	0.686459i
$904$	−340690.			−0.416891
$905$	6453.00	−	11176.9i	0.00787888	−	0.0136466i
$906$	−269438.	+	155560.i	−0.328248	+	0.189514i
$907$	778646.	+	1.34865e6i	0.946511	+	1.63940i	0.752698	+	0.658366i	$0.228752\pi$
$907$	778646.	+	1.34865e6i	0.946511	+	1.63940i	0.193813	+	0.981039i	$0.437915\pi$
$908$	−577274.	−	333289.i	−0.700180	−	0.404249i
$909$			116913.i			0.141494i
$910$	13860.0	+	10911.9i	0.0167371	+	0.0131771i
$911$	491572.			0.592312			0.296156	−	0.955140i	$-0.404295\pi$
$911$	491572.			0.592312			0.296156	+	0.955140i	$0.404295\pi$
$912$	−295713.	+	512190.i	−0.355534	+	0.615802i
$913$	−168296.	+	97165.5i	−0.201898	+	0.116566i
$914$	−441168.	−	764125.i	−0.528094	−	0.914685i
$915$	27810.0	+	16056.1i	0.0332169	+	0.0191778i
$916$		−	215090.i		−	0.256347i
$917$	−1.33652e6	−	192911.i	−1.58942	−	0.229413i
$918$	187110.			0.222030
$919$	516515.	−	894630.i	0.611578	−	1.05928i	−0.379396	−	0.925234i	$-0.623868\pi$
$919$	516515.	−	894630.i	0.611578	−	1.05928i	0.990975	−	0.134050i	$-0.0427983\pi$
$920$	−29400.0	+	16974.1i	−0.0347353	+	0.0200545i
$921$	198126.	+	343164.i	0.233573	+	0.404560i
$922$	−961560.	−	555157.i	−1.13114	−	0.653061i
$923$			20119.5i			0.0236164i
$924$	126724.	+	317046.i	0.148428	+	0.371345i
$925$	1.22534e6			1.43210
$926$	355715.	−	616116.i	0.414840	−	0.718523i
$927$	337932.	−	195105.i	0.393251	−	0.227044i
$928$	−121612.	−	210639.i	−0.141215	−	0.244592i
$929$	−553623.	−	319634.i	−0.641479	−	0.370358i	0.143705	−	0.989621i	$-0.454098\pi$
$929$	−553623.	−	319634.i	−0.641479	−	0.370358i	−0.785184	+	0.619262i	$0.787432\pi$
$930$		−	57911.1i		−	0.0669570i
$931$	−832755.	+	201058.i	−0.960767	+	0.231965i
$932$	867438.			0.998635
$933$	136629.	−	236648.i	0.156957	−	0.271857i
$934$	−1.69095e6	+	976270.i	−1.93837	+	1.11912i
$935$	34419.0	+	59615.5i	0.0393709	+	0.0681923i
$936$	34020.0	+	19641.5i	0.0388314	+	0.0224193i
$937$			656103.i			0.747296i	0.927571	+	0.373648i	$0.121893\pi$
$937$			656103.i			0.747296i	−0.927571	+	0.373648i	$0.878107\pi$
$938$	−945490.	+	377916.i	−1.07461	+	0.429526i
$939$	−482427.			−0.547142
$940$	−32184.0	+	55744.3i	−0.0364237	+	0.0630877i
$941$	429820.	−	248157.i	0.485409	−	0.280251i	−0.237259	−	0.971446i	$-0.576249\pi$
$941$	429820.	−	248157.i	0.485409	−	0.280251i	0.722668	+	0.691195i	$0.242916\pi$
$942$	25830.0	+	44738.9i	0.0291087	+	0.0504177i
$943$	−1.36584e6	−	788568.i	−1.53595	−	0.886780i
$944$		−	440362.i		−	0.494158i
$945$	1701.00	−	11784.9i	0.00190476	−	0.0131966i
$946$	2.08451e6			2.32928
$947$	595411.	−	1.03128e6i	0.663922	−	1.14995i	−0.315655	−	0.948874i	$-0.602224\pi$
$947$	595411.	−	1.03128e6i	0.663922	−	1.14995i	0.979576	−	0.201072i	$-0.0644425\pi$
$948$	175162.	−	101130.i	0.194906	−	0.112529i
$949$	−19728.0	−	34169.9i	−0.0219054	−	0.0379412i
$950$	960990.	+	554828.i	1.06481	+	0.614768i
$951$		−	319995.i		−	0.353819i
$952$	282975.	−	359427.i	0.312230	−	0.396585i
$953$	255670.			0.281510			0.140755	−	0.990044i	$-0.455047\pi$
$953$	255670.			0.281510			0.140755	+	0.990044i	$0.455047\pi$
$954$	−60817.5	+	105339.i	−0.0668239	+	0.115742i
$955$	−43140.0	+	24906.9i	−0.0473013	+	0.0273094i
$956$	199242.	+	345097.i	0.218004	+	0.377595i
$957$	157568.	+	90971.6i	0.172045	+	0.0993304i
$958$			757893.i			0.825804i
$959$	686224.	+	540261.i	0.746154	+	0.587444i
$960$	639.000			0.000693359
$961$	366313.	−	634473.i	0.396648	−	0.687015i
$962$	−354600.	+	204728.i	−0.383167	+	0.221222i
$963$	60277.5	+	104404.i	0.0649984	+	0.112581i
$964$	443866.	+	256266.i	0.477637	+	0.275764i
$965$		−	76364.4i		−	0.0820042i
$966$	705600.	+	101845.i	0.756144	+	0.109140i
$967$	417065.			0.446016			0.223008	−	0.974817i	$-0.428412\pi$
$967$	417065.			0.446016			0.223008	+	0.974817i	$0.428412\pi$
$968$	−132300.	+	229150.i	−0.141192	+	0.244551i
$969$	428274.	−	247264.i	0.456115	−	0.263338i
$970$	23602.5	+	40880.7i	0.0250850	+	0.0434485i
$971$	143530.	+	82867.4i	0.152232	+	0.0878911i	0.574181	−	0.818728i	$-0.305321\pi$
$971$	143530.	+	82867.4i	0.152232	+	0.0878911i	−0.421949	+	0.906620i	$0.638654\pi$
$972$			34092.0i			0.0360844i
$973$	508977.	+	1.27338e6i	0.537616	+	1.34504i
$974$	−1.03014e6			−1.08587
$975$	67176.0	−	116352.i	0.0706651	−	0.122396i
$976$	−985710.	+	569100.i	−1.03478	+	0.597433i
$977$	176185.	+	305161.i	0.184578	+	0.319698i	0.943434	−	0.331560i	$-0.107575\pi$
$977$	176185.	+	305161.i	0.184578	+	0.319698i	−0.758856	+	0.651258i	$0.774242\pi$
$978$	−468000.	−	270200.i	−0.489292	−	0.282493i
$979$			294722.i			0.307502i
$980$	25798.5	+	27116.1i	0.0268622	+	0.0282342i
$981$	−89640.0			−0.0931459
$982$	−1.19278e6	+	2.06596e6i	−1.23691	+	2.14239i
$983$	−480759.	+	277566.i	−0.497531	+	0.287250i	−0.727693	−	0.685902i	$-0.759408\pi$
$983$	−480759.	+	277566.i	−0.497531	+	0.287250i	0.230162	+	0.973152i	$0.426074\pi$
$984$	−256095.	−	443570.i	−0.264491	−	0.458112i
$985$	69717.0	+	40251.1i	0.0718565	+	0.0414864i
$986$			313415.i			0.322378i
$987$	−976248.	+	390210.i	−1.00213	+	0.400557i
$988$	−133488.			−0.136750
$989$	783440.	−	1.35696e6i	0.800964	−	1.38731i
$990$	−30172.5	+	17420.1i	−0.0307851	+	0.0177738i
$991$	−418896.	−	725548.i	−0.426539	−	0.738787i	0.570024	−	0.821628i	$-0.306934\pi$
$991$	−418896.	−	725548.i	−0.426539	−	0.738787i	−0.996563	+	0.0828414i	$0.973601\pi$
$992$	1.15351e6	+	665978.i	1.17219	+	0.676763i
$993$		−	475344.i		−	0.482069i
$994$	−16940.0	+	117364.i	−0.0171451	+	0.118785i
$995$	67956.0			0.0686407
$996$	30496.5	−	52821.5i	0.0307419	−	0.0532466i
$997$	−876990.	+	506330.i	−0.882276	+	0.509382i	−0.871408	−	0.490559i	$-0.836793\pi$
$997$	−876990.	+	506330.i	−0.882276	+	0.509382i	−0.0108676	+	0.999941i	$0.503459\pi$
$998$	412025.	+	713648.i	0.413678	+	0.716511i
$999$	239355.	+	138192.i	0.239834	+	0.138468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.5.f.b.19.1	yes	2
3.2	odd	2		63.5.m.a.19.1		2
4.3	odd	2		336.5.bh.a.145.1		2
7.2	even	3		147.5.d.a.97.2		2
7.3	odd	6	inner	21.5.f.b.10.1	✓	2
7.4	even	3		147.5.f.b.31.1		2
7.5	odd	6		147.5.d.a.97.1		2
7.6	odd	2		147.5.f.b.19.1		2
21.2	odd	6		441.5.d.c.244.1		2
21.5	even	6		441.5.d.c.244.2		2
21.17	even	6		63.5.m.a.10.1		2
28.3	even	6		336.5.bh.a.241.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.5.f.b.10.1	✓	2	7.3	odd	6	inner
21.5.f.b.19.1	yes	2	1.1	even	1	trivial
63.5.m.a.10.1		2	21.17	even	6
63.5.m.a.19.1		2	3.2	odd	2
147.5.d.a.97.1		2	7.5	odd	6
147.5.d.a.97.2		2	7.2	even	3
147.5.f.b.19.1		2	7.6	odd	2
147.5.f.b.31.1		2	7.4	even	3
336.5.bh.a.145.1		2	4.3	odd	2
336.5.bh.a.241.1		2	28.3	even	6
441.5.d.c.244.1		2	21.2	odd	6
441.5.d.c.244.2		2	21.5	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.50000 - 4.33013i) q^{2} +(4.50000 - 2.59808i) q^{3} +(-4.50000 - 7.79423i) q^{4} +(-1.50000 - 0.866025i) q^{5} -25.9808i q^{6} +(-45.5000 + 18.1865i) q^{7} +35.0000 q^{8} +(13.5000 - 23.3827i) q^{9} +O(q^{10})\)	\(q+(2.50000 - 4.33013i) q^{2} +(4.50000 - 2.59808i) q^{3} +(-4.50000 - 7.79423i) q^{4} +(-1.50000 - 0.866025i) q^{5} -25.9808i q^{6} +(-45.5000 + 18.1865i) q^{7} +35.0000 q^{8} +(13.5000 - 23.3827i) q^{9} +(-7.50000 + 4.33013i) q^{10} +(74.5000 + 129.038i) q^{11} +(-40.5000 - 23.3827i) q^{12} +41.5692i q^{13} +(-35.0000 + 242.487i) q^{14} -9.00000 q^{15} +(159.500 - 276.262i) q^{16} +(-231.000 + 133.368i) q^{17} +(-67.5000 - 116.913i) q^{18} +(-309.000 - 178.401i) q^{19} +15.5885i q^{20} +(-157.500 + 200.052i) q^{21} +745.000 q^{22} +(280.000 - 484.974i) q^{23} +(157.500 - 90.9327i) q^{24} +(-311.000 - 538.668i) q^{25} +(180.000 + 103.923i) q^{26} -140.296i q^{27} +(346.500 + 272.798i) q^{28} +235.000 q^{29} +(-22.5000 + 38.9711i) q^{30} +(-1114.50 + 643.457i) q^{31} +(-517.500 - 896.336i) q^{32} +(670.500 + 387.113i) q^{33} +1333.68i q^{34} +(84.0000 + 12.1244i) q^{35} -243.000 q^{36} +(-985.000 + 1706.07i) q^{37} +(-1545.00 + 892.006i) q^{38} +(108.000 + 187.061i) q^{39} +(-52.5000 - 30.3109i) q^{40} -2816.31i q^{41} +(472.500 + 1182.12i) q^{42} +2798.00 q^{43} +(670.500 - 1161.34i) q^{44} +(-40.5000 + 23.3827i) q^{45} +(-1400.00 - 2424.87i) q^{46} +(3576.00 + 2064.60i) q^{47} -1657.57i q^{48} +(1739.50 - 1654.97i) q^{49} -3110.00 q^{50} +(-693.000 + 1200.31i) q^{51} +(324.000 - 187.061i) q^{52} +(-450.500 - 780.289i) q^{53} +(-607.500 - 350.740i) q^{54} -258.076i q^{55} +(-1592.50 + 636.529i) q^{56} -1854.00 q^{57} +(587.500 - 1017.58i) q^{58} +(1195.50 - 690.222i) q^{59} +(40.5000 + 70.1481i) q^{60} +(-3090.00 - 1784.01i) q^{61} +6434.57i q^{62} +(-189.000 + 1309.43i) q^{63} -71.0000 q^{64} +(36.0000 - 62.3538i) q^{65} +(3352.50 - 1935.57i) q^{66} +(2078.00 + 3599.20i) q^{67} +(2079.00 + 1200.31i) q^{68} -2909.85i q^{69} +(262.500 - 333.420i) q^{70} +484.000 q^{71} +(472.500 - 818.394i) q^{72} +(-822.000 + 474.582i) q^{73} +(4925.00 + 8530.35i) q^{74} +(-2799.00 - 1616.00i) q^{75} +3211.22i q^{76} +(-5736.50 - 4516.32i) q^{77} +1080.00 q^{78} +(-2162.50 + 3745.56i) q^{79} +(-478.500 + 276.262i) q^{80} +(-364.500 - 631.333i) q^{81} +(-12195.0 - 7040.79i) q^{82} +1304.23i q^{83} +(2268.00 + 327.358i) q^{84} +462.000 q^{85} +(6995.00 - 12115.7i) q^{86} +(1057.50 - 610.548i) q^{87} +(2607.50 + 4516.32i) q^{88} +(1713.00 + 989.001i) q^{89} +233.827i q^{90} +(-756.000 - 1891.40i) q^{91} -5040.00 q^{92} +(-3343.50 + 5791.11i) q^{93} +(17880.0 - 10323.0i) q^{94} +(309.000 + 535.204i) q^{95} +(-4657.50 - 2689.01i) q^{96} -5450.76i q^{97} +(-2817.50 - 11669.7i) q^{98} +4023.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 5 q^{2} + 9 q^{3} - 9 q^{4} - 3 q^{5} - 91 q^{7} + 70 q^{8} + 27 q^{9}+O(q^{10}) \) 2 * q + 5 * q^2 + 9 * q^3 - 9 * q^4 - 3 * q^5 - 91 * q^7 + 70 * q^8 + 27 * q^9	\( 2 q + 5 q^{2} + 9 q^{3} - 9 q^{4} - 3 q^{5} - 91 q^{7} + 70 q^{8} + 27 q^{9} - 15 q^{10} + 149 q^{11} - 81 q^{12} - 70 q^{14} - 18 q^{15} + 319 q^{16} - 462 q^{17} - 135 q^{18} - 618 q^{19} - 315 q^{21} + 1490 q^{22} + 560 q^{23} + 315 q^{24} - 622 q^{25} + 360 q^{26} + 693 q^{28} + 470 q^{29} - 45 q^{30} - 2229 q^{31} - 1035 q^{32} + 1341 q^{33} + 168 q^{35} - 486 q^{36} - 1970 q^{37} - 3090 q^{38} + 216 q^{39} - 105 q^{40} + 945 q^{42} + 5596 q^{43} + 1341 q^{44} - 81 q^{45} - 2800 q^{46} + 7152 q^{47} + 3479 q^{49} - 6220 q^{50} - 1386 q^{51} + 648 q^{52} - 901 q^{53} - 1215 q^{54} - 3185 q^{56} - 3708 q^{57} + 1175 q^{58} + 2391 q^{59} + 81 q^{60} - 6180 q^{61} - 378 q^{63} - 142 q^{64} + 72 q^{65} + 6705 q^{66} + 4156 q^{67} + 4158 q^{68} + 525 q^{70} + 968 q^{71} + 945 q^{72} - 1644 q^{73} + 9850 q^{74} - 5598 q^{75} - 11473 q^{77} + 2160 q^{78} - 4325 q^{79} - 957 q^{80} - 729 q^{81} - 24390 q^{82} + 4536 q^{84} + 924 q^{85} + 13990 q^{86} + 2115 q^{87} + 5215 q^{88} + 3426 q^{89} - 1512 q^{91} - 10080 q^{92} - 6687 q^{93} + 35760 q^{94} + 618 q^{95} - 9315 q^{96} - 5635 q^{98} + 8046 q^{99}+O(q^{100}) \) 2 * q + 5 * q^2 + 9 * q^3 - 9 * q^4 - 3 * q^5 - 91 * q^7 + 70 * q^8 + 27 * q^9 - 15 * q^10 + 149 * q^11 - 81 * q^12 - 70 * q^14 - 18 * q^15 + 319 * q^16 - 462 * q^17 - 135 * q^18 - 618 * q^19 - 315 * q^21 + 1490 * q^22 + 560 * q^23 + 315 * q^24 - 622 * q^25 + 360 * q^26 + 693 * q^28 + 470 * q^29 - 45 * q^30 - 2229 * q^31 - 1035 * q^32 + 1341 * q^33 + 168 * q^35 - 486 * q^36 - 1970 * q^37 - 3090 * q^38 + 216 * q^39 - 105 * q^40 + 945 * q^42 + 5596 * q^43 + 1341 * q^44 - 81 * q^45 - 2800 * q^46 + 7152 * q^47 + 3479 * q^49 - 6220 * q^50 - 1386 * q^51 + 648 * q^52 - 901 * q^53 - 1215 * q^54 - 3185 * q^56 - 3708 * q^57 + 1175 * q^58 + 2391 * q^59 + 81 * q^60 - 6180 * q^61 - 378 * q^63 - 142 * q^64 + 72 * q^65 + 6705 * q^66 + 4156 * q^67 + 4158 * q^68 + 525 * q^70 + 968 * q^71 + 945 * q^72 - 1644 * q^73 + 9850 * q^74 - 5598 * q^75 - 11473 * q^77 + 2160 * q^78 - 4325 * q^79 - 957 * q^80 - 729 * q^81 - 24390 * q^82 + 4536 * q^84 + 924 * q^85 + 13990 * q^86 + 2115 * q^87 + 5215 * q^88 + 3426 * q^89 - 1512 * q^91 - 10080 * q^92 - 6687 * q^93 + 35760 * q^94 + 618 * q^95 - 9315 * q^96 - 5635 * q^98 + 8046 * q^99

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