LMFDB - Embedded newform 43.4.c.a.36.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,4,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	43.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.53708213025$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 60 x^{18} - 25 x^{17} + 2336 x^{16} - 645 x^{15} + 52478 x^{14} - 2415 x^{13} + \cdots + 589824 $ x^20 - x^19 + 60x^18 - 25x^17 + 2336x^16 - 645x^15 + 52478x^14 - 2415x^13 + 850704x^12 - 4147x^11 + 8670544x^10 + 873865x^9 + 62344097x^8 + 3655316x^7 + 215661012x^6 + 43840208x^5 + 507687824x^4 - 3907840x^3 + 17517568x^2 + 245760x + 589824
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			36.1
Root			$2.65668 + 4.60150i$ of defining polynomial
Character	$\chi$	$=$	43.36
Dual form			43.4.c.a.6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.31336 q^{2} +(-4.02821 - 6.97706i) q^{3} +20.2317 q^{4} +(-7.95967 - 13.7866i) q^{5} +(21.4033 + 37.0716i) q^{6} +(-8.31614 + 14.4040i) q^{7} -64.9916 q^{8} +(-18.9529 + 32.8274i) q^{9} +O(q^{10})$	\(q-5.31336 q^{2} +(-4.02821 - 6.97706i) q^{3} +20.2317 q^{4} +(-7.95967 - 13.7866i) q^{5} +(21.4033 + 37.0716i) q^{6} +(-8.31614 + 14.4040i) q^{7} -64.9916 q^{8} +(-18.9529 + 32.8274i) q^{9} +(42.2926 + 73.2529i) q^{10} +31.4464 q^{11} +(-81.4977 - 141.158i) q^{12} +(-4.55523 + 7.88988i) q^{13} +(44.1866 - 76.5334i) q^{14} +(-64.1265 + 111.070i) q^{15} +183.469 q^{16} +(-15.2129 + 26.3496i) q^{17} +(100.704 - 174.424i) q^{18} +(-3.71590 - 6.43613i) q^{19} +(-161.038 - 278.926i) q^{20} +133.997 q^{21} -167.086 q^{22} +(-27.1516 - 47.0279i) q^{23} +(261.800 + 453.450i) q^{24} +(-64.2128 + 111.220i) q^{25} +(24.2035 - 41.9217i) q^{26} +87.8621 q^{27} +(-168.250 + 291.417i) q^{28} +(-132.378 + 229.286i) q^{29} +(340.727 - 590.156i) q^{30} +(-157.088 - 272.085i) q^{31} -454.906 q^{32} +(-126.673 - 219.403i) q^{33} +(80.8318 - 140.005i) q^{34} +264.775 q^{35} +(-383.451 + 664.156i) q^{36} +(103.086 + 178.550i) q^{37} +(19.7439 + 34.1975i) q^{38} +73.3976 q^{39} +(517.312 + 896.010i) q^{40} -174.881 q^{41} -711.971 q^{42} +(79.8447 - 270.429i) q^{43} +636.215 q^{44} +603.436 q^{45} +(144.266 + 249.876i) q^{46} -356.666 q^{47} +(-739.053 - 1280.08i) q^{48} +(33.1837 + 57.4759i) q^{49} +(341.186 - 590.951i) q^{50} +245.124 q^{51} +(-92.1602 + 159.626i) q^{52} +(84.9673 + 147.168i) q^{53} -466.842 q^{54} +(-250.303 - 433.537i) q^{55} +(540.479 - 936.137i) q^{56} +(-29.9369 + 51.8522i) q^{57} +(703.373 - 1218.28i) q^{58} -673.320 q^{59} +(-1297.39 + 2247.15i) q^{60} +(-80.9557 + 140.219i) q^{61} +(834.665 + 1445.68i) q^{62} +(-315.230 - 545.995i) q^{63} +949.319 q^{64} +145.032 q^{65} +(673.056 + 1165.77i) q^{66} +(-59.1469 - 102.445i) q^{67} +(-307.784 + 533.098i) q^{68} +(-218.744 + 378.876i) q^{69} -1406.84 q^{70} +(45.0809 - 78.0823i) q^{71} +(1231.78 - 2133.51i) q^{72} +(49.0200 - 84.9051i) q^{73} +(-547.733 - 948.701i) q^{74} +1034.65 q^{75} +(-75.1792 - 130.214i) q^{76} +(-261.512 + 452.953i) q^{77} -389.988 q^{78} +(-232.264 + 402.294i) q^{79} +(-1460.36 - 2529.41i) q^{80} +(157.802 + 273.321i) q^{81} +929.203 q^{82} +(74.9171 + 129.760i) q^{83} +2710.98 q^{84} +484.360 q^{85} +(-424.243 + 1436.89i) q^{86} +2132.99 q^{87} -2043.75 q^{88} +(-399.986 - 692.796i) q^{89} -3206.27 q^{90} +(-75.7638 - 131.227i) q^{91} +(-549.324 - 951.457i) q^{92} +(-1265.57 + 2192.03i) q^{93} +1895.09 q^{94} +(-59.1548 + 102.459i) q^{95} +(1832.45 + 3173.90i) q^{96} -862.058 q^{97} +(-176.317 - 305.390i) q^{98} +(-596.001 + 1032.30i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + 27 q^{10} + 54 q^{11} - 72 q^{12} - 15 q^{13} + 96 q^{14} + 65 q^{15} + 134 q^{16} - 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 18 q^{21} + 380 q^{22} - 61 q^{23} + 202 q^{24} - 151 q^{25} - 21 q^{26} - 194 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} + 253 q^{31} - 798 q^{32} - 424 q^{33} - 231 q^{34} + 710 q^{35} - 1092 q^{36} - 129 q^{37} - 854 q^{38} + 1382 q^{39} + 1345 q^{40} + 782 q^{41} + 62 q^{42} + 1025 q^{43} + 754 q^{44} + 1888 q^{45} - 40 q^{46} - 668 q^{47} - 2401 q^{48} - 115 q^{49} + 424 q^{50} + 1590 q^{51} - 564 q^{52} + 773 q^{53} + 364 q^{54} - 1242 q^{55} - 923 q^{56} - 765 q^{57} + 1328 q^{58} - 2966 q^{59} - 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 1476 q^{64} - 2126 q^{65} + 1483 q^{66} - 642 q^{67} - 1052 q^{68} - 3503 q^{69} - 170 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} - 2232 q^{74} + 164 q^{75} - 252 q^{76} + 1448 q^{77} + 5644 q^{78} - 1405 q^{79} - 3157 q^{80} + 974 q^{81} + 6608 q^{82} + 543 q^{83} + 7304 q^{84} + 1946 q^{85} + 2776 q^{86} + 2818 q^{87} - 5372 q^{88} - 2196 q^{89} - 1484 q^{90} - 3513 q^{91} + 2629 q^{92} - 983 q^{93} + 9878 q^{94} - 149 q^{95} + 3540 q^{96} - 850 q^{97} - 213 q^{98} - 3181 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9 + 27 * q^10 + 54 * q^11 - 72 * q^12 - 15 * q^13 + 96 * q^14 + 65 * q^15 + 134 * q^16 - 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 18 * q^21 + 380 * q^22 - 61 * q^23 + 202 * q^24 - 151 * q^25 - 21 * q^26 - 194 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 + 253 * q^31 - 798 * q^32 - 424 * q^33 - 231 * q^34 + 710 * q^35 - 1092 * q^36 - 129 * q^37 - 854 * q^38 + 1382 * q^39 + 1345 * q^40 + 782 * q^41 + 62 * q^42 + 1025 * q^43 + 754 * q^44 + 1888 * q^45 - 40 * q^46 - 668 * q^47 - 2401 * q^48 - 115 * q^49 + 424 * q^50 + 1590 * q^51 - 564 * q^52 + 773 * q^53 + 364 * q^54 - 1242 * q^55 - 923 * q^56 - 765 * q^57 + 1328 * q^58 - 2966 * q^59 - 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 1476 * q^64 - 2126 * q^65 + 1483 * q^66 - 642 * q^67 - 1052 * q^68 - 3503 * q^69 - 170 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 - 2232 * q^74 + 164 * q^75 - 252 * q^76 + 1448 * q^77 + 5644 * q^78 - 1405 * q^79 - 3157 * q^80 + 974 * q^81 + 6608 * q^82 + 543 * q^83 + 7304 * q^84 + 1946 * q^85 + 2776 * q^86 + 2818 * q^87 - 5372 * q^88 - 2196 * q^89 - 1484 * q^90 - 3513 * q^91 + 2629 * q^92 - 983 * q^93 + 9878 * q^94 - 149 * q^95 + 3540 * q^96 - 850 * q^97 - 213 * q^98 - 3181 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

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

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 $

$2$	−5.31336			−1.87855			−0.939277	−	0.343159i	$-0.888503\pi$
$2$	−5.31336			−1.87855			−0.939277	+	0.343159i	$0.888503\pi$
$3$	−4.02821	−	6.97706i	−0.775229	−	1.34274i	−0.934666	−	0.355528i	$-0.884301\pi$
$3$	−4.02821	−	6.97706i	−0.775229	−	1.34274i	0.159437	−	0.987208i	$-0.449032\pi$
$4$	20.2317			2.52897
$5$	−7.95967	−	13.7866i	−0.711935	−	1.23311i	−0.964130	−	0.265431i	$-0.914486\pi$
$5$	−7.95967	−	13.7866i	−0.711935	−	1.23311i	0.252195	−	0.967676i	$-0.418848\pi$
$6$	21.4033	+	37.0716i	1.45631	+	2.52240i
$7$	−8.31614	+	14.4040i	−0.449029	+	0.777741i	−0.998323	−	0.0578879i	$-0.981563\pi$
$7$	−8.31614	+	14.4040i	−0.449029	+	0.777741i	0.549294	+	0.835629i	$0.314897\pi$
$8$	−64.9916			−2.87225
$9$	−18.9529	+	32.8274i	−0.701960	+	1.21583i
$10$	42.2926	+	73.2529i	1.33741	+	2.31646i
$11$	31.4464			0.861949			0.430974	−	0.902364i	$-0.358170\pi$
$11$	31.4464			0.861949			0.430974	+	0.902364i	$0.358170\pi$
$12$	−81.4977	−	141.158i	−1.96053	−	3.39574i
$13$	−4.55523	+	7.88988i	−0.0971840	+	0.168328i	−0.910518	−	0.413469i	$-0.864317\pi$
$13$	−4.55523	+	7.88988i	−0.0971840	+	0.168328i	0.813334	+	0.581797i	$0.197650\pi$
$14$	44.1866	−	76.5334i	0.843526	−	1.46103i
$15$	−64.1265	+	111.070i	−1.10383	+	1.91188i
$16$	183.469			2.86671
$17$	−15.2129	+	26.3496i	−0.217040	+	0.375924i	−0.953902	−	0.300119i	$-0.902974\pi$
$17$	−15.2129	+	26.3496i	−0.217040	+	0.375924i	0.736862	+	0.676044i	$0.236307\pi$
$18$	100.704	−	174.424i	1.31867	−	2.28400i
$19$	−3.71590	−	6.43613i	−0.0448677	−	0.0777132i	0.842719	−	0.538353i	$-0.180953\pi$
$19$	−3.71590	−	6.43613i	−0.0448677	−	0.0777132i	−0.887587	+	0.460640i	$0.847620\pi$
$20$	−161.038	−	278.926i	−1.80046	−	3.11849i
$21$	133.997			1.39240
$22$	−167.086			−1.61922
$23$	−27.1516	−	47.0279i	−0.246152	−	0.426348i	0.716303	−	0.697789i	$-0.245833\pi$
$23$	−27.1516	−	47.0279i	−0.246152	−	0.426348i	−0.962455	+	0.271442i	$0.912500\pi$
$24$	261.800	+	453.450i	2.22665	+	3.85667i
$25$	−64.2128	+	111.220i	−0.513703	+	0.889759i
$26$	24.2035	−	41.9217i	0.182566	−	0.316213i
$27$	87.8621			0.626262
$28$	−168.250	+	291.417i	−1.13558	+	1.96688i
$29$	−132.378	+	229.286i	−0.847657	+	1.46818i	0.0356368	+	0.999365i	$0.488654\pi$
$29$	−132.378	+	229.286i	−0.847657	+	1.46818i	−0.883294	+	0.468820i	$0.844679\pi$
$30$	340.727	−	590.156i	2.07360	−	3.59157i
$31$	−157.088	−	272.085i	−0.910124	−	1.57638i	−0.813887	−	0.581023i	$-0.802653\pi$
$31$	−157.088	−	272.085i	−0.910124	−	1.57638i	−0.0962370	−	0.995358i	$-0.530681\pi$
$32$	−454.906			−2.51302
$33$	−126.673	−	219.403i	−0.668208	−	1.15737i
$34$	80.8318	−	140.005i	0.407722	−	0.706195i
$35$	264.775			1.27872
$36$	−383.451	+	664.156i	−1.77523	+	3.07480i
$37$	103.086	+	178.550i	0.458033	+	0.793337i	0.998857	−	0.0477989i	$-0.0152207\pi$
$37$	103.086	+	178.550i	0.458033	+	0.793337i	−0.540824	+	0.841136i	$0.681887\pi$
$38$	19.7439	+	34.1975i	0.0842865	+	0.145988i
$39$	73.3976			0.301360
$40$	517.312	+	896.010i	2.04485	+	3.54179i
$41$	−174.881			−0.666141			−0.333070	−	0.942902i	$-0.608085\pi$
$41$	−174.881			−0.666141			−0.333070	+	0.942902i	$0.608085\pi$
$42$	−711.971			−2.61570
$43$	79.8447	−	270.429i	0.283168	−	0.959070i
$43$	79.8447	−	270.429i	0.283168	−	0.959070i
$44$	636.215			2.17984
$45$	603.436			1.99900
$46$	144.266	+	249.876i	0.462410	+	0.800917i
$47$	−356.666			−1.10692			−0.553458	−	0.832877i	$-0.686692\pi$
$47$	−356.666			−1.10692			−0.553458	+	0.832877i	$0.686692\pi$
$48$	−739.053	−	1280.08i	−2.22236	−	3.84924i
$49$	33.1837	+	57.4759i	0.0967456	+	0.167568i
$50$	341.186	−	590.951i	0.965019	−	1.67146i
$51$	245.124			0.673023
$52$	−92.1602	+	159.626i	−0.245775	+	0.425695i
$53$	84.9673	+	147.168i	0.220211	+	0.381416i	0.954872	−	0.297018i	$-0.0959922\pi$
$53$	84.9673	+	147.168i	0.220211	+	0.381416i	−0.734661	+	0.678434i	$0.762659\pi$
$54$	−466.842			−1.17647
$55$	−250.303	−	433.537i	−0.613652	−	1.06288i
$56$	540.479	−	936.137i	1.28972	−	2.23387i
$57$	−29.9369	+	51.8522i	−0.0695655	+	0.120491i
$58$	703.373	−	1218.28i	1.59237	−	2.75807i
$59$	−673.320			−1.48574			−0.742871	−	0.669435i	$-0.766536\pi$
$59$	−673.320			−1.48574			−0.742871	+	0.669435i	$0.766536\pi$
$60$	−1297.39	+	2247.15i	−2.79154	+	4.83509i
$61$	−80.9557	+	140.219i	−0.169923	+	0.294316i	−0.938393	−	0.345571i	$-0.887685\pi$
$61$	−80.9557	+	140.219i	−0.169923	+	0.294316i	0.768469	+	0.639886i	$0.221019\pi$
$62$	834.665	+	1445.68i	1.70972	+	2.96132i
$63$	−315.230	−	545.995i	−0.630401	−	1.09189i
$64$	949.319			1.85414
$65$	145.032			0.276755
$66$	673.056	+	1165.77i	1.25527	+	2.17418i
$67$	−59.1469	−	102.445i	−0.107850	−	0.186802i	0.807049	−	0.590484i	$-0.201063\pi$
$67$	−59.1469	−	102.445i	−0.107850	−	0.186802i	−0.914899	+	0.403683i	$0.867730\pi$
$68$	−307.784	+	533.098i	−0.548887	+	0.950701i
$69$	−218.744	+	378.876i	−0.381648	+	0.661034i
$70$	−1406.84			−2.40214
$71$	45.0809	−	78.0823i	0.0753537	−	0.130516i	−0.825886	−	0.563837i	$-0.809325\pi$
$71$	45.0809	−	78.0823i	0.0753537	−	0.130516i	0.901240	+	0.433320i	$0.142658\pi$
$72$	1231.78	−	2133.51i	2.01620	−	3.49217i
$73$	49.0200	−	84.9051i	0.0785939	−	0.136129i	−0.824050	−	0.566518i	$-0.808290\pi$
$73$	49.0200	−	84.9051i	0.0785939	−	0.136129i	0.902643	+	0.430389i	$0.141624\pi$
$74$	−547.733	−	948.701i	−0.860441	−	1.49033i
$75$	1034.65			1.59295
$76$	−75.1792	−	130.214i	−0.113469	−	0.196534i
$77$	−261.512	+	452.953i	−0.387040	+	0.670373i
$78$	−389.988			−0.566120
$79$	−232.264	+	402.294i	−0.330782	+	0.572931i	−0.982665	−	0.185388i	$-0.940646\pi$
$79$	−232.264	+	402.294i	−0.330782	+	0.572931i	0.651883	+	0.758319i	$0.273979\pi$
$80$	−1460.36	−	2529.41i	−2.04091	−	3.53496i
$81$	157.802	+	273.321i	0.216464	+	0.374927i
$82$	929.203			1.25138
$83$	74.9171	+	129.760i	0.0990749	+	0.171603i	0.911302	−	0.411739i	$-0.135078\pi$
$83$	74.9171	+	129.760i	0.0990749	+	0.171603i	−0.812227	+	0.583341i	$0.801745\pi$
$84$	2710.98			3.52134
$85$	484.360			0.618074
$86$	−424.243	+	1436.89i	−0.531946	+	1.80167i
$87$	2132.99			2.62851
$88$	−2043.75			−2.47573
$89$	−399.986	−	692.796i	−0.476387	−	0.825126i	0.523247	−	0.852181i	$-0.324720\pi$
$89$	−399.986	−	692.796i	−0.476387	−	0.825126i	−0.999634	+	0.0270551i	$0.991387\pi$
$90$	−3206.27			−3.75523
$91$	−75.7638	−	131.227i	−0.0872769	−	0.151168i
$92$	−549.324	−	951.457i	−0.622510	−	1.07822i
$93$	−1265.57	+	2192.03i	−1.41111	+	2.44411i
$94$	1895.09			2.07940
$95$	−59.1548	+	102.459i	−0.0638858	+	0.110653i
$96$	1832.45	+	3173.90i	1.94817	+	3.37433i
$97$	−862.058			−0.902358			−0.451179	−	0.892433i	$-0.648996\pi$
$97$	−862.058			−0.902358			−0.451179	+	0.892433i	$0.648996\pi$
$98$	−176.317	−	305.390i	−0.181742	−	0.314786i
$99$	−596.001	+	1032.30i	−0.605054	+	1.04798i
$100$	−1299.14	+	2250.17i	−1.29914	+	2.25017i
$101$	513.995	−	890.266i	0.506380	−	0.877077i	−0.493592	−	0.869693i	$-0.664317\pi$
$101$	513.995	−	890.266i	0.506380	−	0.877077i	0.999973	−	0.00738315i	$-0.00235015\pi$
$102$	−1302.43			−1.26431
$103$	727.316	−	1259.75i	0.695773	−	1.20511i	−0.274147	−	0.961688i	$-0.588395\pi$
$103$	727.316	−	1259.75i	0.695773	−	1.20511i	0.969919	−	0.243426i	$-0.0782713\pi$
$104$	296.051	−	512.776i	0.279137	−	0.483479i
$105$	−1066.57	−	1847.35i	−0.991300	−	1.71698i
$106$	−451.461	−	781.954i	−0.413678	−	0.716510i
$107$	1686.41			1.52366			0.761830	−	0.647778i	$-0.224301\pi$
$107$	1686.41			1.52366			0.761830	+	0.647778i	$0.224301\pi$
$108$	1777.60			1.58380
$109$	−862.106	−	1493.21i	−0.757567	−	1.31214i	−0.944088	−	0.329693i	$-0.893055\pi$
$109$	−862.106	−	1493.21i	−0.757567	−	1.31214i	0.186521	−	0.982451i	$-0.440279\pi$
$110$	1329.95	+	2303.54i	1.15278	+	1.99667i
$111$	830.504	−	1438.47i	0.710162	−	1.23004i
$112$	−1525.76	+	2642.69i	−1.28724	+	2.22956i
$113$	365.815			0.304539			0.152270	−	0.988339i	$-0.451342\pi$
$113$	365.815			0.304539			0.152270	+	0.988339i	$0.451342\pi$
$114$	159.065	−	275.509i	0.130683	−	0.226349i
$115$	−432.235	+	748.654i	−0.350488	+	0.607064i
$116$	−2678.25	+	4638.86i	−2.14370	+	3.71299i
$117$	−172.670	−	299.073i	−0.136439	−	0.236319i
$118$	3577.59			2.79105
$119$	−253.026	−	438.254i	−0.194915	−	0.337602i
$120$	4167.68	−	7218.63i	3.17046	−	5.49140i
$121$	−342.125			−0.257044
$122$	430.146	−	745.035i	0.319210	−	0.552888i
$123$	704.456	+	1220.15i	0.516412	+	0.894451i
$124$	−3178.17	−	5504.74i	−2.30167	−	3.98662i
$125$	54.5347			0.0390219
$126$	1674.93	+	2901.06i	1.18424	+	2.05117i
$127$	−2486.96			−1.73765			−0.868827	−	0.495115i	$-0.835126\pi$
$127$	−2486.96			−1.73765			−0.868827	+	0.495115i	$0.835126\pi$
$128$	−1404.83			−0.970080
$129$	−2208.43	+	532.263i	−1.50730	+	0.363280i
$130$	−770.609			−0.519899
$131$	2385.96			1.59131			0.795657	−	0.605748i	$-0.207126\pi$
$131$	2385.96			1.59131			0.795657	+	0.605748i	$0.207126\pi$
$132$	−2562.81	−	4438.91i	−1.68988	−	2.92695i
$133$	123.608			0.0805877
$134$	314.268	+	544.329i	0.202602	+	0.350917i
$135$	−699.354	−	1211.32i	−0.445858	−	0.772248i
$136$	988.714	−	1712.50i	0.623393	−	1.07975i
$137$	273.052			0.170280			0.0851400	−	0.996369i	$-0.472866\pi$
$137$	273.052			0.170280			0.0851400	+	0.996369i	$0.472866\pi$
$138$	1162.27	−	2013.11i	0.716947	−	1.24179i
$139$	48.4411	+	83.9024i	0.0295591	+	0.0511979i	0.880427	−	0.474183i	$-0.157256\pi$
$139$	48.4411	+	83.9024i	0.0295591	+	0.0511979i	−0.850867	+	0.525380i	$0.823923\pi$
$140$	5356.86			3.23384
$141$	1436.72	+	2488.48i	0.858114	+	1.48630i
$142$	−239.531	+	414.879i	−0.141556	+	0.245182i
$143$	−143.245	+	248.108i	−0.0837677	+	0.145090i
$144$	−3477.28	+	6022.83i	−2.01232	+	3.48543i
$145$	4214.76			2.41391
$146$	−260.460	+	451.131i	−0.147643	+	0.255725i
$147$	267.342	−	463.050i	0.150000	−	0.259808i
$148$	2085.61	+	3612.38i	1.15835	+	2.00632i
$149$	−522.746	−	905.423i	−0.287416	−	0.497820i	0.685776	−	0.727813i	$-0.259463\pi$
$149$	−522.746	−	905.423i	−0.287416	−	0.497820i	−0.973192	+	0.229993i	$0.926130\pi$
$150$	−5497.47			−2.99244
$151$	−2794.03			−1.50580			−0.752898	−	0.658138i	$-0.771344\pi$
$151$	−2794.03			−1.50580			−0.752898	+	0.658138i	$0.771344\pi$
$152$	241.502	+	418.295i	0.128871	+	0.223212i
$153$	−576.660	−	998.804i	−0.304707	−	0.527768i
$154$	1389.51	−	2406.70i	0.727076	−	1.25933i
$155$	−2500.74	+	4331.41i	−1.29590	+	2.24456i
$156$	1484.96			0.762129
$157$	365.696	−	633.404i	0.185896	−	0.321982i	−0.757982	−	0.652276i	$-0.773815\pi$
$157$	365.696	−	633.404i	0.185896	−	0.321982i	0.943878	+	0.330294i	$0.107148\pi$
$158$	1234.10	−	2137.53i	0.621392	−	1.07628i
$159$	684.532	−	1185.64i	0.341427	−	0.591369i
$160$	3620.90	+	6271.58i	1.78911	+	3.09883i
$161$	903.185			0.442118
$162$	−838.459	−	1452.25i	−0.406639	−	0.704320i
$163$	416.532	−	721.455i	0.200155	−	0.346679i	−0.748423	−	0.663222i	$-0.769189\pi$
$163$	416.532	−	721.455i	0.200155	−	0.346679i	0.948578	+	0.316542i	$0.102522\pi$
$164$	−3538.14			−1.68465
$165$	−2016.54	+	3492.76i	−0.951441	+	1.64794i
$166$	−398.061	−	689.462i	−0.186118	−	0.322365i
$167$	1243.05	+	2153.03i	0.575990	+	0.997644i	0.995933	+	0.0900938i	$0.0287167\pi$
$167$	1243.05	+	2153.03i	0.575990	+	0.997644i	−0.419943	+	0.907550i	$0.637950\pi$
$168$	−8708.65			−3.99933
$169$	1057.00	+	1830.78i	0.481111	+	0.833308i
$170$	−2573.58			−1.16109
$171$	281.709			0.125981
$172$	1615.40	−	5471.25i	0.716122	−	2.42546i
$173$	−3354.66			−1.47428			−0.737139	−	0.675741i	$-0.763824\pi$
$173$	−3354.66			−1.47428			−0.737139	+	0.675741i	$0.763824\pi$
$174$	−11333.3			−4.93781
$175$	−1068.01	−	1849.84i	−0.461335	−	0.799056i
$176$	5769.45			2.47096
$177$	2712.27	+	4697.79i	1.15179	+	1.99496i
$178$	2125.27	+	3681.07i	0.894918	+	1.55004i
$179$	1285.02	−	2225.73i	0.536576	−	0.929377i	−0.462509	−	0.886615i	$-0.653051\pi$
$179$	1285.02	−	2225.73i	0.536576	−	0.929377i	0.999085	−	0.0427626i	$-0.0136159\pi$
$180$	12208.6			5.05541
$181$	−1716.57	+	2973.19i	−0.704927	+	1.22097i	0.261791	+	0.965125i	$0.415687\pi$
$181$	−1716.57	+	2973.19i	−0.704927	+	1.22097i	−0.966718	+	0.255844i	$0.917647\pi$
$182$	402.560	+	697.254i	0.163954	+	0.283977i
$183$	1304.43			0.526917
$184$	1764.62	+	3056.42i	0.707010	+	1.22458i
$185$	1641.06	−	2842.40i	0.652180	−	1.12961i
$186$	6724.41	−	11647.0i	2.65085	−	4.59140i
$187$	−478.392	+	828.599i	−0.187077	+	0.324028i
$188$	−7215.97			−2.79936
$189$	−730.673	+	1265.56i	−0.281210	+	0.487070i
$190$	314.310	−	544.401i	0.120013	−	0.207869i
$191$	−1626.00	−	2816.32i	−0.615986	−	1.06692i	−0.990211	−	0.139580i	$-0.955425\pi$
$191$	−1626.00	−	2816.32i	−0.615986	−	1.06692i	0.374225	−	0.927338i	$-0.377909\pi$
$192$	−3824.06	−	6623.46i	−1.43738	−	2.48962i
$193$	−1575.55			−0.587620			−0.293810	−	0.955864i	$-0.594923\pi$
$193$	−1575.55			−0.587620			−0.293810	+	0.955864i	$0.594923\pi$
$194$	4580.42			1.69513
$195$	−584.221	−	1011.90i	−0.214548	−	0.371609i
$196$	671.365	+	1162.84i	0.244667	+	0.423775i
$197$	−309.973	+	536.890i	−0.112105	+	0.194172i	−0.916619	−	0.399762i	$-0.869093\pi$
$197$	−309.973	+	536.890i	−0.112105	+	0.194172i	0.804514	+	0.593934i	$0.202426\pi$
$198$	3166.76	−	5485.00i	1.13663	−	1.96870i
$199$	−734.573			−0.261671			−0.130835	−	0.991404i	$-0.541766\pi$
$199$	−734.573			−0.261671			−0.130835	+	0.991404i	$0.541766\pi$
$200$	4173.29	−	7228.36i	1.47548	−	2.55561i
$201$	−476.512	+	825.343i	−0.167217	+	0.289628i
$202$	−2731.04	+	4730.30i	−0.951263	+	1.64764i
$203$	−2201.75	−	3813.55i	−0.761245	−	1.31852i
$204$	4959.28			1.70205
$205$	1391.99	+	2411.00i	0.474249	+	0.821423i
$206$	−3864.49	+	6693.49i	−1.30705	+	2.26387i
$207$	2058.41			0.691156
$208$	−835.745	+	1447.55i	−0.278598	+	0.482547i
$209$	−116.852	−	202.393i	−0.0386737	−	0.0669848i
$210$	5667.06	+	9815.63i	1.86221	+	3.22544i
$211$	1132.27			0.369425			0.184713	−	0.982793i	$-0.440865\pi$
$211$	1132.27			0.369425			0.184713	+	0.982793i	$0.440865\pi$
$212$	1719.04	+	2977.46i	0.556905	+	0.964588i
$213$	−726.380			−0.233666
$214$	−8960.50			−2.86228
$215$	−4363.82	+	1051.74i	−1.38423	+	0.333620i
$216$	−5710.30			−1.79878
$217$	5225.46			1.63469
$218$	4580.68	+	7933.96i	1.42313	+	2.46493i
$219$	−789.850			−0.243713
$220$	−5064.06	−	8771.22i	−1.55191	−	2.68798i
$221$	−138.597	−	240.057i	−0.0421857	−	0.0730677i
$222$	−4412.76	+	7643.13i	−1.33408	+	2.31069i
$223$	−1053.16			−0.316255			−0.158127	−	0.987419i	$-0.550546\pi$
$223$	−1053.16			−0.316255			−0.158127	+	0.987419i	$0.550546\pi$
$224$	3783.06	−	6552.45i	1.12842	−	1.95448i
$225$	−2434.04	−	4215.89i	−0.721198	−	1.24915i
$226$	−1943.70			−0.572094
$227$	−1899.67	−	3290.33i	−0.555444	−	0.962057i	−0.997869	−	0.0652512i	$-0.979215\pi$
$227$	−1899.67	−	3290.33i	−0.555444	−	0.962057i	0.442425	−	0.896805i	$-0.354118\pi$
$228$	−605.675	+	1049.06i	−0.175929	+	0.304718i
$229$	3162.04	−	5476.81i	0.912460	−	1.58043i	0.101882	−	0.994796i	$-0.467513\pi$
$229$	3162.04	−	5476.81i	0.912460	−	1.58043i	0.810578	−	0.585631i	$-0.199153\pi$
$230$	2296.62	−	3977.86i	0.658412	−	1.14040i
$231$	4213.70			1.20018
$232$	8603.48	−	14901.7i	2.43468	−	4.21699i
$233$	−630.102	+	1091.37i	−0.177164	+	0.306858i	−0.940908	−	0.338662i	$-0.890026\pi$
$233$	−630.102	+	1091.37i	−0.177164	+	0.306858i	0.763744	+	0.645520i	$0.223359\pi$
$234$	917.456	+	1589.08i	0.256307	+	0.443938i
$235$	2838.94	+	4917.20i	0.788052	+	1.36495i
$236$	−13622.4			−3.75739
$237$	3742.44			1.02573
$238$	1344.42	+	2328.60i	0.366158	+	0.634204i
$239$	744.718	+	1289.89i	0.201556	+	0.349105i	0.949030	−	0.315186i	$-0.102067\pi$
$239$	744.718	+	1289.89i	0.201556	+	0.349105i	−0.747474	+	0.664291i	$0.768734\pi$
$240$	−11765.2	+	20378.0i	−3.16435	+	5.48081i
$241$	1305.10	−	2260.50i	0.348833	−	0.604197i	−0.637209	−	0.770691i	$-0.719911\pi$
$241$	1305.10	−	2260.50i	0.348833	−	0.604197i	0.986042	+	0.166494i	$0.0532446\pi$
$242$	1817.83			0.482871
$243$	2457.46	−	4256.44i	0.648749	−	1.12367i
$244$	−1637.87	+	2836.88i	−0.429730	+	0.744314i
$245$	528.264	−	914.980i	0.137753	−	0.238596i
$246$	−3743.02	−	6483.11i	−0.970108	−	1.68028i
$247$	67.7071			0.0174417
$248$	10209.4	+	17683.2i	2.61410	+	4.52776i
$249$	603.563	−	1045.40i	0.153611	−	0.266063i
$250$	−289.762			−0.0733047
$251$	−601.526	+	1041.87i	−0.151267	+	0.262002i	−0.931693	−	0.363246i	$-0.881669\pi$
$251$	−601.526	+	1041.87i	−0.151267	+	0.262002i	0.780427	+	0.625247i	$0.215002\pi$
$252$	−6377.66	−	11046.4i	−1.59426	−	2.76135i
$253$	−853.819	−	1478.86i	−0.212170	−	0.367490i
$254$	13214.1			3.26428
$255$	−1951.10	−	3379.41i	−0.479149	−	0.829910i
$256$	−130.215			−0.0317909
$257$	−2722.72			−0.660851			−0.330426	−	0.943832i	$-0.607192\pi$
$257$	−2722.72			−0.660851			−0.330426	+	0.943832i	$0.607192\pi$
$258$	11734.2	−	2828.10i	2.83154	−	0.682441i
$259$	−3429.11			−0.822681
$260$	2934.26			0.699904
$261$	−5017.92	−	8691.29i	−1.19004	−	2.06121i
$262$	−12677.4			−2.98937
$263$	−1045.30	−	1810.51i	−0.245079	−	0.424490i	0.717075	−	0.696996i	$-0.245481\pi$
$263$	−1045.30	−	1810.51i	−0.245079	−	0.424490i	−0.962154	+	0.272507i	$0.912147\pi$
$264$	8232.65	+	14259.4i	1.91926	+	3.32426i
$265$	1352.62	−	2342.81i	0.313551	−	0.543087i
$266$	−656.772			−0.151388
$267$	−3222.45	+	5581.45i	−0.738617	+	1.27932i
$268$	−1196.64	−	2072.65i	−0.272749	−	0.472415i
$269$	6705.95			1.51996			0.759980	−	0.649947i	$-0.225209\pi$
$269$	6705.95			1.51996			0.759980	+	0.649947i	$0.225209\pi$
$270$	3715.91	+	6436.15i	0.837568	+	1.45071i
$271$	−845.990	+	1465.30i	−0.189632	+	0.328452i	−0.945128	−	0.326702i	$-0.894063\pi$
$271$	−845.990	+	1465.30i	−0.189632	+	0.328452i	0.755496	+	0.655154i	$0.227396\pi$
$272$	−2791.11	+	4834.35i	−0.622191	+	1.07767i
$273$	−610.384	+	1057.22i	−0.135319	+	0.234380i
$274$	−1450.82			−0.319880
$275$	−2019.26	+	3497.46i	−0.442786	+	0.766927i
$276$	−4425.58	+	7665.33i	−0.965176	+	1.67173i
$277$	761.821	+	1319.51i	0.165247	+	0.286216i	0.936743	−	0.350018i	$-0.113825\pi$
$277$	761.821	+	1319.51i	0.165247	+	0.286216i	−0.771496	+	0.636234i	$0.780491\pi$
$278$	−257.385	−	445.803i	−0.0555284	−	0.0961780i
$279$	11909.1			2.55548
$280$	−17208.1			−3.67280
$281$	−2559.19	−	4432.65i	−0.543305	−	0.941032i	−0.998711	−	0.0507481i	$-0.983839\pi$
$281$	−2559.19	−	4432.65i	−0.543305	−	0.941032i	0.455407	−	0.890284i	$-0.349494\pi$
$282$	−7633.83	−	13222.2i	−1.61201	−	2.79209i
$283$	1365.15	−	2364.51i	0.286749	−	0.496663i	−0.686283	−	0.727334i	$-0.740759\pi$
$283$	1365.15	−	2364.51i	0.286749	−	0.496663i	0.973032	+	0.230671i	$0.0740922\pi$
$284$	912.064	−	1579.74i	0.190567	−	0.330072i
$285$	953.151			0.198105
$286$	761.113	−	1318.29i	0.157362	−	0.272559i
$287$	1454.33	−	2518.98i	0.299117	−	0.518085i
$288$	8621.79	−	14933.4i	1.76404	−	3.05541i
$289$	1993.63	+	3453.07i	0.405787	+	0.702844i
$290$	−22394.5			−4.53466
$291$	3472.55	+	6014.63i	0.699534	+	1.21163i
$292$	991.759	−	1717.78i	0.198761	−	0.344265i
$293$	−1885.86			−0.376018			−0.188009	−	0.982167i	$-0.560203\pi$
$293$	−1885.86			−0.376018			−0.188009	+	0.982167i	$0.560203\pi$
$294$	−1420.48	+	2460.35i	−0.281783	+	0.488063i
$295$	5359.41	+	9282.76i	1.05775	+	1.83208i
$296$	−6699.72	−	11604.3i	−1.31559	−	2.27866i
$297$	2762.94			0.539806
$298$	2777.54	+	4810.84i	0.539928	+	0.935182i
$299$	494.726			0.0956882
$300$	20932.8			4.02852
$301$	3231.25	+	3399.01i	0.618758	+	0.650882i
$302$	14845.7			2.82872
$303$	−8281.92			−1.57024
$304$	−681.755	−	1180.83i	−0.128623	−	0.222781i
$305$	2577.52			0.483897
$306$	3064.00	+	5307.00i	0.572409	+	0.991441i
$307$	−2285.60	−	3958.78i	−0.424907	−	0.735960i	0.571505	−	0.820599i	$-0.306360\pi$
$307$	−2285.60	−	3958.78i	−0.424907	−	0.735960i	−0.996412	+	0.0846387i	$0.973026\pi$
$308$	−5290.85	+	9164.02i	−0.978812	+	1.69535i
$309$	−11719.1			−2.15753
$310$	13287.3	−	23014.3i	2.43442	−	4.21653i
$311$	3697.67	+	6404.56i	0.674198	+	1.16775i	0.976702	+	0.214598i	$0.0688441\pi$
$311$	3697.67	+	6404.56i	0.674198	+	1.16775i	−0.302504	+	0.953148i	$0.597823\pi$
$312$	−4770.23			−0.865580
$313$	192.429	+	333.297i	0.0347499	+	0.0601886i	0.882877	−	0.469604i	$-0.155603\pi$
$313$	192.429	+	333.297i	0.0347499	+	0.0601886i	−0.848127	+	0.529792i	$0.822270\pi$
$314$	−1943.07	+	3365.50i	−0.349216	+	0.604860i
$315$	−5018.26	+	8691.88i	−0.897609	+	1.55470i
$316$	−4699.11	+	8139.10i	−0.836537	+	1.44892i
$317$	7188.20			1.27359			0.636797	−	0.771031i	$-0.280259\pi$
$317$	7188.20			1.27359			0.636797	+	0.771031i	$0.280259\pi$
$318$	−3637.16	+	6299.75i	−0.641390	+	1.11092i
$319$	−4162.82	+	7210.22i	−0.730637	+	1.26550i
$320$	−7556.27	−	13087.8i	−1.32003	−	2.28635i
$321$	−6793.22	−	11766.2i	−1.18118	−	2.04587i
$322$	−4798.94			−0.830542
$323$	226.119			0.0389524
$324$	3192.61	+	5529.77i	0.547430	+	0.948177i
$325$	−585.008	−	1013.26i	−0.0998474	−	0.172941i
$326$	−2213.18	+	3833.35i	−0.376003	+	0.651256i
$327$	−6945.49	+	12029.9i	−1.17458	+	2.03442i
$328$	11365.8			1.91332
$329$	2966.08	−	5137.40i	0.497038	−	0.860894i
$330$	10714.6	−	18558.3i	1.78733	−	3.09575i
$331$	3159.17	−	5471.85i	0.524604	−	0.908641i	−0.474986	−	0.879994i	$-0.657547\pi$
$331$	3159.17	−	5471.85i	0.524604	−	0.908641i	0.999590	−	0.0286473i	$-0.00911996\pi$
$332$	1515.70	+	2625.27i	0.250557	+	0.433978i
$333$	−7815.13			−1.28608
$334$	−6604.78	−	11439.8i	−1.08203	−	1.87413i
$335$	−941.580	+	1630.86i	−0.153564	+	0.265981i
$336$	24584.3			3.99161
$337$	148.682	−	257.525i	0.0240333	−	0.0416270i	−0.853759	−	0.520669i	$-0.825683\pi$
$337$	148.682	−	257.525i	0.0240333	−	0.0416270i	0.877792	+	0.479042i	$0.159016\pi$
$338$	−5616.22	−	9727.57i	−0.903792	−	1.56541i
$339$	−1473.58	−	2552.31i	−0.236088	−	0.408916i
$340$	9799.45			1.56309
$341$	−4939.85	−	8556.07i	−0.784481	−	1.35876i
$342$	−1496.82			−0.236663
$343$	−6808.71			−1.07182
$344$	−5189.24	+	17575.6i	−0.813328	+	2.75469i
$345$	6964.54			1.08684
$346$	17824.5			2.76951
$347$	−892.554	−	1545.95i	−0.138083	−	0.239167i	0.788688	−	0.614794i	$-0.210761\pi$
$347$	−892.554	−	1545.95i	−0.138083	−	0.239167i	−0.926771	+	0.375627i	$0.877427\pi$
$348$	43154.1			6.64742
$349$	515.774	+	893.346i	0.0791081	+	0.137019i	0.902865	−	0.429923i	$-0.141459\pi$
$349$	515.774	+	893.346i	0.0791081	+	0.137019i	−0.823757	+	0.566943i	$0.808126\pi$
$350$	5674.69	+	9828.86i	0.866643	+	1.50107i
$351$	−400.232	+	693.222i	−0.0608626	+	0.105417i
$352$	−14305.1			−2.16610
$353$	−4969.39	+	8607.23i	−0.749274	+	1.29778i	0.198897	+	0.980020i	$0.436264\pi$
$353$	−4969.39	+	8607.23i	−0.749274	+	1.29778i	−0.948171	+	0.317760i	$0.897069\pi$
$354$	−14411.3	−	24961.0i	−2.16370	−	3.74764i
$355$	−1435.32			−0.214588
$356$	−8092.41	−	14016.5i	−1.20477	−	2.08672i
$357$	−2038.48	+	3530.75i	−0.302207	+	0.523438i
$358$	−6827.78	+	11826.1i	−1.00799	+	1.74589i
$359$	5459.00	−	9455.27i	0.802549	−	1.39006i	−0.115384	−	0.993321i	$-0.536810\pi$
$359$	5459.00	−	9455.27i	0.802549	−	1.39006i	0.917933	−	0.396735i	$-0.129857\pi$
$360$	−39218.3			−5.74163
$361$	3401.88	−	5892.24i	0.495974	−	0.859052i
$362$	9120.75	−	15797.6i	1.32424	−	2.29366i
$363$	1378.15	+	2387.03i	0.199268	+	0.345142i
$364$	−1532.83	−	2654.94i	−0.220721	−	0.382299i
$365$	−1560.73			−0.223815
$366$	−6930.87			−0.989843
$367$	3544.38	+	6139.05i	0.504129	+	0.873177i	0.999989	+	0.00477448i	$0.00151977\pi$
$367$	3544.38	+	6139.05i	0.504129	+	0.873177i	−0.495859	+	0.868403i	$0.665147\pi$
$368$	−4981.48	−	8628.18i	−0.705646	−	1.22222i
$369$	3314.50	−	5740.88i	0.467604	−	0.809914i
$370$	−8719.55	+	15102.7i	−1.22516	+	2.12203i
$371$	−2826.40			−0.395524
$372$	−25604.6	+	44348.5i	−3.56865	+	6.18108i
$373$	−7164.05	+	12408.5i	−0.994478	+	1.72249i	−0.406357	+	0.913715i	$0.633201\pi$
$373$	−7164.05	+	12408.5i	−0.994478	+	1.72249i	−0.588122	+	0.808772i	$0.700132\pi$
$374$	2541.87	−	4402.64i	0.351435	−	0.608704i
$375$	−219.677	−	380.492i	−0.0302509	−	0.0523961i
$376$	23180.3			3.17934
$377$	−1206.03	−	2088.90i	−0.164757	−	0.285368i
$378$	3882.33	−	6724.39i	0.528268	−	0.914987i
$379$	3776.04			0.511774			0.255887	−	0.966707i	$-0.417633\pi$
$379$	3776.04			0.511774			0.255887	+	0.966707i	$0.417633\pi$
$380$	−1196.80	+	2072.93i	−0.161565	+	0.279839i
$381$	10018.0	+	17351.7i	1.34708	+	2.33321i
$382$	8639.52	+	14964.1i	1.15716	+	2.00426i
$383$	−2959.22			−0.394802			−0.197401	−	0.980323i	$-0.563250\pi$
$383$	−2959.22			−0.394802			−0.197401	+	0.980323i	$0.563250\pi$
$384$	5658.93	+	9801.56i	0.752034	+	1.30256i
$385$	8326.21			1.10219
$386$	8371.46			1.10388
$387$	7364.20	+	7746.52i	0.967295	+	1.01751i
$388$	−17440.9			−2.28203
$389$	−11332.9			−1.47713			−0.738564	−	0.674184i	$-0.764496\pi$
$389$	−11332.9			−1.47713			−0.738564	+	0.674184i	$0.764496\pi$
$390$	3104.17	+	5376.59i	0.403041	+	0.698087i
$391$	1652.22			0.213699
$392$	−2156.66	−	3735.45i	−0.277878	−	0.481298i
$393$	−9611.13	−	16647.0i	−1.23363	−	2.13671i
$394$	1647.00	−	2852.68i	0.210595	−	0.364762i
$395$	7394.99			0.941981
$396$	−12058.1	+	20885.3i	−1.53016	+	2.65032i
$397$	2905.86	+	5033.09i	0.367357	+	0.636281i	0.989151	−	0.146900i	$-0.0469294\pi$
$397$	2905.86	+	5033.09i	0.367357	+	0.636281i	−0.621794	+	0.783180i	$0.713596\pi$
$398$	3903.05			0.491563
$399$	−497.918	−	862.420i	−0.0624739	−	0.108208i
$400$	−11781.1	+	20405.5i	−1.47264	+	2.55068i
$401$	−2921.32	+	5059.88i	−0.363800	+	0.630121i	−0.988583	−	0.150678i	$-0.951854\pi$
$401$	−2921.32	+	5059.88i	−0.363800	+	0.630121i	0.624783	+	0.780799i	$0.285188\pi$
$402$	2531.88	−	4385.34i	0.314126	−	0.544082i
$403$	2862.29			0.353798
$404$	10399.0	−	18011.6i	1.28062	−	2.21810i
$405$	2512.11	−	4351.10i	0.308216	−	0.533847i
$406$	11698.7	+	20262.7i	1.43004	+	2.47690i
$407$	3241.68	+	5614.76i	0.394801	+	0.683816i
$408$	−15931.0			−1.93309
$409$	5605.42			0.677677			0.338839	−	0.940845i	$-0.389966\pi$
$409$	5605.42			0.677677			0.338839	+	0.940845i	$0.389966\pi$
$410$	−7396.15	−	12810.5i	−0.890902	−	1.54309i
$411$	−1099.91	−	1905.10i	−0.132006	−	0.228641i
$412$	14714.9	−	25486.9i	1.75959	−	3.04769i
$413$	5599.42	−	9698.48i	0.667141	−	1.15552i
$414$	−10937.0			−1.29837
$415$	1192.63	−	2065.70i	0.141070	−	0.244340i
$416$	2072.20	−	3589.15i	0.244226	−	0.423011i
$417$	390.261	−	675.952i	0.0458302	−	0.0793802i
$418$	620.875	+	1075.39i	0.0726506	+	0.125835i
$419$	1304.47			0.152094			0.0760471	−	0.997104i	$-0.475770\pi$
$419$	1304.47			0.152094			0.0760471	+	0.997104i	$0.475770\pi$
$420$	−21578.5	−	37375.1i	−2.50696	−	4.34219i
$421$	−2651.39	+	4592.33i	−0.306937	+	0.531631i	−0.977691	−	0.210049i	$-0.932638\pi$
$421$	−2651.39	+	4592.33i	−0.306937	+	0.531631i	0.670753	+	0.741680i	$0.265971\pi$
$422$	−6016.15			−0.693985
$423$	6759.86	−	11708.4i	0.777011	−	1.34582i
$424$	−5522.16	−	9564.66i	−0.632500	−	1.09552i
$425$	−1953.73	−	3383.96i	−0.222988	−	0.386227i
$426$	3859.52			0.438954
$427$	−1346.48	−	2332.17i	−0.152601	−	0.264313i
$428$	34119.0			3.85328
$429$	2308.09			0.259757
$430$	23186.5	−	5588.28i	2.60036	−	0.626723i
$431$	−6201.04			−0.693025			−0.346512	−	0.938045i	$-0.612634\pi$
$431$	−6201.04			−0.693025			−0.346512	+	0.938045i	$0.612634\pi$
$432$	16120.0			1.79531
$433$	−1362.53	−	2359.97i	−0.151221	−	0.261923i	0.780455	−	0.625212i	$-0.214987\pi$
$433$	−1362.53	−	2359.97i	−0.151221	−	0.261923i	−0.931677	+	0.363288i	$0.881654\pi$
$434$	−27764.7			−3.07085
$435$	−16977.9	−	29406.6i	−1.87133	−	3.24124i
$436$	−17441.9	−	30210.3i	−1.91586	−	3.31837i
$437$	−201.785	+	349.502i	−0.0220886	+	0.0382585i
$438$	4196.76			0.457828
$439$	−2267.83	+	3927.99i	−0.246554	+	0.427045i	−0.962568	−	0.271042i	$-0.912632\pi$
$439$	−2267.83	+	3927.99i	−0.246554	+	0.427045i	0.716013	+	0.698087i	$0.245965\pi$
$440$	16267.6	+	28176.3i	1.76256	+	3.05284i
$441$	−2515.72			−0.271646
$442$	736.414	+	1275.51i	0.0792481	+	0.137262i
$443$	2002.43	−	3468.31i	0.214759	−	0.371974i	−0.738439	−	0.674320i	$-0.764437\pi$
$443$	2002.43	−	3468.31i	0.214759	−	0.371974i	0.953198	+	0.302347i	$0.0977700\pi$
$444$	16802.5	−	29102.9i	1.79598	−	3.11072i
$445$	−6367.51	+	11028.9i	−0.678313	+	1.17487i
$446$	5595.82			0.594102
$447$	−4211.46	+	7294.47i	−0.445627	+	0.771849i
$448$	−7894.67	+	13674.0i	−0.832563	+	1.44204i
$449$	−974.753	−	1688.32i	−0.102453	−	0.177454i	0.810242	−	0.586096i	$-0.199336\pi$
$449$	−974.753	−	1688.32i	−0.102453	−	0.177454i	−0.912695	+	0.408642i	$0.866002\pi$
$450$	12932.9	+	22400.5i	1.35481	+	2.34660i
$451$	−5499.36			−0.574179
$452$	7401.07			0.770170
$453$	11254.9	+	19494.1i	1.16734	+	2.02189i
$454$	10093.6	+	17482.7i	1.04343	+	1.80728i
$455$	−1206.11	+	2089.04i	−0.124271	+	0.215244i
$456$	1945.64	−	3369.96i	0.199810	−	0.346080i
$457$	8398.51			0.859662			0.429831	−	0.902909i	$-0.358573\pi$
$457$	8398.51			0.859662			0.429831	+	0.902909i	$0.358573\pi$
$458$	−16801.0	+	29100.2i	−1.71411	+	2.96892i
$459$	−1336.64	+	2315.13i	−0.135924	+	0.235427i
$460$	−8744.88	+	15146.6i	−0.886374	+	1.53524i
$461$	2139.56	+	3705.83i	0.216159	+	0.374398i	0.953630	−	0.300980i	$-0.0973138\pi$
$461$	2139.56	+	3705.83i	0.216159	+	0.374398i	−0.737472	+	0.675378i	$0.763980\pi$
$462$	−22388.9			−2.25460
$463$	−6180.90	−	10705.6i	−0.620412	−	1.07459i	−0.989409	−	0.145154i	$-0.953632\pi$
$463$	−6180.90	−	10705.6i	−0.620412	−	1.07459i	0.368997	−	0.929431i	$-0.379701\pi$
$464$	−24287.4	+	42067.0i	−2.42999	+	4.20886i
$465$	40294.0			4.01847
$466$	3347.95	−	5798.83i	0.332813	−	0.576449i
$467$	−7172.37	−	12422.9i	−0.710702	−	1.23097i	−0.964594	−	0.263739i	$-0.915044\pi$
$467$	−7172.37	−	12422.9i	−0.710702	−	1.23097i	0.253892	−	0.967233i	$-0.418289\pi$
$468$	−3493.41	−	6050.76i	−0.345049	−	0.597642i
$469$	1967.49			0.193711
$470$	−15084.3	−	26126.8i	−1.48040	−	2.56413i
$471$	−5892.40			−0.576449
$472$	43760.1			4.26742
$473$	2510.83	−	8504.01i	0.244076	−	0.826670i
$474$	−19884.9			−1.92688
$475$	954.435			0.0921947
$476$	−5119.15	−	8866.64i	−0.492933	−	0.853785i
$477$	−6441.52			−0.618316
$478$	−3956.95	−	6853.64i	−0.378633	−	0.655812i
$479$	3743.53	+	6483.99i	0.357090	+	0.618499i	0.987473	−	0.157786i	$-0.0504355\pi$
$479$	3743.53	+	6483.99i	0.357090	+	0.618499i	−0.630383	+	0.776284i	$0.717102\pi$
$480$	29171.5	−	50526.5i	2.77394	−	4.80460i
$481$	−1878.32			−0.178054
$482$	−6934.45	+	12010.8i	−0.655302	+	1.13502i
$483$	−3638.22	−	6301.58i	−0.342742	−	0.593647i
$484$	−6921.79			−0.650056
$485$	6861.70	+	11884.8i	0.642420	+	1.11270i
$486$	−13057.3	+	22616.0i	−1.21871	+	2.11087i
$487$	3455.07	−	5984.35i	0.321487	−	0.556831i	−0.659308	−	0.751873i	$-0.729151\pi$
$487$	3455.07	−	5984.35i	0.321487	−	0.556831i	0.980795	+	0.195042i	$0.0624842\pi$
$488$	5261.44	−	9113.08i	0.488062	−	0.845348i
$489$	−6711.51			−0.620665
$490$	−2806.85	+	4861.61i	−0.258777	+	0.448215i
$491$	−8145.25	+	14108.0i	−0.748656	+	1.29671i	0.199811	+	0.979834i	$0.435967\pi$
$491$	−8145.25	+	14108.0i	−0.748656	+	1.29671i	−0.948467	+	0.316875i	$0.897366\pi$
$492$	14252.4	+	24685.8i	1.30599	+	2.26204i
$493$	−4027.73	−	6976.23i	−0.367951	−	0.637310i
$494$	−359.752			−0.0327652
$495$	18975.9			1.72304
$496$	−28820.9	−	49919.2i	−2.60906	−	4.51903i
$497$	749.797	+	1298.69i	0.0676720	+	0.117211i
$498$	−3206.94	+	5554.59i	−0.288568	+	0.499814i
$499$	−6287.05	+	10889.5i	−0.564022	+	0.976915i	0.433118	+	0.901337i	$0.357413\pi$
$499$	−6287.05	+	10889.5i	−0.564022	+	0.976915i	−0.997140	+	0.0755776i	$0.975920\pi$
$500$	1103.33			0.0986850
$501$	10014.6	−	17345.7i	0.893049	−	1.54681i
$502$	3196.12	−	5535.84i	0.284163	−	0.492185i
$503$	−3144.54	+	5446.50i	−0.278744	+	0.482798i	−0.971073	−	0.238784i	$-0.923251\pi$
$503$	−3144.54	+	5446.50i	−0.278744	+	0.482798i	0.692329	+	0.721582i	$0.256585\pi$
$504$	20487.3	+	35485.1i	1.81067	+	3.13617i
$505$	−16364.9			−1.44204
$506$	4536.64	+	7857.69i	0.398574	+	0.690350i
$507$	8515.63	−	14749.5i	0.745942	−	1.29201i
$508$	−50315.6			−4.39447
$509$	−2764.32	+	4787.95i	−0.240720	+	0.416939i	−0.960920	−	0.276828i	$-0.910717\pi$
$509$	−2764.32	+	4787.95i	−0.240720	+	0.416939i	0.720200	+	0.693767i	$0.244050\pi$
$510$	10366.9	+	17956.0i	0.900107	+	1.55903i
$511$	815.313	+	1412.16i	0.0705819	+	0.122251i
$512$	11930.5			1.02980
$513$	−326.487	−	565.492i	−0.0280989	−	0.0486688i
$514$	14466.8			1.24145
$515$	−23156.8			−1.98138
$516$	−44680.4	+	10768.6i	−3.81191	+	0.918723i
$517$	−11215.8			−0.954105
$518$	18220.1			1.54545
$519$	13513.3	+	23405.7i	1.14290	+	1.97957i
$520$	−9425.89			−0.794909
$521$	383.607	+	664.427i	0.0322574	+	0.0558715i	0.881703	−	0.471804i	$-0.156397\pi$
$521$	383.607	+	664.427i	0.0322574	+	0.0558715i	−0.849446	+	0.527676i	$0.823064\pi$
$522$	26662.0	+	46179.9i	2.23556	+	3.87210i
$523$	6162.44	−	10673.7i	0.515229	−	0.892403i	−0.484615	−	0.874728i	$-0.661040\pi$
$523$	6162.44	−	10673.7i	0.515229	−	0.892403i	0.999844	−	0.0176753i	$-0.00562652\pi$
$524$	48272.1			4.02438
$525$	−8604.30	+	14903.1i	−0.715281	+	1.23890i
$526$	5554.04	+	9619.88i	0.460395	+	0.797427i
$527$	9559.09			0.790134
$528$	−23240.5	−	40253.8i	−1.91556	−	3.31784i
$529$	4609.08	−	7983.17i	0.378818	−	0.656133i
$530$	−7186.97	+	12448.2i	−0.589023	+	1.02022i
$531$	12761.4	−	22103.4i	1.04293	−	1.80641i
$532$	2500.80			0.203804
$533$	796.621	−	1379.79i	0.0647382	−	0.112130i
$534$	17122.0	−	29656.2i	1.38753	−	2.40328i
$535$	−13423.3	−	23249.8i	−1.08475	−	1.87884i
$536$	3844.05	+	6658.09i	0.309772	+	0.536541i
$537$	−20705.4			−1.66388
$538$	−35631.1			−2.85533
$539$	1043.51	+	1807.41i	0.0833898	+	0.144435i
$540$	−14149.1	−	24507.0i	−1.12756	−	1.95299i
$541$	−6334.73	+	10972.1i	−0.503422	+	0.871953i	0.496570	+	0.867997i	$0.334593\pi$
$541$	−6334.73	+	10972.1i	−0.503422	+	0.871953i	−0.999992	+	0.00395595i	$0.998741\pi$
$542$	4495.04	−	7785.65i	0.356234	−	0.617015i
$543$	27658.8			2.18592
$544$	6920.45	−	11986.6i	0.545427	−	0.944706i
$545$	−13724.2	+	23771.0i	−1.07868	+	1.86832i
$546$	3243.19	−	5617.37i	0.254205	−	0.440295i
$547$	−1505.38	−	2607.40i	−0.117670	−	0.203810i	0.801174	−	0.598432i	$-0.204209\pi$
$547$	−1505.38	−	2607.40i	−0.117670	−	0.203810i	−0.918844	+	0.394621i	$0.870876\pi$
$548$	5524.31			0.430633
$549$	−3068.69	−	5315.13i	−0.238559	−	0.413196i
$550$	10729.1	−	18583.3i	0.831797	−	1.44071i
$551$	1967.62			0.152130
$552$	14216.5	−	24623.8i	1.09619	−	1.89866i
$553$	−3863.08	−	6691.06i	−0.297061	−	0.514526i
$554$	−4047.83	−	7011.04i	−0.310425	−	0.537673i
$555$	−26442.2			−2.02236
$556$	980.047	+	1697.49i	0.0747540	+	0.129478i
$557$	11347.0			0.863177			0.431589	−	0.902071i	$-0.357953\pi$
$557$	11347.0			0.863177			0.431589	+	0.902071i	$0.357953\pi$
$558$	−63277.4			−4.80062
$559$	1769.94	+	1861.83i	0.133919	+	0.140871i
$560$	48578.1			3.66571
$561$	7708.25			0.580112
$562$	13597.9	+	23552.3i	1.02063	+	1.76778i
$563$	23560.2			1.76366			0.881832	−	0.471565i	$-0.156311\pi$
$563$	23560.2			1.76366			0.881832	+	0.471565i	$0.156311\pi$
$564$	29067.4	+	50346.3i	2.17014	+	3.75880i
$565$	−2911.77	−	5043.33i	−0.216812	−	0.375530i
$566$	−7253.54	+	12563.5i	−0.538673	+	0.933009i
$567$	−5249.22			−0.388794
$568$	−2929.88	+	5074.70i	−0.216435	+	0.374876i
$569$	−6915.50	−	11978.0i	−0.509513	−	0.882503i	−0.999939	−	0.0110199i	$-0.996492\pi$
$569$	−6915.50	−	11978.0i	−0.509513	−	0.882503i	0.490426	−	0.871483i	$-0.336841\pi$
$570$	−5064.43			−0.372150
$571$	4442.68	+	7694.95i	0.325605	+	0.563964i	0.981635	−	0.190771i	$-0.0610987\pi$
$571$	4442.68	+	7694.95i	0.325605	+	0.563964i	−0.656030	+	0.754735i	$0.727765\pi$
$572$	−2898.10	+	5019.66i	−0.211846	+	0.366928i
$573$	−13099.7	+	22689.4i	−0.955060	+	1.65421i
$574$	−7727.38	+	13384.2i	−0.561907	+	0.973251i
$575$	6973.92			0.505796
$576$	−17992.4	+	31163.7i	−1.30153	+	2.25432i
$577$	9374.85	−	16237.7i	0.676396	−	1.17155i	−0.299663	−	0.954045i	$-0.596874\pi$
$577$	9374.85	−	16237.7i	0.676396	−	1.17155i	0.976059	−	0.217507i	$-0.0697923\pi$
$578$	−10592.9	−	18347.4i	−0.762293	−	1.32033i
$579$	6346.65	+	10992.7i	0.455540	+	0.789018i
$580$	85271.9			6.10469
$581$	−2492.08			−0.177950
$582$	−18450.9	−	31957.9i	−1.31411	−	2.27611i
$583$	2671.91	+	4627.89i	0.189810	+	0.328761i
$584$	−3185.88	+	5518.11i	−0.225741	+	0.390995i
$585$	−2748.79	+	4761.04i	−0.194271	+	0.336487i
$586$	10020.3			0.706371
$587$	−7712.47	+	13358.4i	−0.542296	+	0.939284i	0.456476	+	0.889736i	$0.349111\pi$
$587$	−7712.47	+	13358.4i	−0.542296	+	0.939284i	−0.998772	+	0.0495483i	$0.984222\pi$
$588$	5408.80	−	9368.31i	0.379345	−	0.657045i
$589$	−1167.45	+	2022.08i	−0.0816704	+	0.141457i
$590$	−28476.4	−	49322.6i	−1.98704	−	3.44166i
$591$	4994.55			0.347628
$592$	18913.1	+	32758.5i	1.31305	+	2.27427i
$593$	10412.9	−	18035.6i	0.721088	−	1.24896i	−0.239476	−	0.970902i	$-0.576976\pi$
$593$	10412.9	−	18035.6i	0.721088	−	1.24896i	0.960564	−	0.278058i	$-0.0896909\pi$
$594$	−14680.5			−1.01405
$595$	−4028.01	+	6976.71i	−0.277533	+	0.480701i
$596$	−10576.1	−	18318.3i	−0.726867	−	1.25897i
$597$	2959.01	+	5125.16i	0.202855	+	0.351355i
$598$	−2628.66			−0.179755
$599$	−10621.1	−	18396.3i	−0.724484	−	1.25484i	−0.959186	−	0.282775i	$-0.908745\pi$
$599$	−10621.1	−	18396.3i	−0.724484	−	1.25484i	0.234702	−	0.972067i	$-0.424588\pi$
$600$	−67243.6			−4.57535
$601$	1556.16			0.105619			0.0528095	−	0.998605i	$-0.483182\pi$
$601$	1556.16			0.105619			0.0528095	+	0.998605i	$0.483182\pi$
$602$	−17168.8	−	18060.1i	−1.16237	−	1.22272i
$603$	4484.03			0.302825
$604$	−56528.1			−3.80811
$605$	2723.21	+	4716.73i	0.182999	+	0.316963i
$606$	44004.8			2.94979
$607$	5970.51	+	10341.2i	0.399235	+	0.691495i	0.993632	−	0.112677i	$-0.0359424\pi$
$607$	5970.51	+	10341.2i	0.399235	+	0.691495i	−0.594397	+	0.804172i	$0.702609\pi$
$608$	1690.39	+	2927.83i	0.112754	+	0.195295i
$609$	−17738.2	+	30723.5i	−1.18028	+	2.04430i
$610$	−13695.3			−0.909027
$611$	1624.69	−	2814.05i	0.107575	−	0.186325i
$612$	−11666.8	−	20207.5i	−0.770594	−	1.33471i
$613$	−5125.04			−0.337681			−0.168840	−	0.985643i	$-0.554002\pi$
$613$	−5125.04			−0.337681			−0.168840	+	0.985643i	$0.554002\pi$
$614$	12144.2	+	21034.4i	0.798210	+	1.38254i
$615$	11214.5	−	19424.0i	0.735303	−	1.27358i
$616$	16996.1	−	29438.1i	1.11168	−	1.92548i
$617$	10626.7	−	18406.0i	0.693381	−	1.20097i	−0.277343	−	0.960771i	$-0.589454\pi$
$617$	10626.7	−	18406.0i	0.693381	−	1.20097i	0.970724	−	0.240200i	$-0.0772129\pi$
$618$	62267.9			4.05304
$619$	8114.95	−	14055.5i	0.526926	−	0.912663i	−0.472581	−	0.881287i	$-0.656678\pi$
$619$	8114.95	−	14055.5i	0.526926	−	0.912663i	0.999508	−	0.0313761i	$-0.00998897\pi$
$620$	−50594.3	+	87631.9i	−3.27729	+	5.67642i
$621$	−2385.59	−	4131.97i	−0.154156	−	0.267005i
$622$	−19647.0	−	34029.7i	−1.26652	−	2.19367i
$623$	13305.3			0.855646
$624$	13466.2			0.863910
$625$	7592.53	+	13150.6i	0.485922	+	0.841641i
$626$	−1022.44	−	1770.92i	−0.0652796	−	0.113068i
$627$	−941.406	+	1630.56i	−0.0599619	+	0.103857i
$628$	7398.66	−	12814.9i	0.470125	−	0.814281i
$629$	−6272.97			−0.397646
$630$	26663.8	−	46183.1i	1.68621	−	2.92060i
$631$	−5689.63	+	9854.73i	−0.358955	+	0.621728i	−0.987787	−	0.155813i	$-0.950200\pi$
$631$	−5689.63	+	9854.73i	−0.358955	+	0.621728i	0.628831	+	0.777542i	$0.283534\pi$
$632$	15095.2	−	26145.7i	0.950088	−	1.64560i
$633$	−4561.02	−	7899.92i	−0.286389	−	0.496041i
$634$	−38193.5			−2.39252
$635$	19795.4	+	34286.7i	1.23710	+	2.14272i
$636$	13849.3	−	23987.6i	0.863458	−	1.49555i
$637$	−604.638			−0.0376085
$638$	22118.5	−	38310.4i	1.37254	−	2.37731i
$639$	1708.83	+	2959.78i	0.105791	+	0.183235i
$640$	11182.0	+	19367.7i	0.690634	+	1.19621i
$641$	−6841.44			−0.421561			−0.210781	−	0.977533i	$-0.567601\pi$
$641$	−6841.44			−0.421561			−0.210781	+	0.977533i	$0.567601\pi$
$642$	36094.8	+	62518.0i	2.21892	+	3.84328i
$643$	4167.38			0.255592			0.127796	−	0.991800i	$-0.459210\pi$
$643$	4167.38			0.255592			0.127796	+	0.991800i	$0.459210\pi$
$644$	18273.0			1.11810
$645$	24916.5	+	26210.0i	1.52106	+	1.60003i
$646$	−1201.45			−0.0731742
$647$	−17803.0			−1.08178			−0.540888	−	0.841094i	$-0.681912\pi$
$647$	−17803.0			−1.08178			−0.540888	+	0.841094i	$0.681912\pi$
$648$	−10255.8	−	17763.6i	−0.621738	−	1.07688i
$649$	−21173.5			−1.28063
$650$	3108.36	+	5383.83i	0.187569	+	0.324879i
$651$	−21049.3	−	36458.4i	−1.26726	−	2.19496i
$652$	8427.17	−	14596.3i	0.506186	−	0.876741i
$653$	14735.0			0.883037			0.441519	−	0.897252i	$-0.354440\pi$
$653$	14735.0			0.883037			0.441519	+	0.897252i	$0.354440\pi$
$654$	36903.8	−	63919.3i	2.20650	−	3.82178i
$655$	−18991.4	−	32894.1i	−1.13291	−	1.96226i
$656$	−32085.3			−1.90963
$657$	1858.14	+	3218.40i	0.110340	+	0.191114i
$658$	−15759.8	+	27296.9i	−0.933712	+	1.61724i
$659$	5423.39	−	9393.59i	0.320585	−	0.555269i	−0.660024	−	0.751244i	$-0.729454\pi$
$659$	5423.39	−	9393.59i	0.320585	−	0.555269i	0.980609	+	0.195975i	$0.0627873\pi$
$660$	−40798.2	+	70664.6i	−2.40616	+	4.16760i
$661$	8365.45			0.492251			0.246126	−	0.969238i	$-0.420842\pi$
$661$	8365.45			0.492251			0.246126	+	0.969238i	$0.420842\pi$
$662$	−16785.8	+	29073.9i	−0.985497	+	1.70693i
$663$	−1116.59	+	1934.00i	−0.0654071	+	0.113288i
$664$	−4868.98	−	8433.32i	−0.284568	−	0.492886i
$665$	−983.878	−	1704.13i	−0.0573732	−	0.0993732i
$666$	41524.5			2.41598
$667$	14377.1			0.834610
$668$	25149.1	+	43559.6i	1.45666	+	2.52301i
$669$	4242.35	+	7347.97i	0.245170	+	0.424647i
$670$	5002.95	−	8665.36i	0.288479	−	0.499660i
$671$	−2545.76	+	4409.39i	−0.146465	+	0.253685i
$672$	−60955.8			−3.49914
$673$	2152.95	−	3729.02i	0.123314	−	0.213586i	−0.797759	−	0.602977i	$-0.793981\pi$
$673$	2152.95	−	3729.02i	0.123314	−	0.213586i	0.921073	+	0.389391i	$0.127315\pi$
$674$	−790.001	+	1368.32i	−0.0451479	+	0.0781985i
$675$	−5641.87	+	9772.01i	−0.321712	+	0.557222i
$676$	21384.9	+	37039.8i	1.21671	+	2.10741i
$677$	6938.20			0.393880			0.196940	−	0.980416i	$-0.436900\pi$
$677$	6938.20			0.393880			0.196940	+	0.980416i	$0.436900\pi$
$678$	7829.64	+	13561.3i	0.443504	+	0.768171i
$679$	7168.99	−	12417.1i	0.405185	−	0.701801i
$680$	−31479.4			−1.77526
$681$	−15304.6	+	26508.3i	−0.861192	+	1.49163i
$682$	26247.2	+	45461.4i	1.47369	+	2.55251i
$683$	11783.7	+	20409.9i	0.660160	+	1.14343i	0.980573	+	0.196152i	$0.0628447\pi$
$683$	11783.7	+	20409.9i	0.660160	+	1.14343i	−0.320414	+	0.947278i	$0.603822\pi$
$684$	5699.46			0.318603
$685$	−2173.40	−	3764.44i	−0.121228	−	0.209974i
$686$	36177.1			2.01348
$687$	−50949.4			−2.82946
$688$	14649.1	−	49615.4i	0.811759	−	2.74938i
$689$	−1548.18			−0.0856038
$690$	−37005.1			−2.04168
$691$	−11147.6	−	19308.2i	−0.613710	−	1.06298i	−0.990609	−	0.136723i	$-0.956343\pi$
$691$	−11147.6	−	19308.2i	−0.613710	−	1.06298i	0.376899	−	0.926254i	$-0.376990\pi$
$692$	−67870.6			−3.72840
$693$	−9912.85	−	17169.6i	−0.543374	−	0.941151i
$694$	4742.46	+	8214.17i	0.259396	+	0.449288i
$695$	771.150	−	1335.67i	0.0420883	−	0.0728991i
$696$	−138626.			−7.54975
$697$	2660.45	−	4608.03i	0.144579	−	0.250419i
$698$	−2740.49	−	4746.67i	−0.148609	−	0.257398i
$699$	10152.7			0.549372
$700$	−21607.6	−	37425.5i	−1.16670	−	2.02079i
$701$	3693.84	−	6397.92i	0.199022	−	0.344716i	−0.749190	−	0.662356i	$-0.769557\pi$
$701$	3693.84	−	6397.92i	0.199022	−	0.344716i	0.948212	+	0.317639i	$0.102890\pi$
$702$	2126.57	−	3683.33i	0.114334	−	0.198032i
$703$	766.115	−	1326.95i	0.0411018	−	0.0711905i
$704$	29852.7			1.59817
$705$	22871.7	−	39615.0i	1.22184	−	2.11629i
$706$	26404.1	−	45733.3i	1.40755	−	2.43795i
$707$	8548.91	+	14807.1i	0.454759	+	0.787666i
$708$	54874.0	+	95044.5i	2.91284	+	5.04519i
$709$	−20824.0			−1.10305			−0.551525	−	0.834159i	$-0.685954\pi$
$709$	−20824.0			−1.10305			−0.551525	+	0.834159i	$0.685954\pi$
$710$	7626.34			0.403115
$711$	−8804.17	−	15249.3i	−0.464391	−	0.804350i
$712$	25995.7	+	45025.9i	1.36830	+	2.36997i
$713$	−8530.38	+	14775.0i	−0.448058	+	0.776059i
$714$	10831.2	−	18760.2i	0.567712	−	0.983307i
$715$	4560.75			0.238549
$716$	25998.3	−	45030.3i	1.35698	−	2.35036i
$717$	5999.76	−	10391.9i	0.312504	−	0.541272i
$718$	−29005.6	+	50239.2i	−1.50763	+	2.61130i
$719$	10221.4	+	17704.1i	0.530175	+	0.918290i	0.999380	+	0.0352008i	$0.0112071\pi$
$719$	10221.4	+	17704.1i	0.530175	+	0.918290i	−0.469205	+	0.883089i	$0.655460\pi$
$720$	110712.			5.73055
$721$	12096.9	+	20952.5i	0.624845	+	1.08226i
$722$	−18075.4	+	31307.5i	−0.931714	+	1.61378i
$723$	−21028.8			−1.08170
$724$	−34729.2	+	60152.8i	−1.78274	+	3.08779i
$725$	−17000.8	−	29446.2i	−0.870887	−	1.50842i
$726$	−7322.61	−	12683.1i	−0.374336	−	0.648368i
$727$	−6810.77			−0.347452			−0.173726	−	0.984794i	$-0.555581\pi$
$727$	−6810.77			−0.347452			−0.173726	+	0.984794i	$0.555581\pi$
$728$	4924.01	+	8528.63i	0.250681	+	0.434192i
$729$	−31075.3			−1.57879
$730$	8292.72			0.420448
$731$	5911.02	+	6217.90i	0.299079	+	0.314606i
$732$	26390.8			1.33256
$733$	−18357.3			−0.925025			−0.462512	−	0.886613i	$-0.653052\pi$
$733$	−18357.3			−0.925025			−0.462512	+	0.886613i	$0.653052\pi$
$734$	−18832.6	−	32619.0i	−0.947034	−	1.64031i
$735$	−8511.82			−0.427161
$736$	12351.4	+	21393.3i	0.618585	+	1.07142i
$737$	−1859.96	−	3221.54i	−0.0929611	−	0.161013i
$738$	−17611.1	+	30503.3i	−0.878420	+	1.52147i
$739$	18743.1			0.932985			0.466493	−	0.884525i	$-0.345517\pi$
$739$	18743.1			0.932985			0.466493	+	0.884525i	$0.345517\pi$
$740$	33201.5	−	57506.8i	1.64934	−	2.85674i
$741$	−272.738	−	472.397i	−0.0135213	−	0.0234196i
$742$	15017.7			0.743013
$743$	2163.21	+	3746.79i	0.106811	+	0.185002i	0.914477	−	0.404639i	$-0.132603\pi$
$743$	2163.21	+	3746.79i	0.106811	+	0.185002i	−0.807666	+	0.589641i	$0.799269\pi$
$744$	82251.2	−	142463.i	4.05306	−	7.02010i
$745$	−8321.78	+	14413.8i	−0.409244	+	0.708831i
$746$	38065.1	−	65930.8i	1.86818	−	3.23579i
$747$	−5679.59			−0.278186
$748$	−9678.70	+	16764.0i	−0.473113	+	0.819456i
$749$	−14024.4	+	24291.0i	−0.684167	+	1.18501i
$750$	1167.22	+	2021.69i	0.0568279	+	0.0984289i
$751$	−3333.70	−	5774.13i	−0.161982	−	0.280561i	0.773598	−	0.633677i	$-0.218455\pi$
$751$	−3333.70	−	5774.13i	−0.161982	−	0.280561i	−0.935579	+	0.353116i	$0.885122\pi$
$752$	−65437.3			−3.17321
$753$	9692.28			0.469066
$754$	6408.05	+	11099.1i	0.309506	+	0.536080i
$755$	22239.6	+	38520.1i	1.07203	+	1.85681i
$756$	−14782.8	+	25604.5i	−0.711170	+	1.23178i
$757$	20177.1	−	34947.7i	0.968757	−	1.67794i	0.269592	−	0.962975i	$-0.413111\pi$
$757$	20177.1	−	34947.7i	0.968757	−	1.67794i	0.699164	−	0.714961i	$-0.253556\pi$
$758$	−20063.4			−0.961395
$759$	−6878.72	+	11914.3i	−0.328961	+	0.569778i
$760$	3844.56	−	6658.98i	0.183496	−	0.317824i
$761$	−8469.79	+	14670.1i	−0.403455	+	0.698805i	−0.994140	−	0.108097i	$-0.965524\pi$
$761$	−8469.79	+	14670.1i	−0.403455	+	0.698805i	0.590685	+	0.806902i	$0.298858\pi$
$762$	−53229.2	−	92195.7i	−2.53056	−	4.38307i
$763$	28677.6			1.36068
$764$	−32896.8	−	56979.0i	−1.55781	−	2.69820i
$765$	−9180.05	+	15900.3i	−0.433863	+	0.751473i
$766$	15723.4			0.741657
$767$	3067.12	−	5312.41i	0.144390	−	0.250091i
$768$	524.535	+	908.521i	0.0246452	+	0.0426867i
$769$	20783.6	+	35998.3i	0.974613	+	1.68808i	0.681207	+	0.732091i	$0.261456\pi$
$769$	20783.6	+	35998.3i	0.974613	+	1.68808i	0.293406	+	0.955988i	$0.405211\pi$
$770$	−44240.1			−2.07052
$771$	10967.7	+	18996.6i	0.512311	+	0.887349i
$772$	−31876.1			−1.48607
$773$	21859.3			1.01711			0.508555	−	0.861030i	$-0.330180\pi$
$773$	21859.3			1.01711			0.508555	+	0.861030i	$0.330180\pi$
$774$	−39128.6	−	41160.0i	−1.81712	−	1.91145i
$775$	40348.3			1.87013
$776$	56026.5			2.59180
$777$	13813.2	+	23925.1i	0.637767	+	1.10464i
$778$	60215.9			2.77486
$779$	649.840	+	1125.56i	0.0298882	+	0.0517679i
$780$	−11819.8	−	20472.5i	−0.542586	−	0.939786i
$781$	1417.63	−	2455.41i	0.0649511	−	0.112499i
$782$	−8778.84			−0.401446
$783$	−11631.0	+	20145.6i	−0.530855	+	0.919468i
$784$	6088.20	+	10545.1i	0.277342	+	0.480370i
$785$	−11643.3			−0.529384
$786$	51067.4	+	88451.2i	2.31745	+	4.01393i
$787$	−16759.1	+	29027.6i	−0.759081	+	1.31477i	0.184239	+	0.982882i	$0.441018\pi$
$787$	−16759.1	+	29027.6i	−0.759081	+	1.31477i	−0.943320	+	0.331885i	$0.892315\pi$
$788$	−6271.30	+	10862.2i	−0.283510	+	0.491054i
$789$	−8421.36	+	14586.2i	−0.379985	+	0.658154i
$790$	−39292.2			−1.76956
$791$	−3042.16	+	5269.18i	−0.136747	+	0.236853i
$792$	38735.0	−	67091.1i	1.73787	−	3.01007i
$793$	−737.543	−	1277.46i	−0.0330276	−	0.0572055i
$794$	−15439.8	−	26742.6i	−0.690100	−	1.19529i
$795$	−21794.6			−0.972296
$796$	−14861.7			−0.661757
$797$	−2088.61	−	3617.57i	−0.0928259	−	0.160779i	0.815873	−	0.578231i	$-0.196257\pi$
$797$	−2088.61	−	3617.57i	−0.0928259	−	0.160779i	−0.908699	+	0.417452i	$0.862923\pi$
$798$	2645.62	+	4582.34i	0.117361	+	0.203275i
$799$	5425.94	−	9398.00i	0.240245	−	0.416117i
$800$	29210.8	−	50594.6i	1.29095	−	2.23598i
$801$	30323.6			1.33762
$802$	15522.0	−	26884.9i	0.683419	−	1.18372i
$803$	1541.50	−	2669.96i	0.0677439	−	0.117336i
$804$	−9640.67	+	16698.1i	−0.422886	+	0.732460i
$805$	−7189.06	−	12451.8i	−0.314759	−	0.545179i
$806$	−15208.3			−0.664629
$807$	−27013.0	−	46787.9i	−1.17832	−	2.04090i
$808$	−33405.4	+	57859.8i	−1.45445	+	2.51918i
$809$	43230.5			1.87874			0.939372	−	0.342899i	$-0.111409\pi$
$809$	43230.5			1.87874			0.939372	+	0.342899i	$0.111409\pi$
$810$	−13347.7	+	23118.9i	−0.579002	+	1.00286i
$811$	−1126.77	−	1951.62i	−0.0487869	−	0.0845014i	0.840601	−	0.541655i	$-0.182202\pi$
$811$	−1126.77	−	1951.62i	−0.0487869	−	0.0845014i	−0.889388	+	0.457154i	$0.848869\pi$
$812$	−44545.3	−	77154.7i	−1.92516	−	3.33448i
$813$	13631.3			0.588032
$814$	−17224.2	−	29833.2i	−0.741656	−	1.28459i
$815$	−13261.8			−0.569990
$816$	44972.7			1.92936
$817$	−2037.21	+	490.997i	−0.0872375	+	0.0210255i
$818$	−29783.6			−1.27305
$819$	5743.78			0.245060
$820$	28162.4	+	48778.8i	1.19936	+	2.07735i
$821$	−31030.5			−1.31909			−0.659545	−	0.751665i	$-0.729251\pi$
$821$	−31030.5			−1.31909			−0.659545	+	0.751665i	$0.729251\pi$
$822$	5844.20	+	10122.5i	0.247981	+	0.429515i
$823$	−10971.5	−	19003.3i	−0.464695	−	0.804875i	0.534493	−	0.845173i	$-0.320503\pi$
$823$	−10971.5	−	19003.3i	−0.464695	−	0.804875i	−0.999188	+	0.0402983i	$0.987169\pi$
$824$	−47269.4	+	81873.1i	−1.99843	+	3.46139i
$825$	32536.0			1.37304
$826$	−29751.7	+	51531.5i	−1.25326	+	2.17071i
$827$	2146.70	+	3718.20i	0.0902639	+	0.156342i	0.907622	−	0.419788i	$-0.137896\pi$
$827$	2146.70	+	3718.20i	0.0902639	+	0.156342i	−0.817358	+	0.576130i	$0.804562\pi$
$828$	41645.2			1.74791
$829$	−13573.8	−	23510.5i	−0.568682	−	0.984986i	−0.996697	−	0.0812140i	$-0.974120\pi$
$829$	−13573.8	−	23510.5i	−0.568682	−	0.984986i	0.428015	−	0.903772i	$-0.359213\pi$
$830$	−6336.87	+	10975.8i	−0.265007	+	0.459006i
$831$	6137.55	−	10630.5i	0.256208	−	0.443766i
$832$	−4324.36	+	7490.02i	−0.180193	+	0.312103i
$833$	−2019.29			−0.0839907
$834$	−2073.60	+	3591.58i	−0.0860945	+	0.149120i
$835$	19788.6	−	34274.9i	0.820135	−	1.42052i
$836$	−2364.11	−	4094.76i	−0.0978045	−	0.169402i
$837$	−13802.1	−	23905.9i	−0.569976	−	0.987227i
$838$	−6931.11			−0.285717
$839$	37996.0			1.56349			0.781744	−	0.623599i	$-0.214330\pi$
$839$	37996.0			1.56349			0.781744	+	0.623599i	$0.214330\pi$
$840$	69318.0	+	120062.i	2.84726	+	4.93160i
$841$	−22853.6	−	39583.6i	−0.937045	−	1.62301i
$842$	14087.8	−	24400.7i	0.576599	−	0.998698i
$843$	−20617.9	+	35711.3i	−0.842371	+	1.45903i
$844$	22907.8			0.934264
$845$	16826.7	−	29144.8i	0.685039	−	1.18652i
$846$	−35917.5	+	62211.0i	−1.45966	+	2.52820i
$847$	2845.16	−	4927.97i	0.115420	−	0.199914i
$848$	15588.9	+	27000.8i	0.631280	+	1.09341i
$849$	−21996.5			−0.889183
$850$	10380.9	+	17980.2i	0.418895	+	0.725548i
$851$	5597.90	−	9695.84i	0.225492	−	0.390563i
$852$	−14695.9			−0.590933
$853$	−2601.49	+	4505.92i	−0.104424	+	0.180867i	−0.913503	−	0.406833i	$-0.866633\pi$
$853$	−2601.49	+	4505.92i	−0.104424	+	0.180867i	0.809079	+	0.587700i	$0.199966\pi$
$854$	7154.31	+	12391.6i	0.286669	+	0.496525i
$855$	−2242.31	−	3883.80i	−0.0896906	−	0.155349i
$856$	−109603.			−4.37633
$857$	−21197.1	−	36714.5i	−0.844900	−	1.46341i	−0.885708	−	0.464242i	$-0.846327\pi$
$857$	−21197.1	−	36714.5i	−0.844900	−	1.46341i	0.0408085	−	0.999167i	$-0.487007\pi$
$858$	−12263.7			−0.487967
$859$	−39517.4			−1.56964			−0.784818	−	0.619727i	$-0.787243\pi$
$859$	−39517.4			−1.56964			−0.784818	+	0.619727i	$0.787243\pi$
$860$	−88287.7	+	21278.6i	−3.50068	+	0.843713i
$861$	−23433.4			−0.927536
$862$	32948.3			1.30189
$863$	−6784.19	−	11750.6i	−0.267597	−	0.463492i	0.700644	−	0.713512i	$-0.252896\pi$
$863$	−6784.19	−	11750.6i	−0.267597	−	0.463492i	−0.968241	+	0.250019i	$0.919563\pi$
$864$	−39969.0			−1.57381
$865$	26702.0	+	46249.2i	1.04959	+	1.81794i
$866$	7239.59	+	12539.3i	0.284078	+	0.492037i
$867$	16061.5	−	27819.4i	0.629156	−	1.08973i
$868$	105720.			4.13408
$869$	−7303.87	+	12650.7i	−0.285117	+	0.493837i
$870$	90209.7	+	156248.i	3.51540	+	6.08885i
$871$	1077.71			0.0419252
$872$	56029.6	+	97046.2i	2.17592	+	3.76881i
$873$	16338.5	−	28299.1i	0.633419	−	1.09711i
$874$	1072.16	−	1857.03i	0.0414946	−	0.0718707i
$875$	−453.518	+	785.516i	−0.0175220	+	0.0303489i
$876$	−15980.0			−0.616342
$877$	−19334.4	+	33488.2i	−0.744444	+	1.28941i	0.206010	+	0.978550i	$0.433952\pi$
$877$	−19334.4	+	33488.2i	−0.744444	+	1.28941i	−0.950454	+	0.310865i	$0.899381\pi$
$878$	12049.8	−	20870.8i	0.463166	−	0.802227i
$879$	7596.65	+	13157.8i	0.291500	+	0.504893i
$880$	−45922.9	−	79540.9i	−1.75916	−	3.04696i
$881$	−3206.89			−0.122637			−0.0613183	−	0.998118i	$-0.519530\pi$
$881$	−3206.89			−0.122637			−0.0613183	+	0.998118i	$0.519530\pi$
$882$	13366.9			0.510302
$883$	−10535.7	−	18248.3i	−0.401533	−	0.695476i	0.592378	−	0.805660i	$-0.298189\pi$
$883$	−10535.7	−	18248.3i	−0.401533	−	0.695476i	−0.993911	+	0.110184i	$0.964856\pi$
$884$	−2804.06	−	4856.77i	−0.106686	−	0.184786i
$885$	43177.6	−	74785.8i	1.64000	−	2.84056i
$886$	−10639.6	+	18428.4i	−0.403437	+	0.698773i
$887$	−34055.1			−1.28913			−0.644565	−	0.764550i	$-0.722961\pi$
$887$	−34055.1			−1.28913			−0.644565	+	0.764550i	$0.722961\pi$
$888$	−53975.8	+	93488.8i	−2.03976	+	3.53297i
$889$	20681.9	−	35822.1i	0.780258	−	1.35145i
$890$	33832.9	−	58600.2i	1.27425	−	2.20706i
$891$	4962.31	+	8594.97i	0.186581	+	0.323168i
$892$	−21307.3			−0.799799
$893$	1325.34	+	2295.55i	0.0496648	+	0.0860220i
$894$	22377.0	−	38758.1i	0.837135	−	1.44996i
$895$	−40913.5			−1.52803
$896$	11682.7	−	20235.1i	0.435594	−	0.754471i
$897$	−1992.86	−	3451.74i	−0.0741802	−	0.128484i
$898$	5179.21	+	8970.65i	0.192464	+	0.333357i
$899$	83180.3			3.08589
$900$	−49244.9	−	85294.7i	−1.82389	−	3.15906i
$901$	−5170.41			−0.191178
$902$	29220.1			1.07863
$903$	10698.9	−	36236.5i	0.394283	−	1.33541i
$904$	−23774.9			−0.874713
$905$	54653.4			2.00745
$906$	−59801.5	−	103579.i	−2.19291	−	3.79822i
$907$	2553.70			0.0934887			0.0467443	−	0.998907i	$-0.485115\pi$
$907$	2553.70			0.0934887			0.0467443	+	0.998907i	$0.485115\pi$
$908$	−38433.7	−	66569.1i	−1.40470	−	2.43301i
$909$	19483.4	+	33746.3i	0.710918	+	1.23135i
$910$	6408.49	−	11099.8i	0.233450	−	0.404347i
$911$	−27220.5			−0.989960			−0.494980	−	0.868904i	$-0.664825\pi$
$911$	−27220.5			−0.989960			−0.494980	+	0.868904i	$0.664825\pi$
$912$	−5492.50	+	9513.29i	−0.199424	+	0.345413i
$913$	2355.87	+	4080.49i	0.0853975	+	0.147913i
$914$	−44624.3			−1.61492
$915$	−10382.8	−	17983.5i	−0.375131	−	0.649746i
$916$	63973.5	−	110805.i	2.30758	−	3.99685i
$917$	−19841.9	+	34367.3i	−0.714546	+	1.23763i
$918$	7102.05	−	12301.1i	0.255340	−	0.442263i
$919$	23260.3			0.834914			0.417457	−	0.908697i	$-0.362921\pi$
$919$	23260.3			0.834914			0.417457	+	0.908697i	$0.362921\pi$
$920$	28091.7	−	48656.2i	1.00669	−	1.74364i
$921$	−18413.8	+	31893.6i	−0.658800	+	1.14107i
$922$	−11368.2	−	19690.4i	−0.406066	−	0.703327i
$923$	410.707	+	711.365i	0.0146464	+	0.0253682i
$924$	85250.6			3.03521
$925$	−26477.8			−0.941172
$926$	32841.3	+	56882.8i	1.16548	+	2.01867i
$927$	27569.5	+	47751.9i	0.976810	+	1.69188i
$928$	60219.7	−	104304.i	2.13018	−	3.68958i
$929$	−12374.1	+	21432.5i	−0.437008	+	0.756920i	−0.997457	−	0.0712689i	$-0.977295\pi$
$929$	−12374.1	+	21432.5i	−0.437008	+	0.756920i	0.560449	+	0.828189i	$0.310628\pi$
$930$	−214096.			−7.54892
$931$	246.615	−	427.150i	0.00868151	−	0.0150368i
$932$	−12748.1	+	22080.3i	−0.448043	+	0.776034i
$933$	29790.0	−	51597.8i	1.04532	−	1.81054i
$934$	38109.4	+	66007.3i	1.33509	+	2.31245i
$935$	15231.4			0.532748
$936$	11222.1	+	19437.2i	0.391886	+	0.678766i
$937$	8516.69	−	14751.3i	0.296935	−	0.514306i	−0.678498	−	0.734602i	$-0.737369\pi$
$937$	8516.69	−	14751.3i	0.296935	−	0.514306i	0.975433	+	0.220296i	$0.0707022\pi$
$938$	−10454.0			−0.363897
$939$	1550.29	−	2685.18i	0.0538783	−	0.0933200i
$940$	57436.8	+	99483.4i	1.99296	+	3.45191i
$941$	−20700.6	−	35854.5i	−0.717131	−	1.24211i	−0.962132	−	0.272584i	$-0.912122\pi$
$941$	−20700.6	−	35854.5i	−0.717131	−	1.24211i	0.245001	−	0.969523i	$-0.421212\pi$
$942$	31308.4			1.08289
$943$	4748.29	+	8224.27i	0.163972	+	0.284008i
$944$	−123534.			−4.25919
$945$	23263.7			0.800812
$946$	−13340.9	+	45184.8i	−0.458510	+	1.55294i
$947$	−7077.16			−0.242848			−0.121424	−	0.992601i	$-0.538746\pi$
$947$	−7077.16			−0.242848			−0.121424	+	0.992601i	$0.538746\pi$
$948$	75716.0			2.59403
$949$	446.594	+	773.523i	0.0152761	+	0.0264590i
$950$	−5071.25			−0.173193
$951$	−28955.6	−	50152.5i	−0.987328	−	1.71010i
$952$	16444.6	+	28482.8i	0.559844	+	0.969677i
$953$	−11598.2	+	20088.8i	−0.394233	+	0.682832i	−0.993003	−	0.118089i	$-0.962323\pi$
$953$	−11598.2	+	20088.8i	−0.394233	+	0.682832i	0.598770	+	0.800921i	$0.295656\pi$
$954$	34226.1			1.16154
$955$	−25884.9	+	44833.9i	−0.877083	+	1.51915i
$956$	15066.9	+	26096.7i	0.509728	+	0.882874i
$957$	67074.8			2.26564
$958$	−19890.7	−	34451.7i	−0.670814	−	1.16188i
$959$	−2270.73	+	3933.03i	−0.0764607	+	0.132434i
$960$	−60876.5	+	105441.i	−2.04665	+	3.54489i
$961$	−34457.8	+	59682.7i	−1.15665	+	2.00338i
$962$	9980.18			0.334484
$963$	−31962.4	+	55360.5i	−1.06955	+	1.85251i
$964$	26404.4	−	45733.8i	0.882188	−	1.52799i
$965$	12540.9	+	21721.4i	0.418347	+	0.724598i
$966$	19331.1	+	33482.5i	0.643860	+	1.11520i
$967$	−19029.4			−0.632827			−0.316413	−	0.948621i	$-0.602479\pi$
$967$	−19029.4			−0.632827			−0.316413	+	0.948621i	$0.602479\pi$
$968$	22235.3			0.738294
$969$	−910.856	−	1577.65i	−0.0301970	−	0.0523028i
$970$	−36458.7	−	63148.2i	−1.20682	−	2.09028i
$971$	−12267.2	+	21247.4i	−0.405430	+	0.702225i	−0.994371	−	0.105950i	$-0.966212\pi$
$971$	−12267.2	+	21247.4i	−0.405430	+	0.702225i	0.588942	+	0.808176i	$0.299545\pi$
$972$	49718.7	−	86115.3i	1.64067	−	2.84172i
$973$	−1611.37			−0.0530916
$974$	−18358.0	+	31797.0i	−0.603930	+	1.04604i
$975$	−4713.07	+	8163.27i	−0.154809	+	0.268137i
$976$	−14852.9	+	25726.0i	−0.487120	+	0.843717i
$977$	−10358.1	−	17940.8i	−0.339187	−	0.587490i	0.645093	−	0.764104i	$-0.276819\pi$
$977$	−10358.1	−	17940.8i	−0.339187	−	0.587490i	−0.984280	+	0.176614i	$0.943485\pi$
$978$	35660.7			1.16595
$979$	−12578.1	−	21785.9i	−0.410621	−	0.711216i
$980$	10687.7	−	18511.6i	0.348373	−	0.603400i
$981$	65357.7			2.12713
$982$	43278.6	−	74960.7i	1.40639	−	2.43594i
$983$	−4461.51	−	7727.56i	−0.144761	−	0.250733i	0.784523	−	0.620100i	$-0.212908\pi$
$983$	−4461.51	−	7727.56i	−0.144761	−	0.250733i	−0.929284	+	0.369367i	$0.879575\pi$
$984$	−45783.7	−	79299.7i	−1.48326	−	2.56909i
$985$	9869.15			0.319246
$986$	21400.8	+	37067.2i	0.691216	+	1.19722i
$987$	−47792.0			−1.54127
$988$	1369.83			0.0441095
$989$	−14885.6	+	3587.64i	−0.478600	+	0.115349i
$990$	−100826.			−3.23682
$991$	−15414.5			−0.494104			−0.247052	−	0.969002i	$-0.579462\pi$
$991$	−15414.5			−0.494104			−0.247052	+	0.969002i	$0.579462\pi$
$992$	71460.2	+	123773.i	2.28716	+	3.96148i
$993$	−50903.3			−1.62675
$994$	−3983.94	−	6900.38i	−0.127126	−	0.220188i
$995$	5846.96	+	10127.2i	0.186293	+	0.322668i
$996$	12211.1	−	21150.3i	0.388478	−	0.672864i
$997$	672.384			0.0213587			0.0106793	−	0.999943i	$-0.496601\pi$
$997$	672.384			0.0213587			0.0106793	+	0.999943i	$0.496601\pi$
$998$	33405.3	−	57859.7i	1.05955	−	1.83519i
$999$	9057.35	+	15687.8i	0.286849	+	0.496837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.c.a.36.1	yes	20
43.6	even	3	inner	43.4.c.a.6.1	✓	20
43.7	odd	6		1849.4.a.f.1.10		10
43.36	even	3		1849.4.a.d.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.1	✓	20	43.6	even	3	inner
43.4.c.a.36.1	yes	20	1.1	even	1	trivial
1849.4.a.d.1.1		10	43.36	even	3
1849.4.a.f.1.10		10	43.7	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-5.31336 q^{2} +(-4.02821 - 6.97706i) q^{3} +20.2317 q^{4} +(-7.95967 - 13.7866i) q^{5} +(21.4033 + 37.0716i) q^{6} +(-8.31614 + 14.4040i) q^{7} -64.9916 q^{8} +(-18.9529 + 32.8274i) q^{9} +O(q^{10})\)	\(q-5.31336 q^{2} +(-4.02821 - 6.97706i) q^{3} +20.2317 q^{4} +(-7.95967 - 13.7866i) q^{5} +(21.4033 + 37.0716i) q^{6} +(-8.31614 + 14.4040i) q^{7} -64.9916 q^{8} +(-18.9529 + 32.8274i) q^{9} +(42.2926 + 73.2529i) q^{10} +31.4464 q^{11} +(-81.4977 - 141.158i) q^{12} +(-4.55523 + 7.88988i) q^{13} +(44.1866 - 76.5334i) q^{14} +(-64.1265 + 111.070i) q^{15} +183.469 q^{16} +(-15.2129 + 26.3496i) q^{17} +(100.704 - 174.424i) q^{18} +(-3.71590 - 6.43613i) q^{19} +(-161.038 - 278.926i) q^{20} +133.997 q^{21} -167.086 q^{22} +(-27.1516 - 47.0279i) q^{23} +(261.800 + 453.450i) q^{24} +(-64.2128 + 111.220i) q^{25} +(24.2035 - 41.9217i) q^{26} +87.8621 q^{27} +(-168.250 + 291.417i) q^{28} +(-132.378 + 229.286i) q^{29} +(340.727 - 590.156i) q^{30} +(-157.088 - 272.085i) q^{31} -454.906 q^{32} +(-126.673 - 219.403i) q^{33} +(80.8318 - 140.005i) q^{34} +264.775 q^{35} +(-383.451 + 664.156i) q^{36} +(103.086 + 178.550i) q^{37} +(19.7439 + 34.1975i) q^{38} +73.3976 q^{39} +(517.312 + 896.010i) q^{40} -174.881 q^{41} -711.971 q^{42} +(79.8447 - 270.429i) q^{43} +636.215 q^{44} +603.436 q^{45} +(144.266 + 249.876i) q^{46} -356.666 q^{47} +(-739.053 - 1280.08i) q^{48} +(33.1837 + 57.4759i) q^{49} +(341.186 - 590.951i) q^{50} +245.124 q^{51} +(-92.1602 + 159.626i) q^{52} +(84.9673 + 147.168i) q^{53} -466.842 q^{54} +(-250.303 - 433.537i) q^{55} +(540.479 - 936.137i) q^{56} +(-29.9369 + 51.8522i) q^{57} +(703.373 - 1218.28i) q^{58} -673.320 q^{59} +(-1297.39 + 2247.15i) q^{60} +(-80.9557 + 140.219i) q^{61} +(834.665 + 1445.68i) q^{62} +(-315.230 - 545.995i) q^{63} +949.319 q^{64} +145.032 q^{65} +(673.056 + 1165.77i) q^{66} +(-59.1469 - 102.445i) q^{67} +(-307.784 + 533.098i) q^{68} +(-218.744 + 378.876i) q^{69} -1406.84 q^{70} +(45.0809 - 78.0823i) q^{71} +(1231.78 - 2133.51i) q^{72} +(49.0200 - 84.9051i) q^{73} +(-547.733 - 948.701i) q^{74} +1034.65 q^{75} +(-75.1792 - 130.214i) q^{76} +(-261.512 + 452.953i) q^{77} -389.988 q^{78} +(-232.264 + 402.294i) q^{79} +(-1460.36 - 2529.41i) q^{80} +(157.802 + 273.321i) q^{81} +929.203 q^{82} +(74.9171 + 129.760i) q^{83} +2710.98 q^{84} +484.360 q^{85} +(-424.243 + 1436.89i) q^{86} +2132.99 q^{87} -2043.75 q^{88} +(-399.986 - 692.796i) q^{89} -3206.27 q^{90} +(-75.7638 - 131.227i) q^{91} +(-549.324 - 951.457i) q^{92} +(-1265.57 + 2192.03i) q^{93} +1895.09 q^{94} +(-59.1548 + 102.459i) q^{95} +(1832.45 + 3173.90i) q^{96} -862.058 q^{97} +(-176.317 - 305.390i) q^{98} +(-596.001 + 1032.30i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + 27 q^{10} + 54 q^{11} - 72 q^{12} - 15 q^{13} + 96 q^{14} + 65 q^{15} + 134 q^{16} - 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 18 q^{21} + 380 q^{22} - 61 q^{23} + 202 q^{24} - 151 q^{25} - 21 q^{26} - 194 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} + 253 q^{31} - 798 q^{32} - 424 q^{33} - 231 q^{34} + 710 q^{35} - 1092 q^{36} - 129 q^{37} - 854 q^{38} + 1382 q^{39} + 1345 q^{40} + 782 q^{41} + 62 q^{42} + 1025 q^{43} + 754 q^{44} + 1888 q^{45} - 40 q^{46} - 668 q^{47} - 2401 q^{48} - 115 q^{49} + 424 q^{50} + 1590 q^{51} - 564 q^{52} + 773 q^{53} + 364 q^{54} - 1242 q^{55} - 923 q^{56} - 765 q^{57} + 1328 q^{58} - 2966 q^{59} - 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 1476 q^{64} - 2126 q^{65} + 1483 q^{66} - 642 q^{67} - 1052 q^{68} - 3503 q^{69} - 170 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} - 2232 q^{74} + 164 q^{75} - 252 q^{76} + 1448 q^{77} + 5644 q^{78} - 1405 q^{79} - 3157 q^{80} + 974 q^{81} + 6608 q^{82} + 543 q^{83} + 7304 q^{84} + 1946 q^{85} + 2776 q^{86} + 2818 q^{87} - 5372 q^{88} - 2196 q^{89} - 1484 q^{90} - 3513 q^{91} + 2629 q^{92} - 983 q^{93} + 9878 q^{94} - 149 q^{95} + 3540 q^{96} - 850 q^{97} - 213 q^{98} - 3181 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9 + 27 * q^10 + 54 * q^11 - 72 * q^12 - 15 * q^13 + 96 * q^14 + 65 * q^15 + 134 * q^16 - 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 18 * q^21 + 380 * q^22 - 61 * q^23 + 202 * q^24 - 151 * q^25 - 21 * q^26 - 194 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 + 253 * q^31 - 798 * q^32 - 424 * q^33 - 231 * q^34 + 710 * q^35 - 1092 * q^36 - 129 * q^37 - 854 * q^38 + 1382 * q^39 + 1345 * q^40 + 782 * q^41 + 62 * q^42 + 1025 * q^43 + 754 * q^44 + 1888 * q^45 - 40 * q^46 - 668 * q^47 - 2401 * q^48 - 115 * q^49 + 424 * q^50 + 1590 * q^51 - 564 * q^52 + 773 * q^53 + 364 * q^54 - 1242 * q^55 - 923 * q^56 - 765 * q^57 + 1328 * q^58 - 2966 * q^59 - 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 1476 * q^64 - 2126 * q^65 + 1483 * q^66 - 642 * q^67 - 1052 * q^68 - 3503 * q^69 - 170 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 - 2232 * q^74 + 164 * q^75 - 252 * q^76 + 1448 * q^77 + 5644 * q^78 - 1405 * q^79 - 3157 * q^80 + 974 * q^81 + 6608 * q^82 + 543 * q^83 + 7304 * q^84 + 1946 * q^85 + 2776 * q^86 + 2818 * q^87 - 5372 * q^88 - 2196 * q^89 - 1484 * q^90 - 3513 * q^91 + 2629 * q^92 - 983 * q^93 + 9878 * q^94 - 149 * q^95 + 3540 * q^96 - 850 * q^97 - 213 * q^98 - 3181 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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