LMFDB - Embedded newform 22.5.d.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,5,Mod(7,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("22.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	22.d (of order $10$, degree $4$, 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:	$2.27413918784$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 138 x^{14} - 428 x^{13} + 7783 x^{12} - 18620 x^{11} + 235604 x^{10} + \cdots + 1499670491 $ x^16 - 4x^15 + 138x^14 - 428x^13 + 7783x^12 - 18620x^11 + 235604x^10 - 425164x^9 + 4199998x^8 - 5446172x^7 + 45313276x^6 - 38408204x^5 + 290282498x^4 - 132888724x^3 + 1016893202x^2 - 153602264*x + 1499670491
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.2
Root			$-0.309017 - 2.01862i$ of defining polynomial
Character	$\chi$	$=$	22.19
Dual form			22.5.d.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66251 - 2.28825i) q^{2} +(3.38726 + 10.4249i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(17.3145 + 12.5798i) q^{5} +(18.2234 - 25.0824i) q^{6} +(27.3556 + 8.88838i) q^{7} +(21.5200 - 6.99226i) q^{8} +(-31.6748 + 23.0131i) q^{9} +O(q^{10})$	\(q+(-1.66251 - 2.28825i) q^{2} +(3.38726 + 10.4249i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(17.3145 + 12.5798i) q^{5} +(18.2234 - 25.0824i) q^{6} +(27.3556 + 8.88838i) q^{7} +(21.5200 - 6.99226i) q^{8} +(-31.6748 + 23.0131i) q^{9} -60.5339i q^{10} +(-102.318 + 64.5906i) q^{11} -87.6912 q^{12} +(-109.138 - 150.215i) q^{13} +(-25.1401 - 77.3734i) q^{14} +(-72.4939 + 223.113i) q^{15} +(-51.7771 - 37.6183i) q^{16} +(158.359 - 217.962i) q^{17} +(105.319 + 34.2203i) q^{18} +(618.788 - 201.057i) q^{19} +(-138.516 + 100.638i) q^{20} +315.287i q^{21} +(317.904 + 126.747i) q^{22} -644.312 q^{23} +(145.787 + 200.659i) q^{24} +(-51.5923 - 158.785i) q^{25} +(-162.287 + 499.468i) q^{26} +(371.104 + 269.623i) q^{27} +(-135.254 + 186.161i) q^{28} +(-505.956 - 164.395i) q^{29} +(631.060 - 205.044i) q^{30} +(1188.32 - 863.365i) q^{31} +181.019i q^{32} +(-1019.93 - 847.875i) q^{33} -762.024 q^{34} +(361.836 + 498.025i) q^{35} +(-96.7896 - 297.888i) q^{36} +(-367.019 + 1129.57i) q^{37} +(-1488.81 - 1081.68i) q^{38} +(1196.30 - 1646.57i) q^{39} +(460.569 + 149.648i) q^{40} +(-2142.64 + 696.185i) q^{41} +(721.454 - 524.167i) q^{42} +1429.81i q^{43} +(-238.490 - 938.161i) q^{44} -837.934 q^{45} +(1071.17 + 1474.34i) q^{46} +(409.377 + 1259.93i) q^{47} +(216.785 - 667.194i) q^{48} +(-1273.12 - 924.978i) q^{49} +(-277.566 + 382.037i) q^{50} +(2808.64 + 912.582i) q^{51} +(1412.71 - 459.017i) q^{52} +(1896.40 - 1377.82i) q^{53} -1297.43i q^{54} +(-2584.13 - 168.783i) q^{55} +650.841 q^{56} +(4191.99 + 5769.78i) q^{57} +(464.979 + 1431.06i) q^{58} +(-1015.91 + 3126.65i) q^{59} +(-1518.33 - 1103.13i) q^{60} +(2046.30 - 2816.48i) q^{61} +(-3951.18 - 1283.82i) q^{62} +(-1071.03 + 348.000i) q^{63} +(414.217 - 300.946i) q^{64} -3973.84i q^{65} +(-244.503 + 3743.45i) q^{66} +1553.80 q^{67} +(1266.87 + 1743.70i) q^{68} +(-2182.45 - 6716.89i) q^{69} +(538.048 - 1655.94i) q^{70} +(-3993.76 - 2901.63i) q^{71} +(-520.727 + 716.719i) q^{72} +(-3562.52 - 1157.53i) q^{73} +(3194.90 - 1038.09i) q^{74} +(1480.56 - 1075.69i) q^{75} +5205.06i q^{76} +(-3373.09 + 857.472i) q^{77} -5756.62 q^{78} +(-2631.70 - 3622.22i) q^{79} +(-423.268 - 1302.69i) q^{80} +(-2533.76 + 7798.12i) q^{81} +(5155.20 + 3745.47i) q^{82} +(-2119.18 + 2916.80i) q^{83} +(-2398.85 - 779.432i) q^{84} +(5483.82 - 1781.80i) q^{85} +(3271.77 - 2377.08i) q^{86} -5831.39i q^{87} +(-1750.25 + 2105.42i) q^{88} +9594.39 q^{89} +(1393.07 + 1917.40i) q^{90} +(-1650.36 - 5079.29i) q^{91} +(1592.83 - 4902.22i) q^{92} +(13025.7 + 9463.69i) q^{93} +(2202.44 - 3031.40i) q^{94} +(13243.3 + 4303.00i) q^{95} +(-1887.11 + 613.159i) q^{96} +(-10393.5 + 7551.31i) q^{97} +4451.00i q^{98} +(1754.49 - 4400.56i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9} - 30 q^{11} - 384 q^{12} - 510 q^{13} - 96 q^{14} - 1398 q^{15} - 256 q^{16} + 1770 q^{17} + 1120 q^{18} + 1020 q^{19} - 240 q^{20} + 240 q^{22} - 2424 q^{23} - 640 q^{24} - 858 q^{25} + 480 q^{26} + 2224 q^{27} + 1600 q^{28} + 4890 q^{29} + 3360 q^{30} + 602 q^{31} - 2648 q^{33} - 3904 q^{34} - 8670 q^{35} + 720 q^{36} - 4518 q^{37} - 4800 q^{38} - 1130 q^{39} - 1280 q^{40} + 1290 q^{41} - 3808 q^{42} + 720 q^{44} + 12152 q^{45} + 4480 q^{46} + 642 q^{47} - 128 q^{48} + 9534 q^{49} + 6720 q^{50} - 1500 q^{51} + 4000 q^{52} + 2598 q^{53} + 2582 q^{55} - 3072 q^{56} + 9140 q^{57} - 6496 q^{58} + 6660 q^{59} - 5776 q^{60} - 27410 q^{61} - 19680 q^{62} - 27260 q^{63} + 2048 q^{64} + 2528 q^{66} + 21524 q^{67} + 14160 q^{68} + 11416 q^{69} + 34400 q^{70} - 5562 q^{71} + 10240 q^{72} - 7790 q^{73} + 5760 q^{74} + 3576 q^{75} - 1110 q^{77} - 39424 q^{78} - 2770 q^{79} - 3840 q^{80} - 25464 q^{81} - 17472 q^{82} - 36900 q^{83} - 24480 q^{84} - 24750 q^{85} + 624 q^{86} - 5760 q^{88} + 46596 q^{89} + 55360 q^{90} + 32370 q^{91} + 14112 q^{92} + 20722 q^{93} + 58880 q^{94} + 74250 q^{95} - 3732 q^{97} + 45802 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9 - 30 * q^11 - 384 * q^12 - 510 * q^13 - 96 * q^14 - 1398 * q^15 - 256 * q^16 + 1770 * q^17 + 1120 * q^18 + 1020 * q^19 - 240 * q^20 + 240 * q^22 - 2424 * q^23 - 640 * q^24 - 858 * q^25 + 480 * q^26 + 2224 * q^27 + 1600 * q^28 + 4890 * q^29 + 3360 * q^30 + 602 * q^31 - 2648 * q^33 - 3904 * q^34 - 8670 * q^35 + 720 * q^36 - 4518 * q^37 - 4800 * q^38 - 1130 * q^39 - 1280 * q^40 + 1290 * q^41 - 3808 * q^42 + 720 * q^44 + 12152 * q^45 + 4480 * q^46 + 642 * q^47 - 128 * q^48 + 9534 * q^49 + 6720 * q^50 - 1500 * q^51 + 4000 * q^52 + 2598 * q^53 + 2582 * q^55 - 3072 * q^56 + 9140 * q^57 - 6496 * q^58 + 6660 * q^59 - 5776 * q^60 - 27410 * q^61 - 19680 * q^62 - 27260 * q^63 + 2048 * q^64 + 2528 * q^66 + 21524 * q^67 + 14160 * q^68 + 11416 * q^69 + 34400 * q^70 - 5562 * q^71 + 10240 * q^72 - 7790 * q^73 + 5760 * q^74 + 3576 * q^75 - 1110 * q^77 - 39424 * q^78 - 2770 * q^79 - 3840 * q^80 - 25464 * q^81 - 17472 * q^82 - 36900 * q^83 - 24480 * q^84 - 24750 * q^85 + 624 * q^86 - 5760 * q^88 + 46596 * q^89 + 55360 * q^90 + 32370 * q^91 + 14112 * q^92 + 20722 * q^93 + 58880 * q^94 + 74250 * q^95 - 3732 * q^97 + 45802 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−1.66251	−	2.28825i	−0.415627	−	0.572061i
$2$	−1.66251	−	2.28825i	−0.415627	−	0.572061i
$3$	3.38726	+	10.4249i	0.376362	+	1.15832i	0.942555	+	0.334051i	$0.108416\pi$
$3$	3.38726	+	10.4249i	0.376362	+	1.15832i	−0.566193	+	0.824273i	$0.691584\pi$
$4$	−2.47214	+	7.60845i	−0.154508	+	0.475528i
$5$	17.3145	+	12.5798i	0.692582	+	0.503190i	0.877508	−	0.479562i	$-0.159205\pi$
$5$	17.3145	+	12.5798i	0.692582	+	0.503190i	−0.184926	+	0.982752i	$0.559205\pi$
$6$	18.2234	−	25.0824i	0.506206	−	0.696732i
$7$	27.3556	+	8.88838i	0.558278	+	0.181395i	0.574546	−	0.818472i	$-0.305179\pi$
$7$	27.3556	+	8.88838i	0.558278	+	0.181395i	−0.0162683	+	0.999868i	$0.505179\pi$
$8$	21.5200	−	6.99226i	0.336249	−	0.109254i
$9$	−31.6748	+	23.0131i	−0.391047	+	0.284112i
$10$		−	60.5339i		−	0.605339i
$11$	−102.318	+	64.5906i	−0.845606	+	0.533807i
$11$	−102.318	+	64.5906i	−0.845606	+	0.533807i
$12$	−87.6912			−0.608967
$13$	−109.138	−	150.215i	−0.645786	−	0.888848i	0.353122	−	0.935577i	$-0.385120\pi$
$13$	−109.138	−	150.215i	−0.645786	−	0.888848i	−0.998908	+	0.0467295i	$0.985120\pi$
$14$	−25.1401	−	77.3734i	−0.128266	−	0.394762i
$15$	−72.4939	+	223.113i	−0.322195	+	0.991615i
$16$	−51.7771	−	37.6183i	−0.202254	−	0.146946i
$17$	158.359	−	217.962i	0.547954	−	0.754194i	−0.441778	−	0.897124i	$-0.645652\pi$
$17$	158.359	−	217.962i	0.547954	−	0.754194i	0.989733	+	0.142930i	$0.0456523\pi$
$18$	105.319	+	34.2203i	0.325059	+	0.105618i
$19$	618.788	−	201.057i	1.71409	−	0.556943i	0.723088	−	0.690756i	$-0.242722\pi$
$19$	618.788	−	201.057i	1.71409	−	0.556943i	0.991007	+	0.133812i	$0.0427220\pi$
$20$	−138.516	+	100.638i	−0.346291	+	0.251595i
$21$			315.287i			0.714937i
$22$	317.904	+	126.747i	0.656827	+	0.261874i
$23$	−644.312			−1.21798			−0.608991	−	0.793177i	$-0.708425\pi$
$23$	−644.312			−1.21798			−0.608991	+	0.793177i	$0.708425\pi$
$24$	145.787	+	200.659i	0.253103	+	0.348366i
$25$	−51.5923	−	158.785i	−0.0825478	−	0.254056i
$26$	−162.287	+	499.468i	−0.240070	+	0.738858i
$27$	371.104	+	269.623i	0.509059	+	0.369853i
$28$	−135.254	+	186.161i	−0.172517	+	0.237450i
$29$	−505.956	−	164.395i	−0.601612	−	0.195476i	−0.00765295	−	0.999971i	$-0.502436\pi$
$29$	−505.956	−	164.395i	−0.601612	−	0.195476i	−0.593959	+	0.804495i	$0.702436\pi$
$30$	631.060	−	205.044i	0.701178	−	0.227826i
$31$	1188.32	−	863.365i	1.23655	−	0.898403i	0.239182	−	0.970975i	$-0.423121\pi$
$31$	1188.32	−	863.365i	1.23655	−	0.898403i	0.997363	+	0.0725716i	$0.0231206\pi$
$32$			181.019i			0.176777i
$33$	−1019.93	−	847.875i	−0.936575	−	0.778581i
$34$	−762.024			−0.659190
$35$	361.836	+	498.025i	0.295377	+	0.406551i
$36$	−96.7896	−	297.888i	−0.0746834	−	0.229852i
$37$	−367.019	+	1129.57i	−0.268093	+	0.825104i	0.722872	+	0.690982i	$0.242821\pi$
$37$	−367.019	+	1129.57i	−0.268093	+	0.825104i	−0.990965	+	0.134122i	$0.957179\pi$
$38$	−1488.81	−	1081.68i	−1.03103	−	0.749087i
$39$	1196.30	−	1646.57i	0.786524	−	1.08256i
$40$	460.569	+	149.648i	0.287856	+	0.0935300i
$41$	−2142.64	+	696.185i	−1.27462	+	0.414150i	−0.866683	−	0.498860i	$-0.833752\pi$
$41$	−2142.64	+	696.185i	−1.27462	+	0.414150i	−0.407939	+	0.913009i	$0.633752\pi$
$42$	721.454	−	524.167i	0.408988	−	0.297147i
$43$			1429.81i			0.773290i	0.922229	+	0.386645i	$0.126366\pi$
$43$			1429.81i			0.773290i	−0.922229	+	0.386645i	$0.873634\pi$
$44$	−238.490	−	938.161i	−0.123187	−	0.484587i
$45$	−837.934			−0.413795
$46$	1071.17	+	1474.34i	0.506226	+	0.696760i
$47$	409.377	+	1259.93i	0.185322	+	0.570363i	0.999954	−	0.00961570i	$-0.00306082\pi$
$47$	409.377	+	1259.93i	0.185322	+	0.570363i	−0.814632	+	0.579979i	$0.803061\pi$
$48$	216.785	−	667.194i	0.0940905	−	0.289581i
$49$	−1273.12	−	924.978i	−0.530247	−	0.385247i
$50$	−277.566	+	382.037i	−0.111026	+	0.152815i
$51$	2808.64	+	912.582i	1.07983	+	0.350858i
$52$	1412.71	−	459.017i	0.522452	−	0.169755i
$53$	1896.40	−	1377.82i	0.675116	−	0.490500i	−0.196618	−	0.980480i	$-0.562996\pi$
$53$	1896.40	−	1377.82i	0.675116	−	0.490500i	0.871734	+	0.489980i	$0.162996\pi$
$54$		−	1297.43i		−	0.444934i
$55$	−2584.13	−	168.783i	−0.854258	−	0.0557959i
$56$	650.841			0.207539
$57$	4191.99	+	5769.78i	1.29024	+	1.77586i
$58$	464.979	+	1431.06i	0.138222	+	0.425404i
$59$	−1015.91	+	3126.65i	−0.291844	+	0.898204i	0.692419	+	0.721496i	$0.256545\pi$
$59$	−1015.91	+	3126.65i	−0.291844	+	0.898204i	−0.984263	+	0.176709i	$0.943455\pi$
$60$	−1518.33	−	1103.13i	−0.421759	−	0.306426i
$61$	2046.30	−	2816.48i	0.549932	−	0.756916i	−0.440071	−	0.897963i	$-0.645047\pi$
$61$	2046.30	−	2816.48i	0.549932	−	0.756916i	0.990003	+	0.141047i	$0.0450469\pi$
$62$	−3951.18	−	1283.82i	−1.02788	−	0.333980i
$63$	−1071.03	+	348.000i	−0.269850	+	0.0876795i
$64$	414.217	−	300.946i	0.101127	−	0.0734732i
$65$		−	3973.84i		−	0.940553i
$66$	−244.503	+	3743.45i	−0.0561303	+	0.859378i
$67$	1553.80			0.346135			0.173068	−	0.984910i	$-0.444632\pi$
$67$	1553.80			0.346135			0.173068	+	0.984910i	$0.444632\pi$
$68$	1266.87	+	1743.70i	0.273977	+	0.377097i
$69$	−2182.45	−	6716.89i	−0.458402	−	1.41082i
$70$	538.048	−	1655.94i	0.109806	−	0.337947i
$71$	−3993.76	−	2901.63i	−0.792255	−	0.575607i	0.116377	−	0.993205i	$-0.462872\pi$
$71$	−3993.76	−	2901.63i	−0.792255	−	0.575607i	−0.908632	+	0.417598i	$0.862872\pi$
$72$	−520.727	+	716.719i	−0.100449	+	0.138256i
$73$	−3562.52	−	1157.53i	−0.668515	−	0.217214i	−0.0449550	−	0.998989i	$-0.514314\pi$
$73$	−3562.52	−	1157.53i	−0.668515	−	0.217214i	−0.623560	+	0.781775i	$0.714314\pi$
$74$	3194.90	−	1038.09i	0.583437	−	0.189570i
$75$	1480.56	−	1075.69i	0.263211	−	0.191234i
$76$			5205.06i			0.901153i
$77$	−3373.09	+	857.472i	−0.568914	+	0.144623i
$78$	−5756.62			−0.946190
$79$	−2631.70	−	3622.22i	−0.421679	−	0.580391i	0.544340	−	0.838865i	$-0.316780\pi$
$79$	−2631.70	−	3622.22i	−0.421679	−	0.580391i	−0.966018	+	0.258474i	$0.916780\pi$
$80$	−423.268	−	1302.69i	−0.0661357	−	0.203545i
$81$	−2533.76	+	7798.12i	−0.386186	+	1.18856i
$82$	5155.20	+	3745.47i	0.766686	+	0.557030i
$83$	−2119.18	+	2916.80i	−0.307617	+	0.423399i	−0.934636	−	0.355605i	$-0.884275\pi$
$83$	−2119.18	+	2916.80i	−0.307617	+	0.423399i	0.627019	+	0.779004i	$0.284275\pi$
$84$	−2398.85	−	779.432i	−0.339973	−	0.110464i
$85$	5483.82	−	1781.80i	0.759006	−	0.246616i
$86$	3271.77	−	2377.08i	0.442370	−	0.321400i
$87$		−	5831.39i		−	0.770431i
$88$	−1750.25	+	2105.42i	−0.226014	+	0.271878i
$89$	9594.39			1.21126			0.605630	−	0.795746i	$-0.292921\pi$
$89$	9594.39			1.21126			0.605630	+	0.795746i	$0.292921\pi$
$90$	1393.07	+	1917.40i	0.171984	+	0.236716i
$91$	−1650.36	−	5079.29i	−0.199295	−	0.613367i
$92$	1592.83	−	4902.22i	0.188188	−	0.579184i
$93$	13025.7	+	9463.69i	1.50603	+	1.09419i
$94$	2202.44	−	3031.40i	0.249258	−	0.343074i
$95$	13243.3	+	4303.00i	1.46740	+	0.476787i
$96$	−1887.11	+	613.159i	−0.204765	+	0.0665320i
$97$	−10393.5	+	7551.31i	−1.10463	+	0.802562i	−0.981810	−	0.189866i	$-0.939195\pi$
$97$	−10393.5	+	7551.31i	−1.10463	+	0.802562i	−0.122822	+	0.992429i	$0.539195\pi$
$98$			4451.00i			0.463453i
$99$	1754.49	−	4400.56i	0.179011	−	0.448991i
$100$	1335.65			0.133565
$101$	−1851.62	−	2548.54i	−0.181514	−	0.249833i	0.708558	−	0.705653i	$-0.249346\pi$
$101$	−1851.62	−	2548.54i	−0.181514	−	0.249833i	−0.890072	+	0.455820i	$0.849346\pi$
$102$	−2581.17	−	7944.03i	−0.248094	−	0.763555i
$103$	−3997.97	+	12304.5i	−0.376847	+	1.15982i	0.565377	+	0.824833i	$0.308731\pi$
$103$	−3997.97	+	12304.5i	−0.376847	+	1.15982i	−0.942224	+	0.334983i	$0.891269\pi$
$104$	−3398.98	−	2469.51i	−0.314255	−	0.228320i
$105$	−3966.23	+	5459.05i	−0.359749	+	0.495152i
$106$	−6305.56	−	2048.80i	−0.561193	−	0.182343i
$107$	−7121.09	+	2313.78i	−0.621984	+	0.202095i	−0.603021	−	0.797725i	$-0.706036\pi$
$107$	−7121.09	+	2313.78i	−0.621984	+	0.202095i	−0.0189628	+	0.999820i	$0.506036\pi$
$108$	−2968.83	+	2156.98i	−0.254530	+	0.184927i
$109$		−	12658.0i		−	1.06540i	−0.846304	−	0.532700i	$-0.821177\pi$
$109$		−	12658.0i		−	1.06540i	0.846304	−	0.532700i	$-0.178823\pi$
$110$	3909.92	+	6193.73i	0.323134	+	0.511878i
$111$	−13018.8			−1.05664
$112$	−1082.03	−	1489.29i	−0.0862587	−	0.118725i
$113$	6918.47	+	21292.9i	0.541818	+	1.66754i	0.728438	+	0.685112i	$0.240247\pi$
$113$	6918.47	+	21292.9i	0.541818	+	1.66754i	−0.186620	+	0.982432i	$0.559753\pi$
$114$	6233.46	−	19184.6i	0.479644	−	1.47619i
$115$	−11156.0	−	8105.29i	−0.843552	−	0.612876i
$116$	2501.58	−	3443.13i	0.185908	−	0.255881i
$117$	6913.84	+	2246.44i	0.505065	+	0.164106i
$118$	8843.50	−	2873.43i	0.635126	−	0.206365i
$119$	6269.33	−	4554.94i	0.442718	−	0.321654i
$120$			5308.29i			0.368631i
$121$	6297.10	−	13217.6i	0.430100	−	0.902781i
$122$	−9846.79			−0.661569
$123$	−14515.3	−	19978.7i	−0.959438	−	1.32055i
$124$	3631.18	+	11175.6i	0.236159	+	0.726823i
$125$	5237.66	−	16119.9i	0.335210	−	1.03167i
$126$	2576.91	+	1872.24i	0.162315	+	0.117929i
$127$	−3298.12	+	4539.48i	−0.204484	+	0.281448i	−0.898926	−	0.438101i	$-0.855651\pi$
$127$	−3298.12	+	4539.48i	−0.204484	+	0.281448i	0.694442	+	0.719549i	$0.255651\pi$
$128$	−1377.28	−	447.504i	−0.0840623	−	0.0273135i
$129$	−14905.7	+	4843.15i	−0.895720	+	0.291037i
$130$	−9093.11	+	6606.53i	−0.538054	+	0.390919i
$131$			15666.2i			0.912897i	0.889750	+	0.456448i	$0.150879\pi$
$131$			15666.2i			0.912897i	−0.889750	+	0.456448i	$0.849121\pi$
$132$	8972.42	−	5664.03i	0.514946	−	0.325071i
$133$	18714.4			1.05797
$134$	−2583.21	−	3555.48i	−0.143863	−	0.198011i
$135$	3033.71	+	9336.80i	0.166459	+	0.512307i
$136$	1883.83	−	5797.82i	0.101850	−	0.313464i
$137$	3551.82	+	2580.55i	0.189239	+	0.137490i	0.678371	−	0.734720i	$-0.262686\pi$
$137$	3551.82	+	2580.55i	0.189239	+	0.137490i	−0.489132	+	0.872210i	$0.662686\pi$
$138$	−11741.6	+	16160.9i	−0.616549	+	0.848607i
$139$	409.774	+	133.144i	0.0212087	+	0.00689114i	0.319602	−	0.947552i	$-0.396451\pi$
$139$	409.774	+	133.144i	0.0212087	+	0.00689114i	−0.298393	+	0.954443i	$0.596451\pi$
$140$	−4683.71	+	1521.83i	−0.238965	+	0.0776444i
$141$	−11748.0	+	8535.43i	−0.590917	+	0.429326i
$142$			13962.7i			0.692456i
$143$	20869.3	+	8320.51i	1.02055	+	0.406891i
$144$	2505.74			0.120840
$145$	−6692.35	−	9211.23i	−0.318304	−	0.438108i
$146$	3274.00	+	10076.3i	0.153593	+	0.472712i
$147$	5330.42	−	16405.3i	0.246676	−	0.759190i
$148$	−7686.94	−	5584.89i	−0.350938	−	0.254971i
$149$	17319.6	−	23838.3i	0.780126	−	1.07375i	−0.215142	−	0.976583i	$-0.569022\pi$
$149$	17319.6	−	23838.3i	0.780126	−	1.07375i	0.995268	−	0.0971682i	$-0.0309785\pi$
$150$	−4922.89	−	1599.54i	−0.218795	−	0.0710908i
$151$	−18009.7	+	5851.72i	−0.789866	+	0.256643i	−0.676047	−	0.736858i	$-0.736308\pi$
$151$	−18009.7	+	5851.72i	−0.789866	+	0.256643i	−0.113819	+	0.993501i	$0.536308\pi$
$152$	11910.5	−	8653.45i	0.515515	−	0.374543i
$153$			10548.2i			0.450606i
$154$	7569.89	+	6292.90i	0.319189	+	0.265344i
$155$	31436.1			1.30848
$156$	9570.42	+	13172.6i	0.393262	+	0.541279i
$157$	−136.496	−	420.090i	−0.00553757	−	0.0170429i	0.948250	−	0.317526i	$-0.102852\pi$
$157$	−136.496	−	420.090i	−0.00553757	−	0.0170429i	−0.953787	+	0.300483i	$0.902852\pi$
$158$	−3913.31	+	12043.9i	−0.156758	+	0.482452i
$159$	20787.2	+	15102.8i	0.822246	+	0.597396i
$160$	−2277.18	+	3134.27i	−0.0889523	+	0.122432i
$161$	−17625.6	−	5726.89i	−0.679972	−	0.220936i
$162$	22056.4	−	7166.57i	0.840437	−	0.273075i
$163$	−8903.42	+	6468.72i	−0.335106	+	0.243469i	−0.742594	−	0.669742i	$-0.766405\pi$
$163$	−8903.42	+	6468.72i	−0.335106	+	0.243469i	0.407488	+	0.913210i	$0.366405\pi$
$164$		−	18023.2i		−	0.670108i
$165$	−6993.57	−	27511.0i	−0.256881	−	1.01051i
$166$	10197.5			0.370064
$167$	−22027.3	−	30317.9i	−0.789819	−	1.08709i	−0.994131	−	0.108186i	$-0.965496\pi$
$167$	−22027.3	−	30317.9i	−0.789819	−	1.08709i	0.204312	−	0.978906i	$-0.434504\pi$
$168$	2204.57	+	6784.96i	0.0781097	+	0.240397i
$169$	−1827.74	+	5625.21i	−0.0639943	+	0.196954i
$170$	−13194.1	−	9586.07i	−0.456543	−	0.331698i
$171$	−14973.1	+	20608.7i	−0.512058	+	0.704787i
$172$	−10878.7	−	3534.69i	−0.367721	−	0.119480i
$173$	−26415.3	+	8582.84i	−0.882598	+	0.286773i	−0.715035	−	0.699088i	$-0.753589\pi$
$173$	−26415.3	+	8582.84i	−0.882598	+	0.286773i	−0.167562	+	0.985862i	$0.553589\pi$
$174$	−13343.7	+	9694.74i	−0.440734	+	0.320212i
$175$		−	4802.23i		−	0.156808i
$176$	7727.53	+	504.724i	0.249468	+	0.0162940i
$177$	−36036.2			−1.15025
$178$	−15950.8	−	21954.3i	−0.503432	−	0.692915i
$179$	−11589.0	−	35667.3i	−0.361693	−	1.11318i	−0.952026	−	0.306018i	$-0.901003\pi$
$179$	−11589.0	−	35667.3i	−0.361693	−	1.11318i	0.590332	−	0.807160i	$-0.298997\pi$
$180$	2071.49	−	6375.38i	0.0639348	−	0.196771i
$181$	34240.2	+	24876.9i	1.04515	+	0.759346i	0.971284	−	0.237922i	$-0.0764663\pi$
$181$	34240.2	+	24876.9i	1.04515	+	0.759346i	0.0738660	+	0.997268i	$0.476466\pi$
$182$	−8878.93	+	12220.8i	−0.268051	+	0.368941i
$183$	36292.9	+	11792.3i	1.08373	+	0.352124i
$184$	−13865.6	+	4505.20i	−0.409545	+	0.133069i
$185$	−20564.4	+	14940.9i	−0.600860	+	0.436550i
$186$		−	45539.3i		−	1.31632i
$187$	−2124.70	+	32530.0i	−0.0607595	+	0.930254i
$188$	−10598.2			−0.299858
$189$	7755.27	+	10674.2i	0.217107	+	0.298822i
$190$	−12170.7	−	37457.6i	−0.337139	−	1.03761i
$191$	−3526.41	+	10853.2i	−0.0966642	+	0.297502i	−0.987684	−	0.156463i	$-0.949991\pi$
$191$	−3526.41	+	10853.2i	−0.0966642	+	0.297502i	0.891020	+	0.453965i	$0.149991\pi$
$192$	4540.39	+	3298.79i	0.123166	+	0.0894854i
$193$	4955.96	−	6821.30i	0.133050	−	0.183127i	−0.737294	−	0.675572i	$-0.763897\pi$
$193$	4955.96	−	6821.30i	0.133050	−	0.183127i	0.870344	+	0.492445i	$0.163897\pi$
$194$	34558.5	+	11228.7i	0.918230	+	0.298351i
$195$	41426.9	−	13460.4i	1.08946	−	0.353988i
$196$	10185.0	−	7399.83i	0.265124	−	0.192624i
$197$		−	4315.62i		−	0.111202i	−0.998453	−	0.0556008i	$-0.982293\pi$
$197$		−	4315.62i		−	0.111202i	0.998453	−	0.0556008i	$-0.0177074\pi$
$198$	−12986.4	+	3301.27i	−0.331252	+	0.0842075i
$199$	44908.3			1.13402			0.567009	−	0.823711i	$-0.308100\pi$
$199$	44908.3			1.13402			0.567009	+	0.823711i	$0.308100\pi$
$200$	−2220.53	−	3056.30i	−0.0555132	−	0.0764074i
$201$	5263.12	+	16198.2i	0.130272	+	0.400936i
$202$	−2753.35	+	8473.94i	−0.0674775	+	0.207674i
$203$	−12379.5	−	8994.26i	−0.300408	−	0.218260i
$204$	−13886.7	+	19113.4i	−0.333686	+	0.459279i
$205$	−45856.7	−	14899.7i	−1.09118	−	0.354544i
$206$	34802.3	−	11308.0i	0.820114	−	0.266471i
$207$	20408.5	−	14827.6i	0.476288	−	0.346044i
$208$			11883.3i			0.274669i
$209$	−50327.0	+	60539.7i	−1.15215	+	1.38595i
$210$	19085.5			0.432779
$211$	48690.3	+	67016.4i	1.09365	+	1.50528i	0.843547	+	0.537056i	$0.180464\pi$
$211$	48690.3	+	67016.4i	1.09365	+	1.50528i	0.250101	+	0.968220i	$0.419536\pi$
$212$	5794.88	+	17834.8i	0.128936	+	0.396823i
$213$	16721.4	−	51463.1i	0.368564	−	1.13432i
$214$	17133.4	+	12448.1i	0.374124	+	0.271817i
$215$	−17986.7	+	24756.6i	−0.389112	+	0.535567i
$216$	9871.42	+	3207.42i	0.211579	+	0.0687461i
$217$	40181.2	−	13055.6i	0.853302	−	0.277255i
$218$	−28964.7	+	21044.1i	−0.609474	+	0.442809i
$219$		−	41059.8i		−	0.856108i
$220$	7672.50	−	19244.0i	0.158523	−	0.397603i
$221$	−50024.2			−1.02423
$222$	21643.9	+	29790.3i	0.439167	+	0.604461i
$223$	−6741.89	−	20749.4i	−0.135573	−	0.417250i	0.860106	−	0.510115i	$-0.170397\pi$
$223$	−6741.89	−	20749.4i	−0.135573	−	0.417250i	−0.995679	+	0.0928656i	$0.970397\pi$
$224$	−1608.97	+	4951.90i	−0.0320665	+	0.0986905i
$225$	5288.31	+	3842.18i	0.104460	+	0.0758950i
$226$	37221.3	−	51230.7i	0.728744	−	1.00303i
$227$	5049.63	+	1640.72i	0.0979959	+	0.0318408i	0.357605	−	0.933873i	$-0.383594\pi$
$227$	5049.63	+	1640.72i	0.0979959	+	0.0318408i	−0.259609	+	0.965714i	$0.583594\pi$
$228$	−54262.3	+	17630.9i	−1.04383	+	0.339160i
$229$	30669.6	−	22282.8i	0.584841	−	0.424911i	−0.255625	−	0.966776i	$-0.582281\pi$
$229$	30669.6	−	22282.8i	0.584841	−	0.424911i	0.840466	+	0.541864i	$0.182281\pi$
$230$			39002.7i			0.737291i
$231$	−20364.6	−	32259.7i	−0.381638	−	0.604555i
$232$	−12037.6			−0.223648
$233$	−11426.2	−	15726.8i	−0.210470	−	0.289687i	0.690710	−	0.723132i	$-0.257298\pi$
$233$	−11426.2	−	15726.8i	−0.210470	−	0.289687i	−0.901180	+	0.433444i	$0.857298\pi$
$234$	−6353.90	−	19555.3i	−0.116040	−	0.357135i
$235$	−8761.46	+	26965.0i	−0.158650	+	0.488275i
$236$	−21277.5	−	15459.0i	−0.382029	−	0.277560i
$237$	28847.1	−	39704.6i	0.513576	−	0.706877i
$238$	−20845.6	−	6773.16i	−0.368011	−	0.119574i
$239$	−6989.11	+	2270.90i	−0.122356	+	0.0397560i	−0.369555	−	0.929209i	$-0.620490\pi$
$239$	−6989.11	+	2270.90i	−0.122356	+	0.0397560i	0.247199	+	0.968965i	$0.420490\pi$
$240$	12146.7	−	8825.07i	0.210880	−	0.153213i
$241$			44197.4i			0.760961i	0.924789	+	0.380481i	$0.124241\pi$
$241$			44197.4i			0.760961i	−0.924789	+	0.380481i	$0.875759\pi$
$242$	−40714.1	+	7565.08i	−0.695208	+	0.129176i
$243$	−52721.7			−0.892847
$244$	16370.4	+	22531.9i	0.274966	+	0.378458i
$245$	−10407.6	−	32031.2i	−0.173387	−	0.533630i
$246$	−21584.2	+	66429.3i	−0.356669	+	1.09772i
$247$	−97735.0	−	71008.6i	−1.60198	−	1.16390i
$248$	19535.7	−	26888.6i	0.317633	−	0.437185i
$249$	−37585.5	−	12212.3i	−0.606208	−	0.196969i
$250$	−45593.8	+	14814.3i	−0.729501	+	0.237029i
$251$	50887.5	−	36971.9i	0.807725	−	0.586846i	−0.105445	−	0.994425i	$-0.533627\pi$
$251$	50887.5	−	36971.9i	0.807725	−	0.586846i	0.913170	+	0.407579i	$0.133627\pi$
$252$		−	9009.21i		−	0.141868i
$253$	65925.0	−	41616.5i	1.02993	−	0.650167i
$254$	15870.6			0.245995
$255$	37150.2	+	51132.9i	0.571322	+	0.786358i
$256$	1265.73	+	3895.53i	0.0193136	+	0.0594410i
$257$	−10669.6	+	32837.5i	−0.161540	+	0.497169i	−0.998765	−	0.0496899i	$-0.984177\pi$
$257$	−10669.6	+	32837.5i	−0.161540	+	0.497169i	0.837225	+	0.546859i	$0.184177\pi$
$258$	35863.1	+	26056.1i	0.538777	+	0.391444i
$259$	−20080.0	+	27637.8i	−0.299340	+	0.412007i
$260$	30234.7	+	9823.86i	0.447259	+	0.145323i
$261$	19809.3	−	6436.43i	0.290796	−	0.0944853i
$262$	35848.2	−	26045.2i	0.522233	−	0.379425i
$263$		−	29833.5i		−	0.431314i	−0.976469	−	0.215657i	$-0.930811\pi$
$263$		−	29833.5i		−	0.431314i	0.976469	−	0.215657i	$-0.0691892\pi$
$264$	−27877.4	−	11114.6i	−0.399986	−	0.159473i
$265$	50167.9			0.714388
$266$	−31112.8	−	42823.1i	−0.439720	−	0.605223i
$267$	32498.7	+	100021.i	0.455872	+	1.40303i
$268$	−3841.21	+	11822.0i	−0.0534808	+	0.164597i
$269$	−57618.0	−	41861.9i	−0.796258	−	0.578515i	0.113556	−	0.993532i	$-0.463776\pi$
$269$	−57618.0	−	41861.9i	−0.796258	−	0.578515i	−0.909814	+	0.415016i	$0.863776\pi$
$270$	16321.3	−	22464.4i	0.223886	−	0.308153i
$271$	−63339.0	−	20580.1i	−0.862447	−	0.280226i	−0.155797	−	0.987789i	$-0.549794\pi$
$271$	−63339.0	−	20580.1i	−0.862447	−	0.280226i	−0.706650	+	0.707563i	$0.749794\pi$
$272$	−16398.7	+	5328.27i	−0.221652	+	0.0720192i
$273$	47360.9	−	34409.7i	0.635470	−	0.461696i
$274$		−	12417.6i		−	0.165401i
$275$	15534.9	+	12914.2i	0.205420	+	0.170767i
$276$	56500.5			0.741710
$277$	53867.1	+	74141.7i	0.702044	+	0.966280i	0.999932	+	0.0116795i	$0.00371779\pi$
$277$	53867.1	+	74141.7i	0.702044	+	0.966280i	−0.297888	+	0.954601i	$0.596282\pi$
$278$	−376.587	−	1159.02i	−0.00487277	−	0.0149968i
$279$	−17771.1	+	54693.9i	−0.228300	+	0.702636i
$280$	11269.0	+	8187.42i	0.143738	+	0.104431i
$281$	20602.3	−	28356.6i	0.260917	−	0.359121i	−0.658380	−	0.752685i	$-0.728758\pi$
$281$	20602.3	−	28356.6i	0.260917	−	0.359121i	0.919297	+	0.393564i	$0.128758\pi$
$282$	39062.3	+	12692.1i	0.491202	+	0.159601i
$283$	49609.9	−	16119.2i	0.619434	−	0.201266i	0.0175451	−	0.999846i	$-0.494415\pi$
$283$	49609.9	−	16119.2i	0.619434	−	0.201266i	0.601889	+	0.798580i	$0.294415\pi$
$284$	31950.1	−	23213.1i	0.396127	−	0.287803i
$285$			152635.i			1.87917i
$286$	−15656.0	−	61587.0i	−0.191403	−	0.752934i
$287$	−64801.2			−0.786718
$288$	−4165.82	−	5733.76i	−0.0502245	−	0.0691280i
$289$	3379.40	+	10400.7i	0.0404617	+	0.124528i
$290$	−9951.47	+	30627.5i	−0.118329	+	0.364179i
$291$	−113927.	−	82772.9i	−1.34537	−	0.977467i
$292$	17614.1	−	24243.7i	0.206583	−	0.284337i
$293$	130584.	+	42429.5i	1.52110	+	0.494234i	0.946087	−	0.323914i	$-0.104999\pi$
$293$	130584.	+	42429.5i	1.52110	+	0.494234i	0.575008	+	0.818147i	$0.304999\pi$
$294$	−46401.3	+	15076.7i	−0.536828	+	0.174426i
$295$	−56922.5	+	41356.6i	−0.654094	+	0.475227i
$296$			26874.5i			0.306731i
$297$	−55385.9	−	3617.53i	−0.627894	−	0.0410109i
$298$	−83341.9			−0.938493
$299$	70318.8	+	96785.5i	0.786555	+	1.08260i
$300$	4524.19	+	13924.0i	0.0502688	+	0.154712i
$301$	−12708.7	+	39113.4i	−0.140271	+	0.431711i
$302$	43331.5	+	31482.2i	0.475105	+	0.345184i
$303$	20296.4	−	27935.6i	0.221072	−	0.304279i
$304$	−39602.5	−	12867.6i	−0.428524	−	0.139236i
$305$	70861.3	−	23024.2i	0.761745	−	0.247506i
$306$	24137.0	−	17536.5i	0.257774	−	0.187284i
$307$		−	50837.0i		−	0.539390i	−0.962946	−	0.269695i	$-0.913077\pi$
$307$		−	50837.0i		−	0.539390i	0.962946	−	0.269695i	$-0.0869229\pi$
$308$	1814.70	−	27783.8i	0.0191295	−	0.292880i
$309$	−141815.			−1.48527
$310$	−52262.8	−	71933.6i	−0.543838	−	0.748529i
$311$	−24341.8	−	74916.3i	−0.251670	−	0.774561i	−0.994467	−	0.105045i	$-0.966501\pi$
$311$	−24341.8	−	74916.3i	−0.251670	−	0.774561i	0.742797	−	0.669516i	$-0.233499\pi$
$312$	14231.1	−	43799.0i	0.146194	−	0.449940i
$313$	109771.	+	79753.2i	1.12047	+	0.814066i	0.984280	−	0.176617i	$-0.0565155\pi$
$313$	109771.	+	79753.2i	1.12047	+	0.814066i	0.136186	+	0.990683i	$0.456515\pi$
$314$	−734.345	+	1010.74i	−0.00744802	+	0.0102513i
$315$	−22922.2	−	7447.88i	−0.231012	−	0.0750605i
$316$	34065.4	−	11068.5i	0.341145	−	0.110845i
$317$	36448.5	−	26481.4i	0.362711	−	0.263525i	−0.391471	−	0.920190i	$-0.628034\pi$
$317$	36448.5	−	26481.4i	0.362711	−	0.263525i	0.754182	+	0.656665i	$0.228034\pi$
$318$		−	72674.7i		−	0.718669i
$319$	62387.0	−	15859.4i	0.613074	−	0.155849i
$320$	10957.8			0.107010
$321$	−48241.9	−	66399.3i	−0.468182	−	0.644397i
$322$	16198.1	+	49852.6i	0.156226	+	0.480813i
$323$	54167.9	−	166712.i	0.519202	−	1.59794i
$324$	−53067.8	−	38556.0i	−0.505524	−	0.367284i
$325$	−18221.2	+	25079.4i	−0.172509	+	0.237438i
$326$	29604.0	+	9618.93i	0.278558	+	0.0905089i
$327$	131959.	−	42876.0i	1.23408	−	0.400976i
$328$	−41241.6	+	29963.8i	−0.383343	+	0.278515i
$329$			38104.9i			0.352038i
$330$	−51325.1	+	61740.3i	−0.471305	+	0.566945i
$331$	−135226.			−1.23425			−0.617126	−	0.786864i	$-0.711703\pi$
$331$	−135226.			−1.23425			−0.617126	+	0.786864i	$0.711703\pi$
$332$	−16953.4	−	23334.4i	−0.153809	−	0.211700i
$333$	−14369.6	−	44225.1i	−0.129585	−	0.398823i
$334$	−32754.3	+	100808.i	−0.293614	+	0.903649i
$335$	26903.4	+	19546.4i	0.239727	+	0.174172i
$336$	11860.5	−	16324.6i	0.105057	−	0.144599i
$337$	−146208.	−	47505.9i	−1.28739	−	0.418300i	−0.416216	−	0.909266i	$-0.636644\pi$
$337$	−146208.	−	47505.9i	−1.28739	−	0.418300i	−0.871179	+	0.490966i	$0.836644\pi$
$338$	15910.5	−	5169.63i	0.139268	−	0.0452508i
$339$	−198542.	+	144249.i	−1.72764	+	1.25520i
$340$			46128.2i			0.399033i
$341$	−65821.7	+	165093.i	−0.566057	+	1.41977i
$342$	72050.5			0.616006
$343$	−67198.5	−	92490.8i	−0.571178	−	0.786159i
$344$	9997.63	+	30769.5i	0.0844851	+	0.260018i
$345$	46708.7	−	143755.i	0.392428	−	1.20777i
$346$	63555.2	+	46175.6i	0.530883	+	0.385709i
$347$	−29265.5	+	40280.6i	−0.243051	+	0.334531i	−0.913062	−	0.407820i	$-0.866289\pi$
$347$	−29265.5	+	40280.6i	−0.243051	+	0.334531i	0.670011	+	0.742351i	$0.266289\pi$
$348$	44367.9	+	14416.0i	0.366362	+	0.119038i
$349$	−144895.	+	47079.3i	−1.18960	+	0.386526i	−0.835927	−	0.548841i	$-0.815069\pi$
$349$	−144895.	+	47079.3i	−1.18960	+	0.386526i	−0.353678	+	0.935367i	$0.615069\pi$
$350$	−10988.7	+	7983.75i	−0.0897036	+	0.0651735i
$351$		−	85171.6i		−	0.691322i
$352$	−11692.2	−	18521.6i	−0.0943646	−	0.149484i
$353$	111137.			0.891884			0.445942	−	0.895062i	$-0.352869\pi$
$353$	111137.			0.891884			0.445942	+	0.895062i	$0.352869\pi$
$354$	59910.4	+	82459.6i	0.478075	+	0.658014i
$355$	−32648.2	−	100481.i	−0.259062	−	0.797310i
$356$	−23718.6	+	72998.5i	−0.187150	+	0.575989i
$357$	68720.7	+	49928.5i	0.539201	+	0.391753i
$358$	−62348.8	+	85815.7i	−0.486477	+	0.669578i
$359$	148842.	+	48361.7i	1.15488	+	0.375243i	0.822979	−	0.568072i	$-0.192311\pi$
$359$	148842.	+	48361.7i	1.15488	+	0.375243i	0.331899	+	0.943315i	$0.392311\pi$
$360$	−18032.3	+	5859.05i	−0.139138	+	0.0452087i
$361$	237043.	−	172222.i	1.81892	−	1.32152i
$362$		−	119708.i		−	0.913495i
$363$	159122.	+	20875.2i	1.20759	+	0.158423i
$364$	42725.5			0.322466
$365$	−47121.9	−	64857.7i	−0.353702	−	0.486829i
$366$	−33353.6	−	102652.i	−0.248989	−	0.766310i
$367$	−52490.7	+	161550.i	−0.389717	+	1.19943i	0.543282	+	0.839550i	$0.317181\pi$
$367$	−52490.7	+	161550.i	−0.389717	+	1.19943i	−0.933000	+	0.359877i	$0.882819\pi$
$368$	33360.6	+	24237.9i	0.246342	+	0.178978i
$369$	51846.3	−	71360.3i	0.380772	−	0.524088i
$370$	68377.1	+	22217.1i	0.499467	+	0.162287i
$371$	64123.7	−	20835.1i	0.465877	−	0.151373i
$372$	−104205.	+	75709.5i	−0.753015	+	0.547097i
$373$			72850.2i			0.523617i	0.965120	+	0.261808i	$0.0843188\pi$
$373$			72850.2i			0.523617i	−0.965120	+	0.261808i	$0.915681\pi$
$374$	77969.0	−	49219.6i	0.557415	−	0.351880i
$375$	185789.			1.32117
$376$	17619.5	+	24251.2i	0.124629	+	0.171537i
$377$	30524.3	+	93944.0i	0.214765	+	0.660977i
$378$	11532.0	−	35491.9i	0.0807090	−	0.248397i
$379$	126712.	+	92061.9i	0.882146	+	0.640917i	0.933818	−	0.357747i	$-0.116455\pi$
$379$	126712.	+	92061.9i	0.882146	+	0.640917i	−0.0516723	+	0.998664i	$0.516455\pi$
$380$	−65478.4	+	90123.2i	−0.453451	+	0.624122i
$381$	−58495.2	−	19006.3i	−0.402968	−	0.130932i
$382$	30697.4	−	9974.19i	0.210366	−	0.0683519i
$383$	−135728.	+	98612.0i	−0.925276	+	0.672252i	−0.944832	−	0.327557i	$-0.893775\pi$
$383$	−135728.	+	98612.0i	−0.925276	+	0.672252i	0.0195559	+	0.999809i	$0.493775\pi$
$384$		−	15873.8i		−	0.107651i
$385$	−69190.3	−	27585.9i	−0.466792	−	0.186108i
$386$	−23848.1			−0.160059
$387$	−32904.5	−	45289.1i	−0.219701	−	0.302393i
$388$	−31759.7	−	97746.2i	−0.210966	−	0.649286i
$389$	47397.6	−	145875.i	0.313225	−	0.964008i	−0.663253	−	0.748395i	$-0.730825\pi$
$389$	47397.6	−	145875.i	0.313225	−	0.964008i	0.976479	−	0.215614i	$-0.0691751\pi$
$390$	−99673.2	−	72416.8i	−0.655314	−	0.476113i
$391$	−102032.	+	140436.i	−0.667398	+	0.918595i
$392$	−33865.2	−	11003.5i	−0.220385	−	0.0716074i
$393$	−163319.	+	53065.5i	−1.05743	+	0.343580i
$394$	−9875.20	+	7174.76i	−0.0636141	+	0.0462184i
$395$		−	95823.2i		−	0.614153i
$396$	29144.1	+	24227.7i	0.185849	+	0.154498i
$397$	219146.			1.39044			0.695220	−	0.718797i	$-0.255307\pi$
$397$	219146.			1.39044			0.695220	+	0.718797i	$0.255307\pi$
$398$	−74660.3	−	102761.i	−0.471329	−	0.648728i
$399$	63390.5	+	195096.i	0.398179	+	1.22547i
$400$	−3301.91	+	10162.2i	−0.0206369	+	0.0635140i
$401$	−545.447	−	396.290i	−0.00339206	−	0.00246448i	0.586088	−	0.810247i	$-0.300667\pi$
$401$	−545.447	−	396.290i	−0.00339206	−	0.00246448i	−0.589480	+	0.807783i	$0.700667\pi$
$402$	28315.5	−	38973.0i	0.175216	−	0.241164i
$403$	−259381.	−	84278.1i	−1.59709	−	0.518925i
$404$	23967.9	−	7787.65i	0.146848	−	0.0477138i
$405$	−141969.	+	103147.i	−0.865535	+	0.628848i
$406$			43280.4i			0.262567i
$407$	−35406.7	−	139281.i	−0.213745	−	0.840823i
$408$	66822.8			0.401425
$409$	−105058.	−	144600.i	−0.628032	−	0.864412i	0.369874	−	0.929082i	$-0.379401\pi$
$409$	−105058.	−	144600.i	−0.628032	−	0.864412i	−0.997907	+	0.0646695i	$0.979401\pi$
$410$	42142.8	+	129702.i	0.250701	+	0.771578i
$411$	−14871.1	+	45768.4i	−0.0880356	+	0.270946i
$412$	−83734.6	−	60836.7i	−0.493299	−	0.358403i
$413$	−55581.7	+	76501.6i	−0.325860	+	0.448508i
$414$	−67858.5	−	22048.6i	−0.395916	−	0.128641i
$415$	−73385.2	+	23844.3i	−0.426100	+	0.138448i
$416$	27191.9	−	19756.1i	0.157128	−	0.114160i
$417$			4722.85i			0.0271601i
$418$	222199.	+	14512.9i	1.27171	+	0.0830620i
$419$	38184.5			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$419$	38184.5			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$420$	−31729.9	−	43672.4i	−0.179875	−	0.247576i
$421$	−64777.4	−	199364.i	−0.365476	−	1.12482i	−0.949682	−	0.313215i	$-0.898594\pi$
$421$	−64777.4	−	199364.i	−0.365476	−	1.12482i	0.584206	−	0.811605i	$-0.301406\pi$
$422$	72402.0	−	222831.i	0.406561	−	1.25127i
$423$	−41961.9	−	30487.1i	−0.234517	−	0.170387i
$424$	31176.4	−	42910.6i	0.173418	−	0.238689i
$425$	−42779.2	−	13899.8i	−0.236840	−	0.0769540i
$426$	−145560.	+	47295.2i	−0.802088	+	0.260614i
$427$	81011.6	−	58858.4i	0.444316	−	0.322814i
$428$		−	59900.5i		−	0.326996i
$429$	−16050.8	+	245744.i	−0.0872131	+	1.33527i
$430$	86552.2			0.468103
$431$	164680.	+	226663.i	0.886515	+	1.22018i	0.974573	+	0.224068i	$0.0719339\pi$
$431$	164680.	+	226663.i	0.886515	+	1.22018i	−0.0880582	+	0.996115i	$0.528066\pi$
$432$	−9071.95	−	27920.6i	−0.0486108	−	0.149609i
$433$	109016.	−	335518.i	0.581454	−	1.78953i	−0.0316105	−	0.999500i	$-0.510064\pi$
$433$	109016.	−	335518.i	0.581454	−	1.78953i	0.613065	−	0.790033i	$-0.289936\pi$
$434$	−96676.0	−	70239.2i	−0.513262	−	0.372907i
$435$	73357.5	−	100968.i	0.387673	−	0.533587i
$436$	96308.0	+	31292.4i	0.506628	+	0.164613i
$437$	−398693.	+	129543.i	−2.08774	+	0.678346i
$438$	−93954.9	+	68262.2i	−0.489746	+	0.355821i
$439$			56461.4i			0.292969i	0.989213	+	0.146485i	$0.0467959\pi$
$439$			56461.4i			0.292969i	−0.989213	+	0.146485i	$0.953204\pi$
$440$	−56790.5	+	14436.7i	−0.293340	+	0.0745698i
$441$	61612.6			0.316805
$442$	83165.6	+	114468.i	0.425696	+	0.585920i
$443$	79396.8	+	244358.i	0.404572	+	1.24514i	0.921252	+	0.388966i	$0.127168\pi$
$443$	79396.8	+	244358.i	0.404572	+	1.24514i	−0.516680	+	0.856178i	$0.672832\pi$
$444$	32184.3	−	99053.1i	0.163259	−	0.502461i
$445$	166123.	+	120695.i	0.838897	+	0.609494i
$446$	−36271.3	+	49923.2i	−0.182345	+	0.250976i
$447$	307178.	+	99808.3i	1.53736	+	0.499519i
$448$	14006.1	−	4550.85i	0.0697847	−	0.0226744i
$449$	−5782.07	+	4200.92i	−0.0286807	+	0.0208378i	−0.602033	−	0.798471i	$-0.705643\pi$
$449$	−5782.07	+	4200.92i	−0.0286807	+	0.0208378i	0.573353	+	0.819309i	$0.305643\pi$
$450$		−	18488.6i		−	0.0913018i
$451$	174264.	−	209627.i	0.856752	−	1.03061i
$452$	−179109.			−0.876680
$453$	−122007.	−	167929.i	−0.594551	−	0.818330i
$454$	−4640.67	−	14282.5i	−0.0225148	−	0.0692936i
$455$	35321.0	−	108707.i	0.170612	−	0.525090i
$456$	130555.	+	94853.9i	0.627863	+	0.456169i
$457$	−133945.	+	184360.i	−0.641349	+	0.882741i	−0.998687	−	0.0512341i	$-0.983685\pi$
$457$	−133945.	+	184360.i	−0.641349	+	0.882741i	0.357338	+	0.933975i	$0.383685\pi$
$458$	−101977.	−	33134.3i	−0.486151	−	0.157960i
$459$	117535.	−	38189.5i	0.557882	−	0.181267i
$460$	89247.8	−	64842.3i	0.421776	−	0.306438i
$461$			134031.i			0.630673i	0.948980	+	0.315337i	$0.102117\pi$
$461$			134031.i			0.630673i	−0.948980	+	0.315337i	$0.897883\pi$
$462$	−39961.7	+	100231.i	−0.187224	+	0.469590i
$463$	117718.			0.549135			0.274568	−	0.961568i	$-0.411465\pi$
$463$	117718.			0.549135			0.274568	+	0.961568i	$0.411465\pi$
$464$	20012.7	+	27545.1i	0.0929542	+	0.127941i
$465$	106482.	+	327719.i	0.492461	+	1.51564i
$466$	−16990.7	+	52292.0i	−0.0782418	+	0.240804i
$467$	−105205.	−	76436.2i	−0.482396	−	0.350481i	0.319856	−	0.947466i	$-0.396365\pi$
$467$	−105205.	−	76436.2i	−0.482396	−	0.350481i	−0.802253	+	0.596985i	$0.796365\pi$
$468$	−34183.9	+	47050.1i	−0.156074	+	0.214817i
$469$	42505.2	+	13810.8i	0.193240	+	0.0627874i
$470$	76268.6	−	24781.2i	0.345263	−	0.112183i
$471$	3917.06	−	2845.91i	0.0176571	−	0.0128286i
$472$			74388.8i			0.333906i
$473$	−92352.6	−	146296.i	−0.412788	−	0.653899i
$474$	−138812.			−0.617833
$475$	−63849.5	−	87881.3i	−0.282989	−	0.389501i
$476$	19157.4	+	58960.4i	0.0845517	+	0.260223i
$477$	−28360.3	+	87284.1i	−0.124645	+	0.383617i
$478$	16815.8	+	12217.4i	0.0735974	+	0.0534716i
$479$	68011.1	−	93609.2i	0.296421	−	0.407988i	−0.634666	−	0.772787i	$-0.718862\pi$
$479$	68011.1	−	93609.2i	0.296421	−	0.407988i	0.931086	+	0.364799i	$0.118862\pi$
$480$	−40387.8	−	13122.8i	−0.175294	−	0.0569566i
$481$	209734.	−	68146.7i	0.906522	−	0.294547i
$482$	101134.	−	73478.5i	0.435317	−	0.316276i
$483$		−	203143.i		−	0.870779i
$484$	84998.3	+	80586.9i	0.362844	+	0.344012i
$485$	−274952.			−1.16889
$486$	87650.3	+	120640.i	0.371091	+	0.510763i
$487$	−72006.6	−	221613.i	−0.303609	−	0.934411i	−0.980193	−	0.198046i	$-0.936540\pi$
$487$	−72006.6	−	221613.i	−0.303609	−	0.934411i	0.676584	−	0.736365i	$-0.263460\pi$
$488$	24342.6	−	74918.8i	0.102218	−	0.314595i
$489$	−97594.0	−	70906.2i	−0.408136	−	0.296528i
$490$	−55992.5	+	77067.1i	−0.233205	+	0.320979i
$491$	160438.	+	52129.5i	0.665495	+	0.216232i	0.622234	−	0.782831i	$-0.286225\pi$
$491$	160438.	+	52129.5i	0.665495	+	0.216232i	0.0432610	+	0.999064i	$0.486225\pi$
$492$	187891.	−	61049.3i	0.776202	−	0.252203i
$493$	−115955.	+	84245.9i	−0.477083	+	0.346621i
$494$			341694.i			1.40018i
$495$	85736.1	−	54122.7i	0.349907	−	0.220886i
$496$	−94006.1			−0.382114
$497$	−83460.9	−	114874.i	−0.337886	−	0.465060i
$498$	34541.5	+	106308.i	0.139278	+	0.428654i
$499$	−134952.	+	415341.i	−0.541976	+	1.66803i	0.186099	+	0.982531i	$0.440416\pi$
$499$	−134952.	+	415341.i	−0.541976	+	1.66803i	−0.728074	+	0.685498i	$0.759584\pi$
$500$	109699.	+	79700.9i	0.438796	+	0.318804i
$501$	241449.	−	332327.i	0.961946	−	1.32401i
$502$	−169202.	−	54976.9i	−0.671424	−	0.218159i
$503$	−152230.	+	49462.6i	−0.601679	+	0.195497i	−0.593989	−	0.804473i	$-0.702448\pi$
$503$	−152230.	+	49462.6i	−0.601679	+	0.195497i	−0.00769004	+	0.999970i	$0.502448\pi$
$504$	−20615.3	+	14977.9i	−0.0811574	+	0.0589643i
$505$		−	67419.8i		−	0.264366i
$506$	−204830.	−	81664.7i	−0.800003	−	0.318958i
$507$	−64833.3			−0.252222
$508$	−26385.0	−	36315.8i	−0.102242	−	0.140724i
$509$	−135530.	−	417118.i	−0.523118	−	1.60999i	−0.768008	−	0.640441i	$-0.778752\pi$
$509$	−135530.	−	417118.i	−0.523118	−	1.60999i	0.244889	−	0.969551i	$-0.421248\pi$
$510$	55242.1	−	170018.i	0.212388	−	0.653663i
$511$	−87166.3	−	63330.0i	−0.333816	−	0.242531i
$512$	6809.63	−	9372.65i	0.0259767	−	0.0357538i
$513$	283844.	+	92226.6i	1.07856	+	0.350446i
$514$	92878.6	−	30178.1i	0.351552	−	0.114226i
$515$	−224010.	+	162753.i	−0.844605	+	0.613642i
$516$		−	125382.i		−	0.470908i
$517$	−123267.	−	102472.i	−0.461173	−	0.383376i
$518$	96625.3			0.360107
$519$	−178951.	−	246304.i	−0.664352	−	0.914403i
$520$	−27786.1	−	85516.8i	−0.102759	−	0.316260i
$521$	−120228.	+	370024.i	−0.442925	+	1.36318i	0.441818	+	0.897105i	$0.354334\pi$
$521$	−120228.	+	370024.i	−0.442925	+	1.36318i	−0.884743	+	0.466079i	$0.845666\pi$
$522$	−47661.3	−	34627.9i	−0.174914	−	0.127082i
$523$	−243763.	+	335512.i	−0.891180	+	1.22660i	0.0820175	+	0.996631i	$0.473864\pi$
$523$	−243763.	+	335512.i	−0.891180	+	1.22660i	−0.973197	+	0.229973i	$0.926136\pi$
$524$	−119196.	−	38729.0i	−0.434108	−	0.141050i
$525$	50062.8	−	16266.4i	0.181634	−	0.0590164i
$526$	−68266.4	+	49598.5i	−0.246738	+	0.179266i
$527$		−	395730.i		−	1.42488i
$528$	20913.5	+	82268.5i	0.0750167	+	0.295098i
$529$	135297.			0.483478
$530$	−83404.5	−	114796.i	−0.296919	−	0.408674i
$531$	−39775.1	−	122415.i	−0.141066	−	0.434157i
$532$	−46264.5	+	142388.i	−0.163465	+	0.503094i
$533$	338421.	+	245877.i	1.19125	+	0.865493i
$534$	174843.	−	240650.i	0.613147	−	0.843925i
$535$	−152405.	−	49519.5i	−0.532467	−	0.173009i
$536$	33437.7	−	10864.6i	0.116388	−	0.0378167i
$537$	332574.	−	241629.i	1.15329	−	0.837916i
$538$			201440.i			0.695955i
$539$	190009.	+	12410.4i	0.654028	+	0.0427178i
$540$	−78538.3			−0.269336
$541$	224353.	+	308796.i	0.766545	+	1.05506i	0.996641	+	0.0818913i	$0.0260960\pi$
$541$	224353.	+	308796.i	0.766545	+	1.05506i	−0.230096	+	0.973168i	$0.573904\pi$
$542$	58209.2	+	179150.i	0.198150	+	0.609842i
$543$	−143360.	+	441215.i	−0.486213	+	1.49641i
$544$	39455.4	+	28666.0i	0.133324	+	0.0968656i
$545$	159235.	−	219168.i	0.536099	−	0.737877i
$546$	−157476.	−	51167.0i	−0.528237	−	0.171635i
$547$	282409.	−	91760.1i	0.943851	−	0.306676i	0.203636	−	0.979047i	$-0.434724\pi$
$547$	282409.	−	91760.1i	0.943851	−	0.306676i	0.740214	+	0.672371i	$0.234724\pi$
$548$	−28414.6	+	20644.4i	−0.0946195	+	0.0687451i
$549$			136303.i			0.452232i
$550$	3724.11	−	57017.6i	0.0123111	−	0.188488i
$551$	−346132.			−1.14009
$552$	−93932.5	−	129287.i	−0.308275	−	0.424304i
$553$	−39796.0	−	122480.i	−0.130134	−	0.400510i
$554$	80100.0	−	246522.i	0.260983	−	0.803224i
$555$	−225415.	−	163774.i	−0.731807	−	0.531689i
$556$	−2026.03	+	2788.60i	−0.00655386	+	0.00902062i
$557$	186511.	+	60601.0i	0.601164	+	0.195330i	0.593760	−	0.804642i	$-0.297643\pi$
$557$	186511.	+	60601.0i	0.601164	+	0.195330i	0.00740474	+	0.999973i	$0.497643\pi$
$558$	154698.	−	50264.3i	0.496839	−	0.161433i
$559$	214780.	−	156047.i	0.687338	−	0.499380i
$560$		−	39397.9i		−	0.125631i
$561$	−346320.	+	88037.8i	−1.10040	+	0.279733i
$562$	−99138.2			−0.313884
$563$	219272.	+	301802.i	0.691777	+	0.952149i	1.00000		0.000834694i	$0.000265691\pi$
$563$	219272.	+	301802.i	0.691777	+	0.952149i	−0.308223	+	0.951314i	$0.599734\pi$
$564$	−35898.7	−	110485.i	−0.112855	−	0.347332i
$565$	−148069.	+	455709.i	−0.463839	+	1.42755i
$566$	−119362.	−	86721.2i	−0.372590	−	0.270703i
$567$	−138625.	+	190801.i	−0.431198	+	0.593493i
$568$	−106234.	−	34517.7i	−0.329283	−	0.106990i
$569$	120227.	−	39064.2i	0.371346	−	0.120657i	−0.117398	−	0.993085i	$-0.537455\pi$
$569$	120227.	−	39064.2i	0.371346	−	0.120657i	0.488744	+	0.872427i	$0.337455\pi$
$570$	349267.	−	253757.i	1.07500	−	0.781032i
$571$			383915.i			1.17751i	0.808313	+	0.588753i	$0.200381\pi$
$571$			383915.i			1.17751i	−0.808313	+	0.588753i	$0.799619\pi$
$572$	−114898.	+	138214.i	−0.351172	+	0.422434i
$573$	−125088.			−0.380984
$574$	107732.	+	148281.i	0.326981	+	0.450051i
$575$	33241.6	+	102307.i	0.100542	+	0.309435i
$576$	−6194.54	+	19064.8i	−0.0186708	+	0.0574629i
$577$	166603.	+	121044.i	0.500416	+	0.363574i	0.809176	−	0.587566i	$-0.199914\pi$
$577$	166603.	+	121044.i	0.500416	+	0.363574i	−0.308760	+	0.951140i	$0.599914\pi$
$578$	18181.1	−	25024.2i	0.0544208	−	0.0749038i
$579$	87898.5	+	28560.0i	0.262195	+	0.0851923i
$580$	86627.6	−	28147.0i	0.257514	−	0.0836712i
$581$	−83897.0	+	60954.7i	−0.248539	+	0.180574i
$582$			398304.i			1.17589i
$583$	−105043.	+	263465.i	−0.309050	+	0.775152i
$584$	−84759.0			−0.248519
$585$	91450.3	+	125871.i	0.267223	+	0.367801i
$586$	−120009.	−	369349.i	−0.349476	−	1.07558i
$587$	−4259.77	+	13110.2i	−0.0123626	+	0.0380482i	−0.957048	−	0.289931i	$-0.906368\pi$
$587$	−4259.77	+	13110.2i	−0.0123626	+	0.0380482i	0.944685	+	0.327979i	$0.106368\pi$
$588$	111642.	+	81112.4i	0.322903	+	0.234603i
$589$	561734.	−	773160.i	1.61920	−	2.22863i
$590$	189268.	+	61497.0i	0.543718	+	0.176665i
$591$	44990.0	−	14618.1i	0.128807	−	0.0418521i
$592$	61495.5	−	44679.1i	0.175469	−	0.127486i
$593$		−	134754.i		−	0.383207i	−0.981472	−	0.191604i	$-0.938631\pi$
$593$		−	134754.i		−	0.383207i	0.981472	−	0.191604i	$-0.0613688\pi$
$594$	83801.7	+	132751.i	0.237509	+	0.376239i
$595$	165851.			0.468472
$596$	138557.	+	190707.i	0.390063	+	0.536875i
$597$	152116.	+	468165.i	0.426801	+	1.31356i
$598$	104564.	−	321813.i	0.292400	−	0.899915i
$599$	−460224.	−	334372.i	−1.28267	−	0.931916i	−0.283042	−	0.959107i	$-0.591344\pi$
$599$	−460224.	−	334372.i	−1.28267	−	0.931916i	−0.999630	+	0.0271914i	$0.991344\pi$
$600$	24340.1	−	33501.3i	0.0676114	−	0.0930591i
$601$	−364492.	−	118431.i	−1.00911	−	0.327880i	−0.242610	−	0.970124i	$-0.578004\pi$
$601$	−364492.	−	118431.i	−1.00911	−	0.327880i	−0.766500	+	0.642244i	$0.778004\pi$
$602$	110630.	−	35945.7i	0.305266	−	0.0991869i
$603$	−49216.4	+	35757.8i	−0.135355	+	0.0983413i
$604$		−	151493.i		−	0.415257i
$605$	275306.	−	149641.i	0.752150	−	0.408827i
$606$	−97666.4			−0.265950
$607$	−73667.5	−	101395.i	−0.199940	−	0.275193i	0.697260	−	0.716818i	$-0.254402\pi$
$607$	−73667.5	−	101395.i	−0.199940	−	0.275193i	−0.897200	+	0.441625i	$0.854402\pi$
$608$	36395.1	+	112013.i	0.0984546	+	0.303012i
$609$	51831.6	−	159521.i	0.139753	−	0.430115i
$610$	−170493.	−	123870.i	−0.458190	−	0.332895i
$611$	144583.	−	199001.i	0.387288	−	0.533056i
$612$	−80255.8	−	26076.7i	−0.214276	−	0.0696225i
$613$	−460793.	+	149721.i	−1.22627	+	0.398438i	−0.849360	−	0.527814i	$-0.823012\pi$
$613$	−460793.	+	149721.i	−1.22627	+	0.398438i	−0.376906	+	0.926252i	$0.623012\pi$
$614$	−116327.	+	84516.8i	−0.308564	+	0.224185i
$615$		−	528521.i		−	1.39737i
$616$	−66593.0	+	42038.3i	−0.175496	+	0.110786i
$617$	32592.5			0.0856146			0.0428073	−	0.999083i	$-0.486370\pi$
$617$	32592.5			0.0856146			0.0428073	+	0.999083i	$0.486370\pi$
$618$	235769.	+	324508.i	0.617319	+	0.849667i
$619$	−65160.9	−	200545.i	−0.170062	−	0.523395i	0.829312	−	0.558786i	$-0.188733\pi$
$619$	−65160.9	−	200545.i	−0.170062	−	0.523395i	−0.999374	+	0.0353902i	$0.988733\pi$
$620$	−77714.4	+	239180.i	−0.202171	+	0.622218i
$621$	−239107.	−	173721.i	−0.620025	−	0.450474i
$622$	−130959.	+	180249.i	−0.338496	+	0.465899i
$623$	262461.	+	85278.6i	0.676220	+	0.219717i
$624$	−123882.	+	40251.8i	−0.318156	+	0.103375i
$625$	209052.	−	151885.i	0.535174	−	0.388827i
$626$		−	383773.i		−	0.979323i
$627$	−801592.	−	319591.i	−2.03900	−	0.812942i
$628$	3533.67			0.00895998
$629$	188082.	+	258873.i	0.475386	+	0.654313i
$630$	21065.8	+	64833.8i	0.0530758	+	0.163350i
$631$	88340.7	−	271885.i	0.221872	−	0.682851i	−0.776722	−	0.629843i	$-0.783119\pi$
$631$	88340.7	−	271885.i	0.221872	−	0.682851i	0.998594	−	0.0530080i	$-0.0168809\pi$
$632$	−81961.5	−	59548.5i	−0.205199	−	0.149086i
$633$	−533713.	+	734593.i	−1.33199	+	1.83333i
$634$	−121192.	−	39377.6i	−0.301505	−	0.0979649i
$635$	−114211.	+	37109.4i	−0.283244	+	0.0920315i
$636$	−166298.	+	120822.i	−0.411123	+	0.298698i
$637$			292193.i			0.720096i
$638$	−140009.	−	116390.i	−0.343965	−	0.285941i
$639$	193277.			0.473346
$640$	−18217.4	−	25074.1i	−0.0444761	−	0.0612162i
$641$	85162.5	+	262103.i	0.207268	+	0.637906i	0.999613	+	0.0278317i	$0.00886025\pi$
$641$	85162.5	+	262103.i	0.207268	+	0.637906i	−0.792345	+	0.610074i	$0.791140\pi$
$642$	−71735.4	+	220779.i	−0.174046	+	0.535658i
$643$	−109982.	−	79906.6i	−0.266011	−	0.193268i	0.446782	−	0.894643i	$-0.352570\pi$
$643$	−109982.	−	79906.6i	−0.266011	−	0.193268i	−0.712793	+	0.701375i	$0.752570\pi$
$644$	87145.5	−	119946.i	0.210123	−	0.289209i
$645$	−319011.	−	103653.i	−0.766807	−	0.249151i
$646$	−471531.	+	153210.i	−1.12991	+	0.367131i
$647$	208899.	−	151774.i	0.499031	−	0.362567i	−0.309616	−	0.950862i	$-0.600200\pi$
$647$	208899.	−	151774.i	0.499031	−	0.362567i	0.808647	+	0.588295i	$0.200200\pi$
$648$			185532.i			0.441844i
$649$	−98006.0	−	385532.i	−0.232682	−	0.915316i
$650$	87680.8			0.207528
$651$	272208.	+	374662.i	0.642301	+	0.884052i
$652$	−27206.4	−	83732.8i	−0.0639995	−	0.196970i
$653$	166216.	−	511562.i	0.389805	−	1.19970i	−0.543129	−	0.839650i	$-0.682760\pi$
$653$	166216.	−	511562.i	0.389805	−	1.19970i	0.932934	−	0.360048i	$-0.117240\pi$
$654$	−317493.	−	230672.i	−0.742299	−	0.539312i
$655$	−197077.	+	271254.i	−0.459361	+	0.632256i
$656$	137129.	+	44555.9i	0.318655	+	0.103537i
$657$	139481.	−	45320.0i	0.323134	−	0.104993i
$658$	87193.4	−	63349.7i	0.201387	−	0.146316i
$659$		−	209462.i		−	0.482320i	−0.970485	−	0.241160i	$-0.922472\pi$
$659$		−	209462.i		−	0.482320i	0.970485	−	0.241160i	$-0.0775279\pi$
$660$	226605.	+	14800.7i	0.520214	+	0.0339778i
$661$	205891.			0.471231			0.235615	−	0.971846i	$-0.424289\pi$
$661$	205891.			0.471231			0.235615	+	0.971846i	$0.424289\pi$
$662$	224814.	+	309430.i	0.512988	+	0.706068i
$663$	−169445.	−	521498.i	−0.385480	−	1.18638i
$664$	−25209.6	+	77587.1i	−0.0571781	+	0.175976i
$665$	324031.	+	235423.i	0.732730	+	0.532359i
$666$	−77308.3	+	106406.i	−0.174292	+	0.239892i
$667$	325994.	+	105922.i	0.732753	+	0.238086i
$668$	285127.	−	92643.3i	0.638977	−	0.207616i
$669$	193474.	−	140567.i	0.432286	−	0.314074i
$670$		−	94057.6i		−	0.209529i
$671$	−27455.1	+	420350.i	−0.0609788	+	0.933610i
$672$	−57073.1			−0.126384
$673$	−59163.6	−	81431.7i	−0.130624	−	0.179789i	0.738695	−	0.674040i	$-0.235442\pi$
$673$	−59163.6	−	81431.7i	−0.130624	−	0.179789i	−0.869319	+	0.494251i	$0.835442\pi$
$674$	134367.	+	413539.i	0.295783	+	0.910326i
$675$	23665.9	−	72836.2i	0.0519417	−	0.159860i
$676$	−38280.7	−	27812.6i	−0.0837696	−	0.0608622i
$677$	323791.	−	445660.i	0.706460	−	0.972359i	−0.293406	−	0.955988i	$-0.594789\pi$
$677$	323791.	−	445660.i	0.706460	−	0.972359i	0.999866	−	0.0163712i	$-0.00521135\pi$
$678$	660154.	+	214497.i	1.43610	+	0.466618i
$679$	−351439.	+	114189.i	−0.762273	+	0.247677i
$680$	105553.	−	76688.6i	0.228272	−	0.165849i
$681$			58199.5i			0.125495i
$682$	487201.	−	123851.i	1.04747	−	0.266276i
$683$	205165.			0.439806			0.219903	−	0.975522i	$-0.429426\pi$
$683$	205165.			0.439806			0.219903	+	0.975522i	$0.429426\pi$
$684$	−119785.	−	164869.i	−0.256029	−	0.352393i
$685$	29035.5	+	89362.2i	0.0618798	+	0.190446i
$686$	−99923.7	+	307533.i	−0.212334	+	0.653498i
$687$	336182.	+	244250.i	0.712297	+	0.517514i
$688$	53787.1	−	74031.6i	0.113632	−	0.156401i
$689$	−413938.	−	134497.i	−0.871960	−	0.283317i
$690$	−406600.	+	132112.i	−0.854021	+	0.277488i
$691$	465223.	−	338004.i	0.974328	−	0.707891i	0.0178939	−	0.999840i	$-0.494304\pi$
$691$	465223.	−	338004.i	0.974328	−	0.707891i	0.956434	+	0.291949i	$0.0943039\pi$
$692$		−	222197.i		−	0.464009i
$693$	87108.9	−	104786.i	0.181383	−	0.218190i
$694$	140826.			0.292391
$695$	5420.14	+	7460.18i	0.0112212	+	0.0154447i
$696$	−40774.6	−	125491.i	−0.0841727	−	0.259057i
$697$	−187564.	+	577261.i	−0.386085	+	1.18825i
$698$	348618.	+	253286.i	0.715548	+	0.519876i
$699$	125247.	−	172388.i	0.256339	−	0.352820i
$700$	36537.6	+	11871.8i	0.0745664	+	0.0242281i
$701$	77937.1	−	25323.3i	0.158602	−	0.0515329i	−0.228640	−	0.973511i	$-0.573428\pi$
$701$	77937.1	−	25323.3i	0.158602	−	0.0515329i	0.387242	+	0.921978i	$0.373428\pi$
$702$	−194894.	+	141598.i	−0.395479	+	0.287332i
$703$			772754.i			1.56362i
$704$	−22943.7	+	57546.8i	−0.0462933	+	0.116112i
$705$	−310785.			−0.625291
$706$	−184766.	−	254308.i	−0.370691	−	0.510212i
$707$	−27999.9	−	86174.9i	−0.0560168	−	0.172402i
$708$	89086.3	−	274180.i	0.177723	−	0.546976i
$709$	−139644.	−	101457.i	−0.277799	−	0.201832i	0.440158	−	0.897920i	$-0.354922\pi$
$709$	−139644.	−	101457.i	−0.277799	−	0.201832i	−0.717957	+	0.696088i	$0.754922\pi$
$710$	−175647.	+	241758.i	−0.348437	+	0.479583i
$711$	166717.	+	54169.6i	0.329792	+	0.107156i
$712$	206471.	−	67086.5i	0.407285	−	0.132335i
$713$	−765649.	+	556277.i	−1.50609	+	1.09424i
$714$		−	240256.i		−	0.471279i
$715$	256673.	+	406596.i	0.502074	+	0.795338i
$716$	300023.			0.585232
$717$	−47347.9	−	65168.7i	−0.0921005	−	0.126765i
$718$	−136787.	−	420988.i	−0.265337	−	0.816622i
$719$	−53069.6	+	163331.i	−0.102657	+	0.315945i	−0.989173	−	0.146752i	$-0.953118\pi$
$719$	−53069.6	+	163331.i	−0.102657	+	0.315945i	0.886516	+	0.462697i	$0.153118\pi$
$720$	43385.8	+	31521.6i	0.0836917	+	0.0608056i
$721$	−218734.	+	301061.i	−0.420771	+	0.579141i
$722$	−788173.	−	256093.i	−1.51198	−	0.491273i
$723$	−460754.	+	149708.i	−0.881439	+	0.286397i
$724$	−273921.	+	199016.i	−0.522575	+	0.379673i
$725$			88819.7i			0.168979i
$726$	−216775.	−	398816.i	−0.411278	−	0.756658i
$727$	249905.			0.472831			0.236415	−	0.971652i	$-0.424027\pi$
$727$	249905.			0.472831			0.236415	+	0.971652i	$0.424027\pi$
$728$	−71031.4	−	97766.3i	−0.134026	−	0.184470i
$729$	26652.8	+	82028.8i	0.0501519	+	0.154352i
$730$	−70069.9	+	215653.i	−0.131488	+	0.404678i
$731$	311645.	+	226424.i	0.583211	+	0.423728i
$732$	−179442.	+	246981.i	−0.334890	+	0.460936i
$733$	−483123.	−	156976.i	−0.899187	−	0.292164i	−0.177285	−	0.984159i	$-0.556732\pi$
$733$	−483123.	−	156976.i	−0.899187	−	0.292164i	−0.721901	+	0.691996i	$0.756732\pi$
$734$	456931.	−	148466.i	0.848123	−	0.275572i
$735$	298669.	−	216996.i	0.552860	−	0.401676i
$736$		−	116633.i		−	0.215311i
$737$	−158982.	+	100361.i	−0.292694	+	0.184769i
$738$	−249485.			−0.458070
$739$	−360695.	−	496454.i	−0.660467	−	0.909055i	0.339029	−	0.940776i	$-0.389901\pi$
$739$	−360695.	−	496454.i	−0.660467	−	0.909055i	−0.999497	+	0.0317204i	$0.989901\pi$
$740$	−62839.3	−	193400.i	−0.114754	−	0.353177i
$741$	409205.	−	1.25940e6i	0.745254	−	2.29366i
$742$	−154282.	−	112092.i	−0.280225	−	0.203596i
$743$	19765.7	−	27205.1i	0.0358042	−	0.0492802i	−0.790740	−	0.612153i	$-0.790304\pi$
$743$	19765.7	−	27205.1i	0.0358042	−	0.0492802i	0.826544	+	0.562872i	$0.190304\pi$
$744$	346484.	+	112579.i	0.625947	+	0.203382i
$745$	599761.	−	194874.i	1.08060	−	0.351109i
$746$	166699.	−	121114.i	0.299541	−	0.217629i
$747$		−	141158.i		−	0.252967i
$748$	−242251.	−	96584.3i	−0.432974	−	0.172625i
$749$	−215368.			−0.383899
$750$	−308876.	−	425131.i	−0.549113	−	0.755789i
$751$	144056.	+	443358.i	0.255418	+	0.786094i	0.993747	+	0.111654i	$0.0356149\pi$
$751$	144056.	+	443358.i	0.255418	+	0.786094i	−0.738330	+	0.674440i	$0.764385\pi$
$752$	26200.1	−	80635.7i	0.0463306	−	0.142591i
$753$	557798.	+	405264.i	0.983755	+	0.714739i
$754$	164220.	−	226030.i	0.288858	−	0.397578i
$755$	−385444.	−	125238.i	−0.676187	−	0.219707i
$756$	−100386.	+	32617.5i	−0.175643	+	0.0570699i
$757$	−459637.	+	333946.i	−0.802090	+	0.582752i	−0.911526	−	0.411241i	$-0.865095\pi$
$757$	−459637.	+	333946.i	−0.802090	+	0.582752i	0.109437	+	0.993994i	$0.465095\pi$
$758$		−	443003.i		−	0.771024i
$759$	657153.	+	546296.i	1.14073	+	0.948297i
$760$	315082.			0.545503
$761$	−316316.	−	435371.i	−0.546200	−	0.751780i	0.443291	−	0.896378i	$-0.353811\pi$
$761$	−316316.	−	435371.i	−0.546200	−	0.751780i	−0.989490	+	0.144598i	$0.953811\pi$
$762$	53757.8	+	165449.i	0.0925831	+	0.284941i
$763$	112509.	−	346268.i	0.193259	−	0.594789i
$764$	−73858.1	−	53661.0i	−0.126535	−	0.0919332i
$765$	−132694.	+	182638.i	−0.226741	+	0.312082i
$766$	451297.	+	146635.i	0.769139	+	0.249908i
$767$	580545.	−	188630.i	0.986836	−	0.320642i
$768$	−36323.2	+	26390.3i	−0.0615830	+	0.0447427i
$769$			126061.i			0.213171i	0.994304	+	0.106586i	$0.0339918\pi$
$769$			126061.i			0.213171i	−0.994304	+	0.106586i	$0.966008\pi$
$770$	51906.1	+	204186.i	0.0875461	+	0.344385i
$771$	−378469.			−0.636680
$772$	39647.7	+	54570.4i	0.0665248	+	0.0915635i
$773$	−304231.	−	936328.i	−0.509149	−	1.56700i	−0.793682	−	0.608333i	$-0.791838\pi$
$773$	−304231.	−	936328.i	−0.509149	−	1.56700i	0.284532	−	0.958666i	$-0.408162\pi$
$774$	−48928.7	+	150587.i	−0.0816736	+	0.251365i
$775$	−198398.	−	144144.i	−0.330319	−	0.239991i
$776$	−170867.	+	235178.i	−0.283749	+	0.390546i
$777$	−356138.	−	115716.i	−0.589897	−	0.191669i
$778$	−412596.	+	134061.i	−0.681657	+	0.221484i
$779$	−1.18587e6	+	861583.i	−1.95416	+	1.41978i
$780$			348470.i			0.572765i
$781$	596053.	+	38931.2i	0.977199	+	0.0638258i
$782$	490981.			0.802881
$783$	−143438.	−	197425.i	−0.233959	−	0.322017i
$784$	31122.5	+	95785.4i	0.0506341	+	0.155836i
$785$	2921.27	−	8990.76i	0.00474060	−	0.0145901i
$786$	392946.	+	285492.i	0.636045	+	0.462114i
$787$	−122954.	+	169232.i	−0.198515	+	0.273232i	−0.896656	−	0.442728i	$-0.854011\pi$
$787$	−122954.	+	169232.i	−0.198515	+	0.273232i	0.698141	+	0.715960i	$0.254011\pi$
$788$	32835.2	+	10668.8i	0.0528795	+	0.0171816i
$789$	311012.	−	101054.i	0.499601	−	0.162330i
$790$	−219267.	+	159307.i	−0.351333	+	0.255258i
$791$			643974.i			1.02924i
$792$	6986.60	−	106968.i	0.0111382	−	0.170531i
$793$	−646407.			−1.02792
$794$	−364332.	−	501460.i	−0.577905	−	0.795417i
$795$	169932.	+	522996.i	0.268868	+	0.827492i
$796$	−111019.	+	341682.i	−0.175215	+	0.539258i
$797$	−69752.1	−	50677.9i	−0.109810	−	0.0797815i	0.531525	−	0.847042i	$-0.321619\pi$
$797$	−69752.1	−	50677.9i	−0.109810	−	0.0797815i	−0.641335	+	0.767261i	$0.721619\pi$
$798$	341040.	−	469402.i	0.535550	−	0.737121i
$799$	339446.	+	110293.i	0.531713	+	0.172764i
$800$	28743.1	−	9339.21i	0.0449112	−	0.0145925i
$801$	−303901.	+	220797.i	−0.473660	+	0.344134i
$802$			1906.95i			0.00296477i
$803$	439277.	−	111668.i	0.681251	−	0.173181i
$804$	−136255.			−0.210785
$805$	−233136.	−	320884.i	−0.359763	−	0.495172i
$806$	238374.	+	733641.i	0.366935	+	1.12931i
$807$	241240.	−	742460.i	0.370426	−	1.14006i
$808$	−57666.9	−	41897.5i	−0.0883292	−	0.0641749i
$809$	397338.	−	546889.i	0.607104	−	0.835608i	−0.389231	−	0.921140i	$-0.627259\pi$
$809$	397338.	−	546889.i	0.607104	−	0.835608i	0.996335	+	0.0855327i	$0.0272592\pi$
$810$	472051.	+	153379.i	0.719480	+	0.233773i
$811$	673133.	−	218714.i	1.02343	−	0.332534i	0.251242	−	0.967924i	$-0.419161\pi$
$811$	673133.	−	218714.i	1.02343	−	0.332534i	0.772191	+	0.635391i	$0.219161\pi$
$812$	99036.3	−	71954.1i	0.150204	−	0.109130i
$813$		−	730013.i		−	1.10446i
$814$	−259846.	+	312576.i	−0.392164	+	0.471744i
$815$	−235534.			−0.354599
$816$	−111093.	−	152907.i	−0.166843	−	0.229640i
$817$	287473.	+	884752.i	0.430679	+	1.32549i
$818$	−156220.	+	480796.i	−0.233470	+	0.718546i
$819$	169165.	+	122906.i	0.252199	+	0.183233i
$820$	226728.	−	312064.i	0.337192	−	0.464105i
$821$	1.04039e6	+	338044.i	1.54351	+	0.501518i	0.952343	−	0.305028i	$-0.0986657\pi$
$821$	1.04039e6	+	338044.i	1.54351	+	0.501518i	0.591171	+	0.806546i	$0.298666\pi$
$822$	129453.	−	42061.7i	0.191588	−	0.0622506i
$823$	690049.	−	501350.i	1.01878	−	0.740187i	0.0527476	−	0.998608i	$-0.483202\pi$
$823$	690049.	−	501350.i	1.01878	−	0.740187i	0.966032	+	0.258421i	$0.0832021\pi$
$824$			292747.i			0.431159i
$825$	−82009.1	+	205693.i	−0.120491	+	0.302212i
$826$	267460.			0.392011
$827$	−344937.	−	474765.i	−0.504346	−	0.694173i	0.478607	−	0.878029i	$-0.341142\pi$
$827$	−344937.	−	474765.i	−0.504346	−	0.694173i	−0.982953	+	0.183856i	$0.941142\pi$
$828$	62362.7	+	191933.i	0.0909629	+	0.279955i
$829$	−258768.	+	796405.i	−0.376531	+	1.15884i	0.565909	+	0.824468i	$0.308525\pi$
$829$	−258768.	+	796405.i	−0.376531	+	1.15884i	−0.942440	+	0.334375i	$0.891475\pi$
$830$	176565.	+	128282.i	0.256300	+	0.186213i
$831$	−590459.	+	812697.i	−0.855042	+	1.17686i
$832$	−90413.4	−	29377.1i	−0.130613	−	0.0424387i
$833$	−403221.	+	131014.i	−0.581102	+	0.188812i
$834$	10807.0	−	7851.77i	0.0155373	−	0.0112885i
$835$		−	802038.i		−	1.15033i
$836$	−336198.	−	532573.i	−0.481042	−	0.762021i
$837$	673774.			0.961752
$838$	−63482.0	−	87375.5i	−0.0903988	−	0.124423i
$839$	−2177.64	−	6702.07i	−0.00309358	−	0.00952106i	0.949498	−	0.313774i	$-0.101593\pi$
$839$	−2177.64	−	6702.07i	−0.00309358	−	0.00952106i	−0.952591	+	0.304253i	$0.901593\pi$
$840$	−47182.1	+	145211.i	−0.0668680	+	0.205799i
$841$	−343237.	−	249376.i	−0.485290	−	0.352584i
$842$	−348502.	+	479671.i	−0.491564	+	0.676580i
$843$	365400.	+	118726.i	0.514178	+	0.167066i
$844$	−630260.	+	204784.i	−0.884779	+	0.287482i
$845$	−102410.	+	74405.4i	−0.143427	+	0.104206i
$846$			146704.i			0.204975i
$847$	289744.	−	305605.i	0.403876	−	0.425984i
$848$	−150021.			−0.208622
$849$	336083.	+	462578.i	0.466263	+	0.641756i
$850$	39314.6	+	120998.i	0.0544147	+	0.167471i
$851$	236475.	−	727794.i	0.326532	−	1.00496i
$852$	350217.	+	254448.i	0.482457	+	0.350525i
$853$	−177004.	+	243625.i	−0.243268	+	0.334829i	−0.913139	−	0.407648i	$-0.866349\pi$
$853$	−177004.	+	243625.i	−0.243268	+	0.334829i	0.669872	+	0.742477i	$0.266349\pi$
$854$	−269365.	−	87522.0i	−0.369339	−	0.120006i
$855$	−518504.	+	168472.i	−0.709283	+	0.230460i
$856$	−137067.	+	99585.0i	−0.187062	+	0.135908i
$857$		−	22179.5i		−	0.0301988i	−0.999886	−	0.0150994i	$-0.995194\pi$
$857$		−	22179.5i		−	0.0301988i	0.999886	−	0.0150994i	$-0.00480647\pi$
$858$	589008.	−	371824.i	0.800104	−	0.505083i
$859$	518970.			0.703325			0.351663	−	0.936127i	$-0.385616\pi$
$859$	518970.			0.703325			0.351663	+	0.936127i	$0.385616\pi$
$860$	−143894.	−	198053.i	−0.194556	−	0.267783i
$861$	−219498.	−	675546.i	−0.296091	−	0.911273i
$862$	244878.	−	753656.i	0.329560	−	1.01428i
$863$	−527280.	−	383091.i	−0.707978	−	0.514376i	0.174543	−	0.984650i	$-0.444155\pi$
$863$	−527280.	−	383091.i	−0.707978	−	0.514376i	−0.882521	+	0.470273i	$0.844155\pi$
$864$	−48807.0	+	67177.0i	−0.0653814	+	0.0899898i
$865$	−565338.	−	183690.i	−0.755573	−	0.245500i
$866$	−948987.	+	308345.i	−1.26539	+	0.411150i
$867$	−96979.6	+	70459.8i	−0.129016	+	0.0937353i
$868$			337992.i			0.448608i
$869$	503232.	+	200637.i	0.666391	+	0.265687i
$870$	−352997.			−0.466372
$871$	−169578.	−	233405.i	−0.223529	−	0.307662i
$872$	−88508.1	−	272400.i	−0.116399	−	0.358240i
$873$	155433.	−	478373.i	0.203945	−	0.627679i
$874$	959256.	+	696940.i	1.25577	+	0.912374i
$875$	286559.	−	394414.i	0.374281	−	0.515153i
$876$	312401.	+	101505.i	0.407103	+	0.132276i
$877$	−42207.8	+	13714.1i	−0.0548774	+	0.0178307i	−0.336327	−	0.941745i	$-0.609185\pi$
$877$	−42207.8	+	13714.1i	−0.0548774	+	0.0178307i	0.281450	+	0.959576i	$0.409185\pi$
$878$	129197.	−	93867.4i	0.167596	−	0.121766i
$879$			1.50505e6i			1.94793i
$880$	127449.	+	105950.i	0.164578	+	0.136815i
$881$	−145958.			−0.188051			−0.0940254	−	0.995570i	$-0.529973\pi$
$881$	−145958.			−0.188051			−0.0940254	+	0.995570i	$0.529973\pi$
$882$	−102431.	−	140985.i	−0.131673	−	0.181232i
$883$	38325.2	+	117953.i	0.0491545	+	0.151282i	0.972621	−	0.232397i	$-0.0746569\pi$
$883$	38325.2	+	117953.i	0.0491545	+	0.151282i	−0.923467	+	0.383679i	$0.874657\pi$
$884$	123667.	−	380607.i	0.158252	−	0.487048i
$885$	−623950.	−	453326.i	−0.796642	−	0.578794i
$886$	427154.	−	587927.i	0.544148	−	0.748955i
$887$	−1.17770e6	−	382658.i	−1.49688	−	0.486367i	−0.557776	−	0.829991i	$-0.688345\pi$
$887$	−1.17770e6	−	382658.i	−1.49688	−	0.486367i	−0.939107	+	0.343625i	$0.888345\pi$
$888$	−280164.	+	91030.9i	−0.355293	+	0.115442i
$889$	−130571.	+	94865.2i	−0.165212	+	0.120034i
$890$		−	580786.i		−	0.733223i
$891$	−244435.	−	961549.i	−0.307899	−	1.21120i
$892$	174538.			0.219361
$893$	506635.	+	697323.i	0.635320	+	0.874443i
$894$	−282301.	−	868832.i	−0.353213	−	1.08708i
$895$	248028.	−	763351.i	0.309638	−	0.952967i
$896$	−33698.7	−	24483.5i	−0.0419756	−	0.0304970i
$897$	−770792.	+	1.06090e6i	−0.957971	+	1.31853i
$898$	19225.5	+	6246.73i	0.0238410	+	0.00774640i
$899$	−743171.	+	241471.i	−0.919537	+	0.298776i
$900$	−42306.5	+	30737.5i	−0.0522302	+	0.0379475i
$901$		−	631533.i		−	0.777940i
$902$	−769394.	−	50253.0i	−0.945661	−	0.0617659i
$903$	−450802.			−0.552854
$904$	297770.	+	409846.i	0.364372	+	0.501515i
$905$	279907.	+	861466.i	0.341757	+	1.05182i
$906$	−181424.	+	558365.i	−0.221023	+	0.680240i
$907$	231579.	+	168252.i	0.281504	+	0.204525i	0.719573	−	0.694417i	$-0.244337\pi$
$907$	231579.	+	168252.i	0.281504	+	0.204525i	−0.438069	+	0.898941i	$0.644337\pi$
$908$	−24966.8	+	34363.8i	−0.0302824	+	0.0416802i
$909$	117300.	+	38113.0i	0.141961	+	0.0461260i
$910$	−307469.	+	99902.8i	−0.371295	+	0.120641i
$911$	414649.	−	301260.i	0.499625	−	0.362999i	−0.309249	−	0.950981i	$-0.600078\pi$
$911$	414649.	−	301260.i	0.499625	−	0.362999i	0.808874	+	0.587982i	$0.200078\pi$
$912$		−	456438.i		−	0.548772i
$913$	28433.0	−	435321.i	0.0341099	−	0.522237i
$914$	644545.			0.771544
$915$	480051.	+	660734.i	0.573384	+	0.789195i
$916$	93718.0	+	288434.i	0.111695	+	0.343761i
$917$	−139247.	+	428559.i	−0.165595	+	0.509650i
$918$	−282790.	−	205459.i	−0.335567	−	0.243804i
$919$	89108.3	−	122647.i	0.105508	−	0.145220i	−0.752998	−	0.658023i	$-0.771393\pi$
$919$	89108.3	−	122647.i	0.105508	−	0.145220i	0.858506	+	0.512803i	$0.171393\pi$
$920$	−296750.	−	96420.0i	−0.350603	−	0.113918i
$921$	529971.	−	172198.i	0.624788	−	0.203006i
$922$	306697.	−	222828.i	0.360784	−	0.262125i
$923$			916601.i			1.07591i
$924$	295790.	−	75192.7i	0.346449	−	0.0880708i
$925$	198294.			0.231753
$926$	−195706.	−	269367.i	−0.228235	−	0.314139i
$927$	−156529.	−	481748.i	−0.182153	−	0.560610i
$928$	29758.7	−	91587.8i	0.0345555	−	0.106351i
$929$	−656429.	−	476923.i	−0.760600	−	0.552608i	0.138495	−	0.990363i	$-0.455774\pi$
$929$	−656429.	−	476923.i	−0.760600	−	0.552608i	−0.899094	+	0.437755i	$0.855774\pi$
$930$	572874.	−	788493.i	0.662358	−	0.911658i
$931$	−973767.	−	316396.i	−1.12345	−	0.365033i
$932$	147904.	−	48056.9i	0.170274	−	0.0553253i
$933$	698544.	−	507522.i	0.802473	−	0.583031i
$934$			367811.i			0.421630i
$935$	−446008.	+	536515.i	−0.510175	+	0.613703i
$936$	164493.			0.187757
$937$	224637.	+	309186.i	0.255860	+	0.352161i	0.917553	−	0.397614i	$-0.130162\pi$
$937$	224637.	+	309186.i	0.255860	+	0.352161i	−0.661693	+	0.749775i	$0.730162\pi$
$938$	−39062.8	−	120223.i	−0.0443974	−	0.136641i
$939$	−459598.	+	1.41450e6i	−0.521251	+	1.60424i
$940$	−183502.	−	133322.i	−0.207676	−	0.150885i
$941$	−640588.	+	881693.i	−0.723435	+	0.995723i	0.275968	+	0.961167i	$0.411002\pi$
$941$	−640588.	+	881693.i	−0.723435	+	0.995723i	−0.999403	+	0.0345558i	$0.988998\pi$
$942$	−13024.3	−	4231.84i	−0.0146775	−	0.00476901i
$943$	1.38053e6	−	448561.i	1.55246	−	0.504426i
$944$	170220.	−	123672.i	0.191015	−	0.138780i
$945$			282379.i			0.316205i
$946$	−181225.	+	454544.i	−0.202505	+	0.507918i
$947$	−129631.			−0.144547			−0.0722735	−	0.997385i	$-0.523025\pi$
$947$	−129631.			−0.144547			−0.0722735	+	0.997385i	$0.523025\pi$
$948$	230777.	+	317637.i	0.256788	+	0.353439i
$949$	214926.	+	661475.i	0.238648	+	0.734482i
$950$	−94943.7	+	292207.i	−0.105201	+	0.323775i
$951$	399526.	+	290273.i	0.441758	+	0.320956i
$952$	103066.	−	141859.i	0.113722	−	0.156525i
$953$	1.47612e6	+	479621.i	1.62531	+	0.528096i	0.973187	−	0.230016i	$-0.0738779\pi$
$953$	1.47612e6	+	479621.i	1.62531	+	0.528096i	0.652125	+	0.758112i	$0.273878\pi$
$954$	246877.	−	80215.1i	0.271259	−	0.0881372i
$955$	−197588.	+	143556.i	−0.216648	+	0.157404i
$956$		−	58790.3i		−	0.0643265i
$957$	376653.	+	596659.i	0.411261	+	0.651482i
$958$	−327270.			−0.356595
$959$	74225.4	+	102163.i	0.0807078	+	0.111085i
$960$	37116.9	+	114234.i	0.0402744	+	0.123952i
$961$	381322.	−	1.17359e6i	0.412900	−	1.27078i
$962$	−504621.	−	366628.i	−0.545274	−	0.396165i
$963$	172312.	−	237167.i	0.185807	−	0.255742i
$964$	−336274.	−	109262.i	−0.361859	−	0.117575i
$965$	171620.	−	55762.9i	0.184295	−	0.0598812i
$966$	−464842.	+	337727.i	−0.498139	+	0.361919i
$967$		−	477795.i		−	0.510962i	−0.966814	−	0.255481i	$-0.917766\pi$
$967$		−	477795.i		−	0.510962i	0.966814	−	0.255481i	$-0.0822338\pi$
$968$	43092.3	−	328473.i	0.0459885	−	0.350550i
$969$	1.92143e6			2.04634
$970$	457110.	+	629158.i	0.485822	+	0.668677i
$971$	−64875.3	−	199666.i	−0.0688083	−	0.211770i	0.910740	−	0.412981i	$-0.135512\pi$
$971$	−64875.3	−	199666.i	−0.0688083	−	0.211770i	−0.979548	+	0.201211i	$0.935512\pi$
$972$	130335.	−	401131.i	0.137952	−	0.424574i
$973$	10026.2	+	7284.45i	0.0105903	+	0.00769434i
$974$	−387394.	+	533203.i	−0.408353	+	0.562049i
$975$	−323170.	−	105004.i	−0.339956	−	0.110458i
$976$	−211902.	+	68851.3i	−0.222452	+	0.0722790i
$977$	1.00801e6	−	732365.i	1.05603	−	0.767252i	0.0826822	−	0.996576i	$-0.473651\pi$
$977$	1.00801e6	−	732365.i	1.05603	−	0.767252i	0.973350	+	0.229323i	$0.0736514\pi$
$978$			341201.i			0.356724i
$979$	−981683.	+	619708.i	−1.02425	+	0.646579i
$980$	269436.			0.280546
$981$	291300.	+	400941.i	0.302693	+	0.416622i
$982$	−147445.	−	453788.i	−0.152899	−	0.470576i
$983$	−159381.	+	490524.i	−0.164941	+	0.507637i	−0.999032	−	0.0439902i	$-0.985993\pi$
$983$	−159381.	+	490524.i	−0.164941	+	0.507637i	0.834091	+	0.551627i	$0.185993\pi$
$984$	−452065.	−	328445.i	−0.466886	−	0.339213i
$985$	54289.5	−	74723.0i	0.0559555	−	0.0770162i
$986$	385551.	+	125273.i	0.396577	+	0.128856i
$987$	−397240.	+	129071.i	−0.407773	+	0.132494i
$988$	781880.	−	568069.i	0.800988	−	0.581952i
$989$		−	921246.i		−	0.941853i
$990$	−266383.	−	106206.i	−0.271792	−	0.108362i
$991$	−1.65389e6			−1.68407			−0.842035	−	0.539423i	$-0.818642\pi$
$991$	−1.65389e6			−1.68407			−0.842035	+	0.539423i	$0.818642\pi$
$992$	156286.	+	215109.i	0.158817	+	0.218592i
$993$	−458045.	−	1.40972e6i	−0.464525	−	1.42966i
$994$	−124106.	+	381958.i	−0.125608	+	0.386583i
$995$	777566.	+	564935.i	0.785400	+	0.570627i
$996$	185833.	−	255777.i	0.187329	−	0.257836i
$997$	562636.	+	182812.i	0.566027	+	0.183913i	0.578031	−	0.816015i	$-0.303821\pi$
$997$	562636.	+	182812.i	0.566027	+	0.183913i	−0.0120041	+	0.999928i	$0.503821\pi$
$998$	1.17476e6	−	381703.i	1.17947	−	0.383235i
$999$	−440759.	+	320230.i	−0.441642	+	0.320872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.5.d.a.19.2	yes	16
3.2	odd	2		198.5.j.a.19.3		16
4.3	odd	2		176.5.n.c.129.1		16
11.2	odd	10		242.5.b.e.241.7		16
11.7	odd	10	inner	22.5.d.a.7.2	✓	16
11.9	even	5		242.5.b.e.241.15		16
33.29	even	10		198.5.j.a.73.3		16
44.7	even	10		176.5.n.c.161.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.d.a.7.2	✓	16	11.7	odd	10	inner
22.5.d.a.19.2	yes	16	1.1	even	1	trivial
176.5.n.c.129.1		16	4.3	odd	2
176.5.n.c.161.1		16	44.7	even	10
198.5.j.a.19.3		16	3.2	odd	2
198.5.j.a.73.3		16	33.29	even	10
242.5.b.e.241.7		16	11.2	odd	10
242.5.b.e.241.15		16	11.9	even	5

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	22.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66251 - 2.28825i) q^{2} +(3.38726 + 10.4249i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(17.3145 + 12.5798i) q^{5} +(18.2234 - 25.0824i) q^{6} +(27.3556 + 8.88838i) q^{7} +(21.5200 - 6.99226i) q^{8} +(-31.6748 + 23.0131i) q^{9} +O(q^{10})\)	\(q+(-1.66251 - 2.28825i) q^{2} +(3.38726 + 10.4249i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(17.3145 + 12.5798i) q^{5} +(18.2234 - 25.0824i) q^{6} +(27.3556 + 8.88838i) q^{7} +(21.5200 - 6.99226i) q^{8} +(-31.6748 + 23.0131i) q^{9} -60.5339i q^{10} +(-102.318 + 64.5906i) q^{11} -87.6912 q^{12} +(-109.138 - 150.215i) q^{13} +(-25.1401 - 77.3734i) q^{14} +(-72.4939 + 223.113i) q^{15} +(-51.7771 - 37.6183i) q^{16} +(158.359 - 217.962i) q^{17} +(105.319 + 34.2203i) q^{18} +(618.788 - 201.057i) q^{19} +(-138.516 + 100.638i) q^{20} +315.287i q^{21} +(317.904 + 126.747i) q^{22} -644.312 q^{23} +(145.787 + 200.659i) q^{24} +(-51.5923 - 158.785i) q^{25} +(-162.287 + 499.468i) q^{26} +(371.104 + 269.623i) q^{27} +(-135.254 + 186.161i) q^{28} +(-505.956 - 164.395i) q^{29} +(631.060 - 205.044i) q^{30} +(1188.32 - 863.365i) q^{31} +181.019i q^{32} +(-1019.93 - 847.875i) q^{33} -762.024 q^{34} +(361.836 + 498.025i) q^{35} +(-96.7896 - 297.888i) q^{36} +(-367.019 + 1129.57i) q^{37} +(-1488.81 - 1081.68i) q^{38} +(1196.30 - 1646.57i) q^{39} +(460.569 + 149.648i) q^{40} +(-2142.64 + 696.185i) q^{41} +(721.454 - 524.167i) q^{42} +1429.81i q^{43} +(-238.490 - 938.161i) q^{44} -837.934 q^{45} +(1071.17 + 1474.34i) q^{46} +(409.377 + 1259.93i) q^{47} +(216.785 - 667.194i) q^{48} +(-1273.12 - 924.978i) q^{49} +(-277.566 + 382.037i) q^{50} +(2808.64 + 912.582i) q^{51} +(1412.71 - 459.017i) q^{52} +(1896.40 - 1377.82i) q^{53} -1297.43i q^{54} +(-2584.13 - 168.783i) q^{55} +650.841 q^{56} +(4191.99 + 5769.78i) q^{57} +(464.979 + 1431.06i) q^{58} +(-1015.91 + 3126.65i) q^{59} +(-1518.33 - 1103.13i) q^{60} +(2046.30 - 2816.48i) q^{61} +(-3951.18 - 1283.82i) q^{62} +(-1071.03 + 348.000i) q^{63} +(414.217 - 300.946i) q^{64} -3973.84i q^{65} +(-244.503 + 3743.45i) q^{66} +1553.80 q^{67} +(1266.87 + 1743.70i) q^{68} +(-2182.45 - 6716.89i) q^{69} +(538.048 - 1655.94i) q^{70} +(-3993.76 - 2901.63i) q^{71} +(-520.727 + 716.719i) q^{72} +(-3562.52 - 1157.53i) q^{73} +(3194.90 - 1038.09i) q^{74} +(1480.56 - 1075.69i) q^{75} +5205.06i q^{76} +(-3373.09 + 857.472i) q^{77} -5756.62 q^{78} +(-2631.70 - 3622.22i) q^{79} +(-423.268 - 1302.69i) q^{80} +(-2533.76 + 7798.12i) q^{81} +(5155.20 + 3745.47i) q^{82} +(-2119.18 + 2916.80i) q^{83} +(-2398.85 - 779.432i) q^{84} +(5483.82 - 1781.80i) q^{85} +(3271.77 - 2377.08i) q^{86} -5831.39i q^{87} +(-1750.25 + 2105.42i) q^{88} +9594.39 q^{89} +(1393.07 + 1917.40i) q^{90} +(-1650.36 - 5079.29i) q^{91} +(1592.83 - 4902.22i) q^{92} +(13025.7 + 9463.69i) q^{93} +(2202.44 - 3031.40i) q^{94} +(13243.3 + 4303.00i) q^{95} +(-1887.11 + 613.159i) q^{96} +(-10393.5 + 7551.31i) q^{97} +4451.00i q^{98} +(1754.49 - 4400.56i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9} - 30 q^{11} - 384 q^{12} - 510 q^{13} - 96 q^{14} - 1398 q^{15} - 256 q^{16} + 1770 q^{17} + 1120 q^{18} + 1020 q^{19} - 240 q^{20} + 240 q^{22} - 2424 q^{23} - 640 q^{24} - 858 q^{25} + 480 q^{26} + 2224 q^{27} + 1600 q^{28} + 4890 q^{29} + 3360 q^{30} + 602 q^{31} - 2648 q^{33} - 3904 q^{34} - 8670 q^{35} + 720 q^{36} - 4518 q^{37} - 4800 q^{38} - 1130 q^{39} - 1280 q^{40} + 1290 q^{41} - 3808 q^{42} + 720 q^{44} + 12152 q^{45} + 4480 q^{46} + 642 q^{47} - 128 q^{48} + 9534 q^{49} + 6720 q^{50} - 1500 q^{51} + 4000 q^{52} + 2598 q^{53} + 2582 q^{55} - 3072 q^{56} + 9140 q^{57} - 6496 q^{58} + 6660 q^{59} - 5776 q^{60} - 27410 q^{61} - 19680 q^{62} - 27260 q^{63} + 2048 q^{64} + 2528 q^{66} + 21524 q^{67} + 14160 q^{68} + 11416 q^{69} + 34400 q^{70} - 5562 q^{71} + 10240 q^{72} - 7790 q^{73} + 5760 q^{74} + 3576 q^{75} - 1110 q^{77} - 39424 q^{78} - 2770 q^{79} - 3840 q^{80} - 25464 q^{81} - 17472 q^{82} - 36900 q^{83} - 24480 q^{84} - 24750 q^{85} + 624 q^{86} - 5760 q^{88} + 46596 q^{89} + 55360 q^{90} + 32370 q^{91} + 14112 q^{92} + 20722 q^{93} + 58880 q^{94} + 74250 q^{95} - 3732 q^{97} + 45802 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9 - 30 * q^11 - 384 * q^12 - 510 * q^13 - 96 * q^14 - 1398 * q^15 - 256 * q^16 + 1770 * q^17 + 1120 * q^18 + 1020 * q^19 - 240 * q^20 + 240 * q^22 - 2424 * q^23 - 640 * q^24 - 858 * q^25 + 480 * q^26 + 2224 * q^27 + 1600 * q^28 + 4890 * q^29 + 3360 * q^30 + 602 * q^31 - 2648 * q^33 - 3904 * q^34 - 8670 * q^35 + 720 * q^36 - 4518 * q^37 - 4800 * q^38 - 1130 * q^39 - 1280 * q^40 + 1290 * q^41 - 3808 * q^42 + 720 * q^44 + 12152 * q^45 + 4480 * q^46 + 642 * q^47 - 128 * q^48 + 9534 * q^49 + 6720 * q^50 - 1500 * q^51 + 4000 * q^52 + 2598 * q^53 + 2582 * q^55 - 3072 * q^56 + 9140 * q^57 - 6496 * q^58 + 6660 * q^59 - 5776 * q^60 - 27410 * q^61 - 19680 * q^62 - 27260 * q^63 + 2048 * q^64 + 2528 * q^66 + 21524 * q^67 + 14160 * q^68 + 11416 * q^69 + 34400 * q^70 - 5562 * q^71 + 10240 * q^72 - 7790 * q^73 + 5760 * q^74 + 3576 * q^75 - 1110 * q^77 - 39424 * q^78 - 2770 * q^79 - 3840 * q^80 - 25464 * q^81 - 17472 * q^82 - 36900 * q^83 - 24480 * q^84 - 24750 * q^85 + 624 * q^86 - 5760 * q^88 + 46596 * q^89 + 55360 * q^90 + 32370 * q^91 + 14112 * q^92 + 20722 * q^93 + 58880 * q^94 + 74250 * q^95 - 3732 * q^97 + 45802 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more