LMFDB - Embedded newform 22.5.d.a.19.1

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			19.1
Root			$-0.309017 + 2.89265i$ of defining polynomial
Character	$\chi$	$=$	22.19
Dual form			22.5.d.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66251 - 2.28825i) q^{2} +(-1.86966 - 5.75422i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(-23.9466 - 17.3982i) q^{5} +(-10.0587 + 13.8447i) q^{6} +(-38.7210 - 12.5812i) q^{7} +(21.5200 - 6.99226i) q^{8} +(35.9150 - 26.0937i) q^{9} +O(q^{10})$	\(q+(-1.66251 - 2.28825i) q^{2} +(-1.86966 - 5.75422i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(-23.9466 - 17.3982i) q^{5} +(-10.0587 + 13.8447i) q^{6} +(-38.7210 - 12.5812i) q^{7} +(21.5200 - 6.99226i) q^{8} +(35.9150 - 26.0937i) q^{9} +83.7204i q^{10} +(107.823 - 54.9105i) q^{11} +48.4028 q^{12} +(40.3008 + 55.4694i) q^{13} +(35.5851 + 109.520i) q^{14} +(-55.3412 + 170.323i) q^{15} +(-51.7771 - 37.6183i) q^{16} +(207.880 - 286.122i) q^{17} +(-119.418 - 38.8012i) q^{18} +(-171.839 + 55.8338i) q^{19} +(191.573 - 139.186i) q^{20} +246.332i q^{21} +(-304.906 - 155.437i) q^{22} -686.876 q^{23} +(-80.4700 - 110.757i) q^{24} +(77.6058 + 238.846i) q^{25} +(59.9270 - 184.436i) q^{26} +(-613.779 - 445.937i) q^{27} +(191.447 - 263.504i) q^{28} +(1237.04 + 401.939i) q^{29} +(481.745 - 156.529i) q^{30} +(257.323 - 186.956i) q^{31} +181.019i q^{32} +(-517.560 - 517.774i) q^{33} -1000.32 q^{34} +(708.346 + 974.954i) q^{35} +(109.746 + 337.765i) q^{36} +(-644.786 + 1984.45i) q^{37} +(413.444 + 300.385i) q^{38} +(243.834 - 335.609i) q^{39} +(-636.983 - 206.968i) q^{40} +(2400.32 - 779.910i) q^{41} +(563.668 - 409.528i) q^{42} -749.193i q^{43} +(151.230 + 956.114i) q^{44} -1314.03 q^{45} +(1141.94 + 1571.74i) q^{46} +(-955.900 - 2941.96i) q^{47} +(-119.658 + 368.270i) q^{48} +(-601.420 - 436.958i) q^{49} +(417.519 - 574.665i) q^{50} +(-2035.07 - 661.236i) q^{51} +(-521.665 + 169.499i) q^{52} +(2677.53 - 1945.34i) q^{53} +2145.85i q^{54} +(-3537.34 - 561.012i) q^{55} -921.245 q^{56} +(642.560 + 884.407i) q^{57} +(-1136.85 - 3498.88i) q^{58} +(-1902.96 + 5856.70i) q^{59} +(-1159.08 - 842.122i) q^{60} +(1373.23 - 1890.09i) q^{61} +(-855.604 - 278.003i) q^{62} +(-1718.95 + 558.522i) q^{63} +(414.217 - 300.946i) q^{64} -2029.47i q^{65} +(-324.348 + 2045.11i) q^{66} +6271.22 q^{67} +(1663.04 + 2288.98i) q^{68} +(1284.22 + 3952.44i) q^{69} +(1053.30 - 3241.74i) q^{70} +(382.526 + 277.922i) q^{71} +(590.434 - 812.663i) q^{72} +(3786.21 + 1230.22i) q^{73} +(5612.86 - 1823.73i) q^{74} +(1229.28 - 893.122i) q^{75} -1445.45i q^{76} +(-4865.86 + 769.643i) q^{77} -1173.33 q^{78} +(5588.59 + 7692.04i) q^{79} +(585.394 + 1801.66i) q^{80} +(-307.278 + 945.705i) q^{81} +(-5775.17 - 4195.91i) q^{82} +(422.074 - 580.935i) q^{83} +(-1874.20 - 608.966i) q^{84} +(-9956.03 + 3234.91i) q^{85} +(-1714.34 + 1245.54i) q^{86} -7869.69i q^{87} +(1936.40 - 1935.60i) q^{88} -5922.27 q^{89} +(2184.58 + 3006.81i) q^{90} +(-862.617 - 2654.86i) q^{91} +(1698.05 - 5226.06i) q^{92} +(-1556.89 - 1131.15i) q^{93} +(-5142.73 + 7078.37i) q^{94} +(5086.36 + 1652.66i) q^{95} +(1041.63 - 338.445i) q^{96} +(1156.41 - 840.179i) q^{97} +2102.64i q^{98} +(2439.64 - 4785.62i) 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
$3$	−1.86966	−	5.75422i	−0.207740	−	0.639358i	−0.999590	−	0.0286419i	$-0.990882\pi$
$3$	−1.86966	−	5.75422i	−0.207740	−	0.639358i	0.791850	−	0.610716i	$-0.209118\pi$
$4$	−2.47214	+	7.60845i	−0.154508	+	0.475528i
$5$	−23.9466	−	17.3982i	−0.957864	−	0.695929i	−0.00521030	−	0.999986i	$-0.501658\pi$
$5$	−23.9466	−	17.3982i	−0.957864	−	0.695929i	−0.952654	+	0.304058i	$0.901658\pi$
$6$	−10.0587	+	13.8447i	−0.279410	+	0.384574i
$7$	−38.7210	−	12.5812i	−0.790225	−	0.256760i	−0.114025	−	0.993478i	$-0.536374\pi$
$7$	−38.7210	−	12.5812i	−0.790225	−	0.256760i	−0.676200	+	0.736718i	$0.736374\pi$
$8$	21.5200	−	6.99226i	0.336249	−	0.109254i
$9$	35.9150	−	26.0937i	0.443395	−	0.322145i
$10$			83.7204i			0.837204i
$11$	107.823	−	54.9105i	0.891101	−	0.453806i
$11$	107.823	−	54.9105i	0.891101	−	0.453806i
$12$	48.4028			0.336130
$13$	40.3008	+	55.4694i	0.238467	+	0.328221i	0.911430	−	0.411454i	$-0.134979\pi$
$13$	40.3008	+	55.4694i	0.238467	+	0.328221i	−0.672964	+	0.739675i	$0.734979\pi$
$14$	35.5851	+	109.520i	0.181556	+	0.558773i
$15$	−55.3412	+	170.323i	−0.245961	+	0.756990i
$16$	−51.7771	−	37.6183i	−0.202254	−	0.146946i
$17$	207.880	−	286.122i	0.719308	−	0.990042i	−0.280239	−	0.959930i	$-0.590414\pi$
$17$	207.880	−	286.122i	0.719308	−	0.990042i	0.999547	−	0.0301118i	$-0.00958634\pi$
$18$	−119.418	−	38.8012i	−0.368573	−	0.119757i
$19$	−171.839	+	55.8338i	−0.476007	+	0.154664i	−0.537188	−	0.843463i	$-0.680513\pi$
$19$	−171.839	+	55.8338i	−0.476007	+	0.154664i	0.0611806	+	0.998127i	$0.480513\pi$
$20$	191.573	−	139.186i	0.478932	−	0.347964i
$21$			246.332i			0.558575i
$22$	−304.906	−	155.437i	−0.629970	−	0.321150i
$23$	−686.876			−1.29844			−0.649221	−	0.760599i	$-0.724905\pi$
$23$	−686.876			−1.29844			−0.649221	+	0.760599i	$0.724905\pi$
$24$	−80.4700	−	110.757i	−0.139705	−	0.192287i
$25$	77.6058	+	238.846i	0.124169	+	0.382154i
$26$	59.9270	−	184.436i	0.0886495	−	0.272835i
$27$	−613.779	−	445.937i	−0.841947	−	0.611710i
$28$	191.447	−	263.504i	0.244193	−	0.336103i
$29$	1237.04	+	401.939i	1.47092	+	0.477930i	0.931385	−	0.364036i	$-0.118602\pi$
$29$	1237.04	+	401.939i	1.47092	+	0.477930i	0.539531	+	0.841966i	$0.318602\pi$
$30$	481.745	−	156.529i	0.535273	−	0.173921i
$31$	257.323	−	186.956i	0.267766	−	0.194543i	−0.445798	−	0.895134i	$-0.647080\pi$
$31$	257.323	−	186.956i	0.267766	−	0.194543i	0.713564	+	0.700590i	$0.247080\pi$
$32$			181.019i			0.176777i
$33$	−517.560	−	517.774i	−0.475261	−	0.475458i
$34$	−1000.32			−0.865329
$35$	708.346	+	974.954i	0.578241	+	0.795881i
$36$	109.746	+	337.765i	0.0846808	+	0.260621i
$37$	−644.786	+	1984.45i	−0.470991	+	1.44956i	0.380299	+	0.924864i	$0.375821\pi$
$37$	−644.786	+	1984.45i	−0.470991	+	1.44956i	−0.851290	+	0.524696i	$0.824179\pi$
$38$	413.444	+	300.385i	0.286319	+	0.208023i
$39$	243.834	−	335.609i	0.160312	−	0.220650i
$40$	−636.983	−	206.968i	−0.398114	−	0.129355i
$41$	2400.32	−	779.910i	1.42791	−	0.463956i	0.509804	−	0.860291i	$-0.329718\pi$
$41$	2400.32	−	779.910i	1.42791	−	0.463956i	0.918106	+	0.396335i	$0.129718\pi$
$42$	563.668	−	409.528i	0.319539	−	0.232159i
$43$		−	749.193i		−	0.405188i	−0.979263	−	0.202594i	$-0.935063\pi$
$43$		−	749.193i		−	0.405188i	0.979263	−	0.202594i	$-0.0649372\pi$
$44$	151.230	+	956.114i	0.0781149	+	0.493860i
$45$	−1314.03			−0.648902
$46$	1141.94	+	1571.74i	0.539668	+	0.742789i
$47$	−955.900	−	2941.96i	−0.432730	−	1.33181i	−0.895395	−	0.445273i	$-0.853107\pi$
$47$	−955.900	−	2941.96i	−0.432730	−	1.33181i	0.462665	−	0.886533i	$-0.346893\pi$
$48$	−119.658	+	368.270i	−0.0519350	+	0.159839i
$49$	−601.420	−	436.958i	−0.250487	−	0.181990i
$50$	417.519	−	574.665i	0.167007	−	0.229866i
$51$	−2035.07	−	661.236i	−0.782420	−	0.254224i
$52$	−521.665	+	169.499i	−0.192924	+	0.0626846i
$53$	2677.53	−	1945.34i	0.953196	−	0.692537i	0.00163536	−	0.999999i	$-0.499479\pi$
$53$	2677.53	−	1945.34i	0.953196	−	0.692537i	0.951561	+	0.307461i	$0.0994794\pi$
$54$			2145.85i			0.735889i
$55$	−3537.34	−	561.012i	−1.16937	−	0.185458i
$56$	−921.245			−0.293764
$57$	642.560	+	884.407i	0.197771	+	0.272209i
$58$	−1136.85	−	3498.88i	−0.337947	−	1.04009i
$59$	−1902.96	+	5856.70i	−0.546670	+	1.68248i	0.170317	+	0.985389i	$0.445521\pi$
$59$	−1902.96	+	5856.70i	−0.546670	+	1.68248i	−0.716986	+	0.697087i	$0.754479\pi$
$60$	−1159.08	−	842.122i	−0.321967	−	0.233923i
$61$	1373.23	−	1890.09i	0.369049	−	0.507952i	−0.583593	−	0.812046i	$-0.698354\pi$
$61$	1373.23	−	1890.09i	0.369049	−	0.507952i	0.952642	+	0.304094i	$0.0983537\pi$
$62$	−855.604	−	278.003i	−0.222582	−	0.0723212i
$63$	−1718.95	+	558.522i	−0.433095	+	0.140721i
$64$	414.217	−	300.946i	0.101127	−	0.0734732i
$65$		−	2029.47i		−	0.480347i
$66$	−324.348	+	2045.11i	−0.0744600	+	0.469492i
$67$	6271.22			1.39702			0.698509	−	0.715601i	$-0.253847\pi$
$67$	6271.22			1.39702			0.698509	+	0.715601i	$0.253847\pi$
$68$	1663.04	+	2288.98i	0.359654	+	0.495021i
$69$	1284.22	+	3952.44i	0.269738	+	0.830169i
$70$	1053.30	−	3241.74i	0.214960	−	0.661579i
$71$	382.526	+	277.922i	0.0758830	+	0.0551322i	0.625080	−	0.780561i	$-0.285066\pi$
$71$	382.526	+	277.922i	0.0758830	+	0.0551322i	−0.549197	+	0.835693i	$0.685066\pi$
$72$	590.434	−	812.663i	0.113895	−	0.156764i
$73$	3786.21	+	1230.22i	0.710492	+	0.230853i	0.641896	−	0.766792i	$-0.278148\pi$
$73$	3786.21	+	1230.22i	0.710492	+	0.230853i	0.0685962	+	0.997645i	$0.478148\pi$
$74$	5612.86	−	1823.73i	1.02499	−	0.333041i
$75$	1229.28	−	893.122i	0.218538	−	0.158777i
$76$		−	1445.45i		−	0.250252i
$77$	−4865.86	+	769.643i	−0.820689	+	0.129810i
$78$	−1173.33			−0.192855
$79$	5588.59	+	7692.04i	0.895464	+	1.23250i	0.971892	+	0.235426i	$0.0756484\pi$
$79$	5588.59	+	7692.04i	0.895464	+	1.23250i	−0.0764281	+	0.997075i	$0.524352\pi$
$80$	585.394	+	1801.66i	0.0914679	+	0.281509i
$81$	−307.278	+	945.705i	−0.0468340	+	0.144140i
$82$	−5775.17	−	4195.91i	−0.858889	−	0.624019i
$83$	422.074	−	580.935i	0.0612678	−	0.0843279i	−0.777284	−	0.629150i	$-0.783403\pi$
$83$	422.074	−	580.935i	0.0612678	−	0.0843279i	0.838551	+	0.544822i	$0.183403\pi$
$84$	−1874.20	−	608.966i	−0.265618	−	0.0863047i
$85$	−9956.03	+	3234.91i	−1.37800	+	0.447739i
$86$	−1714.34	+	1245.54i	−0.231793	+	0.168407i
$87$		−	7869.69i		−	1.03973i
$88$	1936.40	−	1935.60i	0.250052	−	0.249948i
$89$	−5922.27			−0.747666			−0.373833	−	0.927496i	$-0.621957\pi$
$89$	−5922.27			−0.747666			−0.373833	+	0.927496i	$0.621957\pi$
$90$	2184.58	+	3006.81i	0.269701	+	0.371212i
$91$	−862.617	−	2654.86i	−0.104168	−	0.320597i
$92$	1698.05	−	5226.06i	0.200620	−	0.617446i
$93$	−1556.89	−	1131.15i	−0.180009	−	0.130784i
$94$	−5142.73	+	7078.37i	−0.582021	+	0.801083i
$95$	5086.36	+	1652.66i	0.563586	+	0.183120i
$96$	1041.63	−	338.445i	0.113024	−	0.0367236i
$97$	1156.41	−	840.179i	0.122904	−	0.0892953i	−0.524635	−	0.851327i	$-0.675798\pi$
$97$	1156.41	−	840.179i	0.122904	−	0.0892953i	0.647539	+	0.762032i	$0.275798\pi$
$98$			2102.64i			0.218934i
$99$	2439.64	−	4785.62i	0.248918	−	0.488279i
$100$	−2009.10			−0.200910
$101$	−9915.96	−	13648.1i	−0.972058	−	1.33792i	−0.941001	−	0.338405i	$-0.890113\pi$
$101$	−9915.96	−	13648.1i	−0.972058	−	1.33792i	−0.0310569	−	0.999518i	$-0.509887\pi$
$102$	1870.26	+	5756.06i	0.179763	+	0.553255i
$103$	1299.24	−	3998.66i	0.122466	−	0.376912i	−0.870965	−	0.491345i	$-0.836505\pi$
$103$	1299.24	−	3998.66i	0.122466	−	0.376912i	0.993431	+	0.114433i	$0.0365053\pi$
$104$	1255.13	+	911.904i	0.116044	+	0.0843107i
$105$	4285.74	−	5898.81i	0.388729	−	0.535039i
$106$	−8902.82	−	2892.70i	−0.792348	−	0.257449i
$107$	−5868.10	+	1906.66i	−0.512543	+	0.166535i	−0.553858	−	0.832611i	$-0.686845\pi$
$107$	−5868.10	+	1906.66i	−0.512543	+	0.166535i	0.0413156	+	0.999146i	$0.486845\pi$
$108$	4910.23	−	3567.49i	0.420973	−	0.305855i
$109$			19827.2i			1.66881i	0.551148	+	0.834407i	$0.314190\pi$
$109$			19827.2i			1.66881i	−0.551148	+	0.834407i	$0.685810\pi$
$110$	4597.13	+	9027.00i	0.379928	+	0.746033i
$111$	12624.5			1.02463
$112$	1531.58	+	2108.04i	0.122096	+	0.168051i
$113$	−3452.66	−	10626.2i	−0.270394	−	0.832187i	−0.990401	−	0.138221i	$-0.955862\pi$
$113$	−3452.66	−	10626.2i	−0.270394	−	0.832187i	0.720007	−	0.693966i	$-0.244138\pi$
$114$	955.481	−	2940.67i	0.0735212	−	0.226275i
$115$	16448.3	+	11950.4i	1.24373	+	0.903624i
$116$	−6116.26	+	8418.31i	−0.454538	+	0.625618i
$117$	2894.81	+	940.580i	0.211470	+	0.0687106i
$118$	16565.3	−	5382.38i	1.18969	−	0.386554i
$119$	−11649.1	+	8463.56i	−0.822617	+	0.597667i
$120$			4052.30i			0.281410i
$121$	8610.67	−	11841.2i	0.588121	−	0.808773i
$122$	−6607.99			−0.443966
$123$	−8975.55	−	12353.8i	−0.593268	−	0.816563i
$124$	786.310	+	2420.01i	0.0511388	+	0.157389i
$125$	−3419.64	+	10524.6i	−0.218857	+	0.673572i
$126$	4135.81	+	3004.84i	0.260507	+	0.189269i
$127$	−2505.05	+	3447.91i	−0.155313	+	0.213771i	−0.879582	−	0.475747i	$-0.842178\pi$
$127$	−2505.05	+	3447.91i	−0.155313	+	0.213771i	0.724268	+	0.689518i	$0.242178\pi$
$128$	−1377.28	−	447.504i	−0.0840623	−	0.0273135i
$129$	−4311.02	+	1400.74i	−0.259060	+	0.0841738i
$130$	−4643.92	+	3374.00i	−0.274788	+	0.199645i
$131$		−	14453.4i		−	0.842223i	−0.907009	−	0.421111i	$-0.861640\pi$
$131$		−	14453.4i		−	0.842223i	0.907009	−	0.421111i	$-0.138360\pi$
$132$	5218.94	−	2657.82i	0.299526	−	0.152538i
$133$	7356.22			0.415864
$134$	−10425.9	−	14350.1i	−0.580639	−	0.799180i
$135$	6939.42	+	21357.3i	0.380764	+	1.17187i
$136$	2472.93	−	7610.89i	0.133701	−	0.411488i
$137$	9960.15	+	7236.47i	0.530670	+	0.385554i	0.820608	−	0.571491i	$-0.193635\pi$
$137$	9960.15	+	7236.47i	0.530670	+	0.385554i	−0.289938	+	0.957045i	$0.593635\pi$
$138$	6909.11	−	9509.58i	0.362797	−	0.499348i
$139$	2079.53	+	675.682i	0.107631	+	0.0349714i	0.362337	−	0.932047i	$-0.381979\pi$
$139$	2079.53	+	675.682i	0.107631	+	0.0349714i	−0.254706	+	0.967018i	$0.581979\pi$
$140$	−9169.02	+	2979.19i	−0.467807	+	0.152000i
$141$	−15141.5	+	11000.9i	−0.761605	+	0.553339i
$142$		−	1337.36i		−	0.0663242i
$143$	7391.22	+	3767.94i	0.361446	+	0.184260i
$144$	−2841.17			−0.137016
$145$	−22629.9	−	31147.4i	−1.07633	−	1.48144i
$146$	−3479.57	−	10709.0i	−0.163238	−	0.502394i
$147$	−1389.90	+	4277.67i	−0.0643203	+	0.197958i
$148$	−13504.6	−	9811.65i	−0.616535	−	0.447939i
$149$	−8565.21	+	11789.0i	−0.385803	+	0.531012i	−0.957110	−	0.289724i	$-0.906436\pi$
$149$	−8565.21	+	11789.0i	−0.385803	+	0.531012i	0.571307	+	0.820736i	$0.306436\pi$
$150$	−4087.37	−	1328.07i	−0.181661	−	0.0590251i
$151$	11074.2	−	3598.21i	0.485688	−	0.157809i	−0.0559296	−	0.998435i	$-0.517812\pi$
$151$	11074.2	−	3598.21i	0.485688	−	0.157809i	0.541617	+	0.840625i	$0.317812\pi$
$152$	−3307.56	+	2403.08i	−0.143159	+	0.104011i
$153$		−	15700.4i		−	0.670701i
$154$	9850.67	+	9854.75i	0.415360	+	0.415532i
$155$	−9414.72			−0.391872
$156$	1950.67	+	2684.87i	0.0801558	+	0.110325i
$157$	4580.75	+	14098.1i	0.185839	+	0.571954i	0.999962	−	0.00873891i	$-0.00278172\pi$
$157$	4580.75	+	14098.1i	0.185839	+	0.571954i	−0.814123	+	0.580693i	$0.802782\pi$
$158$	8310.19	−	25576.1i	0.332887	−	1.02452i
$159$	−16200.0	−	11770.0i	−0.640796	−	0.465566i
$160$	3149.41	−	4334.80i	0.123024	−	0.169328i
$161$	26596.5	+	8641.74i	1.02606	+	0.333388i
$162$	2674.86	−	869.114i	0.101923	−	0.0331167i
$163$	−19431.0	+	14117.5i	−0.731341	+	0.531350i	−0.889987	−	0.455985i	$-0.849287\pi$
$163$	−19431.0	+	14117.5i	−0.731341	+	0.531350i	0.158646	+	0.987335i	$0.449287\pi$
$164$			20190.7i			0.750697i
$165$	3385.44	+	21403.6i	0.124351	+	0.786173i
$166$	−2031.02			−0.0737053
$167$	−5002.46	−	6885.29i	−0.179370	−	0.246882i	0.709859	−	0.704344i	$-0.248759\pi$
$167$	−5002.46	−	6885.29i	−0.179370	−	0.246882i	−0.889229	+	0.457462i	$0.848759\pi$
$168$	1722.41	+	5301.05i	0.0610266	+	0.187821i
$169$	7373.14	−	22692.2i	0.258154	−	0.794517i
$170$	23954.3	+	17403.8i	0.828867	+	0.602207i
$171$	−4714.67	+	6489.18i	−0.161235	+	0.221921i
$172$	5700.20	+	1852.11i	0.192678	+	0.0626050i
$173$	−16321.7	+	5303.24i	−0.545347	+	0.177194i	−0.568718	−	0.822533i	$-0.692560\pi$
$173$	−16321.7	+	5303.24i	−0.545347	+	0.177194i	0.0233706	+	0.999727i	$0.492560\pi$
$174$	−18007.8	+	13083.4i	−0.594787	+	0.432138i
$175$		−	10224.7i		−	0.333869i
$176$	−7648.41	−	1213.01i	−0.246914	−	0.0391598i
$177$	37258.6			1.18927
$178$	9845.81	+	13551.6i	0.310750	+	0.427711i
$179$	4615.16	+	14204.0i	0.144039	+	0.443307i	0.996886	−	0.0788539i	$-0.0251261\pi$
$179$	4615.16	+	14204.0i	0.144039	+	0.443307i	−0.852847	+	0.522161i	$0.825126\pi$
$180$	3248.45	−	9997.70i	0.100261	−	0.308571i
$181$	23263.0	+	16901.6i	0.710083	+	0.515906i	0.883201	−	0.468995i	$-0.155384\pi$
$181$	23263.0	+	16901.6i	0.710083	+	0.515906i	−0.173117	+	0.984901i	$0.555384\pi$
$182$	−4640.87	+	6387.61i	−0.140106	+	0.192839i
$183$	−13443.5	−	4368.05i	−0.401429	−	0.130432i
$184$	−14781.5	+	4802.81i	−0.436600	+	0.141860i
$185$	49966.3	−	36302.6i	1.45994	−	1.06071i
$186$			5443.10i			0.157333i
$187$	6703.16	−	42265.4i	0.191689	−	1.20865i
$188$	24746.9			0.700172
$189$	18155.7	+	24989.2i	0.508265	+	0.699566i
$190$	−4674.42	−	14386.4i	−0.129485	−	0.398515i
$191$	6152.61	−	18935.8i	0.168652	−	0.519059i	−0.830634	−	0.556818i	$-0.812022\pi$
$191$	6152.61	−	18935.8i	0.168652	−	0.519059i	0.999287	+	0.0377592i	$0.0120220\pi$
$192$	−2506.15	−	1820.83i	−0.0679838	−	0.0493931i
$193$	−11289.8	+	15539.1i	−0.303090	+	0.417168i	−0.933211	−	0.359329i	$-0.883006\pi$
$193$	−11289.8	+	15539.1i	−0.303090	+	0.417168i	0.630120	+	0.776497i	$0.283006\pi$
$194$	−3845.07	−	1249.34i	−0.102165	−	0.0331953i
$195$	−11678.0	+	3794.41i	−0.307114	+	0.0997872i
$196$	4811.36	−	3495.66i	0.125244	−	0.0909949i
$197$			11569.2i			0.298106i	0.988829	+	0.149053i	$0.0476224\pi$
$197$			11569.2i			0.298106i	−0.988829	+	0.149053i	$0.952378\pi$
$198$	−15006.6	+	2373.62i	−0.382782	+	0.0605454i
$199$	−12541.9			−0.316706			−0.158353	−	0.987383i	$-0.550618\pi$
$199$	−12541.9			−0.316706			−0.158353	+	0.987383i	$0.550618\pi$
$200$	3340.15	+	4597.32i	0.0835037	+	0.114933i
$201$	−11725.0	−	36086.0i	−0.290217	−	0.893195i
$202$	−14745.0	+	45380.3i	−0.361360	+	1.11215i
$203$	−42842.6	−	31126.9i	−1.03964	−	0.755343i
$204$	10062.0	−	13849.1i	0.241781	−	0.332783i
$205$	−71048.5	−	23085.0i	−1.69062	−	0.549317i
$206$	−11309.9	+	3674.81i	−0.266517	+	0.0865966i
$207$	−24669.1	+	17923.2i	−0.575722	+	0.418287i
$208$		−	4388.09i		−	0.101426i
$209$	−15462.3	+	15455.9i	−0.353983	+	0.353836i
$210$	−20623.0			−0.467642
$211$	15075.0	+	20748.9i	0.338603	+	0.466047i	0.944033	−	0.329851i	$-0.106999\pi$
$211$	15075.0	+	20748.9i	0.338603	+	0.466047i	−0.605430	+	0.795899i	$0.706999\pi$
$212$	8181.80	+	25181.0i	0.182044	+	0.560275i
$213$	884.028	−	2720.76i	0.0194853	−	0.0599696i
$214$	14118.7	+	10257.8i	0.308295	+	0.223989i
$215$	−13034.6	+	17940.6i	−0.281982	+	0.388115i
$216$	−16326.6	−	5304.84i	−0.349936	−	0.113701i
$217$	−12316.0	+	4001.70i	−0.261546	+	0.0849815i
$218$	45369.5	−	32962.8i	0.954664	−	0.693604i
$219$		−	24086.8i		−	0.502216i
$220$	13013.2	−	25526.8i	0.268868	−	0.527413i
$221$	24248.8			0.496484
$222$	−20988.3	−	28887.9i	−0.425864	−	0.586152i
$223$	−18830.3	−	57953.8i	−0.378659	−	1.16539i	−0.940977	−	0.338471i	$-0.890090\pi$
$223$	−18830.3	−	57953.8i	−0.378659	−	1.16539i	0.562318	−	0.826921i	$-0.309910\pi$
$224$	2277.44	−	7009.25i	0.0453891	−	0.139693i
$225$	9019.60	+	6553.12i	0.178165	+	0.129444i
$226$	−18575.3	+	25566.7i	−0.363679	+	0.500562i
$227$	74457.8	+	24192.8i	1.44497	+	0.469499i	0.923443	−	0.383736i	$-0.125363\pi$
$227$	74457.8	+	24192.8i	1.44497	+	0.469499i	0.521526	+	0.853235i	$0.325363\pi$
$228$	−8317.47	+	2702.51i	−0.160000	+	0.0519873i
$229$	16694.9	−	12129.5i	0.318356	−	0.231299i	−0.417118	−	0.908852i	$-0.636960\pi$
$229$	16694.9	−	12129.5i	0.318356	−	0.231299i	0.735474	+	0.677553i	$0.236960\pi$
$230$		−	57505.5i		−	1.08706i
$231$	13526.2	+	26560.3i	0.253485	+	0.497747i
$232$	29431.5			0.546810
$233$	51231.9	+	70514.6i	0.943688	+	1.29887i	0.954275	+	0.298931i	$0.0966299\pi$
$233$	51231.9	+	70514.6i	0.943688	+	1.29887i	−0.0105873	+	0.999944i	$0.503370\pi$
$234$	−2660.36	−	8187.75i	−0.0485857	−	0.149532i
$235$	−28294.3	+	87080.9i	−0.512346	+	1.57684i
$236$	−39856.1	−	28957.1i	−0.715600	−	0.519914i
$237$	33812.9	−	46539.5i	0.601985	−	0.828562i
$238$	38733.4	+	12585.2i	0.683804	+	0.222181i
$239$	55365.1	−	17989.2i	0.969259	−	0.314931i	0.218742	−	0.975783i	$-0.429805\pi$
$239$	55365.1	−	17989.2i	0.969259	−	0.314931i	0.750517	+	0.660851i	$0.229805\pi$
$240$	9272.65	−	6736.98i	0.160984	−	0.116961i
$241$			57746.1i			0.994234i	0.867684	+	0.497117i	$0.165608\pi$
$241$			57746.1i			0.994234i	−0.867684	+	0.497117i	$0.834392\pi$
$242$	−41411.0	−	17.1639i	−0.707107	−	0.000293080i
$243$	−55436.2			−0.938817
$244$	10985.8	+	15120.7i	0.184524	+	0.253976i
$245$	6799.69	+	20927.3i	0.113281	+	0.348643i
$246$	−13346.6	+	41076.5i	−0.220546	+	0.678771i
$247$	−10022.3	−	7281.63i	−0.164276	−	0.119353i
$248$	4230.34	−	5822.56i	0.0687815	−	0.0946696i
$249$	−4131.96	−	1342.56i	−0.0666435	−	0.0216538i
$250$	29768.0	−	9672.20i	0.476287	−	0.154755i
$251$	9313.86	−	6766.92i	0.147837	−	0.107410i	−0.511408	−	0.859338i	$-0.670876\pi$
$251$	9313.86	−	6766.92i	0.147837	−	0.107410i	0.659245	+	0.751928i	$0.270876\pi$
$252$		−	14459.3i		−	0.227692i
$253$	−74061.2	+	37716.7i	−1.15704	+	0.589241i
$254$	12054.3			0.186842
$255$	37228.8	+	51241.0i	0.572530	+	0.788020i
$256$	1265.73	+	3895.53i	0.0193136	+	0.0594410i
$257$	24585.0	−	75664.8i	0.372223	−	1.14559i	−0.573109	−	0.819479i	$-0.694263\pi$
$257$	24585.0	−	75664.8i	0.372223	−	1.14559i	0.945333	−	0.326107i	$-0.105737\pi$
$258$	10372.3	+	7535.94i	0.155825	+	0.113213i
$259$	49933.5	−	68727.6i	0.744377	−	1.02455i
$260$	15441.1	+	5017.12i	0.228419	+	0.0742177i
$261$	54916.3	−	17843.4i	0.806159	−	0.261937i
$262$	−33072.9	+	24028.9i	−0.481803	+	0.350051i
$263$			66617.0i			0.963106i	0.876417	+	0.481553i	$0.159927\pi$
$263$			66617.0i			0.963106i	−0.876417	+	0.481553i	$0.840073\pi$
$264$	−14758.3	−	7523.57i	−0.211752	−	0.107948i
$265$	−97963.1			−1.39499
$266$	−12229.8	−	16832.8i	−0.172844	−	0.237900i
$267$	11072.6	+	34078.0i	0.155320	+	0.478026i
$268$	−15503.3	+	47714.2i	−0.215851	+	0.664322i
$269$	−49854.8	−	36221.6i	−0.688973	−	0.500568i	0.187349	−	0.982293i	$-0.440010\pi$
$269$	−49854.8	−	36221.6i	−0.688973	−	0.500568i	−0.876322	+	0.481725i	$0.840010\pi$
$270$	37334.0	−	51385.8i	0.512126	−	0.704881i
$271$	−99210.5	−	32235.4i	−1.35089	−	0.438930i	−0.457897	−	0.889005i	$-0.651397\pi$
$271$	−99210.5	−	32235.4i	−1.35089	−	0.438930i	−0.892990	+	0.450076i	$0.851397\pi$
$272$	−21526.8	+	6994.49i	−0.290966	+	0.0945406i
$273$	−13663.9	+	9927.38i	−0.183336	+	0.133202i
$274$		−	34822.0i		−	0.463823i
$275$	21482.9	+	21491.8i	0.284071	+	0.284189i
$276$	−33246.7			−0.436446
$277$	−21772.3	−	29967.0i	−0.283756	−	0.390557i	0.643217	−	0.765684i	$-0.277599\pi$
$277$	−21772.3	−	29967.0i	−0.283756	−	0.390557i	−0.926974	+	0.375127i	$0.877599\pi$
$278$	−1911.12	−	5881.81i	−0.0247285	−	0.0761065i
$279$	4363.36	−	13429.1i	0.0560548	−	0.172519i
$280$	22060.7	+	16028.0i	0.281386	+	0.204439i
$281$	39428.5	−	54268.7i	0.499341	−	0.687284i	−0.482735	−	0.875766i	$-0.660357\pi$
$281$	39428.5	−	54268.7i	0.499341	−	0.687284i	0.982077	+	0.188482i	$0.0603567\pi$
$282$	50345.6	+	16358.3i	0.633087	+	0.205703i
$283$	96676.0	−	31411.9i	1.20711	−	0.392213i	0.364736	−	0.931111i	$-0.381159\pi$
$283$	96676.0	−	31411.9i	1.20711	−	0.392213i	0.842371	+	0.538898i	$0.181159\pi$
$284$	−3060.21	+	2223.37i	−0.0379415	+	0.0275661i
$285$		−	32357.9i		−	0.398374i
$286$	−3665.98	−	23177.2i	−0.0448185	−	0.283353i
$287$	−102755.			−1.24749
$288$	4723.47	+	6501.30i	0.0569477	+	0.0783818i
$289$	−12842.4	−	39524.9i	−0.153763	−	0.473233i
$290$	−33650.5	+	103565.i	−0.400124	+	1.23146i
$291$	−6996.66	−	5083.37i	−0.0826238	−	0.0600297i
$292$	−18720.1	+	25766.0i	−0.219554	+	0.302190i
$293$	−18247.8	−	5929.06i	−0.212556	−	0.0690638i	0.200803	−	0.979632i	$-0.435645\pi$
$293$	−18247.8	−	5929.06i	−0.212556	−	0.0690638i	−0.413360	+	0.910568i	$0.635645\pi$
$294$	12099.1	−	3931.23i	0.139977	−	0.0454814i
$295$	147466.	−	107140.i	1.69452	−	1.23114i
$296$			47213.7i			0.538871i
$297$	−90666.2	−	14379.4i	−1.02786	−	0.163015i
$298$	41215.9			0.464122
$299$	−27681.7	−	38100.6i	−0.309635	−	0.426176i
$300$	3756.34	+	11560.8i	0.0417371	+	0.128454i
$301$	−9425.76	+	29009.5i	−0.104036	+	0.320190i
$302$	−26644.5	−	19358.3i	−0.292142	−	0.212253i
$303$	−59995.0	+	82576.0i	−0.653476	+	0.899432i
$304$	10997.7	+	3573.36i	0.119002	+	0.0386660i
$305$	−65768.4	+	21369.4i	−0.706997	+	0.229717i
$306$	−35926.4	+	26102.1i	−0.383682	+	0.278761i
$307$			3019.83i			0.0320410i	0.999872	+	0.0160205i	$0.00509970\pi$
$307$			3019.83i			0.0320410i	−0.999872	+	0.0160205i	$0.994900\pi$
$308$	6173.28	−	38924.3i	0.0650751	−	0.410317i
$309$	−25438.3			−0.266423
$310$	15652.1	+	21543.2i	0.162873	+	0.224175i
$311$	474.793	+	1461.26i	0.00490889	+	0.0151080i	0.953481	−	0.301453i	$-0.0974717\pi$
$311$	474.793	+	1461.26i	0.00490889	+	0.0151080i	−0.948572	+	0.316561i	$0.897472\pi$
$312$	2900.63	−	8927.23i	0.0297978	−	0.0917081i
$313$	95549.0	+	69420.4i	0.975299	+	0.708596i	0.956653	−	0.291230i	$-0.0940646\pi$
$313$	95549.0	+	69420.4i	0.975299	+	0.708596i	0.0186456	+	0.999826i	$0.494065\pi$
$314$	24644.4	−	33920.1i	0.249953	−	0.344031i
$315$	50880.4	+	16532.0i	0.512778	+	0.166612i
$316$	−72340.3	+	23504.8i	−0.724446	+	0.235387i
$317$	25763.3	−	18718.2i	0.256380	−	0.186271i	−0.452170	−	0.891932i	$-0.649350\pi$
$317$	25763.3	−	18718.2i	0.256380	−	0.186271i	0.708549	+	0.705661i	$0.249350\pi$
$318$			56637.2i			0.560076i
$319$	155452.	−	24588.2i	1.52762	−	0.241627i
$320$	−15155.0			−0.147998
$321$	21942.7	+	30201.5i	0.212951	+	0.293102i
$322$	−24442.5	−	75226.4i	−0.235741	−	0.725535i
$323$	−19746.5	+	60773.6i	−0.189272	+	0.582519i
$324$	−6435.72	−	4675.82i	−0.0613066	−	0.0445418i
$325$	−10121.1	+	13930.5i	−0.0958207	+	0.131886i
$326$	64608.4	+	20992.5i	0.607930	+	0.197528i
$327$	114090.	−	37070.1i	1.06697	−	0.346679i
$328$	46201.4	−	33567.3i	0.429444	−	0.312010i
$329$			125942.i			1.16353i
$330$	43348.3	−	43330.3i	0.398056	−	0.397891i
$331$	152476.			1.39170			0.695851	−	0.718186i	$-0.255027\pi$
$331$	152476.			1.39170			0.695851	+	0.718186i	$0.255027\pi$
$332$	3376.59	+	4647.48i	0.0306339	+	0.0421640i
$333$	28624.2	+	88096.2i	0.258134	+	0.794454i
$334$	−7438.62	+	22893.7i	−0.0666806	+	0.205222i
$335$	−150174.	−	109108.i	−1.33815	−	0.972226i
$336$	9266.57	−	12754.3i	0.0820806	−	0.112974i
$337$	−169279.	−	55002.0i	−1.49054	−	0.484304i	−0.553294	−	0.832986i	$-0.686630\pi$
$337$	−169279.	−	55002.0i	−1.49054	−	0.484304i	−0.937241	+	0.348681i	$0.886630\pi$
$338$	−64183.2	+	20854.4i	−0.561808	+	0.182543i
$339$	−54690.2	+	39734.8i	−0.475894	+	0.345757i
$340$		−	83747.2i		−	0.724456i
$341$	17479.5	−	34288.0i	0.150322	−	0.294872i
$342$	22687.0			0.193966
$343$	75248.2	+	103570.i	0.639599	+	0.880333i
$344$	−5238.55	−	16122.6i	−0.0442684	−	0.136244i
$345$	38012.6	−	116991.i	0.319366	−	0.982908i
$346$	39270.0	+	28531.4i	0.328027	+	0.238325i
$347$	−86850.6	+	119540.i	−0.721296	+	0.992779i	0.278183	+	0.960528i	$0.410268\pi$
$347$	−86850.6	+	119540.i	−0.721296	+	0.992779i	−0.999480	+	0.0322514i	$0.989732\pi$
$348$	59876.2	+	19454.9i	0.494419	+	0.160647i
$349$	−15274.0	+	4962.84i	−0.125402	+	0.0407454i	−0.371045	−	0.928615i	$-0.621001\pi$
$349$	−15274.0	+	4962.84i	−0.125402	+	0.0407454i	0.245644	+	0.969360i	$0.421001\pi$
$350$	−23396.7	+	16998.7i	−0.190994	+	0.138765i
$351$		−	52017.6i		−	0.422217i
$352$	9939.86	+	19518.1i	0.0802223	+	0.157526i
$353$	−96080.6			−0.771057			−0.385528	−	0.922696i	$-0.625981\pi$
$353$	−96080.6			−0.771057			−0.385528	+	0.922696i	$0.625981\pi$
$354$	−61942.8	−	85256.9i	−0.494292	−	0.680335i
$355$	−4324.86	−	13310.6i	−0.0343175	−	0.105618i
$356$	14640.6	−	45059.3i	0.115521	−	0.355537i
$357$	70481.0	+	51207.4i	0.553013	+	0.401788i
$358$	24829.5	−	34174.9i	0.193732	−	0.266650i
$359$	100517.	+	32660.0i	0.779922	+	0.253412i	0.671807	−	0.740726i	$-0.265518\pi$
$359$	100517.	+	32660.0i	0.779922	+	0.253412i	0.108115	+	0.994138i	$0.465518\pi$
$360$	−28277.8	+	9188.01i	−0.218193	+	0.0708951i
$361$	−79020.8	+	57412.0i	−0.606355	+	0.440543i
$362$		−	81330.6i		−	0.620636i
$363$	−84236.2	−	27408.6i	−0.639272	−	0.208005i
$364$	22331.9			0.168548
$365$	−69263.4	−	95332.9i	−0.519898	−	0.715578i
$366$	12354.7	+	38023.9i	0.0922295	+	0.283853i
$367$	25450.7	−	78329.1i	0.188959	−	0.581555i	−0.811035	−	0.584997i	$-0.801096\pi$
$367$	25450.7	−	78329.1i	0.188959	−	0.581555i	0.999994	+	0.00344191i	$0.00109559\pi$
$368$	35564.5	+	25839.1i	0.262616	+	0.190801i
$369$	65856.5	−	90643.7i	0.483666	−	0.665709i
$370$	−166139.	−	53981.7i	−1.21358	−	0.394315i
$371$	−128151.	+	41638.9i	−0.931055	+	0.302518i
$372$	12455.2	−	9049.20i	0.0900043	−	0.0653920i
$373$			67611.5i			0.485963i	0.970031	+	0.242981i	$0.0781254\pi$
$373$			67611.5i			0.485963i	−0.970031	+	0.242981i	$0.921875\pi$
$374$	−107858.	+	54928.1i	−0.771095	+	0.392691i
$375$	66954.2			0.476119
$376$	−41141.9	−	56626.9i	−0.291010	−	0.400541i
$377$	27558.5	+	84816.3i	0.193898	+	0.596756i
$378$	26997.4	−	83089.5i	0.188946	−	0.581517i
$379$	−89198.5	−	64806.5i	−0.620982	−	0.451170i	0.232282	−	0.972648i	$-0.425381\pi$
$379$	−89198.5	−	64806.5i	−0.620982	−	0.451170i	−0.853265	+	0.521478i	$0.825381\pi$
$380$	−25148.3	+	34613.7i	−0.174158	+	0.239707i
$381$	24523.6	+	7968.20i	0.168941	+	0.0548922i
$382$	−53558.5	+	17402.2i	−0.367030	+	0.119255i
$383$	−163957.	+	119122.i	−1.11772	+	0.812070i	−0.983862	−	0.178931i	$-0.942736\pi$
$383$	−163957.	+	119122.i	−1.11772	+	0.812070i	−0.133856	+	0.991001i	$0.542736\pi$
$384$			8761.84i			0.0594200i
$385$	129911.	+	66227.0i	0.876447	+	0.446801i
$386$	54326.7			0.364618
$387$	−19549.3	−	26907.2i	−0.130529	−	0.179658i
$388$	3533.67	+	10875.5i	0.0234727	+	0.0722414i
$389$	77097.1	−	237280.i	0.509494	−	1.56806i	−0.283589	−	0.958946i	$-0.591525\pi$
$389$	77097.1	−	237280.i	0.509494	−	1.56806i	0.793083	−	0.609114i	$-0.208475\pi$
$390$	28097.3	+	20413.9i	0.184729	+	0.134214i
$391$	−142788.	+	196531.i	−0.933980	+	1.28551i
$392$	−15997.9	−	5198.02i	−0.104109	−	0.0338272i
$393$	−83168.0	+	27022.9i	−0.538482	+	0.174963i
$394$	26473.1	−	19233.9i	0.170535	−	0.123901i
$395$		−	281430.i		−	1.80375i
$396$	30380.0	+	30392.6i	0.193730	+	0.193811i
$397$	184995.			1.17376			0.586879	−	0.809674i	$-0.300356\pi$
$397$	184995.			1.17376			0.586879	+	0.809674i	$0.300356\pi$
$398$	20850.9	+	28698.8i	0.131631	+	0.181175i
$399$	−13753.6	−	42329.3i	−0.0863916	−	0.265886i
$400$	4966.77	−	15286.2i	0.0310423	−	0.0955385i
$401$	190071.	+	138095.i	1.18203	+	0.858792i	0.992399	−	0.123064i	$-0.0392719\pi$
$401$	190071.	+	138095.i	1.18203	+	0.858792i	0.189628	+	0.981856i	$0.439272\pi$
$402$	−63080.6	+	86822.9i	−0.390340	+	0.537257i
$403$	20740.7	+	6739.06i	0.127707	+	0.0414944i
$404$	128355.	−	41705.0i	0.786411	−	0.255520i
$405$	23811.9	−	17300.3i	0.145172	−	0.105474i
$406$			149783.i			0.908679i
$407$	39444.1	+	249375.i	0.238119	+	1.50544i
$408$	−48418.2			−0.290863
$409$	−40048.7	−	55122.3i	−0.239410	−	0.329519i	0.672358	−	0.740227i	$-0.265282\pi$
$409$	−40048.7	−	55122.3i	−0.239410	−	0.329519i	−0.911767	+	0.410707i	$0.865282\pi$
$410$	65294.4	+	200955.i	0.388426	+	1.19545i
$411$	23018.2	−	70842.6i	0.136266	−	0.419383i
$412$	27211.7	+	19770.5i	0.160310	+	0.116472i
$413$	147369.	−	202836.i	0.863984	−	1.18917i
$414$	82025.2	+	26651.6i	0.478571	+	0.155497i
$415$	−20214.5	+	6568.08i	−0.117372	+	0.0381366i
$416$	−10041.0	+	7295.23i	−0.0580218	+	0.0421553i
$417$		−	13229.4i		−	0.0760795i
$418$	61073.2	+	9686.02i	0.349541	+	0.0554361i
$419$	182795.			1.04121			0.520604	−	0.853799i	$-0.325707\pi$
$419$	182795.			1.04121			0.520604	+	0.853799i	$0.325707\pi$
$420$	34285.9	+	47190.5i	0.194364	+	0.267520i
$421$	−32103.3	−	98803.8i	−0.181128	−	0.557454i	0.818732	−	0.574175i	$-0.194677\pi$
$421$	−32103.3	−	98803.8i	−0.181128	−	0.557454i	−0.999860	+	0.0167210i	$0.994677\pi$
$422$	22416.3	−	68990.4i	0.125875	−	0.387404i
$423$	−111098.	−	80717.3i	−0.620905	−	0.451114i
$424$	44018.0	−	60585.5i	0.244849	−	0.337006i
$425$	84471.9	+	27446.6i	0.467664	+	0.151953i
$426$	−7695.47	+	2500.41i	−0.0424049	+	0.0137782i
$427$	−76952.5	+	55909.3i	−0.422053	+	0.306639i
$428$		−	49360.7i		−	0.269460i
$429$	7862.51	−	49575.5i	0.0427215	−	0.269372i
$430$	62722.7			0.339225
$431$	−133745.	−	184084.i	−0.719982	−	0.990971i	−0.999524	−	0.0308373i	$-0.990183\pi$
$431$	−133745.	−	184084.i	−0.719982	−	0.990971i	0.279542	−	0.960133i	$-0.409817\pi$
$432$	15004.3	+	46178.6i	0.0803988	+	0.247442i
$433$	−94654.6	+	291317.i	−0.504854	+	1.55378i	0.296161	+	0.955138i	$0.404293\pi$
$433$	−94654.6	+	291317.i	−0.504854	+	1.55378i	−0.801015	+	0.598644i	$0.795707\pi$
$434$	29632.2	+	21529.1i	0.157320	+	0.114300i
$435$	−136919.	+	188452.i	−0.723576	+	0.995917i
$436$	−150854.	−	49015.5i	−0.793568	−	0.257846i
$437$	118032.	−	38350.9i	0.618068	−	0.200823i
$438$	−55116.5	+	40044.5i	−0.287298	+	0.208735i
$439$		−	102866.i		−	0.533756i	−0.963730	−	0.266878i	$-0.914008\pi$
$439$		−	102866.i		−	0.533756i	0.963730	−	0.266878i	$-0.0859920\pi$
$440$	−80046.2	+	12661.1i	−0.413462	+	0.0653981i
$441$	−33001.8			−0.169692
$442$	−40313.7	−	55487.1i	−0.206352	−	0.284019i
$443$	−81441.7	−	250652.i	−0.414992	−	1.27721i	−0.912258	−	0.409615i	$-0.865663\pi$
$443$	−81441.7	−	250652.i	−0.414992	−	1.27721i	0.497267	−	0.867598i	$-0.334337\pi$
$444$	−31209.4	+	96052.7i	−0.158314	+	0.487241i
$445$	141818.	+	103037.i	0.716163	+	0.520323i
$446$	−101307.	+	139437.i	−0.509295	+	0.700984i
$447$	83850.6	+	27244.7i	0.419654	+	0.136354i
$448$	−19825.2	+	6441.58i	−0.0987781	+	0.0320949i
$449$	−205827.	+	149542.i	−1.02096	+	0.741771i	−0.966479	−	0.256744i	$-0.917350\pi$
$449$	−205827.	+	149542.i	−1.02096	+	0.741771i	−0.0544806	+	0.998515i	$0.517350\pi$
$450$		−	31533.7i		−	0.155722i
$451$	215984.	−	215895.i	1.06187	−	1.06143i
$452$	89384.4			0.437507
$453$	−41409.8	−	56995.7i	−0.201793	−	0.277745i
$454$	−68427.6	−	210598.i	−0.331986	−	1.02175i
$455$	−25533.2	+	78583.0i	−0.123334	+	0.379582i
$456$	20011.9	+	14539.5i	0.0962404	+	0.0699228i
$457$	−66572.9	+	91629.7i	−0.318761	+	0.438736i	−0.938088	−	0.346396i	$-0.887405\pi$
$457$	−66572.9	+	91629.7i	−0.318761	+	0.438736i	0.619328	+	0.785133i	$0.287405\pi$
$458$	−55510.8	−	18036.5i	−0.264634	−	0.0859849i
$459$	−255185.	+	82914.6i	−1.21124	+	0.393555i
$460$	−131587.	+	95603.4i	−0.621866	+	0.451812i
$461$			86262.9i			0.405903i	0.979189	+	0.202951i	$0.0650533\pi$
$461$			86262.9i			0.405903i	−0.979189	+	0.202951i	$0.934947\pi$
$462$	38289.0	−	75107.9i	0.179387	−	0.351886i
$463$	−38050.4			−0.177500			−0.0887499	−	0.996054i	$-0.528287\pi$
$463$	−38050.4			−0.177500			−0.0887499	+	0.996054i	$0.528287\pi$
$464$	−48930.1	−	67346.5i	−0.227269	−	0.312809i
$465$	17602.3	+	54174.4i	0.0814075	+	0.250546i
$466$	76181.4	−	234462.i	0.350814	−	1.07969i
$467$	131850.	+	95794.3i	0.604568	+	0.439244i	0.847497	−	0.530800i	$-0.178108\pi$
$467$	131850.	+	95794.3i	0.604568	+	0.439244i	−0.242930	+	0.970044i	$0.578108\pi$
$468$	−14312.7	+	19699.8i	−0.0653477	+	0.0899434i
$469$	−242828.	−	78899.5i	−1.10396	−	0.358698i
$470$	246302.	−	80028.4i	1.11499	−	0.362283i
$471$	72559.1	−	52717.3i	0.327077	−	0.237635i
$472$			139342.i			0.625457i
$473$	−41138.6	−	80780.4i	−0.183877	−	0.361064i
$474$	−162708.			−0.724189
$475$	−26671.4	−	36710.0i	−0.118211	−	0.162704i
$476$	−35596.4	−	109555.i	−0.157106	−	0.483522i
$477$	45402.1	−	139733.i	0.199544	−	0.614135i
$478$	−133209.	−	96781.7i	−0.583010	−	0.423582i
$479$	108531.	−	149380.i	0.473022	−	0.651059i	−0.504123	−	0.863632i	$-0.668184\pi$
$479$	108531.	−	149380.i	0.473022	−	0.651059i	0.977145	+	0.212573i	$0.0681843\pi$
$480$	−30831.7	−	10017.8i	−0.133818	−	0.0434802i
$481$	−136061.	+	44209.0i	−0.588092	+	0.191083i
$482$	132137.	−	96003.3i	0.568763	−	0.413230i
$483$		−	169199.i		−	0.725278i
$484$	68806.8	+	94787.1i	0.293725	+	0.404630i
$485$	−42309.7			−0.179869
$486$	92163.1	+	126852.i	0.390198	+	0.537061i
$487$	72194.3	+	222191.i	0.304400	+	0.936847i	0.979900	+	0.199487i	$0.0639277\pi$
$487$	72194.3	+	222191.i	0.304400	+	0.936847i	−0.675500	+	0.737360i	$0.736072\pi$
$488$	16335.9	−	50276.6i	0.0685966	−	0.211119i
$489$	117564.	+	85415.4i	0.491652	+	0.357206i
$490$	36582.3	−	50351.2i	0.152363	−	0.209709i
$491$	192877.	+	62669.5i	0.800050	+	0.259952i	0.680378	−	0.732861i	$-0.261816\pi$
$491$	192877.	+	62669.5i	0.800050	+	0.259952i	0.119672	+	0.992813i	$0.461816\pi$
$492$	116182.	−	37749.8i	0.479964	−	0.155950i
$493$	372159.	−	270390.i	1.53121	−	1.11249i
$494$			35039.3i			0.143582i
$495$	−141682.	+	72153.8i	−0.578237	+	0.294475i
$496$	−20356.4			−0.0827443
$497$	−11315.2	−	15574.0i	−0.0458089	−	0.0630505i
$498$	3797.32	+	11687.0i	0.0153115	+	0.0471240i
$499$	−130361.	+	401210.i	−0.523536	+	1.61128i	0.243657	+	0.969862i	$0.421653\pi$
$499$	−130361.	+	401210.i	−0.523536	+	1.61128i	−0.767193	+	0.641417i	$0.778347\pi$
$500$	−71621.8	−	52036.3i	−0.286487	−	0.208145i
$501$	−30266.6	+	41658.4i	−0.120584	+	0.165969i
$502$	−30968.7	−	10062.4i	−0.122890	−	0.0399293i
$503$	136113.	−	44225.7i	0.537976	−	0.174799i	−0.0274118	−	0.999624i	$-0.508727\pi$
$503$	136113.	−	44225.7i	0.537976	−	0.174799i	0.565388	+	0.824825i	$0.308727\pi$
$504$	−33086.5	+	24038.7i	−0.130254	+	0.0946347i
$505$			499347.i			1.95803i
$506$	209432.	+	106766.i	0.817980	+	0.416995i
$507$	−144361.			−0.561610
$508$	−20040.4	−	27583.3i	−0.0776567	−	0.106885i
$509$	101466.	+	312279.i	0.391637	+	1.20533i	0.931550	+	0.363613i	$0.118457\pi$
$509$	101466.	+	312279.i	0.391637	+	1.20533i	−0.539913	+	0.841721i	$0.681543\pi$
$510$	55358.9	−	170377.i	0.212837	−	0.655045i
$511$	−131128.	−	95270.4i	−0.502175	−	0.364851i
$512$	6809.63	−	9372.65i	0.0259767	−	0.0357538i
$513$	130369.	+	42359.6i	0.495383	+	0.160960i
$514$	−214012.	+	69536.8i	−0.810052	+	0.263202i
$515$	−100682.	+	73149.8i	−0.379610	+	0.275803i
$516$		−	36263.0i		−	0.136196i
$517$	−264613.	−	264722.i	−0.989987	−	0.990398i
$518$	−240281.			−0.895487
$519$	61032.0	+	84003.3i	0.226581	+	0.311862i
$520$	−14190.5	−	43674.0i	−0.0524798	−	0.161516i
$521$	14730.2	−	45334.8i	0.0542666	−	0.167015i	−0.920250	−	0.391331i	$-0.872015\pi$
$521$	14730.2	−	45334.8i	0.0542666	−	0.167015i	0.974517	+	0.224316i	$0.0720147\pi$
$522$	−132129.	−	95997.3i	−0.484905	−	0.352304i
$523$	47788.5	−	65775.2i	0.174711	−	0.240469i	−0.712677	−	0.701492i	$-0.752518\pi$
$523$	47788.5	−	65775.2i	0.174711	−	0.240469i	0.887388	+	0.461023i	$0.152518\pi$
$524$	109968.	+	35730.7i	0.400501	+	0.130131i
$525$	−58835.4	+	19116.8i	−0.213462	+	0.0693580i
$526$	152436.	−	110751.i	0.550956	−	0.400293i
$527$		−	112490.i		−	0.405036i
$528$	7319.97	+	46278.5i	0.0262568	+	0.166001i
$529$	191958.			0.685954
$530$	162864.	+	224164.i	0.579795	+	0.798019i
$531$	84478.6	+	259998.i	0.299611	+	0.922108i
$532$	−18185.6	+	55969.5i	−0.0642546	+	0.197755i
$533$	139996.	+	101713.i	0.492789	+	0.358032i
$534$	59570.6	−	81991.8i	0.208905	−	0.287533i
$535$	173694.	+	56436.5i	0.606843	+	0.197175i
$536$	134956.	−	43849.9i	0.469746	−	0.152630i
$537$	73104.1	−	53113.3i	0.253509	−	0.184185i
$538$			174299.i			0.602185i
$539$	−88840.6	−	14089.8i	−0.305798	−	0.0484985i
$540$	−179651.			−0.616089
$541$	−190162.	−	261736.i	−0.649724	−	0.894269i	0.349363	−	0.936988i	$-0.386398\pi$
$541$	−190162.	−	261736.i	−0.649724	−	0.894269i	−0.999087	+	0.0427186i	$0.986398\pi$
$542$	91175.6	+	280610.i	0.310370	+	0.955221i
$543$	53761.5	−	165461.i	0.182336	−	0.561172i
$544$	51793.6	+	37630.3i	0.175016	+	0.127157i
$545$	344958.	−	474794.i	1.16138	−	1.59850i
$546$	45432.6	+	14761.9i	0.152399	+	0.0495174i
$547$	344475.	−	111927.i	1.15129	−	0.374075i	0.329658	−	0.944100i	$-0.393067\pi$
$547$	344475.	−	111927.i	1.15129	−	0.374075i	0.821627	+	0.570025i	$0.193067\pi$
$548$	−79681.2	+	57891.8i	−0.265335	+	0.192777i
$549$		−	103715.i		−	0.344110i
$550$	13463.0	−	84888.3i	0.0445059	−	0.280623i
$551$	−235013.			−0.774085
$552$	55272.9	+	76076.6i	0.181399	+	0.249674i
$553$	−119621.	−	368155.i	−0.391162	−	1.20387i
$554$	−32375.3	+	99640.9i	−0.105486	+	0.324652i
$555$	−302313.	−	219643.i	−0.981457	−	0.713070i
$556$	−10281.8	+	14151.7i	−0.0332597	+	0.0457781i
$557$	−174412.	−	56669.9i	−0.562167	−	0.182659i	0.0141287	−	0.999900i	$-0.495503\pi$
$557$	−174412.	−	56669.9i	−0.562167	−	0.182659i	−0.576296	+	0.817241i	$0.695503\pi$
$558$	−37983.1	+	12341.5i	−0.121989	+	0.0396368i
$559$	41557.3	−	30193.1i	0.132991	−	0.0966239i
$560$		−	77127.0i		−	0.245941i
$561$	−255737.	+	40450.4i	−0.812583	+	0.128528i
$562$	−189730.			−0.600709
$563$	342613.	+	471566.i	1.08090	+	1.48773i	0.858523	+	0.512774i	$0.171382\pi$
$563$	342613.	+	471566.i	1.08090	+	1.48773i	0.222379	+	0.974960i	$0.428618\pi$
$564$	−46268.2	−	142399.i	−0.145454	−	0.447660i
$565$	−102198.	+	314532.i	−0.320143	+	0.985297i
$566$	−232603.	−	168996.i	−0.726076	−	0.527525i
$567$	23796.2	−	32752.7i	0.0740188	−	0.101878i
$568$	10175.2	+	3306.14i	0.0315390	+	0.0102476i
$569$	−456553.	+	148343.i	−1.41015	+	0.458187i	−0.912460	−	0.409167i	$-0.865820\pi$
$569$	−456553.	+	148343.i	−1.41015	+	0.458187i	−0.497693	+	0.867353i	$0.665820\pi$
$570$	−74042.9	+	53795.3i	−0.227894	+	0.165575i
$571$		−	45809.1i		−	0.140501i	−0.997529	−	0.0702505i	$-0.977620\pi$
$571$		−	45809.1i		−	0.140501i	0.997529	−	0.0702505i	$-0.0223799\pi$
$572$	−46940.3	+	46920.8i	−0.143468	+	0.143408i
$573$	−120464.			−0.366900
$574$	170831.	+	235128.i	0.518492	+	0.713643i
$575$	−53305.6	−	164058.i	−0.161227	−	0.496205i
$576$	7023.77	−	21616.9i	0.0211702	−	0.0651552i
$577$	−370083.	−	268881.i	−1.11160	−	0.807624i	−0.128684	−	0.991686i	$-0.541075\pi$
$577$	−370083.	−	268881.i	−1.11160	−	0.807624i	−0.982915	+	0.184062i	$0.941075\pi$
$578$	−69092.1	+	95097.1i	−0.206811	+	0.284650i
$579$	110524.	+	35911.3i	0.329684	+	0.107121i
$580$	292927.	−	95177.9i	0.870771	−	0.282931i
$581$	−23652.0	+	17184.2i	−0.0700673	+	0.0509069i
$582$			24461.2i			0.0722158i
$583$	181880.	−	356777.i	0.535116	−	1.04969i
$584$	90081.1			0.264124
$585$	−52956.4	−	72888.2i	−0.154741	−	0.212983i
$586$	16769.9	+	51612.5i	0.0488355	+	0.150300i
$587$	−117315.	+	361058.i	−0.340468	+	1.04785i	0.623498	+	0.781825i	$0.285711\pi$
$587$	−117315.	+	361058.i	−0.340468	+	1.04785i	−0.963966	+	0.266027i	$0.914289\pi$
$588$	−29110.4	−	21150.0i	−0.0841964	−	0.0611723i
$589$	−33779.6	+	46493.6i	−0.0973698	+	0.134018i
$590$	−490325.	−	159316.i	−1.40858	−	0.457674i
$591$	66571.6	−	21630.4i	0.190596	−	0.0619284i
$592$	108037.	−	78493.2i	0.308267	−	0.223969i
$593$		−	285357.i		−	0.811482i	−0.913988	−	0.405741i	$-0.867014\pi$
$593$		−	285357.i		−	0.811482i	0.913988	−	0.405741i	$-0.132986\pi$
$594$	117830.	+	231372.i	0.333951	+	0.655751i
$595$	426207.			1.20389
$596$	−68521.7	−	94312.0i	−0.192902	−	0.265506i
$597$	23449.0	+	72168.6i	0.0657924	+	0.202488i
$598$	−41162.5	+	126685.i	−0.115106	+	0.354261i
$599$	−93745.5	−	68110.1i	−0.261274	−	0.189827i	0.449434	−	0.893313i	$-0.351626\pi$
$599$	−93745.5	−	68110.1i	−0.261274	−	0.189827i	−0.710709	+	0.703486i	$0.751626\pi$
$600$	20209.0	−	27815.4i	0.0561362	−	0.0772649i
$601$	−61509.4	−	19985.6i	−0.170291	−	0.0553310i	0.222630	−	0.974903i	$-0.428536\pi$
$601$	−61509.4	−	19985.6i	−0.170291	−	0.0553310i	−0.392922	+	0.919572i	$0.628536\pi$
$602$	82051.3	−	26660.1i	0.226408	−	0.0735645i
$603$	225230.	−	163639.i	0.619430	−	0.450042i
$604$			93152.5i			0.255341i
$605$	−412213.	+	133747.i	−1.12619	+	0.365405i
$606$	288696.			0.786133
$607$	−52511.1	−	72275.4i	−0.142519	−	0.196161i	0.731790	−	0.681530i	$-0.238685\pi$
$607$	−52511.1	−	72275.4i	−0.142519	−	0.196161i	−0.874309	+	0.485369i	$0.838685\pi$
$608$	−10107.0	−	31106.1i	−0.0273410	−	0.0841470i
$609$	−99010.3	+	304722.i	−0.266960	+	0.821617i
$610$	158239.	+	114967.i	0.425259	+	0.308969i
$611$	124665.	−	171587.i	0.333935	−	0.459622i
$612$	119456.	+	38813.6i	0.318937	+	0.103629i
$613$	−49567.3	+	16105.4i	−0.131909	+	0.0428598i	−0.374228	−	0.927337i	$-0.622092\pi$
$613$	−49567.3	+	16105.4i	−0.131909	+	0.0428598i	0.242319	+	0.970197i	$0.422092\pi$
$614$	6910.11	−	5020.49i	0.0183294	−	0.0133171i
$615$			451990.i			1.19503i
$616$	−99331.6	+	50586.0i	−0.261774	+	0.133312i
$617$	−147138.			−0.386505			−0.193252	−	0.981149i	$-0.561904\pi$
$617$	−147138.			−0.386505			−0.193252	+	0.981149i	$0.561904\pi$
$618$	42291.4	+	58209.1i	0.110732	+	0.152410i
$619$	−107433.	−	330643.i	−0.280385	−	0.862936i	−0.987744	−	0.156082i	$-0.950114\pi$
$619$	−107433.	−	330643.i	−0.280385	−	0.862936i	0.707359	−	0.706854i	$-0.249886\pi$
$620$	23274.5	−	71631.5i	0.0605476	−	0.186346i
$621$	421590.	+	306303.i	1.09322	+	0.794271i
$622$	2554.38	−	3515.80i	0.00660245	−	0.00908749i
$623$	229316.	+	74509.3i	0.590824	+	0.191971i
$624$	−25250.0	+	8204.23i	−0.0648474	+	0.0210702i
$625$	391982.	−	284791.i	1.00347	−	0.729066i
$626$		−	334052.i		−	0.852442i
$627$	117846.	+	60076.3i	0.299764	+	0.152816i
$628$	−118589.			−0.300694
$629$	433756.	+	597014.i	1.09634	+	1.50898i
$630$	−46759.7	−	143912.i	−0.117812	−	0.362589i
$631$	−182536.	+	561788.i	−0.458448	+	1.41096i	0.408592	+	0.912717i	$0.366020\pi$
$631$	−182536.	+	561788.i	−0.458448	+	1.41096i	−0.867040	+	0.498239i	$0.833980\pi$
$632$	174051.	+	126455.i	0.435755	+	0.316594i
$633$	91208.7	−	125538.i	0.227630	−	0.313305i
$634$	−85663.5	−	27833.8i	−0.213117	−	0.0692458i
$635$	119975.	−	38982.2i	0.297538	−	0.0966761i
$636$	129600.	−	94159.7i	0.320398	−	0.232783i
$637$		−	50970.2i		−	0.125614i
$638$	−314704.	−	314835.i	−0.773146	−	0.773466i
$639$	20990.4			0.0514067
$640$	25195.3	+	34678.4i	0.0615120	+	0.0846640i
$641$	−115996.	−	356999.i	−0.282310	−	0.868862i	−0.987192	−	0.159537i	$-0.949000\pi$
$641$	−115996.	−	356999.i	−0.282310	−	0.868862i	0.704881	−	0.709325i	$-0.251000\pi$
$642$	32628.6	−	100421.i	0.0791642	−	0.243642i
$643$	402905.	+	292727.i	0.974497	+	0.708013i	0.956472	−	0.291824i	$-0.0942622\pi$
$643$	402905.	+	292727.i	0.974497	+	0.708013i	0.0180249	+	0.999838i	$0.494262\pi$
$644$	−131501.	+	180995.i	−0.317070	+	0.436410i
$645$	127605.	+	41461.3i	0.306723	+	0.0996605i
$646$	171894.	−	55851.6i	0.411903	−	0.133835i
$647$	27603.1	−	20054.8i	0.0659400	−	0.0479082i	−0.554327	−	0.832299i	$-0.687024\pi$
$647$	27603.1	−	20054.8i	0.0659400	−	0.0479082i	0.620267	+	0.784391i	$0.287024\pi$
$648$			22500.1i			0.0535839i
$649$	116412.	+	735980.i	0.276380	+	1.74734i
$650$	48702.6			0.115273
$651$	46053.3	+	63386.9i	0.108667	+	0.149568i
$652$	−59375.9	−	182740.i	−0.139674	−	0.429872i
$653$	92460.2	−	284563.i	0.216835	−	0.667348i	−0.782184	−	0.623048i	$-0.785894\pi$
$653$	92460.2	−	284563.i	0.216835	−	0.667348i	0.999018	−	0.0443002i	$-0.0141058\pi$
$654$	−274501.	−	199437.i	−0.641783	−	0.466283i
$655$	−251463.	+	346109.i	−0.586127	+	0.806735i
$656$	−153620.	−	49914.2i	−0.356977	−	0.115989i
$657$	168083.	−	54613.4i	0.389397	−	0.126523i
$658$	288186.	−	209380.i	0.665613	−	0.483596i
$659$		−	187383.i		−	0.431479i	−0.976451	−	0.215740i	$-0.930784\pi$
$659$		−	187383.i		−	0.431479i	0.976451	−	0.215740i	$-0.0692162\pi$
$660$	−171217.	−	27154.5i	−0.393061	−	0.0623382i
$661$	−87569.9			−0.200425			−0.100212	−	0.994966i	$-0.531952\pi$
$661$	−87569.9			−0.200425			−0.100212	+	0.994966i	$0.531952\pi$
$662$	−253493.	−	348903.i	−0.578429	−	0.796139i
$663$	−45336.9	−	139533.i	−0.103139	−	0.317431i
$664$	5020.96	−	15452.9i	0.0113881	−	0.0350489i
$665$	−176157.	−	127985.i	−0.398341	−	0.289412i
$666$	153998.	−	211960.i	0.347189	−	0.477865i
$667$	−849693.	−	276082.i	−1.90990	−	0.620564i
$668$	64753.2	−	21039.6i	0.145114	−	0.0471503i
$669$	−298273.	+	216708.i	−0.666440	+	0.484197i
$670$			525029.i			1.16959i
$671$	44280.3	−	279200.i	0.0983480	−	0.620113i
$672$	−44590.8			−0.0987431
$673$	202939.	+	279321.i	0.448059	+	0.616700i	0.971979	−	0.235067i	$-0.0755311\pi$
$673$	202939.	+	279321.i	0.448059	+	0.616700i	−0.523920	+	0.851767i	$0.675531\pi$
$674$	155569.	+	478792.i	0.342455	+	1.05397i
$675$	58877.4	−	181206.i	0.129223	−	0.397709i
$676$	154425.	+	112196.i	0.337928	+	0.245519i
$677$	−311771.	+	429116.i	−0.680234	+	0.936261i	−0.999937	−	0.0112566i	$-0.996417\pi$
$677$	−311771.	+	429116.i	−0.680234	+	0.936261i	0.319703	+	0.947518i	$0.396417\pi$
$678$	181846.	+	59085.3i	0.395589	+	0.128535i
$679$	−55347.7	+	17983.6i	−0.120049	+	0.0390064i
$680$	−191634.	+	139230.i	−0.414434	+	0.301104i
$681$		−	473679.i		−	1.02139i
$682$	−107519.	+	17006.5i	−0.231162	+	0.0365634i
$683$	−640164.			−1.37230			−0.686151	−	0.727459i	$-0.740701\pi$
$683$	−640164.			−1.37230			−0.686151	+	0.727459i	$0.740701\pi$
$684$	−37717.3	−	51913.4i	−0.0806174	−	0.110960i
$685$	−112610.	−	346578.i	−0.239991	−	0.738617i
$686$	111894.	−	344373.i	0.237770	−	0.731780i
$687$	−101010.	−	73388.0i	−0.214018	−	0.155493i
$688$	−28183.3	+	38791.0i	−0.0595409	+	0.0819510i
$689$	215813.	+	70122.0i	0.454611	+	0.147712i
$690$	−330900.	+	107516.i	−0.695021	+	0.225826i
$691$	−559193.	+	406277.i	−1.17113	+	0.850876i	−0.991144	−	0.132793i	$-0.957605\pi$
$691$	−559193.	+	406277.i	−1.17113	+	0.850876i	−0.179987	+	0.983669i	$0.557605\pi$
$692$		−	137293.i		−	0.286706i
$693$	−154674.	+	154610.i	−0.322071	+	0.321938i
$694$	417926.			0.867721
$695$	−38042.1	−	52360.5i	−0.0787581	−	0.108401i
$696$	−55026.9	−	169355.i	−0.113594	−	0.349607i
$697$	275828.	−	848911.i	0.567770	−	1.74742i
$698$	36749.4	+	26700.0i	0.0754292	+	0.0548025i
$699$	309970.	−	426638.i	0.634404	−	0.873182i
$700$	77794.5	+	25277.0i	0.158764	+	0.0515856i
$701$	−320371.	+	104095.i	−0.651954	+	0.211833i	−0.616275	−	0.787531i	$-0.711359\pi$
$701$	−320371.	+	104095.i	−0.651954	+	0.211833i	−0.0356784	+	0.999363i	$0.511359\pi$
$702$	−119029.	+	86479.6i	−0.241534	+	0.175485i
$703$		−	377006.i		−	0.762847i
$704$	28137.1	−	55193.8i	0.0567719	−	0.111364i
$705$	553983.			1.11460
$706$	159735.	+	219856.i	0.320472	+	0.441092i
$707$	212246.	+	653225.i	0.424619	+	1.30684i
$708$	−92108.4	+	283480.i	−0.183752	+	0.565531i
$709$	−301290.	−	218900.i	−0.599367	−	0.435466i	0.246287	−	0.969197i	$-0.420789\pi$
$709$	−301290.	−	218900.i	−0.599367	−	0.435466i	−0.845654	+	0.533731i	$0.820789\pi$
$710$	−23267.7	+	32025.2i	−0.0461569	+	0.0635295i
$711$	401428.	+	130432.i	0.794088	+	0.258015i
$712$	−127447.	+	41410.0i	−0.251402	+	0.0816856i
$713$	−176749.	+	128416.i	−0.347679	+	0.252604i
$714$		−	246411.i		−	0.483351i
$715$	−111439.	−	218823.i	−0.217984	−	0.428037i
$716$	−119480.			−0.233060
$717$	−207028.	−	284949.i	−0.402708	−	0.554280i
$718$	−92376.4	−	284305.i	−0.179189	−	0.551488i
$719$	18964.4	−	58366.5i	0.0366844	−	0.112903i	−0.931037	−	0.364924i	$-0.881095\pi$
$719$	18964.4	−	58366.5i	0.0366844	−	0.112903i	0.967722	+	0.252021i	$0.0810951\pi$
$720$	68036.4	+	49431.4i	0.131243	+	0.0953537i
$721$	−100616.	+	138486.i	−0.193552	+	0.266401i
$722$	262745.	+	85371.1i	0.504035	+	0.163771i
$723$	332284.	−	107966.i	0.635671	−	0.206542i
$724$	−186104.	+	135213.i	−0.355042	+	0.257953i
$725$			326655.i			0.621460i
$726$	77325.7	+	238320.i	0.146707	+	0.452155i
$727$	163114.			0.308618			0.154309	−	0.988023i	$-0.450685\pi$
$727$	163114.			0.308618			0.154309	+	0.988023i	$0.450685\pi$
$728$	−37127.0	−	51100.9i	−0.0700530	−	0.0964197i
$729$	128536.	+	395594.i	0.241864	+	0.744380i
$730$	−102994.	+	316983.i	−0.193271	+	0.594827i
$731$	−214361.	−	155742.i	−0.401153	−	0.291455i
$732$	66468.1	−	91485.5i	0.124048	−	0.170738i
$733$	521698.	+	169510.i	0.970983	+	0.315492i	0.751213	−	0.660060i	$-0.229469\pi$
$733$	521698.	+	169510.i	0.970983	+	0.315492i	0.219770	+	0.975552i	$0.429469\pi$
$734$	−221548.	+	71985.4i	−0.411222	+	0.133614i
$735$	107707.	−	78253.8i	0.199375	−	0.144854i
$736$		−	124338.i		−	0.229534i
$737$	676182.	−	344356.i	1.24488	−	0.633975i
$738$	−316902.			−0.581851
$739$	−182037.	−	250552.i	−0.333326	−	0.458784i	0.609151	−	0.793054i	$-0.291510\pi$
$739$	−182037.	−	250552.i	−0.333326	−	0.458784i	−0.942477	+	0.334270i	$0.891510\pi$
$740$	152683.	+	469911.i	0.278823	+	0.858129i
$741$	−23161.8	+	71284.7i	−0.0421829	+	0.129826i
$742$	308332.	+	224017.i	0.560030	+	0.406886i
$743$	−135569.	+	186594.i	−0.245573	+	0.338003i	−0.913955	−	0.405816i	$-0.866987\pi$
$743$	−135569.	+	186594.i	−0.245573	+	0.338003i	0.668381	+	0.743819i	$0.266987\pi$
$744$	−41413.6	−	13456.1i	−0.0748164	−	0.0243093i
$745$	410215.	−	133287.i	0.739094	−	0.240146i
$746$	154712.	−	112405.i	0.278001	−	0.201979i
$747$		−	31877.7i		−	0.0571276i
$748$	305003.	+	155486.i	0.545131	+	0.277901i
$749$	251207.			0.447783
$750$	−111312.	−	153208.i	−0.197888	−	0.272369i
$751$	57394.0	+	176640.i	0.101762	+	0.313192i	0.988957	−	0.148203i	$-0.0473490\pi$
$751$	57394.0	+	176640.i	0.101762	+	0.313192i	−0.887195	+	0.461395i	$0.847349\pi$
$752$	−61177.6	+	188285.i	−0.108182	+	0.332951i
$753$	−56352.1	−	40942.2i	−0.0993848	−	0.0722073i
$754$	148264.	−	204068.i	0.260792	−	0.358949i
$755$	−327791.	−	106506.i	−0.575047	−	0.186844i
$756$	−235013.	+	76360.2i	−0.411195	+	0.133605i
$757$	557575.	−	405102.i	0.972997	−	0.706924i	0.0168643	−	0.999858i	$-0.494632\pi$
$757$	557575.	−	405102.i	0.972997	−	0.706924i	0.956133	+	0.292934i	$0.0946317\pi$
$758$			311849.i			0.542758i
$759$	355499.	+	355647.i	0.617100	+	0.617356i
$760$	121014.			0.209512
$761$	329.053	+	452.902i	0.000568193	+	0.000782051i	0.809301	−	0.587394i	$-0.199846\pi$
$761$	329.053	+	452.902i	0.000568193	+	0.000782051i	−0.808733	+	0.588176i	$0.799846\pi$
$762$	−22537.5	−	69363.2i	−0.0388146	−	0.119459i
$763$	249450.	−	767729.i	0.428484	−	1.31874i
$764$	128862.	+	93623.7i	0.220769	+	0.160398i
$765$	−273160.	+	375972.i	−0.466760	+	0.642440i
$766$	545159.	+	177133.i	0.929107	+	0.301885i
$767$	−401558.	+	130474.i	−0.682587	+	0.221786i
$768$	20049.2	−	14566.6i	0.0339919	−	0.0246966i
$769$			632490.i			1.06955i	0.844994	+	0.534775i	$0.179604\pi$
$769$			632490.i			1.06955i	−0.844994	+	0.534775i	$0.820396\pi$
$770$	−64434.8	−	407372.i	−0.108677	−	0.687084i
$771$	−481357.			−0.809765
$772$	−90318.5	−	124313.i	−0.151545	−	0.208584i
$773$	82826.3	+	254913.i	0.138615	+	0.426612i	0.996135	−	0.0878383i	$-0.0279959\pi$
$773$	82826.3	+	254913.i	0.138615	+	0.426612i	−0.857520	+	0.514451i	$0.827996\pi$
$774$	−29069.6	+	89467.0i	−0.0485240	+	0.149342i
$775$	64623.6	+	46951.8i	0.107594	+	0.0781716i
$776$	19011.1	−	26166.5i	0.0315706	−	0.0434533i
$777$	−488832.	−	158831.i	−0.809689	−	0.263084i
$778$	−671130.	+	218063.i	−1.10879	+	0.360266i
$779$	−368922.	+	268037.i	−0.607938	+	0.441693i
$780$		−	98231.7i		−	0.161459i
$781$	56506.0	+	8961.68i	0.0926387	+	0.0146922i
$782$	687096.			1.12358
$783$	−580030.	−	798343.i	−0.946079	−	1.30217i
$784$	14702.2	+	45248.8i	0.0239194	+	0.0736164i
$785$	135588.	−	417298.i	0.220031	−	0.677185i
$786$	200102.	+	145383.i	0.323897	+	0.235325i
$787$	−408989.	+	562926.i	−0.660332	+	0.908870i	−0.999492	−	0.0318591i	$-0.989857\pi$
$787$	−408989.	+	562926.i	−0.660332	+	0.908870i	0.339160	+	0.940729i	$0.389857\pi$
$788$	−88023.6	−	28600.6i	−0.141758	−	0.0460599i
$789$	383329.	−	124551.i	0.615769	−	0.200075i
$790$	−643980.	+	467879.i	−1.03185	+	0.749686i
$791$			454896.i			0.727041i
$792$	19038.7	−	120045.i	0.0303520	−	0.191379i
$793$	160184.			0.254726
$794$	−307555.	−	423314.i	−0.487846	−	0.671462i
$795$	183158.	+	563701.i	0.289795	+	0.891897i
$796$	31005.2	−	95424.1i	0.0489337	−	0.150602i
$797$	138891.	+	100910.i	0.218654	+	0.158862i	0.691721	−	0.722165i	$-0.256853\pi$
$797$	138891.	+	100910.i	0.218654	+	0.158862i	−0.473066	+	0.881027i	$0.656853\pi$
$798$	−73994.4	+	101845.i	−0.116196	+	0.159931i
$799$	−1.04047e6	−	338070.i	−1.62981	−	0.529557i
$800$	−43235.8	+	14048.2i	−0.0675559	+	0.0219502i
$801$	−212698.	+	154534.i	−0.331511	+	0.240857i
$802$		−	664513.i		−	1.03313i
$803$	475793.	−	75257.2i	0.737883	−	0.116712i
$804$	303544.			0.469580
$805$	−486546.	−	669673.i	−0.750813	−	1.03341i
$806$	−19060.9	−	58663.5i	−0.0293410	−	0.0903022i
$807$	−115216.	+	354598.i	−0.176915	+	0.544489i
$808$	−308822.	−	224373.i	−0.473027	−	0.343674i
$809$	651532.	−	896756.i	0.995494	−	1.37018i	0.0674438	−	0.997723i	$-0.478516\pi$
$809$	651532.	−	896756.i	0.995494	−	1.37018i	0.928050	−	0.372456i	$-0.121484\pi$
$810$	−79174.8	−	25725.4i	−0.120675	−	0.0392096i
$811$	97912.6	−	31813.7i	0.148866	−	0.0483696i	−0.233636	−	0.972324i	$-0.575062\pi$
$811$	97912.6	−	31813.7i	0.148866	−	0.0483696i	0.382502	+	0.923955i	$0.375062\pi$
$812$	342741.	−	249016.i	0.519820	−	0.377672i
$813$			631148.i			0.954883i
$814$	505055.	−	504846.i	0.762237	−	0.761921i
$815$	710925.			1.07031
$816$	80495.7	+	110793.i	0.120891	+	0.166392i
$817$	41830.3	+	128740.i	0.0626681	+	0.192873i
$818$	−59552.1	+	183282.i	−0.0890001	+	0.273914i
$819$	−100256.	−	72840.4i	−0.149466	−	0.108594i
$820$	351283.	−	483499.i	0.522431	−	0.719065i
$821$	−116676.	−	37910.3i	−0.173099	−	0.0562433i	0.221185	−	0.975232i	$-0.429007\pi$
$821$	−116676.	−	37910.3i	−0.173099	−	0.0562433i	−0.394284	+	0.918989i	$0.629007\pi$
$822$	−200373.	+	65105.2i	−0.296549	+	0.0963545i
$823$	72509.2	−	52681.0i	0.107052	−	0.0777776i	−0.532972	−	0.846133i	$-0.678925\pi$
$823$	72509.2	−	52681.0i	0.107052	−	0.0777776i	0.640023	+	0.768356i	$0.278925\pi$
$824$		−	95135.6i		−	0.140116i
$825$	83502.8	−	163799.i	0.122685	−	0.240660i
$826$	−709140.			−1.03937
$827$	337437.	+	464442.i	0.493380	+	0.679080i	0.981007	−	0.193973i	$-0.0621373\pi$
$827$	337437.	+	464442.i	0.493380	+	0.679080i	−0.487627	+	0.873052i	$0.662137\pi$
$828$	−75382.2	−	232002.i	−0.109953	−	0.338401i
$829$	14351.4	−	44169.2i	0.0208827	−	0.0642703i	−0.940072	−	0.340976i	$-0.889243\pi$
$829$	14351.4	−	44169.2i	0.0208827	−	0.0642703i	0.960955	+	0.276705i	$0.0892426\pi$
$830$	48636.1	+	35336.2i	0.0705996	+	0.0512936i
$831$	−131730.	+	181311.i	−0.190758	+	0.262556i
$832$	33386.6	+	10848.0i	0.0482309	+	0.0156712i
$833$	−250046.	+	81245.0i	−0.360355	+	0.117086i
$834$	−30272.1	+	21994.0i	−0.0435222	+	0.0316207i
$835$			251913.i			0.361308i
$836$	−79370.7	−	155854.i	−0.113566	−	0.223000i
$837$	−241310.			−0.344449
$838$	−303899.	−	418281.i	−0.432754	−	0.595634i
$839$	−301538.	−	928039.i	−0.428370	−	1.31839i	−0.899731	−	0.436446i	$-0.856237\pi$
$839$	−301538.	−	928039.i	−0.428370	−	1.31839i	0.471361	−	0.881940i	$-0.343763\pi$
$840$	50982.8	−	156909.i	0.0722546	−	0.222377i
$841$	796511.	+	578699.i	1.12616	+	0.818203i
$842$	−172715.	+	237722.i	−0.243617	+	0.335309i
$843$	−385992.	−	125416.i	−0.543154	−	0.176481i
$844$	−195134.	+	63403.0i	−0.273936	+	0.0890071i
$845$	−571366.	+	415121.i	−0.800204	+	0.581382i
$846$			388412.i			0.542691i
$847$	−482391.	+	350172.i	−0.672408	+	0.488107i
$848$	−211815.			−0.294554
$849$	−361502.	−	497565.i	−0.501529	−	0.690295i
$850$	−77630.7	−	238923.i	−0.107447	−	0.330689i
$851$	442888.	−	1.36307e6i	0.611554	−	1.88217i
$852$	18515.3	+	13452.2i	0.0255066	+	0.0185316i
$853$	−760991.	+	1.04741e6i	−1.04588	+	1.43953i	−0.153552	+	0.988140i	$0.549071\pi$
$853$	−760991.	+	1.04741e6i	−1.04588	+	1.43953i	−0.892327	+	0.451389i	$0.850929\pi$
$854$	255868.	+	83136.6i	0.350833	+	0.113993i
$855$	225800.	−	73367.0i	0.308882	−	0.100362i
$856$	−112949.	+	82062.6i	−0.154147	+	0.111995i
$857$			26805.1i			0.0364969i	0.999833	+	0.0182485i	$0.00580898\pi$
$857$			26805.1i			0.0364969i	−0.999833	+	0.0182485i	$0.994191\pi$
$858$	−126512.	+	64428.2i	−0.171853	+	0.0875188i
$859$	−604004.			−0.818566			−0.409283	−	0.912408i	$-0.634221\pi$
$859$	−604004.			−0.818566			−0.409283	+	0.912408i	$0.634221\pi$
$860$	−104277.	−	143525.i	−0.140991	−	0.194058i
$861$	192117.	+	591274.i	0.259154	+	0.797595i
$862$	−198877.	+	612081.i	−0.267652	+	0.823748i
$863$	720560.	+	523518.i	0.967495	+	0.702926i	0.954879	−	0.296994i	$-0.0959842\pi$
$863$	720560.	+	523518.i	0.967495	+	0.702926i	0.0126158	+	0.999920i	$0.495984\pi$
$864$	80723.2	−	111106.i	0.108136	−	0.148837i
$865$	483116.	+	156974.i	0.645683	+	0.209795i
$866$	823969.	−	267724.i	1.09869	−	0.356986i
$867$	−203424.	+	147796.i	−0.270623	+	0.196619i
$868$		−	103598.i		−	0.137503i
$869$	1.02495e6	+	522507.i	1.35726	+	0.691915i
$870$	658853.			0.870463
$871$	252735.	+	347860.i	0.333142	+	0.458531i
$872$	138637.	+	426680.i	0.182325	+	0.561138i
$873$	19608.9	−	60350.0i	0.0257291	−	0.0791861i
$874$	−283985.	−	206327.i	−0.371769	−	0.270106i
$875$	264824.	−	364499.i	0.345892	−	0.476080i
$876$	183263.	+	59545.8i	0.238818	+	0.0775967i
$877$	280503.	−	91140.9i	0.364702	−	0.118499i	−0.120933	−	0.992661i	$-0.538589\pi$
$877$	280503.	−	91140.9i	0.364702	−	0.118499i	0.485635	+	0.874162i	$0.338589\pi$
$878$	−235382.	+	171015.i	−0.305341	+	0.221843i
$879$			116087.i			0.150247i
$880$	162049.	+	162116.i	0.209258	+	0.209344i
$881$	−995350.			−1.28240			−0.641201	−	0.767373i	$-0.721563\pi$
$881$	−995350.			−1.28240			−0.641201	+	0.767373i	$0.721563\pi$
$882$	54865.8	+	75516.3i	0.0705285	+	0.0970742i
$883$	57744.8	+	177720.i	0.0740613	+	0.227937i	0.981234	−	0.192822i	$-0.0617639\pi$
$883$	57744.8	+	177720.i	0.0740613	+	0.227937i	−0.907173	+	0.420759i	$0.861764\pi$
$884$	−59946.2	+	184495.i	−0.0767109	+	0.236092i
$885$	−892217.	−	648234.i	−1.13916	−	0.827647i
$886$	−438155.	+	603069.i	−0.558162	+	0.768245i
$887$	1.25395e6	+	407434.i	1.59380	+	0.517857i	0.965564	−	0.260166i	$-0.0837771\pi$
$887$	1.25395e6	+	407434.i	1.59380	+	0.517857i	0.628236	+	0.778023i	$0.283777\pi$
$888$	271678.	−	88273.6i	0.344531	−	0.111945i
$889$	140377.	−	101990.i	0.177620	−	0.129049i
$890$		−	495814.i		−	0.625949i
$891$	18797.4	+	118842.i	0.0236779	+	0.149697i
$892$	487490.			0.612683
$893$	328521.	+	452171.i	0.411965	+	0.567022i
$894$	−77059.6	−	237165.i	−0.0964166	−	0.296740i
$895$	136607.	−	420433.i	0.170540	−	0.524869i
$896$	47699.4	+	34655.6i	0.0594151	+	0.0431676i
$897$	−167484.	+	230522.i	−0.208156	+	0.286501i
$898$	684377.	+	222367.i	0.848677	+	0.275752i
$899$	393464.	−	127844.i	0.486840	−	0.158184i
$900$	−72156.8	+	52425.0i	−0.0890825	+	0.0647222i
$901$		−	1.17050e6i		−	1.44185i
$902$	−853096.	−	135298.i	−1.04854	−	0.166295i
$903$	184550.			0.226328
$904$	−148602.	−	204533.i	−0.181840	−	0.250281i
$905$	−263013.	−	809471.i	−0.321130	−	0.988335i
$906$	−61576.1	+	189512.i	−0.0750163	+	0.230876i
$907$	745514.	+	541648.i	0.906236	+	0.658419i	0.940060	−	0.341009i	$-0.110769\pi$
$907$	745514.	+	541648.i	0.906236	+	0.658419i	−0.0338240	+	0.999428i	$0.510769\pi$
$908$	−368140.	+	506701.i	−0.446520	+	0.614582i
$909$	−712262.	−	231428.i	−0.862010	−	0.280084i
$910$	222266.	−	72218.7i	0.268405	−	0.0872101i
$911$	463915.	−	337054.i	0.558986	−	0.406127i	−0.272101	−	0.962269i	$-0.587719\pi$
$911$	463915.	−	337054.i	0.558986	−	0.406127i	0.831088	+	0.556141i	$0.187719\pi$
$912$		−	69964.0i		−	0.0841172i
$913$	13609.9	−	85814.5i	0.0163273	−	0.102948i
$914$	320349.			0.383470
$915$	245929.	+	338492.i	0.293743	+	0.404303i
$916$	51015.1	+	157008.i	0.0608005	+	0.187125i
$917$	−181841.	+	559650.i	−0.216249	+	0.665545i
$918$	613976.	+	446079.i	0.728561	+	0.529330i
$919$	935540.	−	1.28766e6i	1.10772	−	1.52465i	0.282996	−	0.959121i	$-0.408672\pi$
$919$	935540.	−	1.28766e6i	1.10772	−	1.52465i	0.824728	−	0.565530i	$-0.191328\pi$
$920$	437528.	+	142162.i	0.516928	+	0.167960i
$921$	17376.8	−	5646.05i	0.0204856	−	0.00665619i
$922$	197391.	−	143413.i	0.232201	−	0.168704i
$923$			32419.0i			0.0380536i
$924$	−235521.	+	37252.9i	−0.275858	+	0.0436331i
$925$	−524017.			−0.612438
$926$	63259.2	+	87068.8i	0.0737737	+	0.101541i
$927$	−57677.7	−	177514.i	−0.0671195	−	0.206573i
$928$	−72758.7	+	223928.i	−0.0844868	+	0.260024i
$929$	−759143.	−	551550.i	−0.879614	−	0.639077i	0.0535354	−	0.998566i	$-0.482951\pi$
$929$	−759143.	−	551550.i	−0.879614	−	0.639077i	−0.933149	+	0.359489i	$0.882951\pi$
$930$	94700.3	−	130344.i	0.109493	−	0.150704i
$931$	127744.	+	41506.6i	0.147381	+	0.0478871i
$932$	−663159.	+	215473.i	−0.763459	+	0.248063i
$933$	7520.73	−	5464.13i	0.00863966	−	0.00627708i
$934$		−	460963.i		−	0.528412i
$935$	−895861.	+	895489.i	−1.02475	+	1.02432i
$936$	68872.9			0.0786134
$937$	−9244.03	−	12723.3i	−0.0105289	−	0.0144918i	0.803720	−	0.595008i	$-0.202851\pi$
$937$	−9244.03	−	12723.3i	−0.0105289	−	0.0144918i	−0.814249	+	0.580516i	$0.802851\pi$
$938$	223162.	+	686821.i	0.253638	+	0.780616i
$939$	220816.	−	679603.i	0.250438	−	0.770768i
$940$	−592603.	−	430552.i	−0.670669	−	0.487270i
$941$	−11190.8	+	15402.8i	−0.0126381	+	0.0173948i	−0.815289	−	0.579054i	$-0.803422\pi$
$941$	−11190.8	+	15402.8i	−0.0126381	+	0.0173948i	0.802651	+	0.596449i	$0.203422\pi$
$942$	−241260.	−	78390.2i	−0.271884	−	0.0883405i
$943$	−1.64872e6	+	535702.i	−1.85406	+	0.602420i
$944$	318848.	−	231657.i	0.357800	−	0.259957i
$945$		−	914284.i		−	1.02381i
$946$	−116452.	+	228433.i	−0.130126	+	0.255257i
$947$	422589.			0.471214			0.235607	−	0.971848i	$-0.424292\pi$
$947$	422589.			0.471214			0.235607	+	0.971848i	$0.424292\pi$
$948$	270503.	+	372316.i	0.300993	+	0.414281i
$949$	84348.4	+	259598.i	0.0936579	+	0.288249i
$950$	−39660.1	+	122061.i	−0.0439447	+	0.135248i
$951$	−155877.	−	113251.i	−0.172354	−	0.125222i
$952$	−191508.	+	263589.i	−0.211307	+	0.290839i
$953$	−682123.	−	221635.i	−0.751064	−	0.244036i	−0.0916252	−	0.995794i	$-0.529206\pi$
$953$	−682123.	−	221635.i	−0.751064	−	0.244036i	−0.659439	+	0.751758i	$0.729206\pi$
$954$	−395226.	+	128417.i	−0.434259	+	0.141099i
$955$	−476783.	+	346403.i	−0.522774	+	0.379818i
$956$			465714.i			0.509570i
$957$	−432129.	−	848535.i	−0.471834	−	0.926501i
$958$	−522250.			−0.569046
$959$	−294623.	−	405514.i	−0.320354	−	0.440929i
$960$	28334.7	+	87205.2i	0.0307451	+	0.0946238i
$961$	−254121.	+	782104.i	−0.275165	+	0.846872i
$962$	327364.	+	237844.i	0.353738	+	0.257005i
$963$	−161001.	+	221598.i	−0.173610	+	0.238954i
$964$	−439358.	−	142756.i	−0.472786	−	0.153618i
$965$	540705.	−	175686.i	0.580639	−	0.188661i
$966$	−387170.	+	281295.i	−0.414904	+	0.301445i
$967$			131854.i			0.141007i	0.997512	+	0.0705033i	$0.0224605\pi$
$967$			131854.i			0.141007i	−0.997512	+	0.0705033i	$0.977539\pi$
$968$	102504.	−	315031.i	0.109393	−	0.336204i
$969$	386624.			0.411757
$970$	70340.1	+	96814.9i	0.0747583	+	0.102896i
$971$	−418337.	−	1.28751e6i	−0.443698	−	1.36556i	−0.883905	−	0.467667i	$-0.845095\pi$
$971$	−418337.	−	1.28751e6i	−0.443698	−	1.36556i	0.440206	−	0.897897i	$-0.354905\pi$
$972$	137046.	−	421784.i	0.145055	−	0.446434i
$973$	−72020.8	−	52326.2i	−0.0760733	−	0.0552705i
$974$	388404.	−	534593.i	0.409417	−	0.563514i
$975$	99081.8	+	32193.6i	0.104228	+	0.0338658i
$976$	−142204.	+	46204.8i	−0.149283	+	0.0485051i
$977$	−134790.	+	97931.0i	−0.141211	+	0.102596i	−0.656148	−	0.754632i	$-0.727815\pi$
$977$	−134790.	+	97931.0i	−0.141211	+	0.102596i	0.514937	+	0.857228i	$0.327815\pi$
$978$		−	411020.i		−	0.429719i
$979$	−638558.	+	325195.i	−0.666246	+	0.339295i
$980$	−176034.			−0.183292
$981$	517365.	+	712092.i	0.537600	+	0.739943i
$982$	−177256.	−	545538.i	−0.183814	−	0.565721i
$983$	−29255.0	+	90037.5i	−0.0302756	+	0.0931786i	−0.965052	−	0.262057i	$-0.915599\pi$
$983$	−29255.0	+	90037.5i	−0.0302756	+	0.0931786i	0.934777	+	0.355235i	$0.115599\pi$
$984$	−279534.	−	203093.i	−0.288699	−	0.209752i
$985$	201283.	−	277043.i	0.207460	−	0.285545i
$986$	−1.23744e6	−	402067.i	−1.27283	−	0.413566i
$987$	724698.	−	235469.i	0.743914	−	0.241712i
$988$	80178.5	−	58253.1i	0.0821379	−	0.0596767i
$989$			514603.i			0.526114i
$990$	400654.	+	204248.i	0.408789	+	0.208395i
$991$	723807.			0.737013			0.368507	−	0.929625i	$-0.379869\pi$
$991$	723807.			0.737013			0.368507	+	0.929625i	$0.379869\pi$
$992$	33842.7	+	46580.5i	0.0343908	+	0.0473348i
$993$	−285079.	−	877382.i	−0.289112	−	0.889796i
$994$	−16825.6	+	51784.0i	−0.0170294	+	0.0524110i
$995$	300335.	+	218206.i	0.303361	+	0.220405i
$996$	20429.5	−	28118.9i	0.0205940	−	0.0283452i
$997$	−15029.6	−	4883.42i	−0.0151202	−	0.00491285i	0.301447	−	0.953483i	$-0.402530\pi$
$997$	−15029.6	−	4883.42i	−0.0151202	−	0.00491285i	−0.316567	+	0.948570i	$0.602530\pi$
$998$	1.13479e6	−	368717.i	1.13935	−	0.370196i
$999$	1.28069e6	−	930479.i	1.28326	−	0.932343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.5.d.a.19.1	yes	16
3.2	odd	2		198.5.j.a.19.4		16
4.3	odd	2		176.5.n.c.129.4		16
11.2	odd	10		242.5.b.e.241.2		16
11.7	odd	10	inner	22.5.d.a.7.1	✓	16
11.9	even	5		242.5.b.e.241.10		16
33.29	even	10		198.5.j.a.73.4		16
44.7	even	10		176.5.n.c.161.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.d.a.7.1	✓	16	11.7	odd	10	inner
22.5.d.a.19.1	yes	16	1.1	even	1	trivial
176.5.n.c.129.4		16	4.3	odd	2
176.5.n.c.161.4		16	44.7	even	10
198.5.j.a.19.4		16	3.2	odd	2
198.5.j.a.73.4		16	33.29	even	10
242.5.b.e.241.2		16	11.2	odd	10
242.5.b.e.241.10		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)

\(f(q)\)	\(=\)	\(q+(-1.66251 - 2.28825i) q^{2} +(-1.86966 - 5.75422i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(-23.9466 - 17.3982i) q^{5} +(-10.0587 + 13.8447i) q^{6} +(-38.7210 - 12.5812i) q^{7} +(21.5200 - 6.99226i) q^{8} +(35.9150 - 26.0937i) q^{9} +O(q^{10})\)	\(q+(-1.66251 - 2.28825i) q^{2} +(-1.86966 - 5.75422i) q^{3} +(-2.47214 + 7.60845i) q^{4} +(-23.9466 - 17.3982i) q^{5} +(-10.0587 + 13.8447i) q^{6} +(-38.7210 - 12.5812i) q^{7} +(21.5200 - 6.99226i) q^{8} +(35.9150 - 26.0937i) q^{9} +83.7204i q^{10} +(107.823 - 54.9105i) q^{11} +48.4028 q^{12} +(40.3008 + 55.4694i) q^{13} +(35.5851 + 109.520i) q^{14} +(-55.3412 + 170.323i) q^{15} +(-51.7771 - 37.6183i) q^{16} +(207.880 - 286.122i) q^{17} +(-119.418 - 38.8012i) q^{18} +(-171.839 + 55.8338i) q^{19} +(191.573 - 139.186i) q^{20} +246.332i q^{21} +(-304.906 - 155.437i) q^{22} -686.876 q^{23} +(-80.4700 - 110.757i) q^{24} +(77.6058 + 238.846i) q^{25} +(59.9270 - 184.436i) q^{26} +(-613.779 - 445.937i) q^{27} +(191.447 - 263.504i) q^{28} +(1237.04 + 401.939i) q^{29} +(481.745 - 156.529i) q^{30} +(257.323 - 186.956i) q^{31} +181.019i q^{32} +(-517.560 - 517.774i) q^{33} -1000.32 q^{34} +(708.346 + 974.954i) q^{35} +(109.746 + 337.765i) q^{36} +(-644.786 + 1984.45i) q^{37} +(413.444 + 300.385i) q^{38} +(243.834 - 335.609i) q^{39} +(-636.983 - 206.968i) q^{40} +(2400.32 - 779.910i) q^{41} +(563.668 - 409.528i) q^{42} -749.193i q^{43} +(151.230 + 956.114i) q^{44} -1314.03 q^{45} +(1141.94 + 1571.74i) q^{46} +(-955.900 - 2941.96i) q^{47} +(-119.658 + 368.270i) q^{48} +(-601.420 - 436.958i) q^{49} +(417.519 - 574.665i) q^{50} +(-2035.07 - 661.236i) q^{51} +(-521.665 + 169.499i) q^{52} +(2677.53 - 1945.34i) q^{53} +2145.85i q^{54} +(-3537.34 - 561.012i) q^{55} -921.245 q^{56} +(642.560 + 884.407i) q^{57} +(-1136.85 - 3498.88i) q^{58} +(-1902.96 + 5856.70i) q^{59} +(-1159.08 - 842.122i) q^{60} +(1373.23 - 1890.09i) q^{61} +(-855.604 - 278.003i) q^{62} +(-1718.95 + 558.522i) q^{63} +(414.217 - 300.946i) q^{64} -2029.47i q^{65} +(-324.348 + 2045.11i) q^{66} +6271.22 q^{67} +(1663.04 + 2288.98i) q^{68} +(1284.22 + 3952.44i) q^{69} +(1053.30 - 3241.74i) q^{70} +(382.526 + 277.922i) q^{71} +(590.434 - 812.663i) q^{72} +(3786.21 + 1230.22i) q^{73} +(5612.86 - 1823.73i) q^{74} +(1229.28 - 893.122i) q^{75} -1445.45i q^{76} +(-4865.86 + 769.643i) q^{77} -1173.33 q^{78} +(5588.59 + 7692.04i) q^{79} +(585.394 + 1801.66i) q^{80} +(-307.278 + 945.705i) q^{81} +(-5775.17 - 4195.91i) q^{82} +(422.074 - 580.935i) q^{83} +(-1874.20 - 608.966i) q^{84} +(-9956.03 + 3234.91i) q^{85} +(-1714.34 + 1245.54i) q^{86} -7869.69i q^{87} +(1936.40 - 1935.60i) q^{88} -5922.27 q^{89} +(2184.58 + 3006.81i) q^{90} +(-862.617 - 2654.86i) q^{91} +(1698.05 - 5226.06i) q^{92} +(-1556.89 - 1131.15i) q^{93} +(-5142.73 + 7078.37i) q^{94} +(5086.36 + 1652.66i) q^{95} +(1041.63 - 338.445i) q^{96} +(1156.41 - 840.179i) q^{97} +2102.64i q^{98} +(2439.64 - 4785.62i) 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

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