LMFDB - Embedded newform 9.5.d.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,5,Mod(2,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("9.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.930329667755$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.39400128.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 $ x^6 - x^5 + 11x^4 + 14x^3 + 98x^2 + 20x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2.2
Root			$-0.102534 + 0.177594i$ of defining polynomial
Character	$\chi$	$=$	9.2
Dual form			9.5.d.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.307601 + 0.177594i) q^{2} +(8.32172 + 3.42768i) q^{3} +(-7.93692 - 13.7472i) q^{4} +(-30.0804 + 17.3669i) q^{5} +(1.95104 + 2.53225i) q^{6} +(15.6054 - 27.0294i) q^{7} -11.3212i q^{8} +(57.5020 + 57.0484i) q^{9} +O(q^{10})$	\(q+(0.307601 + 0.177594i) q^{2} +(8.32172 + 3.42768i) q^{3} +(-7.93692 - 13.7472i) q^{4} +(-30.0804 + 17.3669i) q^{5} +(1.95104 + 2.53225i) q^{6} +(15.6054 - 27.0294i) q^{7} -11.3212i q^{8} +(57.5020 + 57.0484i) q^{9} -12.3370 q^{10} +(49.9968 + 28.8657i) q^{11} +(-18.9279 - 141.605i) q^{12} +(36.6478 + 63.4758i) q^{13} +(9.60051 - 5.54285i) q^{14} +(-309.848 + 41.4165i) q^{15} +(-124.980 + 216.472i) q^{16} -386.985i q^{17} +(7.55625 + 27.7602i) q^{18} +115.791 q^{19} +(477.491 + 275.679i) q^{20} +(222.512 - 171.441i) q^{21} +(10.2527 + 17.7583i) q^{22} +(-474.852 + 274.156i) q^{23} +(38.8055 - 94.2118i) q^{24} +(290.719 - 503.539i) q^{25} +26.0337i q^{26} +(282.971 + 671.839i) q^{27} -495.436 q^{28} +(-680.082 - 392.645i) q^{29} +(-102.665 - 42.2874i) q^{30} +(-272.367 - 471.753i) q^{31} +(-233.759 + 134.961i) q^{32} +(317.117 + 411.585i) q^{33} +(68.7261 - 119.037i) q^{34} +1084.07i q^{35} +(327.865 - 1243.28i) q^{36} +898.827 q^{37} +(35.6175 + 20.5637i) q^{38} +(87.3975 + 653.845i) q^{39} +(196.614 + 340.546i) q^{40} +(2242.01 - 1294.43i) q^{41} +(98.8918 - 13.2186i) q^{42} +(-1000.05 + 1732.14i) q^{43} -916.419i q^{44} +(-2720.43 - 717.406i) q^{45} -194.753 q^{46} +(-702.646 - 405.673i) q^{47} +(-1782.05 + 1373.03i) q^{48} +(713.441 + 1235.72i) q^{49} +(178.851 - 103.260i) q^{50} +(1326.46 - 3220.38i) q^{51} +(581.741 - 1007.61i) q^{52} +2221.00i q^{53} +(-32.2721 + 256.913i) q^{54} -2005.23 q^{55} +(-306.005 - 176.672i) q^{56} +(963.579 + 396.895i) q^{57} +(-139.463 - 241.557i) q^{58} +(1309.65 - 756.128i) q^{59} +(3028.60 + 3930.81i) q^{60} +(951.281 - 1647.67i) q^{61} -193.483i q^{62} +(2439.33 - 663.979i) q^{63} +3903.49 q^{64} +(-2204.76 - 1272.92i) q^{65} +(24.4507 + 182.922i) q^{66} +(-2253.55 - 3903.26i) q^{67} +(-5319.94 + 3071.47i) q^{68} +(-4891.30 + 653.806i) q^{69} +(-192.524 + 333.462i) q^{70} +3993.54i q^{71} +(645.856 - 650.991i) q^{72} -3436.70 q^{73} +(276.480 + 159.626i) q^{74} +(4145.25 - 3193.82i) q^{75} +(-919.023 - 1591.80i) q^{76} +(1560.44 - 900.923i) q^{77} +(-89.2352 + 216.645i) q^{78} +(-601.388 + 1041.63i) q^{79} -8682.07i q^{80} +(51.9555 + 6560.79i) q^{81} +919.529 q^{82} +(8016.22 + 4628.17i) q^{83} +(-4122.88 - 1698.20i) q^{84} +(6720.72 + 11640.6i) q^{85} +(-615.236 + 355.207i) q^{86} +(-4313.58 - 5598.59i) q^{87} +(326.794 - 566.024i) q^{88} -8929.99i q^{89} +(-709.403 - 703.807i) q^{90} +2287.62 q^{91} +(7537.72 + 4351.91i) q^{92} +(-649.539 - 4859.38i) q^{93} +(-144.090 - 249.571i) q^{94} +(-3483.03 + 2010.93i) q^{95} +(-2407.88 + 321.854i) q^{96} +(-3335.14 + 5776.64i) q^{97} +506.811i q^{98} +(1228.18 + 4512.07i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 + 15 * q^4 - 12 * q^5 - 99 * q^6 + 12 * q^7 + 99 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9} - 36 q^{10} + 483 q^{11} + 330 q^{12} - 6 q^{13} - 1146 q^{14} - 1026 q^{15} + 15 q^{16} + 1404 q^{18} - 258 q^{19} + 1614 q^{20} + 480 q^{21} - 369 q^{22} - 282 q^{23} - 1449 q^{24} - 273 q^{25} + 54 q^{27} + 1308 q^{28} - 1056 q^{29} - 1278 q^{30} + 1290 q^{31} - 1161 q^{32} + 279 q^{33} + 513 q^{34} - 2385 q^{36} + 12 q^{37} - 789 q^{38} + 1974 q^{39} - 1314 q^{40} + 7629 q^{41} + 9612 q^{42} - 285 q^{43} - 4212 q^{45} - 5760 q^{46} - 9642 q^{47} - 6771 q^{48} - 1863 q^{49} + 3027 q^{50} + 2457 q^{51} - 240 q^{52} - 405 q^{54} + 2016 q^{55} - 462 q^{56} + 5367 q^{57} + 6462 q^{58} + 6225 q^{59} + 7470 q^{60} + 3630 q^{61} - 7578 q^{63} + 15450 q^{64} - 7158 q^{65} - 13734 q^{66} - 5055 q^{67} - 10503 q^{68} - 13878 q^{69} - 9684 q^{70} + 8451 q^{72} - 14622 q^{73} + 26454 q^{74} + 21021 q^{75} - 4047 q^{76} + 2580 q^{77} - 12060 q^{78} + 4764 q^{79} + 18387 q^{81} - 9702 q^{82} - 1866 q^{83} - 6486 q^{84} + 12366 q^{85} - 37731 q^{86} - 21564 q^{87} + 14787 q^{88} + 20790 q^{90} + 34836 q^{91} + 33636 q^{92} + 19254 q^{93} - 12708 q^{94} - 13362 q^{95} - 3672 q^{96} - 28959 q^{97} - 9126 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 + 15 * q^4 - 12 * q^5 - 99 * q^6 + 12 * q^7 + 99 * q^9 - 36 * q^10 + 483 * q^11 + 330 * q^12 - 6 * q^13 - 1146 * q^14 - 1026 * q^15 + 15 * q^16 + 1404 * q^18 - 258 * q^19 + 1614 * q^20 + 480 * q^21 - 369 * q^22 - 282 * q^23 - 1449 * q^24 - 273 * q^25 + 54 * q^27 + 1308 * q^28 - 1056 * q^29 - 1278 * q^30 + 1290 * q^31 - 1161 * q^32 + 279 * q^33 + 513 * q^34 - 2385 * q^36 + 12 * q^37 - 789 * q^38 + 1974 * q^39 - 1314 * q^40 + 7629 * q^41 + 9612 * q^42 - 285 * q^43 - 4212 * q^45 - 5760 * q^46 - 9642 * q^47 - 6771 * q^48 - 1863 * q^49 + 3027 * q^50 + 2457 * q^51 - 240 * q^52 - 405 * q^54 + 2016 * q^55 - 462 * q^56 + 5367 * q^57 + 6462 * q^58 + 6225 * q^59 + 7470 * q^60 + 3630 * q^61 - 7578 * q^63 + 15450 * q^64 - 7158 * q^65 - 13734 * q^66 - 5055 * q^67 - 10503 * q^68 - 13878 * q^69 - 9684 * q^70 + 8451 * q^72 - 14622 * q^73 + 26454 * q^74 + 21021 * q^75 - 4047 * q^76 + 2580 * q^77 - 12060 * q^78 + 4764 * q^79 + 18387 * q^81 - 9702 * q^82 - 1866 * q^83 - 6486 * q^84 + 12366 * q^85 - 37731 * q^86 - 21564 * q^87 + 14787 * q^88 + 20790 * q^90 + 34836 * q^91 + 33636 * q^92 + 19254 * q^93 - 12708 * q^94 - 13362 * q^95 - 3672 * q^96 - 28959 * q^97 - 9126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.307601	+	0.177594i	0.0769004	+	0.0443984i	0.537957	−	0.842972i	$-0.319196\pi$
$2$	0.307601	+	0.177594i	0.0769004	+	0.0443984i	−0.461057	+	0.887371i	$0.652530\pi$
$3$	8.32172	+	3.42768i	0.924635	+	0.380854i
$3$	8.32172	+	3.42768i	0.924635	+	0.380854i
$4$	−7.93692	−	13.7472i	−0.496058	−	0.859197i
$5$	−30.0804	+	17.3669i	−1.20321	+	0.694676i	−0.961268	−	0.275614i	$-0.911119\pi$
$5$	−30.0804	+	17.3669i	−1.20321	+	0.694676i	−0.241946	+	0.970290i	$0.577786\pi$
$6$	1.95104	+	2.53225i	0.0541955	+	0.0703402i
$7$	15.6054	−	27.0294i	0.318478	−	0.551620i	−0.661693	−	0.749775i	$-0.730162\pi$
$7$	15.6054	−	27.0294i	0.318478	−	0.551620i	0.980171	+	0.198155i	$0.0634949\pi$
$8$		−	11.3212i		−	0.176894i
$9$	57.5020	+	57.0484i	0.709901	+	0.704301i
$10$	−12.3370			−0.123370
$11$	49.9968	+	28.8657i	0.413197	+	0.238559i	0.692162	−	0.721742i	$-0.256658\pi$
$11$	49.9968	+	28.8657i	0.413197	+	0.238559i	−0.278965	+	0.960301i	$0.589991\pi$
$12$	−18.9279	−	141.605i	−0.131444	−	0.983369i
$13$	36.6478	+	63.4758i	0.216851	+	0.375597i	0.953844	−	0.300304i	$-0.0970882\pi$
$13$	36.6478	+	63.4758i	0.216851	+	0.375597i	−0.736993	+	0.675901i	$0.763755\pi$
$14$	9.60051	−	5.54285i	0.0489822	−	0.0282799i
$15$	−309.848	+	41.4165i	−1.37710	+	0.184074i
$16$	−124.980	+	216.472i	−0.488204	+	0.845594i
$17$		−	386.985i		−	1.33905i	−0.742791	−	0.669524i	$-0.766498\pi$
$17$		−	386.985i		−	1.33905i	0.742791	−	0.669524i	$-0.233502\pi$
$18$	7.55625	+	27.7602i	0.0233218	+	0.0856795i
$19$	115.791			0.320750			0.160375	−	0.987056i	$-0.448730\pi$
$19$	115.791			0.320750			0.160375	+	0.987056i	$0.448730\pi$
$20$	477.491	+	275.679i	1.19373	+	0.689199i
$21$	222.512	−	171.441i	0.504563	−	0.388754i
$22$	10.2527	+	17.7583i	0.0211833	+	0.0366906i
$23$	−474.852	+	274.156i	−0.897641	+	0.518253i	−0.876434	−	0.481522i	$-0.840084\pi$
$23$	−474.852	+	274.156i	−0.897641	+	0.518253i	−0.0212066	+	0.999775i	$0.506751\pi$
$24$	38.8055	−	94.2118i	0.0673706	−	0.163562i
$25$	290.719	−	503.539i	0.465150	−	0.805663i
$26$			26.0337i			0.0385113i
$27$	282.971	+	671.839i	0.388164	+	0.921590i
$28$	−495.436			−0.631934
$29$	−680.082	−	392.645i	−0.808658	−	0.466879i	0.0378313	−	0.999284i	$-0.487955\pi$
$29$	−680.082	−	392.645i	−0.808658	−	0.466879i	−0.846490	+	0.532405i	$0.821288\pi$
$30$	−102.665	−	42.2874i	−0.114072	−	0.0469860i
$31$	−272.367	−	471.753i	−0.283420	−	0.490898i	0.688805	−	0.724947i	$-0.258136\pi$
$31$	−272.367	−	471.753i	−0.283420	−	0.490898i	−0.972225	+	0.234049i	$0.924802\pi$
$32$	−233.759	+	134.961i	−0.228280	+	0.131798i
$33$	317.117	+	411.585i	0.291200	+	0.377948i
$34$	68.7261	−	119.037i	0.0594516	−	0.102973i
$35$			1084.07i			0.884957i
$36$	327.865	−	1243.28i	0.252982	−	0.959319i
$37$	898.827			0.656557			0.328279	−	0.944581i	$-0.393532\pi$
$37$	898.827			0.656557			0.328279	+	0.944581i	$0.393532\pi$
$38$	35.6175	+	20.5637i	0.0246658	+	0.0142408i
$39$	87.3975	+	653.845i	0.0574606	+	0.429878i
$40$	196.614	+	340.546i	0.122884	+	0.212841i
$41$	2242.01	−	1294.43i	1.33374	−	0.770034i	0.347867	−	0.937544i	$-0.386906\pi$
$41$	2242.01	−	1294.43i	1.33374	−	0.770034i	0.985870	+	0.167510i	$0.0535727\pi$
$42$	98.8918	−	13.2186i	0.0560611	−	0.00749353i
$43$	−1000.05	+	1732.14i	−0.540862	+	0.936801i	0.457993	+	0.888956i	$0.348569\pi$
$43$	−1000.05	+	1732.14i	−0.540862	+	0.936801i	−0.998855	+	0.0478447i	$0.984765\pi$
$44$		−	916.419i		−	0.473357i
$45$	−2720.43	−	717.406i	−1.34342	−	0.354274i
$46$	−194.753			−0.0920385
$47$	−702.646	−	405.673i	−0.318083	−	0.183645i	0.332455	−	0.943119i	$-0.392123\pi$
$47$	−702.646	−	405.673i	−0.318083	−	0.183645i	−0.650538	+	0.759474i	$0.725456\pi$
$48$	−1782.05	+	1373.03i	−0.773458	+	0.595932i
$49$	713.441	+	1235.72i	0.297143	+	0.514667i
$50$	178.851	−	103.260i	0.0715404	−	0.0413039i
$51$	1326.46	−	3220.38i	0.509981	−	1.23813i
$52$	581.741	−	1007.61i	0.215141	−	0.372635i
$53$			2221.00i			0.790672i	0.918537	+	0.395336i	$0.129372\pi$
$53$			2221.00i			0.790672i	−0.918537	+	0.395336i	$0.870628\pi$
$54$	−32.2721	+	256.913i	−0.0110672	+	0.0881045i
$55$	−2005.23			−0.662886
$56$	−306.005	−	176.672i	−0.0975781	−	0.0563368i
$57$	963.579	+	396.895i	0.296577	+	0.122159i
$58$	−139.463	−	241.557i	−0.0414574	−	0.0718064i
$59$	1309.65	−	756.128i	0.376229	−	0.217216i	−0.299947	−	0.953956i	$-0.596969\pi$
$59$	1309.65	−	756.128i	0.376229	−	0.217216i	0.676176	+	0.736740i	$0.263636\pi$
$60$	3028.60	+	3930.81i	0.841278	+	1.09189i
$61$	951.281	−	1647.67i	0.255652	−	0.442802i	−0.709420	−	0.704786i	$-0.751043\pi$
$61$	951.281	−	1647.67i	0.255652	−	0.442802i	0.965072	+	0.261983i	$0.0843765\pi$
$62$		−	193.483i		−	0.0503337i
$63$	2439.33	−	663.979i	0.614595	−	0.167291i
$64$	3903.49			0.953001
$65$	−2204.76	−	1272.92i	−0.521836	−	0.301282i
$66$	24.4507	+	182.922i	0.00561311	+	0.0419932i
$67$	−2253.55	−	3903.26i	−0.502015	−	0.869516i	−0.999997	−	0.00232883i	$-0.999259\pi$
$67$	−2253.55	−	3903.26i	−0.502015	−	0.869516i	0.497982	−	0.867187i	$-0.334075\pi$
$68$	−5319.94	+	3071.47i	−1.15051	+	0.664244i
$69$	−4891.30	+	653.806i	−1.02737	+	0.137325i
$70$	−192.524	+	333.462i	−0.0392907	+	0.0680535i
$71$			3993.54i			0.792213i	0.918205	+	0.396106i	$0.129639\pi$
$71$			3993.54i			0.792213i	−0.918205	+	0.396106i	$0.870361\pi$
$72$	645.856	−	650.991i	0.124586	−	0.125577i
$73$	−3436.70			−0.644905			−0.322452	−	0.946586i	$-0.604507\pi$
$73$	−3436.70			−0.644905			−0.322452	+	0.946586i	$0.604507\pi$
$74$	276.480	+	159.626i	0.0504895	+	0.0291501i
$75$	4145.25	−	3193.82i	0.736934	−	0.567790i
$76$	−919.023	−	1591.80i	−0.159111	−	0.275588i
$77$	1560.44	−	900.923i	0.263188	−	0.151952i
$78$	−89.2352	+	216.645i	−0.0146672	+	0.0356090i
$79$	−601.388	+	1041.63i	−0.0963608	+	0.166902i	−0.910176	−	0.414222i	$-0.864054\pi$
$79$	−601.388	+	1041.63i	−0.0963608	+	0.166902i	0.813815	+	0.581124i	$0.197387\pi$
$80$		−	8682.07i		−	1.35657i
$81$	51.9555	+	6560.79i	0.00791883	+	0.999969i
$82$	919.529			0.136753
$83$	8016.22	+	4628.17i	1.16363	+	0.671820i	0.952170	−	0.305567i	$-0.0988461\pi$
$83$	8016.22	+	4628.17i	1.16363	+	0.671820i	0.211456	+	0.977387i	$0.432179\pi$
$84$	−4122.88	−	1698.20i	−0.584308	−	0.240674i
$85$	6720.72	+	11640.6i	0.930204	+	1.61116i
$86$	−615.236	+	355.207i	−0.0831850	+	0.0480269i
$87$	−4313.58	−	5598.59i	−0.569902	−	0.739673i
$88$	326.794	−	566.024i	0.0421996	−	0.0730919i
$89$		−	8929.99i		−	1.12738i	−0.825986	−	0.563691i	$-0.809381\pi$
$89$		−	8929.99i		−	1.12738i	0.825986	−	0.563691i	$-0.190619\pi$
$90$	−709.403	−	703.807i	−0.0875806	−	0.0868898i
$91$	2287.62			0.276249
$92$	7537.72	+	4351.91i	0.890563	+	0.514167i
$93$	−649.539	−	4859.38i	−0.0751000	−	0.561843i
$94$	−144.090	−	249.571i	−0.0163071	−	0.0282448i
$95$	−3483.03	+	2010.93i	−0.385932	+	0.222818i
$96$	−2407.88	+	321.854i	−0.261272	+	0.0349234i
$97$	−3335.14	+	5776.64i	−0.354463	+	0.613948i	−0.987026	−	0.160561i	$-0.948670\pi$
$97$	−3335.14	+	5776.64i	−0.354463	+	0.613948i	0.632563	+	0.774509i	$0.282003\pi$
$98$			506.811i			0.0527708i
$99$	1228.18	+	4512.07i	0.125311	+	0.460369i
$100$	−9229.64			−0.922964
$101$	−7924.19	−	4575.03i	−0.776805	−	0.448489i	0.0584918	−	0.998288i	$-0.481371\pi$
$101$	−7924.19	−	4575.03i	−0.776805	−	0.448489i	−0.835297	+	0.549799i	$0.814704\pi$
$102$	979.940	−	755.021i	0.0941888	−	0.0725703i
$103$	−7656.20	−	13260.9i	−0.721670	−	1.24997i	−0.960330	−	0.278866i	$-0.910041\pi$
$103$	−7656.20	−	13260.9i	−0.721670	−	1.24997i	0.238660	−	0.971103i	$-0.423292\pi$
$104$	718.622	−	414.897i	0.0664406	−	0.0383595i
$105$	−3715.85	+	9021.34i	−0.337039	+	0.818262i
$106$	−394.435	+	683.182i	−0.0351046	+	0.0608029i
$107$			6099.28i			0.532735i	0.963872	+	0.266367i	$0.0858234\pi$
$107$			6099.28i			0.532735i	−0.963872	+	0.266367i	$0.914177\pi$
$108$	6989.96	−	9222.39i	0.599276	−	0.790671i
$109$	15169.5			1.27679			0.638393	−	0.769710i	$-0.279599\pi$
$109$	15169.5			1.27679			0.638393	+	0.769710i	$0.279599\pi$
$110$	−616.812	−	356.116i	−0.0509762	−	0.0294311i
$111$	7479.78	+	3080.89i	0.607076	+	0.250052i
$112$	3900.74	+	6756.28i	0.310964	+	0.538606i
$113$	−1189.11	+	686.532i	−0.0931246	+	0.0537655i	−0.545839	−	0.837890i	$-0.683789\pi$
$113$	−1189.11	+	686.532i	−0.0931246	+	0.0537655i	0.452714	+	0.891656i	$0.350456\pi$
$114$	225.912	+	293.211i	0.0173832	+	0.0225616i
$115$	9522.48	−	16493.4i	0.720036	−	1.24714i
$116$			12465.6i			0.926396i
$117$	−1513.88	+	5740.68i	−0.110591	+	0.419365i
$118$	537.135			0.0385762
$119$	−10460.0	−	6039.06i	−0.738646	−	0.426457i
$120$	468.885	+	3507.85i	0.0325614	+	0.243601i
$121$	−5654.04	−	9793.09i	−0.386179	−	0.668881i
$122$	585.231	−	337.883i	0.0393195	−	0.0227011i
$123$	23094.3	−	3086.94i	1.52649	−	0.204042i
$124$	−4323.51	+	7488.53i	−0.281185	+	0.487027i
$125$		−	1513.10i		−	0.0968386i
$126$	868.259	+	228.969i	0.0546900	+	0.0144223i
$127$	−19152.4			−1.18745			−0.593726	−	0.804667i	$-0.702344\pi$
$127$	−19152.4			−1.18745			−0.593726	+	0.804667i	$0.702344\pi$
$128$	4940.87	+	2852.61i	0.301567	+	0.174110i
$129$	−14259.4	+	10986.5i	−0.856884	+	0.660210i
$130$	−452.124	−	783.102i	−0.0267529	−	0.0463374i
$131$	−2615.39	+	1510.00i	−0.152403	+	0.0879902i	−0.574262	−	0.818671i	$-0.694711\pi$
$131$	−2615.39	+	1510.00i	−0.152403	+	0.0879902i	0.421859	+	0.906661i	$0.361378\pi$
$132$	3141.19	−	7626.18i	0.180280	−	0.437682i
$133$	1806.97	−	3129.76i	0.102152	−	0.176932i
$134$		−	1600.86i		−	0.0891548i
$135$	−20179.6	−	15294.8i	−1.10725	−	0.839223i
$136$	−4381.13			−0.236869
$137$	−8788.30	−	5073.93i	−0.468235	−	0.270336i	0.247266	−	0.968948i	$-0.420468\pi$
$137$	−8788.30	−	5073.93i	−0.468235	−	0.270336i	−0.715501	+	0.698612i	$0.753801\pi$
$138$	−1620.68	−	667.553i	−0.0851021	−	0.0350532i
$139$	17563.2	+	30420.3i	0.909021	+	1.57447i	0.815427	+	0.578860i	$0.196502\pi$
$139$	17563.2	+	30420.3i	0.909021	+	1.57447i	0.0935938	+	0.995610i	$0.470165\pi$
$140$	14902.9	−	8604.19i	0.760352	−	0.438989i
$141$	−4456.70	−	5784.34i	−0.224169	−	0.290948i
$142$	−709.229	+	1228.42i	−0.0351730	+	0.0609214i
$143$			4231.45i			0.206927i
$144$	−19536.0	+	5317.65i	−0.942129	+	0.256445i
$145$	27276.1			1.29732
$146$	−1057.13	−	610.336i	−0.0495934	−	0.0286328i
$147$	1701.41	+	12728.7i	0.0787363	+	0.589048i
$148$	−7133.92	−	12356.3i	−0.325690	−	0.564112i
$149$	32373.7	−	18691.0i	1.45821	−	0.841899i	0.459288	−	0.888288i	$-0.348105\pi$
$149$	32373.7	−	18691.0i	1.45821	−	0.841899i	0.998923	+	0.0463890i	$0.0147714\pi$
$150$	1842.29	−	246.253i	0.0818795	−	0.0109446i
$151$	−16635.0	+	28812.7i	−0.729573	+	1.26366i	0.227490	+	0.973780i	$0.426948\pi$
$151$	−16635.0	+	28812.7i	−0.729573	+	1.26366i	−0.957064	+	0.289878i	$0.906385\pi$
$152$		−	1310.89i		−	0.0567387i
$153$	22076.9	−	22252.4i	0.943093	−	0.950591i
$154$	639.993			0.0269857
$155$	16385.8	+	9460.33i	0.682030	+	0.393770i
$156$	8294.84	−	6390.98i	0.340846	−	0.262614i
$157$	−4040.16	−	6997.77i	−0.163908	−	0.283897i	0.772359	−	0.635186i	$-0.219077\pi$
$157$	−4040.16	−	6997.77i	−0.163908	−	0.283897i	−0.936267	+	0.351289i	$0.885743\pi$
$158$	−369.975	+	213.605i	−0.0148204	+	0.00855654i
$159$	−7612.87	+	18482.5i	−0.301130	+	0.731083i
$160$	4687.71	−	8119.35i	0.183114	−	0.317162i
$161$			17113.3i			0.660209i
$162$	−1149.17	+	2027.34i	−0.0437881	+	0.0772495i
$163$	−25427.1			−0.957022			−0.478511	−	0.878081i	$-0.658823\pi$
$163$	−25427.1			−0.957022			−0.478511	+	0.878081i	$0.658823\pi$
$164$	−35589.4	−	20547.5i	−1.32322	−	0.763962i
$165$	−16687.0	−	6873.29i	−0.612928	−	0.252463i
$166$	1643.87	+	2847.26i	0.0596555	+	0.103326i
$167$	−30356.6	+	17526.4i	−1.08848	+	0.628434i	−0.933171	−	0.359432i	$-0.882971\pi$
$167$	−30356.6	+	17526.4i	−1.08848	+	0.628434i	−0.155309	+	0.987866i	$0.549637\pi$
$168$	−1940.91	−	2519.10i	−0.0687681	−	0.0892539i
$169$	11594.4	−	20082.1i	0.405951	−	0.703129i
$170$			4774.24i			0.165198i
$171$	6658.21	+	6605.69i	0.227701	+	0.225905i
$172$	31749.4			1.07319
$173$	12731.0	+	7350.23i	0.425372	+	0.245589i	0.697373	−	0.716708i	$-0.254352\pi$
$173$	12731.0	+	7350.23i	0.425372	+	0.245589i	−0.272001	+	0.962297i	$0.587685\pi$
$174$	−332.590	−	2488.20i	−0.0109853	−	0.0821839i
$175$	−9073.58	−	15715.9i	−0.296280	−	0.513172i
$176$	−12497.2	+	7215.28i	−0.403449	+	0.232931i
$177$	13490.3	−	1803.21i	0.430602	−	0.0575573i
$178$	1585.91	−	2746.88i	0.0500540	−	0.0866960i
$179$		−	37052.5i		−	1.15641i	−0.815892	−	0.578205i	$-0.803753\pi$
$179$		−	37052.5i		−	1.15641i	0.815892	−	0.578205i	$-0.196247\pi$
$180$	11729.6	+	43092.2i	0.362024	+	1.33001i
$181$	−39664.7			−1.21073			−0.605365	−	0.795948i	$-0.706973\pi$
$181$	−39664.7			−1.21073			−0.605365	+	0.795948i	$0.706973\pi$
$182$	703.674	+	406.267i	0.0212436	+	0.0122650i
$183$	13564.0	−	10450.7i	0.405028	−	0.312065i
$184$	3103.77	+	5375.89i	0.0916757	+	0.158787i
$185$	−27037.0	+	15609.8i	−0.789979	+	0.456094i
$186$	663.197	−	1610.11i	0.0191698	−	0.0465403i
$187$	11170.6	−	19348.0i	0.319442	−	0.553290i
$188$			12879.2i			0.364395i
$189$	22575.3	+	2835.80i	0.631990	+	0.0793874i
$190$	−1428.51			−0.0395710
$191$	49915.1	+	28818.5i	1.36825	+	0.789959i	0.990704	−	0.136032i	$-0.0434352\pi$
$191$	49915.1	+	28818.5i	1.36825	+	0.789959i	0.377545	+	0.925991i	$0.376768\pi$
$192$	32483.8	+	13379.9i	0.881178	+	0.362954i
$193$	−2089.81	−	3619.67i	−0.0561039	−	0.0971748i	0.836609	−	0.547800i	$-0.184534\pi$
$193$	−2089.81	−	3619.67i	−0.0561039	−	0.0971748i	−0.892713	+	0.450625i	$0.851201\pi$
$194$	−2051.79	+	1184.60i	−0.0545167	+	0.0314752i
$195$	−13984.2	−	18150.1i	−0.367763	−	0.477319i
$196$	11325.1	−	19615.6i	0.294800	−	0.510609i
$197$		−	22191.5i		−	0.571812i	−0.958258	−	0.285906i	$-0.907705\pi$
$197$		−	22191.5i		−	0.571812i	0.958258	−	0.285906i	$-0.0922945\pi$
$198$	−423.528	+	1606.04i	−0.0108032	+	0.0409662i
$199$	50608.7			1.27797			0.638983	−	0.769221i	$-0.279355\pi$
$199$	50608.7			1.27797			0.638983	+	0.769221i	$0.279355\pi$
$200$	−5700.67	−	3291.28i	−0.142517	−	0.0822820i
$201$	−5374.25	−	40206.3i	−0.133023	−	0.995180i
$202$	−1624.99	−	2814.57i	−0.0398244	−	0.0689779i
$203$	−21225.9	+	12254.8i	−0.515080	+	0.297382i
$204$	−54799.0	+	7324.82i	−1.31678	+	0.176010i
$205$	−44960.4	+	77873.6i	−1.06985	+	1.85303i
$206$		−	5438.77i		−	0.128164i
$207$	−42945.1	−	11325.0i	−1.00224	−	0.264301i
$208$	−18321.0			−0.423469
$209$	5789.18	+	3342.38i	0.132533	+	0.0765180i
$210$	−2745.14	+	2115.06i	−0.0622480	+	0.0479606i
$211$	4459.02	+	7723.26i	0.100156	+	0.173474i	0.911749	−	0.410749i	$-0.134733\pi$
$211$	4459.02	+	7723.26i	0.100156	+	0.173474i	−0.811593	+	0.584223i	$0.801399\pi$
$212$	30532.4	−	17627.9i	0.679343	−	0.392219i
$213$	−13688.6	+	33233.1i	−0.301717	+	0.732508i
$214$	−1083.19	+	1876.15i	−0.0236526	+	0.0409675i
$215$		−	69471.4i		−	1.50290i
$216$	7606.02	−	3203.57i	0.163023	−	0.0686637i
$217$	−17001.6			−0.361052
$218$	4666.16	+	2694.01i	0.0981853	+	0.0566873i
$219$	−28599.2	−	11779.9i	−0.596302	−	0.245614i
$220$	15915.4	+	27566.2i	0.328830	+	0.569550i
$221$	24564.2	−	14182.1i	0.502941	−	0.290373i
$222$	1753.64	+	2276.05i	0.0355824	+	0.0461823i
$223$	4248.76	−	7359.07i	0.0854384	−	0.147984i	−0.820140	−	0.572164i	$-0.806104\pi$
$223$	4248.76	−	7359.07i	0.0854384	−	0.147984i	0.905578	+	0.424180i	$0.139438\pi$
$224$			8424.49i			0.167899i
$225$	45443.0	−	12369.5i	0.897640	−	0.244335i
$226$	−487.695			−0.00954842
$227$	16543.5	+	9551.40i	0.321052	+	0.185360i	0.651862	−	0.758338i	$-0.273988\pi$
$227$	16543.5	+	9551.40i	0.321052	+	0.185360i	−0.330809	+	0.943698i	$0.607322\pi$
$228$	−2191.68	−	16396.6i	−0.0421607	−	0.315416i
$229$	5361.51	+	9286.40i	0.102239	+	0.177083i	0.912607	−	0.408839i	$-0.134066\pi$
$229$	5361.51	+	9286.40i	0.102239	+	0.177083i	−0.810368	+	0.585921i	$0.800733\pi$
$230$	5858.25	−	3382.26i	0.110742	−	0.0639370i
$231$	16073.7	−	2148.52i	0.301225	−	0.0402638i
$232$	−4445.21	+	7699.34i	−0.0825880	+	0.143047i
$233$			102200.i			1.88251i	0.337694	+	0.941256i	$0.390353\pi$
$233$			102200.i			1.88251i	−0.337694	+	0.941256i	$0.609647\pi$
$234$	−1485.18	+	1496.99i	−0.0271236	+	0.0273392i
$235$	28181.1			0.510296
$236$	−20789.2	−	12002.7i	−0.373262	−	0.215503i
$237$	−8574.97	+	6606.82i	−0.152664	+	0.117624i
$238$	−2145.00	−	3715.25i	−0.0378681	−	0.0655894i
$239$	13440.9	−	7760.09i	0.235305	−	0.135854i	−0.377712	−	0.925923i	$-0.623289\pi$
$239$	13440.9	−	7760.09i	0.235305	−	0.135854i	0.613017	+	0.790070i	$0.289956\pi$
$240$	29759.4	−	72249.8i	0.516656	−	1.25434i
$241$	35978.9	−	62317.3i	0.619461	−	1.07294i	−0.370123	−	0.928983i	$-0.620685\pi$
$241$	35978.9	−	62317.3i	0.619461	−	1.07294i	0.989584	−	0.143955i	$-0.0459820\pi$
$242$		−	4016.49i		−	0.0685830i
$243$	−22056.0	+	54775.2i	−0.373520	+	0.927622i
$244$	−30201.0			−0.507272
$245$	−42921.1	−	24780.5i	−0.715054	−	0.412837i
$246$	7652.06	+	3151.85i	0.126447	+	0.0520830i
$247$	4243.48	+	7349.92i	0.0695550	+	0.120473i
$248$	−5340.81	+	3083.52i	−0.0868368	+	0.0501352i
$249$	50844.9	+	65991.4i	0.820065	+	1.06436i
$250$	268.718	−	465.433i	0.00429948	−	0.00744692i
$251$		−	41487.8i		−	0.658526i	−0.944238	−	0.329263i	$-0.893200\pi$
$251$		−	41487.8i		−	0.658526i	0.944238	−	0.329263i	$-0.106800\pi$
$252$	−28488.6	−	28263.9i	−0.448611	−	0.445072i
$253$	−31654.8			−0.494537
$254$	−5891.31	−	3401.35i	−0.0913155	−	0.0527210i
$255$	16027.6	+	119907.i	0.246483	+	1.84401i
$256$	−30214.7	−	52333.4i	−0.461040	−	0.798545i
$257$	−62812.2	+	36264.6i	−0.950994	+	0.549057i	−0.893390	−	0.449283i	$-0.851680\pi$
$257$	−62812.2	+	36264.6i	−0.950994	+	0.549057i	−0.0576045	+	0.998339i	$0.518346\pi$
$258$	−6337.36	+	847.096i	−0.0952070	+	0.0127260i
$259$	14026.6	−	24294.7i	0.209099	−	0.362170i
$260$			40412.2i			0.597813i
$261$	−16706.2	−	61375.5i	−0.245244	−	0.900977i
$262$	−1072.67			−0.0156265
$263$	−74383.1	−	42945.1i	−1.07538	−	0.620872i	−0.145735	−	0.989324i	$-0.546555\pi$
$263$	−74383.1	−	42945.1i	−1.07538	−	0.620872i	−0.929647	+	0.368451i	$0.879888\pi$
$264$	4659.64	−	3590.14i	0.0668566	−	0.0515115i
$265$	−38571.8	−	66808.4i	−0.549261	−	0.951347i
$266$	1111.65	−	641.812i	0.0157111	−	0.00907078i
$267$	30609.2	−	74312.8i	0.429367	−	1.04242i
$268$	−35772.5	+	61959.7i	−0.498057	+	0.862660i
$269$			88967.6i			1.22950i	0.788724	+	0.614748i	$0.210742\pi$
$269$			88967.6i			1.22950i	−0.788724	+	0.614748i	$0.789258\pi$
$270$	−3491.02	−	8288.49i	−0.0478878	−	0.113697i
$271$	96541.6			1.31455			0.657273	−	0.753652i	$-0.271710\pi$
$271$	96541.6			1.31455			0.657273	+	0.753652i	$0.271710\pi$
$272$	83771.3	+	48365.4i	1.13229	+	0.653728i
$273$	19036.9	+	7841.23i	0.255429	+	0.105210i
$274$	−1802.20	−	3121.49i	−0.0240050	−	0.0415778i
$275$	29070.0	−	16783.6i	0.384397	−	0.221932i
$276$	47809.9	+	62052.3i	0.627624	+	0.814591i
$277$	11770.8	−	20387.6i	0.153407	−	0.265710i	−0.779071	−	0.626936i	$-0.784309\pi$
$277$	11770.8	−	20387.6i	0.153407	−	0.265710i	0.932478	+	0.361227i	$0.117642\pi$
$278$			12476.5i			0.161436i
$279$	11251.1	−	42664.8i	0.144540	−	0.548102i
$280$	12273.0			0.156543
$281$	−50584.4	−	29204.9i	−0.640626	−	0.369865i	0.144230	−	0.989544i	$-0.453930\pi$
$281$	−50584.4	−	29204.9i	−0.640626	−	0.369865i	−0.784855	+	0.619679i	$0.787263\pi$
$282$	−343.625	−	2570.75i	−0.00432102	−	0.0323268i
$283$	38058.6	+	65919.5i	0.475204	+	0.823078i	0.999597	−	0.0283989i	$-0.00904087\pi$
$283$	38058.6	+	65919.5i	0.475204	+	0.823078i	−0.524393	+	0.851477i	$0.675708\pi$
$284$	54899.9	−	31696.4i	0.680667	−	0.392983i
$285$	−35877.6	+	4795.66i	−0.441707	+	0.0590417i
$286$	−751.480	+	1301.60i	−0.00918724	+	0.0159128i
$287$		−	80800.3i		−	0.980956i
$288$	−21140.9	−	5575.07i	−0.254882	−	0.0672149i
$289$	−66236.1			−0.793047
$290$	8390.18	+	4844.07i	0.0997643	+	0.0575990i
$291$	−47554.6	+	36639.7i	−0.561573	+	0.432680i
$292$	27276.8	+	47244.8i	0.319910	+	0.554100i
$293$	121166.	−	69955.5i	1.41139	−	0.814866i	0.415871	−	0.909424i	$-0.363477\pi$
$293$	121166.	−	69955.5i	1.41139	−	0.814866i	0.995519	+	0.0945573i	$0.0301436\pi$
$294$	−1737.19	+	4217.54i	−0.0200980	+	0.0487938i
$295$	−26263.2	+	45489.2i	−0.301789	+	0.522714i
$296$		−	10175.8i		−	0.116141i
$297$	−5245.43	+	41758.0i	−0.0594660	+	0.473399i
$298$	13277.6			0.149516
$299$	−34804.5	−	20094.4i	−0.389308	−	0.224767i
$300$	−76806.5	−	31636.3i	−0.853405	−	0.351514i
$301$	31212.5	+	54061.7i	0.344505	+	0.596701i
$302$	−10233.9	+	5908.55i	−0.112209	+	0.0647838i
$303$	−50261.1	−	65233.7i	−0.547453	−	0.710537i
$304$	−14471.6	+	25065.5i	−0.156592	+	0.271225i
$305$			66083.2i			0.710381i
$306$	10742.8	−	2924.15i	0.114729	−	0.0312289i
$307$	−81796.8			−0.867880			−0.433940	−	0.900942i	$-0.642877\pi$
$307$	−81796.8			−0.867880			−0.433940	+	0.900942i	$0.642877\pi$
$308$	−24770.2	−	14301.1i	−0.261113	−	0.150754i
$309$	−18258.5	−	136597.i	−0.191226	−	1.43062i
$310$	3360.19	+	5820.03i	0.0349656	+	0.0605622i
$311$	−1474.59	+	851.354i	−0.0152458	+	0.00880216i	−0.507604	−	0.861591i	$-0.669469\pi$
$311$	−1474.59	+	851.354i	−0.0152458	+	0.00880216i	0.492358	+	0.870393i	$0.336135\pi$
$312$	7402.30	−	989.444i	0.0760427	−	0.0101644i
$313$	34980.1	−	60587.3i	0.357052	−	0.618433i	−0.630415	−	0.776259i	$-0.717115\pi$
$313$	34980.1	−	60587.3i	0.357052	−	0.618433i	0.987467	+	0.157826i	$0.0504484\pi$
$314$		−	2870.03i		−	0.0291090i
$315$	−61844.6	+	62336.3i	−0.623276	+	0.628232i
$316$	19092.7			0.191202
$317$	101004.	+	58314.7i	1.00512	+	0.580309i	0.909760	−	0.415134i	$-0.136265\pi$
$317$	101004.	+	58314.7i	1.00512	+	0.580309i	0.0953639	+	0.995442i	$0.469599\pi$
$318$	−5624.11	+	4333.25i	−0.0556160	+	0.0428508i
$319$	−22668.0	−	39262.1i	−0.222757	−	0.385826i
$320$	−117418.	+	67791.6i	−1.14666	+	0.662027i
$321$	−20906.4	+	50756.5i	−0.202894	+	0.492585i
$322$	−3039.21	+	5264.07i	−0.0293123	+	0.0507703i
$323$		−	44809.3i		−	0.429500i
$324$	89779.9	−	52786.7i	0.855242	−	0.502846i
$325$	42616.8			0.403472
$326$	−7821.42	−	4515.70i	−0.0735954	−	0.0424903i
$327$	126236.	+	51996.2i	1.18056	+	0.486269i
$328$	−14654.5	−	25382.3i	−0.136214	−	0.235930i
$329$	−21930.2	+	12661.4i	−0.202605	+	0.116974i
$330$	−3912.28	−	5077.74i	−0.0359254	−	0.0466275i
$331$	−50418.1	+	87326.8i	−0.460183	+	0.797061i	−0.998970	−	0.0453817i	$-0.985550\pi$
$331$	−50418.1	+	87326.8i	−0.460183	+	0.797061i	0.538787	+	0.842442i	$0.318883\pi$
$332$		−	146934.i		−	1.33305i
$333$	51684.3	+	51276.6i	0.466090	+	0.462414i
$334$	−12450.3			−0.111606
$335$	135575.	+	78274.3i	1.20806	+	0.697476i
$336$	9302.47	+	69594.3i	0.0823986	+	0.616446i
$337$	−20047.2	−	34722.8i	−0.176520	−	0.305742i	0.764166	−	0.645020i	$-0.223151\pi$
$337$	−20047.2	−	34722.8i	−0.176520	−	0.305742i	−0.940686	+	0.339277i	$0.889817\pi$
$338$	7132.90	−	4118.18i	0.0624356	−	0.0360472i
$339$	−12248.6	+	1637.24i	−0.106583	+	0.0142466i
$340$	106684.	−	184782.i	0.922869	−	1.59846i
$341$		−	31448.2i		−	0.270450i
$342$	874.945	+	3214.38i	0.00748046	+	0.0274818i
$343$	119471.			1.01549
$344$	19609.9	+	11321.8i	0.165714	+	0.0956751i
$345$	135778.	−	104613.i	1.14075	−	0.878920i
$346$	2610.71	+	4521.88i	0.0218075	+	0.0377717i
$347$	−196035.	+	113181.i	−1.62808	+	0.939971i	−0.643412	+	0.765520i	$0.722482\pi$
$347$	−196035.	+	113181.i	−1.62808	+	0.939971i	−0.984666	+	0.174451i	$0.944185\pi$
$348$	−42728.1	+	103735.i	−0.352821	+	0.856578i
$349$	−39799.1	+	68934.1i	−0.326755	+	0.565957i	−0.981866	−	0.189576i	$-0.939289\pi$
$349$	−39799.1	+	68934.1i	−0.326755	+	0.565957i	0.655111	+	0.755533i	$0.272622\pi$
$350$		−	6445.64i		−	0.0526175i
$351$	−32275.3	+	42583.3i	−0.261973	+	0.345641i
$352$	−15583.0			−0.125766
$353$	−121173.	−	69959.4i	−0.972427	−	0.561431i	−0.0724520	−	0.997372i	$-0.523082\pi$
$353$	−121173.	−	69959.4i	−0.972427	−	0.561431i	−0.899975	+	0.435941i	$0.856416\pi$
$354$	4469.88	+	1841.13i	0.0356689	+	0.0146919i
$355$	−69355.5	−	120127.i	−0.550331	−	0.953202i
$356$	−122762.	+	70876.6i	−0.968642	+	0.559246i
$357$	−66344.9	−	86108.8i	−0.520560	−	0.675633i
$358$	6580.30	−	11397.4i	0.0513428	−	0.0889283i
$359$			211616.i			1.64195i	0.570963	+	0.820976i	$0.306570\pi$
$359$			211616.i			1.64195i	−0.570963	+	0.820976i	$0.693430\pi$
$360$	−8121.89	+	30798.6i	−0.0626689	+	0.237643i
$361$	−116913.			−0.897119
$362$	−12200.9	−	7044.20i	−0.0931055	−	0.0537545i
$363$	−13483.7	−	100876.i	−0.102329	−	0.765549i
$364$	−18156.6	−	31448.2i	−0.137035	−	0.237352i
$365$	103377.	−	59684.8i	0.775959	−	0.448000i
$366$	6028.28	−	805.783i	0.0450020	−	0.00601528i
$367$	15996.8	−	27707.3i	0.118769	−	0.205713i	−0.800511	−	0.599318i	$-0.795439\pi$
$367$	15996.8	−	27707.3i	0.118769	−	0.205713i	0.919280	+	0.393604i	$0.128772\pi$
$368$		−	137056.i		−	1.01205i
$369$	202765.	+	53471.2i	1.48916	+	0.392706i
$370$	−11088.8			−0.0809995
$371$	60032.2	+	34659.6i	0.436151	+	0.251812i
$372$	−61647.3	+	47497.9i	−0.445480	+	0.343232i
$373$	61573.9	+	106649.i	0.442567	+	0.766548i	0.997879	−	0.0650938i	$-0.0207347\pi$
$373$	61573.9	+	106649.i	0.442567	+	0.766548i	−0.555312	+	0.831642i	$0.687401\pi$
$374$	6872.17	−	3967.65i	0.0491305	−	0.0283655i
$375$	5186.44	−	12591.6i	0.0368813	−	0.0895404i
$376$	−4592.70	+	7954.79i	−0.0324857	+	0.0562669i
$377$		−	57558.3i		−	0.404972i
$378$	6440.58	+	4881.53i	0.0450756	+	0.0341643i
$379$	−116524.			−0.811218			−0.405609	−	0.914047i	$-0.632941\pi$
$379$	−116524.			−0.811218			−0.405609	+	0.914047i	$0.632941\pi$
$380$	55289.1	+	31921.2i	0.382889	+	0.221061i
$381$	−159381.	−	65648.4i	−1.09796	−	0.452246i
$382$	10236.0	+	17729.2i	0.0701459	+	0.121496i
$383$	156848.	−	90556.2i	1.06925	−	0.617334i	0.141277	−	0.989970i	$-0.454879\pi$
$383$	156848.	−	90556.2i	1.06925	−	0.617334i	0.927978	+	0.372636i	$0.121546\pi$
$384$	31338.7	+	40674.3i	0.212529	+	0.275841i
$385$	−31292.5	+	54200.2i	−0.211115	+	0.365661i
$386$		−	1484.55i		−	0.00996371i
$387$	−156321.	+	42550.2i	−1.04375	+	0.284106i
$388$	105883.			0.703336
$389$	−44017.9	−	25413.7i	−0.290891	−	0.167946i	0.347453	−	0.937697i	$-0.387047\pi$
$389$	−44017.9	−	25413.7i	−0.290891	−	0.167946i	−0.638343	+	0.769752i	$0.720380\pi$
$390$	−1078.22	−	8066.49i	−0.00708892	−	0.0530341i
$391$	106094.	+	183760.i	0.693965	+	1.20198i
$392$	13989.8	−	8077.01i	0.0910414	−	0.0525628i
$393$	−26940.4	+	3601.04i	−0.174429	+	0.0233154i
$394$	3941.06	−	6826.12i	0.0253876	−	0.0439726i
$395$		−	41777.0i		−	0.267758i
$396$	52280.2	−	52695.9i	0.333386	−	0.336036i
$397$	228710.			1.45112			0.725561	−	0.688158i	$-0.241580\pi$
$397$	228710.			1.45112			0.725561	+	0.688158i	$0.241580\pi$
$398$	15567.3	+	8987.80i	0.0982761	+	0.0567397i
$399$	25764.9	−	19851.3i	0.161839	−	0.124693i
$400$	72668.1	+	125865.i	0.454176	+	0.786655i
$401$	163618.	−	94464.9i	1.01752	−	0.587465i	0.104134	−	0.994563i	$-0.466793\pi$
$401$	163618.	−	94464.9i	1.01752	−	0.587465i	0.913384	+	0.407099i	$0.133459\pi$
$402$	5487.25	−	13321.9i	0.0339549	−	0.0824357i
$403$	19963.3	−	34577.4i	0.122920	−	0.212903i
$404$			145247.i			0.889904i
$405$	−115504.	−	196449.i	−0.704182	−	1.19768i
$406$	−8705.50			−0.0528131
$407$	44938.5	+	25945.2i	0.271287	+	0.156628i
$408$	−36458.5	−	15017.1i	−0.219017	−	0.0902124i
$409$	−138713.	−	240258.i	−0.829223	−	1.43626i	−0.898649	−	0.438669i	$-0.855450\pi$
$409$	−138713.	−	240258.i	−0.829223	−	1.43626i	0.0694256	−	0.997587i	$-0.477883\pi$
$410$	−27659.7	+	15969.4i	−0.164543	+	0.0949992i
$411$	−55741.9	−	72347.3i	−0.329988	−	0.428291i
$412$	−121533.	+	210502.i	−0.715980	+	1.24011i
$413$		−	47198.8i		−	0.276714i
$414$	−11198.7	−	11110.4i	−0.0653382	−	0.0648229i
$415$	−321508.			−1.86679
$416$	−17133.5	−	9892.04i	−0.0990056	−	0.0571609i
$417$	41884.6	+	313351.i	0.240870	+	1.80201i
$418$	1187.17	+	2056.24i	0.00679456	+	0.0117685i
$419$	−88699.9	+	51210.9i	−0.505237	+	0.291699i	−0.730874	−	0.682513i	$-0.760887\pi$
$419$	−88699.9	+	51210.9i	−0.505237	+	0.291699i	0.225637	+	0.974212i	$0.427554\pi$
$420$	153510.	−	20519.3i	0.870239	−	0.116322i
$421$	−23567.9	+	40820.8i	−0.132971	+	0.230312i	−0.924821	−	0.380404i	$-0.875785\pi$
$421$	−23567.9	+	40820.8i	−0.132971	+	0.230312i	0.791850	+	0.610716i	$0.209118\pi$
$422$			3167.58i			0.0177870i
$423$	−17260.5	−	63411.8i	−0.0964658	−	0.354397i
$424$	25144.3			0.139865
$425$	−194862.	−	112504.i	−1.07882	−	0.622857i
$426$	−10112.6	+	7791.55i	−0.0557244	+	0.0429344i
$427$	−29690.3	−	51425.1i	−0.162839	−	0.282046i
$428$	83847.7	−	48409.5i	0.457724	−	0.264267i
$429$	−14504.1	+	35213.0i	−0.0788090	+	0.191332i
$430$	12337.7	−	21369.5i	0.0667262	−	0.115573i
$431$			45556.1i			0.245240i	0.992454	+	0.122620i	$0.0391297\pi$
$431$			45556.1i			0.245240i	−0.992454	+	0.122620i	$0.960870\pi$
$432$	−180800.	−	22711.2i	−0.968794	−	0.121695i
$433$	209599.			1.11793			0.558965	−	0.829192i	$-0.311199\pi$
$433$	209599.			1.11793			0.558965	+	0.829192i	$0.311199\pi$
$434$	−5229.72	−	3019.38i	−0.0277651	−	0.0160302i
$435$	226984.	+	93493.9i	1.19955	+	0.494089i
$436$	−120399.	−	208537.i	−0.633360	−	1.09701i
$437$	−54983.5	+	31744.8i	−0.287919	+	0.166230i
$438$	−6705.13	−	8702.56i	−0.0349509	−	0.0453627i
$439$	91842.1	−	159075.i	0.476555	−	0.825417i	−0.523084	−	0.852281i	$-0.675219\pi$
$439$	91842.1	−	159075.i	0.476555	−	0.825417i	0.999639	+	0.0268637i	$0.00855202\pi$
$440$			22701.6i			0.117260i
$441$	−29471.4	+	111757.i	−0.151539	+	0.574641i
$442$	10074.6			0.0515685
$443$	−100410.	−	57971.5i	−0.511644	−	0.295398i	0.221865	−	0.975077i	$-0.428785\pi$
$443$	−100410.	−	57971.5i	−0.511644	−	0.295398i	−0.733509	+	0.679680i	$0.762119\pi$
$444$	−17012.9	−	127278.i	−0.0863005	−	0.645638i
$445$	155086.	+	268617.i	0.783165	+	1.35648i
$446$	2613.85	−	1509.11i	0.0131405	−	0.00758666i
$447$	333472.	−	44574.2i	1.66895	−	0.223084i
$448$	60915.7	−	105509.i	0.303510	−	0.525695i
$449$			328940.i			1.63164i	0.578305	+	0.815820i	$0.303714\pi$
$449$			328940.i			1.63164i	−0.578305	+	0.815820i	$0.696286\pi$
$450$	16175.1	+	4265.53i	0.0798769	+	0.0210643i
$451$	149458.			0.734795
$452$	18875.7	+	10897.9i	0.0923903	+	0.0533416i
$453$	−237192.	+	182751.i	−1.15586	+	0.890562i
$454$	3392.54	+	5876.05i	0.0164594	+	0.0285084i
$455$	−68812.3	+	39728.8i	−0.332387	+	0.191904i
$456$	4493.32	−	10908.9i	0.0216091	−	0.0524626i
$457$	106369.	−	184236.i	0.509308	−	0.882148i	−0.490634	−	0.871366i	$-0.663235\pi$
$457$	106369.	−	184236.i	0.509308	−	0.882148i	0.999942	−	0.0107819i	$-0.00343204\pi$
$458$			3808.68i			0.0181570i
$459$	259992.	−	109506.i	1.23405	−	0.519770i
$460$	−302317.			−1.42872
$461$	−41957.2	−	24224.0i	−0.197426	−	0.113984i	0.398028	−	0.917373i	$-0.369695\pi$
$461$	−41957.2	−	24224.0i	−0.197426	−	0.113984i	−0.595454	+	0.803389i	$0.703028\pi$
$462$	5325.84	+	2193.69i	0.0249519	+	0.0102776i
$463$	−84550.6	−	146446.i	−0.394416	−	0.683149i	0.598610	−	0.801040i	$-0.295720\pi$
$463$	−84550.6	−	146446.i	−0.394416	−	0.683149i	−0.993026	+	0.117892i	$0.962386\pi$
$464$	169993.	−	98145.8i	0.789580	−	0.455864i
$465$	103931.	+	134891.i	0.480660	+	0.623848i
$466$	−18150.0	+	31436.8i	−0.0835806	+	0.144766i
$467$		−	54646.4i		−	0.250569i	−0.992121	−	0.125285i	$-0.960016\pi$
$467$		−	54646.4i		−	0.250569i	0.992121	−	0.125285i	$-0.0399844\pi$
$468$	90933.5	−	24751.9i	0.415176	−	0.113010i
$469$	−140670.			−0.639524
$470$	8668.55	+	5004.79i	0.0392420	+	0.0226564i
$471$	−9634.97	−	72081.9i	−0.0434319	−	0.324926i
$472$	−8560.28	−	14826.8i	−0.0384241	−	0.0665525i
$473$	−99999.1	+	57734.5i	−0.446965	+	0.258055i
$474$	−3811.00	+	509.406i	−0.0169622	+	0.00226729i
$475$	33662.6	−	58305.3i	0.149197	−	0.258417i
$476$			191726.i			0.846189i
$477$	−126704.	+	127712.i	−0.556871	+	0.561299i
$478$	5512.58			0.0241268
$479$	−120011.	−	69288.6i	−0.523060	−	0.301989i	0.215126	−	0.976586i	$-0.430984\pi$
$479$	−120011.	−	69288.6i	−0.523060	−	0.301989i	−0.738186	+	0.674597i	$0.764317\pi$
$480$	66840.3	−	51498.9i	0.290106	−	0.223520i
$481$	32940.0	+	57053.7i	0.142375	+	0.246601i
$482$	22134.3	−	12779.3i	0.0952735	−	0.0550062i
$483$	−58658.9	+	142412.i	−0.251443	+	0.610453i
$484$	−89751.4	+	155454.i	−0.383134	+	0.663607i
$485$		−	231684.i		−	0.984948i
$486$	−16512.2	+	12931.9i	−0.0699088	+	0.0547508i
$487$	23464.1			0.0989340			0.0494670	−	0.998776i	$-0.484248\pi$
$487$	23464.1			0.0989340			0.0494670	+	0.998776i	$0.484248\pi$
$488$	−18653.6	−	10769.6i	−0.0783289	−	0.0452232i
$489$	−211597.	−	87156.1i	−0.884897	−	0.364485i
$490$	−8801.74	−	15245.1i	−0.0366586	−	0.0634946i
$491$	64368.8	−	37163.4i	0.267001	−	0.154153i	−0.360523	−	0.932750i	$-0.617402\pi$
$491$	64368.8	−	37163.4i	0.267001	−	0.154153i	0.627524	+	0.778597i	$0.284068\pi$
$492$	−225734.	−	292980.i	−0.932539	−	1.21034i
$493$	−151948.	+	263181.i	−0.625173	+	1.08283i
$494$			3014.46i			0.0123525i
$495$	−115305.	−	114395.i	−0.470583	−	0.466872i
$496$	136162.			0.553467
$497$	107943.	+	62321.0i	0.437001	+	0.252302i
$498$	3920.29	+	29328.8i	0.0158074	+	0.118259i
$499$	9486.01	+	16430.2i	0.0380963	+	0.0659847i	0.884445	−	0.466645i	$-0.154537\pi$
$499$	9486.01	+	16430.2i	0.0380963	+	0.0659847i	−0.846349	+	0.532629i	$0.821204\pi$
$500$	−20800.9	+	12009.4i	−0.0832034	+	0.0480375i
$501$	−312694.	+	41796.9i	−1.24579	+	0.166521i
$502$	7367.97	−	12761.7i	0.0292375	−	0.0506409i
$503$		−	117856.i		−	0.465818i	−0.972498	−	0.232909i	$-0.925175\pi$
$503$		−	117856.i		−	0.465818i	0.972498	−	0.232909i	$-0.0748245\pi$
$504$	−7517.03	−	27616.1i	−0.0295927	−	0.108718i
$505$	317816.			1.24622
$506$	−9737.06	−	5621.69i	−0.0380300	−	0.0219567i
$507$	165320.	−	127375.i	0.643146	−	0.495529i
$508$	152011.	+	263291.i	0.589045	+	1.02026i
$509$	158881.	−	91730.2i	0.613250	−	0.354060i	−0.160986	−	0.986957i	$-0.551468\pi$
$509$	158881.	−	91730.2i	0.613250	−	0.354060i	0.774236	+	0.632897i	$0.218134\pi$
$510$	−16364.6	+	39729.8i	−0.0629164	+	0.152748i
$511$	−53631.2	+	92891.9i	−0.205388	+	0.355743i
$512$		−	112747.i		−	0.430097i
$513$	32765.5	+	77792.9i	0.124504	+	0.295601i
$514$	−25761.5			−0.0975091
$515$	460602.	+	265929.i	1.73665	+	1.00265i
$516$	264210.	+	108827.i	0.992314	+	0.408730i
$517$	−23420.0	−	40564.7i	−0.0876207	−	0.151763i
$518$	8629.19	−	4982.06i	0.0321596	−	0.0185673i
$519$	80749.2	+	104804.i	0.299781	+	0.389085i
$520$	−14410.9	+	24960.5i	−0.0532949	+	0.0923094i
$521$		−	409498.i		−	1.50861i	−0.656526	−	0.754303i	$-0.727975\pi$
$521$		−	409498.i		−	1.50861i	0.656526	−	0.754303i	$-0.272025\pi$
$522$	5761.04	−	21846.1i	0.0211427	−	0.0801739i
$523$	−211852.			−0.774513			−0.387256	−	0.921972i	$-0.626577\pi$
$523$	−211852.			−0.774513			−0.387256	+	0.921972i	$0.626577\pi$
$524$	41516.4	+	23969.5i	0.151202	+	0.0872964i
$525$	−21638.6	−	161885.i	−0.0785075	−	0.587336i
$526$	−15253.6	−	26420.0i	−0.0551315	−	0.0954906i
$527$	−182561.	+	105402.i	−0.657336	+	0.379513i
$528$	−128730.	+	17207.0i	−0.461756	+	0.0617215i
$529$	10402.4	−	18017.4i	0.0371724	−	0.0643845i
$530$		−	27400.5i		−	0.0975453i
$531$	118444.	+	31234.7i	0.420071	+	0.110777i
$532$	−57367.0			−0.202693
$533$	164330.	+	94875.7i	0.578444	+	0.333965i
$534$	22612.9	−	17422.7i	0.0793002	−	0.0610990i
$535$	−105926.	−	183468.i	−0.370078	−	0.640994i
$536$	−44189.5	+	25512.8i	−0.153812	+	0.0888033i
$537$	127004.	−	308341.i	0.440423	−	1.06926i
$538$	−15800.1	+	27366.6i	−0.0545877	+	0.0945487i
$539$			82375.9i			0.283545i
$540$	−50096.1	+	398807.i	−0.171797	+	1.36765i
$541$	44016.5			0.150391			0.0751954	−	0.997169i	$-0.476042\pi$
$541$	44016.5			0.150391			0.0751954	+	0.997169i	$0.476042\pi$
$542$	29696.3	+	17145.2i	0.101089	+	0.0583638i
$543$	−330078.	−	135958.i	−1.11948	−	0.461111i
$544$	52227.8	+	90461.2i	0.176483	+	0.305678i
$545$	−456304.	+	263447.i	−1.53625	+	0.886953i
$546$	4463.23	+	5792.81i	0.0149714	+	0.0194314i
$547$	21429.6	−	37117.1i	0.0716207	−	0.124051i	−0.827991	−	0.560741i	$-0.810516\pi$
$547$	21429.6	−	37117.1i	0.0716207	−	0.124051i	0.899612	+	0.436691i	$0.143850\pi$
$548$			161085.i			0.536408i
$549$	148697.	−	40475.0i	0.493354	−	0.134290i
$550$	11922.6			0.0394137
$551$	−78747.3	−	45464.8i	−0.259378	−	0.149752i
$552$	7401.86	+	55375.4i	0.0242920	+	0.181735i
$553$	18769.8	+	32510.3i	0.0613776	+	0.106309i
$554$	7241.43	−	4180.84i	0.0235942	−	0.0136221i
$555$	−278500.	+	37226.3i	−0.904148	+	0.120855i
$556$	278795.	−	482888.i	0.901853	−	1.56206i
$557$		−	311007.i		−	1.00244i	−0.865319	−	0.501222i	$-0.832884\pi$
$557$		−	311007.i		−	1.00244i	0.865319	−	0.501222i	$-0.167116\pi$
$558$	11037.9	−	11125.6i	0.0354501	−	0.0357319i
$559$	−146599.			−0.469145
$560$	−234671.	−	135487.i	−0.748314	−	0.432039i
$561$	159277.	−	122719.i	0.506090	−	0.389931i
$562$	−10373.2	−	17967.0i	−0.0328429	−	0.0568856i
$563$	−247482.	+	142884.i	−0.780777	+	0.450782i	−0.836705	−	0.547653i	$-0.815521\pi$
$563$	−247482.	+	142884.i	−0.780777	+	0.450782i	0.0559288	+	0.998435i	$0.482188\pi$
$564$	−44145.7	+	107177.i	−0.138781	+	0.336932i
$565$	23845.9	−	41302.2i	0.0746992	−	0.129383i
$566$			27035.9i			0.0843933i
$567$	178145.	+	100980.i	0.554125	+	0.314100i
$568$	45211.7			0.140137
$569$	−118371.	−	68341.3i	−0.365611	−	0.211086i	0.305928	−	0.952055i	$-0.401033\pi$
$569$	−118371.	−	68341.3i	−0.365611	−	0.211086i	−0.671539	+	0.740969i	$0.734367\pi$
$570$	−11887.7	−	4896.49i	−0.0365888	−	0.0150708i
$571$	14255.0	+	24690.4i	0.0437215	+	0.0757279i	0.887058	−	0.461658i	$-0.152745\pi$
$571$	14255.0	+	24690.4i	0.0437215	+	0.0757279i	−0.843337	+	0.537386i	$0.819412\pi$
$572$	58170.4	−	33584.7i	0.177791	−	0.102648i
$573$	316599.	+	410912.i	0.964273	+	1.25153i
$574$	14349.6	−	24854.3i	0.0435529	−	0.0754358i
$575$			318809.i			0.964261i
$576$	224459.	+	222688.i	0.676536	+	0.671200i
$577$	−293742.			−0.882297			−0.441149	−	0.897434i	$-0.645429\pi$
$577$	−293742.			−0.882297			−0.441149	+	0.897434i	$0.645429\pi$
$578$	−20374.3	−	11763.1i	−0.0609856	−	0.0352101i
$579$	−4983.78	−	37285.1i	−0.0148663	−	0.111219i
$580$	−216489.	−	374969.i	−0.643545	−	1.11465i
$581$	250193.	−	144449.i	0.741179	−	0.427920i
$582$	−21134.9	+	2825.03i	−0.0623955	+	0.00834022i
$583$	−64110.6	+	111043.i	−0.188622	+	0.326703i
$584$			38907.5i			0.114080i
$585$	−54160.0	−	198973.i	−0.158258	−	0.581410i
$586$	49694.6			0.144715
$587$	334334.	+	193028.i	0.970295	+	0.560200i	0.899326	−	0.437279i	$-0.144058\pi$
$587$	334334.	+	193028.i	0.970295	+	0.560200i	0.0709687	+	0.997479i	$0.477391\pi$
$588$	161480.	−	124417.i	0.467050	−	0.359852i
$589$	−31537.6	−	54624.7i	−0.0909072	−	0.157456i
$590$	−16157.2	+	9328.37i	−0.0464154	+	0.0267980i
$591$	76065.3	−	184671.i	0.217777	−	0.528718i
$592$	−112335.	+	194571.i	−0.320534	+	0.555180i
$593$			305581.i			0.868995i	0.900673	+	0.434497i	$0.143074\pi$
$593$			305581.i			0.868995i	−0.900673	+	0.434497i	$0.856926\pi$
$594$	−9029.47	+	11913.3i	−0.0255911	+	0.0337643i
$595$	419519.			1.18500
$596$	−513896.	−	296698.i	−1.44671	−	0.835260i
$597$	421152.	+	173471.i	1.18165	+	0.486718i
$598$	−7137.28	−	12362.1i	−0.0199586	−	0.0345693i
$599$	229270.	−	132369.i	0.638988	−	0.368920i	−0.145236	−	0.989397i	$-0.546394\pi$
$599$	229270.	−	132369.i	0.638988	−	0.368920i	0.784225	+	0.620477i	$0.213061\pi$
$600$	−36157.9	−	46929.2i	−0.100439	−	0.130359i
$601$	66101.5	−	114491.i	0.183005	−	0.316973i	−0.759898	−	0.650043i	$-0.774751\pi$
$601$	66101.5	−	114491.i	0.183005	−	0.316973i	0.942902	+	0.333069i	$0.108084\pi$
$602$			22172.6i			0.0611820i
$603$	93091.3	−	353006.i	0.256020	−	0.970841i
$604$	528123.			1.44764
$605$	340151.	+	196386.i	0.929312	+	0.536538i
$606$	−3875.28	−	28992.0i	−0.0105526	−	0.0789466i
$607$	127073.	+	220097.i	0.344886	+	0.597360i	0.985333	−	0.170642i	$-0.0545843\pi$
$607$	127073.	+	220097.i	0.344886	+	0.597360i	−0.640447	+	0.768002i	$0.721251\pi$
$608$	−27067.2	+	15627.3i	−0.0732211	+	0.0422742i
$609$	−218642.	+	29225.2i	−0.589520	+	0.0787994i
$610$	−11736.0	+	20327.3i	−0.0315398	+	0.0546286i
$611$		−	59468.0i		−	0.159295i
$612$	−481129.	−	126879.i	−1.28457	−	0.338755i
$613$	−492878.			−1.31165			−0.655826	−	0.754912i	$-0.727680\pi$
$613$	−492878.			−1.31165			−0.655826	+	0.754912i	$0.727680\pi$
$614$	−25160.8	−	14526.6i	−0.0667403	−	0.0385325i
$615$	−641074.	+	493933.i	−1.69495	+	1.30592i
$616$	−10199.5	−	17666.1i	−0.0268793	−	0.0465564i
$617$	−105029.	+	60638.8i	−0.275893	+	0.159287i	−0.631563	−	0.775325i	$-0.717586\pi$
$617$	−105029.	+	60638.8i	−0.275893	+	0.159287i	0.355670	+	0.934612i	$0.384253\pi$
$618$	18642.4	−	45259.9i	0.0488118	−	0.118505i
$619$	−153682.	+	266185.i	−0.401090	+	0.694709i	−0.993858	−	0.110665i	$-0.964702\pi$
$619$	−153682.	+	266185.i	−0.401090	+	0.694709i	0.592768	+	0.805374i	$0.298035\pi$
$620$		−	300344.i		−	0.781331i
$621$	−318558.	−	241446.i	−0.826049	−	0.626090i
$622$	−604.780			−0.00156321
$623$	−241372.	−	139356.i	−0.621886	−	0.359046i
$624$	−152462.	−	62798.5i	−0.391555	−	0.161280i
$625$	207977.	+	360227.i	0.532421	+	0.922181i
$626$	21519.8	−	12424.5i	0.0549149	−	0.0317051i
$627$	36719.3	+	47657.9i	0.0934026	+	0.121227i
$628$	−64132.9	+	111081.i	−0.162615	+	0.281658i
$629$		−	347832.i		−	0.879161i
$630$	−30094.0	+	8191.52i	−0.0758227	+	0.0206387i
$631$	−254196.			−0.638425			−0.319212	−	0.947683i	$-0.603418\pi$
$631$	−254196.			−0.638425			−0.319212	+	0.947683i	$0.603418\pi$
$632$	11792.5	+	6808.43i	0.0295239	+	0.0170456i
$633$	10633.9	+	79554.9i	0.0265390	+	0.198545i
$634$	20712.6	+	35875.3i	0.0515296	+	0.0892519i
$635$	576112.	−	332618.i	1.42876	−	0.824895i
$636$	314505.	−	42038.9i	0.777522	−	0.103929i
$637$	−52292.1	+	90572.5i	−0.128872	+	0.223212i
$638$		−	16102.8i		−	0.0395602i
$639$	−227825.	+	229637.i	−0.557957	+	0.562393i
$640$	−198164.			−0.483799
$641$	316954.	+	182993.i	0.771400	+	0.445368i	0.833374	−	0.552710i	$-0.186406\pi$
$641$	316954.	+	182993.i	0.771400	+	0.445368i	−0.0619737	+	0.998078i	$0.519739\pi$
$642$	−15444.9	+	11899.9i	−0.0374726	+	0.0288718i
$643$	−115391.	−	199864.i	−0.279094	−	0.483406i	0.692066	−	0.721835i	$-0.256701\pi$
$643$	−115391.	−	199864.i	−0.279094	−	0.483406i	−0.971160	+	0.238429i	$0.923368\pi$
$644$	235259.	−	135827.i	0.567250	−	0.327502i
$645$	238126.	−	578121.i	0.572383	−	1.38963i
$646$	7957.85	−	13783.4i	0.0190691	−	0.0330287i
$647$			278596.i			0.665529i	0.943010	+	0.332764i	$0.107981\pi$
$647$			278596.i			0.665529i	−0.943010	+	0.332764i	$0.892019\pi$
$648$	74276.0	−	588.198i	0.176888	−	0.00140079i
$649$	87304.7			0.207276
$650$	13109.0	+	7568.47i	0.0310272	+	0.0179135i
$651$	−141483.	−	58276.1i	−0.333842	−	0.137508i
$652$	201813.	+	349551.i	0.474738	+	0.822271i
$653$	−67988.8	+	39253.4i	−0.159445	+	0.0920557i	−0.577600	−	0.816320i	$-0.696010\pi$
$653$	−67988.8	+	39253.4i	−0.159445	+	0.0920557i	0.418154	+	0.908376i	$0.362677\pi$
$654$	29596.3	+	38412.9i	0.0691961	+	0.0898094i
$655$	52448.0	−	90842.6i	0.122249	−	0.211742i
$656$			647111.i			1.50373i
$657$	−197617.	−	196058.i	−0.457819	−	0.454208i
$658$	−8994.34			−0.0207739
$659$	−742420.	−	428637.i	−1.70954	−	0.987003i	−0.935121	−	0.354328i	$-0.884710\pi$
$659$	−742420.	−	428637.i	−1.70954	−	0.987003i	−0.774418	−	0.632675i	$-0.781957\pi$
$660$	37954.9	+	283951.i	0.0871324	+	0.651862i
$661$	−11172.0	−	19350.4i	−0.0255698	−	0.0442882i	0.852957	−	0.521981i	$-0.174807\pi$
$661$	−11172.0	−	19350.4i	−0.0255698	−	0.0442882i	−0.878527	+	0.477692i	$0.841473\pi$
$662$	−31017.4	+	17907.9i	−0.0707765	+	0.0408628i
$663$	253028.	−	33821.5i	0.575627	−	0.0769424i
$664$	52396.4	−	90753.2i	0.118841	−	0.205838i
$665$			125526.i			0.283850i
$666$	6791.76	+	24951.6i	0.0153121	+	0.0562535i
$667$	430584.			0.967846
$668$	481876.	+	278211.i	1.07990	+	0.623479i
$669$	60581.6	−	46676.7i	0.135359	−	0.104291i
$670$	27802.0	+	48154.6i	0.0619337	+	0.107272i
$671$	95122.1	−	54918.8i	0.211269	−	0.121976i
$672$	−28876.5	+	70106.3i	−0.0639449	+	0.155245i
$673$	331739.	−	574588.i	0.732430	−	1.26861i	−0.223412	−	0.974724i	$-0.571719\pi$
$673$	331739.	−	574588.i	0.732430	−	1.26861i	0.955842	−	0.293882i	$-0.0949472\pi$
$674$		−	14241.1i		−	0.0313489i
$675$	420563.	+	52829.0i	0.923046	+	0.115948i
$676$	−368095.			−0.805501
$677$	−197558.	−	114060.i	−0.431040	−	0.248861i	0.268749	−	0.963210i	$-0.413390\pi$
$677$	−197558.	−	114060.i	−0.431040	−	0.248861i	−0.699790	+	0.714349i	$0.746723\pi$
$678$	−4058.46	−	1671.66i	−0.00882881	−	0.00363655i
$679$	104093.	+	180294.i	0.225777	+	0.391058i
$680$	131786.	−	76086.6i	0.285004	−	0.164547i
$681$	104931.	+	136190.i	0.226261	+	0.293664i
$682$	5585.01	−	9673.52i	0.0120076	−	0.0207977i
$683$			53606.6i			0.114915i	0.998348	+	0.0574575i	$0.0182994\pi$
$683$			53606.6i			0.114915i	−0.998348	+	0.0574575i	$0.981701\pi$
$684$	37963.7	−	143960.i	0.0811441	−	0.307702i
$685$	352474.			0.751182
$686$	36749.6	+	21217.4i	0.0780916	+	0.0450862i
$687$	12786.1	+	95656.4i	0.0270910	+	0.202675i
$688$	−249974.	−	432967.i	−0.528102	−	0.914699i
$689$	−140980.	+	81394.6i	−0.296974	+	0.171458i
$690$	60344.1	−	8066.02i	0.126747	−	0.0169419i
$691$	−378663.	+	655863.i	−0.793043	+	1.37359i	0.131031	+	0.991378i	$0.458171\pi$
$691$	−378663.	+	655863.i	−0.793043	+	1.37359i	−0.924074	+	0.382213i	$0.875162\pi$
$692$		−	233353.i		−	0.487305i
$693$	141125.	+	37216.0i	0.293858	+	0.0774932i
$694$	−80400.9			−0.166933
$695$	−1.05661e6	−	610036.i	−2.18749	−	1.26295i
$696$	−63382.7	+	48834.9i	−0.130844	+	0.100812i
$697$	−500923.	−	867624.i	−1.03111	−	1.78594i
$698$	−24484.5	+	14136.2i	−0.0502552	+	0.0290149i
$699$	−350308.	+	850477.i	−0.716962	+	1.74064i
$700$	−144033.	+	249472.i	−0.293944	+	0.509126i
$701$			506359.i			1.03044i	0.857058	+	0.515220i	$0.172290\pi$
$701$			506359.i			1.03044i	−0.857058	+	0.515220i	$0.827710\pi$
$702$	−17490.4	+	7366.78i	−0.0354917	+	0.0149487i
$703$	104076.			0.210591
$704$	195162.	+	112677.i	0.393777	+	0.227347i
$705$	234515.	+	96595.9i	0.471838	+	0.194348i
$706$	−24848.7	−	43039.2i	−0.0498534	−	0.0863485i
$707$	−247321.	+	142791.i	−0.494791	+	0.285668i
$708$	−131861.	−	171142.i	−0.263056	−	0.341420i
$709$	325622.	−	563993.i	0.647770	−	1.12197i	−0.335885	−	0.941903i	$-0.609035\pi$
$709$	325622.	−	563993.i	0.647770	−	1.12197i	0.983654	−	0.180067i	$-0.0576314\pi$
$710$		−	49268.4i		−	0.0977354i
$711$	−94004.6	+	25587.8i	−0.185956	+	0.0506167i
$712$	−101098.			−0.199427
$713$	258668.	+	149342.i	0.508819	+	0.293767i
$714$	−5115.39	−	38269.6i	−0.0100342	−	0.0750685i
$715$	−73487.2	−	127284.i	−0.143747	−	0.248978i
$716$	−509367.	+	294083.i	−0.993584	+	0.573646i
$717$	138450.	−	18506.3i	0.269312	−	0.0359981i
$718$	−37581.8	+	65093.5i	−0.0729001	+	0.126267i
$719$		−	69724.6i		−	0.134874i	−0.997724	−	0.0674370i	$-0.978518\pi$
$719$		−	69724.6i		−	0.134874i	0.997724	−	0.0674370i	$-0.0214822\pi$
$720$	495299.	−	499236.i	0.955437	−	0.963033i
$721$	−477913.			−0.919345
$722$	−35962.8	−	20763.1i	−0.0689888	−	0.0398307i
$723$	513010.	−	395263.i	0.981407	−	0.756152i
$724$	314816.	+	545277.i	0.600591	+	1.04025i
$725$	−395425.	+	228299.i	−0.752294	+	0.434337i
$726$	13767.3	−	33424.1i	0.0261201	−	0.0634142i
$727$	373864.	−	647552.i	0.707367	−	1.22520i	−0.258463	−	0.966021i	$-0.583216\pi$
$727$	373864.	−	647552.i	0.707367	−	1.22520i	0.965830	−	0.259175i	$-0.0834506\pi$
$728$		−	25898.6i		−	0.0488667i
$729$	−371295.	+	380223.i	−0.698658	+	0.715456i
$730$	42398.6			0.0795620
$731$	670313.	+	387006.i	1.25442	+	0.724240i
$732$	−251324.	−	103519.i	−0.469042	−	0.193197i
$733$	−32869.3	−	56931.2i	−0.0611761	−	0.105960i	0.833815	−	0.552044i	$-0.186152\pi$
$733$	−32869.3	−	56931.2i	−0.0611761	−	0.105960i	−0.894991	+	0.446083i	$0.852818\pi$
$734$	9841.29	−	5681.87i	0.0182667	−	0.0105463i
$735$	−272238.	−	353337.i	−0.503934	−	0.654054i
$736$	74000.7	−	128173.i	0.136609	−	0.236614i
$737$		−	260201.i		−	0.479042i
$738$	52874.7	+	52457.7i	0.0970812	+	0.0963155i
$739$	977921.			1.79067			0.895334	−	0.445395i	$-0.146937\pi$
$739$	977921.			1.79067			0.895334	+	0.445395i	$0.146937\pi$
$740$	429181.	+	247788.i	0.783750	+	0.452498i
$741$	10119.8	+	75709.3i	0.0184305	+	0.137884i
$742$	12310.7	+	21322.7i	0.0223601	+	0.0387288i
$743$	437233.	−	252437.i	0.792019	−	0.457272i	−0.0486539	−	0.998816i	$-0.515493\pi$
$743$	437233.	−	252437.i	0.792019	−	0.457272i	0.840673	+	0.541543i	$0.182160\pi$
$744$	−55014.0	+	7353.56i	−0.0993865	+	0.0132847i
$745$	−649209.	+	1.12446e6i	−1.16969	+	2.02597i
$746$			43740.5i			0.0785971i
$747$	196919.	+	723442.i	0.352896	+	1.29647i
$748$	−354640.			−0.633847
$749$	164860.	+	95181.9i	0.293867	+	0.169664i
$750$	3831.55	−	2952.12i	0.00681164	−	0.00524822i
$751$	266395.	+	461411.i	0.472332	+	0.818102i	0.999499	−	0.0316593i	$-0.0100792\pi$
$751$	266395.	+	461411.i	0.472332	+	0.818102i	−0.527167	+	0.849762i	$0.676746\pi$
$752$	175634.	−	101402.i	0.310579	−	0.179313i
$753$	142207.	−	345250.i	0.250802	−	0.608896i
$754$	10222.0	−	17705.0i	0.0179801	−	0.0311425i
$755$		−	1.15559e6i		−	2.02727i
$756$	−140194.	−	332854.i	−0.245294	−	0.582384i
$757$	−293571.			−0.512297			−0.256148	−	0.966637i	$-0.582454\pi$
$757$	−293571.			−0.512297			−0.256148	+	0.966637i	$0.582454\pi$
$758$	−35843.0	−	20694.0i	−0.0623830	−	0.0360168i
$759$	−263422.	−	108503.i	−0.457266	−	0.188346i
$760$	22766.1	+	39432.1i	0.0394150	+	0.0682688i
$761$	−22249.2	+	12845.6i	−0.0384190	+	0.0221812i	−0.519086	−	0.854722i	$-0.673728\pi$
$761$	−22249.2	+	12845.6i	−0.0384190	+	0.0221812i	0.480667	+	0.876903i	$0.340394\pi$
$762$	−37367.1	−	48498.6i	−0.0643546	−	0.0835256i
$763$	236727.	−	410022.i	0.406629	−	0.704301i
$764$		−	914920.i		−	1.56746i
$765$	−277625.	+	1.05277e6i	−0.474390	+	1.79891i
$766$	64328.9			0.109635
$767$	95991.7	+	55420.9i	0.163171	+	0.0942069i
$768$	−72056.0	−	539071.i	−0.122165	−	0.913952i
$769$	323572.	+	560443.i	0.547165	+	0.947717i	0.998467	+	0.0553463i	$0.0176263\pi$
$769$	323572.	+	560443.i	0.547165	+	0.947717i	−0.451302	+	0.892371i	$0.649040\pi$
$770$	−19251.2	+	11114.7i	−0.0324696	+	0.0187463i
$771$	−647009.	+	86483.8i	−1.08843	+	0.145488i
$772$	−33173.4	+	57458.0i	−0.0556615	+	0.0964086i
$773$			610238.i			1.02127i	0.859798	+	0.510634i	$0.170589\pi$
$773$			610238.i			1.02127i	−0.859798	+	0.510634i	$0.829411\pi$
$774$	−55641.3	−	14673.2i	−0.0928785	−	0.0244930i
$775$	−316728.			−0.527331
$776$	65398.4	+	37757.8i	0.108604	+	0.0627023i
$777$	200000.	−	154095.i	0.331274	−	0.255239i
$778$	−9026.64	−	15634.6i	−0.0149131	−	0.0258302i
$779$	259605.	−	149883.i	0.427797	−	0.246989i
$780$	−138520.	+	336299.i	−0.227679	+	0.552759i
$781$	−115276.	+	199665.i	−0.188990	+	0.327340i
$782$			75366.6i			0.123244i
$783$	71351.0	−	568013.i	0.116379	−	0.926477i
$784$	−356664.			−0.580266
$785$	243059.	+	140330.i	0.394432	+	0.227726i
$786$	−8926.42	−	3676.76i	−0.0144488	−	0.00595141i
$787$	290160.	+	502572.i	0.468477	+	0.811427i	0.999351	−	0.0360244i	$-0.0114694\pi$
$787$	290160.	+	502572.i	0.468477	+	0.811427i	−0.530874	+	0.847451i	$0.678136\pi$
$788$	−305069.	+	176132.i	−0.491299	+	0.283652i
$789$	−471793.	−	612339.i	−0.757875	−	0.983644i
$790$	7419.33	−	12850.7i	0.0118880	−	0.0205907i
$791$			42854.5i			0.0684926i
$792$	51082.1	−	13904.4i	0.0814363	−	0.0221668i
$793$	139449.			0.221753
$794$	70351.5	+	40617.4i	0.111592	+	0.0644276i
$795$	−91986.0	−	688172.i	−0.145542	−	1.08884i
$796$	−401678.	−	695726.i	−0.633945	−	1.09802i
$797$	−915508.	+	528569.i	−1.44127	+	0.832118i	−0.997935	−	0.0642373i	$-0.979539\pi$
$797$	−915508.	+	528569.i	−1.44127	+	0.832118i	−0.443336	+	0.896355i	$0.646205\pi$
$798$	11450.8	−	1530.59i	0.0179816	−	0.00240355i
$799$	−156989.	+	271913.i	−0.245910	+	0.425928i
$800$			156943.i			0.245223i
$801$	509442.	−	513492.i	0.794016	−	0.800329i
$802$	67105.5			0.104330
$803$	−171824.	−	99202.7i	−0.266473	−	0.153848i
$804$	−510067.	+	392995.i	−0.789069	+	0.607959i
$805$	−297205.	−	514774.i	−0.458631	−	0.794373i
$806$	12281.5	−	7090.71i	0.0189051	−	0.0109149i
$807$	−304953.	+	740363.i	−0.468258	+	1.13684i
$808$	−51794.8	+	89711.2i	−0.0793348	+	0.137412i
$809$		−	355969.i		−	0.543895i	−0.962312	−	0.271947i	$-0.912332\pi$
$809$		−	355969.i		−	0.543895i	0.962312	−	0.271947i	$-0.0876677\pi$
$810$	−640.975	−	80940.6i	−0.000976947	−	0.123366i
$811$	−136417.			−0.207409			−0.103704	−	0.994608i	$-0.533070\pi$
$811$	−136417.			−0.207409			−0.103704	+	0.994608i	$0.533070\pi$
$812$	336937.	+	194531.i	0.511019	+	0.295037i
$813$	803392.	+	330914.i	1.21548	+	0.500650i
$814$	9215.43	+	15961.6i	0.0139081	+	0.0240895i
$815$	764857.	−	441590.i	1.15150	−	0.664820i
$816$	531340.	+	689625.i	0.797981	+	1.03570i
$817$	−115797.	+	200567.i	−0.173482	+	0.300479i
$818$		−	98538.4i		−	0.147265i
$819$	131543.	+	130505.i	0.196109	+	0.194563i
$820$	1.42739e6			2.12282
$821$	−394889.	−	227989.i	−0.585854	−	0.338243i	0.177603	−	0.984102i	$-0.443166\pi$
$821$	−394889.	−	227989.i	−0.585854	−	0.338243i	−0.763456	+	0.645860i	$0.776499\pi$
$822$	−4297.87	−	32153.6i	−0.00636077	−	0.0475867i
$823$	−251795.	−	436122.i	−0.371747	−	0.643885i	0.618087	−	0.786109i	$-0.287908\pi$
$823$	−251795.	−	436122.i	−0.371747	−	0.643885i	−0.989834	+	0.142225i	$0.954574\pi$
$824$	−150129.	+	86677.3i	−0.221112	+	0.127659i
$825$	299441.	−	40025.4i	0.439951	−	0.0588069i
$826$	8382.22	−	14518.4i	0.0122857	−	0.0212794i
$827$			551861.i			0.806898i	0.915002	+	0.403449i	$0.132189\pi$
$827$			551861.i			0.806898i	−0.915002	+	0.403449i	$0.867811\pi$
$828$	185165.	+	680258.i	0.270083	+	0.992232i
$829$	−182308.			−0.265275			−0.132638	−	0.991165i	$-0.542345\pi$
$829$	−182308.			−0.265275			−0.132638	+	0.991165i	$0.542345\pi$
$830$	−98896.3	−	57097.8i	−0.143557	−	0.0828826i
$831$	167836.	−	129314.i	0.243042	−	0.187259i
$832$	143054.	+	247777.i	0.206659	+	0.357944i
$833$	478203.	−	276091.i	0.689164	−	0.397889i
$834$	−42765.3	+	103826.i	−0.0614837	+	0.149270i
$835$	608759.	−	1.05440e6i	0.873117	−	1.51228i
$836$		−	106113.i		−	0.151829i
$837$	239870.	−	316479.i	0.342394	−	0.451746i
$838$	−36379.0			−0.0518039
$839$	−359993.	−	207842.i	−0.511410	−	0.295263i	0.222003	−	0.975046i	$-0.428741\pi$
$839$	−359993.	−	207842.i	−0.511410	−	0.295263i	−0.733413	+	0.679783i	$0.762074\pi$
$840$	102132.	+	42067.9i	0.144745	+	0.0596200i
$841$	−45299.7	−	78461.4i	−0.0640477	−	0.110934i
$842$	−14499.0	+	8371.03i	−0.0204510	+	0.0118074i
$843$	−320844.	−	416423.i	−0.451480	−	0.585975i
$844$	70781.8	−	122598.i	0.0993658	−	0.172107i
$845$			805434.i			1.12802i
$846$	5952.18	−	22570.9i	0.00831640	−	0.0315362i
$847$	−352935.			−0.491958
$848$	−480784.	−	277581.i	−0.668587	−	0.386009i
$849$	90762.1	+	679016.i	0.125918	+	0.942030i
$850$	−39959.9	−	69212.6i	−0.0553078	−	0.0957959i
$851$	−426809.	+	246419.i	−0.589352	+	0.340263i
$852$	565506.	−	75589.6i	0.779038	−	0.104132i
$853$	−75135.3	+	130138.i	−0.103263	+	0.178857i	−0.913027	−	0.407898i	$-0.866262\pi$
$853$	−75135.3	+	130138.i	−0.103263	+	0.178857i	0.809764	+	0.586756i	$0.199595\pi$
$854$		−	21091.3i		−	0.0289192i
$855$	−315002.	−	83069.1i	−0.430904	−	0.113634i
$856$	69051.1			0.0942374
$857$	125373.	+	72383.9i	0.170703	+	0.0985554i	0.582917	−	0.812532i	$-0.301911\pi$
$857$	125373.	+	72383.9i	0.170703	+	0.0985554i	−0.412214	+	0.911087i	$0.635245\pi$
$858$	−10715.1	+	8255.72i	−0.0145553	+	0.0112145i
$859$	−166948.	−	289163.i	−0.226254	−	0.391883i	0.730441	−	0.682976i	$-0.239315\pi$
$859$	−166948.	−	289163.i	−0.226254	−	0.391883i	−0.956695	+	0.291093i	$0.905981\pi$
$860$	−955033.	+	551389.i	−1.29128	+	0.745523i
$861$	276958.	−	672398.i	0.373601	−	0.907026i
$862$	−8090.47	+	14013.1i	−0.0108883	+	0.0188591i
$863$			1.13280e6i			1.52101i	0.649330	+	0.760507i	$0.275049\pi$
$863$			1.13280e6i			1.52101i	−0.649330	+	0.760507i	$0.724951\pi$
$864$	−156819.	−	118859.i	−0.210074	−	0.159222i
$865$	−510603.			−0.682418
$866$	64473.1	+	37223.6i	0.0859692	+	0.0496343i
$867$	−551198.	−	227036.i	−0.733279	−	0.302035i
$868$	134940.	+	233724.i	0.179103	+	0.310215i
$869$	−60135.0	+	34718.9i	−0.0796320	+	0.0459755i
$870$	53216.8	+	69069.9i	0.0703088	+	0.0912536i
$871$	165175.	−	286092.i	0.217725	−	0.377111i
$872$		−	171737.i		−	0.225855i
$873$	−521325.	+	141903.i	−0.684038	+	0.186193i
$874$	−22550.7			−0.0295214
$875$	−40898.3	−	23612.6i	−0.0534181	−	0.0308410i
$876$	65049.6	+	486654.i	0.0847689	+	0.634180i
$877$	−248271.	−	430017.i	−0.322795	−	0.559097i	0.658269	−	0.752783i	$-0.271289\pi$
$877$	−248271.	−	430017.i	−0.322795	−	0.559097i	−0.981064	+	0.193686i	$0.937956\pi$
$878$	56501.5	−	32621.2i	0.0732945	−	0.0423166i
$879$	1.24810e6	−	166830.i	1.61537	−	0.215921i
$880$	250614.	−	434076.i	0.323623	−	0.560532i
$881$		−	1.21533e6i		−	1.56583i	−0.622131	−	0.782913i	$-0.713733\pi$
$881$		−	1.21533e6i		−	1.56583i	0.622131	−	0.782913i	$-0.286267\pi$
$882$	−28912.8	+	29142.6i	−0.0371666	+	0.0374621i
$883$	−999070.			−1.28137			−0.640685	−	0.767804i	$-0.721349\pi$
$883$	−999070.			−1.28137			−0.640685	+	0.767804i	$0.721349\pi$
$884$	−389928.	−	225125.i	−0.498976	−	0.288084i
$885$	−374478.	+	288527.i	−0.478123	+	0.368383i
$886$	−20590.8	−	35664.2i	−0.0262304	−	0.0454324i
$887$	938048.	−	541582.i	1.19228	−	0.688362i	0.233456	−	0.972367i	$-0.424997\pi$
$887$	938048.	−	541582.i	1.19228	−	0.688362i	0.958823	+	0.284005i	$0.0916632\pi$
$888$	34879.4	−	84680.0i	0.0442326	−	0.107388i
$889$	−298882.	+	517678.i	−0.378178	+	0.655023i
$890$			110169.i			0.139085i
$891$	−186784.	+	329519.i	−0.235280	+	0.415073i
$892$	−134888.			−0.169529
$893$	−81360.0	−	46973.2i	−0.102025	−	0.0589044i
$894$	110493.	+	45511.5i	0.138248	+	0.0569437i
$895$	643488.	+	1.11455e6i	0.803330	+	1.39141i
$896$	154209.	−	89032.4i	0.192085	−	0.110900i
$897$	−220756.	−	286519.i	−0.274365	−	0.356097i
$898$	−58417.8	+	101183.i	−0.0724423	+	0.125474i
$899$			427774.i			0.529292i
$900$	−530723.	−	526536.i	−0.655213	−	0.650045i
$901$	859491.			1.05875
$902$	45973.5	+	26542.8i	0.0565060	+	0.0326238i
$903$	74435.6	+	556873.i	0.0912862	+	0.682937i
$904$	7772.36	+	13462.1i	0.00951078	+	0.0164731i
$905$	1.19313e6	−	688853.i	1.45677	−	0.841065i
$906$	−105416.	+	14090.7i	−0.128425	+	0.0171663i
$907$	−638426.	+	1.10579e6i	−0.776061	+	1.34418i	0.158135	+	0.987417i	$0.449452\pi$
$907$	−638426.	+	1.10579e6i	−0.776061	+	1.34418i	−0.934196	+	0.356760i	$0.883882\pi$
$908$		−	303235.i		−	0.367796i
$909$	−194658.	−	715136.i	−0.235583	−	0.865487i
$910$	−28222.4			−0.0340809
$911$	236846.	+	136743.i	0.285383	+	0.164766i	0.635858	−	0.771806i	$-0.280646\pi$
$911$	236846.	+	136743.i	0.285383	+	0.164766i	−0.350475	+	0.936572i	$0.613980\pi$
$912$	−206345.	+	158984.i	−0.248087	+	0.191145i
$913$	267191.	+	462788.i	0.320538	+	0.555188i
$914$	65438.2	−	37780.8i	0.0783320	−	0.0452250i
$915$	−226512.	+	549926.i	−0.270551	+	0.656844i
$916$	85107.7	−	147411.i	0.101433	−	0.175687i
$917$			94256.7i			0.112092i
$918$	99421.3	+	12488.8i	0.117976	+	0.0148196i
$919$	1.15882e6			1.37210			0.686051	−	0.727553i	$-0.259343\pi$
$919$	1.15882e6			1.37210			0.686051	+	0.727553i	$0.259343\pi$
$920$	−186725.	−	107806.i	−0.220611	−	0.127370i
$921$	−680690.	−	280373.i	−0.802472	−	0.330535i
$922$	−8604.07	−	14902.7i	−0.0101214	−	0.0175308i
$923$	−253493.	+	146355.i	−0.297552	+	0.171792i
$924$	−157111.	−	203914.i	−0.184019	−	0.238838i
$925$	261306.	−	452595.i	0.305397	−	0.528964i
$926$		−	60062.6i		−	0.0700459i
$927$	316268.	−	1.19930e6i	0.368041	−	1.39563i
$928$	211967.			0.246135
$929$	738465.	+	426353.i	0.855655	+	0.494012i	0.862555	−	0.505964i	$-0.168863\pi$
$929$	738465.	+	426353.i	0.855655	+	0.494012i	−0.00690018	+	0.999976i	$0.502196\pi$
$930$	8013.38	+	59950.3i	0.00926509	+	0.0693147i
$931$	82610.0	+	143085.i	0.0953089	+	0.165080i
$932$	1.40495e6	−	811151.i	1.61745	−	0.933834i
$933$	−15189.3	+	2030.31i	−0.0174491	+	0.00233237i
$934$	9704.86	−	16809.3i	0.0111249	−	0.0192689i
$935$			775993.i			0.887636i
$936$	64991.4	+	17138.9i	0.0741829	+	0.0195628i
$937$	629989.			0.717552			0.358776	−	0.933424i	$-0.383194\pi$
$937$	629989.			0.717552			0.358776	+	0.933424i	$0.383194\pi$
$938$	−43270.4	−	24982.2i	−0.0491796	−	0.0283939i
$939$	498768.	−	384290.i	0.565676	−	0.435840i
$940$	−223671.	−	387410.i	−0.253136	−	0.438445i
$941$	−366547.	+	211626.i	−0.413953	+	0.238996i	−0.692487	−	0.721431i	$-0.743485\pi$
$941$	−366547.	+	211626.i	−0.413953	+	0.238996i	0.278534	+	0.960426i	$0.410152\pi$
$942$	9837.56	−	23883.6i	0.0110863	−	0.0269152i
$943$	−709749.	+	1.22932e6i	−0.798145	+	1.38243i
$944$			378004.i			0.424182i
$945$	−728322.	+	306761.i	−0.815568	+	0.343508i
$946$	−41013.1			−0.0458290
$947$	−1.20762e6	−	697219.i	−1.34657	−	0.777444i	−0.358810	−	0.933411i	$-0.616817\pi$
$947$	−1.20762e6	−	697219.i	−1.34657	−	0.777444i	−0.987762	+	0.155967i	$0.950151\pi$
$948$	158884.	+	65443.6i	0.176792	+	0.0728200i
$949$	−125947.	−	218147.i	−0.139848	−	0.242224i
$950$	20709.3	−	11956.5i	0.0229466	−	0.0132482i
$951$	640642.	+	831488.i	0.708361	+	0.919379i
$952$	−68369.4	+	118419.i	−0.0754376	+	0.130662i
$953$			24001.0i			0.0264267i	0.999913	+	0.0132134i	$0.00420607\pi$
$953$			24001.0i			0.0264267i	−0.999913	+	0.0132134i	$0.995794\pi$
$954$	−61655.2	+	16782.4i	−0.0677444	+	0.0184398i
$955$	−2.00195e6			−2.19506
$956$	−213358.	−	123183.i	−0.233450	−	0.134782i
$957$	−54058.5	−	404426.i	−0.0590255	−	0.441586i
$958$	−24610.5	−	42626.6i	−0.0268157	−	0.0464461i
$959$	−274290.	+	158362.i	−0.298245	+	0.172192i
$960$	−1.20949e6	+	161669.i	−1.31238	+	0.175422i
$961$	313393.	−	542813.i	0.339346	−	0.587765i
$962$			23399.8i			0.0252849i
$963$	−347954.	+	350721.i	−0.375206	+	0.378189i
$964$	−1.14225e6			−1.22915
$965$	125725.	+	72587.2i	0.135010	+	0.0779481i
$966$	−43335.0	+	33388.6i	−0.0464392	+	0.0357803i
$967$	−522031.	−	904183.i	−0.558268	−	0.966949i	−0.997641	−	0.0686443i	$-0.978133\pi$
$967$	−522031.	−	904183.i	−0.558268	−	0.966949i	0.439373	−	0.898305i	$-0.355201\pi$
$968$	−110869.	+	64010.5i	−0.118321	+	0.0683126i
$969$	153592.	−	372890.i	0.163577	−	0.397131i
$970$	41145.7	−	71266.5i	0.0437302	−	0.0757429i
$971$		−	605213.i		−	0.641904i	−0.947096	−	0.320952i	$-0.895997\pi$
$971$		−	605213.i		−	0.641904i	0.947096	−	0.320952i	$-0.104003\pi$
$972$	928059.	−	131540.i	0.982297	−	0.139227i
$973$	1.09632e6			1.15801
$974$	7217.58	+	4167.07i	0.00760806	+	0.00439251i
$975$	354645.	+	146077.i	0.373065	+	0.153664i
$976$	237783.	+	411851.i	0.249621	+	0.432355i
$977$	41660.2	−	24052.5i	0.0436448	−	0.0251983i	−0.478019	−	0.878350i	$-0.658645\pi$
$977$	41660.2	−	24052.5i	0.0436448	−	0.0251983i	0.521664	+	0.853151i	$0.325312\pi$
$978$	−49609.3	−	64387.7i	−0.0518663	−	0.0673171i
$979$	257770.	−	446471.i	0.268947	−	0.465831i
$980$			786724.i			0.819163i
$981$	872276.	+	865396.i	0.906392	+	0.899243i
$982$	26399.9			0.0273766
$983$	−107286.	−	61941.5i	−0.111029	−	0.0641024i	0.443457	−	0.896295i	$-0.353752\pi$
$983$	−107286.	−	61941.5i	−0.111029	−	0.0641024i	−0.554486	+	0.832193i	$0.687085\pi$
$984$	−34947.9	−	261455.i	−0.0360937	−	0.270027i
$985$	385397.	+	667527.i	0.397224	+	0.688012i
$986$	−93478.7	+	53969.9i	−0.0961521	+	0.0555134i
$987$	−225896.	+	30194.9i	−0.231886	+	0.0309955i
$988$	67360.3	−	116672.i	0.0690066	−	0.119523i
$989$		−	1.09668e6i		−	1.12121i
$990$	−15152.0	−	55665.5i	−0.0154597	−	0.0567958i
$991$	851418.			0.866953			0.433477	−	0.901165i	$-0.357287\pi$
$991$	851418.			0.866953			0.433477	+	0.901165i	$0.357287\pi$
$992$	127336.	+	73517.8i	0.129399	+	0.0747083i
$993$	−718894.	+	553891.i	−0.729065	+	0.561728i
$994$	22135.6	+	38340.0i	0.0224037	+	0.0388043i
$995$	−1.52233e6	+	878917.i	−1.53767	+	0.887773i
$996$	503642.	−	1.22274e6i	0.507695	−	1.23258i
$997$	801524.	−	1.38828e6i	0.806355	−	1.39665i	−0.109018	−	0.994040i	$-0.534771\pi$
$997$	801524.	−	1.38828e6i	0.806355	−	1.39665i	0.915373	−	0.402607i	$-0.131896\pi$
$998$			6738.62i			0.00676566i
$999$	254342.	+	603867.i	0.254852	+	0.605077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.5.d.a.2.2	✓	6
3.2	odd	2		27.5.d.a.8.2		6
4.3	odd	2		144.5.q.a.65.1		6
9.2	odd	6		81.5.b.a.80.4		6
9.4	even	3		27.5.d.a.17.2		6
9.5	odd	6	inner	9.5.d.a.5.2	yes	6
9.7	even	3		81.5.b.a.80.3		6
12.11	even	2		432.5.q.a.305.3		6
36.7	odd	6		1296.5.e.c.161.1		6
36.11	even	6		1296.5.e.c.161.6		6
36.23	even	6		144.5.q.a.113.1		6
36.31	odd	6		432.5.q.a.17.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.5.d.a.2.2	✓	6	1.1	even	1	trivial
9.5.d.a.5.2	yes	6	9.5	odd	6	inner
27.5.d.a.8.2		6	3.2	odd	2
27.5.d.a.17.2		6	9.4	even	3
81.5.b.a.80.3		6	9.7	even	3
81.5.b.a.80.4		6	9.2	odd	6
144.5.q.a.65.1		6	4.3	odd	2
144.5.q.a.113.1		6	36.23	even	6
432.5.q.a.17.3		6	36.31	odd	6
432.5.q.a.305.3		6	12.11	even	2
1296.5.e.c.161.1		6	36.7	odd	6
1296.5.e.c.161.6		6	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.307601 + 0.177594i) q^{2} +(8.32172 + 3.42768i) q^{3} +(-7.93692 - 13.7472i) q^{4} +(-30.0804 + 17.3669i) q^{5} +(1.95104 + 2.53225i) q^{6} +(15.6054 - 27.0294i) q^{7} -11.3212i q^{8} +(57.5020 + 57.0484i) q^{9} +O(q^{10})\)	\(q+(0.307601 + 0.177594i) q^{2} +(8.32172 + 3.42768i) q^{3} +(-7.93692 - 13.7472i) q^{4} +(-30.0804 + 17.3669i) q^{5} +(1.95104 + 2.53225i) q^{6} +(15.6054 - 27.0294i) q^{7} -11.3212i q^{8} +(57.5020 + 57.0484i) q^{9} -12.3370 q^{10} +(49.9968 + 28.8657i) q^{11} +(-18.9279 - 141.605i) q^{12} +(36.6478 + 63.4758i) q^{13} +(9.60051 - 5.54285i) q^{14} +(-309.848 + 41.4165i) q^{15} +(-124.980 + 216.472i) q^{16} -386.985i q^{17} +(7.55625 + 27.7602i) q^{18} +115.791 q^{19} +(477.491 + 275.679i) q^{20} +(222.512 - 171.441i) q^{21} +(10.2527 + 17.7583i) q^{22} +(-474.852 + 274.156i) q^{23} +(38.8055 - 94.2118i) q^{24} +(290.719 - 503.539i) q^{25} +26.0337i q^{26} +(282.971 + 671.839i) q^{27} -495.436 q^{28} +(-680.082 - 392.645i) q^{29} +(-102.665 - 42.2874i) q^{30} +(-272.367 - 471.753i) q^{31} +(-233.759 + 134.961i) q^{32} +(317.117 + 411.585i) q^{33} +(68.7261 - 119.037i) q^{34} +1084.07i q^{35} +(327.865 - 1243.28i) q^{36} +898.827 q^{37} +(35.6175 + 20.5637i) q^{38} +(87.3975 + 653.845i) q^{39} +(196.614 + 340.546i) q^{40} +(2242.01 - 1294.43i) q^{41} +(98.8918 - 13.2186i) q^{42} +(-1000.05 + 1732.14i) q^{43} -916.419i q^{44} +(-2720.43 - 717.406i) q^{45} -194.753 q^{46} +(-702.646 - 405.673i) q^{47} +(-1782.05 + 1373.03i) q^{48} +(713.441 + 1235.72i) q^{49} +(178.851 - 103.260i) q^{50} +(1326.46 - 3220.38i) q^{51} +(581.741 - 1007.61i) q^{52} +2221.00i q^{53} +(-32.2721 + 256.913i) q^{54} -2005.23 q^{55} +(-306.005 - 176.672i) q^{56} +(963.579 + 396.895i) q^{57} +(-139.463 - 241.557i) q^{58} +(1309.65 - 756.128i) q^{59} +(3028.60 + 3930.81i) q^{60} +(951.281 - 1647.67i) q^{61} -193.483i q^{62} +(2439.33 - 663.979i) q^{63} +3903.49 q^{64} +(-2204.76 - 1272.92i) q^{65} +(24.4507 + 182.922i) q^{66} +(-2253.55 - 3903.26i) q^{67} +(-5319.94 + 3071.47i) q^{68} +(-4891.30 + 653.806i) q^{69} +(-192.524 + 333.462i) q^{70} +3993.54i q^{71} +(645.856 - 650.991i) q^{72} -3436.70 q^{73} +(276.480 + 159.626i) q^{74} +(4145.25 - 3193.82i) q^{75} +(-919.023 - 1591.80i) q^{76} +(1560.44 - 900.923i) q^{77} +(-89.2352 + 216.645i) q^{78} +(-601.388 + 1041.63i) q^{79} -8682.07i q^{80} +(51.9555 + 6560.79i) q^{81} +919.529 q^{82} +(8016.22 + 4628.17i) q^{83} +(-4122.88 - 1698.20i) q^{84} +(6720.72 + 11640.6i) q^{85} +(-615.236 + 355.207i) q^{86} +(-4313.58 - 5598.59i) q^{87} +(326.794 - 566.024i) q^{88} -8929.99i q^{89} +(-709.403 - 703.807i) q^{90} +2287.62 q^{91} +(7537.72 + 4351.91i) q^{92} +(-649.539 - 4859.38i) q^{93} +(-144.090 - 249.571i) q^{94} +(-3483.03 + 2010.93i) q^{95} +(-2407.88 + 321.854i) q^{96} +(-3335.14 + 5776.64i) q^{97} +506.811i q^{98} +(1228.18 + 4512.07i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 + 15 * q^4 - 12 * q^5 - 99 * q^6 + 12 * q^7 + 99 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9} - 36 q^{10} + 483 q^{11} + 330 q^{12} - 6 q^{13} - 1146 q^{14} - 1026 q^{15} + 15 q^{16} + 1404 q^{18} - 258 q^{19} + 1614 q^{20} + 480 q^{21} - 369 q^{22} - 282 q^{23} - 1449 q^{24} - 273 q^{25} + 54 q^{27} + 1308 q^{28} - 1056 q^{29} - 1278 q^{30} + 1290 q^{31} - 1161 q^{32} + 279 q^{33} + 513 q^{34} - 2385 q^{36} + 12 q^{37} - 789 q^{38} + 1974 q^{39} - 1314 q^{40} + 7629 q^{41} + 9612 q^{42} - 285 q^{43} - 4212 q^{45} - 5760 q^{46} - 9642 q^{47} - 6771 q^{48} - 1863 q^{49} + 3027 q^{50} + 2457 q^{51} - 240 q^{52} - 405 q^{54} + 2016 q^{55} - 462 q^{56} + 5367 q^{57} + 6462 q^{58} + 6225 q^{59} + 7470 q^{60} + 3630 q^{61} - 7578 q^{63} + 15450 q^{64} - 7158 q^{65} - 13734 q^{66} - 5055 q^{67} - 10503 q^{68} - 13878 q^{69} - 9684 q^{70} + 8451 q^{72} - 14622 q^{73} + 26454 q^{74} + 21021 q^{75} - 4047 q^{76} + 2580 q^{77} - 12060 q^{78} + 4764 q^{79} + 18387 q^{81} - 9702 q^{82} - 1866 q^{83} - 6486 q^{84} + 12366 q^{85} - 37731 q^{86} - 21564 q^{87} + 14787 q^{88} + 20790 q^{90} + 34836 q^{91} + 33636 q^{92} + 19254 q^{93} - 12708 q^{94} - 13362 q^{95} - 3672 q^{96} - 28959 q^{97} - 9126 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 + 15 * q^4 - 12 * q^5 - 99 * q^6 + 12 * q^7 + 99 * q^9 - 36 * q^10 + 483 * q^11 + 330 * q^12 - 6 * q^13 - 1146 * q^14 - 1026 * q^15 + 15 * q^16 + 1404 * q^18 - 258 * q^19 + 1614 * q^20 + 480 * q^21 - 369 * q^22 - 282 * q^23 - 1449 * q^24 - 273 * q^25 + 54 * q^27 + 1308 * q^28 - 1056 * q^29 - 1278 * q^30 + 1290 * q^31 - 1161 * q^32 + 279 * q^33 + 513 * q^34 - 2385 * q^36 + 12 * q^37 - 789 * q^38 + 1974 * q^39 - 1314 * q^40 + 7629 * q^41 + 9612 * q^42 - 285 * q^43 - 4212 * q^45 - 5760 * q^46 - 9642 * q^47 - 6771 * q^48 - 1863 * q^49 + 3027 * q^50 + 2457 * q^51 - 240 * q^52 - 405 * q^54 + 2016 * q^55 - 462 * q^56 + 5367 * q^57 + 6462 * q^58 + 6225 * q^59 + 7470 * q^60 + 3630 * q^61 - 7578 * q^63 + 15450 * q^64 - 7158 * q^65 - 13734 * q^66 - 5055 * q^67 - 10503 * q^68 - 13878 * q^69 - 9684 * q^70 + 8451 * q^72 - 14622 * q^73 + 26454 * q^74 + 21021 * q^75 - 4047 * q^76 + 2580 * q^77 - 12060 * q^78 + 4764 * q^79 + 18387 * q^81 - 9702 * q^82 - 1866 * q^83 - 6486 * q^84 + 12366 * q^85 - 37731 * q^86 - 21564 * q^87 + 14787 * q^88 + 20790 * q^90 + 34836 * q^91 + 33636 * q^92 + 19254 * q^93 - 12708 * q^94 - 13362 * q^95 - 3672 * q^96 - 28959 * q^97 - 9126 * q^99

Introduction

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