LMFDB - Embedded newform 9.5.d.a.5.2

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

$q$-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 $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.307601	−	0.177594i	0.0769004	−	0.0443984i	−0.461057	−	0.887371i	$-0.652530\pi$
$2$	0.307601	−	0.177594i	0.0769004	−	0.0443984i	0.537957	+	0.842972i	$0.319196\pi$
$3$	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	−0.241946	−	0.970290i	$-0.577786\pi$
$5$	−30.0804	−	17.3669i	−1.20321	−	0.694676i	−0.961268	+	0.275614i	$0.911119\pi$
$6$	1.95104	−	2.53225i	0.0541955	−	0.0703402i
$7$	15.6054	+	27.0294i	0.318478	+	0.551620i	0.980171	−	0.198155i	$-0.0634949\pi$
$7$	15.6054	+	27.0294i	0.318478	+	0.551620i	−0.661693	+	0.749775i	$0.730162\pi$
$8$			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	−0.278965	−	0.960301i	$-0.589991\pi$
$11$	49.9968	−	28.8657i	0.413197	−	0.238559i	0.692162	+	0.721742i	$0.256658\pi$
$12$	−18.9279	+	141.605i	−0.131444	+	0.983369i
$13$	36.6478	−	63.4758i	0.216851	−	0.375597i	−0.736993	−	0.675901i	$-0.763755\pi$
$13$	36.6478	−	63.4758i	0.216851	−	0.375597i	0.953844	+	0.300304i	$0.0970882\pi$
$14$	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	$0.233502\pi$
$17$			386.985i			1.33905i	−0.742791	+	0.669524i	$0.766498\pi$
$18$	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	−0.0212066	−	0.999775i	$-0.506751\pi$
$23$	−474.852	−	274.156i	−0.897641	−	0.518253i	−0.876434	+	0.481522i	$0.840084\pi$
$24$	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	−0.846490	−	0.532405i	$-0.821288\pi$
$29$	−680.082	+	392.645i	−0.808658	+	0.466879i	0.0378313	+	0.999284i	$0.487955\pi$
$30$	−102.665	+	42.2874i	−0.114072	+	0.0469860i
$31$	−272.367	+	471.753i	−0.283420	+	0.490898i	−0.972225	−	0.234049i	$-0.924802\pi$
$31$	−272.367	+	471.753i	−0.283420	+	0.490898i	0.688805	+	0.724947i	$0.258136\pi$
$32$	−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	0.985870	−	0.167510i	$-0.0535727\pi$
$41$	2242.01	+	1294.43i	1.33374	+	0.770034i	0.347867	+	0.937544i	$0.386906\pi$
$42$	98.8918	+	13.2186i	0.0560611	+	0.00749353i
$43$	−1000.05	−	1732.14i	−0.540862	−	0.936801i	−0.998855	−	0.0478447i	$-0.984765\pi$
$43$	−1000.05	−	1732.14i	−0.540862	−	0.936801i	0.457993	−	0.888956i	$-0.348569\pi$
$44$			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	−0.650538	−	0.759474i	$-0.725456\pi$
$47$	−702.646	+	405.673i	−0.318083	+	0.183645i	0.332455	+	0.943119i	$0.392123\pi$
$48$	−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	$-0.870628\pi$
$53$		−	2221.00i		−	0.790672i	0.918537	−	0.395336i	$-0.129372\pi$
$54$	−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	0.676176	−	0.736740i	$-0.263636\pi$
$59$	1309.65	+	756.128i	0.376229	+	0.217216i	−0.299947	+	0.953956i	$0.596969\pi$
$60$	3028.60	−	3930.81i	0.841278	−	1.09189i
$61$	951.281	+	1647.67i	0.255652	+	0.442802i	0.965072	−	0.261983i	$-0.0843765\pi$
$61$	951.281	+	1647.67i	0.255652	+	0.442802i	−0.709420	+	0.704786i	$0.751043\pi$
$62$			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	0.497982	+	0.867187i	$0.334075\pi$
$67$	−2253.55	+	3903.26i	−0.502015	+	0.869516i	−0.999997	+	0.00232883i	$0.999259\pi$
$68$	−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	$-0.870361\pi$
$71$		−	3993.54i		−	0.792213i	0.918205	−	0.396106i	$-0.129639\pi$
$72$	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	0.813815	−	0.581124i	$-0.197387\pi$
$79$	−601.388	−	1041.63i	−0.0963608	−	0.166902i	−0.910176	+	0.414222i	$0.864054\pi$
$80$			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	0.211456	−	0.977387i	$-0.432179\pi$
$83$	8016.22	−	4628.17i	1.16363	−	0.671820i	0.952170	+	0.305567i	$0.0988461\pi$
$84$	−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	$0.190619\pi$
$89$			8929.99i			1.12738i	−0.825986	+	0.563691i	$0.809381\pi$
$90$	−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	0.632563	−	0.774509i	$-0.282003\pi$
$97$	−3335.14	−	5776.64i	−0.354463	−	0.613948i	−0.987026	+	0.160561i	$0.948670\pi$
$98$		−	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	−0.835297	−	0.549799i	$-0.814704\pi$
$101$	−7924.19	+	4575.03i	−0.776805	+	0.448489i	0.0584918	+	0.998288i	$0.481371\pi$
$102$	979.940	+	755.021i	0.0941888	+	0.0725703i
$103$	−7656.20	+	13260.9i	−0.721670	+	1.24997i	0.238660	+	0.971103i	$0.423292\pi$
$103$	−7656.20	+	13260.9i	−0.721670	+	1.24997i	−0.960330	+	0.278866i	$0.910041\pi$
$104$	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	$-0.914177\pi$
$107$		−	6099.28i		−	0.532735i	0.963872	−	0.266367i	$-0.0858234\pi$
$108$	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	0.452714	−	0.891656i	$-0.350456\pi$
$113$	−1189.11	−	686.532i	−0.0931246	−	0.0537655i	−0.545839	+	0.837890i	$0.683789\pi$
$114$	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	0.421859	−	0.906661i	$-0.361378\pi$
$131$	−2615.39	−	1510.00i	−0.152403	−	0.0879902i	−0.574262	+	0.818671i	$0.694711\pi$
$132$	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	−0.715501	−	0.698612i	$-0.753801\pi$
$137$	−8788.30	+	5073.93i	−0.468235	+	0.270336i	0.247266	+	0.968948i	$0.420468\pi$
$138$	−1620.68	+	667.553i	−0.0851021	+	0.0350532i
$139$	17563.2	−	30420.3i	0.909021	−	1.57447i	0.0935938	−	0.995610i	$-0.470165\pi$
$139$	17563.2	−	30420.3i	0.909021	−	1.57447i	0.815427	−	0.578860i	$-0.196502\pi$
$140$	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	0.998923	−	0.0463890i	$-0.0147714\pi$
$149$	32373.7	+	18691.0i	1.45821	+	0.841899i	0.459288	+	0.888288i	$0.348105\pi$
$150$	1842.29	+	246.253i	0.0818795	+	0.0109446i
$151$	−16635.0	−	28812.7i	−0.729573	−	1.26366i	−0.957064	−	0.289878i	$-0.906385\pi$
$151$	−16635.0	−	28812.7i	−0.729573	−	1.26366i	0.227490	−	0.973780i	$-0.426948\pi$
$152$			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	−0.936267	−	0.351289i	$-0.885743\pi$
$157$	−4040.16	+	6997.77i	−0.163908	+	0.283897i	0.772359	+	0.635186i	$0.219077\pi$
$158$	−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	−0.155309	−	0.987866i	$-0.549637\pi$
$167$	−30356.6	−	17526.4i	−1.08848	−	0.628434i	−0.933171	+	0.359432i	$0.882971\pi$
$168$	−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	−0.272001	−	0.962297i	$-0.587685\pi$
$173$	12731.0	−	7350.23i	0.425372	−	0.245589i	0.697373	+	0.716708i	$0.254352\pi$
$174$	−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	$0.196247\pi$
$179$			37052.5i			1.15641i	−0.815892	+	0.578205i	$0.803753\pi$
$180$	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	0.377545	−	0.925991i	$-0.376768\pi$
$191$	49915.1	−	28818.5i	1.36825	−	0.789959i	0.990704	+	0.136032i	$0.0434352\pi$
$192$	32483.8	−	13379.9i	0.881178	−	0.362954i
$193$	−2089.81	+	3619.67i	−0.0561039	+	0.0971748i	−0.892713	−	0.450625i	$-0.851201\pi$
$193$	−2089.81	+	3619.67i	−0.0561039	+	0.0971748i	0.836609	+	0.547800i	$0.184534\pi$
$194$	−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	$0.0922945\pi$
$197$			22191.5i			0.571812i	−0.958258	+	0.285906i	$0.907705\pi$
$198$	−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	−0.811593	−	0.584223i	$-0.801399\pi$
$211$	4459.02	−	7723.26i	0.100156	−	0.173474i	0.911749	+	0.410749i	$0.134733\pi$
$212$	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	0.905578	−	0.424180i	$-0.139438\pi$
$223$	4248.76	+	7359.07i	0.0854384	+	0.147984i	−0.820140	+	0.572164i	$0.806104\pi$
$224$		−	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	−0.330809	−	0.943698i	$-0.607322\pi$
$227$	16543.5	−	9551.40i	0.321052	−	0.185360i	0.651862	+	0.758338i	$0.273988\pi$
$228$	−2191.68	+	16396.6i	−0.0421607	+	0.315416i
$229$	5361.51	−	9286.40i	0.102239	−	0.177083i	−0.810368	−	0.585921i	$-0.800733\pi$
$229$	5361.51	−	9286.40i	0.102239	−	0.177083i	0.912607	+	0.408839i	$0.134066\pi$
$230$	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	$-0.609647\pi$
$233$		−	102200.i		−	1.88251i	0.337694	−	0.941256i	$-0.390353\pi$
$234$	−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	0.613017	−	0.790070i	$-0.289956\pi$
$239$	13440.9	+	7760.09i	0.235305	+	0.135854i	−0.377712	+	0.925923i	$0.623289\pi$
$240$	29759.4	+	72249.8i	0.516656	+	1.25434i
$241$	35978.9	+	62317.3i	0.619461	+	1.07294i	0.989584	+	0.143955i	$0.0459820\pi$
$241$	35978.9	+	62317.3i	0.619461	+	1.07294i	−0.370123	+	0.928983i	$0.620685\pi$
$242$			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	$0.106800\pi$
$251$			41487.8i			0.658526i	−0.944238	+	0.329263i	$0.893200\pi$
$252$	−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	−0.0576045	−	0.998339i	$-0.518346\pi$
$257$	−62812.2	−	36264.6i	−0.950994	−	0.549057i	−0.893390	+	0.449283i	$0.851680\pi$
$258$	−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	−0.929647	−	0.368451i	$-0.879888\pi$
$263$	−74383.1	+	42945.1i	−1.07538	+	0.620872i	−0.145735	+	0.989324i	$0.546555\pi$
$264$	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	$-0.789258\pi$
$269$		−	88967.6i		−	1.22950i	0.788724	−	0.614748i	$-0.210742\pi$
$270$	−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	0.932478	−	0.361227i	$-0.117642\pi$
$277$	11770.8	+	20387.6i	0.153407	+	0.265710i	−0.779071	+	0.626936i	$0.784309\pi$
$278$		−	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	−0.784855	−	0.619679i	$-0.787263\pi$
$281$	−50584.4	+	29204.9i	−0.640626	+	0.369865i	0.144230	+	0.989544i	$0.453930\pi$
$282$	−343.625	+	2570.75i	−0.00432102	+	0.0323268i
$283$	38058.6	−	65919.5i	0.475204	−	0.823078i	−0.524393	−	0.851477i	$-0.675708\pi$
$283$	38058.6	−	65919.5i	0.475204	−	0.823078i	0.999597	+	0.0283989i	$0.00904087\pi$
$284$	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	0.995519	−	0.0945573i	$-0.0301436\pi$
$293$	121166.	+	69955.5i	1.41139	+	0.814866i	0.415871	+	0.909424i	$0.363477\pi$
$294$	−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	0.492358	−	0.870393i	$-0.336135\pi$
$311$	−1474.59	−	851.354i	−0.0152458	−	0.00880216i	−0.507604	+	0.861591i	$0.669469\pi$
$312$	7402.30	+	989.444i	0.0760427	+	0.0101644i
$313$	34980.1	+	60587.3i	0.357052	+	0.618433i	0.987467	−	0.157826i	$-0.0504484\pi$
$313$	34980.1	+	60587.3i	0.357052	+	0.618433i	−0.630415	+	0.776259i	$0.717115\pi$
$314$			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	0.0953639	−	0.995442i	$-0.469599\pi$
$317$	101004.	−	58314.7i	1.00512	−	0.580309i	0.909760	+	0.415134i	$0.136265\pi$
$318$	−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	0.538787	−	0.842442i	$-0.318883\pi$
$331$	−50418.1	−	87326.8i	−0.460183	−	0.797061i	−0.998970	+	0.0453817i	$0.985550\pi$
$332$			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	−0.940686	−	0.339277i	$-0.889817\pi$
$337$	−20047.2	+	34722.8i	−0.176520	+	0.305742i	0.764166	+	0.645020i	$0.223151\pi$
$338$	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	−0.984666	−	0.174451i	$-0.944185\pi$
$347$	−196035.	−	113181.i	−1.62808	−	0.939971i	−0.643412	−	0.765520i	$-0.722482\pi$
$348$	−42728.1	−	103735.i	−0.352821	−	0.856578i
$349$	−39799.1	−	68934.1i	−0.326755	−	0.565957i	0.655111	−	0.755533i	$-0.272622\pi$
$349$	−39799.1	−	68934.1i	−0.326755	−	0.565957i	−0.981866	+	0.189576i	$0.939289\pi$
$350$			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	−0.899975	−	0.435941i	$-0.856416\pi$
$353$	−121173.	+	69959.4i	−0.972427	+	0.561431i	−0.0724520	+	0.997372i	$0.523082\pi$
$354$	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	$-0.693430\pi$
$359$		−	211616.i		−	1.64195i	0.570963	−	0.820976i	$-0.306570\pi$
$360$	−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	0.919280	−	0.393604i	$-0.128772\pi$
$367$	15996.8	+	27707.3i	0.118769	+	0.205713i	−0.800511	+	0.599318i	$0.795439\pi$
$368$			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	−0.555312	−	0.831642i	$-0.687401\pi$
$373$	61573.9	−	106649.i	0.442567	−	0.766548i	0.997879	+	0.0650938i	$0.0207347\pi$
$374$	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	0.927978	−	0.372636i	$-0.121546\pi$
$383$	156848.	+	90556.2i	1.06925	+	0.617334i	0.141277	+	0.989970i	$0.454879\pi$
$384$	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	−0.638343	−	0.769752i	$-0.720380\pi$
$389$	−44017.9	+	25413.7i	−0.290891	+	0.167946i	0.347453	+	0.937697i	$0.387047\pi$
$390$	−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	0.913384	−	0.407099i	$-0.133459\pi$
$401$	163618.	+	94464.9i	1.01752	+	0.587465i	0.104134	+	0.994563i	$0.466793\pi$
$402$	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	0.0694256	+	0.997587i	$0.477883\pi$
$409$	−138713.	+	240258.i	−0.829223	+	1.43626i	−0.898649	+	0.438669i	$0.855450\pi$
$410$	−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	0.225637	−	0.974212i	$-0.427554\pi$
$419$	−88699.9	−	51210.9i	−0.505237	−	0.291699i	−0.730874	+	0.682513i	$0.760887\pi$
$420$	153510.	+	20519.3i	0.870239	+	0.116322i
$421$	−23567.9	−	40820.8i	−0.132971	−	0.230312i	0.791850	−	0.610716i	$-0.209118\pi$
$421$	−23567.9	−	40820.8i	−0.132971	−	0.230312i	−0.924821	+	0.380404i	$0.875785\pi$
$422$		−	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	$-0.960870\pi$
$431$		−	45556.1i		−	0.245240i	0.992454	−	0.122620i	$-0.0391297\pi$
$432$	−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	0.999639	−	0.0268637i	$-0.00855202\pi$
$439$	91842.1	+	159075.i	0.476555	+	0.825417i	−0.523084	+	0.852281i	$0.675219\pi$
$440$		−	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	−0.733509	−	0.679680i	$-0.762119\pi$
$443$	−100410.	+	57971.5i	−0.511644	+	0.295398i	0.221865	+	0.975077i	$0.428785\pi$
$444$	−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	$-0.696286\pi$
$449$		−	328940.i		−	1.63164i	0.578305	−	0.815820i	$-0.303714\pi$
$450$	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	0.999942	+	0.0107819i	$0.00343204\pi$
$457$	106369.	+	184236.i	0.509308	+	0.882148i	−0.490634	+	0.871366i	$0.663235\pi$
$458$		−	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	−0.595454	−	0.803389i	$-0.703028\pi$
$461$	−41957.2	+	24224.0i	−0.197426	+	0.113984i	0.398028	+	0.917373i	$0.369695\pi$
$462$	5325.84	−	2193.69i	0.0249519	−	0.0102776i
$463$	−84550.6	+	146446.i	−0.394416	+	0.683149i	−0.993026	−	0.117892i	$-0.962386\pi$
$463$	−84550.6	+	146446.i	−0.394416	+	0.683149i	0.598610	+	0.801040i	$0.295720\pi$
$464$	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	$0.0399844\pi$
$467$			54646.4i			0.250569i	−0.992121	+	0.125285i	$0.960016\pi$
$468$	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	−0.738186	−	0.674597i	$-0.764317\pi$
$479$	−120011.	+	69288.6i	−0.523060	+	0.301989i	0.215126	+	0.976586i	$0.430984\pi$
$480$	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	0.627524	−	0.778597i	$-0.284068\pi$
$491$	64368.8	+	37163.4i	0.267001	+	0.154153i	−0.360523	+	0.932750i	$0.617402\pi$
$492$	−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	−0.846349	−	0.532629i	$-0.821204\pi$
$499$	9486.01	−	16430.2i	0.0380963	−	0.0659847i	0.884445	+	0.466645i	$0.154537\pi$
$500$	−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	$0.0748245\pi$
$503$			117856.i			0.465818i	−0.972498	+	0.232909i	$0.925175\pi$
$504$	−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	0.774236	−	0.632897i	$-0.218134\pi$
$509$	158881.	+	91730.2i	0.613250	+	0.354060i	−0.160986	+	0.986957i	$0.551468\pi$
$510$	−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	$0.272025\pi$
$521$			409498.i			1.50861i	−0.656526	+	0.754303i	$0.727975\pi$
$522$	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	0.899612	−	0.436691i	$-0.143850\pi$
$547$	21429.6	+	37117.1i	0.0716207	+	0.124051i	−0.827991	+	0.560741i	$0.810516\pi$
$548$		−	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	$0.167116\pi$
$557$			311007.i			1.00244i	−0.865319	+	0.501222i	$0.832884\pi$
$558$	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	0.0559288	−	0.998435i	$-0.482188\pi$
$563$	−247482.	−	142884.i	−0.780777	−	0.450782i	−0.836705	+	0.547653i	$0.815521\pi$
$564$	−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	−0.671539	−	0.740969i	$-0.734367\pi$
$569$	−118371.	+	68341.3i	−0.365611	+	0.211086i	0.305928	+	0.952055i	$0.401033\pi$
$570$	−11887.7	+	4896.49i	−0.0365888	+	0.0150708i
$571$	14255.0	−	24690.4i	0.0437215	−	0.0757279i	−0.843337	−	0.537386i	$-0.819412\pi$
$571$	14255.0	−	24690.4i	0.0437215	−	0.0757279i	0.887058	+	0.461658i	$0.152745\pi$
$572$	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	0.0709687	−	0.997479i	$-0.477391\pi$
$587$	334334.	−	193028.i	0.970295	−	0.560200i	0.899326	+	0.437279i	$0.144058\pi$
$588$	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	$-0.856926\pi$
$593$		−	305581.i		−	0.868995i	0.900673	−	0.434497i	$-0.143074\pi$
$594$	−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	0.784225	−	0.620477i	$-0.213061\pi$
$599$	229270.	+	132369.i	0.638988	+	0.368920i	−0.145236	+	0.989397i	$0.546394\pi$
$600$	−36157.9	+	46929.2i	−0.100439	+	0.130359i
$601$	66101.5	+	114491.i	0.183005	+	0.316973i	0.942902	−	0.333069i	$-0.108084\pi$
$601$	66101.5	+	114491.i	0.183005	+	0.316973i	−0.759898	+	0.650043i	$0.774751\pi$
$602$		−	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	−0.640447	−	0.768002i	$-0.721251\pi$
$607$	127073.	−	220097.i	0.344886	−	0.597360i	0.985333	+	0.170642i	$0.0545843\pi$
$608$	−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	0.355670	−	0.934612i	$-0.384253\pi$
$617$	−105029.	−	60638.8i	−0.275893	−	0.159287i	−0.631563	+	0.775325i	$0.717586\pi$
$618$	18642.4	+	45259.9i	0.0488118	+	0.118505i
$619$	−153682.	−	266185.i	−0.401090	−	0.694709i	0.592768	−	0.805374i	$-0.298035\pi$
$619$	−153682.	−	266185.i	−0.401090	−	0.694709i	−0.993858	+	0.110665i	$0.964702\pi$
$620$			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	−0.0619737	−	0.998078i	$-0.519739\pi$
$641$	316954.	−	182993.i	0.771400	−	0.445368i	0.833374	+	0.552710i	$0.186406\pi$
$642$	−15444.9	−	11899.9i	−0.0374726	−	0.0288718i
$643$	−115391.	+	199864.i	−0.279094	+	0.483406i	−0.971160	−	0.238429i	$-0.923368\pi$
$643$	−115391.	+	199864.i	−0.279094	+	0.483406i	0.692066	+	0.721835i	$0.256701\pi$
$644$	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	$-0.892019\pi$
$647$		−	278596.i		−	0.665529i	0.943010	−	0.332764i	$-0.107981\pi$
$648$	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	0.418154	−	0.908376i	$-0.362677\pi$
$653$	−67988.8	−	39253.4i	−0.159445	−	0.0920557i	−0.577600	+	0.816320i	$0.696010\pi$
$654$	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	−0.774418	+	0.632675i	$0.781957\pi$
$659$	−742420.	+	428637.i	−1.70954	+	0.987003i	−0.935121	+	0.354328i	$0.884710\pi$
$660$	37954.9	−	283951.i	0.0871324	−	0.651862i
$661$	−11172.0	+	19350.4i	−0.0255698	+	0.0442882i	−0.878527	−	0.477692i	$-0.841473\pi$
$661$	−11172.0	+	19350.4i	−0.0255698	+	0.0442882i	0.852957	+	0.521981i	$0.174807\pi$
$662$	−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	0.955842	+	0.293882i	$0.0949472\pi$
$673$	331739.	+	574588.i	0.732430	+	1.26861i	−0.223412	+	0.974724i	$0.571719\pi$
$674$			14241.1i			0.0313489i
$675$	420563.	−	52829.0i	0.923046	−	0.115948i
$676$	−368095.			−0.805501
$677$	−197558.	+	114060.i	−0.431040	+	0.248861i	−0.699790	−	0.714349i	$-0.746723\pi$
$677$	−197558.	+	114060.i	−0.431040	+	0.248861i	0.268749	+	0.963210i	$0.413390\pi$
$678$	−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	$-0.981701\pi$
$683$		−	53606.6i		−	0.114915i	0.998348	−	0.0574575i	$-0.0182994\pi$
$684$	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	−0.924074	−	0.382213i	$-0.875162\pi$
$691$	−378663.	−	655863.i	−0.793043	−	1.37359i	0.131031	−	0.991378i	$-0.458171\pi$
$692$			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	$-0.827710\pi$
$701$		−	506359.i		−	1.03044i	0.857058	−	0.515220i	$-0.172290\pi$
$702$	−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	0.983654	+	0.180067i	$0.0576314\pi$
$709$	325622.	+	563993.i	0.647770	+	1.12197i	−0.335885	+	0.941903i	$0.609035\pi$
$710$			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	$0.0214822\pi$
$719$			69724.6i			0.134874i	−0.997724	+	0.0674370i	$0.978518\pi$
$720$	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	0.965830	+	0.259175i	$0.0834506\pi$
$727$	373864.	+	647552.i	0.707367	+	1.22520i	−0.258463	+	0.966021i	$0.583216\pi$
$728$			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	−0.894991	−	0.446083i	$-0.852818\pi$
$733$	−32869.3	+	56931.2i	−0.0611761	+	0.105960i	0.833815	+	0.552044i	$0.186152\pi$
$734$	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	0.840673	−	0.541543i	$-0.182160\pi$
$743$	437233.	+	252437.i	0.792019	+	0.457272i	−0.0486539	+	0.998816i	$0.515493\pi$
$744$	−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	−0.527167	−	0.849762i	$-0.676746\pi$
$751$	266395.	−	461411.i	0.472332	−	0.818102i	0.999499	+	0.0316593i	$0.0100792\pi$
$752$	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	0.480667	−	0.876903i	$-0.340394\pi$
$761$	−22249.2	−	12845.6i	−0.0384190	−	0.0221812i	−0.519086	+	0.854722i	$0.673728\pi$
$762$	−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	−0.451302	−	0.892371i	$-0.649040\pi$
$769$	323572.	−	560443.i	0.547165	−	0.947717i	0.998467	−	0.0553463i	$-0.0176263\pi$
$770$	−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	$-0.829411\pi$
$773$		−	610238.i		−	1.02127i	0.859798	−	0.510634i	$-0.170589\pi$
$774$	−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	−0.530874	−	0.847451i	$-0.678136\pi$
$787$	290160.	−	502572.i	0.468477	−	0.811427i	0.999351	+	0.0360244i	$0.0114694\pi$
$788$	−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	−0.443336	−	0.896355i	$-0.646205\pi$
$797$	−915508.	−	528569.i	−1.44127	−	0.832118i	−0.997935	+	0.0642373i	$0.979539\pi$
$798$	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	$0.0876677\pi$
$809$			355969.i			0.543895i	−0.962312	+	0.271947i	$0.912332\pi$
$810$	−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	−0.763456	−	0.645860i	$-0.776499\pi$
$821$	−394889.	+	227989.i	−0.585854	+	0.338243i	0.177603	+	0.984102i	$0.443166\pi$
$822$	−4297.87	+	32153.6i	−0.00636077	+	0.0475867i
$823$	−251795.	+	436122.i	−0.371747	+	0.643885i	−0.989834	−	0.142225i	$-0.954574\pi$
$823$	−251795.	+	436122.i	−0.371747	+	0.643885i	0.618087	+	0.786109i	$0.287908\pi$
$824$	−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	$-0.867811\pi$
$827$		−	551861.i		−	0.806898i	0.915002	−	0.403449i	$-0.132189\pi$
$828$	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	−0.733413	−	0.679783i	$-0.762074\pi$
$839$	−359993.	+	207842.i	−0.511410	+	0.295263i	0.222003	+	0.975046i	$0.428741\pi$
$840$	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	0.809764	−	0.586756i	$-0.199595\pi$
$853$	−75135.3	−	130138.i	−0.103263	−	0.178857i	−0.913027	+	0.407898i	$0.866262\pi$
$854$			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	−0.412214	−	0.911087i	$-0.635245\pi$
$857$	125373.	−	72383.9i	0.170703	−	0.0985554i	0.582917	+	0.812532i	$0.301911\pi$
$858$	−10715.1	−	8255.72i	−0.0145553	−	0.0112145i
$859$	−166948.	+	289163.i	−0.226254	+	0.391883i	−0.956695	−	0.291093i	$-0.905981\pi$
$859$	−166948.	+	289163.i	−0.226254	+	0.391883i	0.730441	+	0.682976i	$0.239315\pi$
$860$	−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	$-0.724951\pi$
$863$		−	1.13280e6i		−	1.52101i	0.649330	−	0.760507i	$-0.275049\pi$
$864$	−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	−0.981064	−	0.193686i	$-0.937956\pi$
$877$	−248271.	+	430017.i	−0.322795	+	0.559097i	0.658269	+	0.752783i	$0.271289\pi$
$878$	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	$0.286267\pi$
$881$			1.21533e6i			1.56583i	−0.622131	+	0.782913i	$0.713733\pi$
$882$	−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	0.958823	−	0.284005i	$-0.0916632\pi$
$887$	938048.	+	541582.i	1.19228	+	0.688362i	0.233456	+	0.972367i	$0.424997\pi$
$888$	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	−0.934196	−	0.356760i	$-0.883882\pi$
$907$	−638426.	−	1.10579e6i	−0.776061	−	1.34418i	0.158135	−	0.987417i	$-0.449452\pi$
$908$			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	−0.350475	−	0.936572i	$-0.613980\pi$
$911$	236846.	−	136743.i	0.285383	−	0.164766i	0.635858	+	0.771806i	$0.280646\pi$
$912$	−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	−0.00690018	−	0.999976i	$-0.502196\pi$
$929$	738465.	−	426353.i	0.855655	−	0.494012i	0.862555	+	0.505964i	$0.168863\pi$
$930$	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	0.278534	−	0.960426i	$-0.410152\pi$
$941$	−366547.	−	211626.i	−0.413953	−	0.238996i	−0.692487	+	0.721431i	$0.743485\pi$
$942$	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	−0.987762	−	0.155967i	$-0.950151\pi$
$947$	−1.20762e6	+	697219.i	−1.34657	+	0.777444i	−0.358810	+	0.933411i	$0.616817\pi$
$948$	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	$-0.995794\pi$
$953$		−	24001.0i		−	0.0264267i	0.999913	−	0.0132134i	$-0.00420607\pi$
$954$	−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	0.439373	+	0.898305i	$0.355201\pi$
$967$	−522031.	+	904183.i	−0.558268	+	0.966949i	−0.997641	+	0.0686443i	$0.978133\pi$
$968$	−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	$0.104003\pi$
$971$			605213.i			0.641904i	−0.947096	+	0.320952i	$0.895997\pi$
$972$	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	0.521664	−	0.853151i	$-0.325312\pi$
$977$	41660.2	+	24052.5i	0.0436448	+	0.0251983i	−0.478019	+	0.878350i	$0.658645\pi$
$978$	−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	−0.554486	−	0.832193i	$-0.687085\pi$
$983$	−107286.	+	61941.5i	−0.111029	+	0.0641024i	0.443457	+	0.896295i	$0.353752\pi$
$984$	−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	0.915373	+	0.402607i	$0.131896\pi$
$997$	801524.	+	1.38828e6i	0.806355	+	1.39665i	−0.109018	+	0.994040i	$0.534771\pi$
$998$		−	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.5.2	yes	6
3.2	odd	2		27.5.d.a.17.2		6
4.3	odd	2		144.5.q.a.113.1		6
9.2	odd	6	inner	9.5.d.a.2.2	✓	6
9.4	even	3		81.5.b.a.80.4		6
9.5	odd	6		81.5.b.a.80.3		6
9.7	even	3		27.5.d.a.8.2		6
12.11	even	2		432.5.q.a.17.3		6
36.7	odd	6		432.5.q.a.305.3		6
36.11	even	6		144.5.q.a.65.1		6
36.23	even	6		1296.5.e.c.161.1		6
36.31	odd	6		1296.5.e.c.161.6		6

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
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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