LMFDB - Embedded newform 40.6.f.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(29,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("40.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.f (of order $2$, degree $1$, 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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	40.29
Dual form			40.6.f.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.53936 + 1.14695i) q^{2} -16.0077 q^{3} +(29.3690 - 12.7067i) q^{4} +(19.1184 - 52.5308i) q^{5} +(88.6724 - 18.3600i) q^{6} -20.5525i q^{7} +(-148.112 + 104.072i) q^{8} +13.2465 q^{9} +O(q^{10})$	\(q+(-5.53936 + 1.14695i) q^{2} -16.0077 q^{3} +(29.3690 - 12.7067i) q^{4} +(19.1184 - 52.5308i) q^{5} +(88.6724 - 18.3600i) q^{6} -20.5525i q^{7} +(-148.112 + 104.072i) q^{8} +13.2465 q^{9} +(-45.6540 + 312.915i) q^{10} +619.983i q^{11} +(-470.131 + 203.405i) q^{12} -101.664 q^{13} +(23.5726 + 113.848i) q^{14} +(-306.042 + 840.897i) q^{15} +(701.080 - 746.367i) q^{16} +527.303i q^{17} +(-73.3772 + 15.1930i) q^{18} +1703.28i q^{19} +(-106.003 - 1785.71i) q^{20} +328.998i q^{21} +(-711.087 - 3434.31i) q^{22} +1548.24i q^{23} +(2370.93 - 1665.95i) q^{24} +(-2393.97 - 2008.61i) q^{25} +(563.155 - 116.603i) q^{26} +3677.83 q^{27} +(-261.154 - 603.607i) q^{28} +4308.41i q^{29} +(730.815 - 5009.05i) q^{30} +201.464 q^{31} +(-3027.49 + 4938.49i) q^{32} -9924.50i q^{33} +(-604.788 - 2920.92i) q^{34} +(-1079.64 - 392.932i) q^{35} +(389.037 - 168.319i) q^{36} +12439.1 q^{37} +(-1953.57 - 9435.06i) q^{38} +1627.41 q^{39} +(2635.30 + 9770.12i) q^{40} -13917.3 q^{41} +(-377.343 - 1822.44i) q^{42} -16240.5 q^{43} +(7877.94 + 18208.3i) q^{44} +(253.253 - 695.850i) q^{45} +(-1775.75 - 8576.25i) q^{46} +29929.9i q^{47} +(-11222.7 + 11947.6i) q^{48} +16384.6 q^{49} +(15564.8 + 8380.69i) q^{50} -8440.91i q^{51} +(-2985.78 + 1291.82i) q^{52} -23517.7 q^{53} +(-20372.8 + 4218.27i) q^{54} +(32568.2 + 11853.1i) q^{55} +(2138.93 + 3044.06i) q^{56} -27265.5i q^{57} +(-4941.51 - 23865.8i) q^{58} -13712.4i q^{59} +(1696.86 + 28585.1i) q^{60} -30368.5i q^{61} +(-1115.98 + 231.068i) q^{62} -272.249i q^{63} +(11106.2 - 30828.5i) q^{64} +(-1943.66 + 5340.50i) q^{65} +(11382.9 + 54975.4i) q^{66} -7812.39 q^{67} +(6700.28 + 15486.4i) q^{68} -24783.7i q^{69} +(6431.18 + 938.303i) q^{70} +4047.41 q^{71} +(-1961.96 + 1378.59i) q^{72} -49410.9i q^{73} +(-68904.6 + 14267.0i) q^{74} +(38322.0 + 32153.3i) q^{75} +(21643.0 + 50023.6i) q^{76} +12742.2 q^{77} +(-9014.81 + 1866.55i) q^{78} -68775.3 q^{79} +(-25803.7 - 51097.7i) q^{80} -62092.4 q^{81} +(77092.7 - 15962.3i) q^{82} -7597.39 q^{83} +(4180.48 + 9662.35i) q^{84} +(27699.6 + 10081.2i) q^{85} +(89962.0 - 18627.0i) q^{86} -68967.7i q^{87} +(-64522.7 - 91826.8i) q^{88} +80012.0 q^{89} +(-604.756 + 4145.03i) q^{90} +2089.45i q^{91} +(19673.0 + 45470.3i) q^{92} -3224.97 q^{93} +(-34327.9 - 165792. i) q^{94} +(89474.5 + 32564.0i) q^{95} +(48463.2 - 79053.9i) q^{96} +135262. i q^{97} +(-90760.2 + 18792.2i) q^{98} +8212.61i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9}+O(q^{10}) $ 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9	$ 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9} - 16 q^{10} - 692 q^{14} - 488 q^{15} + 1560 q^{16} + 2732 q^{20} - 2224 q^{24} + 1556 q^{25} - 9976 q^{26} - 15012 q^{30} + 4368 q^{31} + 13016 q^{34} - 34116 q^{36} + 23360 q^{39} - 22496 q^{40} - 2480 q^{41} + 10712 q^{44} + 58372 q^{46} - 38420 q^{49} + 45624 q^{50} - 3568 q^{54} - 48776 q^{55} + 110944 q^{56} + 111688 q^{60} - 46944 q^{64} + 37200 q^{65} - 136120 q^{66} - 112852 q^{70} - 69232 q^{71} + 34176 q^{74} - 13944 q^{76} - 35984 q^{79} - 47064 q^{80} + 122596 q^{81} - 165688 q^{84} - 73676 q^{86} - 178744 q^{89} + 51496 q^{90} + 314740 q^{94} + 89416 q^{95} - 236176 q^{96}+O(q^{100}) $ 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9 - 16 * q^10 - 692 * q^14 - 488 * q^15 + 1560 * q^16 + 2732 * q^20 - 2224 * q^24 + 1556 * q^25 - 9976 * q^26 - 15012 * q^30 + 4368 * q^31 + 13016 * q^34 - 34116 * q^36 + 23360 * q^39 - 22496 * q^40 - 2480 * q^41 + 10712 * q^44 + 58372 * q^46 - 38420 * q^49 + 45624 * q^50 - 3568 * q^54 - 48776 * q^55 + 110944 * q^56 + 111688 * q^60 - 46944 * q^64 + 37200 * q^65 - 136120 * q^66 - 112852 * q^70 - 69232 * q^71 + 34176 * q^74 - 13944 * q^76 - 35984 * q^79 - 47064 * q^80 + 122596 * q^81 - 165688 * q^84 - 73676 * q^86 - 178744 * q^89 + 51496 * q^90 + 314740 * q^94 + 89416 * q^95 - 236176 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−5.53936	+	1.14695i	−0.979230	+	0.202753i
$2$	−5.53936	+	1.14695i	−0.979230	+	0.202753i
$3$	−16.0077			−1.02689			−0.513447	−	0.858121i	$-0.671632\pi$
$3$	−16.0077			−1.02689			−0.513447	+	0.858121i	$0.671632\pi$
$4$	29.3690	−	12.7067i	0.917782	−	0.397084i
$5$	19.1184	−	52.5308i	0.342001	−	0.939700i
$5$	19.1184	−	52.5308i	0.342001	−	0.939700i
$6$	88.6724	−	18.3600i	1.00557	−	0.208206i
$7$		−	20.5525i		−	0.158533i	−0.996853	−	0.0792664i	$-0.974742\pi$
$7$		−	20.5525i		−	0.158533i	0.996853	−	0.0792664i	$-0.0252578\pi$
$8$	−148.112	+	104.072i	−0.818210	+	0.574920i
$9$	13.2465			0.0545124
$10$	−45.6540	+	312.915i	−0.144371	+	0.989524i
$11$			619.983i			1.54489i	0.635080	+	0.772446i	$0.280967\pi$
$11$			619.983i			1.54489i	−0.635080	+	0.772446i	$0.719033\pi$
$12$	−470.131	+	203.405i	−0.942466	+	0.407764i
$13$	−101.664			−0.166844			−0.0834218	−	0.996514i	$-0.526585\pi$
$13$	−101.664			−0.166844			−0.0834218	+	0.996514i	$0.526585\pi$
$14$	23.5726	+	113.848i	0.0321431	+	0.155240i
$15$	−306.042	+	840.897i	−0.351199	+	0.964972i
$16$	701.080	−	746.367i	0.684648	−	0.728874i
$17$			527.303i			0.442525i	0.975214	+	0.221263i	$0.0710178\pi$
$17$			527.303i			0.442525i	−0.975214	+	0.221263i	$0.928982\pi$
$18$	−73.3772	+	15.1930i	−0.0533801	+	0.0110526i
$19$			1703.28i			1.08243i	0.840883	+	0.541216i	$0.182036\pi$
$19$			1703.28i			1.08243i	−0.840883	+	0.541216i	$0.817964\pi$
$20$	−106.003	−	1785.71i	−0.0592573	−	0.998243i
$21$			328.998i			0.162797i
$22$	−711.087	−	3434.31i	−0.313232	−	1.51280i
$23$			1548.24i			0.610265i	0.952310	+	0.305132i	$0.0987007\pi$
$23$			1548.24i			0.610265i	−0.952310	+	0.305132i	$0.901299\pi$
$24$	2370.93	−	1665.95i	0.840215	−	0.590382i
$25$	−2393.97	−	2008.61i	−0.766070	−	0.642757i
$26$	563.155	−	116.603i	0.163378	−	0.0338281i
$27$	3677.83			0.970916
$28$	−261.154	−	603.607i	−0.0629509	−	0.145499i
$29$			4308.41i			0.951310i	0.879632	+	0.475655i	$0.157789\pi$
$29$			4308.41i			0.951310i	−0.879632	+	0.475655i	$0.842211\pi$
$30$	730.815	−	5009.05i	0.148253	−	1.01614i
$31$	201.464			0.0376524			0.0188262	−	0.999823i	$-0.494007\pi$
$31$	201.464			0.0376524			0.0188262	+	0.999823i	$0.494007\pi$
$32$	−3027.49	+	4938.49i	−0.522647	+	0.852549i
$33$		−	9924.50i		−	1.58644i
$34$	−604.788	−	2920.92i	−0.0897234	−	0.433334i
$35$	−1079.64	−	392.932i	−0.148973	−	0.0542184i
$36$	389.037	−	168.319i	0.0500305	−	0.0216460i
$37$	12439.1			1.49377			0.746886	−	0.664952i	$-0.231548\pi$
$37$	12439.1			1.49377			0.746886	+	0.664952i	$0.231548\pi$
$38$	−1953.57	−	9435.06i	−0.219467	−	1.05995i
$39$	1627.41			0.171331
$40$	2635.30	+	9770.12i	0.260424	+	0.965494i
$41$	−13917.3			−1.29299			−0.646494	−	0.762919i	$-0.723765\pi$
$41$	−13917.3			−1.29299			−0.646494	+	0.762919i	$0.723765\pi$
$42$	−377.343	−	1822.44i	−0.0330075	−	0.159415i
$43$	−16240.5			−1.33946			−0.669728	−	0.742606i	$-0.733589\pi$
$43$	−16240.5			−1.33946			−0.669728	+	0.742606i	$0.733589\pi$
$44$	7877.94	+	18208.3i	0.613452	+	1.41787i
$45$	253.253	−	695.850i	0.0186433	−	0.0512253i
$46$	−1775.75	−	8576.25i	−0.123733	−	0.597589i
$47$			29929.9i			1.97633i	0.153385	+	0.988167i	$0.450983\pi$
$47$			29929.9i			1.97633i	−0.153385	+	0.988167i	$0.549017\pi$
$48$	−11222.7	+	11947.6i	−0.703062	+	0.748476i
$49$	16384.6			0.974867
$50$	15564.8	+	8380.69i	0.880480	+	0.474083i
$51$		−	8440.91i		−	0.454427i
$52$	−2985.78	+	1291.82i	−0.153126	+	0.0662510i
$53$	−23517.7			−1.15002			−0.575010	−	0.818147i	$-0.695002\pi$
$53$	−23517.7			−1.15002			−0.575010	+	0.818147i	$0.695002\pi$
$54$	−20372.8	+	4218.27i	−0.950750	+	0.196856i
$55$	32568.2	+	11853.1i	1.45173	+	0.528355i
$56$	2138.93	+	3044.06i	0.0911437	+	0.129713i
$57$		−	27265.5i		−	1.11154i
$58$	−4941.51	−	23865.8i	−0.192881	−	0.931551i
$59$		−	13712.4i		−	0.512843i	−0.966565	−	0.256422i	$-0.917456\pi$
$59$		−	13712.4i		−	0.512843i	0.966565	−	0.256422i	$-0.0825435\pi$
$60$	1696.86	+	28585.1i	0.0608510	+	1.02509i
$61$		−	30368.5i		−	1.04496i	−0.852653	−	0.522478i	$-0.825008\pi$
$61$		−	30368.5i		−	1.04496i	0.852653	−	0.522478i	$-0.174992\pi$
$62$	−1115.98	+	231.068i	−0.0368704	+	0.00763415i
$63$		−	272.249i		−	0.00864200i
$64$	11106.2	−	30828.5i	0.338934	−	0.940810i
$65$	−1943.66	+	5340.50i	−0.0570607	+	0.156783i
$66$	11382.9	+	54975.4i	0.321656	+	1.55349i
$67$	−7812.39			−0.212617			−0.106308	−	0.994333i	$-0.533903\pi$
$67$	−7812.39			−0.212617			−0.106308	+	0.994333i	$0.533903\pi$
$68$	6700.28	+	15486.4i	0.175720	+	0.406142i
$69$		−	24783.7i		−	0.626678i
$70$	6431.18	+	938.303i	0.156872	+	0.0228875i
$71$	4047.41			0.0952864			0.0476432	−	0.998864i	$-0.484829\pi$
$71$	4047.41			0.0952864			0.0476432	+	0.998864i	$0.484829\pi$
$72$	−1961.96	+	1378.59i	−0.0446025	+	0.0313403i
$73$		−	49410.9i		−	1.08521i	−0.839986	−	0.542607i	$-0.817437\pi$
$73$		−	49410.9i		−	1.08521i	0.839986	−	0.542607i	$-0.182563\pi$
$74$	−68904.6	+	14267.0i	−1.46275	+	0.302867i
$75$	38322.0	+	32153.3i	0.786674	+	0.660043i
$76$	21643.0	+	50023.6i	0.429817	+	0.993438i
$77$	12742.2			0.244916
$78$	−9014.81	+	1866.55i	−0.167772	+	0.0347379i
$79$	−68775.3			−1.23984			−0.619918	−	0.784666i	$-0.712834\pi$
$79$	−68775.3			−1.23984			−0.619918	+	0.784666i	$0.712834\pi$
$80$	−25803.7	−	51097.7i	−0.450772	−	0.892639i
$81$	−62092.4			−1.05154
$82$	77092.7	−	15962.3i	1.26613	−	0.262157i
$83$	−7597.39			−0.121051			−0.0605256	−	0.998167i	$-0.519278\pi$
$83$	−7597.39			−0.121051			−0.0605256	+	0.998167i	$0.519278\pi$
$84$	4180.48	+	9662.35i	0.0646439	+	0.149412i
$85$	27699.6	+	10081.2i	0.415841	+	0.151344i
$86$	89962.0	−	18627.0i	1.31164	−	0.271579i
$87$		−	68967.7i		−	0.976895i
$88$	−64522.7	−	91826.8i	−0.888189	−	1.26405i
$89$	80012.0			1.07073			0.535365	−	0.844621i	$-0.320174\pi$
$89$	80012.0			1.07073			0.535365	+	0.844621i	$0.320174\pi$
$90$	−604.756	+	4145.03i	−0.00786998	+	0.0539413i
$91$			2089.45i			0.0264502i
$92$	19673.0	+	45470.3i	0.242326	+	0.560090i
$93$	−3224.97			−0.0386651
$94$	−34327.9	−	165792.i	−0.400708	−	1.93528i
$95$	89474.5	+	32564.0i	1.01716	+	0.370193i
$96$	48463.2	−	79053.9i	0.536703	−	0.875478i
$97$			135262.i			1.45965i	0.683636	+	0.729823i	$0.260397\pi$
$97$			135262.i			1.45965i	−0.683636	+	0.729823i	$0.739603\pi$
$98$	−90760.2	+	18792.2i	−0.954619	+	0.197658i
$99$			8212.61i			0.0842157i
$100$	−95831.4	−	28571.6i	−0.958314	−	0.285716i
$101$			74276.1i			0.724512i	0.932079	+	0.362256i	$0.117993\pi$
$101$			74276.1i			0.724512i	−0.932079	+	0.362256i	$0.882007\pi$
$102$	9681.27	+	46757.2i	0.0921365	+	0.444988i
$103$		−	34987.0i		−	0.324948i	−0.986713	−	0.162474i	$-0.948053\pi$
$103$		−	34987.0i		−	0.324948i	0.986713	−	0.162474i	$-0.0519473\pi$
$104$	15057.7	−	10580.4i	0.136513	−	0.0959218i
$105$	17282.5	+	6289.93i	0.152980	+	0.0556766i
$106$	130273.	−	26973.5i	1.12613	−	0.233170i
$107$	−118429.			−0.999995			−0.499998	−	0.866027i	$-0.666666\pi$
$107$	−118429.			−0.999995			−0.499998	+	0.866027i	$0.666666\pi$
$108$	108014.	−	46733.0i	0.891089	−	0.385535i
$109$			188208.i			1.51730i	0.651500	+	0.758649i	$0.274140\pi$
$109$			188208.i			1.51730i	−0.651500	+	0.758649i	$0.725860\pi$
$110$	−194002.	−	28304.7i	−1.52871	−	0.223037i
$111$	−199121.			−1.53395
$112$	−15339.7	−	14408.9i	−0.115550	−	0.108539i
$113$			219409.i			1.61644i	0.588884	+	0.808218i	$0.299567\pi$
$113$			219409.i			1.61644i	−0.588884	+	0.808218i	$0.700433\pi$
$114$	31272.1	+	151034.i	0.225369	+	1.08846i
$115$	81330.2	+	29599.9i	0.573465	+	0.208711i
$116$	54745.7	+	126534.i	0.377750	+	0.873095i
$117$	−1346.70			−0.00909505
$118$	15727.4	+	75958.1i	0.103981	+	0.502191i
$119$	10837.4			0.0701548
$120$	−42185.1	−	156397.i	−0.267427	−	0.991461i
$121$	−223328.			−1.38669
$122$	34831.0	+	168222.i	0.211868	+	1.02325i
$123$	222783.			1.32776
$124$	5916.80	−	2559.94i	0.0345567	−	0.0149512i
$125$	−151283.	+	87355.6i	−0.865995	+	0.500053i
$126$	312.254	+	1508.08i	0.00175219	+	0.00846251i
$127$		−	178729.i		−	0.983301i	−0.870793	−	0.491650i	$-0.836394\pi$
$127$		−	178729.i		−	0.983301i	0.870793	−	0.491650i	$-0.163606\pi$
$128$	−26162.6	+	183508.i	−0.141142	+	0.989989i
$129$	259973.			1.37548
$130$	4641.38	−	31812.2i	0.0240873	−	0.165096i
$131$		−	182659.i		−	0.929957i	−0.885322	−	0.464979i	$-0.846062\pi$
$131$		−	182659.i		−	0.929957i	0.885322	−	0.464979i	$-0.153938\pi$
$132$	−126108.	−	291473.i	−0.629951	−	1.45601i
$133$	35006.6			0.171601
$134$	43275.7	−	8960.39i	0.208201	−	0.0431087i
$135$	70314.3	−	193199.i	0.332054	−	0.912369i
$136$	−54877.3	−	78099.8i	−0.254417	−	0.362078i
$137$		−	107724.i		−	0.490357i	−0.969478	−	0.245178i	$-0.921153\pi$
$137$		−	107724.i		−	0.490357i	0.969478	−	0.245178i	$-0.0788465\pi$
$138$	28425.6	+	137286.i	0.127061	+	0.613661i
$139$			174364.i			0.765455i	0.923861	+	0.382727i	$0.125015\pi$
$139$			174364.i			0.765455i	−0.923861	+	0.382727i	$0.874985\pi$
$140$	−36700.8	+	2178.62i	−0.158254	+	0.00939422i
$141$		−	479108.i		−	2.02949i
$142$	−22420.0	+	4642.16i	−0.0933073	+	0.0193196i
$143$		−	63030.1i		−	0.257755i
$144$	9286.86	−	9886.75i	0.0373218	−	0.0397326i
$145$	226324.	+	82370.1i	0.893946	+	0.325349i
$146$	56671.6	+	273705.i	0.220031	+	1.06267i
$147$	−262280.			−1.00109
$148$	365324.	−	158060.i	1.37096	−	0.593153i
$149$		−	208118.i		−	0.767971i	−0.923339	−	0.383986i	$-0.874551\pi$
$149$		−	208118.i		−	0.767971i	0.923339	−	0.383986i	$-0.125449\pi$
$150$	−249157.	−	134156.i	−0.904160	−	0.486833i
$151$	−309204.			−1.10358			−0.551788	−	0.833985i	$-0.686054\pi$
$151$	−309204.			−1.10358			−0.551788	+	0.833985i	$0.686054\pi$
$152$	−177263.	−	252275.i	−0.622312	−	0.885657i
$153$			6984.92i			0.0241231i
$154$	−70583.6	+	14614.6i	−0.239829	+	0.0496576i
$155$	3851.68	−	10583.1i	0.0128772	−	0.0353820i
$156$	47795.5	−	20679.0i	0.157244	−	0.0680328i
$157$	432444.			1.40017			0.700085	−	0.714059i	$-0.253145\pi$
$157$	432444.			1.40017			0.700085	+	0.714059i	$0.253145\pi$
$158$	380971.	−	78881.5i	1.21409	−	0.251381i
$159$	376464.			1.18095
$160$	201542.	+	253453.i	0.622395	+	0.782704i
$161$	31820.1			0.0967470
$162$	343952.	−	71216.7i	1.02970	−	0.213203i
$163$	131967.			0.389043			0.194521	−	0.980898i	$-0.437685\pi$
$163$	131967.			0.389043			0.194521	+	0.980898i	$0.437685\pi$
$164$	−408737.	+	176842.i	−1.18668	+	0.513425i
$165$	−521342.	−	189741.i	−1.49078	−	0.542565i
$166$	42084.7	−	8713.79i	0.118537	−	0.0245435i
$167$			193263.i			0.536237i	0.963386	+	0.268118i	$0.0864018\pi$
$167$			193263.i			0.536237i	−0.963386	+	0.268118i	$0.913598\pi$
$168$	−34239.4	−	48728.5i	−0.0935950	−	0.133202i
$169$	−360957.			−0.972163
$170$	−165001.	−	24073.5i	−0.437889	−	0.0638876i
$171$			22562.5i			0.0590060i
$172$	−476968.	+	206363.i	−1.22933	+	0.531877i
$173$	−209492.			−0.532172			−0.266086	−	0.963949i	$-0.585731\pi$
$173$	−209492.			−0.532172			−0.266086	+	0.963949i	$0.585731\pi$
$174$	79102.3	+	382037.i	0.198069	+	0.956605i
$175$	−41282.0	+	49202.0i	−0.101898	+	0.121447i
$176$	462735.	+	434658.i	1.12603	+	1.05771i
$177$			219505.i			0.526636i
$178$	−443215.	+	91769.4i	−1.04849	+	0.217094i
$179$		−	437147.i		−	1.01975i	−0.860248	−	0.509876i	$-0.829691\pi$
$179$		−	437147.i		−	1.01975i	0.860248	−	0.509876i	$-0.170309\pi$
$180$	−1404.16	−	23654.4i	−0.00323025	−	0.0544166i
$181$			559164.i			1.26865i	0.773066	+	0.634326i	$0.218722\pi$
$181$			559164.i			1.26865i	−0.773066	+	0.634326i	$0.781278\pi$
$182$	−2396.49	−	11574.2i	−0.00536287	−	0.0259008i
$183$			486129.i			1.07306i
$184$	−161128.	−	229312.i	−0.350853	−	0.499324i
$185$	237816.	−	653435.i	0.510872	−	1.40370i
$186$	17864.3	−	3698.87i	0.0378620	−	0.00783947i
$187$	−326919.			−0.683653
$188$	380310.	+	879011.i	0.784771	+	1.81384i
$189$		−	75588.4i		−	0.153922i
$190$	−532980.	−	77761.3i	−1.07109	−	0.156271i
$191$	330553.			0.655627			0.327814	−	0.944742i	$-0.393688\pi$
$191$	330553.			0.655627			0.327814	+	0.944742i	$0.393688\pi$
$192$	−177784.	+	493493.i	−0.348049	+	0.966113i
$193$		−	407436.i		−	0.787347i	−0.919250	−	0.393673i	$-0.871204\pi$
$193$		−	407436.i		−	0.787347i	0.919250	−	0.393673i	$-0.128796\pi$
$194$	−155139.	−	749267.i	−0.295948	−	1.42933i
$195$	31113.6	−	85489.2i	0.0585954	−	0.161000i
$196$	481200.	−	208194.i	0.894716	−	0.387104i
$197$	843885.			1.54924			0.774618	−	0.632429i	$-0.217942\pi$
$197$	843885.			1.54924			0.774618	+	0.632429i	$0.217942\pi$
$198$	−9419.42	−	45492.6i	−0.0170750	−	0.0824666i
$199$	245445.			0.439362			0.219681	−	0.975572i	$-0.429498\pi$
$199$	245445.			0.439362			0.219681	+	0.975572i	$0.429498\pi$
$200$	563615.	+	48355.0i	0.996340	+	0.0854804i
$201$	125058.			0.218335
$202$	−85190.7	−	411442.i	−0.146897	−	0.709464i
$203$	88548.5			0.150814
$204$	−107256.	−	247901.i	−0.180446	−	0.417065i
$205$	−266076.	+	731085.i	−0.442203	+	1.21502i
$206$	40128.2	+	193806.i	0.0658842	+	0.318199i
$207$			20508.8i			0.0332670i
$208$	−71274.7	+	75878.8i	−0.114229	+	0.121608i
$209$	−1.05600e6			−1.67224
$210$	−102948.	−	15020.1i	−0.161091	−	0.0235030i
$211$		−	73311.6i		−	0.113362i	−0.998392	−	0.0566809i	$-0.981948\pi$
$211$		−	73311.6i		−	0.113362i	0.998392	−	0.0566809i	$-0.0180518\pi$
$212$	−690692.	+	298832.i	−1.05547	+	0.456654i
$213$	−64789.7			−0.0978491
$214$	656020.	−	135831.i	0.979225	−	0.202752i
$215$	−310493.	+	853127.i	−0.458096	+	1.25869i
$216$	−544729.	+	382757.i	−0.794413	+	0.558199i
$217$		−	4140.58i		−	0.00596915i
$218$	−215864.	−	1.04255e6i	−0.307637	−	1.48578i
$219$			790955.i			1.11440i
$220$	1.10711e6	−	65719.8i	1.54218	−	0.0915461i
$221$		−	53607.9i		−	0.0738325i
$222$	1.10300e6	−	228381.i	1.50209	−	0.311013i
$223$			382998.i			0.515744i	0.966179	+	0.257872i	$0.0830212\pi$
$223$			382998.i			0.515744i	−0.966179	+	0.257872i	$0.916979\pi$
$224$	101498.	+	62222.5i	0.135157	+	0.0828566i
$225$	−31711.7	−	26607.1i	−0.0417603	−	0.0350382i
$226$	−251650.	−	1.21539e6i	−0.327738	−	1.58286i
$227$	−1.13601e6			−1.46324			−0.731622	−	0.681711i	$-0.761236\pi$
$227$	−1.13601e6			−1.46324			−0.731622	+	0.681711i	$0.761236\pi$
$228$	−346455.	−	800762.i	−0.441377	−	1.02016i
$229$			151374.i			0.190749i	0.995441	+	0.0953743i	$0.0304048\pi$
$229$			151374.i			0.190749i	−0.995441	+	0.0953743i	$0.969595\pi$
$230$	−484467.	−	70683.2i	−0.603871	−	0.0881042i
$231$	−203973.			−0.251503
$232$	−448383.	−	638126.i	−0.546927	−	0.778371i
$233$		−	684836.i		−	0.826412i	−0.910638	−	0.413206i	$-0.864409\pi$
$233$		−	684836.i		−	0.826412i	0.910638	−	0.413206i	$-0.135591\pi$
$234$	7459.83	−	1544.59i	0.00890614	−	0.00184405i
$235$	1.57224e6	+	572213.i	1.85716	+	0.675908i
$236$	−174240.	−	402721.i	−0.203642	−	0.470678i
$237$	1.10093e6			1.27318
$238$	−60032.2	+	12429.9i	−0.0686976	+	0.0142241i
$239$	136612.			0.154701			0.0773505	−	0.997004i	$-0.475354\pi$
$239$	136612.			0.154701			0.0773505	+	0.997004i	$0.475354\pi$
$240$	413058.	+	817956.i	0.462895	+	0.916646i
$241$	8903.12			0.00987415			0.00493707	−	0.999988i	$-0.498428\pi$
$241$	8903.12			0.00987415			0.00493707	+	0.999988i	$0.498428\pi$
$242$	1.23709e6	−	256145.i	1.35789	−	0.281156i
$243$	100246.			0.108905
$244$	−385883.	−	891892.i	−0.414936	−	0.959042i
$245$	313248.	−	860696.i	0.333406	−	0.916082i
$246$	−1.23408e6	+	255520.i	−1.30018	+	0.269208i
$247$		−	173162.i		−	0.180597i
$248$	−29839.2	+	20966.7i	−0.0308076	+	0.0216471i
$249$	121617.			0.124307
$250$	737820.	−	657408.i	0.746621	−	0.665250i
$251$			1.22945e6i			1.23176i	0.787840	+	0.615880i	$0.211200\pi$
$251$			1.22945e6i			1.23176i	−0.787840	+	0.615880i	$0.788800\pi$
$252$	−3459.38	−	7995.68i	−0.00343160	−	0.00793147i
$253$	−959882.			−0.942793
$254$	204993.	+	990046.i	0.199368	+	0.962878i
$255$	−443408.	−	161377.i	−0.427024	−	0.155414i
$256$	−65550.1	−	1.04653e6i	−0.0625134	−	0.998044i
$257$		−	916382.i		−	0.865453i	−0.901525	−	0.432727i	$-0.857552\pi$
$257$		−	916382.i		−	0.865453i	0.901525	−	0.432727i	$-0.142448\pi$
$258$	−1.44009e6	+	298175.i	−1.34691	+	0.278883i
$259$		−	255654.i		−	0.236812i
$260$	10776.7	+	181543.i	0.00988670	+	0.166551i
$261$			57071.4i			0.0518582i
$262$	209500.	+	1.01181e6i	0.188552	+	0.910642i
$263$		−	820999.i		−	0.731903i	−0.930634	−	0.365951i	$-0.880744\pi$
$263$		−	820999.i		−	0.731903i	0.930634	−	0.365951i	$-0.119256\pi$
$264$	1.03286e6	+	1.46994e6i	0.912077	+	1.29804i
$265$	−449622.	+	1.23540e6i	−0.393308	+	1.08067i
$266$	−193914.	+	40150.6i	−0.168037	+	0.0347927i
$267$	−1.28081e6			−1.09953
$268$	−229442.	+	99269.7i	−0.195136	+	0.0844267i
$269$		−	475703.i		−	0.400825i	−0.979712	−	0.200413i	$-0.935772\pi$
$269$		−	475703.i		−	0.400825i	0.979712	−	0.200413i	$-0.0642283\pi$
$270$	−167907.	+	1.15085e6i	−0.140172	+	0.960744i
$271$	566034.			0.468187			0.234093	−	0.972214i	$-0.424788\pi$
$271$	566034.			0.468187			0.234093	+	0.972214i	$0.424788\pi$
$272$	393561.	+	369681.i	0.322545	+	0.302974i
$273$		−	33447.3i		−	0.0271616i
$274$	123554.	+	596724.i	0.0994215	+	0.480172i
$275$	1.24531e6	−	1.48422e6i	0.992990	−	1.18350i
$276$	−314919.	−	727874.i	−0.248844	−	0.575153i
$277$	−124729.			−0.0976713			−0.0488357	−	0.998807i	$-0.515551\pi$
$277$	−124729.			−0.0976713			−0.0488357	+	0.998807i	$0.515551\pi$
$278$	−199986.	−	965865.i	−0.155199	−	0.749556i
$279$	2668.69			0.00205252
$280$	200800.	−	54162.0i	0.153063	−	0.0412857i
$281$	1.46925e6			1.11002			0.555010	−	0.831844i	$-0.312714\pi$
$281$	1.46925e6			1.11002			0.555010	+	0.831844i	$0.312714\pi$
$282$	549511.	+	2.65395e6i	0.411485	+	1.98733i
$283$	554357.			0.411456			0.205728	−	0.978609i	$-0.434044\pi$
$283$	554357.			0.411456			0.205728	+	0.978609i	$0.434044\pi$
$284$	118868.	−	51429.1i	0.0874522	−	0.0378367i
$285$	−1.43228e6	−	521275.i	−1.04452	−	0.380149i
$286$	72292.1	+	349146.i	0.0522608	+	0.252402i
$287$			286034.i			0.204981i
$288$	−40103.7	+	65417.8i	−0.0284907	+	0.0464745i
$289$	1.14181e6			0.804172
$290$	−1.34817e6	−	196696.i	−0.941344	−	0.137341i
$291$		−	2.16524e6i		−	1.49890i
$292$	−627849.	−	1.45115e6i	−0.430922	−	0.995991i
$293$	−1.42856e6			−0.972144			−0.486072	−	0.873919i	$-0.661571\pi$
$293$	−1.42856e6			−0.972144			−0.486072	+	0.873919i	$0.661571\pi$
$294$	1.45286e6	−	300821.i	0.980293	−	0.202973i
$295$	−720325.	−	262160.i	−0.481918	−	0.175393i
$296$	−1.84238e6	+	1.29456e6i	−1.22222	+	0.858800i
$297$			2.28019e6i			1.49996i
$298$	238701.	+	1.15284e6i	0.155709	+	0.752020i
$299$		−	157400.i		−	0.101819i
$300$	1.53404e6	+	457366.i	0.984088	+	0.293400i
$301$			333783.i			0.212348i
$302$	1.71279e6	−	354640.i	1.08065	−	0.223754i
$303$		−	1.18899e6i		−	0.743997i
$304$	1.27127e6	+	1.19413e6i	0.788957	+	0.741086i
$305$	−1.59528e6	−	580598.i	−0.981945	−	0.357376i
$306$	−8011.33	−	38692.0i	−0.00489104	−	0.0236221i
$307$	−1.98189e6			−1.20015			−0.600073	−	0.799945i	$-0.704862\pi$
$307$	−1.98189e6			−1.20015			−0.600073	+	0.799945i	$0.704862\pi$
$308$	374226.	−	161911.i	0.224780	−	0.0972523i
$309$			560061.i			0.333687i
$310$	−9197.63	+	63041.0i	−0.00543590	+	0.0372580i
$311$	3.02125e6			1.77127			0.885635	−	0.464381i	$-0.153723\pi$
$311$	3.02125e6			1.77127			0.885635	+	0.464381i	$0.153723\pi$
$312$	−241039.	+	169367.i	−0.140185	+	0.0985016i
$313$			2.57822e6i			1.48751i	0.668455	+	0.743753i	$0.266956\pi$
$313$			2.57822e6i			1.48751i	−0.668455	+	0.743753i	$0.733044\pi$
$314$	−2.39546e6	+	495990.i	−1.37109	+	0.283889i
$315$	−14301.4	−	5204.97i	−0.00812088	−	0.00295557i
$316$	−2.01986e6	+	873906.i	−1.13790	+	0.492320i
$317$	2.64595e6			1.47888			0.739442	−	0.673220i	$-0.235089\pi$
$317$	2.64595e6			1.47888			0.739442	+	0.673220i	$0.235089\pi$
$318$	−2.08537e6	+	431784.i	−1.15642	+	0.239441i
$319$	−2.67114e6			−1.46967
$320$	−1.40711e6	−	1.17281e6i	−0.768163	−	0.640254i
$321$	1.89577e6			1.02689
$322$	−176263.	+	36496.0i	−0.0947376	+	0.0196158i
$323$	−898142.			−0.479004
$324$	−1.82359e6	+	788990.i	−0.965085	+	0.417550i
$325$	243381.	+	204204.i	0.127814	+	0.107240i
$326$	−731015.	+	151359.i	−0.380962	+	0.0788797i
$327$		−	3.01277e6i		−	1.55810i
$328$	2.06131e6	−	1.44839e6i	1.05793	−	0.743364i
$329$	615133.			0.313314
$330$	3.10552e6	+	453093.i	1.56982	+	0.229035i
$331$			2.90430e6i			1.45704i	0.685026	+	0.728519i	$0.259791\pi$
$331$			2.90430e6i			1.45704i	−0.685026	+	0.728519i	$0.740209\pi$
$332$	−223128.	+	96537.7i	−0.111099	+	0.0480675i
$333$	164775.			0.0814291
$334$	−221662.	−	1.07055e6i	−0.108724	−	0.525099i
$335$	−149361.	+	410391.i	−0.0727151	+	0.199796i
$336$	245553.	+	230654.i	0.118658	+	0.111458i
$337$			1.76207e6i			0.845177i	0.906322	+	0.422588i	$0.138878\pi$
$337$			1.76207e6i			0.845177i	−0.906322	+	0.422588i	$0.861122\pi$
$338$	1.99947e6	−	413999.i	0.951971	−	0.197109i
$339$		−	3.51223e6i		−	1.65991i
$340$	941611.	−	55895.5i	0.441747	−	0.0262228i
$341$			124904.i			0.0581689i
$342$	−25877.9	−	124982.i	−0.0119637	−	0.0577804i
$343$		−	682170.i		−	0.313081i
$344$	2.40541e6	−	1.69018e6i	1.09596	−	0.770080i
$345$	−1.30191e6	−	473827.i	−0.588889	−	0.214324i
$346$	1.16045e6	−	240276.i	0.521119	−	0.107900i
$347$	1.83299e6			0.817214			0.408607	−	0.912710i	$-0.366015\pi$
$347$	1.83299e6			0.817214			0.408607	+	0.912710i	$0.366015\pi$
$348$	−876352.	−	2.02552e6i	−0.387910	−	0.896577i
$349$		−	145377.i		−	0.0638900i	−0.999490	−	0.0319450i	$-0.989830\pi$
$349$		−	145377.i		−	0.0638900i	0.999490	−	0.0319450i	$-0.0101701\pi$
$350$	172244.	−	319896.i	0.0751577	−	0.139585i
$351$	−373903.			−0.161991
$352$	−3.06178e6	−	1.87699e6i	−1.31710	−	0.807432i
$353$		−	2.82178e6i		−	1.20528i	−0.798015	−	0.602638i	$-0.794116\pi$
$353$		−	2.82178e6i		−	1.20528i	0.798015	−	0.602638i	$-0.205884\pi$
$354$	−251760.	−	1.21591e6i	−0.106777	−	0.515697i
$355$	77380.1	−	212613.i	0.0325881	−	0.0895406i
$356$	2.34987e6	−	1.01669e6i	0.982697	−	0.425170i
$357$	−173482.			−0.0720415
$358$	501384.	+	2.42151e6i	0.206758	+	0.998572i
$359$	−2.95218e6			−1.20894			−0.604472	−	0.796626i	$-0.706616\pi$
$359$	−2.95218e6			−1.20894			−0.604472	+	0.796626i	$0.706616\pi$
$360$	34908.5	+	129420.i	0.0141963	+	0.0526314i
$361$	−425050.			−0.171661
$362$	−641330.	−	3.09741e6i	−0.257223	−	1.24230i
$363$	3.57497e6			1.42399
$364$	26550.0	+	61365.2i	0.0105030	+	0.0242755i
$365$	−2.59559e6	−	944660.i	−1.01978	−	0.371145i
$366$	−557564.	−	2.69285e6i	−0.217566	−	1.05077i
$367$		−	2.33961e6i		−	0.906731i	−0.891325	−	0.453366i	$-0.850223\pi$
$367$		−	2.33961e6i		−	0.906731i	0.891325	−	0.453366i	$-0.149777\pi$
$368$	1.15555e6	+	1.08544e6i	0.444806	+	0.417817i
$369$	−184355.			−0.0704838
$370$	−567894.	+	3.89238e6i	−0.215657	+	1.47812i
$371$			483347.i			0.182316i
$372$	−94714.4	+	40978.8i	−0.0354861	+	0.0153533i
$373$	1.56241e6			0.581463			0.290731	−	0.956805i	$-0.406101\pi$
$373$	1.56241e6			0.581463			0.290731	+	0.956805i	$0.406101\pi$
$374$	1.81092e6	−	374958.i	0.669454	−	0.138613i
$375$	2.42169e6	−	1.39836e6i	0.889286	−	0.513501i
$376$	−3.11485e6	−	4.43297e6i	−1.13623	−	1.61705i
$377$		−	438011.i		−	0.158720i
$378$	86695.9	+	418712.i	0.0312082	+	0.150725i
$379$			4.69434e6i			1.67871i	0.543580	+	0.839357i	$0.317068\pi$
$379$			4.69434e6i			1.67871i	−0.543580	+	0.839357i	$0.682932\pi$
$380$	3.04156e6	−	180552.i	1.08053	−	0.0641420i
$381$			2.86105e6i			1.00975i
$382$	−1.83105e6	+	379126.i	−0.642010	+	0.132931i
$383$			4.36467e6i			1.52039i	0.649696	+	0.760194i	$0.274896\pi$
$383$			4.36467e6i			1.52039i	−0.649696	+	0.760194i	$0.725104\pi$
$384$	418803.	−	2.93754e6i	0.144938	−	1.01661i
$385$	243611.	−	669358.i	0.0837616	−	0.230148i
$386$	467307.	+	2.25693e6i	0.159637	+	0.770993i
$387$	−215130.			−0.0730169
$388$	1.71874e6	+	3.97252e6i	0.579602	+	1.33964i
$389$		−	455452.i		−	0.152605i	−0.997085	−	0.0763024i	$-0.975689\pi$
$389$		−	455452.i		−	0.152605i	0.997085	−	0.0763024i	$-0.0243114\pi$
$390$	−74297.8	+	509241.i	−0.0247351	+	0.169536i
$391$	−816391.			−0.270057
$392$	−2.42675e6	+	1.70517e6i	−0.797646	+	0.560471i
$393$			2.92395e6i			0.954968i
$394$	−4.67458e6	+	967891.i	−1.51706	+	0.314113i
$395$	−1.31488e6	+	3.61282e6i	−0.424026	+	1.16507i
$396$	104355.	+	241196.i	0.0334407	+	0.0772917i
$397$	1.41260e6			0.449824			0.224912	−	0.974379i	$-0.427790\pi$
$397$	1.41260e6			0.449824			0.224912	+	0.974379i	$0.427790\pi$
$398$	−1.35961e6	+	281512.i	−0.430236	+	0.0890820i
$399$	−560374.			−0.176216
$400$	−3.17753e6	+	378580.i	−0.992977	+	0.118306i
$401$	−3.45600e6			−1.07328			−0.536640	−	0.843811i	$-0.680307\pi$
$401$	−3.45600e6			−1.07328			−0.536640	+	0.843811i	$0.680307\pi$
$402$	−692744.	+	143435.i	−0.213800	+	0.0442681i
$403$	−20481.7			−0.00628207
$404$	943804.	+	2.18142e6i	0.287692	+	0.664944i
$405$	−1.18711e6	+	3.26177e6i	−0.359628	+	0.988132i
$406$	−490502.	+	101560.i	−0.147681	+	0.0305780i
$407$			7.71203e6i			2.30772i
$408$	878459.	+	1.25020e6i	0.261259	+	0.371816i
$409$	1.59180e6			0.470523			0.235262	−	0.971932i	$-0.424405\pi$
$409$	1.59180e6			0.470523			0.235262	+	0.971932i	$0.424405\pi$
$410$	635378.	−	4.35492e6i	0.186669	−	1.27944i
$411$			1.72442e6i			0.503545i
$412$	−444569.	−	1.02753e6i	−0.129032	−	0.298231i
$413$	−281825.			−0.0813025
$414$	−23522.4	−	113605.i	−0.00674499	−	0.0325760i
$415$	−145250.	+	399097.i	−0.0413996	+	0.113752i
$416$	307788.	−	502068.i	0.0872003	−	0.142243i
$417$		−	2.79117e6i		−	0.786041i
$418$	5.84958e6	−	1.21118e6i	1.63751	−	0.339053i
$419$		−	2.15084e6i		−	0.598513i	−0.954173	−	0.299256i	$-0.903261\pi$
$419$		−	2.15084e6i		−	0.598513i	0.954173	−	0.299256i	$-0.0967386\pi$
$420$	587495.	−	34874.7i	0.162510	−	0.00964688i
$421$		−	4.61854e6i		−	1.26999i	−0.772517	−	0.634994i	$-0.781003\pi$
$421$		−	4.61854e6i		−	1.26999i	0.772517	−	0.634994i	$-0.218997\pi$
$422$	84084.5	+	406100.i	0.0229845	+	0.111007i
$423$			396466.i			0.107735i
$424$	3.48325e6	−	2.44753e6i	0.940957	−	0.661169i
$425$	1.05915e6	−	1.26235e6i	0.284436	−	0.339005i
$426$	358893.	−	74310.2i	0.0958167	−	0.0198392i
$427$	−624147.			−0.165660
$428$	−3.47814e6	+	1.50484e6i	−0.917778	+	0.397082i
$429$			1.00897e6i			0.264688i
$430$	741444.	−	5.08190e6i	0.193378	−	1.32542i
$431$	2.67275e6			0.693051			0.346525	−	0.938041i	$-0.387361\pi$
$431$	2.67275e6			0.693051			0.346525	+	0.938041i	$0.387361\pi$
$432$	2.57845e6	−	2.74501e6i	0.664736	−	0.707675i
$433$			1.02544e6i			0.262840i	0.991327	+	0.131420i	$0.0419536\pi$
$433$			1.02544e6i			0.262840i	−0.991327	+	0.131420i	$0.958046\pi$
$434$	4749.03	+	22936.2i	0.00121026	+	0.00584517i
$435$	−3.62293e6	−	1.31856e6i	−0.917988	−	0.334099i
$436$	2.39150e6	+	5.52747e6i	0.602495	+	1.39255i
$437$	−2.63708e6			−0.660571
$438$	−907183.	−	4.38139e6i	−0.225949	−	1.09125i
$439$	4.60142e6			1.13954			0.569771	−	0.821803i	$-0.307032\pi$
$439$	4.60142e6			1.13954			0.569771	+	0.821803i	$0.307032\pi$
$440$	−6.05731e6	+	1.63384e6i	−1.49158	+	0.402326i
$441$	217039.			0.0531423
$442$	61485.3	+	296953.i	0.0149698	+	0.0722990i
$443$	−2.12572e6			−0.514631			−0.257315	−	0.966327i	$-0.582838\pi$
$443$	−2.12572e6			−0.514631			−0.257315	+	0.966327i	$0.582838\pi$
$444$	−5.84800e6	+	2.53017e6i	−1.40783	+	0.609106i
$445$	1.52970e6	−	4.20309e6i	0.366191	−	1.00616i
$446$	−439278.	−	2.12156e6i	−0.104569	−	0.505032i
$447$			3.33150e6i			0.788625i
$448$	−633602.	−	228260.i	−0.149149	−	0.0537321i
$449$	−1.97599e6			−0.462561			−0.231280	−	0.972887i	$-0.574291\pi$
$449$	−1.97599e6			−0.462561			−0.231280	+	0.972887i	$0.574291\pi$
$450$	206180.	+	111015.i	0.0479971	+	0.0258434i
$451$		−	8.62847e6i		−	1.99753i
$452$	2.78796e6	+	6.44383e6i	0.641861	+	1.48354i
$453$	4.94964e6			1.13326
$454$	6.29276e6	−	1.30294e6i	1.43285	−	0.296678i
$455$	109761.	+	39947.1i	0.0248552	+	0.00904600i
$456$	2.83757e6	+	4.03835e6i	0.639049	+	0.909476i
$457$		−	6.53536e6i		−	1.46379i	−0.681417	−	0.731895i	$-0.738636\pi$
$457$		−	6.53536e6i		−	1.46379i	0.681417	−	0.731895i	$-0.261364\pi$
$458$	−173617.	−	838513.i	−0.0386749	−	0.186787i
$459$			1.93933e6i			0.429655i
$460$	2.76471e6	−	164117.i	0.609192	−	0.0361626i
$461$			1.38960e6i			0.304535i	0.988339	+	0.152267i	$0.0486575\pi$
$461$			1.38960e6i			0.304535i	−0.988339	+	0.152267i	$0.951343\pi$
$462$	1.12988e6	−	233946.i	0.246279	−	0.0509931i
$463$		−	2.88277e6i		−	0.624968i	−0.949923	−	0.312484i	$-0.898839\pi$
$463$		−	2.88277e6i		−	0.624968i	0.949923	−	0.312484i	$-0.101161\pi$
$464$	3.21565e6	+	3.02054e6i	0.693385	+	0.651313i
$465$	−61656.5	+	169410.i	−0.0132235	+	0.0363336i
$466$	785470.	+	3.79355e6i	0.167558	+	0.809248i
$467$	−1.34330e6			−0.285024			−0.142512	−	0.989793i	$-0.545518\pi$
$467$	−1.34330e6			−0.285024			−0.142512	+	0.989793i	$0.545518\pi$
$468$	−39551.2	+	17112.1i	−0.00834727	+	0.00361150i
$469$			160564.i			0.0337067i
$470$	−9.36550e6	−	1.36642e6i	−1.95563	−	0.285324i
$471$	−6.92244e6			−1.43783
$472$	1.42708e6	+	2.03097e6i	0.294844	+	0.419613i
$473$		−	1.00688e7i		−	2.06932i
$474$	−6.09847e6	+	1.26271e6i	−1.24674	+	0.258142i
$475$	3.42122e6	−	4.07759e6i	0.695741	−	0.829220i
$476$	318284.	−	137707.i	0.0643868	−	0.0278573i
$477$	−311527.			−0.0626903
$478$	−756741.	+	156686.i	−0.151488	+	0.0313661i
$479$	6.70033e6			1.33431			0.667156	−	0.744918i	$-0.267512\pi$
$479$	6.70033e6			1.33431			0.667156	+	0.744918i	$0.267512\pi$
$480$	−3.22623e6	−	4.05720e6i	−0.639134	−	0.803754i
$481$	−1.26461e6			−0.249226
$482$	−49317.6	+	10211.4i	−0.00966906	+	0.00200202i
$483$	−509367.			−0.0993490
$484$	−6.55893e6	+	2.83776e6i	−1.27268	+	0.550633i
$485$	7.10544e6	+	2.58600e6i	1.37163	+	0.499200i
$486$	−555296.	+	114976.i	−0.106643	+	0.0220809i
$487$		−	7.10977e6i		−	1.35842i	−0.733945	−	0.679209i	$-0.762323\pi$
$487$		−	7.10977e6i		−	1.35842i	0.733945	−	0.679209i	$-0.237677\pi$
$488$	3.16050e6	+	4.49793e6i	0.600766	+	0.854993i
$489$	−2.11249e6			−0.399506
$490$	−748022.	+	5.12698e6i	−0.140742	+	0.964654i
$491$			2.40729e6i			0.450634i	0.974285	+	0.225317i	$0.0723418\pi$
$491$			2.40729e6i			0.450634i	−0.974285	+	0.225317i	$0.927658\pi$
$492$	6.54293e6	−	2.83084e6i	1.21860	−	0.527233i
$493$	−2.27184e6			−0.420979
$494$	198608.	+	959208.i	0.0366167	+	0.176846i
$495$	431415.	+	157012.i	0.0791375	+	0.0288019i
$496$	141242.	−	150366.i	0.0257787	−	0.0274439i
$497$		−	83184.2i		−	0.0151060i
$498$	−673679.	+	139488.i	−0.121725	+	0.0252036i
$499$		−	5.17486e6i		−	0.930351i	−0.885218	−	0.465176i	$-0.845991\pi$
$499$		−	5.17486e6i		−	0.930351i	0.885218	−	0.465176i	$-0.154009\pi$
$500$	−3.33304e6	+	4.48786e6i	−0.596232	+	0.802812i
$501$		−	3.09369e6i		−	0.550658i
$502$	−1.41011e6	−	6.81036e6i	−0.249744	−	1.20618i
$503$			9.51641e6i			1.67708i	0.544842	+	0.838539i	$0.316590\pi$
$503$			9.51641e6i			1.67708i	−0.544842	+	0.838539i	$0.683410\pi$
$504$	28333.4	+	40323.2i	0.00496846	+	0.00707097i
$505$	3.90178e6	+	1.42004e6i	0.680824	+	0.247784i
$506$	5.31713e6	−	1.10093e6i	0.923211	−	0.191154i
$507$	5.77810e6			0.998309
$508$	−2.27106e6	−	5.24911e6i	−0.390453	−	0.902456i
$509$		−	977974.i		−	0.167314i	−0.996495	−	0.0836571i	$-0.973340\pi$
$509$		−	977974.i		−	0.167314i	0.996495	−	0.0836571i	$-0.0266601\pi$
$510$	2.64129e6	+	385361.i	0.449666	+	0.0656058i
$511$	−1.01552e6			−0.172042
$512$	1.56341e6	+	5.72190e6i	0.263572	+	0.964640i
$513$			6.26435e6i			1.05095i
$514$	1.05104e6	+	5.07617e6i	0.175473	+	0.847477i
$515$	−1.83789e6	−	668897.i	−0.305353	−	0.111132i
$516$	7.63516e6	−	3.30340e6i	1.26239	−	0.546181i
$517$	−1.85560e7			−3.05322
$518$	293222.	+	1.41616e6i	0.0480144	+	0.231893i
$519$	3.35349e6			0.546485
$520$	−267916.	−	993271.i	−0.0434500	−	0.161087i
$521$	−6.38760e6			−1.03096			−0.515482	−	0.856900i	$-0.672387\pi$
$521$	−6.38760e6			−1.03096			−0.515482	+	0.856900i	$0.672387\pi$
$522$	−65457.8	−	316139.i	−0.0105144	−	0.0507811i
$523$	−2.84665e6			−0.455072			−0.227536	−	0.973770i	$-0.573067\pi$
$523$	−2.84665e6			−0.455072			−0.227536	+	0.973770i	$0.573067\pi$
$524$	−2.32099e6	−	5.36452e6i	−0.369271	−	0.853498i
$525$	660830.	−	787611.i	0.104639	−	0.124714i
$526$	941642.	+	4.54781e6i	0.148396	+	0.716701i
$527$			106233.i			0.0166621i
$528$	−7.40732e6	−	6.95787e6i	−1.15632	−	1.08615i
$529$	4.03930e6			0.627577
$530$	1.07368e6	−	7.35904e6i	0.166029	−	1.13797i
$531$		−	181642.i		−	0.0279563i
$532$	1.02811e6	−	444818.i	0.157493	−	0.0681401i
$533$	1.41489e6			0.215727
$534$	7.09486e6	−	1.46902e6i	1.07669	−	0.222933i
$535$	−2.26418e6	+	6.22116e6i	−0.342000	+	0.939695i
$536$	1.15711e6	−	813049.i	0.173965	−	0.122238i
$537$			6.99771e6i			1.04718i
$538$	545605.	+	2.63509e6i	0.0812686	+	0.392500i
$539$			1.01582e7i			1.50606i
$540$	−389859.	−	6.56753e6i	−0.0575338	−	0.969210i
$541$		−	2.39581e6i		−	0.351933i	−0.984396	−	0.175966i	$-0.943695\pi$
$541$		−	2.39581e6i		−	0.351933i	0.984396	−	0.175966i	$-0.0563050\pi$
$542$	−3.13546e6	+	649210.i	−0.458462	+	0.0949264i
$543$		−	8.95092e6i		−	1.30277i
$544$	−2.60408e6	−	1.59641e6i	−0.377275	−	0.231284i
$545$	9.88669e6	+	3.59824e6i	1.42580	+	0.518918i
$546$	38362.3	+	185277.i	0.00550710	+	0.0265974i
$547$	4.73593e6			0.676763			0.338382	−	0.941009i	$-0.390121\pi$
$547$	4.73593e6			0.676763			0.338382	+	0.941009i	$0.390121\pi$
$548$	−1.36882e6	−	3.16376e6i	−0.194713	−	0.450041i
$549$		−	402276.i		−	0.0569631i
$550$	−5.19588e6	+	9.64993e6i	−0.732407	+	1.36025i
$551$	−7.33841e6			−1.02973
$552$	2.57928e6	+	3.67076e6i	0.360289	+	0.512754i
$553$			1.41350e6i			0.196555i
$554$	690918.	−	143057.i	0.0956427	−	0.0198032i
$555$	−3.80689e6	+	1.04600e7i	−0.524611	+	1.44145i
$556$	2.21559e6	+	5.12090e6i	0.303950	+	0.702521i
$557$	6.50430e6			0.888306			0.444153	−	0.895951i	$-0.353505\pi$
$557$	6.50430e6			0.888306			0.444153	+	0.895951i	$0.353505\pi$
$558$	−14782.9	+	3060.85i	−0.00200989	+	0.000416156i
$559$	1.65108e6			0.223480
$560$	−1.05018e6	+	530330.i	−0.141513	+	0.0714621i
$561$	5.23322e6			0.702040
$562$	−8.13872e6	+	1.68515e6i	−1.08696	+	0.225060i
$563$	−7.39875e6			−0.983756			−0.491878	−	0.870664i	$-0.663689\pi$
$563$	−7.39875e6			−0.983756			−0.491878	+	0.870664i	$0.663689\pi$
$564$	−6.08788e6	−	1.40709e7i	−0.805877	−	1.86263i
$565$	1.15257e7	+	4.19476e6i	1.51896	+	0.552823i
$566$	−3.07078e6	+	635818.i	−0.402910	+	0.0834241i
$567$			1.27615e6i			0.166704i
$568$	−599468.	+	421220.i	−0.0779642	+	0.0547821i
$569$	−8.19657e6			−1.06133			−0.530666	−	0.847581i	$-0.678058\pi$
$569$	−8.19657e6			−1.06133			−0.530666	+	0.847581i	$0.678058\pi$
$570$	8.53179e6	+	1.24478e6i	1.09990	+	0.160474i
$571$			468744.i			0.0601653i	0.999547	+	0.0300826i	$0.00957704\pi$
$571$			468744.i			0.0601653i	−0.999547	+	0.0300826i	$0.990423\pi$
$572$	−800904.	−	1.85113e6i	−0.102351	−	0.236563i
$573$	−5.29139e6			−0.673260
$574$	−328066.	−	1.58445e6i	−0.0415606	−	0.200723i
$575$	3.10981e6	−	3.70644e6i	0.392252	−	0.467506i
$576$	147118.	−	408370.i	0.0184761	−	0.0512858i
$577$			7.11469e6i			0.889645i	0.895619	+	0.444822i	$0.146733\pi$
$577$			7.11469e6i			0.889645i	−0.895619	+	0.444822i	$0.853267\pi$
$578$	−6.32489e6	+	1.30959e6i	−0.787469	+	0.163048i
$579$			6.52211e6i			0.808522i
$580$	7.69358e6	−	456703.i	0.949638	−	0.0563720i
$581$			156145.i			0.0191906i
$582$	2.48341e6	+	1.19940e7i	0.303907	+	1.46777i
$583$		−	1.45806e7i		−	1.77666i
$584$	5.14228e6	+	7.31834e6i	0.623912	+	0.887933i
$585$	−25746.7	+	70743.0i	−0.00311052	+	0.00854661i
$586$	7.91333e6	−	1.63849e6i	0.951953	−	0.197106i
$587$	1.51044e7			1.80929			0.904645	−	0.426166i	$-0.140136\pi$
$587$	1.51044e7			1.80929			0.904645	+	0.426166i	$0.140136\pi$
$588$	−7.70290e6	+	3.33271e6i	−0.918779	+	0.397515i
$589$			343149.i			0.0407562i
$590$	4.29082e6	+	626027.i	0.507470	+	0.0740394i
$591$	−1.35087e7			−1.59090
$592$	8.72080e6	−	9.28412e6i	1.02271	−	1.08877i
$593$			1.95268e6i			0.228031i	0.993479	+	0.114016i	$0.0363714\pi$
$593$			1.95268e6i			0.228031i	−0.993479	+	0.114016i	$0.963629\pi$
$594$	−2.61525e6	−	1.26308e7i	−0.304122	−	1.46881i
$595$	207194.	−	569297.i	0.0239930	−	0.0659244i
$596$	−2.64450e6	−	6.11224e6i	−0.304949	−	0.704830i
$597$	−3.92902e6			−0.451178
$598$	180530.	+	871898.i	0.0206441	+	0.0997040i
$599$	−6.34911e6			−0.723012			−0.361506	−	0.932370i	$-0.617737\pi$
$599$	−6.34911e6			−0.723012			−0.361506	+	0.932370i	$0.617737\pi$
$600$	−9.02218e6	−	774052.i	−1.02314	−	0.0877793i
$601$	−5.25950e6			−0.593961			−0.296981	−	0.954884i	$-0.595980\pi$
$601$	−5.25950e6			−0.593961			−0.296981	+	0.954884i	$0.595980\pi$
$602$	−382831.	−	1.84894e6i	−0.0430542	−	0.207937i
$603$	−103487.			−0.0115902
$604$	−9.08101e6	+	3.92895e6i	−1.01284	+	0.438212i
$605$	−4.26968e6	+	1.17316e7i	−0.474250	+	1.30307i
$606$	1.36371e6	+	6.58624e6i	0.150848	+	0.728545i
$607$			1.91612e6i			0.211081i	0.994415	+	0.105541i	$0.0336573\pi$
$607$			1.91612e6i			0.211081i	−0.994415	+	0.105541i	$0.966343\pi$
$608$	−8.41162e6	−	5.15665e6i	−0.922828	−	0.565730i
$609$	−1.41746e6			−0.154870
$610$	9.50274e6	+	1.38644e6i	1.03401	+	0.150861i
$611$		−	3.04280e6i		−	0.329739i
$612$	88755.3	+	205140.i	0.00957890	+	0.0221397i
$613$	3.26461e6			0.350898			0.175449	−	0.984489i	$-0.443862\pi$
$613$	3.26461e6			0.350898			0.175449	+	0.984489i	$0.443862\pi$
$614$	1.09784e7	−	2.27312e6i	1.17522	−	0.243334i
$615$	4.25927e6	−	1.17030e7i	0.454096	−	1.24770i
$616$	−1.88727e6	+	1.32610e6i	−0.200393	+	0.140807i
$617$		−	6.30937e6i		−	0.667227i	−0.942710	−	0.333613i	$-0.891732\pi$
$617$		−	6.30937e6i		−	0.667227i	0.942710	−	0.333613i	$-0.108268\pi$
$618$	−642360.	−	3.10238e6i	−0.0676562	−	0.326756i
$619$		−	1.61077e7i		−	1.68969i	−0.535011	−	0.844845i	$-0.679692\pi$
$619$		−	1.61077e7i		−	1.68969i	0.535011	−	0.844845i	$-0.320308\pi$
$620$	−21355.7	−	359756.i	−0.00223118	−	0.0375863i
$621$			5.69415e6i			0.592516i
$622$	−1.67358e7	+	3.46520e6i	−1.73448	+	0.359131i
$623$		−	1.64445e6i		−	0.169746i
$624$	1.14094e6	−	1.21464e6i	0.117301	−	0.124879i
$625$	1.69656e6	+	9.61713e6i	0.173728	+	0.984794i
$626$	−2.95708e6	−	1.42817e7i	−0.301597	−	1.45661i
$627$	1.69042e7			1.71722
$628$	1.27005e7	−	5.49494e6i	1.28505	−	0.555986i
$629$			6.55917e6i			0.661032i
$630$	85190.6	+	12429.2i	0.00855147	+	0.00124765i
$631$	6.37953e6			0.637845			0.318923	−	0.947781i	$-0.396679\pi$
$631$	6.37953e6			0.637845			0.318923	+	0.947781i	$0.396679\pi$
$632$	1.01864e7	−	7.15755e6i	1.01445	−	0.712807i
$633$			1.17355e6i			0.116411i
$634$	−1.46569e7	+	3.03477e6i	−1.44817	+	0.299849i
$635$	−9.38879e6	−	3.41703e6i	−0.924007	−	0.336290i
$636$	1.10564e7	−	4.78362e6i	1.08385	−	0.468936i
$637$	−1.66573e6			−0.162650
$638$	1.47964e7	−	3.06365e6i	1.43915	−	0.297981i
$639$	53614.0			0.00519429
$640$	9.13964e6	+	4.88273e6i	0.882022	+	0.471208i
$641$	−4.35064e6			−0.418224			−0.209112	−	0.977892i	$-0.567057\pi$
$641$	−4.35064e6			−0.418224			−0.209112	+	0.977892i	$0.567057\pi$
$642$	−1.05014e7	+	2.17435e6i	−1.00556	+	0.208205i
$643$	−5.59471e6			−0.533642			−0.266821	−	0.963746i	$-0.585973\pi$
$643$	−5.59471e6			−0.533642			−0.266821	+	0.963746i	$0.585973\pi$
$644$	934527.	−	404329.i	0.0887927	−	0.0384167i
$645$	4.97028e6	−	1.36566e7i	0.470416	−	1.29254i
$646$	4.97514e6	−	1.03012e6i	0.469055	−	0.0971196i
$647$			5.34514e6i			0.501994i	0.967988	+	0.250997i	$0.0807584\pi$
$647$			5.34514e6i			0.501994i	−0.967988	+	0.250997i	$0.919242\pi$
$648$	9.19662e6	−	6.46206e6i	0.860381	−	0.604552i
$649$	8.50148e6			0.792287
$650$	−1.58239e6	−	852016.i	−0.146903	−	0.0790978i
$651$			66281.2i			0.00612968i
$652$	3.87575e6	−	1.67687e6i	0.357057	−	0.154483i
$653$	5.04365e6			0.462873			0.231436	−	0.972850i	$-0.425657\pi$
$653$	5.04365e6			0.462873			0.231436	+	0.972850i	$0.425657\pi$
$654$	3.45548e6	+	1.66888e7i	0.315911	+	1.52574i
$655$	−9.59523e6	−	3.49216e6i	−0.873880	−	0.318046i
$656$	−9.75711e6	+	1.03874e7i	−0.885241	+	0.942424i
$657$		−	654522.i		−	0.0591576i
$658$	−3.40744e6	+	705524.i	−0.306806	+	0.0635254i
$659$		−	7.04546e6i		−	0.631969i	−0.948764	−	0.315984i	$-0.897665\pi$
$659$		−	7.04546e6i		−	0.631969i	0.948764	−	0.315984i	$-0.102335\pi$
$660$	−1.77223e7	+	1.05202e6i	−1.58365	+	0.0940082i
$661$			8.20765e6i			0.730660i	0.930878	+	0.365330i	$0.119044\pi$
$661$			8.20765e6i			0.730660i	−0.930878	+	0.365330i	$0.880956\pi$
$662$	−3.33107e6	−	1.60879e7i	−0.295419	−	1.42678i
$663$			858138.i			0.0758182i
$664$	1.12526e6	−	790673.i	0.0990452	−	0.0695948i
$665$	669271.	−	1.83892e6i	0.0586878	−	0.161254i
$666$	−912745.	+	188987.i	−0.0797378	+	0.0165100i
$667$	−6.67045e6			−0.580551
$668$	2.45573e6	+	5.67593e6i	0.212931	+	0.492148i
$669$		−	6.13091e6i		−	0.529614i
$670$	356667.	−	2.44461e6i	0.0306956	−	0.210389i
$671$	1.88279e7			1.61434
$672$	−1.62475e6	−	996039.i	−0.138792	−	0.0850850i
$673$			6.23037e6i			0.530245i	0.964215	+	0.265122i	$0.0854124\pi$
$673$			6.23037e6i			0.530245i	−0.964215	+	0.265122i	$0.914588\pi$
$674$	−2.02100e6	−	9.76072e6i	−0.171362	−	0.827622i
$675$	−8.80460e6	−	7.38733e6i	−0.743790	−	0.624063i
$676$	−1.06010e7	+	4.58658e6i	−0.892234	+	0.386031i
$677$	−1.39112e7			−1.16652			−0.583262	−	0.812284i	$-0.698224\pi$
$677$	−1.39112e7			−1.16652			−0.583262	+	0.812284i	$0.698224\pi$
$678$	4.02834e6	+	1.94555e7i	0.336552	+	1.62543i
$679$	2.77998e6			0.231402
$680$	−5.15181e6	+	1.38960e6i	−0.427256	+	0.115244i
$681$	1.81849e7			1.50260
$682$	−143258.	−	691889.i	−0.0117939	−	0.0569608i
$683$	1.07327e6			0.0880350			0.0440175	−	0.999031i	$-0.485984\pi$
$683$	1.07327e6			0.0880350			0.0440175	+	0.999031i	$0.485984\pi$
$684$	286694.	+	662637.i	0.0234303	+	0.0541546i
$685$	−5.65884e6	−	2.05952e6i	−0.460788	−	0.167703i
$686$	782412.	+	3.77878e6i	0.0634783	+	0.306579i
$687$		−	2.42314e6i		−	0.195879i
$688$	−1.13859e7	+	1.21214e7i	−0.917056	+	0.976294i
$689$	2.39091e6			0.191873
$690$	7.75520e6	+	1.13148e6i	0.620112	+	0.0904738i
$691$			4.51366e6i			0.359611i	0.983702	+	0.179806i	$0.0575469\pi$
$691$			4.51366e6i			0.359611i	−0.983702	+	0.179806i	$0.942453\pi$
$692$	−6.15258e6	+	2.66195e6i	−0.488418	+	0.211317i
$693$	168790.			0.0133510
$694$	−1.01536e7	+	2.10234e6i	−0.800241	+	0.165693i
$695$	9.15948e6	+	3.33357e6i	0.719298	+	0.261786i
$696$	7.17759e6	+	1.02149e7i	0.561637	+	0.799305i
$697$		−	7.33861e6i		−	0.572179i
$698$	166740.	+	805296.i	0.0129539	+	0.0625630i
$699$			1.09627e7i			0.848638i
$700$	−587218.	+	1.96957e6i	−0.0452954	+	0.151924i
$701$		−	2.00796e7i		−	1.54334i	−0.636025	−	0.771668i	$-0.719423\pi$
$701$		−	2.00796e7i		−	1.54334i	0.636025	−	0.771668i	$-0.280577\pi$
$702$	2.07119e6	−	428847.i	0.158627	−	0.0328443i
$703$			2.11872e7i			1.61691i
$704$	1.91131e7	+	6.88565e6i	1.45345	+	0.523616i
$705$	−2.51679e7	−	9.15981e6i	−1.90711	−	0.694086i
$706$	3.23643e6	+	1.56309e7i	0.244374	+	1.18024i
$707$	1.52656e6			0.114859
$708$	2.78918e6	+	6.44663e6i	0.209119	+	0.483337i
$709$		−	7.45228e6i		−	0.556767i	−0.960470	−	0.278384i	$-0.910201\pi$
$709$		−	7.45228e6i		−	0.556767i	0.960470	−	0.278384i	$-0.0897986\pi$
$710$	−184780.	+	1.26649e6i	−0.0137565	+	0.0942881i
$711$	−911032.			−0.0675864
$712$	−1.18507e7	+	8.32698e6i	−0.876082	+	0.615584i
$713$			311914.i			0.0229779i
$714$	960977.	−	198974.i	0.0705452	−	0.0146067i
$715$	−3.31102e6	−	1.20504e6i	−0.242213	−	0.0881527i
$716$	−5.55469e6	−	1.28386e7i	−0.404927	−	0.935910i
$717$	−2.18684e6			−0.158862
$718$	1.63532e7	−	3.38599e6i	1.18383	−	0.245118i
$719$	−2.33956e7			−1.68776			−0.843881	−	0.536531i	$-0.819735\pi$
$719$	−2.33956e7			−1.68776			−0.843881	+	0.536531i	$0.819735\pi$
$720$	−341809.	−	676865.i	−0.0245726	−	0.0486599i
$721$	−719070.			−0.0515149
$722$	2.35451e6	−	487509.i	0.168096	−	0.0348049i
$723$	−142519.			−0.0101397
$724$	7.10512e6	+	1.64221e7i	0.503762	+	1.16435i
$725$	8.65394e6	−	1.03142e7i	0.611461	−	0.728770i
$726$	−1.98030e7	+	4.10030e6i	−1.39441	+	0.288718i
$727$		−	294804.i		−	0.0206870i	−0.999947	−	0.0103435i	$-0.996708\pi$
$727$		−	294804.i		−	0.0206870i	0.999947	−	0.0103435i	$-0.00329250\pi$
$728$	−217453.	−	309472.i	−0.0152068	−	0.0216418i
$729$	1.34838e7			0.939706
$730$	1.54614e7	+	2.25580e6i	1.07385	+	0.156673i
$731$		−	8.56367e6i		−	0.592743i
$732$	6.17710e6	+	1.42771e7i	0.426095	+	0.984835i
$733$	1.28146e7			0.880936			0.440468	−	0.897768i	$-0.354813\pi$
$733$	1.28146e7			0.880936			0.440468	+	0.897768i	$0.354813\pi$
$734$	2.68341e6	+	1.29600e7i	0.183843	+	0.887898i
$735$	−5.01438e6	+	1.37778e7i	−0.342373	+	0.940720i
$736$	−7.64597e6	−	4.68728e6i	−0.520281	−	0.318953i
$737$		−	4.84355e6i		−	0.328470i
$738$	1.02121e6	−	211445.i	0.0690198	−	0.0142908i
$739$			1.38313e7i			0.931648i	0.884878	+	0.465824i	$0.154242\pi$
$739$			1.38313e7i			0.931648i	−0.884878	+	0.465824i	$0.845758\pi$
$740$	−1.31858e6	−	2.22126e7i	−0.0885169	−	1.49115i
$741$			2.77193e6i			0.185454i
$742$	−554373.	−	2.67743e6i	−0.0369651	−	0.178529i
$743$		−	2.75909e6i		−	0.183355i	−0.995789	−	0.0916776i	$-0.970777\pi$
$743$		−	2.75909e6i		−	0.183355i	0.995789	−	0.0916776i	$-0.0292229\pi$
$744$	477657.	−	335628.i	0.0316361	−	0.0222293i
$745$	−1.09326e7	−	3.97890e6i	−0.721662	−	0.262647i
$746$	−8.65473e6	+	1.79199e6i	−0.569386	+	0.117893i
$747$	−100639.			−0.00659879
$748$	−9.60129e6	+	4.15406e6i	−0.627445	+	0.271468i
$749$			2.43401e6i			0.158532i
$750$	−1.18108e7	+	1.05236e7i	−0.766701	+	0.683141i
$751$	2.08472e7			1.34880			0.674400	−	0.738366i	$-0.264402\pi$
$751$	2.08472e7			1.34880			0.674400	+	0.738366i	$0.264402\pi$
$752$	2.23387e7	+	2.09832e7i	1.44050	+	1.35309i
$753$		−	1.96807e7i		−	1.26489i
$754$	502375.	+	2.42630e6i	0.0321810	+	0.155423i
$755$	−5.91149e6	+	1.62427e7i	−0.377424	+	1.03703i
$756$	−960479.	−	2.21996e6i	−0.0611200	−	0.141267i
$757$	−2.19242e7			−1.39054			−0.695270	−	0.718748i	$-0.744715\pi$
$757$	−2.19242e7			−1.39054			−0.695270	+	0.718748i	$0.744715\pi$
$758$	−5.38416e6	−	2.60037e7i	−0.340365	−	1.64385i
$759$	1.53655e7			0.968149
$760$	−1.66412e7	+	4.48864e6i	−1.04508	+	0.281891i
$761$	−8.04798e6			−0.503762			−0.251881	−	0.967758i	$-0.581049\pi$
$761$	−8.04798e6			−0.503762			−0.251881	+	0.967758i	$0.581049\pi$
$762$	−3.28146e6	−	1.58484e7i	−0.204729	−	0.988774i
$763$	3.86813e6			0.240542
$764$	9.70801e6	−	4.20023e6i	0.601723	−	0.260339i
$765$	366924.	+	133541.i	0.0226685	+	0.00825013i
$766$	−5.00604e6	−	2.41775e7i	−0.308264	−	1.48881i
$767$			1.39406e6i			0.0855646i
$768$	1.04931e6	+	1.67525e7i	0.0641947	+	1.02489i
$769$	1.69276e6			0.103224			0.0516119	−	0.998667i	$-0.483564\pi$
$769$	1.69276e6			0.103224			0.0516119	+	0.998667i	$0.483564\pi$
$770$	−581732.	+	3.98722e6i	−0.0353587	+	0.242350i
$771$			1.46692e7i			0.888729i
$772$	−5.17716e6	−	1.19660e7i	−0.312643	−	0.722613i
$773$	1.17341e7			0.706320			0.353160	−	0.935563i	$-0.385107\pi$
$773$	1.17341e7			0.706320			0.353160	+	0.935563i	$0.385107\pi$
$774$	1.19168e6	−	246742.i	0.0715004	−	0.0148044i
$775$	−482299.	−	404663.i	−0.0288444	−	0.0242013i
$776$	−1.40770e7	−	2.00339e7i	−0.839179	−	1.19430i
$777$			4.09244e6i			0.243181i
$778$	522378.	+	2.52291e6i	0.0309411	+	0.149435i
$779$		−	2.37049e7i		−	1.39957i
$780$	−172510.	−	2.90608e6i	−0.0101526	−	0.171030i
$781$			2.50932e6i			0.147207i
$782$	4.52228e6	−	936356.i	0.264448	−	0.0547550i
$783$			1.58456e7i			0.923642i
$784$	1.14869e7	−	1.22289e7i	0.667441	−	0.710555i
$785$	8.26766e6	−	2.27166e7i	0.478860	−	1.31574i
$786$	−3.35361e6	−	1.61968e7i	−0.193623	−	0.935133i
$787$	−4.79782e6			−0.276126			−0.138063	−	0.990423i	$-0.544088\pi$
$787$	−4.79782e6			−0.276126			−0.138063	+	0.990423i	$0.544088\pi$
$788$	2.47841e7	−	1.07230e7i	1.42186	−	0.615177i
$789$			1.31423e7i			0.751587i
$790$	3.13986e6	−	2.15208e7i	0.178996	−	1.22685i
$791$	4.50940e6			0.256258
$792$	−854700.	−	1.21638e6i	−0.0484173	−	0.0689061i
$793$			3.08739e6i			0.174344i
$794$	−7.82490e6	+	1.62018e6i	−0.440481	+	0.0912034i
$795$	7.19741e6	−	1.97760e7i	0.403886	−	1.10974i
$796$	7.20849e6	−	3.11880e6i	0.403238	−	0.174464i
$797$	1.64953e7			0.919845			0.459922	−	0.887959i	$-0.347877\pi$
$797$	1.64953e7			0.919845			0.459922	+	0.887959i	$0.347877\pi$
$798$	3.10412e6	−	642719.i	0.172556	−	0.0357284i
$799$	−1.57821e7			−0.874577
$800$	1.71673e7	−	5.74154e6i	0.948366	−	0.317178i
$801$	1.05988e6			0.0583680
$802$	1.91441e7	−	3.96385e6i	1.05099	−	0.217611i
$803$	3.06339e7			1.67654
$804$	3.67285e6	−	1.58908e6i	0.200384	−	0.0866973i
$805$	608352.	−	1.67154e6i	0.0330876	−	0.0909131i
$806$	113455.	−	23491.4i	0.00615159	−	0.00127371i
$807$			7.61491e6i			0.411605i
$808$	−7.73004e6	−	1.10012e7i	−0.416537	−	0.592803i
$809$	−1.68460e7			−0.904952			−0.452476	−	0.891777i	$-0.649459\pi$
$809$	−1.68460e7			−0.904952			−0.452476	+	0.891777i	$0.649459\pi$
$810$	2.83477e6	−	1.94296e7i	0.151811	−	1.04052i
$811$			1.09892e7i			0.586696i	0.956006	+	0.293348i	$0.0947695\pi$
$811$			1.09892e7i			0.586696i	−0.956006	+	0.293348i	$0.905231\pi$
$812$	2.60058e6	−	1.12516e6i	0.138414	−	0.0598858i
$813$	−9.06090e6			−0.480778
$814$	−8.84528e6	−	4.27197e7i	−0.467897	−	2.25979i
$815$	2.52301e6	−	6.93235e6i	0.133053	−	0.365583i
$816$	−6.30001e6	−	5.91775e6i	−0.331220	−	0.311122i
$817$		−	2.76621e7i		−	1.44987i
$818$	−8.81757e6	+	1.82571e6i	−0.460750	+	0.0954001i
$819$			27677.9i			0.00144186i
$820$	1.47527e6	+	2.48522e7i	0.0766189	+	1.29071i
$821$			3.39298e7i			1.75680i	0.477924	+	0.878401i	$0.341390\pi$
$821$			3.39298e7i			1.75680i	−0.477924	+	0.878401i	$0.658610\pi$
$822$	−1.97781e6	−	9.55217e6i	−0.102095	−	0.493086i
$823$			1.59677e7i			0.821758i	0.911690	+	0.410879i	$0.134778\pi$
$823$			1.59677e7i			0.821758i	−0.911690	+	0.410879i	$0.865222\pi$
$824$	3.64115e6	+	5.18198e6i	0.186819	+	0.265875i
$825$	−1.99345e7	+	2.37590e7i	−1.01970	+	1.21533i
$826$	1.56113e6	−	323238.i	0.0796138	−	0.0164843i
$827$	−1.35172e7			−0.687261			−0.343631	−	0.939105i	$-0.611657\pi$
$827$	−1.35172e7			−0.687261			−0.343631	+	0.939105i	$0.611657\pi$
$828$	260598.	+	602322.i	0.0132098	+	0.0305318i
$829$			1.89399e7i			0.957173i	0.878040	+	0.478587i	$0.158851\pi$
$829$			1.89399e7i			0.957173i	−0.878040	+	0.478587i	$0.841149\pi$
$830$	346851.	−	2.37734e6i	0.0174762	−	0.119783i
$831$	1.99662e6			0.100298
$832$	−1.12910e6	+	3.13415e6i	−0.0565490	+	0.156968i
$833$			8.63965e6i			0.431403i
$834$	3.20132e6	+	1.54613e7i	0.159373	+	0.769715i
$835$	1.01522e7	+	3.69488e6i	0.503901	+	0.183394i
$836$	−3.10138e7	+	1.34183e7i	−1.53475	+	0.664021i
$837$	740949.			0.0365573
$838$	2.46690e6	+	1.19143e7i	0.121350	+	0.586082i
$839$	−2.65584e7			−1.30256			−0.651279	−	0.758839i	$-0.725767\pi$
$839$	−2.65584e7			−1.30256			−0.651279	+	0.758839i	$0.725767\pi$
$840$	−3.21435e6	+	867009.i	−0.157179	+	0.0423960i
$841$	1.94875e6			0.0950093
$842$	5.29721e6	+	2.55838e7i	0.257494	+	1.24361i
$843$	−2.35194e7			−1.13987
$844$	−931548.	−	2.15309e6i	−0.0450142	−	0.104041i
$845$	−6.90094e6	+	1.89614e7i	−0.332481	+	0.913541i
$846$	−454725.	−	2.19617e6i	−0.0218435	−	0.105497i
$847$			4.58995e6i			0.219836i
$848$	−1.64878e7	+	1.75528e7i	−0.787359	+	0.838219i
$849$	−8.87398e6			−0.422522
$850$	−4.41916e6	+	8.20738e6i	−0.209794	+	0.389635i
$851$			1.92587e7i			0.911596i
$852$	−1.90281e6	+	823262.i	−0.0898041	+	0.0388543i
$853$	3.19230e7			1.50221			0.751106	−	0.660182i	$-0.229521\pi$
$853$	3.19230e7			1.50221			0.751106	+	0.660182i	$0.229521\pi$
$854$	3.45738e6	−	715863.i	0.162219	−	0.0335881i
$855$	1.18522e6	+	431359.i	0.0554479	+	0.0201801i
$856$	1.75407e7	−	1.23251e7i	0.818206	−	0.574917i
$857$			1.09419e7i			0.508910i	0.967085	+	0.254455i	$0.0818961\pi$
$857$			1.09419e7i			0.508910i	−0.967085	+	0.254455i	$0.918104\pi$
$858$	−1.15723e6	−	5.58903e6i	−0.0536663	−	0.259190i
$859$			8.02039e6i			0.370862i	0.982657	+	0.185431i	$0.0593682\pi$
$859$			8.02039e6i			0.370862i	−0.982657	+	0.185431i	$0.940632\pi$
$860$	1.72154e6	+	2.90009e7i	0.0793725	+	1.33710i
$861$		−	4.57875e6i		−	0.210494i
$862$	−1.48053e7	+	3.06550e6i	−0.678656	+	0.140518i
$863$		−	3.19608e7i		−	1.46080i	−0.683019	−	0.730401i	$-0.739333\pi$
$863$		−	3.19608e7i		−	1.46080i	0.683019	−	0.730401i	$-0.260667\pi$
$864$	−1.11346e7	+	1.81629e7i	−0.507446	+	0.827754i
$865$	−4.00516e6	+	1.10048e7i	−0.182003	+	0.500082i
$866$	−1.17613e6	−	5.68029e6i	−0.0532916	−	0.257381i
$867$	−1.82777e7			−0.825799
$868$	−52613.1	−	121605.i	−0.00237025	−	0.00547838i
$869$		−	4.26395e7i		−	1.91541i
$870$	2.15810e7	+	3.14865e6i	0.966661	+	0.141035i
$871$	794241.			0.0354737
$872$	−1.95871e7	−	2.78758e7i	−0.872325	−	1.24147i
$873$			1.79175e6i			0.0795687i
$874$	1.46077e7	−	3.02459e6i	0.646851	−	0.133933i
$875$	1.79537e6	+	3.10924e6i	0.0792748	+	0.137289i
$876$	1.00504e7	+	2.32296e7i	0.442511	+	1.02278i
$877$	2.53762e7			1.11411			0.557053	−	0.830477i	$-0.311932\pi$
$877$	2.53762e7			1.11411			0.557053	+	0.830477i	$0.311932\pi$
$878$	−2.54889e7	+	5.27758e6i	−1.11587	+	0.231046i
$879$	2.28680e7			0.998290
$880$	3.16797e7	−	1.59978e7i	1.37903	−	0.696394i
$881$	3.25533e7			1.41304			0.706522	−	0.707691i	$-0.250263\pi$
$881$	3.25533e7			1.41304			0.706522	+	0.707691i	$0.250263\pi$
$882$	−1.20226e6	+	248932.i	−0.0520386	+	0.0107748i
$883$	−3.66593e6			−0.158227			−0.0791137	−	0.996866i	$-0.525209\pi$
$883$	−3.66593e6			−0.158227			−0.0791137	+	0.996866i	$0.525209\pi$
$884$	−681179.	−	1.57441e6i	−0.0293177	−	0.0677622i
$885$	1.15307e7	+	4.19658e6i	0.494879	+	0.180110i
$886$	1.17751e7	−	2.43808e6i	0.503942	−	0.104343i
$887$		−	1.23711e7i		−	0.527957i	−0.964529	−	0.263979i	$-0.914965\pi$
$887$		−	1.23711e7i		−	0.527957i	0.964529	−	0.263979i	$-0.0850348\pi$
$888$	2.94922e7	−	2.07229e7i	1.25509	−	0.881897i
$889$	−3.67333e6			−0.155885
$890$	−3.65286e6	+	2.50369e7i	−0.154582	+	1.05951i
$891$		−	3.84963e7i		−	1.62452i
$892$	4.86663e6	+	1.12483e7i	0.204794	+	0.473340i
$893$	−5.09788e7			−2.13925
$894$	−3.82105e6	−	1.84544e7i	−0.159896	−	0.772246i
$895$	−2.29637e7	−	8.35756e6i	−0.958261	−	0.348756i
$896$	3.77155e6	+	537706.i	0.156946	+	0.0223756i
$897$			2.51962e6i			0.104557i
$898$	1.09457e7	−	2.26635e6i	0.452953	−	0.0937857i
$899$			867989.i			0.0358191i
$900$	−1.26943e6	−	378474.i	−0.0522400	−	0.0155751i
$901$		−	1.24010e7i		−	0.508912i
$902$	9.89639e6	+	4.77962e7i	0.405005	+	1.95604i
$903$		−	5.34310e6i		−	0.218059i
$904$	−2.28343e7	−	3.24970e7i	−0.929321	−	1.32258i
$905$	2.93733e7	+	1.06903e7i	1.19215	+	0.433880i
$906$	−2.74178e7	+	5.67697e6i	−1.10972	+	0.229771i
$907$	−1.12158e6			−0.0452702			−0.0226351	−	0.999744i	$-0.507206\pi$
$907$	−1.12158e6			−0.0452702			−0.0226351	+	0.999744i	$0.507206\pi$
$908$	−3.33635e7	+	1.44349e7i	−1.34294	+	0.581031i
$909$			983899.i			0.0394949i
$910$	−653821.	−	95391.8i	−0.0261731	−	0.00381863i
$911$	3.35511e7			1.33940			0.669700	−	0.742632i	$-0.266423\pi$
$911$	3.35511e7			1.33940			0.669700	+	0.742632i	$0.266423\pi$
$912$	−2.03501e7	−	1.91153e7i	−0.810175	−	0.761017i
$913$		−	4.71025e6i		−	0.187011i
$914$	7.49570e6	+	3.62017e7i	0.296788	+	1.43339i
$915$	2.55368e7	+	9.29404e6i	1.00835	+	0.366988i
$916$	1.92346e6	+	4.44570e6i	0.0757433	+	0.175066i
$917$	−3.75410e6			−0.147429
$918$	−2.22430e6	−	1.07426e7i	−0.0871139	−	0.420731i
$919$	1.22526e6			0.0478562			0.0239281	−	0.999714i	$-0.492383\pi$
$919$	1.22526e6			0.0478562			0.0239281	+	0.999714i	$0.492383\pi$
$920$	−1.51265e7	+	4.08007e6i	−0.589207	+	0.158927i
$921$	3.17255e7			1.23242
$922$	−1.59379e6	−	7.69748e6i	−0.0617454	−	0.298210i
$923$	−411476.			−0.0158979
$924$	−5.99050e6	+	2.59183e6i	−0.230825	+	0.0998679i
$925$	−2.97788e7	−	2.49853e7i	−1.14433	−	0.960132i
$926$	3.30638e6	+	1.59687e7i	0.126714	+	0.611988i
$927$		−	463455.i		−	0.0177137i
$928$	−2.12771e7	−	1.30437e7i	−0.811039	−	0.497199i
$929$	−1.33528e7			−0.507615			−0.253808	−	0.967255i	$-0.581683\pi$
$929$	−1.33528e7			−0.507615			−0.253808	+	0.967255i	$0.581683\pi$
$930$	147233.	−	1.00914e6i	0.00558210	−	0.0382600i
$931$			2.79075e7i			1.05523i
$932$	−8.70200e6	−	2.01130e7i	−0.328155	−	0.758466i
$933$	−4.83632e7			−1.81891
$934$	7.44102e6	−	1.54069e6i	0.279104	−	0.0577895i
$935$	−6.25018e6	+	1.71733e7i	−0.233810	+	0.642429i
$936$	199461.	−	140153.i	0.00744165	−	0.00522892i
$937$			3.30748e7i			1.23069i	0.788258	+	0.615345i	$0.210983\pi$
$937$			3.30748e7i			1.23069i	−0.788258	+	0.615345i	$0.789017\pi$
$938$	−184158.	−	889423.i	−0.00683415	−	0.0330066i
$939$		−	4.12713e7i		−	1.52751i
$940$	5.34461e7	−	3.17264e6i	1.97286	−	0.117112i
$941$		−	7.79508e6i		−	0.286977i	−0.989652	−	0.143488i	$-0.954168\pi$
$941$		−	7.79508e6i		−	0.286977i	0.989652	−	0.143488i	$-0.0458320\pi$
$942$	3.83459e7	−	7.93966e6i	1.40796	−	0.291524i
$943$		−	2.15472e7i		−	0.789064i
$944$	−1.02345e7	−	9.61351e6i	−0.373798	−	0.351117i
$945$	−3.97072e6	−	1.44513e6i	−0.144641	−	0.0526415i
$946$	1.15484e7	+	5.57749e7i	0.419560	+	2.02634i
$947$	1.39656e7			0.506041			0.253021	−	0.967461i	$-0.418576\pi$
$947$	1.39656e7			0.506041			0.253021	+	0.967461i	$0.418576\pi$
$948$	3.23334e7	−	1.39892e7i	1.16850	−	0.505560i
$949$			5.02332e6i			0.181061i
$950$	−1.42746e7	+	2.65112e7i	−0.513163	+	0.953061i
$951$	−4.23556e7			−1.51866
$952$	−1.60514e6	+	1.12786e6i	−0.0574013	+	0.0403334i
$953$			3.59220e7i			1.28123i	0.767861	+	0.640616i	$0.221321\pi$
$953$			3.59220e7i			1.28123i	−0.767861	+	0.640616i	$0.778679\pi$
$954$	1.72566e6	−	357305.i	0.0613882	−	0.0127107i
$955$	6.31965e6	−	1.73642e7i	0.224225	−	0.616093i
$956$	4.01215e6	−	1.73588e6i	0.141982	−	0.0614293i
$957$	4.27588e7			1.50920
$958$	−3.71155e7	+	7.68491e6i	−1.30660	+	0.270536i
$959$	−2.21400e6			−0.0777377
$960$	2.25246e7	+	1.87740e7i	0.788823	+	0.657473i
$961$	−2.85886e7			−0.998582
$962$	7.00513e6	−	1.45044e6i	0.244050	−	0.0505315i
$963$	−1.56877e6			−0.0545121
$964$	261476.	−	113129.i	0.00906232	−	0.00392087i
$965$	−2.14029e7	−	7.78954e6i	−0.739869	−	0.269273i
$966$	2.82157e6	−	584217.i	0.0972855	−	0.0201433i
$967$		−	1.77704e7i		−	0.611127i	−0.952172	−	0.305563i	$-0.901155\pi$
$967$		−	1.77704e7i		−	0.611127i	0.952172	−	0.305563i	$-0.0988448\pi$
$968$	3.30775e7	−	2.32421e7i	1.13460	−	0.797237i
$969$	1.43772e7			0.491886
$970$	−4.23256e7	−	6.17526e6i	−1.44435	−	0.210730i
$971$		−	1.15077e7i		−	0.391690i	−0.980635	−	0.195845i	$-0.937255\pi$
$971$		−	1.15077e7i		−	0.391690i	0.980635	−	0.195845i	$-0.0627449\pi$
$972$	2.94411e6	−	1.27379e6i	0.0999514	−	0.0432446i
$973$	3.58361e6			0.121350
$974$	8.15453e6	+	3.93836e7i	0.275424	+	1.33020i
$975$	−3.89597e6	−	3.26884e6i	−0.131252	−	0.110124i
$976$	−2.26660e7	−	2.12907e7i	−0.761641	−	0.715428i
$977$			4.95837e7i			1.66189i	0.556354	+	0.830945i	$0.312200\pi$
$977$			4.95837e7i			1.66189i	−0.556354	+	0.830945i	$0.687800\pi$
$978$	1.17019e7	−	2.42292e6i	0.391208	−	0.0810011i
$979$			4.96061e7i			1.65416i
$980$	−1.73681e6	−	2.92582e7i	−0.0577680	−	0.973154i
$981$			2.49309e6i			0.0827115i
$982$	−2.76103e6	−	1.33348e7i	−0.0913676	−	0.441275i
$983$		−	3.00805e7i		−	0.992890i	−0.868068	−	0.496445i	$-0.834638\pi$
$983$		−	3.00805e7i		−	0.992890i	0.868068	−	0.496445i	$-0.165362\pi$
$984$	−3.29968e7	+	2.31854e7i	−1.08639	+	0.763357i
$985$	1.61338e7	−	4.43300e7i	0.529841	−	1.45582i
$986$	1.25845e7	−	2.60567e6i	0.412235	−	0.0853548i
$987$	−9.84687e6			−0.321740
$988$	−2.20032e6	−	5.08561e6i	−0.0717123	−	0.165749i
$989$		−	2.51442e7i		−	0.817423i
$990$	−2.56985e6	−	374938.i	−0.0833335	−	0.0121583i
$991$	−1.83106e7			−0.592270			−0.296135	−	0.955146i	$-0.595698\pi$
$991$	−1.83106e7			−0.592270			−0.296135	+	0.955146i	$0.595698\pi$
$992$	−609930.	+	994928.i	−0.0196789	+	0.0321006i
$993$		−	4.64911e7i		−	1.49622i
$994$	95407.8	+	460788.i	0.00306280	+	0.0147923i
$995$	4.69253e6	−	1.28934e7i	0.150262	−	0.412868i
$996$	3.57176e6	−	1.54535e6i	0.114087	−	0.0493603i
$997$	3.42076e7			1.08990			0.544948	−	0.838470i	$-0.316550\pi$
$997$	3.42076e7			1.08990			0.544948	+	0.838470i	$0.316550\pi$
$998$	5.93528e6	+	2.86654e7i	0.188632	+	0.911028i
$999$	4.57488e7			1.45033

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.f.a.29.2	yes	28
4.3	odd	2		160.6.f.a.49.21		28
5.2	odd	4		200.6.d.e.101.13		28
5.3	odd	4		200.6.d.e.101.16		28
5.4	even	2	inner	40.6.f.a.29.27	yes	28
8.3	odd	2		160.6.f.a.49.7		28
8.5	even	2	inner	40.6.f.a.29.28	yes	28
20.3	even	4		800.6.d.e.401.14		28
20.7	even	4		800.6.d.e.401.15		28
20.19	odd	2		160.6.f.a.49.8		28
40.3	even	4		800.6.d.e.401.13		28
40.13	odd	4		200.6.d.e.101.15		28
40.19	odd	2		160.6.f.a.49.22		28
40.27	even	4		800.6.d.e.401.16		28
40.29	even	2	inner	40.6.f.a.29.1	✓	28
40.37	odd	4		200.6.d.e.101.14		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.f.a.29.1	✓	28	40.29	even	2	inner
40.6.f.a.29.2	yes	28	1.1	even	1	trivial
40.6.f.a.29.27	yes	28	5.4	even	2	inner
40.6.f.a.29.28	yes	28	8.5	even	2	inner
160.6.f.a.49.7		28	8.3	odd	2
160.6.f.a.49.8		28	20.19	odd	2
160.6.f.a.49.21		28	4.3	odd	2
160.6.f.a.49.22		28	40.19	odd	2
200.6.d.e.101.13		28	5.2	odd	4
200.6.d.e.101.14		28	40.37	odd	4
200.6.d.e.101.15		28	40.13	odd	4
200.6.d.e.101.16		28	5.3	odd	4
800.6.d.e.401.13		28	40.3	even	4
800.6.d.e.401.14		28	20.3	even	4
800.6.d.e.401.15		28	20.7	even	4
800.6.d.e.401.16		28	40.27	even	4

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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.53936 + 1.14695i) q^{2} -16.0077 q^{3} +(29.3690 - 12.7067i) q^{4} +(19.1184 - 52.5308i) q^{5} +(88.6724 - 18.3600i) q^{6} -20.5525i q^{7} +(-148.112 + 104.072i) q^{8} +13.2465 q^{9} +O(q^{10})\)	\(q+(-5.53936 + 1.14695i) q^{2} -16.0077 q^{3} +(29.3690 - 12.7067i) q^{4} +(19.1184 - 52.5308i) q^{5} +(88.6724 - 18.3600i) q^{6} -20.5525i q^{7} +(-148.112 + 104.072i) q^{8} +13.2465 q^{9} +(-45.6540 + 312.915i) q^{10} +619.983i q^{11} +(-470.131 + 203.405i) q^{12} -101.664 q^{13} +(23.5726 + 113.848i) q^{14} +(-306.042 + 840.897i) q^{15} +(701.080 - 746.367i) q^{16} +527.303i q^{17} +(-73.3772 + 15.1930i) q^{18} +1703.28i q^{19} +(-106.003 - 1785.71i) q^{20} +328.998i q^{21} +(-711.087 - 3434.31i) q^{22} +1548.24i q^{23} +(2370.93 - 1665.95i) q^{24} +(-2393.97 - 2008.61i) q^{25} +(563.155 - 116.603i) q^{26} +3677.83 q^{27} +(-261.154 - 603.607i) q^{28} +4308.41i q^{29} +(730.815 - 5009.05i) q^{30} +201.464 q^{31} +(-3027.49 + 4938.49i) q^{32} -9924.50i q^{33} +(-604.788 - 2920.92i) q^{34} +(-1079.64 - 392.932i) q^{35} +(389.037 - 168.319i) q^{36} +12439.1 q^{37} +(-1953.57 - 9435.06i) q^{38} +1627.41 q^{39} +(2635.30 + 9770.12i) q^{40} -13917.3 q^{41} +(-377.343 - 1822.44i) q^{42} -16240.5 q^{43} +(7877.94 + 18208.3i) q^{44} +(253.253 - 695.850i) q^{45} +(-1775.75 - 8576.25i) q^{46} +29929.9i q^{47} +(-11222.7 + 11947.6i) q^{48} +16384.6 q^{49} +(15564.8 + 8380.69i) q^{50} -8440.91i q^{51} +(-2985.78 + 1291.82i) q^{52} -23517.7 q^{53} +(-20372.8 + 4218.27i) q^{54} +(32568.2 + 11853.1i) q^{55} +(2138.93 + 3044.06i) q^{56} -27265.5i q^{57} +(-4941.51 - 23865.8i) q^{58} -13712.4i q^{59} +(1696.86 + 28585.1i) q^{60} -30368.5i q^{61} +(-1115.98 + 231.068i) q^{62} -272.249i q^{63} +(11106.2 - 30828.5i) q^{64} +(-1943.66 + 5340.50i) q^{65} +(11382.9 + 54975.4i) q^{66} -7812.39 q^{67} +(6700.28 + 15486.4i) q^{68} -24783.7i q^{69} +(6431.18 + 938.303i) q^{70} +4047.41 q^{71} +(-1961.96 + 1378.59i) q^{72} -49410.9i q^{73} +(-68904.6 + 14267.0i) q^{74} +(38322.0 + 32153.3i) q^{75} +(21643.0 + 50023.6i) q^{76} +12742.2 q^{77} +(-9014.81 + 1866.55i) q^{78} -68775.3 q^{79} +(-25803.7 - 51097.7i) q^{80} -62092.4 q^{81} +(77092.7 - 15962.3i) q^{82} -7597.39 q^{83} +(4180.48 + 9662.35i) q^{84} +(27699.6 + 10081.2i) q^{85} +(89962.0 - 18627.0i) q^{86} -68967.7i q^{87} +(-64522.7 - 91826.8i) q^{88} +80012.0 q^{89} +(-604.756 + 4145.03i) q^{90} +2089.45i q^{91} +(19673.0 + 45470.3i) q^{92} -3224.97 q^{93} +(-34327.9 - 165792. i) q^{94} +(89474.5 + 32564.0i) q^{95} +(48463.2 - 79053.9i) q^{96} +135262. i q^{97} +(-90760.2 + 18792.2i) q^{98} +8212.61i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9}+O(q^{10}) \) 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9	\( 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9} - 16 q^{10} - 692 q^{14} - 488 q^{15} + 1560 q^{16} + 2732 q^{20} - 2224 q^{24} + 1556 q^{25} - 9976 q^{26} - 15012 q^{30} + 4368 q^{31} + 13016 q^{34} - 34116 q^{36} + 23360 q^{39} - 22496 q^{40} - 2480 q^{41} + 10712 q^{44} + 58372 q^{46} - 38420 q^{49} + 45624 q^{50} - 3568 q^{54} - 48776 q^{55} + 110944 q^{56} + 111688 q^{60} - 46944 q^{64} + 37200 q^{65} - 136120 q^{66} - 112852 q^{70} - 69232 q^{71} + 34176 q^{74} - 13944 q^{76} - 35984 q^{79} - 47064 q^{80} + 122596 q^{81} - 165688 q^{84} - 73676 q^{86} - 178744 q^{89} + 51496 q^{90} + 314740 q^{94} + 89416 q^{95} - 236176 q^{96}+O(q^{100}) \) 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9 - 16 * q^10 - 692 * q^14 - 488 * q^15 + 1560 * q^16 + 2732 * q^20 - 2224 * q^24 + 1556 * q^25 - 9976 * q^26 - 15012 * q^30 + 4368 * q^31 + 13016 * q^34 - 34116 * q^36 + 23360 * q^39 - 22496 * q^40 - 2480 * q^41 + 10712 * q^44 + 58372 * q^46 - 38420 * q^49 + 45624 * q^50 - 3568 * q^54 - 48776 * q^55 + 110944 * q^56 + 111688 * q^60 - 46944 * q^64 + 37200 * q^65 - 136120 * q^66 - 112852 * q^70 - 69232 * q^71 + 34176 * q^74 - 13944 * q^76 - 35984 * q^79 - 47064 * q^80 + 122596 * q^81 - 165688 * q^84 - 73676 * q^86 - 178744 * q^89 + 51496 * q^90 + 314740 * q^94 + 89416 * q^95 - 236176 * q^96

Introduction

L-functions

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