LMFDB - Embedded newform 40.6.f.a.29.28

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			29.28
Character	$\chi$	$=$	40.29
Dual form			40.6.f.a.29.27

$q$-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} +(-166.154 + 269.059i) 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} +(-1228.98 + 1299.85i) 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} +(-2659.74 + 4307.02i) 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} +(-8298.63 + 5790.74i) 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} +(-10957.3 - 13872.2i) 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} +(-19673.2 + 20807.6i) 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} +(5529.84 + 3414.88i) 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} +(-52610.8 + 22558.9i) 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} +(-2200.96 + 3564.09i) 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	$-0.328368\pi$
$3$	16.0077			1.02689			0.513447	+	0.858121i	$0.328368\pi$
$4$	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
$10$	−166.154	+	269.059i	−0.525425	+	0.850840i
$11$		−	619.983i		−	1.54489i	−0.635080	−	0.772446i	$-0.719033\pi$
$11$		−	619.983i		−	1.54489i	0.635080	−	0.772446i	$-0.280967\pi$
$12$	470.131	+	203.405i	0.942466	+	0.407764i
$13$	101.664			0.166844			0.0834218	−	0.996514i	$-0.473415\pi$
$13$	101.664			0.166844			0.0834218	+	0.996514i	$0.473415\pi$
$14$	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	$-0.817964\pi$
$19$		−	1703.28i		−	1.08243i	0.840883	−	0.541216i	$-0.182036\pi$
$20$	−1228.98	+	1299.85i	−0.687022	+	0.726636i
$21$		−	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	$-0.842211\pi$
$29$		−	4308.41i		−	0.951310i	0.879632	−	0.475655i	$-0.157789\pi$
$30$	−2659.74	+	4307.02i	−0.539556	+	0.873723i
$31$	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	$-0.768452\pi$
$37$	−12439.1			−1.49377			−0.746886	+	0.664952i	$0.768452\pi$
$38$	1953.57	−	9435.06i	0.219467	−	1.05995i
$39$	1627.41			0.171331
$40$	−8298.63	+	5790.74i	−0.820081	+	0.572248i
$41$	−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	$-0.266411\pi$
$43$	16240.5			1.33946			0.669728	+	0.742606i	$0.266411\pi$
$44$	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
$50$	−10957.3	−	13872.2i	−0.619838	−	0.784730i
$51$			8440.91i			0.454427i
$52$	2985.78	+	1291.82i	0.153126	+	0.0662510i
$53$	23517.7			1.15002			0.575010	−	0.818147i	$-0.304998\pi$
$53$	23517.7			1.15002			0.575010	+	0.818147i	$0.304998\pi$
$54$	−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	$0.0825435\pi$
$59$			13712.4i			0.512843i	−0.966565	+	0.256422i	$0.917456\pi$
$60$	−19673.2	+	20807.6i	−0.705500	+	0.746179i
$61$			30368.5i			1.04496i	0.852653	+	0.522478i	$0.174992\pi$
$61$			30368.5i			1.04496i	−0.852653	+	0.522478i	$0.825008\pi$
$62$	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	$-0.466097\pi$
$67$	7812.39			0.212617			0.106308	+	0.994333i	$0.466097\pi$
$68$	−6700.28	+	15486.4i	−0.175720	+	0.406142i
$69$			24783.7i			0.626678i
$70$	5529.84	+	3414.88i	0.134886	+	0.0832971i
$71$	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	$0.712834\pi$
$80$	−52610.8	+	22558.9i	−0.919073	+	0.394088i
$81$	−62092.4			−1.05154
$82$	−77092.7	−	15962.3i	−1.26613	−	0.262157i
$83$	7597.39			0.121051			0.0605256	−	0.998167i	$-0.480722\pi$
$83$	7597.39			0.121051			0.0605256	+	0.998167i	$0.480722\pi$
$84$	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	$0.320174\pi$
$90$	−2200.96	+	3564.09i	−0.0286422	+	0.0463813i
$91$		−	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
$100$	−44785.7	−	89410.5i	−0.447857	−	0.894105i
$101$		−	74276.1i		−	0.724512i	−0.932079	−	0.362256i	$-0.882007\pi$
$101$		−	74276.1i		−	0.724512i	0.932079	−	0.362256i	$-0.117993\pi$
$102$	−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	$-0.333334\pi$
$107$	118429.			0.999995			0.499998	+	0.866027i	$0.333334\pi$
$108$	−108014.	−	46733.0i	−0.891089	−	0.385535i
$109$		−	188208.i		−	1.51730i	−0.651500	−	0.758649i	$-0.725860\pi$
$109$		−	188208.i		−	1.51730i	0.651500	−	0.758649i	$-0.274140\pi$
$110$	166812.	+	103013.i	1.31446	+	0.811725i
$111$	−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
$120$	−132842.	+	92696.5i	−0.842136	+	0.587638i
$121$	−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
$130$	−16891.9	+	27353.7i	−0.0876638	+	0.141957i
$131$			182659.i			0.929957i	0.885322	+	0.464979i	$0.153938\pi$
$131$			182659.i			0.929957i	−0.885322	+	0.464979i	$0.846062\pi$
$132$	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	$-0.874985\pi$
$139$		−	174364.i		−	0.765455i	0.923861	−	0.382727i	$-0.125015\pi$
$140$	26715.1	+	25258.7i	0.115196	+	0.108916i
$141$			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	$0.125449\pi$
$149$			208118.i			0.767971i	−0.923339	+	0.383986i	$0.874551\pi$
$150$	−175401.	−	222062.i	−0.636508	−	0.805835i
$151$	−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	$-0.746855\pi$
$157$	−432444.			−1.40017			−0.700085	+	0.714059i	$0.746855\pi$
$158$	−380971.	−	78881.5i	−1.21409	−	0.251381i
$159$	376464.			1.18095
$160$	−317304.	+	64620.3i	−0.979886	+	0.199558i
$161$	31820.1			0.0967470
$162$	−343952.	−	71216.7i	−1.02970	−	0.213203i
$163$	−131967.			−0.389043			−0.194521	−	0.980898i	$-0.562315\pi$
$163$	−131967.			−0.389043			−0.194521	+	0.980898i	$0.562315\pi$
$164$	−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
$170$	−141876.	−	87613.5i	−0.376518	−	0.232514i
$171$		−	22562.5i		−	0.0590060i
$172$	476968.	+	206363.i	1.22933	+	0.531877i
$173$	209492.			0.532172			0.266086	−	0.963949i	$-0.414269\pi$
$173$	209492.			0.532172			0.266086	+	0.963949i	$0.414269\pi$
$174$	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	$0.170309\pi$
$179$			437147.i			1.01975i	−0.860248	+	0.509876i	$0.829691\pi$
$180$	−16279.7	+	17218.4i	−0.0374512	+	0.0396107i
$181$		−	559164.i		−	1.26865i	−0.773066	−	0.634326i	$-0.781278\pi$
$181$		−	559164.i		−	1.26865i	0.773066	−	0.634326i	$-0.218722\pi$
$182$	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
$190$	458282.	+	283006.i	0.920977	+	0.568737i
$191$	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	$-0.782058\pi$
$197$	−843885.			−1.54924			−0.774618	+	0.632429i	$0.782058\pi$
$198$	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	$0.429498\pi$
$200$	−145535.	−	546644.i	−0.257273	−	0.966339i
$201$	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
$210$	88520.0	+	54664.3i	0.138514	+	0.0855373i
$211$			73311.6i			0.113362i	0.998392	+	0.0566809i	$0.0180518\pi$
$211$			73311.6i			0.113362i	−0.998392	+	0.0566809i	$0.981948\pi$
$212$	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
$220$	805883.	+	761949.i	1.12257	+	1.06138i
$221$			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	$-0.238764\pi$
$227$	1.13601e6			1.46324			0.731622	+	0.681711i	$0.238764\pi$
$228$	346455.	−	800762.i	0.441377	−	1.02016i
$229$		−	151374.i		−	0.190749i	−0.995441	−	0.0953743i	$-0.969595\pi$
$229$		−	151374.i		−	0.190749i	0.995441	−	0.0953743i	$-0.0304048\pi$
$230$	−416568.	−	257246.i	−0.519238	−	0.320648i
$231$	−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	$0.475354\pi$
$240$	−842178.	+	361116.i	−0.943791	+	0.404687i
$241$	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
$250$	938204.	−	310381.i	0.949396	−	0.314083i
$251$		−	1.22945e6i		−	1.23176i	−0.787840	−	0.615880i	$-0.788800\pi$
$251$		−	1.22945e6i		−	1.23176i	0.787840	−	0.615880i	$-0.211200\pi$
$252$	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
$260$	−124944.	+	132148.i	−0.114625	+	0.121235i
$261$		−	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	$0.0642283\pi$
$269$			475703.i			0.400825i	−0.979712	+	0.200413i	$0.935772\pi$
$270$	611085.	−	989553.i	0.510143	−	0.826094i
$271$	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	$-0.484449\pi$
$277$	124729.			0.0976713			0.0488357	+	0.998807i	$0.484449\pi$
$278$	199986.	−	965865.i	0.155199	−	0.749556i
$279$	2668.69			0.00205252
$280$	119014.	+	170558.i	0.0907201	+	0.130010i
$281$	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	$-0.565956\pi$
$283$	−554357.			−0.411456			−0.205728	+	0.978609i	$0.565956\pi$
$284$	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
$290$	1.15922e6	+	715859.i	0.809413	+	0.499842i
$291$			2.16524e6i			1.49890i
$292$	627849.	−	1.45115e6i	0.430922	−	0.995991i
$293$	1.42856e6			0.972144			0.486072	−	0.873919i	$-0.338429\pi$
$293$	1.42856e6			0.972144			0.486072	+	0.873919i	$0.338429\pi$
$294$	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
$300$	−716917.	−	1.43126e6i	−0.459902	−	0.918152i
$301$		−	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	$-0.295138\pi$
$307$	1.98189e6			1.20015			0.600073	+	0.799945i	$0.295138\pi$
$308$	−374226.	−	161911.i	−0.224780	−	0.0972523i
$309$		−	560061.i		−	0.333687i
$310$	−33474.0	+	54205.7i	−0.0197835	+	0.0320362i
$311$	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	$-0.764911\pi$
$317$	−2.64595e6			−1.47888			−0.739442	+	0.673220i	$0.764911\pi$
$318$	2.08537e6	+	431784.i	1.15642	+	0.239441i
$319$	−2.67114e6			−1.46967
$320$	−1.83178e6	−	5975.64i	−0.999995	−	0.00326219i
$321$	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
$330$	2.67028e6	+	1.64900e6i	1.34981	+	0.833556i
$331$		−	2.90430e6i		−	1.45704i	−0.685026	−	0.728519i	$-0.740209\pi$
$331$		−	2.90430e6i		−	1.45704i	0.685026	−	0.728519i	$-0.259791\pi$
$332$	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
$340$	−685413.	−	648046.i	−0.321555	−	0.304025i
$341$		−	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	$-0.633985\pi$
$347$	−1.83299e6			−0.817214			−0.408607	+	0.912710i	$0.633985\pi$
$348$	876352.	−	2.02552e6i	0.387910	−	0.896577i
$349$			145377.i			0.0638900i	0.999490	+	0.0319450i	$0.0101701\pi$
$349$			145377.i			0.0638900i	−0.999490	+	0.0319450i	$0.989830\pi$
$350$	−285108.	+	225200.i	−0.124405	+	0.0982647i
$351$	−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	$0.706616\pi$
$360$	−109928.	+	76707.1i	−0.0447045	+	0.0311946i
$361$	−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
$370$	2.06680e6	−	3.34685e6i	0.784865	−	1.27096i
$371$		−	483347.i		−	0.182316i
$372$	94714.4	+	40978.8i	0.0354861	+	0.0153533i
$373$	−1.56241e6			−0.581463			−0.290731	−	0.956805i	$-0.593899\pi$
$373$	−1.56241e6			−0.581463			−0.290731	+	0.956805i	$0.593899\pi$
$374$	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	$-0.682932\pi$
$379$		−	4.69434e6i		−	1.67871i	0.543580	−	0.839357i	$-0.317068\pi$
$380$	2.21400e6	+	2.09330e6i	0.786535	+	0.743656i
$381$		−	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	$0.0243114\pi$
$389$			455452.i			0.152605i	−0.997085	+	0.0763024i	$0.975689\pi$
$390$	−270401.	+	437870.i	−0.0900215	+	0.145775i
$391$	−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	$-0.572210\pi$
$397$	−1.41260e6			−0.449824			−0.224912	+	0.974379i	$0.572210\pi$
$398$	1.35961e6	+	281512.i	0.430236	+	0.0890820i
$399$	−560374.			−0.176216
$400$	−179202.	−	3.19498e6i	−0.0560005	−	0.998431i
$401$	−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	$0.424405\pi$
$410$	2.31241e6	−	3.74457e6i	0.679368	−	1.10013i
$411$		−	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	$0.0967386\pi$
$419$			2.15084e6i			0.598513i	−0.954173	+	0.299256i	$0.903261\pi$
$420$	427647.	+	404333.i	0.118294	+	0.111845i
$421$			4.61854e6i			1.26999i	0.772517	+	0.634994i	$0.218997\pi$
$421$			4.61854e6i			1.26999i	−0.772517	+	0.634994i	$0.781003\pi$
$422$	−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
$430$	−2.69842e6	+	4.36966e6i	−0.703784	+	1.13966i
$431$	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	$0.307032\pi$
$440$	3.59016e6	+	5.14501e6i	0.884061	+	1.26694i
$441$	217039.			0.0531423
$442$	−61485.3	+	296953.i	−0.0149698	+	0.0722990i
$443$	2.12572e6			0.514631			0.257315	−	0.966327i	$-0.417162\pi$
$443$	2.12572e6			0.514631			0.257315	+	0.966327i	$0.417162\pi$
$444$	−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	$0.574291\pi$
$450$	−145146.	−	183758.i	−0.0337888	−	0.0427775i
$451$			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
$460$	−2.01247e6	−	1.90276e6i	−0.443440	−	0.419266i
$461$		−	1.38960e6i		−	0.304535i	−0.988339	−	0.152267i	$-0.951343\pi$
$461$		−	1.38960e6i		−	0.304535i	0.988339	−	0.152267i	$-0.0486575\pi$
$462$	−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	$-0.454482\pi$
$467$	1.34330e6			0.285024			0.142512	+	0.989793i	$0.454482\pi$
$468$	39551.2	+	17112.1i	0.00834727	+	0.00361150i
$469$		−	160564.i		−	0.0337067i
$470$	−8.05291e6	−	4.97297e6i	−1.68154	−	1.03841i
$471$	−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	$0.267512\pi$
$480$	−5.07931e6	+	1.03442e6i	−1.00624	+	0.204925i
$481$	−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
$490$	−2.72237e6	+	4.40843e6i	−0.512220	+	0.829456i
$491$		−	2.40729e6i		−	0.450634i	−0.974285	−	0.225317i	$-0.927658\pi$
$491$		−	2.40729e6i		−	0.450634i	0.974285	−	0.225317i	$-0.0723418\pi$
$492$	−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	$0.154009\pi$
$499$			5.17486e6i			0.930351i	−0.885218	+	0.465176i	$0.845991\pi$
$500$	5.55304e6	−	643241.i	0.993358	−	0.115066i
$501$			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	$0.0266601\pi$
$509$			977974.i			0.167314i	−0.996495	+	0.0836571i	$0.973340\pi$
$510$	−2.27110e6	−	1.40249e6i	−0.386644	−	0.238767i
$511$	−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
$520$	−843674.	+	588711.i	−0.136825	+	0.0954759i
$521$	−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	$-0.426933\pi$
$523$	2.84665e6			0.455072			0.227536	+	0.973770i	$0.426933\pi$
$524$	−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
$530$	−3.90756e6	+	6.32765e6i	−0.604249	+	0.978482i
$531$			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
$540$	4.51998e6	−	4.78061e6i	0.667041	−	0.705503i
$541$			2.39581e6i			0.351933i	0.984396	+	0.175966i	$0.0563050\pi$
$541$			2.39581e6i			0.351933i	−0.984396	+	0.175966i	$0.943695\pi$
$542$	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	$-0.609879\pi$
$547$	−4.73593e6			−0.676763			−0.338382	+	0.941009i	$0.609879\pi$
$548$	1.36882e6	−	3.16376e6i	0.194713	−	0.450041i
$549$			402276.i			0.0569631i
$550$	−8.60053e6	+	6.79334e6i	−1.21232	+	0.957583i
$551$	−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	$-0.646495\pi$
$557$	−6.50430e6			−0.888306			−0.444153	+	0.895951i	$0.646495\pi$
$558$	14782.9	+	3060.85i	0.00200989	+	0.000416156i
$559$	1.65108e6			0.223480
$560$	463642.	+	1.08128e6i	0.0624759	+	0.145703i
$561$	5.23322e6			0.702040
$562$	8.13872e6	+	1.68515e6i	1.08696	+	0.225060i
$563$	7.39875e6			0.983756			0.491878	−	0.870664i	$-0.336311\pi$
$563$	7.39875e6			0.983756			0.491878	+	0.870664i	$0.336311\pi$
$564$	−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	$0.678058\pi$
$570$	7.33604e6	+	4.53028e6i	0.945747	+	0.584033i
$571$		−	468744.i		−	0.0601653i	−0.999547	−	0.0300826i	$-0.990423\pi$
$571$		−	468744.i		−	0.0601653i	0.999547	−	0.0300826i	$-0.00957704\pi$
$572$	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
$580$	5.60027e6	+	5.29496e6i	0.691256	+	0.653571i
$581$		−	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	$-0.859864\pi$
$587$	−1.51044e7			−1.80929			−0.904645	+	0.426166i	$0.859864\pi$
$588$	7.70290e6	+	3.33271e6i	0.918779	+	0.397515i
$589$		−	343149.i		−	0.0407562i
$590$	−3.68946e6	−	2.27837e6i	−0.436347	−	0.269460i
$591$	−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	$0.617737\pi$
$600$	−2.32969e6	−	8.75051e6i	−0.264192	−	0.992328i
$601$	−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
$610$	−8.17091e6	−	5.04584e6i	−0.889091	−	0.549046i
$611$			3.04280e6i			0.329739i
$612$	−88755.3	+	205140.i	−0.00957890	+	0.0221397i
$613$	−3.26461e6			−0.350898			−0.175449	−	0.984489i	$-0.556138\pi$
$613$	−3.26461e6			−0.350898			−0.175449	+	0.984489i	$0.556138\pi$
$614$	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	$0.320308\pi$
$619$			1.61077e7i			1.68969i	−0.535011	+	0.844845i	$0.679692\pi$
$620$	−247596.	+	261872.i	−0.0258681	+	0.0273596i
$621$		−	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
$630$	73251.0	+	45235.2i	0.00735296	+	0.00454072i
$631$	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
$640$	−1.01400e7	−	2.13405e6i	−0.978563	−	0.205947i
$641$	−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	$-0.414027\pi$
$643$	5.59471e6			0.533642			0.266821	+	0.963746i	$0.414027\pi$
$644$	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
$650$	−1.11396e6	−	1.41031e6i	−0.103416	−	0.130927i
$651$		−	66281.2i		−	0.00612968i
$652$	−3.87575e6	−	1.67687e6i	−0.357057	−	0.154483i
$653$	−5.04365e6			−0.462873			−0.231436	−	0.972850i	$-0.574343\pi$
$653$	−5.04365e6			−0.462873			−0.231436	+	0.972850i	$0.574343\pi$
$654$	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	$0.102335\pi$
$659$			7.04546e6i			0.631969i	−0.948764	+	0.315984i	$0.897665\pi$
$660$	1.29003e7	+	1.21970e7i	1.15277	+	1.08992i
$661$		−	8.20765e6i		−	0.730660i	−0.930878	−	0.365330i	$-0.880956\pi$
$661$		−	8.20765e6i		−	0.730660i	0.930878	−	0.365330i	$-0.119044\pi$
$662$	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
$670$	−1.29806e6	+	2.10200e6i	−0.111714	+	0.180903i
$671$	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	$-0.301776\pi$
$677$	1.39112e7			1.16652			0.583262	+	0.812284i	$0.301776\pi$
$678$	−4.02834e6	+	1.94555e7i	−0.336552	+	1.62543i
$679$	2.77998e6			0.231402
$680$	−3.05347e6	−	4.37589e6i	−0.253234	−	0.362906i
$681$	1.81849e7			1.50260
$682$	143258.	−	691889.i	0.0117939	−	0.0569608i
$683$	−1.07327e6			−0.0880350			−0.0440175	−	0.999031i	$-0.514016\pi$
$683$	−1.07327e6			−0.0880350			−0.0440175	+	0.999031i	$0.514016\pi$
$684$	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
$690$	−6.66829e6	−	4.11792e6i	−0.533202	−	0.329272i
$691$		−	4.51366e6i		−	0.359611i	−0.983702	−	0.179806i	$-0.942453\pi$
$691$		−	4.51366e6i		−	0.359611i	0.983702	−	0.179806i	$-0.0575469\pi$
$692$	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
$700$	−1.83761e6	+	920458.i	−0.141745	+	0.0710001i
$701$			2.00796e7i			1.54334i	0.636025	+	0.771668i	$0.280577\pi$
$701$			2.00796e7i			1.54334i	−0.636025	+	0.771668i	$0.719423\pi$
$702$	−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	$0.0897986\pi$
$709$			7.45228e6i			0.556767i	−0.960470	+	0.278384i	$0.910201\pi$
$710$	−672492.	+	1.08899e6i	−0.0500658	+	0.0810735i
$711$	−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	$0.819735\pi$
$720$	−696909.	+	298827.i	−0.0501008	+	0.0214827i
$721$	−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
$730$	1.32945e7	+	8.20982e6i	0.923344	+	0.570199i
$731$			8.56367e6i			0.592743i
$732$	−6.17710e6	+	1.42771e7i	−0.426095	+	0.984835i
$733$	−1.28146e7			−0.880936			−0.440468	−	0.897768i	$-0.645187\pi$
$733$	−1.28146e7			−0.880936			−0.440468	+	0.897768i	$0.645187\pi$
$734$	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	$-0.845758\pi$
$739$		−	1.38313e7i		−	0.931648i	0.884878	−	0.465824i	$-0.154242\pi$
$740$	1.52874e7	−	1.61689e7i	1.02625	−	1.08543i
$741$		−	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
$750$	1.50185e7	−	4.96848e6i	0.974929	−	0.322530i
$751$	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	$-0.255285\pi$
$757$	2.19242e7			1.39054			0.695270	+	0.718748i	$0.255285\pi$
$758$	5.38416e6	−	2.60037e7i	0.340365	−	1.64385i
$759$	1.53655e7			0.968149
$760$	9.86323e6	+	1.41349e7i	0.619420	+	0.887682i
$761$	−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	$0.483564\pi$
$770$	2.11717e6	−	3.42840e6i	0.128685	−	0.208384i
$771$		−	1.46692e7i		−	0.888729i
$772$	5.17716e6	−	1.19660e7i	0.312643	−	0.722613i
$773$	−1.17341e7			−0.706320			−0.353160	−	0.935563i	$-0.614893\pi$
$773$	−1.17341e7			−0.706320			−0.353160	+	0.935563i	$0.614893\pi$
$774$	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
$780$	−2.00006e6	+	2.11538e6i	−0.117708	+	0.124495i
$781$		−	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	$-0.455912\pi$
$787$	4.79782e6			0.276126			0.138063	+	0.990423i	$0.455912\pi$
$788$	−2.47841e7	−	1.07230e7i	−1.42186	−	0.615177i
$789$		−	1.31423e7i		−	0.751587i
$790$	1.14273e7	−	1.85046e7i	0.651441	−	1.05490i
$791$	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	$-0.652123\pi$
$797$	−1.64953e7			−0.919845			−0.459922	+	0.887959i	$0.652123\pi$
$798$	−3.10412e6	−	642719.i	−0.172556	−	0.0357284i
$799$	−1.57821e7			−0.874577
$800$	2.67181e6	−	1.79037e7i	0.147598	−	0.989047i
$801$	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	$0.649459\pi$
$810$	1.03169e7	−	1.67065e7i	0.552506	−	0.894693i
$811$		−	1.09892e7i		−	0.586696i	−0.956006	−	0.293348i	$-0.905231\pi$
$811$		−	1.09892e7i		−	0.586696i	0.956006	−	0.293348i	$-0.0947695\pi$
$812$	−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
$820$	1.71041e7	−	1.80903e7i	0.888311	−	0.939531i
$821$		−	3.39298e7i		−	1.75680i	−0.477924	−	0.878401i	$-0.658610\pi$
$821$		−	3.39298e7i		−	1.75680i	0.477924	−	0.878401i	$-0.341390\pi$
$822$	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	$-0.388343\pi$
$827$	1.35172e7			0.687261			0.343631	+	0.939105i	$0.388343\pi$
$828$	−260598.	+	602322.i	−0.0132098	+	0.0305318i
$829$		−	1.89399e7i		−	0.957173i	−0.878040	−	0.478587i	$-0.841149\pi$
$829$		−	1.89399e7i		−	0.957173i	0.878040	−	0.478587i	$-0.158851\pi$
$830$	−1.26234e6	+	2.04415e6i	−0.0636033	+	0.102995i
$831$	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	$0.725767\pi$
$840$	1.90514e6	+	2.73023e6i	0.0931599	+	0.133506i
$841$	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
$850$	7.31485e6	−	5.77781e6i	0.347263	−	0.274294i
$851$		−	1.92587e7i		−	0.911596i
$852$	1.90281e6	+	823262.i	0.0898041	+	0.0388543i
$853$	−3.19230e7			−1.50221			−0.751106	−	0.660182i	$-0.770479\pi$
$853$	−3.19230e7			−1.50221			−0.751106	+	0.660182i	$0.770479\pi$
$854$	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	$-0.940632\pi$
$859$		−	8.02039e6i		−	0.370862i	0.982657	−	0.185431i	$-0.0593682\pi$
$860$	−1.99593e7	+	2.11102e7i	−0.920236	+	0.973297i
$861$			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
$870$	1.85564e7	+	1.14593e7i	0.831181	+	0.513285i
$871$	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	$-0.688068\pi$
$877$	−2.53762e7			−1.11411			−0.557053	+	0.830477i	$0.688068\pi$
$878$	2.54889e7	+	5.27758e6i	1.11587	+	0.231046i
$879$	2.28680e7			0.998290
$880$	1.39861e7	+	3.26178e7i	0.608824	+	1.41987i
$881$	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	$-0.474791\pi$
$883$	3.66593e6			0.158227			0.0791137	+	0.996866i	$0.474791\pi$
$884$	−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
$890$	−1.32943e7	+	2.15280e7i	−0.562588	+	0.911020i
$891$			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
$900$	−593255.	−	1.18438e6i	−0.0244138	−	0.0487398i
$901$			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	$-0.492794\pi$
$907$	1.12158e6			0.0452702			0.0226351	+	0.999744i	$0.492794\pi$
$908$	3.33635e7	+	1.44349e7i	1.34294	+	0.581031i
$909$		−	983899.i		−	0.0394949i
$910$	562186.	+	347171.i	0.0225049	+	0.0138976i
$911$	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	$0.492383\pi$
$920$	−8.96545e6	−	1.28483e7i	−0.349223	−	0.500466i
$921$	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	$0.581683\pi$
$930$	−535842.	+	867709.i	−0.0203156	+	0.0328978i
$931$		−	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
$940$	−3.89042e7	−	3.67833e7i	−1.43608	−	1.35779i
$941$			7.79508e6i			0.286977i	0.989652	+	0.143488i	$0.0458320\pi$
$941$			7.79508e6i			0.286977i	−0.989652	+	0.143488i	$0.954168\pi$
$942$	−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	$-0.581424\pi$
$947$	−1.39656e7			−0.506041			−0.253021	+	0.967461i	$0.581424\pi$
$948$	−3.23334e7	−	1.39892e7i	−1.16850	−	0.505560i
$949$		−	5.02332e6i		−	0.181061i
$950$	−2.36282e7	+	1.86633e7i	−0.849417	+	0.670933i
$951$	−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
$960$	−2.93225e7	−	95656.3i	−1.02689	−	0.00334993i
$961$	−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
$970$	−3.63936e7	−	2.24744e7i	−1.24192	−	0.766934i
$971$			1.15077e7i			0.391690i	0.980635	+	0.195845i	$0.0627449\pi$
$971$			1.15077e7i			0.391690i	−0.980635	+	0.195845i	$0.937255\pi$
$972$	−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
$980$	−2.01364e7	+	2.12975e7i	−0.669756	+	0.708374i
$981$		−	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
$990$	2.20968e6	+	1.36456e6i	0.0716541	+	0.0442490i
$991$	−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	$-0.683450\pi$
$997$	−3.42076e7			−1.08990			−0.544948	+	0.838470i	$0.683450\pi$
$998$	−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.29.28	yes	28
4.3	odd	2		160.6.f.a.49.7		28
5.2	odd	4		200.6.d.e.101.14		28
5.3	odd	4		200.6.d.e.101.15		28
5.4	even	2	inner	40.6.f.a.29.1	✓	28
8.3	odd	2		160.6.f.a.49.21		28
8.5	even	2	inner	40.6.f.a.29.2	yes	28
20.3	even	4		800.6.d.e.401.13		28
20.7	even	4		800.6.d.e.401.16		28
20.19	odd	2		160.6.f.a.49.22		28
40.3	even	4		800.6.d.e.401.14		28
40.13	odd	4		200.6.d.e.101.16		28
40.19	odd	2		160.6.f.a.49.8		28
40.27	even	4		800.6.d.e.401.15		28
40.29	even	2	inner	40.6.f.a.29.27	yes	28
40.37	odd	4		200.6.d.e.101.13		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.f.a.29.1	✓	28	5.4	even	2	inner
40.6.f.a.29.2	yes	28	8.5	even	2	inner
40.6.f.a.29.27	yes	28	40.29	even	2	inner
40.6.f.a.29.28	yes	28	1.1	even	1	trivial
160.6.f.a.49.7		28	4.3	odd	2
160.6.f.a.49.8		28	40.19	odd	2
160.6.f.a.49.21		28	8.3	odd	2
160.6.f.a.49.22		28	20.19	odd	2
200.6.d.e.101.13		28	40.37	odd	4
200.6.d.e.101.14		28	5.2	odd	4
200.6.d.e.101.15		28	5.3	odd	4
200.6.d.e.101.16		28	40.13	odd	4
800.6.d.e.401.13		28	20.3	even	4
800.6.d.e.401.14		28	40.3	even	4
800.6.d.e.401.15		28	40.27	even	4
800.6.d.e.401.16		28	20.7	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} +(-166.154 + 269.059i) 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} +(-1228.98 + 1299.85i) 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} +(-2659.74 + 4307.02i) 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} +(-8298.63 + 5790.74i) 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} +(-10957.3 - 13872.2i) 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} +(-19673.2 + 20807.6i) 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} +(5529.84 + 3414.88i) 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} +(-52610.8 + 22558.9i) 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} +(-2200.96 + 3564.09i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more