LMFDB - Embedded newform 40.6.d.a.21.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(21,40)]

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, 0]))

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

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

chi := DirichletCharacter("40.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.d (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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{4}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.4
Root			$-3.90102 - 0.884346i$ of defining polynomial
Character	$\chi$	$=$	40.21
Dual form			40.6.d.a.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.78536 + 3.01667i) q^{2} -25.4343i q^{3} +(13.7994 - 28.8717i) q^{4} -25.0000i q^{5} +(76.7270 + 121.712i) q^{6} -56.4938 q^{7} +(21.0614 + 179.790i) q^{8} -403.904 q^{9} +O(q^{10})$	\(q+(-4.78536 + 3.01667i) q^{2} -25.4343i q^{3} +(13.7994 - 28.8717i) q^{4} -25.0000i q^{5} +(76.7270 + 121.712i) q^{6} -56.4938 q^{7} +(21.0614 + 179.790i) q^{8} -403.904 q^{9} +(75.4168 + 119.634i) q^{10} +261.019i q^{11} +(-734.333 - 350.978i) q^{12} -720.631i q^{13} +(270.343 - 170.423i) q^{14} -635.858 q^{15} +(-643.154 - 796.825i) q^{16} -1876.44 q^{17} +(1932.83 - 1218.45i) q^{18} +1992.33i q^{19} +(-721.793 - 344.985i) q^{20} +1436.88i q^{21} +(-787.408 - 1249.07i) q^{22} +2570.29 q^{23} +(4572.83 - 535.682i) q^{24} -625.000 q^{25} +(2173.91 + 3448.48i) q^{26} +4092.49i q^{27} +(-779.581 + 1631.07i) q^{28} -1700.16i q^{29} +(3042.81 - 1918.17i) q^{30} -7734.68 q^{31} +(5481.48 + 1872.91i) q^{32} +6638.83 q^{33} +(8979.46 - 5660.61i) q^{34} +1412.35i q^{35} +(-5573.63 + 11661.4i) q^{36} -12228.1i q^{37} +(-6010.20 - 9534.02i) q^{38} -18328.8 q^{39} +(4494.75 - 526.535i) q^{40} +14979.3 q^{41} +(-4334.60 - 6876.00i) q^{42} -18113.9i q^{43} +(7536.06 + 3601.90i) q^{44} +10097.6i q^{45} +(-12299.8 + 7753.73i) q^{46} +2141.03 q^{47} +(-20266.7 + 16358.2i) q^{48} -13615.4 q^{49} +(2990.85 - 1885.42i) q^{50} +47726.0i q^{51} +(-20805.9 - 9944.27i) q^{52} -1605.71i q^{53} +(-12345.7 - 19584.1i) q^{54} +6525.47 q^{55} +(-1189.84 - 10157.0i) q^{56} +50673.5 q^{57} +(5128.81 + 8135.87i) q^{58} -2680.90i q^{59} +(-8774.45 + 18358.3i) q^{60} -44521.9i q^{61} +(37013.2 - 23333.0i) q^{62} +22818.1 q^{63} +(-31880.8 + 7573.26i) q^{64} -18015.8 q^{65} +(-31769.2 + 20027.2i) q^{66} +12486.0i q^{67} +(-25893.8 + 54176.2i) q^{68} -65373.7i q^{69} +(-4260.58 - 6758.59i) q^{70} +8189.38 q^{71} +(-8506.79 - 72617.9i) q^{72} -41082.7 q^{73} +(36888.2 + 58516.0i) q^{74} +15896.4i q^{75} +(57522.0 + 27492.9i) q^{76} -14746.0i q^{77} +(87709.7 - 55291.8i) q^{78} +46325.9 q^{79} +(-19920.6 + 16078.8i) q^{80} +5940.95 q^{81} +(-71681.6 + 45187.8i) q^{82} -61655.4i q^{83} +(41485.3 + 19828.1i) q^{84} +46911.1i q^{85} +(54643.7 + 86681.7i) q^{86} -43242.3 q^{87} +(-46928.5 + 5497.42i) q^{88} +53205.4 q^{89} +(-30461.2 - 48320.7i) q^{90} +40711.2i q^{91} +(35468.5 - 74208.8i) q^{92} +196726. i q^{93} +(-10245.6 + 6458.79i) q^{94} +49808.2 q^{95} +(47636.2 - 139418. i) q^{96} -39211.8 q^{97} +(65154.8 - 41073.3i) q^{98} -105427. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9	\( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9} - 50 q^{10} - 1876 q^{12} + 2708 q^{14} + 900 q^{15} + 3080 q^{16} - 5294 q^{18} - 1900 q^{20} + 13836 q^{22} - 4676 q^{23} + 1032 q^{24} - 12500 q^{25} - 8084 q^{26} + 2108 q^{28} + 5800 q^{30} + 7160 q^{31} + 6792 q^{32} + 5672 q^{33} + 21132 q^{34} + 18344 q^{36} - 19580 q^{38} - 44904 q^{39} + 6200 q^{40} + 11608 q^{41} - 17116 q^{42} + 72296 q^{44} - 28516 q^{46} + 44180 q^{47} - 88856 q^{48} + 18756 q^{49} - 1250 q^{50} - 39680 q^{52} - 100584 q^{54} - 24200 q^{55} - 53624 q^{56} + 5032 q^{57} + 59496 q^{58} - 31300 q^{60} + 59824 q^{62} + 240620 q^{63} - 11264 q^{64} - 56688 q^{66} + 11576 q^{68} + 29800 q^{70} - 200312 q^{71} + 235912 q^{72} - 105136 q^{73} + 78876 q^{74} - 153872 q^{76} + 95864 q^{78} + 282080 q^{79} + 16000 q^{80} + 65172 q^{81} - 223032 q^{82} - 297128 q^{84} + 27452 q^{86} - 332592 q^{87} + 86896 q^{88} - 3160 q^{89} + 51750 q^{90} + 107916 q^{92} + 148820 q^{94} + 144400 q^{95} + 395168 q^{96} + 147376 q^{97} + 216942 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9 - 50 * q^10 - 1876 * q^12 + 2708 * q^14 + 900 * q^15 + 3080 * q^16 - 5294 * q^18 - 1900 * q^20 + 13836 * q^22 - 4676 * q^23 + 1032 * q^24 - 12500 * q^25 - 8084 * q^26 + 2108 * q^28 + 5800 * q^30 + 7160 * q^31 + 6792 * q^32 + 5672 * q^33 + 21132 * q^34 + 18344 * q^36 - 19580 * q^38 - 44904 * q^39 + 6200 * q^40 + 11608 * q^41 - 17116 * q^42 + 72296 * q^44 - 28516 * q^46 + 44180 * q^47 - 88856 * q^48 + 18756 * q^49 - 1250 * q^50 - 39680 * q^52 - 100584 * q^54 - 24200 * q^55 - 53624 * q^56 + 5032 * q^57 + 59496 * q^58 - 31300 * q^60 + 59824 * q^62 + 240620 * q^63 - 11264 * q^64 - 56688 * q^66 + 11576 * q^68 + 29800 * q^70 - 200312 * q^71 + 235912 * q^72 - 105136 * q^73 + 78876 * q^74 - 153872 * q^76 + 95864 * q^78 + 282080 * q^79 + 16000 * q^80 + 65172 * q^81 - 223032 * q^82 - 297128 * q^84 + 27452 * q^86 - 332592 * q^87 + 86896 * q^88 - 3160 * q^89 + 51750 * q^90 + 107916 * q^92 + 148820 * q^94 + 144400 * q^95 + 395168 * q^96 + 147376 * q^97 + 216942 * q^98

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 $

$2$	−4.78536	+	3.01667i	−0.845941	+	0.533277i
$2$	−4.78536	+	3.01667i	−0.845941	+	0.533277i
$3$		−	25.4343i		−	1.63161i	−0.578326	−	0.815806i	$-0.696294\pi$
$3$		−	25.4343i		−	1.63161i	0.578326	−	0.815806i	$-0.303706\pi$
$4$	13.7994	−	28.8717i	0.431231	−	0.902242i
$5$		−	25.0000i		−	0.447214i
$5$		−	25.0000i		−	0.447214i
$6$	76.7270	+	121.712i	0.870101	+	1.38025i
$7$	−56.4938			−0.435769			−0.217884	−	0.975975i	$-0.569916\pi$
$7$	−56.4938			−0.435769			−0.217884	+	0.975975i	$0.569916\pi$
$8$	21.0614	+	179.790i	0.116349	+	0.993208i
$9$	−403.904			−1.66216
$10$	75.4168	+	119.634i	0.238489	+	0.378316i
$11$			261.019i			0.650414i	0.945643	+	0.325207i	$0.105434\pi$
$11$			261.019i			0.650414i	−0.945643	+	0.325207i	$0.894566\pi$
$12$	−734.333	−	350.978i	−1.47211	−	0.703602i
$13$		−	720.631i		−	1.18265i	−0.806435	−	0.591323i	$-0.798606\pi$
$13$		−	720.631i		−	1.18265i	0.806435	−	0.591323i	$-0.201394\pi$
$14$	270.343	−	170.423i	0.368634	−	0.232385i
$15$	−635.858			−0.729679
$16$	−643.154	−	796.825i	−0.628080	−	0.778149i
$17$	−1876.44			−1.57476			−0.787378	−	0.616471i	$-0.788562\pi$
$17$	−1876.44			−1.57476			−0.787378	+	0.616471i	$0.788562\pi$
$18$	1932.83	−	1218.45i	1.40609	−	0.886391i
$19$			1992.33i			1.26613i	0.774100	+	0.633063i	$0.218203\pi$
$19$			1992.33i			1.26613i	−0.774100	+	0.633063i	$0.781797\pi$
$20$	−721.793	−	344.985i	−0.403495	−	0.192852i
$21$			1436.88i			0.711005i
$22$	−787.408	−	1249.07i	−0.346851	−	0.550212i
$23$	2570.29			1.01313			0.506563	−	0.862203i	$-0.330916\pi$
$23$	2570.29			1.01313			0.506563	+	0.862203i	$0.330916\pi$
$24$	4572.83	−	535.682i	1.62053	−	0.189836i
$25$	−625.000			−0.200000
$26$	2173.91	+	3448.48i	0.630678	+	1.00045i
$27$			4092.49i			1.08038i
$28$	−779.581	+	1631.07i	−0.187917	+	0.393169i
$29$		−	1700.16i		−	0.375400i	−0.982226	−	0.187700i	$-0.939897\pi$
$29$		−	1700.16i		−	0.375400i	0.982226	−	0.187700i	$-0.0601032\pi$
$30$	3042.81	−	1918.17i	0.617265	−	0.389121i
$31$	−7734.68			−1.44557			−0.722783	−	0.691075i	$-0.757137\pi$
$31$	−7734.68			−1.44557			−0.722783	+	0.691075i	$0.757137\pi$
$32$	5481.48	+	1872.91i	0.946287	+	0.323327i
$33$	6638.83			1.06122
$34$	8979.46	−	5660.61i	1.33215	−	0.839781i
$35$			1412.35i			0.194882i
$36$	−5573.63	+	11661.4i	−0.716774	+	1.49967i
$37$		−	12228.1i		−	1.46844i	−0.678913	−	0.734218i	$-0.737549\pi$
$37$		−	12228.1i		−	1.46844i	0.678913	−	0.734218i	$-0.262451\pi$
$38$	−6010.20	−	9534.02i	−0.675196	−	1.07107i
$39$	−18328.8			−1.92962
$40$	4494.75	−	526.535i	0.444176	−	0.0520328i
$41$	14979.3			1.39166			0.695830	−	0.718206i	$-0.255037\pi$
$41$	14979.3			1.39166			0.695830	+	0.718206i	$0.255037\pi$
$42$	−4334.60	−	6876.00i	−0.379163	−	0.601468i
$43$		−	18113.9i		−	1.49397i	−0.664842	−	0.746984i	$-0.731501\pi$
$43$		−	18113.9i		−	1.49397i	0.664842	−	0.746984i	$-0.268499\pi$
$44$	7536.06	+	3601.90i	0.586831	+	0.280479i
$45$			10097.6i			0.743340i
$46$	−12299.8	+	7753.73i	−0.857044	+	0.540277i
$47$	2141.03			0.141377			0.0706885	−	0.997498i	$-0.477480\pi$
$47$	2141.03			0.141377			0.0706885	+	0.997498i	$0.477480\pi$
$48$	−20266.7	+	16358.2i	−1.26964	+	1.02478i
$49$	−13615.4			−0.810106
$50$	2990.85	−	1885.42i	0.169188	−	0.106655i
$51$			47726.0i			2.56939i
$52$	−20805.9	−	9944.27i	−1.06703	−	0.509993i
$53$		−	1605.71i		−	0.0785192i	−0.999229	−	0.0392596i	$-0.987500\pi$
$53$		−	1605.71i		−	0.0785192i	0.999229	−	0.0392596i	$-0.0124999\pi$
$54$	−12345.7	−	19584.1i	−0.576144	−	0.913941i
$55$	6525.47			0.290874
$56$	−1189.84	−	10157.0i	−0.0507012	−	0.432809i
$57$	50673.5			2.06583
$58$	5128.81	+	8135.87i	0.200192	+	0.317566i
$59$		−	2680.90i		−	0.100265i	−0.998743	−	0.0501327i	$-0.984036\pi$
$59$		−	2680.90i		−	0.100265i	0.998743	−	0.0501327i	$-0.0159644\pi$
$60$	−8774.45	+	18358.3i	−0.314660	+	0.658347i
$61$		−	44521.9i		−	1.53197i	−0.642860	−	0.765984i	$-0.722252\pi$
$61$		−	44521.9i		−	1.53197i	0.642860	−	0.765984i	$-0.277748\pi$
$62$	37013.2	−	23333.0i	1.22286	−	0.770887i
$63$	22818.1			0.724316
$64$	−31880.8	+	7573.26i	−0.972926	+	0.231117i
$65$	−18015.8			−0.528895
$66$	−31769.2	+	20027.2i	−0.897732	+	0.565926i
$67$			12486.0i			0.339809i	0.985461	+	0.169905i	$0.0543460\pi$
$67$			12486.0i			0.339809i	−0.985461	+	0.169905i	$0.945654\pi$
$68$	−25893.8	+	54176.2i	−0.679083	+	1.42081i
$69$		−	65373.7i		−	1.65303i
$70$	−4260.58	−	6758.59i	−0.103926	−	0.164858i
$71$	8189.38			0.192799			0.0963996	−	0.995343i	$-0.469267\pi$
$71$	8189.38			0.192799			0.0963996	+	0.995343i	$0.469267\pi$
$72$	−8506.79	−	72617.9i	−0.193390	−	1.65087i
$73$	−41082.7			−0.902302			−0.451151	−	0.892448i	$-0.648986\pi$
$73$	−41082.7			−0.902302			−0.451151	+	0.892448i	$0.648986\pi$
$74$	36888.2	+	58516.0i	0.783084	+	1.24221i
$75$			15896.4i			0.326322i
$76$	57522.0	+	27492.9i	1.14235	+	0.545993i
$77$		−	14746.0i		−	0.283430i
$78$	87709.7	−	55291.8i	1.63234	−	1.02902i
$79$	46325.9			0.835134			0.417567	−	0.908646i	$-0.362883\pi$
$79$	46325.9			0.835134			0.417567	+	0.908646i	$0.362883\pi$
$80$	−19920.6	+	16078.8i	−0.347999	+	0.280886i
$81$	5940.95			0.100611
$82$	−71681.6	+	45187.8i	−1.17726	+	0.742141i
$83$		−	61655.4i		−	0.982372i	−0.871055	−	0.491186i	$-0.836564\pi$
$83$		−	61655.4i		−	0.982372i	0.871055	−	0.491186i	$-0.163436\pi$
$84$	41485.3	+	19828.1i	0.641499	+	0.306608i
$85$			46911.1i			0.704252i
$86$	54643.7	+	86681.7i	0.796699	+	1.26381i
$87$	−43242.3			−0.612507
$88$	−46928.5	+	5497.42i	−0.645997	+	0.0756750i
$89$	53205.4			0.712001			0.356000	−	0.934486i	$-0.384140\pi$
$89$	53205.4			0.712001			0.356000	+	0.934486i	$0.384140\pi$
$90$	−30461.2	−	48320.7i	−0.396406	−	0.628821i
$91$			40711.2i			0.515360i
$92$	35468.5	−	74208.8i	0.436891	−	0.914084i
$93$			196726.i			2.35860i
$94$	−10245.6	+	6458.79i	−0.119597	+	0.0753931i
$95$	49808.2			0.566229
$96$	47636.2	−	139418.i	0.527545	−	1.54397i
$97$	−39211.8			−0.423143			−0.211571	−	0.977363i	$-0.567858\pi$
$97$	−39211.8			−0.423143			−0.211571	+	0.977363i	$0.567858\pi$
$98$	65154.8	−	41073.3i	0.685301	−	0.432011i
$99$		−	105427.i		−	1.08109i
$100$	−8624.62	+	18044.8i	−0.0862462	+	0.180448i
$101$			41893.0i			0.408637i	0.978904	+	0.204319i	$0.0654979\pi$
$101$			41893.0i			0.408637i	−0.978904	+	0.204319i	$0.934502\pi$
$102$	−143974.	−	228386.i	−1.37020	−	2.17355i
$103$	−118358.			−1.09927			−0.549635	−	0.835405i	$-0.685233\pi$
$103$	−118358.			−1.09927			−0.549635	+	0.835405i	$0.685233\pi$
$104$	129562.	−	15177.5i	1.17461	−	0.137600i
$105$	35922.0			0.317971
$106$	4843.88	+	7683.88i	0.0418725	+	0.0664226i
$107$			147978.i			1.24951i	0.780822	+	0.624754i	$0.214801\pi$
$107$			147978.i			1.24951i	−0.780822	+	0.624754i	$0.785199\pi$
$108$	118157.	+	56473.9i	0.974768	+	0.465895i
$109$		−	126538.i		−	1.02013i	−0.860135	−	0.510066i	$-0.829621\pi$
$109$		−	126538.i		−	1.02013i	0.860135	−	0.510066i	$-0.170379\pi$
$110$	−31226.7	+	19685.2i	−0.246062	+	0.155116i
$111$	−311014.			−2.39592
$112$	36334.2	+	45015.7i	0.273697	+	0.339093i
$113$	−221898.			−1.63478			−0.817388	−	0.576088i	$-0.804579\pi$
$113$	−221898.			−1.63478			−0.817388	+	0.576088i	$0.804579\pi$
$114$	−242491.	+	152865.i	−1.74757	+	1.10166i
$115$		−	64257.4i		−	0.453084i
$116$	−49086.5	−	23461.1i	−0.338701	−	0.161884i
$117$			291066.i			1.96574i
$118$	8087.40	+	12829.1i	0.0534692	+	0.0848185i
$119$	106007.			0.686229
$120$	−13392.1	−	114321.i	−0.0848974	−	0.724723i
$121$	92920.2			0.576961
$122$	134308.	+	213054.i	0.816963	+	1.29595i
$123$		−	380989.i		−	2.27065i
$124$	−106734.	+	223313.i	−0.623373	+	1.30425i
$125$			15625.0i			0.0894427i
$126$	−109193.	+	68834.7i	−0.612728	+	0.386261i
$127$	237825.			1.30842			0.654212	−	0.756312i	$-0.273001\pi$
$127$	237825.			1.30842			0.654212	+	0.756312i	$0.273001\pi$
$128$	129715.	−	132415.i	0.699788	−	0.714351i
$129$	−460715.			−2.43758
$130$	86212.0	−	54347.7i	0.447414	−	0.282048i
$131$		−	151213.i		−	0.769856i	−0.922947	−	0.384928i	$-0.874226\pi$
$131$		−	151213.i		−	0.769856i	0.922947	−	0.384928i	$-0.125774\pi$
$132$	91611.9	−	191675.i	0.457633	−	0.957480i
$133$		−	112554.i		−	0.551738i
$134$	−37666.1	−	59749.9i	−0.181213	−	0.287458i
$135$	102312.			0.483163
$136$	−39520.5	−	337366.i	−0.183221	−	1.56406i
$137$	163216.			0.742954			0.371477	−	0.928442i	$-0.378852\pi$
$137$	163216.			0.742954			0.371477	+	0.928442i	$0.378852\pi$
$138$	197211.	+	312837.i	0.881522	+	1.39836i
$139$			7490.33i			0.0328824i	0.999865	+	0.0164412i	$0.00523364\pi$
$139$			7490.33i			0.0328824i	−0.999865	+	0.0164412i	$0.994766\pi$
$140$	40776.9	+	19489.5i	0.175830	+	0.0840390i
$141$		−	54455.7i		−	0.230672i
$142$	−39189.2	+	24704.7i	−0.163097	+	0.102815i
$143$	188098.			0.769209
$144$	259772.	+	321841.i	1.04397	+	1.29341i
$145$	−42503.9			−0.167884
$146$	196596.	−	123933.i	0.763294	−	0.481177i
$147$			346300.i			1.32178i
$148$	−353047.	−	168741.i	−1.32488	−	0.633236i
$149$		−	35543.3i		−	0.131157i	−0.997847	−	0.0655786i	$-0.979111\pi$
$149$		−	35543.3i		−	0.131157i	0.997847	−	0.0655786i	$-0.0208893\pi$
$150$	−47954.3	−	76070.3i	−0.174020	−	0.276049i
$151$	549802.			1.96229			0.981147	−	0.193263i	$-0.0619070\pi$
$151$	549802.			1.96229			0.981147	+	0.193263i	$0.0619070\pi$
$152$	−358201.	+	41961.3i	−1.25753	+	0.147312i
$153$	757903.			2.61749
$154$	44483.7	+	70564.7i	0.151147	+	0.239765i
$155$			193367.i			0.646477i
$156$	−252926.	+	529183.i	−0.832111	+	1.74098i
$157$			252420.i			0.817287i	0.912694	+	0.408643i	$0.133998\pi$
$157$			252420.i			0.817287i	−0.912694	+	0.408643i	$0.866002\pi$
$158$	−221686.	+	139750.i	−0.706474	+	0.445358i
$159$	−40840.0			−0.128113
$160$	46822.8	−	137037.i	0.144596	−	0.423192i
$161$	−145206.			−0.441488
$162$	−28429.6	+	17921.9i	−0.0851106	+	0.0536533i
$163$			383218.i			1.12974i	0.825182	+	0.564868i	$0.191073\pi$
$163$			383218.i			1.12974i	−0.825182	+	0.564868i	$0.808927\pi$
$164$	206706.	−	432480.i	0.600127	−	1.25561i
$165$		−	165971.i		−	0.474594i
$166$	185994.	+	295043.i	0.523876	+	0.831028i
$167$	108418.			0.300821			0.150411	−	0.988624i	$-0.451940\pi$
$167$	108418.			0.300821			0.150411	+	0.988624i	$0.451940\pi$
$168$	−258337.	+	30262.8i	−0.706176	+	0.0827247i
$169$	−148016.			−0.398650
$170$	−141515.	−	224487.i	−0.375561	−	0.595755i
$171$		−	804710.i		−	2.10450i
$172$	−522980.	−	249961.i	−1.34792	−	0.644245i
$173$		−	305932.i		−	0.777157i	−0.921416	−	0.388579i	$-0.872966\pi$
$173$		−	305932.i		−	0.777157i	0.921416	−	0.388579i	$-0.127034\pi$
$174$	206930.	−	130448.i	0.518144	−	0.326636i
$175$	35308.6			0.0871537
$176$	207986.	−	167875.i	0.506119	−	0.408512i
$177$	−68186.9			−0.163594
$178$	−254607.	+	160503.i	−0.602311	+	0.379694i
$179$			209868.i			0.489568i	0.969578	+	0.244784i	$0.0787170\pi$
$179$			209868.i			0.489568i	−0.969578	+	0.244784i	$0.921283\pi$
$180$	291535.	+	139341.i	0.670672	+	0.320551i
$181$		−	212990.i		−	0.483239i	−0.970371	−	0.241620i	$-0.922321\pi$
$181$		−	212990.i		−	0.483239i	0.970371	−	0.241620i	$-0.0776786\pi$
$182$	−122812.	−	194818.i	−0.274830	−	0.435964i
$183$	−1.13239e6			−2.49958
$184$	54134.0	+	462113.i	0.117876	+	1.00624i
$185$	−305703.			−0.656705
$186$	−593458.	−	941406.i	−1.25779	−	1.99524i
$187$		−	489787.i		−	1.02424i
$188$	29545.0	−	61815.3i	0.0609662	−	0.127556i
$189$		−	231201.i		−	0.470798i
$190$	−238350.	+	150255.i	−0.478996	+	0.301957i
$191$	−177246.			−0.351555			−0.175777	−	0.984430i	$-0.556244\pi$
$191$	−177246.			−0.351555			−0.175777	+	0.984430i	$0.556244\pi$
$192$	192621.	+	810867.i	0.377094	+	1.58744i
$193$	758117.			1.46502			0.732509	−	0.680758i	$-0.238349\pi$
$193$	758117.			1.46502			0.732509	+	0.680758i	$0.238349\pi$
$194$	187643.	−	118289.i	0.357954	−	0.225652i
$195$			458219.i			0.862952i
$196$	−187885.	+	393101.i	−0.349343	+	0.730911i
$197$			353509.i			0.648985i	0.945888	+	0.324492i	$0.105193\pi$
$197$			353509.i			0.648985i	−0.945888	+	0.324492i	$0.894807\pi$
$198$	318037.	+	504505.i	0.576521	+	0.914539i
$199$	233027.			0.417132			0.208566	−	0.978008i	$-0.433120\pi$
$199$	233027.			0.417132			0.208566	+	0.978008i	$0.433120\pi$
$200$	−13163.4	−	112369.i	−0.0232698	−	0.198642i
$201$	317572.			0.554437
$202$	−126377.	−	200473.i	−0.217917	−	0.345683i
$203$			96048.4i			0.163587i
$204$	1.37793e6	+	658590.i	2.31821	+	1.10800i
$205$		−	374484.i		−	0.622369i
$206$	566385.	−	357047.i	0.929917	−	0.586215i
$207$	−1.03815e6			−1.68397
$208$	−574217.	+	463476.i	−0.920274	+	0.742795i
$209$	−520035.			−0.823507
$210$	−171900.	+	108365.i	−0.268985	+	0.169567i
$211$			401222.i			0.620410i	0.950670	+	0.310205i	$0.100398\pi$
$211$			401222.i			0.620410i	−0.950670	+	0.310205i	$0.899602\pi$
$212$	−46359.5	−	22157.8i	−0.0708433	−	0.0338599i
$213$		−	208291.i		−	0.314573i
$214$	−446402.	−	708130.i	−0.666334	−	1.05701i
$215$	−452848.			−0.668123
$216$	−735789.	+	86193.6i	−1.07305	+	0.125702i
$217$	436961.			0.629932
$218$	381725.	+	605533.i	0.544013	+	0.862971i
$219$			1.04491e6i			1.47221i
$220$	90047.5	−	188402.i	0.125434	−	0.262439i
$221$			1.35222e6i			1.86238i
$222$	1.48831e6	−	938226.i	2.02681	−	1.27769i
$223$	−475659.			−0.640521			−0.320260	−	0.947330i	$-0.603770\pi$
$223$	−475659.			−0.640521			−0.320260	+	0.947330i	$0.603770\pi$
$224$	−309670.	−	105808.i	−0.412362	−	0.140896i
$225$	252440.			0.332432
$226$	1.06186e6	−	669395.i	1.38292	−	0.871789i
$227$			28559.0i			0.0367856i	0.999831	+	0.0183928i	$0.00585494\pi$
$227$			28559.0i			0.0367856i	−0.999831	+	0.0183928i	$0.994145\pi$
$228$	699264.	−	1.46303e6i	0.890849	−	1.86388i
$229$		−	969736.i		−	1.22198i	−0.791638	−	0.610991i	$-0.790771\pi$
$229$		−	969736.i		−	1.22198i	0.791638	−	0.610991i	$-0.209229\pi$
$230$	193843.	+	307495.i	0.241619	+	0.383282i
$231$	−375053.			−0.462448
$232$	305671.	−	35807.7i	0.372850	−	0.0436774i
$233$	−16005.7			−0.0193146			−0.00965728	−	0.999953i	$-0.503074\pi$
$233$	−16005.7			−0.0193146			−0.00965728	+	0.999953i	$0.503074\pi$
$234$	−878050.	−	1.39286e6i	−1.04829	−	1.66290i
$235$		−	53525.8i		−	0.0632257i
$236$	−77402.3	−	36994.8i	−0.0904636	−	0.0432375i
$237$		−	1.17827e6i		−	1.36261i
$238$	−507284.	+	319790.i	−0.580509	+	0.365950i
$239$	1.26598e6			1.43361			0.716807	−	0.697272i	$-0.245603\pi$
$239$	1.26598e6			1.43361			0.716807	+	0.697272i	$0.245603\pi$
$240$	408954.	+	506667.i	0.458297	+	0.567799i
$241$	414590.			0.459807			0.229904	−	0.973213i	$-0.426159\pi$
$241$	414590.			0.459807			0.229904	+	0.973213i	$0.426159\pi$
$242$	−444657.	+	280310.i	−0.488075	+	0.307680i
$243$			843371.i			0.916227i
$244$	−1.28543e6	−	614376.i	−1.38220	−	0.660632i
$245$			340386.i			0.362290i
$246$	1.14932e6	+	1.82317e6i	1.21089	+	1.92083i
$247$	1.43573e6			1.49738
$248$	−162903.	−	1.39062e6i	−0.168190	−	1.43575i
$249$	−1.56816e6			−1.60285
$250$	−47135.5	−	74771.3i	−0.0476978	−	0.0756632i
$251$		−	184150.i		−	0.184496i	−0.995736	−	0.0922479i	$-0.970595\pi$
$251$		−	184150.i		−	0.184496i	0.995736	−	0.0922479i	$-0.0294052\pi$
$252$	314876.	−	658798.i	0.312348	−	0.653508i
$253$			670895.i			0.658951i
$254$	−1.13808e6	+	717440.i	−1.10685	+	0.697752i
$255$	1.19315e6			1.14907
$256$	−221283.	+	1.02496e6i	−0.211032	+	0.977479i
$257$	−846268.			−0.799236			−0.399618	−	0.916682i	$-0.630857\pi$
$257$	−846268.			−0.799236			−0.399618	+	0.916682i	$0.630857\pi$
$258$	2.20469e6	−	1.38983e6i	2.06204	−	1.29990i
$259$			690813.i			0.639899i
$260$	−248607.	+	520147.i	−0.228076	+	0.477191i
$261$			686701.i			0.623974i
$262$	456159.	+	723607.i	0.410547	+	0.651253i
$263$	−1.53385e6			−1.36740			−0.683698	−	0.729765i	$-0.739629\pi$
$263$	−1.53385e6			−1.36740			−0.683698	+	0.729765i	$0.739629\pi$
$264$	139823.	+	1.19360e6i	0.123472	+	1.05402i
$265$	−40142.6			−0.0351149
$266$	339539.	+	538613.i	0.294229	+	0.466738i
$267$		−	1.35324e6i		−	1.16171i
$268$	360492.	+	172299.i	0.306590	+	0.146536i
$269$		−	646714.i		−	0.544918i	−0.962167	−	0.272459i	$-0.912163\pi$
$269$		−	646714.i		−	0.544918i	0.962167	−	0.272459i	$-0.0878370\pi$
$270$	−489601.	+	308642.i	−0.408727	+	0.257660i
$271$	−1.58318e6			−1.30950			−0.654752	−	0.755844i	$-0.727227\pi$
$271$	−1.58318e6			−1.30950			−0.654752	+	0.755844i	$0.727227\pi$
$272$	1.20684e6	+	1.49520e6i	0.989072	+	1.22539i
$273$	1.03546e6			0.840867
$274$	−781049.	+	492369.i	−0.628495	+	0.396200i
$275$		−	163137.i		−	0.130083i
$276$	−1.88745e6	−	902117.i	−1.49143	−	0.712837i
$277$		−	1.62475e6i		−	1.27229i	−0.771568	−	0.636147i	$-0.780527\pi$
$277$		−	1.62475e6i		−	1.27229i	0.771568	−	0.636147i	$-0.219473\pi$
$278$	−22595.9	−	35844.0i	−0.0175355	−	0.0278166i
$279$	3.12407e6			2.40276
$280$	−253926.	+	29746.0i	−0.193558	+	0.0226743i
$281$	−1.48375e6			−1.12097			−0.560487	−	0.828163i	$-0.689386\pi$
$281$	−1.48375e6			−1.12097			−0.560487	+	0.828163i	$0.689386\pi$
$282$	164275.	+	260590.i	0.123012	+	0.195135i
$283$		−	1.18244e6i		−	0.877634i	−0.898577	−	0.438817i	$-0.855398\pi$
$283$		−	1.18244e6i		−	0.877634i	0.898577	−	0.438817i	$-0.144602\pi$
$284$	113008.	−	236442.i	0.0831410	−	0.173951i
$285$		−	1.26684e6i		−	0.923866i
$286$	−900118.	+	567430.i	−0.650705	+	0.410202i
$287$	−846241.			−0.606442
$288$	−2.21399e6	−	756478.i	−1.57288	−	0.537421i
$289$	2.10118e6			1.47985
$290$	203397.	−	128220.i	0.142020	−	0.0895286i
$291$			997325.i			0.690405i
$292$	−566916.	+	1.18613e6i	−0.389101	+	0.814094i
$293$			887981.i			0.604275i	0.953264	+	0.302137i	$0.0977002\pi$
$293$			887981.i			0.604275i	−0.953264	+	0.302137i	$0.902300\pi$
$294$	−1.04467e6	−	1.65717e6i	−0.704874	−	1.11815i
$295$	−67022.6			−0.0448400
$296$	2.19849e6	−	257541.i	1.45846	−	0.170851i
$297$	−1.06822e6			−0.702697
$298$	107223.	+	170088.i	0.0699432	+	0.110951i
$299$		−	1.85223e6i		−	1.19817i
$300$	458958.	+	219361.i	0.294422	+	0.140720i
$301$			1.02332e6i			0.651024i
$302$	−2.63100e6	+	1.65857e6i	−1.65998	+	1.04645i
$303$	1.06552e6			0.666738
$304$	1.58754e6	−	1.28137e6i	0.985235	−	0.795228i
$305$	−1.11305e6			−0.685117
$306$	−3.62684e6	+	2.28635e6i	−2.21424	+	1.39585i
$307$		−	1.47690e6i		−	0.894346i	−0.894447	−	0.447173i	$-0.852431\pi$
$307$		−	1.47690e6i		−	0.894346i	0.894447	−	0.447173i	$-0.147569\pi$
$308$	−425741.	−	203485.i	−0.255722	−	0.122224i
$309$			3.01035e6i			1.79358i
$310$	−583324.	−	925331.i	−0.344751	−	0.546881i
$311$	364521.			0.213708			0.106854	−	0.994275i	$-0.465922\pi$
$311$	364521.			0.213708			0.106854	+	0.994275i	$0.465922\pi$
$312$	−386029.	−	3.29533e6i	−0.224509	−	1.91651i
$313$	324246.			0.187074			0.0935371	−	0.995616i	$-0.470183\pi$
$313$	324246.			0.187074			0.0935371	+	0.995616i	$0.470183\pi$
$314$	−761468.	−	1.20792e6i	−0.435840	−	0.691376i
$315$		−	570453.i		−	0.323924i
$316$	639269.	−	1.33751e6i	0.360136	−	0.753493i
$317$			1.55670e6i			0.870074i	0.900413	+	0.435037i	$0.143265\pi$
$317$			1.55670e6i			0.870074i	−0.900413	+	0.435037i	$0.856735\pi$
$318$	195434.	−	123201.i	0.108376	−	0.0683197i
$319$	443773.			0.244165
$320$	189331.	+	797021.i	0.103359	+	0.435106i
$321$	3.76373e6			2.03871
$322$	694862.	−	438038.i	0.373473	−	0.235436i
$323$		−	3.73849e6i		−	1.99384i
$324$	81981.6	−	171526.i	0.0433864	−	0.0907751i
$325$			450394.i			0.236529i
$326$	−1.15604e6	−	1.83384e6i	−0.602462	−	0.955689i
$327$	−3.21842e6			−1.66446
$328$	315486.	+	2.69314e6i	0.161918	+	1.38221i
$329$	−120955.			−0.0616077
$330$	500679.	+	794231.i	0.253090	+	0.401478i
$331$			558769.i			0.280325i	0.990128	+	0.140163i	$0.0447626\pi$
$331$			558769.i			0.280325i	−0.990128	+	0.140163i	$0.955237\pi$
$332$	−1.78010e6	−	850807.i	−0.886336	−	0.423629i
$333$			4.93899e6i			2.44077i
$334$	−518818.	+	327060.i	−0.254477	+	0.160421i
$335$	312149.			0.151967
$336$	1.14494e6	−	924136.i	0.553268	−	0.446568i
$337$	2.18320e6			1.04717			0.523587	−	0.851972i	$-0.324593\pi$
$337$	2.18320e6			1.04717			0.523587	+	0.851972i	$0.324593\pi$
$338$	708310.	−	446516.i	0.337234	−	0.212591i
$339$			5.64384e6i			2.66732i
$340$	1.35440e6	+	647344.i	0.635405	+	0.303695i
$341$		−	2.01890e6i		−	0.940216i
$342$	2.42755e6	+	3.85083e6i	1.12228	+	1.78028i
$343$	1.71868e6			0.788787
$344$	3.25670e6	−	381505.i	1.48382	−	0.173822i
$345$	−1.63434e6			−0.739257
$346$	922895.	+	1.46399e6i	0.414440	+	0.657429i
$347$		−	2.53924e6i		−	1.13209i	−0.824375	−	0.566043i	$-0.808473\pi$
$347$		−	2.53924e6i		−	1.13209i	0.824375	−	0.566043i	$-0.191527\pi$
$348$	−596718.	+	1.24848e6i	−0.264132	+	0.552629i
$349$		−	2.58452e6i		−	1.13584i	−0.823085	−	0.567918i	$-0.807749\pi$
$349$		−	2.58452e6i		−	1.13584i	0.823085	−	0.567918i	$-0.192251\pi$
$350$	−168965.	+	106515.i	−0.0737269	+	0.0464771i
$351$	2.94918e6			1.27771
$352$	−488865.	+	1.43077e6i	−0.210297	+	0.615479i
$353$	284338.			0.121450			0.0607250	−	0.998155i	$-0.480659\pi$
$353$	284338.			0.121450			0.0607250	+	0.998155i	$0.480659\pi$
$354$	326299.	−	205697.i	0.138391	−	0.0872410i
$355$		−	204734.i		−	0.0862224i
$356$	734202.	−	1.53613e6i	0.307037	−	0.642397i
$357$		−	2.69623e6i		−	1.11966i
$358$	−633102.	−	1.00429e6i	−0.261075	−	0.414145i
$359$	−1.97109e6			−0.807179			−0.403590	−	0.914940i	$-0.632238\pi$
$359$	−1.97109e6			−0.807179			−0.403590	+	0.914940i	$0.632238\pi$
$360$	−1.81545e6	+	212670.i	−0.738291	+	0.0864868i
$361$	−1.49328e6			−0.603077
$362$	642520.	+	1.01923e6i	0.257701	+	0.408792i
$363$		−	2.36336e6i		−	0.941377i
$364$	1.17540e6	+	561790.i	0.464979	+	0.222239i
$365$			1.02707e6i			0.403522i
$366$	5.41887e6	−	3.41603e6i	2.11449	−	1.33297i
$367$	1.04179e6			0.403754			0.201877	−	0.979411i	$-0.435296\pi$
$367$	1.04179e6			0.403754			0.201877	+	0.979411i	$0.435296\pi$
$368$	−1.65309e6	−	2.04807e6i	−0.636324	−	0.788363i
$369$	−6.05022e6			−2.31316
$370$	1.46290e6	−	922205.i	0.555533	−	0.350206i
$371$			90712.4i			0.0342162i
$372$	5.67982e6	+	2.71470e6i	2.12803	+	1.01710i
$373$			1.58767e6i			0.590866i	0.955363	+	0.295433i	$0.0954639\pi$
$373$			1.58767e6i			0.590866i	−0.955363	+	0.295433i	$0.904536\pi$
$374$	1.47753e6	+	2.34381e6i	0.546205	+	0.866449i
$375$	397411.			0.145936
$376$	45093.2	+	384936.i	0.0164491	+	0.140417i
$377$	−1.22519e6			−0.443965
$378$	697456.	+	1.10638e6i	0.251066	+	0.398267i
$379$		−	995922.i		−	0.356145i	−0.984017	−	0.178073i	$-0.943014\pi$
$379$		−	995922.i		−	0.356145i	0.984017	−	0.178073i	$-0.0569862\pi$
$380$	687323.	−	1.43805e6i	0.244176	−	0.510875i
$381$		−	6.04892e6i		−	2.13484i
$382$	848186.	−	534692.i	0.297394	−	0.187476i
$383$	1.53418e6			0.534415			0.267208	−	0.963639i	$-0.413899\pi$
$383$	1.53418e6			0.534415			0.267208	+	0.963639i	$0.413899\pi$
$384$	−3.36788e6	−	3.29922e6i	−1.16554	−	1.14178i
$385$	−368649.			−0.126754
$386$	−3.62786e6	+	2.28699e6i	−1.23932	+	0.781260i
$387$			7.31629e6i			2.48321i
$388$	−541099.	+	1.13211e6i	−0.182472	+	0.381777i
$389$			4.70941e6i			1.57795i	0.614428	+	0.788973i	$0.289387\pi$
$389$			4.70941e6i			1.57795i	−0.614428	+	0.788973i	$0.710613\pi$
$390$	−1.38230e6	−	2.19274e6i	−0.460192	−	0.730006i
$391$	−4.82301e6			−1.59542
$392$	−286760.	−	2.44792e6i	−0.0942549	−	0.804604i
$393$	−3.84599e6			−1.25611
$394$	−1.06642e6	−	1.69167e6i	−0.346089	−	0.549002i
$395$		−	1.15815e6i		−	0.373483i
$396$	−3.04385e6	−	1.45482e6i	−0.975405	−	0.466200i
$397$		−	485420.i		−	0.154576i	−0.997009	−	0.0772879i	$-0.975374\pi$
$397$		−	485420.i		−	0.154576i	0.997009	−	0.0772879i	$-0.0246261\pi$
$398$	−1.11512e6	+	702966.i	−0.352869	+	0.222447i
$399$	−2.86274e6			−0.900223
$400$	401971.	+	498015.i	0.125616	+	0.155630i
$401$	1.73402e6			0.538508			0.269254	−	0.963069i	$-0.413223\pi$
$401$	1.73402e6			0.538508			0.269254	+	0.963069i	$0.413223\pi$
$402$	−1.51970e6	+	958010.i	−0.469021	+	0.295669i
$403$			5.57385e6i			1.70959i
$404$	1.20952e6	+	578098.i	0.368690	+	0.176217i
$405$		−	148524.i		−	0.0449944i
$406$	−289746.	−	459626.i	−0.0872374	−	0.138385i
$407$	3.19177e6			0.955092
$408$	−8.58066e6	+	1.00518e6i	−2.55194	+	0.298946i
$409$	−853587.			−0.252313			−0.126156	−	0.992010i	$-0.540264\pi$
$409$	−853587.			−0.252313			−0.126156	+	0.992010i	$0.540264\pi$
$410$	1.12969e6	+	1.79204e6i	0.331895	+	0.526488i
$411$		−	4.15129e6i		−	1.21221i
$412$	−1.63327e6	+	3.41720e6i	−0.474039	+	0.991807i
$413$			151454.i			0.0436925i
$414$	4.96794e6	−	3.13177e6i	1.42454	−	0.898025i
$415$	−1.54138e6			−0.439330
$416$	1.34968e6	−	3.95012e6i	0.382382	−	1.11912i
$417$	190511.			0.0536514
$418$	2.48856e6	−	1.56878e6i	0.696638	−	0.439157i
$419$			3.86903e6i			1.07663i	0.842743	+	0.538316i	$0.180939\pi$
$419$			3.86903e6i			1.07663i	−0.842743	+	0.538316i	$0.819061\pi$
$420$	495702.	−	1.03713e6i	0.137119	−	0.286887i
$421$		−	1.15014e6i		−	0.316260i	−0.987418	−	0.158130i	$-0.949454\pi$
$421$		−	1.15014e6i		−	0.316260i	0.987418	−	0.158130i	$-0.0505464\pi$
$422$	−1.21036e6	−	1.91999e6i	−0.330851	−	0.524830i
$423$	−864773.			−0.234991
$424$	288690.	−	33818.4i	0.0779860	−	0.00913563i
$425$	1.17278e6			0.314951
$426$	628346.	+	996749.i	0.167755	+	0.266110i
$427$			2.51522e6i			0.667583i
$428$	4.27239e6	+	2.04201e6i	1.12736	+	0.538826i
$429$		−	4.78415e6i		−	1.25505i
$430$	2.16704e6	−	1.36609e6i	0.565192	−	0.356295i
$431$	−3.09078e6			−0.801448			−0.400724	−	0.916199i	$-0.631241\pi$
$431$	−3.09078e6			−0.801448			−0.400724	+	0.916199i	$0.631241\pi$
$432$	3.26100e6	−	2.63210e6i	0.840700	−	0.678567i
$433$	2.47892e6			0.635394			0.317697	−	0.948192i	$-0.397090\pi$
$433$	2.47892e6			0.635394			0.317697	+	0.948192i	$0.397090\pi$
$434$	−2.09102e6	+	1.31817e6i	−0.532885	+	0.335928i
$435$			1.08106e6i			0.273921i
$436$	−3.65338e6	−	1.74615e6i	−0.920405	−	0.439913i
$437$			5.12087e6i			1.28275i
$438$	−3.15215e6	−	5.00028e6i	−0.785094	−	1.24540i
$439$	997159.			0.246947			0.123473	−	0.992348i	$-0.460597\pi$
$439$	997159.			0.246947			0.123473	+	0.992348i	$0.460597\pi$
$440$	137436.	+	1.17321e6i	0.0338429	+	0.288899i
$441$	5.49934e6			1.34652
$442$	−4.07921e6	−	6.47088e6i	−0.993163	−	1.57546i
$443$		−	2.10966e6i		−	0.510744i	−0.966843	−	0.255372i	$-0.917802\pi$
$443$		−	2.10966e6i		−	0.510744i	0.966843	−	0.255372i	$-0.0821980\pi$
$444$	−4.29180e6	+	8.97951e6i	−1.03319	+	2.16170i
$445$		−	1.33013e6i		−	0.318416i
$446$	2.27620e6	−	1.43491e6i	0.541843	−	0.341575i
$447$	−904020.			−0.213998
$448$	1.80107e6	−	427842.i	0.423971	−	0.100714i
$449$	6.24963e6			1.46298			0.731490	−	0.681852i	$-0.238825\pi$
$449$	6.24963e6			1.46298			0.731490	+	0.681852i	$0.238825\pi$
$450$	−1.20802e6	+	761529.i	−0.281217	+	0.177278i
$451$			3.90989e6i			0.905156i
$452$	−3.06206e6	+	6.40659e6i	−0.704966	+	1.47496i
$453$		−	1.39838e7i		−	3.20170i
$454$	−86153.0	−	136665.i	−0.0196169	−	0.0311184i
$455$	1.01778e6			0.230476
$456$	1.06726e6	+	9.11059e6i	0.240357	+	2.05180i
$457$	1.87669e6			0.420340			0.210170	−	0.977665i	$-0.432598\pi$
$457$	1.87669e6			0.420340			0.210170	+	0.977665i	$0.432598\pi$
$458$	2.92537e6	+	4.64054e6i	0.651655	+	1.03372i
$459$		−	7.67933e6i		−	1.70134i
$460$	−1.85522e6	−	886713.i	−0.408791	−	0.195384i
$461$			8.54777e6i			1.87327i	0.350307	+	0.936635i	$0.386077\pi$
$461$			8.54777e6i			1.87327i	−0.350307	+	0.936635i	$0.613923\pi$
$462$	1.79477e6	−	1.13141e6i	0.391204	−	0.246613i
$463$	−7.55869e6			−1.63868			−0.819340	−	0.573308i	$-0.805660\pi$
$463$	−7.55869e6			−1.63868			−0.819340	+	0.573308i	$0.805660\pi$
$464$	−1.35473e6	+	1.09346e6i	−0.292117	+	0.235781i
$465$	4.91815e6			1.05480
$466$	76593.1	−	48283.9i	0.0163390	−	0.0103000i
$467$		−	3.29127e6i		−	0.698346i	−0.937058	−	0.349173i	$-0.886462\pi$
$467$		−	3.29127e6i		−	0.698346i	0.937058	−	0.349173i	$-0.113538\pi$
$468$	8.40358e6	+	4.01653e6i	1.77358	+	0.847689i
$469$		−	705380.i		−	0.148078i
$470$	161470.	+	256141.i	0.0337168	+	0.0534852i
$471$	6.42013e6			1.33349
$472$	481999.	−	56463.6i	0.0995844	−	0.0116658i
$473$	4.72807e6			0.971698
$474$	3.55445e6	+	5.63844e6i	0.726651	+	1.15269i
$475$		−	1.24521e6i		−	0.253225i
$476$	1.46284e6	−	3.06062e6i	0.295923	−	0.619144i
$477$			648551.i			0.130511i
$478$	−6.05817e6	+	3.81905e6i	−1.21275	+	0.764513i
$479$	4.95610e6			0.986965			0.493482	−	0.869756i	$-0.335724\pi$
$479$	4.95610e6			0.986965			0.493482	+	0.869756i	$0.335724\pi$
$480$	−3.48544e6	−	1.19091e6i	−0.690486	−	0.235925i
$481$	−8.81196e6			−1.73664
$482$	−1.98396e6	+	1.25068e6i	−0.388970	+	0.245205i
$483$			3.69321e6i			0.720338i
$484$	1.28224e6	−	2.68277e6i	0.248804	−	0.520559i
$485$			980294.i			0.189235i
$486$	−2.54417e6	−	4.03584e6i	−0.488603	−	0.775074i
$487$	−7.56942e6			−1.44624			−0.723120	−	0.690723i	$-0.757293\pi$
$487$	−7.56942e6			−1.44624			−0.723120	+	0.690723i	$0.757293\pi$
$488$	8.00460e6	−	937695.i	1.52156	−	0.178243i
$489$	9.74688e6			1.84329
$490$	−1.02683e6	−	1.62887e6i	−0.193201	−	0.306476i
$491$		−	1.25015e6i		−	0.234023i	−0.993131	−	0.117012i	$-0.962668\pi$
$491$		−	1.25015e6i		−	0.234023i	0.993131	−	0.117012i	$-0.0373315\pi$
$492$	−1.09998e7	−	5.25742e6i	−2.04867	−	0.979175i
$493$			3.19025e6i			0.591163i
$494$	−6.87051e6	+	4.33114e6i	−1.26669	+	0.798518i
$495$	−2.63567e6			−0.483479
$496$	4.97458e6	+	6.16318e6i	0.907930	+	1.12487i
$497$	−462649.			−0.0840158
$498$	7.50423e6	−	4.73063e6i	1.35592	−	0.854763i
$499$		−	5.59295e6i		−	1.00552i	−0.864427	−	0.502758i	$-0.832319\pi$
$499$		−	5.59295e6i		−	1.00552i	0.864427	−	0.502758i	$-0.167681\pi$
$500$	451121.	+	215616.i	0.0806989	+	0.0385705i
$501$		−	2.75753e6i		−	0.490824i
$502$	555519.	+	881223.i	0.0983874	+	0.156073i
$503$	9.76813e6			1.72144			0.860719	−	0.509080i	$-0.170014\pi$
$503$	9.76813e6			1.72144			0.860719	+	0.509080i	$0.170014\pi$
$504$	480581.	+	4.10247e6i	0.0842734	+	0.719397i
$505$	1.04733e6			0.182748
$506$	−2.02387e6	−	3.21048e6i	−0.351404	−	0.557434i
$507$			3.76469e6i			0.650443i
$508$	3.28184e6	−	6.86642e6i	0.564233	−	1.18051i
$509$		−	9.05091e6i		−	1.54845i	−0.632909	−	0.774226i	$-0.718139\pi$
$509$		−	9.05091e6i		−	1.54845i	0.632909	−	0.774226i	$-0.281861\pi$
$510$	−5.70966e6	+	3.59934e6i	−0.972042	+	0.612771i
$511$	2.32092e6			0.393195
$512$	−2.03305e6	−	5.57235e6i	−0.342747	−	0.939428i
$513$	−8.15359e6			−1.36790
$514$	4.04970e6	−	2.55291e6i	0.676106	−	0.426214i
$515$			2.95895e6i			0.491608i
$516$	−6.35759e6	+	1.33016e7i	−1.05116	+	2.19928i
$517$			558850.i			0.0919536i
$518$	−2.08396e6	−	3.30579e6i	−0.341243	−	0.541316i
$519$	−7.78116e6			−1.26802
$520$	−379438.	−	3.23905e6i	−0.0615364	−	0.525303i
$521$	−7.68287e6			−1.24002			−0.620011	−	0.784593i	$-0.712872\pi$
$521$	−7.68287e6			−1.24002			−0.620011	+	0.784593i	$0.712872\pi$
$522$	−2.07155e6	−	3.28611e6i	−0.332751	−	0.527845i
$523$			8.45353e6i			1.35140i	0.737177	+	0.675700i	$0.236159\pi$
$523$			8.45353e6i			1.35140i	−0.737177	+	0.675700i	$0.763841\pi$
$524$	−4.36577e6	−	2.08664e6i	−0.694596	−	0.331986i
$525$		−	898051.i		−	0.142201i
$526$	7.34004e6	−	4.62713e6i	1.15674	−	0.729201i
$527$	1.45137e7			2.27641
$528$	−4.26979e6	−	5.28999e6i	−0.666533	−	0.825790i
$529$	170070.			0.0264234
$530$	192097.	−	121097.i	0.0297051	−	0.0187260i
$531$			1.08283e6i			0.166657i
$532$	−3.24964e6	−	1.55318e6i	−0.497801	−	0.237927i
$533$		−	1.07946e7i		−	1.64584i
$534$	4.08229e6	+	6.47576e6i	0.619513	+	0.982737i
$535$	3.69946e6			0.558797
$536$	−2.24485e6	+	262972.i	−0.337501	+	0.0395365i
$537$	5.33784e6			0.798785
$538$	1.95092e6	+	3.09476e6i	0.290592	+	0.460969i
$539$		−	3.55389e6i		−	0.526904i
$540$	1.41185e6	−	2.95393e6i	0.208355	−	0.435929i
$541$			4.67406e6i			0.686596i	0.939227	+	0.343298i	$0.111544\pi$
$541$			4.67406e6i			0.686596i	−0.939227	+	0.343298i	$0.888456\pi$
$542$	7.57609e6	−	4.77593e6i	1.10776	−	0.698329i
$543$	−5.41725e6			−0.788459
$544$	−1.02857e7	−	3.51441e6i	−1.49017	−	0.509162i
$545$	−3.16346e6			−0.456217
$546$	−4.95506e6	+	3.12365e6i	−0.711324	+	0.448415i
$547$			1.86478e6i			0.266477i	0.991084	+	0.133238i	$0.0425376\pi$
$547$			1.86478e6i			0.266477i	−0.991084	+	0.133238i	$0.957462\pi$
$548$	2.25228e6	−	4.71233e6i	0.320385	−	0.670324i
$549$			1.79826e7i			2.54637i
$550$	492130.	+	780668.i	0.0693702	+	0.110042i
$551$	3.38727e6			0.475304
$552$	1.17535e7	−	1.37686e6i	1.64180	−	0.192328i
$553$	−2.61713e6			−0.363925
$554$	4.90134e6	+	7.77503e6i	0.678486	+	1.07629i
$555$			7.77534e6i			1.07149i
$556$	216259.	+	103362.i	0.0296679	+	0.0141799i
$557$			9.40472e6i			1.28442i	0.766528	+	0.642211i	$0.221983\pi$
$557$			9.40472e6i			1.28442i	−0.766528	+	0.642211i	$0.778017\pi$
$558$	−1.49498e7	+	9.42429e6i	−2.03259	+	1.28134i
$559$	−1.30535e7			−1.76683
$560$	1.12539e6	−	908355.i	0.151647	−	0.122401i
$561$	−1.24574e7			−1.67117
$562$	7.10029e6	−	4.47599e6i	0.948277	−	0.597790i
$563$			849619.i			0.112967i	0.998404	+	0.0564837i	$0.0179889\pi$
$563$			849619.i			0.112967i	−0.998404	+	0.0564837i	$0.982011\pi$
$564$	−1.57223e6	−	751456.i	−0.208122	−	0.0994731i
$565$			5.54746e6i			0.731094i
$566$	3.56703e6	+	5.65841e6i	0.468022	+	0.742426i
$567$	−335627.			−0.0438429
$568$	172480.	+	1.47237e6i	0.0224320	+	0.191490i
$569$	−5.41948e6			−0.701741			−0.350870	−	0.936424i	$-0.614114\pi$
$569$	−5.41948e6			−0.701741			−0.350870	+	0.936424i	$0.614114\pi$
$570$	3.82163e6	+	6.06228e6i	0.492677	+	0.781536i
$571$		−	331372.i		−	0.0425329i	−0.999774	−	0.0212664i	$-0.993230\pi$
$571$		−	331372.i		−	0.0425329i	0.999774	−	0.0212664i	$-0.00676983\pi$
$572$	2.59564e6	−	5.43072e6i	0.331707	−	0.694013i
$573$			4.50813e6i			0.573601i
$574$	4.04957e6	−	2.55283e6i	0.513014	−	0.323402i
$575$	−1.60643e6			−0.202625
$576$	1.28768e7	−	3.05887e6i	1.61716	−	0.384154i
$577$	−1.51001e7			−1.88817			−0.944086	−	0.329701i	$-0.893052\pi$
$577$	−1.51001e7			−1.88817			−0.944086	+	0.329701i	$0.893052\pi$
$578$	−1.00549e7	+	6.33857e6i	−1.25187	+	0.789173i
$579$		−	1.92822e7i		−	2.39034i
$580$	−586528.	+	1.22716e6i	−0.0723967	+	0.151472i
$581$			3.48315e6i			0.428087i
$582$	−3.00860e6	−	4.77256e6i	−0.368177	−	0.584042i
$583$	419119.			0.0510700
$584$	−865260.	−	7.38626e6i	−0.104982	−	0.896174i
$585$	7.27665e6			0.879107
$586$	−2.67875e6	−	4.24931e6i	−0.322246	−	0.511181i
$587$		−	1.51509e7i		−	1.81486i	−0.420199	−	0.907432i	$-0.638040\pi$
$587$		−	1.51509e7i		−	1.81486i	0.420199	−	0.907432i	$-0.361960\pi$
$588$	9.99827e6	+	4.77872e6i	1.19256	+	0.569992i
$589$		−	1.54100e7i		−	1.83027i
$590$	320727.	−	202185.i	0.0379320	−	0.0239122i
$591$	8.99125e6			1.05889
$592$	−9.74367e6	+	7.86456e6i	−1.14266	+	0.922295i
$593$	−1.46568e7			−1.71160			−0.855800	−	0.517307i	$-0.826934\pi$
$593$	−1.46568e7			−1.71160			−0.855800	+	0.517307i	$0.826934\pi$
$594$	5.11181e6	−	3.22246e6i	0.594440	−	0.374732i
$595$		−	2.65019e6i		−	0.306891i
$596$	−1.02620e6	−	490476.i	−0.118336	−	0.0565591i
$597$		−	5.92688e6i		−	0.680597i
$598$	5.58758e6	+	8.86361e6i	0.638956	+	1.01358i
$599$	−5.14552e6			−0.585952			−0.292976	−	0.956120i	$-0.594646\pi$
$599$	−5.14552e6			−0.585952			−0.292976	+	0.956120i	$0.594646\pi$
$600$	−2.85802e6	+	334802.i	−0.324106	+	0.0379673i
$601$	9.03954e6			1.02085			0.510423	−	0.859923i	$-0.329489\pi$
$601$	9.03954e6			1.02085			0.510423	+	0.859923i	$0.329489\pi$
$602$	−3.08703e6	−	4.89698e6i	−0.347176	−	0.550728i
$603$		−	5.04314e6i		−	0.564817i
$604$	7.58694e6	−	1.58737e7i	0.846202	−	1.77046i
$605$		−	2.32301e6i		−	0.258025i
$606$	−5.09890e6	+	3.21432e6i	−0.564021	+	0.355556i
$607$	1.25949e7			1.38747			0.693733	−	0.720232i	$-0.255965\pi$
$607$	1.25949e7			1.38747			0.693733	+	0.720232i	$0.255965\pi$
$608$	−3.73146e6	+	1.09209e7i	−0.409373	+	1.19812i
$609$	2.44292e6			0.266911
$610$	5.32634e6	−	3.35770e6i	0.579568	−	0.365357i
$611$		−	1.54290e6i		−	0.167199i
$612$	1.04586e7	−	2.18820e7i	1.12874	−	2.36161i
$613$		−	8.66424e6i		−	0.931278i	−0.884975	−	0.465639i	$-0.845825\pi$
$613$		−	8.66424e6i		−	0.931278i	0.884975	−	0.465639i	$-0.154175\pi$
$614$	4.45533e6	+	7.06751e6i	0.476934	+	0.756564i
$615$	−9.52474e6			−1.01547
$616$	2.65117e6	−	310570.i	0.281505	−	0.0329768i
$617$	6.86089e6			0.725551			0.362775	−	0.931877i	$-0.381829\pi$
$617$	6.86089e6			0.725551			0.362775	+	0.931877i	$0.381829\pi$
$618$	−9.08124e6	−	1.44056e7i	−0.956476	−	1.51726i
$619$			3.44552e6i			0.361434i	0.983535	+	0.180717i	$0.0578417\pi$
$619$			3.44552e6i			0.361434i	−0.983535	+	0.180717i	$0.942158\pi$
$620$	5.58284e6	+	2.66835e6i	0.583278	+	0.278781i
$621$			1.05189e7i			1.09457i
$622$	−1.74436e6	+	1.09964e6i	−0.180785	+	0.113966i
$623$	−3.00578e6			−0.310268
$624$	1.17882e7	+	1.46048e7i	1.21195	+	1.50153i
$625$	390625.			0.0400000
$626$	−1.55164e6	+	978144.i	−0.158254	+	0.0997624i
$627$			1.32267e7i			1.34364i
$628$	7.28780e6	+	3.48324e6i	0.737390	+	0.352439i
$629$			2.29454e7i			2.31243i
$630$	1.72087e6	+	2.72982e6i	0.172741	+	0.274021i
$631$	−7.79725e6			−0.779593			−0.389797	−	0.920901i	$-0.627455\pi$
$631$	−7.79725e6			−0.779593			−0.389797	+	0.920901i	$0.627455\pi$
$632$	975689.	+	8.32893e6i	0.0971670	+	0.829462i
$633$	1.02048e7			1.01227
$634$	−4.69604e6	−	7.44936e6i	−0.463990	−	0.736031i
$635$		−	5.94563e6i		−	0.585145i
$636$	−563567.	+	1.17912e6i	−0.0552463	+	0.115589i
$637$			9.81171e6i			0.958068i
$638$	−2.12361e6	+	1.33872e6i	−0.206549	+	0.130208i
$639$	−3.30773e6			−0.320463
$640$	−3.31037e6	−	3.24288e6i	−0.319467	−	0.312955i
$641$	7.82134e6			0.751859			0.375929	−	0.926648i	$-0.377324\pi$
$641$	7.82134e6			0.751859			0.375929	+	0.926648i	$0.377324\pi$
$642$	−1.80108e7	+	1.13539e7i	−1.72463	+	1.08720i
$643$			1.35325e7i			1.29078i	0.763854	+	0.645389i	$0.223305\pi$
$643$			1.35325e7i			1.29078i	−0.763854	+	0.645389i	$0.776695\pi$
$644$	−2.00375e6	+	4.19234e6i	−0.190383	+	0.398329i
$645$			1.15179e7i			1.09012i
$646$	1.12778e7	+	1.78900e7i	1.06327	+	1.68667i
$647$	−1.34237e6			−0.126070			−0.0630352	−	0.998011i	$-0.520078\pi$
$647$	−1.34237e6			−0.126070			−0.0630352	+	0.998011i	$0.520078\pi$
$648$	125125.	+	1.06812e6i	0.0117059	+	0.0999273i
$649$	699766.			0.0652140
$650$	−1.35869e6	−	2.15530e6i	−0.126136	−	0.200090i
$651$		−	1.11138e7i		−	1.02780i
$652$	1.10642e7	+	5.28817e6i	1.01929	+	0.487177i
$653$		−	5.36490e6i		−	0.492355i	−0.969225	−	0.246178i	$-0.920825\pi$
$653$		−	5.36490e6i		−	0.492355i	0.969225	−	0.246178i	$-0.0791747\pi$
$654$	1.54013e7	−	9.70891e6i	1.40803	−	0.887618i
$655$	−3.78031e6			−0.344290
$656$	−9.63402e6	−	1.19359e7i	−0.874074	−	1.08292i
$657$	1.65935e7			1.49977
$658$	578815.	−	364882.i	0.0521164	−	0.0328540i
$659$			8.49067e6i			0.761603i	0.924657	+	0.380801i	$0.124352\pi$
$659$			8.49067e6i			0.761603i	−0.924657	+	0.380801i	$0.875648\pi$
$660$	−4.79186e6	−	2.29030e6i	−0.428198	−	0.204659i
$661$		−	9.80254e6i		−	0.872640i	−0.899792	−	0.436320i	$-0.856282\pi$
$661$		−	9.80254e6i		−	0.872640i	0.899792	−	0.436320i	$-0.143718\pi$
$662$	−1.68562e6	−	2.67391e6i	−0.149491	−	0.237139i
$663$	3.43929e7			3.03868
$664$	1.10850e7	−	1.29855e6i	0.975700	−	0.114298i
$665$	−2.81386e6			−0.246745
$666$	−1.48993e7	−	2.36349e7i	−1.30161	−	2.06475i
$667$		−	4.36990e6i		−	0.380327i
$668$	1.49610e6	−	3.13020e6i	0.129723	−	0.271413i
$669$			1.20981e7i			1.04508i
$670$	−1.49375e6	+	941652.i	−0.128555	+	0.0810407i
$671$	1.16211e7			0.996413
$672$	−2.69115e6	+	7.87624e6i	−0.229888	+	0.672815i
$673$	7.99241e6			0.680205			0.340103	−	0.940388i	$-0.389538\pi$
$673$	7.99241e6			0.680205			0.340103	+	0.940388i	$0.389538\pi$
$674$	−1.04474e7	+	6.58600e6i	−0.885848	+	0.558434i
$675$		−	2.55781e6i		−	0.216077i
$676$	−2.04253e6	+	4.27348e6i	−0.171910	+	0.359679i
$677$		−	8.50891e6i		−	0.713514i	−0.934197	−	0.356757i	$-0.883882\pi$
$677$		−	8.50891e6i		−	0.713514i	0.934197	−	0.356757i	$-0.116118\pi$
$678$	−1.70256e7	−	2.70078e7i	−1.42242	−	2.25639i
$679$	2.21522e6			0.184392
$680$	−8.43414e6	+	988013.i	−0.699469	+	0.0819390i
$681$	726378.			0.0600198
$682$	6.09034e6	+	9.66115e6i	0.501396	+	0.795367i
$683$		−	1.39302e7i		−	1.14263i	−0.820732	−	0.571314i	$-0.806434\pi$
$683$		−	1.39302e7i		−	1.14263i	0.820732	−	0.571314i	$-0.193566\pi$
$684$	−2.32334e7	−	1.11045e7i	−1.89877	−	0.907527i
$685$		−	4.08040e6i		−	0.332259i
$686$	−8.22451e6	+	5.18469e6i	−0.667267	+	0.420642i
$687$	−2.46646e7			−1.99380
$688$	−1.44336e7	+	1.16500e7i	−1.16253	+	0.938331i
$689$	−1.15712e6			−0.0928604
$690$	7.82092e6	−	4.93027e6i	0.625367	−	0.394229i
$691$			1.79579e6i			0.143074i	0.997438	+	0.0715371i	$0.0227904\pi$
$691$			1.79579e6i			0.143074i	−0.997438	+	0.0715371i	$0.977210\pi$
$692$	−8.83277e6	−	4.22167e6i	−0.701184	−	0.335134i
$693$			5.95595e6i			0.471106i
$694$	7.66005e6	+	1.21512e7i	0.603716	+	0.957678i
$695$	187258.			0.0147055
$696$	−910744.	−	7.77453e6i	−0.0712645	−	0.608347i
$697$	−2.81079e7			−2.19152
$698$	7.79664e6	+	1.23678e7i	0.605716	+	0.960850i
$699$			407094.i			0.0315139i
$700$	487238.	−	1.01942e6i	0.0375834	−	0.0786337i
$701$		−	1.76628e7i		−	1.35758i	−0.734334	−	0.678789i	$-0.762505\pi$
$701$		−	1.76628e7i		−	1.35758i	0.734334	−	0.678789i	$-0.237495\pi$
$702$	−1.41129e7	+	8.89669e6i	−1.08087	+	0.681374i
$703$	2.43624e7			1.85923
$704$	−1.97676e6	−	8.32150e6i	−0.150322	−	0.632805i
$705$	−1.36139e6			−0.103160
$706$	−1.36066e6	+	857753.i	−0.102740	+	0.0647665i
$707$		−	2.36670e6i		−	0.178071i
$708$	−940938.	+	1.96867e6i	−0.0705469	+	0.147601i
$709$		−	1.67397e7i		−	1.25064i	−0.780369	−	0.625319i	$-0.784969\pi$
$709$		−	1.67397e7i		−	1.25064i	0.780369	−	0.625319i	$-0.215031\pi$
$710$	617617.	+	979729.i	0.0459804	+	0.0729390i
$711$	−1.87112e7			−1.38812
$712$	1.12058e6	+	9.56579e6i	0.0828405	+	0.707165i
$713$	−1.98804e7			−1.46454
$714$	8.13363e6	+	1.29024e7i	0.597089	+	0.947165i
$715$		−	4.70246e6i		−	0.344001i
$716$	6.05924e6	+	2.89605e6i	0.441709	+	0.211117i
$717$		−	3.21993e7i		−	2.33910i
$718$	9.43238e6	−	5.94613e6i	0.682826	−	0.430450i
$719$	−1.41699e7			−1.02222			−0.511111	−	0.859515i	$-0.670766\pi$
$719$	−1.41699e7			−1.02222			−0.511111	+	0.859515i	$0.670766\pi$
$720$	8.04602e6	−	6.49431e6i	0.578429	−	0.466876i
$721$	6.68649e6			0.479027
$722$	7.14588e6	−	4.50473e6i	0.510167	−	0.321607i
$723$		−	1.05448e7i		−	0.750227i
$724$	−6.14938e6	−	2.93913e6i	−0.435999	−	0.208388i
$725$			1.06260e6i			0.0750800i
$726$	7.12948e6	+	1.13095e7i	0.502015	+	0.796349i
$727$	3.78412e6			0.265539			0.132770	−	0.991147i	$-0.457613\pi$
$727$	3.78412e6			0.265539			0.132770	+	0.991147i	$0.457613\pi$
$728$	−7.31947e6	+	857435.i	−0.511860	+	0.0599616i
$729$	2.28942e7			1.59554
$730$	−3.09833e6	−	4.91489e6i	−0.215189	−	0.341355i
$731$			3.39897e7i			2.35263i
$732$	−1.56262e7	+	3.26939e7i	−1.07790	+	2.25522i
$733$			2.58722e7i			1.77858i	0.457345	+	0.889290i	$0.348801\pi$
$733$			2.58722e7i			1.77858i	−0.457345	+	0.889290i	$0.651199\pi$
$734$	−4.98536e6	+	3.14275e6i	−0.341552	+	0.215313i
$735$	8.65749e6			0.591117
$736$	1.40890e7	+	4.81394e6i	0.958708	+	0.327571i
$737$	−3.25907e6			−0.221017
$738$	2.89525e7	−	1.82515e7i	1.95680	−	1.23355i
$739$			5.89215e6i			0.396883i	0.980113	+	0.198441i	$0.0635880\pi$
$739$			5.89215e6i			0.396883i	−0.980113	+	0.198441i	$0.936412\pi$
$740$	−4.21851e6	+	8.82617e6i	−0.283192	+	0.592506i
$741$		−	3.65169e7i		−	2.44314i
$742$	−273650.	−	434092.i	−0.0182467	−	0.0289449i
$743$	−2.47551e7			−1.64510			−0.822551	−	0.568692i	$-0.807450\pi$
$743$	−2.47551e7			−1.64510			−0.822551	+	0.568692i	$0.807450\pi$
$744$	−3.53694e7	+	4.14333e6i	−2.34258	+	0.274421i
$745$	−888583.			−0.0586553
$746$	−4.78949e6	−	7.59759e6i	−0.315095	−	0.499838i
$747$			2.49029e7i			1.63286i
$748$	−1.41410e7	−	6.75876e6i	−0.924115	−	0.441685i
$749$		−	8.35986e6i		−	0.544496i
$750$	−1.90176e6	+	1.19886e6i	−0.123453	+	0.0778242i
$751$	1.98371e6			0.128345			0.0641724	−	0.997939i	$-0.479559\pi$
$751$	1.98371e6			0.128345			0.0641724	+	0.997939i	$0.479559\pi$
$752$	−1.37701e6	−	1.70603e6i	−0.0887960	−	0.110012i
$753$	−4.68372e6			−0.301026
$754$	5.86296e6	−	3.69598e6i	0.375568	−	0.236756i
$755$		−	1.37451e7i		−	0.877565i
$756$	−6.67516e6	−	3.19043e6i	−0.424773	−	0.203023i
$757$			1.85647e7i			1.17746i	0.808328	+	0.588732i	$0.200373\pi$
$757$			1.85647e7i			1.17746i	−0.808328	+	0.588732i	$0.799627\pi$
$758$	3.00437e6	+	4.76585e6i	0.189924	+	0.301278i
$759$	1.70638e7			1.07515
$760$	1.04903e6	+	8.95502e6i	0.0658801	+	0.562383i
$761$	−5.16348e6			−0.323207			−0.161603	−	0.986856i	$-0.551667\pi$
$761$	−5.16348e6			−0.323207			−0.161603	+	0.986856i	$0.551667\pi$
$762$	1.82476e7	+	2.89463e7i	1.13846	+	1.80595i
$763$			7.14864e6i			0.444542i
$764$	−2.44589e6	+	5.11739e6i	−0.151601	+	0.317187i
$765$		−	1.89476e7i		−	1.17058i
$766$	−7.34160e6	+	4.62811e6i	−0.452083	+	0.284991i
$767$	−1.93194e6			−0.118578
$768$	2.60692e7	+	5.62818e6i	1.59487	+	0.344322i
$769$	3.01408e7			1.83797			0.918985	−	0.394293i	$-0.129011\pi$
$769$	3.01408e7			1.83797			0.918985	+	0.394293i	$0.129011\pi$
$770$	1.76412e6	−	1.11209e6i	0.107226	−	0.0675949i
$771$			2.15242e7i			1.30404i
$772$	1.04615e7	−	2.18881e7i	0.631761	−	1.32180i
$773$		−	1.51718e7i		−	0.913246i	−0.889660	−	0.456623i	$-0.849059\pi$
$773$		−	1.51718e7i		−	0.913246i	0.889660	−	0.456623i	$-0.150941\pi$
$774$	−2.20708e7	−	3.50111e7i	−1.32424	−	2.10065i
$775$	4.83417e6			0.289113
$776$	−825855.	−	7.04988e6i	−0.0492322	−	0.420269i
$777$	1.75704e7			1.04407
$778$	−1.42067e7	−	2.25362e7i	−0.841483	−	1.33485i
$779$			2.98438e7i			1.76202i
$780$	1.32296e7	+	6.32314e6i	0.778591	+	0.372132i
$781$			2.13758e6i			0.125399i
$782$	2.30799e7	−	1.45494e7i	1.34963	−	0.850804i
$783$	6.95788e6			0.405576
$784$	8.75682e6	+	1.08491e7i	0.508811	+	0.630383i
$785$	6.31050e6			0.365502
$786$	1.84044e7	−	1.16021e7i	1.06259	−	0.669853i
$787$		−	1.46106e7i		−	0.840874i	−0.907322	−	0.420437i	$-0.861877\pi$
$787$		−	1.46106e7i		−	0.840874i	0.907322	−	0.420437i	$-0.138123\pi$
$788$	1.02064e7	+	4.87820e6i	0.585541	+	0.279862i
$789$			3.90125e7i			2.23106i
$790$	3.49375e6	+	5.54216e6i	0.199170	+	0.315945i
$791$	1.25359e7			0.712384
$792$	1.89546e7	−	2.22043e6i	1.07375	−	0.125784i
$793$	−3.20839e7			−1.81177
$794$	1.46435e6	+	2.32291e6i	0.0824318	+	0.130762i
$795$			1.02100e6i			0.0572939i
$796$	3.21563e6	−	6.72789e6i	0.179880	−	0.376354i
$797$			4.81785e6i			0.268663i	0.990936	+	0.134331i	$0.0428887\pi$
$797$			4.81785e6i			0.268663i	−0.990936	+	0.134331i	$0.957111\pi$
$798$	1.36993e7	−	8.63595e6i	0.761535	−	0.480068i
$799$	−4.01753e6			−0.222634
$800$	−3.42593e6	−	1.17057e6i	−0.189257	−	0.0646655i
$801$	−2.14899e7			−1.18346
$802$	−8.29790e6	+	5.23096e6i	−0.455546	+	0.287174i
$803$		−	1.07234e7i		−	0.586870i
$804$	4.38230e6	−	9.16886e6i	0.239090	−	0.500236i
$805$			3.63014e6i			0.197440i
$806$	−1.68145e7	−	2.66729e7i	−0.911686	−	1.44621i
$807$	−1.64487e7			−0.889095
$808$	−7.53194e6	+	882326.i	−0.405862	+	0.0475445i
$809$	−267715.			−0.0143814			−0.00719072	−	0.999974i	$-0.502289\pi$
$809$	−267715.			−0.0143814			−0.00719072	+	0.999974i	$0.502289\pi$
$810$	448048.	+	710741.i	0.0239945	+	0.0380626i
$811$		−	1.10232e7i		−	0.588514i	−0.955726	−	0.294257i	$-0.904928\pi$
$811$		−	1.10232e7i		−	0.588514i	0.955726	−	0.294257i	$-0.0950722\pi$
$812$	2.77308e6	+	1.32541e6i	0.147595	+	0.0705440i
$813$			4.02671e7i			2.13660i
$814$	−1.52738e7	+	9.62851e6i	−0.807951	+	0.509329i
$815$	9.58044e6			0.505233
$816$	3.80293e7	−	3.06952e7i	1.99937	−	1.61378i
$817$	3.60889e7			1.89155
$818$	4.08472e6	−	2.57499e6i	0.213442	−	0.134553i
$819$		−	1.64434e7i		−	0.856609i
$820$	−1.08120e7	−	5.16765e6i	−0.561528	−	0.268385i
$821$			7.52183e6i			0.389462i	0.980857	+	0.194731i	$0.0623834\pi$
$821$			7.52183e6i			0.389462i	−0.980857	+	0.194731i	$0.937617\pi$
$822$	1.25231e7	+	1.98654e7i	0.646445	+	1.02546i
$823$	−2.86933e7			−1.47666			−0.738331	−	0.674439i	$-0.764386\pi$
$823$	−2.86933e7			−1.47666			−0.738331	+	0.674439i	$0.764386\pi$
$824$	−2.49278e6	−	2.12796e7i	−0.127899	−	1.09180i
$825$	−4.14927e6			−0.212245
$826$	−456888.	−	724764.i	−0.0233002	−	0.0369613i
$827$			1.90830e7i			0.970248i	0.874445	+	0.485124i	$0.161226\pi$
$827$			1.90830e7i			0.970248i	−0.874445	+	0.485124i	$0.838774\pi$
$828$	−1.43259e7	+	2.99733e7i	−0.726182	+	1.51935i
$829$		−	2.31916e7i		−	1.17205i	−0.810295	−	0.586023i	$-0.800693\pi$
$829$		−	2.31916e7i		−	1.17205i	0.810295	−	0.586023i	$-0.199307\pi$
$830$	7.37608e6	−	4.64985e6i	0.371647	−	0.234285i
$831$	−4.13245e7			−2.07589
$832$	5.45752e6	+	2.29743e7i	0.273330	+	1.15063i
$833$	2.55486e7			1.27572
$834$	−911666.	+	574710.i	−0.0453859	+	0.0286111i
$835$		−	2.71044e6i		−	0.134531i
$836$	−7.17617e6	+	1.50143e7i	−0.355122	+	0.743002i
$837$		−	3.16541e7i		−	1.56177i
$838$	−1.16716e7	−	1.85147e7i	−0.574143	−	0.910766i
$839$	−887580.			−0.0435314			−0.0217657	−	0.999763i	$-0.506929\pi$
$839$	−887580.			−0.0435314			−0.0217657	+	0.999763i	$0.506929\pi$
$840$	756569.	+	6.45842e6i	0.0369956	+	0.315812i
$841$	1.76206e7			0.859075
$842$	3.46958e6	+	5.50382e6i	0.168654	+	0.267537i
$843$			3.77382e7i			1.82899i
$844$	1.15840e7	+	5.53663e6i	0.559760	+	0.267540i
$845$			3.70040e6i			0.178282i
$846$	4.13825e6	−	2.60873e6i	0.198788	−	0.125315i
$847$	−5.24942e6			−0.251422
$848$	−1.27947e6	+	1.03271e6i	−0.0610997	+	0.0493163i
$849$	−3.00746e7			−1.43196
$850$	−5.61216e6	+	3.53788e6i	−0.266430	+	0.167956i
$851$		−	3.14299e7i		−	1.48771i
$852$	−6.01373e6	−	2.87429e6i	−0.283821	−	0.135654i
$853$		−	1.39449e7i		−	0.656208i	−0.944642	−	0.328104i	$-0.893590\pi$
$853$		−	1.39449e7i		−	0.656208i	0.944642	−	0.328104i	$-0.106410\pi$
$854$	−7.58758e6	−	1.20362e7i	−0.356007	−	0.564736i
$855$	−2.01178e7			−0.941162
$856$	−2.66050e7	+	3.11663e6i	−1.24102	+	0.145379i
$857$	−3.58423e7			−1.66703			−0.833516	−	0.552495i	$-0.813676\pi$
$857$	−3.58423e7			−1.66703			−0.833516	+	0.552495i	$0.813676\pi$
$858$	1.44322e7	+	2.28939e7i	0.669290	+	1.06170i
$859$			767053.i			0.0354685i	0.999843	+	0.0177342i	$0.00564528\pi$
$859$			767053.i			0.0354685i	−0.999843	+	0.0177342i	$0.994355\pi$
$860$	−6.24903e6	+	1.30745e7i	−0.288115	+	0.602808i
$861$			2.15236e7i			0.989478i
$862$	1.47905e7	−	9.32387e6i	0.677977	−	0.427394i
$863$	−2.90420e7			−1.32739			−0.663697	−	0.748002i	$-0.731013\pi$
$863$	−2.90420e7			−1.32739			−0.663697	+	0.748002i	$0.731013\pi$
$864$	−7.66488e6	+	2.24329e7i	−0.349318	+	1.02235i
$865$	−7.64829e6			−0.347555
$866$	−1.18625e7	+	7.47809e6i	−0.537506	+	0.338841i
$867$		−	5.34421e7i		−	2.41455i
$868$	6.02980e6	−	1.26158e7i	0.271646	−	0.568351i
$869$			1.20919e7i			0.543183i
$870$	−3.26120e6	−	5.17325e6i	−0.146076	−	0.231721i
$871$	8.99778e6			0.401874
$872$	2.27503e7	−	2.66508e6i	1.01320	−	0.118691i
$873$	1.58378e7			0.703330
$874$	−1.54480e7	−	2.45052e7i	−0.684059	−	1.08513i
$875$		−	882716.i		−	0.0389763i
$876$	3.01684e7	+	1.44191e7i	1.32829	+	0.634861i
$877$		−	9.62715e6i		−	0.422667i	−0.977414	−	0.211334i	$-0.932219\pi$
$877$		−	9.62715e6i		−	0.422667i	0.977414	−	0.211334i	$-0.0677807\pi$
$878$	−4.77177e6	+	3.00810e6i	−0.208902	+	0.131691i
$879$	2.25852e7			0.985942
$880$	−4.19688e6	−	5.19965e6i	−0.182692	−	0.226343i
$881$	3.88627e7			1.68691			0.843457	−	0.537196i	$-0.180517\pi$
$881$	3.88627e7			1.68691			0.843457	+	0.537196i	$0.180517\pi$
$882$	−2.63163e7	+	1.65897e7i	−1.13908	+	0.718070i
$883$			4.29023e6i			0.185173i	0.995705	+	0.0925867i	$0.0295135\pi$
$883$			4.29023e6i			0.185173i	−0.995705	+	0.0925867i	$0.970486\pi$
$884$	3.90410e7	+	1.86599e7i	1.68031	+	0.803115i
$885$			1.70467e6i			0.0731615i
$886$	6.36416e6	+	1.00955e7i	0.272368	+	0.432059i
$887$	−1.30883e7			−0.558564			−0.279282	−	0.960209i	$-0.590096\pi$
$887$	−1.30883e7			−0.558564			−0.279282	+	0.960209i	$0.590096\pi$
$888$	−6.55039e6	−	5.59171e7i	−0.278763	−	2.37965i
$889$	−1.34356e7			−0.570170
$890$	4.01258e6	+	6.36518e6i	0.169804	+	0.269361i
$891$			1.55070e6i			0.0654386i
$892$	−6.56380e6	+	1.37331e7i	−0.276212	+	0.577905i
$893$			4.26564e6i			0.179001i
$894$	4.32606e6	−	2.72713e6i	0.181029	−	0.114120i
$895$	5.24669e6			0.218941
$896$	−7.32812e6	+	7.48062e6i	−0.304946	+	0.311292i
$897$	−4.71103e7			−1.95495
$898$	−2.99068e7	+	1.88531e7i	−1.23760	+	0.780174i
$899$			1.31502e7i			0.542665i
$900$	3.48352e6	−	7.28839e6i	0.143355	−	0.299934i
$901$			3.01301e6i			0.123649i
$902$	−1.17949e7	−	1.87102e7i	−0.482699	−	0.765708i
$903$	2.60276e7			1.06222
$904$	−4.67349e6	−	3.98951e7i	−0.190204	−	1.62367i
$905$	−5.32474e6			−0.216111
$906$	4.21846e7	+	6.69178e7i	1.70739	+	2.70845i
$907$		−	2.36895e7i		−	0.956175i	−0.878312	−	0.478087i	$-0.841330\pi$
$907$		−	2.36895e7i		−	0.956175i	0.878312	−	0.478087i	$-0.158670\pi$
$908$	824547.	+	394096.i	0.0331895	+	0.0158631i
$909$		−	1.69208e7i		−	0.679220i
$910$	−4.87045e6	+	3.07031e6i	−0.194969	+	0.122908i
$911$	1.27323e7			0.508289			0.254144	−	0.967166i	$-0.418206\pi$
$911$	1.27323e7			0.508289			0.254144	+	0.967166i	$0.418206\pi$
$912$	−3.25909e7	−	4.03779e7i	−1.29750	−	1.60752i
$913$	1.60932e7			0.638948
$914$	−8.98062e6	+	5.66135e6i	−0.355583	+	0.224158i
$915$			2.83096e7i			1.11784i
$916$	−2.79980e7	−	1.33818e7i	−1.10252	−	0.526957i
$917$			8.54258e6i			0.335479i
$918$	2.31660e7	+	3.67484e7i	0.907286	+	1.43923i
$919$	3.36064e7			1.31260			0.656302	−	0.754499i	$-0.272120\pi$
$919$	3.36064e7			1.31260			0.656302	+	0.754499i	$0.272120\pi$
$920$	1.15528e7	−	1.35335e6i	0.450006	−	0.0527158i
$921$	−3.75640e7			−1.45923
$922$	−2.57858e7	−	4.09042e7i	−0.998972	−	1.58467i
$923$		−	5.90152e6i		−	0.228013i
$924$	−5.17551e6	+	1.08284e7i	−0.199422	+	0.417240i
$925$			7.64257e6i			0.293687i
$926$	3.61711e7	−	2.28021e7i	1.38623	−	0.873871i
$927$	4.78053e7			1.82716
$928$	3.18425e6	−	9.31938e6i	0.121377	−	0.355236i
$929$	2.44326e7			0.928816			0.464408	−	0.885621i	$-0.346267\pi$
$929$	2.44326e7			0.928816			0.464408	+	0.885621i	$0.346267\pi$
$930$	−2.35352e7	+	1.48365e7i	−0.892297	+	0.562500i
$931$		−	2.71265e7i		−	1.02570i
$932$	−220869.	+	462112.i	−0.00832904	+	0.0174264i
$933$		−	9.27134e6i		−	0.348689i
$934$	9.92867e6	+	1.57499e7i	0.372412	+	0.590760i
$935$	−1.22447e7			−0.458055
$936$	−5.23307e7	+	6.13026e6i	−1.95239	+	0.228712i
$937$	−2.46226e7			−0.916188			−0.458094	−	0.888904i	$-0.651468\pi$
$937$	−2.46226e7			−0.916188			−0.458094	+	0.888904i	$0.651468\pi$
$938$	2.12790e6	+	3.37550e6i	0.0789667	+	0.125265i
$939$		−	8.24698e6i		−	0.305233i
$940$	−1.54538e6	−	738624.i	−0.0570449	−	0.0272649i
$941$			3.64578e7i			1.34220i	0.741368	+	0.671098i	$0.234177\pi$
$941$			3.64578e7i			1.34220i	−0.741368	+	0.671098i	$0.765823\pi$
$942$	−3.07226e7	+	1.93674e7i	−1.12806	+	0.711122i
$943$	3.85013e7			1.40993
$944$	−2.13621e6	+	1.72423e6i	−0.0780214	+	0.0629746i
$945$	−5.78001e6			−0.210547
$946$	−2.26255e7	+	1.42630e7i	−0.821999	+	0.518184i
$947$			1.49302e7i			0.540992i	0.962721	+	0.270496i	$0.0871876\pi$
$947$			1.49302e7i			0.540992i	−0.962721	+	0.270496i	$0.912812\pi$
$948$	−3.40186e7	−	1.62594e7i	−1.22941	−	0.587602i
$949$			2.96055e7i			1.06710i
$950$	3.75638e6	+	5.95876e6i	0.135039	+	0.214214i
$951$	3.95935e7			1.41962
$952$	2.23267e6	+	1.90591e7i	0.0798420	+	0.681568i
$953$	2.82853e7			1.00885			0.504426	−	0.863455i	$-0.331704\pi$
$953$	2.82853e7			1.00885			0.504426	+	0.863455i	$0.331704\pi$
$954$	−1.95647e6	−	3.10355e6i	−0.0695987	−	0.110405i
$955$			4.43115e6i			0.157220i
$956$	1.74698e7	−	3.65510e7i	0.618219	−	1.29347i
$957$		−	1.12871e7i		−	0.398383i
$958$	−2.37168e7	+	1.49509e7i	−0.834914	+	0.526326i
$959$	−9.22071e6			−0.323756
$960$	2.02717e7	−	4.81552e6i	0.709924	−	0.168642i
$961$	3.11960e7			1.08966
$962$	4.21684e7	−	2.65828e7i	1.46909	−	0.926110i
$963$		−	5.97691e7i		−	2.07688i
$964$	5.72109e6	−	1.19699e7i	0.198283	−	0.414857i
$965$		−	1.89529e7i		−	0.655176i
$966$	−1.11412e7	−	1.76733e7i	−0.384140	−	0.609363i
$967$	3.47503e7			1.19507			0.597533	−	0.801844i	$-0.296148\pi$
$967$	3.47503e7			1.19507			0.597533	+	0.801844i	$0.296148\pi$
$968$	1.95703e6	+	1.67061e7i	0.0671288	+	0.573043i
$969$	−9.50860e7			−3.25317
$970$	−2.95723e6	−	4.69106e6i	−0.100915	−	0.160082i
$971$			4.65499e7i			1.58442i	0.610247	+	0.792211i	$0.291070\pi$
$971$			4.65499e7i			1.58442i	−0.610247	+	0.792211i	$0.708930\pi$
$972$	2.43496e7	+	1.16380e7i	0.826658	+	0.395106i
$973$		−	423158.i		−	0.0143291i
$974$	3.62224e7	−	2.28345e7i	1.22343	−	0.771247i
$975$	1.14555e7			0.385924
$976$	−3.54762e7	+	2.86344e7i	−1.19210	+	0.962198i
$977$	4.15712e7			1.39334			0.696668	−	0.717394i	$-0.254665\pi$
$977$	4.15712e7			1.39334			0.696668	+	0.717394i	$0.254665\pi$
$978$	−4.66424e7	+	2.94031e7i	−1.55931	+	0.982984i
$979$			1.38876e7i			0.463096i
$980$	9.82754e6	+	4.69712e6i	0.326873	+	0.156231i
$981$			5.11094e7i			1.69562i
$982$	3.77130e6	+	5.98243e6i	0.124799	+	0.197970i
$983$	−2.55186e7			−0.842313			−0.421157	−	0.906988i	$-0.638376\pi$
$983$	−2.55186e7			−0.842313			−0.421157	+	0.906988i	$0.638376\pi$
$984$	6.84981e7	−	8.02417e6i	2.25523	−	0.264188i
$985$	8.83771e6			0.290235
$986$	−9.62393e6	−	1.52665e7i	−0.315254	−	0.500089i
$987$			3.07641e6i			0.100520i
$988$	1.98123e7	−	4.14521e7i	0.645716	−	1.35100i
$989$		−	4.65581e7i		−	1.51358i
$990$	1.26126e7	−	7.95093e6i	0.408994	−	0.257828i
$991$	−3.10296e7			−1.00367			−0.501836	−	0.864963i	$-0.667342\pi$
$991$	−3.10296e7			−1.00367			−0.501836	+	0.864963i	$0.667342\pi$
$992$	−4.23975e7	−	1.44864e7i	−1.36792	−	0.467391i
$993$	1.42119e7			0.457382
$994$	2.21395e6	−	1.39566e6i	0.0710724	−	0.0448037i
$995$		−	5.82567e6i		−	0.186547i
$996$	−2.16397e7	+	4.52756e7i	−0.691198	+	1.44616i
$997$			1.66036e7i			0.529011i	0.964384	+	0.264505i	$0.0852087\pi$
$997$			1.66036e7i			0.529011i	−0.964384	+	0.264505i	$0.914791\pi$
$998$	1.68721e7	+	2.67643e7i	0.536219	+	0.850607i
$999$	5.00435e7			1.58648

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.d.a.21.4	yes	20
3.2	odd	2		360.6.k.b.181.17		20
4.3	odd	2		160.6.d.a.81.19		20
5.2	odd	4		200.6.f.c.149.7		20
5.3	odd	4		200.6.f.b.149.14		20
5.4	even	2		200.6.d.b.101.17		20
8.3	odd	2		160.6.d.a.81.2		20
8.5	even	2	inner	40.6.d.a.21.3	✓	20
20.3	even	4		800.6.f.c.49.1		20
20.7	even	4		800.6.f.b.49.20		20
20.19	odd	2		800.6.d.c.401.2		20
24.5	odd	2		360.6.k.b.181.18		20
40.3	even	4		800.6.f.b.49.19		20
40.13	odd	4		200.6.f.c.149.8		20
40.19	odd	2		800.6.d.c.401.19		20
40.27	even	4		800.6.f.c.49.2		20
40.29	even	2		200.6.d.b.101.18		20
40.37	odd	4		200.6.f.b.149.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.3	✓	20	8.5	even	2	inner
40.6.d.a.21.4	yes	20	1.1	even	1	trivial
160.6.d.a.81.2		20	8.3	odd	2
160.6.d.a.81.19		20	4.3	odd	2
200.6.d.b.101.17		20	5.4	even	2
200.6.d.b.101.18		20	40.29	even	2
200.6.f.b.149.13		20	40.37	odd	4
200.6.f.b.149.14		20	5.3	odd	4
200.6.f.c.149.7		20	5.2	odd	4
200.6.f.c.149.8		20	40.13	odd	4
360.6.k.b.181.17		20	3.2	odd	2
360.6.k.b.181.18		20	24.5	odd	2
800.6.d.c.401.2		20	20.19	odd	2
800.6.d.c.401.19		20	40.19	odd	2
800.6.f.b.49.19		20	40.3	even	4
800.6.f.b.49.20		20	20.7	even	4
800.6.f.c.49.1		20	20.3	even	4
800.6.f.c.49.2		20	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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.78536 + 3.01667i) q^{2} -25.4343i q^{3} +(13.7994 - 28.8717i) q^{4} -25.0000i q^{5} +(76.7270 + 121.712i) q^{6} -56.4938 q^{7} +(21.0614 + 179.790i) q^{8} -403.904 q^{9} +O(q^{10})\)	\(q+(-4.78536 + 3.01667i) q^{2} -25.4343i q^{3} +(13.7994 - 28.8717i) q^{4} -25.0000i q^{5} +(76.7270 + 121.712i) q^{6} -56.4938 q^{7} +(21.0614 + 179.790i) q^{8} -403.904 q^{9} +(75.4168 + 119.634i) q^{10} +261.019i q^{11} +(-734.333 - 350.978i) q^{12} -720.631i q^{13} +(270.343 - 170.423i) q^{14} -635.858 q^{15} +(-643.154 - 796.825i) q^{16} -1876.44 q^{17} +(1932.83 - 1218.45i) q^{18} +1992.33i q^{19} +(-721.793 - 344.985i) q^{20} +1436.88i q^{21} +(-787.408 - 1249.07i) q^{22} +2570.29 q^{23} +(4572.83 - 535.682i) q^{24} -625.000 q^{25} +(2173.91 + 3448.48i) q^{26} +4092.49i q^{27} +(-779.581 + 1631.07i) q^{28} -1700.16i q^{29} +(3042.81 - 1918.17i) q^{30} -7734.68 q^{31} +(5481.48 + 1872.91i) q^{32} +6638.83 q^{33} +(8979.46 - 5660.61i) q^{34} +1412.35i q^{35} +(-5573.63 + 11661.4i) q^{36} -12228.1i q^{37} +(-6010.20 - 9534.02i) q^{38} -18328.8 q^{39} +(4494.75 - 526.535i) q^{40} +14979.3 q^{41} +(-4334.60 - 6876.00i) q^{42} -18113.9i q^{43} +(7536.06 + 3601.90i) q^{44} +10097.6i q^{45} +(-12299.8 + 7753.73i) q^{46} +2141.03 q^{47} +(-20266.7 + 16358.2i) q^{48} -13615.4 q^{49} +(2990.85 - 1885.42i) q^{50} +47726.0i q^{51} +(-20805.9 - 9944.27i) q^{52} -1605.71i q^{53} +(-12345.7 - 19584.1i) q^{54} +6525.47 q^{55} +(-1189.84 - 10157.0i) q^{56} +50673.5 q^{57} +(5128.81 + 8135.87i) q^{58} -2680.90i q^{59} +(-8774.45 + 18358.3i) q^{60} -44521.9i q^{61} +(37013.2 - 23333.0i) q^{62} +22818.1 q^{63} +(-31880.8 + 7573.26i) q^{64} -18015.8 q^{65} +(-31769.2 + 20027.2i) q^{66} +12486.0i q^{67} +(-25893.8 + 54176.2i) q^{68} -65373.7i q^{69} +(-4260.58 - 6758.59i) q^{70} +8189.38 q^{71} +(-8506.79 - 72617.9i) q^{72} -41082.7 q^{73} +(36888.2 + 58516.0i) q^{74} +15896.4i q^{75} +(57522.0 + 27492.9i) q^{76} -14746.0i q^{77} +(87709.7 - 55291.8i) q^{78} +46325.9 q^{79} +(-19920.6 + 16078.8i) q^{80} +5940.95 q^{81} +(-71681.6 + 45187.8i) q^{82} -61655.4i q^{83} +(41485.3 + 19828.1i) q^{84} +46911.1i q^{85} +(54643.7 + 86681.7i) q^{86} -43242.3 q^{87} +(-46928.5 + 5497.42i) q^{88} +53205.4 q^{89} +(-30461.2 - 48320.7i) q^{90} +40711.2i q^{91} +(35468.5 - 74208.8i) q^{92} +196726. i q^{93} +(-10245.6 + 6458.79i) q^{94} +49808.2 q^{95} +(47636.2 - 139418. i) q^{96} -39211.8 q^{97} +(65154.8 - 41073.3i) q^{98} -105427. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9	\( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9} - 50 q^{10} - 1876 q^{12} + 2708 q^{14} + 900 q^{15} + 3080 q^{16} - 5294 q^{18} - 1900 q^{20} + 13836 q^{22} - 4676 q^{23} + 1032 q^{24} - 12500 q^{25} - 8084 q^{26} + 2108 q^{28} + 5800 q^{30} + 7160 q^{31} + 6792 q^{32} + 5672 q^{33} + 21132 q^{34} + 18344 q^{36} - 19580 q^{38} - 44904 q^{39} + 6200 q^{40} + 11608 q^{41} - 17116 q^{42} + 72296 q^{44} - 28516 q^{46} + 44180 q^{47} - 88856 q^{48} + 18756 q^{49} - 1250 q^{50} - 39680 q^{52} - 100584 q^{54} - 24200 q^{55} - 53624 q^{56} + 5032 q^{57} + 59496 q^{58} - 31300 q^{60} + 59824 q^{62} + 240620 q^{63} - 11264 q^{64} - 56688 q^{66} + 11576 q^{68} + 29800 q^{70} - 200312 q^{71} + 235912 q^{72} - 105136 q^{73} + 78876 q^{74} - 153872 q^{76} + 95864 q^{78} + 282080 q^{79} + 16000 q^{80} + 65172 q^{81} - 223032 q^{82} - 297128 q^{84} + 27452 q^{86} - 332592 q^{87} + 86896 q^{88} - 3160 q^{89} + 51750 q^{90} + 107916 q^{92} + 148820 q^{94} + 144400 q^{95} + 395168 q^{96} + 147376 q^{97} + 216942 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9 - 50 * q^10 - 1876 * q^12 + 2708 * q^14 + 900 * q^15 + 3080 * q^16 - 5294 * q^18 - 1900 * q^20 + 13836 * q^22 - 4676 * q^23 + 1032 * q^24 - 12500 * q^25 - 8084 * q^26 + 2108 * q^28 + 5800 * q^30 + 7160 * q^31 + 6792 * q^32 + 5672 * q^33 + 21132 * q^34 + 18344 * q^36 - 19580 * q^38 - 44904 * q^39 + 6200 * q^40 + 11608 * q^41 - 17116 * q^42 + 72296 * q^44 - 28516 * q^46 + 44180 * q^47 - 88856 * q^48 + 18756 * q^49 - 1250 * q^50 - 39680 * q^52 - 100584 * q^54 - 24200 * q^55 - 53624 * q^56 + 5032 * q^57 + 59496 * q^58 - 31300 * q^60 + 59824 * q^62 + 240620 * q^63 - 11264 * q^64 - 56688 * q^66 + 11576 * q^68 + 29800 * q^70 - 200312 * q^71 + 235912 * q^72 - 105136 * q^73 + 78876 * q^74 - 153872 * q^76 + 95864 * q^78 + 282080 * q^79 + 16000 * q^80 + 65172 * q^81 - 223032 * q^82 - 297128 * q^84 + 27452 * q^86 - 332592 * q^87 + 86896 * q^88 - 3160 * q^89 + 51750 * q^90 + 107916 * q^92 + 148820 * q^94 + 144400 * q^95 + 395168 * q^96 + 147376 * q^97 + 216942 * q^98

Introduction

L-functions

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