LMFDB - Embedded newform 40.6.k.a.27.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(3,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("40.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.4
Character	$\chi$	$=$	40.27
Dual form			40.6.k.a.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.95505 - 2.72901i) q^{2} +(-17.2715 + 17.2715i) q^{3} +(17.1050 + 27.0447i) q^{4} +(55.8976 + 0.673734i) q^{5} +(132.715 - 38.4469i) q^{6} +(-135.845 + 135.845i) q^{7} +(-10.9508 - 180.688i) q^{8} -353.606i q^{9} +O(q^{10})$	\(q+(-4.95505 - 2.72901i) q^{2} +(-17.2715 + 17.2715i) q^{3} +(17.1050 + 27.0447i) q^{4} +(55.8976 + 0.673734i) q^{5} +(132.715 - 38.4469i) q^{6} +(-135.845 + 135.845i) q^{7} +(-10.9508 - 180.688i) q^{8} -353.606i q^{9} +(-275.137 - 155.884i) q^{10} -109.728 q^{11} +(-762.531 - 171.674i) q^{12} +(-469.186 - 469.186i) q^{13} +(1043.84 - 302.395i) q^{14} +(-977.070 + 953.797i) q^{15} +(-438.837 + 925.202i) q^{16} +(283.916 + 283.916i) q^{17} +(-964.995 + 1752.14i) q^{18} -2630.80i q^{19} +(937.909 + 1523.26i) q^{20} -4692.47i q^{21} +(543.708 + 299.449i) q^{22} +(-1169.93 - 1169.93i) q^{23} +(3309.88 + 2931.60i) q^{24} +(3124.09 + 75.3203i) q^{25} +(1044.43 + 3605.25i) q^{26} +(1910.33 + 1910.33i) q^{27} +(-5997.51 - 1350.26i) q^{28} -1610.97 q^{29} +(7444.35 - 2059.68i) q^{30} +3805.32i q^{31} +(4699.34 - 3386.83i) q^{32} +(1895.17 - 1895.17i) q^{33} +(-632.008 - 2181.63i) q^{34} +(-7684.92 + 7501.87i) q^{35} +(9563.19 - 6048.44i) q^{36} +(-7125.02 + 7125.02i) q^{37} +(-7179.47 + 13035.7i) q^{38} +16207.0 q^{39} +(-490.390 - 10107.4i) q^{40} -12159.6 q^{41} +(-12805.8 + 23251.4i) q^{42} +(10049.2 - 10049.2i) q^{43} +(-1876.90 - 2967.57i) q^{44} +(238.237 - 19765.8i) q^{45} +(2604.31 + 8989.80i) q^{46} +(-11740.5 + 11740.5i) q^{47} +(-8400.23 - 23558.9i) q^{48} -20100.5i q^{49} +(-15274.5 - 8898.89i) q^{50} -9807.29 q^{51} +(4663.58 - 20714.4i) q^{52} +(-1312.47 - 1312.47i) q^{53} +(-4252.47 - 14679.1i) q^{54} +(-6133.55 - 73.9276i) q^{55} +(26033.1 + 23057.9i) q^{56} +(45437.7 + 45437.7i) q^{57} +(7982.44 + 4396.36i) q^{58} +20595.0i q^{59} +(-42508.0 - 10109.9i) q^{60} -28836.9i q^{61} +(10384.8 - 18855.6i) q^{62} +(48035.5 + 48035.5i) q^{63} +(-32528.2 + 3957.36i) q^{64} +(-25910.3 - 26542.5i) q^{65} +(-14562.6 + 4218.71i) q^{66} +(-27245.0 - 27245.0i) q^{67} +(-2822.05 + 12534.8i) q^{68} +40412.8 q^{69} +(58551.8 - 16199.9i) q^{70} +57260.4i q^{71} +(-63892.3 + 3872.28i) q^{72} +(-25178.5 + 25178.5i) q^{73} +(54749.1 - 15860.6i) q^{74} +(-55258.5 + 52656.7i) q^{75} +(71149.2 - 44999.8i) q^{76} +(14906.0 - 14906.0i) q^{77} +(-80306.7 - 44229.2i) q^{78} -56597.7 q^{79} +(-25153.3 + 51420.9i) q^{80} +19937.9 q^{81} +(60251.2 + 33183.5i) q^{82} +(41952.5 - 41952.5i) q^{83} +(126907. - 80264.7i) q^{84} +(15679.0 + 16061.5i) q^{85} +(-77218.7 + 22369.9i) q^{86} +(27823.8 - 27823.8i) q^{87} +(1201.61 + 19826.5i) q^{88} +28977.6i q^{89} +(-55121.4 + 97290.1i) q^{90} +127473. q^{91} +(11628.8 - 51652.1i) q^{92} +(-65723.5 - 65723.5i) q^{93} +(90214.4 - 26134.7i) q^{94} +(1772.46 - 147055. i) q^{95} +(-22669.0 + 139660. i) q^{96} +(17161.5 + 17161.5i) q^{97} +(-54854.5 + 99599.0i) q^{98} +38800.6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	−4.95505	−	2.72901i	−0.875937	−	0.482425i
$2$	−4.95505	−	2.72901i	−0.875937	−	0.482425i
$3$	−17.2715	+	17.2715i	−1.10796	+	1.10796i	−0.114546	+	0.993418i	$0.536541\pi$
$3$	−17.2715	+	17.2715i	−1.10796	+	1.10796i	−0.993418	+	0.114546i	$0.963459\pi$
$4$	17.1050	+	27.0447i	0.534532	+	0.845148i
$5$	55.8976	+	0.673734i	0.999927	+	0.0120521i
$5$	55.8976	+	0.673734i	0.999927	+	0.0120521i
$6$	132.715	−	38.4469i	1.50502	−	0.435997i
$7$	−135.845	+	135.845i	−1.04785	+	1.04785i	−0.0490492	+	0.998796i	$0.515619\pi$
$7$	−135.845	+	135.845i	−1.04785	+	1.04785i	−0.998796	+	0.0490492i	$0.984381\pi$
$8$	−10.9508	−	180.688i	−0.0604953	−	0.998168i
$9$		−	353.606i		−	1.45517i
$10$	−275.137	−	155.884i	−0.870059	−	0.492947i
$11$	−109.728			−0.273424			−0.136712	−	0.990611i	$-0.543653\pi$
$11$	−109.728			−0.273424			−0.136712	+	0.990611i	$0.543653\pi$
$12$	−762.531	−	171.674i	−1.52864	−	0.344152i
$13$	−469.186	−	469.186i	−0.769992	−	0.769992i	0.208113	−	0.978105i	$-0.433268\pi$
$13$	−469.186	−	469.186i	−0.769992	−	0.769992i	−0.978105	+	0.208113i	$0.933268\pi$
$14$	1043.84	−	302.395i	1.42335	−	0.412340i
$15$	−977.070	+	953.797i	−1.12124	+	1.09453i
$16$	−438.837	+	925.202i	−0.428552	+	0.903517i
$17$	283.916	+	283.916i	0.238269	+	0.238269i	0.816133	−	0.577864i	$-0.196114\pi$
$17$	283.916	+	283.916i	0.238269	+	0.238269i	−0.577864	+	0.816133i	$0.696114\pi$
$18$	−964.995	+	1752.14i	−0.702011	+	1.27464i
$19$		−	2630.80i		−	1.67187i	−0.548827	−	0.835936i	$-0.684925\pi$
$19$		−	2630.80i		−	1.67187i	0.548827	−	0.835936i	$-0.315075\pi$
$20$	937.909	+	1523.26i	0.524307	+	0.851529i
$21$		−	4692.47i		−	2.32195i
$22$	543.708	+	299.449i	0.239502	+	0.131907i
$23$	−1169.93	−	1169.93i	−0.461148	−	0.461148i	0.437884	−	0.899032i	$-0.355728\pi$
$23$	−1169.93	−	1169.93i	−0.461148	−	0.461148i	−0.899032	+	0.437884i	$0.855728\pi$
$24$	3309.88	+	2931.60i	1.17296	+	1.03891i
$25$	3124.09	+	75.3203i	0.999709	+	0.0241025i
$26$	1044.43	+	3605.25i	0.303001	+	1.04593i
$27$	1910.33	+	1910.33i	0.504312	+	0.504312i
$28$	−5997.51	−	1350.26i	−1.44569	−	0.325478i
$29$	−1610.97			−0.355707			−0.177854	−	0.984057i	$-0.556915\pi$
$29$	−1610.97			−0.355707			−0.177854	+	0.984057i	$0.556915\pi$
$30$	7444.35	−	2059.68i	1.51016	−	0.417827i
$31$			3805.32i			0.711193i	0.934640	+	0.355596i	$0.115722\pi$
$31$			3805.32i			0.711193i	−0.934640	+	0.355596i	$0.884278\pi$
$32$	4699.34	−	3386.83i	0.811264	−	0.584680i
$33$	1895.17	−	1895.17i	0.302944	−	0.302944i
$34$	−632.008	−	2181.63i	−0.0937617	−	0.323656i
$35$	−7684.92	+	7501.87i	−1.06040	+	1.03514i
$36$	9563.19	−	6048.44i	1.22983	−	0.777835i
$37$	−7125.02	+	7125.02i	−0.855622	+	0.855622i	−0.990819	−	0.135197i	$-0.956833\pi$
$37$	−7125.02	+	7125.02i	−0.855622	+	0.855622i	0.135197	+	0.990819i	$0.456833\pi$
$38$	−7179.47	+	13035.7i	−0.806554	+	1.46446i
$39$	16207.0			1.70625
$40$	−490.390	−	10107.4i	−0.0484609	−	0.998825i
$41$	−12159.6			−1.12969			−0.564843	−	0.825198i	$-0.691063\pi$
$41$	−12159.6			−1.12969			−0.564843	+	0.825198i	$0.691063\pi$
$42$	−12805.8	+	23251.4i	−1.12017	+	2.03388i
$43$	10049.2	−	10049.2i	0.828821	−	0.828821i	−0.158533	−	0.987354i	$-0.550676\pi$
$43$	10049.2	−	10049.2i	0.828821	−	0.828821i	0.987354	+	0.158533i	$0.0506764\pi$
$44$	−1876.90	−	2967.57i	−0.146154	−	0.231084i
$45$	238.237	−	19765.8i	0.0175379	−	1.45506i
$46$	2604.31	+	8989.80i	0.181467	+	0.626406i
$47$	−11740.5	+	11740.5i	−0.775248	+	0.775248i	−0.979019	−	0.203771i	$-0.934680\pi$
$47$	−11740.5	+	11740.5i	−0.775248	+	0.775248i	0.203771	+	0.979019i	$0.434680\pi$
$48$	−8400.23	−	23558.9i	−0.526245	−	1.47588i
$49$		−	20100.5i		−	1.19596i
$50$	−15274.5	−	8898.89i	−0.864055	−	0.503397i
$51$	−9807.29			−0.527987
$52$	4663.58	−	20714.4i	0.239172	−	1.06234i
$53$	−1312.47	−	1312.47i	−0.0641798	−	0.0641798i	0.674288	−	0.738468i	$-0.264451\pi$
$53$	−1312.47	−	1312.47i	−0.0641798	−	0.0641798i	−0.738468	+	0.674288i	$0.764451\pi$
$54$	−4252.47	−	14679.1i	−0.198453	−	0.685039i
$55$	−6133.55	−	73.9276i	−0.273404	−	0.00329534i
$56$	26033.1	+	23057.9i	1.10932	+	0.982537i
$57$	45437.7	+	45437.7i	1.85238	+	1.85238i
$58$	7982.44	+	4396.36i	0.311577	+	0.171602i
$59$			20595.0i			0.770249i	0.922865	+	0.385125i	$0.125842\pi$
$59$			20595.0i			0.770249i	−0.922865	+	0.385125i	$0.874158\pi$
$60$	−42508.0	−	10109.9i	−1.52438	−	0.362550i
$61$		−	28836.9i		−	0.992256i	−0.868249	−	0.496128i	$-0.834755\pi$
$61$		−	28836.9i		−	0.992256i	0.868249	−	0.496128i	$-0.165245\pi$
$62$	10384.8	−	18855.6i	0.343097	−	0.622960i
$63$	48035.5	+	48035.5i	1.52479	+	1.52479i
$64$	−32528.2	+	3957.36i	−0.992681	+	0.120769i
$65$	−25910.3	−	26542.5i	−0.760656	−	0.779216i
$66$	−14562.6	+	4218.71i	−0.411508	+	0.119212i
$67$	−27245.0	−	27245.0i	−0.741481	−	0.741481i	0.231382	−	0.972863i	$-0.425675\pi$
$67$	−27245.0	−	27245.0i	−0.741481	−	0.741481i	−0.972863	+	0.231382i	$0.925675\pi$
$68$	−2822.05	+	12534.8i	−0.0740103	+	0.328735i
$69$	40412.8			1.02187
$70$	58551.8	−	16199.9i	1.42822	−	0.395155i
$71$			57260.4i			1.34806i	0.738705	+	0.674029i	$0.235438\pi$
$71$			57260.4i			1.34806i	−0.738705	+	0.674029i	$0.764562\pi$
$72$	−63892.3	+	3872.28i	−1.45250	+	0.0880310i
$73$	−25178.5	+	25178.5i	−0.552996	+	0.552996i	−0.927304	−	0.374308i	$-0.877880\pi$
$73$	−25178.5	+	25178.5i	−0.552996	+	0.552996i	0.374308	+	0.927304i	$0.377880\pi$
$74$	54749.1	−	15860.6i	1.16224	−	0.336697i
$75$	−55258.5	+	52656.7i	−1.13435	+	1.08094i
$76$	71149.2	−	44999.8i	1.41298	−	0.893669i
$77$	14906.0	−	14906.0i	0.286506	−	0.286506i
$78$	−80306.7	−	44229.2i	−1.49457	−	0.823137i
$79$	−56597.7			−1.02031			−0.510154	−	0.860083i	$-0.670412\pi$
$79$	−56597.7			−1.02031			−0.510154	+	0.860083i	$0.670412\pi$
$80$	−25153.3	+	51420.9i	−0.439410	+	0.898287i
$81$	19937.9			0.337650
$82$	60251.2	+	33183.5i	0.989534	+	0.544989i
$83$	41952.5	−	41952.5i	0.668440	−	0.668440i	−0.288914	−	0.957355i	$-0.593294\pi$
$83$	41952.5	−	41952.5i	0.668440	−	0.668440i	0.957355	+	0.288914i	$0.0932943\pi$
$84$	126907.	−	80264.7i	1.96239	−	1.24116i
$85$	15679.0	+	16061.5i	0.235380	+	0.241123i
$86$	−77218.7	+	22369.9i	−1.12584	+	0.326151i
$87$	27823.8	−	27823.8i	0.394111	−	0.394111i
$88$	1201.61	+	19826.5i	0.0165409	+	0.272923i
$89$			28977.6i			0.387782i	0.981023	+	0.193891i	$0.0621108\pi$
$89$			28977.6i			0.387782i	−0.981023	+	0.193891i	$0.937889\pi$
$90$	−55121.4	+	97290.1i	−0.717322	+	1.26608i
$91$	127473.			1.61367
$92$	11628.8	−	51652.1i	0.143240	−	0.636236i
$93$	−65723.5	−	65723.5i	−0.787976	−	0.787976i
$94$	90214.4	−	26134.7i	1.05307	−	0.305069i
$95$	1772.46	−	147055.i	0.0201496	−	1.67175i
$96$	−22669.0	+	139660.i	−0.251046	+	1.54666i
$97$	17161.5	+	17161.5i	0.185193	+	0.185193i	0.793614	−	0.608421i	$-0.208197\pi$
$97$	17161.5	+	17161.5i	0.185193	+	0.185193i	−0.608421	+	0.793614i	$0.708197\pi$
$98$	−54854.5	+	99599.0i	−0.576962	+	1.04759i
$99$			38800.6i			0.397878i
$100$	51400.6	+	85778.6i	0.514006	+	0.857786i
$101$			190789.i			1.86101i	0.366275	+	0.930507i	$0.380633\pi$
$101$			190789.i			1.86101i	−0.366275	+	0.930507i	$0.619367\pi$
$102$	48595.6	+	26764.2i	0.462484	+	0.254714i
$103$	−67508.1	−	67508.1i	−0.626993	−	0.626993i	0.320317	−	0.947310i	$-0.396210\pi$
$103$	−67508.1	−	67508.1i	−0.626993	−	0.626993i	−0.947310	+	0.320317i	$0.896210\pi$
$104$	−79638.1	+	89914.1i	−0.722001	+	0.815163i
$105$	3161.48	−	262298.i	0.0279845	−	2.32178i
$106$	2921.60	+	10085.1i	0.0252555	+	0.0871795i
$107$	−21569.7	−	21569.7i	−0.182132	−	0.182132i	0.610152	−	0.792284i	$-0.291108\pi$
$107$	−21569.7	−	21569.7i	−0.182132	−	0.182132i	−0.792284	+	0.610152i	$0.791108\pi$
$108$	−18988.2	+	84340.7i	−0.156648	+	0.695789i
$109$	−159516.			−1.28599			−0.642995	−	0.765871i	$-0.722308\pi$
$109$	−159516.			−1.28599			−0.642995	+	0.765871i	$0.722308\pi$
$110$	30190.3	+	17104.8i	0.237895	+	0.134783i
$111$		−	246119.i		−	1.89600i
$112$	−66070.1	−	185297.i	−0.497691	−	1.39580i
$113$	−5170.07	+	5170.07i	−0.0380891	+	0.0380891i	−0.725895	−	0.687806i	$-0.758574\pi$
$113$	−5170.07	+	5170.07i	−0.0380891	+	0.0380891i	0.687806	+	0.725895i	$0.258574\pi$
$114$	−101146.	−	349146.i	−0.728932	−	2.51620i
$115$	−64608.1	−	66184.5i	−0.455556	−	0.466672i
$116$	−27555.7	−	43568.3i	−0.190137	−	0.300626i
$117$	−165907.	+	165907.i	−1.12047	+	1.12047i
$118$	56203.9	−	102049.i	0.371588	−	0.674690i
$119$	−77136.9			−0.499338
$120$	183039.	+	166100.i	1.16036	+	1.05297i
$121$	−149011.			−0.925239
$122$	−78696.1	+	142888.i	−0.478689	+	0.869154i
$123$	210013.	−	210013.i	1.25165	−	1.25165i
$124$	−102914.	+	65090.1i	−0.601063	+	0.380155i
$125$	174579.	+	6315.04i	0.999346	+	0.0361494i
$126$	−106929.	−	369108.i	−0.600024	−	2.07122i
$127$	−72936.6	+	72936.6i	−0.401270	+	0.401270i	−0.878680	−	0.477411i	$-0.841575\pi$
$127$	−72936.6	+	72936.6i	−0.401270	+	0.401270i	0.477411	+	0.878680i	$0.341575\pi$
$128$	171978.	+	69160.7i	0.927788	+	0.373108i
$129$			347129.i			1.83661i
$130$	55952.0	+	202229.i	0.290373	+	1.04950i
$131$	−273977.			−1.39488			−0.697440	−	0.716644i	$-0.745677\pi$
$131$	−273977.			−1.39488			−0.697440	+	0.716644i	$0.745677\pi$
$132$	83671.1	+	18837.4i	0.417966	+	0.0940994i
$133$	357379.	+	357379.i	1.75186	+	1.75186i
$134$	60648.5	+	209352.i	0.291782	+	1.00720i
$135$	105496.	+	108070.i	0.498197	+	0.510354i
$136$	48191.1	−	54409.3i	0.223418	−	0.252247i
$137$	24762.9	+	24762.9i	0.112720	+	0.112720i	0.761217	−	0.648497i	$-0.224602\pi$
$137$	24762.9	+	24762.9i	0.112720	+	0.112720i	−0.648497	+	0.761217i	$0.724602\pi$
$138$	−200247.	−	110287.i	−0.895094	−	0.492976i
$139$			99830.6i			0.438255i	0.975696	+	0.219127i	$0.0703211\pi$
$139$			99830.6i			0.438255i	−0.975696	+	0.219127i	$0.929679\pi$
$140$	−334337.	−	79517.0i	−1.44166	−	0.342878i
$141$		−	405550.i		−	1.71789i
$142$	156264.	−	283728.i	0.650337	−	1.18081i
$143$	51482.9	+	51482.9i	0.210534	+	0.210534i
$144$	327157.	+	155175.i	1.31477	+	0.623615i
$145$	−90049.5	−	1085.37i	−0.355682	−	0.00428703i
$146$	193473.	−	56048.3i	0.751169	−	0.217611i
$147$	347165.	+	347165.i	1.32508	+	1.32508i
$148$	−314568.	−	70820.8i	−1.18048	−	0.265770i
$149$	−6833.17			−0.0252149			−0.0126074	−	0.999921i	$-0.504013\pi$
$149$	−6833.17			−0.0252149			−0.0126074	+	0.999921i	$0.504013\pi$
$150$	417509.	−	110116.i	1.51509	−	0.399596i
$151$		−	30711.7i		−	0.109613i	−0.998497	−	0.0548064i	$-0.982546\pi$
$151$		−	30711.7i		−	0.109613i	0.998497	−	0.0548064i	$-0.0174542\pi$
$152$	−475353.	+	28809.4i	−1.66881	+	0.101140i
$153$	100395.	−	100395.i	0.346722	−	0.346722i
$154$	−114538.	+	33181.3i	−0.389179	+	0.112744i
$155$	−2563.78	+	212709.i	−0.00857139	+	0.711141i
$156$	277222.	+	438315.i	0.912044	+	1.44203i
$157$	203987.	−	203987.i	0.660470	−	0.660470i	−0.295021	−	0.955491i	$-0.595327\pi$
$157$	203987.	−	203987.i	0.660470	−	0.660470i	0.955491	+	0.295021i	$0.0953265\pi$
$158$	280444.	+	154456.i	0.893726	+	0.492222i
$159$	45336.4			0.142218
$160$	264964.	−	186150.i	0.818252	−	0.574860i
$161$	317857.			0.966423
$162$	−98793.3	−	54410.8i	−0.295760	−	0.162891i
$163$	130313.	−	130313.i	0.384166	−	0.384166i	−0.488434	−	0.872601i	$-0.662432\pi$
$163$	130313.	−	130313.i	0.384166	−	0.384166i	0.872601	+	0.488434i	$0.162432\pi$
$164$	−207989.	−	328852.i	−0.603853	−	0.954753i
$165$	107212.	−	104658.i	0.306573	−	0.299271i
$166$	−322366.	+	93387.9i	−0.907984	+	0.263039i
$167$	177343.	−	177343.i	0.492067	−	0.492067i	−0.416890	−	0.908957i	$-0.636880\pi$
$167$	177343.	−	177343.i	0.492067	−	0.492067i	0.908957	+	0.416890i	$0.136880\pi$
$168$	−847872.	+	51386.4i	−2.31770	+	0.140467i
$169$			68977.3i			0.185776i
$170$	−33857.9	−	122374.i	−0.0898542	−	0.324762i
$171$	−930266.			−2.43286
$172$	443670.	+	99886.4i	1.14351	+	0.257445i
$173$	19021.2	+	19021.2i	0.0483194	+	0.0483194i	0.730854	−	0.682534i	$-0.239122\pi$
$173$	19021.2	+	19021.2i	0.0483194	+	0.0483194i	−0.682534	+	0.730854i	$0.739122\pi$
$174$	−213800.	+	61936.9i	−0.535346	+	0.155087i
$175$	−434623.	+	414159.i	−1.07280	+	1.02229i
$176$	48152.8	−	101521.i	0.117176	−	0.247043i
$177$	−355705.	−	355705.i	−0.853409	−	0.853409i
$178$	79080.2	−	143586.i	0.187076	−	0.339673i
$179$		−	270618.i		−	0.631283i	−0.948878	−	0.315642i	$-0.897780\pi$
$179$		−	270618.i		−	0.631283i	0.948878	−	0.315642i	$-0.102220\pi$
$180$	538635.	−	331651.i	1.23912	−	0.762956i
$181$			454629.i			1.03148i	0.856745	+	0.515740i	$0.172483\pi$
$181$			454629.i			1.03148i	−0.856745	+	0.515740i	$0.827517\pi$
$182$	−631633.	−	347874.i	−1.41347	−	0.778473i
$183$	498055.	+	498055.i	1.09938	+	1.09938i
$184$	−198580.	+	224204.i	−0.432406	+	0.488200i
$185$	−403072.	+	393472.i	−0.865872	+	0.845248i
$186$	146303.	+	505023.i	0.310078	+	1.07036i
$187$	−31153.6	−	31153.6i	−0.0651484	−	0.0651484i
$188$	−518339.	−	116697.i	−1.06959	−	0.240805i
$189$	−519016.			−1.05688
$190$	−410098.	+	723829.i	−0.824145	+	1.45463i
$191$		−	251074.i		−	0.497988i	−0.968505	−	0.248994i	$-0.919900\pi$
$191$		−	251074.i		−	0.497988i	0.968505	−	0.248994i	$-0.0800999\pi$
$192$	493459.	−	630158.i	0.966047	−	1.23366i
$193$	−12037.9	+	12037.9i	−0.0232626	+	0.0232626i	−0.718642	−	0.695380i	$-0.755236\pi$
$193$	−12037.9	+	12037.9i	−0.0232626	+	0.0232626i	0.695380	+	0.718642i	$0.255236\pi$
$194$	−38202.1	−	131870.i	−0.0728758	−	0.251560i
$195$	905935.	+	10919.2i	1.70612	+	0.0205639i
$196$	543613.	−	343820.i	1.01076	−	0.639279i
$197$	3901.52	−	3901.52i	0.00716257	−	0.00716257i	−0.703516	−	0.710679i	$-0.748388\pi$
$197$	3901.52	−	3901.52i	0.00716257	−	0.00716257i	0.710679	+	0.703516i	$0.248388\pi$
$198$	105887.	−	192259.i	0.191946	−	0.348516i
$199$	298621.			0.534550			0.267275	−	0.963620i	$-0.413877\pi$
$199$	298621.			0.534550			0.267275	+	0.963620i	$0.413877\pi$
$200$	−20601.9	−	565310.i	−0.0364194	−	0.999337i
$201$	941122.			1.64307
$202$	520664.	−	945368.i	0.897800	−	1.63013i
$203$	218842.	−	218842.i	0.372727	−	0.372727i
$204$	−167754.	−	265236.i	−0.282226	−	0.446228i
$205$	−679690.	−	8192.31i	−1.12960	−	0.0136151i
$206$	150276.	+	518736.i	0.246729	+	0.851684i
$207$	−413694.	+	413694.i	−0.671048	+	0.671048i
$208$	639987.	−	228195.i	1.02568	−	0.365720i
$209$			288672.i			0.457130i
$210$	−731479.	+	1.29107e6i	−1.14460	+	2.02024i
$211$	−1.05067e6			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$211$	−1.05067e6			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$212$	13045.6	−	57945.1i	0.0199353	−	0.0885476i
$213$	−988971.	−	988971.i	−1.49360	−	1.49360i
$214$	48015.1	+	165743.i	0.0716709	+	0.247401i
$215$	568497.	−	554956.i	0.838750	−	0.818772i
$216$	324254.	−	366093.i	0.472880	−	0.533897i
$217$	−516933.	−	516933.i	−0.745220	−	0.745220i
$218$	790408.	+	435320.i	1.12645	+	0.620394i
$219$		−	869738.i		−	1.22540i
$220$	−102915.	−	167145.i	−0.143358	−	0.232828i
$221$		−	266419.i		−	0.366931i
$222$	−671661.	+	1.21953e6i	−0.914677	+	1.66077i
$223$	−406061.	−	406061.i	−0.546800	−	0.546800i	0.378714	−	0.925514i	$-0.376367\pi$
$223$	−406061.	−	406061.i	−0.546800	−	0.546800i	−0.925514	+	0.378714i	$0.876367\pi$
$224$	−178298.	+	1.09846e6i	−0.237425	+	1.46273i
$225$	26633.7	−	1.10470e6i	0.0350732	−	1.45475i
$226$	39727.1	−	11508.8i	0.0517388	−	0.0149885i
$227$	1.06139e6	+	1.06139e6i	1.36713	+	1.36713i	0.864500	+	0.502634i	$0.167636\pi$
$227$	1.06139e6	+	1.06139e6i	1.36713	+	1.36713i	0.502634	+	0.864500i	$0.332364\pi$
$228$	−451638.	+	2.00606e6i	−0.575378	+	2.55569i
$229$	767294.			0.966881			0.483440	−	0.875377i	$-0.339387\pi$
$229$	767294.			0.966881			0.483440	+	0.875377i	$0.339387\pi$
$230$	139518.	+	504263.i	0.173904	+	0.628547i
$231$			514896.i			0.634877i
$232$	17641.5	+	291083.i	0.0215186	+	0.355056i
$233$	227771.	−	227771.i	0.274858	−	0.274858i	−0.556194	−	0.831052i	$-0.687739\pi$
$233$	227771.	−	227771.i	0.274858	−	0.274858i	0.831052	+	0.556194i	$0.187739\pi$
$234$	1.27484e6	−	369316.i	1.52200	−	0.440918i
$235$	−664174.	+	648354.i	−0.784535	+	0.765848i
$236$	−556986.	+	352278.i	−0.650975	+	0.411723i
$237$	977525.	−	977525.i	1.13046	−	1.13046i
$238$	382217.	+	210507.i	0.437389	+	0.240893i
$239$	−205259.			−0.232438			−0.116219	−	0.993224i	$-0.537077\pi$
$239$	−205259.			−0.232438			−0.116219	+	0.993224i	$0.537077\pi$
$240$	−453681.	−	1.32255e6i	−0.508419	−	1.48212i
$241$	1.47338e6			1.63407			0.817037	−	0.576585i	$-0.195615\pi$
$241$	1.47338e6			1.63407			0.817037	+	0.576585i	$0.195615\pi$
$242$	738355.	+	406652.i	0.810452	+	0.446359i
$243$	−808567.	+	808567.i	−0.878417	+	0.878417i
$244$	779886.	−	493256.i	0.838604	−	0.530393i
$245$	13542.4	−	1.12357e6i	0.0144139	−	1.19587i
$246$	−1.61375e6	+	467498.i	−1.70020	+	0.492540i
$247$	−1.23433e6	+	1.23433e6i	−1.28733	+	1.28733i
$248$	687575.	−	41671.4i	0.709890	−	0.0430238i
$249$			1.44916e6i			1.48122i
$250$	−847812.	−	507718.i	−0.857925	−	0.513775i
$251$	1.12409e6			1.12620			0.563102	−	0.826387i	$-0.309608\pi$
$251$	1.12409e6			1.12620			0.563102	+	0.826387i	$0.309608\pi$
$252$	−477460.	+	2.12076e6i	−0.473626	+	2.10373i
$253$	128374.	+	128374.i	0.126089	+	0.126089i
$254$	560449.	−	162360.i	0.545070	−	0.157904i
$255$	−548204.	−	6607.51i	−0.527949	−	0.00636337i
$256$	−663421.	−	812025.i	−0.632687	−	0.774408i
$257$	−402647.	−	402647.i	−0.380270	−	0.380270i	0.490929	−	0.871199i	$-0.336657\pi$
$257$	−402647.	−	402647.i	−0.380270	−	0.380270i	−0.871199	+	0.490929i	$0.836657\pi$
$258$	947318.	−	1.72004e6i	0.886026	−	1.60875i
$259$		−	1.93579e6i		−	1.79312i
$260$	274639.	−	1.15475e6i	0.251958	−	1.05938i
$261$			569650.i			0.517615i
$262$	1.35757e6	+	747687.i	1.22183	+	0.672925i
$263$	918848.	+	918848.i	0.819133	+	0.819133i	0.985982	−	0.166849i	$-0.0533593\pi$
$263$	918848.	+	918848.i	0.819133	+	0.819133i	−0.166849	+	0.985982i	$0.553359\pi$
$264$	−363187.	−	321680.i	−0.320716	−	0.284062i
$265$	−72479.5	−	74248.0i	−0.0634017	−	0.0649487i
$266$	−795541.	−	2.74612e6i	−0.689379	−	2.37967i
$267$	−500486.	−	500486.i	−0.429649	−	0.429649i
$268$	270808.	−	1.20286e6i	0.230316	−	1.02301i
$269$	−859452.			−0.724171			−0.362085	−	0.932145i	$-0.617935\pi$
$269$	−859452.			−0.724171			−0.362085	+	0.932145i	$0.617935\pi$
$270$	−227813.	−	823392.i	−0.190182	−	0.687381i
$271$		−	133818.i		−	0.110686i	−0.998467	−	0.0553428i	$-0.982375\pi$
$271$		−	133818.i		−	0.110686i	0.998467	−	0.0553428i	$-0.0176252\pi$
$272$	−387272.	+	138087.i	−0.317391	+	0.113170i
$273$	−2.20164e6	+	2.20164e6i	−1.78788	+	1.78788i
$274$	−55123.2	−	190280.i	−0.0443566	−	0.153114i
$275$	−342801.	−	8264.76i	−0.273344	−	0.00659020i
$276$	691261.	+	1.09295e6i	0.546222	+	0.863632i
$277$	−511140.	+	511140.i	−0.400258	+	0.400258i	−0.878324	−	0.478066i	$-0.841338\pi$
$277$	−511140.	+	511140.i	−0.400258	+	0.400258i	0.478066	+	0.878324i	$0.341338\pi$
$278$	272439.	−	494666.i	0.211425	−	0.383884i
$279$	1.34559e6			1.03491
$280$	1.43965e6	+	1.30642e6i	1.09739	+	0.995835i
$281$	1.05360e6			0.795994			0.397997	−	0.917387i	$-0.369705\pi$
$281$	1.05360e6			0.795994			0.397997	+	0.917387i	$0.369705\pi$
$282$	−1.10675e6	+	2.00952e6i	−0.828755	+	1.50477i
$283$	151790.	−	151790.i	0.112662	−	0.112662i	−0.648528	−	0.761190i	$-0.724615\pi$
$283$	151790.	−	151790.i	0.112662	−	0.112662i	0.761190	+	0.648528i	$0.224615\pi$
$284$	−1.54859e6	+	979440.i	−1.13931	+	0.720580i
$285$	2.50925e6	+	2.57047e6i	1.82992	+	1.87457i
$286$	−114603.	−	395597.i	−0.0828477	−	0.285982i
$287$	1.65181e6	−	1.65181e6i	1.18374	−	1.18374i
$288$	−1.19760e6	−	1.66172e6i	−0.850809	−	1.18053i
$289$		−	1.25864e6i		−	0.886456i
$290$	443238.	+	251124.i	0.309487	+	0.175345i
$291$	−592807.			−0.410375
$292$	−1.11162e6	−	250267.i	−0.762958	−	0.171770i
$293$	−1.05639e6	−	1.05639e6i	−0.718881	−	0.718881i	0.249495	−	0.968376i	$-0.419735\pi$
$293$	−1.05639e6	−	1.05639e6i	−0.718881	−	0.718881i	−0.968376	+	0.249495i	$0.919735\pi$
$294$	−772803.	−	2.66764e6i	−0.521435	−	1.79994i
$295$	−13875.6	+	1.15121e6i	−0.00928315	+	0.770194i
$296$	1.36543e6	+	1.20938e6i	0.905816	+	0.802294i
$297$	−209617.	−	209617.i	−0.137891	−	0.137891i
$298$	33858.7	+	18647.8i	0.0220866	+	0.0121643i
$299$			1.09783e6i			0.710160i
$300$	−2.36929e6	−	593758.i	−1.51990	−	0.380896i
$301$			2.73026e6i			1.73695i
$302$	−83812.5	+	152178.i	−0.0528800	+	0.0960140i
$303$	−3.29520e6	−	3.29520e6i	−2.06194	−	2.06194i
$304$	2.43402e6	+	1.15449e6i	1.51057	+	0.716484i
$305$	19428.4	−	1.61191e6i	0.0119588	−	0.992184i
$306$	−771437.	+	223482.i	−0.470974	+	0.136439i
$307$	−460970.	−	460970.i	−0.279143	−	0.279143i	0.553624	−	0.832767i	$-0.313245\pi$
$307$	−460970.	−	460970.i	−0.279143	−	0.279143i	−0.832767	+	0.553624i	$0.813245\pi$
$308$	658095.	+	148161.i	0.395287	+	0.0889935i
$309$	2.33193e6			1.38937
$310$	593187.	−	1.04698e6i	0.350580	−	0.618780i
$311$		−	44810.5i		−	0.0262711i	−0.999914	−	0.0131356i	$-0.995819\pi$
$311$		−	44810.5i		−	0.0262711i	0.999914	−	0.0131356i	$-0.00418130\pi$
$312$	−177480.	−	2.92841e6i	−0.103220	−	1.70312i
$313$	−2.36991e6	+	2.36991e6i	−1.36733	+	1.36733i	−0.503093	+	0.864232i	$0.667805\pi$
$313$	−2.36991e6	+	2.36991e6i	−1.36733	+	1.36733i	−0.864232	+	0.503093i	$0.832195\pi$
$314$	−1.56745e6	+	454083.i	−0.897158	+	0.259903i
$315$	2.65271e6	+	2.71743e6i	1.50631	+	1.54306i
$316$	−968105.	−	1.53067e6i	−0.545387	−	0.862311i
$317$	−2.29735e6	+	2.29735e6i	−1.28404	+	1.28404i	−0.345697	+	0.938346i	$0.612357\pi$
$317$	−2.29735e6	+	2.29735e6i	−1.28404	+	1.28404i	−0.938346	+	0.345697i	$0.887643\pi$
$318$	−224644.	−	123723.i	−0.124574	−	0.0686095i
$319$	176769.			0.0972589
$320$	−1.82091e6	+	199292.i	−0.994064	+	0.108796i
$321$	745081.			0.403591
$322$	−1.57500e6	−	867435.i	−0.846526	−	0.466227i
$323$	746925.	−	746925.i	0.398355	−	0.398355i
$324$	341038.	+	539216.i	0.180485	+	0.285365i
$325$	−1.43044e6	−	1.50112e6i	−0.751210	−	0.788327i
$326$	−1.00133e6	+	290082.i	−0.521837	+	0.151174i
$327$	2.75507e6	−	2.75507e6i	1.42483	−	1.42483i
$328$	133157.	+	2.19708e6i	0.0683407	+	1.12762i
$329$		−	3.18976e6i		−	1.62468i
$330$	−816855.	+	226005.i	−0.412914	+	0.114244i
$331$	−336759.			−0.168947			−0.0844733	−	0.996426i	$-0.526921\pi$
$331$	−336759.			−0.168947			−0.0844733	+	0.996426i	$0.526921\pi$
$332$	1.85219e6	+	416997.i	0.922234	+	0.207629i
$333$	2.51945e6	+	2.51945e6i	1.24508	+	1.24508i
$334$	−1.36272e6	+	394774.i	−0.668405	+	0.193634i
$335$	−1.50458e6	−	1.54129e6i	−0.732491	−	0.750364i
$336$	4.34148e6	+	2.05923e6i	2.09792	+	0.995076i
$337$	1.01889e6	+	1.01889e6i	0.488712	+	0.488712i	0.907900	−	0.419187i	$-0.137685\pi$
$337$	1.01889e6	+	1.01889e6i	0.488712	+	0.488712i	−0.419187	+	0.907900i	$0.637685\pi$
$338$	188240.	−	341786.i	0.0896230	−	0.162728i
$339$		−	178589.i		−	0.0844027i
$340$	−166191.	+	698766.i	−0.0779669	+	0.327819i
$341$		−	417551.i		−	0.194457i
$342$	4.60951e6	+	2.53870e6i	2.13103	+	1.17367i
$343$	447406.	+	447406.i	0.205336	+	0.205336i
$344$	−1.92582e6	−	1.70572e6i	−0.877443	−	0.777163i
$345$	2.25898e6	+	27227.5i	1.02180	+	0.0123157i
$346$	−42341.9	−	146160.i	−0.0190143	−	0.0656353i
$347$	−969632.	−	969632.i	−0.432298	−	0.432298i	0.457111	−	0.889409i	$-0.348884\pi$
$347$	−969632.	−	969632.i	−0.432298	−	0.432298i	−0.889409	+	0.457111i	$0.848884\pi$
$348$	1.22842e6	+	276561.i	0.543747	+	0.122417i
$349$	33463.7			0.0147066			0.00735328	−	0.999973i	$-0.497659\pi$
$349$	33463.7			0.0147066			0.00735328	+	0.999973i	$0.497659\pi$
$350$	3.28382e6	−	866089.i	1.43288	−	0.377914i
$351$		−	1.79260e6i		−	0.776633i
$352$	−515650.	+	371631.i	−0.221819	+	0.159866i
$353$	−1.13980e6	+	1.13980e6i	−0.486845	+	0.486845i	−0.907309	−	0.420464i	$-0.861867\pi$
$353$	−1.13980e6	+	1.13980e6i	−0.486845	+	0.486845i	0.420464	+	0.907309i	$0.361867\pi$
$354$	791814.	+	2.73326e6i	0.335827	+	1.15924i
$355$	−38578.3	+	3.20072e6i	−0.0162470	+	1.34796i
$356$	−783692.	+	495663.i	−0.327733	+	0.207282i
$357$	1.33227e6	−	1.33227e6i	0.553249	−	0.553249i
$358$	−738520.	+	1.34093e6i	−0.304547	+	0.552965i
$359$	3.63472e6			1.48845			0.744226	−	0.667928i	$-0.232818\pi$
$359$	3.63472e6			1.48845			0.744226	+	0.667928i	$0.232818\pi$
$360$	−3.57404e6	+	173405.i	−1.45346	+	0.0705188i
$361$	−4.44499e6			−1.79516
$362$	1.24069e6	−	2.25271e6i	0.497612	−	0.903512i
$363$	2.57363e6	−	2.57363e6i	1.02513	−	1.02513i
$364$	2.18042e6	+	3.44747e6i	0.862556	+	1.36379i
$365$	−1.42438e6	+	1.39045e6i	−0.559621	+	0.546291i
$366$	−1.10869e6	−	3.82708e6i	−0.432621	−	1.49336i
$367$	−3.14879e6	+	3.14879e6i	−1.22034	+	1.22034i	−0.252823	+	0.967513i	$0.581359\pi$
$367$	−3.14879e6	+	3.14879e6i	−1.22034	+	1.22034i	−0.967513	+	0.252823i	$0.918641\pi$
$368$	1.59583e6	−	569012.i	0.614280	−	0.219029i
$369$			4.29969e6i			1.64389i
$370$	3.07103e6	−	849683.i	1.16622	−	0.322666i
$371$	356583.			0.134501
$372$	653274.	−	2.90168e6i	0.244758	−	1.08716i
$373$	−935485.	−	935485.i	−0.348149	−	0.348149i	0.511271	−	0.859420i	$-0.329175\pi$
$373$	−935485.	−	935485.i	−0.348149	−	0.348149i	−0.859420	+	0.511271i	$0.829175\pi$
$374$	69349.1	+	239386.i	0.0256367	+	0.0884952i
$375$	−3.12430e6	+	2.90616e6i	−1.14729	+	1.06719i
$376$	2.24993e6	+	1.99279e6i	0.820727	+	0.726929i
$377$	755845.	+	755845.i	0.273892	+	0.273892i
$378$	2.57175e6	+	1.41640e6i	0.925763	+	0.509867i
$379$		−	1.29738e6i		−	0.463948i	−0.972722	−	0.231974i	$-0.925482\pi$
$379$		−	1.29738e6i		−	0.463948i	0.972722	−	0.231974i	$-0.0745184\pi$
$380$	4.00739e6	−	2.46745e6i	1.42365	−	0.876575i
$381$		−	2.51944e6i		−	0.889185i
$382$	−685184.	+	1.24408e6i	−0.240242	+	0.436206i
$383$	2.38206e6	+	2.38206e6i	0.829766	+	0.829766i	0.987484	−	0.157718i	$-0.0504137\pi$
$383$	2.38206e6	+	2.38206e6i	0.829766	+	0.829766i	−0.157718	+	0.987484i	$0.550414\pi$
$384$	−4.16482e6	+	1.77581e6i	−1.44135	+	0.614565i
$385$	843252.	−	823166.i	0.289938	−	0.283032i
$386$	92500.0	−	26796.9i	0.0315990	−	0.00915410i
$387$	−3.55346e6	−	3.55346e6i	−1.20608	−	1.20608i
$388$	−170581.	+	757675.i	−0.0575241	+	0.255508i
$389$	−3.68559e6			−1.23490			−0.617451	−	0.786609i	$-0.711835\pi$
$389$	−3.68559e6			−1.23490			−0.617451	+	0.786609i	$0.711835\pi$
$390$	−4.45915e6	−	2.52641e6i	−1.48454	−	0.841090i
$391$		−	664323.i		−	0.219754i
$392$	−3.63192e6	+	220117.i	−1.19377	+	0.0723500i
$393$	4.73199e6	−	4.73199e6i	1.54548	−	1.54548i
$394$	−29979.5	+	8684.95i	−0.00972936	+	0.00281856i
$395$	−3.16368e6	−	38131.8i	−1.02023	−	0.0122969i
$396$	−1.04935e6	+	663684.i	−0.336266	+	0.212679i
$397$	4.08468e6	−	4.08468e6i	1.30071	−	1.30071i	0.372802	−	0.927911i	$-0.378397\pi$
$397$	4.08468e6	−	4.08468e6i	1.30071	−	1.30071i	0.927911	−	0.372802i	$-0.121603\pi$
$398$	−1.47968e6	−	814940.i	−0.468232	−	0.257880i
$399$	−1.23449e7			−3.88201
$400$	−1.44065e6	+	2.85736e6i	−0.450204	+	0.892926i
$401$	2.80149e6			0.870017			0.435008	−	0.900426i	$-0.356745\pi$
$401$	2.80149e6			0.870017			0.435008	+	0.900426i	$0.356745\pi$
$402$	−4.66331e6	−	2.56833e6i	−1.43923	−	0.792658i
$403$	1.78540e6	−	1.78540e6i	0.547613	−	0.547613i
$404$	−5.15983e6	+	3.26345e6i	−1.57283	+	0.994771i
$405$	1.11448e6	+	13432.9i	0.337626	+	0.00406941i
$406$	−1.68159e6	+	487151.i	−0.506298	+	0.146672i
$407$	781816.	−	781816.i	0.233947	−	0.233947i
$408$	107398.	+	1.77206e6i	0.0319408	+	0.527020i
$409$		−	4.14449e6i		−	1.22508i	−0.790441	−	0.612538i	$-0.790149\pi$
$409$		−	4.14449e6i		−	1.22508i	0.790441	−	0.612538i	$-0.209851\pi$
$410$	3.34554e6	+	1.89547e6i	0.982894	+	0.556876i
$411$	−855383.			−0.249779
$412$	671012.	−	2.98047e6i	0.194754	−	0.865050i
$413$	−2.79772e6	−	2.79772e6i	−0.807102	−	0.807102i
$414$	3.17885e6	−	920900.i	0.911527	−	0.264065i
$415$	2.37331e6	−	2.31678e6i	0.676448	−	0.660336i
$416$	−3.79392e6	−	615812.i	−1.07487	−	0.174468i
$417$	−1.72422e6	−	1.72422e6i	−0.485571	−	0.485571i
$418$	787790.	−	1.43039e6i	0.220531	−	0.400417i
$419$			1.58235e6i			0.440320i	0.975464	+	0.220160i	$0.0706579\pi$
$419$			1.58235e6i			0.440320i	−0.975464	+	0.220160i	$0.929342\pi$
$420$	7.14786e6	−	4.40111e6i	1.97721	−	1.21742i
$421$		−	4.44020e6i		−	1.22095i	−0.792036	−	0.610475i	$-0.790979\pi$
$421$		−	4.44020e6i		−	1.22095i	0.792036	−	0.610475i	$-0.209021\pi$
$422$	5.20614e6	+	2.86730e6i	1.42310	+	0.783776i
$423$	4.15150e6	+	4.15150e6i	1.12812	+	1.12812i
$424$	−222774.	+	251519.i	−0.0601797	+	0.0679449i
$425$	865595.	+	908365.i	0.232457	+	0.243943i
$426$	2.20149e6	+	7.59931e6i	0.587750	+	2.02885i
$427$	3.91734e6	+	3.91734e6i	1.03973	+	1.03973i
$428$	214397.	−	952298.i	0.0565731	−	0.251283i
$429$	−1.77837e6			−0.466529
$430$	−4.33141e6	+	1.19840e6i	−1.12969	+	0.312558i
$431$			1.63067e6i			0.422838i	0.977396	+	0.211419i	$0.0678084\pi$
$431$			1.63067e6i			0.422838i	−0.977396	+	0.211419i	$0.932192\pi$
$432$	−2.60577e6	+	929118.i	−0.671778	+	0.239531i
$433$	247629.	−	247629.i	0.0634719	−	0.0634719i	−0.674658	−	0.738130i	$-0.735709\pi$
$433$	247629.	−	247629.i	0.0634719	−	0.0634719i	0.738130	+	0.674658i	$0.235709\pi$
$434$	1.15071e6	+	3.97214e6i	0.293253	+	1.01228i
$435$	1.57403e6	−	1.53654e6i	0.398832	−	0.389333i
$436$	−2.72852e6	−	4.31406e6i	−0.687402	−	1.08685i
$437$	−3.07784e6	+	3.07784e6i	−0.770980	+	0.770980i
$438$	−2.37352e6	+	4.30959e6i	−0.591164	+	1.07337i
$439$	5.01088e6			1.24094			0.620472	−	0.784228i	$-0.286941\pi$
$439$	5.01088e6			1.24094			0.620472	+	0.784228i	$0.286941\pi$
$440$	53809.6	+	1.10907e6i	0.0132504	+	0.273103i
$441$	−7.10767e6			−1.74033
$442$	−727059.	+	1.32012e6i	−0.177017	+	0.321408i
$443$	−4.59370e6	+	4.59370e6i	−1.11212	+	1.11212i	−0.119261	+	0.992863i	$0.538053\pi$
$443$	−4.59370e6	+	4.59370e6i	−1.11212	+	1.11212i	−0.992863	+	0.119261i	$0.961947\pi$
$444$	6.65623e6	−	4.20987e6i	1.60240	−	1.01347i
$445$	−19523.2	+	1.61978e6i	−0.00467360	+	0.387754i
$446$	903907.	+	3.12019e6i	0.215172	+	0.742753i
$447$	118019.	−	118019.i	0.0279372	−	0.0279372i
$448$	3.88119e6	−	4.95636e6i	0.913629	−	1.16672i
$449$			5.19864e6i			1.21695i	0.793572	+	0.608476i	$0.208219\pi$
$449$			5.19864e6i			1.21695i	−0.793572	+	0.608476i	$0.791781\pi$
$450$	−3.14670e6	+	5.40115e6i	−0.732529	+	1.25735i
$451$	1.33425e6			0.308883
$452$	−228257.	−	51389.1i	−0.0525508	−	0.0118311i
$453$	530436.	+	530436.i	0.121447	+	0.121447i
$454$	−2.36270e6	−	8.15579e6i	−0.537983	−	1.85706i
$455$	7.12542e6	+	85882.7i	1.61355	+	0.0194481i
$456$	7.71245e6	−	8.70761e6i	1.73692	−	1.96104i
$457$	4.65839e6	+	4.65839e6i	1.04339	+	1.04339i	0.999015	+	0.0443713i	$0.0141285\pi$
$457$	4.65839e6	+	4.65839e6i	1.04339	+	1.04339i	0.0443713	+	0.999015i	$0.485872\pi$
$458$	−3.80198e6	−	2.09395e6i	−0.846927	−	0.466448i
$459$			1.08475e6i			0.240324i
$460$	684821.	−	2.87940e6i	0.150898	−	0.634464i
$461$			1.06915e6i			0.234308i	0.993114	+	0.117154i	$0.0373771\pi$
$461$			1.06915e6i			0.234308i	−0.993114	+	0.117154i	$0.962623\pi$
$462$	1.40516e6	−	2.55133e6i	0.306281	−	0.556112i
$463$	−2.38078e6	−	2.38078e6i	−0.516140	−	0.516140i	0.400261	−	0.916401i	$-0.368919\pi$
$463$	−2.38078e6	−	2.38078e6i	−0.516140	−	0.516140i	−0.916401	+	0.400261i	$0.868919\pi$
$464$	706954.	−	1.49047e6i	0.152439	−	0.321388i
$465$	−3.62951e6	−	3.71807e6i	−0.778422	−	0.797416i
$466$	−1.75021e6	+	507027.i	−0.373357	+	0.108160i
$467$	1.78812e6	+	1.78812e6i	0.379405	+	0.379405i	0.870888	−	0.491482i	$-0.163545\pi$
$467$	1.78812e6	+	1.78812e6i	0.379405	+	0.379405i	−0.491482	+	0.870888i	$0.663545\pi$
$468$	−7.32475e6	−	1.64907e6i	−1.54589	−	0.348036i
$469$	7.40218e6			1.55392
$470$	5.06038e6	−	1.40009e6i	1.05667	−	0.292355i
$471$			7.04630e6i			1.46355i
$472$	3.72126e6	−	225532.i	0.768839	−	0.0465965i
$473$	−1.10268e6	+	1.10268e6i	−0.226619	+	0.226619i
$474$	−7.51136e6	+	2.17601e6i	−1.53558	+	0.444851i
$475$	198152.	−	8.21885e6i	0.0402963	−	1.67139i
$476$	−1.31943e6	−	2.08615e6i	−0.266912	−	0.422015i
$477$	−464096.	+	464096.i	−0.0933926	+	0.0933926i
$478$	1.01707e6	+	560154.i	0.203601	+	0.112134i
$479$	6.71412e6			1.33706			0.668530	−	0.743686i	$-0.266924\pi$
$479$	6.71412e6			1.33706			0.668530	+	0.743686i	$0.266924\pi$
$480$	−1.36124e6	+	7.79139e6i	−0.269669	+	1.54352i
$481$	6.68592e6			1.31764
$482$	−7.30066e6	−	4.02086e6i	−1.43135	−	0.788318i
$483$	−5.48985e6	+	5.48985e6i	−1.07076	+	1.07076i
$484$	−2.54883e6	−	4.02996e6i	−0.494570	−	0.781965i
$485$	947724.	+	970849.i	0.182948	+	0.187412i
$486$	6.21308e6	−	1.79990e6i	1.19321	−	0.345667i
$487$	−2.69373e6	+	2.69373e6i	−0.514672	+	0.514672i	−0.915955	−	0.401282i	$-0.868565\pi$
$487$	−2.69373e6	+	2.69373e6i	−0.514672	+	0.514672i	0.401282	+	0.915955i	$0.368565\pi$
$488$	−5.21047e6	+	315788.i	−0.990439	+	0.0600269i
$489$			4.50140e6i			0.851285i
$490$	−3.13334e6	+	5.53039e6i	−0.589545	+	1.04056i
$491$	−1.95727e6			−0.366393			−0.183196	−	0.983076i	$-0.558644\pi$
$491$	−1.95727e6			−0.366393			−0.183196	+	0.983076i	$0.558644\pi$
$492$	9.27203e6	+	2.08747e6i	1.72688	+	0.388784i
$493$	−457381.	−	457381.i	−0.0847541	−	0.0847541i
$494$	9.48468e6	−	2.74767e6i	1.74866	−	0.506579i
$495$	−26141.3	+	2.16886e6i	−0.00479528	+	0.397849i
$496$	−3.52069e6	−	1.66992e6i	−0.642575	−	0.304783i
$497$	−7.77852e6	−	7.77852e6i	−1.41256	−	1.41256i
$498$	3.95478e6	−	7.18067e6i	0.714576	−	1.29745i
$499$			6.23022e6i			1.12009i	0.828463	+	0.560044i	$0.189216\pi$
$499$			6.23022e6i			1.12009i	−0.828463	+	0.560044i	$0.810784\pi$
$500$	2.81538e6	+	4.82945e6i	0.503631	+	0.863919i
$501$			6.12596e6i			1.09039i
$502$	−5.56993e6	−	3.06765e6i	−0.986484	−	0.543309i
$503$	997584.	+	997584.i	0.175804	+	0.175804i	0.789524	−	0.613720i	$-0.210328\pi$
$503$	997584.	+	997584.i	0.175804	+	0.175804i	−0.613720	+	0.789524i	$0.710328\pi$
$504$	8.15340e6	−	9.20546e6i	1.42976	−	1.61424i
$505$	−128541.	+	1.06646e7i	−0.0224292	+	1.86088i
$506$	−285766.	−	986435.i	−0.0496174	−	0.171274i
$507$	−1.19134e6	−	1.19134e6i	−0.205833	−	0.205833i
$508$	−3.22013e6	−	724970.i	−0.553624	−	0.124641i
$509$	−2.76272e6			−0.472652			−0.236326	−	0.971674i	$-0.575943\pi$
$509$	−2.76272e6			−0.472652			−0.236326	+	0.971674i	$0.575943\pi$
$510$	2.69835e6	+	1.52879e6i	0.459380	+	0.260270i
$511$		−	6.84072e6i		−	1.15891i
$512$	1.07126e6	+	5.83410e6i	0.180600	+	0.983557i
$513$	5.02569e6	−	5.02569e6i	0.843146	−	0.843146i
$514$	896309.	+	3.09397e6i	0.149641	+	0.516545i
$515$	−3.72806e6	−	3.81902e6i	−0.619391	−	0.634504i
$516$	−9.38801e6	+	5.93764e6i	−1.55221	+	0.981725i
$517$	1.28826e6	−	1.28826e6i	0.211971	−	0.211971i
$518$	−5.28279e6	+	9.59194e6i	−0.865046	+	1.57066i
$519$	−657046.			−0.107072
$520$	−4.51216e6	+	4.97233e6i	−0.731773	+	0.806402i
$521$	878624.			0.141811			0.0709053	−	0.997483i	$-0.477411\pi$
$521$	878624.			0.141811			0.0709053	+	0.997483i	$0.477411\pi$
$522$	1.55458e6	−	2.82264e6i	0.249710	−	0.453398i
$523$	1.66656e6	−	1.66656e6i	0.266420	−	0.266420i	−0.561236	−	0.827656i	$-0.689674\pi$
$523$	1.66656e6	−	1.66656e6i	0.266420	−	0.266420i	0.827656	+	0.561236i	$0.189674\pi$
$524$	−4.68639e6	−	7.40965e6i	−0.745607	−	1.17888i
$525$	353438.	−	1.46597e7i	0.0559648	−	2.32128i
$526$	−2.04539e6	−	7.06048e6i	−0.322339	−	1.11268i
$527$	−1.08039e6	+	1.08039e6i	−0.169455	+	0.169455i
$528$	921742.	+	2.58508e6i	0.143888	+	0.403542i
$529$		−	3.69887e6i		−	0.574686i
$530$	156516.	+	565700.i	0.0242030	+	0.0874775i
$531$	7.28252e6			1.12084
$532$	−3.55226e6	+	1.57782e7i	−0.544158	+	2.41701i
$533$	5.70509e6	+	5.70509e6i	0.869850	+	0.869850i
$534$	1.11410e6	+	3.84576e6i	0.169072	+	0.583619i
$535$	−1.19116e6	−	1.22023e6i	−0.179923	−	0.184313i
$536$	−4.62449e6	+	5.22120e6i	−0.695267	+	0.784979i
$537$	4.67397e6	+	4.67397e6i	0.699440	+	0.699440i
$538$	4.25863e6	+	2.34545e6i	0.634328	+	0.349358i
$539$			2.20559e6i			0.327004i
$540$	−1.11822e6	+	4.70165e6i	−0.165022	+	0.693851i
$541$		−	9.33731e6i		−	1.37160i	−0.727789	−	0.685802i	$-0.759452\pi$
$541$		−	9.33731e6i		−	1.37160i	0.727789	−	0.685802i	$-0.240548\pi$
$542$	−365190.	+	663074.i	−0.0533975	+	0.0969536i
$543$	−7.85211e6	−	7.85211e6i	−1.14284	−	1.14284i
$544$	2.29579e6	+	372643.i	0.332610	+	0.0539878i
$545$	−8.91655e6	−	107471.i	−1.28590	−	0.0154989i
$546$	1.69175e7	−	4.90093e6i	2.42859	−	0.703554i
$547$	2.37941e6	+	2.37941e6i	0.340017	+	0.340017i	0.856374	−	0.516357i	$-0.172712\pi$
$547$	2.37941e6	+	2.37941e6i	0.340017	+	0.340017i	−0.516357	+	0.856374i	$0.672712\pi$
$548$	−246137.	+	1.09328e6i	−0.0350127	+	0.155517i
$549$	−1.01969e7			−1.44390
$550$	1.67604e6	+	976459.i	0.236253	+	0.137641i
$551$			4.23814e6i			0.594698i
$552$	−442553.	−	7.30209e6i	−0.0618184	−	1.02000i
$553$	7.68849e6	−	7.68849e6i	1.06912	−	1.06912i
$554$	3.92763e6	−	1.13782e6i	0.543696	−	0.157506i
$555$	165819.	−	1.37575e7i	0.0228508	−	1.89586i
$556$	−2.69989e6	+	1.70760e6i	−0.370391	+	0.234261i
$557$	−2.39984e6	+	2.39984e6i	−0.327752	+	0.327752i	−0.851731	−	0.523979i	$-0.824447\pi$
$557$	−2.39984e6	+	2.39984e6i	−0.327752	+	0.327752i	0.523979	+	0.851731i	$0.324447\pi$
$558$	−6.66745e6	−	3.67212e6i	−0.906513	−	0.499265i
$559$	−9.42989e6			−1.27637
$560$	−3.56832e6	−	1.04022e7i	−0.480832	−	1.40170i
$561$	1.07614e6			0.144364
$562$	−5.22064e6	−	2.87528e6i	−0.697241	−	0.384008i
$563$	7.18484e6	−	7.18484e6i	0.955314	−	0.955314i	−0.0437290	−	0.999043i	$-0.513924\pi$
$563$	7.18484e6	−	7.18484e6i	0.955314	−	0.955314i	0.999043	+	0.0437290i	$0.0139238\pi$
$564$	1.09680e7	−	6.93693e6i	1.45188	−	0.918269i
$565$	−292478.	+	285512.i	−0.0385454	+	0.0376273i
$566$	−1.16636e6	+	337891.i	−0.153036	+	0.0443338i
$567$	−2.70846e6	+	2.70846e6i	−0.353805	+	0.353805i
$568$	1.03463e7	−	627049.i	1.34559	−	0.0815512i
$569$		−	1.34721e7i		−	1.74443i	−0.489122	−	0.872215i	$-0.662683\pi$
$569$		−	1.34721e7i		−	1.74443i	0.489122	−	0.872215i	$-0.337317\pi$
$570$	−5.41859e6	−	1.95846e7i	−0.698553	−	2.52480i
$571$	−8.14236e6			−1.04511			−0.522553	−	0.852607i	$-0.675020\pi$
$571$	−8.14236e6			−1.04511			−0.522553	+	0.852607i	$0.675020\pi$
$572$	−511726.	+	2.27296e6i	−0.0653954	+	0.290470i
$573$	4.33642e6	+	4.33642e6i	0.551753	+	0.551753i
$574$	−1.26926e7	+	3.67699e6i	−1.60794	+	0.465815i
$575$	−3.56685e6	−	3.74309e6i	−0.449899	−	0.472128i
$576$	1.39935e6	+	1.15022e7i	0.175740	+	1.44452i
$577$	4.44335e6	+	4.44335e6i	0.555611	+	0.555611i	0.928055	−	0.372444i	$-0.121480\pi$
$577$	4.44335e6	+	4.44335e6i	0.555611	+	0.555611i	−0.372444	+	0.928055i	$0.621480\pi$
$578$	−3.43484e6	+	6.23662e6i	−0.427649	+	0.776479i
$579$		−	415824.i		−	0.0515482i
$580$	−1.51095e6	−	2.45393e6i	−0.186500	−	0.302895i
$581$			1.13980e7i			1.40084i
$582$	2.93739e6	+	1.61778e6i	0.359463	+	0.197975i
$583$	144015.	+	144015.i	0.0175483	+	0.0175483i
$584$	4.82517e6	+	4.27372e6i	0.585437	+	0.518530i
$585$	−9.38559e6	+	9.16203e6i	−1.13389	+	1.10688i
$586$	2.35158e6	+	8.11740e6i	0.282888	+	0.976501i
$587$	9.00349e6	+	9.00349e6i	1.07849	+	1.07849i	0.996645	+	0.0818437i	$0.0260808\pi$
$587$	9.00349e6	+	9.00349e6i	1.07849	+	1.07849i	0.0818437	+	0.996645i	$0.473919\pi$
$588$	−3.45073e6	+	1.53273e7i	−0.411592	+	1.82819i
$589$	1.00110e7			1.18902
$590$	3.21042e6	−	5.66644e6i	0.379692	−	0.670163i
$591$			134770.i			0.0158717i
$592$	−3.46536e6	−	9.71881e6i	−0.406391	−	1.13975i
$593$	−2.64046e6	+	2.64046e6i	−0.308349	+	0.308349i	−0.844269	−	0.535920i	$-0.819965\pi$
$593$	−2.64046e6	+	2.64046e6i	−0.308349	+	0.308349i	0.535920	+	0.844269i	$0.319965\pi$
$594$	466616.	+	1.61071e6i	0.0542617	+	0.187306i
$595$	−4.31177e6	−	51969.8i	−0.499302	−	0.00601809i
$596$	−116882.	−	184801.i	−0.0134781	−	0.0213103i
$597$	−5.15763e6	+	5.15763e6i	−0.592262	+	0.592262i
$598$	2.99598e6	−	5.43979e6i	0.342599	−	0.622056i
$599$	−8.50368e6			−0.968367			−0.484183	−	0.874966i	$-0.660883\pi$
$599$	−8.50368e6			−0.968367			−0.484183	+	0.874966i	$0.660883\pi$
$600$	1.01196e7	+	9.40790e6i	1.14758	+	1.06688i
$601$	−1.50671e7			−1.70155			−0.850774	−	0.525532i	$-0.823866\pi$
$601$	−1.50671e7			−1.70155			−0.850774	+	0.525532i	$0.823866\pi$
$602$	7.45091e6	−	1.35286e7i	0.837950	−	1.52146i
$603$	−9.63401e6	+	9.63401e6i	−1.07898	+	1.07898i
$604$	830590.	−	525324.i	0.0926391	−	0.0585916i
$605$	−8.32935e6	−	100394.i	−0.925172	−	0.0111511i
$606$	7.33525e6	+	2.53205e7i	0.811396	+	2.80086i
$607$	7.08935e6	−	7.08935e6i	0.780971	−	0.780971i	−0.199024	−	0.979995i	$-0.563777\pi$
$607$	7.08935e6	−	7.08935e6i	0.780971	−	0.780971i	0.979995	+	0.199024i	$0.0637771\pi$
$608$	−8.91006e6	−	1.23630e7i	−0.977511	−	1.35633i
$609$			7.55943e6i			0.825935i
$610$	−4.49520e6	+	7.93409e6i	−0.489130	+	0.863322i
$611$	1.10169e7			1.19387
$612$	4.43239e6	+	997894.i	0.478365	+	0.107698i
$613$	1.16554e7	+	1.16554e7i	1.25279	+	1.25279i	0.954465	+	0.298323i	$0.0964271\pi$
$613$	1.16554e7	+	1.16554e7i	1.25279	+	1.25279i	0.298323	+	0.954465i	$0.403573\pi$
$614$	1.02614e6	+	3.54212e6i	0.109846	+	0.379178i
$615$	1.18807e7	−	1.15977e7i	1.26665	−	1.23648i
$616$	−2.85656e6	−	2.53010e6i	−0.303313	−	0.268649i
$617$	−4.87789e6	−	4.87789e6i	−0.515845	−	0.515845i	0.400466	−	0.916311i	$-0.368848\pi$
$617$	−4.87789e6	−	4.87789e6i	−0.515845	−	0.515845i	−0.916311	+	0.400466i	$0.868848\pi$
$618$	−1.15548e7	−	6.36385e6i	−1.21700	−	0.670268i
$619$		−	4.13340e6i		−	0.433592i	−0.976217	−	0.216796i	$-0.930439\pi$
$619$		−	4.13340e6i		−	0.433592i	0.976217	−	0.216796i	$-0.0695606\pi$
$620$	−5.79650e6	+	3.56905e6i	−0.605601	+	0.372883i
$621$		−	4.46991e6i		−	0.465125i
$622$	−122288.	+	222038.i	−0.0126739	+	0.0230119i
$623$	−3.93645e6	−	3.93645e6i	−0.406336	−	0.406336i
$624$	−7.11224e6	+	1.49948e7i	−0.731215	+	1.54162i
$625$	9.75428e6	+	470615.i	0.998838	+	0.0481910i
$626$	1.82106e7	−	5.27552e6i	1.85732	−	0.538059i
$627$	−4.98579e6	−	4.98579e6i	−0.506484	−	0.506484i
$628$	9.00598e6	+	2.02758e6i	0.911238	+	0.205153i
$629$	−4.04582e6			−0.407737
$630$	−5.72839e6	−	2.07043e7i	−0.575018	−	2.07830i
$631$		−	1.71628e7i		−	1.71599i	−0.513659	−	0.857995i	$-0.671710\pi$
$631$		−	1.71628e7i		−	1.71599i	0.513659	−	0.857995i	$-0.328290\pi$
$632$	619792.	+	1.02265e7i	0.0617239	+	1.01844i
$633$	1.81467e7	−	1.81467e7i	1.80006	−	1.80006i
$634$	1.76530e7	−	5.11400e6i	1.74420	−	0.505286i
$635$	−4.12612e6	+	4.02785e6i	−0.406077	+	0.396404i
$636$	775480.	+	1.22611e6i	0.0760200	+	0.120195i
$637$	−9.43087e6	+	9.43087e6i	−0.920880	+	0.920880i
$638$	−875899.	−	482404.i	−0.0851927	−	0.0469202i
$639$	2.02476e7			1.96165
$640$	9.56658e6	+	3.98179e6i	0.923224	+	0.384263i
$641$	−6.30149e6			−0.605757			−0.302878	−	0.953029i	$-0.597948\pi$
$641$	−6.30149e6			−0.605757			−0.302878	+	0.953029i	$0.597948\pi$
$642$	−3.69191e6	−	2.03333e6i	−0.353520	−	0.194702i
$643$	211405.	−	211405.i	0.0201645	−	0.0201645i	−0.696953	−	0.717117i	$-0.745461\pi$
$643$	211405.	−	211405.i	0.0201645	−	0.0201645i	0.717117	+	0.696953i	$0.245461\pi$
$644$	5.43695e6	+	8.59636e6i	0.516584	+	0.816771i
$645$	−233873.	+	1.94037e7i	−0.0221350	+	1.83647i
$646$	−5.73942e6	+	1.66269e6i	−0.541111	+	0.156758i
$647$	8.61526e6	−	8.61526e6i	0.809110	−	0.809110i	−0.175389	−	0.984499i	$-0.556118\pi$
$647$	8.61526e6	−	8.61526e6i	0.809110	−	0.809110i	0.984499	+	0.175389i	$0.0561184\pi$
$648$	−218337.	−	3.60254e6i	−0.0204263	−	0.337032i
$649$		−	2.25985e6i		−	0.210605i
$650$	2.99133e6	+	1.13418e7i	0.277704	+	1.05293i
$651$	1.78564e7			1.65135
$652$	5.75330e6	+	1.29528e6i	0.530027	+	0.119328i
$653$	−1.20956e7	−	1.20956e7i	−1.11005	−	1.11005i	−0.993143	−	0.116910i	$-0.962701\pi$
$653$	−1.20956e7	−	1.20956e7i	−1.11005	−	1.11005i	−0.116910	−	0.993143i	$-0.537299\pi$
$654$	−2.11701e7	+	6.13289e6i	−1.93544	+	0.560688i
$655$	−1.53147e7	−	184588.i	−1.39478	−	0.0168113i
$656$	5.33606e6	−	1.12500e7i	0.484129	−	1.02069i
$657$	8.90327e6	+	8.90327e6i	0.804704	+	0.804704i
$658$	−8.70488e6	+	1.58054e7i	−0.783787	+	1.42312i
$659$		−	1.46296e6i		−	0.131226i	−0.997845	−	0.0656128i	$-0.979100\pi$
$659$		−	1.46296e6i		−	0.131226i	0.997845	−	0.0656128i	$-0.0209002\pi$
$660$	4.66432e6	+	1.10934e6i	0.416801	+	0.0991299i
$661$		−	7.14270e6i		−	0.635856i	−0.948115	−	0.317928i	$-0.897013\pi$
$661$		−	7.14270e6i		−	0.635856i	0.948115	−	0.317928i	$-0.102987\pi$
$662$	1.66866e6	+	919019.i	0.147987	+	0.0815041i
$663$	4.60144e6	+	4.60144e6i	0.406546	+	0.406546i
$664$	−8.03972e6	−	7.12089e6i	−0.707654	−	0.626779i
$665$	1.97359e7	+	2.02174e7i	1.73062	+	1.77285i
$666$	−5.60840e6	−	1.93596e7i	−0.489952	−	1.69126i
$667$	1.88472e6	+	1.88472e6i	0.164034	+	0.164034i
$668$	7.82967e6	+	1.76275e6i	0.678895	+	0.152844i
$669$	1.40265e7			1.21167
$670$	3.24906e6	+	1.17432e7i	0.279621	+	1.01064i
$671$			3.16422e6i			0.271307i
$672$	−1.58926e7	−	2.20515e7i	−1.35760	−	1.88371i
$673$	−1.41251e7	+	1.41251e7i	−1.20214	+	1.20214i	−0.228624	+	0.973515i	$0.573422\pi$
$673$	−1.41251e7	+	1.41251e7i	−1.20214	+	1.20214i	−0.973515	+	0.228624i	$0.926578\pi$
$674$	−2.26809e6	−	7.82922e6i	−0.192314	−	0.663849i
$675$	5.82417e6	+	6.11194e6i	0.492010	+	0.516321i
$676$	−1.86547e6	+	1.17986e6i	−0.157008	+	0.0993031i
$677$	1.64648e7	−	1.64648e7i	1.38065	−	1.38065i	0.537199	−	0.843456i	$-0.319482\pi$
$677$	1.64648e7	−	1.64648e7i	1.38065	−	1.38065i	0.843456	−	0.537199i	$-0.180518\pi$
$678$	−487372.	+	884919.i	−0.0407180	+	0.0739315i
$679$	−4.66259e6			−0.388108
$680$	2.73042e6	−	3.00888e6i	0.226442	−	0.249536i
$681$	−3.66635e7			−3.02947
$682$	−1.13950e6	+	2.06899e6i	−0.0938110	+	0.170332i
$683$	4.52109e6	−	4.52109e6i	0.370844	−	0.370844i	−0.496941	−	0.867785i	$-0.665543\pi$
$683$	4.52109e6	−	4.52109e6i	0.370844	−	0.370844i	0.867785	+	0.496941i	$0.165543\pi$
$684$	−1.59122e7	−	2.51588e7i	−1.30044	−	2.05613i
$685$	1.36751e6	+	1.40087e6i	0.111353	+	0.114070i
$686$	−995942.	−	3.43789e6i	−0.0808023	−	0.278921i
$687$	−1.32523e7	+	1.32523e7i	−1.07127	+	1.07127i
$688$	4.88758e6	+	1.37075e7i	0.393661	+	1.10405i
$689$			1.23158e6i			0.0988359i
$690$	−1.11190e7	−	6.29968e6i	−0.889088	−	0.503728i
$691$	−8.39292e6			−0.668679			−0.334340	−	0.942453i	$-0.608513\pi$
$691$	−8.39292e6			−0.668679			−0.334340	+	0.942453i	$0.608513\pi$
$692$	−189065.	+	839780.i	−0.0150088	+	0.0666654i
$693$	−5.27085e6	−	5.27085e6i	−0.416915	−	0.416915i
$694$	2.15844e6	+	7.45071e6i	0.170114	+	0.587217i
$695$	−67259.3	+	5.58030e6i	−0.00528191	+	0.438223i
$696$	−5.33212e6	−	4.72273e6i	−0.417231	−	0.369547i
$697$	−3.45229e6	−	3.45229e6i	−0.269169	−	0.269169i
$698$	−165814.	−	91322.8i	−0.0128820	−	0.00709481i
$699$			7.86787e6i			0.609066i
$700$	−1.86351e7	−	4.67007e6i	−1.43743	−	0.360228i
$701$			2.06180e7i			1.58472i	0.610055	+	0.792359i	$0.291148\pi$
$701$			2.06180e7i			1.58472i	−0.610055	+	0.792359i	$0.708852\pi$
$702$	−4.89202e6	+	8.88242e6i	−0.374667	+	0.680281i
$703$	1.87445e7	+	1.87445e7i	1.43049	+	1.43049i
$704$	3.56926e6	−	434234.i	0.271423	−	0.0330211i
$705$	273233.	−	2.26693e7i	0.0207043	−	1.71777i
$706$	8.75827e6	−	2.53723e6i	0.661312	−	0.191579i
$707$	−2.59176e7	−	2.59176e7i	−1.95005	−	1.95005i
$708$	3.53562e6	−	1.57043e7i	0.265083	−	1.17743i
$709$	7.89378e6			0.589752			0.294876	−	0.955535i	$-0.404722\pi$
$709$	7.89378e6			0.589752			0.294876	+	0.955535i	$0.404722\pi$
$710$	8.92596e6	−	1.57545e7i	0.664521	−	1.17289i
$711$			2.00133e7i			1.48472i
$712$	5.23590e6	−	317329.i	0.387072	−	0.0234590i
$713$	4.45196e6	−	4.45196e6i	0.327965	−	0.327965i
$714$	−1.02372e7	+	2.96568e6i	−0.751513	+	0.217710i
$715$	2.84309e6	+	2.91246e6i	0.207982	+	0.213056i
$716$	7.31880e6	−	4.62893e6i	0.533528	−	0.337441i
$717$	3.54512e6	−	3.54512e6i	0.257533	−	0.257533i
$718$	−1.80102e7	−	9.91919e6i	−1.30379	−	0.718067i
$719$	−8.19958e6			−0.591520			−0.295760	−	0.955262i	$-0.595573\pi$
$719$	−8.19958e6			−0.591520			−0.295760	+	0.955262i	$0.595573\pi$
$720$	1.81828e7	+	8.89436e6i	1.30716	+	0.639416i
$721$	1.83412e7			1.31398
$722$	2.20251e7	+	1.21304e7i	1.57245	+	0.866029i
$723$	−2.54474e7	+	2.54474e7i	−1.81050	+	1.81050i
$724$	−1.22953e7	+	7.77644e6i	−0.871754	+	0.551359i
$725$	−5.03283e6	−	121339.i	−0.355604	−	0.00857344i
$726$	−1.97759e7	+	5.72901e6i	−1.39250	+	0.403402i
$727$	−5.89054e6	+	5.89054e6i	−0.413351	+	0.413351i	−0.882904	−	0.469553i	$-0.844415\pi$
$727$	−5.89054e6	+	5.89054e6i	−0.413351	+	0.413351i	0.469553	+	0.882904i	$0.344415\pi$
$728$	−1.39593e6	−	2.30328e7i	−0.0976192	−	1.61071i
$729$		−	2.30854e7i		−	1.60886i
$730$	1.08524e7	−	3.00262e6i	0.753738	−	0.208542i
$731$	5.70626e6			0.394965
$732$	−4.95053e6	+	2.19890e7i	−0.341487	+	1.51680i
$733$	−3.20192e6	−	3.20192e6i	−0.220115	−	0.220115i	0.588432	−	0.808547i	$-0.299746\pi$
$733$	−3.20192e6	−	3.20192e6i	−0.220115	−	0.220115i	−0.808547	+	0.588432i	$0.799746\pi$
$734$	2.41955e7	−	7.00934e6i	1.65766	−	0.480216i
$735$	1.91718e7	+	1.96396e7i	1.30902	+	1.34096i
$736$	−9.46025e6	−	1.53555e6i	−0.643736	−	0.104488i
$737$	2.98955e6	+	2.98955e6i	0.202739	+	0.202739i
$738$	1.17339e7	−	2.13052e7i	0.793052	−	1.43994i
$739$			1.34840e7i			0.908253i	0.890937	+	0.454127i	$0.150049\pi$
$739$			1.34840e7i			0.908253i	−0.890937	+	0.454127i	$0.849951\pi$
$740$	−1.75359e7	−	4.17065e6i	−1.17720	−	0.279978i
$741$		−	4.26374e7i		−	2.85263i
$742$	−1.76689e6	−	973118.i	−0.117815	−	0.0648867i
$743$	−1.39605e7	−	1.39605e7i	−0.927746	−	0.927746i	0.0698140	−	0.997560i	$-0.477759\pi$
$743$	−1.39605e7	−	1.39605e7i	−0.927746	−	0.927746i	−0.997560	+	0.0698140i	$0.977759\pi$
$744$	−1.11557e7	+	1.25952e7i	−0.738864	+	0.834202i
$745$	−381958.	−	4603.74i	−0.0252130	−	0.000303893i
$746$	2.08243e6	+	7.18832e6i	0.137001	+	0.472912i
$747$	−1.48347e7	−	1.48347e7i	−0.972694	−	0.972694i
$748$	309658.	−	1.37542e6i	0.0202362	−	0.0898840i
$749$	5.86026e6			0.381692
$750$	2.34120e7	−	5.87391e6i	1.51979	−	0.381307i
$751$			1.52400e7i			0.986017i	0.870025	+	0.493008i	$0.164103\pi$
$751$			1.52400e7i			0.986017i	−0.870025	+	0.493008i	$0.835897\pi$
$752$	−5.71015e6	−	1.60144e7i	−0.368216	−	1.03268i
$753$	−1.94147e7	+	1.94147e7i	−1.24779	+	1.24779i
$754$	−1.68254e6	−	5.80796e6i	−0.107780	−	0.372045i
$755$	20691.5	−	1.71671e6i	0.00132107	−	0.109605i
$756$	−8.87779e6	−	1.40367e7i	−0.564937	−	0.893222i
$757$	−2.63351e6	+	2.63351e6i	−0.167030	+	0.167030i	−0.785673	−	0.618642i	$-0.787683\pi$
$757$	−2.63351e6	+	2.63351e6i	−0.167030	+	0.167030i	0.618642	+	0.785673i	$0.287683\pi$
$758$	−3.54056e6	+	6.42858e6i	−0.223820	+	0.406389i
$759$	−4.43442e6			−0.279404
$760$	−2.65905e7	+	1.29012e6i	−1.66991	+	0.0810204i
$761$	1.46715e7			0.918357			0.459179	−	0.888344i	$-0.348144\pi$
$761$	1.46715e7			0.918357			0.459179	+	0.888344i	$0.348144\pi$
$762$	−6.87558e6	+	1.24840e7i	−0.428965	+	0.778870i
$763$	2.16693e7	−	2.16693e7i	1.34752	−	1.34752i
$764$	6.79024e6	−	4.29463e6i	0.420874	−	0.266190i
$765$	5.67946e6	−	5.54418e6i	0.350876	−	0.342518i
$766$	−5.30256e6	−	1.83039e7i	−0.326523	−	1.12712i
$767$	9.66287e6	−	9.66287e6i	0.593086	−	0.593086i
$768$	2.54831e7	+	2.56662e6i	1.55901	+	0.157021i
$769$		−	5.83333e6i		−	0.355714i	−0.984056	−	0.177857i	$-0.943084\pi$
$769$		−	5.83333e6i		−	0.355714i	0.984056	−	0.177857i	$-0.0569164\pi$
$770$	−6.42478e6	+	1.77759e6i	−0.390509	+	0.108045i
$771$	1.39086e7			0.842651
$772$	−531471.	−	119654.i	−0.0320949	−	0.00722574i
$773$	−1.08851e7	−	1.08851e7i	−0.655216	−	0.655216i	0.299028	−	0.954244i	$-0.403337\pi$
$773$	−1.08851e7	−	1.08851e7i	−0.655216	−	0.655216i	−0.954244	+	0.299028i	$0.903337\pi$
$774$	7.91015e6	+	2.73050e7i	0.474605	+	1.63829i
$775$	−286618.	+	1.18882e7i	−0.0171415	+	0.710986i
$776$	2.91294e6	−	3.28880e6i	0.173651	−	0.196058i
$777$	3.34339e7	+	3.34339e7i	1.98671	+	1.98671i
$778$	1.82623e7	+	1.00580e7i	1.08170	+	0.595748i
$779$			3.19893e7i			1.88869i
$780$	1.52007e7	+	2.46876e7i	0.894598	+	1.45292i
$781$		−	6.28308e6i		−	0.368591i
$782$	−1.81294e6	+	3.29175e6i	−0.106015	+	0.192491i
$783$	−3.07749e6	−	3.07749e6i	−0.179388	−	0.179388i
$784$	1.85970e7	+	8.82084e6i	1.08057	+	0.512531i
$785$	1.15398e7	−	1.12650e7i	0.668382	−	0.652462i
$786$	−3.63609e7	+	1.05336e7i	−2.09932	+	0.608163i
$787$	3.71537e6	+	3.71537e6i	0.213828	+	0.213828i	0.805891	−	0.592063i	$-0.201686\pi$
$787$	3.71537e6	+	3.71537e6i	0.213828	+	0.213828i	−0.592063	+	0.805891i	$0.701686\pi$
$788$	172251.	+	38780.1i	0.00988205	+	0.00222481i
$789$	−3.17397e7			−1.81514
$790$	1.55721e7	+	8.82265e6i	0.887728	+	0.502958i
$791$		−	1.40465e6i		−	0.0798230i
$792$	7.01079e6	−	424898.i	0.397149	−	0.0240698i
$793$	−1.35299e7	+	1.35299e7i	−0.764030	+	0.764030i
$794$	−3.13869e7	+	9.09265e6i	−1.76684	+	0.511846i
$795$	2.53420e6	+	30544.7i	0.142208	+	0.00171403i
$796$	5.10792e6	+	8.07614e6i	0.285734	+	0.451774i
$797$	8.47263e6	−	8.47263e6i	0.472468	−	0.472468i	−0.430244	−	0.902712i	$-0.641573\pi$
$797$	8.47263e6	−	8.47263e6i	0.472468	−	0.472468i	0.902712	+	0.430244i	$0.141573\pi$
$798$	6.11697e7	+	3.36894e7i	3.40039	+	1.87278i
$799$	−6.66661e6			−0.369435
$800$	1.49363e7	−	1.02268e7i	0.825120	−	0.564957i
$801$	1.02467e7			0.564289
$802$	−1.38815e7	−	7.64528e6i	−0.762080	−	0.419718i
$803$	2.76279e6	−	2.76279e6i	0.151202	−	0.151202i
$804$	1.60979e7	+	2.54524e7i	0.878273	+	1.38864i
$805$	1.77675e7	+	214151.i	0.966353	+	0.0116475i
$806$	−1.37191e7	+	3.97438e6i	−0.743857	+	0.215492i
$807$	1.48440e7	−	1.48440e7i	0.802356	−	0.802356i
$808$	3.44732e7	−	2.08929e6i	1.85760	−	0.112583i
$809$			7.50267e6i			0.403036i	0.979485	+	0.201518i	$0.0645875\pi$
$809$			7.50267e6i			0.403036i	−0.979485	+	0.201518i	$0.935412\pi$
$810$	−5.48566e6	−	3.10799e6i	−0.293776	−	0.166444i
$811$	143609.			0.00766708			0.00383354	−	0.999993i	$-0.498780\pi$
$811$	143609.			0.00766708			0.00383354	+	0.999993i	$0.498780\pi$
$812$	9.66182e6	+	2.17523e6i	0.514243	+	0.115775i
$813$	2.31123e6	+	2.31123e6i	0.122636	+	0.122636i
$814$	−6.00752e6	+	1.74035e6i	−0.317785	+	0.0920611i
$815$	7.37200e6	−	7.19640e6i	0.388769	−	0.379508i
$816$	4.30380e6	−	9.07372e6i	0.226270	−	0.477046i
$817$	−2.64374e7	−	2.64374e7i	−1.38568	−	1.38568i
$818$	−1.13104e7	+	2.05362e7i	−0.591008	+	1.07309i
$819$		−	4.50751e7i		−	2.34816i
$820$	−1.14046e7	−	1.85222e7i	−0.592303	−	0.961961i
$821$		−	3.34075e6i		−	0.172976i	−0.996253	−	0.0864880i	$-0.972436\pi$
$821$		−	3.34075e6i		−	0.172976i	0.996253	−	0.0864880i	$-0.0275644\pi$
$822$	4.23847e6	+	2.33435e6i	0.218791	+	0.120500i
$823$	−7.60023e6	−	7.60023e6i	−0.391136	−	0.391136i	0.483956	−	0.875092i	$-0.339199\pi$
$823$	−7.60023e6	−	7.60023e6i	−0.391136	−	0.391136i	−0.875092	+	0.483956i	$0.839199\pi$
$824$	−1.14586e7	+	1.29372e7i	−0.587914	+	0.663775i
$825$	6.06341e6	−	5.77793e6i	0.310158	−	0.295554i
$826$	6.22783e6	+	2.14978e7i	0.317604	+	1.09634i
$827$	−1.26418e7	−	1.26418e7i	−0.642755	−	0.642755i	0.308477	−	0.951232i	$-0.400181\pi$
$827$	−1.26418e7	−	1.26418e7i	−0.642755	−	0.642755i	−0.951232	+	0.308477i	$0.900181\pi$
$828$	−1.82645e7	−	4.11201e6i	−0.925832	−	0.208439i
$829$	−3.02538e7			−1.52895			−0.764475	−	0.644653i	$-0.777002\pi$
$829$	−3.02538e7			−1.52895			−0.764475	+	0.644653i	$0.777002\pi$
$830$	−1.80824e7	+	5.00298e6i	−0.911089	+	0.252077i
$831$		−	1.76563e7i		−	0.886944i
$832$	1.71185e7	+	1.34050e7i	0.857348	+	0.671365i
$833$	5.70686e6	−	5.70686e6i	0.284960	−	0.284960i
$834$	3.83818e6	+	1.32490e7i	0.191078	+	0.659581i
$835$	1.00326e7	−	9.79360e6i	0.497962	−	0.486101i
$836$	−7.80707e6	+	4.93775e6i	−0.386343	+	0.244350i
$837$	−7.26943e6	+	7.26943e6i	−0.358663	+	0.358663i
$838$	4.31826e6	−	7.84064e6i	0.212421	−	0.385693i
$839$	−2.10849e6			−0.103411			−0.0517055	−	0.998662i	$-0.516466\pi$
$839$	−2.10849e6			−0.103411			−0.0517055	+	0.998662i	$0.516466\pi$
$840$	−4.74286e7	+	2.30114e6i	−2.31922	+	0.112524i
$841$	−1.79159e7			−0.873472
$842$	−1.21174e7	+	2.20014e7i	−0.589017	+	1.06947i
$843$	−1.81972e7	+	1.81972e7i	−0.881933	+	0.881933i
$844$	−1.79718e7	−	2.84152e7i	−0.868431	−	1.37308i
$845$	−46472.4	+	3.85567e6i	−0.00223899	+	0.185762i
$846$	−9.24141e6	−	3.19004e7i	−0.443928	−	1.53239i
$847$	2.02423e7	−	2.02423e7i	0.969508	−	0.969508i
$848$	1.79026e6	−	638338.i	0.0854920	−	0.0304832i
$849$			5.24327e6i			0.249651i
$850$	−1.81013e6	−	6.86321e6i	−0.0859336	−	0.325822i
$851$	1.66715e7			0.789136
$852$	9.83010e6	−	4.36628e7i	0.463937	−	2.06069i
$853$	−1.45964e7	−	1.45964e7i	−0.686868	−	0.686868i	0.274671	−	0.961538i	$-0.411431\pi$
$853$	−1.45964e7	−	1.45964e7i	−0.686868	−	0.686868i	−0.961538	+	0.274671i	$0.911431\pi$
$854$	−8.72014e6	−	3.01010e7i	−0.409147	−	1.41233i
$855$	−5.19997e7	−	626752.i	−2.43268	−	0.0293211i
$856$	−3.66118e6	+	4.13359e6i	−0.170780	+	0.192816i
$857$	−2.56434e7	−	2.56434e7i	−1.19268	−	1.19268i	−0.976312	−	0.216366i	$-0.930580\pi$
$857$	−2.56434e7	−	2.56434e7i	−1.19268	−	1.19268i	−0.216366	−	0.976312i	$-0.569420\pi$
$858$	8.81190e6	+	4.85318e6i	0.408650	+	0.225065i
$859$			8.86065e6i			0.409716i	0.978792	+	0.204858i	$0.0656732\pi$
$859$			8.86065e6i			0.409716i	−0.978792	+	0.204858i	$0.934327\pi$
$860$	2.47328e7	+	5.88233e6i	1.14032	+	0.271208i
$861$			5.70583e7i			2.62308i
$862$	4.45012e6	−	8.08007e6i	0.203988	−	0.370379i
$863$	1.69276e7	+	1.69276e7i	0.773690	+	0.773690i	0.978750	−	0.205059i	$-0.0657387\pi$
$863$	1.69276e7	+	1.69276e7i	0.773690	+	0.773690i	−0.205059	+	0.978750i	$0.565739\pi$
$864$	1.54473e7	+	2.50733e6i	0.703991	+	0.114269i
$865$	1.05042e6	+	1.07605e6i	0.0477336	+	0.0488983i
$866$	−1.90279e6	+	551232.i	−0.0862178	+	0.0249769i
$867$	2.17385e7	+	2.17385e7i	0.982161	+	0.982161i
$868$	5.13817e6	−	2.28225e7i	0.231478	−	1.02817i
$869$	6.21036e6			0.278976
$870$	−1.19926e7	+	3.31808e6i	−0.537176	+	0.148624i
$871$			2.55659e7i			1.14187i
$872$	1.74683e6	+	2.88225e7i	0.0777963	+	1.28363i
$873$	6.06841e6	−	6.06841e6i	0.269488	−	0.269488i
$874$	2.36503e7	−	6.85140e6i	1.04727	−	0.303390i
$875$	−2.45734e7	+	2.28577e7i	−1.08504	+	1.00928i
$876$	2.35218e7	−	1.48769e7i	1.03565	−	0.655015i
$877$	−2.44921e7	+	2.44921e7i	−1.07529	+	1.07529i	−0.0783670	+	0.996925i	$0.524971\pi$
$877$	−2.44921e7	+	2.44921e7i	−1.07529	+	1.07529i	−0.996925	+	0.0783670i	$0.975029\pi$
$878$	−2.48291e7	−	1.36747e7i	−1.08699	−	0.598663i
$879$	3.64909e7			1.59299
$880$	2.76002e6	−	5.64232e6i	0.120145	−	0.245613i
$881$	2.83155e7			1.22909			0.614546	−	0.788881i	$-0.289339\pi$
$881$	2.83155e7			1.22909			0.614546	+	0.788881i	$0.289339\pi$
$882$	3.52188e7	+	1.93969e7i	1.52442	+	0.839577i
$883$	−6.52387e6	+	6.52387e6i	−0.281581	+	0.281581i	−0.833739	−	0.552158i	$-0.813804\pi$
$883$	−6.52387e6	+	6.52387e6i	−0.281581	+	0.281581i	0.552158	+	0.833739i	$0.313804\pi$
$884$	7.20523e6	−	4.55710e6i	0.310111	−	0.196136i
$885$	−1.96434e7	−	2.01227e7i	−0.843062	−	0.863632i
$886$	3.52983e7	−	1.02258e7i	1.51067	−	0.437634i
$887$	−1.30545e7	+	1.30545e7i	−0.557122	+	0.557122i	−0.928487	−	0.371365i	$-0.878890\pi$
$887$	−1.30545e7	+	1.30545e7i	−0.557122	+	0.557122i	0.371365	+	0.928487i	$0.378890\pi$
$888$	−4.44707e7	+	2.69521e6i	−1.89253	+	0.114699i
$889$		−	1.98161e7i		−	0.840937i
$890$	4.51713e6	−	7.97281e6i	0.191156	−	0.337393i
$891$	−2.18775e6			−0.0923217
$892$	4.03613e6	−	1.79275e7i	0.169845	−	0.754410i
$893$	3.08868e7	+	3.08868e7i	1.29612	+	1.29612i
$894$	−906863.	+	262715.i	−0.0379488	+	0.0109936i
$895$	182325.	−	1.51269e7i	0.00760831	−	0.631238i
$896$	−3.27574e7	+	1.39672e7i	−1.36314	+	0.581219i
$897$	−1.89611e7	−	1.89611e7i	−0.786832	−	0.786832i
$898$	1.41871e7	−	2.57595e7i	0.587088	−	1.06597i
$899$		−	6.13027e6i		−	0.252977i
$900$	3.03319e7	−	1.81756e7i	1.24823	−	0.747967i
$901$		−	745261.i		−	0.0305841i
$902$	−6.61125e6	−	3.64117e6i	−0.270562	−	0.149013i
$903$	−4.71556e7	−	4.71556e7i	−1.92448	−	1.92448i
$904$	990786.	+	877552.i	0.0403235	+	0.0357151i
$905$	−306300.	+	2.54127e7i	−0.0124315	+	1.03141i
$906$	−1.18077e6	−	4.07590e6i	−0.0477909	−	0.164969i
$907$	−5.00920e6	−	5.00920e6i	−0.202185	−	0.202185i	0.598750	−	0.800936i	$-0.295664\pi$
$907$	−5.00920e6	−	5.00920e6i	−0.202185	−	0.202185i	−0.800936	+	0.598750i	$0.795664\pi$
$908$	−1.05499e7	+	4.68602e7i	−0.424654	+	1.88621i
$909$	6.74641e7			2.70809
$910$	−3.50724e7	−	1.98709e7i	−1.40398	−	0.795452i
$911$			2.24129e7i			0.894750i	0.894346	+	0.447375i	$0.147641\pi$
$911$			2.24129e7i			0.894750i	−0.894346	+	0.447375i	$0.852359\pi$
$912$	−6.19787e7	+	2.20993e7i	−2.46749	+	0.879815i
$913$	−4.60337e6	+	4.60337e6i	−0.182768	+	0.182768i
$914$	−1.03698e7	−	3.57953e7i	−0.410585	−	1.41730i
$915$	2.75045e7	+	2.81757e7i	1.08605	+	1.11255i
$916$	1.31246e7	+	2.07513e7i	0.516828	+	0.817158i
$917$	3.72184e7	−	3.72184e7i	1.46162	−	1.46162i
$918$	2.96029e6	−	5.37498e6i	0.115938	−	0.210509i
$919$	2.13486e7			0.833835			0.416917	−	0.908944i	$-0.363110\pi$
$919$	2.13486e7			0.833835			0.416917	+	0.908944i	$0.363110\pi$
$920$	−1.12512e7	+	1.23987e7i	−0.438258	+	0.482953i
$921$	1.59233e7			0.618562
$922$	2.91772e6	−	5.29769e6i	0.113036	−	0.205239i
$923$	2.68658e7	−	2.68658e7i	1.03799	−	1.03799i
$924$	−1.39252e7	+	8.80730e6i	−0.536565	+	0.339362i
$925$	−2.27959e7	+	2.17226e7i	−0.875996	+	0.834751i
$926$	5.29972e6	+	1.82941e7i	0.203107	+	0.701105i
$927$	−2.38713e7	+	2.38713e7i	−0.912381	+	0.912381i
$928$	−7.57051e6	+	5.45609e6i	−0.288573	+	0.207975i
$929$			3.61549e7i			1.37445i	0.726446	+	0.687223i	$0.241171\pi$
$929$			3.61549e7i			1.37445i	−0.726446	+	0.687223i	$0.758829\pi$
$930$	7.83774e6	+	2.83282e7i	0.297155	+	1.07402i
$931$	−5.28803e7			−1.99949
$932$	1.00560e7	+	2.26398e6i	0.379216	+	0.0853755i
$933$	773943.	+	773943.i	0.0291075	+	0.0291075i
$934$	−3.98042e6	−	1.37400e7i	−0.149301	−	0.515370i
$935$	−1.72042e6	−	1.76240e6i	−0.0643585	−	0.0659289i
$936$	3.17942e7	+	2.81605e7i	1.18620	+	1.05063i
$937$	2.26100e7	+	2.26100e7i	0.841303	+	0.841303i	0.989028	−	0.147726i	$-0.0471953\pi$
$937$	2.26100e7	+	2.26100e7i	0.841303	+	0.841303i	−0.147726	+	0.989028i	$0.547195\pi$
$938$	−3.66781e7	−	2.02006e7i	−1.36113	−	0.749648i
$939$		−	8.18637e7i		−	3.02990i
$940$	−2.88953e7	−	6.87231e6i	−1.06661	−	0.253678i
$941$		−	2.83736e7i		−	1.04458i	−0.852769	−	0.522288i	$-0.825078\pi$
$941$		−	2.83736e7i		−	1.04458i	0.852769	−	0.522288i	$-0.174922\pi$
$942$	1.92294e7	−	3.49148e7i	0.706056	−	1.28198i
$943$	1.42258e7	+	1.42258e7i	0.520952	+	0.520952i
$944$	−1.90545e7	−	9.03784e6i	−0.695934	−	0.330092i
$945$	−2.90118e7	−	349679.i	−1.05681	−	0.0127377i
$946$	8.47306e6	−	2.45461e6i	0.307831	−	0.0891774i
$947$	2.11646e7	+	2.11646e7i	0.766894	+	0.766894i	0.977558	−	0.210665i	$-0.0675629\pi$
$947$	2.11646e7	+	2.11646e7i	0.766894	+	0.766894i	−0.210665	+	0.977558i	$0.567563\pi$
$948$	4.31575e7	+	9.71634e6i	1.55968	+	0.351141i
$949$	2.36268e7			0.851606
$950$	−2.34112e7	+	4.01840e7i	−0.841616	+	1.44459i
$951$		−	7.93573e7i		−	2.84535i
$952$	844713.	+	1.39377e7i	0.0302076	+	0.498424i
$953$	−2.38547e7	+	2.38547e7i	−0.850827	+	0.850827i	−0.990235	−	0.139408i	$-0.955480\pi$
$953$	−2.38547e7	+	2.38547e7i	−0.850827	+	0.850827i	0.139408	+	0.990235i	$0.455480\pi$
$954$	3.56614e6	−	1.03310e6i	0.126861	−	0.0367511i
$955$	169157.	−	1.40345e7i	0.00600181	−	0.497952i
$956$	−3.51096e6	−	5.55118e6i	−0.124246	−	0.196445i
$957$	−3.05306e6	+	3.05306e6i	−0.107759	+	0.107759i
$958$	−3.32688e7	−	1.83229e7i	−1.17118	−	0.645031i
$959$	−6.72782e6			−0.236226
$960$	2.80078e7	−	3.48919e7i	0.980845	−	1.22193i
$961$	1.41487e7			0.494205
$962$	−3.31290e7	−	1.82459e7i	−1.15417	−	0.635665i
$963$	−7.62719e6	+	7.62719e6i	−0.265032	+	0.265032i
$964$	2.52022e7	+	3.98471e7i	0.873464	+	1.38103i
$965$	−681001.	+	664780.i	−0.0235412	+	0.0229805i
$966$	4.21844e7	−	1.22206e7i	1.45448	−	0.421358i
$967$	−1.56733e7	+	1.56733e7i	−0.539007	+	0.539007i	−0.923237	−	0.384230i	$-0.874467\pi$
$967$	−1.56733e7	+	1.56733e7i	−0.539007	+	0.539007i	0.384230	+	0.923237i	$0.374467\pi$
$968$	1.63179e6	+	2.69244e7i	0.0559727	+	0.923545i
$969$			2.58010e7i			0.882727i
$970$	−2.04656e6	−	7.39695e6i	−0.0698387	−	0.252420i
$971$	−3.04623e7			−1.03685			−0.518423	−	0.855124i	$-0.673481\pi$
$971$	−3.04623e7			−1.03685			−0.518423	+	0.855124i	$0.673481\pi$
$972$	−3.56981e7	−	8.03694e6i	−1.21193	−	0.272851i
$973$	−1.35615e7	−	1.35615e7i	−0.459224	−	0.459224i
$974$	2.06987e7	−	5.99634e6i	0.699112	−	0.202530i
$975$	5.06323e7	+	1.22072e6i	1.70575	+	0.0411248i
$976$	2.66799e7	+	1.26547e7i	0.896521	+	0.425233i
$977$	−1.05653e7	−	1.05653e7i	−0.354117	−	0.354117i	0.507522	−	0.861639i	$-0.330562\pi$
$977$	−1.05653e7	−	1.05653e7i	−0.354117	−	0.354117i	−0.861639	+	0.507522i	$0.830562\pi$
$978$	1.22844e7	−	2.23046e7i	0.410682	−	0.745672i
$979$		−	3.17966e6i		−	0.106029i
$980$	3.06183e7	−	1.88525e7i	1.01840	−	0.627051i
$981$			5.64058e7i			1.87133i
$982$	9.69837e6	+	5.34141e6i	0.320937	+	0.176757i
$983$	2.85839e7	+	2.85839e7i	0.943491	+	0.943491i	0.998487	−	0.0549958i	$-0.0175145\pi$
$983$	2.85839e7	+	2.85839e7i	0.943491	+	0.943491i	−0.0549958	+	0.998487i	$0.517515\pi$
$984$	−4.02466e7	−	3.56470e7i	−1.32508	−	1.17364i
$985$	220715.	−	215457.i	0.00724837	−	0.00707572i
$986$	1.01815e6	+	3.51454e6i	0.0333517	+	0.115127i
$987$	5.50917e7	+	5.50917e7i	1.80009	+	1.80009i
$988$	−5.44955e7	−	1.22689e7i	−1.77610	−	0.399866i
$989$	−2.35137e7			−0.764417
$990$	6.04837e6	−	1.06755e7i	0.196133	−	0.346178i
$991$		−	2.35227e6i		−	0.0760857i	−0.999276	−	0.0380429i	$-0.987888\pi$
$991$		−	2.35227e6i		−	0.0760857i	0.999276	−	0.0380429i	$-0.0121123\pi$
$992$	1.28880e7	+	1.78825e7i	0.415820	+	0.576965i
$993$	5.81632e6	−	5.81632e6i	0.187187	−	0.187187i
$994$	1.73153e7	+	5.97706e7i	0.555858	+	1.91876i
$995$	1.66922e7	+	201192.i	0.534511	+	0.00644246i
$996$	−3.91922e7	+	2.47879e7i	−1.25185	+	0.791757i
$997$	−4.06409e6	+	4.06409e6i	−0.129487	+	0.129487i	−0.768880	−	0.639393i	$-0.779186\pi$
$997$	−4.06409e6	+	4.06409e6i	−0.129487	+	0.129487i	0.639393	+	0.768880i	$0.279186\pi$
$998$	1.70023e7	−	3.08710e7i	0.540359	−	0.981126i
$999$	−2.72223e7			−0.863001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.k.a.27.4	yes	56
4.3	odd	2		160.6.o.a.47.25		56
5.3	odd	4	inner	40.6.k.a.3.10	yes	56
8.3	odd	2	inner	40.6.k.a.27.10	yes	56
8.5	even	2		160.6.o.a.47.26		56
20.3	even	4		160.6.o.a.143.26		56
40.3	even	4	inner	40.6.k.a.3.4	✓	56
40.13	odd	4		160.6.o.a.143.25		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.4	✓	56	40.3	even	4	inner
40.6.k.a.3.10	yes	56	5.3	odd	4	inner
40.6.k.a.27.4	yes	56	1.1	even	1	trivial
40.6.k.a.27.10	yes	56	8.3	odd	2	inner
160.6.o.a.47.25		56	4.3	odd	2
160.6.o.a.47.26		56	8.5	even	2
160.6.o.a.143.25		56	40.13	odd	4
160.6.o.a.143.26		56	20.3	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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.95505 - 2.72901i) q^{2} +(-17.2715 + 17.2715i) q^{3} +(17.1050 + 27.0447i) q^{4} +(55.8976 + 0.673734i) q^{5} +(132.715 - 38.4469i) q^{6} +(-135.845 + 135.845i) q^{7} +(-10.9508 - 180.688i) q^{8} -353.606i q^{9} +O(q^{10})\)	\(q+(-4.95505 - 2.72901i) q^{2} +(-17.2715 + 17.2715i) q^{3} +(17.1050 + 27.0447i) q^{4} +(55.8976 + 0.673734i) q^{5} +(132.715 - 38.4469i) q^{6} +(-135.845 + 135.845i) q^{7} +(-10.9508 - 180.688i) q^{8} -353.606i q^{9} +(-275.137 - 155.884i) q^{10} -109.728 q^{11} +(-762.531 - 171.674i) q^{12} +(-469.186 - 469.186i) q^{13} +(1043.84 - 302.395i) q^{14} +(-977.070 + 953.797i) q^{15} +(-438.837 + 925.202i) q^{16} +(283.916 + 283.916i) q^{17} +(-964.995 + 1752.14i) q^{18} -2630.80i q^{19} +(937.909 + 1523.26i) q^{20} -4692.47i q^{21} +(543.708 + 299.449i) q^{22} +(-1169.93 - 1169.93i) q^{23} +(3309.88 + 2931.60i) q^{24} +(3124.09 + 75.3203i) q^{25} +(1044.43 + 3605.25i) q^{26} +(1910.33 + 1910.33i) q^{27} +(-5997.51 - 1350.26i) q^{28} -1610.97 q^{29} +(7444.35 - 2059.68i) q^{30} +3805.32i q^{31} +(4699.34 - 3386.83i) q^{32} +(1895.17 - 1895.17i) q^{33} +(-632.008 - 2181.63i) q^{34} +(-7684.92 + 7501.87i) q^{35} +(9563.19 - 6048.44i) q^{36} +(-7125.02 + 7125.02i) q^{37} +(-7179.47 + 13035.7i) q^{38} +16207.0 q^{39} +(-490.390 - 10107.4i) q^{40} -12159.6 q^{41} +(-12805.8 + 23251.4i) q^{42} +(10049.2 - 10049.2i) q^{43} +(-1876.90 - 2967.57i) q^{44} +(238.237 - 19765.8i) q^{45} +(2604.31 + 8989.80i) q^{46} +(-11740.5 + 11740.5i) q^{47} +(-8400.23 - 23558.9i) q^{48} -20100.5i q^{49} +(-15274.5 - 8898.89i) q^{50} -9807.29 q^{51} +(4663.58 - 20714.4i) q^{52} +(-1312.47 - 1312.47i) q^{53} +(-4252.47 - 14679.1i) q^{54} +(-6133.55 - 73.9276i) q^{55} +(26033.1 + 23057.9i) q^{56} +(45437.7 + 45437.7i) q^{57} +(7982.44 + 4396.36i) q^{58} +20595.0i q^{59} +(-42508.0 - 10109.9i) q^{60} -28836.9i q^{61} +(10384.8 - 18855.6i) q^{62} +(48035.5 + 48035.5i) q^{63} +(-32528.2 + 3957.36i) q^{64} +(-25910.3 - 26542.5i) q^{65} +(-14562.6 + 4218.71i) q^{66} +(-27245.0 - 27245.0i) q^{67} +(-2822.05 + 12534.8i) q^{68} +40412.8 q^{69} +(58551.8 - 16199.9i) q^{70} +57260.4i q^{71} +(-63892.3 + 3872.28i) q^{72} +(-25178.5 + 25178.5i) q^{73} +(54749.1 - 15860.6i) q^{74} +(-55258.5 + 52656.7i) q^{75} +(71149.2 - 44999.8i) q^{76} +(14906.0 - 14906.0i) q^{77} +(-80306.7 - 44229.2i) q^{78} -56597.7 q^{79} +(-25153.3 + 51420.9i) q^{80} +19937.9 q^{81} +(60251.2 + 33183.5i) q^{82} +(41952.5 - 41952.5i) q^{83} +(126907. - 80264.7i) q^{84} +(15679.0 + 16061.5i) q^{85} +(-77218.7 + 22369.9i) q^{86} +(27823.8 - 27823.8i) q^{87} +(1201.61 + 19826.5i) q^{88} +28977.6i q^{89} +(-55121.4 + 97290.1i) q^{90} +127473. q^{91} +(11628.8 - 51652.1i) q^{92} +(-65723.5 - 65723.5i) q^{93} +(90214.4 - 26134.7i) q^{94} +(1772.46 - 147055. i) q^{95} +(-22669.0 + 139660. i) q^{96} +(17161.5 + 17161.5i) q^{97} +(-54854.5 + 99599.0i) q^{98} +38800.6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Introduction

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