LMFDB - Embedded newform 49.6.g.a.11.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,6,Mod(2,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("49.2");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	49.g (of order $21$, degree $12$, 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:	$7.85880717084$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$22$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			11.22
Character	$\chi$	$=$	49.11
Dual form			49.6.g.a.9.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.75287 - 7.19361i) q^{2} +(-22.4292 + 3.38065i) q^{3} +(5.96758 - 79.6318i) q^{4} +(-24.3614 + 62.0717i) q^{5} +(-149.571 + 187.556i) q^{6} +(-121.085 + 46.3178i) q^{7} +(-315.563 - 395.703i) q^{8} +(259.434 - 80.0247i) q^{9} +O(q^{10})$	\(q+(7.75287 - 7.19361i) q^{2} +(-22.4292 + 3.38065i) q^{3} +(5.96758 - 79.6318i) q^{4} +(-24.3614 + 62.0717i) q^{5} +(-149.571 + 187.556i) q^{6} +(-121.085 + 46.3178i) q^{7} +(-315.563 - 395.703i) q^{8} +(259.434 - 80.0247i) q^{9} +(257.650 + 656.480i) q^{10} +(90.5917 + 27.9438i) q^{11} +(135.360 + 1806.25i) q^{12} +(-185.075 - 810.866i) q^{13} +(-605.567 + 1230.14i) q^{14} +(336.562 - 1474.57i) q^{15} +(-2766.23 - 416.942i) q^{16} +(-1632.63 + 1113.11i) q^{17} +(1435.69 - 2486.69i) q^{18} +(-431.870 - 748.021i) q^{19} +(4797.51 + 2310.36i) q^{20} +(2559.26 - 1448.22i) q^{21} +(903.363 - 435.037i) q^{22} +(-477.276 - 325.402i) q^{23} +(8415.53 + 7808.48i) q^{24} +(-968.635 - 898.762i) q^{25} +(-7267.92 - 4955.19i) q^{26} +(-582.343 + 280.442i) q^{27} +(2965.78 + 9918.65i) q^{28} +(-5163.50 - 2486.61i) q^{29} +(-7998.19 - 13853.3i) q^{30} +(3981.17 - 6895.59i) q^{31} +(-11063.8 + 7543.19i) q^{32} +(-2126.36 - 320.498i) q^{33} +(-4650.30 + 20374.3i) q^{34} +(74.7790 - 8644.34i) q^{35} +(-4824.32 - 21136.7i) q^{36} +(902.679 + 12045.4i) q^{37} +(-8729.21 - 2692.61i) q^{38} +(6892.33 + 17561.4i) q^{39} +(32249.5 - 9947.65i) q^{40} +(-1016.99 - 1275.27i) q^{41} +(9423.69 - 29638.1i) q^{42} +(4848.64 - 6080.00i) q^{43} +(2765.83 - 7047.22i) q^{44} +(-1352.89 + 18053.0i) q^{45} +(-6041.08 + 910.546i) q^{46} +(-4472.04 + 4149.44i) q^{47} +63453.7 q^{48} +(12516.3 - 11216.8i) q^{49} -13975.1 q^{50} +(32855.5 - 30485.4i) q^{51} +(-65675.2 + 9898.95i) q^{52} +(-1971.73 + 26311.0i) q^{53} +(-2497.44 + 6363.38i) q^{54} +(-3941.46 + 4942.43i) q^{55} +(56538.1 + 33297.7i) q^{56} +(12215.3 + 15317.5i) q^{57} +(-57919.7 + 17865.9i) q^{58} +(-5437.25 - 13853.9i) q^{59} +(-115414. - 35600.7i) q^{60} +(-39.3781 - 525.465i) q^{61} +(-18738.7 - 82099.6i) q^{62} +(-27707.1 + 21706.2i) q^{63} +(-11593.7 + 50795.5i) q^{64} +(54840.6 + 8265.88i) q^{65} +(-18791.0 + 12811.5i) q^{66} +(-12931.9 + 22398.7i) q^{67} +(78896.0 + 136652. i) q^{68} +(11805.0 + 5684.98i) q^{69} +(-61604.3 - 67556.4i) q^{70} +(-8424.85 + 4057.19i) q^{71} +(-113534. - 77405.9i) q^{72} +(28444.8 + 26392.9i) q^{73} +(93648.4 + 86893.0i) q^{74} +(24764.1 + 16883.9i) q^{75} +(-62143.5 + 29926.7i) q^{76} +(-12263.6 + 812.417i) q^{77} +(179765. + 86570.3i) q^{78} +(-34930.1 - 60500.7i) q^{79} +(93269.4 - 161547. i) q^{80} +(-42396.4 + 28905.4i) q^{81} +(-17058.4 - 2571.14i) q^{82} +(-3650.88 + 15995.6i) q^{83} +(-100051. - 212441. i) q^{84} +(-29319.5 - 128457. i) q^{85} +(-6146.30 - 82016.7i) q^{86} +(124219. + 38316.6i) q^{87} +(-17529.9 - 44665.4i) q^{88} +(-75313.8 + 23231.2i) q^{89} +(119378. + 149695. i) q^{90} +(59967.4 + 89611.8i) q^{91} +(-28760.5 + 36064.5i) q^{92} +(-65982.7 + 168121. i) q^{93} +(-4821.63 + 64340.2i) q^{94} +(56951.9 - 8584.12i) q^{95} +(222651. - 206590. i) q^{96} -123391. q^{97} +(16348.1 - 177000. i) q^{98} +25738.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q - 13 q^{2} - 22 q^{3} + 307 q^{4} - 52 q^{5} - 130 q^{6} + 154 q^{7} - 320 q^{8} + 6 q^{9}+O(q^{10}) $ 264 * q - 13 * q^2 - 22 * q^3 + 307 * q^4 - 52 * q^5 - 130 * q^6 + 154 * q^7 - 320 * q^8 + 6 * q^9	\( 264 q - 13 q^{2} - 22 q^{3} + 307 q^{4} - 52 q^{5} - 130 q^{6} + 154 q^{7} - 320 q^{8} + 6 q^{9} - 792 q^{10} - 635 q^{11} + 3605 q^{12} + 1834 q^{13} - 875 q^{14} - 2572 q^{15} + 3735 q^{16} - 1023 q^{17} - 1336 q^{18} + 9741 q^{19} + 8330 q^{20} + 1512 q^{21} + 842 q^{22} - 1553 q^{23} + 1756 q^{24} + 13144 q^{25} - 1946 q^{26} - 19849 q^{27} - 31584 q^{28} - 30356 q^{29} + 6129 q^{30} + 43903 q^{31} + 27725 q^{32} - 3412 q^{33} - 73182 q^{34} - 17360 q^{35} - 102868 q^{36} - 22105 q^{37} + 19116 q^{38} + 109165 q^{39} + 77354 q^{40} + 47446 q^{41} + 157738 q^{42} + 6674 q^{43} + 15154 q^{44} - 130923 q^{45} - 136952 q^{46} - 195163 q^{47} - 151484 q^{48} - 131194 q^{49} + 263000 q^{50} - 84276 q^{51} - 58758 q^{52} - 110577 q^{53} + 170313 q^{54} + 290245 q^{55} + 79688 q^{56} + 47310 q^{57} + 252156 q^{58} + 127308 q^{59} + 86254 q^{60} + 166863 q^{61} - 63578 q^{62} - 243033 q^{63} - 293812 q^{64} - 16702 q^{65} - 661788 q^{66} + 46195 q^{67} + 393869 q^{68} + 321394 q^{69} - 64330 q^{70} - 61793 q^{71} + 333944 q^{72} + 21699 q^{73} + 133514 q^{74} - 431136 q^{75} + 3087 q^{76} - 48993 q^{77} - 450576 q^{78} - 181 q^{79} + 264228 q^{80} + 142090 q^{81} - 512442 q^{82} + 102424 q^{83} + 344932 q^{84} - 205502 q^{85} + 611991 q^{86} + 1427200 q^{87} + 685993 q^{88} + 145800 q^{89} + 677844 q^{90} + 732956 q^{91} + 10018 q^{92} - 1233536 q^{93} - 601938 q^{94} - 945265 q^{95} - 2372958 q^{96} - 1932952 q^{97} - 672973 q^{98} + 1090736 q^{99}+O(q^{100}) \) 264 * q - 13 * q^2 - 22 * q^3 + 307 * q^4 - 52 * q^5 - 130 * q^6 + 154 * q^7 - 320 * q^8 + 6 * q^9 - 792 * q^10 - 635 * q^11 + 3605 * q^12 + 1834 * q^13 - 875 * q^14 - 2572 * q^15 + 3735 * q^16 - 1023 * q^17 - 1336 * q^18 + 9741 * q^19 + 8330 * q^20 + 1512 * q^21 + 842 * q^22 - 1553 * q^23 + 1756 * q^24 + 13144 * q^25 - 1946 * q^26 - 19849 * q^27 - 31584 * q^28 - 30356 * q^29 + 6129 * q^30 + 43903 * q^31 + 27725 * q^32 - 3412 * q^33 - 73182 * q^34 - 17360 * q^35 - 102868 * q^36 - 22105 * q^37 + 19116 * q^38 + 109165 * q^39 + 77354 * q^40 + 47446 * q^41 + 157738 * q^42 + 6674 * q^43 + 15154 * q^44 - 130923 * q^45 - 136952 * q^46 - 195163 * q^47 - 151484 * q^48 - 131194 * q^49 + 263000 * q^50 - 84276 * q^51 - 58758 * q^52 - 110577 * q^53 + 170313 * q^54 + 290245 * q^55 + 79688 * q^56 + 47310 * q^57 + 252156 * q^58 + 127308 * q^59 + 86254 * q^60 + 166863 * q^61 - 63578 * q^62 - 243033 * q^63 - 293812 * q^64 - 16702 * q^65 - 661788 * q^66 + 46195 * q^67 + 393869 * q^68 + 321394 * q^69 - 64330 * q^70 - 61793 * q^71 + 333944 * q^72 + 21699 * q^73 + 133514 * q^74 - 431136 * q^75 + 3087 * q^76 - 48993 * q^77 - 450576 * q^78 - 181 * q^79 + 264228 * q^80 + 142090 * q^81 - 512442 * q^82 + 102424 * q^83 + 344932 * q^84 - 205502 * q^85 + 611991 * q^86 + 1427200 * q^87 + 685993 * q^88 + 145800 * q^89 + 677844 * q^90 + 732956 * q^91 + 10018 * q^92 - 1233536 * q^93 - 601938 * q^94 - 945265 * q^95 - 2372958 * q^96 - 1932952 * q^97 - 672973 * q^98 + 1090736 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{20}{21}\right)$

Coefficient data

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

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

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

$2$	7.75287	−	7.19361i	1.37053	−	1.27166i	0.443700	−	0.896176i	$-0.353666\pi$
$2$	7.75287	−	7.19361i	1.37053	−	1.27166i	0.926827	−	0.375488i	$-0.122525\pi$
$3$	−22.4292	+	3.38065i	−1.43883	+	0.216869i	−0.821668	−	0.569967i	$-0.806956\pi$
$3$	−22.4292	+	3.38065i	−1.43883	+	0.216869i	−0.617163	+	0.786835i	$0.711718\pi$
$4$	5.96758	−	79.6318i	0.186487	−	2.48849i
$5$	−24.3614	+	62.0717i	−0.435789	+	1.11037i	0.529296	+	0.848437i	$0.322456\pi$
$5$	−24.3614	+	62.0717i	−0.435789	+	1.11037i	−0.965085	+	0.261936i	$0.915639\pi$
$6$	−149.571	+	187.556i	−1.69617	+	2.12693i
$7$	−121.085	+	46.3178i	−0.933999	+	0.357275i
$7$	−121.085	+	46.3178i	−0.933999	+	0.357275i
$8$	−315.563	−	395.703i	−1.74325	−	2.18597i
$9$	259.434	−	80.0247i	1.06763	−	0.329320i
$10$	257.650	+	656.480i	0.814759	+	2.07597i
$11$	90.5917	+	27.9438i	0.225739	+	0.0696313i	0.405561	−	0.914068i	$-0.367076\pi$
$11$	90.5917	+	27.9438i	0.225739	+	0.0696313i	−0.179822	+	0.983699i	$0.557552\pi$
$12$	135.360	+	1806.25i	0.271354	+	3.62097i
$13$	−185.075	−	810.866i	−0.303731	−	1.33073i	−0.864447	−	0.502725i	$-0.832331\pi$
$13$	−185.075	−	810.866i	−0.303731	−	1.33073i	0.560716	−	0.828009i	$-0.310526\pi$
$14$	−605.567	+	1230.14i	−0.825738	+	1.67739i
$15$	336.562	−	1474.57i	0.386222	−	1.69215i
$16$	−2766.23	−	416.942i	−2.70140	−	0.407170i
$17$	−1632.63	+	1113.11i	−1.37014	+	0.934146i	−0.370154	+	0.928970i	$0.620695\pi$
$17$	−1632.63	+	1113.11i	−1.37014	+	0.934146i	−0.999987	+	0.00517618i	$0.998352\pi$
$18$	1435.69	−	2486.69i	1.04443	−	1.80901i
$19$	−431.870	−	748.021i	−0.274454	−	0.475368i	0.695543	−	0.718484i	$-0.255164\pi$
$19$	−431.870	−	748.021i	−0.274454	−	0.475368i	−0.969997	+	0.243116i	$0.921830\pi$
$20$	4797.51	+	2310.36i	2.68189	+	1.29153i
$21$	2559.26	−	1448.22i	1.26638	−	0.716614i
$22$	903.363	−	435.037i	0.397929	−	0.191632i
$23$	−477.276	−	325.402i	−0.188127	−	0.128263i	0.465594	−	0.884998i	$-0.345841\pi$
$23$	−477.276	−	325.402i	−0.188127	−	0.128263i	−0.653721	+	0.756736i	$0.726793\pi$
$24$	8415.53	+	7808.48i	2.98232	+	2.76718i
$25$	−968.635	−	898.762i	−0.309963	−	0.287604i
$26$	−7267.92	−	4955.19i	−2.10852	−	1.43756i
$27$	−582.343	+	280.442i	−0.153734	+	0.0740343i
$28$	2965.78	+	9918.65i	0.714898	+	2.39088i
$29$	−5163.50	−	2486.61i	−1.14012	−	0.549051i	−0.234066	−	0.972221i	$-0.575203\pi$
$29$	−5163.50	−	2486.61i	−1.14012	−	0.549051i	−0.906051	+	0.423170i	$0.860917\pi$
$30$	−7998.19	−	13853.3i	−1.62251	−	2.81028i
$31$	3981.17	−	6895.59i	0.744058	−	1.28875i	−0.206576	−	0.978431i	$-0.566232\pi$
$31$	3981.17	−	6895.59i	0.744058	−	1.28875i	0.950634	−	0.310315i	$-0.100435\pi$
$32$	−11063.8	+	7543.19i	−1.90999	+	1.30221i
$33$	−2126.36	−	320.498i	−0.339901	−	0.0512318i
$34$	−4650.30	+	20374.3i	−0.689896	+	3.02263i
$35$	74.7790	−	8644.34i	0.0103183	−	1.19278i
$36$	−4824.32	−	21136.7i	−0.620412	−	2.71820i
$37$	902.679	+	12045.4i	0.108400	+	1.44650i	0.740733	+	0.671799i	$0.234478\pi$
$37$	902.679	+	12045.4i	0.108400	+	1.44650i	−0.632333	+	0.774697i	$0.717903\pi$
$38$	−8729.21	−	2692.61i	−0.980655	−	0.302492i
$39$	6892.33	+	17561.4i	0.725612	+	1.84883i
$40$	32249.5	−	9947.65i	3.18693	−	0.983039i
$41$	−1016.99	−	1275.27i	−0.0944840	−	0.118479i	0.732342	−	0.680937i	$-0.238427\pi$
$41$	−1016.99	−	1275.27i	−0.0944840	−	0.118479i	−0.826826	+	0.562458i	$0.809856\pi$
$42$	9423.69	−	29638.1i	0.824324	−	2.59255i
$43$	4848.64	−	6080.00i	0.399898	−	0.501456i	−0.540589	−	0.841287i	$-0.681799\pi$
$43$	4848.64	−	6080.00i	0.399898	−	0.501456i	0.940486	+	0.339831i	$0.110370\pi$
$44$	2765.83	−	7047.22i	0.215374	−	0.548765i
$45$	−1352.89	+	18053.0i	−0.0995933	+	1.32898i
$46$	−6041.08	+	910.546i	−0.420940	+	0.0634464i
$47$	−4472.04	+	4149.44i	−0.295298	+	0.273997i	−0.813882	−	0.581030i	$-0.802650\pi$
$47$	−4472.04	+	4149.44i	−0.295298	+	0.273997i	0.518584	+	0.855027i	$0.326459\pi$
$48$	63453.7			3.97515
$49$	12516.3	−	11216.8i	0.744709	−	0.667389i
$50$	−13975.1			−0.790549
$51$	32855.5	−	30485.4i	1.76881	−	1.64122i
$52$	−65675.2	+	9898.95i	−3.36816	+	0.507669i
$53$	−1971.73	+	26311.0i	−0.0964181	+	1.28661i	0.713745	+	0.700406i	$0.246998\pi$
$53$	−1971.73	+	26311.0i	−0.0964181	+	1.28661i	−0.810163	+	0.586205i	$0.800621\pi$
$54$	−2497.44	+	6363.38i	−0.116550	+	0.296964i
$55$	−3941.46	+	4942.43i	−0.175691	+	0.220310i
$56$	56538.1	+	33297.7i	2.40919	+	1.41887i
$57$	12215.3	+	15317.5i	0.497985	+	0.624454i
$58$	−57919.7	+	17865.9i	−2.26077	+	0.697355i
$59$	−5437.25	−	13853.9i	−0.203352	−	0.518134i	0.792421	−	0.609974i	$-0.208820\pi$
$59$	−5437.25	−	13853.9i	−0.203352	−	0.518134i	−0.995774	+	0.0918406i	$0.970725\pi$
$60$	−115414.	−	35600.7i	−4.13887	−	1.27667i
$61$	−39.3781	−	525.465i	−0.00135497	−	0.0180809i	0.996485	−	0.0837674i	$-0.0266953\pi$
$61$	−39.3781	−	525.465i	−0.00135497	−	0.0180809i	−0.997840	+	0.0656866i	$0.979076\pi$
$62$	−18738.7	−	82099.6i	−0.619099	−	2.71245i
$63$	−27707.1	+	21706.2i	−0.879507	+	0.689022i
$64$	−11593.7	+	50795.5i	−0.353813	+	1.55016i
$65$	54840.6	+	8265.88i	1.60997	+	0.242664i
$66$	−18791.0	+	12811.5i	−0.530993	+	0.362025i
$67$	−12931.9	+	22398.7i	−0.351946	+	0.609588i	−0.986590	−	0.163216i	$-0.947813\pi$
$67$	−12931.9	+	22398.7i	−0.351946	+	0.609588i	0.634645	+	0.772804i	$0.281146\pi$
$68$	78896.0	+	136652.i	2.06910	+	3.58379i
$69$	11805.0	+	5684.98i	0.298499	+	0.143749i
$70$	−61604.3	−	67556.4i	−1.50268	−	1.64786i
$71$	−8424.85	+	4057.19i	−0.198343	+	0.0955168i	−0.530419	−	0.847736i	$-0.677965\pi$
$71$	−8424.85	+	4057.19i	−0.198343	+	0.0955168i	0.332076	+	0.943253i	$0.392251\pi$
$72$	−113534.	−	77405.9i	−2.58103	−	1.75972i
$73$	28444.8	+	26392.9i	0.624735	+	0.579670i	0.927697	−	0.373333i	$-0.121785\pi$
$73$	28444.8	+	26392.9i	0.624735	+	0.579670i	−0.302962	+	0.953003i	$0.597976\pi$
$74$	93648.4	+	86893.0i	1.98802	+	1.84461i
$75$	24764.1	+	16883.9i	0.508357	+	0.346592i
$76$	−62143.5	+	29926.7i	−1.23413	+	0.594327i
$77$	−12263.6	+	812.417i	−0.235718	+	0.0156154i
$78$	179765.	+	86570.3i	3.34556	+	1.61114i
$79$	−34930.1	−	60500.7i	−0.629698	−	1.09067i	−0.987612	−	0.156914i	$-0.949845\pi$
$79$	−34930.1	−	60500.7i	−0.629698	−	1.09067i	0.357914	−	0.933754i	$-0.383488\pi$
$80$	93269.4	−	161547.i	1.62935	−	2.82212i
$81$	−42396.4	+	28905.4i	−0.717987	+	0.489515i
$82$	−17058.4	−	2571.14i	−0.280158	−	0.0422271i
$83$	−3650.88	+	15995.6i	−0.0581705	+	0.254861i	−0.995649	−	0.0931812i	$-0.970296\pi$
$83$	−3650.88	+	15995.6i	−0.0581705	+	0.254861i	0.937479	+	0.348043i	$0.113154\pi$
$84$	−100051.	−	212441.i	−1.54712	−	3.28503i
$85$	−29319.5	−	128457.i	−0.440158	−	1.92846i
$86$	−6146.30	−	82016.7i	−0.0896123	−	1.19579i
$87$	124219.	+	38316.6i	1.75951	+	0.542736i
$88$	−17529.9	−	44665.4i	−0.241308	−	0.614844i
$89$	−75313.8	+	23231.2i	−1.00786	+	0.310883i	−0.754366	−	0.656454i	$-0.772056\pi$
$89$	−75313.8	+	23231.2i	−1.00786	+	0.310883i	−0.253493	+	0.967337i	$0.581579\pi$
$90$	119378.	+	149695.i	1.55352	+	1.94805i
$91$	59967.4	+	89611.8i	0.759122	+	1.13439i
$92$	−28760.5	+	36064.5i	−0.354264	+	0.444233i
$93$	−65982.7	+	168121.i	−0.791084	+	2.01565i
$94$	−4821.63	+	64340.2i	−0.0562826	+	0.751040i
$95$	56951.9	−	8584.12i	0.647440	−	0.0975858i
$96$	222651.	−	206590.i	2.46574	−	2.28787i
$97$	−123391.			−1.33154			−0.665768	−	0.746159i	$-0.731896\pi$
$97$	−123391.			−1.33154			−0.665768	+	0.746159i	$0.731896\pi$
$98$	16348.1	−	177000.i	0.171950	−	1.86169i
$99$	25738.7			0.263936
$100$	−77350.5	+	71770.8i	−0.773505	+	0.717708i
$101$	−59756.0	+	9006.77i	−0.582879	+	0.0878549i	−0.433861	−	0.900980i	$-0.642849\pi$
$101$	−59756.0	+	9006.77i	−0.582879	+	0.0878549i	−0.149018	+	0.988835i	$0.547611\pi$
$102$	35423.9	−	472699.i	0.337129	−	4.49867i
$103$	23449.3	−	59747.7i	0.217789	−	0.554917i	−0.779668	−	0.626194i	$-0.784612\pi$
$103$	23449.3	−	59747.7i	0.217789	−	0.554917i	0.997457	+	0.0712762i	$0.0227072\pi$
$104$	−262460.	+	329114.i	−2.37946	+	2.98375i
$105$	27546.3	+	194138.i	0.243831	+	1.71845i
$106$	173984.	+	218169.i	1.50399	+	1.88595i
$107$	73476.4	−	22664.5i	0.620423	−	0.191375i	0.0314206	−	0.999506i	$-0.489997\pi$
$107$	73476.4	−	22664.5i	0.620423	−	0.191375i	0.589003	+	0.808131i	$0.299521\pi$
$108$	18856.9	+	48046.6i	0.155565	+	0.396372i
$109$	88234.9	+	27216.9i	0.711335	+	0.219418i	0.629245	−	0.777207i	$-0.283364\pi$
$109$	88234.9	+	27216.9i	0.711335	+	0.219418i	0.0820903	+	0.996625i	$0.473840\pi$
$110$	4996.33	+	66671.4i	0.0393703	+	0.525361i
$111$	−60967.6	−	267117.i	−0.469669	−	2.05775i
$112$	354262.	−	77640.0i	2.66857	−	0.584845i
$113$	45793.4	−	200634.i	0.337371	−	1.47812i	−0.467142	−	0.884182i	$-0.654716\pi$
$113$	45793.4	−	200634.i	0.337371	−	1.47812i	0.804513	−	0.593935i	$-0.202426\pi$
$114$	204892.	+	30882.4i	1.47660	+	0.222561i
$115$	31825.3	−	21698.1i	0.224403	−	0.152995i
$116$	−228827.	+	396340.i	−1.57893	+	2.73478i
$117$	−112904.	−	195556.i	−0.762509	−	1.32070i
$118$	−141814.	−	68294.0i	−0.937592	−	0.451520i
$119$	146131.	−	210401.i	0.945964	−	1.36201i
$120$	−689699.	+	332142.i	−4.37227	+	2.10557i
$121$	−125641.	−	85660.3i	−0.780129	−	0.531883i
$122$	−4085.28	−	3790.59i	−0.0248498	−	0.0230572i
$123$	27121.5	+	25165.1i	0.161641	+	0.149981i
$124$	−525350.	−	358178.i	−3.06828	−	2.09192i
$125$	−108358.	+	52182.3i	−0.620275	+	0.298709i
$126$	−58663.2	+	367600.i	−0.329184	+	2.06276i
$127$	−258383.	−	124430.i	−1.42152	−	0.684569i	−0.444123	−	0.895966i	$-0.646485\pi$
$127$	−258383.	−	124430.i	−1.42152	−	0.684569i	−0.977400	+	0.211397i	$0.932199\pi$
$128$	61269.0	+	106121.i	0.330534	+	0.572501i
$129$	−88196.5	+	152761.i	−0.466635	+	0.808235i
$130$	484633.	−	330417.i	2.51510	−	1.71476i
$131$	147145.	+	22178.5i	0.749146	+	0.112916i	0.512508	−	0.858682i	$-0.328716\pi$
$131$	147145.	+	22178.5i	0.749146	+	0.112916i	0.236638	+	0.971598i	$0.423955\pi$
$132$	−38211.0	+	167414.i	−0.190877	+	0.836288i
$133$	86939.9	+	70571.2i	0.426177	+	0.345938i
$134$	60868.3	+	266682.i	0.292839	+	1.28301i
$135$	−3220.83	−	42979.0i	−0.0152101	−	0.202965i
$136$	955657.	+	294781.i	4.43052	+	1.36663i
$137$	−20439.4	−	52078.8i	−0.0930394	−	0.237060i	0.876777	−	0.480897i	$-0.159689\pi$
$137$	−20439.4	−	52078.8i	−0.0930394	−	0.237060i	−0.969816	+	0.243837i	$0.921594\pi$
$138$	132418.	−	40845.5i	0.591901	−	0.182577i
$139$	−4660.41	−	5843.98i	−0.0204591	−	0.0256550i	0.771497	−	0.636233i	$-0.219508\pi$
$139$	−4660.41	−	5843.98i	−0.0204591	−	0.0256550i	−0.791956	+	0.610578i	$0.790937\pi$
$140$	−687918.	−	57540.6i	−2.96631	−	0.248116i
$141$	86276.2	−	108187.i	0.365463	−	0.458276i
$142$	−36130.9	+	92060.0i	−0.150369	+	0.383133i
$143$	5892.46	−	78629.5i	0.0240967	−	0.321548i
$144$	−751019.	+	113198.i	−3.01818	+	0.454917i
$145$	280138.	−	259930.i	1.10650	−	1.02668i
$146$	410390.			1.59336
$147$	−242810.	+	293897.i	−0.926774	+	1.12176i
$148$	964585.			3.61981
$149$	−261260.	+	242414.i	−0.964066	+	0.894523i	−0.994471	−	0.105015i	$-0.966511\pi$
$149$	−261260.	+	242414.i	−0.964066	+	0.894523i	0.0304042	+	0.999538i	$0.490321\pi$
$150$	313449.	−	47244.8i	1.13747	−	0.171445i
$151$	3193.97	−	42620.6i	0.0113996	−	0.152117i	−0.988599	−	0.150571i	$-0.951889\pi$
$151$	3193.97	−	42620.6i	0.0113996	−	0.152117i	0.999999	−	0.00154591i	$-0.000492080\pi$
$152$	−159712.	+	406940.i	−0.560698	+	1.42864i
$153$	−334483.	+	419429.i	−1.15517	+	1.44854i
$154$	−89234.1	+	94518.3i	−0.303200	+	0.321155i
$155$	331034.	+	415104.i	1.10674	+	1.38780i
$156$	1.43957e6	−	444050.i	4.73612	−	1.46090i
$157$	−57538.7	−	146606.i	−0.186299	−	0.474682i	0.806959	−	0.590608i	$-0.201112\pi$
$157$	−57538.7	−	146606.i	−0.186299	−	0.474682i	−0.993258	+	0.115925i	$0.963017\pi$
$158$	−706027.	−	217781.i	−2.24998	−	0.694027i
$159$	−44723.9	−	596798.i	−0.140296	−	1.87212i
$160$	−198689.	−	870513.i	−0.613583	−	2.68828i
$161$	72863.1	+	17295.0i	0.221535	+	0.0525842i
$162$	−120760.	+	529083.i	−0.361522	+	1.58393i
$163$	−263271.	−	39681.7i	−0.776129	−	0.116983i	−0.250979	−	0.967993i	$-0.580753\pi$
$163$	−263271.	−	39681.7i	−0.776129	−	0.116983i	−0.525150	+	0.851010i	$0.675991\pi$
$164$	−107621.	+	73374.7i	−0.312455	+	0.213028i
$165$	71694.9	−	124179.i	0.205012	−	0.355091i
$166$	86761.0	+	150275.i	0.244374	+	0.423268i
$167$	314472.	+	151442.i	0.872550	+	0.420198i	0.815898	−	0.578196i	$-0.196243\pi$
$167$	314472.	+	151442.i	0.872550	+	0.420198i	0.0566521	+	0.998394i	$0.481957\pi$
$168$	−1.38067e6	−	555703.i	−3.77413	−	1.51904i
$169$	−288728.	+	139044.i	−0.777629	+	0.374486i
$170$	−1.15138e6	−	784997.i	−3.05560	−	2.08327i
$171$	−171902.	−	159502.i	−0.449563	−	0.417134i
$172$	−455227.	−	422389.i	−1.17329	−	1.08866i
$173$	91837.3	+	62613.6i	0.233294	+	0.159057i	0.674325	−	0.738435i	$-0.264435\pi$
$173$	91837.3	+	62613.6i	0.233294	+	0.159057i	−0.441031	+	0.897492i	$0.645387\pi$
$174$	1.23869e6	−	596522.i	3.10163	−	1.49367i
$175$	158916.	+	63961.9i	0.392259	+	0.157880i
$176$	−238946.	−	115071.i	−0.581459	−	0.280016i
$177$	168788.	+	292350.i	0.404957	+	0.701406i
$178$	−416782.	+	721887.i	−0.985959	+	1.70773i
$179$	−13836.5	+	9433.58i	−0.0322771	+	0.0220061i	−0.579351	−	0.815078i	$-0.696694\pi$
$179$	−13836.5	+	9433.58i	−0.0322771	+	0.0220061i	0.547074	+	0.837084i	$0.315742\pi$
$180$	1.42952e6	+	215466.i	3.28859	+	0.495675i
$181$	61847.5	−	270972.i	0.140322	−	0.614791i	−0.855038	−	0.518566i	$-0.826466\pi$
$181$	61847.5	−	270972.i	0.140322	−	0.614791i	0.995360	−	0.0962247i	$-0.0306767\pi$
$182$	1.10955e6	+	263366.i	2.48296	+	0.589362i
$183$	2659.63	+	11652.6i	0.00587075	+	0.0257214i
$184$	21848.2	+	291544.i	0.0475742	+	0.634834i
$185$	−769670.	−	237412.i	−1.65339	−	0.510003i
$186$	697843.	+	1.77808e6i	1.47903	+	3.76850i
$187$	−179007.	+	55216.4i	−0.374340	+	0.115469i
$188$	303740.	+	380878.i	0.626770	+	0.785944i
$189$	57523.8	−	60930.2i	0.117137	−	0.124073i
$190$	379790.	−	476242.i	0.763237	−	0.957069i
$191$	3306.28	−	8424.27i	0.00655777	−	0.0167089i	−0.927557	−	0.373681i	$-0.878096\pi$
$191$	3306.28	−	8424.27i	0.00655777	−	0.0167089i	0.934115	+	0.356972i	$0.116191\pi$
$192$	88315.9	−	1.17849e6i	0.172896	−	2.30714i
$193$	767171.	−	115632.i	1.48251	−	0.223453i	0.642612	−	0.766192i	$-0.277851\pi$
$193$	767171.	−	115632.i	1.48251	−	0.223453i	0.839902	+	0.542738i	$0.182613\pi$
$194$	−956632.	+	887625.i	−1.82491	+	1.69327i
$195$	−1.25797e6			−2.36910
$196$	−818523.	−	1.06363e6i	−1.52192	−	1.97766i
$197$	−147804.			−0.271345			−0.135672	−	0.990754i	$-0.543319\pi$
$197$	−147804.			−0.271345			−0.135672	+	0.990754i	$0.543319\pi$
$198$	199549.	−	185155.i	0.361732	−	0.335638i
$199$	115362.	−	17388.0i	0.206505	−	0.0311256i	−0.0449751	−	0.998988i	$-0.514321\pi$
$199$	115362.	−	17388.0i	0.206505	−	0.0311256i	0.251480	+	0.967863i	$0.419083\pi$
$200$	−49977.8	+	666908.i	−0.0883491	+	1.17894i
$201$	214329.	−	546103.i	0.374190	−	0.953420i
$202$	−398490.	+	499690.i	−0.687130	+	0.861633i
$203$	740399.	+	61930.3i	1.26103	+	0.105478i
$204$	−2.23154e6	−	2.79826e6i	−3.75430	−	4.70775i
$205$	103933.	−	32059.2i	0.172731	−	0.0532805i
$206$	−248003.	−	631901.i	−0.407182	−	1.03748i
$207$	−149862.	−	46226.3i	−0.243089	−	0.0749830i
$208$	173876.	+	2.32021e6i	0.278664	+	3.71851i
$209$	−18221.3	−	79832.6i	−0.0288545	−	0.126420i
$210$	1.61012e6	+	1.30697e6i	2.51947	+	2.04511i
$211$	−48333.6	+	211763.i	−0.0747383	+	0.327450i	−0.998451	−	0.0556358i	$-0.982281\pi$
$211$	−48333.6	+	211763.i	−0.0747383	+	0.327450i	0.923713	+	0.383086i	$0.125139\pi$
$212$	2.08342e6	+	314026.i	3.18374	+	0.479872i
$213$	175246.	−	119481.i	0.264667	−	0.180447i
$214$	406613.	−	704275.i	0.606942	−	1.05125i
$215$	259277.	+	449080.i	0.382532	+	0.662564i
$216$	294737.	+	141938.i	0.429834	+	0.206997i
$217$	−162673.	+	1.01935e6i	−0.234513	+	1.46952i
$218$	879862.	−	423719.i	1.25393	−	0.603861i
$219$	−727218.	−	495809.i	−1.02460	−	0.698561i
$220$	370054.	+	343360.i	0.515476	+	0.478292i
$221$	1.20474e6	+	1.11784e6i	1.65925	+	1.53956i
$222$	−2.39421e6	−	1.63234e6i	−3.26046	−	2.22295i
$223$	−85966.9	+	41399.5i	−0.115763	+	0.0557484i	−0.490869	−	0.871233i	$-0.663321\pi$
$223$	−85966.9	+	41399.5i	−0.115763	+	0.0557484i	0.375106	+	0.926982i	$0.377606\pi$
$224$	990283.	−	1.42582e6i	1.31868	−	1.89865i
$225$	−323220.	−	155655.i	−0.425640	−	0.204977i
$226$	−1.08825e6	−	1.88491e6i	−1.41729	−	2.45482i
$227$	−604748.	+	1.04745e6i	−0.778950	+	1.34918i	0.153597	+	0.988133i	$0.450914\pi$
$227$	−604748.	+	1.04745e6i	−0.778950	+	1.34918i	−0.932547	+	0.361047i	$0.882419\pi$
$228$	1.29265e6	−	881317.i	1.64682	−	1.12278i
$229$	860231.	+	129659.i	1.08399	+	0.163386i	0.666656	−	0.745366i	$-0.267725\pi$
$229$	860231.	+	129659.i	1.08399	+	0.163386i	0.417337	+	0.908752i	$0.362963\pi$
$230$	90649.7	−	397162.i	0.112992	−	0.495049i
$231$	272316.	−	59680.8i	0.335771	−	0.0735877i
$232$	645448.	+	2.82789e6i	0.787302	+	3.44940i
$233$	55696.3	+	743216.i	0.0672104	+	0.896861i	0.924293	+	0.381683i	$0.124655\pi$
$233$	55696.3	+	743216.i	0.0672104	+	0.896861i	−0.857083	+	0.515178i	$0.827726\pi$
$234$	−2.28208e6	−	703929.i	−2.72453	−	0.840406i
$235$	−148618.	−	378673.i	−0.175551	−	0.447296i
$236$	−1.13566e6	+	350304.i	−1.32730	+	0.409416i
$237$	987984.	+	1.23889e6i	1.14256	+	1.43273i
$238$	−380609.	−	2.68242e6i	−0.435548	−	3.06962i
$239$	909085.	−	1.13996e6i	1.02946	−	1.29090i	0.0735352	−	0.997293i	$-0.476572\pi$
$239$	909085.	−	1.13996e6i	1.02946	−	1.29090i	0.955925	−	0.293610i	$-0.0948567\pi$
$240$	−1.54582e6	+	3.93868e6i	−1.73233	+	4.41390i
$241$	39044.5	−	521013.i	0.0433029	−	0.577838i	−0.932781	−	0.360444i	$-0.882625\pi$
$241$	39044.5	−	521013.i	0.0433029	−	0.577838i	0.976084	−	0.217394i	$-0.0697556\pi$
$242$	−1.59028e6	+	239697.i	−1.74556	+	0.263101i
$243$	968333.	−	898481.i	1.05198	−	0.976098i
$244$	−42078.7			−0.0452468
$245$	391332.	+	1.05017e6i	0.416515	+	1.11775i
$246$	391298.			0.412258
$247$	−526617.	+	488629.i	−0.549228	+	0.509609i
$248$	−3.98491e6	+	600629.i	−4.11424	+	0.620122i
$249$	27810.8	−	371109.i	0.0284259	−	0.379318i
$250$	−464703.	+	1.18405e6i	−0.470247	+	1.19817i
$251$	−203908.	+	255692.i	−0.204291	+	0.256173i	−0.873414	−	0.486979i	$-0.838099\pi$
$251$	−203908.	+	255692.i	−0.204291	+	0.256173i	0.669122	+	0.743152i	$0.266670\pi$
$252$	1.56316e6	+	2.33590e6i	1.55061	+	2.31714i
$253$	−34144.3	−	42815.6i	−0.0335364	−	0.0420534i
$254$	−2.89831e6	+	894011.i	−2.81878	+	0.869478i
$255$	1.09188e6	+	2.78206e6i	1.05154	+	2.67927i
$256$	−354782.	−	109436.i	−0.338346	−	0.104366i
$257$	19128.6	+	255253.i	0.0180655	+	0.241068i	0.998925	+	0.0463516i	$0.0147595\pi$
$257$	19128.6	+	255253.i	0.0180655	+	0.241068i	−0.980860	+	0.194716i	$0.937621\pi$
$258$	415126.	+	1.81879e6i	0.388267	+	1.70111i
$259$	−667218.	−	1.41671e6i	−0.618042	−	1.31230i
$260$	985493.	−	4.31773e6i	0.904107	−	3.96115i
$261$	−1.53858e6	−	231903.i	−1.39803	−	0.210720i
$262$	1.30034e6	−	886555.i	1.17032	−	0.797908i
$263$	591358.	−	1.02426e6i	0.527183	−	0.913107i	−0.472316	−	0.881430i	$-0.656582\pi$
$263$	591358.	−	1.02426e6i	0.527183	−	0.913107i	0.999498	−	0.0316775i	$-0.0100850\pi$
$264$	544179.	+	942545.i	0.480542	+	0.832324i
$265$	−1.58513e6	−	763360.i	−1.38660	−	0.667751i
$266$	1.18170e6	−	78282.7i	1.02400	−	0.0678362i
$267$	1.61069e6	−	775666.i	1.38272	−	0.665881i
$268$	1.70648e6	+	1.16346e6i	1.45132	+	0.989495i
$269$	951709.	+	883057.i	0.801906	+	0.744060i	0.970364	−	0.241649i	$-0.0776882\pi$
$269$	951709.	+	883057.i	0.801906	+	0.744060i	−0.168458	+	0.985709i	$0.553879\pi$
$270$	−334145.	−	310041.i	−0.278949	−	0.258827i
$271$	−1.67846e6	−	1.14436e6i	−1.38832	−	0.946538i	−0.999684	−	0.0251444i	$-0.991995\pi$
$271$	−1.67846e6	−	1.14436e6i	−1.38832	−	0.946538i	−0.388632	−	0.921393i	$-0.627052\pi$
$272$	4.98033e6	−	2.39840e6i	4.08165	−	1.96562i
$273$	−1.64796e6	−	1.80719e6i	−1.33826	−	1.46756i
$274$	−533099.	−	256727.i	−0.428974	−	0.206583i
$275$	−62635.5	−	108488.i	−0.0499446	−	0.0865066i
$276$	523152.	−	906126.i	0.413386	−	0.716005i
$277$	−1.50761e6	+	1.02787e6i	−1.18056	+	0.804894i	−0.984446	−	0.175686i	$-0.943785\pi$
$277$	−1.50761e6	+	1.02787e6i	−1.18056	+	0.804894i	−0.196117	+	0.980581i	$0.562833\pi$
$278$	−78170.9	−	11782.4i	−0.0606643	−	0.00914367i
$279$	481033.	−	2.10754e6i	0.369968	−	1.62094i
$280$	−3.44419e6	+	2.69824e6i	−2.62538	+	2.05677i
$281$	−144573.	−	633414.i	−0.109225	−	0.478544i	−0.999723	−	0.0235567i	$-0.992501\pi$
$281$	−144573.	−	633414.i	−0.109225	−	0.478544i	0.890498	−	0.454987i	$-0.150356\pi$
$282$	−109367.	−	1.45940e6i	−0.0818959	−	1.09282i
$283$	2.11304e6	+	651787.i	1.56835	+	0.483770i	0.952613	−	0.304185i	$-0.0983841\pi$
$283$	2.11304e6	+	651787.i	1.56835	+	0.483770i	0.615732	+	0.787955i	$0.288860\pi$
$284$	272806.	+	695097.i	0.200705	+	0.511387i
$285$	−1.24836e6	+	385069.i	−0.910393	+	0.280819i
$286$	−519946.	−	651992.i	−0.375875	−	0.471332i
$287$	182210.	+	107311.i	0.130578	+	0.0769027i
$288$	−2.26669e6	+	2.84234e6i	−1.61031	+	2.01927i
$289$	907738.	−	2.31288e6i	0.639316	−	1.62895i
$290$	302037.	−	4.03041e6i	0.210895	−	2.81420i
$291$	2.76755e6	−	417141.i	1.91586	−	0.288769i
$292$	2.27146e6	−	2.10761e6i	1.55901	−	1.44655i
$293$	−1.31511e6			−0.894939			−0.447470	−	0.894299i	$-0.647675\pi$
$293$	−1.31511e6			−0.894939			−0.447470	+	0.894299i	$0.647675\pi$
$294$	231702.	+	4.02523e6i	0.156337	+	2.71595i
$295$	992394.			0.663940
$296$	4.48155e6	−	4.15827e6i	2.97303	−	2.75857i
$297$	−60592.0	+	9132.78i	−0.0398588	+	0.00600775i
$298$	−281683.	+	3.75880e6i	−0.183747	+	2.45194i
$299$	−175525.	+	447231.i	−0.113543	+	0.289304i
$300$	1.49227e6	−	1.87125e6i	0.957294	−	1.20041i
$301$	−305487.	+	960777.i	−0.194346	+	0.611233i
$302$	−281833.	−	353408.i	−0.177818	−	0.222976i
$303$	1.30983e6	−	404029.i	0.819611	−	0.252817i
$304$	882771.	+	2.24926e6i	0.547853	+	1.39591i
$305$	33575.8	+	10356.8i	0.0206670	+	0.00637491i
$306$	424002.	+	5.65792e6i	0.258860	+	3.45424i
$307$	−128538.	−	563163.i	−0.0778370	−	0.341026i	0.920982	−	0.389604i	$-0.127388\pi$
$307$	−128538.	−	563163.i	−0.0778370	−	0.341026i	−0.998819	+	0.0485780i	$0.984531\pi$
$308$	−8489.92	+	981423.i	−0.00509949	+	0.589494i
$309$	−323961.	+	1.41936e6i	−0.193017	+	0.845664i
$310$	5.55257e6	+	836915.i	3.28163	+	0.494626i
$311$	120657.	−	82262.9i	0.0707381	−	0.0482284i	−0.527435	−	0.849596i	$-0.676846\pi$
$311$	120657.	−	82262.9i	0.0707381	−	0.0482284i	0.598173	+	0.801367i	$0.295894\pi$
$312$	4.77413e6	−	8.26903e6i	2.77656	−	4.80915i
$313$	−201147.	−	348396.i	−0.116052	−	0.201008i	0.802148	−	0.597125i	$-0.203691\pi$
$313$	−201147.	−	348396.i	−0.116052	−	0.201008i	−0.918200	+	0.396118i	$0.870357\pi$
$314$	−1.50072e6	−	722708.i	−0.858964	−	0.413655i
$315$	−672361.	−	2.24862e6i	−0.381791	−	1.27685i
$316$	−5.02623e6	+	2.42050e6i	−2.83155	+	1.36360i
$317$	−283257.	−	193121.i	−0.158319	−	0.107940i	0.481569	−	0.876408i	$-0.340067\pi$
$317$	−283257.	−	193121.i	−0.158319	−	0.107940i	−0.639888	+	0.768468i	$0.721019\pi$
$318$	−4.63987e6	−	4.30517e6i	−2.57299	−	2.38739i
$319$	−398285.	−	369554.i	−0.219138	−	0.203330i
$320$	−2.87052e6	−	1.95709e6i	−1.56706	−	1.06841i
$321$	−1.57139e6	+	756742.i	−0.851181	+	0.409907i
$322$	689312.	−	390063.i	0.370489	−	0.209650i
$323$	1.53771e6	+	740523.i	0.820104	+	0.394941i
$324$	2.04879e6	+	3.54860e6i	1.08426	+	1.87800i
$325$	−549506.	+	951772.i	−0.288579	+	0.499833i
$326$	−2.32656e6	+	1.58622e6i	−1.21247	+	0.826647i
$327$	−2.07105e6	−	312160.i	−1.07108	−	0.161439i
$328$	−183703.	+	804854.i	−0.0942824	+	0.413078i
$329$	349305.	−	709572.i	0.177916	−	0.361415i
$330$	−337456.	−	1.47849e6i	−0.170582	−	0.747367i
$331$	76120.2	+	1.01575e6i	0.0381883	+	0.509587i	0.983198	+	0.182544i	$0.0584332\pi$
$331$	76120.2	+	1.01575e6i	0.0381883	+	0.509587i	−0.945009	+	0.327043i	$0.893948\pi$
$332$	1.25197e6	+	386181.i	0.623373	+	0.192285i
$333$	1.19812e6	+	3.05275e6i	0.592091	+	1.50862i
$334$	3.52747e6	−	1.08808e6i	1.73020	−	0.533697i
$335$	−1.07529e6	−	1.34837e6i	−0.523495	−	0.656443i
$336$	−7.68331e6	+	2.93903e6i	−3.71279	+	1.42022i
$337$	−1.84018e6	+	2.30751e6i	−0.882643	+	1.10680i	0.110955	+	0.993825i	$0.464609\pi$
$337$	−1.84018e6	+	2.30751e6i	−0.882643	+	1.10680i	−0.993598	+	0.112974i	$0.963962\pi$
$338$	−1.23824e6	+	3.15499e6i	−0.589541	+	1.50213i
$339$	−348834.	+	4.65487e6i	−0.164862	+	2.19993i
$340$	−1.04042e7	+	1.56818e6i	−4.88104	+	0.735698i
$341$	553350.	−	513434.i	0.257700	−	0.239110i
$342$	−2.48013e6			−1.14659
$343$	−996006.	+	1.93792e6i	−0.457116	+	0.889407i
$344$	−3.93592e6			−1.79329
$345$	−640461.	+	594261.i	−0.289698	+	0.268800i
$346$	1.16242e6	−	175207.i	0.522003	−	0.0786794i
$347$	12906.7	−	172228.i	0.00575429	−	0.0767857i	−0.993587	−	0.113068i	$-0.963932\pi$
$347$	12906.7	−	172228.i	0.00575429	−	0.0767857i	0.999342	+	0.0362818i	$0.0115514\pi$
$348$	3.79251e6	−	9.66315e6i	1.67872	−	4.27731i
$349$	2.00640e6	−	2.51594e6i	0.881766	−	1.10570i	−0.111944	−	0.993714i	$-0.535708\pi$
$349$	2.00640e6	−	2.51594e6i	0.881766	−	1.10570i	0.993710	−	0.111985i	$-0.0357208\pi$
$350$	1.69217e6	−	647294.i	0.738372	−	0.282443i
$351$	335178.	+	420300.i	0.145214	+	0.182092i
$352$	−1.21308e6	+	374184.i	−0.521833	+	0.160964i
$353$	−1.43715e6	−	3.66181e6i	−0.613856	−	1.56408i	−0.811843	−	0.583875i	$-0.801536\pi$
$353$	−1.43715e6	−	3.66181e6i	−0.613856	−	1.56408i	0.197987	−	0.980205i	$-0.436559\pi$
$354$	3.41164e6	+	1.05235e6i	1.44696	+	0.446327i
$355$	−46596.2	−	621783.i	−0.0196237	−	0.261859i
$356$	1.40050e6	+	6.13601e6i	0.585679	+	2.56603i
$357$	−2.56630e6	+	5.21313e6i	−1.06570	+	2.16485i
$358$	−39411.2	+	172672.i	−0.0162522	+	0.0712056i
$359$	2.84783e6	+	429241.i	1.16621	+	0.175778i	0.703476	−	0.710719i	$-0.251630\pi$
$359$	2.84783e6	+	429241.i	1.16621	+	0.175778i	0.462735	+	0.886497i	$0.346868\pi$
$360$	7.57055e6	−	5.16152e6i	3.07873	−	2.09904i
$361$	865025.	−	1.49827e6i	0.349350	−	0.605092i
$362$	−1.46977e6	−	2.54571e6i	−0.589492	−	1.02103i
$363$	3.10760e6	+	1.49654e6i	1.23782	+	0.596104i
$364$	7.49381e6	−	4.24055e6i	2.96448	−	1.67752i
$365$	−2.33121e6	+	1.12265e6i	−0.915902	+	0.441075i
$366$	104444.	+	71208.8i	0.0407550	+	0.0277863i
$367$	−2.81867e6	−	2.61534e6i	−1.09239	−	1.01359i	−0.999840	−	0.0178848i	$-0.994307\pi$
$367$	−2.81867e6	−	2.61534e6i	−1.09239	−	1.01359i	−0.0925529	−	0.995708i	$-0.529503\pi$
$368$	1.18458e6	+	1.09913e6i	0.455980	+	0.423088i
$369$	−365895.	−	249463.i	−0.139891	−	0.0953763i
$370$	−7.67500e6	+	3.69608e6i	−2.91457	+	1.40358i
$371$	−979917.	−	3.27720e6i	−0.369619	−	1.23614i
$372$	1.29940e7	+	6.25760e6i	4.86841	+	2.34450i
$373$	1.15792e6	+	2.00558e6i	0.430932	+	0.746395i	0.996954	−	0.0779946i	$-0.0248517\pi$
$373$	1.15792e6	+	2.00558e6i	0.430932	+	0.746395i	−0.566022	+	0.824390i	$0.691518\pi$
$374$	−990614.	+	1.71579e6i	−0.366206	+	0.634287i
$375$	2.25396e6	−	1.53672e6i	0.827690	−	0.564310i
$376$	3.05315e6	+	460189.i	1.11373	+	0.167867i
$377$	−1.06067e6	+	4.64712e6i	−0.384352	+	1.68395i
$378$	7666.08	−	886188.i	0.00275959	−	0.319004i
$379$	−469338.	−	2.05631e6i	−0.167837	−	0.735342i	−0.986859	−	0.161581i	$-0.948341\pi$
$379$	−469338.	−	2.05631e6i	−0.167837	−	0.735342i	0.819022	−	0.573762i	$-0.194516\pi$
$380$	−343704.	−	4.58641e6i	−0.122103	−	1.62935i
$381$	6.21596e6	+	1.91737e6i	2.19379	+	0.676695i
$382$	−34967.7	−	89096.4i	−0.0122605	−	0.0312393i
$383$	−837894.	+	258456.i	−0.291872	+	0.0900305i	−0.437233	−	0.899348i	$-0.644042\pi$
$383$	−837894.	+	258456.i	−0.291872	+	0.0900305i	0.145362	+	0.989379i	$0.453565\pi$
$384$	−1.73297e6	−	2.17307e6i	−0.599740	−	0.752050i
$385$	248330.	−	781016.i	0.0853843	−	0.268539i
$386$	5.11596e6	−	6.41521e6i	1.74767	−	2.19151i
$387$	771351.	−	1.96537e6i	0.261803	−	0.667063i
$388$	−736344.	+	9.82582e6i	−0.248314	+	3.31352i
$389$	2.75446e6	−	415168.i	0.922917	−	0.139107i	0.329641	−	0.944106i	$-0.393072\pi$
$389$	2.75446e6	−	415168.i	0.922917	−	0.139107i	0.593276	+	0.804999i	$0.297834\pi$
$390$	−9.75289e6	+	9.04936e6i	−3.24692	+	3.01270i
$391$	1.14142e6			0.377576
$392$	−8.38821e6	−	1.41314e6i	−2.75711	−	0.464484i
$393$	−3.37531e6			−1.10238
$394$	−1.14591e6	+	1.06325e6i	−0.371886	+	0.345059i
$395$	4.60633e6	−	694292.i	1.48546	−	0.223898i
$396$	153598.	−	2.04962e6i	0.0492207	−	0.656804i
$397$	1.87910e6	−	4.78786e6i	0.598374	−	1.52463i	−0.235042	−	0.971985i	$-0.575523\pi$
$397$	1.87910e6	−	4.78786e6i	0.598374	−	1.52463i	0.833416	−	0.552647i	$-0.186382\pi$
$398$	769304.	−	964677.i	0.243439	−	0.305263i
$399$	−2.18856e6	−	1.28894e6i	−0.688220	−	0.405322i
$400$	2.30474e6	+	2.89005e6i	0.720230	+	0.903140i
$401$	−2.35806e6	+	727365.i	−0.732308	+	0.225887i	−0.638412	−	0.769695i	$-0.720408\pi$
$401$	−2.35806e6	+	727365.i	−0.732308	+	0.225887i	−0.0938961	+	0.995582i	$0.529932\pi$
$402$	−2.26678e6	−	5.77567e6i	−0.699592	−	1.78253i
$403$	−6.32822e6	−	1.95200e6i	−1.94097	−	0.598710i
$404$	360627.	+	4.81223e6i	0.109927	+	1.46687i
$405$	−761373.	−	3.33579e6i	−0.230653	−	1.01056i
$406$	6.18572e6	−	4.84600e6i	1.86241	−	1.45905i
$407$	−254820.	+	1.11644e6i	−0.0762513	+	0.334079i
$408$	−2.24311e7	−	3.38095e6i	−6.67115	−	1.00551i
$409$	−2.49599e6	+	1.70174e6i	−0.737794	+	0.503020i	−0.872953	−	0.487804i	$-0.837798\pi$
$409$	−2.49599e6	+	1.70174e6i	−0.737794	+	0.503020i	0.135159	+	0.990824i	$0.456846\pi$
$410$	575161.	−	996208.i	0.168978	−	0.292678i
$411$	634499.	+	1.09898e6i	0.185279	+	0.320913i
$412$	−4.61789e6	−	2.22386e6i	−1.34029	−	0.645452i
$413$	1.30005e6	+	1.42566e6i	0.375047	+	0.411284i
$414$	−1.49439e6	+	719662.i	−0.428513	+	0.206361i
$415$	−903931.	−	616290.i	−0.257641	−	0.175657i
$416$	8.16415e6	+	7.57523e6i	2.31301	+	2.14616i
$417$	124286.	+	115320.i	0.0350010	+	0.0324762i
$418$	−715552.	−	487855.i	−0.200309	−	0.136568i
$419$	3.12372e6	−	1.50431e6i	0.869236	−	0.418602i	0.0545546	−	0.998511i	$-0.482626\pi$
$419$	3.12372e6	−	1.50431e6i	0.869236	−	0.418602i	0.814681	+	0.579909i	$0.196912\pi$
$420$	1.56239e7	−	1.03502e6i	4.32183	−	0.286304i
$421$	−4.46136e6	−	2.14848e6i	−1.22677	−	0.590779i	−0.295578	−	0.955319i	$-0.595512\pi$
$421$	−4.46136e6	−	2.14848e6i	−1.22677	−	0.590779i	−0.931188	+	0.364539i	$0.881226\pi$
$422$	1.14862e6	+	1.98947e6i	0.313975	+	0.543821i
$423$	−828139.	+	1.43438e6i	−0.225036	+	0.389774i
$424$	1.10335e7	−	7.52253e6i	2.98057	−	2.03212i
$425$	2.58184e6	+	389150.i	0.693358	+	0.104507i
$426$	499162.	−	2.18697e6i	0.133266	−	0.583874i
$427$	29106.5	+	61802.2i	0.00772538	+	0.0164034i
$428$	−1.36634e6	−	5.98631e6i	−0.360535	−	1.57961i
$429$	133656.	+	1.78351e6i	0.0350626	+	0.467878i
$430$	5.24065e6	+	1.61653e6i	1.36683	+	0.421611i
$431$	1.17845e6	+	3.00264e6i	0.305575	+	0.778592i	0.998349	+	0.0574377i	$0.0182931\pi$
$431$	1.17845e6	+	3.00264e6i	0.305575	+	0.778592i	−0.692774	+	0.721155i	$0.743612\pi$
$432$	1.72782e6	−	532962.i	0.445440	−	0.137400i
$433$	155246.	+	194673.i	0.0397926	+	0.0498983i	0.801330	−	0.598223i	$-0.204126\pi$
$433$	155246.	+	194673.i	0.0397926	+	0.0498983i	−0.761537	+	0.648121i	$0.775555\pi$
$434$	6.07166e6	+	9.07313e6i	1.54733	+	2.31224i
$435$	−5.40453e6	+	6.77706e6i	−1.36941	+	1.71719i
$436$	2.69388e6	−	6.86389e6i	0.678675	−	1.72924i
$437$	−37285.8	+	497544.i	−0.00933985	+	0.124632i
$438$	−9.20469e6	+	1.38738e6i	−2.29258	+	0.345550i
$439$	−2.60580e6	+	2.41782e6i	−0.645326	+	0.598775i	−0.933402	−	0.358833i	$-0.883175\pi$
$439$	−2.60580e6	+	2.41782e6i	−0.645326	+	0.598775i	0.288076	+	0.957607i	$0.406984\pi$
$440$	3.19951e6			0.787865
$441$	2.34954e6	−	3.91164e6i	0.575288	−	0.957772i
$442$	1.73815e7			4.23186
$443$	−3.57626e6	+	3.31828e6i	−0.865804	+	0.803349i	−0.981803	−	0.189901i	$-0.939183\pi$
$443$	−3.57626e6	+	3.31828e6i	−0.865804	+	0.803349i	0.115999	+	0.993249i	$0.462993\pi$
$444$	−2.16348e7	+	3.26092e6i	−5.20830	+	0.785024i
$445$	392744.	−	5.24080e6i	0.0940176	−	1.25458i
$446$	−368678.	+	939377.i	−0.0877628	+	0.223616i
$447$	5.04032e6	−	6.32036e6i	1.19313	−	1.49614i
$448$	−948902.	−	6.68759e6i	−0.223371	−	1.57425i
$449$	1.32161e6	+	1.65724e6i	0.309376	+	0.387945i	0.912075	−	0.410023i	$-0.134479\pi$
$449$	1.32161e6	+	1.65724e6i	0.309376	+	0.387945i	−0.602699	+	0.797969i	$0.705908\pi$
$450$	−3.62560e6	+	1.11835e6i	−0.844013	+	0.260343i
$451$	−56495.2	−	143947.i	−0.0130789	−	0.0333244i
$452$	−1.57036e7	−	4.84392e6i	−3.61537	−	1.11519i
$453$	72447.2	+	966741.i	0.0165873	+	0.221342i
$454$	2.84645e6	+	1.24711e7i	0.648132	+	2.83965i
$455$	−7.02324e6	+	1.53922e6i	−1.59041	+	0.348555i
$456$	2.20649e6	−	9.66725e6i	0.496923	−	2.17716i
$457$	−726391.	−	109486.i	−0.162697	−	0.0245226i	0.0671885	−	0.997740i	$-0.478597\pi$
$457$	−726391.	−	109486.i	−0.162697	−	0.0245226i	−0.229886	+	0.973218i	$0.573835\pi$
$458$	7.60198e6	−	5.18294e6i	1.69341	−	1.15455i
$459$	638588.	−	1.10607e6i	0.141478	−	0.245047i
$460$	−1.53794e6	−	2.66379e6i	−0.338880	−	0.586957i
$461$	2.53915e6	+	1.22279e6i	0.556462	+	0.267978i	0.690908	−	0.722943i	$-0.257211\pi$
$461$	2.53915e6	+	1.22279e6i	0.556462	+	0.267978i	−0.134446	+	0.990921i	$0.542925\pi$
$462$	1.68191e6	−	2.42164e6i	0.366605	−	0.527842i
$463$	−24379.4	+	11740.5i	−0.00528530	+	0.00254527i	−0.436525	−	0.899692i	$-0.643791\pi$
$463$	−24379.4	+	11740.5i	−0.00528530	+	0.00254527i	0.431239	+	0.902238i	$0.358076\pi$
$464$	1.32467e7	+	9.03141e6i	2.85635	+	1.94743i
$465$	−8.82814e6	−	8.19132e6i	−1.89338	−	1.75680i
$466$	5.77821e6	+	5.36140e6i	1.23262	+	1.14370i
$467$	116093.	+	79150.7i	0.0246328	+	0.0167943i	0.575574	−	0.817750i	$-0.304779\pi$
$467$	116093.	+	79150.7i	0.0246328	+	0.0167943i	−0.550941	+	0.834544i	$0.685731\pi$
$468$	−1.62462e7	+	7.82376e6i	−3.42876	+	1.65121i
$469$	528406.	−	3.31113e6i	0.110927	−	0.695096i
$470$	−3.87625e6	−	1.86670e6i	−0.809406	−	0.389790i
$471$	1.78617e6	+	3.09373e6i	0.370997	+	0.642585i
$472$	−3.76623e6	+	6.52331e6i	−0.778130	+	1.34776i
$473$	609145.	−	415308.i	0.125189	−	0.0853527i
$474$	1.65718e7	+	2.49780e6i	3.38785	+	0.510637i
$475$	−253969.	+	1.11271e6i	−0.0516471	+	0.226281i
$476$	−1.58826e7	−	1.28922e7i	−3.21294	−	2.60802i
$477$	1.59399e6	+	6.98374e6i	0.320768	+	1.40537i
$478$	−1.15239e6	−	1.53775e7i	−0.230690	−	3.07834i
$479$	−8.65920e6	−	2.67101e6i	−1.72440	−	0.531908i	−0.735122	−	0.677935i	$-0.762875\pi$
$479$	−8.65920e6	−	2.67101e6i	−1.72440	−	0.531908i	−0.989281	+	0.146027i	$0.953351\pi$
$480$	7.39932e6	+	1.88532e7i	1.46585	+	3.73492i
$481$	9.60015e6	−	2.96126e6i	1.89198	−	0.583597i
$482$	−3.44526e6	−	4.32022e6i	−0.675467	−	0.847009i
$483$	−1.69273e6	−	141587.i	−0.330156	−	0.0276157i
$484$	−7.57106e6	+	9.49380e6i	−1.46907	+	1.84216i
$485$	3.00596e6	−	7.65907e6i	0.580269	−	1.47850i
$486$	1.04403e6	−	1.39316e7i	0.200504	−	2.67554i
$487$	−2.07222e6	+	312336.i	−0.395925	+	0.0596760i	−0.343987	−	0.938974i	$-0.611778\pi$
$487$	−2.07222e6	+	312336.i	−0.395925	+	0.0596760i	−0.0519373	+	0.998650i	$0.516540\pi$
$488$	−195502.	+	181399.i	−0.0371622	+	0.0344814i
$489$	6.03909e6			1.14209
$490$	1.05884e7	+	5.32672e6i	1.99224	+	1.00223i
$491$	1.80936e6			0.338704			0.169352	−	0.985556i	$-0.445832\pi$
$491$	1.80936e6			0.338704			0.169352	+	0.985556i	$0.445832\pi$
$492$	2.16579e6	−	2.00956e6i	0.403370	−	0.374273i
$493$	1.11979e7	−	1.68782e6i	2.07501	−	0.312758i
$494$	−567785.	+	7.57656e6i	−0.104681	+	1.39687i
$495$	−627031.	+	1.59765e6i	−0.115021	+	0.293068i
$496$	−1.38879e7	+	1.74149e7i	−2.53473	+	3.17845i
$497$	832205.	−	881487.i	0.151126	−	0.160075i
$498$	−2.45400e6	−	3.07722e6i	−0.443406	−	0.556014i
$499$	−3.42649e6	+	1.05693e6i	−0.616025	+	0.190019i	−0.587036	−	0.809561i	$-0.699705\pi$
$499$	−3.42649e6	+	1.05693e6i	−0.616025	+	0.190019i	−0.0289896	+	0.999580i	$0.509229\pi$
$500$	3.50874e6	+	8.94011e6i	0.627662	+	1.59926i
$501$	−7.56530e6	−	2.33359e6i	−1.34658	−	0.415365i
$502$	258480.	+	3.44918e6i	0.0457792	+	0.610881i
$503$	−2.23905e6	−	9.80994e6i	−0.394589	−	1.72881i	−0.648173	−	0.761493i	$-0.724467\pi$
$503$	−2.23905e6	−	9.80994e6i	−0.394589	−	1.72881i	0.253585	−	0.967313i	$-0.418390\pi$
$504$	1.73325e7	+	4.11410e6i	3.03938	+	0.721437i
$505$	896672.	−	3.92858e6i	0.156461	−	0.685499i
$506$	−572715.	−	86323.0i	−0.0994403	−	0.0149882i
$507$	6.00587e6	−	4.09473e6i	1.03766	−	0.707466i
$508$	−1.14505e7	+	1.98329e7i	−1.96864	+	3.40979i
$509$	1.54213e6	+	2.67105e6i	0.263831	+	0.456969i	0.967257	−	0.253800i	$-0.0816804\pi$
$509$	1.54213e6	+	2.67105e6i	0.263831	+	0.456969i	−0.703425	+	0.710769i	$0.748347\pi$
$510$	2.84783e7	+	1.37144e7i	4.84828	+	2.33481i
$511$	−4.66671e6	−	1.87830e6i	−0.790604	−	0.318209i
$512$	−7.07071e6	+	3.40507e6i	−1.19203	+	0.574053i
$513$	461273.	+	314491.i	0.0773864	+	0.0527611i
$514$	1.98450e6	+	1.84134e6i	0.331316	+	0.307416i
$515$	3.13739e6	+	2.91107e6i	0.521255	+	0.483654i
$516$	1.16383e7	+	7.93486e6i	1.92427	+	1.31194i
$517$	−521081.	+	250939.i	−0.0857390	+	0.0412897i
$518$	−1.53641e7	−	6.18388e6i	−2.51584	−	1.01260i
$519$	−2.27151e6	−	1.09390e6i	−0.370165	−	0.178262i
$520$	−1.40348e7	−	2.43090e7i	−2.27613	−	3.94238i
$521$	1.88879e6	−	3.27148e6i	0.304852	−	0.528019i	−0.672376	−	0.740210i	$-0.734726\pi$
$521$	1.88879e6	−	3.27148e6i	0.304852	−	0.528019i	0.977228	+	0.212190i	$0.0680596\pi$
$522$	−1.35966e7	+	9.27001e6i	−2.18401	+	1.48903i
$523$	367128.	+	55335.6i	0.0586899	+	0.00884608i	0.178322	−	0.983972i	$-0.442933\pi$
$523$	367128.	+	55335.6i	0.0586899	+	0.00884608i	−0.119632	+	0.992818i	$0.538171\pi$
$524$	2.64421e6	−	1.15850e7i	0.420696	−	1.84319i
$525$	−3.78059e6	−	897371.i	−0.598634	−	0.142093i
$526$	−2.78342e6	−	1.21950e7i	−0.438647	−	1.92184i
$527$	1.17576e6	+	1.56894e7i	0.184413	+	2.46082i
$528$	5.74838e6	+	1.77314e6i	0.897347	+	0.276795i
$529$	−2.22955e6	−	5.68081e6i	−0.346401	−	0.882614i
$530$	−1.77806e7	+	5.48460e6i	−2.74953	+	0.848116i
$531$	−2.51926e6	−	3.15905e6i	−0.387737	−	0.486206i
$532$	6.13853e6	−	6.50204e6i	0.940341	−	0.996026i
$533$	−845852.	+	1.06067e6i	−0.128966	+	0.161719i
$534$	6.90761e6	−	1.76003e7i	1.04827	−	2.67096i
$535$	−383162.	+	5.11294e6i	−0.0578759	+	0.772300i
$536$	1.29441e7	−	1.95100e6i	1.94607	−	0.293323i
$537$	278450.	−	258364.i	0.0416688	−	0.0386630i
$538$	1.37308e7			2.04523
$539$	1.44732e6	−	666396.i	0.214581	−	0.0988007i
$540$	−3.44171e6			−0.507914
$541$	−5.44523e6	+	5.05244e6i	−0.799877	+	0.742177i	−0.969963	−	0.243252i	$-0.921786\pi$
$541$	−5.44523e6	+	5.05244e6i	−0.799877	+	0.742177i	0.170086	+	0.985429i	$0.445595\pi$
$542$	−2.12450e7	+	3.20216e6i	−3.10640	+	0.468215i
$543$	−471126.	+	6.28675e6i	−0.0685706	+	0.915011i
$544$	9.66674e6	−	2.46305e7i	1.40050	−	3.56841i
$545$	−3.83892e6	+	4.81385e6i	−0.553628	+	0.694227i
$546$	−2.57767e7	−	2.15608e6i	−3.70037	−	0.309516i
$547$	1.37941e6	+	1.72973e6i	0.197118	+	0.247178i	0.870560	−	0.492062i	$-0.163756\pi$
$547$	1.37941e6	+	1.72973e6i	0.197118	+	0.247178i	−0.673442	+	0.739240i	$0.735185\pi$
$548$	−4.26910e6	+	1.31684e6i	−0.607274	+	0.187319i
$549$	−52266.2	−	133172.i	−0.00740099	−	0.0188574i
$550$	−1.26602e6	−	390517.i	−0.178458	−	0.0550469i
$551$	369925.	+	4.93630e6i	0.0519080	+	0.692664i
$552$	−1.47565e6	−	6.46523e6i	−0.206127	−	0.903101i
$553$	7.03178e6	+	5.70787e6i	0.977806	+	0.793708i
$554$	−4.29419e6	+	1.88141e7i	−0.594439	+	2.60441i
$555$	1.80656e7	+	2.72296e6i	2.48955	+	0.375239i
$556$	−493178.	+	336243.i	−0.0676576	+	0.0461282i
$557$	4.67968e6	−	8.10545e6i	0.639114	−	1.10698i	−0.346513	−	0.938045i	$-0.612634\pi$
$557$	4.67968e6	−	8.10545e6i	0.639114	−	1.10698i	0.985627	−	0.168933i	$-0.0540323\pi$
$558$	−1.14315e7	−	1.97999e7i	−1.55423	−	2.69201i
$559$	−5.82743e6	−	2.80634e6i	−0.788765	−	0.379849i
$560$	−3.81104e6	+	2.38810e7i	−0.513539	+	3.21798i
$561$	3.82831e6	−	1.84362e6i	0.513570	−	0.247323i
$562$	−5.67739e6	−	3.87078e6i	−0.758242	−	0.516961i
$563$	7.03163e6	+	6.52440e6i	0.934943	+	0.867500i	0.991395	−	0.130905i	$-0.0417883\pi$
$563$	7.03163e6	+	6.52440e6i	0.934943	+	0.867500i	−0.0564520	+	0.998405i	$0.517979\pi$
$564$	−8.10026e6	−	7.51594e6i	−1.07226	−	0.994914i
$565$	1.13381e7	+	7.73020e6i	1.49424	+	1.01875i
$566$	2.10708e7	−	1.01472e7i	2.76465	−	1.33139i
$567$	3.79475e6	−	5.46373e6i	0.495708	−	0.713726i
$568$	4.26401e6	+	2.05344e6i	0.554558	+	0.267061i
$569$	7.36716e6	+	1.27603e7i	0.953937	+	1.65227i	0.736782	+	0.676130i	$0.236344\pi$
$569$	7.36716e6	+	1.27603e7i	0.953937	+	1.65227i	0.217155	+	0.976137i	$0.430322\pi$
$570$	−6.90836e6	+	1.19656e7i	−0.890611	+	1.54258i
$571$	−1.21649e7	+	8.29387e6i	−1.56141	+	1.06455i	−0.596283	+	0.802774i	$0.703356\pi$
$571$	−1.21649e7	+	8.29387e6i	−1.56141	+	1.06455i	−0.965128	+	0.261778i	$0.915691\pi$
$572$	−6.22624e6	−	938455.i	−0.795675	−	0.119929i
$573$	−45677.6	+	200127.i	−0.00581188	+	0.0254635i
$574$	2.18461e6	−	478780.i	0.276754	−	0.0606535i
$575$	169848.	+	744154.i	0.0214235	+	0.0938627i
$576$	1.05709e6	+	1.41059e7i	0.132756	+	1.77151i
$577$	−1.82044e6	−	561532.i	−0.227634	−	0.0702158i	0.178840	−	0.983878i	$-0.442766\pi$
$577$	−1.82044e6	−	561532.i	−0.227634	−	0.0702158i	−0.406474	+	0.913662i	$0.633242\pi$
$578$	−9.60037e6	−	2.44614e7i	−1.19528	−	3.04552i
$579$	−1.68161e7	+	5.18707e6i	−2.08463	+	0.643022i
$580$	−1.90270e7	−	2.38591e7i	−2.34855	−	2.94499i
$581$	−298810.	−	2.10593e6i	−0.0367245	−	0.258823i
$582$	1.84557e7	−	2.31427e7i	2.25851	−	2.83209i
$583$	−913852.	+	2.32846e6i	−0.111354	+	0.283724i
$584$	1.46764e6	−	1.95843e7i	0.178069	−	2.37616i
$585$	1.48890e7	−	2.24415e6i	1.79877	−	0.271121i
$586$	−1.01959e7	+	9.46041e6i	−1.22654	+	1.13806i
$587$	−314124.			−0.0376275			−0.0188138	−	0.999823i	$-0.505989\pi$
$587$	−314124.			−0.0376275			−0.0188138	+	0.999823i	$0.505989\pi$
$588$	2.19545e7	+	2.10893e7i	2.61867	+	2.51547i
$589$	−6.87740e6			−0.816838
$590$	7.69390e6	−	7.13890e6i	0.909948	−	0.844308i
$591$	3.31513e6	−	499675.i	0.390419	−	0.0588463i
$592$	2.52522e6	−	3.36967e7i	0.296139	−	3.95169i
$593$	1.96383e6	−	5.00377e6i	0.229334	−	0.584333i	−0.769168	−	0.639046i	$-0.779329\pi$
$593$	1.96383e6	−	5.00377e6i	0.229334	−	0.584333i	0.998502	+	0.0547134i	$0.0174245\pi$
$594$	−404065.	+	506681.i	−0.0469878	+	0.0589208i
$595$	9.50000e6	+	1.41962e7i	1.10010	+	1.64392i
$596$	1.77448e7	+	2.22512e7i	2.04623	+	2.56589i
$597$	−2.52869e6	+	779997.i	−0.290375	+	0.0895689i
$598$	1.85638e6	+	4.72999e6i	0.212283	+	0.540888i
$599$	−510427.	−	157446.i	−0.0581255	−	0.0179293i	0.265556	−	0.964095i	$-0.414444\pi$
$599$	−510427.	−	157446.i	−0.0581255	−	0.0179293i	−0.323682	+	0.946166i	$0.604921\pi$
$600$	−1.13362e6	−	1.51271e7i	−0.128555	−	1.71545i
$601$	3.40807e6	+	1.49317e7i	0.384878	+	1.68626i	0.681945	+	0.731403i	$0.261134\pi$
$601$	3.40807e6	+	1.49317e7i	0.384878	+	1.68626i	−0.297067	+	0.954856i	$0.596009\pi$
$602$	4.54306e6	+	9.64634e6i	0.510925	+	1.08485i
$603$	−1.56252e6	+	6.84586e6i	−0.174998	+	0.766716i
$604$	−3.37489e6	−	508683.i	−0.376416	−	0.0567355i
$605$	8.37786e6	−	5.71193e6i	0.930560	−	0.634445i
$606$	7.24851e6	−	1.25548e7i	0.801802	−	1.38876i
$607$	5.64953e6	+	9.78527e6i	0.622358	+	1.07796i	0.989045	+	0.147612i	$0.0471587\pi$
$607$	5.64953e6	+	9.78527e6i	0.622358	+	1.07796i	−0.366687	+	0.930344i	$0.619508\pi$
$608$	1.04206e7	+	5.01830e6i	1.14323	+	0.550551i
$609$	−1.68159e7	+	1.11399e6i	−1.83728	+	0.121713i
$610$	334811.	−	161237.i	0.0364314	−	0.0175444i
$611$	4.19231e6	+	2.85827e6i	0.454308	+	0.309742i
$612$	3.14038e7	+	2.91385e7i	3.38925	+	3.14477i
$613$	7.76548e6	+	7.20531e6i	0.834674	+	0.774464i	0.976521	−	0.215424i	$-0.0691134\pi$
$613$	7.76548e6	+	7.20531e6i	0.834674	+	0.774464i	−0.141846	+	0.989889i	$0.545304\pi$
$614$	−5.04771e6	−	3.44147e6i	−0.540348	−	0.368403i
$615$	−2.22276e6	+	1.07042e6i	−0.236976	+	0.114122i
$616$	4.19142e6	+	4.59638e6i	0.445050	+	0.488050i
$617$	−1.07521e7	−	5.17792e6i	−1.13705	−	0.547573i	−0.231929	−	0.972733i	$-0.574504\pi$
$617$	−1.07521e7	−	5.17792e6i	−1.13705	−	0.547573i	−0.905118	+	0.425159i	$0.860218\pi$
$618$	7.69874e6	+	1.33346e7i	0.810864	+	1.40446i
$619$	−1.03052e6	+	1.78491e6i	−0.108101	+	0.187236i	−0.915001	−	0.403452i	$-0.867810\pi$
$619$	−1.03052e6	+	1.78491e6i	−0.108101	+	0.187236i	0.806900	+	0.590688i	$0.201144\pi$
$620$	3.50310e7	−	2.38837e7i	3.65993	−	2.49530i
$621$	369195.	+	55647.1i	0.0384173	+	0.00579047i
$622$	343675.	−	1.50574e6i	0.0356181	−	0.156053i
$623$	8.04338e6	−	6.30133e6i	0.830268	−	0.650447i
$624$	−1.17437e7	−	5.14525e7i	−1.20738	−	5.28987i
$625$	−907888.	−	1.21149e7i	−0.0929677	−	1.24057i
$626$	−4.06569e6	−	1.25410e6i	−0.414666	−	0.127908i
$627$	678574.	+	1.72898e6i	0.0689332	+	0.175639i
$628$	−1.20179e7	+	3.70703e6i	−1.21599	+	0.375082i
$629$	−1.48816e7	−	1.86609e7i	−1.49976	−	1.88064i
$630$	−2.13884e7	−	1.25965e7i	−2.14698	−	1.26445i
$631$	1.96498e6	−	2.46401e6i	0.196465	−	0.246359i	−0.673835	−	0.738882i	$-0.735354\pi$
$631$	1.96498e6	−	2.46401e6i	0.196465	−	0.246359i	0.870299	+	0.492523i	$0.163925\pi$
$632$	−1.29177e7	+	3.29137e7i	−1.28645	+	3.27781i
$633$	368184.	−	4.91307e6i	0.0365221	−	0.487353i
$634$	−3.58529e6	+	540396.i	−0.354243	+	0.0533936i
$635$	1.40182e7	−	1.30070e7i	1.37961	−	1.28009i
$636$	−4.77910e7			−4.68493
$637$	−1.14118e7	−	8.07312e6i	−1.11431	−	0.788302i
$638$	−5.74628e6			−0.558901
$639$	−1.86101e6	+	1.72677e6i	−0.180301	+	0.167295i
$640$	−8.07971e6	+	1.21782e6i	−0.779733	+	0.117526i
$641$	−853810.	+	1.13933e7i	−0.0820760	+	1.09523i	0.792349	+	0.610068i	$0.208858\pi$
$641$	−853810.	+	1.13933e7i	−0.0820760	+	1.09523i	−0.874425	+	0.485160i	$0.838761\pi$
$642$	−6.73909e6	+	1.71709e7i	−0.645303	+	1.64420i
$643$	−1.24172e7	+	1.55707e7i	−1.18439	+	1.48518i	−0.347618	+	0.937636i	$0.613009\pi$
$643$	−1.24172e7	+	1.55707e7i	−1.18439	+	1.48518i	−0.836776	+	0.547546i	$0.815562\pi$
$644$	1.81205e6	−	5.69901e6i	0.172169	−	0.541483i
$645$	−7.33354e6	−	9.19597e6i	−0.694088	−	0.870359i
$646$	1.72487e7	−	5.32053e6i	1.62621	−	0.501618i
$647$	869100.	+	2.21443e6i	0.0816223	+	0.207970i	0.965859	−	0.259069i	$-0.0834158\pi$
$647$	869100.	+	2.21443e6i	0.0816223	+	0.207970i	−0.884236	+	0.467040i	$0.845321\pi$
$648$	2.48167e7	+	7.65493e6i	2.32170	+	0.716150i
$649$	−105439.	−	1.40699e6i	−0.00982629	−	0.131123i
$650$	2.58643e6	+	1.13319e7i	0.240114	+	1.05201i
$651$	202539.	−	2.34132e7i	0.0187308	−	2.16525i
$652$	−4.73101e6	+	2.07279e7i	−0.435848	+	1.90958i
$653$	−9.97385e6	−	1.50332e6i	−0.915335	−	0.137965i	−0.325550	−	0.945525i	$-0.605549\pi$
$653$	−9.97385e6	−	1.50332e6i	−0.915335	−	0.137965i	−0.589785	+	0.807560i	$0.700788\pi$
$654$	−1.83021e7	+	1.24782e7i	−1.67323	+	1.14079i
$655$	−4.96130e6	+	8.59323e6i	−0.451848	+	0.782624i
$656$	2.28152e6	+	3.95171e6i	0.206997	+	0.358530i
$657$	9.49164e6	+	4.57093e6i	0.857882	+	0.413134i
$658$	−2.39627e6	−	8.01398e6i	−0.215760	−	0.721579i
$659$	1.31457e7	−	6.33063e6i	1.17915	−	0.567849i	0.261488	−	0.965207i	$-0.415787\pi$
$659$	1.31457e7	−	6.33063e6i	1.17915	−	0.567849i	0.917664	+	0.397357i	$0.130073\pi$
$660$	−9.46077e6	−	6.45025e6i	−0.845409	−	0.576390i
$661$	−1.15658e7	−	1.07315e7i	−1.02961	−	0.955339i	−0.0305879	−	0.999532i	$-0.509738\pi$
$661$	−1.15658e7	−	1.07315e7i	−1.02961	−	0.955339i	−0.999023	+	0.0441928i	$0.985928\pi$
$662$	7.89709e6	+	7.32743e6i	0.700361	+	0.649840i
$663$	−3.08003e7	−	2.09993e7i	−2.72127	−	1.85533i
$664$	7.48157e6	−	3.60293e6i	0.658525	−	0.317129i
$665$	−6.49845e6	+	3.67730e6i	−0.569843	+	0.322459i
$666$	3.12491e7	+	1.50488e7i	2.72994	+	1.31467i
$667$	1.65527e6	+	2.86701e6i	0.144064	+	0.249526i
$668$	1.39362e7	−	2.41382e7i	1.20838	−	2.09297i
$669$	1.78821e6	−	1.21918e6i	0.154473	−	0.105318i
$670$	−1.80362e7	−	2.71852e6i	−1.55224	−	0.233962i
$671$	11116.2	−	48703.1i	0.000953122	−	0.00417590i
$672$	−1.73910e7	+	3.53278e7i	−1.48560	+	3.01782i
$673$	3.91471e6	+	1.71515e7i	0.333167	+	1.45970i	0.812960	+	0.582319i	$0.197855\pi$
$673$	3.91471e6	+	1.71515e7i	0.333167	+	1.45970i	−0.479793	+	0.877382i	$0.659288\pi$
$674$	2.33267e6	+	3.11274e7i	0.197790	+	2.63932i
$675$	816128.	+	251742.i	0.0689444	+	0.0212665i
$676$	9.34933e6	+	2.38217e7i	0.786890	+	2.00496i
$677$	1.16757e7	−	3.60148e6i	0.979066	−	0.302002i	0.236394	−	0.971657i	$-0.424034\pi$
$677$	1.16757e7	−	3.60148e6i	0.979066	−	0.302002i	0.742672	+	0.669655i	$0.233558\pi$
$678$	3.07808e7	+	3.85980e7i	2.57162	+	3.22471i
$679$	1.49408e7	−	5.71518e6i	1.24365	−	0.475725i
$680$	−4.15787e7	+	5.21380e7i	−3.44825	+	4.32396i
$681$	1.00229e7	−	2.55379e7i	0.828182	−	2.11017i
$682$	596608.	−	7.96118e6i	0.0491166	−	0.655415i
$683$	−2.24047e7	+	3.37697e6i	−1.83776	+	0.276997i	−0.973939	−	0.226808i	$-0.927171\pi$
$683$	−2.24047e7	+	3.37697e6i	−1.83776	+	0.276997i	−0.863817	+	0.503806i	$0.831933\pi$
$684$	−1.37273e7	+	1.27370e7i	−1.12187	+	1.04095i
$685$	3.73055e6			0.303771
$686$	6.21874e6	+	2.21893e7i	0.504536	+	1.80025i
$687$	−1.97326e7			−1.59512
$688$	−1.59475e7	+	1.47971e7i	−1.28446	+	1.19180i
$689$	2.16996e7	−	3.27069e6i	1.74142	−	0.262477i
$690$	−690529.	+	9.21447e6i	−0.0552152	+	0.736796i
$691$	2.13295e6	−	5.43466e6i	0.169936	−	0.432989i	−0.820381	−	0.571818i	$-0.806238\pi$
$691$	2.13295e6	−	5.43466e6i	0.169936	−	0.432989i	0.990316	+	0.138828i	$0.0443337\pi$
$692$	5.53408e6	−	6.93952e6i	0.439319	−	0.550889i
$693$	−3.11659e6	+	1.19216e6i	−0.246516	+	0.0942979i
$694$	−1.13888e6	−	1.42811e6i	−0.0897591	−	0.112554i
$695$	476280.	−	146913.i	0.0374024	−	0.0115371i
$696$	−2.40370e7	−	6.12452e7i	−1.88086	−	4.79236i
$697$	3.07988e6	+	950018.i	0.240133	+	0.0740713i
$698$	−2.54338e6	−	3.39390e7i	−0.197593	−	2.63670i
$699$	−3.76177e6	−	1.64814e7i	−0.291206	−	1.27586i
$700$	6.04175e6	−	1.22731e7i	0.466034	−	0.946692i
$701$	4.46456e6	−	1.95605e7i	0.343150	−	1.50344i	−0.449234	−	0.893414i	$-0.648303\pi$
$701$	4.46456e6	−	1.95605e7i	0.343150	−	1.50344i	0.792384	−	0.610023i	$-0.208840\pi$
$702$	5.62206e6	+	847390.i	0.430579	+	0.0648994i
$703$	8.62038e6	−	5.87728e6i	0.657867	−	0.448526i
$704$	−2.46972e6	+	4.27768e6i	−0.187809	+	0.325294i
$705$	4.61354e6	+	7.99089e6i	0.349592	+	0.605511i
$706$	−3.74837e7	−	1.80512e7i	−2.83029	−	1.36300i
$707$	6.81841e6	−	3.85836e6i	0.513020	−	0.290304i
$708$	2.42876e7	−	1.16963e7i	1.82096	−	0.876930i
$709$	1.09417e7	+	7.45990e6i	0.817463	+	0.557337i	0.898296	−	0.439391i	$-0.144806\pi$
$709$	1.09417e7	+	7.45990e6i	0.817463	+	0.557337i	−0.0808331	+	0.996728i	$0.525758\pi$
$710$	−4.83412e6	−	4.48541e6i	−0.359892	−	0.333931i
$711$	−1.39036e7	−	1.29007e7i	−1.03146	−	0.957057i
$712$	3.29589e7	+	2.24710e7i	2.43653	+	1.66120i
$713$	−4.14396e6	+	1.99562e6i	−0.305275	+	0.147013i
$714$	1.76051e7	+	5.88777e7i	1.29238	+	4.32220i
$715$	4.73712e6	+	2.28128e6i	0.346537	+	0.166883i
$716$	668643.	+	1.15812e6i	0.0487429	+	0.0844252i
$717$	−1.65362e7	+	2.86416e7i	−1.20126	+	2.08065i
$718$	2.51666e7	−	1.71583e7i	1.82185	−	1.24212i
$719$	−9.10726e6	−	1.37270e6i	−0.657000	−	0.0990268i	−0.187922	−	0.982184i	$-0.560175\pi$
$719$	−9.10726e6	−	1.37270e6i	−0.657000	−	0.0990268i	−0.469077	+	0.883157i	$0.655413\pi$
$720$	1.12695e7	−	4.93747e7i	0.810161	−	3.54955i
$721$	−71979.2	+	8.32069e6i	−0.00515667	+	0.596103i
$722$	−4.07153e6	−	1.78385e7i	−0.290680	−	1.27355i
$723$	885627.	+	1.18179e7i	0.0630094	+	0.840801i
$724$	−2.12089e7	−	6.54207e6i	−1.50373	−	0.463841i
$725$	2.76668e6	+	7.04938e6i	0.195485	+	0.498088i
$726$	3.48584e7	−	1.07524e7i	2.45451	−	0.757117i
$727$	1.18121e6	+	1.48119e6i	0.0828879	+	0.103938i	0.821546	−	0.570142i	$-0.193112\pi$
$727$	1.18121e6	+	1.48119e6i	0.0828879	+	0.103938i	−0.738658	+	0.674080i	$0.764540\pi$
$728$	1.65362e7	−	5.20074e7i	1.15640	−	3.63695i
$729$	−1.09072e7	+	1.36771e7i	−0.760139	+	0.953184i
$730$	−9.99765e6	+	2.54736e7i	−0.694370	+	1.76922i
$731$	−1.14833e6	+	1.53234e7i	−0.0794831	+	1.06063i
$732$	943789.	−	142253.i	0.0651025	−	0.00981262i
$733$	2.32580e6	−	2.15803e6i	0.159887	−	0.148353i	−0.596173	−	0.802856i	$-0.703313\pi$
$733$	2.32580e6	−	2.15803e6i	0.159887	−	0.148353i	0.756059	+	0.654503i	$0.227122\pi$
$734$	−4.06665e7			−2.78610
$735$	−1.23275e7	−	2.22314e7i	−0.841698	−	1.51792i
$736$	7.73507e6			0.526344
$737$	−1.79743e6	+	1.66777e6i	−0.121894	+	0.113101i
$738$	−4.63128e6	+	698053.i	−0.313011	+	0.0471789i
$739$	753825.	−	1.00591e7i	0.0507761	−	0.677560i	−0.912505	−	0.409065i	$-0.865855\pi$
$739$	753825.	−	1.00591e7i	0.0507761	−	0.677560i	0.963281	−	0.268495i	$-0.0865261\pi$
$740$	−2.34986e7	+	5.98734e7i	−1.57747	+	4.01934i
$741$	1.01597e7	−	1.27398e7i	0.679728	−	0.852351i
$742$	−3.11721e7	−	1.83586e7i	−2.07853	−	1.22413i
$743$	−2.60018e6	−	3.26052e6i	−0.172795	−	0.216678i	0.687891	−	0.725814i	$-0.258537\pi$
$743$	−2.60018e6	−	3.26052e6i	−0.172795	−	0.216678i	−0.860686	+	0.509136i	$0.829965\pi$
$744$	8.73477e7	−	2.69432e7i	5.78521	−	1.78450i
$745$	−8.68239e6	−	2.21224e7i	−0.573124	−	1.46030i
$746$	2.34046e7	+	7.21938e6i	1.53977	+	0.474955i
$747$	332878.	+	4.44195e6i	0.0218265	+	0.291254i
$748$	3.32874e6	+	1.45842e7i	0.217533	+	0.953077i
$749$	−7.84714e6	+	6.14760e6i	−0.511101	+	0.400406i
$750$	6.42006e6	−	2.81281e7i	0.416760	−	1.82594i
$751$	1.99120e7	+	3.00125e6i	1.28829	+	0.194179i	0.757227	−	0.653152i	$-0.226554\pi$
$751$	1.99120e7	+	3.00125e6i	1.28829	+	0.194179i	0.531065	+	0.847331i	$0.321792\pi$
$752$	1.41008e7	−	9.61373e6i	0.909280	−	0.619937i
$753$	3.70907e6	−	6.42430e6i	0.238384	−	0.412894i
$754$	2.52063e7	+	4.36586e7i	1.61466	+	2.79667i
$755$	2.56772e6	+	1.23655e6i	0.163938	+	0.0789486i
$756$	−4.50870e6	−	4.94433e6i	−0.286911	−	0.314632i
$757$	−3.68808e6	+	1.77609e6i	−0.233917	+	0.112648i	−0.547171	−	0.837021i	$-0.684295\pi$
$757$	−3.68808e6	+	1.77609e6i	−0.233917	+	0.112648i	0.313254	+	0.949669i	$0.398581\pi$
$758$	−1.84310e7	−	1.25660e7i	−1.16513	−	0.794374i
$759$	910573.	+	844888.i	0.0573733	+	0.0532347i
$760$	−2.13687e7	−	1.98272e7i	−1.34197	−	1.24517i
$761$	1.01079e6	+	689146.i	0.0632703	+	0.0431370i	0.594542	−	0.804064i	$-0.297333\pi$
$761$	1.01079e6	+	689146.i	0.0632703	+	0.0431370i	−0.531272	+	0.847201i	$0.678286\pi$
$762$	6.19843e7	−	2.98501e7i	3.86718	−	1.86234i
$763$	−1.19446e7	+	791282.i	−0.742779	+	0.0492062i
$764$	−651109.	−	313558.i	−0.0403571	−	0.0194350i
$765$	−1.78862e7	−	3.09798e7i	−1.10501	−	1.91392i
$766$	−4.63685e6	+	8.03126e6i	−0.285530	+	0.494552i
$767$	−1.02274e7	+	6.97289e6i	−0.627733	+	0.427981i
$768$	8.32742e6	+	1.25516e6i	0.509457	+	0.0767883i
$769$	−2.03289e6	+	8.90666e6i	−0.123965	+	0.543124i	0.874361	+	0.485276i	$0.161281\pi$
$769$	−2.03289e6	+	8.90666e6i	−0.123965	+	0.543124i	−0.998325	+	0.0578478i	$0.981576\pi$
$770$	−3.69305e6	−	7.84151e6i	−0.224470	−	0.476621i
$771$	−1.29196e6	−	5.66045e6i	−0.0782733	−	0.342938i
$772$	−4.62986e6	−	6.17813e7i	−0.279592	−	3.73090i
$773$	381803.	+	117771.i	0.0229821	+	0.00708905i	0.306225	−	0.951959i	$-0.400934\pi$
$773$	381803.	+	117771.i	0.0229821	+	0.00708905i	−0.283243	+	0.959048i	$0.591410\pi$
$774$	−8.15793e6	−	2.07861e7i	−0.489471	−	1.24715i
$775$	−1.00538e7	+	3.10119e6i	−0.601279	+	0.185470i
$776$	3.89375e7	+	4.88261e7i	2.32121	+	2.91070i
$777$	1.97545e7	+	2.95200e7i	1.17385	+	1.75414i
$778$	1.83684e7	−	2.30333e7i	1.08799	−	1.36429i
$779$	−514719.	+	1.31148e6i	−0.0303897	+	0.0774317i
$780$	−7.50704e6	+	1.00175e8i	−0.441807	+	5.89550i
$781$	−876594.	+	132125.i	−0.0514246	+	0.00775102i
$782$	8.84930e6	−	8.21095e6i	0.517478	−	0.480150i
$783$	3.70428e6			0.215923
$784$	−3.92998e7	+	2.58097e7i	−2.28349	+	1.49966i
$785$	1.05018e7			0.608261
$786$	−2.61683e7	+	2.42807e7i	−1.51084	+	1.40186i
$787$	−1.61458e7	+	2.43359e6i	−0.929231	+	0.140059i	−0.596181	−	0.802850i	$-0.703316\pi$
$787$	−1.61458e7	+	2.43359e6i	−0.929231	+	0.140059i	−0.333050	+	0.942909i	$0.608078\pi$
$788$	−882034.	+	1.17699e7i	−0.0506023	+	0.675240i
$789$	−9.80098e6	+	2.49725e7i	−0.560502	+	1.42814i
$790$	3.07178e7	−	3.85189e7i	1.75115	−	2.19587i
$791$	3.74802e6	+	2.64149e7i	0.212990	+	1.50109i
$792$	−8.12219e6	−	1.01849e7i	−0.460108	−	0.576957i
$793$	−418794.	+	129181.i	−0.0236492	+	0.00729482i
$794$	−1.98736e7	−	5.06371e7i	−1.11873	−	2.85048i
$795$	3.81338e7	+	1.17627e7i	2.13990	+	0.660070i
$796$	−696208.	−	9.29025e6i	−0.0389454	−	0.519691i
$797$	−5.80580e6	−	2.54369e7i	−0.323755	−	1.41846i	−0.830813	−	0.556551i	$-0.812124\pi$
$797$	−5.80580e6	−	2.54369e7i	−0.323755	−	1.41846i	0.507059	−	0.861912i	$-0.330733\pi$
$798$	−2.62398e7	+	5.75071e6i	−1.45866	+	0.319679i
$799$	2.68240e6	−	1.17524e7i	0.148647	−	0.651266i
$800$	1.74963e7	+	2.63715e6i	0.966546	+	0.145683i
$801$	−1.76799e7	+	1.20539e7i	−0.973639	+	0.663816i
$802$	−1.30493e7	+	2.26021e7i	−0.716396	+	1.24083i
$803$	1.83934e6	+	3.18584e6i	0.100664	+	0.174355i
$804$	−4.22081e7	−	2.03264e7i	−2.30280	−	1.10897i
$805$	−2.84857e6	+	4.10141e6i	−0.154931	+	0.223071i
$806$	−6.31038e7	+	3.03892e7i	−3.42151	+	1.64771i
$807$	−2.43313e7	−	1.65888e7i	−1.31517	−	0.896668i
$808$	2.24208e7	+	2.08034e7i	1.20815	+	1.12100i
$809$	−1.30543e7	−	1.21126e7i	−0.701266	−	0.650680i	0.246685	−	0.969096i	$-0.420659\pi$
$809$	−1.30543e7	−	1.21126e7i	−0.701266	−	0.650680i	−0.947951	+	0.318416i	$0.896849\pi$
$810$	−2.98992e7	−	2.03850e7i	−1.60121	−	1.09168i
$811$	1.76949e7	−	8.52140e6i	0.944703	−	0.454945i	0.102877	−	0.994694i	$-0.467195\pi$
$811$	1.76949e7	−	8.52140e6i	0.944703	−	0.454945i	0.841826	+	0.539749i	$0.181481\pi$
$812$	9.35001e6	−	5.85897e7i	0.497648	−	3.11840i
$813$	4.15151e7	+	1.99926e7i	2.20283	+	1.06082i
$814$	6.05564e6	+	1.04887e7i	0.320331	+	0.554830i
$815$	8.87674e6	−	1.53750e7i	0.468123	−	0.810812i
$816$	−1.03596e8	+	7.06308e7i	−5.44652	+	3.71337i
$817$	−6.64196e6	−	1.00111e6i	−0.348129	−	0.0524721i
$818$	−7.10946e6	+	3.11486e7i	−0.371496	+	1.62763i
$819$	2.27287e7	+	1.84495e7i	1.18404	+	0.961111i
$820$	−1.93270e6	−	8.46772e6i	−0.100376	−	0.439776i
$821$	−1.72023e6	−	2.29549e7i	−0.0890696	−	1.18855i	−0.845317	−	0.534266i	$-0.820588\pi$
$821$	−1.72023e6	−	2.29549e7i	−0.0890696	−	1.18855i	0.756247	−	0.654286i	$-0.227031\pi$
$822$	1.28249e7	+	3.95594e6i	0.662023	+	0.204207i
$823$	−9.57622e6	−	2.43998e7i	−0.492827	−	1.25570i	−0.933675	−	0.358121i	$-0.883417\pi$
$823$	−9.57622e6	−	2.43998e7i	−0.492827	−	1.25570i	0.440848	−	0.897582i	$-0.354678\pi$
$824$	−3.10421e7	+	9.57521e6i	−1.59269	+	0.491281i
$825$	1.77162e6	+	2.22154e6i	0.0906224	+	0.113637i
$826$	2.03348e7	+	1.70089e6i	1.03703	+	0.0867416i
$827$	5.73780e6	−	7.19497e6i	0.291730	−	0.365818i	−0.614270	−	0.789096i	$-0.710549\pi$
$827$	5.73780e6	−	7.19497e6i	0.291730	−	0.365818i	0.906000	+	0.423278i	$0.139121\pi$
$828$	−4.57539e6	+	1.16579e7i	−0.231928	+	0.590942i
$829$	530746.	−	7.08231e6i	0.0268226	−	0.357922i	−0.967603	−	0.252478i	$-0.918755\pi$
$829$	530746.	−	7.08231e6i	0.0268226	−	0.357922i	0.994425	−	0.105444i	$-0.0336264\pi$
$830$	−1.14414e7	+	1.72452e6i	−0.576480	+	0.0868904i
$831$	3.03395e7	−	2.81509e7i	1.52407	−	1.41413i
$832$	4.33341e7			2.17031
$833$	−7.94900e6	+	3.22449e7i	−0.396917	+	1.61008i
$834$	1.79314e6			0.0892686
$835$	−1.70612e7	+	1.58305e7i	−0.846824	+	0.785738i
$836$	−6.46595e6	+	974586.i	−0.319976	+	0.0482286i
$837$	−384597.	+	5.13208e6i	−0.0189754	+	0.253210i
$838$	1.33964e7	−	3.41336e7i	0.658991	−	1.67908i
$839$	−2.01813e7	+	2.53066e7i	−0.989794	+	1.24116i	−0.0193561	+	0.999813i	$0.506162\pi$
$839$	−2.01813e7	+	2.53066e7i	−0.989794	+	1.24116i	−0.970438	+	0.241350i	$0.922410\pi$
$840$	6.81284e7	−	7.21628e7i	3.33143	−	3.52871i
$841$	7.69001e6	+	9.64297e6i	0.374919	+	0.470133i
$842$	−5.00436e7	+	1.54364e7i	−2.43259	+	0.750354i
$843$	5.38399e6	+	1.37182e7i	0.260937	+	0.664856i
$844$	1.65747e7	+	5.11261e6i	0.800919	+	0.247051i
$845$	−1.59690e6	−	2.13092e7i	−0.0769372	−	1.02666i
$846$	3.89791e6	+	1.70779e7i	0.187243	+	0.820367i
$847$	1.91808e7	+	4.55281e6i	0.918669	+	0.218058i
$848$	1.64244e7	−	7.19600e7i	0.784332	−	3.43638i
$849$	−4.95972e7	−	7.47557e6i	−2.36150	−	0.355939i
$850$	2.28161e7	−	1.55557e7i	1.08316	−	0.738488i
$851$	3.48877e6	−	6.04272e6i	0.165138	−	0.286028i
$852$	−8.46868e6	−	1.46682e7i	−0.399684	−	0.692273i
$853$	1.79641e7	+	8.65106e6i	0.845343	+	0.407096i	0.805847	−	0.592124i	$-0.201710\pi$
$853$	1.79641e7	+	8.65106e6i	0.845343	+	0.407096i	0.0394962	+	0.999220i	$0.487425\pi$
$854$	670240.	+	269764.i	0.0314474	+	0.0126572i
$855$	1.40883e7	−	6.78457e6i	0.659088	−	0.317400i
$856$	−3.21548e7	−	2.19228e7i	−1.49990	−	1.02261i
$857$	9.17306e6	+	8.51136e6i	0.426641	+	0.395865i	0.864057	−	0.503395i	$-0.167916\pi$
$857$	9.17306e6	+	8.51136e6i	0.426641	+	0.395865i	−0.437416	+	0.899259i	$0.644106\pi$
$858$	1.38661e7	+	1.28659e7i	0.643038	+	0.596652i
$859$	2.81273e7	+	1.91769e7i	1.30060	+	0.886736i	0.997799	−	0.0663163i	$-0.0211246\pi$
$859$	2.81273e7	+	1.91769e7i	1.30060	+	0.886736i	0.302805	+	0.953053i	$0.402077\pi$
$860$	3.73083e7	−	1.79668e7i	1.72012	−	0.828368i
$861$	−4.44961e6	−	1.79092e6i	−0.204557	−	0.0823317i
$862$	3.07362e7	+	1.48018e7i	1.40891	+	0.678493i
$863$	−1.00829e7	−	1.74641e7i	−0.460848	−	0.798212i	0.538155	−	0.842846i	$-0.319121\pi$
$863$	−1.00829e7	−	1.74641e7i	−0.460848	−	0.798212i	−0.999003	+	0.0446334i	$0.985788\pi$
$864$	4.32752e6	−	7.49548e6i	0.197222	−	0.341598i
$865$	−6.12382e6	+	4.17515e6i	−0.278280	+	0.189728i
$866$	2.60401e6	+	392491.i	0.117991	+	0.0177842i
$867$	−1.25408e7	+	5.49446e7i	−0.566599	+	2.48243i
$868$	8.02022e7	+	1.90370e7i	3.61316	+	0.857630i
$869$	−1.47376e6	−	6.45694e6i	−0.0662027	−	0.290053i
$870$	6.85096e6	+	9.14198e7i	0.306869	+	4.09489i
$871$	2.05557e7	+	6.34061e6i	0.918095	+	0.283195i
$872$	−1.70738e7	−	4.35035e7i	−0.760397	−	1.93746i
$873$	−3.20117e7	+	9.87431e6i	−1.42159	+	0.438501i
$874$	3.29007e6	+	4.12562e6i	0.145689	+	0.182688i
$875$	1.07036e7	−	1.13374e7i	0.472615	−	0.500602i
$876$	−4.38219e7	+	5.49509e7i	−1.92944	+	2.41944i
$877$	−1.43346e7	+	3.65240e7i	−0.629342	+	1.60354i	0.158291	+	0.987393i	$0.449402\pi$
$877$	−1.43346e7	+	3.65240e7i	−0.629342	+	1.60354i	−0.787633	+	0.616145i	$0.788693\pi$
$878$	−2.80950e6	+	3.74902e7i	−0.122996	+	1.64127i
$879$	2.94968e7	−	4.44593e6i	1.28767	−	0.194084i
$880$	1.29637e7	−	1.20285e7i	0.564315	−	0.523608i
$881$	3.93167e7			1.70662			0.853311	−	0.521403i	$-0.174591\pi$
$881$	3.93167e7			1.70662			0.853311	+	0.521403i	$0.174591\pi$
$882$	−9.92314e6	−	4.72281e7i	−0.429514	−	2.04423i
$883$	−1.09328e7			−0.471879			−0.235940	−	0.971768i	$-0.575817\pi$
$883$	−1.09328e7			−0.471879			−0.235940	+	0.971768i	$0.575817\pi$
$884$	9.62047e7	−	8.92649e7i	4.14062	−	3.84194i
$885$	−2.22585e7	+	3.35494e6i	−0.955298	+	0.143988i
$886$	−3.85583e6	+	5.14524e7i	−0.165019	+	2.20202i
$887$	−3.60843e6	+	9.19412e6i	−0.153996	+	0.392375i	−0.986963	−	0.160948i	$-0.948545\pi$
$887$	−3.60843e6	+	9.19412e6i	−0.153996	+	0.392375i	0.832967	+	0.553322i	$0.186640\pi$
$888$	−8.64598e7	+	1.08417e8i	−3.67944	+	4.61387i
$889$	3.70497e7	+	3.09900e6i	1.57228	+	0.131513i
$890$	−3.46554e7	−	4.34565e7i	−1.46655	−	1.83899i
$891$	−4.64849e6	+	1.43387e6i	−0.196163	+	0.0605084i
$892$	2.78370e6	+	7.09275e6i	0.117141	+	0.298471i
$893$	5.03521e6	+	1.55316e6i	0.211295	+	0.0651759i
$894$	−6.38928e6	−	8.52591e7i	−0.267367	−	3.56777i
$895$	−248482.	−	1.08867e6i	−0.0103690	−	0.0454296i
$896$	−1.23341e7	−	1.00119e7i	−0.513259	−	0.416624i
$897$	2.42495e6	−	1.06244e7i	0.100629	−	0.440883i
$898$	2.21678e7	+	3.34126e6i	0.917344	+	0.138267i
$899$	−3.77034e7	+	2.57058e7i	−1.55590	+	1.06079i
$900$	−1.43239e7	+	2.48097e7i	−0.589461	+	1.02098i
$901$	−2.60678e7	−	4.51508e7i	−1.06978	−	1.85291i
$902$	−1.47350e6	−	709601.i	−0.0603024	−	0.0290401i
$903$	3.60376e6	−	2.25822e7i	0.147074	−	0.921608i
$904$	−9.38423e7	+	4.51920e7i	−3.81924	+	1.83925i
$905$	1.53130e7	+	1.04402e7i	0.621496	+	0.423729i
$906$	7.51603e6	+	6.97386e6i	0.304206	+	0.282262i
$907$	540420.	+	501436.i	0.0218129	+	0.0202394i	0.691004	−	0.722851i	$-0.257169\pi$
$907$	540420.	+	501436.i	0.0218129	+	0.0202394i	−0.669191	+	0.743090i	$0.733359\pi$
$908$	7.98018e7	+	5.44079e7i	3.21216	+	2.19002i
$909$	−1.47820e7	+	7.11862e6i	−0.593366	+	0.285750i
$910$	−4.33778e7	+	6.24559e7i	−1.73646	+	2.50017i
$911$	−2.70185e7	−	1.30114e7i	−1.07861	−	0.519432i	−0.191739	−	0.981446i	$-0.561413\pi$
$911$	−2.70185e7	−	1.30114e7i	−1.07861	−	0.519432i	−0.886873	+	0.462014i	$0.847127\pi$
$912$	−2.74038e7	−	4.74647e7i	−1.09100	−	1.88966i
$913$	−777717.	+	1.34704e6i	−0.0308777	+	0.0534817i
$914$	−6.41921e6	+	4.37655e6i	−0.254165	+	0.173287i
$915$	−788089.	−	118785.i	−0.0311188	−	0.00469040i
$916$	1.54585e7	−	6.77280e7i	0.608735	−	2.66704i
$917$	−1.88443e7	+	4.12993e6i	−0.740044	+	0.162188i
$918$	−3.00573e6	−	1.31690e7i	−0.117718	−	0.515757i
$919$	−3.31806e6	−	4.42764e7i	−0.129597	−	1.72935i	−0.561539	−	0.827450i	$-0.689791\pi$
$919$	−3.31806e6	−	4.42764e7i	−0.129597	−	1.72935i	0.431942	−	0.901901i	$-0.357828\pi$
$920$	−1.86289e7	−	5.74626e6i	−0.725634	−	0.223829i
$921$	4.78686e6	+	1.21967e7i	0.185952	+	0.473799i
$922$	2.84819e7	−	8.78551e6i	1.10342	−	0.340361i
$923$	4.84907e6	+	6.08054e6i	0.187350	+	0.234930i
$924$	−3.12743e6	−	2.20412e7i	−0.120506	−	0.849288i
$925$	9.95159e6	−	1.24789e7i	0.382418	−	0.479537i
$926$	−104554.	+	266398.i	−0.00400693	+	0.0102095i
$927$	1.30223e6	−	1.73771e7i	0.0497725	−	0.664168i
$928$	7.58850e7	−	1.14378e7i	2.89259	−	0.435987i
$929$	−4.50950e6	+	4.18421e6i	−0.171431	+	0.159065i	−0.761222	−	0.648491i	$-0.775400\pi$
$929$	−4.50950e6	+	4.18421e6i	−0.171431	+	0.159065i	0.589791	+	0.807556i	$0.299210\pi$
$930$	−1.27369e8			−4.82898
$931$	−1.37958e7	−	4.51827e6i	−0.521644	−	0.170843i
$932$	5.95160e7			2.24437
$933$	−2.42814e6	+	2.25299e6i	−0.0913209	+	0.0847334i
$934$	1.46943e6	−	221481.i	0.0551166	−	0.00830749i
$935$	933480.	−	1.24564e7i	0.0349201	−	0.465977i
$936$	−4.17536e7	+	1.06387e8i	−1.55777	+	3.96915i
$937$	6.68738e6	−	8.38571e6i	0.248832	−	0.312026i	−0.641691	−	0.766963i	$-0.721767\pi$
$937$	6.68738e6	−	8.38571e6i	0.248832	−	0.312026i	0.890524	+	0.454937i	$0.150338\pi$
$938$	−1.97224e7	−	2.94719e7i	−0.731900	−	1.09371i
$939$	5.68935e6	+	7.13422e6i	0.210571	+	0.264048i
$940$	−3.10413e7	+	9.57498e6i	−1.14583	+	0.353442i
$941$	1.76934e7	+	4.50819e7i	0.651382	+	1.65970i	0.747448	+	0.664320i	$0.231279\pi$
$941$	1.76934e7	+	4.50819e7i	0.651382	+	1.65970i	−0.0960655	+	0.995375i	$0.530626\pi$
$942$	3.61031e7	+	1.11363e7i	1.32561	+	0.408897i
$943$	70412.3	+	939587.i	0.00257851	+	0.0344079i
$944$	9.26442e6	+	4.05901e7i	0.338367	+	1.48248i
$945$	2.38069e6	+	5.05494e6i	0.0867206	+	0.184135i
$946$	1.73506e6	−	7.60178e6i	0.0630356	−	0.276177i
$947$	2.28891e7	+	3.44998e6i	0.829381	+	0.125009i	0.549993	−	0.835169i	$-0.314630\pi$
$947$	2.28891e7	+	3.44998e6i	0.829381	+	0.125009i	0.279388	+	0.960178i	$0.409868\pi$
$948$	1.04551e8	−	7.12818e7i	3.77840	−	2.57607i
$949$	1.61367e7	−	2.79496e7i	0.581634	−	1.00742i
$950$	6.03541e6	+	1.04536e7i	0.216969	+	0.375802i
$951$	7.00609e6	+	3.37395e6i	0.251203	+	0.120973i
$952$	−1.29370e8	+	8.57023e6i	−4.62637	+	0.306479i
$953$	2.62025e7	−	1.26185e7i	0.934567	−	0.450064i	0.0963174	−	0.995351i	$-0.469294\pi$
$953$	2.62025e7	−	1.26185e7i	0.934567	−	0.450064i	0.838249	+	0.545287i	$0.183579\pi$
$954$	6.25964e7	+	4.26775e7i	2.22678	+	1.51820i
$955$	442363.	+	410453.i	0.0156953	+	0.0145631i
$956$	−8.53518e7	−	7.91949e7i	−3.02042	−	2.80254i
$957$	1.01825e7	+	6.94233e6i	0.359398	+	0.245033i
$958$	−8.63478e7	+	4.15829e7i	−3.03975	+	1.46387i
$959$	4.88708e6	+	5.35927e6i	0.171595	+	0.188174i
$960$	7.09997e7	+	3.41916e7i	2.48644	+	1.19741i
$961$	−1.73849e7	−	3.01115e7i	−0.607244	−	1.05178i
$962$	5.31266e7	−	9.20180e7i	1.85086	−	3.20579i
$963$	1.72485e7	−	1.17599e7i	0.599358	−	0.408636i
$964$	−4.12562e7	−	6.21837e6i	−1.42987	−	0.215518i
$965$	−1.15118e7	+	5.04366e7i	−0.397947	+	1.74352i
$966$	−1.41420e7	+	1.10791e7i	−0.487605	+	0.381999i
$967$	4.07237e6	+	1.78422e7i	0.140049	+	0.613596i	0.995422	+	0.0955824i	$0.0304713\pi$
$967$	4.07237e6	+	1.78422e7i	0.140049	+	0.613596i	−0.855372	+	0.518014i	$0.826672\pi$
$968$	5.75143e6	+	7.67475e7i	0.197282	+	2.63255i
$969$	−3.69930e7	−	1.14108e7i	−1.26564	−	0.390399i
$970$	−3.17915e7	−	8.10035e7i	−1.08488	−	2.76423i
$971$	2.99135e6	−	922710.i	0.101817	−	0.0314063i	−0.243428	−	0.969919i	$-0.578272\pi$
$971$	2.99135e6	−	922710.i	0.101817	−	0.0314063i	0.345245	+	0.938513i	$0.387796\pi$
$972$	−6.57691e7	−	8.24718e7i	−2.23283	−	2.79988i
$973$	834988.	+	491760.i	0.0282747	+	0.0166522i
$974$	−1.38188e7	+	1.73282e7i	−0.466738	+	0.585270i
$975$	9.10734e6	−	2.32051e7i	0.306818	−	0.781758i
$976$	−110159.	+	1.46997e6i	−0.00370166	+	0.0493952i
$977$	5.39984e7	−	8.13895e6i	1.80986	−	0.272792i	0.844849	−	0.535005i	$-0.179690\pi$
$977$	5.39984e7	−	8.13895e6i	1.80986	−	0.272792i	0.965010	+	0.262213i	$0.0844523\pi$
$978$	4.68203e7	−	4.34429e7i	1.56526	−	1.45235i
$979$	−7.47197e6			−0.249160
$980$	8.59620e7	−	2.48955e7i	2.85918	−	0.828049i
$981$	2.50692e7			0.831701
$982$	1.40277e7	−	1.30158e7i	0.464203	−	0.430718i
$983$	−4.70734e7	+	7.09517e6i	−1.55379	+	0.234196i	−0.869098	−	0.494640i	$-0.835300\pi$
$983$	−4.70734e7	+	7.09517e6i	−1.55379	+	0.234196i	−0.684689	+	0.728835i	$0.740062\pi$
$984$	1.39936e6	−	1.86732e7i	0.0460726	−	0.614797i
$985$	3.60071e6	−	9.17447e6i	0.118249	−	0.301294i
$986$	7.46747e7	−	9.36392e7i	2.44614	−	3.06736i
$987$	−5.43580e6	+	1.70960e7i	−0.177611	+	0.558600i
$988$	3.57678e7	+	4.48514e7i	1.16574	+	1.46179i
$989$	−4.29258e6	+	1.32409e6i	−0.139549	+	0.0430453i
$990$	6.63158e6	+	1.68970e7i	0.215045	+	0.547925i
$991$	−2.87602e7	−	8.87134e6i	−0.930267	−	0.286949i	−0.207654	−	0.978202i	$-0.566583\pi$
$991$	−2.87602e7	−	8.87134e6i	−0.930267	−	0.286949i	−0.722613	+	0.691253i	$0.757059\pi$
$992$	7.96776e6	+	1.06322e8i	0.257073	+	3.43040i
$993$	−5.14122e6	−	2.25252e7i	−0.165460	−	0.724928i
$994$	110906.	−	1.28206e7i	0.00356033	−	0.411569i
$995$	−1.73107e6	+	7.58432e6i	−0.0554316	+	0.242862i
$996$	−2.93861e7	−	4.42925e6i	−0.938629	−	0.141476i
$997$	−3.93507e7	+	2.68289e7i	−1.25376	+	0.854799i	−0.993839	−	0.110830i	$-0.964649\pi$
$997$	−3.93507e7	+	2.68289e7i	−1.25376	+	0.854799i	−0.259921	+	0.965630i	$0.583697\pi$
$998$	−1.89620e7	+	3.28431e7i	−0.602640	+	1.04380i
$999$	−3.90370e6	−	6.76141e6i	−0.123755	−	0.214350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.g.a.11.22	yes	264
49.9	even	21	inner	49.6.g.a.9.22	✓	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.6.g.a.9.22	✓	264	49.9	even	21	inner
49.6.g.a.11.22	yes	264	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	49.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(7.75287 - 7.19361i) q^{2} +(-22.4292 + 3.38065i) q^{3} +(5.96758 - 79.6318i) q^{4} +(-24.3614 + 62.0717i) q^{5} +(-149.571 + 187.556i) q^{6} +(-121.085 + 46.3178i) q^{7} +(-315.563 - 395.703i) q^{8} +(259.434 - 80.0247i) q^{9} +O(q^{10})\)	\(q+(7.75287 - 7.19361i) q^{2} +(-22.4292 + 3.38065i) q^{3} +(5.96758 - 79.6318i) q^{4} +(-24.3614 + 62.0717i) q^{5} +(-149.571 + 187.556i) q^{6} +(-121.085 + 46.3178i) q^{7} +(-315.563 - 395.703i) q^{8} +(259.434 - 80.0247i) q^{9} +(257.650 + 656.480i) q^{10} +(90.5917 + 27.9438i) q^{11} +(135.360 + 1806.25i) q^{12} +(-185.075 - 810.866i) q^{13} +(-605.567 + 1230.14i) q^{14} +(336.562 - 1474.57i) q^{15} +(-2766.23 - 416.942i) q^{16} +(-1632.63 + 1113.11i) q^{17} +(1435.69 - 2486.69i) q^{18} +(-431.870 - 748.021i) q^{19} +(4797.51 + 2310.36i) q^{20} +(2559.26 - 1448.22i) q^{21} +(903.363 - 435.037i) q^{22} +(-477.276 - 325.402i) q^{23} +(8415.53 + 7808.48i) q^{24} +(-968.635 - 898.762i) q^{25} +(-7267.92 - 4955.19i) q^{26} +(-582.343 + 280.442i) q^{27} +(2965.78 + 9918.65i) q^{28} +(-5163.50 - 2486.61i) q^{29} +(-7998.19 - 13853.3i) q^{30} +(3981.17 - 6895.59i) q^{31} +(-11063.8 + 7543.19i) q^{32} +(-2126.36 - 320.498i) q^{33} +(-4650.30 + 20374.3i) q^{34} +(74.7790 - 8644.34i) q^{35} +(-4824.32 - 21136.7i) q^{36} +(902.679 + 12045.4i) q^{37} +(-8729.21 - 2692.61i) q^{38} +(6892.33 + 17561.4i) q^{39} +(32249.5 - 9947.65i) q^{40} +(-1016.99 - 1275.27i) q^{41} +(9423.69 - 29638.1i) q^{42} +(4848.64 - 6080.00i) q^{43} +(2765.83 - 7047.22i) q^{44} +(-1352.89 + 18053.0i) q^{45} +(-6041.08 + 910.546i) q^{46} +(-4472.04 + 4149.44i) q^{47} +63453.7 q^{48} +(12516.3 - 11216.8i) q^{49} -13975.1 q^{50} +(32855.5 - 30485.4i) q^{51} +(-65675.2 + 9898.95i) q^{52} +(-1971.73 + 26311.0i) q^{53} +(-2497.44 + 6363.38i) q^{54} +(-3941.46 + 4942.43i) q^{55} +(56538.1 + 33297.7i) q^{56} +(12215.3 + 15317.5i) q^{57} +(-57919.7 + 17865.9i) q^{58} +(-5437.25 - 13853.9i) q^{59} +(-115414. - 35600.7i) q^{60} +(-39.3781 - 525.465i) q^{61} +(-18738.7 - 82099.6i) q^{62} +(-27707.1 + 21706.2i) q^{63} +(-11593.7 + 50795.5i) q^{64} +(54840.6 + 8265.88i) q^{65} +(-18791.0 + 12811.5i) q^{66} +(-12931.9 + 22398.7i) q^{67} +(78896.0 + 136652. i) q^{68} +(11805.0 + 5684.98i) q^{69} +(-61604.3 - 67556.4i) q^{70} +(-8424.85 + 4057.19i) q^{71} +(-113534. - 77405.9i) q^{72} +(28444.8 + 26392.9i) q^{73} +(93648.4 + 86893.0i) q^{74} +(24764.1 + 16883.9i) q^{75} +(-62143.5 + 29926.7i) q^{76} +(-12263.6 + 812.417i) q^{77} +(179765. + 86570.3i) q^{78} +(-34930.1 - 60500.7i) q^{79} +(93269.4 - 161547. i) q^{80} +(-42396.4 + 28905.4i) q^{81} +(-17058.4 - 2571.14i) q^{82} +(-3650.88 + 15995.6i) q^{83} +(-100051. - 212441. i) q^{84} +(-29319.5 - 128457. i) q^{85} +(-6146.30 - 82016.7i) q^{86} +(124219. + 38316.6i) q^{87} +(-17529.9 - 44665.4i) q^{88} +(-75313.8 + 23231.2i) q^{89} +(119378. + 149695. i) q^{90} +(59967.4 + 89611.8i) q^{91} +(-28760.5 + 36064.5i) q^{92} +(-65982.7 + 168121. i) q^{93} +(-4821.63 + 64340.2i) q^{94} +(56951.9 - 8584.12i) q^{95} +(222651. - 206590. i) q^{96} -123391. q^{97} +(16348.1 - 177000. i) q^{98} +25738.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q - 13 q^{2} - 22 q^{3} + 307 q^{4} - 52 q^{5} - 130 q^{6} + 154 q^{7} - 320 q^{8} + 6 q^{9}+O(q^{10}) \) 264 * q - 13 * q^2 - 22 * q^3 + 307 * q^4 - 52 * q^5 - 130 * q^6 + 154 * q^7 - 320 * q^8 + 6 * q^9	\( 264 q - 13 q^{2} - 22 q^{3} + 307 q^{4} - 52 q^{5} - 130 q^{6} + 154 q^{7} - 320 q^{8} + 6 q^{9} - 792 q^{10} - 635 q^{11} + 3605 q^{12} + 1834 q^{13} - 875 q^{14} - 2572 q^{15} + 3735 q^{16} - 1023 q^{17} - 1336 q^{18} + 9741 q^{19} + 8330 q^{20} + 1512 q^{21} + 842 q^{22} - 1553 q^{23} + 1756 q^{24} + 13144 q^{25} - 1946 q^{26} - 19849 q^{27} - 31584 q^{28} - 30356 q^{29} + 6129 q^{30} + 43903 q^{31} + 27725 q^{32} - 3412 q^{33} - 73182 q^{34} - 17360 q^{35} - 102868 q^{36} - 22105 q^{37} + 19116 q^{38} + 109165 q^{39} + 77354 q^{40} + 47446 q^{41} + 157738 q^{42} + 6674 q^{43} + 15154 q^{44} - 130923 q^{45} - 136952 q^{46} - 195163 q^{47} - 151484 q^{48} - 131194 q^{49} + 263000 q^{50} - 84276 q^{51} - 58758 q^{52} - 110577 q^{53} + 170313 q^{54} + 290245 q^{55} + 79688 q^{56} + 47310 q^{57} + 252156 q^{58} + 127308 q^{59} + 86254 q^{60} + 166863 q^{61} - 63578 q^{62} - 243033 q^{63} - 293812 q^{64} - 16702 q^{65} - 661788 q^{66} + 46195 q^{67} + 393869 q^{68} + 321394 q^{69} - 64330 q^{70} - 61793 q^{71} + 333944 q^{72} + 21699 q^{73} + 133514 q^{74} - 431136 q^{75} + 3087 q^{76} - 48993 q^{77} - 450576 q^{78} - 181 q^{79} + 264228 q^{80} + 142090 q^{81} - 512442 q^{82} + 102424 q^{83} + 344932 q^{84} - 205502 q^{85} + 611991 q^{86} + 1427200 q^{87} + 685993 q^{88} + 145800 q^{89} + 677844 q^{90} + 732956 q^{91} + 10018 q^{92} - 1233536 q^{93} - 601938 q^{94} - 945265 q^{95} - 2372958 q^{96} - 1932952 q^{97} - 672973 q^{98} + 1090736 q^{99}+O(q^{100}) \) 264 * q - 13 * q^2 - 22 * q^3 + 307 * q^4 - 52 * q^5 - 130 * q^6 + 154 * q^7 - 320 * q^8 + 6 * q^9 - 792 * q^10 - 635 * q^11 + 3605 * q^12 + 1834 * q^13 - 875 * q^14 - 2572 * q^15 + 3735 * q^16 - 1023 * q^17 - 1336 * q^18 + 9741 * q^19 + 8330 * q^20 + 1512 * q^21 + 842 * q^22 - 1553 * q^23 + 1756 * q^24 + 13144 * q^25 - 1946 * q^26 - 19849 * q^27 - 31584 * q^28 - 30356 * q^29 + 6129 * q^30 + 43903 * q^31 + 27725 * q^32 - 3412 * q^33 - 73182 * q^34 - 17360 * q^35 - 102868 * q^36 - 22105 * q^37 + 19116 * q^38 + 109165 * q^39 + 77354 * q^40 + 47446 * q^41 + 157738 * q^42 + 6674 * q^43 + 15154 * q^44 - 130923 * q^45 - 136952 * q^46 - 195163 * q^47 - 151484 * q^48 - 131194 * q^49 + 263000 * q^50 - 84276 * q^51 - 58758 * q^52 - 110577 * q^53 + 170313 * q^54 + 290245 * q^55 + 79688 * q^56 + 47310 * q^57 + 252156 * q^58 + 127308 * q^59 + 86254 * q^60 + 166863 * q^61 - 63578 * q^62 - 243033 * q^63 - 293812 * q^64 - 16702 * q^65 - 661788 * q^66 + 46195 * q^67 + 393869 * q^68 + 321394 * q^69 - 64330 * q^70 - 61793 * q^71 + 333944 * q^72 + 21699 * q^73 + 133514 * q^74 - 431136 * q^75 + 3087 * q^76 - 48993 * q^77 - 450576 * q^78 - 181 * q^79 + 264228 * q^80 + 142090 * q^81 - 512442 * q^82 + 102424 * q^83 + 344932 * q^84 - 205502 * q^85 + 611991 * q^86 + 1427200 * q^87 + 685993 * q^88 + 145800 * q^89 + 677844 * q^90 + 732956 * q^91 + 10018 * q^92 - 1233536 * q^93 - 601938 * q^94 - 945265 * q^95 - 2372958 * q^96 - 1932952 * q^97 - 672973 * q^98 + 1090736 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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