LMFDB - Embedded newform 31.8.g.a.9.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,8,Mod(7,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.7"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.68393579001$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.11
Character	$\chi$	$=$	31.9
Dual form			31.8.g.a.7.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.822068 - 2.53007i) q^{2} +(-31.4883 - 6.69304i) q^{3} +(97.8287 + 71.0767i) q^{4} +(-80.8758 - 140.081i) q^{5} +(-42.8193 + 74.1652i) q^{6} +(-375.195 + 167.047i) q^{7} +(535.733 - 389.233i) q^{8} +(-1051.21 - 468.029i) q^{9} +(-420.900 + 89.4650i) q^{10} +(-641.184 + 6100.45i) q^{11} +(-2604.74 - 2892.85i) q^{12} +(-7749.92 + 8607.16i) q^{13} +(114.205 + 1086.59i) q^{14} +(1609.07 + 4952.21i) q^{15} +(4238.63 + 13045.2i) q^{16} +(1375.02 + 13082.4i) q^{17} +(-2048.31 + 2274.88i) q^{18} +(-22513.7 - 25003.9i) q^{19} +(2044.52 - 19452.3i) q^{20} +(12932.3 - 2748.84i) q^{21} +(14907.5 + 6637.23i) q^{22} +(-70028.2 + 50878.4i) q^{23} +(-19474.4 + 8670.58i) q^{24} +(25980.7 - 44999.9i) q^{25} +(15405.7 + 26683.5i) q^{26} +(86925.7 + 63155.2i) q^{27} +(-48578.0 - 10325.6i) q^{28} +(-6613.86 + 20355.4i) q^{29} +13852.2 q^{30} +(-98792.4 - 133239. i) q^{31} +121251. q^{32} +(61020.3 - 187801. i) q^{33} +(34229.8 + 7275.77i) q^{34} +(53744.3 + 39047.5i) q^{35} +(-69572.6 - 120503. i) q^{36} +(297255. - 514860. i) q^{37} +(-81769.4 + 36406.1i) q^{38} +(301640. - 219154. i) q^{39} +(-97851.9 - 43566.5i) q^{40} +(-149088. + 31689.7i) q^{41} +(3676.47 - 34979.2i) q^{42} +(487347. + 541254. i) q^{43} +(-496327. + 551227. i) q^{44} +(19455.5 + 185107. i) q^{45} +(71157.9 + 219001. i) q^{46} +(75637.4 + 232788. i) q^{47} +(-46155.4 - 439139. i) q^{48} +(-438192. + 486661. i) q^{49} +(-92494.8 - 102726. i) q^{50} +(44264.3 - 421146. i) q^{51} +(-1.36993e6 + 291189. i) q^{52} +(-314851. - 140181. i) q^{53} +(231246. - 168010. i) q^{54} +(906414. - 403562. i) q^{55} +(-135984. + 235531. i) q^{56} +(541564. + 938015. i) q^{57} +(46063.4 + 33467.0i) q^{58} +(-1.30145e6 - 276631. i) q^{59} +(-194574. + 598836. i) q^{60} -1.07357e6 q^{61} +(-418318. + 140420. i) q^{62} +472591. q^{63} +(-442868. + 1.36301e6i) q^{64} +(1.83248e6 + 389506. i) q^{65} +(-424987. - 308771. i) q^{66} +(-208454. - 361053. i) q^{67} +(-795341. + 1.37757e6i) q^{68} +(2.54560e6 - 1.13337e6i) q^{69} +(142974. - 103877. i) q^{70} +(2.22572e6 + 990956. i) q^{71} +(-745339. + 158427. i) q^{72} +(105067. - 999642. i) q^{73} +(-1.05827e6 - 1.17532e6i) q^{74} +(-1.11927e6 + 1.24308e6i) q^{75} +(-425283. - 4.04630e6i) q^{76} +(-778496. - 2.39597e6i) q^{77} +(-306506. - 943328. i) q^{78} +(160488. + 1.52694e6i) q^{79} +(1.48458e6 - 1.64879e6i) q^{80} +(-630529. - 700274. i) q^{81} +(-42383.7 + 403254. i) q^{82} +(9.30302e6 - 1.97742e6i) q^{83} +(1.46053e6 + 650269. i) q^{84} +(1.72140e6 - 1.25067e6i) q^{85} +(1.77004e6 - 788072. i) q^{86} +(344498. - 596688. i) q^{87} +(2.03099e6 + 3.51778e6i) q^{88} +(-8.52640e6 - 6.19479e6i) q^{89} +(484326. + 102947. i) q^{90} +(1.46993e6 - 4.52396e6i) q^{91} -1.04670e7 q^{92} +(2.21903e6 + 4.85669e6i) q^{93} +651148. q^{94} +(-1.68177e6 + 5.17595e6i) q^{95} +(-3.81800e6 - 811540. i) q^{96} +(6.10363e6 + 4.43455e6i) q^{97} +(871061. + 1.50872e6i) q^{98} +(3.52921e6 - 6.11277e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{2} - 8 q^{3} - 2362 q^{4} - 75 q^{5} - 1637 q^{6} + 5518 q^{7} + 3401 q^{8} + 14542 q^{9} - 5312 q^{10} + 1361 q^{11} - 18281 q^{12} + 22457 q^{13} + 28470 q^{14} - 86918 q^{15} - 155730 q^{16}+ \cdots - 102755966 q^{99}+O(q^{100}) $ 144 * q - 6 * q^2 - 8 * q^3 - 2362 * q^4 - 75 * q^5 - 1637 * q^6 + 5518 * q^7 + 3401 * q^8 + 14542 * q^9 - 5312 * q^10 + 1361 * q^11 - 18281 * q^12 + 22457 * q^13 + 28470 * q^14 - 86918 * q^15 - 155730 * q^16 + 51582 * q^17 - 24915 * q^18 + 206748 * q^19 + 53815 * q^20 - 28547 * q^21 + 471441 * q^22 - 10235 * q^23 + 69278 * q^24 - 974301 * q^25 - 279651 * q^26 - 948323 * q^27 + 550632 * q^28 - 32990 * q^29 + 2457990 * q^30 + 899715 * q^31 - 1048518 * q^32 + 780887 * q^33 - 1741528 * q^34 + 40023 * q^35 - 2118881 * q^36 - 787972 * q^37 + 580274 * q^38 + 2541281 * q^39 + 2341817 * q^40 + 1129504 * q^41 - 4390379 * q^42 + 481927 * q^43 - 3123681 * q^44 - 1715971 * q^45 + 2065430 * q^46 - 3123106 * q^47 + 1041890 * q^48 + 76766 * q^49 + 7537425 * q^50 + 6145978 * q^51 + 3260257 * q^52 + 141486 * q^53 - 8979668 * q^54 - 8182779 * q^55 - 5240874 * q^56 - 5487037 * q^57 + 5315215 * q^58 + 7471552 * q^59 + 8590679 * q^60 + 10667852 * q^61 + 27020951 * q^62 - 23783686 * q^63 - 3962521 * q^64 + 935148 * q^65 + 3015728 * q^66 - 17382495 * q^67 - 29462568 * q^68 - 26986306 * q^69 - 31811186 * q^70 - 6186650 * q^71 + 35811589 * q^72 + 6470154 * q^73 + 55339663 * q^74 + 17367737 * q^75 + 2919592 * q^76 + 31865334 * q^77 - 7291717 * q^78 + 4223078 * q^79 + 77431338 * q^80 - 5164601 * q^81 - 19477394 * q^82 - 28867780 * q^83 - 76561164 * q^84 - 45198987 * q^85 - 60993764 * q^86 + 18253055 * q^87 - 45197061 * q^88 - 8429459 * q^89 + 83458809 * q^90 - 53128088 * q^91 + 77469728 * q^92 + 41662009 * q^93 - 16867972 * q^94 - 12744274 * q^95 + 119555444 * q^96 + 20643027 * q^97 + 49624796 * q^98 - 102755966 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	0.822068	−	2.53007i	0.0726612	−	0.223628i	−0.908130	−	0.418688i	$-0.862490\pi$
$2$	0.822068	−	2.53007i	0.0726612	−	0.223628i	0.980791	+	0.195060i	$0.0624901\pi$
$3$	−31.4883	−	6.69304i	−0.673324	−	0.143120i	−0.141453	−	0.989945i	$-0.545178\pi$
$3$	−31.4883	−	6.69304i	−0.673324	−	0.143120i	−0.531871	+	0.846825i	$0.678511\pi$
$4$	97.8287	+	71.0767i	0.764287	+	0.555287i
$5$	−80.8758	−	140.081i	−0.289350	−	0.501169i	0.684305	−	0.729196i	$-0.260106\pi$
$5$	−80.8758	−	140.081i	−0.289350	−	0.501169i	−0.973655	+	0.228027i	$0.926772\pi$
$6$	−42.8193	+	74.1652i	−0.0809302	+	0.140175i
$7$	−375.195	+	167.047i	−0.413441	+	0.184076i	−0.602907	−	0.797812i	$-0.705991\pi$
$7$	−375.195	+	167.047i	−0.413441	+	0.184076i	0.189466	+	0.981887i	$0.439324\pi$
$8$	535.733	−	389.233i	0.369942	−	0.268778i
$9$	−1051.21	−	468.029i	−0.480663	−	0.214005i
$10$	−420.900	+	89.4650i	−0.133100	+	0.0282913i
$11$	−641.184	+	6100.45i	−0.145247	+	1.38194i	0.642665	+	0.766148i	$0.277829\pi$
$11$	−641.184	+	6100.45i	−0.145247	+	1.38194i	−0.787912	+	0.615788i	$0.788838\pi$
$12$	−2604.74	−	2892.85i	−0.435141	−	0.483273i
$13$	−7749.92	+	8607.16i	−0.978353	+	1.08657i	0.0178785	+	0.999840i	$0.494309\pi$
$13$	−7749.92	+	8607.16i	−0.978353	+	1.08657i	−0.996232	+	0.0867312i	$0.972358\pi$
$14$	114.205	+	1086.59i	0.0111234	+	0.105832i
$15$	1609.07	+	4952.21i	0.123099	+	0.378861i
$16$	4238.63	+	13045.2i	0.258706	+	0.796214i
$17$	1375.02	+	13082.4i	0.0678794	+	0.645829i	0.974578	+	0.224050i	$0.0719277\pi$
$17$	1375.02	+	13082.4i	0.0678794	+	0.645829i	−0.906698	+	0.421780i	$0.861406\pi$
$18$	−2048.31	+	2274.88i	−0.0827831	+	0.0919400i
$19$	−22513.7	−	25003.9i	−0.753023	−	0.836317i	0.237824	−	0.971308i	$-0.423566\pi$
$19$	−22513.7	−	25003.9i	−0.753023	−	0.836317i	−0.990847	+	0.134991i	$0.956899\pi$
$20$	2044.52	−	19452.3i	0.0571462	−	0.543709i
$21$	12932.3	−	2748.84i	0.304725	−	0.0647712i
$22$	14907.5	+	6637.23i	0.298486	+	0.132895i
$23$	−70028.2	+	50878.4i	−1.20012	+	0.871940i	−0.994297	−	0.106649i	$-0.965988\pi$
$23$	−70028.2	+	50878.4i	−1.20012	+	0.871940i	−0.205825	+	0.978589i	$0.565988\pi$
$24$	−19474.4	+	8670.58i	−0.287558	+	0.128029i
$25$	25980.7	−	44999.9i	0.332553	−	0.575999i
$26$	15405.7	+	26683.5i	0.171900	+	0.297739i
$27$	86925.7	+	63155.2i	0.849914	+	0.617499i
$28$	−48578.0	−	10325.6i	−0.418202	−	0.0888916i
$29$	−6613.86	+	20355.4i	−0.0503572	+	0.154984i	−0.973073	−	0.230498i	$-0.925965\pi$
$29$	−6613.86	+	20355.4i	−0.0503572	+	0.154984i	0.922716	+	0.385481i	$0.125965\pi$
$30$	13852.2			0.0936686
$31$	−98792.4	−	133239.i	−0.595604	−	0.803278i
$31$	−98792.4	−	133239.i	−0.595604	−	0.803278i
$32$	121251.			0.654127
$33$	61020.3	−	187801.i	0.295580	−	0.909703i
$34$	34229.8	+	7275.77i	0.149358	+	0.0317470i
$35$	53744.3	+	39047.5i	0.211882	+	0.153941i
$36$	−69572.6	−	120503.i	−0.248530	−	0.430467i
$37$	297255.	−	514860.i	0.964768	−	1.67103i	0.254530	−	0.967065i	$-0.418079\pi$
$37$	297255.	−	514860.i	0.964768	−	1.67103i	0.710238	−	0.703962i	$-0.248587\pi$
$38$	−81769.4	+	36406.1i	−0.241740	+	0.107629i
$39$	301640.	−	219154.i	0.814259	−	0.591594i
$40$	−97851.9	−	43566.5i	−0.241746	−	0.107632i
$41$	−149088.	+	31689.7i	−0.337831	+	0.0718082i	−0.373704	−	0.927548i	$-0.621912\pi$
$41$	−149088.	+	31689.7i	−0.337831	+	0.0718082i	0.0358725	+	0.999356i	$0.488579\pi$
$42$	3676.47	−	34979.2i	0.00765699	−	0.0728514i
$43$	487347.	+	541254.i	0.934757	+	1.03815i	0.999190	+	0.0402305i	$0.0128092\pi$
$43$	487347.	+	541254.i	0.934757	+	1.03815i	−0.0644337	+	0.997922i	$0.520524\pi$
$44$	−496327.	+	551227.i	−0.878382	+	0.975542i
$45$	19455.5	+	185107.i	0.0318272	+	0.302816i
$46$	71157.9	+	219001.i	0.107788	+	0.331737i
$47$	75637.4	+	232788.i	0.106266	+	0.327053i	0.990025	−	0.140888i	$-0.0449959\pi$
$47$	75637.4	+	232788.i	0.106266	+	0.327053i	−0.883760	+	0.467941i	$0.844996\pi$
$48$	−46155.4	−	439139.i	−0.0602390	−	0.573136i
$49$	−438192.	+	486661.i	−0.532081	+	0.590936i
$50$	−92494.8	−	102726.i	−0.104646	−	0.116221i
$51$	44264.3	−	421146.i	0.0467259	−	0.444567i
$52$	−1.36993e6	+	291189.i	−1.35110	+	0.287186i
$53$	−314851.	−	140181.i	−0.290495	−	0.129337i	0.256315	−	0.966593i	$-0.417492\pi$
$53$	−314851.	−	140181.i	−0.290495	−	0.129337i	−0.546811	+	0.837256i	$0.684158\pi$
$54$	231246.	−	168010.i	0.199846	−	0.145197i
$55$	906414.	−	403562.i	0.734611	−	0.327070i
$56$	−135984.	+	235531.i	−0.103473	+	0.179221i
$57$	541564.	+	938015.i	0.387336	+	0.670885i
$58$	46063.4	+	33467.0i	0.0309997	+	0.0225226i
$59$	−1.30145e6	−	276631.i	−0.824981	−	0.175355i	−0.223970	−	0.974596i	$-0.571902\pi$
$59$	−1.30145e6	−	276631.i	−0.824981	−	0.175355i	−0.601011	+	0.799241i	$0.705235\pi$
$60$	−194574.	+	598836.i	−0.116293	+	0.357914i
$61$	−1.07357e6			−0.605587			−0.302793	−	0.953056i	$-0.597919\pi$
$61$	−1.07357e6			−0.605587			−0.302793	+	0.953056i	$0.597919\pi$
$62$	−418318.	+	140420.i	−0.222913	+	0.0748268i
$63$	472591.			0.238119
$64$	−442868.	+	1.36301e6i	−0.211176	+	0.649933i
$65$	1.83248e6	+	389506.i	0.827642	+	0.175921i
$66$	−424987.	−	308771.i	−0.181958	−	0.132200i
$67$	−208454.	−	361053.i	−0.0846738	−	0.146659i	0.820578	−	0.571534i	$-0.193651\pi$
$67$	−208454.	−	361053.i	−0.0846738	−	0.146659i	−0.905252	+	0.424875i	$0.860318\pi$
$68$	−795341.	+	1.37757e6i	−0.306741	+	0.531291i
$69$	2.54560e6	−	1.13337e6i	0.932863	−	0.415337i
$70$	142974.	−	103877.i	0.0498213	−	0.0361973i
$71$	2.22572e6	+	990956.i	0.738018	+	0.328587i	0.741087	−	0.671409i	$-0.234310\pi$
$71$	2.22572e6	+	990956.i	0.738018	+	0.328587i	−0.00306947	+	0.999995i	$0.500977\pi$
$72$	−745339.	+	158427.i	−0.235337	+	0.0500224i
$73$	105067.	−	999642.i	0.0316107	−	0.300756i	−0.967282	−	0.253705i	$-0.918351\pi$
$73$	105067.	−	999642.i	0.0316107	−	0.300756i	0.998892	−	0.0470515i	$-0.0149825\pi$
$74$	−1.05827e6	−	1.17532e6i	−0.303588	−	0.337168i
$75$	−1.11927e6	+	1.24308e6i	−0.306353	+	0.340239i
$76$	−425283.	−	4.04630e6i	−0.111130	−	1.05733i
$77$	−778496.	−	2.39597e6i	−0.194330	−	0.598085i
$78$	−306506.	−	943328.i	−0.0731320	−	0.225077i
$79$	160488.	+	1.52694e6i	0.0366224	+	0.348439i	0.997454	+	0.0713074i	$0.0227171\pi$
$79$	160488.	+	1.52694e6i	0.0366224	+	0.348439i	−0.960832	+	0.277132i	$0.910616\pi$
$80$	1.48458e6	−	1.64879e6i	0.324181	−	0.360040i
$81$	−630529.	−	700274.i	−0.131828	−	0.146410i
$82$	−42383.7	+	403254.i	−0.00848888	+	0.0807663i
$83$	9.30302e6	−	1.97742e6i	1.78587	−	0.379599i	0.808063	−	0.589096i	$-0.200516\pi$
$83$	9.30302e6	−	1.97742e6i	1.78587	−	0.379599i	0.977809	+	0.209497i	$0.0671825\pi$
$84$	1.46053e6	+	650269.i	0.268864	+	0.119706i
$85$	1.72140e6	−	1.25067e6i	0.304029	−	0.220890i
$86$	1.77004e6	−	788072.i	0.300081	−	0.133605i
$87$	344498.	−	596688.i	0.0560879	−	0.0971472i
$88$	2.03099e6	+	3.51778e6i	0.317701	+	0.550275i
$89$	−8.52640e6	−	6.19479e6i	−1.28204	−	0.931454i	−0.282424	−	0.959290i	$-0.591139\pi$
$89$	−8.52640e6	−	6.19479e6i	−1.28204	−	0.931454i	−0.999613	+	0.0278353i	$0.991139\pi$
$90$	484326.	+	102947.i	0.0700308	+	0.0148855i
$91$	1.46993e6	−	4.52396e6i	0.204480	−	0.629324i
$92$	−1.04670e7			−1.40141
$93$	2.21903e6	+	4.85669e6i	0.286070	+	0.626109i
$94$	651148.			0.0808597
$95$	−1.68177e6	+	5.17595e6i	−0.201249	+	0.619380i
$96$	−3.81800e6	−	811540.i	−0.440439	−	0.0936183i
$97$	6.10363e6	+	4.43455e6i	0.679027	+	0.493342i	0.873035	−	0.487658i	$-0.162149\pi$
$97$	6.10363e6	+	4.43455e6i	0.679027	+	0.493342i	−0.194008	+	0.981000i	$0.562149\pi$
$98$	871061.	+	1.50872e6i	0.0934883	+	0.161927i
$99$	3.52921e6	−	6.11277e6i	0.365556	−	0.633162i
$100$	5.74011e6	−	2.55566e6i	0.574011	−	0.255566i
$101$	−1.22099e7	+	8.87098e6i	−1.17920	+	0.856736i	−0.992081	−	0.125602i	$-0.959914\pi$
$101$	−1.22099e7	+	8.87098e6i	−1.17920	+	0.856736i	−0.187115	+	0.982338i	$0.559914\pi$
$102$	−1.02914e6	−	458203.i	−0.0960227	−	0.0427520i
$103$	−328378.	+	69799.0i	−0.0296104	+	0.00629388i	−0.222693	−	0.974889i	$-0.571485\pi$
$103$	−328378.	+	69799.0i	−0.0296104	+	0.00629388i	0.193083	+	0.981182i	$0.438151\pi$
$104$	−801699.	+	7.62766e6i	−0.0698867	+	0.664928i
$105$	−1.43097e6	−	1.58925e6i	−0.120633	−	0.133977i
$106$	−613495.	+	681355.i	−0.0500312	+	0.0555652i
$107$	−130884.	−	1.24528e6i	−0.0103286	−	0.0982704i	0.988143	−	0.153536i	$-0.0490661\pi$
$107$	−130884.	−	1.24528e6i	−0.0103286	−	0.0982704i	−0.998472	+	0.0552656i	$0.982399\pi$
$108$	4.01497e6	+	1.23568e7i	0.306689	+	0.943893i
$109$	−5.61723e6	−	1.72881e7i	−0.415460	−	1.27866i	−0.911838	−	0.410549i	$-0.865337\pi$
$109$	−5.61723e6	−	1.72881e7i	−0.415460	−	1.27866i	0.496378	−	0.868106i	$-0.334663\pi$
$110$	−275903.	−	2.62504e6i	−0.0197643	−	0.188045i
$111$	−1.28060e7	+	1.42225e7i	−0.888758	+	0.987066i
$112$	−3.76947e6	−	4.18642e6i	−0.253523	−	0.281566i
$113$	−2.78369e6	+	2.64850e7i	−0.181487	+	1.72673i	0.402887	+	0.915250i	$0.368007\pi$
$113$	−2.78369e6	+	2.64850e7i	−0.181487	+	1.72673i	−0.584374	+	0.811484i	$0.698660\pi$
$114$	2.81844e6	−	599079.i	0.178173	−	0.0378719i
$115$	1.27907e7	+	5.69478e6i	0.784245	+	0.349168i
$116$	−2.09382e6	+	1.52125e6i	−0.124548	+	0.0904893i
$117$	1.21752e7	−	5.42075e6i	0.702790	−	0.312902i
$118$	−1.76977e6	+	3.06533e6i	−0.0991585	+	0.171748i
$119$	−2.70129e6	−	4.67877e6i	−0.146946	−	0.254517i
$120$	2.78959e6	+	2.02676e6i	0.147369	+	0.107070i
$121$	−1.77431e7	−	3.77141e6i	−0.910502	−	0.193533i
$122$	−882549.	+	2.71621e6i	−0.0440027	+	0.135426i
$123$	4.90663e6			0.237747
$124$	−194535.	−	2.00565e7i	−0.00916268	−	0.944666i
$125$	−2.10417e7			−0.963597
$126$	388502.	−	1.19569e6i	0.0173020	−	0.0532501i
$127$	7.70638e6	+	1.63804e6i	0.333839	+	0.0709598i	0.371782	−	0.928320i	$-0.378747\pi$
$127$	7.70638e6	+	1.63804e6i	0.333839	+	0.0709598i	−0.0379423	+	0.999280i	$0.512080\pi$
$128$	1.56405e7	+	1.13635e7i	0.659199	+	0.478936i
$129$	−1.17231e7	−	2.03050e7i	−0.480815	−	0.832795i
$130$	2.49190e6	−	4.31610e6i	0.0994784	−	0.172302i
$131$	7.26730e6	−	3.23561e6i	0.282438	−	0.125750i	−0.260628	−	0.965439i	$-0.583930\pi$
$131$	7.26730e6	−	3.23561e6i	0.282438	−	0.125750i	0.543067	+	0.839690i	$0.317263\pi$
$132$	1.93178e7	−	1.40352e7i	0.731055	−	0.531142i
$133$	1.26238e7	+	5.62050e6i	0.465276	+	0.207154i
$134$	−1.08485e6	+	230592.i	−0.0389497	+	0.00827901i
$135$	1.81666e6	−	1.72844e7i	0.0635485	−	0.604624i
$136$	5.82876e6	+	6.47349e6i	0.198696	+	0.220675i
$137$	−1.60468e7	+	1.78217e7i	−0.533169	+	0.592145i	−0.948204	−	0.317661i	$-0.897103\pi$
$137$	−1.60468e7	+	1.78217e7i	−0.533169	+	0.592145i	0.415035	+	0.909805i	$0.363769\pi$
$138$	−774853.	−	7.37224e6i	−0.0250982	−	0.238793i
$139$	7.57857e6	+	2.33244e7i	0.239351	+	0.736647i	0.996514	+	0.0834214i	$0.0265847\pi$
$139$	7.57857e6	+	2.33244e7i	0.239351	+	0.736647i	−0.757163	+	0.653226i	$0.773415\pi$
$140$	2.48237e6	+	7.63994e6i	0.0764571	+	0.235311i
$141$	−823632.	−	7.83633e6i	−0.0247438	−	0.235421i
$142$	4.33688e6	−	4.81659e6i	0.127107	−	0.141166i
$143$	−4.75385e7	−	5.27968e7i	−1.35947	−	1.50984i
$144$	1.64982e6	−	1.56970e7i	0.0460435	−	0.438075i
$145$	3.38630e6	−	719780.i	0.0922439	−	0.0196070i
$146$	−2.44279e6	−	1.08760e6i	−0.0649607	−	0.0289224i
$147$	1.70551e7	−	1.23913e7i	0.442838	−	0.321740i
$148$	6.56746e7	−	2.92402e7i	1.66526	−	0.741421i
$149$	−2.47083e7	+	4.27960e7i	−0.611914	+	1.05987i	0.379003	+	0.925395i	$0.376267\pi$
$149$	−2.47083e7	+	4.27960e7i	−0.611914	+	1.05987i	−0.990917	+	0.134471i	$0.957066\pi$
$150$	2.22495e6	+	3.85373e6i	0.0538271	+	0.0932313i
$151$	3.66752e7	+	2.66461e7i	0.866869	+	0.629817i	0.929745	−	0.368204i	$-0.120027\pi$
$151$	3.66752e7	+	2.66461e7i	0.866869	+	0.629817i	−0.0628758	+	0.998021i	$0.520027\pi$
$152$	−2.17936e7	−	4.63238e6i	−0.503358	−	0.106992i
$153$	4.67753e6	−	1.43959e7i	0.105584	−	0.324953i
$154$	−6.70193e6			−0.147869
$155$	−1.06744e7	+	2.46148e7i	−0.230240	+	0.530927i
$156$	4.50858e7			0.950831
$157$	4.54762e6	−	1.39961e7i	0.0937854	−	0.288642i	−0.893150	−	0.449759i	$-0.851510\pi$
$157$	4.54762e6	−	1.39961e7i	0.0937854	−	0.288642i	0.986935	+	0.161117i	$0.0515098\pi$
$158$	3.99519e6	+	849203.i	0.0805819	+	0.0171282i
$159$	8.97587e6	+	6.52135e6i	0.177087	+	0.128661i
$160$	−9.80631e6	−	1.69850e7i	−0.189272	−	0.327828i
$161$	1.77751e7	−	3.07873e7i	0.335677	−	0.581409i
$162$	−2.29008e6	+	1.01961e6i	−0.0423202	+	0.0188422i
$163$	−6.10722e7	+	4.43715e7i	−1.10455	+	0.802505i	−0.981797	−	0.189931i	$-0.939173\pi$
$163$	−6.10722e7	+	4.43715e7i	−1.10455	+	0.802505i	−0.122757	+	0.992437i	$0.539173\pi$
$164$	−1.68375e7	−	7.49654e6i	−0.298074	−	0.132711i
$165$	−3.12425e7	+	6.64079e6i	−0.541441	+	0.115087i
$166$	2.64472e6	−	2.51628e7i	0.0448747	−	0.426954i
$167$	1.37201e7	+	1.52377e7i	0.227955	+	0.253170i	0.846262	−	0.532767i	$-0.178848\pi$
$167$	1.37201e7	+	1.52377e7i	0.227955	+	0.253170i	−0.618307	+	0.785937i	$0.712181\pi$
$168$	5.85830e6	−	6.50631e6i	0.0953212	−	0.105865i
$169$	−7.46292e6	−	7.10049e7i	−0.118934	−	1.13158i
$170$	−1.74917e6	−	5.38338e6i	−0.0273061	−	0.0840395i
$171$	1.19640e7	+	3.68214e7i	0.182974	+	0.563137i
$172$	9.20599e6	+	8.75892e7i	0.137950	+	1.31250i
$173$	−5.52138e6	+	6.13211e6i	−0.0810749	+	0.0900428i	−0.782317	−	0.622880i	$-0.785962\pi$
$173$	−5.52138e6	+	6.13211e6i	−0.0810749	+	0.0900428i	0.701242	+	0.712923i	$0.252629\pi$
$174$	−1.22646e6	−	1.36212e6i	−0.0176494	−	0.0196017i
$175$	−2.23070e6	+	2.12237e7i	−0.0314636	+	0.299356i
$176$	−8.22992e7	+	1.74932e7i	−1.13789	+	0.241867i
$177$	3.91287e7	+	1.74212e7i	0.530383	+	0.236142i
$178$	−2.26825e7	+	1.64798e7i	−0.301454	+	0.219019i
$179$	−1.28703e7	+	5.73021e6i	−0.167727	+	0.0746767i	−0.488883	−	0.872350i	$-0.662595\pi$
$179$	−1.28703e7	+	5.73021e6i	−0.167727	+	0.0746767i	0.321156	+	0.947026i	$0.395929\pi$
$180$	−1.12535e7	+	1.94916e7i	−0.143825	+	0.249111i
$181$	1.10399e6	+	1.91216e6i	0.0138385	+	0.0239690i	0.872862	−	0.487968i	$-0.162262\pi$
$181$	1.10399e6	+	1.91216e6i	0.0138385	+	0.0239690i	−0.859023	+	0.511937i	$0.828928\pi$
$182$	−1.02375e7	−	7.43801e6i	−0.125877	−	0.0914549i
$183$	3.38049e7	+	7.18545e6i	0.407756	+	0.0866713i
$184$	−1.77128e7	+	5.45145e7i	−0.209617	+	0.645133i
$185$	−9.61629e7			−1.11662
$186$	1.41119e7	−	1.62175e6i	0.160802	−	0.0184795i
$187$	−8.06905e7			−0.902354
$188$	−9.14630e6	+	2.81494e7i	−0.100391	+	0.308970i
$189$	−4.31640e7	−	9.17479e6i	−0.465056	−	0.0988507i
$190$	1.17130e7	+	8.50997e6i	0.123888	+	0.0900099i
$191$	5.31881e7	+	9.21245e7i	0.552329	+	0.956661i	0.998106	+	0.0615174i	$0.0195940\pi$
$191$	5.31881e7	+	9.21245e7i	0.552329	+	0.956661i	−0.445777	+	0.895144i	$0.647073\pi$
$192$	2.30678e7	−	3.99546e7i	0.235208	−	0.407392i
$193$	1.41411e8	−	6.29603e7i	1.41590	−	0.630400i	0.450884	−	0.892582i	$-0.351109\pi$
$193$	1.41411e8	−	6.29603e7i	1.41590	−	0.630400i	0.965018	+	0.262182i	$0.0844421\pi$
$194$	1.62373e7	−	1.17971e7i	0.159664	−	0.116003i
$195$	−5.50947e7	−	2.45297e7i	−0.532094	−	0.236904i
$196$	−7.74580e7	+	1.64642e7i	−0.734802	+	0.156187i
$197$	−1.41080e7	+	1.34229e8i	−0.131472	+	1.25088i	0.707505	+	0.706708i	$0.249821\pi$
$197$	−1.41080e7	+	1.34229e8i	−0.131472	+	1.25088i	−0.838977	+	0.544167i	$0.816846\pi$
$198$	−1.25645e7	−	1.39542e7i	−0.115031	−	0.127755i
$199$	9.25557e7	−	1.02794e8i	0.832564	−	0.924655i	−0.165541	−	0.986203i	$-0.552937\pi$
$199$	9.25557e7	−	1.02794e8i	0.832564	−	0.924655i	0.998104	+	0.0615475i	$0.0196036\pi$
$200$	−3.59671e6	−	3.42205e7i	−0.0317908	−	0.302469i
$201$	4.14732e6	+	1.27641e7i	0.0360231	+	0.110868i
$202$	1.24068e7	+	3.81843e7i	0.105909	+	0.325953i
$203$	−918826.	−	8.74205e6i	−0.00770899	−	0.0733461i
$204$	3.42640e7	−	3.80541e7i	0.282574	−	0.313831i
$205$	1.64967e7	+	1.83215e7i	0.133740	+	0.148533i
$206$	−93353.4	+	888198.i	−0.000744038	+	0.00707904i
$207$	9.74269e7	−	2.07087e7i	0.763454	−	0.162277i
$208$	−1.45131e8	−	6.46165e7i	−1.11825	−	0.497877i
$209$	1.66971e8	−	1.21311e8i	1.26511	−	0.919157i
$210$	−5.19727e6	+	2.31397e6i	−0.0387264	+	0.0172421i
$211$	6.53310e7	−	1.13157e8i	0.478774	−	0.829262i	−0.520929	−	0.853600i	$-0.674414\pi$
$211$	6.53310e7	−	1.13157e8i	0.478774	−	0.829262i	0.999704	+	0.0243381i	$0.00774783\pi$
$212$	−2.08379e7	−	3.60923e7i	−0.150203	−	0.260159i
$213$	−6.34517e7	−	4.61003e7i	−0.449898	−	0.326870i
$214$	−3.25823e6	−	692558.i	−0.0227265	−	0.00483067i
$215$	3.64048e7	−	1.12042e8i	0.249818	−	0.768861i
$216$	7.11510e7			0.480389
$217$	5.93236e7	+	3.34876e7i	0.394111	+	0.222472i
$218$	−4.83577e7			−0.316131
$219$	−9.99901e6	+	3.07738e7i	−0.0643284	+	0.197982i
$220$	1.17357e8	+	2.49450e7i	0.743071	+	0.157945i
$221$	−1.23259e8	−	8.95529e7i	−0.768149	−	0.558093i
$222$	2.54565e7	+	4.40919e7i	0.156158	+	0.270473i
$223$	3.04499e6	−	5.27408e6i	0.0183873	−	0.0318478i	−0.856685	−	0.515839i	$-0.827480\pi$
$223$	3.04499e6	−	5.27408e6i	0.0183873	−	0.0318478i	0.875073	+	0.483992i	$0.160813\pi$
$224$	−4.54929e7	+	2.02547e7i	−0.270443	+	0.120409i
$225$	−4.83724e7	+	3.51446e7i	−0.283113	+	0.205693i
$226$	6.47204e7	+	2.88154e7i	0.372960	+	0.166052i
$227$	5.55039e7	−	1.17977e7i	0.314944	−	0.0669434i	−0.0477278	−	0.998860i	$-0.515198\pi$
$227$	5.55039e7	−	1.17977e7i	0.314944	−	0.0669434i	0.362672	+	0.931917i	$0.381865\pi$
$228$	−1.36906e7	+	1.30257e8i	−0.0764981	+	0.727831i
$229$	−4.46190e7	−	4.95544e7i	−0.245525	−	0.272683i	0.607768	−	0.794114i	$-0.292065\pi$
$229$	−4.46190e7	−	4.95544e7i	−0.245525	−	0.272683i	−0.853293	+	0.521431i	$0.825398\pi$
$230$	2.49230e7	−	2.76798e7i	0.135068	−	0.150008i
$231$	8.47721e6	+	8.06553e7i	0.0452492	+	0.430518i
$232$	4.37971e6	+	1.34794e7i	0.0230270	+	0.0708698i
$233$	5.07578e7	+	1.56216e8i	0.262880	+	0.809060i	0.992174	+	0.124860i	$0.0398483\pi$
$233$	5.07578e7	+	1.56216e8i	0.262880	+	0.809060i	−0.729295	+	0.684200i	$0.760152\pi$
$234$	−3.70600e6	−	3.52603e7i	−0.0189082	−	0.179900i
$235$	2.64919e7	−	2.94223e7i	0.133161	−	0.147890i
$236$	−1.07657e8	−	1.19565e8i	−0.533150	−	0.592123i
$237$	5.16638e6	−	4.91548e7i	0.0252097	−	0.239854i
$238$	−1.40582e7	+	2.98817e6i	−0.0675945	+	0.0143677i
$239$	1.74066e8	+	7.74993e7i	0.824749	+	0.367202i	0.775314	−	0.631575i	$-0.217591\pi$
$239$	1.74066e8	+	7.74993e7i	0.824749	+	0.367202i	0.0494347	+	0.998777i	$0.484258\pi$
$240$	−5.77822e7	+	4.19812e7i	−0.269808	+	0.196027i
$241$	−1.90918e8	+	8.50020e7i	−0.878591	+	0.391174i	−0.795919	−	0.605403i	$-0.793012\pi$
$241$	−1.90918e8	+	8.50020e7i	−0.878591	+	0.391174i	−0.0826715	+	0.996577i	$0.526345\pi$
$242$	−2.41280e7	+	4.17909e7i	−0.109438	+	0.189552i
$243$	−1.02325e8	−	1.77232e8i	−0.457467	−	0.792356i
$244$	−1.05026e8	−	7.63059e7i	−0.462842	−	0.336274i
$245$	1.03611e8	+	2.20232e7i	0.450117	+	0.0956752i
$246$	4.03358e6	−	1.24141e7i	0.0172750	−	0.0531670i
$247$	3.89692e8			1.64544
$248$	−1.04787e8	−	3.29273e7i	−0.436242	−	0.137080i
$249$	−3.06171e8			−1.25680
$250$	−1.72977e7	+	5.32368e7i	−0.0700162	+	0.215488i
$251$	3.93056e8	+	8.35466e7i	1.56890	+	0.333481i	0.908649	−	0.417561i	$-0.137115\pi$
$251$	3.93056e8	+	8.35466e7i	1.56890	+	0.333481i	0.660255	+	0.751042i	$0.270448\pi$
$252$	4.62330e7	+	3.35902e7i	0.181991	+	0.132224i
$253$	−2.65481e8	−	4.59826e8i	−1.03065	−	1.78514i
$254$	1.04795e7	−	1.81511e7i	0.0401258	−	0.0694999i
$255$	−6.25745e7	+	2.78600e7i	−0.236324	+	0.105218i
$256$	−1.06801e8	+	7.75953e7i	−0.397864	+	0.289065i
$257$	−8.35739e7	−	3.72095e7i	−0.307118	−	0.136738i	0.247391	−	0.968916i	$-0.420427\pi$
$257$	−8.35739e7	−	3.72095e7i	−0.307118	−	0.136738i	−0.554508	+	0.832178i	$0.687094\pi$
$258$	−6.10101e7	+	1.29681e7i	−0.221173	+	0.0470118i
$259$	−2.55223e7	+	2.42828e8i	−0.0912789	+	0.868461i
$260$	1.51585e8	+	1.68352e8i	0.534870	+	0.594033i
$261$	1.64795e7	−	1.83023e7i	0.0573721	−	0.0637182i
$262$	−2.21209e6	−	2.10466e7i	−0.00759886	−	0.0722983i
$263$	2.19062e7	+	6.74202e7i	0.0742542	+	0.228531i	0.981294	−	0.192513i	$-0.0616638\pi$
$263$	2.19062e7	+	6.74202e7i	0.0742542	+	0.228531i	−0.907040	+	0.421044i	$0.861664\pi$
$264$	−4.04078e7	−	1.24362e8i	−0.135161	−	0.415983i
$265$	5.82717e6	+	5.54418e7i	0.0192352	+	0.183011i
$266$	2.45979e7	−	2.73187e7i	0.0801331	−	0.0889968i
$267$	2.27019e8	+	2.52131e8i	0.729917	+	0.810655i
$268$	5.26968e6	−	5.01376e7i	0.0167229	−	0.159108i
$269$	−5.04140e8	+	1.07158e8i	−1.57913	+	0.335654i	−0.912290	−	0.409546i	$-0.865687\pi$
$269$	−5.04140e8	+	1.07158e8i	−1.57913	+	0.335654i	−0.666841	+	0.745200i	$0.732354\pi$
$270$	−4.22372e7	−	1.88052e7i	−0.130594	−	0.0581440i
$271$	−4.44604e8	+	3.23023e8i	−1.35700	+	0.985919i	−0.358372	+	0.933579i	$0.616668\pi$
$271$	−4.44604e8	+	3.23023e8i	−1.35700	+	0.985919i	−0.998629	+	0.0523407i	$0.983332\pi$
$272$	−1.64835e8	+	7.33891e7i	−0.496657	+	0.221126i
$273$	−7.65645e7	+	1.32614e8i	−0.227750	+	0.394474i
$274$	3.18986e7	+	5.52500e7i	0.0936795	+	0.162258i
$275$	2.57862e8	+	1.87347e8i	0.747691	+	0.543229i
$276$	3.29589e8	+	7.00563e7i	0.943606	+	0.200570i
$277$	−2.73504e7	+	8.41757e7i	−0.0773186	+	0.237962i	−0.982244	−	0.187608i	$-0.939926\pi$
$277$	−2.73504e7	+	8.41757e7i	−0.0773186	+	0.237962i	0.904925	+	0.425570i	$0.139926\pi$
$278$	6.52425e7			0.182127
$279$	4.14918e7	+	1.86300e8i	0.114379	+	0.513568i
$280$	4.39912e7			0.119760
$281$	9.12005e7	−	2.80686e8i	0.245203	−	0.754656i	−0.750401	−	0.660983i	$-0.770139\pi$
$281$	9.12005e7	−	2.80686e8i	0.245203	−	0.754656i	0.995603	−	0.0936725i	$-0.0298606\pi$
$282$	−2.05035e7	−	4.35816e6i	−0.0544448	−	0.0115726i
$283$	1.27055e6	+	923108.i	0.00333226	+	0.00242103i	0.589450	−	0.807805i	$-0.299344\pi$
$283$	1.27055e6	+	923108.i	0.00333226	+	0.00242103i	−0.586118	+	0.810226i	$0.699344\pi$
$284$	1.47306e8	+	2.55141e8i	0.381598	+	0.660946i
$285$	8.75988e7	−	1.51726e8i	0.224151	−	0.388241i
$286$	−1.72659e8	+	7.68729e7i	−0.436424	+	0.194309i
$287$	5.06434e7	−	3.67946e7i	0.126455	−	0.0918750i
$288$	−1.27461e8	−	5.67492e7i	−0.314415	−	0.139986i
$289$	2.32112e8	−	4.93370e7i	0.565660	−	0.120235i
$290$	962678.	−	9.15927e6i	0.00231787	−	0.0220530i
$291$	−1.62512e8	−	1.80488e8i	−0.386599	−	0.429361i
$292$	8.13298e7	−	9.03259e7i	0.191166	−	0.212311i
$293$	−4.40928e7	−	4.19515e8i	−0.102407	−	0.974341i	−0.918232	−	0.396042i	$-0.870383\pi$
$293$	−4.40928e7	−	4.19515e8i	−0.102407	−	0.974341i	0.815825	−	0.578299i	$-0.196283\pi$
$294$	−1.73303e7	−	5.33371e7i	−0.0397731	−	0.122409i
$295$	6.65047e7	+	2.04680e8i	0.150826	+	0.464194i
$296$	−4.11513e7	−	3.91529e8i	−0.0922280	−	0.877491i
$297$	−4.41011e8	+	4.89792e8i	−0.976791	+	1.08484i
$298$	8.79648e7	+	9.76948e7i	0.192554	+	0.213853i
$299$	1.04794e8	−	9.97048e8i	0.226719	−	2.15708i
$300$	−1.97851e8	+	4.20546e7i	−0.423072	+	0.0899267i
$301$	−2.73265e8	−	1.21665e8i	−0.577565	−	0.257149i
$302$	9.75660e7	−	7.08858e7i	0.203833	−	0.148093i
$303$	4.43841e8	−	1.97611e8i	0.916597	−	0.408095i
$304$	2.30754e8	−	3.99677e8i	0.471076	−	0.815928i
$305$	8.68259e7	+	1.50387e8i	0.175227	+	0.303501i
$306$	−3.25774e7	−	2.36689e7i	−0.0649968	−	0.0472229i
$307$	1.11342e8	+	2.36665e7i	0.219622	+	0.0466821i	0.316408	−	0.948623i	$-0.397523\pi$
$307$	1.11342e8	+	2.36665e7i	0.219622	+	0.0466821i	−0.0967864	+	0.995305i	$0.530856\pi$
$308$	9.41381e7	−	2.89727e8i	0.183585	−	0.565017i
$309$	1.08072e7			0.0208382
$310$	5.35019e7	+	4.72418e7i	0.102001	+	0.0900660i
$311$	7.01973e8			1.32330			0.661651	−	0.749812i	$-0.269856\pi$
$311$	7.01973e8			1.32330			0.661651	+	0.749812i	$0.269856\pi$
$312$	7.62963e7	−	2.34816e8i	0.142221	−	0.437710i
$313$	−1.17483e8	−	2.49718e7i	−0.216556	−	0.0460303i	0.0983561	−	0.995151i	$-0.468642\pi$
$313$	−1.17483e8	−	2.49718e7i	−0.216556	−	0.0460303i	−0.314912	+	0.949121i	$0.601975\pi$
$314$	−3.16727e7	−	2.30115e7i	−0.0577339	−	0.0419461i
$315$	−3.82212e7	−	6.62011e7i	−0.0688997	−	0.119338i
$316$	−9.28295e7	+	1.60785e8i	−0.165494	+	0.286643i
$317$	−2.41832e8	+	1.07671e8i	−0.426390	+	0.189841i	−0.608701	−	0.793400i	$-0.708309\pi$
$317$	−2.41832e8	+	1.07671e8i	−0.426390	+	0.189841i	0.182311	+	0.983241i	$0.441642\pi$
$318$	2.38782e7	−	1.73486e7i	0.0416397	−	0.0302530i
$319$	−1.19936e8	−	5.33991e7i	−0.206863	−	0.0921014i
$320$	2.26749e8	−	4.81970e7i	0.386830	−	0.0822233i
$321$	−4.21338e6	+	4.00876e7i	−0.00710989	+	0.0676461i
$322$	−6.32817e7	−	7.02814e7i	−0.105629	−	0.117313i
$323$	2.96156e8	−	3.28915e8i	0.489003	−	0.543093i
$324$	−1.19107e7	−	1.13323e8i	−0.0194550	−	0.185101i
$325$	1.85973e8	+	5.72366e8i	0.300509	+	0.924873i
$326$	6.20574e7	+	1.90993e8i	0.0992047	+	0.305321i
$327$	6.11672e7	+	5.81967e8i	0.0967390	+	0.920410i
$328$	−6.75368e7	+	7.50072e7i	−0.105677	+	0.117367i
$329$	−6.72654e7	−	7.47058e7i	−0.104137	−	0.115656i
$330$	−8.88180e6	+	8.45046e7i	−0.0136051	+	0.129444i
$331$	−8.64565e8	+	1.83769e8i	−1.31039	+	0.278531i	−0.809571	−	0.587022i	$-0.800300\pi$
$331$	−8.64565e8	+	1.83769e8i	−1.31039	+	0.278531i	−0.500816	+	0.865554i	$0.666967\pi$
$332$	1.05065e9	+	4.67780e8i	1.57571	+	0.701549i
$333$	−5.53447e8	+	4.02102e8i	−0.821336	+	0.596736i
$334$	4.98312e7	−	2.21863e7i	0.0731794	−	0.0325816i
$335$	−3.37178e7	+	5.84009e7i	−0.0490007	+	0.0848717i
$336$	9.06743e7	+	1.57052e8i	0.130406	+	0.225869i
$337$	−8.58702e8	−	6.23883e8i	−1.22219	−	0.887971i	−0.225907	−	0.974149i	$-0.572535\pi$
$337$	−8.58702e8	−	6.23883e8i	−1.22219	−	0.887971i	−0.996280	+	0.0861781i	$0.972535\pi$
$338$	−1.85782e8	−	3.94892e7i	−0.261695	−	0.0556250i
$339$	2.64919e8	−	8.15335e8i	0.369329	−	1.13668i
$340$	2.57295e8			0.355022
$341$	8.76163e8	−	5.17248e8i	1.19659	−	0.706413i
$342$	1.02996e8			0.139229
$343$	1.87631e8	−	5.77468e8i	0.251058	−	0.772677i
$344$	4.71761e8	+	1.00276e8i	0.624838	+	0.132813i
$345$	−3.64641e8	−	2.64927e8i	−0.478078	−	0.347344i
$346$	1.09757e7	+	1.90105e7i	0.0142451	+	0.0246733i
$347$	−6.78468e8	+	1.17514e9i	−0.871718	+	1.50986i	−0.0115006	+	0.999934i	$0.503661\pi$
$347$	−6.78468e8	+	1.17514e9i	−0.871718	+	1.50986i	−0.860218	+	0.509927i	$0.829672\pi$
$348$	7.61125e7	−	3.38875e7i	0.0968118	−	0.0431034i
$349$	−4.66404e8	+	3.38862e8i	−0.587318	+	0.426712i	−0.841355	−	0.540483i	$-0.818242\pi$
$349$	−4.66404e8	+	3.38862e8i	−0.587318	+	0.426712i	0.254037	+	0.967195i	$0.418242\pi$
$350$	5.18636e7	+	2.30912e7i	0.0646584	+	0.0287878i
$351$	−1.21725e9	+	2.58736e8i	−1.50247	+	0.319360i
$352$	−7.77444e7	+	7.39689e8i	−0.0950101	+	0.903961i
$353$	2.34893e8	+	2.60875e8i	0.284223	+	0.315662i	0.868303	−	0.496035i	$-0.165211\pi$
$353$	2.34893e8	+	2.60875e8i	0.284223	+	0.315662i	−0.584080	+	0.811696i	$0.698544\pi$
$354$	7.62434e7	−	8.46768e7i	0.0913462	−	0.101450i
$355$	−4.11931e7	−	3.91926e8i	−0.0488680	−	0.464948i
$356$	−3.93821e8	−	1.21206e9i	−0.462620	−	1.42380i
$357$	5.37437e7	+	1.65406e8i	0.0625157	+	0.192403i
$358$	3.91758e6	+	3.72733e7i	0.00451260	+	0.0429345i
$359$	−4.10630e8	+	4.56051e8i	−0.468404	+	0.520215i	−0.930340	−	0.366698i	$-0.880488\pi$
$359$	−4.10630e8	+	4.56051e8i	−0.468404	+	0.520215i	0.461936	+	0.886913i	$0.347155\pi$
$360$	8.24725e7	+	9.15950e7i	0.0931645	+	0.103470i
$361$	−2.48976e7	+	2.36885e8i	−0.0278537	+	0.265010i
$362$	5.74545e6	−	1.22123e6i	0.00636567	−	0.00135307i
$363$	5.33457e8	+	2.37511e8i	0.585365	+	0.260621i
$364$	4.65350e8	−	3.38096e8i	0.505737	−	0.367439i
$365$	−1.48528e8	+	6.61290e7i	−0.159876	+	0.0711815i
$366$	4.59696e7	−	7.96217e7i	0.0490102	−	0.0848882i
$367$	7.32202e8	+	1.26821e9i	0.773214	+	1.33925i	0.935793	+	0.352551i	$0.114686\pi$
$367$	7.32202e8	+	1.26821e9i	0.773214	+	1.33925i	−0.162579	+	0.986696i	$0.551981\pi$
$368$	−9.60542e8	−	6.97875e8i	−1.00473	−	0.729978i
$369$	1.71555e8	+	3.64651e7i	0.177750	+	0.0377820i
$370$	−7.90524e7	+	2.43298e8i	−0.0811352	+	0.249708i
$371$	1.41547e8			0.143910
$372$	−1.28113e8	+	6.32845e8i	−0.129031	+	0.637378i
$373$	2.84205e8			0.283564			0.141782	−	0.989898i	$-0.454717\pi$
$373$	2.84205e8			0.283564			0.141782	+	0.989898i	$0.454717\pi$
$374$	−6.63331e7	+	2.04152e8i	−0.0655661	+	0.201792i
$375$	6.62566e8	+	1.40833e8i	0.648813	+	0.137910i
$376$	1.31130e8	+	9.52716e7i	0.127217	+	0.0924285i
$377$	−1.23945e8	−	2.14679e8i	−0.119134	−	0.206345i
$378$	−5.86965e7	+	1.01665e8i	−0.0558973	+	0.0968170i
$379$	−1.33209e9	+	5.93085e8i	−1.25689	+	0.559603i	−0.923649	−	0.383240i	$-0.874808\pi$
$379$	−1.33209e9	+	5.93085e8i	−1.25689	+	0.559603i	−0.333239	+	0.942842i	$0.608142\pi$
$380$	−5.32415e8	+	3.86822e8i	−0.497746	+	0.361633i
$381$	−2.31697e8	−	1.03158e8i	−0.214627	−	0.0955579i
$382$	2.76805e8	−	5.88367e7i	0.254069	−	0.0540041i
$383$	−1.20137e8	+	1.14303e9i	−0.109265	+	1.03959i	0.793240	+	0.608909i	$0.208393\pi$
$383$	−1.20137e8	+	1.14303e9i	−0.109265	+	1.03959i	−0.902505	+	0.430679i	$0.858274\pi$
$384$	−4.16437e8	−	4.62500e8i	−0.375310	−	0.416823i
$385$	−2.72668e8	+	3.02828e8i	−0.243512	+	0.270448i
$386$	−4.30441e7	−	4.09537e8i	−0.0380941	−	0.362442i
$387$	−2.58982e8	−	7.97064e8i	−0.227133	−	0.699044i
$388$	2.81917e8	+	8.67652e8i	0.245025	+	0.754110i
$389$	−1.62191e8	−	1.54315e9i	−0.139702	−	1.32918i	−0.809713	−	0.586827i	$-0.800377\pi$
$389$	−1.62191e8	−	1.54315e9i	−0.139702	−	1.32918i	0.670010	−	0.742352i	$-0.266290\pi$
$390$	−1.07353e8	+	1.19228e8i	−0.0916410	+	0.101778i
$391$	−7.61905e8	−	8.46181e8i	−0.644588	−	0.715887i
$392$	−4.53292e7	+	4.31279e8i	−0.0380082	+	0.361624i
$393$	−2.50491e8	+	5.32435e7i	−0.208170	+	0.0442479i
$394$	3.28010e8	+	1.46039e8i	0.270178	+	0.120291i
$395$	2.00916e8	−	1.45974e8i	0.164030	−	0.119175i
$396$	7.79733e8	−	3.47160e8i	0.630976	−	0.280929i
$397$	3.89638e8	−	6.74873e8i	0.312532	−	0.541322i	−0.666378	−	0.745614i	$-0.732156\pi$
$397$	3.89638e8	−	6.74873e8i	0.312532	−	0.541322i	0.978910	+	0.204293i	$0.0654894\pi$
$398$	−1.83987e8	−	3.18675e8i	−0.146284	−	0.253371i
$399$	−3.59885e8	−	2.61472e8i	−0.283634	−	0.206072i
$400$	6.97154e8	+	1.48185e8i	0.544652	+	0.115769i
$401$	1.48348e8	−	4.56569e8i	0.114889	−	0.353591i	−0.877035	−	0.480426i	$-0.840482\pi$
$401$	1.48348e8	−	4.56569e8i	0.114889	−	0.353591i	0.991924	+	0.126835i	$0.0404819\pi$
$402$	3.57035e7			0.0274106
$403$	1.91244e9	+	1.82271e8i	1.45553	+	0.138723i
$404$	−1.82500e9			−1.37698
$405$	−4.71005e7	+	1.44960e8i	−0.0352316	+	0.108432i
$406$	−2.28733e7	−	4.86187e6i	−0.0169624	−	0.00360547i
$407$	2.95029e9	+	2.14351e9i	2.16912	+	1.57596i
$408$	−1.40210e8	−	2.42851e8i	−0.102204	−	0.177023i
$409$	7.99061e8	−	1.38401e9i	0.577495	−	1.00025i	−0.418271	−	0.908322i	$-0.637364\pi$
$409$	7.99061e8	−	1.38401e9i	0.577495	−	1.00025i	0.995766	−	0.0919280i	$-0.0293030\pi$
$410$	5.99160e7	−	2.66763e7i	0.0429338	−	0.0191154i
$411$	6.24566e8	−	4.53774e8i	0.443743	−	0.322398i
$412$	−3.70859e7	−	1.65117e7i	−0.0261258	−	0.0116319i
$413$	5.34506e8	−	1.13613e8i	0.373359	−	0.0793600i
$414$	2.76971e7	−	2.63520e8i	0.0191837	−	0.182521i
$415$	−1.02939e9	−	1.14325e9i	−0.706986	−	0.785187i
$416$	−9.39689e8	+	1.04363e9i	−0.639967	+	0.710755i
$417$	−8.25247e7	−	7.85170e8i	−0.0557324	−	0.530258i
$418$	−1.69664e8	−	5.22173e8i	−0.113625	−	0.349702i
$419$	−5.97160e8	−	1.83787e9i	−0.396590	−	1.22058i	−0.927716	−	0.373286i	$-0.878231\pi$
$419$	−5.97160e8	−	1.83787e9i	−0.396590	−	1.22058i	0.531126	−	0.847293i	$-0.321769\pi$
$420$	−2.70310e7	−	2.57183e8i	−0.0178029	−	0.169383i
$421$	−8.67119e8	+	9.63033e8i	−0.566358	+	0.629005i	−0.956494	−	0.291753i	$-0.905762\pi$
$421$	−8.67119e8	+	9.63033e8i	−0.566358	+	0.629005i	0.390135	+	0.920758i	$0.372428\pi$
$422$	−2.32587e8	−	2.58314e8i	−0.150658	−	0.167323i
$423$	2.94407e7	−	2.80110e8i	0.0189128	−	0.179944i
$424$	−2.23239e8	+	4.74509e7i	−0.142229	+	0.0302318i
$425$	6.24433e8	+	2.78015e8i	0.394570	+	0.175674i
$426$	−1.68798e8	+	1.22639e8i	−0.105788	+	0.0768592i
$427$	4.02798e8	−	1.79337e8i	0.250374	−	0.111474i
$428$	7.57060e7	−	1.31127e8i	0.0466742	−	0.0808422i
$429$	1.14353e9	+	1.98066e9i	0.699275	+	1.21118i
$430$	−2.53547e8	−	1.84213e8i	−0.153787	−	0.111733i
$431$	1.72718e9	+	3.67123e8i	1.03912	+	0.220872i	0.695718	−	0.718315i	$-0.255086\pi$
$431$	1.72718e9	+	3.67123e8i	1.03912	+	0.220872i	0.343405	+	0.939187i	$0.388420\pi$
$432$	−4.55425e8	+	1.40165e9i	−0.271784	+	0.836464i
$433$	2.00815e9			1.18875			0.594373	−	0.804189i	$-0.297400\pi$
$433$	2.00815e9			1.18875			0.594373	+	0.804189i	$0.297400\pi$
$434$	1.33494e8	−	1.22564e8i	0.0783876	−	0.0719693i
$435$	−1.11446e8			−0.0649162
$436$	6.79252e8	−	2.09052e9i	0.392490	−	1.20796i
$437$	2.84875e9	+	6.05521e8i	1.63294	+	0.347092i
$438$	6.96398e7	+	5.05963e7i	0.0396003	+	0.0287713i
$439$	−1.18019e9	−	2.04414e9i	−0.665772	−	1.15315i	−0.979076	−	0.203497i	$-0.934769\pi$
$439$	−1.18019e9	−	2.04414e9i	−0.665772	−	1.15315i	0.313304	−	0.949653i	$-0.398564\pi$
$440$	3.28516e8	−	5.69007e8i	0.183854	−	0.318444i
$441$	6.88403e8	−	3.06497e8i	0.382215	−	0.170173i
$442$	−3.27902e8	+	2.38235e8i	−0.180620	+	0.131228i
$443$	−3.02640e9	−	1.34744e9i	−1.65392	−	0.736371i	−0.654116	−	0.756394i	$-0.726959\pi$
$443$	−3.02640e9	−	1.34744e9i	−1.65392	−	0.736371i	−0.999800	+	0.0200236i	$0.993626\pi$
$444$	−2.26369e9	+	4.81161e8i	−1.22737	+	0.260886i
$445$	−1.78193e8	+	1.69539e9i	−0.0958586	+	0.912034i
$446$	−1.08406e7	−	1.20397e7i	−0.00578603	−	0.00642603i
$447$	1.06446e9	−	1.18220e9i	0.563704	−	0.626057i
$448$	−6.15252e7	−	5.85373e8i	−0.0323281	−	0.307581i
$449$	−4.98737e7	−	1.53495e8i	−0.0260022	−	0.0800264i	0.937213	−	0.348757i	$-0.113396\pi$
$449$	−4.98737e7	−	1.53495e8i	−0.0260022	−	0.0800264i	−0.963215	+	0.268730i	$0.913396\pi$
$450$	4.91528e7	+	1.51277e8i	0.0254275	+	0.0782579i
$451$	−9.77285e7	−	9.29825e8i	−0.0501653	−	0.477291i
$452$	−2.15479e9	+	2.39314e9i	−1.09754	+	1.21894i
$453$	−9.76496e8	−	1.08451e9i	−0.493545	−	0.548137i
$454$	1.57790e7	−	1.50127e8i	0.00791377	−	0.0752945i
$455$	−7.52603e8	+	1.59971e8i	−0.374564	+	0.0796160i
$456$	6.55239e8	+	2.91731e8i	0.323611	+	0.144081i
$457$	−4.24434e8	+	3.08370e8i	−0.208019	+	0.151135i	−0.686917	−	0.726736i	$-0.741036\pi$
$457$	−4.24434e8	+	3.08370e8i	−0.208019	+	0.151135i	0.478898	+	0.877871i	$0.341036\pi$
$458$	−1.62056e8	+	7.21518e7i	−0.0788197	+	0.0350928i
$459$	−7.06700e8	+	1.22404e9i	−0.341107	+	0.590815i
$460$	8.46530e8	+	1.46623e9i	0.405499	+	0.702346i
$461$	3.26843e8	+	2.37465e8i	0.155377	+	0.112888i	0.662757	−	0.748834i	$-0.269386\pi$
$461$	3.26843e8	+	2.37465e8i	0.155377	+	0.112888i	−0.507381	+	0.861722i	$0.669386\pi$
$462$	2.11032e8	+	4.48562e7i	0.0995638	+	0.0211629i
$463$	3.99878e8	−	1.23070e9i	0.187238	−	0.576259i	−0.812742	−	0.582624i	$-0.802026\pi$
$463$	3.99878e8	−	1.23070e9i	0.187238	−	0.576259i	0.999980	+	0.00636494i	$0.00202604\pi$
$464$	−2.93573e8			−0.136428
$465$	5.00864e8	−	7.03632e8i	0.231012	−	0.324534i
$466$	4.36964e8			0.200030
$467$	−8.85999e8	+	2.72682e9i	−0.402554	+	1.23893i	0.520367	+	0.853943i	$0.325795\pi$
$467$	−8.85999e8	+	2.72682e9i	−0.402554	+	1.23893i	−0.922920	+	0.384991i	$0.874205\pi$
$468$	1.57637e9	+	3.35068e8i	0.710884	+	0.151103i
$469$	1.38524e8	+	1.00643e8i	0.0620040	+	0.0450485i
$470$	−5.26621e7	−	9.12135e7i	−0.0233968	−	0.0405244i
$471$	−2.36873e8	+	4.10276e8i	−0.104458	+	0.180927i
$472$	−8.04900e8	+	3.58365e8i	−0.352326	+	0.156866i
$473$	−3.61437e9	+	2.62599e9i	−1.57043	+	1.14098i
$474$	−1.20118e8	−	5.34799e7i	−0.0518064	−	0.0230657i
$475$	−1.71010e9	+	3.63492e8i	−0.732138	+	0.155621i
$476$	6.82880e7	−	6.49717e8i	0.0290215	−	0.276121i
$477$	2.65366e8	+	2.94719e8i	0.111952	+	0.124335i
$478$	3.39173e8	−	3.76689e8i	0.142044	−	0.157756i
$479$	−3.28390e8	−	3.12443e9i	−0.136526	−	1.29896i	−0.821423	−	0.570320i	$-0.806819\pi$
$479$	−3.28390e8	−	3.12443e9i	−0.136526	−	1.29896i	0.684897	−	0.728640i	$-0.259847\pi$
$480$	1.95102e8	+	6.00463e8i	0.0805226	+	0.247823i
$481$	2.12778e9	+	6.54865e9i	0.871806	+	2.68314i
$482$	5.81134e7	+	5.52912e8i	0.0236380	+	0.224901i
$483$	−7.65767e8	+	8.50471e8i	−0.309230	+	0.343435i
$484$	−1.46773e9	−	1.63007e9i	−0.588418	−	0.653505i
$485$	1.27560e8	−	1.21365e9i	0.0507712	−	0.483056i
$486$	−5.32527e8	+	1.13192e8i	−0.210433	+	0.0447290i
$487$	−1.83750e8	−	8.18109e7i	−0.0720903	−	0.0320967i	0.370375	−	0.928882i	$-0.379229\pi$
$487$	−1.83750e8	−	8.18109e7i	−0.0720903	−	0.0320967i	−0.442465	+	0.896786i	$0.645896\pi$
$488$	−5.75147e8	+	4.17869e8i	−0.224032	+	0.162769i
$489$	2.22004e9	−	9.88425e8i	0.858577	−	0.382263i
$490$	1.40896e8	−	2.44038e8i	0.0541017	−	0.0937069i
$491$	1.29324e9	+	2.23995e9i	0.493053	+	0.853992i	0.999968	−	0.00800373i	$-0.00254769\pi$
$491$	1.29324e9	+	2.23995e9i	0.493053	+	0.853992i	−0.506915	+	0.861996i	$0.669214\pi$
$492$	4.80009e8	+	3.48747e8i	0.181707	+	0.132018i
$493$	−2.75392e8	−	5.85364e7i	−0.103511	−	0.0220020i
$494$	3.20353e8	−	9.85947e8i	0.119560	−	0.367967i
$495$	−1.14171e9			−0.423095
$496$	1.31938e9	−	1.85352e9i	0.485495	−	0.682041i
$497$	−1.00062e9			−0.365612
$498$	−2.51693e8	+	7.74632e8i	−0.0913206	+	0.281056i
$499$	−1.52745e8	−	3.24671e7i	−0.0550321	−	0.0116974i	0.180313	−	0.983609i	$-0.442289\pi$
$499$	−1.52745e8	−	3.24671e7i	−0.0550321	−	0.0116974i	−0.235345	+	0.971912i	$0.575622\pi$
$500$	−2.05848e9	−	1.49557e9i	−0.736465	−	0.535073i
$501$	−3.30035e8	−	5.71638e8i	−0.117254	−	0.203090i
$502$	5.34497e8	−	9.25776e8i	0.188574	−	0.326620i
$503$	−1.48735e9	+	6.62211e8i	−0.521105	+	0.232011i	−0.650395	−	0.759596i	$-0.725397\pi$
$503$	−1.48735e9	+	6.62211e8i	−0.521105	+	0.232011i	0.129290	+	0.991607i	$0.458730\pi$
$504$	2.53183e8	−	1.83948e8i	0.0880900	−	0.0640012i
$505$	2.23014e9	+	9.92922e8i	0.770570	+	0.343080i
$506$	−1.38163e9	+	2.93675e8i	−0.474096	+	0.100772i
$507$	−2.40244e8	+	2.28577e9i	−0.0818701	+	0.778942i
$508$	6.37479e8	+	7.07992e8i	0.215746	+	0.239610i
$509$	3.53171e9	−	3.92236e9i	1.18706	−	1.31836i	0.250393	−	0.968144i	$-0.419440\pi$
$509$	3.53171e9	−	3.92236e9i	1.18706	−	1.31836i	0.936667	−	0.350220i	$-0.113893\pi$
$510$	1.90470e7	+	1.81220e8i	0.00635817	+	0.0604939i
$511$	1.27567e8	+	3.92611e8i	0.0422927	+	0.130164i
$512$	8.73215e8	+	2.68748e9i	0.287525	+	0.884912i
$513$	−3.77886e8	−	3.59534e9i	−0.123580	−	1.17579i
$514$	−1.62846e8	+	1.80859e8i	−0.0528939	+	0.0587447i
$515$	3.63354e7	+	4.03545e7i	0.0117221	+	0.0130187i
$516$	2.96357e8	−	2.81965e9i	0.0949601	−	0.903485i
$517$	−1.46861e9	+	3.12163e8i	−0.467401	+	0.0993492i
$518$	5.93391e8	+	2.64195e8i	0.187580	+	0.0835160i
$519$	2.14901e8	−	1.56135e8i	0.0674766	−	0.0490246i
$520$	1.13333e9	−	5.04590e8i	0.353463	−	0.157372i
$521$	−2.90206e9	+	5.02652e9i	−0.899030	+	1.55717i	−0.0702947	+	0.997526i	$0.522394\pi$
$521$	−2.90206e9	+	5.02652e9i	−0.899030	+	1.55717i	−0.828736	+	0.559640i	$0.810939\pi$
$522$	−3.27587e7	−	5.67398e7i	−0.0100805	−	0.0174599i
$523$	−2.68302e9	−	1.94933e9i	−0.820103	−	0.595840i	0.0966391	−	0.995319i	$-0.469191\pi$
$523$	−2.68302e9	−	1.94933e9i	−0.820103	−	0.595840i	−0.916742	+	0.399480i	$0.869191\pi$
$524$	9.40928e8	+	2.00000e8i	0.285691	+	0.0607255i
$525$	2.12292e8	−	6.53368e8i	0.0640290	−	0.197061i
$526$	1.88586e8			0.0565014
$527$	1.60725e9	−	1.47565e9i	0.478351	−	0.439185i
$528$	2.70854e9			0.800787
$529$	1.26318e9	−	3.88767e9i	0.370997	−	1.14181i
$530$	1.45062e8	+	3.08338e7i	0.0423241	+	0.00899626i
$531$	1.23862e9	+	8.99911e8i	0.359011	+	0.260837i
$532$	8.35488e8	+	1.44711e9i	0.240574	+	0.416687i
$533$	8.82664e8	−	1.52882e9i	0.252493	−	0.437332i
$534$	8.24533e8	−	3.67106e8i	0.234322	−	0.104327i
$535$	−1.63854e8	+	1.19047e8i	−0.0462615	+	0.0336109i
$536$	−2.52209e8	−	1.12291e8i	−0.0707432	−	0.0314969i
$537$	4.43615e8	−	9.42933e7i	0.123622	−	0.0262767i
$538$	−1.43320e8	+	1.36360e9i	−0.0396797	+	0.377527i
$539$	−2.68789e9	−	2.98521e9i	−0.739352	−	0.821134i
$540$	1.40624e9	−	1.56179e9i	0.384309	−	0.426819i
$541$	−6.83201e8	−	6.50022e9i	−0.185506	−	1.76497i	−0.551330	−	0.834287i	$-0.685879\pi$
$541$	−6.83201e8	−	6.50022e9i	−0.185506	−	1.76497i	0.365824	−	0.930684i	$-0.380787\pi$
$542$	4.51776e8	+	1.39042e9i	0.121878	+	0.375102i
$543$	−2.19645e7	−	6.75997e7i	−0.00588737	−	0.0181195i
$544$	1.66723e8	+	1.58626e9i	0.0444017	+	0.422454i
$545$	−1.96743e9	+	2.18505e9i	−0.520609	+	0.578195i
$546$	2.72580e8	+	3.02730e8i	0.0716670	+	0.0795943i
$547$	−3.11393e8	+	2.96271e9i	−0.0813492	+	0.773986i	0.875464	+	0.483283i	$0.160556\pi$
$547$	−3.11393e8	+	2.96271e9i	−0.0813492	+	0.773986i	−0.956813	+	0.290703i	$0.906111\pi$
$548$	−2.83654e9	+	6.02926e8i	−0.736305	+	0.156506i
$549$	1.12855e9	+	5.02462e8i	0.291083	+	0.129599i
$550$	6.85981e8	−	4.98394e8i	0.175810	−	0.127733i
$551$	6.57866e8	−	2.92901e8i	0.167536	−	0.0745917i
$552$	9.22614e8	−	1.59801e9i	0.233471	−	0.404384i
$553$	−3.15285e8	−	5.46090e8i	−0.0792804	−	0.137318i
$554$	1.90486e8	+	1.38396e8i	0.0475970	+	0.0345812i
$555$	3.02800e9	+	6.43622e8i	0.751849	+	0.159810i
$556$	−9.16423e8	+	2.82046e9i	−0.226118	+	0.695918i
$557$	1.29799e9			0.318256			0.159128	−	0.987258i	$-0.449132\pi$
$557$	1.29799e9			0.318256			0.159128	+	0.987258i	$0.449132\pi$
$558$	5.05460e8	+	4.81743e7i	0.123159	+	0.0117380i
$559$	−8.43556e9			−2.04255
$560$	−2.81579e8	+	8.66612e8i	−0.0677552	+	0.208529i
$561$	2.54080e9	+	5.40064e8i	0.607577	+	0.129144i
$562$	−6.35181e8	−	4.61486e8i	−0.150946	−	0.109668i
$563$	−8.48831e8	−	1.47022e9i	−0.200467	−	0.347218i	0.748212	−	0.663459i	$-0.230912\pi$
$563$	−8.48831e8	−	1.47022e9i	−0.200467	−	0.347218i	−0.948679	+	0.316241i	$0.897579\pi$
$564$	4.76406e8	−	8.25160e8i	0.111815	−	0.193669i
$565$	3.93518e9	−	1.75205e9i	0.917899	−	0.408675i
$566$	3.38000e6	−	2.45572e6i	0.000783537	−	0.000569273i
$567$	3.53550e8	+	1.57411e8i	0.0814536	+	0.0362655i
$568$	1.57810e9	−	3.35437e8i	0.361340	−	0.0768053i
$569$	−5.66622e8	+	5.39105e9i	−0.128944	+	1.22682i	0.718345	+	0.695687i	$0.244900\pi$
$569$	−5.66622e8	+	5.39105e9i	−0.128944	+	1.22682i	−0.847289	+	0.531132i	$0.821767\pi$
$570$	−3.11863e8	−	3.46359e8i	−0.0705346	−	0.0783366i
$571$	5.19669e9	−	5.77151e9i	1.16816	−	1.29737i	0.221486	−	0.975164i	$-0.428909\pi$
$571$	5.19669e9	−	5.77151e9i	1.16816	−	1.29737i	0.946670	−	0.322205i	$-0.104424\pi$
$572$	−8.98003e8	−	8.54393e9i	−0.200628	−	1.90885i
$573$	−1.05821e9	−	3.25683e9i	−0.234979	−	0.723192i
$574$	−5.14604e7	−	1.58379e8i	−0.0113575	−	0.0349547i
$575$	4.70144e8	+	4.47312e9i	0.103132	+	0.981235i
$576$	1.10347e9	−	1.22553e9i	0.240593	−	0.267206i
$577$	1.89939e9	+	2.10949e9i	0.411623	+	0.457154i	0.912930	−	0.408116i	$-0.133814\pi$
$577$	1.89939e9	+	2.10949e9i	0.411623	+	0.457154i	−0.501307	+	0.865269i	$0.667147\pi$
$578$	6.59863e7	−	6.27817e8i	0.0142137	−	0.135234i
$579$	−4.87419e9	+	1.03604e9i	−1.04358	+	0.221821i
$580$	3.82437e8	+	1.70272e8i	0.0813883	+	0.0362364i
$581$	−3.16012e9	+	2.29596e9i	−0.668478	+	0.485678i
$582$	−5.90243e8	+	2.62793e8i	−0.124108	+	0.0552565i
$583$	1.05704e9	−	1.83085e9i	0.220929	−	0.382660i
$584$	−3.32806e8	−	5.76436e8i	−0.0691426	−	0.119758i
$585$	−1.74402e9	−	1.26711e9i	−0.360169	−	0.261678i
$586$	−1.09765e9	−	2.33312e8i	−0.225331	−	0.0478956i
$587$	5.48366e8	−	1.68770e9i	0.111902	−	0.344398i	−0.879387	−	0.476109i	$-0.842047\pi$
$587$	5.48366e8	−	1.68770e9i	0.111902	−	0.344398i	0.991288	+	0.131710i	$0.0420469\pi$
$588$	2.54921e9			0.517113
$589$	−1.10733e9	+	5.46990e9i	−0.223291	+	1.10300i
$590$	5.72526e8			0.114766
$591$	1.34264e9	−	4.13221e9i	0.267548	−	0.823428i
$592$	7.97639e9	+	1.69544e9i	1.58009	+	0.335858i
$593$	5.04384e9	+	3.66456e9i	0.993276	+	0.721657i	0.960636	−	0.277810i	$-0.0896086\pi$
$593$	5.04384e9	+	3.66456e9i	0.993276	+	0.721657i	0.0326398	+	0.999467i	$0.489609\pi$
$594$	8.76666e8	+	1.51843e9i	0.171625	+	0.297264i
$595$	−4.36938e8	+	7.56798e8i	−0.0850374	+	0.147289i
$596$	−5.45898e9	+	2.43049e9i	−1.05621	+	0.470254i
$597$	−3.60242e9	+	2.61731e9i	−0.692922	+	0.503437i
$598$	−2.43645e9	−	1.08478e9i	−0.465911	−	0.207437i
$599$	−8.65160e9	+	1.83896e9i	−1.64476	+	0.349605i	−0.934948	−	0.354785i	$-0.884554\pi$
$599$	−8.65160e9	+	1.83896e9i	−1.64476	+	0.349605i	−0.709813	+	0.704390i	$0.751221\pi$
$600$	−1.15784e8	+	1.10162e9i	−0.0218837	+	0.208210i
$601$	1.62004e8	+	1.79924e8i	0.0304414	+	0.0338086i	0.758173	−	0.652053i	$-0.226092\pi$
$601$	1.62004e8	+	1.79924e8i	0.0304414	+	0.0338086i	−0.727732	+	0.685862i	$0.759425\pi$
$602$	−5.32464e8	+	5.91361e8i	−0.0994723	+	0.110475i
$603$	5.01458e7	+	4.77105e8i	0.00931374	+	0.0886143i
$604$	1.69397e9	+	5.21351e9i	0.312808	+	0.962723i
$605$	9.06684e8	+	2.79049e9i	0.166461	+	0.512314i
$606$	−1.35101e8	−	1.28540e9i	−0.0246606	−	0.234630i
$607$	−1.92109e9	+	2.13359e9i	−0.348648	+	0.387213i	−0.891806	−	0.452418i	$-0.850562\pi$
$607$	−1.92109e9	+	2.13359e9i	−0.348648	+	0.387213i	0.543158	+	0.839630i	$0.317228\pi$
$608$	−2.72981e9	−	3.03176e9i	−0.492573	−	0.547057i
$609$	−2.95786e7	+	2.81422e8i	−0.00530661	+	0.0504890i
$610$	4.51866e8	−	9.60470e7i	0.0806037	−	0.0171328i
$611$	−2.58983e9	−	1.15307e9i	−0.459332	−	0.204508i
$612$	1.48081e9	−	1.07587e9i	0.261138	−	0.189728i
$613$	−8.68948e9	+	3.86881e9i	−1.52364	+	0.678368i	−0.986294	−	0.164995i	$-0.947239\pi$
$613$	−8.68948e9	+	3.86881e9i	−1.52364	+	0.678368i	−0.537345	+	0.843363i	$0.680573\pi$
$614$	1.51409e8	−	2.62248e8i	0.0263974	−	0.0457217i
$615$	−3.96828e8	−	6.87325e8i	−0.0687921	−	0.119151i
$616$	−1.34965e9	−	9.80581e8i	−0.232643	−	0.169025i
$617$	5.78840e9	+	1.23036e9i	0.992112	+	0.210880i	0.675248	−	0.737591i	$-0.264037\pi$
$617$	5.78840e9	+	1.23036e9i	0.992112	+	0.210880i	0.316864	+	0.948471i	$0.397370\pi$
$618$	8.88428e6	−	2.73430e7i	0.00151413	−	0.00466001i
$619$	5.01114e9			0.849219			0.424609	−	0.905377i	$-0.360411\pi$
$619$	5.01114e9			0.849219			0.424609	+	0.905377i	$0.360411\pi$
$620$	−2.79380e9	+	1.64933e9i	−0.470786	+	0.277931i
$621$	−9.30049e9			−1.55842
$622$	5.77069e8	−	1.77604e9i	0.0961528	−	0.295928i
$623$	4.23388e9	+	8.99939e8i	0.701505	+	0.149109i
$624$	4.13744e9	+	3.00603e9i	0.681688	+	0.495276i
$625$	−3.27980e8	−	5.68077e8i	−0.0537362	−	0.0930738i
$626$	−1.59759e8	+	2.76711e8i	−0.0260289	+	0.0450833i
$627$	−6.06956e9	+	2.70234e9i	−0.983379	+	0.437829i
$628$	1.43969e9	−	1.04599e9i	0.231958	−	0.168527i
$629$	7.14436e9	+	3.18087e9i	1.14469	+	0.509647i
$630$	−1.98913e8	+	4.22804e7i	−0.0316936	+	0.00673669i
$631$	−9.80933e8	+	9.33295e9i	−0.155431	+	1.47882i	0.587374	+	0.809316i	$0.300162\pi$
$631$	−9.80933e8	+	9.33295e9i	−0.155431	+	1.47882i	−0.742805	+	0.669508i	$0.766505\pi$
$632$	6.80313e8	+	7.55564e8i	0.107201	+	0.119059i
$633$	−2.81452e9	+	3.12584e9i	−0.441054	+	0.489840i
$634$	7.36112e7	+	7.00364e8i	0.0114718	+	0.109147i
$635$	−3.93801e8	−	1.21200e9i	−0.0610336	−	0.187842i
$636$	4.14582e8	+	1.27595e9i	0.0639014	+	0.196668i
$637$	−7.92820e8	−	7.54317e9i	−0.121531	−	1.15629i
$638$	−2.33699e8	+	2.59549e8i	−0.0356274	+	0.0395683i
$639$	−1.87591e9	−	2.08341e9i	−0.284419	−	0.315879i
$640$	3.26871e8	−	3.10997e9i	0.0492886	−	0.468950i
$641$	5.61991e9	−	1.19455e9i	0.842803	−	0.179143i	0.233774	−	0.972291i	$-0.424892\pi$
$641$	5.61991e9	−	1.19455e9i	0.842803	−	0.179143i	0.609029	+	0.793148i	$0.291559\pi$
$642$	9.79606e7	+	4.36149e7i	0.0146110	+	0.00650522i
$643$	−4.46768e8	+	3.24596e8i	−0.0662740	+	0.0481509i	−0.620429	−	0.784263i	$-0.713041\pi$
$643$	−4.46768e8	+	3.24596e8i	−0.0662740	+	0.0481509i	0.554155	+	0.832414i	$0.313041\pi$
$644$	3.92718e9	−	1.74849e9i	0.579402	−	0.257966i
$645$	−1.89623e9	+	3.28436e9i	−0.278247	+	0.481939i
$646$	−5.88715e8	−	1.01968e9i	−0.0859194	−	0.148817i
$647$	−2.23301e8	−	1.62238e8i	−0.0324135	−	0.0235498i	0.571461	−	0.820630i	$-0.306377\pi$
$647$	−2.23301e8	−	1.62238e8i	−0.0324135	−	0.0235498i	−0.603874	+	0.797080i	$0.706377\pi$
$648$	−6.10364e8	−	1.29737e8i	−0.0881204	−	0.0187306i
$649$	2.52204e9	−	7.76204e9i	0.362156	−	1.11460i
$650$	1.60101e9			0.228663
$651$	−1.64386e9	−	1.45152e9i	−0.233525	−	0.206201i
$652$	−9.12840e9			−1.28982
$653$	3.98912e9	−	1.22773e10i	0.560637	−	1.72546i	−0.119936	−	0.992782i	$-0.538269\pi$
$653$	3.98912e9	−	1.22773e10i	0.560637	−	1.72546i	0.680573	−	0.732680i	$-0.261731\pi$
$654$	1.52270e9	+	3.23660e8i	0.212859	+	0.0452446i
$655$	−1.04100e9	−	7.56328e8i	−0.144745	−	0.105164i
$656$	−1.04533e9	−	1.81056e9i	−0.144574	−	0.250409i
$657$	−5.78308e8	+	1.00166e9i	−0.0795574	+	0.137798i
$658$	−2.44307e8	+	1.08773e8i	−0.0334307	+	0.0148843i
$659$	1.14550e9	−	8.32256e8i	0.155918	−	0.113281i	−0.507091	−	0.861893i	$-0.669279\pi$
$659$	1.14550e9	−	8.32256e8i	0.155918	−	0.113281i	0.663009	+	0.748611i	$0.269279\pi$
$660$	−3.52842e9	−	1.57095e9i	−0.477723	−	0.212696i
$661$	1.14667e8	−	2.43731e7i	0.0154430	−	0.00328251i	−0.200184	−	0.979758i	$-0.564154\pi$
$661$	1.14667e8	−	2.43731e7i	0.0154430	−	0.00328251i	0.215627	+	0.976476i	$0.430821\pi$
$662$	−2.45784e8	+	2.33848e9i	−0.0329268	+	0.313278i
$663$	3.28183e9	+	3.64484e9i	0.437340	+	0.485715i
$664$	4.21425e9	−	4.68040e9i	0.558641	−	0.620433i
$665$	−2.33639e8	−	2.22292e9i	−0.0308084	−	0.293122i
$666$	5.62375e8	+	1.73081e9i	0.0737677	+	0.227034i
$667$	−5.72493e8	−	1.76195e9i	−0.0747016	−	0.229908i
$668$	2.59173e8	+	2.46586e9i	0.0336412	+	0.320075i
$669$	−1.31181e8	+	1.45691e8i	−0.0169387	+	0.0188123i
$670$	1.20040e8	+	1.33318e8i	0.0154193	+	0.0171248i
$671$	6.88356e8	−	6.54927e9i	0.0879598	−	0.836882i
$672$	1.56806e9	−	3.33301e8i	0.199329	−	0.0423686i
$673$	8.57379e9	+	3.81730e9i	1.08423	+	0.482729i	0.869494	−	0.493944i	$-0.164445\pi$
$673$	8.57379e9	+	3.81730e9i	1.08423	+	0.482729i	0.214733	+	0.976673i	$0.431112\pi$
$674$	−2.28438e9	+	1.65970e9i	−0.287381	+	0.208795i
$675$	5.10037e9	−	2.27083e9i	0.638320	−	0.284198i
$676$	4.31671e9	−	7.47676e9i	0.537452	−	0.930894i
$677$	−3.72828e9	−	6.45757e9i	−0.461794	−	0.799850i	0.537257	−	0.843419i	$-0.319461\pi$
$677$	−3.72828e9	−	6.45757e9i	−0.461794	−	0.799850i	−0.999050	+	0.0435687i	$0.986127\pi$
$678$	−1.84507e9	−	1.34052e9i	−0.227357	−	0.165185i
$679$	−3.03083e9	−	6.44223e8i	−0.371550	−	0.0789754i
$680$	4.35407e8	−	1.34005e9i	0.0531025	−	0.163433i
$681$	−1.82668e9			−0.221640
$682$	−5.88405e8	−	2.64196e9i	−0.0710283	−	0.318920i
$683$	1.23836e10			1.48722			0.743611	−	0.668613i	$-0.233112\pi$
$683$	1.23836e10			1.48722			0.743611	+	0.668613i	$0.233112\pi$
$684$	−1.44672e9	+	4.45256e9i	−0.172858	+	0.532002i
$685$	3.79428e9	+	8.06499e8i	0.451037	+	0.0958709i
$686$	−1.30679e9	−	9.49435e8i	−0.154550	−	0.112287i
$687$	1.07330e9	+	1.85902e9i	0.126292	+	0.218743i
$688$	−4.99506e9	+	8.65170e9i	−0.584765	+	1.01284i
$689$	3.64663e9	−	1.62358e9i	0.424741	−	0.189107i
$690$	−9.70043e8	+	7.04778e8i	−0.112414	+	0.0816734i
$691$	5.85870e9	+	2.60846e9i	0.675504	+	0.300754i	0.715669	−	0.698439i	$-0.246122\pi$
$691$	5.85870e9	+	2.60846e9i	0.675504	+	0.300754i	−0.0401653	+	0.999193i	$0.512788\pi$
$692$	−9.76000e8	+	2.07455e8i	−0.111964	+	0.0237987i
$693$	−3.03018e8	+	2.88302e9i	−0.0345861	+	0.329065i
$694$	2.41544e9	+	2.68261e9i	0.274307	+	0.304649i
$695$	2.65439e9	−	2.94800e9i	0.299928	−	0.333104i
$696$	−4.76916e7	−	4.53755e8i	−0.00536179	−	0.0510140i
$697$	−6.19578e8	−	1.90686e9i	−0.0693076	−	0.213307i
$698$	4.73928e8	+	1.45860e9i	0.0527495	+	0.162346i
$699$	−5.52712e8	−	5.25870e9i	−0.0612109	−	0.582383i
$700$	−1.72674e9	+	1.91774e9i	−0.190276	+	0.211323i
$701$	2.59142e9	+	2.87806e9i	0.284135	+	0.315564i	0.868269	−	0.496093i	$-0.165233\pi$
$701$	2.59142e9	+	2.87806e9i	0.284135	+	0.315564i	−0.584134	+	0.811657i	$0.698566\pi$
$702$	−3.46049e8	+	3.29243e9i	−0.0377535	+	0.359201i
$703$	−1.95658e10	+	4.15885e9i	−2.12400	+	0.451470i
$704$	−8.03101e9	−	3.57564e9i	−0.867493	−	0.386233i
$705$	−1.03111e9	+	7.49145e8i	−0.110826	+	0.0805200i
$706$	8.53130e8	−	3.79838e8i	0.0912429	−	0.0406239i
$707$	3.09920e9	−	5.36797e9i	0.329823	−	0.571271i
$708$	2.58967e9	+	4.48544e9i	0.274238	+	0.474995i
$709$	5.41982e9	+	3.93773e9i	0.571114	+	0.414939i	0.835510	−	0.549475i	$-0.185172\pi$
$709$	5.41982e9	+	3.93773e9i	0.571114	+	0.414939i	−0.264395	+	0.964414i	$0.585172\pi$
$710$	−1.02546e9	−	2.17969e8i	−0.107526	−	0.0228554i
$711$	5.45945e8	−	1.68025e9i	0.0569646	−	0.175319i
$712$	−6.97908e9			−0.724633
$713$	1.36973e10	+	4.30409e9i	1.41521	+	0.444701i
$714$	4.62669e8			0.0475693
$715$	−3.55112e9	+	1.09292e10i	−0.363324	+	1.11820i
$716$	−1.66637e9	−	3.54197e8i	−0.169658	−	0.0360620i
$717$	−4.96234e9	−	3.60535e9i	−0.502770	−	0.365284i
$718$	8.16273e8	+	1.41383e9i	0.0823000	+	0.142548i
$719$	9.02620e9	−	1.56338e10i	0.905636	−	1.56861i	0.0855756	−	0.996332i	$-0.472727\pi$
$719$	9.02620e9	−	1.56338e10i	0.905636	−	1.56861i	0.820061	−	0.572276i	$-0.193940\pi$
$720$	−2.33228e9	+	1.03840e9i	−0.232872	+	0.103681i
$721$	1.11546e8	−	8.10429e7i	0.0110836	−	0.00805270i
$722$	5.78868e8	+	2.57728e8i	0.0572399	+	0.0254849i
$723$	6.58059e9	−	1.39875e9i	0.647561	−	0.137643i
$724$	−2.79086e7	+	2.65532e8i	−0.00273308	+	0.0260035i
$725$	7.44157e8	+	8.26470e8i	0.0725239	+	0.0805460i
$726$	1.03946e9	−	1.15443e9i	0.100816	−	0.111967i
$727$	−1.09685e9	−	1.04358e10i	−0.105871	−	1.00730i	−0.910498	−	0.413514i	$-0.864301\pi$
$727$	−1.09685e9	−	1.04358e10i	−0.105871	−	1.00730i	0.804627	−	0.593781i	$-0.202365\pi$
$728$	−9.73387e8	−	2.99578e9i	−0.0935031	−	0.287773i
$729$	2.67265e9	+	8.22557e9i	0.255503	+	0.786356i
$730$	4.52104e7	+	4.30149e8i	0.00430139	+	0.0409250i
$731$	−6.41081e9	+	7.11992e9i	−0.607018	+	0.674162i
$732$	2.79637e9	+	3.10568e9i	0.263515	+	0.292664i
$733$	1.75431e9	−	1.66911e10i	0.164529	−	1.56539i	−0.531302	−	0.847182i	$-0.678297\pi$
$733$	1.75431e9	−	1.66911e10i	0.164529	−	1.56539i	0.695831	−	0.718205i	$-0.255036\pi$
$734$	3.81058e9	−	8.09963e8i	0.355676	−	0.0756013i
$735$	−3.11513e9	−	1.38695e9i	−0.289381	−	0.128841i
$736$	−8.49102e9	+	6.16908e9i	−0.785032	+	0.570359i
$737$	2.33625e9	−	1.04016e9i	0.214972	−	0.0957118i
$738$	2.33289e8	−	4.04068e8i	0.0213647	−	0.0370047i
$739$	7.15055e9	+	1.23851e10i	0.651755	+	1.12887i	0.982697	+	0.185221i	$0.0593001\pi$
$739$	7.15055e9	+	1.23851e10i	0.651755	+	1.12887i	−0.330942	+	0.943651i	$0.607367\pi$
$740$	−9.40749e9	−	6.83494e9i	−0.853420	−	0.620046i
$741$	−1.22707e10	−	2.60822e9i	−1.10792	−	0.235495i
$742$	1.16361e8	−	3.58124e8i	0.0104567	−	0.0321825i
$743$	2.70726e9			0.242142			0.121071	−	0.992644i	$-0.461367\pi$
$743$	2.70726e9			0.242142			0.121071	+	0.992644i	$0.461367\pi$
$744$	3.07919e9	+	1.73817e9i	0.274114	+	0.154734i
$745$	7.99321e9			0.708230
$746$	2.33636e8	−	7.19058e8i	0.0206041	−	0.0634129i
$747$	−1.07049e10	−	2.27540e9i	−0.939639	−	0.199726i
$748$	−7.89385e9	−	5.73522e9i	−0.689657	−	0.501065i
$749$	2.57127e8	+	4.45357e8i	0.0223595	+	0.0387277i
$750$	9.00991e8	−	1.56056e9i	0.0779841	−	0.135072i
$751$	−7.79547e9	+	3.47077e9i	−0.671587	+	0.299010i	−0.714057	−	0.700088i	$-0.753144\pi$
$751$	−7.79547e9	+	3.47077e9i	−0.671587	+	0.299010i	0.0424695	+	0.999098i	$0.486477\pi$
$752$	−2.71616e9	+	1.97341e9i	−0.232913	+	0.169221i
$753$	−1.18175e10	−	5.26148e9i	−1.00865	−	0.449081i
$754$	−6.45043e8	+	1.37108e8i	−0.0548011	+	0.0116483i
$755$	7.66476e8	−	7.29253e9i	0.0648163	−	0.616686i
$756$	−3.57056e9	−	3.96551e9i	−0.300546	−	0.333790i
$757$	−5.56028e9	+	6.17532e9i	−0.465866	+	0.517397i	−0.929596	−	0.368580i	$-0.879844\pi$
$757$	−5.56028e9	+	6.17532e9i	−0.465866	+	0.517397i	0.463730	+	0.885977i	$0.346511\pi$
$758$	4.05475e8	+	3.85783e9i	0.0338159	+	0.321737i
$759$	5.28189e9	+	1.62560e10i	0.438474	+	1.34948i
$760$	1.11367e9	+	3.42752e9i	0.0920256	+	0.283226i
$761$	1.23876e9	+	1.17860e10i	0.101892	+	0.969437i	0.919348	+	0.393446i	$0.128717\pi$
$761$	1.23876e9	+	1.17860e10i	0.101892	+	0.969437i	−0.817456	+	0.575991i	$0.804616\pi$
$762$	−4.51468e8	+	5.01406e8i	−0.0369645	+	0.0410532i
$763$	4.99548e9	+	5.54804e9i	0.407138	+	0.452172i
$764$	−1.34458e9	+	1.27929e10i	−0.109084	+	1.03786i
$765$	−2.39490e9	+	5.09051e8i	−0.193407	+	0.0411099i
$766$	2.79318e9	+	1.24360e9i	0.224542	+	0.0999726i
$767$	1.24671e10	−	9.05788e9i	0.997658	−	0.724841i
$768$	3.88232e9	−	1.72852e9i	0.309262	−	0.137693i
$769$	−1.17102e10	+	2.02827e10i	−0.928588	+	1.60836i	−0.142901	+	0.989737i	$0.545643\pi$
$769$	−1.17102e10	+	2.02827e10i	−0.928588	+	1.60836i	−0.785687	+	0.618624i	$0.787690\pi$
$770$	5.42024e8	+	9.38813e8i	0.0427859	+	0.0741074i
$771$	2.38255e9	+	1.73103e9i	0.187220	+	0.136023i
$772$	1.83091e10	+	3.89172e9i	1.43221	+	0.304425i
$773$	−2.45250e9	+	7.54803e9i	−0.190977	+	0.587767i	−1.00000		1.00740e-5i	$-0.999997\pi$
$773$	−2.45250e9	+	7.54803e9i	−0.190977	+	0.587767i	0.809023	+	0.587777i	$0.199997\pi$
$774$	−2.22952e9			−0.172830
$775$	−8.56245e9	+	9.84003e8i	−0.660757	+	0.0759347i
$776$	4.99598e9			0.383800
$777$	2.42891e9	−	7.47542e9i	0.185754	−	0.571692i
$778$	−4.03759e9	−	8.58217e8i	−0.307393	−	0.0653384i
$779$	4.14889e9	+	3.01434e9i	0.314449	+	0.228461i
$780$	−3.64635e9	−	6.31566e9i	−0.275123	−	0.476527i
$781$	−7.47238e9	+	1.29425e10i	−0.561281	+	0.972167i
$782$	−2.76723e9	+	1.23205e9i	−0.206929	+	0.0921308i
$783$	−1.86046e9	+	1.35170e9i	−0.138502	+	0.100627i
$784$	−8.20591e9	−	3.65351e9i	−0.608164	−	0.270772i
$785$	−2.32838e9	+	4.94913e8i	−0.171795	+	0.0365162i
$786$	−7.12110e7	+	6.77528e8i	−0.00523080	+	0.0497678i
$787$	−9.36166e9	−	1.03972e10i	−0.684607	−	0.760333i	0.296240	−	0.955114i	$-0.404267\pi$
$787$	−9.36166e9	−	1.03972e10i	−0.684607	−	0.760333i	−0.980847	+	0.194781i	$0.937601\pi$
$788$	−1.09207e10	+	1.21287e10i	−0.795077	+	0.883023i
$789$	−2.38541e8	−	2.26956e9i	−0.0172899	−	0.164503i
$790$	−2.04157e8	−	6.28330e8i	−0.0147322	−	0.0453412i
$791$	−3.37983e9	−	1.04020e10i	−0.242816	−	0.747310i
$792$	−4.88576e8	−	4.64849e9i	−0.0349457	−	0.332486i
$793$	8.32009e9	−	9.24040e9i	0.592478	−	0.658013i
$794$	−1.38716e9	−	1.54060e9i	−0.0983459	−	0.109224i
$795$	1.87587e8	−	1.78477e9i	0.0132409	−	0.125979i
$796$	1.63608e10	−	3.47760e9i	1.14977	−	0.244390i
$797$	6.98177e9	+	3.10849e9i	0.488497	+	0.217493i	0.636178	−	0.771542i	$-0.280514\pi$
$797$	6.98177e9	+	3.10849e9i	0.488497	+	0.217493i	−0.147681	+	0.989035i	$0.547181\pi$
$798$	−9.57390e8	+	6.95584e8i	−0.0666928	+	0.0484551i
$799$	−2.94143e9	+	1.30961e9i	−0.204007	+	0.0908298i
$800$	3.15020e9	−	5.45630e9i	0.217532	−	0.376776i
$801$	6.06369e9	+	1.05026e10i	0.416892	+	0.722078i
$802$	−1.03320e9	−	7.50662e8i	−0.0707250	−	0.0513847i
$803$	6.03090e9	+	1.28191e9i	0.411034	+	0.0873680i
$804$	−5.01506e8	+	1.54348e9i	−0.0340314	+	0.104738i
$805$	−5.75029e9			−0.388512
$806$	2.03332e9	−	4.68877e9i	0.136783	−	0.315418i
$807$	1.65917e10			1.11131
$808$	−3.08835e9	+	9.50495e9i	−0.205962	+	0.633884i
$809$	−6.22451e8	−	1.32306e8i	−0.0413319	−	0.00878537i	0.187199	−	0.982322i	$-0.440059\pi$
$809$	−6.22451e8	−	1.32306e8i	−0.0413319	−	0.00878537i	−0.228531	+	0.973537i	$0.573392\pi$
$810$	3.28039e8	+	2.38335e8i	0.0216884	+	0.0157576i
$811$	−5.96867e9	−	1.03380e10i	−0.392920	−	0.680558i	0.599913	−	0.800065i	$-0.295202\pi$
$811$	−5.96867e9	−	1.03380e10i	−0.392920	−	0.680558i	−0.992833	+	0.119507i	$0.961868\pi$
$812$	5.31469e8	−	9.20531e8i	0.0348363	−	0.0603382i
$813$	1.61618e10	−	7.19570e9i	1.05481	−	0.469630i
$814$	7.84856e9	−	5.70231e9i	0.510040	−	0.370566i
$815$	1.11549e10	+	4.96647e9i	0.721794	+	0.321363i
$816$	5.68155e9	−	1.20765e9i	0.366059	−	0.0778082i
$817$	2.56152e9	−	2.43712e10i	0.164331	−	1.56351i
$818$	−2.84476e9	−	3.15943e9i	−0.181723	−	0.201824i
$819$	−3.66255e9	+	4.06767e9i	−0.232964	+	0.258733i
$820$	3.11624e8	+	2.96490e9i	0.0197371	+	0.187786i
$821$	−9.39048e9	−	2.89009e10i	−0.592225	−	1.82268i	−0.568082	−	0.822972i	$-0.692315\pi$
$821$	−9.39048e9	−	2.89009e10i	−0.592225	−	1.82268i	−0.0241423	−	0.999709i	$-0.507685\pi$
$822$	−6.34641e8	−	1.95323e9i	−0.0398545	−	0.122659i
$823$	9.33999e7	+	8.88641e8i	0.00584046	+	0.0555683i	0.997054	−	0.0767035i	$-0.0244395\pi$
$823$	9.33999e7	+	8.88641e8i	0.00584046	+	0.0555683i	−0.991213	+	0.132272i	$0.957773\pi$
$824$	−1.48755e8	+	1.65209e8i	−0.00926246	+	0.0102870i
$825$	−6.86569e9	−	7.62512e9i	−0.425692	−	0.472779i
$826$	1.51952e8	−	1.44573e9i	0.00938162	−	0.0892601i
$827$	−4.97116e9	+	1.05665e9i	−0.305625	+	0.0649625i	−0.358171	−	0.933656i	$-0.616600\pi$
$827$	−4.97116e9	+	1.05665e9i	−0.305625	+	0.0649625i	0.0525465	+	0.998618i	$0.483266\pi$
$828$	1.10031e10	+	4.89888e9i	0.673608	+	0.299910i
$829$	−5.74393e9	+	4.17321e9i	−0.350162	+	0.254407i	−0.748937	−	0.662641i	$-0.769435\pi$
$829$	−5.74393e9	+	4.17321e9i	−0.350162	+	0.254407i	0.398775	+	0.917049i	$0.369435\pi$
$830$	−3.73873e9	+	1.66459e9i	−0.226961	+	0.101049i
$831$	1.42461e9	−	2.46749e9i	0.0861175	−	0.149160i
$832$	−8.29944e9	−	1.43750e10i	−0.499594	−	0.865322i
$833$	−6.96924e9	−	5.06345e9i	−0.417761	−	0.303521i
$834$	−2.05437e9	−	4.36670e8i	−0.122630	−	0.0260659i
$835$	1.02489e9	−	3.15428e9i	0.0609220	−	0.187499i
$836$	2.49570e10			1.47730
$837$	−1.72854e8	−	1.78212e10i	−0.0101892	−	1.05050i
$838$	−5.14084e9			−0.301773
$839$	−3.60067e9	+	1.10817e10i	−0.210483	+	0.647799i	0.788961	+	0.614443i	$0.210619\pi$
$839$	−3.60067e9	+	1.10817e10i	−0.210483	+	0.647799i	−0.999444	+	0.0333553i	$0.989381\pi$
$840$	−1.38521e9	−	2.94434e8i	−0.0806374	−	0.0171400i
$841$	1.35848e10	+	9.86997e9i	0.787533	+	0.572176i
$842$	1.72371e9	+	2.98555e9i	0.0995110	+	0.172358i
$843$	−4.75039e9	+	8.22791e9i	−0.273107	+	0.473035i
$844$	1.44341e10	−	6.42646e9i	0.826399	−	0.367937i
$845$	−9.34287e9	+	6.78799e9i	−0.532699	+	0.387028i
$846$	−6.84493e8	−	3.04756e8i	−0.0388663	−	0.0173044i
$847$	7.28712e9	−	1.54893e9i	0.412063	−	0.0875868i
$848$	4.94143e8	−	4.70146e9i	0.0278271	−	0.264757i
$849$	−3.38290e7	−	3.75709e7i	−0.00189720	−	0.00210705i
$850$	1.21672e9	−	1.35131e9i	0.0679557	−	0.0754724i
$851$	5.37909e9	+	5.11786e10i	0.299195	+	2.84665i
$852$	−2.93073e9	−	9.01987e9i	−0.162345	−	0.499645i
$853$	−5.52644e9	−	1.70086e10i	−0.304876	−	0.938313i	−0.979723	−	0.200355i	$-0.935790\pi$
$853$	−5.52644e9	−	1.70086e10i	−0.304876	−	0.938313i	0.674847	−	0.737958i	$-0.264210\pi$
$854$	−1.22608e8	−	1.16653e9i	−0.00673619	−	0.0640906i
$855$	4.19038e9	−	4.65389e9i	0.229283	−	0.254645i
$856$	−5.54821e8	−	6.16191e8i	−0.0302339	−	0.0335782i
$857$	−1.84624e9	+	1.75658e10i	−0.100197	+	0.953312i	0.822755	+	0.568396i	$0.192436\pi$
$857$	−1.84624e9	+	1.75658e10i	−0.100197	+	0.953312i	−0.922952	+	0.384915i	$0.874231\pi$
$858$	5.95125e9	−	1.26498e9i	0.321664	−	0.0683719i
$859$	−3.31290e9	−	1.47500e9i	−0.178333	−	0.0793992i	0.315628	−	0.948883i	$-0.397785\pi$
$859$	−3.31290e9	−	1.47500e9i	−0.178333	−	0.0793992i	−0.493961	+	0.869484i	$0.664452\pi$
$860$	1.15250e10	−	8.37343e9i	0.617871	−	0.448910i
$861$	−1.84094e9	+	8.19639e8i	−0.0982944	+	0.0437635i
$862$	2.34870e9	−	4.06807e9i	0.124897	−	0.216328i
$863$	3.25346e9	+	5.63516e9i	0.172309	+	0.298448i	0.939227	−	0.343297i	$-0.111544\pi$
$863$	3.25346e9	+	5.63516e9i	0.172309	+	0.298448i	−0.766918	+	0.641746i	$0.778211\pi$
$864$	1.05399e10	+	7.65766e9i	0.555952	+	0.403923i
$865$	1.30554e9	+	2.77501e8i	0.0685857	+	0.0145783i
$866$	1.65084e9	−	5.08076e9i	0.0863758	−	0.265837i
$867$	−7.63902e9			−0.398081
$868$	3.42337e9	+	7.49258e9i	0.177678	+	0.388877i
$869$	−9.41792e9			−0.486840
$870$	−9.16164e7	+	2.81966e8i	−0.00471689	+	0.0145171i
$871$	4.72315e9	+	1.00394e9i	0.242197	+	0.0514805i
$872$	−9.73841e9	−	7.07537e9i	−0.497371	−	0.361361i
$873$	−4.34070e9	−	7.51832e9i	−0.220806	−	0.382447i
$874$	3.87388e9	−	6.70975e9i	0.196271	−	0.339951i
$875$	7.89473e9	−	3.51496e9i	0.398390	−	0.177375i
$876$	−3.16549e9	+	2.29986e9i	−0.159102	+	0.115595i
$877$	−3.15805e10	−	1.40605e10i	−1.58096	−	0.703887i	−0.586591	−	0.809884i	$-0.699530\pi$
$877$	−3.15805e10	−	1.40605e10i	−1.58096	−	0.703887i	−0.994367	+	0.105996i	$0.966197\pi$
$878$	−6.14201e9	+	1.30553e9i	−0.306253	+	0.0650960i
$879$	−1.41942e9	+	1.35049e10i	−0.0704938	+	0.670704i
$880$	9.10649e9	+	1.01138e10i	0.450465	+	0.500293i
$881$	−7.94242e9	+	8.82095e9i	−0.391325	+	0.434610i	−0.906326	−	0.422579i	$-0.861125\pi$
$881$	−7.94242e9	+	8.82095e9i	−0.391325	+	0.434610i	0.515001	+	0.857189i	$0.327791\pi$
$882$	−2.09543e8	−	1.99367e9i	−0.0102833	−	0.0978391i
$883$	−1.59809e7	−	4.91841e7i	−0.000781157	−	0.00240415i	0.950665	−	0.310219i	$-0.100402\pi$
$883$	−1.59809e7	−	4.91841e7i	−0.000781157	−	0.00240415i	−0.951446	+	0.307815i	$0.900402\pi$
$884$	−5.69314e9	−	1.75217e10i	−0.277185	−	0.853087i
$885$	−7.24184e8	−	6.89015e9i	−0.0351194	−	0.334139i
$886$	−5.89702e9	+	6.54930e9i	−0.284849	+	0.316357i
$887$	−1.91323e10	−	2.12486e10i	−0.920523	−	1.02234i	−0.999675	−	0.0254823i	$-0.991888\pi$
$887$	−1.91323e10	−	2.12486e10i	−0.920523	−	1.02234i	0.0791518	−	0.996863i	$-0.474779\pi$
$888$	−1.32473e9	+	1.26040e10i	−0.0634867	+	0.604035i
$889$	−3.16502e9	+	6.72747e8i	−0.151085	+	0.0321141i
$890$	4.14297e9	+	1.84457e9i	0.196991	+	0.0877062i
$891$	4.67627e9	−	3.39751e9i	0.221477	−	0.160912i
$892$	6.72752e8	−	2.99529e8i	0.0317379	−	0.0141306i
$893$	4.11774e9	−	7.13214e9i	0.193499	−	0.335151i
$894$	−2.11598e9	−	3.66499e9i	−0.0990446	−	0.171550i
$895$	1.84359e9	+	1.33944e9i	0.0859574	+	0.0624517i
$896$	−7.76648e9	−	1.65082e9i	−0.360700	−	0.0766692i
$897$	−9.97306e9	+	3.06939e10i	−0.461376	+	1.41997i
$898$	−4.29353e8			−0.0197855
$899$	3.36553e9	−	1.12973e9i	0.154488	−	0.0518580i
$900$	−7.23018e9			−0.330598
$901$	1.40098e9	−	4.31177e9i	0.0638109	−	0.196390i
$902$	−2.43286e9	−	5.17120e8i	−0.110381	−	0.0234622i
$903$	7.79033e9	+	5.66000e9i	0.352086	+	0.255805i
$904$	8.81751e9	+	1.52724e10i	0.396969	+	0.687570i
$905$	1.78572e8	−	3.09295e8i	0.00800835	−	0.0138709i
$906$	−3.54662e9	+	1.57906e9i	−0.158441	+	0.0705423i
$907$	2.51342e10	−	1.82610e10i	1.11851	−	0.812644i	0.134526	−	0.990910i	$-0.457049\pi$
$907$	2.51342e10	−	1.82610e10i	1.11851	−	0.812644i	0.983982	+	0.178266i	$0.0570489\pi$
$908$	6.26842e9	+	2.79088e9i	0.277880	+	0.123720i
$909$	1.69870e10	−	3.61070e9i	0.750141	−	0.159447i
$910$	−2.13955e8	+	2.03564e9i	−0.00941189	+	0.0895481i
$911$	−3.05602e9	−	3.39406e9i	−0.133919	−	0.148732i	0.672455	−	0.740138i	$-0.265240\pi$
$911$	−3.05602e9	−	3.39406e9i	−0.133919	−	0.148732i	−0.806374	+	0.591406i	$0.798573\pi$
$912$	−9.94108e9	+	1.10407e10i	−0.433962	+	0.481964i
$913$	6.09820e9	+	5.80205e10i	0.265188	+	2.52310i
$914$	4.31281e8	+	1.32735e9i	0.0186831	+	0.0575007i
$915$	−1.72745e9	−	5.31655e9i	−0.0745474	−	0.229433i
$916$	−8.42853e8	−	8.01921e9i	−0.0362341	−	0.344745i
$917$	−2.18615e9	+	2.42797e9i	−0.0936241	+	0.103980i
$918$	2.51595e9	+	2.79424e9i	0.107338	+	0.119211i
$919$	−2.10708e9	+	2.00475e10i	−0.0895523	+	0.852033i	0.853880	+	0.520469i	$0.174243\pi$
$919$	−2.10708e9	+	2.00475e10i	−0.0895523	+	0.852033i	−0.943433	+	0.331564i	$0.892424\pi$
$920$	9.06898e9	−	1.92767e9i	0.383973	−	0.0816161i
$921$	−3.34757e9	−	1.49044e9i	−0.141196	−	0.0628644i
$922$	8.69489e8	−	6.31721e8i	0.0365347	−	0.0265440i
$923$	−2.57785e10	+	1.14773e10i	−1.07908	+	0.480435i
$924$	−4.90340e9	+	8.49294e9i	−0.204477	+	0.354165i
$925$	−1.54458e10	−	2.67529e10i	−0.641673	−	1.11141i
$926$	−2.78502e9	−	2.02343e9i	−0.115263	−	0.0837434i
$927$	3.77863e8	+	8.03172e7i	0.0155795	+	0.00331153i
$928$	−8.01940e8	+	2.46812e9i	−0.0329400	+	0.101379i
$929$	−1.79069e10			−0.732768			−0.366384	−	0.930464i	$-0.619404\pi$
$929$	−1.79069e10			−0.732768			−0.366384	+	0.930464i	$0.619404\pi$
$930$	−1.36849e9	−	1.84565e9i	−0.0557894	−	0.0752419i
$931$	2.20337e10			0.894879
$932$	−6.13778e9	+	1.88901e10i	−0.248345	+	0.764328i
$933$	−2.21039e10	−	4.69833e9i	−0.891011	−	0.189390i
$934$	6.17069e9	+	4.48327e9i	0.247811	+	0.180045i
$935$	6.52591e9	+	1.13032e10i	0.261096	+	0.452232i
$936$	4.41272e9	−	7.64305e9i	0.175890	−	0.304650i
$937$	−1.99791e10	+	8.89525e9i	−0.793389	+	0.353240i	−0.763083	−	0.646301i	$-0.776315\pi$
$937$	−1.99791e10	+	8.89525e9i	−0.793389	+	0.353240i	−0.0303067	+	0.999541i	$0.509648\pi$
$938$	3.68511e8	−	2.67739e8i	0.0145794	−	0.0105926i
$939$	3.53220e9	+	1.57263e9i	0.139224	+	0.0619867i
$940$	4.68291e9	−	9.95384e8i	0.183894	−	0.0390880i
$941$	4.50506e9	−	4.28627e10i	0.176253	−	1.67694i	−0.446706	−	0.894681i	$-0.647403\pi$
$941$	4.50506e9	−	4.28627e10i	0.176253	−	1.67694i	0.622959	−	0.782254i	$-0.285930\pi$
$942$	8.43300e8	+	9.36580e8i	0.0328703	+	0.0365062i
$943$	8.82805e9	−	9.80455e9i	0.342826	−	0.380747i
$944$	−1.90765e9	−	1.81501e10i	−0.0738070	−	0.702227i
$945$	2.20571e9	+	6.78847e9i	0.0850230	+	0.261674i
$946$	3.67268e9	+	1.13033e10i	0.141047	+	0.434098i
$947$	4.00687e9	+	3.81228e10i	0.153314	+	1.45868i	0.752775	+	0.658278i	$0.228715\pi$
$947$	4.00687e9	+	3.81228e10i	0.153314	+	1.45868i	−0.599462	+	0.800403i	$0.704619\pi$
$948$	3.99918e9	−	4.44154e9i	0.152455	−	0.169319i
$949$	7.78982e9	+	8.65148e9i	0.295867	+	0.328593i
$950$	−4.86156e8	+	4.62547e9i	−0.0183968	+	0.175034i
$951$	8.33552e9	−	1.77177e9i	0.314269	−	0.0667998i
$952$	−3.26830e9	−	1.45514e9i	−0.122770	−	0.0546607i
$953$	2.25141e9	−	1.63574e9i	0.0842615	−	0.0612196i	−0.544857	−	0.838529i	$-0.683416\pi$
$953$	2.25141e9	−	1.63574e9i	0.0842615	−	0.0612196i	0.629118	+	0.777309i	$0.283416\pi$
$954$	9.63806e8	−	4.29114e8i	0.0359394	−	0.0160012i
$955$	8.60326e9	−	1.49013e10i	0.319633	−	0.553620i
$956$	1.15203e10	+	1.99537e10i	0.426443	+	0.738620i
$957$	3.41918e9	+	2.48418e9i	0.126104	+	0.0916203i
$958$	−8.17496e9	−	1.73764e9i	−0.300404	−	0.0638529i
$959$	3.04358e9	−	9.36718e9i	0.111435	−	0.342960i
$960$	−7.46251e9			−0.272230
$961$	−7.99272e9	+	2.63260e10i	−0.290511	+	0.956872i
$962$	1.83177e10			0.663373
$963$	−4.45239e8	+	1.37031e9i	−0.0160658	+	0.0494453i
$964$	−2.47189e10	−	5.25417e9i	−0.888709	−	0.188901i
$965$	−2.02563e10	−	1.47171e10i	−0.725629	−	0.527200i
$966$	1.52223e9	+	2.63659e9i	0.0543327	+	0.0941070i
$967$	−2.47745e9	+	4.29107e9i	−0.0881074	+	0.152607i	−0.906711	−	0.421752i	$-0.861415\pi$
$967$	−2.47745e9	+	4.29107e9i	−0.0881074	+	0.152607i	0.818604	+	0.574359i	$0.194749\pi$
$968$	−1.09735e10	+	4.88572e9i	−0.388850	+	0.173127i
$969$	−1.15269e10	+	8.37476e9i	−0.406985	+	0.295692i
$970$	−2.96575e9	−	1.32044e9i	−0.104336	−	0.0464533i
$971$	−6.14485e9	+	1.30613e9i	−0.215399	+	0.0457845i	−0.314347	−	0.949308i	$-0.601786\pi$
$971$	−6.14485e9	+	1.30613e9i	−0.215399	+	0.0457845i	0.0989479	+	0.995093i	$0.468452\pi$
$972$	2.58675e9	−	2.46113e10i	0.0903490	−	0.859613i
$973$	−6.73973e9	−	7.48522e9i	−0.234556	−	0.260501i
$974$	−3.58042e8	+	3.97646e8i	−0.0124159	+	0.0137892i
$975$	−2.02510e9	−	1.92675e10i	−0.0699730	−	0.665748i
$976$	−4.55047e9	−	1.40049e10i	−0.156669	−	0.482177i
$977$	−6.67937e9	−	2.05570e10i	−0.229142	−	0.705227i	−0.997845	−	0.0656203i	$-0.979097\pi$
$977$	−6.67937e9	−	2.05570e10i	−0.229142	−	0.705227i	0.768703	−	0.639606i	$-0.220903\pi$
$978$	−6.75756e8	−	6.42939e9i	−0.0230996	−	0.219778i
$979$	4.32580e10	−	4.80429e10i	1.47342	−	1.63640i
$980$	8.57080e9	+	9.51884e9i	0.290891	+	0.323067i
$981$	−2.18642e9	+	2.08024e10i	−0.0739422	+	0.703513i
$982$	6.73036e9	−	1.43058e9i	0.226803	−	0.0482084i
$983$	−1.39434e10	−	6.20798e9i	−0.468199	−	0.208455i	0.159056	−	0.987270i	$-0.449155\pi$
$983$	−1.39434e10	−	6.20798e9i	−0.468199	−	0.208455i	−0.627255	+	0.778814i	$0.715822\pi$
$984$	2.62864e9	−	1.90982e9i	0.0879525	−	0.0639013i
$985$	1.99439e10	−	8.87960e9i	0.664941	−	0.296051i
$986$	−3.74492e8	+	6.48639e8i	−0.0124415	+	0.0215493i
$987$	1.61806e9	+	2.80256e9i	0.0535655	+	0.0927781i
$988$	3.81231e10	+	2.76980e10i	1.25759	+	0.913692i
$989$	−6.16662e10	−	1.31075e10i	−2.02703	−	0.430858i
$990$	−9.38563e8	+	2.88860e9i	−0.0307426	+	0.0946160i
$991$	−6.23731e9			−0.203582			−0.101791	−	0.994806i	$-0.532457\pi$
$991$	−6.23731e9			−0.203582			−0.101791	+	0.994806i	$0.532457\pi$
$992$	−1.19787e10	−	1.61554e10i	−0.389601	−	0.525446i
$993$	2.84536e10			0.922179
$994$	−8.22574e8	+	2.53162e9i	−0.0265658	+	0.0817611i
$995$	−2.18849e10	−	4.65179e9i	−0.704311	−	0.149706i
$996$	−2.99523e10	−	2.17616e10i	−0.960556	−	0.697884i
$997$	1.02324e10	+	1.77230e10i	0.326998	+	0.566376i	0.981915	−	0.189324i	$-0.0606298\pi$
$997$	1.02324e10	+	1.77230e10i	0.326998	+	0.566376i	−0.654917	+	0.755701i	$0.727296\pi$
$998$	−2.07711e8	+	3.59766e8i	−0.00661458	+	0.0114568i
$999$	5.83552e10	−	2.59814e10i	1.85183	−	0.824486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.8.g.a.9.11	yes	144
31.7	even	15	inner	31.8.g.a.7.11	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.8.g.a.7.11	✓	144	31.7	even	15	inner
31.8.g.a.9.11	yes	144	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.822068 - 2.53007i) q^{2} +(-31.4883 - 6.69304i) q^{3} +(97.8287 + 71.0767i) q^{4} +(-80.8758 - 140.081i) q^{5} +(-42.8193 + 74.1652i) q^{6} +(-375.195 + 167.047i) q^{7} +(535.733 - 389.233i) q^{8} +(-1051.21 - 468.029i) q^{9} +(-420.900 + 89.4650i) q^{10} +(-641.184 + 6100.45i) q^{11} +(-2604.74 - 2892.85i) q^{12} +(-7749.92 + 8607.16i) q^{13} +(114.205 + 1086.59i) q^{14} +(1609.07 + 4952.21i) q^{15} +(4238.63 + 13045.2i) q^{16} +(1375.02 + 13082.4i) q^{17} +(-2048.31 + 2274.88i) q^{18} +(-22513.7 - 25003.9i) q^{19} +(2044.52 - 19452.3i) q^{20} +(12932.3 - 2748.84i) q^{21} +(14907.5 + 6637.23i) q^{22} +(-70028.2 + 50878.4i) q^{23} +(-19474.4 + 8670.58i) q^{24} +(25980.7 - 44999.9i) q^{25} +(15405.7 + 26683.5i) q^{26} +(86925.7 + 63155.2i) q^{27} +(-48578.0 - 10325.6i) q^{28} +(-6613.86 + 20355.4i) q^{29} +13852.2 q^{30} +(-98792.4 - 133239. i) q^{31} +121251. q^{32} +(61020.3 - 187801. i) q^{33} +(34229.8 + 7275.77i) q^{34} +(53744.3 + 39047.5i) q^{35} +(-69572.6 - 120503. i) q^{36} +(297255. - 514860. i) q^{37} +(-81769.4 + 36406.1i) q^{38} +(301640. - 219154. i) q^{39} +(-97851.9 - 43566.5i) q^{40} +(-149088. + 31689.7i) q^{41} +(3676.47 - 34979.2i) q^{42} +(487347. + 541254. i) q^{43} +(-496327. + 551227. i) q^{44} +(19455.5 + 185107. i) q^{45} +(71157.9 + 219001. i) q^{46} +(75637.4 + 232788. i) q^{47} +(-46155.4 - 439139. i) q^{48} +(-438192. + 486661. i) q^{49} +(-92494.8 - 102726. i) q^{50} +(44264.3 - 421146. i) q^{51} +(-1.36993e6 + 291189. i) q^{52} +(-314851. - 140181. i) q^{53} +(231246. - 168010. i) q^{54} +(906414. - 403562. i) q^{55} +(-135984. + 235531. i) q^{56} +(541564. + 938015. i) q^{57} +(46063.4 + 33467.0i) q^{58} +(-1.30145e6 - 276631. i) q^{59} +(-194574. + 598836. i) q^{60} -1.07357e6 q^{61} +(-418318. + 140420. i) q^{62} +472591. q^{63} +(-442868. + 1.36301e6i) q^{64} +(1.83248e6 + 389506. i) q^{65} +(-424987. - 308771. i) q^{66} +(-208454. - 361053. i) q^{67} +(-795341. + 1.37757e6i) q^{68} +(2.54560e6 - 1.13337e6i) q^{69} +(142974. - 103877. i) q^{70} +(2.22572e6 + 990956. i) q^{71} +(-745339. + 158427. i) q^{72} +(105067. - 999642. i) q^{73} +(-1.05827e6 - 1.17532e6i) q^{74} +(-1.11927e6 + 1.24308e6i) q^{75} +(-425283. - 4.04630e6i) q^{76} +(-778496. - 2.39597e6i) q^{77} +(-306506. - 943328. i) q^{78} +(160488. + 1.52694e6i) q^{79} +(1.48458e6 - 1.64879e6i) q^{80} +(-630529. - 700274. i) q^{81} +(-42383.7 + 403254. i) q^{82} +(9.30302e6 - 1.97742e6i) q^{83} +(1.46053e6 + 650269. i) q^{84} +(1.72140e6 - 1.25067e6i) q^{85} +(1.77004e6 - 788072. i) q^{86} +(344498. - 596688. i) q^{87} +(2.03099e6 + 3.51778e6i) q^{88} +(-8.52640e6 - 6.19479e6i) q^{89} +(484326. + 102947. i) q^{90} +(1.46993e6 - 4.52396e6i) q^{91} -1.04670e7 q^{92} +(2.21903e6 + 4.85669e6i) q^{93} +651148. q^{94} +(-1.68177e6 + 5.17595e6i) q^{95} +(-3.81800e6 - 811540. i) q^{96} +(6.10363e6 + 4.43455e6i) q^{97} +(871061. + 1.50872e6i) q^{98} +(3.52921e6 - 6.11277e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{2} - 8 q^{3} - 2362 q^{4} - 75 q^{5} - 1637 q^{6} + 5518 q^{7} + 3401 q^{8} + 14542 q^{9} - 5312 q^{10} + 1361 q^{11} - 18281 q^{12} + 22457 q^{13} + 28470 q^{14} - 86918 q^{15} - 155730 q^{16}+ \cdots - 102755966 q^{99}+O(q^{100}) \) 144 * q - 6 * q^2 - 8 * q^3 - 2362 * q^4 - 75 * q^5 - 1637 * q^6 + 5518 * q^7 + 3401 * q^8 + 14542 * q^9 - 5312 * q^10 + 1361 * q^11 - 18281 * q^12 + 22457 * q^13 + 28470 * q^14 - 86918 * q^15 - 155730 * q^16 + 51582 * q^17 - 24915 * q^18 + 206748 * q^19 + 53815 * q^20 - 28547 * q^21 + 471441 * q^22 - 10235 * q^23 + 69278 * q^24 - 974301 * q^25 - 279651 * q^26 - 948323 * q^27 + 550632 * q^28 - 32990 * q^29 + 2457990 * q^30 + 899715 * q^31 - 1048518 * q^32 + 780887 * q^33 - 1741528 * q^34 + 40023 * q^35 - 2118881 * q^36 - 787972 * q^37 + 580274 * q^38 + 2541281 * q^39 + 2341817 * q^40 + 1129504 * q^41 - 4390379 * q^42 + 481927 * q^43 - 3123681 * q^44 - 1715971 * q^45 + 2065430 * q^46 - 3123106 * q^47 + 1041890 * q^48 + 76766 * q^49 + 7537425 * q^50 + 6145978 * q^51 + 3260257 * q^52 + 141486 * q^53 - 8979668 * q^54 - 8182779 * q^55 - 5240874 * q^56 - 5487037 * q^57 + 5315215 * q^58 + 7471552 * q^59 + 8590679 * q^60 + 10667852 * q^61 + 27020951 * q^62 - 23783686 * q^63 - 3962521 * q^64 + 935148 * q^65 + 3015728 * q^66 - 17382495 * q^67 - 29462568 * q^68 - 26986306 * q^69 - 31811186 * q^70 - 6186650 * q^71 + 35811589 * q^72 + 6470154 * q^73 + 55339663 * q^74 + 17367737 * q^75 + 2919592 * q^76 + 31865334 * q^77 - 7291717 * q^78 + 4223078 * q^79 + 77431338 * q^80 - 5164601 * q^81 - 19477394 * q^82 - 28867780 * q^83 - 76561164 * q^84 - 45198987 * q^85 - 60993764 * q^86 + 18253055 * q^87 - 45197061 * q^88 - 8429459 * q^89 + 83458809 * q^90 - 53128088 * q^91 + 77469728 * q^92 + 41662009 * q^93 - 16867972 * q^94 - 12744274 * q^95 + 119555444 * q^96 + 20643027 * q^97 + 49624796 * q^98 - 102755966 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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