LMFDB - Embedded newform 4.7.b.a.3.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,7,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	4.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.920216334479$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-15}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 4 $ x^2 - x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.2
Root			$0.500000 + 1.93649i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.7.b.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 7.74597i) q^{2} -30.9839i q^{3} +(-56.0000 + 30.9839i) q^{4} +10.0000 q^{5} +(240.000 - 61.9677i) q^{6} +309.839i q^{7} +(-352.000 - 371.806i) q^{8} -231.000 q^{9} +O(q^{10})$	\(q+(2.00000 + 7.74597i) q^{2} -30.9839i q^{3} +(-56.0000 + 30.9839i) q^{4} +10.0000 q^{5} +(240.000 - 61.9677i) q^{6} +309.839i q^{7} +(-352.000 - 371.806i) q^{8} -231.000 q^{9} +(20.0000 + 77.4597i) q^{10} -960.500i q^{11} +(960.000 + 1735.10i) q^{12} +1466.00 q^{13} +(-2400.00 + 619.677i) q^{14} -309.839i q^{15} +(2176.00 - 3470.19i) q^{16} -4766.00 q^{17} +(-462.000 - 1789.32i) q^{18} +7529.08i q^{19} +(-560.000 + 309.839i) q^{20} +9600.00 q^{21} +(7440.00 - 1921.00i) q^{22} -10472.5i q^{23} +(-11520.0 + 10906.3i) q^{24} -15525.0 q^{25} +(2932.00 + 11355.6i) q^{26} -15430.0i q^{27} +(-9600.00 - 17351.0i) q^{28} +25498.0 q^{29} +(2400.00 - 619.677i) q^{30} +41890.2i q^{31} +(31232.0 + 9914.84i) q^{32} -29760.0 q^{33} +(-9532.00 - 36917.3i) q^{34} +3098.39i q^{35} +(12936.0 - 7157.27i) q^{36} +1994.00 q^{37} +(-58320.0 + 15058.2i) q^{38} -45422.3i q^{39} +(-3520.00 - 3718.06i) q^{40} +29362.0 q^{41} +(19200.0 + 74361.3i) q^{42} -21533.8i q^{43} +(29760.0 + 53788.0i) q^{44} -2310.00 q^{45} +(81120.0 - 20945.1i) q^{46} -7560.06i q^{47} +(-107520. - 67420.9i) q^{48} +21649.0 q^{49} +(-31050.0 - 120256. i) q^{50} +147669. i q^{51} +(-82096.0 + 45422.3i) q^{52} -192854. q^{53} +(119520. - 30859.9i) q^{54} -9605.00i q^{55} +(115200. - 109063. i) q^{56} +233280. q^{57} +(50996.0 + 197507. i) q^{58} -78420.2i q^{59} +(9600.00 + 17351.0i) q^{60} -10918.0 q^{61} +(-324480. + 83780.4i) q^{62} -71572.7i q^{63} +(-14336.0 + 261752. i) q^{64} +14660.0 q^{65} +(-59520.0 - 230520. i) q^{66} -394146. i q^{67} +(266896. - 147669. i) q^{68} -324480. q^{69} +(-24000.0 + 6196.77i) q^{70} +532241. i q^{71} +(81312.0 + 85887.3i) q^{72} +288626. q^{73} +(3988.00 + 15445.5i) q^{74} +481025. i q^{75} +(-233280. - 421628. i) q^{76} +297600. q^{77} +(351840. - 90844.7i) q^{78} -310706. i q^{79} +(21760.0 - 34701.9i) q^{80} -646479. q^{81} +(58724.0 + 227437. i) q^{82} -204153. i q^{83} +(-537600. + 297445. i) q^{84} -47660.0 q^{85} +(166800. - 43067.6i) q^{86} -790027. i q^{87} +(-357120. + 338096. i) q^{88} +310738. q^{89} +(-4620.00 - 17893.2i) q^{90} +454223. i q^{91} +(324480. + 586463. i) q^{92} +1.29792e6 q^{93} +(58560.0 - 15120.1i) q^{94} +75290.8i q^{95} +(307200. - 967688. i) q^{96} -1.45709e6 q^{97} +(43298.0 + 167692. i) q^{98} +221875. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 112 q^{4} + 20 q^{5} + 480 q^{6} - 704 q^{8} - 462 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 - 112 * q^4 + 20 * q^5 + 480 * q^6 - 704 * q^8 - 462 * q^9	\( 2 q + 4 q^{2} - 112 q^{4} + 20 q^{5} + 480 q^{6} - 704 q^{8} - 462 q^{9} + 40 q^{10} + 1920 q^{12} + 2932 q^{13} - 4800 q^{14} + 4352 q^{16} - 9532 q^{17} - 924 q^{18} - 1120 q^{20} + 19200 q^{21} + 14880 q^{22} - 23040 q^{24} - 31050 q^{25} + 5864 q^{26} - 19200 q^{28} + 50996 q^{29} + 4800 q^{30} + 62464 q^{32} - 59520 q^{33} - 19064 q^{34} + 25872 q^{36} + 3988 q^{37} - 116640 q^{38} - 7040 q^{40} + 58724 q^{41} + 38400 q^{42} + 59520 q^{44} - 4620 q^{45} + 162240 q^{46} - 215040 q^{48} + 43298 q^{49} - 62100 q^{50} - 164192 q^{52} - 385708 q^{53} + 239040 q^{54} + 230400 q^{56} + 466560 q^{57} + 101992 q^{58} + 19200 q^{60} - 21836 q^{61} - 648960 q^{62} - 28672 q^{64} + 29320 q^{65} - 119040 q^{66} + 533792 q^{68} - 648960 q^{69} - 48000 q^{70} + 162624 q^{72} + 577252 q^{73} + 7976 q^{74} - 466560 q^{76} + 595200 q^{77} + 703680 q^{78} + 43520 q^{80} - 1292958 q^{81} + 117448 q^{82} - 1075200 q^{84} - 95320 q^{85} + 333600 q^{86} - 714240 q^{88} + 621476 q^{89} - 9240 q^{90} + 648960 q^{92} + 2595840 q^{93} + 117120 q^{94} + 614400 q^{96} - 2914172 q^{97} + 86596 q^{98}+O(q^{100}) \) 2 * q + 4 * q^2 - 112 * q^4 + 20 * q^5 + 480 * q^6 - 704 * q^8 - 462 * q^9 + 40 * q^10 + 1920 * q^12 + 2932 * q^13 - 4800 * q^14 + 4352 * q^16 - 9532 * q^17 - 924 * q^18 - 1120 * q^20 + 19200 * q^21 + 14880 * q^22 - 23040 * q^24 - 31050 * q^25 + 5864 * q^26 - 19200 * q^28 + 50996 * q^29 + 4800 * q^30 + 62464 * q^32 - 59520 * q^33 - 19064 * q^34 + 25872 * q^36 + 3988 * q^37 - 116640 * q^38 - 7040 * q^40 + 58724 * q^41 + 38400 * q^42 + 59520 * q^44 - 4620 * q^45 + 162240 * q^46 - 215040 * q^48 + 43298 * q^49 - 62100 * q^50 - 164192 * q^52 - 385708 * q^53 + 239040 * q^54 + 230400 * q^56 + 466560 * q^57 + 101992 * q^58 + 19200 * q^60 - 21836 * q^61 - 648960 * q^62 - 28672 * q^64 + 29320 * q^65 - 119040 * q^66 + 533792 * q^68 - 648960 * q^69 - 48000 * q^70 + 162624 * q^72 + 577252 * q^73 + 7976 * q^74 - 466560 * q^76 + 595200 * q^77 + 703680 * q^78 + 43520 * q^80 - 1292958 * q^81 + 117448 * q^82 - 1075200 * q^84 - 95320 * q^85 + 333600 * q^86 - 714240 * q^88 + 621476 * q^89 - 9240 * q^90 + 648960 * q^92 + 2595840 * q^93 + 117120 * q^94 + 614400 * q^96 - 2914172 * q^97 + 86596 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	2.00000	+	7.74597i	0.250000	+	0.968246i
$2$	2.00000	+	7.74597i	0.250000	+	0.968246i
$3$		−	30.9839i		−	1.14755i	−0.819013	−	0.573775i	$-0.805478\pi$
$3$		−	30.9839i		−	1.14755i	0.819013	−	0.573775i	$-0.194522\pi$
$4$	−56.0000	+	30.9839i	−0.875000	+	0.484123i
$5$	10.0000			0.0800000			0.0400000	−	0.999200i	$-0.487264\pi$
$5$	10.0000			0.0800000			0.0400000	+	0.999200i	$0.487264\pi$
$6$	240.000	−	61.9677i	1.11111	−	0.286888i
$7$			309.839i			0.903320i	0.892190	+	0.451660i	$0.149168\pi$
$7$			309.839i			0.903320i	−0.892190	+	0.451660i	$0.850832\pi$
$8$	−352.000	−	371.806i	−0.687500	−	0.726184i
$9$	−231.000			−0.316872
$10$	20.0000	+	77.4597i	0.0200000	+	0.0774597i
$11$		−	960.500i		−	0.721638i	−0.932636	−	0.360819i	$-0.882497\pi$
$11$		−	960.500i		−	0.721638i	0.932636	−	0.360819i	$-0.117503\pi$
$12$	960.000	+	1735.10i	0.555556	+	1.00411i
$13$	1466.00			0.667274			0.333637	−	0.942702i	$-0.391724\pi$
$13$	1466.00			0.667274			0.333637	+	0.942702i	$0.391724\pi$
$14$	−2400.00	+	619.677i	−0.874636	+	0.225830i
$15$		−	309.839i		−	0.0918040i
$16$	2176.00	−	3470.19i	0.531250	−	0.847215i
$17$	−4766.00			−0.970079			−0.485040	−	0.874492i	$-0.661195\pi$
$17$	−4766.00			−0.970079			−0.485040	+	0.874492i	$0.661195\pi$
$18$	−462.000	−	1789.32i	−0.0792181	−	0.306810i
$19$			7529.08i			1.09769i	0.835923	+	0.548847i	$0.184933\pi$
$19$			7529.08i			1.09769i	−0.835923	+	0.548847i	$0.815067\pi$
$20$	−560.000	+	309.839i	−0.0700000	+	0.0387298i
$21$	9600.00			1.03661
$22$	7440.00	−	1921.00i	0.698723	−	0.180409i
$23$		−	10472.5i		−	0.860734i	−0.902654	−	0.430367i	$-0.858384\pi$
$23$		−	10472.5i		−	0.860734i	0.902654	−	0.430367i	$-0.141616\pi$
$24$	−11520.0	+	10906.3i	−0.833333	+	0.788941i
$25$	−15525.0			−0.993600
$26$	2932.00	+	11355.6i	0.166818	+	0.646085i
$27$		−	15430.0i		−	0.783923i
$28$	−9600.00	−	17351.0i	−0.437318	−	0.790405i
$29$	25498.0			1.04547			0.522736	−	0.852495i	$-0.324911\pi$
$29$	25498.0			1.04547			0.522736	+	0.852495i	$0.324911\pi$
$30$	2400.00	−	619.677i	0.0888889	−	0.0229510i
$31$			41890.2i			1.40614i	0.711123	+	0.703068i	$0.248187\pi$
$31$			41890.2i			1.40614i	−0.711123	+	0.703068i	$0.751813\pi$
$32$	31232.0	+	9914.84i	0.953125	+	0.302577i
$33$	−29760.0			−0.828116
$34$	−9532.00	−	36917.3i	−0.242520	−	0.939275i
$35$			3098.39i			0.0722656i
$36$	12936.0	−	7157.27i	0.277263	−	0.153405i
$37$	1994.00			0.0393659			0.0196829	−	0.999806i	$-0.493734\pi$
$37$	1994.00			0.0393659			0.0196829	+	0.999806i	$0.493734\pi$
$38$	−58320.0	+	15058.2i	−1.06284	+	0.274423i
$39$		−	45422.3i		−	0.765730i
$40$	−3520.00	−	3718.06i	−0.0550000	−	0.0580948i
$41$	29362.0			0.426024			0.213012	−	0.977050i	$-0.431673\pi$
$41$	29362.0			0.426024			0.213012	+	0.977050i	$0.431673\pi$
$42$	19200.0	+	74361.3i	0.259151	+	1.00369i
$43$		−	21533.8i		−	0.270841i	−0.990788	−	0.135421i	$-0.956761\pi$
$43$		−	21533.8i		−	0.270841i	0.990788	−	0.135421i	$-0.0432386\pi$
$44$	29760.0	+	53788.0i	0.349361	+	0.631433i
$45$	−2310.00			−0.0253498
$46$	81120.0	−	20945.1i	0.833402	−	0.215183i
$47$		−	7560.06i		−	0.0728168i	−0.999337	−	0.0364084i	$-0.988408\pi$
$47$		−	7560.06i		−	0.0728168i	0.999337	−	0.0364084i	$-0.0115917\pi$
$48$	−107520.	−	67420.9i	−0.972222	−	0.609636i
$49$	21649.0			0.184013
$50$	−31050.0	−	120256.i	−0.248400	−	0.962049i
$51$			147669.i			1.11322i
$52$	−82096.0	+	45422.3i	−0.583864	+	0.323042i
$53$	−192854.			−1.29539			−0.647696	−	0.761899i	$-0.724267\pi$
$53$	−192854.			−1.29539			−0.647696	+	0.761899i	$0.724267\pi$
$54$	119520.	−	30859.9i	0.759031	−	0.195981i
$55$		−	9605.00i		−	0.0577310i
$56$	115200.	−	109063.i	0.655977	−	0.621032i
$57$	233280.			1.25966
$58$	50996.0	+	197507.i	0.261368	+	1.01227i
$59$		−	78420.2i		−	0.381831i	−0.981606	−	0.190916i	$-0.938854\pi$
$59$		−	78420.2i		−	0.381831i	0.981606	−	0.190916i	$-0.0611457\pi$
$60$	9600.00	+	17351.0i	0.0444444	+	0.0803285i
$61$	−10918.0			−0.0481009			−0.0240505	−	0.999711i	$-0.507656\pi$
$61$	−10918.0			−0.0481009			−0.0240505	+	0.999711i	$0.507656\pi$
$62$	−324480.	+	83780.4i	−1.36149	+	0.351534i
$63$		−	71572.7i		−	0.286237i
$64$	−14336.0	+	261752.i	−0.0546875	+	0.998504i
$65$	14660.0			0.0533819
$66$	−59520.0	−	230520.i	−0.207029	−	0.801820i
$67$		−	394146.i		−	1.31049i	−0.755418	−	0.655243i	$-0.772566\pi$
$67$		−	394146.i		−	1.31049i	0.755418	−	0.655243i	$-0.227434\pi$
$68$	266896.	−	147669.i	0.848819	−	0.469638i
$69$	−324480.			−0.987735
$70$	−24000.0	+	6196.77i	−0.0699708	+	0.0180664i
$71$			532241.i			1.48708i	0.668694	+	0.743538i	$0.266854\pi$
$71$			532241.i			1.48708i	−0.668694	+	0.743538i	$0.733146\pi$
$72$	81312.0	+	85887.3i	0.217850	+	0.230108i
$73$	288626.			0.741937			0.370968	−	0.928646i	$-0.379026\pi$
$73$	288626.			0.741937			0.370968	+	0.928646i	$0.379026\pi$
$74$	3988.00	+	15445.5i	0.00984147	+	0.0381159i
$75$			481025.i			1.14021i
$76$	−233280.	−	421628.i	−0.531419	−	0.960482i
$77$	297600.			0.651870
$78$	351840.	−	90844.7i	0.741415	−	0.191433i
$79$		−	310706.i		−	0.630186i	−0.949061	−	0.315093i	$-0.897964\pi$
$79$		−	310706.i		−	0.630186i	0.949061	−	0.315093i	$-0.102036\pi$
$80$	21760.0	−	34701.9i	0.0425000	−	0.0677772i
$81$	−646479.			−1.21646
$82$	58724.0	+	227437.i	0.106506	+	0.412496i
$83$		−	204153.i		−	0.357043i	−0.983936	−	0.178522i	$-0.942869\pi$
$83$		−	204153.i		−	0.357043i	0.983936	−	0.178522i	$-0.0571314\pi$
$84$	−537600.	+	297445.i	−0.907029	+	0.501844i
$85$	−47660.0			−0.0776064
$86$	166800.	−	43067.6i	0.262241	−	0.0677104i
$87$		−	790027.i		−	1.19973i
$88$	−357120.	+	338096.i	−0.524042	+	0.496126i
$89$	310738.			0.440783			0.220391	−	0.975412i	$-0.429267\pi$
$89$	310738.			0.440783			0.220391	+	0.975412i	$0.429267\pi$
$90$	−4620.00	−	17893.2i	−0.00633745	−	0.0245448i
$91$			454223.i			0.602761i
$92$	324480.	+	586463.i	0.416701	+	0.753142i
$93$	1.29792e6			1.61361
$94$	58560.0	−	15120.1i	0.0705046	−	0.0182042i
$95$			75290.8i			0.0878155i
$96$	307200.	−	967688.i	0.347222	−	1.09376i
$97$	−1.45709e6			−1.59650			−0.798252	−	0.602324i	$-0.794242\pi$
$97$	−1.45709e6			−1.59650			−0.798252	+	0.602324i	$0.794242\pi$
$98$	43298.0	+	167692.i	0.0460034	+	0.178170i
$99$			221875.i			0.228667i
$100$	869400.	−	481025.i	0.869400	−	0.481025i
$101$	−639158.			−0.620360			−0.310180	−	0.950678i	$-0.600389\pi$
$101$	−639158.			−0.620360			−0.310180	+	0.950678i	$0.600389\pi$
$102$	−1.14384e6	+	295338.i	−1.07787	+	0.278304i
$103$			1.38913e6i			1.27125i	0.771997	+	0.635626i	$0.219258\pi$
$103$			1.38913e6i			1.27125i	−0.771997	+	0.635626i	$0.780742\pi$
$104$	−516032.	−	545068.i	−0.458751	−	0.484564i
$105$	96000.0			0.0829284
$106$	−385708.	−	1.49384e6i	−0.323848	−	1.25426i
$107$		−	1.14935e6i		−	0.938209i	−0.883143	−	0.469105i	$-0.844577\pi$
$107$		−	1.14935e6i		−	0.938209i	0.883143	−	0.469105i	$-0.155423\pi$
$108$	478080.	+	864078.i	0.379515	+	0.685933i
$109$	1.53574e6			1.18587			0.592936	−	0.805250i	$-0.297969\pi$
$109$	1.53574e6			1.18587			0.592936	+	0.805250i	$0.297969\pi$
$110$	74400.0	−	19210.0i	0.0558978	−	0.0144328i
$111$		−	61781.8i		−	0.0451743i
$112$	1.07520e6	+	674209.i	0.765306	+	0.479889i
$113$	−601694.			−0.417004			−0.208502	−	0.978022i	$-0.566859\pi$
$113$	−601694.			−0.417004			−0.208502	+	0.978022i	$0.566859\pi$
$114$	466560.	+	1.80698e6i	0.314915	+	1.21966i
$115$		−	104725.i		−	0.0688587i
$116$	−1.42789e6	+	790027.i	−0.914787	+	0.506137i
$117$	−338646.			−0.211441
$118$	607440.	−	156840.i	0.369707	−	0.0954579i
$119$		−	1.47669e6i		−	0.876292i
$120$	−115200.	+	109063.i	−0.0666667	+	0.0631153i
$121$	849001.			0.479239
$122$	−21836.0	−	84570.5i	−0.0120252	−	0.0465735i
$123$		−	909748.i		−	0.488884i
$124$	−1.29792e6	−	2.34585e6i	−0.680743	−	1.23037i
$125$	−311500.			−0.159488
$126$	554400.	−	143145.i	0.277148	−	0.0715593i
$127$			1.67462e6i			0.817531i	0.912640	+	0.408765i	$0.134041\pi$
$127$			1.67462e6i			0.817531i	−0.912640	+	0.408765i	$0.865959\pi$
$128$	−2.05619e6	+	412457.i	−0.980469	+	0.196675i
$129$	−667200.			−0.310804
$130$	29320.0	+	113556.i	0.0133455	+	0.0516868i
$131$			2.84454e6i			1.26531i	0.774433	+	0.632656i	$0.218035\pi$
$131$			2.84454e6i			1.26531i	−0.774433	+	0.632656i	$0.781965\pi$
$132$	1.66656e6	−	922080.i	0.724601	−	0.400910i
$133$	−2.33280e6			−0.991568
$134$	3.05304e6	−	788292.i	1.26887	−	0.327622i
$135$		−	154300.i		−	0.0627139i
$136$	1.67763e6	+	1.77203e6i	0.666930	+	0.704456i
$137$	3.81003e6			1.48172			0.740862	−	0.671658i	$-0.234417\pi$
$137$	3.81003e6			1.48172			0.740862	+	0.671658i	$0.234417\pi$
$138$	−648960.	−	2.51341e6i	−0.246934	−	0.956371i
$139$			138839.i			0.0516971i	0.999666	+	0.0258485i	$0.00822877\pi$
$139$			138839.i			0.0516971i	−0.999666	+	0.0258485i	$0.991771\pi$
$140$	−96000.0	−	173510.i	−0.0349854	−	0.0632324i
$141$	−234240.			−0.0835610
$142$	−4.12272e6	+	1.06448e6i	−1.43986	+	0.371769i
$143$		−	1.40809e6i		−	0.481530i
$144$	−502656.	+	801615.i	−0.168338	+	0.268459i
$145$	254980.			0.0836377
$146$	577252.	+	2.23569e6i	0.185484	+	0.718377i
$147$		−	670770.i		−	0.211165i
$148$	−111664.	+	61781.8i	−0.0344451	+	0.0190579i
$149$	−3.27426e6			−0.989816			−0.494908	−	0.868945i	$-0.664798\pi$
$149$	−3.27426e6			−0.989816			−0.494908	+	0.868945i	$0.664798\pi$
$150$	−3.72600e6	+	962049.i	−1.10400	+	0.285052i
$151$		−	5.59352e6i		−	1.62463i	−0.583220	−	0.812314i	$-0.698207\pi$
$151$		−	5.59352e6i		−	1.62463i	0.583220	−	0.812314i	$-0.301793\pi$
$152$	2.79936e6	−	2.65024e6i	0.797128	−	0.754664i
$153$	1.10095e6			0.307391
$154$	595200.	+	2.30520e6i	0.162967	+	0.631170i
$155$			418902.i			0.112491i
$156$	1.40736e6	+	2.54365e6i	0.370708	+	0.670014i
$157$	816794.			0.211064			0.105532	−	0.994416i	$-0.466345\pi$
$157$	816794.			0.211064			0.105532	+	0.994416i	$0.466345\pi$
$158$	2.40672e6	−	621412.i	0.610175	−	0.157546i
$159$			5.97536e6i			1.48653i
$160$	312320.	+	99148.4i	0.0762500	+	0.0242061i
$161$	3.24480e6			0.777518
$162$	−1.29296e6	−	5.00760e6i	−0.304116	−	1.17784i
$163$		−	1.84593e6i		−	0.426237i	−0.977026	−	0.213119i	$-0.931638\pi$
$163$		−	1.84593e6i		−	0.426237i	0.977026	−	0.213119i	$-0.0683621\pi$
$164$	−1.64427e6	+	909748.i	−0.372771	+	0.206248i
$165$	−297600.			−0.0662493
$166$	1.58136e6	−	408305.i	0.345706	−	0.0892608i
$167$			7.96515e6i			1.71019i	0.518471	+	0.855095i	$0.326501\pi$
$167$			7.96515e6i			1.71019i	−0.518471	+	0.855095i	$0.673499\pi$
$168$	−3.37920e6	−	3.56934e6i	−0.712666	−	0.752766i
$169$	−2.67765e6			−0.554746
$170$	−95320.0	−	369173.i	−0.0194016	−	0.0751420i
$171$		−	1.73922e6i		−	0.347829i
$172$	667200.	+	1.20589e6i	0.131121	+	0.236986i
$173$	−5.12653e6			−0.990115			−0.495057	−	0.868860i	$-0.664853\pi$
$173$	−5.12653e6			−0.990115			−0.495057	+	0.868860i	$0.664853\pi$
$174$	6.11952e6	−	1.58005e6i	1.16163	−	0.299933i
$175$		−	4.81025e6i		−	0.897538i
$176$	−3.33312e6	−	2.09005e6i	−0.611382	−	0.383370i
$177$	−2.42976e6			−0.438171
$178$	621476.	+	2.40697e6i	0.110196	+	0.426786i
$179$		−	2.33411e6i		−	0.406969i	−0.979078	−	0.203485i	$-0.934773\pi$
$179$		−	2.33411e6i		−	0.406969i	0.979078	−	0.203485i	$-0.0652267\pi$
$180$	129360.	−	71572.7i	0.0221811	−	0.0122724i
$181$	9.69156e6			1.63440			0.817199	−	0.576355i	$-0.195525\pi$
$181$	9.69156e6			1.63440			0.817199	+	0.576355i	$0.195525\pi$
$182$	−3.51840e6	+	908447.i	−0.583621	+	0.150690i
$183$			338282.i			0.0551983i
$184$	−3.89376e6	+	3.68634e6i	−0.625051	+	0.591754i
$185$	19940.0			0.00314927
$186$	2.59584e6	+	1.00536e7i	0.403403	+	1.56237i
$187$			4.57774e6i			0.700046i
$188$	234240.	+	423364.i	0.0352523	+	0.0637147i
$189$	4.78080e6			0.708134
$190$	−583200.	+	150582.i	−0.0850270	+	0.0219539i
$191$		−	1.14164e7i		−	1.63844i	−0.573479	−	0.819220i	$-0.694407\pi$
$191$		−	1.14164e7i		−	1.63844i	0.573479	−	0.819220i	$-0.305593\pi$
$192$	8.11008e6	+	444185.i	1.14583	+	0.0627567i
$193$	−2.43033e6			−0.338060			−0.169030	−	0.985611i	$-0.554064\pi$
$193$	−2.43033e6			−0.338060			−0.169030	+	0.985611i	$0.554064\pi$
$194$	−2.91417e6	−	1.12865e7i	−0.399126	−	1.54581i
$195$		−	454223.i		−	0.0612584i
$196$	−1.21234e6	+	670770.i	−0.161012	+	0.0890851i
$197$	−2.23065e6			−0.291764			−0.145882	−	0.989302i	$-0.546602\pi$
$197$	−2.23065e6			−0.291764			−0.145882	+	0.989302i	$0.546602\pi$
$198$	−1.71864e6	+	443751.i	−0.221406	+	0.0571668i
$199$			4.89576e6i			0.621242i	0.950534	+	0.310621i	$0.100537\pi$
$199$			4.89576e6i			0.621242i	−0.950534	+	0.310621i	$0.899463\pi$
$200$	5.46480e6	+	5.77229e6i	0.683100	+	0.721537i
$201$	−1.22122e7			−1.50385
$202$	−1.27832e6	−	4.95090e6i	−0.155090	−	0.600661i
$203$			7.90027e6i			0.944395i
$204$	−4.57536e6	−	8.26947e6i	−0.538933	−	0.974063i
$205$	293620.			0.0340819
$206$	−1.07602e7	+	2.77826e6i	−1.23088	+	0.317813i
$207$			2.41916e6i			0.272743i
$208$	3.19002e6	−	5.08730e6i	0.354489	−	0.565324i
$209$	7.23168e6			0.792137
$210$	192000.	+	743613.i	0.0207321	+	0.0802951i
$211$			3.90951e6i			0.416174i	0.978110	+	0.208087i	$0.0667238\pi$
$211$			3.90951e6i			0.416174i	−0.978110	+	0.208087i	$0.933276\pi$
$212$	1.07998e7	−	5.97536e6i	1.13347	−	0.627129i
$213$	1.64909e7			1.70650
$214$	8.90280e6	−	2.29869e6i	0.908417	−	0.234552i
$215$		−	215338.i		−	0.0216673i
$216$	−5.73696e6	+	5.43135e6i	−0.569273	+	0.538947i
$217$	−1.29792e7			−1.27019
$218$	3.07148e6	+	1.18958e7i	0.296468	+	1.14822i
$219$		−	8.94275e6i		−	0.851410i
$220$	297600.	+	537880.i	0.0279489	+	0.0505146i
$221$	−6.98696e6			−0.647308
$222$	478560.	−	123564.i	0.0437399	−	0.0112936i
$223$			3.33114e6i			0.300385i	0.988657	+	0.150192i	$0.0479893\pi$
$223$			3.33114e6i			0.300385i	−0.988657	+	0.150192i	$0.952011\pi$
$224$	−3.07200e6	+	9.67688e6i	−0.273324	+	0.860977i
$225$	3.58628e6			0.314844
$226$	−1.20339e6	−	4.66070e6i	−0.104251	−	0.403763i
$227$		−	1.35033e7i		−	1.15442i	−0.816597	−	0.577208i	$-0.804142\pi$
$227$		−	1.35033e7i		−	1.15442i	0.816597	−	0.577208i	$-0.195858\pi$
$228$	−1.30637e7	+	7.22792e6i	−1.10220	+	0.609830i
$229$	1.59598e6			0.132899			0.0664493	−	0.997790i	$-0.478833\pi$
$229$	1.59598e6			0.132899			0.0664493	+	0.997790i	$0.478833\pi$
$230$	811200.	−	209451.i	0.0666721	−	0.0172147i
$231$		−	9.22080e6i		−	0.748053i
$232$	−8.97530e6	−	9.48032e6i	−0.718762	−	0.759205i
$233$	8.04383e6			0.635909			0.317954	−	0.948106i	$-0.397004\pi$
$233$	8.04383e6			0.635909			0.317954	+	0.948106i	$0.397004\pi$
$234$	−677292.	−	2.62314e6i	−0.0528601	−	0.204726i
$235$		−	75600.6i		−	0.00582535i
$236$	2.42976e6	+	4.39153e6i	0.184853	+	0.334103i
$237$	−9.62688e6			−0.723170
$238$	1.14384e7	−	2.95338e6i	0.848466	−	0.219073i
$239$			1.12532e7i			0.824296i	0.911117	+	0.412148i	$0.135221\pi$
$239$			1.12532e7i			0.824296i	−0.911117	+	0.412148i	$0.864779\pi$
$240$	−1.07520e6	−	674209.i	−0.0777778	−	0.0487709i
$241$	5.05104e6			0.360853			0.180426	−	0.983589i	$-0.442252\pi$
$241$	5.05104e6			0.360853			0.180426	+	0.983589i	$0.442252\pi$
$242$	1.69800e6	+	6.57633e6i	0.119810	+	0.464021i
$243$			8.78197e6i			0.612031i
$244$	611408.	−	338282.i	0.0420883	−	0.0232868i
$245$	216490.			0.0147211
$246$	7.04688e6	−	1.81950e6i	0.473360	−	0.122221i
$247$			1.10376e7i			0.732462i
$248$	1.55750e7	−	1.47453e7i	1.02111	−	0.966718i
$249$	−6.32544e6			−0.409725
$250$	−623000.	−	2.41287e6i	−0.0398720	−	0.154424i
$251$			4.71590e6i			0.298225i	0.988820	+	0.149112i	$0.0476416\pi$
$251$			4.71590e6i			0.298225i	−0.988820	+	0.149112i	$0.952358\pi$
$252$	2.21760e6	+	4.00807e6i	0.138574	+	0.250457i
$253$	−1.00589e7			−0.621138
$254$	−1.29715e7	+	3.34923e6i	−0.791571	+	0.204383i
$255$			1.47669e6i			0.0890572i
$256$	−7.30726e6	−	1.51023e7i	−0.435547	−	0.900166i
$257$	2.34552e7			1.38178			0.690892	−	0.722958i	$-0.257218\pi$
$257$	2.34552e7			1.38178			0.690892	+	0.722958i	$0.257218\pi$
$258$	−1.33440e6	−	5.16811e6i	−0.0777011	−	0.300935i
$259$			617818.i			0.0355600i
$260$	−820960.	+	454223.i	−0.0467091	+	0.0258434i
$261$	−5.89004e6			−0.331281
$262$	−2.20337e7	+	5.68907e6i	−1.22513	+	0.316328i
$263$		−	2.16993e7i		−	1.19283i	−0.802676	−	0.596415i	$-0.796591\pi$
$263$		−	2.16993e7i		−	1.19283i	0.802676	−	0.596415i	$-0.203409\pi$
$264$	1.04755e7	+	1.10650e7i	0.569330	+	0.601365i
$265$	−1.92854e6			−0.103631
$266$	−4.66560e6	−	1.80698e7i	−0.247892	−	0.960082i
$267$		−	9.62786e6i		−	0.505820i
$268$	1.22122e7	+	2.20722e7i	0.634436	+	1.14668i
$269$	−2.94278e7			−1.51182			−0.755911	−	0.654674i	$-0.772806\pi$
$269$	−2.94278e7			−1.51182			−0.755911	+	0.654674i	$0.772806\pi$
$270$	1.19520e6	−	308599.i	0.0607225	−	0.0156785i
$271$		−	8.51474e6i		−	0.427822i	−0.976853	−	0.213911i	$-0.931380\pi$
$271$		−	8.51474e6i		−	0.427822i	0.976853	−	0.213911i	$-0.0686203\pi$
$272$	−1.03708e7	+	1.65389e7i	−0.515355	+	0.821866i
$273$	1.40736e7			0.691699
$274$	7.62007e6	+	2.95124e7i	0.370431	+	1.43467i
$275$			1.49118e7i			0.717019i
$276$	1.81709e7	−	1.00536e7i	0.864269	−	0.478185i
$277$	2.76226e7			1.29965			0.649824	−	0.760085i	$-0.274843\pi$
$277$	2.76226e7			1.29965			0.649824	+	0.760085i	$0.274843\pi$
$278$	−1.07544e6	+	277677.i	−0.0500555	+	0.0129243i
$279$		−	9.67663e6i		−	0.445566i
$280$	1.15200e6	−	1.09063e6i	0.0524781	−	0.0496826i
$281$	8.64008e6			0.389403			0.194701	−	0.980863i	$-0.437626\pi$
$281$	8.64008e6			0.389403			0.194701	+	0.980863i	$0.437626\pi$
$282$	−468480.	−	1.81442e6i	−0.0208903	−	0.0809076i
$283$		−	1.27350e7i		−	0.561873i	−0.959726	−	0.280937i	$-0.909355\pi$
$283$		−	1.27350e7i		−	0.561873i	0.959726	−	0.280937i	$-0.0906450\pi$
$284$	−1.64909e7	−	2.98055e7i	−0.719928	−	1.30119i
$285$	2.33280e6			0.100773
$286$	1.09070e7	−	2.81619e6i	0.466239	−	0.120382i
$287$			9.09748e6i			0.384836i
$288$	−7.21459e6	−	2.29033e6i	−0.302019	−	0.0958783i
$289$	−1.42281e6			−0.0589460
$290$	509960.	+	1.97507e6i	0.0209094	+	0.0809819i
$291$			4.51462e7i			1.83207i
$292$	−1.61631e7	+	8.94275e6i	−0.649195	+	0.359189i
$293$	−4.45415e7			−1.77077			−0.885385	−	0.464859i	$-0.846105\pi$
$293$	−4.45415e7			−1.77077			−0.885385	+	0.464859i	$0.846105\pi$
$294$	5.19576e6	−	1.34154e6i	0.204459	−	0.0527912i
$295$		−	784202.i		−	0.0305465i
$296$	−701888.	−	741382.i	−0.0270640	−	0.0285869i
$297$	−1.48205e7			−0.565709
$298$	−6.54852e6	−	2.53623e7i	−0.247454	−	0.958386i
$299$		−	1.53528e7i		−	0.574345i
$300$	−1.49040e7	−	2.69374e7i	−0.552000	−	0.997681i
$301$	6.67200e6			0.244656
$302$	4.33272e7	−	1.11870e7i	1.57304	−	0.406157i
$303$			1.98036e7i			0.711895i
$304$	2.61274e7	+	1.63833e7i	0.929983	+	0.583150i
$305$	−109180.			−0.00384808
$306$	2.20189e6	+	8.52789e6i	0.0768479	+	0.297630i
$307$		−	4.89051e7i		−	1.69020i	−0.534606	−	0.845102i	$-0.679540\pi$
$307$		−	4.89051e7i		−	1.69020i	0.534606	−	0.845102i	$-0.320460\pi$
$308$	−1.66656e7	+	9.22080e6i	−0.570386	+	0.315585i
$309$	4.30406e7			1.45883
$310$	−3.24480e6	+	837804.i	−0.108919	+	0.0281227i
$311$			5.00220e7i			1.66295i	0.555559	+	0.831477i	$0.312504\pi$
$311$			5.00220e7i			1.66295i	−0.555559	+	0.831477i	$0.687496\pi$
$312$	−1.68883e7	+	1.59887e7i	−0.556061	+	0.526440i
$313$	1.12719e6			0.0367589			0.0183795	−	0.999831i	$-0.494149\pi$
$313$	1.12719e6			0.0367589			0.0183795	+	0.999831i	$0.494149\pi$
$314$	1.63359e6	+	6.32686e6i	0.0527659	+	0.204362i
$315$		−	715727.i		−	0.0228990i
$316$	9.62688e6	+	1.73995e7i	0.305087	+	0.551413i
$317$	3.44882e7			1.08266			0.541330	−	0.840810i	$-0.317921\pi$
$317$	3.44882e7			1.08266			0.541330	+	0.840810i	$0.317921\pi$
$318$	−4.62850e7	+	1.19507e7i	−1.43932	+	0.371632i
$319$		−	2.44908e7i		−	0.754452i
$320$	−143360.	+	2.61752e6i	−0.00437500	+	0.0798803i
$321$	−3.56112e7			−1.07664
$322$	6.48960e6	+	2.51341e7i	0.194379	+	0.752828i
$323$		−	3.58836e7i		−	1.06485i
$324$	3.62028e7	−	2.00304e7i	1.06441	−	0.588918i
$325$	−2.27596e7			−0.663003
$326$	1.42985e7	−	3.69185e6i	0.412702	−	0.106559i
$327$		−	4.75831e7i		−	1.36085i
$328$	−1.03354e7	−	1.09170e7i	−0.292891	−	0.309372i
$329$	2.34240e6			0.0657769
$330$	−595200.	−	2.30520e6i	−0.0165623	−	0.0641456i
$331$			4.02696e7i			1.11044i	0.831705	+	0.555218i	$0.187365\pi$
$331$			4.02696e7i			1.11044i	−0.831705	+	0.555218i	$0.812635\pi$
$332$	6.32544e6	+	1.14326e7i	0.172853	+	0.312413i
$333$	−460614.			−0.0124740
$334$	−6.16978e7	+	1.59303e7i	−1.65588	+	0.427547i
$335$		−	3.94146e6i		−	0.104839i
$336$	2.08896e7	−	3.33139e7i	0.550696	−	0.878228i
$337$	−3.42531e7			−0.894973			−0.447487	−	0.894291i	$-0.647681\pi$
$337$	−3.42531e7			−0.894973			−0.447487	+	0.894291i	$0.647681\pi$
$338$	−5.35531e6	−	2.07410e7i	−0.138687	−	0.537131i
$339$			1.86428e7i			0.478533i
$340$	2.66896e6	−	1.47669e6i	0.0679056	−	0.0375710i
$341$	4.02355e7			1.01472
$342$	1.34719e7	−	3.47843e6i	0.336784	−	0.0869572i
$343$			4.31599e7i			1.06954i
$344$	−8.00640e6	+	7.57989e6i	−0.196681	+	0.186203i
$345$	−3.24480e6			−0.0790188
$346$	−1.02531e7	−	3.97100e7i	−0.247529	−	0.958674i
$347$			5.45496e7i			1.30558i	0.757539	+	0.652790i	$0.226401\pi$
$347$			5.45496e7i			1.30558i	−0.757539	+	0.652790i	$0.773599\pi$
$348$	2.44781e7	+	4.42415e7i	0.580817	+	1.04976i
$349$	4.70009e7			1.10568			0.552840	−	0.833287i	$-0.313544\pi$
$349$	4.70009e7			1.10568			0.552840	+	0.833287i	$0.313544\pi$
$350$	3.72600e7	−	9.62049e6i	0.869038	−	0.224385i
$351$		−	2.26203e7i		−	0.523091i
$352$	9.52320e6	−	2.99983e7i	0.218351	−	0.687811i
$353$	−1.27231e7			−0.289248			−0.144624	−	0.989487i	$-0.546197\pi$
$353$	−1.27231e7			−0.289248			−0.144624	+	0.989487i	$0.546197\pi$
$354$	−4.85952e6	−	1.88208e7i	−0.109543	−	0.424257i
$355$			5.32241e6i			0.118966i
$356$	−1.74013e7	+	9.62786e6i	−0.385685	+	0.213393i
$357$	−4.57536e7			−1.00559
$358$	1.80799e7	−	4.66822e6i	0.394046	−	0.101742i
$359$		−	2.02153e7i		−	0.436915i	−0.975846	−	0.218457i	$-0.929898\pi$
$359$		−	2.02153e7i		−	0.436915i	0.975846	−	0.218457i	$-0.0701025\pi$
$360$	813120.	+	858873.i	0.0174280	+	0.0184086i
$361$	−9.64116e6			−0.204931
$362$	1.93831e7	+	7.50705e7i	0.408600	+	1.58250i
$363$		−	2.63053e7i		−	0.549951i
$364$	−1.40736e7	−	2.54365e7i	−0.291811	−	0.527416i
$365$	2.88626e6			0.0593549
$366$	−2.62032e6	+	676564.i	−0.0534455	+	0.0137996i
$367$		−	1.11057e7i		−	0.224672i	−0.993670	−	0.112336i	$-0.964167\pi$
$367$		−	1.11057e7i		−	0.224672i	0.993670	−	0.112336i	$-0.0358333\pi$
$368$	−3.63418e7	−	2.27883e7i	−0.729227	−	0.457265i
$369$	−6.78262e6			−0.134995
$370$	39880.0	+	154455.i	0.000787318	+	0.00304927i
$371$		−	5.97536e7i		−	1.17015i
$372$	−7.26835e7	+	4.02146e7i	−1.41191	+	0.781186i
$373$	687146.			0.0132411			0.00662053	−	0.999978i	$-0.497893\pi$
$373$	687146.			0.0132411			0.00662053	+	0.999978i	$0.497893\pi$
$374$	−3.54590e7	+	9.15548e6i	−0.677817	+	0.175011i
$375$			9.65147e6i			0.183021i
$376$	−2.81088e6	+	2.66114e6i	−0.0528785	+	0.0500616i
$377$	3.73801e7			0.697615
$378$	9.56160e6	+	3.70319e7i	0.177033	+	0.685647i
$379$			1.48499e7i			0.272775i	0.990656	+	0.136388i	$0.0435492\pi$
$379$			1.48499e7i			0.272775i	−0.990656	+	0.136388i	$0.956451\pi$
$380$	−2.33280e6	−	4.21628e6i	−0.0425135	−	0.0768385i
$381$	5.18861e7			0.938158
$382$	8.84314e7	−	2.28329e7i	1.58641	−	0.409610i
$383$		−	3.35885e7i		−	0.597853i	−0.954276	−	0.298926i	$-0.903372\pi$
$383$		−	3.35885e7i		−	0.597853i	0.954276	−	0.298926i	$-0.0966285\pi$
$384$	1.27795e7	+	6.37088e7i	0.225694	+	1.12514i
$385$	2.97600e6			0.0521496
$386$	−4.86067e6	−	1.88253e7i	−0.0845150	−	0.327325i
$387$			4.97430e6i			0.0858222i
$388$	8.15968e7	−	4.51462e7i	1.39694	−	0.772904i
$389$	−1.01122e8			−1.71789			−0.858946	−	0.512066i	$-0.828880\pi$
$389$	−1.01122e8			−1.71789			−0.858946	+	0.512066i	$0.828880\pi$
$390$	3.51840e6	−	908447.i	0.0593132	−	0.0153146i
$391$			4.99122e7i			0.834980i
$392$	−7.62045e6	−	8.04924e6i	−0.126509	−	0.133628i
$393$	8.81347e7			1.45201
$394$	−4.46129e6	−	1.72785e7i	−0.0729410	−	0.282499i
$395$		−	3.10706e6i		−	0.0504149i
$396$	−6.87456e6	−	1.24250e7i	−0.110703	−	0.200084i
$397$	−3.48266e7			−0.556595			−0.278297	−	0.960495i	$-0.589770\pi$
$397$	−3.48266e7			−0.556595			−0.278297	+	0.960495i	$0.589770\pi$
$398$	−3.79224e7	+	9.79152e6i	−0.601515	+	0.155311i
$399$			7.22792e7i			1.13787i
$400$	−3.37824e7	+	5.38747e7i	−0.527850	+	0.841793i
$401$	−6.88398e7			−1.06760			−0.533798	−	0.845612i	$-0.679236\pi$
$401$	−6.88398e7			−1.06760			−0.533798	+	0.845612i	$0.679236\pi$
$402$	−2.44243e7	−	9.45950e7i	−0.375962	−	1.45610i
$403$			6.14110e7i			0.938277i
$404$	3.57928e7	−	1.98036e7i	0.542815	−	0.300331i
$405$	−6.46479e6			−0.0973171
$406$	−6.11952e7	+	1.58005e7i	−0.914406	+	0.236099i
$407$		−	1.91524e6i		−	0.0284079i
$408$	5.49043e7	−	5.19795e7i	0.808399	−	0.765335i
$409$	4.59959e7			0.672278			0.336139	−	0.941812i	$-0.390879\pi$
$409$	4.59959e7			0.672278			0.336139	+	0.941812i	$0.390879\pi$
$410$	587240.	+	2.27437e6i	0.00852048	+	0.0329997i
$411$		−	1.18050e8i		−	1.70035i
$412$	−4.30406e7	−	7.77913e7i	−0.615442	−	1.11234i
$413$	2.42976e7			0.344916
$414$	−1.87387e7	+	4.83832e6i	−0.264082	+	0.0681857i
$415$		−	2.04153e6i		−	0.0285635i
$416$	4.57861e7	+	1.45352e7i	0.635995	+	0.201902i
$417$	4.30176e6			0.0593250
$418$	1.44634e7	+	5.60164e7i	0.198034	+	0.766983i
$419$			2.71153e7i			0.368615i	0.982869	+	0.184307i	$0.0590042\pi$
$419$			2.71153e7i			0.368615i	−0.982869	+	0.184307i	$0.940996\pi$
$420$	−5.37600e6	+	2.97445e6i	−0.0725624	+	0.0401475i
$421$	−9.42078e7			−1.26253			−0.631263	−	0.775569i	$-0.717463\pi$
$421$	−9.42078e7			−1.26253			−0.631263	+	0.775569i	$0.717463\pi$
$422$	−3.02830e7	+	7.81903e6i	−0.402959	+	0.104044i
$423$			1.74637e6i			0.0230737i
$424$	6.78846e7	+	7.17044e7i	0.890582	+	0.940693i
$425$	7.39922e7			0.963871
$426$	3.29818e7	+	1.27738e8i	0.426624	+	1.65231i
$427$		−	3.38282e6i		−	0.0434505i
$428$	3.56112e7	+	6.43634e7i	0.454209	+	0.820933i
$429$	−4.36282e7			−0.552580
$430$	1.66800e6	−	430676.i	0.0209793	−	0.00541683i
$431$		−	5.19187e7i		−	0.648473i	−0.945976	−	0.324236i	$-0.894893\pi$
$431$		−	5.19187e7i		−	0.648473i	0.945976	−	0.324236i	$-0.105107\pi$
$432$	−5.35450e7	−	3.35756e7i	−0.664152	−	0.416459i
$433$	8.40210e7			1.03496			0.517481	−	0.855695i	$-0.326870\pi$
$433$	8.40210e7			1.03496			0.517481	+	0.855695i	$0.326870\pi$
$434$	−2.59584e7	−	1.00536e8i	−0.317548	−	1.22986i
$435$		−	7.90027e6i		−	0.0959785i
$436$	−8.60013e7	+	4.75831e7i	−1.03764	+	0.574108i
$437$	7.88486e7			0.944822
$438$	6.92702e7	−	1.78855e7i	0.824374	−	0.212852i
$439$		−	1.48115e8i		−	1.75068i	−0.483512	−	0.875338i	$-0.660639\pi$
$439$		−	1.48115e8i		−	1.75068i	0.483512	−	0.875338i	$-0.339361\pi$
$440$	−3.57120e6	+	3.38096e6i	−0.0419234	+	0.0396901i
$441$	−5.00092e6			−0.0583088
$442$	−1.39739e7	−	5.41207e7i	−0.161827	−	0.626754i
$443$			8.03735e7i			0.924489i	0.886752	+	0.462245i	$0.152956\pi$
$443$			8.03735e7i			0.924489i	−0.886752	+	0.462245i	$0.847044\pi$
$444$	1.91424e6	+	3.45978e6i	0.0218699	+	0.0395275i
$445$	3.10738e6			0.0352626
$446$	−2.58029e7	+	6.66227e6i	−0.290846	+	0.0750962i
$447$			1.01449e8i			1.13586i
$448$	−8.11008e7	−	4.44185e6i	−0.901968	−	0.0494003i
$449$	−8.80925e7			−0.973196			−0.486598	−	0.873626i	$-0.661762\pi$
$449$	−8.80925e7			−0.973196			−0.486598	+	0.873626i	$0.661762\pi$
$450$	7.17255e6	+	2.77792e7i	0.0787111	+	0.304847i
$451$		−	2.82022e7i		−	0.307435i
$452$	3.36949e7	−	1.86428e7i	0.364879	−	0.201881i
$453$	−1.73309e8			−1.86434
$454$	1.04596e8	−	2.70066e7i	1.11776	−	0.288604i
$455$			4.54223e6i			0.0482209i
$456$	−8.21146e7	−	8.67350e7i	−0.866015	−	0.914745i
$457$	−3.75423e7			−0.393344			−0.196672	−	0.980469i	$-0.563013\pi$
$457$	−3.75423e7			−0.393344			−0.196672	+	0.980469i	$0.563013\pi$
$458$	3.19196e6	+	1.23624e7i	0.0332247	+	0.128679i
$459$			7.35392e7i			0.760468i
$460$	3.24480e6	+	5.86463e6i	0.0333361	+	0.0602514i
$461$	1.15260e8			1.17646			0.588228	−	0.808695i	$-0.299826\pi$
$461$	1.15260e8			1.17646			0.588228	+	0.808695i	$0.299826\pi$
$462$	7.14240e7	−	1.84416e7i	0.724300	−	0.187013i
$463$		−	1.03415e7i		−	0.104194i	−0.998642	−	0.0520970i	$-0.983410\pi$
$463$		−	1.03415e7i		−	0.104194i	0.998642	−	0.0520970i	$-0.0165905\pi$
$464$	5.54836e7	−	8.84830e7i	0.555407	−	0.885739i
$465$	1.29792e7			0.129089
$466$	1.60877e7	+	6.23072e7i	0.158977	+	0.615716i
$467$			1.64223e8i			1.61243i	0.591620	+	0.806217i	$0.298489\pi$
$467$			1.64223e8i			1.61243i	−0.591620	+	0.806217i	$0.701511\pi$
$468$	1.89642e7	−	1.04926e7i	0.185011	−	0.102363i
$469$	1.22122e8			1.18379
$470$	585600.	−	151201.i	0.00564037	−	0.00145634i
$471$		−	2.53074e7i		−	0.242206i
$472$	−2.91571e7	+	2.76039e7i	−0.277280	+	0.262509i
$473$	−2.06832e7			−0.195449
$474$	−1.92538e7	−	7.45695e7i	−0.180793	−	0.700207i
$475$		−	1.16889e8i		−	1.09067i
$476$	4.57536e7	+	8.26947e7i	0.424233	+	0.766755i
$477$	4.45493e7			0.410474
$478$	−8.71670e7	+	2.25064e7i	−0.798121	+	0.206074i
$479$			7.76230e7i			0.706291i	0.935568	+	0.353146i	$0.114888\pi$
$479$			7.76230e7i			0.706291i	−0.935568	+	0.353146i	$0.885112\pi$
$480$	3.07200e6	−	9.67688e6i	0.0277778	−	0.0875007i
$481$	2.92320e6			0.0262678
$482$	1.01021e7	+	3.91252e7i	0.0902132	+	0.349394i
$483$		−	1.00536e8i		−	0.892241i
$484$	−4.75441e7	+	2.63053e7i	−0.419334	+	0.232011i
$485$	−1.45709e7			−0.127720
$486$	−6.80249e7	+	1.75639e7i	−0.592596	+	0.153008i
$487$		−	1.08071e7i		−	0.0935670i	−0.998905	−	0.0467835i	$-0.985103\pi$
$487$		−	1.08071e7i		−	0.0935670i	0.998905	−	0.0467835i	$-0.0148971\pi$
$488$	3.84314e6	+	4.05938e6i	0.0330694	+	0.0349302i
$489$	−5.71939e7			−0.489129
$490$	432980.	+	1.67692e6i	0.00368027	+	0.0142536i
$491$		−	1.85067e8i		−	1.56345i	−0.623624	−	0.781724i	$-0.714340\pi$
$491$		−	1.85067e8i		−	1.56345i	0.623624	−	0.781724i	$-0.285660\pi$
$492$	2.81875e7	+	5.09459e7i	0.236680	+	0.427774i
$493$	−1.21523e8			−1.01419
$494$	−8.54971e7	+	2.20753e7i	−0.709203	+	0.183115i
$495$			2.21875e6i			0.0182934i
$496$	1.45367e8	+	9.11530e7i	1.19130	+	0.747010i
$497$	−1.64909e8			−1.34331
$498$	−1.26509e7	−	4.89966e7i	−0.102431	−	0.396715i
$499$		−	6.83704e7i		−	0.550258i	−0.961407	−	0.275129i	$-0.911279\pi$
$499$		−	6.83704e7i		−	0.550258i	0.961407	−	0.275129i	$-0.0887206\pi$
$500$	1.74440e7	−	9.65147e6i	0.139552	−	0.0772118i
$501$	2.46791e8			1.96253
$502$	−3.65292e7	+	9.43180e6i	−0.288755	+	0.0745561i
$503$			1.31562e7i			0.103377i	0.998663	+	0.0516887i	$0.0164604\pi$
$503$			1.31562e7i			0.103377i	−0.998663	+	0.0516887i	$0.983540\pi$
$504$	−2.66112e7	+	2.51936e7i	−0.207861	+	0.196788i
$505$	−6.39158e6			−0.0496288
$506$	−2.01178e7	−	7.79157e7i	−0.155284	−	0.601414i
$507$			8.29640e7i			0.636599i
$508$	−5.18861e7	−	9.37785e7i	−0.395785	−	0.715339i
$509$	1.34186e8			1.01755			0.508775	−	0.860900i	$-0.330099\pi$
$509$	1.34186e8			1.01755			0.508775	+	0.860900i	$0.330099\pi$
$510$	−1.14384e7	+	2.95338e6i	−0.0862293	+	0.0222643i
$511$			8.94275e7i			0.670206i
$512$	1.02367e8	−	8.68064e7i	0.762695	−	0.646758i
$513$	1.16173e8			0.860508
$514$	4.69105e7	+	1.81683e8i	0.345446	+	1.33791i
$515$			1.38913e7i			0.101700i
$516$	3.73632e7	−	2.06724e7i	0.271954	−	0.150467i
$517$	−7.26144e6			−0.0525474
$518$	−4.78560e6	+	1.23564e6i	−0.0344308	+	0.00888999i
$519$			1.58840e8i			1.13621i
$520$	−5.16032e6	−	5.45068e6i	−0.0367000	−	0.0387651i
$521$	−1.98565e8			−1.40407			−0.702036	−	0.712142i	$-0.747725\pi$
$521$	−1.98565e8			−1.40407			−0.702036	+	0.712142i	$0.747725\pi$
$522$	−1.17801e7	−	4.56240e7i	−0.0828203	−	0.320761i
$523$			2.15512e8i			1.50649i	0.657740	+	0.753245i	$0.271513\pi$
$523$			2.15512e8i			1.50649i	−0.657740	+	0.753245i	$0.728487\pi$
$524$	−8.81347e7	−	1.59294e8i	−0.612566	−	1.10715i
$525$	−1.49040e8			−1.02997
$526$	1.68082e8	−	4.33986e7i	1.15495	−	0.298207i
$527$		−	1.99649e8i		−	1.36406i
$528$	−6.47578e7	+	1.03273e8i	−0.439937	+	0.701592i
$529$	3.83616e7			0.259137
$530$	−3.85708e6	−	1.49384e7i	−0.0259078	−	0.100341i
$531$			1.81151e7i			0.120992i
$532$	1.30637e8	−	7.22792e7i	0.867622	−	0.480041i
$533$	4.30447e7			0.284275
$534$	7.45771e7	−	1.92557e7i	0.489758	−	0.126455i
$535$		−	1.14935e7i		−	0.0750567i
$536$	−1.46546e8	+	1.38739e8i	−0.951655	+	0.900959i
$537$	−7.23197e7			−0.467018
$538$	−5.88556e7	−	2.27947e8i	−0.377956	−	1.46382i
$539$		−	2.07939e7i		−	0.132791i
$540$	4.78080e6	+	8.64078e6i	0.0303612	+	0.0548746i
$541$	1.44188e7			0.0910623			0.0455311	−	0.998963i	$-0.485502\pi$
$541$	1.44188e7			0.0910623			0.0455311	+	0.998963i	$0.485502\pi$
$542$	6.59549e7	−	1.70295e7i	0.414237	−	0.106956i
$543$		−	3.00282e8i		−	1.87556i
$544$	−1.48852e8	−	4.72541e7i	−0.924607	−	0.293524i
$545$	1.53574e7			0.0948697
$546$	2.81472e7	+	1.09014e8i	0.172925	+	0.669735i
$547$			4.24129e7i			0.259141i	0.991570	+	0.129571i	$0.0413599\pi$
$547$			4.24129e7i			0.259141i	−0.991570	+	0.129571i	$0.958640\pi$
$548$	−2.13362e8	+	1.18050e8i	−1.29651	+	0.717336i
$549$	2.52206e6			0.0152419
$550$	−1.15506e8	+	2.98235e7i	−0.694251	+	0.179255i
$551$			1.91976e8i			1.14761i
$552$	1.14217e8	+	1.20644e8i	0.679068	+	0.717278i
$553$	9.62688e7			0.569259
$554$	5.52453e7	+	2.13964e8i	0.324912	+	1.25838i
$555$		−	617818.i		−	0.00361395i
$556$	−4.30176e6	−	7.77497e6i	−0.0250277	−	0.0452350i
$557$	8.90848e7			0.515511			0.257756	−	0.966210i	$-0.417017\pi$
$557$	8.90848e7			0.515511			0.257756	+	0.966210i	$0.417017\pi$
$558$	7.49549e7	−	1.93533e7i	0.431417	−	0.111391i
$559$		−	3.15685e7i		−	0.180725i
$560$	1.07520e7	+	6.74209e6i	0.0612245	+	0.0383911i
$561$	1.41836e8			0.803338
$562$	1.72802e7	+	6.69258e7i	0.0973507	+	0.377037i
$563$		−	2.41576e8i		−	1.35372i	−0.736112	−	0.676860i	$-0.763340\pi$
$563$		−	2.41576e8i		−	1.35372i	0.736112	−	0.676860i	$-0.236660\pi$
$564$	1.31174e7	−	7.25766e6i	0.0731159	−	0.0404538i
$565$	−6.01694e6			−0.0333603
$566$	9.86446e7	−	2.54699e7i	0.544031	−	0.140468i
$567$		−	2.00304e8i		−	1.09886i
$568$	1.97891e8	−	1.87349e8i	1.07989	−	1.02236i
$569$	−2.56141e7			−0.139041			−0.0695203	−	0.997581i	$-0.522147\pi$
$569$	−2.56141e7			−0.139041			−0.0695203	+	0.997581i	$0.522147\pi$
$570$	4.66560e6	+	1.80698e7i	0.0251932	+	0.0975728i
$571$			1.10781e8i			0.595057i	0.954713	+	0.297528i	$0.0961623\pi$
$571$			1.10781e8i			0.595057i	−0.954713	+	0.297528i	$0.903838\pi$
$572$	4.36282e7	+	7.88532e7i	0.233120	+	0.421339i
$573$	−3.53725e8			−1.88019
$574$	−7.04688e7	+	1.81950e7i	−0.372616	+	0.0962090i
$575$			1.62586e8i			0.855225i
$576$	3.31162e6	−	6.04646e7i	0.0173290	−	0.316398i
$577$	1.07272e8			0.558415			0.279208	−	0.960231i	$-0.409928\pi$
$577$	1.07272e8			0.558415			0.279208	+	0.960231i	$0.409928\pi$
$578$	−2.84563e6	−	1.10211e7i	−0.0147365	−	0.0570742i
$579$			7.53011e7i			0.387941i
$580$	−1.42789e7	+	7.90027e6i	−0.0731830	+	0.0404909i
$581$	6.32544e7			0.322524
$582$	−3.49701e8	+	9.02923e7i	−1.77389	+	0.458017i
$583$			1.85236e8i			0.934803i
$584$	−1.01596e8	−	1.07313e8i	−0.510082	−	0.538783i
$585$	−3.38646e6			−0.0169152
$586$	−8.90830e7	−	3.45017e8i	−0.442692	−	1.71454i
$587$			2.16397e7i			0.106988i	0.998568	+	0.0534941i	$0.0170358\pi$
$587$			2.16397e7i			0.106988i	−0.998568	+	0.0534941i	$0.982964\pi$
$588$	2.07830e7	+	3.75631e7i	0.102230	+	0.184769i
$589$	−3.15395e8			−1.54351
$590$	6.07440e6	−	1.56840e6i	0.0295765	−	0.00763663i
$591$			6.91140e7i			0.334814i
$592$	4.33894e6	−	6.91956e6i	0.0209131	−	0.0333514i
$593$	2.00341e8			0.960738			0.480369	−	0.877066i	$-0.340503\pi$
$593$	2.00341e8			0.960738			0.480369	+	0.877066i	$0.340503\pi$
$594$	−2.96410e7	−	1.14799e8i	−0.141427	−	0.547745i
$595$		−	1.47669e7i		−	0.0701033i
$596$	1.83359e8	−	1.01449e8i	0.866089	−	0.479193i
$597$	1.51690e8			0.712907
$598$	1.18922e8	−	3.07055e7i	0.556107	−	0.143586i
$599$		−	1.37592e8i		−	0.640197i	−0.947384	−	0.320098i	$-0.896284\pi$
$599$		−	1.37592e8i		−	0.640197i	0.947384	−	0.320098i	$-0.103716\pi$
$600$	1.78848e8	−	1.69321e8i	0.828000	−	0.783892i
$601$	−1.90306e8			−0.876655			−0.438327	−	0.898815i	$-0.644429\pi$
$601$	−1.90306e8			−0.876655			−0.438327	+	0.898815i	$0.644429\pi$
$602$	1.33440e7	+	5.16811e7i	0.0611641	+	0.236888i
$603$			9.10477e7i			0.415257i
$604$	1.73309e8	+	3.13237e8i	0.786520	+	1.42155i
$605$	8.49001e6			0.0383391
$606$	−1.53398e8	+	3.96072e7i	−0.689289	+	0.177974i
$607$			1.25461e8i			0.560974i	0.959858	+	0.280487i	$0.0904960\pi$
$607$			1.25461e8i			0.560974i	−0.959858	+	0.280487i	$0.909504\pi$
$608$	−7.46496e7	+	2.35148e8i	−0.332137	+	1.04624i
$609$	2.44781e8			1.08374
$610$	−218360.	−	845705.i	−0.000962019	−	0.00372588i
$611$		−	1.10831e7i		−	0.0485888i
$612$	−6.16530e7	+	3.41116e7i	−0.268967	+	0.148815i
$613$	−9.91111e7			−0.430270			−0.215135	−	0.976584i	$-0.569019\pi$
$613$	−9.91111e7			−0.430270			−0.215135	+	0.976584i	$0.569019\pi$
$614$	3.78817e8	−	9.78102e7i	1.63653	−	0.422551i
$615$		−	9.09748e6i		−	0.0391107i
$616$	−1.04755e8	−	1.10650e8i	−0.448160	−	0.473378i
$617$	3.70827e7			0.157876			0.0789379	−	0.996880i	$-0.474847\pi$
$617$	3.70827e7			0.157876			0.0789379	+	0.996880i	$0.474847\pi$
$618$	8.60813e7	+	3.33391e8i	0.364706	+	1.41250i
$619$		−	4.05274e8i		−	1.70874i	−0.519662	−	0.854372i	$-0.673942\pi$
$619$		−	4.05274e8i		−	1.70874i	0.519662	−	0.854372i	$-0.326058\pi$
$620$	−1.29792e7	−	2.34585e7i	−0.0544594	−	0.0984295i
$621$	−1.61591e8			−0.674749
$622$	−3.87469e8	+	1.00044e8i	−1.61015	+	0.415738i
$623$			9.62786e7i			0.398168i
$624$	−1.57624e8	−	9.88390e7i	−0.648738	−	0.406794i
$625$	2.39463e8			0.980841
$626$	2.25437e6	+	8.73115e6i	0.00918973	+	0.0355917i
$627$		−	2.24065e8i		−	0.909017i
$628$	−4.57405e7	+	2.53074e7i	−0.184681	+	0.102181i
$629$	−9.50340e6			−0.0381880
$630$	5.54400e6	−	1.43145e6i	0.0221718	−	0.00572474i
$631$		−	2.52648e7i		−	0.100561i	−0.998735	−	0.0502803i	$-0.983989\pi$
$631$		−	2.52648e7i		−	0.100561i	0.998735	−	0.0502803i	$-0.0160115\pi$
$632$	−1.15523e8	+	1.09369e8i	−0.457631	+	0.433253i
$633$	1.21132e8			0.477581
$634$	6.89763e7	+	2.67144e8i	0.270665	+	1.04828i
$635$			1.67462e7i			0.0654025i
$636$	−1.85140e8	−	3.34620e8i	−0.719662	−	1.30071i
$637$	3.17374e7			0.122787
$638$	1.89705e8	−	4.89817e7i	0.730495	−	0.188613i
$639$		−	1.22948e8i		−	0.471213i
$640$	−2.05619e7	+	4.12457e6i	−0.0784375	+	0.0157340i
$641$	−4.21293e8			−1.59959			−0.799797	−	0.600270i	$-0.795060\pi$
$641$	−4.21293e8			−1.59959			−0.799797	+	0.600270i	$0.795060\pi$
$642$	−7.12224e7	−	2.75843e8i	−0.269161	−	1.04245i
$643$			8.17706e7i			0.307584i	0.988103	+	0.153792i	$0.0491486\pi$
$643$			8.17706e7i			0.307584i	−0.988103	+	0.153792i	$0.950851\pi$
$644$	−1.81709e8	+	1.00536e8i	−0.680328	+	0.376414i
$645$	−6.67200e6			−0.0248643
$646$	2.77953e8	−	7.17672e7i	1.03104	−	0.266212i
$647$		−	1.84284e8i		−	0.680416i	−0.940350	−	0.340208i	$-0.889503\pi$
$647$		−	1.84284e8i		−	0.680416i	0.940350	−	0.340208i	$-0.110497\pi$
$648$	2.27561e8	+	2.40365e8i	0.836319	+	0.883377i
$649$	−7.53226e7			−0.275544
$650$	−4.55193e7	−	1.76295e8i	−0.165751	−	0.641950i
$651$			4.02146e8i			1.45761i
$652$	5.71939e7	+	1.03372e8i	0.206351	+	0.372958i
$653$	6.43842e7			0.231228			0.115614	−	0.993294i	$-0.463117\pi$
$653$	6.43842e7			0.231228			0.115614	+	0.993294i	$0.463117\pi$
$654$	3.68577e8	−	9.51662e7i	1.31764	−	0.340212i
$655$			2.84454e7i			0.101225i
$656$	6.38917e7	−	1.01892e8i	0.226325	−	0.360934i
$657$	−6.66726e7			−0.235099
$658$	4.68480e6	+	1.81442e7i	0.0164442	+	0.0636882i
$659$			5.38099e8i			1.88021i	0.340889	+	0.940103i	$0.389272\pi$
$659$			5.38099e8i			1.88021i	−0.340889	+	0.940103i	$0.610728\pi$
$660$	1.66656e7	−	9.22080e6i	0.0579681	−	0.0320728i
$661$	2.83897e8			0.983008			0.491504	−	0.870875i	$-0.336447\pi$
$661$	2.83897e8			0.983008			0.491504	+	0.870875i	$0.336447\pi$
$662$	−3.11927e8	+	8.05393e7i	−1.07518	+	0.277609i
$663$			2.16483e8i			0.742819i
$664$	−7.59053e7	+	7.18617e7i	−0.259279	+	0.245467i
$665$	−2.33280e7			−0.0793255
$666$	−921228.	−	3.56790e6i	−0.00311849	−	0.0120779i
$667$		−	2.67029e8i		−	0.899872i
$668$	−2.46791e8	−	4.46048e8i	−0.827942	−	1.49642i
$669$	1.03212e8			0.344707
$670$	3.05304e7	−	7.88292e6i	0.101510	−	0.0262097i
$671$			1.04867e7i			0.0347115i
$672$	2.99827e8	+	9.51824e7i	0.988014	+	0.313653i
$673$	2.77693e8			0.911002			0.455501	−	0.890235i	$-0.349460\pi$
$673$	2.77693e8			0.911002			0.455501	+	0.890235i	$0.349460\pi$
$674$	−6.85062e7	−	2.65323e8i	−0.223743	−	0.866554i
$675$			2.39550e8i			0.778906i
$676$	1.49949e8	−	8.29640e7i	0.485403	−	0.268565i
$677$	−9.23026e7			−0.297473			−0.148737	−	0.988877i	$-0.547521\pi$
$677$	−9.23026e7			−0.297473			−0.148737	+	0.988877i	$0.547521\pi$
$678$	−1.44407e8	+	3.72856e7i	−0.463338	+	0.119633i
$679$		−	4.51462e8i		−	1.44215i
$680$	1.67763e7	+	1.77203e7i	0.0533544	+	0.0563565i
$681$	−4.18384e8			−1.32475
$682$	8.04710e7	+	3.11663e8i	0.253680	+	0.982499i
$683$		−	2.70862e8i		−	0.850132i	−0.905162	−	0.425066i	$-0.860251\pi$
$683$		−	2.70862e8i		−	0.850132i	0.905162	−	0.425066i	$-0.139749\pi$
$684$	5.38877e7	+	9.73962e7i	0.168392	+	0.304350i
$685$	3.81003e7			0.118538
$686$	−3.34315e8	+	8.63198e7i	−1.03558	+	0.267386i
$687$		−	4.94496e7i		−	0.152508i
$688$	−7.47264e7	−	4.68575e7i	−0.229461	−	0.143884i
$689$	−2.82724e8			−0.864380
$690$	−6.48960e6	−	2.51341e7i	−0.0197547	−	0.0765097i
$691$		−	1.92568e7i		−	0.0583645i	−0.999574	−	0.0291823i	$-0.990710\pi$
$691$		−	1.92568e7i		−	0.0583645i	0.999574	−	0.0291823i	$-0.00929032\pi$
$692$	2.87086e8	−	1.58840e8i	0.866350	−	0.479337i
$693$	−6.87456e7			−0.206560
$694$	−4.22539e8	+	1.09099e8i	−1.26412	+	0.326395i
$695$			1.38839e6i			0.00413577i
$696$	−2.93737e8	+	2.78089e8i	−0.871226	+	0.824815i
$697$	−1.39939e8			−0.413277
$698$	9.40017e7	+	3.64067e8i	0.276420	+	1.07057i
$699$		−	2.49229e8i		−	0.729738i
$700$	1.49040e8	+	2.69374e8i	0.434519	+	0.785346i
$701$	3.52234e8			1.02253			0.511266	−	0.859423i	$-0.329177\pi$
$701$	3.52234e8			1.02253			0.511266	+	0.859423i	$0.329177\pi$
$702$	1.75216e8	−	4.52407e7i	0.506481	−	0.130773i
$703$			1.50130e7i			0.0432117i
$704$	2.51412e8	+	1.37697e7i	0.720558	+	0.0394646i
$705$	−2.34240e6			−0.00668488
$706$	−2.54463e7	−	9.85530e7i	−0.0723119	−	0.280063i
$707$		−	1.98036e8i		−	0.560384i
$708$	1.36067e8	−	7.52834e7i	0.383400	−	0.212129i
$709$	4.62733e8			1.29835			0.649175	−	0.760639i	$-0.275114\pi$
$709$	4.62733e8			1.29835			0.649175	+	0.760639i	$0.275114\pi$
$710$	−4.12272e7	+	1.06448e7i	−0.115188	+	0.0297415i
$711$			7.17731e7i			0.199689i
$712$	−1.09380e8	−	1.15534e8i	−0.303038	−	0.320089i
$713$	4.38697e8			1.21031
$714$	−9.15072e7	−	3.54406e8i	−0.251397	−	0.973658i
$715$		−	1.40809e7i		−	0.0385224i
$716$	7.23197e7	+	1.30710e8i	0.197023	+	0.356098i
$717$	3.48668e8			0.945921
$718$	1.56587e8	−	4.04306e7i	0.423041	−	0.109229i
$719$			4.60385e8i			1.23861i	0.785150	+	0.619305i	$0.212586\pi$
$719$			4.60385e8i			1.23861i	−0.785150	+	0.619305i	$0.787414\pi$
$720$	−5.02656e6	+	8.01615e6i	−0.0134671	+	0.0214767i
$721$	−4.30406e8			−1.14835
$722$	−1.92823e7	−	7.46801e7i	−0.0512327	−	0.198424i
$723$		−	1.56501e8i		−	0.414097i
$724$	−5.42727e8	+	3.00282e8i	−1.43010	+	0.791250i
$725$	−3.95856e8			−1.03878
$726$	2.03760e8	−	5.26107e7i	0.532488	−	0.137488i
$727$			4.82173e8i			1.25487i	0.778668	+	0.627437i	$0.215896\pi$
$727$			4.82173e8i			1.25487i	−0.778668	+	0.627437i	$0.784104\pi$
$728$	1.68883e8	−	1.59887e8i	0.437716	−	0.414398i
$729$	−1.99184e8			−0.514128
$730$	5.77252e6	+	2.23569e7i	0.0148387	+	0.0574702i
$731$			1.02630e8i			0.262738i
$732$	−1.04813e7	−	1.89438e7i	−0.0267227	−	0.0482985i
$733$	−5.08270e8			−1.29057			−0.645287	−	0.763941i	$-0.723262\pi$
$733$	−5.08270e8			−1.29057			−0.645287	+	0.763941i	$0.723262\pi$
$734$	8.60246e7	−	2.22115e7i	0.217538	−	0.0561680i
$735$		−	6.70770e6i		−	0.0168932i
$736$	1.03834e8	−	3.27079e8i	0.260438	−	0.820387i
$737$	−3.78577e8			−0.945696
$738$	−1.35652e7	−	5.25380e7i	−0.0337488	−	0.130709i
$739$			1.27767e8i			0.316582i	0.987392	+	0.158291i	$0.0505984\pi$
$739$			1.27767e8i			0.316582i	−0.987392	+	0.158291i	$0.949402\pi$
$740$	−1.11664e6	+	617818.i	−0.00275561	+	0.00152463i
$741$	3.41988e8			0.840537
$742$	4.62850e8	−	1.19507e8i	1.13300	−	0.292538i
$743$		−	2.83312e8i		−	0.690716i	−0.938471	−	0.345358i	$-0.887758\pi$
$743$		−	2.83312e8i		−	0.690716i	0.938471	−	0.345358i	$-0.112242\pi$
$744$	−4.56868e8	−	4.82575e8i	−1.10936	−	1.17178i
$745$	−3.27426e7			−0.0791853
$746$	1.37429e6	+	5.32261e6i	0.00331026	+	0.0128206i
$747$			4.71593e7i			0.113137i
$748$	−1.41836e8	−	2.56354e8i	−0.338908	−	0.612540i
$749$	3.56112e8			0.847503
$750$	−7.47600e7	+	1.93029e7i	−0.177209	+	0.0457551i
$751$		−	2.15309e8i		−	0.508325i	−0.967161	−	0.254163i	$-0.918200\pi$
$751$		−	2.15309e8i		−	0.508325i	0.967161	−	0.254163i	$-0.0817999\pi$
$752$	−2.62349e7	−	1.64507e7i	−0.0616915	−	0.0386839i
$753$	1.46117e8			0.342228
$754$	7.47601e7	+	2.89545e8i	0.174404	+	0.675463i
$755$		−	5.59352e7i		−	0.129970i
$756$	−2.67725e8	+	1.48128e8i	−0.619617	+	0.342824i
$757$	−3.03985e8			−0.700753			−0.350377	−	0.936609i	$-0.613946\pi$
$757$	−3.03985e8			−0.700753			−0.350377	+	0.936609i	$0.613946\pi$
$758$	−1.15026e8	+	2.96997e7i	−0.264113	+	0.0681938i
$759$			3.11663e8i			0.712787i
$760$	2.79936e7	−	2.65024e7i	0.0637702	−	0.0603731i
$761$	8.63611e8			1.95959			0.979793	−	0.200014i	$-0.0640988\pi$
$761$	8.63611e8			1.95959			0.979793	+	0.200014i	$0.0640988\pi$
$762$	1.03772e8	+	4.01908e8i	0.234539	+	0.908367i
$763$			4.75831e8i			1.07122i
$764$	3.53725e8	+	6.39321e8i	0.793206	+	1.43364i
$765$	1.10095e7			0.0245913
$766$	2.60175e8	−	6.71770e7i	0.578868	−	0.149463i
$767$		−	1.14964e8i		−	0.254786i
$768$	−4.67927e8	+	2.26407e8i	−1.03299	+	0.499812i
$769$	−1.97898e7			−0.0435174			−0.0217587	−	0.999763i	$-0.506927\pi$
$769$	−1.97898e7			−0.0435174			−0.0217587	+	0.999763i	$0.506927\pi$
$770$	5.95200e6	+	2.30520e7i	0.0130374	+	0.0504936i
$771$		−	7.26734e8i		−	1.58567i
$772$	1.36099e8	−	7.53011e7i	0.295803	−	0.163663i
$773$	−5.64048e8			−1.22117			−0.610587	−	0.791949i	$-0.709067\pi$
$773$	−5.64048e8			−1.22117			−0.610587	+	0.791949i	$0.709067\pi$
$774$	−3.85308e7	+	9.94861e6i	−0.0830970	+	0.0214555i
$775$		−	6.50345e8i		−	1.39714i
$776$	5.12894e8	+	5.41754e8i	1.09760	+	1.15936i
$777$	1.91424e7			0.0408069
$778$	−2.02244e8	−	7.83286e8i	−0.429473	−	1.66334i
$779$			2.21069e8i			0.467644i
$780$	1.40736e7	+	2.54365e7i	0.0296566	+	0.0536011i
$781$	5.11217e8			1.07313
$782$	−3.86618e8	+	9.98243e7i	−0.808466	+	0.208745i
$783$		−	3.93433e8i		−	0.819570i
$784$	4.71082e7	−	7.51262e7i	0.0977572	−	0.155899i
$785$	8.16794e6			0.0168851
$786$	1.76269e8	+	6.82689e8i	0.363002	+	1.40590i
$787$			4.04198e8i			0.829220i	0.909999	+	0.414610i	$0.136082\pi$
$787$			4.04198e8i			0.829220i	−0.909999	+	0.414610i	$0.863918\pi$
$788$	1.24916e8	−	6.91140e7i	0.255294	−	0.141250i
$789$	−6.72328e8			−1.36883
$790$	2.40672e7	−	6.21412e6i	0.0488140	−	0.0126037i
$791$		−	1.86428e8i		−	0.376688i
$792$	8.24947e7	−	7.81002e7i	0.166054	−	0.157209i
$793$	−1.60058e7			−0.0320965
$794$	−6.96531e7	−	2.69765e8i	−0.139149	−	0.538921i
$795$			5.97536e7i			0.118922i
$796$	−1.51690e8	−	2.74163e8i	−0.300758	−	0.543587i
$797$	−2.15998e7			−0.0426654			−0.0213327	−	0.999772i	$-0.506791\pi$
$797$	−2.15998e7			−0.0426654			−0.0213327	+	0.999772i	$0.506791\pi$
$798$	−5.59872e8	+	1.44558e8i	−1.10174	+	0.284469i
$799$			3.60313e7i			0.0706381i
$800$	−4.84877e8	−	1.53928e8i	−0.947025	−	0.300640i
$801$	−7.17805e7			−0.139672
$802$	−1.37680e8	−	5.33231e8i	−0.266899	−	1.03369i
$803$		−	2.77225e8i		−	0.535410i
$804$	6.83881e8	−	3.78380e8i	1.31587	−	0.728048i
$805$	3.24480e7			0.0622014
$806$	−4.75688e8	+	1.22822e8i	−0.908483	+	0.234569i
$807$			9.11786e8i			1.73489i
$808$	2.24984e8	+	2.37643e8i	0.426498	+	0.450496i
$809$	6.51310e8			1.23011			0.615053	−	0.788486i	$-0.289135\pi$
$809$	6.51310e8			1.23011			0.615053	+	0.788486i	$0.289135\pi$
$810$	−1.29296e7	−	5.00760e7i	−0.0243293	−	0.0942269i
$811$			5.52891e8i			1.03652i	0.855223	+	0.518259i	$0.173420\pi$
$811$			5.52891e8i			1.03652i	−0.855223	+	0.518259i	$0.826580\pi$
$812$	−2.44781e8	−	4.42415e8i	−0.457203	−	0.826346i
$813$	−2.63820e8			−0.490948
$814$	1.48354e7	−	3.83047e6i	0.0275058	−	0.00710198i
$815$		−	1.84593e7i		−	0.0340990i
$816$	5.12440e8	+	3.21328e8i	0.943133	+	0.591396i
$817$	1.62130e8			0.297301
$818$	9.19917e7	+	3.56282e8i	0.168069	+	0.650930i
$819$		−	1.04926e8i		−	0.190998i
$820$	−1.64427e7	+	9.09748e6i	−0.0298217	+	0.0164998i
$821$	−8.94865e8			−1.61707			−0.808534	−	0.588450i	$-0.799738\pi$
$821$	−8.94865e8			−1.61707			−0.808534	+	0.588450i	$0.799738\pi$
$822$	9.14408e8	−	2.36099e8i	1.64636	−	0.425088i
$823$			8.44482e8i			1.51492i	0.652879	+	0.757462i	$0.273561\pi$
$823$			8.44482e8i			1.51492i	−0.652879	+	0.757462i	$0.726439\pi$
$824$	5.16488e8	−	4.88974e8i	0.923163	−	0.873985i
$825$	4.62024e8			0.822816
$826$	4.85952e7	+	1.88208e8i	0.0862290	+	0.333963i
$827$		−	3.11099e7i		−	0.0550024i	−0.999622	−	0.0275012i	$-0.991245\pi$
$827$		−	3.11099e7i		−	0.0550024i	0.999622	−	0.0275012i	$-0.00875501\pi$
$828$	−7.49549e7	−	1.35473e8i	−0.132041	−	0.238650i
$829$	−4.05444e7			−0.0711652			−0.0355826	−	0.999367i	$-0.511329\pi$
$829$	−4.05444e7			−0.0711652			−0.0355826	+	0.999367i	$0.511329\pi$
$830$	1.58136e7	−	4.08305e6i	0.0276565	−	0.00714087i
$831$		−	8.55856e8i		−	1.49141i
$832$	−2.10166e7	+	3.83728e8i	−0.0364915	+	0.666275i
$833$	−1.03179e8			−0.178508
$834$	8.60352e6	+	3.33213e7i	0.0148313	+	0.0574412i
$835$			7.96515e7i			0.136815i
$836$	−4.04974e8	+	2.24065e8i	−0.693120	+	0.383492i
$837$	6.46364e8			1.10230
$838$	−2.10034e8	+	5.42306e7i	−0.356910	+	0.0921537i
$839$		−	4.17820e8i		−	0.707463i	−0.935347	−	0.353731i	$-0.884913\pi$
$839$		−	4.17820e8i		−	0.707463i	0.935347	−	0.353731i	$-0.115087\pi$
$840$	−3.37920e7	−	3.56934e7i	−0.0570133	−	0.0602213i
$841$	5.53247e7			0.0930103
$842$	−1.88416e8	−	7.29730e8i	−0.315632	−	1.22244i
$843$		−	2.67703e8i		−	0.446859i
$844$	−1.21132e8	−	2.18933e8i	−0.201480	−	0.364153i
$845$	−2.67765e7			−0.0443797
$846$	−1.35274e7	+	3.49275e6i	−0.0223410	+	0.00576841i
$847$			2.63053e8i			0.432906i
$848$	−4.19650e8	+	6.69241e8i	−0.688177	+	1.09748i
$849$	−3.94578e8			−0.644778
$850$	1.47984e8	+	5.73141e8i	0.240968	+	0.933264i
$851$		−	2.08823e7i		−	0.0338835i
$852$	−9.23489e8	+	5.10951e8i	−1.49318	+	0.826153i
$853$	−4.28994e8			−0.691201			−0.345601	−	0.938382i	$-0.612325\pi$
$853$	−4.28994e8			−0.691201			−0.345601	+	0.938382i	$0.612325\pi$
$854$	2.62032e7	−	6.76564e6i	0.0420708	−	0.0108626i
$855$		−	1.73922e7i		−	0.0278263i
$856$	−4.27334e8	+	4.04570e8i	−0.681313	+	0.645019i
$857$	2.20598e8			0.350476			0.175238	−	0.984526i	$-0.443930\pi$
$857$	2.20598e8			0.350476			0.175238	+	0.984526i	$0.443930\pi$
$858$	−8.72563e7	−	3.37942e8i	−0.138145	−	0.535033i
$859$		−	1.14768e9i		−	1.81068i	−0.424689	−	0.905339i	$-0.639617\pi$
$859$		−	1.14768e9i		−	1.81068i	0.424689	−	0.905339i	$-0.360383\pi$
$860$	6.67200e6	+	1.20589e7i	0.0104896	+	0.0189589i
$861$	2.81875e8			0.441619
$862$	4.02160e8	−	1.03837e8i	0.627881	−	0.162118i
$863$			6.44987e7i			0.100350i	0.998740	+	0.0501752i	$0.0159780\pi$
$863$			6.44987e7i			0.100350i	−0.998740	+	0.0501752i	$0.984022\pi$
$864$	1.52986e8	−	4.81909e8i	0.237197	−	0.747177i
$865$	−5.12653e7			−0.0792092
$866$	1.68042e8	+	6.50824e8i	0.258740	+	1.00210i
$867$			4.40842e7i			0.0676435i
$868$	7.26835e8	−	4.02146e8i	1.11142	−	0.614928i
$869$	−2.98433e8			−0.454766
$870$	6.11952e7	−	1.58005e7i	0.0929308	−	0.0239946i
$871$		−	5.77818e8i		−	0.874453i
$872$	−5.40580e8	−	5.70997e8i	−0.815287	−	0.861161i
$873$	3.36587e8			0.505888
$874$	1.57697e8	+	6.10759e8i	0.236205	+	0.914820i
$875$		−	9.65147e7i		−	0.144069i
$876$	2.77081e8	+	5.00794e8i	0.412187	+	0.744984i
$877$	5.15252e8			0.763873			0.381937	−	0.924189i	$-0.375257\pi$
$877$	5.15252e8			0.763873			0.381937	+	0.924189i	$0.375257\pi$
$878$	1.14729e9	−	2.96230e8i	1.69508	−	0.437669i
$879$			1.38007e9i			2.03205i
$880$	−3.33312e7	−	2.09005e7i	−0.0489106	−	0.0306696i
$881$	−1.18519e8			−0.173324			−0.0866622	−	0.996238i	$-0.527620\pi$
$881$	−1.18519e8			−0.173324			−0.0866622	+	0.996238i	$0.527620\pi$
$882$	−1.00018e7	−	3.87370e7i	−0.0145772	−	0.0564572i
$883$		−	1.28669e8i		−	0.186893i	−0.995624	−	0.0934466i	$-0.970212\pi$
$883$		−	1.28669e8i		−	0.186893i	0.995624	−	0.0934466i	$-0.0297884\pi$
$884$	3.91270e8	−	2.16483e8i	0.566395	−	0.313377i
$885$	−2.42976e7			−0.0350537
$886$	−6.22571e8	+	1.60747e8i	−0.895133	+	0.231122i
$887$			5.09948e8i			0.730727i	0.930865	+	0.365363i	$0.119055\pi$
$887$			5.09948e8i			0.730727i	−0.930865	+	0.365363i	$0.880945\pi$
$888$	−2.29709e7	+	2.17472e7i	−0.0328049	+	0.0310574i
$889$	−5.18861e8			−0.738492
$890$	6.21476e6	+	2.40697e7i	0.00881565	+	0.0341429i
$891$			6.20943e8i			0.877847i
$892$	−1.03212e8	−	1.86544e8i	−0.145423	−	0.262837i
$893$	5.69203e7			0.0799306
$894$	−7.85823e8	+	2.02899e8i	−1.09980	+	0.283966i
$895$		−	2.33411e7i		−	0.0325576i
$896$	−1.27795e8	−	6.37088e8i	−0.177660	−	0.885677i
$897$	−4.75688e8			−0.659090
$898$	−1.76185e8	−	6.82362e8i	−0.243299	−	0.942293i
$899$			1.06812e9i			1.47007i
$900$	−2.00831e8	+	1.11117e8i	−0.275489	+	0.152423i
$901$	9.19142e8			1.25663
$902$	2.18453e8	−	5.64044e7i	0.297673	−	0.0768588i
$903$		−	2.06724e8i		−	0.280756i
$904$	2.11796e8	+	2.23714e8i	0.286690	+	0.302822i
$905$	9.69156e7			0.130752
$906$	−3.46618e8	−	1.34244e9i	−0.466086	−	1.80514i
$907$		−	5.43212e8i		−	0.728027i	−0.931394	−	0.364014i	$-0.881406\pi$
$907$		−	5.43212e8i		−	0.728027i	0.931394	−	0.364014i	$-0.118594\pi$
$908$	4.18384e8	+	7.56185e8i	0.558879	+	1.01011i
$909$	1.47645e8			0.196575
$910$	−3.51840e7	+	9.08447e6i	−0.0466897	+	0.0120552i
$911$		−	5.99585e8i		−	0.793041i	−0.918026	−	0.396520i	$-0.870218\pi$
$911$		−	5.99585e8i		−	0.793041i	0.918026	−	0.396520i	$-0.129782\pi$
$912$	5.07617e8	−	8.09527e8i	0.669194	−	1.06720i
$913$	−1.96089e8			−0.257656
$914$	−7.50846e7	−	2.90801e8i	−0.0983359	−	0.380853i
$915$			3.38282e6i			0.00441586i
$916$	−8.93748e7	+	4.94496e7i	−0.116286	+	0.0643393i
$917$	−8.81347e8			−1.14298
$918$	−5.69632e8	+	1.47078e8i	−0.736320	+	0.190117i
$919$		−	9.66486e8i		−	1.24523i	−0.782529	−	0.622614i	$-0.786071\pi$
$919$		−	9.66486e8i		−	1.24523i	0.782529	−	0.622614i	$-0.213929\pi$
$920$	−3.89376e7	+	3.68634e7i	−0.0500041	+	0.0473404i
$921$	−1.51527e9			−1.93959
$922$	2.30520e8	+	8.92800e8i	0.294114	+	1.13910i
$923$			7.80265e8i			0.992286i
$924$	2.85696e8	+	5.16365e8i	0.362150	+	0.654547i
$925$	−3.09568e7			−0.0391139
$926$	8.01053e7	−	2.06831e7i	0.100885	−	0.0260485i
$927$		−	3.20889e8i		−	0.402825i
$928$	7.96354e8	+	2.52809e8i	0.996465	+	0.316335i
$929$	7.22626e8			0.901295			0.450647	−	0.892702i	$-0.351193\pi$
$929$	7.22626e8			0.901295			0.450647	+	0.892702i	$0.351193\pi$
$930$	2.59584e7	+	1.00536e8i	0.0322722	+	0.124990i
$931$			1.62997e8i			0.201990i
$932$	−4.50454e8	+	2.49229e8i	−0.556420	+	0.307858i
$933$	1.54988e9			1.90832
$934$	−1.27206e9	+	3.28445e8i	−1.56123	+	0.403109i
$935$			4.57774e7i			0.0560037i
$936$	1.19203e8	+	1.25911e8i	0.145365	+	0.153545i
$937$	−4.12016e8			−0.500836			−0.250418	−	0.968138i	$-0.580568\pi$
$937$	−4.12016e8			−0.500836			−0.250418	+	0.968138i	$0.580568\pi$
$938$	2.44243e8	+	9.45950e8i	0.295947	+	1.14620i
$939$		−	3.49246e7i		−	0.0421827i
$940$	2.34240e6	+	4.23364e6i	0.00282018	+	0.00509718i
$941$	7.87666e8			0.945308			0.472654	−	0.881248i	$-0.343296\pi$
$941$	7.87666e8			0.945308			0.472654	+	0.881248i	$0.343296\pi$
$942$	1.96031e8	−	5.06149e7i	0.234515	−	0.0605516i
$943$		−	3.07495e8i		−	0.366693i
$944$	−2.72133e8	−	1.70642e8i	−0.323493	−	0.202848i
$945$	4.78080e7			0.0566507
$946$	−4.13664e7	−	1.60211e8i	−0.0488623	−	0.189243i
$947$		−	5.29504e8i		−	0.623475i	−0.950168	−	0.311738i	$-0.899089\pi$
$947$		−	5.29504e8i		−	0.623475i	0.950168	−	0.311738i	$-0.100911\pi$
$948$	5.39105e8	−	2.98278e8i	0.632774	−	0.350103i
$949$	4.23126e8			0.495075
$950$	9.05418e8	−	2.33778e8i	1.05603	−	0.272667i
$951$		−	1.06858e9i		−	1.24241i
$952$	−5.49043e8	+	5.19795e8i	−0.636349	+	0.602451i
$953$	1.18323e9			1.36706			0.683532	−	0.729920i	$-0.260443\pi$
$953$	1.18323e9			1.36706			0.683532	+	0.729920i	$0.260443\pi$
$954$	8.90985e7	+	3.45077e8i	0.102618	+	0.397440i
$955$		−	1.14164e8i		−	0.131075i
$956$	−3.48668e8	−	6.30180e8i	−0.399060	−	0.721259i
$957$	−7.58820e8			−0.865771
$958$	−6.01265e8	+	1.55246e8i	−0.683864	+	0.176573i
$959$			1.18050e9i			1.33847i
$960$	8.11008e7	+	4.44185e6i	0.0916667	+	0.00502053i
$961$	−8.67284e8			−0.977218
$962$	5.84641e6	+	2.26430e7i	0.00656695	+	0.0254337i
$963$			2.65499e8i			0.297293i
$964$	−2.82858e8	+	1.56501e8i	−0.315746	+	0.174697i
$965$	−2.43033e7			−0.0270448
$966$	7.78752e8	−	2.01073e8i	0.863909	−	0.223060i
$967$			4.78688e8i			0.529387i	0.964333	+	0.264693i	$0.0852708\pi$
$967$			4.78688e8i			0.529387i	−0.964333	+	0.264693i	$0.914729\pi$
$968$	−2.98848e8	−	3.15664e8i	−0.329477	−	0.348016i
$969$	−1.11181e9			−1.22197
$970$	−2.91417e7	−	1.12865e8i	−0.0319301	−	0.123665i
$971$		−	7.02914e8i		−	0.767793i	−0.923376	−	0.383897i	$-0.874582\pi$
$971$		−	7.02914e8i		−	0.767793i	0.923376	−	0.383897i	$-0.125418\pi$
$972$	−2.72100e8	−	4.91791e8i	−0.296298	−	0.535527i
$973$	−4.30176e7			−0.0466990
$974$	8.37115e7	−	2.16142e7i	0.0905959	−	0.0233918i
$975$			7.05182e8i			0.760830i
$976$	−2.37576e7	+	3.78876e7i	−0.0255536	+	0.0407518i
$977$	−9.21323e8			−0.987934			−0.493967	−	0.869481i	$-0.664454\pi$
$977$	−9.21323e8			−0.987934			−0.493967	+	0.869481i	$0.664454\pi$
$978$	−1.14388e8	−	4.43022e8i	−0.122282	−	0.473597i
$979$		−	2.98464e8i		−	0.318085i
$980$	−1.21234e7	+	6.70770e6i	−0.0128809	+	0.00712681i
$981$	−3.54755e8			−0.375770
$982$	1.43352e9	−	3.70133e8i	1.51380	−	0.390862i
$983$			2.44410e8i			0.257311i	0.991689	+	0.128655i	$0.0410661\pi$
$983$			2.44410e8i			0.257311i	−0.991689	+	0.128655i	$0.958934\pi$
$984$	−3.38250e8	+	3.20231e8i	−0.355020	+	0.336108i
$985$	−2.23065e7			−0.0233411
$986$	−2.43047e8	−	9.41317e8i	−0.253548	−	0.981985i
$987$		−	7.25766e7i		−	0.0754823i
$988$	−3.41988e8	−	6.18107e8i	−0.354602	−	0.640904i
$989$	−2.25514e8			−0.233122
$990$	−1.71864e7	+	4.43751e6i	−0.0177125	+	0.00457334i
$991$			1.78184e9i			1.83083i	0.402516	+	0.915413i	$0.368136\pi$
$991$			1.78184e9i			1.83083i	−0.402516	+	0.915413i	$0.631864\pi$
$992$	−4.15334e8	+	1.30831e9i	−0.425464	+	1.34022i
$993$	1.24771e9			1.27428
$994$	−3.29818e8	−	1.27738e9i	−0.335826	−	1.30065i
$995$			4.89576e7i			0.0496994i
$996$	3.54225e8	−	1.95987e8i	0.358510	−	0.198357i
$997$	1.36790e9			1.38029			0.690143	−	0.723673i	$-0.257548\pi$
$997$	1.36790e9			1.38029			0.690143	+	0.723673i	$0.257548\pi$
$998$	5.29595e8	−	1.36741e8i	0.532785	−	0.137565i
$999$		−	3.07674e7i		−	0.0308598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.7.b.a.3.2	yes	2
3.2	odd	2		36.7.d.c.19.1		2
4.3	odd	2	inner	4.7.b.a.3.1	✓	2
5.2	odd	4		100.7.d.a.99.2		4
5.3	odd	4		100.7.d.a.99.3		4
5.4	even	2		100.7.b.c.51.1		2
8.3	odd	2		64.7.c.c.63.1		2
8.5	even	2		64.7.c.c.63.2		2
12.11	even	2		36.7.d.c.19.2		2
16.3	odd	4		256.7.d.f.127.1		4
16.5	even	4		256.7.d.f.127.2		4
16.11	odd	4		256.7.d.f.127.4		4
16.13	even	4		256.7.d.f.127.3		4
20.3	even	4		100.7.d.a.99.1		4
20.7	even	4		100.7.d.a.99.4		4
20.19	odd	2		100.7.b.c.51.2		2
24.5	odd	2		576.7.g.h.127.2		2
24.11	even	2		576.7.g.h.127.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.7.b.a.3.1	✓	2	4.3	odd	2	inner
4.7.b.a.3.2	yes	2	1.1	even	1	trivial
36.7.d.c.19.1		2	3.2	odd	2
36.7.d.c.19.2		2	12.11	even	2
64.7.c.c.63.1		2	8.3	odd	2
64.7.c.c.63.2		2	8.5	even	2
100.7.b.c.51.1		2	5.4	even	2
100.7.b.c.51.2		2	20.19	odd	2
100.7.d.a.99.1		4	20.3	even	4
100.7.d.a.99.2		4	5.2	odd	4
100.7.d.a.99.3		4	5.3	odd	4
100.7.d.a.99.4		4	20.7	even	4
256.7.d.f.127.1		4	16.3	odd	4
256.7.d.f.127.2		4	16.5	even	4
256.7.d.f.127.3		4	16.13	even	4
256.7.d.f.127.4		4	16.11	odd	4
576.7.g.h.127.1		2	24.11	even	2
576.7.g.h.127.2		2	24.5	odd	2

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:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 7.74597i) q^{2} -30.9839i q^{3} +(-56.0000 + 30.9839i) q^{4} +10.0000 q^{5} +(240.000 - 61.9677i) q^{6} +309.839i q^{7} +(-352.000 - 371.806i) q^{8} -231.000 q^{9} +O(q^{10})\)	\(q+(2.00000 + 7.74597i) q^{2} -30.9839i q^{3} +(-56.0000 + 30.9839i) q^{4} +10.0000 q^{5} +(240.000 - 61.9677i) q^{6} +309.839i q^{7} +(-352.000 - 371.806i) q^{8} -231.000 q^{9} +(20.0000 + 77.4597i) q^{10} -960.500i q^{11} +(960.000 + 1735.10i) q^{12} +1466.00 q^{13} +(-2400.00 + 619.677i) q^{14} -309.839i q^{15} +(2176.00 - 3470.19i) q^{16} -4766.00 q^{17} +(-462.000 - 1789.32i) q^{18} +7529.08i q^{19} +(-560.000 + 309.839i) q^{20} +9600.00 q^{21} +(7440.00 - 1921.00i) q^{22} -10472.5i q^{23} +(-11520.0 + 10906.3i) q^{24} -15525.0 q^{25} +(2932.00 + 11355.6i) q^{26} -15430.0i q^{27} +(-9600.00 - 17351.0i) q^{28} +25498.0 q^{29} +(2400.00 - 619.677i) q^{30} +41890.2i q^{31} +(31232.0 + 9914.84i) q^{32} -29760.0 q^{33} +(-9532.00 - 36917.3i) q^{34} +3098.39i q^{35} +(12936.0 - 7157.27i) q^{36} +1994.00 q^{37} +(-58320.0 + 15058.2i) q^{38} -45422.3i q^{39} +(-3520.00 - 3718.06i) q^{40} +29362.0 q^{41} +(19200.0 + 74361.3i) q^{42} -21533.8i q^{43} +(29760.0 + 53788.0i) q^{44} -2310.00 q^{45} +(81120.0 - 20945.1i) q^{46} -7560.06i q^{47} +(-107520. - 67420.9i) q^{48} +21649.0 q^{49} +(-31050.0 - 120256. i) q^{50} +147669. i q^{51} +(-82096.0 + 45422.3i) q^{52} -192854. q^{53} +(119520. - 30859.9i) q^{54} -9605.00i q^{55} +(115200. - 109063. i) q^{56} +233280. q^{57} +(50996.0 + 197507. i) q^{58} -78420.2i q^{59} +(9600.00 + 17351.0i) q^{60} -10918.0 q^{61} +(-324480. + 83780.4i) q^{62} -71572.7i q^{63} +(-14336.0 + 261752. i) q^{64} +14660.0 q^{65} +(-59520.0 - 230520. i) q^{66} -394146. i q^{67} +(266896. - 147669. i) q^{68} -324480. q^{69} +(-24000.0 + 6196.77i) q^{70} +532241. i q^{71} +(81312.0 + 85887.3i) q^{72} +288626. q^{73} +(3988.00 + 15445.5i) q^{74} +481025. i q^{75} +(-233280. - 421628. i) q^{76} +297600. q^{77} +(351840. - 90844.7i) q^{78} -310706. i q^{79} +(21760.0 - 34701.9i) q^{80} -646479. q^{81} +(58724.0 + 227437. i) q^{82} -204153. i q^{83} +(-537600. + 297445. i) q^{84} -47660.0 q^{85} +(166800. - 43067.6i) q^{86} -790027. i q^{87} +(-357120. + 338096. i) q^{88} +310738. q^{89} +(-4620.00 - 17893.2i) q^{90} +454223. i q^{91} +(324480. + 586463. i) q^{92} +1.29792e6 q^{93} +(58560.0 - 15120.1i) q^{94} +75290.8i q^{95} +(307200. - 967688. i) q^{96} -1.45709e6 q^{97} +(43298.0 + 167692. i) q^{98} +221875. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 112 q^{4} + 20 q^{5} + 480 q^{6} - 704 q^{8} - 462 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - 112 * q^4 + 20 * q^5 + 480 * q^6 - 704 * q^8 - 462 * q^9	\( 2 q + 4 q^{2} - 112 q^{4} + 20 q^{5} + 480 q^{6} - 704 q^{8} - 462 q^{9} + 40 q^{10} + 1920 q^{12} + 2932 q^{13} - 4800 q^{14} + 4352 q^{16} - 9532 q^{17} - 924 q^{18} - 1120 q^{20} + 19200 q^{21} + 14880 q^{22} - 23040 q^{24} - 31050 q^{25} + 5864 q^{26} - 19200 q^{28} + 50996 q^{29} + 4800 q^{30} + 62464 q^{32} - 59520 q^{33} - 19064 q^{34} + 25872 q^{36} + 3988 q^{37} - 116640 q^{38} - 7040 q^{40} + 58724 q^{41} + 38400 q^{42} + 59520 q^{44} - 4620 q^{45} + 162240 q^{46} - 215040 q^{48} + 43298 q^{49} - 62100 q^{50} - 164192 q^{52} - 385708 q^{53} + 239040 q^{54} + 230400 q^{56} + 466560 q^{57} + 101992 q^{58} + 19200 q^{60} - 21836 q^{61} - 648960 q^{62} - 28672 q^{64} + 29320 q^{65} - 119040 q^{66} + 533792 q^{68} - 648960 q^{69} - 48000 q^{70} + 162624 q^{72} + 577252 q^{73} + 7976 q^{74} - 466560 q^{76} + 595200 q^{77} + 703680 q^{78} + 43520 q^{80} - 1292958 q^{81} + 117448 q^{82} - 1075200 q^{84} - 95320 q^{85} + 333600 q^{86} - 714240 q^{88} + 621476 q^{89} - 9240 q^{90} + 648960 q^{92} + 2595840 q^{93} + 117120 q^{94} + 614400 q^{96} - 2914172 q^{97} + 86596 q^{98}+O(q^{100}) \) 2 * q + 4 * q^2 - 112 * q^4 + 20 * q^5 + 480 * q^6 - 704 * q^8 - 462 * q^9 + 40 * q^10 + 1920 * q^12 + 2932 * q^13 - 4800 * q^14 + 4352 * q^16 - 9532 * q^17 - 924 * q^18 - 1120 * q^20 + 19200 * q^21 + 14880 * q^22 - 23040 * q^24 - 31050 * q^25 + 5864 * q^26 - 19200 * q^28 + 50996 * q^29 + 4800 * q^30 + 62464 * q^32 - 59520 * q^33 - 19064 * q^34 + 25872 * q^36 + 3988 * q^37 - 116640 * q^38 - 7040 * q^40 + 58724 * q^41 + 38400 * q^42 + 59520 * q^44 - 4620 * q^45 + 162240 * q^46 - 215040 * q^48 + 43298 * q^49 - 62100 * q^50 - 164192 * q^52 - 385708 * q^53 + 239040 * q^54 + 230400 * q^56 + 466560 * q^57 + 101992 * q^58 + 19200 * q^60 - 21836 * q^61 - 648960 * q^62 - 28672 * q^64 + 29320 * q^65 - 119040 * q^66 + 533792 * q^68 - 648960 * q^69 - 48000 * q^70 + 162624 * q^72 + 577252 * q^73 + 7976 * q^74 - 466560 * q^76 + 595200 * q^77 + 703680 * q^78 + 43520 * q^80 - 1292958 * q^81 + 117448 * q^82 - 1075200 * q^84 - 95320 * q^85 + 333600 * q^86 - 714240 * q^88 + 621476 * q^89 - 9240 * q^90 + 648960 * q^92 + 2595840 * q^93 + 117120 * q^94 + 614400 * q^96 - 2914172 * q^97 + 86596 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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