LMFDB - Embedded newform 29.7.c.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,7,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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("29.12");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.67156842498$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	29.17
Dual form			29.7.c.a.12.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.36218 + 5.36218i) q^{2} +(27.0129 - 27.0129i) q^{3} +6.49405i q^{4} -130.759i q^{5} +289.696i q^{6} -330.754 q^{7} +(-378.002 - 378.002i) q^{8} -730.397i q^{9} +O(q^{10})$	\(q+(-5.36218 + 5.36218i) q^{2} +(27.0129 - 27.0129i) q^{3} +6.49405i q^{4} -130.759i q^{5} +289.696i q^{6} -330.754 q^{7} +(-378.002 - 378.002i) q^{8} -730.397i q^{9} +(701.154 + 701.154i) q^{10} +(869.156 - 869.156i) q^{11} +(175.423 + 175.423i) q^{12} -2446.31i q^{13} +(1773.56 - 1773.56i) q^{14} +(-3532.19 - 3532.19i) q^{15} +3638.21 q^{16} +(3363.90 - 3363.90i) q^{17} +(3916.52 + 3916.52i) q^{18} +(-3391.60 + 3391.60i) q^{19} +849.157 q^{20} +(-8934.64 + 8934.64i) q^{21} +9321.14i q^{22} -14145.3 q^{23} -20421.9 q^{24} -1472.96 q^{25} +(13117.6 + 13117.6i) q^{26} +(-37.7443 - 37.7443i) q^{27} -2147.94i q^{28} +(9026.07 + 22657.3i) q^{29} +37880.5 q^{30} +(18915.8 - 18915.8i) q^{31} +(4683.39 - 4683.39i) q^{32} -46956.9i q^{33} +36075.6i q^{34} +43249.1i q^{35} +4743.24 q^{36} +(-35403.5 - 35403.5i) q^{37} -36372.7i q^{38} +(-66082.1 - 66082.1i) q^{39} +(-49427.2 + 49427.2i) q^{40} +(75064.4 + 75064.4i) q^{41} -95818.3i q^{42} +(-38960.8 + 38960.8i) q^{43} +(5644.35 + 5644.35i) q^{44} -95506.1 q^{45} +(75849.6 - 75849.6i) q^{46} +(105441. + 105441. i) q^{47} +(98278.7 - 98278.7i) q^{48} -8250.74 q^{49} +(7898.27 - 7898.27i) q^{50} -181737. i q^{51} +15886.5 q^{52} -193139. q^{53} +404.784 q^{54} +(-113650. - 113650. i) q^{55} +(125026. + 125026. i) q^{56} +183234. i q^{57} +(-169892. - 73093.1i) q^{58} +314055. q^{59} +(22938.2 - 22938.2i) q^{60} +(132513. - 132513. i) q^{61} +202859. i q^{62} +241582. i q^{63} +283072. i q^{64} -319878. q^{65} +(251791. + 251791. i) q^{66} -354672. i q^{67} +(21845.3 + 21845.3i) q^{68} +(-382106. + 382106. i) q^{69} +(-231910. - 231910. i) q^{70} -407240. i q^{71} +(-276091. + 276091. i) q^{72} +(122649. + 122649. i) q^{73} +379680. q^{74} +(-39788.9 + 39788.9i) q^{75} +(-22025.2 - 22025.2i) q^{76} +(-287477. + 287477. i) q^{77} +708688. q^{78} +(-167108. + 167108. i) q^{79} -475729. i q^{80} +530420. q^{81} -805017. q^{82} +287008. q^{83} +(-58022.0 - 58022.0i) q^{84} +(-439860. - 439860. i) q^{85} -417830. i q^{86} +(855861. + 368220. i) q^{87} -657085. q^{88} +(270731. - 270731. i) q^{89} +(512121. - 512121. i) q^{90} +809128. i q^{91} -91860.3i q^{92} -1.02194e6i q^{93} -1.13079e6 q^{94} +(443483. + 443483. i) q^{95} -253024. i q^{96} +(-678551. - 678551. i) q^{97} +(44242.0 - 44242.0i) q^{98} +(-634829. - 634829. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) $ 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−5.36218	+	5.36218i	−0.670272	+	0.670272i	−0.957779	−	0.287506i	$-0.907174\pi$
$2$	−5.36218	+	5.36218i	−0.670272	+	0.670272i	0.287506	+	0.957779i	$0.407174\pi$
$3$	27.0129	−	27.0129i	1.00048	−	1.00048i	0.000479173	−	1.00000i	$-0.499847\pi$
$3$	27.0129	−	27.0129i	1.00048	−	1.00048i	1.00000		0.000479173i	$-0.000152525\pi$
$4$			6.49405i			0.101470i
$5$		−	130.759i		−	1.04607i	−0.852310	−	0.523037i	$-0.824799\pi$
$5$		−	130.759i		−	1.04607i	0.852310	−	0.523037i	$-0.175201\pi$
$6$			289.696i			1.34119i
$7$	−330.754			−0.964298			−0.482149	−	0.876089i	$-0.660144\pi$
$7$	−330.754			−0.964298			−0.482149	+	0.876089i	$0.660144\pi$
$8$	−378.002	−	378.002i	−0.738285	−	0.738285i
$9$		−	730.397i		−	1.00192i
$10$	701.154	+	701.154i	0.701154	+	0.701154i
$11$	869.156	−	869.156i	0.653010	−	0.653010i	−0.300707	−	0.953717i	$-0.597223\pi$
$11$	869.156	−	869.156i	0.653010	−	0.653010i	0.953717	+	0.300707i	$0.0972226\pi$
$12$	175.423	+	175.423i	0.101518	+	0.101518i
$13$		−	2446.31i		−	1.11348i	−0.830687	−	0.556739i	$-0.812052\pi$
$13$		−	2446.31i		−	1.11348i	0.830687	−	0.556739i	$-0.187948\pi$
$14$	1773.56	−	1773.56i	0.646342	−	0.646342i
$15$	−3532.19	−	3532.19i	−1.04657	−	1.04657i
$16$	3638.21			0.888234
$17$	3363.90	−	3363.90i	0.684693	−	0.684693i	−0.276361	−	0.961054i	$-0.589128\pi$
$17$	3363.90	−	3363.90i	0.684693	−	0.684693i	0.961054	+	0.276361i	$0.0891285\pi$
$18$	3916.52	+	3916.52i	0.671557	+	0.671557i
$19$	−3391.60	+	3391.60i	−0.494475	+	0.494475i	−0.909713	−	0.415238i	$-0.863698\pi$
$19$	−3391.60	+	3391.60i	−0.494475	+	0.494475i	0.415238	+	0.909713i	$0.363698\pi$
$20$	849.157			0.106145
$21$	−8934.64	+	8934.64i	−0.964760	+	0.964760i
$22$			9321.14i			0.875389i
$23$	−14145.3			−1.16259			−0.581297	−	0.813691i	$-0.697455\pi$
$23$	−14145.3			−1.16259			−0.581297	+	0.813691i	$0.697455\pi$
$24$	−20421.9			−1.47728
$25$	−1472.96			−0.0942693
$26$	13117.6	+	13117.6i	0.746334	+	0.746334i
$27$	−37.7443	−	37.7443i	−0.00191761	−	0.00191761i
$28$		−	2147.94i		−	0.0978469i
$29$	9026.07	+	22657.3i	0.370088	+	0.928997i
$29$	9026.07	+	22657.3i	0.370088	+	0.928997i
$30$	37880.5			1.40298
$31$	18915.8	−	18915.8i	0.634949	−	0.634949i	−0.314356	−	0.949305i	$-0.601789\pi$
$31$	18915.8	−	18915.8i	0.634949	−	0.634949i	0.949305	+	0.314356i	$0.101789\pi$
$32$	4683.39	−	4683.39i	0.142926	−	0.142926i
$33$		−	46956.9i		−	1.30665i
$34$			36075.6i			0.917862i
$35$			43249.1i			1.00873i
$36$	4743.24			0.101664
$37$	−35403.5	−	35403.5i	−0.698942	−	0.698942i	0.265240	−	0.964182i	$-0.414549\pi$
$37$	−35403.5	−	35403.5i	−0.698942	−	0.698942i	−0.964182	+	0.265240i	$0.914549\pi$
$38$		−	36372.7i		−	0.662865i
$39$	−66082.1	−	66082.1i	−1.11401	−	1.11401i
$40$	−49427.2	+	49427.2i	−0.772300	+	0.772300i
$41$	75064.4	+	75064.4i	1.08914	+	1.08914i	0.995618	+	0.0935186i	$0.0298115\pi$
$41$	75064.4	+	75064.4i	1.08914	+	1.08914i	0.0935186	+	0.995618i	$0.470189\pi$
$42$		−	95818.3i		−	1.29330i
$43$	−38960.8	+	38960.8i	−0.490030	+	0.490030i	−0.908316	−	0.418286i	$-0.862631\pi$
$43$	−38960.8	+	38960.8i	−0.490030	+	0.490030i	0.418286	+	0.908316i	$0.362631\pi$
$44$	5644.35	+	5644.35i	0.0662606	+	0.0662606i
$45$	−95506.1			−1.04808
$46$	75849.6	−	75849.6i	0.779255	−	0.779255i
$47$	105441.	+	105441.i	1.01558	+	1.01558i	0.999877	+	0.0157081i	$0.00500026\pi$
$47$	105441.	+	105441.i	1.01558	+	1.01558i	0.0157081	+	0.999877i	$0.495000\pi$
$48$	98278.7	−	98278.7i	0.888660	−	0.888660i
$49$	−8250.74			−0.0701302
$50$	7898.27	−	7898.27i	0.0631861	−	0.0631861i
$51$		−	181737.i		−	1.37004i
$52$	15886.5			0.112984
$53$	−193139.			−1.29730			−0.648652	−	0.761085i	$-0.724667\pi$
$53$	−193139.			−1.29730			−0.648652	+	0.761085i	$0.724667\pi$
$54$	404.784			0.00257064
$55$	−113650.	−	113650.i	−0.683096	−	0.683096i
$56$	125026.	+	125026.i	0.711926	+	0.711926i
$57$			183234.i			0.989423i
$58$	−169892.	−	73093.1i	−0.870741	−	0.374621i
$59$	314055.			1.52915			0.764574	−	0.644536i	$-0.222950\pi$
$59$	314055.			1.52915			0.764574	+	0.644536i	$0.222950\pi$
$60$	22938.2	−	22938.2i	0.106195	−	0.106195i
$61$	132513.	−	132513.i	0.583807	−	0.583807i	−0.352140	−	0.935947i	$-0.614546\pi$
$61$	132513.	−	132513.i	0.583807	−	0.583807i	0.935947	+	0.352140i	$0.114546\pi$
$62$			202859.i			0.851177i
$63$			241582.i			0.966146i
$64$			283072.i			1.07983i
$65$	−319878.			−1.16478
$66$	251791.	+	251791.i	0.875808	+	0.875808i
$67$		−	354672.i		−	1.17924i	−0.807680	−	0.589621i	$-0.799277\pi$
$67$		−	354672.i		−	1.17924i	0.807680	−	0.589621i	$-0.200723\pi$
$68$	21845.3	+	21845.3i	0.0694755	+	0.0694755i
$69$	−382106.	+	382106.i	−1.16315	+	1.16315i
$70$	−231910.	−	231910.i	−0.676121	−	0.676121i
$71$		−	407240.i		−	1.13782i	−0.822398	−	0.568912i	$-0.807365\pi$
$71$		−	407240.i		−	1.13782i	0.822398	−	0.568912i	$-0.192635\pi$
$72$	−276091.	+	276091.i	−0.739700	+	0.739700i
$73$	122649.	+	122649.i	0.315279	+	0.315279i	0.846950	−	0.531672i	$-0.178436\pi$
$73$	122649.	+	122649.i	0.315279	+	0.315279i	−0.531672	+	0.846950i	$0.678436\pi$
$74$	379680.			0.936963
$75$	−39788.9	+	39788.9i	−0.0943145	+	0.0943145i
$76$	−22025.2	−	22025.2i	−0.0501741	−	0.0501741i
$77$	−287477.	+	287477.i	−0.629696	+	0.629696i
$78$	708688.			1.49338
$79$	−167108.	+	167108.i	−0.338935	+	0.338935i	−0.855966	−	0.517032i	$-0.827037\pi$
$79$	−167108.	+	167108.i	−0.338935	+	0.338935i	0.517032	+	0.855966i	$0.327037\pi$
$80$		−	475729.i		−	0.929158i
$81$	530420.			0.998080
$82$	−805017.			−1.46004
$83$	287008.			0.501949			0.250974	−	0.967994i	$-0.419249\pi$
$83$	287008.			0.501949			0.250974	+	0.967994i	$0.419249\pi$
$84$	−58022.0	−	58022.0i	−0.0978938	−	0.0978938i
$85$	−439860.	−	439860.i	−0.716239	−	0.716239i
$86$		−	417830.i		−	0.656907i
$87$	855861.	+	368220.i	1.29971	+	0.559177i
$88$	−657085.			−0.964214
$89$	270731.	−	270731.i	0.384032	−	0.384032i	−0.488520	−	0.872553i	$-0.662463\pi$
$89$	270731.	−	270731.i	0.384032	−	0.384032i	0.872553	+	0.488520i	$0.162463\pi$
$90$	512121.	−	512121.i	0.702498	−	0.702498i
$91$			809128.i			1.07372i
$92$		−	91860.3i		−	0.117968i
$93$		−	1.02194e6i		−	1.27051i
$94$	−1.13079e6			−1.36144
$95$	443483.	+	443483.i	0.517257	+	0.517257i
$96$		−	253024.i		−	0.285988i
$97$	−678551.	−	678551.i	−0.743477	−	0.743477i	0.229768	−	0.973245i	$-0.426203\pi$
$97$	−678551.	−	678551.i	−0.743477	−	0.743477i	−0.973245	+	0.229768i	$0.926203\pi$
$98$	44242.0	−	44242.0i	0.0470063	−	0.0470063i
$99$	−634829.	−	634829.i	−0.654261	−	0.654261i
$100$		−	9565.47i		−	0.00956547i
$101$	1.05824e6	−	1.05824e6i	1.02712	−	1.02712i	0.0274991	−	0.999622i	$-0.491246\pi$
$101$	1.05824e6	−	1.05824e6i	1.02712	−	1.02712i	0.999622	−	0.0274991i	$-0.00875433\pi$
$102$	974509.	+	974509.i	0.918302	+	0.918302i
$103$	1.98667e6			1.81808			0.909042	−	0.416705i	$-0.136815\pi$
$103$	1.98667e6			1.81808			0.909042	+	0.416705i	$0.136815\pi$
$104$	−924711.	+	924711.i	−0.822064	+	0.822064i
$105$	1.16829e6	+	1.16829e6i	1.00921	+	1.00921i
$106$	1.03565e6	−	1.03565e6i	0.869548	−	0.869548i
$107$	−1.52390e6			−1.24396			−0.621978	−	0.783035i	$-0.713671\pi$
$107$	−1.52390e6			−1.24396			−0.621978	+	0.783035i	$0.713671\pi$
$108$	245.114	−	245.114i	0.000194579	−	0.000194579i
$109$		−	408748.i		−	0.315629i	−0.987469	−	0.157814i	$-0.949555\pi$
$109$		−	408748.i		−	0.315629i	0.987469	−	0.157814i	$-0.0504448\pi$
$110$	1.21882e6			0.915721
$111$	−1.91271e6			−1.39855
$112$	−1.20335e6			−0.856522
$113$	454771.	+	454771.i	0.315179	+	0.315179i	0.846912	−	0.531733i	$-0.178459\pi$
$113$	454771.	+	454771.i	0.315179	+	0.315179i	−0.531733	+	0.846912i	$0.678459\pi$
$114$	−982535.	−	982535.i	−0.663183	−	0.663183i
$115$			1.84963e6i			1.21616i
$116$	−147138.	+	58615.8i	−0.0942649	+	0.0375527i
$117$	−1.78678e6			−1.11561
$118$	−1.68402e6	+	1.68402e6i	−1.02495	+	1.02495i
$119$	−1.11262e6	+	1.11262e6i	−0.660248	+	0.660248i
$120$			2.67035e6i			1.54534i
$121$			260697.i			0.147156i
$122$			1.42112e6i			0.782619i
$123$	4.05542e6			2.17932
$124$	122840.	+	122840.i	0.0644280	+	0.0644280i
$125$		−	1.85051e6i		−	0.947461i
$126$	−1.29541e6	−	1.29541e6i	−0.647581	−	0.647581i
$127$	−814601.	+	814601.i	−0.397680	+	0.397680i	−0.877414	−	0.479734i	$-0.840733\pi$
$127$	−814601.	+	814601.i	−0.397680	+	0.397680i	0.479734	+	0.877414i	$0.340733\pi$
$128$	−1.21814e6	−	1.21814e6i	−0.580856	−	0.580856i
$129$			2.10489e6i			0.980529i
$130$	1.71524e6	−	1.71524e6i	0.780720	−	0.780720i
$131$	732962.	+	732962.i	0.326038	+	0.326038i	0.851078	−	0.525040i	$-0.175950\pi$
$131$	732962.	+	732962.i	0.326038	+	0.326038i	−0.525040	+	0.851078i	$0.675950\pi$
$132$	304941.			0.132585
$133$	1.12179e6	−	1.12179e6i	0.476821	−	0.476821i
$134$	1.90182e6	+	1.90182e6i	0.790413	+	0.790413i
$135$	−4935.41	+	4935.41i	−0.00200596	+	0.00200596i
$136$	−2.54312e6			−1.01100
$137$	2.53771e6	−	2.53771e6i	0.986915	−	0.986915i	−0.0130001	−	0.999915i	$-0.504138\pi$
$137$	2.53771e6	−	2.53771e6i	0.986915	−	0.986915i	0.999915	+	0.0130001i	$0.00413818\pi$
$138$		−	4.09784e6i		−	1.55926i
$139$	−3.98504e6			−1.48384			−0.741922	−	0.670486i	$-0.766086\pi$
$139$	−3.98504e6			−1.48384			−0.741922	+	0.670486i	$0.766086\pi$
$140$	−280862.			−0.102355
$141$	5.69654e6			2.03214
$142$	2.18369e6	+	2.18369e6i	0.762652	+	0.762652i
$143$	−2.12623e6	−	2.12623e6i	−0.727112	−	0.727112i
$144$		−	2.65734e6i		−	0.889937i
$145$	2.96265e6	−	1.18024e6i	0.971799	−	0.387139i
$146$	−1.31533e6			−0.422645
$147$	−222877.	+	222877.i	−0.0701638	+	0.0701638i
$148$	229912.	−	229912.i	0.0709214	−	0.0709214i
$149$			3.14043e6i			0.949360i	0.880159	+	0.474680i	$0.157436\pi$
$149$			3.14043e6i			0.949360i	−0.880159	+	0.474680i	$0.842564\pi$
$150$		−	426711.i		−	0.126433i
$151$			3.85484e6i			1.11963i	0.828616	+	0.559817i	$0.189129\pi$
$151$			3.85484e6i			1.11963i	−0.828616	+	0.559817i	$0.810871\pi$
$152$	2.56406e6			0.730126
$153$	−2.45698e6	−	2.45698e6i	−0.686005	−	0.686005i
$154$		−	3.08301e6i		−	0.844135i
$155$	−2.47341e6	−	2.47341e6i	−0.664203	−	0.664203i
$156$	429141.	−	429141.i	0.113038	−	0.113038i
$157$	−4.64148e6	−	4.64148e6i	−1.19938	−	1.19938i	−0.974351	−	0.225031i	$-0.927752\pi$
$157$	−4.64148e6	−	4.64148e6i	−1.19938	−	1.19938i	−0.225031	−	0.974351i	$-0.572248\pi$
$158$		−	1.79213e6i		−	0.454357i
$159$	−5.21725e6	+	5.21725e6i	−1.29793	+	1.29793i
$160$	−612396.	−	612396.i	−0.149511	−	0.149511i
$161$	4.67861e6			1.12109
$162$	−2.84421e6	+	2.84421e6i	−0.668985	+	0.668985i
$163$	1.00208e6	+	1.00208e6i	0.231388	+	0.231388i	0.813272	−	0.581884i	$-0.197684\pi$
$163$	1.00208e6	+	1.00208e6i	0.231388	+	0.231388i	−0.581884	+	0.813272i	$0.697684\pi$
$164$	−487472.	+	487472.i	−0.110514	+	0.110514i
$165$	−6.14005e6			−1.36685
$166$	−1.53899e6	+	1.53899e6i	−0.336442	+	0.336442i
$167$			4.84100e6i			1.03941i	0.854347	+	0.519703i	$0.173958\pi$
$167$			4.84100e6i			1.03941i	−0.854347	+	0.519703i	$0.826042\pi$
$168$	6.75462e6			1.42453
$169$	−1.15764e6			−0.239835
$170$	4.71722e6			0.960151
$171$	2.47722e6	+	2.47722e6i	0.495422	+	0.495422i
$172$	−253014.	−	253014.i	−0.0497231	−	0.0497231i
$173$		−	2.48816e6i		−	0.480551i	−0.970705	−	0.240275i	$-0.922762\pi$
$173$		−	2.48816e6i		−	0.480551i	0.970705	−	0.240275i	$-0.0772378\pi$
$174$	−6.56374e6	+	2.61482e6i	−1.24596	+	0.496357i
$175$	487187.			0.0909037
$176$	3.16217e6	−	3.16217e6i	0.580026	−	0.580026i
$177$	8.48354e6	−	8.48354e6i	1.52988	−	1.52988i
$178$			2.90342e6i			0.514813i
$179$			5731.24i			0.000999285i	1.00000		0.000499643i	$0.000159041\pi$
$179$			5731.24i			0.000999285i	−1.00000		0.000499643i	$0.999841\pi$
$180$		−	620222.i		−	0.106348i
$181$	3.63228e6			0.612554			0.306277	−	0.951942i	$-0.400917\pi$
$181$	3.63228e6			0.612554			0.306277	+	0.951942i	$0.400917\pi$
$182$	−4.33869e6	−	4.33869e6i	−0.719688	−	0.719688i
$183$		−	7.15913e6i		−	1.16817i
$184$	5.34694e6	+	5.34694e6i	0.858326	+	0.858326i
$185$	−4.62933e6	+	4.62933e6i	−0.731145	+	0.731145i
$186$	5.47983e6	+	5.47983e6i	0.851585	+	0.851585i
$187$		−	5.84750e6i		−	0.894223i
$188$	−684740.	+	684740.i	−0.103051	+	0.103051i
$189$	12484.1	+	12484.1i	0.00184915	+	0.00184915i
$190$	−4.75607e6			−0.693406
$191$	−6.87959e6	+	6.87959e6i	−0.987330	+	0.987330i	−0.999921	−	0.0125905i	$-0.995992\pi$
$191$	−6.87959e6	+	6.87959e6i	−0.987330	+	0.987330i	0.0125905	+	0.999921i	$0.495992\pi$
$192$	7.64660e6	+	7.64660e6i	1.08035	+	1.08035i
$193$	−3.24619e6	+	3.24619e6i	−0.451546	+	0.451546i	−0.895867	−	0.444322i	$-0.853445\pi$
$193$	−3.24619e6	+	3.24619e6i	−0.451546	+	0.451546i	0.444322	+	0.895867i	$0.353445\pi$
$194$	7.27703e6			0.996664
$195$	−8.64084e6	+	8.64084e6i	−1.16534	+	1.16534i
$196$		−	53580.8i		−	0.00711608i
$197$	−1.42589e6			−0.186504			−0.0932520	−	0.995643i	$-0.529726\pi$
$197$	−1.42589e6			−0.186504			−0.0932520	+	0.995643i	$0.529726\pi$
$198$	6.80814e6			0.877067
$199$	−942182.			−0.119557			−0.0597786	−	0.998212i	$-0.519039\pi$
$199$	−942182.			−0.119557			−0.0597786	+	0.998212i	$0.519039\pi$
$200$	556781.	+	556781.i	0.0695976	+	0.0695976i
$201$	−9.58074e6	−	9.58074e6i	−1.17981	−	1.17981i
$202$			1.13490e7i			1.37690i
$203$	−2.98541e6	−	7.49400e6i	−0.356875	−	0.895829i
$204$	1.18021e6			0.139018
$205$	9.81535e6	−	9.81535e6i	1.13932	−	1.13932i
$206$	−1.06529e7	+	1.06529e7i	−1.21861	+	1.21861i
$207$			1.03317e7i			1.16482i
$208$		−	8.90019e6i		−	0.989030i
$209$			5.89566e6i			0.645793i
$210$	−1.25291e7			−1.35289
$211$	−561484.	−	561484.i	−0.0597709	−	0.0597709i	0.676589	−	0.736360i	$-0.263457\pi$
$211$	−561484.	−	561484.i	−0.0597709	−	0.0597709i	−0.736360	+	0.676589i	$0.763457\pi$
$212$		−	1.25425e6i		−	0.131637i
$213$	−1.10007e7	−	1.10007e7i	−1.13837	−	1.13837i
$214$	8.17142e6	−	8.17142e6i	0.833789	−	0.833789i
$215$	5.09448e6	+	5.09448e6i	0.512607	+	0.512607i
$216$			28534.8i			0.00283148i
$217$	−6.25646e6	+	6.25646e6i	−0.612279	+	0.612279i
$218$	2.19178e6	+	2.19178e6i	0.211557	+	0.211557i
$219$	6.62620e6			0.630859
$220$	738050.	−	738050.i	0.0693135	−	0.0693135i
$221$	−8.22914e6	−	8.22914e6i	−0.762391	−	0.762391i
$222$	1.02563e7	−	1.02563e7i	0.937412	−	0.937412i
$223$	1.89202e7			1.70612			0.853062	−	0.521809i	$-0.174743\pi$
$223$	1.89202e7			1.70612			0.853062	+	0.521809i	$0.174743\pi$
$224$	−1.54905e6	+	1.54905e6i	−0.137823	+	0.137823i
$225$			1.07584e6i			0.0944500i
$226$	−4.87713e6			−0.422512
$227$	1.23213e7			1.05336			0.526681	−	0.850063i	$-0.323436\pi$
$227$	1.23213e7			1.05336			0.526681	+	0.850063i	$0.323436\pi$
$228$	−1.18993e6			−0.100396
$229$	−1.47156e7	−	1.47156e7i	−1.22539	−	1.22539i	−0.965691	−	0.259695i	$-0.916378\pi$
$229$	−1.47156e7	−	1.47156e7i	−1.22539	−	1.22539i	−0.259695	−	0.965691i	$-0.583622\pi$
$230$	−9.91803e6	−	9.91803e6i	−0.815158	−	0.815158i
$231$			1.55312e7i			1.25999i
$232$	5.15263e6	−	1.19764e7i	0.412634	−	0.959094i
$233$	1.28490e7			1.01578			0.507891	−	0.861421i	$-0.330425\pi$
$233$	1.28490e7			1.01578			0.507891	+	0.861421i	$0.330425\pi$
$234$	9.58104e6	−	9.58104e6i	0.747765	−	0.747765i
$235$	1.37874e7	−	1.37874e7i	1.06238	−	1.06238i
$236$			2.03949e6i			0.155162i
$237$			9.02816e6i			0.678194i
$238$		−	1.19322e7i		−	0.885092i
$239$	6.85760e6			0.502318			0.251159	−	0.967946i	$-0.419188\pi$
$239$	6.85760e6			0.502318			0.251159	+	0.967946i	$0.419188\pi$
$240$	−1.28508e7	−	1.28508e7i	−0.929603	−	0.929603i
$241$			1.88348e7i			1.34558i	0.739834	+	0.672790i	$0.234904\pi$
$241$			1.88348e7i			1.34558i	−0.739834	+	0.672790i	$0.765096\pi$
$242$	−1.39790e6	−	1.39790e6i	−0.0986349	−	0.0986349i
$243$	1.43557e7	−	1.43557e7i	1.00048	−	1.00048i
$244$	860547.	+	860547.i	0.0592386	+	0.0592386i
$245$			1.07886e6i			0.0733613i
$246$	−2.17459e7	+	2.17459e7i	−1.46074	+	1.46074i
$247$	8.29692e6	+	8.29692e6i	0.550587	+	0.550587i
$248$	−1.43004e7			−0.937546
$249$	7.75292e6	−	7.75292e6i	0.502189	−	0.502189i
$250$	9.92276e6	+	9.92276e6i	0.635057	+	0.635057i
$251$	−1.36973e7	+	1.36973e7i	−0.866194	+	0.866194i	−0.992049	−	0.125854i	$-0.959833\pi$
$251$	−1.36973e7	+	1.36973e7i	−0.866194	+	0.866194i	0.125854	+	0.992049i	$0.459833\pi$
$252$	−1.56885e6			−0.0980344
$253$	−1.22945e7	+	1.22945e7i	−0.759185	+	0.759185i
$254$		−	8.73608e6i		−	0.533108i
$255$	−2.37638e7			−1.43316
$256$	−5.05277e6			−0.301169
$257$	1.42439e7			0.839131			0.419565	−	0.907725i	$-0.362183\pi$
$257$	1.42439e7			0.839131			0.419565	+	0.907725i	$0.362183\pi$
$258$	−1.12868e7	−	1.12868e7i	−0.657222	−	0.657222i
$259$	1.17099e7	+	1.17099e7i	0.673988	+	0.673988i
$260$		−	2.07730e6i		−	0.118190i
$261$	1.65488e7	−	6.59262e6i	0.930777	−	0.370797i
$262$	−7.86055e6			−0.437068
$263$	−2.83169e6	+	2.83169e6i	−0.155660	+	0.155660i	−0.780641	−	0.624980i	$-0.785107\pi$
$263$	−2.83169e6	+	2.83169e6i	−0.155660	+	0.155660i	0.624980	+	0.780641i	$0.285107\pi$
$264$	−1.77498e7	+	1.77498e7i	−0.964676	+	0.964676i
$265$			2.52547e7i			1.35708i
$266$			1.20304e7i			0.639199i
$267$		−	1.46265e7i		−	0.768433i
$268$	2.30326e6			0.119657
$269$	−2.16472e7	−	2.16472e7i	−1.11210	−	1.11210i	−0.992866	−	0.119236i	$-0.961956\pi$
$269$	−2.16472e7	−	2.16472e7i	−1.11210	−	1.11210i	−0.119236	−	0.992866i	$-0.538044\pi$
$270$		−	52929.2i		−	0.00268908i
$271$	8.97334e6	+	8.97334e6i	0.450865	+	0.450865i	0.895641	−	0.444777i	$-0.146717\pi$
$271$	8.97334e6	+	8.97334e6i	0.450865	+	0.450865i	−0.444777	+	0.895641i	$0.646717\pi$
$272$	1.22386e7	−	1.22386e7i	0.608168	−	0.608168i
$273$	2.18569e7	+	2.18569e7i	1.07424	+	1.07424i
$274$			2.72153e7i			1.32300i
$275$	−1.28023e6	+	1.28023e6i	−0.0615588	+	0.0615588i
$276$	−2.48142e6	−	2.48142e6i	−0.118025	−	0.118025i
$277$	2.03396e7			0.956980			0.478490	−	0.878093i	$-0.341184\pi$
$277$	2.03396e7			0.956980			0.478490	+	0.878093i	$0.341184\pi$
$278$	2.13685e7	−	2.13685e7i	0.994580	−	0.994580i
$279$	−1.38160e7	−	1.38160e7i	−0.636166	−	0.636166i
$280$	1.63482e7	−	1.63482e7i	0.744727	−	0.744727i
$281$	−3.49083e6			−0.157329			−0.0786646	−	0.996901i	$-0.525066\pi$
$281$	−3.49083e6			−0.157329			−0.0786646	+	0.996901i	$0.525066\pi$
$282$	−3.05459e7	+	3.05459e7i	−1.36209	+	1.36209i
$283$			3.42742e7i			1.51219i	0.654459	+	0.756097i	$0.272896\pi$
$283$			3.42742e7i			1.51219i	−0.654459	+	0.756097i	$0.727104\pi$
$284$	2.64464e6			0.115455
$285$	2.39595e7			1.03501
$286$	2.28024e7			0.974727
$287$	−2.48278e7	−	2.48278e7i	−1.05025	−	1.05025i
$288$	−3.42074e6	−	3.42074e6i	−0.143200	−	0.143200i
$289$			1.50596e6i			0.0623908i
$290$	−9.55759e6	+	2.22149e7i	−0.391881	+	0.910859i
$291$	−3.66593e7			−1.48767
$292$	−796487.	+	796487.i	−0.0319912	+	0.0319912i
$293$	−1.23409e7	+	1.23409e7i	−0.490617	+	0.490617i	−0.908501	−	0.417883i	$-0.862772\pi$
$293$	−1.23409e7	+	1.23409e7i	−0.490617	+	0.490617i	0.417883	+	0.908501i	$0.362772\pi$
$294$		−	2.39021e6i		−	0.0940577i
$295$		−	4.10655e7i		−	1.59960i
$296$			2.67652e7i			1.03204i
$297$	−65611.4			−0.00250444
$298$	−1.68396e7	−	1.68396e7i	−0.636330	−	0.636330i
$299$			3.46038e7i			1.29452i
$300$	−258391.	−	258391.i	−0.00957005	−	0.00957005i
$301$	1.28864e7	−	1.28864e7i	0.472535	−	0.472535i
$302$	−2.06704e7	−	2.06704e7i	−0.750460	−	0.750460i
$303$		−	5.71725e7i		−	2.05523i
$304$	−1.23393e7	+	1.23393e7i	−0.439209	+	0.439209i
$305$	−1.73273e7	−	1.73273e7i	−0.610705	−	0.610705i
$306$	2.63495e7			0.919621
$307$	−1.46631e7	+	1.46631e7i	−0.506770	+	0.506770i	−0.913533	−	0.406764i	$-0.866657\pi$
$307$	−1.46631e7	+	1.46631e7i	−0.506770	+	0.506770i	0.406764	+	0.913533i	$0.366657\pi$
$308$	−1.86689e6	−	1.86689e6i	−0.0638950	−	0.0638950i
$309$	5.36657e7	−	5.36657e7i	1.81895	−	1.81895i
$310$	2.65257e7			0.890394
$311$	1.23724e7	−	1.23724e7i	0.411312	−	0.411312i	−0.470883	−	0.882196i	$-0.656065\pi$
$311$	1.23724e7	−	1.23724e7i	0.411312	−	0.411312i	0.882196	+	0.470883i	$0.156065\pi$
$312$			4.99583e7i			1.64492i
$313$	3.33164e6			0.108649			0.0543243	−	0.998523i	$-0.482700\pi$
$313$	3.33164e6			0.108649			0.0543243	+	0.998523i	$0.482700\pi$
$314$	4.97769e7			1.60783
$315$	3.15890e7			1.01066
$316$	−1.08521e6	−	1.08521e6i	−0.0343916	−	0.0343916i
$317$	−1.45515e7	−	1.45515e7i	−0.456805	−	0.456805i	0.440800	−	0.897605i	$-0.354695\pi$
$317$	−1.45515e7	−	1.45515e7i	−0.456805	−	0.456805i	−0.897605	+	0.440800i	$0.854695\pi$
$318$		−	5.59516e7i		−	1.73993i
$319$	2.75378e7	+	1.18477e7i	0.848315	+	0.364973i
$320$	3.70142e7			1.12958
$321$	−4.11650e7	+	4.11650e7i	−1.24455	+	1.24455i
$322$	−2.50876e7	+	2.50876e7i	−0.751434	+	0.751434i
$323$			2.28180e7i			0.677127i
$324$			3.44458e6i			0.101275i
$325$			3.60332e6i			0.104967i
$326$	−1.07467e7			−0.310186
$327$	−1.10415e7	−	1.10415e7i	−0.315780	−	0.315780i
$328$		−	5.67489e7i		−	1.60819i
$329$	−3.48751e7	−	3.48751e7i	−0.979326	−	0.979326i
$330$	3.29240e7	−	3.29240e7i	0.916160	−	0.916160i
$331$	−1.31293e7	−	1.31293e7i	−0.362042	−	0.362042i	0.502522	−	0.864564i	$-0.332405\pi$
$331$	−1.31293e7	−	1.31293e7i	−0.362042	−	0.362042i	−0.864564	+	0.502522i	$0.832405\pi$
$332$			1.86384e6i			0.0509325i
$333$	−2.58586e7	+	2.58586e7i	−0.700282	+	0.700282i
$334$	−2.59583e7	−	2.59583e7i	−0.696686	−	0.696686i
$335$	−4.63766e7			−1.23357
$336$	−3.25061e7	+	3.25061e7i	−0.856933	+	0.856933i
$337$	921198.	+	921198.i	0.0240693	+	0.0240693i	0.719039	−	0.694970i	$-0.244582\pi$
$337$	921198.	+	921198.i	0.0240693	+	0.0240693i	−0.694970	+	0.719039i	$0.744582\pi$
$338$	6.20745e6	−	6.20745e6i	0.160755	−	0.160755i
$339$	2.45694e7			0.630661
$340$	2.85648e6	−	2.85648e6i	0.0726765	−	0.0726765i
$341$		−	3.28815e7i		−	0.829255i
$342$	−2.65666e7			−0.664136
$343$	4.16419e7			1.03192
$344$	2.94545e7			0.723563
$345$	4.99638e7	+	4.99638e7i	1.21674	+	1.21674i
$346$	1.33419e7	+	1.33419e7i	0.322100	+	0.322100i
$347$			4.94791e7i			1.18422i	0.805856	+	0.592112i	$0.201706\pi$
$347$			4.94791e7i			1.18422i	−0.805856	+	0.592112i	$0.798294\pi$
$348$	−2.39124e6	+	5.55801e6i	−0.0567394	+	0.131881i
$349$	−6.37912e7			−1.50067			−0.750334	−	0.661059i	$-0.770107\pi$
$349$	−6.37912e7			−1.50067			−0.750334	+	0.661059i	$0.770107\pi$
$350$	−2.61238e6	+	2.61238e6i	−0.0609302	+	0.0609302i
$351$	−92334.4	+	92334.4i	−0.00213522	+	0.00213522i
$352$		−	8.14119e6i		−	0.186664i
$353$		−	5.54404e7i		−	1.26038i	−0.776440	−	0.630191i	$-0.782977\pi$
$353$		−	5.54404e7i		−	1.26038i	0.776440	−	0.630191i	$-0.217023\pi$
$354$			9.09806e7i			2.05087i
$355$	−5.32503e7			−1.19025
$356$	1.75814e6	+	1.75814e6i	0.0389676	+	0.0389676i
$357$			6.01104e7i			1.32113i
$358$	−30731.9	−	30731.9i	−0.000669794	−	0.000669794i
$359$	5.90739e6	−	5.90739e6i	0.127677	−	0.127677i	−0.640381	−	0.768058i	$-0.721223\pi$
$359$	5.90739e6	−	5.90739e6i	0.127677	−	0.127677i	0.768058	+	0.640381i	$0.221223\pi$
$360$	3.61015e7	+	3.61015e7i	0.773780	+	0.773780i
$361$			2.40400e7i			0.510990i
$362$	−1.94770e7	+	1.94770e7i	−0.410578	+	0.410578i
$363$	7.04218e6	+	7.04218e6i	0.147227	+	0.147227i
$364$	−5.25452e6			−0.108950
$365$	1.60374e7	−	1.60374e7i	0.329804	−	0.329804i
$366$	3.83886e7	+	3.83886e7i	0.782994	+	0.782994i
$367$	−2.79767e7	+	2.79767e7i	−0.565977	+	0.565977i	−0.930999	−	0.365022i	$-0.881061\pi$
$367$	−2.79767e7	+	2.79767e7i	−0.565977	+	0.565977i	0.365022	+	0.930999i	$0.381061\pi$
$368$	−5.14635e7			−1.03266
$369$	5.48268e7	−	5.48268e7i	1.09122	−	1.09122i
$370$		−	4.96466e7i		−	0.980132i
$371$	6.38815e7			1.25099
$372$	6.63653e6			0.128918
$373$	−9.15358e7			−1.76386			−0.881931	−	0.471379i	$-0.843756\pi$
$373$	−9.15358e7			−1.76386			−0.881931	+	0.471379i	$0.843756\pi$
$374$	3.13554e7	+	3.13554e7i	0.599373	+	0.599373i
$375$	−4.99877e7	−	4.99877e7i	−0.947915	−	0.947915i
$376$		−	7.97138e7i		−	1.49958i
$377$	5.54268e7	−	2.20806e7i	1.03442	−	0.412085i
$378$	−133884.			−0.00247886
$379$	−2.88941e7	+	2.88941e7i	−0.530751	+	0.530751i	−0.920796	−	0.390045i	$-0.872460\pi$
$379$	−2.88941e7	+	2.88941e7i	−0.530751	+	0.530751i	0.390045	+	0.920796i	$0.372460\pi$
$380$	−2.88000e6	+	2.88000e6i	−0.0524858	+	0.0524858i
$381$			4.40095e7i			0.795741i
$382$		−	7.37792e7i		−	1.32356i
$383$			5.38885e7i			0.959179i	0.877493	+	0.479590i	$0.159214\pi$
$383$			5.38885e7i			0.959179i	−0.877493	+	0.479590i	$0.840786\pi$
$384$	−6.58113e7			−1.16227
$385$	3.75902e7	+	3.75902e7i	0.658708	+	0.658708i
$386$		−	3.48133e7i		−	0.605317i
$387$	2.84569e7	+	2.84569e7i	0.490969	+	0.490969i
$388$	4.40655e6	−	4.40655e6i	0.0754403	−	0.0754403i
$389$	7.90745e7	+	7.90745e7i	1.34335	+	1.34335i	0.892706	+	0.450640i	$0.148804\pi$
$389$	7.90745e7	+	7.90745e7i	1.34335	+	1.34335i	0.450640	+	0.892706i	$0.351196\pi$
$390$		−	9.26674e7i		−	1.56219i
$391$	−4.75833e7	+	4.75833e7i	−0.796020	+	0.796020i
$392$	3.11880e6	+	3.11880e6i	0.0517760	+	0.0517760i
$393$	3.95989e7			0.652388
$394$	7.64589e6	−	7.64589e6i	0.125008	−	0.125008i
$395$	2.18509e7	+	2.18509e7i	0.354551	+	0.354551i
$396$	4.12262e6	−	4.12262e6i	0.0663876	−	0.0663876i
$397$	−1.19942e6			−0.0191691			−0.00958453	−	0.999954i	$-0.503051\pi$
$397$	−1.19942e6			−0.0191691			−0.00958453	+	0.999954i	$0.503051\pi$
$398$	5.05215e6	−	5.05215e6i	0.0801358	−	0.0801358i
$399$		−	6.06055e7i		−	0.954098i
$400$	−5.35893e6			−0.0837332
$401$	4.31073e7			0.668525			0.334262	−	0.942480i	$-0.391513\pi$
$401$	4.31073e7			0.668525			0.334262	+	0.942480i	$0.391513\pi$
$402$	1.02747e8			1.58158
$403$	−4.62738e7	−	4.62738e7i	−0.707002	−	0.707002i
$404$	6.87229e6	+	6.87229e6i	0.104222	+	0.104222i
$405$		−	6.93573e7i		−	1.04406i
$406$	5.61925e7	+	2.41758e7i	0.839653	+	0.361246i
$407$	−6.15423e7			−0.912832
$408$	−6.86971e7	+	6.86971e7i	−1.01148	+	1.01148i
$409$	−6.38206e7	+	6.38206e7i	−0.932805	+	0.932805i	−0.997880	−	0.0650756i	$-0.979271\pi$
$409$	−6.38206e7	+	6.38206e7i	−0.932805	+	0.932805i	0.0650756	+	0.997880i	$0.479271\pi$
$410$			1.05263e8i			1.52730i
$411$		−	1.37102e8i		−	1.97478i
$412$			1.29015e7i			0.184480i
$413$	−1.03875e8			−1.47455
$414$	−5.54003e7	−	5.54003e7i	−0.780749	−	0.780749i
$415$		−	3.75289e7i		−	0.525075i
$416$	−1.14570e7	−	1.14570e7i	−0.159145	−	0.159145i
$417$	−1.07648e8	+	1.07648e8i	−1.48455	+	1.48455i
$418$	−3.16136e7	−	3.16136e7i	−0.432858	−	0.432858i
$419$		−	9.05072e7i		−	1.23039i	−0.788377	−	0.615193i	$-0.789078\pi$
$419$		−	9.05072e7i		−	1.23039i	0.788377	−	0.615193i	$-0.210922\pi$
$420$	−7.58691e6	+	7.58691e6i	−0.102404	+	0.102404i
$421$	3.20880e7	+	3.20880e7i	0.430027	+	0.430027i	0.888638	−	0.458610i	$-0.151653\pi$
$421$	3.20880e7	+	3.20880e7i	0.430027	+	0.430027i	−0.458610	+	0.888638i	$0.651653\pi$
$422$	6.02156e6			0.0801256
$423$	7.70139e7	−	7.70139e7i	1.01753	−	1.01753i
$424$	7.30068e7	+	7.30068e7i	0.957780	+	0.957780i
$425$	−4.95488e6	+	4.95488e6i	−0.0645455	+	0.0645455i
$426$	1.17976e8			1.52603
$427$	−4.38292e7	+	4.38292e7i	−0.562963	+	0.562963i
$428$		−	9.89628e6i		−	0.126224i
$429$	−1.14871e8			−1.45492
$430$	−5.46351e7			−0.687173
$431$	−1.30311e7			−0.162760			−0.0813802	−	0.996683i	$-0.525933\pi$
$431$	−1.30311e7			−0.162760			−0.0813802	+	0.996683i	$0.525933\pi$
$432$	−137322.	−	137322.i	−0.00170329	−	0.00170329i
$433$	−1.32981e7	−	1.32981e7i	−0.163805	−	0.163805i	0.620445	−	0.784250i	$-0.286952\pi$
$433$	−1.32981e7	−	1.32981e7i	−0.163805	−	0.163805i	−0.784250	+	0.620445i	$0.786952\pi$
$434$		−	6.70965e7i		−	0.820788i
$435$	4.81481e7	−	1.11912e8i	0.584940	−	1.35959i
$436$	2.65444e6			0.0320267
$437$	4.79752e7	−	4.79752e7i	0.574873	−	0.574873i
$438$	−3.55309e7	+	3.55309e7i	−0.422847	+	0.422847i
$439$		−	1.51264e8i		−	1.78789i	−0.448174	−	0.893946i	$-0.647926\pi$
$439$		−	1.51264e8i		−	1.78789i	0.448174	−	0.893946i	$-0.352074\pi$
$440$			8.59199e7i			1.00864i
$441$			6.02632e6i			0.0702646i
$442$	8.82523e7			1.02202
$443$	4.24240e7	+	4.24240e7i	0.487979	+	0.487979i	0.907668	−	0.419689i	$-0.137861\pi$
$443$	4.24240e7	+	4.24240e7i	0.487979	+	0.487979i	−0.419689	+	0.907668i	$0.637861\pi$
$444$		−	1.24212e7i		−	0.141911i
$445$	−3.54006e7	−	3.54006e7i	−0.401726	−	0.401726i
$446$	−1.01453e8	+	1.01453e8i	−1.14357	+	1.14357i
$447$	8.48323e7	+	8.48323e7i	0.949815	+	0.949815i
$448$		−	9.36271e7i		−	1.04128i
$449$	1.24150e8	−	1.24150e8i	1.37154	−	1.37154i	0.513372	−	0.858166i	$-0.328396\pi$
$449$	1.24150e8	−	1.24150e8i	1.37154	−	1.37154i	0.858166	−	0.513372i	$-0.171604\pi$
$450$	−5.76887e6	−	5.76887e6i	−0.0633072	−	0.0633072i
$451$	1.30485e8			1.42243
$452$	−2.95331e6	+	2.95331e6i	−0.0319811	+	0.0319811i
$453$	1.04131e8	+	1.04131e8i	1.12017	+	1.12017i
$454$	−6.60688e7	+	6.60688e7i	−0.706039	+	0.706039i
$455$	1.05801e8			1.12319
$456$	6.92629e7	−	6.92629e7i	0.730476	−	0.730476i
$457$		−	5.96646e7i		−	0.625126i	−0.949897	−	0.312563i	$-0.898812\pi$
$457$		−	5.96646e7i		−	0.625126i	0.949897	−	0.312563i	$-0.101188\pi$
$458$	1.57816e8			1.64268
$459$	−253936.			−0.00262595
$460$	−1.20116e7			−0.123403
$461$	−4.26201e7	−	4.26201e7i	−0.435022	−	0.435022i	0.455310	−	0.890333i	$-0.349528\pi$
$461$	−4.26201e7	−	4.26201e7i	−0.435022	−	0.435022i	−0.890333	+	0.455310i	$0.849528\pi$
$462$	−8.32810e7	−	8.32810e7i	−0.844540	−	0.844540i
$463$			5.23620e7i			0.527562i	0.964583	+	0.263781i	$0.0849696\pi$
$463$			5.23620e7i			0.527562i	−0.964583	+	0.263781i	$0.915030\pi$
$464$	3.28387e7	+	8.24320e7i	0.328725	+	0.825167i
$465$	−1.33628e8			−1.32904
$466$	−6.88985e7	+	6.88985e7i	−0.680851	+	0.680851i
$467$	7.31073e7	−	7.31073e7i	0.717811	−	0.717811i	−0.250346	−	0.968156i	$-0.580544\pi$
$467$	7.31073e7	−	7.31073e7i	0.717811	−	0.717811i	0.968156	+	0.250346i	$0.0805443\pi$
$468$		−	1.16034e7i		−	0.113201i
$469$			1.17309e8i			1.13714i
$470$			1.47861e8i			1.42416i
$471$	−2.50760e8			−2.39992
$472$	−1.18713e8	−	1.18713e8i	−1.12895	−	1.12895i
$473$			6.77260e7i			0.639989i
$474$	−4.84106e7	−	4.84106e7i	−0.454575	−	0.454575i
$475$	4.99569e6	−	4.99569e6i	0.0466138	−	0.0466138i
$476$	−7.22543e6	−	7.22543e6i	−0.0669951	−	0.0669951i
$477$			1.41068e8i			1.29979i
$478$	−3.67717e7	+	3.67717e7i	−0.336690	+	0.336690i
$479$	7.42068e7	+	7.42068e7i	0.675207	+	0.675207i	0.958912	−	0.283704i	$-0.0915634\pi$
$479$	7.42068e7	+	7.42068e7i	0.675207	+	0.675207i	−0.283704	+	0.958912i	$0.591563\pi$
$480$	−3.30852e7			−0.299165
$481$	−8.66080e7	+	8.66080e7i	−0.778257	+	0.778257i
$482$	−1.00995e8	−	1.00995e8i	−0.901905	−	0.901905i
$483$	1.26383e8	−	1.26383e8i	1.12162	−	1.12162i
$484$	−1.69298e6			−0.0149319
$485$	−8.87268e7	+	8.87268e7i	−0.777731	+	0.777731i
$486$			1.53956e8i			1.34118i
$487$	−3.41030e7			−0.295261			−0.147630	−	0.989043i	$-0.547165\pi$
$487$	−3.41030e7			−0.295261			−0.147630	+	0.989043i	$0.547165\pi$
$488$	−1.00180e8			−0.862031
$489$	5.41384e7			0.462998
$490$	−5.78504e6	−	5.78504e6i	−0.0491721	−	0.0491721i
$491$	7.17038e7	+	7.17038e7i	0.605756	+	0.605756i	0.941834	−	0.336078i	$-0.109101\pi$
$491$	7.17038e7	+	7.17038e7i	0.605756	+	0.605756i	−0.336078	+	0.941834i	$0.609101\pi$
$492$			2.63361e7i			0.221134i
$493$	1.06580e8	+	4.58541e7i	0.889474	+	0.382681i
$494$	−8.89791e7			−0.738086
$495$	−8.30097e7	+	8.30097e7i	−0.684405	+	0.684405i
$496$	6.88194e7	−	6.88194e7i	0.563983	−	0.563983i
$497$			1.34696e8i			1.09720i
$498$			8.31451e7i			0.673207i
$499$			1.57386e8i			1.26667i	0.773877	+	0.633336i	$0.218315\pi$
$499$			1.57386e8i			1.26667i	−0.773877	+	0.633336i	$0.781685\pi$
$500$	1.20173e7			0.0961385
$501$	1.30770e8	+	1.30770e8i	1.03990	+	1.03990i
$502$		−	1.46895e8i		−	1.16117i
$503$	1.16276e7	+	1.16276e7i	0.0913664	+	0.0913664i	0.751313	−	0.659946i	$-0.229421\pi$
$503$	1.16276e7	+	1.16276e7i	0.0913664	+	0.0913664i	−0.659946	+	0.751313i	$0.729421\pi$
$504$	9.13184e7	−	9.13184e7i	0.713291	−	0.713291i
$505$	−1.38375e8	−	1.38375e8i	−1.07444	−	1.07444i
$506$		−	1.31850e8i		−	1.01772i
$507$	−3.12712e7	+	3.12712e7i	−0.239950	+	0.239950i
$508$	−5.29007e6	−	5.29007e6i	−0.0403525	−	0.0403525i
$509$	−8.61303e7			−0.653135			−0.326567	−	0.945174i	$-0.605892\pi$
$509$	−8.61303e7			−0.653135			−0.326567	+	0.945174i	$0.605892\pi$
$510$	1.27426e8	−	1.27426e8i	0.960611	−	0.960611i
$511$	−4.05666e7	−	4.05666e7i	−0.304022	−	0.304022i
$512$	1.05055e8	−	1.05055e8i	0.782721	−	0.782721i
$513$	256027.			0.00189642
$514$	−7.63784e7	+	7.63784e7i	−0.562446	+	0.562446i
$515$		−	2.59775e8i		−	1.90185i
$516$	−1.36693e7			−0.0994939
$517$	1.83289e8			1.32637
$518$	−1.25581e8			−0.903511
$519$	−6.72124e7	−	6.72124e7i	−0.480781	−	0.480781i
$520$	1.20914e8	+	1.20914e8i	0.859940	+	0.859940i
$521$			9.07225e7i			0.641507i	0.947163	+	0.320754i	$0.103936\pi$
$521$			9.07225e7i			0.641507i	−0.947163	+	0.320754i	$0.896064\pi$
$522$	−5.33870e7	+	1.24089e8i	−0.375339	+	0.872410i
$523$	1.70723e8			1.19340			0.596702	−	0.802463i	$-0.296478\pi$
$523$	1.70723e8			1.19340			0.596702	+	0.802463i	$0.296478\pi$
$524$	−4.75990e6	+	4.75990e6i	−0.0330829	+	0.0330829i
$525$	1.31603e7	−	1.31603e7i	0.0909472	−	0.0909472i
$526$		−	3.03680e7i		−	0.208670i
$527$		−	1.27261e8i		−	0.869490i
$528$		−	1.70839e8i		−	1.16061i
$529$	5.20532e7			0.351626
$530$	−1.35420e8	−	1.35420e8i	−0.909611	−	0.909611i
$531$		−	2.29385e8i		−	1.53208i
$532$	7.28494e6	+	7.28494e6i	0.0483828	+	0.0483828i
$533$	1.83631e8	−	1.83631e8i	1.21273	−	1.21273i
$534$	7.84298e7	+	7.84298e7i	0.515059	+	0.515059i
$535$			1.99264e8i			1.30127i
$536$	−1.34067e8	+	1.34067e8i	−0.870616	+	0.870616i
$537$	154818.	+	154818.i	0.000999764	+	0.000999764i
$538$	2.32152e8			1.49082
$539$	−7.17118e6	+	7.17118e6i	−0.0457957	+	0.0457957i
$540$	−32050.8	−	32050.8i	−0.000203544	−	0.000203544i
$541$	9.32811e7	−	9.32811e7i	0.589117	−	0.589117i	−0.348275	−	0.937392i	$-0.613232\pi$
$541$	9.32811e7	−	9.32811e7i	0.589117	−	0.589117i	0.937392	+	0.348275i	$0.113232\pi$
$542$	−9.62333e7			−0.604404
$543$	9.81187e7	−	9.81187e7i	0.612847	−	0.612847i
$544$		−	3.15089e7i		−	0.195721i
$545$	−5.34476e7			−0.330171
$546$	−2.34401e8			−1.44007
$547$	5.21804e7			0.318820			0.159410	−	0.987212i	$-0.449041\pi$
$547$	5.21804e7			0.318820			0.159410	+	0.987212i	$0.449041\pi$
$548$	1.64800e7	+	1.64800e7i	0.100142	+	0.100142i
$549$	−9.67872e7	−	9.67872e7i	−0.584926	−	0.584926i
$550$		−	1.37296e7i		−	0.0825223i
$551$	−1.07457e8	−	4.62317e7i	−0.642364	−	0.276366i
$552$	2.88873e8			1.71747
$553$	5.52717e7	−	5.52717e7i	0.326834	−	0.326834i
$554$	−1.09064e8	+	1.09064e8i	−0.641437	+	0.641437i
$555$			2.50104e8i			1.46299i
$556$		−	2.58791e7i		−	0.150565i
$557$		−	1.30053e8i		−	0.752586i	−0.926501	−	0.376293i	$-0.877199\pi$
$557$		−	1.30053e8i		−	0.752586i	0.926501	−	0.376293i	$-0.122801\pi$
$558$	1.48168e8			0.852808
$559$	9.53103e7	+	9.53103e7i	0.545638	+	0.545638i
$560$			1.57349e8i			0.895985i
$561$	−1.57958e8	−	1.57958e8i	−0.894651	−	0.894651i
$562$	1.87185e7	−	1.87185e7i	0.105453	−	0.105453i
$563$	−1.08043e8	−	1.08043e8i	−0.605438	−	0.605438i	0.336312	−	0.941750i	$-0.390820\pi$
$563$	−1.08043e8	−	1.08043e8i	−0.605438	−	0.605438i	−0.941750	+	0.336312i	$0.890820\pi$
$564$			3.69937e7i			0.206201i
$565$	5.94655e7	−	5.94655e7i	0.329701	−	0.329701i
$566$	−1.83784e8	−	1.83784e8i	−1.01358	−	1.01358i
$567$	−1.75439e8			−0.962446
$568$	−1.53937e8	+	1.53937e8i	−0.840038	+	0.840038i
$569$	−9.48533e7	−	9.48533e7i	−0.514891	−	0.514891i	0.401130	−	0.916021i	$-0.368618\pi$
$569$	−9.48533e7	−	9.48533e7i	−0.514891	−	0.514891i	−0.916021	+	0.401130i	$0.868618\pi$
$570$	−1.28475e8	+	1.28475e8i	−0.693738	+	0.693738i
$571$	−1.67736e8			−0.900984			−0.450492	−	0.892781i	$-0.648751\pi$
$571$	−1.67736e8			−0.900984			−0.450492	+	0.892781i	$0.648751\pi$
$572$	1.38078e7	−	1.38078e7i	0.0737798	−	0.0737798i
$573$			3.71676e8i			1.97561i
$574$	2.66263e8			1.40791
$575$	2.08354e7			0.109597
$576$	2.06755e8			1.08190
$577$	−1.26937e8	−	1.26937e8i	−0.660786	−	0.660786i	0.294779	−	0.955565i	$-0.404754\pi$
$577$	−1.26937e8	−	1.26937e8i	−0.660786	−	0.660786i	−0.955565	+	0.294779i	$0.904754\pi$
$578$	−8.07524e6	−	8.07524e6i	−0.0418189	−	0.0418189i
$579$			1.75378e8i			0.903524i
$580$	7.66455e6	+	1.92396e7i	0.0392828	+	0.0986080i
$581$	−9.49290e7			−0.484028
$582$	1.96574e8	−	1.96574e8i	0.997142	−	0.997142i
$583$	−1.67868e8	+	1.67868e8i	−0.847153	+	0.847153i
$584$		−	9.27229e7i		−	0.465531i
$585$			2.33638e8i			1.16701i
$586$		−	1.32348e8i		−	0.657695i
$587$	2.34079e8			1.15731			0.578653	−	0.815574i	$-0.303579\pi$
$587$	2.34079e8			1.15731			0.578653	+	0.815574i	$0.303579\pi$
$588$	−1.44737e6	−	1.44737e6i	−0.00711949	−	0.00711949i
$589$			1.28309e8i			0.627932i
$590$	2.20201e8	+	2.20201e8i	1.07217	+	1.07217i
$591$	−3.85175e7	+	3.85175e7i	−0.186593	+	0.186593i
$592$	−1.28805e8	−	1.28805e8i	−0.620824	−	0.620824i
$593$		−	2.19757e8i		−	1.05385i	−0.849912	−	0.526924i	$-0.823345\pi$
$593$		−	2.19757e8i		−	1.05385i	0.849912	−	0.526924i	$-0.176655\pi$
$594$	351820.	−	351820.i	0.00167865	−	0.00167865i
$595$	1.45486e8	+	1.45486e8i	0.690668	+	0.690668i
$596$	−2.03941e7			−0.0963312
$597$	−2.54511e7	+	2.54511e7i	−0.119614	+	0.119614i
$598$	−1.85552e8	−	1.85552e8i	−0.867684	−	0.867684i
$599$	−1.79651e8	+	1.79651e8i	−0.835889	+	0.835889i	−0.988315	−	0.152426i	$-0.951291\pi$
$599$	−1.79651e8	+	1.79651e8i	−0.835889	+	0.835889i	0.152426	+	0.988315i	$0.451291\pi$
$600$	3.00806e7			0.139262
$601$	7.14537e7	−	7.14537e7i	0.329155	−	0.329155i	−0.523110	−	0.852265i	$-0.675228\pi$
$601$	7.14537e7	−	7.14537e7i	0.329155	−	0.329155i	0.852265	+	0.523110i	$0.175228\pi$
$602$			1.38199e8i			0.633454i
$603$	−2.59052e8			−1.18150
$604$	−2.50336e7			−0.113609
$605$	3.40885e7			0.153936
$606$	3.06569e8	+	3.06569e8i	1.37756	+	1.37756i
$607$	4.60597e7	+	4.60597e7i	0.205947	+	0.205947i	0.802542	−	0.596595i	$-0.203480\pi$
$607$	4.60597e7	+	4.60597e7i	0.205947	+	0.205947i	−0.596595	+	0.802542i	$0.703480\pi$
$608$			3.17684e7i			0.141346i
$609$	−2.83079e8	−	1.21790e8i	−1.25330	−	0.539213i
$610$	1.85824e8			0.818677
$611$	2.57942e8	−	2.57942e8i	1.13083	−	1.13083i
$612$	1.59558e7	−	1.59558e7i	0.0696087	−	0.0696087i
$613$			2.50989e8i			1.08962i	0.838561	+	0.544808i	$0.183397\pi$
$613$			2.50989e8i			1.08962i	−0.838561	+	0.544808i	$0.816603\pi$
$614$		−	1.57252e8i		−	0.679348i
$615$		−	5.30283e8i		−	2.27972i
$616$	2.17334e8			0.929790
$617$	4.43878e7	+	4.43878e7i	0.188977	+	0.188977i	0.795254	−	0.606277i	$-0.207338\pi$
$617$	4.43878e7	+	4.43878e7i	0.188977	+	0.188977i	−0.606277	+	0.795254i	$0.707338\pi$
$618$			5.75531e8i			2.43839i
$619$	1.29591e8	+	1.29591e8i	0.546390	+	0.546390i	0.925395	−	0.379005i	$-0.123734\pi$
$619$	1.29591e8	+	1.29591e8i	0.546390	+	0.546390i	−0.379005	+	0.925395i	$0.623734\pi$
$620$	1.60624e7	−	1.60624e7i	0.0673964	−	0.0673964i
$621$	533904.	+	533904.i	0.00222940	+	0.00222940i
$622$			1.32686e8i			0.551383i
$623$	−8.95454e7	+	8.95454e7i	−0.370322	+	0.370322i
$624$	−2.40420e8	−	2.40420e8i	−0.989504	−	0.989504i
$625$	−2.64986e8			−1.08538
$626$	−1.78648e7	+	1.78648e7i	−0.0728242	+	0.0728242i
$627$	1.59259e8	+	1.59259e8i	0.646103	+	0.646103i
$628$	3.01421e7	−	3.01421e7i	0.121701	−	0.121701i
$629$	−2.38188e8			−0.957121
$630$	−1.69386e8	+	1.69386e8i	−0.677417	+	0.677417i
$631$		−	1.21373e8i		−	0.483097i	−0.970389	−	0.241548i	$-0.922345\pi$
$631$		−	1.21373e8i		−	0.483097i	0.970389	−	0.241548i	$-0.0776553\pi$
$632$	1.26334e8			0.500461
$633$	−3.03347e7			−0.119599
$634$	1.56056e8			0.612368
$635$	1.06517e8	+	1.06517e8i	0.416003	+	0.416003i
$636$	−3.38811e7	−	3.38811e7i	−0.131700	−	0.131700i
$637$			2.01839e7i			0.0780884i
$638$	−2.11192e8	+	8.41333e7i	−0.813234	+	0.323971i
$639$	−2.97447e8			−1.14000
$640$	−1.59284e8	+	1.59284e8i	−0.607618	+	0.607618i
$641$	1.91937e8	−	1.91937e8i	0.728759	−	0.728759i	−0.241614	−	0.970373i	$-0.577677\pi$
$641$	1.91937e8	−	1.91937e8i	0.728759	−	0.728759i	0.970373	+	0.241614i	$0.0776767\pi$
$642$		−	4.41468e8i		−	1.66838i
$643$			6.63702e7i			0.249655i	0.992178	+	0.124827i	$0.0398377\pi$
$643$			6.63702e7i			0.249655i	−0.992178	+	0.124827i	$0.960162\pi$
$644$			3.03832e7i			0.113756i
$645$	2.75234e8			1.02571
$646$	−1.22354e8	−	1.22354e8i	−0.453859	−	0.453859i
$647$			3.56666e7i			0.131689i	0.997830	+	0.0658443i	$0.0209741\pi$
$647$			3.56666e7i			0.131689i	−0.997830	+	0.0658443i	$0.979026\pi$
$648$	−2.00500e8	−	2.00500e8i	−0.736867	−	0.736867i
$649$	2.72963e8	−	2.72963e8i	0.998548	−	0.998548i
$650$	−1.93216e7	−	1.93216e7i	−0.0703564	−	0.0703564i
$651$			3.38011e8i			1.22515i
$652$	−6.50758e6	+	6.50758e6i	−0.0234789	+	0.0234789i
$653$	5.66376e7	+	5.66376e7i	0.203407	+	0.203407i	0.801458	−	0.598051i	$-0.204058\pi$
$653$	5.66376e7	+	5.66376e7i	0.203407	+	0.203407i	−0.598051	+	0.801458i	$0.704058\pi$
$654$	1.18413e8			0.423317
$655$	9.58415e7	−	9.58415e7i	0.341059	−	0.341059i
$656$	2.73100e8	+	2.73100e8i	0.967408	+	0.967408i
$657$	8.95823e7	−	8.95823e7i	0.315883	−	0.315883i
$658$	3.74013e8			1.31283
$659$	−2.41295e8	+	2.41295e8i	−0.843126	+	0.843126i	−0.989264	−	0.146138i	$-0.953316\pi$
$659$	−2.41295e8	+	2.41295e8i	−0.843126	+	0.843126i	0.146138	+	0.989264i	$0.453316\pi$
$660$		−	3.98738e7i		−	0.138693i
$661$	−1.61684e8			−0.559840			−0.279920	−	0.960023i	$-0.590308\pi$
$661$	−1.61684e8			−0.559840			−0.279920	+	0.960023i	$0.590308\pi$
$662$	1.40804e8			0.485333
$663$	−4.44587e8			−1.52551
$664$	−1.08489e8	−	1.08489e8i	−0.370581	−	0.370581i
$665$	−1.46684e8	−	1.46684e8i	−0.498789	−	0.498789i
$666$		−	2.77317e8i		−	0.938759i
$667$	−1.27676e8	−	3.20494e8i	−0.430262	−	1.08005i
$668$	−3.14377e7			−0.105468
$669$	5.11090e8	−	5.11090e8i	1.70694	−	1.70694i
$670$	2.48680e8	−	2.48680e8i	0.826830	−	0.826830i
$671$		−	2.30349e8i		−	0.762463i
$672$			8.36888e7i			0.275778i
$673$		−	1.11108e8i		−	0.364501i	−0.983252	−	0.182250i	$-0.941662\pi$
$673$		−	1.11108e8i		−	0.364501i	0.983252	−	0.182250i	$-0.0583381\pi$
$674$	−9.87926e6			−0.0322660
$675$	55595.8	+	55595.8i	0.000180772	+	0.000180772i
$676$		−	7.51775e6i		−	0.0243359i
$677$	6.11655e7	+	6.11655e7i	0.197125	+	0.197125i	0.798766	−	0.601642i	$-0.205486\pi$
$677$	6.11655e7	+	6.11655e7i	0.197125	+	0.197125i	−0.601642	+	0.798766i	$0.705486\pi$
$678$	−1.31746e8	+	1.31746e8i	−0.422715	+	0.422715i
$679$	2.24434e8	+	2.24434e8i	0.716933	+	0.716933i
$680$			3.32536e8i			1.05758i
$681$	3.32833e8	−	3.32833e8i	1.05387	−	1.05387i
$682$	1.76316e8	+	1.76316e8i	0.555827	+	0.555827i
$683$	−2.05936e8			−0.646354			−0.323177	−	0.946339i	$-0.604751\pi$
$683$	−2.05936e8			−0.646354			−0.323177	+	0.946339i	$0.604751\pi$
$684$	−1.60872e7	+	1.60872e7i	−0.0502703	+	0.0502703i
$685$	−3.31829e8	−	3.31829e8i	−1.03239	−	1.03239i
$686$	−2.23291e8	+	2.23291e8i	−0.691670	+	0.691670i
$687$	−7.95026e8			−2.45195
$688$	−1.41747e8	+	1.41747e8i	−0.435261	+	0.435261i
$689$			4.72478e8i			1.44452i
$690$	−5.35830e8			−1.63110
$691$	3.70662e8			1.12343			0.561713	−	0.827332i	$-0.310143\pi$
$691$	3.70662e8			1.12343			0.561713	+	0.827332i	$0.310143\pi$
$692$	1.61582e7			0.0487613
$693$	2.09972e8	+	2.09972e8i	0.630903	+	0.630903i
$694$	−2.65316e8	−	2.65316e8i	−0.793753	−	0.793753i
$695$			5.21080e8i			1.55221i
$696$	−1.84329e8	−	4.62705e8i	−0.546722	−	1.37239i
$697$	5.05017e8			1.49145
$698$	3.42060e8	−	3.42060e8i	1.00586	−	1.00586i
$699$	3.47088e8	−	3.47088e8i	1.01627	−	1.01627i
$700$			3.16382e6i			0.00922396i
$701$			1.18001e7i			0.0342555i	0.999853	+	0.0171278i	$0.00545220\pi$
$701$			1.18001e7i			0.0342555i	−0.999853	+	0.0171278i	$0.994548\pi$
$702$		−	990227.i		−	0.00286235i
$703$	2.40149e8			0.691218
$704$	2.46033e8	+	2.46033e8i	0.705141	+	0.705141i
$705$		−	7.44875e8i		−	2.12577i
$706$	2.97281e8	+	2.97281e8i	0.844800	+	0.844800i
$707$	−3.50018e8	+	3.50018e8i	−0.990450	+	0.990450i
$708$	5.50926e7	+	5.50926e7i	0.155236	+	0.155236i
$709$			2.20625e8i			0.619037i	0.950893	+	0.309518i	$0.100168\pi$
$709$			2.20625e8i			0.619037i	−0.950893	+	0.309518i	$0.899832\pi$
$710$	2.85538e8	−	2.85538e8i	0.797790	−	0.797790i
$711$	1.22055e8	+	1.22055e8i	0.339584	+	0.339584i
$712$	−2.04674e8			−0.567051
$713$	−2.67569e8	+	2.67569e8i	−0.738188	+	0.738188i
$714$	−3.22323e8	−	3.22323e8i	−0.885516	−	0.885516i
$715$	−2.78024e8	+	2.78024e8i	−0.760613	+	0.760613i
$716$	−37219.0			−0.000101397
$717$	1.85244e8	−	1.85244e8i	0.502558	−	0.502558i
$718$			6.33530e7i			0.171157i
$719$	−1.21790e7			−0.0327661			−0.0163830	−	0.999866i	$-0.505215\pi$
$719$	−1.21790e7			−0.0327661			−0.0163830	+	0.999866i	$0.505215\pi$
$720$	−3.47471e8			−0.930939
$721$	−6.57099e8			−1.75317
$722$	−1.28907e8	−	1.28907e8i	−0.342502	−	0.342502i
$723$	5.08783e8	+	5.08783e8i	1.34622	+	1.34622i
$724$			2.35883e7i			0.0621556i
$725$	−1.32950e7	−	3.33733e7i	−0.0348879	−	0.0875759i
$726$	−7.55229e7			−0.197364
$727$	−3.74895e8	+	3.74895e8i	−0.975679	+	0.975679i	−0.999711	−	0.0240323i	$-0.992350\pi$
$727$	−3.74895e8	+	3.74895e8i	−0.975679	+	0.975679i	0.0240323	+	0.999711i	$0.492350\pi$
$728$	3.05852e8	−	3.05852e8i	0.792715	−	0.792715i
$729$		−	3.88904e8i		−	1.00383i
$730$			1.71991e8i			0.442118i
$731$			2.62120e8i			0.671040i
$732$	4.64918e7			0.118534
$733$	3.79009e7	+	3.79009e7i	0.0962359	+	0.0962359i	0.753586	−	0.657350i	$-0.228323\pi$
$733$	3.79009e7	+	3.79009e7i	0.0962359	+	0.0962359i	−0.657350	+	0.753586i	$0.728323\pi$
$734$		−	3.00032e8i		−	0.758717i
$735$	2.91432e7	+	2.91432e7i	0.0733964	+	0.0733964i
$736$	−6.62479e7	+	6.62479e7i	−0.166165	+	0.166165i
$737$	−3.08265e8	−	3.08265e8i	−0.770056	−	0.770056i
$738$			5.87982e8i			1.46283i
$739$	2.58562e8	−	2.58562e8i	0.640666	−	0.640666i	−0.310053	−	0.950719i	$-0.600347\pi$
$739$	2.58562e8	−	2.58562e8i	0.640666	−	0.640666i	0.950719	+	0.310053i	$0.100347\pi$
$740$	−3.00631e7	−	3.00631e7i	−0.0741889	−	0.0741889i
$741$	4.48248e8			1.10170
$742$	−3.42544e8	+	3.42544e8i	−0.838503	+	0.838503i
$743$	1.66124e8	+	1.66124e8i	0.405010	+	0.405010i	0.879994	−	0.474985i	$-0.157546\pi$
$743$	1.66124e8	+	1.66124e8i	0.405010	+	0.405010i	−0.474985	+	0.879994i	$0.657546\pi$
$744$	−3.86295e8	+	3.86295e8i	−0.937995	+	0.937995i
$745$	4.10640e8			0.993100
$746$	4.90831e8	−	4.90831e8i	1.18227	−	1.18227i
$747$		−	2.09630e8i		−	0.502911i
$748$	3.79740e7			0.0907364
$749$	5.04036e8			1.19954
$750$	5.36086e8			1.27072
$751$	−3.36889e8	−	3.36889e8i	−0.795365	−	0.795365i	0.186995	−	0.982361i	$-0.440125\pi$
$751$	−3.36889e8	−	3.36889e8i	−0.795365	−	0.795365i	−0.982361	+	0.186995i	$0.940125\pi$
$752$	3.83616e8	+	3.83616e8i	0.902077	+	0.902077i
$753$			7.40011e8i			1.73322i
$754$	−1.78809e8	+	4.15609e8i	−0.417133	+	0.969551i
$755$	5.04056e8			1.17122
$756$	−81072.3	+	81072.3i	−0.000187632	+	0.000187632i
$757$	−1.23175e8	+	1.23175e8i	−0.283945	+	0.283945i	−0.834680	−	0.550735i	$-0.814347\pi$
$757$	−1.23175e8	+	1.23175e8i	−0.283945	+	0.283945i	0.550735	+	0.834680i	$0.314347\pi$
$758$		−	3.09870e8i		−	0.711496i
$759$			6.64219e8i			1.51910i
$760$		−	3.35275e8i		−	0.763765i
$761$	3.75245e8			0.851454			0.425727	−	0.904852i	$-0.360018\pi$
$761$	3.75245e8			0.851454			0.425727	+	0.904852i	$0.360018\pi$
$762$	−2.35987e8	−	2.35987e8i	−0.533364	−	0.533364i
$763$			1.35195e8i			0.304360i
$764$	−4.46764e7	−	4.46764e7i	−0.100184	−	0.100184i
$765$	−3.21273e8	+	3.21273e8i	−0.717612	+	0.717612i
$766$	−2.88960e8	−	2.88960e8i	−0.642911	−	0.642911i
$767$		−	7.68276e8i		−	1.70267i
$768$	−1.36490e8	+	1.36490e8i	−0.301313	+	0.301313i
$769$	6.56900e7	+	6.56900e7i	0.144451	+	0.144451i	0.775634	−	0.631183i	$-0.217430\pi$
$769$	6.56900e7	+	6.56900e7i	0.144451	+	0.144451i	−0.631183	+	0.775634i	$0.717430\pi$
$770$	−4.03131e8			−0.883028
$771$	3.84770e8	−	3.84770e8i	0.839533	−	0.839533i
$772$	−2.10809e7	−	2.10809e7i	−0.0458182	−	0.0458182i
$773$	−4.11575e7	+	4.11575e7i	−0.0891066	+	0.0891066i	−0.750255	−	0.661148i	$-0.770069\pi$
$773$	−4.11575e7	+	4.11575e7i	−0.0891066	+	0.0891066i	0.661148	+	0.750255i	$0.270069\pi$
$774$	−3.05182e8			−0.658166
$775$	−2.78621e7	+	2.78621e7i	−0.0598562	+	0.0598562i
$776$			5.12987e8i			1.09780i
$777$	6.32635e8			1.34862
$778$	−8.48024e8			−1.80082
$779$	−5.09177e8			−1.07710
$780$	−5.61141e7	−	5.61141e7i	−0.118246	−	0.118246i
$781$	−3.53955e8	−	3.53955e8i	−0.743010	−	0.743010i
$782$		−	5.10300e8i		−	1.06710i
$783$	514501.	−	1.19587e6i	0.00107177	−	0.00249114i
$784$	−3.00179e7			−0.0622920
$785$	−6.06917e8	+	6.06917e8i	−1.25464	+	1.25464i
$786$	−2.12337e8	+	2.12337e8i	−0.437278	+	0.437278i
$787$		−	2.88053e7i		−	0.0590947i	−0.999563	−	0.0295473i	$-0.990593\pi$
$787$		−	2.88053e7i		−	0.0590947i	0.999563	−	0.0295473i	$-0.00940658\pi$
$788$		−	9.25982e6i		−	0.0189245i
$789$			1.52984e8i			0.311470i
$790$	−2.34337e8			−0.475291
$791$	−1.50417e8	−	1.50417e8i	−0.303927	−	0.303927i
$792$			4.79933e8i			0.966062i
$793$	−3.24168e8	−	3.24168e8i	−0.650056	−	0.650056i
$794$	6.43152e6	−	6.43152e6i	0.0128485	−	0.0128485i
$795$	6.82203e8	+	6.82203e8i	1.35773	+	1.35773i
$796$		−	6.11858e6i		−	0.0121314i
$797$	−1.89013e8	+	1.89013e8i	−0.373350	+	0.373350i	−0.868696	−	0.495346i	$-0.835041\pi$
$797$	−1.89013e8	+	1.89013e8i	−0.373350	+	0.373350i	0.495346	+	0.868696i	$0.335041\pi$
$798$	3.24977e8	+	3.24977e8i	0.639506	+	0.639506i
$799$	7.09386e8			1.39073
$800$	−6.89844e6	+	6.89844e6i	−0.0134735	+	0.0134735i
$801$	−1.97741e8	−	1.97741e8i	−0.384769	−	0.384769i
$802$	−2.31149e8	+	2.31149e8i	−0.448094	+	0.448094i
$803$	2.13202e8			0.411760
$804$	6.22178e7	−	6.22178e7i	0.119714	−	0.119714i
$805$		−	6.11771e8i		−	1.17274i
$806$	4.96257e8			0.947767
$807$	−1.16951e9			−2.22527
$808$	−8.00036e8			−1.51662
$809$	3.22745e8	+	3.22745e8i	0.609556	+	0.609556i	0.942830	−	0.333274i	$-0.108153\pi$
$809$	3.22745e8	+	3.22745e8i	0.609556	+	0.609556i	−0.333274	+	0.942830i	$0.608153\pi$
$810$	3.71906e8	+	3.71906e8i	0.699808	+	0.699808i
$811$		−	4.06926e8i		−	0.762874i	−0.924395	−	0.381437i	$-0.875429\pi$
$811$		−	4.06926e8i		−	0.762874i	0.924395	−	0.381437i	$-0.124571\pi$
$812$	4.86664e7	−	1.93874e7i	0.0908995	−	0.0362119i
$813$	4.84792e8			0.902161
$814$	3.30001e8	−	3.30001e8i	0.611846	−	0.611846i
$815$	1.31032e8	−	1.31032e8i	0.242049	−	0.242049i
$816$		−	6.61199e8i		−	1.21692i
$817$		−	2.64279e8i		−	0.484615i
$818$		−	6.84435e8i		−	1.25047i
$819$	5.90985e8			1.07578
$820$	6.37414e7	+	6.37414e7i	0.115606	+	0.115606i
$821$		−	7.69797e8i		−	1.39106i	−0.718495	−	0.695532i	$-0.755169\pi$
$821$		−	7.69797e8i		−	1.39106i	0.718495	−	0.695532i	$-0.244831\pi$
$822$	7.35165e8	+	7.35165e8i	1.32364	+	1.32364i
$823$	−2.58126e8	+	2.58126e8i	−0.463055	+	0.463055i	−0.899656	−	0.436600i	$-0.856182\pi$
$823$	−2.58126e8	+	2.58126e8i	−0.463055	+	0.463055i	0.436600	+	0.899656i	$0.356182\pi$
$824$	−7.50964e8	−	7.50964e8i	−1.34226	−	1.34226i
$825$			6.91656e7i			0.123177i
$826$	5.56996e8	−	5.56996e8i	0.988352	−	0.988352i
$827$	−4.05442e8	−	4.05442e8i	−0.716823	−	0.716823i	0.251130	−	0.967953i	$-0.419198\pi$
$827$	−4.05442e8	−	4.05442e8i	−0.716823	−	0.716823i	−0.967953	+	0.251130i	$0.919198\pi$
$828$	−6.70945e7			−0.118194
$829$	−8.74237e7	+	8.74237e7i	−0.153450	+	0.153450i	−0.779657	−	0.626207i	$-0.784606\pi$
$829$	−8.74237e7	+	8.74237e7i	−0.153450	+	0.153450i	0.626207	+	0.779657i	$0.284606\pi$
$830$	2.01237e8	+	2.01237e8i	0.351943	+	0.351943i
$831$	5.49432e8	−	5.49432e8i	0.957438	−	0.957438i
$832$	6.92482e8			1.20237
$833$	−2.77547e7	+	2.77547e7i	−0.0480176	+	0.0480176i
$834$		−	1.15445e9i		−	1.99011i
$835$	6.33005e8			1.08730
$836$	−3.82867e7			−0.0655284
$837$	−1.42792e6			−0.00243517
$838$	4.85316e8	+	4.85316e8i	0.824693	+	0.824693i
$839$	1.26414e8	+	1.26414e8i	0.214047	+	0.214047i	0.805984	−	0.591937i	$-0.201637\pi$
$839$	1.26414e8	+	1.26414e8i	0.214047	+	0.214047i	−0.591937	+	0.805984i	$0.701637\pi$
$840$		−	8.83228e8i		−	1.49017i
$841$	−4.31883e8	+	4.09013e8i	−0.726070	+	0.687621i
$842$	−3.44123e8			−0.576471
$843$	−9.42975e7	+	9.42975e7i	−0.157405	+	0.157405i
$844$	3.64631e6	−	3.64631e6i	0.00606493	−	0.00606493i
$845$			1.51372e8i			0.250885i
$846$			8.25924e8i			1.36405i
$847$		−	8.62265e7i		−	0.141903i
$848$	−7.02679e8			−1.15231
$849$	9.25846e8	+	9.25846e8i	1.51292	+	1.51292i
$850$		−	5.31379e7i		−	0.0865262i
$851$	5.00793e8	+	5.00793e8i	0.812586	+	0.812586i
$852$	7.14394e7	−	7.14394e7i	0.115510	−	0.115510i
$853$	−5.57852e8	−	5.57852e8i	−0.898818	−	0.898818i	0.0965134	−	0.995332i	$-0.469231\pi$
$853$	−5.57852e8	−	5.57852e8i	−0.898818	−	0.898818i	−0.995332	+	0.0965134i	$0.969231\pi$
$854$		−	4.70040e8i		−	0.754678i
$855$	3.23919e8	−	3.23919e8i	0.518248	−	0.518248i
$856$	5.76037e8	+	5.76037e8i	0.918393	+	0.918393i
$857$	−5.16865e8			−0.821173			−0.410587	−	0.911822i	$-0.634676\pi$
$857$	−5.16865e8			−0.821173			−0.410587	+	0.911822i	$0.634676\pi$
$858$	6.15960e8	−	6.15960e8i	0.975194	−	0.975194i
$859$	−6.10054e8	−	6.10054e8i	−0.962473	−	0.962473i	0.0368480	−	0.999321i	$-0.488268\pi$
$859$	−6.10054e8	−	6.10054e8i	−0.962473	−	0.962473i	−0.999321	+	0.0368480i	$0.988268\pi$
$860$	−3.30838e7	+	3.30838e7i	−0.0520140	+	0.0520140i
$861$	−1.34135e9			−2.10151
$862$	6.98750e7	−	6.98750e7i	0.109094	−	0.109094i
$863$		−	6.08757e8i		−	0.947134i	−0.880758	−	0.473567i	$-0.842966\pi$
$863$		−	6.08757e8i		−	0.947134i	0.880758	−	0.473567i	$-0.157034\pi$
$864$	−353543.			−0.000548152
$865$	−3.25349e8			−0.502691
$866$	1.42614e8			0.219587
$867$	4.06805e7	+	4.06805e7i	0.0624207	+	0.0624207i
$868$	−4.06298e7	−	4.06298e7i	−0.0621277	−	0.0621277i
$869$			2.90486e8i			0.442655i
$870$	3.41912e8	+	8.58269e8i	0.519226	+	1.30336i
$871$	−8.67639e8			−1.31306
$872$	−1.54508e8	+	1.54508e8i	−0.233024	+	0.233024i
$873$	−4.95612e8	+	4.95612e8i	−0.744902	+	0.744902i
$874$			5.14503e8i			0.770644i
$875$			6.12063e8i			0.913634i
$876$			4.30309e7i			0.0640130i
$877$	8.73409e7			0.129485			0.0647424	−	0.997902i	$-0.479377\pi$
$877$	8.73409e7			0.129485			0.0647424	+	0.997902i	$0.479377\pi$
$878$	8.11104e8	+	8.11104e8i	1.19838	+	1.19838i
$879$			6.66726e8i			0.981705i
$880$	−4.13483e8	−	4.13483e8i	−0.606749	−	0.606749i
$881$	1.59929e8	−	1.59929e8i	0.233884	−	0.233884i	−0.580428	−	0.814312i	$-0.697115\pi$
$881$	1.59929e8	−	1.59929e8i	0.233884	−	0.233884i	0.814312	+	0.580428i	$0.197115\pi$
$882$	−3.23142e7	−	3.23142e7i	−0.0470964	−	0.0470964i
$883$		−	1.09247e8i		−	0.158682i	−0.996848	−	0.0793409i	$-0.974718\pi$
$883$		−	1.09247e8i		−	0.158682i	0.996848	−	0.0793409i	$-0.0252816\pi$
$884$	5.34405e7	−	5.34405e7i	0.0773595	−	0.0773595i
$885$	−1.10930e9	−	1.10930e9i	−1.60037	−	1.60037i
$886$	−4.54971e8			−0.654157
$887$	−1.87235e8	+	1.87235e8i	−0.268297	+	0.268297i	−0.828414	−	0.560116i	$-0.810756\pi$
$887$	−1.87235e8	+	1.87235e8i	−0.268297	+	0.268297i	0.560116	+	0.828414i	$0.310756\pi$
$888$	7.23006e8	+	7.23006e8i	1.03253	+	1.03253i
$889$	2.69433e8	−	2.69433e8i	0.383482	−	0.383482i
$890$	3.79648e8			0.538532
$891$	4.61018e8	−	4.61018e8i	0.651756	−	0.651756i
$892$			1.22869e8i			0.173120i
$893$	−7.15228e8			−1.00436
$894$	−9.09772e8			−1.27327
$895$	749412.			0.00104533
$896$	4.02906e8	+	4.02906e8i	0.560118	+	0.560118i
$897$	9.34750e8	+	9.34750e8i	1.29514	+	1.29514i
$898$			1.33143e9i			1.83861i
$899$	5.99315e8	+	2.57845e8i	0.824852	+	0.354878i
$900$	−6.98659e6			−0.00958380
$901$	−6.49699e8	+	6.49699e8i	−0.888256	+	0.888256i
$902$	−6.99685e8	+	6.99685e8i	−0.953418	+	0.953418i
$903$		−	6.96201e8i		−	0.945522i
$904$		−	3.43809e8i		−	0.465384i
$905$		−	4.74954e8i		−	0.640776i
$906$	−1.11673e9			−1.50164
$907$	1.00550e9	+	1.00550e9i	1.34760	+	1.34760i	0.888262	+	0.459338i	$0.151913\pi$
$907$	1.00550e9	+	1.00550e9i	1.34760	+	1.34760i	0.459338	+	0.888262i	$0.348087\pi$
$908$			8.00149e7i			0.106884i
$909$	−7.72938e8	−	7.72938e8i	−1.02909	−	1.02909i
$910$	−5.67323e8	+	5.67323e8i	−0.752847	+	0.752847i
$911$	4.64611e8	+	4.64611e8i	0.614518	+	0.614518i	0.944120	−	0.329602i	$-0.106915\pi$
$911$	4.64611e8	+	4.64611e8i	0.614518	+	0.614518i	−0.329602	+	0.944120i	$0.606915\pi$
$912$			6.66644e8i			0.878839i
$913$	2.49455e8	−	2.49455e8i	0.327777	−	0.327777i
$914$	3.19932e8	+	3.19932e8i	0.419005	+	0.419005i
$915$	−9.36122e8			−1.22199
$916$	9.55642e7	−	9.55642e7i	0.124339	−	0.124339i
$917$	−2.42430e8	−	2.42430e8i	−0.314397	−	0.314397i
$918$	1.36165e6	−	1.36165e6i	0.00176010	−	0.00176010i
$919$	−2.15690e8			−0.277896			−0.138948	−	0.990300i	$-0.544372\pi$
$919$	−2.15690e8			−0.277896			−0.138948	+	0.990300i	$0.544372\pi$
$920$	6.99162e8	−	6.99162e8i	0.897872	−	0.897872i
$921$			7.92187e8i			1.01403i
$922$	4.57073e8			0.583167
$923$	−9.96236e8			−1.26694
$924$	−1.00860e8			−0.127851
$925$	5.21479e7	+	5.21479e7i	0.0658888	+	0.0658888i
$926$	−2.80774e8	−	2.80774e8i	−0.353610	−	0.353610i
$927$		−	1.45106e9i		−	1.82157i
$928$	1.48386e8	+	6.38404e7i	0.185673	+	0.0798825i
$929$	1.31361e9			1.63840			0.819198	−	0.573510i	$-0.194419\pi$
$929$	1.31361e9			1.63840			0.819198	+	0.573510i	$0.194419\pi$
$930$	7.16537e8	−	7.16537e8i	0.890820	−	0.890820i
$931$	2.79832e7	−	2.79832e7i	0.0346776	−	0.0346776i
$932$			8.34419e7i			0.103071i
$933$		−	6.68428e8i		−	0.823019i
$934$			7.84028e8i			0.962257i
$935$	−7.64615e8			−0.935422
$936$	6.75406e8	+	6.75406e8i	0.823640	+	0.823640i
$937$		−	1.86195e8i		−	0.226333i	−0.993576	−	0.113167i	$-0.963901\pi$
$937$		−	1.86195e8i		−	0.226333i	0.993576	−	0.113167i	$-0.0360994\pi$
$938$	−6.29033e8	−	6.29033e8i	−0.762193	−	0.762193i
$939$	8.99972e7	−	8.99972e7i	0.108701	−	0.108701i
$940$	8.95360e7	+	8.95360e7i	0.107799	+	0.107799i
$941$			3.63764e8i			0.436567i	0.975885	+	0.218283i	$0.0700457\pi$
$941$			3.63764e8i			0.436567i	−0.975885	+	0.218283i	$0.929954\pi$
$942$	1.34462e9	−	1.34462e9i	1.60860	−	1.60860i
$943$	−1.06181e9	−	1.06181e9i	−1.26622	−	1.26622i
$944$	1.14260e9			1.35824
$945$	1.63241e6	−	1.63241e6i	0.00193434	−	0.00193434i
$946$	−3.63159e8	−	3.63159e8i	−0.428967	−	0.428967i
$947$	6.20422e8	−	6.20422e8i	0.730529	−	0.730529i	−0.240195	−	0.970725i	$-0.577212\pi$
$947$	6.20422e8	−	6.20422e8i	0.730529	−	0.730529i	0.970725	+	0.240195i	$0.0772115\pi$
$948$	−5.86293e7			−0.0688161
$949$	3.00037e8	−	3.00037e8i	0.351056	−	0.351056i
$950$			5.35755e7i			0.0624879i
$951$	−7.86159e8			−0.914048
$952$	8.41147e8			0.974902
$953$	8.04419e8			0.929402			0.464701	−	0.885468i	$-0.346162\pi$
$953$	8.04419e8			0.929402			0.464701	+	0.885468i	$0.346162\pi$
$954$	−7.56432e8	−	7.56432e8i	−0.871214	−	0.871214i
$955$	8.99569e8	+	8.99569e8i	1.03282	+	1.03282i
$956$			4.45336e7i			0.0509700i
$957$	1.06392e9	−	4.23836e8i	1.21387	−	0.483573i
$958$	−7.95821e8			−0.905146
$959$	−8.39357e8	+	8.39357e8i	−0.951680	+	0.951680i
$960$	9.99863e8	−	9.99863e8i	1.13013	−	1.13013i
$961$			1.71892e8i			0.193681i
$962$		−	9.28816e8i		−	1.04329i
$963$			1.11305e9i			1.24634i
$964$	−1.22314e8			−0.136535
$965$	4.24469e8	+	4.24469e8i	0.472350	+	0.472350i
$966$			1.35538e9i			1.50359i
$967$	7.33550e8	+	7.33550e8i	0.811241	+	0.811241i	0.984820	−	0.173579i	$-0.0555330\pi$
$967$	7.33550e8	+	7.33550e8i	0.811241	+	0.811241i	−0.173579	+	0.984820i	$0.555533\pi$
$968$	9.85438e7	−	9.85438e7i	0.108643	−	0.108643i
$969$	6.16381e8	+	6.16381e8i	0.677451	+	0.677451i
$970$		−	9.51538e8i		−	1.04258i
$971$	−7.38627e8	+	7.38627e8i	−0.806803	+	0.806803i	−0.984149	−	0.177346i	$-0.943249\pi$
$971$	−7.38627e8	+	7.38627e8i	−0.806803	+	0.806803i	0.177346	+	0.984149i	$0.443249\pi$
$972$	9.32269e7	+	9.32269e7i	0.101518	+	0.101518i
$973$	1.31807e9			1.43087
$974$	1.82867e8	−	1.82867e8i	0.197905	−	0.197905i
$975$	9.73361e7	+	9.73361e7i	0.105017	+	0.105017i
$976$	4.82110e8	−	4.82110e8i	0.518557	−	0.518557i
$977$	−8.88297e8			−0.952521			−0.476261	−	0.879304i	$-0.658008\pi$
$977$	−8.88297e8			−0.952521			−0.476261	+	0.879304i	$0.658008\pi$
$978$	−2.90300e8	+	2.90300e8i	−0.310335	+	0.310335i
$979$		−	4.70615e8i		−	0.501554i
$980$	−7.00618e6			−0.00744394
$981$	−2.98549e8			−0.316234
$982$	−7.68977e8			−0.812043
$983$	−3.50247e8	−	3.50247e8i	−0.368735	−	0.368735i	0.498281	−	0.867016i	$-0.333965\pi$
$983$	−3.50247e8	−	3.50247e8i	−0.368735	−	0.368735i	−0.867016	+	0.498281i	$0.833965\pi$
$984$	−1.53295e9	−	1.53295e9i	−1.60896	−	1.60896i
$985$			1.86449e8i			0.195097i
$986$	−8.17377e8	+	3.25621e8i	−0.852691	+	0.339689i
$987$	−1.88416e9			−1.95959
$988$	−5.38806e7	+	5.38806e7i	−0.0558678	+	0.0558678i
$989$	5.51112e8	−	5.51112e8i	0.569706	−	0.569706i
$990$		−	8.90226e8i		−	0.917476i
$991$		−	8.65756e8i		−	0.889558i	−0.895640	−	0.444779i	$-0.853282\pi$
$991$		−	8.65756e8i		−	0.889558i	0.895640	−	0.444779i	$-0.146718\pi$
$992$		−	1.77180e8i		−	0.181501i
$993$	−7.09323e8			−0.724430
$994$	−7.22265e8	−	7.22265e8i	−0.735424	−	0.735424i
$995$			1.23199e8i			0.125065i
$996$	5.03479e7	+	5.03479e7i	0.0509569	+	0.0509569i
$997$	−9.58996e8	+	9.58996e8i	−0.967680	+	0.967680i	−0.999494	−	0.0318143i	$-0.989871\pi$
$997$	−9.58996e8	+	9.58996e8i	−0.967680	+	0.967680i	0.0318143	+	0.999494i	$0.489871\pi$
$998$	−8.43932e8	−	8.43932e8i	−0.849016	−	0.849016i
$999$			2.67256e6i			0.00268060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.7.c.a.17.5	yes	28
29.12	odd	4	inner	29.7.c.a.12.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.7.c.a.12.5	✓	28	29.12	odd	4	inner
29.7.c.a.17.5	yes	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.36218 + 5.36218i) q^{2} +(27.0129 - 27.0129i) q^{3} +6.49405i q^{4} -130.759i q^{5} +289.696i q^{6} -330.754 q^{7} +(-378.002 - 378.002i) q^{8} -730.397i q^{9} +O(q^{10})\)	\(q+(-5.36218 + 5.36218i) q^{2} +(27.0129 - 27.0129i) q^{3} +6.49405i q^{4} -130.759i q^{5} +289.696i q^{6} -330.754 q^{7} +(-378.002 - 378.002i) q^{8} -730.397i q^{9} +(701.154 + 701.154i) q^{10} +(869.156 - 869.156i) q^{11} +(175.423 + 175.423i) q^{12} -2446.31i q^{13} +(1773.56 - 1773.56i) q^{14} +(-3532.19 - 3532.19i) q^{15} +3638.21 q^{16} +(3363.90 - 3363.90i) q^{17} +(3916.52 + 3916.52i) q^{18} +(-3391.60 + 3391.60i) q^{19} +849.157 q^{20} +(-8934.64 + 8934.64i) q^{21} +9321.14i q^{22} -14145.3 q^{23} -20421.9 q^{24} -1472.96 q^{25} +(13117.6 + 13117.6i) q^{26} +(-37.7443 - 37.7443i) q^{27} -2147.94i q^{28} +(9026.07 + 22657.3i) q^{29} +37880.5 q^{30} +(18915.8 - 18915.8i) q^{31} +(4683.39 - 4683.39i) q^{32} -46956.9i q^{33} +36075.6i q^{34} +43249.1i q^{35} +4743.24 q^{36} +(-35403.5 - 35403.5i) q^{37} -36372.7i q^{38} +(-66082.1 - 66082.1i) q^{39} +(-49427.2 + 49427.2i) q^{40} +(75064.4 + 75064.4i) q^{41} -95818.3i q^{42} +(-38960.8 + 38960.8i) q^{43} +(5644.35 + 5644.35i) q^{44} -95506.1 q^{45} +(75849.6 - 75849.6i) q^{46} +(105441. + 105441. i) q^{47} +(98278.7 - 98278.7i) q^{48} -8250.74 q^{49} +(7898.27 - 7898.27i) q^{50} -181737. i q^{51} +15886.5 q^{52} -193139. q^{53} +404.784 q^{54} +(-113650. - 113650. i) q^{55} +(125026. + 125026. i) q^{56} +183234. i q^{57} +(-169892. - 73093.1i) q^{58} +314055. q^{59} +(22938.2 - 22938.2i) q^{60} +(132513. - 132513. i) q^{61} +202859. i q^{62} +241582. i q^{63} +283072. i q^{64} -319878. q^{65} +(251791. + 251791. i) q^{66} -354672. i q^{67} +(21845.3 + 21845.3i) q^{68} +(-382106. + 382106. i) q^{69} +(-231910. - 231910. i) q^{70} -407240. i q^{71} +(-276091. + 276091. i) q^{72} +(122649. + 122649. i) q^{73} +379680. q^{74} +(-39788.9 + 39788.9i) q^{75} +(-22025.2 - 22025.2i) q^{76} +(-287477. + 287477. i) q^{77} +708688. q^{78} +(-167108. + 167108. i) q^{79} -475729. i q^{80} +530420. q^{81} -805017. q^{82} +287008. q^{83} +(-58022.0 - 58022.0i) q^{84} +(-439860. - 439860. i) q^{85} -417830. i q^{86} +(855861. + 368220. i) q^{87} -657085. q^{88} +(270731. - 270731. i) q^{89} +(512121. - 512121. i) q^{90} +809128. i q^{91} -91860.3i q^{92} -1.02194e6i q^{93} -1.13079e6 q^{94} +(443483. + 443483. i) q^{95} -253024. i q^{96} +(-678551. - 678551. i) q^{97} +(44242.0 - 44242.0i) q^{98} +(-634829. - 634829. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Introduction

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