LMFDB - Embedded newform 29.7.c.a.17.4

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			17.4
Character	$\chi$	$=$	29.17
Dual form			29.7.c.a.12.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.25438 + 6.25438i) q^{2} +(-11.2134 + 11.2134i) q^{3} -14.2346i q^{4} +192.776i q^{5} -140.266i q^{6} -54.6116 q^{7} +(-311.252 - 311.252i) q^{8} +477.517i q^{9} +O(q^{10})$	\(q+(-6.25438 + 6.25438i) q^{2} +(-11.2134 + 11.2134i) q^{3} -14.2346i q^{4} +192.776i q^{5} -140.266i q^{6} -54.6116 q^{7} +(-311.252 - 311.252i) q^{8} +477.517i q^{9} +(-1205.69 - 1205.69i) q^{10} +(785.752 - 785.752i) q^{11} +(159.619 + 159.619i) q^{12} -3667.70i q^{13} +(341.562 - 341.562i) q^{14} +(-2161.68 - 2161.68i) q^{15} +4804.39 q^{16} +(-4655.47 + 4655.47i) q^{17} +(-2986.58 - 2986.58i) q^{18} +(-4781.68 + 4781.68i) q^{19} +2744.09 q^{20} +(612.385 - 612.385i) q^{21} +9828.78i q^{22} +20344.2 q^{23} +6980.41 q^{24} -21537.5 q^{25} +(22939.2 + 22939.2i) q^{26} +(-13529.2 - 13529.2i) q^{27} +777.377i q^{28} +(-8538.03 + 22845.7i) q^{29} +27040.0 q^{30} +(-5994.66 + 5994.66i) q^{31} +(-10128.4 + 10128.4i) q^{32} +17622.0i q^{33} -58234.2i q^{34} -10527.8i q^{35} +6797.29 q^{36} +(-13918.2 - 13918.2i) q^{37} -59813.0i q^{38} +(41127.6 + 41127.6i) q^{39} +(60001.8 - 60001.8i) q^{40} +(-32553.5 - 32553.5i) q^{41} +7660.18i q^{42} +(-39247.7 + 39247.7i) q^{43} +(-11184.9 - 11184.9i) q^{44} -92053.7 q^{45} +(-127240. + 127240. i) q^{46} +(7767.76 + 7767.76i) q^{47} +(-53873.8 + 53873.8i) q^{48} -114667. q^{49} +(134704. - 134704. i) q^{50} -104408. i q^{51} -52208.4 q^{52} +197389. q^{53} +169234. q^{54} +(151474. + 151474. i) q^{55} +(16998.0 + 16998.0i) q^{56} -107238. i q^{57} +(-89485.5 - 196286. i) q^{58} -292706. q^{59} +(-30770.8 + 30770.8i) q^{60} +(-94717.5 + 94717.5i) q^{61} -74985.8i q^{62} -26078.0i q^{63} +180787. i q^{64} +707044. q^{65} +(-110215. - 110215. i) q^{66} +147611. i q^{67} +(66269.0 + 66269.0i) q^{68} +(-228128. + 228128. i) q^{69} +(65844.9 + 65844.9i) q^{70} +518240. i q^{71} +(148628. - 148628. i) q^{72} +(-179019. - 179019. i) q^{73} +174099. q^{74} +(241509. - 241509. i) q^{75} +(68065.6 + 68065.6i) q^{76} +(-42911.2 + 42911.2i) q^{77} -514455. q^{78} +(-323054. + 323054. i) q^{79} +926170. i q^{80} -44691.6 q^{81} +407204. q^{82} +278153. q^{83} +(-8717.08 - 8717.08i) q^{84} +(-897462. - 897462. i) q^{85} -490940. i q^{86} +(-160438. - 351920. i) q^{87} -489133. q^{88} +(397771. - 397771. i) q^{89} +(575739. - 575739. i) q^{90} +200299. i q^{91} -289592. i q^{92} -134442. i q^{93} -97165.1 q^{94} +(-921792. - 921792. i) q^{95} -227149. i q^{96} +(-254007. - 254007. i) q^{97} +(717169. - 717169. i) q^{98} +(375210. + 375210. 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 $

$2$	−6.25438	+	6.25438i	−0.781798	+	0.781798i	−0.980134	−	0.198336i	$-0.936446\pi$
$2$	−6.25438	+	6.25438i	−0.781798	+	0.781798i	0.198336	+	0.980134i	$0.436446\pi$
$3$	−11.2134	+	11.2134i	−0.415313	+	0.415313i	−0.883585	−	0.468272i	$-0.844877\pi$
$3$	−11.2134	+	11.2134i	−0.415313	+	0.415313i	0.468272	+	0.883585i	$0.344877\pi$
$4$		−	14.2346i		−	0.222416i
$5$			192.776i			1.54221i	0.636711	+	0.771103i	$0.280295\pi$
$5$			192.776i			1.54221i	−0.636711	+	0.771103i	$0.719705\pi$
$6$		−	140.266i		−	0.649382i
$7$	−54.6116			−0.159218			−0.0796088	−	0.996826i	$-0.525367\pi$
$7$	−54.6116			−0.159218			−0.0796088	+	0.996826i	$0.525367\pi$
$8$	−311.252	−	311.252i	−0.607913	−	0.607913i
$9$			477.517i			0.655030i
$10$	−1205.69	−	1205.69i	−1.20569	−	1.20569i
$11$	785.752	−	785.752i	0.590347	−	0.590347i	−0.347378	−	0.937725i	$-0.612928\pi$
$11$	785.752	−	785.752i	0.590347	−	0.590347i	0.937725	+	0.347378i	$0.112928\pi$
$12$	159.619	+	159.619i	0.0923724	+	0.0923724i
$13$		−	3667.70i		−	1.66941i	−0.550695	−	0.834706i	$-0.685637\pi$
$13$		−	3667.70i		−	1.66941i	0.550695	−	0.834706i	$-0.314363\pi$
$14$	341.562	−	341.562i	0.124476	−	0.124476i
$15$	−2161.68	−	2161.68i	−0.640498	−	0.640498i
$16$	4804.39			1.17295
$17$	−4655.47	+	4655.47i	−0.947582	+	0.947582i	−0.998693	−	0.0511110i	$-0.983724\pi$
$17$	−4655.47	+	4655.47i	−0.947582	+	0.947582i	0.0511110	+	0.998693i	$0.483724\pi$
$18$	−2986.58	−	2986.58i	−0.512101	−	0.512101i
$19$	−4781.68	+	4781.68i	−0.697140	+	0.697140i	−0.963793	−	0.266653i	$-0.914082\pi$
$19$	−4781.68	+	4781.68i	−0.697140	+	0.697140i	0.266653	+	0.963793i	$0.414082\pi$
$20$	2744.09			0.343012
$21$	612.385	−	612.385i	0.0661251	−	0.0661251i
$22$			9828.78i			0.923064i
$23$	20344.2			1.67208			0.836039	−	0.548670i	$-0.184866\pi$
$23$	20344.2			1.67208			0.836039	+	0.548670i	$0.184866\pi$
$24$	6980.41			0.504949
$25$	−21537.5			−1.37840
$26$	22939.2	+	22939.2i	1.30514	+	1.30514i
$27$	−13529.2	−	13529.2i	−0.687355	−	0.687355i
$28$			777.377i			0.0354126i
$29$	−8538.03	+	22845.7i	−0.350077	+	0.936721i
$29$	−8538.03	+	22845.7i	−0.350077	+	0.936721i
$30$	27040.0			1.00148
$31$	−5994.66	+	5994.66i	−0.201224	+	0.201224i	−0.800524	−	0.599300i	$-0.795446\pi$
$31$	−5994.66	+	5994.66i	−0.201224	+	0.201224i	0.599300	+	0.800524i	$0.295446\pi$
$32$	−10128.4	+	10128.4i	−0.309095	+	0.309095i
$33$			17622.0i			0.490357i
$34$		−	58234.2i		−	1.48164i
$35$		−	10527.8i		−	0.245546i
$36$	6797.29			0.145689
$37$	−13918.2	−	13918.2i	−0.274775	−	0.274775i	0.556244	−	0.831019i	$-0.312242\pi$
$37$	−13918.2	−	13918.2i	−0.274775	−	0.274775i	−0.831019	+	0.556244i	$0.812242\pi$
$38$		−	59813.0i		−	1.09005i
$39$	41127.6	+	41127.6i	0.693329	+	0.693329i
$40$	60001.8	−	60001.8i	0.937527	−	0.937527i
$41$	−32553.5	−	32553.5i	−0.472330	−	0.472330i	0.430338	−	0.902668i	$-0.358395\pi$
$41$	−32553.5	−	32553.5i	−0.472330	−	0.472330i	−0.902668	+	0.430338i	$0.858395\pi$
$42$			7660.18i			0.103393i
$43$	−39247.7	+	39247.7i	−0.493638	+	0.493638i	−0.909450	−	0.415812i	$-0.863497\pi$
$43$	−39247.7	+	39247.7i	−0.493638	+	0.493638i	0.415812	+	0.909450i	$0.363497\pi$
$44$	−11184.9	−	11184.9i	−0.131303	−	0.131303i
$45$	−92053.7			−1.01019
$46$	−127240.	+	127240.i	−1.30723	+	1.30723i
$47$	7767.76	+	7767.76i	0.0748173	+	0.0748173i	0.743525	−	0.668708i	$-0.233152\pi$
$47$	7767.76	+	7767.76i	0.0748173	+	0.0748173i	−0.668708	+	0.743525i	$0.733152\pi$
$48$	−53873.8	+	53873.8i	−0.487140	+	0.487140i
$49$	−114667.			−0.974650
$50$	134704.	−	134704.i	1.07763	−	1.07763i
$51$		−	104408.i		−	0.787086i
$52$	−52208.4			−0.371305
$53$	197389.			1.32585			0.662926	−	0.748685i	$-0.269314\pi$
$53$	197389.			1.32585			0.662926	+	0.748685i	$0.269314\pi$
$54$	169234.			1.07475
$55$	151474.	+	151474.i	0.910436	+	0.910436i
$56$	16998.0	+	16998.0i	0.0967905	+	0.0967905i
$57$		−	107238.i		−	0.579062i
$58$	−89485.5	−	196286.i	−0.458637	−	1.00602i
$59$	−292706.			−1.42520			−0.712600	−	0.701571i	$-0.752482\pi$
$59$	−292706.			−1.42520			−0.712600	+	0.701571i	$0.752482\pi$
$60$	−30770.8	+	30770.8i	−0.142457	+	0.142457i
$61$	−94717.5	+	94717.5i	−0.417293	+	0.417293i	−0.884270	−	0.466977i	$-0.845343\pi$
$61$	−94717.5	+	94717.5i	−0.417293	+	0.417293i	0.466977	+	0.884270i	$0.345343\pi$
$62$		−	74985.8i		−	0.314633i
$63$		−	26078.0i		−	0.104292i
$64$			180787.i			0.689648i
$65$	707044.			2.57458
$66$	−110215.	−	110215.i	−0.383360	−	0.383360i
$67$			147611.i			0.490788i	0.969423	+	0.245394i	$0.0789173\pi$
$67$			147611.i			0.490788i	−0.969423	+	0.245394i	$0.921083\pi$
$68$	66269.0	+	66269.0i	0.210758	+	0.210758i
$69$	−228128.	+	228128.i	−0.694435	+	0.694435i
$70$	65844.9	+	65844.9i	0.191968	+	0.191968i
$71$			518240.i			1.44796i	0.689822	+	0.723979i	$0.257689\pi$
$71$			518240.i			1.44796i	−0.689822	+	0.723979i	$0.742311\pi$
$72$	148628.	−	148628.i	0.398202	−	0.398202i
$73$	−179019.	−	179019.i	−0.460184	−	0.460184i	0.438532	−	0.898716i	$-0.355499\pi$
$73$	−179019.	−	179019.i	−0.460184	−	0.460184i	−0.898716	+	0.438532i	$0.855499\pi$
$74$	174099.			0.429638
$75$	241509.	−	241509.i	0.572467	−	0.572467i
$76$	68065.6	+	68065.6i	0.155055	+	0.155055i
$77$	−42911.2	+	42911.2i	−0.0939936	+	0.0939936i
$78$	−514455.			−1.08409
$79$	−323054.	+	323054.i	−0.655230	+	0.655230i	−0.954248	−	0.299017i	$-0.903341\pi$
$79$	−323054.	+	323054.i	−0.655230	+	0.655230i	0.299017	+	0.954248i	$0.403341\pi$
$80$			926170.i			1.80893i
$81$	−44691.6			−0.0840951
$82$	407204.			0.738534
$83$	278153.			0.486462			0.243231	−	0.969968i	$-0.421793\pi$
$83$	278153.			0.486462			0.243231	+	0.969968i	$0.421793\pi$
$84$	−8717.08	−	8717.08i	−0.0147073	−	0.0147073i
$85$	−897462.	−	897462.i	−1.46137	−	1.46137i
$86$		−	490940.i		−	0.771851i
$87$	−160438.	−	351920.i	−0.243641	−	0.534424i
$88$	−489133.			−0.717759
$89$	397771.	−	397771.i	0.564239	−	0.564239i	−0.366269	−	0.930509i	$-0.619365\pi$
$89$	397771.	−	397771.i	0.564239	−	0.564239i	0.930509	+	0.366269i	$0.119365\pi$
$90$	575739.	−	575739.i	0.789766	−	0.789766i
$91$			200299.i			0.265800i
$92$		−	289592.i		−	0.371897i
$93$		−	134442.i		−	0.167142i
$94$	−97165.1			−0.116984
$95$	−921792.	−	921792.i	−1.07513	−	1.07513i
$96$		−	227149.i		−	0.256742i
$97$	−254007.	−	254007.i	−0.278311	−	0.278311i	0.554124	−	0.832434i	$-0.313053\pi$
$97$	−254007.	−	254007.i	−0.278311	−	0.278311i	−0.832434	+	0.554124i	$0.813053\pi$
$98$	717169.	−	717169.i	0.761979	−	0.761979i
$99$	375210.	+	375210.i	0.386695	+	0.386695i
$100$			306578.i			0.306578i
$101$	882077.	−	882077.i	0.856135	−	0.856135i	−0.134745	−	0.990880i	$-0.543022\pi$
$101$	882077.	−	882077.i	0.856135	−	0.856135i	0.990880	+	0.134745i	$0.0430215\pi$
$102$	653006.	+	653006.i	0.615342	+	0.615342i
$103$	123249.			0.112791			0.0563953	−	0.998409i	$-0.482039\pi$
$103$	123249.			0.112791			0.0563953	+	0.998409i	$0.482039\pi$
$104$	−1.14158e6	+	1.14158e6i	−1.01486	+	1.01486i
$105$	118053.	+	118053.i	0.101979	+	0.101979i
$106$	−1.23455e6	+	1.23455e6i	−1.03655	+	1.03655i
$107$	177855.			0.145183			0.0725913	−	0.997362i	$-0.476873\pi$
$107$	177855.			0.145183			0.0725913	+	0.997362i	$0.476873\pi$
$108$	−192584.	+	192584.i	−0.152879	+	0.152879i
$109$		−	130435.i		−	0.100720i	−0.998731	−	0.0503599i	$-0.983963\pi$
$109$		−	130435.i		−	0.100720i	0.998731	−	0.0503599i	$-0.0160368\pi$
$110$	−1.89475e6			−1.42355
$111$	312142.			0.228236
$112$	−262376.			−0.186754
$113$	288388.	+	288388.i	0.199867	+	0.199867i	0.799943	−	0.600076i	$-0.204863\pi$
$113$	288388.	+	288388.i	0.199867	+	0.199867i	−0.600076	+	0.799943i	$0.704863\pi$
$114$	670709.	+	670709.i	0.452710	+	0.452710i
$115$			3.92186e6i			2.57869i
$116$	325200.	+	121536.i	0.208342	+	0.0778629i
$117$	1.75139e6			1.09352
$118$	1.83070e6	−	1.83070e6i	1.11422	−	1.11422i
$119$	254243.	−	254243.i	0.150872	−	0.150872i
$120$			1.34565e6i			0.778735i
$121$			536750.i			0.302981i
$122$		−	1.18480e6i		−	0.652477i
$123$	730074.			0.392330
$124$	85331.9	+	85331.9i	0.0447555	+	0.0447555i
$125$		−	1.13978e6i		−	0.583568i
$126$	163102.	+	163102.i	0.0815356	+	0.0815356i
$127$	522788.	−	522788.i	0.255220	−	0.255220i	−0.567887	−	0.823107i	$-0.692239\pi$
$127$	522788.	−	522788.i	0.255220	−	0.255220i	0.823107	+	0.567887i	$0.192239\pi$
$128$	−1.77893e6	−	1.77893e6i	−0.848260	−	0.848260i
$129$		−	880204.i		−	0.410029i
$130$	−4.42212e6	+	4.42212e6i	−2.01280	+	2.01280i
$131$	1.43380e6	+	1.43380e6i	0.637785	+	0.637785i	0.950009	−	0.312223i	$-0.101074\pi$
$131$	1.43380e6	+	1.43380e6i	0.637785	+	0.637785i	−0.312223	+	0.950009i	$0.601074\pi$
$132$	250843.			0.109063
$133$	261135.	−	261135.i	0.110997	−	0.110997i
$134$	−923215.	−	923215.i	−0.383697	−	0.383697i
$135$	2.60810e6	−	2.60810e6i	1.06004	−	1.06004i
$136$	2.89805e6			1.15210
$137$	−2.51046e6	+	2.51046e6i	−0.976320	+	0.976320i	−0.999726	−	0.0234064i	$-0.992549\pi$
$137$	−2.51046e6	+	2.51046e6i	−0.976320	+	0.976320i	0.0234064	+	0.999726i	$0.492549\pi$
$138$		−	2.85360e6i		−	1.08582i
$139$	4.57024e6			1.70175			0.850874	−	0.525371i	$-0.176073\pi$
$139$	4.57024e6			1.70175			0.850874	+	0.525371i	$0.176073\pi$
$140$	−149859.			−0.0546135
$141$	−174207.			−0.0621452
$142$	−3.24127e6	−	3.24127e6i	−1.13201	−	1.13201i
$143$	−2.88190e6	−	2.88190e6i	−0.985533	−	0.985533i
$144$			2.29418e6i			0.768316i
$145$	−4.40409e6	−	1.64593e6i	−1.44462	−	0.539891i
$146$	2.23931e6			0.719542
$147$	1.28581e6	−	1.28581e6i	0.404785	−	0.404785i
$148$	−198121.	+	198121.i	−0.0611145	+	0.0611145i
$149$			5.65573e6i			1.70974i	0.518843	+	0.854869i	$0.326363\pi$
$149$			5.65573e6i			1.70974i	−0.518843	+	0.854869i	$0.673637\pi$
$150$			3.02098e6i			0.895107i
$151$		−	2.77434e6i		−	0.805802i	−0.915244	−	0.402901i	$-0.868002\pi$
$151$		−	2.77434e6i		−	0.805802i	0.915244	−	0.402901i	$-0.131998\pi$
$152$	2.97661e6			0.847601
$153$	−2.22307e6	−	2.22307e6i	−0.620695	−	0.620695i
$154$		−	536766.i		−	0.146968i
$155$	−1.15562e6	−	1.15562e6i	−0.310329	−	0.310329i
$156$	585436.	−	585436.i	0.154208	−	0.154208i
$157$	−208301.	−	208301.i	−0.0538260	−	0.0538260i	0.679681	−	0.733507i	$-0.262118\pi$
$157$	−208301.	−	208301.i	−0.0538260	−	0.0538260i	−0.733507	+	0.679681i	$0.762118\pi$
$158$		−	4.04101e6i		−	1.02452i
$159$	−2.21341e6	+	2.21341e6i	−0.550643	+	0.550643i
$160$	−1.95251e6	−	1.95251e6i	−0.476687	−	0.476687i
$161$	−1.11103e6			−0.266224
$162$	279518.	−	279518.i	0.0657454	−	0.0657454i
$163$	3.95009e6	+	3.95009e6i	0.912105	+	0.912105i	0.996438	−	0.0843329i	$-0.0268759\pi$
$163$	3.95009e6	+	3.95009e6i	0.912105	+	0.912105i	−0.0843329	+	0.996438i	$0.526876\pi$
$164$	−463387.	+	463387.i	−0.105054	+	0.105054i
$165$	−3.39709e6			−0.756232
$166$	−1.73967e6	+	1.73967e6i	−0.380315	+	0.380315i
$167$			4.55862e6i			0.978778i	0.872066	+	0.489389i	$0.162780\pi$
$167$			4.55862e6i			0.978778i	−0.872066	+	0.489389i	$0.837220\pi$
$168$	−381212.			−0.0803967
$169$	−8.62522e6			−1.78694
$170$	1.12261e7			2.28499
$171$	−2.28333e6	−	2.28333e6i	−0.456648	−	0.456648i
$172$	558677.	+	558677.i	0.109793	+	0.109793i
$173$		−	4.11687e6i		−	0.795113i	−0.917578	−	0.397556i	$-0.869858\pi$
$173$		−	4.11687e6i		−	0.795113i	0.917578	−	0.397556i	$-0.130142\pi$
$174$	3.20448e6	+	1.19760e6i	0.608289	+	0.227334i
$175$	1.17620e6			0.219465
$176$	3.77506e6	−	3.77506e6i	0.692446	−	0.692446i
$177$	3.28224e6	−	3.28224e6i	0.591904	−	0.591904i
$178$			4.97563e6i			0.882243i
$179$			8.77840e6i			1.53058i	0.643685	+	0.765291i	$0.277405\pi$
$179$			8.77840e6i			1.53058i	−0.643685	+	0.765291i	$0.722595\pi$
$180$			1.31035e6i			0.224683i
$181$	1.36687e6			0.230511			0.115255	−	0.993336i	$-0.463231\pi$
$181$	1.36687e6			0.230511			0.115255	+	0.993336i	$0.463231\pi$
$182$	−1.25275e6	−	1.25275e6i	−0.207802	−	0.207802i
$183$		−	2.12422e6i		−	0.346614i
$184$	−6.33216e6	−	6.33216e6i	−1.01648	−	1.01648i
$185$	2.68309e6	−	2.68309e6i	0.423760	−	0.423760i
$186$	840850.	+	840850.i	0.130671	+	0.130671i
$187$			7.31609e6i			1.11880i
$188$	110571.	−	110571.i	0.0166406	−	0.0166406i
$189$	738853.	+	738853.i	0.109439	+	0.109439i
$190$	1.15305e7			1.68107
$191$	−4.16008e6	+	4.16008e6i	−0.597037	+	0.597037i	−0.939523	−	0.342486i	$-0.888731\pi$
$191$	−4.16008e6	+	4.16008e6i	−0.597037	+	0.597037i	0.342486	+	0.939523i	$0.388731\pi$
$192$	−2.02725e6	−	2.02725e6i	−0.286420	−	0.286420i
$193$	8.56877e6	−	8.56877e6i	1.19192	−	1.19192i	0.215390	−	0.976528i	$-0.430898\pi$
$193$	8.56877e6	−	8.56877e6i	1.19192	−	1.19192i	0.976528	−	0.215390i	$-0.0691022\pi$
$194$	3.17731e6			0.435166
$195$	−7.92840e6	+	7.92840e6i	−1.06926	+	1.06926i
$196$			1.63224e6i			0.216778i
$197$	−1.08566e7			−1.42002			−0.710009	−	0.704193i	$-0.751309\pi$
$197$	−1.08566e7			−1.42002			−0.710009	+	0.704193i	$0.751309\pi$
$198$	−4.69341e6			−0.604635
$199$	5.55876e6			0.705372			0.352686	−	0.935742i	$-0.385268\pi$
$199$	5.55876e6			0.705372			0.352686	+	0.935742i	$0.385268\pi$
$200$	6.70357e6	+	6.70357e6i	0.837947	+	0.837947i
$201$	−1.65523e6	−	1.65523e6i	−0.203830	−	0.203830i
$202$			1.10337e7i			1.33865i
$203$	466276.	−	1.24764e6i	0.0557385	−	0.149142i
$204$	−1.48621e6			−0.175061
$205$	6.27552e6	−	6.27552e6i	0.728431	−	0.728431i
$206$	−770849.	+	770849.i	−0.0881795	+	0.0881795i
$207$			9.71469e6i			1.09526i
$208$		−	1.76211e7i		−	1.95813i
$209$			7.51443e6i			0.823108i
$210$	−1.47670e6			−0.159453
$211$	−3.37983e6	−	3.37983e6i	−0.359788	−	0.359788i	0.503947	−	0.863735i	$-0.331881\pi$
$211$	−3.37983e6	−	3.37983e6i	−0.359788	−	0.359788i	−0.863735	+	0.503947i	$0.831881\pi$
$212$		−	2.80976e6i		−	0.294891i
$213$	−5.81126e6	−	5.81126e6i	−0.601356	−	0.601356i
$214$	−1.11237e6	+	1.11237e6i	−0.113503	+	0.113503i
$215$	−7.56600e6	−	7.56600e6i	−0.761291	−	0.761291i
$216$			8.42198e6i			0.835705i
$217$	327378.	−	327378.i	0.0320384	−	0.0320384i
$218$	815792.	+	815792.i	0.0787426	+	0.0787426i
$219$	4.01485e6			0.382241
$220$	2.15618e6	−	2.15618e6i	0.202496	−	0.202496i
$221$	1.70749e7	+	1.70749e7i	1.58191	+	1.58191i
$222$	−1.95226e6	+	1.95226e6i	−0.178434	+	0.178434i
$223$	−1.71433e7			−1.54589			−0.772947	−	0.634471i	$-0.781218\pi$
$223$	−1.71433e7			−1.54589			−0.772947	+	0.634471i	$0.781218\pi$
$224$	553129.	−	553129.i	0.0492133	−	0.0492133i
$225$		−	1.02845e7i		−	0.902893i
$226$	−3.60738e6			−0.312512
$227$	2.15247e7			1.84018			0.920088	−	0.391712i	$-0.128117\pi$
$227$	2.15247e7			1.84018			0.920088	+	0.391712i	$0.128117\pi$
$228$	−1.52650e6			−0.128793
$229$	−1.43577e6	−	1.43577e6i	−0.119558	−	0.119558i	0.644796	−	0.764354i	$-0.276942\pi$
$229$	−1.43577e6	−	1.43577e6i	−0.119558	−	0.119558i	−0.764354	+	0.644796i	$0.776942\pi$
$230$	−2.45288e7	−	2.45288e7i	−2.01601	−	2.01601i
$231$		−	962365.i		−	0.0780735i
$232$	9.76823e6	−	4.45328e6i	0.782262	−	0.356628i
$233$	−1.65569e7			−1.30891			−0.654457	−	0.756099i	$-0.727103\pi$
$233$	−1.65569e7			−1.30891			−0.654457	+	0.756099i	$0.727103\pi$
$234$	−1.09539e7	+	1.09539e7i	−0.854909	+	0.854909i
$235$	−1.49743e6	+	1.49743e6i	−0.115384	+	0.115384i
$236$			4.16657e6i			0.316988i
$237$		−	7.24510e6i		−	0.544251i
$238$			3.18027e6i			0.235902i
$239$	1.00601e7			0.736901			0.368450	−	0.929647i	$-0.379888\pi$
$239$	1.00601e7			0.736901			0.368450	+	0.929647i	$0.379888\pi$
$240$	−1.03856e7	−	1.03856e7i	−0.751270	−	0.751270i
$241$		−	1.56486e7i		−	1.11795i	−0.829184	−	0.558976i	$-0.811194\pi$
$241$		−	1.56486e7i		−	1.11795i	0.829184	−	0.558976i	$-0.188806\pi$
$242$	−3.35704e6	−	3.35704e6i	−0.236870	−	0.236870i
$243$	1.03639e7	−	1.03639e7i	0.722281	−	0.722281i
$244$	1.34827e6	+	1.34827e6i	0.0928127	+	0.0928127i
$245$		−	2.21049e7i		−	1.50311i
$246$	−4.56616e6	+	4.56616e6i	−0.306723	+	0.306723i
$247$	1.75378e7	+	1.75378e7i	1.16381	+	1.16381i
$248$	3.73170e6			0.244653
$249$	−3.11905e6	+	3.11905e6i	−0.202034	+	0.202034i
$250$	7.12863e6	+	7.12863e6i	0.456232	+	0.456232i
$251$	−7.06671e6	+	7.06671e6i	−0.446885	+	0.446885i	−0.894318	−	0.447433i	$-0.852338\pi$
$251$	−7.06671e6	+	7.06671e6i	−0.446885	+	0.446885i	0.447433	+	0.894318i	$0.352338\pi$
$252$	−371211.			−0.0231963
$253$	1.59855e7	−	1.59855e7i	0.987106	−	0.987106i
$254$			6.53943e6i			0.399060i
$255$	2.01273e7			1.21385
$256$	1.06819e7			0.636688
$257$	−3.90772e6			−0.230210			−0.115105	−	0.993353i	$-0.536720\pi$
$257$	−3.90772e6			−0.230210			−0.115105	+	0.993353i	$0.536720\pi$
$258$	5.50513e6	+	5.50513e6i	0.320560	+	0.320560i
$259$	760095.	+	760095.i	0.0437491	+	0.0437491i
$260$		−	1.00645e7i		−	0.572628i
$261$	−1.09092e7	−	4.07706e6i	−0.613581	−	0.229311i
$262$	−1.79351e7			−0.997238
$263$	−1.35628e7	+	1.35628e7i	−0.745561	+	0.745561i	−0.973642	−	0.228081i	$-0.926755\pi$
$263$	−1.35628e7	+	1.35628e7i	−0.745561	+	0.745561i	0.228081	+	0.973642i	$0.426755\pi$
$264$	5.48487e6	−	5.48487e6i	0.298095	−	0.298095i
$265$			3.80518e7i			2.04474i
$266$			3.26648e6i			0.173554i
$267$			8.92078e6i			0.468672i
$268$	2.10119e6			0.109159
$269$	3.35868e6	+	3.35868e6i	0.172549	+	0.172549i	0.788098	−	0.615549i	$-0.211066\pi$
$269$	3.35868e6	+	3.35868e6i	0.172549	+	0.172549i	−0.615549	+	0.788098i	$0.711066\pi$
$270$			3.26242e7i			1.65748i
$271$	1.24844e7	+	1.24844e7i	0.627279	+	0.627279i	0.947382	−	0.320104i	$-0.103718\pi$
$271$	1.24844e7	+	1.24844e7i	0.627279	+	0.627279i	−0.320104	+	0.947382i	$0.603718\pi$
$272$	−2.23667e7	+	2.23667e7i	−1.11146	+	1.11146i
$273$	−2.24604e6	−	2.24604e6i	−0.110390	−	0.110390i
$274$		−	3.14028e7i		−	1.52657i
$275$	−1.69231e7	+	1.69231e7i	−0.813733	+	0.813733i
$276$	3.24733e6	+	3.24733e6i	0.154454	+	0.154454i
$277$	1.39382e6			0.0655796			0.0327898	−	0.999462i	$-0.489561\pi$
$277$	1.39382e6			0.0655796			0.0327898	+	0.999462i	$0.489561\pi$
$278$	−2.85841e7	+	2.85841e7i	−1.33042	+	1.33042i
$279$	−2.86255e6	−	2.86255e6i	−0.131808	−	0.131808i
$280$	−3.27679e6	+	3.27679e6i	−0.149271	+	0.149271i
$281$	3.27581e7			1.47639			0.738193	−	0.674590i	$-0.235680\pi$
$281$	3.27581e7			1.47639			0.738193	+	0.674590i	$0.235680\pi$
$282$	1.08956e6	−	1.08956e6i	0.0485850	−	0.0485850i
$283$		−	6.85630e6i		−	0.302503i	−0.988495	−	0.151252i	$-0.951670\pi$
$283$		−	6.85630e6i		−	0.302503i	0.988495	−	0.151252i	$-0.0483304\pi$
$284$	7.37697e6			0.322050
$285$	2.06729e7			0.893033
$286$	3.60490e7			1.54097
$287$	1.77780e6	+	1.77780e6i	0.0752033	+	0.0752033i
$288$	−4.83649e6	−	4.83649e6i	−0.202466	−	0.202466i
$289$		−	1.92092e7i		−	0.795823i
$290$	3.78391e7	−	1.72506e7i	1.55148	−	0.707312i
$291$	5.69658e6			0.231172
$292$	−2.54828e6	+	2.54828e6i	−0.102352	+	0.102352i
$293$	−2.32052e7	+	2.32052e7i	−0.922533	+	0.922533i	−0.997208	−	0.0746748i	$-0.976208\pi$
$293$	−2.32052e7	+	2.32052e7i	−0.922533	+	0.922533i	0.0746748	+	0.997208i	$0.476208\pi$
$294$			1.60839e7i			0.632920i
$295$		−	5.64266e7i		−	2.19795i
$296$			8.66412e6i			0.334079i
$297$	−2.12612e7			−0.811556
$298$	−3.53731e7	−	3.53731e7i	−1.33667	−	1.33667i
$299$		−	7.46163e7i		−	2.79139i
$300$	−3.43780e6	−	3.43780e6i	−0.127326	−	0.127326i
$301$	2.14338e6	−	2.14338e6i	0.0785959	−	0.0785959i
$302$	1.73518e7	+	1.73518e7i	0.629974	+	0.629974i
$303$			1.97823e7i			0.711128i
$304$	−2.29731e7	+	2.29731e7i	−0.817708	+	0.817708i
$305$	−1.82592e7	−	1.82592e7i	−0.643551	−	0.643551i
$306$	2.78078e7			0.970516
$307$	2.55471e7	−	2.55471e7i	0.882929	−	0.882929i	−0.110903	−	0.993831i	$-0.535374\pi$
$307$	2.55471e7	−	2.55471e7i	0.882929	−	0.882929i	0.993831	+	0.110903i	$0.0353741\pi$
$308$	610825.	+	610825.i	0.0209057	+	0.0209057i
$309$	−1.38205e6	+	1.38205e6i	−0.0468434	+	0.0468434i
$310$	1.44554e7			0.485229
$311$	−2.76074e7	+	2.76074e7i	−0.917792	+	0.917792i	−0.996869	−	0.0790767i	$-0.974803\pi$
$311$	−2.76074e7	+	2.76074e7i	−0.917792	+	0.917792i	0.0790767	+	0.996869i	$0.474803\pi$
$312$		−	2.56020e7i		−	0.842968i
$313$	−3.40228e7			−1.10953			−0.554763	−	0.832009i	$-0.687191\pi$
$313$	−3.40228e7			−1.10953			−0.554763	+	0.832009i	$0.687191\pi$
$314$	2.60559e6			0.0841621
$315$	5.02720e6			0.160840
$316$	4.59856e6	+	4.59856e6i	0.145734	+	0.145734i
$317$	−2.23157e7	−	2.23157e7i	−0.700540	−	0.700540i	0.263986	−	0.964526i	$-0.414963\pi$
$317$	−2.23157e7	−	2.23157e7i	−0.700540	−	0.700540i	−0.964526	+	0.263986i	$0.914963\pi$
$318$		−	2.76870e7i		−	0.860984i
$319$	1.12423e7	+	2.46598e7i	0.346323	+	0.759657i
$320$	−3.48514e7			−1.06358
$321$	−1.99437e6	+	1.99437e6i	−0.0602962	+	0.0602962i
$322$	6.94880e6	−	6.94880e6i	0.208134	−	0.208134i
$323$		−	4.45220e7i		−	1.32119i
$324$			636169.i			0.0187041i
$325$			7.89930e7i			2.30112i
$326$	−4.94108e7			−1.42616
$327$	1.46263e6	+	1.46263e6i	0.0418303	+	0.0418303i
$328$			2.02647e7i			0.574272i
$329$	−424210.	−	424210.i	−0.0119122	−	0.0119122i
$330$	2.12467e7	−	2.12467e7i	0.591221	−	0.591221i
$331$	3.23502e7	+	3.23502e7i	0.892057	+	0.892057i	0.994717	−	0.102660i	$-0.0327352\pi$
$331$	3.23502e7	+	3.23502e7i	0.892057	+	0.892057i	−0.102660	+	0.994717i	$0.532735\pi$
$332$		−	3.95940e6i		−	0.108197i
$333$	6.64618e6	−	6.64618e6i	0.179986	−	0.179986i
$334$	−2.85114e7	−	2.85114e7i	−0.765207	−	0.765207i
$335$	−2.84558e7			−0.756896
$336$	2.94214e6	−	2.94214e6i	0.0775613	−	0.0775613i
$337$	3.65369e7	+	3.65369e7i	0.954645	+	0.954645i	0.999015	−	0.0443704i	$-0.0141282\pi$
$337$	3.65369e7	+	3.65369e7i	0.954645	+	0.954645i	−0.0443704	+	0.999015i	$0.514128\pi$
$338$	5.39454e7	−	5.39454e7i	1.39703	−	1.39703i
$339$	−6.46765e6			−0.166015
$340$	−1.27750e7	+	1.27750e7i	−0.325032	+	0.325032i
$341$			9.42063e6i			0.237584i
$342$	2.85617e7			0.714013
$343$	1.26871e7			0.314399
$344$	2.44318e7			0.600178
$345$	−4.39776e7	−	4.39776e7i	−1.07096	−	1.07096i
$346$	2.57485e7	+	2.57485e7i	0.621617	+	0.621617i
$347$			2.65156e7i			0.634620i	0.948322	+	0.317310i	$0.102780\pi$
$347$			2.65156e7i			0.634620i	−0.948322	+	0.317310i	$0.897220\pi$
$348$	−5.00945e6	+	2.28378e6i	−0.118865	+	0.0541897i
$349$	2.38249e7			0.560473			0.280236	−	0.959931i	$-0.409587\pi$
$349$	2.38249e7			0.560473			0.280236	+	0.959931i	$0.409587\pi$
$350$	−7.35639e6	+	7.35639e6i	−0.171578	+	0.171578i
$351$	−4.96211e7	+	4.96211e7i	−1.14748	+	1.14748i
$352$			1.59168e7i			0.364946i
$353$			5.97729e7i			1.35888i	0.733733	+	0.679438i	$0.237776\pi$
$353$			5.97729e7i			1.35888i	−0.733733	+	0.679438i	$0.762224\pi$
$354$			4.10568e7i			0.925498i
$355$	−9.99041e7			−2.23305
$356$	−5.66213e6	−	5.66213e6i	−0.125496	−	0.125496i
$357$			5.70188e6i			0.125318i
$358$	−5.49035e7	−	5.49035e7i	−1.19661	−	1.19661i
$359$	5.74970e7	−	5.74970e7i	1.24269	−	1.24269i	0.283804	−	0.958882i	$-0.408404\pi$
$359$	5.74970e7	−	5.74970e7i	1.24269	−	1.24269i	0.958882	−	0.283804i	$-0.0915964\pi$
$360$	2.86519e7	+	2.86519e7i	0.614109	+	0.614109i
$361$			1.31692e6i			0.0279923i
$362$	−8.54892e6	+	8.54892e6i	−0.180213	+	0.180213i
$363$	−6.01882e6	−	6.01882e6i	−0.125832	−	0.125832i
$364$	2.85119e6			0.0591182
$365$	3.45106e7	−	3.45106e7i	0.709698	−	0.709698i
$366$	1.32857e7	+	1.32857e7i	0.270982	+	0.270982i
$367$	3.23833e7	−	3.23833e7i	0.655122	−	0.655122i	−0.299100	−	0.954222i	$-0.596686\pi$
$367$	3.23833e7	−	3.23833e7i	0.655122	−	0.655122i	0.954222	+	0.299100i	$0.0966863\pi$
$368$	9.77414e7			1.96126
$369$	1.55448e7	−	1.55448e7i	0.309391	−	0.309391i
$370$			3.35622e7i			0.662590i
$371$	−1.07797e7			−0.211099
$372$	−1.91373e6			−0.0371751
$373$	−8.13184e6			−0.156698			−0.0783488	−	0.996926i	$-0.524965\pi$
$373$	−8.13184e6			−0.156698			−0.0783488	+	0.996926i	$0.524965\pi$
$374$	−4.57576e7	−	4.57576e7i	−0.874679	−	0.874679i
$375$	1.27809e7	+	1.27809e7i	0.242363	+	0.242363i
$376$		−	4.83545e6i		−	0.0909649i
$377$	8.37911e7	+	3.13150e7i	1.56377	+	0.584424i
$378$	−9.24214e6			−0.171119
$379$	−3.63052e6	+	3.63052e6i	−0.0666885	+	0.0666885i	−0.739664	−	0.672976i	$-0.765016\pi$
$379$	−3.63052e6	+	3.63052e6i	−0.0666885	+	0.0666885i	0.672976	+	0.739664i	$0.265016\pi$
$380$	−1.31214e7	+	1.31214e7i	−0.239127	+	0.239127i
$381$			1.17245e7i			0.211992i
$382$		−	5.20375e7i		−	0.933525i
$383$		−	3.24233e7i		−	0.577113i	−0.957463	−	0.288556i	$-0.906825\pi$
$383$		−	3.24233e7i		−	0.577113i	0.957463	−	0.288556i	$-0.0931753\pi$
$384$	3.98959e7			0.704587
$385$	−8.27223e6	−	8.27223e6i	−0.144957	−	0.144957i
$386$			1.07185e8i			1.86368i
$387$	−1.87414e7	−	1.87414e7i	−0.323348	−	0.323348i
$388$	−3.61570e6	+	3.61570e6i	−0.0619009	+	0.0619009i
$389$	6.62169e7	+	6.62169e7i	1.12492	+	1.12492i	0.990992	+	0.133924i	$0.0427578\pi$
$389$	6.62169e7	+	6.62169e7i	1.12492	+	1.12492i	0.133924	+	0.990992i	$0.457242\pi$
$390$		−	9.91745e7i		−	1.67188i
$391$	−9.47117e7	+	9.47117e7i	−1.58443	+	1.58443i
$392$	3.56902e7	+	3.56902e7i	0.592503	+	0.592503i
$393$	−3.21557e7			−0.529761
$394$	6.79011e7	−	6.79011e7i	1.11017	−	1.11017i
$395$	−6.22770e7	−	6.22770e7i	−1.01050	−	1.01050i
$396$	5.34098e6	−	5.34098e6i	0.0860073	−	0.0860073i
$397$	−1.47597e7			−0.235888			−0.117944	−	0.993020i	$-0.537630\pi$
$397$	−1.47597e7			−0.235888			−0.117944	+	0.993020i	$0.537630\pi$
$398$	−3.47666e7	+	3.47666e7i	−0.551459	+	0.551459i
$399$			5.85646e6i			0.0921969i
$400$	−1.03474e8			−1.61679
$401$	5.08319e7			0.788322			0.394161	−	0.919041i	$-0.371035\pi$
$401$	5.08319e7			0.788322			0.394161	+	0.919041i	$0.371035\pi$
$402$	2.07048e7			0.318709
$403$	2.19866e7	+	2.19866e7i	0.335926	+	0.335926i
$404$	−1.25561e7	−	1.25561e7i	−0.190418	−	0.190418i
$405$		−	8.61545e6i		−	0.129692i
$406$	4.88695e6	+	1.07195e7i	0.0730230	+	0.160175i
$407$	−2.18725e7			−0.324425
$408$	−3.24971e7	+	3.24971e7i	−0.478480	+	0.478480i
$409$	−4.04076e7	+	4.04076e7i	−0.590599	+	0.590599i	−0.937793	−	0.347194i	$-0.887134\pi$
$409$	−4.04076e7	+	4.04076e7i	−0.590599	+	0.590599i	0.347194	+	0.937793i	$0.387134\pi$
$410$			7.84990e7i			1.13897i
$411$		−	5.63019e7i		−	0.810956i
$412$		−	1.75441e6i		−	0.0250865i
$413$	1.59852e7			0.226917
$414$	−6.07594e7	−	6.07594e7i	−0.856273	−	0.856273i
$415$			5.36211e7i			0.750224i
$416$	3.71480e7	+	3.71480e7i	0.516006	+	0.516006i
$417$	−5.12482e7	+	5.12482e7i	−0.706758	+	0.706758i
$418$	−4.69981e7	−	4.69981e7i	−0.643505	−	0.643505i
$419$		−	1.15872e8i		−	1.57520i	−0.616184	−	0.787602i	$-0.711322\pi$
$419$		−	1.15872e8i		−	1.57520i	0.616184	−	0.787602i	$-0.288678\pi$
$420$	1.68044e6	−	1.68044e6i	0.0226817	−	0.0226817i
$421$	−5.56826e7	−	5.56826e7i	−0.746230	−	0.746230i	0.227539	−	0.973769i	$-0.426932\pi$
$421$	−5.56826e7	−	5.56826e7i	−0.746230	−	0.746230i	−0.973769	+	0.227539i	$0.926932\pi$
$422$	4.22775e7			0.562564
$423$	−3.70924e6	+	3.70924e6i	−0.0490076	+	0.0490076i
$424$	−6.14376e7	−	6.14376e7i	−0.806003	−	0.806003i
$425$	1.00267e8	−	1.00267e8i	1.30615	−	1.30615i
$426$	7.26917e7			0.940278
$427$	5.17268e6	−	5.17268e6i	0.0664403	−	0.0664403i
$428$		−	2.53170e6i		−	0.0322910i
$429$	6.46321e7			0.818609
$430$	9.46413e7			1.19035
$431$	1.96739e7			0.245731			0.122865	−	0.992423i	$-0.460792\pi$
$431$	1.96739e7			0.245731			0.122865	+	0.992423i	$0.460792\pi$
$432$	−6.49997e7	−	6.49997e7i	−0.806232	−	0.806232i
$433$	1.49949e7	+	1.49949e7i	0.184706	+	0.184706i	0.793403	−	0.608697i	$-0.208308\pi$
$433$	1.49949e7	+	1.49949e7i	0.184706	+	0.184706i	−0.608697	+	0.793403i	$0.708308\pi$
$434$			4.09510e6i			0.0500951i
$435$	6.78416e7	−	3.09286e7i	0.824192	−	0.375744i
$436$	−1.85670e6			−0.0224017
$437$	−9.72793e7	+	9.72793e7i	−1.16567	+	1.16567i
$438$	−2.51104e7	+	2.51104e7i	−0.298835	+	0.298835i
$439$			4.40495e7i			0.520651i	0.965521	+	0.260326i	$0.0838299\pi$
$439$			4.40495e7i			0.520651i	−0.965521	+	0.260326i	$0.916170\pi$
$440$		−	9.42929e7i		−	1.10693i
$441$		−	5.47553e7i		−	0.638425i
$442$	−2.13586e8			−2.47346
$443$	7.91402e6	+	7.91402e6i	0.0910303	+	0.0910303i	0.751156	−	0.660125i	$-0.229497\pi$
$443$	7.91402e6	+	7.91402e6i	0.0910303	+	0.0910303i	−0.660125	+	0.751156i	$0.729497\pi$
$444$		−	4.44323e6i		−	0.0507633i
$445$	7.66806e7	+	7.66806e7i	0.870173	+	0.870173i
$446$	1.07221e8	−	1.07221e8i	1.20858	−	1.20858i
$447$	−6.34202e7	−	6.34202e7i	−0.710077	−	0.710077i
$448$		−	9.87308e6i		−	0.109804i
$449$	−4.10934e7	+	4.10934e7i	−0.453976	+	0.453976i	−0.896672	−	0.442696i	$-0.854022\pi$
$449$	−4.10934e7	+	4.10934e7i	−0.453976	+	0.453976i	0.442696	+	0.896672i	$0.354022\pi$
$450$	6.43233e7	+	6.43233e7i	0.705880	+	0.705880i
$451$	−5.11579e7			−0.557677
$452$	4.10510e6	−	4.10510e6i	0.0444538	−	0.0444538i
$453$	3.11099e7	+	3.11099e7i	0.334660	+	0.334660i
$454$	−1.34624e8	+	1.34624e8i	−1.43865	+	1.43865i
$455$	−3.86128e7			−0.409918
$456$	−3.33781e7	+	3.33781e7i	−0.352020	+	0.352020i
$457$		−	1.81502e7i		−	0.190166i	−0.995469	−	0.0950830i	$-0.969688\pi$
$457$		−	1.81502e7i		−	0.190166i	0.995469	−	0.0950830i	$-0.0303116\pi$
$458$	1.79597e7			0.186940
$459$	1.25970e8			1.30265
$460$	5.58263e7			0.573542
$461$	−6.13412e7	−	6.13412e7i	−0.626109	−	0.626109i	0.320978	−	0.947087i	$-0.395988\pi$
$461$	−6.13412e7	−	6.13412e7i	−0.626109	−	0.626109i	−0.947087	+	0.320978i	$0.895988\pi$
$462$	6.01900e6	+	6.01900e6i	0.0610377	+	0.0610377i
$463$		−	6.22146e7i		−	0.626829i	−0.949616	−	0.313414i	$-0.898527\pi$
$463$		−	6.22146e7i		−	0.626829i	0.949616	−	0.313414i	$-0.101473\pi$
$464$	−4.10201e7	+	1.09760e8i	−0.410622	+	1.09872i
$465$	2.59171e7			0.257767
$466$	1.03553e8	−	1.03553e8i	1.02331	−	1.02331i
$467$	3.49380e7	−	3.49380e7i	0.343042	−	0.343042i	−0.514468	−	0.857510i	$-0.672010\pi$
$467$	3.49380e7	−	3.49380e7i	0.343042	−	0.343042i	0.857510	+	0.514468i	$0.172010\pi$
$468$		−	2.49304e7i		−	0.243216i
$469$		−	8.06127e6i		−	0.0781420i
$470$		−	1.87311e7i		−	0.180413i
$471$	4.67154e6			0.0447092
$472$	9.11052e7	+	9.11052e7i	0.866398	+	0.866398i
$473$			6.16779e7i			0.582835i
$474$	4.53136e7	+	4.53136e7i	0.425494	+	0.425494i
$475$	1.02985e8	−	1.02985e8i	0.960936	−	0.960936i
$476$	−3.61906e6	−	3.61906e6i	−0.0335563	−	0.0335563i
$477$			9.42565e7i			0.868473i
$478$	−6.29198e7	+	6.29198e7i	−0.576108	+	0.576108i
$479$	−4.29697e7	−	4.29697e7i	−0.390981	−	0.390981i	0.484056	−	0.875037i	$-0.339163\pi$
$479$	−4.29697e7	−	4.29697e7i	−0.390981	−	0.390981i	−0.875037	+	0.484056i	$0.839163\pi$
$480$	4.37888e7			0.395949
$481$	−5.10478e7	+	5.10478e7i	−0.458714	+	0.458714i
$482$	9.78721e7	+	9.78721e7i	0.874013	+	0.874013i
$483$	1.24585e7	−	1.24585e7i	0.110566	−	0.110566i
$484$	7.64045e6			0.0673880
$485$	4.89663e7	−	4.89663e7i	0.429212	−	0.429212i
$486$			1.29640e8i			1.12936i
$487$	−4.05429e7			−0.351017			−0.175508	−	0.984478i	$-0.556157\pi$
$487$	−4.05429e7			−0.351017			−0.175508	+	0.984478i	$0.556157\pi$
$488$	5.89619e7			0.507355
$489$	−8.85884e7			−0.757618
$490$	1.38253e8	+	1.38253e8i	1.17513	+	1.17513i
$491$	4.35116e7	+	4.35116e7i	0.367587	+	0.367587i	0.866597	−	0.499009i	$-0.166303\pi$
$491$	4.35116e7	+	4.35116e7i	0.367587	+	0.367587i	−0.499009	+	0.866597i	$0.666303\pi$
$492$		−	1.03923e7i		−	0.0872606i
$493$	−6.66088e7	−	1.46106e8i	−0.555893	−	1.21935i
$494$	−2.19376e8			−1.81974
$495$	−7.23313e7	+	7.23313e7i	−0.596363	+	0.596363i
$496$	−2.88007e7	+	2.88007e7i	−0.236025	+	0.236025i
$497$		−	2.83019e7i		−	0.230540i
$498$		−	3.90155e7i		−	0.315899i
$499$			2.05856e8i			1.65677i	0.560157	+	0.828386i	$0.310741\pi$
$499$			2.05856e8i			1.65677i	−0.560157	+	0.828386i	$0.689259\pi$
$500$	−1.62244e7			−0.129795
$501$	−5.11179e7	−	5.11179e7i	−0.406499	−	0.406499i
$502$		−	8.83958e7i		−	0.698748i
$503$	−1.75489e8	−	1.75489e8i	−1.37894	−	1.37894i	−0.846409	−	0.532534i	$-0.821240\pi$
$503$	−1.75489e8	−	1.75489e8i	−1.37894	−	1.37894i	−0.532534	−	0.846409i	$-0.678760\pi$
$504$	−8.11682e6	+	8.11682e6i	−0.0634007	+	0.0634007i
$505$	1.70043e8	+	1.70043e8i	1.32034	+	1.32034i
$506$			1.99958e8i			1.54343i
$507$	9.67184e7	−	9.67184e7i	0.742139	−	0.742139i
$508$	−7.44170e6	−	7.44170e6i	−0.0567650	−	0.0567650i
$509$	5.62447e7			0.426509			0.213254	−	0.976997i	$-0.431594\pi$
$509$	5.62447e7			0.426509			0.213254	+	0.976997i	$0.431594\pi$
$510$	−1.25884e8	+	1.25884e8i	−0.948985	+	0.948985i
$511$	9.77654e6	+	9.77654e6i	0.0732694	+	0.0732694i
$512$	4.70431e7	−	4.70431e7i	0.350499	−	0.350499i
$513$	1.29385e8			0.958366
$514$	2.44404e7	−	2.44404e7i	0.179978	−	0.179978i
$515$			2.37595e7i			0.173946i
$516$	−1.25294e7			−0.0911971
$517$	1.22071e7			0.0883363
$518$	−9.50786e6			−0.0684059
$519$	4.61643e7	+	4.61643e7i	0.330221	+	0.330221i
$520$	−2.20068e8	−	2.20068e8i	−1.56512	−	1.56512i
$521$		−	1.86893e7i		−	0.132154i	−0.997815	−	0.0660769i	$-0.978952\pi$
$521$		−	1.86893e7i		−	0.132154i	0.997815	−	0.0660769i	$-0.0210483\pi$
$522$	9.37299e7	−	4.27309e7i	0.658971	−	0.300421i
$523$	4.44357e7			0.310618			0.155309	−	0.987866i	$-0.450363\pi$
$523$	4.44357e7			0.310618			0.155309	+	0.987866i	$0.450363\pi$
$524$	2.04096e7	−	2.04096e7i	0.141854	−	0.141854i
$525$	−1.31892e7	+	1.31892e7i	−0.0911468	+	0.0911468i
$526$		−	1.69654e8i		−	1.16576i
$527$		−	5.58159e7i		−	0.381352i
$528$			8.46629e7i			0.575163i
$529$	2.65849e8			1.79584
$530$	−2.37990e8	−	2.37990e8i	−1.59857	−	1.59857i
$531$		−	1.39772e8i		−	0.933549i
$532$	−3.71717e6	−	3.71717e6i	−0.0246875	−	0.0246875i
$533$	−1.19396e8	+	1.19396e8i	−0.788515	+	0.788515i
$534$	−5.57940e7	−	5.57940e7i	−0.366407	−	0.366407i
$535$			3.42861e7i			0.223901i
$536$	4.59441e7	−	4.59441e7i	0.298356	−	0.298356i
$537$	−9.84362e7	−	9.84362e7i	−0.635670	−	0.635670i
$538$	−4.20130e7			−0.269797
$539$	−9.00994e7	+	9.00994e7i	−0.575381	+	0.575381i
$540$	−3.71254e7	−	3.71254e7i	−0.235771	−	0.235771i
$541$	7.92896e7	−	7.92896e7i	0.500754	−	0.500754i	−0.410918	−	0.911672i	$-0.634792\pi$
$541$	7.92896e7	−	7.92896e7i	0.500754	−	0.500754i	0.911672	+	0.410918i	$0.134792\pi$
$542$	−1.56165e8			−0.980810
$543$	−1.53273e7	+	1.53273e7i	−0.0957340	+	0.0957340i
$544$		−	9.43050e7i		−	0.585785i
$545$	2.51447e7			0.155331
$546$	2.80952e7			0.172606
$547$	1.65168e8			1.00917			0.504586	−	0.863362i	$-0.331645\pi$
$547$	1.65168e8			1.00917			0.504586	+	0.863362i	$0.331645\pi$
$548$	3.57355e7	+	3.57355e7i	0.217149	+	0.217149i
$549$	−4.52292e7	−	4.52292e7i	−0.273339	−	0.273339i
$550$		−	2.11687e8i		−	1.27235i
$551$	−6.84146e7	−	1.50067e8i	−0.408973	−	0.897078i
$552$	1.42011e8			0.844313
$553$	1.76425e7	−	1.76425e7i	0.104324	−	0.104324i
$554$	−8.71752e6	+	8.71752e6i	−0.0512700	+	0.0512700i
$555$			6.01734e7i			0.351986i
$556$		−	6.50558e7i		−	0.378496i
$557$		−	1.81071e7i		−	0.104781i	−0.998627	−	0.0523905i	$-0.983316\pi$
$557$		−	1.81071e7i		−	0.104781i	0.998627	−	0.0523905i	$-0.0166840\pi$
$558$	3.58070e7			0.206094
$559$	1.43949e8	+	1.43949e8i	0.824086	+	0.824086i
$560$		−	5.05797e7i		−	0.288013i
$561$	−8.20386e7	−	8.20386e7i	−0.464654	−	0.464654i
$562$	−2.04882e8	+	2.04882e8i	−1.15424	+	1.15424i
$563$	1.67343e8	+	1.67343e8i	0.937739	+	0.937739i	0.998172	−	0.0604330i	$-0.0192481\pi$
$563$	1.67343e8	+	1.67343e8i	0.937739	+	0.937739i	−0.0604330	+	0.998172i	$0.519248\pi$
$564$			2.47977e6i			0.0138221i
$565$	−5.55942e7	+	5.55942e7i	−0.308237	+	0.308237i
$566$	4.28819e7	+	4.28819e7i	0.236497	+	0.236497i
$567$	2.44068e6			0.0133894
$568$	1.61303e8	−	1.61303e8i	0.880233	−	0.880233i
$569$	−6.48196e7	−	6.48196e7i	−0.351860	−	0.351860i	0.508941	−	0.860801i	$-0.330037\pi$
$569$	−6.48196e7	−	6.48196e7i	−0.351860	−	0.351860i	−0.860801	+	0.508941i	$0.830037\pi$
$570$	−1.29296e8	+	1.29296e8i	−0.698172	+	0.698172i
$571$	−2.02900e8			−1.08986			−0.544932	−	0.838480i	$-0.683445\pi$
$571$	−2.02900e8			−1.08986			−0.544932	+	0.838480i	$0.683445\pi$
$572$	−4.10228e7	+	4.10228e7i	−0.219199	+	0.219199i
$573$		−	9.32977e7i		−	0.495915i
$574$	−2.22381e7			−0.117588
$575$	−4.38162e8			−2.30479
$576$	−8.63290e7			−0.451741
$577$	1.02640e8	+	1.02640e8i	0.534306	+	0.534306i	0.921851	−	0.387545i	$-0.126677\pi$
$577$	1.02640e8	+	1.02640e8i	0.534306	+	0.534306i	−0.387545	+	0.921851i	$0.626677\pi$
$578$	1.20142e8	+	1.20142e8i	0.622173	+	0.622173i
$579$			1.92171e8i			0.990038i
$580$	−2.34292e7	+	6.26907e7i	−0.120081	+	0.321306i
$581$	−1.51904e7			−0.0774533
$582$	−3.56286e7	+	3.56286e7i	−0.180730	+	0.180730i
$583$	1.55099e8	−	1.55099e8i	0.782712	−	0.782712i
$584$			1.11440e8i			0.559504i
$585$			3.37625e8i			1.68643i
$586$		−	2.90268e8i		−	1.44247i
$587$	3.00798e8			1.48717			0.743586	−	0.668640i	$-0.233123\pi$
$587$	3.00798e8			1.48717			0.743586	+	0.668640i	$0.233123\pi$
$588$	−1.83030e7	−	1.83030e7i	−0.0900307	−	0.0900307i
$589$		−	5.73291e7i		−	0.280562i
$590$	3.52914e8	+	3.52914e8i	1.71835	+	1.71835i
$591$	1.21740e8	−	1.21740e8i	0.589752	−	0.589752i
$592$	−6.68685e7	−	6.68685e7i	−0.322297	−	0.322297i
$593$		−	4.46655e7i		−	0.214195i	−0.994249	−	0.107097i	$-0.965844\pi$
$593$		−	4.46655e7i		−	0.214195i	0.994249	−	0.107097i	$-0.0341556\pi$
$594$	1.32976e8	−	1.32976e8i	0.634473	−	0.634473i
$595$	4.90118e7	+	4.90118e7i	0.232675	+	0.232675i
$596$	8.05073e7			0.380274
$597$	−6.23328e7	+	6.23328e7i	−0.292950	+	0.292950i
$598$	4.66679e8	+	4.66679e8i	2.18230	+	2.18230i
$599$	−2.80470e8	+	2.80470e8i	−1.30499	+	1.30499i	−0.380000	+	0.924987i	$0.624076\pi$
$599$	−2.80470e8	+	2.80470e8i	−1.30499	+	1.30499i	−0.924987	+	0.380000i	$0.875924\pi$
$600$	−1.50340e8			−0.696020
$601$	9.12404e6	−	9.12404e6i	0.0420304	−	0.0420304i	−0.685779	−	0.727810i	$-0.740538\pi$
$601$	9.12404e6	−	9.12404e6i	0.0420304	−	0.0420304i	0.727810	+	0.685779i	$0.240538\pi$
$602$			2.68110e7i			0.122892i
$603$	−7.04867e7			−0.321481
$604$	−3.94917e7			−0.179224
$605$	−1.03472e8			−0.467260
$606$	−1.23726e8	−	1.23726e8i	−0.555959	−	0.555959i
$607$	−3.14651e7	−	3.14651e7i	−0.140690	−	0.140690i	0.633254	−	0.773944i	$-0.281719\pi$
$607$	−3.14651e7	−	3.14651e7i	−0.140690	−	0.140690i	−0.773944	+	0.633254i	$0.781719\pi$
$608$		−	9.68617e7i		−	0.430964i
$609$	8.76179e6	+	1.92189e7i	0.0387919	+	0.0850897i
$610$	2.28401e8			1.00625
$611$	2.84898e7	−	2.84898e7i	0.124901	−	0.124901i
$612$	−3.16446e7	+	3.16446e7i	−0.138053	+	0.138053i
$613$			6.68885e7i			0.290382i	0.989404	+	0.145191i	$0.0463797\pi$
$613$			6.68885e7i			0.290382i	−0.989404	+	0.145191i	$0.953620\pi$
$614$			3.19562e8i			1.38054i
$615$			1.40740e8i			0.605053i
$616$	2.67123e7			0.114280
$617$	−1.91447e8	−	1.91447e8i	−0.815068	−	0.815068i	0.170321	−	0.985389i	$-0.445520\pi$
$617$	−1.91447e8	−	1.91447e8i	−0.815068	−	0.815068i	−0.985389	+	0.170321i	$0.945520\pi$
$618$		−	1.72877e7i		−	0.0732441i
$619$	−1.54440e8	−	1.54440e8i	−0.651162	−	0.651162i	0.302111	−	0.953273i	$-0.402309\pi$
$619$	−1.54440e8	−	1.54440e8i	−0.651162	−	0.651162i	−0.953273	+	0.302111i	$0.902309\pi$
$620$	−1.64499e7	+	1.64499e7i	−0.0690222	+	0.0690222i
$621$	−2.75241e8	−	2.75241e8i	−1.14931	−	1.14931i
$622$		−	3.45334e8i		−	1.43506i
$623$	−2.17229e7	+	2.17229e7i	−0.0898368	+	0.0898368i
$624$	1.97593e8	+	1.97593e8i	0.813238	+	0.813238i
$625$	−1.16801e8			−0.478416
$626$	2.12792e8	−	2.12792e8i	0.867425	−	0.867425i
$627$	−8.42627e7	−	8.42627e7i	−0.341848	−	0.341848i
$628$	−2.96509e6	+	2.96509e6i	−0.0119718	+	0.0119718i
$629$	1.29592e8			0.520744
$630$	−3.14421e7	+	3.14421e7i	−0.125745	+	0.125745i
$631$		−	9.89707e7i		−	0.393930i	−0.980411	−	0.196965i	$-0.936892\pi$
$631$		−	9.89707e7i		−	0.393930i	0.980411	−	0.196965i	$-0.0631085\pi$
$632$	2.01102e8			0.796646
$633$	7.57990e7			0.298849
$634$	2.79142e8			1.09536
$635$	1.00781e8	+	1.00781e8i	0.393601	+	0.393601i
$636$	3.15071e7	+	3.15071e7i	0.122472	+	0.122472i
$637$			4.20563e8i			1.62709i
$638$	−2.24545e8	−	8.39185e7i	−0.864653	−	0.323144i
$639$	−2.47469e8			−0.948457
$640$	3.42935e8	−	3.42935e8i	1.30819	−	1.30819i
$641$	1.82846e8	−	1.82846e8i	0.694244	−	0.694244i	−0.268919	−	0.963163i	$-0.586666\pi$
$641$	1.82846e8	−	1.82846e8i	0.694244	−	0.694244i	0.963163	+	0.268919i	$0.0866663\pi$
$642$		−	2.49471e7i		−	0.0942789i
$643$		−	1.90830e8i		−	0.717818i	−0.933373	−	0.358909i	$-0.883149\pi$
$643$		−	1.90830e8i		−	0.717818i	0.933373	−	0.358909i	$-0.116851\pi$
$644$			1.58151e7i			0.0592126i
$645$	1.69682e8			0.632348
$646$	2.78457e8	+	2.78457e8i	1.03291	+	1.03291i
$647$		−	3.01493e8i		−	1.11318i	−0.830788	−	0.556589i	$-0.812110\pi$
$647$		−	3.01493e8i		−	1.11318i	0.830788	−	0.556589i	$-0.187890\pi$
$648$	1.39103e7	+	1.39103e7i	0.0511225	+	0.0511225i
$649$	−2.29994e8	+	2.29994e8i	−0.841362	+	0.841362i
$650$	−4.94053e8	−	4.94053e8i	−1.79901	−	1.79901i
$651$			7.34208e6i			0.0266119i
$652$	5.62282e7	−	5.62282e7i	0.202867	−	0.202867i
$653$	2.51506e8	+	2.51506e8i	0.903252	+	0.903252i	0.995716	−	0.0924643i	$-0.0294744\pi$
$653$	2.51506e8	+	2.51506e8i	0.903252	+	0.903252i	−0.0924643	+	0.995716i	$0.529474\pi$
$654$	−1.82957e7			−0.0654056
$655$	−2.76402e8	+	2.76402e8i	−0.983596	+	0.983596i
$656$	−1.56400e8	−	1.56400e8i	−0.554019	−	0.554019i
$657$	8.54848e7	−	8.54848e7i	0.301435	−	0.301435i
$658$	5.30634e6			0.0186259
$659$	2.24474e8	−	2.24474e8i	0.784350	−	0.784350i	−0.196212	−	0.980562i	$-0.562864\pi$
$659$	2.24474e8	−	2.24474e8i	0.784350	−	0.784350i	0.980562	+	0.196212i	$0.0628640\pi$
$660$			4.83563e7i			0.168198i
$661$	−2.32508e8			−0.805069			−0.402534	−	0.915405i	$-0.631871\pi$
$661$	−2.32508e8			−0.805069			−0.402534	+	0.915405i	$0.631871\pi$
$662$	−4.04661e8			−1.39482
$663$	−3.82936e8			−1.31397
$664$	−8.65755e7	−	8.65755e7i	−0.295727	−	0.295727i
$665$	5.03406e7	+	5.03406e7i	0.171180	+	0.171180i
$666$			8.31355e7i			0.281426i
$667$	−1.73699e8	+	4.64776e8i	−0.585356	+	1.56627i
$668$	6.48904e7			0.217696
$669$	1.92235e8	−	1.92235e8i	0.642030	−	0.642030i
$670$	1.77973e8	−	1.77973e8i	0.591739	−	0.591739i
$671$			1.48849e8i			0.492695i
$672$			1.24050e7i			0.0408778i
$673$		−	2.56372e8i		−	0.841057i	−0.907279	−	0.420529i	$-0.861845\pi$
$673$		−	2.56372e8i		−	0.841057i	0.907279	−	0.420529i	$-0.138155\pi$
$674$	−4.57031e8			−1.49268
$675$	2.91385e8	+	2.91385e8i	0.947450	+	0.947450i
$676$			1.22777e8i			0.397445i
$677$	−1.42757e8	−	1.42757e8i	−0.460076	−	0.460076i	0.438604	−	0.898680i	$-0.355473\pi$
$677$	−1.42757e8	−	1.42757e8i	−0.460076	−	0.460076i	−0.898680	+	0.438604i	$0.855473\pi$
$678$	4.04512e7	−	4.04512e7i	0.129790	−	0.129790i
$679$	1.38717e7	+	1.38717e7i	0.0443120	+	0.0443120i
$680$			5.58673e8i			1.77677i
$681$	−2.41366e8	+	2.41366e8i	−0.764249	+	0.764249i
$682$	−5.89202e7	−	5.89202e7i	−0.185742	−	0.185742i
$683$	5.52130e8			1.73292			0.866461	−	0.499245i	$-0.166389\pi$
$683$	5.52130e8			1.73292			0.866461	+	0.499245i	$0.166389\pi$
$684$	−3.25025e7	+	3.25025e7i	−0.101566	+	0.101566i
$685$	−4.83956e8	−	4.83956e8i	−1.50569	−	1.50569i
$686$	−7.93502e7	+	7.93502e7i	−0.245797	+	0.245797i
$687$	3.21999e7			0.0993079
$688$	−1.88561e8	+	1.88561e8i	−0.579011	+	0.579011i
$689$		−	7.23963e8i		−	2.21339i
$690$	5.50105e8			1.67455
$691$	−2.14897e8			−0.651323			−0.325661	−	0.945487i	$-0.605587\pi$
$691$	−2.14897e8			−0.651323			−0.325661	+	0.945487i	$0.605587\pi$
$692$	−5.86022e7			−0.176846
$693$	−2.04908e7	−	2.04908e7i	−0.0615687	−	0.0615687i
$694$	−1.65839e8	−	1.65839e8i	−0.496145	−	0.496145i
$695$			8.81032e8i			2.62444i
$696$	−5.95990e7	+	1.59472e8i	−0.176771	+	0.472996i
$697$	3.03104e8			0.895144
$698$	−1.49010e8	+	1.49010e8i	−0.438177	+	0.438177i
$699$	1.85660e8	−	1.85660e8i	0.543609	−	0.543609i
$700$		−	1.67427e7i		−	0.0488127i
$701$			3.05315e8i			0.886327i	0.896441	+	0.443164i	$0.146144\pi$
$701$			3.05315e8i			0.886327i	−0.896441	+	0.443164i	$0.853856\pi$
$702$		−	6.20699e8i		−	1.79420i
$703$	1.33105e8			0.383114
$704$	1.42054e8	+	1.42054e8i	0.407132	+	0.407132i
$705$		−	3.35828e7i		−	0.0958407i
$706$	−3.73842e8	−	3.73842e8i	−1.06237	−	1.06237i
$707$	−4.81717e7	+	4.81717e7i	−0.136312	+	0.136312i
$708$	−4.67216e7	−	4.67216e7i	−0.131649	−	0.131649i
$709$		−	3.65886e8i		−	1.02661i	−0.858205	−	0.513307i	$-0.828420\pi$
$709$		−	3.65886e8i		−	1.02661i	0.858205	−	0.513307i	$-0.171580\pi$
$710$	6.24839e8	−	6.24839e8i	1.74579	−	1.74579i
$711$	−1.54264e8	−	1.54264e8i	−0.429196	−	0.429196i
$712$	−2.47614e8			−0.686017
$713$	−1.21956e8	+	1.21956e8i	−0.336462	+	0.336462i
$714$	−3.56617e7	−	3.56617e7i	−0.0979733	−	0.0979733i
$715$	5.55561e8	−	5.55561e8i	1.51989	−	1.51989i
$716$	1.24957e8			0.340426
$717$	−1.12809e8	+	1.12809e8i	−0.306044	+	0.306044i
$718$			7.19216e8i			1.94306i
$719$	8.41475e7			0.226389			0.113194	−	0.993573i	$-0.463892\pi$
$719$	8.41475e7			0.226389			0.113194	+	0.993573i	$0.463892\pi$
$720$	−4.42262e8			−1.18490
$721$	−6.73085e6			−0.0179582
$722$	−8.23653e6	−	8.23653e6i	−0.0218843	−	0.0218843i
$723$	1.75474e8	+	1.75474e8i	0.464300	+	0.464300i
$724$		−	1.94569e7i		−	0.0512693i
$725$	1.83888e8	−	4.92038e8i	0.482546	−	1.29117i
$726$	7.52880e7			0.196751
$727$	2.82989e8	−	2.82989e8i	0.736488	−	0.736488i	−0.235409	−	0.971896i	$-0.575643\pi$
$727$	2.82989e8	−	2.82989e8i	0.736488	−	0.736488i	0.971896	+	0.235409i	$0.0756428\pi$
$728$	6.23434e7	−	6.23434e7i	0.161583	−	0.161583i
$729$			1.99851e8i			0.515850i
$730$			4.31685e8i			1.10968i
$731$		−	3.65433e8i		−	0.935525i
$732$	−3.02375e7			−0.0770926
$733$	4.94778e8	+	4.94778e8i	1.25631	+	1.25631i	0.952840	+	0.303474i	$0.0981465\pi$
$733$	4.94778e8	+	4.94778e8i	1.25631	+	1.25631i	0.303474	+	0.952840i	$0.401853\pi$
$734$			4.05075e8i			1.02435i
$735$	2.47872e8	+	2.47872e8i	0.624261	+	0.624261i
$736$	−2.06054e8	+	2.06054e8i	−0.516830	+	0.516830i
$737$	1.15985e8	+	1.15985e8i	0.289735	+	0.289735i
$738$			1.94447e8i			0.483762i
$739$	5.41598e8	−	5.41598e8i	1.34197	−	1.34197i	0.447879	−	0.894094i	$-0.352179\pi$
$739$	5.41598e8	−	5.41598e8i	1.34197	−	1.34197i	0.894094	−	0.447879i	$-0.147821\pi$
$740$	−3.81928e7	−	3.81928e7i	−0.0942512	−	0.0942512i
$741$	−3.93318e8			−0.966694
$742$	6.74206e7	−	6.74206e7i	0.165037	−	0.165037i
$743$	1.15210e8	+	1.15210e8i	0.280883	+	0.280883i	0.833461	−	0.552578i	$-0.186356\pi$
$743$	1.15210e8	+	1.15210e8i	0.280883	+	0.280883i	−0.552578	+	0.833461i	$0.686356\pi$
$744$	−4.18452e7	+	4.18452e7i	−0.101608	+	0.101608i
$745$	−1.09029e9			−2.63677
$746$	5.08596e7	−	5.08596e7i	0.122506	−	0.122506i
$747$			1.32823e8i			0.318647i
$748$	1.04142e8			0.248840
$749$	−9.71294e6			−0.0231156
$750$	−1.59873e8			−0.378958
$751$	−3.73749e7	−	3.73749e7i	−0.0882390	−	0.0882390i	0.661610	−	0.749849i	$-0.269874\pi$
$751$	−3.73749e7	−	3.73749e7i	−0.0882390	−	0.0882390i	−0.749849	+	0.661610i	$0.769874\pi$
$752$	3.73193e7	+	3.73193e7i	0.0877567	+	0.0877567i
$753$		−	1.58484e8i		−	0.371194i
$754$	−7.19918e8	+	3.28206e8i	−1.67946	+	0.765654i
$755$	5.34825e8			1.24271
$756$	1.05173e7	−	1.05173e7i	0.0243410	−	0.0243410i
$757$	−2.06004e7	+	2.06004e7i	−0.0474884	+	0.0474884i	−0.730452	−	0.682964i	$-0.760691\pi$
$757$	−2.06004e7	+	2.06004e7i	−0.0474884	+	0.0474884i	0.682964	+	0.730452i	$0.260691\pi$
$758$		−	4.54133e7i		−	0.104274i
$759$			3.58504e8i			0.819915i
$760$			5.73819e8i			1.30718i
$761$	3.05021e8			0.692111			0.346055	−	0.938214i	$-0.387521\pi$
$761$	3.05021e8			0.692111			0.346055	+	0.938214i	$0.387521\pi$
$762$	−7.33296e7	−	7.33296e7i	−0.165735	−	0.165735i
$763$			7.12328e6i			0.0160364i
$764$	5.92173e7	+	5.92173e7i	0.132791	+	0.132791i
$765$	4.28553e8	−	4.28553e8i	0.957239	−	0.957239i
$766$	2.02788e8	+	2.02788e8i	0.451186	+	0.451186i
$767$			1.07356e9i			2.37925i
$768$	−1.19780e8	+	1.19780e8i	−0.264425	+	0.264425i
$769$	−6.15939e7	−	6.15939e7i	−0.135444	−	0.135444i	0.636134	−	0.771578i	$-0.280532\pi$
$769$	−6.15939e7	−	6.15939e7i	−0.135444	−	0.135444i	−0.771578	+	0.636134i	$0.780532\pi$
$770$	1.03475e8			0.226655
$771$	4.38190e7	−	4.38190e7i	0.0956092	−	0.0956092i
$772$	−1.21973e8	−	1.21973e8i	−0.265102	−	0.265102i
$773$	−5.50659e8	+	5.50659e8i	−1.19219	+	1.19219i	−0.215736	+	0.976452i	$0.569215\pi$
$773$	−5.50659e8	+	5.50659e8i	−1.19219	+	1.19219i	−0.976452	+	0.215736i	$0.930785\pi$
$774$	2.34432e8			0.505586
$775$	1.29110e8	−	1.29110e8i	0.277367	−	0.277367i
$776$			1.58120e8i			0.338378i
$777$	−1.70466e7			−0.0363391
$778$	−8.28292e8			−1.75891
$779$	3.11321e8			0.658561
$780$	1.12858e8	+	1.12858e8i	0.237820	+	0.237820i
$781$	4.07208e8	+	4.07208e8i	0.854797	+	0.854797i
$782$		−	1.18473e9i		−	2.47741i
$783$	4.24597e8	−	1.93571e8i	0.884488	−	0.403233i
$784$	−5.50903e8			−1.14321
$785$	4.01553e7	−	4.01553e7i	0.0830107	−	0.0830107i
$786$	2.01114e8	−	2.01114e8i	0.414166	−	0.414166i
$787$		−	3.42436e8i		−	0.702515i	−0.936279	−	0.351257i	$-0.885754\pi$
$787$		−	3.42436e8i		−	0.702515i	0.936279	−	0.351257i	$-0.114246\pi$
$788$			1.54539e8i			0.315835i
$789$		−	3.04172e8i		−	0.619282i
$790$	7.79008e8			1.58001
$791$	−1.57493e7	−	1.57493e7i	−0.0318224	−	0.0318224i
$792$		−	2.33569e8i		−	0.470154i
$793$	3.47395e8	+	3.47395e8i	0.696634	+	0.696634i
$794$	9.23129e7	−	9.23129e7i	0.184417	−	0.184417i
$795$	−4.26692e8	−	4.26692e8i	−0.849205	−	0.849205i
$796$		−	7.91269e7i		−	0.156886i
$797$	−1.96550e8	+	1.96550e8i	−0.388238	+	0.388238i	−0.874059	−	0.485821i	$-0.838521\pi$
$797$	−1.96550e8	+	1.96550e8i	−0.388238	+	0.388238i	0.485821	+	0.874059i	$0.338521\pi$
$798$	−3.66285e7	−	3.66285e7i	−0.0720794	−	0.0720794i
$799$	−7.23251e7			−0.141791
$800$	2.18140e8	−	2.18140e8i	0.426055	−	0.426055i
$801$	1.89943e8	+	1.89943e8i	0.369594	+	0.369594i
$802$	−3.17923e8	+	3.17923e8i	−0.616309	+	0.616309i
$803$	−2.81330e8			−0.543336
$804$	−2.35616e7	+	2.35616e7i	−0.0453352	+	0.0453352i
$805$		−	2.14179e8i		−	0.410572i
$806$	−2.75025e8			−0.525252
$807$	−7.53248e7			−0.143323
$808$	−5.49096e8			−1.04091
$809$	−2.26227e8	−	2.26227e8i	−0.427267	−	0.427267i	0.460430	−	0.887696i	$-0.347695\pi$
$809$	−2.26227e8	−	2.26227e8i	−0.427267	−	0.427267i	−0.887696	+	0.460430i	$0.847695\pi$
$810$	5.38844e7	+	5.38844e7i	0.101393	+	0.101393i
$811$			2.35205e8i			0.440945i	0.975393	+	0.220472i	$0.0707599\pi$
$811$			2.35205e8i			0.440945i	−0.975393	+	0.220472i	$0.929240\pi$
$812$	−1.77597e7	−	6.63727e6i	−0.0331717	−	0.0123971i
$813$	−2.79987e8			−0.521034
$814$	1.36799e8	−	1.36799e8i	0.253635	−	0.253635i
$815$	−7.61482e8	+	7.61482e8i	−1.40665	+	1.40665i
$816$		−	5.01616e8i		−	0.923211i
$817$		−	3.75340e8i		−	0.688269i
$818$		−	5.05449e8i		−	0.923458i
$819$	−9.56463e7			−0.174107
$820$	−8.93298e7	−	8.93298e7i	−0.162015	−	0.162015i
$821$		−	1.47068e8i		−	0.265759i	−0.991132	−	0.132879i	$-0.957578\pi$
$821$		−	1.47068e8i		−	0.265759i	0.991132	−	0.132879i	$-0.0424223\pi$
$822$	3.52134e8	+	3.52134e8i	0.634004	+	0.634004i
$823$	−4.95193e8	+	4.95193e8i	−0.888332	+	0.888332i	−0.994363	−	0.106031i	$-0.966186\pi$
$823$	−4.95193e8	+	4.95193e8i	−0.888332	+	0.888332i	0.106031	+	0.994363i	$0.466186\pi$
$824$	−3.83616e7	−	3.83616e7i	−0.0685669	−	0.0685669i
$825$		−	3.79533e8i		−	0.675908i
$826$	−9.99773e7	+	9.99773e7i	−0.177403	+	0.177403i
$827$	−4.21922e8	−	4.21922e8i	−0.745960	−	0.745960i	0.227758	−	0.973718i	$-0.426860\pi$
$827$	−4.21922e8	−	4.21922e8i	−0.745960	−	0.745960i	−0.973718	+	0.227758i	$0.926860\pi$
$828$	1.38285e8			0.243604
$829$	6.03043e8	−	6.03043e8i	1.05848	−	1.05848i	0.0603048	−	0.998180i	$-0.480793\pi$
$829$	6.03043e8	−	6.03043e8i	1.05848	−	1.05848i	0.998180	−	0.0603048i	$-0.0192073\pi$
$830$	−3.35367e8	−	3.35367e8i	−0.586524	−	0.586524i
$831$	−1.56296e7	+	1.56296e7i	−0.0272361	+	0.0272361i
$832$	6.63073e8			1.15131
$833$	5.33827e8	−	5.33827e8i	0.923561	−	0.923561i
$834$		−	6.41052e8i		−	1.10508i
$835$	−8.78792e8			−1.50948
$836$	1.06965e8			0.183073
$837$	1.62206e8			0.276625
$838$	7.24709e8	+	7.24709e8i	1.23149	+	1.23149i
$839$	8.84824e7	+	8.84824e7i	0.149820	+	0.149820i	0.778038	−	0.628217i	$-0.216215\pi$
$839$	8.84824e7	+	8.84824e7i	0.149820	+	0.149820i	−0.628217	+	0.778038i	$0.716215\pi$
$840$		−	7.34883e7i		−	0.123988i
$841$	−4.49027e8	−	3.90114e8i	−0.754892	−	0.655849i
$842$	6.96520e8			1.16680
$843$	−3.67331e8	+	3.67331e8i	−0.613162	+	0.613162i
$844$	−4.81106e7	+	4.81106e7i	−0.0800228	+	0.0800228i
$845$		−	1.66273e9i		−	2.75583i
$846$		−	4.63980e7i		−	0.0766281i
$847$		−	2.93128e7i		−	0.0482400i
$848$	9.48333e8			1.55515
$849$	7.68827e7	+	7.68827e7i	0.125634	+	0.125634i
$850$			1.25422e9i			2.04228i
$851$	−2.83154e8	−	2.83154e8i	−0.459446	−	0.459446i
$852$	−8.27212e7	+	8.27212e7i	−0.133751	+	0.133751i
$853$	−8.22199e7	−	8.22199e7i	−0.132474	−	0.132474i	0.637761	−	0.770235i	$-0.279861\pi$
$853$	−8.22199e7	−	8.22199e7i	−0.132474	−	0.132474i	−0.770235	+	0.637761i	$0.779861\pi$
$854$			6.47038e7i			0.103886i
$855$	4.40172e8	−	4.40172e8i	0.704245	−	0.704245i
$856$	−5.53576e7	−	5.53576e7i	−0.0882584	−	0.0882584i
$857$	−9.87790e8			−1.56936			−0.784679	−	0.619902i	$-0.787172\pi$
$857$	−9.87790e8			−1.56936			−0.784679	+	0.619902i	$0.787172\pi$
$858$	−4.04234e8	+	4.04234e8i	−0.639987	+	0.639987i
$859$	3.32483e7	+	3.32483e7i	0.0524554	+	0.0524554i	0.732848	−	0.680393i	$-0.238191\pi$
$859$	3.32483e7	+	3.32483e7i	0.0524554	+	0.0524554i	−0.680393	+	0.732848i	$0.738191\pi$
$860$	−1.07699e8	+	1.07699e8i	−0.169324	+	0.169324i
$861$	−3.98705e7			−0.0624658
$862$	−1.23048e8	+	1.23048e8i	−0.192112	+	0.192112i
$863$			4.50256e8i			0.700531i	0.936650	+	0.350266i	$0.113909\pi$
$863$			4.50256e8i			0.700531i	−0.936650	+	0.350266i	$0.886091\pi$
$864$	2.74059e8			0.424916
$865$	7.93632e8			1.22623
$866$	−1.87568e8			−0.288805
$867$	2.15402e8	+	2.15402e8i	0.330516	+	0.330516i
$868$	−4.66011e6	−	4.66011e6i	−0.00712586	−	0.00712586i
$869$			5.07680e8i			0.773626i
$870$	−2.30868e8	+	6.17746e8i	−0.350595	+	0.938107i
$871$	5.41392e8			0.819327
$872$	−4.05982e7	+	4.05982e7i	−0.0612290	+	0.0612290i
$873$	1.21293e8	−	1.21293e8i	0.182302	−	0.182302i
$874$		−	1.21684e9i		−	1.82264i
$875$			6.22453e7i			0.0929143i
$876$		−	5.71500e7i		−	0.0850166i
$877$	−2.13229e8			−0.316116			−0.158058	−	0.987430i	$-0.550523\pi$
$877$	−2.13229e8			−0.316116			−0.158058	+	0.987430i	$0.550523\pi$
$878$	−2.75502e8	−	2.75502e8i	−0.407044	−	0.407044i
$879$		−	5.20420e8i		−	0.766280i
$880$	7.27740e8	+	7.27740e8i	1.06789	+	1.06789i
$881$	−4.92334e8	+	4.92334e8i	−0.719999	+	0.719999i	−0.968605	−	0.248606i	$-0.920028\pi$
$881$	−4.92334e8	+	4.92334e8i	−0.719999	+	0.719999i	0.248606	+	0.968605i	$0.420028\pi$
$882$	3.42460e8	+	3.42460e8i	0.499120	+	0.499120i
$883$			8.28784e8i			1.20381i	0.798566	+	0.601907i	$0.205592\pi$
$883$			8.28784e8i			1.20381i	−0.798566	+	0.601907i	$0.794408\pi$
$884$	2.43055e8	−	2.43055e8i	0.351842	−	0.351842i
$885$	6.32737e8	+	6.32737e8i	0.912837	+	0.912837i
$886$	−9.89946e7			−0.142335
$887$	−8.24304e8	+	8.24304e8i	−1.18118	+	1.18118i	−0.201743	+	0.979438i	$0.564661\pi$
$887$	−8.24304e8	+	8.24304e8i	−1.18118	+	1.18118i	−0.979438	+	0.201743i	$0.935339\pi$
$888$	−9.71547e7	−	9.71547e7i	−0.138747	−	0.138747i
$889$	−2.85503e7	+	2.85503e7i	−0.0406355	+	0.0406355i
$890$	−9.59180e8			−1.36060
$891$	−3.51165e7	+	3.51165e7i	−0.0496453	+	0.0496453i
$892$			2.44029e8i			0.343832i
$893$	−7.42859e7			−0.104316
$894$	7.93309e8			1.11027
$895$	−1.69226e9			−2.36047
$896$	9.71503e7	+	9.71503e7i	0.135058	+	0.135058i
$897$	8.36706e8	+	8.36706e8i	1.15930	+	1.15930i
$898$		−	5.14028e8i		−	0.709835i
$899$	−8.57695e7	−	1.88135e8i	−0.118047	−	0.258934i
$900$	−1.46396e8			−0.200818
$901$	−9.18938e8	+	9.18938e8i	−1.25635	+	1.25635i
$902$	3.19961e8	−	3.19961e8i	0.435991	−	0.435991i
$903$			4.80694e7i			0.0652838i
$904$		−	1.79523e8i		−	0.243004i
$905$			2.63499e8i			0.355495i
$906$	−3.89146e8			−0.523273
$907$	9.98862e7	+	9.98862e7i	0.133870	+	0.133870i	0.770867	−	0.636997i	$-0.219823\pi$
$907$	9.98862e7	+	9.98862e7i	0.133870	+	0.133870i	−0.636997	+	0.770867i	$0.719823\pi$
$908$		−	3.06396e8i		−	0.409285i
$909$	4.21207e8	+	4.21207e8i	0.560795	+	0.560795i
$910$	2.41499e8	−	2.41499e8i	0.320473	−	0.320473i
$911$	7.33060e8	+	7.33060e8i	0.969582	+	0.969582i	0.999551	−	0.0299691i	$-0.00954089\pi$
$911$	7.33060e8	+	7.33060e8i	0.969582	+	0.969582i	−0.0299691	+	0.999551i	$0.509541\pi$
$912$		−	5.15215e8i		−	0.679210i
$913$	2.18559e8	−	2.18559e8i	0.287181	−	0.287181i
$914$	1.13518e8	+	1.13518e8i	0.148671	+	0.148671i
$915$	4.09498e8			0.534550
$916$	−2.04377e7	+	2.04377e7i	−0.0265916	+	0.0265916i
$917$	−7.83021e7	−	7.83021e7i	−0.101547	−	0.101547i
$918$	−7.87863e8	+	7.87863e8i	−1.01841	+	1.01841i
$919$	5.89725e8			0.759807			0.379903	−	0.925026i	$-0.375957\pi$
$919$	5.89725e8			0.759807			0.379903	+	0.925026i	$0.375957\pi$
$920$	1.22069e9	−	1.22069e9i	1.56762	−	1.56762i
$921$			5.72941e8i			0.733383i
$922$	7.67303e8			0.978981
$923$	1.90075e9			2.41724
$924$	−1.36989e7			−0.0173648
$925$	2.99763e8	+	2.99763e8i	0.378750	+	0.378750i
$926$	3.89114e8	+	3.89114e8i	0.490054	+	0.490054i
$927$			5.88537e7i			0.0738813i
$928$	−1.44914e8	−	3.17867e8i	−0.181328	−	0.397742i
$929$	−4.19168e8			−0.522807			−0.261403	−	0.965230i	$-0.584185\pi$
$929$	−4.19168e8			−0.522807			−0.261403	+	0.965230i	$0.584185\pi$
$930$	−1.62095e8	+	1.62095e8i	−0.201522	+	0.201522i
$931$	5.48299e8	−	5.48299e8i	0.679467	−	0.679467i
$932$			2.35681e8i			0.291124i
$933$		−	6.19148e8i		−	0.762342i
$934$			4.37031e8i			0.536379i
$935$	−1.41036e9			−1.72543
$936$	−5.45123e8	−	5.45123e8i	−0.664763	−	0.664763i
$937$		−	2.34529e8i		−	0.285087i	−0.989789	−	0.142544i	$-0.954472\pi$
$937$		−	2.34529e8i		−	0.285087i	0.989789	−	0.142544i	$-0.0455281\pi$
$938$	5.04183e7	+	5.04183e7i	0.0610913	+	0.0610913i
$939$	3.81513e8	−	3.81513e8i	0.460800	−	0.460800i
$940$	2.13155e7	+	2.13155e7i	0.0256632	+	0.0256632i
$941$		−	9.79271e8i		−	1.17526i	−0.809130	−	0.587630i	$-0.800061\pi$
$941$		−	9.79271e8i		−	1.17526i	0.809130	−	0.587630i	$-0.199939\pi$
$942$	−2.92176e7	+	2.92176e7i	−0.0349536	+	0.0349536i
$943$	−6.62274e8	−	6.62274e8i	−0.789773	−	0.789773i
$944$	−1.40627e9			−1.67168
$945$	−1.42433e8	+	1.42433e8i	−0.168778	+	0.168778i
$946$	−3.85757e8	−	3.85757e8i	−0.455660	−	0.455660i
$947$	4.01485e8	−	4.01485e8i	0.472737	−	0.472737i	−0.430062	−	0.902799i	$-0.641508\pi$
$947$	4.01485e8	−	4.01485e8i	0.472737	−	0.472737i	0.902799	+	0.430062i	$0.141508\pi$
$948$	−1.03131e8			−0.121050
$949$	−6.56590e8	+	6.56590e8i	−0.768237	+	0.768237i
$950$			1.28822e9i			1.50252i
$951$	5.00472e8			0.581887
$952$	−1.58267e8			−0.183434
$953$	−7.33647e8			−0.847635			−0.423817	−	0.905748i	$-0.639310\pi$
$953$	−7.33647e8			−0.847635			−0.423817	+	0.905748i	$0.639310\pi$
$954$	−5.89517e8	−	5.89517e8i	−0.678971	−	0.678971i
$955$	−8.01962e8	−	8.01962e8i	−0.920755	−	0.920755i
$956$		−	1.43202e8i		−	0.163899i
$957$	−4.02586e8	−	1.50457e8i	−0.459328	−	0.171663i
$958$	5.37498e8			0.611336
$959$	1.37100e8	−	1.37100e8i	0.155447	−	0.155447i
$960$	3.90804e8	−	3.90804e8i	0.441718	−	0.441718i
$961$			8.15632e8i			0.919018i
$962$		−	6.38545e8i		−	0.717243i
$963$			8.49287e7i			0.0950990i
$964$	−2.22752e8			−0.248651
$965$	1.65185e9	+	1.65185e9i	1.83818	+	1.83818i
$966$			1.55840e8i			0.172881i
$967$	−6.56789e8	−	6.56789e8i	−0.726351	−	0.726351i	0.243540	−	0.969891i	$-0.421691\pi$
$967$	−6.56789e8	−	6.56789e8i	−0.726351	−	0.726351i	−0.969891	+	0.243540i	$0.921691\pi$
$968$	1.67064e8	−	1.67064e8i	0.184186	−	0.184186i
$969$	4.99245e8	+	4.99245e8i	0.548709	+	0.548709i
$970$			6.12508e8i			0.671115i
$971$	5.83962e8	−	5.83962e8i	0.637862	−	0.637862i	−0.312166	−	0.950028i	$-0.601054\pi$
$971$	5.83962e8	−	5.83962e8i	0.637862	−	0.637862i	0.950028	+	0.312166i	$0.101054\pi$
$972$	−1.47527e8	−	1.47527e8i	−0.160647	−	0.160647i
$973$	−2.49589e8			−0.270948
$974$	2.53571e8	−	2.53571e8i	0.274424	−	0.274424i
$975$	−8.85784e8	−	8.85784e8i	−0.955683	−	0.955683i
$976$	−4.55060e8	+	4.55060e8i	−0.489462	+	0.489462i
$977$	6.40413e8			0.686715			0.343357	−	0.939205i	$-0.388436\pi$
$977$	6.40413e8			0.686715			0.343357	+	0.939205i	$0.388436\pi$
$978$	5.54066e8	−	5.54066e8i	0.592304	−	0.592304i
$979$		−	6.25099e8i		−	0.666194i
$980$	−3.14656e8			−0.334316
$981$	6.22850e7			0.0659746
$982$	−5.44276e8			−0.574758
$983$	−3.28274e8	−	3.28274e8i	−0.345602	−	0.345602i	0.512866	−	0.858468i	$-0.328584\pi$
$983$	−3.28274e8	−	3.28274e8i	−0.345602	−	0.345602i	−0.858468	+	0.512866i	$0.828584\pi$
$984$	−2.27237e8	−	2.27237e8i	−0.238503	−	0.238503i
$985$		−	2.09288e9i		−	2.18996i
$986$	1.33040e9	+	4.97206e8i	1.38788	+	0.518687i
$987$	9.51371e6			0.00989461
$988$	2.49644e8	−	2.49644e8i	0.258851	−	0.258851i
$989$	−7.98461e8	+	7.98461e8i	−0.825401	+	0.825401i
$990$		−	9.04776e8i		−	0.932471i
$991$		−	2.42243e8i		−	0.248903i	−0.992226	−	0.124452i	$-0.960283\pi$
$991$		−	2.42243e8i		−	0.248903i	0.992226	−	0.124452i	$-0.0397172\pi$
$992$		−	1.21433e8i		−	0.124394i
$993$	−7.25514e8			−0.740966
$994$	1.77011e8	+	1.77011e8i	0.180236	+	0.180236i
$995$			1.07159e9i			1.08783i
$996$	4.43986e7	+	4.43986e7i	0.0449356	+	0.0449356i
$997$	−2.62949e8	+	2.62949e8i	−0.265329	+	0.265329i	−0.827215	−	0.561886i	$-0.810076\pi$
$997$	−2.62949e8	+	2.62949e8i	−0.265329	+	0.265329i	0.561886	+	0.827215i	$0.310076\pi$
$998$	−1.28751e9	−	1.28751e9i	−1.29526	−	1.29526i
$999$			3.76605e8i			0.377737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.7.c.a.17.4	yes	28
29.12	odd	4	inner	29.7.c.a.12.4	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.7.c.a.12.4	✓	28	29.12	odd	4	inner
29.7.c.a.17.4	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)

\(f(q)\)	\(=\)	\(q+(-6.25438 + 6.25438i) q^{2} +(-11.2134 + 11.2134i) q^{3} -14.2346i q^{4} +192.776i q^{5} -140.266i q^{6} -54.6116 q^{7} +(-311.252 - 311.252i) q^{8} +477.517i q^{9} +O(q^{10})\)	\(q+(-6.25438 + 6.25438i) q^{2} +(-11.2134 + 11.2134i) q^{3} -14.2346i q^{4} +192.776i q^{5} -140.266i q^{6} -54.6116 q^{7} +(-311.252 - 311.252i) q^{8} +477.517i q^{9} +(-1205.69 - 1205.69i) q^{10} +(785.752 - 785.752i) q^{11} +(159.619 + 159.619i) q^{12} -3667.70i q^{13} +(341.562 - 341.562i) q^{14} +(-2161.68 - 2161.68i) q^{15} +4804.39 q^{16} +(-4655.47 + 4655.47i) q^{17} +(-2986.58 - 2986.58i) q^{18} +(-4781.68 + 4781.68i) q^{19} +2744.09 q^{20} +(612.385 - 612.385i) q^{21} +9828.78i q^{22} +20344.2 q^{23} +6980.41 q^{24} -21537.5 q^{25} +(22939.2 + 22939.2i) q^{26} +(-13529.2 - 13529.2i) q^{27} +777.377i q^{28} +(-8538.03 + 22845.7i) q^{29} +27040.0 q^{30} +(-5994.66 + 5994.66i) q^{31} +(-10128.4 + 10128.4i) q^{32} +17622.0i q^{33} -58234.2i q^{34} -10527.8i q^{35} +6797.29 q^{36} +(-13918.2 - 13918.2i) q^{37} -59813.0i q^{38} +(41127.6 + 41127.6i) q^{39} +(60001.8 - 60001.8i) q^{40} +(-32553.5 - 32553.5i) q^{41} +7660.18i q^{42} +(-39247.7 + 39247.7i) q^{43} +(-11184.9 - 11184.9i) q^{44} -92053.7 q^{45} +(-127240. + 127240. i) q^{46} +(7767.76 + 7767.76i) q^{47} +(-53873.8 + 53873.8i) q^{48} -114667. q^{49} +(134704. - 134704. i) q^{50} -104408. i q^{51} -52208.4 q^{52} +197389. q^{53} +169234. q^{54} +(151474. + 151474. i) q^{55} +(16998.0 + 16998.0i) q^{56} -107238. i q^{57} +(-89485.5 - 196286. i) q^{58} -292706. q^{59} +(-30770.8 + 30770.8i) q^{60} +(-94717.5 + 94717.5i) q^{61} -74985.8i q^{62} -26078.0i q^{63} +180787. i q^{64} +707044. q^{65} +(-110215. - 110215. i) q^{66} +147611. i q^{67} +(66269.0 + 66269.0i) q^{68} +(-228128. + 228128. i) q^{69} +(65844.9 + 65844.9i) q^{70} +518240. i q^{71} +(148628. - 148628. i) q^{72} +(-179019. - 179019. i) q^{73} +174099. q^{74} +(241509. - 241509. i) q^{75} +(68065.6 + 68065.6i) q^{76} +(-42911.2 + 42911.2i) q^{77} -514455. q^{78} +(-323054. + 323054. i) q^{79} +926170. i q^{80} -44691.6 q^{81} +407204. q^{82} +278153. q^{83} +(-8717.08 - 8717.08i) q^{84} +(-897462. - 897462. i) q^{85} -490940. i q^{86} +(-160438. - 351920. i) q^{87} -489133. q^{88} +(397771. - 397771. i) q^{89} +(575739. - 575739. i) q^{90} +200299. i q^{91} -289592. i q^{92} -134442. i q^{93} -97165.1 q^{94} +(-921792. - 921792. i) q^{95} -227149. i q^{96} +(-254007. - 254007. i) q^{97} +(717169. - 717169. i) q^{98} +(375210. + 375210. 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more