LMFDB - Embedded newform 29.7.c.a.17.3

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			17.3
Character	$\chi$	$=$	29.17
Dual form			29.7.c.a.12.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.90454 + 6.90454i) q^{2} +(11.2332 - 11.2332i) q^{3} -31.3454i q^{4} -10.9400i q^{5} +155.120i q^{6} +617.401 q^{7} +(-225.465 - 225.465i) q^{8} +476.632i q^{9} +O(q^{10})$	\(q+(-6.90454 + 6.90454i) q^{2} +(11.2332 - 11.2332i) q^{3} -31.3454i q^{4} -10.9400i q^{5} +155.120i q^{6} +617.401 q^{7} +(-225.465 - 225.465i) q^{8} +476.632i q^{9} +(75.5356 + 75.5356i) q^{10} +(-913.761 + 913.761i) q^{11} +(-352.109 - 352.109i) q^{12} +3606.76i q^{13} +(-4262.87 + 4262.87i) q^{14} +(-122.891 - 122.891i) q^{15} +5119.57 q^{16} +(3543.05 - 3543.05i) q^{17} +(-3290.92 - 3290.92i) q^{18} +(-6399.82 + 6399.82i) q^{19} -342.919 q^{20} +(6935.37 - 6935.37i) q^{21} -12618.2i q^{22} +16351.8 q^{23} -5065.37 q^{24} +15505.3 q^{25} +(-24903.0 - 24903.0i) q^{26} +(13543.1 + 13543.1i) q^{27} -19352.7i q^{28} +(-6039.13 - 23629.5i) q^{29} +1697.01 q^{30} +(-21451.2 + 21451.2i) q^{31} +(-20918.5 + 20918.5i) q^{32} +20528.9i q^{33} +48926.3i q^{34} -6754.35i q^{35} +14940.2 q^{36} +(-34488.3 - 34488.3i) q^{37} -88375.7i q^{38} +(40515.3 + 40515.3i) q^{39} +(-2466.58 + 2466.58i) q^{40} +(8953.75 + 8953.75i) q^{41} +95771.1i q^{42} +(38744.0 - 38744.0i) q^{43} +(28642.2 + 28642.2i) q^{44} +5214.34 q^{45} +(-112902. + 112902. i) q^{46} +(-24711.8 - 24711.8i) q^{47} +(57509.0 - 57509.0i) q^{48} +263534. q^{49} +(-107057. + 107057. i) q^{50} -79599.4i q^{51} +113055. q^{52} -145487. q^{53} -187017. q^{54} +(9996.54 + 9996.54i) q^{55} +(-139202. - 139202. i) q^{56} +143781. i q^{57} +(204848. + 121453. i) q^{58} -166041. q^{59} +(-3852.06 + 3852.06i) q^{60} +(60451.4 - 60451.4i) q^{61} -296221. i q^{62} +294273. i q^{63} +38786.6i q^{64} +39457.9 q^{65} +(-141743. - 141743. i) q^{66} -457131. i q^{67} +(-111058. - 111058. i) q^{68} +(183683. - 183683. i) q^{69} +(46635.7 + 46635.7i) q^{70} -228114. i q^{71} +(107464. - 107464. i) q^{72} +(143925. + 143925. i) q^{73} +476251. q^{74} +(174174. - 174174. i) q^{75} +(200605. + 200605. i) q^{76} +(-564157. + 564157. i) q^{77} -559479. q^{78} +(171232. - 171232. i) q^{79} -56008.1i q^{80} -43201.0 q^{81} -123643. q^{82} +229141. q^{83} +(-217392. - 217392. i) q^{84} +(-38760.9 - 38760.9i) q^{85} +535020. i q^{86} +(-333273. - 197596. i) q^{87} +412042. q^{88} +(489097. - 489097. i) q^{89} +(-36002.7 + 36002.7i) q^{90} +2.22681e6i q^{91} -512554. i q^{92} +481930. i q^{93} +341248. q^{94} +(70014.0 + 70014.0i) q^{95} +469963. i q^{96} +(-135073. - 135073. i) q^{97} +(-1.81958e6 + 1.81958e6i) q^{98} +(-435527. - 435527. 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 $

$2$	−6.90454	+	6.90454i	−0.863068	+	0.863068i	−0.991693	−	0.128625i	$-0.958944\pi$
$2$	−6.90454	+	6.90454i	−0.863068	+	0.863068i	0.128625	+	0.991693i	$0.458944\pi$
$3$	11.2332	−	11.2332i	0.416044	−	0.416044i	−0.467794	−	0.883838i	$-0.654951\pi$
$3$	11.2332	−	11.2332i	0.416044	−	0.416044i	0.883838	+	0.467794i	$0.154951\pi$
$4$		−	31.3454i		−	0.489772i
$5$		−	10.9400i		−	0.0875199i	−0.999042	−	0.0437600i	$-0.986066\pi$
$5$		−	10.9400i		−	0.0875199i	0.999042	−	0.0437600i	$-0.0139337\pi$
$6$			155.120i			0.718148i
$7$	617.401			1.80000			0.900001	−	0.435888i	$-0.143566\pi$
$7$	617.401			1.80000			0.900001	+	0.435888i	$0.143566\pi$
$8$	−225.465	−	225.465i	−0.440361	−	0.440361i
$9$			476.632i			0.653816i
$10$	75.5356	+	75.5356i	0.0755356	+	0.0755356i
$11$	−913.761	+	913.761i	−0.686522	+	0.686522i	−0.961462	−	0.274939i	$-0.911342\pi$
$11$	−913.761	+	913.761i	−0.686522	+	0.686522i	0.274939	+	0.961462i	$0.411342\pi$
$12$	−352.109	−	352.109i	−0.203767	−	0.203767i
$13$			3606.76i			1.64167i	0.571163	+	0.820836i	$0.306492\pi$
$13$			3606.76i			1.64167i	−0.571163	+	0.820836i	$0.693508\pi$
$14$	−4262.87	+	4262.87i	−1.55352	+	1.55352i
$15$	−122.891	−	122.891i	−0.0364121	−	0.0364121i
$16$	5119.57			1.24990
$17$	3543.05	−	3543.05i	0.721158	−	0.721158i	−0.247683	−	0.968841i	$-0.579669\pi$
$17$	3543.05	−	3543.05i	0.721158	−	0.721158i	0.968841	+	0.247683i	$0.0796692\pi$
$18$	−3290.92	−	3290.92i	−0.564287	−	0.564287i
$19$	−6399.82	+	6399.82i	−0.933055	+	0.933055i	−0.997896	−	0.0648408i	$-0.979346\pi$
$19$	−6399.82	+	6399.82i	−0.933055	+	0.933055i	0.0648408	+	0.997896i	$0.479346\pi$
$20$	−342.919			−0.0428648
$21$	6935.37	−	6935.37i	0.748879	−	0.748879i
$22$		−	12618.2i		−	1.18503i
$23$	16351.8			1.34395			0.671973	−	0.740576i	$-0.265447\pi$
$23$	16351.8			1.34395			0.671973	+	0.740576i	$0.265447\pi$
$24$	−5065.37			−0.366419
$25$	15505.3			0.992340
$26$	−24903.0	−	24903.0i	−1.41687	−	1.41687i
$27$	13543.1	+	13543.1i	0.688059	+	0.688059i
$28$		−	19352.7i		−	0.881591i
$29$	−6039.13	−	23629.5i	−0.247617	−	0.968858i
$29$	−6039.13	−	23629.5i	−0.247617	−	0.968858i
$30$	1697.01			0.0628522
$31$	−21451.2	+	21451.2i	−0.720056	+	0.720056i	−0.968616	−	0.248560i	$-0.920043\pi$
$31$	−21451.2	+	21451.2i	−0.720056	+	0.720056i	0.248560	+	0.968616i	$0.420043\pi$
$32$	−20918.5	+	20918.5i	−0.638383	+	0.638383i
$33$			20528.9i			0.571246i
$34$			48926.3i			1.24482i
$35$		−	6754.35i		−	0.157536i
$36$	14940.2			0.320221
$37$	−34488.3	−	34488.3i	−0.680873	−	0.680873i	0.279324	−	0.960197i	$-0.409890\pi$
$37$	−34488.3	−	34488.3i	−0.680873	−	0.680873i	−0.960197	+	0.279324i	$0.909890\pi$
$38$		−	88375.7i		−	1.61058i
$39$	40515.3	+	40515.3i	0.683007	+	0.683007i
$40$	−2466.58	+	2466.58i	−0.0385404	+	0.0385404i
$41$	8953.75	+	8953.75i	0.129913	+	0.129913i	0.769074	−	0.639160i	$-0.220718\pi$
$41$	8953.75	+	8953.75i	0.129913	+	0.129913i	−0.639160	+	0.769074i	$0.720718\pi$
$42$			95771.1i			1.29267i
$43$	38744.0	−	38744.0i	0.487303	−	0.487303i	−0.420151	−	0.907454i	$-0.638023\pi$
$43$	38744.0	−	38744.0i	0.487303	−	0.487303i	0.907454	+	0.420151i	$0.138023\pi$
$44$	28642.2	+	28642.2i	0.336240	+	0.336240i
$45$	5214.34			0.0572219
$46$	−112902.	+	112902.i	−1.15992	+	1.15992i
$47$	−24711.8	−	24711.8i	−0.238019	−	0.238019i	0.578010	−	0.816029i	$-0.303829\pi$
$47$	−24711.8	−	24711.8i	−0.238019	−	0.238019i	−0.816029	+	0.578010i	$0.803829\pi$
$48$	57509.0	−	57509.0i	0.520011	−	0.520011i
$49$	263534.			2.24001
$50$	−107057.	+	107057.i	−0.856457	+	0.856457i
$51$		−	79599.4i		−	0.600066i
$52$	113055.			0.804046
$53$	−145487.			−0.977233			−0.488616	−	0.872499i	$-0.662498\pi$
$53$	−145487.			−0.977233			−0.488616	+	0.872499i	$0.662498\pi$
$54$	−187017.			−1.18768
$55$	9996.54	+	9996.54i	0.0600844	+	0.0600844i
$56$	−139202.	−	139202.i	−0.792651	−	0.792651i
$57$			143781.i			0.776383i
$58$	204848.	+	121453.i	1.04990	+	0.622480i
$59$	−166041.			−0.808463			−0.404232	−	0.914657i	$-0.632461\pi$
$59$	−166041.			−0.808463			−0.404232	+	0.914657i	$0.632461\pi$
$60$	−3852.06	+	3852.06i	−0.0178336	+	0.0178336i
$61$	60451.4	−	60451.4i	0.266328	−	0.266328i	−0.561291	−	0.827619i	$-0.689695\pi$
$61$	60451.4	−	60451.4i	0.266328	−	0.266328i	0.827619	+	0.561291i	$0.189695\pi$
$62$		−	296221.i		−	1.24291i
$63$			294273.i			1.17687i
$64$			38786.6i			0.147959i
$65$	39457.9			0.143679
$66$	−141743.	−	141743.i	−0.493024	−	0.493024i
$67$		−	457131.i		−	1.51990i	−0.649979	−	0.759952i	$-0.725222\pi$
$67$		−	457131.i		−	1.51990i	0.649979	−	0.759952i	$-0.274778\pi$
$68$	−111058.	−	111058.i	−0.353203	−	0.353203i
$69$	183683.	−	183683.i	0.559140	−	0.559140i
$70$	46635.7	+	46635.7i	0.135964	+	0.135964i
$71$		−	228114.i		−	0.637348i	−0.947864	−	0.318674i	$-0.896763\pi$
$71$		−	228114.i		−	0.637348i	0.947864	−	0.318674i	$-0.103237\pi$
$72$	107464.	−	107464.i	0.287915	−	0.287915i
$73$	143925.	+	143925.i	0.369971	+	0.369971i	0.867466	−	0.497496i	$-0.165747\pi$
$73$	143925.	+	143925.i	0.369971	+	0.369971i	−0.497496	+	0.867466i	$0.665747\pi$
$74$	476251.			1.17528
$75$	174174.	−	174174.i	0.412857	−	0.412857i
$76$	200605.	+	200605.i	0.456984	+	0.456984i
$77$	−564157.	+	564157.i	−1.23574	+	1.23574i
$78$	−559479.			−1.17896
$79$	171232.	−	171232.i	0.347299	−	0.347299i	−0.511804	−	0.859102i	$-0.671022\pi$
$79$	171232.	−	171232.i	0.347299	−	0.347299i	0.859102	+	0.511804i	$0.171022\pi$
$80$		−	56008.1i		−	0.109391i
$81$	−43201.0			−0.0812903
$82$	−123643.			−0.224248
$83$	229141.			0.400746			0.200373	−	0.979720i	$-0.435785\pi$
$83$	229141.			0.400746			0.200373	+	0.979720i	$0.435785\pi$
$84$	−217392.	−	217392.i	−0.366780	−	0.366780i
$85$	−38760.9	−	38760.9i	−0.0631157	−	0.0631157i
$86$			535020.i			0.841152i
$87$	−333273.	−	197596.i	−0.506107	−	0.300068i
$88$	412042.			0.604636
$89$	489097.	−	489097.i	0.693785	−	0.693785i	−0.269278	−	0.963063i	$-0.586785\pi$
$89$	489097.	−	489097.i	0.693785	−	0.693785i	0.963063	+	0.269278i	$0.0867849\pi$
$90$	−36002.7	+	36002.7i	−0.0493864	+	0.0493864i
$91$			2.22681e6i			2.95501i
$92$		−	512554.i		−	0.658227i
$93$			481930.i			0.599149i
$94$	341248.			0.410853
$95$	70014.0	+	70014.0i	0.0816609	+	0.0816609i
$96$			469963.i			0.531191i
$97$	−135073.	−	135073.i	−0.147997	−	0.147997i	0.629226	−	0.777223i	$-0.283372\pi$
$97$	−135073.	−	135073.i	−0.147997	−	0.147997i	−0.777223	+	0.629226i	$0.783372\pi$
$98$	−1.81958e6	+	1.81958e6i	−1.93328	+	1.93328i
$99$	−435527.	−	435527.i	−0.448859	−	0.448859i
$100$		−	486021.i		−	0.486021i
$101$	−129929.	+	129929.i	−0.126108	+	0.126108i	−0.767344	−	0.641236i	$-0.778422\pi$
$101$	−129929.	+	129929.i	−0.126108	+	0.126108i	0.641236	+	0.767344i	$0.278422\pi$
$102$	549597.	+	549597.i	0.517898	+	0.517898i
$103$	−1.03313e6			−0.945460			−0.472730	−	0.881207i	$-0.656731\pi$
$103$	−1.03313e6			−0.945460			−0.472730	+	0.881207i	$0.656731\pi$
$104$	813197.	−	813197.i	0.722929	−	0.722929i
$105$	−75872.9	−	75872.9i	−0.0655418	−	0.0655418i
$106$	1.00452e6	−	1.00452e6i	0.843418	−	0.843418i
$107$	−1.02946e6			−0.840346			−0.420173	−	0.907444i	$-0.638031\pi$
$107$	−1.02946e6			−0.840346			−0.420173	+	0.907444i	$0.638031\pi$
$108$	424513.	−	424513.i	0.336992	−	0.336992i
$109$		−	1.69275e6i		−	1.30712i	−0.756876	−	0.653558i	$-0.773275\pi$
$109$		−	1.69275e6i		−	1.30712i	0.756876	−	0.653558i	$-0.226725\pi$
$110$	−138043.			−0.103714
$111$	−774826.			−0.566546
$112$	3.16083e6			2.24981
$113$	1.38835e6	+	1.38835e6i	0.962198	+	0.962198i	0.999311	−	0.0371134i	$-0.0118163\pi$
$113$	1.38835e6	+	1.38835e6i	0.962198	+	0.962198i	−0.0371134	+	0.999311i	$0.511816\pi$
$114$	−992740.	−	992740.i	−0.670071	−	0.670071i
$115$		−	178888.i		−	0.117622i
$116$	−740676.	+	189299.i	−0.474520	+	0.121276i
$117$	−1.71909e6			−1.07335
$118$	1.14644e6	−	1.14644e6i	0.697759	−	0.697759i
$119$	2.18748e6	−	2.18748e6i	1.29809	−	1.29809i
$120$			55415.1i			0.0320689i
$121$			101642.i			0.0573743i
$122$			834778.i			0.459718i
$123$	201158.			0.108099
$124$	672397.	+	672397.i	0.352663	+	0.352663i
$125$		−	340565.i		−	0.174369i
$126$	−2.03182e6	−	2.03182e6i	−1.01572	−	1.01572i
$127$	1.73439e6	−	1.73439e6i	0.846712	−	0.846712i	−0.143010	−	0.989721i	$-0.545678\pi$
$127$	1.73439e6	−	1.73439e6i	0.846712	−	0.846712i	0.989721	+	0.143010i	$0.0456780\pi$
$128$	−1.60659e6	−	1.60659e6i	−0.766082	−	0.766082i
$129$		−	870437.i		−	0.405479i
$130$	−272438.	+	272438.i	−0.124005	+	0.124005i
$131$	−930760.	−	930760.i	−0.414023	−	0.414023i	0.469115	−	0.883137i	$-0.344573\pi$
$131$	−930760.	−	930760.i	−0.414023	−	0.414023i	−0.883137	+	0.469115i	$0.844573\pi$
$132$	643486.			0.279781
$133$	−3.95125e6	+	3.95125e6i	−1.67950	+	1.67950i
$134$	3.15628e6	+	3.15628e6i	1.31178	+	1.31178i
$135$	148161.	−	148161.i	0.0602189	−	0.0602189i
$136$	−1.59767e6			−0.635140
$137$	−2.14717e6	+	2.14717e6i	−0.835034	+	0.835034i	−0.988200	−	0.153166i	$-0.951053\pi$
$137$	−2.14717e6	+	2.14717e6i	−0.835034	+	0.835034i	0.153166	+	0.988200i	$0.451053\pi$
$138$			2.53649e6i			0.965152i
$139$	1.91500e6			0.713058			0.356529	−	0.934284i	$-0.383960\pi$
$139$	1.91500e6			0.713058			0.356529	+	0.934284i	$0.383960\pi$
$140$	−211718.			−0.0771567
$141$	−555185.			−0.198052
$142$	1.57502e6	+	1.57502e6i	0.550074	+	0.550074i
$143$	−3.29571e6	−	3.29571e6i	−1.12704	−	1.12704i
$144$			2.44015e6i			0.817201i
$145$	−258506.	+	66068.0i	−0.0847944	+	0.0216714i
$146$	−1.98747e6			−0.638620
$147$	2.96033e6	−	2.96033e6i	0.931940	−	0.931940i
$148$	−1.08105e6	+	1.08105e6i	−0.333473	+	0.333473i
$149$			5.39796e6i			1.63182i	0.578182	+	0.815908i	$0.303762\pi$
$149$			5.39796e6i			1.63182i	−0.578182	+	0.815908i	$0.696238\pi$
$150$			2.40518e6i			0.712647i
$151$		−	1.82637e6i		−	0.530468i	−0.964184	−	0.265234i	$-0.914551\pi$
$151$		−	1.82637e6i		−	0.530468i	0.964184	−	0.265234i	$-0.0854492\pi$
$152$	2.88587e6			0.821762
$153$	1.68873e6	+	1.68873e6i	0.471504	+	0.471504i
$154$		−	7.79049e6i		−	2.13306i
$155$	234676.	+	234676.i	0.0630192	+	0.0630192i
$156$	1.26997e6	−	1.26997e6i	0.334518	−	0.334518i
$157$	−504555.	−	504555.i	−0.130380	−	0.130380i	0.638906	−	0.769285i	$-0.279387\pi$
$157$	−504555.	−	504555.i	−0.130380	−	0.130380i	−0.769285	+	0.638906i	$0.779387\pi$
$158$			2.36456e6i			0.599485i
$159$	−1.63429e6	+	1.63429e6i	−0.406571	+	0.406571i
$160$	228849.	+	228849.i	0.0558713	+	0.0558713i
$161$	1.00956e7			2.41910
$162$	298283.	−	298283.i	0.0701590	−	0.0701590i
$163$	685957.	+	685957.i	0.158392	+	0.158392i	0.781854	−	0.623462i	$-0.214274\pi$
$163$	685957.	+	685957.i	0.158392	+	0.158392i	−0.623462	+	0.781854i	$0.714274\pi$
$164$	280659.	−	280659.i	0.0636279	−	0.0636279i
$165$	224586.			0.0499954
$166$	−1.58212e6	+	1.58212e6i	−0.345871	+	0.345871i
$167$		−	1.21170e6i		−	0.260162i	−0.991503	−	0.130081i	$-0.958476\pi$
$167$		−	1.21170e6i		−	0.260162i	0.991503	−	0.130081i	$-0.0415237\pi$
$168$	−3.12736e6			−0.659554
$169$	−8.18187e6			−1.69509
$170$	535253.			0.108946
$171$	−3.05036e6	−	3.05036e6i	−0.610046	−	0.610046i
$172$	−1.21445e6	−	1.21445e6i	−0.238668	−	0.238668i
$173$			1.85131e6i			0.357553i	0.983890	+	0.178776i	$0.0572139\pi$
$173$			1.85131e6i			0.357553i	−0.983890	+	0.178776i	$0.942786\pi$
$174$	3.66540e6	−	936789.i	0.695783	−	0.177825i
$175$	9.57299e6			1.78621
$176$	−4.67807e6	+	4.67807e6i	−0.858081	+	0.858081i
$177$	−1.86517e6	+	1.86517e6i	−0.336356	+	0.336356i
$178$			6.75398e6i			1.19757i
$179$		−	6.23252e6i		−	1.08669i	−0.839510	−	0.543344i	$-0.817158\pi$
$179$		−	6.23252e6i		−	1.08669i	0.839510	−	0.543344i	$-0.182842\pi$
$180$		−	163446.i		−	0.0280257i
$181$	9.28324e6			1.56554			0.782769	−	0.622312i	$-0.213807\pi$
$181$	9.28324e6			1.56554			0.782769	+	0.622312i	$0.213807\pi$
$182$	−1.53751e7	−	1.53751e7i	−2.55038	−	2.55038i
$183$		−	1.35812e6i		−	0.221608i
$184$	−3.68675e6	−	3.68675e6i	−0.591822	−	0.591822i
$185$	−377301.	+	377301.i	−0.0595900	+	0.0595900i
$186$	−3.32751e6	−	3.32751e6i	−0.517107	−	0.517107i
$187$			6.47500e6i			0.990182i
$188$	−774603.	+	774603.i	−0.116575	+	0.116575i
$189$	8.36150e6	+	8.36150e6i	1.23851	+	1.23851i
$190$	−966829.			−0.140958
$191$	−4.60442e6	+	4.60442e6i	−0.660807	+	0.660807i	−0.955570	−	0.294764i	$-0.904759\pi$
$191$	−4.60442e6	+	4.60442e6i	−0.660807	+	0.660807i	0.294764	+	0.955570i	$0.404759\pi$
$192$	435696.	+	435696.i	0.0615574	+	0.0615574i
$193$	−1.62474e6	+	1.62474e6i	−0.226001	+	0.226001i	−0.811020	−	0.585019i	$-0.801087\pi$
$193$	−1.62474e6	+	1.62474e6i	−0.226001	+	0.226001i	0.585019	+	0.811020i	$0.301087\pi$
$194$	1.86523e6			0.255463
$195$	443237.	−	443237.i	0.0597767	−	0.0597767i
$196$		−	8.26060e6i		−	1.09709i
$197$	7.54382e6			0.986717			0.493359	−	0.869826i	$-0.335769\pi$
$197$	7.54382e6			0.986717			0.493359	+	0.869826i	$0.335769\pi$
$198$	6.01423e6			0.774791
$199$	7.73732e6			0.981819			0.490909	−	0.871211i	$-0.336665\pi$
$199$	7.73732e6			0.981819			0.490909	+	0.871211i	$0.336665\pi$
$200$	−3.49590e6	−	3.49590e6i	−0.436988	−	0.436988i
$201$	−5.13503e6	−	5.13503e6i	−0.632347	−	0.632347i
$202$		−	1.79421e6i		−	0.217680i
$203$	−3.72856e6	−	1.45889e7i	−0.445711	−	1.74395i
$204$	−2.49508e6			−0.293896
$205$	97954.0	−	97954.0i	0.0113700	−	0.0113700i
$206$	7.13329e6	−	7.13329e6i	0.815996	−	0.815996i
$207$			7.79378e6i			0.878693i
$208$			1.84650e7i			2.05192i
$209$		−	1.16958e7i		−	1.28113i
$210$	1.04773e6			0.113134
$211$	−4.17113e6	−	4.17113e6i	−0.444024	−	0.444024i	0.449338	−	0.893362i	$-0.351660\pi$
$211$	−4.17113e6	−	4.17113e6i	−0.444024	−	0.444024i	−0.893362	+	0.449338i	$0.851660\pi$
$212$			4.56037e6i			0.478621i
$213$	−2.56244e6	−	2.56244e6i	−0.265164	−	0.265164i
$214$	7.10795e6	−	7.10795e6i	0.725276	−	0.725276i
$215$	−423859.	−	423859.i	−0.0426487	−	0.0426487i
$216$		−	6.10697e6i		−	0.605989i
$217$	−1.32440e7	+	1.32440e7i	−1.29610	+	1.29610i
$218$	1.16877e7	+	1.16877e7i	1.12813	+	1.12813i
$219$	3.23347e6			0.307848
$220$	313346.	−	313346.i	0.0294277	−	0.0294277i
$221$	1.27789e7	+	1.27789e7i	1.18391	+	1.18391i
$222$	5.34982e6	−	5.34982e6i	0.488967	−	0.488967i
$223$	4.02935e6			0.363346			0.181673	−	0.983359i	$-0.441849\pi$
$223$	4.02935e6			0.363346			0.181673	+	0.983359i	$0.441849\pi$
$224$	−1.29151e7	+	1.29151e7i	−1.14909	+	1.14909i
$225$			7.39032e6i			0.648807i
$226$	−1.91719e7			−1.66088
$227$	9.98502e6			0.853633			0.426817	−	0.904338i	$-0.359635\pi$
$227$	9.98502e6			0.853633			0.426817	+	0.904338i	$0.359635\pi$
$228$	4.50687e6			0.380251
$229$	−6.73092e6	−	6.73092e6i	−0.560490	−	0.560490i	0.368957	−	0.929447i	$-0.379715\pi$
$229$	−6.73092e6	−	6.73092e6i	−0.560490	−	0.560490i	−0.929447	+	0.368957i	$0.879715\pi$
$230$	1.23514e6	+	1.23514e6i	0.101516	+	0.101516i
$231$			1.26745e7i			1.02824i
$232$	−3.96601e6	+	6.68923e6i	−0.317607	+	0.535688i
$233$	−1.72317e7			−1.36226			−0.681131	−	0.732161i	$-0.738512\pi$
$233$	−1.72317e7			−1.36226			−0.681131	+	0.732161i	$0.738512\pi$
$234$	1.18696e7	−	1.18696e7i	0.926375	−	0.926375i
$235$	−270347.	+	270347.i	−0.0208314	+	0.0208314i
$236$			5.20464e6i			0.395963i
$237$		−	3.84696e6i		−	0.288983i
$238$			3.02071e7i			2.24067i
$239$	−3.14347e6			−0.230258			−0.115129	−	0.993351i	$-0.536728\pi$
$239$	−3.14347e6			−0.230258			−0.115129	+	0.993351i	$0.536728\pi$
$240$	−629148.	−	629148.i	−0.0455113	−	0.0455113i
$241$		−	1.60511e7i		−	1.14671i	−0.819307	−	0.573355i	$-0.805642\pi$
$241$		−	1.60511e7i		−	1.14671i	0.819307	−	0.573355i	$-0.194358\pi$
$242$	−701792.	−	701792.i	−0.0495179	−	0.0495179i
$243$	−1.03582e7	+	1.03582e7i	−0.721880	+	0.721880i
$244$	−1.89487e6	−	1.89487e6i	−0.130440	−	0.130440i
$245$		−	2.88306e6i		−	0.196045i
$246$	−1.38891e6	+	1.38891e6i	−0.0932969	+	0.0932969i
$247$	−2.30826e7	−	2.30826e7i	−1.53177	−	1.53177i
$248$	9.67298e6			0.634169
$249$	2.57399e6	−	2.57399e6i	0.166728	−	0.166728i
$250$	2.35145e6	+	2.35145e6i	0.150493	+	0.150493i
$251$	9.30962e6	−	9.30962e6i	0.588723	−	0.588723i	−0.348563	−	0.937285i	$-0.613330\pi$
$251$	9.30962e6	−	9.30962e6i	0.588723	−	0.588723i	0.937285	+	0.348563i	$0.113330\pi$
$252$	9.22410e6			0.576398
$253$	−1.49416e7	+	1.49416e7i	−0.922649	+	0.922649i
$254$			2.39503e7i			1.46154i
$255$	−870816.			−0.0525177
$256$	1.97032e7			1.17440
$257$	3.64400e6			0.214674			0.107337	−	0.994223i	$-0.465768\pi$
$257$	3.64400e6			0.214674			0.107337	+	0.994223i	$0.465768\pi$
$258$	6.00997e6	+	6.00997e6i	0.349956	+	0.349956i
$259$	−2.12931e7	−	2.12931e7i	−1.22557	−	1.22557i
$260$		−	1.23682e6i		−	0.0703700i
$261$	1.12626e7	−	2.87844e6i	0.633454	−	0.161896i
$262$	1.28529e7			0.714659
$263$	1.14369e7	−	1.14369e7i	0.628699	−	0.628699i	−0.319042	−	0.947741i	$-0.603361\pi$
$263$	1.14369e7	−	1.14369e7i	0.628699	−	0.628699i	0.947741	+	0.319042i	$0.103361\pi$
$264$	4.62854e6	−	4.62854e6i	0.251555	−	0.251555i
$265$			1.59163e6i			0.0855273i
$266$		−	5.45632e7i		−	2.89904i
$267$		−	1.09882e7i		−	0.577290i
$268$	−1.43290e7			−0.744407
$269$	1.14133e7	+	1.14133e7i	0.586346	+	0.586346i	0.936640	−	0.350294i	$-0.113918\pi$
$269$	1.14133e7	+	1.14133e7i	0.586346	+	0.586346i	−0.350294	+	0.936640i	$0.613918\pi$
$270$			2.04597e6i			0.103946i
$271$	−7.90483e6	−	7.90483e6i	−0.397177	−	0.397177i	0.480059	−	0.877236i	$-0.340615\pi$
$271$	−7.90483e6	−	7.90483e6i	−0.397177	−	0.397177i	−0.877236	+	0.480059i	$0.840615\pi$
$272$	1.81389e7	−	1.81389e7i	0.901372	−	0.901372i
$273$	2.50142e7	+	2.50142e7i	1.22941	+	1.22941i
$274$		−	2.96504e7i		−	1.44138i
$275$	−1.41682e7	+	1.41682e7i	−0.681264	+	0.681264i
$276$	−5.75761e6	−	5.75761e6i	−0.273851	−	0.273851i
$277$	−1.12490e7			−0.529267			−0.264634	−	0.964349i	$-0.585251\pi$
$277$	−1.12490e7			−0.529267			−0.264634	+	0.964349i	$0.585251\pi$
$278$	−1.32222e7	+	1.32222e7i	−0.615417	+	0.615417i
$279$	−1.02243e7	−	1.02243e7i	−0.470784	−	0.470784i
$280$	−1.52287e6	+	1.52287e6i	−0.0693727	+	0.0693727i
$281$	−1.22250e7			−0.550970			−0.275485	−	0.961305i	$-0.588839\pi$
$281$	−1.22250e7			−0.550970			−0.275485	+	0.961305i	$0.588839\pi$
$282$	3.83330e6	−	3.83330e6i	0.170933	−	0.170933i
$283$			390113.i			0.0172120i	0.999963	+	0.00860599i	$0.00273940\pi$
$283$			390113.i			0.0172120i	−0.999963	+	0.00860599i	$0.997261\pi$
$284$	−7.15032e6			−0.312155
$285$	1.57296e6			0.0679490
$286$	4.55108e7			1.94543
$287$	5.52805e6	+	5.52805e6i	0.233844	+	0.233844i
$288$	−9.97044e6	−	9.97044e6i	−0.417385	−	0.417385i
$289$		−	968828.i		−	0.0401378i
$290$	1.32870e6	−	2.24104e6i	0.0544794	−	0.0918872i
$291$	−3.03459e6			−0.123146
$292$	4.51139e6	−	4.51139e6i	0.181201	−	0.181201i
$293$	1.89409e6	−	1.89409e6i	0.0753003	−	0.0753003i	−0.668454	−	0.743754i	$-0.733043\pi$
$293$	1.89409e6	−	1.89409e6i	0.0753003	−	0.0753003i	0.743754	+	0.668454i	$0.233043\pi$
$294$			4.08794e7i			1.60865i
$295$			1.81649e6i			0.0707566i
$296$			1.55518e7i			0.599660i
$297$	−2.47503e7			−0.944736
$298$	−3.72705e7	−	3.72705e7i	−1.40837	−	1.40837i
$299$			5.89769e7i			2.20632i
$300$	−5.45956e6	−	5.45956e6i	−0.202206	−	0.202206i
$301$	2.39206e7	−	2.39206e7i	0.877147	−	0.877147i
$302$	1.26103e7	+	1.26103e7i	0.457830	+	0.457830i
$303$			2.91904e6i			0.104933i
$304$	−3.27643e7	+	3.27643e7i	−1.16622	+	1.16622i
$305$	−661337.	−	661337.i	−0.0233090	−	0.0233090i
$306$	−2.33198e7			−0.813880
$307$	1.83887e7	−	1.83887e7i	0.635529	−	0.635529i	−0.313920	−	0.949449i	$-0.601642\pi$
$307$	1.83887e7	−	1.83887e7i	0.635529	−	0.635529i	0.949449	+	0.313920i	$0.101642\pi$
$308$	1.76837e7	+	1.76837e7i	0.605232	+	0.605232i
$309$	−1.16053e7	+	1.16053e7i	−0.393352	+	0.393352i
$310$	−3.24066e6			−0.108780
$311$	2.15150e7	−	2.15150e7i	0.715254	−	0.715254i	−0.252375	−	0.967629i	$-0.581212\pi$
$311$	2.15150e7	−	2.15150e7i	0.715254	−	0.715254i	0.967629	+	0.252375i	$0.0812118\pi$
$312$		−	1.82696e7i		−	0.601540i
$313$	8.51921e6			0.277822			0.138911	−	0.990305i	$-0.455640\pi$
$313$	8.51921e6			0.277822			0.138911	+	0.990305i	$0.455640\pi$
$314$	6.96745e6			0.225053
$315$	3.21934e6			0.102999
$316$	−5.36734e6	−	5.36734e6i	−0.170097	−	0.170097i
$317$	1.80959e7	+	1.80959e7i	0.568071	+	0.568071i	0.931588	−	0.363517i	$-0.118424\pi$
$317$	1.80959e7	+	1.80959e7i	0.568071	+	0.568071i	−0.363517	+	0.931588i	$0.618424\pi$
$318$		−	2.25680e7i		−	0.701797i
$319$	2.71100e7	+	1.60734e7i	0.835137	+	0.495148i
$320$	424325.			0.0129494
$321$	−1.15641e7	+	1.15641e7i	−0.349621	+	0.349621i
$322$	−6.97055e7	+	6.97055e7i	−2.08785	+	2.08785i
$323$			4.53498e7i			1.34576i
$324$			1.35415e6i			0.0398137i
$325$			5.59239e7i			1.62910i
$326$	−9.47244e6			−0.273407
$327$	−1.90150e7	−	1.90150e7i	−0.543818	−	0.543818i
$328$		−	4.03751e6i		−	0.114418i
$329$	−1.52571e7	−	1.52571e7i	−0.428434	−	0.428434i
$330$	−1.55066e6	+	1.55066e6i	−0.0431494	+	0.0431494i
$331$	3.47554e6	+	3.47554e6i	0.0958382	+	0.0958382i	0.753400	−	0.657562i	$-0.228412\pi$
$331$	3.47554e6	+	3.47554e6i	0.0958382	+	0.0958382i	−0.657562	+	0.753400i	$0.728412\pi$
$332$		−	7.18253e6i		−	0.196274i
$333$	1.64382e7	−	1.64382e7i	0.445165	−	0.445165i
$334$	8.36620e6	+	8.36620e6i	0.224538	+	0.224538i
$335$	−5.00101e6			−0.133022
$336$	3.55061e7	−	3.55061e7i	0.936020	−	0.936020i
$337$	−1.64739e7	−	1.64739e7i	−0.430434	−	0.430434i	0.458342	−	0.888776i	$-0.348444\pi$
$337$	−1.64739e7	−	1.64739e7i	−0.430434	−	0.430434i	−0.888776	+	0.458342i	$0.848444\pi$
$338$	5.64921e7	−	5.64921e7i	1.46298	−	1.46298i
$339$	3.11912e7			0.800632
$340$	−1.21498e6	+	1.21498e6i	−0.0309123	+	0.0309123i
$341$		−	3.92025e7i		−	0.988669i
$342$	4.21226e7			1.05302
$343$	9.00697e7			2.23201
$344$	−1.74708e7			−0.429179
$345$	−2.00948e6	−	2.00948e6i	−0.0489359	−	0.0489359i
$346$	−1.27824e7	−	1.27824e7i	−0.308592	−	0.308592i
$347$		−	3.15709e7i		−	0.755611i	−0.925885	−	0.377805i	$-0.876679\pi$
$347$		−	3.15709e7i		−	0.755611i	0.925885	−	0.377805i	$-0.123321\pi$
$348$	−6.19372e6	+	1.04466e7i	−0.146965	+	0.247877i
$349$	−6.25571e7			−1.47164			−0.735818	−	0.677179i	$-0.763202\pi$
$349$	−6.25571e7			−1.47164			−0.735818	+	0.677179i	$0.763202\pi$
$350$	−6.60971e7	+	6.60971e7i	−1.54162	+	1.54162i
$351$	−4.88465e7	+	4.88465e7i	−1.12957	+	1.12957i
$352$		−	3.82291e7i		−	0.876529i
$353$		−	2.13876e7i		−	0.486227i	−0.969998	−	0.243113i	$-0.921831\pi$
$353$		−	2.13876e7i		−	0.486227i	0.969998	−	0.243113i	$-0.0781687\pi$
$354$		−	2.57563e7i		−	0.580596i
$355$	−2.49556e6			−0.0557806
$356$	−1.53310e7	−	1.53310e7i	−0.339797	−	0.339797i
$357$		−	4.91447e7i		−	1.08012i
$358$	4.30327e7	+	4.30327e7i	0.937885	+	0.937885i
$359$	2.27121e7	−	2.27121e7i	0.490878	−	0.490878i	−0.417705	−	0.908583i	$-0.637165\pi$
$359$	2.27121e7	−	2.27121e7i	0.490878	−	0.490878i	0.908583	+	0.417705i	$0.137165\pi$
$360$	−1.17565e6	−	1.17565e6i	−0.0251983	−	0.0251983i
$361$		−	3.48696e7i		−	0.741182i
$362$	−6.40965e7	+	6.40965e7i	−1.35117	+	1.35117i
$363$	1.14176e6	+	1.14176e6i	0.0238702	+	0.0238702i
$364$	6.98004e7			1.44728
$365$	1.57454e6	−	1.57454e6i	0.0323798	−	0.0323798i
$366$	9.37721e6	+	9.37721e6i	0.191263	+	0.191263i
$367$	9.95058e6	−	9.95058e6i	0.201303	−	0.201303i	−0.599255	−	0.800558i	$-0.704536\pi$
$367$	9.95058e6	−	9.95058e6i	0.201303	−	0.201303i	0.800558	+	0.599255i	$0.204536\pi$
$368$	8.37142e7			1.67979
$369$	−4.26764e6	+	4.26764e6i	−0.0849393	+	0.0849393i
$370$		−	5.21019e6i		−	0.102860i
$371$	−8.98240e7			−1.75902
$372$	1.51063e7			0.293447
$373$	3.10171e7			0.597689			0.298845	−	0.954302i	$-0.403399\pi$
$373$	3.10171e7			0.597689			0.298845	+	0.954302i	$0.403399\pi$
$374$	−4.47069e7	−	4.47069e7i	−0.854594	−	0.854594i
$375$	−3.82563e6	−	3.82563e6i	−0.0725453	−	0.0725453i
$376$			1.11433e7i			0.209629i
$377$	8.52257e7	−	2.17816e7i	1.59055	−	0.406506i
$378$	−1.15465e8			−2.13783
$379$	−4.87165e7	+	4.87165e7i	−0.894866	+	0.894866i	−0.994976	−	0.100110i	$-0.968081\pi$
$379$	−4.87165e7	+	4.87165e7i	−0.894866	+	0.894866i	0.100110	+	0.994976i	$0.468081\pi$
$380$	2.19462e6	−	2.19462e6i	0.0399952	−	0.0399952i
$381$		−	3.89654e7i		−	0.704538i
$382$		−	6.35828e7i		−	1.14064i
$383$			7.30726e7i			1.30064i	0.759659	+	0.650321i	$0.225366\pi$
$383$			7.30726e7i			1.30064i	−0.759659	+	0.650321i	$0.774634\pi$
$384$	−3.60942e7			−0.637447
$385$	6.17187e6	+	6.17187e6i	0.108152	+	0.108152i
$386$		−	2.24361e7i		−	0.390109i
$387$	1.84666e7	+	1.84666e7i	0.318606	+	0.318606i
$388$	−4.23391e6	+	4.23391e6i	−0.0724847	+	0.0724847i
$389$	6.54976e6	+	6.54976e6i	0.111270	+	0.111270i	0.760550	−	0.649280i	$-0.224930\pi$
$389$	6.54976e6	+	6.54976e6i	0.111270	+	0.111270i	−0.649280	+	0.760550i	$0.724930\pi$
$390$			6.12070e6i			0.103183i
$391$	5.79352e7	−	5.79352e7i	0.969197	−	0.969197i
$392$	−5.94178e7	−	5.94178e7i	−0.986411	−	0.986411i
$393$	−2.09108e7			−0.344503
$394$	−5.20866e7	+	5.20866e7i	−0.851604	+	0.851604i
$395$	−1.87327e6	−	1.87327e6i	−0.0303956	−	0.0303956i
$396$	−1.36518e7	+	1.36518e7i	−0.219839	+	0.219839i
$397$	2.59646e7			0.414963			0.207482	−	0.978239i	$-0.433473\pi$
$397$	2.59646e7			0.414963			0.207482	+	0.978239i	$0.433473\pi$
$398$	−5.34227e7	+	5.34227e7i	−0.847376	+	0.847376i
$399$			8.87703e7i			1.39749i
$400$	7.93806e7			1.24032
$401$	−1.45981e6			−0.0226392			−0.0113196	−	0.999936i	$-0.503603\pi$
$401$	−1.45981e6			−0.0226392			−0.0113196	+	0.999936i	$0.503603\pi$
$402$	7.09101e7			1.09152
$403$	−7.73692e7	−	7.73692e7i	−1.18210	−	1.18210i
$404$	4.07269e6	+	4.07269e6i	0.0617643	+	0.0617643i
$405$			472618.i			0.00711452i
$406$	1.26473e8	+	7.49854e7i	1.88982	+	1.12047i
$407$	6.30281e7			0.934869
$408$	−1.79469e7	+	1.79469e7i	−0.264246	+	0.264246i
$409$	7.33822e7	−	7.33822e7i	1.07256	−	1.07256i	0.0754053	−	0.997153i	$-0.475975\pi$
$409$	7.33822e7	−	7.33822e7i	1.07256	−	1.07256i	0.997153	−	0.0754053i	$-0.0240250\pi$
$410$			1.35265e6i			0.0196262i
$411$			4.82390e7i			0.694821i
$412$			3.23839e7i			0.463060i
$413$	−1.02514e8			−1.45523
$414$	−5.38125e7	−	5.38125e7i	−0.758371	−	0.758371i
$415$		−	2.50680e6i		−	0.0350733i
$416$	−7.54481e7	−	7.54481e7i	−1.04802	−	1.04802i
$417$	2.15116e7	−	2.15116e7i	0.296663	−	0.296663i
$418$	8.07543e7	+	8.07543e7i	1.10570	+	1.10570i
$419$		−	5.96627e7i		−	0.811074i	−0.914079	−	0.405537i	$-0.867085\pi$
$419$		−	5.96627e7i		−	0.811074i	0.914079	−	0.405537i	$-0.132915\pi$
$420$	−2.37827e6	+	2.37827e6i	−0.0321006	+	0.0321006i
$421$	8.73129e7	+	8.73129e7i	1.17012	+	1.17012i	0.982180	+	0.187945i	$0.0601827\pi$
$421$	8.73129e7	+	8.73129e7i	1.17012	+	1.17012i	0.187945	+	0.982180i	$0.439817\pi$
$422$	5.75995e7			0.766445
$423$	1.17784e7	−	1.17784e7i	0.155620	−	0.155620i
$424$	3.28023e7	+	3.28023e7i	0.430335	+	0.430335i
$425$	5.49361e7	−	5.49361e7i	0.715634	−	0.715634i
$426$	3.53850e7			0.457710
$427$	3.73227e7	−	3.73227e7i	0.479391	−	0.479391i
$428$			3.22689e7i			0.411578i
$429$	−7.40426e7			−0.937800
$430$	5.85311e6			0.0736175
$431$	−1.40591e8			−1.75600			−0.878001	−	0.478660i	$-0.841123\pi$
$431$	−1.40591e8			−1.75600			−0.878001	+	0.478660i	$0.841123\pi$
$432$	6.93347e7	+	6.93347e7i	0.860002	+	0.860002i
$433$	2.61606e7	+	2.61606e7i	0.322243	+	0.322243i	0.849627	−	0.527384i	$-0.176827\pi$
$433$	2.61606e7	+	2.61606e7i	0.322243	+	0.322243i	−0.527384	+	0.849627i	$0.676827\pi$
$434$		−	1.82887e8i		−	2.23725i
$435$	−2.16169e6	+	3.64600e6i	−0.0262619	+	0.0442944i
$436$	−5.30601e7			−0.640190
$437$	−1.04649e8	+	1.04649e8i	−1.25398	+	1.25398i
$438$	−2.23256e7	+	2.23256e7i	−0.265694	+	0.265694i
$439$			8.39687e7i			0.992485i	0.868184	+	0.496243i	$0.165287\pi$
$439$			8.39687e7i			0.992485i	−0.868184	+	0.496243i	$0.834713\pi$
$440$		−	4.50774e6i		−	0.0529176i
$441$			1.25609e8i			1.46455i
$442$	−1.76465e8			−2.04358
$443$	3.09131e7	+	3.09131e7i	0.355575	+	0.355575i	0.862179	−	0.506604i	$-0.169099\pi$
$443$	3.09131e7	+	3.09131e7i	0.355575	+	0.355575i	−0.506604	+	0.862179i	$0.669099\pi$
$444$			2.42872e7i			0.277478i
$445$	−5.35072e6	−	5.35072e6i	−0.0607200	−	0.0607200i
$446$	−2.78208e7	+	2.78208e7i	−0.313592	+	0.313592i
$447$	6.06363e7	+	6.06363e7i	0.678907	+	0.678907i
$448$			2.39469e7i			0.266327i
$449$	−9.55953e7	+	9.55953e7i	−1.05608	+	1.05608i	−0.0577504	+	0.998331i	$0.518393\pi$
$449$	−9.55953e7	+	9.55953e7i	−1.05608	+	1.05608i	−0.998331	+	0.0577504i	$0.981607\pi$
$450$	−5.10268e7	−	5.10268e7i	−0.559965	−	0.559965i
$451$	−1.63632e7			−0.178377
$452$	4.35185e7	−	4.35185e7i	0.471258	−	0.471258i
$453$	−2.05160e7	−	2.05160e7i	−0.220698	−	0.220698i
$454$	−6.89420e7	+	6.89420e7i	−0.736744	+	0.736744i
$455$	2.43613e7			0.258623
$456$	3.24175e7	−	3.24175e7i	0.341889	−	0.341889i
$457$		−	1.23432e8i		−	1.29324i	−0.762811	−	0.646621i	$-0.776181\pi$
$457$		−	1.23432e8i		−	1.29324i	0.762811	−	0.646621i	$-0.223819\pi$
$458$	9.29478e7			0.967481
$459$	9.59675e7			0.992399
$460$	−5.60733e6			−0.0576080
$461$	1.05518e7	+	1.05518e7i	0.107702	+	0.107702i	0.758904	−	0.651202i	$-0.225735\pi$
$461$	1.05518e7	+	1.05518e7i	0.107702	+	0.107702i	−0.651202	+	0.758904i	$0.725735\pi$
$462$	−8.75119e7	−	8.75119e7i	−0.887445	−	0.887445i
$463$			1.96248e7i			0.197725i	0.995101	+	0.0988626i	$0.0315204\pi$
$463$			1.96248e7i			0.197725i	−0.995101	+	0.0988626i	$0.968480\pi$
$464$	−3.09177e7	−	1.20973e8i	−0.309495	−	1.21097i
$465$	5.27231e6			0.0524375
$466$	1.18977e8	−	1.18977e8i	1.17573	−	1.17573i
$467$	−7.77961e7	+	7.77961e7i	−0.763849	+	0.763849i	−0.977016	−	0.213167i	$-0.931622\pi$
$467$	−7.77961e7	+	7.77961e7i	−0.763849	+	0.763849i	0.213167	+	0.977016i	$0.431622\pi$
$468$			5.38857e7i			0.525698i
$469$		−	2.82233e8i		−	2.73583i
$470$		−	3.73325e6i		−	0.0359578i
$471$	−1.13355e7			−0.108487
$472$	3.74365e7	+	3.74365e7i	0.356016	+	0.356016i
$473$			7.08056e7i			0.669089i
$474$	2.65615e7	+	2.65615e7i	0.249412	+	0.249412i
$475$	−9.92313e7	+	9.92313e7i	−0.925908	+	0.925908i
$476$	−6.85675e7	−	6.85675e7i	−0.635766	−	0.635766i
$477$		−	6.93439e7i		−	0.638930i
$478$	2.17042e7	−	2.17042e7i	0.198729	−	0.198729i
$479$	6.25405e7	+	6.25405e7i	0.569056	+	0.569056i	0.931864	−	0.362808i	$-0.118182\pi$
$479$	6.25405e7	+	6.25405e7i	0.569056	+	0.569056i	−0.362808	+	0.931864i	$0.618182\pi$
$480$	5.14139e6			0.0464898
$481$	1.24391e8	−	1.24391e8i	1.11777	−	1.11777i
$482$	1.10825e8	+	1.10825e8i	0.989689	+	0.989689i
$483$	1.13406e8	−	1.13406e8i	1.00645	−	1.00645i
$484$	3.18601e6			0.0281003
$485$	−1.47769e6	+	1.47769e6i	−0.0129527	+	0.0129527i
$486$		−	1.43037e8i		−	1.24606i
$487$	−8.37942e7			−0.725483			−0.362741	−	0.931890i	$-0.618159\pi$
$487$	−8.37942e7			−0.725483			−0.362741	+	0.931890i	$0.618159\pi$
$488$	−2.72593e7			−0.234561
$489$	1.54110e7			0.131796
$490$	1.99062e7	+	1.99062e7i	0.169200	+	0.169200i
$491$	5.19829e7	+	5.19829e7i	0.439153	+	0.439153i	0.891727	−	0.452574i	$-0.149494\pi$
$491$	5.19829e7	+	5.19829e7i	0.439153	+	0.439153i	−0.452574	+	0.891727i	$0.649494\pi$
$492$		−	6.30539e6i		−	0.0529440i
$493$	−1.05117e8	−	6.23235e7i	−0.877271	−	0.520129i
$494$	3.18750e8			2.64404
$495$	−4.76466e6	+	4.76466e6i	−0.0392841	+	0.0392841i
$496$	−1.09821e8	+	1.09821e8i	−0.899995	+	0.899995i
$497$		−	1.40838e8i		−	1.14723i
$498$			3.55444e7i			0.287795i
$499$		−	8.46731e7i		−	0.681466i	−0.940160	−	0.340733i	$-0.889325\pi$
$499$		−	8.46731e7i		−	0.681466i	0.940160	−	0.340733i	$-0.110675\pi$
$500$	−1.06752e7			−0.0854013
$501$	−1.36112e7	−	1.36112e7i	−0.108239	−	0.108239i
$502$			1.28557e8i			1.01622i
$503$	−1.62238e8	−	1.62238e8i	−1.27482	−	1.27482i	−0.943530	−	0.331288i	$-0.892517\pi$
$503$	−1.62238e8	−	1.62238e8i	−1.27482	−	1.27482i	−0.331288	−	0.943530i	$-0.607483\pi$
$504$	6.63481e7	−	6.63481e7i	0.518247	−	0.518247i
$505$	1.42143e6	+	1.42143e6i	0.0110370	+	0.0110370i
$506$		−	2.06330e8i		−	1.59262i
$507$	−9.19084e7	+	9.19084e7i	−0.705231	+	0.705231i
$508$	−5.43652e7	−	5.43652e7i	−0.414696	−	0.414696i
$509$	263411.			0.00199747			0.000998734	−	1.00000i	$-0.499682\pi$
$509$	263411.			0.00199747			0.000998734		1.00000i	$0.499682\pi$
$510$	6.01259e6	−	6.01259e6i	0.0453264	−	0.0453264i
$511$	8.88593e7	+	8.88593e7i	0.665948	+	0.665948i
$512$	−3.32198e7	+	3.32198e7i	−0.247507	+	0.247507i
$513$	−1.73347e8			−1.28399
$514$	−2.51602e7	+	2.51602e7i	−0.185278	+	0.185278i
$515$			1.13024e7i			0.0827465i
$516$	−2.72842e7			−0.198592
$517$	4.51614e7			0.326811
$518$	2.94038e8			2.11550
$519$	2.07961e7	+	2.07961e7i	0.148758	+	0.148758i
$520$	−8.89636e6	−	8.89636e6i	−0.0632707	−	0.0632707i
$521$			2.40436e8i			1.70015i	0.526662	+	0.850074i	$0.323443\pi$
$521$			2.40436e8i			1.70015i	−0.526662	+	0.850074i	$0.676557\pi$
$522$	−5.78885e7	+	9.76371e7i	−0.406987	+	0.686441i
$523$	−2.63856e8			−1.84443			−0.922213	−	0.386681i	$-0.873621\pi$
$523$	−2.63856e8			−1.84443			−0.922213	+	0.386681i	$0.873621\pi$
$524$	−2.91751e7	+	2.91751e7i	−0.202777	+	0.202777i
$525$	1.07535e8	−	1.07535e8i	0.743143	−	0.743143i
$526$			1.57934e8i			1.08522i
$527$			1.52005e8i			1.03855i
$528$			1.05099e8i			0.713998i
$529$	1.19345e8			0.806190
$530$	−1.09895e7	−	1.09895e7i	−0.0738159	−	0.0738159i
$531$		−	7.91405e7i		−	0.528586i
$532$	1.23854e8	+	1.23854e8i	0.822572	+	0.822572i
$533$	−3.22940e7	+	3.22940e7i	−0.213275	+	0.213275i
$534$	7.58687e7	+	7.58687e7i	0.498240	+	0.498240i
$535$			1.12623e7i			0.0735470i
$536$	−1.03067e8	+	1.03067e8i	−0.669307	+	0.669307i
$537$	−7.00110e7	−	7.00110e7i	−0.452109	−	0.452109i
$538$	−1.57607e8			−1.01211
$539$	−2.40808e8	+	2.40808e8i	−1.53781	+	1.53781i
$540$	−4.64417e6	−	4.64417e6i	−0.0294935	−	0.0294935i
$541$	−2.66522e7	+	2.66522e7i	−0.168322	+	0.168322i	−0.786241	−	0.617919i	$-0.787976\pi$
$541$	−2.66522e7	+	2.66522e7i	−0.168322	+	0.168322i	0.617919	+	0.786241i	$0.287976\pi$
$542$	1.09158e8			0.685582
$543$	1.04280e8	−	1.04280e8i	0.651332	−	0.651332i
$544$			1.48231e8i			0.920751i
$545$	−1.85187e7			−0.114399
$546$	−3.45423e8			−2.12214
$547$	−1.10750e8			−0.676677			−0.338338	−	0.941025i	$-0.609865\pi$
$547$	−1.10750e8			−0.676677			−0.338338	+	0.941025i	$0.609865\pi$
$548$	6.73039e7	+	6.73039e7i	0.408976	+	0.408976i
$549$	2.88130e7	+	2.88130e7i	0.174129	+	0.174129i
$550$		−	1.95649e8i		−	1.17595i
$551$	1.89874e8	+	1.12575e8i	1.13504	+	0.672958i
$552$	−8.28279e7			−0.492447
$553$	1.05719e8	−	1.05719e8i	0.625138	−	0.625138i
$554$	7.76693e7	−	7.76693e7i	0.456794	−	0.456794i
$555$			8.47658e6i			0.0495840i
$556$		−	6.00266e7i		−	0.349236i
$557$		−	2.55721e8i		−	1.47979i	−0.672722	−	0.739895i	$-0.734875\pi$
$557$		−	2.55721e8i		−	1.47979i	0.672722	−	0.739895i	$-0.265125\pi$
$558$	1.41188e8			0.812637
$559$	1.39740e8	+	1.39740e8i	0.799993	+	0.799993i
$560$		−	3.45794e7i		−	0.196903i
$561$	7.27348e7	+	7.27348e7i	0.411959	+	0.411959i
$562$	8.44077e7	−	8.44077e7i	0.475525	−	0.475525i
$563$	−1.75955e8	−	1.75955e8i	−0.985997	−	0.985997i	0.0139062	−	0.999903i	$-0.495573\pi$
$563$	−1.75955e8	−	1.75955e8i	−0.985997	−	0.985997i	−0.999903	+	0.0139062i	$0.995573\pi$
$564$			1.74025e7i			0.0970006i
$565$	1.51886e7	−	1.51886e7i	0.0842115	−	0.0842115i
$566$	−2.69355e6	−	2.69355e6i	−0.0148551	−	0.0148551i
$567$	−2.66723e7			−0.146323
$568$	−5.14316e7	+	5.14316e7i	−0.280663	+	0.280663i
$569$	7.18615e7	+	7.18615e7i	0.390085	+	0.390085i	0.874718	−	0.484633i	$-0.161047\pi$
$569$	7.18615e7	+	7.18615e7i	0.390085	+	0.390085i	−0.484633	+	0.874718i	$0.661047\pi$
$570$	−1.08606e7	+	1.08606e7i	−0.0586446	+	0.0586446i
$571$	−7.79764e7			−0.418846			−0.209423	−	0.977825i	$-0.567159\pi$
$571$	−7.79764e7			−0.418846			−0.209423	+	0.977825i	$0.567159\pi$
$572$	−1.03306e8	+	1.03306e8i	−0.551995	+	0.551995i
$573$			1.03444e8i			0.549849i
$574$	−7.63373e7			−0.403647
$575$	2.53540e8			1.33365
$576$	−1.84869e7			−0.0967379
$577$	−5.27893e7	−	5.27893e7i	−0.274801	−	0.274801i	0.556228	−	0.831029i	$-0.312248\pi$
$577$	−5.27893e7	−	5.27893e7i	−0.274801	−	0.274801i	−0.831029	+	0.556228i	$0.812248\pi$
$578$	6.68932e6	+	6.68932e6i	0.0346416	+	0.0346416i
$579$			3.65019e7i			0.188053i
$580$	2.07093e6	+	8.10299e6i	0.0106141	+	0.0415299i
$581$	1.41472e8			0.721344
$582$	2.09525e7	−	2.09525e7i	0.106284	−	0.106284i
$583$	1.32941e8	−	1.32941e8i	0.670892	−	0.670892i
$584$		−	6.49001e7i		−	0.325842i
$585$			1.88069e7i			0.0939396i
$586$			2.61556e7i			0.129979i
$587$	2.03863e8			1.00792			0.503958	−	0.863728i	$-0.331877\pi$
$587$	2.03863e8			1.00792			0.503958	+	0.863728i	$0.331877\pi$
$588$	−9.27927e7	−	9.27927e7i	−0.456438	−	0.456438i
$589$		−	2.74568e8i		−	1.34370i
$590$	−1.25420e7	−	1.25420e7i	−0.0610678	−	0.0610678i
$591$	8.47411e7	−	8.47411e7i	0.410517	−	0.410517i
$592$	−1.76565e8	−	1.76565e8i	−0.851020	−	0.851020i
$593$			3.80986e8i			1.82703i	0.406807	+	0.913514i	$0.366642\pi$
$593$			3.80986e8i			1.82703i	−0.406807	+	0.913514i	$0.633358\pi$
$594$	1.70889e8	−	1.70889e8i	0.815371	−	0.815371i
$595$	−2.39310e7	−	2.39310e7i	−0.113608	−	0.113608i
$596$	1.69201e8			0.799218
$597$	8.69147e7	−	8.69147e7i	0.408479	−	0.408479i
$598$	−4.07209e8	−	4.07209e8i	−1.90420	−	1.90420i
$599$	1.03951e8	−	1.03951e8i	0.483671	−	0.483671i	−0.422631	−	0.906302i	$-0.638893\pi$
$599$	1.03951e8	−	1.03951e8i	0.483671	−	0.483671i	0.906302	+	0.422631i	$0.138893\pi$
$600$	−7.85402e7			−0.363612
$601$	−3.00401e8	+	3.00401e8i	−1.38381	+	1.38381i	−0.546085	+	0.837730i	$0.683882\pi$
$601$	−3.00401e8	+	3.00401e8i	−1.38381	+	1.38381i	−0.837730	+	0.546085i	$0.816118\pi$
$602$			3.30321e8i			1.51407i
$603$	2.17883e8			0.993737
$604$	−5.72485e7			−0.259808
$605$	1.11196e6			0.00502139
$606$	−2.01546e7	−	2.01546e7i	−0.0905643	−	0.0905643i
$607$	−2.34010e8	−	2.34010e8i	−1.04633	−	1.04633i	−0.998873	−	0.0474554i	$-0.984889\pi$
$607$	−2.34010e8	−	2.34010e8i	−1.04633	−	1.04633i	−0.0474554	−	0.998873i	$-0.515111\pi$
$608$		−	2.67750e8i		−	1.19129i
$609$	−2.05763e8	−	1.21996e8i	−0.910993	−	0.540122i
$610$	9.13247e6			0.0402345
$611$	8.91295e7	−	8.91295e7i	0.390749	−	0.390749i
$612$	5.29339e7	−	5.29339e7i	0.230930	−	0.230930i
$613$			2.41320e8i			1.04764i	0.851829	+	0.523820i	$0.175494\pi$
$613$			2.41320e8i			1.04764i	−0.851829	+	0.523820i	$0.824506\pi$
$614$			2.53931e8i			1.09701i
$615$		−	2.20067e6i		−	0.00946083i
$616$	2.54395e8			1.08834
$617$	−1.12626e8	−	1.12626e8i	−0.479494	−	0.479494i	0.425476	−	0.904970i	$-0.360107\pi$
$617$	−1.12626e8	−	1.12626e8i	−0.479494	−	0.479494i	−0.904970	+	0.425476i	$0.860107\pi$
$618$		−	1.60259e8i		−	0.678980i
$619$	−2.00082e8	−	2.00082e8i	−0.843597	−	0.843597i	0.145727	−	0.989325i	$-0.453448\pi$
$619$	−2.00082e8	−	2.00082e8i	−0.843597	−	0.843597i	−0.989325	+	0.145727i	$0.953448\pi$
$620$	7.35601e6	−	7.35601e6i	0.0308651	−	0.0308651i
$621$	2.21453e8	+	2.21453e8i	0.924714	+	0.924714i
$622$			2.97103e8i			1.23463i
$623$	3.01969e8	−	3.01969e8i	1.24881	−	1.24881i
$624$	2.07421e8	+	2.07421e8i	0.853688	+	0.853688i
$625$	2.38545e8			0.977079
$626$	−5.88213e7	+	5.88213e7i	−0.239779	+	0.239779i
$627$	−1.31381e8	−	1.31381e8i	−0.533004	−	0.533004i
$628$	−1.58155e7	+	1.58155e7i	−0.0638563	+	0.0638563i
$629$	−2.44387e8			−0.982034
$630$	−2.22281e7	+	2.22281e7i	−0.0888955	+	0.0888955i
$631$		−	2.63831e8i		−	1.05012i	−0.851066	−	0.525058i	$-0.824044\pi$
$631$		−	2.63831e8i		−	1.05012i	0.851066	−	0.525058i	$-0.175956\pi$
$632$	−7.72136e7			−0.305874
$633$	−9.37100e7			−0.369466
$634$	−2.49888e8			−0.980568
$635$	−1.89742e7	−	1.89742e7i	−0.0741041	−	0.0741041i
$636$	5.12274e7	+	5.12274e7i	0.199127	+	0.199127i
$637$			9.50504e8i			3.67736i
$638$	−2.98162e8	+	7.62029e7i	−1.14813	+	0.293434i
$639$	1.08726e8			0.416708
$640$	−1.75761e7	+	1.75761e7i	−0.0670474	+	0.0670474i
$641$	−6.79901e7	+	6.79901e7i	−0.258150	+	0.258150i	−0.824301	−	0.566152i	$-0.808432\pi$
$641$	−6.79901e7	+	6.79901e7i	−0.258150	+	0.258150i	0.566152	+	0.824301i	$0.308432\pi$
$642$		−	1.59690e8i		−	0.603493i
$643$			4.03370e8i			1.51730i	0.651499	+	0.758649i	$0.274140\pi$
$643$			4.03370e8i			1.51730i	−0.651499	+	0.758649i	$0.725860\pi$
$644$		−	3.16451e8i		−	1.18481i
$645$	−9.52257e6			−0.0354875
$646$	−3.13119e8	−	3.13119e8i	−1.16148	−	1.16148i
$647$			1.27162e8i			0.469508i	0.972055	+	0.234754i	$0.0754284\pi$
$647$			1.27162e8i			0.469508i	−0.972055	+	0.234754i	$0.924572\pi$
$648$	9.74030e6	+	9.74030e6i	0.0357971	+	0.0357971i
$649$	1.51722e8	−	1.51722e8i	0.555028	−	0.555028i
$650$	−3.86129e8	−	3.86129e8i	−1.40602	−	1.40602i
$651$			2.97544e8i			1.07847i
$652$	2.15016e7	−	2.15016e7i	0.0775762	−	0.0775762i
$653$	−1.85368e7	−	1.85368e7i	−0.0665726	−	0.0665726i	0.673037	−	0.739609i	$-0.264990\pi$
$653$	−1.85368e7	−	1.85368e7i	−0.0665726	−	0.0665726i	−0.739609	+	0.673037i	$0.764990\pi$
$654$	2.62580e8			0.938703
$655$	−1.01825e7	+	1.01825e7i	−0.0362352	+	0.0362352i
$656$	4.58394e7	+	4.58394e7i	0.162378	+	0.162378i
$657$	−6.85992e7	+	6.85992e7i	−0.241893	+	0.241893i
$658$	2.10687e8			0.739536
$659$	2.91451e8	−	2.91451e8i	1.01838	−	1.01838i	0.0185521	−	0.999828i	$-0.494094\pi$
$659$	2.91451e8	−	2.91451e8i	1.01838	−	1.01838i	0.999828	−	0.0185521i	$-0.00590566\pi$
$660$		−	7.03973e6i		−	0.0244864i
$661$	2.54440e8			0.881009			0.440504	−	0.897750i	$-0.354800\pi$
$661$	2.54440e8			0.881009			0.440504	+	0.897750i	$0.354800\pi$
$662$	−4.79941e7			−0.165430
$663$	2.87096e8			0.985112
$664$	−5.16633e7	−	5.16633e7i	−0.176473	−	0.176473i
$665$	4.32267e7	+	4.32267e7i	0.146990	+	0.146990i
$666$			2.26996e8i			0.768416i
$667$	−9.87505e7	−	3.86384e8i	−0.332784	−	1.30209i
$668$	−3.79811e7			−0.127420
$669$	4.52624e7	−	4.52624e7i	0.151168	−	0.151168i
$670$	3.45297e7	−	3.45297e7i	0.114807	−	0.114807i
$671$			1.10476e8i			0.365680i
$672$			2.90156e8i			0.956144i
$673$			1.73379e8i			0.568789i	0.958707	+	0.284394i	$0.0917925\pi$
$673$			1.73379e8i			0.568789i	−0.958707	+	0.284394i	$0.908208\pi$
$674$	2.27490e8			0.742988
$675$	2.09990e8	+	2.09990e8i	0.682789	+	0.682789i
$676$			2.56464e8i			0.830208i
$677$	2.70931e8	+	2.70931e8i	0.873159	+	0.873159i	0.992815	−	0.119657i	$-0.0381793\pi$
$677$	2.70931e8	+	2.70931e8i	0.873159	+	0.873159i	−0.119657	+	0.992815i	$0.538179\pi$
$678$	−2.15361e8	+	2.15361e8i	−0.691000	+	0.691000i
$679$	−8.33940e7	−	8.33940e7i	−0.266395	−	0.266395i
$680$			1.74785e7i			0.0555874i
$681$	1.12164e8	−	1.12164e8i	0.355149	−	0.355149i
$682$	2.70676e8	+	2.70676e8i	0.853289	+	0.853289i
$683$	−3.67004e8			−1.15188			−0.575941	−	0.817491i	$-0.695364\pi$
$683$	−3.67004e8			−1.15188			−0.575941	+	0.817491i	$0.695364\pi$
$684$	−9.56147e7	+	9.56147e7i	−0.298783	+	0.298783i
$685$	2.34900e7	+	2.34900e7i	0.0730821	+	0.0730821i
$686$	−6.21890e8	+	6.21890e8i	−1.92638	+	1.92638i
$687$	−1.51219e8			−0.466376
$688$	1.98353e8	−	1.98353e8i	0.609078	−	0.609078i
$689$		−	5.24738e8i		−	1.60430i
$690$	2.77491e7			0.0844700
$691$	−3.17313e8			−0.961731			−0.480866	−	0.876794i	$-0.659677\pi$
$691$	−3.17313e8			−0.961731			−0.480866	+	0.876794i	$0.659677\pi$
$692$	5.80300e7			0.175119
$693$	−2.68895e8	−	2.68895e8i	−0.807947	−	0.807947i
$694$	2.17982e8	+	2.17982e8i	0.652143	+	0.652143i
$695$		−	2.09501e7i		−	0.0624068i
$696$	3.05904e7	+	1.19692e8i	0.0907315	+	0.355008i
$697$	6.34472e7			0.187376
$698$	4.31928e8	−	4.31928e8i	1.27012	−	1.27012i
$699$	−1.93567e8	+	1.93567e8i	−0.566761	+	0.566761i
$700$		−	3.00069e8i		−	0.874838i
$701$		−	3.08585e8i		−	0.895821i	−0.894078	−	0.447911i	$-0.852168\pi$
$701$		−	3.08585e8i		−	0.895821i	0.894078	−	0.447911i	$-0.147832\pi$
$702$		−	6.74526e8i		−	1.94979i
$703$	4.41438e8			1.27058
$704$	−3.54417e7	−	3.54417e7i	−0.101577	−	0.101577i
$705$			6.07372e6i			0.0173335i
$706$	1.47672e8	+	1.47672e8i	0.419647	+	0.419647i
$707$	−8.02185e7	+	8.02185e7i	−0.226995	+	0.226995i
$708$	5.84646e7	+	5.84646e7i	0.164738	+	0.164738i
$709$			2.81793e7i			0.0790663i	0.999218	+	0.0395331i	$0.0125871\pi$
$709$			2.81793e7i			0.0790663i	−0.999218	+	0.0395331i	$0.987413\pi$
$710$	1.72307e7	−	1.72307e7i	0.0481425	−	0.0481425i
$711$	8.16145e7	+	8.16145e7i	0.227069	+	0.227069i
$712$	−2.20548e8			−0.611032
$713$	−3.50765e8	+	3.50765e8i	−0.967716	+	0.967716i
$714$	3.39322e8	+	3.39322e8i	0.932217	+	0.932217i
$715$	−3.60551e7	+	3.60551e7i	−0.0986389	+	0.0986389i
$716$	−1.95361e8			−0.532229
$717$	−3.53112e7	+	3.53112e7i	−0.0957976	+	0.0957976i
$718$			3.13633e8i			0.847322i
$719$	−4.47387e8			−1.20364			−0.601820	−	0.798632i	$-0.705557\pi$
$719$	−4.47387e8			−1.20364			−0.601820	+	0.798632i	$0.705557\pi$
$720$	2.66952e7			0.0715214
$721$	−6.37855e8			−1.70183
$722$	2.40759e8	+	2.40759e8i	0.639691	+	0.639691i
$723$	−1.80305e8	−	1.80305e8i	−0.477081	−	0.477081i
$724$		−	2.90987e8i		−	0.766757i
$725$	−9.36386e7	−	3.66383e8i	−0.245720	−	0.961437i
$726$	−1.57667e7			−0.0412032
$727$	3.09341e8	−	3.09341e8i	0.805071	−	0.805071i	−0.178812	−	0.983883i	$-0.557225\pi$
$727$	3.09341e8	−	3.09341e8i	0.805071	−	0.805071i	0.983883	+	0.178812i	$0.0572255\pi$
$728$	5.02068e8	−	5.02068e8i	1.30127	−	1.30127i
$729$			2.01217e8i			0.519376i
$730$			2.17429e7i			0.0558920i
$731$		−	2.74544e8i		−	0.702845i
$732$	−4.25709e7			−0.108537
$733$	2.98498e8	+	2.98498e8i	0.757932	+	0.757932i	0.975946	−	0.218014i	$-0.0699579\pi$
$733$	2.98498e8	+	2.98498e8i	0.757932	+	0.757932i	−0.218014	+	0.975946i	$0.569958\pi$
$734$			1.37408e8i			0.347476i
$735$	−3.23860e7	−	3.23860e7i	−0.0815633	−	0.0815633i
$736$	−3.42056e8	+	3.42056e8i	−0.857953	+	0.857953i
$737$	4.17709e8	+	4.17709e8i	1.04345	+	1.04345i
$738$		−	5.89322e7i		−	0.146617i
$739$	−2.27802e8	+	2.27802e8i	−0.564448	+	0.564448i	−0.930568	−	0.366119i	$-0.880686\pi$
$739$	−2.27802e8	+	2.27802e8i	−0.564448	+	0.564448i	0.366119	+	0.930568i	$0.380686\pi$
$740$	1.18267e7	+	1.18267e7i	0.0291855	+	0.0291855i
$741$	−5.18582e8			−1.27457
$742$	6.20194e8	−	6.20194e8i	1.51815	−	1.51815i
$743$	−5.04192e8	−	5.04192e8i	−1.22922	−	1.22922i	−0.964259	−	0.264960i	$-0.914641\pi$
$743$	−5.04192e8	−	5.04192e8i	−1.22922	−	1.22922i	−0.264960	−	0.964259i	$-0.585359\pi$
$744$	1.08658e8	−	1.08658e8i	0.263842	−	0.263842i
$745$	5.90537e7			0.142816
$746$	−2.14159e8	+	2.14159e8i	−0.515846	+	0.515846i
$747$			1.09216e8i			0.262014i
$748$	2.02962e8			0.484964
$749$	−6.35589e8			−1.51262
$750$	5.28285e7			0.125223
$751$	4.97776e8	+	4.97776e8i	1.17521	+	1.17521i	0.980951	+	0.194256i	$0.0622291\pi$
$751$	4.97776e8	+	4.97776e8i	1.17521	+	1.17521i	0.194256	+	0.980951i	$0.437771\pi$
$752$	−1.26514e8	−	1.26514e8i	−0.297499	−	0.297499i
$753$		−	2.09153e8i		−	0.489869i
$754$	−4.38052e8	+	7.38837e8i	−1.02191	+	1.72359i
$755$	−1.99805e7			−0.0464265
$756$	2.62095e8	−	2.62095e8i	0.606587	−	0.606587i
$757$	3.43905e8	−	3.43905e8i	0.792776	−	0.792776i	−0.189169	−	0.981945i	$-0.560579\pi$
$757$	3.43905e8	−	3.43905e8i	0.792776	−	0.792776i	0.981945	+	0.189169i	$0.0605793\pi$
$758$		−	6.72730e8i		−	1.54466i
$759$			3.35684e8i			0.767724i
$760$		−	3.15714e7i		−	0.0719206i
$761$	5.14375e8			1.16715			0.583574	−	0.812060i	$-0.301654\pi$
$761$	5.14375e8			1.16715			0.583574	+	0.812060i	$0.301654\pi$
$762$	2.69038e8	+	2.69038e8i	0.608064	+	0.608064i
$763$		−	1.04511e9i		−	2.35281i
$764$	1.44327e8	+	1.44327e8i	0.323645	+	0.323645i
$765$	1.84747e7	−	1.84747e7i	0.0412660	−	0.0412660i
$766$	−5.04533e8	−	5.04533e8i	−1.12254	−	1.12254i
$767$		−	5.98870e8i		−	1.32723i
$768$	2.21330e8	−	2.21330e8i	0.488603	−	0.488603i
$769$	−2.98630e8	−	2.98630e8i	−0.656682	−	0.656682i	0.297912	−	0.954593i	$-0.403710\pi$
$769$	−2.98630e8	−	2.98630e8i	−0.656682	−	0.656682i	−0.954593	+	0.297912i	$0.903710\pi$
$770$	−8.52278e7			−0.186685
$771$	4.09337e7	−	4.09337e7i	0.0893137	−	0.0893137i
$772$	5.09281e7	+	5.09281e7i	0.110689	+	0.110689i
$773$	−1.33051e8	+	1.33051e8i	−0.288058	+	0.288058i	−0.836312	−	0.548254i	$-0.815293\pi$
$773$	−1.33051e8	+	1.33051e8i	−0.288058	+	0.288058i	0.548254	+	0.836312i	$0.315293\pi$
$774$	−2.55007e8			−0.549958
$775$	−3.32608e8	+	3.32608e8i	−0.714541	+	0.714541i
$776$			6.09083e7i			0.130344i
$777$	−4.78378e8			−1.01978
$778$	−9.04463e7			−0.192067
$779$	−1.14605e8			−0.242432
$780$	−1.38935e7	−	1.38935e7i	−0.0292770	−	0.0292770i
$781$	2.08441e8	+	2.08441e8i	0.437553	+	0.437553i
$782$			8.00032e8i			1.67297i
$783$	2.38227e8	−	4.01804e8i	0.496257	−	0.837007i
$784$	1.34918e9			2.79977
$785$	−5.51983e6	+	5.51983e6i	−0.0114108	+	0.0114108i
$786$	1.44379e8	−	1.44379e8i	0.297329	−	0.297329i
$787$		−	1.71032e6i		−	0.00350876i	−0.999998	−	0.00175438i	$-0.999442\pi$
$787$		−	1.71032e6i		−	0.00350876i	0.999998	−	0.00175438i	$-0.000558436\pi$
$788$		−	2.36464e8i		−	0.483267i
$789$		−	2.56946e8i		−	0.523132i
$790$	2.58682e7			0.0524669
$791$	8.57169e8	+	8.57169e8i	1.73196	+	1.73196i
$792$			1.96392e8i			0.395320i
$793$	2.18033e8	+	2.18033e8i	0.437223	+	0.437223i
$794$	−1.79273e8	+	1.79273e8i	−0.358141	+	0.358141i
$795$	1.78791e7	+	1.78791e7i	0.0355831	+	0.0355831i
$796$		−	2.42530e8i		−	0.480868i
$797$	9.07015e7	−	9.07015e7i	0.179159	−	0.179159i	−0.611830	−	0.790989i	$-0.709566\pi$
$797$	9.07015e7	−	9.07015e7i	0.179159	−	0.179159i	0.790989	+	0.611830i	$0.209566\pi$
$798$	−6.12918e8	−	6.12918e8i	−1.20613	−	1.20613i
$799$	−1.75111e8			−0.343298
$800$	−3.24349e8	+	3.24349e8i	−0.633494	+	0.633494i
$801$	2.33119e8	+	2.33119e8i	0.453607	+	0.453607i
$802$	1.00793e7	−	1.00793e7i	0.0195392	−	0.0195392i
$803$	−2.63026e8			−0.507987
$804$	−1.60960e8	+	1.60960e8i	−0.309706	+	0.309706i
$805$		−	1.10446e8i		−	0.211720i
$806$	1.06840e9			2.04046
$807$	2.56415e8			0.487891
$808$	5.85891e7			0.111066
$809$	2.95921e8	+	2.95921e8i	0.558894	+	0.558894i	0.928993	−	0.370098i	$-0.120676\pi$
$809$	2.95921e8	+	2.95921e8i	0.558894	+	0.558894i	−0.370098	+	0.928993i	$0.620676\pi$
$810$	−3.26321e6	−	3.26321e6i	−0.00614031	−	0.00614031i
$811$		−	7.39222e8i		−	1.38584i	−0.721016	−	0.692918i	$-0.756325\pi$
$811$		−	7.39222e8i		−	1.38584i	0.721016	−	0.692918i	$-0.243675\pi$
$812$	−4.57294e8	+	1.16873e8i	−0.854136	+	0.218297i
$813$	−1.77593e8			−0.330486
$814$	−4.35180e8	+	4.35180e8i	−0.806856	+	0.806856i
$815$	7.50436e6	−	7.50436e6i	0.0138625	−	0.0138625i
$816$		−	4.07515e8i		−	0.750020i
$817$			4.95910e8i			0.909361i
$818$			1.01334e9i			1.85138i
$819$	−1.06137e9			−1.93203
$820$	−3.07041e6	−	3.07041e6i	−0.00556871	−	0.00556871i
$821$			5.89279e8i			1.06486i	0.846475	+	0.532429i	$0.178721\pi$
$821$			5.89279e8i			1.06486i	−0.846475	+	0.532429i	$0.821279\pi$
$822$	−3.33068e8	−	3.33068e8i	−0.599678	−	0.599678i
$823$	−2.80724e8	+	2.80724e8i	−0.503594	+	0.503594i	−0.912553	−	0.408959i	$-0.865892\pi$
$823$	−2.80724e8	+	2.80724e8i	−0.503594	+	0.503594i	0.408959	+	0.912553i	$0.365892\pi$
$824$	2.32934e8	+	2.32934e8i	0.416344	+	0.416344i
$825$			3.18307e8i			0.566871i
$826$	7.07812e8	−	7.07812e8i	1.25597	−	1.25597i
$827$	−7.94539e7	−	7.94539e7i	−0.140475	−	0.140475i	0.633372	−	0.773847i	$-0.281670\pi$
$827$	−7.94539e7	−	7.94539e7i	−0.140475	−	0.140475i	−0.773847	+	0.633372i	$0.781670\pi$
$828$	2.44299e8			0.430359
$829$	−5.49081e8	+	5.49081e8i	−0.963769	+	0.963769i	−0.999366	−	0.0355970i	$-0.988667\pi$
$829$	−5.49081e8	+	5.49081e8i	−0.963769	+	0.963769i	0.0355970	+	0.999366i	$0.488667\pi$
$830$	1.73083e7	+	1.73083e7i	0.0302706	+	0.0302706i
$831$	−1.26362e8	+	1.26362e8i	−0.220198	+	0.220198i
$832$	−1.39894e8			−0.242900
$833$	9.33715e8	−	9.33715e8i	1.61540	−	1.61540i
$834$			2.97055e8i			0.512081i
$835$	−1.32559e7			−0.0227694
$836$	−3.66610e8			−0.627460
$837$	−5.81030e8			−0.990883
$838$	4.11943e8	+	4.11943e8i	0.700012	+	0.700012i
$839$	6.87348e8	+	6.87348e8i	1.16383	+	1.16383i	0.983629	+	0.180205i	$0.0576761\pi$
$839$	6.87348e8	+	6.87348e8i	1.16383	+	1.16383i	0.180205	+	0.983629i	$0.442324\pi$
$840$			3.42133e7i			0.0577242i
$841$	−5.21881e8	+	2.85403e8i	−0.877372	+	0.479811i
$842$	−1.20571e9			−2.01979
$843$	−1.37325e8	+	1.37325e8i	−0.229228	+	0.229228i
$844$	−1.30746e8	+	1.30746e8i	−0.217470	+	0.217470i
$845$			8.95096e7i			0.148354i
$846$			1.62649e8i			0.268622i
$847$			6.27538e7i			0.103274i
$848$	−7.44833e8			−1.22144
$849$	4.38220e6	+	4.38220e6i	0.00716093	+	0.00716093i
$850$			7.58617e8i			1.23528i
$851$	−5.63945e8	−	5.63945e8i	−0.915057	−	0.915057i
$852$	−8.03208e7	+	8.03208e7i	−0.129870	+	0.129870i
$853$	1.08077e8	+	1.08077e8i	0.174135	+	0.174135i	0.788793	−	0.614658i	$-0.210706\pi$
$853$	1.08077e8	+	1.08077e8i	0.174135	+	0.174135i	−0.614658	+	0.788793i	$0.710706\pi$
$854$			5.15393e8i			0.827493i
$855$	−3.33709e7	+	3.33709e7i	−0.0533911	+	0.0533911i
$856$	2.32107e8	+	2.32107e8i	0.370056	+	0.370056i
$857$	7.15568e8			1.13686			0.568432	−	0.822730i	$-0.307550\pi$
$857$	7.15568e8			1.13686			0.568432	+	0.822730i	$0.307550\pi$
$858$	5.11231e8	−	5.11231e8i	0.809385	−	0.809385i
$859$	−4.77828e8	−	4.77828e8i	−0.753862	−	0.753862i	0.221335	−	0.975198i	$-0.428958\pi$
$859$	−4.77828e8	−	4.77828e8i	−0.753862	−	0.753862i	−0.975198	+	0.221335i	$0.928958\pi$
$860$	−1.32860e7	+	1.32860e7i	−0.0208882	+	0.0208882i
$861$	1.24195e8			0.194579
$862$	9.70714e8	−	9.70714e8i	1.51555	−	1.51555i
$863$			1.15308e7i			0.0179402i	0.999960	+	0.00897011i	$0.00285531\pi$
$863$			1.15308e7i			0.0179402i	−0.999960	+	0.00897011i	$0.997145\pi$
$864$	−5.66603e8			−0.878491
$865$	2.02533e7			0.0312930
$866$	−3.61254e8			−0.556236
$867$	−1.08830e7	−	1.08830e7i	−0.0166991	−	0.0166991i
$868$	4.15138e8	+	4.15138e8i	0.634795	+	0.634795i
$869$			3.12930e8i			0.476857i
$870$	−1.02485e7	−	4.00995e7i	−0.0155633	−	0.0608949i
$871$	1.64876e9			2.49519
$872$	−3.81657e8	+	3.81657e8i	−0.575604	+	0.575604i
$873$	6.43799e7	−	6.43799e7i	0.0967626	−	0.0967626i
$874$		−	1.44510e9i		−	2.16453i
$875$		−	2.10265e8i		−	0.313865i
$876$		−	1.01354e8i		−	0.150775i
$877$	6.30768e8			0.935128			0.467564	−	0.883959i	$-0.345132\pi$
$877$	6.30768e8			0.935128			0.467564	+	0.883959i	$0.345132\pi$
$878$	−5.79766e8	−	5.79766e8i	−0.856582	−	0.856582i
$879$		−	4.25532e7i		−	0.0626564i
$880$	5.11780e7	+	5.11780e7i	0.0750992	+	0.0750992i
$881$	1.65385e8	−	1.65385e8i	0.241862	−	0.241862i	−0.575758	−	0.817620i	$-0.695293\pi$
$881$	1.65385e8	−	1.65385e8i	0.241862	−	0.241862i	0.817620	+	0.575758i	$0.195293\pi$
$882$	−8.67271e8	−	8.67271e8i	−1.26401	−	1.26401i
$883$			6.73181e8i			0.977799i	0.872340	+	0.488899i	$0.162602\pi$
$883$			6.73181e8i			0.977799i	−0.872340	+	0.488899i	$0.837398\pi$
$884$	4.00560e8	−	4.00560e8i	0.579844	−	0.579844i
$885$	2.04050e7	+	2.04050e7i	0.0294378	+	0.0294378i
$886$	−4.26881e8			−0.613770
$887$	7.32579e8	−	7.32579e8i	1.04975	−	1.04975i	0.0510489	−	0.998696i	$-0.483744\pi$
$887$	7.32579e8	−	7.32579e8i	1.04975	−	1.04975i	0.998696	−	0.0510489i	$-0.0162564\pi$
$888$	1.74696e8	+	1.74696e8i	0.249485	+	0.249485i
$889$	1.07081e9	−	1.07081e9i	1.52408	−	1.52408i
$890$	7.38885e7			0.104811
$891$	3.94754e7	−	3.94754e7i	0.0558076	−	0.0558076i
$892$		−	1.26302e8i		−	0.177957i
$893$	3.16303e8			0.444169
$894$	−8.37332e8			−1.17188
$895$	−6.81837e7			−0.0951068
$896$	−9.91910e8	−	9.91910e8i	−1.37895	−	1.37895i
$897$	6.62498e8	+	6.62498e8i	0.917925	+	0.917925i
$898$		−	1.32008e9i		−	1.82294i
$899$	6.36427e8	+	3.77334e8i	0.875930	+	0.519334i
$900$	2.31653e8			0.317768
$901$	−5.15469e8	+	5.15469e8i	−0.704739	+	0.704739i
$902$	1.12980e8	−	1.12980e8i	0.153951	−	0.153951i
$903$		−	5.37408e8i		−	0.729862i
$904$		−	6.26049e8i		−	0.847429i
$905$		−	1.01558e8i		−	0.137016i
$906$	2.83307e8			0.380954
$907$	6.97953e8	+	6.97953e8i	0.935415	+	0.935415i	0.998037	−	0.0626219i	$-0.0199462\pi$
$907$	6.97953e8	+	6.97953e8i	0.935415	+	0.935415i	−0.0626219	+	0.998037i	$0.519946\pi$
$908$		−	3.12985e8i		−	0.418086i
$909$	−6.19285e7	−	6.19285e7i	−0.0824515	−	0.0824515i
$910$	−1.68204e8	+	1.68204e8i	−0.223209	+	0.223209i
$911$	−2.08682e8	−	2.08682e8i	−0.276013	−	0.276013i	0.555502	−	0.831515i	$-0.312526\pi$
$911$	−2.08682e8	−	2.08682e8i	−0.276013	−	0.276013i	−0.831515	+	0.555502i	$0.812526\pi$
$912$			7.36095e8i			0.970397i
$913$	−2.09381e8	+	2.09381e8i	−0.275121	+	0.275121i
$914$	8.52243e8	+	8.52243e8i	1.11616	+	1.11616i
$915$	−1.48578e7			−0.0193951
$916$	−2.10983e8	+	2.10983e8i	−0.274512	+	0.274512i
$917$	−5.74652e8	−	5.74652e8i	−0.745241	−	0.745241i
$918$	−6.62612e8	+	6.62612e8i	−0.856508	+	0.856508i
$919$	−2.84238e8			−0.366214			−0.183107	−	0.983093i	$-0.558616\pi$
$919$	−2.84238e8			−0.366214			−0.183107	+	0.983093i	$0.558616\pi$
$920$	−4.03331e7	+	4.03331e7i	−0.0517962	+	0.0517962i
$921$		−	4.13127e8i		−	0.528816i
$922$	−1.45710e8			−0.185908
$923$	8.22750e8			1.04632
$924$	3.97289e8			0.503606
$925$	−5.34751e8	−	5.34751e8i	−0.675658	−	0.675658i
$926$	−1.35500e8	−	1.35500e8i	−0.170650	−	0.170650i
$927$		−	4.92422e8i		−	0.618156i
$928$	6.20624e8	+	3.67965e8i	0.776577	+	0.460428i
$929$	−1.03881e9			−1.29566			−0.647830	−	0.761785i	$-0.724323\pi$
$929$	−1.03881e9			−1.29566			−0.647830	+	0.761785i	$0.724323\pi$
$930$	−3.64029e7	+	3.64029e7i	−0.0452571	+	0.0452571i
$931$	−1.68657e9	+	1.68657e9i	−2.09005	+	2.09005i
$932$			5.40136e8i			0.667198i
$933$		−	4.83364e8i		−	0.595154i
$934$		−	1.07429e9i		−	1.31851i
$935$	7.08364e7			0.0866607
$936$	3.87595e8	+	3.87595e8i	0.472662	+	0.472662i
$937$		−	8.40955e8i		−	1.02224i	−0.859509	−	0.511121i	$-0.829230\pi$
$937$		−	8.40955e8i		−	1.02224i	0.859509	−	0.511121i	$-0.170770\pi$
$938$	1.94869e9	+	1.94869e9i	2.36121	+	2.36121i
$939$	9.56978e7	−	9.56978e7i	0.115586	−	0.115586i
$940$	8.47415e6	+	8.47415e6i	0.0102026	+	0.0102026i
$941$		−	9.40596e8i		−	1.12884i	−0.825486	−	0.564422i	$-0.809099\pi$
$941$		−	9.40596e8i		−	1.12884i	0.825486	−	0.564422i	$-0.190901\pi$
$942$	7.82665e7	−	7.82665e7i	0.0936318	−	0.0936318i
$943$	1.46410e8	+	1.46410e8i	0.174596	+	0.174596i
$944$	−8.50061e8			−1.01049
$945$	9.14747e7	−	9.14747e7i	0.108394	−	0.108394i
$946$	−4.88880e8	−	4.88880e8i	−0.577469	−	0.577469i
$947$	−4.36143e8	+	4.36143e8i	−0.513546	+	0.513546i	−0.915611	−	0.402065i	$-0.868292\pi$
$947$	−4.36143e8	+	4.36143e8i	−0.513546	+	0.513546i	0.402065	+	0.915611i	$0.368292\pi$
$948$	−1.20584e8			−0.141536
$949$	−5.19102e8	+	5.19102e8i	−0.607371	+	0.607371i
$950$		−	1.37029e9i		−	1.59824i
$951$	4.06549e8			0.472685
$952$	−9.86400e8			−1.14325
$953$	−1.19474e9			−1.38037			−0.690183	−	0.723635i	$-0.742470\pi$
$953$	−1.19474e9			−1.38037			−0.690183	+	0.723635i	$0.742470\pi$
$954$	4.78788e8	+	4.78788e8i	0.551440	+	0.551440i
$955$	5.03723e7	+	5.03723e7i	0.0578337	+	0.0578337i
$956$			9.85334e7i			0.112774i
$957$	4.85087e8	−	1.23977e8i	0.553457	−	0.141450i
$958$	−8.63628e8			−0.982268
$959$	−1.32566e9	+	1.32566e9i	−1.50306	+	1.50306i
$960$	4.76651e6	−	4.76651e6i	0.00538750	−	0.00538750i
$961$		−	3.28035e7i		−	0.0369616i
$962$			1.71772e9i			1.92942i
$963$		−	4.90673e8i		−	0.549431i
$964$	−5.03128e8			−0.561627
$965$	1.77746e7	+	1.77746e7i	0.0197796	+	0.0197796i
$966$			1.56603e9i			1.73727i
$967$	1.36268e8	+	1.36268e8i	0.150701	+	0.150701i	0.778431	−	0.627730i	$-0.216016\pi$
$967$	1.36268e8	+	1.36268e8i	0.150701	+	0.150701i	−0.627730	+	0.778431i	$0.716016\pi$
$968$	2.29167e7	−	2.29167e7i	0.0252654	−	0.0252654i
$969$	5.09422e8	+	5.09422e8i	0.559895	+	0.559895i
$970$		−	2.04056e7i		−	0.0223581i
$971$	5.95877e8	−	5.95877e8i	0.650877	−	0.650877i	−0.302327	−	0.953204i	$-0.597763\pi$
$971$	5.95877e8	−	5.95877e8i	0.650877	−	0.650877i	0.953204	+	0.302327i	$0.0977635\pi$
$972$	3.24682e8	+	3.24682e8i	0.353557	+	0.353557i
$973$	1.18232e9			1.28351
$974$	5.78561e8	−	5.78561e8i	0.626141	−	0.626141i
$975$	6.28203e8	+	6.28203e8i	0.677776	+	0.677776i
$976$	3.09485e8	−	3.09485e8i	0.332882	−	0.332882i
$977$	−4.62516e7			−0.0495956			−0.0247978	−	0.999692i	$-0.507894\pi$
$977$	−4.62516e7			−0.0495956			−0.0247978	+	0.999692i	$0.507894\pi$
$978$	−1.06406e8	+	1.06406e8i	−0.113749	+	0.113749i
$979$			8.93836e8i			0.952598i
$980$	−9.03708e7			−0.0960174
$981$	8.06820e8			0.854613
$982$	−7.17836e8			−0.758037
$983$	5.66244e7	+	5.66244e7i	0.0596133	+	0.0596133i	0.736285	−	0.676672i	$-0.236578\pi$
$983$	5.66244e7	+	5.66244e7i	0.0596133	+	0.0596133i	−0.676672	+	0.736285i	$0.736578\pi$
$984$	−4.53541e7	−	4.53541e7i	−0.0476027	−	0.0476027i
$985$		−	8.25293e7i		−	0.0863574i
$986$	1.15610e9	−	2.95472e8i	1.20605	−	0.308238i
$987$	−3.42771e8			−0.356495
$988$	−7.23534e8	+	7.23534e8i	−0.750219	+	0.750219i
$989$	6.33534e8	−	6.33534e8i	0.654909	−	0.654909i
$990$		−	6.57957e7i		−	0.0678097i
$991$		−	4.98287e8i		−	0.511987i	−0.966678	−	0.255994i	$-0.917597\pi$
$991$		−	4.98287e8i		−	0.511987i	0.966678	−	0.255994i	$-0.0824026\pi$
$992$		−	8.97455e8i		−	0.919344i
$993$	7.80828e7			0.0797457
$994$	9.72419e8	+	9.72419e8i	0.990135	+	0.990135i
$995$		−	8.46462e7i		−	0.0859287i
$996$	−8.06827e7	−	8.06827e7i	−0.0816587	−	0.0816587i
$997$	−4.20740e8	+	4.20740e8i	−0.424550	+	0.424550i	−0.886767	−	0.462217i	$-0.847054\pi$
$997$	−4.20740e8	+	4.20740e8i	−0.424550	+	0.424550i	0.462217	+	0.886767i	$0.347054\pi$
$998$	5.84629e8	+	5.84629e8i	0.588151	+	0.588151i
$999$		−	9.34154e8i		−	0.936962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.7.c.a.17.3	yes	28
29.12	odd	4	inner	29.7.c.a.12.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.7.c.a.12.3	✓	28	29.12	odd	4	inner
29.7.c.a.17.3	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)

\(f(q)\)	\(=\)	\(q+(-6.90454 + 6.90454i) q^{2} +(11.2332 - 11.2332i) q^{3} -31.3454i q^{4} -10.9400i q^{5} +155.120i q^{6} +617.401 q^{7} +(-225.465 - 225.465i) q^{8} +476.632i q^{9} +O(q^{10})\)	\(q+(-6.90454 + 6.90454i) q^{2} +(11.2332 - 11.2332i) q^{3} -31.3454i q^{4} -10.9400i q^{5} +155.120i q^{6} +617.401 q^{7} +(-225.465 - 225.465i) q^{8} +476.632i q^{9} +(75.5356 + 75.5356i) q^{10} +(-913.761 + 913.761i) q^{11} +(-352.109 - 352.109i) q^{12} +3606.76i q^{13} +(-4262.87 + 4262.87i) q^{14} +(-122.891 - 122.891i) q^{15} +5119.57 q^{16} +(3543.05 - 3543.05i) q^{17} +(-3290.92 - 3290.92i) q^{18} +(-6399.82 + 6399.82i) q^{19} -342.919 q^{20} +(6935.37 - 6935.37i) q^{21} -12618.2i q^{22} +16351.8 q^{23} -5065.37 q^{24} +15505.3 q^{25} +(-24903.0 - 24903.0i) q^{26} +(13543.1 + 13543.1i) q^{27} -19352.7i q^{28} +(-6039.13 - 23629.5i) q^{29} +1697.01 q^{30} +(-21451.2 + 21451.2i) q^{31} +(-20918.5 + 20918.5i) q^{32} +20528.9i q^{33} +48926.3i q^{34} -6754.35i q^{35} +14940.2 q^{36} +(-34488.3 - 34488.3i) q^{37} -88375.7i q^{38} +(40515.3 + 40515.3i) q^{39} +(-2466.58 + 2466.58i) q^{40} +(8953.75 + 8953.75i) q^{41} +95771.1i q^{42} +(38744.0 - 38744.0i) q^{43} +(28642.2 + 28642.2i) q^{44} +5214.34 q^{45} +(-112902. + 112902. i) q^{46} +(-24711.8 - 24711.8i) q^{47} +(57509.0 - 57509.0i) q^{48} +263534. q^{49} +(-107057. + 107057. i) q^{50} -79599.4i q^{51} +113055. q^{52} -145487. q^{53} -187017. q^{54} +(9996.54 + 9996.54i) q^{55} +(-139202. - 139202. i) q^{56} +143781. i q^{57} +(204848. + 121453. i) q^{58} -166041. q^{59} +(-3852.06 + 3852.06i) q^{60} +(60451.4 - 60451.4i) q^{61} -296221. i q^{62} +294273. i q^{63} +38786.6i q^{64} +39457.9 q^{65} +(-141743. - 141743. i) q^{66} -457131. i q^{67} +(-111058. - 111058. i) q^{68} +(183683. - 183683. i) q^{69} +(46635.7 + 46635.7i) q^{70} -228114. i q^{71} +(107464. - 107464. i) q^{72} +(143925. + 143925. i) q^{73} +476251. q^{74} +(174174. - 174174. i) q^{75} +(200605. + 200605. i) q^{76} +(-564157. + 564157. i) q^{77} -559479. q^{78} +(171232. - 171232. i) q^{79} -56008.1i q^{80} -43201.0 q^{81} -123643. q^{82} +229141. q^{83} +(-217392. - 217392. i) q^{84} +(-38760.9 - 38760.9i) q^{85} +535020. i q^{86} +(-333273. - 197596. i) q^{87} +412042. q^{88} +(489097. - 489097. i) q^{89} +(-36002.7 + 36002.7i) q^{90} +2.22681e6i q^{91} -512554. i q^{92} +481930. i q^{93} +341248. q^{94} +(70014.0 + 70014.0i) q^{95} +469963. i q^{96} +(-135073. - 135073. i) q^{97} +(-1.81958e6 + 1.81958e6i) q^{98} +(-435527. - 435527. 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