LMFDB - Embedded newform 5.9.c.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,9,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	5.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:	$2.03689305031$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} - 30x^{3} + 1089x^{2} - 3168x + 4608 $ x^6 - 2x^5 + 2x^4 - 30x^3 + 1089x^2 - 3168*x + 4608
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.2
Root			$-4.23471 + 4.23471i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.9.c.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.39608 - 4.39608i) q^{2} +(75.2981 - 75.2981i) q^{3} -217.349i q^{4} +(-14.1685 + 624.839i) q^{5} -662.032 q^{6} +(730.992 + 730.992i) q^{7} +(-2080.88 + 2080.88i) q^{8} -4778.60i q^{9} +O(q^{10})$	\(q+(-4.39608 - 4.39608i) q^{2} +(75.2981 - 75.2981i) q^{3} -217.349i q^{4} +(-14.1685 + 624.839i) q^{5} -662.032 q^{6} +(730.992 + 730.992i) q^{7} +(-2080.88 + 2080.88i) q^{8} -4778.60i q^{9} +(2809.13 - 2684.56i) q^{10} +19599.8 q^{11} +(-16366.0 - 16366.0i) q^{12} +(-24915.1 + 24915.1i) q^{13} -6426.99i q^{14} +(45982.3 + 48116.1i) q^{15} -37346.0 q^{16} +(-11288.6 - 11288.6i) q^{17} +(-21007.1 + 21007.1i) q^{18} -171525. i q^{19} +(135808. + 3079.51i) q^{20} +110085. q^{21} +(-86162.2 - 86162.2i) q^{22} +(-132074. + 132074. i) q^{23} +313372. i q^{24} +(-390224. - 17706.1i) q^{25} +219057. q^{26} +(134211. + 134211. i) q^{27} +(158880. - 158880. i) q^{28} -127019. i q^{29} +(9380.00 - 413664. i) q^{30} -960715. q^{31} +(696880. + 696880. i) q^{32} +(1.47583e6 - 1.47583e6i) q^{33} +99251.5i q^{34} +(-467110. + 446396. i) q^{35} -1.03862e6 q^{36} +(-243873. - 243873. i) q^{37} +(-754036. + 754036. i) q^{38} +3.75212e6i q^{39} +(-1.27073e6 - 1.32970e6i) q^{40} +2.50747e6 q^{41} +(-483940. - 483940. i) q^{42} +(-6763.95 + 6763.95i) q^{43} -4.26000e6i q^{44} +(2.98586e6 + 67705.6i) q^{45} +1.16122e6 q^{46} +(-1.79394e6 - 1.79394e6i) q^{47} +(-2.81208e6 + 2.81208e6i) q^{48} -4.69610e6i q^{49} +(1.63761e6 + 1.79329e6i) q^{50} -1.70003e6 q^{51} +(5.41527e6 + 5.41527e6i) q^{52} +(-2.97161e6 + 2.97161e6i) q^{53} -1.18001e6i q^{54} +(-277700. + 1.22467e7i) q^{55} -3.04221e6 q^{56} +(-1.29155e7 - 1.29155e7i) q^{57} +(-558385. + 558385. i) q^{58} +313805. i q^{59} +(1.04580e7 - 9.99422e6i) q^{60} +1.76977e7 q^{61} +(4.22338e6 + 4.22338e6i) q^{62} +(3.49312e6 - 3.49312e6i) q^{63} +3.43349e6i q^{64} +(-1.52149e7 - 1.59209e7i) q^{65} -1.29757e7 q^{66} +(4.41349e6 + 4.41349e6i) q^{67} +(-2.45358e6 + 2.45358e6i) q^{68} +1.98899e7i q^{69} +(4.01584e6 + 91060.8i) q^{70} -8.89315e6 q^{71} +(9.94368e6 + 9.94368e6i) q^{72} +(1.95076e7 - 1.95076e7i) q^{73} +2.14417e6i q^{74} +(-3.07163e7 + 2.80498e7i) q^{75} -3.72808e7 q^{76} +(1.43273e7 + 1.43273e7i) q^{77} +(1.64946e7 - 1.64946e7i) q^{78} -1.11272e7i q^{79} +(529136. - 2.33352e7i) q^{80} +5.15641e7 q^{81} +(-1.10230e7 - 1.10230e7i) q^{82} +(1.58712e7 - 1.58712e7i) q^{83} -2.39268e7i q^{84} +(7.21353e6 - 6.89365e6i) q^{85} +59469.7 q^{86} +(-9.56429e6 - 9.56429e6i) q^{87} +(-4.07848e7 + 4.07848e7i) q^{88} +4.85032e7i q^{89} +(-1.28284e7 - 1.34237e7i) q^{90} -3.64255e7 q^{91} +(2.87062e7 + 2.87062e7i) q^{92} +(-7.23400e7 + 7.23400e7i) q^{93} +1.57726e7i q^{94} +(1.07176e8 + 2.43025e6i) q^{95} +1.04948e8 q^{96} +(-1.07411e8 - 1.07411e8i) q^{97} +(-2.06444e7 + 2.06444e7i) q^{98} -9.36596e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 72 q^{3} + 220 q^{5} + 1752 q^{6} - 2352 q^{7} - 8220 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 72 * q^3 + 220 * q^5 + 1752 * q^6 - 2352 * q^7 - 8220 * q^8	\( 6 q - 2 q^{2} - 72 q^{3} + 220 q^{5} + 1752 q^{6} - 2352 q^{7} - 8220 q^{8} + 30870 q^{10} + 23192 q^{11} - 45912 q^{12} - 119142 q^{13} + 241440 q^{15} + 218616 q^{16} - 265502 q^{17} - 454062 q^{18} + 412260 q^{20} + 231672 q^{21} - 35664 q^{22} + 28888 q^{23} - 340350 q^{25} - 801388 q^{26} + 392040 q^{27} + 1305192 q^{28} - 2549760 q^{30} - 747648 q^{31} + 3033928 q^{32} + 4269096 q^{33} - 4971680 q^{35} - 3972804 q^{36} - 454002 q^{37} + 1443720 q^{38} + 2683500 q^{40} + 2489432 q^{41} + 4223856 q^{42} + 792648 q^{43} + 210690 q^{45} - 3149928 q^{46} - 15313352 q^{47} - 21677712 q^{48} + 29537650 q^{50} + 35567712 q^{51} - 735732 q^{52} - 13509122 q^{53} + 4448040 q^{55} - 18454800 q^{56} - 34625520 q^{57} - 23903520 q^{58} + 13688520 q^{60} + 24111192 q^{61} + 53913416 q^{62} + 44837688 q^{63} - 30943610 q^{65} - 55047936 q^{66} - 32827752 q^{67} + 8118692 q^{68} - 44156280 q^{70} - 13992928 q^{71} + 82596420 q^{72} + 111859638 q^{73} - 126793200 q^{75} - 56470800 q^{76} + 26260136 q^{77} + 31125576 q^{78} + 23045920 q^{80} + 65834226 q^{81} + 38023056 q^{82} - 14768432 q^{83} - 19713030 q^{85} - 135560008 q^{86} - 133207680 q^{87} - 44555040 q^{88} + 135147990 q^{90} + 167542032 q^{91} + 69931048 q^{92} - 96798024 q^{93} + 239661000 q^{95} + 184867872 q^{96} - 186656202 q^{97} - 345959698 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 72 * q^3 + 220 * q^5 + 1752 * q^6 - 2352 * q^7 - 8220 * q^8 + 30870 * q^10 + 23192 * q^11 - 45912 * q^12 - 119142 * q^13 + 241440 * q^15 + 218616 * q^16 - 265502 * q^17 - 454062 * q^18 + 412260 * q^20 + 231672 * q^21 - 35664 * q^22 + 28888 * q^23 - 340350 * q^25 - 801388 * q^26 + 392040 * q^27 + 1305192 * q^28 - 2549760 * q^30 - 747648 * q^31 + 3033928 * q^32 + 4269096 * q^33 - 4971680 * q^35 - 3972804 * q^36 - 454002 * q^37 + 1443720 * q^38 + 2683500 * q^40 + 2489432 * q^41 + 4223856 * q^42 + 792648 * q^43 + 210690 * q^45 - 3149928 * q^46 - 15313352 * q^47 - 21677712 * q^48 + 29537650 * q^50 + 35567712 * q^51 - 735732 * q^52 - 13509122 * q^53 + 4448040 * q^55 - 18454800 * q^56 - 34625520 * q^57 - 23903520 * q^58 + 13688520 * q^60 + 24111192 * q^61 + 53913416 * q^62 + 44837688 * q^63 - 30943610 * q^65 - 55047936 * q^66 - 32827752 * q^67 + 8118692 * q^68 - 44156280 * q^70 - 13992928 * q^71 + 82596420 * q^72 + 111859638 * q^73 - 126793200 * q^75 - 56470800 * q^76 + 26260136 * q^77 + 31125576 * q^78 + 23045920 * q^80 + 65834226 * q^81 + 38023056 * q^82 - 14768432 * q^83 - 19713030 * q^85 - 135560008 * q^86 - 133207680 * q^87 - 44555040 * q^88 + 135147990 * q^90 + 167542032 * q^91 + 69931048 * q^92 - 96798024 * q^93 + 239661000 * q^95 + 184867872 * q^96 - 186656202 * q^97 - 345959698 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−4.39608	−	4.39608i	−0.274755	−	0.274755i	0.556256	−	0.831011i	$-0.312237\pi$
$2$	−4.39608	−	4.39608i	−0.274755	−	0.274755i	−0.831011	+	0.556256i	$0.812237\pi$
$3$	75.2981	−	75.2981i	0.929606	−	0.929606i	−0.0680745	−	0.997680i	$-0.521686\pi$
$3$	75.2981	−	75.2981i	0.929606	−	0.929606i	0.997680	+	0.0680745i	$0.0216855\pi$
$4$		−	217.349i		−	0.849020i
$5$	−14.1685	+	624.839i	−0.0226696	+	0.999743i
$5$	−14.1685	+	624.839i	−0.0226696	+	0.999743i
$6$	−662.032			−0.510827
$7$	730.992	+	730.992i	0.304453	+	0.304453i	0.842753	−	0.538300i	$-0.180933\pi$
$7$	730.992	+	730.992i	0.304453	+	0.304453i	−0.538300	+	0.842753i	$0.680933\pi$
$8$	−2080.88	+	2080.88i	−0.508027	+	0.508027i
$9$		−	4778.60i		−	0.728334i
$10$	2809.13	−	2684.56i	0.280913	−	0.268456i
$11$	19599.8			1.33869			0.669347	−	0.742950i	$-0.266574\pi$
$11$	19599.8			1.33869			0.669347	+	0.742950i	$0.266574\pi$
$12$	−16366.0	−	16366.0i	−0.789254	−	0.789254i
$13$	−24915.1	+	24915.1i	−0.872347	+	0.872347i	−0.992728	−	0.120381i	$-0.961588\pi$
$13$	−24915.1	+	24915.1i	−0.872347	+	0.872347i	0.120381	+	0.992728i	$0.461588\pi$
$14$		−	6426.99i		−	0.167300i
$15$	45982.3	+	48116.1i	0.908293	+	0.950441i
$16$	−37346.0			−0.569854
$17$	−11288.6	−	11288.6i	−0.135159	−	0.135159i	0.636290	−	0.771450i	$-0.280468\pi$
$17$	−11288.6	−	11288.6i	−0.135159	−	0.135159i	−0.771450	+	0.636290i	$0.780468\pi$
$18$	−21007.1	+	21007.1i	−0.200113	+	0.200113i
$19$		−	171525.i		−	1.31617i	−0.752943	−	0.658086i	$-0.771366\pi$
$19$		−	171525.i		−	1.31617i	0.752943	−	0.658086i	$-0.228634\pi$
$20$	135808.	+	3079.51i	0.848802	+	0.0192469i
$21$	110085.			0.566043
$22$	−86162.2	−	86162.2i	−0.367812	−	0.367812i
$23$	−132074.	+	132074.i	−0.471961	+	0.471961i	−0.902549	−	0.430587i	$-0.858306\pi$
$23$	−132074.	+	132074.i	−0.471961	+	0.471961i	0.430587	+	0.902549i	$0.358306\pi$
$24$			313372.i			0.944529i
$25$	−390224.	−	17706.1i	−0.998972	−	0.0453275i
$26$	219057.			0.479363
$27$	134211.	+	134211.i	0.252542	+	0.252542i
$28$	158880.	−	158880.i	0.258487	−	0.258487i
$29$		−	127019.i		−	0.179588i	−0.995960	−	0.0897939i	$-0.971379\pi$
$29$		−	127019.i		−	0.179588i	0.995960	−	0.0897939i	$-0.0286208\pi$
$30$	9380.00	−	413664.i	0.0115802	−	0.510696i
$31$	−960715.			−1.04027			−0.520137	−	0.854083i	$-0.674119\pi$
$31$	−960715.			−1.04027			−0.520137	+	0.854083i	$0.674119\pi$
$32$	696880.	+	696880.i	0.664597	+	0.664597i
$33$	1.47583e6	−	1.47583e6i	1.24446	−	1.24446i
$34$			99251.5i			0.0742713i
$35$	−467110.	+	446396.i	−0.311277	+	0.297473i
$36$	−1.03862e6			−0.618370
$37$	−243873.	−	243873.i	−0.130124	−	0.130124i	0.639045	−	0.769169i	$-0.279330\pi$
$37$	−243873.	−	243873.i	−0.130124	−	0.130124i	−0.769169	+	0.639045i	$0.779330\pi$
$38$	−754036.	+	754036.i	−0.361625	+	0.361625i
$39$			3.75212e6i			1.62188i
$40$	−1.27073e6	−	1.32970e6i	−0.496380	−	0.519413i
$41$	2.50747e6			0.887360			0.443680	−	0.896185i	$-0.353673\pi$
$41$	2.50747e6			0.887360			0.443680	+	0.896185i	$0.353673\pi$
$42$	−483940.	−	483940.i	−0.155523	−	0.155523i
$43$	−6763.95	+	6763.95i	−0.00197846	+	0.00197846i	−0.708095	−	0.706117i	$-0.750445\pi$
$43$	−6763.95	+	6763.95i	−0.00197846	+	0.00197846i	0.706117	+	0.708095i	$0.250445\pi$
$44$		−	4.26000e6i		−	1.13658i
$45$	2.98586e6	+	67705.6i	0.728147	+	0.0165110i
$46$	1.16122e6			0.259347
$47$	−1.79394e6	−	1.79394e6i	−0.367635	−	0.367635i	0.498979	−	0.866614i	$-0.333709\pi$
$47$	−1.79394e6	−	1.79394e6i	−0.367635	−	0.367635i	−0.866614	+	0.498979i	$0.833709\pi$
$48$	−2.81208e6	+	2.81208e6i	−0.529740	+	0.529740i
$49$		−	4.69610e6i		−	0.814617i
$50$	1.63761e6	+	1.79329e6i	0.262018	+	0.286926i
$51$	−1.70003e6			−0.251290
$52$	5.41527e6	+	5.41527e6i	0.740640	+	0.740640i
$53$	−2.97161e6	+	2.97161e6i	−0.376608	+	0.376608i	−0.869877	−	0.493269i	$-0.835802\pi$
$53$	−2.97161e6	+	2.97161e6i	−0.376608	+	0.376608i	0.493269	+	0.869877i	$0.335802\pi$
$54$		−	1.18001e6i		−	0.138774i
$55$	−277700.	+	1.22467e7i	−0.0303476	+	1.33835i
$56$	−3.04221e6			−0.309341
$57$	−1.29155e7	−	1.29155e7i	−1.22352	−	1.22352i
$58$	−558385.	+	558385.i	−0.0493426	+	0.0493426i
$59$			313805.i			0.0258972i	0.999916	+	0.0129486i	$0.00412178\pi$
$59$			313805.i			0.0258972i	−0.999916	+	0.0129486i	$0.995878\pi$
$60$	1.04580e7	−	9.99422e6i	0.806943	−	0.771159i
$61$	1.76977e7			1.27820			0.639098	−	0.769125i	$-0.279308\pi$
$61$	1.76977e7			1.27820			0.639098	+	0.769125i	$0.279308\pi$
$62$	4.22338e6	+	4.22338e6i	0.285820	+	0.285820i
$63$	3.49312e6	−	3.49312e6i	0.221744	−	0.221744i
$64$			3.43349e6i			0.204652i
$65$	−1.52149e7	−	1.59209e7i	−0.852347	−	0.891899i
$66$	−1.29757e7			−0.683841
$67$	4.41349e6	+	4.41349e6i	0.219020	+	0.219020i	0.808085	−	0.589066i	$-0.200504\pi$
$67$	4.41349e6	+	4.41349e6i	0.219020	+	0.219020i	−0.589066	+	0.808085i	$0.700504\pi$
$68$	−2.45358e6	+	2.45358e6i	−0.114753	+	0.114753i
$69$			1.98899e7i			0.877476i
$70$	4.01584e6	+	91060.8i	0.167257	+	0.00379262i
$71$	−8.89315e6			−0.349963			−0.174982	−	0.984572i	$-0.555987\pi$
$71$	−8.89315e6			−0.349963			−0.174982	+	0.984572i	$0.555987\pi$
$72$	9.94368e6	+	9.94368e6i	0.370013	+	0.370013i
$73$	1.95076e7	−	1.95076e7i	0.686928	−	0.686928i	−0.274624	−	0.961552i	$-0.588553\pi$
$73$	1.95076e7	−	1.95076e7i	0.686928	−	0.686928i	0.961552	+	0.274624i	$0.0885532\pi$
$74$			2.14417e6i			0.0715043i
$75$	−3.07163e7	+	2.80498e7i	−0.970787	+	0.886514i
$76$	−3.72808e7			−1.11746
$77$	1.43273e7	+	1.43273e7i	0.407569	+	0.407569i
$78$	1.64946e7	−	1.64946e7i	0.445619	−	0.445619i
$79$		−	1.11272e7i		−	0.285680i	−0.989746	−	0.142840i	$-0.954377\pi$
$79$		−	1.11272e7i		−	0.285680i	0.989746	−	0.142840i	$-0.0456234\pi$
$80$	529136.	−	2.33352e7i	0.0129184	−	0.569708i
$81$	5.15641e7			1.19786
$82$	−1.10230e7	−	1.10230e7i	−0.243806	−	0.243806i
$83$	1.58712e7	−	1.58712e7i	0.334423	−	0.334423i	−0.519840	−	0.854264i	$-0.674008\pi$
$83$	1.58712e7	−	1.58712e7i	0.334423	−	0.334423i	0.854264	+	0.519840i	$0.174008\pi$
$84$		−	2.39268e7i		−	0.480581i
$85$	7.21353e6	−	6.89365e6i	0.138189	−	0.132061i
$86$	59469.7			0.00108718
$87$	−9.56429e6	−	9.56429e6i	−0.166946	−	0.166946i
$88$	−4.07848e7	+	4.07848e7i	−0.680092	+	0.680092i
$89$			4.85032e7i			0.773056i	0.922278	+	0.386528i	$0.126326\pi$
$89$			4.85032e7i			0.773056i	−0.922278	+	0.386528i	$0.873674\pi$
$90$	−1.28284e7	−	1.34237e7i	−0.195525	−	0.204598i
$91$	−3.64255e7			−0.531178
$92$	2.87062e7	+	2.87062e7i	0.400704	+	0.400704i
$93$	−7.23400e7	+	7.23400e7i	−0.967045	+	0.967045i
$94$			1.57726e7i			0.202019i
$95$	1.07176e8	+	2.43025e6i	1.31583	+	0.0298371i
$96$	1.04948e8			1.23563
$97$	−1.07411e8	−	1.07411e8i	−1.21329	−	1.21329i	−0.969939	−	0.243348i	$-0.921754\pi$
$97$	−1.07411e8	−	1.07411e8i	−1.21329	−	1.21329i	−0.243348	−	0.969939i	$-0.578246\pi$
$98$	−2.06444e7	+	2.06444e7i	−0.223820	+	0.223820i
$99$		−	9.36596e7i		−	0.975016i
$100$	−3.84840e6	+	8.48147e7i	−0.0384840	+	0.848147i
$101$	−7.16023e7			−0.688084			−0.344042	−	0.938954i	$-0.611796\pi$
$101$	−7.16023e7			−0.688084			−0.344042	+	0.938954i	$0.611796\pi$
$102$	7.47344e6	+	7.47344e6i	0.0690431	+	0.0690431i
$103$	9.89158e7	−	9.89158e7i	0.878854	−	0.878854i	−0.114562	−	0.993416i	$-0.536546\pi$
$103$	9.89158e7	−	9.89158e7i	0.878854	−	0.878854i	0.993416	+	0.114562i	$0.0365464\pi$
$104$		−	1.03691e8i		−	0.886352i
$105$	−1.55973e6	+	6.87852e7i	−0.0128320	+	0.565897i
$106$	2.61269e7			0.206949
$107$	4.73497e7	+	4.73497e7i	0.361228	+	0.361228i	0.864265	−	0.503037i	$-0.167784\pi$
$107$	4.73497e7	+	4.73497e7i	0.361228	+	0.361228i	−0.503037	+	0.864265i	$0.667784\pi$
$108$	2.91707e7	−	2.91707e7i	0.214414	−	0.214414i
$109$			2.29072e7i			0.162280i	0.996703	+	0.0811401i	$0.0258561\pi$
$109$			2.29072e7i			0.162280i	−0.996703	+	0.0811401i	$0.974144\pi$
$110$	5.50583e7	−	5.26168e7i	0.376056	−	0.359380i
$111$	−3.67264e7			−0.241928
$112$	−2.72996e7	−	2.72996e7i	−0.173494	−	0.173494i
$113$	−1.95361e8	+	1.95361e8i	−1.19819	+	1.19819i	−0.223480	+	0.974709i	$0.571742\pi$
$113$	−1.95361e8	+	1.95361e8i	−1.19819	+	1.19819i	−0.974709	+	0.223480i	$0.928258\pi$
$114$			1.13555e8i			0.672337i
$115$	−8.06538e7	−	8.43964e7i	−0.461141	−	0.482539i
$116$	−2.76075e7			−0.152474
$117$	1.19059e8	+	1.19059e8i	0.635360	+	0.635360i
$118$	1.37951e6	−	1.37951e6i	0.00711537	−	0.00711537i
$119$		−	1.65038e7i		−	0.0822994i
$120$	−1.95807e8	−	4.44001e6i	−0.944287	−	0.0214121i
$121$	1.69794e8			0.792100
$122$	−7.78004e7	−	7.78004e7i	−0.351190	−	0.351190i
$123$	1.88808e8	−	1.88808e8i	0.824895	−	0.824895i
$124$			2.08811e8i			0.883213i
$125$	1.65923e7	−	2.43576e8i	0.0679622	−	0.997688i
$126$	−3.07120e7			−0.121850
$127$	1.84792e8	+	1.84792e8i	0.710343	+	0.710343i	0.966607	−	0.256264i	$-0.0824917\pi$
$127$	1.84792e8	+	1.84792e8i	0.710343	+	0.710343i	−0.256264	+	0.966607i	$0.582492\pi$
$128$	1.93495e8	−	1.93495e8i	0.720826	−	0.720826i
$129$			1.01862e6i			0.00367837i
$130$	−3.10371e6	+	1.36876e8i	−0.0108670	+	0.479240i
$131$	−3.05076e8			−1.03591			−0.517956	−	0.855407i	$-0.673307\pi$
$131$	−3.05076e8			−1.03591			−0.517956	+	0.855407i	$0.673307\pi$
$132$	−3.20770e8	−	3.20770e8i	−1.05657	−	1.05657i
$133$	1.25383e8	−	1.25383e8i	0.400713	−	0.400713i
$134$		−	3.88041e7i		−	0.120353i
$135$	−8.57622e7	+	8.19590e7i	−0.258203	+	0.246753i
$136$	4.69806e7			0.137329
$137$	3.75735e8	+	3.75735e8i	1.06659	+	1.06659i	0.997618	+	0.0689766i	$0.0219734\pi$
$137$	3.75735e8	+	3.75735e8i	1.06659	+	1.06659i	0.0689766	+	0.997618i	$0.478027\pi$
$138$	8.74373e7	−	8.74373e7i	0.241091	−	0.241091i
$139$			1.10575e8i			0.296208i	0.988972	+	0.148104i	$0.0473171\pi$
$139$			1.10575e8i			0.296208i	−0.988972	+	0.148104i	$0.952683\pi$
$140$	9.70236e7	+	1.01526e8i	0.252560	+	0.264280i
$141$	−2.70161e8			−0.683512
$142$	3.90950e7	+	3.90950e7i	0.0961540	+	0.0961540i
$143$	−4.88331e8	+	4.88331e8i	−1.16781	+	1.16781i
$144$			1.78461e8i			0.415044i
$145$	7.93665e7	+	1.79967e6i	0.179542	+	0.00407118i
$146$	−1.71513e8			−0.377474
$147$	−3.53607e8	−	3.53607e8i	−0.757272	−	0.757272i
$148$	−5.30056e7	+	5.30056e7i	−0.110478	+	0.110478i
$149$		−	7.23744e8i		−	1.46838i	−0.678942	−	0.734192i	$-0.737561\pi$
$149$		−	7.23744e8i		−	1.46838i	0.678942	−	0.734192i	$-0.262439\pi$
$150$	2.58340e8	+	1.17220e7i	0.510302	+	0.0231545i
$151$	7.67246e8			1.47580			0.737899	−	0.674911i	$-0.235818\pi$
$151$	7.67246e8			1.47580			0.737899	+	0.674911i	$0.235818\pi$
$152$	3.56922e8	+	3.56922e8i	0.668651	+	0.668651i
$153$	−5.39439e7	+	5.39439e7i	−0.0984411	+	0.0984411i
$154$		−	1.25968e8i		−	0.223963i
$155$	1.36119e7	−	6.00293e8i	0.0235826	−	1.04001i
$156$	8.15519e8			1.37701
$157$	−8.03264e8	−	8.03264e8i	−1.32209	−	1.32209i	−0.912085	−	0.410001i	$-0.865528\pi$
$157$	−8.03264e8	−	8.03264e8i	−1.32209	−	1.32209i	−0.410001	−	0.912085i	$-0.634472\pi$
$158$	−4.89162e7	+	4.89162e7i	−0.0784918	+	0.0784918i
$159$			4.47514e8i			0.700193i
$160$	−4.45312e8	+	4.25565e8i	−0.679492	+	0.649360i
$161$	−1.93090e8			−0.287380
$162$	−2.26680e8	−	2.26680e8i	−0.329119	−	0.329119i
$163$	−4.34915e8	+	4.34915e8i	−0.616103	+	0.616103i	−0.944530	−	0.328426i	$-0.893482\pi$
$163$	−4.34915e8	+	4.34915e8i	−0.616103	+	0.616103i	0.328426	+	0.944530i	$0.393482\pi$
$164$		−	5.44996e8i		−	0.753386i
$165$	9.01245e8	+	9.43066e8i	1.21593	+	1.27235i
$166$	−1.39542e8			−0.183769
$167$	7.16803e8	+	7.16803e8i	0.921582	+	0.921582i	0.997141	−	0.0755590i	$-0.0240741\pi$
$167$	7.16803e8	+	7.16803e8i	0.921582	+	0.921582i	−0.0755590	+	0.997141i	$0.524074\pi$
$168$	−2.29073e8	+	2.29073e8i	−0.287565	+	0.287565i
$169$		−	4.25794e8i		−	0.521979i
$170$	−6.20162e7	−	1.40624e6i	−0.0742522	−	0.00168370i
$171$	−8.19649e8			−0.958613
$172$	1.47014e6	+	1.47014e6i	0.00167975	+	0.00167975i
$173$	3.40359e8	−	3.40359e8i	0.379973	−	0.379973i	−0.491119	−	0.871092i	$-0.663412\pi$
$173$	3.40359e8	−	3.40359e8i	0.379973	−	0.379973i	0.871092	+	0.491119i	$0.163412\pi$
$174$			8.40907e7i			0.0917383i
$175$	−2.72307e8	−	2.98193e8i	−0.290340	−	0.317940i
$176$	−7.31974e8			−0.762860
$177$	2.36289e7	+	2.36289e7i	0.0240741	+	0.0240741i
$178$	2.13224e8	−	2.13224e8i	0.212401	−	0.212401i
$179$			1.29181e9i			1.25830i	0.777283	+	0.629151i	$0.216597\pi$
$179$			1.29181e9i			1.25830i	−0.777283	+	0.629151i	$0.783403\pi$
$180$	1.47157e7	−	6.48973e8i	0.0140182	−	0.618211i
$181$	1.92912e8			0.179740			0.0898700	−	0.995954i	$-0.471355\pi$
$181$	1.92912e8			0.179740			0.0898700	+	0.995954i	$0.471355\pi$
$182$	1.60129e8	+	1.60129e8i	0.145944	+	0.145944i
$183$	1.33260e9	−	1.33260e9i	1.18822	−	1.18822i
$184$		−	5.49660e8i		−	0.479538i
$185$	1.55837e8	−	1.48926e8i	0.133040	−	0.127141i
$186$	6.36024e8			0.531400
$187$	−2.21255e8	−	2.21255e8i	−0.180937	−	0.180937i
$188$	−3.89912e8	+	3.89912e8i	−0.312130	+	0.312130i
$189$			1.96215e8i			0.153775i
$190$	−4.60468e8	−	4.81835e8i	−0.353334	−	0.369729i
$191$	7.64646e8			0.574549			0.287274	−	0.957848i	$-0.407251\pi$
$191$	7.64646e8			0.574549			0.287274	+	0.957848i	$0.407251\pi$
$192$	2.58535e8	+	2.58535e8i	0.190246	+	0.190246i
$193$	1.15389e8	−	1.15389e8i	0.0831641	−	0.0831641i	−0.664301	−	0.747465i	$-0.731271\pi$
$193$	1.15389e8	−	1.15389e8i	0.0831641	−	0.0831641i	0.747465	+	0.664301i	$0.231271\pi$
$194$			9.44378e8i			0.666713i
$195$	−2.34447e9	−	5.31619e7i	−1.62146	−	0.0367673i
$196$	−1.02069e9			−0.691626
$197$	−9.95415e7	−	9.95415e7i	−0.0660906	−	0.0660906i	0.673289	−	0.739379i	$-0.264881\pi$
$197$	−9.95415e7	−	9.95415e7i	−0.0660906	−	0.0660906i	−0.739379	+	0.673289i	$0.764881\pi$
$198$	−4.11735e8	+	4.11735e8i	−0.267890	+	0.267890i
$199$			1.71187e9i			1.09159i	0.837919	+	0.545795i	$0.183772\pi$
$199$			1.71187e9i			1.09159i	−0.837919	+	0.545795i	$0.816228\pi$
$200$	8.48852e8	−	7.75163e8i	0.530532	−	0.484477i
$201$	6.64655e8			0.407204
$202$	3.14769e8	+	3.14769e8i	0.189054	+	0.189054i
$203$	9.28499e7	−	9.28499e7i	0.0546761	−	0.0546761i
$204$			3.69499e8i			0.213350i
$205$	−3.55271e7	+	1.56676e9i	−0.0201161	+	0.887132i
$206$	−8.69683e8			−0.482939
$207$	6.31129e8	+	6.31129e8i	0.343745	+	0.343745i
$208$	9.30479e8	−	9.30479e8i	0.497111	−	0.497111i
$209$		−	3.36185e9i		−	1.76195i
$210$	3.09242e8	−	2.95528e8i	0.159009	−	0.151957i
$211$	−6.81230e8			−0.343688			−0.171844	−	0.985124i	$-0.554972\pi$
$211$	−6.81230e8			−0.343688			−0.171844	+	0.985124i	$0.554972\pi$
$212$	6.45878e8	+	6.45878e8i	0.319747	+	0.319747i
$213$	−6.69637e8	+	6.69637e8i	−0.325328	+	0.325328i
$214$		−	4.16305e8i		−	0.198498i
$215$	−4.13055e6	−	4.32222e6i	−0.00193310	−	0.00202280i
$216$	−5.58555e8			−0.256597
$217$	−7.02275e8	−	7.02275e8i	−0.316715	−	0.316715i
$218$	1.00702e8	−	1.00702e8i	0.0445872	−	0.0445872i
$219$		−	2.93776e9i		−	1.27715i
$220$	2.66182e9	+	6.03578e7i	1.13628	+	0.0257657i
$221$	5.62515e8			0.235812
$222$	1.61452e8	+	1.61452e8i	0.0664708	+	0.0664708i
$223$	9.37608e8	−	9.37608e8i	0.379142	−	0.379142i	−0.491651	−	0.870793i	$-0.663606\pi$
$223$	9.37608e8	−	9.37608e8i	0.379142	−	0.379142i	0.870793	+	0.491651i	$0.163606\pi$
$224$			1.01883e9i			0.404677i
$225$	−8.46102e7	+	1.86472e9i	−0.0330136	+	0.727585i
$226$	1.71765e9			0.658416
$227$	−3.47956e9	−	3.47956e9i	−1.31045	−	1.31045i	−0.921082	−	0.389368i	$-0.872693\pi$
$227$	−3.47956e9	−	3.47956e9i	−1.31045	−	1.31045i	−0.389368	−	0.921082i	$-0.627307\pi$
$228$	−2.80717e9	+	2.80717e9i	−1.03879	+	1.03879i
$229$			3.67273e9i			1.33551i	0.744382	+	0.667754i	$0.232744\pi$
$229$			3.67273e9i			1.33551i	−0.744382	+	0.667754i	$0.767256\pi$
$230$	−1.64527e7	+	7.25573e8i	−0.00587930	+	0.259281i
$231$	2.15764e9			0.757758
$232$	2.64311e8	+	2.64311e8i	0.0912354	+	0.0912354i
$233$	−3.62893e9	+	3.62893e9i	−1.23128	+	1.23128i	−0.267801	+	0.963474i	$0.586297\pi$
$233$	−3.62893e9	+	3.62893e9i	−1.23128	+	1.23128i	−0.963474	+	0.267801i	$0.913703\pi$
$234$		−	1.04679e9i		−	0.349136i
$235$	1.14634e9	−	1.09551e9i	0.375875	−	0.359207i
$236$	6.82053e7			0.0219872
$237$	−8.37860e8	−	8.37860e8i	−0.265569	−	0.265569i
$238$	−7.25520e7	+	7.25520e7i	−0.0226121	+	0.0226121i
$239$			2.64336e9i			0.810148i	0.914284	+	0.405074i	$0.132754\pi$
$239$			2.64336e9i			0.810148i	−0.914284	+	0.405074i	$0.867246\pi$
$240$	−1.71725e9	−	1.79694e9i	−0.517595	−	0.541613i
$241$	−7.20231e7			−0.0213503			−0.0106751	−	0.999943i	$-0.503398\pi$
$241$	−7.20231e7			−0.0213503			−0.0106751	+	0.999943i	$0.503398\pi$
$242$	−7.46425e8	−	7.46425e8i	−0.217633	−	0.217633i
$243$	3.00212e9	−	3.00212e9i	0.860999	−	0.860999i
$244$		−	3.84658e9i		−	1.08521i
$245$	2.93431e9	+	6.65367e7i	0.814407	+	0.0184670i
$246$	−1.66002e9			−0.453288
$247$	4.27356e9	+	4.27356e9i	1.14816	+	1.14816i
$248$	1.99913e9	−	1.99913e9i	0.528487	−	0.528487i
$249$		−	2.39014e9i		−	0.621764i
$250$	−1.14372e9	+	9.97838e8i	−0.292792	+	0.255447i
$251$	5.78911e7			0.0145854			0.00729268	−	0.999973i	$-0.497679\pi$
$251$	5.78911e7			0.0145854			0.00729268	+	0.999973i	$0.497679\pi$
$252$	−7.59226e8	−	7.59226e8i	−0.188265	−	0.188265i
$253$	−2.58863e9	+	2.58863e9i	−0.631811	+	0.631811i
$254$		−	1.62472e9i		−	0.390340i
$255$	2.40868e7	−	1.06224e9i	0.00569664	−	0.251225i
$256$	−8.22267e8			−0.191449
$257$	−4.73425e8	−	4.73425e8i	−0.108522	−	0.108522i	0.650761	−	0.759283i	$-0.274450\pi$
$257$	−4.73425e8	−	4.73425e8i	−0.108522	−	0.108522i	−0.759283	+	0.650761i	$0.774450\pi$
$258$	4.47795e6	−	4.47795e6i	0.00101065	−	0.00101065i
$259$		−	3.56539e8i		−	0.0792333i
$260$	−3.46040e9	+	3.30695e9i	−0.757240	+	0.723660i
$261$	−6.06973e8			−0.130800
$262$	1.34114e9	+	1.34114e9i	0.284622	+	0.284622i
$263$	6.55957e9	−	6.55957e9i	1.37105	−	1.37105i	0.512155	−	0.858893i	$-0.328847\pi$
$263$	6.55957e9	−	6.55957e9i	1.37105	−	1.37105i	0.858893	−	0.512155i	$-0.171153\pi$
$264$			6.14204e9i			1.26444i
$265$	−1.81468e9	−	1.89889e9i	−0.367973	−	0.385048i
$266$	−1.10239e9			−0.220195
$267$	3.65220e9	+	3.65220e9i	0.718637	+	0.718637i
$268$	9.59269e8	−	9.59269e8i	0.185952	−	0.185952i
$269$			5.38818e9i			1.02904i	0.857478	+	0.514521i	$0.172030\pi$
$269$			5.38818e9i			1.02904i	−0.857478	+	0.514521i	$0.827970\pi$
$270$	7.37315e8	+	1.67189e7i	0.138739	+	0.00314596i
$271$	−8.79497e9			−1.63064			−0.815318	−	0.579013i	$-0.803438\pi$
$271$	−8.79497e9			−1.63064			−0.815318	+	0.579013i	$0.803438\pi$
$272$	4.21585e8	+	4.21585e8i	0.0770211	+	0.0770211i
$273$	−2.74277e9	+	2.74277e9i	−0.493786	+	0.493786i
$274$		−	3.30352e9i		−	0.586104i
$275$	−7.64831e9	−	3.47036e8i	−1.33732	−	0.0606797i
$276$	4.32304e9			0.744994
$277$	−4.78151e9	−	4.78151e9i	−0.812168	−	0.812168i	0.172790	−	0.984959i	$-0.444722\pi$
$277$	−4.78151e9	−	4.78151e9i	−0.812168	−	0.812168i	−0.984959	+	0.172790i	$0.944722\pi$
$278$	4.86096e8	−	4.86096e8i	0.0813846	−	0.0813846i
$279$			4.59087e9i			0.757667i
$280$	4.31035e7	−	1.90089e9i	0.00701263	−	0.309261i
$281$	1.22255e10			1.96083			0.980416	−	0.196936i	$-0.0630990\pi$
$281$	1.22255e10			1.96083			0.980416	+	0.196936i	$0.0630990\pi$
$282$	1.18765e9	+	1.18765e9i	0.187798	+	0.187798i
$283$	−2.86857e8	+	2.86857e8i	−0.0447219	+	0.0447219i	−0.729114	−	0.684392i	$-0.760068\pi$
$283$	−2.86857e8	+	2.86857e8i	−0.0447219	+	0.0447219i	0.684392	+	0.729114i	$0.260068\pi$
$284$			1.93292e9i			0.297126i
$285$	8.25310e9	−	7.88712e9i	1.25094	−	1.19547i
$286$	4.29348e9			0.641720
$287$	1.83294e9	+	1.83294e9i	0.270160	+	0.270160i
$288$	3.33011e9	−	3.33011e9i	0.484048	−	0.484048i
$289$		−	6.72089e9i		−	0.963464i
$290$	−3.40990e8	−	3.56813e8i	−0.0482113	−	0.0504485i
$291$	−1.61757e10			−2.25576
$292$	−4.23995e9	−	4.23995e9i	−0.583216	−	0.583216i
$293$	−1.02814e9	+	1.02814e9i	−0.139503	+	0.139503i	−0.773410	−	0.633907i	$-0.781450\pi$
$293$	−1.02814e9	+	1.02814e9i	−0.139503	+	0.139503i	0.633907	+	0.773410i	$0.281450\pi$
$294$			3.10897e9i			0.416128i
$295$	−1.96078e8	−	4.44615e6i	−0.0258905	−	0.000587078i
$296$	1.01494e9			0.132213
$297$	2.63052e9	+	2.63052e9i	0.338077	+	0.338077i
$298$	−3.18163e9	+	3.18163e9i	−0.403445	+	0.403445i
$299$		−	6.58128e9i		−	0.823428i
$300$	6.09661e9	+	6.67616e9i	0.752667	+	0.824217i
$301$	−9.88879e6			−0.00120469
$302$	−3.37287e9	−	3.37287e9i	−0.405482	−	0.405482i
$303$	−5.39151e9	+	5.39151e9i	−0.639647	+	0.639647i
$304$			6.40576e9i			0.750026i
$305$	−2.50750e8	+	1.10582e10i	−0.0289762	+	1.27787i
$306$	4.74283e8			0.0540943
$307$	7.92159e9	+	7.92159e9i	0.891783	+	0.891783i	0.994691	−	0.102908i	$-0.0328148\pi$
$307$	7.92159e9	+	7.92159e9i	0.891783	+	0.891783i	−0.102908	+	0.994691i	$0.532815\pi$
$308$	3.11403e9	−	3.11403e9i	0.346034	−	0.346034i
$309$		−	1.48963e10i		−	1.63398i
$310$	−2.69877e9	+	2.57909e9i	−0.292226	+	0.279267i
$311$	3.74059e9			0.399851			0.199926	−	0.979811i	$-0.435930\pi$
$311$	3.74059e9			0.399851			0.199926	+	0.979811i	$0.435930\pi$
$312$	−7.80770e9	−	7.80770e9i	−0.823958	−	0.823958i
$313$	−4.79633e9	+	4.79633e9i	−0.499725	+	0.499725i	−0.911352	−	0.411627i	$-0.864961\pi$
$313$	−4.79633e9	+	4.79633e9i	−0.499725	+	0.499725i	0.411627	+	0.911352i	$0.364961\pi$
$314$			7.06242e9i			0.726499i
$315$	2.13314e9	+	2.23213e9i	0.216660	+	0.226713i
$316$	−2.41850e9			−0.242548
$317$	−5.54903e9	−	5.54903e9i	−0.549516	−	0.549516i	0.376785	−	0.926301i	$-0.377030\pi$
$317$	−5.54903e9	−	5.54903e9i	−0.549516	−	0.549516i	−0.926301	+	0.376785i	$0.877030\pi$
$318$	1.96730e9	−	1.96730e9i	0.192381	−	0.192381i
$319$		−	2.48955e9i		−	0.240413i
$320$	−2.14538e9	−	4.86474e7i	−0.204599	−	0.00463937i
$321$	7.13068e9			0.671600
$322$	8.48839e8	+	8.48839e8i	0.0789591	+	0.0789591i
$323$	−1.93628e9	+	1.93628e9i	−0.177893	+	0.177893i
$324$		−	1.12074e10i		−	1.01701i
$325$	1.01636e10	−	9.28131e9i	0.910992	−	0.831909i
$326$	3.82384e9			0.338555
$327$	1.72487e9	+	1.72487e9i	0.150857	+	0.150857i
$328$	−5.21774e9	+	5.21774e9i	−0.450803	+	0.450803i
$329$		−	2.62272e9i		−	0.223855i
$330$	1.83846e8	−	8.10773e9i	0.0155024	−	0.683665i
$331$	1.49782e10			1.24780			0.623902	−	0.781503i	$-0.285546\pi$
$331$	1.49782e10			1.24780			0.623902	+	0.781503i	$0.285546\pi$
$332$	−3.44958e9	−	3.44958e9i	−0.283932	−	0.283932i
$333$	−1.16537e9	+	1.16537e9i	−0.0947737	+	0.0947737i
$334$		−	6.30224e9i		−	0.506418i
$335$	−2.82026e9	+	2.69519e9i	−0.223929	+	0.213998i
$336$	−4.11121e9			−0.322562
$337$	6.29203e9	+	6.29203e9i	0.487833	+	0.487833i	0.907622	−	0.419789i	$-0.137896\pi$
$337$	6.29203e9	+	6.29203e9i	0.487833	+	0.487833i	−0.419789	+	0.907622i	$0.637896\pi$
$338$	−1.87182e9	+	1.87182e9i	−0.143416	+	0.143416i
$339$			2.94207e10i			2.22769i
$340$	−1.49833e9	−	1.56785e9i	−0.112122	−	0.117325i
$341$	−1.88298e10			−1.39261
$342$	3.60324e9	+	3.60324e9i	0.263383	+	0.263383i
$343$	7.64684e9	−	7.64684e9i	0.552466	−	0.552466i
$344$		−	2.81499e7i		−	0.00201022i
$345$	−1.24280e10	−	2.81809e8i	−0.877251	−	0.0198920i
$346$	−2.99249e9			−0.208799
$347$	−8.28230e9	−	8.28230e9i	−0.571259	−	0.571259i	0.361221	−	0.932480i	$-0.382360\pi$
$347$	−8.28230e9	−	8.28230e9i	−0.571259	−	0.571259i	−0.932480	+	0.361221i	$0.882360\pi$
$348$	−2.07879e9	+	2.07879e9i	−0.141740	+	0.141740i
$349$			1.11611e10i			0.752328i	0.926553	+	0.376164i	$0.122757\pi$
$349$			1.11611e10i			0.752328i	−0.926553	+	0.376164i	$0.877243\pi$
$350$	−1.13797e8	+	2.50796e9i	−0.00758329	+	0.167128i
$351$	−6.68778e9			−0.440609
$352$	1.36587e10	+	1.36587e10i	0.889692	+	0.889692i
$353$	1.05904e10	−	1.05904e10i	0.682047	−	0.682047i	−0.278414	−	0.960461i	$-0.589809\pi$
$353$	1.05904e10	−	1.05904e10i	0.682047	−	0.682047i	0.960461	+	0.278414i	$0.0898088\pi$
$354$		−	2.07749e8i		−	0.0132290i
$355$	1.26003e8	−	5.55679e9i	0.00793352	−	0.349873i
$356$	1.05421e10			0.656339
$357$	−1.24271e9	−	1.24271e9i	−0.0765060	−	0.0765060i
$358$	5.67888e9	−	5.67888e9i	0.345725	−	0.345725i
$359$		−	9.48530e9i		−	0.571049i	−0.958371	−	0.285524i	$-0.907832\pi$
$359$		−	9.48530e9i		−	0.571049i	0.958371	−	0.285524i	$-0.0921677\pi$
$360$	−6.35409e9	+	6.07232e9i	−0.378306	+	0.361530i
$361$	−1.24372e10			−0.732309
$362$	−8.48055e8	−	8.48055e8i	−0.0493844	−	0.0493844i
$363$	1.27851e10	−	1.27851e10i	0.736340	−	0.736340i
$364$			7.91704e9i			0.450980i
$365$	1.19127e10	+	1.24655e10i	0.671179	+	0.702324i
$366$	−1.17164e10			−0.652937
$367$	−9.59996e9	−	9.59996e9i	−0.529182	−	0.529182i	0.391146	−	0.920329i	$-0.372079\pi$
$367$	−9.59996e9	−	9.59996e9i	−0.529182	−	0.529182i	−0.920329	+	0.391146i	$0.872079\pi$
$368$	4.93244e9	−	4.93244e9i	0.268949	−	0.268949i
$369$		−	1.19822e10i		−	0.646295i
$370$	−1.33976e9	−	3.03797e7i	−0.0714860	−	0.00162097i
$371$	−4.34445e9			−0.229319
$372$	1.57230e10	+	1.57230e10i	0.821040	+	0.821040i
$373$	8.48382e9	−	8.48382e9i	0.438285	−	0.438285i	−0.453150	−	0.891434i	$-0.649700\pi$
$373$	8.48382e9	−	8.48382e9i	0.438285	−	0.438285i	0.891434	+	0.453150i	$0.149700\pi$
$374$			1.94531e9i			0.0994265i
$375$	−1.70914e10	−	1.95902e10i	−0.864278	−	0.990634i
$376$	7.46595e9			0.373537
$377$	3.16469e9	+	3.16469e9i	0.156663	+	0.156663i
$378$	8.62576e8	−	8.62576e8i	0.0422503	−	0.0422503i
$379$			2.19075e10i			1.06178i	0.847440	+	0.530891i	$0.178143\pi$
$379$			2.19075e10i			1.06178i	−0.847440	+	0.530891i	$0.821857\pi$
$380$	5.28212e8	−	2.32945e10i	0.0253323	−	1.11717i
$381$	2.78289e10			1.32068
$382$	−3.36144e9	−	3.36144e9i	−0.157860	−	0.157860i
$383$	−2.31285e10	+	2.31285e10i	−1.07486	+	1.07486i	−0.0778987	+	0.996961i	$0.524821\pi$
$383$	−2.31285e10	+	2.31285e10i	−1.07486	+	1.07486i	−0.996961	+	0.0778987i	$0.975179\pi$
$384$		−	2.91396e10i		−	1.34017i
$385$	−9.15526e9	+	8.74927e9i	−0.416704	+	0.398225i
$386$	−1.01452e9			−0.0456995
$387$	3.23222e7	+	3.23222e7i	0.00144098	+	0.00144098i
$388$	−2.33458e10	+	2.33458e10i	−1.03010	+	1.03010i
$389$			2.23175e10i			0.974647i	0.873221	+	0.487324i	$0.162027\pi$
$389$			2.23175e10i			0.974647i	−0.873221	+	0.487324i	$0.837973\pi$
$390$	1.00728e10	+	1.05402e10i	0.435402	+	0.455606i
$391$	2.98188e9			0.127580
$392$	9.77202e9	+	9.77202e9i	0.413847	+	0.413847i
$393$	−2.29716e10	+	2.29716e10i	−0.962989	+	0.962989i
$394$			8.75184e8i			0.0363174i
$395$	6.95274e9	+	1.57656e8i	0.285606	+	0.00647624i
$396$	−2.03568e10			−0.827807
$397$	−2.26036e10	−	2.26036e10i	−0.909947	−	0.909947i	0.0863200	−	0.996267i	$-0.472489\pi$
$397$	−2.26036e10	−	2.26036e10i	−0.909947	−	0.909947i	−0.996267	+	0.0863200i	$0.972489\pi$
$398$	7.52553e9	−	7.52553e9i	0.299919	−	0.299919i
$399$		−	1.88822e10i		−	0.745010i
$400$	1.45733e10	+	6.61250e8i	0.569268	+	0.0258301i
$401$	1.77913e10			0.688064			0.344032	−	0.938958i	$-0.388207\pi$
$401$	1.77913e10			0.688064			0.344032	+	0.938958i	$0.388207\pi$
$402$	−2.92187e9	−	2.92187e9i	−0.111881	−	0.111881i
$403$	2.39363e10	−	2.39363e10i	0.907480	−	0.907480i
$404$			1.55627e10i			0.584197i
$405$	−7.30586e8	+	3.22193e10i	−0.0271551	+	1.19756i
$406$	−8.16350e8			−0.0300450
$407$	−4.77987e9	−	4.77987e9i	−0.174196	−	0.174196i
$408$	3.53755e9	−	3.53755e9i	0.127662	−	0.127662i
$409$		−	4.37112e10i		−	1.56206i	−0.624490	−	0.781032i	$-0.714693\pi$
$409$		−	4.37112e10i		−	1.56206i	0.624490	−	0.781032i	$-0.285307\pi$
$410$	7.04380e9	−	6.73144e9i	0.249271	−	0.238217i
$411$	5.65843e10			1.98303
$412$	−2.14993e10	−	2.14993e10i	−0.746165	−	0.746165i
$413$	−2.29389e8	+	2.29389e8i	−0.00788447	+	0.00788447i
$414$		−	5.54898e9i		−	0.188891i
$415$	9.69206e9	+	1.01418e10i	0.326756	+	0.341919i
$416$	−3.47257e10			−1.15952
$417$	8.32607e9	+	8.32607e9i	0.275357	+	0.275357i
$418$	−1.47790e10	+	1.47790e10i	−0.484104	+	0.484104i
$419$		−	2.98593e10i		−	0.968776i	−0.874853	−	0.484388i	$-0.839042\pi$
$419$		−	2.98593e10i		−	0.968776i	0.874853	−	0.484388i	$-0.160958\pi$
$420$	1.49504e10	+	3.39006e8i	0.480458	+	0.0108946i
$421$	−5.33816e10			−1.69927			−0.849637	−	0.527368i	$-0.823179\pi$
$421$	−5.33816e10			−1.69927			−0.849637	+	0.527368i	$0.823179\pi$
$422$	2.99474e9	+	2.99474e9i	0.0944298	+	0.0944298i
$423$	−8.57253e9	+	8.57253e9i	−0.267761	+	0.267761i
$424$		−	1.23671e10i		−	0.382654i
$425$	4.20522e9	+	4.60497e9i	0.128894	+	0.141147i
$426$	5.88755e9			0.178771
$427$	1.29369e10	+	1.29369e10i	0.389151	+	0.389151i
$428$	1.02914e10	−	1.02914e10i	0.306690	−	0.306690i
$429$			7.35408e10i			2.17120i
$430$	−842596.	+	3.71590e7i	−2.46459e−5	+	0.00108690i
$431$	1.68739e10			0.488997			0.244499	−	0.969650i	$-0.421377\pi$
$431$	1.68739e10			0.488997			0.244499	+	0.969650i	$0.421377\pi$
$432$	−5.01225e9	−	5.01225e9i	−0.143912	−	0.143912i
$433$	7.15187e9	−	7.15187e9i	0.203455	−	0.203455i	−0.598024	−	0.801478i	$-0.704047\pi$
$433$	7.15187e9	−	7.15187e9i	0.203455	−	0.203455i	0.801478	+	0.598024i	$0.204047\pi$
$434$			6.17451e9i			0.174038i
$435$	6.11165e9	−	5.84063e9i	0.170688	−	0.163118i
$436$	4.97885e9			0.137779
$437$	2.26540e10	+	2.26540e10i	0.621182	+	0.621182i
$438$	−1.29146e10	+	1.29146e10i	−0.350902	+	0.350902i
$439$			2.62124e9i			0.0705747i	0.999377	+	0.0352873i	$0.0112346\pi$
$439$			2.62124e9i			0.0705747i	−0.999377	+	0.0352873i	$0.988765\pi$
$440$	−2.49061e10	−	2.60618e10i	−0.664500	−	0.695335i
$441$	−2.24408e10			−0.593313
$442$	−2.47286e9	−	2.47286e9i	−0.0647904	−	0.0647904i
$443$	−3.30317e10	+	3.30317e10i	−0.857663	+	0.857663i	−0.991062	−	0.133400i	$-0.957411\pi$
$443$	−3.30317e10	+	3.30317e10i	−0.857663	+	0.857663i	0.133400	+	0.991062i	$0.457411\pi$
$444$			7.98244e9i			0.205402i
$445$	−3.03067e10	−	6.87218e8i	−0.772857	−	0.0175249i
$446$	−8.24359e9			−0.208342
$447$	−5.44965e10	−	5.44965e10i	−1.36502	−	1.36502i
$448$	−2.50985e9	+	2.50985e9i	−0.0623069	+	0.0623069i
$449$		−	2.56081e10i		−	0.630074i	−0.949079	−	0.315037i	$-0.897983\pi$
$449$		−	2.56081e10i		−	0.630074i	0.949079	−	0.315037i	$-0.102017\pi$
$450$	8.56941e9	−	7.82550e9i	0.208978	−	0.190837i
$451$	4.91459e10			1.18790
$452$	4.24616e10	+	4.24616e10i	1.01729	+	1.01729i
$453$	5.77721e10	−	5.77721e10i	1.37191	−	1.37191i
$454$			3.05928e10i			0.720105i
$455$	5.16094e8	−	2.27601e10i	0.0120416	−	0.531041i
$456$	5.37511e10			1.24316
$457$	1.31162e10	+	1.31162e10i	0.300707	+	0.300707i	0.841290	−	0.540583i	$-0.181796\pi$
$457$	1.31162e10	+	1.31162e10i	0.300707	+	0.300707i	−0.540583	+	0.841290i	$0.681796\pi$
$458$	1.61456e10	−	1.61456e10i	0.366937	−	0.366937i
$459$		−	3.03013e9i		−	0.0682669i
$460$	−1.83435e10	+	1.75300e10i	−0.409685	+	0.391518i
$461$	−3.99207e10			−0.883883			−0.441942	−	0.897044i	$-0.645710\pi$
$461$	−3.99207e10			−0.883883			−0.441942	+	0.897044i	$0.645710\pi$
$462$	−9.48513e9	−	9.48513e9i	−0.208197	−	0.208197i
$463$	1.43482e10	−	1.43482e10i	0.312229	−	0.312229i	−0.533544	−	0.845772i	$-0.679140\pi$
$463$	1.43482e10	−	1.43482e10i	0.312229	−	0.312229i	0.845772	+	0.533544i	$0.179140\pi$
$464$			4.74365e9i			0.102339i
$465$	−4.41759e10	−	4.62258e10i	−0.944874	−	0.988719i
$466$	3.19061e10			0.676597
$467$	2.44200e10	+	2.44200e10i	0.513427	+	0.513427i	0.915575	−	0.402148i	$-0.131736\pi$
$467$	2.44200e10	+	2.44200e10i	0.513427	+	0.513427i	−0.402148	+	0.915575i	$0.631736\pi$
$468$	2.58774e10	−	2.58774e10i	0.539433	−	0.539433i
$469$			6.45246e9i			0.133363i
$470$	−9.85535e9	−	2.23474e8i	−0.201967	−	0.00457969i
$471$	−1.20968e11			−2.45804
$472$	−6.52990e8	−	6.52990e8i	−0.0131565	−	0.0131565i
$473$	−1.32572e8	+	1.32572e8i	−0.00264855	+	0.00264855i
$474$			7.36659e9i			0.145933i
$475$	−3.03703e9	+	6.69330e10i	−0.0596588	+	1.31482i
$476$	−3.58709e9			−0.0698738
$477$	1.42002e10	+	1.42002e10i	0.274296	+	0.274296i
$478$	1.16204e10	−	1.16204e10i	0.222592	−	0.222592i
$479$		−	9.03857e9i		−	0.171695i	−0.996308	−	0.0858475i	$-0.972640\pi$
$479$		−	9.03857e9i		−	0.171695i	0.996308	−	0.0858475i	$-0.0273598\pi$
$480$	−1.48695e9	+	6.55753e10i	−0.0280111	+	1.23531i
$481$	1.21523e10			0.227026
$482$	3.16619e8	+	3.16619e8i	0.00586609	+	0.00586609i
$483$	−1.45393e10	+	1.45393e10i	−0.267150	+	0.267150i
$484$		−	3.69045e10i		−	0.672508i
$485$	6.86368e10	−	6.55930e10i	1.24048	−	1.18547i
$486$	−2.63951e10			−0.473127
$487$	3.53950e10	+	3.53950e10i	0.629255	+	0.629255i	0.947881	−	0.318626i	$-0.103221\pi$
$487$	3.53950e10	+	3.53950e10i	0.629255	+	0.629255i	−0.318626	+	0.947881i	$0.603221\pi$
$488$	−3.68268e10	+	3.68268e10i	−0.649358	+	0.649358i
$489$			6.54965e10i			1.14547i
$490$	−1.26069e10	−	1.31919e10i	−0.218688	−	0.228836i
$491$	−5.87159e10			−1.01025			−0.505126	−	0.863045i	$-0.668554\pi$
$491$	−5.87159e10			−1.01025			−0.505126	+	0.863045i	$0.668554\pi$
$492$	−4.10371e10	−	4.10371e10i	−0.700352	−	0.700352i
$493$	−1.43387e9	+	1.43387e9i	−0.0242730	+	0.0242730i
$494$		−	3.75738e10i		−	0.630924i
$495$	5.85222e10	+	1.32702e9i	0.974765	+	0.0221032i
$496$	3.58788e10			0.592805
$497$	−6.50082e9	−	6.50082e9i	−0.106547	−	0.106547i
$498$	−1.05072e10	+	1.05072e10i	−0.170833	+	0.170833i
$499$			2.57394e10i			0.415141i	0.978220	+	0.207571i	$0.0665557\pi$
$499$			2.57394e10i			0.415141i	−0.978220	+	0.207571i	$0.933444\pi$
$500$	−5.29410e10	−	3.60633e9i	−0.847057	−	0.0577012i
$501$	1.07948e11			1.71342
$502$	−2.54494e8	−	2.54494e8i	−0.00400740	−	0.00400740i
$503$	−4.75499e10	+	4.75499e10i	−0.742810	+	0.742810i	−0.973118	−	0.230308i	$-0.926027\pi$
$503$	−4.75499e10	+	4.75499e10i	−0.742810	+	0.742810i	0.230308	+	0.973118i	$0.426027\pi$
$504$			1.45375e10i			0.225303i
$505$	1.01450e9	−	4.47399e10i	0.0155986	−	0.687907i
$506$	2.27596e10			0.347186
$507$	−3.20615e10	−	3.20615e10i	−0.485235	−	0.485235i
$508$	4.01643e10	−	4.01643e10i	0.603095	−	0.603095i
$509$		−	8.69280e10i		−	1.29506i	−0.762042	−	0.647528i	$-0.775803\pi$
$509$		−	8.69280e10i		−	1.29506i	0.762042	−	0.647528i	$-0.224197\pi$
$510$	−4.77559e9	+	4.56381e9i	−0.0705905	+	0.0674601i
$511$	2.85197e10			0.418275
$512$	−4.59200e10	−	4.59200e10i	−0.668225	−	0.668225i
$513$	2.30206e10	−	2.30206e10i	0.332389	−	0.332389i
$514$			4.16243e9i			0.0596340i
$515$	6.04050e10	+	6.32080e10i	0.858705	+	0.898552i
$516$	2.21397e8			0.00312301
$517$	−3.51609e10	−	3.51609e10i	−0.492151	−	0.492151i
$518$	−1.56737e9	+	1.56737e9i	−0.0217697	+	0.0217697i
$519$		−	5.12568e10i		−	0.706451i
$520$	6.47900e10	+	1.46914e9i	0.886124	+	0.0200932i
$521$	6.44123e10			0.874214			0.437107	−	0.899409i	$-0.356003\pi$
$521$	6.44123e10			0.874214			0.437107	+	0.899409i	$0.356003\pi$
$522$	2.66830e9	+	2.66830e9i	0.0359379	+	0.0359379i
$523$	−5.99903e10	+	5.99903e10i	−0.801815	+	0.801815i	−0.983379	−	0.181564i	$-0.941884\pi$
$523$	−5.99903e10	+	5.99903e10i	−0.801815	+	0.801815i	0.181564	+	0.983379i	$0.441884\pi$
$524$			6.63079e10i			0.879509i
$525$	−4.29576e10	−	1.94917e9i	−0.565461	−	0.0256573i
$526$	−5.76728e10			−0.753404
$527$	1.08452e10	+	1.08452e10i	0.140603	+	0.140603i
$528$	−5.51162e10	+	5.51162e10i	−0.709159	+	0.709159i
$529$			4.34238e10i			0.554505i
$530$	−3.70179e8	+	1.63251e10i	−0.00469146	+	0.206896i
$531$	1.49955e9			0.0188618
$532$	−2.72519e10	−	2.72519e10i	−0.340213	−	0.340213i
$533$	−6.24738e10	+	6.24738e10i	−0.774086	+	0.774086i
$534$		−	3.21107e10i		−	0.394898i
$535$	−3.02568e10	+	2.89151e10i	−0.369324	+	0.352947i
$536$	−1.83679e10			−0.222536
$537$	9.72705e10	+	9.72705e10i	1.16973	+	1.16973i
$538$	2.36869e10	−	2.36869e10i	0.282734	−	0.282734i
$539$		−	9.20427e10i		−	1.09052i
$540$	1.78137e10	+	1.86403e10i	0.209498	+	0.219219i
$541$	−9.38341e10			−1.09540			−0.547698	−	0.836676i	$-0.684496\pi$
$541$	−9.38341e10			−1.09540			−0.547698	+	0.836676i	$0.684496\pi$
$542$	3.86633e10	+	3.86633e10i	0.448025	+	0.448025i
$543$	1.45259e10	−	1.45259e10i	0.167087	−	0.167087i
$544$		−	1.57337e10i		−	0.179653i
$545$	−1.43133e10	−	3.24560e8i	−0.162238	−	0.00367883i
$546$	2.41148e10			0.271340
$547$	1.86813e10	+	1.86813e10i	0.208669	+	0.208669i	0.803702	−	0.595032i	$-0.202861\pi$
$547$	1.86813e10	+	1.86813e10i	0.208669	+	0.208669i	−0.595032	+	0.803702i	$0.702861\pi$
$548$	8.16657e10	−	8.16657e10i	0.905560	−	0.905560i
$549$		−	8.45702e10i		−	0.930954i
$550$	3.20969e10	+	3.51481e10i	0.350762	+	0.384106i
$551$	−2.17869e10			−0.236368
$552$	−4.13884e10	−	4.13884e10i	−0.445781	−	0.445781i
$553$	8.13393e9	−	8.13393e9i	0.0869761	−	0.0869761i
$554$			4.20398e10i			0.446294i
$555$	5.20357e8	−	2.29481e10i	0.00548441	−	0.241866i
$556$	2.40333e10			0.251487
$557$	−4.32331e9	−	4.32331e9i	−0.0449154	−	0.0449154i	0.684292	−	0.729208i	$-0.260111\pi$
$557$	−4.32331e9	−	4.32331e9i	−0.0449154	−	0.0449154i	−0.729208	+	0.684292i	$0.760111\pi$
$558$	2.01818e10	−	2.01818e10i	0.208173	−	0.208173i
$559$		−	3.37049e8i		−	0.00345180i
$560$	1.74447e10	−	1.66711e10i	0.177382	−	0.169516i
$561$	−3.33202e10			−0.336400
$562$	−5.37441e10	−	5.37441e10i	−0.538748	−	0.538748i
$563$	5.85471e10	−	5.85471e10i	0.582736	−	0.582736i	−0.352918	−	0.935654i	$-0.614811\pi$
$563$	5.85471e10	−	5.85471e10i	0.582736	−	0.582736i	0.935654	+	0.352918i	$0.114811\pi$
$564$			5.87192e10i			0.580315i
$565$	−1.19302e11	−	1.24837e11i	−1.17072	−	1.22504i
$566$	2.52209e9			0.0245751
$567$	3.76929e10	+	3.76929e10i	0.364693	+	0.364693i
$568$	1.85056e10	−	1.85056e10i	0.177791	−	0.177791i
$569$			1.98793e11i			1.89650i	0.317524	+	0.948250i	$0.397149\pi$
$569$			1.98793e11i			1.89650i	−0.317524	+	0.948250i	$0.602851\pi$
$570$	−7.09536e10	−	1.60890e9i	−0.672164	−	0.0152416i
$571$	6.21842e10			0.584973			0.292487	−	0.956270i	$-0.405517\pi$
$571$	6.21842e10			0.584973			0.292487	+	0.956270i	$0.405517\pi$
$572$	1.06138e11	+	1.06138e11i	0.991490	+	0.991490i
$573$	5.75764e10	−	5.75764e10i	0.534104	−	0.534104i
$574$		−	1.61155e10i		−	0.148455i
$575$	5.38769e10	−	4.91999e10i	0.492869	−	0.450083i
$576$	1.64073e10			0.149055
$577$	−1.02056e11	−	1.02056e11i	−0.920739	−	0.920739i	0.0763427	−	0.997082i	$-0.475676\pi$
$577$	−1.02056e11	−	1.02056e11i	−0.920739	−	0.920739i	−0.997082	+	0.0763427i	$0.975676\pi$
$578$	−2.95455e10	+	2.95455e10i	−0.264716	+	0.264716i
$579$		−	1.73772e10i		−	0.154620i
$580$	3.91156e8	−	1.72502e10i	0.00345651	−	0.152434i
$581$	2.32034e10			0.203633
$582$	7.11098e10	+	7.11098e10i	0.619780	+	0.619780i
$583$	−5.82431e10	+	5.82431e10i	−0.504162	+	0.504162i
$584$			8.11857e10i			0.697956i
$585$	−7.60798e10	+	7.27060e10i	−0.649600	+	0.620793i
$586$	9.03959e9			0.0766581
$587$	−1.52761e11	−	1.52761e11i	−1.28665	−	1.28665i	−0.936811	−	0.349837i	$-0.886237\pi$
$587$	−1.52761e11	−	1.52761e11i	−1.28665	−	1.28665i	−0.349837	−	0.936811i	$-0.613763\pi$
$588$	−7.68562e10	+	7.68562e10i	−0.642939	+	0.642939i
$589$			1.64787e11i			1.36918i
$590$	8.42427e8	+	8.81518e8i	0.00695223	+	0.00727484i
$591$	−1.49906e10			−0.122876
$592$	9.10768e9	+	9.10768e9i	0.0741517	+	0.0741517i
$593$	9.35153e10	−	9.35153e10i	0.756247	−	0.756247i	−0.219390	−	0.975637i	$-0.570407\pi$
$593$	9.35153e10	−	9.35153e10i	0.756247	−	0.756247i	0.975637	+	0.219390i	$0.0704067\pi$
$594$		−	2.31279e10i		−	0.185776i
$595$	1.03122e10	+	2.33834e8i	0.0822782	+	0.00186569i
$596$	−1.57305e11			−1.24669
$597$	1.28901e11	+	1.28901e11i	1.01475	+	1.01475i
$598$	−2.89318e10	+	2.89318e10i	−0.226241	+	0.226241i
$599$		−	5.65120e10i		−	0.438968i	−0.975616	−	0.219484i	$-0.929563\pi$
$599$		−	5.65120e10i		−	0.438968i	0.975616	−	0.219484i	$-0.0704374\pi$
$600$	5.54859e9	−	1.22285e11i	0.0428132	−	0.943559i
$601$	−9.99220e10			−0.765884			−0.382942	−	0.923772i	$-0.625089\pi$
$601$	−9.99220e10			−0.765884			−0.382942	+	0.923772i	$0.625089\pi$
$602$	4.34719e7	+	4.34719e7i	0.000330996	+	0.000330996i
$603$	2.10903e10	−	2.10903e10i	0.159520	−	0.159520i
$604$		−	1.66760e11i		−	1.25298i
$605$	−2.40572e9	+	1.06094e11i	−0.0179566	+	0.791896i
$606$	4.74030e10			0.351492
$607$	1.27776e11	+	1.27776e11i	0.941229	+	0.941229i	0.998366	−	0.0571370i	$-0.0181972\pi$
$607$	1.27776e11	+	1.27776e11i	0.941229	+	0.941229i	−0.0571370	+	0.998366i	$0.518197\pi$
$608$	1.19532e11	−	1.19532e11i	0.874724	−	0.874724i
$609$		−	1.39828e10i		−	0.101654i
$610$	4.97151e10	−	4.75105e10i	0.359062	−	0.343139i
$611$	8.93925e10			0.641411
$612$	1.17247e10	+	1.17247e10i	0.0835784	+	0.0835784i
$613$	6.34636e10	−	6.34636e10i	0.449452	−	0.449452i	−0.445720	−	0.895172i	$-0.647052\pi$
$613$	6.34636e10	−	6.34636e10i	0.449452	−	0.449452i	0.895172	+	0.445720i	$0.147052\pi$
$614$		−	6.96478e10i		−	0.490043i
$615$	1.15299e11	+	1.20649e11i	0.805983	+	0.843383i
$616$	−5.96267e10			−0.414112
$617$	−6.39126e10	−	6.39126e10i	−0.441007	−	0.441007i	0.451343	−	0.892350i	$-0.350945\pi$
$617$	−6.39126e10	−	6.39126e10i	−0.441007	−	0.441007i	−0.892350	+	0.451343i	$0.850945\pi$
$618$	−6.54854e10	+	6.54854e10i	−0.448943	+	0.448943i
$619$		−	5.76225e10i		−	0.392491i	−0.980555	−	0.196245i	$-0.937125\pi$
$619$		−	5.76225e10i		−	0.392491i	0.980555	−	0.196245i	$-0.0628749\pi$
$620$	−1.30473e11	−	2.95853e9i	−0.882986	−	0.0200221i
$621$	−3.54517e10			−0.238381
$622$	−1.64439e10	−	1.64439e10i	−0.109861	−	0.109861i
$623$	−3.54555e10	+	3.54555e10i	−0.235359	+	0.235359i
$624$		−	1.40126e11i		−	0.924234i
$625$	1.51961e11	+	1.38186e10i	0.995891	+	0.0905619i
$626$	4.21700e10			0.274604
$627$	−2.53141e11	−	2.53141e11i	−1.63792	−	1.63792i
$628$	−1.74589e11	+	1.74589e11i	−1.12248	+	1.12248i
$629$			5.50600e9i			0.0351749i
$630$	4.35143e8	−	1.91901e10i	0.00276229	−	0.121819i
$631$	1.53061e11			0.965486			0.482743	−	0.875762i	$-0.339641\pi$
$631$	1.53061e11			0.965486			0.482743	+	0.875762i	$0.339641\pi$
$632$	2.31544e10	+	2.31544e10i	0.145133	+	0.145133i
$633$	−5.12953e10	+	5.12953e10i	−0.319494	+	0.319494i
$634$			4.87880e10i			0.301964i
$635$	−1.18083e11	+	1.12847e11i	−0.726263	+	0.694057i
$636$	9.72667e10			0.594478
$637$	1.17004e11	+	1.17004e11i	0.710628	+	0.710628i
$638$	−1.09442e10	+	1.09442e10i	−0.0660546	+	0.0660546i
$639$			4.24968e10i			0.254890i
$640$	1.18162e11	+	1.23645e11i	0.704300	+	0.736982i
$641$	1.10388e11			0.653867			0.326934	−	0.945047i	$-0.393985\pi$
$641$	1.10388e11			0.653867			0.326934	+	0.945047i	$0.393985\pi$
$642$	−3.13470e10	−	3.13470e10i	−0.184525	−	0.184525i
$643$	4.62452e10	−	4.62452e10i	0.270535	−	0.270535i	−0.558781	−	0.829315i	$-0.688731\pi$
$643$	4.62452e10	−	4.62452e10i	0.270535	−	0.270535i	0.829315	+	0.558781i	$0.188731\pi$
$644$			4.19680e10i			0.243991i
$645$	−6.36477e8	−	1.44324e7i	−0.00367743	−	8.33872e-5i
$646$	1.70241e10			0.0977539
$647$	−9.64071e10	−	9.64071e10i	−0.550164	−	0.550164i	0.376324	−	0.926488i	$-0.377188\pi$
$647$	−9.64071e10	−	9.64071e10i	−0.550164	−	0.550164i	−0.926488	+	0.376324i	$0.877188\pi$
$648$	−1.07299e11	+	1.07299e11i	−0.608547	+	0.608547i
$649$			6.15052e9i			0.0346683i
$650$	−8.54813e10	−	3.87864e9i	−0.478870	−	0.0217283i
$651$	−1.05760e11			−0.588840
$652$	9.45283e10	+	9.45283e10i	0.523084	+	0.523084i
$653$	−2.02786e11	+	2.02786e11i	−1.11528	+	1.11528i	−0.122857	+	0.992424i	$0.539206\pi$
$653$	−2.02786e11	+	2.02786e11i	−1.11528	+	1.11528i	−0.992424	+	0.122857i	$0.960794\pi$
$654$		−	1.51653e10i		−	0.0828971i
$655$	4.32247e9	−	1.90623e11i	0.0234837	−	1.03565i
$656$	−9.36438e10			−0.505666
$657$	−9.32188e10	−	9.32188e10i	−0.500313	−	0.500313i
$658$	−1.15297e10	+	1.15297e10i	−0.0615053	+	0.0615053i
$659$			5.78139e10i			0.306542i	0.988184	+	0.153271i	$0.0489808\pi$
$659$			5.78139e10i			0.306542i	−0.988184	+	0.153271i	$0.951019\pi$
$660$	2.04974e11	−	1.95885e11i	1.08025	−	1.03234i
$661$	3.80376e10			0.199254			0.0996271	−	0.995025i	$-0.468235\pi$
$661$	3.80376e10			0.199254			0.0996271	+	0.995025i	$0.468235\pi$
$662$	−6.58451e10	−	6.58451e10i	−0.342840	−	0.342840i
$663$	4.23563e10	−	4.23563e10i	0.219212	−	0.219212i
$664$			6.60520e10i			0.339792i
$665$	7.65679e10	+	8.01209e10i	0.391526	+	0.409694i
$666$	1.02461e10			0.0520790
$667$	1.67759e10	+	1.67759e10i	0.0847585	+	0.0847585i
$668$	1.55797e11	−	1.55797e11i	0.782442	−	0.782442i
$669$		−	1.41200e11i		−	0.704905i
$670$	2.42463e10	+	5.49796e8i	0.120323	+	0.00272836i
$671$	3.46872e11			1.71111
$672$	7.67158e10	+	7.67158e10i	0.376190	+	0.376190i
$673$	1.23735e11	−	1.23735e11i	0.603158	−	0.603158i	−0.337991	−	0.941149i	$-0.609747\pi$
$673$	1.23735e11	−	1.23735e11i	0.603158	−	0.603158i	0.941149	+	0.337991i	$0.109747\pi$
$674$		−	5.53205e10i		−	0.268069i
$675$	−4.99961e10	−	5.47488e10i	−0.240836	−	0.263730i
$676$	−9.25460e10			−0.443170
$677$	−8.44279e10	−	8.44279e10i	−0.401912	−	0.401912i	0.476994	−	0.878906i	$-0.341726\pi$
$677$	−8.44279e10	−	8.44279e10i	−0.401912	−	0.401912i	−0.878906	+	0.476994i	$0.841726\pi$
$678$	1.29336e11	−	1.29336e11i	0.612067	−	0.612067i
$679$		−	1.57034e11i		−	0.738778i
$680$	−6.65644e8	+	2.93553e10i	−0.00311320	+	0.137294i
$681$	−5.24008e11			−2.43640
$682$	8.27774e10	+	8.27774e10i	0.382626	+	0.382626i
$683$	−2.87370e10	+	2.87370e10i	−0.132056	+	0.132056i	−0.770045	−	0.637989i	$-0.779766\pi$
$683$	−2.87370e10	+	2.87370e10i	−0.132056	+	0.132056i	0.637989	+	0.770045i	$0.279766\pi$
$684$			1.78150e11i			0.813881i
$685$	−2.40098e11	+	2.29450e11i	−1.09050	+	1.04214i
$686$	−6.72321e10			−0.303585
$687$	2.76549e11	+	2.76549e11i	1.24150	+	1.24150i
$688$	2.52606e8	−	2.52606e8i	0.00112743	−	0.00112743i
$689$		−	1.48076e11i		−	0.657065i
$690$	5.33954e10	+	5.58731e10i	0.235563	+	0.246494i
$691$	−8.87703e10			−0.389364			−0.194682	−	0.980866i	$-0.562367\pi$
$691$	−8.87703e10			−0.389364			−0.194682	+	0.980866i	$0.562367\pi$
$692$	−7.39768e10	−	7.39768e10i	−0.322605	−	0.322605i
$693$	6.84644e10	−	6.84644e10i	0.296847	−	0.296847i
$694$			7.28192e10i			0.313912i
$695$	−6.90915e10	−	1.56668e9i	−0.296132	−	0.00671492i
$696$	3.98042e10			0.169626
$697$	−2.83059e10	−	2.83059e10i	−0.119935	−	0.119935i
$698$	4.90652e10	−	4.90652e10i	0.206706	−	0.206706i
$699$			5.46503e11i			2.28920i
$700$	−6.48120e10	+	5.91857e10i	−0.269938	+	0.246504i
$701$	1.22790e11			0.508499			0.254249	−	0.967139i	$-0.418172\pi$
$701$	1.22790e11			0.508499			0.254249	+	0.967139i	$0.418172\pi$
$702$	2.94000e10	+	2.94000e10i	0.121060	+	0.121060i
$703$	−4.18303e10	+	4.18303e10i	−0.171266	+	0.171266i
$704$			6.72957e10i			0.273966i
$705$	3.82777e9	−	1.68807e11i	0.0154949	−	0.683336i
$706$	−9.31125e10			−0.374791
$707$	−5.23407e10	−	5.23407e10i	−0.209489	−	0.209489i
$708$	5.13572e9	−	5.13572e9i	0.0204394	−	0.0204394i
$709$		−	2.07670e11i		−	0.821842i	−0.911671	−	0.410921i	$-0.865207\pi$
$709$		−	2.07670e11i		−	0.821842i	0.911671	−	0.410921i	$-0.134793\pi$
$710$	−2.49820e10	+	2.38742e10i	−0.0983091	+	0.0939495i
$711$	−5.31726e10			−0.208070
$712$	−1.00929e11	−	1.00929e11i	−0.392733	−	0.392733i
$713$	1.26886e11	−	1.26886e11i	0.490969	−	0.490969i
$714$			1.09261e10i			0.0420408i
$715$	−2.98210e11	−	3.12048e11i	−1.14103	−	1.19398i
$716$	2.80773e11			1.06832
$717$	1.99040e11	+	1.99040e11i	0.753119	+	0.753119i
$718$	−4.16981e10	+	4.16981e10i	−0.156898	+	0.156898i
$719$			1.66571e11i			0.623281i	0.950200	+	0.311640i	$0.100878\pi$
$719$			1.66571e11i			0.623281i	−0.950200	+	0.311640i	$0.899122\pi$
$720$	−1.11510e11	−	2.52853e9i	−0.414937	−	0.00940888i
$721$	1.44613e11			0.535140
$722$	5.46750e10	+	5.46750e10i	0.201205	+	0.201205i
$723$	−5.42320e9	+	5.42320e9i	−0.0198474	+	0.0198474i
$724$		−	4.19292e10i		−	0.152603i
$725$	−2.24901e9	+	4.95658e10i	−0.00814027	+	0.179403i
$726$	−1.12409e11			−0.404626
$727$	1.61369e11	+	1.61369e11i	0.577673	+	0.577673i	0.934262	−	0.356588i	$-0.116060\pi$
$727$	1.61369e11	+	1.61369e11i	0.577673	+	0.577673i	−0.356588	+	0.934262i	$0.616060\pi$
$728$	7.57970e10	−	7.57970e10i	0.269853	−	0.269853i
$729$		−	1.13795e11i		−	0.402915i
$730$	2.43009e9	−	1.07168e11i	0.00855717	−	0.377377i
$731$	1.52712e8			0.000534814
$732$	−2.89640e11	−	2.89640e11i	−1.00882	−	1.00882i
$733$	4.72057e10	−	4.72057e10i	0.163523	−	0.163523i	−0.620603	−	0.784125i	$-0.713112\pi$
$733$	4.72057e10	−	4.72057e10i	0.163523	−	0.163523i	0.784125	+	0.620603i	$0.213112\pi$
$734$			8.44043e10i			0.290791i
$735$	2.25958e11	−	2.15938e11i	0.774245	−	0.739911i
$736$	−1.84080e11			−0.627328
$737$	8.65036e10	+	8.65036e10i	0.293200	+	0.293200i
$738$	−5.26746e10	+	5.26746e10i	−0.177572	+	0.177572i
$739$		−	2.13693e11i		−	0.716494i	−0.933627	−	0.358247i	$-0.883375\pi$
$739$		−	2.13693e11i		−	0.716494i	0.933627	−	0.358247i	$-0.116625\pi$
$740$	−3.23690e10	−	3.38710e10i	−0.107945	−	0.112954i
$741$	6.43582e11			2.13467
$742$	1.90985e10	+	1.90985e10i	0.0630064	+	0.0630064i
$743$	−3.10741e11	+	3.10741e11i	−1.01963	+	1.01963i	−0.0198284	+	0.999803i	$0.506312\pi$
$743$	−3.10741e11	+	3.10741e11i	−1.01963	+	1.01963i	−0.999803	+	0.0198284i	$0.993688\pi$
$744$		−	3.01061e11i		−	0.982570i
$745$	4.52224e11	+	1.02544e10i	1.46801	+	0.0332877i
$746$	−7.45910e10			−0.240841
$747$	−7.58420e10	−	7.58420e10i	−0.243572	−	0.243572i
$748$	−4.80896e10	+	4.80896e10i	−0.153619	+	0.153619i
$749$			6.92245e10i			0.219954i
$750$	−1.09847e10	+	1.61255e11i	−0.0347169	+	0.509646i
$751$	−5.29510e11			−1.66462			−0.832308	−	0.554313i	$-0.812981\pi$
$751$	−5.29510e11			−1.66462			−0.832308	+	0.554313i	$0.812981\pi$
$752$	6.69965e10	+	6.69965e10i	0.209498	+	0.209498i
$753$	4.35909e9	−	4.35909e9i	0.0135586	−	0.0135586i
$754$		−	2.78245e10i		−	0.0860877i
$755$	−1.08707e10	+	4.79405e11i	−0.0334557	+	1.47542i
$756$	4.26471e10			0.130558
$757$	−1.66172e11	−	1.66172e11i	−0.506029	−	0.506029i	0.407276	−	0.913305i	$-0.366479\pi$
$757$	−1.66172e11	−	1.66172e11i	−0.506029	−	0.506029i	−0.913305	+	0.407276i	$0.866479\pi$
$758$	9.63068e10	−	9.63068e10i	0.291729	−	0.291729i
$759$			3.89837e11i			1.17467i
$760$	−2.28076e11	+	2.17962e11i	−0.683637	+	0.653321i
$761$	−3.61095e11			−1.07667			−0.538335	−	0.842731i	$-0.680946\pi$
$761$	−3.61095e11			−1.07667			−0.538335	+	0.842731i	$0.680946\pi$
$762$	−1.22338e11	−	1.22338e11i	−0.362862	−	0.362862i
$763$	−1.67450e10	+	1.67450e10i	−0.0494067	+	0.0494067i
$764$		−	1.66195e11i		−	0.487803i
$765$	−3.29420e10	−	3.44706e10i	−0.0961842	−	0.100647i
$766$	2.03349e11			0.590646
$767$	−7.81849e9	−	7.81849e9i	−0.0225913	−	0.0225913i
$768$	−6.19151e10	+	6.19151e10i	−0.177972	+	0.177972i
$769$			2.04700e11i			0.585345i	0.956213	+	0.292672i	$0.0945446\pi$
$769$			2.04700e11i			0.585345i	−0.956213	+	0.292672i	$0.905455\pi$
$770$	7.87096e10	+	1.78477e9i	0.223906	+	0.00507716i
$771$	−7.12960e10			−0.201766
$772$	−2.50797e10	−	2.50797e10i	−0.0706080	−	0.0706080i
$773$	−8.07889e10	+	8.07889e10i	−0.226274	+	0.226274i	−0.811134	−	0.584860i	$-0.801149\pi$
$773$	−8.07889e10	+	8.07889e10i	−0.226274	+	0.226274i	0.584860	+	0.811134i	$0.301149\pi$
$774$		−	2.84182e8i		−	0.000791831i
$775$	3.74894e11	+	1.70105e10i	1.03921	+	0.0471531i
$776$	4.47020e11			1.23276
$777$	−2.68467e10	−	2.68467e10i	−0.0736557	−	0.0736557i
$778$	9.81095e10	−	9.81095e10i	0.267789	−	0.267789i
$779$		−	4.30093e11i		−	1.16792i
$780$	−1.15547e10	+	5.09569e11i	−0.0312162	+	1.37665i
$781$	−1.74304e11			−0.468493
$782$	−1.31086e10	−	1.31086e10i	−0.0350532	−	0.0350532i
$783$	1.70474e10	−	1.70474e10i	0.0453535	−	0.0453535i
$784$			1.75380e11i			0.464213i
$785$	5.13292e11	−	4.90530e11i	1.35172	−	1.29177i
$786$	2.01970e11			0.529172
$787$	−1.41727e11	−	1.41727e11i	−0.369448	−	0.369448i	0.497828	−	0.867276i	$-0.334131\pi$
$787$	−1.41727e11	−	1.41727e11i	−0.369448	−	0.369448i	−0.867276	+	0.497828i	$0.834131\pi$
$788$	−2.16353e10	+	2.16353e10i	−0.0561122	+	0.0561122i
$789$		−	9.87846e11i		−	2.54907i
$790$	−2.98717e10	−	3.12578e10i	−0.0766923	−	0.0802510i
$791$	−2.85615e11			−0.729584
$792$	1.94894e11	+	1.94894e11i	0.495334	+	0.495334i
$793$	−4.40940e11	+	4.40940e11i	−1.11503	+	1.11503i
$794$			1.98735e11i			0.500025i
$795$	−2.79624e11	−	6.34060e9i	−0.700013	−	0.0158731i
$796$	3.72074e11			0.926781
$797$	−2.66505e11	−	2.66505e11i	−0.660499	−	0.660499i	0.294998	−	0.955498i	$-0.404681\pi$
$797$	−2.66505e11	−	2.66505e11i	−0.660499	−	0.660499i	−0.955498	+	0.294998i	$0.904681\pi$
$798$	−8.30078e10	+	8.30078e10i	−0.204695	+	0.204695i
$799$			4.05024e10i			0.0993787i
$800$	−2.59600e11	−	2.84278e11i	−0.633789	−	0.694038i
$801$	2.31778e11			0.563043
$802$	−7.82117e10	−	7.82117e10i	−0.189049	−	0.189049i
$803$	3.82344e11	−	3.82344e11i	0.919586	−	0.919586i
$804$		−	1.44462e11i		−	0.345724i
$805$	2.73580e9	−	1.20650e11i	0.00651479	−	0.287306i
$806$	−2.10452e11			−0.498669
$807$	4.05720e11	+	4.05720e11i	0.956604	+	0.956604i
$808$	1.48996e11	−	1.48996e11i	0.349565	−	0.349565i
$809$			6.78011e11i			1.58286i	0.611259	+	0.791431i	$0.290663\pi$
$809$			6.78011e11i			1.58286i	−0.611259	+	0.791431i	$0.709337\pi$
$810$	1.44850e11	−	1.38427e11i	0.336495	−	0.321573i
$811$	4.62623e11			1.06941			0.534704	−	0.845039i	$-0.320423\pi$
$811$	4.62623e11			1.06941			0.534704	+	0.845039i	$0.320423\pi$
$812$	−2.01808e10	−	2.01808e10i	−0.0464211	−	0.0464211i
$813$	−6.62244e11	+	6.62244e11i	−1.51585	+	1.51585i
$814$			4.20253e10i			0.0957224i
$815$	−2.65590e11	−	2.77914e11i	−0.601978	−	0.629912i
$816$	6.34891e10			0.143199
$817$	1.16019e9	+	1.16019e9i	0.00260399	+	0.00260399i
$818$	−1.92158e11	+	1.92158e11i	−0.429185	+	0.429185i
$819$			1.74063e11i			0.386875i
$820$	3.40535e11	+	7.72177e9i	0.753193	+	0.0170790i
$821$	−2.02486e11			−0.445678			−0.222839	−	0.974855i	$-0.571532\pi$
$821$	−2.02486e11			−0.445678			−0.222839	+	0.974855i	$0.571532\pi$
$822$	−2.48749e11	−	2.48749e11i	−0.544846	−	0.544846i
$823$	5.67731e11	−	5.67731e11i	1.23749	−	1.23749i	0.276473	−	0.961022i	$-0.410834\pi$
$823$	5.67731e11	−	5.67731e11i	1.23749	−	1.23749i	0.961022	−	0.276473i	$-0.0891657\pi$
$824$			4.11664e11i			0.892963i
$825$	−6.02034e11	+	5.49772e11i	−1.29959	+	1.18677i
$826$	2.01682e9			0.00433259
$827$	5.76065e11	+	5.76065e11i	1.23154	+	1.23154i	0.963371	+	0.268173i	$0.0864198\pi$
$827$	5.76065e11	+	5.76065e11i	1.23154	+	1.23154i	0.268173	+	0.963371i	$0.413580\pi$
$828$	1.37175e11	−	1.37175e11i	0.291847	−	0.291847i
$829$			2.12691e11i			0.450330i	0.974321	+	0.225165i	$0.0722922\pi$
$829$			2.12691e11i			0.450330i	−0.974321	+	0.225165i	$0.927708\pi$
$830$	1.97710e9	−	8.71912e10i	0.00416596	−	0.183722i
$831$	−7.20077e11			−1.50999
$832$	−8.55457e10	−	8.55457e10i	−0.178527	−	0.178527i
$833$	−5.30126e10	+	5.30126e10i	−0.110103	+	0.110103i
$834$		−	7.32041e10i		−	0.151311i
$835$	−4.58043e11	+	4.37731e11i	−0.942237	+	0.900454i
$836$	−7.30696e11			−1.49593
$837$	−1.28939e11	−	1.28939e11i	−0.262713	−	0.262713i
$838$	−1.31264e11	+	1.31264e11i	−0.266176	+	0.266176i
$839$		−	8.36816e11i		−	1.68881i	−0.535701	−	0.844407i	$-0.679953\pi$
$839$		−	8.36816e11i		−	1.68881i	0.535701	−	0.844407i	$-0.320047\pi$
$840$	−1.39888e11	−	1.46379e11i	−0.280972	−	0.294010i
$841$	4.84113e11			0.967748
$842$	2.34670e11	+	2.34670e11i	0.466883	+	0.466883i
$843$	9.20555e11	−	9.20555e11i	1.82280	−	1.82280i
$844$			1.48065e11i			0.291797i
$845$	2.66053e11	+	6.03286e9i	0.521845	+	0.0118331i
$846$	7.53710e10			0.147137
$847$	1.24118e11	+	1.24118e11i	0.241157	+	0.241157i
$848$	1.10978e11	−	1.10978e11i	0.214611	−	0.214611i
$849$			4.31996e10i			0.0831475i
$850$	1.75735e9	−	3.87303e10i	0.00336654	−	0.0741950i
$851$	6.44187e10			0.122827
$852$	1.45545e11	+	1.45545e11i	0.276210	+	0.276210i
$853$	2.74662e11	−	2.74662e11i	0.518803	−	0.518803i	−0.398406	−	0.917209i	$-0.630436\pi$
$853$	2.74662e11	−	2.74662e11i	0.518803	−	0.518803i	0.917209	+	0.398406i	$0.130436\pi$
$854$		−	1.13743e11i		−	0.213842i
$855$	1.16132e10	−	5.12149e11i	0.0217314	−	0.958366i
$856$	−1.97058e11			−0.367027
$857$	−9.65564e10	−	9.65564e10i	−0.179002	−	0.179002i	0.611919	−	0.790921i	$-0.290398\pi$
$857$	−9.65564e10	−	9.65564e10i	−0.179002	−	0.179002i	−0.790921	+	0.611919i	$0.790398\pi$
$858$	3.23291e11	−	3.23291e11i	0.596547	−	0.596547i
$859$			7.22383e11i			1.32677i	0.748280	+	0.663383i	$0.230880\pi$
$859$			7.22383e11i			1.32677i	−0.748280	+	0.663383i	$0.769120\pi$
$860$	−9.39430e8	+	8.97771e8i	−0.00171740	+	0.00164124i
$861$	2.76034e11			0.502284
$862$	−7.41790e10	−	7.41790e10i	−0.134354	−	0.134354i
$863$	−9.33124e10	+	9.33124e10i	−0.168227	+	0.168227i	−0.786200	−	0.617973i	$-0.787954\pi$
$863$	−9.33124e10	+	9.33124e10i	−0.168227	+	0.168227i	0.617973	+	0.786200i	$0.287954\pi$
$864$			1.87059e11i			0.335678i
$865$	2.07848e11	+	2.17492e11i	0.371262	+	0.388490i
$866$	−6.28803e10			−0.111800
$867$	−5.06070e11	−	5.06070e11i	−0.895642	−	0.895642i
$868$	−1.52639e11	+	1.52639e11i	−0.268897	+	0.268897i
$869$		−	2.18092e11i		−	0.382437i
$870$	−5.25432e10	−	1.19144e9i	−0.0917147	−	0.00207967i
$871$	−2.19925e11			−0.382123
$872$	−4.76670e10	−	4.76670e10i	−0.0824427	−	0.0824427i
$873$	−5.13276e11	+	5.13276e11i	−0.883678	+	0.883678i
$874$		−	1.99177e11i		−	0.341346i
$875$	1.90181e11	−	1.65923e11i	0.324441	−	0.283058i
$876$	−6.38520e11			−1.08432
$877$	5.23388e11	+	5.23388e11i	0.884760	+	0.884760i	0.994014	−	0.109254i	$-0.0348463\pi$
$877$	5.23388e11	+	5.23388e11i	0.884760	+	0.884760i	−0.109254	+	0.994014i	$0.534846\pi$
$878$	1.15232e10	−	1.15232e10i	0.0193907	−	0.0193907i
$879$			1.54834e11i			0.259365i
$880$	1.03710e10	−	4.57366e11i	0.0172937	−	0.762664i
$881$	−8.15621e10			−0.135389			−0.0676947	−	0.997706i	$-0.521564\pi$
$881$	−8.15621e10			−0.135389			−0.0676947	+	0.997706i	$0.521564\pi$
$882$	9.86514e10	+	9.86514e10i	0.163015	+	0.163015i
$883$	−3.22895e11	+	3.22895e11i	−0.531151	+	0.531151i	−0.920915	−	0.389764i	$-0.872557\pi$
$883$	−3.22895e11	+	3.22895e11i	−0.531151	+	0.531151i	0.389764	+	0.920915i	$0.372557\pi$
$884$		−	1.22262e11i		−	0.200209i
$885$	−1.50991e10	+	1.44295e10i	−0.0246137	+	0.0235222i
$886$	2.90420e11			0.471294
$887$	4.59932e11	+	4.59932e11i	0.743018	+	0.743018i	0.973158	−	0.230140i	$-0.0739183\pi$
$887$	4.59932e11	+	4.59932e11i	0.743018	+	0.743018i	−0.230140	+	0.973158i	$0.573918\pi$
$888$	7.64231e10	−	7.64231e10i	0.122906	−	0.122906i
$889$			2.70163e11i			0.432532i
$890$	1.30210e11	+	1.36252e11i	0.207531	+	0.217161i
$891$	1.01065e12			1.60357
$892$	−2.03788e11	−	2.03788e11i	−0.321899	−	0.321899i
$893$	−3.07706e11	+	3.07706e11i	−0.483871	+	0.483871i
$894$			4.79141e11i			0.750091i
$895$	−8.07171e11	−	1.83029e10i	−1.25798	−	0.0285252i
$896$	2.82887e11			0.438915
$897$	−4.95558e11	−	4.95558e11i	−0.765464	−	0.765464i
$898$	−1.12575e11	+	1.12575e11i	−0.173116	+	0.173116i
$899$			1.22029e11i			0.186821i
$900$	4.05295e11	+	1.83899e10i	0.617734	+	0.0280292i
$901$	6.70910e10			0.101804
$902$	−2.16049e11	−	2.16049e11i	−0.326382	−	0.326382i
$903$	−7.44607e8	+	7.44607e8i	−0.00111989	+	0.00111989i
$904$		−	8.13047e11i		−	1.21742i
$905$	−2.73327e9	+	1.20539e11i	−0.00407463	+	0.179694i
$906$	−5.07941e11			−0.753877
$907$	−7.98076e11	−	7.98076e11i	−1.17928	−	1.17928i	−0.979929	−	0.199347i	$-0.936118\pi$
$907$	−7.98076e11	−	7.98076e11i	−1.17928	−	1.17928i	−0.199347	−	0.979929i	$-0.563882\pi$
$908$	−7.56278e11	+	7.56278e11i	−1.11260	+	1.11260i
$909$			3.42159e11i			0.501155i
$910$	−1.02324e11	+	9.77862e10i	−0.149215	+	0.142598i
$911$	−1.50243e11			−0.218132			−0.109066	−	0.994034i	$-0.534786\pi$
$911$	−1.50243e11			−0.218132			−0.109066	+	0.994034i	$0.534786\pi$
$912$	4.82341e11	+	4.82341e11i	0.697229	+	0.697229i
$913$	3.11072e11	−	3.11072e11i	0.447690	−	0.447690i
$914$		−	1.15320e11i		−	0.165241i
$915$	8.13782e11	+	8.51544e11i	1.16098	+	1.21485i
$916$	7.98264e11			1.13387
$917$	−2.23008e11	−	2.23008e11i	−0.315387	−	0.315387i
$918$	−1.33207e10	+	1.33207e10i	−0.0187567	+	0.0187567i
$919$		−	1.02471e12i		−	1.43662i	−0.695725	−	0.718308i	$-0.744917\pi$
$919$		−	1.02471e12i		−	1.43662i	0.695725	−	0.718308i	$-0.255083\pi$
$920$	3.43449e11	+	7.78786e9i	0.479415	+	0.0108709i
$921$	1.19296e12			1.65801
$922$	1.75495e11	+	1.75495e11i	0.242851	+	0.242851i
$923$	2.21574e11	−	2.21574e11i	0.305289	−	0.305289i
$924$		−	4.68960e11i		−	0.643351i
$925$	9.08470e10	+	9.94831e10i	0.124092	+	0.135888i
$926$	−1.26151e11			−0.171573
$927$	−4.72679e11	−	4.72679e11i	−0.640099	−	0.640099i
$928$	8.85171e10	−	8.85171e10i	0.119353	−	0.119353i
$929$		−	1.38553e12i		−	1.86017i	−0.367346	−	0.930084i	$-0.619734\pi$
$929$		−	1.38553e12i		−	1.86017i	0.367346	−	0.930084i	$-0.380266\pi$
$930$	−9.01151e9	+	3.97413e11i	−0.0120466	+	0.531264i
$931$	−8.05498e11			−1.07218
$932$	7.88745e11	+	7.88745e11i	1.04538	+	1.04538i
$933$	2.81659e11	−	2.81659e11i	0.371704	−	0.371704i
$934$		−	2.14705e11i		−	0.282133i
$935$	1.41384e11	−	1.35114e11i	0.184992	−	0.176789i
$936$	−4.95496e11			−0.645560
$937$	−7.72786e11	−	7.72786e11i	−1.00254	−	1.00254i	−0.999997	−	0.00254091i	$-0.999191\pi$
$937$	−7.72786e11	−	7.72786e11i	−1.00254	−	1.00254i	−0.00254091	−	0.999997i	$-0.500809\pi$
$938$	2.83655e10	−	2.83655e10i	0.0366420	−	0.0366420i
$939$			7.22308e11i			0.929095i
$940$	−2.38108e11	−	2.49157e11i	−0.304973	−	0.319125i
$941$	−6.91185e11			−0.881528			−0.440764	−	0.897623i	$-0.645292\pi$
$941$	−6.91185e11			−0.881528			−0.440764	+	0.897623i	$0.645292\pi$
$942$	5.31786e11	+	5.31786e11i	0.675357	+	0.675357i
$943$	−3.31172e11	+	3.31172e11i	−0.418800	+	0.418800i
$944$		−	1.17194e10i		−	0.0147576i
$945$	−1.22603e11	−	2.78007e9i	−0.153735	−	0.00348601i
$946$	1.16559e9			0.00145540
$947$	6.05426e11	+	6.05426e11i	0.752768	+	0.752768i	0.974995	−	0.222227i	$-0.0713327\pi$
$947$	6.05426e11	+	6.05426e11i	0.752768	+	0.752768i	−0.222227	+	0.974995i	$0.571333\pi$
$948$	−1.82108e11	+	1.82108e11i	−0.225474	+	0.225474i
$949$			9.72066e11i			1.19848i
$950$	3.07594e11	−	2.80892e11i	0.377644	−	0.344861i
$951$	−8.35663e11			−1.02167
$952$	3.43424e10	+	3.43424e10i	0.0418103	+	0.0418103i
$953$	−3.45330e11	+	3.45330e11i	−0.418661	+	0.418661i	−0.884742	−	0.466081i	$-0.845665\pi$
$953$	−3.45330e11	+	3.45330e11i	−0.418661	+	0.418661i	0.466081	+	0.884742i	$0.345665\pi$
$954$		−	1.24850e11i		−	0.150728i
$955$	−1.08339e10	+	4.77781e11i	−0.0130248	+	0.574401i
$956$	5.74532e11			0.687832
$957$	−1.87458e11	−	1.87458e11i	−0.223489	−	0.223489i
$958$	−3.97343e10	+	3.97343e10i	−0.0471740	+	0.0471740i
$959$			5.49319e11i			0.649456i
$960$	−1.65206e11	+	1.57880e11i	−0.194509	+	0.185884i
$961$	7.00825e10			0.0821705
$962$	−5.34222e10	−	5.34222e10i	−0.0623766	−	0.0623766i
$963$	2.26265e11	−	2.26265e11i	0.263095	−	0.263095i
$964$			1.56542e10i			0.0181268i
$965$	7.04648e10	+	7.37346e10i	0.0812575	+	0.0850281i
$966$	1.27832e11			0.146802
$967$	−1.77273e10	−	1.77273e10i	−0.0202739	−	0.0202739i	0.696897	−	0.717171i	$-0.254563\pi$
$967$	−1.77273e10	−	1.77273e10i	−0.0202739	−	0.0202739i	−0.717171	+	0.696897i	$0.754563\pi$
$968$	−3.53320e11	+	3.53320e11i	−0.402408	+	0.402408i
$969$			2.91597e11i			0.330741i
$970$	−5.90084e11	−	1.33804e10i	−0.666541	−	0.0151141i
$971$	1.52187e12			1.71199			0.855994	−	0.516986i	$-0.172946\pi$
$971$	1.52187e12			1.71199			0.855994	+	0.516986i	$0.172946\pi$
$972$	−6.52507e11	−	6.52507e11i	−0.731005	−	0.731005i
$973$	−8.08294e10	+	8.08294e10i	−0.0901816	+	0.0901816i
$974$		−	3.11199e11i		−	0.345782i
$975$	6.64353e10	−	1.46416e12i	0.0735157	−	1.62021i
$976$	−6.60938e11			−0.728385
$977$	2.88131e11	+	2.88131e11i	0.316237	+	0.316237i	0.847320	−	0.531083i	$-0.178215\pi$
$977$	2.88131e11	+	2.88131e11i	0.316237	+	0.316237i	−0.531083	+	0.847320i	$0.678215\pi$
$978$	2.87927e11	−	2.87927e11i	0.314722	−	0.314722i
$979$			9.50654e11i			1.03488i
$980$	1.44617e10	−	6.37769e11i	0.0156789	−	0.691448i
$981$	1.09464e11			0.118194
$982$	2.58120e11	+	2.58120e11i	0.277572	+	0.277572i
$983$	−2.15222e9	+	2.15222e9i	−0.00230501	+	0.00230501i	−0.708258	−	0.705953i	$-0.750519\pi$
$983$	−2.15222e9	+	2.15222e9i	−0.00230501	+	0.00230501i	0.705953	+	0.708258i	$0.250519\pi$
$984$			7.85771e11i			0.838138i
$985$	6.36078e10	−	6.07871e10i	0.0675718	−	0.0645753i
$986$	1.26068e10			0.0133382
$987$	−1.97485e11	−	1.97485e11i	−0.208097	−	0.208097i
$988$	9.28854e11	−	9.28854e11i	0.974810	−	0.974810i
$989$		−	1.78669e9i		−	0.00186751i
$990$	−2.51434e11	−	2.63102e11i	−0.261748	−	0.273894i
$991$	1.40286e10			0.0145452			0.00727261	−	0.999974i	$-0.497685\pi$
$991$	1.40286e10			0.0145452			0.00727261	+	0.999974i	$0.497685\pi$
$992$	−6.69504e11	−	6.69504e11i	−0.691363	−	0.691363i
$993$	1.12783e12	−	1.12783e12i	1.15997	−	1.15997i
$994$			5.71562e10i			0.0585488i
$995$	−1.06965e12	−	2.42547e10i	−1.09131	−	0.0247459i
$996$	−5.19494e11			−0.527890
$997$	7.09850e11	+	7.09850e11i	0.718433	+	0.718433i	0.968284	−	0.249851i	$-0.0803818\pi$
$997$	7.09850e11	+	7.09850e11i	0.718433	+	0.718433i	−0.249851	+	0.968284i	$0.580382\pi$
$998$	1.13152e11	−	1.13152e11i	0.114062	−	0.114062i
$999$		−	6.54611e10i		−	0.0657236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.9.c.a.2.2	✓	6
3.2	odd	2		45.9.g.a.37.2		6
4.3	odd	2		80.9.p.c.17.1		6
5.2	odd	4		25.9.c.b.18.2		6
5.3	odd	4	inner	5.9.c.a.3.2	yes	6
5.4	even	2		25.9.c.b.7.2		6
15.8	even	4		45.9.g.a.28.2		6
20.3	even	4		80.9.p.c.33.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.9.c.a.2.2	✓	6	1.1	even	1	trivial
5.9.c.a.3.2	yes	6	5.3	odd	4	inner
25.9.c.b.7.2		6	5.4	even	2
25.9.c.b.18.2		6	5.2	odd	4
45.9.g.a.28.2		6	15.8	even	4
45.9.g.a.37.2		6	3.2	odd	2
80.9.p.c.17.1		6	4.3	odd	2
80.9.p.c.33.1		6	20.3	even	4

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.39608 - 4.39608i) q^{2} +(75.2981 - 75.2981i) q^{3} -217.349i q^{4} +(-14.1685 + 624.839i) q^{5} -662.032 q^{6} +(730.992 + 730.992i) q^{7} +(-2080.88 + 2080.88i) q^{8} -4778.60i q^{9} +O(q^{10})\)	\(q+(-4.39608 - 4.39608i) q^{2} +(75.2981 - 75.2981i) q^{3} -217.349i q^{4} +(-14.1685 + 624.839i) q^{5} -662.032 q^{6} +(730.992 + 730.992i) q^{7} +(-2080.88 + 2080.88i) q^{8} -4778.60i q^{9} +(2809.13 - 2684.56i) q^{10} +19599.8 q^{11} +(-16366.0 - 16366.0i) q^{12} +(-24915.1 + 24915.1i) q^{13} -6426.99i q^{14} +(45982.3 + 48116.1i) q^{15} -37346.0 q^{16} +(-11288.6 - 11288.6i) q^{17} +(-21007.1 + 21007.1i) q^{18} -171525. i q^{19} +(135808. + 3079.51i) q^{20} +110085. q^{21} +(-86162.2 - 86162.2i) q^{22} +(-132074. + 132074. i) q^{23} +313372. i q^{24} +(-390224. - 17706.1i) q^{25} +219057. q^{26} +(134211. + 134211. i) q^{27} +(158880. - 158880. i) q^{28} -127019. i q^{29} +(9380.00 - 413664. i) q^{30} -960715. q^{31} +(696880. + 696880. i) q^{32} +(1.47583e6 - 1.47583e6i) q^{33} +99251.5i q^{34} +(-467110. + 446396. i) q^{35} -1.03862e6 q^{36} +(-243873. - 243873. i) q^{37} +(-754036. + 754036. i) q^{38} +3.75212e6i q^{39} +(-1.27073e6 - 1.32970e6i) q^{40} +2.50747e6 q^{41} +(-483940. - 483940. i) q^{42} +(-6763.95 + 6763.95i) q^{43} -4.26000e6i q^{44} +(2.98586e6 + 67705.6i) q^{45} +1.16122e6 q^{46} +(-1.79394e6 - 1.79394e6i) q^{47} +(-2.81208e6 + 2.81208e6i) q^{48} -4.69610e6i q^{49} +(1.63761e6 + 1.79329e6i) q^{50} -1.70003e6 q^{51} +(5.41527e6 + 5.41527e6i) q^{52} +(-2.97161e6 + 2.97161e6i) q^{53} -1.18001e6i q^{54} +(-277700. + 1.22467e7i) q^{55} -3.04221e6 q^{56} +(-1.29155e7 - 1.29155e7i) q^{57} +(-558385. + 558385. i) q^{58} +313805. i q^{59} +(1.04580e7 - 9.99422e6i) q^{60} +1.76977e7 q^{61} +(4.22338e6 + 4.22338e6i) q^{62} +(3.49312e6 - 3.49312e6i) q^{63} +3.43349e6i q^{64} +(-1.52149e7 - 1.59209e7i) q^{65} -1.29757e7 q^{66} +(4.41349e6 + 4.41349e6i) q^{67} +(-2.45358e6 + 2.45358e6i) q^{68} +1.98899e7i q^{69} +(4.01584e6 + 91060.8i) q^{70} -8.89315e6 q^{71} +(9.94368e6 + 9.94368e6i) q^{72} +(1.95076e7 - 1.95076e7i) q^{73} +2.14417e6i q^{74} +(-3.07163e7 + 2.80498e7i) q^{75} -3.72808e7 q^{76} +(1.43273e7 + 1.43273e7i) q^{77} +(1.64946e7 - 1.64946e7i) q^{78} -1.11272e7i q^{79} +(529136. - 2.33352e7i) q^{80} +5.15641e7 q^{81} +(-1.10230e7 - 1.10230e7i) q^{82} +(1.58712e7 - 1.58712e7i) q^{83} -2.39268e7i q^{84} +(7.21353e6 - 6.89365e6i) q^{85} +59469.7 q^{86} +(-9.56429e6 - 9.56429e6i) q^{87} +(-4.07848e7 + 4.07848e7i) q^{88} +4.85032e7i q^{89} +(-1.28284e7 - 1.34237e7i) q^{90} -3.64255e7 q^{91} +(2.87062e7 + 2.87062e7i) q^{92} +(-7.23400e7 + 7.23400e7i) q^{93} +1.57726e7i q^{94} +(1.07176e8 + 2.43025e6i) q^{95} +1.04948e8 q^{96} +(-1.07411e8 - 1.07411e8i) q^{97} +(-2.06444e7 + 2.06444e7i) q^{98} -9.36596e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 72 q^{3} + 220 q^{5} + 1752 q^{6} - 2352 q^{7} - 8220 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 72 * q^3 + 220 * q^5 + 1752 * q^6 - 2352 * q^7 - 8220 * q^8	\( 6 q - 2 q^{2} - 72 q^{3} + 220 q^{5} + 1752 q^{6} - 2352 q^{7} - 8220 q^{8} + 30870 q^{10} + 23192 q^{11} - 45912 q^{12} - 119142 q^{13} + 241440 q^{15} + 218616 q^{16} - 265502 q^{17} - 454062 q^{18} + 412260 q^{20} + 231672 q^{21} - 35664 q^{22} + 28888 q^{23} - 340350 q^{25} - 801388 q^{26} + 392040 q^{27} + 1305192 q^{28} - 2549760 q^{30} - 747648 q^{31} + 3033928 q^{32} + 4269096 q^{33} - 4971680 q^{35} - 3972804 q^{36} - 454002 q^{37} + 1443720 q^{38} + 2683500 q^{40} + 2489432 q^{41} + 4223856 q^{42} + 792648 q^{43} + 210690 q^{45} - 3149928 q^{46} - 15313352 q^{47} - 21677712 q^{48} + 29537650 q^{50} + 35567712 q^{51} - 735732 q^{52} - 13509122 q^{53} + 4448040 q^{55} - 18454800 q^{56} - 34625520 q^{57} - 23903520 q^{58} + 13688520 q^{60} + 24111192 q^{61} + 53913416 q^{62} + 44837688 q^{63} - 30943610 q^{65} - 55047936 q^{66} - 32827752 q^{67} + 8118692 q^{68} - 44156280 q^{70} - 13992928 q^{71} + 82596420 q^{72} + 111859638 q^{73} - 126793200 q^{75} - 56470800 q^{76} + 26260136 q^{77} + 31125576 q^{78} + 23045920 q^{80} + 65834226 q^{81} + 38023056 q^{82} - 14768432 q^{83} - 19713030 q^{85} - 135560008 q^{86} - 133207680 q^{87} - 44555040 q^{88} + 135147990 q^{90} + 167542032 q^{91} + 69931048 q^{92} - 96798024 q^{93} + 239661000 q^{95} + 184867872 q^{96} - 186656202 q^{97} - 345959698 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 72 * q^3 + 220 * q^5 + 1752 * q^6 - 2352 * q^7 - 8220 * q^8 + 30870 * q^10 + 23192 * q^11 - 45912 * q^12 - 119142 * q^13 + 241440 * q^15 + 218616 * q^16 - 265502 * q^17 - 454062 * q^18 + 412260 * q^20 + 231672 * q^21 - 35664 * q^22 + 28888 * q^23 - 340350 * q^25 - 801388 * q^26 + 392040 * q^27 + 1305192 * q^28 - 2549760 * q^30 - 747648 * q^31 + 3033928 * q^32 + 4269096 * q^33 - 4971680 * q^35 - 3972804 * q^36 - 454002 * q^37 + 1443720 * q^38 + 2683500 * q^40 + 2489432 * q^41 + 4223856 * q^42 + 792648 * q^43 + 210690 * q^45 - 3149928 * q^46 - 15313352 * q^47 - 21677712 * q^48 + 29537650 * q^50 + 35567712 * q^51 - 735732 * q^52 - 13509122 * q^53 + 4448040 * q^55 - 18454800 * q^56 - 34625520 * q^57 - 23903520 * q^58 + 13688520 * q^60 + 24111192 * q^61 + 53913416 * q^62 + 44837688 * q^63 - 30943610 * q^65 - 55047936 * q^66 - 32827752 * q^67 + 8118692 * q^68 - 44156280 * q^70 - 13992928 * q^71 + 82596420 * q^72 + 111859638 * q^73 - 126793200 * q^75 - 56470800 * q^76 + 26260136 * q^77 + 31125576 * q^78 + 23045920 * q^80 + 65834226 * q^81 + 38023056 * q^82 - 14768432 * q^83 - 19713030 * q^85 - 135560008 * q^86 - 133207680 * q^87 - 44555040 * q^88 + 135147990 * q^90 + 167542032 * q^91 + 69931048 * q^92 - 96798024 * q^93 + 239661000 * q^95 + 184867872 * q^96 - 186656202 * q^97 - 345959698 * q^98

Introduction

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