LMFDB - Embedded newform 24.8.d.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,8,Mod(13,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("24.13");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	24.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.49724061162$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 52 x^{12} + 300 x^{11} - 1005 x^{10} - 23250 x^{9} + 349930 x^{8} + \cdots + 3813237677250 $ x^14 - 6x^13 - 52x^12 + 300x^11 - 1005x^10 - 23250x^9 + 349930x^8 + 2867784x^7 - 20463993x^6 - 78987210x^5 + 94608296x^4 - 6477861300x^3 - 21982316987x^2 + 613270661346*x + 3813237677250
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{37}\cdot 3^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.5
Root			$2.71713 - 7.81354i$ of defining polynomial
Character	$\chi$	$=$	24.13
Dual form			24.8.d.a.13.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.09641 - 9.53067i) q^{2} +27.0000i q^{3} +(-53.6675 + 116.206i) q^{4} -137.155i q^{5} +(257.328 - 164.603i) q^{6} +808.153 q^{7} +(1434.70 - 196.951i) q^{8} -729.000 q^{9} +O(q^{10})$	\(q+(-6.09641 - 9.53067i) q^{2} +27.0000i q^{3} +(-53.6675 + 116.206i) q^{4} -137.155i q^{5} +(257.328 - 164.603i) q^{6} +808.153 q^{7} +(1434.70 - 196.951i) q^{8} -729.000 q^{9} +(-1307.18 + 836.155i) q^{10} -8242.25i q^{11} +(-3137.56 - 1449.02i) q^{12} -3408.20i q^{13} +(-4926.84 - 7702.25i) q^{14} +3703.19 q^{15} +(-10623.6 - 12473.0i) q^{16} +20783.8 q^{17} +(4444.29 + 6947.86i) q^{18} -6307.04i q^{19} +(15938.2 + 7360.78i) q^{20} +21820.1i q^{21} +(-78554.2 + 50248.2i) q^{22} +68891.6 q^{23} +(5317.69 + 38736.9i) q^{24} +59313.5 q^{25} +(-32482.5 + 20777.8i) q^{26} -19683.0i q^{27} +(-43371.6 + 93912.2i) q^{28} -42047.6i q^{29} +(-22576.2 - 35293.9i) q^{30} -214737. q^{31} +(-54109.8 + 177290. i) q^{32} +222541. q^{33} +(-126707. - 198084. i) q^{34} -110842. i q^{35} +(39123.6 - 84714.1i) q^{36} +182746. i q^{37} +(-60110.3 + 38450.3i) q^{38} +92021.5 q^{39} +(-27012.9 - 196776. i) q^{40} +395877. q^{41} +(207961. - 133025. i) q^{42} -433527. i q^{43} +(957798. + 442341. i) q^{44} +99986.1i q^{45} +(-419992. - 656584. i) q^{46} -1.32987e6 q^{47} +(336770. - 286837. i) q^{48} -170431. q^{49} +(-361599. - 565297. i) q^{50} +561163. i q^{51} +(396053. + 182910. i) q^{52} +225062. i q^{53} +(-187592. + 119996. i) q^{54} -1.13047e6 q^{55} +(1.15946e6 - 159167. i) q^{56} +170290. q^{57} +(-400742. + 256340. i) q^{58} -2.06725e6i q^{59} +(-198741. + 430332. i) q^{60} +3.11174e6i q^{61} +(1.30913e6 + 2.04659e6i) q^{62} -589144. q^{63} +(2.01957e6 - 565132. i) q^{64} -467453. q^{65} +(-1.35670e6 - 2.12096e6i) q^{66} +1.22034e6i q^{67} +(-1.11542e6 + 2.41520e6i) q^{68} +1.86007e6i q^{69} +(-1.05640e6 + 675741. i) q^{70} -1.63667e6 q^{71} +(-1.04590e6 + 143578. i) q^{72} +3.43311e6 q^{73} +(1.74169e6 - 1.11409e6i) q^{74} +1.60146e6i q^{75} +(732915. + 338483. i) q^{76} -6.66100e6i q^{77} +(-561001. - 877027. i) q^{78} +6.60063e6 q^{79} +(-1.71073e6 + 1.45708e6i) q^{80} +531441. q^{81} +(-2.41343e6 - 3.77298e6i) q^{82} -3.38713e6i q^{83} +(-2.53563e6 - 1.17103e6i) q^{84} -2.85061e6i q^{85} +(-4.13180e6 + 2.64296e6i) q^{86} +1.13529e6 q^{87} +(-1.62332e6 - 1.18252e7i) q^{88} -688852. q^{89} +(952935. - 609557. i) q^{90} -2.75435e6i q^{91} +(-3.69724e6 + 8.00561e6i) q^{92} -5.79791e6i q^{93} +(8.10744e6 + 1.26746e7i) q^{94} -865043. q^{95} +(-4.78684e6 - 1.46096e6i) q^{96} -3.48055e6 q^{97} +(1.03902e6 + 1.62432e6i) q^{98} +6.00860e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9	\( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9} + 5020 q^{10} + 7668 q^{12} + 4636 q^{14} - 13500 q^{15} - 43336 q^{16} - 2908 q^{17} + 10206 q^{18} + 175096 q^{20} - 128480 q^{22} - 143416 q^{23} - 29268 q^{24} - 202626 q^{25} + 424984 q^{26} + 567520 q^{28} - 250668 q^{30} - 89468 q^{31} - 893944 q^{32} + 1109820 q^{34} + 151632 q^{36} - 823816 q^{38} + 474552 q^{39} - 860888 q^{40} - 441284 q^{41} + 427788 q^{42} + 1275264 q^{44} - 2167992 q^{46} - 1056408 q^{47} - 233280 q^{48} + 2158134 q^{49} + 324610 q^{50} - 2059248 q^{52} + 39366 q^{54} + 4757504 q^{55} + 1643704 q^{56} + 1551096 q^{57} - 5494676 q^{58} - 3203712 q^{60} + 5767172 q^{62} - 1000188 q^{63} + 3852224 q^{64} - 2520464 q^{65} - 3615840 q^{66} - 3735840 q^{68} + 12890312 q^{70} + 5172696 q^{71} + 312012 q^{72} - 5446196 q^{73} - 6468800 q^{74} - 9084624 q^{76} + 3542184 q^{78} - 14373548 q^{79} + 14369088 q^{80} + 7440174 q^{81} - 7935708 q^{82} - 2775816 q^{84} + 4738312 q^{86} + 7902036 q^{87} + 12598720 q^{88} - 11952620 q^{89} - 3659580 q^{90} + 11004480 q^{92} - 15440088 q^{94} - 69327376 q^{95} + 1341576 q^{96} + 133732 q^{97} + 53030538 q^{98}+O(q^{100}) \) 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9 + 5020 * q^10 + 7668 * q^12 + 4636 * q^14 - 13500 * q^15 - 43336 * q^16 - 2908 * q^17 + 10206 * q^18 + 175096 * q^20 - 128480 * q^22 - 143416 * q^23 - 29268 * q^24 - 202626 * q^25 + 424984 * q^26 + 567520 * q^28 - 250668 * q^30 - 89468 * q^31 - 893944 * q^32 + 1109820 * q^34 + 151632 * q^36 - 823816 * q^38 + 474552 * q^39 - 860888 * q^40 - 441284 * q^41 + 427788 * q^42 + 1275264 * q^44 - 2167992 * q^46 - 1056408 * q^47 - 233280 * q^48 + 2158134 * q^49 + 324610 * q^50 - 2059248 * q^52 + 39366 * q^54 + 4757504 * q^55 + 1643704 * q^56 + 1551096 * q^57 - 5494676 * q^58 - 3203712 * q^60 + 5767172 * q^62 - 1000188 * q^63 + 3852224 * q^64 - 2520464 * q^65 - 3615840 * q^66 - 3735840 * q^68 + 12890312 * q^70 + 5172696 * q^71 + 312012 * q^72 - 5446196 * q^73 - 6468800 * q^74 - 9084624 * q^76 + 3542184 * q^78 - 14373548 * q^79 + 14369088 * q^80 + 7440174 * q^81 - 7935708 * q^82 - 2775816 * q^84 + 4738312 * q^86 + 7902036 * q^87 + 12598720 * q^88 - 11952620 * q^89 - 3659580 * q^90 + 11004480 * q^92 - 15440088 * q^94 - 69327376 * q^95 + 1341576 * q^96 + 133732 * q^97 + 53030538 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−6.09641	−	9.53067i	−0.538852	−	0.842401i
$2$	−6.09641	−	9.53067i	−0.538852	−	0.842401i
$3$			27.0000i			0.577350i
$3$			27.0000i			0.577350i
$4$	−53.6675	+	116.206i	−0.419277	+	0.907858i
$5$		−	137.155i		−	0.490701i	−0.969434	−	0.245351i	$-0.921097\pi$
$5$		−	137.155i		−	0.490701i	0.969434	−	0.245351i	$-0.0789031\pi$
$6$	257.328	−	164.603i	0.486360	−	0.311106i
$7$	808.153			0.890534			0.445267	−	0.895398i	$-0.353109\pi$
$7$	808.153			0.890534			0.445267	+	0.895398i	$0.353109\pi$
$8$	1434.70	−	196.951i	0.990709	−	0.136002i
$9$	−729.000			−0.333333
$10$	−1307.18	+	836.155i	−0.413367	+	0.264415i
$11$		−	8242.25i		−	1.86712i	−0.358426	−	0.933558i	$-0.616686\pi$
$11$		−	8242.25i		−	1.86712i	0.358426	−	0.933558i	$-0.383314\pi$
$12$	−3137.56	−	1449.02i	−0.524152	−	0.242070i
$13$		−	3408.20i		−	0.430253i	−0.976586	−	0.215127i	$-0.930984\pi$
$13$		−	3408.20i		−	0.430253i	0.976586	−	0.215127i	$-0.0690164\pi$
$14$	−4926.84	−	7702.25i	−0.479866	−	0.750187i
$15$	3703.19			0.283307
$16$	−10623.6	−	12473.0i	−0.648413	−	0.761289i
$17$	20783.8			1.02602			0.513008	−	0.858384i	$-0.328531\pi$
$17$	20783.8			1.02602			0.513008	+	0.858384i	$0.328531\pi$
$18$	4444.29	+	6947.86i	0.179617	+	0.280800i
$19$		−	6307.04i		−	0.210954i	−0.994422	−	0.105477i	$-0.966363\pi$
$19$		−	6307.04i		−	0.210954i	0.994422	−	0.105477i	$-0.0336370\pi$
$20$	15938.2	+	7360.78i	0.445487	+	0.205740i
$21$			21820.1i			0.514150i
$22$	−78554.2	+	50248.2i	−1.57286	+	1.00610i
$23$	68891.6			1.18064			0.590322	−	0.807168i	$-0.299001\pi$
$23$	68891.6			1.18064			0.590322	+	0.807168i	$0.299001\pi$
$24$	5317.69	+	38736.9i	0.0785206	+	0.571986i
$25$	59313.5			0.759212
$26$	−32482.5	+	20777.8i	−0.362445	+	0.231843i
$27$		−	19683.0i		−	0.192450i
$28$	−43371.6	+	93912.2i	−0.373381	+	0.808479i
$29$		−	42047.6i		−	0.320146i	−0.987105	−	0.160073i	$-0.948827\pi$
$29$		−	42047.6i		−	0.320146i	0.987105	−	0.160073i	$-0.0511730\pi$
$30$	−22576.2	−	35293.9i	−0.152660	−	0.238658i
$31$	−214737.			−1.29462			−0.647309	−	0.762228i	$-0.724106\pi$
$31$	−214737.			−1.29462			−0.647309	+	0.762228i	$0.724106\pi$
$32$	−54109.8	+	177290.i	−0.291911	+	0.956445i
$33$	222541.			1.07798
$34$	−126707.	−	198084.i	−0.552871	−	0.864317i
$35$		−	110842.i		−	0.436986i
$36$	39123.6	−	84714.1i	0.139759	−	0.302619i
$37$			182746.i			0.593118i	0.955015	+	0.296559i	$0.0958391\pi$
$37$			182746.i			0.593118i	−0.955015	+	0.296559i	$0.904161\pi$
$38$	−60110.3	+	38450.3i	−0.177708	+	0.113673i
$39$	92021.5			0.248407
$40$	−27012.9	−	196776.i	−0.0667362	−	0.486142i
$41$	395877.			0.897051			0.448525	−	0.893770i	$-0.351949\pi$
$41$	395877.			0.897051			0.448525	+	0.893770i	$0.351949\pi$
$42$	207961.	−	133025.i	0.433120	−	0.277051i
$43$		−	433527.i		−	0.831527i	−0.909473	−	0.415763i	$-0.863514\pi$
$43$		−	433527.i		−	0.831527i	0.909473	−	0.415763i	$-0.136486\pi$
$44$	957798.	+	442341.i	1.69508	+	0.782840i
$45$			99986.1i			0.163567i
$46$	−419992.	−	656584.i	−0.636192	−	0.994575i
$47$	−1.32987e6			−1.86839			−0.934194	−	0.356766i	$-0.883880\pi$
$47$	−1.32987e6			−1.86839			−0.934194	+	0.356766i	$0.883880\pi$
$48$	336770.	−	286837.i	0.439530	−	0.374361i
$49$	−170431.			−0.206949
$50$	−361599.	−	565297.i	−0.409103	−	0.639561i
$51$			561163.i			0.592371i
$52$	396053.	+	182910.i	0.390609	+	0.180395i
$53$			225062.i			0.207652i	0.994595	+	0.103826i	$0.0331085\pi$
$53$			225062.i			0.207652i	−0.994595	+	0.103826i	$0.966891\pi$
$54$	−187592.	+	119996.i	−0.162120	+	0.103702i
$55$	−1.13047e6			−0.916197
$56$	1.15946e6	−	159167.i	0.882260	−	0.121114i
$57$	170290.			0.121794
$58$	−400742.	+	256340.i	−0.269691	+	0.172511i
$59$		−	2.06725e6i		−	1.31042i	−0.755445	−	0.655212i	$-0.772579\pi$
$59$		−	2.06725e6i		−	1.31042i	0.755445	−	0.655212i	$-0.227421\pi$
$60$	−198741.	+	430332.i	−0.118784	+	0.257202i
$61$			3.11174e6i			1.75529i	0.479310	+	0.877646i	$0.340887\pi$
$61$			3.11174e6i			1.75529i	−0.479310	+	0.877646i	$0.659113\pi$
$62$	1.30913e6	+	2.04659e6i	0.697607	+	1.09059i
$63$	−589144.			−0.296845
$64$	2.01957e6	−	565132.i	0.963007	−	0.269476i
$65$	−467453.			−0.211126
$66$	−1.35670e6	−	2.12096e6i	−0.580872	−	0.908091i
$67$			1.22034e6i			0.495699i	0.968798	+	0.247850i	$0.0797239\pi$
$67$			1.22034e6i			0.495699i	−0.968798	+	0.247850i	$0.920276\pi$
$68$	−1.11542e6	+	2.41520e6i	−0.430185	+	0.931478i
$69$			1.86007e6i			0.681645i
$70$	−1.05640e6	+	675741.i	−0.368118	+	0.235471i
$71$	−1.63667e6			−0.542695			−0.271348	−	0.962481i	$-0.587469\pi$
$71$	−1.63667e6			−0.542695			−0.271348	+	0.962481i	$0.587469\pi$
$72$	−1.04590e6	+	143578.i	−0.330236	+	0.0453339i
$73$	3.43311e6			1.03290			0.516450	−	0.856318i	$-0.327253\pi$
$73$	3.43311e6			1.03290			0.516450	+	0.856318i	$0.327253\pi$
$74$	1.74169e6	−	1.11409e6i	0.499643	−	0.319603i
$75$			1.60146e6i			0.438331i
$76$	732915.	+	338483.i	0.191516	+	0.0884483i
$77$		−	6.66100e6i		−	1.66273i
$78$	−561001.	−	877027.i	−0.133854	−	0.209258i
$79$	6.60063e6			1.50623			0.753113	−	0.657891i	$-0.228551\pi$
$79$	6.60063e6			1.50623			0.753113	+	0.657891i	$0.228551\pi$
$80$	−1.71073e6	+	1.45708e6i	−0.373565	+	0.318177i
$81$	531441.			0.111111
$82$	−2.41343e6	−	3.77298e6i	−0.483377	−	0.755676i
$83$		−	3.38713e6i		−	0.650217i	−0.945677	−	0.325108i	$-0.894599\pi$
$83$		−	3.38713e6i		−	0.650217i	0.945677	−	0.325108i	$-0.105401\pi$
$84$	−2.53563e6	−	1.17103e6i	−0.466776	−	0.215572i
$85$		−	2.85061e6i		−	0.503468i
$86$	−4.13180e6	+	2.64296e6i	−0.700478	+	0.448070i
$87$	1.13529e6			0.184836
$88$	−1.62332e6	−	1.18252e7i	−0.253931	−	1.84977i
$89$	−688852.			−0.103576			−0.0517882	−	0.998658i	$-0.516492\pi$
$89$	−688852.			−0.103576			−0.0517882	+	0.998658i	$0.516492\pi$
$90$	952935.	−	609557.i	0.137789	−	0.0881384i
$91$		−	2.75435e6i		−	0.383155i
$92$	−3.69724e6	+	8.00561e6i	−0.495017	+	1.07186i
$93$		−	5.79791e6i		−	0.747448i
$94$	8.10744e6	+	1.26746e7i	1.00678	+	1.57393i
$95$	−865043.			−0.103515
$96$	−4.78684e6	−	1.46096e6i	−0.552204	−	0.168535i
$97$	−3.48055e6			−0.387210			−0.193605	−	0.981080i	$-0.562018\pi$
$97$	−3.48055e6			−0.387210			−0.193605	+	0.981080i	$0.562018\pi$
$98$	1.03902e6	+	1.62432e6i	0.111515	+	0.174334i
$99$			6.00860e6i			0.622372i
$100$	−3.18320e6	+	6.89257e6i	−0.318320	+	0.689257i
$101$		−	6.80385e6i		−	0.657098i	−0.944487	−	0.328549i	$-0.893440\pi$
$101$		−	6.80385e6i		−	0.657098i	0.944487	−	0.328549i	$-0.106560\pi$
$102$	5.34827e6	−	3.42108e6i	0.499014	−	0.319200i
$103$	1.85092e7			1.66900			0.834502	−	0.551005i	$-0.185756\pi$
$103$	1.85092e7			1.66900			0.834502	+	0.551005i	$0.185756\pi$
$104$	−671251.	−	4.88975e6i	−0.0585151	−	0.426255i
$105$	2.99275e6			0.252294
$106$	2.14499e6	−	1.37207e6i	0.174926	−	0.111894i
$107$			1.69583e7i			1.33826i	0.743146	+	0.669129i	$0.233333\pi$
$107$			1.69583e7i			1.33826i	−0.743146	+	0.669129i	$0.766667\pi$
$108$	2.28728e6	+	1.05634e6i	0.174717	+	0.0806900i
$109$			2.40588e7i			1.77943i	0.456512	+	0.889717i	$0.349099\pi$
$109$			2.40588e7i			1.77943i	−0.456512	+	0.889717i	$0.650901\pi$
$110$	6.89180e6	+	1.07741e7i	0.493694	+	0.771804i
$111$	−4.93413e6			−0.342437
$112$	−8.58550e6	−	1.00801e7i	−0.577434	−	0.677954i
$113$	−1.97853e7			−1.28993			−0.644967	−	0.764211i	$-0.723129\pi$
$113$	−1.97853e7			−1.28993			−0.644967	+	0.764211i	$0.723129\pi$
$114$	−1.03816e6	−	1.62298e6i	−0.0656291	−	0.102600i
$115$		−	9.44885e6i		−	0.579344i
$116$	4.88618e6	+	2.25659e6i	0.290647	+	0.134230i
$117$			2.48458e6i			0.143418i
$118$	−1.97023e7	+	1.26028e7i	−1.10390	+	0.706125i
$119$	1.67965e7			0.913703
$120$	5.31296e6	−	729349.i	0.280674	−	0.0385302i
$121$	−4.84475e7			−2.48612
$122$	2.96570e7	−	1.89705e7i	1.47866	−	0.945842i
$123$			1.06887e7i			0.517912i
$124$	1.15244e7	−	2.49537e7i	0.542804	−	1.17533i
$125$		−	1.88504e7i		−	0.863248i
$126$	3.59166e6	+	5.61494e6i	0.159955	+	0.250062i
$127$	−2.74201e7			−1.18783			−0.593917	−	0.804526i	$-0.702419\pi$
$127$	−2.74201e7			−1.18783			−0.593917	+	0.804526i	$0.702419\pi$
$128$	−1.76982e7	−	1.58026e7i	−0.745925	−	0.666030i
$129$	1.17052e7			0.480082
$130$	2.84979e6	+	4.45514e6i	0.113766	+	0.177852i
$131$			1.22444e7i			0.475868i	0.971281	+	0.237934i	$0.0764703\pi$
$131$			1.22444e7i			0.475868i	−0.971281	+	0.237934i	$0.923530\pi$
$132$	−1.19432e7	+	2.58605e7i	−0.451973	+	0.978653i
$133$		−	5.09705e6i		−	0.187862i
$134$	1.16306e7	−	7.43969e6i	0.417577	−	0.267109i
$135$	−2.69963e6			−0.0944355
$136$	2.98185e7	−	4.09341e6i	1.01648	−	0.139540i
$137$	4.83466e7			1.60636			0.803182	−	0.595733i	$-0.203138\pi$
$137$	4.83466e7			1.60636			0.803182	+	0.595733i	$0.203138\pi$
$138$	1.77278e7	−	1.13398e7i	0.574218	−	0.367306i
$139$		−	2.54730e7i		−	0.804503i	−0.915529	−	0.402252i	$-0.868228\pi$
$139$		−	2.54730e7i		−	0.804503i	0.915529	−	0.402252i	$-0.131772\pi$
$140$	1.28805e7	+	5.94864e6i	0.396722	+	0.183218i
$141$		−	3.59065e7i		−	1.07871i
$142$	9.97779e6	+	1.55985e7i	0.292432	+	0.457167i
$143$	−2.80913e7			−0.803333
$144$	7.74460e6	+	9.09278e6i	0.216138	+	0.253763i
$145$	−5.76705e6			−0.157096
$146$	−2.09297e7	−	3.27199e7i	−0.556580	−	0.870115i
$147$		−	4.60164e6i		−	0.119482i
$148$	−2.12361e7	−	9.80750e6i	−0.538467	−	0.248681i
$149$			5.26513e7i			1.30394i	0.758245	+	0.651969i	$0.226057\pi$
$149$			5.26513e7i			1.30394i	−0.758245	+	0.651969i	$0.773943\pi$
$150$	1.52630e7	−	9.76318e6i	0.369251	−	0.236196i
$151$	2.75769e7			0.651817			0.325909	−	0.945401i	$-0.394330\pi$
$151$	2.75769e7			0.651817			0.325909	+	0.945401i	$0.394330\pi$
$152$	−1.24218e6	−	9.04870e6i	−0.0286901	−	0.208994i
$153$	−1.51514e7			−0.342006
$154$	−6.34838e7	+	4.06082e7i	−1.40069	+	0.895966i
$155$			2.94523e7i			0.635271i
$156$	−4.93857e6	+	1.06934e7i	−0.104151	+	0.225518i
$157$			1.50946e7i			0.311296i	0.987813	+	0.155648i	$0.0497466\pi$
$157$			1.50946e7i			0.311296i	−0.987813	+	0.155648i	$0.950253\pi$
$158$	−4.02401e7	−	6.29084e7i	−0.811633	−	1.26885i
$159$	−6.07667e6			−0.119888
$160$	2.43163e7	+	7.42144e6i	0.469329	+	0.143241i
$161$	5.56750e7			1.05140
$162$	−3.23988e6	−	5.06499e6i	−0.0598724	−	0.0936001i
$163$		−	7.23758e7i		−	1.30899i	−0.756066	−	0.654496i	$-0.772881\pi$
$163$		−	7.23758e7i		−	1.30899i	0.756066	−	0.654496i	$-0.227119\pi$
$164$	−2.12457e7	+	4.60032e7i	−0.376113	+	0.814395i
$165$		−	3.05226e7i		−	0.528966i
$166$	−3.22816e7	+	2.06493e7i	−0.547743	+	0.350370i
$167$	−2.87007e7			−0.476854			−0.238427	−	0.971160i	$-0.576632\pi$
$167$	−2.87007e7			−0.476854			−0.238427	+	0.971160i	$0.576632\pi$
$168$	4.29751e6	+	3.13053e7i	0.0699253	+	0.509373i
$169$	5.11327e7			0.814882
$170$	−2.71682e7	+	1.73785e7i	−0.424121	+	0.271295i
$171$			4.59783e6i			0.0703180i
$172$	5.03783e7	+	2.32663e7i	0.754908	+	0.348640i
$173$			1.61003e7i			0.236414i	0.992989	+	0.118207i	$0.0377146\pi$
$173$			1.61003e7i			0.236414i	−0.992989	+	0.118207i	$0.962285\pi$
$174$	−6.92117e6	−	1.08200e7i	−0.0995995	−	0.155706i
$175$	4.79344e7			0.676104
$176$	−1.02805e8	+	8.75624e7i	−1.42141	+	1.21066i
$177$	5.58159e7			0.756574
$178$	4.19953e6	+	6.56522e6i	0.0558124	+	0.0872528i
$179$			5.41747e7i			0.706010i	0.935622	+	0.353005i	$0.114840\pi$
$179$			5.41747e7i			0.706010i	−0.935622	+	0.353005i	$0.885160\pi$
$180$	−1.16190e7	−	5.36601e6i	−0.148496	−	0.0685800i
$181$			1.36783e8i			1.71458i	0.514836	+	0.857288i	$0.327853\pi$
$181$			1.36783e8i			1.71458i	−0.514836	+	0.857288i	$0.672147\pi$
$182$	−2.62508e7	+	1.67917e7i	−0.322770	+	0.206464i
$183$	−8.40171e7			−1.01342
$184$	9.88388e7	−	1.35683e7i	1.16967	−	0.160570i
$185$	2.50645e7			0.291044
$186$	−5.52580e7	+	3.53464e7i	−0.629651	+	0.402764i
$187$		−	1.71306e8i		−	1.91569i
$188$	7.13709e7	−	1.54539e8i	0.783373	−	1.69623i
$189$		−	1.59069e7i		−	0.171383i
$190$	5.27366e6	+	8.24444e6i	0.0557795	+	0.0872015i
$191$	9.18294e6			0.0953597			0.0476799	−	0.998863i	$-0.484817\pi$
$191$	9.18294e6			0.0953597			0.0476799	+	0.998863i	$0.484817\pi$
$192$	1.52586e7	+	5.45285e7i	0.155582	+	0.555992i
$193$	3.02678e7			0.303062			0.151531	−	0.988453i	$-0.451580\pi$
$193$	3.02678e7			0.303062			0.151531	+	0.988453i	$0.451580\pi$
$194$	2.12189e7	+	3.31720e7i	0.208649	+	0.326186i
$195$		−	1.26212e7i		−	0.121894i
$196$	9.14661e6	−	1.98051e7i	0.0867689	−	0.187880i
$197$		−	5.72982e7i		−	0.533960i	−0.963702	−	0.266980i	$-0.913974\pi$
$197$		−	5.72982e7i		−	0.533960i	0.963702	−	0.266980i	$-0.0860258\pi$
$198$	5.72660e7	−	3.66309e7i	0.524287	−	0.335366i
$199$	−2.41023e6			−0.0216807			−0.0108403	−	0.999941i	$-0.503451\pi$
$199$	−2.41023e6			−0.0216807			−0.0108403	+	0.999941i	$0.503451\pi$
$200$	8.50970e7	−	1.16819e7i	0.752158	−	0.103254i
$201$	−3.29491e7			−0.286192
$202$	−6.48453e7	+	4.14791e7i	−0.553540	+	0.354078i
$203$		−	3.39809e7i		−	0.285101i
$204$	−6.52105e7	−	3.01162e7i	−0.537789	−	0.248368i
$205$		−	5.42966e7i		−	0.440184i
$206$	−1.12840e8	−	1.76405e8i	−0.899346	−	1.40597i
$207$	−5.02220e7			−0.393548
$208$	−4.25104e7	+	3.62074e7i	−0.327547	+	0.278982i
$209$	−5.19842e7			−0.393876
$210$	−1.82450e7	−	2.85229e7i	−0.135949	−	0.212533i
$211$			1.41783e8i			1.03905i	0.854457	+	0.519523i	$0.173890\pi$
$211$			1.41783e8i			1.03905i	−0.854457	+	0.519523i	$0.826110\pi$
$212$	−2.61535e7	−	1.20785e7i	−0.188519	−	0.0870638i
$213$		−	4.41900e7i		−	0.313325i
$214$	1.61624e8	−	1.03385e8i	1.12735	−	0.721123i
$215$	−5.94604e7			−0.408031
$216$	−3.87660e6	−	2.82392e7i	−0.0261735	−	0.190662i
$217$	−1.73541e8			−1.15290
$218$	2.29297e8	−	1.46673e8i	1.49900	−	0.958852i
$219$			9.26940e7i			0.596345i
$220$	6.06694e7	−	1.31367e8i	0.384140	−	0.831777i
$221$		−	7.08356e7i		−	0.441447i
$222$	3.00805e7	+	4.70256e7i	0.184523	+	0.288469i
$223$	−2.72134e7			−0.164330			−0.0821649	−	0.996619i	$-0.526183\pi$
$223$	−2.72134e7			−0.164330			−0.0821649	+	0.996619i	$0.526183\pi$
$224$	−4.37290e7	+	1.43278e8i	−0.259957	+	0.851747i
$225$	−4.32395e7			−0.253071
$226$	1.20619e8	+	1.88567e8i	0.695083	+	1.08664i
$227$		−	4.60299e6i		−	0.0261186i	−0.999915	−	0.0130593i	$-0.995843\pi$
$227$		−	4.60299e6i		−	0.0261186i	0.999915	−	0.0130593i	$-0.00415702\pi$
$228$	−9.13904e6	+	1.97887e7i	−0.0510656	+	0.110572i
$229$			1.66323e8i			0.915224i	0.889152	+	0.457612i	$0.151295\pi$
$229$			1.66323e8i			0.915224i	−0.889152	+	0.457612i	$0.848705\pi$
$230$	−9.00539e7	+	5.76041e7i	−0.488039	+	0.312180i
$231$	1.79847e8			0.959978
$232$	−8.28134e6	−	6.03257e7i	−0.0435404	−	0.317172i
$233$	−5.18994e7			−0.268792			−0.134396	−	0.990928i	$-0.542909\pi$
$233$	−5.18994e7			−0.268792			−0.134396	+	0.990928i	$0.542909\pi$
$234$	2.36797e7	−	1.51470e7i	0.120815	−	0.0772809i
$235$			1.82399e8i			0.916820i
$236$	2.40227e8	+	1.10944e8i	1.18968	+	0.549431i
$237$			1.78217e8i			0.869620i
$238$	−1.02399e8	−	1.60082e8i	−0.492351	−	0.769704i
$239$	−2.02994e7			−0.0961811			−0.0480906	−	0.998843i	$-0.515314\pi$
$239$	−2.02994e7			−0.0961811			−0.0480906	+	0.998843i	$0.515314\pi$
$240$	−3.93412e7	−	4.61897e7i	−0.183700	−	0.215678i
$241$	−3.40237e7			−0.156575			−0.0782875	−	0.996931i	$-0.524945\pi$
$241$	−3.40237e7			−0.156575			−0.0782875	+	0.996931i	$0.524945\pi$
$242$	2.95356e8	+	4.61738e8i	1.33965	+	2.09431i
$243$			1.43489e7i			0.0641500i
$244$	−3.61603e8	−	1.66999e8i	−1.59356	−	0.735954i
$245$			2.33755e7i			0.101550i
$246$	1.01870e8	−	6.51626e7i	0.436290	−	0.279078i
$247$	−2.14957e7			−0.0907636
$248$	−3.08083e8	+	4.22928e7i	−1.28259	+	0.176070i
$249$	9.14524e7			0.375403
$250$	−1.79657e8	+	1.14920e8i	−0.727200	+	0.465163i
$251$			5.06937e7i			0.202347i	0.994869	+	0.101173i	$0.0322596\pi$
$251$			5.06937e7i			0.202347i	−0.994869	+	0.101173i	$0.967740\pi$
$252$	3.16179e7	−	6.84620e7i	0.124460	−	0.269493i
$253$		−	5.67822e8i		−	2.20440i
$254$	1.67164e8	+	2.61332e8i	0.640067	+	1.00063i
$255$	7.69665e7			0.290677
$256$	−4.27137e7	+	2.65015e8i	−0.159121	+	0.987259i
$257$	−4.16956e8			−1.53223			−0.766116	−	0.642702i	$-0.777813\pi$
$257$	−4.16956e8			−1.53223			−0.766116	+	0.642702i	$0.777813\pi$
$258$	−7.13598e7	−	1.11559e8i	−0.258693	−	0.404421i
$259$			1.47687e8i			0.528192i
$260$	2.50870e7	−	5.43208e7i	0.0885202	−	0.191672i
$261$			3.06527e7i			0.106715i
$262$	1.16697e8	−	7.46467e7i	0.400872	−	0.256423i
$263$	3.30240e8			1.11940			0.559699	−	0.828696i	$-0.310917\pi$
$263$	3.30240e8			1.11940			0.559699	+	0.828696i	$0.310917\pi$
$264$	3.19279e8	−	4.38297e7i	1.06796	−	0.146607i
$265$	3.08684e7			0.101895
$266$	−4.85784e7	+	3.10738e7i	−0.158255	+	0.101230i
$267$		−	1.85990e7i		−	0.0597999i
$268$	−1.41810e8	−	6.54925e7i	−0.450025	−	0.207835i
$269$		−	3.55998e8i		−	1.11510i	−0.830143	−	0.557551i	$-0.811741\pi$
$269$		−	3.55998e8i		−	1.11510i	0.830143	−	0.557551i	$-0.188259\pi$
$270$	1.64580e7	+	2.57293e7i	0.0508868	+	0.0795525i
$271$	2.92692e8			0.893343			0.446671	−	0.894698i	$-0.352609\pi$
$271$	2.92692e8			0.893343			0.446671	+	0.894698i	$0.352609\pi$
$272$	−2.20799e8	−	2.59236e8i	−0.665283	−	0.781095i
$273$	7.43675e7			0.221215
$274$	−2.94741e8	−	4.60776e8i	−0.865593	−	1.35320i
$275$		−	4.88876e8i		−	1.41754i
$276$	−2.16152e8	−	9.98255e7i	−0.618837	−	0.285798i
$277$			3.30724e8i			0.934947i	0.884007	+	0.467473i	$0.154836\pi$
$277$			3.30724e8i			0.934947i	−0.884007	+	0.467473i	$0.845164\pi$
$278$	−2.42775e8	+	1.55294e8i	−0.677714	+	0.433508i
$279$	1.56543e8			0.431539
$280$	−2.18306e7	−	1.59026e8i	−0.0594309	−	0.432926i
$281$	2.85026e8			0.766325			0.383163	−	0.923681i	$-0.374835\pi$
$281$	2.85026e8			0.766325			0.383163	+	0.923681i	$0.374835\pi$
$282$	−3.42213e8	+	2.18901e8i	−0.908709	+	0.581267i
$283$			4.02132e7i			0.105467i	0.998609	+	0.0527334i	$0.0167934\pi$
$283$			4.02132e7i			0.105467i	−0.998609	+	0.0527334i	$0.983207\pi$
$284$	8.78358e7	−	1.90190e8i	0.227540	−	0.492690i
$285$		−	2.33562e7i		−	0.0597647i
$286$	1.71256e8	+	2.67729e8i	0.432877	+	0.676728i
$287$	3.19929e8			0.798854
$288$	3.94460e7	−	1.29245e8i	0.0973038	−	0.318815i
$289$	2.16289e7			0.0527100
$290$	3.51583e7	+	5.49639e7i	0.0846516	+	0.132338i
$291$		−	9.39749e7i		−	0.223556i
$292$	−1.84247e8	+	3.98948e8i	−0.433071	+	0.937726i
$293$			1.53923e8i			0.357493i	0.983895	+	0.178747i	$0.0572043\pi$
$293$			1.53923e8i			0.357493i	−0.983895	+	0.178747i	$0.942796\pi$
$294$	−4.38567e7	+	2.80535e7i	−0.100652	+	0.0643830i
$295$	−2.83535e8			−0.643027
$296$	3.59920e7	+	2.62185e8i	0.0806650	+	0.587607i
$297$	−1.62232e8			−0.359327
$298$	5.01802e8	−	3.20984e8i	1.09844	−	0.702630i
$299$		−	2.34797e8i		−	0.507976i
$300$	−1.86099e8	−	8.59465e7i	−0.397943	−	0.183782i
$301$		−	3.50356e8i		−	0.740503i
$302$	−1.68120e8	−	2.62826e8i	−0.351233	−	0.549091i
$303$	1.83704e8			0.379376
$304$	−7.86674e7	+	6.70035e7i	−0.160597	+	0.136785i
$305$	4.26792e8			0.861324
$306$	9.23693e7	+	1.44403e8i	0.184290	+	0.288106i
$307$			2.93832e8i			0.579583i	0.957090	+	0.289791i	$0.0935859\pi$
$307$			2.93832e8i			0.579583i	−0.957090	+	0.289791i	$0.906414\pi$
$308$	7.74047e8	+	3.57479e8i	1.50952	+	0.697145i
$309$			4.99748e8i			0.963600i
$310$	2.80701e8	−	1.79554e8i	0.535152	−	0.342317i
$311$	−9.52586e8			−1.79574			−0.897869	−	0.440263i	$-0.854885\pi$
$311$	−9.52586e8			−1.79574			−0.897869	+	0.440263i	$0.854885\pi$
$312$	1.32023e8	−	1.81238e7i	0.246099	−	0.0337837i
$313$	7.11814e8			1.31208			0.656041	−	0.754725i	$-0.272230\pi$
$313$	7.11814e8			1.31208			0.656041	+	0.754725i	$0.272230\pi$
$314$	1.43862e8	−	9.20231e7i	0.262236	−	0.167742i
$315$			8.08041e7i			0.145662i
$316$	−3.54239e8	+	7.67031e8i	−0.631527	+	1.36744i
$317$		−	1.92856e7i		−	0.0340037i	−0.999855	−	0.0170018i	$-0.994588\pi$
$317$		−	1.92856e7i		−	0.0340037i	0.999855	−	0.0170018i	$-0.00541212\pi$
$318$	3.70459e7	+	5.79147e7i	0.0646018	+	0.100994i
$319$	−3.46567e8			−0.597750
$320$	−7.75108e7	−	2.76995e8i	−0.132232	−	0.472549i
$321$	−4.57875e8			−0.772643
$322$	−3.39418e8	−	5.30620e8i	−0.566551	−	0.885703i
$323$		−	1.31084e8i		−	0.216442i
$324$	−2.85211e7	+	6.17566e7i	−0.0465864	+	0.100873i
$325$		−	2.02152e8i		−	0.326653i
$326$	−6.89790e8	+	4.41233e8i	−1.10270	+	0.705353i
$327$	−6.49589e8			−1.02736
$328$	5.67965e8	−	7.79686e7i	0.888716	−	0.122000i
$329$	−1.07474e9			−1.66386
$330$	−2.90901e8	+	1.86079e8i	−0.445602	+	0.285035i
$331$			6.26075e8i			0.948918i	0.880278	+	0.474459i	$0.157356\pi$
$331$			6.26075e8i			0.948918i	−0.880278	+	0.474459i	$0.842644\pi$
$332$	3.93604e8	+	1.81779e8i	0.590304	+	0.272621i
$333$		−	1.33222e8i		−	0.197706i
$334$	1.74971e8	+	2.73537e8i	0.256953	+	0.401702i
$335$	1.67376e8			0.243240
$336$	2.72162e8	−	2.31808e8i	0.391417	−	0.333382i
$337$	6.06096e8			0.862655			0.431327	−	0.902196i	$-0.358045\pi$
$337$	6.06096e8			0.862655			0.431327	+	0.902196i	$0.358045\pi$
$338$	−3.11726e8	−	4.87329e8i	−0.439101	−	0.686457i
$339$		−	5.34202e8i		−	0.744743i
$340$	3.31258e8	+	1.52985e8i	0.457077	+	0.211093i
$341$			1.76992e9i			2.41720i
$342$	4.38204e7	−	2.80303e7i	0.0592359	−	0.0378910i
$343$	−8.03284e8			−1.07483
$344$	−8.53837e7	−	6.21980e8i	−0.113089	−	0.823801i
$345$	2.55119e8			0.334484
$346$	1.53447e8	−	9.81542e7i	0.199155	−	0.127392i
$347$			5.46595e8i			0.702283i	0.936322	+	0.351142i	$0.114206\pi$
$347$			5.46595e8i			0.702283i	−0.936322	+	0.351142i	$0.885794\pi$
$348$	−6.09279e7	+	1.31927e8i	−0.0774977	+	0.167805i
$349$		−	2.67022e8i		−	0.336246i	−0.985766	−	0.168123i	$-0.946229\pi$
$349$		−	2.67022e8i		−	0.336246i	0.985766	−	0.168123i	$-0.0537706\pi$
$350$	−2.92228e8	−	4.56847e8i	−0.364320	−	0.569551i
$351$	−6.70837e7			−0.0828022
$352$	1.46127e9	+	4.45987e8i	1.78579	+	0.545033i
$353$	4.23784e8			0.512783			0.256391	−	0.966573i	$-0.417466\pi$
$353$	4.23784e8			0.512783			0.256391	+	0.966573i	$0.417466\pi$
$354$	−3.40277e8	−	5.31963e8i	−0.407681	−	0.637338i
$355$			2.24477e8i			0.266301i
$356$	3.69690e7	−	8.00486e7i	0.0434272	−	0.0940327i
$357$			4.53506e8i			0.527527i
$358$	5.16321e8	−	3.30271e8i	0.594743	−	0.380435i
$359$	2.46440e8			0.281113			0.140557	−	0.990073i	$-0.455111\pi$
$359$	2.46440e8			0.281113			0.140557	+	0.990073i	$0.455111\pi$
$360$	1.96924e7	+	1.43450e8i	0.0222454	+	0.162047i
$361$	8.54093e8			0.955498
$362$	1.30363e9	−	8.33885e8i	1.44436	−	0.923903i
$363$		−	1.30808e9i		−	1.43536i
$364$	3.20072e8	+	1.47819e8i	0.347851	+	0.160648i
$365$		−	4.70869e8i		−	0.506845i
$366$	5.12203e8	+	8.00739e8i	0.546082	+	0.853704i
$367$	−9.48483e8			−1.00161			−0.500805	−	0.865560i	$-0.666963\pi$
$367$	−9.48483e8			−1.00161			−0.500805	+	0.865560i	$0.666963\pi$
$368$	−7.31877e8	−	8.59282e8i	−0.765545	−	0.898811i
$369$	−2.88594e8			−0.299017
$370$	−1.52804e8	−	2.38882e8i	−0.156829	−	0.245175i
$371$			1.81884e8i			0.184921i
$372$	6.73751e8	+	3.11159e8i	0.678577	+	0.313388i
$373$		−	4.22758e8i		−	0.421804i	−0.977507	−	0.210902i	$-0.932360\pi$
$373$		−	4.22758e8i		−	0.421804i	0.977507	−	0.210902i	$-0.0676401\pi$
$374$	−1.63266e9	+	1.04435e9i	−1.61378	+	1.03227i
$375$	5.08961e8			0.498396
$376$	−1.90797e9	+	2.61920e8i	−1.85103	+	0.254104i
$377$	−1.43307e8			−0.137744
$378$	−1.51603e8	+	9.69749e7i	−0.144373	+	0.0923503i
$379$		−	1.90673e9i		−	1.79909i	−0.436828	−	0.899545i	$-0.643898\pi$
$379$		−	1.90673e9i		−	1.79909i	0.436828	−	0.899545i	$-0.356102\pi$
$380$	4.64247e7	−	1.00523e8i	0.0434017	−	0.0939773i
$381$		−	7.40343e8i		−	0.685797i
$382$	−5.59830e7	−	8.75196e7i	−0.0513848	−	0.0803311i
$383$	−4.96320e7			−0.0451405			−0.0225702	−	0.999745i	$-0.507185\pi$
$383$	−4.96320e7			−0.0451405			−0.0225702	+	0.999745i	$0.507185\pi$
$384$	4.26670e8	−	4.77852e8i	0.384533	−	0.430660i
$385$	−9.13591e8			−0.815904
$386$	−1.84525e8	−	2.88473e8i	−0.163305	−	0.255299i
$387$			3.16041e8i			0.277176i
$388$	1.86792e8	−	4.04460e8i	0.162348	−	0.351532i
$389$			1.83253e9i			1.57844i	0.614112	+	0.789219i	$0.289514\pi$
$389$			1.83253e9i			1.57844i	−0.614112	+	0.789219i	$0.710486\pi$
$390$	−1.20289e8	+	7.69442e7i	−0.102683	+	0.0656825i
$391$	1.43183e9			1.21136
$392$	−2.44517e8	+	3.35667e7i	−0.205026	+	0.0281454i
$393$	−3.30598e8			−0.274743
$394$	−5.46090e8	+	3.49313e8i	−0.449808	+	0.287726i
$395$		−	9.05310e8i		−	0.739107i
$396$	−6.98235e8	−	3.22467e8i	−0.565026	−	0.260947i
$397$		−	1.24041e9i		−	0.994942i	−0.867481	−	0.497471i	$-0.834262\pi$
$397$		−	1.24041e9i		−	0.994942i	0.867481	−	0.497471i	$-0.165738\pi$
$398$	1.46938e7	+	2.29711e7i	0.0116827	+	0.0182638i
$399$	1.37620e8			0.108462
$400$	−6.30122e8	−	7.39814e8i	−0.492283	−	0.577980i
$401$	1.72908e9			1.33909			0.669544	−	0.742772i	$-0.266489\pi$
$401$	1.72908e9			1.33909			0.669544	+	0.742772i	$0.266489\pi$
$402$	2.00872e8	+	3.14027e8i	0.154215	+	0.241088i
$403$			7.31869e8i			0.557013i
$404$	7.90648e8	+	3.65146e8i	0.596552	+	0.275506i
$405$		−	7.28899e7i		−	0.0545224i
$406$	−3.23861e8	+	2.07162e8i	−0.240169	+	0.153627i
$407$	1.50624e9			1.10742
$408$	1.10522e8	+	8.05101e8i	0.0805634	+	0.586867i
$409$	−1.59861e9			−1.15534			−0.577670	−	0.816271i	$-0.696038\pi$
$409$	−1.59861e9			−1.15534			−0.577670	+	0.816271i	$0.696038\pi$
$410$	−5.17483e8	+	3.31015e8i	−0.370811	+	0.237194i
$411$			1.30536e9i			0.927435i
$412$	−9.93342e8	+	2.15088e9i	−0.699775	+	1.51522i
$413$		−	1.67066e9i		−	1.16698i
$414$	3.06174e8	+	4.78650e8i	0.212064	+	0.331525i
$415$	−4.64562e8			−0.319062
$416$	6.04242e8	+	1.84417e8i	0.411514	+	0.125596i
$417$	6.87770e8			0.464480
$418$	3.16917e8	+	4.95444e8i	0.212241	+	0.331801i
$419$			1.44325e9i			0.958501i	0.877678	+	0.479250i	$0.159091\pi$
$419$			1.44325e9i			0.958501i	−0.877678	+	0.479250i	$0.840909\pi$
$420$	−1.60613e8	+	3.47775e8i	−0.105781	+	0.229047i
$421$			8.96348e8i			0.585450i	0.956197	+	0.292725i	$0.0945620\pi$
$421$			8.96348e8i			0.585450i	−0.956197	+	0.292725i	$0.905438\pi$
$422$	1.35128e9	−	8.64366e8i	0.875292	−	0.559892i
$423$	9.69476e8			0.622796
$424$	4.43262e7	+	3.22896e8i	0.0282410	+	0.205723i
$425$	1.23276e9			0.778964
$426$	−4.21160e8	+	2.69400e8i	−0.263945	+	0.168836i
$427$			2.51477e9i			1.56315i
$428$	−1.97066e9	−	9.10111e8i	−1.21495	−	0.561101i
$429$		−	7.58465e8i		−	0.463804i
$430$	3.62495e8	+	5.66698e8i	0.219868	+	0.343726i
$431$	7.07247e8			0.425501			0.212751	−	0.977107i	$-0.431758\pi$
$431$	7.07247e8			0.425501			0.212751	+	0.977107i	$0.431758\pi$
$432$	−2.45505e8	+	2.09104e8i	−0.146510	+	0.124787i
$433$	−4.90457e8			−0.290331			−0.145166	−	0.989407i	$-0.546371\pi$
$433$	−4.90457e8			−0.290331			−0.145166	+	0.989407i	$0.546371\pi$
$434$	1.05798e9	+	1.65396e9i	0.621243	+	0.971205i
$435$		−	1.55710e8i		−	0.0906995i
$436$	−2.79578e9	−	1.29118e9i	−1.61547	−	0.746077i
$437$		−	4.34502e8i		−	0.249062i
$438$	8.83437e8	−	5.65101e8i	0.502361	−	0.321342i
$439$	1.06892e9			0.603002			0.301501	−	0.953466i	$-0.402512\pi$
$439$	1.06892e9			0.603002			0.301501	+	0.953466i	$0.402512\pi$
$440$	−1.62188e9	+	2.22647e8i	−0.907684	+	0.124604i
$441$	1.24244e8			0.0689829
$442$	−6.75111e8	+	4.31843e8i	−0.371875	+	0.237874i
$443$			1.01920e9i			0.556989i	0.960438	+	0.278495i	$0.0898355\pi$
$443$			1.01920e9i			0.556989i	−0.960438	+	0.278495i	$0.910165\pi$
$444$	2.64803e8	−	5.73375e8i	0.143576	−	0.310884i
$445$			9.44796e7i			0.0508251i
$446$	1.65904e8	+	2.59362e8i	0.0885494	+	0.138432i
$447$	−1.42158e9			−0.752829
$448$	1.63212e9	−	4.56714e8i	0.857591	−	0.239978i
$449$	−2.46756e9			−1.28649			−0.643244	−	0.765661i	$-0.722412\pi$
$449$	−2.46756e9			−1.28649			−0.643244	+	0.765661i	$0.722412\pi$
$450$	2.63606e8	+	4.12102e8i	0.136368	+	0.213187i
$451$		−	3.26292e9i		−	1.67490i
$452$	1.06183e9	−	2.29916e9i	0.540840	−	1.17108i
$453$			7.44576e8i			0.376327i
$454$	−4.38696e7	+	2.80617e7i	−0.0220023	+	0.0140740i
$455$	−3.77774e8			−0.188015
$456$	2.44315e8	−	3.35389e7i	0.120663	−	0.0165642i
$457$	−1.08845e9			−0.533460			−0.266730	−	0.963771i	$-0.585943\pi$
$457$	−1.08845e9			−0.533460			−0.266730	+	0.963771i	$0.585943\pi$
$458$	1.58517e9	−	1.01397e9i	0.770985	−	0.493170i
$459$		−	4.09088e8i		−	0.197457i
$460$	1.09801e9	+	5.07096e8i	0.525962	+	0.242906i
$461$		−	2.65805e9i		−	1.26360i	−0.775131	−	0.631801i	$-0.782316\pi$
$461$		−	2.65805e9i		−	1.26360i	0.775131	−	0.631801i	$-0.217684\pi$
$462$	−1.09642e9	−	1.71406e9i	−0.517286	−	0.808686i
$463$	1.27045e9			0.594871			0.297435	−	0.954742i	$-0.403869\pi$
$463$	1.27045e9			0.594871			0.297435	+	0.954742i	$0.403869\pi$
$464$	−5.24458e8	+	4.46697e8i	−0.243724	+	0.207587i
$465$	−7.95213e8			−0.366774
$466$	3.16400e8	+	4.94637e8i	0.144839	+	0.226431i
$467$			6.33304e8i			0.287742i	0.989596	+	0.143871i	$0.0459550\pi$
$467$			6.33304e8i			0.287742i	−0.989596	+	0.143871i	$0.954045\pi$
$468$	−2.88723e8	−	1.33341e8i	−0.130203	−	0.0601318i
$469$			9.86220e8i			0.441437i
$470$	1.73838e9	−	1.11198e9i	0.772330	−	0.494030i
$471$	−4.07555e8			−0.179727
$472$	−4.07149e8	−	2.96589e9i	−0.178220	−	1.29825i
$473$	−3.57323e9			−1.55256
$474$	1.69853e9	−	1.08648e9i	0.732569	−	0.468596i
$475$		−	3.74092e8i		−	0.160159i
$476$	−9.01427e8	+	1.95185e9i	−0.383095	+	0.829513i
$477$		−	1.64070e8i		−	0.0692173i
$478$	1.23753e8	+	1.93467e8i	0.0518274	+	0.0810230i
$479$	−2.97478e6			−0.00123674			−0.000618372	−	1.00000i	$-0.500197\pi$
$479$	−2.97478e6			−0.00123674			−0.000618372		1.00000i	$0.500197\pi$
$480$	−2.00379e8	+	6.56540e8i	−0.0827004	+	0.270967i
$481$	6.22835e8			0.255191
$482$	2.07423e8	+	3.24269e8i	0.0843707	+	0.131899i
$483$			1.50323e9i			0.607029i
$484$	2.60006e9	−	5.62989e9i	1.04238	−	2.25705i
$485$			4.77376e8i			0.190005i
$486$	1.36755e8	−	8.74769e7i	0.0540400	−	0.0345674i
$487$	−7.68410e8			−0.301468			−0.150734	−	0.988574i	$-0.548164\pi$
$487$	−7.68410e8			−0.301468			−0.150734	+	0.988574i	$0.548164\pi$
$488$	6.12862e8	+	4.46442e9i	0.238723	+	1.73898i
$489$	1.95415e9			0.755747
$490$	2.22784e8	−	1.42507e8i	0.0855458	−	0.0547204i
$491$		−	1.44626e9i		−	0.551391i	−0.961245	−	0.275696i	$-0.911092\pi$
$491$		−	1.44626e9i		−	0.551391i	0.961245	−	0.275696i	$-0.0889081\pi$
$492$	−1.24209e9	−	5.73635e8i	−0.470191	−	0.217149i
$493$		−	8.73910e8i		−	0.328475i
$494$	1.31047e8	+	2.04868e8i	0.0489082	+	0.0764593i
$495$	8.24111e8			0.305399
$496$	2.28128e9	+	2.67841e9i	0.839447	+	0.985578i
$497$	−1.32268e9			−0.483289
$498$	−5.57532e8	−	8.71603e8i	−0.202286	−	0.316239i
$499$			9.02518e8i			0.325165i	0.986695	+	0.162583i	$0.0519824\pi$
$499$			9.02518e8i			0.325165i	−0.986695	+	0.162583i	$0.948018\pi$
$500$	2.19053e9	+	1.01165e9i	0.783707	+	0.361940i
$501$		−	7.74919e8i		−	0.275312i
$502$	4.83145e8	−	3.09050e8i	0.170457	−	0.109035i
$503$	−3.71023e9			−1.29991			−0.649954	−	0.759974i	$-0.725212\pi$
$503$	−3.71023e9			−1.29991			−0.649954	+	0.759974i	$0.725212\pi$
$504$	−8.45244e8	+	1.16033e8i	−0.294087	+	0.0403714i
$505$	−9.33184e8			−0.322439
$506$	−5.41173e9	+	3.46168e9i	−1.85699	+	1.18785i
$507$			1.38058e9i			0.470473i
$508$	1.47157e9	−	3.18638e9i	0.498032	−	1.07839i
$509$		−	7.61723e8i		−	0.256027i	−0.991772	−	0.128013i	$-0.959140\pi$
$509$		−	7.61723e8i		−	0.256027i	0.991772	−	0.128013i	$-0.0408600\pi$
$510$	−4.69219e8	−	7.33542e8i	−0.156632	−	0.244867i
$511$	2.77448e9			0.919832
$512$	2.78618e9	−	1.20855e9i	0.917410	−	0.397943i
$513$	−1.24141e8			−0.0405981
$514$	2.54194e9	+	3.97387e9i	0.825646	+	1.29075i
$515$		−	2.53863e9i		−	0.818982i
$516$	−6.28190e8	+	1.36021e9i	−0.201288	+	0.435846i
$517$			1.09611e10i			3.48850i
$518$	1.40755e9	−	9.00358e8i	0.444949	−	0.284617i
$519$	−4.34708e8			−0.136494
$520$	−6.70655e8	+	9.20656e7i	−0.209164	+	0.0287135i
$521$	4.48514e9			1.38945			0.694726	−	0.719274i	$-0.255525\pi$
$521$	4.48514e9			1.38945			0.694726	+	0.719274i	$0.255525\pi$
$522$	2.92141e8	−	1.86872e8i	0.0898971	−	0.0575038i
$523$			3.54373e8i			0.108319i	0.998532	+	0.0541595i	$0.0172479\pi$
$523$			3.54373e8i			0.108319i	−0.998532	+	0.0541595i	$0.982752\pi$
$524$	−1.42287e9	−	6.57125e8i	−0.432021	−	0.199521i
$525$			1.29423e9i			0.390349i
$526$	−2.01328e9	−	3.14741e9i	−0.603190	−	0.942981i
$527$	−4.46306e9			−1.32830
$528$	−2.36418e9	−	2.77574e9i	−0.698976	−	0.820654i
$529$	1.34123e9			0.393921
$530$	−1.88186e8	−	2.94197e8i	−0.0549064	−	0.0858365i
$531$			1.50703e9i			0.436808i
$532$	5.92308e8	+	2.73546e8i	0.170552	+	0.0787662i
$533$		−	1.34923e9i		−	0.385959i
$534$	−1.77261e8	+	1.13387e8i	−0.0503755	+	0.0322233i
$535$	2.32592e9			0.656685
$536$	2.40347e8	+	1.75082e9i	0.0674160	+	0.491094i
$537$	−1.46272e9			−0.407615
$538$	−3.39290e9	+	2.17031e9i	−0.939362	+	0.600875i
$539$			1.40474e9i			0.386397i
$540$	1.44882e8	−	3.13712e8i	0.0395947	−	0.0857341i
$541$		−	2.98685e9i		−	0.811005i	−0.914094	−	0.405502i	$-0.867097\pi$
$541$		−	2.98685e9i		−	0.811005i	0.914094	−	0.405502i	$-0.132903\pi$
$542$	−1.78437e9	−	2.78955e9i	−0.481379	−	0.752552i
$543$	−3.69314e9			−0.989911
$544$	−1.12461e9	+	3.68477e9i	−0.299506	+	0.981329i
$545$	3.29980e9			0.873171
$546$	−4.53375e8	−	7.08773e8i	−0.119202	−	0.186351i
$547$		−	5.14992e9i		−	1.34538i	−0.739925	−	0.672690i	$-0.765139\pi$
$547$		−	5.14992e9i		−	1.34538i	0.739925	−	0.672690i	$-0.234861\pi$
$548$	−2.59464e9	+	5.61816e9i	−0.673512	+	1.45835i
$549$		−	2.26846e9i		−	0.585097i
$550$	−4.65932e9	+	2.98039e9i	−1.19413	+	0.763843i
$551$	−2.65196e8			−0.0675361
$552$	3.66344e8	+	2.66865e9i	0.0927049	+	0.675312i
$553$	5.33432e9			1.34135
$554$	3.15202e9	−	2.01623e9i	0.787600	−	0.503798i
$555$			6.76742e8i			0.168034i
$556$	2.96011e9	+	1.36707e9i	0.730375	+	0.337310i
$557$		−	3.21644e9i		−	0.788647i	−0.918972	−	0.394323i	$-0.870979\pi$
$557$		−	3.21644e9i		−	0.788647i	0.918972	−	0.394323i	$-0.129021\pi$
$558$	−9.54354e8	−	1.49197e9i	−0.232536	−	0.363529i
$559$	−1.47755e9			−0.357767
$560$	−1.38253e9	+	1.17755e9i	−0.332673	+	0.283348i
$561$	4.62525e9			1.10603
$562$	−1.73764e9	−	2.71649e9i	−0.412936	−	0.645553i
$563$		−	6.23693e8i		−	0.147296i	−0.997284	−	0.0736481i	$-0.976536\pi$
$563$		−	6.23693e8i		−	0.147296i	0.997284	−	0.0736481i	$-0.0234642\pi$
$564$	4.17255e9	+	1.92701e9i	0.979320	+	0.452280i
$565$			2.71365e9i			0.632972i
$566$	3.83259e8	−	2.45156e8i	0.0888453	−	0.0568310i
$567$	4.29486e8			0.0989483
$568$	−2.34812e9	+	3.22344e8i	−0.537653	+	0.0738074i
$569$	2.58144e9			0.587449			0.293724	−	0.955890i	$-0.405105\pi$
$569$	2.58144e9			0.587449			0.293724	+	0.955890i	$0.405105\pi$
$570$	−2.22600e8	+	1.42389e8i	−0.0503458	+	0.0322043i
$571$		−	4.51863e9i		−	1.01573i	−0.861436	−	0.507867i	$-0.830434\pi$
$571$		−	4.51863e9i		−	1.01573i	0.861436	−	0.507867i	$-0.169566\pi$
$572$	1.50759e9	−	3.26437e9i	0.336819	−	0.729312i
$573$			2.47939e8i			0.0550560i
$574$	−1.95042e9	−	3.04914e9i	−0.430464	−	0.672955i
$575$	4.08620e9			0.896360
$576$	−1.47227e9	+	4.11981e8i	−0.321002	+	0.0898254i
$577$	−5.58211e9			−1.20972			−0.604858	−	0.796334i	$-0.706770\pi$
$577$	−5.58211e9			−1.20972			−0.604858	+	0.796334i	$0.706770\pi$
$578$	−1.31859e8	−	2.06138e8i	−0.0284029	−	0.0444029i
$579$			8.17232e8i			0.174973i
$580$	3.09503e8	−	6.70165e8i	0.0658669	−	0.142621i
$581$		−	2.73732e9i		−	0.579040i
$582$	−8.95644e8	+	5.72910e8i	−0.188324	+	0.120464i
$583$	1.85502e9			0.387710
$584$	4.92548e9	−	6.76157e8i	1.02330	−	0.140476i
$585$	3.40773e8			0.0703753
$586$	1.46699e9	−	9.38381e8i	0.301153	−	0.192636i
$587$		−	3.49384e9i		−	0.712967i	−0.934302	−	0.356484i	$-0.883976\pi$
$587$		−	3.49384e9i		−	0.712967i	0.934302	−	0.356484i	$-0.116024\pi$
$588$	5.34738e8	+	2.46958e8i	0.108473	+	0.0500960i
$589$			1.35436e9i			0.273105i
$590$	1.72854e9	+	2.70228e9i	0.346496	+	0.541686i
$591$	1.54705e9			0.308282
$592$	2.27938e9	−	1.94142e9i	0.451534	−	0.384585i
$593$	6.78437e8			0.133604			0.0668018	−	0.997766i	$-0.478720\pi$
$593$	6.78437e8			0.133604			0.0668018	+	0.997766i	$0.478720\pi$
$594$	9.89035e8	+	1.54618e9i	0.193624	+	0.302697i
$595$		−	2.30373e9i		−	0.448355i
$596$	−6.11839e9	−	2.82566e9i	−1.18379	−	0.546712i
$597$		−	6.50762e7i		−	0.0125173i
$598$	−2.23777e9	+	1.43142e9i	−0.427919	+	0.273724i
$599$	2.98442e8			0.0567370			0.0283685	−	0.999598i	$-0.490969\pi$
$599$	2.98442e8			0.0567370			0.0283685	+	0.999598i	$0.490969\pi$
$600$	3.15411e8	+	2.29762e9i	0.0596138	+	0.434259i
$601$	−4.58275e8			−0.0861123			−0.0430561	−	0.999073i	$-0.513709\pi$
$601$	−4.58275e8			−0.0861123			−0.0430561	+	0.999073i	$0.513709\pi$
$602$	−3.33913e9	+	2.13591e9i	−0.623800	+	0.399021i
$603$		−	8.89627e8i		−	0.165233i
$604$	−1.47998e9	+	3.20459e9i	−0.273292	+	0.591758i
$605$			6.64483e9i			1.21994i
$606$	−1.11994e9	−	1.75082e9i	−0.204427	−	0.319586i
$607$	−8.38542e9			−1.52182			−0.760912	−	0.648855i	$-0.775248\pi$
$607$	−8.38542e9			−1.52182			−0.760912	+	0.648855i	$0.775248\pi$
$608$	1.11818e9	+	3.41273e8i	0.201766	+	0.0615799i
$609$	9.17485e8			0.164603
$610$	−2.60190e9	−	4.06761e9i	−0.464126	−	0.725580i
$611$			4.53247e9i			0.803880i
$612$	8.13138e8	−	1.76068e9i	0.143395	−	0.310493i
$613$		−	5.53124e9i		−	0.969865i	−0.874552	−	0.484932i	$-0.838844\pi$
$613$		−	5.53124e9i		−	0.969865i	0.874552	−	0.484932i	$-0.161156\pi$
$614$	2.80042e9	−	1.79132e9i	0.488241	−	0.312309i
$615$	1.46601e9			0.254140
$616$	−1.31189e9	−	9.55654e9i	−0.226134	−	1.64728i
$617$	4.15289e9			0.711791			0.355896	−	0.934526i	$-0.384176\pi$
$617$	4.15289e9			0.711791			0.355896	+	0.934526i	$0.384176\pi$
$618$	4.76294e9	−	3.04667e9i	0.811737	−	0.519237i
$619$			2.84793e9i			0.482627i	0.970447	+	0.241314i	$0.0775782\pi$
$619$			2.84793e9i			0.482627i	−0.970447	+	0.241314i	$0.922422\pi$
$620$	−3.42253e9	−	1.58063e9i	−0.576736	−	0.266355i
$621$		−	1.35599e9i		−	0.227215i
$622$	5.80736e9	+	9.07879e9i	0.967637	+	1.51273i
$623$	−5.56698e8			−0.0922384
$624$	−9.77600e8	−	1.14778e9i	−0.161070	−	0.189109i
$625$	2.04843e9			0.335615
$626$	−4.33951e9	−	6.78406e9i	−0.707018	−	1.10530i
$627$		−	1.40357e9i		−	0.227404i
$628$	−1.75408e9	−	8.10091e8i	−0.282613	−	0.130519i
$629$			3.79815e9i			0.608549i
$630$	7.70118e8	−	4.92615e8i	0.122706	−	0.0784903i
$631$	8.88293e8			0.140752			0.0703758	−	0.997521i	$-0.477580\pi$
$631$	8.88293e8			0.140752			0.0703758	+	0.997521i	$0.477580\pi$
$632$	9.46991e9	−	1.30000e9i	1.49223	−	0.204849i
$633$	−3.82813e9			−0.599893
$634$	−1.83805e8	+	1.17573e8i	−0.0286447	+	0.0183230i
$635$			3.76081e9i			0.582872i
$636$	3.26119e8	−	7.06144e8i	0.0502663	−	0.108841i
$637$			5.80864e8i			0.0890403i
$638$	2.11282e9	+	3.30302e9i	0.322099	+	0.503545i
$639$	1.19313e9			0.180898
$640$	−2.16741e9	+	2.42741e9i	−0.326822	+	0.366026i
$641$	−1.13079e10			−1.69582			−0.847910	−	0.530139i	$-0.822140\pi$
$641$	−1.13079e10			−1.69582			−0.847910	+	0.530139i	$0.822140\pi$
$642$	2.79139e9	+	4.36385e9i	0.416340	+	0.650875i
$643$			8.67974e9i			1.28756i	0.765209	+	0.643781i	$0.222635\pi$
$643$			8.67974e9i			1.28756i	−0.765209	+	0.643781i	$0.777365\pi$
$644$	−2.98794e9	+	6.46976e9i	−0.440830	+	0.954526i
$645$		−	1.60543e9i		−	0.235577i
$646$	−1.24932e9	+	7.99145e8i	−0.182331	+	0.116630i
$647$	−9.12604e9			−1.32470			−0.662350	−	0.749195i	$-0.730441\pi$
$647$	−9.12604e9			−1.32470			−0.662350	+	0.749195i	$0.730441\pi$
$648$	7.62458e8	−	1.04668e8i	0.110079	−	0.0151113i
$649$	−1.70388e10			−2.44671
$650$	−1.92665e9	+	1.23240e9i	−0.275173	+	0.176018i
$651$		−	4.68560e9i		−	0.665628i
$652$	8.41049e9	+	3.88423e9i	1.18838	+	0.548831i
$653$			9.07309e9i			1.27514i	0.770391	+	0.637572i	$0.220061\pi$
$653$			9.07309e9i			1.27514i	−0.770391	+	0.637572i	$0.779939\pi$
$654$	3.96016e9	+	6.19102e9i	0.553593	+	0.865446i
$655$	1.67938e9			0.233509
$656$	−4.20564e9	−	4.93776e9i	−0.581659	−	0.682915i
$657$	−2.50274e9			−0.344300
$658$	6.55206e9	+	1.02430e10i	0.896576	+	1.40164i
$659$			5.93620e9i			0.807996i	0.914760	+	0.403998i	$0.132380\pi$
$659$			5.93620e9i			0.807996i	−0.914760	+	0.403998i	$0.867620\pi$
$660$	3.54691e9	+	1.63807e9i	0.480226	+	0.221784i
$661$		−	4.99352e9i		−	0.672515i	−0.941770	−	0.336257i	$-0.890839\pi$
$661$		−	4.99352e9i		−	0.672515i	0.941770	−	0.336257i	$-0.109161\pi$
$662$	5.96692e9	−	3.81681e9i	0.799369	−	0.511326i
$663$	1.91256e9			0.254869
$664$	−6.67099e8	−	4.85951e9i	−0.0884305	−	0.644175i
$665$	−6.99088e8			−0.0921841
$666$	−1.26969e9	+	8.12174e8i	−0.166548	+	0.106534i
$667$		−	2.89673e9i		−	0.377979i
$668$	1.54030e9	−	3.33519e9i	0.199934	−	0.432915i
$669$		−	7.34763e8i		−	0.0948759i
$670$	−1.02039e9	−	1.59520e9i	−0.131071	−	0.204906i
$671$	2.56478e10			3.27733
$672$	−3.86850e9	−	1.18068e9i	−0.491757	−	0.150086i
$673$	2.02208e9			0.255708			0.127854	−	0.991793i	$-0.459191\pi$
$673$	2.02208e9			0.255708			0.127854	+	0.991793i	$0.459191\pi$
$674$	−3.69501e9	−	5.77651e9i	−0.464843	−	0.726701i
$675$		−	1.16747e9i		−	0.146110i
$676$	−2.74416e9	+	5.94191e9i	−0.341662	+	0.739798i
$677$			2.99982e9i			0.371565i	0.982591	+	0.185783i	$0.0594820\pi$
$677$			2.99982e9i			0.371565i	−0.982591	+	0.185783i	$0.940518\pi$
$678$	−5.09131e9	+	3.25672e9i	−0.627372	+	0.401306i
$679$	−2.81282e9			−0.344824
$680$	−5.61432e8	−	4.08977e9i	−0.0684725	−	0.498790i
$681$	1.24281e8			0.0150796
$682$	1.68685e10	−	1.07902e10i	2.03625	−	1.30251i
$683$			7.77019e9i			0.933166i	0.884477	+	0.466583i	$0.154515\pi$
$683$			7.77019e9i			0.933166i	−0.884477	+	0.466583i	$0.845485\pi$
$684$	−5.34295e8	−	2.46754e8i	−0.0638388	−	0.0294828i
$685$		−	6.63099e9i		−	0.788245i
$686$	4.89715e9	+	7.65583e9i	0.579174	+	0.905437i
$687$	−4.49071e9			−0.528405
$688$	−5.40736e9	+	4.60561e9i	−0.633032	+	0.539173i
$689$	7.67056e8			0.0893429
$690$	−1.55531e9	−	2.43145e9i	−0.180237	−	0.281770i
$691$			4.29400e9i			0.495095i	0.968876	+	0.247547i	$0.0796246\pi$
$691$			4.29400e9i			0.495095i	−0.968876	+	0.247547i	$0.920375\pi$
$692$	−1.87095e9	−	8.64063e8i	−0.214630	−	0.0991230i
$693$			4.85587e9i			0.554244i
$694$	5.20942e9	−	3.33227e9i	0.591604	−	0.378427i
$695$	−3.49375e9			−0.394771
$696$	1.62879e9	−	2.23596e8i	0.183119	−	0.0251381i
$697$	8.22784e9			0.920389
$698$	−2.54489e9	+	1.62787e9i	−0.283254	+	0.181187i
$699$		−	1.40129e9i		−	0.155187i
$700$	−2.57252e9	+	5.57025e9i	−0.283475	+	0.613807i
$701$		−	1.78556e10i		−	1.95777i	−0.204420	−	0.978883i	$-0.565531\pi$
$701$		−	1.78556e10i		−	1.95777i	0.204420	−	0.978883i	$-0.434469\pi$
$702$	4.08970e8	+	6.39353e8i	0.0446181	+	0.0697527i
$703$	1.15258e9			0.125121
$704$	−4.65796e9	−	1.66458e10i	−0.503143	−	1.79805i
$705$	−4.92477e9			−0.529327
$706$	−2.58356e9	−	4.03895e9i	−0.276314	−	0.431968i
$707$		−	5.49856e9i		−	0.585168i
$708$	−2.99550e9	+	6.48613e9i	−0.317214	+	0.686862i
$709$		−	1.41108e10i		−	1.48693i	−0.668775	−	0.743465i	$-0.733181\pi$
$709$		−	1.41108e10i		−	1.48693i	0.668775	−	0.743465i	$-0.266819\pi$
$710$	2.13942e9	−	1.36851e9i	0.224332	−	0.143497i
$711$	−4.81186e9			−0.502075
$712$	−9.88296e8	+	1.35670e8i	−0.102614	+	0.0140866i
$713$	−1.47936e10			−1.52848
$714$	4.32222e9	−	2.76476e9i	0.444389	−	0.284259i
$715$			3.85286e9i			0.394196i
$716$	−6.29541e9	−	2.90742e9i	−0.640957	−	0.296014i
$717$		−	5.48083e8i		−	0.0555302i
$718$	−1.50240e9	−	2.34874e9i	−0.151478	−	0.236810i
$719$	3.78839e9			0.380105			0.190052	−	0.981774i	$-0.439134\pi$
$719$	3.78839e9			0.380105			0.190052	+	0.981774i	$0.439134\pi$
$720$	1.24712e9	−	1.06221e9i	0.124522	−	0.106059i
$721$	1.49583e10			1.48630
$722$	−5.20690e9	−	8.14008e9i	−0.514872	−	0.804912i
$723$		−	9.18641e8i		−	0.0903986i
$724$	−1.58950e10	−	7.34080e9i	−1.55659	−	0.718883i
$725$		−	2.49399e9i		−	0.243059i
$726$	−1.24669e10	+	7.97461e9i	−1.20915	+	0.773449i
$727$	3.16436e9			0.305433			0.152716	−	0.988270i	$-0.451198\pi$
$727$	3.16436e9			0.305433			0.152716	+	0.988270i	$0.451198\pi$
$728$	−5.42474e8	−	3.95167e9i	−0.0521097	−	0.379595i
$729$	−3.87420e8			−0.0370370
$730$	−4.48770e9	+	2.87061e9i	−0.426967	+	0.273114i
$731$		−	9.01034e9i		−	0.853160i
$732$	4.50898e9	−	9.76327e9i	0.424903	−	0.920040i
$733$			1.63026e10i			1.52895i	0.644654	+	0.764474i	$0.277001\pi$
$733$			1.63026e10i			1.52895i	−0.644654	+	0.764474i	$0.722999\pi$
$734$	5.78235e9	+	9.03968e9i	0.539719	+	0.843756i
$735$	−6.31139e8			−0.0586299
$736$	−3.72771e9	+	1.22138e10i	−0.344644	+	1.12922i
$737$	1.00583e10			0.925528
$738$	1.75939e9	+	2.75050e9i	0.161126	+	0.251892i
$739$		−	6.96883e9i		−	0.635191i	−0.948226	−	0.317595i	$-0.897125\pi$
$739$		−	6.96883e9i		−	0.635191i	0.948226	−	0.317595i	$-0.102875\pi$
$740$	−1.34515e9	+	2.91264e9i	−0.122028	+	0.264226i
$741$		−	5.80383e8i		−	0.0524024i
$742$	1.73348e9	−	1.10884e9i	0.155778	−	0.0996451i
$743$	2.95248e9			0.264074			0.132037	−	0.991245i	$-0.457848\pi$
$743$	2.95248e9			0.264074			0.132037	+	0.991245i	$0.457848\pi$
$744$	−1.14191e9	−	8.31825e9i	−0.101654	−	0.740503i
$745$	7.22140e9			0.639844
$746$	−4.02917e9	+	2.57731e9i	−0.355328	+	0.227290i
$747$			2.46921e9i			0.216739i
$748$	1.99067e10	+	9.19354e9i	1.73918	+	0.803206i
$749$			1.37049e10i			1.19176i
$750$	−3.10283e9	−	4.85074e9i	−0.268562	−	0.419849i
$751$	1.61693e10			1.39300			0.696502	−	0.717555i	$-0.254739\pi$
$751$	1.61693e10			1.39300			0.696502	+	0.717555i	$0.254739\pi$
$752$	1.41280e10	+	1.65874e10i	1.21149	+	1.42238i
$753$	−1.36873e9			−0.116825
$754$	8.73658e8	+	1.36581e9i	0.0742235	+	0.116036i
$755$		−	3.78231e9i		−	0.319848i
$756$	1.84847e9	+	8.53683e8i	0.155592	+	0.0718572i
$757$		−	2.26203e10i		−	1.89523i	−0.319412	−	0.947616i	$-0.603485\pi$
$757$		−	2.26203e10i		−	1.89523i	0.319412	−	0.947616i	$-0.396515\pi$
$758$	−1.81725e10	+	1.16242e10i	−1.51555	+	0.969443i
$759$	1.53312e10			1.27271
$760$	−1.24108e9	+	1.70372e8i	−0.102554	+	0.0140783i
$761$	8.62411e9			0.709362			0.354681	−	0.934987i	$-0.384589\pi$
$761$	8.62411e9			0.709362			0.354681	+	0.934987i	$0.384589\pi$
$762$	−7.05596e9	+	4.51343e9i	−0.577715	+	0.369543i
$763$			1.94432e10i			1.58465i
$764$	−4.92826e8	+	1.06711e9i	−0.0399822	+	0.0865731i
$765$			2.07809e9i			0.167823i
$766$	3.02577e8	+	4.73026e8i	0.0243240	+	0.0380263i
$767$	−7.04563e9			−0.563814
$768$	−7.15541e9	−	1.15327e9i	−0.569994	−	0.0918685i
$769$	−7.71654e9			−0.611900			−0.305950	−	0.952048i	$-0.598974\pi$
$769$	−7.71654e9			−0.611900			−0.305950	+	0.952048i	$0.598974\pi$
$770$	5.56963e9	+	8.70714e9i	0.439652	+	0.687318i
$771$		−	1.12578e10i		−	0.884635i
$772$	−1.62440e9	+	3.51730e9i	−0.127067	+	0.275137i
$773$		−	6.35693e8i		−	0.0495016i	−0.999694	−	0.0247508i	$-0.992121\pi$
$773$		−	6.35693e8i		−	0.0495016i	0.999694	−	0.0247508i	$-0.00787923\pi$
$774$	3.01208e9	−	1.92672e9i	0.233493	−	0.149357i
$775$	−1.27368e10			−0.982890
$776$	−4.99354e9	+	6.85499e8i	−0.383613	+	0.0526612i
$777$	−3.98754e9			−0.304952
$778$	1.74652e10	−	1.11719e10i	1.32968	−	0.850544i
$779$		−	2.49681e9i		−	0.189236i
$780$	1.46666e9	+	6.77350e8i	0.110662	+	0.0511072i
$781$			1.34898e10i			1.01327i
$782$	−8.72904e9	−	1.36463e10i	−0.652744	−	1.02045i
$783$	−8.27623e8			−0.0616122
$784$	1.81059e9	+	2.12578e9i	0.134188	+	0.157548i
$785$	2.07031e9			0.152753
$786$	2.01546e9	+	3.15082e9i	0.148046	+	0.231443i
$787$			1.72173e10i			1.25908i	0.776968	+	0.629540i	$0.216757\pi$
$787$			1.72173e10i			1.25908i	−0.776968	+	0.629540i	$0.783243\pi$
$788$	6.65838e9	+	3.07505e9i	0.484760	+	0.223877i
$789$			8.91648e9i			0.646285i
$790$	−8.62821e9	+	5.51914e9i	−0.622624	+	0.398269i
$791$	−1.59895e10			−1.14873
$792$	1.18340e9	+	8.62054e9i	0.0846437	+	0.616589i
$793$	1.06055e10			0.755220
$794$	−1.18219e10	+	7.56204e9i	−0.838139	+	0.536126i
$795$			8.33446e8i			0.0588292i
$796$	1.29351e8	−	2.80083e8i	0.00909021	−	0.0196830i
$797$			2.34758e10i			1.64254i	0.570537	+	0.821272i	$0.306735\pi$
$797$			2.34758e10i			1.64254i	−0.570537	+	0.821272i	$0.693265\pi$
$798$	−8.38991e8	−	1.31162e9i	−0.0584450	−	0.0913685i
$799$	−2.76398e10			−1.91700
$800$	−3.20944e9	+	1.05157e10i	−0.221623	+	0.726145i
$801$	5.02173e8			0.0345255
$802$	−1.05412e10	−	1.64793e10i	−0.721571	−	1.12805i
$803$		−	2.82966e10i		−	1.92854i
$804$	1.76830e9	−	3.82888e9i	0.119994	−	0.259822i
$805$		−	7.63612e9i		−	0.515925i
$806$	6.97520e9	−	4.46177e9i	0.469228	−	0.300148i
$807$	9.61194e9			0.643804
$808$	−1.34003e9	−	9.76148e9i	−0.0893664	−	0.650993i
$809$	−7.71245e9			−0.512121			−0.256060	−	0.966661i	$-0.582425\pi$
$809$	−7.71245e9			−0.512121			−0.256060	+	0.966661i	$0.582425\pi$
$810$	−6.94690e8	+	4.44367e8i	−0.0459297	+	0.0293795i
$811$		−	2.49188e10i		−	1.64041i	−0.572067	−	0.820207i	$-0.693858\pi$
$811$		−	2.49188e10i		−	1.64041i	0.572067	−	0.820207i	$-0.306142\pi$
$812$	3.94878e9	+	1.82367e9i	0.258831	+	0.119536i
$813$			7.90268e9i			0.515772i
$814$	−9.18263e9	−	1.43554e10i	−0.596735	−	0.932891i
$815$	−9.92672e9			−0.642324
$816$	6.99937e9	−	5.96158e9i	0.450965	−	0.384101i
$817$	−2.73427e9			−0.175414
$818$	9.74576e9	+	1.52358e10i	0.622557	+	0.973259i
$819$			2.00792e9i			0.127718i
$820$	6.30958e9	+	2.91396e9i	0.399625	+	0.184559i
$821$		−	1.20840e9i		−	0.0762098i	−0.999274	−	0.0381049i	$-0.987868\pi$
$821$		−	1.20840e9i		−	0.0762098i	0.999274	−	0.0381049i	$-0.0121321\pi$
$822$	1.24410e10	−	7.95801e9i	0.781272	−	0.499750i
$823$	8.05412e9			0.503638			0.251819	−	0.967774i	$-0.418971\pi$
$823$	8.05412e9			0.503638			0.251819	+	0.967774i	$0.418971\pi$
$824$	2.65551e10	−	3.64541e9i	1.65350	−	0.226987i
$825$	1.31997e10			0.818416
$826$	−1.59225e10	+	1.01850e10i	−0.983063	+	0.628828i
$827$		−	2.99837e9i		−	0.184338i	−0.995743	−	0.0921692i	$-0.970620\pi$
$827$		−	2.99837e9i		−	0.184338i	0.995743	−	0.0921692i	$-0.0293801\pi$
$828$	2.69529e9	−	5.83609e9i	0.165006	−	0.357286i
$829$			7.99710e8i			0.0487519i	0.999703	+	0.0243760i	$0.00775987\pi$
$829$			7.99710e8i			0.0487519i	−0.999703	+	0.0243760i	$0.992240\pi$
$830$	2.83216e9	+	4.42759e9i	0.171927	+	0.268778i
$831$	−8.92955e9			−0.539792
$832$	−1.92609e9	−	6.88312e9i	−0.115943	−	0.414337i
$833$	−3.54221e9			−0.212333
$834$	−4.19293e9	−	6.55491e9i	−0.250286	−	0.391278i
$835$			3.93645e9i			0.233993i
$836$	2.78986e9	−	6.04087e9i	0.165143	−	0.357583i
$837$			4.22667e9i			0.249149i
$838$	1.37551e10	−	8.79865e9i	0.807442	−	0.516490i
$839$	7.15014e9			0.417972			0.208986	−	0.977919i	$-0.432984\pi$
$839$	7.15014e9			0.417972			0.208986	+	0.977919i	$0.432984\pi$
$840$	4.29369e9	−	5.89426e8i	0.249950	−	0.0343124i
$841$	1.54819e10			0.897506
$842$	8.54280e9	−	5.46451e9i	0.493183	−	0.315471i
$843$			7.69571e9i			0.442438i
$844$	−1.64760e10	−	7.60912e9i	−0.943306	−	0.435648i
$845$		−	7.01311e9i		−	0.399864i
$846$	−5.91033e9	−	9.23976e9i	−0.335595	−	0.524644i
$847$	−3.91530e10			−2.21398
$848$	2.80718e9	−	2.39097e9i	0.158083	−	0.134644i
$849$	−1.08576e9			−0.0608913
$850$	−7.51542e9	−	1.17490e10i	−0.419746	−	0.656200i
$851$			1.25896e10i			0.700261i
$852$	5.13513e9	+	2.37157e9i	0.284455	+	0.131370i
$853$			5.59947e9i			0.308905i	0.988000	+	0.154453i	$0.0493614\pi$
$853$			5.59947e9i			0.308905i	−0.988000	+	0.154453i	$0.950639\pi$
$854$	2.39674e10	−	1.53310e10i	1.31680	−	0.842305i
$855$	6.30616e8			0.0345051
$856$	3.33997e9	+	2.43301e10i	0.182005	+	1.32582i
$857$	−1.20730e10			−0.655213			−0.327606	−	0.944814i	$-0.606242\pi$
$857$	−1.20730e10			−0.655213			−0.327606	+	0.944814i	$0.606242\pi$
$858$	−7.22868e9	+	4.62391e9i	−0.390709	+	0.249922i
$859$			2.95709e10i			1.59180i	0.605427	+	0.795901i	$0.293002\pi$
$859$			2.95709e10i			1.59180i	−0.605427	+	0.795901i	$0.706998\pi$
$860$	3.19109e9	−	6.90965e9i	0.171078	−	0.370434i
$861$			8.63810e9i			0.461219i
$862$	−4.31167e9	−	6.74054e9i	−0.229282	−	0.358442i
$863$	1.10938e10			0.587546			0.293773	−	0.955875i	$-0.405089\pi$
$863$	1.10938e10			0.587546			0.293773	+	0.955875i	$0.405089\pi$
$864$	3.48961e9	+	1.06504e9i	0.184068	+	0.0561784i
$865$	2.20824e9			0.116009
$866$	2.99003e9	+	4.67439e9i	0.156445	+	0.244575i
$867$			5.83982e8i			0.0304321i
$868$	9.31349e9	−	2.01664e10i	0.483385	−	1.04667i
$869$		−	5.44040e10i		−	2.81230i
$870$	−1.48402e9	+	9.49274e8i	−0.0764053	+	0.0488736i
$871$	4.15916e9			0.213276
$872$	4.73843e9	+	3.45172e10i	0.242006	+	1.76290i
$873$	2.53732e9			0.129070
$874$	−4.14110e9	+	2.64891e9i	−0.209810	+	0.134207i
$875$		−	1.52340e10i		−	0.768752i
$876$	−1.07716e10	−	4.97466e9i	−0.541397	−	0.250034i
$877$			1.31675e10i			0.659179i	0.944124	+	0.329589i	$0.106910\pi$
$877$			1.31675e10i			0.659179i	−0.944124	+	0.329589i	$0.893090\pi$
$878$	−6.51657e9	−	1.01875e10i	−0.324929	−	0.507969i
$879$	−4.15593e9			−0.206399
$880$	1.20096e10	+	1.41003e10i	0.594074	+	0.697490i
$881$	6.99376e9			0.344584			0.172292	−	0.985046i	$-0.444883\pi$
$881$	6.99376e9			0.344584			0.172292	+	0.985046i	$0.444883\pi$
$882$	−7.57444e8	−	1.18413e9i	−0.0371716	−	0.0581112i
$883$		−	4.62869e9i		−	0.226254i	−0.993581	−	0.113127i	$-0.963913\pi$
$883$		−	4.62869e9i		−	0.226254i	0.993581	−	0.113127i	$-0.0360866\pi$
$884$	8.23151e9	+	3.80157e9i	0.400771	+	0.185089i
$885$		−	7.65544e9i		−	0.371252i
$886$	9.71368e9	−	6.21347e9i	0.469208	−	0.300135i
$887$	−2.71747e10			−1.30747			−0.653735	−	0.756724i	$-0.726799\pi$
$887$	−2.71747e10			−1.30747			−0.653735	+	0.756724i	$0.726799\pi$
$888$	−7.07900e9	+	9.71785e8i	−0.339255	+	0.0465720i
$889$	−2.21596e10			−1.05781
$890$	9.00455e8	−	5.75987e8i	0.0428151	−	0.0273872i
$891$		−	4.38027e9i		−	0.207457i
$892$	1.46048e9	−	3.16236e9i	0.0688998	−	0.149188i
$893$			8.38755e9i			0.394144i
$894$	8.66657e9	+	1.35487e10i	0.405663	+	0.634184i
$895$	7.43034e9			0.346440
$896$	−1.43029e10	−	1.27709e10i	−0.664272	−	0.593123i
$897$	6.33951e9			0.293280
$898$	1.50433e10	+	2.35175e10i	0.693227	+	1.08374i
$899$			9.02919e9i			0.414467i
$900$	2.32056e9	−	5.02468e9i	0.106107	−	0.229752i
$901$			4.67764e9i			0.213054i
$902$	−3.10978e10	+	1.98921e10i	−1.41093	+	0.902522i
$903$	9.45961e9			0.427530
$904$	−2.83859e10	+	3.89674e9i	−1.27795	+	0.175433i
$905$	1.87605e10			0.841345
$906$	7.09631e9	−	4.53924e9i	0.317018	−	0.202784i
$907$		−	3.63626e10i		−	1.61819i	−0.587679	−	0.809095i	$-0.699958\pi$
$907$		−	3.63626e10i		−	1.61819i	0.587679	−	0.809095i	$-0.300042\pi$
$908$	5.34894e8	+	2.47031e8i	0.0237120	+	0.0109509i
$909$			4.96001e9i			0.219033i
$910$	2.30306e9	+	3.60044e9i	0.101312	+	0.158384i
$911$	3.56701e10			1.56311			0.781556	−	0.623834i	$-0.214426\pi$
$911$	3.56701e10			1.56311			0.781556	+	0.623834i	$0.214426\pi$
$912$	−1.80909e9	−	2.12402e9i	−0.0789731	−	0.0927207i
$913$	−2.79175e10			−1.21403
$914$	6.63564e9	+	1.03737e10i	0.287456	+	0.449387i
$915$			1.15234e10i			0.497286i
$916$	−1.93277e10	−	8.92612e9i	−0.830894	−	0.383733i
$917$			9.89533e9i			0.423777i
$918$	−3.89889e9	+	2.49397e9i	−0.166338	+	0.106400i
$919$	3.65009e10			1.55131			0.775657	−	0.631155i	$-0.217419\pi$
$919$	3.65009e10			1.55131			0.775657	+	0.631155i	$0.217419\pi$
$920$	−1.86096e9	−	1.35563e10i	−0.0787917	−	0.573961i
$921$	−7.93347e9			−0.334622
$922$	−2.53330e10	+	1.62046e10i	−1.06446	+	0.680894i
$923$			5.57809e9i			0.233496i
$924$	−9.65194e9	+	2.08993e10i	−0.402497	+	0.871524i
$925$			1.08393e10i			0.450302i
$926$	−7.74516e9	−	1.21082e10i	−0.320547	−	0.501119i
$927$	−1.34932e10			−0.556334
$928$	7.45464e9	+	2.27519e9i	0.306202	+	0.0934543i
$929$	6.38374e8			0.0261228			0.0130614	−	0.999915i	$-0.495842\pi$
$929$	6.38374e8			0.0261228			0.0130614	+	0.999915i	$0.495842\pi$
$930$	4.84795e9	+	7.57892e9i	0.197637	+	0.308970i
$931$			1.07492e9i			0.0436567i
$932$	2.78531e9	−	6.03102e9i	0.112699	−	0.244025i
$933$		−	2.57198e10i		−	1.03677i
$934$	6.03582e9	−	3.86088e9i	0.242394	−	0.155050i
$935$	−2.34954e10			−0.940033
$936$	4.89342e8	+	3.56463e9i	0.0195050	+	0.142085i
$937$	1.01827e10			0.404367			0.202183	−	0.979348i	$-0.435196\pi$
$937$	1.01827e10			0.404367			0.202183	+	0.979348i	$0.435196\pi$
$938$	9.39935e9	−	6.01241e9i	0.371867	−	0.237869i
$939$			1.92190e10i			0.757531i
$940$	−2.11958e10	−	9.78888e9i	−0.832343	−	0.384402i
$941$			3.07639e10i			1.20359i	0.798652	+	0.601793i	$0.205547\pi$
$941$			3.07639e10i			1.20359i	−0.798652	+	0.601793i	$0.794453\pi$
$942$	2.48462e9	+	3.88427e9i	0.0968462	+	0.151402i
$943$	2.72726e10			1.05910
$944$	−2.57848e10	+	2.19617e10i	−0.997611	+	0.849696i
$945$	−2.18171e9			−0.0840981
$946$	2.17839e10	+	3.40553e10i	0.836598	+	1.30787i
$947$			1.28317e10i			0.490974i	0.969400	+	0.245487i	$0.0789479\pi$
$947$			1.28317e10i			0.490974i	−0.969400	+	0.245487i	$0.921052\pi$
$948$	−2.07098e10	−	9.56445e9i	−0.789492	−	0.364612i
$949$		−	1.17008e10i		−	0.444408i
$950$	−3.56535e9	+	2.28062e9i	−0.134918	+	0.0863019i
$951$	5.20712e8			0.0196320
$952$	2.40980e10	−	3.30810e9i	0.905213	−	0.124265i
$953$	−1.24916e10			−0.467511			−0.233756	−	0.972295i	$-0.575102\pi$
$953$	−1.24916e10			−0.467511			−0.233756	+	0.972295i	$0.575102\pi$
$954$	−1.56370e9	+	1.00024e9i	−0.0583087	+	0.0372979i
$955$		−	1.25949e9i		−	0.0467932i
$956$	1.08942e9	−	2.35891e9i	0.0403266	−	0.0873188i
$957$		−	9.35731e9i		−	0.345111i
$958$	1.81355e7	+	2.83516e7i	0.000666422	+	0.00104183i
$959$	3.90715e10			1.43052
$960$	7.47886e9	−	2.09279e9i	0.272826	−	0.0763443i
$961$	1.85995e10			0.676035
$962$	−3.79706e9	−	5.93603e9i	−0.137510	−	0.214973i
$963$		−	1.23626e10i		−	0.446086i
$964$	1.82597e9	−	3.95376e9i	0.0656483	−	0.142148i
$965$		−	4.15139e9i		−	0.148713i
$966$	1.43267e10	−	9.16428e9i	0.511361	−	0.327098i
$967$	4.23912e10			1.50759			0.753795	−	0.657110i	$-0.228221\pi$
$967$	4.23912e10			1.50759			0.753795	+	0.657110i	$0.228221\pi$
$968$	−6.95076e10	+	9.54181e9i	−2.46302	+	0.338117i
$969$	3.53928e9			0.124963
$970$	4.54971e9	−	2.91028e9i	0.160060	−	0.102384i
$971$			3.64229e10i			1.27676i	0.769723	+	0.638378i	$0.220394\pi$
$971$			3.64229e10i			1.27676i	−0.769723	+	0.638378i	$0.779606\pi$
$972$	−1.66743e9	−	7.70070e8i	−0.0582391	−	0.0268967i
$973$		−	2.05861e10i		−	0.716438i
$974$	4.68454e9	+	7.32346e9i	0.162447	+	0.253957i
$975$	5.45811e9			0.188593
$976$	3.88126e10	−	3.30579e10i	1.33628	−	1.13815i
$977$	−9.15850e9			−0.314191			−0.157095	−	0.987583i	$-0.550213\pi$
$977$	−9.15850e9			−0.314191			−0.157095	+	0.987583i	$0.550213\pi$
$978$	−1.19133e10	−	1.86243e10i	−0.407236	−	0.636641i
$979$			5.67769e9i			0.193389i
$980$	−2.71637e9	−	1.25451e9i	−0.0921930	−	0.0425776i
$981$		−	1.75389e10i		−	0.593145i
$982$	−1.37838e10	+	8.81697e9i	−0.464492	+	0.297118i
$983$	1.91841e9			0.0644176			0.0322088	−	0.999481i	$-0.489746\pi$
$983$	1.91841e9			0.0644176			0.0322088	+	0.999481i	$0.489746\pi$
$984$	2.10515e9	+	1.53350e10i	0.0704370	+	0.513100i
$985$	−7.85874e9			−0.262015
$986$	−8.32896e9	+	5.32772e9i	−0.276708	+	0.177000i
$987$		−	2.90180e10i		−	0.960632i
$988$	1.15362e9	−	2.49792e9i	0.0380551	−	0.0824005i
$989$		−	2.98664e10i		−	0.981737i
$990$	−5.02412e9	−	7.85433e9i	−0.164565	−	0.257268i
$991$	4.46181e9			0.145631			0.0728154	−	0.997345i	$-0.476802\pi$
$991$	4.46181e9			0.145631			0.0728154	+	0.997345i	$0.476802\pi$
$992$	1.16194e10	−	3.80709e10i	0.377914	−	1.23823i
$993$	−1.69040e10			−0.547858
$994$	8.06359e9	+	1.26060e10i	0.260421	+	0.407123i
$995$			3.30576e8i			0.0106387i
$996$	−4.90802e9	+	1.06273e10i	−0.157398	+	0.340812i
$997$			2.09203e10i			0.668552i	0.942475	+	0.334276i	$0.108492\pi$
$997$			2.09203e10i			0.668552i	−0.942475	+	0.334276i	$0.891508\pi$
$998$	8.60161e9	−	5.50212e9i	0.273919	−	0.175216i
$999$	3.59698e9			0.114146

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.8.d.a.13.5	✓	14
3.2	odd	2		72.8.d.d.37.10		14
4.3	odd	2		96.8.d.a.49.2		14
8.3	odd	2		96.8.d.a.49.13		14
8.5	even	2	inner	24.8.d.a.13.6	yes	14
12.11	even	2		288.8.d.d.145.11		14
24.5	odd	2		72.8.d.d.37.9		14
24.11	even	2		288.8.d.d.145.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.8.d.a.13.5	✓	14	1.1	even	1	trivial
24.8.d.a.13.6	yes	14	8.5	even	2	inner
72.8.d.d.37.9		14	24.5	odd	2
72.8.d.d.37.10		14	3.2	odd	2
96.8.d.a.49.2		14	4.3	odd	2
96.8.d.a.49.13		14	8.3	odd	2
288.8.d.d.145.4		14	24.11	even	2
288.8.d.d.145.11		14	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	24.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.09641 - 9.53067i) q^{2} +27.0000i q^{3} +(-53.6675 + 116.206i) q^{4} -137.155i q^{5} +(257.328 - 164.603i) q^{6} +808.153 q^{7} +(1434.70 - 196.951i) q^{8} -729.000 q^{9} +O(q^{10})\)	\(q+(-6.09641 - 9.53067i) q^{2} +27.0000i q^{3} +(-53.6675 + 116.206i) q^{4} -137.155i q^{5} +(257.328 - 164.603i) q^{6} +808.153 q^{7} +(1434.70 - 196.951i) q^{8} -729.000 q^{9} +(-1307.18 + 836.155i) q^{10} -8242.25i q^{11} +(-3137.56 - 1449.02i) q^{12} -3408.20i q^{13} +(-4926.84 - 7702.25i) q^{14} +3703.19 q^{15} +(-10623.6 - 12473.0i) q^{16} +20783.8 q^{17} +(4444.29 + 6947.86i) q^{18} -6307.04i q^{19} +(15938.2 + 7360.78i) q^{20} +21820.1i q^{21} +(-78554.2 + 50248.2i) q^{22} +68891.6 q^{23} +(5317.69 + 38736.9i) q^{24} +59313.5 q^{25} +(-32482.5 + 20777.8i) q^{26} -19683.0i q^{27} +(-43371.6 + 93912.2i) q^{28} -42047.6i q^{29} +(-22576.2 - 35293.9i) q^{30} -214737. q^{31} +(-54109.8 + 177290. i) q^{32} +222541. q^{33} +(-126707. - 198084. i) q^{34} -110842. i q^{35} +(39123.6 - 84714.1i) q^{36} +182746. i q^{37} +(-60110.3 + 38450.3i) q^{38} +92021.5 q^{39} +(-27012.9 - 196776. i) q^{40} +395877. q^{41} +(207961. - 133025. i) q^{42} -433527. i q^{43} +(957798. + 442341. i) q^{44} +99986.1i q^{45} +(-419992. - 656584. i) q^{46} -1.32987e6 q^{47} +(336770. - 286837. i) q^{48} -170431. q^{49} +(-361599. - 565297. i) q^{50} +561163. i q^{51} +(396053. + 182910. i) q^{52} +225062. i q^{53} +(-187592. + 119996. i) q^{54} -1.13047e6 q^{55} +(1.15946e6 - 159167. i) q^{56} +170290. q^{57} +(-400742. + 256340. i) q^{58} -2.06725e6i q^{59} +(-198741. + 430332. i) q^{60} +3.11174e6i q^{61} +(1.30913e6 + 2.04659e6i) q^{62} -589144. q^{63} +(2.01957e6 - 565132. i) q^{64} -467453. q^{65} +(-1.35670e6 - 2.12096e6i) q^{66} +1.22034e6i q^{67} +(-1.11542e6 + 2.41520e6i) q^{68} +1.86007e6i q^{69} +(-1.05640e6 + 675741. i) q^{70} -1.63667e6 q^{71} +(-1.04590e6 + 143578. i) q^{72} +3.43311e6 q^{73} +(1.74169e6 - 1.11409e6i) q^{74} +1.60146e6i q^{75} +(732915. + 338483. i) q^{76} -6.66100e6i q^{77} +(-561001. - 877027. i) q^{78} +6.60063e6 q^{79} +(-1.71073e6 + 1.45708e6i) q^{80} +531441. q^{81} +(-2.41343e6 - 3.77298e6i) q^{82} -3.38713e6i q^{83} +(-2.53563e6 - 1.17103e6i) q^{84} -2.85061e6i q^{85} +(-4.13180e6 + 2.64296e6i) q^{86} +1.13529e6 q^{87} +(-1.62332e6 - 1.18252e7i) q^{88} -688852. q^{89} +(952935. - 609557. i) q^{90} -2.75435e6i q^{91} +(-3.69724e6 + 8.00561e6i) q^{92} -5.79791e6i q^{93} +(8.10744e6 + 1.26746e7i) q^{94} -865043. q^{95} +(-4.78684e6 - 1.46096e6i) q^{96} -3.48055e6 q^{97} +(1.03902e6 + 1.62432e6i) q^{98} +6.00860e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9	\( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9} + 5020 q^{10} + 7668 q^{12} + 4636 q^{14} - 13500 q^{15} - 43336 q^{16} - 2908 q^{17} + 10206 q^{18} + 175096 q^{20} - 128480 q^{22} - 143416 q^{23} - 29268 q^{24} - 202626 q^{25} + 424984 q^{26} + 567520 q^{28} - 250668 q^{30} - 89468 q^{31} - 893944 q^{32} + 1109820 q^{34} + 151632 q^{36} - 823816 q^{38} + 474552 q^{39} - 860888 q^{40} - 441284 q^{41} + 427788 q^{42} + 1275264 q^{44} - 2167992 q^{46} - 1056408 q^{47} - 233280 q^{48} + 2158134 q^{49} + 324610 q^{50} - 2059248 q^{52} + 39366 q^{54} + 4757504 q^{55} + 1643704 q^{56} + 1551096 q^{57} - 5494676 q^{58} - 3203712 q^{60} + 5767172 q^{62} - 1000188 q^{63} + 3852224 q^{64} - 2520464 q^{65} - 3615840 q^{66} - 3735840 q^{68} + 12890312 q^{70} + 5172696 q^{71} + 312012 q^{72} - 5446196 q^{73} - 6468800 q^{74} - 9084624 q^{76} + 3542184 q^{78} - 14373548 q^{79} + 14369088 q^{80} + 7440174 q^{81} - 7935708 q^{82} - 2775816 q^{84} + 4738312 q^{86} + 7902036 q^{87} + 12598720 q^{88} - 11952620 q^{89} - 3659580 q^{90} + 11004480 q^{92} - 15440088 q^{94} - 69327376 q^{95} + 1341576 q^{96} + 133732 q^{97} + 53030538 q^{98}+O(q^{100}) \) 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9 + 5020 * q^10 + 7668 * q^12 + 4636 * q^14 - 13500 * q^15 - 43336 * q^16 - 2908 * q^17 + 10206 * q^18 + 175096 * q^20 - 128480 * q^22 - 143416 * q^23 - 29268 * q^24 - 202626 * q^25 + 424984 * q^26 + 567520 * q^28 - 250668 * q^30 - 89468 * q^31 - 893944 * q^32 + 1109820 * q^34 + 151632 * q^36 - 823816 * q^38 + 474552 * q^39 - 860888 * q^40 - 441284 * q^41 + 427788 * q^42 + 1275264 * q^44 - 2167992 * q^46 - 1056408 * q^47 - 233280 * q^48 + 2158134 * q^49 + 324610 * q^50 - 2059248 * q^52 + 39366 * q^54 + 4757504 * q^55 + 1643704 * q^56 + 1551096 * q^57 - 5494676 * q^58 - 3203712 * q^60 + 5767172 * q^62 - 1000188 * q^63 + 3852224 * q^64 - 2520464 * q^65 - 3615840 * q^66 - 3735840 * q^68 + 12890312 * q^70 + 5172696 * q^71 + 312012 * q^72 - 5446196 * q^73 - 6468800 * q^74 - 9084624 * q^76 + 3542184 * q^78 - 14373548 * q^79 + 14369088 * q^80 + 7440174 * q^81 - 7935708 * q^82 - 2775816 * q^84 + 4738312 * q^86 + 7902036 * q^87 + 12598720 * q^88 - 11952620 * q^89 - 3659580 * q^90 + 11004480 * q^92 - 15440088 * q^94 - 69327376 * q^95 + 1341576 * q^96 + 133732 * q^97 + 53030538 * q^98

Introduction

L-functions

Modular forms

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