LMFDB - Embedded newform 26.8.c.b.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,8,Mod(3,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("26.3");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	26.c (of order $3$, 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:	$8.12201066259$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4654x^{6} + 7012369x^{4} + 3763719168x^{2} + 637953638400 $ x^8 + 4654x^6 + 7012369x^4 + 3763719168*x^2 + 637953638400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3.3
Root			$23.0850i$ of defining polynomial
Character	$\chi$	$=$	26.3
Dual form			26.8.c.b.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 + 6.92820i) q^{2} +(19.9922 + 34.6275i) q^{3} +(-32.0000 + 55.4256i) q^{4} -323.700 q^{5} +(-159.938 + 277.020i) q^{6} +(-284.296 + 492.415i) q^{7} -512.000 q^{8} +(294.123 - 509.436i) q^{9} +O(q^{10})$	\(q+(4.00000 + 6.92820i) q^{2} +(19.9922 + 34.6275i) q^{3} +(-32.0000 + 55.4256i) q^{4} -323.700 q^{5} +(-159.938 + 277.020i) q^{6} +(-284.296 + 492.415i) q^{7} -512.000 q^{8} +(294.123 - 509.436i) q^{9} +(-1294.80 - 2242.66i) q^{10} +(119.113 + 206.309i) q^{11} -2559.00 q^{12} +(-5815.88 + 5378.11i) q^{13} -4548.73 q^{14} +(-6471.49 - 11208.9i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(-10233.3 + 17724.6i) q^{17} +4705.97 q^{18} +(4821.16 - 8350.49i) q^{19} +(10358.4 - 17941.3i) q^{20} -22734.8 q^{21} +(-952.901 + 1650.47i) q^{22} +(39132.3 + 67779.1i) q^{23} +(-10236.0 - 17729.3i) q^{24} +26657.0 q^{25} +(-60524.2 - 18781.2i) q^{26} +110967. q^{27} +(-18194.9 - 31514.5i) q^{28} +(69432.3 + 120260. i) q^{29} +(51771.9 - 89671.6i) q^{30} +160571. q^{31} +(16384.0 - 28377.9i) q^{32} +(-4762.65 + 8249.15i) q^{33} -163733. q^{34} +(92026.6 - 159395. i) q^{35} +(18823.9 + 32603.9i) q^{36} +(76477.6 + 132463. i) q^{37} +77138.6 q^{38} +(-302503. - 93869.2i) q^{39} +165735. q^{40} +(-92718.0 - 160592. i) q^{41} +(-90939.2 - 157511. i) q^{42} +(-42504.5 + 73620.0i) q^{43} -15246.4 q^{44} +(-95207.7 + 164905. i) q^{45} +(-313058. + 542233. i) q^{46} -1.20335e6 q^{47} +(81888.1 - 141834. i) q^{48} +(250123. + 433227. i) q^{49} +(106628. + 184685. i) q^{50} -818346. q^{51} +(-111977. - 494448. i) q^{52} -665967. q^{53} +(443866. + 768799. i) q^{54} +(-38556.8 - 66782.3i) q^{55} +(145559. - 252116. i) q^{56} +385543. q^{57} +(-555458. + 962082. i) q^{58} +(1.24309e6 - 2.15310e6i) q^{59} +828351. q^{60} +(1.52300e6 - 2.63791e6i) q^{61} +(642282. + 1.11247e6i) q^{62} +(167236. + 289661. i) q^{63} +262144. q^{64} +(1.88260e6 - 1.74090e6i) q^{65} -76202.4 q^{66} +(193938. + 335910. i) q^{67} +(-654932. - 1.13437e6i) q^{68} +(-1.56468e6 + 2.71011e6i) q^{69} +1.47243e6 q^{70} +(-1.84016e6 + 3.18724e6i) q^{71} +(-150591. + 260831. i) q^{72} +1.57546e6 q^{73} +(-611821. + 1.05970e6i) q^{74} +(532932. + 923066. i) q^{75} +(308554. + 534432. i) q^{76} -135453. q^{77} +(-559667. - 2.47128e6i) q^{78} +2.29576e6 q^{79} +(662939. + 1.14824e6i) q^{80} +(1.57522e6 + 2.72836e6i) q^{81} +(741744. - 1.28474e6i) q^{82} -7.93544e6 q^{83} +(727514. - 1.26009e6i) q^{84} +(3.31253e6 - 5.73746e6i) q^{85} -680072. q^{86} +(-2.77621e6 + 4.80854e6i) q^{87} +(-60985.6 - 105630. i) q^{88} +(-4.07541e6 - 7.05882e6i) q^{89} -1.52332e6 q^{90} +(-994830. - 4.39280e6i) q^{91} -5.00893e6 q^{92} +(3.21016e6 + 5.56016e6i) q^{93} +(-4.81339e6 - 8.33704e6i) q^{94} +(-1.56061e6 + 2.70306e6i) q^{95} +1.31021e6 q^{96} +(669795. - 1.16012e6i) q^{97} +(-2.00099e6 + 3.46581e6i) q^{98} +140135. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 32 q^{2} - 256 q^{4} + 556 q^{5} - 548 q^{7} - 4096 q^{8} - 5214 q^{9}+O(q^{10}) $ 8 * q + 32 * q^2 - 256 * q^4 + 556 * q^5 - 548 * q^7 - 4096 * q^8 - 5214 * q^9	\( 8 q + 32 q^{2} - 256 q^{4} + 556 q^{5} - 548 q^{7} - 4096 q^{8} - 5214 q^{9} + 2224 q^{10} - 7392 q^{11} - 25818 q^{13} - 8768 q^{14} + 15528 q^{15} - 16384 q^{16} + 28316 q^{17} - 83424 q^{18} - 99888 q^{19} - 17792 q^{20} + 182148 q^{21} + 59136 q^{22} - 33388 q^{23} + 173756 q^{25} - 156000 q^{26} + 212544 q^{27} - 35072 q^{28} + 93140 q^{29} - 124224 q^{30} + 622320 q^{31} + 131072 q^{32} + 238638 q^{33} + 453056 q^{34} + 141544 q^{35} - 333696 q^{36} - 9636 q^{37} - 1598208 q^{38} - 22932 q^{39} - 284672 q^{40} + 82892 q^{41} + 728592 q^{42} - 569264 q^{43} + 946176 q^{44} - 2303394 q^{45} + 267104 q^{46} - 1148400 q^{47} - 717798 q^{49} + 695024 q^{50} - 5459856 q^{51} + 404352 q^{52} + 2470700 q^{53} + 850176 q^{54} - 1092512 q^{55} + 280576 q^{56} + 7056924 q^{57} - 745120 q^{58} + 231504 q^{59} - 1987584 q^{60} + 685684 q^{61} + 2489280 q^{62} - 5951712 q^{63} + 2097152 q^{64} - 6216678 q^{65} + 3818208 q^{66} + 3271056 q^{67} + 1812224 q^{68} + 5600034 q^{69} + 2264704 q^{70} - 175012 q^{71} + 2669568 q^{72} + 14275780 q^{73} + 77088 q^{74} + 22200960 q^{75} - 6392832 q^{76} - 27830412 q^{77} + 5028192 q^{78} - 14107904 q^{79} - 1138688 q^{80} + 3758004 q^{81} - 663136 q^{82} + 1314576 q^{83} - 5828736 q^{84} + 11814998 q^{85} - 9108224 q^{86} - 7182900 q^{87} + 3784704 q^{88} - 11452234 q^{89} - 36854304 q^{90} + 16457168 q^{91} + 4273664 q^{92} + 2984688 q^{93} - 4593600 q^{94} - 23334088 q^{95} - 428002 q^{97} + 5742384 q^{98} - 20715312 q^{99}+O(q^{100}) \) 8 * q + 32 * q^2 - 256 * q^4 + 556 * q^5 - 548 * q^7 - 4096 * q^8 - 5214 * q^9 + 2224 * q^10 - 7392 * q^11 - 25818 * q^13 - 8768 * q^14 + 15528 * q^15 - 16384 * q^16 + 28316 * q^17 - 83424 * q^18 - 99888 * q^19 - 17792 * q^20 + 182148 * q^21 + 59136 * q^22 - 33388 * q^23 + 173756 * q^25 - 156000 * q^26 + 212544 * q^27 - 35072 * q^28 + 93140 * q^29 - 124224 * q^30 + 622320 * q^31 + 131072 * q^32 + 238638 * q^33 + 453056 * q^34 + 141544 * q^35 - 333696 * q^36 - 9636 * q^37 - 1598208 * q^38 - 22932 * q^39 - 284672 * q^40 + 82892 * q^41 + 728592 * q^42 - 569264 * q^43 + 946176 * q^44 - 2303394 * q^45 + 267104 * q^46 - 1148400 * q^47 - 717798 * q^49 + 695024 * q^50 - 5459856 * q^51 + 404352 * q^52 + 2470700 * q^53 + 850176 * q^54 - 1092512 * q^55 + 280576 * q^56 + 7056924 * q^57 - 745120 * q^58 + 231504 * q^59 - 1987584 * q^60 + 685684 * q^61 + 2489280 * q^62 - 5951712 * q^63 + 2097152 * q^64 - 6216678 * q^65 + 3818208 * q^66 + 3271056 * q^67 + 1812224 * q^68 + 5600034 * q^69 + 2264704 * q^70 - 175012 * q^71 + 2669568 * q^72 + 14275780 * q^73 + 77088 * q^74 + 22200960 * q^75 - 6392832 * q^76 - 27830412 * q^77 + 5028192 * q^78 - 14107904 * q^79 - 1138688 * q^80 + 3758004 * q^81 - 663136 * q^82 + 1314576 * q^83 - 5828736 * q^84 + 11814998 * q^85 - 9108224 * q^86 - 7182900 * q^87 + 3784704 * q^88 - 11452234 * q^89 - 36854304 * q^90 + 16457168 * q^91 + 4273664 * q^92 + 2984688 * q^93 - 4593600 * q^94 - 23334088 * q^95 - 428002 * q^97 + 5742384 * q^98 - 20715312 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$3$	19.9922	+	34.6275i	0.427500	+	0.740452i	0.996650	−	0.0817814i	$-0.0260609\pi$
$3$	19.9922	+	34.6275i	0.427500	+	0.740452i	−0.569150	+	0.822234i	$0.692728\pi$
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−323.700			−1.15811			−0.579053	−	0.815290i	$-0.696578\pi$
$5$	−323.700			−1.15811			−0.579053	+	0.815290i	$0.696578\pi$
$6$	−159.938	+	277.020i	−0.302288	+	0.523579i
$7$	−284.296	+	492.415i	−0.313276	+	0.542610i	−0.979070	−	0.203526i	$-0.934760\pi$
$7$	−284.296	+	492.415i	−0.313276	+	0.542610i	0.665794	+	0.746136i	$0.268093\pi$
$8$	−512.000			−0.353553
$9$	294.123	−	509.436i	0.134487	−	0.232938i
$10$	−1294.80	−	2242.66i	−0.409452	−	0.709192i
$11$	119.113	+	206.309i	0.0269826	+	0.0467352i	0.879201	−	0.476450i	$-0.158077\pi$
$11$	119.113	+	206.309i	0.0269826	+	0.0467352i	−0.852219	+	0.523186i	$0.824743\pi$
$12$	−2559.00			−0.427500
$13$	−5815.88	+	5378.11i	−0.734199	+	0.678935i
$13$	−5815.88	+	5378.11i	−0.734199	+	0.678935i
$14$	−4548.73			−0.443039
$15$	−6471.49	−	11208.9i	−0.495091	−	0.857522i
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	−10233.3	+	17724.6i	−0.505178	+	0.874994i	0.494804	+	0.869005i	$0.335240\pi$
$17$	−10233.3	+	17724.6i	−0.505178	+	0.874994i	−0.999982	+	0.00598975i	$0.998093\pi$
$18$	4705.97			0.190193
$19$	4821.16	−	8350.49i	0.161255	−	0.279302i	−0.774064	−	0.633108i	$-0.781779\pi$
$19$	4821.16	−	8350.49i	0.161255	−	0.279302i	0.935319	+	0.353805i	$0.115112\pi$
$20$	10358.4	−	17941.3i	0.289527	−	0.501475i
$21$	−22734.8			−0.535702
$22$	−952.901	+	1650.47i	−0.0190796	+	0.0330468i
$23$	39132.3	+	67779.1i	0.670638	+	1.16158i	0.977724	+	0.209897i	$0.0673128\pi$
$23$	39132.3	+	67779.1i	0.670638	+	1.16158i	−0.307086	+	0.951682i	$0.599354\pi$
$24$	−10236.0	−	17729.3i	−0.151144	−	0.261789i
$25$	26657.0			0.341210
$26$	−60524.2	−	18781.2i	−0.675339	−	0.209563i
$27$	110967.			1.08497
$28$	−18194.9	−	31514.5i	−0.156638	−	0.271305i
$29$	69432.3	+	120260.i	0.528650	+	0.915649i	0.999442	+	0.0334046i	$0.0106350\pi$
$29$	69432.3	+	120260.i	0.528650	+	0.915649i	−0.470792	+	0.882244i	$0.656032\pi$
$30$	51771.9	−	89671.6i	0.350082	−	0.606360i
$31$	160571.			0.968055			0.484027	−	0.875053i	$-0.339174\pi$
$31$	160571.			0.968055			0.484027	+	0.875053i	$0.339174\pi$
$32$	16384.0	−	28377.9i	0.0883883	−	0.153093i
$33$	−4762.65	+	8249.15i	−0.0230701	+	0.0399586i
$34$	−163733.			−0.714430
$35$	92026.6	−	159395.i	0.362807	−	0.628400i
$36$	18823.9	+	32603.9i	0.0672435	+	0.116469i
$37$	76477.6	+	132463.i	0.248215	+	0.429921i	0.963031	−	0.269392i	$-0.0868227\pi$
$37$	76477.6	+	132463.i	0.248215	+	0.429921i	−0.714816	+	0.699313i	$0.753489\pi$
$38$	77138.6			0.228049
$39$	−302503.	−	93869.2i	−0.816589	−	0.253394i
$40$	165735.			0.409452
$41$	−92718.0	−	160592.i	−0.210097	−	0.363899i	0.741647	−	0.670790i	$-0.234045\pi$
$41$	−92718.0	−	160592.i	−0.210097	−	0.363899i	−0.951745	+	0.306891i	$0.900711\pi$
$42$	−90939.2	−	157511.i	−0.189399	−	0.328049i
$43$	−42504.5	+	73620.0i	−0.0815259	+	0.141207i	−0.903906	−	0.427732i	$-0.859313\pi$
$43$	−42504.5	+	73620.0i	−0.0815259	+	0.141207i	0.822380	+	0.568939i	$0.192646\pi$
$44$	−15246.4			−0.0269826
$45$	−95207.7	+	164905.i	−0.155750	+	0.269767i
$46$	−313058.	+	542233.i	−0.474212	+	0.821360i
$47$	−1.20335e6			−1.69063			−0.845315	−	0.534268i	$-0.820587\pi$
$47$	−1.20335e6			−1.69063			−0.845315	+	0.534268i	$0.820587\pi$
$48$	81888.1	−	141834.i	0.106875	−	0.185113i
$49$	250123.	+	433227.i	0.303716	+	0.526052i
$50$	106628.	+	184685.i	0.120636	+	0.208947i
$51$	−818346.			−0.863856
$52$	−111977.	−	494448.i	−0.110438	−	0.487651i
$53$	−665967.			−0.614451			−0.307225	−	0.951637i	$-0.599401\pi$
$53$	−665967.			−0.614451			−0.307225	+	0.951637i	$0.599401\pi$
$54$	443866.	+	768799.i	0.383596	+	0.664408i
$55$	−38556.8	−	66782.3i	−0.0312487	−	0.0541243i
$56$	145559.	−	252116.i	0.110760	−	0.191842i
$57$	385543.			0.275747
$58$	−555458.	+	962082.i	−0.373812	+	0.647462i
$59$	1.24309e6	−	2.15310e6i	0.787992	−	1.36484i	−0.139204	−	0.990264i	$-0.544454\pi$
$59$	1.24309e6	−	2.15310e6i	0.787992	−	1.36484i	0.927195	−	0.374578i	$-0.122212\pi$
$60$	828351.			0.495091
$61$	1.52300e6	−	2.63791e6i	0.859104	−	1.48801i	−0.0136811	−	0.999906i	$-0.504355\pi$
$61$	1.52300e6	−	2.63791e6i	0.859104	−	1.48801i	0.872785	−	0.488105i	$-0.162312\pi$
$62$	642282.	+	1.11247e6i	0.342259	+	0.592810i
$63$	167236.	+	289661.i	0.0842630	+	0.145948i
$64$	262144.			0.125000
$65$	1.88260e6	−	1.74090e6i	0.850280	−	0.786278i
$66$	−76202.4			−0.0326261
$67$	193938.	+	335910.i	0.0787772	+	0.136446i	0.902723	−	0.430223i	$-0.141565\pi$
$67$	193938.	+	335910.i	0.0787772	+	0.136446i	−0.823945	+	0.566669i	$0.808232\pi$
$68$	−654932.	−	1.13437e6i	−0.252589	−	0.437497i
$69$	−1.56468e6	+	2.71011e6i	−0.573396	+	0.993150i
$70$	1.47243e6			0.513086
$71$	−1.84016e6	+	3.18724e6i	−0.610170	+	1.05684i	0.381042	+	0.924558i	$0.375565\pi$
$71$	−1.84016e6	+	3.18724e6i	−0.610170	+	1.05684i	−0.991211	+	0.132287i	$0.957768\pi$
$72$	−150591.	+	260831.i	−0.0475483	+	0.0823561i
$73$	1.57546e6			0.473998			0.236999	−	0.971510i	$-0.423836\pi$
$73$	1.57546e6			0.473998			0.236999	+	0.971510i	$0.423836\pi$
$74$	−611821.	+	1.05970e6i	−0.175515	+	0.304000i
$75$	532932.	+	923066.i	0.145867	+	0.252649i
$76$	308554.	+	534432.i	0.0806276	+	0.139651i
$77$	−135453.			−0.0338120
$78$	−559667.	−	2.47128e6i	−0.133536	−	0.589645i
$79$	2.29576e6			0.523880			0.261940	−	0.965084i	$-0.415638\pi$
$79$	2.29576e6			0.523880			0.261940	+	0.965084i	$0.415638\pi$
$80$	662939.	+	1.14824e6i	0.144763	+	0.250737i
$81$	1.57522e6	+	2.72836e6i	0.329340	+	0.570433i
$82$	741744.	−	1.28474e6i	0.148561	−	0.257316i
$83$	−7.93544e6			−1.52334			−0.761672	−	0.647963i	$-0.775621\pi$
$83$	−7.93544e6			−1.52334			−0.761672	+	0.647963i	$0.775621\pi$
$84$	727514.	−	1.26009e6i	0.133926	−	0.231966i
$85$	3.31253e6	−	5.73746e6i	0.585050	−	1.01334i
$86$	−680072.			−0.115295
$87$	−2.77621e6	+	4.80854e6i	−0.451996	+	0.782881i
$88$	−60985.6	−	105630.i	−0.00953978	−	0.0165234i
$89$	−4.07541e6	−	7.05882e6i	−0.612782	−	1.06137i	−0.990769	−	0.135559i	$-0.956717\pi$
$89$	−4.07541e6	−	7.05882e6i	−0.612782	−	1.06137i	0.377987	−	0.925811i	$-0.376616\pi$
$90$	−1.52332e6			−0.220264
$91$	−994830.	−	4.39280e6i	−0.138390	−	0.611077i
$92$	−5.00893e6			−0.670638
$93$	3.21016e6	+	5.56016e6i	0.413844	+	0.716798i
$94$	−4.81339e6	−	8.33704e6i	−0.597728	−	1.03530i
$95$	−1.56061e6	+	2.70306e6i	−0.186751	+	0.323462i
$96$	1.31021e6			0.151144
$97$	669795.	−	1.16012e6i	0.0745145	−	0.129063i	−0.826361	−	0.563141i	$-0.809593\pi$
$97$	669795.	−	1.16012e6i	0.0745145	−	0.129063i	0.900875	+	0.434079i	$0.142926\pi$
$98$	−2.00099e6	+	3.46581e6i	−0.214760	+	0.371975i
$99$	140135.			0.0145152
$100$	−853024.	+	1.47748e6i	−0.0853024	+	0.147748i
$101$	9.63841e6	+	1.66942e7i	0.930852	+	1.61228i	0.781868	+	0.623444i	$0.214267\pi$
$101$	9.63841e6	+	1.66942e7i	0.930852	+	1.61228i	0.148984	+	0.988840i	$0.452400\pi$
$102$	−3.27338e6	−	5.66966e6i	−0.305419	−	0.529001i
$103$	−1.54295e7			−1.39130			−0.695652	−	0.718379i	$-0.744884\pi$
$103$	−1.54295e7			−1.39130			−0.695652	+	0.718379i	$0.744884\pi$
$104$	2.97773e6	−	2.75359e6i	0.259578	−	0.240040i
$105$	7.35926e6			0.620400
$106$	−2.66387e6	−	4.61395e6i	−0.217241	−	0.376273i
$107$	5.21244e6	+	9.02820e6i	0.411337	+	0.712456i	0.995036	−	0.0995137i	$-0.0317287\pi$
$107$	5.21244e6	+	9.02820e6i	0.411337	+	0.712456i	−0.583699	+	0.811970i	$0.698395\pi$
$108$	−3.55093e6	+	6.15039e6i	−0.271243	+	0.469807i
$109$	1.55544e7			1.15043			0.575216	−	0.818001i	$-0.304918\pi$
$109$	1.55544e7			1.15043			0.575216	+	0.818001i	$0.304918\pi$
$110$	308454.	−	534259.i	0.0220961	−	0.0382716i
$111$	−3.05791e6	+	5.29646e6i	−0.212224	+	0.367583i
$112$	2.32895e6			0.156638
$113$	468038.	−	810666.i	0.0305145	−	0.0528527i	−0.850365	−	0.526194i	$-0.823619\pi$
$113$	468038.	−	810666.i	0.0305145	−	0.0528527i	0.880879	+	0.473341i	$0.156952\pi$
$114$	1.54217e6	+	2.67112e6i	0.0974912	+	0.168860i
$115$	−1.26671e7	−	2.19401e7i	−0.776670	−	1.34523i
$116$	−8.88733e6			−0.528650
$117$	1.02922e6	+	4.54464e6i	0.0594096	+	0.262331i
$118$	1.98895e7			1.11439
$119$	−5.81857e6	−	1.00781e7i	−0.316520	−	0.548230i
$120$	3.31340e6	+	5.73898e6i	0.175041	+	0.303180i
$121$	9.71521e6	−	1.68272e7i	0.498544	−	0.863503i
$122$	2.43680e7			1.21496
$123$	3.70727e6	−	6.42119e6i	0.179633	−	0.311134i
$124$	−5.13826e6	+	8.89972e6i	−0.242014	+	0.419180i
$125$	1.66602e7			0.762949
$126$	−1.33789e6	+	2.31729e6i	−0.0595830	+	0.103201i
$127$	4.23586e6	+	7.33673e6i	0.183497	+	0.317826i	0.943069	−	0.332597i	$-0.107925\pi$
$127$	4.23586e6	+	7.33673e6i	0.183497	+	0.317826i	−0.759572	+	0.650423i	$0.774592\pi$
$128$	1.04858e6	+	1.81619e6i	0.0441942	+	0.0765466i
$129$	−3.39904e6			−0.139409
$130$	1.95917e7	+	6.07947e6i	0.782114	+	0.242697i
$131$	1.17131e7			0.455219			0.227610	−	0.973752i	$-0.426909\pi$
$131$	1.17131e7			0.455219			0.227610	+	0.973752i	$0.426909\pi$
$132$	−304809.	−	527945.i	−0.0115351	−	0.0199793i
$133$	2.74127e6	+	4.74802e6i	0.101035	+	0.174997i
$134$	−1.55150e6	+	2.68728e6i	−0.0557039	+	0.0964820i
$135$	−3.59199e7			−1.25651
$136$	5.23945e6	−	9.07500e6i	0.178608	−	0.309357i
$137$	−1.87496e7	+	3.24753e7i	−0.622975	+	1.07902i	0.365954	+	0.930633i	$0.380743\pi$
$137$	−1.87496e7	+	3.24753e7i	−0.622975	+	1.07902i	−0.988929	+	0.148391i	$0.952591\pi$
$138$	−2.50349e7			−0.810904
$139$	1.40529e7	−	2.43404e7i	0.443828	−	0.768733i	−0.554142	−	0.832422i	$-0.686953\pi$
$139$	1.40529e7	−	2.43404e7i	0.443828	−	0.768733i	0.997970	+	0.0636896i	$0.0202867\pi$
$140$	5.88970e6	+	1.02013e7i	0.181403	+	0.314200i
$141$	−2.40576e7	−	4.16690e7i	−0.722745	−	1.25183i
$142$	−2.94425e7			−0.862910
$143$	−1.80230e6	−	559268.i	−0.0515407	−	0.0159935i
$144$	−2.40945e6			−0.0672435
$145$	−2.24753e7	−	3.89283e7i	−0.612233	−	1.06042i
$146$	6.30182e6	+	1.09151e7i	0.167584	+	0.290263i
$147$	−1.00010e7	+	1.73223e7i	−0.259678	+	0.449775i
$148$	−9.78913e6			−0.248215
$149$	−2.29505e7	+	3.97514e7i	−0.568381	+	0.984465i	0.428345	+	0.903615i	$0.359097\pi$
$149$	−2.29505e7	+	3.97514e7i	−0.568381	+	0.984465i	−0.996726	+	0.0808495i	$0.974237\pi$
$150$	−4.26346e6	+	7.38453e6i	−0.103144	+	0.178650i
$151$	4.77305e7			1.12818			0.564088	−	0.825714i	$-0.309228\pi$
$151$	4.77305e7			1.12818			0.564088	+	0.825714i	$0.309228\pi$
$152$	−2.46843e6	+	4.27545e6i	−0.0570124	+	0.0987483i
$153$	6.01970e6	+	1.04264e7i	0.135880	+	0.235351i
$154$	−541811.	−	938444.i	−0.0119543	−	0.0207055i
$155$	−5.19768e7			−1.12111
$156$	1.48829e7	−	1.37626e7i	0.313870	−	0.290245i
$157$	7.12033e7			1.46842			0.734212	−	0.678921i	$-0.237552\pi$
$157$	7.12033e7			1.46842			0.734212	+	0.678921i	$0.237552\pi$
$158$	9.18305e6	+	1.59055e7i	0.185220	+	0.320810i
$159$	−1.33141e7	−	2.30608e7i	−0.262678	−	0.454971i
$160$	−5.30351e6	+	9.18595e6i	−0.102363	+	0.177298i
$161$	−4.45006e7			−0.840379
$162$	−1.26018e7	+	2.18269e7i	−0.232878	+	0.403357i
$163$	−3.11031e7	+	5.38721e7i	−0.562531	+	0.974332i	0.434744	+	0.900554i	$0.356839\pi$
$163$	−3.11031e7	+	5.38721e7i	−0.562531	+	0.974332i	−0.997275	+	0.0737781i	$0.976494\pi$
$164$	1.18679e7			0.210097
$165$	1.54167e6	−	2.67025e6i	0.0267176	−	0.0462763i
$166$	−3.17418e7	−	5.49784e7i	−0.538583	−	0.932854i
$167$	−1.12288e7	−	1.94489e7i	−0.186563	−	0.323137i	0.757539	−	0.652790i	$-0.226402\pi$
$167$	−1.12288e7	−	1.94489e7i	−0.186563	−	0.323137i	−0.944102	+	0.329653i	$0.893068\pi$
$168$	1.16402e7			0.189399
$169$	4.90039e6	−	6.25569e7i	0.0780957	−	0.996946i
$170$	5.30004e7			0.827386
$171$	−2.83603e6	−	4.91214e6i	−0.0433734	−	0.0751250i
$172$	−2.72029e6	−	4.71168e6i	−0.0407629	−	0.0706035i
$173$	−4.30844e7	+	7.46244e7i	−0.632643	+	1.09577i	0.354366	+	0.935107i	$0.384697\pi$
$173$	−4.30844e7	+	7.46244e7i	−0.632643	+	1.09577i	−0.987009	+	0.160664i	$0.948637\pi$
$174$	−4.44194e7			−0.639219
$175$	−7.57847e6	+	1.31263e7i	−0.106893	+	0.185144i
$176$	487885.	−	845042.i	0.00674564	−	0.0116838i
$177$	9.94087e7			1.34747
$178$	3.26033e7	−	5.64705e7i	0.433303	−	0.750502i
$179$	3.55570e7	+	6.15865e7i	0.463382	+	0.802602i	0.999127	−	0.0417785i	$-0.0133024\pi$
$179$	3.55570e7	+	6.15865e7i	0.463382	+	0.802602i	−0.535745	+	0.844380i	$0.679969\pi$
$180$	−6.09329e6	−	1.05539e7i	−0.0778750	−	0.134884i
$181$	1.39420e8			1.74763			0.873817	−	0.486254i	$-0.161637\pi$
$181$	1.39420e8			1.74763			0.873817	+	0.486254i	$0.161637\pi$
$182$	2.64549e7	−	2.44636e7i	0.325279	−	0.300795i
$183$	1.21793e8			1.46907
$184$	−2.00357e7	−	3.47029e7i	−0.237106	−	0.410680i
$185$	−2.47558e7	−	4.28784e7i	−0.287459	−	0.497894i
$186$	−2.56813e7	+	4.44813e7i	−0.292632	+	0.506853i
$187$	−4.87566e6			−0.0545240
$188$	3.85071e7	−	6.66963e7i	0.422658	−	0.732064i
$189$	−3.15473e7	+	5.46416e7i	−0.339896	+	0.588717i
$190$	−2.49698e7			−0.264105
$191$	4.29014e7	−	7.43074e7i	0.445507	−	0.771641i	−0.552580	−	0.833460i	$-0.686357\pi$
$191$	4.29014e7	−	7.43074e7i	0.445507	−	0.771641i	0.998087	+	0.0618185i	$0.0196900\pi$
$192$	5.24084e6	+	9.07740e6i	0.0534375	+	0.0925565i
$193$	−1.17723e7	−	2.03903e7i	−0.117872	−	0.204161i	0.801052	−	0.598595i	$-0.204274\pi$
$193$	−1.17723e7	−	2.03903e7i	−0.117872	−	0.204161i	−0.918924	+	0.394434i	$0.870941\pi$
$194$	1.07167e7			0.105379
$195$	9.79203e7	+	3.03855e7i	0.945697	+	0.293458i
$196$	−3.20158e7			−0.303716
$197$	−3.57372e7	−	6.18986e7i	−0.333034	−	0.576832i	0.650071	−	0.759873i	$-0.274739\pi$
$197$	−3.57372e7	−	6.18986e7i	−0.333034	−	0.576832i	−0.983105	+	0.183041i	$0.941406\pi$
$198$	560540.	+	970883.i	0.00513190	+	0.00888871i
$199$	−1.07802e8	+	1.86718e8i	−0.969706	+	1.67958i	−0.273306	+	0.961927i	$0.588117\pi$
$199$	−1.07802e8	+	1.86718e8i	−0.969706	+	1.67958i	−0.696400	+	0.717654i	$0.745216\pi$
$200$	−1.36484e7			−0.120636
$201$	−7.75449e6	+	1.34312e7i	−0.0673546	+	0.116662i
$202$	−7.71073e7	+	1.33554e8i	−0.658212	+	1.14006i
$203$	−7.89572e7			−0.662454
$204$	2.61871e7	−	4.53573e7i	0.215964	−	0.374060i
$205$	3.00129e7	+	5.19838e7i	0.243315	+	0.421434i
$206$	−6.17180e7	−	1.06899e8i	−0.491900	−	0.851996i
$207$	4.60388e7			0.360768
$208$	3.09884e7	+	9.61595e6i	0.238768	+	0.0740919i
$209$	2.29704e6			0.0174043
$210$	2.94371e7	+	5.09865e7i	0.219345	+	0.379916i
$211$	−4.46978e7	−	7.74188e7i	−0.327565	−	0.567359i	0.654463	−	0.756094i	$-0.272895\pi$
$211$	−4.46978e7	−	7.74188e7i	−0.327565	−	0.567359i	−0.982028	+	0.188735i	$0.939561\pi$
$212$	2.13109e7	−	3.69116e7i	0.153613	−	0.266065i
$213$	−1.47155e8			−1.04339
$214$	−4.16995e7	+	7.22256e7i	−0.290859	+	0.503783i
$215$	1.37587e7	−	2.38308e7i	0.0944156	−	0.163533i
$216$	−5.68149e7			−0.383596
$217$	−4.56495e7	+	7.90673e7i	−0.303268	+	0.525276i
$218$	6.22177e7	+	1.07764e8i	0.406739	+	0.704493i
$219$	3.14969e7	+	5.45541e7i	0.202634	+	0.350973i
$220$	4.93527e6			0.0312487
$221$	−3.58092e7	−	1.58120e8i	−0.223163	−	0.985403i
$222$	−4.89266e7			−0.300130
$223$	−5.37637e7	−	9.31215e7i	−0.324655	−	0.562319i	0.656787	−	0.754076i	$-0.271915\pi$
$223$	−5.37637e7	−	9.31215e7i	−0.324655	−	0.562319i	−0.981443	+	0.191757i	$0.938582\pi$
$224$	9.31580e6	+	1.61354e7i	0.0553799	+	0.0959208i
$225$	7.84043e6	−	1.35800e7i	0.0458882	−	0.0794807i
$226$	7.48861e6			0.0431541
$227$	1.07539e8	−	1.86264e8i	0.610207	−	1.05691i	−0.380999	−	0.924576i	$-0.624420\pi$
$227$	1.07539e8	−	1.86264e8i	0.610207	−	1.05691i	0.991205	−	0.132333i	$-0.0422470\pi$
$228$	−1.23374e7	+	2.13689e7i	−0.0689367	+	0.119402i
$229$	−3.12216e8			−1.71803			−0.859016	−	0.511949i	$-0.828924\pi$
$229$	−3.12216e8			−1.71803			−0.859016	+	0.511949i	$0.828924\pi$
$230$	1.01337e8	−	1.75521e8i	0.549188	−	0.951222i
$231$	−2.70800e6	−	4.69039e6i	−0.0144546	−	0.0250361i
$232$	−3.55493e7	−	6.15732e7i	−0.186906	−	0.323731i
$233$	−2.62733e8			−1.36072			−0.680360	−	0.732878i	$-0.738177\pi$
$233$	−2.62733e8			−1.36072			−0.680360	+	0.732878i	$0.738177\pi$
$234$	−2.73693e7	+	2.53092e7i	−0.139640	+	0.129129i
$235$	3.89524e8			1.95793
$236$	7.95580e7	+	1.37798e8i	0.393996	+	0.682421i
$237$	4.58974e7	+	7.94965e7i	0.223959	+	0.387908i
$238$	4.65485e7	−	8.06244e7i	0.223814	−	0.387657i
$239$	−8.68087e7			−0.411311			−0.205656	−	0.978624i	$-0.565933\pi$
$239$	−8.68087e7			−0.411311			−0.205656	+	0.978624i	$0.565933\pi$
$240$	−2.65072e7	+	4.59118e7i	−0.123773	+	0.214381i
$241$	−1.06288e8	+	1.84096e8i	−0.489130	+	0.847198i	−0.999922	−	0.0125066i	$-0.996019\pi$
$241$	−1.06288e8	+	1.84096e8i	−0.489130	+	0.847198i	0.510792	+	0.859704i	$0.329352\pi$
$242$	1.55443e8			0.705048
$243$	5.83577e7	−	1.01078e8i	0.260901	−	0.451894i
$244$	9.74720e7	+	1.68827e8i	0.429552	+	0.744006i
$245$	−8.09651e7	−	1.40236e8i	−0.351736	−	0.609224i
$246$	5.93164e7			0.254040
$247$	1.68706e7	+	7.44942e7i	0.0712346	+	0.314545i
$248$	−8.22121e7			−0.342259
$249$	−1.58647e8	−	2.74785e8i	−0.651230	−	1.12796i
$250$	6.66409e7	+	1.15425e8i	0.269743	+	0.467209i
$251$	5.96185e7	−	1.03262e8i	0.237970	−	0.412177i	−0.722161	−	0.691725i	$-0.756851\pi$
$251$	5.96185e7	−	1.03262e8i	0.237970	−	0.412177i	0.960132	+	0.279548i	$0.0901846\pi$
$252$	−2.14062e7			−0.0842630
$253$	−9.32230e6	+	1.61467e7i	−0.0361910	+	0.0626847i
$254$	−3.38869e7	+	5.86938e7i	−0.129752	+	0.224737i
$255$	2.64899e8			1.00044
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	1.72292e8	+	2.98419e8i	0.633139	+	1.09663i	0.986906	+	0.161296i	$0.0515673\pi$
$257$	1.72292e8	+	2.98419e8i	0.633139	+	1.09663i	−0.353767	+	0.935334i	$0.615099\pi$
$258$	−1.35962e7	−	2.35492e7i	−0.0492887	−	0.0853705i
$259$	−8.69690e7			−0.311039
$260$	3.62470e7	+	1.60053e8i	0.127898	+	0.564752i
$261$	8.16865e7			0.284386
$262$	4.68522e7	+	8.11504e7i	0.160944	+	0.278764i
$263$	−1.51825e7	−	2.62969e7i	−0.0514634	−	0.0891373i	0.839146	−	0.543906i	$-0.183055\pi$
$263$	−1.51825e7	−	2.62969e7i	−0.0514634	−	0.0891373i	−0.890610	+	0.454769i	$0.849722\pi$
$264$	2.43848e6	−	4.22356e6i	0.00815652	−	0.0141275i
$265$	2.15574e8			0.711599
$266$	−2.19302e7	+	3.79841e7i	−0.0714424	+	0.123742i
$267$	1.62953e8	−	2.82243e8i	0.523929	−	0.907472i
$268$	−2.48240e7			−0.0787772
$269$	−2.52890e8	+	4.38018e8i	−0.792134	+	1.37202i	0.132510	+	0.991182i	$0.457696\pi$
$269$	−2.52890e8	+	4.38018e8i	−0.792134	+	1.37202i	−0.924643	+	0.380834i	$0.875637\pi$
$270$	−1.43680e8	−	2.48861e8i	−0.444245	−	0.769455i
$271$	1.82110e8	+	3.15424e8i	0.555829	+	0.962724i	0.997839	+	0.0657138i	$0.0209324\pi$
$271$	1.82110e8	+	3.15424e8i	0.555829	+	0.962724i	−0.442009	+	0.897010i	$0.645734\pi$
$272$	8.38312e7			0.252589
$273$	1.32223e8	−	1.22270e8i	0.393312	−	0.363707i
$274$	−2.99994e8			−0.881020
$275$	3.17518e6	+	5.49958e6i	0.00920671	+	0.0159465i
$276$	−1.00140e8	−	1.73447e8i	−0.286698	−	0.496575i
$277$	5.83761e7	−	1.01110e8i	0.165027	−	0.285836i	−0.771638	−	0.636062i	$-0.780562\pi$
$277$	5.83761e7	−	1.01110e8i	0.165027	−	0.285836i	0.936665	+	0.350227i	$0.113895\pi$
$278$	2.24847e8			0.627668
$279$	4.72275e7	−	8.18004e7i	0.130191	−	0.225497i
$280$	−4.71176e7	+	8.16101e7i	−0.128272	+	0.222173i
$281$	3.12559e8			0.840349			0.420174	−	0.907443i	$-0.361969\pi$
$281$	3.12559e8			0.840349			0.420174	+	0.907443i	$0.361969\pi$
$282$	1.92461e8	−	3.33352e8i	0.511058	−	0.885178i
$283$	−1.05637e8	−	1.82969e8i	−0.277054	−	0.479872i	0.693597	−	0.720363i	$-0.256025\pi$
$283$	−1.05637e8	−	1.82969e8i	−0.277054	−	0.479872i	−0.970651	+	0.240491i	$0.922692\pi$
$284$	−1.17770e8	−	2.03984e8i	−0.305085	−	0.528422i
$285$	−1.24800e8			−0.319344
$286$	−3.33447e6	−	1.47238e7i	−0.00842840	−	0.0372167i
$287$	1.05437e8			0.263274
$288$	−9.63782e6	−	1.66932e7i	−0.0237742	−	0.0411780i
$289$	−4.27172e6	−	7.39884e6i	−0.0104102	−	0.0180311i
$290$	1.79802e8	−	3.11426e8i	0.432914	−	0.749829i
$291$	5.35627e7			0.127420
$292$	−5.04146e7	+	8.73206e7i	−0.118499	+	0.205247i
$293$	3.49752e8	−	6.05788e8i	0.812313	−	1.40697i	−0.0989278	−	0.995095i	$-0.531541\pi$
$293$	3.49752e8	−	6.05788e8i	0.812313	−	1.40697i	0.911241	−	0.411873i	$-0.135125\pi$
$294$	−1.60017e8			−0.367240
$295$	−4.02390e8	+	6.96960e8i	−0.912578	+	1.58063i
$296$	−3.91565e7	−	6.78211e7i	−0.0877573	−	0.152000i
$297$	1.32175e7	+	2.28934e7i	0.0292754	+	0.0507064i
$298$	−3.67207e8			−0.803812
$299$	−5.92112e8	−	1.83737e8i	−1.28102	−	0.397510i
$300$	−6.82153e7			−0.145867
$301$	−2.41677e7	−	4.18597e7i	−0.0510802	−	0.0884735i
$302$	1.90922e8	+	3.30687e8i	0.398871	+	0.690864i
$303$	−3.85386e8	+	6.67509e8i	−0.795879	+	1.37850i
$304$	−3.94949e7			−0.0806276
$305$	−4.92996e8	+	8.53894e8i	−0.994933	+	1.72327i
$306$	−4.81576e7	+	8.34114e7i	−0.0960815	+	0.166418i
$307$	4.84159e8			0.955001			0.477500	−	0.878632i	$-0.341543\pi$
$307$	4.84159e8			0.955001			0.477500	+	0.878632i	$0.341543\pi$
$308$	4.33449e6	−	7.50755e6i	0.00845299	−	0.0146410i
$309$	−3.08470e8	−	5.34286e8i	−0.594783	−	1.03019i
$310$	−2.07907e8	−	3.60106e8i	−0.396372	−	0.686537i
$311$	−5.82462e8			−1.09801			−0.549005	−	0.835819i	$-0.684993\pi$
$311$	−5.82462e8			−1.09801			−0.549005	+	0.835819i	$0.684993\pi$
$312$	1.54882e8	+	4.80610e7i	0.288708	+	0.0895885i
$313$	−6.04523e8			−1.11431			−0.557157	−	0.830407i	$-0.688108\pi$
$313$	−6.04523e8			−1.11431			−0.557157	+	0.830407i	$0.688108\pi$
$314$	2.84813e8	+	4.93311e8i	0.519166	+	0.899222i
$315$	−5.41343e7	−	9.37633e7i	−0.0975855	−	0.169023i
$316$	−7.34644e7	+	1.27244e8i	−0.130970	+	0.226847i
$317$	9.32561e8			1.64426			0.822129	−	0.569301i	$-0.192786\pi$
$317$	9.32561e8			1.64426			0.822129	+	0.569301i	$0.192786\pi$
$318$	1.06513e8	−	1.84486e8i	0.185741	−	0.321713i
$319$	−1.65405e7	+	2.86490e7i	−0.0285287	+	0.0494131i
$320$	−8.48561e7			−0.144763
$321$	−2.08416e8	+	3.60988e8i	−0.351693	+	0.609150i
$322$	−1.78002e8	−	3.08309e8i	−0.297119	−	0.514625i
$323$	9.86728e7	+	1.70906e8i	0.162925	+	0.282195i
$324$	−2.01628e8			−0.329340
$325$	−1.55034e8	+	1.43364e8i	−0.250516	+	0.231659i
$326$	−4.97649e8			−0.795539
$327$	3.10967e8	+	5.38611e8i	0.491810	+	0.851840i
$328$	4.74716e7	+	8.22232e7i	0.0742806	+	0.128658i
$329$	3.42107e8	−	5.92546e8i	0.529634	−	0.917353i
$330$	2.46667e7			0.0377844
$331$	3.41829e8	−	5.92065e8i	0.518096	−	0.897369i	−0.481683	−	0.876346i	$-0.659974\pi$
$331$	3.41829e8	−	5.92065e8i	0.518096	−	0.897369i	0.999779	−	0.0210234i	$-0.00669245\pi$
$332$	2.53934e8	−	4.39827e8i	0.380836	−	0.659627i
$333$	8.99753e7			0.133527
$334$	8.98305e7	−	1.55591e8i	0.131920	−	0.228492i
$335$	−6.27778e7	−	1.08734e8i	−0.0912324	−	0.158019i
$336$	4.65609e7	+	8.06458e7i	0.0669628	+	0.115983i
$337$	1.36368e9			1.94092			0.970459	−	0.241264i	$-0.0775621\pi$
$337$	1.36368e9			1.94092			0.970459	+	0.241264i	$0.0775621\pi$
$338$	4.53008e8	−	2.16277e8i	0.638113	−	0.304650i
$339$	3.74285e7			0.0521799
$340$	2.12002e8	+	3.67198e8i	0.292525	+	0.506668i
$341$	1.91260e7	+	3.31271e7i	0.0261206	+	0.0452422i
$342$	2.26882e7	−	3.92971e7i	0.0306697	−	0.0531214i
$343$	−7.52695e8			−1.00714
$344$	2.17623e7	−	3.76934e7i	0.0288238	−	0.0499242i
$345$	5.06488e8	−	8.77264e8i	0.664053	−	1.15017i
$346$	−6.89351e8			−0.894693
$347$	9.07095e7	−	1.57113e8i	0.116547	−	0.201865i	−0.801850	−	0.597525i	$-0.796151\pi$
$347$	9.07095e7	−	1.57113e8i	0.116547	−	0.201865i	0.918397	+	0.395660i	$0.129484\pi$
$348$	−1.77677e8	−	3.07746e8i	−0.225998	−	0.391440i
$349$	2.23486e8	+	3.87090e8i	0.281425	+	0.487442i	0.971736	−	0.236071i	$-0.0758598\pi$
$349$	2.23486e8	+	3.87090e8i	0.281425	+	0.487442i	−0.690311	+	0.723512i	$0.742526\pi$
$350$	−1.21255e8			−0.151169
$351$	−6.45368e8	+	5.96791e8i	−0.796586	+	0.736626i
$352$	7.80616e6			0.00953978
$353$	−6.06158e7	−	1.04990e8i	−0.0733456	−	0.127038i	0.827020	−	0.562172i	$-0.190034\pi$
$353$	−6.06158e7	−	1.04990e8i	−0.0733456	−	0.127038i	−0.900366	+	0.435134i	$0.856701\pi$
$354$	3.97635e8	+	6.88724e8i	0.476402	+	0.825152i
$355$	5.95660e8	−	1.03171e9i	0.706641	−	1.22394i
$356$	5.21653e8			0.612782
$357$	2.32652e8	−	4.02965e8i	0.270625	−	0.468737i
$358$	−2.84456e8	+	4.92692e8i	−0.327661	+	0.567525i
$359$	−1.84724e8			−0.210714			−0.105357	−	0.994434i	$-0.533599\pi$
$359$	−1.84724e8			−0.210714			−0.105357	+	0.994434i	$0.533599\pi$
$360$	4.87463e7	−	8.44312e7i	0.0550660	−	0.0953771i
$361$	4.00449e8	+	6.93597e8i	0.447993	+	0.775947i
$362$	5.57681e8	+	9.65932e8i	0.617882	+	1.07020i
$363$	7.76914e8			0.852511
$364$	2.75308e8	+	8.54304e7i	0.299202	+	0.0928448i
$365$	−5.09976e8			−0.548940
$366$	4.87170e8	+	8.43804e8i	0.519394	+	0.899617i
$367$	−4.45347e8	−	7.71364e8i	−0.470292	−	0.814569i	0.529131	−	0.848540i	$-0.322518\pi$
$367$	−4.45347e8	−	7.71364e8i	−0.470292	−	0.814569i	−0.999423	+	0.0339709i	$0.989185\pi$
$368$	1.60286e8	−	2.77623e8i	0.167659	−	0.290395i
$369$	−1.09082e8			−0.113021
$370$	1.98047e8	−	3.43027e8i	0.203265	−	0.352064i
$371$	1.89331e8	−	3.27932e8i	0.192493	−	0.333407i
$372$	−4.10901e8			−0.413844
$373$	−2.21327e8	+	3.83349e8i	−0.220828	+	0.382485i	−0.955060	−	0.296414i	$-0.904209\pi$
$373$	−2.21327e8	+	3.83349e8i	−0.220828	+	0.382485i	0.734232	+	0.678899i	$0.237542\pi$
$374$	−1.95026e7	−	3.37796e7i	−0.0192772	−	0.0333890i
$375$	3.33075e8	+	5.76902e8i	0.326161	+	0.564928i
$376$	6.16114e8			0.597728
$377$	−1.05058e9	−	3.26005e8i	−1.00980	−	0.313349i
$378$	−5.04757e8			−0.480686
$379$	−7.43553e8	−	1.28787e9i	−0.701576	−	1.21517i	−0.967913	−	0.251285i	$-0.919147\pi$
$379$	−7.43553e8	−	1.28787e9i	−0.701576	−	1.21517i	0.266337	−	0.963880i	$-0.414187\pi$
$380$	−9.98792e7	−	1.72996e8i	−0.0933754	−	0.161731i
$381$	−1.69368e8	+	2.93355e8i	−0.156890	+	0.271741i
$382$	6.86423e8			0.630042
$383$	−4.46769e8	+	7.73827e8i	−0.406338	+	0.703798i	−0.994476	−	0.104962i	$-0.966528\pi$
$383$	−4.46769e8	+	7.73827e8i	−0.406338	+	0.703798i	0.588138	+	0.808761i	$0.299861\pi$
$384$	−4.19267e7	+	7.26192e7i	−0.0377860	+	0.0654474i
$385$	4.38461e7			0.0391578
$386$	9.41787e7	−	1.63122e8i	0.0833484	−	0.144364i
$387$	2.50031e7	+	4.33066e7i	0.0219283	+	0.0379810i
$388$	4.28669e7	+	7.42476e7i	0.0372572	+	0.0645314i
$389$	−5.98070e8			−0.515143			−0.257572	−	0.966259i	$-0.582922\pi$
$389$	−5.98070e8			−0.515143			−0.257572	+	0.966259i	$0.582922\pi$
$390$	1.81164e8	+	7.99954e8i	0.154649	+	0.682871i
$391$	−1.60181e9			−1.35517
$392$	−1.28063e8	−	2.21812e8i	−0.107380	−	0.185988i
$393$	2.34170e8	+	4.05594e8i	0.194606	+	0.337068i
$394$	2.85898e8	−	4.95189e8i	0.235491	−	0.407882i
$395$	−7.43139e8			−0.606709
$396$	−4.48432e6	+	7.76707e6i	−0.00362880	+	0.00628527i
$397$	1.02106e9	−	1.76852e9i	0.818999	−	1.41855i	−0.0874217	−	0.996171i	$-0.527863\pi$
$397$	1.02106e9	−	1.76852e9i	0.818999	−	1.41855i	0.906421	−	0.422376i	$-0.138804\pi$
$398$	−1.72483e9			−1.37137
$399$	−1.09608e8	+	1.89847e8i	−0.0863848	+	0.149623i
$400$	−5.45935e7	−	9.45588e7i	−0.0426512	−	0.0738740i
$401$	8.12903e8	+	1.40799e9i	0.629555	+	1.09042i	0.987641	+	0.156732i	$0.0500960\pi$
$401$	8.12903e8	+	1.40799e9i	0.629555	+	1.09042i	−0.358086	+	0.933689i	$0.616571\pi$
$402$	−1.24072e8			−0.0952538
$403$	−9.33859e8	+	8.63566e8i	−0.710745	+	0.657246i
$404$	−1.23372e9			−0.930852
$405$	−5.09900e8	−	8.83172e8i	−0.381410	−	0.660622i
$406$	−3.15829e8	−	5.47031e8i	−0.234213	−	0.405668i
$407$	−1.82189e7	+	3.15560e7i	−0.0133950	+	0.0232008i
$408$	4.18993e8			0.305419
$409$	3.53619e7	−	6.12486e7i	0.0255567	−	0.0442655i	−0.852964	−	0.521969i	$-0.825198\pi$
$409$	3.53619e7	−	6.12486e7i	0.0255567	−	0.0442655i	0.878521	+	0.477704i	$0.158531\pi$
$410$	−2.40103e8	+	4.15870e8i	−0.172050	+	0.297999i
$411$	−1.49939e9			−1.06529
$412$	4.93744e8	−	8.55190e8i	0.347826	−	0.602452i
$413$	7.06812e8	+	1.22423e9i	0.493718	+	0.855144i
$414$	1.84155e8	+	3.18966e8i	0.127551	+	0.220924i
$415$	2.56871e9			1.76419
$416$	5.73322e7	+	2.53158e8i	0.0390456	+	0.172411i
$417$	1.12380e9			0.758947
$418$	9.18817e6	+	1.59144e7i	0.00615336	+	0.0106579i
$419$	−7.58892e8	−	1.31444e9i	−0.504000	−	0.872954i	−0.999989	−	0.00462522i	$-0.998528\pi$
$419$	−7.58892e8	−	1.31444e9i	−0.504000	−	0.872954i	0.495989	−	0.868329i	$-0.334806\pi$
$420$	−2.35496e8	+	4.07892e8i	−0.155100	+	0.268641i
$421$	−6.23005e8			−0.406916			−0.203458	−	0.979084i	$-0.565218\pi$
$421$	−6.23005e8			−0.406916			−0.203458	+	0.979084i	$0.565218\pi$
$422$	3.57582e8	−	6.19351e8i	0.231623	−	0.401183i
$423$	−3.53932e8	+	6.13028e8i	−0.227368	+	0.393812i
$424$	3.40975e8			0.217241
$425$	−2.72789e8	+	4.72485e8i	−0.172372	+	0.298556i
$426$	−5.88621e8	−	1.01952e9i	−0.368894	−	0.638944i
$427$	8.65965e8	+	1.49990e9i	0.538273	+	0.932316i
$428$	−6.67192e8			−0.411337
$429$	−1.66658e7	−	7.35901e7i	−0.0101912	−	0.0450007i
$430$	2.20140e8			0.133524
$431$	3.99315e8	+	6.91634e8i	0.240240	+	0.416108i	0.960783	−	0.277303i	$-0.0894406\pi$
$431$	3.99315e8	+	6.91634e8i	0.240240	+	0.416108i	−0.720543	+	0.693411i	$0.756107\pi$
$432$	−2.27260e8	−	3.93625e8i	−0.135622	−	0.234904i
$433$	5.32611e8	−	9.22509e8i	0.315284	−	0.546088i	−0.664214	−	0.747543i	$-0.731233\pi$
$433$	5.32611e8	−	9.22509e8i	0.315284	−	0.546088i	0.979498	+	0.201455i	$0.0645668\pi$
$434$	−7.30392e8			−0.428886
$435$	8.98660e8	−	1.55653e9i	0.523460	−	0.906659i
$436$	−4.97741e8	+	8.62114e8i	−0.287608	+	0.498152i
$437$	7.54652e8			0.432575
$438$	−2.51975e8	+	4.36433e8i	−0.143284	+	0.248175i
$439$	−1.39630e9	−	2.41846e9i	−0.787685	−	1.36431i	−0.927382	−	0.374115i	$-0.877946\pi$
$439$	−1.39630e9	−	2.41846e9i	−0.787685	−	1.36431i	0.139698	−	0.990194i	$-0.455387\pi$
$440$	1.97411e7	+	3.41926e7i	0.0110481	+	0.0191358i
$441$	2.94268e8			0.163383
$442$	9.52251e8	−	8.80573e8i	0.524534	−	0.485051i
$443$	1.37114e9			0.749323			0.374661	−	0.927162i	$-0.377759\pi$
$443$	1.37114e9			0.749323			0.374661	+	0.927162i	$0.377759\pi$
$444$	−1.95706e8	−	3.38973e8i	−0.106112	−	0.183791i
$445$	1.31921e9	+	2.28494e9i	0.709667	+	1.22918i
$446$	4.30110e8	−	7.44972e8i	0.229566	−	0.397620i
$447$	−1.83532e9			−0.971932
$448$	−7.45264e7	+	1.29084e8i	−0.0391595	+	0.0678262i
$449$	4.30186e8	−	7.45104e8i	0.224282	−	0.388467i	−0.731822	−	0.681496i	$-0.761330\pi$
$449$	4.30186e8	−	7.45104e8i	0.224282	−	0.388467i	0.956104	+	0.293028i	$0.0946631\pi$
$450$	1.25447e8			0.0648957
$451$	2.20878e7	−	3.82571e7i	0.0113379	−	0.0196379i
$452$	2.99545e7	+	5.18826e7i	0.0152573	+	0.0264264i
$453$	9.54239e8	+	1.65279e9i	0.482296	+	0.835361i
$454$	1.72063e9			0.862963
$455$	3.22027e8	+	1.42195e9i	0.160270	+	0.707692i
$456$	−1.97398e8			−0.0974912
$457$	4.03429e8	+	6.98760e8i	0.197725	+	0.342469i	0.947790	−	0.318894i	$-0.103311\pi$
$457$	4.03429e8	+	6.98760e8i	0.197725	+	0.342469i	−0.750066	+	0.661363i	$0.769978\pi$
$458$	−1.24886e9	−	2.16310e9i	−0.607416	−	1.05208i
$459$	−1.13556e9	+	1.96684e9i	−0.548105	+	0.949346i
$460$	1.62139e9			0.776670
$461$	7.54447e7	−	1.30674e8i	0.0358654	−	0.0621207i	−0.847536	−	0.530739i	$-0.821915\pi$
$461$	7.54447e7	−	1.30674e8i	0.0358654	−	0.0621207i	0.883401	+	0.468618i	$0.155248\pi$
$462$	2.16640e7	−	3.75231e7i	0.0102210	−	0.0177032i
$463$	2.52574e9			1.18265			0.591324	−	0.806434i	$-0.298605\pi$
$463$	2.52574e9			1.18265			0.591324	+	0.806434i	$0.298605\pi$
$464$	2.84395e8	−	4.92586e8i	0.132163	−	0.228912i
$465$	−1.03913e9	−	1.79983e9i	−0.479275	−	0.830129i
$466$	−1.05093e9	−	1.82027e9i	−0.481087	−	0.833268i
$467$	2.68879e9			1.22165			0.610827	−	0.791764i	$-0.290837\pi$
$467$	2.68879e9			1.22165			0.610827	+	0.791764i	$0.290837\pi$
$468$	−2.84825e8	−	8.83835e7i	−0.128445	−	0.0398576i
$469$	−2.20543e8			−0.0987161
$470$	1.55810e9	+	2.69870e9i	0.692233	+	1.19898i
$471$	1.42351e9	+	2.46559e9i	0.627751	+	1.08730i
$472$	−6.36464e8	+	1.10239e9i	−0.278597	+	0.482544i
$473$	−2.02513e7			−0.00879911
$474$	−3.67179e8	+	6.35972e8i	−0.158363	+	0.274293i
$475$	1.28518e8	−	2.22599e8i	0.0550218	−	0.0953006i
$476$	7.44777e8			0.316520
$477$	−1.95876e8	+	3.39267e8i	−0.0826356	+	0.143129i
$478$	−3.47235e8	−	6.01428e8i	−0.145420	−	0.251876i
$479$	−1.31293e8	−	2.27405e8i	−0.0545841	−	0.0945424i	0.837442	−	0.546526i	$-0.184050\pi$
$479$	−1.31293e8	−	2.27405e8i	−0.0545841	−	0.0945424i	−0.892026	+	0.451983i	$0.850717\pi$
$480$	−4.24115e8			−0.175041
$481$	−1.15719e9	−	3.59084e8i	−0.474128	−	0.147126i
$482$	−1.70061e9			−0.691734
$483$	−8.89665e8	−	1.54094e9i	−0.359262	−	0.622260i
$484$	6.21773e8	+	1.07694e9i	0.249272	+	0.431752i
$485$	−2.16813e8	+	3.75531e8i	−0.0862957	+	0.149468i
$486$	9.33723e8			0.368970
$487$	−1.13272e9	+	1.96193e9i	−0.444398	+	0.769720i	−0.998010	−	0.0630549i	$-0.979916\pi$
$487$	−1.13272e9	+	1.96193e9i	−0.444398	+	0.769720i	0.553612	+	0.832775i	$0.313249\pi$
$488$	−7.79776e8	+	1.35061e9i	−0.303739	+	0.526091i
$489$	−2.48728e9			−0.961929
$490$	6.47721e8	−	1.12189e9i	0.248715	−	0.430786i
$491$	−1.38389e9	−	2.39696e9i	−0.527613	−	0.913852i	−0.999482	−	0.0321836i	$-0.989754\pi$
$491$	−1.38389e9	−	2.39696e9i	−0.527613	−	0.913852i	0.471869	−	0.881669i	$-0.343579\pi$
$492$	2.37266e8	+	4.10956e8i	0.0898167	+	0.155567i
$493$	−2.84209e9			−1.06825
$494$	−4.48629e8	+	4.14860e8i	−0.167434	+	0.154831i
$495$	−4.53617e7			−0.0168101
$496$	−3.28848e8	−	5.69582e8i	−0.121007	−	0.209590i
$497$	−1.04630e9	−	1.81224e9i	−0.382303	−	0.662168i
$498$	1.26918e9	−	2.19828e9i	0.460489	−	0.797590i
$499$	1.33804e9			0.482078			0.241039	−	0.970515i	$-0.422512\pi$
$499$	1.33804e9			0.482078			0.241039	+	0.970515i	$0.422512\pi$
$500$	−5.33127e8	+	9.23403e8i	−0.190737	+	0.330367i
$501$	4.48978e8	−	7.77652e8i	0.159512	−	0.276283i
$502$	9.53896e8			0.336541
$503$	−2.20403e8	+	3.81749e8i	−0.0772199	+	0.133749i	−0.902049	−	0.431633i	$-0.857938\pi$
$503$	−2.20403e8	+	3.81749e8i	−0.0772199	+	0.133749i	0.824830	+	0.565381i	$0.191271\pi$
$504$	−8.56247e7	−	1.48306e8i	−0.0297915	−	0.0516004i
$505$	−3.11996e9	−	5.40393e9i	−1.07803	−	1.86719i
$506$	−1.49157e8			−0.0511819
$507$	2.26416e9	−	1.08096e9i	0.771577	−	0.368369i
$508$	−5.42190e8			−0.183497
$509$	1.62285e8	+	2.81086e8i	0.0545464	+	0.0944771i	0.892009	−	0.452017i	$-0.149295\pi$
$509$	1.62285e8	+	2.81086e8i	0.0545464	+	0.0944771i	−0.837463	+	0.546494i	$0.815962\pi$
$510$	1.05960e9	+	1.83527e9i	0.353708	+	0.612640i
$511$	−4.47895e8	+	7.75777e8i	−0.148492	+	0.257196i
$512$	−1.34218e8			−0.0441942
$513$	5.34988e8	−	9.26626e8i	0.174958	−	0.303036i
$514$	−1.37834e9	+	2.38735e9i	−0.447697	+	0.775434i
$515$	4.99454e9			1.61128
$516$	1.08769e8	−	1.88394e8i	0.0348523	−	0.0603660i
$517$	−1.43334e8	−	2.48262e8i	−0.0456175	−	0.0790119i
$518$	−3.47876e8	−	6.02539e8i	−0.109969	−	0.190472i
$519$	−3.44541e9			−1.08182
$520$	−9.63893e8	+	8.91339e8i	−0.300619	+	0.277991i
$521$	1.45685e9			0.451320			0.225660	−	0.974206i	$-0.427546\pi$
$521$	1.45685e9			0.451320			0.225660	+	0.974206i	$0.427546\pi$
$522$	3.26746e8	+	5.65941e8i	0.100546	+	0.174150i
$523$	−9.45984e8	−	1.63849e9i	−0.289153	−	0.500828i	0.684455	−	0.729055i	$-0.260040\pi$
$523$	−9.45984e8	−	1.63849e9i	−0.289153	−	0.500828i	−0.973608	+	0.228227i	$0.926707\pi$
$524$	−3.74818e8	+	6.49203e8i	−0.113805	+	0.197116i
$525$	−6.06041e8			−0.182787
$526$	1.21460e8	−	2.10375e8i	0.0363901	−	0.0630296i
$527$	−1.64317e9	+	2.84605e9i	−0.489040	+	0.847043i
$528$	3.90156e7			0.0115351
$529$	−1.36026e9	+	2.35604e9i	−0.399510	+	0.691971i
$530$	8.62295e8	+	1.49354e9i	0.251588	+	0.435764i
$531$	−7.31244e8	−	1.26655e9i	−0.211949	−	0.367107i
$532$	−3.50883e8			−0.101035
$533$	1.40292e9	+	4.35338e8i	0.401317	+	0.124532i
$534$	2.60725e9			0.740948
$535$	−1.68727e9	−	2.92243e9i	−0.476372	−	0.825100i
$536$	−9.92962e7	−	1.71986e8i	−0.0278520	−	0.0482410i
$537$	−1.42173e9	+	2.46250e9i	−0.396192	+	0.686225i
$538$	−4.04624e9			−1.12025
$539$	−5.95857e7	+	1.03205e8i	−0.0163901	+	0.0283885i
$540$	1.14944e9	−	1.99089e9i	0.314129	−	0.544087i
$541$	−1.32498e9			−0.359765			−0.179883	−	0.983688i	$-0.557572\pi$
$541$	−1.32498e9			−0.359765			−0.179883	+	0.983688i	$0.557572\pi$
$542$	−1.45688e9	+	2.52339e9i	−0.393030	+	0.680749i
$543$	2.78732e9	+	4.82778e9i	0.747115	+	1.29404i
$544$	3.35325e8	+	5.80800e8i	0.0893038	+	0.154679i
$545$	−5.03497e9			−1.33232
$546$	1.37600e9	+	4.26986e8i	0.361781	+	0.112264i
$547$	1.87811e9			0.490643			0.245321	−	0.969442i	$-0.421107\pi$
$547$	1.87811e9			0.490643			0.245321	+	0.969442i	$0.421107\pi$
$548$	−1.19998e9	−	2.07842e9i	−0.311487	−	0.539512i
$549$	−8.95899e8	−	1.55174e9i	−0.231076	−	0.400236i
$550$	−2.54015e7	+	4.39966e7i	−0.00651013	+	0.0112759i
$551$	1.33898e9			0.340991
$552$	8.01117e8	−	1.38758e9i	0.202726	−	0.351132i
$553$	−6.52675e8	+	1.13047e9i	−0.164119	+	0.284263i
$554$	9.34018e8			0.233384
$555$	9.89848e8	−	1.71447e9i	0.245778	−	0.425700i
$556$	8.99387e8	+	1.55778e9i	0.221914	+	0.384366i
$557$	7.25064e7	+	1.25585e8i	0.0177780	+	0.0307924i	0.874778	−	0.484525i	$-0.161007\pi$
$557$	7.25064e7	+	1.25585e8i	0.0177780	+	0.0307924i	−0.857000	+	0.515317i	$0.827674\pi$
$558$	7.55639e8			0.184117
$559$	−1.48735e8	−	6.56759e8i	−0.0360141	−	0.159025i
$560$	−7.53882e8			−0.181403
$561$	−9.74752e7	−	1.68832e8i	−0.0233090	−	0.0403724i
$562$	1.25023e9	+	2.16547e9i	0.297108	+	0.514606i
$563$	2.40050e9	−	4.15779e9i	0.566921	−	0.981936i	−0.429947	−	0.902854i	$-0.641468\pi$
$563$	2.40050e9	−	4.15779e9i	0.566921	−	0.981936i	0.996868	−	0.0790818i	$-0.0251988\pi$
$564$	3.07937e9			0.722745
$565$	−1.51504e8	+	2.62413e8i	−0.0353391	+	0.0612091i
$566$	8.45099e8	−	1.46375e9i	0.195907	−	0.339321i
$567$	−1.79131e9			−0.412697
$568$	9.42160e8	−	1.63187e9i	0.215728	−	0.373651i
$569$	3.18665e9	+	5.51944e9i	0.725173	+	1.25604i	0.958903	+	0.283735i	$0.0915736\pi$
$569$	3.18665e9	+	5.51944e9i	0.725173	+	1.25604i	−0.233730	+	0.972302i	$0.575093\pi$
$570$	−4.99201e8	−	8.64642e8i	−0.112905	−	0.195557i
$571$	3.01445e9			0.677613			0.338807	−	0.940856i	$-0.389977\pi$
$571$	3.01445e9			0.677613			0.338807	+	0.940856i	$0.389977\pi$
$572$	8.86713e7	−	8.19969e7i	0.0198106	−	0.0183194i
$573$	3.43078e9			0.761818
$574$	4.21749e8	+	7.30491e8i	0.0930813	+	0.161222i
$575$	1.04315e9	+	1.80679e9i	0.228828	+	0.396342i
$576$	7.71025e7	−	1.33546e8i	0.0168109	−	0.0291173i
$577$	5.46768e9			1.18492			0.592458	−	0.805601i	$-0.298158\pi$
$577$	5.46768e9			1.18492			0.592458	+	0.805601i	$0.298158\pi$
$578$	3.41738e7	−	5.91907e7i	0.00736115	−	0.0127499i
$579$	4.70710e8	−	8.15294e8i	0.100781	−	0.174558i
$580$	2.87683e9			0.612233
$581$	2.25601e9	−	3.90753e9i	0.477227	−	0.826581i
$582$	2.14251e8	+	3.71093e8i	0.0450497	+	0.0780284i
$583$	−7.93250e7	−	1.37395e8i	−0.0165794	−	0.0287164i
$584$	−8.06634e8			−0.167584
$585$	−3.33158e8	−	1.47110e9i	−0.0688027	−	0.303807i
$586$	5.59603e9			1.14878
$587$	−2.05914e9	−	3.56654e9i	−0.420197	−	0.727803i	0.575761	−	0.817618i	$-0.304706\pi$
$587$	−2.05914e9	−	3.56654e9i	−0.420197	−	0.727803i	−0.995958	+	0.0898148i	$0.971372\pi$
$588$	−6.40067e8	−	1.10863e9i	−0.129839	−	0.224887i
$589$	7.74136e8	−	1.34084e9i	0.156104	−	0.270380i
$590$	−6.43824e9			−1.29058
$591$	1.42893e9	−	2.47498e9i	0.284744	−	0.493192i
$592$	3.13252e8	−	5.42569e8i	0.0620538	−	0.107480i
$593$	6.94912e8			0.136848			0.0684240	−	0.997656i	$-0.478203\pi$
$593$	6.94912e8			0.136848			0.0684240	+	0.997656i	$0.478203\pi$
$594$	−1.05740e8	+	1.83147e8i	−0.0207008	+	0.0358549i
$595$	1.88347e9	+	3.26227e9i	0.366564	+	0.634908i
$596$	−1.46883e9	−	2.54409e9i	−0.284190	−	0.492232i
$597$	−8.62079e9			−1.65820
$598$	−1.09548e9	−	4.83722e9i	−0.209484	−	0.925001i
$599$	5.53945e9			1.05311			0.526554	−	0.850142i	$-0.323484\pi$
$599$	5.53945e9			1.05311			0.526554	+	0.850142i	$0.323484\pi$
$600$	−2.72861e8	−	4.72610e8i	−0.0515718	−	0.0893250i
$601$	−9.34647e8	−	1.61886e9i	−0.175625	−	0.304192i	0.764752	−	0.644324i	$-0.222861\pi$
$601$	−9.34647e8	−	1.61886e9i	−0.175625	−	0.304192i	−0.940377	+	0.340133i	$0.889528\pi$
$602$	1.93342e8	−	3.34878e8i	0.0361192	−	0.0625602i
$603$	2.28166e8			0.0423780
$604$	−1.52738e9	+	2.64550e9i	−0.282044	+	0.488515i
$605$	−3.14482e9	+	5.44698e9i	−0.577367	+	1.00003i
$606$	−6.16618e9			−1.12554
$607$	−3.92775e9	+	6.80306e9i	−0.712825	+	1.23465i	0.250967	+	0.967996i	$0.419251\pi$
$607$	−3.92775e9	+	6.80306e9i	−0.712825	+	1.23465i	−0.963792	+	0.266654i	$0.914082\pi$
$608$	−1.57980e8	−	2.73629e8i	−0.0285062	−	0.0493741i
$609$	−1.57853e9	−	2.73409e9i	−0.283199	−	0.490515i
$610$	−7.88794e9			−1.40705
$611$	6.99853e9	−	6.47174e9i	1.24126	−	1.14783i
$612$	−7.70521e8			−0.135880
$613$	5.55641e9	+	9.62398e9i	0.974277	+	1.68750i	0.682302	+	0.731070i	$0.260979\pi$
$613$	5.55641e9	+	9.62398e9i	0.974277	+	1.68750i	0.291974	+	0.956426i	$0.405688\pi$
$614$	1.93664e9	+	3.35435e9i	0.337644	+	0.584816i
$615$	−1.20005e9	+	2.07854e9i	−0.208034	+	0.360326i
$616$	6.93518e7			0.0119543
$617$	−1.49482e9	+	2.58911e9i	−0.256207	+	0.443764i	−0.965223	−	0.261429i	$-0.915806\pi$
$617$	−1.49482e9	+	2.58911e9i	−0.256207	+	0.443764i	0.709016	+	0.705193i	$0.249140\pi$
$618$	2.46776e9	−	4.27429e9i	0.420575	−	0.728457i
$619$	−4.26716e9			−0.723138			−0.361569	−	0.932345i	$-0.617759\pi$
$619$	−4.26716e9			−0.723138			−0.361569	+	0.932345i	$0.617759\pi$
$620$	1.66326e9	−	2.88084e9i	0.280278	−	0.485455i
$621$	4.34238e9	+	7.52122e9i	0.727624	+	1.26028i
$622$	−2.32985e9	−	4.03541e9i	−0.388205	−	0.672391i
$623$	4.63449e9			0.767880
$624$	2.86549e8	+	1.26529e9i	0.0472121	+	0.208471i
$625$	−7.47550e9			−1.22479
$626$	−2.41809e9	−	4.18826e9i	−0.393970	−	0.682375i
$627$	4.59230e7	+	7.95409e7i	0.00744035	+	0.0128871i
$628$	−2.27850e9	+	3.94649e9i	−0.367106	+	0.635846i
$629$	−3.13047e9			−0.501572
$630$	4.33074e8	−	7.50107e8i	0.0690034	−	0.119517i
$631$	−3.57540e9	+	6.19277e9i	−0.566528	+	0.981256i	0.430377	+	0.902649i	$0.358380\pi$
$631$	−3.57540e9	+	6.19277e9i	−0.566528	+	0.981256i	−0.996906	+	0.0786066i	$0.974953\pi$
$632$	−1.17543e9			−0.185220
$633$	1.78721e9	−	3.09555e9i	0.280068	−	0.485092i
$634$	3.73024e9	+	6.46097e9i	0.581333	+	1.00690i
$635$	−1.37115e9	−	2.37490e9i	−0.212509	−	0.368076i
$636$	1.70421e9			0.262678
$637$	−3.78463e9	−	1.17440e9i	−0.580143	−	0.180023i
$638$	−2.64648e8			−0.0403456
$639$	1.08246e9	+	1.87488e9i	0.164120	+	0.284264i
$640$	−3.39425e8	−	5.87901e8i	−0.0511815	−	0.0886490i
$641$	−1.54411e9	+	2.67448e9i	−0.231566	+	0.401085i	−0.958269	−	0.285867i	$-0.907718\pi$
$641$	−1.54411e9	+	2.67448e9i	−0.231566	+	0.401085i	0.726703	+	0.686952i	$0.241052\pi$
$642$	−3.33466e9			−0.497369
$643$	−3.08662e9	+	5.34619e9i	−0.457873	+	0.793060i	−0.998848	−	0.0479788i	$-0.984722\pi$
$643$	−3.08662e9	+	5.34619e9i	−0.457873	+	0.793060i	0.540975	+	0.841039i	$0.318055\pi$
$644$	1.42402e9	−	2.46647e9i	0.210095	−	0.363895i
$645$	1.10027e9			0.161451
$646$	−7.89382e8	+	1.36725e9i	−0.115206	+	0.199542i
$647$	−1.89760e9	−	3.28675e9i	−0.275449	−	0.477091i	0.694800	−	0.719203i	$-0.255493\pi$
$647$	−1.89760e9	−	3.28675e9i	−0.275449	−	0.477091i	−0.970248	+	0.242112i	$0.922160\pi$
$648$	−8.06513e8	−	1.39692e9i	−0.116439	−	0.201679i
$649$	5.92272e8			0.0850481
$650$	−1.61339e9	−	5.00649e8i	−0.230432	−	0.0715051i
$651$	−3.65054e9			−0.518589
$652$	−1.99060e9	−	3.44781e9i	−0.281266	−	0.487166i
$653$	−5.33607e9	−	9.24234e9i	−0.749938	−	1.29893i	−0.947852	−	0.318711i	$-0.896750\pi$
$653$	−5.33607e9	−	9.24234e9i	−0.749938	−	1.29893i	0.197914	−	0.980219i	$-0.436583\pi$
$654$	−2.48774e9	+	4.30889e9i	−0.347762	+	0.602342i
$655$	−3.79152e9			−0.527192
$656$	−3.79773e8	+	6.57786e8i	−0.0525243	+	0.0909748i
$657$	4.63378e8	−	8.02594e8i	0.0637465	−	0.110412i
$658$	5.47371e9			0.749015
$659$	6.14106e9	−	1.06366e10i	0.835880	−	1.44779i	−0.0574313	−	0.998349i	$-0.518291\pi$
$659$	6.14106e9	−	1.06366e10i	0.835880	−	1.44779i	0.893312	−	0.449438i	$-0.148376\pi$
$660$	9.86670e7	+	1.70896e8i	0.0133588	+	0.0231381i
$661$	−3.63672e9	−	6.29899e9i	−0.489785	−	0.848332i	0.510146	−	0.860088i	$-0.329591\pi$
$661$	−3.63672e9	−	6.29899e9i	−0.489785	−	0.848332i	−0.999931	+	0.0117556i	$0.996258\pi$
$662$	5.46926e9			0.732699
$663$	4.75940e9	−	4.40115e9i	0.634242	−	0.586501i
$664$	4.06295e9			0.538583
$665$	−8.87350e8	−	1.53694e9i	−0.117009	−	0.202666i
$666$	3.59901e8	+	6.23367e8i	0.0472088	+	0.0817681i
$667$	−5.43409e9	+	9.41212e9i	−0.709065	+	1.22814i
$668$	1.43729e9			0.186563
$669$	2.14971e9	−	3.72341e9i	0.277580	−	0.480783i
$670$	5.02222e8	−	8.69874e8i	0.0645110	−	0.111736i
$671$	7.25634e8			0.0927233
$672$	−3.72487e8	+	6.45166e8i	−0.0473498	+	0.0820123i
$673$	2.43285e8	+	4.21381e8i	0.0307654	+	0.0532872i	0.880998	−	0.473120i	$-0.156872\pi$
$673$	2.43285e8	+	4.21381e8i	0.0307654	+	0.0532872i	−0.850233	+	0.526407i	$0.823539\pi$
$674$	5.45471e9	+	9.44784e9i	0.686218	+	1.18857i
$675$	2.95804e9			0.370203
$676$	3.31044e9	+	2.27343e9i	0.412166	+	0.283053i
$677$	4.31885e9			0.534944			0.267472	−	0.963566i	$-0.413812\pi$
$677$	4.31885e9			0.534944			0.267472	+	0.963566i	$0.413812\pi$
$678$	1.49714e8	+	2.59312e8i	0.0184484	+	0.0319535i
$679$	3.80839e8	+	6.59633e8i	0.0466872	+	0.0808646i
$680$	−1.69601e9	+	2.93758e9i	−0.206846	+	0.358269i
$681$	8.59980e9			1.04345
$682$	−1.53008e8	+	2.65017e8i	−0.0184701	+	0.0319911i
$683$	−3.89016e9	+	6.73796e9i	−0.467192	+	0.809201i	−0.999297	−	0.0374776i	$-0.988068\pi$
$683$	−3.89016e9	+	6.73796e9i	−0.467192	+	0.809201i	0.532105	+	0.846678i	$0.321401\pi$
$684$	3.63011e8			0.0433734
$685$	6.06926e9	−	1.05123e10i	0.721471	−	1.24962i
$686$	−3.01078e9	−	5.21483e9i	−0.356078	−	0.616745i
$687$	−6.24189e9	−	1.08113e10i	−0.734459	−	1.27212i
$688$	3.48197e8			0.0407629
$689$	3.87318e9	−	3.58164e9i	0.451129	−	0.417172i
$690$	8.10382e9			0.939113
$691$	7.63764e9	+	1.32288e10i	0.880614	+	1.52527i	0.850659	+	0.525718i	$0.176203\pi$
$691$	7.63764e9	+	1.32288e10i	0.880614	+	1.52527i	0.0299552	+	0.999551i	$0.490464\pi$
$692$	−2.75740e9	−	4.77596e9i	−0.316322	−	0.547885i
$693$	−3.98397e7	+	6.90045e7i	−0.00454727	+	0.00787609i
$694$	1.45135e9			0.164822
$695$	−4.54894e9	+	7.87899e9i	−0.514000	+	0.890274i
$696$	1.42142e9	−	2.46197e9i	0.159805	−	0.276790i
$697$	3.79525e9			0.424546
$698$	−1.78789e9	+	3.09672e9i	−0.198997	+	0.344673i
$699$	−5.25262e9	−	9.09780e9i	−0.581709	−	1.00755i
$700$	−4.85022e8	−	8.40083e8i	−0.0534464	−	0.0925718i
$701$	−1.39687e9			−0.153159			−0.0765794	−	0.997063i	$-0.524400\pi$
$701$	−1.39687e9			−0.153159			−0.0765794	+	0.997063i	$0.524400\pi$
$702$	−6.71616e9	−	2.08408e9i	−0.732725	−	0.227371i
$703$	1.47484e9			0.160104
$704$	3.12246e7	+	5.40827e7i	0.00337282	+	0.00584190i
$705$	7.78745e9	+	1.34883e10i	0.837015	+	1.44975i
$706$	4.84926e8	−	8.39917e8i	0.0518632	−	0.0898297i
$707$	−1.09606e10			−1.16645
$708$	−3.18108e9	+	5.50979e9i	−0.336867	+	0.583470i
$709$	6.96858e8	−	1.20699e9i	0.0734315	−	0.127187i	−0.826972	−	0.562244i	$-0.809938\pi$
$709$	6.96858e8	−	1.20699e9i	0.0734315	−	0.127187i	0.900403	+	0.435057i	$0.143272\pi$
$710$	9.53055e9			0.999341
$711$	6.75236e8	−	1.16954e9i	0.0704550	−	0.122032i
$712$	2.08661e9	+	3.61411e9i	0.216651	+	0.375251i
$713$	6.28349e9	+	1.08833e10i	0.649214	+	1.12447i
$714$	3.72243e9			0.382722
$715$	5.83404e8	+	1.81035e8i	0.0596896	+	0.0185222i
$716$	−4.55129e9			−0.463382
$717$	−1.73550e9	−	3.00597e9i	−0.175836	−	0.304556i
$718$	−7.38898e8	−	1.27981e9i	−0.0744987	−	0.129036i
$719$	4.06923e9	−	7.04812e9i	0.408283	−	0.707167i	−0.586414	−	0.810011i	$-0.699461\pi$
$719$	4.06923e9	−	7.04812e9i	0.408283	−	0.707167i	0.994697	+	0.102844i	$0.0327943\pi$
$720$	7.79942e8			0.0778750
$721$	4.38654e9	−	7.59771e9i	0.435862	−	0.754935i
$722$	−3.20359e9	+	5.54878e9i	−0.316779	+	0.548678i
$723$	−8.49972e9			−0.836413
$724$	−4.46145e9	+	7.72745e9i	−0.436909	+	0.756748i
$725$	1.85086e9	+	3.20578e9i	0.180380	+	0.312428i
$726$	3.10766e9	+	5.38262e9i	0.301408	+	0.522054i
$727$	−9.98246e9			−0.963534			−0.481767	−	0.876299i	$-0.660005\pi$
$727$	−9.98246e9			−0.963534			−0.481767	+	0.876299i	$0.660005\pi$
$728$	5.09353e8	+	2.24911e9i	0.0489282	+	0.216048i
$729$	1.15568e10			1.10482
$730$	−2.03990e9	−	3.53322e9i	−0.194079	−	0.336156i
$731$	−8.69923e8	−	1.50675e9i	−0.0823702	−	0.142669i
$732$	−3.89736e9	+	6.75043e9i	−0.367267	+	0.636125i
$733$	6.61890e9			0.620758			0.310379	−	0.950613i	$-0.399544\pi$
$733$	6.61890e9			0.620758			0.310379	+	0.950613i	$0.399544\pi$
$734$	3.56278e9	−	6.17091e9i	0.332546	−	0.575987i
$735$	3.23734e9	−	5.60724e9i	0.300734	−	0.520887i
$736$	2.56457e9			0.237106
$737$	−4.62009e7	+	8.00222e7i	−0.00425122	+	0.00736333i
$738$	−4.36328e8	−	7.55742e8i	−0.0399591	−	0.0692112i
$739$	2.02110e9	+	3.50065e9i	0.184218	+	0.319075i	0.943313	−	0.331905i	$-0.107691\pi$
$739$	2.02110e9	+	3.50065e9i	0.184218	+	0.319075i	−0.759095	+	0.650980i	$0.774358\pi$
$740$	3.16875e9			0.287459
$741$	−2.24227e9	+	2.07349e9i	−0.202453	+	0.187214i
$742$	3.02930e9			0.272226
$743$	−5.12883e9	−	8.88339e9i	−0.458730	−	0.794544i	0.540164	−	0.841560i	$-0.318362\pi$
$743$	−5.12883e9	−	8.88339e9i	−0.458730	−	0.794544i	−0.998894	+	0.0470156i	$0.985029\pi$
$744$	−1.64360e9	−	2.84680e9i	−0.146316	−	0.253426i
$745$	7.42908e9	−	1.28675e10i	0.658245	−	1.14011i
$746$	−3.54123e9			−0.312297
$747$	−2.33400e9	+	4.04260e9i	−0.204870	+	0.354845i
$748$	1.56021e8	−	2.70237e8i	0.0136310	−	0.0236096i
$749$	−5.92749e9			−0.515448
$750$	−2.66460e9	+	4.61522e9i	−0.230631	+	0.399464i
$751$	−8.25795e9	−	1.43032e10i	−0.711431	−	1.23223i	−0.964320	−	0.264739i	$-0.914714\pi$
$751$	−8.25795e9	−	1.43032e10i	−0.711431	−	1.23223i	0.252890	−	0.967495i	$-0.418619\pi$
$752$	2.46446e9	+	4.26856e9i	0.211329	+	0.366032i
$753$	4.76762e9			0.406930
$754$	−1.94370e9	−	8.58267e9i	−0.165132	−	0.729160i
$755$	−1.54504e10			−1.30655
$756$	−2.01903e9	−	3.49706e9i	−0.169948	−	0.294359i
$757$	−1.73903e9	−	3.01209e9i	−0.145704	−	0.252367i	0.783931	−	0.620848i	$-0.213211\pi$
$757$	−1.73903e9	−	3.01209e9i	−0.145704	−	0.252367i	−0.929635	+	0.368481i	$0.879878\pi$
$758$	5.94842e9	−	1.03030e10i	0.496089	−	0.859251i
$759$	−7.45493e8

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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	26.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 + 6.92820i) q^{2} +(19.9922 + 34.6275i) q^{3} +(-32.0000 + 55.4256i) q^{4} -323.700 q^{5} +(-159.938 + 277.020i) q^{6} +(-284.296 + 492.415i) q^{7} -512.000 q^{8} +(294.123 - 509.436i) q^{9} +O(q^{10})\)	\(q+(4.00000 + 6.92820i) q^{2} +(19.9922 + 34.6275i) q^{3} +(-32.0000 + 55.4256i) q^{4} -323.700 q^{5} +(-159.938 + 277.020i) q^{6} +(-284.296 + 492.415i) q^{7} -512.000 q^{8} +(294.123 - 509.436i) q^{9} +(-1294.80 - 2242.66i) q^{10} +(119.113 + 206.309i) q^{11} -2559.00 q^{12} +(-5815.88 + 5378.11i) q^{13} -4548.73 q^{14} +(-6471.49 - 11208.9i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(-10233.3 + 17724.6i) q^{17} +4705.97 q^{18} +(4821.16 - 8350.49i) q^{19} +(10358.4 - 17941.3i) q^{20} -22734.8 q^{21} +(-952.901 + 1650.47i) q^{22} +(39132.3 + 67779.1i) q^{23} +(-10236.0 - 17729.3i) q^{24} +26657.0 q^{25} +(-60524.2 - 18781.2i) q^{26} +110967. q^{27} +(-18194.9 - 31514.5i) q^{28} +(69432.3 + 120260. i) q^{29} +(51771.9 - 89671.6i) q^{30} +160571. q^{31} +(16384.0 - 28377.9i) q^{32} +(-4762.65 + 8249.15i) q^{33} -163733. q^{34} +(92026.6 - 159395. i) q^{35} +(18823.9 + 32603.9i) q^{36} +(76477.6 + 132463. i) q^{37} +77138.6 q^{38} +(-302503. - 93869.2i) q^{39} +165735. q^{40} +(-92718.0 - 160592. i) q^{41} +(-90939.2 - 157511. i) q^{42} +(-42504.5 + 73620.0i) q^{43} -15246.4 q^{44} +(-95207.7 + 164905. i) q^{45} +(-313058. + 542233. i) q^{46} -1.20335e6 q^{47} +(81888.1 - 141834. i) q^{48} +(250123. + 433227. i) q^{49} +(106628. + 184685. i) q^{50} -818346. q^{51} +(-111977. - 494448. i) q^{52} -665967. q^{53} +(443866. + 768799. i) q^{54} +(-38556.8 - 66782.3i) q^{55} +(145559. - 252116. i) q^{56} +385543. q^{57} +(-555458. + 962082. i) q^{58} +(1.24309e6 - 2.15310e6i) q^{59} +828351. q^{60} +(1.52300e6 - 2.63791e6i) q^{61} +(642282. + 1.11247e6i) q^{62} +(167236. + 289661. i) q^{63} +262144. q^{64} +(1.88260e6 - 1.74090e6i) q^{65} -76202.4 q^{66} +(193938. + 335910. i) q^{67} +(-654932. - 1.13437e6i) q^{68} +(-1.56468e6 + 2.71011e6i) q^{69} +1.47243e6 q^{70} +(-1.84016e6 + 3.18724e6i) q^{71} +(-150591. + 260831. i) q^{72} +1.57546e6 q^{73} +(-611821. + 1.05970e6i) q^{74} +(532932. + 923066. i) q^{75} +(308554. + 534432. i) q^{76} -135453. q^{77} +(-559667. - 2.47128e6i) q^{78} +2.29576e6 q^{79} +(662939. + 1.14824e6i) q^{80} +(1.57522e6 + 2.72836e6i) q^{81} +(741744. - 1.28474e6i) q^{82} -7.93544e6 q^{83} +(727514. - 1.26009e6i) q^{84} +(3.31253e6 - 5.73746e6i) q^{85} -680072. q^{86} +(-2.77621e6 + 4.80854e6i) q^{87} +(-60985.6 - 105630. i) q^{88} +(-4.07541e6 - 7.05882e6i) q^{89} -1.52332e6 q^{90} +(-994830. - 4.39280e6i) q^{91} -5.00893e6 q^{92} +(3.21016e6 + 5.56016e6i) q^{93} +(-4.81339e6 - 8.33704e6i) q^{94} +(-1.56061e6 + 2.70306e6i) q^{95} +1.31021e6 q^{96} +(669795. - 1.16012e6i) q^{97} +(-2.00099e6 + 3.46581e6i) q^{98} +140135. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 32 q^{2} - 256 q^{4} + 556 q^{5} - 548 q^{7} - 4096 q^{8} - 5214 q^{9}+O(q^{10}) \) 8 * q + 32 * q^2 - 256 * q^4 + 556 * q^5 - 548 * q^7 - 4096 * q^8 - 5214 * q^9	\( 8 q + 32 q^{2} - 256 q^{4} + 556 q^{5} - 548 q^{7} - 4096 q^{8} - 5214 q^{9} + 2224 q^{10} - 7392 q^{11} - 25818 q^{13} - 8768 q^{14} + 15528 q^{15} - 16384 q^{16} + 28316 q^{17} - 83424 q^{18} - 99888 q^{19} - 17792 q^{20} + 182148 q^{21} + 59136 q^{22} - 33388 q^{23} + 173756 q^{25} - 156000 q^{26} + 212544 q^{27} - 35072 q^{28} + 93140 q^{29} - 124224 q^{30} + 622320 q^{31} + 131072 q^{32} + 238638 q^{33} + 453056 q^{34} + 141544 q^{35} - 333696 q^{36} - 9636 q^{37} - 1598208 q^{38} - 22932 q^{39} - 284672 q^{40} + 82892 q^{41} + 728592 q^{42} - 569264 q^{43} + 946176 q^{44} - 2303394 q^{45} + 267104 q^{46} - 1148400 q^{47} - 717798 q^{49} + 695024 q^{50} - 5459856 q^{51} + 404352 q^{52} + 2470700 q^{53} + 850176 q^{54} - 1092512 q^{55} + 280576 q^{56} + 7056924 q^{57} - 745120 q^{58} + 231504 q^{59} - 1987584 q^{60} + 685684 q^{61} + 2489280 q^{62} - 5951712 q^{63} + 2097152 q^{64} - 6216678 q^{65} + 3818208 q^{66} + 3271056 q^{67} + 1812224 q^{68} + 5600034 q^{69} + 2264704 q^{70} - 175012 q^{71} + 2669568 q^{72} + 14275780 q^{73} + 77088 q^{74} + 22200960 q^{75} - 6392832 q^{76} - 27830412 q^{77} + 5028192 q^{78} - 14107904 q^{79} - 1138688 q^{80} + 3758004 q^{81} - 663136 q^{82} + 1314576 q^{83} - 5828736 q^{84} + 11814998 q^{85} - 9108224 q^{86} - 7182900 q^{87} + 3784704 q^{88} - 11452234 q^{89} - 36854304 q^{90} + 16457168 q^{91} + 4273664 q^{92} + 2984688 q^{93} - 4593600 q^{94} - 23334088 q^{95} - 428002 q^{97} + 5742384 q^{98} - 20715312 q^{99}+O(q^{100}) \) 8 * q + 32 * q^2 - 256 * q^4 + 556 * q^5 - 548 * q^7 - 4096 * q^8 - 5214 * q^9 + 2224 * q^10 - 7392 * q^11 - 25818 * q^13 - 8768 * q^14 + 15528 * q^15 - 16384 * q^16 + 28316 * q^17 - 83424 * q^18 - 99888 * q^19 - 17792 * q^20 + 182148 * q^21 + 59136 * q^22 - 33388 * q^23 + 173756 * q^25 - 156000 * q^26 + 212544 * q^27 - 35072 * q^28 + 93140 * q^29 - 124224 * q^30 + 622320 * q^31 + 131072 * q^32 + 238638 * q^33 + 453056 * q^34 + 141544 * q^35 - 333696 * q^36 - 9636 * q^37 - 1598208 * q^38 - 22932 * q^39 - 284672 * q^40 + 82892 * q^41 + 728592 * q^42 - 569264 * q^43 + 946176 * q^44 - 2303394 * q^45 + 267104 * q^46 - 1148400 * q^47 - 717798 * q^49 + 695024 * q^50 - 5459856 * q^51 + 404352 * q^52 + 2470700 * q^53 + 850176 * q^54 - 1092512 * q^55 + 280576 * q^56 + 7056924 * q^57 - 745120 * q^58 + 231504 * q^59 - 1987584 * q^60 + 685684 * q^61 + 2489280 * q^62 - 5951712 * q^63 + 2097152 * q^64 - 6216678 * q^65 + 3818208 * q^66 + 3271056 * q^67 + 1812224 * q^68 + 5600034 * q^69 + 2264704 * q^70 - 175012 * q^71 + 2669568 * q^72 + 14275780 * q^73 + 77088 * q^74 + 22200960 * q^75 - 6392832 * q^76 - 27830412 * q^77 + 5028192 * q^78 - 14107904 * q^79 - 1138688 * q^80 + 3758004 * q^81 - 663136 * q^82 + 1314576 * q^83 - 5828736 * q^84 + 11814998 * q^85 - 9108224 * q^86 - 7182900 * q^87 + 3784704 * q^88 - 11452234 * q^89 - 36854304 * q^90 + 16457168 * q^91 + 4273664 * q^92 + 2984688 * q^93 - 4593600 * q^94 - 23334088 * q^95 - 428002 * q^97 + 5742384 * q^98 - 20715312 * q^99

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