LMFDB - Embedded newform 26.8.c.b.9.2

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			9.2
Root			$18.4011i$ of defining polynomial
Character	$\chi$	$=$	26.9
Dual form			26.8.c.b.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 - 6.92820i) q^{2} +(-15.9358 + 27.6017i) q^{3} +(-32.0000 - 55.4256i) q^{4} -54.4265 q^{5} +(127.487 + 220.813i) q^{6} +(556.354 + 963.633i) q^{7} -512.000 q^{8} +(585.599 + 1014.29i) q^{9} +O(q^{10})$	\(q+(4.00000 - 6.92820i) q^{2} +(-15.9358 + 27.6017i) q^{3} +(-32.0000 - 55.4256i) q^{4} -54.4265 q^{5} +(127.487 + 220.813i) q^{6} +(556.354 + 963.633i) q^{7} -512.000 q^{8} +(585.599 + 1014.29i) q^{9} +(-217.706 + 377.078i) q^{10} +(-3566.84 + 6177.94i) q^{11} +2039.79 q^{12} +(7565.86 - 2346.53i) q^{13} +8901.66 q^{14} +(867.331 - 1502.26i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(10252.8 + 17758.4i) q^{17} +9369.59 q^{18} +(-14035.8 - 24310.8i) q^{19} +(1741.65 + 3016.62i) q^{20} -35463.8 q^{21} +(28534.7 + 49423.6i) q^{22} +(-16961.2 + 29377.7i) q^{23} +(8159.14 - 14132.0i) q^{24} -75162.8 q^{25} +(14006.2 - 61804.0i) q^{26} -107031. q^{27} +(35606.6 - 61672.5i) q^{28} +(87734.9 - 151961. i) q^{29} +(-6938.65 - 12018.1i) q^{30} +15690.1 q^{31} +(16384.0 + 28377.9i) q^{32} +(-113681. - 196901. i) q^{33} +164045. q^{34} +(-30280.4 - 52447.2i) q^{35} +(37478.3 - 64914.4i) q^{36} +(-998.478 + 1729.41i) q^{37} -224573. q^{38} +(-55800.0 + 246224. i) q^{39} +27866.4 q^{40} +(-111820. + 193678. i) q^{41} +(-141855. + 245701. i) q^{42} +(268966. + 465862. i) q^{43} +456555. q^{44} +(-31872.1 - 55204.1i) q^{45} +(135690. + 235022. i) q^{46} +542249. q^{47} +(-65273.1 - 113056. i) q^{48} +(-207288. + 359033. i) q^{49} +(-300651. + 520743. i) q^{50} -653549. q^{51} +(-372166. - 344254. i) q^{52} +1.85685e6 q^{53} +(-428125. + 741535. i) q^{54} +(194131. - 336244. i) q^{55} +(-284853. - 493380. i) q^{56} +894691. q^{57} +(-701879. - 1.21569e6i) q^{58} +(665225. + 1.15220e6i) q^{59} -111018. q^{60} +(-1.43331e6 - 2.48257e6i) q^{61} +(62760.3 - 108704. i) q^{62} +(-651601. + 1.12861e6i) q^{63} +262144. q^{64} +(-411784. + 127714. i) q^{65} -1.81890e6 q^{66} +(1.41579e6 - 2.45222e6i) q^{67} +(656181. - 1.13654e6i) q^{68} +(-540583. - 936317. i) q^{69} -484486. q^{70} +(800929. + 1.38725e6i) q^{71} +(-299827. - 519315. i) q^{72} +1.39213e6 q^{73} +(7987.82 + 13835.3i) q^{74} +(1.19778e6 - 2.07462e6i) q^{75} +(-898294. + 1.55589e6i) q^{76} -7.93770e6 q^{77} +(1.48269e6 + 1.37149e6i) q^{78} -2.33505e6 q^{79} +(111466. - 193064. i) q^{80} +(424927. - 735994. i) q^{81} +(894559. + 1.54942e6i) q^{82} +2.37338e6 q^{83} +(1.13484e6 + 1.96560e6i) q^{84} +(-558025. - 966528. i) q^{85} +4.30345e6 q^{86} +(2.79625e6 + 4.84325e6i) q^{87} +(1.82622e6 - 3.16311e6i) q^{88} +(-3.52575e6 + 6.10678e6i) q^{89} -509954. q^{90} +(6.47050e6 + 5.98521e6i) q^{91} +2.17104e6 q^{92} +(-250034. + 433072. i) q^{93} +(2.16899e6 - 3.75681e6i) q^{94} +(763922. + 1.32315e6i) q^{95} -1.04437e6 q^{96} +(-4.25685e6 - 7.37308e6i) q^{97} +(1.65830e6 + 2.87226e6i) q^{98} -8.35495e6 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 $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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
$3$	−15.9358	+	27.6017i	−0.340761	+	0.590216i	−0.984574	−	0.174967i	$-0.944018\pi$
$3$	−15.9358	+	27.6017i	−0.340761	+	0.590216i	0.643813	+	0.765183i	$0.277351\pi$
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	−54.4265			−0.194722			−0.0973611	−	0.995249i	$-0.531040\pi$
$5$	−54.4265			−0.194722			−0.0973611	+	0.995249i	$0.531040\pi$
$6$	127.487	+	220.813i	0.240955	+	0.417345i
$7$	556.354	+	963.633i	0.613067	+	1.06186i	0.990720	+	0.135916i	$0.0433978\pi$
$7$	556.354	+	963.633i	0.613067	+	1.06186i	−0.377653	+	0.925947i	$0.623269\pi$
$8$	−512.000			−0.353553
$9$	585.599	+	1014.29i	0.267764	+	0.463780i
$10$	−217.706	+	377.078i	−0.0688447	+	0.119243i
$11$	−3566.84	+	6177.94i	−0.807996	+	1.39949i	0.106255	+	0.994339i	$0.466114\pi$
$11$	−3566.84	+	6177.94i	−0.807996	+	1.39949i	−0.914250	+	0.405150i	$0.867219\pi$
$12$	2039.79			0.340761
$13$	7565.86	−	2346.53i	0.955117	−	0.296227i
$13$	7565.86	−	2346.53i	0.955117	−	0.296227i
$14$	8901.66			0.867008
$15$	867.331	−	1502.26i	0.0663538	−	0.114928i
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	10252.8	+	17758.4i	0.506142	+	0.876663i	0.999975	+	0.00710642i	$0.00226206\pi$
$17$	10252.8	+	17758.4i	0.506142	+	0.876663i	−0.493833	+	0.869557i	$0.664405\pi$
$18$	9369.59			0.378675
$19$	−14035.8	−	24310.8i	−0.469462	−	0.813133i	0.529928	−	0.848043i	$-0.322219\pi$
$19$	−14035.8	−	24310.8i	−0.469462	−	0.813133i	−0.999390	+	0.0349098i	$0.988886\pi$
$20$	1741.65	+	3016.62i	0.0486806	+	0.0843172i
$21$	−35463.8			−0.835638
$22$	28534.7	+	49423.6i	0.571339	+	0.989588i
$23$	−16961.2	+	29377.7i	−0.290677	+	0.503467i	−0.973970	−	0.226677i	$-0.927214\pi$
$23$	−16961.2	+	29377.7i	−0.290677	+	0.503467i	0.683293	+	0.730144i	$0.260547\pi$
$24$	8159.14	−	14132.0i	0.120477	−	0.208673i
$25$	−75162.8			−0.962083
$26$	14006.2	−	61804.0i	0.156284	−	0.689620i
$27$	−107031.			−1.04650
$28$	35606.6	−	61672.5i	0.306534	−	0.530932i
$29$	87734.9	−	151961.i	0.668004	−	1.15702i	−0.310457	−	0.950587i	$-0.600482\pi$
$29$	87734.9	−	151961.i	0.668004	−	1.15702i	0.978461	−	0.206430i	$-0.0661845\pi$
$30$	−6938.65	−	12018.1i	−0.0469192	−	0.0812664i
$31$	15690.1			0.0945930			0.0472965	−	0.998881i	$-0.484939\pi$
$31$	15690.1			0.0945930			0.0472965	+	0.998881i	$0.484939\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$	−113681.	−	196901.i	−0.550667	−	0.953783i
$34$	164045.			0.715792
$35$	−30280.4	−	52447.2i	−0.119378	−	0.206768i
$36$	37478.3	−	64914.4i	0.133882	−	0.231890i
$37$	−998.478	+	1729.41i	−0.00324065	+	0.00561297i	−0.867641	−	0.497191i	$-0.834365\pi$
$37$	−998.478	+	1729.41i	−0.00324065	+	0.00561297i	0.864401	+	0.502804i	$0.167698\pi$
$38$	−224573.			−0.663920
$39$	−55800.0	+	246224.i	−0.150629	+	0.664668i
$40$	27866.4			0.0688447
$41$	−111820.	+	193678.i	−0.253382	+	0.438870i	−0.964455	−	0.264248i	$-0.914876\pi$
$41$	−111820.	+	193678.i	−0.253382	+	0.438870i	0.711073	+	0.703118i	$0.248210\pi$
$42$	−141855.	+	245701.i	−0.295443	+	0.511722i
$43$	268966.	+	465862.i	0.515890	+	0.893548i	0.999830	+	0.0184468i	$0.00587213\pi$
$43$	268966.	+	465862.i	0.515890	+	0.893548i	−0.483940	+	0.875101i	$0.660795\pi$
$44$	456555.			0.807996
$45$	−31872.1	−	55204.1i	−0.0521395	−	0.0903083i
$46$	135690.	+	235022.i	0.205540	+	0.356005i
$47$	542249.			0.761826			0.380913	−	0.924611i	$-0.375610\pi$
$47$	542249.			0.761826			0.380913	+	0.924611i	$0.375610\pi$
$48$	−65273.1	−	113056.i	−0.0851903	−	0.147554i
$49$	−207288.	+	359033.i	−0.251702	+	0.435961i
$50$	−300651.	+	520743.i	−0.340148	+	0.589153i
$51$	−653549.			−0.689894
$52$	−372166.	−	344254.i	−0.367050	−	0.339521i
$53$	1.85685e6			1.71322			0.856609	−	0.515967i	$-0.172567\pi$
$53$	1.85685e6			1.71322			0.856609	+	0.515967i	$0.172567\pi$
$54$	−428125.	+	741535.i	−0.369992	+	0.640845i
$55$	194131.	−	336244.i	0.157335	−	0.272512i
$56$	−284853.	−	493380.i	−0.216752	−	0.375425i
$57$	894691.			0.639898
$58$	−701879.	−	1.21569e6i	−0.472350	−	0.818135i
$59$	665225.	+	1.15220e6i	0.421684	+	0.730377i	0.996104	−	0.0881828i	$-0.0281060\pi$
$59$	665225.	+	1.15220e6i	0.421684	+	0.730377i	−0.574421	+	0.818560i	$0.694773\pi$
$60$	−111018.			−0.0663538
$61$	−1.43331e6	−	2.48257e6i	−0.808512	−	1.40038i	−0.913895	−	0.405952i	$-0.866940\pi$
$61$	−1.43331e6	−	2.48257e6i	−0.808512	−	1.40038i	0.105383	−	0.994432i	$-0.466393\pi$
$62$	62760.3	−	108704.i	0.0334437	−	0.0579261i
$63$	−651601.	+	1.12861e6i	−0.328314	+	0.568657i
$64$	262144.			0.125000
$65$	−411784.	+	127714.i	−0.185983	+	0.0576821i
$66$	−1.81890e6			−0.778761
$67$	1.41579e6	−	2.45222e6i	0.575091	−	0.996086i	−0.420941	−	0.907088i	$-0.638300\pi$
$67$	1.41579e6	−	2.45222e6i	0.575091	−	0.996086i	0.996032	−	0.0889982i	$-0.0283665\pi$
$68$	656181.	−	1.13654e6i	0.253071	−	0.438332i
$69$	−540583.	−	936317.i	−0.198103	−	0.343124i
$70$	−484486.			−0.168826
$71$	800929.	+	1.38725e6i	0.265576	+	0.459992i	0.967714	−	0.252049i	$-0.0811044\pi$
$71$	800929.	+	1.38725e6i	0.265576	+	0.459992i	−0.702138	+	0.712041i	$0.747771\pi$
$72$	−299827.	−	519315.i	−0.0946687	−	0.163971i
$73$	1.39213e6			0.418841			0.209420	−	0.977826i	$-0.432842\pi$
$73$	1.39213e6			0.418841			0.209420	+	0.977826i	$0.432842\pi$
$74$	7987.82	+	13835.3i	0.00229149	+	0.00396897i
$75$	1.19778e6	−	2.07462e6i	0.327841	−	0.567837i
$76$	−898294.	+	1.55589e6i	−0.234731	+	0.406566i
$77$	−7.93770e6			−1.98142
$78$	1.48269e6	+	1.37149e6i	0.353769	+	0.327237i
$79$	−2.33505e6			−0.532847			−0.266423	−	0.963856i	$-0.585842\pi$
$79$	−2.33505e6			−0.532847			−0.266423	+	0.963856i	$0.585842\pi$
$80$	111466.	−	193064.i	0.0243403	−	0.0421586i
$81$	424927.	−	735994.i	0.0888416	−	0.153878i
$82$	894559.	+	1.54942e6i	0.179168	+	0.310328i
$83$	2.37338e6			0.455610			0.227805	−	0.973707i	$-0.426845\pi$
$83$	2.37338e6			0.455610			0.227805	+	0.973707i	$0.426845\pi$
$84$	1.13484e6	+	1.96560e6i	0.208909	+	0.361842i
$85$	−558025.	−	966528.i	−0.0985570	−	0.170706i
$86$	4.30345e6			0.729579
$87$	2.79625e6	+	4.84325e6i	0.455260	+	0.788533i
$88$	1.82622e6	−	3.16311e6i	0.285670	−	0.494794i
$89$	−3.52575e6	+	6.10678e6i	−0.530135	+	0.918221i	0.469247	+	0.883067i	$0.344526\pi$
$89$	−3.52575e6	+	6.10678e6i	−0.530135	+	0.918221i	−0.999382	+	0.0351542i	$0.988808\pi$
$90$	−509954.			−0.0737364
$91$	6.47050e6	+	5.98521e6i	0.900104	+	0.832597i
$92$	2.17104e6			0.290677
$93$	−250034.	+	433072.i	−0.0322336	+	0.0558302i
$94$	2.16899e6	−	3.75681e6i	0.269346	−	0.466521i
$95$	763922.	+	1.32315e6i	0.0914148	+	0.158335i
$96$	−1.04437e6			−0.120477
$97$	−4.25685e6	−	7.37308e6i	−0.473573	−	0.820253i	0.525969	−	0.850504i	$-0.323703\pi$
$97$	−4.25685e6	−	7.37308e6i	−0.473573	−	0.820253i	−0.999542	+	0.0302508i	$0.990369\pi$
$98$	1.65830e6	+	2.87226e6i	0.177980	+	0.308271i
$99$	−8.35495e6			−0.865407
$100$	2.40521e6	+	4.16594e6i	0.240521	+	0.416594i
$101$	5.28711e6	−	9.15754e6i	0.510615	−	0.884411i	−0.489309	−	0.872110i	$-0.662751\pi$
$101$	5.28711e6	−	9.15754e6i	0.510615	−	0.884411i	0.999924	−	0.0123007i	$-0.00391555\pi$
$102$	−2.61419e6	+	4.52792e6i	−0.243914	+	0.422472i
$103$	3.01542e6			0.271905			0.135952	−	0.990715i	$-0.456591\pi$
$103$	3.01542e6			0.271905			0.135952	+	0.990715i	$0.456591\pi$
$104$	−3.87372e6	+	1.20143e6i	−0.337685	+	0.104732i
$105$	1.93017e6			0.162717
$106$	7.42742e6	−	1.28647e7i	0.605714	−	1.04913i
$107$	−1.14119e7	+	1.97661e7i	−0.900568	+	1.55983i	−0.0738099	+	0.997272i	$0.523516\pi$
$107$	−1.14119e7	+	1.97661e7i	−0.900568	+	1.55983i	−0.826758	+	0.562557i	$0.809818\pi$
$108$	3.42500e6	+	5.93228e6i	0.261624	+	0.453146i
$109$	4.55907e6			0.337197			0.168598	−	0.985685i	$-0.446076\pi$
$109$	4.55907e6			0.337197			0.168598	+	0.985685i	$0.446076\pi$
$110$	−1.55304e6	−	2.68995e6i	−0.111252	−	0.192695i
$111$	−31823.1	−	55119.3i	−0.00220858	−	0.00382537i
$112$	−4.55765e6			−0.306534
$113$	−1.03660e7	−	1.79544e7i	−0.675826	−	1.17056i	−0.976227	−	0.216752i	$-0.930454\pi$
$113$	−1.03660e7	−	1.79544e7i	−0.675826	−	1.17056i	0.300401	−	0.953813i	$-0.402880\pi$
$114$	3.57876e6	−	6.19860e6i	0.226238	−	0.391856i
$115$	923142.	−	1.59893e6i	0.0566012	−	0.0980362i
$116$	−1.12301e7			−0.668004
$117$	6.81062e6	+	6.29983e6i	0.393130	+	0.363646i
$118$	1.06436e7			0.596351
$119$	−1.14084e7	+	1.97599e7i	−0.620598	+	1.07491i
$120$	−444074.	+	769158.i	−0.0234596	+	0.0406332i
$121$	−1.57011e7	−	2.71951e7i	−0.805714	−	1.39554i
$122$	−2.29330e7			−1.14341
$123$	−3.56388e6	−	6.17283e6i	−0.172685	−	0.299100i
$124$	−502082.	−	869632.i	−0.0236482	−	0.0409600i
$125$	8.34292e6			0.382061
$126$	5.21281e6	+	9.02884e6i	0.232153	+	0.402101i
$127$	2.03935e7	−	3.53227e7i	0.883445	−	1.53017i	0.0359603	−	0.999353i	$-0.488551\pi$
$127$	2.03935e7	−	3.53227e7i	0.883445	−	1.53017i	0.847485	−	0.530819i	$-0.178116\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$	−1.71448e7			−0.703182
$130$	−762308.	+	3.36378e6i	−0.0304319	+	0.134284i
$131$	4.11026e7			1.59742			0.798711	−	0.601715i	$-0.205516\pi$
$131$	4.11026e7			1.59742			0.798711	+	0.601715i	$0.205516\pi$
$132$	−7.27558e6	+	1.26017e7i	−0.275333	+	0.476892i
$133$	1.56178e7	−	2.70508e7i	0.575624	−	0.997010i
$134$	−1.13263e7	−	1.96177e7i	−0.406650	−	0.704339i
$135$	5.82534e6			0.203776
$136$	−5.24944e6	−	9.09230e6i	−0.178948	−	0.309947i
$137$	−7.36036e6	−	1.27485e7i	−0.244555	−	0.423582i	0.717451	−	0.696609i	$-0.245309\pi$
$137$	−7.36036e6	−	1.27485e7i	−0.244555	−	0.423582i	−0.962006	+	0.273027i	$0.911975\pi$
$138$	−8.64933e6			−0.280160
$139$	2.84245e7	+	4.92326e7i	0.897719	+	1.55490i	0.830403	+	0.557164i	$0.188110\pi$
$139$	2.84245e7	+	4.92326e7i	0.897719	+	1.55490i	0.0673168	+	0.997732i	$0.478556\pi$
$140$	−1.93795e6	+	3.35662e6i	−0.0596889	+	0.103384i
$141$	−8.64118e6	+	1.49670e7i	−0.259601	+	0.449642i
$142$	1.28149e7			0.375582
$143$	−1.24894e7	+	5.51112e7i	−0.357164	+	1.57603i
$144$	−4.79723e6			−0.133882
$145$	−4.77510e6	+	8.27072e6i	−0.130075	+	0.225297i
$146$	5.56851e6	−	9.64494e6i	0.148082	−	0.256486i
$147$	−6.60660e6	−	1.14430e7i	−0.171541	−	0.297117i
$148$	127805.			0.00324065
$149$	1.92631e7	+	3.33646e7i	0.477061	+	0.826294i	0.999654	−	0.0262884i	$-0.00836881\pi$
$149$	1.92631e7	+	3.33646e7i	0.477061	+	0.826294i	−0.522594	+	0.852582i	$0.675035\pi$
$150$	−9.58224e6	−	1.65969e7i	−0.231818	−	0.401521i
$151$	2.94587e7			0.696297			0.348148	−	0.937439i	$-0.386811\pi$
$151$	2.94587e7			0.696297			0.348148	+	0.937439i	$0.386811\pi$
$152$	7.18635e6	+	1.24471e7i	0.165980	+	0.287486i
$153$	−1.20081e7	+	2.07986e7i	−0.271053	+	0.469477i
$154$	−3.17508e7	+	5.49940e7i	−0.700538	+	1.21337i
$155$	−853956.			−0.0184194
$156$	1.54327e7	−	4.78643e6i	0.325467	−	0.100943i
$157$	6.77251e7			1.39669			0.698346	−	0.715760i	$-0.253919\pi$
$157$	6.77251e7			1.39669			0.698346	+	0.715760i	$0.253919\pi$
$158$	−9.34022e6	+	1.61777e7i	−0.188390	+	0.326301i
$159$	−2.95905e7	+	5.12523e7i	−0.583798	+	1.01117i
$160$	−891724.	−	1.54451e6i	−0.0172112	−	0.0298106i
$161$	−3.77458e7			−0.712817
$162$	−3.39941e6	−	5.88796e6i	−0.0628205	−	0.108808i
$163$	−4.98183e7	−	8.62878e7i	−0.901015	−	1.56060i	−0.826179	−	0.563408i	$-0.809490\pi$
$163$	−4.98183e7	−	8.62878e7i	−0.901015	−	1.56060i	−0.0748357	−	0.997196i	$-0.523843\pi$
$164$	1.43129e7			0.253382
$165$	6.18726e6	+	1.07166e7i	0.107227	+	0.185723i
$166$	9.49351e6	−	1.64432e7i	0.161083	−	0.279003i
$167$	−1.65811e7	+	2.87193e7i	−0.275490	+	0.477162i	−0.970259	−	0.242071i	$-0.922173\pi$
$167$	−1.65811e7	+	2.87193e7i	−0.275490	+	0.477162i	0.694769	+	0.719233i	$0.255507\pi$
$168$	1.81575e7			0.295443
$169$	5.17361e7	−	3.55071e7i	0.824499	−	0.565864i
$170$	−8.92840e6			−0.139381
$171$	1.64388e7	−	2.84728e7i	0.251410	−	0.435455i
$172$	1.72138e7	−	2.98152e7i	0.257945	−	0.446774i
$173$	−2.13081e7	−	3.69067e7i	−0.312884	−	0.541931i	0.666101	−	0.745861i	$-0.267962\pi$
$173$	−2.13081e7	−	3.69067e7i	−0.312884	−	0.541931i	−0.978985	+	0.203930i	$0.934628\pi$
$174$	4.47401e7			0.643834
$175$	−4.18171e7	−	7.24293e7i	−0.589822	−	1.02160i
$176$	−1.46098e7	−	2.53049e7i	−0.201999	−	0.349872i
$177$	−4.24037e7			−0.574774
$178$	2.82060e7	+	4.88543e7i	0.374862	+	0.649281i
$179$	1.01329e7	−	1.75507e7i	0.132053	−	0.228722i	−0.792415	−	0.609982i	$-0.791177\pi$
$179$	1.01329e7	−	1.75507e7i	0.132053	−	0.228722i	0.924468	+	0.381260i	$0.124510\pi$
$180$	−2.03982e6	+	3.53306e6i	−0.0260698	+	0.0451542i
$181$	−3.09055e7			−0.387401			−0.193700	−	0.981061i	$-0.562049\pi$
$181$	−3.09055e7			−0.387401			−0.193700	+	0.981061i	$0.562049\pi$
$182$	6.73488e7	−	2.08881e7i	0.828094	−	0.256831i
$183$	9.13640e7			1.10204
$184$	8.68416e6	−	1.50414e7i	0.102770	−	0.178002i
$185$	54343.7	−	94126.0i	0.000631027	−	0.00109297i
$186$	2.00027e6	+	3.46457e6i	0.0227926	+	0.0394779i
$187$	−1.46281e8			−1.63584
$188$	−1.73520e7	−	3.00545e7i	−0.190457	−	0.329881i
$189$	−5.95473e7	−	1.03139e8i	−0.641572	−	1.11124i
$190$	1.22228e7			0.129280
$191$	−4.03566e7	−	6.98997e7i	−0.419081	−	0.725870i	0.576766	−	0.816909i	$-0.304314\pi$
$191$	−4.03566e7	−	6.98997e7i	−0.419081	−	0.725870i	−0.995847	+	0.0910397i	$0.970981\pi$
$192$	−4.17748e6	+	7.23561e6i	−0.0425951	+	0.0737770i
$193$	−6.91934e7	+	1.19846e8i	−0.692810	+	1.19998i	0.278104	+	0.960551i	$0.410294\pi$
$193$	−6.91934e7	+	1.19846e8i	−0.692810	+	1.19998i	−0.970913	+	0.239431i	$0.923039\pi$
$194$	−6.81096e7			−0.669734
$195$	3.03700e6	−	1.34011e7i	0.0293308	−	0.129426i
$196$	2.65328e7			0.251702
$197$	−8.69235e7	+	1.50556e8i	−0.810038	+	1.40303i	0.102798	+	0.994702i	$0.467220\pi$
$197$	−8.69235e7	+	1.50556e8i	−0.810038	+	1.40303i	−0.912837	+	0.408325i	$0.866113\pi$
$198$	−3.34198e7	+	5.78848e7i	−0.305968	+	0.529952i
$199$	−1.19505e7	−	2.06988e7i	−0.107498	−	0.186191i	0.807258	−	0.590198i	$-0.200950\pi$
$199$	−1.19505e7	−	2.06988e7i	−0.107498	−	0.186191i	−0.914756	+	0.404007i	$0.867617\pi$
$200$	3.84833e7			0.340148
$201$	4.51235e7	+	7.81562e7i	0.391937	+	0.678855i
$202$	−4.22969e7	−	7.32603e7i	−0.361059	−	0.625373i
$203$	1.95246e8			1.63813
$204$	2.09136e7	+	3.62233e7i	0.172473	+	0.298733i
$205$	6.08596e6	−	1.05412e7i	0.0493391	−	0.0854578i
$206$	1.20617e7	−	2.08914e7i	0.0961329	−	0.166507i
$207$	−3.97300e7			−0.311331
$208$	−7.17117e6	+	3.16436e7i	−0.0552546	+	0.243817i
$209$	2.00254e8			1.51729
$210$	7.72069e6	−	1.33726e7i	0.0575292	−	0.0996436i
$211$	2.73880e7	−	4.74375e7i	0.200711	−	0.347642i	−0.748046	−	0.663646i	$-0.769008\pi$
$211$	2.73880e7	−	4.74375e7i	0.200711	−	0.347642i	0.948758	+	0.316004i	$0.102341\pi$
$212$	−5.94194e7	−	1.02917e8i	−0.428304	−	0.741845i
$213$	−5.10538e7			−0.361993
$214$	9.12956e7	+	1.58129e8i	0.636798	+	1.10297i
$215$	−1.46389e7	−	2.53553e7i	−0.100455	−	0.173994i
$216$	5.48000e7			0.369992
$217$	8.72923e6	+	1.51195e7i	0.0579918	+	0.100445i
$218$	1.82363e7	−	3.15862e7i	0.119217	−	0.206490i
$219$	−2.21847e7	+	3.84250e7i	−0.142725	+	0.247206i
$220$	−2.48487e7			−0.157335
$221$	1.19242e8	+	1.10299e8i	0.743116	+	0.687383i
$222$	−509170.			−0.00312340
$223$	−1.36109e8	+	2.35747e8i	−0.821901	+	1.42357i	0.0823641	+	0.996602i	$0.473753\pi$
$223$	−1.36109e8	+	2.35747e8i	−0.821901	+	1.42357i	−0.904265	+	0.426972i	$0.859580\pi$
$224$	−1.82306e7	+	3.15763e7i	−0.108376	+	0.187713i
$225$	−4.40152e7	−	7.62366e7i	−0.257611	−	0.446195i
$226$	−1.65855e8			−0.955762
$227$	2.24777e7	+	3.89325e7i	0.127544	+	0.220914i	0.922725	−	0.385460i	$-0.125957\pi$
$227$	2.24777e7	+	3.89325e7i	0.127544	+	0.220914i	−0.795180	+	0.606373i	$0.792624\pi$
$228$	−2.86301e7	−	4.95888e7i	−0.159975	−	0.277084i
$229$	1.23460e8			0.679362			0.339681	−	0.940541i	$-0.389681\pi$
$229$	1.23460e8			0.679362			0.339681	+	0.940541i	$0.389681\pi$
$230$	−7.38513e6	−	1.27914e7i	−0.0400231	−	0.0693221i
$231$	1.26494e8	−	2.19094e8i	0.675192	−	1.16947i
$232$	−4.49202e7	+	7.78041e7i	−0.236175	+	0.409067i
$233$	1.26541e8			0.655371			0.327685	−	0.944787i	$-0.393731\pi$
$233$	1.26541e8			0.655371			0.327685	+	0.944787i	$0.393731\pi$
$234$	7.08890e7	−	2.19861e7i	0.361679	−	0.112174i
$235$	−2.95127e7			−0.148345
$236$	4.25744e7	−	7.37411e7i	0.210842	−	0.365189i
$237$	3.72110e7	−	6.44514e7i	0.181573	−	0.314494i
$238$	9.12671e7	+	1.58079e8i	0.438829	+	0.760074i
$239$	8.04943e6			0.0381393			0.0190696	−	0.999818i	$-0.493930\pi$
$239$	8.04943e6			0.0381393			0.0190696	+	0.999818i	$0.493930\pi$
$240$	3.55259e6	+	6.15326e6i	0.0165884	+	0.0287320i
$241$	1.93788e8	+	3.35651e8i	0.891801	+	1.54464i	0.837715	+	0.546108i	$0.183891\pi$
$241$	1.93788e8	+	3.35651e8i	0.891801	+	1.54464i	0.0540864	+	0.998536i	$0.482775\pi$
$242$	−2.51217e8			−1.13945
$243$	−1.03496e8	−	1.79260e8i	−0.462701	−	0.801421i
$244$	−9.17320e7	+	1.58884e8i	−0.404256	+	0.700192i
$245$	1.12819e7	−	1.95409e7i	0.0490120	−	0.0848913i
$246$	−5.70221e7			−0.244214
$247$	−1.63239e8	−	1.50997e8i	−0.689264	−	0.637570i
$248$	−8.03331e6			−0.0334437
$249$	−3.78217e7	+	6.55091e7i	−0.155254	+	0.268908i
$250$	3.33717e7	−	5.78014e7i	0.135079	−	0.233964i
$251$	−3.70235e7	−	6.41265e7i	−0.147781	−	0.255965i	0.782626	−	0.622492i	$-0.213880\pi$
$251$	−3.70235e7	−	6.41265e7i	−0.147781	−	0.255965i	−0.930407	+	0.366528i	$0.880546\pi$
$252$	8.34049e7			0.328314
$253$	−1.20996e8	−	2.09571e8i	−0.469731	−	0.813598i
$254$	−1.63148e8	−	2.82581e8i	−0.624690	−	1.08200i
$255$	3.55704e7			0.134338
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	7.46504e7	−	1.29298e8i	0.274326	−	0.475146i	−0.695639	−	0.718391i	$-0.744879\pi$
$257$	7.46504e7	−	1.29298e8i	0.274326	−	0.475146i	0.969965	+	0.243246i	$0.0782121\pi$
$258$	−6.85790e7	+	1.18782e8i	−0.248612	+	0.430609i
$259$	−2.22203e6			−0.00794695
$260$	2.02557e7	+	1.87365e7i	0.0714727	+	0.0661123i
$261$	2.05510e8			0.715469
$262$	1.64410e8	−	2.84767e8i	0.564774	−	0.978217i
$263$	−8.67285e7	+	1.50218e8i	−0.293979	+	0.509187i	−0.974747	−	0.223313i	$-0.928313\pi$
$263$	−8.67285e7	+	1.50218e8i	−0.293979	+	0.509187i	0.680768	+	0.732499i	$0.261646\pi$
$264$	5.82047e7	+	1.00813e8i	0.194690	+	0.337213i
$265$	−1.01062e8			−0.333601
$266$	−1.24942e8	−	2.16406e8i	−0.407028	−	0.704992i
$267$	−1.12372e8	−	1.94633e8i	−0.361299	−	0.625788i
$268$	−1.81221e8			−0.575091
$269$	2.15455e8	+	3.73179e8i	0.674875	+	1.16892i	0.976506	+	0.215492i	$0.0691357\pi$
$269$	2.15455e8	+	3.73179e8i	0.674875	+	1.16892i	−0.301631	+	0.953425i	$0.597531\pi$
$270$	2.33014e7	−	4.03591e7i	0.0720457	−	0.124787i
$271$	−1.55116e8	+	2.68669e8i	−0.473439	+	0.820021i	−0.999538	−	0.0304029i	$-0.990321\pi$
$271$	−1.55116e8	+	2.68669e8i	−0.473439	+	0.820021i	0.526099	+	0.850424i	$0.323654\pi$
$272$	−8.39911e7			−0.253071
$273$	−2.68314e8	+	8.32171e7i	−0.798132	+	0.247539i
$274$	−1.17766e8			−0.345853
$275$	2.68093e8	−	4.64351e8i	0.777359	−	1.34643i
$276$	−3.45973e7	+	5.99243e7i	−0.0990514	+	0.171562i
$277$	−1.95019e8	−	3.37783e8i	−0.551313	−	0.954902i	−0.998180	−	0.0603016i	$-0.980794\pi$
$277$	−1.95019e8	−	3.37783e8i	−0.551313	−	0.954902i	0.446867	−	0.894600i	$-0.352540\pi$
$278$	4.54792e8			1.26957
$279$	9.18809e6	+	1.59142e7i	0.0253286	+	0.0438704i
$280$	1.55036e7	+	2.68530e7i	0.0422064	+	0.0731037i
$281$	−2.24392e8			−0.603303			−0.301652	−	0.953418i	$-0.597538\pi$
$281$	−2.24392e8			−0.603303			−0.301652	+	0.953418i	$0.597538\pi$
$282$	6.91294e7	+	1.19736e8i	0.183566	+	0.317945i
$283$	6.25944e6	−	1.08417e7i	0.0164166	−	0.0284344i	−0.857700	−	0.514150i	$-0.828108\pi$
$283$	6.25944e6	−	1.08417e7i	0.0164166	−	0.0284344i	0.874117	+	0.485715i	$0.161441\pi$
$284$	5.12594e7	−	8.87839e7i	0.132788	−	0.229996i
$285$	−4.86949e7			−0.124602
$286$	3.31864e8	+	3.06974e8i	0.838839	+	0.775927i
$287$	−2.48846e8			−0.621360
$288$	−1.91889e7	+	3.32362e7i	−0.0473344	+	0.0819855i
$289$	−5.07133e6	+	8.78379e6i	−0.0123589	+	0.0214062i
$290$	3.82008e7	+	6.61658e7i	0.0919771	+	0.159309i
$291$	2.71346e8			0.645501
$292$	−4.45481e7	−	7.71595e7i	−0.104710	−	0.181363i
$293$	2.13337e8	+	3.69510e8i	0.495483	+	0.858201i	0.999986	−	0.00520823i	$-0.00165784\pi$
$293$	2.13337e8	+	3.69510e8i	0.495483	+	0.858201i	−0.504504	+	0.863410i	$0.668325\pi$
$294$	−1.05706e8			−0.242595
$295$	−3.62059e7	−	6.27105e7i	−0.0821112	−	0.142221i
$296$	511221.	−	885460.i	0.00114574	−	0.00198449i
$297$	3.81763e8	−	6.61233e8i	0.845564	−	1.46456i
$298$	3.08209e8			0.674666
$299$	−5.93906e7	+	2.62068e8i	−0.128490	+	0.566977i
$300$	−1.53316e8			−0.327841
$301$	−2.99280e8	+	5.18369e8i	−0.632551	+	1.09561i
$302$	1.17835e8	−	2.04096e8i	0.246178	−	0.426393i
$303$	1.68509e8	+	2.91866e8i	0.347995	+	0.602746i
$304$	1.14982e8			0.234731
$305$	7.80102e7	+	1.35118e8i	0.157435	+	0.272686i
$306$	9.60647e7	+	1.66389e8i	0.191663	+	0.331970i
$307$	2.83423e8			0.559051			0.279525	−	0.960138i	$-0.409823\pi$
$307$	2.83423e8			0.559051			0.279525	+	0.960138i	$0.409823\pi$
$308$	2.54006e8	+	4.39952e8i	0.495355	+	0.857981i
$309$	−4.80532e7	+	8.32305e7i	−0.0926547	+	0.160483i
$310$	−3.41582e6	+	5.91638e6i	−0.00651222	+	0.0112795i
$311$	−7.14238e8			−1.34642			−0.673212	−	0.739450i	$-0.735086\pi$
$311$	−7.14238e8			−1.34642			−0.673212	+	0.739450i	$0.735086\pi$
$312$	2.85696e7	−	1.26067e8i	0.0532554	−	0.234996i
$313$	−3.51984e8			−0.648811			−0.324406	−	0.945918i	$-0.605164\pi$
$313$	−3.51984e8			−0.648811			−0.324406	+	0.945918i	$0.605164\pi$
$314$	2.70900e8	−	4.69213e8i	0.493806	−	0.855296i
$315$	3.54644e7	−	6.14261e7i	0.0639301	−	0.110730i
$316$	7.47217e7	+	1.29422e8i	0.133212	+	0.230729i
$317$	−4.55628e8			−0.803346			−0.401673	−	0.915783i	$-0.631571\pi$
$317$	−4.55628e8			−0.803346			−0.401673	+	0.915783i	$0.631571\pi$
$318$	2.36724e8	+	4.10018e8i	0.412807	+	0.715003i
$319$	6.25872e8	+	1.08404e9i	1.07949	+	1.86973i
$320$	−1.42676e7			−0.0243403
$321$	−3.63718e8	−	6.29977e8i	−0.613757	−	1.06306i
$322$	−1.50983e8	+	2.61511e8i	−0.252019	+	0.436510i
$323$	2.87814e8	−	4.98508e8i	0.475229	−	0.823121i
$324$	−5.43906e7			−0.0888416
$325$	−5.68671e8	+	1.76372e8i	−0.918902	+	0.284995i
$326$	−7.97092e8			−1.27423
$327$	−7.26526e7	+	1.25838e8i	−0.114904	+	0.199019i
$328$	5.72518e7	−	9.91630e7i	0.0895840	−	0.155164i
$329$	3.01682e8	+	5.22529e8i	0.467051	+	0.808955i
$330$	9.89962e7			0.151642
$331$	−3.32605e8	−	5.76089e8i	−0.504117	−	0.873156i	−0.999989	−	0.00476004i	$-0.998485\pi$
$331$	−3.32605e8	−	5.76089e8i	−0.504117	−	0.873156i	0.495872	−	0.868396i	$-0.334849\pi$
$332$	−7.59481e7	−	1.31546e8i	−0.113903	−	0.197285i
$333$	−2.33883e6			−0.00347091
$334$	1.32649e8	+	2.29754e8i	0.194801	+	0.337405i
$335$	−7.70564e7	+	1.33466e8i	−0.111983	+	0.193960i
$336$	7.26299e7	−	1.25799e8i	0.104455	−	0.180921i
$337$	9.20291e8			1.30985			0.654924	−	0.755695i	$-0.272701\pi$
$337$	9.20291e8			1.30985			0.654924	+	0.755695i	$0.272701\pi$
$338$	−3.90563e7	−	5.00466e8i	−0.0550152	−	0.704963i
$339$	6.60760e8			0.921181
$340$	−3.57136e7	+	6.18578e7i	−0.0492785	+	0.0853529i
$341$	−5.59639e7	+	9.69324e7i	−0.0764307	+	0.132382i
$342$	−1.31510e8	−	2.27782e8i	−0.177774	−	0.307913i
$343$	4.55061e8			0.608892
$344$	−1.37710e8	−	2.38522e8i	−0.182395	−	0.315917i
$345$	2.94220e7	+	5.09605e7i	0.0385750	+	0.0668139i
$346$	−3.40930e8			−0.442485
$347$	−6.82493e8	−	1.18211e9i	−0.876890	−	1.51882i	−0.854736	−	0.519063i	$-0.826281\pi$
$347$	−6.82493e8	−	1.18211e9i	−0.876890	−	1.51882i	−0.0221539	−	0.999755i	$-0.507052\pi$
$348$	1.78960e8	−	3.09968e8i	0.227630	−	0.394266i
$349$	4.48612e8	−	7.77018e8i	0.564913	−	0.978458i	−0.432145	−	0.901804i	$-0.642243\pi$
$349$	4.48612e8	−	7.77018e8i	0.564913	−	0.978458i	0.997058	−	0.0766537i	$-0.0244236\pi$
$350$	−6.69073e8			−0.834134
$351$	−8.09784e8	+	2.51153e8i	−0.999527	+	0.310001i
$352$	−2.33756e8			−0.285670
$353$	1.34803e8	−	2.33485e8i	0.163112	−	0.282519i	−0.772871	−	0.634563i	$-0.781180\pi$
$353$	1.34803e8	−	2.33485e8i	0.163112	−	0.282519i	0.935983	+	0.352044i	$0.114513\pi$
$354$	−1.69615e8	+	2.93781e8i	−0.203213	+	0.351976i
$355$	−4.35918e7	−	7.55031e7i	−0.0517136	−	0.0895707i
$356$	4.51296e8			0.530135
$357$	−3.63604e8	−	6.29781e8i	−0.422951	−	0.732573i
$358$	−8.10630e7	−	1.40405e8i	−0.0933753	−	0.161731i
$359$	−2.23928e8			−0.255433			−0.127717	−	0.991811i	$-0.540765\pi$
$359$	−2.23928e8			−0.255433			−0.127717	+	0.991811i	$0.540765\pi$
$360$	1.63185e7	+	2.82645e7i	0.0184341	+	0.0319288i
$361$	5.29262e7	−	9.16708e7i	0.0592100	−	0.102555i
$362$	−1.23622e8	+	2.14119e8i	−0.136967	+	0.237234i
$363$	1.00084e9			1.09822
$364$	1.24678e8	−	5.50158e8i	0.135499	−	0.597906i
$365$	−7.57686e7			−0.0815576
$366$	3.65456e8	−	6.32989e8i	0.389629	−	0.674857i
$367$	1.40428e8	−	2.43229e8i	0.148294	−	0.256853i	−0.782303	−	0.622898i	$-0.785955\pi$
$367$	1.40428e8	−	2.43229e8i	0.148294	−	0.256853i	0.930597	+	0.366045i	$0.119288\pi$
$368$	−6.94733e7	−	1.20331e8i	−0.0726692	−	0.125867i
$369$	−2.61926e8			−0.271386
$370$	−434749.	−	753008.i	−0.000446203	−	0.000772847i
$371$	1.03307e9	+	1.78933e9i	1.05032	+	1.81920i
$372$	3.20044e7			0.0322336
$373$	−8.77622e8	−	1.52009e9i	−0.875642	−	1.51666i	−0.856077	−	0.516848i	$-0.827105\pi$
$373$	−8.77622e8	−	1.52009e9i	−0.875642	−	1.51666i	−0.0195647	−	0.999809i	$-0.506228\pi$
$374$	−5.85122e8	+	1.01346e9i	−0.578357	+	1.00174i
$375$	−1.32951e8	+	2.30278e8i	−0.130192	+	0.225499i
$376$	−2.77631e8			−0.269346
$377$	3.07208e8	−	1.35559e9i	0.295282	−	1.30297i
$378$	−9.52756e8			−0.907320
$379$	−1.79617e8	+	3.11105e8i	−0.169477	+	0.293542i	−0.938236	−	0.345996i	$-0.887541\pi$
$379$	−1.79617e8	+	3.11105e8i	−0.169477	+	0.293542i	0.768759	+	0.639538i	$0.220874\pi$
$380$	4.88910e7	−	8.46817e7i	0.0457074	−	0.0791675i
$381$	6.49976e8	+	1.12579e9i	0.602088	+	1.04285i
$382$	−6.45706e8			−0.592670
$383$	9.39346e8	+	1.62699e9i	0.854338	+	1.47976i	0.877258	+	0.480020i	$0.159370\pi$
$383$	9.39346e8	+	1.62699e9i	0.854338	+	1.47976i	−0.0229197	+	0.999737i	$0.507296\pi$
$384$	3.34198e7	+	5.78849e7i	0.0301193	+	0.0521682i
$385$	4.32021e8			0.385827
$386$	5.53547e8	+	9.58772e8i	0.489891	+	0.848515i
$387$	−3.15012e8	+	5.45617e8i	−0.276273	+	0.478519i
$388$	−2.72438e8	+	4.71877e8i	−0.236787	+	0.410126i
$389$	4.34490e8			0.374245			0.187122	−	0.982337i	$-0.440084\pi$
$389$	4.34490e8			0.374245			0.187122	+	0.982337i	$0.440084\pi$
$390$	−8.06978e7	−	7.46455e7i	−0.0688867	−	0.0637202i
$391$	−6.95603e8			−0.588495
$392$	1.06131e8	−	1.83825e8i	0.0889902	−	0.154136i
$393$	−6.55004e8	+	1.13450e9i	−0.544339	+	0.942824i
$394$	6.95388e8	+	1.20445e9i	0.572784	+	0.992090i
$395$	1.27089e8			0.103757
$396$	2.67358e8	+	4.63078e8i	0.216352	+	0.374732i
$397$	−1.01579e9	−	1.75940e9i	−0.814772	−	1.41123i	−0.909491	−	0.415723i	$-0.863529\pi$
$397$	−1.01579e9	−	1.75940e9i	−0.814772	−	1.41123i	0.0947188	−	0.995504i	$-0.469805\pi$
$398$	−1.91207e8			−0.152025
$399$	4.97765e8	+	8.62154e8i	0.392301	+	0.679484i
$400$	1.53933e8	−	2.66620e8i	0.120260	−	0.208297i
$401$	4.01539e8	−	6.95485e8i	0.310973	−	0.538620i	−0.667601	−	0.744520i	$-0.732679\pi$
$401$	4.01539e8	−	6.95485e8i	0.310973	−	0.538620i	0.978573	+	0.205899i	$0.0660119\pi$
$402$	7.21976e8			0.554283
$403$	1.18709e8	−	3.68173e7i	0.0903474	−	0.0280210i
$404$	−6.76750e8			−0.510615
$405$	−2.31273e7	+	4.00576e7i	−0.0172994	+	0.0299635i
$406$	7.80986e8	−	1.35271e9i	0.579165	−	1.00314i
$407$	−7.12282e6	−	1.23371e7i	−0.00523686	−	0.00907051i
$408$	3.34617e8			0.243914
$409$	1.26870e9	+	2.19745e9i	0.916912	+	1.58814i	0.804077	+	0.594525i	$0.202660\pi$
$409$	1.26870e9	+	2.19745e9i	0.916912	+	1.58814i	0.112835	+	0.993614i	$0.464007\pi$
$410$	−4.86877e7	−	8.43296e7i	−0.0348880	−	0.0604278i
$411$	4.69174e8			0.333340
$412$	−9.64934e7	−	1.67131e8i	−0.0679762	−	0.117738i
$413$	−7.40201e8	+	1.28207e9i	−0.517041	+	0.895541i
$414$	−1.58920e8	+	2.75257e8i	−0.110072	+	0.190650i
$415$	−1.29175e8			−0.0887174
$416$	1.90549e8	+	1.76258e8i	0.129772	+	0.120039i
$417$	−1.81187e9			−1.22363
$418$	8.01017e8	−	1.38740e9i	0.536445	−	0.929149i
$419$	8.92968e7	−	1.54667e8i	0.0593044	−	0.102718i	−0.834849	−	0.550479i	$-0.814445\pi$
$419$	8.92968e7	−	1.54667e8i	0.0593044	−	0.102718i	0.894153	+	0.447761i	$0.147778\pi$
$420$	−6.17655e7	−	1.06981e8i	−0.0406793	−	0.0704586i
$421$	2.07782e9			1.35713			0.678563	−	0.734542i	$-0.262603\pi$
$421$	2.07782e9			1.35713			0.678563	+	0.734542i	$0.262603\pi$
$422$	−2.19104e8	−	3.79500e8i	−0.141924	−	0.245820i
$423$	3.17540e8	+	5.49996e8i	0.203989	+	0.353320i
$424$	−9.50710e8			−0.605714
$425$	−7.70630e8	−	1.33477e9i	−0.486950	−	0.843423i
$426$	−2.04215e8	+	3.53711e8i	−0.127984	+	0.221674i
$427$	1.59486e9	−	2.76237e9i	0.991344	−	1.71706i
$428$	1.46073e9			0.900568
$429$	−1.32213e9	−	1.22297e9i	−0.808488	−	0.747852i
$430$	−2.34222e8			−0.142065
$431$	−7.90928e8	+	1.36993e9i	−0.475846	+	0.824190i	−0.999617	−	0.0276692i	$-0.991192\pi$
$431$	−7.90928e8	+	1.36993e9i	−0.475846	+	0.824190i	0.523771	+	0.851859i	$0.324525\pi$
$432$	2.19200e8	−	3.79666e8i	0.130812	−	0.226573i
$433$	−6.68261e8	−	1.15746e9i	−0.395584	−	0.685171i	0.597592	−	0.801801i	$-0.296124\pi$
$433$	−6.68261e8	−	1.15746e9i	−0.395584	−	0.685171i	−0.993176	+	0.116629i	$0.962791\pi$
$434$	1.39668e8			0.0820128
$435$	−1.52190e8	−	2.63601e8i	−0.0886492	−	0.153545i
$436$	−1.45890e8	−	2.52689e8i	−0.0842992	−	0.146011i
$437$	9.52262e8			0.545847
$438$	1.77477e8	+	3.07400e8i	0.100922	+	0.174801i
$439$	−9.97662e8	+	1.72800e9i	−0.562805	+	0.974806i	0.434445	+	0.900698i	$0.356944\pi$
$439$	−9.97662e8	+	1.72800e9i	−0.562805	+	0.974806i	−0.997250	+	0.0741082i	$0.976389\pi$
$440$	−9.93948e7	+	1.72157e8i	−0.0556262	+	0.0963474i
$441$	−4.85550e8			−0.269587
$442$	1.24114e9	−	3.84938e8i	0.683666	−	0.212037i
$443$	1.51862e8			0.0829921			0.0414960	−	0.999139i	$-0.486788\pi$
$443$	1.51862e8			0.0829921			0.0414960	+	0.999139i	$0.486788\pi$
$444$	−2.03668e6	+	3.52763e6i	−0.00110429	+	0.00191268i
$445$	1.91894e8	−	3.32371e8i	0.103229	−	0.178798i
$446$	1.08887e9	+	1.88598e9i	0.581172	+	1.00662i
$447$	−1.22789e9			−0.650255
$448$	1.45845e8	+	2.52611e8i	0.0766334	+	0.132733i
$449$	8.03256e7	+	1.39128e8i	0.0418786	+	0.0725358i	0.886205	−	0.463293i	$-0.153332\pi$
$449$	8.03256e7	+	1.39128e8i	0.0418786	+	0.0725358i	−0.844326	+	0.535829i	$0.819999\pi$
$450$	−7.04244e8			−0.364317
$451$	−7.97686e8	−	1.38163e9i	−0.409463	−	0.709210i
$452$	−6.63421e8	+	1.14908e9i	−0.337913	+	0.585282i
$453$	−4.69449e8	+	8.13109e8i	−0.237271	+	0.410965i
$454$	3.59643e8			0.180375
$455$	−3.52167e8	−	3.25754e8i	−0.175270	−	0.162125i
$456$	−4.58082e8			−0.226238
$457$	−5.10839e8	+	8.84800e8i	−0.250367	+	0.433649i	−0.963627	−	0.267251i	$-0.913885\pi$
$457$	−5.10839e8	+	8.84800e8i	−0.250367	+	0.433649i	0.713260	+	0.700900i	$0.247218\pi$
$458$	4.93839e8	−	8.55354e8i	0.240191	−	0.416022i
$459$	−1.09737e9	−	1.90071e9i	−0.529675	−	0.917425i
$460$	−1.18162e8			−0.0566012
$461$	−1.35144e9	−	2.34077e9i	−0.642458	−	1.11277i	−0.984882	−	0.173225i	$-0.944581\pi$
$461$	−1.35144e9	−	2.34077e9i	−0.642458	−	1.11277i	0.342424	−	0.939546i	$-0.388752\pi$
$462$	−1.01195e9	−	1.75275e9i	−0.477433	−	0.826937i
$463$	−2.68582e9			−1.25760			−0.628801	−	0.777566i	$-0.716454\pi$
$463$	−2.68582e9			−1.25760			−0.628801	+	0.777566i	$0.716454\pi$
$464$	3.59362e8	+	6.22433e8i	0.167001	+	0.289254i
$465$	1.36085e7	−	2.35706e7i	0.00627660	−	0.0108714i
$466$	5.06166e8	−	8.76705e8i	0.231709	−	0.401331i
$467$	−4.54161e8			−0.206348			−0.103174	−	0.994663i	$-0.532900\pi$
$467$	−4.54161e8			−0.206348			−0.103174	+	0.994663i	$0.532900\pi$
$468$	1.31232e8	−	5.79078e8i	0.0591807	−	0.261142i
$469$	3.15072e9			1.41028
$470$	−1.18051e8	+	2.04470e8i	−0.0524477	+	0.0908421i
$471$	−1.07926e9	+	1.86933e9i	−0.475939	+	0.824350i
$472$	−3.40595e8	−	5.89928e8i	−0.149088	−	0.258227i
$473$	−3.83743e9			−1.66735
$474$	−2.97688e8	−	5.15611e8i	−0.128392	−	0.222381i
$475$	1.05497e9	+	1.82727e9i	0.451662	+	0.782301i
$476$	1.46027e9			0.620598
$477$	1.08737e9	+	1.88338e9i	0.458737	+	0.794556i
$478$	3.21977e7	−	5.57681e7i	0.0134843	−	0.0233554i
$479$	9.98214e8	−	1.72896e9i	0.415001	−	0.718803i	−0.580427	−	0.814312i	$-0.697114\pi$
$479$	9.98214e8	−	1.72896e9i	0.415001	−	0.718803i	0.995429	+	0.0955088i	$0.0304478\pi$
$480$	5.68414e7			0.0234596
$481$	−3.49622e6	+	1.54275e7i	−0.00143249	+	0.00632102i
$482$	3.10061e9			1.26120
$483$	6.01511e8	−	1.04185e9i	0.242901	−	0.420716i
$484$	−1.00487e9	+	1.74048e9i	−0.402857	+	0.697768i
$485$	2.31685e8	+	4.01291e8i	0.0922152	+	0.159721i
$486$	−1.65593e9			−0.654357
$487$	−8.06060e8	−	1.39614e9i	−0.316240	−	0.547743i	0.663461	−	0.748211i	$-0.269087\pi$
$487$	−8.06060e8	−	1.39614e9i	−0.316240	−	0.547743i	−0.979700	+	0.200468i	$0.935754\pi$
$488$	7.33856e8	+	1.27108e9i	0.285852	+	0.495110i
$489$	3.17558e9			1.22812
$490$	−9.02556e7	−	1.56327e8i	−0.0346567	−	0.0600272i
$491$	2.59072e9	−	4.48725e9i	0.987722	−	1.71078i	0.358570	−	0.933503i	$-0.383264\pi$
$491$	2.59072e9	−	4.48725e9i	0.987722	−	1.71078i	0.629152	−	0.777282i	$-0.283402\pi$
$492$	−2.28088e8	+	3.95061e8i	−0.0863427	+	0.149550i
$493$	3.59812e9			1.35242
$494$	−1.69909e9	+	5.26969e8i	−0.634122	+	0.196671i
$495$	4.54731e8			0.168514
$496$	−3.21333e7	+	5.56564e7i	−0.0118241	+	0.0204800i
$497$	−8.91199e8	+	1.54360e9i	−0.325632	+	0.564012i
$498$	3.02574e8	+	5.24073e8i	0.109781	+	0.190147i
$499$	2.11935e9			0.763574			0.381787	−	0.924250i	$-0.375309\pi$
$499$	2.11935e9			0.763574			0.381787	+	0.924250i	$0.375309\pi$
$500$	−2.66973e8	−	4.62411e8i	−0.0955153	−	0.165437i
$501$	−5.28466e8	−	9.15331e8i	−0.187752	−	0.325197i
$502$	−5.92376e8			−0.208994
$503$	9.53790e7	+	1.65201e8i	0.0334168	+	0.0578796i	0.882250	−	0.470781i	$-0.156028\pi$
$503$	9.53790e7	+	1.65201e8i	0.0334168	+	0.0578796i	−0.848833	+	0.528661i	$0.822694\pi$
$504$	3.33620e8	−	5.77846e8i	0.116077	−	0.201051i
$505$	−2.87759e8	+	4.98413e8i	−0.0994281	+	0.172214i
$506$	−1.93594e9			−0.664300
$507$	1.55598e8	+	1.99384e9i	0.0530246	+	0.679456i
$508$	−2.61037e9			−0.883445
$509$	−2.57239e9	+	4.45550e9i	−0.864617	+	1.49756i	0.00280918	+	0.999996i	$0.499106\pi$
$509$	−2.57239e9	+	4.45550e9i	−0.864617	+	1.49756i	−0.867427	+	0.497565i	$0.834228\pi$
$510$	1.42281e8	−	2.46439e8i	0.0474955	−	0.0822647i
$511$	7.74515e8	+	1.34150e9i	0.256777	+	0.444751i
$512$	−1.34218e8			−0.0441942
$513$	1.50227e9	+	2.60202e9i	0.491291	+	0.850940i
$514$	−5.97203e8	−	1.03439e9i	−0.193977	−	0.335979i
$515$	−1.64119e8			−0.0529459
$516$	5.48632e8	+	9.50259e8i	0.175795	+	0.304487i
$517$	−1.93411e9	+	3.34998e9i	−0.615552	+	1.06617i
$518$	−8.88811e6	+	1.53947e7i	−0.00280967	+	0.00486649i
$519$	1.35825e9			0.426475
$520$	2.10833e8	−	6.53894e7i	0.0657548	−	0.0203937i
$521$	1.41370e9			0.437950			0.218975	−	0.975730i	$-0.429729\pi$
$521$	1.41370e9			0.437950			0.218975	+	0.975730i	$0.429729\pi$
$522$	8.22039e8	−	1.42381e9i	0.252956	−	0.438133i
$523$	1.73475e9	−	3.00468e9i	0.530251	−	0.918421i	−0.469126	−	0.883131i	$-0.655431\pi$
$523$	1.73475e9	−	3.00468e9i	0.530251	−	0.918421i	0.999377	−	0.0352902i	$-0.0112356\pi$
$524$	−1.31528e9	−	2.27814e9i	−0.399356	−	0.691704i
$525$	2.66556e9			0.803953
$526$	6.93828e8	+	1.20174e9i	0.207875	+	0.360049i
$527$	1.60867e8	+	2.78631e8i	0.0478774	+	0.0829262i
$528$	9.31275e8			0.275333
$529$	1.12704e9	+	1.95210e9i	0.331014	+	0.573333i
$530$	−4.04249e8	+	7.00179e8i	−0.117946	+	0.204288i
$531$	−7.79111e8	+	1.34946e9i	−0.225823	+	0.391137i
$532$	−1.99908e9			−0.575624
$533$	−3.91542e8	+	1.72773e9i	−0.112004	+	0.494231i
$534$	−1.79794e9			−0.510954
$535$	6.21113e8	−	1.07580e9i	0.175361	−	0.303734i
$536$	−7.24883e8	+	1.25553e9i	−0.203325	+	0.352170i
$537$	3.22951e8	+	5.59368e8i	0.0899968	+	0.155879i
$538$	3.44728e9			0.954417
$539$	−1.47872e9	−	2.56122e9i	−0.406749	−	0.704510i
$540$	−1.86411e8	−	3.22873e8i	−0.0509440	−	0.0882376i
$541$	−2.01148e9			−0.546166			−0.273083	−	0.961990i	$-0.588043\pi$
$541$	−2.01148e9			−0.546166			−0.273083	+	0.961990i	$0.588043\pi$
$542$	1.24093e9	+	2.14935e9i	0.334772	+	0.579842i
$543$	4.92504e8	−	8.53042e8i	0.132011	−	0.228650i
$544$	−3.35964e8	+	5.81907e8i	−0.0894741	+	0.154974i
$545$	−2.48134e8			−0.0656597
$546$	−4.96713e8	+	2.19181e9i	−0.130596	+	0.576272i
$547$	−1.25989e8			−0.0329137			−0.0164569	−	0.999865i	$-0.505239\pi$
$547$	−1.25989e8			−0.0329137			−0.0164569	+	0.999865i	$0.505239\pi$
$548$	−4.71063e8	+	8.15905e8i	−0.122278	+	0.211791i
$549$	1.67869e9	−	2.90758e9i	0.432980	−	0.749944i
$550$	−2.14475e9	−	3.71481e9i	−0.549676	−	0.952066i
$551$	−4.92573e9			−1.25441
$552$	2.76778e8	+	4.79394e8i	0.0700399	+	0.121313i
$553$	−1.29912e9	−	2.25014e9i	−0.326671	−	0.565810i
$554$	−3.12031e9			−0.779674
$555$	1.73202e6	+	2.99995e6i	0.000430059	+	0.000744884i
$556$	1.81917e9	−	3.15089e9i	0.448860	−	0.777448i
$557$	1.13089e7	−	1.95875e7i	0.00277284	−	0.00480270i	−0.864636	−	0.502399i	$-0.832451\pi$
$557$	1.13089e7	−	1.95875e7i	0.00277284	−	0.00480270i	0.867408	+	0.497597i	$0.165784\pi$
$558$	1.47009e8			0.0358200
$559$	3.12812e9	+	2.89351e9i	0.757429	+	0.700623i
$560$	2.48057e8			0.0596889
$561$	2.33110e9	−	4.03759e9i	0.557431	−	0.965499i
$562$	−8.97569e8	+	1.55463e9i	−0.213300	+	0.369446i
$563$	−1.70004e9	−	2.94455e9i	−0.401494	−	0.695408i	0.592412	−	0.805635i	$-0.298176\pi$
$563$	−1.70004e9	−	2.94455e9i	−0.401494	−	0.695408i	−0.993906	+	0.110227i	$0.964842\pi$
$564$	1.10607e9			0.259601
$565$	5.64183e8	+	9.77194e8i	0.131598	+	0.227935i
$566$	−5.00755e7	−	8.67333e7i	−0.0116083	−	0.0201061i
$567$	9.45638e8			0.217863
$568$	−4.10075e8	−	7.10272e8i	−0.0938955	−	0.162632i
$569$	4.22095e9	−	7.31090e9i	0.960544	−	1.66371i	0.239406	−	0.970919i	$-0.423047\pi$
$569$	4.22095e9	−	7.31090e9i	0.960544	−	1.66371i	0.721138	−	0.692792i	$-0.243619\pi$
$570$	−1.94780e8	+	3.37368e8i	−0.0440536	+	0.0763031i
$571$	−8.49495e9			−1.90956			−0.954782	−	0.297307i	$-0.903912\pi$
$571$	−8.49495e9			−1.90956			−0.954782	+	0.297307i	$0.903912\pi$
$572$	3.45423e9	−	1.07132e9i	0.771731	−	0.239350i
$573$	2.57246e9			0.571226
$574$	−9.95382e8	+	1.72405e9i	−0.219684	+	0.380504i
$575$	1.27485e9	−	2.20811e9i	0.279655	−	0.484377i
$576$	1.53511e8	+	2.65889e8i	0.0334705	+	0.0579725i
$577$	−3.24606e9			−0.703462			−0.351731	−	0.936101i	$-0.614407\pi$
$577$	−3.24606e9			−0.703462			−0.351731	+	0.936101i	$0.614407\pi$
$578$	4.05706e7	+	7.02704e7i	0.00873905	+	0.0151365i
$579$	−2.20531e9	−	3.81970e9i	−0.472165	−	0.817814i
$580$	6.11213e8			0.130075
$581$	1.32044e9	+	2.28707e9i	0.279320	+	0.483796i
$582$	1.08538e9	−	1.87994e9i	0.228219	−	0.395287i
$583$	−6.62310e9	+	1.14715e10i	−1.38427	+	2.39763i
$584$	−7.12769e8			−0.148082
$585$	−3.70679e8	−	3.42878e8i	−0.0765512	−	0.0708099i
$586$	3.41338e9			0.700718
$587$	2.87126e9	−	4.97318e9i	0.585922	−	1.01485i	−0.408838	−	0.912607i	$-0.634066\pi$
$587$	2.87126e9	−	4.97318e9i	0.585922	−	1.01485i	0.994760	−	0.102240i	$-0.0326009\pi$
$588$	−4.22822e8	+	7.32350e8i	−0.0857704	+	0.148559i
$589$	−2.20223e8	−	3.81438e8i	−0.0444078	−	0.0769166i
$590$	−5.79294e8			−0.116123
$591$	−2.77040e9	−	4.79847e9i	−0.552059	−	0.956195i
$592$	−4.08976e6	−	7.08368e6i	−0.000810163	−	0.00140324i
$593$	−5.53884e9			−1.09076			−0.545378	−	0.838190i	$-0.683614\pi$
$593$	−5.53884e9			−1.09076			−0.545378	+	0.838190i	$0.683614\pi$
$594$	−3.05411e9	−	5.28987e9i	−0.597904	−	1.03560i
$595$	6.20919e8	−	1.07546e9i	0.120844	−	0.209308i
$596$	1.23284e9	−	2.13534e9i	0.238530	−	0.413147i
$597$	7.61761e8			0.146524
$598$	1.57810e9	+	1.45974e9i	0.301773	+	0.279140i
$599$	−5.75425e8			−0.109394			−0.0546971	−	0.998503i	$-0.517419\pi$
$599$	−5.75425e8			−0.109394			−0.0546971	+	0.998503i	$0.517419\pi$
$600$	−6.13264e8	+	1.06220e9i	−0.115909	+	0.200761i
$601$	−1.81762e9	+	3.14821e9i	−0.341541	+	0.591566i	−0.984719	−	0.174150i	$-0.944282\pi$
$601$	−1.81762e9	+	3.14821e9i	−0.341541	+	0.591566i	0.643178	+	0.765717i	$0.277615\pi$
$602$	2.39424e9	+	4.14695e9i	0.447281	+	0.774713i
$603$	3.31634e9			0.615953
$604$	−9.42679e8	−	1.63277e9i	−0.174074	−	0.301505i
$605$	8.54555e8	+	1.48013e9i	0.156890	+	0.271742i
$606$	2.69614e9			0.492140
$607$	−4.49966e8	−	7.79364e8i	−0.0816619	−	0.141443i	0.822302	−	0.569051i	$-0.192689\pi$
$607$	−4.49966e8	−	7.79364e8i	−0.0816619	−	0.141443i	−0.903964	+	0.427609i	$0.859356\pi$
$608$	4.59926e8	−	7.96616e8i	0.0829900	−	0.143743i
$609$	−3.11141e9	+	5.38913e9i	−0.558209	+	0.966847i
$610$	1.24816e9			0.222647
$611$	4.10258e9	−	1.27241e9i	0.727634	−	0.225674i
$612$	1.53703e9			0.271053
$613$	−9.74743e8	+	1.68830e9i	−0.170914	+	0.296032i	−0.938740	−	0.344627i	$-0.888005\pi$
$613$	−9.74743e8	+	1.68830e9i	−0.170914	+	0.296032i	0.767825	+	0.640659i	$0.221339\pi$
$614$	1.13369e9	−	1.96361e9i	0.197654	−	0.342347i
$615$	1.93970e8	+	3.35965e8i	0.0336257	+	0.0582414i
$616$	4.06410e9			0.700538
$617$	2.94732e9	+	5.10490e9i	0.505160	+	0.874962i	0.999982	+	0.00596820i	$0.00189975\pi$
$617$	2.94732e9	+	5.10490e9i	0.505160	+	0.874962i	−0.494822	+	0.868994i	$0.664767\pi$
$618$	3.84425e8	+	6.65844e8i	0.0655167	+	0.113478i
$619$	5.43625e9			0.921259			0.460630	−	0.887592i	$-0.347624\pi$
$619$	5.43625e9			0.921259			0.460630	+	0.887592i	$0.347624\pi$
$620$	2.73266e7	+	4.73310e7i	0.00460484	+	0.00797581i
$621$	1.81538e9	−	3.14434e9i	0.304192	−	0.526876i
$622$	−2.85695e9	+	4.94839e9i	−0.476033	+	0.824512i
$623$	−7.84626e9			−1.30003
$624$	−7.59138e8	−	7.02203e8i	−0.125076	−	0.115696i
$625$	5.41801e9			0.887687
$626$	−1.40794e9	+	2.43862e9i	−0.229389	+	0.397314i
$627$	−3.19122e9	+	5.52735e9i	−0.517035	+	0.895531i
$628$	−2.16720e9	−	3.75371e9i	−0.349173	−	0.604786i
$629$	−4.09488e7			−0.00656092
$630$	−2.83715e8	−	4.91408e8i	−0.0452054	−	0.0782980i
$631$	5.81666e8	+	1.00747e9i	0.0921660	+	0.159636i	0.908422	−	0.418054i	$-0.137288\pi$
$631$	5.81666e8	+	1.00747e9i	0.0921660	+	0.159636i	−0.816256	+	0.577690i	$0.803954\pi$
$632$	1.19555e9			0.188390
$633$	8.72901e8	+	1.51191e9i	0.136789	+	0.236926i
$634$	−1.82251e9	+	3.15668e9i	−0.284026	+	0.491947i
$635$	−1.10995e9	+	1.92249e9i	−0.172026	+	0.297959i
$636$	3.78759e9			0.583798
$637$	−7.25828e8	+	3.20280e9i	−0.111262	+	0.490955i
$638$	1.00140e10			1.52663
$639$	−9.38046e8	+	1.62474e9i	−0.142223	+	0.246338i
$640$	−5.70703e7	+	9.88487e7i	−0.00860559	+	0.0149053i
$641$	−1.31488e9	−	2.27743e9i	−0.197189	−	0.341541i	0.750427	−	0.660953i	$-0.229848\pi$
$641$	−1.31488e9	−	2.27743e9i	−0.197189	−	0.341541i	−0.947616	+	0.319412i	$0.896515\pi$
$642$	−5.81948e9			−0.867984
$643$	1.46295e9	+	2.53391e9i	0.217016	+	0.375883i	0.953894	−	0.300143i	$-0.0970343\pi$
$643$	1.46295e9	+	2.53391e9i	0.217016	+	0.375883i	−0.736878	+	0.676025i	$0.763701\pi$
$644$	1.20787e9	+	2.09209e9i	0.178204	+	0.308659i
$645$	9.33130e8			0.136925
$646$	−2.30251e9	−	3.98807e9i	−0.336038	−	0.582034i
$647$	6.86472e8	−	1.18900e9i	0.0996455	−	0.172591i	−0.811892	−	0.583807i	$-0.801562\pi$
$647$	6.86472e8	−	1.18900e9i	0.0996455	−	0.172591i	0.911538	+	0.411216i	$0.134896\pi$
$648$	−2.17562e8	+	3.76829e8i	−0.0314102	+	0.0544041i
$649$	−9.49100e9			−1.36287
$650$	−1.05274e9	+	4.64536e9i	−0.150358	+	0.663472i
$651$	−5.56430e8			−0.0790455
$652$	−3.18837e9	+	5.52242e9i	−0.450507	+	0.780302i
$653$	2.25639e9	−	3.90819e9i	0.317116	−	0.549262i	−0.662769	−	0.748824i	$-0.730619\pi$
$653$	2.25639e9	−	3.90819e9i	0.317116	−	0.549262i	0.979885	+	0.199563i	$0.0639521\pi$
$654$	5.81220e8	+	1.00670e9i	0.0812491	+	0.140728i
$655$	−2.23707e9			−0.311054
$656$	−4.58014e8	−	7.93304e8i	−0.0633454	−	0.109718i
$657$	8.15228e8	+	1.41202e9i	0.112150	+	0.194250i
$658$	4.82691e9			0.660509
$659$	2.70823e9	+	4.69079e9i	0.368626	+	0.638479i	0.989351	−	0.145549i	$-0.0464949\pi$
$659$	2.70823e9	+	4.69079e9i	0.368626	+	0.638479i	−0.620725	+	0.784028i	$0.713162\pi$
$660$	3.95985e8	−	6.85866e8i	0.0536136	−	0.0928614i
$661$	7.09561e8	−	1.22900e9i	0.0955618	−	0.165518i	−0.814281	−	0.580471i	$-0.802869\pi$
$661$	7.09561e8	−	1.22900e9i	0.0955618	−	0.165518i	0.909843	+	0.414953i	$0.136202\pi$
$662$	−5.32168e9			−0.712929
$663$	−4.94466e9	+	1.53357e9i	−0.658930	+	0.204365i
$664$	−1.21517e9			−0.161083
$665$	−8.50022e8	+	1.47228e9i	−0.112087	+	0.194140i
$666$	−9.35532e6	+	1.62039e7i	−0.00122715	+	0.00212549i
$667$	2.97619e9	+	5.15490e9i	0.388347	+	0.672636i
$668$	2.12238e9			0.275490
$669$	−4.33801e9	−	7.51366e9i	−0.560144	−	0.970198i
$670$	6.16451e8	+	1.06772e9i	0.0791839	+	0.137151i
$671$	2.04496e10			2.61310
$672$	−5.81039e8	−	1.00639e9i	−0.0738606	−	0.127930i
$673$	2.75030e9	−	4.76366e9i	0.347799	−	0.602405i	−0.638060	−	0.769987i	$-0.720263\pi$
$673$	2.75030e9	−	4.76366e9i	0.347799	−	0.602405i	0.985858	+	0.167582i	$0.0535960\pi$
$674$	3.68117e9	−	6.37597e9i	0.463101	−	0.802114i
$675$	8.04477e9			1.00682
$676$	−3.62356e9	−	1.73128e9i	−0.451151	−	0.215552i
$677$	−8.33416e9			−1.03229			−0.516145	−	0.856501i	$-0.672633\pi$
$677$	−8.33416e9			−1.03229			−0.516145	+	0.856501i	$0.672633\pi$
$678$	2.64304e9	−	4.57788e9i	0.325687	−	0.564106i
$679$	4.73663e9	−	8.20408e9i	0.580664	−	1.00574i
$680$	2.85709e8	+	4.94862e8i	0.0348452	+	0.0603536i
$681$	−1.43280e9			−0.173849
$682$	4.47711e8	+	7.75459e8i	0.0540447	+	0.0936081i
$683$	−7.46024e9	−	1.29215e10i	−0.895943	−	1.55182i	−0.832633	−	0.553825i	$-0.813168\pi$
$683$	−7.46024e9	−	1.29215e10i	−0.895943	−	1.55182i	−0.0633104	−	0.997994i	$-0.520166\pi$
$684$	−2.10416e9			−0.251410
$685$	4.00599e8	+	6.93857e8i	0.0476204	+	0.0824809i
$686$	1.82025e9	−	3.15276e9i	0.215276	−	0.372869i
$687$	−1.96743e9	+	3.40769e9i	−0.231500	+	0.400970i
$688$	−2.20337e9			−0.257945
$689$	1.40487e10	−	4.35717e9i	1.63632	−	0.507502i
$690$	4.70753e8			0.0545533
$691$	−2.44866e9	+	4.24121e9i	−0.282329	+	0.489009i	−0.971958	−	0.235154i	$-0.924440\pi$
$691$	−2.44866e9	+	4.24121e9i	−0.282329	+	0.489009i	0.689629	+	0.724163i	$0.257774\pi$
$692$	−1.36372e9	+	2.36203e9i	−0.156442	+	0.270965i
$693$	−4.64831e9	−	8.05111e9i	−0.530553	−	0.918944i
$694$	−1.09199e10			−1.24011
$695$	−1.54704e9	−	2.67956e9i	−0.174806	−	0.302773i
$696$	−1.43168e9	−	2.47975e9i	−0.160959	−	0.278789i
$697$	−4.58588e9			−0.512988
$698$	−3.58889e9	−	6.21615e9i	−0.399454	−	0.691874i
$699$	−2.01654e9	+	3.49275e9i	−0.223325	+	0.386810i
$700$	−2.67629e9	+	4.63548e9i	−0.294911	+	0.510800i
$701$	−2.20310e9			−0.241558			−0.120779	−	0.992679i	$-0.538539\pi$
$701$	−2.20310e9			−0.241558			−0.120779	+	0.992679i	$0.538539\pi$
$702$	−1.49910e9	+	6.61496e9i	−0.163550	+	0.721684i
$703$	5.60579e7			0.00608546
$704$	−9.35025e8	+	1.61951e9i	−0.100999	+	0.174936i
$705$	4.70309e8	−	8.14600e8i	0.0505501	−	0.0875553i
$706$	−1.07842e9	−	1.86788e9i	−0.115338	−	0.199771i
$707$	1.17660e10			1.25216
$708$	1.35692e9	+	2.35025e9i	0.143693	+	0.248884i
$709$	−4.34938e9	−	7.53334e9i	−0.458316	−	0.793827i	0.540556	−	0.841308i	$-0.318214\pi$
$709$	−4.34938e9	−	7.53334e9i	−0.458316	−	0.793827i	−0.998872	+	0.0474812i	$0.984881\pi$
$710$	−6.97468e8			−0.0731341
$711$	−1.36741e9	−	2.36842e9i	−0.142677	−	0.247124i
$712$	1.80519e9	−	3.12667e9i	0.187431	−	0.324640i
$713$	−2.66123e8	+	4.60939e8i	−0.0274960	+	0.0476244i
$714$	−5.81767e9			−0.598143
$715$	6.79757e8	−	2.99951e9i	0.0695477	−	0.306887i
$716$	−1.29701e9			−0.132053
$717$	−1.28274e8	+	2.22177e8i	−0.0129964	+	0.0225104i
$718$	−8.95711e8	+	1.55142e9i	−0.0903093	+	0.156420i
$719$	5.46812e8	+	9.47107e8i	0.0548640	+	0.0950272i	0.892153	−	0.451733i	$-0.149194\pi$
$719$	5.46812e8	+	9.47107e8i	0.0548640	+	0.0950272i	−0.837289	+	0.546761i	$0.815861\pi$
$720$	2.61096e8			0.0260698
$721$	1.67764e9	+	2.90576e9i	0.166696	+	0.288726i
$722$	−4.23409e8	−	7.33367e8i	−0.0418678	−	0.0725172i
$723$	−1.23527e10			−1.21556
$724$	9.88975e8	+	1.71296e9i	0.0968502	+	0.167749i
$725$	−6.59439e9	+	1.14218e10i	−0.642676	+	1.11315i
$726$	4.00335e9	−	6.93401e9i	0.388281	−	0.672522i
$727$	9.47790e9			0.914832			0.457416	−	0.889253i	$-0.348775\pi$
$727$	9.47790e9			0.914832			0.457416	+	0.889253i	$0.348775\pi$
$728$	−3.31289e9	−	3.06443e9i	−0.318235	−	0.294367i
$729$	8.45578e9			0.808365
$730$	−3.03074e8	+	5.24940e8i	−0.0288350	+	0.0499436i
$731$	−5.51532e9	+	9.55281e9i	−0.522227	+	0.904524i
$732$	−2.92365e9	−	5.06391e9i	−0.275509	−	0.477196i
$733$	5.75895e9			0.540107			0.270053	−	0.962845i	$-0.412959\pi$
$733$	5.75895e9			0.540107			0.270053	+	0.962845i	$0.412959\pi$
$734$	−1.12343e9	−	1.94583e9i	−0.104860	−	0.181622i
$735$	3.59574e8	+	6.22801e8i	0.0334028	+	0.0578553i
$736$	−1.11157e9			−0.102770
$737$	1.00998e10	+	1.74933e10i	0.929341	+	1.60967i
$738$	−1.04771e9	+	1.81468e9i	−0.0959493	+	0.166189i
$739$	−3.55253e9	+	6.15316e9i	−0.323804	+	0.560845i	−0.981270	−	0.192640i	$-0.938295\pi$
$739$	−3.55253e9	+	6.15316e9i	−0.323804	+	0.560845i	0.657466	+	0.753485i	$0.271628\pi$
$740$	−6.95599e6			−0.000631027
$741$	6.76911e9	−	2.09942e9i	0.611178	−	0.189555i
$742$	1.65291e10			1.48537
$743$	4.92054e9	−	8.52263e9i	0.440101	−	0.762277i	−0.557596	−	0.830113i	$-0.688276\pi$
$743$	4.92054e9	−	8.52263e9i	0.440101	−	0.762277i	0.997697	+	0.0678357i	$0.0216094\pi$
$744$	1.28017e8	−	2.21733e8i	0.0113963	−	0.0197390i
$745$	−1.04842e9	−	1.81592e9i	−0.0928943	−	0.160898i
$746$	−1.40420e10			−1.23834
$747$	1.38985e9	+	2.40729e9i	0.121996	+	0.211303i
$748$	4.68098e9	+	8.10769e9i	0.408960	+	0.708340i
$749$	−2.53963e10			−2.20843
$750$	1.06361e9	+	1.84223e9i	0.0920594	+	0.159452i
$751$	−6.46148e9	+	1.11916e10i	−0.556663	+	0.964169i	0.441109	+	0.897454i	$0.354585\pi$
$751$	−6.46148e9	+	1.11916e10i	−0.556663	+	0.964169i	−0.997772	+	0.0667151i	$0.978748\pi$
$752$	−1.11053e9	+	1.92349e9i	−0.0952283	+	0.164940i
$753$	2.36000e9			0.201432
$754$	−8.16298e9	−	7.55076e9i	−0.693504	−	0.641492i
$755$	−1.60333e9			−0.135584
$756$	−3.81103e9	+	6.60089e9i	−0.320786	+	0.555618i
$757$	7.59753e9	−	1.31593e10i	0.636556	−	1.10255i	−0.349627	−	0.936889i	$-0.613692\pi$
$757$	7.59753e9	−	1.31593e10i	0.636556	−	1.10255i	0.986183	−	0.165659i	$-0.0529750\pi$
$758$	1.43693e9	+	2.48884e9i	0.119838	+	0.207565i

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)

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(-15.9358 + 27.6017i) q^{3} +(-32.0000 - 55.4256i) q^{4} -54.4265 q^{5} +(127.487 + 220.813i) q^{6} +(556.354 + 963.633i) q^{7} -512.000 q^{8} +(585.599 + 1014.29i) q^{9} +O(q^{10})\)	\(q+(4.00000 - 6.92820i) q^{2} +(-15.9358 + 27.6017i) q^{3} +(-32.0000 - 55.4256i) q^{4} -54.4265 q^{5} +(127.487 + 220.813i) q^{6} +(556.354 + 963.633i) q^{7} -512.000 q^{8} +(585.599 + 1014.29i) q^{9} +(-217.706 + 377.078i) q^{10} +(-3566.84 + 6177.94i) q^{11} +2039.79 q^{12} +(7565.86 - 2346.53i) q^{13} +8901.66 q^{14} +(867.331 - 1502.26i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(10252.8 + 17758.4i) q^{17} +9369.59 q^{18} +(-14035.8 - 24310.8i) q^{19} +(1741.65 + 3016.62i) q^{20} -35463.8 q^{21} +(28534.7 + 49423.6i) q^{22} +(-16961.2 + 29377.7i) q^{23} +(8159.14 - 14132.0i) q^{24} -75162.8 q^{25} +(14006.2 - 61804.0i) q^{26} -107031. q^{27} +(35606.6 - 61672.5i) q^{28} +(87734.9 - 151961. i) q^{29} +(-6938.65 - 12018.1i) q^{30} +15690.1 q^{31} +(16384.0 + 28377.9i) q^{32} +(-113681. - 196901. i) q^{33} +164045. q^{34} +(-30280.4 - 52447.2i) q^{35} +(37478.3 - 64914.4i) q^{36} +(-998.478 + 1729.41i) q^{37} -224573. q^{38} +(-55800.0 + 246224. i) q^{39} +27866.4 q^{40} +(-111820. + 193678. i) q^{41} +(-141855. + 245701. i) q^{42} +(268966. + 465862. i) q^{43} +456555. q^{44} +(-31872.1 - 55204.1i) q^{45} +(135690. + 235022. i) q^{46} +542249. q^{47} +(-65273.1 - 113056. i) q^{48} +(-207288. + 359033. i) q^{49} +(-300651. + 520743. i) q^{50} -653549. q^{51} +(-372166. - 344254. i) q^{52} +1.85685e6 q^{53} +(-428125. + 741535. i) q^{54} +(194131. - 336244. i) q^{55} +(-284853. - 493380. i) q^{56} +894691. q^{57} +(-701879. - 1.21569e6i) q^{58} +(665225. + 1.15220e6i) q^{59} -111018. q^{60} +(-1.43331e6 - 2.48257e6i) q^{61} +(62760.3 - 108704. i) q^{62} +(-651601. + 1.12861e6i) q^{63} +262144. q^{64} +(-411784. + 127714. i) q^{65} -1.81890e6 q^{66} +(1.41579e6 - 2.45222e6i) q^{67} +(656181. - 1.13654e6i) q^{68} +(-540583. - 936317. i) q^{69} -484486. q^{70} +(800929. + 1.38725e6i) q^{71} +(-299827. - 519315. i) q^{72} +1.39213e6 q^{73} +(7987.82 + 13835.3i) q^{74} +(1.19778e6 - 2.07462e6i) q^{75} +(-898294. + 1.55589e6i) q^{76} -7.93770e6 q^{77} +(1.48269e6 + 1.37149e6i) q^{78} -2.33505e6 q^{79} +(111466. - 193064. i) q^{80} +(424927. - 735994. i) q^{81} +(894559. + 1.54942e6i) q^{82} +2.37338e6 q^{83} +(1.13484e6 + 1.96560e6i) q^{84} +(-558025. - 966528. i) q^{85} +4.30345e6 q^{86} +(2.79625e6 + 4.84325e6i) q^{87} +(1.82622e6 - 3.16311e6i) q^{88} +(-3.52575e6 + 6.10678e6i) q^{89} -509954. q^{90} +(6.47050e6 + 5.98521e6i) q^{91} +2.17104e6 q^{92} +(-250034. + 433072. i) q^{93} +(2.16899e6 - 3.75681e6i) q^{94} +(763922. + 1.32315e6i) q^{95} -1.04437e6 q^{96} +(-4.25685e6 - 7.37308e6i) q^{97} +(1.65830e6 + 2.87226e6i) q^{98} -8.35495e6 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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