LMFDB - Embedded newform 162.6.c.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,6,Mod(55,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("162.55");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not 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:	$25.9821788097$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.109
Dual form			162.6.c.a.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(-48.0000 + 83.1384i) q^{5} +(74.0000 + 128.172i) q^{7} +64.0000 q^{8} +O(q^{10})$	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(-48.0000 + 83.1384i) q^{5} +(74.0000 + 128.172i) q^{7} +64.0000 q^{8} +384.000 q^{10} +(192.000 + 332.554i) q^{11} +(167.000 - 289.252i) q^{13} +(296.000 - 512.687i) q^{14} +(-128.000 - 221.703i) q^{16} -576.000 q^{17} -664.000 q^{19} +(-768.000 - 1330.22i) q^{20} +(768.000 - 1330.22i) q^{22} +(-1920.00 + 3325.54i) q^{23} +(-3045.50 - 5274.96i) q^{25} -1336.00 q^{26} -2368.00 q^{28} +(48.0000 + 83.1384i) q^{29} +(2282.00 - 3952.54i) q^{31} +(-512.000 + 886.810i) q^{32} +(1152.00 + 1995.32i) q^{34} -14208.0 q^{35} +5798.00 q^{37} +(1328.00 + 2300.16i) q^{38} +(-3072.00 + 5320.86i) q^{40} +(-3360.00 + 5819.69i) q^{41} +(7436.00 + 12879.5i) q^{43} -6144.00 q^{44} +15360.0 q^{46} +(-9600.00 - 16627.7i) q^{47} +(-2548.50 + 4414.13i) q^{49} +(-12182.0 + 21099.8i) q^{50} +(2672.00 + 4628.04i) q^{52} -7776.00 q^{53} -36864.0 q^{55} +(4736.00 + 8202.99i) q^{56} +(192.000 - 332.554i) q^{58} +(-6528.00 + 11306.8i) q^{59} +(-21391.0 - 37050.3i) q^{61} -18256.0 q^{62} +4096.00 q^{64} +(16032.0 + 27768.2i) q^{65} +(-18328.0 + 31745.0i) q^{67} +(4608.00 - 7981.29i) q^{68} +(28416.0 + 49218.0i) q^{70} -64512.0 q^{71} -16810.0 q^{73} +(-11596.0 - 20084.9i) q^{74} +(5312.00 - 9200.65i) q^{76} +(-28416.0 + 49218.0i) q^{77} +(-14038.0 - 24314.5i) q^{79} +24576.0 q^{80} +26880.0 q^{82} +(-33216.0 - 57531.8i) q^{83} +(27648.0 - 47887.7i) q^{85} +(29744.0 - 51518.1i) q^{86} +(12288.0 + 21283.4i) q^{88} +81792.0 q^{89} +49432.0 q^{91} +(-30720.0 - 53208.6i) q^{92} +(-38400.0 + 66510.8i) q^{94} +(31872.0 - 55203.9i) q^{95} +(14969.0 + 25927.1i) q^{97} +20388.0 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 16 q^{4} - 96 q^{5} + 148 q^{7} + 128 q^{8}+O(q^{10}) $ 2 * q - 4 * q^2 - 16 * q^4 - 96 * q^5 + 148 * q^7 + 128 * q^8	$ 2 q - 4 q^{2} - 16 q^{4} - 96 q^{5} + 148 q^{7} + 128 q^{8} + 768 q^{10} + 384 q^{11} + 334 q^{13} + 592 q^{14} - 256 q^{16} - 1152 q^{17} - 1328 q^{19} - 1536 q^{20} + 1536 q^{22} - 3840 q^{23} - 6091 q^{25} - 2672 q^{26} - 4736 q^{28} + 96 q^{29} + 4564 q^{31} - 1024 q^{32} + 2304 q^{34} - 28416 q^{35} + 11596 q^{37} + 2656 q^{38} - 6144 q^{40} - 6720 q^{41} + 14872 q^{43} - 12288 q^{44} + 30720 q^{46} - 19200 q^{47} - 5097 q^{49} - 24364 q^{50} + 5344 q^{52} - 15552 q^{53} - 73728 q^{55} + 9472 q^{56} + 384 q^{58} - 13056 q^{59} - 42782 q^{61} - 36512 q^{62} + 8192 q^{64} + 32064 q^{65} - 36656 q^{67} + 9216 q^{68} + 56832 q^{70} - 129024 q^{71} - 33620 q^{73} - 23192 q^{74} + 10624 q^{76} - 56832 q^{77} - 28076 q^{79} + 49152 q^{80} + 53760 q^{82} - 66432 q^{83} + 55296 q^{85} + 59488 q^{86} + 24576 q^{88} + 163584 q^{89} + 98864 q^{91} - 61440 q^{92} - 76800 q^{94} + 63744 q^{95} + 29938 q^{97} + 40776 q^{98}+O(q^{100}) $ 2 * q - 4 * q^2 - 16 * q^4 - 96 * q^5 + 148 * q^7 + 128 * q^8 + 768 * q^10 + 384 * q^11 + 334 * q^13 + 592 * q^14 - 256 * q^16 - 1152 * q^17 - 1328 * q^19 - 1536 * q^20 + 1536 * q^22 - 3840 * q^23 - 6091 * q^25 - 2672 * q^26 - 4736 * q^28 + 96 * q^29 + 4564 * q^31 - 1024 * q^32 + 2304 * q^34 - 28416 * q^35 + 11596 * q^37 + 2656 * q^38 - 6144 * q^40 - 6720 * q^41 + 14872 * q^43 - 12288 * q^44 + 30720 * q^46 - 19200 * q^47 - 5097 * q^49 - 24364 * q^50 + 5344 * q^52 - 15552 * q^53 - 73728 * q^55 + 9472 * q^56 + 384 * q^58 - 13056 * q^59 - 42782 * q^61 - 36512 * q^62 + 8192 * q^64 + 32064 * q^65 - 36656 * q^67 + 9216 * q^68 + 56832 * q^70 - 129024 * q^71 - 33620 * q^73 - 23192 * q^74 + 10624 * q^76 - 56832 * q^77 - 28076 * q^79 + 49152 * q^80 + 53760 * q^82 - 66432 * q^83 + 55296 * q^85 + 59488 * q^86 + 24576 * q^88 + 163584 * q^89 + 98864 * q^91 - 61440 * q^92 - 76800 * q^94 + 63744 * q^95 + 29938 * q^97 + 40776 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−48.0000	+	83.1384i	−0.858650	+	1.48723i	0.0145668	+	0.999894i	$0.495363\pi$
$5$	−48.0000	+	83.1384i	−0.858650	+	1.48723i	−0.873217	+	0.487332i	$0.837970\pi$
$6$		0			0
$7$	74.0000	+	128.172i	0.570803	+	0.988661i	0.996484	+	0.0837870i	$0.0267015\pi$
$7$	74.0000	+	128.172i	0.570803	+	0.988661i	−0.425680	+	0.904874i	$0.639965\pi$
$8$	64.0000			0.353553
$9$		0			0
$10$	384.000			1.21431
$11$	192.000	+	332.554i	0.478431	+	0.828667i	0.999694	−	0.0247289i	$-0.00787226\pi$
$11$	192.000	+	332.554i	0.478431	+	0.828667i	−0.521263	+	0.853396i	$0.674539\pi$
$12$		0			0
$13$	167.000	−	289.252i	0.274068	−	0.474699i	−0.695832	−	0.718205i	$-0.744964\pi$
$13$	167.000	−	289.252i	0.274068	−	0.474699i	0.969900	+	0.243505i	$0.0782974\pi$
$14$	296.000	−	512.687i	0.403619	−	0.699089i
$15$		0			0
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−576.000			−0.483393			−0.241696	−	0.970352i	$-0.577704\pi$
$17$	−576.000			−0.483393			−0.241696	+	0.970352i	$0.577704\pi$
$18$		0			0
$19$	−664.000			−0.421972			−0.210986	−	0.977489i	$-0.567668\pi$
$19$	−664.000			−0.421972			−0.210986	+	0.977489i	$0.567668\pi$
$20$	−768.000	−	1330.22i	−0.429325	−	0.743613i
$21$		0			0
$22$	768.000	−	1330.22i	0.338302	−	0.585956i
$23$	−1920.00	+	3325.54i	−0.756801	+	1.31082i	0.187673	+	0.982232i	$0.439905\pi$
$23$	−1920.00	+	3325.54i	−0.756801	+	1.31082i	−0.944474	+	0.328586i	$0.893428\pi$
$24$		0			0
$25$	−3045.50	−	5274.96i	−0.974560	−	1.68799i
$26$	−1336.00			−0.387590
$27$		0			0
$28$	−2368.00			−0.570803
$29$	48.0000	+	83.1384i	0.0105985	+	0.0183572i	0.871276	−	0.490793i	$-0.163293\pi$
$29$	48.0000	+	83.1384i	0.0105985	+	0.0183572i	−0.860677	+	0.509151i	$0.829960\pi$
$30$		0			0
$31$	2282.00	−	3952.54i	0.426493	−	0.738707i	−0.570066	−	0.821599i	$-0.693082\pi$
$31$	2282.00	−	3952.54i	0.426493	−	0.738707i	0.996559	+	0.0828922i	$0.0264157\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$		0			0
$34$	1152.00	+	1995.32i	0.170905	+	0.296016i
$35$	−14208.0			−1.96048
$36$		0			0
$37$	5798.00			0.696264			0.348132	−	0.937446i	$-0.386816\pi$
$37$	5798.00			0.696264			0.348132	+	0.937446i	$0.386816\pi$
$38$	1328.00	+	2300.16i	0.149190	+	0.258404i
$39$		0			0
$40$	−3072.00	+	5320.86i	−0.303579	+	0.525814i
$41$	−3360.00	+	5819.69i	−0.312162	+	0.540680i	−0.978830	−	0.204675i	$-0.934386\pi$
$41$	−3360.00	+	5819.69i	−0.312162	+	0.540680i	0.666668	+	0.745354i	$0.267720\pi$
$42$		0			0
$43$	7436.00	+	12879.5i	0.613293	+	1.06226i	0.990681	+	0.136200i	$0.0434890\pi$
$43$	7436.00	+	12879.5i	0.613293	+	1.06226i	−0.377388	+	0.926055i	$0.623178\pi$
$44$	−6144.00			−0.478431
$45$		0			0
$46$	15360.0			1.07028
$47$	−9600.00	−	16627.7i	−0.633909	−	1.09796i	−0.986745	−	0.162277i	$-0.948116\pi$
$47$	−9600.00	−	16627.7i	−0.633909	−	1.09796i	0.352837	−	0.935685i	$-0.385217\pi$
$48$		0			0
$49$	−2548.50	+	4414.13i	−0.151633	+	0.262636i
$50$	−12182.0	+	21099.8i	−0.689118	+	1.19359i
$51$		0			0
$52$	2672.00	+	4628.04i	0.137034	+	0.237350i
$53$	−7776.00			−0.380248			−0.190124	−	0.981760i	$-0.560889\pi$
$53$	−7776.00			−0.380248			−0.190124	+	0.981760i	$0.560889\pi$
$54$		0			0
$55$	−36864.0			−1.64322
$56$	4736.00	+	8202.99i	0.201810	+	0.349544i
$57$		0			0
$58$	192.000	−	332.554i	0.00749430	−	0.0129805i
$59$	−6528.00	+	11306.8i	−0.244146	+	0.422874i	−0.961891	−	0.273432i	$-0.911841\pi$
$59$	−6528.00	+	11306.8i	−0.244146	+	0.422874i	0.717745	+	0.696306i	$0.245174\pi$
$60$		0			0
$61$	−21391.0	−	37050.3i	−0.736049	−	1.27487i	−0.954262	−	0.298972i	$-0.903356\pi$
$61$	−21391.0	−	37050.3i	−0.736049	−	1.27487i	0.218213	−	0.975901i	$-0.429977\pi$
$62$	−18256.0			−0.603151
$63$		0			0
$64$	4096.00			0.125000
$65$	16032.0	+	27768.2i	0.470657	+	0.815201i
$66$		0			0
$67$	−18328.0	+	31745.0i	−0.498802	+	0.863950i	−0.999999	−	0.00138293i	$-0.999560\pi$
$67$	−18328.0	+	31745.0i	−0.498802	+	0.863950i	0.501197	+	0.865333i	$0.332893\pi$
$68$	4608.00	−	7981.29i	0.120848	−	0.209315i
$69$		0			0
$70$	28416.0	+	49218.0i	0.693135	+	1.20055i
$71$	−64512.0			−1.51878			−0.759390	−	0.650636i	$-0.774502\pi$
$71$	−64512.0			−1.51878			−0.759390	+	0.650636i	$0.774502\pi$
$72$		0			0
$73$	−16810.0			−0.369199			−0.184600	−	0.982814i	$-0.559099\pi$
$73$	−16810.0			−0.369199			−0.184600	+	0.982814i	$0.559099\pi$
$74$	−11596.0	−	20084.9i	−0.246166	−	0.426373i
$75$		0			0
$76$	5312.00	−	9200.65i	0.105493	−	0.182719i
$77$	−28416.0	+	49218.0i	−0.546180	+	0.946012i
$78$		0			0
$79$	−14038.0	−	24314.5i	−0.253068	−	0.438327i	0.711301	−	0.702888i	$-0.248106\pi$
$79$	−14038.0	−	24314.5i	−0.253068	−	0.438327i	−0.964369	+	0.264561i	$0.914773\pi$
$80$	24576.0			0.429325
$81$		0			0
$82$	26880.0			0.441463
$83$	−33216.0	−	57531.8i	−0.529239	−	0.916669i	−0.999418	−	0.0340984i	$-0.989144\pi$
$83$	−33216.0	−	57531.8i	−0.529239	−	0.916669i	0.470179	−	0.882571i	$-0.344189\pi$
$84$		0			0
$85$	27648.0	−	47887.7i	0.415065	−	0.718914i
$86$	29744.0	−	51518.1i	0.433664	−	0.751128i
$87$		0			0
$88$	12288.0	+	21283.4i	0.169151	+	0.292978i
$89$	81792.0			1.09455			0.547275	−	0.836953i	$-0.315665\pi$
$89$	81792.0			1.09455			0.547275	+	0.836953i	$0.315665\pi$
$90$		0			0
$91$	49432.0			0.625756
$92$	−30720.0	−	53208.6i	−0.378400	−	0.655409i
$93$		0			0
$94$	−38400.0	+	66510.8i	−0.448241	+	0.776376i
$95$	31872.0	−	55203.9i	0.362327	−	0.627568i
$96$		0			0
$97$	14969.0	+	25927.1i	0.161534	+	0.279785i	0.935419	−	0.353541i	$-0.115023\pi$
$97$	14969.0	+	25927.1i	0.161534	+	0.279785i	−0.773885	+	0.633326i	$0.781689\pi$
$98$	20388.0			0.214442
$99$		0			0
$100$	97456.0			0.974560
$101$	89328.0	+	154721.i	0.871333	+	1.50919i	0.860618	+	0.509250i	$0.170077\pi$
$101$	89328.0	+	154721.i	0.871333	+	1.50919i	0.0107147	+	0.999943i	$0.496589\pi$
$102$		0			0
$103$	57614.0	−	99790.4i	0.535100	−	0.926820i	−0.464058	−	0.885805i	$-0.653607\pi$
$103$	57614.0	−	99790.4i	0.535100	−	0.926820i	0.999158	−	0.0410159i	$-0.0130594\pi$
$104$	10688.0	−	18512.2i	0.0968976	−	0.167832i
$105$		0			0
$106$	15552.0	+	26936.9i	0.134438	+	0.232853i
$107$	76032.0			0.642003			0.321001	−	0.947079i	$-0.395981\pi$
$107$	76032.0			0.642003			0.321001	+	0.947079i	$0.395981\pi$
$108$		0			0
$109$	−231118.			−1.86323			−0.931617	−	0.363441i	$-0.881602\pi$
$109$	−231118.			−1.86323			−0.931617	+	0.363441i	$0.881602\pi$
$110$	73728.0	+	127701.i	0.580966	+	1.00626i
$111$		0			0
$112$	18944.0	−	32812.0i	0.142701	−	0.247165i
$113$	71232.0	−	123377.i	0.524782	−	0.908949i	−0.474801	−	0.880093i	$-0.657480\pi$
$113$	71232.0	−	123377.i	0.524782	−	0.908949i	0.999584	−	0.0288564i	$-0.00918654\pi$
$114$		0			0
$115$	−184320.	−	319252.i	−1.29965	−	2.25107i
$116$	−1536.00			−0.0105985
$117$		0			0
$118$	52224.0			0.345275
$119$	−42624.0	−	73826.9i	−0.275922	−	0.477911i
$120$		0			0
$121$	6797.50	−	11773.6i	0.0422071	−	0.0731049i
$122$	−85564.0	+	148201.i	−0.520465	+	0.901472i
$123$		0			0
$124$	36512.0	+	63240.6i	0.213246	+	0.369353i
$125$	284736.			1.62992
$126$		0			0
$127$	−988.000			−0.00543560			−0.00271780	−	0.999996i	$-0.500865\pi$
$127$	−988.000			−0.00543560			−0.00271780	+	0.999996i	$0.500865\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	64128.0	−	111073.i	0.332805	−	0.576434i
$131$	112128.	−	194211.i	0.570868	−	0.988773i	−0.425609	−	0.904907i	$-0.639940\pi$
$131$	112128.	−	194211.i	0.570868	−	0.988773i	0.996477	−	0.0838655i	$-0.0267266\pi$
$132$		0			0
$133$	−49136.0	−	85106.0i	−0.240863	−	0.417188i
$134$	146624.			0.705412
$135$		0			0
$136$	−36864.0			−0.170905
$137$	−139488.	−	241600.i	−0.634944	−	1.09976i	−0.986527	−	0.163599i	$-0.947690\pi$
$137$	−139488.	−	241600.i	−0.634944	−	1.09976i	0.351583	−	0.936157i	$-0.385644\pi$
$138$		0			0
$139$	−88600.0	+	153460.i	−0.388953	+	0.673686i	−0.992309	−	0.123786i	$-0.960496\pi$
$139$	−88600.0	+	153460.i	−0.388953	+	0.673686i	0.603356	+	0.797472i	$0.293830\pi$
$140$	113664.	−	196872.i	0.490120	−	0.848914i
$141$		0			0
$142$	129024.	+	223476.i	0.536970	+	0.930059i
$143$	128256.			0.524490
$144$		0			0
$145$	−9216.00			−0.0364018
$146$	33620.0	+	58231.5i	0.130532	+	0.226087i
$147$		0			0
$148$	−46384.0	+	80339.4i	−0.174066	+	0.301491i
$149$	118032.	−	204437.i	0.435546	−	0.754388i	−0.561794	−	0.827277i	$-0.689889\pi$
$149$	118032.	−	204437.i	0.435546	−	0.754388i	0.997340	+	0.0728893i	$0.0232220\pi$
$150$		0			0
$151$	241418.	+	418148.i	0.861643	+	1.49241i	0.870342	+	0.492447i	$0.163897\pi$
$151$	241418.	+	418148.i	0.861643	+	1.49241i	−0.00869960	+	0.999962i	$0.502769\pi$
$152$	−42496.0			−0.149190
$153$		0			0
$154$	227328.			0.772416
$155$	219072.	+	379444.i	0.732416	+	1.26858i
$156$		0			0
$157$	−190543.	+	330030.i	−0.616941	+	1.06857i	0.373099	+	0.927791i	$0.378295\pi$
$157$	−190543.	+	330030.i	−0.616941	+	1.06857i	−0.990041	+	0.140782i	$0.955038\pi$
$158$	−56152.0	+	97258.1i	−0.178946	+	0.309944i
$159$		0			0
$160$	−49152.0	−	85133.8i	−0.151789	−	0.262907i
$161$	−568320.			−1.72794
$162$		0			0
$163$	162920.			0.480292			0.240146	−	0.970737i	$-0.422805\pi$
$163$	162920.			0.480292			0.240146	+	0.970737i	$0.422805\pi$
$164$	−53760.0	−	93115.1i	−0.156081	−	0.270340i
$165$		0			0
$166$	−132864.	+	230127.i	−0.374229	+	0.648183i
$167$	−283008.	+	490184.i	−0.785249	+	1.36009i	0.143601	+	0.989636i	$0.454132\pi$
$167$	−283008.	+	490184.i	−0.785249	+	1.36009i	−0.928850	+	0.370456i	$0.879201\pi$
$168$		0			0
$169$	129868.	+	224939.i	0.349774	+	0.605826i
$170$	−221184.			−0.586991
$171$		0			0
$172$	−237952.			−0.613293
$173$	−109104.	−	188974.i	−0.277157	−	0.480050i	0.693520	−	0.720437i	$-0.256059\pi$
$173$	−109104.	−	188974.i	−0.277157	−	0.480050i	−0.970677	+	0.240388i	$0.922725\pi$
$174$		0			0
$175$	450734.	−	780694.i	1.11256	−	1.92702i
$176$	49152.0	−	85133.8i	0.119608	−	0.207167i
$177$		0			0
$178$	−163584.	−	283336.i	−0.386982	−	0.670273i
$179$	412416.			0.962062			0.481031	−	0.876704i	$-0.340262\pi$
$179$	412416.			0.962062			0.481031	+	0.876704i	$0.340262\pi$
$180$		0			0
$181$	−25558.0			−0.0579870			−0.0289935	−	0.999580i	$-0.509230\pi$
$181$	−25558.0			−0.0579870			−0.0289935	+	0.999580i	$0.509230\pi$
$182$	−98864.0	−	171237.i	−0.221238	−	0.383195i
$183$		0			0
$184$	−122880.	+	212834.i	−0.267570	+	0.463444i
$185$	−278304.	+	482037.i	−0.597847	+	1.03550i
$186$		0			0
$187$	−110592.	−	191551.i	−0.231270	−	0.400572i
$188$	307200.			0.633909
$189$		0			0
$190$	−254976.			−0.512407
$191$	200064.	+	346521.i	0.396813	+	0.687300i	0.993331	−	0.115300i	$-0.0367829\pi$
$191$	200064.	+	346521.i	0.396813	+	0.687300i	−0.596518	+	0.802600i	$0.703450\pi$
$192$		0			0
$193$	−349825.	+	605915.i	−0.676017	+	1.17090i	0.300154	+	0.953891i	$0.402962\pi$
$193$	−349825.	+	605915.i	−0.676017	+	1.17090i	−0.976171	+	0.217005i	$0.930371\pi$
$194$	59876.0	−	103708.i	0.114222	−	0.197838i
$195$		0			0
$196$	−40776.0	−	70626.1i	−0.0758166	−	0.131318i
$197$	−406368.			−0.746026			−0.373013	−	0.927826i	$-0.621675\pi$
$197$	−406368.			−0.746026			−0.373013	+	0.927826i	$0.621675\pi$
$198$		0			0
$199$	−361996.			−0.647994			−0.323997	−	0.946058i	$-0.605027\pi$
$199$	−361996.			−0.647994			−0.323997	+	0.946058i	$0.605027\pi$
$200$	−194912.	−	337597.i	−0.344559	−	0.596794i
$201$		0			0
$202$	357312.	−	618883.i	0.616125	−	1.06716i
$203$	−7104.00	+	12304.5i	−0.0120994	+	0.0209567i
$204$		0			0
$205$	−322560.	−	558690.i	−0.536075	−	0.928510i
$206$	−460912.			−0.756746
$207$		0			0
$208$	−85504.0			−0.137034
$209$	−127488.	−	220816.i	−0.201885	−	0.349675i
$210$		0			0
$211$	−75928.0	+	131511.i	−0.117407	+	0.203356i	−0.918740	−	0.394864i	$-0.870792\pi$
$211$	−75928.0	+	131511.i	−0.117407	+	0.203356i	0.801332	+	0.598220i	$0.204125\pi$
$212$	62208.0	−	107747.i	0.0950619	−	0.164652i
$213$		0			0
$214$	−152064.	−	263383.i	−0.226982	−	0.393145i
$215$	−1.42771e6			−2.10642
$216$		0			0
$217$	675472.			0.973774
$218$	462236.	+	800616.i	0.658753	+	1.14099i
$219$		0			0
$220$	294912.	−	510803.i	0.410805	−	0.711535i
$221$	−96192.0	+	166609.i	−0.132482	+	0.229466i
$222$		0			0
$223$	546662.	+	946846.i	0.736134	+	1.27502i	0.954224	+	0.299092i	$0.0966839\pi$
$223$	546662.	+	946846.i	0.736134	+	1.27502i	−0.218090	+	0.975929i	$0.569983\pi$
$224$	−151552.			−0.201810
$225$		0			0
$226$	−569856.			−0.742154
$227$	−283200.	−	490517.i	−0.364778	−	0.631814i	0.623963	−	0.781454i	$-0.285522\pi$
$227$	−283200.	−	490517.i	−0.364778	−	0.631814i	−0.988741	+	0.149640i	$0.952188\pi$
$228$		0			0
$229$	293603.	−	508535.i	0.369974	−	0.640815i	−0.619587	−	0.784928i	$-0.712700\pi$
$229$	293603.	−	508535.i	0.369974	−	0.640815i	0.989561	+	0.144114i	$0.0460331\pi$
$230$	−737280.	+	1.27701e6i	−0.918994	+	1.59174i
$231$		0			0
$232$	3072.00	+	5320.86i	0.00374715	+	0.00649026i
$233$	−579456.			−0.699247			−0.349624	−	0.936890i	$-0.613691\pi$
$233$	−579456.			−0.699247			−0.349624	+	0.936890i	$0.613691\pi$
$234$		0			0
$235$	1.84320e6			2.17722
$236$	−104448.	−	180909.i	−0.122073	−	0.211437i
$237$		0			0
$238$	−170496.	+	295308.i	−0.195107	+	0.337934i
$239$	−292224.	+	506147.i	−0.330919	+	0.573168i	−0.982692	−	0.185246i	$-0.940692\pi$
$239$	−292224.	+	506147.i	−0.330919	+	0.573168i	0.651774	+	0.758414i	$0.274025\pi$
$240$		0			0
$241$	207065.	+	358647.i	0.229649	+	0.397763i	0.957704	−	0.287755i	$-0.0929089\pi$
$241$	207065.	+	358647.i	0.229649	+	0.397763i	−0.728055	+	0.685518i	$0.759576\pi$
$242$	−54380.0			−0.0596899
$243$		0			0
$244$	684512.			0.736049
$245$	−244656.	−	423757.i	−0.260400	−	0.451026i
$246$		0			0
$247$	−110888.	+	192064.i	−0.115649	+	0.200310i
$248$	146048.	−	252963.i	0.150788	−	0.261172i
$249$		0			0
$250$	−569472.	−	986354.i	−0.576265	−	0.998121i
$251$	1.89965e6			1.90322			0.951610	−	0.307309i	$-0.0994287\pi$
$251$	1.89965e6			1.90322			0.951610	+	0.307309i	$0.0994287\pi$
$252$		0			0
$253$	−1.47456e6			−1.44831
$254$	1976.00	+	3422.53i	0.00192178	+	0.00332861i
$255$		0			0
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	223872.	−	387758.i	0.211430	−	0.366208i	−0.740732	−	0.671800i	$-0.765521\pi$
$257$	223872.	−	387758.i	0.211430	−	0.366208i	0.952162	+	0.305593i	$0.0988546\pi$
$258$		0			0
$259$	429052.	+	743140.i	0.397430	+	0.688369i
$260$	−513024.			−0.470657
$261$		0			0
$262$	−897024.			−0.807330
$263$	−33792.0	−	58529.5i	−0.0301248	−	0.0521777i	0.850570	−	0.525862i	$-0.176257\pi$
$263$	−33792.0	−	58529.5i	−0.0301248	−	0.0521777i	−0.880695	+	0.473684i	$0.842924\pi$
$264$		0			0
$265$	373248.	−	646484.i	0.326500	−	0.565514i
$266$	−196544.	+	340424.i	−0.170316	+	0.294996i
$267$		0			0
$268$	−293248.	−	507920.i	−0.249401	−	0.431975i
$269$	−564192.			−0.475386			−0.237693	−	0.971340i	$-0.576391\pi$
$269$	−564192.			−0.475386			−0.237693	+	0.971340i	$0.576391\pi$
$270$		0			0
$271$	720308.			0.595792			0.297896	−	0.954598i	$-0.403715\pi$
$271$	720308.			0.595792			0.297896	+	0.954598i	$0.403715\pi$
$272$	73728.0	+	127701.i	0.0604241	+	0.104658i
$273$		0			0
$274$	−557952.	+	966401.i	−0.448973	+	0.777644i
$275$	1.16947e6	−	2.02558e6i	0.932520	−	1.61517i
$276$		0			0
$277$	70571.0	+	122233.i	0.0552620	+	0.0957166i	0.892333	−	0.451378i	$-0.149067\pi$
$277$	70571.0	+	122233.i	0.0552620	+	0.0957166i	−0.837071	+	0.547094i	$0.815734\pi$
$278$	708800.			0.550062
$279$		0			0
$280$	−909312.			−0.693135
$281$	292224.	+	506147.i	0.220775	+	0.382394i	0.955044	−	0.296466i	$-0.0958080\pi$
$281$	292224.	+	506147.i	0.220775	+	0.382394i	−0.734268	+	0.678859i	$0.762475\pi$
$282$		0			0
$283$	−88528.0	+	153335.i	−0.0657074	+	0.113809i	−0.897008	−	0.442015i	$-0.854264\pi$
$283$	−88528.0	+	153335.i	−0.0657074	+	0.113809i	0.831300	+	0.555824i	$0.187597\pi$
$284$	516096.	−	893904.i	0.379695	−	0.657651i
$285$		0			0
$286$	−256512.	−	444292.i	−0.185435	−	0.321184i
$287$	−994560.			−0.712732
$288$		0			0
$289$	−1.08808e6			−0.766331
$290$	18432.0	+	31925.2i	0.0128700	+	0.0222914i
$291$		0			0
$292$	134480.	−	232926.i	0.0922998	−	0.159868i
$293$	−478416.	+	828641.i	−0.325564	+	0.563894i	−0.981626	−	0.190813i	$-0.938888\pi$
$293$	−478416.	+	828641.i	−0.325564	+	0.563894i	0.656062	+	0.754707i	$0.272221\pi$
$294$		0			0
$295$	−626688.	−	1.08546e6i	−0.419272	−	0.726201i
$296$	371072.			0.246166
$297$		0			0
$298$	−944256.			−0.615955
$299$	641280.	+	1.11073e6i	0.414830	+	0.718506i
$300$		0			0
$301$	−1.10053e6	+	1.90617e6i	−0.700140	+	1.21268i
$302$	965672.	−	1.67259e6i	0.609273	−	1.05529i
$303$		0			0
$304$	84992.0	+	147210.i	0.0527466	+	0.0913597i
$305$	4.10707e6			2.52803
$306$		0			0
$307$	2.88286e6			1.74573			0.872867	−	0.487958i	$-0.162258\pi$
$307$	2.88286e6			1.74573			0.872867	+	0.487958i	$0.162258\pi$
$308$	−454656.	−	787487.i	−0.273090	−	0.473006i
$309$		0			0
$310$	876288.	−	1.51778e6i	0.517896	−	0.897022i
$311$	−1.30022e6	+	2.25205e6i	−0.762285	+	1.32032i	0.179386	+	0.983779i	$0.442589\pi$
$311$	−1.30022e6	+	2.25205e6i	−0.762285	+	1.32032i	−0.941670	+	0.336537i	$0.890744\pi$
$312$		0			0
$313$	1.29040e6	+	2.23503e6i	0.744495	+	1.28950i	0.950430	+	0.310938i	$0.100643\pi$
$313$	1.29040e6	+	2.23503e6i	0.744495	+	1.28950i	−0.205935	+	0.978566i	$0.566024\pi$
$314$	1.52434e6			0.872487
$315$		0			0
$316$	449216.			0.253068
$317$	1.15550e6	+	2.00139e6i	0.645838	+	1.11862i	0.984107	+	0.177574i	$0.0568250\pi$
$317$	1.15550e6	+	2.00139e6i	0.645838	+	1.11862i	−0.338270	+	0.941049i	$0.609842\pi$
$318$		0			0
$319$	−18432.0	+	31925.2i	−0.0101413	+	0.0175653i
$320$	−196608.	+	340535.i	−0.107331	+	0.185903i
$321$		0			0
$322$	1.13664e6	+	1.96872e6i	0.610918	+	1.05814i
$323$	382464.			0.203978
$324$		0			0
$325$	−2.03439e6			−1.06838
$326$	−325840.	−	564371.i	−0.169809	−	0.294118i
$327$		0			0
$328$	−215040.	+	372460.i	−0.110366	+	0.191159i
$329$	1.42080e6	−	2.46090e6i	0.723674	−	1.25344i
$330$		0			0
$331$	318512.	+	551679.i	0.159792	+	0.276768i	0.934794	−	0.355191i	$-0.115584\pi$
$331$	318512.	+	551679.i	0.159792	+	0.276768i	−0.775001	+	0.631960i	$0.782251\pi$
$332$	1.06291e6			0.529239
$333$		0			0
$334$	2.26406e6			1.11051
$335$	−1.75949e6	−	3.04752e6i	−0.856593	−	1.48366i
$336$		0			0
$337$	−1.69333e6	+	2.93293e6i	−0.812206	+	1.40678i	0.0991112	+	0.995076i	$0.468400\pi$
$337$	−1.69333e6	+	2.93293e6i	−0.812206	+	1.40678i	−0.911317	+	0.411705i	$0.864933\pi$
$338$	519474.	−	899755.i	0.247327	−	0.428383i
$339$		0			0
$340$	442368.	+	766204.i	0.207533	+	0.359457i
$341$	1.75258e6			0.816189
$342$		0			0
$343$	1.73308e6			0.795396
$344$	475904.	+	824290.i	0.216832	+	0.375564i
$345$		0			0
$346$	−436416.	+	755895.i	−0.195979	+	0.339446i
$347$	1.38912e6	−	2.40603e6i	0.619321	−	1.07270i	−0.370288	−	0.928917i	$-0.620741\pi$
$347$	1.38912e6	−	2.40603e6i	0.619321	−	1.07270i	0.989610	−	0.143779i	$-0.0459255\pi$
$348$		0			0
$349$	−777679.	−	1.34698e6i	−0.341772	−	0.591967i	0.642990	−	0.765875i	$-0.277694\pi$
$349$	−777679.	−	1.34698e6i	−0.341772	−	0.591967i	−0.984762	+	0.173908i	$0.944360\pi$
$350$	−3.60587e6			−1.57340
$351$		0			0
$352$	−393216.			−0.169151
$353$	1.05888e6	+	1.83403e6i	0.452283	+	0.783377i	0.998527	−	0.0542490i	$-0.0172765\pi$
$353$	1.05888e6	+	1.83403e6i	0.452283	+	0.783377i	−0.546245	+	0.837626i	$0.683943\pi$
$354$		0			0
$355$	3.09658e6	−	5.36343e6i	1.30410	−	2.25877i
$356$	−654336.	+	1.13334e6i	−0.273638	+	0.473954i
$357$		0			0
$358$	−824832.	−	1.42865e6i	−0.340140	−	0.589140i
$359$	−2.17498e6			−0.890673			−0.445337	−	0.895363i	$-0.646916\pi$
$359$	−2.17498e6			−0.890673			−0.445337	+	0.895363i	$0.646916\pi$
$360$		0			0
$361$	−2.03520e6			−0.821939
$362$	51116.0	+	88535.5i	0.0205015	+	0.0355096i
$363$		0			0
$364$	−395456.	+	684950.i	−0.156439	+	0.270960i
$365$	806880.	−	1.39756e6i	0.317013	−	0.549082i
$366$		0			0
$367$	−526678.	−	912233.i	−0.204117	−	0.353542i	0.745734	−	0.666244i	$-0.232099\pi$
$367$	−526678.	−	912233.i	−0.204117	−	0.353542i	−0.949851	+	0.312702i	$0.898766\pi$
$368$	983040.			0.378400
$369$		0			0
$370$	2.22643e6			0.845483
$371$	−575424.	−	996664.i	−0.217047	−	0.375936i
$372$		0			0
$373$	338549.	−	586384.i	0.125994	−	0.218228i	−0.796127	−	0.605129i	$-0.793121\pi$
$373$	338549.	−	586384.i	0.125994	−	0.218228i	0.922121	+	0.386902i	$0.126455\pi$
$374$	−442368.	+	766204.i	−0.163533	+	0.283247i
$375$		0			0
$376$	−614400.	−	1.06417e6i	−0.224121	−	0.388188i
$377$	32064.0			0.0116189
$378$		0			0
$379$	−5.10748e6			−1.82645			−0.913227	−	0.407452i	$-0.866418\pi$
$379$	−5.10748e6			−1.82645			−0.913227	+	0.407452i	$0.866418\pi$
$380$	509952.	+	883263.i	0.181163	+	0.313784i
$381$		0			0
$382$	800256.	−	1.38608e6i	0.280589	−	0.485994i
$383$	816000.	−	1.41335e6i	0.284245	−	0.492327i	−0.688181	−	0.725539i	$-0.741590\pi$
$383$	816000.	−	1.41335e6i	0.284245	−	0.492327i	0.972426	+	0.233212i	$0.0749237\pi$
$384$		0			0
$385$	−2.72794e6	−	4.72492e6i	−0.937956	−	1.62459i
$386$	2.79860e6			0.956032
$387$		0			0
$388$	−479008.			−0.161534
$389$	−2.23282e6	−	3.86735e6i	−0.748133	−	1.29580i	−0.948717	−	0.316128i	$-0.897617\pi$
$389$	−2.23282e6	−	3.86735e6i	−0.748133	−	1.29580i	0.200583	−	0.979677i	$-0.435716\pi$
$390$		0			0
$391$	1.10592e6	−	1.91551e6i	0.365832	−	0.633640i
$392$	−163104.	+	282504.i	−0.0536104	+	0.0928560i
$393$		0			0
$394$	812736.	+	1.40770e6i	0.263760	+	0.456846i
$395$	2.69530e6			0.869188
$396$		0			0
$397$	−611026.			−0.194573			−0.0972867	−	0.995256i	$-0.531016\pi$
$397$	−611026.			−0.194573			−0.0972867	+	0.995256i	$0.531016\pi$
$398$	723992.	+	1.25399e6i	0.229101	+	0.396814i
$399$		0			0
$400$	−779648.	+	1.35039e6i	−0.243640	+	0.421997i
$401$	−3.04579e6	+	5.27547e6i	−0.945887	+	1.63832i	−0.191922	+	0.981410i	$0.561472\pi$
$401$	−3.04579e6	+	5.27547e6i	−0.945887	+	1.63832i	−0.753965	+	0.656914i	$0.771861\pi$
$402$		0			0
$403$	−762188.	−	1.32015e6i	−0.233776	−	0.404912i
$404$	−2.85850e6			−0.871333
$405$		0			0
$406$	56832.0			0.0171111
$407$	1.11322e6	+	1.92815e6i	0.333114	+	0.576971i
$408$		0			0
$409$	−1.44554e6	+	2.50375e6i	−0.427289	+	0.740086i	−0.996631	−	0.0820146i	$-0.973865\pi$
$409$	−1.44554e6	+	2.50375e6i	−0.427289	+	0.740086i	0.569342	+	0.822101i	$0.307198\pi$
$410$	−1.29024e6	+	2.23476e6i	−0.379063	+	0.656556i
$411$		0			0
$412$	921824.	+	1.59665e6i	0.267550	+	0.463410i
$413$	−1.93229e6			−0.557438
$414$		0			0
$415$	6.37747e6			1.81773
$416$	171008.	+	296195.i	0.0484488	+	0.0839158i
$417$		0			0
$418$	−509952.	+	883263.i	−0.142754	+	0.247257i
$419$	−1.49203e6	+	2.58428e6i	−0.415186	+	0.719124i	−0.995448	−	0.0953063i	$-0.969617\pi$
$419$	−1.49203e6	+	2.58428e6i	−0.415186	+	0.719124i	0.580262	+	0.814430i	$0.302950\pi$
$420$		0			0
$421$	−411037.	−	711937.i	−0.113025	−	0.195766i	0.803963	−	0.594679i	$-0.202721\pi$
$421$	−411037.	−	711937.i	−0.113025	−	0.195766i	−0.916989	+	0.398913i	$0.869387\pi$
$422$	607424.			0.166039
$423$		0			0
$424$	−497664.			−0.134438
$425$	1.75421e6	+	3.03838e6i	0.471095	+	0.815961i
$426$		0			0
$427$	3.16587e6	−	5.48344e6i	0.840278	−	1.45540i
$428$	−608256.	+	1.05353e6i	−0.160501	+	0.277995i
$429$		0			0
$430$	2.85542e6	+	4.94574e6i	0.744731	+	1.28991i
$431$	−6.32448e6			−1.63995			−0.819977	−	0.572397i	$-0.806014\pi$
$431$	−6.32448e6			−1.63995			−0.819977	+	0.572397i	$0.806014\pi$
$432$		0			0
$433$	−851902.			−0.218358			−0.109179	−	0.994022i	$-0.534822\pi$
$433$	−851902.			−0.218358			−0.109179	+	0.994022i	$0.534822\pi$
$434$	−1.35094e6	−	2.33990e6i	−0.344281	−	0.596312i
$435$		0			0
$436$	1.84894e6	−	3.20246e6i	0.465809	−	0.806804i
$437$	1.27488e6	−	2.20816e6i	0.319349	−	0.553129i
$438$		0			0
$439$	167366.	+	289886.i	0.0414482	+	0.0717904i	0.886005	−	0.463675i	$-0.153470\pi$
$439$	167366.	+	289886.i	0.0414482	+	0.0717904i	−0.844557	+	0.535466i	$0.820136\pi$
$440$	−2.35930e6			−0.580966
$441$		0			0
$442$	769536.			0.187358
$443$	−881088.	−	1.52609e6i	−0.213309	−	0.369463i	0.739439	−	0.673224i	$-0.235091\pi$
$443$	−881088.	−	1.52609e6i	−0.213309	−	0.369463i	−0.952748	+	0.303761i	$0.901758\pi$
$444$		0			0
$445$	−3.92602e6	+	6.80006e6i	−0.939836	+	1.62784i
$446$	2.18665e6	−	3.78739e6i	0.520525	−	0.901576i
$447$		0			0
$448$	303104.	+	524992.i	0.0713504	+	0.123583i
$449$	−6.51859e6			−1.52594			−0.762971	−	0.646433i	$-0.776260\pi$
$449$	−6.51859e6			−1.52594			−0.762971	+	0.646433i	$0.776260\pi$
$450$		0			0
$451$	−2.58048e6			−0.597392
$452$	1.13971e6	+	1.97404e6i	0.262391	+	0.454475i
$453$		0			0
$454$	−1.13280e6	+	1.96207e6i	−0.257937	+	0.446760i
$455$	−2.37274e6	+	4.10970e6i	−0.537305	+	0.930640i
$456$		0			0
$457$	46037.0	+	79738.4i	0.0103114	+	0.0178598i	0.871135	−	0.491044i	$-0.163384\pi$
$457$	46037.0	+	79738.4i	0.0103114	+	0.0178598i	−0.860824	+	0.508903i	$0.830051\pi$
$458$	−2.34882e6			−0.523223
$459$		0			0
$460$	5.89824e6			1.29965
$461$	128784.	+	223060.i	0.0282234	+	0.0488844i	0.879792	−	0.475359i	$-0.157682\pi$
$461$	128784.	+	223060.i	0.0282234	+	0.0488844i	−0.851569	+	0.524243i	$0.824348\pi$
$462$		0			0
$463$	−1.98114e6	+	3.43143e6i	−0.429499	+	0.743914i	−0.996829	−	0.0795765i	$-0.974643\pi$
$463$	−1.98114e6	+	3.43143e6i	−0.429499	+	0.743914i	0.567330	+	0.823491i	$0.307977\pi$
$464$	12288.0	−	21283.4i	0.00264964	−	0.00458930i
$465$		0			0
$466$	1.15891e6	+	2.00729e6i	0.247221	+	0.428200i
$467$	3.48941e6			0.740388			0.370194	−	0.928954i	$-0.379291\pi$
$467$	3.48941e6			0.740388			0.370194	+	0.928954i	$0.379291\pi$
$468$		0			0
$469$	−5.42509e6			−1.13887
$470$	−3.68640e6	−	6.38503e6i	−0.769764	−	1.33327i
$471$		0			0
$472$	−417792.	+	723637.i	−0.0863187	+	0.149508i
$473$	−2.85542e6	+	4.94574e6i	−0.586837	+	1.01643i
$474$		0			0
$475$	2.02221e6	+	3.50257e6i	0.411237	+	0.712284i
$476$	1.36397e6			0.275922
$477$		0			0
$478$	2.33779e6			0.467990
$479$	256512.	+	444292.i	0.0510821	+	0.0884768i	0.890436	−	0.455109i	$-0.150400\pi$
$479$	256512.	+	444292.i	0.0510821	+	0.0884768i	−0.839354	+	0.543586i	$0.817066\pi$
$480$		0			0
$481$	968266.	−	1.67709e6i	0.190824	−	0.330516i
$482$	828260.	−	1.43459e6i	0.162386	−	0.281261i
$483$		0			0
$484$	108760.	+	188378.i	0.0211036	+	0.0365524i
$485$	−2.87405e6			−0.554804
$486$		0			0
$487$	4.14499e6			0.791956			0.395978	−	0.918260i	$-0.370406\pi$
$487$	4.14499e6			0.791956			0.395978	+	0.918260i	$0.370406\pi$
$488$	−1.36902e6	−	2.37122e6i	−0.260232	−	0.450736i
$489$		0			0
$490$	−978624.	+	1.69503e6i	−0.184130	+	0.318923i
$491$	1.37933e6	−	2.38907e6i	0.258205	−	0.447223i	−0.707556	−	0.706657i	$-0.750202\pi$
$491$	1.37933e6	−	2.38907e6i	0.258205	−	0.447223i	0.965761	+	0.259433i	$0.0835358\pi$
$492$		0			0
$493$	−27648.0	−	47887.7i	−0.00512326	−	0.00887375i
$494$	887104.			0.163552
$495$		0			0
$496$	−1.16838e6			−0.213246
$497$	−4.77389e6	−	8.26862e6i	−0.866924	−	1.50156i
$498$		0			0
$499$	−330448.	+	572353.i	−0.0594089	+	0.102899i	−0.894200	−	0.447667i	$-0.852255\pi$
$499$	−330448.	+	572353.i	−0.0594089	+	0.102899i	0.834791	+	0.550567i	$0.185588\pi$
$500$	−2.27789e6	+	3.94542e6i	−0.407481	+	0.705778i
$501$		0			0
$502$	−3.79930e6	−	6.58057e6i	−0.672890	−	1.16548i
$503$	944640.			0.166474			0.0832370	−	0.996530i	$-0.473474\pi$
$503$	944640.			0.166474			0.0832370	+	0.996530i	$0.473474\pi$
$504$		0			0
$505$	−1.71510e7			−2.99268
$506$	2.94912e6	+	5.10803e6i	0.512054	+	0.886904i
$507$		0			0
$508$	7904.00	−	13690.1i	0.00135890	−	0.00235368i
$509$	−3.91886e6	+	6.78767e6i	−0.670449	+	1.16125i	0.307328	+	0.951604i	$0.400565\pi$
$509$	−3.91886e6	+	6.78767e6i	−0.670449	+	1.16125i	−0.977777	+	0.209648i	$0.932768\pi$
$510$		0			0
$511$	−1.24394e6	−	2.15457e6i	−0.210740	−	0.365013i
$512$	262144.			0.0441942
$513$		0			0
$514$	−1.79098e6			−0.299007
$515$	5.53094e6	+	9.57988e6i	0.918927	+	1.59163i
$516$		0			0
$517$	3.68640e6	−	6.38503e6i	0.606563	−	1.05060i
$518$	1.71621e6	−	2.97256e6i	0.281025	−	0.486750i
$519$		0			0
$520$	1.02605e6	+	1.77717e6i	0.166402	+	0.288217i
$521$	−3.29645e6			−0.532049			−0.266025	−	0.963966i	$-0.585710\pi$
$521$	−3.29645e6			−0.532049			−0.266025	+	0.963966i	$0.585710\pi$
$522$		0			0
$523$	6.50238e6			1.03948			0.519742	−	0.854323i	$-0.326028\pi$
$523$	6.50238e6			1.03948			0.519742	+	0.854323i	$0.326028\pi$
$524$	1.79405e6	+	3.10738e6i	0.285434	+	0.494386i
$525$		0			0
$526$	−135168.	+	234118.i	−0.0213015	+	0.0368952i
$527$	−1.31443e6	+	2.27666e6i	−0.206163	+	0.357085i
$528$		0			0
$529$	−4.15463e6	−	7.19603e6i	−0.645495	−	1.11803i
$530$	−2.98598e6			−0.461740
$531$		0			0
$532$	1.57235e6			0.240863
$533$	1.12224e6	+	1.94378e6i	0.171107	+	0.296366i
$534$		0			0
$535$	−3.64954e6	+	6.32118e6i	−0.551256	+	0.954803i
$536$	−1.17299e6	+	2.03168e6i	−0.176353	+	0.305453i
$537$		0			0
$538$	1.12838e6	+	1.95442e6i	0.168074	+	0.291113i
$539$	−1.95725e6			−0.290184
$540$		0			0
$541$	9.82714e6			1.44356			0.721778	−	0.692124i	$-0.243325\pi$
$541$	9.82714e6			1.44356			0.721778	+	0.692124i	$0.243325\pi$
$542$	−1.44062e6	−	2.49522e6i	−0.210644	−	0.364847i
$543$		0			0
$544$	294912.	−	510803.i	0.0427263	−	0.0740041i
$545$	1.10937e7	−	1.92148e7i	1.59987	−	2.77105i
$546$		0			0
$547$	1.71290e6	+	2.96683e6i	0.244773	+	0.423959i	0.962068	−	0.272810i	$-0.0879532\pi$
$547$	1.71290e6	+	2.96683e6i	0.244773	+	0.423959i	−0.717295	+	0.696770i	$0.754620\pi$
$548$	4.46362e6			0.634944
$549$		0			0
$550$	−9.35578e6			−1.31878
$551$	−31872.0	−	55203.9i	−0.00447229	−	0.00774624i
$552$		0			0
$553$	2.07762e6	−	3.59855e6i	0.288904	−	0.500397i
$554$	282284.	−	488930.i	0.0390762	−	0.0676819i
$555$		0			0
$556$	−1.41760e6	−	2.45536e6i	−0.194476	−	0.336843i
$557$	6.43363e6			0.878655			0.439327	−	0.898327i	$-0.355217\pi$
$557$	6.43363e6			0.878655			0.439327	+	0.898327i	$0.355217\pi$
$558$		0			0
$559$	4.96725e6			0.672336
$560$	1.81862e6	+	3.14995e6i	0.245060	+	0.424457i
$561$		0			0
$562$	1.16890e6	−	2.02459e6i	0.156112	−	0.270393i
$563$	376512.	−	652138.i	0.0500620	−	0.0867099i	−0.839909	−	0.542728i	$-0.817391\pi$
$563$	376512.	−	652138.i	0.0500620	−	0.0867099i	0.889970	+	0.456018i	$0.150725\pi$
$564$		0			0
$565$	6.83827e6	+	1.18442e7i	0.901208	+	1.56094i
$566$	708224.			0.0929244
$567$		0			0
$568$	−4.12877e6			−0.536970
$569$	−5.57405e6	−	9.65453e6i	−0.721755	−	1.25012i	−0.960296	−	0.278984i	$-0.910002\pi$
$569$	−5.57405e6	−	9.65453e6i	−0.721755	−	1.25012i	0.238540	−	0.971133i	$-0.423331\pi$
$570$		0			0
$571$	−95512.0	+	165432.i	−0.0122594	+	0.0212338i	−0.872090	−	0.489346i	$-0.837236\pi$
$571$	−95512.0	+	165432.i	−0.0122594	+	0.0212338i	0.859831	+	0.510579i	$0.170569\pi$
$572$	−1.02605e6	+	1.77717e6i	−0.131123	+	0.227111i
$573$		0			0
$574$	1.98912e6	+	3.44526e6i	0.251989	+	0.436457i
$575$	2.33894e7			2.95019
$576$		0			0
$577$	1.03722e7			1.29697			0.648486	−	0.761227i	$-0.275403\pi$
$577$	1.03722e7			1.29697			0.648486	+	0.761227i	$0.275403\pi$
$578$	2.17616e6	+	3.76922e6i	0.270939	+	0.469280i
$579$		0			0
$580$	73728.0	−	127701.i	0.00910044	−	0.0157624i
$581$	4.91597e6	−	8.51471e6i	0.604183	−	1.04648i
$582$		0			0
$583$	−1.49299e6	−	2.58594e6i	−0.181922	−	0.315099i
$584$	−1.07584e6			−0.130532
$585$		0			0
$586$	3.82733e6			0.460417
$587$	−1.48531e6	−	2.57264e6i	−0.177919	−	0.308165i	0.763249	−	0.646105i	$-0.223603\pi$
$587$	−1.48531e6	−	2.57264e6i	−0.177919	−	0.308165i	−0.941168	+	0.337940i	$0.890270\pi$
$588$		0			0
$589$	−1.51525e6	+	2.62449e6i	−0.179968	+	0.311714i
$590$	−2.50675e6	+	4.34182e6i	−0.296470	+	0.513502i
$591$		0			0
$592$	−742144.	−	1.28543e6i	−0.0870330	−	0.150746i
$593$	7.55827e6			0.882644			0.441322	−	0.897349i	$-0.354510\pi$
$593$	7.55827e6			0.882644			0.441322	+	0.897349i	$0.354510\pi$
$594$		0			0
$595$	8.18381e6			0.947683
$596$	1.88851e6	+	3.27100e6i	0.217773	+	0.377194i
$597$		0			0
$598$	2.56512e6	−	4.44292e6i	0.293329	−	0.508060i
$599$	3.34579e6	−	5.79508e6i	0.381006	−	0.659922i	−0.610200	−	0.792247i	$-0.708911\pi$
$599$	3.34579e6	−	5.79508e6i	0.381006	−	0.659922i	0.991206	+	0.132325i	$0.0422444\pi$
$600$		0			0
$601$	1.60180e6	+	2.77439e6i	0.180893	+	0.313315i	0.942185	−	0.335094i	$-0.108768\pi$
$601$	1.60180e6	+	2.77439e6i	0.180893	+	0.313315i	−0.761292	+	0.648409i	$0.775435\pi$
$602$	8.80422e6			0.990147
$603$		0			0
$604$	−7.72538e6			−0.861643
$605$	652560.	+	1.13027e6i	0.0724823	+	0.125543i
$606$		0			0
$607$	6.77925e6	−	1.17420e7i	0.746809	−	1.29351i	−0.202535	−	0.979275i	$-0.564918\pi$
$607$	6.77925e6	−	1.17420e7i	0.746809	−	1.29351i	0.949345	−	0.314237i	$-0.101749\pi$
$608$	339968.	−	588842.i	0.0372974	−	0.0646011i
$609$		0			0
$610$	−8.21414e6	−	1.42273e7i	−0.893795	−	1.54810i
$611$	−6.41280e6			−0.694936
$612$		0			0
$613$	−1.07654e7			−1.15712			−0.578561	−	0.815639i	$-0.696385\pi$
$613$	−1.07654e7			−1.15712			−0.578561	+	0.815639i	$0.696385\pi$
$614$	−5.76573e6	−	9.98653e6i	−0.617210	−	1.06904i
$615$		0			0
$616$	−1.81862e6	+	3.14995e6i	−0.193104	+	0.334466i
$617$	−4.66752e6	+	8.08438e6i	−0.493598	+	0.854937i	−0.999973	−	0.00737683i	$-0.997652\pi$
$617$	−4.66752e6	+	8.08438e6i	−0.493598	+	0.854937i	0.506375	+	0.862313i	$0.330985\pi$
$618$		0			0
$619$	−4.53832e6	−	7.86060e6i	−0.476067	−	0.824573i	0.523557	−	0.851991i	$-0.324605\pi$
$619$	−4.53832e6	−	7.86060e6i	−0.476067	−	0.824573i	−0.999624	+	0.0274179i	$0.991272\pi$
$620$	−7.01030e6			−0.732416
$621$		0			0
$622$	1.04018e7			1.07803
$623$	6.05261e6	+	1.04834e7i	0.624773	+	1.08214i
$624$		0			0
$625$	−4.15014e6	+	7.18825e6i	−0.424974	+	0.736077i
$626$	5.16158e6	−	8.94012e6i	0.526438	−	0.911817i
$627$		0			0
$628$	−3.04869e6	−	5.28048e6i	−0.308471	−	0.534287i
$629$	−3.33965e6			−0.336569
$630$		0			0
$631$	−1.13367e7			−1.13348			−0.566741	−	0.823896i	$-0.691796\pi$
$631$	−1.13367e7			−1.13348			−0.566741	+	0.823896i	$0.691796\pi$
$632$	−898432.	−	1.55613e6i	−0.0894731	−	0.154972i
$633$		0			0
$634$	4.62202e6	−	8.00557e6i	0.456676	−	0.790986i
$635$	47424.0	−	82140.8i	0.00466728	−	0.00808397i
$636$		0			0
$637$	851199.	+	1.47432e6i	0.0831156	+	0.143960i
$638$	147456.			0.0143420
$639$		0			0
$640$	1.57286e6			0.151789
$641$	7.77245e6	+	1.34623e7i	0.747159	+	1.29412i	0.949179	+	0.314735i	$0.101916\pi$
$641$	7.77245e6	+	1.34623e7i	0.747159	+	1.29412i	−0.202021	+	0.979381i	$0.564751\pi$
$642$		0			0
$643$	4.40013e6	−	7.62125e6i	0.419699	−	0.726941i	−0.576210	−	0.817302i	$-0.695469\pi$
$643$	4.40013e6	−	7.62125e6i	0.419699	−	0.726941i	0.995909	+	0.0903613i	$0.0288022\pi$
$644$	4.54656e6	−	7.87487e6i	0.431985	−	0.748219i
$645$		0			0
$646$	−764928.	−	1.32489e6i	−0.0721173	−	0.124911i
$647$	−1.08449e7			−1.01851			−0.509256	−	0.860615i	$-0.670079\pi$
$647$	−1.08449e7			−1.01851			−0.509256	+	0.860615i	$0.670079\pi$
$648$		0			0
$649$	−5.01350e6			−0.467229
$650$	4.06879e6	+	7.04735e6i	0.377730	+	0.654248i
$651$		0			0
$652$	−1.30336e6	+	2.25749e6i	−0.120073	+	0.207973i
$653$	−4.94386e6	+	8.56301e6i	−0.453715	+	0.785857i	−0.998613	−	0.0526450i	$-0.983235\pi$
$653$	−4.94386e6	+	8.56301e6i	−0.453715	+	0.785857i	0.544899	+	0.838502i	$0.316568\pi$
$654$		0			0
$655$	1.07643e7	+	1.86443e7i	0.980352	+	1.69802i
$656$	1.72032e6			0.156081
$657$		0			0
$658$	−1.13664e7			−1.02343
$659$	−7.30752e6	−	1.26570e7i	−0.655476	−	1.13532i	−0.981774	−	0.190050i	$-0.939135\pi$
$659$	−7.30752e6	−	1.26570e7i	−0.655476	−	1.13532i	0.326299	−	0.945267i	$-0.394198\pi$
$660$		0			0
$661$	−7.88961e6	+	1.36652e7i	−0.702347	+	1.21650i	0.265293	+	0.964168i	$0.414531\pi$
$661$	−7.88961e6	+	1.36652e7i	−0.702347	+	1.21650i	−0.967640	+	0.252333i	$0.918802\pi$
$662$	1.27405e6	−	2.20672e6i	0.112990	−	0.195705i
$663$		0			0
$664$	−2.12582e6	−	3.68204e6i	−0.187114	−	0.324092i
$665$	9.43411e6			0.827269
$666$		0			0
$667$	−368640.			−0.0320840
$668$	−4.52813e6	−	7.84295e6i	−0.392625	−	0.680046i
$669$		0			0
$670$	−7.03795e6	+	1.21901e7i	−0.605702	+	1.04911i
$671$	8.21414e6	−	1.42273e7i	0.704297	−	1.21988i
$672$		0			0
$673$	−3.32470e6	−	5.75854e6i	−0.282953	−	0.490089i	0.689158	−	0.724611i	$-0.257981\pi$
$673$	−3.32470e6	−	5.75854e6i	−0.282953	−	0.490089i	−0.972111	+	0.234522i	$0.924647\pi$
$674$	1.35466e7			1.14863
$675$		0			0
$676$	−4.15579e6			−0.349774
$677$	2.21275e6	+	3.83260e6i	0.185550	+	0.321382i	0.943762	−	0.330626i	$-0.107260\pi$
$677$	2.21275e6	+	3.83260e6i	0.185550	+	0.321382i	−0.758212	+	0.652008i	$0.773927\pi$
$678$		0			0
$679$	−2.21541e6	+	3.83721e6i	−0.184408	+	0.319404i
$680$	1.76947e6	−	3.06482e6i	0.146748	−	0.254175i
$681$		0			0
$682$	−3.50515e6	−	6.07110e6i	−0.288567	−	0.499812i
$683$	4.67827e6			0.383737			0.191869	−	0.981421i	$-0.438545\pi$
$683$	4.67827e6			0.383737			0.191869	+	0.981421i	$0.438545\pi$
$684$		0			0
$685$	2.67817e7			2.18078
$686$	−3.46616e6	−	6.00357e6i	−0.281215	−	0.487078i
$687$		0			0
$688$	1.90362e6	−	3.29716e6i	0.153323	−	0.265564i
$689$	−1.29859e6	+	2.24923e6i	−0.104214	+	0.180503i
$690$		0			0
$691$	2.77051e6	+	4.79866e6i	0.220731	+	0.382318i	0.955030	−	0.296508i	$-0.0958222\pi$
$691$	2.77051e6	+	4.79866e6i	0.220731	+	0.382318i	−0.734299	+	0.678826i	$0.762489\pi$
$692$	3.49133e6			0.277157
$693$		0			0
$694$	−1.11130e7			−0.875853
$695$	−8.50560e6	−	1.47321e7i	−0.667948	−	1.15692i
$696$		0			0
$697$	1.93536e6	−	3.35214e6i	0.150897	−	0.261361i
$698$	−3.11072e6	+	5.38792e6i	−0.241669	+	0.418584i
$699$		0			0
$700$	7.21174e6	+	1.24911e7i	0.556282	+	0.963509i
$701$	6.53443e6			0.502242			0.251121	−	0.967956i	$-0.419201\pi$
$701$	6.53443e6			0.502242			0.251121	+	0.967956i	$0.419201\pi$
$702$		0			0
$703$	−3.84987e6			−0.293804
$704$	786432.	+	1.36214e6i	0.0598039	+	0.103583i
$705$		0			0
$706$	4.23552e6	−	7.33614e6i	0.319812	−	0.553931i
$707$	−1.32205e7	+	2.28987e7i	−0.994720	+	1.72291i
$708$		0			0
$709$	1.93271e6	+	3.34755e6i	0.144394	+	0.250098i	0.929147	−	0.369711i	$-0.120543\pi$
$709$	1.93271e6	+	3.34755e6i	0.144394	+	0.250098i	−0.784752	+	0.619809i	$0.787210\pi$
$710$	−2.47726e7			−1.84428
$711$		0			0
$712$	5.23469e6			0.386982
$713$	8.76288e6	+	1.51778e7i	0.645540	+	1.11811i
$714$		0			0
$715$	−6.15629e6	+	1.06630e7i	−0.450354	+	0.780036i
$716$	−3.29933e6	+	5.71460e6i	−0.240515	+	0.416585i
$717$		0			0
$718$	4.34995e6	+	7.53434e6i	0.314901	+	0.545424i
$719$	−4.80614e6			−0.346717			−0.173358	−	0.984859i	$-0.555462\pi$
$719$	−4.80614e6			−0.346717			−0.173358	+	0.984859i	$0.555462\pi$
$720$		0			0
$721$	1.70537e7			1.22175
$722$	4.07041e6	+	7.05015e6i	0.290599	+	0.503333i
$723$		0			0
$724$	204464.	−	354142.i	0.0144967	−	0.0251091i
$725$	292368.	−	506396.i	0.0206578	−	0.0357804i
$726$		0			0
$727$	9.52949e6	+	1.65056e7i	0.668704	+	1.15823i	0.978267	+	0.207350i	$0.0664838\pi$
$727$	9.52949e6	+	1.65056e7i	0.668704	+	1.15823i	−0.309563	+	0.950879i	$0.600183\pi$
$728$	3.16365e6			0.221238
$729$		0			0
$730$	−6.45504e6			−0.448324
$731$	−4.28314e6	−	7.41861e6i	−0.296462	−	0.513487i
$732$		0			0
$733$	−2.84808e6	+	4.93302e6i	−0.195791	+	0.339120i	−0.947159	−	0.320763i	$-0.896061\pi$
$733$	−2.84808e6	+	4.93302e6i	−0.195791	+	0.339120i	0.751369	+	0.659883i	$0.229394\pi$
$734$	−2.10671e6	+	3.64893e6i	−0.144333	+	0.249992i
$735$		0			0
$736$	−1.96608e6	−	3.40535e6i	−0.133785	−	0.231722i
$737$	−1.40759e7			−0.954570
$738$		0			0
$739$	1.84902e7			1.24546			0.622730	−	0.782437i	$-0.286024\pi$
$739$	1.84902e7			1.24546			0.622730	+	0.782437i	$0.286024\pi$
$740$	−4.45286e6	−	7.71259e6i	−0.298924	−	0.517751i
$741$		0			0
$742$	−2.30170e6	+	3.98665e6i	−0.153475	+	0.265827i
$743$	4.95168e6	−	8.57656e6i	0.329064	−	0.569956i	−0.653262	−	0.757132i	$-0.726600\pi$
$743$	4.95168e6	−	8.57656e6i	0.329064	−	0.569956i	0.982326	+	0.187176i	$0.0599334\pi$
$744$		0			0
$745$	1.13311e7	+	1.96260e7i	0.747963	+	1.29551i
$746$	−2.70839e6			−0.178182
$747$		0			0
$748$	3.53894e6			0.231270
$749$	5.62637e6	+	9.74516e6i	0.366457	+	0.634723i
$750$		0			0
$751$	4.52957e6	−	7.84545e6i	0.293060	−	0.507595i	−0.681471	−	0.731845i	$-0.738660\pi$
$751$	4.52957e6	−	7.84545e6i	0.293060	−	0.507595i	0.974532	+	0.224249i	$0.0719930\pi$
$752$	−2.45760e6	+	4.25669e6i	−0.158477	+	0.274490i
$753$		0			0
$754$	−64128.0	−	111073.i	−0.00410789	−	0.00711508i
$755$	−4.63523e7			−2.95940
$756$		0			0
$757$	−1.16677e7			−0.740022			−0.370011	−	0.929027i	$-0.620646\pi$
$757$	−1.16677e7			−0.740022			−0.370011	+	0.929027i	$0.620646\pi$
$758$	1.02150e7	+	1.76928e7i	0.645749	+	1.11847i
$759$		0			0
$760$	2.03981e6	−	3.53305e6i	0.128102	−	0.221879i
$761$	−6.36989e6	+	1.10330e7i	−0.398722	+	0.690607i	−0.993569	−	0.113233i	$-0.963879\pi$
$761$	−6.36989e6	+	1.10330e7i	−0.398722	+	0.690607i	0.594847	+	0.803839i	$0.297213\pi$
$762$		0			0
$763$	−1.71027e7	−	2.96228e7i	−1.06354	−	1.84211i
$764$	−6.40205e6			−0.396813
$765$		0			0
$766$	−6.52800e6			−0.401983
$767$	2.18035e6	+	3.77648e6i	0.133825	+	0.231792i
$768$		0			0
$769$	−5.33914e6	+	9.24766e6i	−0.325578	+	0.563918i	−0.981629	−	0.190799i	$-0.938892\pi$
$769$	−5.33914e6	+	9.24766e6i	−0.325578	+	0.563918i	0.656051	+	0.754716i	$0.272226\pi$
$770$	−1.09117e7	+	1.88997e7i	−0.663235	+	1.14876i
$771$		0			0
$772$	−5.59720e6	−	9.69463e6i	−0.338008	−	0.585448i
$773$	9.18634e6			0.552960			0.276480	−	0.961020i	$-0.410832\pi$
$773$	9.18634e6			0.552960			0.276480	+	0.961020i	$0.410832\pi$
$774$		0			0
$775$	−2.77993e7			−1.66257
$776$	958016.	+	1.65933e6i	0.0571108	+	0.0989189i
$777$		0			0
$778$	−8.93126e6	+	1.54694e7i	−0.529010	+	0.916272i
$779$	2.23104e6	−	3.86427e6i	0.131724	−	0.228152i
$780$		0			0
$781$	−1.23863e7	−	2.14537e7i	−0.726631	−	1.25856i
$782$	−8.84736e6			−0.517365
$783$		0			0
$784$	1.30483e6			0.0758166
$785$	−1.82921e7	−	3.16829e7i	−1.05947	−	1.83506i
$786$		0			0
$787$	4.64104e6	−	8.03852e6i	0.267103	−	0.462636i	−0.701009	−	0.713152i	$-0.747267\pi$
$787$	4.64104e6	−	8.03852e6i	0.267103	−	0.462636i	0.968112	+	0.250516i	$0.0806003\pi$
$788$	3.25094e6	−	5.63080e6i	0.186506	−	0.323039i
$789$		0			0
$790$	−5.39059e6	−	9.33678e6i	−0.307304	−	0.532267i
$791$	2.10847e7			1.19819
$792$		0			0
$793$	−1.42892e7			−0.806909
$794$	1.22205e6	+	2.11666e6i	0.0687921	+	0.119151i
$795$		0			0
$796$	2.89597e6	−	5.01596e6i	0.161999	−	0.280590i
$797$	10896.0	−	18872.4i	0.000607605	−	0.00105240i	−0.865721	−	0.500526i	$-0.833140\pi$
$797$	10896.0	−	18872.4i	0.000607605	−	0.00105240i	0.866329	+	0.499474i	$0.166473\pi$
$798$		0			0
$799$	5.52960e6	+	9.57755e6i	0.306427	+	0.530747i
$800$	6.23718e6			0.344559
$801$		0			0
$802$	2.43663e7			1.33769
$803$	−3.22752e6	−	5.59023e6i	−0.176636	−	0.305943i
$804$		0			0
$805$	2.72794e7	−	4.72492e7i	1.48369	−	2.56983i
$806$	−3.04875e6	+	5.28059e6i	−0.165304	+	0.286316i
$807$		0			0
$808$	5.71699e6	+	9.90212e6i	0.308063	+	0.533580i
$809$	−1.23085e7			−0.661204			−0.330602	−	0.943770i	$-0.607252\pi$
$809$	−1.23085e7			−0.661204			−0.330602	+	0.943770i	$0.607252\pi$
$810$		0			0
$811$	−2.34636e7			−1.25269			−0.626343	−	0.779547i	$-0.715449\pi$
$811$	−2.34636e7			−1.25269			−0.626343	+	0.779547i	$0.715449\pi$
$812$	−113664.	−	196872.i	−0.00604969	−	0.0104784i
$813$		0			0
$814$	4.45286e6	−	7.71259e6i	0.235547	−	0.407980i
$815$	−7.82016e6	+	1.35449e7i	−0.412403	+	0.714303i
$816$		0			0
$817$	−4.93750e6	−	8.55201e6i	−0.258793	−	0.448242i
$818$	1.15643e7			0.604278
$819$		0			0
$820$	1.03219e7			0.536075
$821$	−7.21032e6	−	1.24886e7i	−0.373333	−	0.646632i	0.616743	−	0.787165i	$-0.288452\pi$
$821$	−7.21032e6	−	1.24886e7i	−0.373333	−	0.646632i	−0.990076	+	0.140533i	$0.955119\pi$
$822$		0			0
$823$	−1.71709e7	+	2.97409e7i	−0.883679	+	1.53058i	−0.0364587	+	0.999335i	$0.511608\pi$
$823$	−1.71709e7	+	2.97409e7i	−0.883679	+	1.53058i	−0.847220	+	0.531242i	$0.821726\pi$
$824$	3.68730e6	−	6.38658e6i	0.189186	−	0.327681i
$825$		0			0
$826$	3.86458e6	+	6.69364e6i	0.197084	+	0.341360i
$827$	−2.13327e7			−1.08463			−0.542316	−	0.840174i	$-0.682453\pi$
$827$	−2.13327e7			−1.08463			−0.542316	+	0.840174i	$0.682453\pi$
$828$		0			0
$829$	2.63751e6			0.133293			0.0666465	−	0.997777i	$-0.478770\pi$
$829$	2.63751e6			0.133293			0.0666465	+	0.997777i	$0.478770\pi$
$830$	−1.27549e7	−	2.20922e7i	−0.642663	−	1.11313i
$831$		0			0
$832$	684032.	−	1.18478e6i	0.0342585	−	0.0593374i
$833$	1.46794e6	−	2.54254e6i	0.0732984	−	0.126957i
$834$		0			0
$835$	−2.71688e7	−	4.70577e7i	−1.34851	−	2.33569i
$836$	4.07962e6			0.201885
$837$		0			0
$838$	1.19363e7			0.587162
$839$	−5.02886e6	−	8.71025e6i	−0.246641	−	0.427194i	0.715951	−	0.698151i	$-0.245993\pi$
$839$	−5.02886e6	−	8.71025e6i	−0.246641	−	0.427194i	−0.962592	+	0.270956i	$0.912660\pi$
$840$		0			0
$841$	1.02510e7	−	1.77552e7i	0.499775	−	0.865636i
$842$	−1.64415e6	+	2.84775e6i	−0.0799210	+	0.138427i
$843$		0			0
$844$	−1.21485e6	−	2.10418e6i	−0.0587037	−	0.101678i
$845$	−2.49348e7			−1.20133
$846$		0			0
$847$	2.01206e6			0.0963679
$848$	995328.	+	1.72396e6i	0.0475310	+	0.0823260i
$849$		0			0
$850$	7.01683e6	−	1.21535e7i	0.333115	−	0.576972i
$851$	−1.11322e7	+	1.92815e7i	−0.526933	+	0.912675i
$852$		0			0
$853$	1.15374e7	+	1.99833e7i	0.542919	+	0.940362i	0.998735	+	0.0502885i	$0.0160141\pi$
$853$	1.15374e7	+	1.99833e7i	0.542919	+	0.940362i	−0.455816	+	0.890074i	$0.650653\pi$
$854$	−2.53269e7			−1.18833
$855$		0			0
$856$	4.86605e6			0.226982
$857$	1.75823e7	+	3.04534e7i	0.817756	+	1.41639i	0.907332	+	0.420415i	$0.138115\pi$
$857$	1.75823e7	+	3.04534e7i	0.817756	+	1.41639i	−0.0895760	+	0.995980i	$0.528551\pi$
$858$		0			0
$859$	−8.30110e6	+	1.43779e7i	−0.383842	+	0.664834i	−0.991608	−	0.129282i	$-0.958733\pi$
$859$	−8.30110e6	+	1.43779e7i	−0.383842	+	0.664834i	0.607766	+	0.794116i	$0.292066\pi$
$860$	1.14217e7	−	1.97830e7i	0.526604	−	0.912106i
$861$		0			0
$862$	1.26490e7	+	2.19086e7i	0.579811	+	1.00426i
$863$	2.97009e7			1.35751			0.678754	−	0.734366i	$-0.262520\pi$
$863$	2.97009e7			1.35751			0.678754	+	0.734366i	$0.262520\pi$
$864$		0			0
$865$	2.09480e7			0.951923
$866$	1.70380e6	+	2.95108e6i	0.0772014	+	0.133717i
$867$		0			0
$868$	−5.40378e6	+	9.35961e6i	−0.243443	+	0.421656i
$869$	5.39059e6	−	9.33678e6i	0.242151	−	0.419419i
$870$		0			0
$871$	6.12155e6	+	1.06028e7i	0.273411	+	0.473562i
$872$	−1.47916e7			−0.658753
$873$		0			0
$874$	−1.01990e7			−0.451628
$875$	2.10705e7	+	3.64951e7i	0.930366	+	1.61144i
$876$		0			0
$877$	5.89713e6	−	1.02141e7i	0.258906	−	0.448438i	−0.707043	−	0.707170i	$-0.749971\pi$
$877$	5.89713e6	−	1.02141e7i	0.258906	−	0.448438i	0.965949	+	0.258732i	$0.0833048\pi$
$878$	669464.	−	1.15955e6i	0.0293083	−	0.0507635i
$879$		0			0
$880$	4.71859e6	+	8.17284e6i	0.205403	+	0.355768i
$881$	2.10378e7			0.913190			0.456595	−	0.889675i	$-0.349069\pi$
$881$	2.10378e7			0.913190			0.456595	+	0.889675i	$0.349069\pi$
$882$		0			0
$883$	2.12192e7			0.915855			0.457928	−	0.888990i	$-0.348592\pi$
$883$	2.12192e7			0.915855			0.457928	+	0.888990i	$0.348592\pi$
$884$	−1.53907e6	−	2.66575e6i	−0.0662412	−	0.114733i
$885$		0			0
$886$	−3.52435e6	+	6.10436e6i	−0.150833	+	0.261250i
$887$	1.14409e7	−	1.98162e7i	0.488260	−	0.845691i	−0.511649	−	0.859195i	$-0.670965\pi$
$887$	1.14409e7	−	1.98162e7i	0.488260	−	0.845691i	0.999909	+	0.0135037i	$0.00429851\pi$
$888$		0			0
$889$	−73112.0	−	126634.i	−0.00310266	−	0.00537397i
$890$	3.14081e7			1.32913
$891$		0			0
$892$	−1.74932e7			−0.736134
$893$	6.37440e6	+	1.10408e7i	0.267492	+	0.463310i
$894$		0			0
$895$	−1.97960e7	+	3.42876e7i	−0.826074	+	1.43080i
$896$	1.21242e6	−	2.09997e6i	0.0504524	−	0.0873861i
$897$		0			0
$898$	1.30372e7	+	2.25811e7i	0.539502	+	0.934445i
$899$	438144.			0.0180808
$900$		0			0
$901$	4.47898e6			0.183809
$902$	5.16096e6	+	8.93904e6i	0.211210	+	0.365826i
$903$		0			0
$904$	4.55885e6	−	7.89616e6i	0.185538	−	0.321362i
$905$	1.22678e6	−	2.12485e6i	0.0497905	−	0.0862397i
$906$		0			0
$907$	4.84346e6	+	8.38912e6i	0.195496	+	0.338609i	0.947063	−	0.321048i	$-0.104035\pi$
$907$	4.84346e6	+	8.38912e6i	0.195496	+	0.338609i	−0.751567	+	0.659657i	$0.770702\pi$
$908$	9.06240e6			0.364778
$909$		0			0
$910$	1.89819e7			0.759864
$911$	4.69056e6	+	8.12429e6i	0.187253	+	0.324332i	0.944333	−	0.328990i	$-0.106708\pi$
$911$	4.69056e6	+	8.12429e6i	0.187253	+	0.324332i	−0.757080	+	0.653322i	$0.773375\pi$
$912$		0			0
$913$	1.27549e7	−	2.20922e7i	0.506409	−	0.877127i
$914$	184148.	−	318954.i	0.00729124	−	0.0126288i
$915$		0			0
$916$	4.69765e6	+	8.13657e6i	0.184987	+	0.320407i
$917$	3.31899e7			1.30341
$918$		0			0
$919$	−4.21870e7			−1.64774			−0.823872	−	0.566775i	$-0.808191\pi$
$919$	−4.21870e7			−1.64774			−0.823872	+	0.566775i	$0.808191\pi$
$920$	−1.17965e7	−	2.04321e7i	−0.459497	−	0.795872i
$921$		0			0
$922$	515136.	−	892242.i	0.0199570	−	0.0345665i
$923$	−1.07735e7	+	1.86603e7i	−0.416249	+	0.720964i
$924$		0			0
$925$	−1.76578e7	−	3.05842e7i	−0.678551	−	1.17528i
$926$	1.58491e7			0.607403
$927$		0			0
$928$	−98304.0			−0.00374715
$929$	−1.52278e7	−	2.63753e7i	−0.578893	−	1.00267i	−0.995607	−	0.0936340i	$-0.970152\pi$
$929$	−1.52278e7	−	2.63753e7i	−0.578893	−	1.00267i	0.416714	−	0.909038i	$-0.363182\pi$
$930$		0			0
$931$	1.69220e6	−	2.93098e6i	0.0639851	−	0.110825i
$932$	4.63565e6	−	8.02918e6i	0.174812	−	0.302783i
$933$		0			0
$934$	−6.97882e6	−	1.20877e7i	−0.261767	−	0.453393i
$935$	2.12337e7			0.794321
$936$		0			0
$937$	1.47847e7			0.550128			0.275064	−	0.961426i	$-0.411301\pi$
$937$	1.47847e7			0.550128			0.275064	+	0.961426i	$0.411301\pi$
$938$	1.08502e7	+	1.87931e7i	0.402652	+	0.697413i
$939$		0			0
$940$	−1.47456e7	+	2.55401e7i	−0.544306	+	0.942765i
$941$	−4.95998e6	+	8.59094e6i	−0.182602	+	0.316276i	−0.942766	−	0.333455i	$-0.891785\pi$
$941$	−4.95998e6	+	8.59094e6i	−0.182602	+	0.316276i	0.760164	+	0.649732i	$0.225119\pi$
$942$		0			0
$943$	−1.29024e7	−	2.23476e7i	−0.472489	−	0.818374i
$944$	3.34234e6			0.122073
$945$		0			0
$946$	2.28434e7			0.829913
$947$	1.45805e6	+	2.52541e6i	0.0528320	+	0.0915077i	0.891232	−	0.453548i	$-0.149842\pi$
$947$	1.45805e6	+	2.52541e6i	0.0528320	+	0.0915077i	−0.838400	+	0.545056i	$0.816509\pi$
$948$		0			0
$949$	−2.80727e6	+	4.86233e6i	−0.101186	+	0.175259i
$950$	8.08885e6	−	1.40103e7i	0.290789	−	0.503661i
$951$		0			0
$952$	−2.72794e6	−	4.72492e6i	−0.0975533	−	0.168967i
$953$	−1.40861e7			−0.502410			−0.251205	−	0.967934i	$-0.580827\pi$
$953$	−1.40861e7			−0.502410			−0.251205	+	0.967934i	$0.580827\pi$
$954$		0			0
$955$	−3.84123e7			−1.36289
$956$	−4.67558e6	−	8.09835e6i	−0.165459	−	0.286584i
$957$		0			0
$958$	1.02605e6	−	1.77717e6i	0.0361205	−	0.0625626i
$959$	2.06442e7	−	3.57568e7i	0.724857	−	1.25549i
$960$		0			0
$961$	3.89953e6	+	6.75418e6i	0.136208	+	0.235920i
$962$	−7.74613e6			−0.269865
$963$		0			0
$964$	−6.62608e6			−0.229649
$965$	−3.35832e7	−	5.81678e7i	−1.16092	−	2.01078i
$966$		0			0
$967$	−7.59743e6	+	1.31591e7i	−0.261276	+	0.452544i	−0.966581	−	0.256360i	$-0.917477\pi$
$967$	−7.59743e6	+	1.31591e7i	−0.261276	+	0.452544i	0.705305	+	0.708904i	$0.250810\pi$
$968$	435040.	−	753511.i	0.0149225	−	0.0258465i
$969$		0			0
$970$	5.74810e6	+	9.95599e6i	0.196153	+	0.339747i
$971$	5.61220e7			1.91023			0.955113	−	0.296240i	$-0.0957329\pi$
$971$	5.61220e7			1.91023			0.955113	+	0.296240i	$0.0957329\pi$
$972$		0			0
$973$	−2.62256e7			−0.888062
$974$	−8.28998e6	−	1.43587e7i	−0.279999	−	0.484972i
$975$		0			0
$976$	−5.47610e6	+	9.48488e6i	−0.184012	+	0.318718i
$977$	1.72812e7	−	2.99320e7i	0.579214	−	1.00323i	−0.416356	−	0.909202i	$-0.636693\pi$
$977$	1.72812e7	−	2.99320e7i	0.579214	−	1.00323i	0.995570	−	0.0940257i	$-0.0299736\pi$
$978$		0			0
$979$	1.57041e7	+	2.72002e7i	0.523667	+	0.907018i
$980$	7.82899e6			0.260400
$981$		0			0
$982$	−1.10346e7			−0.365156
$983$	2.78193e7	+	4.81844e7i	0.918252	+	1.59046i	0.802069	+	0.597231i	$0.203732\pi$
$983$	2.78193e7	+	4.81844e7i	0.918252	+	1.59046i	0.116183	+	0.993228i	$0.462934\pi$
$984$		0			0
$985$	1.95057e7	−	3.37848e7i	0.640575	−	1.10951i
$986$	−110592.	+	191551.i	−0.00362269	+	0.00627469i
$987$		0			0
$988$	−1.77421e6	−	3.07302e6i	−0.0578245	−	0.100155i
$989$	−5.71085e7			−1.85656
$990$		0			0
$991$	−3.60028e7			−1.16453			−0.582267	−	0.812998i	$-0.697834\pi$
$991$	−3.60028e7			−1.16453			−0.582267	+	0.812998i	$0.697834\pi$
$992$	2.33677e6	+	4.04740e6i	0.0753939	+	0.130586i
$993$		0			0
$994$	−1.90956e7	+	3.30745e7i	−0.613008	+	1.06176i
$995$	1.73758e7	−	3.00958e7i	0.556400	−	0.963713i
$996$		0			0
$997$	−1.17905e7	−	2.04218e7i	−0.375661	−	0.650664i	0.614765	−	0.788711i	$-0.289251\pi$
$997$	−1.17905e7	−	2.04218e7i	−0.375661	−	0.650664i	−0.990426	+	0.138047i	$0.955918\pi$
$998$	2.64358e6			0.0840169
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.6.c.a.109.1		2
3.2	odd	2		162.6.c.l.109.1		2
9.2	odd	6		162.6.c.l.55.1		2
9.4	even	3		18.6.a.c.1.1	yes	1
9.5	odd	6		18.6.a.a.1.1	✓	1
9.7	even	3	inner	162.6.c.a.55.1		2
36.23	even	6		144.6.a.a.1.1		1
36.31	odd	6		144.6.a.l.1.1		1
45.4	even	6		450.6.a.k.1.1		1
45.13	odd	12		450.6.c.c.199.1		2
45.14	odd	6		450.6.a.v.1.1		1
45.22	odd	12		450.6.c.c.199.2		2
45.23	even	12		450.6.c.m.199.2		2
45.32	even	12		450.6.c.m.199.1		2
63.13	odd	6		882.6.a.l.1.1		1
63.41	even	6		882.6.a.k.1.1		1
72.5	odd	6		576.6.a.bh.1.1		1
72.13	even	6		576.6.a.a.1.1		1
72.59	even	6		576.6.a.bi.1.1		1
72.67	odd	6		576.6.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.6.a.a.1.1	✓	1	9.5	odd	6
18.6.a.c.1.1	yes	1	9.4	even	3
144.6.a.a.1.1		1	36.23	even	6
144.6.a.l.1.1		1	36.31	odd	6
162.6.c.a.55.1		2	9.7	even	3	inner
162.6.c.a.109.1		2	1.1	even	1	trivial
162.6.c.l.55.1		2	9.2	odd	6
162.6.c.l.109.1		2	3.2	odd	2
450.6.a.k.1.1		1	45.4	even	6
450.6.a.v.1.1		1	45.14	odd	6
450.6.c.c.199.1		2	45.13	odd	12
450.6.c.c.199.2		2	45.22	odd	12
450.6.c.m.199.1		2	45.32	even	12
450.6.c.m.199.2		2	45.23	even	12
576.6.a.a.1.1		1	72.13	even	6
576.6.a.b.1.1		1	72.67	odd	6
576.6.a.bh.1.1		1	72.5	odd	6
576.6.a.bi.1.1		1	72.59	even	6
882.6.a.k.1.1		1	63.41	even	6
882.6.a.l.1.1		1	63.13	odd	6

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(-48.0000 + 83.1384i) q^{5} +(74.0000 + 128.172i) q^{7} +64.0000 q^{8} +O(q^{10})\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(-48.0000 + 83.1384i) q^{5} +(74.0000 + 128.172i) q^{7} +64.0000 q^{8} +384.000 q^{10} +(192.000 + 332.554i) q^{11} +(167.000 - 289.252i) q^{13} +(296.000 - 512.687i) q^{14} +(-128.000 - 221.703i) q^{16} -576.000 q^{17} -664.000 q^{19} +(-768.000 - 1330.22i) q^{20} +(768.000 - 1330.22i) q^{22} +(-1920.00 + 3325.54i) q^{23} +(-3045.50 - 5274.96i) q^{25} -1336.00 q^{26} -2368.00 q^{28} +(48.0000 + 83.1384i) q^{29} +(2282.00 - 3952.54i) q^{31} +(-512.000 + 886.810i) q^{32} +(1152.00 + 1995.32i) q^{34} -14208.0 q^{35} +5798.00 q^{37} +(1328.00 + 2300.16i) q^{38} +(-3072.00 + 5320.86i) q^{40} +(-3360.00 + 5819.69i) q^{41} +(7436.00 + 12879.5i) q^{43} -6144.00 q^{44} +15360.0 q^{46} +(-9600.00 - 16627.7i) q^{47} +(-2548.50 + 4414.13i) q^{49} +(-12182.0 + 21099.8i) q^{50} +(2672.00 + 4628.04i) q^{52} -7776.00 q^{53} -36864.0 q^{55} +(4736.00 + 8202.99i) q^{56} +(192.000 - 332.554i) q^{58} +(-6528.00 + 11306.8i) q^{59} +(-21391.0 - 37050.3i) q^{61} -18256.0 q^{62} +4096.00 q^{64} +(16032.0 + 27768.2i) q^{65} +(-18328.0 + 31745.0i) q^{67} +(4608.00 - 7981.29i) q^{68} +(28416.0 + 49218.0i) q^{70} -64512.0 q^{71} -16810.0 q^{73} +(-11596.0 - 20084.9i) q^{74} +(5312.00 - 9200.65i) q^{76} +(-28416.0 + 49218.0i) q^{77} +(-14038.0 - 24314.5i) q^{79} +24576.0 q^{80} +26880.0 q^{82} +(-33216.0 - 57531.8i) q^{83} +(27648.0 - 47887.7i) q^{85} +(29744.0 - 51518.1i) q^{86} +(12288.0 + 21283.4i) q^{88} +81792.0 q^{89} +49432.0 q^{91} +(-30720.0 - 53208.6i) q^{92} +(-38400.0 + 66510.8i) q^{94} +(31872.0 - 55203.9i) q^{95} +(14969.0 + 25927.1i) q^{97} +20388.0 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 16 q^{4} - 96 q^{5} + 148 q^{7} + 128 q^{8}+O(q^{10}) \) 2 * q - 4 * q^2 - 16 * q^4 - 96 * q^5 + 148 * q^7 + 128 * q^8	\( 2 q - 4 q^{2} - 16 q^{4} - 96 q^{5} + 148 q^{7} + 128 q^{8} + 768 q^{10} + 384 q^{11} + 334 q^{13} + 592 q^{14} - 256 q^{16} - 1152 q^{17} - 1328 q^{19} - 1536 q^{20} + 1536 q^{22} - 3840 q^{23} - 6091 q^{25} - 2672 q^{26} - 4736 q^{28} + 96 q^{29} + 4564 q^{31} - 1024 q^{32} + 2304 q^{34} - 28416 q^{35} + 11596 q^{37} + 2656 q^{38} - 6144 q^{40} - 6720 q^{41} + 14872 q^{43} - 12288 q^{44} + 30720 q^{46} - 19200 q^{47} - 5097 q^{49} - 24364 q^{50} + 5344 q^{52} - 15552 q^{53} - 73728 q^{55} + 9472 q^{56} + 384 q^{58} - 13056 q^{59} - 42782 q^{61} - 36512 q^{62} + 8192 q^{64} + 32064 q^{65} - 36656 q^{67} + 9216 q^{68} + 56832 q^{70} - 129024 q^{71} - 33620 q^{73} - 23192 q^{74} + 10624 q^{76} - 56832 q^{77} - 28076 q^{79} + 49152 q^{80} + 53760 q^{82} - 66432 q^{83} + 55296 q^{85} + 59488 q^{86} + 24576 q^{88} + 163584 q^{89} + 98864 q^{91} - 61440 q^{92} - 76800 q^{94} + 63744 q^{95} + 29938 q^{97} + 40776 q^{98}+O(q^{100}) \) 2 * q - 4 * q^2 - 16 * q^4 - 96 * q^5 + 148 * q^7 + 128 * q^8 + 768 * q^10 + 384 * q^11 + 334 * q^13 + 592 * q^14 - 256 * q^16 - 1152 * q^17 - 1328 * q^19 - 1536 * q^20 + 1536 * q^22 - 3840 * q^23 - 6091 * q^25 - 2672 * q^26 - 4736 * q^28 + 96 * q^29 + 4564 * q^31 - 1024 * q^32 + 2304 * q^34 - 28416 * q^35 + 11596 * q^37 + 2656 * q^38 - 6144 * q^40 - 6720 * q^41 + 14872 * q^43 - 12288 * q^44 + 30720 * q^46 - 19200 * q^47 - 5097 * q^49 - 24364 * q^50 + 5344 * q^52 - 15552 * q^53 - 73728 * q^55 + 9472 * q^56 + 384 * q^58 - 13056 * q^59 - 42782 * q^61 - 36512 * q^62 + 8192 * q^64 + 32064 * q^65 - 36656 * q^67 + 9216 * q^68 + 56832 * q^70 - 129024 * q^71 - 33620 * q^73 - 23192 * q^74 + 10624 * q^76 - 56832 * q^77 - 28076 * q^79 + 49152 * q^80 + 53760 * q^82 - 66432 * q^83 + 55296 * q^85 + 59488 * q^86 + 24576 * q^88 + 163584 * q^89 + 98864 * q^91 - 61440 * q^92 - 76800 * q^94 + 63744 * q^95 + 29938 * q^97 + 40776 * q^98

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