LMFDB - Embedded newform 108.6.h.a.71.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, 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:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.9
Character	$\chi$	$=$	108.71
Dual form			108.6.h.a.35.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.65969 - 4.31354i) q^{2} +(-5.21330 + 31.5725i) q^{4} +(51.8636 + 29.9435i) q^{5} +(33.8827 - 19.5622i) q^{7} +(155.268 - 93.0578i) q^{8} +O(q^{10})$	\(q+(-3.65969 - 4.31354i) q^{2} +(-5.21330 + 31.5725i) q^{4} +(51.8636 + 29.9435i) q^{5} +(33.8827 - 19.5622i) q^{7} +(155.268 - 93.0578i) q^{8} +(-60.6425 - 333.300i) q^{10} +(-108.537 - 187.992i) q^{11} +(-532.156 + 921.721i) q^{13} +(-208.383 - 74.5629i) q^{14} +(-969.643 - 329.194i) q^{16} +315.283i q^{17} +1889.72i q^{19} +(-1215.77 + 1481.36i) q^{20} +(-413.698 + 1156.17i) q^{22} +(1200.19 - 2078.79i) q^{23} +(230.725 + 399.628i) q^{25} +(5923.41 - 1077.74i) q^{26} +(440.986 + 1171.75i) q^{28} +(-5185.33 + 2993.75i) q^{29} +(6949.56 + 4012.33i) q^{31} +(2128.60 + 5387.34i) q^{32} +(1359.99 - 1153.84i) q^{34} +2343.04 q^{35} +5243.91 q^{37} +(8151.40 - 6915.81i) q^{38} +(10839.3 - 177.040i) q^{40} +(7589.92 + 4382.04i) q^{41} +(-8780.43 + 5069.38i) q^{43} +(6501.20 - 2446.73i) q^{44} +(-13359.2 + 2430.66i) q^{46} +(7272.14 + 12595.7i) q^{47} +(-7638.14 + 13229.6i) q^{49} +(879.429 - 2457.76i) q^{50} +(-26326.7 - 21606.7i) q^{52} +19631.3i q^{53} -12999.9i q^{55} +(3440.50 - 6190.44i) q^{56} +(31890.4 + 11410.9i) q^{58} +(909.551 - 1575.39i) q^{59} +(24421.5 + 42299.3i) q^{61} +(-8125.89 - 44661.1i) q^{62} +(15448.5 - 28897.8i) q^{64} +(-55199.1 + 31869.2i) q^{65} +(-37065.9 - 21400.0i) q^{67} +(-9954.28 - 1643.67i) q^{68} +(-8574.81 - 10106.8i) q^{70} -29409.1 q^{71} +38022.9 q^{73} +(-19191.1 - 22619.8i) q^{74} +(-59663.3 - 9851.70i) q^{76} +(-7355.06 - 4246.45i) q^{77} +(12858.2 - 7423.70i) q^{79} +(-40432.0 - 46107.7i) q^{80} +(-8874.65 - 48776.4i) q^{82} +(-60168.3 - 104215. i) q^{83} +(-9440.69 + 16351.7i) q^{85} +(54000.6 + 19322.4i) q^{86} +(-34346.5 - 19089.0i) q^{88} -35496.5i q^{89} +41640.5i q^{91} +(59375.5 + 48730.2i) q^{92} +(27718.3 - 77465.1i) q^{94} +(-56584.9 + 98008.0i) q^{95} +(1491.62 + 2583.55i) q^{97} +(85019.9 - 15469.0i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−3.65969	−	4.31354i	−0.646948	−	0.762534i
$2$	−3.65969	−	4.31354i	−0.646948	−	0.762534i
$3$		0			0
$3$		0			0
$4$	−5.21330	+	31.5725i	−0.162916	+	0.986640i
$5$	51.8636	+	29.9435i	0.927765	+	0.535645i	0.886104	−	0.463486i	$-0.153402\pi$
$5$	51.8636	+	29.9435i	0.927765	+	0.535645i	0.0416611	+	0.999132i	$0.486735\pi$
$6$		0			0
$7$	33.8827	−	19.5622i	0.261356	−	0.150894i	−0.363597	−	0.931556i	$-0.618451\pi$
$7$	33.8827	−	19.5622i	0.261356	−	0.150894i	0.624953	+	0.780662i	$0.285118\pi$
$8$	155.268	−	93.0578i	0.857744	−	0.514076i
$9$		0			0
$10$	−60.6425	−	333.300i	−0.191768	−	1.05399i
$11$	−108.537	−	187.992i	−0.270456	−	0.468443i	0.698523	−	0.715588i	$-0.253841\pi$
$11$	−108.537	−	187.992i	−0.270456	−	0.468443i	−0.968979	+	0.247144i	$0.920508\pi$
$12$		0			0
$13$	−532.156	+	921.721i	−0.873334	+	1.51266i	−0.0148071	+	0.999890i	$0.504713\pi$
$13$	−532.156	+	921.721i	−0.873334	+	1.51266i	−0.858527	+	0.512769i	$0.828620\pi$
$14$	−208.383	−	74.5629i	−0.284146	−	0.101672i
$15$		0			0
$16$	−969.643	−	329.194i	−0.946917	−	0.321478i
$17$			315.283i			0.264593i	0.991210	+	0.132297i	$0.0422351\pi$
$17$			315.283i			0.264593i	−0.991210	+	0.132297i	$0.957765\pi$
$18$		0			0
$19$			1889.72i			1.20092i	0.799655	+	0.600460i	$0.205016\pi$
$19$			1889.72i			1.20092i	−0.799655	+	0.600460i	$0.794984\pi$
$20$	−1215.77	+	1481.36i	−0.679637	+	0.828105i
$21$		0			0
$22$	−413.698	+	1156.17i	−0.182233	+	0.509291i
$23$	1200.19	−	2078.79i	0.473074	−	0.819389i	−0.526451	−	0.850206i	$-0.676478\pi$
$23$	1200.19	−	2078.79i	0.473074	−	0.819389i	0.999525	+	0.0308168i	$0.00981084\pi$
$24$		0			0
$25$	230.725	+	399.628i	0.0738321	+	0.127881i
$26$	5923.41	−	1077.74i	1.71846	−	0.312665i
$27$		0			0
$28$	440.986	+	1171.75i	0.106299	+	0.282448i
$29$	−5185.33	+	2993.75i	−1.14494	+	0.661030i	−0.947648	−	0.319315i	$-0.896547\pi$
$29$	−5185.33	+	2993.75i	−1.14494	+	0.661030i	−0.197289	+	0.980345i	$0.563214\pi$
$30$		0			0
$31$	6949.56	+	4012.33i	1.29883	+	0.749881i	0.980202	−	0.197999i	$-0.0634442\pi$
$31$	6949.56	+	4012.33i	1.29883	+	0.749881i	0.318629	+	0.947879i	$0.396778\pi$
$32$	2128.60	+	5387.34i	0.367468	+	0.930036i
$33$		0			0
$34$	1359.99	−	1153.84i	0.201761	−	0.171178i
$35$	2343.04			0.323303
$36$		0			0
$37$	5243.91			0.629725			0.314862	−	0.949137i	$-0.398042\pi$
$37$	5243.91			0.629725			0.314862	+	0.949137i	$0.398042\pi$
$38$	8151.40	−	6915.81i	0.915743	−	0.776934i
$39$		0			0
$40$	10839.3	−	177.040i	1.07115	−	0.0174953i
$41$	7589.92	+	4382.04i	0.705144	+	0.407115i	0.809260	−	0.587450i	$-0.199868\pi$
$41$	7589.92	+	4382.04i	0.705144	+	0.407115i	−0.104117	+	0.994565i	$0.533202\pi$
$42$		0			0
$43$	−8780.43	+	5069.38i	−0.724176	+	0.418103i	−0.816288	−	0.577645i	$-0.803972\pi$
$43$	−8780.43	+	5069.38i	−0.724176	+	0.418103i	0.0921115	+	0.995749i	$0.470638\pi$
$44$	6501.20	−	2446.73i	0.506247	−	0.190526i
$45$		0			0
$46$	−13359.2	+	2430.66i	−0.930866	+	0.169367i
$47$	7272.14	+	12595.7i	0.480195	+	0.831721i	0.999742	−	0.0227202i	$-0.00723270\pi$
$47$	7272.14	+	12595.7i	0.480195	+	0.831721i	−0.519547	+	0.854442i	$0.673899\pi$
$48$		0			0
$49$	−7638.14	+	13229.6i	−0.454462	+	0.787151i
$50$	879.429	−	2457.76i	0.0497480	−	0.139032i
$51$		0			0
$52$	−26326.7	−	21606.7i	−1.35017	−	1.10810i
$53$			19631.3i			0.959974i	0.877276	+	0.479987i	$0.159359\pi$
$53$			19631.3i			0.959974i	−0.877276	+	0.479987i	$0.840641\pi$
$54$		0			0
$55$		−	12999.9i		−	0.579474i
$56$	3440.50	−	6190.44i	0.146606	−	0.263786i
$57$		0			0
$58$	31890.4	+	11410.9i	1.24477	+	0.445401i
$59$	909.551	−	1575.39i	0.0340171	−	0.0589193i	−0.848516	−	0.529170i	$-0.822503\pi$
$59$	909.551	−	1575.39i	0.0340171	−	0.0589193i	0.882533	+	0.470251i	$0.155837\pi$
$60$		0			0
$61$	24421.5	+	42299.3i	0.840327	+	1.45549i	0.889619	+	0.456704i	$0.150970\pi$
$61$	24421.5	+	42299.3i	0.840327	+	1.45549i	−0.0492921	+	0.998784i	$0.515697\pi$
$62$	−8125.89	−	44661.1i	−0.268467	−	1.47554i
$63$		0			0
$64$	15448.5	−	28897.8i	0.471451	−	0.881892i
$65$	−55199.1	+	31869.2i	−1.62050	+	0.935595i
$66$		0			0
$67$	−37065.9	−	21400.0i	−1.00876	−	0.582407i	−0.0979310	−	0.995193i	$-0.531222\pi$
$67$	−37065.9	−	21400.0i	−1.00876	−	0.582407i	−0.910828	+	0.412786i	$0.864556\pi$
$68$	−9954.28	−	1643.67i	−0.261058	−	0.0431064i
$69$		0			0
$70$	−8574.81	−	10106.8i	−0.209160	−	0.246530i
$71$	−29409.1			−0.692365			−0.346183	−	0.938167i	$-0.612522\pi$
$71$	−29409.1			−0.692365			−0.346183	+	0.938167i	$0.612522\pi$
$72$		0			0
$73$	38022.9			0.835099			0.417550	−	0.908654i	$-0.362889\pi$
$73$	38022.9			0.835099			0.417550	+	0.908654i	$0.362889\pi$
$74$	−19191.1	−	22619.8i	−0.407399	−	0.480186i
$75$		0			0
$76$	−59663.3	−	9851.70i	−1.18488	−	0.195649i
$77$	−7355.06	−	4246.45i	−0.141371	−	0.0816205i
$78$		0			0
$79$	12858.2	−	7423.70i	0.231800	−	0.133830i	−0.379602	−	0.925150i	$-0.623939\pi$
$79$	12858.2	−	7423.70i	0.231800	−	0.133830i	0.611402	+	0.791320i	$0.290606\pi$
$80$	−40432.0	−	46107.7i	−0.706318	−	0.805468i
$81$		0			0
$82$	−8874.65	−	48776.4i	−0.145753	−	0.801078i
$83$	−60168.3	−	104215.i	−0.958677	−	1.66048i	−0.725719	−	0.687991i	$-0.758493\pi$
$83$	−60168.3	−	104215.i	−0.958677	−	1.66048i	−0.232959	−	0.972487i	$-0.574841\pi$
$84$		0			0
$85$	−9440.69	+	16351.7i	−0.141728	+	0.245480i
$86$	54000.6	+	19322.4i	0.787323	+	0.281718i
$87$		0			0
$88$	−34346.5	−	19089.0i	−0.472798	−	0.262770i
$89$		−	35496.5i		−	0.475019i	−0.971385	−	0.237509i	$-0.923669\pi$
$89$		−	35496.5i		−	0.475019i	0.971385	−	0.237509i	$-0.0763311\pi$
$90$		0			0
$91$			41640.5i			0.527124i
$92$	59375.5	+	48730.2i	0.731371	+	0.600245i
$93$		0			0
$94$	27718.3	−	77465.1i	0.323555	−	0.904245i
$95$	−56584.9	+	98008.0i	−0.643268	+	1.11417i
$96$		0			0
$97$	1491.62	+	2583.55i	0.0160964	+	0.0278797i	0.873961	−	0.485995i	$-0.161543\pi$
$97$	1491.62	+	2583.55i	0.0160964	+	0.0278797i	−0.857865	+	0.513875i	$0.828209\pi$
$98$	85019.9	−	15469.0i	0.894243	−	0.162704i
$99$		0			0
$100$	−13820.1	+	5201.19i	−0.138201	+	0.0520119i
$101$	−45537.2	+	26290.9i	−0.444184	+	0.256450i	−0.705371	−	0.708838i	$-0.749220\pi$
$101$	−45537.2	+	26290.9i	−0.444184	+	0.256450i	0.261187	+	0.965288i	$0.415886\pi$
$102$		0			0
$103$	−10418.1	−	6014.90i	−0.0967600	−	0.0558644i	0.450839	−	0.892605i	$-0.351125\pi$
$103$	−10418.1	−	6014.90i	−0.0967600	−	0.0558644i	−0.547599	+	0.836741i	$0.684458\pi$
$104$	3146.35	+	192635.i	0.0285248	+	1.74644i
$105$		0			0
$106$	84680.5	−	71844.5i	0.732013	−	0.621054i
$107$	89559.8			0.756229			0.378115	−	0.925759i	$-0.376572\pi$
$107$	89559.8			0.756229			0.378115	+	0.925759i	$0.376572\pi$
$108$		0			0
$109$	−29876.1			−0.240856			−0.120428	−	0.992722i	$-0.538427\pi$
$109$	−29876.1			−0.240856			−0.120428	+	0.992722i	$0.538427\pi$
$110$	−56075.7	+	47575.7i	−0.441869	+	0.374890i
$111$		0			0
$112$	−39293.9	+	7814.37i	−0.295992	+	0.0588639i
$113$	214387.	+	123776.i	1.57943	+	0.911886i	0.994938	+	0.100490i	$0.0320409\pi$
$113$	214387.	+	123776.i	1.57943	+	0.911886i	0.584496	+	0.811397i	$0.301292\pi$
$114$		0			0
$115$	124492.	−	71875.6i	0.877804	−	0.506800i
$116$	−67487.5	−	179321.i	−0.465670	−	1.23733i
$117$		0			0
$118$	−10124.2	+	1842.05i	−0.0669352	+	0.0121786i
$119$	6167.64	+	10682.7i	0.0399256	+	0.0691531i
$120$		0			0
$121$	56964.9	−	98666.1i	0.353707	−	0.612639i
$122$	93084.6	−	260146.i	0.566211	−	1.58240i
$123$		0			0
$124$	−162909.	+	198497.i	−0.951462	+	1.15931i
$125$		−	159512.i		−	0.913100i
$126$		0			0
$127$			265961.i			1.46322i	0.681724	+	0.731610i	$0.261231\pi$
$127$			265961.i			1.46322i	−0.681724	+	0.731610i	$0.738769\pi$
$128$	−181189.	+	39119.4i	−0.977477	+	0.211041i
$129$		0			0
$130$	339481.	+	121472.i	1.76180	+	0.630403i
$131$	37162.9	−	64368.0i	0.189204	−	0.327712i	−0.755781	−	0.654825i	$-0.772742\pi$
$131$	37162.9	−	64368.0i	0.189204	−	0.327712i	0.944985	+	0.327113i	$0.106076\pi$
$132$		0			0
$133$	36967.1	+	64029.0i	0.181212	+	0.313868i
$134$	43339.9	+	238203.i	0.208510	+	1.14600i
$135$		0			0
$136$	29339.6	+	48953.5i	0.136021	+	0.226953i
$137$	−20104.8	+	11607.5i	−0.0915163	+	0.0528370i	−0.545060	−	0.838397i	$-0.683493\pi$
$137$	−20104.8	+	11607.5i	−0.0915163	+	0.0528370i	0.453543	+	0.891234i	$0.350160\pi$
$138$		0			0
$139$	−287391.	−	165925.i	−1.26164	−	0.728410i	−0.288251	−	0.957555i	$-0.593074\pi$
$139$	−287391.	−	165925.i	−1.26164	−	0.728410i	−0.973392	+	0.229145i	$0.926407\pi$
$140$	−12215.0	+	73975.6i	−0.0526712	+	0.318984i
$141$		0			0
$142$	107628.	+	126857.i	0.447924	+	0.527952i
$143$	231035.			0.944794
$144$		0			0
$145$	−358574.			−1.41631
$146$	−139152.	−	164013.i	−0.540266	−	0.636791i
$147$		0			0
$148$	−27338.1	+	165563.i	−0.102592	+	0.621312i
$149$	−287800.	−	166162.i	−1.06200	−	0.613147i	−0.136017	−	0.990707i	$-0.543430\pi$
$149$	−287800.	−	166162.i	−1.06200	−	0.613147i	−0.925985	+	0.377559i	$0.876763\pi$
$150$		0			0
$151$	300515.	−	173503.i	1.07257	−	0.619247i	0.143685	−	0.989623i	$-0.454105\pi$
$151$	300515.	−	173503.i	1.07257	−	0.619247i	0.928882	+	0.370377i	$0.120771\pi$
$152$	175853.	+	293414.i	0.617365	+	1.03008i
$153$		0			0
$154$	8600.04	+	47267.1i	0.0292212	+	0.160604i
$155$	240286.	+	416188.i	0.803340	+	1.39143i
$156$		0			0
$157$	72572.9	−	125700.i	0.234977	−	0.406992i	−0.724289	−	0.689497i	$-0.757832\pi$
$157$	72572.9	−	125700.i	0.234977	−	0.406992i	0.959266	+	0.282504i	$0.0911651\pi$
$158$	−79079.6	−	28296.0i	−0.252012	−	0.0901743i
$159$		0			0
$160$	−50918.7	+	343145.i	−0.157245	+	1.05969i
$161$		−	93913.2i		−	0.285537i
$162$		0			0
$163$			240037.i			0.707635i	0.935314	+	0.353818i	$0.115117\pi$
$163$			240037.i			0.707635i	−0.935314	+	0.353818i	$0.884883\pi$
$164$	−177920.	+	216788.i	−0.516555	+	0.629397i
$165$		0			0
$166$	−229336.	+	640932.i	−0.645956	+	1.80527i
$167$	144730.	−	250679.i	0.401575	−	0.695548i	−0.592341	−	0.805687i	$-0.701796\pi$
$167$	144730.	−	250679.i	0.401575	−	0.695548i	0.993916	+	0.110139i	$0.0351296\pi$
$168$		0			0
$169$	−380733.	−	659449.i	−1.02542	−	1.77609i
$170$	105084.	−	19119.6i	0.278878	−	0.0507406i
$171$		0			0
$172$	−114278.	−	303648.i	−0.294538	−	0.782617i
$173$	490809.	−	283369.i	1.24680	−	0.719841i	0.276332	−	0.961062i	$-0.410881\pi$
$173$	490809.	−	283369.i	1.24680	−	0.719841i	0.970470	+	0.241221i	$0.0775479\pi$
$174$		0			0
$175$	15635.2	+	9026.99i	0.0385930	+	0.0222817i
$176$	43356.5	+	218015.i	0.105505	+	0.530523i
$177$		0			0
$178$	−153116.	+	129906.i	−0.362218	+	0.307313i
$179$	−440866.			−1.02843			−0.514214	−	0.857662i	$-0.671916\pi$
$179$	−440866.			−1.02843			−0.514214	+	0.857662i	$0.671916\pi$
$180$		0			0
$181$	103852.			0.235623			0.117812	−	0.993036i	$-0.462412\pi$
$181$	103852.			0.235623			0.117812	+	0.993036i	$0.462412\pi$
$182$	179618.	−	152392.i	0.401950	−	0.341022i
$183$		0			0
$184$	−7096.05	−	434456.i	−0.0154516	−	0.946023i
$185$	271968.	+	157021.i	0.584237	+	0.337309i
$186$		0			0
$187$	59270.7	−	34220.0i	0.123947	−	0.0715608i
$188$	−435590.	+	163934.i	−0.898841	+	0.338279i
$189$		0			0
$190$	629845.	−	114598.i	1.26576	−	0.230299i
$191$	−215522.	−	373294.i	−0.427472	−	0.740403i	0.569176	−	0.822216i	$-0.307262\pi$
$191$	−215522.	−	373294.i	−0.427472	−	0.740403i	−0.996648	+	0.0818131i	$0.973929\pi$
$192$		0			0
$193$	20745.9	−	35932.9i	0.0400903	−	0.0694384i	−0.845284	−	0.534317i	$-0.820569\pi$
$193$	20745.9	−	35932.9i	0.0400903	−	0.0694384i	0.885374	+	0.464879i	$0.153902\pi$
$194$	5685.42	−	15889.2i	0.0108457	−	0.0303107i
$195$		0			0
$196$	−377873.	−	310125.i	−0.702596	−	0.576630i
$197$		−	353610.i		−	0.649170i	−0.945856	−	0.324585i	$-0.894775\pi$
$197$		−	353610.i		−	0.649170i	0.945856	−	0.324585i	$-0.105225\pi$
$198$		0			0
$199$		−	167614.i		−	0.300038i	−0.988683	−	0.150019i	$-0.952066\pi$
$199$		−	167614.i		−	0.300038i	0.988683	−	0.150019i	$-0.0479336\pi$
$200$	73012.8	+	40578.8i	0.129070	+	0.0717338i
$201$		0			0
$202$	280059.	+	100210.i	0.482916	+	0.172796i
$203$	−117129.	+	202873.i	−0.199491	+	0.345529i
$204$		0			0
$205$	262427.	+	454537.i	0.436138	+	0.755414i
$206$	12181.6	+	66951.7i	0.0200002	+	0.109924i
$207$		0			0
$208$	819426.	−	718558.i	1.31326	−	1.15160i
$209$	355253.	−	205105.i	0.562563	−	0.324796i
$210$		0			0
$211$	−60893.8	−	35157.0i	−0.0941601	−	0.0543633i	0.452181	−	0.891926i	$-0.350646\pi$
$211$	−60893.8	−	35157.0i	−0.0941601	−	0.0543633i	−0.546341	+	0.837563i	$0.683980\pi$
$212$	−619809.	−	102344.i	−0.947149	−	0.156395i
$213$		0			0
$214$	−327761.	−	386320.i	−0.489241	−	0.576651i
$215$	−607180.			−0.895821
$216$		0			0
$217$	313960.			0.452611
$218$	109337.	+	128872.i	0.155822	+	0.183661i
$219$		0			0
$220$	410440.	+	67772.5i	0.571732	+	0.0944054i
$221$	−290603.	−	167780.i	−0.400239	−	0.231078i
$222$		0			0
$223$	439612.	−	253810.i	0.591980	−	0.341780i	−0.173900	−	0.984763i	$-0.555637\pi$
$223$	439612.	−	253810.i	0.591980	−	0.341780i	0.765880	+	0.642983i	$0.222304\pi$
$224$	177511.	+	140898.i	0.236377	+	0.187622i
$225$		0			0
$226$	−250675.	−	1.37775e6i	−0.326468	−	1.79432i
$227$	−54791.0	−	94900.8i	−0.0705739	−	0.122238i	0.828579	−	0.559872i	$-0.189150\pi$
$227$	−54791.0	−	94900.8i	−0.0705739	−	0.122238i	−0.899153	+	0.437634i	$0.855816\pi$
$228$		0			0
$229$	180234.	−	312174.i	0.227116	−	0.393376i	−0.729836	−	0.683622i	$-0.760404\pi$
$229$	180234.	−	312174.i	0.227116	−	0.393376i	0.956952	+	0.290246i	$0.0937370\pi$
$230$	−765642.	−	273960.i	−0.954346	−	0.341482i
$231$		0			0
$232$	−526526.	+	947371.i	−0.642244	+	1.15558i
$233$			938716.i			1.13278i	0.824138	+	0.566389i	$0.191660\pi$
$233$			938716.i			1.13278i	−0.824138	+	0.566389i	$0.808340\pi$
$234$		0			0
$235$			871012.i			1.02886i
$236$	44997.1	+	36929.7i	0.0525902	+	0.0431615i
$237$		0			0
$238$	23508.5	−	65699.6i	0.0269018	−	0.0751831i
$239$	−163017.	+	282354.i	−0.184603	+	0.319742i	−0.943443	−	0.331536i	$-0.892433\pi$
$239$	−163017.	+	282354.i	−0.184603	+	0.319742i	0.758840	+	0.651278i	$0.225767\pi$
$240$		0			0
$241$	37903.3	+	65650.4i	0.0420373	+	0.0728107i	0.886279	−	0.463153i	$-0.153282\pi$
$241$	37903.3	+	65650.4i	0.0420373	+	0.0728107i	−0.844241	+	0.535963i	$0.819949\pi$
$242$	−634074.	+	115367.i	−0.695988	+	0.126632i
$243$		0			0
$244$	−1.46281e6	+	550529.i	−1.57295	+	0.591978i
$245$	−792284.	+	457425.i	−0.843268	+	0.486861i
$246$		0			0
$247$	−1.74180e6	−	1.00563e6i	−1.81658	−	1.04880i
$248$	1.45242e6	−	23722.7i	1.49956	−	0.0244926i
$249$		0			0
$250$	−688062.	+	583765.i	−0.696269	+	0.590728i
$251$	971568.			0.973394			0.486697	−	0.873571i	$-0.338202\pi$
$251$	971568.			0.973394			0.486697	+	0.873571i	$0.338202\pi$
$252$		0			0
$253$	−521060.			−0.511783
$254$	1.14724e6	−	973337.i	1.11575	−	0.946627i
$255$		0			0
$256$	831839.	+	638401.i	0.793303	+	0.608826i
$257$	−1.19547e6	−	690206.i	−1.12903	−	0.651848i	−0.185342	−	0.982674i	$-0.559339\pi$
$257$	−1.19547e6	−	690206.i	−1.12903	−	0.651848i	−0.943692	+	0.330826i	$0.892673\pi$
$258$		0			0
$259$	177678.	−	102582.i	0.164583	−	0.0950218i
$260$	−718420.	−	1.90892e6i	−0.659091	−	1.75127i
$261$		0			0
$262$	−413659.	+	75263.4i	−0.372297	+	0.0677377i
$263$	−240670.	−	416853.i	−0.214552	−	0.371615i	0.738582	−	0.674164i	$-0.235496\pi$
$263$	−240670.	−	416853.i	−0.214552	−	0.371615i	−0.953134	+	0.302549i	$0.902163\pi$
$264$		0			0
$265$	−587830.	+	1.01815e6i	−0.514206	+	0.890631i
$266$	140903.	−	393786.i	0.122100	−	0.341237i
$267$		0			0
$268$	868887.	−	1.05870e6i	0.738969	−	0.900399i
$269$			1.12150e6i			0.944969i	0.881339	+	0.472484i	$0.156643\pi$
$269$			1.12150e6i			0.944969i	−0.881339	+	0.472484i	$0.843357\pi$
$270$		0			0
$271$		−	873330.i		−	0.722362i	−0.932496	−	0.361181i	$-0.882374\pi$
$271$		−	873330.i		−	0.722362i	0.932496	−	0.361181i	$-0.117626\pi$
$272$	103789.	−	305712.i	0.0850610	−	0.250548i
$273$		0			0
$274$	123647.	+	44243.0i	0.0994963	+	0.0356015i
$275$	50084.5	−	86748.9i	0.0399367	−	0.0691723i
$276$		0			0
$277$	900195.	+	1.55918e6i	0.704915	+	1.22095i	0.966722	+	0.255829i	$0.0823483\pi$
$277$	900195.	+	1.55918e6i	0.704915	+	1.22095i	−0.261807	+	0.965120i	$0.584318\pi$
$278$	336037.	+	1.84691e6i	0.260781	+	1.43329i
$279$		0			0
$280$	363800.	−	218038.i	0.277311	−	0.166203i
$281$	236453.	−	136516.i	0.178640	−	0.103138i	−0.408014	−	0.912976i	$-0.633778\pi$
$281$	236453.	−	136516.i	0.178640	−	0.103138i	0.586654	+	0.809838i	$0.300445\pi$
$282$		0			0
$283$	644438.	+	372067.i	0.478316	+	0.276156i	0.719715	−	0.694270i	$-0.244273\pi$
$283$	644438.	+	372067.i	0.478316	+	0.276156i	−0.241398	+	0.970426i	$0.577606\pi$
$284$	153318.	−	928517.i	0.112797	−	0.683115i
$285$		0			0
$286$	−845516.	−	996578.i	−0.611233	−	0.720437i
$287$	342889.			0.245725
$288$		0			0
$289$	1.32045e6			0.929990
$290$	1.31227e6	+	1.54672e6i	0.916280	+	1.07998i
$291$		0			0
$292$	−198225.	+	1.20048e6i	−0.136051	+	0.823942i
$293$	330601.	+	190873.i	0.224976	+	0.129890i	0.608252	−	0.793744i	$-0.291871\pi$
$293$	330601.	+	190873.i	0.224976	+	0.129890i	−0.383276	+	0.923634i	$0.625204\pi$
$294$		0			0
$295$	94345.2	−	54470.2i	0.0631197	−	0.0364422i
$296$	814213.	−	487986.i	0.540143	−	0.323727i
$297$		0			0
$298$	336515.	+	1.84954e6i	0.219515	+	1.20649i
$299$	1.27737e6	+	2.21248e6i	0.826304	+	1.43120i
$300$		0			0
$301$	−198336.	+	343529.i	−0.126179	+	0.218548i
$302$	−1.84820e6	−	661319.i	−1.16609	−	0.417248i
$303$		0			0
$304$	622085.	−	1.83236e6i	0.386070	−	1.13717i
$305$			2.92506e6i			1.80047i
$306$		0			0
$307$			3.21986e6i			1.94980i	0.222640	+	0.974901i	$0.428533\pi$
$307$			3.21986e6i			1.94980i	−0.222640	+	0.974901i	$0.571467\pi$
$308$	172415.	−	210080.i	0.103562	−	0.126185i
$309$		0			0
$310$	915871.	−	2.55960e6i	0.541290	−	1.51276i
$311$	775835.	−	1.34378e6i	0.454850	−	0.787823i	−0.543830	−	0.839196i	$-0.683026\pi$
$311$	775835.	−	1.34378e6i	0.454850	−	0.787823i	0.998680	+	0.0513724i	$0.0163596\pi$
$312$		0			0
$313$	263995.	+	457253.i	0.152312	+	0.263813i	0.932077	−	0.362260i	$-0.117995\pi$
$313$	263995.	+	457253.i	0.152312	+	0.263813i	−0.779765	+	0.626073i	$0.784661\pi$
$314$	−807807.	+	146977.i	−0.462364	+	0.0841250i
$315$		0			0
$316$	167351.	+	444668.i	0.0942779	+	0.250506i
$317$	−764737.	+	441521.i	−0.427429	+	0.246776i	−0.698251	−	0.715853i	$-0.746038\pi$
$317$	−764737.	+	441521.i	−0.427429	+	0.246776i	0.270822	+	0.962630i	$0.412705\pi$
$318$		0			0
$319$	1.12560e6	+	649867.i	0.619310	+	0.357559i
$320$	1.66652e6	−	1.03617e6i	0.909777	−	0.565658i
$321$		0			0
$322$	−405099.	+	343693.i	−0.217731	+	0.184727i
$323$	−595799.			−0.317756
$324$		0			0
$325$	−491127.			−0.257920
$326$	1.03541e6	−	878462.i	0.539596	−	0.457803i
$327$		0			0
$328$	1.58626e6	−	25908.6i	0.814121	−	0.0132972i
$329$	492799.	+	284518.i	0.251004	+	0.144917i
$330$		0			0
$331$	−128289.	+	74067.9i	−0.0643607	+	0.0371587i	−0.531835	−	0.846848i	$-0.678497\pi$
$331$	−128289.	+	74067.9i	−0.0643607	+	0.0371587i	0.467474	+	0.884007i	$0.345164\pi$
$332$	3.60399e6	−	1.35636e6i	1.79448	−	0.675352i
$333$		0			0
$334$	−1.61098e6	+	293111.i	−0.790177	+	0.143769i
$335$	−1.28158e6	−	2.21976e6i	−0.623928	−	1.08067i
$336$		0			0
$337$	191733.	−	332092.i	0.0919651	−	0.159288i	−0.816373	−	0.577525i	$-0.804019\pi$
$337$	191733.	−	332092.i	0.0919651	−	0.159288i	0.908338	+	0.418237i	$0.137352\pi$
$338$	−1.45120e6	+	4.05569e6i	−0.690930	+	1.93096i
$339$		0			0
$340$	−467048.	−	383312.i	−0.219111	−	0.179827i
$341$		−	1.74195e6i		−	0.811239i
$342$		0			0
$343$			1.25524e6i			0.576091i
$344$	−891577.	+	1.60420e6i	−0.406221	+	0.730908i
$345$		0			0
$346$	−3.01853e6	−	1.08008e6i	−1.35552	−	0.485028i
$347$	−602848.	+	1.04416e6i	−0.268772	+	0.465527i	−0.968545	−	0.248839i	$-0.919951\pi$
$347$	−602848.	+	1.04416e6i	−0.268772	+	0.465527i	0.699773	+	0.714365i	$0.253284\pi$
$348$		0			0
$349$	−145755.	−	252456.i	−0.0640562	−	0.110949i	0.832219	−	0.554447i	$-0.187070\pi$
$349$	−145755.	−	252456.i	−0.0640562	−	0.110949i	−0.896275	+	0.443499i	$0.853737\pi$
$350$	−18281.7	−	100479.i	−0.00797714	−	0.0438435i
$351$		0			0
$352$	781744.	−	984887.i	0.336285	−	0.423672i
$353$	162770.	−	93975.5i	0.0695246	−	0.0401400i	−0.464835	−	0.885397i	$-0.653886\pi$
$353$	162770.	−	93975.5i	0.0695246	−	0.0401400i	0.534359	+	0.845257i	$0.320553\pi$
$354$		0			0
$355$	−1.52526e6	−	880610.i	−0.642352	−	0.370862i
$356$	1.12071e6	+	185054.i	0.468673	+	0.0773880i
$357$		0			0
$358$	1.61343e6	+	1.90169e6i	0.665340	+	0.784211i
$359$	−1.70884e6			−0.699786			−0.349893	−	0.936790i	$-0.613782\pi$
$359$	−1.70884e6			−0.699786			−0.349893	+	0.936790i	$0.613782\pi$
$360$		0			0
$361$	−1.09496e6			−0.442211
$362$	−380066.	−	447970.i	−0.152436	−	0.179671i
$363$		0			0
$364$	−1.31470e6	−	217085.i	−0.520082	−	0.0858768i
$365$	1.97201e6	+	1.13854e6i	0.774776	+	0.447317i
$366$		0			0
$367$	3.26612e6	−	1.88569e6i	1.26581	−	0.730813i	0.291614	−	0.956536i	$-0.405808\pi$
$367$	3.26612e6	−	1.88569e6i	1.26581	−	0.730813i	0.974191	+	0.225723i	$0.0724745\pi$
$368$	−1.84808e6	+	1.62059e6i	−0.711378	+	0.623810i
$369$		0			0
$370$	−318004.	−	1.74779e6i	−0.120761	−	0.663722i
$371$	384031.	+	665162.i	0.144855	+	0.250895i
$372$		0			0
$373$	1.13464e6	−	1.96526e6i	0.422267	−	0.731388i	−0.573894	−	0.818930i	$-0.694568\pi$
$373$	1.13464e6	−	1.96526e6i	0.422267	−	0.731388i	0.996161	+	0.0875420i	$0.0279012\pi$
$374$	−364522.	−	130432.i	−0.134755	−	0.0482176i
$375$		0			0
$376$	2.30126e6	+	1.27899e6i	0.839453	+	0.466548i
$377$		−	6.37257e6i		−	2.30920i
$378$		0			0
$379$		−	4.07165e6i		−	1.45604i	−0.685557	−	0.728019i	$-0.740441\pi$
$379$		−	4.07165e6i		−	1.45604i	0.685557	−	0.728019i	$-0.259559\pi$
$380$	−2.79936e6	−	2.29747e6i	−0.994489	−	0.816190i
$381$		0			0
$382$	−821478.	+	2.29580e6i	−0.288030	+	0.804964i
$383$	1.22056e6	−	2.11407e6i	0.425170	−	0.736415i	−0.571267	−	0.820765i	$-0.693548\pi$
$383$	1.22056e6	−	2.11407e6i	0.425170	−	0.736415i	0.996436	+	0.0843491i	$0.0268811\pi$
$384$		0			0
$385$	−254307.	−	440473.i	−0.0874393	−	0.151449i
$386$	−230922.	+	42015.2i	−0.0788854	+	0.0143529i
$387$		0			0
$388$	−89345.5	+	33625.2i	−0.0301296	+	0.0113393i
$389$	−924047.	+	533499.i	−0.309614	+	0.178756i	−0.646754	−	0.762699i	$-0.723874\pi$
$389$	−924047.	+	533499.i	−0.309614	+	0.178756i	0.337140	+	0.941455i	$0.390540\pi$
$390$		0			0
$391$	655407.	+	378399.i	0.216805	+	0.125172i
$392$	45160.2	+	2.76493e6i	0.0148436	+	0.908803i
$393$		0			0
$394$	−1.52531e6	+	1.29410e6i	−0.495014	+	0.419980i
$395$	889166.			0.286741
$396$		0			0
$397$	−2.64187e6			−0.841271			−0.420635	−	0.907230i	$-0.638193\pi$
$397$	−2.64187e6			−0.841271			−0.420635	+	0.907230i	$0.638193\pi$
$398$	−723009.	+	613415.i	−0.228789	+	0.194109i
$399$		0			0
$400$	−92166.1	−	463450.i	−0.0288019	−	0.144828i
$401$	−2.41745e6	−	1.39571e6i	−0.750751	−	0.433446i	0.0752142	−	0.997167i	$-0.476036\pi$
$401$	−2.41745e6	−	1.39571e6i	−0.750751	−	0.433446i	−0.825965	+	0.563721i	$0.809369\pi$
$402$		0			0
$403$	−7.39649e6	+	4.27037e6i	−2.26863	+	1.30979i
$404$	−592671.	−	1.57479e6i	−0.180659	−	0.480030i
$405$		0			0
$406$	1.30376e6	−	237213.i	0.392538	−	0.0714205i
$407$	−569159.	−	985812.i	−0.170313	−	0.294990i
$408$		0			0
$409$	−502887.	+	871025.i	−0.148649	+	0.257468i	−0.930728	−	0.365711i	$-0.880826\pi$
$409$	−502887.	+	871025.i	−0.148649	+	0.257468i	0.782079	+	0.623179i	$0.214159\pi$
$410$	1.00026e6	−	2.79546e6i	0.293870	−	0.821284i
$411$		0			0
$412$	244218.	−	297568.i	0.0708818	−	0.0863661i
$413$		−	71171.2i		−	0.0205319i
$414$		0			0
$415$		−	7.20660e6i		−	2.05404i
$416$	−6.09838e6	−	904928.i	−1.72775	−	0.256378i
$417$		0			0
$418$	−2.18485e6	−	781775.i	−0.611618	−	0.218847i
$419$	−2.85052e6	+	4.93724e6i	−0.793210	+	1.37388i	0.130759	+	0.991414i	$0.458259\pi$
$419$	−2.85052e6	+	4.93724e6i	−0.793210	+	1.37388i	−0.923969	+	0.382466i	$0.875075\pi$
$420$		0			0
$421$	−2.95835e6	−	5.12400e6i	−0.813474	−	1.40898i	−0.910419	−	0.413688i	$-0.864240\pi$
$421$	−2.95835e6	−	5.12400e6i	−0.813474	−	1.40898i	0.0969446	−	0.995290i	$-0.469093\pi$
$422$	71201.1	+	391332.i	0.0194628	+	0.106971i
$423$		0			0
$424$	1.82685e6	+	3.04812e6i	0.493500	+	0.823412i
$425$	−125996.	+	72743.8i	−0.0338364	+	0.0195355i
$426$		0			0
$427$	1.65493e6	+	955477.i	0.439249	+	0.253601i
$428$	−466902.	+	2.82762e6i	−0.123202	+	0.746126i
$429$		0			0
$430$	2.22209e6	+	2.61910e6i	0.579550	+	0.683094i
$431$	−516224.			−0.133858			−0.0669291	−	0.997758i	$-0.521320\pi$
$431$	−516224.			−0.133858			−0.0669291	+	0.997758i	$0.521320\pi$
$432$		0			0
$433$	6.50137e6			1.66642			0.833212	−	0.552954i	$-0.186499\pi$
$433$	6.50137e6			1.66642			0.833212	+	0.552954i	$0.186499\pi$
$434$	−1.14900e6	−	1.35428e6i	−0.292816	−	0.345131i
$435$		0			0
$436$	155753.	−	943264.i	0.0392393	−	0.237639i
$437$	3.92833e6	+	2.26802e6i	0.984021	+	0.568125i
$438$		0			0
$439$	−762498.	+	440228.i	−0.188833	+	0.109023i	−0.591436	−	0.806352i	$-0.701439\pi$
$439$	−762498.	+	440228.i	−0.188833	+	0.109023i	0.402603	+	0.915375i	$0.368105\pi$
$440$	−1.20974e6	−	2.01848e6i	−0.297894	−	0.497041i
$441$		0			0
$442$	339793.	+	1.86755e6i	0.0827292	+	0.454692i
$443$	372571.	+	645312.i	0.0901985	+	0.156228i	0.907595	−	0.419848i	$-0.137917\pi$
$443$	372571.	+	645312.i	0.0901985	+	0.156228i	−0.817396	+	0.576076i	$0.804583\pi$
$444$		0			0
$445$	1.06289e6	−	1.84098e6i	0.254442	−	0.440706i
$446$	−2.70366e6	−	967418.i	−0.643599	−	0.230291i
$447$		0			0
$448$	−41868.0	−	1.28134e6i	−0.00985570	−	0.301627i
$449$		−	3.80614e6i		−	0.890983i	−0.895286	−	0.445492i	$-0.853029\pi$
$449$		−	3.80614e6i		−	0.890983i	0.895286	−	0.445492i	$-0.146971\pi$
$450$		0			0
$451$		−	1.90246e6i		−	0.440427i
$452$	−5.02558e6	+	6.12343e6i	−1.15702	+	1.40977i
$453$		0			0
$454$	−208840.	+	583651.i	−0.0475527	+	0.132896i
$455$	−1.24686e6	+	2.15963e6i	−0.282352	+	0.489047i
$456$		0			0
$457$	−1.54711e6	−	2.67967e6i	−0.346521	−	0.600192i	0.639108	−	0.769117i	$-0.279304\pi$
$457$	−1.54711e6	−	2.67967e6i	−0.346521	−	0.600192i	−0.985629	+	0.168925i	$0.945970\pi$
$458$	−2.00618e6	+	365015.i	−0.446895	+	0.0813106i
$459$		0			0
$460$	1.62028e6	+	4.30524e6i	0.357021	+	0.948642i
$461$	6.16631e6	−	3.56012e6i	1.35137	−	0.780212i	0.362926	−	0.931818i	$-0.381778\pi$
$461$	6.16631e6	−	3.56012e6i	1.35137	−	0.780212i	0.988441	+	0.151606i	$0.0484445\pi$
$462$		0			0
$463$	4.12079e6	+	2.37914e6i	0.893363	+	0.515784i	0.875041	−	0.484049i	$-0.160834\pi$
$463$	4.12079e6	+	2.37914e6i	0.893363	+	0.515784i	0.0183222	+	0.999832i	$0.494168\pi$
$464$	6.01345e6	−	1.19589e6i	1.29667	−	0.257868i
$465$		0			0
$466$	4.04919e6	−	3.43541e6i	0.863781	−	0.732848i
$467$	7.37952e6			1.56580			0.782900	−	0.622148i	$-0.213740\pi$
$467$	7.37952e6			1.56580			0.782900	+	0.622148i	$0.213740\pi$
$468$		0			0
$469$	−1.67452e6			−0.351528
$470$	3.75715e6	−	3.18764e6i	0.784538	−	0.665617i
$471$		0			0
$472$	−5377.68	−	329249.i	−0.00111107	−	0.0680251i
$473$	1.90600e6	+	1.10043e6i	0.391716	+	0.226157i
$474$		0			0
$475$	−755186.	+	436007.i	−0.153575	+	0.0886665i
$476$	−369432.	+	139036.i	−0.0747338	+	0.0281260i
$477$		0			0
$478$	1.81454e6	−	330148.i	0.363243	−	0.0660904i
$479$	553793.	+	959197.i	0.110283	+	0.191016i	0.915884	−	0.401442i	$-0.131491\pi$
$479$	553793.	+	959197.i	0.110283	+	0.191016i	−0.805601	+	0.592458i	$0.798158\pi$
$480$		0			0
$481$	−2.79058e6	+	4.83342e6i	−0.549960	+	0.952559i
$482$	144472.	−	403758.i	0.0283247	−	0.0791596i
$483$		0			0
$484$	2.81816e6	+	2.31290e6i	0.546829	+	0.448790i
$485$			178657.i			0.0344878i
$486$		0			0
$487$		−	763869.i		−	0.145948i	−0.997334	−	0.0729738i	$-0.976751\pi$
$487$		−	763869.i		−	0.145948i	0.997334	−	0.0729738i	$-0.0232489\pi$
$488$	7.72817e6	+	4.29513e6i	1.46902	+	0.816445i
$489$		0			0
$490$	4.87264e6	+	1.74351e6i	0.916799	+	0.328046i
$491$	3.47276e6	−	6.01500e6i	0.650087	−	1.12598i	−0.333015	−	0.942922i	$-0.608066\pi$
$491$	3.47276e6	−	6.01500e6i	0.650087	−	1.12598i	0.983101	−	0.183061i	$-0.0586007\pi$
$492$		0			0
$493$	−943881.	−	1.63485e6i	−0.174904	−	0.302943i
$494$	2.03663e6	+	1.11936e7i	0.375486	+	2.06373i
$495$		0			0
$496$	−5.41775e6	−	6.17828e6i	−0.988815	−	1.12762i
$497$	−996459.	+	575306.i	−0.180954	+	0.104474i
$498$		0			0
$499$	5.34730e6	+	3.08727e6i	0.961354	+	0.555038i	0.896590	−	0.442862i	$-0.146037\pi$
$499$	5.34730e6	+	3.08727e6i	0.961354	+	0.555038i	0.0647647	+	0.997901i	$0.479370\pi$
$500$	5.03619e6	+	831584.i	0.900901	+	0.148758i
$501$		0			0
$502$	−3.55564e6	−	4.19090e6i	−0.629736	−	0.742246i
$503$	−3.43627e6			−0.605574			−0.302787	−	0.953058i	$-0.597917\pi$
$503$	−3.43627e6			−0.605574			−0.302787	+	0.953058i	$0.597917\pi$
$504$		0			0
$505$	−3.14897e6			−0.549465
$506$	1.90692e6	+	2.24761e6i	0.331097	+	0.390252i
$507$		0			0
$508$	−8.39706e6	−	1.38654e6i	−1.44367	−	0.238381i
$509$	−2.45696e6	−	1.41853e6i	−0.420343	−	0.242685i	0.274881	−	0.961478i	$-0.411362\pi$
$509$	−2.45696e6	−	1.41853e6i	−0.420343	−	0.242685i	−0.695224	+	0.718793i	$0.744695\pi$
$510$		0			0
$511$	1.28832e6	−	743811.i	0.218259	−	0.126012i
$512$	−290506.	−	5.92452e6i	−0.0489756	−	0.998800i
$513$		0			0
$514$	1.39783e6	+	7.68266e6i	0.233370	+	1.28264i
$515$	−360214.	−	623909.i	−0.0598470	−	0.103658i
$516$		0			0
$517$	1.57859e6	−	2.73420e6i	0.259743	−	0.449888i
$518$	−1.09274e6	−	391001.i	−0.178934	−	0.0640256i
$519$		0			0
$520$	−5.60499e6	+	1.00850e7i	−0.909006	+	1.63556i
$521$			1.84176e6i			0.297261i	0.988893	+	0.148631i	$0.0474866\pi$
$521$			1.84176e6i			0.297261i	−0.988893	+	0.148631i	$0.952513\pi$
$522$		0			0
$523$			1.03954e7i			1.66183i	0.556398	+	0.830916i	$0.312183\pi$
$523$			1.03954e7i			1.66183i	−0.556398	+	0.830916i	$0.687817\pi$
$524$	1.83852e6	+	1.50889e6i	0.292509	+	0.240066i
$525$		0			0
$526$	−917335.	+	2.56370e6i	−0.144565	+	0.404019i
$527$	−1.26502e6	+	2.19108e6i	−0.198413	+	0.343662i
$528$		0			0
$529$	337272.	+	584172.i	0.0524012	+	0.0907615i
$530$	6.54312e6	−	1.19049e6i	1.01180	−	0.184093i
$531$		0			0
$532$	−2.21427e6	+	833342.i	−0.339197	+	0.127657i
$533$	−8.07804e6	+	4.66386e6i	−1.23165	+	0.711094i
$534$		0			0
$535$	4.64490e6	+	2.68173e6i	0.701603	+	0.405071i
$536$	−7.74660e6	+	126527.i	−1.16466	+	0.0190226i
$537$		0			0
$538$	4.83762e6	−	4.10433e6i	0.720570	−	0.611346i
$539$	3.31609e6			0.491648
$540$		0			0
$541$	330411.			0.0485357			0.0242679	−	0.999705i	$-0.492275\pi$
$541$	330411.			0.0485357			0.0242679	+	0.999705i	$0.492275\pi$
$542$	−3.76715e6	+	3.19612e6i	−0.550826	+	0.467331i
$543$		0			0
$544$	−1.69854e6	+	671113.i	−0.246081	+	0.0972296i
$545$	−1.54949e6	−	894596.i	−0.223458	−	0.129014i
$546$		0			0
$547$	−1.06834e7	+	6.16808e6i	−1.52666	+	0.881417i	−0.527160	+	0.849766i	$0.676743\pi$
$547$	−1.06834e7	+	6.16808e6i	−1.52666	+	0.881417i	−0.999499	+	0.0316507i	$0.989924\pi$
$548$	−261666.	−	695272.i	−0.0372216	−	0.0989017i
$549$		0			0
$550$	−557489.	+	101433.i	−0.0785832	+	0.0142979i
$551$	−5.65737e6	−	9.79885e6i	−0.793845	−	1.37498i
$552$		0			0
$553$	290448.	−	503070.i	0.0403883	−	0.0699545i
$554$	3.43117e6	−	9.58916e6i	0.474971	−	1.32741i
$555$		0			0
$556$	6.73693e6	−	8.20863e6i	0.924220	−	1.12612i
$557$			5.94173e6i			0.811474i	0.913990	+	0.405737i	$0.132985\pi$
$557$			5.94173e6i			0.811474i	−0.913990	+	0.405737i	$0.867015\pi$
$558$		0			0
$559$		−	1.07908e7i		−	1.46058i
$560$	−2.27191e6	−	771315.i	−0.306141	−	0.103935i
$561$		0			0
$562$	−1.45421e6	−	520343.i	−0.194217	−	0.0694942i
$563$	−66573.9	+	115309.i	−0.00885182	+	0.0153318i	−0.870417	−	0.492315i	$-0.836151\pi$
$563$	−66573.9	+	115309.i	−0.00885182	+	0.0153318i	0.861566	+	0.507646i	$0.169484\pi$
$564$		0			0
$565$	7.41258e6	+	1.28390e7i	0.976896	+	1.69203i
$566$	−753521.	−	4.14146e6i	−0.0988676	−	0.543391i
$567$		0			0
$568$	−4.56629e6	+	2.73674e6i	−0.593872	+	0.355929i
$569$	−3.70587e6	+	2.13959e6i	−0.479854	+	0.277044i	−0.720356	−	0.693605i	$-0.756021\pi$
$569$	−3.70587e6	+	2.13959e6i	−0.479854	+	0.277044i	0.240501	+	0.970649i	$0.422688\pi$
$570$		0			0
$571$	−525371.	−	303323.i	−0.0674335	−	0.0389328i	0.465904	−	0.884835i	$-0.345729\pi$
$571$	−525371.	−	303323.i	−0.0674335	−	0.0389328i	−0.533338	+	0.845902i	$0.679062\pi$
$572$	−1.20445e6	+	7.29434e6i	−0.153922	+	0.932171i
$573$		0			0
$574$	−1.25487e6	−	1.47907e6i	−0.158971	−	0.187374i
$575$	1.10765e6			0.139712
$576$		0			0
$577$	−496600.			−0.0620965			−0.0310483	−	0.999518i	$-0.509885\pi$
$577$	−496600.			−0.0620965			−0.0310483	+	0.999518i	$0.509885\pi$
$578$	−4.83245e6	−	5.69583e6i	−0.601656	−	0.709149i
$579$		0			0
$580$	1.86935e6	−	1.13211e7i	0.230739	−	1.39739i
$581$	−4.07733e6	−	2.35405e6i	−0.501113	−	0.289318i
$582$		0			0
$583$	3.69053e6	−	2.13073e6i	0.449694	−	0.259631i
$584$	5.90375e6	−	3.53833e6i	0.716302	−	0.429305i
$585$		0			0
$586$	−386561.	−	2.12460e6i	−0.0465023	−	0.255583i
$587$	7.37488e6	+	1.27737e7i	0.883405	+	1.53010i	0.847531	+	0.530746i	$0.178088\pi$
$587$	7.37488e6	+	1.27737e7i	0.883405	+	1.53010i	0.0358744	+	0.999356i	$0.488578\pi$
$588$		0			0
$589$	−7.58219e6	+	1.31327e7i	−0.900547	+	1.55979i
$590$	−580234.	−	207618.i	−0.0686236	−	0.0245547i
$591$		0			0
$592$	−5.08472e6	−	1.72626e6i	−0.596297	−	0.202443i
$593$			1.01532e7i			1.18568i	0.805322	+	0.592838i	$0.201992\pi$
$593$			1.01532e7i			1.18568i	−0.805322	+	0.592838i	$0.798008\pi$
$594$		0			0
$595$			738722.i			0.0855438i
$596$	6.74652e6	−	8.22032e6i	0.777973	−	0.947923i
$597$		0			0
$598$	4.86881e6	−	1.36070e7i	0.556763	−	1.55600i
$599$	5.29325e6	−	9.16817e6i	0.602775	−	1.04404i	−0.389624	−	0.920974i	$-0.627395\pi$
$599$	5.29325e6	−	9.16817e6i	0.602775	−	1.04404i	0.992399	−	0.123062i	$-0.0392715\pi$
$600$		0			0
$601$	6.67071e6	+	1.15540e7i	0.753331	+	1.30481i	0.946200	+	0.323583i	$0.104887\pi$
$601$	6.67071e6	+	1.15540e7i	0.753331	+	1.30481i	−0.192869	+	0.981224i	$0.561779\pi$
$602$	2.20768e6	−	401677.i	0.248281	−	0.0451737i
$603$		0			0
$604$	3.91123e6	+	1.03925e7i	0.436235	+	1.15912i
$605$	5.90881e6	−	3.41146e6i	0.656314	−	0.378923i
$606$		0			0
$607$	−6.57795e6	−	3.79778e6i	−0.724635	−	0.418368i	0.0918216	−	0.995775i	$-0.470731\pi$
$607$	−6.57795e6	−	3.79778e6i	−0.724635	−	0.418368i	−0.816456	+	0.577408i	$0.804064\pi$
$608$	−1.01806e7	+	4.02247e6i	−1.11690	+	0.441300i
$609$		0			0
$610$	1.26174e7	−	1.07048e7i	1.37292	−	1.16481i
$611$	−1.54796e7			−1.67748
$612$		0			0
$613$	1.15773e7			1.24438			0.622192	−	0.782865i	$-0.286242\pi$
$613$	1.15773e7			1.24438			0.622192	+	0.782865i	$0.286242\pi$
$614$	1.38890e7	−	1.17837e7i	1.48679	−	1.26142i
$615$		0			0
$616$	−1.53717e6	+	25106.9i	−0.163219	+	0.00266589i
$617$	4.79775e6	+	2.76998e6i	0.507370	+	0.292930i	0.731752	−	0.681571i	$-0.238703\pi$
$617$	4.79775e6	+	2.76998e6i	0.507370	+	0.292930i	−0.224382	+	0.974501i	$0.572036\pi$
$618$		0			0
$619$	−399838.	+	230847.i	−0.0419428	+	0.0242157i	−0.520825	−	0.853664i	$-0.674376\pi$
$619$	−399838.	+	230847.i	−0.0419428	+	0.0242157i	0.478882	+	0.877879i	$0.341042\pi$
$620$	−1.43928e7	+	5.41672e6i	−1.50371	+	0.565923i
$621$		0			0
$622$	−8.63579e6	+	1.57124e6i	−0.895006	+	0.162842i
$623$	−694390.	−	1.20272e6i	−0.0716776	−	0.124149i
$624$		0			0
$625$	5.49736e6	−	9.52171e6i	0.562930	−	0.975023i
$626$	1.00624e6	−	2.81216e6i	0.102628	−	0.286816i
$627$		0			0
$628$	3.59032e6	+	2.94662e6i	0.363273	+	0.298143i
$629$			1.65332e6i			0.166621i
$630$		0			0
$631$		−	1.33405e7i		−	1.33383i	−0.745136	−	0.666913i	$-0.767615\pi$
$631$		−	1.33405e7i		−	1.33383i	0.745136	−	0.666913i	$-0.232385\pi$
$632$	1.30564e6	−	2.34922e6i	0.130026	−	0.233955i
$633$		0			0
$634$	4.70322e6	+	1.68289e6i	0.464700	+	0.166278i
$635$	−7.96382e6	+	1.37937e7i	−0.783767	+	1.35752i
$636$		0			0
$637$	−8.12936e6	−	1.40805e7i	−0.793794	−	1.37489i
$638$	−1.31613e6	−	7.23365e6i	−0.128011	−	0.703567i
$639$		0			0
$640$	−1.05685e7	−	3.39655e6i	−1.01991	−	0.327784i
$641$	2.31892e6	−	1.33883e6i	0.222915	−	0.128700i	−0.384384	−	0.923173i	$-0.625586\pi$
$641$	2.31892e6	−	1.33883e6i	0.222915	−	0.128700i	0.607299	+	0.794473i	$0.292253\pi$
$642$		0			0
$643$	−1.46328e7	−	8.44826e6i	−1.39573	−	0.805824i	−0.401786	−	0.915734i	$-0.631610\pi$
$643$	−1.46328e7	−	8.44826e6i	−1.39573	−	0.805824i	−0.993942	+	0.109910i	$0.964944\pi$
$644$	2.96507e6	+	489598.i	0.281722	+	0.0465184i
$645$		0			0
$646$	2.18044e6	+	2.57000e6i	0.205571	+	0.242299i
$647$	−7.65712e6			−0.719126			−0.359563	−	0.933121i	$-0.617074\pi$
$647$	−7.65712e6			−0.719126			−0.359563	+	0.933121i	$0.617074\pi$
$648$		0			0
$649$	−394880.			−0.0368005
$650$	1.79737e6	+	2.11850e6i	0.166861	+	0.196673i
$651$		0			0
$652$	−7.57857e6	−	1.25139e6i	−0.698181	−	0.115285i
$653$	−957462.	−	552791.i	−0.0878696	−	0.0507315i	0.455421	−	0.890276i	$-0.349489\pi$
$653$	−957462.	−	552791.i	−0.0878696	−	0.0507315i	−0.543291	+	0.839544i	$0.682822\pi$
$654$		0			0
$655$	3.85480e6	−	2.22557e6i	0.351074	−	0.202693i
$656$	−5.91697e6	−	6.74757e6i	−0.536834	−	0.612192i
$657$		0			0
$658$	−576214.	−	3.16696e6i	−0.0518823	−	0.285153i
$659$	7.66650e6	+	1.32788e7i	0.687675	+	1.19109i	0.972588	+	0.232535i	$0.0747021\pi$
$659$	7.66650e6	+	1.32788e7i	0.687675	+	1.19109i	−0.284912	+	0.958554i	$0.591965\pi$
$660$		0			0
$661$	3.77496e6	−	6.53842e6i	0.336054	−	0.582062i	−0.647633	−	0.761952i	$-0.724241\pi$
$661$	3.77496e6	−	6.53842e6i	0.336054	−	0.582062i	0.983687	+	0.179890i	$0.0575743\pi$
$662$	788995.	+	282316.i	0.0699728	+	0.0250375i
$663$		0			0
$664$	−1.90402e7	−	1.05821e7i	−1.67591	−	0.931432i
$665$			4.42770e6i			0.388261i
$666$		0			0
$667$			1.43723e7i			1.25087i
$668$	7.16005e6	+	5.87634e6i	0.620833	+	0.509526i
$669$		0			0
$670$	−4.88485e6	+	1.36518e7i	−0.420402	+	1.17491i
$671$	5.30128e6	−	9.18209e6i	0.454543	−	0.787291i
$672$		0			0
$673$	1.45359e6	+	2.51769e6i	0.123710	+	0.214271i	0.921228	−	0.389023i	$-0.127188\pi$
$673$	1.45359e6	+	2.51769e6i	0.123710	+	0.214271i	−0.797518	+	0.603295i	$0.793854\pi$
$674$	−2.13418e6	+	388304.i	−0.180959	+	0.0329248i
$675$		0			0
$676$	2.28053e7	−	8.58278e6i	1.91942	−	0.722372i
$677$	−8.20582e6	+	4.73763e6i	−0.688098	+	0.397274i	−0.802899	−	0.596115i	$-0.796710\pi$
$677$	−8.20582e6	+	4.73763e6i	−0.688098	+	0.397274i	0.114801	+	0.993389i	$0.463377\pi$
$678$		0			0
$679$	101080.	+	58358.6i	0.00841377	+	0.00485769i
$680$	55817.6	+	3.41744e6i	0.00462913	+	0.283419i
$681$		0			0
$682$	−7.51396e6	+	6.37499e6i	−0.618597	+	0.524830i
$683$	6.62953e6			0.543789			0.271895	−	0.962327i	$-0.412350\pi$
$683$	6.62953e6			0.543789			0.271895	+	0.962327i	$0.412350\pi$
$684$		0			0
$685$	−1.39028e6			−0.113208
$686$	5.41453e6	−	4.59379e6i	0.439289	−	0.372701i
$687$		0			0
$688$	1.01827e7	−	2.02503e6i	0.820146	−	0.163102i
$689$	−1.80946e7	−	1.04469e7i	−1.45211	−	0.838378i
$690$		0			0
$691$	6.59285e6	−	3.80638e6i	0.525264	−	0.303261i	−0.213822	−	0.976873i	$-0.568591\pi$
$691$	6.59285e6	−	3.80638e6i	0.525264	−	0.303261i	0.739086	+	0.673611i	$0.235258\pi$
$692$	6.38792e6	+	1.69733e7i	0.507101	+	1.34742i
$693$		0			0
$694$	6.71028e6	−	1.22091e6i	0.528861	−	0.0962240i
$695$	−9.93677e6	−	1.72110e7i	−0.780339	−	1.35159i
$696$		0			0
$697$	−1.38159e6	+	2.39298e6i	−0.107720	+	0.186576i
$698$	−555559.	+	1.55263e6i	−0.0431610	+	0.120623i
$699$		0			0
$700$	−366515.	+	446582.i	−0.0282714	+	0.0344473i
$701$		−	3.35628e6i		−	0.257966i	−0.991647	−	0.128983i	$-0.958829\pi$
$701$		−	3.35628e6i		−	0.257966i	0.991647	−	0.128983i	$-0.0411713\pi$
$702$		0			0
$703$			9.90954e6i			0.756249i
$704$	−7.10929e6	+	232297.i	−0.540623	+	0.0176649i
$705$		0			0
$706$	−1.00106e6	−	358195.i	−0.0755869	−	0.0270463i
$707$	−1.02862e6	+	1.78162e6i	−0.0773936	+	0.134050i
$708$		0			0
$709$	3.57561e6	+	6.19313e6i	0.267137	+	0.462695i	0.968121	−	0.250482i	$-0.0805890\pi$
$709$	3.57561e6	+	6.19313e6i	0.267137	+	0.462695i	−0.700984	+	0.713177i	$0.747256\pi$
$710$	1.78344e6	+	9.80204e6i	0.132774	+	0.729744i
$711$		0			0
$712$	−3.30323e6	−	5.51149e6i	−0.244196	−	0.407445i
$713$	1.66815e7	−	9.63109e6i	1.22889	−	0.709499i
$714$		0			0
$715$	1.19823e7	+	6.91798e6i	0.876547	+	0.506074i
$716$	2.29837e6	−	1.39192e7i	0.167547	−	1.01469i
$717$		0			0
$718$	6.25383e6	+	7.37116e6i	0.452725	+	0.533611i
$719$	−1.05572e7			−0.761603			−0.380801	−	0.924657i	$-0.624352\pi$
$719$	−1.05572e7			−0.761603			−0.380801	+	0.924657i	$0.624352\pi$
$720$		0			0
$721$	−470659.			−0.0337185
$722$	4.00721e6	+	4.72314e6i	0.286087	+	0.337200i
$723$		0			0
$724$	−541412.	+	3.27887e6i	−0.0383868	+	0.232475i
$725$	−2.39278e6	−	1.38147e6i	−0.169066	−	0.0976104i
$726$		0			0
$727$	−457178.	+	263952.i	−0.0320811	+	0.0185220i	−0.515955	−	0.856616i	$-0.672563\pi$
$727$	−457178.	+	263952.i	−0.0320811	+	0.0185220i	0.483874	+	0.875138i	$0.339229\pi$
$728$	3.87498e6	+	6.46546e6i	0.270982	+	0.452138i
$729$		0			0
$730$	−2.30580e6	−	1.26730e7i	−0.160146	−	0.880184i
$731$	−1.59829e6	−	2.76832e6i	−0.110627	−	0.191612i
$732$		0			0
$733$	−1.01725e7	+	1.76192e7i	−0.699304	+	1.21123i	0.269404	+	0.963027i	$0.413173\pi$
$733$	−1.01725e7	+	1.76192e7i	−0.699304	+	1.21123i	−0.968708	+	0.248202i	$0.920160\pi$
$734$	−2.00870e7	−	7.18748e6i	−1.37618	−	0.492421i
$735$		0			0
$736$	1.37539e7	+	2.04091e6i	0.935901	+	0.138877i
$737$			9.29078e6i			0.630062i
$738$		0			0
$739$		−	4.56621e6i		−	0.307570i	−0.988104	−	0.153785i	$-0.950854\pi$
$739$		−	4.56621e6i		−	0.307570i	0.988104	−	0.153785i	$-0.0491464\pi$
$740$	−6.37539e6	+	7.76811e6i	−0.427984	+	0.521478i
$741$		0			0
$742$	1.46377e6	−	4.09082e6i	0.0976028	−	0.272773i
$743$	8.52924e6	−	1.47731e7i	0.566811	−	0.981745i	−0.430068	−	0.902797i	$-0.641510\pi$
$743$	8.52924e6	−	1.47731e7i	0.566811	−	0.981745i	0.996879	−	0.0789485i	$-0.0251563\pi$
$744$		0			0
$745$	−9.95091e6	−	1.72355e7i	−0.656859	−	1.13771i
$746$	−1.26297e7	+	2.29791e6i	−0.830893	+	0.151177i
$747$		0			0
$748$	771413.	+	2.04972e6i	0.0504119	+	0.133949i
$749$	3.03453e6	−	1.75199e6i	0.197645	−	0.114111i
$750$		0			0
$751$	−4.42935e6	−	2.55729e6i	−0.286576	−	0.165455i	0.349821	−	0.936817i	$-0.386243\pi$
$751$	−4.42935e6	−	2.55729e6i	−0.286576	−	0.165455i	−0.636397	+	0.771362i	$0.719576\pi$
$752$	−2.90495e6	−	1.46073e7i	−0.187324	−	0.941943i
$753$		0			0
$754$	−2.74884e7	+	2.33217e7i	−1.76084	+	1.49393i
$755$	2.07811e7			1.32679
$756$		0			0
$757$	6.36558e6			0.403736			0.201868	−	0.979413i	$-0.435299\pi$
$757$	6.36558e6			0.403736			0.201868	+	0.979413i	$0.435299\pi$
$758$	−1.75633e7	+	1.49010e7i	−1.11028	+	0.941981i
$759$		0			0
$760$	334556.	+	2.04832e7i	0.0210104	+	1.28636i
$761$	9.28199e6	+	5.35896e6i	0.581005	+	0.335443i	0.761533	−	0.648127i	$-0.224447\pi$
$761$	9.28199e6	+	5.35896e6i	0.581005	+	0.335443i	−0.180528	+	0.983570i	$0.557781\pi$
$762$		0			0
$763$	−1.01228e6	+	584443.i	−0.0629494	+	0.0363438i
$764$	1.29094e7	−	4.85845e6i	0.800153	−	0.301137i
$765$		0			0
$766$	−1.35860e7	+	2.47192e6i	−0.836605	+	0.152217i
$767$	968045.	+	1.67670e6i	0.0594165	+	0.102912i
$768$		0			0
$769$	7.59857e6	−	1.31611e7i	0.463358	−	0.802559i	−0.535768	−	0.844365i	$-0.679978\pi$
$769$	7.59857e6	−	1.31611e7i	0.463358	−	0.802559i	0.999126	+	0.0418063i	$0.0133112\pi$
$770$	−969312.	+	2.70896e6i	−0.0589165	+	0.164655i
$771$		0			0
$772$	1.02634e6	+	842329.i	0.0619794	+	0.0508673i
$773$		−	2.52966e7i		−	1.52270i	−0.648342	−	0.761349i	$-0.724537\pi$
$773$		−	2.52966e7i		−	1.52270i	0.648342	−	0.761349i	$-0.275463\pi$
$774$		0			0
$775$			3.70298e6i			0.221461i
$776$	472020.	+	262338.i	0.0281389	+	0.0156389i
$777$		0			0
$778$	5.68300e6	+	2.03348e6i	0.336611	+	0.120445i
$779$	−8.28085e6	+	1.43429e7i	−0.488913	+	0.846822i
$780$		0			0
$781$	3.19197e6	+	5.52866e6i	0.187254	+	0.324334i
$782$	−766345.	−	4.21195e6i	−0.0448134	−	0.246301i
$783$		0			0
$784$	1.17614e7	−	1.03136e7i	0.683390	−	0.599267i
$785$	7.52780e6	−	4.34617e6i	0.436007	−	0.251729i
$786$		0			0
$787$	1.86663e7	+	1.07770e7i	1.07429	+	0.620240i	0.929350	−	0.369201i	$-0.120369\pi$
$787$	1.86663e7	+	1.07770e7i	1.07429	+	0.620240i	0.144938	+	0.989441i	$0.453702\pi$
$788$	1.11643e7	+	1.84347e6i	0.640497	+	0.105760i
$789$		0			0
$790$	−3.25407e6	−	3.83545e6i	−0.185507	−	0.218650i
$791$	9.68533e6			0.550393
$792$		0			0
$793$	−5.19842e7			−2.93554
$794$	9.66845e6	+	1.13958e7i	0.544259	+	0.641497i
$795$		0			0
$796$	5.29198e6	+	873821.i	0.296030	+	0.0488810i
$797$	2.02403e7	+	1.16857e7i	1.12868	+	0.651643i	0.943602	−	0.331081i	$-0.107413\pi$
$797$	2.02403e7	+	1.16857e7i	1.12868	+	0.651643i	0.185077	+	0.982724i	$0.440747\pi$
$798$		0			0
$799$	−3.97122e6	+	2.29278e6i	−0.220068	+	0.127056i
$800$	−1.66181e6	+	2.09365e6i	−0.0918029	+	0.115659i
$801$		0			0
$802$	2.82664e6	+	1.55356e7i	0.155180	+	0.852890i
$803$	−4.12690e6	−	7.14799e6i	−0.225858	−	0.391197i
$804$		0			0
$805$	2.81209e6	−	4.87068e6i	0.152946	−	0.264911i
$806$	4.54893e7	+	1.62769e7i	2.46645	+	0.882537i
$807$		0			0
$808$	−4.62392e6	+	8.31975e6i	−0.249162	+	0.448313i
$809$			1.04327e7i			0.560434i	0.959937	+	0.280217i	$0.0904064\pi$
$809$			1.04327e7i			0.560434i	−0.959937	+	0.280217i	$0.909594\pi$
$810$		0			0
$811$			2.11443e7i			1.12886i	0.825480	+	0.564431i	$0.190904\pi$
$811$			2.11443e7i			1.12886i	−0.825480	+	0.564431i	$0.809096\pi$
$812$	−5.79458e6	−	4.75569e6i	−0.308412	−	0.253118i
$813$		0			0
$814$	−2.16940e6	+	6.06286e6i	−0.114757	+	0.320713i
$815$	−7.18755e6	+	1.24492e7i	−0.379042	+	0.656519i
$816$		0			0
$817$	−9.57973e6	−	1.65926e7i	−0.502109	−	0.869679i
$818$	5.59761e6	−	1.01846e6i	0.292496	−	0.0532183i
$819$		0			0
$820$	−1.57190e7	+	5.91584e6i	−0.816375	+	0.307243i
$821$	−1.20134e7	+	6.93595e6i	−0.622027	+	0.359127i	−0.777658	−	0.628688i	$-0.783592\pi$
$821$	−1.20134e7	+	6.93595e6i	−0.622027	+	0.359127i	0.155631	+	0.987815i	$0.450259\pi$
$822$		0			0
$823$	−5.96052e6	−	3.44131e6i	−0.306750	−	0.177102i	0.338721	−	0.940887i	$-0.390006\pi$
$823$	−5.96052e6	−	3.44131e6i	−0.306750	−	0.177102i	−0.645471	+	0.763785i	$0.723339\pi$
$824$	−2.17734e6	+	35562.8i	−0.111714	+	0.00182464i
$825$		0			0
$826$	−307000.	+	260465.i	−0.0156563	+	0.0132831i
$827$	2.50557e7			1.27392			0.636962	−	0.770895i	$-0.280191\pi$
$827$	2.50557e7			1.27392			0.636962	+	0.770895i	$0.280191\pi$
$828$		0			0
$829$	8.56223e6			0.432714			0.216357	−	0.976314i	$-0.430583\pi$
$829$	8.56223e6			0.432714			0.216357	+	0.976314i	$0.430583\pi$
$830$	−3.10860e7	+	2.63739e7i	−1.56628	+	1.32886i
$831$		0			0
$832$	1.84147e7	+	2.96174e7i	0.922268	+	1.48333i
$833$	−4.17109e6	−	2.40818e6i	−0.208275	−	0.120248i
$834$		0			0
$835$	1.50124e7	−	8.66743e6i	0.745134	−	0.430204i
$836$	4.62364e6	+	1.22855e7i	0.228806	+	0.607962i
$837$		0			0
$838$	3.17290e7	−	5.77295e6i	1.56080	−	0.283980i
$839$	1.86706e7	+	3.23384e7i	0.915701	+	1.58604i	0.805872	+	0.592090i	$0.201697\pi$
$839$	1.86706e7	+	3.23384e7i	0.915701	+	1.58604i	0.109828	+	0.993951i	$0.464970\pi$
$840$		0			0
$841$	7.66955e6	−	1.32841e7i	0.373921	−	0.647650i
$842$	−1.12760e7	+	3.15132e7i	−0.548118	+	1.53184i
$843$		0			0
$844$	1.42745e6	−	1.73928e6i	0.0689772	−	0.0840454i
$845$		−	4.56019e7i		−	2.19706i
$846$		0			0
$847$		−	4.45743e6i		−	0.213489i
$848$	6.46250e6	−	1.90354e7i	0.308611	−	0.909016i
$849$		0			0
$850$	774890.	+	277269.i	0.0367869	+	0.0131630i
$851$	6.29367e6	−	1.09010e7i	0.297907	−	0.515989i
$852$		0			0
$853$	−8.88097e6	−	1.53823e7i	−0.417915	−	0.723850i	0.577815	−	0.816168i	$-0.303906\pi$
$853$	−8.88097e6	−	1.53823e7i	−0.417915	−	0.723850i	−0.995730	+	0.0923182i	$0.970572\pi$
$854$	−1.93506e6	−	1.06354e7i	−0.0907925	−	0.499009i
$855$		0			0
$856$	1.39058e7	−	8.33423e6i	0.648652	−	0.388760i
$857$	2.38271e7	−	1.37566e7i	1.10820	−	0.639822i	0.169840	−	0.985472i	$-0.445675\pi$
$857$	2.38271e7	−	1.37566e7i	1.10820	−	0.639822i	0.938363	+	0.345650i	$0.112342\pi$
$858$		0			0
$859$	−3.17405e7	−	1.83254e7i	−1.46768	−	0.847365i	−0.468334	−	0.883551i	$-0.655146\pi$
$859$	−3.17405e7	−	1.83254e7i	−1.46768	−	0.847365i	−0.999345	+	0.0361865i	$0.988479\pi$
$860$	3.16541e6	−	1.91702e7i	0.145943	−	0.883853i
$861$		0			0
$862$	1.88922e6	+	2.22675e6i	0.0865993	+	0.102071i
$863$	5.86388e6			0.268015			0.134007	−	0.990980i	$-0.457215\pi$
$863$	5.86388e6			0.268015			0.134007	+	0.990980i	$0.457215\pi$
$864$		0			0
$865$	3.39402e7			1.54232
$866$	−2.37930e7	−	2.80440e7i	−1.07809	−	1.27070i
$867$		0			0
$868$	−1.63677e6	+	9.91249e6i	−0.0737374	+	0.446564i
$869$	−2.79119e6	−	1.61149e6i	−0.125383	−	0.0723901i
$870$		0			0
$871$	3.94497e7	−	2.27763e7i	1.76197	−	1.01727i
$872$	−4.63882e6	+	2.78021e6i	−0.206593	+	0.123819i
$873$		0			0
$874$	−4.59327e6	−	2.52453e7i	−0.203396	−	1.11790i
$875$	−3.12040e6	−	5.40470e6i	−0.137781	−	0.238644i
$876$		0			0
$877$	1.52615e7	−	2.64338e7i	0.670038	−	1.16054i	−0.307855	−	0.951433i	$-0.599611\pi$
$877$	1.52615e7	−	2.64338e7i	0.670038	−	1.16054i	0.977893	−	0.209106i	$-0.0670555\pi$
$878$	4.68945e6	+	1.67797e6i	0.205298	+	0.0734593i
$879$		0			0
$880$	−4.27949e6	+	1.26053e7i	−0.186288	+	0.548714i
$881$			940107.i			0.0408073i	0.999792	+	0.0204036i	$0.00649513\pi$
$881$			940107.i			0.0408073i	−0.999792	+	0.0204036i	$0.993505\pi$
$882$		0			0
$883$		−	1.57094e6i		−	0.0678045i	−0.999425	−	0.0339022i	$-0.989207\pi$
$883$		−	1.57094e6i		−	0.0678045i	0.999425	−	0.0339022i	$-0.0107935\pi$
$884$	6.81223e6	−	8.30038e6i	0.293196	−	0.357246i
$885$		0			0
$886$	1.42008e6	−	3.96874e6i	0.0607757	−	0.169851i
$887$	−1.53981e7	+	2.66703e7i	−0.657140	+	1.13820i	0.324213	+	0.945984i	$0.394901\pi$
$887$	−1.53981e7	+	2.66703e7i	−0.657140	+	1.13820i	−0.981353	+	0.192216i	$0.938433\pi$
$888$		0			0
$889$	5.20279e6	+	9.01150e6i	0.220791	+	0.382422i
$890$	−1.18310e7	+	2.15260e6i	−0.500664	+	0.0910936i
$891$		0			0
$892$	5.72158e6	+	1.52028e7i	0.240771	+	0.639753i
$893$	−2.38024e7	+	1.37423e7i	−0.998832	+	0.576676i
$894$		0			0
$895$	−2.28649e7	−	1.32011e7i	−0.954140	−	0.550873i
$896$	−5.37391e6	+	4.86993e6i	−0.223625	+	0.202653i
$897$		0			0
$898$	−1.64180e7	+	1.39293e7i	−0.679405	+	0.576420i
$899$	−4.80477e7			−1.98277
$900$		0			0
$901$	−6.18943e6			−0.254003
$902$	−8.20633e6	+	6.96241e6i	−0.335840	+	0.284933i
$903$		0			0
$904$	4.48058e7	−	731821.i	1.82353	−	0.0297840i
$905$	5.38614e6	+	3.10969e6i	0.218603	+	0.126211i
$906$		0			0
$907$	−1.63670e7	+	9.44950e6i	−0.660619	+	0.381409i	−0.792513	−	0.609855i	$-0.791228\pi$
$907$	−1.63670e7	+	9.44950e6i	−0.660619	+	0.381409i	0.131894	+	0.991264i	$0.457894\pi$
$908$	3.28189e6	−	1.23514e6i	0.132102	−	0.0497166i
$909$		0			0
$910$	1.38788e7	−	2.52519e6i	0.555582	−	0.101086i
$911$	−2.19197e7	−	3.79660e7i	−0.875060	−	1.51565i	−0.856699	−	0.515817i	$-0.827489\pi$
$911$	−2.19197e7	−	3.79660e7i	−0.875060	−	1.51565i	−0.0183608	−	0.999831i	$-0.505845\pi$
$912$		0			0
$913$	−1.30610e7	+	2.26223e7i	−0.518560	+	0.898172i
$914$	−5.89692e6	+	1.64803e7i	−0.233486	+	0.652527i
$915$		0			0
$916$	8.91650e6	+	7.31789e6i	0.351120	+	0.288169i
$917$		−	2.90795e6i		−	0.114199i
$918$		0			0
$919$			3.62995e7i			1.41779i	0.705313	+	0.708896i	$0.250806\pi$
$919$			3.62995e7i			1.41779i	−0.705313	+	0.708896i	$0.749194\pi$
$920$	1.26411e7	−	2.27450e7i	0.492397	−	0.885963i
$921$		0			0
$922$	−3.79236e7	−	1.35697e7i	−1.46920	−	0.525706i
$923$	1.56502e7	−	2.71069e7i	0.604666	−	1.04731i
$924$		0			0
$925$	1.20990e6	+	2.09561e6i	0.0464939	+	0.0805298i
$926$	−4.81831e6	−	2.64821e7i	−0.184658	−	1.01491i
$927$		0			0
$928$	−2.71659e7	−	2.15627e7i	−1.03551	−	0.821926i
$929$	−3.32057e7	+	1.91713e7i	−1.26233	+	0.728807i	−0.973525	−	0.228581i	$-0.926591\pi$
$929$	−3.32057e7	+	1.91713e7i	−1.26233	+	0.728807i	−0.288805	+	0.957388i	$0.593258\pi$
$930$		0			0
$931$	−2.50004e7	−	1.44340e7i	−0.945306	−	0.545773i
$932$	−2.96376e7	−	4.89381e6i	−1.11764	−	0.184547i
$933$		0			0
$934$	−2.70068e7	−	3.18319e7i	−1.01299	−	1.19397i
$935$	4.09866e6			0.153325
$936$		0			0
$937$	−102797.			−0.00382500			−0.00191250	−	0.999998i	$-0.500609\pi$
$937$	−102797.			−0.00382500			−0.00191250	+	0.999998i	$0.500609\pi$
$938$	6.12824e6	+	7.22313e6i	0.227420	+	0.268052i
$939$		0			0
$940$	−2.75000e7	−	4.54085e6i	−1.01511	−	0.167617i
$941$	1.82125e7	+	1.05150e7i	0.670496	+	0.387111i	0.796265	−	0.604948i	$-0.206806\pi$
$941$	1.82125e7	+	1.05150e7i	0.670496	+	0.387111i	−0.125768	+	0.992060i	$0.540140\pi$
$942$		0			0
$943$	1.82187e7	−	1.05185e7i	0.667171	−	0.385191i
$944$	−1.40055e6	+	1.22815e6i	−0.0511526	+	0.0448559i
$945$		0			0
$946$	−2.22863e6	−	1.22489e7i	−0.0809673	−	0.445008i
$947$	7.49577e6	+	1.29831e7i	0.271607	+	0.470438i	0.969274	−	0.245985i	$-0.0791115\pi$
$947$	7.49577e6	+	1.29831e7i	0.271607	+	0.470438i	−0.697666	+	0.716423i	$0.745778\pi$
$948$		0			0
$949$	−2.02341e7	+	3.50465e7i	−0.729321	+	1.26322i
$950$	4.64449e6	+	1.66188e6i	0.166966	+	0.0597434i
$951$		0			0
$952$	1.95174e6	+	1.08473e6i	0.0697959	+	0.0387909i
$953$			716587.i			0.0255586i	0.999918	+	0.0127793i	$0.00406788\pi$
$953$			716587.i			0.0255586i	−0.999918	+	0.0127793i	$0.995932\pi$
$954$		0			0
$955$		−	2.58139e7i		−	0.915893i
$956$	−8.06476e6	−	6.61886e6i	−0.285395	−	0.234228i
$957$		0			0
$958$	2.11083e6	−	5.89917e6i	0.0743085	−	0.207672i
$959$	−454137.	+	786589.i	−0.0159456	+	0.0276186i
$960$		0			0
$961$	1.78830e7	+	3.09742e7i	0.624642	+	1.08191i
$962$	3.10618e7	−	5.65156e6i	1.08215	−	0.196893i
$963$		0			0
$964$	−2.27035e6	+	854445.i	−0.0786864	+	0.0296136i
$965$	2.15192e6	−	1.24241e6i	0.0743887	−	0.0429483i
$966$		0			0
$967$	7.27307e6	+	4.19911e6i	0.250122	+	0.144408i	0.619820	−	0.784744i	$-0.287206\pi$
$967$	7.27307e6	+	4.19911e6i	0.250122	+	0.144408i	−0.369698	+	0.929152i	$0.620539\pi$
$968$	−336802.	−	2.06207e7i	−0.0115528	−	0.707320i
$969$		0			0
$970$	770643.	−	653829.i	0.0262981	−	0.0223118i
$971$	−1.84209e7			−0.626992			−0.313496	−	0.949590i	$-0.601500\pi$
$971$	−1.84209e7			−0.626992			−0.313496	+	0.949590i	$0.601500\pi$
$972$		0			0
$973$	−1.29835e7			−0.439651
$974$	−3.29498e6	+	2.79553e6i	−0.111290	+	0.0944205i
$975$		0			0
$976$	−9.75549e6	−	4.90546e7i	−0.327812	−	1.64837i
$977$	−1.70913e6	−	986767.i	−0.0572848	−	0.0330734i	0.471084	−	0.882088i	$-0.343863\pi$
$977$	−1.70913e6	−	986767.i	−0.0572848	−	0.0330734i	−0.528369	+	0.849015i	$0.677196\pi$
$978$		0			0
$979$	−6.67306e6	+	3.85269e6i	−0.222519	+	0.128472i
$980$	−1.03116e7	−	2.73991e7i	−0.342975	−	0.911319i
$981$		0			0
$982$	−3.86552e7	+	7.03314e6i	−1.27917	+	0.232740i
$983$	1.64275e7	+	2.84533e7i	0.542236	+	0.939181i	0.998775	+	0.0494775i	$0.0157556\pi$
$983$	1.64275e7	+	2.84533e7i	0.542236	+	0.939181i	−0.456539	+	0.889703i	$0.650911\pi$
$984$		0			0
$985$	1.05883e7	−	1.83395e7i	0.347725	−	0.602278i
$986$	−3.59768e6	+	1.00545e7i	−0.117850	+	0.329359i
$987$		0			0
$988$	4.08307e7	−	4.97502e7i	1.33074	−	1.62145i
$989$			2.43368e7i			0.791176i
$990$		0			0
$991$			1.19722e7i			0.387250i	0.981076	+	0.193625i	$0.0620244\pi$
$991$			1.19722e7i			0.387250i	−0.981076	+	0.193625i	$0.937976\pi$
$992$	−6.82294e6	+	4.59803e7i	−0.220137	+	1.48352i
$993$		0			0
$994$	6.12834e6	+	2.19282e6i	0.196733	+	0.0703944i
$995$	5.01894e6	−	8.69306e6i	0.160714	−	0.278365i
$996$		0			0
$997$	1.60260e7	+	2.77579e7i	0.510608	+	0.884400i	0.999924	+	0.0122932i	$0.00391315\pi$
$997$	1.60260e7	+	2.77579e7i	0.510608	+	0.884400i	−0.489316	+	0.872107i	$0.662754\pi$
$998$	−6.25243e6	−	3.43643e7i	−0.198711	−	1.09215i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.71.9		56
3.2	odd	2		36.6.h.a.23.20	yes	56
4.3	odd	2	inner	108.6.h.a.71.18		56
9.2	odd	6	inner	108.6.h.a.35.18		56
9.7	even	3		36.6.h.a.11.11	✓	56
12.11	even	2		36.6.h.a.23.11	yes	56
36.7	odd	6		36.6.h.a.11.20	yes	56
36.11	even	6	inner	108.6.h.a.35.9		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.11	✓	56	9.7	even	3
36.6.h.a.11.20	yes	56	36.7	odd	6
36.6.h.a.23.11	yes	56	12.11	even	2
36.6.h.a.23.20	yes	56	3.2	odd	2
108.6.h.a.35.9		56	36.11	even	6	inner
108.6.h.a.35.18		56	9.2	odd	6	inner
108.6.h.a.71.9		56	1.1	even	1	trivial
108.6.h.a.71.18		56	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.65969 - 4.31354i) q^{2} +(-5.21330 + 31.5725i) q^{4} +(51.8636 + 29.9435i) q^{5} +(33.8827 - 19.5622i) q^{7} +(155.268 - 93.0578i) q^{8} +O(q^{10})\)	\(q+(-3.65969 - 4.31354i) q^{2} +(-5.21330 + 31.5725i) q^{4} +(51.8636 + 29.9435i) q^{5} +(33.8827 - 19.5622i) q^{7} +(155.268 - 93.0578i) q^{8} +(-60.6425 - 333.300i) q^{10} +(-108.537 - 187.992i) q^{11} +(-532.156 + 921.721i) q^{13} +(-208.383 - 74.5629i) q^{14} +(-969.643 - 329.194i) q^{16} +315.283i q^{17} +1889.72i q^{19} +(-1215.77 + 1481.36i) q^{20} +(-413.698 + 1156.17i) q^{22} +(1200.19 - 2078.79i) q^{23} +(230.725 + 399.628i) q^{25} +(5923.41 - 1077.74i) q^{26} +(440.986 + 1171.75i) q^{28} +(-5185.33 + 2993.75i) q^{29} +(6949.56 + 4012.33i) q^{31} +(2128.60 + 5387.34i) q^{32} +(1359.99 - 1153.84i) q^{34} +2343.04 q^{35} +5243.91 q^{37} +(8151.40 - 6915.81i) q^{38} +(10839.3 - 177.040i) q^{40} +(7589.92 + 4382.04i) q^{41} +(-8780.43 + 5069.38i) q^{43} +(6501.20 - 2446.73i) q^{44} +(-13359.2 + 2430.66i) q^{46} +(7272.14 + 12595.7i) q^{47} +(-7638.14 + 13229.6i) q^{49} +(879.429 - 2457.76i) q^{50} +(-26326.7 - 21606.7i) q^{52} +19631.3i q^{53} -12999.9i q^{55} +(3440.50 - 6190.44i) q^{56} +(31890.4 + 11410.9i) q^{58} +(909.551 - 1575.39i) q^{59} +(24421.5 + 42299.3i) q^{61} +(-8125.89 - 44661.1i) q^{62} +(15448.5 - 28897.8i) q^{64} +(-55199.1 + 31869.2i) q^{65} +(-37065.9 - 21400.0i) q^{67} +(-9954.28 - 1643.67i) q^{68} +(-8574.81 - 10106.8i) q^{70} -29409.1 q^{71} +38022.9 q^{73} +(-19191.1 - 22619.8i) q^{74} +(-59663.3 - 9851.70i) q^{76} +(-7355.06 - 4246.45i) q^{77} +(12858.2 - 7423.70i) q^{79} +(-40432.0 - 46107.7i) q^{80} +(-8874.65 - 48776.4i) q^{82} +(-60168.3 - 104215. i) q^{83} +(-9440.69 + 16351.7i) q^{85} +(54000.6 + 19322.4i) q^{86} +(-34346.5 - 19089.0i) q^{88} -35496.5i q^{89} +41640.5i q^{91} +(59375.5 + 48730.2i) q^{92} +(27718.3 - 77465.1i) q^{94} +(-56584.9 + 98008.0i) q^{95} +(1491.62 + 2583.55i) q^{97} +(85019.9 - 15469.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Introduction

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