LMFDB - Embedded newform 567.2.p.c.404.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(80,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("567.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			404.4
Root			$0.187540 - 0.324828i$ of defining polynomial
Character	$\chi$	$=$	567.404
Dual form			567.2.p.c.80.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.621951 + 0.359083i) q^{2} +(-0.742118 - 1.28539i) q^{4} +(0.723774 - 1.25361i) q^{5} +(-2.37721 - 1.16142i) q^{7} -2.50226i q^{8} +O(q^{10})$	\(q+(0.621951 + 0.359083i) q^{2} +(-0.742118 - 1.28539i) q^{4} +(0.723774 - 1.25361i) q^{5} +(-2.37721 - 1.16142i) q^{7} -2.50226i q^{8} +(0.900304 - 0.519791i) q^{10} +(-1.55933 + 0.900281i) q^{11} +2.18085i q^{13} +(-1.06146 - 1.57596i) q^{14} +(-0.585716 + 1.01449i) q^{16} +(-1.95230 - 3.38149i) q^{17} +(-3.47456 - 2.00604i) q^{19} -2.14850 q^{20} -1.29310 q^{22} +(-4.91522 - 2.83781i) q^{23} +(1.45230 + 2.51546i) q^{25} +(-0.783106 + 1.35638i) q^{26} +(0.271298 + 3.91754i) q^{28} -9.80824i q^{29} +(2.45129 - 1.41525i) q^{31} +(-5.06262 + 2.92290i) q^{32} -2.80416i q^{34} +(-3.17653 + 2.13949i) q^{35} +(-0.411767 + 0.713202i) q^{37} +(-1.44067 - 2.49531i) q^{38} +(-3.13687 - 1.81107i) q^{40} +11.8123 q^{41} +7.53532 q^{43} +(2.31442 + 1.33623i) q^{44} +(-2.03802 - 3.52995i) q^{46} +(1.16920 - 2.02511i) q^{47} +(4.30222 + 5.52186i) q^{49} +2.08599i q^{50} +(2.80323 - 1.61845i) q^{52} +(-0.996713 + 0.575453i) q^{53} +2.60640i q^{55} +(-2.90617 + 5.94839i) q^{56} +(3.52198 - 6.10024i) q^{58} +(-4.89555 - 8.47934i) q^{59} +(-2.03980 - 1.17768i) q^{61} +2.03277 q^{62} -1.85540 q^{64} +(2.73394 + 1.57844i) q^{65} +(0.156402 + 0.270897i) q^{67} +(-2.89768 + 5.01893i) q^{68} +(-2.74390 + 0.190021i) q^{70} -1.94933i q^{71} +(2.42847 - 1.40208i) q^{73} +(-0.512198 + 0.295717i) q^{74} +5.95486i q^{76} +(4.75246 - 0.329118i) q^{77} +(-6.21583 + 10.7661i) q^{79} +(0.847852 + 1.46852i) q^{80} +(7.34669 + 4.24162i) q^{82} +7.21832 q^{83} -5.65210 q^{85} +(4.68660 + 2.70581i) q^{86} +(2.25274 + 3.90186i) q^{88} +(5.28999 - 9.16253i) q^{89} +(2.53287 - 5.18433i) q^{91} +8.42395i q^{92} +(1.45436 - 0.839677i) q^{94} +(-5.02959 + 2.90383i) q^{95} -15.5102i q^{97} +(0.692961 + 4.97918i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} + 3 q^{7}+O(q^{10}) $ 10 * q + 4 * q^4 + 3 * q^7	$ 10 q + 4 q^{4} + 3 q^{7} - 15 q^{10} - 12 q^{11} + 18 q^{14} - 6 q^{16} - 12 q^{17} + 3 q^{19} + 6 q^{20} - 10 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 2 q^{28} + 9 q^{31} - 48 q^{32} - 15 q^{35} + 6 q^{37} - 18 q^{38} - 15 q^{40} + 18 q^{41} - 6 q^{43} + 24 q^{44} - 13 q^{46} + 15 q^{47} + 19 q^{49} + 12 q^{52} - 9 q^{53} + 21 q^{56} + 8 q^{58} - 18 q^{59} - 12 q^{61} + 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} + 27 q^{68} - 15 q^{70} + 3 q^{73} - 30 q^{74} - 6 q^{77} + 20 q^{79} - 30 q^{80} + 9 q^{82} + 30 q^{83} - 36 q^{85} + 54 q^{86} - 8 q^{88} + 24 q^{89} - 24 q^{91} + 3 q^{94} + 45 q^{98}+O(q^{100}) $ 10 * q + 4 * q^4 + 3 * q^7 - 15 * q^10 - 12 * q^11 + 18 * q^14 - 6 * q^16 - 12 * q^17 + 3 * q^19 + 6 * q^20 - 10 * q^22 - 15 * q^23 + 7 * q^25 + 3 * q^26 + 2 * q^28 + 9 * q^31 - 48 * q^32 - 15 * q^35 + 6 * q^37 - 18 * q^38 - 15 * q^40 + 18 * q^41 - 6 * q^43 + 24 * q^44 - 13 * q^46 + 15 * q^47 + 19 * q^49 + 12 * q^52 - 9 * q^53 + 21 * q^56 + 8 * q^58 - 18 * q^59 - 12 * q^61 + 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 + 27 * q^68 - 15 * q^70 + 3 * q^73 - 30 * q^74 - 6 * q^77 + 20 * q^79 - 30 * q^80 + 9 * q^82 + 30 * q^83 - 36 * q^85 + 54 * q^86 - 8 * q^88 + 24 * q^89 - 24 * q^91 + 3 * q^94 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.621951	+	0.359083i	0.439785	+	0.253910i	0.703507	−	0.710689i	$-0.251617\pi$
$2$	0.621951	+	0.359083i	0.439785	+	0.253910i	−0.263721	+	0.964599i	$0.584950\pi$
$3$		0			0
$3$		0			0
$4$	−0.742118	−	1.28539i	−0.371059	−	0.642693i
$5$	0.723774	−	1.25361i	0.323682	−	0.560633i	−0.657563	−	0.753400i	$-0.728413\pi$
$5$	0.723774	−	1.25361i	0.323682	−	0.560633i	0.981245	+	0.192766i	$0.0617460\pi$
$6$		0			0
$7$	−2.37721	−	1.16142i	−0.898500	−	0.438974i
$7$	−2.37721	−	1.16142i	−0.898500	−	0.438974i
$8$		−	2.50226i		−	0.884683i
$9$		0			0
$10$	0.900304	−	0.519791i	0.284701	−	0.164372i
$11$	−1.55933	+	0.900281i	−0.470156	+	0.271445i	−0.716305	−	0.697787i	$-0.754168\pi$
$11$	−1.55933	+	0.900281i	−0.470156	+	0.271445i	0.246149	+	0.969232i	$0.420835\pi$
$12$		0			0
$13$			2.18085i			0.604858i	0.953172	+	0.302429i	$0.0977976\pi$
$13$			2.18085i			0.604858i	−0.953172	+	0.302429i	$0.902202\pi$
$14$	−1.06146	−	1.57596i	−0.283687	−	0.421193i
$15$		0			0
$16$	−0.585716	+	1.01449i	−0.146429	+	0.253622i
$17$	−1.95230	−	3.38149i	−0.473503	−	0.820131i	0.526037	−	0.850462i	$-0.323677\pi$
$17$	−1.95230	−	3.38149i	−0.473503	−	0.820131i	−0.999540	+	0.0303308i	$0.990344\pi$
$18$		0			0
$19$	−3.47456	−	2.00604i	−0.797118	−	0.460216i	0.0453446	−	0.998971i	$-0.485561\pi$
$19$	−3.47456	−	2.00604i	−0.797118	−	0.460216i	−0.842462	+	0.538755i	$0.818895\pi$
$20$	−2.14850			−0.480420
$21$		0			0
$22$	−1.29310			−0.275691
$23$	−4.91522	−	2.83781i	−1.02490	−	0.591723i	−0.109377	−	0.994000i	$-0.534886\pi$
$23$	−4.91522	−	2.83781i	−1.02490	−	0.591723i	−0.915518	+	0.402277i	$0.868219\pi$
$24$		0			0
$25$	1.45230	+	2.51546i	0.290460	+	0.503092i
$26$	−0.783106	+	1.35638i	−0.153580	+	0.266008i
$27$		0			0
$28$	0.271298	+	3.91754i	0.0512705	+	0.740345i
$29$		−	9.80824i		−	1.82134i	−0.413130	−	0.910672i	$-0.635564\pi$
$29$		−	9.80824i		−	1.82134i	0.413130	−	0.910672i	$-0.364436\pi$
$30$		0			0
$31$	2.45129	−	1.41525i	0.440264	−	0.254187i	−0.263445	−	0.964674i	$-0.584859\pi$
$31$	2.45129	−	1.41525i	0.440264	−	0.254187i	0.703710	+	0.710488i	$0.251526\pi$
$32$	−5.06262	+	2.92290i	−0.894953	+	0.516701i
$33$		0			0
$34$		−	2.80416i		−	0.480909i
$35$	−3.17653	+	2.13949i	−0.536931	+	0.361641i
$36$		0			0
$37$	−0.411767	+	0.713202i	−0.0676941	+	0.117250i	−0.897886	−	0.440228i	$-0.854898\pi$
$37$	−0.411767	+	0.713202i	−0.0676941	+	0.117250i	0.830192	+	0.557478i	$0.188231\pi$
$38$	−1.44067	−	2.49531i	−0.233707	−	0.404793i
$39$		0			0
$40$	−3.13687	−	1.81107i	−0.495983	−	0.286356i
$41$	11.8123			1.84478			0.922389	−	0.386262i	$-0.126234\pi$
$41$	11.8123			1.84478			0.922389	+	0.386262i	$0.126234\pi$
$42$		0			0
$43$	7.53532			1.14913			0.574563	−	0.818461i	$-0.305172\pi$
$43$	7.53532			1.14913			0.574563	+	0.818461i	$0.305172\pi$
$44$	2.31442	+	1.33623i	0.348912	+	0.201444i
$45$		0			0
$46$	−2.03802	−	3.52995i	−0.300489	−	0.520463i
$47$	1.16920	−	2.02511i	0.170545	−	0.295392i	−0.768066	−	0.640371i	$-0.778781\pi$
$47$	1.16920	−	2.02511i	0.170545	−	0.295392i	0.938610	+	0.344979i	$0.112114\pi$
$48$		0			0
$49$	4.30222	+	5.52186i	0.614603	+	0.788837i
$50$			2.08599i			0.295003i
$51$		0			0
$52$	2.80323	−	1.61845i	0.388738	−	0.224438i
$53$	−0.996713	+	0.575453i	−0.136909	+	0.0790445i	−0.566890	−	0.823793i	$-0.691854\pi$
$53$	−0.996713	+	0.575453i	−0.136909	+	0.0790445i	0.429981	+	0.902838i	$0.358520\pi$
$54$		0			0
$55$			2.60640i			0.351447i
$56$	−2.90617	+	5.94839i	−0.388353	+	0.794888i
$57$		0			0
$58$	3.52198	−	6.10024i	0.462458	−	0.801001i
$59$	−4.89555	−	8.47934i	−0.637346	−	1.10392i	−0.986013	−	0.166669i	$-0.946699\pi$
$59$	−4.89555	−	8.47934i	−0.637346	−	1.10392i	0.348666	−	0.937247i	$-0.386635\pi$
$60$		0			0
$61$	−2.03980	−	1.17768i	−0.261170	−	0.150786i	0.363698	−	0.931517i	$-0.381514\pi$
$61$	−2.03980	−	1.17768i	−0.261170	−	0.150786i	−0.624868	+	0.780730i	$0.714847\pi$
$62$	2.03277			0.258163
$63$		0			0
$64$	−1.85540			−0.231925
$65$	2.73394	+	1.57844i	0.339104	+	0.195782i
$66$		0			0
$67$	0.156402	+	0.270897i	0.0191076	+	0.0330953i	0.875421	−	0.483361i	$-0.160584\pi$
$67$	0.156402	+	0.270897i	0.0191076	+	0.0330953i	−0.856313	+	0.516456i	$0.827251\pi$
$68$	−2.89768	+	5.01893i	−0.351395	+	0.608634i
$69$		0			0
$70$	−2.74390	+	0.190021i	−0.327959	+	0.0227119i
$71$		−	1.94933i		−	0.231343i	−0.993288	−	0.115671i	$-0.963098\pi$
$71$		−	1.94933i		−	0.231343i	0.993288	−	0.115671i	$-0.0369019\pi$
$72$		0			0
$73$	2.42847	−	1.40208i	0.284231	−	0.164101i	−0.351106	−	0.936336i	$-0.614194\pi$
$73$	2.42847	−	1.40208i	0.284231	−	0.164101i	0.635337	+	0.772235i	$0.280861\pi$
$74$	−0.512198	+	0.295717i	−0.0595418	+	0.0343765i
$75$		0			0
$76$			5.95486i			0.683070i
$77$	4.75246	−	0.329118i	0.541593	−	0.0375065i
$78$		0			0
$79$	−6.21583	+	10.7661i	−0.699336	+	1.21128i	0.269361	+	0.963039i	$0.413187\pi$
$79$	−6.21583	+	10.7661i	−0.699336	+	1.21128i	−0.968697	+	0.248246i	$0.920146\pi$
$80$	0.847852	+	1.46852i	0.0947927	+	0.164186i
$81$		0			0
$82$	7.34669	+	4.24162i	0.811306	+	0.468408i
$83$	7.21832			0.792313			0.396157	−	0.918183i	$-0.370344\pi$
$83$	7.21832			0.792313			0.396157	+	0.918183i	$0.370344\pi$
$84$		0			0
$85$	−5.65210			−0.613057
$86$	4.68660	+	2.70581i	0.505369	+	0.291775i
$87$		0			0
$88$	2.25274	+	3.90186i	0.240143	+	0.415939i
$89$	5.28999	−	9.16253i	0.560737	−	0.971226i	−0.436695	−	0.899610i	$-0.643851\pi$
$89$	5.28999	−	9.16253i	0.560737	−	0.971226i	0.997432	−	0.0716161i	$-0.0228156\pi$
$90$		0			0
$91$	2.53287	−	5.18433i	0.265517	−	0.543465i
$92$			8.42395i			0.878258i
$93$		0			0
$94$	1.45436	−	0.839677i	0.150006	−	0.0866061i
$95$	−5.02959	+	2.90383i	−0.516025	+	0.297927i
$96$		0			0
$97$		−	15.5102i		−	1.57482i	−0.616428	−	0.787411i	$-0.711421\pi$
$97$		−	15.5102i		−	1.57482i	0.616428	−	0.787411i	$-0.288579\pi$
$98$	0.692961	+	4.97918i	0.0699997	+	0.502973i
$99$		0			0
$100$	2.15556	−	3.73354i	0.215556	−	0.373354i
$101$	1.97309	+	3.41749i	0.196330	+	0.340053i	0.947336	−	0.320242i	$-0.103764\pi$
$101$	1.97309	+	3.41749i	0.196330	+	0.340053i	−0.751006	+	0.660295i	$0.770431\pi$
$102$		0			0
$103$	−3.59853	−	2.07761i	−0.354573	−	0.204713i	0.312124	−	0.950041i	$-0.398959\pi$
$103$	−3.59853	−	2.07761i	−0.354573	−	0.204713i	−0.666698	+	0.745328i	$0.732293\pi$
$104$	5.45705			0.535108
$105$		0			0
$106$	−0.826542			−0.0802809
$107$	4.91092	+	2.83532i	0.474757	+	0.274101i	0.718229	−	0.695807i	$-0.244953\pi$
$107$	4.91092	+	2.83532i	0.474757	+	0.274101i	−0.243472	+	0.969908i	$0.578286\pi$
$108$		0			0
$109$	5.99916	+	10.3908i	0.574615	+	0.995262i	0.996083	+	0.0884193i	$0.0281815\pi$
$109$	5.99916	+	10.3908i	0.574615	+	0.995262i	−0.421468	+	0.906843i	$0.638485\pi$
$110$	−0.935915	+	1.62105i	−0.0892360	+	0.154561i
$111$		0			0
$112$	2.57061	−	1.73139i	0.242900	−	0.163601i
$113$			7.24921i			0.681948i	0.940073	+	0.340974i	$0.110757\pi$
$113$			7.24921i			0.681948i	−0.940073	+	0.340974i	$0.889243\pi$
$114$		0			0
$115$	−7.11502	+	4.10786i	−0.663479	+	0.383060i
$116$	−12.6074	+	7.27887i	−1.17057	+	0.675826i
$117$		0			0
$118$		−	7.03164i		−	0.647315i
$119$	0.713708	+	10.3059i	0.0654255	+	0.944743i
$120$		0			0
$121$	−3.87899	+	6.71861i	−0.352635	+	0.610782i
$122$	−0.845770	−	1.46492i	−0.0765724	−	0.132627i
$123$		0			0
$124$	−3.63829	−	2.10057i	−0.326728	−	0.188637i
$125$	11.4423			1.02343
$126$		0			0
$127$	−0.881336			−0.0782059			−0.0391030	−	0.999235i	$-0.512450\pi$
$127$	−0.881336			−0.0782059			−0.0391030	+	0.999235i	$0.512450\pi$
$128$	8.97127	+	5.17956i	0.792956	+	0.457813i
$129$		0			0
$130$	1.13358	+	1.96343i	0.0994219	+	0.172204i
$131$	1.48721	−	2.57592i	0.129938	−	0.225059i	−0.793714	−	0.608291i	$-0.791856\pi$
$131$	1.48721	−	2.57592i	0.129938	−	0.225059i	0.923652	+	0.383232i	$0.125189\pi$
$132$		0			0
$133$	5.92989	+	8.80417i	0.514187	+	0.763418i
$134$			0.224646i			0.0194065i
$135$		0			0
$136$	−8.46137	+	4.88517i	−0.725556	+	0.418900i
$137$	−10.3045	+	5.94930i	−0.880372	+	0.508283i	−0.870781	−	0.491671i	$-0.836386\pi$
$137$	−10.3045	+	5.94930i	−0.880372	+	0.508283i	−0.00959114	+	0.999954i	$0.503053\pi$
$138$		0			0
$139$		−	12.0254i		−	1.01998i	−0.860181	−	0.509989i	$-0.829649\pi$
$139$		−	12.0254i		−	1.01998i	0.860181	−	0.509989i	$-0.170351\pi$
$140$	5.10744	+	2.49531i	0.431657	+	0.210892i
$141$		0			0
$142$	0.699971	−	1.21239i	0.0587403	−	0.101741i
$143$	−1.96338	−	3.40067i	−0.164186	−	0.284378i
$144$		0			0
$145$	−12.2957	−	7.09895i	−1.02111	−	0.589536i
$146$	2.01385			0.166668
$147$		0			0
$148$	1.22232			0.100474
$149$	6.13061	+	3.53951i	0.502239	+	0.289968i	0.729638	−	0.683834i	$-0.239689\pi$
$149$	6.13061	+	3.53951i	0.502239	+	0.289968i	−0.227399	+	0.973802i	$0.573022\pi$
$150$		0			0
$151$	−7.79093	−	13.4943i	−0.634017	−	1.09815i	−0.986723	−	0.162415i	$-0.948072\pi$
$151$	−7.79093	−	13.4943i	−0.634017	−	1.09815i	0.352706	−	0.935734i	$-0.385262\pi$
$152$	−5.01963	+	8.69425i	−0.407146	+	0.705197i
$153$		0			0
$154$	3.07397	+	1.50183i	0.247708	+	0.121021i
$155$		−	4.09729i		−	0.329102i
$156$		0			0
$157$	−1.80677	+	1.04314i	−0.144196	+	0.0832517i	−0.570362	−	0.821393i	$-0.693197\pi$
$157$	−1.80677	+	1.04314i	−0.144196	+	0.0832517i	0.426166	+	0.904645i	$0.359864\pi$
$158$	−7.73188	+	4.46400i	−0.615115	+	0.355137i
$159$		0			0
$160$			8.46209i			0.668987i
$161$	8.38862	+	12.4547i	0.661116	+	0.981566i
$162$		0			0
$163$	−5.58983	+	9.68188i	−0.437830	+	0.758343i	−0.997522	−	0.0703575i	$-0.977586\pi$
$163$	−5.58983	+	9.68188i	−0.437830	+	0.758343i	0.559692	+	0.828700i	$0.310919\pi$
$164$	−8.76616	−	15.1834i	−0.684522	−	1.18563i
$165$		0			0
$166$	4.48944	+	2.59198i	0.348448	+	0.201176i
$167$	−1.92150			−0.148690			−0.0743450	−	0.997233i	$-0.523687\pi$
$167$	−1.92150			−0.148690			−0.0743450	+	0.997233i	$0.523687\pi$
$168$		0			0
$169$	8.24390			0.634146
$170$	−3.51533	−	2.02958i	−0.269613	−	0.155661i
$171$		0			0
$172$	−5.59210	−	9.68580i	−0.426393	−	0.738535i
$173$	7.61290	−	13.1859i	0.578798	−	1.00251i	−0.416820	−	0.908989i	$-0.636855\pi$
$173$	7.61290	−	13.1859i	0.578798	−	1.00251i	0.995618	−	0.0935182i	$-0.0298113\pi$
$174$		0			0
$175$	−0.530922	−	7.66650i	−0.0401339	−	0.579533i
$176$		−	2.10923i		−	0.158990i
$177$		0			0
$178$	6.58022	−	3.79909i	0.493208	−	0.284754i
$179$	−0.299401	+	0.172859i	−0.0223783	+	0.0129201i	−0.511147	−	0.859493i	$-0.670779\pi$
$179$	−0.299401	+	0.172859i	−0.0223783	+	0.0129201i	0.488769	+	0.872413i	$0.337446\pi$
$180$		0			0
$181$			3.27661i			0.243548i	0.992558	+	0.121774i	$0.0388583\pi$
$181$			3.27661i			0.243548i	−0.992558	+	0.121774i	$0.961142\pi$
$182$	3.43693	−	2.31488i	0.254762	−	0.171590i
$183$		0			0
$184$	−7.10094	+	12.2992i	−0.523488	+	0.906708i
$185$	0.596053	+	1.03239i	0.0438227	+	0.0759031i
$186$		0			0
$187$	6.08857	+	3.51524i	0.445241	+	0.257060i
$188$	−3.47073			−0.253129
$189$		0			0
$190$	−4.17087			−0.302587
$191$	−6.40096	−	3.69560i	−0.463158	−	0.267404i	0.250213	−	0.968191i	$-0.419499\pi$
$191$	−6.40096	−	3.69560i	−0.463158	−	0.267404i	−0.713371	+	0.700787i	$0.752833\pi$
$192$		0			0
$193$	−6.51425	−	11.2830i	−0.468906	−	0.812169i	0.530462	−	0.847708i	$-0.322018\pi$
$193$	−6.51425	−	11.2830i	−0.468906	−	0.812169i	−0.999368	+	0.0355398i	$0.988685\pi$
$194$	5.56945	−	9.64658i	0.399863	−	0.692584i
$195$		0			0
$196$	3.90496	−	9.62789i	0.278926	−	0.687706i
$197$			4.03035i			0.287151i	0.989639	+	0.143575i	$0.0458599\pi$
$197$			4.03035i			0.287151i	−0.989639	+	0.143575i	$0.954140\pi$
$198$		0			0
$199$	14.2096	−	8.20390i	1.00729	−	0.581559i	0.0968925	−	0.995295i	$-0.469110\pi$
$199$	14.2096	−	8.20390i	1.00729	−	0.581559i	0.910397	+	0.413736i	$0.135776\pi$
$200$	6.29434	−	3.63404i	0.445077	−	0.256965i
$201$		0			0
$202$			2.83401i			0.199401i
$203$	−11.3915	+	23.3162i	−0.799524	+	1.63648i
$204$		0			0
$205$	8.54947	−	14.8081i	0.597121	−	1.03424i
$206$	−1.49207	−	2.58434i	−0.103957	−	0.180060i
$207$		0			0
$208$	−2.21245	−	1.27736i	−0.153406	−	0.0885688i
$209$	7.22398			0.499693
$210$		0			0
$211$	12.0165			0.827253			0.413627	−	0.910447i	$-0.364262\pi$
$211$	12.0165			0.827253			0.413627	+	0.910447i	$0.364262\pi$
$212$	1.47936	+	0.854108i	0.101603	+	0.0586604i
$213$		0			0
$214$	2.03623	+	3.52686i	0.139194	+	0.241091i
$215$	5.45387	−	9.44638i	0.371951	−	0.644238i
$216$		0			0
$217$	−7.47092	+	0.517377i	−0.507159	+	0.0351219i
$218$			8.61679i			0.583603i
$219$		0			0
$220$	3.35023	−	1.93426i	0.225873	−	0.130408i
$221$	7.37451	−	4.25767i	0.496063	−	0.286402i
$222$		0			0
$223$			26.3193i			1.76247i	0.472675	+	0.881237i	$0.343288\pi$
$223$			26.3193i			1.76247i	−0.472675	+	0.881237i	$0.656712\pi$
$224$	15.4296	−	1.06853i	1.03093	−	0.0713944i
$225$		0			0
$226$	−2.60307	+	4.50865i	−0.173154	+	0.299911i
$227$	−5.40410	−	9.36018i	−0.358683	−	0.621257i	0.629058	−	0.777358i	$-0.283441\pi$
$227$	−5.40410	−	9.36018i	−0.358683	−	0.621257i	−0.987741	+	0.156101i	$0.950107\pi$
$228$		0			0
$229$	8.39777	+	4.84846i	0.554941	+	0.320395i	0.751112	−	0.660174i	$-0.229518\pi$
$229$	8.39777	+	4.84846i	0.554941	+	0.320395i	−0.196172	+	0.980570i	$0.562851\pi$
$230$	−5.90026			−0.389052
$231$		0			0
$232$	−24.5428			−1.61131
$233$	−1.92897	−	1.11369i	−0.126371	−	0.0729605i	0.435482	−	0.900198i	$-0.356578\pi$
$233$	−1.92897	−	1.11369i	−0.126371	−	0.0729605i	−0.561853	+	0.827237i	$0.689911\pi$
$234$		0			0
$235$	−1.69247	−	2.93144i	−0.110404	−	0.191226i
$236$	−7.26616	+	12.5854i	−0.472986	+	0.819237i
$237$		0			0
$238$	−3.25680	+	6.66606i	−0.211107	+	0.432096i
$239$		−	18.4402i		−	1.19280i	−0.802689	−	0.596398i	$-0.796598\pi$
$239$		−	18.4402i		−	1.19280i	0.802689	−	0.596398i	$-0.203402\pi$
$240$		0			0
$241$	−5.60475	+	3.23591i	−0.361034	+	0.208443i	−0.669534	−	0.742781i	$-0.733506\pi$
$241$	−5.60475	+	3.23591i	−0.361034	+	0.208443i	0.308500	+	0.951224i	$0.400173\pi$
$242$	−4.82508	+	2.78576i	−0.310168	+	0.179075i
$243$		0			0
$244$			3.49591i			0.223803i
$245$	10.0361	−	1.39674i	0.641184	−	0.0892347i
$246$		0			0
$247$	4.37486	−	7.57748i	0.278366	−	0.482143i
$248$	−3.54133	−	6.13377i	−0.224875	−	0.389495i
$249$		0			0
$250$	7.11654	+	4.10874i	0.450090	+	0.259859i
$251$	0.416679			0.0263005			0.0131503	−	0.999914i	$-0.495814\pi$
$251$	0.416679			0.0263005			0.0131503	+	0.999914i	$0.495814\pi$
$252$		0			0
$253$	10.2193			0.642481
$254$	−0.548147	−	0.316473i	−0.0343938	−	0.0198573i
$255$		0			0
$256$	5.57519	+	9.65652i	0.348449	+	0.603532i
$257$	10.5642	−	18.2977i	0.658976	−	1.14138i	−0.321906	−	0.946772i	$-0.604323\pi$
$257$	10.5642	−	18.2977i	0.658976	−	1.14138i	0.980881	−	0.194607i	$-0.0623433\pi$
$258$		0			0
$259$	1.80718	−	1.21719i	0.112293	−	0.0756328i
$260$		−	4.68556i		−	0.290586i
$261$		0			0
$262$	1.84994	−	1.06806i	0.114290	−	0.0659851i
$263$	−19.2653	+	11.1228i	−1.18795	+	0.685862i	−0.957840	−	0.287304i	$-0.907241\pi$
$263$	−19.2653	+	11.1228i	−1.18795	+	0.685862i	−0.230108	+	0.973165i	$0.573908\pi$
$264$		0			0
$265$			1.66599i			0.102341i
$266$	0.526669	+	7.60508i	0.0322921	+	0.466298i
$267$		0			0
$268$	0.232138	−	0.402075i	0.0141801	−	0.0245607i
$269$	−14.5164	−	25.1432i	−0.885083	−	1.53301i	−0.845619	−	0.533788i	$-0.820768\pi$
$269$	−14.5164	−	25.1432i	−0.885083	−	1.53301i	−0.0394642	−	0.999221i	$-0.512565\pi$
$270$		0			0
$271$	20.8174	+	12.0189i	1.26456	+	0.730097i	0.973954	−	0.226745i	$-0.0728084\pi$
$271$	20.8174	+	12.0189i	1.26456	+	0.730097i	0.290610	+	0.956842i	$0.406142\pi$
$272$	4.57398			0.277338
$273$		0			0
$274$	−8.54518			−0.516233
$275$	−4.52924	−	2.61496i	−0.273124	−	0.157688i
$276$		0			0
$277$	−4.03243	−	6.98437i	−0.242285	−	0.419650i	0.719080	−	0.694928i	$-0.244564\pi$
$277$	−4.03243	−	6.98437i	−0.242285	−	0.419650i	−0.961365	+	0.275278i	$0.911230\pi$
$278$	4.31811	−	7.47918i	0.258983	−	0.448572i
$279$		0			0
$280$	5.35358	+	7.94851i	0.319937	+	0.475014i
$281$			13.9576i			0.832639i	0.909218	+	0.416320i	$0.136680\pi$
$281$			13.9576i			0.832639i	−0.909218	+	0.416320i	$0.863320\pi$
$282$		0			0
$283$	−13.4559	+	7.76876i	−0.799869	+	0.461805i	−0.843425	−	0.537246i	$-0.819465\pi$
$283$	−13.4559	+	7.76876i	−0.799869	+	0.461805i	0.0435563	+	0.999051i	$0.486131\pi$
$284$	−2.50564	+	1.44663i	−0.148682	+	0.0858418i
$285$		0			0
$286$		−	2.82006i		−	0.166754i
$287$	−28.0804	−	13.7191i	−1.65753	−	0.809810i
$288$		0			0
$289$	0.877036	−	1.51907i	0.0515904	−	0.0893571i
$290$	−5.09823	−	8.83039i	−0.299378	−	0.518539i
$291$		0			0
$292$	−3.60442	−	2.08102i	−0.210933	−	0.121782i
$293$	−13.4742			−0.787173			−0.393587	−	0.919288i	$-0.628766\pi$
$293$	−13.4742			−0.787173			−0.393587	+	0.919288i	$0.628766\pi$
$294$		0			0
$295$	−14.1731			−0.825189
$296$	1.78462	+	1.03035i	0.103729	+	0.0598879i
$297$		0			0
$298$	2.54196	+	4.40280i	0.147252	+	0.255047i
$299$	6.18882	−	10.7194i	0.357909	−	0.619916i
$300$		0			0
$301$	−17.9130	−	8.75165i	−1.03249	−	0.504437i
$302$		−	11.1904i		−	0.643933i
$303$		0			0
$304$	4.07020	−	2.34993i	0.233442	−	0.134778i
$305$	−2.95271	+	1.70475i	−0.169072	+	0.0976136i
$306$		0			0
$307$		−	8.62791i		−	0.492421i	−0.969216	−	0.246210i	$-0.920815\pi$
$307$		−	8.62791i		−	0.492421i	0.969216	−	0.246210i	$-0.0791854\pi$
$308$	−3.94993	−	5.86450i	−0.225068	−	0.334161i
$309$		0			0
$310$	1.47127	−	2.54831i	0.0835625	−	0.144734i
$311$	−8.12200	−	14.0677i	−0.460556	−	0.797707i	0.538432	−	0.842669i	$-0.319017\pi$
$311$	−8.12200	−	14.0677i	−0.460556	−	0.797707i	−0.998989	+	0.0449616i	$0.985683\pi$
$312$		0			0
$313$	−5.86899	−	3.38846i	−0.331735	−	0.191527i	0.324876	−	0.945757i	$-0.394677\pi$
$313$	−5.86899	−	3.38846i	−0.331735	−	0.191527i	−0.656611	+	0.754229i	$0.728011\pi$
$314$	−1.49830			−0.0845538
$315$		0			0
$316$	18.4515			1.03798
$317$	−19.0245	−	10.9838i	−1.06852	−	0.616911i	−0.140744	−	0.990046i	$-0.544949\pi$
$317$	−19.0245	−	10.9838i	−1.06852	−	0.616911i	−0.927777	+	0.373135i	$0.878283\pi$
$318$		0			0
$319$	8.83017	+	15.2943i	0.494395	+	0.856316i
$320$	−1.34289	+	2.32596i	−0.0750699	+	0.130025i
$321$		0			0
$322$	0.745044	+	10.7584i	0.0415197	+	0.599543i
$323$			15.6655i			0.871654i
$324$		0			0
$325$	−5.48584	+	3.16725i	−0.304299	+	0.175687i
$326$	−6.95320	+	4.01443i	−0.385102	+	0.222339i
$327$		0			0
$328$		−	29.5576i		−	1.63204i
$329$	−5.13141	+	3.45617i	−0.282904	+	0.190545i
$330$		0			0
$331$	7.30179	−	12.6471i	0.401342	−	0.695145i	−0.592546	−	0.805537i	$-0.701877\pi$
$331$	7.30179	−	12.6471i	0.401342	−	0.695145i	0.993888	+	0.110391i	$0.0352104\pi$
$332$	−5.35684	−	9.27833i	−0.293995	−	0.509214i
$333$		0			0
$334$	−1.19508	−	0.689978i	−0.0653917	−	0.0377539i
$335$	0.452800			0.0247391
$336$		0			0
$337$	32.5257			1.77179			0.885894	−	0.463887i	$-0.153546\pi$
$337$	32.5257			1.77179			0.885894	+	0.463887i	$0.153546\pi$
$338$	5.12730	+	2.96025i	0.278888	+	0.161016i
$339$		0			0
$340$	4.19453	+	7.26514i	0.227480	+	0.394007i
$341$	−2.54825	+	4.41370i	−0.137995	+	0.239015i
$342$		0			0
$343$	−3.81408	−	18.1233i	−0.205941	−	0.978564i
$344$		−	18.8553i		−	1.01661i
$345$		0			0
$346$	9.46969	−	5.46733i	0.509094	−	0.293925i
$347$	−2.76005	+	1.59352i	−0.148167	+	0.0855444i	−0.572251	−	0.820079i	$-0.693930\pi$
$347$	−2.76005	+	1.59352i	−0.148167	+	0.0855444i	0.424084	+	0.905623i	$0.360596\pi$
$348$		0			0
$349$			7.48504i			0.400665i	0.979728	+	0.200333i	$0.0642023\pi$
$349$			7.48504i			0.400665i	−0.979728	+	0.200333i	$0.935798\pi$
$350$	2.42270	−	4.95883i	0.129499	−	0.265060i
$351$		0			0
$352$	5.26287	−	9.11556i	0.280512	−	0.485861i
$353$	5.69040	+	9.85606i	0.302869	+	0.524585i	0.976785	−	0.214223i	$-0.0687220\pi$
$353$	5.69040	+	9.85606i	0.302869	+	0.524585i	−0.673915	+	0.738809i	$0.735389\pi$
$354$		0			0
$355$	−2.44370	−	1.41087i	−0.129698	−	0.0748814i
$356$	−15.7032			−0.832267
$357$		0			0
$358$	−0.248283			−0.0131222
$359$	−4.77569	−	2.75725i	−0.252051	−	0.145522i	0.368652	−	0.929568i	$-0.379819\pi$
$359$	−4.77569	−	2.75725i	−0.252051	−	0.145522i	−0.620703	+	0.784046i	$0.713153\pi$
$360$		0			0
$361$	−1.45164	−	2.51432i	−0.0764022	−	0.132332i
$362$	−1.17657	+	2.03789i	−0.0618394	+	0.107109i
$363$		0			0
$364$	−8.54356	+	0.591660i	−0.447804	+	0.0310114i
$365$		−	4.05915i		−	0.212466i
$366$		0			0
$367$	18.2753	−	10.5512i	0.953962	−	0.550770i	0.0596526	−	0.998219i	$-0.481001\pi$
$367$	18.2753	−	10.5512i	0.953962	−	0.550770i	0.894309	+	0.447449i	$0.147667\pi$
$368$	5.75785	−	3.32430i	0.300149	−	0.173291i
$369$		0			0
$370$			0.856131i			0.0445081i
$371$	3.03773	−	0.210370i	0.157711	−	0.0109219i
$372$		0			0
$373$	−7.68498	+	13.3108i	−0.397913	+	0.689206i	−0.993468	−	0.114109i	$-0.963599\pi$
$373$	−7.68498	+	13.3108i	−0.397913	+	0.689206i	0.595555	+	0.803314i	$0.296932\pi$
$374$	2.52453	+	4.37261i	0.130540	+	0.226102i
$375$		0			0
$376$	−5.06735	−	2.92563i	−0.261328	−	0.150878i
$377$	21.3903			1.10166
$378$		0			0
$379$	−32.3630			−1.66238			−0.831188	−	0.555991i	$-0.812339\pi$
$379$	−32.3630			−1.66238			−0.831188	+	0.555991i	$0.812339\pi$
$380$	7.46510	+	4.30998i	0.382951	+	0.221097i
$381$		0			0
$382$	−2.65406	−	4.59696i	−0.135793	−	0.235201i
$383$	−9.91730	+	17.1773i	−0.506750	+	0.877718i	0.493219	+	0.869905i	$0.335820\pi$
$383$	−9.91730	+	17.1773i	−0.506750	+	0.877718i	−0.999969	+	0.00781236i	$0.997513\pi$
$384$		0			0
$385$	3.02712	−	6.19595i	0.154276	−	0.315775i
$386$		−	9.35663i		−	0.476240i
$387$		0			0
$388$	−19.9366	+	11.5104i	−1.01213	+	0.584352i
$389$	4.41918	−	2.55141i	0.224061	−	0.129362i	−0.383768	−	0.923429i	$-0.625374\pi$
$389$	4.41918	−	2.55141i	0.224061	−	0.129362i	0.607829	+	0.794068i	$0.292040\pi$
$390$		0			0
$391$			22.1610i			1.12073i
$392$	13.8171	−	10.7653i	0.697871	−	0.543729i
$393$		0			0
$394$	−1.44723	+	2.50668i	−0.0729105	+	0.126285i
$395$	8.99772	+	15.5845i	0.452724	+	0.784141i
$396$		0			0
$397$	−11.5288	−	6.65615i	−0.578613	−	0.334062i	0.181969	−	0.983304i	$-0.441753\pi$
$397$	−11.5288	−	6.65615i	−0.578613	−	0.334062i	−0.760582	+	0.649242i	$0.775086\pi$
$398$	11.7835			0.590655
$399$		0			0
$400$	−3.40254			−0.170127
$401$	14.1750	+	8.18392i	0.707864	+	0.408685i	0.810270	−	0.586057i	$-0.199321\pi$
$401$	14.1750	+	8.18392i	0.707864	+	0.408685i	−0.102406	+	0.994743i	$0.532654\pi$
$402$		0			0
$403$	3.08645	+	5.34589i	0.153747	+	0.266298i
$404$	2.92853	−	5.07237i	0.145700	−	0.252360i
$405$		0			0
$406$	−15.4574	+	10.4110i	−0.767137	+	0.516692i
$407$		−	1.48282i		−	0.0735009i
$408$		0			0
$409$	−3.75604	+	2.16855i	−0.185724	+	0.107228i	−0.589979	−	0.807418i	$-0.700864\pi$
$409$	−3.75604	+	2.16855i	−0.185724	+	0.107228i	0.404255	+	0.914646i	$0.367531\pi$
$410$	10.6347	−	6.13994i	0.525210	−	0.303230i
$411$		0			0
$412$			6.16733i			0.303843i
$413$	1.78968	+	25.8429i	0.0880644	+	1.27165i
$414$		0			0
$415$	5.22443	−	9.04898i	0.256457	−	0.444197i
$416$	−6.37441	−	11.0408i	−0.312531	−	0.541320i
$417$		0			0
$418$	4.49296	+	2.59401i	0.219758	+	0.126877i
$419$	18.8259			0.919705			0.459852	−	0.887995i	$-0.347902\pi$
$419$	18.8259			0.919705			0.459852	+	0.887995i	$0.347902\pi$
$420$		0			0
$421$	−1.82691			−0.0890380			−0.0445190	−	0.999009i	$-0.514176\pi$
$421$	−1.82691			−0.0890380			−0.0445190	+	0.999009i	$0.514176\pi$
$422$	7.47370	+	4.31494i	0.363814	+	0.210048i
$423$		0			0
$424$	1.43993	+	2.49404i	0.0699294	+	0.121121i
$425$	5.67066	−	9.82187i	0.275068	−	0.476431i
$426$		0			0
$427$	3.48125	+	5.16865i	0.168469	+	0.250128i
$428$		−	8.41658i		−	0.406831i
$429$		0			0
$430$	6.78407	−	3.91679i	0.327157	−	0.188884i
$431$	−12.4526	+	7.18954i	−0.599823	+	0.346308i	−0.768972	−	0.639283i	$-0.779231\pi$
$431$	−12.4526	+	7.18954i	−0.599823	+	0.346308i	0.169149	+	0.985590i	$0.445898\pi$
$432$		0			0
$433$			2.22130i			0.106749i	0.998575	+	0.0533745i	$0.0169977\pi$
$433$			2.22130i			0.106749i	−0.998575	+	0.0533745i	$0.983002\pi$
$434$	−4.83232	−	2.36090i	−0.231959	−	0.113327i
$435$		0			0
$436$	8.90417	−	15.4225i	0.426432	−	0.738602i
$437$	11.3855	+	19.7202i	0.544641	+	0.943347i
$438$		0			0
$439$	−8.69907	−	5.02241i	−0.415184	−	0.239706i	0.277831	−	0.960630i	$-0.410385\pi$
$439$	−8.69907	−	5.02241i	−0.415184	−	0.239706i	−0.693015	+	0.720924i	$0.743718\pi$
$440$	6.52190			0.310919
$441$		0			0
$442$	6.11544			0.290882
$443$	−12.0321	−	6.94672i	−0.571661	−	0.330049i	0.186151	−	0.982521i	$-0.440398\pi$
$443$	−12.0321	−	6.94672i	−0.571661	−	0.330049i	−0.757812	+	0.652472i	$0.773732\pi$
$444$		0			0
$445$	−7.65751	−	13.2632i	−0.363001	−	0.628736i
$446$	−9.45084	+	16.3693i	−0.447510	+	0.775110i
$447$		0			0
$448$	4.41067	+	2.15490i	0.208385	+	0.101809i
$449$			10.5630i			0.498498i	0.968439	+	0.249249i	$0.0801837\pi$
$449$			10.5630i			0.498498i	−0.968439	+	0.249249i	$0.919816\pi$
$450$		0			0
$451$	−18.4194	+	10.6344i	−0.867334	+	0.500755i
$452$	9.31804	−	5.37977i	0.438284	−	0.253043i
$453$		0			0
$454$		−	7.76210i		−	0.364293i
$455$	−4.66591	−	6.92753i	−0.218741	−	0.324768i
$456$		0			0
$457$	−2.55654	+	4.42805i	−0.119590	+	0.207135i	−0.919605	−	0.392844i	$-0.871491\pi$
$457$	−2.55654	+	4.42805i	−0.119590	+	0.207135i	0.800015	+	0.599979i	$0.204825\pi$
$458$	3.48200	+	6.03100i	0.162703	+	0.281810i
$459$		0			0
$460$	10.5604	+	6.09704i	0.492380	+	0.284276i
$461$	8.33382			0.388145			0.194072	−	0.980987i	$-0.437830\pi$
$461$	8.33382			0.388145			0.194072	+	0.980987i	$0.437830\pi$
$462$		0			0
$463$	−20.0286			−0.930806			−0.465403	−	0.885099i	$-0.654091\pi$
$463$	−20.0286			−0.930806			−0.465403	+	0.885099i	$0.654091\pi$
$464$	9.95036	+	5.74484i	0.461934	+	0.266698i
$465$		0			0
$466$	−0.799817	−	1.38532i	−0.0370508	−	0.0641739i
$467$	−10.3896	+	17.9953i	−0.480773	+	0.832723i	−0.999757	−	0.0220611i	$-0.992977\pi$
$467$	−10.3896	+	17.9953i	−0.480773	+	0.832723i	0.518984	+	0.854784i	$0.326310\pi$
$468$		0			0
$469$	−0.0571765	−	0.825627i	−0.00264016	−	0.0381239i
$470$		−	2.43095i		−	0.112131i
$471$		0			0
$472$	−21.2175	+	12.2500i	−0.976616	+	0.563850i
$473$	−11.7501	+	6.78390i	−0.540268	+	0.311924i
$474$		0			0
$475$		−	11.6535i		−	0.534698i
$476$	12.7174	−	8.56561i	0.582903	−	0.392604i
$477$		0			0
$478$	6.62156	−	11.4689i	0.302863	−	0.524574i
$479$	16.0308	+	27.7662i	0.732468	+	1.26867i	0.955825	+	0.293935i	$0.0949650\pi$
$479$	16.0308	+	27.7662i	0.732468	+	1.26867i	−0.223357	+	0.974737i	$0.571702\pi$
$480$		0			0
$481$	−1.55538	−	0.898002i	−0.0709194	−	0.0409454i
$482$	−4.64784			−0.211703
$483$		0			0
$484$	11.5147			0.523394
$485$	−19.4438	−	11.2259i	−0.882897	−	0.509741i
$486$		0			0
$487$	11.8375	+	20.5032i	0.536408	+	0.929087i	0.999094	+	0.0425641i	$0.0135527\pi$
$487$	11.8375	+	20.5032i	0.536408	+	0.929087i	−0.462685	+	0.886523i	$0.653114\pi$
$488$	−2.94686	+	5.10412i	−0.133398	+	0.231052i
$489$		0			0
$490$	6.74351	+	2.73509i	0.304641	+	0.123559i
$491$			17.8590i			0.805966i	0.915207	+	0.402983i	$0.132027\pi$
$491$			17.8590i			0.805966i	−0.915207	+	0.402983i	$0.867973\pi$
$492$		0			0
$493$	−33.1664	+	19.1486i	−1.49374	+	0.862411i
$494$	5.44189	−	3.14188i	0.244842	−	0.141360i
$495$		0			0
$496$			3.31574i			0.148881i
$497$	−2.26398	+	4.63395i	−0.101554	+	0.207861i
$498$		0			0
$499$	11.5602	−	20.0229i	0.517506	−	0.896346i	−0.482288	−	0.876013i	$-0.660194\pi$
$499$	11.5602	−	20.0229i	0.517506	−	0.896346i	0.999793	−	0.0203330i	$-0.00647265\pi$
$500$	−8.49154	−	14.7078i	−0.379753	−	0.657752i
$501$		0			0
$502$	0.259154	+	0.149622i	0.0115666	+	0.00667798i
$503$	−13.9995			−0.624206			−0.312103	−	0.950048i	$-0.601033\pi$
$503$	−13.9995			−0.624206			−0.312103	+	0.950048i	$0.601033\pi$
$504$		0			0
$505$	5.71228			0.254193
$506$	6.35589	+	3.66958i	0.282554	+	0.163133i
$507$		0			0
$508$	0.654056	+	1.13286i	0.0290190	+	0.0502624i
$509$	6.79171	−	11.7636i	0.301037	−	0.521411i	−0.675334	−	0.737512i	$-0.736001\pi$
$509$	6.79171	−	11.7636i	0.301037	−	0.521411i	0.976371	+	0.216100i	$0.0693339\pi$
$510$		0			0
$511$	−7.40137	+	0.512561i	−0.327417	+	0.0226744i
$512$		−	12.7104i		−	0.561727i
$513$		0			0
$514$	13.1408	−	7.58684i	0.579616	−	0.334641i
$515$	−5.20904	+	3.00744i	−0.229538	+	0.132524i
$516$		0			0
$517$			4.21042i			0.185174i
$518$	1.56105	−	0.108106i	0.0685886	−	0.00474992i
$519$		0			0
$520$	3.94968	−	6.84104i	0.173205	−	0.299999i
$521$	15.9477	+	27.6222i	0.698682	+	1.21015i	0.968924	+	0.247360i	$0.0795630\pi$
$521$	15.9477	+	27.6222i	0.698682	+	1.21015i	−0.270242	+	0.962792i	$0.587104\pi$
$522$		0			0
$523$	−1.20531	−	0.695886i	−0.0527046	−	0.0304290i	0.473416	−	0.880839i	$-0.343021\pi$
$523$	−1.20531	−	0.695886i	−0.0527046	−	0.0304290i	−0.526121	+	0.850410i	$0.676354\pi$
$524$	−4.41473			−0.192859
$525$		0			0
$526$	−15.9761			−0.696589
$527$	−9.57131	−	5.52600i	−0.416933	−	0.240716i
$528$		0			0
$529$	4.60628	+	7.97832i	0.200273	+	0.346883i
$530$	−0.598230	+	1.03616i	−0.0259854	+	0.0450081i
$531$		0			0
$532$	6.91608	−	14.1559i	0.299850	−	0.613738i
$533$			25.7609i			1.11583i
$534$		0			0
$535$	7.10880	−	4.10427i	0.307340	−	0.177443i
$536$	0.677855	−	0.391360i	0.0292789	−	0.0169042i
$537$		0			0
$538$		−	20.8504i		−	0.898926i
$539$	−11.6798	−	4.73720i	−0.503085	−	0.204046i
$540$		0			0
$541$	12.9736	−	22.4709i	0.557779	−	0.966101i	−0.439903	−	0.898045i	$-0.644987\pi$
$541$	12.9736	−	22.4709i	0.557779	−	0.966101i	0.997682	−	0.0680555i	$-0.0216795\pi$
$542$	8.63158	+	14.9503i	0.370758	+	0.642172i
$543$		0			0
$544$	19.7675	+	11.4128i	0.847525	+	0.489319i
$545$	17.3681			0.743969
$546$		0			0
$547$	18.6488			0.797363			0.398682	−	0.917089i	$-0.369468\pi$
$547$	18.6488			0.797363			0.398682	+	0.917089i	$0.369468\pi$
$548$	15.2943	+	8.83017i	0.653340	+	0.377206i
$549$		0			0
$550$	−1.87798	−	3.25275i	−0.0800772	−	0.138698i
$551$	−19.6757	+	34.0793i	−0.838212	+	1.45183i
$552$		0			0
$553$	27.2803	−	18.3742i	1.16008	−	0.781348i
$554$		−	5.79191i		−	0.246075i
$555$		0			0
$556$	−15.4572	+	8.92424i	−0.655533	+	0.378472i
$557$	36.3567	−	20.9905i	1.54048	−	0.889398i	0.541674	−	0.840589i	$-0.317791\pi$
$557$	36.3567	−	20.9905i	1.54048	−	0.889398i	0.998808	−	0.0488092i	$-0.0155426\pi$
$558$		0			0
$559$			16.4334i			0.695058i
$560$	−0.309952	−	4.47569i	−0.0130978	−	0.189133i
$561$		0			0
$562$	−5.01193	+	8.68092i	−0.211416	+	0.366183i
$563$	19.3006	+	33.4295i	0.813422	+	1.40889i	0.910456	+	0.413606i	$0.135731\pi$
$563$	19.3006	+	33.4295i	0.813422	+	1.40889i	−0.0970343	+	0.995281i	$0.530936\pi$
$564$		0			0
$565$	9.08771	+	5.24679i	0.382323	+	0.220734i
$566$	−11.1585			−0.469028
$567$		0			0
$568$	−4.87773			−0.204665
$569$	30.4460	+	17.5780i	1.27636	+	0.736908i	0.976178	−	0.216973i	$-0.0696185\pi$
$569$	30.4460	+	17.5780i	1.27636	+	0.736908i	0.300184	+	0.953881i	$0.402952\pi$
$570$		0			0
$571$	17.6766	+	30.6167i	0.739742	+	1.28127i	0.952611	+	0.304190i	$0.0983857\pi$
$571$	17.6766	+	30.6167i	0.739742	+	1.28127i	−0.212870	+	0.977081i	$0.568281\pi$
$572$	−2.91411	+	5.04739i	−0.121845	+	0.211042i
$573$		0			0
$574$	−12.5383	−	18.6158i	−0.523339	−	0.777007i
$575$		−	16.4854i		−	0.687489i
$576$		0			0
$577$	23.2557	−	13.4267i	0.968147	−	0.558960i	0.0694761	−	0.997584i	$-0.477867\pi$
$577$	23.2557	−	13.4267i	0.968147	−	0.558960i	0.898671	+	0.438624i	$0.144534\pi$
$578$	1.09095	−	0.629858i	0.0453774	−	0.0261986i
$579$		0			0
$580$			21.0730i			0.875011i
$581$	−17.1594	−	8.38348i	−0.711893	−	0.347805i
$582$		0			0
$583$	1.03614	−	1.79464i	0.0429125	−	0.0743266i
$584$	−3.50837	−	6.07667i	−0.145177	−	0.251454i
$585$		0			0
$586$	−8.38031	−	4.83837i	−0.346187	−	0.199871i
$587$	−31.3576			−1.29427			−0.647134	−	0.762377i	$-0.724032\pi$
$587$	−31.3576			−1.29427			−0.647134	+	0.762377i	$0.724032\pi$
$588$		0			0
$589$	−11.3562			−0.467923
$590$	−8.81496	−	5.08932i	−0.362906	−	0.209524i
$591$		0			0
$592$	−0.482357	−	0.835467i	−0.0198248	−	0.0343375i
$593$	−4.56131	+	7.90043i	−0.187311	+	0.324432i	−0.944353	−	0.328935i	$-0.893310\pi$
$593$	−4.56131	+	7.90043i	−0.187311	+	0.324432i	0.757042	+	0.653366i	$0.226644\pi$
$594$		0			0
$595$	13.4362	+	6.56445i	0.550831	+	0.269116i
$596$		−	10.5069i		−	0.430381i
$597$		0			0
$598$	7.69828	−	4.44461i	0.314806	−	0.181753i
$599$	−1.11316	+	0.642683i	−0.0454825	+	0.0262593i	−0.522569	−	0.852597i	$-0.675026\pi$
$599$	−1.11316	+	0.642683i	−0.0454825	+	0.0262593i	0.477086	+	0.878856i	$0.341693\pi$
$600$		0			0
$601$			19.2981i			0.787184i	0.919285	+	0.393592i	$0.128768\pi$
$601$			19.2981i			0.787184i	−0.919285	+	0.393592i	$0.871232\pi$
$602$	−7.99843	−	11.8754i	−0.325992	−	0.484003i
$603$		0			0
$604$	−11.5636	+	20.0287i	−0.470515	+	0.814956i
$605$	5.61502	+	9.72551i	0.228283	+	0.395398i
$606$		0			0
$607$	−33.7319	−	19.4751i	−1.36913	−	0.790470i	−0.378317	−	0.925676i	$-0.623497\pi$
$607$	−33.7319	−	19.4751i	−1.36913	−	0.790470i	−0.990817	+	0.135206i	$0.956830\pi$
$608$	23.4538			0.951177
$609$		0			0
$610$	−2.44859			−0.0991404
$611$	4.41645	+	2.54984i	0.178670	+	0.103155i
$612$		0			0
$613$	−3.65018	−	6.32229i	−0.147429	−	0.255355i	0.782847	−	0.622214i	$-0.213767\pi$
$613$	−3.65018	−	6.32229i	−0.147429	−	0.255355i	−0.930277	+	0.366859i	$0.880433\pi$
$614$	3.09814	−	5.36613i	0.125031	−	0.216560i
$615$		0			0
$616$	−0.823540	−	11.8919i	−0.0331814	−	0.479138i
$617$			44.2990i			1.78341i	0.452616	+	0.891706i	$0.350491\pi$
$617$			44.2990i			1.78341i	−0.452616	+	0.891706i	$0.649509\pi$
$618$		0			0
$619$	0.408449	−	0.235818i	0.0164169	−	0.00947832i	−0.491769	−	0.870726i	$-0.663650\pi$
$619$	0.408449	−	0.235818i	0.0164169	−	0.00947832i	0.508186	+	0.861247i	$0.330316\pi$
$620$	−5.26660	+	3.04068i	−0.211512	+	0.122116i
$621$		0			0
$622$		−	11.6659i		−	0.467760i
$623$	−23.2169	+	15.6373i	−0.930166	+	0.626496i
$624$		0			0
$625$	1.02013	−	1.76692i	0.0408052	−	0.0706768i
$626$	−2.43348	−	4.21491i	−0.0972614	−	0.168462i
$627$		0			0
$628$	2.68168	+	1.54827i	0.107011	+	0.0617826i
$629$	3.21558			0.128213
$630$		0			0
$631$	10.2247			0.407038			0.203519	−	0.979071i	$-0.434762\pi$
$631$	10.2247			0.407038			0.203519	+	0.979071i	$0.434762\pi$
$632$	26.9397	+	15.5536i	1.07160	+	0.618691i
$633$		0			0
$634$	−7.88819	−	13.6627i	−0.313280	−	0.542617i
$635$	−0.637888	+	1.10485i	−0.0253138	+	0.0438448i
$636$		0			0
$637$	−12.0423	+	9.38249i	−0.477135	+	0.371748i
$638$			12.6831i			0.502127i
$639$		0			0
$640$	12.9863	−	7.49767i	0.513330	−	0.296371i
$641$	43.4584	−	25.0907i	1.71651	−	0.991025i	0.791414	−	0.611280i	$-0.209345\pi$
$641$	43.4584	−	25.0907i	1.71651	−	0.991025i	0.925091	−	0.379745i	$-0.123988\pi$
$642$		0			0
$643$			10.6075i			0.418318i	0.977882	+	0.209159i	$0.0670726\pi$
$643$			10.6075i			0.418318i	−0.977882	+	0.209159i	$0.932927\pi$
$644$	9.78372	−	20.0255i	0.385533	−	0.789114i
$645$		0			0
$646$	−5.62524	+	9.74320i	−0.221322	+	0.383341i
$647$	14.9203	+	25.8427i	0.586577	+	1.01598i	0.994677	+	0.103044i	$0.0328582\pi$
$647$	14.9203	+	25.8427i	0.586577	+	1.01598i	−0.408100	+	0.912937i	$0.633809\pi$
$648$		0			0
$649$	15.2676	+	8.81474i	0.599305	+	0.346009i
$650$	−4.54923			−0.178435
$651$		0			0
$652$	16.5933			0.649843
$653$	−30.5327	−	17.6281i	−1.19484	−	0.689839i	−0.235437	−	0.971890i	$-0.575652\pi$
$653$	−30.5327	−	17.6281i	−1.19484	−	0.689839i	−0.959400	+	0.282050i	$0.908986\pi$
$654$		0			0
$655$	−2.15280	−	3.72877i	−0.0841170	−	0.145695i
$656$	−6.91868	+	11.9835i	−0.270129	+	0.467877i
$657$		0			0
$658$	−4.43254	+	0.306963i	−0.172798	+	0.0119667i
$659$		−	33.9194i		−	1.32131i	−0.750688	−	0.660656i	$-0.770278\pi$
$659$		−	33.9194i		−	1.32131i	0.750688	−	0.660656i	$-0.229722\pi$
$660$		0			0
$661$	13.6550	−	7.88371i	0.531117	−	0.306641i	−0.210354	−	0.977625i	$-0.567462\pi$
$661$	13.6550	−	7.88371i	0.531117	−	0.306641i	0.741471	+	0.670985i	$0.234128\pi$
$662$	9.08270	−	5.24390i	0.353009	−	0.203810i
$663$		0			0
$664$		−	18.0621i		−	0.700946i
$665$	15.3289	−	1.06156i	0.594430	−	0.0411656i
$666$		0			0
$667$	−27.8339	+	48.2097i	−1.07773	+	1.86669i
$668$	1.42598	+	2.46987i	0.0551728	+	0.0955621i
$669$		0			0
$670$	0.281619	+	0.162593i	0.0108799	+	0.00628152i
$671$	4.24097			0.163721
$672$		0			0
$673$	14.7125			0.567127			0.283563	−	0.958954i	$-0.408483\pi$
$673$	14.7125			0.567127			0.283563	+	0.958954i	$0.408483\pi$
$674$	20.2294	+	11.6794i	0.779207	+	0.449875i
$675$		0			0
$676$	−6.11795	−	10.5966i	−0.235306	−	0.407562i
$677$	1.99217	−	3.45054i	0.0765654	−	0.132615i	−0.825201	−	0.564840i	$-0.808938\pi$
$677$	1.99217	−	3.45054i	0.0765654	−	0.132615i	0.901766	+	0.432225i	$0.142271\pi$
$678$		0			0
$679$	−18.0138	+	36.8709i	−0.691307	+	1.41498i
$680$			14.1430i			0.542361i
$681$		0			0
$682$	−3.16977	+	1.83007i	−0.121377	+	0.0700769i
$683$	−19.2812	+	11.1320i	−0.737774	+	0.425954i	−0.821259	−	0.570555i	$-0.806728\pi$
$683$	−19.2812	+	11.1320i	−0.737774	+	0.425954i	0.0834856	+	0.996509i	$0.473395\pi$
$684$		0			0
$685$			17.2238i			0.658088i
$686$	4.13559	−	12.6413i	0.157898	−	0.482649i
$687$		0			0
$688$	−4.41356	+	7.64450i	−0.168265	+	0.291444i
$689$	−1.25498	−	2.17368i	−0.0478107	−	0.0828106i
$690$		0			0
$691$	41.9003	+	24.1912i	1.59396	+	0.920275i	0.992618	+	0.121287i	$0.0387020\pi$
$691$	41.9003	+	24.1912i	1.59396	+	0.920275i	0.601346	+	0.798989i	$0.294631\pi$
$692$	−22.5987			−0.859073
$693$		0			0
$694$	−2.28882			−0.0868824
$695$	−15.0752	−	8.70365i	−0.571834	−	0.330148i
$696$		0			0
$697$	−23.0613	−	39.9433i	−0.873507	−	1.51296i
$698$	−2.68775	+	4.65533i	−0.101733	+	0.176207i
$699$		0			0
$700$	−9.46041	+	6.37189i	−0.357570	+	0.240835i
$701$		−	23.3129i		−	0.880514i	−0.897872	−	0.440257i	$-0.854887\pi$
$701$		−	23.3129i		−	0.880514i	0.897872	−	0.440257i	$-0.145113\pi$
$702$		0			0
$703$	2.86142	−	1.65204i	0.107920	−	0.0623079i
$704$	2.89319	−	1.67038i	0.109041	−	0.0629549i
$705$		0			0
$706$			8.17331i			0.307607i
$707$	−0.721308	−	10.4157i	−0.0271276	−	0.391721i
$708$		0			0
$709$	−8.83884	+	15.3093i	−0.331949	+	0.574953i	−0.982894	−	0.184172i	$-0.941040\pi$
$709$	−8.83884	+	15.3093i	−0.331949	+	0.574953i	0.650945	+	0.759125i	$0.274373\pi$
$710$	−1.01324	−	1.75499i	−0.0380263	−	0.0658635i
$711$		0			0
$712$	−22.9270	−	13.2369i	−0.859227	−	0.496075i
$713$	−16.0648			−0.601633
$714$		0			0
$715$	−5.68416			−0.212576
$716$	0.444382	+	0.256564i	0.0166073	+	0.00958824i
$717$		0			0
$718$	−1.98016	−	3.42974i	−0.0738990	−	0.127997i
$719$	15.2102	−	26.3449i	0.567246	−	0.982498i	−0.429591	−	0.903024i	$-0.641342\pi$
$719$	15.2102	−	26.3449i	0.567246	−	0.982498i	0.996837	−	0.0794749i	$-0.0253244\pi$
$720$		0			0
$721$	6.14147	+	9.11830i	0.228720	+	0.339583i
$722$		−	2.08504i		−	0.0775972i
$723$		0			0
$724$	4.21171	−	2.43163i	0.156527	−	0.0903708i
$725$	24.6722	−	14.2445i	0.916304	−	0.529028i
$726$		0			0
$727$		−	44.4813i		−	1.64972i	−0.565338	−	0.824859i	$-0.691254\pi$
$727$		−	44.4813i		−	1.64972i	0.565338	−	0.824859i	$-0.308746\pi$
$728$	−12.9725	−	6.33792i	−0.480795	−	0.234899i
$729$		0			0
$730$	1.45757	−	2.52459i	0.0539472	−	0.0934393i
$731$	−14.7112	−	25.4806i	−0.544114	−	0.942433i
$732$		0			0
$733$	39.2270	+	22.6477i	1.44888	+	0.836512i	0.998415	−	0.0562818i	$-0.0179245\pi$
$733$	39.2270	+	22.6477i	1.44888	+	0.836512i	0.450466	+	0.892794i	$0.351258\pi$
$734$	15.1551			0.559385
$735$		0			0
$736$	33.1785			1.22298
$737$	−0.487767	−	0.281612i	−0.0179671	−	0.0103733i
$738$		0			0
$739$	−10.3086	−	17.8550i	−0.379208	−	0.656808i	0.611739	−	0.791060i	$-0.290470\pi$
$739$	−10.3086	−	17.8550i	−0.379208	−	0.656808i	−0.990947	+	0.134252i	$0.957137\pi$
$740$	0.884684	−	1.53232i	0.0325216	−	0.0563291i
$741$		0			0
$742$	1.96486	+	0.959960i	0.0721323	+	0.0352412i
$743$			8.88987i			0.326138i	0.986615	+	0.163069i	$0.0521392\pi$
$743$			8.88987i			0.326138i	−0.986615	+	0.163069i	$0.947861\pi$
$744$		0			0
$745$	8.87435	−	5.12361i	0.325131	−	0.187714i
$746$	−9.55935	+	5.51909i	−0.349993	+	0.202068i
$747$		0			0
$748$		−	10.4349i		−	0.381538i
$749$	−8.38129	−	12.4438i	−0.306246	−	0.454686i
$750$		0			0
$751$	12.5008	−	21.6521i	0.456162	−	0.790095i	−0.542592	−	0.839996i	$-0.682557\pi$
$751$	12.5008	−	21.6521i	0.456162	−	0.790095i	0.998754	+	0.0499007i	$0.0158905\pi$
$752$	1.36963	+	2.37227i	0.0499454	+	0.0865079i
$753$		0			0
$754$	13.3037	+	7.68089i	0.484492	+	0.279722i
$755$	−22.5555			−0.820878
$756$		0			0
$757$	−27.1262			−0.985919			−0.492959	−	0.870052i	$-0.664085\pi$
$757$	−27.1262			−0.985919			−0.492959	+	0.870052i	$0.664085\pi$
$758$	−20.1282	−	11.6210i	−0.731089	−	0.422094i
$759$		0			0
$760$	7.26616	+	12.5854i	0.263571	+	0.456519i
$761$	1.58366	−	2.74298i	0.0574075	−	0.0994328i	−0.835893	−	0.548892i	$-0.815050\pi$
$761$	1.58366	−	2.74298i	0.0574075	−	0.0994328i	0.893301	+	0.449459i	$0.148383\pi$
$762$		0			0
$763$	−2.19313	−	31.6687i	−0.0793966	−	1.14648i
$764$			10.9703i			0.396891i
$765$		0			0
$766$	−12.3361	+	7.12228i	−0.445723	+	0.257338i
$767$	18.4922	−	10.6765i	0.667713	−	0.385504i
$768$		0			0
$769$			2.87374i			0.103630i	0.998657	+	0.0518149i	$0.0165006\pi$
$769$			2.87374i			0.103630i	−0.998657	+	0.0518149i	$0.983499\pi$
$770$	4.10758	−	2.76659i	0.148027	−	0.0997009i
$771$		0			0
$772$	−9.66868	+	16.7467i	−0.347984	+	0.602725i
$773$	6.15679	+	10.6639i	0.221444	+	0.383553i	0.955247	−	0.295810i	$-0.0955895\pi$
$773$	6.15679	+	10.6639i	0.221444	+	0.383553i	−0.733802	+	0.679363i	$0.762256\pi$
$774$		0			0
$775$	7.12002	+	4.11075i	0.255759	+	0.147662i
$776$	−38.8106			−1.39322
$777$		0			0
$778$	3.66468			0.131385
$779$	−41.0426	−	23.6960i	−1.47051	−	0.848997i
$780$		0			0
$781$	1.75494	+	3.03965i	0.0627968	+	0.108767i
$782$	−7.95765	+	13.7831i	−0.284565	+	0.492881i
$783$		0			0
$784$	−8.12174	+	1.13032i	−0.290062	+	0.0403685i
$785$			3.01999i			0.107788i
$786$		0			0
$787$	3.30450	−	1.90785i	0.117793	−	0.0680076i	−0.439946	−	0.898024i	$-0.645002\pi$
$787$	3.30450	−	1.90785i	0.117793	−	0.0680076i	0.557739	+	0.830017i	$0.311669\pi$
$788$	5.18056	−	2.99100i	0.184550	−	0.106550i
$789$		0			0
$790$			12.9237i			0.459805i
$791$	8.41936	−	17.2329i	0.299358	−	0.612730i
$792$		0			0
$793$	2.56834	−	4.44849i	0.0912044	−	0.157971i
$794$	−4.78022	−	8.27959i	−0.169644	−	0.293832i
$795$		0			0
$796$	−21.0904	−	12.1765i	−0.747528	−	0.431585i
$797$	−49.1365			−1.74050			−0.870252	−	0.492607i	$-0.836044\pi$
$797$	−49.1365			−1.74050			−0.870252	+	0.492607i	$0.836044\pi$
$798$		0			0
$799$	−9.13049			−0.323013
$800$	−14.7049	−	8.48988i	−0.519897	−	0.300162i
$801$		0			0
$802$	5.87742	+	10.1800i	0.207539	+	0.359468i
$803$	−2.52453	+	4.37261i	−0.0890886	+	0.154306i
$804$		0			0
$805$	21.6848	−	1.50172i	0.764290	−	0.0529287i
$806$			4.43317i			0.156152i
$807$		0			0
$808$	8.55146	−	4.93719i	0.300839	−	0.173690i
$809$	39.4929	−	22.8012i	1.38850	−	0.801648i	0.395350	−	0.918531i	$-0.370623\pi$
$809$	39.4929	−	22.8012i	1.38850	−	0.801648i	0.993146	+	0.116882i	$0.0372900\pi$
$810$		0			0
$811$		−	39.1391i		−	1.37436i	−0.726488	−	0.687180i	$-0.758849\pi$
$811$		−	39.1391i		−	1.37436i	0.726488	−	0.687180i	$-0.241151\pi$
$812$	38.4242	−	2.66096i	1.34842	−	0.0933813i
$813$		0			0
$814$	0.532458	−	0.922243i	0.0186626	−	0.0323246i
$815$	8.09155	+	14.0150i	0.283435	+	0.490923i
$816$		0			0
$817$	−26.1819	−	15.1161i	−0.915988	−	0.528846i
$818$	−3.11476			−0.108905
$819$		0			0
$820$	−25.3789			−0.886269
$821$	−10.2976	−	5.94530i	−0.359387	−	0.207492i	0.309425	−	0.950924i	$-0.399864\pi$
$821$	−10.2976	−	5.94530i	−0.359387	−	0.207492i	−0.668812	+	0.743432i	$0.733197\pi$
$822$		0			0
$823$	−1.51195	−	2.61877i	−0.0527031	−	0.0912844i	0.838470	−	0.544947i	$-0.183450\pi$
$823$	−1.51195	−	2.61877i	−0.0527031	−	0.0912844i	−0.891173	+	0.453663i	$0.850117\pi$
$824$	−5.19873	+	9.00446i	−0.181106	+	0.313685i
$825$		0			0
$826$	−8.16667	+	16.7157i	−0.284155	+	0.581612i
$827$			15.2436i			0.530071i	0.964239	+	0.265035i	$0.0853836\pi$
$827$			15.2436i			0.530071i	−0.964239	+	0.265035i	$0.914616\pi$
$828$		0			0
$829$	−29.7306	+	17.1649i	−1.03259	+	0.596163i	−0.917724	−	0.397218i	$-0.869976\pi$
$829$	−29.7306	+	17.1649i	−1.03259	+	0.596163i	−0.114861	+	0.993382i	$0.536642\pi$
$830$	6.49868	−	3.75201i	0.225572	−	0.130234i
$831$		0			0
$832$		−	4.04635i		−	0.140282i
$833$	10.2728	−	25.3282i	0.355933	−	0.877571i
$834$		0			0
$835$	−1.39073	+	2.40882i	−0.0481283	+	0.0833606i
$836$	−5.36105	−	9.28561i	−0.185416	−	0.321150i
$837$		0			0
$838$	11.7088	+	6.76006i	0.404473	+	0.233522i
$839$	12.3205			0.425350			0.212675	−	0.977123i	$-0.431782\pi$
$839$	12.3205			0.425350			0.212675	+	0.977123i	$0.431782\pi$
$840$		0			0
$841$	−67.2016			−2.31729
$842$	−1.13625	−	0.656012i	−0.0391576	−	0.0226077i
$843$		0			0
$844$	−8.91770	−	15.4459i	−0.306960	−	0.531670i
$845$	5.96672	−	10.3347i	0.205262	−	0.355523i
$846$		0			0
$847$	17.0243	−	11.4664i	0.584961	−	0.393990i
$848$		−	1.34821i		−	0.0462976i
$849$		0			0
$850$	7.05374	−	4.07248i	0.241941	−	0.139685i
$851$	4.04786	−	2.33703i	0.138759	−	0.0801124i
$852$		0			0
$853$			4.53263i			0.155194i	0.996985	+	0.0775971i	$0.0247248\pi$
$853$			4.53263i			0.155194i	−0.996985	+	0.0775971i	$0.975275\pi$
$854$	0.309190	+	4.46470i	0.0105803	+	0.152779i
$855$		0			0
$856$	7.09472	−	12.2884i	0.242493	−	0.420010i
$857$	16.1307	+	27.9392i	0.551014	+	0.954384i	0.998202	+	0.0599442i	$0.0190923\pi$
$857$	16.1307	+	27.9392i	0.551014	+	0.954384i	−0.447188	+	0.894440i	$0.647574\pi$
$858$		0			0
$859$	−15.2711	−	8.81675i	−0.521042	−	0.300824i	0.216319	−	0.976323i	$-0.430595\pi$
$859$	−15.2711	−	8.81675i	−0.521042	−	0.300824i	−0.737361	+	0.675499i	$0.763928\pi$
$860$	−16.1897			−0.552063
$861$		0			0
$862$	−10.3266			−0.351724
$863$	−26.4091	−	15.2473i	−0.898975	−	0.519023i	−0.0221074	−	0.999756i	$-0.507038\pi$
$863$	−26.4091	−	15.2473i	−0.898975	−	0.519023i	−0.876867	+	0.480732i	$0.840371\pi$
$864$		0			0
$865$	−11.0200	−	19.0873i	−0.374693	−	0.648987i
$866$	−0.797632	+	1.38154i	−0.0271046	+	0.0469466i
$867$		0			0
$868$	6.20933	+	9.21906i	0.210759	+	0.312915i
$869$		−	22.3840i		−	0.759324i
$870$		0			0
$871$	−0.590785	+	0.341090i	−0.0200180	+	0.0115574i
$872$	26.0006	−	15.0115i	0.880492	−	0.508352i
$873$		0			0
$874$			16.3533i			0.553160i
$875$	−27.2007	−	13.2893i	−0.919552	−	0.449260i
$876$		0			0
$877$	−4.40363	+	7.62730i	−0.148700	+	0.257556i	−0.930747	−	0.365663i	$-0.880842\pi$
$877$	−4.40363	+	7.62730i	−0.148700	+	0.257556i	0.782047	+	0.623219i	$0.214176\pi$
$878$	−3.60693	−	6.24738i	−0.121728	−	0.210839i
$879$		0			0
$880$	−2.64417	−	1.52661i	−0.0891348	−	0.0514620i
$881$	−38.6776			−1.30308			−0.651540	−	0.758614i	$-0.725877\pi$
$881$	−38.6776			−1.30308			−0.651540	+	0.758614i	$0.725877\pi$
$882$		0			0
$883$	37.4489			1.26026			0.630128	−	0.776491i	$-0.283002\pi$
$883$	37.4489			1.26026			0.630128	+	0.776491i	$0.283002\pi$
$884$	−10.9455	−	6.31940i	−0.368137	−	0.212544i
$885$		0			0
$886$	−4.98890	−	8.64103i	−0.167605	−	0.290301i
$887$	−13.7025	+	23.7335i	−0.460086	+	0.796892i	−0.998965	−	0.0454915i	$-0.985515\pi$
$887$	−13.7025	+	23.7335i	−0.460086	+	0.796892i	0.538879	+	0.842383i	$0.318848\pi$
$888$		0			0
$889$	2.09512	+	1.02360i	0.0702680	+	0.0343304i
$890$		−	10.9987i		−	0.368679i
$891$		0			0
$892$	33.8305	−	19.5321i	1.13273	−	0.653982i
$893$	−8.12487	+	4.69090i	−0.271888	+	0.156975i
$894$		0			0
$895$			0.500444i			0.0167280i
$896$	−15.3109	−	22.7323i	−0.511502	−	0.759432i
$897$		0			0
$898$	−3.79299	+	6.56965i	−0.126574	+	0.219232i
$899$	−13.8811	−	24.0428i	−0.462962	−	0.801873i
$900$		0			0
$901$	3.89177	+	2.24691i	0.129654	+	0.0748556i
$902$	−15.2746			−0.508588
$903$		0			0
$904$	18.1394			0.603308
$905$	4.10760	+	2.37152i	0.136541	+	0.0788321i
$906$		0			0
$907$	11.8216	+	20.4757i	0.392531	+	0.679883i	0.992783	−	0.119928i	$-0.0382663\pi$
$907$	11.8216	+	20.4757i	0.392531	+	0.679883i	−0.600252	+	0.799811i	$0.704933\pi$
$908$	−8.02097	+	13.8927i	−0.266185	+	0.461046i
$909$		0			0
$910$	−0.414407	−	5.98403i	−0.0137375	−	0.198369i
$911$			4.52930i			0.150063i	0.997181	+	0.0750313i	$0.0239057\pi$
$911$			4.52930i			0.150063i	−0.997181	+	0.0750313i	$0.976094\pi$
$912$		0			0
$913$	−11.2557	+	6.49851i	−0.372511	+	0.215069i
$914$	−3.18008	+	1.83602i	−0.105188	+	0.0607301i
$915$		0			0
$916$		−	14.3925i		−	0.475542i
$917$	−6.52711	+	4.39622i	−0.215544	+	0.145176i
$918$		0			0
$919$	16.9149	−	29.2975i	0.557971	−	0.966434i	−0.439695	−	0.898147i	$-0.644913\pi$
$919$	16.9149	−	29.2975i	0.557971	−	0.966434i	0.997666	−	0.0682866i	$-0.0217532\pi$
$920$	10.2789	+	17.8037i	0.338887	+	0.586969i
$921$		0			0
$922$	5.18323	+	2.99254i	0.170700	+	0.0985540i
$923$	4.25119			0.139930
$924$		0			0
$925$	−2.39204			−0.0786498
$926$	−12.4568	−	7.19192i	−0.409355	−	0.236341i
$927$		0			0
$928$	28.6685	+	49.6554i	0.941091	+	1.63002i
$929$	16.4582	−	28.5064i	0.539976	−	0.935266i	−0.458928	−	0.888473i	$-0.651767\pi$
$929$	16.4582	−	28.5064i	0.539976	−	0.935266i	0.998905	−	0.0467929i	$-0.0149001\pi$
$930$		0			0
$931$	−3.87126	−	27.8164i	−0.126875	−	0.911646i
$932$			3.30597i			0.108291i
$933$		0			0
$934$	−12.9236	+	7.46146i	−0.422874	+	0.244146i
$935$	8.81350	−	5.08848i	0.288232	−	0.166411i
$936$		0			0
$937$			38.1057i			1.24486i	0.782676	+	0.622430i	$0.213854\pi$
$937$			38.1057i			1.24486i	−0.782676	+	0.622430i	$0.786146\pi$
$938$	0.260908	−	0.534030i	0.00851894	−	0.0174367i
$939$		0			0
$940$	−2.51202	+	4.35095i	−0.0819331	+	0.141912i
$941$	−9.93855	−	17.2141i	−0.323987	−	0.561163i	0.657319	−	0.753612i	$-0.271690\pi$
$941$	−9.93855	−	17.2141i	−0.323987	−	0.561163i	−0.981307	+	0.192449i	$0.938357\pi$
$942$		0			0
$943$	−58.0603	−	33.5211i	−1.89070	−	1.09160i
$944$	11.4696			0.373304
$945$		0			0
$946$	−9.74394			−0.316803
$947$	−17.9696	−	10.3747i	−0.583933	−	0.337134i	0.178762	−	0.983892i	$-0.442791\pi$
$947$	−17.9696	−	10.3747i	−0.583933	−	0.337134i	−0.762695	+	0.646759i	$0.776124\pi$
$948$		0			0
$949$	3.05772	+	5.29613i	0.0992578	+	0.171919i
$950$	4.18457	−	7.24789i	0.135765	−	0.235152i
$951$		0			0
$952$	25.7881	−	1.78589i	0.835798	−	0.0578809i
$953$			12.8345i			0.415751i	0.978155	+	0.207876i	$0.0666549\pi$
$953$			12.8345i			0.415751i	−0.978155	+	0.207876i	$0.933345\pi$
$954$		0			0
$955$	−9.26571	+	5.34956i	−0.299831	+	0.173108i
$956$	−23.7027	+	13.6848i	−0.766602	+	0.442598i
$957$		0			0
$958$			23.0256i			0.743925i
$959$	31.4055	−	2.17490i	1.01414	−	0.0702313i
$960$		0			0
$961$	−11.4941	+	19.9084i	−0.370778	+	0.642207i
$962$	−0.644915	−	1.11703i	−0.0207929	−	0.0360143i
$963$		0			0
$964$	8.31878	+	4.80285i	0.267930	+	0.154689i
$965$	−18.8594			−0.607105
$966$		0			0
$967$	35.7883			1.15087			0.575437	−	0.817846i	$-0.304832\pi$
$967$	35.7883			1.15087			0.575437	+	0.817846i	$0.304832\pi$
$968$	16.8117	+	9.70625i	0.540349	+	0.311971i
$969$		0			0
$970$	−8.06205	−	13.9639i	−0.258857	−	0.448353i
$971$	14.5129	−	25.1370i	0.465740	−	0.806686i	−0.533494	−	0.845804i	$-0.679121\pi$
$971$	14.5129	−	25.1370i	0.465740	−	0.806686i	0.999235	+	0.0391177i	$0.0124547\pi$
$972$		0			0
$973$	−13.9665	+	28.5868i	−0.447744	+	0.916450i
$974$			17.0026i			0.544798i
$975$		0			0
$976$	2.38949	−	1.37957i	0.0764856	−	0.0441590i
$977$	−7.73439	+	4.46545i	−0.247445	+	0.142862i	−0.618594	−	0.785711i	$-0.712297\pi$
$977$	−7.73439	+	4.46545i	−0.247445	+	0.142862i	0.371149	+	0.928573i	$0.378964\pi$
$978$		0			0
$979$			19.0499i			0.608837i
$980$	−9.24334	−	11.8637i	−0.295268	−	0.378973i
$981$		0			0
$982$	−6.41288	+	11.1074i	−0.204643	+	0.354452i
$983$	26.1346	+	45.2665i	0.833566	+	1.44378i	0.895193	+	0.445679i	$0.147038\pi$
$983$	26.1346	+	45.2665i	0.833566	+	1.44378i	−0.0616269	+	0.998099i	$0.519629\pi$
$984$		0			0
$985$	5.05250	+	2.91707i	0.160986	+	0.0929454i
$986$	−27.5038			−0.875900
$987$		0			0
$988$	−12.9867			−0.413160
$989$	−37.0378	−	21.3838i	−1.17773	−	0.679964i
$990$		0			0
$991$	−21.9151	−	37.9581i	−0.696158	−	1.20578i	−0.969789	−	0.243946i	$-0.921558\pi$
$991$	−21.9151	−	37.9581i	−0.696158	−	1.20578i	0.273631	−	0.961835i	$-0.411775\pi$
$992$	−8.27329	+	14.3298i	−0.262677	+	0.454970i
$993$		0			0
$994$	−3.07206	+	2.06913i	−0.0974399	+	0.0656289i
$995$		−	23.7511i		−	0.752960i
$996$		0			0
$997$	38.9689	−	22.4987i	1.23416	−	0.712542i	0.266264	−	0.963900i	$-0.414211\pi$
$997$	38.9689	−	22.4987i	1.23416	−	0.712542i	0.967894	+	0.251358i	$0.0808772\pi$
$998$	14.3797	−	8.30215i	0.455183	−	0.262800i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.p.c.404.4		10
3.2	odd	2		567.2.p.d.404.2		10
7.3	odd	6		567.2.p.d.80.2		10
9.2	odd	6		63.2.i.b.5.4	✓	10
9.4	even	3		63.2.s.b.47.2	yes	10
9.5	odd	6		189.2.s.b.89.4		10
9.7	even	3		189.2.i.b.152.2		10
21.17	even	6	inner	567.2.p.c.80.4		10
36.7	odd	6		3024.2.ca.b.2609.4		10
36.11	even	6		1008.2.ca.b.257.3		10
36.23	even	6		3024.2.df.b.1601.4		10
36.31	odd	6		1008.2.df.b.929.2		10
63.2	odd	6		441.2.o.d.293.4		10
63.4	even	3		441.2.i.b.227.2		10
63.5	even	6		1323.2.o.c.440.2		10
63.11	odd	6		441.2.s.b.374.2		10
63.13	odd	6		441.2.s.b.362.2		10
63.16	even	3		1323.2.o.c.881.2		10
63.20	even	6		441.2.i.b.68.4		10
63.23	odd	6		1323.2.o.d.440.2		10
63.25	even	3		1323.2.s.b.962.4		10
63.31	odd	6		63.2.i.b.38.2	yes	10
63.32	odd	6		1323.2.i.b.521.4		10
63.34	odd	6		1323.2.i.b.1097.2		10
63.38	even	6		63.2.s.b.59.2	yes	10
63.40	odd	6		441.2.o.d.146.4		10
63.41	even	6		1323.2.s.b.656.4		10
63.47	even	6		441.2.o.c.293.4		10
63.52	odd	6		189.2.s.b.17.4		10
63.58	even	3		441.2.o.c.146.4		10
63.59	even	6		189.2.i.b.143.4		10
63.61	odd	6		1323.2.o.d.881.2		10
252.31	even	6		1008.2.ca.b.353.3		10
252.59	odd	6		3024.2.ca.b.2033.4		10
252.115	even	6		3024.2.df.b.17.4		10
252.227	odd	6		1008.2.df.b.689.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.4	✓	10	9.2	odd	6
63.2.i.b.38.2	yes	10	63.31	odd	6
63.2.s.b.47.2	yes	10	9.4	even	3
63.2.s.b.59.2	yes	10	63.38	even	6
189.2.i.b.143.4		10	63.59	even	6
189.2.i.b.152.2		10	9.7	even	3
189.2.s.b.17.4		10	63.52	odd	6
189.2.s.b.89.4		10	9.5	odd	6
441.2.i.b.68.4		10	63.20	even	6
441.2.i.b.227.2		10	63.4	even	3
441.2.o.c.146.4		10	63.58	even	3
441.2.o.c.293.4		10	63.47	even	6
441.2.o.d.146.4		10	63.40	odd	6
441.2.o.d.293.4		10	63.2	odd	6
441.2.s.b.362.2		10	63.13	odd	6
441.2.s.b.374.2		10	63.11	odd	6
567.2.p.c.80.4		10	21.17	even	6	inner
567.2.p.c.404.4		10	1.1	even	1	trivial
567.2.p.d.80.2		10	7.3	odd	6
567.2.p.d.404.2		10	3.2	odd	2
1008.2.ca.b.257.3		10	36.11	even	6
1008.2.ca.b.353.3		10	252.31	even	6
1008.2.df.b.689.2		10	252.227	odd	6
1008.2.df.b.929.2		10	36.31	odd	6
1323.2.i.b.521.4		10	63.32	odd	6
1323.2.i.b.1097.2		10	63.34	odd	6
1323.2.o.c.440.2		10	63.5	even	6
1323.2.o.c.881.2		10	63.16	even	3
1323.2.o.d.440.2		10	63.23	odd	6
1323.2.o.d.881.2		10	63.61	odd	6
1323.2.s.b.656.4		10	63.41	even	6
1323.2.s.b.962.4		10	63.25	even	3
3024.2.ca.b.2033.4		10	252.59	odd	6
3024.2.ca.b.2609.4		10	36.7	odd	6
3024.2.df.b.17.4		10	252.115	even	6
3024.2.df.b.1601.4		10	36.23	even	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.621951 + 0.359083i) q^{2} +(-0.742118 - 1.28539i) q^{4} +(0.723774 - 1.25361i) q^{5} +(-2.37721 - 1.16142i) q^{7} -2.50226i q^{8} +O(q^{10})\)	\(q+(0.621951 + 0.359083i) q^{2} +(-0.742118 - 1.28539i) q^{4} +(0.723774 - 1.25361i) q^{5} +(-2.37721 - 1.16142i) q^{7} -2.50226i q^{8} +(0.900304 - 0.519791i) q^{10} +(-1.55933 + 0.900281i) q^{11} +2.18085i q^{13} +(-1.06146 - 1.57596i) q^{14} +(-0.585716 + 1.01449i) q^{16} +(-1.95230 - 3.38149i) q^{17} +(-3.47456 - 2.00604i) q^{19} -2.14850 q^{20} -1.29310 q^{22} +(-4.91522 - 2.83781i) q^{23} +(1.45230 + 2.51546i) q^{25} +(-0.783106 + 1.35638i) q^{26} +(0.271298 + 3.91754i) q^{28} -9.80824i q^{29} +(2.45129 - 1.41525i) q^{31} +(-5.06262 + 2.92290i) q^{32} -2.80416i q^{34} +(-3.17653 + 2.13949i) q^{35} +(-0.411767 + 0.713202i) q^{37} +(-1.44067 - 2.49531i) q^{38} +(-3.13687 - 1.81107i) q^{40} +11.8123 q^{41} +7.53532 q^{43} +(2.31442 + 1.33623i) q^{44} +(-2.03802 - 3.52995i) q^{46} +(1.16920 - 2.02511i) q^{47} +(4.30222 + 5.52186i) q^{49} +2.08599i q^{50} +(2.80323 - 1.61845i) q^{52} +(-0.996713 + 0.575453i) q^{53} +2.60640i q^{55} +(-2.90617 + 5.94839i) q^{56} +(3.52198 - 6.10024i) q^{58} +(-4.89555 - 8.47934i) q^{59} +(-2.03980 - 1.17768i) q^{61} +2.03277 q^{62} -1.85540 q^{64} +(2.73394 + 1.57844i) q^{65} +(0.156402 + 0.270897i) q^{67} +(-2.89768 + 5.01893i) q^{68} +(-2.74390 + 0.190021i) q^{70} -1.94933i q^{71} +(2.42847 - 1.40208i) q^{73} +(-0.512198 + 0.295717i) q^{74} +5.95486i q^{76} +(4.75246 - 0.329118i) q^{77} +(-6.21583 + 10.7661i) q^{79} +(0.847852 + 1.46852i) q^{80} +(7.34669 + 4.24162i) q^{82} +7.21832 q^{83} -5.65210 q^{85} +(4.68660 + 2.70581i) q^{86} +(2.25274 + 3.90186i) q^{88} +(5.28999 - 9.16253i) q^{89} +(2.53287 - 5.18433i) q^{91} +8.42395i q^{92} +(1.45436 - 0.839677i) q^{94} +(-5.02959 + 2.90383i) q^{95} -15.5102i q^{97} +(0.692961 + 4.97918i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} + 3 q^{7}+O(q^{10}) \) 10 * q + 4 * q^4 + 3 * q^7	\( 10 q + 4 q^{4} + 3 q^{7} - 15 q^{10} - 12 q^{11} + 18 q^{14} - 6 q^{16} - 12 q^{17} + 3 q^{19} + 6 q^{20} - 10 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 2 q^{28} + 9 q^{31} - 48 q^{32} - 15 q^{35} + 6 q^{37} - 18 q^{38} - 15 q^{40} + 18 q^{41} - 6 q^{43} + 24 q^{44} - 13 q^{46} + 15 q^{47} + 19 q^{49} + 12 q^{52} - 9 q^{53} + 21 q^{56} + 8 q^{58} - 18 q^{59} - 12 q^{61} + 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} + 27 q^{68} - 15 q^{70} + 3 q^{73} - 30 q^{74} - 6 q^{77} + 20 q^{79} - 30 q^{80} + 9 q^{82} + 30 q^{83} - 36 q^{85} + 54 q^{86} - 8 q^{88} + 24 q^{89} - 24 q^{91} + 3 q^{94} + 45 q^{98}+O(q^{100}) \) 10 * q + 4 * q^4 + 3 * q^7 - 15 * q^10 - 12 * q^11 + 18 * q^14 - 6 * q^16 - 12 * q^17 + 3 * q^19 + 6 * q^20 - 10 * q^22 - 15 * q^23 + 7 * q^25 + 3 * q^26 + 2 * q^28 + 9 * q^31 - 48 * q^32 - 15 * q^35 + 6 * q^37 - 18 * q^38 - 15 * q^40 + 18 * q^41 - 6 * q^43 + 24 * q^44 - 13 * q^46 + 15 * q^47 + 19 * q^49 + 12 * q^52 - 9 * q^53 + 21 * q^56 + 8 * q^58 - 18 * q^59 - 12 * q^61 + 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 + 27 * q^68 - 15 * q^70 + 3 * q^73 - 30 * q^74 - 6 * q^77 + 20 * q^79 - 30 * q^80 + 9 * q^82 + 30 * q^83 - 36 * q^85 + 54 * q^86 - 8 * q^88 + 24 * q^89 - 24 * q^91 + 3 * q^94 + 45 * q^98

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