LMFDB - Embedded newform 567.2.p.c.80.4

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			80.4
Root			$0.187540 + 0.324828i$ of defining polynomial
Character	$\chi$	$=$	567.80
Dual form			567.2.p.c.404.4

$q$-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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

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

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	−0.263721	−	0.964599i	$-0.584950\pi$
$2$	0.621951	−	0.359083i	0.439785	−	0.253910i	0.703507	+	0.710689i	$0.251617\pi$
$3$		0			0
$3$		0			0
$4$	−0.742118	+	1.28539i	−0.371059	+	0.642693i
$5$	0.723774	+	1.25361i	0.323682	+	0.560633i	0.981245	−	0.192766i	$-0.0617460\pi$
$5$	0.723774	+	1.25361i	0.323682	+	0.560633i	−0.657563	+	0.753400i	$0.728413\pi$
$6$		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	0.246149	−	0.969232i	$-0.420835\pi$
$11$	−1.55933	−	0.900281i	−0.470156	−	0.271445i	−0.716305	+	0.697787i	$0.754168\pi$
$12$		0			0
$13$		−	2.18085i		−	0.604858i	−0.953172	−	0.302429i	$-0.902202\pi$
$13$		−	2.18085i		−	0.604858i	0.953172	−	0.302429i	$-0.0977976\pi$
$14$	−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	−0.999540	−	0.0303308i	$-0.990344\pi$
$17$	−1.95230	+	3.38149i	−0.473503	+	0.820131i	0.526037	+	0.850462i	$0.323677\pi$
$18$		0			0
$19$	−3.47456	+	2.00604i	−0.797118	+	0.460216i	−0.842462	−	0.538755i	$-0.818895\pi$
$19$	−3.47456	+	2.00604i	−0.797118	+	0.460216i	0.0453446	+	0.998971i	$0.485561\pi$
$20$	−2.14850			−0.480420
$21$		0			0
$22$	−1.29310			−0.275691
$23$	−4.91522	+	2.83781i	−1.02490	+	0.591723i	−0.915518	−	0.402277i	$-0.868219\pi$
$23$	−4.91522	+	2.83781i	−1.02490	+	0.591723i	−0.109377	+	0.994000i	$0.534886\pi$
$24$		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	$0.364436\pi$
$29$			9.80824i			1.82134i	−0.413130	+	0.910672i	$0.635564\pi$
$30$		0			0
$31$	2.45129	+	1.41525i	0.440264	+	0.254187i	0.703710	−	0.710488i	$-0.251526\pi$
$31$	2.45129	+	1.41525i	0.440264	+	0.254187i	−0.263445	+	0.964674i	$0.584859\pi$
$32$	−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	0.830192	−	0.557478i	$-0.188231\pi$
$37$	−0.411767	−	0.713202i	−0.0676941	−	0.117250i	−0.897886	+	0.440228i	$0.854898\pi$
$38$	−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	0.938610	−	0.344979i	$-0.112114\pi$
$47$	1.16920	+	2.02511i	0.170545	+	0.295392i	−0.768066	+	0.640371i	$0.778781\pi$
$48$		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	0.429981	−	0.902838i	$-0.358520\pi$
$53$	−0.996713	−	0.575453i	−0.136909	−	0.0790445i	−0.566890	+	0.823793i	$0.691854\pi$
$54$		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	0.348666	+	0.937247i	$0.386635\pi$
$59$	−4.89555	+	8.47934i	−0.637346	+	1.10392i	−0.986013	+	0.166669i	$0.946699\pi$
$60$		0			0
$61$	−2.03980	+	1.17768i	−0.261170	+	0.150786i	−0.624868	−	0.780730i	$-0.714847\pi$
$61$	−2.03980	+	1.17768i	−0.261170	+	0.150786i	0.363698	+	0.931517i	$0.381514\pi$
$62$	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	−0.856313	−	0.516456i	$-0.827251\pi$
$67$	0.156402	−	0.270897i	0.0191076	−	0.0330953i	0.875421	+	0.483361i	$0.160584\pi$
$68$	−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	$0.0369019\pi$
$71$			1.94933i			0.231343i	−0.993288	+	0.115671i	$0.963098\pi$
$72$		0			0
$73$	2.42847	+	1.40208i	0.284231	+	0.164101i	0.635337	−	0.772235i	$-0.280861\pi$
$73$	2.42847	+	1.40208i	0.284231	+	0.164101i	−0.351106	+	0.936336i	$0.614194\pi$
$74$	−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	−0.968697	−	0.248246i	$-0.920146\pi$
$79$	−6.21583	−	10.7661i	−0.699336	−	1.21128i	0.269361	−	0.963039i	$-0.413187\pi$
$80$	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	0.997432	+	0.0716161i	$0.0228156\pi$
$89$	5.28999	+	9.16253i	0.560737	+	0.971226i	−0.436695	+	0.899610i	$0.643851\pi$
$90$		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	$0.288579\pi$
$97$			15.5102i			1.57482i	−0.616428	+	0.787411i	$0.711421\pi$
$98$	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	−0.751006	−	0.660295i	$-0.770431\pi$
$101$	1.97309	−	3.41749i	0.196330	−	0.340053i	0.947336	+	0.320242i	$0.103764\pi$
$102$		0			0
$103$	−3.59853	+	2.07761i	−0.354573	+	0.204713i	−0.666698	−	0.745328i	$-0.732293\pi$
$103$	−3.59853	+	2.07761i	−0.354573	+	0.204713i	0.312124	+	0.950041i	$0.398959\pi$
$104$	5.45705			0.535108
$105$		0			0
$106$	−0.826542			−0.0802809
$107$	4.91092	−	2.83532i	0.474757	−	0.274101i	−0.243472	−	0.969908i	$-0.578286\pi$
$107$	4.91092	−	2.83532i	0.474757	−	0.274101i	0.718229	+	0.695807i	$0.244953\pi$
$108$		0			0
$109$	5.99916	−	10.3908i	0.574615	−	0.995262i	−0.421468	−	0.906843i	$-0.638485\pi$
$109$	5.99916	−	10.3908i	0.574615	−	0.995262i	0.996083	−	0.0884193i	$-0.0281815\pi$
$110$	−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	$-0.889243\pi$
$113$		−	7.24921i		−	0.681948i	0.940073	−	0.340974i	$-0.110757\pi$
$114$		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	0.923652	−	0.383232i	$-0.125189\pi$
$131$	1.48721	+	2.57592i	0.129938	+	0.225059i	−0.793714	+	0.608291i	$0.791856\pi$
$132$		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	−0.00959114	−	0.999954i	$-0.503053\pi$
$137$	−10.3045	−	5.94930i	−0.880372	−	0.508283i	−0.870781	+	0.491671i	$0.836386\pi$
$138$		0			0
$139$			12.0254i			1.01998i	0.860181	+	0.509989i	$0.170351\pi$
$139$			12.0254i			1.01998i	−0.860181	+	0.509989i	$0.829649\pi$
$140$	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	−0.227399	−	0.973802i	$-0.573022\pi$
$149$	6.13061	−	3.53951i	0.502239	−	0.289968i	0.729638	+	0.683834i	$0.239689\pi$
$150$		0			0
$151$	−7.79093	+	13.4943i	−0.634017	+	1.09815i	0.352706	+	0.935734i	$0.385262\pi$
$151$	−7.79093	+	13.4943i	−0.634017	+	1.09815i	−0.986723	+	0.162415i	$0.948072\pi$
$152$	−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	0.426166	−	0.904645i	$-0.359864\pi$
$157$	−1.80677	−	1.04314i	−0.144196	−	0.0832517i	−0.570362	+	0.821393i	$0.693197\pi$
$158$	−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	0.559692	−	0.828700i	$-0.310919\pi$
$163$	−5.58983	−	9.68188i	−0.437830	−	0.758343i	−0.997522	+	0.0703575i	$0.977586\pi$
$164$	−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	0.995618	+	0.0935182i	$0.0298113\pi$
$173$	7.61290	+	13.1859i	0.578798	+	1.00251i	−0.416820	+	0.908989i	$0.636855\pi$
$174$		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	0.488769	−	0.872413i	$-0.337446\pi$
$179$	−0.299401	−	0.172859i	−0.0223783	−	0.0129201i	−0.511147	+	0.859493i	$0.670779\pi$
$180$		0			0
$181$		−	3.27661i		−	0.243548i	−0.992558	−	0.121774i	$-0.961142\pi$
$181$		−	3.27661i		−	0.243548i	0.992558	−	0.121774i	$-0.0388583\pi$
$182$	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	−0.713371	−	0.700787i	$-0.752833\pi$
$191$	−6.40096	+	3.69560i	−0.463158	+	0.267404i	0.250213	+	0.968191i	$0.419499\pi$
$192$		0			0
$193$	−6.51425	+	11.2830i	−0.468906	+	0.812169i	−0.999368	−	0.0355398i	$-0.988685\pi$
$193$	−6.51425	+	11.2830i	−0.468906	+	0.812169i	0.530462	+	0.847708i	$0.322018\pi$
$194$	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	$-0.954140\pi$
$197$		−	4.03035i		−	0.287151i	0.989639	−	0.143575i	$-0.0458599\pi$
$198$		0			0
$199$	14.2096	+	8.20390i	1.00729	+	0.581559i	0.910397	−	0.413736i	$-0.135776\pi$
$199$	14.2096	+	8.20390i	1.00729	+	0.581559i	0.0968925	+	0.995295i	$0.469110\pi$
$200$	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	$-0.656712\pi$
$223$		−	26.3193i		−	1.76247i	0.472675	−	0.881237i	$-0.343288\pi$
$224$	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	−0.987741	−	0.156101i	$-0.950107\pi$
$227$	−5.40410	+	9.36018i	−0.358683	+	0.621257i	0.629058	+	0.777358i	$0.283441\pi$
$228$		0			0
$229$	8.39777	−	4.84846i	0.554941	−	0.320395i	−0.196172	−	0.980570i	$-0.562851\pi$
$229$	8.39777	−	4.84846i	0.554941	−	0.320395i	0.751112	+	0.660174i	$0.229518\pi$
$230$	−5.90026			−0.389052
$231$		0			0
$232$	−24.5428			−1.61131
$233$	−1.92897	+	1.11369i	−0.126371	+	0.0729605i	−0.561853	−	0.827237i	$-0.689911\pi$
$233$	−1.92897	+	1.11369i	−0.126371	+	0.0729605i	0.435482	+	0.900198i	$0.356578\pi$
$234$		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	$0.203402\pi$
$239$			18.4402i			1.19280i	−0.802689	+	0.596398i	$0.796598\pi$
$240$		0			0
$241$	−5.60475	−	3.23591i	−0.361034	−	0.208443i	0.308500	−	0.951224i	$-0.400173\pi$
$241$	−5.60475	−	3.23591i	−0.361034	−	0.208443i	−0.669534	+	0.742781i	$0.733506\pi$
$242$	−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	0.980881	+	0.194607i	$0.0623433\pi$
$257$	10.5642	+	18.2977i	0.658976	+	1.14138i	−0.321906	+	0.946772i	$0.604323\pi$
$258$		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	−0.230108	−	0.973165i	$-0.573908\pi$
$263$	−19.2653	−	11.1228i	−1.18795	−	0.685862i	−0.957840	+	0.287304i	$0.907241\pi$
$264$		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	−0.0394642	+	0.999221i	$0.512565\pi$
$269$	−14.5164	+	25.1432i	−0.885083	+	1.53301i	−0.845619	+	0.533788i	$0.820768\pi$
$270$		0			0
$271$	20.8174	−	12.0189i	1.26456	−	0.730097i	0.290610	−	0.956842i	$-0.406142\pi$
$271$	20.8174	−	12.0189i	1.26456	−	0.730097i	0.973954	+	0.226745i	$0.0728084\pi$
$272$	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	−0.961365	−	0.275278i	$-0.911230\pi$
$277$	−4.03243	+	6.98437i	−0.242285	+	0.419650i	0.719080	+	0.694928i	$0.244564\pi$
$278$	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	$-0.863320\pi$
$281$		−	13.9576i		−	0.832639i	0.909218	−	0.416320i	$-0.136680\pi$
$282$		0			0
$283$	−13.4559	−	7.76876i	−0.799869	−	0.461805i	0.0435563	−	0.999051i	$-0.486131\pi$
$283$	−13.4559	−	7.76876i	−0.799869	−	0.461805i	−0.843425	+	0.537246i	$0.819465\pi$
$284$	−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	$0.0791854\pi$
$307$			8.62791i			0.492421i	−0.969216	+	0.246210i	$0.920815\pi$
$308$	−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	−0.998989	−	0.0449616i	$-0.985683\pi$
$311$	−8.12200	+	14.0677i	−0.460556	+	0.797707i	0.538432	+	0.842669i	$0.319017\pi$
$312$		0			0
$313$	−5.86899	+	3.38846i	−0.331735	+	0.191527i	−0.656611	−	0.754229i	$-0.728011\pi$
$313$	−5.86899	+	3.38846i	−0.331735	+	0.191527i	0.324876	+	0.945757i	$0.394677\pi$
$314$	−1.49830			−0.0845538
$315$		0			0
$316$	18.4515			1.03798
$317$	−19.0245	+	10.9838i	−1.06852	+	0.616911i	−0.927777	−	0.373135i	$-0.878283\pi$
$317$	−19.0245	+	10.9838i	−1.06852	+	0.616911i	−0.140744	+	0.990046i	$0.544949\pi$
$318$		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	0.993888	−	0.110391i	$-0.0352104\pi$
$331$	7.30179	+	12.6471i	0.401342	+	0.695145i	−0.592546	+	0.805537i	$0.701877\pi$
$332$	−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	0.424084	−	0.905623i	$-0.360596\pi$
$347$	−2.76005	−	1.59352i	−0.148167	−	0.0855444i	−0.572251	+	0.820079i	$0.693930\pi$
$348$		0			0
$349$		−	7.48504i		−	0.400665i	−0.979728	−	0.200333i	$-0.935798\pi$
$349$		−	7.48504i		−	0.400665i	0.979728	−	0.200333i	$-0.0642023\pi$
$350$	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	−0.673915	−	0.738809i	$-0.735389\pi$
$353$	5.69040	−	9.85606i	0.302869	−	0.524585i	0.976785	+	0.214223i	$0.0687220\pi$
$354$		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	−0.620703	−	0.784046i	$-0.713153\pi$
$359$	−4.77569	+	2.75725i	−0.252051	+	0.145522i	0.368652	+	0.929568i	$0.379819\pi$
$360$		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	0.894309	−	0.447449i	$-0.147667\pi$
$367$	18.2753	+	10.5512i	0.953962	+	0.550770i	0.0596526	+	0.998219i	$0.481001\pi$
$368$	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	0.595555	−	0.803314i	$-0.296932\pi$
$373$	−7.68498	−	13.3108i	−0.397913	−	0.689206i	−0.993468	+	0.114109i	$0.963599\pi$
$374$	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	−0.999969	−	0.00781236i	$-0.997513\pi$
$383$	−9.91730	−	17.1773i	−0.506750	−	0.877718i	0.493219	−	0.869905i	$-0.335820\pi$
$384$		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	0.607829	−	0.794068i	$-0.292040\pi$
$389$	4.41918	+	2.55141i	0.224061	+	0.129362i	−0.383768	+	0.923429i	$0.625374\pi$
$390$		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	−0.760582	−	0.649242i	$-0.775086\pi$
$397$	−11.5288	+	6.65615i	−0.578613	+	0.334062i	0.181969	+	0.983304i	$0.441753\pi$
$398$	11.7835			0.590655
$399$		0			0
$400$	−3.40254			−0.170127
$401$	14.1750	−	8.18392i	0.707864	−	0.408685i	−0.102406	−	0.994743i	$-0.532654\pi$
$401$	14.1750	−	8.18392i	0.707864	−	0.408685i	0.810270	+	0.586057i	$0.199321\pi$
$402$		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	0.404255	−	0.914646i	$-0.367531\pi$
$409$	−3.75604	−	2.16855i	−0.185724	−	0.107228i	−0.589979	+	0.807418i	$0.700864\pi$
$410$	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	0.169149	−	0.985590i	$-0.445898\pi$
$431$	−12.4526	−	7.18954i	−0.599823	−	0.346308i	−0.768972	+	0.639283i	$0.779231\pi$
$432$		0			0
$433$		−	2.22130i		−	0.106749i	−0.998575	−	0.0533745i	$-0.983002\pi$
$433$		−	2.22130i		−	0.106749i	0.998575	−	0.0533745i	$-0.0169977\pi$
$434$	−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	−0.693015	−	0.720924i	$-0.743718\pi$
$439$	−8.69907	+	5.02241i	−0.415184	+	0.239706i	0.277831	+	0.960630i	$0.410385\pi$
$440$	6.52190			0.310919
$441$		0			0
$442$	6.11544			0.290882
$443$	−12.0321	+	6.94672i	−0.571661	+	0.330049i	−0.757812	−	0.652472i	$-0.773732\pi$
$443$	−12.0321	+	6.94672i	−0.571661	+	0.330049i	0.186151	+	0.982521i	$0.440398\pi$
$444$		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	$-0.919816\pi$
$449$		−	10.5630i		−	0.498498i	0.968439	−	0.249249i	$-0.0801837\pi$
$450$		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	0.800015	−	0.599979i	$-0.204825\pi$
$457$	−2.55654	−	4.42805i	−0.119590	−	0.207135i	−0.919605	+	0.392844i	$0.871491\pi$
$458$	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	0.518984	−	0.854784i	$-0.326310\pi$
$467$	−10.3896	−	17.9953i	−0.480773	−	0.832723i	−0.999757	+	0.0220611i	$0.992977\pi$
$468$		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	−0.223357	−	0.974737i	$-0.571702\pi$
$479$	16.0308	−	27.7662i	0.732468	−	1.26867i	0.955825	−	0.293935i	$-0.0949650\pi$
$480$		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	−0.462685	−	0.886523i	$-0.653114\pi$
$487$	11.8375	−	20.5032i	0.536408	−	0.929087i	0.999094	−	0.0425641i	$-0.0135527\pi$
$488$	−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	$-0.867973\pi$
$491$		−	17.8590i		−	0.805966i	0.915207	−	0.402983i	$-0.132027\pi$
$492$		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	0.999793	+	0.0203330i	$0.00647265\pi$
$499$	11.5602	+	20.0229i	0.517506	+	0.896346i	−0.482288	+	0.876013i	$0.660194\pi$
$500$	−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	0.976371	−	0.216100i	$-0.0693339\pi$
$509$	6.79171	+	11.7636i	0.301037	+	0.521411i	−0.675334	+	0.737512i	$0.736001\pi$
$510$		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	−0.270242	−	0.962792i	$-0.587104\pi$
$521$	15.9477	−	27.6222i	0.698682	−	1.21015i	0.968924	−	0.247360i	$-0.0795630\pi$
$522$		0			0
$523$	−1.20531	+	0.695886i	−0.0527046	+	0.0304290i	−0.526121	−	0.850410i	$-0.676354\pi$
$523$	−1.20531	+	0.695886i	−0.0527046	+	0.0304290i	0.473416	+	0.880839i	$0.343021\pi$
$524$	−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	0.997682	+	0.0680555i	$0.0216795\pi$
$541$	12.9736	+	22.4709i	0.557779	+	0.966101i	−0.439903	+	0.898045i	$0.644987\pi$
$542$	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	0.998808	+	0.0488092i	$0.0155426\pi$
$557$	36.3567	+	20.9905i	1.54048	+	0.889398i	0.541674	+	0.840589i	$0.317791\pi$
$558$		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	−0.0970343	−	0.995281i	$-0.530936\pi$
$563$	19.3006	−	33.4295i	0.813422	−	1.40889i	0.910456	−	0.413606i	$-0.135731\pi$
$564$		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	0.300184	−	0.953881i	$-0.402952\pi$
$569$	30.4460	−	17.5780i	1.27636	−	0.736908i	0.976178	+	0.216973i	$0.0696185\pi$
$570$		0			0
$571$	17.6766	−	30.6167i	0.739742	−	1.28127i	−0.212870	−	0.977081i	$-0.568281\pi$
$571$	17.6766	−	30.6167i	0.739742	−	1.28127i	0.952611	−	0.304190i	$-0.0983857\pi$
$572$	−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	0.898671	−	0.438624i	$-0.144534\pi$
$577$	23.2557	+	13.4267i	0.968147	+	0.558960i	0.0694761	+	0.997584i	$0.477867\pi$
$578$	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	0.757042	−	0.653366i	$-0.226644\pi$
$593$	−4.56131	−	7.90043i	−0.187311	−	0.324432i	−0.944353	+	0.328935i	$0.893310\pi$
$594$		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	0.477086	−	0.878856i	$-0.341693\pi$
$599$	−1.11316	−	0.642683i	−0.0454825	−	0.0262593i	−0.522569	+	0.852597i	$0.675026\pi$
$600$		0			0
$601$		−	19.2981i		−	0.787184i	−0.919285	−	0.393592i	$-0.871232\pi$
$601$		−	19.2981i		−	0.787184i	0.919285	−	0.393592i	$-0.128768\pi$
$602$	−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	−0.990817	−	0.135206i	$-0.956830\pi$
$607$	−33.7319	+	19.4751i	−1.36913	+	0.790470i	−0.378317	+	0.925676i	$0.623497\pi$
$608$	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	−0.930277	−	0.366859i	$-0.880433\pi$
$613$	−3.65018	+	6.32229i	−0.147429	+	0.255355i	0.782847	+	0.622214i	$0.213767\pi$
$614$	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	$-0.649509\pi$
$617$		−	44.2990i		−	1.78341i	0.452616	−	0.891706i	$-0.350491\pi$
$618$		0			0
$619$	0.408449	+	0.235818i	0.0164169	+	0.00947832i	0.508186	−	0.861247i	$-0.330316\pi$
$619$	0.408449	+	0.235818i	0.0164169	+	0.00947832i	−0.491769	+	0.870726i	$0.663650\pi$
$620$	−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	0.925091	+	0.379745i	$0.123988\pi$
$641$	43.4584	+	25.0907i	1.71651	+	0.991025i	0.791414	+	0.611280i	$0.209345\pi$
$642$		0			0
$643$		−	10.6075i		−	0.418318i	−0.977882	−	0.209159i	$-0.932927\pi$
$643$		−	10.6075i		−	0.418318i	0.977882	−	0.209159i	$-0.0670726\pi$
$644$	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	−0.408100	−	0.912937i	$-0.633809\pi$
$647$	14.9203	−	25.8427i	0.586577	−	1.01598i	0.994677	−	0.103044i	$-0.0328582\pi$
$648$		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	−0.959400	−	0.282050i	$-0.908986\pi$
$653$	−30.5327	+	17.6281i	−1.19484	+	0.689839i	−0.235437	+	0.971890i	$0.575652\pi$
$654$		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	$0.229722\pi$
$659$			33.9194i			1.32131i	−0.750688	+	0.660656i	$0.770278\pi$
$660$		0			0
$661$	13.6550	+	7.88371i	0.531117	+	0.306641i	0.741471	−	0.670985i	$-0.234128\pi$
$661$	13.6550	+	7.88371i	0.531117	+	0.306641i	−0.210354	+	0.977625i	$0.567462\pi$
$662$	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	0.901766	−	0.432225i	$-0.142271\pi$
$677$	1.99217	+	3.45054i	0.0765654	+	0.132615i	−0.825201	+	0.564840i	$0.808938\pi$
$678$		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	0.0834856	−	0.996509i	$-0.473395\pi$
$683$	−19.2812	−	11.1320i	−0.737774	−	0.425954i	−0.821259	+	0.570555i	$0.806728\pi$
$684$		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	0.601346	−	0.798989i	$-0.294631\pi$
$691$	41.9003	−	24.1912i	1.59396	−	0.920275i	0.992618	−	0.121287i	$-0.0387020\pi$
$692$	−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	$0.145113\pi$
$701$			23.3129i			0.880514i	−0.897872	+	0.440257i	$0.854887\pi$
$702$		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	0.650945	−	0.759125i	$-0.274373\pi$
$709$	−8.83884	−	15.3093i	−0.331949	−	0.574953i	−0.982894	+	0.184172i	$0.941040\pi$
$710$	−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	0.996837	+	0.0794749i	$0.0253244\pi$
$719$	15.2102	+	26.3449i	0.567246	+	0.982498i	−0.429591	+	0.903024i	$0.641342\pi$
$720$		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	$0.308746\pi$
$727$			44.4813i			1.64972i	−0.565338	+	0.824859i	$0.691254\pi$
$728$	−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	0.450466	−	0.892794i	$-0.351258\pi$
$733$	39.2270	−	22.6477i	1.44888	−	0.836512i	0.998415	+	0.0562818i	$0.0179245\pi$
$734$	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	−0.990947	−	0.134252i	$-0.957137\pi$
$739$	−10.3086	+	17.8550i	−0.379208	+	0.656808i	0.611739	+	0.791060i	$0.290470\pi$
$740$	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	$-0.947861\pi$
$743$		−	8.88987i		−	0.326138i	0.986615	−	0.163069i	$-0.0521392\pi$
$744$		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	0.998754	−	0.0499007i	$-0.0158905\pi$
$751$	12.5008	+	21.6521i	0.456162	+	0.790095i	−0.542592	+	0.839996i	$0.682557\pi$
$752$	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	0.893301	−	0.449459i	$-0.148383\pi$
$761$	1.58366	+	2.74298i	0.0574075	+	0.0994328i	−0.835893	+	0.548892i	$0.815050\pi$
$762$		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	$-0.983499\pi$
$769$		−	2.87374i		−	0.103630i	0.998657	−	0.0518149i	$-0.0165006\pi$
$770$	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	−0.733802	−	0.679363i	$-0.762256\pi$
$773$	6.15679	−	10.6639i	0.221444	−	0.383553i	0.955247	+	0.295810i	$0.0955895\pi$
$774$		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	0.557739	−	0.830017i	$-0.311669\pi$
$787$	3.30450	+	1.90785i	0.117793	+	0.0680076i	−0.439946	+	0.898024i	$0.645002\pi$
$788$	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	0.993146	−	0.116882i	$-0.0372900\pi$
$809$	39.4929	+	22.8012i	1.38850	+	0.801648i	0.395350	+	0.918531i	$0.370623\pi$
$810$		0			0
$811$			39.1391i			1.37436i	0.726488	+	0.687180i	$0.241151\pi$
$811$			39.1391i			1.37436i	−0.726488	+	0.687180i	$0.758849\pi$
$812$	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	−0.668812	−	0.743432i	$-0.733197\pi$
$821$	−10.2976	+	5.94530i	−0.359387	+	0.207492i	0.309425	+	0.950924i	$0.399864\pi$
$822$		0			0
$823$	−1.51195	+	2.61877i	−0.0527031	+	0.0912844i	−0.891173	−	0.453663i	$-0.850117\pi$
$823$	−1.51195	+	2.61877i	−0.0527031	+	0.0912844i	0.838470	+	0.544947i	$0.183450\pi$
$824$	−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	$-0.914616\pi$
$827$		−	15.2436i		−	0.530071i	0.964239	−	0.265035i	$-0.0853836\pi$
$828$		0			0
$829$	−29.7306	−	17.1649i	−1.03259	−	0.596163i	−0.114861	−	0.993382i	$-0.536642\pi$
$829$	−29.7306	−	17.1649i	−1.03259	−	0.596163i	−0.917724	+	0.397218i	$0.869976\pi$
$830$	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	$-0.975275\pi$
$853$		−	4.53263i		−	0.155194i	0.996985	−	0.0775971i	$-0.0247248\pi$
$854$	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	−0.447188	−	0.894440i	$-0.647574\pi$
$857$	16.1307	−	27.9392i	0.551014	−	0.954384i	0.998202	−	0.0599442i	$-0.0190923\pi$
$858$		0			0
$859$	−15.2711	+	8.81675i	−0.521042	+	0.300824i	−0.737361	−	0.675499i	$-0.763928\pi$
$859$	−15.2711	+	8.81675i	−0.521042	+	0.300824i	0.216319	+	0.976323i	$0.430595\pi$
$860$	−16.1897			−0.552063
$861$		0			0
$862$	−10.3266			−0.351724
$863$	−26.4091	+	15.2473i	−0.898975	+	0.519023i	−0.876867	−	0.480732i	$-0.840371\pi$
$863$	−26.4091	+	15.2473i	−0.898975	+	0.519023i	−0.0221074	+	0.999756i	$0.507038\pi$
$864$		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	0.782047	−	0.623219i	$-0.214176\pi$
$877$	−4.40363	−	7.62730i	−0.148700	−	0.257556i	−0.930747	+	0.365663i	$0.880842\pi$
$878$	−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	0.538879	−	0.842383i	$-0.318848\pi$
$887$	−13.7025	−	23.7335i	−0.460086	−	0.796892i	−0.998965	+	0.0454915i	$0.985515\pi$
$888$		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	−0.600252	−	0.799811i	$-0.704933\pi$
$907$	11.8216	−	20.4757i	0.392531	−	0.679883i	0.992783	+	0.119928i	$0.0382663\pi$
$908$	−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	$-0.976094\pi$
$911$		−	4.52930i		−	0.150063i	0.997181	−	0.0750313i	$-0.0239057\pi$
$912$		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	0.997666	+	0.0682866i	$0.0217532\pi$
$919$	16.9149	+	29.2975i	0.557971	+	0.966434i	−0.439695	+	0.898147i	$0.644913\pi$
$920$	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	0.998905	+	0.0467929i	$0.0149001\pi$
$929$	16.4582	+	28.5064i	0.539976	+	0.935266i	−0.458928	+	0.888473i	$0.651767\pi$
$930$		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	$-0.786146\pi$
$937$		−	38.1057i		−	1.24486i	0.782676	−	0.622430i	$-0.213854\pi$
$938$	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	−0.981307	−	0.192449i	$-0.938357\pi$
$941$	−9.93855	+	17.2141i	−0.323987	+	0.561163i	0.657319	+	0.753612i	$0.271690\pi$
$942$		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	−0.762695	−	0.646759i	$-0.776124\pi$
$947$	−17.9696	+	10.3747i	−0.583933	+	0.337134i	0.178762	+	0.983892i	$0.442791\pi$
$948$		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	$-0.933345\pi$
$953$		−	12.8345i		−	0.415751i	0.978155	−	0.207876i	$-0.0666549\pi$
$954$		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	0.999235	−	0.0391177i	$-0.0124547\pi$
$971$	14.5129	+	25.1370i	0.465740	+	0.806686i	−0.533494	+	0.845804i	$0.679121\pi$
$972$		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	0.371149	−	0.928573i	$-0.378964\pi$
$977$	−7.73439	−	4.46545i	−0.247445	−	0.142862i	−0.618594	+	0.785711i	$0.712297\pi$
$978$		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	−0.0616269	−	0.998099i	$-0.519629\pi$
$983$	26.1346	−	45.2665i	0.833566	−	1.44378i	0.895193	−	0.445679i	$-0.147038\pi$
$984$		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	0.273631	+	0.961835i	$0.411775\pi$
$991$	−21.9151	+	37.9581i	−0.696158	+	1.20578i	−0.969789	+	0.243946i	$0.921558\pi$
$992$	−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	0.967894	−	0.251358i	$-0.0808772\pi$
$997$	38.9689	+	22.4987i	1.23416	+	0.712542i	0.266264	+	0.963900i	$0.414211\pi$
$998$	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.80.4		10
3.2	odd	2		567.2.p.d.80.2		10
7.5	odd	6		567.2.p.d.404.2		10
9.2	odd	6		189.2.s.b.17.4		10
9.4	even	3		189.2.i.b.143.4		10
9.5	odd	6		63.2.i.b.38.2	yes	10
9.7	even	3		63.2.s.b.59.2	yes	10
21.5	even	6	inner	567.2.p.c.404.4		10
36.7	odd	6		1008.2.df.b.689.2		10
36.11	even	6		3024.2.df.b.17.4		10
36.23	even	6		1008.2.ca.b.353.3		10
36.31	odd	6		3024.2.ca.b.2033.4		10
63.2	odd	6		1323.2.i.b.1097.2		10
63.4	even	3		1323.2.o.c.440.2		10
63.5	even	6		63.2.s.b.47.2	yes	10
63.11	odd	6		1323.2.o.d.881.2		10
63.13	odd	6		1323.2.i.b.521.4		10
63.16	even	3		441.2.i.b.68.4		10
63.20	even	6		1323.2.s.b.962.4		10
63.23	odd	6		441.2.s.b.362.2		10
63.25	even	3		441.2.o.c.293.4		10
63.31	odd	6		1323.2.o.d.440.2		10
63.32	odd	6		441.2.o.d.146.4		10
63.34	odd	6		441.2.s.b.374.2		10
63.38	even	6		1323.2.o.c.881.2		10
63.40	odd	6		189.2.s.b.89.4		10
63.41	even	6		441.2.i.b.227.2		10
63.47	even	6		189.2.i.b.152.2		10
63.52	odd	6		441.2.o.d.293.4		10
63.58	even	3		1323.2.s.b.656.4		10
63.59	even	6		441.2.o.c.146.4		10
63.61	odd	6		63.2.i.b.5.4	✓	10
252.47	odd	6		3024.2.ca.b.2609.4		10
252.103	even	6		3024.2.df.b.1601.4		10
252.131	odd	6		1008.2.df.b.929.2		10
252.187	even	6		1008.2.ca.b.257.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.4	✓	10	63.61	odd	6
63.2.i.b.38.2	yes	10	9.5	odd	6
63.2.s.b.47.2	yes	10	63.5	even	6
63.2.s.b.59.2	yes	10	9.7	even	3
189.2.i.b.143.4		10	9.4	even	3
189.2.i.b.152.2		10	63.47	even	6
189.2.s.b.17.4		10	9.2	odd	6
189.2.s.b.89.4		10	63.40	odd	6
441.2.i.b.68.4		10	63.16	even	3
441.2.i.b.227.2		10	63.41	even	6
441.2.o.c.146.4		10	63.59	even	6
441.2.o.c.293.4		10	63.25	even	3
441.2.o.d.146.4		10	63.32	odd	6
441.2.o.d.293.4		10	63.52	odd	6
441.2.s.b.362.2		10	63.23	odd	6
441.2.s.b.374.2		10	63.34	odd	6
567.2.p.c.80.4		10	1.1	even	1	trivial
567.2.p.c.404.4		10	21.5	even	6	inner
567.2.p.d.80.2		10	3.2	odd	2
567.2.p.d.404.2		10	7.5	odd	6
1008.2.ca.b.257.3		10	252.187	even	6
1008.2.ca.b.353.3		10	36.23	even	6
1008.2.df.b.689.2		10	36.7	odd	6
1008.2.df.b.929.2		10	252.131	odd	6
1323.2.i.b.521.4		10	63.13	odd	6
1323.2.i.b.1097.2		10	63.2	odd	6
1323.2.o.c.440.2		10	63.4	even	3
1323.2.o.c.881.2		10	63.38	even	6
1323.2.o.d.440.2		10	63.31	odd	6
1323.2.o.d.881.2		10	63.11	odd	6
1323.2.s.b.656.4		10	63.58	even	3
1323.2.s.b.962.4		10	63.20	even	6
3024.2.ca.b.2033.4		10	36.31	odd	6
3024.2.ca.b.2609.4		10	252.47	odd	6
3024.2.df.b.17.4		10	36.11	even	6
3024.2.df.b.1601.4		10	252.103	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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