LMFDB - Embedded newform 165.2.f.a.131.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(131,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("165.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.f (of order $2$, degree $1$, 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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.5
Root			$1.18254 - 1.18254i$ of defining polynomial
Character	$\chi$	$=$	165.131
Dual form			165.2.f.a.131.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.796815 q^{2} +(-1.55654 - 0.759725i) q^{3} -1.36509 q^{4} -1.00000i q^{5} +(-1.24027 - 0.605361i) q^{6} -4.36509i q^{7} -2.68135 q^{8} +(1.84564 + 2.36509i) q^{9} +O(q^{10})$	\(q+0.796815 q^{2} +(-1.55654 - 0.759725i) q^{3} -1.36509 q^{4} -1.00000i q^{5} +(-1.24027 - 0.605361i) q^{6} -4.36509i q^{7} -2.68135 q^{8} +(1.84564 + 2.36509i) q^{9} -0.796815i q^{10} +(-3.31627 - 0.0488202i) q^{11} +(2.12481 + 1.03709i) q^{12} -2.26745i q^{13} -3.47817i q^{14} +(-0.759725 + 1.55654i) q^{15} +0.593630 q^{16} +5.57581 q^{17} +(1.47063 + 1.88454i) q^{18} -2.48055i q^{19} +1.36509i q^{20} +(-3.31627 + 6.79443i) q^{21} +(-2.64245 - 0.0389007i) q^{22} +6.80435i q^{23} +(4.17363 + 2.03709i) q^{24} -1.00000 q^{25} -1.80673i q^{26} +(-1.07599 - 5.08353i) q^{27} +5.95872i q^{28} -1.21072 q^{29} +(-0.605361 + 1.24027i) q^{30} +1.59363 q^{31} +5.83572 q^{32} +(5.12481 + 2.59544i) q^{33} +4.44289 q^{34} -4.36509 q^{35} +(-2.51945 - 3.22854i) q^{36} +4.63253 q^{37} -1.97654i q^{38} +(-1.72264 + 3.52937i) q^{39} +2.68135i q^{40} +0.460711 q^{41} +(-2.64245 + 5.41391i) q^{42} -11.3214i q^{43} +(4.52699 + 0.0666438i) q^{44} +(2.36509 - 1.84564i) q^{45} +5.42181i q^{46} -3.74561i q^{47} +(-0.924009 - 0.450996i) q^{48} -12.0540 q^{49} -0.796815 q^{50} +(-8.67897 - 4.23608i) q^{51} +3.09526i q^{52} -9.36270i q^{53} +(-0.857366 - 4.05063i) q^{54} +(-0.0488202 + 3.31627i) q^{55} +11.7043i q^{56} +(-1.88454 + 3.86108i) q^{57} -0.964721 q^{58} +7.51106i q^{59} +(1.03709 - 2.12481i) q^{60} -1.67143i q^{61} +1.26983 q^{62} +(10.3238 - 8.05636i) q^{63} +3.46273 q^{64} -2.26745 q^{65} +(4.08353 + 2.06809i) q^{66} +4.48055 q^{67} -7.61145 q^{68} +(5.16944 - 10.5912i) q^{69} -3.47817 q^{70} -6.63253i q^{71} +(-4.94880 - 6.34163i) q^{72} +7.87615i q^{73} +3.69127 q^{74} +(1.55654 + 0.759725i) q^{75} +3.38616i q^{76} +(-0.213104 + 14.4758i) q^{77} +(-1.37262 + 2.81226i) q^{78} -5.66781i q^{79} -0.593630i q^{80} +(-2.18726 + 8.73017i) q^{81} +0.367101 q^{82} -1.56073 q^{83} +(4.52699 - 9.27498i) q^{84} -5.57581i q^{85} -9.02108i q^{86} +(1.88454 + 0.919815i) q^{87} +(8.89207 + 0.130904i) q^{88} +8.80797i q^{89} +(1.88454 - 1.47063i) q^{90} -9.89759 q^{91} -9.28852i q^{92} +(-2.48055 - 1.21072i) q^{93} -2.98456i q^{94} -2.48055 q^{95} +(-9.08353 - 4.43354i) q^{96} -12.0151 q^{97} -9.60479 q^{98} +(-6.00515 - 7.93336i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 8 q^{4} - 14 q^{6} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 8 * q^4 - 14 * q^6 + 12 * q^8 + 4 * q^9	$ 8 q - 2 q^{3} + 8 q^{4} - 14 q^{6} + 12 q^{8} + 4 q^{9} - 12 q^{11} - 6 q^{12} - 2 q^{15} - 8 q^{16} - 4 q^{17} + 8 q^{18} - 12 q^{21} - 4 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{27} + 20 q^{29} + 10 q^{30} + 24 q^{32} + 18 q^{33} - 16 q^{34} - 16 q^{35} - 12 q^{36} + 8 q^{37} - 12 q^{39} - 12 q^{41} - 4 q^{42} - 8 q^{44} - 26 q^{48} - 8 q^{49} + 12 q^{51} + 6 q^{54} + 4 q^{55} + 12 q^{57} + 4 q^{58} + 6 q^{60} + 48 q^{62} + 32 q^{63} - 8 q^{65} - 22 q^{66} + 44 q^{67} - 84 q^{68} - 20 q^{69} + 12 q^{70} + 4 q^{72} + 8 q^{74} + 2 q^{75} - 20 q^{77} + 44 q^{78} + 8 q^{81} - 28 q^{82} - 36 q^{83} - 8 q^{84} - 12 q^{87} + 8 q^{88} - 12 q^{90} + 8 q^{91} - 28 q^{93} - 28 q^{95} - 18 q^{96} - 24 q^{97} + 36 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 8 * q^4 - 14 * q^6 + 12 * q^8 + 4 * q^9 - 12 * q^11 - 6 * q^12 - 2 * q^15 - 8 * q^16 - 4 * q^17 + 8 * q^18 - 12 * q^21 - 4 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^27 + 20 * q^29 + 10 * q^30 + 24 * q^32 + 18 * q^33 - 16 * q^34 - 16 * q^35 - 12 * q^36 + 8 * q^37 - 12 * q^39 - 12 * q^41 - 4 * q^42 - 8 * q^44 - 26 * q^48 - 8 * q^49 + 12 * q^51 + 6 * q^54 + 4 * q^55 + 12 * q^57 + 4 * q^58 + 6 * q^60 + 48 * q^62 + 32 * q^63 - 8 * q^65 - 22 * q^66 + 44 * q^67 - 84 * q^68 - 20 * q^69 + 12 * q^70 + 4 * q^72 + 8 * q^74 + 2 * q^75 - 20 * q^77 + 44 * q^78 + 8 * q^81 - 28 * q^82 - 36 * q^83 - 8 * q^84 - 12 * q^87 + 8 * q^88 - 12 * q^90 + 8 * q^91 - 28 * q^93 - 28 * q^95 - 18 * q^96 - 24 * q^97 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	0.796815			0.563433			0.281717	−	0.959498i	$-0.409096\pi$
$2$	0.796815			0.563433			0.281717	+	0.959498i	$0.409096\pi$
$3$	−1.55654	−	0.759725i	−0.898669	−	0.438628i
$3$	−1.55654	−	0.759725i	−0.898669	−	0.438628i
$4$	−1.36509			−0.682543
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.24027	−	0.605361i	−0.506340	−	0.247137i
$7$		−	4.36509i		−	1.64985i	−0.565244	−	0.824924i	$-0.691218\pi$
$7$		−	4.36509i		−	1.64985i	0.565244	−	0.824924i	$-0.308782\pi$
$8$	−2.68135			−0.948001
$9$	1.84564	+	2.36509i	0.615212	+	0.788362i
$10$		−	0.796815i		−	0.251975i
$11$	−3.31627	−	0.0488202i	−0.999892	−	0.0147198i
$11$	−3.31627	−	0.0488202i	−0.999892	−	0.0147198i
$12$	2.12481	+	1.03709i	0.613380	+	0.299382i
$13$		−	2.26745i		−	0.628876i	−0.949278	−	0.314438i	$-0.898184\pi$
$13$		−	2.26745i		−	0.628876i	0.949278	−	0.314438i	$-0.101816\pi$
$14$		−	3.47817i		−	0.929579i
$15$	−0.759725	+	1.55654i	−0.196160	+	0.401897i
$16$	0.593630			0.148408
$17$	5.57581			1.35233			0.676166	−	0.736749i	$-0.263640\pi$
$17$	5.57581			1.35233			0.676166	+	0.736749i	$0.263640\pi$
$18$	1.47063	+	1.88454i	0.346631	+	0.444189i
$19$		−	2.48055i		−	0.569077i	−0.958665	−	0.284539i	$-0.908160\pi$
$19$		−	2.48055i		−	0.569077i	0.958665	−	0.284539i	$-0.0918404\pi$
$20$			1.36509i			0.305242i
$21$	−3.31627	+	6.79443i	−0.723668	+	1.48267i
$22$	−2.64245	−	0.0389007i	−0.563372	−	0.00829365i
$23$			6.80435i			1.41881i	0.704803	+	0.709403i	$0.251035\pi$
$23$			6.80435i			1.41881i	−0.704803	+	0.709403i	$0.748965\pi$
$24$	4.17363	+	2.03709i	0.851939	+	0.415819i
$25$	−1.00000			−0.200000
$26$		−	1.80673i		−	0.354330i
$27$	−1.07599	−	5.08353i	−0.207074	−	0.978325i
$28$			5.95872i			1.12609i
$29$	−1.21072			−0.224825			−0.112413	−	0.993662i	$-0.535858\pi$
$29$	−1.21072			−0.224825			−0.112413	+	0.993662i	$0.535858\pi$
$30$	−0.605361	+	1.24027i	−0.110523	+	0.226442i
$31$	1.59363			0.286224			0.143112	−	0.989706i	$-0.454289\pi$
$31$	1.59363			0.286224			0.143112	+	0.989706i	$0.454289\pi$
$32$	5.83572			1.03162
$33$	5.12481	+	2.59544i	0.892115	+	0.451808i
$34$	4.44289			0.761949
$35$	−4.36509			−0.737834
$36$	−2.51945	−	3.22854i	−0.419908	−	0.538091i
$37$	4.63253			0.761583			0.380792	−	0.924661i	$-0.375651\pi$
$37$	4.63253			0.761583			0.380792	+	0.924661i	$0.375651\pi$
$38$		−	1.97654i		−	0.320637i
$39$	−1.72264	+	3.52937i	−0.275842	+	0.565151i
$40$			2.68135i			0.423959i
$41$	0.460711			0.0719509			0.0359755	−	0.999353i	$-0.488546\pi$
$41$	0.460711			0.0719509			0.0359755	+	0.999353i	$0.488546\pi$
$42$	−2.64245	+	5.41391i	−0.407739	+	0.835384i
$43$		−	11.3214i		−	1.72650i	−0.504777	−	0.863250i	$-0.668425\pi$
$43$		−	11.3214i		−	1.72650i	0.504777	−	0.863250i	$-0.331575\pi$
$44$	4.52699	+	0.0666438i	0.682469	+	0.0100469i
$45$	2.36509	−	1.84564i	0.352566	−	0.275131i
$46$			5.42181i			0.799402i
$47$		−	3.74561i		−	0.546354i	−0.961964	−	0.273177i	$-0.911926\pi$
$47$		−	3.74561i		−	0.546354i	0.961964	−	0.273177i	$-0.0880744\pi$
$48$	−0.924009	−	0.450996i	−0.133369	−	0.0650956i
$49$	−12.0540			−1.72200
$50$	−0.796815			−0.112687
$51$	−8.67897	−	4.23608i	−1.21530	−	0.593170i
$52$			3.09526i			0.429235i
$53$		−	9.36270i		−	1.28607i	−0.765838	−	0.643033i	$-0.777676\pi$
$53$		−	9.36270i		−	1.28607i	0.765838	−	0.643033i	$-0.222324\pi$
$54$	−0.857366	−	4.05063i	−0.116673	−	0.551221i
$55$	−0.0488202	+	3.31627i	−0.00658292	+	0.447165i
$56$			11.7043i			1.56406i
$57$	−1.88454	+	3.86108i	−0.249613	+	0.511412i
$58$	−0.964721			−0.126674
$59$			7.51106i			0.977857i	0.872324	+	0.488928i	$0.162612\pi$
$59$			7.51106i			0.977857i	−0.872324	+	0.488928i	$0.837388\pi$
$60$	1.03709	−	2.12481i	0.133888	−	0.274312i
$61$		−	1.67143i		−	0.214005i	−0.994259	−	0.107002i	$-0.965875\pi$
$61$		−	1.67143i		−	0.214005i	0.994259	−	0.107002i	$-0.0341253\pi$
$62$	1.26983			0.161268
$63$	10.3238	−	8.05636i	1.30068	−	1.01501i
$64$	3.46273			0.432841
$65$	−2.26745			−0.281242
$66$	4.08353	+	2.06809i	0.502647	+	0.254564i
$67$	4.48055			0.547386			0.273693	−	0.961817i	$-0.411755\pi$
$67$	4.48055			0.547386			0.273693	+	0.961817i	$0.411755\pi$
$68$	−7.61145			−0.923024
$69$	5.16944	−	10.5912i	0.622327	−	1.27504i
$70$	−3.47817			−0.415720
$71$		−	6.63253i		−	0.787137i	−0.919295	−	0.393568i	$-0.871240\pi$
$71$		−	6.63253i		−	0.787137i	0.919295	−	0.393568i	$-0.128760\pi$
$72$	−4.94880	−	6.34163i	−0.583221	−	0.747368i
$73$			7.87615i			0.921833i	0.887443	+	0.460917i	$0.152479\pi$
$73$			7.87615i			0.921833i	−0.887443	+	0.460917i	$0.847521\pi$
$74$	3.69127			0.429101
$75$	1.55654	+	0.759725i	0.179734	+	0.0877255i
$76$			3.38616i			0.388420i
$77$	−0.213104	+	14.4758i	−0.0242855	+	1.64967i
$78$	−1.37262	+	2.81226i	−0.155419	+	0.318425i
$79$		−	5.66781i		−	0.637678i	−0.947809	−	0.318839i	$-0.896707\pi$
$79$		−	5.66781i		−	0.637678i	0.947809	−	0.318839i	$-0.103293\pi$
$80$		−	0.593630i		−	0.0663699i
$81$	−2.18726	+	8.73017i	−0.243029	+	0.970019i
$82$	0.367101			0.0405395
$83$	−1.56073			−0.171313			−0.0856564	−	0.996325i	$-0.527299\pi$
$83$	−1.56073			−0.171313			−0.0856564	+	0.996325i	$0.527299\pi$
$84$	4.52699	−	9.27498i	0.493935	−	1.01198i
$85$		−	5.57581i		−	0.604781i
$86$		−	9.02108i		−	0.972768i
$87$	1.88454	+	0.919815i	0.202043	+	0.0986145i
$88$	8.89207	+	0.130904i	0.947898	+	0.0139544i
$89$			8.80797i			0.933643i	0.884351	+	0.466822i	$0.154601\pi$
$89$			8.80797i			0.933643i	−0.884351	+	0.466822i	$0.845399\pi$
$90$	1.88454	−	1.47063i	0.198648	−	0.155018i
$91$	−9.89759			−1.03755
$92$		−	9.28852i		−	0.968395i
$93$	−2.48055	−	1.21072i	−0.257221	−	0.125546i
$94$		−	2.98456i		−	0.307834i
$95$	−2.48055			−0.254499
$96$	−9.08353	−	4.43354i	−0.927084	−	0.452496i
$97$	−12.0151			−1.21995			−0.609973	−	0.792422i	$-0.708820\pi$
$97$	−12.0151			−1.21995			−0.609973	+	0.792422i	$0.708820\pi$
$98$	−9.60479			−0.970230
$99$	−6.00515	−	7.93336i	−0.603541	−	0.797332i
$100$	1.36509			0.136509
$101$	12.4805			1.24186			0.620931	−	0.783866i	$-0.286755\pi$
$101$	12.4805			1.24186			0.620931	+	0.783866i	$0.286755\pi$
$102$	−6.91553	−	3.37537i	−0.684740	−	0.334212i
$103$	16.0187			1.57837			0.789184	−	0.614156i	$-0.210504\pi$
$103$	16.0187			1.57837			0.789184	+	0.614156i	$0.210504\pi$
$104$			6.07982i			0.596175i
$105$	6.79443	+	3.31627i	0.663069	+	0.323634i
$106$		−	7.46034i		−	0.724613i
$107$	−8.51707			−0.823376			−0.411688	−	0.911325i	$-0.635061\pi$
$107$	−8.51707			−0.823376			−0.411688	+	0.911325i	$0.635061\pi$
$108$	1.46882	+	6.93945i	0.141337	+	0.667749i
$109$			12.1754i			1.16620i	0.812402	+	0.583098i	$0.198160\pi$
$109$			12.1754i			1.16620i	−0.812402	+	0.583098i	$0.801840\pi$
$110$	−0.0389007	+	2.64245i	−0.00370903	+	0.251948i
$111$	−7.21072	−	3.51945i	−0.684411	−	0.334051i
$112$		−	2.59125i		−	0.244850i
$113$		−	2.12852i		−	0.200234i	−0.994976	−	0.100117i	$-0.968078\pi$
$113$		−	2.12852i		−	0.200234i	0.994976	−	0.100117i	$-0.0319218\pi$
$114$	−1.50163	+	3.07656i	−0.140640	+	0.288147i
$115$	6.80435			0.634509
$116$	1.65274			0.153453
$117$	5.36270	−	4.18488i	0.495782	−	0.386892i
$118$			5.98493i			0.550957i
$119$		−	24.3389i		−	2.23114i
$120$	2.03709	−	4.17363i	0.185960	−	0.380999i
$121$	10.9952	+	0.323802i	0.999567	+	0.0294365i
$122$		−	1.33182i		−	0.120577i
$123$	−0.717115	−	0.350013i	−0.0646600	−	0.0315596i
$124$	−2.17544			−0.195360
$125$			1.00000i			0.0894427i
$126$	8.22616	−	6.41943i	0.732845	−	0.571888i
$127$			8.89998i			0.789745i	0.918736	+	0.394873i	$0.129211\pi$
$127$			8.89998i			0.789745i	−0.918736	+	0.394873i	$0.870789\pi$
$128$	−8.91228			−0.787742
$129$	−8.60117	+	17.6222i	−0.757290	+	1.55155i
$130$	−1.80673			−0.158461
$131$	6.95633			0.607778			0.303889	−	0.952708i	$-0.401715\pi$
$131$	6.95633			0.607778			0.303889	+	0.952708i	$0.401715\pi$
$132$	−6.99581	−	3.54300i	−0.608907	−	0.308379i
$133$	−10.8278			−0.938890
$134$	3.57017			0.308416
$135$	−5.08353	+	1.07599i	−0.437520	+	0.0926065i
$136$	−14.9507			−1.28201
$137$		−	9.38254i		−	0.801605i	−0.916165	−	0.400802i	$-0.868731\pi$
$137$		−	9.38254i		−	0.801605i	0.916165	−	0.400802i	$-0.131269\pi$
$138$	4.11909	−	8.43927i	0.350640	−	0.718398i
$139$			12.3003i			1.04330i	0.853159	+	0.521651i	$0.174684\pi$
$139$			12.3003i			1.04330i	−0.853159	+	0.521651i	$0.825316\pi$
$140$	5.95872			0.503603
$141$	−2.84564	+	5.83020i	−0.239646	+	0.490991i
$142$		−	5.28490i		−	0.443499i
$143$	−0.110697	+	7.51945i	−0.00925696	+	0.628808i
$144$	1.09562	+	1.40399i	0.0913021	+	0.116999i
$145$			1.21072i			0.100545i
$146$			6.27583i			0.519392i
$147$	18.7625	+	9.15771i	1.54750	+	0.755315i
$148$	−6.32380			−0.519813
$149$	−7.26144			−0.594880			−0.297440	−	0.954740i	$-0.596133\pi$
$149$	−7.26144			−0.594880			−0.297440	+	0.954740i	$0.596133\pi$
$150$	1.24027	+	0.605361i	0.101268	+	0.0494275i
$151$			10.1869i			0.828998i	0.910050	+	0.414499i	$0.136043\pi$
$151$			10.1869i			0.828998i	−0.910050	+	0.414499i	$0.863957\pi$
$152$			6.65122i			0.539486i
$153$	10.2909	+	13.1873i	0.831970	+	1.06613i
$154$	−0.169805	+	11.5345i	−0.0136833	+	0.929478i
$155$		−	1.59363i		−	0.128003i
$156$	2.35154	−	4.81789i	0.188274	−	0.385740i
$157$	11.9127			0.950734			0.475367	−	0.879788i	$-0.342315\pi$
$157$	11.9127			0.950734			0.475367	+	0.879788i	$0.342315\pi$
$158$		−	4.51620i		−	0.359289i
$159$	−7.11308	+	14.5734i	−0.564104	+	1.15575i
$160$		−	5.83572i		−	0.461354i
$161$	29.7016			2.34081
$162$	−1.74284	+	6.95633i	−0.136931	+	0.546541i
$163$	−11.8234			−0.926081			−0.463041	−	0.886337i	$-0.653242\pi$
$163$	−11.8234			−0.926081			−0.463041	+	0.886337i	$0.653242\pi$
$164$	−0.628909			−0.0491096
$165$	2.59544	−	5.12481i	0.202055	−	0.398966i
$166$	−1.24362			−0.0965234
$167$	10.2909			0.796334			0.398167	−	0.917313i	$-0.369646\pi$
$167$	10.2909			0.796334			0.398167	+	0.917313i	$0.369646\pi$
$168$	8.89207	−	18.2183i	0.686038	−	1.40557i
$169$	7.85869			0.604515
$170$		−	4.44289i		−	0.340754i
$171$	5.86671	−	4.57819i	0.448639	−	0.350103i
$172$			15.4547i			1.17841i
$173$	3.58057			0.272226			0.136113	−	0.990693i	$-0.456539\pi$
$173$	3.58057			0.272226			0.136113	+	0.990693i	$0.456539\pi$
$174$	1.50163	+	0.732923i	0.113838	+	0.0555627i
$175$			4.36509i			0.329969i
$176$	−1.96864	−	0.0289812i	−0.148391	−	0.00218454i
$177$	5.70634	−	11.6913i	0.428915	−	0.878770i
$178$			7.01833i			0.526046i
$179$			1.59363i			0.119114i	0.998225	+	0.0595568i	$0.0189687\pi$
$179$			1.59363i			0.119114i	−0.998225	+	0.0595568i	$0.981031\pi$
$180$	−3.22854	+	2.51945i	−0.240642	+	0.187789i
$181$	18.1238			1.34713			0.673564	−	0.739129i	$-0.264763\pi$
$181$	18.1238			1.34713			0.673564	+	0.739129i	$0.264763\pi$
$182$	−7.88655			−0.584590
$183$	−1.26983	+	2.60165i	−0.0938684	+	0.192320i
$184$		−	18.2449i		−	1.34503i
$185$		−	4.63253i		−	0.340590i
$186$	−1.97654	−	0.964721i	−0.144927	−	0.0707368i
$187$	−18.4909	−	0.272212i	−1.35219	−	0.0199061i
$188$			5.11308i			0.372910i
$189$	−22.1900	+	4.69679i	−1.61409	+	0.341641i
$190$	−1.97654			−0.143393
$191$			17.8976i			1.29502i	0.762055	+	0.647512i	$0.224191\pi$
$191$			17.8976i			1.29502i	−0.762055	+	0.647512i	$0.775809\pi$
$192$	−5.38987	−	2.63072i	−0.388981	−	0.189856i
$193$			1.50163i			0.108089i	0.998539	+	0.0540447i	$0.0172114\pi$
$193$			1.50163i			0.108089i	−0.998539	+	0.0540447i	$0.982789\pi$
$194$	−9.57379			−0.687358
$195$	3.52937	+	1.72264i	0.252743	+	0.123360i
$196$	16.4547			1.17534
$197$	−20.6147			−1.46874			−0.734369	−	0.678751i	$-0.762522\pi$
$197$	−20.6147			−1.46874			−0.734369	+	0.678751i	$0.762522\pi$
$198$	−4.78500	−	6.32142i	−0.340055	−	0.449244i
$199$	2.42144			0.171651			0.0858257	−	0.996310i	$-0.472647\pi$
$199$	2.42144			0.171651			0.0858257	+	0.996310i	$0.472647\pi$
$200$	2.68135			0.189600
$201$	−6.97416	−	3.40399i	−0.491919	−	0.240099i
$202$	9.94469			0.699706
$203$			5.28490i			0.370927i
$204$	11.8475	+	5.78261i	0.829493	+	0.404864i
$205$		−	0.460711i		−	0.0321774i
$206$	12.7639			0.889306
$207$	−16.0929	+	12.5584i	−1.11853	+	0.872866i
$208$		−	1.34602i		−	0.0933300i
$209$	−0.121101	+	8.22616i	−0.00837673	+	0.569015i
$210$	5.41391	+	2.64245i	0.373595	+	0.182346i
$211$		−	25.8734i		−	1.78120i	−0.454789	−	0.890599i	$-0.650285\pi$
$211$		−	25.8734i		−	1.78120i	0.454789	−	0.890599i	$-0.349715\pi$
$212$			12.7809i			0.877795i
$213$	−5.03890	+	10.3238i	−0.345260	+	0.707375i
$214$	−6.78653			−0.463917
$215$	−11.3214			−0.772114
$216$	2.88511	+	13.6307i	0.196307	+	0.927453i
$217$		−	6.95633i		−	0.472227i
$218$			9.70158i			0.657074i
$219$	5.98371	−	12.2595i	0.404341	−	0.828423i
$220$	0.0666438	−	4.52699i	0.00449312	−	0.305209i
$221$		−	12.6428i		−	0.850449i
$222$	−5.74561	−	2.80435i	−0.385620	−	0.188216i
$223$	−7.45672			−0.499339			−0.249669	−	0.968331i	$-0.580322\pi$
$223$	−7.45672			−0.499339			−0.249669	+	0.968331i	$0.580322\pi$
$224$		−	25.4734i		−	1.70201i
$225$	−1.84564	−	2.36509i	−0.123042	−	0.157672i
$226$		−	1.69604i		−	0.112819i
$227$	−13.0520			−0.866289			−0.433144	−	0.901325i	$-0.642596\pi$
$227$	−13.0520			−0.866289			−0.433144	+	0.901325i	$0.642596\pi$
$228$	2.57255	−	5.27070i	0.170371	−	0.349061i
$229$	6.87853			0.454546			0.227273	−	0.973831i	$-0.427019\pi$
$229$	6.87853			0.454546			0.227273	+	0.973831i	$0.427019\pi$
$230$	5.42181			0.357504
$231$	11.3293	−	22.3702i	0.745415	−	1.47185i
$232$	3.24637			0.213135
$233$	−21.1067			−1.38275			−0.691373	−	0.722498i	$-0.742994\pi$
$233$	−21.1067			−1.38275			−0.691373	+	0.722498i	$0.742994\pi$
$234$	4.27308	−	3.33457i	0.279340	−	0.217988i
$235$	−3.74561			−0.244337
$236$		−	10.2532i		−	0.667429i
$237$	−4.30598	+	8.82217i	−0.279703	+	0.573062i
$238$		−	19.3936i		−	1.25710i
$239$	−3.87148			−0.250425			−0.125213	−	0.992130i	$-0.539961\pi$
$239$	−3.87148			−0.250425			−0.125213	+	0.992130i	$0.539961\pi$
$240$	−0.450996	+	0.924009i	−0.0291117	+	0.0596445i
$241$		−	27.4357i		−	1.76729i	−0.468156	−	0.883646i	$-0.655082\pi$
$241$		−	27.4357i		−	1.76729i	0.468156	−	0.883646i	$-0.344918\pi$
$242$	8.76117	+	0.258010i	0.563189	+	0.0165855i
$243$	10.0371	−	11.9271i	0.643880	−	0.765127i
$244$			2.28165i			0.146068i
$245$			12.0540i			0.770100i
$246$	−0.571408	−	0.278896i	−0.0364316	−	0.0177818i
$247$	−5.62451			−0.357879
$248$	−4.27308			−0.271341
$249$	2.42935	+	1.18573i	0.153954	+	0.0751425i
$250$			0.796815i			0.0503950i
$251$		−	9.17219i		−	0.578943i	−0.957187	−	0.289472i	$-0.906520\pi$
$251$		−	9.17219i		−	0.578943i	0.957187	−	0.289472i	$-0.0934796\pi$
$252$	−14.0929	+	10.9976i	−0.887768	+	0.692785i
$253$	0.332190	−	22.5650i	0.0208846	−	1.41865i
$254$			7.09164i			0.444969i
$255$	−4.23608	+	8.67897i	−0.265274	+	0.543498i
$256$	−14.0269			−0.876681
$257$		−	17.0389i		−	1.06286i	−0.847103	−	0.531429i	$-0.821655\pi$
$257$		−	17.0389i		−	1.06286i	0.847103	−	0.531429i	$-0.178345\pi$
$258$	−6.85354	+	14.0417i	−0.426683	+	0.874196i
$259$		−	20.2214i		−	1.25650i
$260$	3.09526			0.191960
$261$	−2.23455	−	2.86346i	−0.138315	−	0.177244i
$262$	5.54291			0.342442
$263$	32.3519			1.99491			0.997453	−	0.0713303i	$-0.0227244\pi$
$263$	32.3519			1.99491			0.997453	+	0.0713303i	$0.0227244\pi$
$264$	−13.7414	−	6.95929i	−0.845726	−	0.428315i
$265$	−9.36270			−0.575146
$266$	−8.62776			−0.529002
$267$	6.69164	−	13.7100i	0.409522	−	0.839036i
$268$	−6.11633			−0.373615
$269$			6.41741i			0.391276i	0.980676	+	0.195638i	$0.0626778\pi$
$269$			6.41741i			0.391276i	−0.980676	+	0.195638i	$0.937322\pi$
$270$	−4.05063	+	0.857366i	−0.246514	+	0.0521776i
$271$			16.8352i			1.02267i	0.859382	+	0.511334i	$0.170848\pi$
$271$			16.8352i			1.02267i	−0.859382	+	0.511334i	$0.829152\pi$
$272$	3.30997			0.200696
$273$	15.4060	+	7.51945i	0.932414	+	0.455098i
$274$		−	7.47615i		−	0.451651i
$275$	3.31627	+	0.0488202i	0.199978	+	0.00294397i
$276$	−7.05672	+	14.4580i	−0.424765	+	0.870267i
$277$		−	4.53328i		−	0.272379i	−0.990683	−	0.136189i	$-0.956514\pi$
$277$		−	4.53328i		−	0.272379i	0.990683	−	0.136189i	$-0.0434855\pi$
$278$			9.80110i			0.587831i
$279$	2.94126	+	3.76907i	0.176089	+	0.225648i
$280$	11.7043			0.699467
$281$	2.72655			0.162652			0.0813262	−	0.996688i	$-0.474084\pi$
$281$	2.72655			0.162652			0.0813262	+	0.996688i	$0.474084\pi$
$282$	−2.26745	+	4.64559i	−0.135024	+	0.276641i
$283$			8.89998i			0.529049i	0.964379	+	0.264524i	$0.0852149\pi$
$283$			8.89998i			0.529049i	−0.964379	+	0.264524i	$0.914785\pi$
$284$			9.05397i			0.537254i
$285$	3.86108	+	1.88454i	0.228710	+	0.111630i
$286$	−0.0882052	+	5.99161i	−0.00521568	+	0.354291i
$287$		−	2.01104i		−	0.118708i
$288$	10.7706	+	13.8020i	0.634664	+	0.813289i
$289$	14.0896			0.828801
$290$			0.964721i			0.0566504i
$291$	18.7019	+	9.12815i	1.09633	+	0.535102i
$292$		−	10.7516i		−	0.629191i
$293$	−11.8845			−0.694302			−0.347151	−	0.937809i	$-0.612851\pi$
$293$	−11.8845			−0.694302			−0.347151	+	0.937809i	$0.612851\pi$
$294$	14.9502	+	7.29700i	0.871916	+	0.425570i
$295$	7.51106			0.437311
$296$	−12.4214			−0.721982
$297$	3.32009	+	16.9109i	0.192651	+	0.981267i
$298$	−5.78603			−0.335175
$299$	15.4285			0.892253
$300$	−2.12481	−	1.03709i	−0.122676	−	0.0598764i
$301$	−49.4190			−2.84846
$302$			8.11707i			0.467085i
$303$	−19.4265	−	9.48179i	−1.11602	−	0.544714i
$304$		−	1.47253i		−	0.0844553i
$305$	−1.67143			−0.0957059
$306$	8.19995	+	10.5078i	0.468760	+	0.600691i
$307$			10.9818i			0.626765i	0.949627	+	0.313382i	$0.101462\pi$
$307$			10.9818i			0.626765i	−0.949627	+	0.313382i	$0.898538\pi$
$308$	0.290906	−	19.7607i	0.0165759	−	1.12597i
$309$	−24.9337	−	12.1698i	−1.41843	−	0.692316i
$310$		−	1.26983i		−	0.0721214i
$311$			21.8928i			1.24143i	0.784037	+	0.620714i	$0.213157\pi$
$311$			21.8928i			1.24143i	−0.784037	+	0.620714i	$0.786843\pi$
$312$	4.61899	−	9.46348i	0.261499	−	0.535764i
$313$	10.2111			0.577165			0.288582	−	0.957455i	$-0.406816\pi$
$313$	10.2111			0.577165			0.288582	+	0.957455i	$0.406816\pi$
$314$	9.49219			0.535675
$315$	−8.05636	−	10.3238i	−0.453924	−	0.581680i
$316$			7.73705i			0.435243i
$317$			2.51908i			0.141486i	0.997495	+	0.0707429i	$0.0225370\pi$
$317$			2.51908i			0.141486i	−0.997495	+	0.0707429i	$0.977463\pi$
$318$	−5.66781	+	11.6123i	−0.317835	+	0.651187i
$319$	4.01507	+	0.0591077i	0.224801	+	0.00330939i
$320$		−	3.46273i		−	0.193572i
$321$	13.2572	+	6.47063i	0.739942	+	0.361155i
$322$	23.6667			1.31889
$323$		−	13.8311i		−	0.769581i
$324$	2.98580	−	11.9174i	0.165878	−	0.662080i
$325$			2.26745i			0.125775i
$326$	−9.42107			−0.521785
$327$	9.24999	−	18.9516i	0.511526	−	1.04802i
$328$	−1.23533			−0.0682095
$329$	−16.3499			−0.901400
$330$	2.06809	−	4.08353i	0.113844	−	0.224791i
$331$	16.3587			0.899156			0.449578	−	0.893241i	$-0.351574\pi$
$331$	16.3587			0.899156			0.449578	+	0.893241i	$0.351574\pi$
$332$	2.13054			0.116928
$333$	8.54996	+	10.9563i	0.468535	+	0.600403i
$334$	8.19995			0.448681
$335$		−	4.48055i		−	0.244799i
$336$	−1.96864	+	4.03338i	−0.107398	+	0.220039i
$337$		−	10.9976i		−	0.599078i	−0.954084	−	0.299539i	$-0.903167\pi$
$337$		−	10.9976i		−	0.599078i	0.954084	−	0.299539i	$-0.0968329\pi$
$338$	6.26192			0.340604
$339$	−1.61709	+	3.31313i	−0.0878283	+	0.179944i
$340$			7.61145i			0.412789i
$341$	−5.28490	−	0.0778014i	−0.286193	−	0.00421318i
$342$	4.67469	−	3.64797i	0.252778	−	0.197260i
$343$			22.0610i			1.19118i
$344$			30.3567i			1.63672i
$345$	−10.5912	−	5.16944i	−0.570214	−	0.278313i
$346$	2.85306			0.153381
$347$	16.6654			0.894647			0.447323	−	0.894372i	$-0.352377\pi$
$347$	16.6654			0.894647			0.447323	+	0.894372i	$0.352377\pi$
$348$	−2.57255	−	1.25563i	−0.137903	−	0.0673086i
$349$			8.36975i			0.448023i	0.974587	+	0.224011i	$0.0719153\pi$
$349$			8.36975i			0.448023i	−0.974587	+	0.224011i	$0.928085\pi$
$350$			3.47817i			0.185916i
$351$	−11.5266	+	2.43975i	−0.615245	+	0.130224i
$352$	−19.3528	−	0.284901i	−1.03151	−	0.0151853i
$353$		−	13.9634i		−	0.743196i	−0.928394	−	0.371598i	$-0.878810\pi$
$353$		−	13.9634i		−	0.743196i	0.928394	−	0.371598i	$-0.121190\pi$
$354$	4.54690	−	9.31578i	0.241665	−	0.495128i
$355$	−6.63253			−0.352018
$356$		−	12.0236i		−	0.637252i
$357$	−18.4909	+	37.8844i	−0.978640	+	2.00506i
$358$			1.26983i			0.0671125i
$359$	25.4405			1.34270			0.671349	−	0.741141i	$-0.265715\pi$
$359$	25.4405			1.34270			0.671349	+	0.741141i	$0.265715\pi$
$360$	−6.34163	+	4.94880i	−0.334233	+	0.260824i
$361$	12.8469			0.676151
$362$	14.4413			0.759017
$363$	−16.8685	−	8.85737i	−0.885368	−	0.464891i
$364$	13.5111			0.708172
$365$	7.87615			0.412256
$366$	−1.01182	+	2.07303i	−0.0528886	+	0.108359i
$367$	3.07340			0.160430			0.0802152	−	0.996778i	$-0.474439\pi$
$367$	3.07340			0.160430			0.0802152	+	0.996778i	$0.474439\pi$
$368$			4.03927i			0.210561i
$369$	0.850304	+	1.08962i	0.0442650	+	0.0567234i
$370$		−	3.69127i		−	0.191900i
$371$	−40.8690			−2.12181
$372$	3.38616	+	1.65274i	0.175564	+	0.0856905i
$373$			9.98960i			0.517242i	0.965979	+	0.258621i	$0.0832680\pi$
$373$			9.98960i			0.517242i	−0.965979	+	0.258621i	$0.916732\pi$
$374$	−14.7338	−	0.216903i	−0.761866	−	0.0112158i
$375$	0.759725	−	1.55654i	0.0392320	−	0.0803794i
$376$			10.0433i			0.517944i
$377$			2.74524i			0.141387i
$378$	−17.6814	+	3.74247i	−0.909431	+	0.192492i
$379$	−17.8657			−0.917702			−0.458851	−	0.888513i	$-0.651739\pi$
$379$	−17.8657			−0.917702			−0.458851	+	0.888513i	$0.651739\pi$
$380$	3.38616			0.173706
$381$	6.76154	−	13.8532i	0.346404	−	0.709719i
$382$			14.2611i			0.729660i
$383$		−	26.8345i		−	1.37118i	−0.727989	−	0.685589i	$-0.759545\pi$
$383$		−	26.8345i		−	1.37118i	0.727989	−	0.685589i	$-0.240455\pi$
$384$	13.8723	+	6.77088i	0.707919	+	0.345525i
$385$	14.4758	+	0.213104i	0.737754	+	0.0108608i
$386$			1.19652i			0.0609012i
$387$	26.7761	−	20.8952i	1.36111	−	1.06216i
$388$	16.4016			0.832665
$389$		−	16.5650i		−	0.839881i	−0.907552	−	0.419940i	$-0.862051\pi$
$389$		−	16.5650i		−	0.839881i	0.907552	−	0.419940i	$-0.137949\pi$
$390$	2.81226	+	1.37262i	0.142404	+	0.0695054i
$391$			37.9397i			1.91870i
$392$	32.3209			1.63245
$393$	−10.8278	−	5.28490i	−0.546191	−	0.266588i
$394$	−16.4261			−0.827535
$395$	−5.66781			−0.285178
$396$	8.19755	+	10.8297i	0.411942	+	0.544213i
$397$	−12.1707			−0.610829			−0.305414	−	0.952220i	$-0.598795\pi$
$397$	−12.1707			−0.610829			−0.305414	+	0.952220i	$0.598795\pi$
$398$	1.92944			0.0967142
$399$	16.8539	+	8.22616i	0.843752	+	0.411823i
$400$	−0.593630			−0.0296815
$401$			3.02689i			0.151156i	0.997140	+	0.0755779i	$0.0240801\pi$
$401$			3.02689i			0.151156i	−0.997140	+	0.0755779i	$0.975920\pi$
$402$	−5.55711	−	2.71235i	−0.277164	−	0.135280i
$403$		−	3.61347i		−	0.180000i
$404$	−17.0370			−0.847623
$405$	8.73017	+	2.18726i	0.433806	+	0.108686i
$406$			4.21109i			0.208993i
$407$	−15.3627	−	0.226161i	−0.761501	−	0.0112104i
$408$	23.2714	+	11.3584i	1.15210	+	0.562326i
$409$			6.29292i			0.311165i	0.987823	+	0.155582i	$0.0497254\pi$
$409$			6.29292i			0.311165i	−0.987823	+	0.155582i	$0.950275\pi$
$410$		−	0.367101i		−	0.0181298i
$411$	−7.12815	+	14.6043i	−0.351606	+	0.720377i
$412$	−21.8669			−1.07730
$413$	32.7864			1.61331
$414$	−12.8230	+	10.0067i	−0.630218	+	0.491802i
$415$			1.56073i			0.0766134i
$416$		−	13.2322i		−	0.648760i
$417$	9.34488	−	19.1460i	0.457621	−	0.937582i
$418$	−0.0964951	+	6.55473i	−0.00471973	+	0.320602i
$419$		−	23.0444i		−	1.12579i	−0.826527	−	0.562897i	$-0.809687\pi$
$419$		−	23.0444i		−	1.12579i	0.826527	−	0.562897i	$-0.190313\pi$
$420$	−9.27498	−	4.52699i	−0.452573	−	0.220894i
$421$	−1.24522			−0.0606884			−0.0303442	−	0.999540i	$-0.509660\pi$
$421$	−1.24522			−0.0606884			−0.0303442	+	0.999540i	$0.509660\pi$
$422$		−	20.6163i		−	1.00359i
$423$	8.85869	−	6.91303i	0.430724	−	0.336123i
$424$			25.1047i			1.21919i
$425$	−5.57581			−0.270466
$426$	−4.01507	+	8.22616i	−0.194531	+	0.398559i
$427$	−7.29594			−0.353075
$428$	11.6265			0.561989
$429$	5.88502	−	11.6202i	0.284131	−	0.561030i
$430$	−9.02108			−0.435035
$431$	−27.2801			−1.31404			−0.657019	−	0.753874i	$-0.728183\pi$
$431$	−27.2801			−1.31404			−0.657019	+	0.753874i	$0.728183\pi$
$432$	−0.638741	−	3.01774i	−0.0307314	−	0.145191i
$433$	21.1245			1.01518			0.507590	−	0.861599i	$-0.330536\pi$
$433$	21.1245			1.01518			0.507590	+	0.861599i	$0.330536\pi$
$434$		−	5.54291i		−	0.266068i
$435$	0.919815	−	1.88454i	0.0441018	−	0.0903566i
$436$		−	16.6205i		−	0.795979i
$437$	16.8785			0.807410
$438$	4.76791	−	9.76859i	0.227819	−	0.466761i
$439$			16.4090i			0.783160i	0.920144	+	0.391580i	$0.128071\pi$
$439$			16.4090i			0.783160i	−0.920144	+	0.391580i	$0.871929\pi$
$440$	0.130904	−	8.89207i	0.00624061	−	0.423913i
$441$	−22.2472	−	28.5087i	−1.05939	−	1.35756i
$442$		−	10.0740i		−	0.479171i
$443$			28.6773i			1.36250i	0.732050	+	0.681251i	$0.238564\pi$
$443$			28.6773i			1.36250i	−0.732050	+	0.681251i	$0.761436\pi$
$444$	9.84325	+	4.80435i	0.467140	+	0.228004i
$445$	8.80797			0.417538
$446$	−5.94163			−0.281344
$447$	11.3027	+	5.51670i	0.534601	+	0.260931i
$448$		−	15.1151i		−	0.714121i
$449$			24.4047i			1.15173i	0.817546	+	0.575864i	$0.195334\pi$
$449$			24.4047i			1.15173i	−0.817546	+	0.575864i	$0.804666\pi$
$450$	−1.47063	−	1.88454i	−0.0693262	−	0.0888379i
$451$	−1.52784	−	0.0224920i	−0.0719431	−	0.00105911i
$452$			2.90561i			0.136669i
$453$	7.73924	−	15.8563i	0.363621	−	0.744994i
$454$	−10.4000			−0.488096
$455$			9.89759i			0.464006i
$456$	5.05310	−	10.3529i	0.236633	−	0.484819i
$457$		−	11.0634i		−	0.517524i	−0.965941	−	0.258762i	$-0.916685\pi$
$457$		−	11.0634i		−	0.517524i	0.965941	−	0.258762i	$-0.0833146\pi$
$458$	5.48092			0.256106
$459$	−5.99952	−	28.3448i	−0.280033	−	1.32302i
$460$	−9.28852			−0.433080
$461$	2.55835			0.119154			0.0595771	−	0.998224i	$-0.481025\pi$
$461$	2.55835			0.119154			0.0595771	+	0.998224i	$0.481025\pi$
$462$	9.02738	−	17.8249i	0.419992	−	0.829291i
$463$	−9.50438			−0.441706			−0.220853	−	0.975307i	$-0.570884\pi$
$463$	−9.50438			−0.441706			−0.220853	+	0.975307i	$0.570884\pi$
$464$	−0.718721			−0.0333658
$465$	−1.21072	+	2.48055i	−0.0561458	+	0.115033i
$466$	−16.8181			−0.779085
$467$			26.3822i			1.22082i	0.792085	+	0.610411i	$0.208996\pi$
$467$			26.3822i			1.22082i	−0.792085	+	0.610411i	$0.791004\pi$
$468$	−7.32055	+	5.71272i	−0.338392	+	0.264070i
$469$		−	19.5580i		−	0.903104i
$470$	−2.98456			−0.137667
$471$	−18.5425	−	9.05035i	−0.854395	−	0.417018i
$472$		−	20.1398i		−	0.927009i
$473$	−0.552714	+	37.5448i	−0.0254138	+	1.72631i
$474$	−3.43107	+	7.02964i	−0.157594	+	0.322882i
$475$			2.48055i			0.113815i
$476$			33.2246i			1.52285i
$477$	22.1436	−	17.2801i	1.01389	−	0.791203i
$478$	−3.08485			−0.141098
$479$	−11.6594			−0.532733			−0.266366	−	0.963872i	$-0.585823\pi$
$479$	−11.6594			−0.532733			−0.266366	+	0.963872i	$0.585823\pi$
$480$	−4.43354	+	9.08353i	−0.202362	+	0.414604i
$481$		−	10.5040i		−	0.478942i
$482$		−	21.8612i		−	0.995751i
$483$	−46.2317	−	22.5650i	−2.10362	−	1.02674i
$484$	−15.0094	−	0.442017i	−0.682247	−	0.0200917i
$485$			12.0151i			0.545576i
$486$	7.99770	−	9.50373i	0.362783	−	0.431098i
$487$	33.3139			1.50960			0.754798	−	0.655957i	$-0.227735\pi$
$487$	33.3139			1.50960			0.754798	+	0.655957i	$0.227735\pi$
$488$			4.48170i			0.202877i
$489$	18.4036	+	8.98254i	0.832240	+	0.406205i
$490$			9.60479i			0.433900i
$491$	−38.0055			−1.71517			−0.857583	−	0.514346i	$-0.828035\pi$
$491$	−38.0055			−1.71517			−0.857583	+	0.514346i	$0.828035\pi$
$492$	0.978923	+	0.477798i	0.0441333	+	0.0215408i
$493$	−6.75075			−0.304038
$494$	−4.48170			−0.201641
$495$	−7.93336	+	6.00515i	−0.356578	+	0.269912i
$496$	0.946027			0.0424779
$497$	−28.9516			−1.29866
$498$	1.93574	+	0.944807i	0.0867426	+	0.0423378i
$499$	26.7723			1.19849			0.599247	−	0.800564i	$-0.295467\pi$
$499$	26.7723			1.19849			0.599247	+	0.800564i	$0.295467\pi$
$500$		−	1.36509i		−	0.0610485i
$501$	−16.0182	−	7.81826i	−0.715641	−	0.349294i
$502$		−	7.30854i		−	0.326196i
$503$	21.9377			0.978155			0.489078	−	0.872240i	$-0.337334\pi$
$503$	21.9377			0.978155			0.489078	+	0.872240i	$0.337334\pi$
$504$	−27.6817	+	21.6019i	−1.23304	+	0.962226i
$505$		−	12.4805i		−	0.555377i
$506$	0.264694	−	17.9802i	0.0117671	−	0.799316i
$507$	−12.2324	−	5.97045i	−0.543259	−	0.265157i
$508$		−	12.1492i		−	0.539035i
$509$		−	26.7254i		−	1.18458i	−0.805724	−	0.592291i	$-0.798223\pi$
$509$		−	26.7254i		−	1.18458i	0.805724	−	0.592291i	$-0.201777\pi$
$510$	−3.37537	+	6.91553i	−0.149464	+	0.306225i
$511$	34.3801			1.52088
$512$	6.64772			0.293790
$513$	−12.6099	+	2.66905i	−0.556742	+	0.117841i
$514$		−	13.5769i		−	0.598849i
$515$		−	16.0187i		−	0.705868i
$516$	11.7413	−	24.0559i	0.516883	−	1.05900i
$517$	−0.182862	+	12.4214i	−0.00804224	+	0.546294i
$518$		−	16.1127i		−	0.707952i
$519$	−5.57331	−	2.72025i	−0.244641	−	0.119406i
$520$	6.07982			0.266618
$521$			3.34763i			0.146662i	0.997308	+	0.0733312i	$0.0233630\pi$
$521$			3.34763i			0.146662i	−0.997308	+	0.0733312i	$0.976637\pi$
$522$	−1.78052	−	2.28165i	−0.0779314	−	0.0998650i
$523$		−	7.12614i		−	0.311604i	−0.987788	−	0.155802i	$-0.950204\pi$
$523$		−	7.12614i		−	0.311604i	0.987788	−	0.155802i	$-0.0497962\pi$
$524$	−9.49599			−0.414834
$525$	3.31627	−	6.79443i	0.144734	−	0.296533i
$526$	25.7785			1.12400
$527$	8.88577			0.387070
$528$	3.04224	+	1.54073i	0.132397	+	0.0670518i
$529$	−23.2992			−1.01301
$530$	−7.46034			−0.324057
$531$	−17.7643	+	13.8627i	−0.770905	+	0.601589i
$532$	14.7809			0.640833
$533$		−	1.04464i		−	0.0452482i
$534$	5.33200	−	10.9243i	0.230738	−	0.472741i
$535$			8.51707i			0.368225i
$536$	−12.0139			−0.518923
$537$	1.21072	−	2.48055i	0.0522465	−	0.107044i
$538$			5.11349i			0.220458i
$539$	39.9742	+	0.588478i	1.72181	+	0.0253475i
$540$	6.93945	−	1.46882i	0.298626	−	0.0632079i
$541$			27.6697i			1.18961i	0.803868	+	0.594807i	$0.202772\pi$
$541$			27.6697i			1.18961i	−0.803868	+	0.594807i	$0.797228\pi$
$542$			13.4146i			0.576205i
$543$	−28.2104	−	13.7691i	−1.21062	−	0.590887i
$544$	32.5388			1.39509
$545$	12.1754			0.521539
$546$	12.2757	+	5.99161i	0.525353	+	0.256417i
$547$		−	3.25966i		−	0.139373i	−0.997569	−	0.0696864i	$-0.977800\pi$
$547$		−	3.25966i		−	0.139373i	0.997569	−	0.0696864i	$-0.0221999\pi$
$548$			12.8080i			0.547129i
$549$	3.95308	−	3.08485i	0.168713	−	0.131658i
$550$	2.64245	+	0.0389007i	0.112674	+	0.00165873i
$551$			3.00325i			0.127943i
$552$	−13.8611	+	28.3989i	−0.589967	+	1.20874i
$553$	−24.7405			−1.05207
$554$		−	3.61219i		−	0.153467i
$555$	−3.51945	+	7.21072i	−0.149392	+	0.306078i
$556$		−	16.7910i		−	0.712098i
$557$	−37.5590			−1.59143			−0.795714	−	0.605673i	$-0.792904\pi$
$557$	−37.5590			−1.59143			−0.795714	+	0.605673i	$0.792904\pi$
$558$	2.34364	+	3.00325i	0.0992142	+	0.127138i
$559$	−25.6707			−1.08575
$560$	−2.59125			−0.109500
$561$	28.5750	+	14.4717i	1.20644	+	0.610995i
$562$	2.17256			0.0916437
$563$	7.52985			0.317346			0.158673	−	0.987331i	$-0.449279\pi$
$563$	7.52985			0.317346			0.158673	+	0.987331i	$0.449279\pi$
$564$	3.88454	−	7.95872i	0.163568	−	0.335122i
$565$	−2.12852			−0.0895475
$566$			7.09164i			0.298084i
$567$	38.1079	+	9.54758i	1.60038	+	0.400961i
$568$			17.7841i			0.746206i
$569$	41.2115			1.72768			0.863838	−	0.503770i	$-0.168054\pi$
$569$	41.2115			1.72768			0.863838	+	0.503770i	$0.168054\pi$
$570$	3.07656	+	1.50163i	0.128863	+	0.0628962i
$571$			45.6844i			1.91183i	0.293640	+	0.955916i	$0.405133\pi$
$571$			45.6844i			1.91183i	−0.293640	+	0.955916i	$0.594867\pi$
$572$	0.151111	−	10.2647i	0.00631827	−	0.429188i
$573$	13.5973	−	27.8583i	0.568033	−	1.16380i
$574$		−	1.60243i		−	0.0668841i
$575$		−	6.80435i		−	0.283761i
$576$	6.39093	+	8.18964i	0.266289	+	0.341235i
$577$	−25.2643			−1.05177			−0.525884	−	0.850556i	$-0.676265\pi$
$577$	−25.2643			−1.05177			−0.525884	+	0.850556i	$0.676265\pi$
$578$	11.2268			0.466974
$579$	1.14082	−	2.33734i	0.0474110	−	0.0971366i
$580$		−	1.65274i		−	0.0686262i
$581$			6.81274i			0.282640i
$582$	14.9020	+	7.27345i	0.617707	+	0.301494i
$583$	−0.457089	+	31.0492i	−0.0189307	+	1.28593i
$584$		−	21.1187i		−	0.873899i
$585$	−4.18488	−	5.36270i	−0.173023	−	0.221720i
$586$	−9.46978			−0.391193
$587$			39.6472i			1.63642i	0.574922	+	0.818208i	$0.305032\pi$
$587$			39.6472i			1.63642i	−0.574922	+	0.818208i	$0.694968\pi$
$588$	−25.6124	−	12.5011i	−1.05624	−	0.515535i
$589$		−	3.95308i		−	0.162884i
$590$	5.98493			0.246396
$591$	32.0876	+	15.6615i	1.31991	+	0.644229i
$592$	2.75001			0.113025
$593$	−10.3529			−0.425143			−0.212571	−	0.977146i	$-0.568184\pi$
$593$	−10.3529			−0.425143			−0.212571	+	0.977146i	$0.568184\pi$
$594$	2.64550	+	13.4748i	0.108546	+	0.552879i
$595$	−24.3389			−0.997797
$596$	9.91249			0.406031
$597$	−3.76907	−	1.83963i	−0.154258	−	0.0752911i
$598$	12.2937			0.502725
$599$			18.8700i			0.771006i	0.922707	+	0.385503i	$0.125972\pi$
$599$			18.8700i			0.771006i	−0.922707	+	0.385503i	$0.874028\pi$
$600$	−4.17363	−	2.03709i	−0.170388	−	0.0831638i
$601$		−	0.663411i		−	0.0270611i	−0.999908	−	0.0135306i	$-0.995693\pi$
$601$		−	0.663411i		−	0.0270611i	0.999908	−	0.0135306i	$-0.00430704\pi$
$602$	−39.3778			−1.60492
$603$	8.26946	+	10.5969i	0.336758	+	0.431538i
$604$		−	13.9060i		−	0.565826i
$605$	0.323802	−	10.9952i	0.0131644	−	0.447020i
$606$	−15.4793	−	7.55523i	−0.628804	−	0.306910i
$607$			43.6651i			1.77231i	0.463389	+	0.886155i	$0.346633\pi$
$607$			43.6651i			1.77231i	−0.463389	+	0.886155i	$0.653367\pi$
$608$		−	14.4758i		−	0.587071i
$609$	4.01507	−	8.22616i	0.162699	−	0.333341i
$610$	−1.33182			−0.0539239
$611$	−8.49297			−0.343589
$612$	−14.0480	−	18.0017i	−0.567855	−	0.727677i
$613$		−	7.72376i		−	0.311960i	−0.987760	−	0.155980i	$-0.950147\pi$
$613$		−	7.72376i		−	0.311960i	0.987760	−	0.155980i	$-0.0498535\pi$
$614$			8.75047i			0.353140i
$615$	−0.350013	+	0.717115i	−0.0141139	+	0.0289169i
$616$	0.571408	−	38.8147i	0.0230227	−	1.56389i
$617$		−	15.3150i		−	0.616561i	−0.951296	−	0.308280i	$-0.900247\pi$
$617$		−	15.3150i		−	0.616561i	0.951296	−	0.308280i	$-0.0997535\pi$
$618$	−19.8676	−	9.69708i	−0.799191	−	0.390074i
$619$	−0.867490			−0.0348674			−0.0174337	−	0.999848i	$-0.505550\pi$
$619$	−0.867490			−0.0348674			−0.0174337	+	0.999848i	$0.505550\pi$
$620$			2.17544i			0.0873678i
$621$	34.5901	−	7.32142i	1.38805	−	0.293798i
$622$			17.4445i			0.699462i
$623$	38.4476			1.54037
$624$	−1.02261	+	2.09514i	−0.0409371	+	0.0838728i
$625$	1.00000			0.0400000
$626$	8.13635			0.325194
$627$	6.43812	−	12.7123i	0.257114	−	0.507682i
$628$	−16.2618			−0.648917
$629$	25.8301			1.02991
$630$	−6.41943	−	8.22616i	−0.255756	−	0.327738i
$631$	−37.4905			−1.49247			−0.746236	−	0.665681i	$-0.768141\pi$
$631$	−37.4905			−1.49247			−0.746236	+	0.665681i	$0.768141\pi$
$632$			15.1974i			0.604520i
$633$	−19.6567	+	40.2730i	−0.781283	+	1.60071i
$634$			2.00724i			0.0797178i
$635$	8.89998			0.353185
$636$	9.70996	−	19.8940i	0.385025	−	0.788847i
$637$			27.3317i			1.08292i
$638$	3.19927	+	0.0470979i	0.126660	+	0.00186462i
$639$	15.6865	−	12.2412i	0.620549	−	0.484256i
$640$			8.91228i			0.352289i
$641$		−	26.6381i		−	1.05214i	−0.850441	−	0.526070i	$-0.823665\pi$
$641$		−	26.6381i		−	1.05214i	0.850441	−	0.526070i	$-0.176335\pi$
$642$	10.5635	+	5.15590i	0.416908	+	0.203487i
$643$	30.4234			1.19978			0.599890	−	0.800082i	$-0.295211\pi$
$643$	30.4234			1.19978			0.599890	+	0.800082i	$0.295211\pi$
$644$	−40.5452			−1.59770
$645$	17.6222	+	8.60117i	0.693875	+	0.338671i
$646$		−	11.0208i		−	0.433608i
$647$		−	20.3661i		−	0.800675i	−0.916368	−	0.400338i	$-0.868893\pi$
$647$		−	20.3661i		−	0.800675i	0.916368	−	0.400338i	$-0.131107\pi$
$648$	5.86481	−	23.4087i	0.230392	−	0.919579i
$649$	0.366692	−	24.9087i	0.0143939	−	0.977751i
$650$			1.80673i			0.0708660i
$651$	−5.28490	+	10.8278i	−0.207132	+	0.424375i
$652$	16.1400			0.632090
$653$		−	8.53966i		−	0.334183i	−0.985941	−	0.167091i	$-0.946563\pi$
$653$		−	8.53966i		−	0.334183i	0.985941	−	0.167091i	$-0.0534375\pi$
$654$	7.37053	−	15.1009i	0.288211	−	0.590492i
$655$		−	6.95633i		−	0.271806i
$656$	0.273492			0.0106781
$657$	−18.6278	+	14.5365i	−0.726738	+	0.567123i
$658$	−13.0279			−0.507879
$659$	6.85315			0.266961			0.133480	−	0.991051i	$-0.457385\pi$
$659$	6.85315			0.266961			0.133480	+	0.991051i	$0.457385\pi$
$660$	−3.54300	+	6.99581i	−0.137911	+	0.272311i
$661$	25.7691			1.00230			0.501150	−	0.865360i	$-0.332910\pi$
$661$	25.7691			1.00230			0.501150	+	0.865360i	$0.332910\pi$
$662$	13.0349			0.506615
$663$	−9.60508	+	19.6791i	−0.373030	+	0.764272i
$664$	4.18488			0.162405
$665$			10.8278i			0.419885i
$666$	6.81274	+	8.73017i	0.263988	+	0.338287i
$667$		−	8.23817i		−	0.318983i
$668$	−14.0480			−0.543532
$669$	11.6067	+	5.66506i	0.448740	+	0.219024i
$670$		−	3.57017i		−	0.137928i
$671$	−0.0815996	+	5.54291i	−0.00315012	+	0.213982i
$672$	−19.3528	+	39.6504i	−0.746550	+	1.52955i
$673$		−	37.4753i		−	1.44457i	−0.691597	−	0.722284i	$-0.743093\pi$
$673$		−	37.4753i		−	1.44457i	0.691597	−	0.722284i	$-0.256907\pi$
$674$		−	8.76307i		−	0.337541i
$675$	1.07599	+	5.08353i	0.0414149	+	0.195665i
$676$	−10.7278			−0.412607
$677$	−41.0575			−1.57797			−0.788984	−	0.614414i	$-0.789393\pi$
$677$	−41.0575			−1.57797			−0.788984	+	0.614414i	$0.789393\pi$
$678$	−1.28852	+	2.63995i	−0.0494854	+	0.101387i
$679$			52.4468i			2.01272i
$680$			14.9507i			0.573333i
$681$	20.3159	+	9.91590i	0.778507	+	0.379978i
$682$	−4.21109	−	0.0619933i	−0.161251	−	0.00237385i
$683$			13.6583i			0.522619i	0.965255	+	0.261310i	$0.0841544\pi$
$683$			13.6583i			0.522619i	−0.965255	+	0.261310i	$0.915846\pi$
$684$	−8.00857	+	6.24962i	−0.306215	+	0.238960i
$685$	−9.38254			−0.358488
$686$			17.5786i			0.671152i
$687$	−10.7067	−	5.22579i	−0.408486	−	0.199376i
$688$		−	6.72074i		−	0.256226i
$689$	−21.2294			−0.808776
$690$	−8.43927	−	4.11909i	−0.321277	−	0.156811i
$691$	10.9920			0.418155			0.209077	−	0.977899i	$-0.432954\pi$
$691$	10.9920			0.418155			0.209077	+	0.977899i	$0.432954\pi$
$692$	−4.88779			−0.185806
$693$	−34.6298	+	26.2130i	−1.31548	+	0.995750i
$694$	13.2793			0.504074
$695$	12.3003			0.466579
$696$	−5.05310	−	2.46635i	−0.191537	−	0.0934867i
$697$	2.56883			0.0973015
$698$			6.66915i			0.252431i
$699$	32.8534	+	16.0353i	1.24263	+	0.606511i
$700$		−	5.95872i		−	0.225218i
$701$	37.1552			1.40333			0.701667	−	0.712505i	$-0.252439\pi$
$701$	37.1552			1.40333			0.701667	+	0.712505i	$0.252439\pi$
$702$	−9.18458	+	1.94403i	−0.346650	+	0.0733727i
$703$		−	11.4912i		−	0.433400i
$704$	−11.4833	−	0.169051i	−0.432794	−	0.00637135i
$705$	5.83020	+	2.84564i	0.219578	+	0.107173i
$706$		−	11.1262i		−	0.418741i
$707$		−	54.4787i		−	2.04888i
$708$	−7.78965	+	15.9596i	−0.292753	+	0.599798i
$709$	−17.3467			−0.651468			−0.325734	−	0.945462i	$-0.605611\pi$
$709$	−17.3467			−0.651468			−0.325734	+	0.945462i	$0.605611\pi$
$710$	−5.28490			−0.198339
$711$	13.4049	−	10.4607i	0.502721	−	0.392307i
$712$		−	23.6173i		−	0.885095i
$713$			10.8436i			0.406097i
$714$	−14.7338	+	30.1869i	−0.551398	+	1.12972i
$715$	7.51945	+	0.110697i	0.281211	+	0.00413984i
$716$		−	2.17544i		−	0.0813001i
$717$	6.02611	+	2.94126i	0.225049	+	0.109843i
$718$	20.2714			0.756521
$719$			23.9285i			0.892381i	0.894938	+	0.446191i	$0.147220\pi$
$719$			23.9285i			0.892381i	−0.894938	+	0.446191i	$0.852780\pi$
$720$	1.40399	−	1.09562i	0.0523235	−	0.0408315i
$721$		−	69.9230i		−	2.60407i
$722$	10.2366			0.380966
$723$	−20.8436	+	42.7048i	−0.775183	+	1.58821i
$724$	−24.7405			−0.919473
$725$	1.21072			0.0449650
$726$	−13.4411	−	7.05768i	−0.498846	−	0.261935i
$727$	12.3854			0.459349			0.229674	−	0.973268i	$-0.426234\pi$
$727$	12.3854			0.459349			0.229674	+	0.973268i	$0.426234\pi$
$728$	26.5389			0.983598
$729$	−24.6845	+	10.9397i	−0.914240	+	0.405172i
$730$	6.27583			0.232279
$731$		−	63.1260i		−	2.33480i
$732$	1.73342	−	3.55148i	0.0640692	−	0.131266i
$733$			19.8460i			0.733029i	0.930412	+	0.366514i	$0.119449\pi$
$733$			19.8460i			0.733029i	−0.930412	+	0.366514i	$0.880551\pi$
$734$	2.44893			0.0903918
$735$	9.15771	−	18.7625i	0.337787	−	0.692065i
$736$			39.7083i			1.46367i
$737$	−14.8587	−	0.218741i	−0.547327	−	0.00805744i
$738$	0.677535	+	0.868226i	0.0249404	+	0.0319598i
$739$		−	2.09096i		−	0.0769171i	−0.999260	−	0.0384585i	$-0.987755\pi$
$739$		−	2.09096i		−	0.0769171i	0.999260	−	0.0384585i	$-0.0122448\pi$
$740$			6.32380i			0.232468i
$741$	8.75478	+	4.27308i	0.321615	+	0.156976i
$742$	−32.5650			−1.19550
$743$	−11.9465			−0.438276			−0.219138	−	0.975694i	$-0.570324\pi$
$743$	−11.9465			−0.438276			−0.219138	+	0.975694i	$0.570324\pi$
$744$	6.65122	+	3.24637i	0.243846	+	0.119018i
$745$			7.26144i			0.266039i
$746$			7.95986i			0.291431i
$747$	−2.88055	−	3.69127i	−0.105394	−	0.135057i
$748$	25.2416	+	0.371593i	0.922924	+	0.0135868i
$749$			37.1777i			1.35844i
$750$	0.605361	−	1.24027i	0.0221046	−	0.0452884i
$751$	−14.1792			−0.517408			−0.258704	−	0.965957i	$-0.583295\pi$
$751$	−14.1792			−0.517408			−0.258704	+	0.965957i	$0.583295\pi$
$752$		−	2.22351i		−	0.0810830i
$753$	−6.96834	+	14.2769i	−0.253941	+	0.520278i
$754$			2.18745i			0.0796623i
$755$	10.1869			0.370739
$756$	30.2913	−	6.41152i	1.10168	−	0.233185i
$757$	47.4436			1.72437			0.862183	−	0.506597i	$-0.169097\pi$
$757$	47.4436			1.72437			0.862183	+	0.506597i	$0.169097\pi$
$758$	−14.2357			−0.517064
$759$	−17.6603	+	34.8710i	−0.641028	+	1.26574i
$760$	6.65122			0.241265
$761$	26.0328			0.943688			0.471844	−	0.881682i	$-0.343589\pi$
$761$	26.0328			0.943688			0.471844	+	0.881682i	$0.343589\pi$
$762$	5.38769	−	11.0384i	0.195176	−	0.399880i
$763$	53.1468			1.92405
$764$		−	24.4317i		−	0.883910i
$765$	13.1873	−	10.2909i	0.476786	−	0.372068i
$766$		−	21.3821i		−	0.772568i
$767$	17.0309			0.614951
$768$	21.8334	+	10.6566i	0.787846	+	0.384536i
$769$		−	33.7287i		−	1.21629i	−0.793827	−	0.608143i	$-0.791915\pi$
$769$		−	33.7287i		−	1.21629i	0.793827	−	0.608143i	$-0.208085\pi$
$770$	11.5345	+	0.169805i	0.415675	+	0.00611934i
$771$	−12.9449	+	26.5217i	−0.466199	+	0.955157i
$772$		−	2.04985i		−	0.0737757i
$773$		−	33.6396i		−	1.20993i	−0.796251	−	0.604966i	$-0.793187\pi$
$773$		−	33.6396i		−	1.20993i	0.796251	−	0.604966i	$-0.206813\pi$
$774$	21.3356	−	16.6496i	0.766893	−	0.598458i
$775$	−1.59363			−0.0572449
$776$	32.2166			1.15651
$777$	−15.3627	+	31.4754i	−0.551134	+	1.12917i
$778$		−	13.1993i		−	0.473217i
$779$		−	1.14282i		−	0.0409456i
$780$	−4.81789	−	2.35154i	−0.172508	−	0.0841988i
$781$	−0.323802	+	21.9952i	−0.0115865	+	0.787051i
$782$			30.2310i			1.08106i
$783$	1.30272	+	6.15473i	0.0465556	+	0.219952i
$784$	−7.15560			−0.255557
$785$		−	11.9127i		−	0.425181i
$786$	−8.62776	−	4.21109i	−0.307742	−	0.150205i
$787$		−	43.5468i		−	1.55228i	−0.630562	−	0.776139i	$-0.717176\pi$
$787$		−	43.5468i		−	1.55228i	0.630562	−	0.776139i	$-0.282824\pi$
$788$	28.1408			1.00248
$789$	−50.3571	−	24.5786i	−1.79276	−	0.875020i
$790$	−4.51620			−0.160679
$791$	−9.29118			−0.330356
$792$	16.1019	+	21.2721i	0.572157	+	0.755872i
$793$	−3.78988			−0.134583
$794$	−9.69778			−0.344161
$795$	14.5734	+	7.11308i	0.516866	+	0.252275i
$796$	−3.30548			−0.117159
$797$			37.0397i			1.31201i	0.754755	+	0.656006i	$0.227756\pi$
$797$			37.0397i			1.31201i	−0.754755	+	0.656006i	$0.772244\pi$
$798$	13.4295	+	6.55473i	0.475398	+	0.232035i
$799$		−	20.8848i		−	0.738851i
$800$	−5.83572			−0.206324
$801$	−20.8316	+	16.2563i	−0.736049	+	0.574388i
$802$			2.41187i			0.0851662i
$803$	0.384515	−	26.1194i	0.0135692	−	0.921733i
$804$	9.52032	+	4.64673i	0.335756	+	0.163878i
$805$		−	29.7016i		−	1.04684i
$806$		−	2.87927i		−	0.101418i
$807$	4.87547	−	9.98896i	0.171625	−	0.351628i
$808$	−33.4647			−1.17729
$809$	−31.4575			−1.10599			−0.552993	−	0.833186i	$-0.686514\pi$
$809$	−31.4575			−1.10599			−0.552993	+	0.833186i	$0.686514\pi$
$810$	6.95633	+	1.74284i	0.244421	+	0.0612372i
$811$		−	33.1535i		−	1.16418i	−0.813125	−	0.582089i	$-0.802236\pi$
$811$		−	33.1535i		−	1.16418i	0.813125	−	0.582089i	$-0.197764\pi$
$812$		−	7.21434i		−	0.253174i
$813$	12.7901	−	26.2047i	0.448570	−	0.919040i
$814$	−12.2412	−	0.180209i	−0.429055	−	0.00631631i
$815$			11.8234i			0.414156i
$816$	−5.15210	−	2.51467i	−0.180359	−	0.0880309i
$817$	−28.0833			−0.982512
$818$			5.01429i			0.175321i
$819$	−18.2673	−	23.4087i	−0.638313	−	0.817965i
$820$			0.628909i			0.0219625i
$821$	−15.7418			−0.549393			−0.274697	−	0.961531i	$-0.588577\pi$
$821$	−15.7418			−0.549393			−0.274697	+	0.961531i	$0.588577\pi$
$822$	−5.67982	+	11.6369i	−0.198106	+	0.405885i
$823$	−47.6487			−1.66093			−0.830465	−	0.557070i	$-0.811925\pi$
$823$	−47.6487			−1.66093			−0.830465	+	0.557070i	$0.811925\pi$
$824$	−42.9517			−1.49629
$825$	−5.12481	−	2.59544i	−0.178423	−	0.0903617i
$826$	26.1247			0.908995
$827$	−32.0439			−1.11428			−0.557138	−	0.830420i	$-0.688101\pi$
$827$	−32.0439			−1.11428			−0.557138	+	0.830420i	$0.688101\pi$
$828$	21.9682	−	17.1432i	0.763446	−	0.595768i
$829$	−15.9842			−0.555154			−0.277577	−	0.960703i	$-0.589531\pi$
$829$	−15.9842			−0.555154			−0.277577	+	0.960703i	$0.589531\pi$
$830$			1.24362i			0.0431666i
$831$	−3.44405	+	7.05624i	−0.119473	+	0.244778i
$832$		−	7.85154i		−	0.272203i
$833$	−67.2106			−2.32871
$834$	7.44614	−	15.2558i	0.257839	−	0.528265i
$835$		−	10.2909i		−	0.356131i
$836$	0.165313	−	11.2294i	0.00571748	−	0.388377i
$837$	−1.71473	−	8.10126i	−0.0592698	−	0.280021i
$838$		−	18.3622i		−	0.634310i
$839$			3.70634i			0.127957i	0.997951	+	0.0639786i	$0.0203789\pi$
$839$			3.70634i			0.127957i	−0.997951	+	0.0639786i	$0.979621\pi$
$840$	−18.2183	−	8.89207i	−0.628590	−	0.306806i
$841$	−27.5342			−0.949454
$842$	−0.992212			−0.0341939
$843$	−4.24398	−	2.07143i	−0.146171	−	0.0713438i
$844$			35.3194i			1.21574i
$845$		−	7.85869i		−	0.270347i
$846$	7.05874	−	5.50841i	0.242684	−	0.189383i
$847$	1.41342	−	47.9951i	0.0485657	−	1.64913i
$848$		−	5.55798i		−	0.190862i
$849$	6.76154	−	13.8532i	0.232055	−	0.475440i
$850$	−4.44289			−0.152390
$851$			31.5214i			1.08054i
$852$	6.87853	−	14.0929i	0.235655	−	0.482814i
$853$			0.223000i			0.00763538i	0.999993	+	0.00381769i	$0.00121521\pi$
$853$			0.223000i			0.00763538i	−0.999993	+	0.00381769i	$0.998785\pi$
$854$	−5.81352			−0.198934
$855$	−4.57819	−	5.86671i	−0.156571	−	0.200637i
$856$	22.8372			0.780561
$857$	−14.0846			−0.481120			−0.240560	−	0.970634i	$-0.577331\pi$
$857$	−14.0846			−0.481120			−0.240560	+	0.970634i	$0.577331\pi$
$858$	4.68927	−	9.25917i	0.160089	−	0.316103i
$859$	15.9136			0.542966			0.271483	−	0.962443i	$-0.412486\pi$
$859$	15.9136			0.542966			0.271483	+	0.962443i	$0.412486\pi$
$860$	15.4547			0.527001
$861$	−1.52784	+	3.13027i	−0.0520686	+	0.106679i
$862$	−21.7372			−0.740373
$863$		−	39.2471i		−	1.33599i	−0.744167	−	0.667994i	$-0.767153\pi$
$863$		−	39.2471i		−	1.33599i	0.744167	−	0.667994i	$-0.232847\pi$
$864$	−6.27918	−	29.6660i	−0.213622	−	1.00926i
$865$		−	3.58057i		−	0.121743i
$866$	16.8323			0.571986
$867$	−21.9311	−	10.7042i	−0.744818	−	0.363535i
$868$			9.49599i			0.322315i
$869$	−0.276704	+	18.7960i	−0.00938653	+	0.637609i
$870$	0.732923	−	1.50163i	0.0248484	−	0.0509099i
$871$		−	10.1594i		−	0.344238i
$872$		−	32.6466i		−	1.10555i
$873$	−22.1754	−	28.4167i	−0.750525	−	0.961759i
$874$	13.4491			0.454922
$875$	4.36509			0.147567
$876$	−8.16827	+	16.7353i	−0.275980	+	0.565434i
$877$			28.5762i			0.964949i	0.875910	+	0.482474i	$0.160262\pi$
$877$			28.5762i			0.964949i	−0.875910	+	0.482474i	$0.839738\pi$
$878$			13.0750i			0.441258i
$879$	18.4988	+	9.02898i	0.623948	+	0.304540i
$880$	−0.0289812	+	1.96864i	−0.000976955	+	0.0663627i
$881$			28.2142i			0.950559i	0.879835	+	0.475279i	$0.157653\pi$
$881$			28.2142i			0.950559i	−0.879835	+	0.475279i	$0.842347\pi$
$882$	−17.7269	−	22.7161i	−0.596897	−	0.764892i
$883$	−16.6203			−0.559319			−0.279660	−	0.960099i	$-0.590222\pi$
$883$	−16.6203			−0.559319			−0.279660	+	0.960099i	$0.590222\pi$
$884$			17.2586i			0.580468i
$885$	−11.6913	−	5.70634i	−0.392998	−	0.191817i
$886$			22.8505i			0.767679i
$887$	44.6464			1.49908			0.749539	−	0.661960i	$-0.230275\pi$
$887$	44.6464			1.49908			0.749539	+	0.661960i	$0.230275\pi$
$888$	19.3345	+	9.43688i	0.648822	+	0.316681i
$889$	38.8492			1.30296
$890$	7.01833			0.235255
$891$	7.67975	−	28.8448i	0.257281	−	0.966337i
$892$	10.1791			0.340820
$893$	−9.29118			−0.310917
$894$	9.00618	+	4.39579i	0.301212	+	0.147017i
$895$	1.59363			0.0532692
$896$			38.9029i			1.29965i
$897$	−24.0151	−	11.7214i	−0.801840	−	0.391367i
$898$			19.4460i			0.648922i
$899$	−1.92944			−0.0643505
$900$	2.51945	+	3.22854i	0.0839817	+	0.107618i
$901$		−	52.2046i		−	1.73919i
$902$	−1.21740	−	0.0179220i	−0.0405352	−	0.000596736i
$903$	76.9226	+	37.5448i	2.55982	+	1.24941i
$904$			5.70731i			0.189822i
$905$		−	18.1238i		−	0.602454i
$906$	6.16674	−	12.6345i	0.204876	−	0.419755i
$907$	−3.12032			−0.103609			−0.0518043	−	0.998657i	$-0.516497\pi$
$907$	−3.12032			−0.103609			−0.0518043	+	0.998657i	$0.516497\pi$
$908$	17.8170			0.591279
$909$	23.0345	+	29.5176i	0.764008	+	0.979036i
$910$			7.88655i			0.261437i
$911$			13.4754i			0.446460i	0.974766	+	0.223230i	$0.0716602\pi$
$911$			13.4754i			0.446460i	−0.974766	+	0.223230i	$0.928340\pi$
$912$	−1.11872	+	2.29205i	−0.0370444	+	0.0758974i
$913$	5.17581	+	0.0761954i	0.171294	+	0.00252170i
$914$		−	8.81549i		−	0.291591i
$915$	2.60165	+	1.26983i	0.0860079	+	0.0419792i
$916$	−9.38978			−0.310247
$917$		−	30.3650i		−	1.00274i
$918$	−4.78050	−	22.5855i	−0.157780	−	0.745434i
$919$			31.2115i			1.02957i	0.857319	+	0.514786i	$0.172129\pi$
$919$			31.2115i			1.02957i	−0.857319	+	0.514786i	$0.827871\pi$
$920$	−18.2449			−0.601515
$921$	8.34316	−	17.0936i	0.274916	−	0.563254i
$922$	2.03853			0.0671355
$923$	−15.0389			−0.495011
$924$	−15.4655	+	30.5373i	−0.508777	+	1.00460i
$925$	−4.63253			−0.152317
$926$	−7.57323			−0.248872
$927$	29.5647	+	37.8856i	0.971031	+	1.24433i
$928$	−7.06542			−0.231934
$929$		−	50.2207i		−	1.64769i	−0.566818	−	0.823843i	$-0.691826\pi$
$929$		−	50.2207i		−	1.64769i	0.566818	−	0.823843i	$-0.308174\pi$
$930$	−0.964721	+	1.97654i	−0.0316344	+	0.0648133i
$931$			29.9005i			0.979949i
$932$	28.8125			0.943784
$933$	16.6325	−	34.0771i	0.544525	−	1.11563i
$934$			21.0217i			0.687852i
$935$	−0.272212	+	18.4909i	−0.00890229	+	0.604716i
$936$	−14.3793	+	11.2211i	−0.470002	+	0.366774i
$937$		−	7.74456i		−	0.253004i	−0.991966	−	0.126502i	$-0.959625\pi$
$937$		−	7.74456i		−	0.253004i	0.991966	−	0.126502i	$-0.0403750\pi$
$938$		−	15.5841i		−	0.508839i
$939$	−15.8940	−	7.75762i	−0.518680	−	0.253160i
$940$	5.11308			0.166770
$941$	33.2838			1.08502			0.542510	−	0.840050i	$-0.317474\pi$
$941$	33.2838			1.08502			0.542510	+	0.840050i	$0.317474\pi$
$942$	−14.7750	−	7.21146i	−0.481395	−	0.234962i
$943$			3.13484i			0.102084i
$944$			4.45879i			0.145121i
$945$	4.69679	+	22.1900i	0.152787	+	0.721842i
$946$	−0.440411	+	29.9163i	−0.0143190	+	0.972662i
$947$			45.6884i			1.48467i	0.670027	+	0.742337i	$0.266283\pi$
$947$			45.6884i			1.48467i	−0.670027	+	0.742337i	$0.733717\pi$
$948$	5.87803	−	12.0430i	0.190910	−	0.391139i
$949$	17.8587			0.579719
$950$			1.97654i			0.0641274i
$951$	1.91381	−	3.92105i	0.0620596	−	0.127149i
$952$			65.2611i			2.11512i
$953$	1.89333			0.0613311			0.0306655	−	0.999530i	$-0.490237\pi$
$953$	1.89333			0.0613311			0.0306655	+	0.999530i	$0.490237\pi$
$954$	17.6443	−	13.7691i	0.571257	−	0.445790i
$955$	17.8976			0.579153
$956$	5.28490			0.170926
$957$	−6.20472	−	3.14235i	−0.200570	−	0.101578i
$958$	−9.29040			−0.300159
$959$	−40.9556			−1.32253
$960$	−2.63072	+	5.38987i	−0.0849061	+	0.173957i
$961$	−28.4603			−0.918076
$962$		−	8.36975i		−	0.269852i
$963$	−15.7194	−	20.1436i	−0.506551	−	0.649118i
$964$			37.4521i			1.20625i
$965$	1.50163			0.0483391
$966$	−36.8381	−	17.9802i	−1.18525	−	0.578502i
$967$		−	3.87309i		−	0.124550i	−0.998059	−	0.0622750i	$-0.980164\pi$
$967$		−	3.87309i		−	0.124550i	0.998059	−	0.0622750i	$-0.0198356\pi$
$968$	−29.4821	−	0.868226i	−0.947590	−	0.0279058i
$969$	−10.5078	+	21.5286i	−0.337559	+	0.691599i
$970$			9.57379i			0.307396i
$971$		−	48.1278i		−	1.54449i	−0.635322	−	0.772247i	$-0.719133\pi$
$971$		−	48.1278i		−	1.54449i	0.635322	−	0.772247i	$-0.280867\pi$
$972$	−13.7015	+	16.2816i	−0.439475	+	0.522232i
$973$	53.6920			1.72129
$974$	26.5450			0.850557
$975$	1.72264	−	3.52937i	0.0551685	−	0.113030i
$976$		−	0.992212i		−	0.0317599i
$977$			51.3570i			1.64305i	0.570169	+	0.821527i	$0.306878\pi$
$977$			51.3570i			1.64305i	−0.570169	+	0.821527i	$0.693122\pi$
$978$	14.6643	+	7.15743i	0.468912	+	0.228869i
$979$	0.430007	−	29.2096i	0.0137431	−	0.933542i
$980$		−	16.4547i		−	0.525626i
$981$	−28.7960	+	22.4714i	−0.919384	+	0.717457i
$982$	−30.2834			−0.966382
$983$			57.9519i			1.84838i	0.381933	+	0.924190i	$0.375258\pi$
$983$			57.9519i			1.84838i	−0.381933	+	0.924190i	$0.624742\pi$
$984$	1.92284	+	0.938509i	0.0612978	+	0.0299186i
$985$			20.6147i			0.656839i
$986$	−5.37910			−0.171305
$987$	25.4493	+	12.4214i	0.810060	+	0.395379i
$988$	7.67794			0.244268
$989$	77.0349			2.44957
$990$	−6.32142	+	4.78500i	−0.200908	+	0.152077i
$991$	28.4842			0.904830			0.452415	−	0.891808i	$-0.350563\pi$
$991$	28.4842			0.904830			0.452415	+	0.891808i	$0.350563\pi$
$992$	9.29997			0.295274
$993$	−25.4630	−	12.4281i	−0.808044	−	0.394395i
$994$	−23.0690			−0.731706
$995$		−	2.42144i		−	0.0767649i
$996$	−3.31627	−	1.61862i	−0.105080	−	0.0512880i
$997$			33.2142i			1.05191i	0.850514	+	0.525953i	$0.176291\pi$
$997$			33.2142i			1.05191i	−0.850514	+	0.525953i	$0.823709\pi$
$998$	21.3326			0.675271
$999$	−4.98456	−	23.5496i	−0.157704	−	0.745076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.f.a.131.5	✓	8
3.2	odd	2		165.2.f.b.131.4	yes	8
4.3	odd	2		2640.2.f.d.1121.8		8
5.2	odd	4		825.2.d.b.824.5		8
5.3	odd	4		825.2.d.d.824.4		8
5.4	even	2		825.2.f.c.626.4		8
11.10	odd	2		165.2.f.b.131.3	yes	8
12.11	even	2		2640.2.f.c.1121.7		8
15.2	even	4		825.2.d.e.824.4		8
15.8	even	4		825.2.d.c.824.5		8
15.14	odd	2		825.2.f.d.626.5		8
33.32	even	2	inner	165.2.f.a.131.6	yes	8
44.43	even	2		2640.2.f.c.1121.8		8
55.32	even	4		825.2.d.c.824.4		8
55.43	even	4		825.2.d.e.824.5		8
55.54	odd	2		825.2.f.d.626.6		8
132.131	odd	2		2640.2.f.d.1121.7		8
165.32	odd	4		825.2.d.d.824.5		8
165.98	odd	4		825.2.d.b.824.4		8
165.164	even	2		825.2.f.c.626.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.f.a.131.5	✓	8	1.1	even	1	trivial
165.2.f.a.131.6	yes	8	33.32	even	2	inner
165.2.f.b.131.3	yes	8	11.10	odd	2
165.2.f.b.131.4	yes	8	3.2	odd	2
825.2.d.b.824.4		8	165.98	odd	4
825.2.d.b.824.5		8	5.2	odd	4
825.2.d.c.824.4		8	55.32	even	4
825.2.d.c.824.5		8	15.8	even	4
825.2.d.d.824.4		8	5.3	odd	4
825.2.d.d.824.5		8	165.32	odd	4
825.2.d.e.824.4		8	15.2	even	4
825.2.d.e.824.5		8	55.43	even	4
825.2.f.c.626.3		8	165.164	even	2
825.2.f.c.626.4		8	5.4	even	2
825.2.f.d.626.5		8	15.14	odd	2
825.2.f.d.626.6		8	55.54	odd	2
2640.2.f.c.1121.7		8	12.11	even	2
2640.2.f.c.1121.8		8	44.43	even	2
2640.2.f.d.1121.7		8	132.131	odd	2
2640.2.f.d.1121.8		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.796815 q^{2} +(-1.55654 - 0.759725i) q^{3} -1.36509 q^{4} -1.00000i q^{5} +(-1.24027 - 0.605361i) q^{6} -4.36509i q^{7} -2.68135 q^{8} +(1.84564 + 2.36509i) q^{9} +O(q^{10})\)	\(q+0.796815 q^{2} +(-1.55654 - 0.759725i) q^{3} -1.36509 q^{4} -1.00000i q^{5} +(-1.24027 - 0.605361i) q^{6} -4.36509i q^{7} -2.68135 q^{8} +(1.84564 + 2.36509i) q^{9} -0.796815i q^{10} +(-3.31627 - 0.0488202i) q^{11} +(2.12481 + 1.03709i) q^{12} -2.26745i q^{13} -3.47817i q^{14} +(-0.759725 + 1.55654i) q^{15} +0.593630 q^{16} +5.57581 q^{17} +(1.47063 + 1.88454i) q^{18} -2.48055i q^{19} +1.36509i q^{20} +(-3.31627 + 6.79443i) q^{21} +(-2.64245 - 0.0389007i) q^{22} +6.80435i q^{23} +(4.17363 + 2.03709i) q^{24} -1.00000 q^{25} -1.80673i q^{26} +(-1.07599 - 5.08353i) q^{27} +5.95872i q^{28} -1.21072 q^{29} +(-0.605361 + 1.24027i) q^{30} +1.59363 q^{31} +5.83572 q^{32} +(5.12481 + 2.59544i) q^{33} +4.44289 q^{34} -4.36509 q^{35} +(-2.51945 - 3.22854i) q^{36} +4.63253 q^{37} -1.97654i q^{38} +(-1.72264 + 3.52937i) q^{39} +2.68135i q^{40} +0.460711 q^{41} +(-2.64245 + 5.41391i) q^{42} -11.3214i q^{43} +(4.52699 + 0.0666438i) q^{44} +(2.36509 - 1.84564i) q^{45} +5.42181i q^{46} -3.74561i q^{47} +(-0.924009 - 0.450996i) q^{48} -12.0540 q^{49} -0.796815 q^{50} +(-8.67897 - 4.23608i) q^{51} +3.09526i q^{52} -9.36270i q^{53} +(-0.857366 - 4.05063i) q^{54} +(-0.0488202 + 3.31627i) q^{55} +11.7043i q^{56} +(-1.88454 + 3.86108i) q^{57} -0.964721 q^{58} +7.51106i q^{59} +(1.03709 - 2.12481i) q^{60} -1.67143i q^{61} +1.26983 q^{62} +(10.3238 - 8.05636i) q^{63} +3.46273 q^{64} -2.26745 q^{65} +(4.08353 + 2.06809i) q^{66} +4.48055 q^{67} -7.61145 q^{68} +(5.16944 - 10.5912i) q^{69} -3.47817 q^{70} -6.63253i q^{71} +(-4.94880 - 6.34163i) q^{72} +7.87615i q^{73} +3.69127 q^{74} +(1.55654 + 0.759725i) q^{75} +3.38616i q^{76} +(-0.213104 + 14.4758i) q^{77} +(-1.37262 + 2.81226i) q^{78} -5.66781i q^{79} -0.593630i q^{80} +(-2.18726 + 8.73017i) q^{81} +0.367101 q^{82} -1.56073 q^{83} +(4.52699 - 9.27498i) q^{84} -5.57581i q^{85} -9.02108i q^{86} +(1.88454 + 0.919815i) q^{87} +(8.89207 + 0.130904i) q^{88} +8.80797i q^{89} +(1.88454 - 1.47063i) q^{90} -9.89759 q^{91} -9.28852i q^{92} +(-2.48055 - 1.21072i) q^{93} -2.98456i q^{94} -2.48055 q^{95} +(-9.08353 - 4.43354i) q^{96} -12.0151 q^{97} -9.60479 q^{98} +(-6.00515 - 7.93336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 8 q^{4} - 14 q^{6} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 8 * q^4 - 14 * q^6 + 12 * q^8 + 4 * q^9	\( 8 q - 2 q^{3} + 8 q^{4} - 14 q^{6} + 12 q^{8} + 4 q^{9} - 12 q^{11} - 6 q^{12} - 2 q^{15} - 8 q^{16} - 4 q^{17} + 8 q^{18} - 12 q^{21} - 4 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{27} + 20 q^{29} + 10 q^{30} + 24 q^{32} + 18 q^{33} - 16 q^{34} - 16 q^{35} - 12 q^{36} + 8 q^{37} - 12 q^{39} - 12 q^{41} - 4 q^{42} - 8 q^{44} - 26 q^{48} - 8 q^{49} + 12 q^{51} + 6 q^{54} + 4 q^{55} + 12 q^{57} + 4 q^{58} + 6 q^{60} + 48 q^{62} + 32 q^{63} - 8 q^{65} - 22 q^{66} + 44 q^{67} - 84 q^{68} - 20 q^{69} + 12 q^{70} + 4 q^{72} + 8 q^{74} + 2 q^{75} - 20 q^{77} + 44 q^{78} + 8 q^{81} - 28 q^{82} - 36 q^{83} - 8 q^{84} - 12 q^{87} + 8 q^{88} - 12 q^{90} + 8 q^{91} - 28 q^{93} - 28 q^{95} - 18 q^{96} - 24 q^{97} + 36 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 8 * q^4 - 14 * q^6 + 12 * q^8 + 4 * q^9 - 12 * q^11 - 6 * q^12 - 2 * q^15 - 8 * q^16 - 4 * q^17 + 8 * q^18 - 12 * q^21 - 4 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^27 + 20 * q^29 + 10 * q^30 + 24 * q^32 + 18 * q^33 - 16 * q^34 - 16 * q^35 - 12 * q^36 + 8 * q^37 - 12 * q^39 - 12 * q^41 - 4 * q^42 - 8 * q^44 - 26 * q^48 - 8 * q^49 + 12 * q^51 + 6 * q^54 + 4 * q^55 + 12 * q^57 + 4 * q^58 + 6 * q^60 + 48 * q^62 + 32 * q^63 - 8 * q^65 - 22 * q^66 + 44 * q^67 - 84 * q^68 - 20 * q^69 + 12 * q^70 + 4 * q^72 + 8 * q^74 + 2 * q^75 - 20 * q^77 + 44 * q^78 + 8 * q^81 - 28 * q^82 - 36 * q^83 - 8 * q^84 - 12 * q^87 + 8 * q^88 - 12 * q^90 + 8 * q^91 - 28 * q^93 - 28 * q^95 - 18 * q^96 - 24 * q^97 + 36 * q^99

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