LMFDB - Embedded newform 1470.2.m.f.1273.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1470,2,Mod(97,1470)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1470.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1470, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,8,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 32 x^{13} + 2 x^{12} + 352 x^{10} - 288 x^{9} + 2 x^{8} - 1440 x^{7} + 8800 x^{6} + \cdots + 390625 $ x^16 - 32x^13 + 2x^12 + 352x^10 - 288x^9 + 2x^8 - 1440x^7 + 8800x^6 + 1250x^4 - 100000*x^3 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1273.7
Root			$-1.12594 + 1.93191i$ of defining polynomial
Character	$\chi$	$=$	1470.1273
Dual form			1470.2.m.f.97.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(1.35397 + 1.77954i) q^{5} +1.00000i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(2.21573 + 0.300921i) q^{10} +2.44960 q^{11} +(0.707107 + 0.707107i) q^{12} +(1.28575 - 1.28575i) q^{13} +(-2.21573 - 0.300921i) q^{15} -1.00000 q^{16} +(5.33117 + 5.33117i) q^{17} +(-0.707107 - 0.707107i) q^{18} -0.690213 q^{19} +(1.77954 - 1.35397i) q^{20} +(1.73213 - 1.73213i) q^{22} +(-5.65016 - 5.65016i) q^{23} +1.00000 q^{24} +(-1.33352 + 4.81889i) q^{25} -1.81833i q^{26} +(0.707107 + 0.707107i) q^{27} +5.08030i q^{29} +(-1.77954 + 1.35397i) q^{30} +1.26497i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.73213 + 1.73213i) q^{33} +7.53941 q^{34} -1.00000 q^{36} +(7.16021 - 7.16021i) q^{37} +(-0.488054 + 0.488054i) q^{38} +1.81833i q^{39} +(0.300921 - 2.21573i) q^{40} +1.15796i q^{41} +(0.893060 + 0.893060i) q^{43} -2.44960i q^{44} +(1.77954 - 1.35397i) q^{45} -7.99053 q^{46} +(4.95521 + 4.95521i) q^{47} +(0.707107 - 0.707107i) q^{48} +(2.46453 + 4.35041i) q^{50} -7.53941 q^{51} +(-1.28575 - 1.28575i) q^{52} +(6.74356 + 6.74356i) q^{53} +1.00000 q^{54} +(3.31669 + 4.35916i) q^{55} +(0.488054 - 0.488054i) q^{57} +(3.59232 + 3.59232i) q^{58} +8.06376 q^{59} +(-0.300921 + 2.21573i) q^{60} +1.09779i q^{61} +(0.894469 + 0.894469i) q^{62} +1.00000i q^{64} +(4.02892 + 0.547173i) q^{65} +2.44960i q^{66} +(-7.41414 + 7.41414i) q^{67} +(5.33117 - 5.33117i) q^{68} +7.99053 q^{69} +4.24084 q^{71} +(-0.707107 + 0.707107i) q^{72} +(4.58803 - 4.58803i) q^{73} -10.1261i q^{74} +(-2.46453 - 4.35041i) q^{75} +0.690213i q^{76} +(1.28575 + 1.28575i) q^{78} +2.31721i q^{79} +(-1.35397 - 1.77954i) q^{80} -1.00000 q^{81} +(0.818802 + 0.818802i) q^{82} +(7.39632 - 7.39632i) q^{83} +(-2.26877 + 16.7053i) q^{85} +1.26298 q^{86} +(-3.59232 - 3.59232i) q^{87} +(-1.73213 - 1.73213i) q^{88} -16.8162 q^{89} +(0.300921 - 2.21573i) q^{90} +(-5.65016 + 5.65016i) q^{92} +(-0.894469 - 0.894469i) q^{93} +7.00773 q^{94} +(-0.934530 - 1.22826i) q^{95} -1.00000i q^{96} +(4.74063 + 4.74063i) q^{97} -2.44960i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{5} + 8 q^{13} - 16 q^{16} - 8 q^{17} - 48 q^{19} - 8 q^{22} - 8 q^{23} + 16 q^{24} + 8 q^{25} + 8 q^{33} - 16 q^{36} + 8 q^{37} - 8 q^{38} + 16 q^{47} - 8 q^{52} + 8 q^{53} + 16 q^{54} + 8 q^{57}+ \cdots - 64 q^{97}+O(q^{100}) $ 16 * q + 8 * q^5 + 8 * q^13 - 16 * q^16 - 8 * q^17 - 48 * q^19 - 8 * q^22 - 8 * q^23 + 16 * q^24 + 8 * q^25 + 8 * q^33 - 16 * q^36 + 8 * q^37 - 8 * q^38 + 16 * q^47 - 8 * q^52 + 8 * q^53 + 16 * q^54 + 8 * q^57 + 24 * q^58 + 48 * q^59 - 8 * q^62 + 72 * q^65 - 48 * q^67 - 8 * q^68 + 16 * q^73 + 8 * q^78 - 8 * q^80 - 16 * q^81 - 16 * q^82 - 72 * q^85 - 24 * q^87 + 8 * q^88 - 64 * q^89 - 8 * q^92 + 8 * q^93 + 64 * q^94 + 48 * q^95 - 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	1.35397	+	1.77954i	0.605515	+	0.795834i
$5$	1.35397	+	1.77954i	0.605515	+	0.795834i
$6$			1.00000i			0.408248i
$7$		0			0
$7$		0			0
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	2.21573	+	0.300921i	0.700674	+	0.0951596i
$11$	2.44960			0.738583			0.369291	−	0.929314i	$-0.379600\pi$
$11$	2.44960			0.738583			0.369291	+	0.929314i	$0.379600\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	1.28575	−	1.28575i	0.356604	−	0.356604i	−0.505956	−	0.862559i	$-0.668860\pi$
$13$	1.28575	−	1.28575i	0.356604	−	0.356604i	0.862559	+	0.505956i	$0.168860\pi$
$14$		0			0
$15$	−2.21573	−	0.300921i	−0.572098	−	0.0776975i
$16$	−1.00000			−0.250000
$17$	5.33117	+	5.33117i	1.29300	+	1.29300i	0.932923	+	0.360075i	$0.117249\pi$
$17$	5.33117	+	5.33117i	1.29300	+	1.29300i	0.360075	+	0.932923i	$0.382751\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−0.690213			−0.158346			−0.0791729	−	0.996861i	$-0.525228\pi$
$19$	−0.690213			−0.158346			−0.0791729	+	0.996861i	$0.525228\pi$
$20$	1.77954	−	1.35397i	0.397917	−	0.302757i
$21$		0			0
$22$	1.73213	−	1.73213i	0.369291	−	0.369291i
$23$	−5.65016	−	5.65016i	−1.17814	−	1.17814i	−0.980218	−	0.197922i	$-0.936581\pi$
$23$	−5.65016	−	5.65016i	−1.17814	−	1.17814i	−0.197922	−	0.980218i	$-0.563419\pi$
$24$	1.00000			0.204124
$25$	−1.33352	+	4.81889i	−0.266704	+	0.963779i
$26$		−	1.81833i		−	0.356604i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$			5.08030i			0.943388i	0.881762	+	0.471694i	$0.156357\pi$
$29$			5.08030i			0.943388i	−0.881762	+	0.471694i	$0.843643\pi$
$30$	−1.77954	+	1.35397i	−0.324898	+	0.247200i
$31$			1.26497i			0.227195i	0.993527	+	0.113598i	$0.0362375\pi$
$31$			1.26497i			0.227195i	−0.993527	+	0.113598i	$0.963762\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.73213	+	1.73213i	−0.301525	+	0.301525i
$34$	7.53941			1.29300
$35$		0			0
$36$	−1.00000			−0.166667
$37$	7.16021	−	7.16021i	1.17713	−	1.17713i	0.196659	−	0.980472i	$-0.436991\pi$
$37$	7.16021	−	7.16021i	1.17713	−	1.17713i	0.980472	−	0.196659i	$-0.0630093\pi$
$38$	−0.488054	+	0.488054i	−0.0791729	+	0.0791729i
$39$			1.81833i			0.291166i
$40$	0.300921	−	2.21573i	0.0475798	−	0.350337i
$41$			1.15796i			0.180843i	0.995904	+	0.0904216i	$0.0288215\pi$
$41$			1.15796i			0.180843i	−0.995904	+	0.0904216i	$0.971179\pi$
$42$		0			0
$43$	0.893060	+	0.893060i	0.136190	+	0.136190i	0.771915	−	0.635725i	$-0.219299\pi$
$43$	0.893060	+	0.893060i	0.136190	+	0.136190i	−0.635725	+	0.771915i	$0.719299\pi$
$44$		−	2.44960i		−	0.369291i
$45$	1.77954	−	1.35397i	0.265278	−	0.201838i
$46$	−7.99053			−1.17814
$47$	4.95521	+	4.95521i	0.722792	+	0.722792i	0.969173	−	0.246381i	$-0.0792414\pi$
$47$	4.95521	+	4.95521i	0.722792	+	0.722792i	−0.246381	+	0.969173i	$0.579241\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$		0			0
$50$	2.46453	+	4.35041i	0.348538	+	0.615241i
$51$	−7.53941			−1.05573
$52$	−1.28575	−	1.28575i	−0.178302	−	0.178302i
$53$	6.74356	+	6.74356i	0.926299	+	0.926299i	0.997465	−	0.0711657i	$-0.0226719\pi$
$53$	6.74356	+	6.74356i	0.926299	+	0.926299i	−0.0711657	+	0.997465i	$0.522672\pi$
$54$	1.00000			0.136083
$55$	3.31669	+	4.35916i	0.447223	+	0.587789i
$56$		0			0
$57$	0.488054	−	0.488054i	0.0646444	−	0.0646444i
$58$	3.59232	+	3.59232i	0.471694	+	0.471694i
$59$	8.06376			1.04981			0.524906	−	0.851160i	$-0.324101\pi$
$59$	8.06376			1.04981			0.524906	+	0.851160i	$0.324101\pi$
$60$	−0.300921	+	2.21573i	−0.0388487	+	0.286049i
$61$			1.09779i			0.140557i	0.997527	+	0.0702785i	$0.0223888\pi$
$61$			1.09779i			0.140557i	−0.997527	+	0.0702785i	$0.977611\pi$
$62$	0.894469	+	0.894469i	0.113598	+	0.113598i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	4.02892	+	0.547173i	0.499726	+	0.0678685i
$66$			2.44960i			0.301525i
$67$	−7.41414	+	7.41414i	−0.905782	+	0.905782i	−0.995929	−	0.0901466i	$-0.971266\pi$
$67$	−7.41414	+	7.41414i	−0.905782	+	0.905782i	0.0901466	+	0.995929i	$0.471266\pi$
$68$	5.33117	−	5.33117i	0.646499	−	0.646499i
$69$	7.99053			0.961947
$70$		0			0
$71$	4.24084			0.503296			0.251648	−	0.967819i	$-0.419028\pi$
$71$	4.24084			0.503296			0.251648	+	0.967819i	$0.419028\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	4.58803	−	4.58803i	0.536989	−	0.536989i	−0.385654	−	0.922643i	$-0.626024\pi$
$73$	4.58803	−	4.58803i	0.536989	−	0.536989i	0.922643	+	0.385654i	$0.126024\pi$
$74$		−	10.1261i		−	1.17713i
$75$	−2.46453	−	4.35041i	−0.284580	−	0.502342i
$76$			0.690213i			0.0791729i
$77$		0			0
$78$	1.28575	+	1.28575i	0.145583	+	0.145583i
$79$			2.31721i			0.260706i	0.991468	+	0.130353i	$0.0416111\pi$
$79$			2.31721i			0.260706i	−0.991468	+	0.130353i	$0.958389\pi$
$80$	−1.35397	−	1.77954i	−0.151379	−	0.198959i
$81$	−1.00000			−0.111111
$82$	0.818802	+	0.818802i	0.0904216	+	0.0904216i
$83$	7.39632	−	7.39632i	0.811852	−	0.811852i	−0.173060	−	0.984911i	$-0.555365\pi$
$83$	7.39632	−	7.39632i	0.811852	−	0.811852i	0.984911	+	0.173060i	$0.0553653\pi$
$84$		0			0
$85$	−2.26877	+	16.7053i	−0.246082	+	1.81194i
$86$	1.26298			0.136190
$87$	−3.59232	−	3.59232i	−0.385137	−	0.385137i
$88$	−1.73213	−	1.73213i	−0.184646	−	0.184646i
$89$	−16.8162			−1.78251			−0.891255	−	0.453503i	$-0.850174\pi$
$89$	−16.8162			−1.78251			−0.891255	+	0.453503i	$0.850174\pi$
$90$	0.300921	−	2.21573i	0.0317199	−	0.233558i
$91$		0			0
$92$	−5.65016	+	5.65016i	−0.589070	+	0.589070i
$93$	−0.894469	−	0.894469i	−0.0927522	−	0.0927522i
$94$	7.00773			0.722792
$95$	−0.934530	−	1.22826i	−0.0958807	−	0.126017i
$96$		−	1.00000i		−	0.102062i
$97$	4.74063	+	4.74063i	0.481338	+	0.481338i	0.905559	−	0.424221i	$-0.139452\pi$
$97$	4.74063	+	4.74063i	0.481338	+	0.481338i	−0.424221	+	0.905559i	$0.639452\pi$
$98$		0			0
$99$		−	2.44960i		−	0.246194i
$100$	4.81889	+	1.33352i	0.481889	+	0.133352i
$101$			18.8914i			1.87977i	0.341494	+	0.939884i	$0.389067\pi$
$101$			18.8914i			1.87977i	−0.341494	+	0.939884i	$0.610933\pi$
$102$	−5.33117	+	5.33117i	−0.527864	+	0.527864i
$103$	−6.84553	+	6.84553i	−0.674510	+	0.674510i	−0.958752	−	0.284242i	$-0.908258\pi$
$103$	−6.84553	+	6.84553i	−0.674510	+	0.674510i	0.284242	+	0.958752i	$0.408258\pi$
$104$	−1.81833			−0.178302
$105$		0			0
$106$	9.53683			0.926299
$107$	10.7995	−	10.7995i	1.04402	−	1.04402i	0.0450393	−	0.998985i	$-0.485659\pi$
$107$	10.7995	−	10.7995i	1.04402	−	1.04402i	0.998985	−	0.0450393i	$-0.0143413\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$			0.964378i			0.0923706i	0.998933	+	0.0461853i	$0.0147065\pi$
$109$			0.964378i			0.0923706i	−0.998933	+	0.0461853i	$0.985294\pi$
$110$	5.42765	+	0.737137i	0.517506	+	0.0702832i
$111$			10.1261i			0.961124i
$112$		0			0
$113$	−10.0903	−	10.0903i	−0.949215	−	0.949215i	0.0495565	−	0.998771i	$-0.484219\pi$
$113$	−10.0903	−	10.0903i	−0.949215	−	0.949215i	−0.998771	+	0.0495565i	$0.984219\pi$
$114$		−	0.690213i		−	0.0646444i
$115$	2.40452	−	17.7048i	0.224223	−	1.65098i
$116$	5.08030			0.471694
$117$	−1.28575	−	1.28575i	−0.118868	−	0.118868i
$118$	5.70194	−	5.70194i	0.524906	−	0.524906i
$119$		0			0
$120$	1.35397	+	1.77954i	0.123600	+	0.162449i
$121$	−4.99945			−0.454496
$122$	0.776251	+	0.776251i	0.0702785	+	0.0702785i
$123$	−0.818802	−	0.818802i	−0.0738289	−	0.0738289i
$124$	1.26497			0.113598
$125$	−10.3810	+	4.15160i	−0.928501	+	0.371330i
$126$		0			0
$127$	5.47457	−	5.47457i	0.485790	−	0.485790i	−0.421185	−	0.906975i	$-0.638386\pi$
$127$	5.47457	−	5.47457i	0.485790	−	0.485790i	0.906975	+	0.421185i	$0.138386\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−1.26298			−0.111199
$130$	3.23579	−	2.46197i	0.283797	−	0.215929i
$131$		−	5.14115i		−	0.449185i	−0.974453	−	0.224592i	$-0.927895\pi$
$131$		−	5.14115i		−	0.449185i	0.974453	−	0.224592i	$-0.0721050\pi$
$132$	1.73213	+	1.73213i	0.150763	+	0.150763i
$133$		0			0
$134$			10.4852i			0.905782i
$135$	−0.300921	+	2.21573i	−0.0258992	+	0.190699i
$136$		−	7.53941i		−	0.646499i
$137$	16.2051	−	16.2051i	1.38450	−	1.38450i	0.548058	−	0.836440i	$-0.315367\pi$
$137$	16.2051	−	16.2051i	1.38450	−	1.38450i	0.836440	−	0.548058i	$-0.184633\pi$
$138$	5.65016	−	5.65016i	0.480974	−	0.480974i
$139$	−5.66867			−0.480810			−0.240405	−	0.970673i	$-0.577280\pi$
$139$	−5.66867			−0.480810			−0.240405	+	0.970673i	$0.577280\pi$
$140$		0			0
$141$	−7.00773			−0.590157
$142$	2.99873	−	2.99873i	0.251648	−	0.251648i
$143$	3.14958	−	3.14958i	0.263381	−	0.263381i
$144$			1.00000i			0.0833333i
$145$	−9.04059	+	6.87859i	−0.750780	+	0.571236i
$146$		−	6.48846i		−	0.536989i
$147$		0			0
$148$	−7.16021	−	7.16021i	−0.588566	−	0.588566i
$149$		−	11.6944i		−	0.958045i	−0.877803	−	0.479022i	$-0.840991\pi$
$149$		−	11.6944i		−	0.958045i	0.877803	−	0.479022i	$-0.159009\pi$
$150$	−4.81889	−	1.33352i	−0.393461	−	0.108881i
$151$	16.6297			1.35331			0.676654	−	0.736302i	$-0.263430\pi$
$151$	16.6297			1.35331			0.676654	+	0.736302i	$0.263430\pi$
$152$	0.488054	+	0.488054i	0.0395864	+	0.0395864i
$153$	5.33117	−	5.33117i	0.431000	−	0.431000i
$154$		0			0
$155$	−2.25106	+	1.71274i	−0.180810	+	0.137570i
$156$	1.81833			0.145583
$157$	−5.17869	−	5.17869i	−0.413304	−	0.413304i	0.469584	−	0.882888i	$-0.344404\pi$
$157$	−5.17869	−	5.17869i	−0.413304	−	0.413304i	−0.882888	+	0.469584i	$0.844404\pi$
$158$	1.63851	+	1.63851i	0.130353	+	0.130353i
$159$	−9.53683			−0.756320
$160$	−2.21573	−	0.300921i	−0.175169	−	0.0237899i
$161$		0			0
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−7.70934	−	7.70934i	−0.603842	−	0.603842i	0.337488	−	0.941330i	$-0.390423\pi$
$163$	−7.70934	−	7.70934i	−0.603842	−	0.603842i	−0.941330	+	0.337488i	$0.890423\pi$
$164$	1.15796			0.0904216
$165$	−5.42765	−	0.737137i	−0.422542	−	0.0573860i
$166$		−	10.4600i		−	0.811852i
$167$	−10.3891	−	10.3891i	−0.803931	−	0.803931i	0.179777	−	0.983707i	$-0.442463\pi$
$167$	−10.3891	−	10.3891i	−0.803931	−	0.803931i	−0.983707	+	0.179777i	$0.942463\pi$
$168$		0			0
$169$			9.69368i			0.745668i
$170$	10.2082	+	13.4167i	0.782930	+	1.02901i
$171$			0.690213i			0.0527819i
$172$	0.893060	−	0.893060i	0.0680952	−	0.0680952i
$173$	−1.60887	+	1.60887i	−0.122320	+	0.122320i	−0.765617	−	0.643297i	$-0.777566\pi$
$173$	−1.60887	+	1.60887i	−0.122320	+	0.122320i	0.643297	+	0.765617i	$0.277566\pi$
$174$	−5.08030			−0.385137
$175$		0			0
$176$	−2.44960			−0.184646
$177$	−5.70194	+	5.70194i	−0.428584	+	0.428584i
$178$	−11.8908	+	11.8908i	−0.891255	+	0.891255i
$179$		−	9.60469i		−	0.717888i	−0.933359	−	0.358944i	$-0.883137\pi$
$179$		−	9.60469i		−	0.717888i	0.933359	−	0.358944i	$-0.116863\pi$
$180$	−1.35397	−	1.77954i	−0.100919	−	0.132639i
$181$			6.19591i			0.460539i	0.973127	+	0.230269i	$0.0739607\pi$
$181$			6.19591i			0.460539i	−0.973127	+	0.230269i	$0.926039\pi$
$182$		0			0
$183$	−0.776251	−	0.776251i	−0.0573821	−	0.0573821i
$184$			7.99053i			0.589070i
$185$	22.4366	+	3.04715i	1.64957	+	0.224031i
$186$	−1.26497			−0.0927522
$187$	13.0592	+	13.0592i	0.954986	+	0.954986i
$188$	4.95521	−	4.95521i	0.361396	−	0.361396i
$189$		0			0
$190$	−1.52932	−	0.207700i	−0.110949	−	0.0150681i
$191$	−6.57026			−0.475408			−0.237704	−	0.971338i	$-0.576395\pi$
$191$	−6.57026			−0.475408			−0.237704	+	0.971338i	$0.576395\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	0.214493	+	0.214493i	0.0154395	+	0.0154395i	0.714784	−	0.699345i	$-0.246525\pi$
$193$	0.214493	+	0.214493i	0.0154395	+	0.0154395i	−0.699345	+	0.714784i	$0.746525\pi$
$194$	6.70426			0.481338
$195$	−3.23579	+	2.46197i	−0.231719	+	0.176305i
$196$		0			0
$197$	1.65688	−	1.65688i	0.118048	−	0.118048i	−0.645615	−	0.763663i	$-0.723399\pi$
$197$	1.65688	−	1.65688i	0.118048	−	0.118048i	0.763663	+	0.645615i	$0.223399\pi$
$198$	−1.73213	−	1.73213i	−0.123097	−	0.123097i
$199$	−19.6397			−1.39222			−0.696110	−	0.717935i	$-0.745087\pi$
$199$	−19.6397			−1.39222			−0.696110	+	0.717935i	$0.745087\pi$
$200$	4.35041	−	2.46453i	0.307621	−	0.174269i
$201$		−	10.4852i		−	0.739568i
$202$	13.3583	+	13.3583i	0.939884	+	0.939884i
$203$		0			0
$204$			7.53941i			0.527864i
$205$	−2.06064	+	1.56785i	−0.143921	+	0.109503i
$206$			9.68104i			0.674510i
$207$	−5.65016	+	5.65016i	−0.392713	+	0.392713i
$208$	−1.28575	+	1.28575i	−0.0891509	+	0.0891509i
$209$	−1.69075			−0.116951
$210$		0			0
$211$	−1.71203			−0.117861			−0.0589306	−	0.998262i	$-0.518769\pi$
$211$	−1.71203			−0.117861			−0.0589306	+	0.998262i	$0.518769\pi$
$212$	6.74356	−	6.74356i	0.463149	−	0.463149i
$213$	−2.99873	+	2.99873i	−0.205470	+	0.205470i
$214$		−	15.2728i		−	1.04402i
$215$	−0.380057	+	2.79841i	−0.0259196	+	0.190850i
$216$		−	1.00000i		−	0.0680414i
$217$		0			0
$218$	0.681918	+	0.681918i	0.0461853	+	0.0461853i
$219$			6.48846i			0.438450i
$220$	4.35916	−	3.31669i	0.293895	−	0.223611i
$221$	13.7091			0.922176
$222$	7.16021	+	7.16021i	0.480562	+	0.480562i
$223$	−19.7204	+	19.7204i	−1.32058	+	1.32058i	−0.407270	+	0.913308i	$0.633519\pi$
$223$	−19.7204	+	19.7204i	−1.32058	+	1.32058i	−0.913308	+	0.407270i	$0.866481\pi$
$224$		0			0
$225$	4.81889	+	1.33352i	0.321260	+	0.0889012i
$226$	−14.2698			−0.949215
$227$	−19.7598	−	19.7598i	−1.31150	−	1.31150i	−0.920308	−	0.391195i	$-0.872062\pi$
$227$	−19.7598	−	19.7598i	−1.31150	−	1.31150i	−0.391195	−	0.920308i	$-0.627938\pi$
$228$	−0.488054	−	0.488054i	−0.0323222	−	0.0323222i
$229$	−2.04335			−0.135029			−0.0675143	−	0.997718i	$-0.521507\pi$
$229$	−2.04335			−0.135029			−0.0675143	+	0.997718i	$0.521507\pi$
$230$	−10.8190	−	14.2195i	−0.713381	−	0.937604i
$231$		0			0
$232$	3.59232	−	3.59232i	0.235847	−	0.235847i
$233$	−2.26245	−	2.26245i	−0.148218	−	0.148218i	0.629104	−	0.777321i	$-0.283422\pi$
$233$	−2.26245	−	2.26245i	−0.148218	−	0.148218i	−0.777321	+	0.629104i	$0.783422\pi$
$234$	−1.81833			−0.118868
$235$	−2.10877	+	15.5272i	−0.137561	+	1.01288i
$236$		−	8.06376i		−	0.524906i
$237$	−1.63851	−	1.63851i	−0.106433	−	0.106433i
$238$		0			0
$239$		−	19.7009i		−	1.27434i	−0.770721	−	0.637172i	$-0.780104\pi$
$239$		−	19.7009i		−	1.27434i	0.770721	−	0.637172i	$-0.219896\pi$
$240$	2.21573	+	0.300921i	0.143025	+	0.0194244i
$241$		−	6.04502i		−	0.389394i	−0.980863	−	0.194697i	$-0.937628\pi$
$241$		−	6.04502i		−	0.389394i	0.980863	−	0.194697i	$-0.0623723\pi$
$242$	−3.53515	+	3.53515i	−0.227248	+	0.227248i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	1.09779			0.0702785
$245$		0			0
$246$	−1.15796			−0.0738289
$247$	−0.887443	+	0.887443i	−0.0564667	+	0.0564667i
$248$	0.894469	−	0.894469i	0.0567989	−	0.0567989i
$249$			10.4600i			0.662874i
$250$	−4.40482	+	10.2761i	−0.278585	+	0.649916i
$251$		−	12.7796i		−	0.806644i	−0.915058	−	0.403322i	$-0.867855\pi$
$251$		−	12.7796i		−	0.806644i	0.915058	−	0.403322i	$-0.132145\pi$
$252$		0			0
$253$	−13.8406	−	13.8406i	−0.870153	−	0.870153i
$254$		−	7.74221i		−	0.485790i
$255$	−10.2082	−	13.4167i	−0.639260	−	0.840185i
$256$	1.00000			0.0625000
$257$	13.3999	+	13.3999i	0.835861	+	0.835861i	0.988311	−	0.152450i	$-0.0487163\pi$
$257$	13.3999	+	13.3999i	0.835861	+	0.835861i	−0.152450	+	0.988311i	$0.548716\pi$
$258$	−0.893060	+	0.893060i	−0.0555995	+	0.0555995i
$259$		0			0
$260$	0.547173	−	4.02892i	0.0339342	−	0.249863i
$261$	5.08030			0.314463
$262$	−3.63534	−	3.63534i	−0.224592	−	0.224592i
$263$	−12.2716	−	12.2716i	−0.756697	−	0.756697i	0.219023	−	0.975720i	$-0.429713\pi$
$263$	−12.2716	−	12.2716i	−0.756697	−	0.756697i	−0.975720	+	0.219023i	$0.929713\pi$
$264$	2.44960			0.150763
$265$	−2.86983	+	21.1310i	−0.176292	+	1.29807i
$266$		0			0
$267$	11.8908	−	11.8908i	0.727706	−	0.727706i
$268$	7.41414	+	7.41414i	0.452891	+	0.452891i
$269$	−16.3231			−0.995235			−0.497617	−	0.867397i	$-0.665792\pi$
$269$	−16.3231			−0.995235			−0.497617	+	0.867397i	$0.665792\pi$
$270$	1.35397	+	1.77954i	0.0824001	+	0.108299i
$271$		−	17.1242i		−	1.04022i	−0.854098	−	0.520112i	$-0.825890\pi$
$271$		−	17.1242i		−	1.04022i	0.854098	−	0.520112i	$-0.174110\pi$
$272$	−5.33117	−	5.33117i	−0.323250	−	0.323250i
$273$		0			0
$274$		−	22.9175i		−	1.38450i
$275$	−3.26659	+	11.8044i	−0.196983	+	0.711830i
$276$		−	7.99053i		−	0.480974i
$277$	−19.7015	+	19.7015i	−1.18375	+	1.18375i	−0.204985	+	0.978765i	$0.565714\pi$
$277$	−19.7015	+	19.7015i	−1.18375	+	1.18375i	−0.978765	+	0.204985i	$0.934286\pi$
$278$	−4.00836	+	4.00836i	−0.240405	+	0.240405i
$279$	1.26497			0.0757318
$280$		0			0
$281$	−11.2741			−0.672559			−0.336279	−	0.941762i	$-0.609169\pi$
$281$	−11.2741			−0.672559			−0.336279	+	0.941762i	$0.609169\pi$
$282$	−4.95521	+	4.95521i	−0.295079	+	0.295079i
$283$	−18.4416	+	18.4416i	−1.09624	+	1.09624i	−0.101395	+	0.994846i	$0.532330\pi$
$283$	−18.4416	+	18.4416i	−1.09624	+	1.09624i	−0.994846	+	0.101395i	$0.967670\pi$
$284$		−	4.24084i		−	0.251648i
$285$	1.52932	+	0.207700i	0.0905893	+	0.0123031i
$286$		−	4.45418i		−	0.263381i
$287$		0			0
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$			39.8427i			2.34369i
$290$	−1.52877	+	11.2566i	−0.0897724	+	0.661008i
$291$	−6.70426			−0.393011
$292$	−4.58803	−	4.58803i	−0.268494	−	0.268494i
$293$	1.48873	−	1.48873i	0.0869726	−	0.0869726i	−0.662282	−	0.749255i	$-0.730412\pi$
$293$	1.48873	−	1.48873i	0.0869726	−	0.0869726i	0.749255	+	0.662282i	$0.230412\pi$
$294$		0			0
$295$	10.9181	+	14.3498i	0.635676	+	0.835476i
$296$	−10.1261			−0.588566
$297$	1.73213	+	1.73213i	0.100508	+	0.100508i
$298$	−8.26921	−	8.26921i	−0.479022	−	0.479022i
$299$	−14.5294			−0.840257
$300$	−4.35041	+	2.46453i	−0.251171	+	0.142290i
$301$		0			0
$302$	11.7590	−	11.7590i	0.676654	−	0.676654i
$303$	−13.3583	−	13.3583i	−0.767412	−	0.767412i
$304$	0.690213			0.0395864
$305$	−1.95355	+	1.48637i	−0.111860	+	0.0851093i
$306$		−	7.53941i		−	0.431000i
$307$	−22.1348	−	22.1348i	−1.26330	−	1.26330i	−0.949483	−	0.313818i	$-0.898392\pi$
$307$	−22.1348	−	22.1348i	−1.26330	−	1.26330i	−0.313818	−	0.949483i	$-0.601608\pi$
$308$		0			0
$309$		−	9.68104i		−	0.550735i
$310$	−0.380656	+	2.80283i	−0.0216198	+	0.159190i
$311$			29.4930i			1.67239i	0.548429	+	0.836197i	$0.315226\pi$
$311$			29.4930i			1.67239i	−0.548429	+	0.836197i	$0.684774\pi$
$312$	1.28575	−	1.28575i	0.0727914	−	0.0727914i
$313$	22.8714	−	22.8714i	1.29277	−	1.29277i	0.359701	−	0.933068i	$-0.382879\pi$
$313$	22.8714	−	22.8714i	1.29277	−	1.29277i	0.933068	−	0.359701i	$-0.117121\pi$
$314$	−7.32377			−0.413304
$315$		0			0
$316$	2.31721			0.130353
$317$	16.8344	−	16.8344i	0.945514	−	0.945514i	−0.0530763	−	0.998590i	$-0.516903\pi$
$317$	16.8344	−	16.8344i	0.945514	−	0.945514i	0.998590	+	0.0530763i	$0.0169026\pi$
$318$	−6.74356	+	6.74356i	−0.378160	+	0.378160i
$319$			12.4447i			0.696770i
$320$	−1.77954	+	1.35397i	−0.0994793	+	0.0756894i
$321$			15.2728i			0.852442i
$322$		0			0
$323$	−3.67964	−	3.67964i	−0.204741	−	0.204741i
$324$			1.00000i			0.0555556i
$325$	4.48133	+	7.91048i	0.248579	+	0.438794i
$326$	−10.9027			−0.603842
$327$	−0.681918	−	0.681918i	−0.0377101	−	0.0377101i
$328$	0.818802	−	0.818802i	0.0452108	−	0.0452108i
$329$		0			0
$330$	−4.35916	+	3.31669i	−0.239964	+	0.182578i
$331$	−29.1019			−1.59958			−0.799792	−	0.600277i	$-0.795057\pi$
$331$	−29.1019			−1.59958			−0.799792	+	0.600277i	$0.795057\pi$
$332$	−7.39632	−	7.39632i	−0.405926	−	0.405926i
$333$	−7.16021	−	7.16021i	−0.392377	−	0.392377i
$334$	−14.6924			−0.803931
$335$	−23.2323	−	3.15521i	−1.26932	−	0.172388i
$336$		0			0
$337$	−5.11616	+	5.11616i	−0.278695	+	0.278695i	−0.832588	−	0.553893i	$-0.813142\pi$
$337$	−5.11616	+	5.11616i	−0.278695	+	0.278695i	0.553893	+	0.832588i	$0.313142\pi$
$338$	6.85447	+	6.85447i	0.372834	+	0.372834i
$339$	14.2698			0.775031
$340$	16.7053	+	2.26877i	0.905971	+	0.123041i
$341$			3.09867i			0.167803i
$342$	0.488054	+	0.488054i	0.0263910	+	0.0263910i
$343$		0			0
$344$		−	1.26298i		−	0.0680952i
$345$	10.8190	+	14.2195i	0.582473	+	0.765550i
$346$			2.27529i			0.122320i
$347$	25.1758	−	25.1758i	1.35151	−	1.35151i	0.467530	−	0.883977i	$-0.345144\pi$
$347$	25.1758	−	25.1758i	1.35151	−	1.35151i	0.883977	−	0.467530i	$-0.154856\pi$
$348$	−3.59232	+	3.59232i	−0.192568	+	0.192568i
$349$	−8.57090			−0.458790			−0.229395	−	0.973333i	$-0.573675\pi$
$349$	−8.57090			−0.458790			−0.229395	+	0.973333i	$0.573675\pi$
$350$		0			0
$351$	1.81833			0.0970552
$352$	−1.73213	+	1.73213i	−0.0923228	+	0.0923228i
$353$	11.7033	−	11.7033i	0.622903	−	0.622903i	−0.323370	−	0.946273i	$-0.604816\pi$
$353$	11.7033	−	11.7033i	0.622903	−	0.622903i	0.946273	+	0.323370i	$0.104816\pi$
$354$			8.06376i			0.428584i
$355$	5.74199	+	7.54675i	0.304753	+	0.400540i
$356$			16.8162i			0.891255i
$357$		0			0
$358$	−6.79154	−	6.79154i	−0.358944	−	0.358944i
$359$			34.1296i			1.80129i	0.434553	+	0.900646i	$0.356906\pi$
$359$			34.1296i			1.80129i	−0.434553	+	0.900646i	$0.643094\pi$
$360$	−2.21573	−	0.300921i	−0.116779	−	0.0158599i
$361$	−18.5236			−0.974927
$362$	4.38117	+	4.38117i	0.230269	+	0.230269i
$363$	3.53515	−	3.53515i	0.185547	−	0.185547i
$364$		0			0
$365$	14.3767	+	1.95251i	0.752509	+	0.102199i
$366$	−1.09779			−0.0573821
$367$	−4.69129	−	4.69129i	−0.244883	−	0.244883i	0.573983	−	0.818867i	$-0.305397\pi$
$367$	−4.69129	−	4.69129i	−0.244883	−	0.244883i	−0.818867	+	0.573983i	$0.805397\pi$
$368$	5.65016	+	5.65016i	0.294535	+	0.294535i
$369$	1.15796			0.0602811
$370$	18.0197	−	13.7104i	0.936801	−	0.712770i
$371$		0			0
$372$	−0.894469	+	0.894469i	−0.0463761	+	0.0463761i
$373$	−14.9324	−	14.9324i	−0.773169	−	0.773169i	0.205490	−	0.978659i	$-0.434121\pi$
$373$	−14.9324	−	14.9324i	−0.773169	−	0.773169i	−0.978659	+	0.205490i	$0.934121\pi$
$374$	18.4686			0.954986
$375$	4.40482	−	10.2761i	0.227464	−	0.530654i
$376$		−	7.00773i		−	0.361396i
$377$	6.53201	+	6.53201i	0.336416	+	0.336416i
$378$		0			0
$379$		−	18.2436i		−	0.937112i	−0.883434	−	0.468556i	$-0.844774\pi$
$379$		−	18.2436i		−	0.937112i	0.883434	−	0.468556i	$-0.155226\pi$
$380$	−1.22826	+	0.934530i	−0.0630085	+	0.0479404i
$381$			7.74221i			0.396646i
$382$	−4.64588	+	4.64588i	−0.237704	+	0.237704i
$383$	20.2850	−	20.2850i	1.03652	−	1.03652i	0.0372095	−	0.999307i	$-0.488153\pi$
$383$	20.2850	−	20.2850i	1.03652	−	1.03652i	0.999307	−	0.0372095i	$-0.0118469\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	0.303338			0.0154395
$387$	0.893060	−	0.893060i	0.0453968	−	0.0453968i
$388$	4.74063	−	4.74063i	0.240669	−	0.240669i
$389$		−	1.87927i		−	0.0952830i	−0.998864	−	0.0476415i	$-0.984829\pi$
$389$		−	1.87927i		−	0.0952830i	0.998864	−	0.0476415i	$-0.0151705\pi$
$390$	−0.547173	+	4.02892i	−0.0277072	+	0.204012i
$391$		−	60.2439i		−	3.04667i
$392$		0			0
$393$	3.63534	+	3.63534i	0.183379	+	0.183379i
$394$		−	2.34319i		−	0.118048i
$395$	−4.12356	+	3.13743i	−0.207479	+	0.157861i
$396$	−2.44960			−0.123097
$397$	9.50826	+	9.50826i	0.477206	+	0.477206i	0.904237	−	0.427031i	$-0.140441\pi$
$397$	9.50826	+	9.50826i	0.477206	+	0.477206i	−0.427031	+	0.904237i	$0.640441\pi$
$398$	−13.8873	+	13.8873i	−0.696110	+	0.696110i
$399$		0			0
$400$	1.33352	−	4.81889i	0.0666759	−	0.240945i
$401$	23.5306			1.17506			0.587531	−	0.809202i	$-0.300100\pi$
$401$	23.5306			1.17506			0.587531	+	0.809202i	$0.300100\pi$
$402$	−7.41414	−	7.41414i	−0.369784	−	0.369784i
$403$	1.62644	+	1.62644i	0.0810187	+	0.0810187i
$404$	18.8914			0.939884
$405$	−1.35397	−	1.77954i	−0.0672794	−	0.0884260i
$406$		0			0
$407$	17.5397	−	17.5397i	0.869409	−	0.869409i
$408$	5.33117	+	5.33117i	0.263932	+	0.263932i
$409$	10.3255			0.510561			0.255281	−	0.966867i	$-0.417832\pi$
$409$	10.3255			0.510561			0.255281	+	0.966867i	$0.417832\pi$
$410$	−0.348455	+	2.56573i	−0.0172090	+	0.126712i
$411$			22.9175i			1.13044i
$412$	6.84553	+	6.84553i	0.337255	+	0.337255i
$413$		0			0
$414$			7.99053i			0.392713i
$415$	23.1765	+	3.14763i	1.13769	+	0.154511i
$416$			1.81833i			0.0891509i
$417$	4.00836	−	4.00836i	0.196290	−	0.196290i
$418$	−1.19554	+	1.19554i	−0.0584757	+	0.0584757i
$419$	−13.4099			−0.655115			−0.327557	−	0.944831i	$-0.606225\pi$
$419$	−13.4099			−0.655115			−0.327557	+	0.944831i	$0.606225\pi$
$420$		0			0
$421$	20.8227			1.01484			0.507419	−	0.861699i	$-0.330600\pi$
$421$	20.8227			1.01484			0.507419	+	0.861699i	$0.330600\pi$
$422$	−1.21059	+	1.21059i	−0.0589306	+	0.0589306i
$423$	4.95521	−	4.95521i	0.240931	−	0.240931i
$424$		−	9.53683i		−	0.463149i
$425$	−32.7995	+	18.5811i	−1.59101	+	0.901317i
$426$			4.24084i			0.205470i
$427$		0			0
$428$	−10.7995	−	10.7995i	−0.522012	−	0.522012i
$429$			4.45418i			0.215050i
$430$	1.71004	+	2.24752i	0.0824653	+	0.108385i
$431$	6.90210			0.332462			0.166231	−	0.986087i	$-0.446840\pi$
$431$	6.90210			0.332462			0.166231	+	0.986087i	$0.446840\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−8.92851	+	8.92851i	−0.429077	+	0.429077i	−0.888314	−	0.459237i	$-0.848123\pi$
$433$	−8.92851	+	8.92851i	−0.429077	+	0.429077i	0.459237	+	0.888314i	$0.348123\pi$
$434$		0			0
$435$	1.52877	−	11.2566i	0.0732989	−	0.539711i
$436$	0.964378			0.0461853
$437$	3.89981	+	3.89981i	0.186553	+	0.186553i
$438$	4.58803	+	4.58803i	0.219225	+	0.219225i
$439$	25.3064			1.20781			0.603903	−	0.797058i	$-0.293611\pi$
$439$	25.3064			1.20781			0.603903	+	0.797058i	$0.293611\pi$
$440$	0.737137	−	5.42765i	0.0351416	−	0.258753i
$441$		0			0
$442$	9.69382	−	9.69382i	0.461088	−	0.461088i
$443$	6.31933	+	6.31933i	0.300241	+	0.300241i	0.841108	−	0.540867i	$-0.181904\pi$
$443$	6.31933	+	6.31933i	0.300241	+	0.300241i	−0.540867	+	0.841108i	$0.681904\pi$
$444$	10.1261			0.480562
$445$	−22.7686	−	29.9250i	−1.07934	−	1.41858i
$446$			27.8889i			1.32058i
$447$	8.26921	+	8.26921i	0.391120	+	0.391120i
$448$		0			0
$449$			15.5429i			0.733514i	0.930317	+	0.366757i	$0.119532\pi$
$449$			15.5429i			0.733514i	−0.930317	+	0.366757i	$0.880468\pi$
$450$	4.35041	−	2.46453i	0.205080	−	0.116179i
$451$			2.83654i			0.133568i
$452$	−10.0903	+	10.0903i	−0.474607	+	0.474607i
$453$	−11.7590	+	11.7590i	−0.552485	+	0.552485i
$454$	−27.9446			−1.31150
$455$		0			0
$456$	−0.690213			−0.0323222
$457$	22.6684	−	22.6684i	1.06039	−	1.06039i	0.0623294	−	0.998056i	$-0.480147\pi$
$457$	22.6684	−	22.6684i	1.06039	−	1.06039i	0.998056	−	0.0623294i	$-0.0198529\pi$
$458$	−1.44487	+	1.44487i	−0.0675143	+	0.0675143i
$459$			7.53941i			0.351910i
$460$	−17.7048	−	2.40452i	−0.825492	−	0.112111i
$461$			11.0867i			0.516361i	0.966097	+	0.258181i	$0.0831229\pi$
$461$			11.0867i			0.516361i	−0.966097	+	0.258181i	$0.916877\pi$
$462$		0			0
$463$	7.15110	+	7.15110i	0.332340	+	0.332340i	0.853474	−	0.521135i	$-0.174491\pi$
$463$	7.15110	+	7.15110i	0.332340	+	0.332340i	−0.521135	+	0.853474i	$0.674491\pi$
$464$		−	5.08030i		−	0.235847i
$465$	0.380656	−	2.80283i	0.0176525	−	0.129978i
$466$	−3.19959			−0.148218
$467$	1.01418	+	1.01418i	0.0469309	+	0.0469309i	0.730183	−	0.683252i	$-0.239435\pi$
$467$	1.01418	+	1.01418i	0.0469309	+	0.0469309i	−0.683252	+	0.730183i	$0.739435\pi$
$468$	−1.28575	+	1.28575i	−0.0594339	+	0.0594339i
$469$		0			0
$470$	9.48827	+	12.4705i	0.437661	+	0.575223i
$471$	7.32377			0.337462
$472$	−5.70194	−	5.70194i	−0.262453	−	0.262453i
$473$	2.18764	+	2.18764i	0.100588	+	0.100588i
$474$	−2.31721			−0.106433
$475$	0.920412	−	3.32606i	0.0422314	−	0.152610i
$476$		0			0
$477$	6.74356	−	6.74356i	0.308766	−	0.308766i
$478$	−13.9306	−	13.9306i	−0.637172	−	0.637172i
$479$	−5.61498			−0.256555			−0.128277	−	0.991738i	$-0.540945\pi$
$479$	−5.61498			−0.256555			−0.128277	+	0.991738i	$0.540945\pi$
$480$	1.77954	−	1.35397i	0.0812245	−	0.0618001i
$481$		−	18.4125i		−	0.839538i
$482$	−4.27447	−	4.27447i	−0.194697	−	0.194697i
$483$		0			0
$484$			4.99945i			0.227248i
$485$	−2.01745	+	14.8548i	−0.0916078	+	0.674522i
$486$		−	1.00000i		−	0.0453609i
$487$	19.7480	−	19.7480i	0.894867	−	0.894867i	−0.100110	−	0.994976i	$-0.531919\pi$
$487$	19.7480	−	19.7480i	0.894867	−	0.894867i	0.994976	+	0.100110i	$0.0319193\pi$
$488$	0.776251	−	0.776251i	0.0351392	−	0.0351392i
$489$	10.9027			0.493035
$490$		0			0
$491$	−13.7125			−0.618838			−0.309419	−	0.950926i	$-0.600135\pi$
$491$	−13.7125			−0.618838			−0.309419	+	0.950926i	$0.600135\pi$
$492$	−0.818802	+	0.818802i	−0.0369145	+	0.0369145i
$493$	−27.0839	+	27.0839i	−1.21980	+	1.21980i
$494$			1.25503i			0.0564667i
$495$	4.35916	−	3.31669i	0.195930	−	0.149074i
$496$		−	1.26497i		−	0.0567989i
$497$		0			0
$498$	7.39632	+	7.39632i	0.331437	+	0.331437i
$499$			32.2153i			1.44215i	0.692855	+	0.721077i	$0.256352\pi$
$499$			32.2153i			1.44215i	−0.692855	+	0.721077i	$0.743648\pi$
$500$	4.15160	+	10.3810i	0.185665	+	0.464250i
$501$	14.6924			0.656407
$502$	−9.03657	−	9.03657i	−0.403322	−	0.403322i
$503$	10.2179	−	10.2179i	0.455593	−	0.455593i	−0.441613	−	0.897206i	$-0.645594\pi$
$503$	10.2179	−	10.2179i	0.455593	−	0.455593i	0.897206	+	0.441613i	$0.145594\pi$
$504$		0			0
$505$	−33.6180	+	25.5785i	−1.49598	+	1.13823i
$506$	−19.5736			−0.870153
$507$	−6.85447	−	6.85447i	−0.304418	−	0.304418i
$508$	−5.47457	−	5.47457i	−0.242895	−	0.242895i
$509$	−5.73735			−0.254304			−0.127152	−	0.991883i	$-0.540584\pi$
$509$	−5.73735			−0.254304			−0.127152	+	0.991883i	$0.540584\pi$
$510$	−16.7053	−	2.26877i	−0.739722	−	0.100463i
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−0.488054	−	0.488054i	−0.0215481	−	0.0215481i
$514$	18.9503			0.835861
$515$	−21.4505	−	2.91323i	−0.945224	−	0.128372i
$516$			1.26298i			0.0555995i
$517$	12.1383	+	12.1383i	0.533842	+	0.533842i
$518$		0			0
$519$		−	2.27529i		−	0.0998741i
$520$	−2.46197	−	3.23579i	−0.107964	−	0.141899i
$521$		−	4.35849i		−	0.190949i	−0.995432	−	0.0954745i	$-0.969563\pi$
$521$		−	4.35849i		−	0.190949i	0.995432	−	0.0954745i	$-0.0304368\pi$
$522$	3.59232	−	3.59232i	0.157231	−	0.157231i
$523$	−13.8496	+	13.8496i	−0.605601	+	0.605601i	−0.941793	−	0.336192i	$-0.890861\pi$
$523$	−13.8496	+	13.8496i	−0.605601	+	0.605601i	0.336192	+	0.941793i	$0.390861\pi$
$524$	−5.14115			−0.224592
$525$		0			0
$526$	−17.3546			−0.756697
$527$	−6.74377	+	6.74377i	−0.293763	+	0.293763i
$528$	1.73213	−	1.73213i	0.0753813	−	0.0753813i
$529$			40.8486i			1.77603i
$530$	12.9126	+	16.9712i	0.560888	+	0.737180i
$531$		−	8.06376i		−	0.349937i
$532$		0			0
$533$	1.48885	+	1.48885i	0.0644893	+	0.0644893i
$534$		−	16.8162i		−	0.727706i
$535$	33.8403	+	4.59590i	1.46304	+	0.198698i
$536$	10.4852			0.452891
$537$	6.79154	+	6.79154i	0.293077	+	0.293077i
$538$	−11.5422	+	11.5422i	−0.497617	+	0.497617i
$539$		0			0
$540$	2.21573	+	0.300921i	0.0953497	+	0.0129496i
$541$	−12.1108			−0.520684			−0.260342	−	0.965516i	$-0.583835\pi$
$541$	−12.1108			−0.520684			−0.260342	+	0.965516i	$0.583835\pi$
$542$	−12.1087	−	12.1087i	−0.520112	−	0.520112i
$543$	−4.38117	−	4.38117i	−0.188014	−	0.188014i
$544$	−7.53941			−0.323250
$545$	−1.71615	+	1.30574i	−0.0735117	+	0.0559318i
$546$		0			0
$547$	−2.16237	+	2.16237i	−0.0924565	+	0.0924565i	−0.751822	−	0.659366i	$-0.770825\pi$
$547$	−2.16237	+	2.16237i	−0.0924565	+	0.0924565i	0.659366	+	0.751822i	$0.270825\pi$
$548$	−16.2051	−	16.2051i	−0.692249	−	0.692249i
$549$	1.09779			0.0468523
$550$	6.03712	+	10.6568i	0.257424	+	0.454406i
$551$		−	3.50649i		−	0.149382i
$552$	−5.65016	−	5.65016i	−0.240487	−	0.240487i
$553$		0			0
$554$			27.8622i			1.18375i
$555$	−18.0197	+	13.7104i	−0.764895	+	0.581975i
$556$			5.66867i			0.240405i
$557$	−10.0772	+	10.0772i	−0.426985	+	0.426985i	−0.887600	−	0.460615i	$-0.847629\pi$
$557$	−10.0772	+	10.0772i	−0.426985	+	0.426985i	0.460615	+	0.887600i	$0.347629\pi$
$558$	0.894469	−	0.894469i	0.0378659	−	0.0378659i
$559$	2.29651			0.0971319
$560$		0			0
$561$	−18.4686			−0.779743
$562$	−7.97202	+	7.97202i	−0.336279	+	0.336279i
$563$	20.9737	−	20.9737i	0.883938	−	0.883938i	−0.109994	−	0.993932i	$-0.535083\pi$
$563$	20.9737	−	20.9737i	0.883938	−	0.883938i	0.993932	+	0.109994i	$0.0350832\pi$
$564$			7.00773i			0.295079i
$565$	4.29409	−	31.6180i	0.180654	−	1.33018i
$566$			26.0804i			1.09624i
$567$		0			0
$568$	−2.99873	−	2.99873i	−0.125824	−	0.125824i
$569$		−	16.7597i		−	0.702603i	−0.936262	−	0.351301i	$-0.885739\pi$
$569$		−	16.7597i		−	0.702603i	0.936262	−	0.351301i	$-0.114261\pi$
$570$	1.22826	−	0.934530i	0.0514462	−	0.0391431i
$571$	36.4781			1.52656			0.763280	−	0.646068i	$-0.223588\pi$
$571$	36.4781			1.52656			0.763280	+	0.646068i	$0.223588\pi$
$572$	−3.14958	−	3.14958i	−0.131691	−	0.131691i
$573$	4.64588	−	4.64588i	0.194084	−	0.194084i
$574$		0			0
$575$	34.7621	−	19.6929i	1.44968	−	0.821252i
$576$	1.00000			0.0416667
$577$	16.1203	+	16.1203i	0.671098	+	0.671098i	0.957969	−	0.286871i	$-0.0926152\pi$
$577$	16.1203	+	16.1203i	0.671098	+	0.671098i	−0.286871	+	0.957969i	$0.592615\pi$
$578$	28.1731	+	28.1731i	1.17185	+	1.17185i
$579$	−0.303338			−0.0126063
$580$	6.87859	+	9.04059i	0.285618	+	0.375390i
$581$		0			0
$582$	−4.74063	+	4.74063i	−0.196505	+	0.196505i
$583$	16.5190	+	16.5190i	0.684148	+	0.684148i
$584$	−6.48846			−0.268494
$585$	0.547173	−	4.02892i	0.0226228	−	0.166575i
$586$		−	2.10538i		−	0.0869726i
$587$	7.12788	+	7.12788i	0.294199	+	0.294199i	0.838737	−	0.544537i	$-0.183295\pi$
$587$	7.12788	+	7.12788i	0.294199	+	0.294199i	−0.544537	+	0.838737i	$0.683295\pi$
$588$		0			0
$589$		−	0.873100i		−	0.0359754i
$590$	17.8671	+	2.42655i	0.735576	+	0.0998996i
$591$			2.34319i			0.0963859i
$592$	−7.16021	+	7.16021i	−0.294283	+	0.294283i
$593$	24.3485	−	24.3485i	0.999874	−	0.999874i	−0.000126141	−	1.00000i	$-0.500040\pi$
$593$	24.3485	−	24.3485i	0.999874	−	0.999874i	1.00000		0.000126141i	$4.01518e-5\pi$
$594$	2.44960			0.100508
$595$		0			0
$596$	−11.6944			−0.479022
$597$	13.8873	−	13.8873i	0.568371	−	0.568371i
$598$	−10.2738	+	10.2738i	−0.420129	+	0.420129i
$599$			10.8206i			0.442117i	0.975261	+	0.221058i	$0.0709511\pi$
$599$			10.8206i			0.442117i	−0.975261	+	0.221058i	$0.929049\pi$
$600$	−1.33352	+	4.81889i	−0.0544406	+	0.196730i
$601$		−	4.06861i		−	0.165962i	−0.996551	−	0.0829811i	$-0.973556\pi$
$601$		−	4.06861i		−	0.165962i	0.996551	−	0.0829811i	$-0.0264441\pi$
$602$		0			0
$603$	7.41414	+	7.41414i	0.301927	+	0.301927i
$604$		−	16.6297i		−	0.676654i
$605$	−6.76912	−	8.89672i	−0.275204	−	0.361703i
$606$	−18.8914			−0.767412
$607$	−12.9641	−	12.9641i	−0.526197	−	0.526197i	0.393239	−	0.919436i	$-0.371355\pi$
$607$	−12.9641	−	12.9641i	−0.526197	−	0.526197i	−0.919436	+	0.393239i	$0.871355\pi$
$608$	0.488054	−	0.488054i	0.0197932	−	0.0197932i
$609$		0			0
$610$	−0.330347	+	2.43239i	−0.0133753	+	0.0984847i
$611$	12.7424			0.515500
$612$	−5.33117	−	5.33117i	−0.215500	−	0.215500i
$613$	−26.7072	−	26.7072i	−1.07870	−	1.07870i	−0.996627	−	0.0820683i	$-0.973847\pi$
$613$	−26.7072	−	26.7072i	−1.07870	−	1.07870i	−0.0820683	−	0.996627i	$-0.526153\pi$
$614$	−31.3034			−1.26330
$615$	0.348455	−	2.56573i	0.0140511	−	0.103460i
$616$		0			0
$617$	−10.0471	+	10.0471i	−0.404479	+	0.404479i	−0.879808	−	0.475329i	$-0.842329\pi$
$617$	−10.0471	+	10.0471i	−0.404479	+	0.404479i	0.475329	+	0.879808i	$0.342329\pi$
$618$	−6.84553	−	6.84553i	−0.275368	−	0.275368i
$619$	−18.1838			−0.730869			−0.365434	−	0.930837i	$-0.619079\pi$
$619$	−18.1838			−0.730869			−0.365434	+	0.930837i	$0.619079\pi$
$620$	1.71274	+	2.25106i	0.0687851	+	0.0904049i
$621$		−	7.99053i		−	0.320649i
$622$	20.8547	+	20.8547i	0.836197	+	0.836197i
$623$		0			0
$624$		−	1.81833i		−	0.0727914i
$625$	−21.4435	−	12.8522i	−0.857738	−	0.514086i
$626$		−	32.3451i		−	1.29277i
$627$	1.19554	−	1.19554i	0.0477452	−	0.0477452i
$628$	−5.17869	+	5.17869i	−0.206652	+	0.206652i
$629$	76.3446			3.04406
$630$		0			0
$631$	−27.7104			−1.10314			−0.551568	−	0.834130i	$-0.685970\pi$
$631$	−27.7104			−1.10314			−0.551568	+	0.834130i	$0.685970\pi$
$632$	1.63851	−	1.63851i	0.0651765	−	0.0651765i
$633$	1.21059	−	1.21059i	0.0481166	−	0.0481166i
$634$		−	23.8074i		−	0.945514i
$635$	17.1546	+	2.32980i	0.680761	+	0.0924551i
$636$			9.53683i			0.378160i
$637$		0			0
$638$	8.79974	+	8.79974i	0.348385	+	0.348385i
$639$		−	4.24084i		−	0.167765i
$640$	−0.300921	+	2.21573i	−0.0118949	+	0.0875843i
$641$	−5.23987			−0.206962			−0.103481	−	0.994631i	$-0.532998\pi$
$641$	−5.23987			−0.206962			−0.103481	+	0.994631i	$0.532998\pi$
$642$	10.7995	+	10.7995i	0.426221	+	0.426221i
$643$	12.9239	−	12.9239i	0.509669	−	0.509669i	−0.404756	−	0.914425i	$-0.632643\pi$
$643$	12.9239	−	12.9239i	0.509669	−	0.509669i	0.914425	+	0.404756i	$0.132643\pi$
$644$		0			0
$645$	−1.71004	−	2.24752i	−0.0673326	−	0.0884959i
$646$	−5.20380			−0.204741
$647$	−30.7971	−	30.7971i	−1.21076	−	1.21076i	−0.970778	−	0.239979i	$-0.922859\pi$
$647$	−30.7971	−	30.7971i	−1.21076	−	1.21076i	−0.239979	−	0.970778i	$-0.577141\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	19.7530			0.775372
$650$	8.76233	+	2.42477i	0.343687	+	0.0951074i
$651$		0			0
$652$	−7.70934	+	7.70934i	−0.301921	+	0.301921i
$653$	−20.7989	−	20.7989i	−0.813925	−	0.813925i	0.171295	−	0.985220i	$-0.445205\pi$
$653$	−20.7989	−	20.7989i	−0.813925	−	0.813925i	−0.985220	+	0.171295i	$0.945205\pi$
$654$	−0.964378			−0.0377101
$655$	9.14888	−	6.96098i	0.357476	−	0.271988i
$656$		−	1.15796i		−	0.0452108i
$657$	−4.58803	−	4.58803i	−0.178996	−	0.178996i
$658$		0			0
$659$			43.4005i			1.69064i	0.534258	+	0.845321i	$0.320591\pi$
$659$			43.4005i			1.69064i	−0.534258	+	0.845321i	$0.679409\pi$
$660$	−0.737137	+	5.42765i	−0.0286930	+	0.211271i
$661$		−	30.7709i		−	1.19685i	−0.801179	−	0.598425i	$-0.795793\pi$
$661$		−	30.7709i		−	1.19685i	0.801179	−	0.598425i	$-0.204207\pi$
$662$	−20.5781	+	20.5781i	−0.799792	+	0.799792i
$663$	−9.69382	+	9.69382i	−0.376477	+	0.376477i
$664$	−10.4600			−0.405926
$665$		0			0
$666$	−10.1261			−0.392377
$667$	28.7045	−	28.7045i	1.11144	−	1.11144i
$668$	−10.3891	+	10.3891i	−0.401965	+	0.401965i
$669$		−	27.8889i		−	1.07825i
$670$	−18.6588	+	14.1966i	−0.720852	+	0.548464i
$671$			2.68914i			0.103813i
$672$		0			0
$673$	10.5593	+	10.5593i	0.407032	+	0.407032i	0.880702	−	0.473670i	$-0.157071\pi$
$673$	10.5593	+	10.5593i	0.407032	+	0.407032i	−0.473670	+	0.880702i	$0.657071\pi$
$674$			7.23534i			0.278695i
$675$	−4.35041	+	2.46453i	−0.167447	+	0.0948599i
$676$	9.69368			0.372834
$677$	−10.3276	−	10.3276i	−0.396922	−	0.396922i	0.480224	−	0.877146i	$-0.340555\pi$
$677$	−10.3276	−	10.3276i	−0.396922	−	0.396922i	−0.877146	+	0.480224i	$0.840555\pi$
$678$	10.0903	−	10.0903i	0.387515	−	0.387515i
$679$		0			0
$680$	13.4167	−	10.2082i	0.514506	−	0.391465i
$681$	27.9446			1.07084
$682$	2.19109	+	2.19109i	0.0839013	+	0.0839013i
$683$	−1.17090	−	1.17090i	−0.0448034	−	0.0448034i	0.684350	−	0.729154i	$-0.260086\pi$
$683$	−1.17090	−	1.17090i	−0.0448034	−	0.0448034i	−0.729154	+	0.684350i	$0.760086\pi$
$684$	0.690213			0.0263910
$685$	50.7790	+	6.89637i	1.94017	+	0.263497i
$686$		0			0
$687$	1.44487	−	1.44487i	0.0551252	−	0.0551252i
$688$	−0.893060	−	0.893060i	−0.0340476	−	0.0340476i
$689$	17.3411			0.660643
$690$	17.7048	+	2.40452i	0.674012	+	0.0915385i
$691$			7.91595i			0.301137i	0.988600	+	0.150569i	$0.0481104\pi$
$691$			7.91595i			0.301137i	−0.988600	+	0.150569i	$0.951890\pi$
$692$	1.60887	+	1.60887i	0.0611602	+	0.0611602i
$693$		0			0
$694$		−	35.6039i		−	1.35151i
$695$	−7.67522	−	10.0876i	−0.291138	−	0.382645i
$696$			5.08030i			0.192568i
$697$	−6.17329	+	6.17329i	−0.233830	+	0.233830i
$698$	−6.06054	+	6.06054i	−0.229395	+	0.229395i
$699$	3.19959			0.121019
$700$		0			0
$701$	−32.9545			−1.24467			−0.622337	−	0.782750i	$-0.713816\pi$
$701$	−32.9545			−1.24467			−0.622337	+	0.782750i	$0.713816\pi$
$702$	1.28575	−	1.28575i	0.0485276	−	0.0485276i
$703$	−4.94207	+	4.94207i	−0.186394	+	0.186394i
$704$			2.44960i			0.0923228i
$705$	−9.48827	−	12.4705i	−0.357349	−	0.469667i
$706$		−	16.5509i		−	0.622903i
$707$		0			0
$708$	5.70194	+	5.70194i	0.214292	+	0.214292i
$709$		−	21.6205i		−	0.811974i	−0.913879	−	0.405987i	$-0.866928\pi$
$709$		−	21.6205i		−	0.811974i	0.913879	−	0.405987i	$-0.133072\pi$
$710$	9.39655	+	1.27616i	0.352646	+	0.0478934i
$711$	2.31721			0.0869020
$712$	11.8908	+	11.8908i	0.445627	+	0.445627i
$713$	7.14729	−	7.14729i	0.267668	−	0.267668i
$714$		0			0
$715$	9.86925	+	1.34036i	0.369089	+	0.0501265i
$716$	−9.60469			−0.358944
$717$	13.9306	+	13.9306i	0.520249	+	0.520249i
$718$	24.1333	+	24.1333i	0.900646	+	0.900646i
$719$	−9.49541			−0.354119			−0.177060	−	0.984200i	$-0.556659\pi$
$719$	−9.49541			−0.354119			−0.177060	+	0.984200i	$0.556659\pi$
$720$	−1.77954	+	1.35397i	−0.0663195	+	0.0504596i
$721$		0			0
$722$	−13.0982	+	13.0982i	−0.487463	+	0.487463i
$723$	4.27447	+	4.27447i	0.158969	+	0.158969i
$724$	6.19591			0.230269
$725$	−24.4814	−	6.77467i	−0.909217	−	0.251605i
$726$		−	4.99945i		−	0.185547i
$727$	3.23075	+	3.23075i	0.119822	+	0.119822i	0.764475	−	0.644653i	$-0.222998\pi$
$727$	3.23075	+	3.23075i	0.119822	+	0.119822i	−0.644653	+	0.764475i	$0.722998\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	11.5465	−	8.78520i	0.427354	−	0.325155i
$731$			9.52211i			0.352188i
$732$	−0.776251	+	0.776251i	−0.0286911	+	0.0286911i
$733$	15.1024	−	15.1024i	0.557820	−	0.557820i	−0.370866	−	0.928686i	$-0.620939\pi$
$733$	15.1024	−	15.1024i	0.557820	−	0.557820i	0.928686	+	0.370866i	$0.120939\pi$
$734$	−6.63449			−0.244883
$735$		0			0
$736$	7.99053			0.294535
$737$	−18.1617	+	18.1617i	−0.668995	+	0.668995i
$738$	0.818802	−	0.818802i	0.0301405	−	0.0301405i
$739$		−	7.42649i		−	0.273188i	−0.990627	−	0.136594i	$-0.956384\pi$
$739$		−	7.42649i		−	0.273188i	0.990627	−	0.136594i	$-0.0436155\pi$
$740$	3.04715	−	22.4366i	0.112015	−	0.824786i
$741$		−	1.25503i		−	0.0461048i
$742$		0			0
$743$	14.3245	+	14.3245i	0.525515	+	0.525515i	0.919232	−	0.393717i	$-0.128811\pi$
$743$	14.3245	+	14.3245i	0.525515	+	0.525515i	−0.393717	+	0.919232i	$0.628811\pi$
$744$			1.26497i			0.0463761i
$745$	20.8107	−	15.8339i	0.762444	−	0.580110i
$746$	−21.1176			−0.773169
$747$	−7.39632	−	7.39632i	−0.270617	−	0.270617i
$748$	13.0592	−	13.0592i	0.477493	−	0.477493i
$749$		0			0
$750$	−4.15160	−	10.3810i	−0.151595	−	0.379059i
$751$	−35.9783			−1.31287			−0.656433	−	0.754384i	$-0.727936\pi$
$751$	−35.9783			−1.31287			−0.656433	+	0.754384i	$0.727936\pi$
$752$	−4.95521	−	4.95521i	−0.180698	−	0.180698i
$753$	9.03657	+	9.03657i	0.329311	+	0.329311i
$754$	9.23765			0.336416
$755$	22.5162	+	29.5932i	0.819447	+	1.07701i
$756$		0			0
$757$	−10.7626	+	10.7626i	−0.391172	+	0.391172i	−0.875105	−	0.483933i	$-0.839208\pi$
$757$	−10.7626	+	10.7626i	−0.391172	+	0.391172i	0.483933	+	0.875105i	$0.339208\pi$
$758$	−12.9002	−	12.9002i	−0.468556	−	0.468556i
$759$	19.5736			0.710477
$760$	−0.207700	+	1.52932i	−0.00753406	+	0.0554744i
$761$		−	23.9419i		−	0.867891i	−0.900939	−	0.433946i	$-0.857121\pi$
$761$		−	23.9419i		−	0.867891i	0.900939	−	0.433946i	$-0.142879\pi$
$762$	5.47457	+	5.47457i	0.198323	+	0.198323i
$763$		0			0
$764$			6.57026i			0.237704i
$765$	16.7053	+	2.26877i	0.603981	+	0.0820275i
$766$		−	28.6874i		−	1.03652i
$767$	10.3680	−	10.3680i	0.374366	−	0.374366i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−4.82317			−0.173928			−0.0869639	−	0.996211i	$-0.527716\pi$
$769$	−4.82317			−0.173928			−0.0869639	+	0.996211i	$0.527716\pi$
$770$		0			0
$771$	−18.9503			−0.682478
$772$	0.214493	−	0.214493i	0.00771976	−	0.00771976i
$773$	−26.8007	+	26.8007i	−0.963953	+	0.963953i	−0.999373	−	0.0354198i	$-0.988723\pi$
$773$	−26.8007	+	26.8007i	−0.963953	+	0.963953i	0.0354198	+	0.999373i	$0.488723\pi$
$774$		−	1.26298i		−	0.0453968i
$775$	−6.09576	−	1.68686i	−0.218966	−	0.0605938i
$776$		−	6.70426i		−	0.240669i
$777$		0			0
$778$	−1.32885	−	1.32885i	−0.0476415	−	0.0476415i
$779$		−	0.799240i		−	0.0286358i
$780$	2.46197	+	3.23579i	0.0881525	+	0.115860i
$781$	10.3884			0.371725
$782$	−42.5989	−	42.5989i	−1.52333	−	1.52333i
$783$	−3.59232	+	3.59232i	−0.128379	+	0.128379i
$784$		0			0
$785$	2.20388	−	16.2275i	0.0786598	−	0.579184i
$786$	5.14115			0.183379
$787$	10.8448	+	10.8448i	0.386574	+	0.386574i	0.873463	−	0.486890i	$-0.161869\pi$
$787$	10.8448	+	10.8448i	0.386574	+	0.386574i	−0.486890	+	0.873463i	$0.661869\pi$
$788$	−1.65688	−	1.65688i	−0.0590240	−	0.0590240i
$789$	17.3546			0.617840
$790$	−0.697296	+	5.13429i	−0.0248087	+	0.182670i
$791$		0			0
$792$	−1.73213	+	1.73213i	−0.0615485	+	0.0615485i
$793$	1.41148	+	1.41148i	0.0501231	+	0.0501231i
$794$	13.4467			0.477206
$795$	−12.9126	−	16.9712i	−0.457963	−	0.601905i
$796$			19.6397i			0.696110i
$797$	16.6466	+	16.6466i	0.589653	+	0.589653i	0.937538	−	0.347884i	$-0.113100\pi$
$797$	16.6466	+	16.6466i	0.589653	+	0.589653i	−0.347884	+	0.937538i	$0.613100\pi$
$798$		0			0
$799$			52.8342i			1.86914i
$800$	−2.46453	−	4.35041i	−0.0871344	−	0.153810i
$801$			16.8162i			0.594170i
$802$	16.6386	−	16.6386i	0.587531	−	0.587531i
$803$	11.2389	−	11.2389i	0.396611	−	0.396611i
$804$	−10.4852			−0.369784
$805$		0			0
$806$	2.30013			0.0810187
$807$	11.5422	−	11.5422i	0.406303	−	0.406303i
$808$	13.3583	−	13.3583i	0.469942	−	0.469942i
$809$			46.0937i			1.62057i	0.586036	+	0.810285i	$0.300688\pi$
$809$			46.0937i			1.62057i	−0.586036	+	0.810285i	$0.699312\pi$
$810$	−2.21573	−	0.300921i	−0.0778527	−	0.0105733i
$811$		−	51.4810i		−	1.80774i	−0.427805	−	0.903871i	$-0.640713\pi$
$811$		−	51.4810i		−	1.80774i	0.427805	−	0.903871i	$-0.359287\pi$
$812$		0			0
$813$	12.1087	+	12.1087i	0.424670	+	0.424670i
$814$		−	24.8048i		−	0.869409i
$815$	3.28084	−	24.1573i	0.114923	−	0.846193i
$816$	7.53941			0.263932
$817$	−0.616402	−	0.616402i	−0.0215652	−	0.0215652i
$818$	7.30120	−	7.30120i	0.255281	−	0.255281i
$819$		0			0
$820$	1.56785	+	2.06064i	0.0547516	+	0.0719606i
$821$	35.1335			1.22617			0.613083	−	0.790018i	$-0.289929\pi$
$821$	35.1335			1.22617			0.613083	+	0.790018i	$0.289929\pi$
$822$	16.2051	+	16.2051i	0.565219	+	0.565219i
$823$	21.7533	+	21.7533i	0.758272	+	0.758272i	0.976008	−	0.217736i	$-0.0698671\pi$
$823$	21.7533	+	21.7533i	0.758272	+	0.758272i	−0.217736	+	0.976008i	$0.569867\pi$
$824$	9.68104			0.337255
$825$	−6.03712	−	10.6568i	−0.210186	−	0.371021i
$826$		0			0
$827$	−1.51688	+	1.51688i	−0.0527471	+	0.0527471i	−0.732988	−	0.680241i	$-0.761875\pi$
$827$	−1.51688	+	1.51688i	−0.0527471	+	0.0527471i	0.680241	+	0.732988i	$0.261875\pi$
$828$	5.65016	+	5.65016i	0.196357	+	0.196357i
$829$	−16.8789			−0.586227			−0.293114	−	0.956078i	$-0.594691\pi$
$829$	−16.8789			−0.586227			−0.293114	+	0.956078i	$0.594691\pi$
$830$	18.6139	−	14.1625i	0.646099	−	0.491588i
$831$		−	27.8622i		−	0.966528i
$832$	1.28575	+	1.28575i	0.0445754	+	0.0445754i
$833$		0			0
$834$		−	5.66867i		−	0.196290i
$835$	4.42125	−	32.5543i	0.153003	−	1.12659i
$836$			1.69075i			0.0584757i
$837$	−0.894469	+	0.894469i	−0.0309174	+	0.0309174i
$838$	−9.48221	+	9.48221i	−0.327557	+	0.327557i
$839$	21.1069			0.728691			0.364346	−	0.931264i	$-0.381293\pi$
$839$	21.1069			0.728691			0.364346	+	0.931264i	$0.381293\pi$
$840$		0			0
$841$	3.19054			0.110019
$842$	14.7239	−	14.7239i	0.507419	−	0.507419i
$843$	7.97202	−	7.97202i	0.274571	−	0.274571i
$844$			1.71203i			0.0589306i
$845$	−17.2503	+	13.1250i	−0.593428	+	0.451513i
$846$		−	7.00773i		−	0.240931i
$847$		0			0
$848$	−6.74356	−	6.74356i	−0.231575	−	0.231575i
$849$		−	26.0804i		−	0.895077i
$850$	−10.0539	+	36.3316i	−0.344847	+	1.24616i
$851$	−80.9127			−2.77365
$852$	2.99873	+	2.99873i	0.102735	+	0.102735i
$853$	−35.4946	+	35.4946i	−1.21531	+	1.21531i	−0.246058	+	0.969255i	$0.579135\pi$
$853$	−35.4946	+	35.4946i	−1.21531	+	1.21531i	−0.969255	+	0.246058i	$0.920865\pi$
$854$		0			0
$855$	−1.22826	+	0.934530i	−0.0420057	+	0.0319602i
$856$	−15.2728			−0.522012
$857$	15.1895	+	15.1895i	0.518863	+	0.518863i	0.917227	−	0.398364i	$-0.130422\pi$
$857$	15.1895	+	15.1895i	0.518863	+	0.518863i	−0.398364	+	0.917227i	$0.630422\pi$
$858$	3.14958	+	3.14958i	0.107525	+	0.107525i
$859$	9.24777			0.315530			0.157765	−	0.987477i	$-0.449571\pi$
$859$	9.24777			0.315530			0.157765	+	0.987477i	$0.449571\pi$
$860$	2.79841	+	0.380057i	0.0954251	+	0.0129598i
$861$		0			0
$862$	4.88052	−	4.88052i	0.166231	−	0.166231i
$863$	−1.12455	−	1.12455i	−0.0382801	−	0.0382801i	0.687708	−	0.725988i	$-0.258617\pi$
$863$	−1.12455	−	1.12455i	−0.0382801	−	0.0382801i	−0.725988	+	0.687708i	$0.758617\pi$
$864$	−1.00000			−0.0340207
$865$	−5.04142	−	0.684682i	−0.171413	−	0.0232799i
$866$			12.6268i			0.429077i
$867$	−28.1731	−	28.1731i	−0.956808	−	0.956808i
$868$		0			0
$869$			5.67623i			0.192553i
$870$	−6.87859	−	9.04059i	−0.233206	−	0.306505i
$871$			19.0655i			0.646010i
$872$	0.681918	−	0.681918i	0.0230927	−	0.0230927i
$873$	4.74063	−	4.74063i	0.160446	−	0.160446i
$874$	5.51517			0.186553
$875$		0			0
$876$	6.48846			0.219225
$877$	18.4475	−	18.4475i	0.622928	−	0.622928i	−0.323351	−	0.946279i	$-0.604809\pi$
$877$	18.4475	−	18.4475i	0.622928	−	0.622928i	0.946279	+	0.323351i	$0.104809\pi$
$878$	17.8943	−	17.8943i	0.603903	−	0.603903i
$879$			2.10538i			0.0710129i
$880$	−3.31669	−	4.35916i	−0.111806	−	0.146947i
$881$		−	3.50861i		−	0.118208i	−0.998252	−	0.0591040i	$-0.981176\pi$
$881$		−	3.50861i		−	0.118208i	0.998252	−	0.0591040i	$-0.0188244\pi$
$882$		0			0
$883$	−16.4167	−	16.4167i	−0.552465	−	0.552465i	0.374687	−	0.927152i	$-0.377750\pi$
$883$	−16.4167	−	16.4167i	−0.552465	−	0.552465i	−0.927152	+	0.374687i	$0.877750\pi$
$884$		−	13.7091i		−	0.461088i
$885$	−17.8671	−	2.42655i	−0.600595	−	0.0815677i
$886$	8.93689			0.300241
$887$	4.94287	+	4.94287i	0.165965	+	0.165965i	0.785203	−	0.619238i	$-0.212558\pi$
$887$	4.94287	+	4.94287i	0.165965	+	0.165965i	−0.619238	+	0.785203i	$0.712558\pi$
$888$	7.16021	−	7.16021i	0.240281	−	0.240281i
$889$		0			0
$890$	−37.2600	−	5.06034i	−1.24896	−	0.169623i
$891$	−2.44960			−0.0820647
$892$	19.7204	+	19.7204i	0.660289	+	0.660289i
$893$	−3.42015	−	3.42015i	−0.114451	−	0.114451i
$894$	11.6944			0.391120
$895$	17.0919	−	13.0045i	0.571320	−	0.434692i
$896$		0			0
$897$	10.2738	−	10.2738i	0.343034	−	0.343034i
$898$	10.9905	+	10.9905i	0.366757	+	0.366757i
$899$	−6.42643			−0.214334
$900$	1.33352	−	4.81889i	0.0444506	−	0.160630i
$901$			71.9021i			2.39541i
$902$	2.00574	+	2.00574i	0.0667838	+	0.0667838i
$903$		0			0
$904$			14.2698i			0.474607i
$905$	−11.0259	+	8.38909i	−0.366512	+	0.278863i
$906$			16.6297i			0.552485i
$907$	27.5421	−	27.5421i	0.914521	−	0.914521i	−0.0821024	−	0.996624i	$-0.526163\pi$
$907$	27.5421	−	27.5421i	0.914521	−	0.914521i	0.996624	+	0.0821024i	$0.0261635\pi$
$908$	−19.7598	+	19.7598i	−0.655751	+	0.655751i
$909$	18.8914			0.626589
$910$		0			0
$911$	47.0579			1.55910			0.779549	−	0.626342i	$-0.215449\pi$
$911$	47.0579			1.55910			0.779549	+	0.626342i	$0.215449\pi$
$912$	−0.488054	+	0.488054i	−0.0161611	+	0.0161611i
$913$	18.1180	−	18.1180i	0.599620	−	0.599620i
$914$		−	32.0580i		−	1.06039i
$915$	0.330347	−	2.43239i	0.0109209	−	0.0804124i
$916$			2.04335i			0.0675143i
$917$		0			0
$918$	5.33117	+	5.33117i	0.175955	+	0.175955i
$919$			19.0621i			0.628802i	0.949290	+	0.314401i	$0.101804\pi$
$919$			19.0621i			0.628802i	−0.949290	+	0.314401i	$0.898196\pi$
$920$	−14.2195	+	10.8190i	−0.468802	+	0.356691i
$921$	31.3034			1.03148
$922$	7.83951	+	7.83951i	0.258181	+	0.258181i
$923$	5.45268	−	5.45268i	0.179477	−	0.179477i
$924$		0			0
$925$	24.9560	+	44.0526i	0.820549	+	1.44844i
$926$	10.1132			0.332340
$927$	6.84553	+	6.84553i	0.224837	+	0.224837i
$928$	−3.59232	−	3.59232i	−0.117924	−	0.117924i
$929$	44.4638			1.45881			0.729405	−	0.684082i	$-0.239797\pi$
$929$	44.4638			1.45881			0.729405	+	0.684082i	$0.239797\pi$
$930$	−1.71274	−	2.25106i	−0.0561628	−	0.0738153i
$931$		0			0
$932$	−2.26245	+	2.26245i	−0.0741090	+	0.0741090i
$933$	−20.8547	−	20.8547i	−0.682752	−	0.682752i
$934$	1.43427			0.0469309
$935$	−5.55758	+	40.9213i	−0.181752	+	1.33827i
$936$			1.81833i			0.0594339i
$937$	13.5674	+	13.5674i	0.443228	+	0.443228i	0.893095	−	0.449867i	$-0.148529\pi$
$937$	13.5674	+	13.5674i	0.443228	+	0.443228i	−0.449867	+	0.893095i	$0.648529\pi$
$938$		0			0
$939$			32.3451i			1.05554i
$940$	15.5272	+	2.10877i	0.506442	+	0.0687806i
$941$			11.3958i			0.371492i	0.982598	+	0.185746i	$0.0594702\pi$
$941$			11.3958i			0.371492i	−0.982598	+	0.185746i	$0.940530\pi$
$942$	5.17869	−	5.17869i	0.168731	−	0.168731i
$943$	6.54267	−	6.54267i	0.213059	−	0.213059i
$944$	−8.06376			−0.262453
$945$		0			0
$946$	3.09379			0.100588
$947$	−25.1853	+	25.1853i	−0.818412	+	0.818412i	−0.985878	−	0.167466i	$-0.946442\pi$
$947$	−25.1853	+	25.1853i	−0.818412	+	0.818412i	0.167466	+	0.985878i	$0.446442\pi$
$948$	−1.63851	+	1.63851i	−0.0532164	+	0.0532164i
$949$		−	11.7982i		−	0.382984i
$950$	−1.70105	−	3.00271i	−0.0551894	−	0.0974208i
$951$			23.8074i			0.772009i
$952$		0			0
$953$	−8.47549	−	8.47549i	−0.274548	−	0.274548i	0.556380	−	0.830928i	$-0.312190\pi$
$953$	−8.47549	−	8.47549i	−0.274548	−	0.274548i	−0.830928	+	0.556380i	$0.812190\pi$
$954$		−	9.53683i		−	0.308766i
$955$	−8.89596	−	11.6920i	−0.287866	−	0.378346i
$956$	−19.7009			−0.637172
$957$	−8.79974	−	8.79974i	−0.284455	−	0.284455i
$958$	−3.97039	+	3.97039i	−0.128277	+	0.128277i
$959$		0			0
$960$	0.300921	−	2.21573i	0.00971219	−	0.0715123i
$961$	29.3998			0.948382
$962$	−13.0196	−	13.0196i	−0.419769	−	0.419769i
$963$	−10.7995	−	10.7995i	−0.348008	−	0.348008i
$964$	−6.04502			−0.194697
$965$	−0.0912809	+	0.672115i	−0.00293844	+	0.0216361i
$966$		0			0
$967$	−26.7576	+	26.7576i	−0.860467	+	0.860467i	−0.991392	−	0.130925i	$-0.958205\pi$
$967$	−26.7576	+	26.7576i	−0.860467	+	0.860467i	0.130925	+	0.991392i	$0.458205\pi$
$968$	3.53515	+	3.53515i	0.113624	+	0.113624i
$969$	5.20380			0.167170
$970$	9.07738	+	11.9305i	0.291457	+	0.383065i
$971$		−	30.2895i		−	0.972037i	−0.873949	−	0.486018i	$-0.838449\pi$
$971$		−	30.2895i		−	0.972037i	0.873949	−	0.486018i	$-0.161551\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$		0			0
$974$		−	27.9279i		−	0.894867i
$975$	−8.76233	−	2.42477i	−0.280619	−	0.0776549i
$976$		−	1.09779i		−	0.0351392i
$977$	9.93182	−	9.93182i	0.317747	−	0.317747i	−0.530154	−	0.847901i	$-0.677866\pi$
$977$	9.93182	−	9.93182i	0.317747	−	0.317747i	0.847901	+	0.530154i	$0.177866\pi$
$978$	7.70934	−	7.70934i	0.246517	−	0.246517i
$979$	−41.1929			−1.31653
$980$		0			0
$981$	0.964378			0.0307902
$982$	−9.69623	+	9.69623i	−0.309419	+	0.309419i
$983$	36.9236	−	36.9236i	1.17768	−	1.17768i	0.197347	−	0.980334i	$-0.436767\pi$
$983$	36.9236	−	36.9236i	1.17768	−	1.17768i	0.980334	−	0.197347i	$-0.0632326\pi$
$984$			1.15796i			0.0369145i
$985$	5.19186	+	0.705115i	0.165427	+	0.0224668i
$986$			38.3025i			1.21980i
$987$		0			0
$988$	0.887443	+	0.887443i	0.0282333	+	0.0282333i
$989$		−	10.0919i		−	0.320903i
$990$	0.737137	−	5.42765i	0.0234277	−	0.172502i
$991$	−11.1384			−0.353822			−0.176911	−	0.984227i	$-0.556611\pi$
$991$	−11.1384			−0.353822			−0.176911	+	0.984227i	$0.556611\pi$
$992$	−0.894469	−	0.894469i	−0.0283994	−	0.0283994i
$993$	20.5781	−	20.5781i	0.653027	−	0.653027i
$994$		0			0
$995$	−26.5916	−	34.9496i	−0.843010	−	1.10798i
$996$	10.4600			0.331437
$997$	29.8135	+	29.8135i	0.944202	+	0.944202i	0.998524	−	0.0543212i	$-0.0172995\pi$
$997$	29.8135	+	29.8135i	0.944202	+	0.944202i	−0.0543212	+	0.998524i	$0.517299\pi$
$998$	22.7796	+	22.7796i	0.721077	+	0.721077i
$999$	10.1261			0.320375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.f.1273.7	yes	16
5.2	odd	4		1470.2.m.c.97.6	✓	16
7.6	odd	2		1470.2.m.c.1273.6	yes	16
35.27	even	4	inner	1470.2.m.f.97.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.c.97.6	✓	16	5.2	odd	4
1470.2.m.c.1273.6	yes	16	7.6	odd	2
1470.2.m.f.97.7	yes	16	35.27	even	4	inner
1470.2.m.f.1273.7	yes	16	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(1.35397 + 1.77954i) q^{5} +1.00000i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(2.21573 + 0.300921i) q^{10} +2.44960 q^{11} +(0.707107 + 0.707107i) q^{12} +(1.28575 - 1.28575i) q^{13} +(-2.21573 - 0.300921i) q^{15} -1.00000 q^{16} +(5.33117 + 5.33117i) q^{17} +(-0.707107 - 0.707107i) q^{18} -0.690213 q^{19} +(1.77954 - 1.35397i) q^{20} +(1.73213 - 1.73213i) q^{22} +(-5.65016 - 5.65016i) q^{23} +1.00000 q^{24} +(-1.33352 + 4.81889i) q^{25} -1.81833i q^{26} +(0.707107 + 0.707107i) q^{27} +5.08030i q^{29} +(-1.77954 + 1.35397i) q^{30} +1.26497i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.73213 + 1.73213i) q^{33} +7.53941 q^{34} -1.00000 q^{36} +(7.16021 - 7.16021i) q^{37} +(-0.488054 + 0.488054i) q^{38} +1.81833i q^{39} +(0.300921 - 2.21573i) q^{40} +1.15796i q^{41} +(0.893060 + 0.893060i) q^{43} -2.44960i q^{44} +(1.77954 - 1.35397i) q^{45} -7.99053 q^{46} +(4.95521 + 4.95521i) q^{47} +(0.707107 - 0.707107i) q^{48} +(2.46453 + 4.35041i) q^{50} -7.53941 q^{51} +(-1.28575 - 1.28575i) q^{52} +(6.74356 + 6.74356i) q^{53} +1.00000 q^{54} +(3.31669 + 4.35916i) q^{55} +(0.488054 - 0.488054i) q^{57} +(3.59232 + 3.59232i) q^{58} +8.06376 q^{59} +(-0.300921 + 2.21573i) q^{60} +1.09779i q^{61} +(0.894469 + 0.894469i) q^{62} +1.00000i q^{64} +(4.02892 + 0.547173i) q^{65} +2.44960i q^{66} +(-7.41414 + 7.41414i) q^{67} +(5.33117 - 5.33117i) q^{68} +7.99053 q^{69} +4.24084 q^{71} +(-0.707107 + 0.707107i) q^{72} +(4.58803 - 4.58803i) q^{73} -10.1261i q^{74} +(-2.46453 - 4.35041i) q^{75} +0.690213i q^{76} +(1.28575 + 1.28575i) q^{78} +2.31721i q^{79} +(-1.35397 - 1.77954i) q^{80} -1.00000 q^{81} +(0.818802 + 0.818802i) q^{82} +(7.39632 - 7.39632i) q^{83} +(-2.26877 + 16.7053i) q^{85} +1.26298 q^{86} +(-3.59232 - 3.59232i) q^{87} +(-1.73213 - 1.73213i) q^{88} -16.8162 q^{89} +(0.300921 - 2.21573i) q^{90} +(-5.65016 + 5.65016i) q^{92} +(-0.894469 - 0.894469i) q^{93} +7.00773 q^{94} +(-0.934530 - 1.22826i) q^{95} -1.00000i q^{96} +(4.74063 + 4.74063i) q^{97} -2.44960i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5} + 8 q^{13} - 16 q^{16} - 8 q^{17} - 48 q^{19} - 8 q^{22} - 8 q^{23} + 16 q^{24} + 8 q^{25} + 8 q^{33} - 16 q^{36} + 8 q^{37} - 8 q^{38} + 16 q^{47} - 8 q^{52} + 8 q^{53} + 16 q^{54} + 8 q^{57}+ \cdots - 64 q^{97}+O(q^{100}) \) 16 * q + 8 * q^5 + 8 * q^13 - 16 * q^16 - 8 * q^17 - 48 * q^19 - 8 * q^22 - 8 * q^23 + 16 * q^24 + 8 * q^25 + 8 * q^33 - 16 * q^36 + 8 * q^37 - 8 * q^38 + 16 * q^47 - 8 * q^52 + 8 * q^53 + 16 * q^54 + 8 * q^57 + 24 * q^58 + 48 * q^59 - 8 * q^62 + 72 * q^65 - 48 * q^67 - 8 * q^68 + 16 * q^73 + 8 * q^78 - 8 * q^80 - 16 * q^81 - 16 * q^82 - 72 * q^85 - 24 * q^87 + 8 * q^88 - 64 * q^89 - 8 * q^92 + 8 * q^93 + 64 * q^94 + 48 * q^95 - 64 * q^97

Introduction

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